LMFDB - Embedded newform 1216.2.i.o.961.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(577,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("1216.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.i (of order $3$, degree $2$, 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:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.41342275584.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 13x^{6} + 2x^{5} + 81x^{4} - 8x^{3} + 208x^{2} + 128x + 256 $ x^8 - 2x^7 + 13x^6 + 2x^5 + 81x^4 - 8x^3 + 208x^2 + 128*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 608)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.3
Root			$-1.10890 - 1.92067i$ of defining polynomial
Character	$\chi$	$=$	1216.961
Dual form			1216.2.i.o.577.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.207107 - 0.358719i) q^{3} +(-1.60890 + 2.78670i) q^{5} -3.13644 q^{7} +(1.41421 + 2.44949i) q^{9} +O(q^{10})$	\(q+(0.207107 - 0.358719i) q^{3} +(-1.60890 + 2.78670i) q^{5} -3.13644 q^{7} +(1.41421 + 2.44949i) q^{9} -2.21780 q^{11} +(-1.37354 - 2.37903i) q^{13} +(0.666429 + 1.15429i) q^{15} +(3.59134 - 6.22038i) q^{17} +(-4.32670 + 0.528817i) q^{19} +(-0.649579 + 1.12510i) q^{21} +(-4.29844 - 7.44512i) q^{23} +(-2.67712 - 4.63691i) q^{25} +2.41421 q^{27} +(3.33113 + 5.76969i) q^{29} +10.7933 q^{31} +(-0.459322 + 0.795569i) q^{33} +(5.04623 - 8.74032i) q^{35} +0.308018 q^{37} -1.13787 q^{39} +(2.30359 - 3.98993i) q^{41} +(4.31601 - 7.47554i) q^{43} -9.10132 q^{45} +(-2.47002 - 4.27819i) q^{47} +2.83729 q^{49} +(-1.48758 - 2.57656i) q^{51} +(-4.00555 - 6.93782i) q^{53} +(3.56822 - 6.18034i) q^{55} +(-0.706392 + 1.66159i) q^{57} +(-1.01069 + 1.75057i) q^{59} +(-0.780474 - 1.35182i) q^{61} +(-4.43560 - 7.68269i) q^{63} +8.83953 q^{65} +(-3.81428 - 6.60653i) q^{67} -3.56095 q^{69} +(-4.84183 + 8.38629i) q^{71} +(-4.85425 + 8.40780i) q^{73} -2.21780 q^{75} +6.95601 q^{77} +(2.98315 - 5.16697i) q^{79} +(-3.74264 + 6.48244i) q^{81} -6.49069 q^{83} +(11.5562 + 20.0159i) q^{85} +2.75960 q^{87} +(0.762910 + 1.32140i) q^{89} +(4.30802 + 7.46171i) q^{91} +(2.23537 - 3.87177i) q^{93} +(5.48758 - 12.9080i) q^{95} +(-2.69296 + 4.66435i) q^{97} +(-3.13644 - 5.43248i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 2 q^{5} - 8 q^{7}+O(q^{10}) $ 8 * q - 4 * q^3 - 2 * q^5 - 8 * q^7	$ 8 q - 4 q^{3} - 2 q^{5} - 8 q^{7} + 4 q^{11} - 2 q^{13} + 2 q^{15} - 2 q^{17} - 2 q^{19} + 8 q^{21} + 2 q^{23} - 2 q^{25} + 8 q^{27} + 10 q^{29} + 24 q^{31} - 6 q^{33} - 4 q^{35} + 8 q^{37} - 12 q^{39} + 8 q^{41} + 18 q^{43} - 16 q^{45} - 6 q^{47} + 32 q^{49} - 18 q^{51} + 10 q^{53} + 20 q^{55} + 10 q^{57} + 8 q^{59} - 18 q^{61} + 8 q^{63} - 36 q^{65} - 4 q^{67} - 52 q^{69} - 6 q^{71} + 4 q^{75} - 16 q^{77} + 14 q^{79} + 4 q^{81} + 4 q^{83} + 22 q^{85} - 60 q^{87} - 2 q^{89} + 40 q^{91} + 16 q^{93} + 50 q^{95} - 12 q^{97} - 8 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 - 2 * q^5 - 8 * q^7 + 4 * q^11 - 2 * q^13 + 2 * q^15 - 2 * q^17 - 2 * q^19 + 8 * q^21 + 2 * q^23 - 2 * q^25 + 8 * q^27 + 10 * q^29 + 24 * q^31 - 6 * q^33 - 4 * q^35 + 8 * q^37 - 12 * q^39 + 8 * q^41 + 18 * q^43 - 16 * q^45 - 6 * q^47 + 32 * q^49 - 18 * q^51 + 10 * q^53 + 20 * q^55 + 10 * q^57 + 8 * q^59 - 18 * q^61 + 8 * q^63 - 36 * q^65 - 4 * q^67 - 52 * q^69 - 6 * q^71 + 4 * q^75 - 16 * q^77 + 14 * q^79 + 4 * q^81 + 4 * q^83 + 22 * q^85 - 60 * q^87 - 2 * q^89 + 40 * q^91 + 16 * q^93 + 50 * q^95 - 12 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.207107	−	0.358719i	0.119573	−	0.207107i	−0.800025	−	0.599966i	$-0.795181\pi$
$3$	0.207107	−	0.358719i	0.119573	−	0.207107i	0.919599	+	0.392859i	$0.128514\pi$
$4$		0			0
$5$	−1.60890	+	2.78670i	−0.719522	+	1.24625i	0.241667	+	0.970359i	$0.422306\pi$
$5$	−1.60890	+	2.78670i	−0.719522	+	1.24625i	−0.961189	+	0.275890i	$0.911027\pi$
$6$		0			0
$7$	−3.13644			−1.18546			−0.592732	−	0.805399i	$-0.701951\pi$
$7$	−3.13644			−1.18546			−0.592732	+	0.805399i	$0.701951\pi$
$8$		0			0
$9$	1.41421	+	2.44949i	0.471405	+	0.816497i
$10$		0			0
$11$	−2.21780			−0.668692			−0.334346	−	0.942450i	$-0.608515\pi$
$11$	−2.21780			−0.668692			−0.334346	+	0.942450i	$0.608515\pi$
$12$		0			0
$13$	−1.37354	−	2.37903i	−0.380950	−	0.659825i	0.610248	−	0.792210i	$-0.291070\pi$
$13$	−1.37354	−	2.37903i	−0.380950	−	0.659825i	−0.991198	+	0.132385i	$0.957736\pi$
$14$		0			0
$15$	0.666429	+	1.15429i	0.172071	+	0.298036i
$16$		0			0
$17$	3.59134	−	6.22038i	0.871027	−	1.50866i	0.0100916	−	0.999949i	$-0.496788\pi$
$17$	3.59134	−	6.22038i	0.871027	−	1.50866i	0.860935	−	0.508714i	$-0.169879\pi$
$18$		0			0
$19$	−4.32670	+	0.528817i	−0.992614	+	0.121319i
$19$	−4.32670	+	0.528817i	−0.992614	+	0.121319i
$20$		0			0
$21$	−0.649579	+	1.12510i	−0.141750	+	0.245518i
$22$		0			0
$23$	−4.29844	−	7.44512i	−0.896287	−	1.55242i	−0.832203	−	0.554471i	$-0.812921\pi$
$23$	−4.29844	−	7.44512i	−0.896287	−	1.55242i	−0.0640843	−	0.997944i	$-0.520413\pi$
$24$		0			0
$25$	−2.67712	−	4.63691i	−0.535425	−	0.927383i
$26$		0			0
$27$	2.41421			0.464616
$28$		0			0
$29$	3.33113	+	5.76969i	0.618576	+	1.07140i	0.989746	+	0.142840i	$0.0456233\pi$
$29$	3.33113	+	5.76969i	0.618576	+	1.07140i	−0.371170	+	0.928565i	$0.621043\pi$
$30$		0			0
$31$	10.7933			1.93853			0.969267	−	0.246012i	$-0.0791201\pi$
$31$	10.7933			1.93853			0.969267	+	0.246012i	$0.0791201\pi$
$32$		0			0
$33$	−0.459322	+	0.795569i	−0.0799576	+	0.138491i
$34$		0			0
$35$	5.04623	−	8.74032i	0.852968	−	1.47738i
$36$		0			0
$37$	0.308018			0.0506378			0.0253189	−	0.999679i	$-0.491940\pi$
$37$	0.308018			0.0506378			0.0253189	+	0.999679i	$0.491940\pi$
$38$		0			0
$39$	−1.13787			−0.182206
$40$		0			0
$41$	2.30359	−	3.98993i	0.359760	−	0.623123i	−0.628161	−	0.778084i	$-0.716192\pi$
$41$	2.30359	−	3.98993i	0.359760	−	0.623123i	0.987921	+	0.154961i	$0.0495252\pi$
$42$		0			0
$43$	4.31601	−	7.47554i	0.658185	−	1.14001i	−0.322900	−	0.946433i	$-0.604658\pi$
$43$	4.31601	−	7.47554i	0.658185	−	1.14001i	0.981085	−	0.193577i	$-0.0620089\pi$
$44$		0			0
$45$	−9.10132			−1.35674
$46$		0			0
$47$	−2.47002	−	4.27819i	−0.360289	−	0.624039i	0.627719	−	0.778440i	$-0.283989\pi$
$47$	−2.47002	−	4.27819i	−0.360289	−	0.624039i	−0.988008	+	0.154401i	$0.950655\pi$
$48$		0			0
$49$	2.83729			0.405327
$50$		0			0
$51$	−1.48758	−	2.57656i	−0.208303	−	0.360791i
$52$		0			0
$53$	−4.00555	−	6.93782i	−0.550205	−	0.952982i	−0.998259	−	0.0589763i	$-0.981216\pi$
$53$	−4.00555	−	6.93782i	−0.550205	−	0.952982i	0.448055	−	0.894006i	$-0.352117\pi$
$54$		0			0
$55$	3.56822	−	6.18034i	0.481139	−	0.833357i
$56$		0			0
$57$	−0.706392	+	1.66159i	−0.0935639	+	0.220083i
$58$		0			0
