LMFDB - Embedded newform 735.2.p.c.374.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(374,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("735.374");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.p (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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			374.4
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	735.374
Dual form			735.2.p.c.509.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 1.50000i) q^{2} +(1.72474 - 0.158919i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.09077 + 0.792893i) q^{5} +(1.73205 + 2.44949i) q^{6} +1.73205 q^{8} +(2.94949 - 0.548188i) q^{9} +O(q^{10})$	\(q+(0.866025 + 1.50000i) q^{2} +(1.72474 - 0.158919i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.09077 + 0.792893i) q^{5} +(1.73205 + 2.44949i) q^{6} +1.73205 q^{8} +(2.94949 - 0.548188i) q^{9} +(0.621320 + 3.82282i) q^{10} +(-2.44949 - 1.41421i) q^{11} +(-0.724745 + 1.57313i) q^{12} -4.00000 q^{13} +(3.73205 + 1.03528i) q^{15} +(2.50000 + 4.33013i) q^{16} +(-2.44949 - 1.41421i) q^{17} +(3.37662 + 3.94949i) q^{18} +(-1.73205 + 1.41421i) q^{20} -4.89898i q^{22} +(1.73205 + 3.00000i) q^{23} +(2.98735 - 0.275255i) q^{24} +(3.74264 + 3.31552i) q^{25} +(-3.46410 - 6.00000i) q^{26} +(5.00000 - 1.41421i) q^{27} -5.65685i q^{29} +(1.67914 + 6.49465i) q^{30} +(-8.48528 - 4.89898i) q^{31} +(-2.59808 + 4.50000i) q^{32} +(-4.44949 - 2.04989i) q^{33} -4.89898i q^{34} +(-1.00000 + 2.82843i) q^{36} +(-6.89898 + 0.635674i) q^{39} +(3.62132 + 1.37333i) q^{40} -3.46410 q^{41} +4.89898i q^{43} +(2.44949 - 1.41421i) q^{44} +(6.60136 + 1.19249i) q^{45} +(-3.00000 + 5.19615i) q^{46} +(2.44949 - 1.41421i) q^{47} +(5.00000 + 7.07107i) q^{48} +(-1.73205 + 8.48528i) q^{50} +(-4.44949 - 2.04989i) q^{51} +(2.00000 - 3.46410i) q^{52} +(6.45145 + 6.27526i) q^{54} +(-4.00000 - 4.89898i) q^{55} +(8.48528 - 4.89898i) q^{58} +(-3.46410 + 6.00000i) q^{59} +(-2.76260 + 2.71441i) q^{60} +(-8.48528 + 4.89898i) q^{61} -16.9706i q^{62} +1.00000 q^{64} +(-8.36308 - 3.17157i) q^{65} +(-0.778539 - 8.44949i) q^{66} +(4.24264 + 2.44949i) q^{67} +(2.44949 - 1.41421i) q^{68} +(3.46410 + 4.89898i) q^{69} +2.82843i q^{71} +(5.10867 - 0.949490i) q^{72} +(-4.00000 + 6.92820i) q^{73} +(6.98200 + 5.12364i) q^{75} +(-6.92820 - 9.79796i) q^{78} +(-4.00000 - 6.92820i) q^{79} +(1.79360 + 11.0355i) q^{80} +(8.39898 - 3.23375i) q^{81} +(-3.00000 - 5.19615i) q^{82} +2.82843i q^{83} +(-4.00000 - 4.89898i) q^{85} +(-7.34847 + 4.24264i) q^{86} +(-0.898979 - 9.75663i) q^{87} +(-4.24264 - 2.44949i) q^{88} +(-5.19615 - 9.00000i) q^{89} +(3.92820 + 10.9348i) q^{90} -3.46410 q^{92} +(-15.4135 - 7.10102i) q^{93} +(4.24264 + 2.44949i) q^{94} +(-3.76588 + 8.17423i) q^{96} +8.00000 q^{97} +(-8.00000 - 2.82843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 4 q^{4} + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 - 4 * q^4 + 4 * q^9	$ 8 q + 4 q^{3} - 4 q^{4} + 4 q^{9} - 12 q^{10} + 4 q^{12} - 32 q^{13} + 16 q^{15} + 20 q^{16} - 4 q^{25} + 40 q^{27} + 12 q^{30} - 16 q^{33} - 8 q^{36} - 16 q^{39} + 12 q^{40} + 16 q^{45} - 24 q^{46} + 40 q^{48} - 16 q^{51} + 16 q^{52} - 32 q^{55} - 8 q^{60} + 8 q^{64} - 32 q^{73} + 4 q^{75} - 32 q^{79} + 28 q^{81} - 24 q^{82} - 32 q^{85} + 32 q^{87} - 24 q^{90} + 64 q^{97} - 64 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 4 * q^4 + 4 * q^9 - 12 * q^10 + 4 * q^12 - 32 * q^13 + 16 * q^15 + 20 * q^16 - 4 * q^25 + 40 * q^27 + 12 * q^30 - 16 * q^33 - 8 * q^36 - 16 * q^39 + 12 * q^40 + 16 * q^45 - 24 * q^46 + 40 * q^48 - 16 * q^51 + 16 * q^52 - 32 * q^55 - 8 * q^60 + 8 * q^64 - 32 * q^73 + 4 * q^75 - 32 * q^79 + 28 * q^81 - 24 * q^82 - 32 * q^85 + 32 * q^87 - 24 * q^90 + 64 * q^97 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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	+	1.50000i	0.612372	+	1.06066i	0.990839	+	0.135045i	$0.0431180\pi$
$2$	0.866025	+	1.50000i	0.612372	+	1.06066i	−0.378467	+	0.925615i	$0.623549\pi$
$3$	1.72474	−	0.158919i	0.995782	−	0.0917517i
$3$	1.72474	−	0.158919i	0.995782	−	0.0917517i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.09077	+	0.792893i	0.935021	+	0.354593i
$5$	2.09077	+	0.792893i	0.935021	+	0.354593i
$6$	1.73205	+	2.44949i	0.707107	+	1.00000i
$7$		0			0
$7$		0			0
$8$	1.73205			0.612372
$9$	2.94949	−	0.548188i	0.983163	−	0.182729i
$10$	0.621320	+	3.82282i	0.196479	+	1.20888i
$11$	−2.44949	−	1.41421i	−0.738549	−	0.426401i	0.0829925	−	0.996550i	$-0.473552\pi$
$11$	−2.44949	−	1.41421i	−0.738549	−	0.426401i	−0.821541	+	0.570149i	$0.806886\pi$
$12$	−0.724745	+	1.57313i	−0.209216	+	0.454124i
$13$	−4.00000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$		0			0
$15$	3.73205	+	1.03528i	0.963611	+	0.267307i
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	−2.44949	−	1.41421i	−0.594089	−	0.342997i	0.172624	−	0.984988i	$-0.444775\pi$
$17$	−2.44949	−	1.41421i	−0.594089	−	0.342997i	−0.766712	+	0.641991i	$0.778109\pi$
$18$	3.37662	+	3.94949i	0.795876	+	0.930904i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$	−1.73205	+	1.41421i	−0.387298	+	0.316228i
$21$		0			0
$22$		−	4.89898i		−	1.04447i
$23$	1.73205	+	3.00000i	0.361158	+	0.625543i	0.988152	−	0.153481i	$-0.0490483\pi$
$23$	1.73205	+	3.00000i	0.361158	+	0.625543i	−0.626994	+	0.779024i	$0.715715\pi$
$24$	2.98735	−	0.275255i	0.609789	−	0.0561862i
$25$	3.74264	+	3.31552i	0.748528	+	0.663103i
$26$	−3.46410	−	6.00000i	−0.679366	−	1.17670i
$27$	5.00000	−	1.41421i	0.962250	−	0.272166i
$28$		0			0
$29$		−	5.65685i		−	1.05045i	−0.850963	−	0.525226i	$-0.823981\pi$
$29$		−	5.65685i		−	1.05045i	0.850963	−	0.525226i	$-0.176019\pi$
$30$	1.67914	+	6.49465i	0.306567	+	1.18576i
$31$	−8.48528	−	4.89898i	−1.52400	−	0.879883i	−0.999596	−	0.0284139i	$-0.990954\pi$
$31$	−8.48528	−	4.89898i	−1.52400	−	0.879883i	−0.524405	−	0.851469i	$-0.675712\pi$
$32$	−2.59808	+	4.50000i	−0.459279	+	0.795495i
$33$	−4.44949	−	2.04989i	−0.774557	−	0.356840i
$34$		−	4.89898i		−	0.840168i
$35$		0			0
$36$	−1.00000	+	2.82843i	−0.166667	+	0.471405i
$37$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$37$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$38$		0			0
$39$	−6.89898	+	0.635674i	−1.10472	+	0.101789i
$40$	3.62132	+	1.37333i	0.572581	+	0.217143i
$41$	−3.46410			−0.541002			−0.270501	−	0.962720i	$-0.587189\pi$
$41$	−3.46410			−0.541002			−0.270501	+	0.962720i	$0.587189\pi$
$42$		0			0
$43$			4.89898i			0.747087i	0.927613	+	0.373544i	$0.121857\pi$
$43$			4.89898i			0.747087i	−0.927613	+	0.373544i	$0.878143\pi$
$44$	2.44949	−	1.41421i	0.369274	−	0.213201i
$45$	6.60136	+	1.19249i	0.984073	+	0.177767i
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$	2.44949	−	1.41421i	0.357295	−	0.206284i	−0.310599	−	0.950541i	$-0.600530\pi$
$47$	2.44949	−	1.41421i	0.357295	−	0.206284i	0.667893	+	0.744257i	$0.267196\pi$
$48$	5.00000	+	7.07107i	0.721688	+	1.02062i
$49$		0			0
$50$	−1.73205	+	8.48528i	−0.244949	+	1.20000i
$51$	−4.44949	−	2.04989i	−0.623053	−	0.287042i
$52$	2.00000	−	3.46410i	0.277350	−	0.480384i
$53$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$53$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$54$	6.45145	+	6.27526i	0.877931	+	0.853954i
$55$	−4.00000	−	4.89898i	−0.539360	−	0.660578i
$56$		0			0
$57$		0			0
$58$	8.48528	−	4.89898i	1.11417	−	0.643268i
$59$	−3.46410	+	6.00000i	−0.450988	+	0.781133i	−0.998448	−	0.0556984i	$-0.982261\pi$
$59$	−3.46410	+	6.00000i	−0.450988	+	0.781133i	0.547460	+	0.836832i	$0.315595\pi$
$60$	−2.76260	+	2.71441i	−0.356650	+	0.350429i
$61$	−8.48528	+	4.89898i	−1.08643	+	0.627250i	−0.932623	−	0.360851i	$-0.882486\pi$
$61$	−8.48528	+	4.89898i	−1.08643	+	0.627250i	−0.153806	+	0.988101i	$0.549153\pi$
$62$		−	16.9706i		−	2.15526i
$63$		0			0
$64$	1.00000			0.125000
$65$	−8.36308	−	3.17157i	−1.03731	−	0.393385i
$66$	−0.778539	−	8.44949i	−0.0958315	−	1.04006i
$67$	4.24264	+	2.44949i	0.518321	+	0.299253i	0.736247	−	0.676712i	$-0.236596\pi$
$67$	4.24264	+	2.44949i	0.518321	+	0.299253i	−0.217926	+	0.975965i	$0.569929\pi$
$68$	2.44949	−	1.41421i	0.297044	−	0.171499i
$69$	3.46410	+	4.89898i	0.417029	+	0.589768i
$70$		0			0
