LMFDB - Embedded newform 45.5.g.e.28.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,5,Mod(28,45)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("45.28"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	45.g (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.65164833877$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 60x^{5} + 1973x^{4} - 3300x^{3} + 1800x^{2} + 31560x + 276676 $ x^8 - 60x^5 + 1973x^4 - 3300x^3 + 1800x^2 + 31560*x + 276676
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			28.3
Root			$-2.08045 - 2.08045i$ of defining polynomial
Character	$\chi$	$=$	45.28
Dual form			45.5.g.e.37.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.08045 - 2.08045i) q^{2} +7.34348i q^{4} +(8.43390 - 23.5344i) q^{5} +(65.1093 - 65.1093i) q^{7} +(48.5649 + 48.5649i) q^{8} +(-31.4158 - 66.5084i) q^{10} -56.3999 q^{11} +(0.983822 + 0.983822i) q^{13} -270.913i q^{14} +84.5776 q^{16} +(-159.144 + 159.144i) q^{17} +265.552i q^{19} +(172.825 + 61.9342i) q^{20} +(-117.337 + 117.337i) q^{22} +(185.430 + 185.430i) q^{23} +(-482.739 - 396.974i) q^{25} +4.09358 q^{26} +(478.129 + 478.129i) q^{28} +544.071i q^{29} -710.805 q^{31} +(-601.079 + 601.079i) q^{32} +662.183i q^{34} +(-983.184 - 2081.43i) q^{35} +(-639.026 + 639.026i) q^{37} +(552.467 + 552.467i) q^{38} +(1552.54 - 733.355i) q^{40} +1325.70 q^{41} +(-22.3358 - 22.3358i) q^{43} -414.172i q^{44} +771.553 q^{46} +(-456.136 + 456.136i) q^{47} -6077.44i q^{49} +(-1830.20 + 178.428i) q^{50} +(-7.22468 + 7.22468i) q^{52} +(424.212 + 424.212i) q^{53} +(-475.672 + 1327.34i) q^{55} +6324.05 q^{56} +(1131.91 + 1131.91i) q^{58} -3460.30i q^{59} +4937.82 q^{61} +(-1478.79 + 1478.79i) q^{62} +3854.27i q^{64} +(31.4511 - 14.8562i) q^{65} +(-3801.58 + 3801.58i) q^{67} +(-1168.67 - 1168.67i) q^{68} +(-6375.78 - 2284.85i) q^{70} -7950.20 q^{71} +(-1940.65 - 1940.65i) q^{73} +2658.92i q^{74} -1950.08 q^{76} +(-3672.16 + 3672.16i) q^{77} +4083.83i q^{79} +(713.319 - 1990.48i) q^{80} +(2758.05 - 2758.05i) q^{82} +(9103.10 + 9103.10i) q^{83} +(2403.16 + 5087.58i) q^{85} -92.9369 q^{86} +(-2739.06 - 2739.06i) q^{88} -7016.23i q^{89} +128.112 q^{91} +(-1361.70 + 1361.70i) q^{92} +1897.93i q^{94} +(6249.62 + 2239.64i) q^{95} +(2571.87 - 2571.87i) q^{97} +(-12643.8 - 12643.8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 84 q^{5} + 20 q^{7} - 180 q^{8} + 104 q^{10} + 288 q^{11} - 340 q^{13} + 620 q^{16} - 900 q^{17} - 564 q^{20} - 1100 q^{22} + 1560 q^{23} - 1204 q^{25} + 3024 q^{26} + 3580 q^{28} - 512 q^{31} - 4980 q^{32}+ \cdots - 46440 q^{98}+O(q^{100}) $ 8 * q + 84 * q^5 + 20 * q^7 - 180 * q^8 + 104 * q^10 + 288 * q^11 - 340 * q^13 + 620 * q^16 - 900 * q^17 - 564 * q^20 - 1100 * q^22 + 1560 * q^23 - 1204 * q^25 + 3024 * q^26 + 3580 * q^28 - 512 * q^31 - 4980 * q^32 - 6600 * q^35 - 3820 * q^37 + 7680 * q^38 - 2952 * q^40 + 2712 * q^41 - 1240 * q^43 + 13528 * q^46 - 4800 * q^47 - 3744 * q^50 - 1240 * q^52 - 1020 * q^53 - 3644 * q^55 + 30720 * q^56 + 2340 * q^58 - 4760 * q^61 - 28680 * q^62 + 1212 * q^65 - 8920 * q^67 + 1920 * q^68 + 7380 * q^70 - 7536 * q^71 + 11600 * q^73 + 4344 * q^76 + 360 * q^77 - 10644 * q^80 - 27200 * q^82 + 32400 * q^83 - 15628 * q^85 - 14592 * q^86 - 14340 * q^88 + 16528 * q^91 + 31800 * q^92 - 18864 * q^95 + 58640 * q^97 - 46440 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	2.08045	−	2.08045i	0.520112	−	0.520112i	−0.397493	−	0.917605i	$-0.630120\pi$
$2$	2.08045	−	2.08045i	0.520112	−	0.520112i	0.917605	+	0.397493i	$0.130120\pi$
$3$		0			0
$3$		0			0
$4$			7.34348i			0.458968i
$5$	8.43390	−	23.5344i	0.337356	−	0.941377i
$5$	8.43390	−	23.5344i	0.337356	−	0.941377i
$6$		0			0
$7$	65.1093	−	65.1093i	1.32876	−	1.32876i	0.422309	−	0.906452i	$-0.361220\pi$
$7$	65.1093	−	65.1093i	1.32876	−	1.32876i	0.906452	−	0.422309i	$-0.138780\pi$
$8$	48.5649	+	48.5649i	0.758826	+	0.758826i
$9$		0			0
$10$	−31.4158	−	66.5084i	−0.314158	−	0.665084i
$11$	−56.3999			−0.466115			−0.233058	−	0.972463i	$-0.574873\pi$
$11$	−56.3999			−0.466115			−0.233058	+	0.972463i	$0.574873\pi$
$12$		0			0
$13$	0.983822	+	0.983822i	0.00582143	+	0.00582143i	0.710012	−	0.704190i	$-0.248690\pi$
$13$	0.983822	+	0.983822i	0.00582143	+	0.00582143i	−0.704190	+	0.710012i	$0.748690\pi$
$14$		−	270.913i		−	1.38221i
$15$		0			0
$16$	84.5776			0.330381
$17$	−159.144	+	159.144i	−0.550673	+	0.550673i	−0.926635	−	0.375962i	$-0.877312\pi$
$17$	−159.144	+	159.144i	−0.550673	+	0.550673i	0.375962	+	0.926635i	$0.377312\pi$
$18$		0			0
$19$			265.552i			0.735602i	0.929905	+	0.367801i	$0.119889\pi$
$19$			265.552i			0.735602i	−0.929905	+	0.367801i	$0.880111\pi$
$20$	172.825	+	61.9342i	0.432062	+	0.154836i
$21$		0			0
$22$	−117.337	+	117.337i	−0.242432	+	0.242432i
$23$	185.430	+	185.430i	0.350529	+	0.350529i	0.860306	−	0.509778i	$-0.170272\pi$
$23$	185.430	+	185.430i	0.350529	+	0.350529i	−0.509778	+	0.860306i	$0.670272\pi$
$24$		0			0
$25$	−482.739	−	396.974i	−0.772382	−	0.635159i
$26$	4.09358			0.00605559
$27$		0			0
$28$	478.129	+	478.129i	0.609858	+	0.609858i
$29$			544.071i			0.646933i	0.946240	+	0.323467i	$0.104848\pi$
$29$			544.071i			0.646933i	−0.946240	+	0.323467i	$0.895152\pi$
$30$		0			0
$31$	−710.805			−0.739651			−0.369826	−	0.929101i	$-0.620583\pi$
$31$	−710.805			−0.739651			−0.369826	+	0.929101i	$0.620583\pi$
$32$	−601.079	+	601.079i	−0.586991	+	0.586991i
$33$		0			0
$34$			662.183i			0.572823i
$35$	−983.184	−	2081.43i	−0.802599	−	1.69913i
$36$		0			0
$37$	−639.026	+	639.026i	−0.466783	+	0.466783i	−0.900871	−	0.434088i	$-0.857071\pi$
$37$	−639.026	+	639.026i	−0.466783	+	0.466783i	0.434088	+	0.900871i	$0.357071\pi$
$38$	552.467	+	552.467i	0.382595	+	0.382595i
$39$		0			0
$40$	1552.54	−	733.355i	0.970336	−	0.458347i
$41$	1325.70			0.788638			0.394319	−	0.918974i	$-0.370981\pi$
$41$	1325.70			0.788638			0.394319	+	0.918974i	$0.370981\pi$
$42$		0			0
$43$	−22.3358	−	22.3358i	−0.0120799	−	0.0120799i	0.701041	−	0.713121i	$-0.252719\pi$
$43$	−22.3358	−	22.3358i	−0.0120799	−	0.0120799i	−0.713121	+	0.701041i	$0.752719\pi$
$44$		−	414.172i		−	0.213932i
$45$		0			0
$46$	771.553			0.364628
$47$	−456.136	+	456.136i	−0.206490	+	0.206490i	−0.802774	−	0.596284i	$-0.796643\pi$
$47$	−456.136	+	456.136i	−0.206490	+	0.206490i	0.596284	+	0.802774i	$0.296643\pi$
$48$		0			0
$49$		−	6077.44i		−	2.53121i
$50$	−1830.20	+	178.428i	−0.732078	+	0.0713713i
$51$		0			0
$52$	−7.22468	+	7.22468i	−0.00267185	+	0.00267185i
$53$	424.212	+	424.212i	0.151019	+	0.151019i	0.778573	−	0.627554i	$-0.215944\pi$
$53$	424.212	+	424.212i	0.151019	+	0.151019i	−0.627554	+	0.778573i	$0.715944\pi$
$54$		0			0
$55$	−475.672	+	1327.34i	−0.157247	+	0.438790i
$56$	6324.05			2.01660
$57$		0			0
$58$	1131.91	+	1131.91i	0.336478	+	0.336478i
$59$		−	3460.30i		−	0.994054i	−0.867735	−	0.497027i	$-0.834425\pi$
$59$		−	3460.30i		−	0.994054i	0.867735	−	0.497027i	$-0.165575\pi$
$60$		0			0
$61$	4937.82			1.32701			0.663507	−	0.748170i	$-0.269067\pi$
$61$	4937.82			1.32701			0.663507	+	0.748170i	$0.269067\pi$
$62$	−1478.79	+	1478.79i	−0.384701	+	0.384701i
$63$		0			0
