LMFDB - Embedded newform 630.2.p.d.307.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(307,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, 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("630.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.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:	$5.03057532734$
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} - 8 x^{15} + 44 x^{14} - 160 x^{13} + 468 x^{12} - 1060 x^{11} + 2038 x^{10} - 3208 x^{9} + \cdots + 2468 $ x^16 - 8x^15 + 44x^14 - 160x^13 + 468x^12 - 1060x^11 + 2038x^10 - 3208x^9 + 4381x^8 - 3980x^7 - 390x^6 + 9000x^5 - 10018x^4 - 2304x^3 + 9396x^2 - 4200*x + 2468
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.2
Root			$0.131441 + 2.64318i$ of defining polynomial
Character	$\chi$	$=$	630.307
Dual form			630.2.p.d.433.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-1.28422 - 1.83051i) q^{5} +(0.0564123 + 2.64515i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-1.28422 - 1.83051i) q^{5} +(0.0564123 + 2.64515i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.386289 + 2.20245i) q^{10} -1.41421 q^{11} +(-0.772577 - 0.772577i) q^{13} +(1.83051 - 1.91029i) q^{14} -1.00000 q^{16} +(0.546295 - 0.546295i) q^{17} -5.95005 q^{19} +(1.83051 - 1.28422i) q^{20} +(1.00000 + 1.00000i) q^{22} +(-5.23480 + 5.23480i) q^{23} +(-1.70156 + 4.70156i) q^{25} +1.09259i q^{26} +(-2.64515 + 0.0564123i) q^{28} -0.992159i q^{29} +2.85974i q^{31} +(0.707107 + 0.707107i) q^{32} -0.772577 q^{34} +(4.76954 - 3.50022i) q^{35} +(5.70156 + 5.70156i) q^{37} +(4.20732 + 4.20732i) q^{38} +(-2.20245 - 0.386289i) q^{40} -2.18518i q^{41} +(-2.00000 + 2.00000i) q^{43} -1.41421i q^{44} +7.40312 q^{46} +(-7.32206 + 7.32206i) q^{47} +(-6.99364 + 0.298438i) q^{49} +(4.52769 - 2.12132i) q^{50} +(0.772577 - 0.772577i) q^{52} +(-2.40637 + 2.40637i) q^{53} +(1.81616 + 2.58874i) q^{55} +(1.91029 + 1.83051i) q^{56} +(-0.701562 + 0.701562i) q^{58} -12.0757 q^{59} -3.63232i q^{61} +(2.02214 - 2.02214i) q^{62} -1.00000i q^{64} +(-0.422055 + 2.40637i) q^{65} +(-4.00000 - 4.00000i) q^{67} +(0.546295 + 0.546295i) q^{68} +(-5.84760 - 0.897546i) q^{70} +8.06323 q^{71} +(11.3985 + 11.3985i) q^{73} -8.06323i q^{74} -5.95005i q^{76} +(-0.0797790 - 3.74081i) q^{77} -5.40312i q^{79} +(1.28422 + 1.83051i) q^{80} +(-1.54515 + 1.54515i) q^{82} +(8.79790 + 8.79790i) q^{83} +(-1.70156 - 0.298438i) q^{85} +2.82843 q^{86} +(-1.00000 + 1.00000i) q^{88} -11.3663 q^{89} +(2.00000 - 2.08717i) q^{91} +(-5.23480 - 5.23480i) q^{92} +10.3550 q^{94} +(7.64117 + 10.8917i) q^{95} +(7.76621 - 7.76621i) q^{97} +(5.15627 + 4.73422i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{7}+O(q^{10}) $ 16 * q - 4 * q^7	$ 16 q - 4 q^{7} - 16 q^{16} + 16 q^{22} + 24 q^{25} + 4 q^{28} + 40 q^{37} - 32 q^{43} + 16 q^{46} + 40 q^{58} - 64 q^{67} - 12 q^{70} + 24 q^{85} - 16 q^{88} + 32 q^{91}+O(q^{100}) $ 16 * q - 4 * q^7 - 16 * q^16 + 16 * q^22 + 24 * q^25 + 4 * q^28 + 40 * q^37 - 32 * q^43 + 16 * q^46 + 40 * q^58 - 64 * q^67 - 12 * q^70 + 24 * q^85 - 16 * q^88 + 32 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	−	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
$5$	−1.28422	−	1.83051i	−0.574320	−	0.818631i
$5$	−1.28422	−	1.83051i	−0.574320	−	0.818631i
$6$		0			0
$7$	0.0564123	+	2.64515i	0.0213218	+	0.999773i
$7$	0.0564123	+	2.64515i	0.0213218	+	0.999773i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−0.386289	+	2.20245i	−0.122155	+	0.696475i
$11$	−1.41421			−0.426401			−0.213201	−	0.977008i	$-0.568389\pi$
$11$	−1.41421			−0.426401			−0.213201	+	0.977008i	$0.568389\pi$
$12$		0			0
$13$	−0.772577	−	0.772577i	−0.214274	−	0.214274i	0.591806	−	0.806080i	$-0.298415\pi$
$13$	−0.772577	−	0.772577i	−0.214274	−	0.214274i	−0.806080	+	0.591806i	$0.798415\pi$
$14$	1.83051	−	1.91029i	0.489225	−	0.510547i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	0.546295	−	0.546295i	0.132496	−	0.132496i	−0.637749	−	0.770245i	$-0.720134\pi$
$17$	0.546295	−	0.546295i	0.132496	−	0.132496i	0.770245	+	0.637749i	$0.220134\pi$
$18$		0			0
$19$	−5.95005			−1.36504			−0.682518	−	0.730869i	$-0.739115\pi$
$19$	−5.95005			−1.36504			−0.682518	+	0.730869i	$0.739115\pi$
$20$	1.83051	−	1.28422i	0.409315	−	0.287160i
$21$		0			0
$22$	1.00000	+	1.00000i	0.213201	+	0.213201i
$23$	−5.23480	+	5.23480i	−1.09153	+	1.09153i	−0.0961658	+	0.995365i	$0.530658\pi$
$23$	−5.23480	+	5.23480i	−1.09153	+	1.09153i	−0.995365	+	0.0961658i	$0.969342\pi$
$24$		0			0
$25$	−1.70156	+	4.70156i	−0.340312	+	0.940312i
$26$			1.09259i			0.214274i
$27$		0			0
$28$	−2.64515	+	0.0564123i	−0.499886	+	0.0106609i
$29$		−	0.992159i		−	0.184239i	−0.995748	−	0.0921196i	$-0.970636\pi$
$29$		−	0.992159i		−	0.184239i	0.995748	−	0.0921196i	$-0.0293642\pi$
$30$		0			0
$31$			2.85974i			0.513625i	0.966461	+	0.256813i	$0.0826723\pi$
$31$			2.85974i			0.513625i	−0.966461	+	0.256813i	$0.917328\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$	−0.772577			−0.132496
$35$	4.76954	−	3.50022i	0.806199	−	0.591644i
$36$		0			0
$37$	5.70156	+	5.70156i	0.937331	+	0.937331i	0.998149	−	0.0608178i	$-0.0193709\pi$
$37$	5.70156	+	5.70156i	0.937331	+	0.937331i	−0.0608178	+	0.998149i	$0.519371\pi$
$38$	4.20732	+	4.20732i	0.682518	+	0.682518i
$39$		0			0
$40$	−2.20245	−	0.386289i	−0.348238	−	0.0610776i
$41$		−	2.18518i		−	0.341268i	−0.985335	−	0.170634i	$-0.945418\pi$
$41$		−	2.18518i		−	0.341268i	0.985335	−	0.170634i	$-0.0545815\pi$
$42$		0			0
$43$	−2.00000	+	2.00000i	−0.304997	+	0.304997i	−0.842965	−	0.537968i	$-0.819192\pi$
$43$	−2.00000	+	2.00000i	−0.304997	+	0.304997i	0.537968	+	0.842965i	$0.319192\pi$
$44$		−	1.41421i		−	0.213201i
$45$		0			0
$46$	7.40312			1.09153
$47$	−7.32206	+	7.32206i	−1.06803	+	1.06803i	−0.0705213	+	0.997510i	$0.522466\pi$
$47$	−7.32206	+	7.32206i	−1.06803	+	1.06803i	−0.997510	+	0.0705213i	$0.977534\pi$
$48$		0			0
$49$	−6.99364	+	0.298438i	−0.999091	+	0.0426340i
$50$	4.52769	−	2.12132i	0.640312	−	0.300000i
$51$		0			0
$52$	0.772577	−	0.772577i	0.107137	−	0.107137i
$53$	−2.40637	+	2.40637i	−0.330541	+	0.330541i	−0.852792	−	0.522251i	$-0.825092\pi$
$53$	−2.40637	+	2.40637i	−0.330541	+	0.330541i	0.522251	+	0.852792i	$0.325092\pi$
$54$		0			0
$55$	1.81616	+	2.58874i	0.244891	+	0.349065i
$56$	1.91029	+	1.83051i	0.255274	+	0.244613i
$57$		0			0
$58$	−0.701562	+	0.701562i	−0.0921196	+	0.0921196i
$59$	−12.0757			−1.57212			−0.786059	−	0.618151i	$-0.787882\pi$
$59$	−12.0757			−1.57212			−0.786059	+	0.618151i	$0.787882\pi$
$60$		0			0
$61$		−	3.63232i		−	0.465071i	−0.972588	−	0.232535i	$-0.925298\pi$
$61$		−	3.63232i		−	0.465071i	0.972588	−	0.232535i	$-0.0747022\pi$
$62$	2.02214	−	2.02214i	0.256813	−	0.256813i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−0.422055	+	2.40637i	−0.0523495	+	0.298474i
$66$		0			0
$67$	−4.00000	−	4.00000i	−0.488678	−	0.488678i	0.419211	−	0.907889i	$-0.362307\pi$
$67$	−4.00000	−	4.00000i	−0.488678	−	0.488678i	−0.907889	+	0.419211i	$0.862307\pi$
$68$	0.546295	+	0.546295i	0.0662480	+	0.0662480i
$69$		0			0
