LMFDB - Embedded newform 1350.2.j.f.1099.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,2,Mod(199,1350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1350, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("1350.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1350.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.7798042729$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.303595776.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1099.2
Root			$1.26217 + 1.18614i$ of defining polynomial
Character	$\chi$	$=$	1350.1099
Dual form			1350.2.j.f.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.05446 + 1.18614i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.05446 + 1.18614i) q^{7} -1.00000i q^{8} +(0.686141 - 1.18843i) q^{11} +(-4.10891 + 2.37228i) q^{13} +(-1.18614 - 2.05446i) q^{14} +(-0.500000 + 0.866025i) q^{16} +7.37228i q^{17} -3.37228 q^{19} +(-1.18843 + 0.686141i) q^{22} +(-3.78651 + 2.18614i) q^{23} +4.74456 q^{26} +2.37228i q^{28} +(2.18614 - 3.78651i) q^{29} +(3.37228 + 5.84096i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.68614 - 6.38458i) q^{34} -4.00000i q^{37} +(2.92048 + 1.68614i) q^{38} +(-1.50000 - 2.59808i) q^{41} +(-9.84868 - 5.68614i) q^{43} +1.37228 q^{44} +4.37228 q^{46} +(-1.40965 - 0.813859i) q^{47} +(-0.686141 - 1.18843i) q^{49} +(-4.10891 - 2.37228i) q^{52} +11.4891i q^{53} +(1.18614 - 2.05446i) q^{56} +(-3.78651 + 2.18614i) q^{58} +(0.686141 + 1.18843i) q^{59} +(-4.55842 + 7.89542i) q^{61} -6.74456i q^{62} -1.00000 q^{64} +(-6.06218 + 3.50000i) q^{67} +(-6.38458 + 3.68614i) q^{68} +6.00000 q^{71} +14.1168i q^{73} +(-2.00000 + 3.46410i) q^{74} +(-1.68614 - 2.92048i) q^{76} +(2.81929 - 1.62772i) q^{77} +(1.00000 - 1.73205i) q^{79} +3.00000i q^{82} +(-1.40965 - 0.813859i) q^{83} +(5.68614 + 9.84868i) q^{86} +(-1.18843 - 0.686141i) q^{88} -1.11684 q^{89} -11.2554 q^{91} +(-3.78651 - 2.18614i) q^{92} +(0.813859 + 1.40965i) q^{94} +(2.27567 + 1.31386i) q^{97} +1.37228i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} - 6 q^{11} + 2 q^{14} - 4 q^{16} - 4 q^{19} - 8 q^{26} + 6 q^{29} + 4 q^{31} + 18 q^{34} - 12 q^{41} - 12 q^{44} + 12 q^{46} + 6 q^{49} - 2 q^{56} - 6 q^{59} - 2 q^{61} - 8 q^{64} + 48 q^{71} - 16 q^{74} - 2 q^{76} + 8 q^{79} + 34 q^{86} + 60 q^{89} - 136 q^{91} + 18 q^{94}+O(q^{100}) $ 8 * q + 4 * q^4 - 6 * q^11 + 2 * q^14 - 4 * q^16 - 4 * q^19 - 8 * q^26 + 6 * q^29 + 4 * q^31 + 18 * q^34 - 12 * q^41 - 12 * q^44 + 12 * q^46 + 6 * q^49 - 2 * q^56 - 6 * q^59 - 2 * q^61 - 8 * q^64 + 48 * q^71 - 16 * q^74 - 2 * q^76 + 8 * q^79 + 34 * q^86 + 60 * q^89 - 136 * q^91 + 18 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.05446	+	1.18614i	0.776511	+	0.448319i	0.835192	−	0.549958i	$-0.185356\pi$
$7$	2.05446	+	1.18614i	0.776511	+	0.448319i	−0.0586811	+	0.998277i	$0.518690\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$		0			0
$11$	0.686141	−	1.18843i	0.206879	−	0.358325i	−0.743851	−	0.668346i	$-0.767003\pi$
$11$	0.686141	−	1.18843i	0.206879	−	0.358325i	0.950730	+	0.310021i	$0.100336\pi$
$12$		0			0
$13$	−4.10891	+	2.37228i	−1.13961	+	0.657952i	−0.946333	−	0.323192i	$-0.895244\pi$
$13$	−4.10891	+	2.37228i	−1.13961	+	0.657952i	−0.193274	+	0.981145i	$0.561911\pi$
$14$	−1.18614	−	2.05446i	−0.317009	−	0.549076i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$			7.37228i			1.78804i	0.448026	+	0.894020i	$0.352127\pi$
$17$			7.37228i			1.78804i	−0.448026	+	0.894020i	$0.647873\pi$
$18$		0			0
$19$	−3.37228			−0.773654			−0.386827	−	0.922152i	$-0.626429\pi$
$19$	−3.37228			−0.773654			−0.386827	+	0.922152i	$0.626429\pi$
$20$		0			0
$21$		0			0
$22$	−1.18843	+	0.686141i	−0.253374	+	0.146286i
$23$	−3.78651	+	2.18614i	−0.789541	+	0.455842i	−0.839801	−	0.542894i	$-0.817328\pi$
$23$	−3.78651	+	2.18614i	−0.789541	+	0.455842i	0.0502598	+	0.998736i	$0.483995\pi$
$24$		0			0
$25$		0			0
$26$	4.74456			0.930485
$27$		0			0
$28$			2.37228i			0.448319i
$29$	2.18614	−	3.78651i	0.405956	−	0.703137i	−0.588476	−	0.808515i	$-0.700272\pi$
$29$	2.18614	−	3.78651i	0.405956	−	0.703137i	0.994432	+	0.105378i	$0.0336052\pi$
$30$		0			0
$31$	3.37228	+	5.84096i	0.605680	+	1.04907i	0.991944	+	0.126680i	$0.0404320\pi$
$31$	3.37228	+	5.84096i	0.605680	+	1.04907i	−0.386264	+	0.922388i	$0.626235\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	3.68614	−	6.38458i	0.632168	−	1.09495i
$35$		0			0
$36$		0			0
$37$		−	4.00000i		−	0.657596i	−0.944400	−	0.328798i	$-0.893356\pi$
$37$		−	4.00000i		−	0.657596i	0.944400	−	0.328798i	$-0.106644\pi$
$38$	2.92048	+	1.68614i	0.473765	+	0.273528i
$39$		0			0
$40$		0			0
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$		0			0
$43$	−9.84868	−	5.68614i	−1.50191	−	0.867128i	−0.999998	−	0.00221007i	$-0.999297\pi$
$43$	−9.84868	−	5.68614i	−1.50191	−	0.867128i	−0.501913	−	0.864918i	$-0.667370\pi$
$44$	1.37228			0.206879
$45$		0			0
$46$	4.37228			0.644658
$47$	−1.40965	−	0.813859i	−0.205618	−	0.118714i	0.393655	−	0.919258i	$-0.371210\pi$
$47$	−1.40965	−	0.813859i	−0.205618	−	0.118714i	−0.599273	+	0.800545i	$0.704544\pi$
$48$		0			0
$49$	−0.686141	−	1.18843i	−0.0980201	−	0.169776i
$50$		0			0
$51$		0			0
$52$	−4.10891	−	2.37228i	−0.569804	−	0.328976i
$53$			11.4891i			1.57815i	0.614295	+	0.789076i	$0.289440\pi$
$53$			11.4891i			1.57815i	−0.614295	+	0.789076i	$0.710560\pi$
$54$		0			0
$55$		0			0
$56$	1.18614	−	2.05446i	0.158505	−	0.274538i
$57$		0			0
$58$	−3.78651	+	2.18614i	−0.497193	+	0.287054i
$59$	0.686141	+	1.18843i	0.0893279	+	0.154720i	0.907227	−	0.420641i	$-0.138195\pi$
$59$	0.686141	+	1.18843i	0.0893279	+	0.154720i	−0.817899	+	0.575361i	$0.804861\pi$
$60$		0			0
$61$	−4.55842	+	7.89542i	−0.583646	+	1.01090i	0.411397	+	0.911456i	$0.365041\pi$
$61$	−4.55842	+	7.89542i	−0.583646	+	1.01090i	−0.995043	+	0.0994483i	$0.968292\pi$
$62$		−	6.74456i		−	0.856560i
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	−6.06218	+	3.50000i	−0.740613	+	0.427593i	−0.822292	−	0.569066i	$-0.807305\pi$
$67$	−6.06218	+	3.50000i	−0.740613	+	0.427593i	0.0816792	+	0.996659i	$0.473972\pi$
$68$	−6.38458	+	3.68614i	−0.774244	+	0.447010i
$69$		0			0
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$			14.1168i			1.65225i	0.563486	+	0.826126i	$0.309460\pi$
$73$			14.1168i			1.65225i	−0.563486	+	0.826126i	$0.690540\pi$
$74$	−2.00000	+	3.46410i	−0.232495	+	0.402694i
$75$		0			0
$76$	−1.68614	−	2.92048i	−0.193414	−	0.335002i
$77$	2.81929	−	1.62772i	0.321288	−	0.185496i
$78$		0			0
$79$	1.00000	−	1.73205i	0.112509	−	0.194871i	−0.804272	−	0.594261i	$-0.797445\pi$
$79$	1.00000	−	1.73205i	0.112509	−	0.194871i	0.916781	+	0.399390i	$0.130778\pi$
$80$		0			0
$81$		0			0
$82$			3.00000i			0.331295i
