LMFDB - Embedded newform 912.2.bo.c.769.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(289,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("912.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bo (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			769.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	912.769
Dual form			912.2.bo.c.625.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{3} +(1.55303 + 0.565258i) q^{5} +(0.0923963 - 0.160035i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{3} +(1.55303 + 0.565258i) q^{5} +(0.0923963 - 0.160035i) q^{7} +(0.173648 - 0.984808i) q^{9} +(-2.17365 - 3.76487i) q^{11} +(-4.96064 - 4.16247i) q^{13} +(-1.55303 + 0.565258i) q^{15} +(-0.368241 - 2.08840i) q^{17} +(4.11721 - 1.43128i) q^{19} +(0.0320889 + 0.181985i) q^{21} +(0.0996702 - 0.0362770i) q^{23} +(-1.73783 - 1.45821i) q^{25} +(0.500000 + 0.866025i) q^{27} +(0.692066 - 3.92490i) q^{29} +(-1.61334 + 2.79439i) q^{31} +(4.08512 + 1.48686i) q^{33} +(0.233956 - 0.196312i) q^{35} +4.06418 q^{37} +6.47565 q^{39} +(-6.61721 + 5.55250i) q^{41} +(0.0393628 + 0.0143269i) q^{43} +(0.826352 - 1.43128i) q^{45} +(1.37551 - 7.80093i) q^{47} +(3.48293 + 6.03260i) q^{49} +(1.62449 + 1.36310i) q^{51} +(8.65657 - 3.15074i) q^{53} +(-1.24763 - 7.07564i) q^{55} +(-2.23396 + 3.74292i) q^{57} +(-1.75237 - 9.93821i) q^{59} +(-3.37939 + 1.23000i) q^{61} +(-0.141559 - 0.118782i) q^{63} +(-5.35117 - 9.26849i) q^{65} +(1.38666 - 7.86414i) q^{67} +(-0.0530334 + 0.0918566i) q^{69} +(-3.79813 - 1.38241i) q^{71} +(11.6420 - 9.76882i) q^{73} +2.26857 q^{75} -0.803348 q^{77} +(-9.49660 + 7.96859i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(4.22803 - 7.32316i) q^{83} +(0.608593 - 3.45150i) q^{85} +(1.99273 + 3.45150i) q^{87} +(-13.7404 - 11.5295i) q^{89} +(-1.12449 + 0.409279i) q^{91} +(-0.560307 - 3.17766i) q^{93} +(7.20321 + 0.104455i) q^{95} +(1.85591 + 10.5254i) q^{97} +(-4.08512 + 1.48686i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} - 3 q^{7}+O(q^{10}) $ 6 * q - 3 * q^5 - 3 * q^7	$ 6 q - 3 q^{5} - 3 q^{7} - 12 q^{11} - 21 q^{13} + 3 q^{15} + 3 q^{17} - 6 q^{19} - 9 q^{21} + 15 q^{23} + 9 q^{25} + 3 q^{27} + 15 q^{29} - 3 q^{31} + 3 q^{33} + 6 q^{35} + 6 q^{37} - 9 q^{41} + 9 q^{43} + 6 q^{45} + 21 q^{47} - 3 q^{51} + 30 q^{53} + 9 q^{55} - 18 q^{57} - 27 q^{59} - 9 q^{61} - 9 q^{63} - 6 q^{65} + 15 q^{67} + 12 q^{69} - 9 q^{71} + 12 q^{73} - 6 q^{75} + 42 q^{77} - 15 q^{79} + 3 q^{83} - 36 q^{85} - 6 q^{87} - 48 q^{89} + 6 q^{91} - 9 q^{93} + 48 q^{95} + 18 q^{97} - 3 q^{99}+O(q^{100}) $ 6 * q - 3 * q^5 - 3 * q^7 - 12 * q^11 - 21 * q^13 + 3 * q^15 + 3 * q^17 - 6 * q^19 - 9 * q^21 + 15 * q^23 + 9 * q^25 + 3 * q^27 + 15 * q^29 - 3 * q^31 + 3 * q^33 + 6 * q^35 + 6 * q^37 - 9 * q^41 + 9 * q^43 + 6 * q^45 + 21 * q^47 - 3 * q^51 + 30 * q^53 + 9 * q^55 - 18 * q^57 - 27 * q^59 - 9 * q^61 - 9 * q^63 - 6 * q^65 + 15 * q^67 + 12 * q^69 - 9 * q^71 + 12 * q^73 - 6 * q^75 + 42 * q^77 - 15 * q^79 + 3 * q^83 - 36 * q^85 - 6 * q^87 - 48 * q^89 + 6 * q^91 - 9 * q^93 + 48 * q^95 + 18 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$	$1$	$1$

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			0
$2$		0			0
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$4$		0			0
$5$	1.55303	+	0.565258i	0.694538	+	0.252791i	0.665077	−	0.746775i	$-0.268399\pi$
$5$	1.55303	+	0.565258i	0.694538	+	0.252791i	0.0294608	+	0.999566i	$0.490621\pi$
$6$		0			0
$7$	0.0923963	−	0.160035i	0.0349225	−	0.0604876i	−0.848036	−	0.529939i	$-0.822215\pi$
$7$	0.0923963	−	0.160035i	0.0349225	−	0.0604876i	0.882958	+	0.469451i	$0.155548\pi$
$8$		0			0
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$		0			0
$11$	−2.17365	−	3.76487i	−0.655380	−	1.13515i	−0.981798	−	0.189926i	$-0.939175\pi$
$11$	−2.17365	−	3.76487i	−0.655380	−	1.13515i	0.326419	−	0.945225i	$-0.394158\pi$
$12$		0			0
$13$	−4.96064	−	4.16247i	−1.37583	−	1.15446i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−4.96064	−	4.16247i	−1.37583	−	1.15446i	−0.405108	−	0.914269i	$-0.632766\pi$
$14$		0			0
$15$	−1.55303	+	0.565258i	−0.400992	+	0.145949i
$16$		0			0
$17$	−0.368241	−	2.08840i	−0.0893115	−	0.506511i	−0.996343	−	0.0854474i	$-0.972768\pi$
$17$	−0.368241	−	2.08840i	−0.0893115	−	0.506511i	0.907031	−	0.421064i	$-0.138343\pi$
$18$		0			0
$19$	4.11721	−	1.43128i	0.944553	−	0.328359i
$19$	4.11721	−	1.43128i	0.944553	−	0.328359i
$20$		0			0
$21$	0.0320889	+	0.181985i	0.00700237	+	0.0397124i
$22$		0			0
$23$	0.0996702	−	0.0362770i	0.0207827	−	0.00756428i	−0.331608	−	0.943417i	$-0.607591\pi$
$23$	0.0996702	−	0.0362770i	0.0207827	−	0.00756428i	0.352391	+	0.935853i	$0.385369\pi$
$24$		0			0
$25$	−1.73783	−	1.45821i	−0.347565	−	0.291642i
$26$		0			0
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$		0			0
$29$	0.692066	−	3.92490i	0.128514	−	0.728836i	−0.850645	−	0.525740i	$-0.823788\pi$
$29$	0.692066	−	3.92490i	0.128514	−	0.728836i	0.979159	−	0.203096i	$-0.0651004\pi$
$30$		0			0
$31$	−1.61334	+	2.79439i	−0.289765	+	0.501887i	−0.973753	−	0.227606i	$-0.926910\pi$
$31$	−1.61334	+	2.79439i	−0.289765	+	0.501887i	0.683989	+	0.729492i	$0.260244\pi$
$32$		0			0
$33$	4.08512	+	1.48686i	0.711129	+	0.258830i
$34$		0			0
$35$	0.233956	−	0.196312i	0.0395457	−	0.0331828i
$36$		0			0
$37$	4.06418			0.668147			0.334073	−	0.942547i	$-0.391577\pi$
$37$	4.06418			0.668147			0.334073	+	0.942547i	$0.391577\pi$
$38$		0			0
$39$	6.47565			1.03693
$40$		0			0
$41$	−6.61721	+	5.55250i	−1.03343	+	0.867155i	−0.991256	−	0.131955i	$-0.957874\pi$
$41$	−6.61721	+	5.55250i	−1.03343	+	0.867155i	−0.0421791	+	0.999110i	$0.513430\pi$
$42$		0			0
$43$	0.0393628	+	0.0143269i	0.00600278	+	0.00218483i	0.345020	−	0.938595i	$-0.387872\pi$
$43$	0.0393628	+	0.0143269i	0.00600278	+	0.00218483i	−0.339017	+	0.940780i	$0.610094\pi$
$44$		0			0
$45$	0.826352	−	1.43128i	0.123185	−	0.213363i
$46$		0			0
$47$	1.37551	−	7.80093i	0.200639	−	1.13788i	−0.703516	−	0.710679i	$-0.748388\pi$
$47$	1.37551	−	7.80093i	0.200639	−	1.13788i	0.904155	−	0.427204i	$-0.140501\pi$
$48$		0			0
$49$	3.48293	+	6.03260i	0.497561	+	0.861801i
$50$		0			0
$51$	1.62449	+	1.36310i	0.227473	+	0.190873i
$52$		0			0
$53$	8.65657	−	3.15074i	1.18907	−	0.432787i	0.329674	−	0.944095i	$-0.393061\pi$
$53$	8.65657	−	3.15074i	1.18907	−	0.432787i	0.859398	+	0.511308i	$0.170839\pi$
$54$		0			0
$55$	−1.24763	−	7.07564i	−0.168230	−	0.954079i
$56$		0			0
$57$	−2.23396	+	3.74292i	−0.295895	+	0.495762i
$58$		0			0
$59$	−1.75237	−	9.93821i	−0.228140	−	1.29384i	−0.856591	−	0.515996i	$-0.827422\pi$
$59$	−1.75237	−	9.93821i	−0.228140	−	1.29384i	0.628452	−	0.777849i	$-0.283689\pi$
$60$		0			0
$61$	−3.37939	+	1.23000i	−0.432686	+	0.157485i	−0.549175	−	0.835707i	$-0.685058\pi$
$61$	−3.37939	+	1.23000i	−0.432686	+	0.157485i	0.116489	+	0.993192i	$0.462836\pi$
$62$		0			0
$63$	−0.141559	−	0.118782i	−0.0178348	−	0.0149652i
$64$		0			0
$65$	−5.35117	−	9.26849i	−0.663731	−	1.14962i
$66$		0			0
$67$	1.38666	−	7.86414i	0.169407	−	0.960757i	−0.774996	−	0.631967i	$-0.782248\pi$