$59$	−1.01069	+	1.75057i	−0.131581	+	0.227905i	−0.924286	−	0.381700i	$-0.875339\pi$
$59$	−1.01069	+	1.75057i	−0.131581	+	0.227905i	0.792705	+	0.609605i	$0.208672\pi$
$60$		0			0
$61$	−0.780474	−	1.35182i	−0.0999294	−	0.173083i	0.811726	−	0.584039i	$-0.198528\pi$
$61$	−0.780474	−	1.35182i	−0.0999294	−	0.173083i	−0.911655	+	0.410956i	$0.865195\pi$
$62$		0			0
$63$	−4.43560	−	7.68269i	−0.558833	−	0.967928i
$64$		0			0
$65$	8.83953			1.09641
$66$		0			0
$67$	−3.81428	−	6.60653i	−0.465989	−	0.807116i	0.533257	−	0.845953i	$-0.320968\pi$
$67$	−3.81428	−	6.60653i	−0.465989	−	0.807116i	−0.999246	+	0.0388372i	$0.987635\pi$
$68$		0			0
$69$	−3.56095			−0.428688
$70$		0			0
$71$	−4.84183	+	8.38629i	−0.574619	+	0.995270i	0.421464	+	0.906845i	$0.361516\pi$
$71$	−4.84183	+	8.38629i	−0.574619	+	0.995270i	−0.996083	+	0.0884243i	$0.971817\pi$
$72$		0			0
$73$	−4.85425	+	8.40780i	−0.568147	+	0.984059i	0.428603	+	0.903493i	$0.359006\pi$
$73$	−4.85425	+	8.40780i	−0.568147	+	0.984059i	−0.996749	+	0.0805657i	$0.974327\pi$
$74$		0			0
$75$	−2.21780			−0.256090
$76$		0			0
$77$	6.95601			0.792711
$78$		0			0
$79$	2.98315	−	5.16697i	0.335631	−	0.581329i	−0.647975	−	0.761662i	$-0.724384\pi$
$79$	2.98315	−	5.16697i	0.335631	−	0.581329i	0.983606	+	0.180332i	$0.0577173\pi$
$80$		0			0
$81$	−3.74264	+	6.48244i	−0.415849	+	0.720272i
$82$		0			0
$83$	−6.49069			−0.712446			−0.356223	−	0.934401i	$-0.615936\pi$
$83$	−6.49069			−0.712446			−0.356223	+	0.934401i	$0.615936\pi$
$84$		0			0
$85$	11.5562	+	20.0159i	1.25345	+	2.17103i
$86$		0			0
$87$	2.75960			0.295860
$88$		0			0
$89$	0.762910	+	1.32140i	0.0808683	+	0.140068i	0.903623	−	0.428328i	$-0.140897\pi$
$89$	0.762910	+	1.32140i	0.0808683	+	0.140068i	−0.822755	+	0.568396i	$0.807564\pi$
$90$		0			0
$91$	4.30802	+	7.46171i	0.451603	+	0.782199i
$92$		0			0
$93$	2.23537	−	3.87177i	0.231797	−	0.401483i
$94$		0			0
$95$	5.48758	−	12.9080i	0.563014	−	1.32434i
$96$		0			0
$97$	−2.69296	+	4.66435i	−0.273429	+	0.473593i	−0.969738	−	0.244150i	$-0.921491\pi$
$97$	−2.69296	+	4.66435i	−0.273429	+	0.473593i	0.696309	+	0.717742i	$0.254824\pi$
$98$		0			0
$99$	−3.13644	−	5.43248i	−0.315225	−	0.545985i
$100$		0			0
$101$	−4.24092	−	7.34548i	−0.421987	−	0.730903i	0.574147	−	0.818752i	$-0.305334\pi$
$101$	−4.24092	−	7.34548i	−0.421987	−	0.730903i	−0.996134	+	0.0878496i	$0.972001\pi$
$102$		0			0
$103$	−10.0925			−0.994439			−0.497220	−	0.867625i	$-0.665646\pi$
$103$	−10.0925			−0.994439			−0.497220	+	0.867625i	$0.665646\pi$
$104$		0			0
$105$	−2.09022	−	3.62036i	−0.203984	−	0.353311i
$106$		0			0
$107$	−14.5983			−1.41127			−0.705636	−	0.708574i	$-0.749339\pi$
$107$	−14.5983			−1.41127			−0.705636	+	0.708574i	$0.749339\pi$
$108$		0			0
$109$	3.15228	−	5.45992i	0.301934	−	0.522965i	−0.674640	−	0.738147i	$-0.735701\pi$
$109$	3.15228	−	5.45992i	0.301934	−	0.522965i	0.976574	+	0.215182i	$0.0690344\pi$
$110$		0			0
$111$	0.0637926	−	0.110492i	0.00605492	−	0.0104874i
$112$		0			0
$113$	−20.1124			−1.89202			−0.946009	−	0.324142i	$-0.894925\pi$
$113$	−20.1124			−1.89202			−0.946009	+	0.324142i	$0.894925\pi$
$114$		0			0
$115$	27.6631			2.57960
$116$		0			0
$117$	3.88494	−	6.72892i	0.359163	−	0.622089i
$118$		0			0
$119$	−11.2640	+	19.5099i	−1.03257	+	1.78847i
$120$		0			0
$121$	−6.08136			−0.552851
$122$		0			0
$123$	−0.954177	−	1.65268i	−0.0860353	−	0.149017i
$124$		0			0
$125$	1.13989			0.101955
$126$		0			0
$127$	0.961761	+	1.66582i	0.0853425	+	0.147818i	0.905537	−	0.424267i	$-0.139468\pi$
$127$	0.961761	+	1.66582i	0.0853425	+	0.147818i	−0.820195	+	0.572085i	$0.806135\pi$
$128$		0			0
$129$	−1.78775	−	3.09647i	−0.157403	−	0.272629i
$130$		0			0
$131$	−0.656448	+	1.13700i	−0.0573542	+	0.0993403i	−0.893277	−	0.449507i	$-0.851600\pi$
$131$	−0.656448	+	1.13700i	−0.0573542	+	0.0993403i	0.835923	+	0.548847i	$0.184933\pi$
$132$		0			0
$133$	13.5705	−	1.65861i	1.17671	−	0.143819i
$134$		0			0
$135$	−3.88423	+	6.72768i	−0.334301	+	0.579027i
$136$		0			0
$137$	0.393804	+	0.682089i	0.0336450	+	0.0582748i	0.882358	−	0.470580i	$-0.155955\pi$
$137$	0.393804	+	0.682089i	0.0336450	+	0.0582748i	−0.848713	+	0.528854i	$0.822622\pi$
$138$		0			0
$139$	1.22850	+	2.12782i	0.104200	+	0.180479i	0.913411	−	0.407039i	$-0.133439\pi$
$139$	1.22850	+	2.12782i	0.104200	+	0.180479i	−0.809211	+	0.587518i	$0.800105\pi$
$140$		0			0
$141$	−2.04623			−0.172324
$142$		0			0
$143$	3.04623	+	5.27622i	0.254738	+	0.441220i
$144$		0			0
$145$	−21.4378			−1.78032
$146$		0			0
$147$	0.587621	−	1.01779i	0.0484662	−	0.0839459i
$148$		0			0
$149$	4.77018	−	8.26220i	0.390789	−	0.676866i	−0.601765	−	0.798673i	$-0.705536\pi$
$149$	4.77018	−	8.26220i	0.390789	−	0.676866i	0.992554	+	0.121807i	$0.0388690\pi$
$150$		0			0
$151$	13.8449			1.12669			0.563343	−	0.826223i	$-0.309515\pi$
$151$	13.8449			1.12669			0.563343	+	0.826223i	$0.309515\pi$
$152$		0			0
$153$	20.3157			1.64242
$154$		0			0
$155$	−17.3653	+	30.0777i	−1.39482	+	2.41590i
$156$		0			0
$157$	2.61273	−	4.52537i	0.208518	−	0.361164i	−0.742730	−	0.669591i	$-0.766469\pi$
$157$	2.61273	−	4.52537i	0.208518	−	0.361164i	0.951248	+	0.308427i	$0.0998026\pi$
$158$		0			0
$159$	−3.31831			−0.263159
$160$		0			0
$161$	13.4818	+	23.3512i	1.06252	+	1.84033i
$162$		0			0
$163$	9.60177			0.752068			0.376034	−	0.926606i	$-0.377288\pi$
$163$	9.60177			0.752068			0.376034	+	0.926606i	$0.377288\pi$
$164$		0			0
$165$	−1.47801	−	2.55998i	−0.115063	−	0.199294i
$166$		0			0
$167$	−4.95147	−	8.57620i	−0.383156	−	0.663646i	0.608355	−	0.793665i	$-0.291830\pi$
$167$	−4.95147	−	8.57620i	−0.383156	−	0.663646i	−0.991512	+	0.130019i	$0.958496\pi$
$168$		0			0
$169$	2.72680	−	4.72296i	0.209754	−	0.363305i
$170$		0			0
$171$	−7.41421	−	9.85035i	−0.566979	−	0.753275i
$172$		0			0
$173$	−2.00555	+	3.47372i	−0.152479	+	0.264102i	−0.932138	−	0.362103i	$-0.882059\pi$
$173$	−2.00555	+	3.47372i	−0.152479	+	0.264102i	0.779659	+	0.626204i	$0.215392\pi$
$174$		0			0
$175$	8.39665	+	14.5434i	0.634727	+	1.09938i
$176$		0			0
$177$	0.418643	+	0.725112i	0.0314672	+	0.0545027i
$178$		0			0
$179$	3.33970			0.249621			0.124810	−	0.992181i	$-0.460168\pi$
$179$	3.33970			0.249621			0.124810	+	0.992181i	$0.460168\pi$
$180$		0			0
$181$	−9.32084	−	16.1442i	−0.692813	−	1.19999i	−0.970912	−	0.239435i	$-0.923038\pi$
$181$	−9.32084	−	16.1442i	−0.692813	−	1.19999i	0.278100	−	0.960552i	$-0.410295\pi$
$182$		0			0
$183$	−0.646566			−0.0477955
$184$		0			0
$185$	−0.495570	+	0.858353i	−0.0364350	+	0.0631073i
$186$		0			0
$187$	−7.96487	+	13.7956i	−0.582449	+	1.00883i
$188$		0			0
$189$	−7.57205			−0.550785
$190$		0			0
$191$	−8.00000			−0.578860			−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000			−0.578860			−0.289430	+	0.957199i	$0.593466\pi$