$83$	−1.40965	−	0.813859i	−0.154729	−	0.0893327i	0.420637	−	0.907229i	$-0.361807\pi$
$83$	−1.40965	−	0.813859i	−0.154729	−	0.0893327i	−0.575365	+	0.817897i	$0.695140\pi$
$84$		0			0
$85$		0			0
$86$	5.68614	+	9.84868i	0.613152	+	1.06201i
$87$		0			0
$88$	−1.18843	−	0.686141i	−0.126687	−	0.0731428i
$89$	−1.11684			−0.118385			−0.0591926	−	0.998247i	$-0.518853\pi$
$89$	−1.11684			−0.118385			−0.0591926	+	0.998247i	$0.518853\pi$
$90$		0			0
$91$	−11.2554			−1.17989
$92$	−3.78651	−	2.18614i	−0.394771	−	0.227921i
$93$		0			0
$94$	0.813859	+	1.40965i	0.0839432	+	0.145394i
$95$		0			0
$96$		0			0
$97$	2.27567	+	1.31386i	0.231059	+	0.133402i	0.611061	−	0.791584i	$-0.290743\pi$
$97$	2.27567	+	1.31386i	0.231059	+	0.133402i	−0.380001	+	0.924986i	$0.624076\pi$
$98$			1.37228i			0.138621i
$99$		0			0
$100$		0			0
$101$	−4.37228	+	7.57301i	−0.435058	+	0.753543i	−0.997300	−	0.0734297i	$-0.976606\pi$
$101$	−4.37228	+	7.57301i	−0.435058	+	0.753543i	0.562242	+	0.826973i	$0.309939\pi$
$102$		0			0
$103$	13.8564	−	8.00000i	1.36531	−	0.788263i	0.374987	−	0.927030i	$-0.377647\pi$
$103$	13.8564	−	8.00000i	1.36531	−	0.788263i	0.990325	+	0.138767i	$0.0443138\pi$
$104$	2.37228	+	4.10891i	0.232621	+	0.402912i
$105$		0			0
$106$	5.74456	−	9.94987i	0.557961	−	0.966417i
$107$			14.4891i			1.40072i	0.713791	+	0.700358i	$0.246976\pi$
$107$			14.4891i			1.40072i	−0.713791	+	0.700358i	$0.753024\pi$
$108$		0			0
$109$	−9.62772			−0.922168			−0.461084	−	0.887356i	$-0.652539\pi$
$109$	−9.62772			−0.922168			−0.461084	+	0.887356i	$0.652539\pi$
$110$		0			0
$111$		0			0
$112$	−2.05446	+	1.18614i	−0.194128	+	0.112080i
$113$	12.7692	−	7.37228i	1.20122	−	0.693526i	0.240395	−	0.970675i	$-0.422723\pi$
$113$	12.7692	−	7.37228i	1.20122	−	0.693526i	0.960827	+	0.277149i	$0.0893896\pi$
$114$		0			0
$115$		0			0
$116$	4.37228			0.405956
$117$		0			0
$118$		−	1.37228i		−	0.126329i
$119$	−8.74456	+	15.1460i	−0.801613	+	1.38843i
$120$		0			0
$121$	4.55842	+	7.89542i	0.414402	+	0.717765i
$122$	7.89542	−	4.55842i	0.714818	−	0.412700i
$123$		0			0
$124$	−3.37228	+	5.84096i	−0.302840	+	0.524534i
$125$		0			0
$126$		0			0
$127$			9.11684i			0.808989i	0.914540	+	0.404495i	$0.132553\pi$
$127$			9.11684i			0.808989i	−0.914540	+	0.404495i	$0.867447\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$		0			0
$131$	4.37228	+	7.57301i	0.382008	+	0.661657i	0.991349	−	0.131251i	$-0.0418993\pi$
$131$	4.37228	+	7.57301i	0.382008	+	0.661657i	−0.609341	+	0.792908i	$0.708566\pi$
$132$		0			0
$133$	−6.92820	−	4.00000i	−0.600751	−	0.346844i
$134$	7.00000			0.604708
$135$		0			0
$136$	7.37228			0.632168
$137$	−1.63086	−	0.941578i	−0.139334	−	0.0804444i	0.428713	−	0.903441i	$-0.358967\pi$
$137$	−1.63086	−	0.941578i	−0.139334	−	0.0804444i	−0.568046	+	0.822996i	$0.692301\pi$
$138$		0			0
$139$	9.05842	+	15.6896i	0.768325	+	1.33078i	0.938470	+	0.345359i	$0.112243\pi$
$139$	9.05842	+	15.6896i	0.768325	+	1.33078i	−0.170145	+	0.985419i	$0.554424\pi$
$140$		0			0
$141$		0			0
$142$	−5.19615	−	3.00000i	−0.436051	−	0.251754i
$143$			6.51087i			0.544467i
$144$		0			0
$145$		0			0
$146$	7.05842	−	12.2255i	0.584159	−	1.01179i
$147$		0			0
$148$	3.46410	−	2.00000i	0.284747	−	0.164399i
$149$	−9.55842	−	16.5557i	−0.783056	−	1.35629i	−0.930153	−	0.367171i	$-0.880326\pi$
$149$	−9.55842	−	16.5557i	−0.783056	−	1.35629i	0.147097	−	0.989122i	$-0.453007\pi$
$150$		0			0
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	−0.587646	−	0.809118i	$-0.699945\pi$
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	0.994540	+	0.104357i	$0.0332784\pi$
$152$			3.37228i			0.273528i
$153$		0			0
$154$	−3.25544			−0.262331
$155$		0			0
$156$		0			0
$157$	4.10891	−	2.37228i	0.327927	−	0.189329i	−0.326993	−	0.945027i	$-0.606036\pi$
$157$	4.10891	−	2.37228i	0.327927	−	0.189329i	0.654920	+	0.755698i	$0.272702\pi$
$158$	−1.73205	+	1.00000i	−0.137795	+	0.0795557i
$159$		0			0
$160$		0			0
$161$	−10.3723			−0.817450
$162$		0			0
$163$		−	1.48913i		−	0.116637i	−0.998298	−	0.0583186i	$-0.981426\pi$
$163$		−	1.48913i		−	0.116637i	0.998298	−	0.0583186i	$-0.0185739\pi$
$164$	1.50000	−	2.59808i	0.117130	−	0.202876i
$165$		0			0
$166$	0.813859	+	1.40965i	0.0631677	+	0.109410i
$167$	−6.60580	+	3.81386i	−0.511172	+	0.295125i	−0.733315	−	0.679889i	$-0.762028\pi$
$167$	−6.60580	+	3.81386i	−0.511172	+	0.295125i	0.222143	+	0.975014i	$0.428695\pi$
$168$		0			0
$169$	4.75544	−	8.23666i	0.365803	−	0.633589i
$170$		0			0
$171$		0			0
$172$		−	11.3723i		−	0.867128i
$173$	−8.01544	−	4.62772i	−0.609403	−	0.351839i	0.163329	−	0.986572i	$-0.447777\pi$
$173$	−8.01544	−	4.62772i	−0.609403	−	0.351839i	−0.772732	+	0.634733i	$0.781110\pi$
$174$		0			0
$175$		0			0
$176$	0.686141	+	1.18843i	0.0517198	+	0.0895813i
$177$		0			0
$178$	0.967215	+	0.558422i	0.0724958	+	0.0418555i
$179$	−3.25544			−0.243323			−0.121661	−	0.992572i	$-0.538822\pi$
$179$	−3.25544			−0.243323			−0.121661	+	0.992572i	$0.538822\pi$
$180$		0			0
$181$	−7.86141			−0.584334			−0.292167	−	0.956367i	$-0.594376\pi$
$181$	−7.86141			−0.584334			−0.292167	+	0.956367i	$0.594376\pi$
$182$	9.74749	+	5.62772i	0.722532	+	0.417154i
$183$		0			0
$184$	2.18614	+	3.78651i	0.161164	+	0.279145i
$185$		0			0
$186$		0			0
$187$	8.76144	+	5.05842i	0.640700	+	0.369908i
$188$		−	1.62772i		−	0.118714i
$189$		0			0
$190$		0			0
$191$	−2.74456	+	4.75372i	−0.198590	+	0.343967i	−0.948071	−	0.318058i	$-0.896969\pi$
$191$	−2.74456	+	4.75372i	−0.198590	+	0.343967i	0.749482	+	0.662025i	$0.230303\pi$
$192$		0			0
$193$	−3.36291	+	1.94158i	−0.242068	+	0.139758i	−0.616127	−	0.787647i	$-0.711299\pi$
$193$	−3.36291	+	1.94158i	−0.242068	+	0.139758i	0.374059	+	0.927405i	$0.377966\pi$
$194$	−1.31386	−	2.27567i	−0.0943296	−	0.163384i
$195$		0			0
$196$	0.686141	−	1.18843i	0.0490100	−	0.0848879i
$197$		−	17.4891i		−	1.24605i	−0.782202	−	0.623024i	$-0.785904\pi$
$197$		−	17.4891i		−	1.24605i	0.782202	−	0.623024i	$-0.214096\pi$
$198$		0			0
$199$	9.48913			0.672666			0.336333	−	0.941743i	$-0.390813\pi$
$199$	9.48913			0.672666			0.336333	+	0.941743i	$0.390813\pi$
$200$		0			0
$201$		0			0
$202$	7.57301	−	4.37228i	0.532835	−	0.307633i
$203$	8.98266	−	5.18614i	0.630459	−	0.363996i
$204$		0			0
$205$		0			0
$206$	−16.0000			−1.11477
$207$		0			0
$208$		−	4.74456i		−	0.328976i
$209$	−2.31386	+	4.00772i	−0.160053	+	0.277220i
$210$		0			0
$211$	3.62772	+	6.28339i	0.249742	+	0.432567i	0.963454	−	0.267873i	$-0.0863207\pi$
$211$	3.62772	+	6.28339i	0.249742	+	0.432567i	−0.713712	+	0.700439i	$0.752987\pi$
$212$	−9.94987	+	5.74456i	−0.683360	+	0.394538i
$213$		0			0
$214$	7.24456	−	12.5480i	0.495228	−	0.857760i
$215$		0			0
$216$		0			0
$217$			16.0000i			1.08615i
$218$	8.33785	+	4.81386i	0.564710	+	0.326036i
$219$		0			0
$220$		0			0
