LMFDB - Embedded newform 630.2.bo.b.269.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(89,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("630.89");

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.bo (of order $6$, 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 $\Q(\zeta_{6})$
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} - 6 x^{15} + 21 x^{14} - 54 x^{13} + 113 x^{12} - 168 x^{11} + 186 x^{10} - 84 x^{9} + \cdots + 390625 $ x^16 - 6x^15 + 21x^14 - 54x^13 + 113x^12 - 168x^11 + 186x^10 - 84x^9 - 6x^8 - 420x^7 + 4650x^6 - 21000x^5 + 70625x^4 - 168750x^3 + 328125x^2 - 468750*x + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.5
Root			$0.948234 + 2.02506i$ of defining polynomial
Character	$\chi$	$=$	630.269
Dual form			630.2.bo.b.89.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.948234 + 2.02506i) q^{5} +(0.732536 - 2.54232i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.948234 + 2.02506i) q^{5} +(0.732536 - 2.54232i) q^{7} -1.00000 q^{8} +(-1.27963 + 1.83372i) q^{10} +(2.07577 + 1.19845i) q^{11} +5.67714 q^{13} +(2.56798 - 0.636766i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.79434 + 1.03596i) q^{17} +(-5.12164 + 2.95698i) q^{19} +(-2.22787 - 0.191334i) q^{20} +2.39690i q^{22} +(0.930877 + 1.61233i) q^{23} +(-3.20171 + 3.84045i) q^{25} +(2.83857 + 4.91654i) q^{26} +(1.83545 + 1.90555i) q^{28} +4.88913i q^{29} +(-3.92008 - 2.26326i) q^{31} +(0.500000 - 0.866025i) q^{32} +2.07192i q^{34} +(5.84296 - 0.927288i) q^{35} +(-2.57132 + 1.48455i) q^{37} +(-5.12164 - 2.95698i) q^{38} +(-0.948234 - 2.02506i) q^{40} +7.04428 q^{41} -8.55956i q^{43} +(-2.07577 + 1.19845i) q^{44} +(-0.930877 + 1.61233i) q^{46} +(-4.83140 + 2.78941i) q^{47} +(-5.92678 - 3.72468i) q^{49} +(-4.92678 - 0.852531i) q^{50} +(-2.83857 + 4.91654i) q^{52} +(2.09538 - 3.62931i) q^{53} +(-0.458606 + 5.33996i) q^{55} +(-0.732536 + 2.54232i) q^{56} +(-4.23411 + 2.44457i) q^{58} +(1.00312 - 1.73746i) q^{59} +(10.7862 - 6.22739i) q^{61} -4.52651i q^{62} +1.00000 q^{64} +(5.38325 + 11.4965i) q^{65} +(-6.60103 - 3.81111i) q^{67} +(-1.79434 + 1.03596i) q^{68} +(3.72453 + 4.59650i) q^{70} +9.14126i q^{71} +(-0.541173 + 0.937339i) q^{73} +(-2.57132 - 1.48455i) q^{74} -5.91397i q^{76} +(4.56742 - 4.39937i) q^{77} +(8.38392 + 14.5214i) q^{79} +(1.27963 - 1.83372i) q^{80} +(3.52214 + 6.10053i) q^{82} -13.6122i q^{83} +(-0.396428 + 4.61597i) q^{85} +(7.41279 - 4.27978i) q^{86} +(-2.07577 - 1.19845i) q^{88} +(-6.63129 - 11.4857i) q^{89} +(4.15870 - 14.4331i) q^{91} -1.86175 q^{92} +(-4.83140 - 2.78941i) q^{94} +(-10.8446 - 7.56771i) q^{95} +12.8260 q^{97} +(0.262276 - 6.99508i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - 8 q^{4} + 6 q^{5} - 16 q^{8}+O(q^{10}) $ 16 * q + 8 * q^2 - 8 * q^4 + 6 * q^5 - 16 * q^8	$ 16 q + 8 q^{2} - 8 q^{4} + 6 q^{5} - 16 q^{8} + 6 q^{10} - 8 q^{16} + 24 q^{19} + 8 q^{23} - 6 q^{25} + 12 q^{31} + 8 q^{32} - 4 q^{35} + 24 q^{38} - 6 q^{40} - 8 q^{46} - 60 q^{47} - 28 q^{49} - 12 q^{50} - 16 q^{53} + 24 q^{61} + 16 q^{64} + 20 q^{65} - 14 q^{70} + 88 q^{77} + 4 q^{79} - 6 q^{80} + 64 q^{85} - 28 q^{91} - 16 q^{92} - 60 q^{94} + 12 q^{95} - 20 q^{98}+O(q^{100}) $ 16 * q + 8 * q^2 - 8 * q^4 + 6 * q^5 - 16 * q^8 + 6 * q^10 - 8 * q^16 + 24 * q^19 + 8 * q^23 - 6 * q^25 + 12 * q^31 + 8 * q^32 - 4 * q^35 + 24 * q^38 - 6 * q^40 - 8 * q^46 - 60 * q^47 - 28 * q^49 - 12 * q^50 - 16 * q^53 + 24 * q^61 + 16 * q^64 + 20 * q^65 - 14 * q^70 + 88 * q^77 + 4 * q^79 - 6 * q^80 + 64 * q^85 - 28 * q^91 - 16 * q^92 - 60 * q^94 + 12 * q^95 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.948234	+	2.02506i	0.424063	+	0.905633i
$5$	0.948234	+	2.02506i	0.424063	+	0.905633i
$6$		0			0
$7$	0.732536	−	2.54232i	0.276872	−	0.960907i
$7$	0.732536	−	2.54232i	0.276872	−	0.960907i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.27963	+	1.83372i	−0.404656	+	0.579874i
$11$	2.07577	+	1.19845i	0.625869	+	0.361346i	0.779150	−	0.626837i	$-0.215651\pi$
$11$	2.07577	+	1.19845i	0.625869	+	0.361346i	−0.153282	+	0.988183i	$0.548984\pi$
$12$		0			0
$13$	5.67714			1.57455			0.787277	−	0.616599i	$-0.211490\pi$
$13$	5.67714			1.57455			0.787277	+	0.616599i	$0.211490\pi$
$14$	2.56798	−	0.636766i	0.686322	−	0.170183i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.79434	+	1.03596i	0.435191	+	0.251258i	0.701556	−	0.712615i	$-0.252489\pi$
$17$	1.79434	+	1.03596i	0.435191	+	0.251258i	−0.266365	+	0.963872i	$0.585823\pi$
$18$		0			0
$19$	−5.12164	+	2.95698i	−1.17499	+	0.678378i	−0.954849	−	0.297091i	$-0.903984\pi$
$19$	−5.12164	+	2.95698i	−1.17499	+	0.678378i	−0.220136	+	0.975469i	$0.570650\pi$
$20$	−2.22787	−	0.191334i	−0.498166	−	0.0427835i
$21$		0			0
$22$			2.39690i			0.511020i
$23$	0.930877	+	1.61233i	0.194101	+	0.336193i	0.946606	−	0.322394i	$-0.104488\pi$
$23$	0.930877	+	1.61233i	0.194101	+	0.336193i	−0.752504	+	0.658587i	$0.771154\pi$
$24$		0			0
$25$	−3.20171	+	3.84045i	−0.640341	+	0.768091i
$26$	2.83857	+	4.91654i	0.556689	+	0.964214i
$27$		0			0
$28$	1.83545	+	1.90555i	0.346867	+	0.360116i
$29$			4.88913i			0.907889i	0.891030	+	0.453944i	$0.149984\pi$
$29$			4.88913i			0.907889i	−0.891030	+	0.453944i	$0.850016\pi$
$30$		0			0
$31$	−3.92008	−	2.26326i	−0.704067	−	0.406493i	0.104794	−	0.994494i	$-0.466582\pi$
$31$	−3.92008	−	2.26326i	−0.704067	−	0.406493i	−0.808860	+	0.588001i	$0.799915\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$			2.07192i			0.355332i
$35$	5.84296	−	0.927288i	0.987640	−	0.156740i
$36$		0			0
$37$	−2.57132	+	1.48455i	−0.422723	+	0.244059i	−0.696242	−	0.717807i	$-0.745146\pi$
$37$	−2.57132	+	1.48455i	−0.422723	+	0.244059i	0.273519	+	0.961867i	$0.411812\pi$
$38$	−5.12164	−	2.95698i	−0.830840	−	0.479686i
$39$		0			0
$40$	−0.948234	−	2.02506i	−0.149929	−	0.320189i
$41$	7.04428			1.10013			0.550066	−	0.835121i	$-0.314603\pi$
$41$	7.04428			1.10013			0.550066	+	0.835121i	$0.314603\pi$
$42$		0			0
$43$		−	8.55956i		−	1.30532i	−0.757651	−	0.652660i	$-0.773653\pi$
$43$		−	8.55956i		−	1.30532i	0.757651	−	0.652660i	$-0.226347\pi$
$44$	−2.07577	+	1.19845i	−0.312934	+	0.180673i
$45$		0			0
$46$	−0.930877	+	1.61233i	−0.137250	+	0.237725i
$47$	−4.83140	+	2.78941i	−0.704732	+	0.406877i	−0.809107	−	0.587661i	$-0.800049\pi$
$47$	−4.83140	+	2.78941i	−0.704732	+	0.406877i	0.104375	+	0.994538i	$0.466716\pi$
$48$		0			0
$49$	−5.92678	−	3.72468i	−0.846683	−	0.532097i
$50$	−4.92678	−	0.852531i	−0.696752	−	0.120566i
$51$		0			0
$52$	−2.83857	+	4.91654i	−0.393639	+	0.681802i
$53$	2.09538	−	3.62931i	0.287823	−	0.498524i	−0.685467	−	0.728104i	$-0.740402\pi$
$53$	2.09538	−	3.62931i	0.287823	−	0.498524i	0.973290	+	0.229580i	$0.0737352\pi$
$54$		0			0
$55$	−0.458606	+	5.33996i	−0.0618385	+	0.720041i
$56$	−0.732536	+	2.54232i	−0.0978892	+	0.339732i
$57$		0			0
$58$	−4.23411	+	2.44457i	−0.555966	+	0.320987i
$59$	1.00312	−	1.73746i	0.130595	−	0.226198i	−0.793311	−	0.608817i	$-0.791644\pi$
$59$	1.00312	−	1.73746i	0.130595	−	0.226198i	0.923906	+	0.382619i	$0.124978\pi$
$60$		0			0
$61$	10.7862	−	6.22739i	1.38103	−	0.797335i	0.388744	−	0.921346i	$-0.372909\pi$
$61$	10.7862	−	6.22739i	1.38103	−	0.797335i	0.992281	+	0.124011i	$0.0395757\pi$
$62$		−	4.52651i		−	0.574868i
$63$		0			0
$64$	1.00000			0.125000
$65$	5.38325	+	11.4965i	0.667710	+	1.42597i
$66$		0			0
$67$	−6.60103	−	3.81111i	−0.806445	−	0.465601i	0.0392750	−	0.999228i	$-0.487495\pi$
$67$	−6.60103	−	3.81111i	−0.806445	−	0.465601i	−0.845720	+	0.533627i	$0.820829\pi$
$68$	−1.79434	+	1.03596i	−0.217596	+	0.125629i
$69$		0			0