$192$		0			0
$193$	6.95932	−	12.0539i	0.500943	−	0.867659i	−0.499056	−	0.866569i	$-0.666320\pi$
$193$	6.95932	−	12.0539i	0.500943	−	0.867659i	0.999999	−	0.00108916i	$-0.000346689\pi$
$194$		0			0
$195$	1.83073	−	3.17091i	0.131101	−	0.227074i
$196$		0			0
$197$	−2.03513			−0.144997			−0.0724984	−	0.997369i	$-0.523097\pi$
$197$	−2.03513			−0.144997			−0.0724984	+	0.997369i	$0.523097\pi$
$198$		0			0
$199$	−4.34085	−	7.51857i	−0.307714	−	0.532977i	0.670148	−	0.742228i	$-0.266231\pi$
$199$	−4.34085	−	7.51857i	−0.307714	−	0.532977i	−0.977862	+	0.209251i	$0.932897\pi$
$200$		0			0
$201$	−3.15986			−0.222879
$202$		0			0
$203$	−10.4479	−	18.0963i	−0.733300	−	1.27011i
$204$		0			0
$205$	7.41249	+	12.8388i	0.517711	+	0.896701i
$206$		0			0
$207$	12.1578	−	21.0580i	0.845028	−	1.46363i
$208$		0			0
$209$	9.59577	−	1.17281i	0.663753	−	0.0811251i
$210$		0			0
$211$	−1.47729	+	2.55874i	−0.101701	+	0.176151i	−0.912386	−	0.409332i	$-0.865762\pi$
$211$	−1.47729	+	2.55874i	−0.101701	+	0.176151i	0.810685	+	0.585483i	$0.199095\pi$
$212$		0			0
$213$	2.00555	+	3.47372i	0.137418	+	0.238015i
$214$		0			0
$215$	13.8881	+	24.0548i	0.947158	+	1.64052i
$216$		0			0
$217$	−33.8526			−2.29806
$218$		0			0
$219$	2.01069	+	3.48263i	0.135870	+	0.235334i
$220$		0			0
$221$	−19.7313			−1.32727
$222$		0			0
$223$	0.252215	−	0.436849i	0.0168896	−	0.0292536i	−0.857457	−	0.514555i	$-0.827957\pi$
$223$	0.252215	−	0.436849i	0.0168896	−	0.0292536i	0.874347	+	0.485302i	$0.161290\pi$
$224$		0			0
$225$	7.57205	−	13.1152i	0.504803	−	0.874345i
$226$		0			0
$227$	26.6933			1.77170			0.885849	−	0.463973i	$-0.153577\pi$
$227$	26.6933			1.77170			0.885849	+	0.463973i	$0.153577\pi$
$228$		0			0
$229$	20.3157			1.34250			0.671249	−	0.741232i	$-0.265758\pi$
$229$	20.3157			1.34250			0.671249	+	0.741232i	$0.265758\pi$
$230$		0			0
$231$	1.44064	−	2.49526i	0.0947870	−	0.164176i
$232$		0			0
$233$	3.65783	−	6.33555i	0.239633	−	0.415056i	−0.720976	−	0.692960i	$-0.756306\pi$
$233$	3.65783	−	6.33555i	0.239633	−	0.415056i	0.960609	+	0.277904i	$0.0896397\pi$
$234$		0			0
$235$	15.8960			1.03694
$236$		0			0
$237$	−1.23566	−	2.14023i	−0.0802648	−	0.139023i
$238$		0			0
$239$	−7.29151			−0.471648			−0.235824	−	0.971796i	$-0.575779\pi$
$239$	−7.29151			−0.471648			−0.235824	+	0.971796i	$0.575779\pi$
$240$		0			0
$241$	1.99557	+	3.45643i	0.128546	+	0.222648i	0.923113	−	0.384528i	$-0.125636\pi$
$241$	1.99557	+	3.45643i	0.128546	+	0.222648i	−0.794567	+	0.607176i	$0.792302\pi$
$242$		0			0
$243$	5.17157	+	8.95743i	0.331757	+	0.574619i
$244$		0			0
$245$	−4.56491	+	7.90666i	−0.291642	+	0.505138i
$246$		0			0
$247$	7.20095	+	9.56702i	0.458186	+	0.608735i
$248$		0			0
$249$	−1.34427	+	2.32834i	−0.0851894	+	0.147552i
$250$		0			0
$251$	−0.120340	−	0.208435i	−0.00759581	−	0.0131563i	0.862203	−	0.506564i	$-0.169085\pi$
$251$	−0.120340	−	0.208435i	−0.00759581	−	0.0131563i	−0.869798	+	0.493407i	$0.835751\pi$
$252$		0			0
$253$	9.53309	+	16.5118i	0.599341	+	1.03809i
$254$		0			0
$255$	9.57348			0.599514
$256$		0			0
$257$	4.68267	+	8.11063i	0.292097	+	0.505927i	0.974305	−	0.225231i	$-0.0723136\pi$
$257$	4.68267	+	8.11063i	0.292097	+	0.505927i	−0.682208	+	0.731158i	$0.738980\pi$
$258$		0			0
$259$	−0.966081			−0.0600293
$260$		0			0
$261$	−9.42186	+	16.3191i	−0.583199	+	1.01013i
$262$		0			0
$263$	−4.74434	+	8.21743i	−0.292548	+	0.506708i	−0.974412	−	0.224771i	$-0.927837\pi$
$263$	−4.74434	+	8.21743i	−0.292548	+	0.506708i	0.681863	+	0.731480i	$0.261170\pi$
$264$		0			0
$265$	25.7781			1.58354
$266$		0			0
$267$	0.632015			0.0386787
$268$		0			0
$269$	13.4749	−	23.3391i	0.821576	−	1.42301i	−0.0829318	−	0.996555i	$-0.526428\pi$
$269$	13.4749	−	23.3391i	0.821576	−	1.42301i	0.904508	−	0.426457i	$-0.140238\pi$
$270$		0			0
$271$	−3.05925	+	5.29878i	−0.185836	+	0.321878i	−0.943858	−	0.330351i	$-0.892833\pi$
$271$	−3.05925	+	5.29878i	−0.185836	+	0.321878i	0.758022	+	0.652229i	$0.226166\pi$
$272$		0			0
$273$	3.56888			0.215998
$274$		0			0
$275$	5.93733	+	10.2838i	0.358034	+	0.620134i
$276$		0			0
$277$	9.06905			0.544906			0.272453	−	0.962169i	$-0.412165\pi$
$277$	9.06905			0.544906			0.272453	+	0.962169i	$0.412165\pi$
$278$		0			0
$279$	15.2640	+	26.4381i	0.913834	+	1.58281i
$280$		0			0
$281$	8.29675	+	14.3704i	0.494943	+	0.857266i	0.999983	−	0.00583003i	$-0.00185577\pi$
$281$	8.29675	+	14.3704i	0.494943	+	0.857266i	−0.505040	+	0.863096i	$0.668522\pi$
$282$		0			0
$283$	−8.78403	+	15.2144i	−0.522157	+	0.904402i	0.477511	+	0.878626i	$0.341539\pi$
$283$	−8.78403	+	15.2144i	−0.522157	+	0.904402i	−0.999668	+	0.0257761i	$0.991794\pi$
$284$		0			0
$285$	−3.49385	−	4.64184i	−0.206958	−	0.274959i
$286$		0			0
$287$	−7.22508	+	12.5142i	−0.426483	+	0.738690i
$288$		0			0
$289$	−17.2954	−	29.9565i	−1.01738	−	1.76215i
$290$		0			0
$291$	1.11546	+	1.93204i	0.0653895	+	0.113258i
$292$		0			0
$293$	−24.0573			−1.40544			−0.702722	−	0.711464i	$-0.748032\pi$
$293$	−24.0573			−1.40544			−0.702722	+	0.711464i	$0.748032\pi$
$294$		0			0
$295$	−3.25221	−	5.63300i	−0.189351	−	0.327966i
$296$		0			0
$297$	−5.35425			−0.310685
$298$		0			0
$299$	−11.8081	+	20.4523i	−0.682882	+	1.18279i
$300$		0			0
$301$	−13.5369	+	23.4466i	−0.780255	+	1.35144i
$302$		0			0
$303$	−3.51329			−0.201833
$304$		0			0
$305$	5.02282			0.287606
$306$		0			0
$307$	9.88047	−	17.1135i	0.563908	−	0.976718i	−0.433242	−	0.901278i	$-0.642630\pi$
$307$	9.88047	−	17.1135i	0.563908	−	0.976718i	0.997150	−	0.0754402i	$-0.0240362\pi$
$308$		0			0
$309$	−2.09022	+	3.62036i	−0.118908	+	0.205955i
$310$		0			0
$311$	−17.2358			−0.977353			−0.488676	−	0.872465i	$-0.662520\pi$
$311$	−17.2358			−0.977353			−0.488676	+	0.872465i	$0.662520\pi$
$312$		0			0
$313$	−4.96044	−	8.59174i	−0.280381	−	0.485634i	0.691098	−	0.722761i	$-0.257127\pi$
$313$	−4.96044	−	8.59174i	−0.280381	−	0.485634i	−0.971479	+	0.237128i	$0.923794\pi$
$314$		0			0
$315$	28.5458			1.60837
$316$		0			0
$317$	9.33496	+	16.1686i	0.524303	+	0.908120i	0.999600	+	0.0282944i	$0.00900758\pi$
$317$	9.33496	+	16.1686i	0.524303	+	0.908120i	−0.475296	+	0.879826i	$0.657659\pi$
$318$		0			0
$319$	−7.38779	−	12.7960i	−0.413637	−	0.716440i
$320$		0			0
$321$	−3.02341	+	5.23670i	−0.168750	+	0.292284i
$322$		0			0
$323$	−12.2492	+	28.8129i	−0.681564	+	1.60319i
$324$		0			0
$325$	−7.35425	+	12.7379i	−0.407940	+	0.706573i
$326$		0			0
$327$	−1.30572	−	2.26157i	−0.0722064	−	0.125065i
$328$		0			0
$329$	7.74707	+	13.4183i	0.427110	+	0.739776i
$330$		0			0
$331$	−23.7341			−1.30455			−0.652273	−	0.757984i	$-0.726185\pi$
$331$	−23.7341			−1.30455			−0.652273	+	0.757984i	$0.726185\pi$
