LMFDB - Embedded newform 450.2.j.c.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(49,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, 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("450.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	450.49
Dual form			450.2.j.c.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.73205i q^{6} +(0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-3.00000 - 5.19615i) q^{11} +(0.866025 + 1.50000i) q^{12} +(-1.73205 - 1.00000i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.59808 + 1.50000i) q^{18} +4.00000 q^{19} +1.73205i q^{21} +(5.19615 + 3.00000i) q^{22} +(-7.79423 - 4.50000i) q^{23} +(-1.50000 - 0.866025i) q^{24} +2.00000 q^{26} +5.19615 q^{27} -1.00000i q^{28} +(1.50000 + 2.59808i) q^{29} +(2.00000 - 3.46410i) q^{31} +(0.866025 + 0.500000i) q^{32} +10.3923 q^{33} -3.00000 q^{36} -8.00000i q^{37} +(-3.46410 + 2.00000i) q^{38} +(3.00000 - 1.73205i) q^{39} +(1.50000 - 2.59808i) q^{41} +(-0.866025 - 1.50000i) q^{42} +(6.92820 - 4.00000i) q^{43} -6.00000 q^{44} +9.00000 q^{46} +(2.59808 - 1.50000i) q^{47} +1.73205 q^{48} +(-3.00000 + 5.19615i) q^{49} +(-1.73205 + 1.00000i) q^{52} +6.00000i q^{53} +(-4.50000 + 2.59808i) q^{54} +(0.500000 + 0.866025i) q^{56} +(-3.46410 + 6.00000i) q^{57} +(-2.59808 - 1.50000i) q^{58} +(3.00000 - 5.19615i) q^{59} +(6.50000 + 11.2583i) q^{61} +4.00000i q^{62} +(-2.59808 - 1.50000i) q^{63} -1.00000 q^{64} +(-9.00000 + 5.19615i) q^{66} +(-11.2583 - 6.50000i) q^{67} +(13.5000 - 7.79423i) q^{69} -6.00000 q^{71} +(2.59808 - 1.50000i) q^{72} -4.00000i q^{73} +(4.00000 + 6.92820i) q^{74} +(2.00000 - 3.46410i) q^{76} +(-5.19615 - 3.00000i) q^{77} +(-1.73205 + 3.00000i) q^{78} +(-5.00000 - 8.66025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +3.00000i q^{82} +(-7.79423 + 4.50000i) q^{83} +(1.50000 + 0.866025i) q^{84} +(-4.00000 + 6.92820i) q^{86} -5.19615 q^{87} +(5.19615 - 3.00000i) q^{88} -9.00000 q^{89} -2.00000 q^{91} +(-7.79423 + 4.50000i) q^{92} +(3.46410 + 6.00000i) q^{93} +(-1.50000 + 2.59808i) q^{94} +(-1.50000 + 0.866025i) q^{96} +(-1.73205 + 1.00000i) q^{97} -6.00000i q^{98} +(-9.00000 + 15.5885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 6 q^{9} - 12 q^{11} - 2 q^{14} - 2 q^{16} + 16 q^{19} - 6 q^{24} + 8 q^{26} + 6 q^{29} + 8 q^{31} - 12 q^{36} + 12 q^{39} + 6 q^{41} - 24 q^{44} + 36 q^{46} - 12 q^{49} - 18 q^{54} + 2 q^{56}+ \cdots - 36 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 6 * q^9 - 12 * q^11 - 2 * q^14 - 2 * q^16 + 16 * q^19 - 6 * q^24 + 8 * q^26 + 6 * q^29 + 8 * q^31 - 12 * q^36 + 12 * q^39 + 6 * q^41 - 24 * q^44 + 36 * q^46 - 12 * q^49 - 18 * q^54 + 2 * q^56 + 12 * q^59 + 26 * q^61 - 4 * q^64 - 36 * q^66 + 54 * q^69 - 24 * q^71 + 16 * q^74 + 8 * q^76 - 20 * q^79 - 18 * q^81 + 6 * q^84 - 16 * q^86 - 36 * q^89 - 8 * q^91 - 6 * q^94 - 6 * q^96 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		−	1.73205i		−	0.707107i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i	−0.327327	−	0.944911i	$-0.606148\pi$
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i	0.654654	+	0.755929i	$0.272814\pi$
$8$			1.00000i			0.353553i
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$		0			0
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.821541	−	0.570149i	$-0.806886\pi$
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.0829925	−	0.996550i	$-0.526448\pi$
$12$	0.866025	+	1.50000i	0.250000	+	0.433013i
$13$	−1.73205	−	1.00000i	−0.480384	−	0.277350i	0.240192	−	0.970725i	$-0.422790\pi$
$13$	−1.73205	−	1.00000i	−0.480384	−	0.277350i	−0.720577	+	0.693375i	$0.756123\pi$
$14$	−0.500000	+	0.866025i	−0.133631	+	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$	2.59808	+	1.50000i	0.612372	+	0.353553i
$19$	4.00000			0.917663			0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000			0.917663			0.458831	+	0.888523i	$0.348268\pi$
$20$		0			0
$21$			1.73205i			0.377964i
$22$	5.19615	+	3.00000i	1.10782	+	0.639602i
$23$	−7.79423	−	4.50000i	−1.62521	−	0.938315i	−0.985496	−	0.169701i	$-0.945720\pi$
$23$	−7.79423	−	4.50000i	−1.62521	−	0.938315i	−0.639713	−	0.768613i	$-0.720947\pi$
$24$	−1.50000	−	0.866025i	−0.306186	−	0.176777i
$25$		0			0
$26$	2.00000			0.392232
$27$	5.19615			1.00000
$28$		−	1.00000i		−	0.188982i
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$		0			0
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	10.3923			1.80907
$34$		0			0
$35$		0			0
$36$	−3.00000			−0.500000
$37$		−	8.00000i		−	1.31519i	−0.753371	−	0.657596i	$-0.771573\pi$
$37$		−	8.00000i		−	1.31519i	0.753371	−	0.657596i	$-0.228427\pi$
$38$	−3.46410	+	2.00000i	−0.561951	+	0.324443i
$39$	3.00000	−	1.73205i	0.480384	−	0.277350i
$40$		0			0
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$	−0.866025	−	1.50000i	−0.133631	−	0.231455i
$43$	6.92820	−	4.00000i	1.05654	−	0.609994i	0.132068	−	0.991241i	$-0.457838\pi$
$43$	6.92820	−	4.00000i	1.05654	−	0.609994i	0.924473	+	0.381246i	$0.124505\pi$
$44$	−6.00000			−0.904534
$45$		0			0
$46$	9.00000			1.32698
$47$	2.59808	−	1.50000i	0.378968	−	0.218797i	−0.298401	−	0.954441i	$-0.596453\pi$
$47$	2.59808	−	1.50000i	0.378968	−	0.218797i	0.677369	+	0.735643i	$0.263120\pi$
$48$	1.73205			0.250000
$49$	−3.00000	+	5.19615i	−0.428571	+	0.742307i
$50$		0			0
$51$		0			0
$52$	−1.73205	+	1.00000i	−0.240192	+	0.138675i
$53$			6.00000i			0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$			6.00000i			0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$	−4.50000	+	2.59808i	−0.612372	+	0.353553i
$55$		0			0
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$	−3.46410	+	6.00000i	−0.458831	+	0.794719i
$58$	−2.59808	−	1.50000i	−0.341144	−	0.196960i
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	0.992524	+	0.122047i	$0.0389457\pi$
$60$		0			0
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	0.896258	+	0.443533i	$0.146275\pi$
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$			4.00000i			0.508001i
$63$	−2.59808	−	1.50000i	−0.327327	−	0.188982i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−9.00000	+	5.19615i	−1.10782	+	0.639602i
$67$	−11.2583	−	6.50000i	−1.37542	−	0.794101i	−0.383819	−	0.923408i	$-0.625391\pi$
$67$	−11.2583	−	6.50000i	−1.37542	−	0.794101i	−0.991605	+	0.129307i	$0.958725\pi$
$68$		0			0
$69$	13.5000	−	7.79423i	1.62521	−	0.938315i
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	2.59808	−	1.50000i	0.306186	−	0.176777i
$73$		−	4.00000i		−	0.468165i	−0.972217	−	0.234082i	$-0.924791\pi$
$73$		−	4.00000i		−	0.468165i	0.972217	−	0.234082i	$-0.0752085\pi$
$74$	4.00000	+	6.92820i	0.464991	+	0.805387i
$75$		0			0
$76$	2.00000	−	3.46410i	0.229416	−	0.397360i
$77$	−5.19615	−	3.00000i	−0.592157	−	0.341882i
$78$	−1.73205	+	3.00000i	−0.196116	+	0.339683i
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	−0.997274	−	0.0737937i	$-0.976489\pi$
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	0.434730	−	0.900561i	$-0.356844\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$			3.00000i			0.331295i
$83$	−7.79423	+	4.50000i	−0.855528	+	0.493939i	−0.862512	−	0.506036i	$-0.831110\pi$
$83$	−7.79423	+	4.50000i	−0.855528	+	0.493939i	0.00698436	+	0.999976i	$0.497777\pi$
$84$	1.50000	+	0.866025i	0.163663	+	0.0944911i
$85$		0			0
$86$	−4.00000	+	6.92820i	−0.431331	+	0.747087i
$87$	−5.19615			−0.557086
$88$	5.19615	−	3.00000i	0.553912	−	0.319801i