$71$			2.82843i			0.335673i	0.985815	+	0.167836i	$0.0536780\pi$
$71$			2.82843i			0.335673i	−0.985815	+	0.167836i	$0.946322\pi$
$72$	5.10867	−	0.949490i	0.602062	−	0.111898i
$73$	−4.00000	+	6.92820i	−0.468165	+	0.810885i	−0.999338	−	0.0363782i	$-0.988418\pi$
$73$	−4.00000	+	6.92820i	−0.468165	+	0.810885i	0.531174	+	0.847263i	$0.321751\pi$
$74$		0			0
$75$	6.98200	+	5.12364i	0.806212	+	0.591627i
$76$		0			0
$77$		0			0
$78$	−6.92820	−	9.79796i	−0.784465	−	1.10940i
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	1.79360	+	11.0355i	0.200530	+	1.23381i
$81$	8.39898	−	3.23375i	0.933220	−	0.359306i
$82$	−3.00000	−	5.19615i	−0.331295	−	0.573819i
$83$			2.82843i			0.310460i	0.987878	+	0.155230i	$0.0496119\pi$
$83$			2.82843i			0.310460i	−0.987878	+	0.155230i	$0.950388\pi$
$84$		0			0
$85$	−4.00000	−	4.89898i	−0.433861	−	0.531369i
$86$	−7.34847	+	4.24264i	−0.792406	+	0.457496i
$87$	−0.898979	−	9.75663i	−0.0963807	−	1.04602i
$88$	−4.24264	−	2.44949i	−0.452267	−	0.261116i
$89$	−5.19615	−	9.00000i	−0.550791	−	0.953998i	−0.998218	−	0.0596775i	$-0.980993\pi$
$89$	−5.19615	−	9.00000i	−0.550791	−	0.953998i	0.447427	−	0.894321i	$-0.352341\pi$
$90$	3.92820	+	10.9348i	0.414069	+	1.15263i
$91$		0			0
$92$	−3.46410			−0.361158
$93$	−15.4135	−	7.10102i	−1.59830	−	0.736342i
$94$	4.24264	+	2.44949i	0.437595	+	0.252646i
$95$		0			0
$96$	−3.76588	+	8.17423i	−0.384354	+	0.834279i
$97$	8.00000			0.812277			0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000			0.812277			0.406138	+	0.913812i	$0.366875\pi$
$98$		0			0
$99$	−8.00000	−	2.82843i	−0.804030	−	0.284268i
$100$	−4.74264	+	1.58346i	−0.474264	+	0.158346i
$101$	8.66025	−	15.0000i	0.861727	−	1.49256i	−0.00853278	−	0.999964i	$-0.502716\pi$
$101$	8.66025	−	15.0000i	0.861727	−	1.49256i	0.870260	−	0.492592i	$-0.163951\pi$
$102$	−0.778539	−	8.44949i	−0.0770869	−	0.836624i
$103$	5.00000	+	8.66025i	0.492665	+	0.853320i	0.999964	−	0.00844953i	$-0.00268960\pi$
$103$	5.00000	+	8.66025i	0.492665	+	0.853320i	−0.507300	+	0.861770i	$0.669356\pi$
$104$	−6.92820			−0.679366
$105$		0			0
$106$		0			0
$107$	−5.19615	−	9.00000i	−0.502331	−	0.870063i	−0.999996	−	0.00269372i	$-0.999143\pi$
$107$	−5.19615	−	9.00000i	−0.502331	−	0.870063i	0.497665	−	0.867369i	$-0.334191\pi$
$108$	−1.27526	+	5.03723i	−0.122711	+	0.484708i
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	−0.520794	−	0.853682i	$-0.674364\pi$
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	0.999708	+	0.0241802i	$0.00769755\pi$
$110$	3.88437	−	10.2426i	0.370360	−	0.976597i
$111$		0			0
$112$		0			0
$113$	6.92820			0.651751			0.325875	−	0.945413i	$-0.394341\pi$
$113$	6.92820			0.651751			0.325875	+	0.945413i	$0.394341\pi$
$114$		0			0
$115$	1.24264	+	7.64564i	0.115877	+	0.712960i
$116$	4.89898	+	2.82843i	0.454859	+	0.262613i
$117$	−11.7980	+	2.19275i	−1.09072	+	0.202720i
$118$	−12.0000			−1.10469
$119$		0			0
$120$	6.46410	+	1.79315i	0.590089	+	0.163692i
$121$	−1.50000	−	2.59808i	−0.136364	−	0.236189i
$122$	−14.6969	−	8.48528i	−1.33060	−	0.768221i
$123$	−5.97469	+	0.550510i	−0.538720	+	0.0496378i
$124$	8.48528	−	4.89898i	0.762001	−	0.439941i
$125$	5.19615	+	9.89949i	0.464758	+	0.885438i
$126$		0			0
$127$			14.6969i			1.30414i	0.758158	+	0.652071i	$0.226100\pi$
$127$			14.6969i			1.30414i	−0.758158	+	0.652071i	$0.773900\pi$
$128$	6.06218	+	10.5000i	0.535826	+	0.928078i
$129$	0.778539	+	8.44949i	0.0685465	+	0.743936i
$130$	−2.48528	−	15.2913i	−0.217974	−	1.34113i
$131$	−3.46410	−	6.00000i	−0.302660	−	0.524222i	0.674078	−	0.738661i	$-0.264541\pi$
$131$	−3.46410	−	6.00000i	−0.302660	−	0.524222i	−0.976738	+	0.214438i	$0.931208\pi$
$132$	4.00000	−	2.82843i	0.348155	−	0.246183i
$133$		0			0
$134$			8.48528i			0.733017i
$135$	11.5752	+	1.00767i	0.996232	+	0.0867265i
$136$	−4.24264	−	2.44949i	−0.363803	−	0.210042i
$137$	3.46410	−	6.00000i	0.295958	−	0.512615i	−0.679249	−	0.733908i	$-0.737694\pi$
$137$	3.46410	−	6.00000i	0.295958	−	0.512615i	0.975207	+	0.221293i	$0.0710278\pi$
$138$	−4.34847	+	9.43879i	−0.370166	+	0.803483i
$139$			9.79796i			0.831052i	0.909581	+	0.415526i	$0.136402\pi$
$139$			9.79796i			0.831052i	−0.909581	+	0.415526i	$0.863598\pi$
$140$		0			0
$141$	4.00000	−	2.82843i	0.336861	−	0.238197i
$142$	−4.24264	+	2.44949i	−0.356034	+	0.205557i
$143$	9.79796	+	5.65685i	0.819346	+	0.473050i
$144$	9.74745	+	11.4012i	0.812287	+	0.950100i
$145$	4.48528	−	11.8272i	0.372482	−	0.982194i
$146$	−13.8564			−1.14676
$147$		0			0
$148$		0			0
$149$	9.79796	−	5.65685i	0.802680	−	0.463428i	−0.0417274	−	0.999129i	$-0.513286\pi$
$149$	9.79796	−	5.65685i	0.802680	−	0.463428i	0.844407	+	0.535701i	$0.179953\pi$
$150$	−1.63888	+	14.9102i	−0.133814	+	1.21741i
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	−0.981617	−	0.190864i	$-0.938871\pi$
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	0.656101	+	0.754673i	$0.272204\pi$
$152$		0			0
$153$	−8.00000	−	2.82843i	−0.646762	−	0.228665i
$154$		0			0
$155$	−13.8564	−	16.9706i	−1.11297	−	1.36311i
$156$	2.89898	−	6.29253i	0.232104	−	0.503806i
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	−0.775113	−	0.631822i	$-0.782307\pi$
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	0.934731	+	0.355357i	$0.115641\pi$
$158$	6.92820	−	12.0000i	0.551178	−	0.954669i
$159$		0			0
$160$	−9.00000	+	7.34847i	−0.711512	+	0.580948i
$161$		0			0
$162$	12.1244	+	9.79796i	0.952579	+	0.769800i
$163$	−12.7279	+	7.34847i	−0.996928	+	0.575577i	−0.907338	−	0.420402i	$-0.861889\pi$
$163$	−12.7279	+	7.34847i	−0.996928	+	0.575577i	−0.0895899	+	0.995979i	$0.528556\pi$
$164$	1.73205	−	3.00000i	0.135250	−	0.234261i
$165$	−7.67752	−	7.81382i	−0.597694	−	0.608305i
$166$	−4.24264	+	2.44949i	−0.329293	+	0.190117i
$167$		−	14.1421i		−	1.09435i	−0.837018	−	0.547176i	$-0.815703\pi$
$167$		−	14.1421i		−	1.09435i	0.837018	−	0.547176i	$-0.184297\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$	3.88437	−	10.2426i	0.297917	−	0.785575i
$171$		0			0
$172$	−4.24264	−	2.44949i	−0.323498	−	0.186772i
$173$	17.1464	−	9.89949i	1.30362	−	0.752645i	0.322596	−	0.946537i	$-0.395445\pi$
$173$	17.1464	−	9.89949i	1.30362	−	0.752645i	0.981023	+	0.193892i	$0.0621112\pi$
$174$	13.8564	−	9.79796i	1.05045	−	0.742781i
$175$		0			0
$176$		−	14.1421i		−	1.06600i
$177$	−5.02118	+	10.8990i	−0.377415	+	0.819217i
$178$	9.00000	−	15.5885i	0.674579	−	1.16840i
$179$	−2.44949	−	1.41421i	−0.183083	−	0.105703i	0.405657	−	0.914025i	$-0.367043\pi$
$179$	−2.44949	−	1.41421i	−0.183083	−	0.105703i	−0.588741	+	0.808322i	$0.700376\pi$
$180$	−4.33341	+	5.12070i	−0.322993	+	0.381674i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$	−13.8564	+	9.79796i	−1.02430	+	0.724286i
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$		0			0
$186$	−2.69694	−	29.2699i	−0.197749	−	2.14617i
$187$	4.00000	+	6.92820i	0.292509	+	0.506640i
$188$			2.82843i			0.206284i
$189$		0			0
$190$		0			0
$191$	17.1464	−	9.89949i	1.24067	−	0.716302i	0.271441	−	0.962455i	$-0.412500\pi$
$191$	17.1464	−	9.89949i	1.24067	−	0.716302i	0.969231	+	0.246153i	$0.0791665\pi$
$192$	1.72474	−	0.158919i	0.124473	−	0.0114690i
$193$	−8.48528	−	4.89898i	−0.610784	−	0.352636i	0.162488	−	0.986710i	$-0.448048\pi$
$193$	−8.48528	−	4.89898i	−0.610784	−	0.352636i	−0.773272	+	0.634074i	$0.781381\pi$
$194$	6.92820	+	12.0000i	0.497416	+	0.861550i
$195$	−14.9282	−	4.14110i	−1.06903	−	0.296551i
$196$		0			0
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$	−2.68556	−	14.4495i	−0.190855	−	1.02688i
$199$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$199$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$200$	6.48244	+	5.74264i	0.458378	+	0.406066i
$201$	7.70674	+	3.55051i	0.543592	+	0.250434i
$202$	30.0000			2.11079
$203$		0			0
$204$	4.00000	−	2.82843i	0.280056	−	0.198030i
$205$	−7.24264	−	2.74666i	−0.505848	−	0.191835i
$206$	−8.66025	+	15.0000i	−0.603388	+	1.04510i
$207$	6.75323	+	7.89898i	0.469382	+	0.549017i
$208$	−10.0000	−	17.3205i	−0.693375	−	1.20096i
$209$		0			0
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$	0.449490	+	4.87832i	0.0307985	+	0.334257i
$214$	9.00000	−	15.5885i	0.615227	−	1.06561i
$215$	−3.88437	+	10.2426i	−0.264912	+	0.698542i