$221$	−17.4891	−	30.2921i	−1.17645	−	2.03766i
$222$		0			0
$223$	10.7147	+	6.18614i	0.717510	+	0.414255i	0.813836	−	0.581095i	$-0.197376\pi$
$223$	10.7147	+	6.18614i	0.717510	+	0.414255i	−0.0963255	+	0.995350i	$0.530709\pi$
$224$	2.37228			0.158505
$225$		0			0
$226$	−14.7446			−0.980794
$227$	1.63086	+	0.941578i	0.108244	+	0.0624947i	0.553145	−	0.833085i	$-0.313428\pi$
$227$	1.63086	+	0.941578i	0.108244	+	0.0624947i	−0.444901	+	0.895580i	$0.646761\pi$
$228$		0			0
$229$	9.18614	+	15.9109i	0.607037	+	1.05142i	0.991726	+	0.128373i	$0.0409755\pi$
$229$	9.18614	+	15.9109i	0.607037	+	1.05142i	−0.384689	+	0.923046i	$0.625691\pi$
$230$		0			0
$231$		0			0
$232$	−3.78651	−	2.18614i	−0.248596	−	0.143527i
$233$		−	10.1168i		−	0.662776i	−0.943494	−	0.331388i	$-0.892483\pi$
$233$		−	10.1168i		−	0.662776i	0.943494	−	0.331388i	$-0.107517\pi$
$234$		0			0
$235$		0			0
$236$	−0.686141	+	1.18843i	−0.0446640	+	0.0773602i
$237$		0			0
$238$	15.1460	−	8.74456i	0.981771	−	0.566826i
$239$	7.37228	+	12.7692i	0.476873	+	0.825969i	0.999649	−	0.0265017i	$-0.00843674\pi$
$239$	7.37228	+	12.7692i	0.476873	+	0.825969i	−0.522776	+	0.852470i	$0.675103\pi$
$240$		0			0
$241$	−5.24456	+	9.08385i	−0.337832	+	0.585142i	−0.984025	−	0.178032i	$-0.943027\pi$
$241$	−5.24456	+	9.08385i	−0.337832	+	0.585142i	0.646193	+	0.763174i	$0.276360\pi$
$242$		−	9.11684i		−	0.586053i
$243$		0			0
$244$	−9.11684			−0.583646
$245$		0			0
$246$		0			0
$247$	13.8564	−	8.00000i	0.881662	−	0.509028i
$248$	5.84096	−	3.37228i	0.370901	−	0.214140i
$249$		0			0
$250$		0			0
$251$	−15.6060			−0.985040			−0.492520	−	0.870301i	$-0.663924\pi$
$251$	−15.6060			−0.985040			−0.492520	+	0.870301i	$0.663924\pi$
$252$		0			0
$253$			6.00000i			0.377217i
$254$	4.55842	−	7.89542i	0.286021	−	0.495403i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.18843	−	0.686141i	0.0741323	−	0.0428003i	−0.462476	−	0.886632i	$-0.653039\pi$
$257$	1.18843	−	0.686141i	0.0741323	−	0.0428003i	0.536608	+	0.843832i	$0.319705\pi$
$258$		0			0
$259$	4.74456	−	8.21782i	0.294813	−	0.510631i
$260$		0			0
$261$		0			0
$262$		−	8.74456i		−	0.540241i
$263$	−4.75372	−	2.74456i	−0.293127	−	0.169237i	0.346224	−	0.938152i	$-0.387464\pi$
$263$	−4.75372	−	2.74456i	−0.293127	−	0.169237i	−0.639351	+	0.768915i	$0.720797\pi$
$264$		0			0
$265$		0			0
$266$	4.00000	+	6.92820i	0.245256	+	0.424795i
$267$		0			0
$268$	−6.06218	−	3.50000i	−0.370306	−	0.213797i
$269$	4.37228			0.266583			0.133291	−	0.991077i	$-0.457445\pi$
$269$	4.37228			0.266583			0.133291	+	0.991077i	$0.457445\pi$
$270$		0			0
$271$	8.00000			0.485965			0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000			0.485965			0.242983	+	0.970031i	$0.421874\pi$
$272$	−6.38458	−	3.68614i	−0.387122	−	0.223505i
$273$		0			0
$274$	0.941578	+	1.63086i	0.0568828	+	0.0985239i
$275$		0			0
$276$		0			0
$277$	−4.55134	−	2.62772i	−0.273464	−	0.157884i	0.356997	−	0.934106i	$-0.383801\pi$
$277$	−4.55134	−	2.62772i	−0.273464	−	0.157884i	−0.630461	+	0.776221i	$0.717134\pi$
$278$		−	18.1168i		−	1.08658i
$279$		0			0
$280$		0			0
$281$	2.18614	−	3.78651i	0.130414	−	0.225884i	−0.793422	−	0.608672i	$-0.791703\pi$
$281$	2.18614	−	3.78651i	0.130414	−	0.225884i	0.923836	+	0.382788i	$0.125036\pi$
$282$		0			0
$283$	27.5928	−	15.9307i	1.64022	−	0.946982i	0.659467	−	0.751733i	$-0.270782\pi$
$283$	27.5928	−	15.9307i	1.64022	−	0.946982i	0.980754	−	0.195249i	$-0.0625514\pi$
$284$	3.00000	+	5.19615i	0.178017	+	0.308335i
$285$		0			0
$286$	3.25544	−	5.63858i	0.192498	−	0.333416i
$287$		−	7.11684i		−	0.420094i
$288$		0			0
$289$	−37.3505			−2.19709
$290$		0			0
$291$		0			0
$292$	−12.2255	+	7.05842i	−0.715446	+	0.413063i
$293$	−7.13058	+	4.11684i	−0.416573	+	0.240509i	−0.693610	−	0.720351i	$-0.743981\pi$
$293$	−7.13058	+	4.11684i	−0.416573	+	0.240509i	0.277037	+	0.960859i	$0.410648\pi$
$294$		0			0
$295$		0			0
$296$	−4.00000			−0.232495
$297$		0			0
$298$			19.1168i			1.10741i
$299$	10.3723	−	17.9653i	0.599845	−	1.03896i
$300$		0			0
$301$	−13.4891	−	23.3639i	−0.777500	−	1.34667i
$302$	−8.66025	+	5.00000i	−0.498342	+	0.287718i
$303$		0			0
$304$	1.68614	−	2.92048i	0.0967068	−	0.167501i
$305$		0			0
$306$		0			0
$307$		−	33.2337i		−	1.89675i	−0.317156	−	0.948373i	$-0.602728\pi$
$307$		−	33.2337i		−	1.89675i	0.317156	−	0.948373i	$-0.397272\pi$
$308$	2.81929	+	1.62772i	0.160644	+	0.0927479i
$309$		0			0
$310$		0			0
$311$	−4.62772	−	8.01544i	−0.262414	−	0.454514i	0.704469	−	0.709735i	$-0.251185\pi$
$311$	−4.62772	−	8.01544i	−0.262414	−	0.454514i	−0.966883	+	0.255221i	$0.917852\pi$
$312$		0			0
$313$	8.11663	+	4.68614i	0.458779	+	0.264876i	0.711531	−	0.702655i	$-0.248002\pi$
$313$	8.11663	+	4.68614i	0.458779	+	0.264876i	−0.252752	+	0.967531i	$0.581336\pi$
$314$	−4.74456			−0.267751
$315$		0			0
$316$	2.00000			0.112509
$317$	−7.57301	−	4.37228i	−0.425343	−	0.245572i	0.272018	−	0.962292i	$-0.412309\pi$
$317$	−7.57301	−	4.37228i	−0.425343	−	0.245572i	−0.697361	+	0.716720i	$0.745642\pi$
$318$		0			0
$319$	−3.00000	−	5.19615i	−0.167968	−	0.290929i
$320$		0			0
$321$		0			0
$322$	8.98266	+	5.18614i	0.500584	+	0.289012i
$323$		−	24.8614i		−	1.38333i
$324$		0			0
$325$		0			0
$326$	−0.744563	+	1.28962i	−0.0412375	+	0.0714255i
$327$		0			0
$328$	−2.59808	+	1.50000i	−0.143455	+	0.0828236i
$329$	−1.93070	−	3.34408i	−0.106443	−	0.184365i
$330$		0			0
$331$	9.11684	−	15.7908i	0.501107	−	0.867943i	−0.498892	−	0.866664i	$-0.666260\pi$
$331$	9.11684	−	15.7908i	0.501107	−	0.867943i	0.999999	−	0.00127880i	$-0.000407055\pi$
$332$		−	1.62772i		−	0.0893327i
$333$		0			0
$334$	7.62772			0.417370
$335$		0			0
$336$		0			0
$337$	2.92048	−	1.68614i	0.159089	−	0.0918499i	−0.418342	−	0.908290i	$-0.637389\pi$
$337$	2.92048	−	1.68614i	0.159089	−	0.0918499i	0.577431	+	0.816440i	$0.304055\pi$
$338$	−8.23666	+	4.75544i	−0.448015	+	0.258662i
$339$		0			0
$340$		0			0
$341$	9.25544			0.501210
$342$		0			0
$343$		−	19.8614i		−	1.07242i
$344$	−5.68614	+	9.84868i	−0.306576	+	0.531005i
$345$		0			0
$346$	4.62772	+	8.01544i	0.248788	+	0.430913i
$347$	19.1537	−	11.0584i	1.02823	−	0.593647i	0.111751	−	0.993736i	$-0.464354\pi$
$347$	19.1537	−	11.0584i	1.02823	−	0.593647i	0.916476	+	0.400089i	$0.131021\pi$
$348$		0			0
$349$	0.441578	−	0.764836i	0.0236371	−	0.0409407i	−0.853965	−	0.520331i	$-0.825809\pi$
$349$	0.441578	−	0.764836i	0.0236371	−	0.0409407i	0.877602	+	0.479390i	$0.159142\pi$
$350$		0			0
$351$		0			0
$352$		−	1.37228i		−	0.0731428i
$353$	−26.2843	−	15.1753i	−1.39897	−	0.807698i	−0.404689	−	0.914455i	$-0.632620\pi$
$353$	−26.2843	−	15.1753i	−1.39897	−	0.807698i	−0.994285	+	0.106757i	$0.965953\pi$
$354$		0			0
$355$		0			0
$356$	−0.558422	−	0.967215i	−0.0295963	−	0.0512623i
$357$		0			0