$64$			3854.27i			0.940983i
$65$	31.4511	−	14.8562i	0.00744406	−	0.00351627i
$66$		0			0
$67$	−3801.58	+	3801.58i	−0.846866	+	0.846866i	−0.989741	−	0.142874i	$-0.954366\pi$
$67$	−3801.58	+	3801.58i	−0.846866	+	0.846866i	0.142874	+	0.989741i	$0.454366\pi$
$68$	−1168.67	−	1168.67i	−0.252741	−	0.252741i
$69$		0			0
$70$	−6375.78	−	2284.85i	−1.30118	−	0.466296i
$71$	−7950.20			−1.57711			−0.788554	−	0.614966i	$-0.789170\pi$
$71$	−7950.20			−1.57711			−0.788554	+	0.614966i	$0.789170\pi$
$72$		0			0
$73$	−1940.65	−	1940.65i	−0.364168	−	0.364168i	0.501177	−	0.865345i	$-0.332901\pi$
$73$	−1940.65	−	1940.65i	−0.364168	−	0.364168i	−0.865345	+	0.501177i	$0.832901\pi$
$74$			2658.92i			0.485558i
$75$		0			0
$76$	−1950.08			−0.337617
$77$	−3672.16	+	3672.16i	−0.619355	+	0.619355i
$78$		0			0
$79$			4083.83i			0.654355i	0.944963	+	0.327178i	$0.106098\pi$
$79$			4083.83i			0.654355i	−0.944963	+	0.327178i	$0.893902\pi$
$80$	713.319	−	1990.48i	0.111456	−	0.311013i
$81$		0			0
$82$	2758.05	−	2758.05i	0.410180	−	0.410180i
$83$	9103.10	+	9103.10i	1.32140	+	1.32140i	0.912646	+	0.408750i	$0.134035\pi$
$83$	9103.10	+	9103.10i	1.32140	+	1.32140i	0.408750	+	0.912646i	$0.365965\pi$
$84$		0			0
$85$	2403.16	+	5087.58i	0.332618	+	0.704164i
$86$	−92.9369			−0.0125658
$87$		0			0
$88$	−2739.06	−	2739.06i	−0.353700	−	0.353700i
$89$		−	7016.23i		−	0.885775i	−0.896577	−	0.442888i	$-0.853954\pi$
$89$		−	7016.23i		−	0.885775i	0.896577	−	0.442888i	$-0.146046\pi$
$90$		0			0
$91$	128.112			0.0154706
$92$	−1361.70	+	1361.70i	−0.160881	+	0.160881i
$93$		0			0
$94$			1897.93i			0.214796i
$95$	6249.62	+	2239.64i	0.692479	+	0.248160i
$96$		0			0
$97$	2571.87	−	2571.87i	0.273342	−	0.273342i	−0.557102	−	0.830444i	$-0.688087\pi$
$97$	2571.87	−	2571.87i	0.273342	−	0.273342i	0.830444	+	0.557102i	$0.188087\pi$
$98$	−12643.8	−	12643.8i	−1.31651	−	1.31651i
$99$		0			0
$100$	2915.17	−	3544.98i	0.291517	−	0.354498i
$101$	7459.58			0.731260			0.365630	−	0.930760i	$-0.380854\pi$
$101$	7459.58			0.731260			0.365630	+	0.930760i	$0.380854\pi$
$102$		0			0
$103$	4637.29	+	4637.29i	0.437109	+	0.437109i	0.891038	−	0.453929i	$-0.149978\pi$
$103$	4637.29	+	4637.29i	0.437109	+	0.437109i	−0.453929	+	0.891038i	$0.649978\pi$
$104$			95.5584i			0.00883491i
$105$		0			0
$106$	1765.10			0.157093
$107$	8804.34	−	8804.34i	0.769005	−	0.769005i	−0.208926	−	0.977931i	$-0.566997\pi$
$107$	8804.34	−	8804.34i	0.769005	−	0.769005i	0.977931	+	0.208926i	$0.0669969\pi$
$108$		0			0
$109$		−	7981.01i		−	0.671746i	−0.941907	−	0.335873i	$-0.890969\pi$
$109$		−	7981.01i		−	0.671746i	0.941907	−	0.335873i	$-0.109031\pi$
$110$	1771.85	+	3751.07i	0.146434	+	0.310006i
$111$		0			0
$112$	5506.78	−	5506.78i	0.438997	−	0.438997i
$113$	−1867.37	−	1867.37i	−0.146242	−	0.146242i	0.630195	−	0.776437i	$-0.282975\pi$
$113$	−1867.37	−	1867.37i	−0.146242	−	0.146242i	−0.776437	+	0.630195i	$0.782975\pi$
$114$		0			0
$115$	5927.88	−	2800.09i	0.448233	−	0.211727i
$116$	−3995.38			−0.296921
$117$		0			0
$118$	−7198.98	−	7198.98i	−0.517019	−	0.517019i
$119$			20723.6i			1.46342i
$120$		0			0
$121$	−11460.0			−0.782737
$122$	10272.9	−	10272.9i	0.690195	−	0.690195i
$123$		0			0
$124$		−	5219.78i		−	0.339476i
$125$	−13413.9	+	8012.93i	−0.858492	+	0.512828i
$126$		0			0
$127$	3139.44	−	3139.44i	0.194646	−	0.194646i	−0.603054	−	0.797700i	$-0.706050\pi$
$127$	3139.44	−	3139.44i	0.194646	−	0.194646i	0.797700	+	0.603054i	$0.206050\pi$
$128$	−1598.67	−	1598.67i	−0.0975748	−	0.0975748i
$129$		0			0
$130$	34.5248	−	96.3400i	0.00204289	−	0.00570059i
$131$	−28716.4			−1.67335			−0.836676	−	0.547698i	$-0.815504\pi$
$131$	−28716.4			−1.67335			−0.836676	+	0.547698i	$0.815504\pi$
$132$		0			0
$133$	17289.9	+	17289.9i	0.977439	+	0.977439i
$134$			15818.0i			0.880930i
$135$		0			0
$136$	−15457.7			−0.835730
$137$	25626.6	−	25626.6i	1.36537	−	1.36537i	0.498453	−	0.866917i	$-0.333902\pi$
$137$	25626.6	−	25626.6i	1.36537	−	1.36537i	0.866917	−	0.498453i	$-0.166098\pi$
$138$		0			0
$139$			16504.6i			0.854229i	0.904197	+	0.427115i	$0.140470\pi$
$139$			16504.6i			0.854229i	−0.904197	+	0.427115i	$0.859530\pi$
$140$	15285.0	−	7220.00i	0.779846	−	0.368367i
$141$		0			0
$142$	−16540.0	+	16540.0i	−0.820272	+	0.820272i
$143$	−55.4875	−	55.4875i	−0.00271346	−	0.00271346i
$144$		0			0
$145$	12804.4	+	4588.64i	0.609008	+	0.218247i
$146$	−8074.84			−0.378816
$147$		0			0
$148$	−4692.67	−	4692.67i	−0.214238	−	0.214238i
$149$		−	10599.1i		−	0.477413i	−0.971092	−	0.238707i	$-0.923277\pi$
$149$		−	10599.1i		−	0.477413i	0.971092	−	0.238707i	$-0.0767235\pi$
$150$		0			0
$151$	−30610.3			−1.34250			−0.671248	−	0.741233i	$-0.734242\pi$
$151$	−30610.3			−1.34250			−0.671248	+	0.741233i	$0.734242\pi$
$152$	−12896.5	+	12896.5i	−0.558194	+	0.558194i
$153$		0			0
$154$			15279.5i			0.644268i
$155$	−5994.86	+	16728.4i	−0.249526	+	0.696291i
$156$		0			0
$157$	17506.2	−	17506.2i	0.710220	−	0.710220i	−0.256361	−	0.966581i	$-0.582524\pi$
$157$	17506.2	−	17506.2i	0.710220	−	0.710220i	0.966581	+	0.256361i	$0.0825237\pi$
$158$	8496.20	+	8496.20i	0.340338	+	0.340338i
$159$		0			0
$160$	9076.61	+	19215.5i	0.354555	+	0.750605i
$161$	24146.4			0.931538
$162$		0			0
$163$	−13776.0	−	13776.0i	−0.518500	−	0.518500i	0.398618	−	0.917117i	$-0.369490\pi$
$163$	−13776.0	−	13776.0i	−0.518500	−	0.518500i	−0.917117	+	0.398618i	$0.869490\pi$
$164$			9735.26i			0.361959i
$165$		0			0
$166$	37877.0			1.37455
$167$	−22076.9	+	22076.9i	−0.791598	+	0.791598i	−0.981754	−	0.190156i	$-0.939101\pi$
$167$	−22076.9	+	22076.9i	−0.791598	+	0.791598i	0.190156	+	0.981754i	$0.439101\pi$
$168$		0			0
$169$		−	28559.1i		−	0.999932i
$170$	15584.1	+	5584.79i	0.539242	+	0.193245i
$171$		0			0
$172$	164.023	−	164.023i	0.00554430	−	0.00554430i
$173$	−26956.5	−	26956.5i	−0.900682	−	0.900682i	0.0948128	−	0.995495i	$-0.469775\pi$
$173$	−26956.5	−	26956.5i	−0.900682	−	0.900682i	−0.995495	+	0.0948128i	$0.969775\pi$
$174$		0			0
$175$	−57277.5	+	5584.06i	−1.87028	+	0.182337i
$176$	−4770.17			−0.153996
$177$		0			0
$178$	−14596.9	−	14596.9i	−0.460702	−	0.460702i
$179$		−	43705.2i		−	1.36404i	−0.731333	−	0.682020i	$-0.761102\pi$
$179$		−	43705.2i		−	1.36404i	0.731333	−	0.682020i	$-0.238898\pi$
$180$		0			0
$181$	30384.4			0.927456			0.463728	−	0.885978i	$-0.346512\pi$
$181$	30384.4			0.927456			0.463728	+	0.885978i	$0.346512\pi$
$182$	266.530	−	266.530i	0.00804643	−	0.00804643i
$183$		0			0
$184$			18010.7i			0.531981i
$185$	9649.62	+	20428.6i	0.281947	+	0.596891i
$186$		0			0
$187$	8975.73	−	8975.73i	0.256677	−	0.256677i
$188$	−3349.63	−	3349.63i	−0.0947722	−	0.0947722i
$189$		0			0
$190$	17661.5	−	8342.55i	0.489237	−	0.231096i
$191$	−4369.57			−0.119777			−0.0598883	−	0.998205i	$-0.519074\pi$
$191$	−4369.57			−0.119777			−0.0598883	+	0.998205i	$0.519074\pi$
$192$		0			0
$193$	−5475.99	−	5475.99i	−0.147011	−	0.147011i	0.629771	−	0.776781i	$-0.283149\pi$
$193$	−5475.99	−	5475.99i	−0.147011	−	0.147011i	−0.776781	+	0.629771i	$0.783149\pi$
$194$		−	10701.3i		−	0.284337i
$195$		0			0
$196$	44629.5			1.16174
$197$	11188.4	−	11188.4i	0.288295	−	0.288295i	−0.548111	−	0.836406i	$-0.684653\pi$
