LMFDB - Embedded newform 273.2.p.c.265.1

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			265.1
Root			$1.58114 - 1.58114i$ of defining polynomial
Character	$\chi$	$=$	273.265
Dual form			273.2.p.c.34.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{3} +2.00000i q^{4} +(-0.581139 - 0.581139i) q^{5} +(-2.58114 + 0.581139i) q^{7} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{3} +2.00000i q^{4} +(-0.581139 - 0.581139i) q^{5} +(-2.58114 + 0.581139i) q^{7} -1.00000 q^{9} +(4.16228 + 4.16228i) q^{11} -2.00000 q^{12} +(-3.58114 + 0.418861i) q^{13} +(0.581139 - 0.581139i) q^{15} -4.00000 q^{16} -1.16228 q^{17} +(-0.418861 - 0.418861i) q^{19} +(1.16228 - 1.16228i) q^{20} +(-0.581139 - 2.58114i) q^{21} +4.16228i q^{23} -4.32456i q^{25} -1.00000i q^{27} +(-1.16228 - 5.16228i) q^{28} +1.83772 q^{29} +(5.58114 + 5.58114i) q^{31} +(-4.16228 + 4.16228i) q^{33} +(1.83772 + 1.16228i) q^{35} -2.00000i q^{36} +(4.32456 + 4.32456i) q^{37} +(-0.418861 - 3.58114i) q^{39} +(7.16228 + 7.16228i) q^{41} -5.32456i q^{43} +(-8.32456 + 8.32456i) q^{44} +(0.581139 + 0.581139i) q^{45} +(6.58114 - 6.58114i) q^{47} -4.00000i q^{48} +(6.32456 - 3.00000i) q^{49} -1.16228i q^{51} +(-0.837722 - 7.16228i) q^{52} -4.16228 q^{53} -4.83772i q^{55} +(0.418861 - 0.418861i) q^{57} +(8.32456 - 8.32456i) q^{59} +(1.16228 + 1.16228i) q^{60} +3.16228i q^{61} +(2.58114 - 0.581139i) q^{63} -8.00000i q^{64} +(2.32456 + 1.83772i) q^{65} +(-6.32456 + 6.32456i) q^{67} -2.32456i q^{68} -4.16228 q^{69} +(6.00000 - 6.00000i) q^{71} +(-5.58114 + 5.58114i) q^{73} +4.32456 q^{75} +(0.837722 - 0.837722i) q^{76} +(-13.1623 - 8.32456i) q^{77} -11.3246 q^{79} +(2.32456 + 2.32456i) q^{80} +1.00000 q^{81} +(6.58114 + 6.58114i) q^{83} +(5.16228 - 1.16228i) q^{84} +(0.675445 + 0.675445i) q^{85} +1.83772i q^{87} +(5.41886 - 5.41886i) q^{89} +(9.00000 - 3.16228i) q^{91} -8.32456 q^{92} +(-5.58114 + 5.58114i) q^{93} +0.486833i q^{95} +(0.418861 + 0.418861i) q^{97} +(-4.16228 - 4.16228i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 36 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 + 36 * 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 $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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	$-0.750000\pi$
$2$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$3$			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	$-0.308831\pi$
$5$	−0.581139	−	0.581139i	−0.259893	−	0.259893i	−0.825011	+	0.565117i	$0.808831\pi$
$6$		0			0
$7$	−2.58114	+	0.581139i	−0.975579	+	0.219650i
$7$	−2.58114	+	0.581139i	−0.975579	+	0.219650i
$8$		0			0
$9$	−1.00000			−0.333333
$10$		0			0
$11$	4.16228	+	4.16228i	1.25497	+	1.25497i	0.953463	+	0.301511i	$0.0974911\pi$
$11$	4.16228	+	4.16228i	1.25497	+	1.25497i	0.301511	+	0.953463i	$0.402509\pi$
$12$	−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	$-0.545015\pi$
$17$	−1.16228			−0.281894			−0.140947	+	0.990017i	$0.545015\pi$
$18$		0			0
$19$	−0.418861	−	0.418861i	−0.0960933	−	0.0960933i	0.657426	−	0.753519i	$-0.271645\pi$
$19$	−0.418861	−	0.418861i	−0.0960933	−	0.0960933i	−0.753519	+	0.657426i	$0.771645\pi$
$20$	1.16228	−	1.16228i	0.259893	−	0.259893i
$21$	−0.581139	−	2.58114i	−0.126815	−	0.563251i
$22$		0			0
$23$			4.16228i			0.867895i	0.900938	+	0.433947i	$0.142880\pi$
$23$			4.16228i			0.867895i	−0.900938	+	0.433947i	$0.857120\pi$
$24$		0			0
$25$		−	4.32456i		−	0.864911i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$	−1.16228	−	5.16228i	−0.219650	−	0.975579i
$29$	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	0.999997	+	0.00240502i	$0.000765542\pi$
$31$	5.58114	+	5.58114i	1.00240	+	1.00240i	0.00240502	+	0.999997i	$0.499234\pi$
$32$		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	0.966734	−	0.255782i	$-0.0823329\pi$
$37$	4.32456	+	4.32456i	0.710953	+	0.710953i	−0.255782	+	0.966734i	$0.582333\pi$
$38$		0			0
$39$	−0.418861	−	3.58114i	−0.0670715	−	0.573441i
$40$		0			0
$41$	7.16228	+	7.16228i	1.11856	+	1.11856i	0.991953	+	0.126607i	$0.0404087\pi$
$41$	7.16228	+	7.16228i	1.11856	+	1.11856i	0.126607	+	0.991953i	$0.459591\pi$
