LMFDB - Embedded newform 273.2.p.b.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.b.34.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{3} +2.00000i q^{4} +(-2.58114 - 2.58114i) q^{5} +(-2.58114 + 0.581139i) q^{7} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{3} +2.00000i q^{4} +(-2.58114 - 2.58114i) q^{5} +(-2.58114 + 0.581139i) q^{7} -1.00000 q^{9} +(-2.16228 - 2.16228i) q^{11} +2.00000 q^{12} +(0.418861 - 3.58114i) q^{13} +(-2.58114 + 2.58114i) q^{15} -4.00000 q^{16} -5.16228 q^{17} +(3.58114 + 3.58114i) q^{19} +(5.16228 - 5.16228i) q^{20} +(0.581139 + 2.58114i) q^{21} -2.16228i q^{23} +8.32456i q^{25} +1.00000i q^{27} +(-1.16228 - 5.16228i) q^{28} +8.16228 q^{29} +(-2.41886 - 2.41886i) q^{31} +(-2.16228 + 2.16228i) q^{33} +(8.16228 + 5.16228i) q^{35} -2.00000i q^{36} +(-8.32456 - 8.32456i) q^{37} +(-3.58114 - 0.418861i) q^{39} +(-0.837722 - 0.837722i) q^{41} +7.32456i q^{43} +(4.32456 - 4.32456i) q^{44} +(2.58114 + 2.58114i) q^{45} +(-3.41886 + 3.41886i) q^{47} +4.00000i q^{48} +(6.32456 - 3.00000i) q^{49} +5.16228i q^{51} +(7.16228 + 0.837722i) q^{52} +2.16228 q^{53} +11.1623i q^{55} +(3.58114 - 3.58114i) q^{57} +(4.32456 - 4.32456i) q^{59} +(-5.16228 - 5.16228i) q^{60} +3.16228i q^{61} +(2.58114 - 0.581139i) q^{63} -8.00000i q^{64} +(-10.3246 + 8.16228i) q^{65} +(6.32456 - 6.32456i) q^{67} -10.3246i q^{68} -2.16228 q^{69} +(6.00000 - 6.00000i) q^{71} +(2.41886 - 2.41886i) q^{73} +8.32456 q^{75} +(-7.16228 + 7.16228i) q^{76} +(6.83772 + 4.32456i) q^{77} +1.32456 q^{79} +(10.3246 + 10.3246i) q^{80} +1.00000 q^{81} +(-3.41886 - 3.41886i) q^{83} +(-5.16228 + 1.16228i) q^{84} +(13.3246 + 13.3246i) q^{85} -8.16228i q^{87} +(-8.58114 + 8.58114i) q^{89} +(1.00000 + 9.48683i) q^{91} +4.32456 q^{92} +(-2.41886 + 2.41886i) q^{93} -18.4868i q^{95} +(-3.58114 - 3.58114i) q^{97} +(2.16228 + 2.16228i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

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

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
$5$	−2.58114	−	2.58114i	−1.15432	−	1.15432i	−0.985677	−	0.168643i	$-0.946061\pi$
$5$	−2.58114	−	2.58114i	−1.15432	−	1.15432i	−0.168643	−	0.985677i	$-0.553939\pi$
$6$		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
$11$	−2.16228	−	2.16228i	−0.651951	−	0.651951i	0.301511	−	0.953463i	$-0.402509\pi$
$11$	−2.16228	−	2.16228i	−0.651951	−	0.651951i	−0.953463	+	0.301511i	$0.902509\pi$
$12$	2.00000			0.577350
$13$	0.418861	−	3.58114i	0.116171	−	0.993229i
$13$	0.418861	−	3.58114i	0.116171	−	0.993229i
$14$		0			0
$15$	−2.58114	+	2.58114i	−0.666447	+	0.666447i
$16$	−4.00000			−1.00000
$17$	−5.16228			−1.25204			−0.626018	−	0.779809i	$-0.715316\pi$
$17$	−5.16228			−1.25204			−0.626018	+	0.779809i	$0.715316\pi$
$18$		0			0
$19$	3.58114	+	3.58114i	0.821570	+	0.821570i	0.986333	−	0.164764i	$-0.0526861\pi$
$19$	3.58114	+	3.58114i	0.821570	+	0.821570i	−0.164764	+	0.986333i	$0.552686\pi$
$20$	5.16228	−	5.16228i	1.15432	−	1.15432i
$21$	0.581139	+	2.58114i	0.126815	+	0.563251i
$22$		0			0
$23$		−	2.16228i		−	0.450866i	−0.974259	−	0.225433i	$-0.927620\pi$
$23$		−	2.16228i		−	0.450866i	0.974259	−	0.225433i	$-0.0723797\pi$
$24$		0			0
$25$			8.32456i			1.66491i
$26$		0			0
$27$			1.00000i			0.192450i
$28$	−1.16228	−	5.16228i	−0.219650	−	0.975579i
$29$	8.16228			1.51570			0.757848	−	0.652431i	$-0.226251\pi$
$29$	8.16228			1.51570			0.757848	+	0.652431i	$0.226251\pi$
$30$		0			0
$31$	−2.41886	−	2.41886i	−0.434440	−	0.434440i	0.455695	−	0.890136i	$-0.349391\pi$
$31$	−2.41886	−	2.41886i	−0.434440	−	0.434440i	−0.890136	+	0.455695i	$0.849391\pi$
$32$		0			0
$33$	−2.16228	+	2.16228i	−0.376404	+	0.376404i
$34$		0			0
$35$	8.16228	+	5.16228i	1.37968	+	0.872584i
$36$		−	2.00000i		−	0.333333i
$37$	−8.32456	−	8.32456i	−1.36855	−	1.36855i	−0.862512	−	0.506036i	$-0.831110\pi$
$37$	−8.32456	−	8.32456i	−1.36855	−	1.36855i	−0.506036	−	0.862512i	$-0.668890\pi$
$38$		0			0
$39$	−3.58114	−	0.418861i	−0.573441	−	0.0670715i
$40$		0			0
$41$	−0.837722	−	0.837722i	−0.130830	−	0.130830i	0.638659	−	0.769490i	$-0.279489\pi$
$41$	−0.837722	−	0.837722i	−0.130830	−	0.130830i	−0.769490	+	0.638659i	$0.779489\pi$
$42$		0			0
$43$			7.32456i			1.11698i	0.829510	+	0.558492i	$0.188620\pi$
$43$			7.32456i			1.11698i	−0.829510	+	0.558492i	$0.811380\pi$
$44$	4.32456	−	4.32456i	0.651951	−	0.651951i
$45$	2.58114	+	2.58114i	0.384773	+	0.384773i
$46$		0			0
$47$	−3.41886	+	3.41886i	−0.498692	+	0.498692i	−0.911031	−	0.412339i	$-0.864712\pi$
$47$	−3.41886	+	3.41886i	−0.498692	+	0.498692i	0.412339	+	0.911031i	$0.364712\pi$
$48$			4.00000i			0.577350i
$49$	6.32456	−	3.00000i	0.903508	−	0.428571i
$50$		0			0
$51$			5.16228i			0.722863i
$52$	7.16228	+	0.837722i	0.993229	+	0.116171i
$53$	2.16228			0.297012			0.148506	−	0.988912i	$-0.452554\pi$
$53$	2.16228			0.297012			0.148506	+	0.988912i	$0.452554\pi$
$54$		0			0
$55$			11.1623i			1.50512i
$56$		0			0
$57$	3.58114	−	3.58114i	0.474333	−	0.474333i
$58$		0			0
$59$	4.32456	−	4.32456i	0.563009	−	0.563009i	−0.367152	−	0.930161i	$-0.619667\pi$
$59$	4.32456	−	4.32456i	0.563009	−	0.563009i	0.930161	+	0.367152i	$0.119667\pi$
$60$	−5.16228	−	5.16228i	−0.666447	−	0.666447i
$61$			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
$65$	−10.3246	+	8.16228i	−1.28060	+	1.01241i
$66$		0			0
$67$	6.32456	−	6.32456i	0.772667	−	0.772667i	−0.205905	−	0.978572i	$-0.566014\pi$
$67$	6.32456	−	6.32456i	0.772667	−	0.772667i	0.978572	+	0.205905i	$0.0660137\pi$
$68$		−	10.3246i		−	1.25204i
$69$	−2.16228			−0.260308
$70$		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
$73$	2.41886	−	2.41886i	0.283106	−	0.283106i	−0.551240	−	0.834347i	$-0.685845\pi$
$73$	2.41886	−	2.41886i	0.283106	−	0.283106i	0.834347	+	0.551240i	$0.185845\pi$
$74$		0			0
$75$	8.32456			0.961237
$76$	−7.16228	+	7.16228i	−0.821570	+	0.821570i
$77$	6.83772	+	4.32456i	0.779231	+	0.492829i
$78$		0			0
$79$	1.32456			0.149024			0.0745121	−	0.997220i	$-0.476260\pi$
$79$	1.32456			0.149024			0.0745121	+	0.997220i	$0.476260\pi$
$80$	10.3246	+	10.3246i	1.15432	+	1.15432i
$81$	1.00000			0.111111
$82$		0			0
$83$	−3.41886	−	3.41886i	−0.375269	−	0.375269i	0.494123	−	0.869392i	$-0.335489\pi$
$83$	−3.41886	−	3.41886i	−0.375269	−	0.375269i	−0.869392	+	0.494123i	$0.835489\pi$
$84$	−5.16228	+	1.16228i	−0.563251	+	0.126815i
$85$	13.3246	+	13.3246i	1.44525	+	1.44525i
$86$		0			0
$87$		−	8.16228i		−	0.875088i
