LMFDB - Embedded newform 273.2.p.b.34.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(34,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("273.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.p (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 25 $ x^4 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			34.2
Root			$1.58114 - 1.58114i$ of defining polynomial
Character	$\chi$	$=$	273.34
Dual form			273.2.p.b.265.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{3} -2.00000i q^{4} +(0.581139 - 0.581139i) q^{5} +(0.581139 + 2.58114i) q^{7} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{3} -2.00000i q^{4} +(0.581139 - 0.581139i) q^{5} +(0.581139 + 2.58114i) q^{7} -1.00000 q^{9} +(4.16228 - 4.16228i) q^{11} +2.00000 q^{12} +(3.58114 + 0.418861i) q^{13} +(0.581139 + 0.581139i) q^{15} -4.00000 q^{16} +1.16228 q^{17} +(0.418861 - 0.418861i) q^{19} +(-1.16228 - 1.16228i) q^{20} +(-2.58114 + 0.581139i) q^{21} -4.16228i q^{23} +4.32456i q^{25} -1.00000i q^{27} +(5.16228 - 1.16228i) q^{28} +1.83772 q^{29} +(-5.58114 + 5.58114i) q^{31} +(4.16228 + 4.16228i) q^{33} +(1.83772 + 1.16228i) q^{35} +2.00000i q^{36} +(4.32456 - 4.32456i) q^{37} +(-0.418861 + 3.58114i) q^{39} +(-7.16228 + 7.16228i) q^{41} +5.32456i q^{43} +(-8.32456 - 8.32456i) q^{44} +(-0.581139 + 0.581139i) q^{45} +(-6.58114 - 6.58114i) q^{47} -4.00000i q^{48} +(-6.32456 + 3.00000i) q^{49} +1.16228i q^{51} +(0.837722 - 7.16228i) q^{52} -4.16228 q^{53} -4.83772i q^{55} +(0.418861 + 0.418861i) q^{57} +(-8.32456 - 8.32456i) q^{59} +(1.16228 - 1.16228i) q^{60} +3.16228i q^{61} +(-0.581139 - 2.58114i) q^{63} +8.00000i q^{64} +(2.32456 - 1.83772i) q^{65} +(-6.32456 - 6.32456i) q^{67} -2.32456i q^{68} +4.16228 q^{69} +(6.00000 + 6.00000i) q^{71} +(5.58114 + 5.58114i) q^{73} -4.32456 q^{75} +(-0.837722 - 0.837722i) q^{76} +(13.1623 + 8.32456i) q^{77} -11.3246 q^{79} +(-2.32456 + 2.32456i) q^{80} +1.00000 q^{81} +(-6.58114 + 6.58114i) q^{83} +(1.16228 + 5.16228i) q^{84} +(0.675445 - 0.675445i) q^{85} +1.83772i q^{87} +(-5.41886 - 5.41886i) q^{89} +(1.00000 + 9.48683i) q^{91} -8.32456 q^{92} +(-5.58114 - 5.58114i) q^{93} -0.486833i q^{95} +(-0.418861 + 0.418861i) q^{97} +(-4.16228 + 4.16228i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^5 - 4 * q^7 - 4 * q^9	$ 4 q - 4 q^{5} - 4 q^{7} - 4 q^{9} + 4 q^{11} + 8 q^{12} + 8 q^{13} - 4 q^{15} - 16 q^{16} - 8 q^{17} + 8 q^{19} + 8 q^{20} - 4 q^{21} + 8 q^{28} + 20 q^{29} - 16 q^{31} + 4 q^{33} + 20 q^{35} - 8 q^{37} - 8 q^{39} - 16 q^{41} - 8 q^{44} + 4 q^{45} - 20 q^{47} + 16 q^{52} - 4 q^{53} + 8 q^{57} - 8 q^{59} - 8 q^{60} + 4 q^{63} - 16 q^{65} + 4 q^{69} + 24 q^{71} + 16 q^{73} + 8 q^{75} - 16 q^{76} + 40 q^{77} - 20 q^{79} + 16 q^{80} + 4 q^{81} - 20 q^{83} - 8 q^{84} + 28 q^{85} - 28 q^{89} + 4 q^{91} - 8 q^{92} - 16 q^{93} - 8 q^{97} - 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^5 - 4 * q^7 - 4 * q^9 + 4 * q^11 + 8 * q^12 + 8 * q^13 - 4 * q^15 - 16 * q^16 - 8 * q^17 + 8 * q^19 + 8 * q^20 - 4 * q^21 + 8 * q^28 + 20 * q^29 - 16 * q^31 + 4 * q^33 + 20 * q^35 - 8 * q^37 - 8 * q^39 - 16 * q^41 - 8 * q^44 + 4 * q^45 - 20 * q^47 + 16 * q^52 - 4 * q^53 + 8 * q^57 - 8 * q^59 - 8 * q^60 + 4 * q^63 - 16 * q^65 + 4 * q^69 + 24 * q^71 + 16 * q^73 + 8 * q^75 - 16 * q^76 + 40 * q^77 - 20 * q^79 + 16 * q^80 + 4 * q^81 - 20 * q^83 - 8 * q^84 + 28 * q^85 - 28 * q^89 + 4 * q^91 - 8 * q^92 - 16 * q^93 - 8 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$2$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$		−	2.00000i		−	1.00000i
$5$	0.581139	−	0.581139i	0.259893	−	0.259893i	−0.565117	−	0.825011i	$-0.691169\pi$
$5$	0.581139	−	0.581139i	0.259893	−	0.259893i	0.825011	+	0.565117i	$0.191169\pi$
$6$		0			0
$7$	0.581139	+	2.58114i	0.219650	+	0.975579i
$7$	0.581139	+	2.58114i	0.219650	+	0.975579i
$8$		0			0
$9$	−1.00000			−0.333333
$10$		0			0
$11$	4.16228	−	4.16228i	1.25497	−	1.25497i	0.301511	−	0.953463i	$-0.402509\pi$
$11$	4.16228	−	4.16228i	1.25497	−	1.25497i	0.953463	−	0.301511i	$-0.0974911\pi$
$12$	2.00000			0.577350
$13$	3.58114	+	0.418861i	0.993229	+	0.116171i
$13$	3.58114	+	0.418861i	0.993229	+	0.116171i
$14$		0			0
$15$	0.581139	+	0.581139i	0.150049	+	0.150049i
$16$	−4.00000			−1.00000
$17$	1.16228			0.281894			0.140947	−	0.990017i	$-0.454985\pi$
$17$	1.16228			0.281894			0.140947	+	0.990017i	$0.454985\pi$
$18$		0			0
$19$	0.418861	−	0.418861i	0.0960933	−	0.0960933i	−0.657426	−	0.753519i	$-0.728355\pi$
$19$	0.418861	−	0.418861i	0.0960933	−	0.0960933i	0.753519	+	0.657426i	$0.228355\pi$
$20$	−1.16228	−	1.16228i	−0.259893	−	0.259893i
$21$	−2.58114	+	0.581139i	−0.563251	+	0.126815i
$22$		0			0
$23$		−	4.16228i		−	0.867895i	−0.900938	−	0.433947i	$-0.857120\pi$
$23$		−	4.16228i		−	0.867895i	0.900938	−	0.433947i	$-0.142880\pi$
$24$		0			0
$25$			4.32456i			0.864911i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$	5.16228	−	1.16228i	0.975579	−	0.219650i
$29$	1.83772			0.341256			0.170628	−	0.985335i	$-0.445420\pi$
$29$	1.83772			0.341256			0.170628	+	0.985335i	$0.445420\pi$
$30$		0			0
$31$	−5.58114	+	5.58114i	−1.00240	+	1.00240i	−0.00240502	+	0.999997i	$0.500766\pi$
$31$	−5.58114	+	5.58114i	−1.00240	+	1.00240i	−0.999997	+	0.00240502i	$0.999234\pi$
$32$		0			0
$33$	4.16228	+	4.16228i	0.724560	+	0.724560i
$34$		0			0
$35$	1.83772	+	1.16228i	0.310632	+	0.196461i
$36$			2.00000i			0.333333i
$37$	4.32456	−	4.32456i	0.710953	−	0.710953i	−0.255782	−	0.966734i	$-0.582333\pi$
$37$	4.32456	−	4.32456i	0.710953	−	0.710953i	0.966734	+	0.255782i	$0.0823329\pi$
$38$		0			0
$39$	−0.418861	+	3.58114i	−0.0670715	+	0.573441i
$40$		0			0
$41$	−7.16228	+	7.16228i	−1.11856	+	1.11856i	−0.126607	+	0.991953i	$0.540409\pi$
$41$	−7.16228	+	7.16228i	−1.11856	+	1.11856i	−0.991953	+	0.126607i	$0.959591\pi$
$42$		0			0
$43$			5.32456i			0.811987i	0.913876	+	0.405994i	$0.133074\pi$
$43$			5.32456i			0.811987i	−0.913876	+	0.405994i	$0.866926\pi$
$44$	−8.32456	−	8.32456i	−1.25497	−	1.25497i
$45$	−0.581139	+	0.581139i	−0.0866311	+	0.0866311i
$46$		0			0
$47$	−6.58114	−	6.58114i	−0.959958	−	0.959958i	0.0392708	−	0.999229i	$-0.487496\pi$
$47$	−6.58114	−	6.58114i	−0.959958	−	0.959958i	−0.999229	+	0.0392708i	$0.987496\pi$
$48$		−	4.00000i		−	0.577350i
$49$	−6.32456	+	3.00000i	−0.903508	+	0.428571i
$50$		0			0
$51$			1.16228i			0.162751i
$52$	0.837722	−	7.16228i	0.116171	−	0.993229i
$53$	−4.16228			−0.571733			−0.285866	−	0.958269i	$-0.592281\pi$
$53$	−4.16228			−0.571733			−0.285866	+	0.958269i	$0.592281\pi$
$54$		0			0
$55$		−	4.83772i		−	0.652318i
$56$		0			0
$57$	0.418861	+	0.418861i	0.0554795	+	0.0554795i
$58$		0			0
$59$	−8.32456	−	8.32456i	−1.08376	−	1.08376i	−0.996155	−	0.0876099i	$-0.972077\pi$
$59$	−8.32456	−	8.32456i	−1.08376	−	1.08376i	−0.0876099	−	0.996155i	$-0.527923\pi$
$60$	1.16228	−	1.16228i	0.150049	−	0.150049i
$61$			3.16228i			0.404888i	0.979294	+	0.202444i	$0.0648884\pi$
$61$			3.16228i			0.404888i	−0.979294	+	0.202444i	$0.935112\pi$
$62$		0			0
$63$	−0.581139	−	2.58114i	−0.0732166	−	0.325193i
$64$			8.00000i			1.00000i