$216$	8.66025	−	2.44949i	0.589256	−	0.166667i
$217$		0			0
$218$	17.3205			1.17309
$219$	−5.79796	+	12.5851i	−0.391790	+	0.850419i
$220$	6.24264	−	1.01461i	0.420879	−	0.0684051i
$221$	9.79796	+	5.65685i	0.659082	+	0.380521i
$222$		0			0
$223$	26.0000			1.74109			0.870544	−	0.492090i	$-0.163767\pi$
$223$	26.0000			1.74109			0.870544	+	0.492090i	$0.163767\pi$
$224$		0			0
$225$	12.8564	+	7.72741i	0.857094	+	0.515160i
$226$	6.00000	+	10.3923i	0.399114	+	0.691286i
$227$	−2.44949	−	1.41421i	−0.162578	−	0.0938647i	0.416503	−	0.909134i	$-0.363255\pi$
$227$	−2.44949	−	1.41421i	−0.162578	−	0.0938647i	−0.579082	+	0.815270i	$0.696589\pi$
$228$		0			0
$229$	−16.9706	+	9.79796i	−1.12145	+	0.647467i	−0.941770	−	0.336258i	$-0.890838\pi$
$229$	−16.9706	+	9.79796i	−1.12145	+	0.647467i	−0.179677	+	0.983726i	$0.557505\pi$
$230$	−10.3923	+	8.48528i	−0.685248	+	0.559503i
$231$		0			0
$232$		−	9.79796i		−	0.643268i
$233$	10.3923	+	18.0000i	0.680823	+	1.17922i	0.974730	+	0.223385i	$0.0717108\pi$
$233$	10.3923	+	18.0000i	0.680823	+	1.17922i	−0.293908	+	0.955834i	$0.594956\pi$
$234$	−13.5065	−	15.7980i	−0.882945	−	1.03274i
$235$	6.24264	−	1.01461i	0.407225	−	0.0661860i
$236$	−3.46410	−	6.00000i	−0.225494	−	0.390567i
$237$	−8.00000	−	11.3137i	−0.519656	−	0.734904i
$238$		0			0
$239$			2.82843i			0.182956i	0.995807	+	0.0914779i	$0.0291591\pi$
$239$			2.82843i			0.182956i	−0.995807	+	0.0914779i	$0.970841\pi$
$240$	4.84725	+	18.7484i	0.312889	+	1.21021i
$241$	8.48528	+	4.89898i	0.546585	+	0.315571i	0.747743	−	0.663988i	$-0.231137\pi$
$241$	8.48528	+	4.89898i	0.546585	+	0.315571i	−0.201158	+	0.979559i	$0.564471\pi$
$242$	2.59808	−	4.50000i	0.167011	−	0.289271i
$243$	13.9722	−	6.91215i	0.896317	−	0.443415i
$244$		−	9.79796i		−	0.627250i
$245$		0			0
$246$	−6.00000	−	8.48528i	−0.382546	−	0.541002i
$247$		0			0
$248$	−14.6969	−	8.48528i	−0.933257	−	0.538816i
$249$	0.449490	+	4.87832i	0.0284853	+	0.309151i
$250$	−10.3492	+	16.3674i	−0.654544	+	1.03517i
$251$	20.7846			1.31191			0.655956	−	0.754799i	$-0.272265\pi$
$251$	20.7846			1.31191			0.655956	+	0.754799i	$0.272265\pi$
$252$		0			0
$253$		−	9.79796i		−	0.615992i
$254$	−22.0454	+	12.7279i	−1.38325	+	0.798621i
$255$	−7.67752	−	7.81382i	−0.480785	−	0.489320i
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	−12.2474	+	7.07107i	−0.763975	+	0.441081i	−0.830721	−	0.556689i	$-0.812072\pi$
$257$	−12.2474	+	7.07107i	−0.763975	+	0.441081i	0.0667462	+	0.997770i	$0.478738\pi$
$258$	−12.0000	+	8.48528i	−0.747087	+	0.528271i
$259$		0			0
$260$	6.92820	−	5.65685i	0.429669	−	0.350823i
$261$	−3.10102	−	16.6848i	−0.191948	−	1.03277i
$262$	6.00000	−	10.3923i	0.370681	−	0.642039i
$263$	−1.73205	+	3.00000i	−0.106803	+	0.184988i	−0.914473	−	0.404646i	$-0.867395\pi$
$263$	−1.73205	+	3.00000i	−0.106803	+	0.184988i	0.807671	+	0.589634i	$0.200728\pi$
$264$	−7.70674	−	3.55051i	−0.474317	−	0.218519i
$265$		0			0
$266$		0			0
$267$	−10.3923	−	14.6969i	−0.635999	−	0.899438i
$268$	−4.24264	+	2.44949i	−0.259161	+	0.149626i
$269$	5.19615	−	9.00000i	0.316815	−	0.548740i	−0.663007	−	0.748614i	$-0.730720\pi$
$269$	5.19615	−	9.00000i	0.316815	−	0.548740i	0.979822	+	0.199874i	$0.0640532\pi$
$270$	8.51289	+	18.2354i	0.518078	+	1.10977i
$271$	25.4558	−	14.6969i	1.54633	−	0.892775i	0.547915	−	0.836534i	$-0.315422\pi$
$271$	25.4558	−	14.6969i	1.54633	−	0.892775i	0.998417	−	0.0562416i	$-0.0179117\pi$
$272$		−	14.1421i		−	0.857493i
$273$		0			0
$274$	12.0000			0.724947
$275$	−4.47871	−	13.4142i	−0.270077	−	0.808908i
$276$	−5.97469	+	0.550510i	−0.359634	+	0.0331368i
$277$	−16.9706	−	9.79796i	−1.01966	−	0.588702i	−0.105656	−	0.994403i	$-0.533694\pi$
$277$	−16.9706	−	9.79796i	−1.01966	−	0.588702i	−0.914006	+	0.405700i	$0.867028\pi$
$278$	−14.6969	+	8.48528i	−0.881464	+	0.508913i
$279$	−27.7128	−	9.79796i	−1.65912	−	0.586588i
$280$		0			0
$281$			28.2843i			1.68730i	0.536895	+	0.843649i	$0.319597\pi$
$281$			28.2843i			1.68730i	−0.536895	+	0.843649i	$0.680403\pi$
$282$	7.70674	+	3.55051i	0.458930	+	0.211430i
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	−0.995544	−	0.0942988i	$-0.969939\pi$
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	0.579437	+	0.815017i	$0.303272\pi$
$284$	−2.44949	−	1.41421i	−0.145350	−	0.0839181i
$285$		0			0
$286$			19.5959i			1.15873i
$287$		0			0
$288$	−5.19615	+	14.6969i	−0.306186	+	0.866025i
$289$	−4.50000	−	7.79423i	−0.264706	−	0.458484i
$290$	21.6251	−	3.51472i	1.26987	−	0.206391i
$291$	13.7980	−	1.27135i	0.808851	−	0.0745278i
$292$	−4.00000	−	6.92820i	−0.234082	−	0.405442i
$293$			2.82843i			0.165238i	0.996581	+	0.0826192i	$0.0263285\pi$
$293$			2.82843i			0.165238i	−0.996581	+	0.0826192i	$0.973671\pi$
$294$		0			0
$295$	−12.0000	+	9.79796i	−0.698667	+	0.570459i
$296$		0			0
$297$	−14.2474	−	3.60697i	−0.826721	−	0.209297i
$298$	16.9706	+	9.79796i	0.983078	+	0.567581i
$299$	−6.92820	−	12.0000i	−0.400668	−	0.693978i
$300$	−7.92820	+	3.48477i	−0.457735	+	0.201193i
$301$		0			0
$302$	−13.8564			−0.797347
$303$	12.5529	−	27.2474i	0.721148	−	1.56533i
$304$		0			0
$305$	−21.6251	+	3.51472i	−1.23825	+	0.201252i
$306$	−2.68556	−	14.4495i	−0.153523	−	0.826022i
$307$	−10.0000			−0.570730			−0.285365	−	0.958419i	$-0.592115\pi$
$307$	−10.0000			−0.570730			−0.285365	+	0.958419i	$0.592115\pi$
$308$		0			0
$309$	10.0000	+	14.1421i	0.568880	+	0.804518i
$310$	13.4558	−	35.4815i	0.764241	−	2.01522i
$311$	−13.8564	+	24.0000i	−0.785725	+	1.36092i	0.142840	+	0.989746i	$0.454376\pi$
$311$	−13.8564	+	24.0000i	−0.785725	+	1.36092i	−0.928565	+	0.371169i	$0.878957\pi$
$312$	−11.9494	+	1.10102i	−0.676501	+	0.0623330i
$313$	8.00000	+	13.8564i	0.452187	+	0.783210i	0.998522	−	0.0543564i	$-0.0173107\pi$
$313$	8.00000	+	13.8564i	0.452187	+	0.783210i	−0.546335	+	0.837567i	$0.683977\pi$
$314$	6.92820			0.390981
$315$		0			0
$316$	8.00000			0.450035
$317$	−6.92820	−	12.0000i	−0.389127	−	0.673987i	0.603206	−	0.797586i	$-0.293890\pi$
$317$	−6.92820	−	12.0000i	−0.389127	−	0.673987i	−0.992332	+	0.123599i	$0.960556\pi$
$318$		0			0
$319$	−8.00000	+	13.8564i	−0.447914	+	0.775810i
$320$	2.09077	+	0.792893i	0.116878	+	0.0443241i
$321$	−10.3923	−	14.6969i	−0.580042	−	0.820303i
$322$		0			0
$323$		0			0
$324$	−1.39898	+	8.89060i	−0.0777211	+	0.493922i
$325$	−14.9706	−	13.2621i	−0.830417	−	0.735647i
$326$	−22.0454	−	12.7279i	−1.22098	−	0.704934i
$327$	7.24745	−	15.7313i	0.400785	−	0.869944i
$328$	−6.00000			−0.331295
$329$		0			0
$330$	5.07180	−	18.2832i	0.279193	−	1.00646i
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	0.937829	+	0.347097i	$0.112833\pi$
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	−0.168320	+	0.985732i	$0.553834\pi$
$332$	−2.44949	−	1.41421i	−0.134433	−	0.0776151i
$333$		0			0
$334$	21.2132	−	12.2474i	1.16073	−	0.670151i
$335$	6.92820	+	8.48528i	0.378528	+	0.463600i
$336$		0			0
$337$		−	19.5959i		−	1.06746i	−0.845656	−	0.533729i	$-0.820790\pi$
$337$		−	19.5959i		−	1.06746i	0.845656	−	0.533729i	$-0.179210\pi$
$338$	2.59808	+	4.50000i	0.141317	+	0.244768i
$339$	11.9494	−	1.10102i	0.649001	−	0.0597992i
$340$	6.24264	−	1.01461i	0.338555	−	0.0550251i
$341$	13.8564	+	24.0000i	0.750366	+	1.29967i
$342$		0			0
$343$		0			0
$344$			8.48528i			0.457496i
$345$	3.35827	+	12.9893i	0.180803	+	0.699321i
$346$	29.6985	+	17.1464i	1.59660	+	0.921798i
$347$	−8.66025	+	15.0000i	−0.464907	+	0.805242i	−0.999197	−	0.0400587i	$-0.987246\pi$
$347$	−8.66025	+	15.0000i	−0.464907	+	0.805242i	0.534291	+	0.845301i	$0.320579\pi$
$348$	8.89898	+	4.09978i	0.477035	+	0.219771i
$349$			19.5959i			1.04895i	0.851427	+	0.524473i	$0.175738\pi$
$349$			19.5959i			1.04895i	−0.851427	+	0.524473i	$0.824262\pi$
$350$		0			0
$351$	−20.0000	+	5.65685i	−1.06752	+	0.301941i
$352$	12.7279	−	7.34847i	0.678401	−	0.391675i
$353$	26.9444	+	15.5563i	1.43411	+	0.827981i	0.997431	−	0.0716387i	$-0.0228229\pi$
$353$	26.9444	+	15.5563i	1.43411	+	0.827981i	0.436674	+	0.899620i	$0.356156\pi$
$354$	−20.6969	+	1.90702i	−1.10003	+	0.101357i
$355$	−2.24264	+	5.91359i	−0.119027	+	0.313861i
$356$	10.3923			0.550791
$357$		0			0
$358$		−	4.89898i		−	0.258919i
$359$	−26.9444	+	15.5563i	−1.42207	+	0.821033i	−0.996476	−	0.0838812i	$-0.973268\pi$