$88$		0			0
$89$	−8.58114	+	8.58114i	−0.909599	+	0.909599i	−0.996240	−	0.0866407i	$-0.972387\pi$
$89$	−8.58114	+	8.58114i	−0.909599	+	0.909599i	0.0866407	+	0.996240i	$0.472387\pi$
$90$		0			0
$91$	1.00000	+	9.48683i	0.104828	+	0.994490i
$92$	4.32456			0.450866
$93$	−2.41886	+	2.41886i	−0.250824	+	0.250824i
$94$		0			0
$95$		−	18.4868i		−	1.89671i
$96$		0			0
$97$	−3.58114	−	3.58114i	−0.363610	−	0.363610i	0.501530	−	0.865140i	$-0.332771\pi$
$97$	−3.58114	−	3.58114i	−0.363610	−	0.363610i	−0.865140	+	0.501530i	$0.832771\pi$
$98$		0			0
$99$	2.16228	+	2.16228i	0.217317	+	0.217317i
$100$	−16.6491			−1.66491
$101$	−13.8114			−1.37428			−0.687142	−	0.726523i	$-0.741135\pi$
$101$	−13.8114			−1.37428			−0.687142	+	0.726523i	$0.741135\pi$
$102$		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
$105$	5.16228	−	8.16228i	0.503787	−	0.796557i
$106$		0			0
$107$	−14.6491			−1.41618			−0.708091	−	0.706121i	$-0.750444\pi$
$107$	−14.6491			−1.41618			−0.708091	+	0.706121i	$0.750444\pi$
$108$	−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
$111$	−8.32456	+	8.32456i	−0.790132	+	0.790132i
$112$	10.3246	−	2.32456i	0.975579	−	0.219650i
$113$	−16.8114			−1.58148			−0.790741	−	0.612151i	$-0.790305\pi$
$113$	−16.8114			−1.58148			−0.790741	+	0.612151i	$0.790305\pi$
$114$		0			0
$115$	−5.58114	+	5.58114i	−0.520444	+	0.520444i
$116$			16.3246i			1.51570i
$117$	−0.418861	+	3.58114i	−0.0387237	+	0.331076i
$118$		0			0
$119$	13.3246	−	3.00000i	1.22146	−	0.275010i
$120$		0			0
$121$		−	1.64911i		−	0.149919i
$122$		0			0
$123$	−0.837722	+	0.837722i	−0.0755349	+	0.0755349i
$124$	4.83772	−	4.83772i	0.434440	−	0.434440i
$125$	8.58114	−	8.58114i	0.767520	−	0.767520i
$126$		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
$129$	7.32456			0.644891
$130$		0			0
$131$		−	6.83772i		−	0.597415i	−0.954345	−	0.298707i	$-0.903445\pi$
$131$		−	6.83772i		−	0.597415i	0.954345	−	0.298707i	$-0.0965554\pi$
$132$	−4.32456	−	4.32456i	−0.376404	−	0.376404i
$133$	−11.3246	−	7.16228i	−0.981963	−	0.621048i
$134$		0			0
$135$	2.58114	−	2.58114i	0.222149	−	0.222149i
$136$		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
$139$			0.837722i			0.0710547i	0.999369	+	0.0355273i	$0.0113111\pi$
$139$			0.837722i			0.0710547i	−0.999369	+	0.0355273i	$0.988689\pi$
$140$	−10.3246	+	16.3246i	−0.872584	+	1.37968i
$141$	3.41886	+	3.41886i	0.287920	+	0.287920i
$142$		0			0
$143$	−8.64911	+	6.83772i	−0.723275	+	0.571799i
$144$	4.00000			0.333333
$145$	−21.0680	−	21.0680i	−1.74960	−	1.74960i
$146$		0			0
$147$	−3.00000	−	6.32456i	−0.247436	−	0.521641i
$148$	16.6491	−	16.6491i	1.36855	−	1.36855i
$149$	−3.83772	+	3.83772i	−0.314398	+	0.314398i	−0.846611	−	0.532212i	$-0.821361\pi$
$149$	−3.83772	+	3.83772i	−0.314398	+	0.314398i	0.532212	+	0.846611i	$0.321361\pi$
$150$		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
$153$	5.16228			0.417345
$154$		0			0
$155$			12.4868i			1.00297i
$156$	0.837722	−	7.16228i	0.0670715	−	0.573441i
$157$		−	21.4868i		−	1.71484i	−0.514621	−	0.857418i	$-0.672067\pi$
$157$		−	21.4868i		−	1.71484i	0.514621	−	0.857418i	$-0.327933\pi$
$158$		0			0
$159$		−	2.16228i		−	0.171480i
$160$		0			0
$161$	1.25658	+	5.58114i	0.0990327	+	0.439855i
$162$		0			0
$163$	11.3246	+	11.3246i	0.887008	+	0.887008i	0.994235	−	0.107227i	$-0.0341971\pi$
$163$	11.3246	+	11.3246i	0.887008	+	0.887008i	−0.107227	+	0.994235i	$0.534197\pi$
$164$	1.67544	−	1.67544i	0.130830	−	0.130830i
$165$	11.1623			0.868982
$166$		0			0
$167$	12.9057	−	12.9057i	0.998673	−	0.998673i	−0.00132652	−	0.999999i	$-0.500422\pi$
$167$	12.9057	−	12.9057i	0.998673	−	0.998673i	0.999999	+	0.00132652i	$0.000422246\pi$
$168$		0			0
$169$	−12.6491	−	3.00000i	−0.973009	−	0.230769i
$170$		0			0
$171$	−3.58114	−	3.58114i	−0.273857	−	0.273857i
$172$	−14.6491			−1.11698
$173$	10.3246			0.784961			0.392481	−	0.919760i	$-0.371617\pi$
$173$	10.3246			0.784961			0.392481	+	0.919760i	$0.371617\pi$
$174$		0			0
$175$	−4.83772	−	21.4868i	−0.365697	−	1.62425i
$176$	8.64911	+	8.64911i	0.651951	+	0.651951i
$177$	−4.32456	−	4.32456i	−0.325053	−	0.325053i
$178$		0			0
$179$			18.4868i			1.38177i	0.722964	+	0.690885i	$0.242779\pi$
$179$			18.4868i			1.38177i	−0.722964	+	0.690885i	$0.757221\pi$
$180$	−5.16228	+	5.16228i	−0.384773	+	0.384773i
$181$	8.83772			0.656903			0.328451	−	0.944521i	$-0.393473\pi$
$181$	8.83772			0.656903			0.328451	+	0.944521i	$0.393473\pi$
$182$		0			0
$183$	3.16228			0.233762
$184$		0			0
$185$			42.9737i			3.15949i
$186$		0			0
$187$	11.1623	+	11.1623i	0.816267	+	0.816267i
$188$	−6.83772	−	6.83772i	−0.498692	−	0.498692i
$189$	−0.581139	−	2.58114i	−0.0422716	−	0.187750i
$190$		0			0
$191$	−1.67544			−0.121231			−0.0606155	−	0.998161i	$-0.519306\pi$
$191$	−1.67544			−0.121231			−0.0606155	+	0.998161i	$0.519306\pi$
$192$	−8.00000			−0.577350
$193$	−6.32456	−	6.32456i	−0.455251	−	0.455251i	0.441842	−	0.897093i	$-0.354325\pi$
$193$	−6.32456	−	6.32456i	−0.455251	−	0.455251i	−0.897093	+	0.441842i	$0.854325\pi$
$194$		0			0
$195$	8.16228	+	10.3246i	0.584513	+	0.739357i
$196$	6.00000	+	12.6491i	0.428571	+	0.903508i
$197$	−8.16228	+	8.16228i	−0.581538	+	0.581538i	−0.935326	−	0.353788i	$-0.884894\pi$
$197$	−8.16228	+	8.16228i	−0.581538	+	0.581538i	0.353788	+	0.935326i	$0.384894\pi$
$198$		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
$203$	−21.0680	+	4.74342i	−1.47868	+	0.332923i
$204$	−10.3246			−0.722863
$205$			4.32456i			0.302040i
$206$		0			0
$207$			2.16228i			0.150289i
$208$	−1.67544	+	14.3246i	−0.116171	+	0.993229i
$209$		−	15.4868i		−	1.07125i
$210$		0			0
$211$	−5.64911			−0.388901			−0.194450	−	0.980912i	$-0.562292\pi$
$211$	−5.64911			−0.388901			−0.194450	+	0.980912i	$0.562292\pi$
$212$			4.32456i			0.297012i
$213$	−6.00000	−	6.00000i	−0.411113	−	0.411113i
$214$		0			0
$215$	18.9057	−	18.9057i	1.28936	−	1.28936i
$216$		0			0
$217$	7.64911	+	4.83772i	0.519255	+	0.328406i
$218$		0			0
$219$	−2.41886	−	2.41886i	−0.163451	−	0.163451i
$220$	−22.3246			−1.50512
$221$	−2.16228	+	18.4868i	−0.145451	+	1.24356i
$222$		0			0
$223$	14.7434	+	14.7434i	0.987292	+	0.987292i	0.999920	−	0.0126281i	$-0.00401975\pi$
$223$	14.7434	+	14.7434i	0.987292	+	0.987292i	−0.0126281	+	0.999920i	$0.504020\pi$
$224$		0			0
$225$		−	8.32456i		−	0.554970i
$226$		0			0
$227$	11.1623	+	11.1623i	0.740866	+	0.740866i	0.972745	−	0.231878i	$-0.0744871\pi$
$227$	11.1623	+	11.1623i	0.740866	+	0.740866i	−0.231878	+	0.972745i	$0.574487\pi$