$65$	2.32456	−	1.83772i	0.288326	−	0.227941i
$66$		0			0
$67$	−6.32456	−	6.32456i	−0.772667	−	0.772667i	0.205905	−	0.978572i	$-0.433986\pi$
$67$	−6.32456	−	6.32456i	−0.772667	−	0.772667i	−0.978572	+	0.205905i	$0.933986\pi$
$68$		−	2.32456i		−	0.281894i
$69$	4.16228			0.501079
$70$		0			0
$71$	6.00000	+	6.00000i	0.712069	+	0.712069i	0.966968	−	0.254899i	$-0.0820421\pi$
$71$	6.00000	+	6.00000i	0.712069	+	0.712069i	−0.254899	+	0.966968i	$0.582042\pi$
$72$		0			0
$73$	5.58114	+	5.58114i	0.653223	+	0.653223i	0.953768	−	0.300545i	$-0.0971685\pi$
$73$	5.58114	+	5.58114i	0.653223	+	0.653223i	−0.300545	+	0.953768i	$0.597168\pi$
$74$		0			0
$75$	−4.32456			−0.499357
$76$	−0.837722	−	0.837722i	−0.0960933	−	0.0960933i
$77$	13.1623	+	8.32456i	1.49998	+	0.948671i
$78$		0			0
$79$	−11.3246			−1.27411			−0.637056	−	0.770818i	$-0.719848\pi$
$79$	−11.3246			−1.27411			−0.637056	+	0.770818i	$0.719848\pi$
$80$	−2.32456	+	2.32456i	−0.259893	+	0.259893i
$81$	1.00000			0.111111
$82$		0			0
$83$	−6.58114	+	6.58114i	−0.722374	+	0.722374i	−0.969088	−	0.246714i	$-0.920649\pi$
$83$	−6.58114	+	6.58114i	−0.722374	+	0.722374i	0.246714	+	0.969088i	$0.420649\pi$
$84$	1.16228	+	5.16228i	0.126815	+	0.563251i
$85$	0.675445	−	0.675445i	0.0732623	−	0.0732623i
$86$		0			0
$87$			1.83772i			0.197025i
$88$		0			0
$89$	−5.41886	−	5.41886i	−0.574398	−	0.574398i	0.358956	−	0.933354i	$-0.383133\pi$
$89$	−5.41886	−	5.41886i	−0.574398	−	0.574398i	−0.933354	+	0.358956i	$0.883133\pi$
$90$		0			0
$91$	1.00000	+	9.48683i	0.104828	+	0.994490i
$92$	−8.32456			−0.867895
$93$	−5.58114	−	5.58114i	−0.578737	−	0.578737i
$94$		0			0
$95$		−	0.486833i		−	0.0499480i
$96$		0			0
$97$	−0.418861	+	0.418861i	−0.0425289	+	0.0425289i	−0.728051	−	0.685523i	$-0.759574\pi$
$97$	−0.418861	+	0.418861i	−0.0425289	+	0.0425289i	0.685523	+	0.728051i	$0.259574\pi$
$98$		0			0
$99$	−4.16228	+	4.16228i	−0.418325	+	0.418325i
$100$	8.64911			0.864911
$101$	17.8114			1.77230			0.886150	−	0.463399i	$-0.153370\pi$
$101$	17.8114			1.77230			0.886150	+	0.463399i	$0.153370\pi$
$102$		0			0
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$		0			0
$105$	−1.16228	+	1.83772i	−0.113427	+	0.179343i
$106$		0			0
$107$	10.6491			1.02949			0.514744	−	0.857344i	$-0.327887\pi$
$107$	10.6491			1.02949			0.514744	+	0.857344i	$0.327887\pi$
$108$	−2.00000			−0.192450
$109$	−2.00000	−	2.00000i	−0.191565	−	0.191565i	0.604807	−	0.796372i	$-0.293250\pi$
$109$	−2.00000	−	2.00000i	−0.191565	−	0.191565i	−0.796372	+	0.604807i	$0.793250\pi$
$110$		0			0
$111$	4.32456	+	4.32456i	0.410469	+	0.410469i
$112$	−2.32456	−	10.3246i	−0.219650	−	0.975579i
$113$	14.8114			1.39334			0.696669	−	0.717393i	$-0.254665\pi$
$113$	14.8114			1.39334			0.696669	+	0.717393i	$0.254665\pi$
$114$		0			0
$115$	−2.41886	−	2.41886i	−0.225560	−	0.225560i
$116$		−	3.67544i		−	0.341256i
$117$	−3.58114	−	0.418861i	−0.331076	−	0.0387237i
$118$		0			0
$119$	0.675445	+	3.00000i	0.0619179	+	0.275010i
$120$		0			0
$121$		−	23.6491i		−	2.14992i
$122$		0			0
$123$	−7.16228	−	7.16228i	−0.645801	−	0.645801i
$124$	11.1623	+	11.1623i	1.00240	+	1.00240i
$125$	5.41886	+	5.41886i	0.484678	+	0.484678i
$126$		0			0
$127$			2.00000i			0.177471i	0.996055	+	0.0887357i	$0.0282826\pi$
$127$			2.00000i			0.177471i	−0.996055	+	0.0887357i	$0.971717\pi$
$128$		0			0
$129$	−5.32456			−0.468801
$130$		0			0
$131$			13.1623i			1.14999i	0.818156	+	0.574997i	$0.194997\pi$
$131$			13.1623i			1.14999i	−0.818156	+	0.574997i	$0.805003\pi$
$132$	8.32456	−	8.32456i	0.724560	−	0.724560i
$133$	1.32456	+	0.837722i	0.114854	+	0.0726397i
$134$		0			0
$135$	−0.581139	−	0.581139i	−0.0500165	−	0.0500165i
$136$		0			0
$137$	−12.0000	+	12.0000i	−1.02523	+	1.02523i	−0.0255558	+	0.999673i	$0.508136\pi$
$137$	−12.0000	+	12.0000i	−1.02523	+	1.02523i	−0.999673	+	0.0255558i	$0.991864\pi$
$138$		0			0
$139$		−	7.16228i		−	0.607496i	−0.952752	−	0.303748i	$-0.901762\pi$
$139$		−	7.16228i		−	0.607496i	0.952752	−	0.303748i	$-0.0982382\pi$
$140$	2.32456	−	3.67544i	0.196461	−	0.310632i
$141$	6.58114	−	6.58114i	0.554232	−	0.554232i
$142$		0			0
$143$	16.6491	−	13.1623i	1.39227	−	1.10068i
$144$	4.00000			0.333333
$145$	1.06797	−	1.06797i	0.0886902	−	0.0886902i
$146$		0			0
$147$	−3.00000	−	6.32456i	−0.247436	−	0.521641i
$148$	−8.64911	−	8.64911i	−0.710953	−	0.710953i
$149$	−10.1623	−	10.1623i	−0.832526	−	0.832526i	0.155336	−	0.987862i	$-0.450354\pi$
$149$	−10.1623	−	10.1623i	−0.832526	−	0.832526i	−0.987862	+	0.155336i	$0.950354\pi$
$150$		0			0
$151$	−4.00000	+	4.00000i	−0.325515	+	0.325515i	−0.850878	−	0.525363i	$-0.823930\pi$
$151$	−4.00000	+	4.00000i	−0.325515	+	0.325515i	0.525363	+	0.850878i	$0.323930\pi$
$152$		0			0
$153$	−1.16228			−0.0939646
$154$		0			0
$155$			6.48683i			0.521035i
$156$	7.16228	+	0.837722i	0.573441	+	0.0670715i
$157$			2.51317i			0.200573i	0.994959	+	0.100286i	$0.0319759\pi$
$157$			2.51317i			0.200573i	−0.994959	+	0.100286i	$0.968024\pi$
$158$		0			0
$159$		−	4.16228i		−	0.330090i
$160$		0			0
$161$	10.7434	−	2.41886i	0.846700	−	0.190633i
$162$		0			0
$163$	−1.32456	+	1.32456i	−0.103747	+	0.103747i	−0.757075	−	0.653328i	$-0.773372\pi$
$163$	−1.32456	+	1.32456i	−0.103747	+	0.103747i	0.653328	+	0.757075i	$0.273372\pi$
$164$	14.3246	+	14.3246i	1.11856	+	1.11856i
$165$	4.83772			0.376616
$166$		0			0
$167$	−2.90569	−	2.90569i	−0.224849	−	0.224849i	0.585688	−	0.810537i	$-0.300825\pi$
$167$	−2.90569	−	2.90569i	−0.224849	−	0.224849i	−0.810537	+	0.585688i	$0.800825\pi$
$168$		0			0
$169$	12.6491	+	3.00000i	0.973009	+	0.230769i
$170$		0			0
$171$	−0.418861	+	0.418861i	−0.0320311	+	0.0320311i
$172$	10.6491			0.811987
$173$	−2.32456			−0.176733			−0.0883663	−	0.996088i	$-0.528165\pi$
$173$	−2.32456			−0.176733			−0.0883663	+	0.996088i	$0.528165\pi$
$174$		0			0
$175$	−11.1623	+	2.51317i	−0.843789	+	0.189978i
$176$	−16.6491	+	16.6491i	−1.25497	+	1.25497i
$177$	8.32456	−	8.32456i	0.625712	−	0.625712i
$178$		0			0
$179$			0.486833i			0.0363876i	0.999834	+	0.0181938i	$0.00579159\pi$
$179$			0.486833i			0.0363876i	−0.999834	+	0.0181938i	$0.994208\pi$
$180$	1.16228	+	1.16228i	0.0866311	+	0.0866311i
$181$	15.1623			1.12700			0.563502	−	0.826115i	$-0.309454\pi$
$181$	15.1623			1.12700			0.563502	+	0.826115i	$0.309454\pi$
$182$		0			0
$183$	−3.16228			−0.233762
$184$		0			0
$185$		−	5.02633i		−	0.369543i
$186$		0			0
$187$	4.83772	−	4.83772i	0.353769	−	0.353769i
$188$	−13.1623	+	13.1623i	−0.959958	+	0.959958i
$189$	2.58114	−	0.581139i	0.187750	−	0.0422716i
$190$		0			0
$191$	−14.3246			−1.03649			−0.518244	−	0.855233i	$-0.673414\pi$
$191$	−14.3246			−1.03649			−0.518244	+	0.855233i	$0.673414\pi$
$192$	−8.00000			−0.577350
$193$	6.32456	−	6.32456i	0.455251	−	0.455251i	−0.441842	−	0.897093i	$-0.645675\pi$
$193$	6.32456	−	6.32456i	0.455251	−	0.455251i	0.897093	+	0.441842i	$0.145675\pi$
$194$		0			0
$195$	1.83772	+	2.32456i	0.131602	+	0.166465i
$196$	6.00000	+	12.6491i	0.428571	+	0.903508i
$197$	−1.83772	−	1.83772i	−0.130932	−	0.130932i	0.638604	−	0.769536i	$-0.279512\pi$
$197$	−1.83772	−	1.83772i	−0.130932	−	0.130932i	−0.769536	+	0.638604i	$0.779512\pi$