$359$	−26.9444	+	15.5563i	−1.42207	+	0.821033i	−0.425595	+	0.904914i	$0.639935\pi$
$360$	11.4339	+	2.06546i	0.602619	+	0.108859i
$361$	−9.50000	+	16.4545i	−0.500000	+	0.866025i
$362$		0			0
$363$	−3.00000	−	4.24264i	−0.157459	−	0.222681i
$364$		0			0
$365$	−13.8564	+	11.3137i	−0.725277	+	0.592187i
$366$	−26.6969	−	12.2993i	−1.39547	−	0.642896i
$367$	5.00000	−	8.66025i	0.260998	−	0.452062i	−0.705509	−	0.708700i	$-0.749282\pi$
$367$	5.00000	−	8.66025i	0.260998	−	0.452062i	0.966507	+	0.256639i	$0.0826151\pi$
$368$	−8.66025	+	15.0000i	−0.451447	+	0.781929i
$369$	−10.2173	+	1.89898i	−0.531893	+	0.0988569i
$370$		0			0
$371$		0			0
$372$	13.8564	−	9.79796i	0.718421	−	0.508001i
$373$	8.48528	−	4.89898i	0.439351	−	0.253660i	−0.263971	−	0.964531i	$-0.585032\pi$
$373$	8.48528	−	4.89898i	0.439351	−	0.253660i	0.703322	+	0.710871i	$0.251699\pi$
$374$	−6.92820	+	12.0000i	−0.358249	+	0.620505i
$375$	10.5353	+	16.2483i	0.544038	+	0.839061i
$376$	4.24264	−	2.44949i	0.218797	−	0.126323i
$377$			22.6274i			1.16537i
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$		0			0
$381$	2.33562	+	25.3485i	0.119657	+	1.29864i
$382$	29.6985	+	17.1464i	1.51951	+	0.877288i
$383$	−12.2474	+	7.07107i	−0.625815	+	0.361315i	−0.779130	−	0.626863i	$-0.784339\pi$
$383$	−12.2474	+	7.07107i	−0.625815	+	0.361315i	0.153314	+	0.988177i	$0.451005\pi$
$384$	12.1244	+	17.1464i	0.618718	+	0.875000i
$385$		0			0
$386$		−	16.9706i		−	0.863779i
$387$	2.68556	+	14.4495i	0.136515	+	0.734509i
$388$	−4.00000	+	6.92820i	−0.203069	+	0.351726i
$389$	19.5959	+	11.3137i	0.993552	+	0.573628i	0.906334	−	0.422561i	$-0.138869\pi$
$389$	19.5959	+	11.3137i	0.993552	+	0.573628i	0.0872182	+	0.996189i	$0.472202\pi$
$390$	−6.71655	−	25.9786i	−0.340106	−	1.31548i
$391$		−	9.79796i		−	0.495504i
$392$		0			0
$393$	−6.92820	−	9.79796i	−0.349482	−	0.494242i
$394$		0			0
$395$	−2.86976	−	17.6569i	−0.144393	−	0.888413i
$396$	6.44949	−	5.51399i	0.324099	−	0.277088i
$397$	−10.0000	−	17.3205i	−0.501886	−	0.869291i	−0.999998	−	0.00217869i	$-0.999307\pi$
$397$	−10.0000	−	17.3205i	−0.501886	−	0.869291i	0.498112	−	0.867113i	$-0.334027\pi$
$398$		0			0
$399$		0			0
$400$	−5.00000	+	24.4949i	−0.250000	+	1.22474i
$401$	−19.5959	+	11.3137i	−0.978573	+	0.564980i	−0.901839	−	0.432072i	$-0.857783\pi$
$401$	−19.5959	+	11.3137i	−0.978573	+	0.564980i	−0.0767343	+	0.997052i	$0.524449\pi$
$402$	1.34847	+	14.6349i	0.0672555	+	0.729925i
$403$	33.9411	+	19.5959i	1.69073	+	0.976142i
$404$	8.66025	+	15.0000i	0.430864	+	0.746278i
$405$	20.1244	−	0.101536i	0.999987	−	0.00504536i
$406$		0			0
$407$		0			0
$408$	−7.70674	−	3.55051i	−0.381541	−	0.175776i
$409$	−8.48528	−	4.89898i	−0.419570	−	0.242239i	0.275323	−	0.961352i	$-0.411215\pi$
$409$	−8.48528	−	4.89898i	−0.419570	−	0.242239i	−0.694893	+	0.719113i	$0.744548\pi$
$410$	−2.15232	−	13.2426i	−0.106295	−	0.654007i
$411$	5.02118	−	10.8990i	0.247677	−	0.537607i
$412$	−10.0000			−0.492665
$413$		0			0
$414$	−6.00000	+	16.9706i	−0.294884	+	0.834058i
$415$	−2.24264	+	5.91359i	−0.110087	+	0.290287i
$416$	10.3923	−	18.0000i	0.509525	−	0.882523i
$417$	1.55708	+	16.8990i	0.0762504	+	0.827547i
$418$		0			0
$419$	6.92820			0.338465			0.169232	−	0.985576i	$-0.445871\pi$
$419$	6.92820			0.338465			0.169232	+	0.985576i	$0.445871\pi$
$420$		0			0
$421$	26.0000			1.26716			0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000			1.26716			0.633581	+	0.773676i	$0.281584\pi$
$422$	−3.46410	−	6.00000i	−0.168630	−	0.292075i
$423$	6.44949	−	5.51399i	0.313585	−	0.268099i
$424$		0			0
$425$	−4.47871	−	13.4142i	−0.217250	−	0.650685i
$426$	−6.92820	+	4.89898i	−0.335673	+	0.237356i
$427$		0			0
$428$	10.3923			0.502331
$429$	17.7980	+	8.19955i	0.859294	+	0.395878i
$430$	−18.7279	+	3.04384i	−0.903141	+	0.146787i
$431$	−2.44949	−	1.41421i	−0.117988	−	0.0681203i	0.439845	−	0.898074i	$-0.355033\pi$
$431$	−2.44949	−	1.41421i	−0.117988	−	0.0681203i	−0.557832	+	0.829954i	$0.688367\pi$
$432$	18.6237	+	18.1151i	0.896034	+	0.871563i
$433$	−16.0000			−0.768911			−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000			−0.768911			−0.384455	+	0.923144i	$0.625611\pi$
$434$		0			0
$435$	5.85641	−	21.1117i	0.280793	−	1.01223i
$436$	5.00000	+	8.66025i	0.239457	+	0.414751i
$437$		0			0
$438$	−23.8988	+	2.20204i	−1.14193	+	0.105218i
$439$	−33.9411	+	19.5959i	−1.61992	+	0.935262i	−0.632983	+	0.774166i	$0.718170\pi$
$439$	−33.9411	+	19.5959i	−1.61992	+	0.935262i	−0.986939	+	0.161096i	$0.948497\pi$
$440$	−6.92820	−	8.48528i	−0.330289	−	0.404520i
$441$		0			0
$442$			19.5959i			0.932083i
$443$	8.66025	+	15.0000i	0.411461	+	0.712672i	0.995050	−	0.0993779i	$-0.0316853\pi$
$443$	8.66025	+	15.0000i	0.411461	+	0.712672i	−0.583589	+	0.812049i	$0.698352\pi$
$444$		0			0
$445$	−3.72792	−	22.9369i	−0.176720	−	1.08731i
$446$	22.5167	+	39.0000i	1.06619	+	1.84670i
$447$	16.0000	−	11.3137i	0.756774	−	0.535120i
$448$		0			0
$449$		−	5.65685i		−	0.266963i	−0.991051	−	0.133482i	$-0.957384\pi$
$449$		−	5.65685i		−	0.266963i	0.991051	−	0.133482i	$-0.0426157\pi$
$450$	−0.457135	+	25.9767i	−0.0215496	+	1.22456i
$451$	8.48528	+	4.89898i	0.399556	+	0.230684i
$452$	−3.46410	+	6.00000i	−0.162938	+	0.282216i
$453$	−5.79796	+	12.5851i	−0.272412	+	0.591298i
$454$		−	4.89898i		−	0.229920i
$455$		0			0
$456$		0			0
$457$	16.9706	−	9.79796i	0.793849	−	0.458329i	−0.0474665	−	0.998873i	$-0.515115\pi$
$457$	16.9706	−	9.79796i	0.793849	−	0.458329i	0.841316	+	0.540544i	$0.181781\pi$
$458$	−29.3939	−	16.9706i	−1.37349	−	0.792982i
$459$	−14.2474	−	3.60697i	−0.665014	−	0.168359i
$460$	−7.24264	−	2.74666i	−0.337690	−	0.128064i
$461$	3.46410			0.161339			0.0806696	−	0.996741i	$-0.474294\pi$
$461$	3.46410			0.161339			0.0806696	+	0.996741i	$0.474294\pi$
$462$		0			0
$463$		−	4.89898i		−	0.227675i	−0.993499	−	0.113837i	$-0.963686\pi$
$463$		−	4.89898i		−	0.227675i	0.993499	−	0.113837i	$-0.0363143\pi$
$464$	24.4949	−	14.1421i	1.13715	−	0.656532i
$465$	−26.5957	−	27.0679i	−1.23335	−	1.25524i
$466$	−18.0000	+	31.1769i	−0.833834	+	1.44424i
$467$	2.44949	−	1.41421i	0.113349	−	0.0654420i	−0.442254	−	0.896890i	$-0.645821\pi$
$467$	2.44949	−	1.41421i	0.113349	−	0.0654420i	0.555603	+	0.831448i	$0.312488\pi$
$468$	4.00000	−	11.3137i	0.184900	−	0.522976i
$469$		0			0
$470$	6.92820	+	8.48528i	0.319574	+	0.391397i
$471$	2.89898	−	6.29253i	0.133578	−	0.289944i
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$	6.92820	−	12.0000i	0.318559	−	0.551761i
$474$	10.0424	−	21.7980i	0.461261	−	1.00121i
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−4.24264	+	2.44949i	−0.194054	+	0.112037i
$479$	13.8564	−	24.0000i	0.633115	−	1.09659i	−0.353796	−	0.935323i	$-0.615109\pi$
$479$	13.8564	−	24.0000i	0.633115	−	1.09659i	0.986911	−	0.161265i	$-0.0515575\pi$
$480$	−14.3549	+	14.1045i	−0.655208	+	0.643780i
$481$		0			0
$482$			16.9706i			0.772988i
$483$		0			0
$484$	3.00000			0.136364
$485$	16.7262	+	6.34315i	0.759496	+	0.288027i
$486$	22.4685	+	14.9722i	1.01919	+	0.679152i
$487$	−12.7279	−	7.34847i	−0.576757	−	0.332991i	0.183086	−	0.983097i	$-0.441391\pi$
$487$	−12.7279	−	7.34847i	−0.576757	−	0.332991i	−0.759844	+	0.650106i	$0.774725\pi$
$488$	−14.6969	+	8.48528i	−0.665299	+	0.384111i
$489$	−20.7846	+	14.6969i	−0.939913	+	0.664619i
$490$		0			0
$491$		−	14.1421i		−	0.638226i	−0.947717	−	0.319113i	$-0.896615\pi$
$491$		−	14.1421i		−	0.638226i	0.947717	−	0.319113i	$-0.103385\pi$
$492$	2.51059	−	5.44949i	0.113186	−	0.245682i
$493$	−8.00000	+	13.8564i	−0.360302	+	0.624061i
$494$		0			0
$495$	−14.4835	−	12.2567i	−0.650986	−	0.550899i
$496$		−	48.9898i		−	2.19971i
$497$		0			0
$498$	−6.92820	+	4.89898i	−0.310460	+	0.219529i
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	0.907314	−	0.420455i	$-0.138129\pi$
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	−0.817781	+	0.575529i	$0.804796\pi$
$500$	−11.1713	−	0.449747i	−0.499595	−	0.0201133i
$501$	−2.24745	−	24.3916i	−0.100409	−	1.08974i
$502$	18.0000	+	31.1769i	0.803379	+	1.39149i
$503$			19.7990i			0.882793i	0.897312	+	0.441397i	$0.145517\pi$
$503$			19.7990i			0.882793i	−0.897312	+	0.441397i	$0.854483\pi$
$504$		0			0
$505$	30.0000	−	24.4949i	1.33498	−	1.09001i