$228$	7.16228	+	7.16228i	0.474333	+	0.474333i
$229$	−5.67544	+	5.67544i	−0.375044	+	0.375044i	−0.869310	−	0.494266i	$-0.835437\pi$
$229$	−5.67544	+	5.67544i	−0.375044	+	0.375044i	0.494266	+	0.869310i	$0.335437\pi$
$230$		0			0
$231$	4.32456	−	6.83772i	0.284535	−	0.449889i
$232$		0			0
$233$		−	15.8377i		−	1.03756i	−0.854907	−	0.518782i	$-0.826386\pi$
$233$		−	15.8377i		−	1.03756i	0.854907	−	0.518782i	$-0.173614\pi$
$234$		0			0
$235$	17.6491			1.15130
$236$	8.64911	+	8.64911i	0.563009	+	0.563009i
$237$		−	1.32456i		−	0.0860391i
$238$		0			0
$239$	12.4868	−	12.4868i	0.807706	−	0.807706i	−0.176580	−	0.984286i	$-0.556503\pi$
$239$	12.4868	−	12.4868i	0.807706	−	0.807706i	0.984286	+	0.176580i	$0.0565035\pi$
$240$	10.3246	−	10.3246i	0.666447	−	0.666447i
$241$	−11.9057	+	11.9057i	−0.766913	+	0.766913i	−0.977562	−	0.210649i	$-0.932442\pi$
$241$	−11.9057	+	11.9057i	−0.766913	+	0.766913i	0.210649	+	0.977562i	$0.432442\pi$
$242$		0			0
$243$		−	1.00000i		−	0.0641500i
$244$	−6.32456			−0.404888
$245$	−24.0680	−	8.58114i	−1.53765	−	0.548229i
$246$		0			0
$247$	14.3246	−	11.3246i	0.911450	−	0.720564i
$248$		0			0
$249$	−3.41886	+	3.41886i	−0.216662	+	0.216662i
$250$		0			0
$251$	−8.51317			−0.537346			−0.268673	−	0.963231i	$-0.586585\pi$
$251$	−8.51317			−0.537346			−0.268673	+	0.963231i	$0.586585\pi$
$252$	1.16228	+	5.16228i	0.0732166	+	0.325193i
$253$	−4.67544	+	4.67544i	−0.293943	+	0.293943i
$254$		0			0
$255$	13.3246	−	13.3246i	0.834416	−	0.834416i
$256$	16.0000			1.00000
$257$	8.51317			0.531037			0.265518	−	0.964106i	$-0.414457\pi$
$257$	8.51317			0.531037			0.265518	+	0.964106i	$0.414457\pi$
$258$		0			0
$259$	26.3246	+	16.6491i	1.63573	+	1.03453i
$260$	−16.3246	−	20.6491i	−1.01241	−	1.28060i
$261$	−8.16228			−0.505232
$262$		0			0
$263$	−0.486833			−0.0300194			−0.0150097	−	0.999887i	$-0.504778\pi$
$263$	−0.486833			−0.0300194			−0.0150097	+	0.999887i	$0.504778\pi$
$264$		0			0
$265$	−5.58114	−	5.58114i	−0.342847	−	0.342847i
$266$		0			0
$267$	8.58114	+	8.58114i	0.525157	+	0.525157i
$268$	12.6491	+	12.6491i	0.772667	+	0.772667i
$269$		−	15.4868i		−	0.944249i	−0.881532	−	0.472124i	$-0.843487\pi$
$269$		−	15.4868i		−	0.944249i	0.881532	−	0.472124i	$-0.156513\pi$
$270$		0			0
$271$	5.48683	−	5.48683i	0.333301	−	0.333301i	−0.520537	−	0.853839i	$-0.674268\pi$
$271$	5.48683	−	5.48683i	0.333301	−	0.333301i	0.853839	+	0.520537i	$0.174268\pi$
$272$	20.6491			1.25204
$273$	9.48683	−	1.00000i	0.574169	−	0.0605228i
$274$		0			0
$275$	18.0000	−	18.0000i	1.08544	−	1.08544i
$276$		−	4.32456i		−	0.260308i
$277$		−	29.6491i		−	1.78144i	−0.454550	−	0.890721i	$-0.650200\pi$
$277$		−	29.6491i		−	1.78144i	0.454550	−	0.890721i	$-0.349800\pi$
$278$		0			0
$279$	2.41886	+	2.41886i	0.144813	+	0.144813i
$280$		0			0
$281$	22.3246	+	22.3246i	1.33177	+	1.33177i	0.903785	+	0.427986i	$0.140777\pi$
$281$	22.3246	+	22.3246i	1.33177	+	1.33177i	0.427986	+	0.903785i	$0.359223\pi$
$282$		0			0
$283$	29.2982			1.74160			0.870799	−	0.491639i	$-0.163602\pi$
$283$	29.2982			1.74160			0.870799	+	0.491639i	$0.163602\pi$
$284$	12.0000	+	12.0000i	0.712069	+	0.712069i
$285$	−18.4868			−1.09507
$286$		0			0
$287$	2.64911	+	1.67544i	0.156372	+	0.0988984i
$288$		0			0
$289$	9.64911			0.567595
$290$		0			0
$291$	−3.58114	+	3.58114i	−0.209930	+	0.209930i
$292$	4.83772	+	4.83772i	0.283106	+	0.283106i
$293$	0.0679718	−	0.0679718i	0.00397096	−	0.00397096i	−0.705119	−	0.709089i	$-0.749106\pi$
$293$	0.0679718	−	0.0679718i	0.00397096	−	0.00397096i	0.709089	+	0.705119i	$0.249106\pi$
$294$		0			0
$295$	−22.3246			−1.29979
$296$		0			0
$297$	2.16228	−	2.16228i	0.125468	−	0.125468i
$298$		0			0
$299$	−7.74342	−	0.905694i	−0.447813	−	0.0523776i
$300$			16.6491i			0.961237i
$301$	−4.25658	−	18.9057i	−0.245345	−	1.08971i
$302$		0			0
$303$			13.8114i			0.793444i
$304$	−14.3246	−	14.3246i	−0.821570	−	0.821570i
$305$	8.16228	−	8.16228i	0.467371	−	0.467371i
$306$		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	$0.397389\pi$
$308$	−8.64911	+	13.6754i	−0.492829	+	0.779231i
$309$		−	4.00000i		−	0.227552i
$310$		0			0
$311$	−1.67544			−0.0950058			−0.0475029	−	0.998871i	$-0.515126\pi$
$311$	−1.67544			−0.0950058			−0.0475029	+	0.998871i	$0.515126\pi$
$312$		0			0
$313$			11.8114i			0.667619i	0.942641	+	0.333810i	$0.108334\pi$
$313$			11.8114i			0.667619i	−0.942641	+	0.333810i	$0.891666\pi$
$314$		0			0
$315$	−8.16228	−	5.16228i	−0.459892	−	0.290861i
$316$			2.64911i			0.149024i
$317$	−8.16228	+	8.16228i	−0.458439	+	0.458439i	−0.898143	−	0.439704i	$-0.855083\pi$
$317$	−8.16228	+	8.16228i	−0.458439	+	0.458439i	0.439704	+	0.898143i	$0.355083\pi$
$318$		0			0
$319$	−17.6491	−	17.6491i	−0.988160	−	0.988160i
$320$	−20.6491	+	20.6491i	−1.15432	+	1.15432i
$321$			14.6491i			0.817634i
$322$		0			0
$323$	−18.4868	−	18.4868i	−1.02863	−	1.02863i
$324$			2.00000i			0.111111i
$325$	29.8114	+	3.48683i	1.65364	+	0.193415i
$326$		0			0
$327$	2.00000	+	2.00000i	0.110600	+	0.110600i
$328$		0			0
$329$	6.83772	−	10.8114i	0.376976	−	0.596051i
$330$		0			0
$331$	−1.64911	+	1.64911i	−0.0906433	+	0.0906433i	−0.750975	−	0.660331i	$-0.770416\pi$
$331$	−1.64911	+	1.64911i	−0.0906433	+	0.0906433i	0.660331	+	0.750975i	$0.270416\pi$
$332$	6.83772	−	6.83772i	0.375269	−	0.375269i
$333$	8.32456	+	8.32456i	0.456183	+	0.456183i
$334$		0			0
$335$	−32.6491			−1.78381
$336$	−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
$339$			16.8114i			0.913069i
$340$	−26.6491	+	26.6491i	−1.44525	+	1.44525i
$341$			10.4605i			0.566468i
$342$		0			0
$343$	−14.5811	+	11.4189i	−0.787307	+	0.616561i
$344$		0			0
$345$	5.58114	+	5.58114i	0.300478	+	0.300478i
$346$		0			0
$347$	6.97367			0.374366			0.187183	−	0.982325i	$-0.440064\pi$
$347$	6.97367			0.374366			0.187183	+	0.982325i	$0.440064\pi$
$348$	16.3246			0.875088
$349$	3.25658	−	3.25658i	0.174321	−	0.174321i	−0.614554	−	0.788875i	$-0.710664\pi$
$349$	3.25658	−	3.25658i	0.174321	−	0.174321i	0.788875	+	0.614554i	$0.210664\pi$
$350$		0			0
$351$	3.58114	+	0.418861i	0.191147	+	0.0223572i
$352$		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
$355$	−30.9737			−1.64391
$356$	−17.1623	−	17.1623i	−0.909599	−	0.909599i
$357$	−3.00000	−	13.3246i	−0.158777	−	0.705210i
$358$		0			0
$359$	3.83772	+	3.83772i	0.202547	+	0.202547i	0.801090	−	0.598543i	$-0.204254\pi$
$359$	3.83772	+	3.83772i	0.202547	+	0.202547i	−0.598543	+	0.801090i	$0.704254\pi$