$198$		0			0
$199$	−9.48683			−0.672504			−0.336252	−	0.941772i	$-0.609159\pi$
$199$	−9.48683			−0.672504			−0.336252	+	0.941772i	$0.609159\pi$
$200$		0			0
$201$	6.32456	−	6.32456i	0.446100	−	0.446100i
$202$		0			0
$203$	1.06797	+	4.74342i	0.0749569	+	0.332923i
$204$	2.32456			0.162751
$205$			8.32456i			0.581412i
$206$		0			0
$207$			4.16228i			0.289298i
$208$	−14.3246	−	1.67544i	−0.993229	−	0.116171i
$209$		−	3.48683i		−	0.241189i
$210$		0			0
$211$	19.6491			1.35270			0.676350	−	0.736580i	$-0.263561\pi$
$211$	19.6491			1.35270			0.676350	+	0.736580i	$0.263561\pi$
$212$			8.32456i			0.571733i
$213$	−6.00000	+	6.00000i	−0.411113	+	0.411113i
$214$		0			0
$215$	3.09431	+	3.09431i	0.211030	+	0.211030i
$216$		0			0
$217$	−17.6491	−	11.1623i	−1.19810	−	0.757745i
$218$		0			0
$219$	−5.58114	+	5.58114i	−0.377138	+	0.377138i
$220$	−9.67544			−0.652318
$221$	4.16228	+	0.486833i	0.279985	+	0.0327479i
$222$		0			0
$223$	5.25658	−	5.25658i	0.352007	−	0.352007i	−0.508849	−	0.860856i	$-0.669929\pi$
$223$	5.25658	−	5.25658i	0.352007	−	0.352007i	0.860856	+	0.508849i	$0.169929\pi$
$224$		0			0
$225$		−	4.32456i		−	0.288304i
$226$		0			0
$227$	4.83772	−	4.83772i	0.321091	−	0.321091i	−0.528095	−	0.849186i	$-0.677093\pi$
$227$	4.83772	−	4.83772i	0.321091	−	0.321091i	0.849186	+	0.528095i	$0.177093\pi$
$228$	0.837722	−	0.837722i	0.0554795	−	0.0554795i
$229$	−18.3246	−	18.3246i	−1.21092	−	1.21092i	−0.970724	−	0.240196i	$-0.922788\pi$
$229$	−18.3246	−	18.3246i	−1.21092	−	1.21092i	−0.240196	−	0.970724i	$-0.577212\pi$
$230$		0			0
$231$	−8.32456	+	13.1623i	−0.547716	+	0.866014i
$232$		0			0
$233$			22.1623i			1.45190i	0.687748	+	0.725950i	$0.258599\pi$
$233$			22.1623i			1.45190i	−0.687748	+	0.725950i	$0.741401\pi$
$234$		0			0
$235$	−7.64911			−0.498973
$236$	−16.6491	+	16.6491i	−1.08376	+	1.08376i
$237$		−	11.3246i		−	0.735609i
$238$		0			0
$239$	−6.48683	−	6.48683i	−0.419598	−	0.419598i	0.465467	−	0.885065i	$-0.345886\pi$
$239$	−6.48683	−	6.48683i	−0.419598	−	0.419598i	−0.885065	+	0.465467i	$0.845886\pi$
$240$	−2.32456	−	2.32456i	−0.150049	−	0.150049i
$241$	3.90569	+	3.90569i	0.251588	+	0.251588i	0.821621	−	0.570034i	$-0.193070\pi$
$241$	3.90569	+	3.90569i	0.251588	+	0.251588i	−0.570034	+	0.821621i	$0.693070\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$	6.32456			0.404888
$245$	−1.93203	+	5.41886i	−0.123433	+	0.346198i
$246$		0			0
$247$	1.67544	−	1.32456i	0.106606	−	0.0842794i
$248$		0			0
$249$	−6.58114	−	6.58114i	−0.417063	−	0.417063i
$250$		0			0
$251$	−27.4868			−1.73495			−0.867477	−	0.497478i	$-0.834260\pi$
$251$	−27.4868			−1.73495			−0.867477	+	0.497478i	$0.834260\pi$
$252$	−5.16228	+	1.16228i	−0.325193	+	0.0732166i
$253$	−17.3246	−	17.3246i	−1.08919	−	1.08919i
$254$		0			0
$255$	0.675445	+	0.675445i	0.0422980	+	0.0422980i
$256$	16.0000			1.00000
$257$	27.4868			1.71458			0.857291	−	0.514833i	$-0.172146\pi$
$257$	27.4868			1.71458			0.857291	+	0.514833i	$0.172146\pi$
$258$		0			0
$259$	13.6754	+	8.64911i	0.849751	+	0.537430i
$260$	−3.67544	−	4.64911i	−0.227941	−	0.288326i
$261$	−1.83772			−0.113752
$262$		0			0
$263$	18.4868			1.13995			0.569973	−	0.821663i	$-0.306953\pi$
$263$	18.4868			1.13995			0.569973	+	0.821663i	$0.306953\pi$
$264$		0			0
$265$	−2.41886	+	2.41886i	−0.148589	+	0.148589i
$266$		0			0
$267$	5.41886	−	5.41886i	0.331629	−	0.331629i
$268$	−12.6491	+	12.6491i	−0.772667	+	0.772667i
$269$		−	3.48683i		−	0.212596i	−0.994334	−	0.106298i	$-0.966100\pi$
$269$		−	3.48683i		−	0.212596i	0.994334	−	0.106298i	$-0.0338997\pi$
$270$		0			0
$271$	−13.4868	−	13.4868i	−0.819267	−	0.819267i	0.166735	−	0.986002i	$-0.446678\pi$
$271$	−13.4868	−	13.4868i	−0.819267	−	0.819267i	−0.986002	+	0.166735i	$0.946678\pi$
$272$	−4.64911			−0.281894
$273$	−9.48683	+	1.00000i	−0.574169	+	0.0605228i
$274$		0			0
$275$	18.0000	+	18.0000i	1.08544	+	1.08544i
$276$		−	8.32456i		−	0.501079i
$277$			4.35089i			0.261420i	0.991421	+	0.130710i	$0.0417256\pi$
$277$			4.35089i			0.261420i	−0.991421	+	0.130710i	$0.958274\pi$
$278$		0			0
$279$	5.58114	−	5.58114i	0.334134	−	0.334134i
$280$		0			0
$281$	9.67544	−	9.67544i	0.577189	−	0.577189i	−0.356939	−	0.934128i	$-0.616180\pi$
$281$	9.67544	−	9.67544i	0.577189	−	0.577189i	0.934128	+	0.356939i	$0.116180\pi$
$282$		0			0
$283$	−21.2982			−1.26605			−0.633024	−	0.774132i	$-0.718187\pi$
$283$	−21.2982			−1.26605			−0.633024	+	0.774132i	$0.718187\pi$
$284$	12.0000	−	12.0000i	0.712069	−	0.712069i
$285$	0.486833			0.0288375
$286$		0			0
$287$	−22.6491	−	14.3246i	−1.33693	−	0.845552i
$288$		0			0
$289$	−15.6491			−0.920536
$290$		0			0
$291$	−0.418861	−	0.418861i	−0.0245541	−	0.0245541i
$292$	11.1623	−	11.1623i	0.653223	−	0.653223i
$293$	−22.0680	−	22.0680i	−1.28922	−	1.28922i	−0.935258	−	0.353967i	$-0.884833\pi$
$293$	−22.0680	−	22.0680i	−1.28922	−	1.28922i	−0.353967	−	0.935258i	$-0.615167\pi$
$294$		0			0
$295$	−9.67544			−0.563326
$296$		0			0
$297$	−4.16228	−	4.16228i	−0.241520	−	0.241520i
$298$		0			0
$299$	1.74342	−	14.9057i	0.100824	−	0.862019i
$300$			8.64911i			0.499357i
$301$	−13.7434	+	3.09431i	−0.792157	+	0.178353i
$302$		0			0
$303$			17.8114i			1.02324i
$304$	−1.67544	+	1.67544i	−0.0960933	+	0.0960933i
$305$	1.83772	+	1.83772i	0.105228	+	0.105228i
$306$		0			0
$307$	11.0680	+	11.0680i	0.631683	+	0.631683i	0.948490	−	0.316807i	$-0.102611\pi$
$307$	11.0680	+	11.0680i	0.631683	+	0.631683i	−0.316807	+	0.948490i	$0.602611\pi$
$308$	16.6491	−	26.3246i	0.948671	−	1.49998i
$309$			4.00000i			0.227552i
$310$		0			0
$311$	−14.3246			−0.812271			−0.406136	−	0.913813i	$-0.633124\pi$
$311$	−14.3246			−0.812271			−0.406136	+	0.913813i	$0.633124\pi$
$312$		0			0
$313$			19.8114i			1.11981i	0.828558	+	0.559903i	$0.189162\pi$
$313$			19.8114i			1.11981i	−0.828558	+	0.559903i	$0.810838\pi$
$314$		0			0
$315$	−1.83772	−	1.16228i	−0.103544	−	0.0654869i
$316$			22.6491i			1.27411i
$317$	−1.83772	−	1.83772i	−0.103217	−	0.103217i	0.653613	−	0.756829i	$-0.273253\pi$
$317$	−1.83772	−	1.83772i	−0.103217	−	0.103217i	−0.756829	+	0.653613i	$0.773253\pi$
$318$		0			0
$319$	7.64911	−	7.64911i	0.428268	−	0.428268i
$320$	4.64911	+	4.64911i	0.259893	+	0.259893i
$321$			10.6491i			0.594375i
$322$		0			0
$323$	0.486833	−	0.486833i	0.0270881	−	0.0270881i
$324$		−	2.00000i		−	0.111111i
$325$	−1.81139	+	15.4868i	−0.100478	+	0.859055i
$326$		0			0
$327$	2.00000	−	2.00000i	0.110600	−	0.110600i
$328$		0			0
$329$	13.1623	−	20.8114i	0.725660	−	1.14737i
$330$		0			0
$331$	23.6491	+	23.6491i	1.29987	+	1.29987i	0.928473	+	0.371400i	$0.121122\pi$
$331$	23.6491	+	23.6491i	1.29987	+	1.29987i	0.371400	+	0.928473i	$0.378878\pi$
$332$	13.1623	+	13.1623i	0.722374	+	0.722374i
$333$	−4.32456	+	4.32456i	−0.236984	+	0.236984i
$334$		0			0
$335$	−7.35089			−0.401622
$336$	10.3246	−	2.32456i	0.563251	−	0.126815i
$337$		−	13.0000i		−	0.708155i	−0.935216	−	0.354078i	$-0.884795\pi$
$337$		−	13.0000i		−	0.708155i	0.935216	−	0.354078i	$-0.115205\pi$
$338$		0			0
$339$			14.8114i			0.804444i
$340$	−1.35089	−	1.35089i	−0.0732623	−	0.0732623i
$341$			46.4605i			2.51598i
$342$		0			0