$70$	3.72453	+	4.59650i	0.445167	+	0.549387i
$71$			9.14126i			1.08487i	0.840099	+	0.542434i	$0.182497\pi$
$71$			9.14126i			1.08487i	−0.840099	+	0.542434i	$0.817503\pi$
$72$		0			0
$73$	−0.541173	+	0.937339i	−0.0633395	+	0.109707i	−0.895956	−	0.444142i	$-0.853508\pi$
$73$	−0.541173	+	0.937339i	−0.0633395	+	0.109707i	0.832617	+	0.553850i	$0.186842\pi$
$74$	−2.57132	−	1.48455i	−0.298910	−	0.172576i
$75$		0			0
$76$		−	5.91397i		−	0.678378i
$77$	4.56742	−	4.39937i	0.520505	−	0.501355i
$78$		0			0
$79$	8.38392	+	14.5214i	0.943265	+	1.63378i	0.759189	+	0.650870i	$0.225596\pi$
$79$	8.38392	+	14.5214i	0.943265	+	1.63378i	0.184076	+	0.982912i	$0.441071\pi$
$80$	1.27963	−	1.83372i	0.143067	−	0.205016i
$81$		0			0
$82$	3.52214	+	6.10053i	0.388955	+	0.673690i
$83$		−	13.6122i		−	1.49414i	−0.664747	−	0.747068i	$-0.731461\pi$
$83$		−	13.6122i		−	1.49414i	0.664747	−	0.747068i	$-0.268539\pi$
$84$		0			0
$85$	−0.396428	+	4.61597i	−0.0429987	+	0.500672i
$86$	7.41279	−	4.27978i	0.799342	−	0.461500i
$87$		0			0
$88$	−2.07577	−	1.19845i	−0.221278	−	0.127755i
$89$	−6.63129	−	11.4857i	−0.702916	−	1.21749i	−0.967438	−	0.253106i	$-0.918548\pi$
$89$	−6.63129	−	11.4857i	−0.702916	−	1.21749i	0.264523	−	0.964379i	$-0.414786\pi$
$90$		0			0
$91$	4.15870	−	14.4331i	0.435951	−	1.51300i
$92$	−1.86175			−0.194101
$93$		0			0
$94$	−4.83140	−	2.78941i	−0.498321	−	0.287706i
$95$	−10.8446	−	7.56771i	−1.11263	−	0.776430i
$96$		0			0
$97$	12.8260			1.30229			0.651143	−	0.758955i	$-0.274290\pi$
$97$	12.8260			1.30229			0.651143	+	0.758955i	$0.274290\pi$
$98$	0.262276	−	6.99508i	0.0264939	−	0.706610i
$99$		0			0
$100$	−1.72508	−	4.69298i	−0.172508	−	0.469298i
$101$	4.45573	−	7.71756i	0.443362	−	0.767926i	−0.554574	−	0.832134i	$-0.687119\pi$
$101$	4.45573	−	7.71756i	0.443362	−	0.767926i	0.997937	+	0.0642084i	$0.0204523\pi$
$102$		0			0
$103$	−5.40989	−	9.37021i	−0.533053	−	0.923274i	−0.999255	−	0.0385960i	$-0.987711\pi$
$103$	−5.40989	−	9.37021i	−0.533053	−	0.923274i	0.466202	−	0.884678i	$-0.345622\pi$
$104$	−5.67714			−0.556689
$105$		0			0
$106$	4.19077			0.407043
$107$	2.78854	+	4.82989i	0.269578	+	0.466923i	0.968753	−	0.248028i	$-0.0797825\pi$
$107$	2.78854	+	4.82989i	0.269578	+	0.466923i	−0.699175	+	0.714951i	$0.746449\pi$
$108$		0			0
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	0.814152	+	0.580651i	$0.197202\pi$
$110$	−4.85385	+	2.27282i	−0.462796	+	0.216705i
$111$		0			0
$112$	−2.56798	+	0.636766i	−0.242651	+	0.0601687i
$113$	−14.5030			−1.36432			−0.682161	−	0.731202i	$-0.738960\pi$
$113$	−14.5030			−1.36432			−0.682161	+	0.731202i	$0.738960\pi$
$114$		0			0
$115$	−2.38236	+	3.41394i	−0.222156	+	0.318352i
$116$	−4.23411	−	2.44457i	−0.393127	−	0.226972i
$117$		0			0
$118$	2.00624			0.184690
$119$	3.94816	−	3.80290i	0.361928	−	0.348612i
$120$		0			0
$121$	−2.62745	−	4.55087i	−0.238859	−	0.413715i
$122$	10.7862	+	6.22739i	0.976532	+	0.563801i
$123$		0			0
$124$	3.92008	−	2.26326i	0.352033	−	0.203247i
$125$	−10.8131	−	2.84199i	−0.967153	−	0.254195i
$126$		0			0
$127$		−	19.2462i		−	1.70783i	−0.520416	−	0.853913i	$-0.674223\pi$
$127$		−	19.2462i		−	1.70783i	0.520416	−	0.853913i	$-0.325777\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−7.26465	+	10.4103i	−0.637152	+	0.913043i
$131$	−2.34970	−	4.06980i	−0.205294	−	0.355580i	0.744932	−	0.667140i	$-0.232482\pi$
$131$	−2.34970	−	4.06980i	−0.205294	−	0.355580i	−0.950226	+	0.311560i	$0.899149\pi$
$132$		0			0
$133$	3.76581	+	15.1870i	0.326537	+	1.31688i
$134$		−	7.62222i		−	0.658459i
$135$		0			0
$136$	−1.79434	−	1.03596i	−0.153863	−	0.0888330i
$137$	−11.4422	+	19.8185i	−0.977577	+	1.69321i	−0.306421	+	0.951896i	$0.599132\pi$
$137$	−11.4422	+	19.8185i	−0.977577	+	1.69321i	−0.671155	+	0.741317i	$0.734202\pi$
$138$		0			0
$139$		−	9.13862i		−	0.775127i	−0.921843	−	0.387564i	$-0.873317\pi$
$139$		−	9.13862i		−	0.775127i	0.921843	−	0.387564i	$-0.126683\pi$
$140$	−2.11842	+	5.52379i	−0.179039	+	0.466846i
$141$		0			0
$142$	−7.91656	+	4.57063i	−0.664343	+	0.383559i
$143$	11.7844	+	6.80375i	0.985465	+	0.568958i
$144$		0			0
$145$	−9.90076	+	4.63604i	−0.822214	+	0.385002i
$146$	−1.08235			−0.0895756
$147$		0			0
$148$		−	2.96911i		−	0.244059i
$149$	−9.05052	+	5.22532i	−0.741448	+	0.428075i	−0.822596	−	0.568627i	$-0.807475\pi$
$149$	−9.05052	+	5.22532i	−0.741448	+	0.428075i	0.0811477	+	0.996702i	$0.474141\pi$
$150$		0			0
$151$	8.85937	−	15.3449i	0.720965	−	1.24875i	−0.239648	−	0.970860i	$-0.577032\pi$
$151$	8.85937	−	15.3449i	0.720965	−	1.24875i	0.960613	−	0.277888i	$-0.0896346\pi$
$152$	5.12164	−	2.95698i	0.415420	−	0.239843i
$153$		0			0
$154$	6.09368	+	1.75581i	0.491042	+	0.141487i
$155$	0.866074	−	10.0845i	0.0695647	−	0.810004i
$156$		0			0
$157$	3.04149	−	5.26801i	0.242737	−	0.420433i	−0.718756	−	0.695263i	$-0.755288\pi$
$157$	3.04149	−	5.26801i	0.242737	−	0.420433i	0.961493	+	0.274830i	$0.0886214\pi$
$158$	−8.38392	+	14.5214i	−0.666989	+	1.15526i
$159$		0			0
$160$	2.22787	+	0.191334i	0.176128	+	0.0151262i
$161$	4.78095	−	1.18550i	0.376792	−	0.0934305i
$162$		0			0
$163$	0.811759	−	0.468670i	0.0635819	−	0.0367090i	−0.467872	−	0.883796i	$-0.654979\pi$
$163$	0.811759	−	0.468670i	0.0635819	−	0.0367090i	0.531454	+	0.847087i	$0.321646\pi$
$164$	−3.52214	+	6.10053i	−0.275033	+	0.476371i
$165$		0			0
$166$	11.7885	−	6.80611i	0.914968	−	0.528257i
$167$		−	17.2101i		−	1.33176i	−0.746060	−	0.665879i	$-0.768057\pi$
$167$		−	17.2101i		−	1.33176i	0.746060	−	0.665879i	$-0.231943\pi$
$168$		0			0
$169$	19.2299			1.47922
$170$	−4.19576	+	1.96467i	−0.321800	+	0.150683i
$171$		0			0
$172$	7.41279	+	4.27978i	0.565220	+	0.326330i
$173$	1.71146	−	0.988114i	0.130120	−	0.0751249i	−0.433527	−	0.901141i	$-0.642731\pi$
$173$	1.71146	−	0.988114i	0.130120	−	0.0751249i	0.563647	+	0.826016i	$0.309398\pi$
$174$		0			0
$175$	7.41830	+	10.9530i	0.560771	+	0.827971i
$176$		−	2.39690i		−	0.180673i
$177$		0			0
$178$	6.63129	−	11.4857i	0.497037	−	0.860893i
$179$	−0.768461	−	0.443671i	−0.0574375	−	0.0331615i	0.471006	−	0.882130i	$-0.343891\pi$
$179$	−0.768461	−	0.443671i	−0.0574375	−	0.0331615i	−0.528444	+	0.848968i	$0.677224\pi$
$180$		0			0
$181$		−	4.89973i		−	0.364194i	−0.983281	−	0.182097i	$-0.941712\pi$
$181$		−	4.89973i		−	0.364194i	0.983281	−	0.182097i	$-0.0582885\pi$
$182$	14.5788	−	3.61500i	1.08065	−	0.267962i
$183$		0			0
$184$	−0.930877	−	1.61233i	−0.0686252	−	0.118862i
$185$	−5.44452	−	3.79937i	−0.400289	−	0.279335i
$186$		0			0
$187$	2.48309	+	4.30084i	0.181582	+	0.314509i
$188$		−	5.57882i		−	0.406877i
$189$		0			0
$190$	1.13154	−	13.1755i	0.0820905	−	0.955853i
$191$	−2.44949	+	1.41421i	−0.177239	+	0.102329i	−0.585995	−	0.810315i	$-0.699296\pi$
$191$	−2.44949	+	1.41421i	−0.177239	+	0.102329i	0.408756	+	0.912644i	$0.365963\pi$
$192$		0			0
$193$	16.8845	+	9.74828i	1.21537	+	0.701697i	0.963925	−	0.266174i	$-0.0857595\pi$
$193$	16.8845	+	9.74828i	1.21537	+	0.701697i	0.251449	+	0.967871i	$0.419093\pi$
$194$	6.41301	+	11.1077i	0.460428	+	0.797484i
$195$		0			0
$196$	6.18906	−	3.27040i	0.442076	−	0.233600i
$197$	−27.1576			−1.93490			−0.967448	−	0.253069i	$-0.918560\pi$
$197$	−27.1576			−1.93490			−0.967448	+	0.253069i	$0.918560\pi$
$198$		0			0
$199$	−3.00000	−	1.73205i	−0.212664	−	0.122782i	0.389885	−	0.920864i	$-0.372515\pi$
$199$	−3.00000	−	1.73205i	−0.212664	−	0.122782i	−0.602549	+	0.798082i	$0.705848\pi$
$200$	3.20171	−	3.84045i	0.226395	−	0.271561i
$201$		0			0
$202$	8.91147			0.627009
$203$	12.4297	+	3.58146i	0.872396	+	0.251369i
$204$		0			0
$205$	6.67962	+	14.2651i	0.466525	+	0.996315i