$360$		0			0
$361$			6.64911i			0.349953i
$362$		0			0
$363$	−1.64911			−0.0865559
$364$	−18.9737	+	2.00000i	−0.994490	+	0.104828i
$365$	−12.4868			−0.653591
$366$		0			0
$367$		−	17.2982i		−	0.902960i	−0.892281	−	0.451480i	$-0.850896\pi$
$367$		−	17.2982i		−	0.902960i	0.892281	−	0.451480i	$-0.149104\pi$
$368$			8.64911i			0.450866i
$369$	0.837722	+	0.837722i	0.0436101	+	0.0436101i
$370$		0			0
$371$	−5.58114	+	1.25658i	−0.289758	+	0.0652386i
$372$	−4.83772	−	4.83772i	−0.250824	−	0.250824i
$373$	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
$375$	−8.58114	−	8.58114i	−0.443128	−	0.443128i
$376$		0			0
$377$	3.41886	−	29.2302i	0.176080	−	1.50543i
$378$		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	$0.331829\pi$
$380$	36.9737			1.89671
$381$	−2.00000			−0.102463
$382$		0			0
$383$	16.3246	+	16.3246i	0.834146	+	0.834146i	0.988081	−	0.153935i	$-0.0491947\pi$
$383$	16.3246	+	16.3246i	0.834146	+	0.834146i	−0.153935	+	0.988081i	$0.549195\pi$
$384$		0			0
$385$	−6.48683	−	28.8114i	−0.330600	−	1.46836i
$386$		0			0
$387$		−	7.32456i		−	0.372328i
$388$	7.16228	−	7.16228i	0.363610	−	0.363610i
$389$		−	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
$391$			11.1623i			0.564501i
$392$		0			0
$393$	−6.83772			−0.344917
$394$		0			0
$395$	−3.41886	−	3.41886i	−0.172022	−	0.172022i
$396$	−4.32456	+	4.32456i	−0.217317	+	0.217317i
$397$	14.7434	−	14.7434i	0.739951	−	0.739951i	−0.232617	−	0.972568i	$-0.574729\pi$
$397$	14.7434	−	14.7434i	0.739951	−	0.739951i	0.972568	+	0.232617i	$0.0747290\pi$
$398$		0			0
$399$	−7.16228	+	11.3246i	−0.358562	+	0.566937i
$400$		−	33.2982i		−	1.66491i
$401$	14.1623	+	14.1623i	0.707230	+	0.707230i	0.965952	−	0.258722i	$-0.0833012\pi$
$401$	14.1623	+	14.1623i	0.707230	+	0.707230i	−0.258722	+	0.965952i	$0.583301\pi$
$402$		0			0
$403$	−9.67544	+	7.64911i	−0.481968	+	0.381029i
$404$		−	27.6228i		−	1.37428i
$405$	−2.58114	−	2.58114i	−0.128258	−	0.128258i
$406$		0			0
$407$			36.0000i			1.78445i
$408$		0			0
$409$	−15.3925	−	15.3925i	−0.761111	−	0.761111i	0.215412	−	0.976523i	$-0.430891\pi$
$409$	−15.3925	−	15.3925i	−0.761111	−	0.761111i	−0.976523	+	0.215412i	$0.930891\pi$
$410$		0			0
$411$	−12.0000	+	12.0000i	−0.591916	+	0.591916i
$412$			8.00000i			0.394132i
$413$	−8.64911	+	13.6754i	−0.425595	+	0.672925i
$414$		0			0
$415$			17.6491i			0.866361i
$416$		0			0
$417$	0.837722			0.0410234
$418$		0			0
$419$			3.48683i			0.170343i	0.996366	+	0.0851715i	$0.0271438\pi$
$419$			3.48683i			0.170343i	−0.996366	+	0.0851715i	$0.972856\pi$
$420$	16.3246	+	10.3246i	0.796557	+	0.503787i
$421$	−5.32456	+	5.32456i	−0.259503	+	0.259503i	−0.824852	−	0.565349i	$-0.808742\pi$
$421$	−5.32456	+	5.32456i	−0.259503	+	0.259503i	0.565349	+	0.824852i	$0.308742\pi$
$422$		0			0
$423$	3.41886	−	3.41886i	0.166231	−	0.166231i
$424$		0			0
$425$		−	42.9737i		−	2.08453i
$426$		0			0
$427$	−1.83772	−	8.16228i	−0.0889336	−	0.395000i
$428$		−	29.2982i		−	1.41618i
$429$	6.83772	+	8.64911i	0.330128	+	0.417583i
$430$		0			0
$431$	16.8114	−	16.8114i	0.809776	−	0.809776i	−0.174824	−	0.984600i	$-0.555936\pi$
$431$	16.8114	−	16.8114i	0.809776	−	0.809776i	0.984600	+	0.174824i	$0.0559355\pi$
$432$		−	4.00000i		−	0.192450i
$433$	0.837722			0.0402584			0.0201292	−	0.999797i	$-0.493592\pi$
$433$	0.837722			0.0402584			0.0201292	+	0.999797i	$0.493592\pi$
$434$		0			0
$435$	−21.0680	+	21.0680i	−1.01013	+	1.01013i
$436$	−4.00000	−	4.00000i	−0.191565	−	0.191565i
$437$	7.74342	−	7.74342i	0.370418	−	0.370418i
$438$		0			0
$439$	10.5132			0.501766			0.250883	−	0.968017i	$-0.419279\pi$
$439$	10.5132			0.501766			0.250883	+	0.968017i	$0.419279\pi$
$440$		0			0
$441$	−6.32456	+	3.00000i	−0.301169	+	0.142857i
$442$		0			0
$443$	32.1623			1.52808			0.764038	−	0.645171i	$-0.223214\pi$
$443$	32.1623			1.52808			0.764038	+	0.645171i	$0.223214\pi$
$444$	−16.6491	−	16.6491i	−0.790132	−	0.790132i
$445$	44.2982			2.09994
$446$		0			0
$447$	3.83772	+	3.83772i	0.181518	+	0.181518i
$448$	4.64911	+	20.6491i	0.219650	+	0.975579i
$449$	−28.8114	−	28.8114i	−1.35969	−	1.35969i	−0.874291	−	0.485403i	$-0.838673\pi$
$449$	−28.8114	−	28.8114i	−1.35969	−	1.35969i	−0.485403	−	0.874291i	$-0.661327\pi$
$450$		0			0
$451$			3.62278i			0.170590i
$452$		−	33.6228i		−	1.58148i
$453$	−4.00000	+	4.00000i	−0.187936	+	0.187936i
$454$		0			0
$455$	21.9057	−	27.0680i	1.02695	−	1.26897i
$456$		0			0
$457$	−11.3246	+	11.3246i	−0.529740	+	0.529740i	−0.920495	−	0.390755i	$-0.872214\pi$
$457$	−11.3246	+	11.3246i	−0.529740	+	0.529740i	0.390755	+	0.920495i	$0.372214\pi$
$458$		0			0
$459$		−	5.16228i		−	0.240954i
$460$	−11.1623	−	11.1623i	−0.520444	−	0.520444i
$461$	−7.67544	−	7.67544i	−0.357481	−	0.357481i	0.505403	−	0.862884i	$-0.331344\pi$
$461$	−7.67544	−	7.67544i	−0.357481	−	0.357481i	−0.862884	+	0.505403i	$0.831344\pi$
$462$		0			0
$463$	−22.6491	−	22.6491i	−1.05259	−	1.05259i	−0.998538	−	0.0540555i	$-0.982785\pi$
$463$	−22.6491	−	22.6491i	−1.05259	−	1.05259i	−0.0540555	−	0.998538i	$-0.517215\pi$
$464$	−32.6491			−1.51570
$465$	12.4868			0.579063
$466$		0			0
$467$	6.97367			0.322703			0.161351	−	0.986897i	$-0.448415\pi$
$467$	6.97367			0.322703			0.161351	+	0.986897i	$0.448415\pi$
$468$	−7.16228	−	0.837722i	−0.331076	−	0.0387237i
$469$	−12.6491	+	20.0000i	−0.584082	+	0.923514i
$470$		0			0
$471$	−21.4868			−0.990061
$472$		0			0
$473$	15.8377	−	15.8377i	0.728219	−	0.728219i
$474$		0			0
$475$	−29.8114	+	29.8114i	−1.36784	+	1.36784i
$476$	6.00000	+	26.6491i	0.275010	+	1.22146i
$477$	−2.16228			−0.0990039
$478$		0			0
$479$	−8.58114	+	8.58114i	−0.392082	+	0.392082i	−0.875429	−	0.483347i	$-0.839421\pi$
$479$	−8.58114	+	8.58114i	−0.392082	+	0.392082i	0.483347	+	0.875429i	$0.339421\pi$
$480$		0			0
$481$	−33.2982	+	26.3246i	−1.51827	+	1.20030i
$482$		0			0
$483$	5.58114	−	1.25658i	0.253951	−	0.0571765i
$484$	3.29822			0.149919
$485$			18.4868i			0.839444i
$486$		0			0
$487$	−11.3246	+	11.3246i	−0.513165	+	0.513165i	−0.915495	−	0.402330i	$-0.868200\pi$
$487$	−11.3246	+	11.3246i	−0.513165	+	0.513165i	0.402330	+	0.915495i	$0.368200\pi$
$488$		0			0
$489$	11.3246	−	11.3246i	0.512114	−	0.512114i
$490$		0			0
$491$			13.6754i			0.617164i	0.951198	+	0.308582i	$0.0998545\pi$
$491$			13.6754i			0.617164i	−0.951198	+	0.308582i	$0.900146\pi$
$492$	−1.67544	−	1.67544i	−0.0755349	−	0.0755349i
$493$	−42.1359			−1.89771
$494$		0			0