$67$	1.38666	−	7.86414i	0.169407	−	0.960757i	0.944403	−	0.328790i	$-0.106641\pi$
$68$		0			0
$69$	−0.0530334	+	0.0918566i	−0.00638447	+	0.0110582i
$70$		0			0
$71$	−3.79813	−	1.38241i	−0.450755	−	0.164062i	0.106659	−	0.994296i	$-0.465985\pi$
$71$	−3.79813	−	1.38241i	−0.450755	−	0.164062i	−0.557415	+	0.830234i	$0.688207\pi$
$72$		0			0
$73$	11.6420	−	9.76882i	1.36260	−	1.14335i	0.387425	−	0.921901i	$-0.373365\pi$
$73$	11.6420	−	9.76882i	1.36260	−	1.14335i	0.975171	−	0.221453i	$-0.0710798\pi$
$74$		0			0
$75$	2.26857			0.261952
$76$		0			0
$77$	−0.803348			−0.0915500
$78$		0			0
$79$	−9.49660	+	7.96859i	−1.06845	+	0.896536i	−0.994911	−	0.100756i	$-0.967874\pi$
$79$	−9.49660	+	7.96859i	−1.06845	+	0.896536i	−0.0735394	+	0.997292i	$0.523429\pi$
$80$		0			0
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$		0			0
$83$	4.22803	−	7.32316i	0.464086	−	0.803821i	−0.535074	−	0.844805i	$-0.679716\pi$
$83$	4.22803	−	7.32316i	0.464086	−	0.803821i	0.999160	+	0.0409847i	$0.0130495\pi$
$84$		0			0
$85$	0.608593	−	3.45150i	0.0660112	−	0.374368i
$86$		0			0
$87$	1.99273	+	3.45150i	0.213643	+	0.370040i
$88$		0			0
$89$	−13.7404	−	11.5295i	−1.45647	−	1.22213i	−0.927679	−	0.373378i	$-0.878200\pi$
$89$	−13.7404	−	11.5295i	−1.45647	−	1.22213i	−0.528795	−	0.848750i	$-0.677356\pi$
$90$		0			0
$91$	−1.12449	+	0.409279i	−0.117878	+	0.0429041i
$92$		0			0
$93$	−0.560307	−	3.17766i	−0.0581012	−	0.329508i
$94$		0			0
$95$	7.20321	+	0.104455i	0.739034	+	0.0107169i
$96$		0			0
$97$	1.85591	+	10.5254i	0.188440	+	1.06869i	0.921456	+	0.388483i	$0.127001\pi$
$97$	1.85591	+	10.5254i	0.188440	+	1.06869i	−0.733016	+	0.680211i	$0.761888\pi$
$98$		0			0
$99$	−4.08512	+	1.48686i	−0.410570	+	0.149435i
$100$		0			0
$101$	6.17752	+	5.18355i	0.614686	+	0.515783i	0.896128	−	0.443795i	$-0.146368\pi$
$101$	6.17752	+	5.18355i	0.614686	+	0.515783i	−0.281442	+	0.959578i	$0.590813\pi$
$102$		0			0
$103$	8.96451	+	15.5270i	0.883299	+	1.52992i	0.847651	+	0.530555i	$0.178016\pi$
$103$	8.96451	+	15.5270i	0.883299	+	1.52992i	0.0356484	+	0.999364i	$0.488650\pi$
$104$		0			0
$105$	−0.0530334	+	0.300767i	−0.00517553	+	0.0293519i
$106$		0			0
$107$	−6.99407	+	12.1141i	−0.676142	+	1.17111i	0.299991	+	0.953942i	$0.403016\pi$
$107$	−6.99407	+	12.1141i	−0.676142	+	1.17111i	−0.976134	+	0.217171i	$0.930317\pi$
$108$		0			0
$109$	4.48545	+	1.63257i	0.429628	+	0.156372i	0.547778	−	0.836624i	$-0.315474\pi$
$109$	4.48545	+	1.63257i	0.429628	+	0.156372i	−0.118149	+	0.992996i	$0.537696\pi$
$110$		0			0
$111$	−3.11334	+	2.61240i	−0.295505	+	0.247958i
$112$		0			0
$113$	−0.753718			−0.0709038			−0.0354519	−	0.999371i	$-0.511287\pi$
$113$	−0.753718			−0.0709038			−0.0354519	+	0.999371i	$0.511287\pi$
$114$		0			0
$115$	0.175297			0.0163465
$116$		0			0
$117$	−4.96064	+	4.16247i	−0.458611	+	0.384820i
$118$		0			0
$119$	−0.368241	−	0.134029i	−0.0337566	−	0.0122864i
$120$		0			0
$121$	−3.94949	+	6.84072i	−0.359045	+	0.621884i
$122$		0			0
$123$	1.50000	−	8.50692i	0.135250	−	0.767043i
$124$		0			0
$125$	−6.00640	−	10.4034i	−0.537228	−	0.930507i
$126$		0			0
$127$	8.29086	+	6.95686i	0.735695	+	0.617321i	0.931678	−	0.363286i	$-0.118345\pi$
$127$	8.29086	+	6.95686i	0.735695	+	0.617321i	−0.195983	+	0.980607i	$0.562790\pi$
$128$		0			0
$129$	−0.0393628	+	0.0143269i	−0.00346571	+	0.00126141i
$130$		0			0
$131$	−1.88326	−	10.6805i	−0.164541	−	0.933157i	−0.949537	−	0.313656i	$-0.898446\pi$
$131$	−1.88326	−	10.6805i	−0.164541	−	0.933157i	0.784996	−	0.619501i	$-0.212665\pi$
$132$		0			0
$133$	0.151359	−	0.791143i	0.0131245	−	0.0686008i
$134$		0			0
$135$	0.286989	+	1.62760i	0.0247001	+	0.140081i
$136$		0			0
$137$	13.1099	−	4.77163i	1.12006	−	0.407668i	0.285384	−	0.958413i	$-0.407879\pi$
$137$	13.1099	−	4.77163i	1.12006	−	0.407668i	0.834673	+	0.550746i	$0.185657\pi$
$138$		0			0
$139$	−4.57011	−	3.83478i	−0.387631	−	0.325261i	0.428058	−	0.903751i	$-0.359198\pi$
$139$	−4.57011	−	3.83478i	−0.387631	−	0.325261i	−0.815690	+	0.578490i	$0.803642\pi$
$140$		0			0
$141$	3.96064	+	6.86002i	0.333546	+	0.577718i
$142$		0			0
$143$	−4.88847	+	27.7239i	−0.408794	+	2.31839i
$144$		0			0
$145$	3.29339	−	5.70431i	0.273501	−	0.473717i
$146$		0			0
$147$	−6.54576	−	2.38246i	−0.539885	−	0.196502i
$148$		0			0
$149$	−10.8931	+	9.14036i	−0.892394	+	0.748807i	−0.968689	−	0.248278i	$-0.920135\pi$
$149$	−10.8931	+	9.14036i	−0.892394	+	0.748807i	0.0762949	+	0.997085i	$0.475691\pi$
$150$		0			0
$151$	15.2003			1.23698			0.618490	−	0.785792i	$-0.287745\pi$
$151$	15.2003			1.23698			0.618490	+	0.785792i	$0.287745\pi$
$152$		0			0
$153$	−2.12061			−0.171442
$154$		0			0
$155$	−4.08512	+	3.42782i	−0.328125	+	0.275329i
$156$		0			0
$157$	−8.83662	−	3.21627i	−0.705239	−	0.256686i	−0.0355929	−	0.999366i	$-0.511332\pi$
$157$	−8.83662	−	3.21627i	−0.705239	−	0.256686i	−0.669646	+	0.742680i	$0.733554\pi$
$158$		0			0
$159$	−4.60607	+	7.97794i	−0.365285	+	0.632692i
$160$		0			0
$161$	0.00340357	−	0.0193026i	0.000268239	−	0.00152126i
$162$		0			0
$163$	−3.81180	−	6.60224i	−0.298564	−	0.517127i	0.677244	−	0.735758i	$-0.263174\pi$
$163$	−3.81180	−	6.60224i	−0.298564	−	0.517127i	−0.975808	+	0.218631i	$0.929841\pi$
$164$		0			0
$165$	5.50387	+	4.61830i	0.428476	+	0.359534i
$166$		0			0
$167$	−16.1630	+	5.88284i	−1.25073	+	0.455228i	−0.880648	−	0.473772i	$-0.842892\pi$
$167$	−16.1630	+	5.88284i	−1.25073	+	0.455228i	−0.370081	+	0.929000i	$0.620670\pi$
$168$		0			0
$169$	5.02435	+	28.4945i	0.386488	+	2.19188i
$170$		0			0
$171$	−0.694593	−	4.30320i	−0.0531168	−	0.329074i
$172$		0			0
$173$	−1.15018	−	6.52298i	−0.0874464	−	0.495933i	−0.996802	−	0.0799130i	$-0.974536\pi$
$173$	−1.15018	−	6.52298i	−0.0874464	−	0.495933i	0.909355	−	0.416020i	$-0.136575\pi$
$174$		0			0
$175$	−0.393933	+	0.143380i	−0.0297785	+	0.0108385i
$176$		0			0
$177$	7.73055	+	6.48670i	0.581064	+	0.487570i
$178$		0			0
$179$	−10.7121	−	18.5540i	−0.800662	−	1.38679i	−0.919181	−	0.393836i	$-0.871148\pi$
$179$	−10.7121	−	18.5540i	−0.800662	−	1.38679i	0.118518	−	0.992952i	$-0.462186\pi$
$180$		0			0
$181$	−2.98411	+	16.9237i	−0.221807	+	1.25793i	0.646889	+	0.762584i	$0.276070\pi$
$181$	−2.98411	+	16.9237i	−0.221807	+	1.25793i	−0.868696	+	0.495346i	$0.835041\pi$
$182$		0			0
$183$	1.79813	−	3.11446i	0.132922	−	0.230227i
$184$		0			0
$185$	6.31180	+	2.29731i	0.464053	+	0.168901i
$186$		0			0
$187$	−7.06212	+	5.92582i	−0.516433	+	0.433339i
$188$		0			0
$189$	0.184793			0.0134417
$190$		0			0
$191$	6.57398			0.475676			0.237838	−	0.971305i	$-0.423561\pi$
$191$	6.57398			0.475676			0.237838	+	0.971305i	$0.423561\pi$
$192$		0			0
$193$	−8.69253	+	7.29390i	−0.625702	+	0.525027i	−0.899590	−	0.436735i	$-0.856135\pi$
$193$	−8.69253	+	7.29390i	−0.625702	+	0.525027i	0.273888	+	0.961762i	$0.411690\pi$
$194$		0			0
$195$	10.0569	+	3.66041i	0.720190	+	0.262128i
$196$		0			0
$197$	−3.22416	+	5.58440i	−0.229712	+	0.397872i	−0.957723	−	0.287693i	$-0.907112\pi$
$197$	−3.22416	+	5.58440i	−0.229712	+	0.397872i	0.728011	+	0.685565i	$0.240445\pi$
$198$		0			0