$206$	5.40989	−	9.37021i	0.376925	−	0.652853i
$207$		0			0
$208$	−2.83857	−	4.91654i	−0.196819	−	0.340901i
$209$	−14.1752			−0.980516
$210$		0			0
$211$	−4.06071			−0.279551			−0.139775	−	0.990183i	$-0.544638\pi$
$211$	−4.06071			−0.279551			−0.139775	+	0.990183i	$0.544638\pi$
$212$	2.09538	+	3.62931i	0.143912	+	0.249262i
$213$		0			0
$214$	−2.78854	+	4.82989i	−0.190620	+	0.330164i
$215$	17.3336	−	8.11646i	1.18214	−	0.553538i
$216$		0			0
$217$	−8.62552	+	8.30817i	−0.585538	+	0.563996i
$218$	−2.00000			−0.135457
$219$		0			0
$220$	−4.39524	−	3.06715i	−0.296327	−	0.206787i
$221$	10.1867	+	5.88130i	0.685232	+	0.395619i
$222$		0			0
$223$	−16.1486			−1.08139			−0.540696	−	0.841218i	$-0.681839\pi$
$223$	−16.1486			−1.08139			−0.540696	+	0.841218i	$0.681839\pi$
$224$	−1.83545	−	1.90555i	−0.122636	−	0.127320i
$225$		0			0
$226$	−7.25148	−	12.5599i	−0.482361	−	0.835474i
$227$	−1.45475	−	0.839901i	−0.0965552	−	0.0557462i	0.450945	−	0.892552i	$-0.351087\pi$
$227$	−1.45475	−	0.839901i	−0.0965552	−	0.0557462i	−0.547500	+	0.836806i	$0.684420\pi$
$228$		0			0
$229$	−10.9143	+	6.30136i	−0.721236	+	0.416406i	−0.815207	−	0.579169i	$-0.803377\pi$
$229$	−10.9143	+	6.30136i	−0.721236	+	0.416406i	0.0939717	+	0.995575i	$0.470044\pi$
$230$	−4.14774	−	0.356216i	−0.273494	−	0.0234882i
$231$		0			0
$232$		−	4.88913i		−	0.320987i
$233$	7.25818	+	12.5715i	0.475499	+	0.823589i	0.999606	−	0.0280635i	$-0.00893407\pi$
$233$	7.25818	+	12.5715i	0.475499	+	0.823589i	−0.524107	+	0.851653i	$0.675601\pi$
$234$		0			0
$235$	−10.2300	−	7.13884i	−0.667332	−	0.465687i
$236$	1.00312	+	1.73746i	0.0652977	+	0.113099i
$237$		0			0
$238$	5.26749	+	1.51776i	0.341441	+	0.0983816i
$239$		−	0.207089i		−	0.0133955i	−0.999978	−	0.00669774i	$-0.997868\pi$
$239$		−	0.207089i		−	0.0133955i	0.999978	−	0.00669774i	$-0.00213197\pi$
$240$		0			0
$241$	9.04172	+	5.22024i	0.582428	+	0.336265i	0.762098	−	0.647462i	$-0.224169\pi$
$241$	9.04172	+	5.22024i	0.582428	+	0.336265i	−0.179669	+	0.983727i	$0.557503\pi$
$242$	2.62745	−	4.55087i	0.168899	−	0.292541i
$243$		0			0
$244$			12.4548i			0.797335i
$245$	1.92271	−	15.5339i	0.122838	−	0.992427i
$246$		0			0
$247$	−29.0763	+	16.7872i	−1.85008	+	1.06814i
$248$	3.92008	+	2.26326i	0.248925	+	0.143717i
$249$		0			0
$250$	−2.94532	−	10.7854i	−0.186278	−	0.682129i
$251$	28.6464			1.80815			0.904074	−	0.427377i	$-0.140562\pi$
$251$	28.6464			1.80815			0.904074	+	0.427377i	$0.140562\pi$
$252$		0			0
$253$			4.46243i			0.280551i
$254$	16.6677	−	9.62311i	1.04583	−	0.603808i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−21.5805	+	12.4595i	−1.34615	+	0.777202i	−0.987702	−	0.156346i	$-0.950029\pi$
$257$	−21.5805	+	12.4595i	−1.34615	+	0.777202i	−0.358452	+	0.933548i	$0.616695\pi$
$258$		0			0
$259$	1.89063	+	7.62462i	0.117478	+	0.473771i
$260$	−12.6479	−	1.08623i	−0.784390	−	0.0673649i
$261$		0			0
$262$	2.34970	−	4.06980i	0.145165	−	0.251433i
$263$	−9.59538	+	16.6197i	−0.591677	+	1.02481i	0.402330	+	0.915495i	$0.368200\pi$
$263$	−9.59538	+	16.6197i	−0.591677	+	1.02481i	−0.994007	+	0.109319i	$0.965133\pi$
$264$		0			0
$265$	9.33647	+	0.801834i	0.573535	+	0.0492563i
$266$	−11.2694	+	10.8548i	−0.690970	+	0.665548i
$267$		0			0
$268$	6.60103	−	3.81111i	0.403222	−	0.232801i
$269$	2.42744	−	4.20446i	0.148004	−	0.256350i	−0.782486	−	0.622668i	$-0.786049\pi$
$269$	2.42744	−	4.20446i	0.148004	−	0.256350i	0.930490	+	0.366318i	$0.119382\pi$
$270$		0			0
$271$	−11.8344	+	6.83257i	−0.718886	+	0.415049i	−0.814342	−	0.580385i	$-0.802902\pi$
$271$	−11.8344	+	6.83257i	−0.718886	+	0.415049i	0.0954567	+	0.995434i	$0.469569\pi$
$272$		−	2.07192i		−	0.125629i
$273$		0			0
$274$	−22.8845			−1.38250
$275$	−11.2486	+	4.13483i	−0.678316	+	0.249340i
$276$		0			0
$277$	−10.5047	−	6.06491i	−0.631168	−	0.364405i	0.150036	−	0.988680i	$-0.452061\pi$
$277$	−10.5047	−	6.06491i	−0.631168	−	0.364405i	−0.781204	+	0.624276i	$0.785394\pi$
$278$	7.91427	−	4.56931i	0.474667	−	0.274049i
$279$		0			0
$280$	−5.84296	+	0.927288i	−0.349183	+	0.0554161i
$281$			32.6206i			1.94598i	0.230839	+	0.972992i	$0.425853\pi$
$281$			32.6206i			1.94598i	−0.230839	+	0.972992i	$0.574147\pi$
$282$		0			0
$283$	−6.33045	+	10.9647i	−0.376306	+	0.651781i	−0.990522	−	0.137357i	$-0.956139\pi$
$283$	−6.33045	+	10.9647i	−0.376306	+	0.651781i	0.614216	+	0.789138i	$0.289473\pi$
$284$	−7.91656	−	4.57063i	−0.469761	−	0.271217i
$285$		0			0
$286$			13.6075i			0.804628i
$287$	5.16019	−	17.9088i	0.304596	−	1.05712i
$288$		0			0
$289$	−6.35357	−	11.0047i	−0.373739	−	0.647335i
$290$	−8.96531	−	6.25629i	−0.526461	−	0.367382i
$291$		0			0
$292$	−0.541173	−	0.937339i	−0.0316698	−	0.0548536i
$293$		−	25.1151i		−	1.46724i	−0.679559	−	0.733621i	$-0.737829\pi$
$293$		−	25.1151i		−	1.46724i	0.679559	−	0.733621i	$-0.262171\pi$
$294$		0			0
$295$	4.46965	+	0.383862i	0.260233	+	0.0223493i
$296$	2.57132	−	1.48455i	0.149455	−	0.0862880i
$297$		0			0
$298$	−9.05052	−	5.22532i	−0.524283	−	0.302695i
$299$	5.28472	+	9.15340i	0.305623	+	0.529355i
$300$		0			0
$301$	−21.7611	−	6.27018i	−1.25429	−	0.361407i
$302$	17.7187			1.01960
$303$		0			0
$304$	5.12164	+	2.95698i	0.293746	+	0.169595i
$305$	22.8386	+	15.9375i	1.30773	+	0.912581i
$306$		0			0
$307$	18.5674			1.05970			0.529849	−	0.848092i	$-0.322249\pi$
$307$	18.5674			1.05970			0.529849	+	0.848092i	$0.322249\pi$
$308$	1.52626	+	6.15518i	0.0869668	+	0.350724i
$309$		0			0
$310$	9.16645	−	4.29219i	0.520619	−	0.243780i
$311$	−6.21831	+	10.7704i	−0.352608	+	0.610735i	−0.986706	−	0.162518i	$-0.948038\pi$
$311$	−6.21831	+	10.7704i	−0.352608	+	0.610735i	0.634098	+	0.773253i	$0.281372\pi$
$312$		0			0
$313$	6.20675	+	10.7504i	0.350826	+	0.607649i	0.986394	−	0.164396i	$-0.0525674\pi$
$313$	6.20675	+	10.7504i	0.350826	+	0.607649i	−0.635568	+	0.772045i	$0.719234\pi$
$314$	6.08297			0.343282
$315$		0			0
$316$	−16.7678			−0.943265
$317$	−12.3232	−	21.3444i	−0.692141	−	1.19882i	−0.971135	−	0.238530i	$-0.923335\pi$
$317$	−12.3232	−	21.3444i	−0.692141	−	1.19882i	0.278995	−	0.960293i	$-0.409999\pi$
$318$		0			0
$319$	−5.85937	+	10.1487i	−0.328062	+	0.568219i
$320$	0.948234	+	2.02506i	0.0530079	+	0.113204i
$321$		0			0
$322$	3.41715	+	3.54767i	0.190430	+	0.197704i
$323$	−12.2533			−0.681791
$324$		0			0
$325$	−18.1765	+	21.8028i	−1.00825	+	1.20940i
$326$	0.811759	+	0.468670i	0.0449592	+	0.0259572i
$327$		0			0
$328$	−7.04428			−0.388955
$329$	3.55240	+	14.3263i	0.195850	+	0.789835i
$330$		0			0
$331$	12.5788	+	21.7871i	0.691392	+	1.19753i	0.971382	+	0.237524i	$0.0763357\pi$
$331$	12.5788	+	21.7871i	0.691392	+	1.19753i	−0.279989	+	0.960003i	$0.590331\pi$
$332$	11.7885	+	6.80611i	0.646980	+	0.373534i
$333$		0			0
$334$	14.9044	−	8.60505i	0.815531	−	0.470847i
$335$	1.45839	−	16.9813i	0.0796801	−	0.927787i
$336$		0			0
$337$		−	14.4214i		−	0.785584i	−0.919627	−	0.392792i	$-0.871509\pi$
$337$		−	14.4214i		−	0.785584i	0.919627	−	0.392792i	$-0.128491\pi$
$338$	9.61494	+	16.6536i	0.522984	+	0.905834i
$339$		0			0
$340$	−3.79933	−	2.65130i	−0.206048	−	0.143787i
$341$	−5.42479	−	9.39601i	−0.293769	−	0.508823i
$342$		0			0
$343$	−13.8109	+	12.3393i	−0.745719	+	0.666261i
$344$			8.55956i			0.461500i
$345$		0			0
$346$	1.71146	+	0.988114i	0.0920088	+	0.0531213i
$347$	7.24329	−	12.5457i	0.388840	−	0.673491i	−0.603454	−	0.797398i	$-0.706209\pi$
$347$	7.24329	−	12.5457i	0.388840	−	0.673491i	0.992294	+	0.123907i	$0.0395425\pi$
$348$		0			0
$349$			2.12483i			0.113739i	0.998382	+	0.0568697i	$0.0181119\pi$
$349$			2.12483i			0.113739i	−0.998382	+	0.0568697i	$0.981888\pi$