$197$	11188.4	−	11188.4i	0.288295	−	0.288295i	0.836406	+	0.548111i	$0.184653\pi$
$198$		0			0
$199$			17995.1i			0.454409i	0.973847	+	0.227205i	$0.0729586\pi$
$199$			17995.1i			0.454409i	−0.973847	+	0.227205i	$0.927041\pi$
$200$	−4165.14	−	42723.1i	−0.104128	−	1.06808i
$201$		0			0
$202$	15519.3	−	15519.3i	0.380337	−	0.380337i
$203$	35424.1	+	35424.1i	0.859620	+	0.859620i
$204$		0			0
$205$	11180.8	−	31199.6i	0.266052	−	0.742406i
$206$	19295.3			0.454691
$207$		0			0
$208$	83.2093	+	83.2093i	0.00192329	+	0.00192329i
$209$		−	14977.1i		−	0.342875i
$210$		0			0
$211$	−12455.8			−0.279774			−0.139887	−	0.990167i	$-0.544674\pi$
$211$	−12455.8			−0.279774			−0.139887	+	0.990167i	$0.544674\pi$
$212$	−3115.19	+	3115.19i	−0.0693128	+	0.0693128i
$213$		0			0
$214$		−	36633.9i		−	0.799937i
$215$	−714.039	+	337.282i	−0.0154470	+	0.00729654i
$216$		0			0
$217$	−46280.0	+	46280.0i	−0.982820	+	0.982820i
$218$	−16604.1	−	16604.1i	−0.349383	−	0.349383i
$219$		0			0
$220$	−9747.30	−	3493.09i	−0.201390	−	0.0721712i
$221$	−313.140			−0.00641141
$222$		0			0
$223$	26399.5	+	26399.5i	0.530867	+	0.530867i	0.920830	−	0.389963i	$-0.127512\pi$
$223$	26399.5	+	26399.5i	0.530867	+	0.530867i	−0.389963	+	0.920830i	$0.627512\pi$
$224$			78271.6i			1.55994i
$225$		0			0
$226$	−7769.92			−0.152125
$227$	−32267.3	+	32267.3i	−0.626197	+	0.626197i	−0.947109	−	0.320912i	$-0.896011\pi$
$227$	−32267.3	+	32267.3i	−0.626197	+	0.626197i	0.320912	+	0.947109i	$0.396011\pi$
$228$		0			0
$229$		−	68117.5i		−	1.29894i	−0.760389	−	0.649468i	$-0.774992\pi$
$229$		−	68117.5i		−	1.29894i	0.760389	−	0.649468i	$-0.225008\pi$
$230$	6507.21	−	18158.1i	0.123010	−	0.343253i
$231$		0			0
$232$	−26422.7	+	26422.7i	−0.490910	+	0.490910i
$233$	65936.0	+	65936.0i	1.21454	+	1.21454i	0.969518	+	0.245019i	$0.0787941\pi$
$233$	65936.0	+	65936.0i	1.21454	+	1.21454i	0.245019	+	0.969518i	$0.421206\pi$
$234$		0			0
$235$	6887.90	+	14581.9i	0.124724	+	0.264045i
$236$	25410.7			0.456239
$237$		0			0
$238$	43114.3	+	43114.3i	0.761144	+	0.761144i
$239$		−	64820.9i		−	1.13480i	−0.823443	−	0.567400i	$-0.807950\pi$
$239$		−	64820.9i		−	1.13480i	0.823443	−	0.567400i	$-0.192050\pi$
$240$		0			0
$241$	−59597.9			−1.02612			−0.513058	−	0.858354i	$-0.671488\pi$
$241$	−59597.9			−1.02612			−0.513058	+	0.858354i	$0.671488\pi$
$242$	−23842.0	+	23842.0i	−0.407111	+	0.407111i
$243$		0			0
$244$			36260.8i			0.609056i
$245$	−143029.	−	51256.5i	−2.38282	−	0.853919i
$246$		0			0
$247$	−261.256	+	261.256i	−0.00428226	+	0.00428226i
$248$	−34520.1	−	34520.1i	−0.561267	−	0.561267i
$249$		0			0
$250$	−11236.5	+	44577.5i	−0.179784	+	0.713239i
$251$	33922.6			0.538445			0.269223	−	0.963078i	$-0.413233\pi$
$251$	33922.6			0.538445			0.269223	+	0.963078i	$0.413233\pi$
$252$		0			0
$253$	−10458.2	−	10458.2i	−0.163387	−	0.163387i
$254$		−	13062.9i		−	0.202475i
$255$		0			0
$256$	−68320.1			−1.04248
$257$	−26107.3	+	26107.3i	−0.395272	+	0.395272i	−0.876562	−	0.481290i	$-0.840168\pi$
$257$	−26107.3	+	26107.3i	−0.395272	+	0.395272i	0.481290	+	0.876562i	$0.340168\pi$
$258$		0			0
$259$			83213.0i			1.24049i
$260$	109.096	+	230.961i	0.00161385	+	0.00341658i
$261$		0			0
$262$	−59743.0	+	59743.0i	−0.870330	+	0.870330i
$263$	−25675.0	−	25675.0i	−0.371192	−	0.371192i	0.496719	−	0.867911i	$-0.334538\pi$
$263$	−25675.0	−	25675.0i	−0.371192	−	0.371192i	−0.867911	+	0.496719i	$0.834538\pi$
$264$		0			0
$265$	13561.4	−	6405.83i	0.193113	−	0.0912186i
$266$	71941.5			1.01675
$267$		0			0
$268$	−27916.9	−	27916.9i	−0.388684	−	0.388684i
$269$			84488.9i			1.16760i	0.811896	+	0.583801i	$0.198435\pi$
$269$			84488.9i			1.16760i	−0.811896	+	0.583801i	$0.801565\pi$
$270$		0			0
$271$	105918.			1.44222			0.721109	−	0.692821i	$-0.243633\pi$
$271$	105918.			1.44222			0.721109	+	0.692821i	$0.243633\pi$
$272$	−13460.0	+	13460.0i	−0.181932	+	0.181932i
$273$		0			0
$274$		−	106630.i		−	1.42029i
$275$	27226.4	+	22389.3i	0.360019	+	0.296057i
$276$		0			0
$277$	71448.5	−	71448.5i	0.931180	−	0.931180i	−0.0665996	−	0.997780i	$-0.521215\pi$
$277$	71448.5	−	71448.5i	0.931180	−	0.931180i	0.997780	+	0.0665996i	$0.0212150\pi$
$278$	34336.9	+	34336.9i	0.444295	+	0.444295i
$279$		0			0
$280$	53336.4	−	148833.i	0.680311	−	1.89838i
$281$	−6316.20			−0.0799914			−0.0399957	−	0.999200i	$-0.512734\pi$
$281$	−6316.20			−0.0799914			−0.0399957	+	0.999200i	$0.512734\pi$
$282$		0			0
$283$	51729.2	+	51729.2i	0.645896	+	0.645896i	0.951999	−	0.306102i	$-0.0990250\pi$
$283$	51729.2	+	51729.2i	0.645896	+	0.645896i	−0.306102	+	0.951999i	$0.599025\pi$
$284$		−	58382.2i		−	0.723841i
$285$		0			0
$286$	−230.878			−0.00282260
$287$	86315.4	−	86315.4i	1.04791	−	1.04791i
$288$		0			0
$289$			32867.1i			0.393519i
$290$	36185.3	−	17092.4i	0.430265	−	0.203240i
$291$		0			0
$292$	14251.1	−	14251.1i	0.167141	−	0.167141i
$293$	71710.7	+	71710.7i	0.835312	+	0.835312i	0.988238	−	0.152926i	$-0.0488696\pi$
$293$	71710.7	+	71710.7i	0.835312	+	0.835312i	−0.152926	+	0.988238i	$0.548870\pi$
$294$		0			0
$295$	−81436.3	−	29183.9i	−0.935780	−	0.335350i
$296$	−62068.4			−0.708414
$297$		0			0
$298$	−22050.8	−	22050.8i	−0.248308	−	0.248308i
$299$			364.860i			0.00408116i
$300$		0			0
$301$	−2908.54			−0.0321027
$302$	−63683.0	+	63683.0i	−0.698248	+	0.698248i
$303$		0			0
$304$			22459.8i			0.243029i
$305$	41645.1	−	116209.i	0.447676	−	1.24922i
$306$		0			0
$307$	22058.5	−	22058.5i	0.234045	−	0.234045i	−0.580334	−	0.814379i	$-0.697078\pi$
$307$	22058.5	−	22058.5i	0.234045	−	0.234045i	0.814379	+	0.580334i	$0.197078\pi$
$308$	−26966.4	−	26966.4i	−0.284264	−	0.284264i
$309$		0			0
$310$	22330.5	+	47274.5i	0.232368	+	0.491930i
$311$	−100432.			−1.03837			−0.519184	−	0.854663i	$-0.673764\pi$
$311$	−100432.			−1.03837			−0.519184	+	0.854663i	$0.673764\pi$
$312$		0			0
$313$	32532.8	+	32532.8i	0.332072	+	0.332072i	0.853373	−	0.521301i	$-0.174553\pi$
$313$	32532.8	+	32532.8i	0.332072	+	0.332072i	−0.521301	+	0.853373i	$0.674553\pi$
$314$		−	72841.4i		−	0.738787i
$315$		0			0
$316$	−29989.5			−0.300328
$317$	72670.5	−	72670.5i	0.723169	−	0.723169i	−0.246080	−	0.969249i	$-0.579143\pi$
$317$	72670.5	−	72670.5i	0.723169	−	0.723169i	0.969249	+	0.246080i	$0.0791428\pi$
$318$		0			0
$319$		−	30685.6i		−	0.301545i
$320$	90707.9	+	32506.5i	0.885820	+	0.317446i
$321$		0			0
$322$	50235.3	−	50235.3i	0.484504	−	0.484504i
$323$	−42261.2	−	42261.2i	−0.405076	−	0.405076i
$324$		0			0
$325$	−84.3769	−	865.481i	−0.000798834	−	0.00819390i
$326$	−57320.5			−0.539355
$327$		0			0
$328$	64382.5	+	64382.5i	0.598439	+	0.598439i
$329$			59397.4i			0.548751i
$330$		0			0
$331$	114400.			1.04417			0.522085	−	0.852893i	$-0.325154\pi$
$331$	114400.			1.04417			0.522085	+	0.852893i	$0.325154\pi$
$332$	−66848.5	+	66848.5i	−0.606478	+	0.606478i
$333$		0			0
$334$			91859.5i			0.823439i
$335$	57405.9	+	121530.i	0.511525	+	1.08292i
$336$		0			0
$337$	−75745.0	+	75745.0i	−0.666952	+	0.666952i	−0.957009	−	0.290058i	$-0.906326\pi$
$337$	−75745.0	+	75745.0i	−0.666952	+	0.666952i	0.290058	+	0.957009i	$0.406326\pi$
$338$	−59415.6	−	59415.6i	−0.520076	−	0.520076i
