LMFDB - Embedded newform 912.3.be.j.145.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,3,Mod(145,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("912.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	912.be (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:	$24.8502001097$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 154 x^{18} - 24 x^{17} + 16374 x^{16} - 4328 x^{15} + 911836 x^{14} - 590088 x^{13} + \cdots + 338560000 $ x^20 + 154x^18 - 24x^17 + 16374x^16 - 4328x^15 + 911836x^14 - 590088x^13 + 36808708x^12 - 29040960x^11 + 727387008x^10 - 1003792064x^9 + 10261479936x^8 - 7069668864x^7 + 36940887936x^6 + 52280031232x^5 + 60574204416x^4 + 32700144640x^3 + 13448832000x^2 + 2490624000x + 338560000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{18} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.8
Root			$-2.60694 + 4.51535i$ of defining polynomial
Character	$\chi$	$=$	912.145
Dual form			912.3.be.j.673.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{3} +(2.60694 + 4.51535i) q^{5} +5.77889 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 - 0.866025i) q^{3} +(2.60694 + 4.51535i) q^{5} +5.77889 q^{7} +(1.50000 - 2.59808i) q^{9} +14.2461 q^{11} +(1.04810 + 0.605123i) q^{13} +(7.82081 + 4.51535i) q^{15} +(-0.848521 - 1.46968i) q^{17} +(-0.755894 + 18.9850i) q^{19} +(8.66833 - 5.00466i) q^{21} +(1.02569 - 1.77655i) q^{23} +(-1.09223 + 1.89180i) q^{25} -5.19615i q^{27} +(-15.6272 - 9.02238i) q^{29} -4.61701i q^{31} +(21.3691 - 12.3375i) q^{33} +(15.0652 + 26.0937i) q^{35} -20.1693i q^{37} +2.09621 q^{39} +(7.14184 - 4.12335i) q^{41} +(37.2972 + 64.6007i) q^{43} +15.6416 q^{45} +(-0.118605 + 0.205430i) q^{47} -15.6045 q^{49} +(-2.54556 - 1.46968i) q^{51} +(-38.2035 - 22.0568i) q^{53} +(37.1387 + 64.3260i) q^{55} +(15.3076 + 29.1321i) q^{57} +(23.8258 - 13.7558i) q^{59} +(-33.0094 + 57.1740i) q^{61} +(8.66833 - 15.0140i) q^{63} +6.31007i q^{65} +(89.0894 + 51.4358i) q^{67} -3.55311i q^{69} +(-88.2180 + 50.9327i) q^{71} +(-25.0249 - 43.3443i) q^{73} +3.78361i q^{75} +82.3266 q^{77} +(134.815 - 77.8357i) q^{79} +(-4.50000 - 7.79423i) q^{81} -9.99542 q^{83} +(4.42408 - 7.66273i) q^{85} -31.2545 q^{87} +(103.182 + 59.5720i) q^{89} +(6.05687 + 3.49694i) q^{91} +(-3.99845 - 6.92552i) q^{93} +(-87.6942 + 46.0795i) q^{95} +(-0.945906 + 0.546119i) q^{97} +(21.3691 - 37.0124i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9}+O(q^{10}) $ 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9	$ 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9} + 8 q^{11} + 18 q^{13} + 8 q^{17} - 28 q^{19} - 30 q^{21} + 8 q^{23} - 58 q^{25} + 108 q^{29} + 12 q^{33} - 20 q^{35} + 36 q^{39} - 36 q^{41} + 2 q^{43} + 296 q^{49} + 24 q^{51} - 72 q^{53} - 216 q^{55} - 30 q^{57} - 72 q^{59} - 26 q^{61} - 30 q^{63} - 138 q^{67} + 204 q^{71} + 218 q^{73} - 8 q^{77} + 78 q^{79} - 90 q^{81} + 112 q^{83} + 224 q^{85} + 216 q^{87} - 432 q^{89} + 330 q^{91} - 126 q^{93} - 220 q^{95} + 132 q^{97} + 12 q^{99}+O(q^{100}) $ 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9 + 8 * q^11 + 18 * q^13 + 8 * q^17 - 28 * q^19 - 30 * q^21 + 8 * q^23 - 58 * q^25 + 108 * q^29 + 12 * q^33 - 20 * q^35 + 36 * q^39 - 36 * q^41 + 2 * q^43 + 296 * q^49 + 24 * q^51 - 72 * q^53 - 216 * q^55 - 30 * q^57 - 72 * q^59 - 26 * q^61 - 30 * q^63 - 138 * q^67 + 204 * q^71 + 218 * q^73 - 8 * q^77 + 78 * q^79 - 90 * q^81 + 112 * q^83 + 224 * q^85 + 216 * q^87 - 432 * q^89 + 330 * q^91 - 126 * q^93 - 220 * q^95 + 132 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$		0			0
$5$	2.60694	+	4.51535i	0.521387	+	0.903069i	0.999691	+	0.0248745i	$0.00791862\pi$
$5$	2.60694	+	4.51535i	0.521387	+	0.903069i	−0.478303	+	0.878195i	$0.658748\pi$
$6$		0			0
$7$	5.77889			0.825555			0.412778	−	0.910832i	$-0.364559\pi$
$7$	5.77889			0.825555			0.412778	+	0.910832i	$0.364559\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	14.2461			1.29510			0.647550	−	0.762023i	$-0.275794\pi$
$11$	14.2461			1.29510			0.647550	+	0.762023i	$0.275794\pi$
$12$		0			0
$13$	1.04810	+	0.605123i	0.0806233	+	0.0465479i	0.539770	−	0.841813i	$-0.318511\pi$
$13$	1.04810	+	0.605123i	0.0806233	+	0.0465479i	−0.459146	+	0.888361i	$0.651845\pi$
$14$		0			0
$15$	7.82081	+	4.51535i	0.521387	+	0.301023i
$16$		0			0
$17$	−0.848521	−	1.46968i	−0.0499130	−	0.0864518i	0.839989	−	0.542603i	$-0.182561\pi$
$17$	−0.848521	−	1.46968i	−0.0499130	−	0.0864518i	−0.889902	+	0.456151i	$0.849228\pi$
$18$		0			0
$19$	−0.755894	+	18.9850i	−0.0397839	+	0.999208i
$19$	−0.755894	+	18.9850i	−0.0397839	+	0.999208i
$20$		0			0
$21$	8.66833	−	5.00466i	0.412778	−	0.238317i
$22$		0			0
$23$	1.02569	−	1.77655i	0.0445954	−	0.0772415i	−0.842866	−	0.538123i	$-0.819133\pi$
$23$	1.02569	−	1.77655i	0.0445954	−	0.0772415i	0.887462	+	0.460882i	$0.152467\pi$
$24$		0			0
$25$	−1.09223	+	1.89180i	−0.0436893	+	0.0756722i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	−15.6272	−	9.02238i	−0.538870	−	0.311117i	0.205751	−	0.978604i	$-0.434036\pi$
$29$	−15.6272	−	9.02238i	−0.538870	−	0.311117i	−0.744621	+	0.667488i	$0.767370\pi$
$30$		0			0
$31$		−	4.61701i		−	0.148936i	−0.997223	−	0.0744680i	$-0.976274\pi$
$31$		−	4.61701i		−	0.148936i	0.997223	−	0.0744680i	$-0.0237259\pi$
$32$		0			0
$33$	21.3691	−	12.3375i	0.647550	−	0.373863i
$34$		0			0
$35$	15.0652	+	26.0937i	0.430434	+	0.745534i
$36$		0			0
$37$		−	20.1693i		−	0.545117i	−0.962139	−	0.272558i	$-0.912130\pi$
$37$		−	20.1693i		−	0.545117i	0.962139	−	0.272558i	$-0.0878698\pi$
$38$		0			0
$39$	2.09621			0.0537489
$40$		0			0
$41$	7.14184	−	4.12335i	0.174191	−	0.100569i	−0.410369	−	0.911919i	$-0.634600\pi$
$41$	7.14184	−	4.12335i	0.174191	−	0.100569i	0.584561	+	0.811350i	$0.301267\pi$
$42$		0			0
$43$	37.2972	+	64.6007i	0.867377	+	1.50234i	0.864667	+	0.502345i	$0.167529\pi$
$43$	37.2972	+	64.6007i	0.867377	+	1.50234i	0.00271032	+	0.999996i	$0.499137\pi$
$44$		0			0
$45$	15.6416			0.347592
$46$		0			0
$47$	−0.118605	+	0.205430i	−0.00252352	+	0.00437086i	−0.867284	−	0.497813i	$-0.834137\pi$
$47$	−0.118605	+	0.205430i	−0.00252352	+	0.00437086i	0.864761	+	0.502184i	$0.167470\pi$
$48$		0			0
$49$	−15.6045			−0.318458
$50$		0			0
$51$	−2.54556	−	1.46968i	−0.0499130	−	0.0288173i
$52$		0			0
$53$	−38.2035	−	22.0568i	−0.720820	−	0.416166i	0.0942344	−	0.995550i	$-0.469960\pi$
$53$	−38.2035	−	22.0568i	−0.720820	−	0.416166i	−0.815054	+	0.579384i	$0.803293\pi$
$54$		0			0
$55$	37.1387	+	64.3260i	0.675248	+	1.16956i
$56$		0			0
$57$	15.3076	+	29.1321i	0.268555	+	0.511089i
$58$		0			0
$59$	23.8258	−	13.7558i	0.403827	−	0.233149i	−0.284307	−	0.958733i	$-0.591764\pi$