$495$		−	11.1623i		−	0.501707i
$496$	9.67544	+	9.67544i	0.434440	+	0.434440i
$497$	−12.0000	+	18.9737i	−0.538274	+	0.851085i
$498$		0			0
$499$	6.67544	−	6.67544i	0.298834	−	0.298834i	−0.541723	−	0.840557i	$-0.682228\pi$
$499$	6.67544	−	6.67544i	0.298834	−	0.298834i	0.840557	+	0.541723i	$0.182228\pi$
$500$	17.1623	+	17.1623i	0.767520	+	0.767520i
$501$	−12.9057	−	12.9057i	−0.576584	−	0.576584i
$502$		0			0
$503$		−	22.4605i		−	1.00146i	−0.865602	−	0.500732i	$-0.833064\pi$
$503$		−	22.4605i		−	1.00146i	0.865602	−	0.500732i	$-0.166936\pi$
$504$		0			0
$505$	35.6491	+	35.6491i	1.58636	+	1.58636i
$506$		0			0
$507$	−3.00000	+	12.6491i	−0.133235	+	0.561767i
$508$	4.00000			0.177471
$509$	−5.09431	−	5.09431i	−0.225801	−	0.225801i	0.585135	−	0.810936i	$-0.301042\pi$
$509$	−5.09431	−	5.09431i	−0.225801	−	0.225801i	−0.810936	+	0.585135i	$0.801042\pi$
$510$		0			0
$511$	−4.83772	+	7.64911i	−0.214008	+	0.338377i
$512$		0			0
$513$	−3.58114	+	3.58114i	−0.158111	+	0.158111i
$514$		0			0
$515$	−10.3246	−	10.3246i	−0.454954	−	0.454954i
$516$			14.6491i			0.644891i
$517$	14.7851			0.650246
$518$		0			0
$519$		−	10.3246i		−	0.453198i
$520$		0			0
$521$			32.6491i			1.43038i	0.698928	+	0.715192i	$0.253661\pi$
$521$			32.6491i			1.43038i	−0.698928	+	0.715192i	$0.746339\pi$
$522$		0			0
$523$		−	33.4868i		−	1.46428i	−0.681156	−	0.732138i	$-0.738522\pi$
$523$		−	33.4868i		−	1.46428i	0.681156	−	0.732138i	$-0.261478\pi$
$524$	13.6754			0.597415
$525$	−21.4868	+	4.83772i	−0.937762	+	0.211136i
$526$		0			0
$527$	12.4868	+	12.4868i	0.543935	+	0.543935i
$528$	8.64911	−	8.64911i	0.376404	−	0.376404i
$529$	18.3246			0.796720
$530$		0			0
$531$	−4.32456	+	4.32456i	−0.187670	+	0.187670i
$532$	14.3246	−	22.6491i	0.621048	−	0.981963i
$533$	−3.35089	+	2.64911i	−0.145143	+	0.114746i
$534$		0			0
$535$	37.8114	+	37.8114i	1.63473	+	1.63473i
$536$		0			0
$537$	18.4868			0.797766
$538$		0			0
$539$	−20.1623	−	7.18861i	−0.868451	−	0.309635i
$540$	5.16228	+	5.16228i	0.222149	+	0.222149i
$541$	−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
$543$		−	8.83772i		−	0.379263i
$544$		0			0
$545$	10.3246			0.442255
$546$		0			0
$547$	−9.64911			−0.412566			−0.206283	−	0.978492i	$-0.566137\pi$
$547$	−9.64911			−0.412566			−0.206283	+	0.978492i	$0.566137\pi$
$548$	24.0000	−	24.0000i	1.02523	−	1.02523i
$549$		−	3.16228i		−	0.134963i
$550$		0			0
$551$	29.2302	+	29.2302i	1.24525	+	1.24525i
$552$		0			0
$553$	−3.41886	+	0.769751i	−0.145385	+	0.0327331i
$554$		0			0
$555$	42.9737			1.82413
$556$	−1.67544			−0.0710547
$557$	20.6491	+	20.6491i	0.874931	+	0.874931i	0.993005	−	0.118074i	$-0.0376720\pi$
$557$	20.6491	+	20.6491i	0.874931	+	0.874931i	−0.118074	+	0.993005i	$0.537672\pi$
$558$		0			0
$559$	26.2302	+	3.06797i	1.10942	+	0.129761i
$560$	−32.6491	−	20.6491i	−1.37968	−	0.872584i
$561$	11.1623	−	11.1623i	0.471272	−	0.471272i
$562$		0			0
$563$	−34.4605			−1.45234			−0.726168	−	0.687517i	$-0.758701\pi$
$563$	−34.4605			−1.45234			−0.726168	+	0.687517i	$0.758701\pi$
$564$	−6.83772	+	6.83772i	−0.287920	+	0.287920i
$565$	43.3925	+	43.3925i	1.82554	+	1.82554i
$566$		0			0
$567$	−2.58114	+	0.581139i	−0.108398	+	0.0244055i
$568$		0			0
$569$		−	11.5132i		−	0.482657i	−0.970443	−	0.241329i	$-0.922417\pi$
$569$		−	11.5132i		−	0.482657i	0.970443	−	0.241329i	$-0.0775831\pi$
$570$		0			0
$571$			8.67544i			0.363056i	0.983386	+	0.181528i	$0.0581043\pi$
$571$			8.67544i			0.363056i	−0.983386	+	0.181528i	$0.941896\pi$
$572$	−13.6754	−	17.2982i	−0.571799	−	0.723275i
$573$			1.67544i			0.0699927i
$574$		0			0
$575$	18.0000			0.750652
$576$			8.00000i			0.333333i
$577$	8.00000	+	8.00000i	0.333044	+	0.333044i	0.853741	−	0.520697i	$-0.174328\pi$
$577$	8.00000	+	8.00000i	0.333044	+	0.333044i	−0.520697	+	0.853741i	$0.674328\pi$
$578$		0			0
$579$	−6.32456	+	6.32456i	−0.262840	+	0.262840i
$580$	42.1359	−	42.1359i	1.74960	−	1.74960i
$581$	10.8114	+	6.83772i	0.448532	+	0.283677i
$582$		0			0
$583$	−4.67544	−	4.67544i	−0.193637	−	0.193637i
$584$		0			0
$585$	10.3246	−	8.16228i	0.426868	−	0.337469i
$586$		0			0
$587$	7.74342	+	7.74342i	0.319605	+	0.319605i	0.848615	−	0.529010i	$-0.177437\pi$
$587$	7.74342	+	7.74342i	0.319605	+	0.319605i	−0.529010	+	0.848615i	$0.677437\pi$
$588$	12.6491	−	6.00000i	0.521641	−	0.247436i
$589$		−	17.3246i		−	0.713846i
$590$		0			0
$591$	8.16228	+	8.16228i	0.335751	+	0.335751i
$592$	33.2982	+	33.2982i	1.36855	+	1.36855i
$593$	−18.9057	+	18.9057i	−0.776364	+	0.776364i	−0.979211	−	0.202847i	$-0.934981\pi$
$593$	−18.9057	+	18.9057i	−0.776364	+	0.776364i	0.202847	+	0.979211i	$0.434981\pi$
$594$		0			0
$595$	−42.1359	−	26.6491i	−1.72741	−	1.09251i
$596$	−7.67544	−	7.67544i	−0.314398	−	0.314398i
$597$		−	9.48683i		−	0.388270i
$598$		0			0
$599$	−40.8114			−1.66751			−0.833754	−	0.552136i	$-0.813813\pi$
$599$	−40.8114			−1.66751			−0.833754	+	0.552136i	$0.813813\pi$
$600$		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
$605$	−4.25658	+	4.25658i	−0.173055	+	0.173055i
$606$		0			0
$607$		−	35.1623i		−	1.42719i	−0.700557	−	0.713596i	$-0.747065\pi$
$607$		−	35.1623i		−	1.42719i	0.700557	−	0.713596i	$-0.252935\pi$
$608$		0			0
$609$	4.74342	+	21.0680i	0.192213	+	0.853717i
$610$		0			0
$611$	10.8114	+	13.6754i	0.437382	+	0.553249i
$612$			10.3246i			0.417345i
$613$	5.32456	−	5.32456i	0.215057	−	0.215057i	−0.591355	−	0.806412i	$-0.701407\pi$
$613$	5.32456	−	5.32456i	0.215057	−	0.215057i	0.806412	+	0.591355i	$0.201407\pi$
$614$		0			0
$615$	4.32456			0.174383
$616$		0			0
$617$	5.51317	−	5.51317i	0.221952	−	0.221952i	−0.587368	−	0.809320i	$-0.699836\pi$
$617$	5.51317	−	5.51317i	0.221952	−	0.221952i	0.809320	+	0.587368i	$0.199836\pi$
$618$		0			0
$619$	−18.3246	+	18.3246i	−0.736526	+	0.736526i	−0.971904	−	0.235378i	$-0.924367\pi$
$619$	−18.3246	+	18.3246i	−0.736526	+	0.736526i	0.235378	+	0.971904i	$0.424367\pi$
$620$	−24.9737			−1.00297
$621$	2.16228			0.0867692
$622$		0			0
$623$	17.1623	−	27.1359i	0.687592	−	1.08718i
$624$	14.3246	+	1.67544i	0.573441	+	0.0670715i
$625$	−2.67544			−0.107018
$626$		0			0
$627$	−15.4868			−0.618485
$628$	42.9737			1.71484
$629$	42.9737	+	42.9737i	1.71347	+	1.71347i
$630$		0			0
$631$	−21.6491	−	21.6491i	−0.861837	−	0.861837i	0.129714	−	0.991551i	$-0.458594\pi$
$631$	−21.6491	−	21.6491i	−0.861837	−	0.861837i	−0.991551	+	0.129714i	$0.958594\pi$
$632$		0			0
$633$			5.64911i			0.224532i
$634$		0			0
$635$	−5.16228	+	5.16228i	−0.204859	+	0.204859i