$343$	−11.4189	−	14.5811i	−0.616561	−	0.787307i
$344$		0			0
$345$	2.41886	−	2.41886i	0.130227	−	0.130227i
$346$		0			0
$347$	−30.9737			−1.66275			−0.831377	−	0.555709i	$-0.812447\pi$
$347$	−30.9737			−1.66275			−0.831377	+	0.555709i	$0.812447\pi$
$348$	3.67544			0.197025
$349$	12.7434	+	12.7434i	0.682139	+	0.682139i	0.960482	−	0.278342i	$-0.0897850\pi$
$349$	12.7434	+	12.7434i	0.682139	+	0.682139i	−0.278342	+	0.960482i	$0.589785\pi$
$350$		0			0
$351$	0.418861	−	3.58114i	0.0223572	−	0.191147i
$352$		0			0
$353$	9.48683	−	9.48683i	0.504933	−	0.504933i	−0.408034	−	0.912967i	$-0.633785\pi$
$353$	9.48683	−	9.48683i	0.504933	−	0.504933i	0.912967	+	0.408034i	$0.133785\pi$
$354$		0			0
$355$	6.97367			0.370124
$356$	−10.8377	+	10.8377i	−0.574398	+	0.574398i
$357$	−3.00000	+	0.675445i	−0.158777	+	0.0357483i
$358$		0			0
$359$	10.1623	−	10.1623i	0.536345	−	0.536345i	−0.386109	−	0.922453i	$-0.626181\pi$
$359$	10.1623	−	10.1623i	0.536345	−	0.536345i	0.922453	+	0.386109i	$0.126181\pi$
$360$		0			0
$361$			18.6491i			0.981532i
$362$		0			0
$363$	23.6491			1.24126
$364$	18.9737	−	2.00000i	0.994490	−	0.104828i
$365$	6.48683			0.339536
$366$		0			0
$367$		−	33.2982i		−	1.73815i	−0.494678	−	0.869077i	$-0.664714\pi$
$367$		−	33.2982i		−	1.73815i	0.494678	−	0.869077i	$-0.335286\pi$
$368$			16.6491i			0.867895i
$369$	7.16228	−	7.16228i	0.372853	−	0.372853i
$370$		0			0
$371$	−2.41886	−	10.7434i	−0.125581	−	0.557770i
$372$	−11.1623	+	11.1623i	−0.578737	+	0.578737i
$373$	24.0000			1.24267			0.621336	−	0.783544i	$-0.286590\pi$
$373$	24.0000			1.24267			0.621336	+	0.783544i	$0.286590\pi$
$374$		0			0
$375$	−5.41886	+	5.41886i	−0.279829	+	0.279829i
$376$		0			0
$377$	6.58114	+	0.769751i	0.338946	+	0.0396442i
$378$		0			0
$379$	−7.00000	−	7.00000i	−0.359566	−	0.359566i	0.504087	−	0.863653i	$-0.331829\pi$
$379$	−7.00000	−	7.00000i	−0.359566	−	0.359566i	−0.863653	+	0.504087i	$0.831829\pi$
$380$	−0.973666			−0.0499480
$381$	−2.00000			−0.102463
$382$		0			0
$383$	3.67544	−	3.67544i	0.187806	−	0.187806i	−0.606941	−	0.794747i	$-0.707603\pi$
$383$	3.67544	−	3.67544i	0.187806	−	0.187806i	0.794747	+	0.606941i	$0.207603\pi$
$384$		0			0
$385$	12.4868	−	2.81139i	0.636388	−	0.143282i
$386$		0			0
$387$		−	5.32456i		−	0.270662i
$388$	0.837722	+	0.837722i	0.0425289	+	0.0425289i
$389$			6.00000i			0.304212i	0.988364	+	0.152106i	$0.0486055\pi$
$389$			6.00000i			0.304212i	−0.988364	+	0.152106i	$0.951394\pi$
$390$		0			0
$391$		−	4.83772i		−	0.244654i
$392$		0			0
$393$	−13.1623			−0.663949
$394$		0			0
$395$	−6.58114	+	6.58114i	−0.331133	+	0.331133i
$396$	8.32456	+	8.32456i	0.418325	+	0.418325i
$397$	5.25658	+	5.25658i	0.263820	+	0.263820i	0.826604	−	0.562784i	$-0.190270\pi$
$397$	5.25658	+	5.25658i	0.263820	+	0.263820i	−0.562784	+	0.826604i	$0.690270\pi$
$398$		0			0
$399$	−0.837722	+	1.32456i	−0.0419386	+	0.0663107i
$400$		−	17.2982i		−	0.864911i
$401$	7.83772	−	7.83772i	0.391397	−	0.391397i	−0.483788	−	0.875185i	$-0.660739\pi$
$401$	7.83772	−	7.83772i	0.391397	−	0.391397i	0.875185	+	0.483788i	$0.160739\pi$
$402$		0			0
$403$	−22.3246	+	17.6491i	−1.11207	+	0.879165i
$404$		−	35.6228i		−	1.77230i
$405$	0.581139	−	0.581139i	0.0288770	−	0.0288770i
$406$		0			0
$407$		−	36.0000i		−	1.78445i
$408$		0			0
$409$	19.3925	−	19.3925i	0.958899	−	0.958899i	−0.0402893	−	0.999188i	$-0.512828\pi$
$409$	19.3925	−	19.3925i	0.958899	−	0.958899i	0.999188	+	0.0402893i	$0.0128280\pi$
$410$		0			0
$411$	−12.0000	−	12.0000i	−0.591916	−	0.591916i
$412$		−	8.00000i		−	0.394132i
$413$	16.6491	−	26.3246i	0.819249	−	1.29535i
$414$		0			0
$415$			7.64911i			0.375480i
$416$		0			0
$417$	7.16228			0.350738
$418$		0			0
$419$			15.4868i			0.756581i	0.925687	+	0.378291i	$0.123488\pi$
$419$			15.4868i			0.756581i	−0.925687	+	0.378291i	$0.876512\pi$
$420$	3.67544	+	2.32456i	0.179343	+	0.113427i
$421$	7.32456	+	7.32456i	0.356977	+	0.356977i	0.862697	−	0.505720i	$-0.168773\pi$
$421$	7.32456	+	7.32456i	0.356977	+	0.356977i	−0.505720	+	0.862697i	$0.668773\pi$
$422$		0			0
$423$	6.58114	+	6.58114i	0.319986	+	0.319986i
$424$		0			0
$425$			5.02633i			0.243813i
$426$		0			0
$427$	−8.16228	+	1.83772i	−0.395000	+	0.0889336i
$428$		−	21.2982i		−	1.02949i
$429$	13.1623	+	16.6491i	0.635481	+	0.803827i
$430$		0			0
$431$	−14.8114	−	14.8114i	−0.713439	−	0.713439i	0.253814	−	0.967253i	$-0.418315\pi$
$431$	−14.8114	−	14.8114i	−0.713439	−	0.713439i	−0.967253	+	0.253814i	$0.918315\pi$
$432$			4.00000i			0.192450i
$433$	7.16228			0.344197			0.172099	−	0.985080i	$-0.444945\pi$
$433$	7.16228			0.344197			0.172099	+	0.985080i	$0.444945\pi$
$434$		0			0
$435$	1.06797	+	1.06797i	0.0512053	+	0.0512053i
$436$	−4.00000	+	4.00000i	−0.191565	+	0.191565i
$437$	−1.74342	−	1.74342i	−0.0833989	−	0.0833989i
$438$		0			0
$439$	29.4868			1.40733			0.703665	−	0.710532i	$-0.251546\pi$
$439$	29.4868			1.40733			0.703665	+	0.710532i	$0.251546\pi$
$440$		0			0
$441$	6.32456	−	3.00000i	0.301169	−	0.142857i
$442$		0			0
$443$	25.8377			1.22759			0.613794	−	0.789467i	$-0.289643\pi$
$443$	25.8377			1.22759			0.613794	+	0.789467i	$0.289643\pi$
$444$	8.64911	−	8.64911i	0.410469	−	0.410469i
$445$	−6.29822			−0.298564
$446$		0			0
$447$	10.1623	−	10.1623i	0.480659	−	0.480659i
$448$	−20.6491	+	4.64911i	−0.975579	+	0.219650i
$449$	2.81139	−	2.81139i	0.132678	−	0.132678i	−0.637649	−	0.770327i	$-0.720093\pi$
$449$	2.81139	−	2.81139i	0.132678	−	0.132678i	0.770327	+	0.637649i	$0.220093\pi$
$450$		0			0
$451$			59.6228i			2.80753i
$452$		−	29.6228i		−	1.39334i
$453$	−4.00000	−	4.00000i	−0.187936	−	0.187936i
$454$		0			0
$455$	6.09431	+	4.93203i	0.285705	+	0.231217i
$456$		0			0
$457$	1.32456	+	1.32456i	0.0619601	+	0.0619601i	0.737408	−	0.675448i	$-0.236050\pi$
$457$	1.32456	+	1.32456i	0.0619601	+	0.0619601i	−0.675448	+	0.737408i	$0.736050\pi$
$458$		0			0
$459$		−	1.16228i		−	0.0542505i
$460$	−4.83772	+	4.83772i	−0.225560	+	0.225560i
$461$	−20.3246	+	20.3246i	−0.946609	+	0.946609i	−0.998645	−	0.0520363i	$-0.983429\pi$
$461$	−20.3246	+	20.3246i	−0.946609	+	0.946609i	0.0520363	+	0.998645i	$0.483429\pi$
$462$		0			0
$463$	2.64911	−	2.64911i	0.123115	−	0.123115i	−0.642865	−	0.765980i	$-0.722254\pi$
$463$	2.64911	−	2.64911i	0.123115	−	0.123115i	0.765980	+	0.642865i	$0.222254\pi$
$464$	−7.35089			−0.341256
$465$	−6.48683			−0.300820
$466$		0			0
$467$	−30.9737			−1.43329			−0.716645	−	0.697438i	$-0.754323\pi$
$467$	−30.9737			−1.43329			−0.716645	+	0.697438i	$0.754323\pi$
$468$	−0.837722	+	7.16228i	−0.0387237	+	0.331076i
$469$	12.6491	−	20.0000i	0.584082	−	0.923514i
$470$		0			0
$471$	−2.51317			−0.115801
$472$		0			0
$473$	22.1623	+	22.1623i	1.01902	+	1.01902i
$474$		0			0
$475$	1.81139	+	1.81139i	0.0831122	+	0.0831122i
$476$	6.00000	−	1.35089i	0.275010	−	0.0619179i
$477$	4.16228			0.190578
$478$		0			0
$479$	−5.41886	−	5.41886i	−0.247594	−	0.247594i	0.572388	−	0.819983i	$-0.306017\pi$
$479$	−5.41886	−	5.41886i	−0.247594	−	0.247594i	−0.819983	+	0.572388i	$0.806017\pi$
$480$		0			0
$481$	17.2982	−	13.6754i	0.788731	−	0.623547i
$482$		0			0
$483$	2.41886	+	10.7434i	0.110062	+	0.488842i