$332$		0			0
$333$	0.435603	+	0.754486i	0.0238709	+	0.0413456i
$334$		0			0
$335$	24.5472			1.34116
$336$		0			0
$337$	8.82400	−	15.2836i	0.480674	−	0.832551i	−0.519080	−	0.854725i	$-0.673725\pi$
$337$	8.82400	−	15.2836i	0.480674	−	0.832551i	0.999754	+	0.0221741i	$0.00705880\pi$
$338$		0			0
$339$	−4.16542	+	7.21472i	−0.226234	+	0.391850i
$340$		0			0
$341$	−23.9374			−1.29628
$342$		0			0
$343$	13.0561			0.704964
$344$		0			0
$345$	5.72921	−	9.92328i	0.308450	−	0.534252i
$346$		0			0
$347$	1.02443	−	1.77437i	0.0549945	−	0.0952532i	−0.837218	−	0.546870i	$-0.815819\pi$
$347$	1.02443	−	1.77437i	0.0549945	−	0.0952532i	0.892212	+	0.451617i	$0.149153\pi$
$348$		0			0
$349$	−0.00975744			−0.000522304			−0.000261152	−	1.00000i	$-0.500083\pi$
$349$	−0.00975744			−0.000522304			−0.000261152		1.00000i	$0.500083\pi$
$350$		0			0
$351$	−3.31601	−	5.74349i	−0.176995	−	0.306565i
$352$		0			0
$353$	5.47418			0.291361			0.145681	−	0.989332i	$-0.453463\pi$
$353$	5.47418			0.291361			0.145681	+	0.989332i	$0.453463\pi$
$354$		0			0
$355$	−15.5800	−	26.9854i	−0.826903	−	1.43224i
$356$		0			0
$357$	4.66571	+	8.08125i	0.246936	+	0.427705i
$358$		0			0
$359$	−4.92701	+	8.53383i	−0.260038	+	0.450398i	−0.966252	−	0.257600i	$-0.917068\pi$
$359$	−4.92701	+	8.53383i	−0.260038	+	0.450398i	0.706214	+	0.707998i	$0.250402\pi$
$360$		0			0
$361$	18.4407	−	4.57607i	0.970563	−	0.240846i
$362$		0			0
$363$	−1.25949	+	2.18150i	−0.0661061	+	0.114499i
$364$		0			0
$365$	−15.6200	−	27.0546i	−0.817588	−	1.41610i
$366$		0			0
$367$	13.4046	+	23.2175i	0.699716	+	1.21194i	0.968565	+	0.248762i	$0.0800237\pi$
$367$	13.4046	+	23.2175i	0.699716	+	1.21194i	−0.268848	+	0.963183i	$0.586643\pi$
$368$		0			0
$369$	13.0311			0.678370
$370$		0			0
$371$	12.5632	+	21.7601i	0.652248	+	1.12973i
$372$		0			0
$373$	−23.1510			−1.19871			−0.599357	−	0.800482i	$-0.704577\pi$
$373$	−23.1510			−1.19871			−0.599357	+	0.800482i	$0.704577\pi$
$374$		0			0
$375$	0.236080	−	0.408902i	0.0121911	−	0.0211156i
$376$		0			0
$377$	9.15086	−	15.8497i	0.471293	−	0.816303i
$378$		0			0
$379$	−21.6968			−1.11449			−0.557244	−	0.830349i	$-0.688141\pi$
$379$	−21.6968			−1.11449			−0.557244	+	0.830349i	$0.688141\pi$
$380$		0			0
$381$	0.796749			0.0408187
$382$		0			0
$383$	−8.62785	+	14.9439i	−0.440863	+	0.763596i	−0.997754	−	0.0669891i	$-0.978661\pi$
$383$	−8.62785	+	14.9439i	−0.440863	+	0.763596i	0.556891	+	0.830586i	$0.311994\pi$
$384$		0			0
$385$	−11.1915	+	19.3843i	−0.570373	+	0.987916i
$386$		0			0
$387$	24.4150			1.24109
$388$		0			0
$389$	1.90423	+	3.29823i	0.0965485	+	0.167227i	0.910254	−	0.414051i	$-0.135886\pi$
$389$	1.90423	+	3.29823i	0.0965485	+	0.167227i	−0.813705	+	0.581278i	$0.802553\pi$
$390$		0			0
$391$	−61.7486			−3.12276
$392$		0			0
$393$	0.271910	+	0.470962i	0.0137160	+	0.0237569i
$394$		0			0
$395$	9.59919	+	16.6263i	0.482987	+	0.836559i
$396$		0			0
$397$	10.6517	−	18.4493i	0.534592	−	0.925941i	−0.464590	−	0.885526i	$-0.653798\pi$
$397$	10.6517	−	18.4493i	0.534592	−	0.925941i	0.999183	−	0.0404157i	$-0.0128682\pi$
$398$		0			0
$399$	2.21556	−	5.21150i	0.110917	−	0.260901i
$400$		0			0
$401$	11.4277	−	19.7934i	0.570673	−	0.988435i	−0.425824	−	0.904806i	$-0.640016\pi$
$401$	11.4277	−	19.7934i	0.570673	−	0.988435i	0.996497	−	0.0836289i	$-0.0266510\pi$
$402$		0			0
$403$	−14.8250	−	25.6776i	−0.738485	−	1.27909i
$404$		0			0
$405$	−12.0431	−	20.8592i	−0.598425	−	1.03650i
$406$		0			0
$407$	−0.683122			−0.0338611
$408$		0			0
$409$	−0.919092	−	1.59191i	−0.0454462	−	0.0787151i	0.842408	−	0.538841i	$-0.181138\pi$
$409$	−0.919092	−	1.59191i	−0.0454462	−	0.0787151i	−0.887854	+	0.460126i	$0.847804\pi$
$410$		0			0
$411$	0.326238			0.0160921
$412$		0			0
$413$	3.16999	−	5.49058i	0.155985	−	0.270174i
$414$		0			0
$415$	10.4429	−	18.0876i	0.512621	−	0.887885i
$416$		0			0
$417$	1.01772			0.0498379
$418$		0			0
$419$	−32.4053			−1.58310			−0.791550	−	0.611104i	$-0.790726\pi$
$419$	−32.4053			−1.58310			−0.791550	+	0.611104i	$0.790726\pi$
$420$		0			0
$421$	9.47246	−	16.4068i	0.461659	−	0.799617i	−0.537385	−	0.843337i	$-0.680588\pi$
$421$	9.47246	−	16.4068i	0.461659	−	0.799617i	0.999044	+	0.0437200i	$0.0139210\pi$
$422$		0			0
$423$	6.98626	−	12.1006i	0.339684	−	0.588349i
$424$		0			0
$425$	−38.4578			−1.86548
$426$		0			0
$427$	2.44791	+	4.23991i	0.118463	+	0.205184i
$428$		0			0
$429$	2.52358			0.121840
$430$		0			0
$431$	6.13333	+	10.6232i	0.295432	+	0.511704i	0.975085	−	0.221830i	$-0.0712030\pi$
$431$	6.13333	+	10.6232i	0.295432	+	0.511704i	−0.679653	+	0.733534i	$0.737870\pi$
$432$		0			0
$433$	5.43005	+	9.40513i	0.260952	+	0.451982i	0.966495	−	0.256685i	$-0.0826303\pi$
$433$	5.43005	+	9.40513i	0.260952	+	0.451982i	−0.705543	+	0.708667i	$0.749297\pi$
$434$		0			0
$435$	−4.43992	+	7.69017i	−0.212878	+	0.368716i
$436$		0			0
$437$	22.5352	+	29.9397i	1.07800	+	1.43221i
$438$		0			0
$439$	0.734047	−	1.27141i	0.0350341	−	0.0606809i	−0.847977	−	0.530034i	$-0.822179\pi$
$439$	0.734047	−	1.27141i	0.0350341	−	0.0606809i	0.883011	+	0.469353i	$0.155513\pi$
$440$		0			0
$441$	4.01253	+	6.94991i	0.191073	+	0.330948i
$442$		0			0
$443$	−16.0004	−	27.7135i	−0.760202	−	1.31671i	−0.942746	−	0.333511i	$-0.891767\pi$
$443$	−16.0004	−	27.7135i	−0.760202	−	1.31671i	0.182544	−	0.983198i	$-0.441567\pi$
$444$		0			0
$445$	−4.90978			−0.232746
$446$		0			0
$447$	−1.97588	−	3.42232i	−0.0934557	−	0.161870i
$448$		0			0
$449$	−38.4556			−1.81483			−0.907415	−	0.420235i	$-0.861947\pi$
$449$	−38.4556			−1.81483			−0.907415	+	0.420235i	$0.861947\pi$
$450$		0			0
$451$	−5.10890	+	8.84888i	−0.240569	+	0.416677i
$452$		0			0
$453$	2.86738	−	4.96645i	0.134721	−	0.233344i
$454$		0			0
$455$	−27.7247			−1.29975
$456$		0			0
$457$	−23.2948			−1.08969			−0.544843	−	0.838538i	$-0.683411\pi$
$457$	−23.2948			−1.08969			−0.544843	+	0.838538i	$0.683411\pi$
$458$		0			0
$459$	8.67025	−	15.0173i	0.404693	−	0.700948i
$460$		0			0
$461$	−14.5879	+	25.2670i	−0.679426	+	1.17680i	0.295728	+	0.955272i	$0.404438\pi$
$461$	−14.5879	+	25.2670i	−0.679426	+	1.17680i	−0.975154	+	0.221528i	$0.928896\pi$
$462$		0			0
$463$	−1.28461			−0.0597008			−0.0298504	−	0.999554i	$-0.509503\pi$
$463$	−1.28461			−0.0597008			−0.0298504	+	0.999554i	$0.509503\pi$
$464$		0			0
$465$	7.19296	+	12.4586i	0.333566	+	0.577753i
$466$		0			0
$467$	11.3289			0.524238			0.262119	−	0.965036i	$-0.415579\pi$
$467$	11.3289			0.524238			0.262119	+	0.965036i	$0.415579\pi$
$468$		0			0
$469$	11.9633	+	20.7210i	0.552413	+	0.956808i
$470$		0			0
$471$	−1.08223	−	1.87447i	−0.0498664	−	0.0863711i
$472$		0			0
$473$	−9.57205	+	16.5793i	−0.440123	+	0.762316i