$59$	23.8258	−	13.7558i	0.403827	−	0.233149i	0.688134	+	0.725584i	$0.258430\pi$
$60$		0			0
$61$	−33.0094	+	57.1740i	−0.541138	+	0.937278i	0.457701	+	0.889106i	$0.348673\pi$
$61$	−33.0094	+	57.1740i	−0.541138	+	0.937278i	−0.998839	+	0.0481721i	$0.984660\pi$
$62$		0			0
$63$	8.66833	−	15.0140i	0.137593	−	0.238317i
$64$		0			0
$65$			6.31007i			0.0970779i
$66$		0			0
$67$	89.0894	+	51.4358i	1.32969	+	0.767698i	0.985252	−	0.171110i	$-0.0547353\pi$
$67$	89.0894	+	51.4358i	1.32969	+	0.767698i	0.344440	+	0.938808i	$0.388069\pi$
$68$		0			0
$69$		−	3.55311i		−	0.0514943i
$70$		0			0
$71$	−88.2180	+	50.9327i	−1.24251	+	0.717362i	−0.969604	−	0.244680i	$-0.921317\pi$
$71$	−88.2180	+	50.9327i	−1.24251	+	0.717362i	−0.272903	+	0.962042i	$0.587984\pi$
$72$		0			0
$73$	−25.0249	−	43.3443i	−0.342806	−	0.593758i	0.642146	−	0.766582i	$-0.278044\pi$
$73$	−25.0249	−	43.3443i	−0.342806	−	0.593758i	−0.984953	+	0.172824i	$0.944711\pi$
$74$		0			0
$75$			3.78361i			0.0504481i
$76$		0			0
$77$	82.3266			1.06918
$78$		0			0
$79$	134.815	−	77.8357i	1.70652	−	0.985262i	0.767734	−	0.640768i	$-0.221384\pi$
$79$	134.815	−	77.8357i	1.70652	−	0.985262i	0.938789	−	0.344493i	$-0.111949\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−9.99542			−0.120427			−0.0602134	−	0.998186i	$-0.519178\pi$
$83$	−9.99542			−0.120427			−0.0602134	+	0.998186i	$0.519178\pi$
$84$		0			0
$85$	4.42408	−	7.66273i	0.0520480	−	0.0901497i
$86$		0			0
$87$	−31.2545			−0.359247
$88$		0			0
$89$	103.182	+	59.5720i	1.15935	+	0.669349i	0.951147	−	0.308738i	$-0.0999066\pi$
$89$	103.182	+	59.5720i	1.15935	+	0.669349i	0.208199	+	0.978087i	$0.433240\pi$
$90$		0			0
$91$	6.05687	+	3.49694i	0.0665590	+	0.0384279i
$92$		0			0
$93$	−3.99845	−	6.92552i	−0.0429941	−	0.0744680i
$94$		0			0
$95$	−87.6942	+	46.0795i	−0.923097	+	0.485047i
$96$		0			0
$97$	−0.945906	+	0.546119i	−0.00975161	+	0.00563010i	−0.504868	−	0.863197i	$-0.668459\pi$
$97$	−0.945906	+	0.546119i	−0.00975161	+	0.00563010i	0.495116	+	0.868827i	$0.335125\pi$
$98$		0			0
$99$	21.3691	−	37.0124i	0.215850	−	0.373863i
$100$		0			0
$101$	−9.82466	+	17.0168i	−0.0972739	+	0.168483i	−0.910555	−	0.413387i	$-0.864346\pi$
$101$	−9.82466	+	17.0168i	−0.0972739	+	0.168483i	0.813281	+	0.581870i	$0.197679\pi$
$102$		0			0
$103$		−	69.3824i		−	0.673616i	−0.941573	−	0.336808i	$-0.890653\pi$
$103$		−	69.3824i		−	0.673616i	0.941573	−	0.336808i	$-0.109347\pi$
$104$		0			0
$105$	45.1956	+	26.0937i	0.430434	+	0.248511i
$106$		0			0
$107$		−	98.1984i		−	0.917742i	−0.888503	−	0.458871i	$-0.848254\pi$
$107$		−	98.1984i		−	0.917742i	0.888503	−	0.458871i	$-0.151746\pi$
$108$		0			0
$109$	58.4100	−	33.7231i	0.535872	−	0.309386i	−0.207532	−	0.978228i	$-0.566543\pi$
$109$	58.4100	−	33.7231i	0.535872	−	0.309386i	0.743404	+	0.668842i	$0.233210\pi$
$110$		0			0
$111$	−17.4671	−	30.2540i	−0.157362	−	0.272558i
$112$		0			0
$113$			22.2700i			0.197079i	0.995133	+	0.0985397i	$0.0314171\pi$
$113$			22.2700i			0.197079i	−0.995133	+	0.0985397i	$0.968583\pi$
$114$		0			0
$115$	10.6957			0.0930059
$116$		0			0
$117$	3.14431	−	1.81537i	0.0268744	−	0.0155160i
$118$		0			0
$119$	−4.90350	−	8.49312i	−0.0412059	−	0.0713707i
$120$		0			0
$121$	81.9512			0.677283
$122$		0			0
$123$	7.14184	−	12.3700i	0.0580638	−	0.100569i
$124$		0			0
$125$	118.957			0.951658
$126$		0			0
$127$	−4.24096	−	2.44852i	−0.0333934	−	0.0192797i	0.483210	−	0.875504i	$-0.339471\pi$
$127$	−4.24096	−	2.44852i	−0.0333934	−	0.0192797i	−0.516604	+	0.856225i	$0.672804\pi$
$128$		0			0
$129$	111.892	+	64.6007i	0.867377	+	0.500781i
$130$		0			0
$131$	−59.8843	−	103.723i	−0.457132	−	0.791776i	0.541676	−	0.840587i	$-0.317790\pi$
$131$	−59.8843	−	103.723i	−0.457132	−	0.791776i	−0.998808	+	0.0488113i	$0.984457\pi$
$132$		0			0
$133$	−4.36823	+	109.712i	−0.0328438	+	0.824902i
$134$		0			0
$135$	23.4624	−	13.5460i	0.173796	−	0.100341i
$136$		0			0
$137$	−56.2021	+	97.3448i	−0.410234	+	0.710546i	−0.994915	−	0.100717i	$-0.967886\pi$
$137$	−56.2021	+	97.3448i	−0.410234	+	0.710546i	0.584681	+	0.811263i	$0.301220\pi$
$138$		0			0
$139$	46.8442	−	81.1365i	0.337008	−	0.583716i	−0.646860	−	0.762609i	$-0.723918\pi$
$139$	46.8442	−	81.1365i	0.337008	−	0.583716i	0.983869	+	0.178893i	$0.0572516\pi$
$140$		0			0
$141$			0.410861i			0.00291390i
$142$		0			0
$143$	14.9314	+	8.62064i	0.104415	+	0.0602842i
$144$		0			0
$145$		−	94.0831i		−	0.648849i
$146$		0			0
$147$	−23.4067	+	13.5139i	−0.159229	+	0.0919310i
$148$		0			0
$149$	−25.8728	−	44.8131i	−0.173643	−	0.300759i	0.766048	−	0.642784i	$-0.222221\pi$
$149$	−25.8728	−	44.8131i	−0.173643	−	0.300759i	−0.939691	+	0.342025i	$0.888887\pi$
$150$		0			0
$151$		−	3.92008i		−	0.0259608i	−0.999916	−	0.0129804i	$-0.995868\pi$
$151$		−	3.92008i		−	0.0259608i	0.999916	−	0.0129804i	$-0.00413191\pi$
$152$		0			0
$153$	−5.09112			−0.0332753
$154$		0			0
$155$	20.8474	−	12.0363i	0.134499	−	0.0776533i
$156$		0			0
$157$	61.3232	+	106.215i	0.390594	+	0.676528i	0.992528	−	0.122017i	$-0.0389364\pi$
$157$	61.3232	+	106.215i	0.390594	+	0.676528i	−0.601934	+	0.798546i	$0.705603\pi$
$158$		0			0
$159$	−76.4069			−0.480547
$160$		0			0
$161$	5.92737	−	10.2665i	0.0368160	−	0.0637671i
$162$		0			0
$163$	54.7784			0.336064			0.168032	−	0.985782i	$-0.446259\pi$
$163$	54.7784			0.336064			0.168032	+	0.985782i	$0.446259\pi$
$164$		0			0
$165$	111.416	+	64.3260i	0.675248	+	0.389855i
$166$		0			0
$167$	94.2369	+	54.4077i	0.564293	+	0.325795i	0.754867	−	0.655878i	$-0.227702\pi$
$167$	94.2369	+	54.4077i	0.564293	+	0.325795i	−0.190574	+	0.981673i	$0.561035\pi$
$168$		0			0
$169$	−83.7677	−	145.090i	−0.495667	−	0.858520i
$170$		0			0
$171$	48.1905	+	30.4413i	0.281816	+	0.178019i
$172$		0			0
$173$	−229.769	+	132.657i	−1.32815	+	0.766806i	−0.985013	−	0.172481i	$-0.944822\pi$
$173$	−229.769	+	132.657i	−1.32815	+	0.766806i	−0.343133	+	0.939287i	$0.611488\pi$
$174$		0			0
$175$	−6.31189	+	10.9325i	−0.0360680	+	0.0624715i
$176$		0			0
$177$	23.8258	−	41.2675i	0.134609	−	0.233149i
$178$		0			0
$179$		−	33.6741i		−	0.188123i	−0.995566	−	0.0940617i	$-0.970015\pi$
$179$		−	33.6741i		−	0.188123i	0.995566	−	0.0940617i	$-0.0299851\pi$
$180$		0			0
$181$	−135.262	−	78.0934i	−0.747303	−	0.431455i	0.0774157	−	0.996999i	$-0.475333\pi$
$181$	−135.262	−	78.0934i	−0.747303	−	0.431455i	−0.824719	+	0.565543i	$0.808666\pi$
$182$		0			0
$183$			114.348i			0.624852i
$184$		0			0
$185$	91.0715	−	52.5801i	0.492278	−	0.284217i
$186$		0			0
$187$	−12.0881	−	20.9372i	−0.0646423	−	0.111964i
$188$		0			0
$189$		−	30.0280i		−	0.158878i
$190$		0			0
$191$	−352.346			−1.84474			−0.922372	−	0.386302i	$-0.873752\pi$
$191$	−352.346			−1.84474			−0.922372	+	0.386302i	$0.873752\pi$
$192$		0			0