$339$		0			0
$340$	−37360.6	+	17647.6i	−0.323188	+	0.152661i
$341$	40089.3			0.344763
$342$		0			0
$343$	−239370.	−	239370.i	−2.03461	−	2.03461i
$344$		−	2169.47i		−	0.0183332i
$345$		0			0
$346$	−112163.			−0.936911
$347$	−49964.9	+	49964.9i	−0.414960	+	0.414960i	−0.883462	−	0.468502i	$-0.844794\pi$
$347$	−49964.9	+	49964.9i	−0.414960	+	0.414960i	0.468502	+	0.883462i	$0.344794\pi$
$348$		0			0
$349$			74192.9i			0.609132i	0.952491	+	0.304566i	$0.0985115\pi$
$349$			74192.9i			0.609132i	−0.952491	+	0.304566i	$0.901489\pi$
$350$	−107545.	+	130780.i	−0.877921	+	1.06759i
$351$		0			0
$352$	33900.8	−	33900.8i	0.273605	−	0.273605i
$353$	15476.1	+	15476.1i	0.124198	+	0.124198i	0.766473	−	0.642276i	$-0.222010\pi$
$353$	15476.1	+	15476.1i	0.124198	+	0.124198i	−0.642276	+	0.766473i	$0.722010\pi$
$354$		0			0
$355$	−67051.2	+	187103.i	−0.532047	+	1.48465i
$356$	51523.5			0.406542
$357$		0			0
$358$	−90926.4	−	90926.4i	−0.709453	−	0.709453i
$359$		−	46469.2i		−	0.360559i	−0.983615	−	0.180279i	$-0.942300\pi$
$359$		−	46469.2i		−	0.360559i	0.983615	−	0.180279i	$-0.0577002\pi$
$360$		0			0
$361$	59803.0			0.458890
$362$	63213.1	−	63213.1i	0.482381	−	0.482381i
$363$		0			0
$364$			940.787i			0.00710049i
$365$	−62039.4	+	29304.9i	−0.465674	+	0.219965i
$366$		0			0
$367$	57731.0	−	57731.0i	0.428624	−	0.428624i	−0.459535	−	0.888160i	$-0.651984\pi$
$367$	57731.0	−	57731.0i	0.428624	−	0.428624i	0.888160	+	0.459535i	$0.151984\pi$
$368$	15683.2	+	15683.2i	0.115808	+	0.115808i
$369$		0			0
$370$	62576.1	+	22425.1i	0.457093	+	0.163806i
$371$	55240.3			0.401336
$372$		0			0
$373$	166181.	+	166181.i	1.19444	+	1.19444i	0.975807	+	0.218634i	$0.0701600\pi$
$373$	166181.	+	166181.i	1.19444	+	1.19444i	0.218634	+	0.975807i	$0.429840\pi$
$374$		−	37347.1i		−	0.267001i
$375$		0			0
$376$	−44304.4			−0.313380
$377$	−535.269	+	535.269i	−0.00376608	+	0.00376608i
$378$		0			0
$379$		−	41316.4i		−	0.287636i	−0.989604	−	0.143818i	$-0.954062\pi$
$379$		−	41316.4i		−	0.287636i	0.989604	−	0.143818i	$-0.0459380\pi$
$380$	−16446.8	+	45894.0i	−0.113897	+	0.317825i
$381$		0			0
$382$	−9090.66	+	9090.66i	−0.0622972	+	0.0622972i
$383$	−72155.3	−	72155.3i	−0.491893	−	0.491893i	0.417009	−	0.908902i	$-0.363078\pi$
$383$	−72155.3	−	72155.3i	−0.491893	−	0.491893i	−0.908902	+	0.417009i	$0.863078\pi$
$384$		0			0
$385$	55451.5	+	117393.i	0.374104	+	0.791990i
$386$	−22785.0			−0.152924
$387$		0			0
$388$	18886.5	+	18886.5i	0.125455	+	0.125455i
$389$			192183.i			1.27004i	0.772497	+	0.635018i	$0.219007\pi$
$389$			192183.i			1.27004i	−0.772497	+	0.635018i	$0.780993\pi$
$390$		0			0
$391$	−59020.2			−0.386053
$392$	295150.	−	295150.i	1.92075	−	1.92075i
$393$		0			0
$394$		−	46553.9i		−	0.299891i
$395$	96110.7	+	34442.6i	0.615995	+	0.220751i
$396$		0			0
$397$	−177091.	+	177091.i	−1.12361	+	1.12361i	−0.132416	+	0.991194i	$0.542274\pi$
$397$	−177091.	+	177091.i	−1.12361	+	1.12361i	−0.991194	+	0.132416i	$0.957726\pi$
$398$	37437.8	+	37437.8i	0.236344	+	0.236344i
$399$		0			0
$400$	−40828.8	−	33575.1i	−0.255180	−	0.209844i
$401$	−208300.			−1.29539			−0.647694	−	0.761900i	$-0.724267\pi$
$401$	−208300.			−1.29539			−0.647694	+	0.761900i	$0.724267\pi$
$402$		0			0
$403$	−699.305	−	699.305i	−0.00430583	−	0.00430583i
$404$			54779.3i			0.335624i
$405$		0			0
$406$	147396.			0.894197
$407$	36041.0	−	36041.0i	0.217574	−	0.217574i
$408$		0			0
$409$		−	265733.i		−	1.58854i	−0.607563	−	0.794271i	$-0.707853\pi$
$409$		−	265733.i		−	1.58854i	0.607563	−	0.794271i	$-0.292147\pi$
$410$	−41648.0	−	88170.2i	−0.247757	−	0.524511i
$411$		0			0
$412$	−34053.8	+	34053.8i	−0.200619	+	0.200619i
$413$	−225298.	−	225298.i	−1.32086	−	1.32086i
$414$		0			0
$415$	291011.	−	137462.i	1.68971	−	0.798151i
$416$	−1182.71			−0.00683426
$417$		0			0
$418$	−31159.1	−	31159.1i	−0.178333	−	0.178333i
$419$			125608.i			0.715467i	0.933824	+	0.357734i	$0.116450\pi$
$419$			125608.i			0.715467i	−0.933824	+	0.357734i	$0.883550\pi$
$420$		0			0
$421$	−278634.			−1.57206			−0.786031	−	0.618187i	$-0.787868\pi$
$421$	−278634.			−1.57206			−0.786031	+	0.618187i	$0.787868\pi$
$422$	−25913.7	+	25913.7i	−0.145514	+	0.145514i
$423$		0			0
$424$			41203.6i			0.229194i
$425$	140001.	−	13648.9i	0.775094	−	0.0755650i
$426$		0			0
$427$	321498.	−	321498.i	1.76328	−	1.76328i
$428$	64654.5	+	64654.5i	0.352948	+	0.352948i
$429$		0			0
$430$	−783.821	+	2187.22i	−0.00423916	+	0.0118292i
$431$	−100603.			−0.541575			−0.270787	−	0.962639i	$-0.587284\pi$
$431$	−100603.			−0.541575			−0.270787	+	0.962639i	$0.587284\pi$
$432$		0			0
$433$	−116014.	−	116014.i	−0.618777	−	0.618777i	0.326440	−	0.945218i	$-0.394151\pi$
$433$	−116014.	−	116014.i	−0.618777	−	0.618777i	−0.945218	+	0.326440i	$0.894151\pi$
$434$			192566.i			1.02235i
$435$		0			0
$436$	58608.4			0.308310
$437$	−49241.3	+	49241.3i	−0.257850	+	0.257850i
$438$		0			0
$439$		−	163656.i		−	0.849184i	−0.905385	−	0.424592i	$-0.860418\pi$
$439$		−	163656.i		−	0.849184i	0.905385	−	0.424592i	$-0.139582\pi$
$440$	−87563.0	+	41361.2i	−0.452288	+	0.213642i
$441$		0			0
$442$	−651.470	+	651.470i	−0.00333465	+	0.00333465i
$443$	117313.	+	117313.i	0.597775	+	0.597775i	0.939720	−	0.341945i	$-0.111086\pi$
$443$	117313.	+	117313.i	0.597775	+	0.597775i	−0.341945	+	0.939720i	$0.611086\pi$
$444$		0			0
$445$	−165123.	−	59174.2i	−0.833849	−	0.298822i
$446$	109845.			0.552220
$447$		0			0
$448$	250948.	+	250948.i	1.25034	+	1.25034i
$449$		−	342550.i		−	1.69915i	−0.527468	−	0.849575i	$-0.676859\pi$
$449$		−	342550.i		−	1.69915i	0.527468	−	0.849575i	$-0.323141\pi$
$450$		0			0
$451$	−74769.4			−0.367596
$452$	13713.0	−	13713.0i	0.0671204	−	0.0671204i
$453$		0			0
$454$			134261.i			0.651385i
$455$	1080.48	−	3015.04i	0.00521909	−	0.0145636i
$456$		0			0
$457$	−162804.	+	162804.i	−0.779530	+	0.779530i	−0.979751	−	0.200221i	$-0.935834\pi$
$457$	−162804.	+	162804.i	−0.779530	+	0.779530i	0.200221	+	0.979751i	$0.435834\pi$
$458$	−141715.	−	141715.i	−0.675592	−	0.675592i
$459$		0			0
$460$	20562.4	+	43531.3i	0.0971757	+	0.205724i
$461$	283688.			1.33487			0.667436	−	0.744667i	$-0.267392\pi$
$461$	283688.			1.33487			0.667436	+	0.744667i	$0.267392\pi$
$462$		0			0
$463$	−34085.9	−	34085.9i	−0.159006	−	0.159006i	0.623120	−	0.782126i	$-0.285865\pi$
$463$	−34085.9	−	34085.9i	−0.159006	−	0.159006i	−0.782126	+	0.623120i	$0.785865\pi$
$464$			46016.2i			0.213735i
$465$		0			0
$466$	274353.			1.26339
$467$	124988.	−	124988.i	0.573107	−	0.573107i	−0.359889	−	0.932995i	$-0.617185\pi$
$467$	124988.	−	124988.i	0.573107	−	0.573107i	0.932995	+	0.359889i	$0.117185\pi$
$468$		0			0
$469$			495037.i			2.25057i
$470$	44666.8	+	16007.0i	0.202204	+	0.0724626i
$471$		0			0
$472$	168049.	−	168049.i	0.754314	−	0.754314i
$473$	1259.74	+	1259.74i	0.00563064	+	0.00563064i
$474$		0			0
$475$	105417.	−	128192.i	0.467224	−	0.568165i
$476$	−152183.			−0.671665
$477$		0			0
$478$	−134856.	−	134856.i	−0.590222	−	0.590222i
$479$		−	248368.i		−	1.08249i	−0.840864	−	0.541247i	$-0.817953\pi$
$479$		−	248368.i		−	1.08249i	0.840864	−	0.541247i	$-0.182047\pi$
$480$		0			0