$474$		0			0
$475$	14.0352	+	18.6468i	0.643979	+	0.855575i
$476$		0			0
$477$	11.3294	−	19.6231i	0.518738	−	0.898480i
$478$		0			0
$479$	6.97827	+	12.0867i	0.318845	+	0.552256i	0.980247	−	0.197775i	$-0.0633716\pi$
$479$	6.97827	+	12.0867i	0.318845	+	0.552256i	−0.661402	+	0.750032i	$0.730038\pi$
$480$		0			0
$481$	−0.423073	−	0.732785i	−0.0192905	−	0.0334121i
$482$		0			0
$483$	11.1687			0.508194
$484$		0			0
$485$	−8.66542	−	15.0089i	−0.393476	−	0.681521i
$486$		0			0
$487$	18.1139			0.820819			0.410410	−	0.911901i	$-0.365386\pi$
$487$	18.1139			0.820819			0.410410	+	0.911901i	$0.365386\pi$
$488$		0			0
$489$	1.98859	−	3.44434i	0.0899272	−	0.155758i
$490$		0			0
$491$	18.9928	−	32.8965i	0.857134	−	1.48460i	−0.0175169	−	0.999847i	$-0.505576\pi$
$491$	18.9928	−	32.8965i	0.857134	−	1.48460i	0.874651	−	0.484753i	$-0.161091\pi$
$492$		0			0
$493$	47.8529			2.15518
$494$		0			0
$495$	20.1849			0.907244
$496$		0			0
$497$	15.1861	−	26.3031i	0.681191	−	1.17986i
$498$		0			0
$499$	13.8728	−	24.0284i	0.621033	−	1.07566i	−0.368261	−	0.929722i	$-0.620047\pi$
$499$	13.8728	−	24.0284i	0.621033	−	1.07566i	0.989294	−	0.145938i	$-0.0466199\pi$
$500$		0			0
$501$	−4.10193			−0.183261
$502$		0			0
$503$	11.7092	+	20.2809i	0.522088	+	0.904283i	0.999670	+	0.0256954i	$0.00817999\pi$
$503$	11.7092	+	20.2809i	0.522088	+	0.904283i	−0.477582	+	0.878587i	$0.658487\pi$
$504$		0			0
$505$	27.2929			1.21452
$506$		0			0
$507$	−1.12948	−	1.95631i	−0.0501619	−	0.0868829i
$508$		0			0
$509$	18.8588	+	32.6644i	0.835902	+	1.44783i	0.893294	+	0.449474i	$0.148388\pi$
$509$	18.8588	+	32.6644i	0.835902	+	1.44783i	−0.0573913	+	0.998352i	$0.518278\pi$
$510$		0			0
$511$	15.2251	−	26.3706i	0.673518	−	1.16657i
$512$		0			0
$513$	−10.4456	+	1.27668i	−0.461184	+	0.0563667i
$514$		0			0
$515$	16.2378	−	28.1246i	0.715521	−	1.23932i
$516$		0			0
$517$	5.47801	+	9.48818i	0.240922	+	0.417290i
$518$		0			0
$519$	0.830726	+	1.43886i	0.0364648	+	0.0631589i
$520$		0			0
$521$	−14.8376			−0.650046			−0.325023	−	0.945706i	$-0.605372\pi$
$521$	−14.8376			−0.650046			−0.325023	+	0.945706i	$0.605372\pi$
$522$		0			0
$523$	18.7964	+	32.5563i	0.821910	+	1.42359i	0.904258	+	0.426986i	$0.140425\pi$
$523$	18.7964	+	32.5563i	0.821910	+	1.42359i	−0.0823488	+	0.996604i	$0.526242\pi$
$524$		0			0
$525$	6.95601			0.303585
$526$		0			0
$527$	38.7624	−	67.1384i	1.68852	−	2.92459i
$528$		0			0
$529$	−25.4532	+	44.0863i	−1.10666	+	1.91680i
$530$		0			0
$531$	−5.71735			−0.248112
$532$		0			0
$533$	−12.6562			−0.548202
$534$		0			0
$535$	23.4872	−	40.6811i	1.01544	−	1.75880i
$536$		0			0
$537$	0.691674	−	1.19801i	0.0298479	−	0.0516981i
$538$		0			0
$539$	−6.29254			−0.271039
$540$		0			0
$541$	−14.5473	−	25.1967i	−0.625439	−	1.08329i	−0.988456	−	0.151510i	$-0.951586\pi$
$541$	−14.5473	−	25.1967i	−0.625439	−	1.08329i	0.363016	−	0.931783i	$-0.381747\pi$
$542$		0			0
$543$	−7.72164			−0.331367
$544$		0			0
$545$	10.1434	+	17.5689i	0.434497	+	0.752570i
$546$		0			0
$547$	−11.2974	−	19.5677i	−0.483042	−	0.836652i	0.516769	−	0.856125i	$-0.327135\pi$
$547$	−11.2974	−	19.5677i	−0.483042	−	0.836652i	−0.999810	+	0.0194725i	$0.993801\pi$
$548$		0			0
$549$	2.20751	−	3.82352i	0.0942143	−	0.163184i
$550$		0			0
$551$	−17.4639	−	23.2022i	−0.743988	−	0.988446i
$552$		0			0
$553$	−9.35649	+	16.2059i	−0.397878	+	0.689145i
$554$		0			0
$555$	0.205272	+	0.355541i	0.00871331	+	0.0150919i
$556$		0			0
$557$	7.12548	+	12.3417i	0.301916	+	0.522935i	0.976570	−	0.215200i	$-0.0690403\pi$
$557$	7.12548	+	12.3417i	0.301916	+	0.522935i	−0.674654	+	0.738135i	$0.735707\pi$
$558$		0			0
$559$	−23.7128			−1.00294
$560$		0			0
$561$	3.29916	+	5.71431i	0.139291	+	0.241258i
$562$		0			0
$563$	−32.0196			−1.34947			−0.674734	−	0.738061i	$-0.735742\pi$
$563$	−32.0196			−1.34947			−0.674734	+	0.738061i	$0.735742\pi$
$564$		0			0
$565$	32.3589	−	56.0472i	1.36135	−	2.35792i
$566$		0			0
$567$	11.7386	−	20.3318i	0.492974	−	0.853857i
$568$		0			0
$569$	5.59636			0.234611			0.117306	−	0.993096i	$-0.462574\pi$
$569$	5.59636			0.234611			0.117306	+	0.993096i	$0.462574\pi$
$570$		0			0
$571$	22.8521			0.956331			0.478166	−	0.878270i	$-0.341302\pi$
$571$	22.8521			0.956331			0.478166	+	0.878270i	$0.341302\pi$
$572$		0			0
$573$	−1.65685	+	2.86976i	−0.0692161	+	0.119886i
$574$		0			0
$575$	−23.0149	+	39.8630i	−0.959789	+	1.66240i
$576$		0			0
$577$	−25.5489			−1.06362			−0.531808	−	0.846865i	$-0.678487\pi$
$577$	−25.5489			−1.06362			−0.531808	+	0.846865i	$0.678487\pi$
$578$		0			0
$579$	−2.88265	−	4.99289i	−0.119799	−	0.207497i
$580$		0			0
$581$	20.3577			0.844580
$582$		0			0
$583$	8.88352	+	15.3867i	0.367918	+	0.637252i
$584$		0			0
$585$	12.5010	+	21.6523i	0.516852	+	0.895214i
$586$		0			0
$587$	−10.7040	+	18.5398i	−0.441799	+	0.765219i	−0.997823	−	0.0659474i	$-0.978993\pi$
$587$	−10.7040	+	18.5398i	−0.441799	+	0.765219i	0.556024	+	0.831166i	$0.312326\pi$
$588$		0			0
$589$	−46.6994	+	5.70768i	−1.92421	+	0.235181i
$590$		0			0
$591$	−0.421489	+	0.730040i	−0.0173377	+	0.0300298i
$592$		0			0
$593$	1.31469	+	2.27711i	0.0539878	+	0.0935096i	0.891756	−	0.452516i	$-0.149473\pi$
$593$	1.31469	+	2.27711i	0.0539878	+	0.0935096i	−0.837768	+	0.546026i	$0.816140\pi$
$594$		0			0
$595$	−36.2454	−	62.7789i	−1.48592	−	2.57368i
$596$		0			0
$597$	−3.59608			−0.147178
$598$		0			0
$599$	−17.0421	−	29.5177i	−0.696320	−	1.20606i	−0.969734	−	0.244165i	$-0.921486\pi$
$599$	−17.0421	−	29.5177i	−0.696320	−	1.20606i	0.273414	−	0.961896i	$-0.411847\pi$
$600$		0			0
$601$	25.9251			1.05751			0.528753	−	0.848776i	$-0.322660\pi$
$601$	25.9251			1.05751			0.528753	+	0.848776i	$0.322660\pi$
$602$		0			0
$603$	10.7884	−	18.6861i	0.439338	−	0.760957i
$604$		0			0
$605$	9.78430	−	16.9469i	0.397788	−	0.688990i
$606$		0			0
$607$	−25.1695			−1.02160			−0.510799	−	0.859700i	$-0.670650\pi$
$607$	−25.1695			−1.02160			−0.510799	+	0.859700i	$0.670650\pi$
$608$		0			0
$609$	−8.65533			−0.350732
$610$		0			0
$611$	−6.78531	+	11.7525i	−0.274504	+	0.475455i
$612$		0			0
$613$	8.50653	−	14.7337i	0.343576	−	0.595090i	−0.641518	−	0.767108i	$-0.721695\pi$
$613$	8.50653	−	14.7337i	0.343576	−	0.595090i	0.985094	+	0.172017i	$0.0550285\pi$
$614$		0			0
$615$	6.14071			0.247617
$616$		0			0
$617$	−4.21682	−	7.30375i	−0.169763	−	0.294038i	0.768574	−	0.639761i	$-0.220967\pi$
$617$	−4.21682	−	7.30375i	−0.169763	−	0.294038i	−0.938336	+	0.345724i	$0.887634\pi$
$618$		0			0
$619$	31.9297			1.28336			0.641682	−	0.766970i	$-0.278237\pi$
$619$	31.9297			1.28336			0.641682	+	0.766970i	$0.278237\pi$
$620$		0			0
$621$	−10.3774	−	17.9741i	−0.416429	−	0.721276i
$622$		0			0
$623$	−2.39282	−	4.14449i	−0.0958665	−	0.166046i