$42$		0			0
$43$		−	5.32456i		−	0.811987i	−0.913876	−	0.405994i	$-0.866926\pi$
$43$		−	5.32456i		−	0.811987i	0.913876	−	0.405994i	$-0.133074\pi$
$44$	−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	$-0.512504\pi$
$47$	6.58114	−	6.58114i	0.959958	−	0.959958i	0.999229	+	0.0392708i	$0.0125035\pi$
$48$		−	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	0.0876099	−	0.996155i	$-0.472077\pi$
$59$	8.32456	−	8.32456i	1.08376	−	1.08376i	0.996155	−	0.0876099i	$-0.0279229\pi$
$60$	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
$63$	2.58114	−	0.581139i	0.325193	−	0.0732166i
$64$		−	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	−0.978572	−	0.205905i	$-0.933986\pi$
$67$	−6.32456	+	6.32456i	−0.772667	+	0.772667i	0.205905	+	0.978572i	$0.433986\pi$
$68$		−	2.32456i		−	0.281894i
$69$	−4.16228			−0.501079
$70$		0			0
$71$	6.00000	−	6.00000i	0.712069	−	0.712069i	−0.254899	−	0.966968i	$-0.582042\pi$
$71$	6.00000	−	6.00000i	0.712069	−	0.712069i	0.966968	+	0.254899i	$0.0820421\pi$
$72$		0			0
$73$	−5.58114	+	5.58114i	−0.653223	+	0.653223i	−0.953768	−	0.300545i	$-0.902832\pi$
$73$	−5.58114	+	5.58114i	−0.653223	+	0.653223i	0.300545	+	0.953768i	$0.402832\pi$
$74$		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	$-0.0793510\pi$
$83$	6.58114	+	6.58114i	0.722374	+	0.722374i	−0.246714	+	0.969088i	$0.579351\pi$
$84$	5.16228	−	1.16228i	0.563251	−	0.126815i
$85$	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	$-0.616867\pi$
$89$	5.41886	−	5.41886i	0.574398	−	0.574398i	0.933354	+	0.358956i	$0.116867\pi$
$90$		0			0
$91$	9.00000	−	3.16228i	0.943456	−	0.331497i
$92$	−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	$-0.240426\pi$
$97$	0.418861	+	0.418861i	0.0425289	+	0.0425289i	−0.685523	+	0.728051i	$0.740426\pi$
$98$		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	$-0.846630\pi$
$101$	−17.8114			−1.77230			−0.886150	+	0.463399i	$0.846630\pi$
$102$		0			0
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$		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	−0.796372	−	0.604807i	$-0.793250\pi$
$109$	−2.00000	+	2.00000i	−0.191565	+	0.191565i	0.604807	+	0.796372i	$0.293250\pi$
$110$		0			0
$111$	−4.32456	+	4.32456i	−0.410469	+	0.410469i
$112$	10.3246	−	2.32456i	0.975579	−	0.219650i
$113$	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
$119$	3.00000	−	0.675445i	0.275010	−	0.0619179i
$120$		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	$-0.971717\pi$
$127$		−	2.00000i		−	0.177471i	0.996055	−	0.0887357i	$-0.0282826\pi$
$128$		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	−0.999673	−	0.0255558i	$-0.991864\pi$
$137$	−12.0000	−	12.0000i	−1.02523	−	1.02523i	−0.0255558	−	0.999673i	$-0.508136\pi$
$138$		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	−0.987862	−	0.155336i	$-0.950354\pi$
$149$	−10.1623	+	10.1623i	−0.832526	+	0.832526i	0.155336	+	0.987862i	$0.450354\pi$
$150$		0			0
$151$	−4.00000	−	4.00000i	−0.325515	−	0.325515i	0.525363	−	0.850878i	$-0.323930\pi$
$151$	−4.00000	−	4.00000i	−0.325515	−	0.325515i	−0.850878	+	0.525363i	$0.823930\pi$
$152$		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
$161$	−2.41886	−	10.7434i	−0.190633	−	0.846700i
$162$		0			0
$163$	−1.32456	−	1.32456i	−0.103747	−	0.103747i	0.653328	−	0.757075i	$-0.273372\pi$
$163$	−1.32456	−	1.32456i	−0.103747	−	0.103747i	−0.757075	+	0.653328i	$0.773372\pi$
$164$	−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	$-0.699175\pi$
$167$	2.90569	−	2.90569i	0.224849	−	0.224849i	0.810537	+	0.585688i	$0.199175\pi$
$168$		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	$-0.471835\pi$
$173$	2.32456			0.176733			0.0883663	+	0.996088i	$0.471835\pi$
$174$		0			0
$175$	2.51317	+	11.1623i	0.189978	+	0.843789i
$176$	−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	$-0.994208\pi$
$179$		−	0.486833i		−	0.0363876i	0.999834	−	0.0181938i	$-0.00579159\pi$
$180$	−1.16228	+	1.16228i	−0.0866311	+	0.0866311i
$181$	−15.1623			−1.12700			−0.563502	−	0.826115i	$-0.690546\pi$
$181$	−15.1623			−1.12700			−0.563502	+	0.826115i	$0.690546\pi$