$70$	−5.84760	−	0.897546i	−0.698922	−	0.107277i
$71$	8.06323			0.956929			0.478464	−	0.878107i	$-0.341194\pi$
$71$	8.06323			0.956929			0.478464	+	0.878107i	$0.341194\pi$
$72$		0			0
$73$	11.3985	+	11.3985i	1.33410	+	1.33410i	0.901668	+	0.432430i	$0.142344\pi$
$73$	11.3985	+	11.3985i	1.33410	+	1.33410i	0.432430	+	0.901668i	$0.357656\pi$
$74$		−	8.06323i		−	0.937331i
$75$		0			0
$76$		−	5.95005i		−	0.682518i
$77$	−0.0797790	−	3.74081i	−0.00909166	−	0.426304i
$78$		0			0
$79$		−	5.40312i		−	0.607899i	−0.952688	−	0.303949i	$-0.901695\pi$
$79$		−	5.40312i		−	0.607899i	0.952688	−	0.303949i	$-0.0983054\pi$
$80$	1.28422	+	1.83051i	0.143580	+	0.204658i
$81$		0			0
$82$	−1.54515	+	1.54515i	−0.170634	+	0.170634i
$83$	8.79790	+	8.79790i	0.965695	+	0.965695i	0.999431	−	0.0337353i	$-0.0107403\pi$
$83$	8.79790	+	8.79790i	0.965695	+	0.965695i	−0.0337353	+	0.999431i	$0.510740\pi$
$84$		0			0
$85$	−1.70156	−	0.298438i	−0.184560	−	0.0323701i
$86$	2.82843			0.304997
$87$		0			0
$88$	−1.00000	+	1.00000i	−0.106600	+	0.106600i
$89$	−11.3663			−1.20483			−0.602415	−	0.798183i	$-0.705795\pi$
$89$	−11.3663			−1.20483			−0.602415	+	0.798183i	$0.705795\pi$
$90$		0			0
$91$	2.00000	−	2.08717i	0.209657	−	0.218794i
$92$	−5.23480	−	5.23480i	−0.545766	−	0.545766i
$93$		0			0
$94$	10.3550			1.06803
$95$	7.64117	+	10.8917i	0.783968	+	1.11746i
$96$		0			0
$97$	7.76621	−	7.76621i	0.788539	−	0.788539i	−0.192715	−	0.981255i	$-0.561729\pi$
$97$	7.76621	−	7.76621i	0.788539	−	0.788539i	0.981255	+	0.192715i	$0.0617294\pi$
$98$	5.15627	+	4.73422i	0.520862	+	0.478228i
$99$		0			0
$100$	−4.70156	−	1.70156i	−0.470156	−	0.170156i
$101$		−	8.79790i		−	0.875424i	−0.899115	−	0.437712i	$-0.855789\pi$
$101$		−	8.79790i		−	0.875424i	0.899115	−	0.437712i	$-0.144211\pi$
$102$		0			0
$103$	−9.85338	−	9.85338i	−0.970882	−	0.970882i	0.0287057	−	0.999588i	$-0.490861\pi$
$103$	−9.85338	−	9.85338i	−0.970882	−	0.970882i	−0.999588	+	0.0287057i	$0.990861\pi$
$104$	−1.09259			−0.107137
$105$		0			0
$106$	3.40312			0.330541
$107$	0.422055	+	0.422055i	0.0408016	+	0.0408016i	0.727213	−	0.686412i	$-0.240815\pi$
$107$	0.422055	+	0.422055i	0.0408016	+	0.0408016i	−0.686412	+	0.727213i	$0.740815\pi$
$108$		0			0
$109$		−	13.4031i		−	1.28379i	−0.766794	−	0.641893i	$-0.778149\pi$
$109$		−	13.4031i		−	1.28379i	0.766794	−	0.641893i	$-0.221851\pi$
$110$	0.546295	−	3.11473i	0.0520872	−	0.296978i
$111$		0			0
$112$	−0.0564123	−	2.64515i	−0.00533046	−	0.249943i
$113$	−11.8838	+	11.8838i	−1.11794	+	1.11794i	−0.125891	+	0.992044i	$0.540179\pi$
$113$	−11.8838	+	11.8838i	−1.11794	+	1.11794i	−0.992044	+	0.125891i	$0.959821\pi$
$114$		0			0
$115$	16.3050	+	2.85974i	1.52045	+	0.266672i
$116$	0.992159			0.0921196
$117$		0			0
$118$	8.53879	+	8.53879i	0.786059	+	0.786059i
$119$	1.47585	+	1.41421i	0.135291	+	0.129641i
$120$		0			0
$121$	−9.00000			−0.818182
$122$	−2.56844	+	2.56844i	−0.232535	+	0.232535i
$123$		0			0
$124$	−2.85974			−0.256813
$125$	10.7915	−	2.92310i	0.965217	−	0.261450i
$126$		0			0
$127$	0.701562	+	0.701562i	0.0622536	+	0.0622536i	0.737548	−	0.675295i	$-0.235983\pi$
$127$	0.701562	+	0.701562i	0.0622536	+	0.0622536i	−0.675295	+	0.737548i	$0.735983\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	2.00000	−	1.40312i	0.175412	−	0.123062i
$131$			2.56844i			0.224406i	0.993685	+	0.112203i	$0.0357906\pi$
$131$			2.56844i			0.224406i	−0.993685	+	0.112203i	$0.964209\pi$
$132$		0			0
$133$	−0.335656	−	15.7388i	−0.0291051	−	1.36473i
$134$			5.65685i			0.488678i
$135$		0			0
$136$		−	0.772577i		−	0.0662480i
$137$	−6.22696	−	6.22696i	−0.532005	−	0.532005i	0.389164	−	0.921169i	$-0.372764\pi$
$137$	−6.22696	−	6.22696i	−0.532005	−	0.532005i	−0.921169	+	0.389164i	$0.872764\pi$
$138$		0			0
$139$	7.49521			0.635735			0.317868	−	0.948135i	$-0.397033\pi$
$139$	7.49521			0.635735			0.317868	+	0.948135i	$0.397033\pi$
$140$	3.50022	+	4.76954i	0.295822	+	0.403100i
$141$		0			0
$142$	−5.70156	−	5.70156i	−0.478464	−	0.478464i
$143$	1.09259	+	1.09259i	0.0913669	+	0.0913669i
$144$		0			0
$145$	−1.81616	+	1.27415i	−0.150824	+	0.105812i
$146$		−	16.1200i		−	1.33410i
$147$		0			0
$148$	−5.70156	+	5.70156i	−0.468666	+	0.468666i
$149$		−	17.1186i		−	1.40241i	−0.712959	−	0.701206i	$-0.752645\pi$
$149$		−	17.1186i		−	1.40241i	0.712959	−	0.701206i	$-0.247355\pi$
$150$		0			0
$151$	−6.80625			−0.553885			−0.276942	−	0.960887i	$-0.589321\pi$
$151$	−6.80625			−0.553885			−0.276942	+	0.960887i	$0.589321\pi$
$152$	−4.20732	+	4.20732i	−0.341259	+	0.341259i
$153$		0			0
$154$	−2.58874	+	2.70156i	−0.208606	+	0.217698i
$155$	5.23480	−	3.67254i	0.420469	−	0.294985i
$156$		0			0
$157$	12.6727	−	12.6727i	1.01139	−	1.01139i	0.0114558	−	0.999934i	$-0.496353\pi$
$157$	12.6727	−	12.6727i	1.01139	−	1.01139i	0.999934	−	0.0114558i	$-0.00364656\pi$
$158$	−3.82059	+	3.82059i	−0.303949	+	0.303949i
$159$		0			0
$160$	0.386289	−	2.20245i	0.0305388	−	0.174119i
$161$	−14.1421	−	13.5515i	−1.11456	−	1.06801i
$162$		0			0
$163$	11.4031	−	11.4031i	0.893162	−	0.893162i	−0.101658	−	0.994819i	$-0.532415\pi$
$163$	11.4031	−	11.4031i	0.893162	−	0.893162i	0.994819	+	0.101658i	$0.0324147\pi$
$164$	2.18518			0.170634
$165$		0			0
$166$		−	12.4421i		−	0.965695i
$167$	−6.22947	+	6.22947i	−0.482051	+	0.482051i	−0.905786	−	0.423735i	$-0.860719\pi$
$167$	−6.22947	+	6.22947i	−0.482051	+	0.482051i	0.423735	+	0.905786i	$0.360719\pi$
$168$		0			0
$169$		−	11.8062i		−	0.908173i
$170$	0.992159	+	1.41421i	0.0760951	+	0.108465i
$171$		0			0
$172$	−2.00000	−	2.00000i	−0.152499	−	0.152499i
$173$	6.39250	+	6.39250i	0.486013	+	0.486013i	0.907045	−	0.421033i	$-0.138332\pi$
$173$	6.39250	+	6.39250i	0.486013	+	0.486013i	−0.421033	+	0.907045i	$0.638332\pi$
$174$		0			0
$175$	−12.5323	−	4.23566i	−0.947355	−	0.320186i
$176$	1.41421			0.106600
$177$		0			0
$178$	8.03722	+	8.03722i	0.602415	+	0.602415i
$179$		−	14.7122i		−	1.09964i	−0.835282	−	0.549822i	$-0.814695\pi$
$179$		−	14.7122i		−	1.09964i	0.835282	−	0.549822i	$-0.185305\pi$
$180$		0			0
$181$			15.5324i			1.15452i	0.816562	+	0.577258i	$0.195877\pi$
$181$			15.5324i			1.15452i	−0.816562	+	0.577258i	$0.804123\pi$
$182$	−2.89006	+	0.0616355i	−0.214226	+	0.00456872i
$183$		0			0
$184$			7.40312i			0.545766i
$185$	3.11473	−	17.7588i	0.229000	−	1.30566i
$186$		0			0
$187$	−0.772577	+	0.772577i	−0.0564965	+	0.0564965i
$188$	−7.32206	−	7.32206i	−0.534016	−	0.534016i
$189$		0			0
$190$	2.29844	−	13.1047i	0.166746	−	0.950714i
$191$	24.1897			1.75030			0.875152	−	0.483848i	$-0.160761\pi$
$191$	24.1897			1.75030			0.875152	+	0.483848i	$0.160761\pi$
$192$		0			0
$193$	−11.0000	+	11.0000i	−0.791797	+	0.791797i	−0.981786	−	0.189989i	$-0.939155\pi$
$193$	−11.0000	+	11.0000i	−0.791797	+	0.791797i	0.189989	+	0.981786i	$0.439155\pi$
$194$	−10.9831			−0.788539
$195$		0			0
$196$	−0.298438	−	6.99364i	−0.0213170	−	0.499545i
$197$	−16.5485	−	16.5485i	−1.17903	−	1.17903i	−0.979991	−	0.199041i	$-0.936217\pi$
$197$	−16.5485	−	16.5485i	−1.17903	−	1.17903i	−0.199041	−	0.979991i	$-0.563783\pi$
$198$		0			0
$199$	27.2020			1.92830			0.964148	−	0.265365i	$-0.0854924\pi$