$193$	10.1890	−	5.88262i	0.0527927	−	0.0304799i	−0.473371	−	0.880863i	$-0.656963\pi$
$193$	10.1890	−	5.88262i	0.0527927	−	0.0304799i	0.526164	+	0.850383i	$0.323630\pi$
$194$		0			0
$195$	5.46468	+	9.46510i	0.0280240	+	0.0485390i
$196$		0			0
$197$	−243.285			−1.23495			−0.617475	−	0.786590i	$-0.711844\pi$
$197$	−243.285			−1.23495			−0.617475	+	0.786590i	$0.711844\pi$
$198$		0			0
$199$	−98.7324	+	171.010i	−0.496143	+	0.859345i	−0.999990	−	0.00444821i	$-0.998584\pi$
$199$	−98.7324	+	171.010i	−0.496143	+	0.859345i	0.503847	+	0.863793i	$0.331917\pi$
$200$		0			0
$201$	178.179			0.886462
$202$		0			0
$203$	−90.3080	−	52.1393i	−0.444867	−	0.256844i
$204$		0			0
$205$	37.2367	+	21.4986i	0.181642	+	0.104871i
$206$		0			0
$207$	−3.07708	−	5.32966i	−0.0148651	−	0.0257472i
$208$		0			0
$209$	−10.7685	+	270.461i	−0.0515241	+	1.29407i
$210$		0			0
$211$	319.747	−	184.606i	1.51539	−	0.874910i	0.515552	−	0.856858i	$-0.327587\pi$
$211$	319.747	−	184.606i	1.51539	−	0.874910i	0.999837	−	0.0180524i	$-0.00574656\pi$
$212$		0			0
$213$	−88.2180	+	152.798i	−0.414169	+	0.717362i
$214$		0			0
$215$	−194.463	+	336.820i	−0.904479	+	1.56660i
$216$		0			0
$217$		−	26.6812i		−	0.122955i
$218$		0			0
$219$	−75.0746	−	43.3443i	−0.342806	−	0.197919i
$220$		0			0
$221$		−	2.05384i		−	0.00929338i
$222$		0			0
$223$	−137.458	+	79.3613i	−0.616402	+	0.355880i	−0.775467	−	0.631388i	$-0.782485\pi$
$223$	−137.458	+	79.3613i	−0.616402	+	0.355880i	0.159065	+	0.987268i	$0.449152\pi$
$224$		0			0
$225$	3.27670	+	5.67541i	0.0145631	+	0.0252241i
$226$		0			0
$227$		−	399.097i		−	1.75814i	−0.476697	−	0.879068i	$-0.658166\pi$
$227$		−	399.097i		−	1.75814i	0.476697	−	0.879068i	$-0.341834\pi$
$228$		0			0
$229$	29.0706			0.126946			0.0634730	−	0.997984i	$-0.479782\pi$
$229$	29.0706			0.126946			0.0634730	+	0.997984i	$0.479782\pi$
$230$		0			0
$231$	123.490	−	71.2969i	0.534588	−	0.308645i
$232$		0			0
$233$	153.331	+	265.577i	0.658072	+	1.13981i	0.981114	+	0.193430i	$0.0619612\pi$
$233$	153.331	+	265.577i	0.658072	+	1.13981i	−0.323042	+	0.946385i	$0.604705\pi$
$234$		0			0
$235$	−1.23679			−0.00526292
$236$		0			0
$237$	134.815	−	233.507i	0.568841	−	0.985262i
$238$		0			0
$239$	−247.751			−1.03662			−0.518308	−	0.855194i	$-0.673438\pi$
$239$	−247.751			−1.03662			−0.518308	+	0.855194i	$0.673438\pi$
$240$		0			0
$241$	3.04012	+	1.75521i	0.0126146	+	0.00728304i	0.506294	−	0.862361i	$-0.331015\pi$
$241$	3.04012	+	1.75521i	0.0126146	+	0.00728304i	−0.493679	+	0.869644i	$0.664348\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	−40.6798	−	70.4595i	−0.166040	−	0.287590i
$246$		0			0
$247$	−12.2805	+	19.4408i	−0.0497186	+	0.0787077i
$248$		0			0
$249$	−14.9931	+	8.65629i	−0.0602134	+	0.0347642i
$250$		0			0
$251$	−146.209	+	253.242i	−0.582507	+	1.00893i	0.412675	+	0.910879i	$0.364595\pi$
$251$	−146.209	+	253.242i	−0.582507	+	1.00893i	−0.995181	+	0.0980526i	$0.968739\pi$
$252$		0			0
$253$	14.6121	−	25.3090i	0.0577555	−	0.100035i
$254$		0			0
$255$		−	15.3255i		−	0.0600998i
$256$		0			0
$257$	−316.010	−	182.448i	−1.22961	−	0.709916i	−0.262662	−	0.964888i	$-0.584600\pi$
$257$	−316.010	−	182.448i	−1.22961	−	0.709916i	−0.966948	+	0.254972i	$0.917934\pi$
$258$		0			0
$259$		−	116.556i		−	0.450024i
$260$		0			0
$261$	−46.8817	+	27.0672i	−0.179623	+	0.103706i
$262$		0			0
$263$	29.3405	+	50.8192i	0.111561	+	0.193229i	0.916400	−	0.400264i	$-0.131082\pi$
$263$	29.3405	+	50.8192i	0.111561	+	0.193229i	−0.804839	+	0.593493i	$0.797748\pi$
$264$		0			0
$265$		−	230.002i		−	0.867934i
$266$		0			0
$267$	206.364			0.772897
$268$		0			0
$269$	−126.984	+	73.3145i	−0.472061	+	0.272545i	−0.717102	−	0.696968i	$-0.754532\pi$
$269$	−126.984	+	73.3145i	−0.472061	+	0.272545i	0.245041	+	0.969513i	$0.421199\pi$
$270$		0			0
$271$	125.646	+	217.626i	0.463640	+	0.803048i	0.999139	−	0.0414878i	$-0.0132098\pi$
$271$	125.646	+	217.626i	0.463640	+	0.803048i	−0.535499	+	0.844536i	$0.679876\pi$
$272$		0			0
$273$	12.1137			0.0443727
$274$		0			0
$275$	−15.5601	+	26.9508i	−0.0565820	+	0.0980030i
$276$		0			0
$277$	−248.879			−0.898480			−0.449240	−	0.893411i	$-0.648305\pi$
$277$	−248.879			−0.898480			−0.449240	+	0.893411i	$0.648305\pi$
$278$		0			0
$279$	−11.9954	−	6.92552i	−0.0429941	−	0.0248227i
$280$		0			0
$281$	−377.933	−	218.200i	−1.34496	−	0.776512i	−0.357428	−	0.933941i	$-0.616346\pi$
$281$	−377.933	−	218.200i	−1.34496	−	0.776512i	−0.987530	+	0.157428i	$0.949680\pi$
$282$		0			0
$283$	−6.57376	−	11.3861i	−0.0232288	−	0.0402335i	0.854177	−	0.519982i	$-0.174061\pi$
$283$	−6.57376	−	11.3861i	−0.0232288	−	0.0402335i	−0.877406	+	0.479748i	$0.840728\pi$
$284$		0			0
$285$	−91.6354	+	145.065i	−0.321528	+	0.508999i
$286$		0			0
$287$	41.2719	−	23.8283i	0.143805	−	0.0830256i
$288$		0			0
$289$	143.060	−	247.787i	0.495017	−	0.857395i
$290$		0			0
$291$	−0.945906	+	1.63836i	−0.00325054	+	0.00563010i
$292$		0			0
$293$		−	500.830i		−	1.70932i	−0.519191	−	0.854658i	$-0.673767\pi$
$293$		−	500.830i		−	1.70932i	0.519191	−	0.854658i	$-0.326233\pi$
$294$		0			0
$295$	124.225	+	71.7211i	0.421100	+	0.243122i
$296$		0			0
$297$		−	74.0249i		−	0.249242i
$298$		0			0
$299$	2.15007	−	1.24134i	0.00719086	−	0.00415164i
$300$		0			0
$301$	215.536	+	373.320i	0.716068	+	1.24027i
$302$		0			0
$303$			34.0336i			0.112322i
$304$		0			0
$305$	−344.214			−1.12857
$306$		0			0
$307$	503.724	−	290.825i	1.64079	−	0.947313i	0.660243	−	0.751052i	$-0.270453\pi$
$307$	503.724	−	290.825i	1.64079	−	0.947313i	0.980552	−	0.196261i	$-0.0628799\pi$
$308$		0			0
$309$	−60.0869	−	104.074i	−0.194456	−	0.336808i
$310$		0			0
$311$	−149.216			−0.479793			−0.239897	−	0.970798i	$-0.577114\pi$
$311$	−149.216			−0.479793			−0.239897	+	0.970798i	$0.577114\pi$
$312$		0			0
$313$	50.8651	−	88.1010i	0.162508	−	0.281473i	−0.773259	−	0.634090i	$-0.781375\pi$
$313$	50.8651	−	88.1010i	0.162508	−	0.281473i	0.935768	+	0.352617i	$0.114708\pi$
$314$		0			0
$315$	90.3911			0.286956
$316$		0			0
$317$	−253.747	−	146.501i	−0.800465	−	0.462149i	0.0431689	−	0.999068i	$-0.486255\pi$
$317$	−253.747	−	146.501i	−0.800465	−	0.462149i	−0.843634	+	0.536919i	$0.819588\pi$
$318$		0			0
$319$	−222.627	−	128.534i	−0.697890	−	0.402927i
$320$		0			0
$321$	−85.0423	−	147.298i	−0.264929	−	0.458871i
$322$		0			0
$323$	28.5432	−	14.9982i	0.0883691	−	0.0464341i
$324$		0			0
$325$	−2.28955	+	1.32187i	−0.00704476	+	0.00406729i
$326$		0			0
$327$	58.4100	−	101.169i	0.178624	−	0.309386i
$328$		0			0
$329$	−0.685406	+	1.18716i	−0.00208330	+	0.00360838i
$330$		0			0
$331$		−	133.158i		−	0.402290i	−0.979561	−	0.201145i	$-0.935534\pi$
$331$		−	133.158i		−	0.402290i	0.979561	−	0.201145i	$-0.0644663\pi$
$332$		0			0