$481$	−1257.37			−0.00543469
$482$	−123990.	+	123990.i	−0.533695	+	0.533695i
$483$		0			0
$484$		−	84156.7i		−	0.359251i
$485$	−38836.6	−	82218.5i	−0.165104	−	0.349531i
$486$		0			0
$487$	−159374.	+	159374.i	−0.671983	+	0.671983i	−0.958173	−	0.286190i	$-0.907611\pi$
$487$	−159374.	+	159374.i	−0.671983	+	0.671983i	0.286190	+	0.958173i	$0.407611\pi$
$488$	239804.	+	239804.i	1.00697	+	1.00697i
$489$		0			0
$490$	−404201.	+	190928.i	−1.68347	+	0.795201i
$491$	16577.9			0.0687647			0.0343823	−	0.999409i	$-0.489054\pi$
$491$	16577.9			0.0687647			0.0343823	+	0.999409i	$0.489054\pi$
$492$		0			0
$493$	−86585.9	−	86585.9i	−0.356249	−	0.356249i
$494$			1087.06i			0.00445450i
$495$		0			0
$496$	−60118.1			−0.244367
$497$	−517632.	+	517632.i	−2.09560	+	2.09560i
$498$		0			0
$499$			202437.i			0.812998i	0.913651	+	0.406499i	$0.133250\pi$
$499$			202437.i			0.812998i	−0.913651	+	0.406499i	$0.866750\pi$
$500$	−58842.8	−	98505.0i	−0.235371	−	0.394020i
$501$		0			0
$502$	70574.2	−	70574.2i	0.280052	−	0.280052i
$503$	33478.6	+	33478.6i	0.132322	+	0.132322i	0.770166	−	0.637844i	$-0.220173\pi$
$503$	33478.6	+	33478.6i	0.132322	+	0.132322i	−0.637844	+	0.770166i	$0.720173\pi$
$504$		0			0
$505$	62913.4	−	175557.i	0.246695	−	0.688391i
$506$	−43515.5			−0.169959
$507$		0			0
$508$	23054.4	+	23054.4i	0.0893361	+	0.0893361i
$509$			57834.5i			0.223229i	0.993752	+	0.111615i	$0.0356022\pi$
$509$			57834.5i			0.223229i	−0.993752	+	0.111615i	$0.964398\pi$
$510$		0			0
$511$	−252709.			−0.967784
$512$	−116558.	+	116558.i	−0.444633	+	0.444633i
$513$		0			0
$514$			108630.i			0.411171i
$515$	148246.	−	70025.4i	0.558945	−	0.264023i
$516$		0			0
$517$	25726.0	−	25726.0i	0.0962481	−	0.0962481i
$518$	173120.	+	173120.i	0.645191	+	0.645191i
$519$		0			0
$520$	2248.91	+	805.930i	0.00831698	+	0.00298051i
$521$	56237.4			0.207181			0.103591	−	0.994620i	$-0.466967\pi$
$521$	56237.4			0.207181			0.103591	+	0.994620i	$0.466967\pi$
$522$		0			0
$523$	210047.	+	210047.i	0.767914	+	0.767914i	0.977739	−	0.209825i	$-0.0672894\pi$
$523$	210047.	+	210047.i	0.767914	+	0.767914i	−0.209825	+	0.977739i	$0.567289\pi$
$524$		−	210878.i		−	0.768015i
$525$		0			0
$526$	−106831.			−0.386123
$527$	113121.	−	113121.i	0.407306	−	0.407306i
$528$		0			0
$529$		−	211073.i		−	0.754259i
$530$	14886.7	−	41540.7i	0.0529964	−	0.147884i
$531$		0			0
$532$	−126968.	+	126968.i	−0.448613	+	0.448613i
$533$	1304.25	+	1304.25i	0.00459100	+	0.00459100i
$534$		0			0
$535$	−132950.	−	281460.i	−0.464495	−	0.983352i
$536$	−369247.			−1.28525
$537$		0			0
$538$	175775.	+	175775.i	0.607284	+	0.607284i
$539$			342767.i			1.17984i
$540$		0			0
$541$	263561.			0.900505			0.450252	−	0.892901i	$-0.351334\pi$
$541$	263561.			0.900505			0.450252	+	0.892901i	$0.351334\pi$
$542$	220357.	−	220357.i	0.750115	−	0.750115i
$543$		0			0
$544$		−	191317.i		−	0.646480i
$545$	−187829.	−	67311.1i	−0.632366	−	0.226618i
$546$		0			0
$547$	−155327.	+	155327.i	−0.519125	+	0.519125i	−0.917306	−	0.398182i	$-0.869641\pi$
$547$	−155327.	+	155327.i	−0.519125	+	0.519125i	0.398182	+	0.917306i	$0.369641\pi$
$548$	188189.	+	188189.i	0.626660	+	0.626660i
$549$		0			0
$550$	103223.	−	10063.3i	0.341233	−	0.0332672i
$551$	−144479.			−0.475885
$552$		0			0
$553$	265895.	+	265895.i	0.869482	+	0.869482i
$554$		−	297290.i		−	0.968635i
$555$		0			0
$556$	−121201.			−0.392064
$557$	−144074.	+	144074.i	−0.464381	+	0.464381i	−0.900088	−	0.435707i	$-0.856498\pi$
$557$	−144074.	+	144074.i	−0.464381	+	0.464381i	0.435707	+	0.900088i	$0.356498\pi$
$558$		0			0
$559$		−	43.9489i		−	0.000140645i
$560$	−83155.3	−	176043.i	−0.265164	−	0.561361i
$561$		0			0
$562$	−13140.5	+	13140.5i	−0.0416044	+	0.0416044i
$563$	−348774.	−	348774.i	−1.10034	−	1.10034i	−0.994369	−	0.105970i	$-0.966205\pi$
$563$	−348774.	−	348774.i	−1.10034	−	1.10034i	−0.105970	−	0.994369i	$-0.533795\pi$
$564$		0			0
$565$	−59696.6	+	28198.2i	−0.187005	+	0.0883334i
$566$	215240.			0.671876
$567$		0			0
$568$	−386101.	−	386101.i	−1.19675	−	1.19675i
$569$		−	183209.i		−	0.565878i	−0.959138	−	0.282939i	$-0.908691\pi$
$569$		−	183209.i		−	0.565878i	0.959138	−	0.282939i	$-0.0913095\pi$
$570$		0			0
$571$	363497.			1.11488			0.557440	−	0.830217i	$-0.311784\pi$
$571$	363497.			1.11488			0.557440	+	0.830217i	$0.311784\pi$
$572$	407.471	−	407.471i	0.00124539	−	0.00124539i
$573$		0			0
$574$		−	359149.i		−	1.09006i
$575$	−15903.3	−	163125.i	−0.0481006	−	0.493383i
$576$		0			0
$577$	168516.	−	168516.i	0.506161	−	0.506161i	−0.407184	−	0.913346i	$-0.633489\pi$
$577$	168516.	−	168516.i	0.506161	−	0.506161i	0.913346	+	0.407184i	$0.133489\pi$
$578$	68378.2	+	68378.2i	0.204674	+	0.204674i
$579$		0			0
$580$	−33696.6	+	94028.9i	−0.100168	+	0.279515i
$581$	1.18539e6			3.51164
$582$		0			0
$583$	−23925.5	−	23925.5i	−0.0703922	−	0.0703922i
$584$		−	188495.i		−	0.552680i
$585$		0			0
$586$	298380.			0.868911
$587$	129891.	−	129891.i	0.376966	−	0.376966i	−0.493040	−	0.870007i	$-0.664114\pi$
$587$	129891.	−	129891.i	0.376966	−	0.376966i	0.870007	+	0.493040i	$0.164114\pi$
$588$		0			0
$589$		−	188756.i		−	0.544089i
$590$	−230139.	+	108708.i	−0.661130	+	0.312291i
$591$		0			0
$592$	−54047.2	+	54047.2i	−0.154216	+	0.154216i
$593$	299982.	+	299982.i	0.853072	+	0.853072i	0.990510	−	0.137438i	$-0.0438868\pi$
$593$	299982.	+	299982.i	0.853072	+	0.853072i	−0.137438	+	0.990510i	$0.543887\pi$
$594$		0			0
$595$	487717.	+	174780.i	1.37763	+	0.493695i
$596$	77834.0			0.219117
$597$		0			0
$598$	759.071	+	759.071i	0.00212266	+	0.00212266i
$599$			642365.i			1.79031i	0.445754	+	0.895155i	$0.352935\pi$
$599$			642365.i			1.79031i	−0.445754	+	0.895155i	$0.647065\pi$
$600$		0			0
$601$	624794.			1.72977			0.864884	−	0.501971i	$-0.167392\pi$
$601$	624794.			1.72977			0.864884	+	0.501971i	$0.167392\pi$
$602$	−6051.06	+	6051.06i	−0.0166970	+	0.0166970i
$603$		0			0
$604$		−	224786.i		−	0.616163i
$605$	−96652.9	+	269706.i	−0.264061	+	0.736850i
$606$		0			0
$607$	−133169.	+	133169.i	−0.361431	+	0.361431i	−0.864340	−	0.502909i	$-0.832263\pi$
$607$	−133169.	+	133169.i	−0.361431	+	0.361431i	0.502909	+	0.864340i	$0.332263\pi$
$608$	−159618.	−	159618.i	−0.431792	−	0.431792i
$609$		0			0
$610$	−155126.	−	328406.i	−0.416892	−	0.882575i
$611$	−897.513			−0.00240413
$612$		0			0
$613$	−394586.	−	394586.i	−1.05008	−	1.05008i	−0.998678	−	0.0513978i	$-0.983632\pi$
$613$	−394586.	−	394586.i	−1.05008	−	1.05008i	−0.0513978	−	0.998678i	$-0.516368\pi$
$614$		−	91783.0i		−	0.243459i
$615$		0			0
$616$	−356676.			−0.939966
$617$	−246284.	+	246284.i	−0.646942	+	0.646942i	−0.952253	−	0.305311i	$-0.901240\pi$
$617$	−246284.	+	246284.i	−0.646942	+	0.646942i	0.305311	+	0.952253i	$0.401240\pi$
$618$		0			0
$619$			135789.i			0.354391i	0.984176	+	0.177195i	$0.0567025\pi$
$619$			135789.i			0.354391i	−0.984176	+	0.177195i	$0.943298\pi$
$620$	−122845.	−	44023.1i	−0.319575	−	0.114524i
$621$		0			0
$622$	−208943.	+	208943.i	−0.540067	+	0.540067i
$623$	−456821.	−	456821.i	−1.17698	−	1.17698i
$624$		0			0
$625$	75448.0	+	383269.i	0.193147	+	0.981170i
$626$	135365.			0.345429
$627$		0			0