$350$	−5.77645	+	11.9009i	−0.308764	+	0.636133i
$351$		0			0
$352$	2.07577	−	1.19845i	0.110639	−	0.0638775i
$353$	12.5805	+	7.26335i	0.669592	+	0.386589i	0.795922	−	0.605399i	$-0.206987\pi$
$353$	12.5805	+	7.26335i	0.669592	+	0.386589i	−0.126330	+	0.991988i	$0.540320\pi$
$354$		0			0
$355$	−18.5116	+	8.66805i	−0.982491	+	0.460052i
$356$	13.2626			0.702916
$357$		0			0
$358$		−	0.887342i		−	0.0468975i
$359$	3.42054	−	1.97485i	0.180529	−	0.104228i	−0.407012	−	0.913423i	$-0.633429\pi$
$359$	3.42054	−	1.97485i	0.180529	−	0.104228i	0.587541	+	0.809194i	$0.300096\pi$
$360$		0			0
$361$	7.98749	−	13.8347i	0.420394	−	0.728144i
$362$	4.24329	−	2.44986i	0.223022	−	0.128762i
$363$		0			0
$364$	10.4201	+	10.8181i	0.546160	+	0.567022i
$365$	−2.41132	−	0.207089i	−0.126214	−	0.0108395i
$366$		0			0
$367$	13.8464	−	23.9826i	0.722775	−	1.25188i	−0.237109	−	0.971483i	$-0.576200\pi$
$367$	13.8464	−	23.9826i	0.722775	−	1.25188i	0.959883	−	0.280400i	$-0.0904669\pi$
$368$	0.930877	−	1.61233i	0.0485253	−	0.0840483i
$369$		0			0
$370$	0.568090	−	6.61478i	0.0295336	−	0.343886i
$371$	−7.69193	−	7.98574i	−0.399345	−	0.414599i
$372$		0			0
$373$	−10.5047	+	6.06491i	−0.543914	+	0.314029i	−0.746664	−	0.665202i	$-0.768346\pi$
$373$	−10.5047	+	6.06491i	−0.543914	+	0.314029i	0.202750	+	0.979231i	$0.435012\pi$
$374$	−2.48309	+	4.30084i	−0.128398	+	0.222391i
$375$		0			0
$376$	4.83140	−	2.78941i	0.249160	−	0.143853i
$377$			27.7563i			1.42952i
$378$		0			0
$379$	−18.6821			−0.959636			−0.479818	−	0.877368i	$-0.659297\pi$
$379$	−18.6821			−0.959636			−0.479818	+	0.877368i	$0.659297\pi$
$380$	11.9761	−	5.60782i	0.614362	−	0.287675i
$381$		0			0
$382$	−2.44949	−	1.41421i	−0.125327	−	0.0723575i
$383$	9.55162	−	5.51463i	0.488065	−	0.281784i	−0.235706	−	0.971824i	$-0.575740\pi$
$383$	9.55162	−	5.51463i	0.488065	−	0.281784i	0.723771	+	0.690040i	$0.242407\pi$
$384$		0			0
$385$	13.2400	+	5.07764i	0.674771	+	0.258780i
$386$			19.4966i			0.992349i
$387$		0			0
$388$	−6.41301	+	11.1077i	−0.325571	+	0.563906i
$389$	29.7662	+	17.1855i	1.50921	+	0.871341i	0.999942	+	0.0107299i	$0.00341551\pi$
$389$	29.7662	+	17.1855i	1.50921	+	0.871341i	0.509264	+	0.860611i	$0.329918\pi$
$390$		0			0
$391$			3.85741i			0.195078i
$392$	5.92678	+	3.72468i	0.299348	+	0.188125i
$393$		0			0
$394$	−13.5788	−	23.5191i	−0.684089	−	1.18488i
$395$	−21.4567	+	30.7476i	−1.07960	+	1.54708i
$396$		0			0
$397$	15.5054	+	26.8561i	0.778191	+	1.34787i	0.932983	+	0.359920i	$0.117196\pi$
$397$	15.5054	+	26.8561i	0.778191	+	1.34787i	−0.154792	+	0.987947i	$0.549471\pi$
$398$		−	3.46410i		−	0.173640i
$399$		0			0
$400$	4.92678	+	0.852531i	0.246339	+	0.0426266i
$401$	8.20771	−	4.73872i	0.409873	−	0.236641i	−0.280862	−	0.959748i	$-0.590620\pi$
$401$	8.20771	−	4.73872i	0.409873	−	0.236641i	0.690735	+	0.723108i	$0.257287\pi$
$402$		0			0
$403$	−22.2548	−	12.8488i	−1.10859	−	0.640045i
$404$	4.45573	+	7.71756i	0.221681	+	0.383963i
$405$		0			0
$406$	3.11323	+	12.5552i	0.154507	+	0.623104i
$407$	−7.11665			−0.352759
$408$		0			0
$409$	8.20805	+	4.73892i	0.405862	+	0.234324i	0.689010	−	0.724752i	$-0.258046\pi$
$409$	8.20805	+	4.73892i	0.405862	+	0.234324i	−0.283148	+	0.959076i	$0.591379\pi$
$410$	−9.01409	+	12.9173i	−0.445174	+	0.637938i
$411$		0			0
$412$	10.8198			0.533053
$413$	−3.68235	−	3.82301i	−0.181197	−	0.188118i
$414$		0			0
$415$	27.5655	−	12.9076i	1.35314	−	0.633608i
$416$	2.83857	−	4.91654i	0.139172	−	0.241053i
$417$		0			0
$418$	−7.08758	−	12.2760i	−0.346665	−	0.600441i
$419$	−2.54445			−0.124305			−0.0621523	−	0.998067i	$-0.519796\pi$
$419$	−2.54445			−0.124305			−0.0621523	+	0.998067i	$0.519796\pi$
$420$		0			0
$421$	−5.08573			−0.247863			−0.123932	−	0.992291i	$-0.539550\pi$
$421$	−5.08573			−0.247863			−0.123932	+	0.992291i	$0.539550\pi$
$422$	−2.03035	−	3.51668i	−0.0988361	−	0.171189i
$423$		0			0
$424$	−2.09538	+	3.62931i	−0.101761	+	0.176255i
$425$	−9.72351	+	3.57423i	−0.471659	+	0.173376i
$426$		0			0
$427$	−7.93077	−	31.9836i	−0.383797	−	1.54780i
$428$	−5.57707			−0.269578
$429$		0			0
$430$	15.6959	+	10.9531i	0.756921	+	0.528205i
$431$	−11.5164	−	6.64902i	−0.554727	−	0.320272i	0.196299	−	0.980544i	$-0.437108\pi$
$431$	−11.5164	−	6.64902i	−0.554727	−	0.320272i	−0.751027	+	0.660272i	$0.770441\pi$
$432$		0			0
$433$	12.7895			0.614626			0.307313	−	0.951608i	$-0.400570\pi$
$433$	12.7895			0.614626			0.307313	+	0.951608i	$0.400570\pi$
$434$	−11.5078	−	3.31583i	−0.552394	−	0.159165i
$435$		0			0
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$	−9.53524	−	5.50517i	−0.456132	−	0.263348i
$438$		0			0
$439$	0.323211	−	0.186606i	0.0154260	−	0.00890623i	−0.492267	−	0.870444i	$-0.663832\pi$
$439$	0.323211	−	0.186606i	0.0154260	−	0.00890623i	0.507693	+	0.861538i	$0.330498\pi$
$440$	0.458606	−	5.33996i	0.0218632	−	0.254573i
$441$		0			0
$442$			11.7626i			0.559490i
$443$	12.3165	+	21.3328i	0.585175	+	1.01355i	0.994854	+	0.101323i	$0.0323075\pi$
$443$	12.3165	+	21.3328i	0.585175	+	1.01355i	−0.409679	+	0.912230i	$0.634359\pi$
$444$		0			0
$445$	16.9712	−	24.3199i	0.804514	−	1.15287i
$446$	−8.07432	−	13.9851i	−0.382330	−	0.662215i
$447$		0			0
$448$	0.732536	−	2.54232i	0.0346091	−	0.120113i
$449$		−	40.6223i		−	1.91708i	−0.284950	−	0.958542i	$-0.591977\pi$
$449$		−	40.6223i		−	1.91708i	0.284950	−	0.958542i	$-0.408023\pi$
$450$		0			0
$451$	14.6223	+	8.44220i	0.688538	+	0.397528i
$452$	7.25148	−	12.5599i	0.341081	−	0.590769i
$453$		0			0
$454$		−	1.67980i		−	0.0788370i
$455$	33.1713	−	5.26434i	1.55509	−	0.246796i
$456$		0			0
$457$	0.857843	−	0.495276i	0.0401282	−	0.0231680i	−0.479802	−	0.877377i	$-0.659291\pi$
$457$	0.857843	−	0.495276i	0.0401282	−	0.0231680i	0.519930	+	0.854209i	$0.325958\pi$
$458$	−10.9143	−	6.30136i	−0.509991	−	0.294443i
$459$		0			0
$460$	−1.76538	−	3.77016i	−0.0823112	−	0.175784i
$461$	−20.7397			−0.965945			−0.482972	−	0.875636i	$-0.660443\pi$
$461$	−20.7397			−0.965945			−0.482972	+	0.875636i	$0.660443\pi$
$462$		0			0
$463$			1.46421i			0.0680476i	0.999421	+	0.0340238i	$0.0108322\pi$
$463$			1.46421i			0.0680476i	−0.999421	+	0.0340238i	$0.989168\pi$
$464$	4.23411	−	2.44457i	0.196564	−	0.113486i
$465$		0			0
$466$	−7.25818	+	12.5715i	−0.336229	+	0.582365i
$467$	−31.4090	+	18.1340i	−1.45344	+	0.839142i	−0.998675	−	0.0514705i	$-0.983609\pi$
$467$	−31.4090	+	18.1340i	−1.45344	+	0.839142i	−0.454762	+	0.890613i	$0.650276\pi$
$468$		0			0
$469$	−14.5246	+	13.9902i	−0.670682	+	0.646006i
$470$	1.06742	−	12.4289i	0.0492362	−	0.573301i
$471$		0			0
$472$	−1.00312	+	1.73746i	−0.0461724	+	0.0799730i
$473$	10.2582	−	17.7677i	0.471672	−	0.816959i
$474$		0			0
$475$	5.04184	−	29.1368i	0.231336	−	1.33689i
$476$	1.31933	+	5.32066i	0.0604714	+	0.243872i
$477$		0			0
$478$	0.179344	−	0.103545i	0.00820302	−	0.00473602i
$479$	−5.16288	+	8.94237i	−0.235898	+	0.408587i	−0.959533	−	0.281595i	$-0.909136\pi$
$479$	−5.16288	+	8.94237i	−0.235898	+	0.408587i	0.723635	+	0.690183i	$0.242470\pi$
$480$		0			0
$481$	−14.5978	+	8.42802i	−0.665600	+	0.384285i
$482$			10.4405i			0.475551i
$483$		0			0
$484$	5.25489			0.238859
$485$	12.1621	+	25.9734i	0.552251	+	1.17939i
$486$		0			0
$487$	17.6055	+	10.1645i	0.797781	+	0.460599i	0.842695	−	0.538392i	$-0.180968\pi$
$487$	17.6055	+	10.1645i	0.797781	+	0.460599i	−0.0449135	+	0.998991i	$0.514301\pi$
$488$	−10.7862	+	6.22739i	−0.488266	+	0.281901i
$489$		0			0
$490$	14.4141	−	6.10185i	0.651164	−	0.275654i
$491$		−	34.6034i		−	1.56163i	−0.624764	−	0.780814i	$-0.714805\pi$
$491$		−	34.6034i		−	1.56163i	0.624764	−	0.780814i	$-0.285195\pi$
$492$		0			0