$199$	−2.90420	+	16.4705i	−0.205873	+	1.16757i	0.690186	+	0.723632i	$0.257529\pi$
$199$	−2.90420	+	16.4705i	−0.205873	+	1.16757i	−0.896060	+	0.443934i	$0.853583\pi$
$200$		0			0
$201$	3.99273	+	6.91560i	0.281625	+	0.487789i
$202$		0			0
$203$	−0.564178	−	0.473401i	−0.0395975	−	0.0332263i
$204$		0			0
$205$	−13.4153	+	4.88279i	−0.936968	+	0.341029i
$206$		0			0
$207$	−0.0184183	−	0.104455i	−0.00128016	−	0.00726016i
$208$		0			0
$209$	−14.3380	−	12.3897i	−0.991778	−	0.857010i
$210$		0			0
$211$	0.847296	+	4.80526i	0.0583303	+	0.330807i	0.999983	−	0.00577769i	$-0.00183911\pi$
$211$	0.847296	+	4.80526i	0.0583303	+	0.330807i	−0.941653	+	0.336585i	$0.890728\pi$
$212$		0			0
$213$	3.79813	−	1.38241i	0.260244	−	0.0947210i
$214$		0			0
$215$	0.0530334	+	0.0445003i	0.00361685	+	0.00303490i
$216$		0			0
$217$	0.298133	+	0.516382i	0.0202386	+	0.0350543i
$218$		0			0
$219$	−2.63903	+	14.9667i	−0.178329	+	1.01136i
$220$		0			0
$221$	−6.86618	+	11.8926i	−0.461869	+	0.799981i
$222$		0			0
$223$	27.0453	+	9.84370i	1.81109	+	0.659183i	0.996908	+	0.0785736i	$0.0250366\pi$
$223$	27.0453	+	9.84370i	1.81109	+	0.659183i	0.814182	+	0.580609i	$0.197186\pi$
$224$		0			0
$225$	−1.73783	+	1.45821i	−0.115855	+	0.0972139i
$226$		0			0
$227$	3.75608			0.249300			0.124650	−	0.992201i	$-0.460219\pi$
$227$	3.75608			0.249300			0.124650	+	0.992201i	$0.460219\pi$
$228$		0			0
$229$	17.5175			1.15759			0.578796	−	0.815472i	$-0.303523\pi$
$229$	17.5175			1.15759			0.578796	+	0.815472i	$0.303523\pi$
$230$		0			0
$231$	0.615400	−	0.516382i	0.0404904	−	0.0339754i
$232$		0			0
$233$	6.58260	+	2.39587i	0.431240	+	0.156959i	0.548515	−	0.836141i	$-0.315193\pi$
$233$	6.58260	+	2.39587i	0.431240	+	0.156959i	−0.117274	+	0.993100i	$0.537416\pi$
$234$		0			0
$235$	6.54576	−	11.3376i	0.426998	−	0.739583i
$236$		0			0
$237$	2.15270	−	12.2086i	0.139833	−	0.793033i
$238$		0			0
$239$	0.467911	+	0.810446i	0.0302667	+	0.0524234i	0.880762	−	0.473559i	$-0.157031\pi$
$239$	0.467911	+	0.810446i	0.0302667	+	0.0524234i	−0.850495	+	0.525983i	$0.823698\pi$
$240$		0			0
$241$	−22.0082	−	18.4671i	−1.41767	−	1.18957i	−0.952573	−	0.304311i	$-0.901574\pi$
$241$	−22.0082	−	18.4671i	−1.41767	−	1.18957i	−0.465101	−	0.885258i	$-0.653982\pi$
$242$		0			0
$243$	0.939693	−	0.342020i	0.0602813	−	0.0219406i
$244$		0			0
$245$	1.99912	+	11.3376i	0.127719	+	0.724332i
$246$		0			0
$247$	−26.3817	−	10.0377i	−1.67863	−	0.638683i
$248$		0			0
$249$	1.46838	+	8.32759i	0.0930547	+	0.527739i
$250$		0			0
$251$	22.7271	−	8.27201i	1.43452	−	0.522124i	0.496300	−	0.868151i	$-0.334692\pi$
$251$	22.7271	−	8.27201i	1.43452	−	0.522124i	0.938225	+	0.346027i	$0.112469\pi$
$252$		0			0
$253$	−0.353226	−	0.296392i	−0.0222071	−	0.0186340i
$254$		0			0
$255$	1.75237	+	3.03520i	0.109738	+	0.190072i
$256$		0			0
$257$	1.52822	−	8.66696i	0.0953277	−	0.540630i	−0.899319	−	0.437294i	$-0.855937\pi$
$257$	1.52822	−	8.66696i	0.0953277	−	0.540630i	0.994646	−	0.103336i	$-0.0329518\pi$
$258$		0			0
$259$	0.375515	−	0.650411i	0.0233334	−	0.0404146i
$260$		0			0
$261$	−3.74510	−	1.36310i	−0.231816	−	0.0843741i
$262$		0			0
$263$	−1.00206	+	0.840828i	−0.0617896	+	0.0518477i	−0.673159	−	0.739497i	$-0.735063\pi$
$263$	−1.00206	+	0.840828i	−0.0617896	+	0.0518477i	0.611370	+	0.791345i	$0.290619\pi$
$264$		0			0
$265$	15.2249			0.935260
$266$		0			0
$267$	17.9368			1.09771
$268$		0			0
$269$	6.70368	−	5.62505i	0.408730	−	0.342966i	−0.415126	−	0.909764i	$-0.636263\pi$
$269$	6.70368	−	5.62505i	0.408730	−	0.342966i	0.823857	+	0.566798i	$0.191818\pi$
$270$		0			0
$271$	−12.9179	−	4.70172i	−0.784705	−	0.285609i	−0.0815717	−	0.996667i	$-0.525994\pi$
$271$	−12.9179	−	4.70172i	−0.784705	−	0.285609i	−0.703133	+	0.711058i	$0.748216\pi$
$272$		0			0
$273$	0.598326	−	1.03633i	0.0362123	−	0.0627216i
$274$		0			0
$275$	−1.71254	+	9.71232i	−0.103270	+	0.585675i
$276$		0			0
$277$	−12.5039	−	21.6573i	−0.751285	−	1.30126i	−0.947200	−	0.320643i	$-0.896101\pi$
$277$	−12.5039	−	21.6573i	−0.751285	−	1.30126i	0.195915	−	0.980621i	$-0.437232\pi$
$278$		0			0
$279$	2.47178	+	2.07407i	0.147982	+	0.124171i
$280$		0			0
$281$	−11.4226	+	4.15749i	−0.681416	+	0.248015i	−0.659456	−	0.751744i	$-0.729213\pi$
$281$	−11.4226	+	4.15749i	−0.681416	+	0.248015i	−0.0219608	+	0.999759i	$0.506991\pi$
$282$		0			0
$283$	1.85756	+	10.5348i	0.110421	+	0.626227i	0.988916	+	0.148476i	$0.0474367\pi$
$283$	1.85756	+	10.5348i	0.110421	+	0.626227i	−0.878495	+	0.477751i	$0.841452\pi$
$284$		0			0
$285$	−5.58512	+	4.55012i	−0.330834	+	0.269526i
$286$		0			0
$287$	0.277189	+	1.57202i	0.0163619	+	0.0927932i
$288$		0			0
$289$	11.7490	−	4.27628i	0.691116	−	0.251546i
$290$		0			0
$291$	−8.18732	−	6.86998i	−0.479949	−	0.402725i
$292$		0			0
$293$	6.67365	+	11.5591i	0.389879	+	0.675290i	0.992433	−	0.122788i	$-0.0391836\pi$
$293$	6.67365	+	11.5591i	0.389879	+	0.675290i	−0.602554	+	0.798078i	$0.705850\pi$
$294$		0			0
$295$	2.89615	−	16.4249i	0.168621	−	0.956295i
$296$		0			0
$297$	2.17365	−	3.76487i	0.126128	−	0.218460i
$298$		0			0
$299$	−0.645430	−	0.234917i	−0.0373262	−	0.0135856i
$300$		0			0
$301$	0.00592979	−	0.00497568i	0.000341787	−	0.000286794i
$302$		0			0
$303$	−8.06418			−0.463275
$304$		0			0
$305$	−5.94356			−0.340327
$306$		0			0
$307$	−11.9987	+	10.0681i	−0.684799	+	0.574615i	−0.917404	−	0.397956i	$-0.869720\pi$
$307$	−11.9987	+	10.0681i	−0.684799	+	0.574615i	0.232605	+	0.972571i	$0.425275\pi$
$308$		0			0
$309$	−16.8478	−	6.13208i	−0.958436	−	0.348842i
$310$		0			0
$311$	4.55303	−	7.88609i	0.258179	−	0.447179i	−0.707575	−	0.706638i	$-0.750211\pi$
$311$	4.55303	−	7.88609i	0.258179	−	0.447179i	0.965754	+	0.259459i	$0.0835443\pi$
$312$		0			0
$313$	3.08172	−	17.4773i	0.174189	−	0.987875i	−0.764887	−	0.644165i	$-0.777205\pi$
$313$	3.08172	−	17.4773i	0.174189	−	0.987875i	0.939076	−	0.343710i	$-0.111684\pi$
$314$		0			0
$315$	−0.152704	−	0.264490i	−0.00860388	−	0.0149023i
$316$		0			0
$317$	23.7822	+	19.9557i	1.33574	+	1.12082i	0.982698	+	0.185216i	$0.0592985\pi$
$317$	23.7822	+	19.9557i	1.33574	+	1.12082i	0.353046	+	0.935606i	$0.385146\pi$
$318$		0			0
$319$	−16.2811	+	5.92582i	−0.911564	+	0.331782i
$320$		0			0
$321$	−2.42902	−	13.7756i	−0.135574	−	0.768881i
$322$		0			0
$323$	−4.50521	−	8.07132i	−0.250677	−	0.449100i
$324$		0			0
$325$	2.55097	+	14.4673i	0.141503	+	0.802501i
$326$		0			0
$327$	−4.48545	+	1.63257i	−0.248046	+	0.0902814i
$328$		0			0
$329$	−1.12133	−	0.940908i	−0.0618209	−	0.0518739i
$330$		0			0
$331$	−5.03983	−	8.72924i	−0.277014	−	0.479802i	0.693627	−	0.720334i	$-0.256012\pi$
$331$	−5.03983	−	8.72924i	−0.277014	−	0.479802i	−0.970641	+	0.240532i	$0.922678\pi$
$332$		0			0
$333$	0.705737	−	4.00243i	0.0386742	−	0.219332i
$334$		0			0
$335$	6.59879	−	11.4294i	0.360531	−	0.624457i
$336$		0			0
$337$	7.87211	+	2.86521i	0.428821	+	0.156078i	0.547409	−	0.836865i	$-0.315614\pi$
$337$	7.87211	+	2.86521i	0.428821	+	0.156078i	−0.118587	+	0.992944i	$0.537837\pi$
$338$		0			0
$339$	0.577382	−	0.484481i	0.0313591	−	0.0263134i
$340$		0			0