$89$	−9.00000			−0.953998			−0.476999	−	0.878904i	$-0.658275\pi$
$89$	−9.00000			−0.953998			−0.476999	+	0.878904i	$0.658275\pi$
$90$		0			0
$91$	−2.00000			−0.209657
$92$	−7.79423	+	4.50000i	−0.812605	+	0.469157i
$93$	3.46410	+	6.00000i	0.359211	+	0.622171i
$94$	−1.50000	+	2.59808i	−0.154713	+	0.267971i
$95$		0			0
$96$	−1.50000	+	0.866025i	−0.153093	+	0.0883883i
$97$	−1.73205	+	1.00000i	−0.175863	+	0.101535i	−0.585348	−	0.810782i	$-0.699042\pi$
$97$	−1.73205	+	1.00000i	−0.175863	+	0.101535i	0.409484	+	0.912317i	$0.365709\pi$
$98$		−	6.00000i		−	0.606092i
$99$	−9.00000	+	15.5885i	−0.904534	+	1.56670i
$100$		0			0
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$		0			0
$103$	−6.92820	−	4.00000i	−0.682656	−	0.394132i	0.118199	−	0.992990i	$-0.462288\pi$
$103$	−6.92820	−	4.00000i	−0.682656	−	0.394132i	−0.800855	+	0.598858i	$0.795621\pi$
$104$	1.00000	−	1.73205i	0.0980581	−	0.169842i
$105$		0			0
$106$	−3.00000	−	5.19615i	−0.291386	−	0.504695i
$107$			3.00000i			0.290021i	0.989430	+	0.145010i	$0.0463216\pi$
$107$			3.00000i			0.290021i	−0.989430	+	0.145010i	$0.953678\pi$
$108$	2.59808	−	4.50000i	0.250000	−	0.433013i
$109$	7.00000			0.670478			0.335239	−	0.942133i	$-0.391183\pi$
$109$	7.00000			0.670478			0.335239	+	0.942133i	$0.391183\pi$
$110$		0			0
$111$	12.0000	+	6.92820i	1.13899	+	0.657596i
$112$	−0.866025	−	0.500000i	−0.0818317	−	0.0472456i
$113$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$113$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$114$		−	6.92820i		−	0.648886i
$115$		0			0
$116$	3.00000			0.278543
$117$			6.00000i			0.554700i
$118$			6.00000i			0.552345i
$119$		0			0
$120$		0			0
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$	−11.2583	−	6.50000i	−1.01928	−	0.588482i
$123$	2.59808	+	4.50000i	0.234261	+	0.405751i
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$		0			0
$126$	3.00000			0.267261
$127$			7.00000i			0.621150i	0.950549	+	0.310575i	$0.100522\pi$
$127$			7.00000i			0.621150i	−0.950549	+	0.310575i	$0.899478\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$			13.8564i			1.21999i
$130$		0			0
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	−0.141865	−	0.989886i	$-0.545310\pi$
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	0.928199	−	0.372084i	$-0.121357\pi$
$132$	5.19615	−	9.00000i	0.452267	−	0.783349i
$133$	3.46410	−	2.00000i	0.300376	−	0.173422i
$134$	13.0000			1.12303
$135$		0			0
$136$		0			0
$137$	10.3923	−	6.00000i	0.887875	−	0.512615i	0.0146279	−	0.999893i	$-0.495344\pi$
$137$	10.3923	−	6.00000i	0.887875	−	0.512615i	0.873247	+	0.487278i	$0.162010\pi$
$138$	−7.79423	+	13.5000i	−0.663489	+	1.14920i
$139$	−8.00000	+	13.8564i	−0.678551	+	1.17529i	0.296866	+	0.954919i	$0.404058\pi$
$139$	−8.00000	+	13.8564i	−0.678551	+	1.17529i	−0.975417	+	0.220366i	$0.929275\pi$
$140$		0			0
$141$			5.19615i			0.437595i
$142$	5.19615	−	3.00000i	0.436051	−	0.251754i
$143$			12.0000i			1.00349i
$144$	−1.50000	+	2.59808i	−0.125000	+	0.216506i
$145$		0			0
$146$	2.00000	+	3.46410i	0.165521	+	0.286691i
$147$	−5.19615	−	9.00000i	−0.428571	−	0.742307i
$148$	−6.92820	−	4.00000i	−0.569495	−	0.328798i
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	−0.920904	−	0.389789i	$-0.872548\pi$
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	0.798019	+	0.602632i	$0.205881\pi$
$150$		0			0
$151$	−7.00000	−	12.1244i	−0.569652	−	0.986666i	−0.996600	−	0.0823900i	$-0.973745\pi$
$151$	−7.00000	−	12.1244i	−0.569652	−	0.986666i	0.426948	−	0.904276i	$-0.359589\pi$
$152$			4.00000i			0.324443i
$153$		0			0
$154$	6.00000			0.483494
$155$		0			0
$156$		−	3.46410i		−	0.277350i
$157$	12.1244	+	7.00000i	0.967629	+	0.558661i	0.898513	−	0.438948i	$-0.144649\pi$
$157$	12.1244	+	7.00000i	0.967629	+	0.558661i	0.0691164	+	0.997609i	$0.477982\pi$
$158$	8.66025	+	5.00000i	0.688973	+	0.397779i
$159$	−9.00000	−	5.19615i	−0.713746	−	0.412082i
$160$		0			0
$161$	−9.00000			−0.709299
$162$		−	9.00000i		−	0.707107i
$163$		−	4.00000i		−	0.313304i	−0.987654	−	0.156652i	$-0.949930\pi$
$163$		−	4.00000i		−	0.313304i	0.987654	−	0.156652i	$-0.0500701\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$		0			0
$166$	4.50000	−	7.79423i	0.349268	−	0.604949i
$167$	−2.59808	−	1.50000i	−0.201045	−	0.116073i	0.396098	−	0.918208i	$-0.370364\pi$
$167$	−2.59808	−	1.50000i	−0.201045	−	0.116073i	−0.597143	+	0.802135i	$0.703697\pi$
$168$	−1.73205			−0.133631
$169$	−4.50000	−	7.79423i	−0.346154	−	0.599556i
$170$		0			0
$171$	−6.00000	−	10.3923i	−0.458831	−	0.794719i
$172$		−	8.00000i		−	0.609994i
$173$	20.7846	−	12.0000i	1.58022	−	0.912343i	0.585399	−	0.810745i	$-0.300938\pi$
$173$	20.7846	−	12.0000i	1.58022	−	0.912343i	0.994826	−	0.101598i	$-0.0323955\pi$
$174$	4.50000	−	2.59808i	0.341144	−	0.196960i
$175$		0			0
$176$	−3.00000	+	5.19615i	−0.226134	+	0.391675i
$177$	5.19615	+	9.00000i	0.390567	+	0.676481i
$178$	7.79423	−	4.50000i	0.584202	−	0.337289i
$179$	18.0000			1.34538			0.672692	−	0.739923i	$-0.265138\pi$
$179$	18.0000			1.34538			0.672692	+	0.739923i	$0.265138\pi$
$180$		0			0
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$	1.73205	−	1.00000i	0.128388	−	0.0741249i
$183$	−22.5167			−1.66448
$184$	4.50000	−	7.79423i	0.331744	−	0.574598i
$185$		0			0
$186$	−6.00000	−	3.46410i	−0.439941	−	0.254000i
$187$		0			0
$188$		−	3.00000i		−	0.218797i
$189$	4.50000	−	2.59808i	0.327327	−	0.188982i
$190$		0			0
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	0.997225	−	0.0744412i	$-0.0237173\pi$
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	−0.563081	+	0.826402i	$0.690384\pi$
$192$	0.866025	−	1.50000i	0.0625000	−	0.108253i
$193$	−1.73205	−	1.00000i	−0.124676	−	0.0719816i	0.436365	−	0.899770i	$-0.356266\pi$
$193$	−1.73205	−	1.00000i	−0.124676	−	0.0719816i	−0.561041	+	0.827788i	$0.689599\pi$
$194$	1.00000	−	1.73205i	0.0717958	−	0.124354i
$195$		0			0
$196$	3.00000	+	5.19615i	0.214286	+	0.371154i
$197$			12.0000i			0.854965i	0.904024	+	0.427482i	$0.140599\pi$
$197$			12.0000i			0.854965i	−0.904024	+	0.427482i	$0.859401\pi$
$198$		−	18.0000i		−	1.27920i
$199$	−8.00000			−0.567105			−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000			−0.567105			−0.283552	+	0.958957i	$0.591513\pi$
$200$		0			0
$201$	19.5000	−	11.2583i	1.37542	−	0.794101i
$202$	5.19615	+	3.00000i	0.365600	+	0.211079i
$203$	2.59808	+	1.50000i	0.182349	+	0.105279i
$204$		0			0
$205$		0			0
$206$	8.00000			0.557386
$207$			27.0000i			1.87663i
$208$			2.00000i			0.138675i
$209$	−12.0000	−	20.7846i	−0.830057	−	1.43770i
$210$		0			0
$211$	−1.00000	+	1.73205i	−0.0688428	+	0.119239i	−0.898392	−	0.439194i	$-0.855264\pi$
$211$	−1.00000	+	1.73205i	−0.0688428	+	0.119239i	0.829549	+	0.558433i	$0.188597\pi$
$212$	5.19615	+	3.00000i	0.356873	+	0.206041i
$213$	5.19615	−	9.00000i	0.356034	−	0.616670i
$214$	−1.50000	−	2.59808i	−0.102538	−	0.177601i
$215$		0			0
$216$			5.19615i			0.353553i
$217$		−	4.00000i		−	0.271538i
$218$	−6.06218	+	3.50000i	−0.410582	+	0.237050i
$219$	6.00000	+	3.46410i	0.405442	+	0.234082i
$220$		0			0
$221$		0			0
$222$	−13.8564			−0.929981
$223$	−0.866025	+	0.500000i	−0.0579934	+	0.0334825i	−0.528716	−	0.848799i	$-0.677326\pi$
$223$	−0.866025	+	0.500000i	−0.0579934	+	0.0334825i	0.470723	+	0.882281i	$0.343993\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$		0			0
$227$	10.3923	−	6.00000i	0.689761	−	0.398234i	−0.113761	−	0.993508i	$-0.536290\pi$