$506$	14.6969	−	8.48528i	0.653359	−	0.377217i
$507$	5.17423	−	0.476756i	0.229796	−	0.0211735i
$508$	−12.7279	−	7.34847i	−0.564710	−	0.326036i
$509$	1.73205	+	3.00000i	0.0767718	+	0.132973i	0.901855	−	0.432038i	$-0.142205\pi$
$509$	1.73205	+	3.00000i	0.0767718	+	0.132973i	−0.825084	+	0.565011i	$0.808872\pi$
$510$	5.07180	−	18.2832i	0.224583	−	0.809595i
$511$		0			0
$512$	−8.66025			−0.382733
$513$		0			0
$514$	−21.2132	−	12.2474i	−0.935674	−	0.540212i
$515$	3.58719	+	22.0711i	0.158071	+	0.972567i
$516$	−7.70674	−	3.55051i	−0.339270	−	0.156302i
$517$	−8.00000			−0.351840
$518$		0			0
$519$	28.0000	−	19.7990i	1.22906	−	0.869079i
$520$	−14.4853	−	5.49333i	−0.635222	−	0.240898i
$521$	5.19615	−	9.00000i	0.227648	−	0.394297i	−0.729463	−	0.684020i	$-0.760230\pi$
$521$	5.19615	−	9.00000i	0.227648	−	0.394297i	0.957110	+	0.289723i	$0.0935633\pi$
$522$	22.3417	−	19.1010i	0.977869	−	0.836029i
$523$	−13.0000	−	22.5167i	−0.568450	−	0.984585i	−0.996719	−	0.0809336i	$-0.974210\pi$
$523$	−13.0000	−	22.5167i	−0.568450	−	0.984585i	0.428269	−	0.903651i	$-0.359124\pi$
$524$	6.92820			0.302660
$525$		0			0
$526$	−6.00000			−0.261612
$527$	13.8564	+	24.0000i	0.603595	+	1.04546i
$528$	−2.24745	−	24.3916i	−0.0978077	−	1.06151i
$529$	5.50000	−	9.52628i	0.239130	−	0.414186i
$530$		0			0
$531$	−6.92820	+	19.5959i	−0.300658	+	0.850390i
$532$		0			0
$533$	13.8564			0.600188
$534$	13.0454	−	28.3164i	0.564530	−	1.22537i
$535$	−3.72792	−	22.9369i	−0.161172	−	0.991650i
$536$	7.34847	+	4.24264i	0.317406	+	0.183254i
$537$	−4.44949	−	2.04989i	−0.192010	−	0.0884592i
$538$	18.0000			0.776035
$539$		0			0
$540$	−6.66025	+	9.52056i	−0.286612	+	0.409700i
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	0.953262	−	0.302144i	$-0.0977023\pi$
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	−0.738296	+	0.674477i	$0.764369\pi$
$542$	44.0908	+	25.4558i	1.89386	+	1.09342i
$543$		0			0
$544$	12.7279	−	7.34847i	0.545705	−	0.315063i
$545$	17.3205	−	14.1421i	0.741929	−	0.605783i
$546$		0			0
$547$			34.2929i			1.46626i	0.680090	+	0.733128i	$0.261941\pi$
$547$			34.2929i			1.46626i	−0.680090	+	0.733128i	$0.738059\pi$
$548$	3.46410	+	6.00000i	0.147979	+	0.256307i
$549$	−22.3417	+	19.1010i	−0.953520	+	0.815212i
$550$	16.2426	−	18.3351i	0.692589	−	0.781812i
$551$		0			0
$552$	6.00000	+	8.48528i	0.255377	+	0.361158i
$553$		0			0
$554$		−	33.9411i		−	1.44202i
$555$		0			0
$556$	−8.48528	−	4.89898i	−0.359856	−	0.207763i
$557$	20.7846	−	36.0000i	0.880672	−	1.52537i	0.0300772	−	0.999548i	$-0.490425\pi$
$557$	20.7846	−	36.0000i	0.880672	−	1.52537i	0.850595	−	0.525821i	$-0.176242\pi$
$558$	−9.30306	−	50.0545i	−0.393830	−	2.11898i
$559$		−	19.5959i		−	0.828819i
$560$		0			0
$561$	8.00000	+	11.3137i	0.337760	+	0.477665i
$562$	−42.4264	+	24.4949i	−1.78965	+	1.03325i
$563$	12.2474	+	7.07107i	0.516168	+	0.298010i	0.735366	−	0.677671i	$-0.237010\pi$
$563$	12.2474	+	7.07107i	0.516168	+	0.298010i	−0.219197	+	0.975681i	$0.570344\pi$
$564$	0.449490	+	4.87832i	0.0189269	+	0.205414i
$565$	14.4853	+	5.49333i	0.609400	+	0.231106i
$566$	−24.2487			−1.01925
$567$		0			0
$568$			4.89898i			0.205557i
$569$	24.4949	−	14.1421i	1.02688	−	0.592869i	0.110790	−	0.993844i	$-0.464662\pi$
$569$	24.4949	−	14.1421i	1.02688	−	0.592869i	0.916089	+	0.400975i	$0.131328\pi$
$570$		0			0
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	−0.821138	−	0.570730i	$-0.806660\pi$
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	0.904835	+	0.425762i	$0.139994\pi$
$572$	−9.79796	+	5.65685i	−0.409673	+	0.236525i
$573$	28.0000	−	19.7990i	1.16972	−	0.827115i
$574$		0			0
$575$	−3.46410	+	16.9706i	−0.144463	+	0.707721i
$576$	2.94949	−	0.548188i	0.122895	−	0.0228412i
$577$	−4.00000	+	6.92820i	−0.166522	+	0.288425i	−0.937195	−	0.348806i	$-0.886587\pi$
$577$	−4.00000	+	6.92820i	−0.166522	+	0.288425i	0.770673	+	0.637231i	$0.219920\pi$
$578$	7.79423	−	13.5000i	0.324197	−	0.561526i
$579$	−15.4135	−	7.10102i	−0.640563	−	0.295108i
$580$	8.00000	+	9.79796i	0.332182	+	0.406838i
$581$		0			0
$582$	13.8564	+	19.5959i	0.574367	+	0.812277i
$583$		0			0
$584$	−6.92820	+	12.0000i	−0.286691	+	0.496564i
$585$	−26.4054	−	4.76998i	−1.09173	−	0.197214i
$586$	−4.24264	+	2.44949i	−0.175262	+	0.101187i
$587$			19.7990i			0.817192i	0.912715	+	0.408596i	$0.133981\pi$
$587$			19.7990i			0.817192i	−0.912715	+	0.408596i	$0.866019\pi$
$588$		0			0
$589$		0			0
$590$	−25.0892	−	9.51472i	−1.03291	−	0.391715i
$591$		0			0
$592$		0			0
$593$	17.1464	−	9.89949i	0.704119	−	0.406524i	−0.104760	−	0.994497i	$-0.533408\pi$
$593$	17.1464	−	9.89949i	0.704119	−	0.406524i	0.808880	+	0.587974i	$0.200074\pi$
$594$	−6.92820	−	24.4949i	−0.284268	−	1.00504i
$595$		0			0
$596$			11.3137i			0.463428i
$597$		0			0
$598$	12.0000	−	20.7846i	0.490716	−	0.849946i
$599$	−31.8434	−	18.3848i	−1.30108	−	0.751182i	−0.320495	−	0.947250i	$-0.603849\pi$
$599$	−31.8434	−	18.3848i	−1.30108	−	0.751182i	−0.980590	+	0.196069i	$0.937182\pi$
$600$	12.0932	+	8.87441i	0.493702	+	0.362296i
$601$		−	9.79796i		−	0.399667i	−0.979830	−	0.199834i	$-0.935960\pi$
$601$		−	9.79796i		−	0.399667i	0.979830	−	0.199834i	$-0.0640401\pi$
$602$		0			0
$603$	13.8564	+	4.89898i	0.564276	+	0.199502i
$604$	−4.00000	−	6.92820i	−0.162758	−	0.281905i
$605$	−1.07616	−	6.62132i	−0.0437521	−	0.269195i
$606$	51.7423	−	4.76756i	2.10189	−	0.193669i
$607$	5.00000	+	8.66025i	0.202944	+	0.351509i	0.949476	−	0.313841i	$-0.101616\pi$
$607$	5.00000	+	8.66025i	0.202944	+	0.351509i	−0.746532	+	0.665350i	$0.768282\pi$
$608$		0			0
$609$		0			0
$610$	−24.0000	−	29.3939i	−0.971732	−	1.19012i
$611$	−9.79796	+	5.65685i	−0.396383	+	0.228852i
$612$	6.44949	−	5.51399i	0.260705	−	0.222890i
$613$	−25.4558	−	14.6969i	−1.02815	−	0.593604i	−0.111697	−	0.993742i	$-0.535629\pi$
$613$	−25.4558	−	14.6969i	−1.02815	−	0.593604i	−0.916455	+	0.400139i	$0.868962\pi$
$614$	−8.66025	−	15.0000i	−0.349499	−	0.605351i
$615$	−12.9282	−	3.58630i	−0.521315	−	0.144614i
$616$		0			0
$617$	48.4974			1.95243			0.976216	−	0.216799i	$-0.0695615\pi$
$617$	48.4974			1.95243			0.976216	+	0.216799i	$0.0695615\pi$
$618$	−12.5529	+	27.2474i	−0.504954	+	1.09605i
$619$	8.48528	+	4.89898i	0.341052	+	0.196907i	0.660737	−	0.750617i	$-0.270244\pi$
$619$	8.48528	+	4.89898i	0.341052	+	0.196907i	−0.319685	+	0.947524i	$0.603577\pi$
$620$	21.6251	−	3.51472i	0.868487	−	0.141154i
$621$	12.9029	+	12.5505i	0.517775	+	0.503635i
$622$	−48.0000			−1.92462
$623$		0			0
$624$	−20.0000	−	28.2843i	−0.800641	−	1.13228i
$625$	3.01472	+	24.8176i	0.120589	+	0.992703i
$626$	−13.8564	+	24.0000i	−0.553813	+	0.959233i
$627$		0			0
$628$	2.00000	+	3.46410i	0.0798087	+	0.138233i
$629$		0			0
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	−6.92820	−	12.0000i	−0.275589	−	0.477334i
$633$	−6.89898	+	0.635674i	−0.274210	+	0.0252658i
$634$	12.0000	−	20.7846i	0.476581	−	0.825462i
$635$	−11.6531	+	30.7279i	−0.462439	+	1.21940i
$636$		0			0
$637$		0			0
$638$	−27.7128			−1.09716
$639$	1.55051	+	8.34242i	0.0613372	+	0.330021i
$640$	4.34924	+	26.7597i	0.171919	+	1.05777i
$641$	4.89898	+	2.82843i	0.193498	+	0.111716i	0.593619	−	0.804746i	$-0.297699\pi$
$641$	4.89898	+	2.82843i	0.193498	+	0.111716i	−0.400121	+	0.916462i	$0.631032\pi$
$642$	13.0454	−	28.3164i	0.514861	−	1.11756i
$643$	−22.0000			−0.867595			−0.433798	−	0.901010i	$-0.642827\pi$
$643$	−22.0000			−0.867595			−0.433798	+	0.901010i	$0.642827\pi$
$644$		0			0
$645$	−5.07180	+	18.2832i	−0.199702	+	0.719902i
$646$		0			0
$647$	−17.1464	−	9.89949i	−0.674096	−	0.389189i	0.123531	−	0.992341i	$-0.460578\pi$
$647$	−17.1464	−	9.89949i	−0.674096	−	0.389189i	−0.797627	+	0.603151i	$0.793911\pi$
$648$	14.5475	−	5.60102i	0.571478	−	0.220029i
$649$	16.9706	−	9.79796i	0.666153	−	0.384604i
$650$	6.92820	−	33.9411i	0.271746	−	1.33128i
$651$		0			0
$652$		−	14.6969i		−	0.575577i
$653$	−13.8564	−	24.0000i	−0.542243	−	0.939193i	−0.998775	−	0.0494855i	$-0.984242\pi$
$653$	−13.8564	−	24.0000i	−0.542243	−	0.939193i	0.456532	−	0.889707i	$-0.349091\pi$
$654$	29.8735	−	2.75255i	1.16814	−	0.107633i
$655$	−2.48528	−	15.2913i	−0.0971080	−	0.597480i
$656$	−8.66025	−	15.0000i	−0.338126	−	0.585652i