$484$	−47.2982			−2.14992
$485$			0.486833i			0.0221059i
$486$		0			0
$487$	1.32456	+	1.32456i	0.0600213	+	0.0600213i	0.736480	−	0.676459i	$-0.236486\pi$
$487$	1.32456	+	1.32456i	0.0600213	+	0.0600213i	−0.676459	+	0.736480i	$0.736486\pi$
$488$		0			0
$489$	−1.32456	−	1.32456i	−0.0598985	−	0.0598985i
$490$		0			0
$491$		−	26.3246i		−	1.18801i	−0.804461	−	0.594005i	$-0.797546\pi$
$491$		−	26.3246i		−	1.18801i	0.804461	−	0.594005i	$-0.202454\pi$
$492$	−14.3246	+	14.3246i	−0.645801	+	0.645801i
$493$	2.13594			0.0961981
$494$		0			0
$495$			4.83772i			0.217439i
$496$	22.3246	−	22.3246i	1.00240	−	1.00240i
$497$	−12.0000	+	18.9737i	−0.538274	+	0.851085i
$498$		0			0
$499$	19.3246	+	19.3246i	0.865086	+	0.865086i	0.991923	−	0.126838i	$-0.0404827\pi$
$499$	19.3246	+	19.3246i	0.865086	+	0.865086i	−0.126838	+	0.991923i	$0.540483\pi$
$500$	10.8377	−	10.8377i	0.484678	−	0.484678i
$501$	2.90569	−	2.90569i	0.129817	−	0.129817i
$502$		0			0
$503$		−	34.4605i		−	1.53652i	−0.640139	−	0.768259i	$-0.721123\pi$
$503$		−	34.4605i		−	1.53652i	0.640139	−	0.768259i	$-0.278877\pi$
$504$		0			0
$505$	10.3509	−	10.3509i	0.460609	−	0.460609i
$506$		0			0
$507$	−3.00000	+	12.6491i	−0.133235	+	0.561767i
$508$	4.00000			0.177471
$509$	−20.9057	+	20.9057i	−0.926629	+	0.926629i	−0.997486	−	0.0708578i	$-0.977426\pi$
$509$	−20.9057	+	20.9057i	−0.926629	+	0.926629i	0.0708578	+	0.997486i	$0.477426\pi$
$510$		0			0
$511$	−11.1623	+	17.6491i	−0.493790	+	0.780751i
$512$		0			0
$513$	−0.418861	−	0.418861i	−0.0184932	−	0.0184932i
$514$		0			0
$515$	2.32456	−	2.32456i	0.102432	−	0.102432i
$516$			10.6491i			0.468801i
$517$	−54.7851			−2.40944
$518$		0			0
$519$		−	2.32456i		−	0.102037i
$520$		0			0
$521$		−	7.35089i		−	0.322048i	−0.986950	−	0.161024i	$-0.948520\pi$
$521$		−	7.35089i		−	0.322048i	0.986950	−	0.161024i	$-0.0514797\pi$
$522$		0			0
$523$			14.5132i			0.634616i	0.948322	+	0.317308i	$0.102779\pi$
$523$			14.5132i			0.634616i	−0.948322	+	0.317308i	$0.897221\pi$
$524$	26.3246			1.14999
$525$	−2.51317	−	11.1623i	−0.109684	−	0.487162i
$526$		0			0
$527$	−6.48683	+	6.48683i	−0.282571	+	0.282571i
$528$	−16.6491	−	16.6491i	−0.724560	−	0.724560i
$529$	5.67544			0.246758
$530$		0			0
$531$	8.32456	+	8.32456i	0.361255	+	0.361255i
$532$	1.67544	−	2.64911i	0.0726397	−	0.114854i
$533$	−28.6491	+	22.6491i	−1.24093	+	0.981042i
$534$		0			0
$535$	6.18861	−	6.18861i	0.267557	−	0.267557i
$536$		0			0
$537$	−0.486833			−0.0210084
$538$		0			0
$539$	−13.8377	+	38.8114i	−0.596033	+	1.67172i
$540$	−1.16228	+	1.16228i	−0.0500165	+	0.0500165i
$541$	−4.00000	+	4.00000i	−0.171973	+	0.171973i	−0.787846	−	0.615872i	$-0.788804\pi$
$541$	−4.00000	+	4.00000i	−0.171973	+	0.171973i	0.615872	+	0.787846i	$0.288804\pi$
$542$		0			0
$543$			15.1623i			0.650676i
$544$		0			0
$545$	−2.32456			−0.0995730
$546$		0			0
$547$	15.6491			0.669108			0.334554	−	0.942377i	$-0.391414\pi$
$547$	15.6491			0.669108			0.334554	+	0.942377i	$0.391414\pi$
$548$	24.0000	+	24.0000i	1.02523	+	1.02523i
$549$		−	3.16228i		−	0.134963i
$550$		0			0
$551$	0.769751	−	0.769751i	0.0327925	−	0.0327925i
$552$		0			0
$553$	−6.58114	−	29.2302i	−0.279858	−	1.24300i
$554$		0			0
$555$	5.02633			0.213356
$556$	−14.3246			−0.607496
$557$	−4.64911	+	4.64911i	−0.196989	+	0.196989i	−0.798708	−	0.601719i	$-0.794483\pi$
$557$	−4.64911	+	4.64911i	−0.196989	+	0.196989i	0.601719	+	0.798708i	$0.294483\pi$
$558$		0			0
$559$	−2.23025	+	19.0680i	−0.0943295	+	0.806489i
$560$	−7.35089	−	4.64911i	−0.310632	−	0.196461i
$561$	4.83772	+	4.83772i	0.204249	+	0.204249i
$562$		0			0
$563$	22.4605			0.946597			0.473299	−	0.880902i	$-0.343063\pi$
$563$	22.4605			0.946597			0.473299	+	0.880902i	$0.343063\pi$
$564$	−13.1623	−	13.1623i	−0.554232	−	0.554232i
$565$	8.60747	−	8.60747i	0.362119	−	0.362119i
$566$		0			0
$567$	0.581139	+	2.58114i	0.0244055	+	0.108398i
$568$		0			0
$569$			30.4868i			1.27807i	0.769176	+	0.639037i	$0.220667\pi$
$569$			30.4868i			1.27807i	−0.769176	+	0.639037i	$0.779333\pi$
$570$		0			0
$571$		−	21.3246i		−	0.892405i	−0.894932	−	0.446202i	$-0.852776\pi$
$571$		−	21.3246i		−	0.892405i	0.894932	−	0.446202i	$-0.147224\pi$
$572$	−26.3246	−	33.2982i	−1.10068	−	1.39227i
$573$		−	14.3246i		−	0.598417i
$574$		0			0
$575$	18.0000			0.750652
$576$		−	8.00000i		−	0.333333i
$577$	8.00000	−	8.00000i	0.333044	−	0.333044i	−0.520697	−	0.853741i	$-0.674328\pi$
$577$	8.00000	−	8.00000i	0.333044	−	0.333044i	0.853741	+	0.520697i	$0.174328\pi$
$578$		0			0
$579$	6.32456	+	6.32456i	0.262840	+	0.262840i
$580$	−2.13594	−	2.13594i	−0.0886902	−	0.0886902i
$581$	−20.8114	−	13.1623i	−0.863402	−	0.546063i
$582$		0			0
$583$	−17.3246	+	17.3246i	−0.717510	+	0.717510i
$584$		0			0
$585$	−2.32456	+	1.83772i	−0.0961085	+	0.0759805i
$586$		0			0
$587$	−1.74342	+	1.74342i	−0.0719585	+	0.0719585i	−0.742170	−	0.670212i	$-0.766203\pi$
$587$	−1.74342	+	1.74342i	−0.0719585	+	0.0719585i	0.670212	+	0.742170i	$0.266203\pi$
$588$	−12.6491	+	6.00000i	−0.521641	+	0.247436i
$589$			4.67544i			0.192648i
$590$		0			0
$591$	1.83772	−	1.83772i	0.0755938	−	0.0755938i
$592$	−17.2982	+	17.2982i	−0.710953	+	0.710953i
$593$	−3.09431	−	3.09431i	−0.127068	−	0.127068i	0.640713	−	0.767781i	$-0.278639\pi$
$593$	−3.09431	−	3.09431i	−0.127068	−	0.127068i	−0.767781	+	0.640713i	$0.778639\pi$
$594$		0			0
$595$	2.13594	+	1.35089i	0.0875652	+	0.0553811i
$596$	−20.3246	+	20.3246i	−0.832526	+	0.832526i
$597$		−	9.48683i		−	0.388270i
$598$		0			0
$599$	−9.18861			−0.375436			−0.187718	−	0.982223i	$-0.560109\pi$
$599$	−9.18861			−0.375436			−0.187718	+	0.982223i	$0.560109\pi$
$600$		0			0
$601$		−	31.6228i		−	1.28992i	−0.764216	−	0.644960i	$-0.776874\pi$
$601$		−	31.6228i		−	1.28992i	0.764216	−	0.644960i	$-0.223126\pi$
$602$		0			0
$603$	6.32456	+	6.32456i	0.257556	+	0.257556i
$604$	8.00000	+	8.00000i	0.325515	+	0.325515i
$605$	−13.7434	−	13.7434i	−0.558749	−	0.558749i
$606$		0			0
$607$			28.8377i			1.17049i	0.810858	+	0.585244i	$0.199001\pi$
$607$			28.8377i			1.17049i	−0.810858	+	0.585244i	$0.800999\pi$
$608$		0			0
$609$	−4.74342	+	1.06797i	−0.192213	+	0.0432764i
$610$		0			0
$611$	−20.8114	−	26.3246i	−0.841939	−	1.06498i
$612$			2.32456i			0.0939646i
$613$	−7.32456	−	7.32456i	−0.295836	−	0.295836i	0.543544	−	0.839380i	$-0.317082\pi$
$613$	−7.32456	−	7.32456i	−0.295836	−	0.295836i	−0.839380	+	0.543544i	$0.817082\pi$
$614$		0			0
$615$	−8.32456			−0.335678
$616$		0			0
$617$	24.4868	+	24.4868i	0.985803	+	0.985803i	0.999901	−	0.0140978i	$-0.00448763\pi$
$617$	24.4868	+	24.4868i	0.985803	+	0.985803i	−0.0140978	+	0.999901i	$0.504488\pi$
$618$		0			0
$619$	−5.67544	−	5.67544i	−0.228115	−	0.228115i	0.583790	−	0.811905i	$-0.301569\pi$
$619$	−5.67544	−	5.67544i	−0.228115	−	0.228115i	−0.811905	+	0.583790i	$0.801569\pi$
$620$	12.9737			0.521035
$621$	−4.16228			−0.167026
$622$		0			0
$623$	10.8377	−	17.1359i	0.434204	−	0.686537i
$624$	1.67544	−	14.3246i	0.0670715	−	0.573441i
$625$	−15.3246			−0.612982
$626$		0			0
$627$	3.48683			0.139251
$628$	5.02633			0.200573
$629$	5.02633	−	5.02633i	0.200413	−	0.200413i
$630$		0			0