$624$		0			0
$625$	11.5516	−	20.0080i	0.462066	−	0.800321i
$626$		0			0
$627$	1.56664	−	3.68509i	0.0625655	−	0.147168i
$628$		0			0
$629$	1.10620	−	1.91599i	0.0441069	−	0.0763954i
$630$		0			0
$631$	12.3584	+	21.4054i	0.491981	+	0.852135i	0.999957	−	0.00923543i	$-0.00293977\pi$
$631$	12.3584	+	21.4054i	0.491981	+	0.852135i	−0.507977	+	0.861371i	$0.669606\pi$
$632$		0			0
$633$	0.611914	+	1.05987i	0.0243214	+	0.0421259i
$634$		0			0
$635$	−6.18951			−0.245623
$636$		0			0
$637$	−3.89711	−	6.75000i	−0.154409	−	0.267445i
$638$		0			0
$639$	−27.3895			−1.08351
$640$		0			0
$641$	13.6013	−	23.5582i	0.537220	−	0.930492i	−0.461833	−	0.886967i	$-0.652808\pi$
$641$	13.6013	−	23.5582i	0.537220	−	0.930492i	0.999052	−	0.0435248i	$-0.0138587\pi$
$642$		0			0
$643$	−17.1988	+	29.7892i	−0.678254	+	1.17477i	0.297253	+	0.954799i	$0.403930\pi$
$643$	−17.1988	+	29.7892i	−0.678254	+	1.17477i	−0.975506	+	0.219971i	$0.929404\pi$
$644$		0			0
$645$	11.5052			0.453018
$646$		0			0
$647$	−40.7415			−1.60171			−0.800857	−	0.598855i	$-0.795622\pi$
$647$	−40.7415			−1.60171			−0.800857	+	0.598855i	$0.795622\pi$
$648$		0			0
$649$	2.24152	−	3.88243i	0.0879874	−	0.152399i
$650$		0			0
$651$	−7.01110	+	12.1436i	−0.274787	+	0.475945i
$652$		0			0
$653$	−37.7465			−1.47713			−0.738566	−	0.674181i	$-0.764497\pi$
$653$	−37.7465			−1.47713			−0.738566	+	0.674181i	$0.764497\pi$
$654$		0			0
$655$	−2.11232	−	3.65865i	−0.0825352	−	0.142955i
$656$		0			0
$657$	−27.4598			−1.07131
$658$		0			0
$659$	2.61915	+	4.53650i	0.102027	+	0.176717i	0.912520	−	0.409032i	$-0.134134\pi$
$659$	2.61915	+	4.53650i	0.102027	+	0.176717i	−0.810492	+	0.585749i	$0.800800\pi$
$660$		0			0
$661$	−9.46982	−	16.4022i	−0.368333	−	0.637972i	0.620972	−	0.783833i	$-0.286738\pi$
$661$	−9.46982	−	16.4022i	−0.368333	−	0.637972i	−0.989305	+	0.145861i	$0.953405\pi$
$662$		0			0
$663$	−4.08649	+	7.07801i	−0.158706	+	0.274887i
$664$		0			0
$665$	−17.2115	+	40.4853i	−0.667433	+	1.56995i
$666$		0			0
$667$	28.6374	−	49.6014i	1.10884	−	1.92057i
$668$		0			0
$669$	−0.104471	−	0.180949i	−0.00403908	−	0.00699589i
$670$		0			0
$671$	1.73094	+	2.99807i	0.0668220	+	0.115739i
$672$		0			0
$673$	1.32739			0.0511670			0.0255835	−	0.999673i	$-0.491856\pi$
$673$	1.32739			0.0511670			0.0255835	+	0.999673i	$0.491856\pi$
$674$		0			0
$675$	−6.46315	−	11.1945i	−0.248767	−	0.430876i
$676$		0			0
$677$	18.2385			0.700963			0.350482	−	0.936570i	$-0.386018\pi$
$677$	18.2385			0.700963			0.350482	+	0.936570i	$0.386018\pi$
$678$		0			0
$679$	8.44633	−	14.6295i	0.324140	−	0.561428i
$680$		0			0
$681$	5.52837	−	9.57542i	0.211848	−	0.366931i
$682$		0			0
$683$	−3.92284			−0.150103			−0.0750517	−	0.997180i	$-0.523912\pi$
$683$	−3.92284			−0.150103			−0.0750517	+	0.997180i	$0.523912\pi$
$684$		0			0
$685$	−2.53437			−0.0968332
$686$		0			0
$687$	4.20751	−	7.28763i	0.160527	−	0.278040i
$688$		0			0
$689$	−11.0035	+	19.0587i	−0.419201	+	0.726078i
$690$		0			0
$691$	1.65685			0.0630297			0.0315149	−	0.999503i	$-0.489967\pi$
$691$	1.65685			0.0630297			0.0315149	+	0.999503i	$0.489967\pi$
$692$		0			0
$693$	9.83729	+	17.0387i	0.373688	+	0.647246i
$694$		0			0
$695$	−7.90611			−0.299896
$696$		0			0
$697$	−16.5459	−	28.6584i	−0.626721	−	1.08551i
$698$		0			0
$699$	−1.51512	−	2.62427i	−0.0573073	−	0.0992591i
$700$		0			0
$701$	3.23551	−	5.60406i	0.122203	−	0.211662i	−0.798433	−	0.602084i	$-0.794337\pi$
$701$	3.23551	−	5.60406i	0.122203	−	0.211662i	0.920636	+	0.390421i	$0.127671\pi$
$702$		0			0
$703$	−1.33270	+	0.162885i	−0.0502638	+	0.00614333i
$704$		0			0
$705$	3.29218	−	5.70222i	0.123991	−	0.214758i
$706$		0			0
$707$	13.3014	+	23.0387i	0.500251	+	0.866459i
$708$		0			0
$709$	21.1975	+	36.7151i	0.796087	+	1.37886i	0.922146	+	0.386841i	$0.126434\pi$
$709$	21.1975	+	36.7151i	0.796087	+	1.37886i	−0.126059	+	0.992023i	$0.540233\pi$
$710$		0			0
$711$	16.8752			0.632871
$712$		0			0
$713$	−46.3944	−	80.3574i	−1.73748	−	3.00941i
$714$		0			0
$715$	−19.6043			−0.733160
$716$		0			0
$717$	−1.51012	+	2.61561i	−0.0563965	+	0.0976816i
$718$		0			0
$719$	−9.08590	+	15.7372i	−0.338847	+	0.586900i	−0.984216	−	0.176971i	$-0.943370\pi$
$719$	−9.08590	+	15.7372i	−0.338847	+	0.586900i	0.645369	+	0.763871i	$0.276703\pi$
$720$		0			0
$721$	31.6544			1.17887
$722$		0			0
$723$	1.65318			0.0614826
$724$		0			0
$725$	17.8357	−	30.8923i	0.662401	−	1.14731i
$726$		0			0
$727$	5.21746	−	9.03691i	0.193505	−	0.335160i	−0.752904	−	0.658130i	$-0.771348\pi$
$727$	5.21746	−	9.03691i	0.193505	−	0.335160i	0.946409	+	0.322969i	$0.104681\pi$
$728$		0			0
$729$	−18.1716			−0.673021
$730$		0			0
$731$	−31.0005	−	53.6944i	−1.14659	−	1.98596i
$732$		0			0
$733$	24.6625			0.910932			0.455466	−	0.890253i	$-0.349473\pi$
$733$	24.6625			0.910932			0.455466	+	0.890253i	$0.349473\pi$
$734$		0			0
$735$	1.89085	+	3.27505i	0.0697450	+	0.120802i
$736$		0			0
$737$	8.45932	+	14.6520i	0.311603	+	0.539712i
$738$		0			0
$739$	−14.9259	+	25.8524i	−0.549058	+	0.950996i	0.449282	+	0.893390i	$0.351680\pi$
$739$	−14.9259	+	25.8524i	−0.549058	+	0.950996i	−0.998339	+	0.0576057i	$0.981653\pi$
$740$		0			0
$741$	4.92324	−	0.601727i	0.180860	−	0.0221050i
$742$		0			0
$743$	8.10405	−	14.0366i	0.297309	−	0.514954i	−0.678210	−	0.734868i	$-0.737244\pi$
$743$	8.10405	−	14.0366i	0.297309	−	0.514954i	0.975519	+	0.219914i	$0.0705776\pi$
$744$		0			0
$745$	15.3495	+	26.5861i	0.562362	+	0.974040i
$746$		0			0
$747$	−9.17922	−	15.8989i	−0.335850	−	0.581710i
$748$		0			0
$749$	45.7868			1.67301
$750$		0			0
$751$	−2.42220	−	4.19538i	−0.0883875	−	0.153092i	0.818442	−	0.574589i	$-0.194838\pi$
$751$	−2.42220	−	4.19538i	−0.0883875	−	0.153092i	−0.906830	+	0.421497i	$0.861505\pi$
$752$		0			0
$753$	−0.0996931			−0.00363302
$754$		0			0
$755$	−22.2751	+	38.5817i	−0.810675	+	1.40413i
$756$		0			0
$757$	−9.82512	+	17.0176i	−0.357100	+	0.618515i	−0.987475	−	0.157775i	$-0.949568\pi$
$757$	−9.82512	+	17.0176i	−0.357100	+	0.618515i	0.630375	+	0.776291i	$0.282901\pi$
$758$		0			0
$759$	7.89747			0.286660
$760$		0			0
$761$	30.5702			1.10817			0.554085	−	0.832460i	$-0.313068\pi$
$761$	30.5702			1.10817			0.554085	+	0.832460i	$0.313068\pi$
$762$		0			0
$763$	−9.88697	+	17.1247i	−0.357932	+	0.619957i
$764$		0			0
$765$	−32.6859	+	56.6136i	−1.18176	+	2.04687i
$766$		0			0
$767$	5.55290			0.200504
$768$		0			0
$769$	−12.9284	−	22.3926i	−0.466210	−	0.807499i	0.533045	−	0.846087i	$-0.321047\pi$
$769$	−12.9284	−	22.3926i	−0.466210	−	0.807499i	−0.999255	+	0.0385875i	$0.987714\pi$
$770$		0			0
$771$	3.87925			0.139708
$772$		0			0
$773$	−16.2326	−	28.1157i	−0.583846	−	1.01125i	−0.995018	−	0.0996927i	$-0.968214\pi$
