LMFDB - Embedded newform 224.2.t.a.177.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(81,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("224.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.t (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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.951588245534976.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 2 x^{10} - 9 x^{9} + 8 x^{8} - 13 x^{7} + 35 x^{6} - 26 x^{5} + 32 x^{4} - 72 x^{3} + \cdots + 64 $ x^12 - x^11 + 2x^10 - 9x^9 + 8x^8 - 13x^7 + 35x^6 - 26x^5 + 32x^4 - 72x^3 + 32x^2 - 32x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			177.5
Root			$-0.0950561 - 1.41102i$ of defining polynomial
Character	$\chi$	$=$	224.177
Dual form			224.2.t.a.81.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36456 - 0.787829i) q^{3} +(-0.476087 - 0.274869i) q^{5} +(2.60755 + 0.447998i) q^{7} +(-0.258652 + 0.447998i) q^{9} +O(q^{10})$	\(q+(1.36456 - 0.787829i) q^{3} +(-0.476087 - 0.274869i) q^{5} +(2.60755 + 0.447998i) q^{7} +(-0.258652 + 0.447998i) q^{9} +(2.07045 - 1.19538i) q^{11} -3.96641i q^{13} -0.866198 q^{15} +(2.10755 + 3.65038i) q^{17} +(-5.75174 - 3.32077i) q^{19} +(3.91110 - 1.44298i) q^{21} +(-1.17445 + 2.03420i) q^{23} +(-2.34889 - 4.06840i) q^{25} +5.54207i q^{27} +8.21720i q^{29} +(0.433099 + 0.750150i) q^{31} +(1.88350 - 3.26232i) q^{33} +(-1.11828 - 0.930019i) q^{35} +(-0.229805 - 0.132678i) q^{37} +(-3.12485 - 5.41240i) q^{39} -6.24970 q^{41} +5.35027i q^{43} +(0.246282 - 0.142191i) q^{45} +(1.29930 - 2.25045i) q^{47} +(6.59859 + 2.33635i) q^{49} +(5.75174 + 3.32077i) q^{51} +(-9.36933 + 5.40939i) q^{53} -1.31429 q^{55} -10.4648 q^{57} +(3.26891 - 1.88730i) q^{59} +(-6.18061 - 3.56837i) q^{61} +(-0.875150 + 1.05230i) q^{63} +(-1.09024 + 1.88835i) q^{65} +(-2.31673 + 1.33757i) q^{67} +3.70105i q^{69} -8.76700 q^{71} +(-2.33159 - 4.03843i) q^{73} +(-6.41041 - 3.70105i) q^{75} +(5.93432 - 2.18944i) q^{77} +(0.308249 - 0.533903i) q^{79} +(3.59024 + 6.21848i) q^{81} +1.09948i q^{83} -2.31720i q^{85} +(6.47374 + 11.2129i) q^{87} +(3.19779 - 5.53873i) q^{89} +(1.77694 - 10.3426i) q^{91} +(1.18198 + 0.682416i) q^{93} +(1.82555 + 3.16195i) q^{95} +12.9475 q^{97} +1.23675i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{7}+O(q^{10}) $ 12 * q + 4 * q^7	$ 12 q + 4 q^{7} + 20 q^{15} - 2 q^{17} - 2 q^{23} - 4 q^{25} - 10 q^{31} - 14 q^{33} - 4 q^{39} - 8 q^{41} - 30 q^{47} - 12 q^{49} - 4 q^{55} - 4 q^{57} - 44 q^{63} + 8 q^{65} - 32 q^{71} - 10 q^{73} + 22 q^{79} + 22 q^{81} + 