$493$	−5.06495	+	8.77276i	−0.228114	+	0.395105i
$494$	−29.0763	−	16.7872i	−1.30820	−	0.755292i
$495$		0			0
$496$			4.52651i			0.203247i
$497$	23.2400	+	6.69630i	1.04246	+	0.300370i
$498$		0			0
$499$	−1.47545	−	2.55555i	−0.0660501	−	0.114402i	0.831109	−	0.556109i	$-0.187706\pi$
$499$	−1.47545	−	2.55555i	−0.0660501	−	0.114402i	−0.897159	+	0.441707i	$0.854373\pi$
$500$	7.86778	−	7.94343i	0.351858	−	0.355241i
$501$		0			0
$502$	14.3232	+	24.8085i	0.639277	+	1.10726i
$503$			31.8907i			1.42193i	0.703225	+	0.710967i	$0.251742\pi$
$503$			31.8907i			1.42193i	−0.703225	+	0.710967i	$0.748258\pi$
$504$		0			0
$505$	19.8536	+	1.70506i	0.883472	+	0.0758743i
$506$	−3.86458	+	2.23121i	−0.171801	+	0.0991896i
$507$		0			0
$508$	16.6677	+	9.62311i	0.739510	+	0.426957i
$509$	0.421199	+	0.729538i	0.0186693	+	0.0323362i	0.875209	−	0.483745i	$-0.160724\pi$
$509$	0.421199	+	0.729538i	0.0186693	+	0.0323362i	−0.856540	+	0.516081i	$0.827390\pi$
$510$		0			0
$511$	1.98659	+	2.06247i	0.0878815	+	0.0912383i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−21.5805	−	12.4595i	−0.951875	−	0.549565i
$515$	13.8454	−	19.8405i	0.610099	−	0.874276i
$516$		0			0
$517$	−13.3718			−0.588093
$518$	−5.65780	+	5.44964i	−0.248589	+	0.239443i
$519$		0			0
$520$	−5.38325	−	11.4965i	−0.236071	−	0.504156i
$521$	−2.81499	+	4.87571i	−0.123327	+	0.213609i	−0.921078	−	0.389379i	$-0.872690\pi$
$521$	−2.81499	+	4.87571i	−0.123327	+	0.213609i	0.797751	+	0.602987i	$0.206023\pi$
$522$		0			0
$523$	−8.91899	−	15.4482i	−0.390000	−	0.675500i	0.602449	−	0.798158i	$-0.294192\pi$
$523$	−8.91899	−	15.4482i	−0.390000	−	0.675500i	−0.992449	+	0.122657i	$0.960858\pi$
$524$	4.69940			0.205294
$525$		0			0
$526$	−19.1908			−0.836757
$527$	−4.68930	−	8.12210i	−0.204269	−	0.353804i
$528$		0			0
$529$	9.76694	−	16.9168i	0.424649	−	0.735514i
$530$	3.97383	+	8.48654i	0.172612	+	0.368632i
$531$		0			0
$532$	−15.0352	−	4.33219i	−0.651858	−	0.187824i
$533$	39.9913			1.73222
$534$		0			0
$535$	−7.13661	+	10.2268i	−0.308542	+	0.442143i
$536$	6.60103	+	3.81111i	0.285121	+	0.164615i
$537$		0			0
$538$	4.85489			0.209309
$539$	−7.83882	−	14.8345i	−0.337642	−	0.638968i
$540$		0			0
$541$	12.7120	+	22.0179i	0.546533	+	0.946623i	0.998509	+	0.0545925i	$0.0173860\pi$
$541$	12.7120	+	22.0179i	0.546533	+	0.946623i	−0.451976	+	0.892030i	$0.649281\pi$
$542$	−11.8344	−	6.83257i	−0.508329	−	0.293484i
$543$		0			0
$544$	1.79434	−	1.03596i	0.0769316	−	0.0444165i
$545$	−4.45573	−	0.382667i	−0.190863	−	0.0163917i
$546$		0			0
$547$			12.1182i			0.518138i	0.965859	+	0.259069i	$0.0834158\pi$
$547$			12.1182i			0.518138i	−0.965859	+	0.259069i	$0.916584\pi$
$548$	−11.4422	−	19.8185i	−0.488788	−	0.846606i
$549$		0			0
$550$	−9.20517	−	7.67415i	−0.392510	−	0.327227i
$551$	−14.4571	−	25.0404i	−0.615892	−	1.06676i
$552$		0			0
$553$	43.0595	−	10.6772i	1.83108	−	0.454040i
$554$		−	12.1298i		−	0.515346i
$555$		0			0
$556$	7.91427	+	4.56931i	0.335640	+	0.193782i
$557$	−0.769786	+	1.33331i	−0.0326169	+	0.0564941i	−0.881873	−	0.471487i	$-0.843717\pi$
$557$	−0.769786	+	1.33331i	−0.0326169	+	0.0564941i	0.849256	+	0.527981i	$0.177051\pi$
$558$		0			0
$559$		−	48.5938i		−	2.05530i
$560$	−3.72453	−	4.59650i	−0.157390	−	0.194238i
$561$		0			0
$562$	−28.2503	+	16.3103i	−1.19167	+	0.688009i
$563$	−19.4548	−	11.2322i	−0.819920	−	0.473381i	0.0304689	−	0.999536i	$-0.490300\pi$
$563$	−19.4548	−	11.2322i	−0.819920	−	0.473381i	−0.850389	+	0.526155i	$0.823633\pi$
$564$		0			0
$565$	−13.7522	−	29.3693i	−0.578559	−	1.23558i
$566$	−12.6609			−0.532177
$567$		0			0
$568$		−	9.14126i		−	0.383559i
$569$	−9.35810	+	5.40290i	−0.392312	+	0.226501i	−0.683161	−	0.730267i	$-0.739395\pi$
$569$	−9.35810	+	5.40290i	−0.392312	+	0.226501i	0.290849	+	0.956769i	$0.406062\pi$
$570$		0			0
$571$	3.98169	−	6.89649i	0.166629	−	0.288609i	−0.770604	−	0.637314i	$-0.780045\pi$
$571$	3.98169	−	6.89649i	0.166629	−	0.288609i	0.937232	+	0.348705i	$0.113379\pi$
$572$	−11.7844	+	6.80375i	−0.492732	+	0.284479i
$573$		0			0
$574$	18.0896	−	4.48555i	0.755045	−	0.187223i
$575$	−9.17246	−	1.58720i	−0.382518	−	0.0661910i
$576$		0			0
$577$	12.2964	−	21.2980i	0.511906	−	0.886648i	−0.487998	−	0.872845i	$-0.662273\pi$
$577$	12.2964	−	21.2980i	0.511906	−	0.886648i	0.999905	−	0.0138033i	$-0.00439386\pi$
$578$	6.35357	−	11.0047i	0.264274	−	0.457735i
$579$		0			0
$580$	0.935455	−	10.8923i	0.0388426	−	0.452280i
$581$	−34.6066	−	9.97144i	−1.43573	−	0.413685i
$582$		0			0
$583$	8.69908	−	5.02242i	0.360279	−	0.208007i
$584$	0.541173	−	0.937339i	0.0223939	−	0.0387874i
$585$		0			0
$586$	21.7503	−	12.5576i	0.898498	−	0.518748i
$587$			12.8469i			0.530248i	0.964214	+	0.265124i	$0.0854129\pi$
$587$			12.8469i			0.530248i	−0.964214	+	0.265124i	$0.914587\pi$
$588$		0			0
$589$	26.7696			1.10302
$590$	1.90239	+	4.06276i	0.0783201	+	0.167261i
$591$		0			0
$592$	2.57132	+	1.48455i	0.105681	+	0.0610148i
$593$	14.8637	−	8.58155i	0.610379	−	0.352402i	−0.162735	−	0.986670i	$-0.552032\pi$
$593$	14.8637	−	8.58155i	0.610379	−	0.352402i	0.773114	+	0.634268i	$0.218698\pi$
$594$		0			0
$595$	11.4449	+	4.38921i	0.469194	+	0.179940i
$596$		−	10.4506i		−	0.428075i
$597$		0			0
$598$	−5.28472	+	9.15340i	−0.216108	+	0.374310i
$599$	16.9813	+	9.80416i	0.693837	+	0.400587i	0.805048	−	0.593210i	$-0.202140\pi$
$599$	16.9813	+	9.80416i	0.693837	+	0.400587i	−0.111211	+	0.993797i	$0.535473\pi$
$600$		0			0
$601$			28.2340i			1.15169i	0.817560	+	0.575844i	$0.195326\pi$
$601$			28.2340i			1.15169i	−0.817560	+	0.575844i	$0.804674\pi$
$602$	−5.45043	−	21.9808i	−0.222143	−	0.895870i
$603$		0			0
$604$	8.85937	+	15.3449i	0.360483	+	0.624374i
$605$	6.72433	−	9.63601i	0.273383	−	0.391760i
$606$		0			0
$607$	−4.82657	−	8.35987i	−0.195904	−	0.339316i	0.751292	−	0.659970i	$-0.229431\pi$
$607$	−4.82657	−	8.35987i	−0.195904	−	0.339316i	−0.947197	+	0.320653i	$0.896098\pi$
$608$			5.91397i			0.239843i
$609$		0			0
$610$	−2.38302	+	27.7476i	−0.0964855	+	1.12347i
$611$	−27.4285	+	15.8359i	−1.10964	+	0.640650i
$612$		0			0
$613$	−7.84262	−	4.52794i	−0.316761	−	0.182882i	0.333187	−	0.942861i	$-0.391876\pi$
$613$	−7.84262	−	4.52794i	−0.316761	−	0.182882i	−0.649948	+	0.759979i	$0.725209\pi$
$614$	9.28370	+	16.0798i	0.374660	+	0.648930i
$615$		0			0
$616$	−4.56742	+	4.39937i	−0.184026	+	0.177256i
$617$	25.3122			1.01903			0.509515	−	0.860462i	$-0.329825\pi$
$617$	25.3122			1.01903			0.509515	+	0.860462i	$0.329825\pi$
$618$		0			0
$619$	33.6634	+	19.4356i	1.35304	+	0.781181i	0.988675	−	0.150073i	$-0.0479510\pi$
$619$	33.6634	+	19.4356i	1.35304	+	0.781181i	0.364370	+	0.931254i	$0.381284\pi$
$620$	8.30037	+	5.79228i	0.333351	+	0.232624i
$621$		0			0
$622$	−12.4366			−0.498663
$623$	−34.0581	+	8.44516i	−1.36451	+	0.338348i
$624$		0			0
$625$	−4.49817	−	24.5920i	−0.179927	−	0.983680i
$626$	−6.20675	+	10.7504i	−0.248072	+	0.429673i
$627$		0			0
$628$	3.04149	+	5.26801i	0.121369	+	0.210216i
$629$	−6.15177			−0.245287
$630$		0			0
$631$	−23.8670			−0.950129			−0.475065	−	0.879951i	$-0.657575\pi$
$631$	−23.8670			−0.950129			−0.475065	+	0.879951i	$0.657575\pi$
$632$	−8.38392	−	14.5214i	−0.333494	−	0.577629i
$633$		0			0
$634$	12.3232	−	21.3444i	0.489417	−	0.847696i
$635$	38.9747	−	18.2499i	1.54666	−	0.724226i
$636$		0			0
$637$	−33.6472	−	21.1455i	−1.33315	−	0.837816i
$638$	−11.7187			−0.463949
$639$		0			0
$640$	−1.27963	+	1.83372i	−0.0505819	+	0.0724843i
$641$	−30.2066	−	17.4398i	−1.19309	−	0.688830i	−0.234083	−	0.972217i	$-0.575209\pi$
$641$	−30.2066	−	17.4398i	−1.19309	−	0.688830i	−0.959006	+	0.283386i	$0.908542\pi$