$333$	−52.4014	−	30.2540i	−0.157362	−	0.0908528i
$334$		0			0
$335$			536.359i			1.60107i
$336$		0			0
$337$	−392.126	+	226.394i	−1.16358	+	0.671792i	−0.952159	−	0.305603i	$-0.901142\pi$
$337$	−392.126	+	226.394i	−1.16358	+	0.671792i	−0.211419	+	0.977395i	$0.567809\pi$
$338$		0			0
$339$	19.2864	+	33.4049i	0.0568919	+	0.0985397i
$340$		0			0
$341$		−	65.7744i		−	0.192887i
$342$		0			0
$343$	−373.342			−1.08846
$344$		0			0
$345$	16.0435	−	9.26273i	0.0465029	−	0.0268485i
$346$		0			0
$347$	−1.12787	−	1.95353i	−0.00325034	−	0.00562976i	0.864396	−	0.502812i	$-0.167701\pi$
$347$	−1.12787	−	1.95353i	−0.00325034	−	0.00562976i	−0.867646	+	0.497182i	$0.834368\pi$
$348$		0			0
$349$	620.015			1.77655			0.888274	−	0.459315i	$-0.151905\pi$
$349$	620.015			1.77655			0.888274	+	0.459315i	$0.151905\pi$
$350$		0			0
$351$	3.14431	−	5.44610i	0.00895815	−	0.0155160i
$352$		0			0
$353$	−607.326			−1.72047			−0.860235	−	0.509897i	$-0.829683\pi$
$353$	−607.326			−1.72047			−0.860235	+	0.509897i	$0.829683\pi$
$354$		0			0
$355$	−459.957	−	265.556i	−1.29565	−	0.748046i
$356$		0			0
$357$	−14.7105	−	8.49312i	−0.0412059	−	0.0237902i
$358$		0			0
$359$	−285.181	−	493.948i	−0.794377	−	1.37590i	−0.923234	−	0.384238i	$-0.874464\pi$
$359$	−285.181	−	493.948i	−0.794377	−	1.37590i	0.128857	−	0.991663i	$-0.458869\pi$
$360$		0			0
$361$	−359.857	−	28.7012i	−0.996834	−	0.0795048i
$362$		0			0
$363$	122.927	−	70.9718i	0.338641	−	0.195515i
$364$		0			0
$365$	130.476	−	225.992i	0.357470	−	0.619156i
$366$		0			0
$367$	−324.726	+	562.442i	−0.884811	+	1.53254i	−0.0388817	+	0.999244i	$0.512380\pi$
$367$	−324.726	+	562.442i	−0.884811	+	1.53254i	−0.845930	+	0.533294i	$0.820954\pi$
$368$		0			0
$369$		−	24.7401i		−	0.0670463i
$370$		0			0
$371$	−220.773	−	127.464i	−0.595077	−	0.343568i
$372$		0			0
$373$		−	681.904i		−	1.82816i	−0.405534	−	0.914080i	$-0.632914\pi$
$373$		−	681.904i		−	1.82816i	0.405534	−	0.914080i	$-0.367086\pi$
$374$		0			0
$375$	178.436	−	103.020i	0.475829	−	0.274720i
$376$		0			0
$377$	−10.9193	−	18.9128i	−0.0289637	−	0.0501665i
$378$		0			0
$379$		−	33.0792i		−	0.0872801i	−0.999047	−	0.0436401i	$-0.986105\pi$
$379$		−	33.0792i		−	0.0872801i	0.999047	−	0.0436401i	$-0.0138955\pi$
$380$		0			0
$381$	−8.48192			−0.0222623
$382$		0			0
$383$	−50.5675	+	29.1952i	−0.132030	+	0.0762276i	−0.564560	−	0.825392i	$-0.690954\pi$
$383$	−50.5675	+	29.1952i	−0.132030	+	0.0762276i	0.432530	+	0.901619i	$0.357621\pi$
$384$		0			0
$385$	214.620	+	371.733i	0.557455	+	0.965540i
$386$		0			0
$387$	223.783			0.578252
$388$		0			0
$389$	275.881	−	477.841i	0.709207	−	1.22838i	−0.255945	−	0.966691i	$-0.582387\pi$
$389$	275.881	−	477.841i	0.709207	−	1.22838i	0.965152	−	0.261691i	$-0.0842801\pi$
$390$		0			0
$391$	−3.48129			−0.00890355
$392$		0			0
$393$	−179.653	−	103.723i	−0.457132	−	0.263925i
$394$		0			0
$395$	702.910	+	405.825i	1.77952	+	1.02741i
$396$		0			0
$397$	4.07470	+	7.05758i	0.0102637	+	0.0177773i	0.871112	−	0.491085i	$-0.163400\pi$
$397$	4.07470	+	7.05758i	0.0102637	+	0.0177773i	−0.860848	+	0.508862i	$0.830066\pi$
$398$		0			0
$399$	88.4610	+	168.351i	0.221707	+	0.421932i
$400$		0			0
$401$	−107.507	+	62.0692i	−0.268097	+	0.154786i	−0.628023	−	0.778195i	$-0.716136\pi$
$401$	−107.507	+	62.0692i	−0.268097	+	0.154786i	0.359925	+	0.932981i	$0.382802\pi$
$402$		0			0
$403$	2.79386	−	4.83911i	0.00693266	−	0.0120077i
$404$		0			0
$405$	23.4624	−	40.6381i	0.0579319	−	0.100341i
$406$		0			0
$407$		−	287.334i		−	0.705981i
$408$		0			0
$409$	−137.773	−	79.5436i	−0.336855	−	0.194483i	0.322026	−	0.946731i	$-0.395636\pi$
$409$	−137.773	−	79.5436i	−0.336855	−	0.194483i	−0.658880	+	0.752248i	$0.728970\pi$
$410$		0			0
$411$			194.690i			0.473697i
$412$		0			0
$413$	137.686	−	79.4933i	0.333381	−	0.192478i
$414$		0			0
$415$	−26.0574	−	45.1328i	−0.0627890	−	0.108754i
$416$		0			0
$417$		−	162.273i		−	0.389144i
$418$		0			0
$419$	−358.130			−0.854724			−0.427362	−	0.904080i	$-0.640557\pi$
$419$	−358.130			−0.854724			−0.427362	+	0.904080i	$0.640557\pi$
$420$		0			0
$421$	−269.779	+	155.757i	−0.640804	+	0.369968i	−0.784924	−	0.619592i	$-0.787298\pi$
$421$	−269.779	+	155.757i	−0.640804	+	0.369968i	0.144120	+	0.989560i	$0.453965\pi$
$422$		0			0
$423$	0.355816	+	0.616291i	0.000841172	+	0.00145695i
$424$		0			0
$425$	3.70713			0.00872266
$426$		0			0
$427$	−190.758	+	330.402i	−0.446739	+	0.773775i
$428$		0			0
$429$	29.8628			0.0696102
$430$		0			0
$431$	−39.2672	−	22.6709i	−0.0911071	−	0.0526007i	0.453754	−	0.891127i	$-0.350084\pi$
$431$	−39.2672	−	22.6709i	−0.0911071	−	0.0526007i	−0.544861	+	0.838526i	$0.683418\pi$
$432$		0			0
$433$	318.577	+	183.931i	0.735744	+	0.424782i	0.820520	−	0.571618i	$-0.193684\pi$
$433$	318.577	+	183.931i	0.735744	+	0.424782i	−0.0847761	+	0.996400i	$0.527017\pi$
$434$		0			0
$435$	−81.4784	−	141.125i	−0.187307	−	0.324425i
$436$		0			0
$437$	32.9525	+	20.8156i	0.0754062	+	0.0476331i
$438$		0			0
$439$	−732.595	+	422.964i	−1.66878	+	0.963472i	−0.700486	+	0.713666i	$0.747033\pi$
$439$	−732.595	+	422.964i	−1.66878	+	0.963472i	−0.968296	+	0.249806i	$0.919633\pi$
$440$		0			0
$441$	−23.4067	+	40.5416i	−0.0530764	+	0.0919310i
$442$		0			0
$443$	133.313	−	230.905i	0.300933	−	0.521231i	−0.675415	−	0.737438i	$-0.736035\pi$
$443$	133.313	−	230.905i	0.300933	−	0.521231i	0.976348	+	0.216207i	$0.0693686\pi$
$444$		0			0
$445$			621.202i			1.39596i
$446$		0			0
$447$	−77.6185	−	44.8131i	−0.173643	−	0.100253i
$448$		0			0
$449$			121.961i			0.271628i	0.990734	+	0.135814i	$0.0433650\pi$
$449$			121.961i			0.271628i	−0.990734	+	0.135814i	$0.956635\pi$
$450$		0			0
$451$	101.743	−	58.7416i	0.225595	−	0.130247i
$452$		0			0
$453$	−3.39489	−	5.88013i	−0.00749424	−	0.0129804i
$454$		0			0
$455$			36.4652i			0.0801432i
$456$		0			0
$457$	59.6689			0.130566			0.0652832	−	0.997867i	$-0.479205\pi$
$457$	59.6689			0.130566			0.0652832	+	0.997867i	$0.479205\pi$
$458$		0			0
$459$	−7.63668	+	4.40904i	−0.0166377	+	0.00960576i
$460$		0			0
$461$	125.279	+	216.990i	0.271756	+	0.470695i	0.969312	−	0.245836i	$-0.0790623\pi$
$461$	125.279	+	216.990i	0.271756	+	0.470695i	−0.697556	+	0.716531i	$0.745729\pi$
$462$		0			0
$463$	126.520			0.273262			0.136631	−	0.990622i	$-0.456373\pi$
$463$	126.520			0.273262			0.136631	+	0.990622i	$0.456373\pi$
$464$		0			0
$465$	20.8474	−	36.1088i	0.0448331	−	0.0776533i
$466$		0			0
$467$	598.831			1.28229			0.641147	−	0.767418i	$-0.278459\pi$
$467$	598.831			1.28229			0.641147	+	0.767418i	$0.278459\pi$
$468$		0			0
$469$	514.838	+	297.242i	1.09773	+	0.633777i
$470$		0			0
$471$	183.970	+	106.215i	0.390594	+	0.225509i
$472$		0			0
$473$	531.340	+	920.308i	1.12334	+	1.94568i