$199$	27.2020			1.92830			0.964148	+	0.265365i	$0.0854924\pi$
$200$	2.12132	+	4.52769i	0.150000	+	0.320156i
$201$		0			0
$202$	−6.22106	+	6.22106i	−0.437712	+	0.437712i
$203$	2.62441	−	0.0559699i	0.184197	−	0.00392832i
$204$		0			0
$205$	−4.00000	+	2.80625i	−0.279372	+	0.195997i
$206$			13.9348i			0.970882i
$207$		0			0
$208$	0.772577	+	0.772577i	0.0535686	+	0.0535686i
$209$	8.41464			0.582053
$210$		0			0
$211$	−10.8062			−0.743933			−0.371966	−	0.928246i	$-0.621316\pi$
$211$	−10.8062			−0.743933			−0.371966	+	0.928246i	$0.621316\pi$
$212$	−2.40637	−	2.40637i	−0.165270	−	0.165270i
$213$		0			0
$214$		−	0.596876i		−	0.0408016i
$215$	6.22947	+	1.09259i	0.424846	+	0.0745140i
$216$		0			0
$217$	−7.56445	+	0.161325i	−0.513508	+	0.0109514i
$218$	−9.47744	+	9.47744i	−0.641893	+	0.641893i
$219$		0			0
$220$	−2.58874	+	1.81616i	−0.174533	+	0.122445i
$221$	−0.844110			−0.0567810
$222$		0			0
$223$	−3.36131	−	3.36131i	−0.225090	−	0.225090i	0.585548	−	0.810638i	$-0.300879\pi$
$223$	−3.36131	−	3.36131i	−0.225090	−	0.225090i	−0.810638	+	0.585548i	$0.800879\pi$
$224$	−1.83051	+	1.91029i	−0.122306	+	0.127637i
$225$		0			0
$226$	16.8062			1.11794
$227$	−10.5998	+	10.5998i	−0.703535	+	0.703535i	−0.965168	−	0.261633i	$-0.915739\pi$
$227$	−10.5998	+	10.5998i	−0.703535	+	0.703535i	0.261633	+	0.965168i	$0.415739\pi$
$228$		0			0
$229$	−24.3422			−1.60858			−0.804290	−	0.594238i	$-0.797454\pi$
$229$	−24.3422			−1.60858			−0.804290	+	0.594238i	$0.797454\pi$
$230$	−9.50723	−	13.5515i	−0.626888	−	0.893561i
$231$		0			0
$232$	−0.701562	−	0.701562i	−0.0460598	−	0.0460598i
$233$	−4.24264	+	4.24264i	−0.277945	+	0.277945i	−0.832288	−	0.554343i	$-0.812969\pi$
$233$	−4.24264	+	4.24264i	−0.277945	+	0.277945i	0.554343	+	0.832288i	$0.312969\pi$
$234$		0			0
$235$	22.8062	+	4.00000i	1.48772	+	0.260931i
$236$		−	12.0757i		−	0.786059i
$237$		0			0
$238$	−0.0435829	−	2.04358i	−0.00282506	−	0.132466i
$239$			14.5642i			0.942079i	0.882112	+	0.471040i	$0.156121\pi$
$239$			14.5642i			0.942079i	−0.882112	+	0.471040i	$0.843879\pi$
$240$		0			0
$241$			19.7068i			1.26942i	0.772749	+	0.634712i	$0.218881\pi$
$241$			19.7068i			1.26942i	−0.772749	+	0.634712i	$0.781119\pi$
$242$	6.36396	+	6.36396i	0.409091	+	0.409091i
$243$		0			0
$244$	3.63232			0.232535
$245$	9.52766	+	12.4187i	0.608700	+	0.793401i
$246$		0			0
$247$	4.59688	+	4.59688i	0.292492	+	0.292492i
$248$	2.02214	+	2.02214i	0.128406	+	0.128406i
$249$		0			0
$250$	−9.69766	−	5.56376i	−0.613334	−	0.351883i
$251$			24.5346i			1.54861i	0.632812	+	0.774305i	$0.281900\pi$
$251$			24.5346i			1.54861i	−0.632812	+	0.774305i	$0.718100\pi$
$252$		0			0
$253$	7.40312	−	7.40312i	0.465430	−	0.465430i
$254$		−	0.992159i		−	0.0622536i
$255$		0			0
$256$	1.00000			0.0625000
$257$	1.63888	−	1.63888i	0.102231	−	0.102231i	−0.654141	−	0.756372i	$-0.726970\pi$
$257$	1.63888	−	1.63888i	0.102231	−	0.102231i	0.756372	+	0.654141i	$0.226970\pi$
$258$		0			0
$259$	−14.7598	+	15.4031i	−0.917132	+	0.957104i
$260$	−2.40637	−	0.422055i	−0.149237	−	0.0261747i
$261$		0			0
$262$	1.81616	−	1.81616i	0.112203	−	0.112203i
$263$	11.3137	−	11.3137i	0.697633	−	0.697633i	−0.266266	−	0.963899i	$-0.585790\pi$
$263$	11.3137	−	11.3137i	0.697633	−	0.697633i	0.963899	+	0.266266i	$0.0857901\pi$
$264$		0			0
$265$	7.49521	+	1.31459i	0.460427	+	0.0807545i
$266$	−10.8917	+	11.3663i	−0.667810	+	0.696915i
$267$		0			0
$268$	4.00000	−	4.00000i	0.244339	−	0.244339i
$269$	18.3051			1.11608			0.558042	−	0.829813i	$-0.311553\pi$
$269$	18.3051			1.11608			0.558042	+	0.829813i	$0.311553\pi$
$270$		0			0
$271$			12.6727i			0.769811i	0.922956	+	0.384905i	$0.125766\pi$
$271$			12.6727i			0.769811i	−0.922956	+	0.384905i	$0.874234\pi$
$272$	−0.546295	+	0.546295i	−0.0331240	+	0.0331240i
$273$		0			0
$274$			8.80625i			0.532005i
$275$	2.40637	−	6.64901i	0.145110	−	0.400951i
$276$		0			0
$277$	5.10469	+	5.10469i	0.306711	+	0.306711i	0.843632	−	0.536921i	$-0.180413\pi$
$277$	5.10469	+	5.10469i	0.306711	+	0.306711i	−0.536921	+	0.843632i	$0.680413\pi$
$278$	−5.29991	−	5.29991i	−0.317868	−	0.317868i
$279$		0			0
$280$	0.897546	−	5.84760i	0.0536386	−	0.349461i
$281$	19.7990			1.18111			0.590554	−	0.806998i	$-0.298909\pi$
$281$	19.7990			1.18111			0.590554	+	0.806998i	$0.298909\pi$
$282$		0			0
$283$	0.542011	+	0.542011i	0.0322192	+	0.0322192i	0.723033	−	0.690814i	$-0.242748\pi$
$283$	0.542011	+	0.542011i	0.0322192	+	0.0322192i	−0.690814	+	0.723033i	$0.742748\pi$
$284$			8.06323i			0.478464i
$285$		0			0
$286$		−	1.54515i		−	0.0913669i
$287$	5.78013	−	0.123271i	0.341190	−	0.00727645i
$288$		0			0
$289$			16.4031i			0.964890i
$290$	2.18518	+	0.383260i	0.128318	+	0.0225058i
$291$		0			0
$292$	−11.3985	+	11.3985i	−0.667049	+	0.667049i
$293$	17.3756	+	17.3756i	1.01509	+	1.01509i	0.999884	+	0.0152081i	$0.00484109\pi$
$293$	17.3756	+	17.3756i	1.01509	+	1.01509i	0.0152081	+	0.999884i	$0.495159\pi$
$294$		0			0
$295$	15.5078	+	22.1047i	0.902900	+	1.28698i
$296$	8.06323			0.468666
$297$		0			0
$298$	−12.1047	+	12.1047i	−0.701206	+	0.701206i
$299$	8.08857			0.467774
$300$		0			0
$301$	−5.40312	−	5.17748i	−0.311431	−	0.298425i
$302$	4.81274	+	4.81274i	0.276942	+	0.276942i
$303$		0			0
$304$	5.95005			0.341259
$305$	−6.64901	+	4.66470i	−0.380721	+	0.267100i
$306$		0			0
$307$	−14.7598	+	14.7598i	−0.842389	+	0.842389i	−0.989169	−	0.146780i	$-0.953109\pi$
$307$	−14.7598	+	14.7598i	−0.842389	+	0.842389i	0.146780	+	0.989169i	$0.453109\pi$
$308$	3.74081	−	0.0797790i	0.213152	−	0.00454583i
$309$		0			0
$310$	−6.29844	−	1.10469i	−0.357727	−	0.0627420i
$311$		−	2.95170i		−	0.167375i	−0.996492	−	0.0836877i	$-0.973330\pi$
$311$		−	2.95170i		−	0.167375i	0.996492	−	0.0836877i	$-0.0266698\pi$
$312$		0			0
$313$	−14.4888	−	14.4888i	−0.818958	−	0.818958i	0.166999	−	0.985957i	$-0.446592\pi$
$313$	−14.4888	−	14.4888i	−0.818958	−	0.818958i	−0.985957	+	0.166999i	$0.946592\pi$
$314$	−17.9219			−1.01139
$315$		0			0
$316$	5.40312			0.303949
$317$	1.41421	+	1.41421i	0.0794301	+	0.0794301i	0.745706	−	0.666276i	$-0.232113\pi$
$317$	1.41421	+	1.41421i	0.0794301	+	0.0794301i	−0.666276	+	0.745706i	$0.732113\pi$
$318$		0			0
$319$			1.40312i			0.0785599i
$320$	−1.83051	+	1.28422i	−0.102329	+	0.0717900i
$321$		0			0
$322$	0.417627	+	19.5824i	0.0232735	+	1.09128i
$323$	−3.25048	+	3.25048i	−0.180862	+	0.180862i
$324$		0			0
$325$	4.94691	−	2.31773i	0.274405	−	0.128565i
$326$	−16.1265			−0.893162
$327$		0			0
$328$	−1.54515	−	1.54515i	−0.0853169	−	0.0853169i
$329$	−19.7810	−	18.9549i	−1.09056	−	1.04502i
$330$		0			0
$331$	−25.6125			−1.40779			−0.703895	−	0.710304i	$-0.748557\pi$
$331$	−25.6125			−1.40779			−0.703895	+	0.710304i	$0.748557\pi$
$332$	−8.79790	+	8.79790i	−0.482848	+	0.482848i
$333$		0			0
$334$	8.80980			0.482051
$335$	−2.18518	+	12.4589i	−0.119389	+	0.680704i
$336$		0			0
$337$	−1.00000	−	1.00000i	−0.0544735	−	0.0544735i	0.679345	−	0.733819i	$-0.262264\pi$
$337$	−1.00000	−	1.00000i	−0.0544735	−	0.0544735i	−0.733819	+	0.679345i	$0.762264\pi$
$338$	−8.34828	+	8.34828i	−0.454086	+	0.454086i
$339$		0			0