20 q^{87} - 10 q^{89} + 34 q^{95} + 40 q^{97}+O(q^{100}) $ 12 * q + 4 * q^7 + 20 * q^15 - 2 * q^17 - 2 * q^23 - 4 * q^25 - 10 * q^31 - 14 * q^33 - 4 * q^39 - 8 * q^41 - 30 * q^47 - 12 * q^49 - 4 * q^55 - 4 * q^57 - 44 * q^63 + 8 * q^65 - 32 * q^71 - 10 * q^73 + 22 * q^79 + 22 * q^81 + 20 * q^87 - 10 * q^89 + 34 * q^95 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.36456	−	0.787829i	0.787829	−	0.454853i	−0.0513689	−	0.998680i	$-0.516358\pi$
$3$	1.36456	−	0.787829i	0.787829	−	0.454853i	0.839198	+	0.543827i	$0.183025\pi$
$4$		0			0
$5$	−0.476087	−	0.274869i	−0.212913	−	0.122925i	0.389752	−	0.920920i	$-0.372561\pi$
$5$	−0.476087	−	0.274869i	−0.212913	−	0.122925i	−0.602664	+	0.797995i	$0.705894\pi$
$6$		0			0
$7$	2.60755	+	0.447998i	0.985560	+	0.169327i
$7$	2.60755	+	0.447998i	0.985560	+	0.169327i
$8$		0			0
$9$	−0.258652	+	0.447998i	−0.0862173	+	0.149333i
$10$		0			0
$11$	2.07045	−	1.19538i	0.624265	−	0.360419i	−0.154263	−	0.988030i	$-0.549300\pi$
$11$	2.07045	−	1.19538i	0.624265	−	0.360419i	0.778527	+	0.627611i	$0.215967\pi$
$12$		0			0
$13$		−	3.96641i		−	1.10008i	−0.835137	−	0.550042i	$-0.814612\pi$
$13$		−	3.96641i		−	1.10008i	0.835137	−	0.550042i	$-0.185388\pi$
$14$		0			0
$15$	−0.866198			−0.223651
$16$		0			0
$17$	2.10755	+	3.65038i	0.511155	+	0.885347i	0.999916	+	0.0129290i	$0.00411554\pi$
$17$	2.10755	+	3.65038i	0.511155	+	0.885347i	−0.488761	+	0.872418i	$0.662551\pi$
$18$		0			0
$19$	−5.75174	−	3.32077i	−1.31954	−	0.761837i	−0.335886	−	0.941903i	$-0.609036\pi$
$19$	−5.75174	−	3.32077i	−1.31954	−	0.761837i	−0.983655	+	0.180066i	$0.942369\pi$
$20$		0			0
$21$	3.91110	−	1.44298i	0.853471	−	0.314884i
$22$		0			0
$23$	−1.17445	+	2.03420i	−0.244889	+	0.424160i	−0.962100	−	0.272695i	$-0.912085\pi$
$23$	−1.17445	+	2.03420i	−0.244889	+	0.424160i	0.717211	+	0.696856i	$0.245418\pi$
$24$		0			0
$25$	−2.34889	−	4.06840i	−0.469779	−	0.813681i
$26$		0			0
$27$			5.54207i			1.06657i
$28$		0			0
$29$			8.21720i			1.52590i	0.646460	+	0.762948i	$0.276249\pi$
$29$			8.21720i			1.52590i	−0.646460	+	0.762948i	$0.723751\pi$
$30$		0			0
$31$	0.433099	+	0.750150i	0.0777869	+	0.134731i	0.902295	−	0.431120i	$-0.141881\pi$
$31$	0.433099	+	0.750150i	0.0777869	+	0.134731i	−0.824508	+	0.565850i	$0.808548\pi$
$32$		0			0
$33$	1.88350	−	3.26232i	0.327876	−	0.567897i
$34$		0			0
$35$	−1.11828	−	0.930019i	−0.189023	−	0.157202i
$36$		0			0
$37$	−0.229805	−	0.132678i	−0.0377797	−	0.0218121i	0.480991	−	0.876725i	$-0.340277\pi$
$37$	−0.229805	−	0.132678i	−0.0377797	−	0.0218121i	−0.518771	+	0.854913i	$0.673610\pi$