$182$		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
$189$	0.581139	+	2.58114i	0.0422716	+	0.187750i
$190$		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	0.897093	−	0.441842i	$-0.145675\pi$
$193$	6.32456	+	6.32456i	0.455251	+	0.455251i	−0.441842	+	0.897093i	$0.645675\pi$
$194$		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	−0.769536	−	0.638604i	$-0.779512\pi$
$197$	−1.83772	+	1.83772i	−0.130932	+	0.130932i	0.638604	+	0.769536i	$0.279512\pi$
$198$		0			0
$199$	9.48683			0.672504			0.336252	−	0.941772i	$-0.390841\pi$
$199$	9.48683			0.672504			0.336252	+	0.941772i	$0.390841\pi$
$200$		0			0
$201$	−6.32456	−	6.32456i	−0.446100	−	0.446100i
$202$		0			0
$203$	−4.74342	+	1.06797i	−0.332923	+	0.0749569i
$204$	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	$-0.330071\pi$
$223$	−5.25658	−	5.25658i	−0.352007	−	0.352007i	−0.860856	+	0.508849i	$0.830071\pi$
$224$		0			0
$225$			4.32456i			0.288304i
$226$		0			0
$227$	−4.83772	−	4.83772i	−0.321091	−	0.321091i	0.528095	−	0.849186i	$-0.322907\pi$
$227$	−4.83772	−	4.83772i	−0.321091	−	0.321091i	−0.849186	+	0.528095i	$0.822907\pi$
$228$	0.837722	+	0.837722i	0.0554795	+	0.0554795i
$229$	18.3246	−	18.3246i	1.21092	−	1.21092i	0.240196	−	0.970724i	$-0.422788\pi$
$229$	18.3246	−	18.3246i	1.21092	−	1.21092i	0.970724	−	0.240196i	$-0.0772118\pi$
$230$		0			0
$231$	8.32456	−	13.1623i	0.547716	−	0.866014i
$232$		0			0
$233$		−	22.1623i		−	1.45190i	−0.687748	−	0.725950i	$-0.741401\pi$
$233$		−	22.1623i		−	1.45190i	0.687748	−	0.725950i	$-0.258599\pi$
$234$		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	−0.885065	−	0.465467i	$-0.845886\pi$
$239$	−6.48683	+	6.48683i	−0.419598	+	0.419598i	0.465467	+	0.885065i	$0.345886\pi$
$240$	−2.32456	+	2.32456i	−0.150049	+	0.150049i
$241$	−3.90569	+	3.90569i	−0.251588	+	0.251588i	−0.821621	−	0.570034i	$-0.806930\pi$
$241$	−3.90569	+	3.90569i	−0.251588	+	0.251588i	0.570034	+	0.821621i	$0.306930\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$	−6.32456			−0.404888
$245$	−5.41886	−	1.93203i	−0.346198	−	0.123433i
$246$		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	$-0.165740\pi$
$251$	27.4868			1.73495			0.867477	+	0.497478i	$0.165740\pi$
$252$	1.16228	+	5.16228i	0.0732166	+	0.325193i
$253$	−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	$-0.827854\pi$
$257$	−27.4868			−1.71458			−0.857291	+	0.514833i	$0.827854\pi$
$258$		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	$-0.553322\pi$
$271$	13.4868	−	13.4868i	0.819267	−	0.819267i	0.986002	+	0.166735i	$0.0533224\pi$
$272$	4.64911			0.281894
$273$	3.16228	+	9.00000i	0.191390	+	0.544705i
$274$		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	$-0.958274\pi$
$277$		−	4.35089i		−	0.261420i	0.991421	−	0.130710i	$-0.0417256\pi$
$278$		0			0
$279$	−5.58114	−	5.58114i	−0.334134	−	0.334134i
$280$		0			0
$281$	9.67544	+	9.67544i	0.577189	+	0.577189i	0.934128	−	0.356939i	$-0.116180\pi$
$281$	9.67544	+	9.67544i	0.577189	+	0.577189i	−0.356939	+	0.934128i	$0.616180\pi$
$282$		0			0
$283$	21.2982			1.26605			0.633024	−	0.774132i	$-0.281813\pi$
$283$	21.2982			1.26605			0.633024	+	0.774132i	$0.281813\pi$
$284$	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	0.353967	−	0.935258i	$-0.384833\pi$
$293$	22.0680	−	22.0680i	1.28922	−	1.28922i	0.935258	−	0.353967i	$-0.115167\pi$
$294$		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
$301$	3.09431	+	13.7434i	0.178353	+	0.792157i
$302$		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	$-0.897389\pi$
$307$	−11.0680	+	11.0680i	−0.631683	+	0.631683i	0.316807	+	0.948490i	$0.397389\pi$
$308$	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	$-0.366876\pi$
$311$	14.3246			0.812271			0.406136	+	0.913813i	$0.366876\pi$
$312$		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	−0.756829	−	0.653613i	$-0.773253\pi$
$317$	−1.83772	+	1.83772i	−0.103217	+	0.103217i	0.653613	+	0.756829i	$0.273253\pi$
$318$		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	0.371400	−	0.928473i	$-0.378878\pi$
$331$	23.6491	−	23.6491i	1.29987	−	1.29987i	0.928473	−	0.371400i	$-0.121122\pi$