$227$	10.3923	−	6.00000i	0.689761	−	0.398234i	0.803523	+	0.595274i	$0.202957\pi$
$228$	3.46410	+	6.00000i	0.229416	+	0.397360i
$229$	−6.50000	+	11.2583i	−0.429532	+	0.743971i	−0.996832	−	0.0795401i	$-0.974655\pi$
$229$	−6.50000	+	11.2583i	−0.429532	+	0.743971i	0.567300	+	0.823511i	$0.307988\pi$
$230$		0			0
$231$	9.00000	−	5.19615i	0.592157	−	0.341882i
$232$	−2.59808	+	1.50000i	−0.170572	+	0.0984798i
$233$		−	12.0000i		−	0.786146i	−0.919507	−	0.393073i	$-0.871412\pi$
$233$		−	12.0000i		−	0.786146i	0.919507	−	0.393073i	$-0.128588\pi$
$234$	−3.00000	−	5.19615i	−0.196116	−	0.339683i
$235$		0			0
$236$	−3.00000	−	5.19615i	−0.195283	−	0.338241i
$237$	17.3205			1.12509
$238$		0			0
$239$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$239$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$240$		0			0
$241$	−14.5000	−	25.1147i	−0.934027	−	1.61778i	−0.776360	−	0.630290i	$-0.782936\pi$
$241$	−14.5000	−	25.1147i	−0.934027	−	1.61778i	−0.157667	−	0.987492i	$-0.550397\pi$
$242$		−	25.0000i		−	1.60706i
$243$	−7.79423	−	13.5000i	−0.500000	−	0.866025i
$244$	13.0000			0.832240
$245$		0			0
$246$	−4.50000	−	2.59808i	−0.286910	−	0.165647i
$247$	−6.92820	−	4.00000i	−0.440831	−	0.254514i
$248$	3.46410	+	2.00000i	0.219971	+	0.127000i
$249$		−	15.5885i		−	0.987878i
$250$		0			0
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$	−2.59808	+	1.50000i	−0.163663	+	0.0944911i
$253$			54.0000i			3.39495i
$254$	−3.50000	−	6.06218i	−0.219610	−	0.380375i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	15.5885	+	9.00000i	0.972381	+	0.561405i	0.899961	−	0.435970i	$-0.143595\pi$
$257$	15.5885	+	9.00000i	0.972381	+	0.561405i	0.0724199	+	0.997374i	$0.476928\pi$
$258$	−6.92820	−	12.0000i	−0.431331	−	0.747087i
$259$	−4.00000	−	6.92820i	−0.248548	−	0.430498i
$260$		0			0
$261$	4.50000	−	7.79423i	0.278543	−	0.482451i
$262$			18.0000i			1.11204i
$263$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$263$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$264$			10.3923i			0.639602i
$265$		0			0
$266$	−2.00000	+	3.46410i	−0.122628	+	0.212398i
$267$	7.79423	−	13.5000i	0.476999	−	0.826187i
$268$	−11.2583	+	6.50000i	−0.687712	+	0.397051i
$269$	−21.0000			−1.28039			−0.640196	−	0.768211i	$-0.721147\pi$
$269$	−21.0000			−1.28039			−0.640196	+	0.768211i	$0.721147\pi$
$270$		0			0
$271$	−4.00000			−0.242983			−0.121491	−	0.992592i	$-0.538768\pi$
$271$	−4.00000			−0.242983			−0.121491	+	0.992592i	$0.538768\pi$
$272$		0			0
$273$	1.73205	−	3.00000i	0.104828	−	0.181568i
$274$	−6.00000	+	10.3923i	−0.362473	+	0.627822i
$275$		0			0
$276$		−	15.5885i		−	0.938315i
$277$	−6.92820	+	4.00000i	−0.416275	+	0.240337i	−0.693482	−	0.720473i	$-0.743925\pi$
$277$	−6.92820	+	4.00000i	−0.416275	+	0.240337i	0.277207	+	0.960810i	$0.410591\pi$
$278$		−	16.0000i		−	0.959616i
$279$	−12.0000			−0.718421
$280$		0			0
$281$	7.50000	+	12.9904i	0.447412	+	0.774941i	0.998217	−	0.0596933i	$-0.0190123\pi$
$281$	7.50000	+	12.9904i	0.447412	+	0.774941i	−0.550804	+	0.834634i	$0.685679\pi$
$282$	−2.59808	−	4.50000i	−0.154713	−	0.267971i
$283$	11.2583	+	6.50000i	0.669238	+	0.386385i	0.795788	−	0.605575i	$-0.207057\pi$
$283$	11.2583	+	6.50000i	0.669238	+	0.386385i	−0.126550	+	0.991960i	$0.540390\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$	−6.00000	−	10.3923i	−0.354787	−	0.614510i
$287$		−	3.00000i		−	0.177084i
$288$		−	3.00000i		−	0.176777i
$289$	17.0000			1.00000
$290$		0			0
$291$		−	3.46410i		−	0.203069i
$292$	−3.46410	−	2.00000i	−0.202721	−	0.117041i
$293$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$293$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$294$	9.00000	+	5.19615i	0.524891	+	0.303046i
$295$		0			0
$296$	8.00000			0.464991
$297$	−15.5885	−	27.0000i	−0.904534	−	1.56670i
$298$		−	3.00000i		−	0.173785i
$299$	9.00000	+	15.5885i	0.520483	+	0.901504i
$300$		0			0
$301$	4.00000	−	6.92820i	0.230556	−	0.399335i
$302$	12.1244	+	7.00000i	0.697678	+	0.402805i
$303$	10.3923			0.597022
$304$	−2.00000	−	3.46410i	−0.114708	−	0.198680i
$305$		0			0
$306$		0			0
$307$			7.00000i			0.399511i	0.979846	+	0.199756i	$0.0640148\pi$
$307$			7.00000i			0.399511i	−0.979846	+	0.199756i	$0.935985\pi$
$308$	−5.19615	+	3.00000i	−0.296078	+	0.170941i
$309$	12.0000	−	6.92820i	0.682656	−	0.394132i
$310$		0			0
$311$	−6.00000	+	10.3923i	−0.340229	+	0.589294i	−0.984475	−	0.175525i	$-0.943838\pi$
$311$	−6.00000	+	10.3923i	−0.340229	+	0.589294i	0.644246	+	0.764818i	$0.277171\pi$
$312$	1.73205	+	3.00000i	0.0980581	+	0.169842i
$313$	1.73205	−	1.00000i	0.0979013	−	0.0565233i	−0.450250	−	0.892903i	$-0.648665\pi$
$313$	1.73205	−	1.00000i	0.0979013	−	0.0565233i	0.548151	+	0.836379i	$0.315332\pi$
$314$	−14.0000			−0.790066
$315$		0			0
$316$	−10.0000			−0.562544
$317$	5.19615	−	3.00000i	0.291845	−	0.168497i	−0.346929	−	0.937892i	$-0.612775\pi$
$317$	5.19615	−	3.00000i	0.291845	−	0.168497i	0.638774	+	0.769395i	$0.279442\pi$
$318$	10.3923			0.582772
$319$	9.00000	−	15.5885i	0.503903	−	0.872786i
$320$		0			0
$321$	−4.50000	−	2.59808i	−0.251166	−	0.145010i
$322$	7.79423	−	4.50000i	0.434355	−	0.250775i
$323$		0			0
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$		0			0
$326$	2.00000	+	3.46410i	0.110770	+	0.191859i
$327$	−6.06218	+	10.5000i	−0.335239	+	0.580651i
$328$	2.59808	+	1.50000i	0.143455	+	0.0828236i
$329$	1.50000	−	2.59808i	0.0826977	−	0.143237i
$330$		0			0
$331$	5.00000	+	8.66025i	0.274825	+	0.476011i	0.970091	−	0.242742i	$-0.0780468\pi$
$331$	5.00000	+	8.66025i	0.274825	+	0.476011i	−0.695266	+	0.718752i	$0.744713\pi$
$332$			9.00000i			0.493939i
$333$	−20.7846	+	12.0000i	−1.13899	+	0.657596i
$334$	3.00000			0.164153
$335$		0			0
$336$	1.50000	−	0.866025i	0.0818317	−	0.0472456i
$337$	6.92820	+	4.00000i	0.377403	+	0.217894i	0.676688	−	0.736270i	$-0.263415\pi$
$337$	6.92820	+	4.00000i	0.377403	+	0.217894i	−0.299285	+	0.954164i	$0.596748\pi$
$338$	7.79423	+	4.50000i	0.423950	+	0.244768i
$339$		0			0
$340$		0			0
$341$	−24.0000			−1.29967
$342$	10.3923	+	6.00000i	0.561951	+	0.324443i
$343$			13.0000i			0.701934i
$344$	4.00000	+	6.92820i	0.215666	+	0.373544i
$345$		0			0
$346$	−12.0000	+	20.7846i	−0.645124	+	1.11739i
$347$	10.3923	+	6.00000i	0.557888	+	0.322097i	0.752297	−	0.658824i	$-0.228946\pi$
$347$	10.3923	+	6.00000i	0.557888	+	0.322097i	−0.194409	+	0.980921i	$0.562279\pi$
$348$	−2.59808	+	4.50000i	−0.139272	+	0.241225i
$349$	11.5000	+	19.9186i	0.615581	+	1.06622i	0.990282	+	0.139072i	$0.0444119\pi$
$349$	11.5000	+	19.9186i	0.615581	+	1.06622i	−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$	−9.00000	−	5.19615i	−0.480384	−	0.277350i
$352$		−	6.00000i		−	0.319801i
$353$	20.7846	−	12.0000i	1.10625	−	0.638696i	0.168397	−	0.985719i	$-0.446141\pi$
$353$	20.7846	−	12.0000i	1.10625	−	0.638696i	0.937856	+	0.347024i	$0.112808\pi$
$354$	−9.00000	−	5.19615i	−0.478345	−	0.276172i
$355$		0			0
$356$	−4.50000	+	7.79423i	−0.238500	+	0.413093i
$357$		0			0
$358$	−15.5885	+	9.00000i	−0.823876	+	0.475665i
$359$	12.0000			0.633336			0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000			0.633336			0.316668	+	0.948536i	$0.397436\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$	−4.33013	+	2.50000i	−0.227586	+	0.131397i
$363$	−21.6506	−	37.5000i	−1.13636	−	1.96824i
$364$	−1.00000	+	1.73205i	−0.0524142	+	0.0907841i
$365$		0			0
$366$	19.5000	−	11.2583i	1.01928	−	0.588482i