$474$		0			0
$475$	−35.0902	−	22.1660i	−0.0738741	−	0.0466653i
$476$		0			0
$477$	−114.610	+	66.1703i	−0.240273	+	0.138722i
$478$		0			0
$479$	102.168	−	176.960i	0.213294	−	0.369437i	−0.739449	−	0.673212i	$-0.764914\pi$
$479$	102.168	−	176.960i	0.213294	−	0.369437i	0.952744	+	0.303776i	$0.0982473\pi$
$480$		0			0
$481$	12.2049	−	21.1395i	0.0253740	−	0.0439491i
$482$		0			0
$483$		−	20.5330i		−	0.0425114i
$484$		0			0
$485$	−4.93184	−	2.84740i	−0.0101687	−	0.00587092i
$486$		0			0
$487$		−	468.435i		−	0.961879i	−0.876754	−	0.480939i	$-0.840296\pi$
$487$		−	468.435i		−	0.961879i	0.876754	−	0.480939i	$-0.159704\pi$
$488$		0			0
$489$	82.1676	−	47.4395i	0.168032	−	0.0970133i
$490$		0			0
$491$	353.053	+	611.505i	0.719048	+	1.24543i	0.961377	+	0.275234i	$0.0887554\pi$
$491$	353.053	+	611.505i	0.719048	+	1.24543i	−0.242329	+	0.970194i	$0.577911\pi$
$492$		0			0
$493$			30.6227i			0.0621150i
$494$		0			0
$495$	222.832			0.450166
$496$		0			0
$497$	−509.802	+	294.334i	−1.02576	+	0.592222i
$498$		0			0
$499$	−287.984	−	498.803i	−0.577122	−	0.999604i	−0.995808	−	0.0914732i	$-0.970842\pi$
$499$	−287.984	−	498.803i	−0.577122	−	0.999604i	0.418686	−	0.908131i	$-0.362491\pi$
$500$		0			0
$501$	188.474			0.376195
$502$		0			0
$503$	160.903	−	278.692i	0.319886	−	0.554059i	−0.660578	−	0.750758i	$-0.729689\pi$
$503$	160.903	−	278.692i	0.319886	−	0.554059i	0.980464	+	0.196698i	$0.0630219\pi$
$504$		0			0
$505$	−102.449			−0.202869
$506$		0			0
$507$	−251.303	−	145.090i	−0.495667	−	0.286173i
$508$		0			0
$509$	81.5619	+	47.0898i	0.160240	+	0.0925144i	0.577975	−	0.816054i	$-0.303843\pi$
$509$	81.5619	+	47.0898i	0.160240	+	0.0925144i	−0.417736	+	0.908569i	$0.637176\pi$
$510$		0			0
$511$	−144.616	−	250.482i	−0.283006	−	0.490180i
$512$		0			0
$513$	98.6487	+	3.92774i	0.192298	+	0.00765641i
$514$		0			0
$515$	313.286	−	180.876i	0.608322	−	0.351215i
$516$		0			0
$517$	−1.68966	+	2.92658i	−0.00326820	+	0.00566069i
$518$		0			0
$519$	−229.769	+	397.972i	−0.442715	+	0.766806i
$520$		0			0
$521$			253.020i			0.485643i	0.970071	+	0.242821i	$0.0780729\pi$
$521$			253.020i			0.485643i	−0.970071	+	0.242821i	$0.921927\pi$
$522$		0			0
$523$	−43.5687	−	25.1544i	−0.0833054	−	0.0480964i	0.457769	−	0.889071i	$-0.348649\pi$
$523$	−43.5687	−	25.1544i	−0.0833054	−	0.0480964i	−0.541074	+	0.840975i	$0.681982\pi$
$524$		0			0
$525$			21.8650i			0.0416477i
$526$		0			0
$527$	−6.78554	+	3.91763i	−0.0128758	+	0.00743383i
$528$		0			0
$529$	262.396	+	454.483i	0.496023	+	0.859136i
$530$		0			0
$531$		−	82.5349i		−	0.155433i
$532$		0			0
$533$	9.98052			0.0187252
$534$		0			0
$535$	443.400	−	255.997i	0.828784	−	0.478499i
$536$		0			0
$537$	−29.1626	−	50.5111i	−0.0543065	−	0.0940617i
$538$		0			0
$539$	−222.303			−0.412435
$540$		0			0
$541$	−74.5980	+	129.207i	−0.137889	+	0.238831i	−0.926697	−	0.375808i	$-0.877365\pi$
$541$	−74.5980	+	129.207i	−0.137889	+	0.238831i	0.788808	+	0.614639i	$0.210698\pi$
$542$		0			0
$543$	−270.524			−0.498202
$544$		0			0
$545$	304.543	+	175.828i	0.558794	+	0.322620i
$546$		0			0
$547$	283.239	+	163.528i	0.517804	+	0.298954i	0.736036	−	0.676943i	$-0.236695\pi$
$547$	283.239	+	163.528i	0.517804	+	0.298954i	−0.218232	+	0.975897i	$0.570029\pi$
$548$		0			0
$549$	99.0282	+	171.522i	0.180379	+	0.312426i
$550$		0			0
$551$	183.102	−	289.862i	0.332309	−	0.526066i
$552$		0			0
$553$	779.083	−	449.804i	1.40883	−	0.813388i
$554$		0			0
$555$	91.0715	−	157.740i	0.164093	−	0.284217i
$556$		0			0
$557$	−70.0091	+	121.259i	−0.125690	+	0.217701i	−0.922002	−	0.387184i	$-0.873448\pi$
$557$	−70.0091	+	121.259i	−0.125690	+	0.217701i	0.796313	+	0.604885i	$0.206781\pi$
$558$		0			0
$559$			90.2776i			0.161498i
$560$		0			0
$561$	−36.2643	−	20.9372i	−0.0646423	−	0.0373212i
$562$		0			0
$563$			643.577i			1.14312i	0.820560	+	0.571560i	$0.193662\pi$
$563$			643.577i			1.14312i	−0.820560	+	0.571560i	$0.806338\pi$
$564$		0			0
$565$	−100.557	+	58.0564i	−0.177976	+	0.102755i
$566$		0			0
$567$	−26.0050	−	45.0420i	−0.0458642	−	0.0794391i
$568$		0			0
$569$		−	206.874i		−	0.363575i	−0.983338	−	0.181787i	$-0.941812\pi$
$569$		−	206.874i		−	0.363575i	0.983338	−	0.181787i	$-0.0581883\pi$
$570$		0			0
$571$	−597.454			−1.04633			−0.523164	−	0.852232i	$-0.675249\pi$
$571$	−597.454			−1.04633			−0.523164	+	0.852232i	$0.675249\pi$
$572$		0			0
$573$	−528.519	+	305.141i	−0.922372	+	0.532532i
$574$		0			0
$575$	2.24059	+	3.88082i	0.00389669	+	0.00674926i
$576$		0			0
$577$	1042.56			1.80686			0.903430	−	0.428735i	$-0.141040\pi$
$577$	1042.56			1.80686			0.903430	+	0.428735i	$0.141040\pi$
$578$		0			0
$579$	10.1890	−	17.6479i	0.0175976	−	0.0304799i
$580$		0			0
$581$	−57.7624			−0.0994190
$582$		0			0
$583$	−544.250	−	314.223i	−0.933534	−	0.538976i
$584$		0			0
$585$	16.3940	+	9.46510i	0.0280240	+	0.0161797i
$586$		0			0
$587$	−406.294	−	703.721i	−0.692153	−	1.19884i	−0.971131	−	0.238546i	$-0.923329\pi$
$587$	−406.294	−	703.721i	−0.692153	−	1.19884i	0.278978	−	0.960297i	$-0.410004\pi$
$588$		0			0
$589$	87.6538	+	3.48997i	0.148818	+	0.00592525i
$590$		0			0
$591$	−364.928	+	210.691i	−0.617475	+	0.356499i
$592$		0			0
$593$	37.4912	−	64.9367i	0.0632229	−	0.109505i	−0.832681	−	0.553752i	$-0.813195\pi$
$593$	37.4912	−	64.9367i	0.0632229	−	0.109505i	0.895904	+	0.444247i	$0.146529\pi$
$594$		0			0
$595$	25.5662	−	44.2820i	0.0429685	−	0.0744236i
$596$		0			0
$597$			342.019i			0.572896i
$598$		0			0
$599$	−25.1947	−	14.5462i	−0.0420613	−	0.0242841i	0.478822	−	0.877912i	$-0.341064\pi$
$599$	−25.1947	−	14.5462i	−0.0420613	−	0.0242841i	−0.520883	+	0.853628i	$0.674397\pi$
$600$		0			0
$601$		−	614.451i		−	1.02238i	−0.859467	−	0.511191i	$-0.829205\pi$
$601$		−	614.451i		−	1.02238i	0.859467	−	0.511191i	$-0.170795\pi$
$602$		0			0
$603$	267.268	−	154.307i	0.443231	−	0.255899i
$604$		0			0
$605$	213.642	+	370.038i	0.353127	+	0.611633i
$606$		0			0
$607$			186.325i			0.306960i	0.988152	+	0.153480i	$0.0490481\pi$
$607$			186.325i			0.306960i	−0.988152	+	0.153480i	$0.950952\pi$
$608$		0			0
$609$	−180.616			−0.296578
$610$		0			0
$611$	−0.248621	+	0.143541i	−0.000406908	+	0.000234929i
$612$		0			0
$613$	279.584	+	484.253i	0.456091	+	0.789972i	0.998750	−	0.0499805i	$-0.0159159\pi$
$613$	279.584	+	484.253i	0.456091	+	0.789972i	−0.542659	+	0.839953i	$0.682583\pi$
$614$		0			0
$615$	74.4733			0.121095
$616$		0			0
$617$	283.544	−	491.113i	0.459553	−	0.795969i	−0.539384	−	0.842060i	$-0.681343\pi$
$617$	283.544	−	491.113i	0.459553	−	0.795969i	0.998937	+	0.0460906i	$0.0146763\pi$
$618$		0			0
$619$	671.562			1.08491			0.542457	−	0.840083i	$-0.317494\pi$
$619$	671.562			1.08491			0.542457	+	0.840083i	$0.317494\pi$