$340$	0.298438	−	1.70156i	0.0161851	−	0.0922802i
$341$		−	4.04429i		−	0.219010i
$342$		0			0
$343$	−1.18394	−	18.4824i	−0.0639267	−	0.997955i
$344$			2.82843i			0.152499i
$345$		0			0
$346$		−	9.04036i		−	0.486013i
$347$	17.1186	+	17.1186i	0.918975	+	0.918975i	0.996955	−	0.0779797i	$-0.0248469\pi$
$347$	17.1186	+	17.1186i	0.918975	+	0.918975i	−0.0779797	+	0.996955i	$0.524847\pi$
$348$		0			0
$349$	−9.81294			−0.525275			−0.262637	−	0.964895i	$-0.584592\pi$
$349$	−9.81294			−0.525275			−0.262637	+	0.964895i	$0.584592\pi$
$350$	5.86663	+	11.8568i	0.313584	+	0.633770i
$351$		0			0
$352$	−1.00000	−	1.00000i	−0.0533002	−	0.0533002i
$353$	−10.0535	−	10.0535i	−0.535095	−	0.535095i	0.386989	−	0.922084i	$-0.373515\pi$
$353$	−10.0535	−	10.0535i	−0.535095	−	0.535095i	−0.922084	+	0.386989i	$0.873515\pi$
$354$		0			0
$355$	−10.3550	−	14.7598i	−0.549584	−	0.783371i
$356$		−	11.3663i		−	0.602415i
$357$		0			0
$358$	−10.4031	+	10.4031i	−0.549822	+	0.549822i
$359$		−	1.26616i		−	0.0668256i	−0.999442	−	0.0334128i	$-0.989362\pi$
$359$		−	1.26616i		−	0.0668256i	0.999442	−	0.0334128i	$-0.0106376\pi$
$360$		0			0
$361$	16.4031			0.863322
$362$	10.9831	−	10.9831i	0.577258	−	0.577258i
$363$		0			0
$364$	2.08717	+	2.00000i	0.109397	+	0.104828i
$365$	6.22696	−	35.5034i	0.325934	−	1.85833i
$366$		0			0
$367$	−10.6260	+	10.6260i	−0.554670	+	0.554670i	−0.927785	−	0.373115i	$-0.878290\pi$
$367$	−10.6260	+	10.6260i	−0.554670	+	0.554670i	0.373115	+	0.927785i	$0.378290\pi$
$368$	5.23480	−	5.23480i	0.272883	−	0.272883i
$369$		0			0
$370$	−14.7598	+	10.3550i	−0.767328	+	0.538328i
$371$	−6.50096	−	6.22947i	−0.337513	−	0.323418i
$372$		0			0
$373$	−3.70156	+	3.70156i	−0.191660	+	0.191660i	−0.796413	−	0.604753i	$-0.793272\pi$
$373$	−3.70156	+	3.70156i	−0.191660	+	0.191660i	0.604753	+	0.796413i	$0.293272\pi$
$374$	1.09259			0.0564965
$375$		0			0
$376$			10.3550i			0.534016i
$377$	−0.766519	+	0.766519i	−0.0394778	+	0.0394778i
$378$		0			0
$379$			17.6125i			0.904693i	0.891842	+	0.452347i	$0.149413\pi$
$379$			17.6125i			0.904693i	−0.891842	+	0.452347i	$0.850587\pi$
$380$	−10.8917	+	7.64117i	−0.558730	+	0.391984i
$381$		0			0
$382$	−17.1047	−	17.1047i	−0.875152	−	0.875152i
$383$	16.5032	+	16.5032i	0.843275	+	0.843275i	0.989283	−	0.146008i	$-0.0466426\pi$
$383$	16.5032	+	16.5032i	0.843275	+	0.843275i	−0.146008	+	0.989283i	$0.546643\pi$
$384$		0			0
$385$	−6.74514	+	4.95005i	−0.343764	+	0.252278i
$386$	15.5563			0.791797
$387$		0			0
$388$	7.76621	+	7.76621i	0.394270	+	0.394270i
$389$		−	13.1500i		−	0.666730i	−0.942798	−	0.333365i	$-0.891816\pi$
$389$		−	13.1500i		−	0.666730i	0.942798	−	0.333365i	$-0.108184\pi$
$390$		0			0
$391$			5.71949i			0.289247i
$392$	−4.73422	+	5.15627i	−0.239114	+	0.260431i
$393$		0			0
$394$			23.4031i			1.17903i
$395$	−9.89049	+	6.93880i	−0.497645	+	0.349129i
$396$		0			0
$397$	−5.95005	+	5.95005i	−0.298625	+	0.298625i	−0.840475	−	0.541850i	$-0.817724\pi$
$397$	−5.95005	+	5.95005i	−0.298625	+	0.298625i	0.541850	+	0.840475i	$0.317724\pi$
$398$	−19.2347	−	19.2347i	−0.964148	−	0.964148i
$399$		0			0
$400$	1.70156	−	4.70156i	0.0850781	−	0.235078i
$401$	−22.9235			−1.14475			−0.572373	−	0.819993i	$-0.693977\pi$
$401$	−22.9235			−1.14475			−0.572373	+	0.819993i	$0.693977\pi$
$402$		0			0
$403$	2.20937	−	2.20937i	0.110057	−	0.110057i
$404$	8.79790			0.437712
$405$		0			0
$406$	−1.89531	−	1.81616i	−0.0940628	−	0.0901345i
$407$	−8.06323	−	8.06323i	−0.399679	−	0.399679i
$408$		0			0
$409$	−3.63232			−0.179607			−0.0898033	−	0.995960i	$-0.528624\pi$
$409$	−3.63232			−0.179607			−0.0898033	+	0.995960i	$0.528624\pi$
$410$	4.81274	+	0.844110i	0.237685	+	0.0416876i
$411$		0			0
$412$	9.85338	−	9.85338i	0.485441	−	0.485441i
$413$	−0.681216	−	31.9420i	−0.0335205	−	1.57176i
$414$		0			0
$415$	4.80625	−	27.4031i	0.235929	−	1.34517i
$416$		−	1.09259i		−	0.0535686i
$417$		0			0
$418$	−5.95005	−	5.95005i	−0.291027	−	0.291027i
$419$	−5.52014			−0.269676			−0.134838	−	0.990868i	$-0.543051\pi$
$419$	−5.52014			−0.269676			−0.134838	+	0.990868i	$0.543051\pi$
$420$		0			0
$421$	6.59688			0.321512			0.160756	−	0.986994i	$-0.448607\pi$
$421$	6.59688			0.321512			0.160756	+	0.986994i	$0.448607\pi$
$422$	7.64117	+	7.64117i	0.371966	+	0.371966i
$423$		0			0
$424$			3.40312i			0.165270i
$425$	1.63888	+	3.49799i	0.0794976	+	0.169678i
$426$		0			0
$427$	9.60803	−	0.204907i	0.464965	−	0.00991617i
$428$	−0.422055	+	0.422055i	−0.0204008	+	0.0204008i
$429$		0			0
$430$	−3.63232	−	5.17748i	−0.175166	−	0.249680i
$431$	−27.0181			−1.30142			−0.650708	−	0.759328i	$-0.725528\pi$
$431$	−27.0181			−1.30142			−0.650708	+	0.759328i	$0.725528\pi$
$432$		0			0
$433$	9.31137	+	9.31137i	0.447476	+	0.447476i	0.894515	−	0.447039i	$-0.147521\pi$
$433$	9.31137	+	9.31137i	0.447476	+	0.447476i	−0.447039	+	0.894515i	$0.647521\pi$
$434$	5.46295	+	5.23480i	0.262230	+	0.251278i
$435$		0			0
$436$	13.4031			0.641893
$437$	31.1473	−	31.1473i	1.48998	−	1.48998i
$438$		0			0
$439$	9.58237			0.457342			0.228671	−	0.973504i	$-0.426562\pi$
$439$	9.58237			0.457342			0.228671	+	0.973504i	$0.426562\pi$
$440$	3.11473	+	0.546295i	0.148489	+	0.0260436i
$441$		0			0
$442$	0.596876	+	0.596876i	0.0283905	+	0.0283905i
$443$	−7.49312	+	7.49312i	−0.356009	+	0.356009i	−0.862340	−	0.506331i	$-0.831002\pi$
$443$	−7.49312	+	7.49312i	−0.356009	+	0.356009i	0.506331	+	0.862340i	$0.331002\pi$
$444$		0			0
$445$	14.5969	+	20.8062i	0.691958	+	0.986311i
$446$			4.75362i			0.225090i
$447$		0			0
$448$	2.64515	−	0.0564123i	0.124972	−	0.00266523i
$449$			35.9254i			1.69543i	0.530455	+	0.847713i	$0.322021\pi$
$449$			35.9254i			1.69543i	−0.530455	+	0.847713i	$0.677979\pi$
$450$		0			0
$451$			3.09031i			0.145517i
$452$	−11.8838	−	11.8838i	−0.558968	−	0.558968i
$453$		0			0
$454$	14.9904			0.703535
$455$	−6.38902	−	0.980649i	−0.299522	−	0.0459736i
$456$		0			0
$457$	19.8062	+	19.8062i	0.926497	+	0.926497i	0.997478	−	0.0709805i	$-0.0226128\pi$
$457$	19.8062	+	19.8062i	0.926497	+	0.926497i	−0.0709805	+	0.997478i	$0.522613\pi$
$458$	17.2125	+	17.2125i	0.804290	+	0.804290i
$459$		0			0
$460$	−2.85974	+	16.3050i	−0.133336	+	0.760225i
$461$			17.2125i			0.801668i	0.916151	+	0.400834i	$0.131280\pi$
$461$			17.2125i			0.801668i	−0.916151	+	0.400834i	$0.868720\pi$
$462$		0			0
$463$	6.10469	−	6.10469i	0.283709	−	0.283709i	−0.550877	−	0.834586i	$-0.685707\pi$
$463$	6.10469	−	6.10469i	0.283709	−	0.283709i	0.834586	+	0.550877i	$0.185707\pi$
$464$			0.992159i			0.0460598i
$465$		0			0
$466$	6.00000			0.277945
$467$	25.6272	−	25.6272i	1.18589	−	1.18589i	0.207691	−	0.978195i	$-0.433405\pi$
$467$	25.6272	−	25.6272i	1.18589	−	1.18589i	0.978195	−	0.207691i	$-0.0665947\pi$
$468$		0			0
$469$	10.3550	−	10.8062i	0.478147	−	0.498986i
$470$	−13.2980	−	18.9549i	−0.613392	−	0.874323i
$471$		0			0
$472$	−8.53879	+	8.53879i	−0.393030	+	0.393030i
$473$	2.82843	−	2.82843i	0.130051	−	0.130051i
$474$		0			0
$475$	10.1244	−	27.9745i	0.464539	−	1.28356i
$476$	−1.41421	+	1.47585i	−0.0648204	+	0.0676454i
$477$		0			0
$478$	10.2984	−	10.2984i	0.471040	−	0.471040i