$636$	4.32456			0.171480
$637$	−8.09431	−	23.9057i	−0.320708	−	0.947178i
$638$		0			0
$639$	−6.00000	+	6.00000i	−0.237356	+	0.237356i
$640$		0			0
$641$		−	5.51317i		−	0.217757i	−0.994055	−	0.108879i	$-0.965274\pi$
$641$		−	5.51317i		−	0.217757i	0.994055	−	0.108879i	$-0.0347259\pi$
$642$		0			0
$643$	−35.8114	−	35.8114i	−1.41226	−	1.41226i	−0.743254	−	0.669009i	$-0.766719\pi$
$643$	−35.8114	−	35.8114i	−1.41226	−	1.41226i	−0.669009	−	0.743254i	$-0.733281\pi$
$644$	−11.1623	+	2.51317i	−0.439855	+	0.0990327i
$645$	−18.9057	−	18.9057i	−0.744411	−	0.744411i
$646$		0			0
$647$	−30.9737			−1.21770			−0.608850	−	0.793285i	$-0.708369\pi$
$647$	−30.9737			−1.21770			−0.608850	+	0.793285i	$0.708369\pi$
$648$		0			0
$649$	−18.7018			−0.734109
$650$		0			0
$651$	4.83772	−	7.64911i	0.189605	−	0.299792i
$652$	−22.6491	+	22.6491i	−0.887008	+	0.887008i
$653$	−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
$655$	−17.6491	+	17.6491i	−0.689608	+	0.689608i
$656$	3.35089	+	3.35089i	0.130830	+	0.130830i
$657$	−2.41886	+	2.41886i	−0.0943688	+	0.0943688i
$658$		0			0
$659$	43.4605			1.69298			0.846490	−	0.532404i	$-0.178711\pi$
$659$	43.4605			1.69298			0.846490	+	0.532404i	$0.178711\pi$
$660$			22.3246i			0.868982i
$661$	−11.9057	+	11.9057i	−0.463078	+	0.463078i	−0.899663	−	0.436585i	$-0.856188\pi$
$661$	−11.9057	+	11.9057i	−0.463078	+	0.463078i	0.436585	+	0.899663i	$0.356188\pi$
$662$		0			0
$663$	18.4868	+	2.16228i	0.717969	+	0.0839759i
$664$		0			0
$665$	10.7434	+	47.7171i	0.416612	+	1.85039i
$666$		0			0
$667$		−	17.6491i		−	0.683376i
$668$	25.8114	+	25.8114i	0.998673	+	0.998673i
$669$	14.7434	−	14.7434i	0.570013	−	0.570013i
$670$		0			0
$671$	6.83772	−	6.83772i	0.263967	−	0.263967i
$672$		0			0
$673$			42.6228i			1.64299i	0.570218	+	0.821494i	$0.306859\pi$
$673$			42.6228i			1.64299i	−0.570218	+	0.821494i	$0.693141\pi$
$674$		0			0
$675$	−8.32456			−0.320412
$676$	6.00000	−	25.2982i	0.230769	−	0.973009i
$677$		−	12.0000i		−	0.461197i	−0.973049	−	0.230599i	$-0.925932\pi$
$677$		−	12.0000i		−	0.461197i	0.973049	−	0.230599i	$-0.0740685\pi$
$678$		0			0
$679$	11.3246	+	7.16228i	0.434597	+	0.274863i
$680$		0			0
$681$	11.1623	−	11.1623i	0.427739	−	0.427739i
$682$		0			0
$683$	−2.64911	−	2.64911i	−0.101365	−	0.101365i	0.654605	−	0.755971i	$-0.272835\pi$
$683$	−2.64911	−	2.64911i	−0.101365	−	0.101365i	−0.755971	+	0.654605i	$0.772835\pi$
$684$	7.16228	−	7.16228i	0.273857	−	0.273857i
$685$			61.9473i			2.36689i
$686$		0			0
$687$	5.67544	+	5.67544i	0.216532	+	0.216532i
$688$		−	29.2982i		−	1.11698i
$689$	0.905694	−	7.74342i	0.0345042	−	0.295001i
$690$		0			0
$691$	−15.5811	−	15.5811i	−0.592734	−	0.592734i	0.345635	−	0.938369i	$-0.387664\pi$
$691$	−15.5811	−	15.5811i	−0.592734	−	0.592734i	−0.938369	+	0.345635i	$0.887664\pi$
$692$			20.6491i			0.784961i
$693$	−6.83772	−	4.32456i	−0.259744	−	0.164276i
$694$		0			0
$695$	2.16228	−	2.16228i	0.0820199	−	0.0820199i
$696$		0			0
$697$	4.32456	+	4.32456i	0.163804	+	0.163804i
$698$		0			0
$699$	−15.8377			−0.599038
$700$	42.9737	−	9.67544i	1.62425	−	0.365697i
$701$		−	8.16228i		−	0.308285i	−0.988049	−	0.154142i	$-0.950739\pi$
$701$		−	8.16228i		−	0.308285i	0.988049	−	0.154142i	$-0.0492615\pi$
$702$		0			0
$703$		−	59.6228i		−	2.24872i
$704$	−17.2982	+	17.2982i	−0.651951	+	0.651951i
$705$		−	17.6491i		−	0.664704i
$706$		0			0
$707$	35.6491	−	8.02633i	1.34072	−	0.301861i
$708$	8.64911	−	8.64911i	0.325053	−	0.325053i
$709$	−18.2982	−	18.2982i	−0.687204	−	0.687204i	0.274409	−	0.961613i	$-0.411518\pi$
$709$	−18.2982	−	18.2982i	−0.687204	−	0.687204i	−0.961613	+	0.274409i	$0.911518\pi$
$710$		0			0
$711$	−1.32456			−0.0496747
$712$		0			0
$713$	−5.23025	+	5.23025i	−0.195874	+	0.195874i
$714$		0			0
$715$	39.9737	+	4.67544i	1.49493	+	0.174852i
$716$	−36.9737			−1.38177
$717$	−12.4868	−	12.4868i	−0.466329	−	0.466329i
$718$		0			0
$719$	−18.9737			−0.707598			−0.353799	−	0.935321i	$-0.615110\pi$
$719$	−18.9737			−0.707598			−0.353799	+	0.935321i	$0.615110\pi$
$720$	−10.3246	−	10.3246i	−0.384773	−	0.384773i
$721$	−10.3246	+	2.32456i	−0.384507	+	0.0865710i
$722$		0			0
$723$	11.9057	+	11.9057i	0.442778	+	0.442778i
$724$			17.6754i			0.656903i
$725$			67.9473i			2.52350i
$726$		0			0
$727$	−17.2982			−0.641556			−0.320778	−	0.947154i	$-0.603944\pi$
$727$	−17.2982			−0.641556			−0.320778	+	0.947154i	$0.603944\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$		−	37.8114i		−	1.39850i
$732$			6.32456i			0.233762i
$733$	12.0943	+	12.0943i	0.446713	+	0.446713i	0.894260	−	0.447547i	$-0.147702\pi$
$733$	12.0943	+	12.0943i	0.446713	+	0.446713i	−0.447547	+	0.894260i	$0.647702\pi$
$734$		0			0
$735$	−8.58114	+	24.0680i	−0.316520	+	0.887761i
$736$		0			0
$737$	−27.3509			−1.00748
$738$		0			0
$739$	19.6491	+	19.6491i	0.722804	+	0.722804i	0.969176	−	0.246371i	$-0.0792383\pi$
$739$	19.6491	+	19.6491i	0.722804	+	0.722804i	−0.246371	+	0.969176i	$0.579238\pi$
$740$	−85.9473			−3.15949
$741$	−11.3246	−	14.3246i	−0.416018	−	0.526226i
$742$		0			0
$743$	−14.1623	+	14.1623i	−0.519564	+	0.519564i	−0.917439	−	0.397876i	$-0.869748\pi$
$743$	−14.1623	+	14.1623i	−0.519564	+	0.519564i	0.397876	+	0.917439i	$0.369748\pi$
$744$		0			0
$745$	19.8114			0.725833
$746$		0			0
$747$	3.41886	+	3.41886i	0.125090	+	0.125090i
$748$	−22.3246	+	22.3246i	−0.816267	+	0.816267i
$749$	37.8114	−	8.51317i	1.38160	−	0.311064i
$750$		0			0
$751$		−	1.32456i		−	0.0483337i	−0.999708	−	0.0241669i	$-0.992307\pi$
$751$		−	1.32456i		−	0.0483337i	0.999708	−	0.0241669i	$-0.00769330\pi$
$752$	13.6754	−	13.6754i	0.498692	−	0.498692i
$753$			8.51317i			0.310237i
$754$		0			0
$755$			20.6491i			0.751498i
$756$	5.16228	−	1.16228i	0.187750	−	0.0422716i
$757$	0.350889			0.0127533			0.00637665	−	0.999980i	$-0.497970\pi$
$757$	0.350889			0.0127533			0.00637665	+	0.999980i	$0.497970\pi$
$758$		0			0
$759$	4.67544	+	4.67544i	0.169708	+	0.169708i
$760$		0			0
$761$	35.2302	−	35.2302i	1.27710	−	1.27710i	0.334810	−	0.942286i	$-0.391328\pi$
$761$	35.2302	−	35.2302i	1.27710	−	1.27710i	0.942286	−	0.334810i	$-0.108672\pi$
$762$		0			0
$763$	4.00000	−	6.32456i	0.144810	−	0.228964i
$764$		−	3.35089i		−	0.121231i
$765$	−13.3246	−	13.3246i	−0.481750	−	0.481750i
$766$		0			0
$767$	−13.6754	−	17.2982i	−0.493792	−	0.624603i
$768$		−	16.0000i		−	0.577350i
$769$	−35.9057	−	35.9057i	−1.29479	−	1.29479i	−0.931787	−	0.363005i	$-0.881751\pi$