$620$		0			0
$621$	−9.23125	−	5.32966i	−0.0148651	−	0.00858239i
$622$		0			0
$623$	596.276	+	344.260i	0.957104	+	0.552584i
$624$		0			0
$625$	337.420	+	584.428i	0.539872	+	0.935085i
$626$		0			0
$627$	218.074	+	415.018i	0.347805	+	0.661911i
$628$		0			0
$629$	−29.6425	+	17.1141i	−0.0471263	+	0.0272084i
$630$		0			0
$631$	223.838	−	387.699i	0.354735	−	0.614419i	−0.632337	−	0.774693i	$-0.717904\pi$
$631$	223.838	−	387.699i	0.354735	−	0.614419i	0.987073	+	0.160274i	$0.0512377\pi$
$632$		0			0
$633$	319.747	−	553.818i	0.505130	−	0.874910i
$634$		0			0
$635$		−	25.5325i		−	0.0402087i
$636$		0			0
$637$	−16.3551	−	9.44261i	−0.0256752	−	0.0148236i
$638$		0			0
$639$			305.596i			0.478241i
$640$		0			0
$641$	716.415	−	413.622i	1.11765	−	0.645277i	0.176852	−	0.984238i	$-0.443409\pi$
$641$	716.415	−	413.622i	1.11765	−	0.645277i	0.940801	+	0.338961i	$0.110075\pi$
$642$		0			0
$643$	551.486	+	955.202i	0.857676	+	1.48554i	0.874140	+	0.485675i	$0.161426\pi$
$643$	551.486	+	955.202i	0.857676	+	1.48554i	−0.0164633	+	0.999864i	$0.505241\pi$
$644$		0			0
$645$			673.640i			1.04440i
$646$		0			0
$647$	494.083			0.763652			0.381826	−	0.924234i	$-0.375295\pi$
$647$	494.083			0.763652			0.381826	+	0.924234i	$0.375295\pi$
$648$		0			0
$649$	339.424	−	195.967i	0.522996	−	0.301952i
$650$		0			0
$651$	−23.1066	−	40.0218i	−0.0354940	−	0.0614774i
$652$		0			0
$653$	1270.54			1.94569			0.972845	−	0.231458i	$-0.0743496\pi$
$653$	1270.54			1.94569			0.972845	+	0.231458i	$0.0743496\pi$
$654$		0			0
$655$	312.229	−	540.797i	0.476686	−	0.825644i
$656$		0			0
$657$	−150.149			−0.228538
$658$		0			0
$659$	−36.4788	−	21.0610i	−0.0553548	−	0.0319591i	0.472067	−	0.881563i	$-0.343508\pi$
$659$	−36.4788	−	21.0610i	−0.0553548	−	0.0319591i	−0.527422	+	0.849603i	$0.676841\pi$
$660$		0			0
$661$	−164.771	−	95.1307i	−0.249276	−	0.143919i	0.370157	−	0.928969i	$-0.379304\pi$
$661$	−164.771	−	95.1307i	−0.249276	−	0.143919i	−0.619433	+	0.785050i	$0.712637\pi$
$662$		0			0
$663$	−1.77867	−	3.08075i	−0.00268277	−	0.00464669i
$664$		0			0
$665$	−506.775	+	266.288i	−0.762068	+	0.400433i
$666$		0			0
$667$	−32.0575	+	18.5084i	−0.0480622	+	0.0277487i
$668$		0			0
$669$	−137.458	+	238.084i	−0.205467	+	0.355880i
$670$		0			0
$671$	−470.255	+	814.506i	−0.700827	+	1.21387i
$672$		0			0
$673$			143.637i			0.213427i	0.994290	+	0.106714i	$0.0340328\pi$
$673$			143.637i			0.213427i	−0.994290	+	0.106714i	$0.965967\pi$
$674$		0			0
$675$	9.83010	+	5.67541i	0.0145631	+	0.00840802i
$676$		0			0
$677$		−	866.720i		−	1.28024i	−0.768277	−	0.640118i	$-0.778885\pi$
$677$		−	866.720i		−	1.28024i	0.768277	−	0.640118i	$-0.221115\pi$
$678$		0			0
$679$	−5.46629	+	3.15596i	−0.00805050	+	0.00464796i
$680$		0			0
$681$	−345.628	−	598.645i	−0.507530	−	0.879068i
$682$		0			0
$683$		−	143.568i		−	0.210203i	−0.994462	−	0.105101i	$-0.966483\pi$
$683$		−	143.568i		−	0.210203i	0.994462	−	0.105101i	$-0.0335167\pi$
$684$		0			0
$685$	−586.061			−0.855563
$686$		0			0
$687$	43.6059	−	25.1759i	0.0634730	−	0.0366461i
$688$		0			0
$689$	−26.6941	−	46.2356i	−0.0387433	−	0.0671053i
$690$		0			0
$691$	838.199			1.21302			0.606512	−	0.795075i	$-0.292568\pi$
$691$	838.199			1.21302			0.606512	+	0.795075i	$0.292568\pi$
$692$		0			0
$693$	123.490	−	213.891i	0.178196	−	0.308645i
$694$		0			0
$695$	488.479			0.702847
$696$		0			0
$697$	−12.1200	−	6.99749i	−0.0173888	−	0.0100394i
$698$		0			0
$699$	459.992	+	265.577i	0.658072	+	0.379938i
$700$		0			0
$701$	314.646	+	544.982i	0.448853	+	0.777435i	0.998312	−	0.0580852i	$-0.0184995\pi$
$701$	314.646	+	544.982i	0.448853	+	0.777435i	−0.549459	+	0.835521i	$0.685166\pi$
$702$		0			0
$703$	382.914	+	15.2459i	0.544685	+	0.0216869i
$704$		0			0
$705$	−1.85518	+	1.07109i	−0.00263146	+	0.00151927i
$706$		0			0
$707$	−56.7756	+	98.3383i	−0.0803050	+	0.139092i
$708$		0			0
$709$	451.150	−	781.415i	0.636319	−	1.10214i	−0.349915	−	0.936781i	$-0.613790\pi$
$709$	451.150	−	781.415i	0.636319	−	1.10214i	0.986234	−	0.165355i	$-0.0528771\pi$
$710$		0			0
$711$		−	467.014i		−	0.656841i
$712$		0			0
$713$	−8.20237	−	4.73564i	−0.0115040	−	0.00664186i
$714$		0			0
$715$			89.8938i			0.125726i
$716$		0			0
$717$	−371.627	+	214.559i	−0.518308	+	0.299246i
$718$		0			0
$719$	331.413	+	574.024i	0.460936	+	0.798364i	0.999008	−	0.0445348i	$-0.0141806\pi$
$719$	331.413	+	574.024i	0.460936	+	0.798364i	−0.538072	+	0.842899i	$0.680847\pi$
$720$		0			0
$721$		−	400.953i		−	0.556107i
$722$		0			0
$723$	6.08023			0.00840973
$724$		0			0
$725$	34.1372	−	19.7091i	0.0470857	−	0.0271850i
$726$		0			0
$727$	−94.3208	−	163.368i	−0.129740	−	0.224716i	0.793836	−	0.608132i	$-0.208081\pi$
$727$	−94.3208	−	163.368i	−0.129740	−	0.224716i	−0.923576	+	0.383416i	$0.874748\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	63.2949	−	109.630i	0.0865868	−	0.149973i
$732$		0			0
$733$	−643.296			−0.877621			−0.438810	−	0.898580i	$-0.644600\pi$
$733$	−643.296			−0.877621			−0.438810	+	0.898580i	$0.644600\pi$
$734$		0			0
$735$	−122.040	−	70.4595i	−0.166040	−	0.0958633i
$736$		0			0
$737$	1269.18	+	732.759i	1.72208	+	0.994246i
$738$		0			0
$739$	−435.613	−	754.504i	−0.589463	−	1.02098i	−0.994303	−	0.106592i	$-0.966006\pi$
$739$	−435.613	−	754.504i	−0.589463	−	1.02098i	0.404840	−	0.914387i	$-0.367327\pi$
$740$		0			0
$741$	−1.58451	+	39.7964i	−0.00213834	+	0.0537063i
$742$		0			0
$743$	−562.192	+	324.582i	−0.756652	+	0.436853i	−0.828092	−	0.560592i	$-0.810574\pi$
$743$	−562.192	+	324.582i	−0.756652	+	0.436853i	0.0714406	+	0.997445i	$0.477240\pi$
$744$		0			0
$745$	134.898	−	233.650i	0.181071	−	0.313624i
$746$		0			0
$747$	−14.9931	+	25.9689i	−0.0200711	+	0.0347642i
$748$		0			0
$749$		−	567.477i		−	0.757647i
$750$		0			0
$751$	887.484	+	512.389i	1.18174	+	0.682276i	0.956416	−	0.292009i	$-0.0943236\pi$
$751$	887.484	+	512.389i	1.18174	+	0.682276i	0.225321	+	0.974285i	$0.427657\pi$
$752$		0			0
$753$			506.483i			0.672621i
$754$		0			0
$755$	17.7005	−	10.2194i	0.0234444	−	0.0135356i
$756$		0			0
$757$	−541.728	−	938.300i	−0.715624	−	1.23950i	−0.962718	−	0.270506i	$-0.912809\pi$
$757$	−541.728	−	938.300i	−0.715624	−	1.23950i	0.247094	−	0.968992i	$-0.420524\pi$
$758$		0			0
$759$		−	50.6179i		−	0.0666903i
$760$		0			0
$761$	−1289.83			−1.69492			−0.847461	−	0.530858i	$-0.821870\pi$
$761$	−1289.83			−1.69492			−0.847461	+	0.530858i	$0.821870\pi$
$762$		0			0
$763$	337.545	−	194.882i	0.442392	−	0.255415i
$764$		0			0
$765$	−13.2722	−	22.9882i	−0.0173493	−	0.0300499i
$766$		0			0
$767$	33.2958			0.0434105
$768$		0			0
$769$	−212.474	+	368.016i	−0.276299	+	0.478564i	−0.970462	−	0.241254i	$-0.922441\pi$
$769$	−212.474	+	368.016i	−0.276299	+	0.478564i	0.694163	+	0.719818i	$0.255775\pi$