$358$	2.81929	+	1.62772i	0.149004	+	0.0860276i
$359$	5.48913			0.289705			0.144852	−	0.989453i	$-0.453729\pi$
$359$	5.48913			0.289705			0.144852	+	0.989453i	$0.453729\pi$
$360$		0			0
$361$	−7.62772			−0.401459
$362$	6.80818	+	3.93070i	0.357830	+	0.206593i
$363$		0			0
$364$	−5.62772	−	9.74749i	−0.294973	−	0.510908i
$365$		0			0
$366$		0			0
$367$	13.8564	+	8.00000i	0.723299	+	0.417597i	0.815966	−	0.578101i	$-0.196206\pi$
$367$	13.8564	+	8.00000i	0.723299	+	0.417597i	−0.0926670	+	0.995697i	$0.529539\pi$
$368$		−	4.37228i		−	0.227921i
$369$		0			0
$370$		0			0
$371$	−13.6277	+	23.6039i	−0.707516	+	1.22545i
$372$		0			0
$373$	−6.48577	+	3.74456i	−0.335821	+	0.193886i	−0.658422	−	0.752649i	$-0.728776\pi$
$373$	−6.48577	+	3.74456i	−0.335821	+	0.193886i	0.322602	+	0.946535i	$0.395443\pi$
$374$	−5.05842	−	8.76144i	−0.261565	−	0.453043i
$375$		0			0
$376$	−0.813859	+	1.40965i	−0.0419716	+	0.0726969i
$377$			20.7446i			1.06840i
$378$		0			0
$379$	10.8614			0.557913			0.278956	−	0.960304i	$-0.410011\pi$
$379$	10.8614			0.557913			0.278956	+	0.960304i	$0.410011\pi$
$380$		0			0
$381$		0			0
$382$	4.75372	−	2.74456i	0.243222	−	0.140424i
$383$	19.8997	−	11.4891i	1.01683	−	0.587067i	0.103646	−	0.994614i	$-0.466949\pi$
$383$	19.8997	−	11.4891i	1.01683	−	0.587067i	0.913184	+	0.407547i	$0.133616\pi$
$384$		0			0
$385$		0			0
$386$	3.88316			0.197647
$387$		0			0
$388$			2.62772i			0.133402i
$389$	5.18614	−	8.98266i	0.262948	−	0.455439i	−0.704076	−	0.710124i	$-0.748639\pi$
$389$	5.18614	−	8.98266i	0.262948	−	0.455439i	0.967024	+	0.254686i	$0.0819720\pi$
$390$		0			0
$391$	−16.1168	−	27.9152i	−0.815064	−	1.41173i
$392$	−1.18843	+	0.686141i	−0.0600248	+	0.0346553i
$393$		0			0
$394$	−8.74456	+	15.1460i	−0.440545	+	0.763046i
$395$		0			0
$396$		0			0
$397$			11.2554i			0.564894i	0.959283	+	0.282447i	$0.0911462\pi$
$397$			11.2554i			0.564894i	−0.959283	+	0.282447i	$0.908854\pi$
$398$	−8.21782	−	4.74456i	−0.411922	−	0.237823i
$399$		0			0
$400$		0			0
$401$	8.05842	+	13.9576i	0.402418	+	0.697009i	0.994017	−	0.109223i	$-0.0348364\pi$
$401$	8.05842	+	13.9576i	0.402418	+	0.697009i	−0.591599	+	0.806232i	$0.701503\pi$
$402$		0			0
$403$	−27.7128	−	16.0000i	−1.38047	−	0.797017i
$404$	−8.74456			−0.435058
$405$		0			0
$406$	−10.3723			−0.514768
$407$	−4.75372	−	2.74456i	−0.235633	−	0.136043i
$408$		0			0
$409$	−5.43070	−	9.40625i	−0.268531	−	0.465109i	0.699952	−	0.714190i	$-0.253205\pi$
$409$	−5.43070	−	9.40625i	−0.268531	−	0.465109i	−0.968483	+	0.249081i	$0.919872\pi$
$410$		0			0
$411$		0			0
$412$	13.8564	+	8.00000i	0.682656	+	0.394132i
$413$			3.25544i			0.160190i
$414$		0			0
$415$		0			0
$416$	−2.37228	+	4.10891i	−0.116311	+	0.201456i
$417$		0			0
$418$	4.00772	−	2.31386i	0.196024	−	0.113175i
$419$	15.8614	+	27.4728i	0.774880	+	1.34213i	0.934862	+	0.355012i	$0.115523\pi$
$419$	15.8614	+	27.4728i	0.774880	+	1.34213i	−0.159981	+	0.987120i	$0.551143\pi$
$420$		0			0
$421$	19.2337	−	33.3137i	0.937393	−	1.62361i	0.167082	−	0.985943i	$-0.446566\pi$
$421$	19.2337	−	33.3137i	0.937393	−	1.62361i	0.770311	−	0.637669i	$-0.220101\pi$
$422$		−	7.25544i		−	0.353189i
$423$		0			0
$424$	11.4891			0.557961
$425$		0			0
$426$		0			0
$427$	−18.7302	+	10.8139i	−0.906416	+	0.523319i
$428$	−12.5480	+	7.24456i	−0.606528	+	0.350179i
$429$		0			0
$430$		0			0
$431$	26.2337			1.26363			0.631816	−	0.775118i	$-0.282310\pi$
$431$	26.2337			1.26363			0.631816	+	0.775118i	$0.282310\pi$
$432$		0			0
$433$		−	0.627719i		−	0.0301662i	−0.999886	−	0.0150831i	$-0.995199\pi$
$433$		−	0.627719i		−	0.0301662i	0.999886	−	0.0150831i	$-0.00480129\pi$
$434$	8.00000	−	13.8564i	0.384012	−	0.665129i
$435$		0			0
$436$	−4.81386	−	8.33785i	−0.230542	−	0.399311i
$437$	12.7692	−	7.37228i	0.610832	−	0.352664i
$438$		0			0
$439$	8.11684	−	14.0588i	0.387396	−	0.670989i	−0.604703	−	0.796451i	$-0.706708\pi$
$439$	8.11684	−	14.0588i	0.387396	−	0.670989i	0.992098	+	0.125462i	$0.0400414\pi$
$440$		0			0
$441$		0			0
$442$			34.9783i			1.66375i
$443$	22.9403	+	13.2446i	1.08992	+	0.629268i	0.933556	−	0.358431i	$-0.116688\pi$
$443$	22.9403	+	13.2446i	1.08992	+	0.629268i	0.156368	+	0.987699i	$0.450021\pi$
$444$		0			0
$445$		0			0
$446$	−6.18614	−	10.7147i	−0.292922	−	0.507356i
$447$		0			0
$448$	−2.05446	−	1.18614i	−0.0970639	−	0.0560399i
$449$	−18.8614			−0.890125			−0.445062	−	0.895500i	$-0.646819\pi$
$449$	−18.8614			−0.890125			−0.445062	+	0.895500i	$0.646819\pi$
$450$		0			0
$451$	−4.11684			−0.193855
$452$	12.7692	+	7.37228i	0.600611	+	0.346763i
$453$		0			0
$454$	−0.941578	−	1.63086i	−0.0441904	−	0.0765401i
$455$		0			0
$456$		0			0
$457$	−26.0820	−	15.0584i	−1.22006	−	0.704403i	−0.255131	−	0.966906i	$-0.582119\pi$
$457$	−26.0820	−	15.0584i	−1.22006	−	0.704403i	−0.964931	+	0.262503i	$0.915452\pi$
$458$		−	18.3723i		−	0.858480i
$459$		0			0
$460$		0			0
$461$	9.55842	−	16.5557i	0.445180	−	0.771075i	−0.552885	−	0.833258i	$-0.686473\pi$
$461$	9.55842	−	16.5557i	0.445180	−	0.771075i	0.998065	+	0.0621833i	$0.0198063\pi$
$462$		0			0
$463$	−17.3205	+	10.0000i	−0.804952	+	0.464739i	−0.845200	−	0.534450i	$-0.820519\pi$
$463$	−17.3205	+	10.0000i	−0.804952	+	0.464739i	0.0402476	+	0.999190i	$0.487185\pi$
$464$	2.18614	+	3.78651i	0.101489	+	0.175784i
$465$		0			0
$466$	−5.05842	+	8.76144i	−0.234327	+	0.405866i
$467$		−	25.8832i		−	1.19773i	−0.800850	−	0.598865i	$-0.795619\pi$
$467$		−	25.8832i		−	1.19773i	0.800850	−	0.598865i	$-0.204381\pi$
$468$		0			0
$469$	−16.6060			−0.766792
$470$		0			0
$471$		0			0
$472$	1.18843	−	0.686141i	0.0547019	−	0.0315822i
$473$	−13.5152	+	7.80298i	−0.621428	+	0.358782i
$474$		0			0
$475$		0			0
$476$	−17.4891			−0.801613
$477$		0			0
$478$		−	14.7446i		−	0.674401i
$479$	11.7446	−	20.3422i	0.536623	−	0.929458i	−0.462460	−	0.886640i	$-0.653033\pi$
$479$	11.7446	−	20.3422i	0.536623	−	0.929458i	0.999083	−	0.0428178i	$-0.0136335\pi$
$480$		0			0
$481$	9.48913	+	16.4356i	0.432667	+	0.749401i
$482$	9.08385	−	5.24456i	0.413758	−	0.238883i
$483$		0			0
$484$	−4.55842	+	7.89542i	−0.207201	+	0.358883i
$485$		0			0
$486$		0			0
$487$		−	1.25544i		−	0.0568893i	−0.999595	−	0.0284446i	$-0.990945\pi$
$487$		−	1.25544i		−	0.0568893i	0.999595	−	0.0284446i	$-0.00905543\pi$
$488$	7.89542	+	4.55842i	0.357409	+	0.206350i
$489$		0			0
$490$		0			0
$491$	1.80298	+	3.12286i	0.0813676	+	0.140933i	0.903838	−	0.427876i	$-0.140738\pi$
$491$	1.80298	+	3.12286i	0.0813676	+	0.140933i	−0.822470	+	0.568808i	$0.807405\pi$
$492$		0			0
$493$	27.9152	+	16.1168i	1.25724	+	0.725866i
$494$	−16.0000			−0.719874
$495$		0			0
$496$	−6.74456			−0.302840
$497$	12.3267	+	7.11684i	0.552930	+	0.319234i
$498$		0			0
$499$	−1.05842	−	1.83324i	−0.0473815	−	0.0820671i	0.841362	−	0.540472i	$-0.181754\pi$