$769$	−35.9057	−	35.9057i	−1.29479	−	1.29479i	−0.363005	−	0.931787i	$-0.618249\pi$
$770$		0			0
$771$		−	8.51317i		−	0.306594i
$772$	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
$775$	20.1359	−	20.1359i	0.723304	−	0.723304i
$776$		0			0
$777$	16.6491	−	26.3246i	0.597284	−	0.944388i
$778$		0			0
$779$		−	6.00000i		−	0.214972i
$780$	−20.6491	+	16.3246i	−0.739357	+	0.584513i
$781$	−25.9473			−0.928469
$782$		0			0
$783$			8.16228i			0.291696i
$784$	−25.2982	+	12.0000i	−0.903508	+	0.428571i
$785$	−55.4605	+	55.4605i	−1.97947	+	1.97947i
$786$		0			0
$787$	−1.06797	+	1.06797i	−0.0380691	+	0.0380691i	−0.725885	−	0.687816i	$-0.758570\pi$
$787$	−1.06797	+	1.06797i	−0.0380691	+	0.0380691i	0.687816	+	0.725885i	$0.258570\pi$
$788$	−16.3246	−	16.3246i	−0.581538	−	0.581538i
$789$			0.486833i			0.0173317i
$790$		0			0
$791$	43.3925	−	9.76975i	1.54286	−	0.347372i
$792$		0			0
$793$	11.3246	+	1.32456i	0.402147	+	0.0470363i
$794$		0			0
$795$	−5.58114	+	5.58114i	−0.197943	+	0.197943i
$796$			18.9737i			0.672504i
$797$	−17.2982			−0.612734			−0.306367	−	0.951913i	$-0.599114\pi$
$797$	−17.2982			−0.612734			−0.306367	+	0.951913i	$0.599114\pi$
$798$		0			0
$799$	17.6491	−	17.6491i	0.624381	−	0.624381i
$800$		0			0
$801$	8.58114	−	8.58114i	0.303200	−	0.303200i
$802$		0			0
$803$	−10.4605			−0.369143
$804$	12.6491	−	12.6491i	0.446100	−	0.446100i
$805$	11.1623	−	17.6491i	0.393419	−	0.622049i
$806$		0			0
$807$	−15.4868			−0.545162
$808$		0			0
$809$	43.4605			1.52799			0.763995	−	0.645222i	$-0.223235\pi$
$809$	43.4605			1.52799			0.763995	+	0.645222i	$0.223235\pi$
$810$		0			0
$811$	0.188612	+	0.188612i	0.00662305	+	0.00662305i	0.710411	−	0.703788i	$-0.248509\pi$
$811$	0.188612	+	0.188612i	0.00662305	+	0.00662305i	−0.703788	+	0.710411i	$0.748509\pi$
$812$	−9.48683	−	42.1359i	−0.332923	−	1.47868i
$813$	−5.48683	−	5.48683i	−0.192432	−	0.192432i
$814$		0			0
$815$		−	58.4605i		−	2.04778i
$816$		−	20.6491i		−	0.722863i
$817$	−26.2302	+	26.2302i	−0.917680	+	0.917680i
$818$		0			0
$819$	−1.00000	−	9.48683i	−0.0349428	−	0.331497i
$820$	−8.64911			−0.302040
$821$	−7.67544	+	7.67544i	−0.267875	+	0.267875i	−0.828243	−	0.560369i	$-0.810660\pi$
$821$	−7.67544	+	7.67544i	−0.267875	+	0.267875i	0.560369	+	0.828243i	$0.310660\pi$
$822$		0			0
$823$			38.6491i			1.34722i	0.739085	+	0.673612i	$0.235258\pi$
$823$			38.6491i			1.34722i	−0.739085	+	0.673612i	$0.764742\pi$
$824$		0			0
$825$	−18.0000	−	18.0000i	−0.626680	−	0.626680i
$826$		0			0
$827$	9.83772	+	9.83772i	0.342091	+	0.342091i	0.857153	−	0.515062i	$-0.172231\pi$
$827$	9.83772	+	9.83772i	0.342091	+	0.342091i	−0.515062	+	0.857153i	$0.672231\pi$
$828$	−4.32456			−0.150289
$829$	46.3246			1.60892			0.804459	−	0.594008i	$-0.202455\pi$
$829$	46.3246			1.60892			0.804459	+	0.594008i	$0.202455\pi$
$830$		0			0
$831$	−29.6491			−1.02852
$832$	−28.6491	−	3.35089i	−0.993229	−	0.116171i
$833$	−32.6491	+	15.4868i	−1.13122	+	0.536587i
$834$		0			0
$835$	−66.6228			−2.30558
$836$	30.9737			1.07125
$837$	2.41886	−	2.41886i	0.0836081	−	0.0836081i
$838$		0			0
$839$	−2.51317	+	2.51317i	−0.0867642	+	0.0867642i	−0.749157	−	0.662393i	$-0.769541\pi$
$839$	−2.51317	+	2.51317i	−0.0867642	+	0.0867642i	0.662393	+	0.749157i	$0.269541\pi$
$840$		0			0
$841$	37.6228			1.29734
$842$		0			0
$843$	22.3246	−	22.3246i	0.768899	−	0.768899i
$844$		−	11.2982i		−	0.388901i
$845$	24.9057	+	40.3925i	0.856782	+	1.38955i
$846$		0			0
$847$	0.958362	+	4.25658i	0.0329297	+	0.146258i
$848$	−8.64911			−0.297012
$849$		−	29.2982i		−	1.00551i
$850$		0			0
$851$	−18.0000	+	18.0000i	−0.617032	+	0.617032i
$852$	12.0000	−	12.0000i	0.411113	−	0.411113i
$853$	−13.9057	+	13.9057i	−0.476122	+	0.476122i	−0.903889	−	0.427767i	$-0.859300\pi$
$853$	−13.9057	+	13.9057i	−0.476122	+	0.476122i	0.427767	+	0.903889i	$0.359300\pi$
$854$		0			0
$855$			18.4868i			0.632236i
$856$		0			0
$857$	32.7851			1.11992			0.559958	−	0.828521i	$-0.310817\pi$
$857$	32.7851			1.11992			0.559958	+	0.828521i	$0.310817\pi$
$858$		0			0
$859$			49.2982i			1.68203i	0.541009	+	0.841017i	$0.318042\pi$
$859$			49.2982i			1.68203i	−0.541009	+	0.841017i	$0.681958\pi$
$860$	37.8114	+	37.8114i	1.28936	+	1.28936i
$861$	1.67544	−	2.64911i	0.0570990	−	0.0902814i
$862$		0			0
$863$	−41.2982	+	41.2982i	−1.40581	+	1.40581i	−0.625923	+	0.779885i	$0.715277\pi$
$863$	−41.2982	+	41.2982i	−1.40581	+	1.40581i	−0.779885	+	0.625923i	$0.784723\pi$
$864$		0			0
$865$	−26.6491	−	26.6491i	−0.906097	−	0.906097i
$866$		0			0
$867$		−	9.64911i		−	0.327701i
$868$	−9.67544	+	15.2982i	−0.328406	+	0.519255i
$869$	−2.86406	−	2.86406i	−0.0971565	−	0.0971565i
$870$		0			0
$871$	−20.0000	−	25.2982i	−0.677674	−	0.857198i
$872$		0			0
$873$	3.58114	+	3.58114i	0.121203	+	0.121203i
$874$		0			0
$875$	−17.1623	+	27.1359i	−0.580191	+	0.917362i
$876$	4.83772	−	4.83772i	0.163451	−	0.163451i
$877$	−18.6754	+	18.6754i	−0.630625	+	0.630625i	−0.948225	−	0.317600i	$-0.897123\pi$
$877$	−18.6754	+	18.6754i	−0.630625	+	0.630625i	0.317600	+	0.948225i	$0.397123\pi$
$878$		0			0
$879$	−0.0679718	−	0.0679718i	−0.00229263	−	0.00229263i
$880$		−	44.6491i		−	1.50512i
$881$	−39.6228			−1.33493			−0.667463	−	0.744643i	$-0.732620\pi$
$881$	−39.6228			−1.33493			−0.667463	+	0.744643i	$0.732620\pi$
$882$		0			0
$883$		−	6.64911i		−	0.223760i	−0.993722	−	0.111880i	$-0.964313\pi$
$883$		−	6.64911i		−	0.223760i	0.993722	−	0.111880i	$-0.0356873\pi$
$884$	−36.9737	−	4.32456i	−1.24356	−	0.145451i
$885$			22.3246i			0.750432i
$886$		0			0
$887$			8.51317i			0.285844i	0.989734	+	0.142922i	$0.0456498\pi$
$887$			8.51317i			0.285844i	−0.989734	+	0.142922i	$0.954350\pi$
$888$		0			0
$889$	1.16228	+	5.16228i	0.0389815	+	0.173137i
$890$		0			0
$891$	−2.16228	−	2.16228i	−0.0724390	−	0.0724390i
$892$	−29.4868	+	29.4868i	−0.987292	+	0.987292i
$893$	−24.4868			−0.819421
$894$		0			0
$895$	47.7171	−	47.7171i	1.59501	−	1.59501i
$896$		0			0
$897$	−0.905694	+	7.74342i	−0.0302402	+	0.258545i
$898$		0			0
$899$	−19.7434	−	19.7434i	−0.658480	−	0.658480i
$900$	16.6491			0.554970
$901$	−11.1623			−0.371869
$902$		0			0
$903$	−18.9057	+	4.25658i	−0.629142	+	0.141650i
$904$		0			0
$905$	−22.8114	−	22.8114i	−0.758276	−	0.758276i
$906$		0			0
$907$		−	44.9473i		−	1.49245i	−0.665693	−	0.746226i	$-0.731864\pi$
$907$		−	44.9473i		−	1.49245i	0.665693	−	0.746226i	$-0.268136\pi$
$908$	−22.3246	+	22.3246i	−0.740866	+	0.740866i
$909$	13.8114			0.458095