$628$	128556.	+	128556.i	0.325968	+	0.325968i
$629$		−	203395.i		−	0.514089i
$630$		0			0
$631$	−566102.			−1.42179			−0.710896	−	0.703297i	$-0.751710\pi$
$631$	−566102.			−1.42179			−0.710896	+	0.703297i	$0.751710\pi$
$632$	−198331.	+	198331.i	−0.496542	+	0.496542i
$633$		0			0
$634$		−	302374.i		−	0.752257i
$635$	−47407.2	−	100363.i	−0.117570	−	0.248900i
$636$		0			0
$637$	5979.11	−	5979.11i	0.0147353	−	0.0147353i
$638$	−63839.7	−	63839.7i	−0.156837	−	0.156837i
$639$		0			0
$640$	−51106.7	+	24140.7i	−0.124772	+	0.0589372i
$641$	−398483.			−0.969826			−0.484913	−	0.874562i	$-0.661149\pi$
$641$	−398483.			−0.969826			−0.484913	+	0.874562i	$0.661149\pi$
$642$		0			0
$643$	270770.	+	270770.i	0.654905	+	0.654905i	0.954170	−	0.299265i	$-0.0967415\pi$
$643$	270770.	+	270770.i	0.654905	+	0.654905i	−0.299265	+	0.954170i	$0.596741\pi$
$644$			177319.i			0.427546i
$645$		0			0
$646$	−175844.			−0.421370
$647$	−22129.0	+	22129.0i	−0.0528632	+	0.0528632i	−0.733044	−	0.680181i	$-0.761901\pi$
$647$	−22129.0	+	22129.0i	−0.0528632	+	0.0528632i	0.680181	+	0.733044i	$0.261901\pi$
$648$		0			0
$649$			195161.i			0.463344i
$650$	−1976.13	−	1625.04i	−0.00467723	−	0.00384626i
$651$		0			0
$652$	101164.	−	101164.i	0.237974	−	0.237974i
$653$	168610.	+	168610.i	0.395418	+	0.395418i	0.876613	−	0.481195i	$-0.159797\pi$
$653$	168610.	+	168610.i	0.395418	+	0.395418i	−0.481195	+	0.876613i	$0.659797\pi$
$654$		0			0
$655$	−242191.	+	675824.i	−0.564516	+	1.57526i
$656$	112125.			0.260551
$657$		0			0
$658$	123573.	+	123573.i	0.285412	+	0.285412i
$659$		−	106032.i		−	0.244155i	−0.992521	−	0.122078i	$-0.961044\pi$
$659$		−	106032.i		−	0.244155i	0.992521	−	0.122078i	$-0.0389557\pi$
$660$		0			0
$661$	−360211.			−0.824432			−0.412216	−	0.911086i	$-0.635245\pi$
$661$	−360211.			−0.824432			−0.412216	+	0.911086i	$0.635245\pi$
$662$	238004.	−	238004.i	0.543085	−	0.543085i
$663$		0			0
$664$			884182.i			2.00542i
$665$	552730.	−	261087.i	1.24988	−	0.590394i
$666$		0			0
$667$	−100887.	+	100887.i	−0.226769	+	0.226769i
$668$	−162121.	−	162121.i	−0.363318	−	0.363318i
$669$		0			0
$670$	372267.	+	133407.i	0.829288	+	0.297187i
$671$	−278492.			−0.618541
$672$		0			0
$673$	−174418.	−	174418.i	−0.385090	−	0.385090i	0.487842	−	0.872932i	$-0.337784\pi$
$673$	−174418.	−	174418.i	−0.385090	−	0.385090i	−0.872932	+	0.487842i	$0.837784\pi$
$674$			315167.i			0.693779i
$675$		0			0
$676$	209723.			0.458937
$677$	−118882.	+	118882.i	−0.259382	+	0.259382i	−0.824803	−	0.565421i	$-0.808714\pi$
$677$	−118882.	+	118882.i	−0.259382	+	0.259382i	0.565421	+	0.824803i	$0.308714\pi$
$678$		0			0
$679$		−	334906.i		−	0.726412i
$680$	−130368.	+	363787.i	−0.281939	+	0.786737i
$681$		0			0
$682$	83403.7	−	83403.7i	0.179315	−	0.179315i
$683$	464368.	+	464368.i	0.995453	+	0.995453i	0.999990	−	0.00453640i	$-0.00144399\pi$
$683$	464368.	+	464368.i	0.995453	+	0.995453i	−0.00453640	+	0.999990i	$0.501444\pi$
$684$		0			0
$685$	−386975.	−	819240.i	−0.824712	−	1.74594i
$686$	−995993.			−2.11645
$687$		0			0
$688$	−1889.11	−	1889.11i	−0.00399098	−	0.00399098i
$689$			834.698i			0.00175829i
$690$		0			0
$691$	112733.			0.236099			0.118050	−	0.993008i	$-0.462336\pi$
$691$	112733.			0.236099			0.118050	+	0.993008i	$0.462336\pi$
$692$	197955.	−	197955.i	0.413384	−	0.413384i
$693$		0			0
$694$			207899.i			0.431651i
$695$	388425.	+	139198.i	0.804152	+	0.288179i
$696$		0			0
$697$	−210978.	+	210978.i	−0.434282	+	0.434282i
$698$	154354.	+	154354.i	0.316817	+	0.316817i
$699$		0			0
$700$	−41006.4	−	420616.i	−0.0836866	−	0.858400i
$701$	−540863.			−1.10065			−0.550327	−	0.834949i	$-0.685497\pi$
$701$	−540863.			−1.10065			−0.550327	+	0.834949i	$0.685497\pi$
$702$		0			0
$703$	−169695.	−	169695.i	−0.343366	−	0.343366i
$704$		−	217380.i		−	0.438606i
$705$		0			0
$706$	64394.5			0.129193
$707$	485688.	−	485688.i	0.971669	−	0.971669i
$708$		0			0
$709$			209535.i			0.416835i	0.978040	+	0.208418i	$0.0668313\pi$
$709$			209535.i			0.416835i	−0.978040	+	0.208418i	$0.933169\pi$
$710$	249762.	+	528755.i	0.495462	+	1.04891i
$711$		0			0
$712$	340742.	−	340742.i	0.672150	−	0.672150i
$713$	−131804.	−	131804.i	−0.259269	−	0.259269i
$714$		0			0
$715$	−1773.84	+	837.890i	−0.00346979	+	0.00163898i
$716$	320948.			0.626050
$717$		0			0
$718$	−96676.7	−	96676.7i	−0.187531	−	0.187531i
$719$			579641.i			1.12125i	0.828071	+	0.560623i	$0.189438\pi$
$719$			579641.i			1.12125i	−0.828071	+	0.560623i	$0.810562\pi$
$720$		0			0
$721$	603861.			1.16163
$722$	124417.	−	124417.i	0.238674	−	0.238674i
$723$		0			0
$724$			223127.i			0.425672i
$725$	215982.	−	262644.i	0.410905	−	0.499680i
$726$		0			0
$727$	666638.	−	666638.i	1.26131	−	1.26131i	0.310848	−	0.950460i	$-0.399387\pi$
$727$	666638.	−	666638.i	1.26131	−	1.26131i	0.950460	−	0.310848i	$-0.100613\pi$
$728$	6221.74	+	6221.74i	0.0117395	+	0.0117395i
$729$		0			0
$730$	−68102.5	+	190037.i	−0.127796	+	0.356609i
$731$	7109.24			0.0133042
$732$		0			0
$733$	184382.	+	184382.i	0.343171	+	0.343171i	0.857558	−	0.514387i	$-0.171981\pi$
$733$	184382.	+	184382.i	0.343171	+	0.343171i	−0.514387	+	0.857558i	$0.671981\pi$
$734$		−	240212.i		−	0.445865i
$735$		0			0
$736$	−222916.			−0.411514
$737$	214409.	−	214409.i	0.394737	−	0.394737i
$738$		0			0
$739$			175164.i			0.320742i	0.987057	+	0.160371i	$0.0512691\pi$
$739$			175164.i			0.320742i	−0.987057	+	0.160371i	$0.948731\pi$
$740$	−150017.	+	70861.8i	−0.273953	+	0.129404i
$741$		0			0
$742$	114924.	−	114924.i	0.208740	−	0.208740i
$743$	−540487.	−	540487.i	−0.979057	−	0.979057i	0.0207283	−	0.999785i	$-0.493402\pi$
$743$	−540487.	−	540487.i	−0.979057	−	0.979057i	−0.999785	+	0.0207283i	$0.993402\pi$
$744$		0			0
$745$	−249443.	−	89391.4i	−0.449426	−	0.161058i
$746$	691463.			1.24249
$747$		0			0
$748$	65913.1	+	65913.1i	0.117806	+	0.117806i
$749$		−	1.14649e6i		−	2.04365i
$750$		0			0
$751$	−588360.			−1.04319			−0.521595	−	0.853193i	$-0.674663\pi$
$751$	−588360.			−1.04319			−0.521595	+	0.853193i	$0.674663\pi$
$752$	−38578.9	+	38578.9i	−0.0682204	+	0.0682204i
$753$		0			0
$754$			2227.20i			0.00391756i
$755$	−258164.	+	720395.i	−0.452899	+	1.26380i
$756$		0			0
$757$	497479.	−	497479.i	0.868126	−	0.868126i	−0.124139	−	0.992265i	$-0.539617\pi$
$757$	497479.	−	497479.i	0.868126	−	0.868126i	0.992265	+	0.124139i	$0.0396168\pi$
$758$	−85956.5	−	85956.5i	−0.149603	−	0.149603i
$759$		0			0
$760$	194744.	+	412280.i	0.337161	+	0.713781i
$761$	−968464.			−1.67230			−0.836150	−	0.548501i	$-0.815199\pi$
$761$	−968464.			−1.67230			−0.836150	+	0.548501i	$0.815199\pi$
$762$		0			0
$763$	−519638.	−	519638.i	−0.892589	−	0.892589i
$764$		−	32087.9i		−	0.0549736i
$765$		0			0
$766$	−300231.			−0.511679
$767$	3404.32	−	3404.32i	0.00578682	−	0.00578682i
$768$		0			0
$769$		−	63796.8i		−	0.107881i	−0.998544	−	0.0539406i	$-0.982822\pi$
$769$		−	63796.8i		−	0.107881i	0.998544	−	0.0539406i	$-0.0171782\pi$
$770$	359593.	+	128865.i	0.606499	+	0.217348i
$771$		0			0
$772$	40212.9	−	40212.9i	0.0674731	−	0.0674731i
$773$	−142221.	−	142221.i	−0.238015	−	0.238015i	0.578013	−	0.816028i	$-0.303828\pi$