$38$		0			0
$39$	−3.12485	−	5.41240i	−0.500377	−	0.866678i
$40$		0			0
$41$	−6.24970			−0.976039			−0.488020	−	0.872833i	$-0.662281\pi$
$41$	−6.24970			−0.976039			−0.488020	+	0.872833i	$0.662281\pi$
$42$		0			0
$43$			5.35027i			0.815908i	0.913003	+	0.407954i	$0.133758\pi$
$43$			5.35027i			0.815908i	−0.913003	+	0.407954i	$0.866242\pi$
$44$		0			0
$45$	0.246282	−	0.142191i	0.0367135	−	0.0211965i
$46$		0			0
$47$	1.29930	−	2.25045i	0.189522	−	0.328262i	−0.755569	−	0.655069i	$-0.772639\pi$
$47$	1.29930	−	2.25045i	0.189522	−	0.328262i	0.945091	+	0.326807i	$0.105973\pi$
$48$		0			0
$49$	6.59859	+	2.33635i	0.942656	+	0.333765i
$50$		0			0
$51$	5.75174	+	3.32077i	0.805405	+	0.465001i
$52$		0			0
$53$	−9.36933	+	5.40939i	−1.28698	+	0.743037i	−0.978114	−	0.208070i	$-0.933282\pi$
$53$	−9.36933	+	5.40939i	−1.28698	+	0.743037i	−0.308863	+	0.951107i	$0.599948\pi$
$54$		0			0
$55$	−1.31429			−0.177218
$56$		0			0
$57$	−10.4648			−1.38610
$58$		0			0
$59$	3.26891	−	1.88730i	0.425575	−	0.245706i	−0.271884	−	0.962330i	$-0.587647\pi$
$59$	3.26891	−	1.88730i	0.425575	−	0.245706i	0.697460	+	0.716624i	$0.254314\pi$
$60$		0			0
$61$	−6.18061	−	3.56837i	−0.791345	−	0.456884i	0.0490905	−	0.998794i	$-0.484368\pi$
$61$	−6.18061	−	3.56837i	−0.791345	−	0.456884i	−0.840436	+	0.541911i	$0.817701\pi$
$62$		0			0
$63$	−0.875150	+	1.05230i	−0.110259	+	0.132577i
$64$		0			0
$65$	−1.09024	+	1.88835i	−0.135228	+	0.234222i
$66$		0			0
$67$	−2.31673	+	1.33757i	−0.283034	+	0.163410i	−0.634796	−	0.772680i	$-0.718916\pi$
$67$	−2.31673	+	1.33757i	−0.283034	+	0.163410i	0.351762	+	0.936089i	$0.385583\pi$
$68$		0			0
$69$			3.70105i			0.445554i
$70$		0			0
$71$	−8.76700			−1.04045			−0.520226	−	0.854029i	$-0.674152\pi$
$71$	−8.76700			−1.04045			−0.520226	+	0.854029i	$0.674152\pi$
$72$		0			0
$73$	−2.33159	−	4.03843i	−0.272892	−	0.472663i	0.696709	−	0.717354i	$-0.254647\pi$
$73$	−2.33159	−	4.03843i	−0.272892	−	0.472663i	−0.969601	+	0.244691i	$0.921313\pi$
$74$		0			0
$75$	−6.41041	−	3.70105i	−0.740210	−	0.427361i
$76$		0			0
$77$	5.93432	−	2.18944i	0.676279	−	0.249510i
$78$		0			0
$79$	0.308249	−	0.533903i	0.0346807	−	0.0600687i	−0.848164	−	0.529734i	$-0.822292\pi$
$79$	0.308249	−	0.533903i	0.0346807	−	0.0600687i	0.882845	+	0.469665i	$0.155625\pi$
$80$		0			0
$81$	3.59024	+	6.21848i	0.398916	+	0.690942i
$82$		0			0
$83$			1.09948i			0.120683i	0.998178	+	0.0603416i	$0.0192190\pi$
$83$			1.09948i			0.120683i	−0.998178	+	0.0603416i	$0.980781\pi$
$84$		0			0
$85$		−	2.31720i		−	0.251335i