$773$	−16.2326	−	28.1157i	−0.583846	−	1.01125i	0.411173	−	0.911557i	$-0.365119\pi$
$774$		0			0
$775$	−28.8950	−	50.0476i	−1.03794	−	1.79776i
$776$		0			0
$777$	−0.200082	+	0.346552i	−0.00717790	+	0.0124325i
$778$		0			0
$779$	−7.85699	+	18.4814i	−0.281506	+	0.662166i
$780$		0			0
$781$	10.7382	−	18.5991i	0.384243	−	0.665529i
$782$		0			0
$783$	8.04206	+	13.9293i	0.287400	+	0.497791i
$784$		0			0
$785$	8.40723	+	14.5618i	0.300067	+	0.519731i
$786$		0			0
$787$	22.6534			0.807507			0.403753	−	0.914868i	$-0.367705\pi$
$787$	22.6534			0.807507			0.403753	+	0.914868i	$0.367705\pi$
$788$		0			0
$789$	1.96517	+	3.40377i	0.0699618	+	0.121177i
$790$		0			0
$791$	63.0815			2.24292
$792$		0			0
$793$	−2.14402	+	3.71354i	−0.0761362	+	0.131872i
$794$		0			0
$795$	5.33883	−	9.24712i	0.189349	−	0.327961i
$796$		0			0
$797$	2.55181			0.0903896			0.0451948	−	0.998978i	$-0.485609\pi$
$797$	2.55181			0.0903896			0.0451948	+	0.998978i	$0.485609\pi$
$798$		0			0
$799$	−35.4826			−1.25529
$800$		0			0
$801$	−2.15783	+	3.73748i	−0.0762433	+	0.132057i
$802$		0			0
$803$	10.7658	−	18.6468i	0.379915	−	0.658033i
$804$		0			0
$805$	−86.7637			−3.05802
$806$		0			0
$807$	−5.58147	−	9.66738i	−0.196477	−	0.340308i
$808$		0			0
$809$	36.8734			1.29640			0.648201	−	0.761470i	$-0.275522\pi$
$809$	36.8734			1.29640			0.648201	+	0.761470i	$0.275522\pi$
$810$		0			0
$811$	1.25949	+	2.18150i	0.0442267	+	0.0766029i	0.887291	−	0.461209i	$-0.152584\pi$
$811$	1.25949	+	2.18150i	0.0442267	+	0.0766029i	−0.843065	+	0.537812i	$0.819251\pi$
$812$		0			0
$813$	1.26718	+	2.19483i	0.0444421	+	0.0769759i
$814$		0			0
$815$	−15.4483	+	26.7572i	−0.541130	+	0.937265i
$816$		0			0
$817$	−14.7209	+	34.6268i	−0.515018	+	1.21144i
$818$		0			0
$819$	−12.1849	+	21.1049i	−0.425775	+	0.737465i
$820$		0			0
$821$	2.27642	+	3.94287i	0.0794476	+	0.137607i	0.903012	−	0.429616i	$-0.141351\pi$
$821$	2.27642	+	3.94287i	0.0794476	+	0.137607i	−0.823564	+	0.567223i	$0.808018\pi$
$822$		0			0
$823$	1.43594	+	2.48712i	0.0500538	+	0.0866957i	0.889967	−	0.456025i	$-0.150727\pi$
$823$	1.43594	+	2.48712i	0.0500538	+	0.0866957i	−0.839913	+	0.542721i	$0.817394\pi$
$824$		0			0
$825$	4.91864			0.171245
$826$		0			0
$827$	−13.4097	−	23.2264i	−0.466302	−	0.807659i	0.532957	−	0.846142i	$-0.321081\pi$
$827$	−13.4097	−	23.2264i	−0.466302	−	0.807659i	−0.999259	+	0.0384830i	$0.987747\pi$
$828$		0			0
$829$	−35.8817			−1.24622			−0.623111	−	0.782133i	$-0.714132\pi$
$829$	−35.8817			−1.24622			−0.623111	+	0.782133i	$0.714132\pi$
$830$		0			0
$831$	1.87826	−	3.25324i	0.0651562	−	0.112854i
$832$		0			0
$833$	10.1897	−	17.6490i	0.353051	−	0.611501i
$834$		0			0
$835$	31.8657			1.10276
$836$		0			0
$837$	26.0573			0.900673
$838$		0			0
$839$	−14.3309	+	24.8219i	−0.494759	+	0.856947i	−0.999982	−	0.00604151i	$-0.998077\pi$
$839$	−14.3309	+	24.8219i	−0.494759	+	0.856947i	0.505223	+	0.862989i	$0.331410\pi$
$840$		0			0
$841$	−7.69288	+	13.3245i	−0.265272	+	0.459464i
$842$		0			0
$843$	6.87325			0.236727
$844$		0			0
$845$	8.77431	+	15.1975i	0.301845	+	0.522811i
$846$		0			0
$847$	19.0738			0.655385
$848$		0			0
$849$	3.63847	+	6.30201i	0.124872	+	0.216284i
$850$		0			0
$851$	−1.32400	−	2.29323i	−0.0453860	−	0.0786109i
$852$		0			0
$853$	−27.1924	+	47.0987i	−0.931051	+	1.61263i	−0.149522	+	0.988758i	$0.547773\pi$
$853$	−27.1924	+	47.0987i	−0.931051	+	1.61263i	−0.781529	+	0.623869i	$0.785560\pi$
$854$		0			0
$855$	39.3787	−	4.81293i	1.34672	−	0.164599i
$856$		0			0
$857$	9.30847	−	16.1227i	0.317971	−	0.550742i	−0.662093	−	0.749421i	$-0.730332\pi$
$857$	9.30847	−	16.1227i	0.317971	−	0.550742i	0.980065	+	0.198679i	$0.0636651\pi$
$858$		0			0
$859$	−18.5174	−	32.0730i	−0.631804	−	1.09432i	−0.987183	−	0.159595i	$-0.948981\pi$
$859$	−18.5174	−	32.0730i	−0.631804	−	1.09432i	0.355378	−	0.934723i	$-0.384352\pi$
$860$		0			0
$861$	2.99272	+	5.18355i	0.101992	+	0.176655i
$862$		0			0
$863$	−24.7053			−0.840979			−0.420490	−	0.907297i	$-0.638142\pi$
$863$	−24.7053			−0.840979			−0.420490	+	0.907297i	$0.638142\pi$
$864$		0			0
$865$	−6.45346	−	11.1777i	−0.219424	−	0.380054i
$866$		0			0
$867$	−14.3280			−0.486604
$868$		0			0
$869$	−6.61604	+	11.4593i	−0.224434	+	0.388730i
$870$		0			0
$871$	−10.4781	+	18.1486i	−0.355037	+	0.614942i
$872$		0			0
$873$	−15.2337			−0.515582
$874$		0			0
$875$	−3.57522			−0.120864
$876$		0			0
$877$	−22.6668	+	39.2600i	−0.765402	+	1.32572i	0.174632	+	0.984634i	$0.444127\pi$
$877$	−22.6668	+	39.2600i	−0.765402	+	1.32572i	−0.940034	+	0.341082i	$0.889207\pi$
$878$		0			0
$879$	−4.98244	+	8.62983i	−0.168053	+	0.291077i
$880$		0			0
$881$	−0.632076			−0.0212952			−0.0106476	−	0.999943i	$-0.503389\pi$
$881$	−0.632076			−0.0212952			−0.0106476	+	0.999943i	$0.503389\pi$
$882$		0			0
$883$	27.1308	+	46.9919i	0.913023	+	1.58140i	0.809770	+	0.586747i	$0.199592\pi$
$883$	27.1308	+	46.9919i	0.913023	+	1.58140i	0.103252	+	0.994655i	$0.467075\pi$
$884$		0			0
$885$	−2.69422			−0.0905653
$886$		0			0
$887$	17.9061	+	31.0142i	0.601227	+	1.04135i	0.992636	+	0.121138i	$0.0386544\pi$
$887$	17.9061	+	31.0142i	0.601227	+	1.04135i	−0.391409	+	0.920217i	$0.628012\pi$
$888$		0			0
$889$	−3.01651	−	5.22475i	−0.101171	−	0.175232i
$890$		0			0
$891$	8.30043	−	14.3768i	0.278075	−	0.481640i
$892$		0			0
$893$	12.9494	+	17.2043i	0.433335	+	0.575719i
$894$		0			0
$895$	−5.37324	+	9.30672i	−0.179608	+	0.311089i
$896$		0			0
$897$	4.89109	+	8.47161i	0.163309	+	0.282859i
$898$		0			0
$899$	35.9539	+	62.2740i	1.19913	+	2.07695i
$900$		0			0
$901$	−57.5411			−1.91697
$902$		0			0
$903$	5.60718	+	9.71191i	0.186595	+	0.323192i
$904$		0			0
$905$	59.9852			1.99398
$906$		0			0
$907$	23.1300	−	40.0623i	0.768017	−	1.33025i	−0.170619	−	0.985337i	$-0.554577\pi$
$907$	23.1300	−	40.0623i	0.768017	−	1.33025i	0.938636	−	0.344908i	$-0.112090\pi$
$908$		0			0
$909$	11.9951	−	20.7762i	0.397853	−	0.689102i
$910$		0			0
$911$	11.0416			0.365824			0.182912	−	0.983129i	$-0.441448\pi$
$911$	11.0416			0.365824			0.182912	+	0.983129i	$0.441448\pi$
$912$		0			0
$913$	14.3951			0.476407
$914$		0			0
$915$	1.04026	−	1.80178i	0.0343899	−	0.0595651i
$916$		0			0
$917$	2.05891	−	3.56614i	0.0679913	−	0.117764i
$918$		0			0
$919$	35.2252			1.16197			0.580986	−	0.813914i	$-0.302667\pi$
$919$	35.2252			1.16197			0.580986	+	0.813914i	$0.302667\pi$
$920$		0			0
$921$	−4.09263	−	7.08864i	−0.134857	−	0.233578i
$922$		0			0
$923$	26.6017			0.875605
$924$		0			0
$925$	−0.824602	−	1.42825i	−0.0271127	−	0.0469606i
$926$		0			0
$927$	−14.2729	−	24.7214i	−0.468783	−	0.811956i
$928$		0			0
$929$	12.6827	−	21.9670i	0.416105	−	0.720715i	−0.579439	−	0.815016i	$-0.696728\pi$