$499$	−1.05842	−	1.83324i	−0.0473815	−	0.0820671i	−0.888743	+	0.458405i	$0.848421\pi$
$500$		0			0
$501$		0			0
$502$	13.5152	+	7.80298i	0.603211	+	0.348264i
$503$			21.8614i			0.974752i	0.873192	+	0.487376i	$0.162046\pi$
$503$			21.8614i			0.974752i	−0.873192	+	0.487376i	$0.837954\pi$
$504$		0			0
$505$		0			0
$506$	3.00000	−	5.19615i	0.133366	−	0.230997i
$507$		0			0
$508$	−7.89542	+	4.55842i	−0.350303	+	0.202247i
$509$	−4.67527	−	8.09780i	−0.207228	−	0.358929i	0.743613	−	0.668611i	$-0.233111\pi$
$509$	−4.67527	−	8.09780i	−0.207228	−	0.358929i	−0.950840	+	0.309682i	$0.899777\pi$
$510$		0			0
$511$	−16.7446	+	29.0024i	−0.740736	+	1.28299i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−1.37228			−0.0605287
$515$		0			0
$516$		0			0
$517$	−1.93443	+	1.11684i	−0.0850762	+	0.0491187i
$518$	−8.21782	+	4.74456i	−0.361070	+	0.208464i
$519$		0			0
$520$		0			0
$521$	41.2337			1.80648			0.903240	−	0.429135i	$-0.141182\pi$
$521$	41.2337			1.80648			0.903240	+	0.429135i	$0.141182\pi$
$522$		0			0
$523$			11.1168i			0.486106i	0.970013	+	0.243053i	$0.0781488\pi$
$523$			11.1168i			0.486106i	−0.970013	+	0.243053i	$0.921851\pi$
$524$	−4.37228	+	7.57301i	−0.191004	+	0.330829i
$525$		0			0
$526$	2.74456	+	4.75372i	0.119669	+	0.207272i
$527$	−43.0612	+	24.8614i	−1.87578	+	1.08298i
$528$		0			0
$529$	−1.94158	+	3.36291i	−0.0844164	+	0.146214i
$530$		0			0
$531$		0			0
$532$		−	8.00000i		−	0.346844i
$533$	12.3267	+	7.11684i	0.533930	+	0.308265i
$534$		0			0
$535$		0			0
$536$	3.50000	+	6.06218i	0.151177	+	0.261846i
$537$		0			0
$538$	−3.78651	−	2.18614i	−0.163248	−	0.0942512i
$539$	−1.88316			−0.0811133
$540$		0			0
$541$	21.6277			0.929848			0.464924	−	0.885351i	$-0.346082\pi$
$541$	21.6277			0.929848			0.464924	+	0.885351i	$0.346082\pi$
$542$	−6.92820	−	4.00000i	−0.297592	−	0.171815i
$543$		0			0
$544$	3.68614	+	6.38458i	0.158042	+	0.273737i
$545$		0			0
$546$		0			0
$547$	−34.1798	−	19.7337i	−1.46142	−	0.843752i	−0.462343	−	0.886701i	$-0.652991\pi$
$547$	−34.1798	−	19.7337i	−1.46142	−	0.843752i	−0.999077	+	0.0429494i	$0.986325\pi$
$548$		−	1.88316i		−	0.0804444i
$549$		0			0
$550$		0			0
$551$	−7.37228	+	12.7692i	−0.314070	+	0.543985i
$552$		0			0
$553$	4.10891	−	2.37228i	0.174729	−	0.100880i
$554$	2.62772	+	4.55134i	0.111641	+	0.193368i
$555$		0			0
$556$	−9.05842	+	15.6896i	−0.384163	+	0.665389i
$557$			9.76631i			0.413812i	0.978361	+	0.206906i	$0.0663394\pi$
$557$			9.76631i			0.413812i	−0.978361	+	0.206906i	$0.933661\pi$
$558$		0			0
$559$	53.9565			2.28212
$560$		0			0
$561$		0			0
$562$	−3.78651	+	2.18614i	−0.159724	+	0.0922168i
$563$	14.4824	−	8.36141i	0.610360	−	0.352391i	−0.162747	−	0.986668i	$-0.552035\pi$
$563$	14.4824	−	8.36141i	0.610360	−	0.352391i	0.773106	+	0.634277i	$0.218702\pi$
$564$		0			0
$565$		0			0
$566$	−31.8614			−1.33923
$567$		0			0
$568$		−	6.00000i		−	0.251754i
$569$	−4.80298	+	8.31901i	−0.201352	+	0.348751i	−0.948964	−	0.315384i	$-0.897867\pi$
$569$	−4.80298	+	8.31901i	−0.201352	+	0.348751i	0.747613	+	0.664135i	$0.231200\pi$
$570$		0			0
$571$	15.8030	+	27.3716i	0.661334	+	1.14546i	0.980265	+	0.197687i	$0.0633429\pi$
$571$	15.8030	+	27.3716i	0.661334	+	1.14546i	−0.318931	+	0.947778i	$0.603324\pi$
$572$	−5.63858	+	3.25544i	−0.235761	+	0.136117i
$573$		0			0
$574$	−3.55842	+	6.16337i	−0.148526	+	0.257254i
$575$		0			0
$576$		0			0
$577$		−	23.8832i		−	0.994269i	−0.867674	−	0.497134i	$-0.834386\pi$
$577$		−	23.8832i		−	0.994269i	0.867674	−	0.497134i	$-0.165614\pi$
$578$	32.3465	+	18.6753i	1.34544	+	0.776789i
$579$		0			0
$580$		0			0
$581$	−1.93070	−	3.34408i	−0.0800991	−	0.138736i
$582$		0			0
$583$	13.6540	+	7.88316i	0.565492	+	0.326487i
$584$	14.1168			0.584159
$585$		0			0
$586$	8.23369			0.340131
$587$	23.3827	+	13.5000i	0.965107	+	0.557205i	0.897741	−	0.440524i	$-0.145207\pi$
$587$	23.3827	+	13.5000i	0.965107	+	0.557205i	0.0673658	+	0.997728i	$0.478541\pi$
$588$		0			0
$589$	−11.3723	−	19.6974i	−0.468587	−	0.811616i
$590$		0			0
$591$		0			0
$592$	3.46410	+	2.00000i	0.142374	+	0.0821995i
$593$			37.7228i			1.54909i	0.632519	+	0.774545i	$0.282021\pi$
$593$			37.7228i			1.54909i	−0.632519	+	0.774545i	$0.717979\pi$
$594$		0			0
$595$		0			0
$596$	9.55842	−	16.5557i	0.391528	−	0.678147i
$597$		0			0
$598$	−17.9653	+	10.3723i	−0.734656	+	0.424154i
$599$	19.1168	+	33.1113i	0.781093	+	1.35289i	0.931305	+	0.364239i	$0.118671\pi$
$599$	19.1168	+	33.1113i	0.781093	+	1.35289i	−0.150212	+	0.988654i	$0.547996\pi$
$600$		0			0
$601$	−13.4307	+	23.2627i	−0.547850	+	0.948904i	0.450572	+	0.892740i	$0.351220\pi$
$601$	−13.4307	+	23.2627i	−0.547850	+	0.948904i	−0.998422	+	0.0561635i	$0.982113\pi$
$602$			26.9783i			1.09955i
$603$		0			0
$604$	10.0000			0.406894
$605$		0			0
$606$		0			0
$607$	0.764836	−	0.441578i	0.0310437	−	0.0179231i	−0.484398	−	0.874848i	$-0.660961\pi$
$607$	0.764836	−	0.441578i	0.0310437	−	0.0179231i	0.515442	+	0.856925i	$0.327628\pi$
$608$	−2.92048	+	1.68614i	−0.118441	+	0.0683820i
$609$		0			0
$610$		0			0
$611$	7.72281			0.312432
$612$		0			0
$613$			0.233688i			0.00943857i	0.999989	+	0.00471928i	$0.00150220\pi$
$613$			0.233688i			0.00943857i	−0.999989	+	0.00471928i	$0.998498\pi$
$614$	−16.6168	+	28.7812i	−0.670601	+	1.16152i
$615$		0			0
$616$	−1.62772	−	2.81929i	−0.0655827	−	0.113592i
$617$	19.1537	−	11.0584i	0.771101	−	0.445195i	−0.0621663	−	0.998066i	$-0.519801\pi$
$617$	19.1537	−	11.0584i	0.771101	−	0.445195i	0.833267	+	0.552870i	$0.186468\pi$
$618$		0			0
$619$	−19.0584	+	33.0102i	−0.766023	+	1.32679i	0.173682	+	0.984802i	$0.444434\pi$
$619$	−19.0584	+	33.0102i	−0.766023	+	1.32679i	−0.939704	+	0.341988i	$0.888900\pi$
$620$		0			0
$621$		0			0
$622$			9.25544i			0.371109i
$623$	−2.29451	−	1.32473i	−0.0919275	−	0.0530743i
$624$		0			0
$625$		0			0
$626$	−4.68614	−	8.11663i	−0.187296	−	0.324406i
$627$		0			0
$628$	4.10891	+	2.37228i	0.163963	+	0.0946643i
$629$	29.4891			1.17581
$630$		0			0
$631$	33.7228			1.34248			0.671242	−	0.741238i	$-0.265761\pi$
$631$	33.7228			1.34248			0.671242	+	0.741238i	$0.265761\pi$
$632$	−1.73205	−	1.00000i	−0.0688973	−	0.0397779i
$633$		0			0
$634$	4.37228	+	7.57301i	0.173645	+	0.300763i
$635$		0			0
$636$		0			0
$637$	5.63858	+	3.25544i	0.223409	+	0.128985i
$638$			6.00000i			0.237542i
$639$		0			0
$640$		0			0
$641$	−19.5000	+	33.7750i	−0.770204	+	1.33403i	0.167247	+	0.985915i	$0.446512\pi$
$641$	−19.5000	+	33.7750i	−0.770204	+	1.33403i	−0.937451	+	0.348117i	$0.886821\pi$
$642$		0			0
$643$	−9.52628	+	5.50000i	−0.375680	+	0.216899i	−0.675937	−	0.736959i	$-0.736261\pi$
$643$	−9.52628	+	5.50000i	−0.375680	+	0.216899i	0.300257	+	0.953858i	$0.402928\pi$
$644$	−5.18614	−	8.98266i	−0.204363	−	0.353966i
$645$		0			0