$341$	14.0273			0.759623
$342$		0			0
$343$	2.58079			0.139349
$344$		0			0
$345$	−0.134285	+	0.112679i	−0.00722968	+	0.00606642i
$346$		0			0
$347$	12.2306	+	4.45156i	0.656570	+	0.238972i	0.648755	−	0.760997i	$-0.275290\pi$
$347$	12.2306	+	4.45156i	0.656570	+	0.238972i	0.00781546	+	0.999969i	$0.497512\pi$
$348$		0			0
$349$	3.35369	−	5.80877i	0.179519	−	0.310936i	−0.762197	−	0.647345i	$-0.775879\pi$
$349$	3.35369	−	5.80877i	0.179519	−	0.310936i	0.941716	+	0.336409i	$0.109213\pi$
$350$		0			0
$351$	1.12449	−	6.37727i	0.0600206	−	0.340394i
$352$		0			0
$353$	−5.32295	−	9.21962i	−0.283312	−	0.490711i	0.688886	−	0.724869i	$-0.258100\pi$
$353$	−5.32295	−	9.21962i	−0.283312	−	0.490711i	−0.972198	+	0.234159i	$0.924767\pi$
$354$		0			0
$355$	−5.11721	−	4.29385i	−0.271593	−	0.227894i
$356$		0			0
$357$	0.368241	−	0.134029i	0.0194894	−	0.00709355i
$358$		0			0
$359$	5.06418	+	28.7204i	0.267277	+	1.51580i	0.762472	+	0.647022i	$0.223986\pi$
$359$	5.06418	+	28.7204i	0.267277	+	1.51580i	−0.495195	+	0.868782i	$0.664903\pi$
$360$		0			0
$361$	14.9029	−	11.7858i	0.784361	−	0.620305i
$362$		0			0
$363$	−1.37164	−	7.77898i	−0.0719927	−	0.408291i
$364$		0			0
$365$	23.6024	−	8.59056i	1.23540	−	0.449650i
$366$		0			0
$367$	2.71095	+	2.27476i	0.141511	+	0.118741i	0.710795	−	0.703399i	$-0.248335\pi$
$367$	2.71095	+	2.27476i	0.141511	+	0.118741i	−0.569285	+	0.822141i	$0.692780\pi$
$368$		0			0
$369$	4.31908	+	7.48086i	0.224842	+	0.389438i
$370$		0			0
$371$	0.295607	−	1.67647i	0.0153472	−	0.0870380i
$372$		0			0
$373$	−5.10472	+	8.84164i	−0.264313	+	0.457803i	−0.967383	−	0.253317i	$-0.918478\pi$
$373$	−5.10472	+	8.84164i	−0.264313	+	0.457803i	0.703071	+	0.711120i	$0.251812\pi$
$374$		0			0
$375$	11.2883	+	4.10862i	0.582927	+	0.212168i
$376$		0			0
$377$	−19.7704	+	16.5893i	−1.01823	+	0.854393i
$378$		0			0
$379$	−12.6287			−0.648691			−0.324345	−	0.945939i	$-0.605144\pi$
$379$	−12.6287			−0.648691			−0.324345	+	0.945939i	$0.605144\pi$
$380$		0			0
$381$	−10.8229			−0.554476
$382$		0			0
$383$	6.67546	−	5.60138i	0.341100	−	0.286217i	−0.456105	−	0.889926i	$-0.650756\pi$
$383$	6.67546	−	5.60138i	0.341100	−	0.286217i	0.797205	+	0.603709i	$0.206311\pi$
$384$		0			0
$385$	−1.24763	−	0.454099i	−0.0635849	−	0.0231430i
$386$		0			0
$387$	0.0209445	−	0.0362770i	0.00106467	−	0.00184406i
$388$		0			0
$389$	−1.50118	+	8.51363i	−0.0761130	+	0.431658i	0.922810	+	0.385256i	$0.125887\pi$
$389$	−1.50118	+	8.51363i	−0.0761130	+	0.431658i	−0.998923	+	0.0464023i	$0.985224\pi$
$390$		0			0
$391$	−0.112463	−	0.194792i	−0.00568752	−	0.00985108i
$392$		0			0
$393$	8.30793	+	6.97118i	0.419080	+	0.351650i
$394$		0			0
$395$	−19.2528	+	7.00746i	−0.968716	+	0.352584i
$396$		0			0
$397$	−1.19372	−	6.76990i	−0.0599109	−	0.339771i	0.940088	−	0.340931i	$-0.110742\pi$
$397$	−1.19372	−	6.76990i	−0.0599109	−	0.339771i	−0.999999	+	0.00115924i	$0.999631\pi$
$398$		0			0
$399$	0.392589	+	0.703343i	0.0196540	+	0.0352112i
$400$		0			0
$401$	−5.11200	−	28.9916i	−0.255281	−	1.44777i	−0.795351	−	0.606150i	$-0.792713\pi$
$401$	−5.11200	−	28.9916i	−0.255281	−	1.44777i	0.540070	−	0.841620i	$-0.318398\pi$
$402$		0			0
$403$	19.6348	−	7.14647i	0.978077	−	0.355991i
$404$		0			0
$405$	−1.26604	−	1.06234i	−0.0629103	−	0.0527880i
$406$		0			0
$407$	−8.83409	−	15.3011i	−0.437890	−	0.758447i
$408$		0			0
$409$	−3.69459	+	20.9531i	−0.182686	+	1.03606i	0.746207	+	0.665714i	$0.231873\pi$
$409$	−3.69459	+	20.9531i	−0.182686	+	1.03606i	−0.928893	+	0.370349i	$0.879238\pi$
$410$		0			0
$411$	−6.97565	+	12.0822i	−0.344084	+	0.595970i
$412$		0			0
$413$	−1.75237	−	0.637812i	−0.0862287	−	0.0313847i
$414$		0			0
$415$	10.7057	−	8.98318i	0.525524	−	0.440967i
$416$		0			0
$417$	5.96585			0.292149
$418$		0			0
$419$	−15.8922			−0.776384			−0.388192	−	0.921579i	$-0.626900\pi$
$419$	−15.8922			−0.776384			−0.388192	+	0.921579i	$0.626900\pi$
$420$		0			0
$421$	15.0103	−	12.5951i	0.731556	−	0.613848i	−0.199000	−	0.980000i	$-0.563769\pi$
$421$	15.0103	−	12.5951i	0.731556	−	0.613848i	0.930555	+	0.366151i	$0.119325\pi$
$422$		0			0
$423$	−7.44356	−	2.70924i	−0.361918	−	0.131728i
$424$		0			0
$425$	−2.40538	+	4.16624i	−0.116678	+	0.202093i
$426$		0			0
$427$	−0.115400	+	0.654467i	−0.00558461	+	0.0316719i
$428$		0			0
$429$	−14.0758	−	24.3800i	−0.679585	−	1.17708i
$430$		0			0
$431$	3.18273	+	2.67063i	0.153307	+	0.128640i	0.716215	−	0.697880i	$-0.245873\pi$
$431$	3.18273	+	2.67063i	0.153307	+	0.128640i	−0.562908	+	0.826520i	$0.690317\pi$
$432$		0			0
$433$	3.34730	−	1.21832i	0.160861	−	0.0585485i	−0.260335	−	0.965518i	$-0.583833\pi$
$433$	3.34730	−	1.21832i	0.160861	−	0.0585485i	0.421195	+	0.906970i	$0.361611\pi$
$434$		0			0
$435$	1.14378	+	6.48670i	0.0548401	+	0.311014i
$436$		0			0
$437$	0.358441	−	0.292016i	0.0171465	−	0.0139690i
$438$		0			0
$439$	1.42649	+	8.09002i	0.0680826	+	0.386116i	0.999741	+	0.0227790i	$0.00725140\pi$
$439$	1.42649	+	8.09002i	0.0680826	+	0.386116i	−0.931658	+	0.363337i	$0.881637\pi$
$440$		0			0
$441$	6.54576	−	2.38246i	0.311703	−	0.113451i
$442$		0			0
$443$	14.5137	+	12.1784i	0.689565	+	0.578614i	0.918784	−	0.394761i	$-0.129173\pi$
$443$	14.5137	+	12.1784i	0.689565	+	0.578614i	−0.229219	+	0.973375i	$0.573617\pi$
$444$		0			0
$445$	−14.8221	−	25.6726i	−0.702634	−	1.21700i
$446$		0			0
$447$	2.46926	−	14.0038i	0.116792	−	0.662359i
$448$		0			0
$449$	−5.24628	+	9.08683i	−0.247587	+	0.428834i	−0.962856	−	0.270016i	$-0.912971\pi$
$449$	−5.24628	+	9.08683i	−0.247587	+	0.428834i	0.715269	+	0.698850i	$0.246304\pi$
$450$		0			0
$451$	35.2879	+	12.8438i	1.66164	+	0.604789i
$452$		0			0
$453$	−11.6441	+	9.77055i	−0.547087	+	0.459060i
$454$		0			0
$455$	−1.97771			−0.0927165
$456$		0			0
$457$	−0.415593			−0.0194406			−0.00972031	−	0.999953i	$-0.503094\pi$
$457$	−0.415593			−0.0194406			−0.00972031	+	0.999953i	$0.503094\pi$
$458$		0			0
$459$	1.62449	−	1.36310i	0.0758245	−	0.0636243i
$460$		0			0
$461$	−23.7344	−	8.63862i	−1.10542	−	0.402341i	−0.276110	−	0.961126i	$-0.589045\pi$
$461$	−23.7344	−	8.63862i	−1.10542	−	0.402341i	−0.829312	+	0.558785i	$0.811268\pi$
$462$		0			0
$463$	9.39558	−	16.2736i	0.436650	−	0.756300i	−0.560779	−	0.827966i	$-0.689498\pi$
$463$	9.39558	−	16.2736i	0.436650	−	0.756300i	0.997429	+	0.0716660i	$0.0228316\pi$
$464$		0			0
$465$	0.926022	−	5.25173i	0.0429432	−	0.243543i
$466$		0			0
$467$	−8.56670	−	14.8380i	−0.396420	−	0.686619i	0.596861	−	0.802344i	$-0.296414\pi$
$467$	−8.56670	−	14.8380i	−0.396420	−	0.686619i	−0.993281	+	0.115725i	$0.963081\pi$
$468$		0			0
$469$	−1.13041	−	0.948531i	−0.0521977	−	0.0437991i
$470$		0			0
$471$	8.83662	−	3.21627i	0.407170	−	0.148198i
$472$		0			0
$473$	−0.0316221	−	0.179338i	−0.00145398	−	0.00824595i
$474$		0			0
$475$	−9.24211	−	3.51643i	−0.424057	−	0.161345i
$476$		0			0
$477$	−1.59967	−	9.07218i	−0.0732439	−	0.415387i
$478$		0			0
$479$	−10.2973	+	3.74789i	−0.470494	+	0.171246i	−0.566376	−	0.824147i	$-0.691655\pi$
$479$	−10.2973	+	3.74789i	−0.470494	+	0.171246i	0.0958823	+	0.995393i	$0.469433\pi$