$642$		0			0
$643$	6.25944			0.246848			0.123424	−	0.992354i	$-0.460612\pi$
$643$	6.25944			0.246848			0.123424	+	0.992354i	$0.460612\pi$
$644$	−1.36380	+	4.73317i	−0.0537413	+	0.186513i
$645$		0			0
$646$	−6.12664	−	10.6117i	−0.241050	−	0.417510i
$647$	32.4778	+	18.7511i	1.27683	+	0.737181i	0.976265	−	0.216579i	$-0.0694898\pi$
$647$	32.4778	+	18.7511i	1.27683	+	0.737181i	0.300570	+	0.953760i	$0.402823\pi$
$648$		0			0
$649$	4.16451	−	2.40438i	0.163471	−	0.0943801i
$650$	−27.9700	−	4.83994i	−1.09707	−	0.189838i
$651$		0			0
$652$			0.937339i			0.0367090i
$653$	−13.2258	−	22.9077i	−0.517565	−	0.896449i	−0.999792	−	0.0204023i	$-0.993505\pi$
$653$	−13.2258	−	22.9077i	−0.517565	−	0.896449i	0.482227	−	0.876046i	$-0.339828\pi$
$654$		0			0
$655$	6.01351	−	8.61740i	0.234967	−	0.336710i
$656$	−3.52214	−	6.10053i	−0.137516	−	0.238186i
$657$		0			0
$658$	−10.6307	+	10.2396i	−0.414430	+	0.399182i
$659$			19.9524i			0.777234i	0.921399	+	0.388617i	$0.127047\pi$
$659$			19.9524i			0.777234i	−0.921399	+	0.388617i	$0.872953\pi$
$660$		0			0
$661$	4.71203	+	2.72049i	0.183277	+	0.105815i	0.588831	−	0.808256i	$-0.299588\pi$
$661$	4.71203	+	2.72049i	0.183277	+	0.105815i	−0.405555	+	0.914071i	$0.632922\pi$
$662$	−12.5788	+	21.7871i	−0.488888	+	0.846779i
$663$		0			0
$664$			13.6122i			0.528257i
$665$	−27.1836	+	22.0268i	−1.05413	+	0.854161i
$666$		0			0
$667$	−7.88287	+	4.55118i	−0.305226	+	0.176222i
$668$	14.9044	+	8.60505i	0.576668	+	0.332939i
$669$		0			0
$670$	15.4354	−	7.22765i	0.596322	−	0.279228i
$671$	29.8528			1.15245
$672$		0			0
$673$			8.50635i			0.327896i	0.986469	+	0.163948i	$0.0524228\pi$
$673$			8.50635i			0.327896i	−0.986469	+	0.163948i	$0.947577\pi$
$674$	12.4893	−	7.21070i	0.481070	−	0.277746i
$675$		0			0
$676$	−9.61494	+	16.6536i	−0.369805	+	0.640522i
$677$	4.40495	−	2.54320i	0.169296	−	0.0977430i	−0.412958	−	0.910750i	$-0.635504\pi$
$677$	4.40495	−	2.54320i	0.169296	−	0.0977430i	0.582254	+	0.813007i	$0.302171\pi$
$678$		0			0
$679$	9.39552	−	32.6079i	0.360567	−	1.25138i
$680$	0.396428	−	4.61597i	0.0152023	−	0.177014i
$681$		0			0
$682$	5.42479	−	9.39601i	0.207726	−	0.359792i
$683$	−10.5073	+	18.1991i	−0.402050	+	0.696370i	−0.993973	−	0.109624i	$-0.965035\pi$
$683$	−10.5073	+	18.1991i	−0.402050	+	0.696370i	0.591924	+	0.805994i	$0.298369\pi$
$684$		0			0
$685$	−50.9836	−	4.37857i	−1.94798	−	0.167297i
$686$	−17.5916	−	5.79094i	−0.671651	−	0.221099i
$687$		0			0
$688$	−7.41279	+	4.27978i	−0.282610	+	0.163165i
$689$	11.8958	−	20.6041i	0.453193	−	0.784953i
$690$		0			0
$691$	−21.5723	+	12.4548i	−0.820649	+	0.473802i	−0.850640	−	0.525748i	$-0.823785\pi$
$691$	−21.5723	+	12.4548i	−0.820649	+	0.473802i	0.0299912	+	0.999550i	$0.490452\pi$
$692$			1.97623i			0.0751249i
$693$		0			0
$694$	14.4866			0.549903
$695$	18.5062	−	8.66555i	0.701981	−	0.328703i
$696$		0			0
$697$	12.6398	+	7.29761i	0.478767	+	0.276417i
$698$	−1.84015	+	1.06241i	−0.0696508	+	0.0402129i
$699$		0			0
$700$	−13.1948	+	0.947921i	−0.498715	+	0.0358280i
$701$			22.5321i			0.851025i	0.904953	+	0.425512i	$0.139906\pi$
$701$			22.5321i			0.851025i	−0.904953	+	0.425512i	$0.860094\pi$
$702$		0			0
$703$	8.77961	−	15.2067i	0.331129	−	0.573532i
$704$	2.07577	+	1.19845i	0.0782336	+	0.0451682i
$705$		0			0
$706$			14.5267i			0.546719i
$707$	−16.3565	−	16.9813i	−0.615150	−	0.638647i
$708$		0			0
$709$	−12.4504	−	21.5648i	−0.467586	−	0.809882i	0.531728	−	0.846915i	$-0.321543\pi$
$709$	−12.4504	−	21.5648i	−0.467586	−	0.809882i	−0.999314	+	0.0370327i	$0.988209\pi$
$710$	−16.7625	−	11.6975i	−0.629086	−	0.438998i
$711$		0			0
$712$	6.63129	+	11.4857i	0.248518	+	0.430446i
$713$		−	8.42726i		−	0.315603i
$714$		0			0
$715$	−2.60357	+	30.3157i	−0.0973681	+	1.13374i
$716$	0.768461	−	0.443671i	0.0287187	−	0.0165808i
$717$		0			0
$718$	3.42054	+	1.97485i	0.127653	+	0.0737007i
$719$	−19.9241	−	34.5096i	−0.743045	−	1.28699i	−0.951103	−	0.308875i	$-0.900047\pi$
$719$	−19.9241	−	34.5096i	−0.743045	−	1.28699i	0.208057	−	0.978117i	$-0.433286\pi$
$720$		0			0
$721$	−27.7850	+	6.88967i	−1.03477	+	0.256585i
$722$	15.9750			0.594527
$723$		0			0
$724$	4.24329	+	2.44986i	0.157701	+	0.0910485i
$725$	−18.7765	−	15.6536i	−0.697341	−	0.581358i
$726$		0			0
$727$	−0.124004			−0.00459906			−0.00229953	−	0.999997i	$-0.500732\pi$
$727$	−0.124004			−0.00459906			−0.00229953	+	0.999997i	$0.500732\pi$
$728$	−4.15870	+	14.4331i	−0.154132	+	0.534926i
$729$		0			0
$730$	−1.02632	−	2.19181i	−0.0379857	−	0.0811226i
$731$	8.86738	−	15.3587i	0.327972	−	0.568064i
$732$		0			0
$733$	−14.2739	−	24.7231i	−0.527218	−	0.913168i	−0.999497	−	0.0317189i	$-0.989902\pi$
$733$	−14.2739	−	24.7231i	−0.527218	−	0.913168i	0.472279	−	0.881449i	$-0.343431\pi$
$734$	27.6927			1.02216
$735$		0			0
$736$	1.86175			0.0686252
$737$	−9.13483	−	15.8220i	−0.336486	−	0.582811i
$738$		0			0
$739$	9.51807	−	16.4858i	0.350128	−	0.606439i	−0.636144	−	0.771571i	$-0.719471\pi$
$739$	9.51807	−	16.4858i	0.350128	−	0.606439i	0.986272	+	0.165131i	$0.0528048\pi$
$740$	6.01261	−	2.81541i	0.221028	−	0.103497i
$741$		0			0
$742$	3.06989	−	10.6543i	0.112699	−	0.391131i
$743$	17.0800			0.626605			0.313303	−	0.949653i	$-0.398565\pi$
$743$	17.0800			0.626605			0.313303	+	0.949653i	$0.398565\pi$
$744$		0			0
$745$	−19.1636	−	13.3730i	−0.702099	−	0.489949i
$746$	−10.5047	−	6.06491i	−0.384605	−	0.222052i
$747$		0			0
$748$	−4.96618			−0.181582
$749$	14.3218	−	3.55129i	0.523308	−	0.129761i
$750$		0			0
$751$	8.44463	+	14.6265i	0.308149	+	0.533730i	0.977957	−	0.208804i	$-0.0669572\pi$
$751$	8.44463	+	14.6265i	0.308149	+	0.533730i	−0.669809	+	0.742534i	$0.733624\pi$
$752$	4.83140	+	2.78941i	0.176183	+	0.101719i
$753$		0			0
$754$	−24.0376	+	13.8781i	−0.875399	+	0.505412i
$755$	39.4750	+	3.39019i	1.43664	+	0.123382i
$756$		0			0
$757$		−	33.4057i		−	1.21415i	−0.794644	−	0.607076i	$-0.792342\pi$
$757$		−	33.4057i		−	1.21415i	0.794644	−	0.607076i	$-0.207658\pi$
$758$	−9.34106	−	16.1792i	−0.339282	−	0.587655i
$759$		0			0
$760$	10.8446	+	7.56771i	0.393374	+	0.274510i
$761$	−16.3074	−	28.2453i	−0.591143	−	1.02389i	−0.994079	−	0.108662i	$-0.965343\pi$
$761$	−16.3074	−	28.2453i	−0.591143	−	1.02389i	0.402935	−	0.915228i	$-0.367990\pi$
$762$		0			0
$763$	3.67089	+	3.81111i	0.132895	+	0.137971i
$764$		−	2.82843i		−	0.102329i
$765$		0			0
$766$	9.55162	+	5.51463i	0.345114	+	0.199252i
$767$	5.69486	−	9.86379i	0.205630	−	0.356161i
$768$		0			0
$769$			22.4396i			0.809192i	0.914495	+	0.404596i	$0.132588\pi$
$769$			22.4396i			0.809192i	−0.914495	+	0.404596i	$0.867412\pi$
$770$	2.22261	+	14.0050i	0.0800974	+	0.504704i
$771$		0			0
$772$	−16.8845	+	9.74828i	−0.607687	+	0.350848i
$773$	−34.4965	−	19.9165i	−1.24075	−	0.716348i	−0.271505	−	0.962437i	$-0.587521\pi$
$773$	−34.4965	−	19.9165i	−1.24075	−	0.716348i	−0.969247	+	0.246089i	$0.920855\pi$
$774$		0			0
$775$	21.2429	−	7.80859i	0.763066	−	0.280493i
$776$	−12.8260			−0.460428
$777$		0			0
$778$			34.3710i			1.23226i
$779$	−36.0783	+	20.8298i	−1.29264	+	0.746306i
$780$		0			0
$781$	−10.9553	+	18.9752i	−0.392012	+	0.678985i
$782$	−3.34062	+	1.92871i	−0.119460	+	0.0689704i
$783$		0			0
$784$	−0.262276	+	6.99508i	−0.00936701	+	0.249824i
$785$	13.5521	+	1.16388i	0.483694	+	0.0415405i
$786$		0			0
$787$	8.36649	−	14.4912i	0.298233	−	0.516555i	−0.677499	−	0.735524i	$-0.736936\pi$
$787$	8.36649	−	14.4912i	0.298233	−	0.516555i	0.975732	+	0.218969i	$0.0702694\pi$
$788$	13.5788	−	23.5191i	0.483724	−	0.837835i
$789$		0			0
$790$	−37.3565	−	3.20825i	−1.32909	−	0.114144i
$791$	−10.6239	+	36.8711i	−0.377743	+	1.31099i