$646$	−12.4307	+	21.5306i	−0.489079	+	0.847111i
$647$		−	24.0951i		−	0.947276i	−0.880720	−	0.473638i	$-0.842941\pi$
$647$		−	24.0951i		−	0.947276i	0.880720	−	0.473638i	$-0.157059\pi$
$648$		0			0
$649$	1.88316			0.0739203
$650$		0			0
$651$		0			0
$652$	1.28962	−	0.744563i	0.0505054	−	0.0291593i
$653$	−32.6689	+	18.8614i	−1.27843	+	0.738104i	−0.976560	−	0.215244i	$-0.930945\pi$
$653$	−32.6689	+	18.8614i	−1.27843	+	0.738104i	−0.301873	+	0.953348i	$0.597612\pi$
$654$		0			0
$655$		0			0
$656$	3.00000			0.117130
$657$		0			0
$658$			3.86141i			0.150533i
$659$	2.74456	−	4.75372i	0.106913	−	0.185179i	−0.807605	−	0.589724i	$-0.799237\pi$
$659$	2.74456	−	4.75372i	0.106913	−	0.185179i	0.914518	+	0.404545i	$0.132570\pi$
$660$		0			0
$661$	−11.1168	−	19.2549i	−0.432395	−	0.748930i	0.564684	−	0.825307i	$-0.308998\pi$
$661$	−11.1168	−	19.2549i	−0.432395	−	0.748930i	−0.997079	+	0.0763770i	$0.975665\pi$
$662$	−15.7908	+	9.11684i	−0.613728	+	0.354336i
$663$		0			0
$664$	−0.813859	+	1.40965i	−0.0315839	+	0.0547049i
$665$		0			0
$666$		0			0
$667$			19.1168i			0.740207i
$668$	−6.60580	−	3.81386i	−0.255586	−	0.147563i
$669$		0			0
$670$		0			0
$671$	6.25544	+	10.8347i	0.241488	+	0.418270i
$672$		0			0
$673$	−8.66025	−	5.00000i	−0.333828	−	0.192736i	0.323711	−	0.946156i	$-0.395069\pi$
$673$	−8.66025	−	5.00000i	−0.333828	−	0.192736i	−0.657539	+	0.753420i	$0.728403\pi$
$674$	−3.37228			−0.129895
$675$		0			0
$676$	9.51087			0.365803
$677$	−37.8651	−	21.8614i	−1.45527	−	0.840202i	−0.456500	−	0.889724i	$-0.650897\pi$
$677$	−37.8651	−	21.8614i	−1.45527	−	0.840202i	−0.998773	+	0.0495215i	$0.984230\pi$
$678$		0			0
$679$	3.11684	+	5.39853i	0.119613	+	0.207177i
$680$		0			0
$681$		0			0
$682$	−8.01544	−	4.62772i	−0.306927	−	0.177205i
$683$			33.0951i			1.26635i	0.774009	+	0.633174i	$0.218248\pi$
$683$			33.0951i			1.26635i	−0.774009	+	0.633174i	$0.781752\pi$
$684$		0			0
$685$		0			0
$686$	−9.93070	+	17.2005i	−0.379156	+	0.656717i
$687$		0			0
$688$	9.84868	−	5.68614i	0.375478	−	0.216782i
$689$	−27.2554	−	47.2078i	−1.03835	−	1.79847i
$690$		0			0
$691$	0.883156	−	1.52967i	0.0335968	−	0.0581914i	−0.848738	−	0.528813i	$-0.822637\pi$
$691$	0.883156	−	1.52967i	0.0335968	−	0.0581914i	0.882335	+	0.470622i	$0.155970\pi$
$692$		−	9.25544i		−	0.351839i
$693$		0			0
$694$	−22.1168			−0.839544
$695$		0			0
$696$		0			0
$697$	19.1537	−	11.0584i	0.725500	−	0.418868i
$698$	−0.764836	+	0.441578i	−0.0289495	+	0.0167140i
$699$		0			0
$700$		0			0
$701$	−14.1386			−0.534007			−0.267004	−	0.963696i	$-0.586034\pi$
$701$	−14.1386			−0.534007			−0.267004	+	0.963696i	$0.586034\pi$
$702$		0			0
$703$			13.4891i			0.508752i
$704$	−0.686141	+	1.18843i	−0.0258599	+	0.0447907i
$705$		0			0
$706$	15.1753	+	26.2843i	0.571129	+	0.989224i
$707$	−17.9653	+	10.3723i	−0.675655	+	0.390090i
$708$		0			0
$709$	−12.9307	+	22.3966i	−0.485623	+	0.841123i	−0.999863	−	0.0165226i	$-0.994740\pi$
$709$	−12.9307	+	22.3966i	−0.485623	+	0.841123i	0.514241	+	0.857646i	$0.328074\pi$
$710$		0			0
$711$		0			0
$712$			1.11684i			0.0418555i
$713$	−25.5383	−	14.7446i	−0.956418	−	0.552188i
$714$		0			0
$715$		0			0
$716$	−1.62772	−	2.81929i	−0.0608307	−	0.105362i
$717$		0			0
$718$	−4.75372	−	2.74456i	−0.177407	−	0.102426i
$719$	−38.2337			−1.42588			−0.712938	−	0.701227i	$-0.752636\pi$
$719$	−38.2337			−1.42588			−0.712938	+	0.701227i	$0.752636\pi$
$720$		0			0
$721$	37.9565			1.41357
$722$	6.60580	+	3.81386i	0.245842	+	0.141937i
$723$		0			0
$724$	−3.93070	−	6.80818i	−0.146083	−	0.253024i
$725$		0			0
$726$		0			0
$727$	−0.764836	−	0.441578i	−0.0283662	−	0.0163772i	0.485750	−	0.874098i	$-0.338547\pi$
$727$	−0.764836	−	0.441578i	−0.0283662	−	0.0163772i	−0.514116	+	0.857721i	$0.671880\pi$
$728$			11.2554i			0.417154i
$729$		0			0
$730$		0			0
$731$	41.9198	−	72.6073i	1.55046	−	2.68548i
$732$		0			0
$733$	−29.6472	+	17.1168i	−1.09505	+	0.632225i	−0.934915	−	0.354871i	$-0.884525\pi$
$733$	−29.6472	+	17.1168i	−1.09505	+	0.632225i	−0.160131	+	0.987096i	$0.551192\pi$
$734$	−8.00000	−	13.8564i	−0.295285	−	0.511449i
$735$		0			0
$736$	−2.18614	+	3.78651i	−0.0805822	+	0.139572i
$737$			9.60597i			0.353840i
$738$		0			0
$739$	23.8832			0.878556			0.439278	−	0.898351i	$-0.355234\pi$
$739$	23.8832			0.878556			0.439278	+	0.898351i	$0.355234\pi$
$740$		0			0
$741$		0			0
$742$	23.6039	−	13.6277i	0.866526	−	0.500289i
$743$	21.7518	−	12.5584i	0.797997	−	0.460724i	−0.0447732	−	0.998997i	$-0.514257\pi$
$743$	21.7518	−	12.5584i	0.797997	−	0.460724i	0.842770	+	0.538273i	$0.180923\pi$
$744$		0			0
$745$		0			0
$746$	7.48913			0.274196
$747$		0			0
$748$			10.1168i			0.369908i
$749$	−17.1861	+	29.7673i	−0.627968	+	1.08767i
$750$		0			0
$751$	9.11684	+	15.7908i	0.332678	+	0.576216i	0.983036	−	0.183412i	$-0.0587143\pi$
$751$	9.11684	+	15.7908i	0.332678	+	0.576216i	−0.650358	+	0.759628i	$0.725381\pi$
$752$	1.40965	−	0.813859i	0.0514045	−	0.0296784i
$753$		0			0
$754$	10.3723	−	17.9653i	0.377736	−	0.654258i
$755$		0			0
$756$		0			0
$757$		−	10.0000i		−	0.363456i	−0.983349	−	0.181728i	$-0.941831\pi$
$757$		−	10.0000i		−	0.363456i	0.983349	−	0.181728i	$-0.0581691\pi$
$758$	−9.40625	−	5.43070i	−0.341651	−	0.197252i
$759$		0			0
$760$		0			0
$761$	6.04755	+	10.4747i	0.219223	+	0.379706i	0.954571	−	0.297984i	$-0.0963143\pi$
$761$	6.04755	+	10.4747i	0.219223	+	0.379706i	−0.735347	+	0.677690i	$0.762981\pi$
$762$		0			0
$763$	−19.7797	−	11.4198i	−0.716074	−	0.413426i
$764$	−5.48913			−0.198590
$765$		0			0
$766$	−22.9783			−0.830238
$767$	−5.63858	−	3.25544i	−0.203597	−	0.117547i
$768$		0			0
$769$	−9.06930	−	15.7085i	−0.327047	−	0.566462i	0.654877	−	0.755735i	$-0.272720\pi$
$769$	−9.06930	−	15.7085i	−0.327047	−	0.566462i	−0.981925	+	0.189273i	$0.939387\pi$
$770$		0			0
$771$		0			0
$772$	−3.36291	−	1.94158i	−0.121034	−	0.0698789i
$773$			14.7446i			0.530325i	0.964204	+	0.265163i	$0.0854256\pi$
$773$			14.7446i			0.530325i	−0.964204	+	0.265163i	$0.914574\pi$
$774$		0			0
$775$		0			0
$776$	1.31386	−	2.27567i	0.0471648	−	0.0816918i
$777$		0			0
$778$	−8.98266	+	5.18614i	−0.322044	+	0.185932i
$779$	5.05842	+	8.76144i	0.181237	+	0.313911i
$780$		0			0
$781$	4.11684	−	7.13058i	0.147312	−	0.255152i
$782$			32.2337i			1.15267i
$783$		0			0
$784$	1.37228			0.0490100
$785$		0			0
$786$		0			0
$787$	−24.2487	+	14.0000i	−0.864373	+	0.499046i	−0.865474	−	0.500953i	$-0.832983\pi$
$787$	−24.2487	+	14.0000i	−0.864373	+	0.499046i	0.00110111	+	0.999999i	$0.499650\pi$
$788$	15.1460	−	8.74456i	0.539555	−	0.311512i
$789$		0			0
$790$		0			0
$791$	34.9783			1.24368
$792$		0			0
$793$		−	43.2554i		−	1.53605i
$794$	5.62772	−	9.74749i	0.199720	−	0.345926i
$795$		0			0
$796$	4.74456	+	8.21782i	0.168167	+	0.291273i