$631$	3.64911	−	3.64911i	0.145269	−	0.145269i	−0.630732	−	0.776001i	$-0.717245\pi$
$631$	3.64911	−	3.64911i	0.145269	−	0.145269i	0.776001	+	0.630732i	$0.217245\pi$
$632$		0			0
$633$			19.6491i			0.780982i
$634$		0			0
$635$	1.16228	+	1.16228i	0.0461236	+	0.0461236i
$636$	−8.32456			−0.330090
$637$	−23.9057	+	8.09431i	−0.947178	+	0.320708i
$638$		0			0
$639$	−6.00000	−	6.00000i	−0.237356	−	0.237356i
$640$		0			0
$641$			24.4868i			0.967172i	0.875297	+	0.483586i	$0.160666\pi$
$641$			24.4868i			0.967172i	−0.875297	+	0.483586i	$0.839334\pi$
$642$		0			0
$643$	−4.18861	+	4.18861i	−0.165183	+	0.165183i	−0.784858	−	0.619675i	$-0.787264\pi$
$643$	−4.18861	+	4.18861i	−0.165183	+	0.165183i	0.619675	+	0.784858i	$0.287264\pi$
$644$	−4.83772	−	21.4868i	−0.190633	−	0.846700i
$645$	−3.09431	+	3.09431i	−0.121838	+	0.121838i
$646$		0			0
$647$	6.97367			0.274163			0.137082	−	0.990560i	$-0.456228\pi$
$647$	6.97367			0.274163			0.137082	+	0.990560i	$0.456228\pi$
$648$		0			0
$649$	−69.2982			−2.72019
$650$		0			0
$651$	11.1623	−	17.6491i	0.437484	−	0.691723i
$652$	2.64911	+	2.64911i	0.103747	+	0.103747i
$653$	−6.00000			−0.234798			−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000			−0.234798			−0.117399	+	0.993085i	$0.537456\pi$
$654$		0			0
$655$	7.64911	+	7.64911i	0.298875	+	0.298875i
$656$	28.6491	−	28.6491i	1.11856	−	1.11856i
$657$	−5.58114	−	5.58114i	−0.217741	−	0.217741i
$658$		0			0
$659$	−13.4605			−0.524347			−0.262173	−	0.965021i	$-0.584439\pi$
$659$	−13.4605			−0.524347			−0.262173	+	0.965021i	$0.584439\pi$
$660$		−	9.67544i		−	0.376616i
$661$	3.90569	+	3.90569i	0.151914	+	0.151914i	0.778972	−	0.627058i	$-0.215741\pi$
$661$	3.90569	+	3.90569i	0.151914	+	0.151914i	−0.627058	+	0.778972i	$0.715741\pi$
$662$		0			0
$663$	−0.486833	+	4.16228i	−0.0189070	+	0.161649i
$664$		0			0
$665$	1.25658	−	0.282918i	0.0487282	−	0.0109711i
$666$		0			0
$667$		−	7.64911i		−	0.296175i
$668$	−5.81139	+	5.81139i	−0.224849	+	0.224849i
$669$	5.25658	+	5.25658i	0.203231	+	0.203231i
$670$		0			0
$671$	13.1623	+	13.1623i	0.508124	+	0.508124i
$672$		0			0
$673$			20.6228i			0.794950i	0.917613	+	0.397475i	$0.130113\pi$
$673$			20.6228i			0.794950i	−0.917613	+	0.397475i	$0.869887\pi$
$674$		0			0
$675$	4.32456			0.166452
$676$	6.00000	−	25.2982i	0.230769	−	0.973009i
$677$			12.0000i			0.461197i	0.973049	+	0.230599i	$0.0740685\pi$
$677$			12.0000i			0.461197i	−0.973049	+	0.230599i	$0.925932\pi$
$678$		0			0
$679$	−1.32456	−	0.837722i	−0.0508318	−	0.0321488i
$680$		0			0
$681$	4.83772	+	4.83772i	0.185382	+	0.185382i
$682$		0			0
$683$	22.6491	−	22.6491i	0.866644	−	0.866644i	−0.125455	−	0.992099i	$-0.540039\pi$
$683$	22.6491	−	22.6491i	0.866644	−	0.866644i	0.992099	+	0.125455i	$0.0400391\pi$
$684$	0.837722	+	0.837722i	0.0320311	+	0.0320311i
$685$			13.9473i			0.532900i
$686$		0			0
$687$	18.3246	−	18.3246i	0.699125	−	0.699125i
$688$		−	21.2982i		−	0.811987i
$689$	−14.9057	−	1.74342i	−0.567862	−	0.0664189i
$690$		0			0
$691$	−12.4189	+	12.4189i	−0.472436	+	0.472436i	−0.902702	−	0.430266i	$-0.858420\pi$
$691$	−12.4189	+	12.4189i	−0.472436	+	0.472436i	0.430266	+	0.902702i	$0.358420\pi$
$692$			4.64911i			0.176733i
$693$	−13.1623	−	8.32456i	−0.499994	−	0.316224i
$694$		0			0
$695$	−4.16228	−	4.16228i	−0.157884	−	0.157884i
$696$		0			0
$697$	−8.32456	+	8.32456i	−0.315315	+	0.315315i
$698$		0			0
$699$	−22.1623			−0.838254
$700$	5.02633	+	22.3246i	0.189978	+	0.843789i
$701$			1.83772i			0.0694098i	0.999398	+	0.0347049i	$0.0110491\pi$
$701$			1.83772i			0.0694098i	−0.999398	+	0.0347049i	$0.988951\pi$
$702$		0			0
$703$		−	3.62278i		−	0.136636i
$704$	33.2982	+	33.2982i	1.25497	+	1.25497i
$705$		−	7.64911i		−	0.288082i
$706$		0			0
$707$	10.3509	+	45.9737i	0.389285	+	1.72902i
$708$	−16.6491	−	16.6491i	−0.625712	−	0.625712i
$709$	32.2982	−	32.2982i	1.21299	−	1.21299i	0.242945	−	0.970040i	$-0.421887\pi$
$709$	32.2982	−	32.2982i	1.21299	−	1.21299i	0.970040	−	0.242945i	$-0.0781135\pi$
$710$		0			0
$711$	11.3246			0.424704
$712$		0			0
$713$	23.2302	+	23.2302i	0.869980	+	0.869980i
$714$		0			0
$715$	2.02633	−	17.3246i	0.0757806	−	0.647902i
$716$	0.973666			0.0363876
$717$	6.48683	−	6.48683i	0.242255	−	0.242255i
$718$		0			0
$719$	18.9737			0.707598			0.353799	−	0.935321i	$-0.384890\pi$
$719$	18.9737			0.707598			0.353799	+	0.935321i	$0.384890\pi$
$720$	2.32456	−	2.32456i	0.0866311	−	0.0866311i
$721$	2.32456	+	10.3246i	0.0865710	+	0.384507i
$722$		0			0
$723$	−3.90569	+	3.90569i	−0.145254	+	0.145254i
$724$		−	30.3246i		−	1.12700i
$725$			7.94733i			0.295156i
$726$		0			0
$727$	33.2982			1.23496			0.617481	−	0.786586i	$-0.288153\pi$
$727$	33.2982			1.23496			0.617481	+	0.786586i	$0.288153\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$			6.18861i			0.228894i
$732$			6.32456i			0.233762i
$733$	27.9057	−	27.9057i	1.03072	−	1.03072i	0.0312074	−	0.999513i	$-0.490065\pi$
$733$	27.9057	−	27.9057i	1.03072	−	1.03072i	0.999513	−	0.0312074i	$-0.00993524\pi$
$734$		0			0
$735$	−5.41886	−	1.93203i	−0.199878	−	0.0712639i
$736$		0			0
$737$	−52.6491			−1.93935
$738$		0			0
$739$	−5.64911	+	5.64911i	−0.207806	+	0.207806i	−0.803334	−	0.595528i	$-0.796943\pi$
$739$	−5.64911	+	5.64911i	−0.207806	+	0.207806i	0.595528	+	0.803334i	$0.296943\pi$
$740$	−10.0527			−0.369543
$741$	1.32456	+	1.67544i	0.0486588	+	0.0615490i
$742$		0			0
$743$	−7.83772	−	7.83772i	−0.287538	−	0.287538i	0.548568	−	0.836106i	$-0.315173\pi$
$743$	−7.83772	−	7.83772i	−0.287538	−	0.287538i	−0.836106	+	0.548568i	$0.815173\pi$
$744$		0			0
$745$	−11.8114			−0.432736
$746$		0			0
$747$	6.58114	−	6.58114i	0.240791	−	0.240791i
$748$	−9.67544	−	9.67544i	−0.353769	−	0.353769i
$749$	6.18861	+	27.4868i	0.226127	+	1.00435i
$750$		0			0
$751$		−	11.3246i		−	0.413239i	−0.978421	−	0.206619i	$-0.933754\pi$
$751$		−	11.3246i		−	0.413239i	0.978421	−	0.206619i	$-0.0662462\pi$
$752$	26.3246	+	26.3246i	0.959958	+	0.959958i
$753$		−	27.4868i		−	1.00168i
$754$		0			0
$755$			4.64911i			0.169198i
$756$	−1.16228	−	5.16228i	−0.0422716	−	0.187750i
$757$	25.6491			0.932233			0.466116	−	0.884723i	$-0.345653\pi$
$757$	25.6491			0.932233			0.466116	+	0.884723i	$0.345653\pi$
$758$		0			0
$759$	17.3246	−	17.3246i	0.628842	−	0.628842i
$760$		0			0
$761$	6.76975	+	6.76975i	0.245403	+	0.245403i	0.819081	−	0.573678i	$-0.194484\pi$
$761$	6.76975	+	6.76975i	0.245403	+	0.245403i	−0.573678	+	0.819081i	$0.694484\pi$
$762$		0			0
$763$	4.00000	−	6.32456i	0.144810	−	0.228964i
$764$			28.6491i			1.03649i
$765$	−0.675445	+	0.675445i	−0.0244208	+	0.0244208i
$766$		0			0
$767$	−26.3246	−	33.2982i	−0.950525	−	1.20233i
$768$			16.0000i			0.577350i
$769$	−20.0943	+	20.0943i	−0.724619	+	0.724619i	−0.969542	−	0.244923i	$-0.921237\pi$
$769$	−20.0943	+	20.0943i	−0.724619	+	0.724619i	0.244923	+	0.969542i	$0.421237\pi$
$770$		0			0
$771$			27.4868i			0.989914i
$772$	−12.6491	−	12.6491i	−0.455251	−	0.455251i
$773$	−9.48683	+	9.48683i	−0.341218	+	0.341218i	−0.856825	−	0.515607i	$-0.827566\pi$
$773$	−9.48683	+	9.48683i	−0.341218	+	0.341218i	0.515607	+	0.856825i	$0.327566\pi$
$774$		0			0
$775$	−24.1359	−	24.1359i	−0.866989	−	0.866989i