$332$	−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
$336$	2.32456	+	10.3246i	0.126815	+	0.563251i
$337$			13.0000i			0.708155i	0.935216	+	0.354078i	$0.115205\pi$
$337$			13.0000i			0.708155i	−0.935216	+	0.354078i	$0.884795\pi$
$338$		0			0
$339$			14.8114i			0.804444i
$340$	−1.35089	+	1.35089i	−0.0732623	+	0.0732623i
$341$			46.4605i			2.51598i
$342$		0			0
$343$	−14.5811	+	11.4189i	−0.787307	+	0.616561i
$344$		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	$-0.910215\pi$
$349$	−12.7434	+	12.7434i	−0.682139	+	0.682139i	0.278342	+	0.960482i	$0.410215\pi$
$350$		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	$-0.366215\pi$
$353$	−9.48683	−	9.48683i	−0.504933	−	0.504933i	−0.912967	+	0.408034i	$0.866215\pi$
$354$		0			0
$355$	−6.97367			−0.370124
$356$	10.8377	+	10.8377i	0.574398	+	0.574398i
$357$	0.675445	+	3.00000i	0.0357483	+	0.158777i
$358$		0			0
$359$	10.1623	+	10.1623i	0.536345	+	0.536345i	0.922453	−	0.386109i	$-0.126181\pi$
$359$	10.1623	+	10.1623i	0.536345	+	0.536345i	−0.386109	+	0.922453i	$0.626181\pi$
$360$		0			0
$361$		−	18.6491i		−	0.981532i
$362$		0			0
$363$	−23.6491			−1.24126
$364$	6.32456	+	18.0000i	0.331497	+	0.943456i
$365$	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
$371$	10.7434	−	2.41886i	0.557770	−	0.125581i
$372$	−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	−0.863653	−	0.504087i	$-0.831829\pi$
$379$	−7.00000	+	7.00000i	−0.359566	+	0.359566i	0.504087	+	0.863653i	$0.331829\pi$
$380$	−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	$-0.292397\pi$
$383$	−3.67544	−	3.67544i	−0.187806	−	0.187806i	−0.794747	+	0.606941i	$0.792397\pi$
$384$		0			0
$385$	2.81139	+	12.4868i	0.143282	+	0.636388i
$386$		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	$-0.951394\pi$
$389$		−	6.00000i		−	0.304212i	0.988364	−	0.152106i	$-0.0486055\pi$
$390$		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	$-0.809730\pi$
$397$	−5.25658	+	5.25658i	−0.263820	+	0.263820i	0.562784	+	0.826604i	$0.309730\pi$
$398$		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	0.875185	−	0.483788i	$-0.160739\pi$
$401$	7.83772	+	7.83772i	0.391397	+	0.391397i	−0.483788	+	0.875185i	$0.660739\pi$
$402$		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	$-0.487172\pi$
$409$	−19.3925	−	19.3925i	−0.958899	−	0.958899i	−0.999188	+	0.0402893i	$0.987172\pi$
$410$		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	−0.505720	−	0.862697i	$-0.668773\pi$
$421$	7.32456	−	7.32456i	0.356977	−	0.356977i	0.862697	+	0.505720i	$0.168773\pi$
$422$		0			0
$423$	−6.58114	+	6.58114i	−0.319986	+	0.319986i
$424$		0			0
$425$			5.02633i			0.243813i
$426$		0			0
$427$	−1.83772	−	8.16228i	−0.0889336	−	0.395000i
$428$			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	−0.967253	−	0.253814i	$-0.918315\pi$
$431$	−14.8114	+	14.8114i	−0.713439	+	0.713439i	0.253814	+	0.967253i	$0.418315\pi$
$432$			4.00000i			0.192450i
$433$	−7.16228			−0.344197			−0.172099	−	0.985080i	$-0.555055\pi$
$433$	−7.16228			−0.344197			−0.172099	+	0.985080i	$0.555055\pi$
$434$		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	$-0.748454\pi$
$439$	−29.4868			−1.40733			−0.703665	+	0.710532i	$0.748454\pi$
$440$		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
$448$	4.64911	+	20.6491i	0.219650	+	0.975579i
$449$	2.81139	+	2.81139i	0.132678	+	0.132678i	0.770327	−	0.637649i	$-0.220093\pi$
$449$	2.81139	+	2.81139i	0.132678	+	0.132678i	−0.637649	+	0.770327i	$0.720093\pi$
$450$		0			0
$451$			59.6228i			2.80753i
$452$			29.6228i			1.39334i
$453$	4.00000	−	4.00000i	0.187936	−	0.187936i
$454$		0			0
$455$	−7.06797	−	3.39253i	−0.331352	−	0.159044i
$456$		0			0
$457$	1.32456	−	1.32456i	0.0619601	−	0.0619601i	−0.675448	−	0.737408i	$-0.736050\pi$
$457$	1.32456	−	1.32456i	0.0619601	−	0.0619601i	0.737408	+	0.675448i	$0.236050\pi$
$458$		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	$-0.0165711\pi$
$461$	20.3246	+	20.3246i	0.946609	+	0.946609i	−0.0520363	+	0.998645i	$0.516571\pi$
$462$		0			0
$463$	2.64911	+	2.64911i	0.123115	+	0.123115i	0.765980	−	0.642865i	$-0.222254\pi$