$479$	−21.9662			−1.00366			−0.501830	−	0.864966i	$-0.667340\pi$
$479$	−21.9662			−1.00366			−0.501830	+	0.864966i	$0.667340\pi$
$480$		0			0
$481$		−	8.80980i		−	0.401692i
$482$	13.9348	−	13.9348i	0.634712	−	0.634712i
$483$		0			0
$484$		−	9.00000i		−	0.409091i
$485$	−24.1897	−	4.24264i	−1.09840	−	0.192648i
$486$		0			0
$487$	−15.5078	−	15.5078i	−0.702726	−	0.702726i	0.262269	−	0.964995i	$-0.415529\pi$
$487$	−15.5078	−	15.5078i	−0.702726	−	0.702726i	−0.964995	+	0.262269i	$0.915529\pi$
$488$	−2.56844	−	2.56844i	−0.116268	−	0.116268i
$489$		0			0
$490$	2.04427	−	15.5184i	0.0923506	−	0.701050i
$491$	22.0573			0.995433			0.497716	−	0.867340i	$-0.334172\pi$
$491$	22.0573			0.995433			0.497716	+	0.867340i	$0.334172\pi$
$492$		0			0
$493$	−0.542011	−	0.542011i	−0.0244109	−	0.0244109i
$494$		−	6.50096i		−	0.292492i
$495$		0			0
$496$		−	2.85974i		−	0.128406i
$497$	0.454865	+	21.3284i	0.0204035	+	0.956711i
$498$		0			0
$499$		−	8.00000i		−	0.358129i	−0.983837	−	0.179065i	$-0.942693\pi$
$499$		−	8.00000i		−	0.358129i	0.983837	−	0.179065i	$-0.0573071\pi$
$500$	2.92310	+	10.7915i	0.130725	+	0.482608i
$501$		0			0
$502$	17.3486	−	17.3486i	0.774305	−	0.774305i
$503$	−4.04429	−	4.04429i	−0.180326	−	0.180326i	0.611172	−	0.791498i	$-0.290698\pi$
$503$	−4.04429	−	4.04429i	−0.180326	−	0.180326i	−0.791498	+	0.611172i	$0.790698\pi$
$504$		0			0
$505$	−16.1047	+	11.2984i	−0.716649	+	0.502774i
$506$	−10.4696			−0.465430
$507$		0			0
$508$	−0.701562	+	0.701562i	−0.0311268	+	0.0311268i
$509$	28.9050			1.28119			0.640595	−	0.767879i	$-0.278688\pi$
$509$	28.9050			1.28119			0.640595	+	0.767879i	$0.278688\pi$
$510$		0			0
$511$	−29.5078	+	30.7938i	−1.30535	+	1.36224i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	−2.31773			−0.102231
$515$	−5.38285	+	30.6906i	−0.237197	+	1.35239i
$516$		0			0
$517$	10.3550	−	10.3550i	0.455410	−	0.455410i
$518$	21.3284	−	0.454865i	0.937118	−	0.0199856i
$519$		0			0
$520$	1.40312	+	2.00000i	0.0615311	+	0.0877058i
$521$		−	22.2922i		−	0.976641i	−0.872664	−	0.488320i	$-0.837610\pi$
$521$		−	22.2922i		−	0.976641i	0.872664	−	0.488320i	$-0.162390\pi$
$522$		0			0
$523$	11.1275	+	11.1275i	0.486573	+	0.486573i	0.907223	−	0.420650i	$-0.138198\pi$
$523$	11.1275	+	11.1275i	0.486573	+	0.486573i	−0.420650	+	0.907223i	$0.638198\pi$
$524$	−2.56844			−0.112203
$525$		0			0
$526$	−16.0000			−0.697633
$527$	1.56226	+	1.56226i	0.0680532	+	0.0680532i
$528$		0			0
$529$		−	31.8062i		−	1.38288i
$530$	−4.37036	−	6.22947i	−0.189836	−	0.270591i
$531$		0			0
$532$	15.7388	−	0.335656i	0.682363	−	0.0145525i
$533$	−1.68822	+	1.68822i	−0.0731249	+	0.0731249i
$534$		0			0
$535$	0.230566	−	1.31459i	0.00996825	−	0.0568346i
$536$	−5.65685			−0.244339
$537$		0			0
$538$	−12.9437	−	12.9437i	−0.558042	−	0.558042i
$539$	9.89049	−	0.422055i	0.426014	−	0.0181792i
$540$		0			0
$541$	−18.0000			−0.773880			−0.386940	−	0.922105i	$-0.626468\pi$
$541$	−18.0000			−0.773880			−0.386940	+	0.922105i	$0.626468\pi$
$542$	8.96094	−	8.96094i	0.384905	−	0.384905i
$543$		0			0
$544$	0.772577			0.0331240
$545$	−24.5346	+	17.2125i	−1.05095	+	0.737305i
$546$		0			0
$547$	−29.4031	−	29.4031i	−1.25719	−	1.25719i	−0.952430	−	0.304757i	$-0.901425\pi$
$547$	−29.4031	−	29.4031i	−1.25719	−	1.25719i	−0.304757	−	0.952430i	$-0.598575\pi$
$548$	6.22696	−	6.22696i	0.266002	−	0.266002i
$549$		0			0
$550$	−6.40312	+	3.00000i	−0.273030	+	0.127920i
$551$			5.90340i			0.251493i
$552$		0			0
$553$	14.2921	−	0.304803i	0.607761	−	0.0129615i
$554$		−	7.21912i		−	0.306711i
$555$		0			0
$556$			7.49521i			0.317868i
$557$	10.8917	+	10.8917i	0.461494	+	0.461494i	0.899145	−	0.437651i	$-0.144189\pi$
$557$	10.8917	+	10.8917i	0.461494	+	0.461494i	−0.437651	+	0.899145i	$0.644189\pi$
$558$		0			0
$559$	3.09031			0.130706
$560$	−4.76954	+	3.50022i	−0.201550	+	0.147911i
$561$		0			0
$562$	−14.0000	−	14.0000i	−0.590554	−	0.590554i
$563$	−24.9179	−	24.9179i	−1.05016	−	1.05016i	−0.998674	−	0.0514892i	$-0.983603\pi$
$563$	−24.9179	−	24.9179i	−1.05016	−	1.05016i	−0.0514892	−	0.998674i	$-0.516397\pi$
$564$		0			0
$565$	37.0149	+	6.49206i	1.55723	+	0.273123i
$566$		−	0.766519i		−	0.0322192i
$567$		0			0
$568$	5.70156	−	5.70156i	0.239232	−	0.239232i
$569$			45.5509i			1.90959i	0.297258	+	0.954797i	$0.403928\pi$
$569$			45.5509i			1.90959i	−0.297258	+	0.954797i	$0.596072\pi$
$570$		0			0
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$	−1.09259	+	1.09259i	−0.0456835	+	0.0456835i
$573$		0			0
$574$	−4.17433	−	4.00000i	−0.174233	−	0.166957i
$575$	−15.7044	−	33.5191i	−0.654919	−	1.39784i
$576$		0			0
$577$	15.0309	−	15.0309i	0.625743	−	0.625743i	−0.321251	−	0.946994i	$-0.604103\pi$
$577$	15.0309	−	15.0309i	0.625743	−	0.625743i	0.946994	+	0.321251i	$0.104103\pi$
$578$	11.5988	−	11.5988i	0.482445	−	0.482445i
$579$		0			0
$580$	−1.27415	−	1.81616i	−0.0529062	−	0.0754119i
$581$	−22.7755	+	23.7681i	−0.944886	+	0.986066i
$582$		0			0
$583$	3.40312	−	3.40312i	0.140943	−	0.140943i
$584$	16.1200			0.667049
$585$		0			0
$586$		−	24.5728i		−	1.01509i
$587$	−15.0274	+	15.0274i	−0.620246	+	0.620246i	−0.945594	−	0.325348i	$-0.894518\pi$
$587$	−15.0274	+	15.0274i	−0.620246	+	0.620246i	0.325348	+	0.945594i	$0.394518\pi$
$588$		0			0
$589$		−	17.0156i		−	0.701116i
$590$	4.66470	−	26.5961i	0.192042	−	1.09494i
$591$		0			0
$592$	−5.70156	−	5.70156i	−0.234333	−	0.234333i
$593$	−32.0197	−	32.0197i	−1.31489	−	1.31489i	−0.917763	−	0.397128i	$-0.870007\pi$
$593$	−32.0197	−	32.0197i	−1.31489	−	1.31489i	−0.397128	−	0.917763i	$-0.629993\pi$
$594$		0			0
$595$	0.693424	−	4.51772i	0.0284276	−	0.185209i
$596$	17.1186			0.701206
$597$		0			0
$598$	−5.71949	−	5.71949i	−0.233887	−	0.233887i
$599$		−	11.7358i		−	0.479510i	−0.970833	−	0.239755i	$-0.922933\pi$
$599$		−	11.7358i		−	0.479510i	0.970833	−	0.239755i	$-0.0770672\pi$
$600$		0			0
$601$		−	33.6940i		−	1.37441i	−0.726464	−	0.687204i	$-0.758838\pi$
$601$		−	33.6940i		−	1.37441i	0.726464	−	0.687204i	$-0.241162\pi$
$602$	0.159558	+	7.48161i	0.00650310	+	0.304928i
$603$		0			0
$604$		−	6.80625i		−	0.276942i
$605$	11.5580	+	16.4746i	0.469898	+	0.669789i
$606$		0			0
$607$	6.99364	−	6.99364i	0.283863	−	0.283863i	−0.550785	−	0.834647i	$-0.685671\pi$
$607$	6.99364	−	6.99364i	0.283863	−	0.283863i	0.834647	+	0.550785i	$0.185671\pi$
$608$	−4.20732	−	4.20732i	−0.170629	−	0.170629i
$609$		0			0
$610$	8.00000	+	1.40312i	0.323911	+	0.0568108i
$611$	11.3137			0.457704
$612$		0			0
$613$	−21.7016	+	21.7016i	−0.876518	+	0.876518i	−0.993173	−	0.116655i	$-0.962783\pi$
$613$	−21.7016	+	21.7016i	−0.876518	+	0.876518i	0.116655	+	0.993173i	$0.462783\pi$
$614$	20.8736			0.842389
$615$		0			0
$616$	−2.70156	−	2.58874i	−0.108849	−	0.104303i
$617$	5.38285	+	5.38285i	0.216705	+	0.216705i	0.807108	−	0.590403i	$-0.201031\pi$
$617$	5.38285	+	5.38285i	0.216705	+	0.216705i	−0.590403	+	0.807108i	$0.701031\pi$
$618$		0			0
$619$	−17.3890			−0.698924			−0.349462	−	0.936951i	$-0.613636\pi$
$619$	−17.3890			−0.698924			−0.349462	+	0.936951i	$0.613636\pi$
$620$	3.67254	+	5.23480i	0.147493	+	0.210235i
$621$		0			0
$622$	−2.08717	+	2.08717i	−0.0836877	+	0.0836877i