$770$		0			0
$771$	−632.020			−0.819740
$772$		0			0
$773$	−615.409	−	355.306i	−0.796130	−	0.459646i	0.0459860	−	0.998942i	$-0.485357\pi$
$773$	−615.409	−	355.306i	−0.796130	−	0.459646i	−0.842116	+	0.539296i	$0.818690\pi$
$774$		0			0
$775$	8.73448	+	5.04286i	0.0112703	+	0.00650691i
$776$		0			0
$777$	−100.941	−	174.834i	−0.129911	−	0.225012i
$778$		0			0
$779$	72.8831	+	138.704i	0.0935598	+	0.178054i
$780$		0			0
$781$	−1256.76	+	725.592i	−1.60917	+	0.929055i
$782$		0			0
$783$	−46.8817	+	81.2015i	−0.0598744	+	0.103706i
$784$		0			0
$785$	−319.731	+	553.791i	−0.407301	+	0.705466i
$786$		0			0
$787$			1176.18i			1.49451i	0.664538	+	0.747255i	$0.268628\pi$
$787$			1176.18i			1.49451i	−0.664538	+	0.747255i	$0.731372\pi$
$788$		0			0
$789$	88.0215	+	50.8192i	0.111561	+	0.0644097i
$790$		0			0
$791$			128.696i			0.162700i
$792$		0			0
$793$	−69.1945	+	39.9495i	−0.0872567	+	0.0503777i
$794$		0			0
$795$	−199.188	−	345.004i	−0.250551	−	0.433967i
$796$		0			0
$797$		−	181.131i		−	0.227266i	−0.993523	−	0.113633i	$-0.963751\pi$
$797$		−	181.131i		−	0.227266i	0.993523	−	0.113633i	$-0.0362488\pi$
$798$		0			0
$799$	0.402556			0.000503825
$800$		0			0
$801$	309.545	−	178.716i	0.386449	−	0.223116i
$802$		0			0
$803$	−356.507	−	617.488i	−0.443968	−	0.768976i
$804$		0			0
$805$	61.8091			0.0767815
$806$		0			0
$807$	−126.984	+	219.943i	−0.157354	+	0.272545i
$808$		0			0
$809$	485.435			0.600043			0.300022	−	0.953932i	$-0.403006\pi$
$809$	485.435			0.600043			0.300022	+	0.953932i	$0.403006\pi$
$810$		0			0
$811$	−1261.00	−	728.040i	−1.55487	−	0.897706i	−0.997734	−	0.0672866i	$-0.978566\pi$
$811$	−1261.00	−	728.040i	−1.55487	−	0.897706i	−0.557139	−	0.830419i	$-0.688101\pi$
$812$		0			0
$813$	376.939	+	217.626i	0.463640	+	0.267683i
$814$		0			0
$815$	142.804	+	247.343i	0.175219	+	0.303489i
$816$		0			0
$817$	−1254.63	+	659.255i	−1.53566	+	0.806922i
$818$		0			0
$819$	18.1706	−	10.4908i	0.0221863	−	0.0128093i
$820$		0			0
$821$	−140.760	+	243.804i	−0.171450	+	0.296959i	−0.938927	−	0.344117i	$-0.888178\pi$
$821$	−140.760	+	243.804i	−0.171450	+	0.296959i	0.767477	+	0.641076i	$0.221512\pi$
$822$		0			0
$823$	−629.927	+	1091.07i	−0.765403	+	1.32572i	0.174630	+	0.984634i	$0.444127\pi$
$823$	−629.927	+	1091.07i	−0.765403	+	1.32572i	−0.940033	+	0.341083i	$0.889206\pi$
$824$		0			0
$825$			53.9016i			0.0653353i
$826$		0			0
$827$	1091.40	+	630.120i	1.31971	+	0.761934i	0.983682	−	0.179918i	$-0.0575832\pi$
$827$	1091.40	+	630.120i	1.31971	+	0.761934i	0.336027	+	0.941852i	$0.390917\pi$
$828$		0			0
$829$		−	656.578i		−	0.792012i	−0.918248	−	0.396006i	$-0.870396\pi$
$829$		−	656.578i		−	0.792012i	0.918248	−	0.396006i	$-0.129604\pi$
$830$		0			0
$831$	−373.319	+	215.536i	−0.449240	+	0.259369i
$832$		0			0
$833$	13.2407	+	22.9336i	0.0158952	+	0.0275313i
$834$		0			0
$835$			567.350i			0.679461i
$836$		0			0
$837$	−23.9907			−0.0286627
$838$		0			0
$839$	653.054	−	377.041i	0.778372	−	0.449393i	−0.0574812	−	0.998347i	$-0.518307\pi$
$839$	653.054	−	377.041i	0.778372	−	0.449393i	0.835853	+	0.548953i	$0.184974\pi$
$840$		0			0
$841$	−257.693	−	446.338i	−0.306413	−	0.530722i
$842$		0			0
$843$	−755.867			−0.896639
$844$		0			0
$845$	436.754	−	756.480i	0.516868	−	0.895242i
$846$		0			0
$847$	473.587			0.559134
$848$		0			0
$849$	−19.7213	−	11.3861i	−0.0232288	−	0.0134112i
$850$		0			0
$851$	−35.8319	−	20.6876i	−0.0421056	−	0.0243097i
$852$		0			0
$853$	−348.689	−	603.948i	−0.408780	−	0.708028i	0.585973	−	0.810330i	$-0.300712\pi$
$853$	−348.689	−	603.948i	−0.408780	−	0.708028i	−0.994753	+	0.102303i	$0.967379\pi$
$854$		0			0
$855$	−11.8234	+	296.955i	−0.0138285	+	0.347316i
$856$		0			0
$857$	−817.383	+	471.916i	−0.953773	+	0.550661i	−0.894251	−	0.447566i	$-0.852291\pi$
$857$	−817.383	+	471.916i	−0.953773	+	0.550661i	−0.0595218	+	0.998227i	$0.518958\pi$
$858$		0			0
$859$	−496.987	+	860.807i	−0.578565	+	1.00210i	0.417080	+	0.908870i	$0.363054\pi$
$859$	−496.987	+	860.807i	−0.578565	+	1.00210i	−0.995644	+	0.0932333i	$0.970280\pi$
$860$		0			0
$861$	41.2719	−	71.4850i	0.0479349	−	0.0830256i
$862$		0			0
$863$		−	1261.81i		−	1.46212i	−0.682316	−	0.731058i	$-0.739027\pi$
$863$		−	1261.81i		−	1.46212i	0.682316	−	0.731058i	$-0.260973\pi$
$864$		0			0
$865$	−1197.99	−	691.659i	−1.38496	−	0.799605i
$866$		0			0
$867$		−	495.574i		−	0.571597i
$868$		0			0
$869$	1920.59	−	1108.85i	2.21012	−	1.27601i
$870$		0			0
$871$	62.2499	+	107.820i	0.0714695	+	0.123789i
$872$		0			0
$873$			3.27672i			0.00375340i
$874$		0			0
$875$	687.441			0.785647
$876$		0			0
$877$	−1370.23	+	791.104i	−1.56241	+	0.902057i	−0.565395	+	0.824820i	$0.691276\pi$
$877$	−1370.23	+	791.104i	−1.56241	+	0.902057i	−0.997013	+	0.0772365i	$0.975390\pi$
$878$		0			0
$879$	−433.731	−	751.245i	−0.493437	−	0.854658i
$880$		0			0
$881$	453.592			0.514861			0.257430	−	0.966297i	$-0.417124\pi$
$881$	453.592			0.514861			0.257430	+	0.966297i	$0.417124\pi$
$882$		0			0
$883$	−171.942	+	297.812i	−0.194724	+	0.337273i	−0.946810	−	0.321793i	$-0.895715\pi$
$883$	−171.942	+	297.812i	−0.194724	+	0.337273i	0.752086	+	0.659065i	$0.229048\pi$
$884$		0			0
$885$	248.449			0.280733
$886$		0			0
$887$	56.2325	+	32.4659i	0.0633963	+	0.0366019i	0.531363	−	0.847144i	$-0.321680\pi$
$887$	56.2325	+	32.4659i	0.0633963	+	0.0366019i	−0.467967	+	0.883746i	$0.655013\pi$
$888$		0			0
$889$	−24.5080	−	14.1497i	−0.0275681	−	0.0159164i
$890$		0			0
$891$	−64.1074	−	111.037i	−0.0719500	−	0.124621i
$892$		0			0
$893$	−3.81043	−	2.40700i	−0.00426700	−	0.00269541i
$894$		0			0
$895$	152.050	−	87.7862i	0.169888	−	0.0980851i
$896$		0			0
$897$	2.15007	−	3.72402i	0.00239695	−	0.00415164i
$898$		0			0
$899$	−41.6565	+	72.1511i	−0.0463365	+	0.0802571i
$900$		0			0
$901$			74.8625i			0.0830882i
$902$		0			0
$903$	646.609	+	373.320i	0.716068	+	0.413422i
$904$		0			0
$905$		−	814.338i		−	0.899821i
$906$		0			0
$907$	−578.484	+	333.988i	−0.637799	+	0.368234i	−0.783766	−	0.621056i	$-0.786704\pi$
$907$	−578.484	+	333.988i	−0.637799	+	0.368234i	0.145967	+	0.989289i	$0.453371\pi$
$908$		0			0
$909$	29.4740	+	51.0504i	0.0324246	+	0.0561611i
$910$		0			0
$911$		−	713.121i		−	0.782789i	−0.920223	−	0.391395i	$-0.871993\pi$
$911$		−	713.121i		−	0.782789i	0.920223	−	0.391395i	$-0.128007\pi$
$912$		0			0
$913$	−142.396			−0.155965
$914$		0			0
$915$	−516.320	+	298.098i	−0.564285	+	0.325790i
$916$		0			0
$917$	−346.065	−	599.402i	−0.377388	−	0.653655i
$918$		0			0
$919$	894.138			0.972946			0.486473	−	0.873696i	$-0.338283\pi$
$919$	894.138			0.972946			0.486473	+	0.873696i	$0.338283\pi$
$920$		0			0
$921$	503.724	−	872.475i	0.546931	−	0.947313i
$922$		0			0