$776$		0			0
$777$	−8.64911	+	13.6754i	−0.310285	+	0.490604i
$778$		0			0
$779$			6.00000i			0.214972i
$780$	4.64911	−	3.67544i	0.166465	−	0.131602i
$781$	49.9473			1.78726
$782$		0			0
$783$		−	1.83772i		−	0.0656748i
$784$	25.2982	−	12.0000i	0.903508	−	0.428571i
$785$	1.46050	+	1.46050i	0.0521274	+	0.0521274i
$786$		0			0
$787$	21.0680	+	21.0680i	0.750992	+	0.750992i	0.974664	−	0.223672i	$-0.0718045\pi$
$787$	21.0680	+	21.0680i	0.750992	+	0.750992i	−0.223672	+	0.974664i	$0.571805\pi$
$788$	−3.67544	+	3.67544i	−0.130932	+	0.130932i
$789$			18.4868i			0.658149i
$790$		0			0
$791$	8.60747	+	38.2302i	0.306047	+	1.35931i
$792$		0			0
$793$	−1.32456	+	11.3246i	−0.0470363	+	0.402147i
$794$		0			0
$795$	−2.41886	−	2.41886i	−0.0857882	−	0.0857882i
$796$			18.9737i			0.672504i
$797$	33.2982			1.17948			0.589742	−	0.807592i	$-0.299230\pi$
$797$	33.2982			1.17948			0.589742	+	0.807592i	$0.299230\pi$
$798$		0			0
$799$	−7.64911	−	7.64911i	−0.270606	−	0.270606i
$800$		0			0
$801$	5.41886	+	5.41886i	0.191466	+	0.191466i
$802$		0			0
$803$	46.4605			1.63956
$804$	−12.6491	−	12.6491i	−0.446100	−	0.446100i
$805$	4.83772	−	7.64911i	0.170507	−	0.269596i
$806$		0			0
$807$	3.48683			0.122742
$808$		0			0
$809$	−13.4605			−0.473246			−0.236623	−	0.971602i	$-0.576041\pi$
$809$	−13.4605			−0.473246			−0.236623	+	0.971602i	$0.576041\pi$
$810$		0			0
$811$	31.8114	−	31.8114i	1.11705	−	1.11705i	0.124877	−	0.992172i	$-0.460146\pi$
$811$	31.8114	−	31.8114i	1.11705	−	1.11705i	0.992172	−	0.124877i	$-0.0398535\pi$
$812$	9.48683	−	2.13594i	0.332923	−	0.0749569i
$813$	13.4868	−	13.4868i	0.473004	−	0.473004i
$814$		0			0
$815$			1.53950i			0.0539264i
$816$		−	4.64911i		−	0.162751i
$817$	2.23025	+	2.23025i	0.0780266	+	0.0780266i
$818$		0			0
$819$	−1.00000	−	9.48683i	−0.0349428	−	0.331497i
$820$	16.6491			0.581412
$821$	−20.3246	−	20.3246i	−0.709332	−	0.709332i	0.257063	−	0.966395i	$-0.417245\pi$
$821$	−20.3246	−	20.3246i	−0.709332	−	0.709332i	−0.966395	+	0.257063i	$0.917245\pi$
$822$		0			0
$823$		−	13.3509i		−	0.465383i	−0.972551	−	0.232691i	$-0.925247\pi$
$823$		−	13.3509i		−	0.465383i	0.972551	−	0.232691i	$-0.0747532\pi$
$824$		0			0
$825$	−18.0000	+	18.0000i	−0.626680	+	0.626680i
$826$		0			0
$827$	16.1623	−	16.1623i	0.562017	−	0.562017i	−0.367863	−	0.929880i	$-0.619910\pi$
$827$	16.1623	−	16.1623i	0.562017	−	0.562017i	0.929880	+	0.367863i	$0.119910\pi$
$828$	8.32456			0.289298
$829$	33.6754			1.16960			0.584798	−	0.811179i	$-0.301174\pi$
$829$	33.6754			1.16960			0.584798	+	0.811179i	$0.301174\pi$
$830$		0			0
$831$	−4.35089			−0.150931
$832$	−3.35089	+	28.6491i	−0.116171	+	0.993229i
$833$	−7.35089	+	3.48683i	−0.254693	+	0.120812i
$834$		0			0
$835$	−3.37722			−0.116874
$836$	−6.97367			−0.241189
$837$	5.58114	+	5.58114i	0.192912	+	0.192912i
$838$		0			0
$839$	−21.4868	−	21.4868i	−0.741808	−	0.741808i	0.231118	−	0.972926i	$-0.425762\pi$
$839$	−21.4868	−	21.4868i	−0.741808	−	0.741808i	−0.972926	+	0.231118i	$0.925762\pi$
$840$		0			0
$841$	−25.6228			−0.883544
$842$		0			0
$843$	9.67544	+	9.67544i	0.333240	+	0.333240i
$844$		−	39.2982i		−	1.35270i
$845$	9.09431	−	5.60747i	0.312854	−	0.192903i
$846$		0			0
$847$	61.0416	−	13.7434i	2.09742	−	0.472229i
$848$	16.6491			0.571733
$849$		−	21.2982i		−	0.730953i
$850$		0			0
$851$	−18.0000	−	18.0000i	−0.617032	−	0.617032i
$852$	12.0000	+	12.0000i	0.411113	+	0.411113i
$853$	1.90569	+	1.90569i	0.0652497	+	0.0652497i	0.738979	−	0.673729i	$-0.235308\pi$
$853$	1.90569	+	1.90569i	0.0652497	+	0.0652497i	−0.673729	+	0.738979i	$0.735308\pi$
$854$		0			0
$855$			0.486833i			0.0166493i
$856$		0			0
$857$	−36.7851			−1.25655			−0.628277	−	0.777990i	$-0.716239\pi$
$857$	−36.7851			−1.25655			−0.628277	+	0.777990i	$0.716239\pi$
$858$		0			0
$859$			1.29822i			0.0442947i	0.999755	+	0.0221474i	$0.00705030\pi$
$859$			1.29822i			0.0442947i	−0.999755	+	0.0221474i	$0.992950\pi$
$860$	6.18861	−	6.18861i	0.211030	−	0.211030i
$861$	14.3246	−	22.6491i	0.488180	−	0.771880i
$862$		0			0
$863$	9.29822	+	9.29822i	0.316515	+	0.316515i	0.847427	−	0.530912i	$-0.178150\pi$
$863$	9.29822	+	9.29822i	0.316515	+	0.316515i	−0.530912	+	0.847427i	$0.678150\pi$
$864$		0			0
$865$	−1.35089	+	1.35089i	−0.0459316	+	0.0459316i
$866$		0			0
$867$		−	15.6491i		−	0.531472i
$868$	−22.3246	+	35.2982i	−0.757745	+	1.19810i
$869$	−47.1359	+	47.1359i	−1.59898	+	1.59898i
$870$		0			0
$871$	−20.0000	−	25.2982i	−0.677674	−	0.857198i
$872$		0			0
$873$	0.418861	−	0.418861i	0.0141763	−	0.0141763i
$874$		0			0
$875$	−10.8377	+	17.1359i	−0.366382	+	0.579301i
$876$	11.1623	+	11.1623i	0.377138	+	0.377138i
$877$	−31.3246	−	31.3246i	−1.05776	−	1.05776i	−0.998227	−	0.0595285i	$-0.981040\pi$
$877$	−31.3246	−	31.3246i	−1.05776	−	1.05776i	−0.0595285	−	0.998227i	$-0.518960\pi$
$878$		0			0
$879$	22.0680	−	22.0680i	0.744334	−	0.744334i
$880$			19.3509i			0.652318i
$881$	23.6228			0.795872			0.397936	−	0.917413i	$-0.369727\pi$
$881$	23.6228			0.795872			0.397936	+	0.917413i	$0.369727\pi$
$882$		0			0
$883$		−	18.6491i		−	0.627593i	−0.949490	−	0.313796i	$-0.898399\pi$
$883$		−	18.6491i		−	0.627593i	0.949490	−	0.313796i	$-0.101601\pi$
$884$	0.973666	−	8.32456i	0.0327479	−	0.279985i
$885$		−	9.67544i		−	0.325237i
$886$		0			0
$887$		−	27.4868i		−	0.922918i	−0.887162	−	0.461459i	$-0.847326\pi$
$887$		−	27.4868i		−	0.922918i	0.887162	−	0.461459i	$-0.152674\pi$
$888$		0			0
$889$	−5.16228	+	1.16228i	−0.173137	+	0.0389815i
$890$		0			0
$891$	4.16228	−	4.16228i	0.139442	−	0.139442i
$892$	−10.5132	−	10.5132i	−0.352007	−	0.352007i
$893$	−5.51317			−0.184491
$894$		0			0
$895$	0.282918	+	0.282918i	0.00945689	+	0.00945689i
$896$		0			0
$897$	14.9057	+	1.74342i	0.497687	+	0.0582110i
$898$		0			0
$899$	−10.2566	+	10.2566i	−0.342076	+	0.342076i
$900$	−8.64911			−0.288304
$901$	−4.83772			−0.161168
$902$		0			0
$903$	−3.09431	−	13.7434i	−0.102972	−	0.457352i
$904$		0			0
$905$	8.81139	−	8.81139i	0.292900	−	0.292900i
$906$		0			0
$907$		−	30.9473i		−	1.02759i	−0.857913	−	0.513795i	$-0.828239\pi$
$907$		−	30.9473i		−	1.02759i	0.857913	−	0.513795i	$-0.171761\pi$
$908$	−9.67544	−	9.67544i	−0.321091	−	0.321091i
$909$	−17.8114			−0.590766
$910$		0			0
$911$	17.5132			0.580237			0.290119	−	0.956991i	$-0.406305\pi$
$911$	17.5132			0.580237			0.290119	+	0.956991i	$0.406305\pi$
$912$	−1.67544	−	1.67544i	−0.0554795	−	0.0554795i
$913$			54.7851i			1.81312i
$914$		0			0
$915$	−1.83772	+	1.83772i	−0.0607532	+	0.0607532i
$916$	−36.6491	+	36.6491i	−1.21092	+	1.21092i
$917$	−33.9737	+	7.64911i	−1.12191	+	0.252596i
$918$		0			0
$919$	−15.2982			−0.504642			−0.252321	−	0.967644i	$-0.581194\pi$
$919$	−15.2982			−0.504642			−0.252321	+	0.967644i	$0.581194\pi$
$920$		0			0
$921$	−11.0680	+	11.0680i	−0.364702	+	0.364702i
$922$		0			0
$923$	18.9737	+	24.0000i	0.624526	+	0.789970i
$924$	26.3246	+	16.6491i	0.866014	+	0.547716i
$925$	18.7018	+	18.7018i	0.614911	+	0.614911i
$926$		0			0
$927$	−4.00000			−0.131377
$928$		0			0
$929$	22.2566	−	22.2566i	0.730215	−	0.730215i	−0.240447	−	0.970662i	$-0.577294\pi$