$623$	−0.641201	−	30.0657i	−0.0256892	−	1.20456i
$624$		0			0
$625$	−19.2094	−	16.0000i	−0.768375	−	0.640000i
$626$			20.4903i			0.818958i
$627$		0			0
$628$	12.6727	+	12.6727i	0.505695	+	0.505695i
$629$	6.22947			0.248385
$630$		0			0
$631$	21.4031			0.852045			0.426022	−	0.904713i	$-0.359914\pi$
$631$	21.4031			0.852045			0.426022	+	0.904713i	$0.359914\pi$
$632$	−3.82059	−	3.82059i	−0.151975	−	0.151975i
$633$		0			0
$634$		−	2.00000i		−	0.0794301i
$635$	0.383260	−	2.18518i	0.0152092	−	0.0867162i
$636$		0			0
$637$	5.63369	+	5.17256i	0.223215	+	0.204944i
$638$	0.992159	−	0.992159i	0.0392799	−	0.0392799i
$639$		0			0
$640$	2.20245	+	0.386289i	0.0870594	+	0.0152694i
$641$	−29.1284			−1.15050			−0.575251	−	0.817977i	$-0.695096\pi$
$641$	−29.1284			−1.15050			−0.575251	+	0.817977i	$0.695096\pi$
$642$		0			0
$643$	2.31773	+	2.31773i	0.0914024	+	0.0914024i	0.751330	−	0.659927i	$-0.229413\pi$
$643$	2.31773	+	2.31773i	0.0914024	+	0.0914024i	−0.659927	+	0.751330i	$0.729413\pi$
$644$	13.5515	−	14.1421i	0.534005	−	0.557278i
$645$		0			0
$646$	4.59688			0.180862
$647$	−9.18116	+	9.18116i	−0.360949	+	0.360949i	−0.864162	−	0.503213i	$-0.832151\pi$
$647$	−9.18116	+	9.18116i	−0.360949	+	0.360949i	0.503213	+	0.864162i	$0.332151\pi$
$648$		0			0
$649$	17.0776			0.670354
$650$	−5.13688	−	1.85911i	−0.201485	−	0.0729202i
$651$		0			0
$652$	11.4031	+	11.4031i	0.446581	+	0.446581i
$653$	17.5407	−	17.5407i	0.686419	−	0.686419i	−0.275019	−	0.961439i	$-0.588684\pi$
$653$	17.5407	−	17.5407i	0.686419	−	0.686419i	0.961439	+	0.275019i	$0.0886843\pi$
$654$		0			0
$655$	4.70156	−	3.29844i	0.183705	−	0.128881i
$656$			2.18518i			0.0853169i
$657$		0			0
$658$	0.584146	+	27.3904i	0.0227724	+	1.06779i
$659$			38.4799i			1.49896i	0.662025	+	0.749481i	$0.269697\pi$
$659$			38.4799i			1.49896i	−0.662025	+	0.749481i	$0.730303\pi$
$660$		0			0
$661$		−	18.1616i		−	0.706404i	−0.935547	−	0.353202i	$-0.885093\pi$
$661$		−	18.1616i		−	0.706404i	0.935547	−	0.353202i	$-0.114907\pi$
$662$	18.1108	+	18.1108i	0.703895	+	0.703895i
$663$		0			0
$664$	12.4421			0.482848
$665$	−28.3790	+	20.8265i	−1.10049	+	0.807616i
$666$		0			0
$667$	5.19375	+	5.19375i	0.201103	+	0.201103i
$668$	−6.22947	−	6.22947i	−0.241025	−	0.241025i
$669$		0			0
$670$	10.3550	−	7.26464i	0.400047	−	0.280658i
$671$			5.13688i			0.198307i
$672$		0			0
$673$	8.19375	−	8.19375i	0.315846	−	0.315846i	−0.531323	−	0.847169i	$-0.678305\pi$
$673$	8.19375	−	8.19375i	0.315846	−	0.315846i	0.847169	+	0.531323i	$0.178305\pi$
$674$			1.41421i			0.0544735i
$675$		0			0
$676$	11.8062			0.454086
$677$	−28.3587	+	28.3587i	−1.08991	+	1.08991i	−0.0943755	+	0.995537i	$0.530085\pi$
$677$	−28.3587	+	28.3587i	−1.08991	+	1.08991i	−0.995537	+	0.0943755i	$0.969915\pi$
$678$		0			0
$679$	20.9809	+	20.1047i	0.805173	+	0.771547i
$680$	−1.41421	+	0.992159i	−0.0542326	+	0.0380475i
$681$		0			0
$682$	−2.85974	+	2.85974i	−0.109505	+	0.109505i
$683$	23.7676	−	23.7676i	0.909443	−	0.909443i	−0.0867843	−	0.996227i	$-0.527659\pi$
$683$	23.7676	−	23.7676i	0.909443	−	0.909443i	0.996227	+	0.0867843i	$0.0276591\pi$
$684$		0			0
$685$	−3.40175	+	19.3953i	−0.129974	+	0.741057i
$686$	−12.2318	+	13.9062i	−0.467014	+	0.530941i
$687$		0			0
$688$	2.00000	−	2.00000i	0.0762493	−	0.0762493i
$689$	3.71822			0.141653
$690$		0			0
$691$			10.1244i			0.385150i	0.981282	+	0.192575i	$0.0616838\pi$
$691$			10.1244i			0.385150i	−0.981282	+	0.192575i	$0.938316\pi$
$692$	−6.39250	+	6.39250i	−0.243006	+	0.243006i
$693$		0			0
$694$		−	24.2094i		−	0.918975i
$695$	−9.62549	−	13.7201i	−0.365116	−	0.520432i
$696$		0			0
$697$	−1.19375	−	1.19375i	−0.0452166	−	0.0452166i
$698$	6.93880	+	6.93880i	0.262637	+	0.262637i
$699$		0			0
$700$	4.23566	−	12.5323i	0.160093	−	0.473677i
$701$	25.3078			0.955862			0.477931	−	0.878397i	$-0.341387\pi$
$701$	25.3078			0.955862			0.477931	+	0.878397i	$0.341387\pi$
$702$		0			0
$703$	−33.9246	−	33.9246i	−1.27949	−	1.27949i
$704$			1.41421i			0.0533002i
$705$		0			0
$706$			14.2178i			0.535095i
$707$	23.2718	−	0.496310i	0.875225	−	0.0186657i
$708$		0			0
$709$		−	23.0156i		−	0.864370i	−0.901785	−	0.432185i	$-0.857743\pi$
$709$		−	23.0156i		−	0.864370i	0.901785	−	0.432185i	$-0.142257\pi$
$710$	−3.11473	+	17.7588i	−0.116894	+	0.666478i
$711$		0			0
$712$	−8.03722	+	8.03722i	−0.301207	+	0.301207i
$713$	−14.9702	−	14.9702i	−0.560638	−	0.560638i
$714$		0			0
$715$	0.596876	−	3.40312i	0.0223219	−	0.127270i
$716$	14.7122			0.549822
$717$		0			0
$718$	−0.895314	+	0.895314i	−0.0334128	+	0.0334128i
$719$	27.1030			1.01077			0.505386	−	0.862893i	$-0.331350\pi$
$719$	27.1030			1.01077			0.505386	+	0.862893i	$0.331350\pi$
$720$		0			0
$721$	25.5078	−	26.6195i	0.949961	−	0.991362i
$722$	−11.5988	−	11.5988i	−0.431661	−	0.431661i
$723$		0			0
$724$	−15.5324			−0.577258
$725$	4.66470	+	1.68822i	0.173242	+	0.0626989i
$726$		0			0
$727$	17.8906	−	17.8906i	0.663525	−	0.663525i	−0.292684	−	0.956209i	$-0.594548\pi$
$727$	17.8906	−	17.8906i	0.663525	−	0.663525i	0.956209	+	0.292684i	$0.0945483\pi$
$728$	−0.0616355	−	2.89006i	−0.00228436	−	0.107113i
$729$		0			0
$730$	−29.5078	+	20.7016i	−1.09213	+	0.766199i
$731$			2.18518i			0.0808218i
$732$		0			0
$733$	25.1148	+	25.1148i	0.927636	+	0.927636i	0.997553	−	0.0699166i	$-0.0222733\pi$
$733$	25.1148	+	25.1148i	0.927636	+	0.927636i	−0.0699166	+	0.997553i	$0.522273\pi$
$734$	15.0274			0.554670
$735$		0			0
$736$	−7.40312			−0.272883
$737$	5.65685	+	5.65685i	0.208373	+	0.208373i
$738$		0			0
$739$		−	9.19375i		−	0.338198i	−0.985599	−	0.169099i	$-0.945914\pi$
$739$		−	9.19375i		−	0.338198i	0.985599	−	0.169099i	$-0.0540857\pi$
$740$	17.7588	+	3.11473i	0.652828	+	0.114500i
$741$		0			0
$742$	0.191978	+	9.00177i	0.00704773	+	0.330466i
$743$	−22.6274	+	22.6274i	−0.830119	+	0.830119i	−0.987533	−	0.157413i	$-0.949684\pi$
$743$	−22.6274	+	22.6274i	−0.830119	+	0.830119i	0.157413	+	0.987533i	$0.449684\pi$
$744$		0			0
$745$	−31.3359	+	21.9840i	−1.14806	+	0.805433i
$746$	5.23480			0.191660
$747$		0			0
$748$	−0.772577	−	0.772577i	−0.0282482	−	0.0282482i
$749$	−1.09259	+	1.14021i	−0.0399223	+	0.0416623i
$750$		0			0
$751$	4.20937			0.153602			0.0768011	−	0.997046i	$-0.475529\pi$
$751$	4.20937			0.153602			0.0768011	+	0.997046i	$0.475529\pi$
$752$	7.32206	−	7.32206i	0.267008	−	0.267008i
$753$		0			0
$754$	1.08402			0.0394778
$755$	8.74071	+	12.4589i	0.318107	+	0.453427i
$756$		0			0
$757$	0.507811	+	0.507811i	0.0184567	+	0.0184567i	0.716275	−	0.697818i	$-0.245846\pi$
$757$	0.507811	+	0.507811i	0.0184567	+	0.0184567i	−0.697818	+	0.716275i	$0.745846\pi$
$758$	12.4539	−	12.4539i	0.452347	−	0.452347i
$759$		0			0
$760$	13.1047	+	2.29844i	0.475357	+	0.0833731i
$761$			34.4251i			1.24791i	0.781461	+	0.623954i	$0.214475\pi$
$761$			34.4251i			1.24791i	−0.781461	+	0.623954i	$0.785525\pi$
$762$		0			0
$763$	35.4533	−	0.756101i	1.28349	−	0.0273727i
$764$			24.1897i			0.875152i
$765$		0			0
$766$		−	23.3391i		−	0.843275i
$767$	9.32939	+	9.32939i	0.336865	+	0.336865i
$768$		0			0
$769$	−35.7003			−1.28739			−0.643693	−	0.765284i	$-0.722599\pi$