$463$	2.64911	+	2.64911i	0.123115	+	0.123115i	−0.642865	+	0.765980i	$0.722254\pi$
$464$	−7.35089			−0.341256
$465$	6.48683			0.300820
$466$		0			0
$467$	30.9737			1.43329			0.716645	−	0.697438i	$-0.245677\pi$
$467$	30.9737			1.43329			0.716645	+	0.697438i	$0.245677\pi$
$468$	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
$476$	1.35089	+	6.00000i	0.0619179	+	0.275010i
$477$	4.16228			0.190578
$478$		0			0
$479$	5.41886	−	5.41886i	0.247594	−	0.247594i	−0.572388	−	0.819983i	$-0.693983\pi$
$479$	5.41886	−	5.41886i	0.247594	−	0.247594i	0.819983	+	0.572388i	$0.193983\pi$
$480$		0			0
$481$	−17.2982	−	13.6754i	−0.788731	−	0.623547i
$482$		0			0
$483$	10.7434	−	2.41886i	0.488842	−	0.110062i
$484$	−47.2982			−2.14992
$485$		−	0.486833i		−	0.0221059i
$486$		0			0
$487$	1.32456	−	1.32456i	0.0600213	−	0.0600213i	−0.676459	−	0.736480i	$-0.736486\pi$
$487$	1.32456	−	1.32456i	0.0600213	−	0.0600213i	0.736480	+	0.676459i	$0.236486\pi$
$488$		0			0
$489$	1.32456	−	1.32456i	0.0598985	−	0.0598985i
$490$		0			0
$491$			26.3246i			1.18801i	0.804461	+	0.594005i	$0.202454\pi$
$491$			26.3246i			1.18801i	−0.804461	+	0.594005i	$0.797546\pi$
$492$	−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	−0.126838	−	0.991923i	$-0.540483\pi$
$499$	19.3246	−	19.3246i	0.865086	−	0.865086i	0.991923	+	0.126838i	$0.0404827\pi$
$500$	−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	$-0.0225737\pi$
$509$	20.9057	+	20.9057i	0.926629	+	0.926629i	−0.0708578	+	0.997486i	$0.522574\pi$
$510$		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
$525$	−11.1623	+	2.51317i	−0.487162	+	0.109684i
$526$		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
$539$	38.8114	+	13.8377i	1.67172	+	0.596033i
$540$	−1.16228	−	1.16228i	−0.0500165	−	0.0500165i
$541$	−4.00000	−	4.00000i	−0.171973	−	0.171973i	0.615872	−	0.787846i	$-0.288804\pi$
$541$	−4.00000	−	4.00000i	−0.171973	−	0.171973i	−0.787846	+	0.615872i	$0.788804\pi$
$542$		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
$553$	29.2302	−	6.58114i	1.24300	−	0.279858i
$554$		0			0
$555$	5.02633			0.213356
$556$	14.3246			0.607496
$557$	−4.64911	−	4.64911i	−0.196989	−	0.196989i	0.601719	−	0.798708i	$-0.294483\pi$
$557$	−4.64911	−	4.64911i	−0.196989	−	0.196989i	−0.798708	+	0.601719i	$0.794483\pi$
$558$		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	$-0.656937\pi$
$563$	−22.4605			−0.946597			−0.473299	+	0.880902i	$0.656937\pi$
$564$	−13.1623	+	13.1623i	−0.554232	+	0.554232i
$565$	−8.60747	−	8.60747i	−0.362119	−	0.362119i
$566$		0			0
$567$	−2.58114	+	0.581139i	−0.108398	+	0.0244055i
$568$		0			0
$569$		−	30.4868i		−	1.27807i	−0.769176	−	0.639037i	$-0.779333\pi$
$569$		−	30.4868i		−	1.27807i	0.769176	−	0.639037i	$-0.220667\pi$
$570$		0			0
$571$			21.3246i			0.892405i	0.894932	+	0.446202i	$0.147224\pi$
$571$			21.3246i			0.892405i	−0.894932	+	0.446202i	$0.852776\pi$
$572$	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	$-0.325672\pi$
$577$	−8.00000	−	8.00000i	−0.333044	−	0.333044i	−0.853741	+	0.520697i	$0.825672\pi$
$578$		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	$-0.233797\pi$
$587$	1.74342	+	1.74342i	0.0719585	+	0.0719585i	−0.670212	+	0.742170i	$0.733797\pi$
$588$	−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	$-0.721361\pi$
$593$	3.09431	−	3.09431i	0.127068	−	0.127068i	0.767781	+	0.640713i	$0.221361\pi$
$594$		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
$609$	−1.06797	−	4.74342i	−0.0432764	−	0.192213i
$610$		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	−0.839380	−	0.543544i	$-0.817082\pi$
$613$	−7.32456	+	7.32456i	−0.295836	+	0.295836i	0.543544	+	0.839380i	$0.317082\pi$
$614$		0			0
$615$	8.32456			0.335678
$616$		0			0
$617$	24.4868	−	24.4868i	0.985803	−	0.985803i	−0.0140978	−	0.999901i	$-0.504488\pi$
$617$	24.4868	−	24.4868i	0.985803	−	0.985803i	0.999901	+	0.0140978i	$0.00448763\pi$
$618$		0			0
$619$	5.67544	−	5.67544i	0.228115	−	0.228115i	−0.583790	−	0.811905i	$-0.698431\pi$
$619$	5.67544	−	5.67544i	0.228115	−	0.228115i	0.811905	+	0.583790i	$0.198431\pi$
$620$	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	0.776001	−	0.630732i	$-0.217245\pi$