$792$		0			0
$793$	61.2344	−	35.3537i	2.17450	−	1.25545i
$794$	−15.5054	+	26.8561i	−0.550264	+	0.953086i
$795$		0			0
$796$	3.00000	−	1.73205i	0.106332	−	0.0613909i
$797$			2.68812i			0.0952182i	0.998866	+	0.0476091i	$0.0151602\pi$
$797$			2.68812i			0.0952182i	−0.998866	+	0.0476091i	$0.984840\pi$
$798$		0			0
$799$	−11.5589			−0.408924
$800$	1.72508	+	4.69298i	0.0609907	+	0.165922i
$801$		0			0
$802$	8.20771	+	4.73872i	0.289824	+	0.167330i
$803$	−2.24670	+	1.29714i	−0.0792845	+	0.0457749i
$804$		0			0
$805$	6.93416	+	8.55756i	0.244397	+	0.301614i
$806$		−	25.6976i		−	0.905161i
$807$		0			0
$808$	−4.45573	+	7.71756i	−0.156752	+	0.271503i
$809$	27.2213	+	15.7162i	0.957051	+	0.552554i	0.895264	−	0.445536i	$-0.146987\pi$
$809$	27.2213	+	15.7162i	0.957051	+	0.552554i	0.0617867	+	0.998089i	$0.480320\pi$
$810$		0			0
$811$			49.3830i			1.73407i	0.498246	+	0.867036i	$0.333978\pi$
$811$			49.3830i			1.73407i	−0.498246	+	0.867036i	$0.666022\pi$
$812$	−9.31651	+	8.97374i	−0.326945	+	0.314916i
$813$		0			0
$814$	−3.55832	−	6.16320i	−0.124719	−	0.216020i
$815$	1.71882	+	1.19945i	0.0602076	+	0.0420149i
$816$		0			0
$817$	25.3105	+	43.8390i	0.885501	+	1.53373i
$818$			9.47784i			0.331385i
$819$		0			0
$820$	−15.6937	−	1.34781i	−0.548048	−	0.0470675i
$821$	38.7342	−	22.3632i	1.35183	−	0.780480i	0.363325	−	0.931662i	$-0.381641\pi$
$821$	38.7342	−	22.3632i	1.35183	−	0.780480i	0.988506	+	0.151182i	$0.0483080\pi$
$822$		0			0
$823$	11.3808	+	6.57071i	0.396710	+	0.229041i	0.685063	−	0.728483i	$-0.259774\pi$
$823$	11.3808	+	6.57071i	0.396710	+	0.229041i	−0.288353	+	0.957524i	$0.593108\pi$
$824$	5.40989	+	9.37021i	0.188463	+	0.326427i
$825$		0			0
$826$	1.46965	−	5.10052i	0.0511355	−	0.177470i
$827$	47.4125			1.64869			0.824346	−	0.566086i	$-0.191543\pi$
$827$	47.4125			1.64869			0.824346	+	0.566086i	$0.191543\pi$
$828$		0			0
$829$	7.11516	+	4.10794i	0.247120	+	0.142675i	0.618445	−	0.785828i	$-0.287763\pi$
$829$	7.11516	+	4.10794i	0.247120	+	0.142675i	−0.371325	+	0.928503i	$0.621096\pi$
$830$	24.9611	+	17.4187i	0.866411	+	0.604611i
$831$		0			0
$832$	5.67714			0.196819
$833$	−6.77603	−	12.8233i	−0.234775	−	0.444300i
$834$		0			0
$835$	34.8514	−	16.3192i	1.20608	−	0.564749i
$836$	7.08758	−	12.2760i	0.245129	−	0.424576i
$837$		0			0
$838$	−1.27223	−	2.20356i	−0.0439483	−	0.0761208i
$839$	−17.6943			−0.610875			−0.305437	−	0.952212i	$-0.598803\pi$
$839$	−17.6943			−0.610875			−0.305437	+	0.952212i	$0.598803\pi$
$840$		0			0
$841$	5.09640			0.175738
$842$	−2.54286	−	4.40437i	−0.0876328	−	0.151785i
$843$		0			0
$844$	2.03035	−	3.51668i	0.0698877	−	0.121049i
$845$	18.2344	+	38.9416i	0.627283	+	1.33963i
$846$		0			0
$847$	−13.4945	+	3.34613i	−0.463675	+	0.114975i
$848$	−4.19077			−0.143912
$849$		0			0
$850$	−7.95713	−	6.63369i	−0.272927	−	0.227534i
$851$	−4.78717	−	2.76388i	−0.164102	−	0.0947444i
$852$		0			0
$853$	−40.1129			−1.37344			−0.686720	−	0.726922i	$-0.740950\pi$
$853$	−40.1129			−1.37344			−0.686720	+	0.726922i	$0.740950\pi$
$854$	23.7333	−	22.8601i	0.812135	−	0.782255i
$855$		0			0
$856$	−2.78854	−	4.82989i	−0.0953102	−	0.165082i
$857$	38.2184	+	22.0654i	1.30552	+	0.753740i	0.981344	−	0.192259i	$-0.0615813\pi$
$857$	38.2184	+	22.0654i	1.30552	+	0.753740i	0.324171	+	0.945998i	$0.394915\pi$
$858$		0			0
$859$	−12.4339	+	7.17873i	−0.424240	+	0.244935i	−0.696890	−	0.717178i	$-0.745433\pi$
$859$	−12.4339	+	7.17873i	−0.424240	+	0.244935i	0.272650	+	0.962113i	$0.412100\pi$
$860$	−1.63773	+	19.0696i	−0.0558461	+	0.650266i
$861$		0			0
$862$		−	13.2980i		−	0.452933i
$863$	−6.40143	−	11.0876i	−0.217907	−	0.377426i	0.736261	−	0.676698i	$-0.236590\pi$
$863$	−6.40143	−	11.0876i	−0.217907	−	0.377426i	−0.954168	+	0.299272i	$0.903256\pi$
$864$		0			0
$865$	3.62385	+	2.52885i	0.123215	+	0.0859834i
$866$	6.39477	+	11.0761i	0.217303	+	0.376380i
$867$		0			0
$868$	−2.88233	−	11.6240i	−0.0978326	−	0.394544i
$869$			40.1908i			1.36338i
$870$		0			0
$871$	−37.4750	−	21.6362i	−1.26979	−	0.733114i
$872$	1.00000	−	1.73205i	0.0338643	−	0.0586546i
$873$		0			0
$874$		−	11.0103i		−	0.372431i
$875$	−15.1462	+	25.4085i	−0.512036	+	0.858964i
$876$		0			0
$877$	−50.4650	+	29.1360i	−1.70408	+	0.983853i	−0.762551	+	0.646928i	$0.776053\pi$
$877$	−50.4650	+	29.1360i	−1.70408	+	0.983853i	−0.941532	+	0.336925i	$0.890613\pi$
$878$	0.323211	+	0.186606i	0.0109079	+	0.00629765i
$879$		0			0
$880$	4.85385	−	2.27282i	0.163623	−	0.0766167i
$881$	1.80667			0.0608682			0.0304341	−	0.999537i	$-0.490311\pi$
$881$	1.80667			0.0608682			0.0304341	+	0.999537i	$0.490311\pi$
$882$		0			0
$883$			13.8997i			0.467761i	0.972265	+	0.233881i	$0.0751425\pi$
$883$			13.8997i			0.467761i	−0.972265	+	0.233881i	$0.924858\pi$
$884$	−10.1867	+	5.88130i	−0.342616	+	0.197809i
$885$		0			0
$886$	−12.3165	+	21.3328i	−0.413781	+	0.716690i
$887$	−22.9426	+	13.2459i	−0.770337	+	0.444754i	−0.832995	−	0.553281i	$-0.813376\pi$
$887$	−22.9426	+	13.2459i	−0.770337	+	0.444754i	0.0626581	+	0.998035i	$0.480042\pi$
$888$		0			0
$889$	−48.9301	−	14.0985i	−1.64106	−	0.472850i
$890$	29.5473	+	2.53758i	0.990427	+	0.0850598i
$891$		0			0
$892$	8.07432	−	13.9851i	0.270348	−	0.468257i
$893$	16.4965	−	28.5727i	0.552033	−	0.956150i
$894$		0			0
$895$	0.169778	−	1.97688i	0.00567506	−	0.0660798i
$896$	2.56798	−	0.636766i	0.0857902	−	0.0212728i
$897$		0			0
$898$	35.1799	−	20.3111i	1.17397	−	0.677792i
$899$	11.0654	−	19.1658i	0.369050	−	0.639214i
$900$		0			0
$901$	7.51966	−	4.34148i	0.250516	−	0.144636i
$902$			16.8844i			0.562189i
$903$		0			0
$904$	14.5030			0.482361
$905$	9.92222	−	4.64609i	0.329826	−	0.154441i
$906$		0			0
$907$	31.8091	+	18.3650i	1.05620	+	0.609800i	0.924380	−	0.381474i	$-0.124583\pi$
$907$	31.8091	+	18.3650i	1.05620	+	0.609800i	0.131824	+	0.991273i	$0.457917\pi$
$908$	1.45475	−	0.839901i	0.0482776	−	0.0278731i
$909$		0			0
$910$	21.1447	+	26.0950i	0.700939	+	0.865040i
$911$			39.8018i			1.31869i	0.751839	+	0.659347i	$0.229167\pi$
$911$			39.8018i			1.31869i	−0.751839	+	0.659347i	$0.770833\pi$
$912$		0			0
$913$	16.3135	−	28.2559i	0.539900	−	0.935134i
$914$	0.857843	+	0.495276i	0.0283749	+	0.0163823i
$915$		0			0
$916$		−	12.6027i		−	0.416406i
$917$	−12.0680	+	2.99242i	−0.398520	+	0.0988184i
$918$		0			0
$919$	30.1692	+	52.2545i	0.995189	+	1.72372i	0.582442	+	0.812872i	$0.302097\pi$
$919$	30.1692	+	52.2545i	0.995189	+	1.72372i	0.412747	+	0.910846i	$0.364570\pi$
$920$	2.38236	−	3.41394i	0.0785442	−	0.112554i
$921$		0			0
$922$	−10.3699	−	17.9611i	−0.341513	−	0.591518i
$923$			51.8962i			1.70818i
$924$		0			0
$925$	2.53126	−	14.6282i	0.0832273	−	0.480971i
$926$	−1.26804	+	0.732105i	−0.0416705	+	0.0240585i
$927$		0			0
$928$	4.23411	+	2.44457i	0.138992	+	0.0802468i
$929$	22.1749	+	38.4080i	0.727533	+	1.26012i	0.957923	+	0.287026i	$0.0926667\pi$
$929$	22.1749	+	38.4080i	0.727533	+	1.26012i	−0.230389	+	0.973099i	$0.574000\pi$
$930$		0			0
$931$	41.3687	+	1.55109i	1.35580	+	0.0508350i
$932$	−14.5164			−0.475499
$933$		0			0
$934$	−31.4090	−	18.1340i	−1.02774	−	0.593363i
$935$	−6.35490	+	9.10661i	−0.207827	+	0.297818i
$936$		0			0
$937$	2.54073			0.0830021			0.0415010	−	0.999138i	$-0.486786\pi$
$937$	2.54073			0.0830021			0.0415010	+	0.999138i	$0.486786\pi$
$938$	−19.3781	−	5.58355i	−0.632718	−	0.182309i
$939$		0			0
$940$	11.2974	−	5.29003i	0.368481	−	0.172542i
$941$	−16.9488	+	29.3563i	−0.552516	+	0.956987i	0.445576	+	0.895244i	$0.352999\pi$
$941$	−16.9488	+	29.3563i	−0.552516	+	0.956987i	−0.998092	+	0.0617423i	$0.980334\pi$
$942$		0			0
$943$	6.55736	+	11.3577i	0.213537	+	0.369857i