$86$		0			0
$87$	6.47374	+	11.2129i	0.694058	+	1.20214i
$88$		0			0
$89$	3.19779	−	5.53873i	0.338965	−	0.587104i	−0.645273	−	0.763952i	$-0.723257\pi$
$89$	3.19779	−	5.53873i	0.338965	−	0.587104i	0.984238	+	0.176847i	$0.0565899\pi$
$90$		0			0
$91$	1.77694	−	10.3426i	0.186274	−	1.08420i
$92$		0			0
$93$	1.18198	+	0.682416i	0.122565	+	0.0707632i
$94$		0			0
$95$	1.82555	+	3.16195i	0.187298	+	0.324409i
$96$		0			0
$97$	12.9475			1.31462			0.657309	−	0.753621i	$-0.271695\pi$
$97$	12.9475			1.31462			0.657309	+	0.753621i	$0.271695\pi$
$98$		0			0
$99$			1.23675i			0.124298i
$100$		0			0
$101$	13.7565	−	7.94233i	1.36882	−	0.790291i	0.378047	−	0.925787i	$-0.376596\pi$
$101$	13.7565	−	7.94233i	1.36882	−	0.790291i	0.990778	+	0.135495i	$0.0432625\pi$
$102$		0			0
$103$	9.38954	−	16.2632i	0.925179	−	1.60246i	0.133906	−	0.990994i	$-0.457248\pi$
$103$	9.38954	−	16.2632i	0.925179	−	1.60246i	0.791273	−	0.611463i	$-0.209419\pi$
$104$		0			0
$105$	−2.25865	−	0.388055i	−0.220422	−	0.0378703i
$106$		0			0
$107$	−0.293506	−	0.169456i	−0.0283743	−	0.0163819i	0.485746	−	0.874100i	$-0.338548\pi$
$107$	−0.293506	−	0.169456i	−0.0283743	−	0.0163819i	−0.514120	+	0.857718i	$0.671881\pi$
$108$		0			0
$109$	6.75910	−	3.90237i	0.647404	−	0.373779i	−0.140057	−	0.990143i	$-0.544729\pi$
$109$	6.75910	−	3.90237i	0.647404	−	0.373779i	0.787461	+	0.616365i	$0.211395\pi$
$110$		0			0
$111$	−0.418110			−0.0396853
$112$		0			0
$113$	2.51730			0.236808			0.118404	−	0.992966i	$-0.462222\pi$
$113$	2.51730			0.236808			0.118404	+	0.992966i	$0.462222\pi$
$114$		0			0
$115$	1.11828	−	0.645638i	0.104280	−	0.0602060i
$116$		0			0
$117$	1.77694	+	1.02592i	0.164279	+	0.0948463i
$118$		0			0
$119$	3.86016	+	10.4627i	0.353860	+	0.959115i
$120$		0			0
$121$	−2.64215	+	4.57635i	−0.240196	+	0.416031i
$122$		0			0
$123$	−8.52809	+	4.92369i	−0.768952	+	0.443954i
$124$		0			0
$125$			5.33124i			0.476841i
$126$		0			0
$127$	5.30221			0.470495			0.235248	−	0.971935i	$-0.424410\pi$
$127$	5.30221			0.470495			0.235248	+	0.971935i	$0.424410\pi$
$128$		0			0
$129$	4.21509	+	7.30075i	0.371118	+	0.642796i
$130$		0			0
$131$	8.69419	+	5.01959i	0.759615	+	0.438564i	0.829157	−	0.559015i	$-0.188821\pi$
$131$	8.69419	+	5.01959i	0.759615	+	0.438564i	−0.0695425	+	0.997579i	$0.522154\pi$
$132$		0			0
$133$	−13.5102	−	11.2358i	−1.17149	−	0.974270i
$134$		0			0
$135$	1.52334	−	2.63850i	0.131108	−	0.227086i
$136$		0			0
$137$	−1.62485	−	2.81432i	−0.138820	−	0.240444i	0.788230	−	0.615381i	$-0.210998\pi$