$631$	3.64911	+	3.64911i	0.145269	+	0.145269i	−0.630732	+	0.776001i	$0.717245\pi$
$632$		0			0
$633$			19.6491i			0.780982i
$634$		0			0
$635$	−1.16228	+	1.16228i	−0.0461236	+	0.0461236i
$636$	8.32456			0.330090
$637$	−21.3925	+	13.3925i	−0.847603	+	0.530631i
$638$		0			0
$639$	−6.00000	+	6.00000i	−0.237356	+	0.237356i
$640$		0			0
$641$		−	24.4868i		−	0.967172i	−0.875297	−	0.483586i	$-0.839334\pi$
$641$		−	24.4868i		−	0.967172i	0.875297	−	0.483586i	$-0.160666\pi$
$642$		0			0
$643$	4.18861	+	4.18861i	0.165183	+	0.165183i	0.784858	−	0.619675i	$-0.212736\pi$
$643$	4.18861	+	4.18861i	0.165183	+	0.165183i	−0.619675	+	0.784858i	$0.712736\pi$
$644$	21.4868	−	4.83772i	0.846700	−	0.190633i
$645$	−3.09431	−	3.09431i	−0.121838	−	0.121838i
$646$		0			0
$647$	−6.97367			−0.274163			−0.137082	−	0.990560i	$-0.543772\pi$
$647$	−6.97367			−0.274163			−0.137082	+	0.990560i	$0.543772\pi$
$648$		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	$-0.784259\pi$
$661$	−3.90569	+	3.90569i	−0.151914	+	0.151914i	0.627058	+	0.778972i	$0.284259\pi$
$662$		0			0
$663$	0.486833	+	4.16228i	0.0189070	+	0.161649i
$664$		0			0
$665$	−0.282918	−	1.25658i	−0.0109711	−	0.0487282i
$666$		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	$-0.869887\pi$
$673$		−	20.6228i		−	0.794950i	0.917613	−	0.397475i	$-0.130113\pi$
$674$		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	0.992099	−	0.125455i	$-0.0400391\pi$
$683$	22.6491	+	22.6491i	0.866644	+	0.866644i	−0.125455	+	0.992099i	$0.540039\pi$
$684$	−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	$-0.141580\pi$
$691$	12.4189	+	12.4189i	0.472436	+	0.472436i	−0.430266	+	0.902702i	$0.641580\pi$
$692$			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
$700$	−22.3246	+	5.02633i	−0.843789	+	0.189978i
$701$		−	1.83772i		−	0.0694098i	−0.999398	−	0.0347049i	$-0.988951\pi$
$701$		−	1.83772i		−	0.0694098i	0.999398	−	0.0347049i	$-0.0110491\pi$
$702$		0			0
$703$		−	3.62278i		−	0.136636i
$704$	33.2982	−	33.2982i	1.25497	−	1.25497i
$705$		−	7.64911i		−	0.288082i
$706$		0			0
$707$	45.9737	−	10.3509i	1.72902	−	0.389285i
$708$	−16.6491	+	16.6491i	−0.625712	+	0.625712i
$709$	32.2982	+	32.2982i	1.21299	+	1.21299i	0.970040	+	0.242945i	$0.0781135\pi$
$709$	32.2982	+	32.2982i	1.21299	+	1.21299i	0.242945	+	0.970040i	$0.421887\pi$
$710$		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	$-0.615110\pi$
$719$	−18.9737			−0.707598			−0.353799	+	0.935321i	$0.615110\pi$
$720$	−2.32456	−	2.32456i	−0.0866311	−	0.0866311i
$721$	10.3246	−	2.32456i	0.384507	−	0.0865710i
$722$		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	$-0.711847\pi$
$727$	−33.2982			−1.23496			−0.617481	+	0.786586i	$0.711847\pi$
$728$		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	−0.999513	−	0.0312074i	$-0.990065\pi$
$733$	−27.9057	−	27.9057i	−1.03072	−	1.03072i	−0.0312074	−	0.999513i	$-0.509935\pi$
$734$		0			0
$735$	1.93203	−	5.41886i	0.0712639	−	0.199878i
$736$		0			0
$737$	−52.6491			−1.93935
$738$		0			0
$739$	−5.64911	−	5.64911i	−0.207806	−	0.207806i	0.595528	−	0.803334i	$-0.296943\pi$
$739$	−5.64911	−	5.64911i	−0.207806	−	0.207806i	−0.803334	+	0.595528i	$0.796943\pi$
$740$	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	−0.836106	−	0.548568i	$-0.815173\pi$
$743$	−7.83772	+	7.83772i	−0.287538	+	0.287538i	0.548568	+	0.836106i	$0.315173\pi$
$744$		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
$749$	−27.4868	+	6.18861i	−1.00435	+	0.226127i
$750$		0			0
$751$			11.3246i			0.413239i	0.978421	+	0.206619i	$0.0662462\pi$
$751$			11.3246i			0.413239i	−0.978421	+	0.206619i	$0.933754\pi$
$752$	−26.3246	+	26.3246i	−0.959958	+	0.959958i
$753$			27.4868i			1.00168i
$754$		0			0
$755$			4.64911i			0.169198i
$756$	−5.16228	+	1.16228i	−0.187750	+	0.0422716i
$757$	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	$-0.805516\pi$
$761$	−6.76975	+	6.76975i	−0.245403	+	0.245403i	0.573678	+	0.819081i	$0.305516\pi$
$762$		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	$-0.0787628\pi$
$769$	20.0943	+	20.0943i	0.724619	+	0.724619i	−0.244923	+	0.969542i	$0.578763\pi$