$929$	12.6827	−	21.9670i	0.416105	−	0.720715i	0.995544	+	0.0943008i	$0.0300615\pi$
$930$		0			0
$931$	−12.2761	+	1.50041i	−0.402333	+	0.0491738i
$932$		0			0
$933$	−3.56965	+	6.18282i	−0.116865	+	0.202416i
$934$		0			0
$935$	−25.6294	−	44.3914i	−0.838170	−	1.45175i
$936$		0			0
$937$	14.8951	+	25.7990i	0.486601	+	0.842817i	0.999881	−	0.0154038i	$-0.00490339\pi$
$937$	14.8951	+	25.7990i	0.486601	+	0.842817i	−0.513281	+	0.858221i	$0.671570\pi$
$938$		0			0
$939$	−4.10936			−0.134104
$940$		0			0
$941$	−17.7327	−	30.7139i	−0.578068	−	1.00124i	−0.995701	−	0.0926275i	$-0.970473\pi$
$941$	−17.7327	−	30.7139i	−0.578068	−	1.00124i	0.417633	−	0.908616i	$-0.362860\pi$
$942$		0			0
$943$	−39.6074			−1.28979
$944$		0			0
$945$	12.1827	−	21.1010i	0.396302	−	0.686416i
$946$		0			0
$947$	9.00995	−	15.6057i	0.292784	−	0.507117i	−0.681683	−	0.731648i	$-0.738752\pi$
$947$	9.00995	−	15.6057i	0.292784	−	0.507117i	0.974467	+	0.224531i	$0.0720850\pi$
$948$		0			0
$949$	26.6699			0.865742
$950$		0			0
$951$	7.73333			0.250770
$952$		0			0
$953$	−7.19963	+	12.4701i	−0.233219	+	0.403947i	−0.958754	−	0.284239i	$-0.908259\pi$
$953$	−7.19963	+	12.4701i	−0.233219	+	0.403947i	0.725535	+	0.688186i	$0.241593\pi$
$954$		0			0
$955$	12.8712	−	22.2936i	0.416502	−	0.721403i
$956$		0			0
$957$	−6.12025			−0.197839
$958$		0			0
$959$	−1.23515	−	2.13933i	−0.0398849	−	0.0690827i
$960$		0			0
$961$	85.4953			2.75791
$962$		0			0
$963$	−20.6451	−	35.7584i	−0.665280	−	1.15230i
$964$		0			0
$965$	22.3937	+	38.7871i	0.720879	+	1.24860i
$966$		0			0
$967$	13.2010	−	22.8647i	0.424514	−	0.735280i	−0.571861	−	0.820351i	$-0.693778\pi$
$967$	13.2010	−	22.8647i	0.424514	−	0.735280i	0.996375	+	0.0850708i	$0.0271116\pi$
$968$		0			0
$969$	7.79885	+	10.3614i	0.250535	+	0.332855i
$970$		0			0
$971$	−13.3912	+	23.1943i	−0.429744	+	0.744339i	−0.996850	−	0.0793058i	$-0.974730\pi$
$971$	−13.3912	+	23.1943i	−0.429744	+	0.744339i	0.567106	+	0.823645i	$0.308063\pi$
$972$		0			0
$973$	−3.85311	−	6.67378i	−0.123525	−	0.213952i
$974$		0			0
$975$	3.04623	+	5.27622i	0.0975574	+	0.168974i
$976$		0			0
$977$	−38.2049			−1.22228			−0.611141	−	0.791522i	$-0.709289\pi$
$977$	−38.2049			−1.22228			−0.611141	+	0.791522i	$0.709289\pi$
$978$		0			0
$979$	−1.69198	−	2.93060i	−0.0540760	−	0.0936624i
$980$		0			0
$981$	17.8320			0.569332
$982$		0			0
$983$	−6.49327	+	11.2467i	−0.207103	+	0.358713i	−0.950801	−	0.309803i	$-0.899737\pi$
$983$	−6.49327	+	11.2467i	−0.207103	+	0.358713i	0.743698	+	0.668516i	$0.233070\pi$
$984$		0			0
$985$	3.27432	−	5.67129i	0.104328	−	0.180702i
$986$		0			0
$987$	6.41788			0.204283
$988$		0			0
$989$	−74.2085			−2.35969
$990$		0			0
$991$	11.0328	−	19.1094i	0.350469	−	0.607031i	−0.635862	−	0.771802i	$-0.719355\pi$
$991$	11.0328	−	19.1094i	0.350469	−	0.607031i	0.986332	+	0.164772i	$0.0526887\pi$
$992$		0			0
$993$	−4.91550	+	8.51390i	−0.155989	+	0.270180i
$994$		0			0
$995$	27.9360			0.885630
$996$		0			0
$997$	−7.61655	−	13.1923i	−0.241219	−	0.417803i	0.719843	−	0.694137i	$-0.244214\pi$
$997$	−7.61655	−	13.1923i	−0.241219	−	0.417803i	−0.961062	+	0.276334i	$0.910880\pi$
$998$		0			0
$999$	0.743621			0.0235271

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.i.o.961.3		8
4.3	odd	2		1216.2.i.q.961.1		8
8.3	odd	2		608.2.i.c.353.4	✓	8
8.5	even	2		608.2.i.e.353.2	yes	8
19.7	even	3	inner	1216.2.i.o.577.3		8
76.7	odd	6		1216.2.i.q.577.1		8
152.45	even	6		608.2.i.e.577.2	yes	8
152.83	odd	6		608.2.i.c.577.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
608.2.i.c.353.4	✓	8	8.3	odd	2
608.2.i.c.577.4	yes	8	152.83	odd	6
608.2.i.e.353.2	yes	8	8.5	even	2
608.2.i.e.577.2	yes	8	152.45	even	6
1216.2.i.o.577.3		8	19.7	even	3	inner
1216.2.i.o.961.3		8	1.1	even	1	trivial
1216.2.i.q.577.1		8	76.7	odd	6
1216.2.i.q.961.1		8	4.3	odd	2

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:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.207107 - 0.358719i) q^{3} +(-1.60890 + 2.78670i) q^{5} -3.13644 q^{7} +(1.41421 + 2.44949i) q^{9} +O(q^{10})\)	\(q+(0.207107 - 0.358719i) q^{3} +(-1.60890 + 2.78670i) q^{5} -3.13644 q^{7} +(1.41421 + 2.44949i) q^{9} -2.21780 q^{11} +(-1.37354 - 2.37903i) q^{13} +(0.666429 + 1.15429i) q^{15} +(3.59134 - 6.22038i) q^{17} +(-4.32670 + 0.528817i) q^{19} +(-0.649579 + 1.12510i) q^{21} +(-4.29844 - 7.44512i) q^{23} +(-2.67712 - 4.63691i) q^{25} +2.41421 q^{27} +(3.33113 + 5.76969i) q^{29} +10.7933 q^{31} +(-0.459322 + 0.795569i) q^{33} +(5.04623 - 8.74032i) q^{35} +0.308018 q^{37} -1.13787 q^{39} +(2.30359 - 3.98993i) q^{41} +(4.31601 - 7.47554i) q^{43} -9.10132 q^{45} +(-2.47002 - 4.27819i) q^{47} +2.83729 q^{49} +(-1.48758 - 2.57656i) q^{51} +(-4.00555 - 6.93782i) q^{53} +(3.56822 - 6.18034i) q^{55} +(-0.706392 + 1.66159i) q^{57} +(-1.01069 + 1.75057i) q^{59} +(-0.780474 - 1.35182i) q^{61} +(-4.43560 - 7.68269i) q^{63} +8.83953 q^{65} +(-3.81428 - 6.60653i) q^{67} -3.56095 q^{69} +(-4.84183 + 8.38629i) q^{71} +(-4.85425 + 8.40780i) q^{73} -2.21780 q^{75} +6.95601 q^{77} +(2.98315 - 5.16697i) q^{79} +(-3.74264 + 6.48244i) q^{81} -6.49069 q^{83} +(11.5562 + 20.0159i) q^{85} +2.75960 q^{87} +(0.762910 + 1.32140i) q^{89} +(4.30802 + 7.46171i) q^{91} +(2.23537 - 3.87177i) q^{93} +(5.48758 - 12.9080i) q^{95} +(-2.69296 + 4.66435i) q^{97} +(-3.13644 - 5.43248i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 2 q^{5} - 8 q^{7}+O(q^{10}) \) 8 * q - 4 * q^3 - 2 * q^5 - 8 * q^7	\( 8 q - 4 q^{3} - 2 q^{5} - 8 q^{7} + 4 q^{11} - 2 q^{13} + 2 q^{15} - 2 q^{17} - 2 q^{19} + 8 q^{21} + 2 q^{23} - 2 q^{25} + 8 q^{27} + 10 q^{29} + 24 q^{31} - 6 q^{33} - 4 q^{35} + 8 q^{37} - 12 q^{39} + 8 q^{41} + 18 q^{43} - 16 q^{45} - 6 q^{47} + 32 q^{49} - 18 q^{51} + 10 q^{53} + 20 q^{55} + 10 q^{57} + 8 q^{59} - 18 q^{61} + 8 q^{63} - 36 q^{65} - 4 q^{67} - 52 q^{69} - 6 q^{71} + 4 q^{75} - 16 q^{77} + 14 q^{79} + 4 q^{81} + 4 q^{83} + 22 q^{85} - 60 q^{87} - 2 q^{89} + 40 q^{91} + 16 q^{93} + 50 q^{95} - 12 q^{97} - 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 - 2 * q^5 - 8 * q^7 + 4 * q^11 - 2 * q^13 + 2 * q^15 - 2 * q^17 - 2 * q^19 + 8 * q^21 + 2 * q^23 - 2 * q^25 + 8 * q^27 + 10 * q^29 + 24 * q^31 - 6 * q^33 - 4 * q^35 + 8 * q^37 - 12 * q^39 + 8 * q^41 + 18 * q^43 - 16 * q^45 - 6 * q^47 + 32 * q^49 - 18 * q^51 + 10 * q^53 + 20 * q^55 + 10 * q^57 + 8 * q^59 - 18 * q^61 + 8 * q^63 - 36 * q^65 - 4 * q^67 - 52 * q^69 - 6 * q^71 + 4 * q^75 - 16 * q^77 + 14 * q^79 + 4 * q^81 + 4 * q^83 + 22 * q^85 - 60 * q^87 - 2 * q^89 + 40 * q^91 + 16 * q^93 + 50 * q^95 - 12 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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