$657$	−8.00000	+	22.6274i	−0.312110	+	0.882780i
$658$		0			0
$659$			2.82843i			0.110180i	0.998481	+	0.0550899i	$0.0175446\pi$
$659$			2.82843i			0.110180i	−0.998481	+	0.0550899i	$0.982455\pi$
$660$	10.6057	−	2.74202i	0.412827	−	0.106733i
$661$	−8.48528	−	4.89898i	−0.330039	−	0.190548i	0.325819	−	0.945432i	$-0.394360\pi$
$661$	−8.48528	−	4.89898i	−0.330039	−	0.190548i	−0.655859	+	0.754884i	$0.727693\pi$
$662$	−24.2487	+	42.0000i	−0.942453	+	1.63238i
$663$	17.7980	+	8.19955i	0.691215	+	0.318444i
$664$			4.89898i			0.190117i
$665$		0			0
$666$		0			0
$667$	16.9706	−	9.79796i	0.657103	−	0.379378i
$668$	12.2474	+	7.07107i	0.473868	+	0.273588i
$669$	44.8434	−	4.13188i	1.73374	−	0.159748i
$670$	−6.72792	+	17.7408i	−0.259922	+	0.685386i
$671$	27.7128			1.06984
$672$		0			0
$673$		−	9.79796i		−	0.377684i	−0.982008	−	0.188842i	$-0.939527\pi$
$673$		−	9.79796i		−	0.377684i	0.982008	−	0.188842i	$-0.0604733\pi$
$674$	29.3939	−	16.9706i	1.13221	−	0.653682i
$675$	23.4020	+	11.2847i	0.900745	+	0.434348i
$676$	−1.50000	+	2.59808i	−0.0576923	+	0.0999260i
$677$	2.44949	−	1.41421i	0.0941415	−	0.0543526i	−0.452190	−	0.891922i	$-0.649357\pi$
$677$	2.44949	−	1.41421i	0.0941415	−	0.0543526i	0.546332	+	0.837569i	$0.316024\pi$
$678$	12.0000	+	16.9706i	0.460857	+	0.651751i
$679$		0			0
$680$	−6.92820	−	8.48528i	−0.265684	−	0.325396i
$681$	−4.44949	−	2.04989i	−0.170505	−	0.0785519i
$682$	−24.0000	+	41.5692i	−0.919007	+	1.59177i
$683$	−5.19615	+	9.00000i	−0.198825	+	0.344375i	−0.948148	−	0.317830i	$-0.897046\pi$
$683$	−5.19615	+	9.00000i	−0.198825	+	0.344375i	0.749323	+	0.662205i	$0.230379\pi$
$684$		0			0
$685$	12.0000	−	9.79796i	0.458496	−	0.374361i
$686$		0			0
$687$	−27.7128	+	19.5959i	−1.05731	+	0.747631i
$688$	−21.2132	+	12.2474i	−0.808746	+	0.466930i
$689$		0			0
$690$	−16.5756	+	16.2865i	−0.631023	+	0.620016i
$691$	−8.48528	+	4.89898i	−0.322795	+	0.186366i	−0.652638	−	0.757670i	$-0.726338\pi$
$691$	−8.48528	+	4.89898i	−0.322795	+	0.186366i	0.329843	+	0.944036i	$0.393004\pi$
$692$			19.7990i			0.752645i
$693$		0			0
$694$	−30.0000			−1.13878
$695$	−7.76874	+	20.4853i	−0.294685	+	0.777051i
$696$	−1.55708	−	16.8990i	−0.0590209	−	0.640554i
$697$	8.48528	+	4.89898i	0.321403	+	0.185562i
$698$	−29.3939	+	16.9706i	−1.11257	+	0.642345i
$699$	20.7846	+	29.3939i	0.786146	+	1.11178i
$700$		0			0
$701$		−	22.6274i		−	0.854626i	−0.904104	−	0.427313i	$-0.859460\pi$
$701$		−	22.6274i		−	0.854626i	0.904104	−	0.427313i	$-0.140540\pi$
$702$	−25.8058	−	25.1010i	−0.973977	−	0.947377i
$703$		0			0
$704$	−2.44949	−	1.41421i	−0.0923186	−	0.0533002i
$705$	10.6057	−	2.74202i	0.399435	−	0.103270i
$706$			53.8888i			2.02813i
$707$		0			0
$708$	−6.92820	−	9.79796i	−0.260378	−	0.368230i
$709$	−19.0000	−	32.9090i	−0.713560	−	1.23592i	−0.963512	−	0.267664i	$-0.913748\pi$
$709$	−19.0000	−	32.9090i	−0.713560	−	1.23592i	0.249952	−	0.968258i	$-0.419585\pi$
$710$	−10.8126	+	1.75736i	−0.405789	+	0.0659525i
$711$	−15.5959	−	18.2419i	−0.584893	−	0.684125i
$712$	−9.00000	−	15.5885i	−0.337289	−	0.584202i
$713$		−	33.9411i		−	1.27111i
$714$		0			0
$715$	16.0000	+	19.5959i	0.598366	+	0.732846i
$716$	2.44949	−	1.41421i	0.0915417	−	0.0528516i
$717$	0.449490	+	4.87832i	0.0167865	+	0.182184i
$718$	−46.6690	−	26.9444i	−1.74167	−	1.00556i
$719$	20.7846	+	36.0000i	0.775135	+	1.34257i	0.934718	+	0.355389i	$0.115652\pi$
$719$	20.7846	+	36.0000i	0.775135	+	1.34257i	−0.159583	+	0.987184i	$0.551015\pi$
$720$	11.3397	+	31.5660i	0.422607	+	1.17639i
$721$		0			0
$722$	−32.9090			−1.22474
$723$	15.4135	+	7.10102i	0.573234	+	0.264090i
$724$		0			0
$725$	18.7554	−	21.1716i	0.696558	−	0.786292i
$726$	3.76588	−	8.17423i	0.139765	−	0.303374i
$727$	−10.0000			−0.370879			−0.185440	−	0.982656i	$-0.559371\pi$
$727$	−10.0000			−0.370879			−0.185440	+	0.982656i	$0.559371\pi$
$728$		0			0
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$	−28.9706	−	10.9867i	−1.07225	−	0.406634i
$731$	6.92820	−	12.0000i	0.256249	−	0.443836i
$732$	−1.55708	−	16.8990i	−0.0575513	−	0.624604i
$733$	14.0000	+	24.2487i	0.517102	+	0.895647i	0.999803	+	0.0198613i	$0.00632248\pi$
$733$	14.0000	+	24.2487i	0.517102	+	0.895647i	−0.482701	+	0.875785i	$0.660344\pi$
$734$	17.3205			0.639312
$735$		0			0
$736$	−18.0000			−0.663489
$737$	−6.92820	−	12.0000i	−0.255204	−	0.442026i
$738$	−11.6969	−	13.6814i	−0.430570	−	0.503621i
$739$	−10.0000	+	17.3205i	−0.367856	+	0.637145i	−0.989230	−	0.146369i	$-0.953241\pi$
$739$	−10.0000	+	17.3205i	−0.367856	+	0.637145i	0.621374	+	0.783514i	$0.286575\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−24.2487			−0.889599			−0.444799	−	0.895630i	$-0.646725\pi$
$743$	−24.2487			−0.889599			−0.444799	+	0.895630i	$0.646725\pi$
$744$	−26.6969	−	12.2993i	−0.978757	−	0.450915i
$745$	24.9706	−	4.05845i	0.914851	−	0.148690i
$746$	14.6969	+	8.48528i	0.538093	+	0.310668i
$747$	1.55051	+	8.34242i	0.0567302	+	0.305233i
$748$	−8.00000			−0.292509
$749$		0			0
$750$	−15.2487	+	29.8744i	−0.556804	+	1.09086i
$751$	−4.00000	−	6.92820i	−0.145962	−	0.252814i	0.783769	−	0.621052i	$-0.213294\pi$
$751$	−4.00000	−	6.92820i	−0.145962	−	0.252814i	−0.929731	+	0.368238i	$0.879961\pi$
$752$	12.2474	+	7.07107i	0.446619	+	0.257855i
$753$	35.8481	−	3.30306i	1.30638	−	0.120370i
$754$	−33.9411	+	19.5959i	−1.23606	+	0.713641i
$755$	−13.8564	+	11.3137i	−0.504286	+	0.411748i
$756$		0			0
$757$		−	29.3939i		−	1.06834i	−0.845378	−	0.534169i	$-0.820624\pi$
$757$		−	29.3939i		−	1.06834i	0.845378	−	0.534169i	$-0.179376\pi$
$758$	−24.2487	−	42.0000i	−0.880753	−	1.52551i
$759$	−1.55708	−	16.8990i	−0.0565184	−	0.613394i
$760$		0			0
$761$	−19.0526	−	33.0000i	−0.690655	−	1.19625i	−0.971624	−	0.236532i	$-0.923989\pi$
$761$	−19.0526	−	33.0000i	−0.690655	−	1.19625i	0.280969	−	0.959717i	$-0.409344\pi$
$762$	−36.0000	+	25.4558i	−1.30414	+	0.922168i
$763$		0			0
$764$			19.7990i			0.716302i
$765$	−14.4835	−	12.2567i	−0.523653	−	0.443143i
$766$	−21.2132	−	12.2474i	−0.766464	−	0.442518i
$767$	13.8564	−	24.0000i	0.500326	−	0.866590i
$768$	−13.7702	+	29.8895i	−0.496888	+	1.07854i
$769$		−	19.5959i		−	0.706647i	−0.935501	−	0.353323i	$-0.885052\pi$
$769$		−	19.5959i		−	0.706647i	0.935501	−	0.353323i	$-0.114948\pi$
$770$		0			0
$771$	−20.0000	+	14.1421i	−0.720282	+	0.509317i
$772$	8.48528	−	4.89898i	0.305392	−	0.176318i
$773$	−2.44949	−	1.41421i	−0.0881020	−	0.0508657i	0.455302	−	0.890337i	$-0.349531\pi$
$773$	−2.44949	−	1.41421i	−0.0881020	−	0.0508657i	−0.543404	+	0.839471i	$0.682865\pi$
$774$	−19.3485	+	16.5420i	−0.695466	+	0.594589i
$775$	−15.5147	−	46.4682i	−0.557305	−	1.66919i
$776$	13.8564			0.497416
$777$		0			0
$778$			39.1918i			1.40510i
$779$		0			0
$780$	11.0504	−	10.8577i	0.395668	−	0.388766i
$781$	4.00000	−	6.92820i	0.143131	−	0.247911i
$782$	14.6969	−	8.48528i	0.525561	−	0.303433i
$783$	−8.00000	−	28.2843i	−0.285897	−	1.01080i
$784$		0			0
$785$	6.92820	−	5.65685i	0.247278	−	0.201902i
$786$	8.69694	−	18.8776i	0.310210	−	0.673341i
$787$	−7.00000	+	12.1244i	−0.249523	+	0.432187i	−0.963394	−	0.268091i	$-0.913607\pi$
$787$	−7.00000	+	12.1244i	−0.249523	+	0.432187i	0.713871	+	0.700278i	$0.246941\pi$
$788$		0			0
$789$	−2.51059	+	5.44949i	−0.0893794	+	0.194007i
$790$	24.0000	−	19.5959i	0.853882	−	0.697191i
$791$		0			0
$792$	−13.8564	−	4.89898i	−0.492366	−	0.174078i
$793$	33.9411	−	19.5959i	1.20528	−	0.695871i
$794$	17.3205	−	30.0000i	0.614682	−	1.06466i
$795$		0			0
$796$		0			0
$797$			36.7696i			1.30244i	0.758887	+	0.651222i	$0.225743\pi$
$797$			36.7696i			1.30244i	−0.758887	+	0.651222i	$0.774257\pi$
$798$		0			0
$799$	−8.00000			−0.283020
$800$	−24.6435	+	8.22792i	−0.871279	+	0.290901i
$801$	−20.2597	−	23.6969i	−0.715841	−	0.837290i
$802$	−33.9411	−	19.5959i	−1.19850	−	0.691956i
$803$	19.5959	−	11.3137i	0.691525	−	0.399252i
$804$	−6.92820	+	4.89898i	−0.244339	+	0.172774i
$805$		0			0
$806$			67.8823i			2.39105i
$807$	7.53177	−	16.3485i	0.265131	−	0.575493i
$808$	15.0000	−	25.9808i	0.527698	−	0.914000i
$809$	19.5959	+	11.3137i	0.688956	+	0.397769i	0.803221	−	0.595682i	$-0.203118\pi$
$809$	19.5959	+	11.3137i	0.688956	+	0.397769i	−0.114265	+	0.993450i	$0.536451\pi$
$810$	17.5805	+	30.0986i	0.617716	+	1.05756i