$770$		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	$-0.172434\pi$
$773$	9.48683	+	9.48683i	0.341218	+	0.341218i	−0.515607	+	0.856825i	$0.672434\pi$
$774$		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	$-0.928195\pi$
$787$	−21.0680	+	21.0680i	−0.750992	+	0.750992i	0.223672	+	0.974664i	$0.428195\pi$
$788$	−3.67544	−	3.67544i	−0.130932	−	0.130932i
$789$			18.4868i			0.658149i
$790$		0			0
$791$	−38.2302	+	8.60747i	−1.35931	+	0.306047i
$792$		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	$-0.700770\pi$
$797$	−33.2982			−1.17948			−0.589742	+	0.807592i	$0.700770\pi$
$798$		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	−0.992172	−	0.124877i	$-0.960146\pi$
$811$	−31.8114	−	31.8114i	−1.11705	−	1.11705i	−0.124877	−	0.992172i	$-0.539854\pi$
$812$	−2.13594	−	9.48683i	−0.0749569	−	0.332923i
$813$	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
$819$	−9.00000	+	3.16228i	−0.314485	+	0.110499i
$820$	16.6491			0.581412
$821$	−20.3246	+	20.3246i	−0.709332	+	0.709332i	−0.966395	−	0.257063i	$-0.917245\pi$
$821$	−20.3246	+	20.3246i	−0.709332	+	0.709332i	0.257063	+	0.966395i	$0.417245\pi$
$822$		0			0
$823$			13.3509i			0.465383i	0.972551	+	0.232691i	$0.0747532\pi$
$823$			13.3509i			0.465383i	−0.972551	+	0.232691i	$0.925247\pi$
$824$		0			0
$825$	18.0000	+	18.0000i	0.626680	+	0.626680i
$826$		0			0
$827$	16.1623	+	16.1623i	0.562017	+	0.562017i	0.929880	−	0.367863i	$-0.119910\pi$
$827$	16.1623	+	16.1623i	0.562017	+	0.562017i	−0.367863	+	0.929880i	$0.619910\pi$
$828$	8.32456			0.289298
$829$	−33.6754			−1.16960			−0.584798	−	0.811179i	$-0.698826\pi$
$829$	−33.6754			−1.16960			−0.584798	+	0.811179i	$0.698826\pi$
$830$		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	$-0.574238\pi$
$839$	21.4868	−	21.4868i	0.741808	−	0.741808i	0.972926	+	0.231118i	$0.0742383\pi$
$840$		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
$847$	−13.7434	−	61.0416i	−0.472229	−	2.09742i
$848$	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	$-0.764692\pi$
$853$	−1.90569	+	1.90569i	−0.0652497	+	0.0652497i	0.673729	+	0.738979i	$0.264692\pi$
$854$		0			0
$855$		−	0.486833i		−	0.0166493i
$856$		0			0
$857$	36.7851			1.25655			0.628277	−	0.777990i	$-0.283761\pi$
$857$	36.7851			1.25655			0.628277	+	0.777990i	$0.283761\pi$
$858$		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	−0.530912	−	0.847427i	$-0.678150\pi$
$863$	9.29822	−	9.29822i	0.316515	−	0.316515i	0.847427	+	0.530912i	$0.178150\pi$
$864$		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	−0.0595285	+	0.998227i	$0.518960\pi$
$877$	−31.3246	+	31.3246i	−1.05776	+	1.05776i	−0.998227	+	0.0595285i	$0.981040\pi$
$878$		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	$-0.630273\pi$
$881$	−23.6228			−0.795872			−0.397936	+	0.917413i	$0.630273\pi$
$882$		0			0
$883$			18.6491i			0.627593i	0.949490	+	0.313796i	$0.101601\pi$
$883$			18.6491i			0.627593i	−0.949490	+	0.313796i	$0.898399\pi$
$884$	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
$889$	1.16228	+	5.16228i	0.0389815	+	0.173137i
$890$		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
$903$	−13.7434	+	3.09431i	−0.457352	+	0.102972i
$904$		0			0
$905$	8.81139	+	8.81139i	0.292900	+	0.292900i
$906$		0			0
$907$			30.9473i			1.02759i	0.857913	+	0.513795i	$0.171761\pi$
$907$			30.9473i			1.02759i	−0.857913	+	0.513795i	$0.828239\pi$
$908$	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
$917$	−7.64911	−	33.9737i	−0.252596	−	1.12191i
$918$		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	$-0.422706\pi$
$929$	−22.2566	−	22.2566i	−0.730215	−	0.730215i	−0.970662	+	0.240447i	$0.922706\pi$
$930$		0			0
$931$	−3.90569	−	1.39253i	−0.128004	−	0.0456382i
$932$	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	$-0.360171\pi$
$941$	−14.7171	−	14.7171i	−0.479763	−	0.479763i	−0.905056	+	0.425293i	$0.860171\pi$
$942$		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	0.965343	−	0.260985i	$-0.0840475\pi$
$947$	21.6754	+	21.6754i	0.704357	+	0.704357i	−0.260985	+	0.965343i	$0.584047\pi$
$948$	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	$0.00250991\pi$