$367$	−6.92820	+	4.00000i	−0.361649	+	0.208798i	−0.669804	−	0.742538i	$-0.733622\pi$
$367$	−6.92820	+	4.00000i	−0.361649	+	0.208798i	0.308155	+	0.951336i	$0.400289\pi$
$368$			9.00000i			0.469157i
$369$	−9.00000			−0.468521
$370$		0			0
$371$	3.00000	+	5.19615i	0.155752	+	0.269771i
$372$	6.92820			0.359211
$373$	−22.5167	−	13.0000i	−1.16587	−	0.673114i	−0.213165	−	0.977016i	$-0.568377\pi$
$373$	−22.5167	−	13.0000i	−1.16587	−	0.673114i	−0.952703	+	0.303902i	$0.901711\pi$
$374$		0			0
$375$		0			0
$376$	1.50000	+	2.59808i	0.0773566	+	0.133986i
$377$		−	6.00000i		−	0.309016i
$378$	−2.59808	+	4.50000i	−0.133631	+	0.231455i
$379$	22.0000			1.13006			0.565032	−	0.825069i	$-0.308864\pi$
$379$	22.0000			1.13006			0.565032	+	0.825069i	$0.308864\pi$
$380$		0			0
$381$	−10.5000	−	6.06218i	−0.537931	−	0.310575i
$382$	−10.3923	−	6.00000i	−0.531717	−	0.306987i
$383$	10.3923	+	6.00000i	0.531022	+	0.306586i	0.741433	−	0.671027i	$-0.234147\pi$
$383$	10.3923	+	6.00000i	0.531022	+	0.306586i	−0.210411	+	0.977613i	$0.567480\pi$
$384$			1.73205i			0.0883883i
$385$		0			0
$386$	2.00000			0.101797
$387$	−20.7846	−	12.0000i	−1.05654	−	0.609994i
$388$			2.00000i			0.101535i
$389$	10.5000	+	18.1865i	0.532371	+	0.922094i	0.999286	+	0.0377914i	$0.0120322\pi$
$389$	10.5000	+	18.1865i	0.532371	+	0.922094i	−0.466915	+	0.884302i	$0.654634\pi$
$390$		0			0
$391$		0			0
$392$	−5.19615	−	3.00000i	−0.262445	−	0.151523i
$393$	15.5885	+	27.0000i	0.786334	+	1.36197i
$394$	−6.00000	−	10.3923i	−0.302276	−	0.523557i
$395$		0			0
$396$	9.00000	+	15.5885i	0.452267	+	0.783349i
$397$		−	2.00000i		−	0.100377i	−0.998740	−	0.0501886i	$-0.984018\pi$
$397$		−	2.00000i		−	0.100377i	0.998740	−	0.0501886i	$-0.0159822\pi$
$398$	6.92820	−	4.00000i	0.347279	−	0.200502i
$399$			6.92820i			0.346844i
$400$		0			0
$401$	−3.00000	+	5.19615i	−0.149813	+	0.259483i	−0.931158	−	0.364615i	$-0.881200\pi$
$401$	−3.00000	+	5.19615i	−0.149813	+	0.259483i	0.781345	+	0.624099i	$0.214534\pi$
$402$	−11.2583	+	19.5000i	−0.561514	+	0.972572i
$403$	−6.92820	+	4.00000i	−0.345118	+	0.199254i
$404$	−6.00000			−0.298511
$405$		0			0
$406$	−3.00000			−0.148888
$407$	−41.5692	+	24.0000i	−2.06051	+	1.18964i
$408$		0			0
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	−0.962757	−	0.270367i	$-0.912855\pi$
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	0.715523	+	0.698589i	$0.246188\pi$
$410$		0			0
$411$			20.7846i			1.02523i
$412$	−6.92820	+	4.00000i	−0.341328	+	0.197066i
$413$		−	6.00000i		−	0.295241i
$414$	−13.5000	−	23.3827i	−0.663489	−	1.14920i
$415$		0			0
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$	−13.8564	−	24.0000i	−0.678551	−	1.17529i
$418$	20.7846	+	12.0000i	1.01661	+	0.586939i
$419$	−15.0000	+	25.9808i	−0.732798	+	1.26924i	0.222885	+	0.974845i	$0.428453\pi$
$419$	−15.0000	+	25.9808i	−0.732798	+	1.26924i	−0.955683	+	0.294398i	$0.904881\pi$
$420$		0			0
$421$	11.0000	+	19.0526i	0.536107	+	0.928565i	0.999109	+	0.0422075i	$0.0134391\pi$
$421$	11.0000	+	19.0526i	0.536107	+	0.928565i	−0.463002	+	0.886357i	$0.653228\pi$
$422$		−	2.00000i		−	0.0973585i
$423$	−7.79423	−	4.50000i	−0.378968	−	0.218797i
$424$	−6.00000			−0.291386
$425$		0			0
$426$			10.3923i			0.503509i
$427$	11.2583	+	6.50000i	0.544829	+	0.314557i
$428$	2.59808	+	1.50000i	0.125583	+	0.0725052i
$429$	−18.0000	−	10.3923i	−0.869048	−	0.501745i
$430$		0			0
$431$	6.00000			0.289010			0.144505	−	0.989504i	$-0.453841\pi$
$431$	6.00000			0.289010			0.144505	+	0.989504i	$0.453841\pi$
$432$	−2.59808	−	4.50000i	−0.125000	−	0.216506i
$433$		−	16.0000i		−	0.768911i	−0.923144	−	0.384455i	$-0.874389\pi$
$433$		−	16.0000i		−	0.768911i	0.923144	−	0.384455i	$-0.125611\pi$
$434$	2.00000	+	3.46410i	0.0960031	+	0.166282i
$435$		0			0
$436$	3.50000	−	6.06218i	0.167620	−	0.290326i
$437$	−31.1769	−	18.0000i	−1.49139	−	0.861057i
$438$	−6.92820			−0.331042
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	0.310228	−	0.950662i	$-0.399595\pi$
$440$		0			0
$441$	18.0000			0.857143
$442$		0			0
$443$	7.79423	−	4.50000i	0.370315	−	0.213801i	−0.303281	−	0.952901i	$-0.598082\pi$
$443$	7.79423	−	4.50000i	0.370315	−	0.213801i	0.673596	+	0.739100i	$0.264749\pi$
$444$	12.0000	−	6.92820i	0.569495	−	0.328798i
$445$		0			0
$446$	0.500000	−	0.866025i	0.0236757	−	0.0410075i
$447$	−2.59808	−	4.50000i	−0.122885	−	0.212843i
$448$	−0.866025	+	0.500000i	−0.0409159	+	0.0236228i
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$		0			0
$451$	−18.0000			−0.847587
$452$		0			0
$453$	24.2487			1.13930
$454$	−6.00000	+	10.3923i	−0.281594	+	0.487735i
$455$		0			0
$456$	−6.00000	−	3.46410i	−0.280976	−	0.162221i
$457$	−6.92820	+	4.00000i	−0.324088	+	0.187112i	−0.653213	−	0.757174i	$-0.726579\pi$
$457$	−6.92820	+	4.00000i	−0.324088	+	0.187112i	0.329125	+	0.944286i	$0.393246\pi$
$458$		−	13.0000i		−	0.607450i
$459$		0			0
$460$		0			0
$461$	13.5000	+	23.3827i	0.628758	+	1.08904i	0.987801	+	0.155719i	$0.0497696\pi$
$461$	13.5000	+	23.3827i	0.628758	+	1.08904i	−0.359044	+	0.933321i	$0.616897\pi$
$462$	−5.19615	+	9.00000i	−0.241747	+	0.418718i
$463$	3.46410	+	2.00000i	0.160990	+	0.0929479i	0.578331	−	0.815802i	$-0.303704\pi$
$463$	3.46410	+	2.00000i	0.160990	+	0.0929479i	−0.417340	+	0.908750i	$0.637038\pi$
$464$	1.50000	−	2.59808i	0.0696358	−	0.120613i
$465$		0			0
$466$	6.00000	+	10.3923i	0.277945	+	0.481414i
$467$		−	36.0000i		−	1.66588i	−0.553362	−	0.832941i	$-0.686655\pi$
$467$		−	36.0000i		−	1.66588i	0.553362	−	0.832941i	$-0.313345\pi$
$468$	5.19615	+	3.00000i	0.240192	+	0.138675i
$469$	−13.0000			−0.600284
$470$		0			0
$471$	−21.0000	+	12.1244i	−0.967629	+	0.558661i
$472$	5.19615	+	3.00000i	0.239172	+	0.138086i
$473$	−41.5692	−	24.0000i	−1.91135	−	1.10352i
$474$	−15.0000	+	8.66025i	−0.688973	+	0.397779i
$475$		0			0
$476$		0			0
$477$	15.5885	−	9.00000i	0.713746	−	0.412082i
$478$		0			0
$479$	−15.0000	−	25.9808i	−0.685367	−	1.18709i	−0.973321	−	0.229447i	$-0.926308\pi$
$479$	−15.0000	−	25.9808i	−0.685367	−	1.18709i	0.287954	−	0.957644i	$-0.407025\pi$
$480$		0			0
$481$	−8.00000	+	13.8564i	−0.364769	+	0.631798i
$482$	25.1147	+	14.5000i	1.14394	+	0.660457i
$483$	7.79423	−	13.5000i	0.354650	−	0.614271i
$484$	12.5000	+	21.6506i	0.568182	+	0.984120i
$485$		0			0
$486$	13.5000	+	7.79423i	0.612372	+	0.353553i
$487$		−	8.00000i		−	0.362515i	−0.983436	−	0.181257i	$-0.941983\pi$
$487$		−	8.00000i		−	0.362515i	0.983436	−	0.181257i	$-0.0580167\pi$
$488$	−11.2583	+	6.50000i	−0.509641	+	0.294241i
$489$	6.00000	+	3.46410i	0.271329	+	0.156652i
$490$		0			0
$491$	−6.00000	+	10.3923i	−0.270776	+	0.468998i	−0.969061	−	0.246822i	$-0.920614\pi$
$491$	−6.00000	+	10.3923i	−0.270776	+	0.468998i	0.698285	+	0.715820i	$0.253947\pi$
$492$	5.19615			0.234261
$493$		0			0
$494$	8.00000			0.359937
$495$		0			0
$496$	−4.00000			−0.179605
$497$	−5.19615	+	3.00000i	−0.233079	+	0.134568i
$498$	7.79423	+	13.5000i	0.349268	+	0.604949i
$499$	16.0000	−	27.7128i	0.716258	−	1.24060i	−0.246214	−	0.969216i	$-0.579187\pi$
$499$	16.0000	−	27.7128i	0.716258	−	1.24060i	0.962472	−	0.271380i	$-0.0874801\pi$
$500$		0			0
$501$	4.50000	−	2.59808i	0.201045	−	0.116073i
$502$	−10.3923	+	6.00000i	−0.463831	+	0.267793i
$503$			27.0000i			1.20387i	0.798545	+	0.601935i	$0.205603\pi$
$503$			27.0000i			1.20387i	−0.798545	+	0.601935i	$0.794397\pi$
$504$	1.50000	−	2.59808i	0.0668153	−	0.115728i
$505$		0			0
$506$	−27.0000	−	46.7654i	−1.20030	−	2.07897i