$797$	−2.81929	+	1.62772i	−0.0998644	+	0.0576568i	−0.549100	−	0.835756i	$-0.685030\pi$
$797$	−2.81929	+	1.62772i	−0.0998644	+	0.0576568i	0.449236	+	0.893413i	$0.351696\pi$
$798$		0			0
$799$	6.00000	−	10.3923i	0.212265	−	0.367653i
$800$		0			0
$801$		0			0
$802$		−	16.1168i		−	0.569106i
$803$	16.7769	+	9.68614i	0.592044	+	0.341816i
$804$		0			0
$805$		0			0
$806$	16.0000	+	27.7128i	0.563576	+	0.976142i
$807$		0			0
$808$	7.57301	+	4.37228i	0.266418	+	0.153816i
$809$	−12.3505			−0.434222			−0.217111	−	0.976147i	$-0.569663\pi$
$809$	−12.3505			−0.434222			−0.217111	+	0.976147i	$0.569663\pi$
$810$		0			0
$811$	9.37228			0.329105			0.164553	−	0.986368i	$-0.447382\pi$
$811$	9.37228			0.329105			0.164553	+	0.986368i	$0.447382\pi$
$812$	8.98266	+	5.18614i	0.315230	+	0.181998i
$813$		0			0
$814$	2.74456	+	4.75372i	0.0961969	+	0.166618i
$815$		0			0
$816$		0			0
$817$	33.2125	+	19.1753i	1.16196	+	0.670858i
$818$			10.8614i			0.379760i
$819$		0			0
$820$		0			0
$821$	25.4198	−	44.0284i	0.887158	−	1.53660i	0.0439382	−	0.999034i	$-0.486010\pi$
$821$	25.4198	−	44.0284i	0.887158	−	1.53660i	0.843220	−	0.537569i	$-0.180657\pi$
$822$		0			0
$823$	−32.9913	+	19.0475i	−1.15001	+	0.663956i	−0.948888	−	0.315612i	$-0.897790\pi$
$823$	−32.9913	+	19.0475i	−1.15001	+	0.663956i	−0.201117	+	0.979567i	$0.564457\pi$
$824$	−8.00000	−	13.8564i	−0.278693	−	0.482711i
$825$		0			0
$826$	1.62772	−	2.81929i	0.0566356	−	0.0980957i
$827$		−	8.13859i		−	0.283007i	−0.989938	−	0.141503i	$-0.954806\pi$
$827$		−	8.13859i		−	0.283007i	0.989938	−	0.141503i	$-0.0451936\pi$
$828$		0			0
$829$	32.8832			1.14208			0.571040	−	0.820923i	$-0.306540\pi$
$829$	32.8832			1.14208			0.571040	+	0.820923i	$0.306540\pi$
$830$		0			0
$831$		0			0
$832$	4.10891	−	2.37228i	0.142451	−	0.0822441i
$833$	8.76144	−	5.05842i	0.303566	−	0.175264i
$834$		0			0
$835$		0			0
$836$	−4.62772			−0.160053
$837$		0			0
$838$		−	31.7228i		−	1.09585i
$839$	−22.1168	+	38.3075i	−0.763558	+	1.32252i	0.177447	+	0.984130i	$0.443216\pi$
$839$	−22.1168	+	38.3075i	−0.763558	+	1.32252i	−0.941005	+	0.338391i	$0.890117\pi$
$840$		0			0
$841$	4.94158	+	8.55906i	0.170399	+	0.295140i
$842$	−33.3137	+	19.2337i	−1.14807	+	0.662837i
$843$		0			0
$844$	−3.62772	+	6.28339i	−0.124871	+	0.216283i
$845$		0			0
$846$		0			0
$847$			21.6277i			0.743137i
$848$	−9.94987	−	5.74456i	−0.341680	−	0.197269i
$849$		0			0
$850$		0			0
$851$	8.74456	+	15.1460i	0.299760	+	0.519199i
$852$		0			0
$853$	−1.52967	−	0.883156i	−0.0523749	−	0.0302387i	0.473584	−	0.880749i	$-0.342960\pi$
$853$	−1.52967	−	0.883156i	−0.0523749	−	0.0302387i	−0.525959	+	0.850510i	$0.676293\pi$
$854$	21.6277			0.740085
$855$		0			0
$856$	14.4891			0.495228
$857$	20.3422	+	11.7446i	0.694876	+	0.401187i	0.805436	−	0.592683i	$-0.201931\pi$
$857$	20.3422	+	11.7446i	0.694876	+	0.401187i	−0.110560	+	0.993869i	$0.535265\pi$
$858$		0			0
$859$	0.0584220	+	0.101190i	0.00199333	+	0.00345255i	0.867020	−	0.498273i	$-0.166032\pi$
$859$	0.0584220	+	0.101190i	0.00199333	+	0.00345255i	−0.865027	+	0.501725i	$0.832699\pi$
$860$		0			0
$861$		0			0
$862$	−22.7190	−	13.1168i	−0.773814	−	0.446761i
$863$		−	42.6060i		−	1.45032i	−0.688578	−	0.725162i	$-0.741765\pi$
$863$		−	42.6060i		−	1.45032i	0.688578	−	0.725162i	$-0.258235\pi$
$864$		0			0
$865$		0			0
$866$	−0.313859	+	0.543620i	−0.0106654	+	0.0184730i
$867$		0			0
$868$	−13.8564	+	8.00000i	−0.470317	+	0.271538i
$869$	−1.37228	−	2.37686i	−0.0465515	−	0.0806295i
$870$		0			0
$871$	16.6060	−	28.7624i	0.562672	−	0.974576i
$872$			9.62772i			0.326036i
$873$		0			0
$874$	−14.7446			−0.498742
$875$		0			0
$876$		0			0
$877$	−48.4598	+	27.9783i	−1.63637	+	0.944758i	−0.654301	+	0.756234i	$0.727037\pi$
$877$	−48.4598	+	27.9783i	−1.63637	+	0.944758i	−0.982069	+	0.188524i	$0.939630\pi$
$878$	−14.0588	+	8.11684i	−0.474461	+	0.273930i
$879$		0			0
$880$		0			0
$881$	−27.3505			−0.921463			−0.460731	−	0.887540i	$-0.652413\pi$
$881$	−27.3505			−0.921463			−0.460731	+	0.887540i	$0.652413\pi$
$882$		0			0
$883$		−	12.7228i		−	0.428157i	−0.976816	−	0.214078i	$-0.931325\pi$
$883$		−	12.7228i		−	0.428157i	0.976816	−	0.214078i	$-0.0686748\pi$
$884$	17.4891	−	30.2921i	0.588223	−	1.01883i
$885$		0			0
$886$	−13.2446	−	22.9403i	−0.444960	−	0.770693i
$887$	32.6689	−	18.8614i	1.09691	−	0.633304i	0.161506	−	0.986872i	$-0.448365\pi$
$887$	32.6689	−	18.8614i	1.09691	−	0.633304i	0.935409	+	0.353568i	$0.115032\pi$
$888$		0			0
$889$	−10.8139	+	18.7302i	−0.362685	+	0.628189i
$890$		0			0
$891$		0			0
$892$			12.3723i			0.414255i
$893$	4.75372	+	2.74456i	0.159077	+	0.0918433i
$894$		0			0
$895$		0			0
$896$	1.18614	+	2.05446i	0.0396262	+	0.0686346i
$897$		0			0
$898$	16.3345	+	9.43070i	0.545088	+	0.314707i
$899$	29.4891			0.983517
$900$		0			0
$901$	−84.7011			−2.82180
$902$	3.56529	+	2.05842i	0.118711	+	0.0685380i
$903$		0			0
$904$	−7.37228	−	12.7692i	−0.245198	−	0.424696i
$905$		0			0
$906$		0			0
$907$	6.06218	+	3.50000i	0.201291	+	0.116216i	0.597258	−	0.802049i	$-0.296257\pi$
$907$	6.06218	+	3.50000i	0.201291	+	0.116216i	−0.395966	+	0.918265i	$0.629590\pi$
$908$			1.88316i			0.0624947i
$909$		0			0
$910$		0			0
$911$	−21.0000	+	36.3731i	−0.695761	+	1.20509i	0.274162	+	0.961683i	$0.411599\pi$
$911$	−21.0000	+	36.3731i	−0.695761	+	1.20509i	−0.969923	+	0.243410i	$0.921734\pi$
$912$		0			0
$913$	−1.93443	+	1.11684i	−0.0640203	+	0.0369621i
$914$	15.0584	+	26.0820i	0.498088	+	0.862714i
$915$		0			0
$916$	−9.18614	+	15.9109i	−0.303519	+	0.525710i
$917$			20.7446i			0.685046i
$918$		0			0
$919$	−42.4674			−1.40087			−0.700435	−	0.713716i	$-0.747011\pi$
$919$	−42.4674			−1.40087			−0.700435	+	0.713716i	$0.747011\pi$
$920$		0			0
$921$		0			0
$922$	−16.5557	+	9.55842i	−0.545232	+	0.314790i
$923$	−24.6535	+	14.2337i	−0.811479	+	0.468508i
$924$		0			0
$925$		0			0
$926$	20.0000			0.657241
$927$		0			0
$928$		−	4.37228i		−	0.143527i
$929$	19.9783	−	34.6033i	0.655465	−	1.13530i	−0.326312	−	0.945262i	$-0.605806\pi$
$929$	19.9783	−	34.6033i	0.655465	−	1.13530i	0.981777	−	0.190037i	$-0.0608607\pi$
$930$		0			0
$931$	2.31386	+	4.00772i	0.0758337	+	0.131348i
$932$	8.76144	−	5.05842i	0.286991	−	0.165694i
$933$		0			0
$934$	−12.9416	+	22.4155i	−0.423461	+	0.733457i
$935$		0			0
$936$		0			0
$937$		−	17.7228i		−	0.578979i	−0.957181	−	0.289490i	$-0.906514\pi$
$937$		−	17.7228i		−	0.578979i	0.957181	−	0.289490i	$-0.0934855\pi$
$938$	14.3812	+	8.30298i	0.469563	+	0.271102i
$939$		0			0
$940$		0			0
$941$	18.8139	+	32.5866i	0.613314	+	1.06229i	0.990678	+	0.136226i	$0.0434974\pi$
$941$	18.8139	+	32.5866i	0.613314	+	1.06229i	−0.377363	+	0.926065i	$0.623169\pi$
$942$		0			0
$943$	11.3595	+	6.55842i	0.369917	+	0.213572i
$944$	−1.37228			−0.0446640
$945$		0			0
$946$	15.6060			0.507394