$953$			0.486833i			0.0157701i	−0.999969	+	0.00788503i	$0.997490\pi$
$954$		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	0.538410	−	0.842683i	$-0.319025\pi$
$967$	42.9473	−	42.9473i	1.38109	−	1.38109i	0.842683	−	0.538410i	$-0.180975\pi$
$968$		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
$973$	4.16228	+	18.4868i	0.133436	+	0.592661i
$974$		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	−0.677098	−	0.735892i	$-0.736763\pi$
$977$	1.83772	−	1.83772i	0.0587939	−	0.0587939i	0.735892	+	0.677098i	$0.236763\pi$
$978$		0			0
$979$	45.1096			1.44171
$980$	3.86406	−	10.8377i	0.123433	−	0.346198i
$981$	2.00000	−	2.00000i	0.0638551	−	0.0638551i
$982$		0			0
$983$	25.7434	−	25.7434i	0.821087	−	0.821087i	−0.165177	−	0.986264i	$-0.552819\pi$
$983$	25.7434	−	25.7434i	0.821087	−	0.821087i	0.986264	+	0.165177i	$0.0528194\pi$
$984$		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.c.265.1	yes	4
3.2	odd	2		819.2.y.b.811.2		4
7.6	odd	2		273.2.p.b.265.2	yes	4
13.8	odd	4		273.2.p.b.34.2	✓	4
21.20	even	2		819.2.y.c.811.1		4
39.8	even	4		819.2.y.c.307.1		4
91.34	even	4	inner	273.2.p.c.34.1	yes	4
273.125	odd	4		819.2.y.b.307.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.p.b.34.2	✓	4	13.8	odd	4
273.2.p.b.265.2	yes	4	7.6	odd	2
273.2.p.c.34.1	yes	4	91.34	even	4	inner
273.2.p.c.265.1	yes	4	1.1	even	1	trivial
819.2.y.b.307.2		4	273.125	odd	4
819.2.y.b.811.2		4	3.2	odd	2
819.2.y.c.307.1		4	39.8	even	4
819.2.y.c.811.1		4	21.20	even	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{3} +2.00000i q^{4} +(-0.581139 - 0.581139i) q^{5} +(-2.58114 + 0.581139i) q^{7} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{3} +2.00000i q^{4} +(-0.581139 - 0.581139i) q^{5} +(-2.58114 + 0.581139i) q^{7} -1.00000 q^{9} +(4.16228 + 4.16228i) q^{11} -2.00000 q^{12} +(-3.58114 + 0.418861i) q^{13} +(0.581139 - 0.581139i) q^{15} -4.00000 q^{16} -1.16228 q^{17} +(-0.418861 - 0.418861i) q^{19} +(1.16228 - 1.16228i) q^{20} +(-0.581139 - 2.58114i) q^{21} +4.16228i q^{23} -4.32456i q^{25} -1.00000i q^{27} +(-1.16228 - 5.16228i) q^{28} +1.83772 q^{29} +(5.58114 + 5.58114i) q^{31} +(-4.16228 + 4.16228i) q^{33} +(1.83772 + 1.16228i) q^{35} -2.00000i q^{36} +(4.32456 + 4.32456i) q^{37} +(-0.418861 - 3.58114i) q^{39} +(7.16228 + 7.16228i) q^{41} -5.32456i q^{43} +(-8.32456 + 8.32456i) q^{44} +(0.581139 + 0.581139i) q^{45} +(6.58114 - 6.58114i) q^{47} -4.00000i q^{48} +(6.32456 - 3.00000i) q^{49} -1.16228i q^{51} +(-0.837722 - 7.16228i) q^{52} -4.16228 q^{53} -4.83772i q^{55} +(0.418861 - 0.418861i) q^{57} +(8.32456 - 8.32456i) q^{59} +(1.16228 + 1.16228i) q^{60} +3.16228i q^{61} +(2.58114 - 0.581139i) q^{63} -8.00000i q^{64} +(2.32456 + 1.83772i) q^{65} +(-6.32456 + 6.32456i) q^{67} -2.32456i q^{68} -4.16228 q^{69} +(6.00000 - 6.00000i) q^{71} +(-5.58114 + 5.58114i) q^{73} +4.32456 q^{75} +(0.837722 - 0.837722i) q^{76} +(-13.1623 - 8.32456i) q^{77} -11.3246 q^{79} +(2.32456 + 2.32456i) q^{80} +1.00000 q^{81} +(6.58114 + 6.58114i) q^{83} +(5.16228 - 1.16228i) q^{84} +(0.675445 + 0.675445i) q^{85} +1.83772i q^{87} +(5.41886 - 5.41886i) q^{89} +(9.00000 - 3.16228i) q^{91} -8.32456 q^{92} +(-5.58114 + 5.58114i) q^{93} +0.486833i q^{95} +(0.418861 + 0.418861i) q^{97} +(-4.16228 - 4.16228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^5 - 4 * q^7 - 4 * q^9	\( 4 q + 4 q^{5} - 4 q^{7} - 4 q^{9} + 4 q^{11} - 8 q^{12} - 8 q^{13} - 4 q^{15} - 16 q^{16} + 8 q^{17} - 8 q^{19} - 8 q^{20} + 4 q^{21} + 8 q^{28} + 20 q^{29} + 16 q^{31} - 4 q^{33} + 20 q^{35} - 8 q^{37} - 8 q^{39} + 16 q^{41} - 8 q^{44} - 4 q^{45} + 20 q^{47} - 16 q^{52} - 4 q^{53} + 8 q^{57} + 8 q^{59} - 8 q^{60} + 4 q^{63} - 16 q^{65} - 4 q^{69} + 24 q^{71} - 16 q^{73} - 8 q^{75} + 16 q^{76} - 40 q^{77} - 20 q^{79} - 16 q^{80} + 4 q^{81} + 20 q^{83} + 8 q^{84} + 28 q^{85} + 28 q^{89} + 36 q^{91} - 8 q^{92} - 16 q^{93} + 8 q^{97} - 4 q^{99}+O(q^{100}) \) 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 + 36 * q^91 - 8 * q^92 - 16 * q^93 + 8 * q^97 - 4 * q^99

Introduction

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