$480$		0			0
$481$	−20.1609	−	16.9170i	−0.919258	−	0.771349i
$482$		0			0
$483$	0.00980018	+	0.0169744i	0.000445924	+	0.000772362i
$484$		0			0
$485$	−3.06728	+	17.3954i	−0.139278	+	0.789884i
$486$		0			0
$487$	8.44016	−	14.6188i	0.382460	−	0.662440i	−0.608953	−	0.793206i	$-0.708410\pi$
$487$	8.44016	−	14.6188i	0.382460	−	0.662440i	0.991413	+	0.130766i	$0.0417436\pi$
$488$		0			0
$489$	7.16385	+	2.60743i	0.323960	+	0.117912i
$490$		0			0
$491$	8.62314	−	7.23567i	0.389157	−	0.326541i	−0.427128	−	0.904191i	$-0.640475\pi$
$491$	8.62314	−	7.23567i	0.389157	−	0.326541i	0.816285	+	0.577650i	$0.196030\pi$
$492$		0			0
$493$	−8.45161			−0.380641
$494$		0			0
$495$	−7.18479			−0.322932
$496$		0			0
$497$	−0.572167	+	0.480105i	−0.0256652	+	0.0215357i
$498$		0			0
$499$	−9.18139	−	3.34175i	−0.411015	−	0.149597i	0.128233	−	0.991744i	$-0.459069\pi$
$499$	−9.18139	−	3.34175i	−0.411015	−	0.149597i	−0.539249	+	0.842147i	$0.681292\pi$
$500$		0			0
$501$	8.60014	−	14.8959i	0.384226	−	0.665499i
$502$		0			0
$503$	6.50093	−	36.8686i	0.289862	−	1.64389i	−0.397519	−	0.917594i	$-0.630129\pi$
$503$	6.50093	−	36.8686i	0.289862	−	1.64389i	0.687381	−	0.726297i	$-0.258760\pi$
$504$		0			0
$505$	6.66385	+	11.5421i	0.296537	+	0.513618i
$506$		0			0
$507$	−22.1648	−	18.5985i	−0.984373	−	0.825987i
$508$		0			0
$509$	3.49273	−	1.27125i	0.154812	−	0.0563471i	−0.263452	−	0.964673i	$-0.584861\pi$
$509$	3.49273	−	1.27125i	0.154812	−	0.0563471i	0.418264	+	0.908326i	$0.362639\pi$
$510$		0			0
$511$	−0.487674	−	2.76573i	−0.0215734	−	0.122349i
$512$		0			0
$513$	3.29813	+	2.84997i	0.145616	+	0.125829i
$514$		0			0
$515$	5.14543	+	29.1812i	0.226735	+	1.28588i
$516$		0			0
$517$	−32.3594	+	11.7778i	−1.42316	+	0.517989i
$518$		0			0
$519$	5.07398	+	4.25757i	0.222723	+	0.186887i
$520$		0			0
$521$	0.446089	+	0.772649i	0.0195435	+	0.0338504i	0.875632	−	0.482979i	$-0.160445\pi$
$521$	0.446089	+	0.772649i	0.0195435	+	0.0338504i	−0.856088	+	0.516830i	$0.827112\pi$
$522$		0			0
$523$	2.44238	−	13.8514i	0.106798	−	0.605681i	−0.883689	−	0.468074i	$-0.844948\pi$
$523$	2.44238	−	13.8514i	0.106798	−	0.605681i	0.990487	−	0.137606i	$-0.0439409\pi$
$524$		0			0
$525$	0.209607	−	0.363051i	0.00914802	−	0.0158448i
$526$		0			0
$527$	6.42989	+	2.34029i	0.280091	+	0.101945i
$528$		0			0
$529$	−17.6104	+	14.7769i	−0.765670	+	0.642473i
$530$		0			0
$531$	−10.0915			−0.437935
$532$		0			0
$533$	55.9377			2.42293
$534$		0			0
$535$	−17.7096	+	14.8601i	−0.765653	+	0.642459i
$536$		0			0
$537$	20.1322	+	7.32753i	0.868770	+	0.316206i
$538$		0			0
$539$	15.1413	−	26.2255i	0.652182	−	1.12961i
$540$		0			0
$541$	4.44862	−	25.2294i	0.191261	−	1.08469i	−0.726383	−	0.687290i	$-0.758800\pi$
$541$	4.44862	−	25.2294i	0.191261	−	1.08469i	0.917644	−	0.397404i	$-0.130089\pi$
$542$		0			0
$543$	−8.59240	−	14.8825i	−0.368735	−	0.638668i
$544$		0			0
$545$	6.04323	+	5.07087i	0.258864	+	0.217212i
$546$		0			0
$547$	34.1263	−	12.4210i	1.45914	−	0.531082i	0.514008	−	0.857785i	$-0.328160\pi$
$547$	34.1263	−	12.4210i	1.45914	−	0.531082i	0.945127	+	0.326704i	$0.105938\pi$
$548$		0			0
$549$	0.624485	+	3.54163i	0.0266524	+	0.151153i
$550$		0			0
$551$	−2.76827	−	17.1502i	−0.117932	−	0.730623i
$552$		0			0
$553$	0.397804	+	2.25606i	0.0169163	+	0.0959373i
$554$		0			0
$555$	−6.31180	+	2.29731i	−0.267921	+	0.0975153i
$556$		0			0
$557$	17.8635	+	14.9893i	0.756900	+	0.635115i	0.937318	−	0.348475i	$-0.113300\pi$
$557$	17.8635	+	14.9893i	0.756900	+	0.635115i	−0.180418	+	0.983590i	$0.557745\pi$
$558$		0			0
$559$	−0.135630	−	0.234917i	−0.00573652	−	0.00993594i
$560$		0			0
$561$	1.60085	−	9.07888i	0.0675880	−	0.383311i
$562$		0			0
$563$	2.26991	−	3.93161i	0.0956655	−	0.165698i	−0.814221	−	0.580556i	$-0.802835\pi$
$563$	2.26991	−	3.93161i	0.0956655	−	0.165698i	0.909886	+	0.414858i	$0.136169\pi$
$564$		0			0
$565$	−1.17055	−	0.426045i	−0.0492454	−	0.0179239i
$566$		0			0
$567$	−0.141559	+	0.118782i	−0.00594493	+	0.00498839i
$568$		0			0
$569$	−6.26621			−0.262693			−0.131347	−	0.991337i	$-0.541930\pi$
$569$	−6.26621			−0.262693			−0.131347	+	0.991337i	$0.541930\pi$
$570$		0			0
$571$	−1.03777			−0.0434293			−0.0217147	−	0.999764i	$-0.506913\pi$
$571$	−1.03777			−0.0434293			−0.0217147	+	0.999764i	$0.506913\pi$
$572$		0			0
$573$	−5.03596	+	4.22567i	−0.210380	+	0.176530i
$574$		0			0
$575$	−0.226109	−	0.0822969i	−0.00942940	−	0.00343202i
$576$		0			0
$577$	20.1211	−	34.8507i	0.837652	−	1.45086i	−0.0542015	−	0.998530i	$-0.517261\pi$
$577$	20.1211	−	34.8507i	0.837652	−	1.45086i	0.891853	−	0.452325i	$-0.149405\pi$
$578$		0			0
$579$	1.97044	−	11.1749i	0.0818886	−	0.464413i
$580$		0			0
$581$	−0.781308	−	1.35326i	−0.0324141	−	0.0561429i
$582$		0			0
$583$	−30.6785	−	25.7423i	−1.27057	−	1.06614i
$584$		0			0
$585$	−10.0569	+	3.66041i	−0.415802	+	0.151339i
$586$		0			0
$587$	8.37598	+	47.5026i	0.345714	+	1.96064i	0.266766	+	0.963761i	$0.414045\pi$
$587$	8.37598	+	47.5026i	0.345714	+	1.96064i	0.0789482	+	0.996879i	$0.474844\pi$
$588$		0			0
$589$	−2.64290	+	13.8142i	−0.108899	+	0.569206i
$590$		0			0
$591$	−1.11974	−	6.35035i	−0.0460598	−	0.261218i
$592$		0			0
$593$	16.4217	−	5.97702i	0.674360	−	0.245447i	0.0179361	−	0.999839i	$-0.494290\pi$
$593$	16.4217	−	5.97702i	0.674360	−	0.245447i	0.656424	+	0.754392i	$0.272068\pi$
$594$		0			0
$595$	−0.496130	−	0.416302i	−0.0203393	−	0.0170667i
$596$		0			0
$597$	−8.36231	−	14.4839i	−0.342247	−	0.592789i
$598$		0			0
$599$	−3.80376	+	21.5722i	−0.155417	+	0.881416i	0.802986	+	0.595998i	$0.203243\pi$
$599$	−3.80376	+	21.5722i	−0.155417	+	0.881416i	−0.958403	+	0.285418i	$0.907868\pi$
$600$		0			0
$601$	−4.63903	+	8.03504i	−0.189230	+	0.327756i	−0.944994	−	0.327088i	$-0.893933\pi$
$601$	−4.63903	+	8.03504i	−0.189230	+	0.327756i	0.755764	+	0.654844i	$0.227266\pi$
$602$		0			0
$603$	−7.50387	−	2.73119i	−0.305581	−	0.111222i
$604$		0			0
$605$	−10.0005	+	8.39139i	−0.406577	+	0.341158i
$606$		0			0
$607$	−29.3354			−1.19069			−0.595344	−	0.803471i	$-0.702984\pi$
$607$	−29.3354			−1.19069			−0.595344	+	0.803471i	$0.702984\pi$
$608$		0			0
$609$	0.736482			0.0298437
$610$		0			0
$611$	−39.2946	+	32.9721i	−1.58969	+	1.33391i
$612$		0			0
$613$	22.7875	+	8.29396i	0.920377	+	0.334990i	0.758388	−	0.651803i	$-0.225987\pi$
$613$	22.7875	+	8.29396i	0.920377	+	0.334990i	0.161988	+	0.986793i	$0.448209\pi$
$614$		0			0
$615$	7.13816	−	12.3636i	0.287838	−	0.498550i
$616$		0			0
$617$	3.47834	−	19.7266i	0.140033	−	0.794165i	−0.831189	−	0.555989i	$-0.812340\pi$
$617$	3.47834	−	19.7266i	0.140033	−	0.794165i	0.971222	−	0.238176i	$-0.0765494\pi$
$618$		0			0
$619$	−4.00774	−	6.94161i	−0.161085	−	0.279007i	0.774173	−	0.632974i	$-0.218166\pi$
$619$	−4.00774	−	6.94161i	−0.161085	−	0.279007i	−0.935258	+	0.353967i	$0.884833\pi$
$620$		0			0
$621$	0.0812519	+	0.0681784i	0.00326053	+	0.00273591i
$622$		0			0
$623$	−3.11468	+	1.13365i	−0.124787	+	0.0454188i
$624$		0			0
$625$	−1.47787	−	8.38144i	−0.0591149	−	0.335257i
$626$		0			0
$627$	18.9474	+	0.274761i	0.756688	+	0.0109729i