$507$	15.5885			0.692308
$508$	6.06218	+	3.50000i	0.268966	+	0.155287i
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	−0.650556	−	0.759458i	$-0.725464\pi$
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	0.982988	+	0.183669i	$0.0587976\pi$
$510$		0			0
$511$	−2.00000	−	3.46410i	−0.0884748	−	0.153243i
$512$		−	1.00000i		−	0.0441942i
$513$	20.7846			0.917663
$514$	−18.0000			−0.793946
$515$		0			0
$516$	12.0000	+	6.92820i	0.528271	+	0.304997i
$517$	−15.5885	−	9.00000i	−0.685580	−	0.395820i
$518$	6.92820	+	4.00000i	0.304408	+	0.175750i
$519$			41.5692i			1.82469i
$520$		0			0
$521$	27.0000			1.18289			0.591446	−	0.806345i	$-0.298557\pi$
$521$	27.0000			1.18289			0.591446	+	0.806345i	$0.298557\pi$
$522$			9.00000i			0.393919i
$523$		−	19.0000i		−	0.830812i	−0.909636	−	0.415406i	$-0.863640\pi$
$523$		−	19.0000i		−	0.830812i	0.909636	−	0.415406i	$-0.136360\pi$
$524$	−9.00000	−	15.5885i	−0.393167	−	0.680985i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−5.19615	−	9.00000i	−0.226134	−	0.391675i
$529$	29.0000	+	50.2295i	1.26087	+	2.18389i
$530$		0			0
$531$	−18.0000			−0.781133
$532$		−	4.00000i		−	0.173422i
$533$	−5.19615	+	3.00000i	−0.225070	+	0.129944i
$534$			15.5885i			0.674579i
$535$		0			0
$536$	6.50000	−	11.2583i	0.280757	−	0.486286i
$537$	−15.5885	+	27.0000i	−0.672692	+	1.16514i
$538$	18.1865	−	10.5000i	0.784077	−	0.452687i
$539$	36.0000			1.55063
$540$		0			0
$541$	29.0000			1.24681			0.623404	−	0.781900i	$-0.285749\pi$
$541$	29.0000			1.24681			0.623404	+	0.781900i	$0.285749\pi$
$542$	3.46410	−	2.00000i	0.148796	−	0.0859074i
$543$	−4.33013	+	7.50000i	−0.185824	+	0.321856i
$544$		0			0
$545$		0			0
$546$			3.46410i			0.148250i
$547$	37.2391	−	21.5000i	1.59223	−	0.919274i	0.599305	−	0.800521i	$-0.295444\pi$
$547$	37.2391	−	21.5000i	1.59223	−	0.919274i	0.992924	−	0.118753i	$-0.0378896\pi$
$548$		−	12.0000i		−	0.512615i
$549$	19.5000	−	33.7750i	0.832240	−	1.44148i
$550$		0			0
$551$	6.00000	+	10.3923i	0.255609	+	0.442727i
$552$	7.79423	+	13.5000i	0.331744	+	0.574598i
$553$	−8.66025	−	5.00000i	−0.368271	−	0.212622i
$554$	4.00000	−	6.92820i	0.169944	−	0.294351i
$555$		0			0
$556$	8.00000	+	13.8564i	0.339276	+	0.587643i
$557$			6.00000i			0.254228i	0.991888	+	0.127114i	$0.0405714\pi$
$557$			6.00000i			0.254228i	−0.991888	+	0.127114i	$0.959429\pi$
$558$	10.3923	−	6.00000i	0.439941	−	0.254000i
$559$	−16.0000			−0.676728
$560$		0			0
$561$		0			0
$562$	−12.9904	−	7.50000i	−0.547966	−	0.316368i
$563$	2.59808	+	1.50000i	0.109496	+	0.0632175i	0.553748	−	0.832684i	$-0.313197\pi$
$563$	2.59808	+	1.50000i	0.109496	+	0.0632175i	−0.444252	+	0.895902i	$0.646530\pi$
$564$	4.50000	+	2.59808i	0.189484	+	0.109399i
$565$		0			0
$566$	−13.0000			−0.546431
$567$			9.00000i			0.377964i
$568$		−	6.00000i		−	0.251754i
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	0.796266	−	0.604947i	$-0.206806\pi$
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	−0.922032	+	0.387113i	$0.873472\pi$
$570$		0			0
$571$	20.0000	−	34.6410i	0.836974	−	1.44968i	−0.0554391	−	0.998462i	$-0.517656\pi$
$571$	20.0000	−	34.6410i	0.836974	−	1.44968i	0.892413	−	0.451219i	$-0.149011\pi$
$572$	10.3923	+	6.00000i	0.434524	+	0.250873i
$573$	−20.7846			−0.868290
$574$	1.50000	+	2.59808i	0.0626088	+	0.108442i
$575$		0			0
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$			10.0000i			0.416305i	0.978096	+	0.208153i	$0.0667451\pi$
$577$			10.0000i			0.416305i	−0.978096	+	0.208153i	$0.933255\pi$
$578$	−14.7224	+	8.50000i	−0.612372	+	0.353553i
$579$	3.00000	−	1.73205i	0.124676	−	0.0719816i
$580$		0			0
$581$	−4.50000	+	7.79423i	−0.186691	+	0.323359i
$582$	1.73205	+	3.00000i	0.0717958	+	0.124354i
$583$	31.1769	−	18.0000i	1.29122	−	0.745484i
$584$	4.00000			0.165521
$585$		0			0
$586$		0			0
$587$	12.9904	−	7.50000i	0.536170	−	0.309558i	−0.207355	−	0.978266i	$-0.566486\pi$
$587$	12.9904	−	7.50000i	0.536170	−	0.309558i	0.743525	+	0.668708i	$0.233152\pi$
$588$	−10.3923			−0.428571
$589$	8.00000	−	13.8564i	0.329634	−	0.570943i
$590$		0			0
$591$	−18.0000	−	10.3923i	−0.740421	−	0.427482i
$592$	−6.92820	+	4.00000i	−0.284747	+	0.164399i
$593$			24.0000i			0.985562i	0.870153	+	0.492781i	$0.164020\pi$
$593$			24.0000i			0.985562i	−0.870153	+	0.492781i	$0.835980\pi$
$594$	27.0000	+	15.5885i	1.10782	+	0.639602i
$595$		0			0
$596$	1.50000	+	2.59808i	0.0614424	+	0.106421i
$597$	6.92820	−	12.0000i	0.283552	−	0.491127i
$598$	−15.5885	−	9.00000i	−0.637459	−	0.368037i
$599$	−3.00000	+	5.19615i	−0.122577	+	0.212309i	−0.920783	−	0.390075i	$-0.872449\pi$
$599$	−3.00000	+	5.19615i	−0.122577	+	0.212309i	0.798206	+	0.602384i	$0.205782\pi$
$600$		0			0
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	−0.999376	−	0.0353259i	$-0.988753\pi$
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	0.469095	−	0.883148i	$-0.344580\pi$
$602$			8.00000i			0.326056i
$603$			39.0000i			1.58820i
$604$	−14.0000			−0.569652
$605$		0			0
$606$	−9.00000	+	5.19615i	−0.365600	+	0.211079i
$607$	25.1147	+	14.5000i	1.01938	+	0.588537i	0.913923	−	0.405887i	$-0.133038\pi$
$607$	25.1147	+	14.5000i	1.01938	+	0.588537i	0.105453	+	0.994424i	$0.466371\pi$
$608$	3.46410	+	2.00000i	0.140488	+	0.0811107i
$609$	−4.50000	+	2.59808i	−0.182349	+	0.105279i
$610$		0			0
$611$	−6.00000			−0.242734
$612$		0			0
$613$		−	40.0000i		−	1.61558i	−0.589467	−	0.807792i	$-0.700662\pi$
$613$		−	40.0000i		−	1.61558i	0.589467	−	0.807792i	$-0.299338\pi$
$614$	−3.50000	−	6.06218i	−0.141249	−	0.244650i
$615$		0			0
$616$	3.00000	−	5.19615i	0.120873	−	0.209359i
$617$	10.3923	+	6.00000i	0.418378	+	0.241551i	0.694383	−	0.719605i	$-0.255677\pi$
$617$	10.3923	+	6.00000i	0.418378	+	0.241551i	−0.276005	+	0.961156i	$0.589011\pi$
$618$	−6.92820	+	12.0000i	−0.278693	+	0.482711i
$619$	−20.0000	−	34.6410i	−0.803868	−	1.39234i	−0.917053	−	0.398766i	$-0.869439\pi$
$619$	−20.0000	−	34.6410i	−0.803868	−	1.39234i	0.113185	−	0.993574i	$-0.463895\pi$
$620$		0			0
$621$	−40.5000	−	23.3827i	−1.62521	−	0.938315i
$622$		−	12.0000i		−	0.481156i
$623$	−7.79423	+	4.50000i	−0.312269	+	0.180289i
$624$	−3.00000	−	1.73205i	−0.120096	−	0.0693375i
$625$		0			0
$626$	−1.00000	+	1.73205i	−0.0399680	+	0.0692267i
$627$	41.5692			1.66011
$628$	12.1244	−	7.00000i	0.483814	−	0.279330i
$629$		0			0
$630$		0			0
$631$	32.0000			1.27390			0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000			1.27390			0.636950	+	0.770905i	$0.280196\pi$
$632$	8.66025	−	5.00000i	0.344486	−	0.198889i
$633$	−1.73205	−	3.00000i	−0.0688428	−	0.119239i
$634$	−3.00000	+	5.19615i	−0.119145	+	0.206366i
$635$		0			0
$636$	−9.00000	+	5.19615i	−0.356873	+	0.206041i
$637$	10.3923	−	6.00000i	0.411758	−	0.237729i
$638$			18.0000i			0.712627i
$639$	9.00000	+	15.5885i	0.356034	+	0.616670i
$640$		0			0
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	−0.982708	−	0.185164i	$-0.940718\pi$
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	0.330997	−	0.943632i	$-0.392615\pi$
$642$	5.19615			0.205076
$643$	26.8468	+	15.5000i	1.05873	+	0.611260i	0.925082	−	0.379768i	$-0.123996\pi$
$643$	26.8468	+	15.5000i	1.05873	+	0.611260i	0.133652	+	0.991028i	$0.457330\pi$
$644$	−4.50000	+	7.79423i	−0.177325	+	0.307136i
$645$		0			0
$646$		0			0
$647$			3.00000i			0.117942i	0.998260	+	0.0589711i	$0.0187820\pi$
$647$			3.00000i			0.117942i	−0.998260	+	0.0589711i	$0.981218\pi$
$648$	−7.79423	−	4.50000i	−0.306186	−	0.176777i