$137$	−1.62485	−	2.81432i	−0.138820	−	0.240444i	−0.927050	+	0.374937i	$0.877664\pi$
$138$		0			0
$139$		−	15.3349i		−	1.30069i	−0.759639	−	0.650346i	$-0.774624\pi$
$139$		−	15.3349i		−	1.30069i	0.759639	−	0.650346i	$-0.225376\pi$
$140$		0			0
$141$		−	4.09449i		−	0.344819i
$142$		0			0
$143$	−4.74135	−	8.21226i	−0.396491	−	0.686743i
$144$		0			0
$145$	2.25865	−	3.91210i	0.187571	−	0.324882i
$146$		0			0
$147$	10.8448	−	2.01047i	0.894466	−	0.165821i
$148$		0			0
$149$	6.39393	+	3.69154i	0.523812	+	0.302423i	0.738493	−	0.674261i	$-0.235538\pi$
$149$	6.39393	+	3.69154i	0.523812	+	0.302423i	−0.214681	+	0.976684i	$0.568871\pi$
$150$		0			0
$151$	4.16550	+	7.21485i	0.338983	+	0.587136i	0.984242	−	0.176828i	$-0.0565837\pi$
$151$	4.16550	+	7.21485i	0.338983	+	0.587136i	−0.645259	+	0.763964i	$0.723250\pi$
$152$		0			0
$153$	−2.18048			−0.176282
$154$		0			0
$155$		−	0.476182i		−	0.0382478i
$156$		0			0
$157$	−6.18061	+	3.56837i	−0.493266	+	0.284787i	−0.725928	−	0.687770i	$-0.758590\pi$
$157$	−6.18061	+	3.56837i	−0.493266	+	0.284787i	0.232662	+	0.972558i	$0.425256\pi$
$158$		0			0
$159$	−8.52334	+	14.7629i	−0.675945	+	1.17077i
$160$		0			0
$161$	−3.97374	+	4.77813i	−0.313175	+	0.376569i
$162$		0			0
$163$	−6.33023	−	3.65476i	−0.495822	−	0.286263i	0.231164	−	0.972915i	$-0.425746\pi$
$163$	−6.33023	−	3.65476i	−0.495822	−	0.286263i	−0.726987	+	0.686652i	$0.759080\pi$
$164$		0			0
$165$	−1.79342	+	1.03543i	−0.139618	+	0.0806083i
$166$		0			0
$167$	−1.88873			−0.146154			−0.0730772	−	0.997326i	$-0.523282\pi$
$167$	−1.88873			−0.146154			−0.0730772	+	0.997326i	$0.523282\pi$
$168$		0			0
$169$	−2.73240			−0.210184
$170$		0			0
$171$	2.97540	−	1.71785i	0.227535	−	0.131367i
$172$		0			0
$173$	−14.3350	−	8.27632i	−1.08987	−	0.629237i	−0.156329	−	0.987705i	$-0.549966\pi$
$173$	−14.3350	−	8.27632i	−1.08987	−	0.629237i	−0.933542	+	0.358468i	$0.883299\pi$
$174$		0			0
$175$	−4.30221	−	11.6609i	−0.325217	−	0.881478i
$176$		0			0
$177$	2.97374	−	5.15068i	0.223520	−	0.387149i
$178$		0			0
$179$	−4.79957	+	2.77103i	−0.358737	+	0.207117i	−0.668526	−	0.743688i	$-0.733075\pi$
$179$	−4.79957	+	2.77103i	−0.358737	+	0.207117i	0.309790	+	0.950805i	$0.399741\pi$
$180$		0			0
$181$			9.98466i			0.742154i	0.928602	+	0.371077i	$0.121011\pi$
$181$			9.98466i			0.742154i	−0.928602	+	0.371077i	$0.878989\pi$
$182$		0			0
$183$	−11.2451			−0.831259
$184$		0			0
$185$	0.0729381	+	0.126333i	0.00536252	+	0.00928816i
$186$		0			0
$187$	8.72714	+	5.03862i	0.638192	+	0.368460i
$188$		0			0
$189$	−2.48284	+	14.4512i	−0.180600	+	1.05117i
$190$		0			0