$944$	−2.00624			−0.0652977
$945$		0			0
$946$	20.5164			0.667045
$947$	−24.7544	−	42.8759i	−0.804411	−	1.39328i	−0.916688	−	0.399604i	$-0.869148\pi$
$947$	−24.7544	−	42.8759i	−0.804411	−	1.39328i	0.112277	−	0.993677i	$-0.464186\pi$
$948$		0			0
$949$	−3.07231	+	5.32140i	−0.0997315	+	0.172740i
$950$	27.7541	−	10.2020i	0.900463	−	0.330998i
$951$		0			0
$952$	−3.94816	+	3.80290i	−0.127961	+	0.123253i
$953$	17.0625			0.552709			0.276355	−	0.961056i	$-0.410874\pi$
$953$	17.0625			0.552709			0.276355	+	0.961056i	$0.410874\pi$
$954$		0			0
$955$	−5.18655	−	3.61935i	−0.167833	−	0.117119i
$956$	0.179344	+	0.103545i	0.00580041	+	0.00334887i
$957$		0			0
$958$	−10.3258			−0.333610
$959$	42.0032	+	43.6076i	1.35636	+	1.40816i
$960$		0			0
$961$	−5.25533	−	9.10250i	−0.169527	−	0.293629i
$962$	−14.5978	−	8.42802i	−0.470651	−	0.271730i
$963$		0			0
$964$	−9.04172	+	5.22024i	−0.291214	+	0.168133i
$965$	−3.73035	+	43.4357i	−0.120084	+	1.39825i
$966$		0			0
$967$			49.6639i			1.59708i	0.601940	+	0.798541i	$0.294394\pi$
$967$			49.6639i			1.59708i	−0.601940	+	0.798541i	$0.705606\pi$
$968$	2.62745	+	4.55087i	0.0844493	+	0.146270i
$969$		0			0
$970$	−16.4126	+	23.5194i	−0.526977	+	0.755162i
$971$	14.2930	+	24.7561i	0.458683	+	0.794462i	0.998892	−	0.0470689i	$-0.0149880\pi$
$971$	14.2930	+	24.7561i	0.458683	+	0.794462i	−0.540209	+	0.841531i	$0.681655\pi$
$972$		0			0
$973$	−23.2333	−	6.69436i	−0.744825	−	0.214611i
$974$			20.3291i			0.651386i
$975$		0			0
$976$	−10.7862	−	6.22739i	−0.345256	−	0.199334i
$977$	−13.8603	+	24.0067i	−0.443429	+	0.768042i	−0.997941	−	0.0641335i	$-0.979572\pi$
$977$	−13.8603	+	24.0067i	−0.443429	+	0.768042i	0.554512	+	0.832176i	$0.312905\pi$
$978$		0			0
$979$		−	31.7890i		−	1.01598i
$980$	12.4914	+	9.43208i	0.399024	+	0.301297i
$981$		0			0
$982$	29.9674	−	17.3017i	0.956298	−	0.552119i
$983$	−37.0891	−	21.4134i	−1.18296	−	0.682982i	−0.226262	−	0.974067i	$-0.572650\pi$
$983$	−37.0891	−	21.4134i	−1.18296	−	0.682982i	−0.956697	+	0.291085i	$0.905984\pi$
$984$		0			0
$985$	−25.7517	−	54.9956i	−0.820518	−	1.75231i
$986$	−10.1299			−0.322602
$987$		0			0
$988$		−	33.5744i		−	1.06814i
$989$	13.8008	−	7.96789i	0.438840	−	0.253364i
$990$		0			0
$991$	−21.3723	+	37.0179i	−0.678914	+	1.17591i	0.296394	+	0.955066i	$0.404216\pi$
$991$	−21.3723	+	37.0179i	−0.678914	+	1.17591i	−0.975308	+	0.220848i	$0.929118\pi$
$992$	−3.92008	+	2.26326i	−0.124463	+	0.0718585i
$993$		0			0
$994$	5.82084	+	23.4746i	0.184626	+	0.744568i
$995$	0.662799	−	7.71756i	0.0210121	−	0.244663i
$996$		0			0
$997$	16.4359	−	28.4679i	0.520531	−	0.901587i	−0.479184	−	0.877715i	$-0.659067\pi$
$997$	16.4359	−	28.4679i	0.520531	−	0.901587i	0.999715	−	0.0238722i	$-0.00759947\pi$
$998$	1.47545	−	2.55555i	0.0467045	−	0.0808945i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bo.b.269.5	yes	16
3.2	odd	2		630.2.bo.a.269.4	yes	16
5.2	odd	4		3150.2.bf.f.1151.2		32
5.3	odd	4		3150.2.bf.f.1151.11		32
5.4	even	2		630.2.bo.a.269.7	yes	16
7.3	odd	6		4410.2.d.a.4409.16		16
7.4	even	3		4410.2.d.a.4409.1		16
7.5	odd	6	inner	630.2.bo.b.89.2	yes	16
15.2	even	4		3150.2.bf.f.1151.12		32
15.8	even	4		3150.2.bf.f.1151.1		32
15.14	odd	2	inner	630.2.bo.b.269.2	yes	16
21.5	even	6		630.2.bo.a.89.7	yes	16
21.11	odd	6		4410.2.d.b.4409.16		16
21.17	even	6		4410.2.d.b.4409.1		16
35.4	even	6		4410.2.d.b.4409.2		16
35.12	even	12		3150.2.bf.f.1601.12		32
35.19	odd	6		630.2.bo.a.89.4	✓	16
35.24	odd	6		4410.2.d.b.4409.15		16
35.33	even	12		3150.2.bf.f.1601.1		32
105.47	odd	12		3150.2.bf.f.1601.2		32
105.59	even	6		4410.2.d.a.4409.2		16
105.68	odd	12		3150.2.bf.f.1601.11		32
105.74	odd	6		4410.2.d.a.4409.15		16
105.89	even	6	inner	630.2.bo.b.89.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bo.a.89.4	✓	16	35.19	odd	6
630.2.bo.a.89.7	yes	16	21.5	even	6
630.2.bo.a.269.4	yes	16	3.2	odd	2
630.2.bo.a.269.7	yes	16	5.4	even	2
630.2.bo.b.89.2	yes	16	7.5	odd	6	inner
630.2.bo.b.89.5	yes	16	105.89	even	6	inner
630.2.bo.b.269.2	yes	16	15.14	odd	2	inner
630.2.bo.b.269.5	yes	16	1.1	even	1	trivial
3150.2.bf.f.1151.1		32	15.8	even	4
3150.2.bf.f.1151.2		32	5.2	odd	4
3150.2.bf.f.1151.11		32	5.3	odd	4
3150.2.bf.f.1151.12		32	15.2	even	4
3150.2.bf.f.1601.1		32	35.33	even	12
3150.2.bf.f.1601.2		32	105.47	odd	12
3150.2.bf.f.1601.11		32	105.68	odd	12
3150.2.bf.f.1601.12		32	35.12	even	12
4410.2.d.a.4409.1		16	7.4	even	3
4410.2.d.a.4409.2		16	105.59	even	6
4410.2.d.a.4409.15		16	105.74	odd	6
4410.2.d.a.4409.16		16	7.3	odd	6
4410.2.d.b.4409.1		16	21.17	even	6
4410.2.d.b.4409.2		16	35.4	even	6
4410.2.d.b.4409.15		16	35.24	odd	6
4410.2.d.b.4409.16		16	21.11	odd	6

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.bo (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.948234 + 2.02506i) q^{5} +(0.732536 - 2.54232i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.948234 + 2.02506i) q^{5} +(0.732536 - 2.54232i) q^{7} -1.00000 q^{8} +(-1.27963 + 1.83372i) q^{10} +(2.07577 + 1.19845i) q^{11} +5.67714 q^{13} +(2.56798 - 0.636766i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.79434 + 1.03596i) q^{17} +(-5.12164 + 2.95698i) q^{19} +(-2.22787 - 0.191334i) q^{20} +2.39690i q^{22} +(0.930877 + 1.61233i) q^{23} +(-3.20171 + 3.84045i) q^{25} +(2.83857 + 4.91654i) q^{26} +(1.83545 + 1.90555i) q^{28} +4.88913i q^{29} +(-3.92008 - 2.26326i) q^{31} +(0.500000 - 0.866025i) q^{32} +2.07192i q^{34} +(5.84296 - 0.927288i) q^{35} +(-2.57132 + 1.48455i) q^{37} +(-5.12164 - 2.95698i) q^{38} +(-0.948234 - 2.02506i) q^{40} +7.04428 q^{41} -8.55956i q^{43} +(-2.07577 + 1.19845i) q^{44} +(-0.930877 + 1.61233i) q^{46} +(-4.83140 + 2.78941i) q^{47} +(-5.92678 - 3.72468i) q^{49} +(-4.92678 - 0.852531i) q^{50} +(-2.83857 + 4.91654i) q^{52} +(2.09538 - 3.62931i) q^{53} +(-0.458606 + 5.33996i) q^{55} +(-0.732536 + 2.54232i) q^{56} +(-4.23411 + 2.44457i) q^{58} +(1.00312 - 1.73746i) q^{59} +(10.7862 - 6.22739i) q^{61} -4.52651i q^{62} +1.00000 q^{64} +(5.38325 + 11.4965i) q^{65} +(-6.60103 - 3.81111i) q^{67} +(-1.79434 + 1.03596i) q^{68} +(3.72453 + 4.59650i) q^{70} +9.14126i q^{71} +(-0.541173 + 0.937339i) q^{73} +(-2.57132 - 1.48455i) q^{74} -5.91397i q^{76} +(4.56742 - 4.39937i) q^{77} +(8.38392 + 14.5214i) q^{79} +(1.27963 - 1.83372i) q^{80} +(3.52214 + 6.10053i) q^{82} -13.6122i q^{83} +(-0.396428 + 4.61597i) q^{85} +(7.41279 - 4.27978i) q^{86} +(-2.07577 - 1.19845i) q^{88} +(-6.63129 - 11.4857i) q^{89} +(4.15870 - 14.4331i) q^{91} -1.86175 q^{92} +(-4.83140 - 2.78941i) q^{94} +(-10.8446 - 7.56771i) q^{95} +12.8260 q^{97} +(0.262276 - 6.99508i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 8 q^{4} + 6 q^{5} - 16 q^{8}+O(q^{10}) \) 16 * q + 8 * q^2 - 8 * q^4 + 6 * q^5 - 16 * q^8	\( 16 q + 8 q^{2} - 8 q^{4} + 6 q^{5} - 16 q^{8} + 6 q^{10} - 8 q^{16} + 24 q^{19} + 8 q^{23} - 6 q^{25} + 12 q^{31} + 8 q^{32} - 4 q^{35} + 24 q^{38} - 6 q^{40} - 8 q^{46} - 60 q^{47} - 28 q^{49} - 12 q^{50} - 16 q^{53} + 24 q^{61} + 16 q^{64} + 20 q^{65} - 14 q^{70} + 88 q^{77} + 4 q^{79} - 6 q^{80} + 64 q^{85} - 28 q^{91} - 16 q^{92} - 60 q^{94} + 12 q^{95} - 20 q^{98}+O(q^{100}) \) 16 * q + 8 * q^2 - 8 * q^4 + 6 * q^5 - 16 * q^8 + 6 * q^10 - 8 * q^16 + 24 * q^19 + 8 * q^23 - 6 * q^25 + 12 * q^31 + 8 * q^32 - 4 * q^35 + 24 * q^38 - 6 * q^40 - 8 * q^46 - 60 * q^47 - 28 * q^49 - 12 * q^50 - 16 * q^53 + 24 * q^61 + 16 * q^64 + 20 * q^65 - 14 * q^70 + 88 * q^77 + 4 * q^79 - 6 * q^80 + 64 * q^85 - 28 * q^91 - 16 * q^92 - 60 * q^94 + 12 * q^95 - 20 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more