$773$	−142221.	−	142221.i	−0.238015	−	0.238015i	−0.816028	+	0.578013i	$0.803828\pi$
$774$		0			0
$775$	343133.	+	282171.i	0.571293	+	0.469796i
$776$	249805.			0.414838
$777$		0			0
$778$	399827.	+	399827.i	0.660561	+	0.660561i
$779$			352043.i			0.580124i
$780$		0			0
$781$	448391.			0.735114
$782$	−122788.	+	122788.i	−0.200791	+	0.200791i
$783$		0			0
$784$		−	514015.i		−	0.836264i
$785$	−264353.	−	559644.i	−0.428988	−	0.908181i
$786$		0			0
$787$	−171318.	+	171318.i	−0.276601	+	0.276601i	−0.831751	−	0.555150i	$-0.812661\pi$
$787$	−171318.	+	171318.i	−0.276601	+	0.276601i	0.555150	+	0.831751i	$0.312661\pi$
$788$	82162.1	+	82162.1i	0.132318	+	0.132318i
$789$		0			0
$790$	271609.	−	128297.i	0.435201	−	0.205571i
$791$	−243166.			−0.388642
$792$		0			0
$793$	4857.93	+	4857.93i	0.00772512	+	0.00772512i
$794$			736857.i			1.16881i
$795$		0			0
$796$	−132146.			−0.208559
$797$	396832.	−	396832.i	0.624727	−	0.624727i	−0.322010	−	0.946736i	$-0.604358\pi$
$797$	396832.	−	396832.i	0.624727	−	0.624727i	0.946736	+	0.322010i	$0.104358\pi$
$798$		0			0
$799$		−	145183.i		−	0.227417i
$800$	528777.	−	51551.2i	0.826214	−	0.0805487i
$801$		0			0
$802$	−433357.	+	433357.i	−0.673747	+	0.673747i
$803$	109453.	+	109453.i	0.169744	+	0.169744i
$804$		0			0
$805$	203648.	−	568271.i	0.314260	−	0.876928i
$806$	−2909.74			−0.00447902
$807$		0			0
$808$	362274.	+	362274.i	0.554899	+	0.554899i
$809$			571851.i			0.873748i	0.899523	+	0.436874i	$0.143914\pi$
$809$			571851.i			0.873748i	−0.899523	+	0.436874i	$0.856086\pi$
$810$		0			0
$811$	−851039.			−1.29392			−0.646960	−	0.762524i	$-0.723960\pi$
$811$	−851039.			−1.29392			−0.646960	+	0.762524i	$0.723960\pi$
$812$	−260136.	+	260136.i	−0.394538	+	0.394538i
$813$		0			0
$814$		−	149963.i		−	0.226326i
$815$	−440396.	+	208025.i	−0.663023	+	0.313185i
$816$		0			0
$817$	5931.33	−	5931.33i	0.00888603	−	0.00888603i
$818$	−552843.	−	552843.i	−0.826220	−	0.826220i
$819$		0			0
$820$	229114.	+	82106.2i	0.340740	+	0.122109i
$821$	422213.			0.626391			0.313195	−	0.949689i	$-0.398601\pi$
$821$	422213.			0.626391			0.313195	+	0.949689i	$0.398601\pi$
$822$		0			0
$823$	−742417.	−	742417.i	−1.09609	−	1.09609i	−0.994863	−	0.101231i	$-0.967722\pi$
$823$	−742417.	−	742417.i	−1.09609	−	1.09609i	−0.101231	−	0.994863i	$-0.532278\pi$
$824$			450418.i			0.663379i
$825$		0			0
$826$	−937440.			−1.37399
$827$	422050.	−	422050.i	0.617097	−	0.617097i	−0.327689	−	0.944786i	$-0.606270\pi$
$827$	422050.	−	422050.i	0.617097	−	0.617097i	0.944786	+	0.327689i	$0.106270\pi$
$828$		0			0
$829$			310239.i			0.451427i	0.974194	+	0.225713i	$0.0724712\pi$
$829$			310239.i			0.451427i	−0.974194	+	0.225713i	$0.927529\pi$
$830$	319451.	−	891414.i	0.463712	−	1.29397i
$831$		0			0
$832$	−3791.91	+	3791.91i	−0.00547787	+	0.00547787i
$833$	967190.	+	967190.i	1.39387	+	1.39387i
$834$		0			0
$835$	333372.	+	705761.i	0.478142	+	1.01224i
$836$	109984.			0.157369
$837$		0			0
$838$	261321.	+	261321.i	0.372123	+	0.372123i
$839$			1.20455e6i			1.71120i	0.517636	+	0.855601i	$0.326812\pi$
$839$			1.20455e6i			1.71120i	−0.517636	+	0.855601i	$0.673188\pi$
$840$		0			0
$841$	411268.			0.581477
$842$	−579683.	+	579683.i	−0.817648	+	0.817648i
$843$		0			0
$844$		−	91469.1i		−	0.128407i
$845$	−672121.	−	240864.i	−0.941313	−	0.337333i
$846$		0			0
$847$	−746155.	+	746155.i	−1.04007	+	1.04007i
$848$	35878.8	+	35878.8i	0.0498938	+	0.0498938i
$849$		0			0
$850$	262870.	−	319661.i	0.363833	−	0.442438i
$851$	−236989.			−0.327242
$852$		0			0
$853$	460012.	+	460012.i	0.632224	+	0.632224i	0.948625	−	0.316402i	$-0.102475\pi$
$853$	460012.	+	460012.i	0.632224	+	0.632224i	−0.316402	+	0.948625i	$0.602475\pi$
$854$		−	1.33772e6i		−	1.83421i
$855$		0			0
$856$	855163.			1.16708
$857$	398341.	−	398341.i	0.542367	−	0.542367i	−0.381855	−	0.924222i	$-0.624715\pi$
$857$	398341.	−	398341.i	0.542367	−	0.542367i	0.924222	+	0.381855i	$0.124715\pi$
$858$		0			0
$859$			323065.i			0.437828i	0.975744	+	0.218914i	$0.0702514\pi$
$859$			323065.i			0.437828i	−0.975744	+	0.218914i	$0.929749\pi$
$860$	−2476.83	−	5243.53i	−0.00334887	−	0.00708968i
$861$		0			0
$862$	−209300.	+	209300.i	−0.281679	+	0.281679i
$863$	−414986.	−	414986.i	−0.557200	−	0.557200i	0.371309	−	0.928509i	$-0.378909\pi$
$863$	−414986.	−	414986.i	−0.557200	−	0.557200i	−0.928509	+	0.371309i	$0.878909\pi$
$864$		0			0
$865$	−861755.	+	407058.i	−1.15173	+	0.544031i
$866$	−482722.			−0.643667
$867$		0			0
$868$	−339856.	−	339856.i	−0.451082	−	0.451082i
$869$		−	230328.i		−	0.305005i
$870$		0			0
$871$	−7480.16			−0.00985995
$872$	387597.	−	387597.i	0.509738	−	0.509738i
$873$		0			0
$874$			204888.i			0.268221i
$875$	−351655.	+	1.39509e6i	−0.459304	+	1.82216i
$876$		0			0
$877$	−257142.	+	257142.i	−0.334328	+	0.334328i	−0.854228	−	0.519899i	$-0.825969\pi$
$877$	−257142.	+	257142.i	−0.334328	+	0.334328i	0.519899	+	0.854228i	$0.325969\pi$
$878$	−340477.	−	340477.i	−0.441671	−	0.441671i
$879$		0			0
$880$	−40231.1	+	112263.i	−0.0519514	+	0.144968i
$881$	831152.			1.07085			0.535425	−	0.844583i	$-0.320152\pi$
$881$	831152.			1.07085			0.535425	+	0.844583i	$0.320152\pi$
$882$		0			0
$883$	908952.	+	908952.i	1.16579	+	1.16579i	0.983187	+	0.182601i	$0.0584518\pi$
$883$	908952.	+	908952.i	1.16579	+	1.16579i	0.182601	+	0.983187i	$0.441548\pi$
$884$		−	2299.53i		−	0.00294263i
$885$		0			0
$886$	488126.			0.621820
$887$	93115.5	−	93115.5i	0.118352	−	0.118352i	−0.645450	−	0.763802i	$-0.723330\pi$
$887$	93115.5	−	93115.5i	0.118352	−	0.118352i	0.763802	+	0.645450i	$0.223330\pi$
$888$		0			0
$889$		−	408814.i		−	0.517276i
$890$	−466638.	+	220421.i	−0.589115	+	0.278274i
$891$		0			0
$892$	−193864.	+	193864.i	−0.243651	+	0.243651i
$893$	−121128.	−	121128.i	−0.151894	−	0.151894i
$894$		0			0
$895$	−1.02858e6	−	368606.i	−1.28408	−	0.460167i
$896$	−208176.			−0.259307
$897$		0			0
$898$	−712658.	−	712658.i	−0.883748	−	0.883748i
$899$		−	386728.i		−	0.478505i
$900$		0			0
$901$	−135022.			−0.166324
$902$	−155554.	+	155554.i	−0.191191	+	0.191191i
$903$		0			0
$904$		−	181377.i		−	0.221945i
$905$	256259.	−	715079.i	0.312883	−	0.873086i
$906$		0			0
$907$	−62370.3	+	62370.3i	−0.0758164	+	0.0758164i	−0.743998	−	0.668182i	$-0.767073\pi$
$907$	−62370.3	+	62370.3i	−0.0758164	+	0.0758164i	0.668182	+	0.743998i	$0.267073\pi$
$908$	−236954.	−	236954.i	−0.287404	−	0.287404i
$909$		0			0
$910$	−4024.74	−	8520.52i	−0.00486021	−	0.0102892i
$911$	1.18436e6			1.42708			0.713540	−	0.700615i	$-0.247091\pi$
$911$	1.18436e6			1.42708			0.713540	+	0.700615i	$0.247091\pi$
$912$		0			0
$913$	−513414.	−	513414.i	−0.615923	−	0.615923i
$914$			677411.i			0.810886i
$915$		0			0
$916$	500220.			0.596170
$917$	−1.86970e6	+	1.86970e6i	−2.22349	+	2.22349i
$918$		0			0
$919$		−	773358.i		−	0.915692i	−0.889031	−	0.457846i	$-0.848621\pi$
$919$		−	773358.i		−	0.915692i	0.889031	−	0.457846i	$-0.151379\pi$
$920$	423872.	+	151901.i	0.500794	+	0.179467i
$921$		0			0
$922$	590199.	−	590199.i	0.694283	−	0.694283i
$923$	−7821.58	−	7821.58i	−0.00918103	−	0.00918103i
$924$		0			0
$925$	562159.	−	54805.6i	0.657016	−	0.0640533i
$926$	−141828.			−0.165401