$649$	−36.0000			−1.41312
$650$		0			0
$651$	6.00000	+	3.46410i	0.235159	+	0.135769i
$652$	−3.46410	−	2.00000i	−0.135665	−	0.0783260i
$653$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$653$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$654$		−	12.1244i		−	0.474100i
$655$		0			0
$656$	−3.00000			−0.117130
$657$	−10.3923	+	6.00000i	−0.405442	+	0.234082i
$658$			3.00000i			0.116952i
$659$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$659$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$660$		0			0
$661$	23.0000	−	39.8372i	0.894596	−	1.54949i	0.0602929	−	0.998181i	$-0.480797\pi$
$661$	23.0000	−	39.8372i	0.894596	−	1.54949i	0.834303	−	0.551306i	$-0.185870\pi$
$662$	−8.66025	−	5.00000i	−0.336590	−	0.194331i
$663$		0			0
$664$	−4.50000	−	7.79423i	−0.174634	−	0.302475i
$665$		0			0
$666$	12.0000	−	20.7846i	0.464991	−	0.805387i
$667$		−	27.0000i		−	1.04544i
$668$	−2.59808	+	1.50000i	−0.100523	+	0.0580367i
$669$		−	1.73205i		−	0.0669650i
$670$		0			0
$671$	39.0000	−	67.5500i	1.50558	−	2.60774i
$672$	−0.866025	+	1.50000i	−0.0334077	+	0.0578638i
$673$	−39.8372	+	23.0000i	−1.53561	+	0.886585i	−0.536522	+	0.843886i	$0.680262\pi$
$673$	−39.8372	+	23.0000i	−1.53561	+	0.886585i	−0.999088	+	0.0426985i	$0.986405\pi$
$674$	−8.00000			−0.308148
$675$		0			0
$676$	−9.00000			−0.346154
$677$	−15.5885	+	9.00000i	−0.599113	+	0.345898i	−0.768693	−	0.639618i	$-0.779092\pi$
$677$	−15.5885	+	9.00000i	−0.599113	+	0.345898i	0.169580	+	0.985517i	$0.445759\pi$
$678$		0			0
$679$	−1.00000	+	1.73205i	−0.0383765	+	0.0664700i
$680$		0			0
$681$			20.7846i			0.796468i
$682$	20.7846	−	12.0000i	0.795884	−	0.459504i
$683$			12.0000i			0.459167i	0.973289	+	0.229584i	$0.0737364\pi$
$683$			12.0000i			0.459167i	−0.973289	+	0.229584i	$0.926264\pi$
$684$	−12.0000			−0.458831
$685$		0			0
$686$	−6.50000	−	11.2583i	−0.248171	−	0.429845i
$687$	−11.2583	−	19.5000i	−0.429532	−	0.743971i
$688$	−6.92820	−	4.00000i	−0.264135	−	0.152499i
$689$	6.00000	−	10.3923i	0.228582	−	0.395915i
$690$		0			0
$691$	5.00000	+	8.66025i	0.190209	+	0.329452i	0.945319	−	0.326146i	$-0.105750\pi$
$691$	5.00000	+	8.66025i	0.190209	+	0.329452i	−0.755110	+	0.655598i	$0.772417\pi$
$692$		−	24.0000i		−	0.912343i
$693$			18.0000i			0.683763i
$694$	−12.0000			−0.455514
$695$		0			0
$696$		−	5.19615i		−	0.196960i
$697$		0			0
$698$	−19.9186	−	11.5000i	−0.753930	−	0.435281i
$699$	18.0000	+	10.3923i	0.680823	+	0.393073i
$700$		0			0
$701$	−45.0000			−1.69963			−0.849813	−	0.527084i	$-0.823285\pi$
$701$	−45.0000			−1.69963			−0.849813	+	0.527084i	$0.823285\pi$
$702$	10.3923			0.392232
$703$		−	32.0000i		−	1.20690i
$704$	3.00000	+	5.19615i	0.113067	+	0.195837i
$705$		0			0
$706$	−12.0000	+	20.7846i	−0.451626	+	0.782239i
$707$	−5.19615	−	3.00000i	−0.195421	−	0.112827i
$708$	10.3923			0.390567
$709$	5.50000	+	9.52628i	0.206557	+	0.357767i	0.950628	−	0.310334i	$-0.100441\pi$
$709$	5.50000	+	9.52628i	0.206557	+	0.357767i	−0.744071	+	0.668101i	$0.767108\pi$
$710$		0			0
$711$	−15.0000	+	25.9808i	−0.562544	+	0.974355i
$712$		−	9.00000i		−	0.337289i
$713$	−31.1769	+	18.0000i	−1.16758	+	0.674105i
$714$		0			0
$715$		0			0
$716$	9.00000	−	15.5885i	0.336346	−	0.582568i
$717$		0			0
$718$	−10.3923	+	6.00000i	−0.387837	+	0.223918i
$719$	6.00000			0.223762			0.111881	−	0.993722i	$-0.464312\pi$
$719$	6.00000			0.223762			0.111881	+	0.993722i	$0.464312\pi$
$720$		0			0
$721$	−8.00000			−0.297936
$722$	2.59808	−	1.50000i	0.0966904	−	0.0558242i
$723$	50.2295			1.86805
$724$	2.50000	−	4.33013i	0.0929118	−	0.160928i
$725$		0			0
$726$	37.5000	+	21.6506i	1.39176	+	0.803530i
$727$	−45.8993	+	26.5000i	−1.70231	+	0.982831i	−0.758901	+	0.651206i	$0.774263\pi$
$727$	−45.8993	+	26.5000i	−1.70231	+	0.982831i	−0.943411	+	0.331625i	$0.892403\pi$
$728$		−	2.00000i		−	0.0741249i
$729$	27.0000			1.00000
$730$		0			0
$731$		0			0
$732$	−11.2583	+	19.5000i	−0.416120	+	0.720741i
$733$	−12.1244	−	7.00000i	−0.447823	−	0.258551i	0.259087	−	0.965854i	$-0.416578\pi$
$733$	−12.1244	−	7.00000i	−0.447823	−	0.258551i	−0.706910	+	0.707303i	$0.749912\pi$
$734$	4.00000	−	6.92820i	0.147643	−	0.255725i
$735$		0			0
$736$	−4.50000	−	7.79423i	−0.165872	−	0.287299i
$737$			78.0000i			2.87317i
$738$	7.79423	−	4.50000i	0.286910	−	0.165647i
$739$	−2.00000			−0.0735712			−0.0367856	−	0.999323i	$-0.511712\pi$
$739$	−2.00000			−0.0735712			−0.0367856	+	0.999323i	$0.511712\pi$
$740$		0			0
$741$	12.0000	−	6.92820i	0.440831	−	0.254514i
$742$	−5.19615	−	3.00000i	−0.190757	−	0.110133i
$743$	12.9904	+	7.50000i	0.476571	+	0.275148i	0.718986	−	0.695024i	$-0.244606\pi$
$743$	12.9904	+	7.50000i	0.476571	+	0.275148i	−0.242415	+	0.970173i	$0.577940\pi$
$744$	−6.00000	+	3.46410i	−0.219971	+	0.127000i
$745$		0			0
$746$	26.0000			0.951928
$747$	23.3827	+	13.5000i	0.855528	+	0.493939i
$748$		0			0
$749$	1.50000	+	2.59808i	0.0548088	+	0.0949316i
$750$		0			0
$751$	−1.00000	+	1.73205i	−0.0364905	+	0.0632034i	−0.883694	−	0.468065i	$-0.844951\pi$
$751$	−1.00000	+	1.73205i	−0.0364905	+	0.0632034i	0.847203	+	0.531269i	$0.178285\pi$
$752$	−2.59808	−	1.50000i	−0.0947421	−	0.0546994i
$753$	−10.3923	+	18.0000i	−0.378717	+	0.655956i
$754$	3.00000	+	5.19615i	0.109254	+	0.189233i
$755$		0			0
$756$		−	5.19615i		−	0.188982i
$757$			46.0000i			1.67190i	0.548807	+	0.835949i	$0.315082\pi$
$757$			46.0000i			1.67190i	−0.548807	+	0.835949i	$0.684918\pi$
$758$	−19.0526	+	11.0000i	−0.692020	+	0.399538i
$759$	−81.0000	−	46.7654i	−2.94011	−	1.69748i
$760$		0			0
$761$	16.5000	−	28.5788i	0.598125	−	1.03598i	−0.394973	−	0.918693i	$-0.629246\pi$
$761$	16.5000	−	28.5788i	0.598125	−	1.03598i	0.993098	−	0.117289i	$-0.0374205\pi$
$762$	12.1244			0.439219
$763$	6.06218	−	3.50000i	0.219466	−	0.126709i
$764$	12.0000			0.434145
$765$		0			0
$766$	−12.0000			−0.433578
$767$	−10.3923	+	6.00000i	−0.375244	+	0.216647i
$768$	−0.866025	−	1.50000i	−0.0312500	−	0.0541266i
$769$	14.5000	−	25.1147i	0.522883	−	0.905661i	−0.476762	−	0.879032i	$-0.658190\pi$
$769$	14.5000	−	25.1147i	0.522883	−	0.905661i	0.999645	−	0.0266282i	$-0.00847701\pi$
$770$		0			0
$771$	−27.0000	+	15.5885i	−0.972381	+	0.561405i
$772$	−1.73205	+	1.00000i	−0.0623379	+	0.0359908i
$773$		−	48.0000i		−	1.72644i	−0.504828	−	0.863220i	$-0.668444\pi$
$773$		−	48.0000i		−	1.72644i	0.504828	−	0.863220i	$-0.331556\pi$
$774$	24.0000			0.862662
$775$		0			0
$776$	−1.00000	−	1.73205i	−0.0358979	−	0.0621770i
$777$	13.8564			0.497096
$778$	−18.1865	−	10.5000i	−0.652019	−	0.376443i
$779$	6.00000	−	10.3923i	0.214972	−	0.372343i
$780$		0			0
$781$	18.0000	+	31.1769i	0.644091	+	1.11560i
$782$		0			0
$783$	7.79423	+	13.5000i	0.278543	+	0.482451i
$784$	6.00000			0.214286
$785$		0			0
$786$	−27.0000	−	15.5885i	−0.963058	−	0.556022i
$787$	17.3205	+	10.0000i	0.617409	+	0.356462i	0.775860	−	0.630905i	$-0.217316\pi$
$787$	17.3205	+	10.0000i	0.617409	+	0.356462i	−0.158450	+	0.987367i	$0.550650\pi$
$788$	10.3923	+	6.00000i	0.370211	+	0.213741i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−15.5885	−	9.00000i	−0.553912	−	0.319801i
$793$		−	26.0000i		−	0.923287i
$794$	1.00000	+	1.73205i	0.0354887	+	0.0614682i
$795$		0			0
$796$	−4.00000	+	6.92820i	−0.141776	+	0.245564i
$797$	−36.3731	−	21.0000i	−1.28840	−	0.743858i	−0.310031	−	0.950726i	$-0.600340\pi$
$797$	−36.3731	−	21.0000i	−1.28840	−	0.743858i	−0.978369	+	0.206868i	$0.933673\pi$