$947$	19.6785	+	11.3614i	0.639466	+	0.369196i	0.784409	−	0.620244i	$-0.212966\pi$
$947$	19.6785	+	11.3614i	0.639466	+	0.369196i	−0.144943	+	0.989440i	$0.546300\pi$
$948$		0			0
$949$	−33.4891	−	58.0049i	−1.08710	−	1.88292i
$950$		0			0
$951$		0			0
$952$	15.1460	+	8.74456i	0.490886	+	0.283413i
$953$			30.8614i			0.999699i	0.866112	+	0.499850i	$0.166611\pi$
$953$			30.8614i			0.999699i	−0.866112	+	0.499850i	$0.833389\pi$
$954$		0			0
$955$		0			0
$956$	−7.37228	+	12.7692i	−0.238437	+	0.412984i
$957$		0			0
$958$	−20.3422	+	11.7446i	−0.657226	+	0.379450i
$959$	−2.23369	−	3.86886i	−0.0721295	−	0.124932i
$960$		0			0
$961$	−7.24456	+	12.5480i	−0.233696	+	0.404773i
$962$		−	18.9783i		−	0.611883i
$963$		0			0
$964$	−10.4891			−0.337832
$965$		0			0
$966$		0			0
$967$	16.3533	−	9.44158i	0.525886	−	0.303621i	−0.213453	−	0.976953i	$-0.568471\pi$
$967$	16.3533	−	9.44158i	0.525886	−	0.303621i	0.739340	+	0.673333i	$0.235138\pi$
$968$	7.89542	−	4.55842i	0.253768	−	0.146513i
$969$		0			0
$970$		0			0
$971$	−22.9783			−0.737407			−0.368704	−	0.929547i	$-0.620198\pi$
$971$	−22.9783			−0.737407			−0.368704	+	0.929547i	$0.620198\pi$
$972$		0			0
$973$			42.9783i			1.37782i
$974$	−0.627719	+	1.08724i	−0.0201134	+	0.0348374i
$975$		0			0
$976$	−4.55842	−	7.89542i	−0.145912	−	0.252726i
$977$	34.7422	−	20.0584i	1.11150	−	0.641726i	0.172284	−	0.985047i	$-0.444885\pi$
$977$	34.7422	−	20.0584i	1.11150	−	0.641726i	0.939218	+	0.343322i	$0.111552\pi$
$978$		0			0
$979$	−0.766312	+	1.32729i	−0.0244914	+	0.0424204i
$980$		0			0
$981$		0			0
$982$		−	3.60597i		−	0.115071i
$983$	−13.7364	−	7.93070i	−0.438123	−	0.252950i	0.264678	−	0.964337i	$-0.414734\pi$
$983$	−13.7364	−	7.93070i	−0.438123	−	0.252950i	−0.702801	+	0.711387i	$0.748068\pi$
$984$		0			0
$985$		0			0
$986$	−16.1168	−	27.9152i	−0.513265	−	0.889001i
$987$		0			0
$988$	13.8564	+	8.00000i	0.440831	+	0.254514i
$989$	49.7228			1.58109
$990$		0			0
$991$	−18.2337			−0.579212			−0.289606	−	0.957146i	$-0.593524\pi$
$991$	−18.2337			−0.579212			−0.289606	+	0.957146i	$0.593524\pi$
$992$	5.84096	+	3.37228i	0.185451	+	0.107070i
$993$		0			0
$994$	−7.11684	−	12.3267i	−0.225733	−	0.390980i
$995$		0			0
$996$		0			0
$997$	−12.1244	−	7.00000i	−0.383982	−	0.221692i	0.295567	−	0.955322i	$-0.404491\pi$
$997$	−12.1244	−	7.00000i	−0.383982	−	0.221692i	−0.679549	+	0.733630i	$0.737825\pi$
$998$			2.11684i			0.0670075i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.2.j.f.1099.2		8
3.2	odd	2		450.2.j.g.349.4		8
5.2	odd	4		1350.2.e.l.451.1		4
5.3	odd	4		270.2.e.c.181.2		4
5.4	even	2	inner	1350.2.j.f.1099.3		8
9.2	odd	6		4050.2.c.v.649.1		4
9.4	even	3	inner	1350.2.j.f.199.3		8
9.5	odd	6		450.2.j.g.49.1		8
9.7	even	3		4050.2.c.ba.649.3		4
15.2	even	4		450.2.e.j.151.1		4
15.8	even	4		90.2.e.c.61.2	yes	4
15.14	odd	2		450.2.j.g.349.1		8
20.3	even	4		2160.2.q.f.721.1		4
45.2	even	12		4050.2.a.bw.1.2		2
45.4	even	6	inner	1350.2.j.f.199.2		8
45.7	odd	12		4050.2.a.bo.1.2		2
45.13	odd	12		270.2.e.c.91.2		4
45.14	odd	6		450.2.j.g.49.4		8
45.22	odd	12		1350.2.e.l.901.1		4
45.23	even	12		90.2.e.c.31.1	✓	4
45.29	odd	6		4050.2.c.v.649.4		4
45.32	even	12		450.2.e.j.301.2		4
45.34	even	6		4050.2.c.ba.649.2		4
45.38	even	12		810.2.a.i.1.1		2
45.43	odd	12		810.2.a.k.1.1		2
60.23	odd	4		720.2.q.f.241.1		4
180.23	odd	12		720.2.q.f.481.2		4
180.43	even	12		6480.2.a.bn.1.2		2
180.83	odd	12		6480.2.a.be.1.2		2
180.103	even	12		2160.2.q.f.1441.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.e.c.31.1	✓	4	45.23	even	12
90.2.e.c.61.2	yes	4	15.8	even	4
270.2.e.c.91.2		4	45.13	odd	12
270.2.e.c.181.2		4	5.3	odd	4
450.2.e.j.151.1		4	15.2	even	4
450.2.e.j.301.2		4	45.32	even	12
450.2.j.g.49.1		8	9.5	odd	6
450.2.j.g.49.4		8	45.14	odd	6
450.2.j.g.349.1		8	15.14	odd	2
450.2.j.g.349.4		8	3.2	odd	2
720.2.q.f.241.1		4	60.23	odd	4
720.2.q.f.481.2		4	180.23	odd	12
810.2.a.i.1.1		2	45.38	even	12
810.2.a.k.1.1		2	45.43	odd	12
1350.2.e.l.451.1		4	5.2	odd	4
1350.2.e.l.901.1		4	45.22	odd	12
1350.2.j.f.199.2		8	45.4	even	6	inner
1350.2.j.f.199.3		8	9.4	even	3	inner
1350.2.j.f.1099.2		8	1.1	even	1	trivial
1350.2.j.f.1099.3		8	5.4	even	2	inner
2160.2.q.f.721.1		4	20.3	even	4
2160.2.q.f.1441.1		4	180.103	even	12
4050.2.a.bo.1.2		2	45.7	odd	12
4050.2.a.bw.1.2		2	45.2	even	12
4050.2.c.v.649.1		4	9.2	odd	6
4050.2.c.v.649.4		4	45.29	odd	6
4050.2.c.ba.649.2		4	45.34	even	6
4050.2.c.ba.649.3		4	9.7	even	3
6480.2.a.be.1.2		2	180.83	odd	12
6480.2.a.bn.1.2		2	180.43	even	12

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:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1350.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.05446 + 1.18614i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.05446 + 1.18614i) q^{7} -1.00000i q^{8} +(0.686141 - 1.18843i) q^{11} +(-4.10891 + 2.37228i) q^{13} +(-1.18614 - 2.05446i) q^{14} +(-0.500000 + 0.866025i) q^{16} +7.37228i q^{17} -3.37228 q^{19} +(-1.18843 + 0.686141i) q^{22} +(-3.78651 + 2.18614i) q^{23} +4.74456 q^{26} +2.37228i q^{28} +(2.18614 - 3.78651i) q^{29} +(3.37228 + 5.84096i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.68614 - 6.38458i) q^{34} -4.00000i q^{37} +(2.92048 + 1.68614i) q^{38} +(-1.50000 - 2.59808i) q^{41} +(-9.84868 - 5.68614i) q^{43} +1.37228 q^{44} +4.37228 q^{46} +(-1.40965 - 0.813859i) q^{47} +(-0.686141 - 1.18843i) q^{49} +(-4.10891 - 2.37228i) q^{52} +11.4891i q^{53} +(1.18614 - 2.05446i) q^{56} +(-3.78651 + 2.18614i) q^{58} +(0.686141 + 1.18843i) q^{59} +(-4.55842 + 7.89542i) q^{61} -6.74456i q^{62} -1.00000 q^{64} +(-6.06218 + 3.50000i) q^{67} +(-6.38458 + 3.68614i) q^{68} +6.00000 q^{71} +14.1168i q^{73} +(-2.00000 + 3.46410i) q^{74} +(-1.68614 - 2.92048i) q^{76} +(2.81929 - 1.62772i) q^{77} +(1.00000 - 1.73205i) q^{79} +3.00000i q^{82} +(-1.40965 - 0.813859i) q^{83} +(5.68614 + 9.84868i) q^{86} +(-1.18843 - 0.686141i) q^{88} -1.11684 q^{89} -11.2554 q^{91} +(-3.78651 - 2.18614i) q^{92} +(0.813859 + 1.40965i) q^{94} +(2.27567 + 1.31386i) q^{97} +1.37228i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} - 6 q^{11} + 2 q^{14} - 4 q^{16} - 4 q^{19} - 8 q^{26} + 6 q^{29} + 4 q^{31} + 18 q^{34} - 12 q^{41} - 12 q^{44} + 12 q^{46} + 6 q^{49} - 2 q^{56} - 6 q^{59} - 2 q^{61} - 8 q^{64} + 48 q^{71} - 16 q^{74} - 2 q^{76} + 8 q^{79} + 34 q^{86} + 60 q^{89} - 136 q^{91} + 18 q^{94}+O(q^{100}) \) 8 * q + 4 * q^4 - 6 * q^11 + 2 * q^14 - 4 * q^16 - 4 * q^19 - 8 * q^26 + 6 * q^29 + 4 * q^31 + 18 * q^34 - 12 * q^41 - 12 * q^44 + 12 * q^46 + 6 * q^49 - 2 * q^56 - 6 * q^59 - 2 * q^61 - 8 * q^64 + 48 * q^71 - 16 * q^74 - 2 * q^76 + 8 * q^79 + 34 * q^86 + 60 * q^89 - 136 * q^91 + 18 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more