$927$		0			0
$928$	−327030.	−	327030.i	−0.379744	−	0.379744i
$929$		−	881163.i		−	1.02100i	−0.859878	−	0.510499i	$-0.829461\pi$
$929$		−	881163.i		−	1.02100i	0.859878	−	0.510499i	$-0.170539\pi$
$930$		0			0
$931$	1.61388e6			1.86196
$932$	−484200.	+	484200.i	−0.557433	+	0.557433i
$933$		0			0
$934$		−	520063.i		−	0.596159i
$935$	−135538.	−	286939.i	−0.155038	−	0.328221i
$936$		0			0
$937$	992967.	−	992967.i	1.13098	−	1.13098i	0.140967	−	0.990014i	$-0.454979\pi$
$937$	992967.	−	992967.i	1.13098	−	1.13098i	0.990014	−	0.140967i	$-0.0450212\pi$
$938$	1.02990e6	+	1.02990e6i	1.17055	+	1.17055i
$939$		0			0
$940$	−107082.	+	50581.1i	−0.121188	+	0.0572444i
$941$	1.13615e6			1.28309			0.641545	−	0.767085i	$-0.278294\pi$
$941$	1.13615e6			1.28309			0.641545	+	0.767085i	$0.278294\pi$
$942$		0			0
$943$	245824.	+	245824.i	0.276440	+	0.276440i
$944$		−	292664.i		−	0.328417i
$945$		0			0
$946$	5241.64			0.00585713
$947$	208361.	−	208361.i	0.232336	−	0.232336i	−0.581331	−	0.813667i	$-0.697468\pi$
$947$	208361.	−	208361.i	0.232336	−	0.232336i	0.813667	+	0.581331i	$0.197468\pi$
$948$		0			0
$949$		−	3818.51i		−	0.00423996i
$950$	−47382.0	−	486013.i	−0.0525009	−	0.538518i
$951$		0			0
$952$	−1.00644e6	+	1.00644e6i	−1.11049	+	1.11049i
$953$	761064.	+	761064.i	0.837983	+	0.837983i	0.988593	−	0.150610i	$-0.0481237\pi$
$953$	761064.	+	761064.i	0.837983	+	0.837983i	−0.150610	+	0.988593i	$0.548124\pi$
$954$		0			0
$955$	−36852.6	+	102835.i	−0.0404074	+	0.112755i
$956$	476011.			0.520836
$957$		0			0
$958$	−516717.	−	516717.i	−0.563018	−	0.563018i
$959$		−	3.33706e6i		−	3.62850i
$960$		0			0
$961$	−418277.			−0.452916
$962$	−2615.90	+	2615.90i	−0.00282664	+	0.00282664i
$963$		0			0
$964$		−	437656.i		−	0.470954i
$965$	−175058.	+	82690.4i	−0.187987	+	0.0887974i
$966$		0			0
$967$	456976.	−	456976.i	0.488698	−	0.488698i	−0.419197	−	0.907895i	$-0.637688\pi$
$967$	456976.	−	456976.i	0.488698	−	0.488698i	0.907895	+	0.419197i	$0.137688\pi$
$968$	−556556.	−	556556.i	−0.593961	−	0.593961i
$969$		0			0
$970$	−251849.	−	90253.6i	−0.267668	−	0.0959227i
$971$	−1.23029e6			−1.30488			−0.652439	−	0.757841i	$-0.726254\pi$
$971$	−1.23029e6			−1.30488			−0.652439	+	0.757841i	$0.726254\pi$
$972$		0			0
$973$	1.07460e6	+	1.07460e6i	1.13507	+	1.13507i
$974$			663136.i			0.699012i
$975$		0			0
$976$	417628.			0.438420
$977$	−120924.	+	120924.i	−0.126684	+	0.126684i	−0.767606	−	0.640922i	$-0.778552\pi$
$977$	−120924.	+	120924.i	−0.126684	+	0.126684i	0.640922	+	0.767606i	$0.278552\pi$
$978$		0			0
$979$			395715.i			0.412873i
$980$	376401.	−	1.05033e6i	0.391921	−	1.09364i
$981$		0			0
$982$	34489.4	−	34489.4i	0.0357653	−	0.0357653i
$983$	607621.	+	607621.i	0.628819	+	0.628819i	0.947771	−	0.318952i	$-0.103331\pi$
$983$	607621.	+	607621.i	0.628819	+	0.628819i	−0.318952	+	0.947771i	$0.603331\pi$
$984$		0			0
$985$	−168951.	−	357676.i	−0.174136	−	0.368652i
$986$	−360275.			−0.370578
$987$		0			0
$988$	−1918.53	−	1918.53i	−0.00196542	−	0.00196542i
$989$		−	8283.45i		−	0.00846873i
$990$		0			0
$991$	−32696.1			−0.0332927			−0.0166464	−	0.999861i	$-0.505299\pi$
$991$	−32696.1			−0.0332927			−0.0166464	+	0.999861i	$0.505299\pi$
$992$	427250.	−	427250.i	0.434169	−	0.434169i
$993$		0			0
$994$			2.15381e6i			2.17989i
$995$	423504.	+	151769.i	0.427771	+	0.153298i
$996$		0			0
$997$	196213.	−	196213.i	0.197395	−	0.197395i	−0.601487	−	0.798882i	$-0.705425\pi$
$997$	196213.	−	196213.i	0.197395	−	0.197395i	0.798882	+	0.601487i	$0.205425\pi$
$998$	421160.	+	421160.i	0.422850	+	0.422850i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.g.e.28.3		8
3.2	odd	2		15.5.f.a.13.2	yes	8
5.2	odd	4	inner	45.5.g.e.37.3		8
5.3	odd	4		225.5.g.m.82.2		8
5.4	even	2		225.5.g.m.118.2		8
12.11	even	2		240.5.bg.c.193.2		8
15.2	even	4		15.5.f.a.7.2	✓	8
15.8	even	4		75.5.f.e.7.3		8
15.14	odd	2		75.5.f.e.43.3		8
60.47	odd	4		240.5.bg.c.97.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.5.f.a.7.2	✓	8	15.2	even	4
15.5.f.a.13.2	yes	8	3.2	odd	2
45.5.g.e.28.3		8	1.1	even	1	trivial
45.5.g.e.37.3		8	5.2	odd	4	inner
75.5.f.e.7.3		8	15.8	even	4
75.5.f.e.43.3		8	15.14	odd	2
225.5.g.m.82.2		8	5.3	odd	4
225.5.g.m.118.2		8	5.4	even	2
240.5.bg.c.97.2		8	60.47	odd	4
240.5.bg.c.193.2		8	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	45.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.08045 - 2.08045i) q^{2} +7.34348i q^{4} +(8.43390 - 23.5344i) q^{5} +(65.1093 - 65.1093i) q^{7} +(48.5649 + 48.5649i) q^{8} +(-31.4158 - 66.5084i) q^{10} -56.3999 q^{11} +(0.983822 + 0.983822i) q^{13} -270.913i q^{14} +84.5776 q^{16} +(-159.144 + 159.144i) q^{17} +265.552i q^{19} +(172.825 + 61.9342i) q^{20} +(-117.337 + 117.337i) q^{22} +(185.430 + 185.430i) q^{23} +(-482.739 - 396.974i) q^{25} +4.09358 q^{26} +(478.129 + 478.129i) q^{28} +544.071i q^{29} -710.805 q^{31} +(-601.079 + 601.079i) q^{32} +662.183i q^{34} +(-983.184 - 2081.43i) q^{35} +(-639.026 + 639.026i) q^{37} +(552.467 + 552.467i) q^{38} +(1552.54 - 733.355i) q^{40} +1325.70 q^{41} +(-22.3358 - 22.3358i) q^{43} -414.172i q^{44} +771.553 q^{46} +(-456.136 + 456.136i) q^{47} -6077.44i q^{49} +(-1830.20 + 178.428i) q^{50} +(-7.22468 + 7.22468i) q^{52} +(424.212 + 424.212i) q^{53} +(-475.672 + 1327.34i) q^{55} +6324.05 q^{56} +(1131.91 + 1131.91i) q^{58} -3460.30i q^{59} +4937.82 q^{61} +(-1478.79 + 1478.79i) q^{62} +3854.27i q^{64} +(31.4511 - 14.8562i) q^{65} +(-3801.58 + 3801.58i) q^{67} +(-1168.67 - 1168.67i) q^{68} +(-6375.78 - 2284.85i) q^{70} -7950.20 q^{71} +(-1940.65 - 1940.65i) q^{73} +2658.92i q^{74} -1950.08 q^{76} +(-3672.16 + 3672.16i) q^{77} +4083.83i q^{79} +(713.319 - 1990.48i) q^{80} +(2758.05 - 2758.05i) q^{82} +(9103.10 + 9103.10i) q^{83} +(2403.16 + 5087.58i) q^{85} -92.9369 q^{86} +(-2739.06 - 2739.06i) q^{88} -7016.23i q^{89} +128.112 q^{91} +(-1361.70 + 1361.70i) q^{92} +1897.93i q^{94} +(6249.62 + 2239.64i) q^{95} +(2571.87 - 2571.87i) q^{97} +(-12643.8 - 12643.8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 84 q^{5} + 20 q^{7} - 180 q^{8} + 104 q^{10} + 288 q^{11} - 340 q^{13} + 620 q^{16} - 900 q^{17} - 564 q^{20} - 1100 q^{22} + 1560 q^{23} - 1204 q^{25} + 3024 q^{26} + 3580 q^{28} - 512 q^{31} - 4980 q^{32}+ \cdots - 46440 q^{98}+O(q^{100}) \) 8 * q + 84 * q^5 + 20 * q^7 - 180 * q^8 + 104 * q^10 + 288 * q^11 - 340 * q^13 + 620 * q^16 - 900 * q^17 - 564 * q^20 - 1100 * q^22 + 1560 * q^23 - 1204 * q^25 + 3024 * q^26 + 3580 * q^28 - 512 * q^31 - 4980 * q^32 - 6600 * q^35 - 3820 * q^37 + 7680 * q^38 - 2952 * q^40 + 2712 * q^41 - 1240 * q^43 + 13528 * q^46 - 4800 * q^47 - 3744 * q^50 - 1240 * q^52 - 1020 * q^53 - 3644 * q^55 + 30720 * q^56 + 2340 * q^58 - 4760 * q^61 - 28680 * q^62 + 1212 * q^65 - 8920 * q^67 + 1920 * q^68 + 7380 * q^70 - 7536 * q^71 + 11600 * q^73 + 4344 * q^76 + 360 * q^77 - 10644 * q^80 - 27200 * q^82 + 32400 * q^83 - 15628 * q^85 - 14592 * q^86 - 14340 * q^88 + 16528 * q^91 + 31800 * q^92 - 18864 * q^95 + 58640 * q^97 - 46440 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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