$923$	−123.282			−0.133567
$924$		0			0
$925$	38.1564	+	22.0296i	0.0412502	+	0.0238158i
$926$		0			0
$927$	−180.261	−	104.074i	−0.194456	−	0.112269i
$928$		0			0
$929$	721.650	+	1249.93i	0.776803	+	1.34546i	0.933776	+	0.357859i	$0.116493\pi$
$929$	721.650	+	1249.93i	0.776803	+	1.34546i	−0.156973	+	0.987603i	$0.550174\pi$
$930$		0			0
$931$	11.7953	−	296.250i	0.0126695	−	0.318206i
$932$		0			0
$933$	−223.824	+	129.225i	−0.239897	+	0.138504i
$934$		0			0
$935$	63.0258	−	109.164i	0.0674073	−	0.116753i
$936$		0			0
$937$	−235.948	+	408.674i	−0.251812	+	0.436152i	−0.964025	−	0.265812i	$-0.914360\pi$
$937$	−235.948	+	408.674i	−0.251812	+	0.436152i	0.712212	+	0.701964i	$0.247693\pi$
$938$		0			0
$939$		−	176.202i		−	0.187649i
$940$		0			0
$941$	366.753	+	211.745i	0.389748	+	0.225021i	0.682051	−	0.731305i	$-0.261088\pi$
$941$	366.753	+	211.745i	0.389748	+	0.225021i	−0.292303	+	0.956326i	$0.594421\pi$
$942$		0			0
$943$		−	16.9172i		−	0.0179397i
$944$		0			0
$945$	135.587	−	78.2810i	0.143478	−	0.0828371i
$946$		0			0
$947$	70.4344	+	121.996i	0.0743764	+	0.128824i	0.900815	−	0.434203i	$-0.142970\pi$
$947$	70.4344	+	121.996i	0.0743764	+	0.128824i	−0.826439	+	0.563027i	$0.809637\pi$
$948$		0			0
$949$		−	60.5725i		−	0.0638277i
$950$		0			0
$951$	−507.495			−0.533643
$952$		0			0
$953$	−224.723	+	129.744i	−0.235805	+	0.136142i	−0.613247	−	0.789891i	$-0.710137\pi$
$953$	−224.723	+	129.744i	−0.235805	+	0.136142i	0.377442	+	0.926033i	$0.376804\pi$
$954$		0			0
$955$	−918.544	−	1590.96i	−0.961826	−	1.66593i
$956$		0			0
$957$	−445.254			−0.465260
$958$		0			0
$959$	−324.785	+	562.545i	−0.338671	+	0.586595i
$960$		0			0
$961$	939.683			0.977818
$962$		0			0
$963$	−255.127	−	147.298i	−0.264929	−	0.152957i
$964$		0			0
$965$	53.1241	+	30.6712i	0.0550509	+	0.0317837i
$966$		0			0
$967$	675.421	+	1169.86i	0.698471	+	1.20979i	0.968997	+	0.247074i	$0.0794690\pi$
$967$	675.421	+	1169.86i	0.698471	+	1.20979i	−0.270526	+	0.962713i	$0.587198\pi$
$968$		0			0
$969$	29.8260	−	47.2165i	0.0307802	−	0.0487270i
$970$		0			0
$971$	−51.9550	+	29.9962i	−0.0535067	+	0.0308921i	−0.526515	−	0.850166i	$-0.676501\pi$
$971$	−51.9550	+	29.9962i	−0.0535067	+	0.0308921i	0.473008	+	0.881058i	$0.343168\pi$
$972$		0			0
$973$	270.707	−	468.878i	0.278219	−	0.481889i
$974$		0			0
$975$	−2.28955	+	3.96561i	−0.00234825	+	0.00406729i
$976$		0			0
$977$			943.392i			0.965601i	0.875730	+	0.482801i	$0.160380\pi$
$977$			943.392i			0.965601i	−0.875730	+	0.482801i	$0.839620\pi$
$978$		0			0
$979$	1469.94	+	848.669i	1.50147	+	0.866873i
$980$		0			0
$981$		−	202.338i		−	0.206257i
$982$		0			0
$983$	855.382	−	493.855i	0.870175	−	0.502396i	0.00276861	−	0.999996i	$-0.499119\pi$
$983$	855.382	−	493.855i	0.870175	−	0.502396i	0.867406	+	0.497600i	$0.165785\pi$
$984$		0			0
$985$	−634.229	−	1098.52i	−0.643887	−	1.11525i
$986$		0			0
$987$			2.37432i			0.00240559i
$988$		0			0
$989$	153.022			0.154724
$990$		0			0
$991$	−520.740	+	300.649i	−0.525469	+	0.303380i	−0.739169	−	0.673520i	$-0.764782\pi$
$991$	−520.740	+	300.649i	−0.525469	+	0.303380i	0.213701	+	0.976899i	$0.431448\pi$
$992$		0			0
$993$	−115.318	−	199.737i	−0.116131	−	0.201145i
$994$		0			0
$995$	−1029.56			−1.03473
$996$		0			0
$997$	−680.988	+	1179.51i	−0.683037	+	1.18305i	0.291012	+	0.956719i	$0.406008\pi$
$997$	−680.988	+	1179.51i	−0.683037	+	1.18305i	−0.974049	+	0.226335i	$0.927325\pi$
$998$		0			0
$999$	−104.803			−0.104908

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.j.145.8		20
4.3	odd	2		456.3.w.a.145.8	✓	20
12.11	even	2		1368.3.bv.c.145.3		20
19.8	odd	6	inner	912.3.be.j.673.8		20
76.27	even	6		456.3.w.a.217.8	yes	20
228.179	odd	6		1368.3.bv.c.217.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.3.w.a.145.8	✓	20	4.3	odd	2
456.3.w.a.217.8	yes	20	76.27	even	6
912.3.be.j.145.8		20	1.1	even	1	trivial
912.3.be.j.673.8		20	19.8	odd	6	inner
1368.3.bv.c.145.3		20	12.11	even	2
1368.3.bv.c.217.3		20	228.179	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	912.be (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +(2.60694 + 4.51535i) q^{5} +5.77889 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 0.866025i) q^{3} +(2.60694 + 4.51535i) q^{5} +5.77889 q^{7} +(1.50000 - 2.59808i) q^{9} +14.2461 q^{11} +(1.04810 + 0.605123i) q^{13} +(7.82081 + 4.51535i) q^{15} +(-0.848521 - 1.46968i) q^{17} +(-0.755894 + 18.9850i) q^{19} +(8.66833 - 5.00466i) q^{21} +(1.02569 - 1.77655i) q^{23} +(-1.09223 + 1.89180i) q^{25} -5.19615i q^{27} +(-15.6272 - 9.02238i) q^{29} -4.61701i q^{31} +(21.3691 - 12.3375i) q^{33} +(15.0652 + 26.0937i) q^{35} -20.1693i q^{37} +2.09621 q^{39} +(7.14184 - 4.12335i) q^{41} +(37.2972 + 64.6007i) q^{43} +15.6416 q^{45} +(-0.118605 + 0.205430i) q^{47} -15.6045 q^{49} +(-2.54556 - 1.46968i) q^{51} +(-38.2035 - 22.0568i) q^{53} +(37.1387 + 64.3260i) q^{55} +(15.3076 + 29.1321i) q^{57} +(23.8258 - 13.7558i) q^{59} +(-33.0094 + 57.1740i) q^{61} +(8.66833 - 15.0140i) q^{63} +6.31007i q^{65} +(89.0894 + 51.4358i) q^{67} -3.55311i q^{69} +(-88.2180 + 50.9327i) q^{71} +(-25.0249 - 43.3443i) q^{73} +3.78361i q^{75} +82.3266 q^{77} +(134.815 - 77.8357i) q^{79} +(-4.50000 - 7.79423i) q^{81} -9.99542 q^{83} +(4.42408 - 7.66273i) q^{85} -31.2545 q^{87} +(103.182 + 59.5720i) q^{89} +(6.05687 + 3.49694i) q^{91} +(-3.99845 - 6.92552i) q^{93} +(-87.6942 + 46.0795i) q^{95} +(-0.945906 + 0.546119i) q^{97} +(21.3691 - 37.0124i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9}+O(q^{10}) \) 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9	\( 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9} + 8 q^{11} + 18 q^{13} + 8 q^{17} - 28 q^{19} - 30 q^{21} + 8 q^{23} - 58 q^{25} + 108 q^{29} + 12 q^{33} - 20 q^{35} + 36 q^{39} - 36 q^{41} + 2 q^{43} + 296 q^{49} + 24 q^{51} - 72 q^{53} - 216 q^{55} - 30 q^{57} - 72 q^{59} - 26 q^{61} - 30 q^{63} - 138 q^{67} + 204 q^{71} + 218 q^{73} - 8 q^{77} + 78 q^{79} - 90 q^{81} + 112 q^{83} + 224 q^{85} + 216 q^{87} - 432 q^{89} + 330 q^{91} - 126 q^{93} - 220 q^{95} + 132 q^{97} + 12 q^{99}+O(q^{100}) \) 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9 + 8 * q^11 + 18 * q^13 + 8 * q^17 - 28 * q^19 - 30 * q^21 + 8 * q^23 - 58 * q^25 + 108 * q^29 + 12 * q^33 - 20 * q^35 + 36 * q^39 - 36 * q^41 + 2 * q^43 + 296 * q^49 + 24 * q^51 - 72 * q^53 - 216 * q^55 - 30 * q^57 - 72 * q^59 - 26 * q^61 - 30 * q^63 - 138 * q^67 + 204 * q^71 + 218 * q^73 - 8 * q^77 + 78 * q^79 - 90 * q^81 + 112 * q^83 + 224 * q^85 + 216 * q^87 - 432 * q^89 + 330 * q^91 - 126 * q^93 - 220 * q^95 + 132 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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