$628$		0			0
$629$	−1.49660	−	8.48762i	−0.0596732	−	0.338424i
$630$		0			0
$631$	3.74763	−	1.36402i	0.149191	−	0.0543010i	−0.266345	−	0.963878i	$-0.585816\pi$
$631$	3.74763	−	1.36402i	0.149191	−	0.0543010i	0.415536	+	0.909577i	$0.363594\pi$
$632$		0			0
$633$	−3.73783	−	3.13641i	−0.148565	−	0.124661i
$634$		0			0
$635$	8.94356	+	15.4907i	0.354914	+	0.614730i
$636$		0			0
$637$	7.83300	−	44.4231i	0.310355	−	1.76011i
$638$		0			0
$639$	−2.02094	+	3.50038i	−0.0799473	+	0.138473i
$640$		0			0
$641$	26.2221	+	9.54406i	1.03571	+	0.376968i	0.803253	−	0.595639i	$-0.203101\pi$
$641$	26.2221	+	9.54406i	1.03571	+	0.376968i	0.232458	+	0.972606i	$0.425323\pi$
$642$		0			0
$643$	8.27584	−	6.94426i	0.326367	−	0.273855i	−0.464850	−	0.885389i	$-0.653892\pi$
$643$	8.27584	−	6.94426i	0.326367	−	0.273855i	0.791218	+	0.611534i	$0.209447\pi$
$644$		0			0
$645$	−0.0692302			−0.00272594
$646$		0			0
$647$	34.4662			1.35500			0.677502	−	0.735521i	$-0.263062\pi$
$647$	34.4662			1.35500			0.677502	+	0.735521i	$0.263062\pi$
$648$		0			0
$649$	−33.6070	+	28.1996i	−1.31919	+	1.10693i
$650$		0			0
$651$	−0.560307	−	0.203935i	−0.0219602	−	0.00799285i
$652$		0			0
$653$	11.4971	−	19.9135i	0.449915	−	0.779275i	−0.548465	−	0.836173i	$-0.684788\pi$
$653$	11.4971	−	19.9135i	0.449915	−	0.779275i	0.998380	+	0.0568980i	$0.0181210\pi$
$654$		0			0
$655$	3.11246	−	17.6517i	0.121614	−	0.689707i
$656$		0			0
$657$	−7.59879	−	13.1615i	−0.296457	−	0.513479i
$658$		0			0
$659$	26.0742	+	21.8788i	1.01571	+	0.852279i	0.989082	−	0.147367i	$-0.0470797\pi$
$659$	26.0742	+	21.8788i	1.01571	+	0.852279i	0.0266245	+	0.999646i	$0.491524\pi$
$660$		0			0
$661$	−8.04411	+	2.92782i	−0.312880	+	0.113879i	−0.493687	−	0.869640i	$-0.664351\pi$
$661$	−8.04411	+	2.92782i	−0.312880	+	0.113879i	0.180807	+	0.983519i	$0.442129\pi$
$662$		0			0
$663$	−2.38460	−	13.5237i	−0.0926102	−	0.525218i
$664$		0			0
$665$	0.682266	−	1.14311i	0.0264572	−	0.0443281i
$666$		0			0
$667$	−0.0734053	−	0.416302i	−0.00284226	−	0.0161193i
$668$		0			0
$669$	−27.0453	+	9.84370i	−1.04563	+	0.380580i
$670$		0			0
$671$	11.9764	+	10.0494i	0.462343	+	0.387951i
$672$		0			0
$673$	6.07011	+	10.5137i	0.233985	+	0.405275i	0.958977	−	0.283483i	$-0.0914899\pi$
$673$	6.07011	+	10.5137i	0.233985	+	0.405275i	−0.724992	+	0.688757i	$0.758157\pi$
$674$		0			0
$675$	0.393933	−	2.23411i	0.0151625	−	0.0859908i
$676$		0			0
$677$	−0.776722	+	1.34532i	−0.0298519	+	0.0517049i	−0.880565	−	0.473925i	$-0.842837\pi$
$677$	−0.776722	+	1.34532i	−0.0298519	+	0.0517049i	0.850714	+	0.525630i	$0.176170\pi$
$678$		0			0
$679$	1.85591	+	0.675498i	0.0712235	+	0.0259232i
$680$		0			0
$681$	−2.87733	+	2.41436i	−0.110259	+	0.0925186i
$682$		0			0
$683$	35.3892			1.35413			0.677065	−	0.735923i	$-0.263252\pi$
$683$	35.3892			1.35413			0.677065	+	0.735923i	$0.263252\pi$
$684$		0			0
$685$	23.0574			0.880977
$686$		0			0
$687$	−13.4192	+	11.2601i	−0.511975	+	0.429598i
$688$		0			0
$689$	−56.0570	−	20.4031i	−2.13560	−	0.777295i
$690$		0			0
$691$	−19.6411	+	34.0195i	−0.747185	+	1.29416i	0.201983	+	0.979389i	$0.435262\pi$
$691$	−19.6411	+	34.0195i	−0.747185	+	1.29416i	−0.949167	+	0.314772i	$0.898072\pi$
$692$		0			0
$693$	−0.139500	+	0.791143i	−0.00529916	+	0.0300530i
$694$		0			0
$695$	−4.92989	−	8.53882i	−0.187001	−	0.323896i
$696$		0			0
$697$	14.0326	+	11.7747i	0.531521	+	0.445999i
$698$		0			0
$699$	−6.58260	+	2.39587i	−0.248977	+	0.0906201i
$700$		0			0
$701$	2.89171	+	16.3997i	0.109218	+	0.619409i	0.989451	+	0.144866i	$0.0462752\pi$
$701$	2.89171	+	16.3997i	0.109218	+	0.619409i	−0.880233	+	0.474542i	$0.842614\pi$
$702$		0			0
$703$	16.7331	−	5.81699i	0.631100	−	0.219392i
$704$		0			0
$705$	2.27332	+	12.8926i	0.0856181	+	0.485565i
$706$		0			0
$707$	1.40033	−	0.509678i	0.0526648	−	0.0191684i
$708$		0			0
$709$	33.3723	+	28.0027i	1.25332	+	1.05166i	0.996360	+	0.0852428i	$0.0271666\pi$
$709$	33.3723	+	28.0027i	1.25332	+	1.05166i	0.256964	+	0.966421i	$0.417278\pi$
$710$		0			0
$711$	6.19846	+	10.7361i	0.232461	+	0.402633i
$712$		0			0
$713$	−0.0594300	+	0.337044i	−0.00222567	+	0.0126224i
$714$		0			0
$715$	−23.2631	+	40.2929i	−0.869991	+	1.50687i
$716$		0			0
$717$	−0.879385	−	0.320070i	−0.0328412	−	0.0119532i
$718$		0			0
$719$	−4.94949	+	4.15312i	−0.184585	+	0.154885i	−0.730398	−	0.683022i	$-0.760665\pi$
$719$	−4.94949	+	4.15312i	−0.184585	+	0.154885i	0.545813	+	0.837907i	$0.316221\pi$
$720$		0			0
$721$	3.31315			0.123388
$722$		0			0
$723$	28.7297			1.06847
$724$		0			0
$725$	−6.92602	+	5.81162i	−0.257226	+	0.215838i
$726$		0			0
$727$	1.73308	+	0.630789i	0.0642763	+	0.0233947i	0.373958	−	0.927446i	$-0.378000\pi$
$727$	1.73308	+	0.630789i	0.0642763	+	0.0233947i	−0.309682	+	0.950840i	$0.600223\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	0.0154253	−	0.0874810i	0.000570524	−	0.00323560i
$732$		0			0
$733$	−16.1793	−	28.0234i	−0.597597	−	1.03507i	−0.993175	−	0.116636i	$-0.962789\pi$
$733$	−16.1793	−	28.0234i	−0.597597	−	1.03507i	0.395578	−	0.918433i	$-0.370544\pi$
$734$		0			0
$735$	−8.81908	−	7.40008i	−0.325297	−	0.272956i
$736$		0			0
$737$	−32.6215	+	11.8733i	−1.20163	+	0.437358i
$738$		0			0
$739$	1.89899	+	10.7697i	0.0698553	+	0.396169i	0.999608	+	0.0279854i	$0.00890918\pi$
$739$	1.89899	+	10.7697i	0.0698553	+	0.396169i	−0.929753	+	0.368184i	$0.879980\pi$
$740$		0			0
$741$	26.6616	−	9.26849i	0.979439	−	0.340487i
$742$		0			0
$743$	1.81820	+	10.3115i	0.0667033	+	0.378293i	0.999825	+	0.0187314i	$0.00596273\pi$
$743$	1.81820	+	10.3115i	0.0667033	+	0.378293i	−0.933121	+	0.359562i	$0.882926\pi$
$744$		0			0
$745$	−22.0839	+	8.03790i	−0.809093	+	0.294486i
$746$		0			0
$747$	−6.47771	−	5.43545i	−0.237007	−	0.198873i
$748$		0			0
$749$	1.29245	+	2.23859i	0.0472252	+	0.0817964i
$750$		0			0
$751$	4.58079	−	25.9789i	0.167155	−	0.947984i	−0.779659	−	0.626204i	$-0.784608\pi$
$751$	4.58079	−	25.9789i	0.167155	−	0.947984i	0.946814	−	0.321780i	$-0.104281\pi$
$752$		0			0
$753$	−12.0929	+	20.9455i	−0.440688	+	0.763295i
$754$		0			0
$755$	23.6065	+	8.59208i	0.859130	+	0.312698i
$756$		0			0
$757$	17.4715	−	14.6604i	0.635014	−	0.532840i	−0.267469	−	0.963567i	$-0.586187\pi$
$757$	17.4715	−	14.6604i	0.635014	−	0.532840i	0.902482	+	0.430727i	$0.141743\pi$
$758$		0			0
$759$	0.461104			0.0167370
$760$		0			0
$761$	41.5012			1.50442			0.752209	−	0.658924i	$-0.228988\pi$
$761$	41.5012			1.50442			0.752209	+	0.658924i	$0.228988\pi$
$762$		0			0
$763$	0.675708	−	0.566986i	0.0244623	−	0.0205263i
$764$		0			0
$765$	−3.29339	−	1.19869i	−0.119073	−	0.0433389i
$766$		0			0
$767$	−32.6746	+	56.5940i	−1.17981	+	2.04349i
$768$		0			0
$769$	3.29948	−	18.7123i	0.118982	−	0.674782i	−0.865719	−	0.500530i	$-0.833138\pi$
$769$	3.29948	−	18.7123i	0.118982	−	0.674782i	0.984701	−	0.174251i	$-0.0557505\pi$
$770$		0			0
$771$	4.40033	+	7.62159i	0.158474	+	0.274485i
$772$		0			0
$773$	13.1329	+	11.0198i	0.472359	+	0.396356i	0.847654	−	0.530549i	$-0.178014\pi$
$773$	13.1329	+	11.0198i	0.472359	+	0.396356i	−0.375295	+	0.926905i	$0.622459\pi$
$774$		0			0