$929$	22.2566	−	22.2566i	0.730215	−	0.730215i	0.970662	+	0.240447i	$0.0772941\pi$
$930$		0			0
$931$	−1.39253	+	3.90569i	−0.0456382	+	0.128004i
$932$	44.3246			1.45190
$933$		−	14.3246i		−	0.468965i
$934$		0			0
$935$		−	5.62278i		−	0.183884i
$936$		0			0
$937$		−	26.9737i		−	0.881191i	−0.897706	−	0.440596i	$-0.854767\pi$
$937$		−	26.9737i		−	0.881191i	0.897706	−	0.440596i	$-0.145233\pi$
$938$		0			0
$939$	−19.8114			−0.646520
$940$			15.2982i			0.498973i
$941$	14.7171	−	14.7171i	0.479763	−	0.479763i	−0.425293	−	0.905056i	$-0.639829\pi$
$941$	14.7171	−	14.7171i	0.479763	−	0.479763i	0.905056	+	0.425293i	$0.139829\pi$
$942$		0			0
$943$	29.8114	+	29.8114i	0.970792	+	0.970792i
$944$	33.2982	+	33.2982i	1.08376	+	1.08376i
$945$	1.16228	−	1.83772i	0.0378089	−	0.0597811i
$946$		0			0
$947$	21.6754	−	21.6754i	0.704357	−	0.704357i	−0.260985	−	0.965343i	$-0.584047\pi$
$947$	21.6754	−	21.6754i	0.704357	−	0.704357i	0.965343	+	0.260985i	$0.0840475\pi$
$948$	−22.6491			−0.735609
$949$	17.6491	+	22.3246i	0.572914	+	0.724686i
$950$		0			0
$951$	1.83772	−	1.83772i	0.0595922	−	0.0595922i
$952$		0			0
$953$		−	0.486833i		−	0.0157701i	−0.999969	−	0.00788503i	$-0.997490\pi$
$953$		−	0.486833i		−	0.0157701i	0.999969	−	0.00788503i	$-0.00250991\pi$
$954$		0			0
$955$	−8.32456	+	8.32456i	−0.269376	+	0.269376i
$956$	−12.9737	+	12.9737i	−0.419598	+	0.419598i
$957$	7.64911	+	7.64911i	0.247261	+	0.247261i
$958$		0			0
$959$	−37.9473	−	24.0000i	−1.22538	−	0.775000i
$960$	−4.64911	+	4.64911i	−0.150049	+	0.150049i
$961$		−	31.2982i		−	1.00962i
$962$		0			0
$963$	−10.6491			−0.343163
$964$	7.81139	−	7.81139i	0.251588	−	0.251588i
$965$		−	7.35089i		−	0.236634i
$966$		0			0
$967$	42.9473	+	42.9473i	1.38109	+	1.38109i	0.842683	+	0.538410i	$0.180975\pi$
$967$	42.9473	+	42.9473i	1.38109	+	1.38109i	0.538410	+	0.842683i	$0.319025\pi$
$968$		0			0
$969$	0.486833	+	0.486833i	0.0156393	+	0.0156393i
$970$		0			0
$971$			39.4868i			1.26719i	0.773664	+	0.633596i	$0.218422\pi$
$971$			39.4868i			1.26719i	−0.773664	+	0.633596i	$0.781578\pi$
$972$	2.00000			0.0641500
$973$	18.4868	−	4.16228i	0.592661	−	0.133436i
$974$		0			0
$975$	−15.4868	−	1.81139i	−0.495976	−	0.0580109i
$976$		−	12.6491i		−	0.404888i
$977$	1.83772	+	1.83772i	0.0587939	+	0.0587939i	0.735892	−	0.677098i	$-0.236763\pi$
$977$	1.83772	+	1.83772i	0.0587939	+	0.0587939i	−0.677098	+	0.735892i	$0.736763\pi$
$978$		0			0
$979$	−45.1096			−1.44171
$980$	10.8377	+	3.86406i	0.346198	+	0.123433i
$981$	2.00000	+	2.00000i	0.0638551	+	0.0638551i
$982$		0			0
$983$	−25.7434	−	25.7434i	−0.821087	−	0.821087i	0.165177	−	0.986264i	$-0.447181\pi$
$983$	−25.7434	−	25.7434i	−0.821087	−	0.821087i	−0.986264	+	0.165177i	$0.947181\pi$
$984$		0			0
$985$	−2.13594			−0.0680568
$986$		0			0
$987$	20.8114	+	13.1623i	0.662434	+	0.418960i
$988$	−2.64911	−	3.35089i	−0.0842794	−	0.106606i
$989$	22.1623			0.704719
$990$		0			0
$991$	−38.0000			−1.20711			−0.603555	−	0.797321i	$-0.706250\pi$
$991$	−38.0000			−1.20711			−0.603555	+	0.797321i	$0.706250\pi$
$992$		0			0
$993$	−23.6491	+	23.6491i	−0.750482	+	0.750482i
$994$		0			0
$995$	−5.51317	+	5.51317i	−0.174779	+	0.174779i
$996$	−13.1623	+	13.1623i	−0.417063	+	0.417063i
$997$		−	33.2982i		−	1.05457i	−0.849690	−	0.527283i	$-0.823211\pi$
$997$		−	33.2982i		−	1.05457i	0.849690	−	0.527283i	$-0.176789\pi$
$998$		0			0
$999$	−4.32456	−	4.32456i	−0.136823	−	0.136823i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.p.b.34.2	✓	4
3.2	odd	2		819.2.y.c.307.1		4
7.6	odd	2		273.2.p.c.34.1	yes	4
13.5	odd	4		273.2.p.c.265.1	yes	4
21.20	even	2		819.2.y.b.307.2		4
39.5	even	4		819.2.y.b.811.2		4
91.83	even	4	inner	273.2.p.b.265.2	yes	4
273.83	odd	4		819.2.y.c.811.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.p.b.34.2	✓	4	1.1	even	1	trivial
273.2.p.b.265.2	yes	4	91.83	even	4	inner
273.2.p.c.34.1	yes	4	7.6	odd	2
273.2.p.c.265.1	yes	4	13.5	odd	4
819.2.y.b.307.2		4	21.20	even	2
819.2.y.b.811.2		4	39.5	even	4
819.2.y.c.307.1		4	3.2	odd	2
819.2.y.c.811.1		4	273.83	odd	4

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{3} -2.00000i q^{4} +(0.581139 - 0.581139i) q^{5} +(0.581139 + 2.58114i) q^{7} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{3} -2.00000i q^{4} +(0.581139 - 0.581139i) q^{5} +(0.581139 + 2.58114i) q^{7} -1.00000 q^{9} +(4.16228 - 4.16228i) q^{11} +2.00000 q^{12} +(3.58114 + 0.418861i) q^{13} +(0.581139 + 0.581139i) q^{15} -4.00000 q^{16} +1.16228 q^{17} +(0.418861 - 0.418861i) q^{19} +(-1.16228 - 1.16228i) q^{20} +(-2.58114 + 0.581139i) q^{21} -4.16228i q^{23} +4.32456i q^{25} -1.00000i q^{27} +(5.16228 - 1.16228i) q^{28} +1.83772 q^{29} +(-5.58114 + 5.58114i) q^{31} +(4.16228 + 4.16228i) q^{33} +(1.83772 + 1.16228i) q^{35} +2.00000i q^{36} +(4.32456 - 4.32456i) q^{37} +(-0.418861 + 3.58114i) q^{39} +(-7.16228 + 7.16228i) q^{41} +5.32456i q^{43} +(-8.32456 - 8.32456i) q^{44} +(-0.581139 + 0.581139i) q^{45} +(-6.58114 - 6.58114i) q^{47} -4.00000i q^{48} +(-6.32456 + 3.00000i) q^{49} +1.16228i q^{51} +(0.837722 - 7.16228i) q^{52} -4.16228 q^{53} -4.83772i q^{55} +(0.418861 + 0.418861i) q^{57} +(-8.32456 - 8.32456i) q^{59} +(1.16228 - 1.16228i) q^{60} +3.16228i q^{61} +(-0.581139 - 2.58114i) q^{63} +8.00000i q^{64} +(2.32456 - 1.83772i) q^{65} +(-6.32456 - 6.32456i) q^{67} -2.32456i q^{68} +4.16228 q^{69} +(6.00000 + 6.00000i) q^{71} +(5.58114 + 5.58114i) q^{73} -4.32456 q^{75} +(-0.837722 - 0.837722i) q^{76} +(13.1623 + 8.32456i) q^{77} -11.3246 q^{79} +(-2.32456 + 2.32456i) q^{80} +1.00000 q^{81} +(-6.58114 + 6.58114i) q^{83} +(1.16228 + 5.16228i) q^{84} +(0.675445 - 0.675445i) q^{85} +1.83772i q^{87} +(-5.41886 - 5.41886i) q^{89} +(1.00000 + 9.48683i) q^{91} -8.32456 q^{92} +(-5.58114 - 5.58114i) q^{93} -0.486833i q^{95} +(-0.418861 + 0.418861i) q^{97} +(-4.16228 + 4.16228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^5 - 4 * q^7 - 4 * q^9	\( 4 q - 4 q^{5} - 4 q^{7} - 4 q^{9} + 4 q^{11} + 8 q^{12} + 8 q^{13} - 4 q^{15} - 16 q^{16} - 8 q^{17} + 8 q^{19} + 8 q^{20} - 4 q^{21} + 8 q^{28} + 20 q^{29} - 16 q^{31} + 4 q^{33} + 20 q^{35} - 8 q^{37} - 8 q^{39} - 16 q^{41} - 8 q^{44} + 4 q^{45} - 20 q^{47} + 16 q^{52} - 4 q^{53} + 8 q^{57} - 8 q^{59} - 8 q^{60} + 4 q^{63} - 16 q^{65} + 4 q^{69} + 24 q^{71} + 16 q^{73} + 8 q^{75} - 16 q^{76} + 40 q^{77} - 20 q^{79} + 16 q^{80} + 4 q^{81} - 20 q^{83} - 8 q^{84} + 28 q^{85} - 28 q^{89} + 4 q^{91} - 8 q^{92} - 16 q^{93} - 8 q^{97} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^5 - 4 * q^7 - 4 * q^9 + 4 * q^11 + 8 * q^12 + 8 * q^13 - 4 * q^15 - 16 * q^16 - 8 * q^17 + 8 * q^19 + 8 * q^20 - 4 * q^21 + 8 * q^28 + 20 * q^29 - 16 * q^31 + 4 * q^33 + 20 * q^35 - 8 * q^37 - 8 * q^39 - 16 * q^41 - 8 * q^44 + 4 * q^45 - 20 * q^47 + 16 * q^52 - 4 * q^53 + 8 * q^57 - 8 * q^59 - 8 * q^60 + 4 * q^63 - 16 * q^65 + 4 * q^69 + 24 * q^71 + 16 * q^73 + 8 * q^75 - 16 * q^76 + 40 * q^77 - 20 * q^79 + 16 * q^80 + 4 * q^81 - 20 * q^83 - 8 * q^84 + 28 * q^85 - 28 * q^89 + 4 * q^91 - 8 * q^92 - 16 * q^93 - 8 * q^97 - 4 * q^99

Introduction

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