$811$			29.3939i			1.03216i	0.856541	+	0.516079i	$0.172609\pi$
$811$			29.3939i			1.03216i	−0.856541	+	0.516079i	$0.827391\pi$
$812$		0			0
$813$	41.5692	−	29.3939i	1.45790	−	1.03089i
$814$		0			0
$815$	−32.4377	+	5.27208i	−1.13624	+	0.184673i
$816$	−2.24745	−	24.3916i	−0.0786764	−	0.853876i
$817$		0			0
$818$		−	16.9706i		−	0.593362i
$819$		0			0
$820$	6.00000	−	4.89898i	0.209529	−	0.171080i
$821$	−19.5959	+	11.3137i	−0.683902	+	0.394851i	−0.801324	−	0.598231i	$-0.795871\pi$
$821$	−19.5959	+	11.3137i	−0.683902	+	0.394851i	0.117421	+	0.993082i	$0.462537\pi$
$822$	20.6969	−	1.90702i	0.721889	−	0.0665151i
$823$	4.24264	+	2.44949i	0.147889	+	0.0853838i	0.572119	−	0.820171i	$-0.306122\pi$
$823$	4.24264	+	2.44949i	0.147889	+	0.0853838i	−0.424229	+	0.905555i	$0.639455\pi$
$824$	8.66025	+	15.0000i	0.301694	+	0.522550i
$825$	−9.85641	−	22.4243i	−0.343156	−	0.780715i
$826$		0			0
$827$	10.3923			0.361376			0.180688	−	0.983540i	$-0.442168\pi$
$827$	10.3923			0.361376			0.180688	+	0.983540i	$0.442168\pi$
$828$	−10.2173	+	1.89898i	−0.355077	+	0.0659941i
$829$	25.4558	+	14.6969i	0.884118	+	0.510446i	0.872014	−	0.489481i	$-0.162814\pi$
$829$	25.4558	+	14.6969i	0.884118	+	0.510446i	0.0121040	+	0.999927i	$0.496147\pi$
$830$	−10.8126	+	1.75736i	−0.375310	+	0.0609988i
$831$	−30.8270	−	14.2020i	−1.06938	−	0.492663i
$832$	−4.00000			−0.138675
$833$		0			0
$834$	−24.0000	+	16.9706i	−0.831052	+	0.587643i
$835$	11.2132	−	29.5680i	0.388049	−	1.02324i
$836$		0			0
$837$	−49.3546	−	12.4949i	−1.70594	−	0.431887i
$838$	6.00000	+	10.3923i	0.207267	+	0.358996i
$839$	−27.7128			−0.956753			−0.478376	−	0.878155i	$-0.658774\pi$
$839$	−27.7128			−0.956753			−0.478376	+	0.878155i	$0.658774\pi$
$840$		0			0
$841$	−3.00000			−0.103448
$842$	22.5167	+	39.0000i	0.775975	+	1.34403i
$843$	4.49490	+	48.7832i	0.154812	+	1.68018i
$844$	2.00000	−	3.46410i	0.0688428	−	0.119239i
$845$	6.27231	+	2.37868i	0.215774	+	0.0818291i
$846$	13.8564	+	4.89898i	0.476393	+	0.168430i
$847$		0			0
$848$		0			0
$849$	−10.1464	+	22.0239i	−0.348225	+	0.755857i
$850$	16.2426	−	18.3351i	0.557118	−	0.628889i
$851$		0			0
$852$	−4.44949	−	2.04989i	−0.152437	−	0.0702280i
$853$	20.0000			0.684787			0.342393	−	0.939557i	$-0.388762\pi$
$853$	20.0000			0.684787			0.342393	+	0.939557i	$0.388762\pi$
$854$		0			0
$855$		0			0
$856$	−9.00000	−	15.5885i	−0.307614	−	0.532803i
$857$	41.6413	+	24.0416i	1.42244	+	0.821246i	0.996507	−	0.0835080i	$-0.0266124\pi$
$857$	41.6413	+	24.0416i	1.42244	+	0.821246i	0.425933	+	0.904754i	$0.359946\pi$
$858$	3.11416	+	33.7980i	0.106316	+	1.15384i
$859$	33.9411	−	19.5959i	1.15806	−	0.668604i	0.207219	−	0.978295i	$-0.433559\pi$
$859$	33.9411	−	19.5959i	1.15806	−	0.668604i	0.950837	+	0.309691i	$0.100225\pi$
$860$	−6.92820	−	8.48528i	−0.236250	−	0.289346i
$861$		0			0
$862$		−	4.89898i		−	0.166860i
$863$	−5.19615	−	9.00000i	−0.176879	−	0.306364i	0.763931	−	0.645298i	$-0.223267\pi$
$863$	−5.19615	−	9.00000i	−0.176879	−	0.306364i	−0.940810	+	0.338935i	$0.889933\pi$
$864$	−6.62642	+	26.1742i	−0.225435	+	0.890466i
$865$	43.6985	−	7.10228i	1.48579	−	0.241485i
$866$	−13.8564	−	24.0000i	−0.470860	−	0.815553i
$867$	−9.00000	−	12.7279i	−0.305656	−	0.432263i
$868$		0			0
$869$			22.6274i			0.767583i
$870$	36.7393	−	9.49863i	1.24558	−	0.322034i
$871$	−16.9706	−	9.79796i	−0.575026	−	0.331991i
$872$	8.66025	−	15.0000i	0.293273	−	0.507964i
$873$	23.5959	−	4.38551i	0.798601	−	0.148427i
$874$		0			0
$875$		0			0
$876$	−8.00000	−	11.3137i	−0.270295	−	0.382255i
$877$	−42.4264	+	24.4949i	−1.43264	+	0.827134i	−0.997321	−	0.0731435i	$-0.976697\pi$
$877$	−42.4264	+	24.4949i	−1.43264	+	0.827134i	−0.435317	+	0.900277i	$0.643364\pi$
$878$	−58.7878	−	33.9411i	−1.98399	−	1.14546i
$879$	0.449490	+	4.87832i	0.0151609	+	0.164541i
$880$	11.2132	−	29.5680i	0.377997	−	0.996736i
$881$	−10.3923			−0.350126			−0.175063	−	0.984557i	$-0.556013\pi$
$881$	−10.3923			−0.350126			−0.175063	+	0.984557i	$0.556013\pi$
$882$		0			0
$883$			14.6969i			0.494591i	0.968940	+	0.247296i	$0.0795419\pi$
$883$			14.6969i			0.494591i	−0.968940	+	0.247296i	$0.920458\pi$
$884$	−9.79796	+	5.65685i	−0.329541	+	0.190261i
$885$	−19.1399	+	18.8060i	−0.643379	+	0.632157i
$886$	−15.0000	+	25.9808i	−0.503935	+	0.872841i
$887$	2.44949	−	1.41421i	0.0822458	−	0.0474846i	−0.458313	−	0.888791i	$-0.651546\pi$
$887$	2.44949	−	1.41421i	0.0822458	−	0.0474846i	0.540559	+	0.841306i	$0.318213\pi$
$888$		0			0
$889$		0			0
$890$	31.1769	−	25.4558i	1.04505	−	0.853282i
$891$	−25.1464	−	3.95691i	−0.842437	−	0.132562i
$892$	−13.0000	+	22.5167i	−0.435272	+	0.753914i
$893$		0			0
$894$	30.8270	+	14.2020i	1.03101	+	0.474987i
$895$	−4.00000	−	4.89898i	−0.133705	−	0.163755i
$896$		0			0
$897$	−13.8564	−	19.5959i	−0.462652	−	0.654289i
$898$	8.48528	−	4.89898i	0.283158	−	0.163481i
$899$	−27.7128	+	48.0000i	−0.924274	+	1.60089i
$900$	−13.1203	+	7.27027i	−0.437344	+	0.242342i
$901$		0			0
$902$			16.9706i			0.565058i
$903$		0			0
$904$	12.0000			0.399114
$905$		0			0
$906$	−23.8988	+	2.20204i	−0.793983	+	0.0731579i
$907$	21.2132	+	12.2474i	0.704373	+	0.406670i	0.808974	−	0.587844i	$-0.200023\pi$
$907$	21.2132	+	12.2474i	0.704373	+	0.406670i	−0.104601	+	0.994514i	$0.533357\pi$
$908$	2.44949	−	1.41421i	0.0812892	−	0.0469323i
$909$	17.3205	−	48.9898i	0.574485	−	1.62489i
$910$		0			0
$911$		−	48.0833i		−	1.59307i	−0.604593	−	0.796535i	$-0.706664\pi$
$911$		−	48.0833i		−	1.59307i	0.604593	−	0.796535i	$-0.293336\pi$
$912$		0			0
$913$	4.00000	−	6.92820i	0.132381	−	0.229290i
$914$	29.3939	+	16.9706i	0.972263	+	0.561336i
$915$	−36.7393	+	9.49863i	−1.21456	+	0.314015i
$916$		−	19.5959i		−	0.647467i
$917$		0			0
$918$	−6.92820	−	24.4949i	−0.228665	−	0.808452i
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	0.967274	−	0.253735i	$-0.0816592\pi$
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	−0.703378	+	0.710816i	$0.748326\pi$
$920$	2.15232	+	13.2426i	0.0709598	+	0.436597i
$921$	−17.2474	+	1.58919i	−0.568323	+	0.0523655i
$922$	3.00000	+	5.19615i	0.0987997	+	0.171126i
$923$		−	11.3137i		−	0.372395i
$924$		0			0
$925$		0			0
$926$	7.34847	−	4.24264i	0.241486	−	0.139422i
$927$	19.4949	+	22.8024i	0.640296	+	0.748929i
$928$	25.4558	+	14.6969i	0.835629	+	0.482451i
$929$	−22.5167	−	39.0000i	−0.738748	−	1.27955i	−0.953059	−	0.302783i	$-0.902084\pi$
$929$	−22.5167	−	39.0000i	−0.738748	−	1.27955i	0.214312	−	0.976765i	$-0.431249\pi$
$930$	17.5692	−	63.3350i	0.576117	−	2.07684i
$931$		0			0
$932$	−20.7846			−0.680823
$933$	−20.0847	+	43.5959i	−0.657544	+	1.42727i
$934$	4.24264	+	2.44949i	0.138823	+	0.0801498i
$935$	2.86976	+	17.6569i	0.0938510	+	0.577441i
$936$	−20.4347	+	3.79796i	−0.667928	+	0.124140i
$937$	8.00000			0.261349			0.130674	−	0.991425i	$-0.458286\pi$
$937$	8.00000			0.261349			0.130674	+	0.991425i	$0.458286\pi$
$938$		0			0
$939$	16.0000	+	22.6274i	0.522140	+	0.738418i
$940$	−2.24264	+	5.91359i	−0.0731469	+	0.192880i
$941$	12.1244	−	21.0000i	0.395243	−	0.684580i	−0.597889	−	0.801579i	$-0.703994\pi$
$941$	12.1244	−	21.0000i	0.395243	−	0.684580i	0.993132	+	0.116998i	$0.0373272\pi$
$942$	11.9494	−	1.10102i	0.389332	−	0.0358732i
$943$	−6.00000	−	10.3923i	−0.195387	−	0.338420i
$944$	−34.6410			−1.12747
$945$		0			0
$946$	24.0000			0.780307
$947$	−1.73205	−	3.00000i	−0.0562841	−	0.0974869i	0.836511	−	0.547951i	$-0.184592\pi$
$947$	−1.73205	−	3.00000i	−0.0562841	−	0.0974869i	−0.892795	+	0.450464i	$0.851259\pi$
$948$	13.7980	−	1.27135i	0.448137	−	0.0412915i
$949$	16.0000	−	27.7128i	0.519382	−	0.899596i
$950$		0			0
$951$	−13.8564	−	19.5959i	−0.449325	−	0.635441i
$952$		0			0
$953$	−20.7846			−0.673280			−0.336640	−	0.941634i	$-0.609290\pi$
$953$	−20.7846			−0.673280			−0.336640	+	0.941634i	$0.609290\pi$
$954$		0			0
$955$	43.6985	−	7.10228i	1.41405	−	0.229824i
$956$	−2.44949	−	1.41421i	−0.0792222	−	0.0457389i
$957$	−11.5959	+	25.1701i	−0.374843	+	0.813634i
$958$	48.0000			1.55081
$959$		0			0
$960$	3.73205	+	1.03528i	0.120451	+	0.0334134i
$961$	32.5000	+	56.2917i	1.04839	+	1.81586i
$962$		0			0
$963$	−20.2597	−	23.6969i	−0.652859	−	0.763623i
$964$	−8.48528	+	4.89898i	−0.273293	+	0.157786i
$965$	−13.8564	−	16.9706i	−0.446054	−	0.546302i