$769$	−35.7003			−1.28739			−0.643693	+	0.765284i	$0.722599\pi$
$770$	8.26975	+	1.26932i	0.298021	+	0.0457432i
$771$		0			0
$772$	−11.0000	−	11.0000i	−0.395899	−	0.395899i
$773$	14.4811	+	14.4811i	0.520848	+	0.520848i	0.917828	−	0.396979i	$-0.129942\pi$
$773$	14.4811	+	14.4811i	0.520848	+	0.520848i	−0.396979	+	0.917828i	$0.629942\pi$
$774$		0			0
$775$	−13.4453	−	4.86603i	−0.482968	−	0.174793i
$776$		−	10.9831i		−	0.394270i
$777$		0			0
$778$	−9.29844	+	9.29844i	−0.333365	+	0.333365i
$779$			13.0019i			0.465842i
$780$		0			0
$781$	−11.4031			−0.408036
$782$	4.04429	−	4.04429i	0.144623	−	0.144623i
$783$		0			0
$784$	6.99364	−	0.298438i	0.249773	−	0.0106585i
$785$	−39.4720	−	6.92302i	−1.40882	−	0.247093i
$786$		0			0
$787$	−17.3081	+	17.3081i	−0.616969	+	0.616969i	−0.944753	−	0.327784i	$-0.893698\pi$
$787$	−17.3081	+	17.3081i	−0.616969	+	0.616969i	0.327784	+	0.944753i	$0.393698\pi$
$788$	16.5485	−	16.5485i	0.589516	−	0.589516i
$789$		0			0
$790$	11.9001	+	2.08717i	0.423387	+	0.0742580i
$791$	−32.1049	−	30.7641i	−1.14152	−	1.09384i
$792$		0			0
$793$	−2.80625	+	2.80625i	−0.0996528	+	0.0996528i
$794$	8.41464			0.298625
$795$		0			0
$796$			27.2020i			0.964148i
$797$	14.4811	−	14.4811i	0.512946	−	0.512946i	−0.402482	−	0.915428i	$-0.631852\pi$
$797$	14.4811	−	14.4811i	0.512946	−	0.512946i	0.915428	+	0.402482i	$0.131852\pi$
$798$		0			0
$799$			8.00000i			0.283020i
$800$	−4.52769	+	2.12132i	−0.160078	+	0.0750000i
$801$		0			0
$802$	16.2094	+	16.2094i	0.572373	+	0.572373i
$803$	−16.1200	−	16.1200i	−0.568861	−	0.568861i
$804$		0			0
$805$	−6.64465	+	43.2905i	−0.234193	+	1.52579i
$806$	−3.12452			−0.110057
$807$		0			0
$808$	−6.22106	−	6.22106i	−0.218856	−	0.218856i
$809$			20.0951i			0.706506i	0.935528	+	0.353253i	$0.114924\pi$
$809$			20.0951i			0.706506i	−0.935528	+	0.353253i	$0.885076\pi$
$810$		0			0
$811$			10.1244i			0.355515i	0.984074	+	0.177758i	$0.0568843\pi$
$811$			10.1244i			0.355515i	−0.984074	+	0.177758i	$0.943116\pi$
$812$	0.0559699	+	2.62441i	0.00196416	+	0.0920987i
$813$		0			0
$814$			11.4031i			0.399679i
$815$	−35.5177	−	6.22947i	−1.24413	−	0.218209i
$816$		0			0
$817$	11.9001	−	11.9001i	0.416332	−	0.416332i
$818$	2.56844	+	2.56844i	0.0898033	+	0.0898033i
$819$		0			0
$820$	−2.80625	−	4.00000i	−0.0979984	−	0.139686i
$821$	46.5431			1.62437			0.812183	−	0.583403i	$-0.198279\pi$
$821$	46.5431			1.62437			0.812183	+	0.583403i	$0.198279\pi$
$822$		0			0
$823$	−16.9109	+	16.9109i	−0.589478	+	0.589478i	−0.937490	−	0.348012i	$-0.886857\pi$
$823$	−16.9109	+	16.9109i	−0.589478	+	0.589478i	0.348012	+	0.937490i	$0.386857\pi$
$824$	−13.9348			−0.485441
$825$		0			0
$826$	−22.1047	+	23.0681i	−0.769120	+	0.802641i
$827$	−7.91518	−	7.91518i	−0.275238	−	0.275238i	0.555967	−	0.831204i	$-0.312348\pi$
$827$	−7.91518	−	7.91518i	−0.275238	−	0.275238i	−0.831204	+	0.555967i	$0.812348\pi$
$828$		0			0
$829$	−49.6876			−1.72572			−0.862861	−	0.505442i	$-0.831329\pi$
$829$	−49.6876			−1.72572			−0.862861	+	0.505442i	$0.831329\pi$
$830$	−22.7755	+	15.9784i	−0.790548	+	0.554619i
$831$		0			0
$832$	−0.772577	+	0.772577i	−0.0267843	+	0.0267843i
$833$	−3.65755	+	3.98362i	−0.126727	+	0.138024i
$834$		0			0
$835$	19.4031	+	3.40312i	0.671473	+	0.117770i
$836$			8.41464i			0.291027i
$837$		0			0
$838$	3.90333	+	3.90333i	0.134838	+	0.134838i
$839$	19.0145			0.656452			0.328226	−	0.944599i	$-0.393549\pi$
$839$	19.0145			0.656452			0.328226	+	0.944599i	$0.393549\pi$
$840$		0			0
$841$	28.0156			0.966056
$842$	−4.66470	−	4.66470i	−0.160756	−	0.160756i
$843$		0			0
$844$		−	10.8062i		−	0.371966i
$845$	−21.6115	+	15.1618i	−0.743458	+	0.521582i
$846$		0			0
$847$	−0.507711	−	23.8063i	−0.0174451	−	0.817996i
$848$	2.40637	−	2.40637i	0.0826352	−	0.0826352i
$849$		0			0
$850$	1.31459	−	3.63232i	0.0450900	−	0.124588i
$851$	−59.6931			−2.04625
$852$		0			0
$853$	−20.9405	−	20.9405i	−0.716988	−	0.716988i	0.250999	−	0.967987i	$-0.419241\pi$
$853$	−20.9405	−	20.9405i	−0.716988	−	0.716988i	−0.967987	+	0.250999i	$0.919241\pi$
$854$	−6.93880	−	6.64901i	−0.237441	−	0.227525i
$855$		0			0
$856$	0.596876			0.0204008
$857$	7.86835	−	7.86835i	0.268778	−	0.268778i	−0.559830	−	0.828608i	$-0.689134\pi$
$857$	7.86835	−	7.86835i	0.268778	−	0.268778i	0.828608	+	0.559830i	$0.189134\pi$
$858$		0			0
$859$	26.6600			0.909626			0.454813	−	0.890587i	$-0.349706\pi$
$859$	26.6600			0.909626			0.454813	+	0.890587i	$0.349706\pi$
$860$	−1.09259	+	6.22947i	−0.0372570	+	0.212423i
$861$		0			0
$862$	19.1047	+	19.1047i	0.650708	+	0.650708i
$863$	1.56226	−	1.56226i	0.0531800	−	0.0531800i	−0.680017	−	0.733197i	$-0.738027\pi$
$863$	1.56226	−	1.56226i	0.0531800	−	0.0531800i	0.733197	+	0.680017i	$0.238027\pi$
$864$		0			0
$865$	3.49219	−	19.9109i	0.118738	−	0.676992i
$866$		−	13.1683i		−	0.447476i
$867$		0			0
$868$	−0.161325	−	7.56445i	−0.00547571	−	0.256754i
$869$			7.64117i			0.259209i
$870$		0			0
$871$			6.18062i			0.209422i
$872$	−9.47744	−	9.47744i	−0.320947	−	0.320947i
$873$		0			0
$874$	−44.0490			−1.48998
$875$	8.34082	+	28.3801i	0.281971	+	0.959423i
$876$		0			0
$877$	38.5078	+	38.5078i	1.30032	+	1.30032i	0.928177	+	0.372140i	$0.121376\pi$
$877$	38.5078	+	38.5078i	1.30032	+	1.30032i	0.372140	+	0.928177i	$0.378624\pi$
$878$	−6.77576	−	6.77576i	−0.228671	−	0.228671i
$879$		0			0
$880$	−1.81616	−	2.58874i	−0.0612227	−	0.0872663i
$881$			4.81081i			0.162080i	0.996711	+	0.0810401i	$0.0258242\pi$
$881$			4.81081i			0.162080i	−0.996711	+	0.0810401i	$0.974176\pi$
$882$		0			0
$883$	−26.8062	+	26.8062i	−0.902102	+	0.902102i	−0.995618	−	0.0935157i	$-0.970189\pi$
$883$	−26.8062	+	26.8062i	−0.902102	+	0.902102i	0.0935157	+	0.995618i	$0.470189\pi$
$884$		−	0.844110i		−	0.0283905i
$885$		0			0
$886$	10.5969			0.356009
$887$	33.6586	−	33.6586i	1.13014	−	1.13014i	0.139992	−	0.990153i	$-0.455292\pi$
$887$	33.6586	−	33.6586i	1.13014	−	1.13014i	0.990153	−	0.139992i	$-0.0447076\pi$
$888$		0			0
$889$	−1.81616	+	1.89531i	−0.0609121	+	0.0635668i
$890$	4.39069	−	25.0338i	0.147176	−	0.839135i
$891$		0			0
$892$	3.36131	−	3.36131i	0.112545	−	0.112545i
$893$	43.5666	−	43.5666i	1.45790	−	1.45790i
$894$		0			0
$895$	−26.9310	+	18.8937i	−0.900203	+	0.631548i
$896$	−1.91029	−	1.83051i	−0.0638184	−	0.0611532i
$897$		0			0
$898$	25.4031	−	25.4031i	0.847713	−	0.847713i
$899$	2.83732			0.0946299
$900$		0			0
$901$			2.62918i			0.0875906i
$902$	2.18518	−	2.18518i	0.0727585	−	0.0727585i
$903$		0			0
$904$			16.8062i			0.558968i
$905$	28.4323	−	19.9470i	0.945122	−	0.663062i
$906$		0			0
$907$	29.4031	+	29.4031i	0.976315	+	0.976315i	0.999726	−	0.0234112i	$-0.00745270\pi$
$907$	29.4031	+	29.4031i	0.976315	+	0.976315i	−0.0234112	+	0.999726i	$0.507453\pi$
$908$	−10.5998	−	10.5998i	−0.351768	−	0.351768i
$909$		0			0
$910$	3.82430	+	5.21115i	0.126774	+	0.172748i
$911$	39.1759			1.29796			0.648978	−	0.760807i	$-0.275197\pi$
$911$	39.1759			1.29796			0.648978	+	0.760807i	$0.275197\pi$
$912$		0			0
$913$	−12.4421	−	12.4421i	−0.411774	−	0.411774i
$914$		−	28.0103i		−	0.926497i
$915$		0			0
$916$		−	24.3422i		−	0.804290i