$910$		0			0
$911$	36.4868			1.20886			0.604431	−	0.796657i	$-0.293400\pi$
$911$	36.4868			1.20886			0.604431	+	0.796657i	$0.293400\pi$
$912$	−14.3246	+	14.3246i	−0.474333	+	0.474333i
$913$			14.7851i			0.489314i
$914$		0			0
$915$	−8.16228	−	8.16228i	−0.269837	−	0.269837i
$916$	−11.3509	−	11.3509i	−0.375044	−	0.375044i
$917$	3.97367	+	17.6491i	0.131222	+	0.582825i
$918$		0			0
$919$	35.2982			1.16438			0.582190	−	0.813052i	$-0.302196\pi$
$919$	35.2982			1.16438			0.582190	+	0.813052i	$0.302196\pi$
$920$		0			0
$921$	11.0680	+	11.0680i	0.364702	+	0.364702i
$922$		0			0
$923$	−18.9737	−	24.0000i	−0.624526	−	0.789970i
$924$	13.6754	+	8.64911i	0.449889	+	0.284535i
$925$	69.2982	−	69.2982i	2.27851	−	2.27851i
$926$		0			0
$927$	−4.00000			−0.131377
$928$		0			0
$929$	31.7434	+	31.7434i	1.04147	+	1.04147i	0.999102	+	0.0423655i	$0.0134894\pi$
$929$	31.7434	+	31.7434i	1.04147	+	1.04147i	0.0423655	+	0.999102i	$0.486511\pi$
$930$		0			0
$931$	33.3925	+	11.9057i	1.09440	+	0.390193i
$932$	31.6754			1.03756
$933$			1.67544i			0.0548516i
$934$		0			0
$935$		−	57.6228i		−	1.88447i
$936$		0			0
$937$		−	10.9737i		−	0.358494i	−0.983804	−	0.179247i	$-0.942634\pi$
$937$		−	10.9737i		−	0.358494i	0.983804	−	0.179247i	$-0.0573661\pi$
$938$		0			0
$939$	11.8114			0.385450
$940$			35.2982i			1.15130i
$941$	−32.7171	−	32.7171i	−1.06655	−	1.06655i	−0.997622	−	0.0689245i	$-0.978043\pi$
$941$	−32.7171	−	32.7171i	−1.06655	−	1.06655i	−0.0689245	−	0.997622i	$-0.521957\pi$
$942$		0			0
$943$	−1.81139	+	1.81139i	−0.0589869	+	0.0589869i
$944$	−17.2982	+	17.2982i	−0.563009	+	0.563009i
$945$	−5.16228	+	8.16228i	−0.167929	+	0.265519i
$946$		0			0
$947$	34.3246	+	34.3246i	1.11540	+	1.11540i	0.992408	+	0.122990i	$0.0392484\pi$
$947$	34.3246	+	34.3246i	1.11540	+	1.11540i	0.122990	+	0.992408i	$0.460752\pi$
$948$	2.64911			0.0860391
$949$	−7.64911	−	9.67544i	−0.248301	−	0.314078i
$950$		0			0
$951$	8.16228	+	8.16228i	0.264680	+	0.264680i
$952$		0			0
$953$		−	18.4868i		−	0.598847i	−0.954120	−	0.299424i	$-0.903206\pi$
$953$		−	18.4868i		−	0.598847i	0.954120	−	0.299424i	$-0.0967944\pi$
$954$		0			0
$955$	4.32456	+	4.32456i	0.139939	+	0.139939i
$956$	24.9737	+	24.9737i	0.807706	+	0.807706i
$957$	−17.6491	+	17.6491i	−0.570515	+	0.570515i
$958$		0			0
$959$	37.9473	+	24.0000i	1.22538	+	0.775000i
$960$	20.6491	+	20.6491i	0.666447	+	0.666447i
$961$		−	19.2982i		−	0.622523i
$962$		0			0
$963$	14.6491			0.472061
$964$	−23.8114	−	23.8114i	−0.766913	−	0.766913i
$965$			32.6491i			1.05101i
$966$		0			0
$967$	−32.9473	+	32.9473i	−1.05951	+	1.05951i	−0.0614016	+	0.998113i	$0.519557\pi$
$967$	−32.9473	+	32.9473i	−1.05951	+	1.05951i	−0.998113	+	0.0614016i	$0.980443\pi$
$968$		0			0
$969$	−18.4868	+	18.4868i	−0.593883	+	0.593883i
$970$		0			0
$971$		−	20.5132i		−	0.658299i	−0.944278	−	0.329149i	$-0.893238\pi$
$971$		−	20.5132i		−	0.658299i	0.944278	−	0.329149i	$-0.106762\pi$
$972$	2.00000			0.0641500
$973$	−0.486833	−	2.16228i	−0.0156071	−	0.0693194i
$974$		0			0
$975$	3.48683	−	29.8114i	0.111668	−	0.954729i
$976$		−	12.6491i		−	0.404888i
$977$	8.16228	−	8.16228i	0.261134	−	0.261134i	−0.564380	−	0.825515i	$-0.690885\pi$
$977$	8.16228	−	8.16228i	0.261134	−	0.261134i	0.825515	+	0.564380i	$0.190885\pi$
$978$		0			0
$979$	37.1096			1.18603
$980$	17.1623	−	48.1359i	0.548229	−	1.53765i
$981$	2.00000	−	2.00000i	0.0638551	−	0.0638551i
$982$		0			0
$983$	−16.2566	+	16.2566i	−0.518504	+	0.518504i	−0.917119	−	0.398614i	$-0.869491\pi$
$983$	−16.2566	+	16.2566i	−0.518504	+	0.518504i	0.398614	+	0.917119i	$0.369491\pi$
$984$		0			0
$985$	42.1359			1.34256
$986$		0			0
$987$	−10.8114	−	6.83772i	−0.344130	−	0.217647i
$988$	22.6491	+	28.6491i	0.720564	+	0.911450i
$989$	15.8377			0.503610
$990$		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
$993$	1.64911	+	1.64911i	0.0523329	+	0.0523329i
$994$		0			0
$995$	−24.4868	−	24.4868i	−0.776285	−	0.776285i
$996$	−6.83772	−	6.83772i	−0.216662	−	0.216662i
$997$		−	17.2982i		−	0.547840i	−0.961752	−	0.273920i	$-0.911680\pi$
$997$		−	17.2982i		−	0.547840i	0.961752	−	0.273920i	$-0.0883204\pi$
$998$		0			0
$999$	8.32456	−	8.32456i	0.263377	−	0.263377i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.p.b.34.1	✓	4	91.34	even	4	inner
273.2.p.b.265.1	yes	4	1.1	even	1	trivial
273.2.p.c.34.2	yes	4	13.8	odd	4
273.2.p.c.265.2	yes	4	7.6	odd	2
819.2.y.b.307.1		4	39.8	even	4
819.2.y.b.811.1		4	21.20	even	2
819.2.y.c.307.2		4	273.125	odd	4
819.2.y.c.811.2		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.00000i q^{3} +2.00000i q^{4} +(-2.58114 - 2.58114i) q^{5} +(-2.58114 + 0.581139i) q^{7} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{3} +2.00000i q^{4} +(-2.58114 - 2.58114i) q^{5} +(-2.58114 + 0.581139i) q^{7} -1.00000 q^{9} +(-2.16228 - 2.16228i) q^{11} +2.00000 q^{12} +(0.418861 - 3.58114i) q^{13} +(-2.58114 + 2.58114i) q^{15} -4.00000 q^{16} -5.16228 q^{17} +(3.58114 + 3.58114i) q^{19} +(5.16228 - 5.16228i) q^{20} +(0.581139 + 2.58114i) q^{21} -2.16228i q^{23} +8.32456i q^{25} +1.00000i q^{27} +(-1.16228 - 5.16228i) q^{28} +8.16228 q^{29} +(-2.41886 - 2.41886i) q^{31} +(-2.16228 + 2.16228i) q^{33} +(8.16228 + 5.16228i) q^{35} -2.00000i q^{36} +(-8.32456 - 8.32456i) q^{37} +(-3.58114 - 0.418861i) q^{39} +(-0.837722 - 0.837722i) q^{41} +7.32456i q^{43} +(4.32456 - 4.32456i) q^{44} +(2.58114 + 2.58114i) q^{45} +(-3.41886 + 3.41886i) q^{47} +4.00000i q^{48} +(6.32456 - 3.00000i) q^{49} +5.16228i q^{51} +(7.16228 + 0.837722i) q^{52} +2.16228 q^{53} +11.1623i q^{55} +(3.58114 - 3.58114i) q^{57} +(4.32456 - 4.32456i) q^{59} +(-5.16228 - 5.16228i) q^{60} +3.16228i q^{61} +(2.58114 - 0.581139i) q^{63} -8.00000i q^{64} +(-10.3246 + 8.16228i) q^{65} +(6.32456 - 6.32456i) q^{67} -10.3246i q^{68} -2.16228 q^{69} +(6.00000 - 6.00000i) q^{71} +(2.41886 - 2.41886i) q^{73} +8.32456 q^{75} +(-7.16228 + 7.16228i) q^{76} +(6.83772 + 4.32456i) q^{77} +1.32456 q^{79} +(10.3246 + 10.3246i) q^{80} +1.00000 q^{81} +(-3.41886 - 3.41886i) q^{83} +(-5.16228 + 1.16228i) q^{84} +(13.3246 + 13.3246i) q^{85} -8.16228i q^{87} +(-8.58114 + 8.58114i) q^{89} +(1.00000 + 9.48683i) q^{91} +4.32456 q^{92} +(-2.41886 + 2.41886i) q^{93} -18.4868i q^{95} +(-3.58114 - 3.58114i) q^{97} +(2.16228 + 2.16228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 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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