$191$	0.0842049	−	0.145847i	0.00609285	−	0.0105531i	−0.862963	−	0.505267i	$-0.831394\pi$
$191$	0.0842049	−	0.145847i	0.00609285	−	0.0105531i	0.869056	+	0.494714i	$0.164727\pi$
$192$		0			0
$193$	−3.75865	−	6.51018i	−0.270554	−	0.468613i	0.698450	−	0.715659i	$-0.253873\pi$
$193$	−3.75865	−	6.51018i	−0.270554	−	0.468613i	−0.969004	+	0.247046i	$0.920540\pi$
$194$		0			0
$195$			3.43570i			0.246035i
$196$		0			0
$197$			1.34581i			0.0958847i	0.998850	+	0.0479424i	$0.0152664\pi$
$197$			1.34581i			0.0958847i	−0.998850	+	0.0479424i	$0.984734\pi$
$198$		0			0
$199$	−6.38059	−	11.0515i	−0.452308	−	0.783420i	0.546221	−	0.837641i	$-0.316066\pi$
$199$	−6.38059	−	11.0515i	−0.452308	−	0.783420i	−0.998529	+	0.0542208i	$0.982733\pi$
$200$		0			0
$201$	−2.10755	+	3.65038i	−0.148655	+	0.257478i
$202$		0			0
$203$	−3.68129	+	21.4267i	−0.258376	+	1.50386i
$204$		0			0
$205$	2.97540	+	1.71785i	0.207811	+	0.119980i
$206$		0			0
$207$	−0.607546	−	1.05230i	−0.0422274	−	0.0731400i
$208$		0			0
$209$	−15.8783			−1.09832
$210$		0			0
$211$			8.46353i			0.582653i	0.956624	+	0.291327i	$0.0940967\pi$
$211$			8.46353i			0.582653i	−0.956624	+	0.291327i	$0.905903\pi$
$212$		0			0
$213$	−11.9631	+	6.90690i	−0.819698	+	0.473253i
$214$		0			0
$215$	1.47062	−	2.54719i	0.100296	−	0.173717i
$216$		0			0
$217$	0.793260	+	2.15008i	0.0538500	+	0.145957i
$218$		0			0
$219$	−6.36319	−	3.67379i	−0.429984	−	0.248252i
$220$		0			0
$221$	14.4789	−	8.35939i	0.973955	−	0.562313i
$222$		0			0
$223$	5.80161			0.388505			0.194252	−	0.980952i	$-0.437772\pi$
$223$	5.80161			0.388505			0.194252	+	0.980952i	$0.437772\pi$
$224$		0			0
$225$	2.43018			0.162012
$226$		0			0
$227$	−9.89265	+	5.71152i	−0.656598	+	0.379087i	−0.790980	−	0.611843i	$-0.790429\pi$
$227$	−9.89265	+	5.71152i	−0.656598	+	0.379087i	0.134382	+	0.990930i	$0.457095\pi$
$228$		0			0
$229$	16.0260	+	9.25263i	1.05903	+	0.611431i	0.925164	−	0.379568i	$-0.123928\pi$
$229$	16.0260	+	9.25263i	1.05903	+	0.611431i	0.133866	+	0.990999i	$0.457261\pi$
$230$		0			0
$231$	6.37283	−	7.66285i	0.419302	−	0.504178i
$232$		0			0
$233$	5.52566	−	9.57072i	0.361998	−	0.626999i	−0.626292	−	0.779589i	$-0.715428\pi$
$233$	5.52566	−	9.57072i	0.361998	−	0.626999i	0.988290	+	0.152590i	$0.0487615\pi$
$234$		0			0
$235$	−1.23716	+	0.714273i	−0.0807032	+	0.0465940i
$236$		0			0
$237$		−	0.971389i		−	0.0630985i
$238$		0			0
$239$	22.6107			1.46256			0.731281	−	0.682076i	$-0.238923\pi$
$239$	22.6107			1.46256			0.731281	+	0.682076i	$0.238923\pi$
$240$		0			0