$966$		0			0
$967$		−	34.2929i		−	1.10278i	−0.834246	−	0.551392i	$-0.814097\pi$
$967$		−	34.2929i		−	1.10278i	0.834246	−	0.551392i	$-0.185903\pi$
$968$	−2.59808	−	4.50000i	−0.0835053	−	0.144635i
$969$		0			0
$970$	4.97056	+	30.5826i	0.159595	+	0.981947i
$971$	10.3923	+	18.0000i	0.333505	+	0.577647i	0.983196	−	0.182550i	$-0.0584353\pi$
$971$	10.3923	+	18.0000i	0.333505	+	0.577647i	−0.649692	+	0.760198i	$0.725102\pi$
$972$	−1.00000	+	15.5563i	−0.0320750	+	0.498970i
$973$		0			0
$974$		−	25.4558i		−	0.815658i
$975$	−27.9280	−	20.4946i	−0.894411	−	0.656352i
$976$	−42.4264	−	24.4949i	−1.35804	−	0.784063i
$977$	−24.2487	+	42.0000i	−0.775785	+	1.34370i	0.158567	+	0.987348i	$0.449313\pi$
$977$	−24.2487	+	42.0000i	−0.775785	+	1.34370i	−0.934352	+	0.356351i	$0.884021\pi$
$978$	−40.0454	−	18.4490i	−1.28051	−	0.589934i
$979$			29.3939i			0.939432i
$980$		0			0
$981$	10.0000	−	28.2843i	0.319275	−	0.903047i
$982$	21.2132	−	12.2474i	0.676941	−	0.390832i
$983$	−2.44949	−	1.41421i	−0.0781266	−	0.0451064i	0.460428	−	0.887697i	$-0.347696\pi$
$983$	−2.44949	−	1.41421i	−0.0781266	−	0.0451064i	−0.538554	+	0.842591i	$0.681029\pi$
$984$	−10.3485	+	0.953512i	−0.329897	+	0.0303968i
$985$		0			0
$986$	−27.7128			−0.882556
$987$		0			0
$988$		0			0
$989$	−14.6969	+	8.48528i	−0.467335	+	0.269816i
$990$	5.84201	−	32.3399i	0.185671	−	1.02783i
$991$	−4.00000	+	6.92820i	−0.127064	+	0.220082i	−0.922538	−	0.385906i	$-0.873889\pi$
$991$	−4.00000	+	6.92820i	−0.127064	+	0.220082i	0.795474	+	0.605988i	$0.207222\pi$
$992$	44.0908	−	25.4558i	1.39988	−	0.808224i
$993$	28.0000	+	39.5980i	0.888553	+	1.25660i
$994$		0			0
$995$		0			0
$996$	−4.44949	−	2.04989i	−0.140987	−	0.0649532i
$997$	26.0000	−	45.0333i	0.823428	−	1.42622i	−0.0796863	−	0.996820i	$-0.525392\pi$
$997$	26.0000	−	45.0333i	0.823428	−	1.42622i	0.903115	−	0.429400i	$-0.141275\pi$
$998$	−3.46410	+	6.00000i	−0.109654	+	0.189927i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.p.c.374.4		8
3.2	odd	2	inner	735.2.p.c.374.1		8
5.4	even	2		735.2.p.a.374.1		8
7.2	even	3	inner	735.2.p.c.509.3		8
7.3	odd	6		105.2.g.c.104.2	yes	4
7.4	even	3		105.2.g.a.104.1	✓	4
7.5	odd	6		735.2.p.a.509.4		8
7.6	odd	2		735.2.p.a.374.3		8
15.14	odd	2		735.2.p.a.374.4		8
21.2	odd	6	inner	735.2.p.c.509.2		8
21.5	even	6		735.2.p.a.509.1		8
21.11	odd	6		105.2.g.a.104.4	yes	4
21.17	even	6		105.2.g.c.104.3	yes	4
21.20	even	2		735.2.p.a.374.2		8
28.3	even	6		1680.2.k.a.209.2		4
28.11	odd	6		1680.2.k.c.209.3		4
35.3	even	12		525.2.b.j.251.6		8
35.4	even	6		105.2.g.c.104.4	yes	4
35.9	even	6		735.2.p.a.509.2		8
35.17	even	12		525.2.b.j.251.3		8
35.18	odd	12		525.2.b.j.251.7		8
35.19	odd	6	inner	735.2.p.c.509.1		8
35.24	odd	6		105.2.g.a.104.3	yes	4
35.32	odd	12		525.2.b.j.251.2		8
35.34	odd	2	inner	735.2.p.c.374.2		8
84.11	even	6		1680.2.k.c.209.2		4
84.59	odd	6		1680.2.k.a.209.3		4
105.17	odd	12		525.2.b.j.251.5		8
105.32	even	12		525.2.b.j.251.8		8
105.38	odd	12		525.2.b.j.251.4		8
105.44	odd	6		735.2.p.a.509.3		8
105.53	even	12		525.2.b.j.251.1		8
105.59	even	6		105.2.g.a.104.2	yes	4
105.74	odd	6		105.2.g.c.104.1	yes	4
105.89	even	6	inner	735.2.p.c.509.4		8
105.104	even	2	inner	735.2.p.c.374.3		8
140.39	odd	6		1680.2.k.a.209.1		4
140.59	even	6		1680.2.k.c.209.4		4
420.59	odd	6		1680.2.k.c.209.1		4
420.179	even	6		1680.2.k.a.209.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.g.a.104.1	✓	4	7.4	even	3
105.2.g.a.104.2	yes	4	105.59	even	6
105.2.g.a.104.3	yes	4	35.24	odd	6
105.2.g.a.104.4	yes	4	21.11	odd	6
105.2.g.c.104.1	yes	4	105.74	odd	6
105.2.g.c.104.2	yes	4	7.3	odd	6
105.2.g.c.104.3	yes	4	21.17	even	6
105.2.g.c.104.4	yes	4	35.4	even	6
525.2.b.j.251.1		8	105.53	even	12
525.2.b.j.251.2		8	35.32	odd	12
525.2.b.j.251.3		8	35.17	even	12
525.2.b.j.251.4		8	105.38	odd	12
525.2.b.j.251.5		8	105.17	odd	12
525.2.b.j.251.6		8	35.3	even	12
525.2.b.j.251.7		8	35.18	odd	12
525.2.b.j.251.8		8	105.32	even	12
735.2.p.a.374.1		8	5.4	even	2
735.2.p.a.374.2		8	21.20	even	2
735.2.p.a.374.3		8	7.6	odd	2
735.2.p.a.374.4		8	15.14	odd	2
735.2.p.a.509.1		8	21.5	even	6
735.2.p.a.509.2		8	35.9	even	6
735.2.p.a.509.3		8	105.44	odd	6
735.2.p.a.509.4		8	7.5	odd	6
735.2.p.c.374.1		8	3.2	odd	2	inner
735.2.p.c.374.2		8	35.34	odd	2	inner
735.2.p.c.374.3		8	105.104	even	2	inner
735.2.p.c.374.4		8	1.1	even	1	trivial
735.2.p.c.509.1		8	35.19	odd	6	inner
735.2.p.c.509.2		8	21.2	odd	6	inner
735.2.p.c.509.3		8	7.2	even	3	inner
735.2.p.c.509.4		8	105.89	even	6	inner
1680.2.k.a.209.1		4	140.39	odd	6
1680.2.k.a.209.2		4	28.3	even	6
1680.2.k.a.209.3		4	84.59	odd	6
1680.2.k.a.209.4		4	420.179	even	6
1680.2.k.c.209.1		4	420.59	odd	6
1680.2.k.c.209.2		4	84.11	even	6
1680.2.k.c.209.3		4	28.11	odd	6
1680.2.k.c.209.4		4	140.59	even	6

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 1.50000i) q^{2} +(1.72474 - 0.158919i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.09077 + 0.792893i) q^{5} +(1.73205 + 2.44949i) q^{6} +1.73205 q^{8} +(2.94949 - 0.548188i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 1.50000i) q^{2} +(1.72474 - 0.158919i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.09077 + 0.792893i) q^{5} +(1.73205 + 2.44949i) q^{6} +1.73205 q^{8} +(2.94949 - 0.548188i) q^{9} +(0.621320 + 3.82282i) q^{10} +(-2.44949 - 1.41421i) q^{11} +(-0.724745 + 1.57313i) q^{12} -4.00000 q^{13} +(3.73205 + 1.03528i) q^{15} +(2.50000 + 4.33013i) q^{16} +(-2.44949 - 1.41421i) q^{17} +(3.37662 + 3.94949i) q^{18} +(-1.73205 + 1.41421i) q^{20} -4.89898i q^{22} +(1.73205 + 3.00000i) q^{23} +(2.98735 - 0.275255i) q^{24} +(3.74264 + 3.31552i) q^{25} +(-3.46410 - 6.00000i) q^{26} +(5.00000 - 1.41421i) q^{27} -5.65685i q^{29} +(1.67914 + 6.49465i) q^{30} +(-8.48528 - 4.89898i) q^{31} +(-2.59808 + 4.50000i) q^{32} +(-4.44949 - 2.04989i) q^{33} -4.89898i q^{34} +(-1.00000 + 2.82843i) q^{36} +(-6.89898 + 0.635674i) q^{39} +(3.62132 + 1.37333i) q^{40} -3.46410 q^{41} +4.89898i q^{43} +(2.44949 - 1.41421i) q^{44} +(6.60136 + 1.19249i) q^{45} +(-3.00000 + 5.19615i) q^{46} +(2.44949 - 1.41421i) q^{47} +(5.00000 + 7.07107i) q^{48} +(-1.73205 + 8.48528i) q^{50} +(-4.44949 - 2.04989i) q^{51} +(2.00000 - 3.46410i) q^{52} +(6.45145 + 6.27526i) q^{54} +(-4.00000 - 4.89898i) q^{55} +(8.48528 - 4.89898i) q^{58} +(-3.46410 + 6.00000i) q^{59} +(-2.76260 + 2.71441i) q^{60} +(-8.48528 + 4.89898i) q^{61} -16.9706i q^{62} +1.00000 q^{64} +(-8.36308 - 3.17157i) q^{65} +(-0.778539 - 8.44949i) q^{66} +(4.24264 + 2.44949i) q^{67} +(2.44949 - 1.41421i) q^{68} +(3.46410 + 4.89898i) q^{69} +2.82843i q^{71} +(5.10867 - 0.949490i) q^{72} +(-4.00000 + 6.92820i) q^{73} +(6.98200 + 5.12364i) q^{75} +(-6.92820 - 9.79796i) q^{78} +(-4.00000 - 6.92820i) q^{79} +(1.79360 + 11.0355i) q^{80} +(8.39898 - 3.23375i) q^{81} +(-3.00000 - 5.19615i) q^{82} +2.82843i q^{83} +(-4.00000 - 4.89898i) q^{85} +(-7.34847 + 4.24264i) q^{86} +(-0.898979 - 9.75663i) q^{87} +(-4.24264 - 2.44949i) q^{88} +(-5.19615 - 9.00000i) q^{89} +(3.92820 + 10.9348i) q^{90} -3.46410 q^{92} +(-15.4135 - 7.10102i) q^{93} +(4.24264 + 2.44949i) q^{94} +(-3.76588 + 8.17423i) q^{96} +8.00000 q^{97} +(-8.00000 - 2.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 4 q^{4} + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 - 4 * q^4 + 4 * q^9	\( 8 q + 4 q^{3} - 4 q^{4} + 4 q^{9} - 12 q^{10} + 4 q^{12} - 32 q^{13} + 16 q^{15} + 20 q^{16} - 4 q^{25} + 40 q^{27} + 12 q^{30} - 16 q^{33} - 8 q^{36} - 16 q^{39} + 12 q^{40} + 16 q^{45} - 24 q^{46} + 40 q^{48} - 16 q^{51} + 16 q^{52} - 32 q^{55} - 8 q^{60} + 8 q^{64} - 32 q^{73} + 4 q^{75} - 32 q^{79} + 28 q^{81} - 24 q^{82} - 32 q^{85} + 32 q^{87} - 24 q^{90} + 64 q^{97} - 64 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 4 * q^4 + 4 * q^9 - 12 * q^10 + 4 * q^12 - 32 * q^13 + 16 * q^15 + 20 * q^16 - 4 * q^25 + 40 * q^27 + 12 * q^30 - 16 * q^33 - 8 * q^36 - 16 * q^39 + 12 * q^40 + 16 * q^45 - 24 * q^46 + 40 * q^48 - 16 * q^51 + 16 * q^52 - 32 * q^55 - 8 * q^60 + 8 * q^64 - 32 * q^73 + 4 * q^75 - 32 * q^79 + 28 * q^81 - 24 * q^82 - 32 * q^85 + 32 * q^87 - 24 * q^90 + 64 * q^97 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more