$798$	−3.46410	−	6.00000i	−0.122628	−	0.212398i
$799$		0			0
$800$		0			0
$801$	13.5000	+	23.3827i	0.476999	+	0.826187i
$802$		−	6.00000i		−	0.211867i
$803$	−20.7846	+	12.0000i	−0.733473	+	0.423471i
$804$		−	22.5167i		−	0.794101i
$805$		0			0
$806$	4.00000	−	6.92820i	0.140894	−	0.244036i
$807$	18.1865	−	31.5000i	0.640196	−	1.10885i
$808$	5.19615	−	3.00000i	0.182800	−	0.105540i
$809$	−18.0000			−0.632846			−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000			−0.632846			−0.316423	+	0.948618i	$0.602482\pi$
$810$		0			0
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$	2.59808	−	1.50000i	0.0911746	−	0.0526397i
$813$	3.46410	−	6.00000i	0.121491	−	0.210429i
$814$	24.0000	−	41.5692i	0.841200	−	1.45700i
$815$		0			0
$816$		0			0
$817$	27.7128	−	16.0000i	0.969549	−	0.559769i
$818$		−	10.0000i		−	0.349642i
$819$	3.00000	+	5.19615i	0.104828	+	0.181568i
$820$		0			0
$821$	−13.5000	−	23.3827i	−0.471153	−	0.816061i	0.528302	−	0.849056i	$-0.322829\pi$
$821$	−13.5000	−	23.3827i	−0.471153	−	0.816061i	−0.999456	+	0.0329950i	$0.989495\pi$
$822$	−10.3923	−	18.0000i	−0.362473	−	0.627822i
$823$	21.6506	+	12.5000i	0.754694	+	0.435723i	0.827387	−	0.561632i	$-0.189826\pi$
$823$	21.6506	+	12.5000i	0.754694	+	0.435723i	−0.0726937	+	0.997354i	$0.523160\pi$
$824$	4.00000	−	6.92820i	0.139347	−	0.241355i
$825$		0			0
$826$	3.00000	+	5.19615i	0.104383	+	0.180797i
$827$		−	3.00000i		−	0.104320i	−0.998639	−	0.0521601i	$-0.983389\pi$
$827$		−	3.00000i		−	0.104320i	0.998639	−	0.0521601i	$-0.0166106\pi$
$828$	23.3827	+	13.5000i	0.812605	+	0.469157i
$829$	7.00000			0.243120			0.121560	−	0.992584i	$-0.461210\pi$
$829$	7.00000			0.243120			0.121560	+	0.992584i	$0.461210\pi$
$830$		0			0
$831$		−	13.8564i		−	0.480673i
$832$	1.73205	+	1.00000i	0.0600481	+	0.0346688i
$833$		0			0
$834$	24.0000	+	13.8564i	0.831052	+	0.479808i
$835$		0			0
$836$	−24.0000			−0.830057
$837$	10.3923	−	18.0000i	0.359211	−	0.622171i
$838$		−	30.0000i		−	1.03633i
$839$	18.0000	+	31.1769i	0.621429	+	1.07635i	0.989220	+	0.146438i	$0.0467809\pi$
$839$	18.0000	+	31.1769i	0.621429	+	1.07635i	−0.367791	+	0.929909i	$0.619886\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−19.0526	−	11.0000i	−0.656595	−	0.379085i
$843$	−25.9808			−0.894825
$844$	1.00000	+	1.73205i	0.0344214	+	0.0596196i
$845$		0			0
$846$	9.00000			0.309426
$847$			25.0000i			0.859010i
$848$	5.19615	−	3.00000i	0.178437	−	0.103020i
$849$	−19.5000	+	11.2583i	−0.669238	+	0.386385i
$850$		0			0
$851$	−36.0000	+	62.3538i	−1.23406	+	2.13746i
$852$	−5.19615	−	9.00000i	−0.178017	−	0.308335i
$853$	−8.66025	+	5.00000i	−0.296521	+	0.171197i	−0.640879	−	0.767642i	$-0.721430\pi$
$853$	−8.66025	+	5.00000i	−0.296521	+	0.171197i	0.344358	+	0.938839i	$0.388097\pi$
$854$	−13.0000			−0.444851
$855$		0			0
$856$	−3.00000			−0.102538
$857$	36.3731	−	21.0000i	1.24248	−	0.717346i	0.272882	−	0.962048i	$-0.412023\pi$
$857$	36.3731	−	21.0000i	1.24248	−	0.717346i	0.969599	+	0.244701i	$0.0786899\pi$
$858$	20.7846			0.709575
$859$	−17.0000	+	29.4449i	−0.580033	+	1.00465i	0.415442	+	0.909620i	$0.363627\pi$
$859$	−17.0000	+	29.4449i	−0.580033	+	1.00465i	−0.995475	+	0.0950262i	$0.969707\pi$
$860$		0			0
$861$	4.50000	+	2.59808i	0.153360	+	0.0885422i
$862$	−5.19615	+	3.00000i	−0.176982	+	0.102180i
$863$			3.00000i			0.102121i	0.998696	+	0.0510606i	$0.0162602\pi$
$863$			3.00000i			0.102121i	−0.998696	+	0.0510606i	$0.983740\pi$
$864$	4.50000	+	2.59808i	0.153093	+	0.0883883i
$865$		0			0
$866$	8.00000	+	13.8564i	0.271851	+	0.470860i
$867$	−14.7224	+	25.5000i	−0.500000	+	0.866025i
$868$	−3.46410	−	2.00000i	−0.117579	−	0.0678844i
$869$	−30.0000	+	51.9615i	−1.01768	+	1.76267i
$870$		0			0
$871$	13.0000	+	22.5167i	0.440488	+	0.762948i
$872$			7.00000i			0.237050i
$873$	5.19615	+	3.00000i	0.175863	+	0.101535i
$874$	36.0000			1.21772
$875$		0			0
$876$	6.00000	−	3.46410i	0.202721	−	0.117041i
$877$	−19.0526	−	11.0000i	−0.643359	−	0.371444i	0.142548	−	0.989788i	$-0.454470\pi$
$877$	−19.0526	−	11.0000i	−0.643359	−	0.371444i	−0.785907	+	0.618344i	$0.787804\pi$
$878$	24.2487	+	14.0000i	0.818354	+	0.472477i
$879$		0			0
$880$		0			0
$881$	21.0000			0.707508			0.353754	−	0.935339i	$-0.384905\pi$
$881$	21.0000			0.707508			0.353754	+	0.935339i	$0.384905\pi$
$882$	−15.5885	+	9.00000i	−0.524891	+	0.303046i
$883$		−	31.0000i		−	1.04323i	−0.853180	−	0.521617i	$-0.825329\pi$
$883$		−	31.0000i		−	1.04323i	0.853180	−	0.521617i	$-0.174671\pi$
$884$		0			0
$885$		0			0
$886$	−4.50000	+	7.79423i	−0.151180	+	0.261852i
$887$	31.1769	+	18.0000i	1.04682	+	0.604381i	0.921757	−	0.387768i	$-0.126754\pi$
$887$	31.1769	+	18.0000i	1.04682	+	0.604381i	0.125061	+	0.992149i	$0.460087\pi$
$888$	−6.92820	+	12.0000i	−0.232495	+	0.402694i
$889$	3.50000	+	6.06218i	0.117386	+	0.203319i
$890$		0			0
$891$	54.0000			1.80907
$892$			1.00000i			0.0334825i
$893$	10.3923	−	6.00000i	0.347765	−	0.200782i
$894$	4.50000	+	2.59808i	0.150503	+	0.0868927i
$895$		0			0
$896$	0.500000	−	0.866025i	0.0167038	−	0.0289319i
$897$	−31.1769			−1.04097
$898$	5.19615	−	3.00000i	0.173398	−	0.100111i
$899$	12.0000			0.400222
$900$		0			0
$901$		0			0
$902$	15.5885	−	9.00000i	0.519039	−	0.299667i
$903$	6.92820	+	12.0000i	0.230556	+	0.399335i
$904$		0			0
$905$		0			0
$906$	−21.0000	+	12.1244i	−0.697678	+	0.402805i
$907$	32.0429	−	18.5000i	1.06397	−	0.614282i	0.137441	−	0.990510i	$-0.456112\pi$
$907$	32.0429	−	18.5000i	1.06397	−	0.614282i	0.926527	+	0.376228i	$0.122779\pi$
$908$		−	12.0000i		−	0.398234i
$909$	−9.00000	+	15.5885i	−0.298511	+	0.517036i
$910$		0			0
$911$	15.0000	+	25.9808i	0.496972	+	0.860781i	0.999994	−	0.00349271i	$-0.00111177\pi$
$911$	15.0000	+	25.9808i	0.496972	+	0.860781i	−0.503022	+	0.864274i	$0.667778\pi$
$912$	6.92820			0.229416
$913$	46.7654	+	27.0000i	1.54771	+	0.893570i
$914$	4.00000	−	6.92820i	0.132308	−	0.229165i
$915$		0			0
$916$	6.50000	+	11.2583i	0.214766	+	0.371986i
$917$		−	18.0000i		−	0.594412i
$918$		0			0
$919$	−38.0000			−1.25350			−0.626752	−	0.779219i	$-0.715616\pi$
$919$	−38.0000			−1.25350			−0.626752	+	0.779219i	$0.715616\pi$
$920$		0			0
$921$	−10.5000	−	6.06218i	−0.345987	−	0.199756i
$922$	−23.3827	−	13.5000i	−0.770068	−	0.444599i
$923$	10.3923	+	6.00000i	0.342067	+	0.197492i
$924$		−	10.3923i		−	0.341882i
$925$		0			0
$926$	−4.00000			−0.131448
$927$			24.0000i			0.788263i
$928$			3.00000i			0.0984798i
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	0.911034	−	0.412332i	$-0.135286\pi$
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	−0.812607	+	0.582812i	$0.801952\pi$
$930$		0			0
$931$	−12.0000	+	20.7846i	−0.393284	+	0.681188i
$932$	−10.3923	−	6.00000i	−0.340411	−	0.196537i
$933$	−10.3923	−	18.0000i	−0.340229	−	0.589294i
$934$	18.0000	+	31.1769i	0.588978	+	1.02014i
$935$		0			0
$936$	−6.00000			−0.196116
$937$		−	56.0000i		−	1.82944i	−0.404088	−	0.914720i	$-0.632411\pi$
$937$		−	56.0000i		−	1.82944i	0.404088	−	0.914720i	$-0.367589\pi$
$938$	11.2583	−	6.50000i	0.367598	−	0.212233i
$939$			3.46410i			0.113047i
$940$		0			0
$941$	−10.5000	+	18.1865i	−0.342290	+	0.592864i	−0.984858	−	0.173365i	$-0.944536\pi$
$941$	−10.5000	+	18.1865i	−0.342290	+	0.592864i	0.642567	+	0.766229i	$0.277869\pi$
$942$	12.1244	−	21.0000i	0.395033	−	0.684217i
$943$	−23.3827	+	13.5000i	−0.761445	+	0.439620i
$944$	−6.00000			−0.195283
$945$		0			0
$946$	48.0000			1.56061
$947$	−33.7750	+	19.5000i	−1.09754	+	0.633665i	−0.935574	−	0.353131i	$-0.885117\pi$