$241$	−6.96479	−	12.0634i	−0.448642	−	0.777070i	0.549656	−	0.835391i	$-0.314759\pi$
$241$	−6.96479	−	12.0634i	−0.448642	−	0.777070i	−0.998298	+	0.0583207i	$0.981425\pi$
$242$		0			0
$243$	−4.60051	−	2.65611i	−0.295123	−	0.170389i
$244$		0			0
$245$	−2.49931	−	2.92606i	−0.159675	−	0.186939i
$246$		0			0
$247$	−13.1715	+	22.8138i	−0.838085	+	1.45161i
$248$		0			0
$249$	0.866198	+	1.50030i	0.0548931	+	0.0950776i
$250$		0			0
$251$			0.706033i			0.0445644i	0.999752	+	0.0222822i	$0.00709323\pi$
$251$			0.706033i			0.0445644i	−0.999752	+	0.0222822i	$0.992907\pi$
$252$		0			0
$253$			5.61562i			0.353051i
$254$		0			0
$255$	−1.82555	−	3.16195i	−0.114321	−	0.198009i
$256$		0			0
$257$	−10.3919	+	17.9992i	−0.648226	+	1.12276i	0.335320	+	0.942104i	$0.391156\pi$
$257$	−10.3919	+	17.9992i	−0.648226	+	1.12276i	−0.983546	+	0.180656i	$0.942178\pi$
$258$		0			0
$259$	−0.539788	−	0.448917i	−0.0335408	−	0.0278943i
$260$		0			0
$261$	−3.68129	−	2.12540i	−0.227866	−	0.131559i
$262$		0			0
$263$	−11.3895	−	19.7273i	−0.702309	−	1.21644i	−0.967654	−	0.252281i	$-0.918819\pi$
$263$	−11.3895	−	19.7273i	−0.702309	−	1.21644i	0.265345	−	0.964154i	$-0.414514\pi$
$264$		0			0
$265$	5.94749			0.365351
$266$		0			0
$267$		−	10.0772i		−	0.616717i
$268$		0			0
$269$	2.59376	−	1.49751i	0.158145	−	0.0913048i	−0.418839	−	0.908060i	$-0.637563\pi$
$269$	2.59376	−	1.49751i	0.158145	−	0.0913048i	0.576984	+	0.816756i	$0.304230\pi$
$270$		0			0
$271$	−12.5926	+	21.8109i	−0.764943	+	1.32492i	0.175333	+	0.984509i	$0.443900\pi$
$271$	−12.5926	+	21.8109i	−0.764943	+	1.32492i	−0.940277	+	0.340412i	$0.889434\pi$
$272$		0			0
$273$	−5.72345	−	15.5130i	−0.346399	−	0.938890i
$274$		0			0
$275$	−9.72654	−	5.61562i	−0.586533	−	0.338635i
$276$		0			0
$277$	8.17940	−	4.72238i	0.491453	−	0.283740i	−0.233724	−	0.972303i	$-0.575091\pi$
$277$	8.17940	−	4.72238i	0.491453	−	0.283740i	0.725177	+	0.688563i	$0.241758\pi$
$278$		0			0
$279$	−0.448088			−0.0268263
$280$		0			0
$281$	26.8425			1.60129			0.800644	−	0.599141i	$-0.204491\pi$
$281$	26.8425			1.60129			0.800644	+	0.599141i	$0.204491\pi$
$282$		0			0
$283$	−11.2429	+	6.49111i	−0.668323	+	0.385856i	−0.795441	−	0.606031i	$-0.792761\pi$
$283$	−11.2429	+	6.49111i	−0.668323	+	0.385856i	0.127118	+	0.991888i	$0.459427\pi$
$284$		0			0
$285$	4.98215	+	2.87645i	0.295117	+	0.170386i
$286$		0			0
$287$	−16.2964	−	2.79986i	−0.961945	−	0.165270i
$288$		0			0
$289$	−0.383502	+	0.664245i	−0.0225590	+	0.0390733i
$290$		0			0
$291$	17.6676	−	10.2004i	1.03569	−	0.597958i
$292$		0			0
$293$		−	9.56300i		−	0.558677i	−0.960193	−	0.279338i	$-0.909885\pi$