$917$	−6.79390	+	0.144891i	−0.224354	+	0.00478474i
$918$		0			0
$919$			49.8219i			1.64347i	0.569868	+	0.821736i	$0.306994\pi$
$919$			49.8219i			1.64347i	−0.569868	+	0.821736i	$0.693006\pi$
$920$	13.5515	−	9.50723i	0.446780	−	0.313444i
$921$		0			0
$922$	12.1711	−	12.1711i	0.400834	−	0.400834i
$923$	−6.22947	−	6.22947i	−0.205045	−	0.205045i
$924$		0			0
$925$	−36.5078	+	17.1047i	−1.20037	+	0.562399i
$926$	−8.63333			−0.283709
$927$		0			0
$928$	0.701562	−	0.701562i	0.0230299	−	0.0230299i
$929$	−59.3430			−1.94698			−0.973490	−	0.228731i	$-0.926542\pi$
$929$	−59.3430			−1.94698			−0.973490	+	0.228731i	$0.926542\pi$
$930$		0			0
$931$	41.6125	−	1.77572i	1.36379	−	0.0581969i
$932$	−4.24264	−	4.24264i	−0.138972	−	0.138972i
$933$		0			0
$934$	−36.2423			−1.18589
$935$	2.40637	+	0.422055i	0.0786968	+	0.0138027i
$936$		0			0
$937$	−34.7376	+	34.7376i	−1.13483	+	1.13483i	−0.145465	+	0.989363i	$0.546468\pi$
$937$	−34.7376	+	34.7376i	−1.13483	+	1.13483i	−0.989363	+	0.145465i	$0.953532\pi$
$938$	−14.9632	+	0.319116i	−0.488567	+	0.0104195i
$939$		0			0
$940$	−4.00000	+	22.8062i	−0.130466	+	0.743858i
$941$			1.80192i			0.0587409i	0.999569	+	0.0293704i	$0.00935025\pi$
$941$			1.80192i			0.0587409i	−0.999569	+	0.0293704i	$0.990650\pi$
$942$		0			0
$943$	11.4390	+	11.4390i	0.372504	+	0.372504i
$944$	12.0757			0.393030
$945$		0			0
$946$	−4.00000			−0.130051
$947$	−28.4323	−	28.4323i	−0.923926	−	0.923926i	0.0733779	−	0.997304i	$-0.476622\pi$
$947$	−28.4323	−	28.4323i	−0.923926	−	0.923926i	−0.997304	+	0.0733779i	$0.976622\pi$
$948$		0			0
$949$		−	17.6125i		−	0.571726i
$950$	−26.9400	+	12.6220i	−0.874049	+	0.409511i
$951$		0			0
$952$	2.04358	−	0.0435829i	0.0662329	−	0.00141253i
$953$	−32.5269	+	32.5269i	−1.05365	+	1.05365i	−0.0551732	+	0.998477i	$0.517571\pi$
$953$	−32.5269	+	32.5269i	−1.05365	+	1.05365i	−0.998477	+	0.0551732i	$0.982429\pi$
$954$		0			0
$955$	−31.0649	−	44.2795i	−1.00523	−	1.43285i
$956$	−14.5642			−0.471040
$957$		0			0
$958$	15.5324	+	15.5324i	0.501830	+	0.501830i
$959$	16.1200	−	16.8225i	0.520541	−	0.543227i
$960$		0			0
$961$	22.8219			0.736189
$962$	−6.22947	+	6.22947i	−0.200846	+	0.200846i
$963$		0			0
$964$	−19.7068			−0.634712
$965$	34.2621	+	6.00924i	1.10293	+	0.193444i
$966$		0			0
$967$	−4.10469	−	4.10469i	−0.131998	−	0.131998i	0.638021	−	0.770019i	$-0.279753\pi$
$967$	−4.10469	−	4.10469i	−0.131998	−	0.131998i	−0.770019	+	0.638021i	$0.779753\pi$
$968$	−6.36396	+	6.36396i	−0.204545	+	0.204545i
$969$		0			0
$970$	14.1047	+	20.1047i	0.452874	+	0.645523i
$971$		−	45.0821i		−	1.44675i	−0.690453	−	0.723377i	$-0.742589\pi$
$971$		−	45.0821i		−	1.44675i	0.690453	−	0.723377i	$-0.257411\pi$
$972$		0			0
$973$	0.422822	+	19.8259i	0.0135550	+	0.635591i
$974$			21.9314i			0.702726i
$975$		0			0
$976$			3.63232i			0.116268i
$977$	28.0103	+	28.0103i	0.896128	+	0.896128i	0.995091	−	0.0989633i	$-0.0315526\pi$
$977$	28.0103	+	28.0103i	0.896128	+	0.896128i	−0.0989633	+	0.995091i	$0.531553\pi$
$978$		0			0
$979$	16.0744			0.513741
$980$	−12.4187	+	9.52766i	−0.396700	+	0.304350i
$981$		0			0
$982$	−15.5969	−	15.5969i	−0.497716	−	0.497716i
$983$	−20.5475	−	20.5475i	−0.655364	−	0.655364i	0.298916	−	0.954279i	$-0.403375\pi$
$983$	−20.5475	−	20.5475i	−0.655364	−	0.655364i	−0.954279	+	0.298916i	$0.903375\pi$
$984$		0			0
$985$	−9.04036	+	51.5442i	−0.288050	+	1.64233i
$986$			0.766519i			0.0244109i
$987$		0			0
$988$	−4.59688	+	4.59688i	−0.146246	+	0.146246i
$989$		−	20.9392i		−	0.665828i
$990$		0			0
$991$	−22.8062			−0.724464			−0.362232	−	0.932088i	$-0.617985\pi$
$991$	−22.8062			−0.724464			−0.362232	+	0.932088i	$0.617985\pi$
$992$	−2.02214	+	2.02214i	−0.0642031	+	0.0642031i
$993$		0			0
$994$	14.7598	−	15.4031i	0.468154	−	0.488557i
$995$	−34.9333	−	49.7936i	−1.10746	−	1.57856i
$996$		0			0
$997$	−23.0276	+	23.0276i	−0.729292	+	0.729292i	−0.970479	−	0.241186i	$-0.922463\pi$
$997$	−23.0276	+	23.0276i	−0.729292	+	0.729292i	0.241186	+	0.970479i	$0.422463\pi$
$998$	−5.65685	+	5.65685i	−0.179065	+	0.179065i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.p.d.307.2	✓	16
3.2	odd	2	inner	630.2.p.d.307.7	yes	16
5.3	odd	4	inner	630.2.p.d.433.3	yes	16
7.6	odd	2	inner	630.2.p.d.307.3	yes	16
15.8	even	4	inner	630.2.p.d.433.6	yes	16
21.20	even	2	inner	630.2.p.d.307.6	yes	16
35.13	even	4	inner	630.2.p.d.433.2	yes	16
105.83	odd	4	inner	630.2.p.d.433.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.p.d.307.2	✓	16	1.1	even	1	trivial
630.2.p.d.307.3	yes	16	7.6	odd	2	inner
630.2.p.d.307.6	yes	16	21.20	even	2	inner
630.2.p.d.307.7	yes	16	3.2	odd	2	inner
630.2.p.d.433.2	yes	16	35.13	even	4	inner
630.2.p.d.433.3	yes	16	5.3	odd	4	inner
630.2.p.d.433.6	yes	16	15.8	even	4	inner
630.2.p.d.433.7	yes	16	105.83	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-1.28422 - 1.83051i) q^{5} +(0.0564123 + 2.64515i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-1.28422 - 1.83051i) q^{5} +(0.0564123 + 2.64515i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.386289 + 2.20245i) q^{10} -1.41421 q^{11} +(-0.772577 - 0.772577i) q^{13} +(1.83051 - 1.91029i) q^{14} -1.00000 q^{16} +(0.546295 - 0.546295i) q^{17} -5.95005 q^{19} +(1.83051 - 1.28422i) q^{20} +(1.00000 + 1.00000i) q^{22} +(-5.23480 + 5.23480i) q^{23} +(-1.70156 + 4.70156i) q^{25} +1.09259i q^{26} +(-2.64515 + 0.0564123i) q^{28} -0.992159i q^{29} +2.85974i q^{31} +(0.707107 + 0.707107i) q^{32} -0.772577 q^{34} +(4.76954 - 3.50022i) q^{35} +(5.70156 + 5.70156i) q^{37} +(4.20732 + 4.20732i) q^{38} +(-2.20245 - 0.386289i) q^{40} -2.18518i q^{41} +(-2.00000 + 2.00000i) q^{43} -1.41421i q^{44} +7.40312 q^{46} +(-7.32206 + 7.32206i) q^{47} +(-6.99364 + 0.298438i) q^{49} +(4.52769 - 2.12132i) q^{50} +(0.772577 - 0.772577i) q^{52} +(-2.40637 + 2.40637i) q^{53} +(1.81616 + 2.58874i) q^{55} +(1.91029 + 1.83051i) q^{56} +(-0.701562 + 0.701562i) q^{58} -12.0757 q^{59} -3.63232i q^{61} +(2.02214 - 2.02214i) q^{62} -1.00000i q^{64} +(-0.422055 + 2.40637i) q^{65} +(-4.00000 - 4.00000i) q^{67} +(0.546295 + 0.546295i) q^{68} +(-5.84760 - 0.897546i) q^{70} +8.06323 q^{71} +(11.3985 + 11.3985i) q^{73} -8.06323i q^{74} -5.95005i q^{76} +(-0.0797790 - 3.74081i) q^{77} -5.40312i q^{79} +(1.28422 + 1.83051i) q^{80} +(-1.54515 + 1.54515i) q^{82} +(8.79790 + 8.79790i) q^{83} +(-1.70156 - 0.298438i) q^{85} +2.82843 q^{86} +(-1.00000 + 1.00000i) q^{88} -11.3663 q^{89} +(2.00000 - 2.08717i) q^{91} +(-5.23480 - 5.23480i) q^{92} +10.3550 q^{94} +(7.64117 + 10.8917i) q^{95} +(7.76621 - 7.76621i) q^{97} +(5.15627 + 4.73422i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{7}+O(q^{10}) \) 16 * q - 4 * q^7	\( 16 q - 4 q^{7} - 16 q^{16} + 16 q^{22} + 24 q^{25} + 4 q^{28} + 40 q^{37} - 32 q^{43} + 16 q^{46} + 40 q^{58} - 64 q^{67} - 12 q^{70} + 24 q^{85} - 16 q^{88} + 32 q^{91}+O(q^{100}) \) 16 * q - 4 * q^7 - 16 * q^16 + 16 * q^22 + 24 * q^25 + 4 * q^28 + 40 * q^37 - 32 * q^43 + 16 * q^46 + 40 * q^58 - 64 * q^67 - 12 * q^70 + 24 * q^85 - 16 * q^88 + 32 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more