$947$	−33.7750	+	19.5000i	−1.09754	+	0.633665i	−0.161966	+	0.986796i	$0.551783\pi$
$948$	8.66025	−	15.0000i	0.281272	−	0.487177i
$949$	−4.00000	+	6.92820i	−0.129845	+	0.224899i
$950$		0			0
$951$			10.3923i			0.336994i
$952$		0			0
$953$		−	6.00000i		−	0.194359i	−0.995267	−	0.0971795i	$-0.969018\pi$
$953$		−	6.00000i		−	0.194359i	0.995267	−	0.0971795i	$-0.0309821\pi$
$954$	−9.00000	+	15.5885i	−0.291386	+	0.504695i
$955$		0			0
$956$		0			0
$957$	15.5885	+	27.0000i	0.503903	+	0.872786i
$958$	25.9808	+	15.0000i	0.839400	+	0.484628i
$959$	6.00000	−	10.3923i	0.193750	−	0.335585i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		−	16.0000i		−	0.515861i
$963$	7.79423	−	4.50000i	0.251166	−	0.145010i
$964$	−29.0000			−0.934027
$965$		0			0
$966$			15.5885i			0.501550i
$967$	−32.0429	−	18.5000i	−1.03043	−	0.594920i	−0.113323	−	0.993558i	$-0.536150\pi$
$967$	−32.0429	−	18.5000i	−1.03043	−	0.594920i	−0.917108	+	0.398638i	$0.869483\pi$
$968$	−21.6506	−	12.5000i	−0.695878	−	0.401765i
$969$		0			0
$970$		0			0
$971$	−24.0000			−0.770197			−0.385098	−	0.922876i	$-0.625832\pi$
$971$	−24.0000			−0.770197			−0.385098	+	0.922876i	$0.625832\pi$
$972$	−15.5885			−0.500000
$973$			16.0000i			0.512936i
$974$	4.00000	+	6.92820i	0.128168	+	0.221994i
$975$		0			0
$976$	6.50000	−	11.2583i	0.208060	−	0.360370i
$977$	−36.3731	−	21.0000i	−1.16368	−	0.671850i	−0.211495	−	0.977379i	$-0.567833\pi$
$977$	−36.3731	−	21.0000i	−1.16368	−	0.671850i	−0.952183	+	0.305530i	$0.901167\pi$
$978$	−6.92820			−0.221540
$979$	27.0000	+	46.7654i	0.862924	+	1.49463i
$980$		0			0
$981$	−10.5000	−	18.1865i	−0.335239	−	0.580651i
$982$		−	12.0000i		−	0.382935i
$983$	7.79423	−	4.50000i	0.248597	−	0.143528i	−0.370525	−	0.928823i	$-0.620822\pi$
$983$	7.79423	−	4.50000i	0.248597	−	0.143528i	0.619122	+	0.785295i	$0.287489\pi$
$984$	−4.50000	+	2.59808i	−0.143455	+	0.0828236i
$985$		0			0
$986$		0			0
$987$	2.59808	+	4.50000i	0.0826977	+	0.143237i
$988$	−6.92820	+	4.00000i	−0.220416	+	0.127257i
$989$	−72.0000			−2.28947
$990$		0			0
$991$	−10.0000			−0.317660			−0.158830	−	0.987306i	$-0.550772\pi$
$991$	−10.0000			−0.317660			−0.158830	+	0.987306i	$0.550772\pi$
$992$	3.46410	−	2.00000i	0.109985	−	0.0635001i
$993$	−17.3205			−0.549650
$994$	3.00000	−	5.19615i	0.0951542	−	0.164812i
$995$		0			0
$996$	−13.5000	−	7.79423i	−0.427764	−	0.246970i
$997$	8.66025	−	5.00000i	0.274273	−	0.158352i	−0.356555	−	0.934274i	$-0.616049\pi$
$997$	8.66025	−	5.00000i	0.274273	−	0.158352i	0.630828	+	0.775923i	$0.282715\pi$
$998$			32.0000i			1.01294i
$999$		−	41.5692i		−	1.31519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.j.c.49.1		4
3.2	odd	2		1350.2.j.e.199.2		4
5.2	odd	4		90.2.e.a.31.1	✓	2
5.3	odd	4		450.2.e.e.301.1		2
5.4	even	2	inner	450.2.j.c.49.2		4
9.2	odd	6		1350.2.j.e.1099.1		4
9.4	even	3		4050.2.c.t.649.1		2
9.5	odd	6		4050.2.c.a.649.2		2
9.7	even	3	inner	450.2.j.c.349.2		4
15.2	even	4		270.2.e.b.91.1		2
15.8	even	4		1350.2.e.b.901.1		2
15.14	odd	2		1350.2.j.e.199.1		4
20.7	even	4		720.2.q.b.481.1		2
45.2	even	12		270.2.e.b.181.1		2
45.4	even	6		4050.2.c.t.649.2		2
45.7	odd	12		90.2.e.a.61.1	yes	2
45.13	odd	12		4050.2.a.n.1.1		1
45.14	odd	6		4050.2.c.a.649.1		2
45.22	odd	12		810.2.a.g.1.1		1
45.23	even	12		4050.2.a.ba.1.1		1
45.29	odd	6		1350.2.j.e.1099.2		4
45.32	even	12		810.2.a.b.1.1		1
45.34	even	6	inner	450.2.j.c.349.1		4
45.38	even	12		1350.2.e.b.451.1		2
45.43	odd	12		450.2.e.e.151.1		2
60.47	odd	4		2160.2.q.b.1441.1		2
180.7	even	12		720.2.q.b.241.1		2
180.47	odd	12		2160.2.q.b.721.1		2
180.67	even	12		6480.2.a.g.1.1		1
180.167	odd	12		6480.2.a.v.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.e.a.31.1	✓	2	5.2	odd	4
90.2.e.a.61.1	yes	2	45.7	odd	12
270.2.e.b.91.1		2	15.2	even	4
270.2.e.b.181.1		2	45.2	even	12
450.2.e.e.151.1		2	45.43	odd	12
450.2.e.e.301.1		2	5.3	odd	4
450.2.j.c.49.1		4	1.1	even	1	trivial
450.2.j.c.49.2		4	5.4	even	2	inner
450.2.j.c.349.1		4	45.34	even	6	inner
450.2.j.c.349.2		4	9.7	even	3	inner
720.2.q.b.241.1		2	180.7	even	12
720.2.q.b.481.1		2	20.7	even	4
810.2.a.b.1.1		1	45.32	even	12
810.2.a.g.1.1		1	45.22	odd	12
1350.2.e.b.451.1		2	45.38	even	12
1350.2.e.b.901.1		2	15.8	even	4
1350.2.j.e.199.1		4	15.14	odd	2
1350.2.j.e.199.2		4	3.2	odd	2
1350.2.j.e.1099.1		4	9.2	odd	6
1350.2.j.e.1099.2		4	45.29	odd	6
2160.2.q.b.721.1		2	180.47	odd	12
2160.2.q.b.1441.1		2	60.47	odd	4
4050.2.a.n.1.1		1	45.13	odd	12
4050.2.a.ba.1.1		1	45.23	even	12
4050.2.c.a.649.1		2	45.14	odd	6
4050.2.c.a.649.2		2	9.5	odd	6
4050.2.c.t.649.1		2	9.4	even	3
4050.2.c.t.649.2		2	45.4	even	6
6480.2.a.g.1.1		1	180.67	even	12
6480.2.a.v.1.1		1	180.167	odd	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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.73205i q^{6} +(0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-3.00000 - 5.19615i) q^{11} +(0.866025 + 1.50000i) q^{12} +(-1.73205 - 1.00000i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.59808 + 1.50000i) q^{18} +4.00000 q^{19} +1.73205i q^{21} +(5.19615 + 3.00000i) q^{22} +(-7.79423 - 4.50000i) q^{23} +(-1.50000 - 0.866025i) q^{24} +2.00000 q^{26} +5.19615 q^{27} -1.00000i q^{28} +(1.50000 + 2.59808i) q^{29} +(2.00000 - 3.46410i) q^{31} +(0.866025 + 0.500000i) q^{32} +10.3923 q^{33} -3.00000 q^{36} -8.00000i q^{37} +(-3.46410 + 2.00000i) q^{38} +(3.00000 - 1.73205i) q^{39} +(1.50000 - 2.59808i) q^{41} +(-0.866025 - 1.50000i) q^{42} +(6.92820 - 4.00000i) q^{43} -6.00000 q^{44} +9.00000 q^{46} +(2.59808 - 1.50000i) q^{47} +1.73205 q^{48} +(-3.00000 + 5.19615i) q^{49} +(-1.73205 + 1.00000i) q^{52} +6.00000i q^{53} +(-4.50000 + 2.59808i) q^{54} +(0.500000 + 0.866025i) q^{56} +(-3.46410 + 6.00000i) q^{57} +(-2.59808 - 1.50000i) q^{58} +(3.00000 - 5.19615i) q^{59} +(6.50000 + 11.2583i) q^{61} +4.00000i q^{62} +(-2.59808 - 1.50000i) q^{63} -1.00000 q^{64} +(-9.00000 + 5.19615i) q^{66} +(-11.2583 - 6.50000i) q^{67} +(13.5000 - 7.79423i) q^{69} -6.00000 q^{71} +(2.59808 - 1.50000i) q^{72} -4.00000i q^{73} +(4.00000 + 6.92820i) q^{74} +(2.00000 - 3.46410i) q^{76} +(-5.19615 - 3.00000i) q^{77} +(-1.73205 + 3.00000i) q^{78} +(-5.00000 - 8.66025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +3.00000i q^{82} +(-7.79423 + 4.50000i) q^{83} +(1.50000 + 0.866025i) q^{84} +(-4.00000 + 6.92820i) q^{86} -5.19615 q^{87} +(5.19615 - 3.00000i) q^{88} -9.00000 q^{89} -2.00000 q^{91} +(-7.79423 + 4.50000i) q^{92} +(3.46410 + 6.00000i) q^{93} +(-1.50000 + 2.59808i) q^{94} +(-1.50000 + 0.866025i) q^{96} +(-1.73205 + 1.00000i) q^{97} -6.00000i q^{98} +(-9.00000 + 15.5885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 6 q^{9} - 12 q^{11} - 2 q^{14} - 2 q^{16} + 16 q^{19} - 6 q^{24} + 8 q^{26} + 6 q^{29} + 8 q^{31} - 12 q^{36} + 12 q^{39} + 6 q^{41} - 24 q^{44} + 36 q^{46} - 12 q^{49} - 18 q^{54} + 2 q^{56}+ \cdots - 36 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 6 * q^9 - 12 * q^11 - 2 * q^14 - 2 * q^16 + 16 * q^19 - 6 * q^24 + 8 * q^26 + 6 * q^29 + 8 * q^31 - 12 * q^36 + 12 * q^39 + 6 * q^41 - 24 * q^44 + 36 * q^46 - 12 * q^49 - 18 * q^54 + 2 * q^56 + 12 * q^59 + 26 * q^61 - 4 * q^64 - 36 * q^66 + 54 * q^69 - 24 * q^71 + 16 * q^74 + 8 * q^76 - 20 * q^79 - 18 * q^81 + 6 * q^84 - 16 * q^86 - 36 * q^89 - 8 * q^91 - 6 * q^94 - 6 * q^96 - 36 * q^99

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