$775$	6.87851	−	2.50357i	0.247083	−	0.0899310i
$776$		0			0
$777$	0.130415	+	0.739620i	0.00467861	+	0.0265337i
$778$		0			0
$779$	−19.2973	+	32.3319i	−0.691396	+	1.15841i
$780$		0			0
$781$	3.05122	+	17.3043i	0.109181	+	0.619198i
$782$		0			0
$783$	3.74510	−	1.36310i	0.133839	−	0.0487134i
$784$		0			0
$785$	−11.9055	−	9.98994i	−0.424927	−	0.356556i
$786$		0			0
$787$	−9.10014	−	15.7619i	−0.324385	−	0.561851i	0.657003	−	0.753888i	$-0.271824\pi$
$787$	−9.10014	−	15.7619i	−0.324385	−	0.561851i	−0.981388	+	0.192037i	$0.938491\pi$
$788$		0			0
$789$	0.227148	−	1.28822i	0.00808670	−	0.0458619i
$790$		0			0
$791$	−0.0696407	+	0.120621i	−0.00247614	+	0.00428880i
$792$		0			0
$793$	21.8837	+	7.96502i	0.777114	+	0.282846i
$794$		0			0
$795$	−11.6630	+	9.78639i	−0.413643	+	0.347088i
$796$		0			0
$797$	−26.4584			−0.937205			−0.468603	−	0.883409i	$-0.655242\pi$
$797$	−26.4584			−0.937205			−0.468603	+	0.883409i	$0.655242\pi$
$798$		0			0
$799$	−16.7980			−0.594270
$800$		0			0
$801$	−13.7404	+	11.5295i	−0.485491	+	0.407376i
$802$		0			0
$803$	−62.0840	−	22.5967i	−2.19090	−	0.797421i
$804$		0			0
$805$	0.0161968	−	0.0280537i	0.000570862	−	0.000988762i
$806$		0			0
$807$	−1.51960	+	8.61808i	−0.0534925	+	0.303371i
$808$		0			0
$809$	15.2836	+	26.4719i	0.537342	+	0.930704i	0.999046	+	0.0436699i	$0.0139050\pi$
$809$	15.2836	+	26.4719i	0.537342	+	0.930704i	−0.461704	+	0.887034i	$0.652762\pi$
$810$		0			0
$811$	5.25284	+	4.40766i	0.184452	+	0.154774i	0.730338	−	0.683086i	$-0.239362\pi$
$811$	5.25284	+	4.40766i	0.184452	+	0.154774i	−0.545886	+	0.837859i	$0.683807\pi$
$812$		0			0
$813$	12.9179	−	4.70172i	0.453050	−	0.164897i
$814$		0			0
$815$	−2.18789	−	12.4081i	−0.0766385	−	0.434638i
$816$		0			0
$817$	0.182571	+	0.00264750i	0.00638735	+	9.26245e-5i
$818$		0			0
$819$	0.207796	+	1.17847i	0.00726100	+	0.0411792i
$820$		0			0
$821$	−37.2870	+	13.5714i	−1.30133	+	0.473644i	−0.897429	−	0.441160i	$-0.854567\pi$
$821$	−37.2870	+	13.5714i	−1.30133	+	0.473644i	−0.403898	+	0.914804i	$0.632345\pi$
$822$		0			0
$823$	35.7900	+	30.0314i	1.24756	+	1.04683i	0.996894	+	0.0787539i	$0.0250941\pi$
$823$	35.7900	+	30.0314i	1.24756	+	1.04683i	0.250666	+	0.968074i	$0.419350\pi$
$824$		0			0
$825$	−4.93107	−	8.54087i	−0.171678	−	0.297355i
$826$		0			0
$827$	7.27884	−	41.2803i	0.253110	−	1.43546i	−0.547768	−	0.836630i	$-0.684522\pi$
$827$	7.27884	−	41.2803i	0.253110	−	1.43546i	0.800878	−	0.598828i	$-0.204367\pi$
$828$		0			0
$829$	0.251030	−	0.434796i	0.00871862	−	0.0151011i	−0.861633	−	0.507532i	$-0.830558\pi$
$829$	0.251030	−	0.434796i	0.00871862	−	0.0151011i	0.870352	+	0.492430i	$0.163891\pi$
$830$		0			0
$831$	23.4996	+	8.55315i	0.815192	+	0.296706i
$832$		0			0
$833$	11.3159	−	9.49519i	0.392073	−	0.328989i
$834$		0			0
$835$	−28.4270			−0.983755
$836$		0			0
$837$	−3.22668			−0.111530
$838$		0			0
$839$	24.0646	−	20.1926i	0.830804	−	0.697127i	−0.124672	−	0.992198i	$-0.539788\pi$
$839$	24.0646	−	20.1926i	0.830804	−	0.697127i	0.955475	+	0.295071i	$0.0953433\pi$
$840$		0			0
$841$	12.3252	+	4.48599i	0.425006	+	0.154689i
$842$		0			0
$843$	6.07785	−	10.5271i	0.209332	−	0.362574i
$844$		0			0
$845$	−8.30376	+	47.0930i	−0.285658	+	1.62005i
$846$		0			0
$847$	0.729837	+	1.26411i	0.0250775	+	0.0434355i
$848$		0			0
$849$	−8.19459	−	6.87608i	−0.281238	−	0.235986i
$850$		0			0
$851$	0.405078	−	0.147436i	0.0138859	−	0.00505405i
$852$		0			0
$853$	3.26682	+	18.5270i	0.111854	+	0.634354i	0.988260	+	0.152781i	$0.0488230\pi$
$853$	3.26682	+	18.5270i	0.111854	+	0.634354i	−0.876406	+	0.481572i	$0.840066\pi$
$854$		0			0
$855$	1.35369	−	7.07564i	0.0462953	−	0.241982i
$856$		0			0
$857$	5.20305	+	29.5080i	0.177733	+	1.00797i	0.934942	+	0.354800i	$0.115451\pi$
$857$	5.20305	+	29.5080i	0.177733	+	1.00797i	−0.757209	+	0.653172i	$0.773438\pi$
$858$		0			0
$859$	−31.1698	+	11.3449i	−1.06350	+	0.387083i	−0.813743	−	0.581225i	$-0.802573\pi$
$859$	−31.1698	+	11.3449i	−1.06350	+	0.387083i	−0.249758	+	0.968308i	$0.580351\pi$
$860$		0			0
$861$	−1.22281	−	1.02606i	−0.0416733	−	0.0349680i
$862$		0			0
$863$	−19.1238	−	33.1233i	−0.650981	−	1.12753i	−0.982885	−	0.184219i	$-0.941025\pi$
$863$	−19.1238	−	33.1233i	−0.650981	−	1.12753i	0.331905	−	0.943313i	$-0.392309\pi$
$864$		0			0
$865$	1.90090	−	10.7806i	0.0646326	−	0.366550i
$866$		0			0
$867$	−6.25150	+	10.8279i	−0.212312	+	0.367735i
$868$		0			0
$869$	50.6430	+	18.4325i	1.71794	+	0.625281i
$870$		0			0
$871$	−39.6129	+	33.2392i	−1.34223	+	1.12627i
$872$		0			0
$873$	10.6878			0.361727
$874$		0			0
$875$	−2.21987			−0.0750455
$876$		0			0
$877$	−36.8981	+	30.9612i	−1.24596	+	1.04549i	−0.248927	+	0.968522i	$0.580078\pi$
$877$	−36.8981	+	30.9612i	−1.24596	+	1.04549i	−0.997034	+	0.0769627i	$0.975478\pi$
$878$		0			0
$879$	−12.5424	−	4.56504i	−0.423043	−	0.153975i
$880$		0			0
$881$	−18.8542	+	32.6564i	−0.635213	+	1.10022i	0.351257	+	0.936279i	$0.385754\pi$
$881$	−18.8542	+	32.6564i	−0.635213	+	1.10022i	−0.986470	+	0.163942i	$0.947579\pi$
$882$		0			0
$883$	5.27022	−	29.8889i	0.177357	−	1.00584i	−0.758031	−	0.652219i	$-0.773838\pi$
$883$	5.27022	−	29.8889i	0.177357	−	1.00584i	0.935388	−	0.353623i	$-0.115050\pi$
$884$		0			0
$885$	8.33915	+	14.4438i	0.280317	+	0.485524i
$886$		0			0
$887$	0.709856	+	0.595640i	0.0238346	+	0.0199996i	0.654627	−	0.755952i	$-0.272826\pi$
$887$	0.709856	+	0.595640i	0.0238346	+	0.0199996i	−0.630793	+	0.775952i	$0.717270\pi$
$888$		0			0
$889$	1.87939	−	0.684040i	0.0630326	−	0.0229420i
$890$		0			0
$891$	0.754900	+	4.28125i	0.0252901	+	0.143427i
$892$		0			0
$893$	−5.50206	−	34.0868i	−0.184119	−	1.14067i
$894$		0			0
$895$	−6.14853	−	34.8700i	−0.205523	−	1.16558i
$896$		0			0
$897$	0.645430	−	0.234917i	0.0215503	−	0.00784366i
$898$		0			0
$899$	9.85117	+	8.26611i	0.328555	+	0.275690i
$900$		0			0
$901$	−9.76769	−	16.9181i	−0.325409	−	0.563625i
$902$		0			0
$903$	−0.00134417	+	0.00762319i	−4.47313e−5	+	0.000253684i
$904$		0			0
$905$	−14.2007	+	24.5963i	−0.472047	+	0.817609i
$906$		0			0
$907$	−3.98932	−	1.45199i	−0.132463	−	0.0482127i	0.274938	−	0.961462i	$-0.411343\pi$
$907$	−3.98932	−	1.45199i	−0.132463	−	0.0482127i	−0.407401	+	0.913249i	$0.633565\pi$
$908$		0			0
$909$	6.17752	−	5.18355i	0.204895	−	0.171928i
$910$		0			0
$911$	56.5509			1.87361			0.936807	−	0.349847i	$-0.113766\pi$
$911$	56.5509			1.87361			0.936807	+	0.349847i	$0.113766\pi$
$912$		0			0
$913$	−36.7610			−1.21661
$914$		0			0
$915$	4.55303	−	3.82045i	0.150519	−	0.126300i
$916$		0			0
$917$	−1.88326	−	0.685449i	−0.0621906	−	0.0226355i
$918$		0			0
$919$	29.4778	−	51.0570i	0.972382	−	1.68421i	0.284064	−	0.958805i	$-0.408317\pi$
$919$	29.4778	−	51.0570i	0.972382	−	1.68421i	0.688318	−	0.725409i	$-0.258350\pi$
$920$		0			0
$921$	2.71987	−	15.4252i	0.0896229	−	0.508277i
$922$		0			0
$923$	13.0869	+	22.6672i	0.430762	+	0.746101i
$924$		0			0
$925$	−7.06283	−	5.92642i	−0.232225	−	0.194860i
$926$		0			0
$927$	16.8478	−	6.13208i	0.553353	−	0.201404i
$928$		0			0
$929$	−2.15446	−	12.2185i	−0.0706855	−	0.400877i	−0.999537	−	0.0304252i	$-0.990314\pi$
$929$	−2.15446	−	12.2185i	−0.0706855	−	0.400877i	0.928852	−	0.370452i	$-0.120797\pi$
$930$		0			0
$931$	22.9743	+	19.8525i	0.752953	+	0.650638i
$932$		0			0
$933$	1.58125	+	8.96773i	0.0517679	+	0.293590i
$934$		0			0
$935$	−14.3173	+	5.21108i	−0.468227	+	0.170421i
$936$		0			0
$937$	21.2973	+	17.8705i	0.695751	+	0.583804i	0.920561	−	0.390598i	$-0.127732\pi$
$937$	21.2973	+	17.8705i	0.695751	+	0.583804i	−0.224810	+	0.974403i	$0.572176\pi$
$938$		0			0
$939$	8.87346	+	15.3693i	0.289574	+	0.501557i
$940$		0			0
$941$	−3.46632	+	19.6585i	−0.112999	+	0.640848i	0.874723	+	0.484623i	$0.161043\pi$
$941$	−3.46632	+	19.6585i	−0.112999	+	0.640848i	−0.987722	+	0.156224i	$0.950068\pi$
$942$		0			0
$943$	−0.458111	+	0.793471i	−0.0149181	+	0.0258390i
$944$		0			0
$945$	0.286989	+	0.104455i	0.00933575	+	0.00339794i
$946$		0			0
$947$	−22.9807	+	19.2831i	−0.746773	+	0.626617i	−0.934647	−	0.355576i	$-0.884285\pi$
$947$	−22.9807	+	19.2831i	−0.746773	+	0.626617i	0.187875	+	0.982193i	$0.439840\pi$
$948$		0			0
$949$	−98.4143			−3.19466
$950$		0			0
$951$	−31.0455			−1.00672
$952$		0			0
$953$	17.5713	−	14.7441i	0.569190	−	0.477607i	−0.312187	−	0.950021i	$-0.601062\pi$
$953$	17.5713	−	14.7441i	0.569190	−	0.477607i	0.881377	+	0.472414i	$0.156617\pi$
$954$		0			0
$955$	10.2096	+	3.71599i	0.330375	+	0.120247i
$956$		0			0
$957$	8.66297	−	15.0047i	0.280034	−	0.485033i
$958$		0			0
$959$	0.447682	−	2.53893i	0.0144564	−	0.0819863i
$960$		0			0
$961$	10.2943	+	17.8302i	0.332073	+	0.575167i
$962$		0			0
$963$	10.7155	+	8.99140i	0.345303	+	0.289744i
$964$		0			0
$965$	−17.6227	+	6.41415i	−0.567296	+	0.206479i
$966$		0			0
$967$	6.57233	+	37.2735i	0.211352	+	1.19864i	0.887126	+	0.461527i	$0.152698\pi$
$967$	6.57233	+	37.2735i	0.211352	+	1.19864i	−0.675774	+	0.737109i	$0.736191\pi$
$968$		0			0
$969$	8.63934	+	3.28709i	0.277536	+	0.105597i
$970$		0			0
$971$	5.09421	+	28.8907i	0.163481	+	0.927146i	0.950617	+	0.310367i	$0.100452\pi$
$971$	5.09421	+	28.8907i	0.163481	+	0.927146i	−0.787136	+	0.616779i	$0.788437\pi$
$972$		0			0
$973$	−1.03596	+	0.377058i	−0.0332113	+	0.0120879i
$974$		0			0
$975$	−11.2536	−	9.44285i	−0.360402	−	0.302413i
$976$		0			0
$977$	−7.08054	−	12.2638i	−0.226526	−	0.392355i	0.730250	−	0.683180i	$-0.239404\pi$
$977$	−7.08054	−	12.2638i	−0.226526	−	0.392355i	−0.956776	+	0.290825i	$0.906070\pi$
$978$		0			0
$979$	−13.5405	+	76.7918i	−0.432755	+	2.45428i
$980$		0			0
$981$	2.38666	−	4.13381i	0.0762002	−	0.131983i
$982$		0			0
$983$	−32.6724	−	11.8918i	−1.04209	−	0.379288i	−0.236416	−	0.971652i	$-0.575973\pi$
$983$	−32.6724	−	11.8918i	−1.04209	−	0.379288i	−0.805671	+	0.592364i	$0.798195\pi$
$984$		0			0
$985$	−8.16385	+	6.85028i	−0.260122	+	0.218268i
$986$		0			0
$987$	1.46379			0.0465930
$988$		0			0
$989$	0.00444304			0.000141280
$990$		0			0
$991$	4.20393	−	3.52751i	0.133542	−	0.112055i	−0.573570	−	0.819156i	$-0.694442\pi$
$991$	4.20393	−	3.52751i	0.133542	−	0.112055i	0.707112	+	0.707101i	$0.249998\pi$
$992$		0			0
$993$	9.47178	+	3.44745i	0.300578	+	0.109401i
$994$		0			0
$995$	−13.8204	+	23.9377i	−0.438137	+	0.758875i
$996$		0			0
$997$	−1.67128	+	9.47832i	−0.0529301	+	0.300182i	−0.999768	−	0.0215289i	$-0.993147\pi$
$997$	−1.67128	+	9.47832i	−0.0529301	+	0.300182i	0.946838	+	0.321710i	$0.104258\pi$
$998$		0			0
$999$	2.03209	+	3.51968i	0.0642924	+	0.111358i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bo.c.769.1		6
4.3	odd	2		114.2.i.b.85.1	yes	6
12.11	even	2		342.2.u.d.199.1		6
19.17	even	9	inner	912.2.bo.c.625.1		6
76.51	even	18		2166.2.a.n.1.2		3
76.55	odd	18		114.2.i.b.55.1	✓	6
76.63	odd	18		2166.2.a.t.1.2		3
228.131	even	18		342.2.u.d.55.1		6
228.203	odd	18		6498.2.a.bt.1.2		3
228.215	even	18		6498.2.a.bo.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.b.55.1	✓	6	76.55	odd	18
114.2.i.b.85.1	yes	6	4.3	odd	2
342.2.u.d.55.1		6	228.131	even	18
342.2.u.d.199.1		6	12.11	even	2
912.2.bo.c.625.1		6	19.17	even	9	inner
912.2.bo.c.769.1		6	1.1	even	1	trivial
2166.2.a.n.1.2		3	76.51	even	18
2166.2.a.t.1.2		3	76.63	odd	18
6498.2.a.bo.1.2		3	228.215	even	18
6498.2.a.bt.1.2		3	228.203	odd	18

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bo (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{3} +(1.55303 + 0.565258i) q^{5} +(0.0923963 - 0.160035i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{3} +(1.55303 + 0.565258i) q^{5} +(0.0923963 - 0.160035i) q^{7} +(0.173648 - 0.984808i) q^{9} +(-2.17365 - 3.76487i) q^{11} +(-4.96064 - 4.16247i) q^{13} +(-1.55303 + 0.565258i) q^{15} +(-0.368241 - 2.08840i) q^{17} +(4.11721 - 1.43128i) q^{19} +(0.0320889 + 0.181985i) q^{21} +(0.0996702 - 0.0362770i) q^{23} +(-1.73783 - 1.45821i) q^{25} +(0.500000 + 0.866025i) q^{27} +(0.692066 - 3.92490i) q^{29} +(-1.61334 + 2.79439i) q^{31} +(4.08512 + 1.48686i) q^{33} +(0.233956 - 0.196312i) q^{35} +4.06418 q^{37} +6.47565 q^{39} +(-6.61721 + 5.55250i) q^{41} +(0.0393628 + 0.0143269i) q^{43} +(0.826352 - 1.43128i) q^{45} +(1.37551 - 7.80093i) q^{47} +(3.48293 + 6.03260i) q^{49} +(1.62449 + 1.36310i) q^{51} +(8.65657 - 3.15074i) q^{53} +(-1.24763 - 7.07564i) q^{55} +(-2.23396 + 3.74292i) q^{57} +(-1.75237 - 9.93821i) q^{59} +(-3.37939 + 1.23000i) q^{61} +(-0.141559 - 0.118782i) q^{63} +(-5.35117 - 9.26849i) q^{65} +(1.38666 - 7.86414i) q^{67} +(-0.0530334 + 0.0918566i) q^{69} +(-3.79813 - 1.38241i) q^{71} +(11.6420 - 9.76882i) q^{73} +2.26857 q^{75} -0.803348 q^{77} +(-9.49660 + 7.96859i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(4.22803 - 7.32316i) q^{83} +(0.608593 - 3.45150i) q^{85} +(1.99273 + 3.45150i) q^{87} +(-13.7404 - 11.5295i) q^{89} +(-1.12449 + 0.409279i) q^{91} +(-0.560307 - 3.17766i) q^{93} +(7.20321 + 0.104455i) q^{95} +(1.85591 + 10.5254i) q^{97} +(-4.08512 + 1.48686i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} - 3 q^{7}+O(q^{10}) \) 6 * q - 3 * q^5 - 3 * q^7	\( 6 q - 3 q^{5} - 3 q^{7} - 12 q^{11} - 21 q^{13} + 3 q^{15} + 3 q^{17} - 6 q^{19} - 9 q^{21} + 15 q^{23} + 9 q^{25} + 3 q^{27} + 15 q^{29} - 3 q^{31} + 3 q^{33} + 6 q^{35} + 6 q^{37} - 9 q^{41} + 9 q^{43} + 6 q^{45} + 21 q^{47} - 3 q^{51} + 30 q^{53} + 9 q^{55} - 18 q^{57} - 27 q^{59} - 9 q^{61} - 9 q^{63} - 6 q^{65} + 15 q^{67} + 12 q^{69} - 9 q^{71} + 12 q^{73} - 6 q^{75} + 42 q^{77} - 15 q^{79} + 3 q^{83} - 36 q^{85} - 6 q^{87} - 48 q^{89} + 6 q^{91} - 9 q^{93} + 48 q^{95} + 18 q^{97} - 3 q^{99}+O(q^{100}) \) 6 * q - 3 * q^5 - 3 * q^7 - 12 * q^11 - 21 * q^13 + 3 * q^15 + 3 * q^17 - 6 * q^19 - 9 * q^21 + 15 * q^23 + 9 * q^25 + 3 * q^27 + 15 * q^29 - 3 * q^31 + 3 * q^33 + 6 * q^35 + 6 * q^37 - 9 * q^41 + 9 * q^43 + 6 * q^45 + 21 * q^47 - 3 * q^51 + 30 * q^53 + 9 * q^55 - 18 * q^57 - 27 * q^59 - 9 * q^61 - 9 * q^63 - 6 * q^65 + 15 * q^67 + 12 * q^69 - 9 * q^71 + 12 * q^73 - 6 * q^75 + 42 * q^77 - 15 * q^79 + 3 * q^83 - 36 * q^85 - 6 * q^87 - 48 * q^89 + 6 * q^91 - 9 * q^93 + 48 * q^95 + 18 * q^97 - 3 * q^99

Introduction

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