$293$		−	9.56300i		−	0.558677i	0.960193	−	0.279338i	$-0.0901151\pi$
$294$		0			0
$295$	−2.07504			−0.120814
$296$		0			0
$297$	6.62485	+	11.4746i	0.384413	+	0.665823i
$298$		0			0
$299$	8.06848	+	4.65834i	0.466612	+	0.269399i
$300$		0			0
$301$	−2.39691	+	13.9511i	−0.138156	+	0.804126i
$302$		0			0
$303$	12.5144	−	21.6756i	0.718933	−	1.24523i
$304$		0			0
$305$	1.96167	+	3.39771i	0.112325	+	0.194552i
$306$		0			0
$307$		−	12.2217i		−	0.697527i	−0.937211	−	0.348763i	$-0.886602\pi$
$307$		−	12.2217i		−	0.697527i	0.937211	−	0.348763i	$-0.113398\pi$
$308$		0			0
$309$		−	29.5894i		−	1.68328i
$310$		0			0
$311$	15.9415	+	27.6114i	0.903957	+	1.56570i	0.822311	+	0.569038i	$0.192684\pi$
$311$	15.9415	+	27.6114i	0.903957	+	1.56570i	0.0816453	+	0.996661i	$0.473983\pi$
$312$		0			0
$313$	−10.7618	+	18.6399i	−0.608291	+	1.05359i	0.383230	+	0.923653i	$0.374811\pi$
$313$	−10.7618	+	18.6399i	−0.608291	+	1.05359i	−0.991522	+	0.129939i	$0.958522\pi$
$314$		0			0
$315$	0.705892	−	0.260435i	0.0397725	−	0.0146739i
$316$		0			0
$317$	−20.0481	−	11.5747i	−1.12601	−	0.650103i	−0.183082	−	0.983098i	$-0.558607\pi$
$317$	−20.0481	−	11.5747i	−1.12601	−	0.650103i	−0.942929	+	0.332995i	$0.891941\pi$
$318$		0			0
$319$	9.82264	+	17.0133i	0.549962	+	0.952562i
$320$		0			0
$321$	−0.534009			−0.0298055
$322$		0			0
$323$		−	27.9947i		−	1.55767i
$324$		0			0
$325$	−16.1370	+	9.31667i	−0.895117	+	0.516796i
$326$		0			0
$327$	6.14879	−	10.6500i	0.340029	−	0.588947i
$328$		0			0
$329$	4.39618	−	5.28607i	0.242369	−	0.291430i
$330$		0			0
$331$	25.5615	+	14.7579i	1.40499	+	0.811169i	0.994899	−	0.100878i	$-0.0321652\pi$
$331$	25.5615	+	14.7579i	1.40499	+	0.811169i	0.410086	+	0.912047i	$0.365499\pi$
$332$		0			0
$333$	0.118879	−	0.0686349i	0.00651454	−	0.00376117i
$334$		0			0
$335$	1.47062			0.0803486
$336$		0			0
$337$	−3.28431			−0.178908			−0.0894538	−	0.995991i	$-0.528512\pi$
$337$	−3.28431			−0.178908			−0.0894538	+	0.995991i	$0.528512\pi$
$338$		0			0
$339$	3.43501	−	1.98320i	0.186564	−	0.107713i
$340$		0			0
$341$	1.79342	+	1.03543i	0.0971192	+	0.0560718i
$342$		0			0
$343$	16.1595	+	9.04831i	0.872529	+	0.488563i
$344$		0			0
$345$	1.01730	−	1.76202i	0.0547698	−	0.0948641i
$346$		0			0
$347$	27.4329	−	15.8384i	1.47267	−	0.850248i	0.473146	−	0.880984i	$-0.343118\pi$
$347$	27.4329	−	15.8384i	1.47267	−	0.850248i	0.999528	+	0.0307361i	$0.00978515\pi$
$348$		0			0
$349$		−	28.4807i		−	1.52454i	−0.647260	−	0.762269i	$-0.724085\pi$
$349$		−	28.4807i		−	1.52454i	0.647260	−	0.762269i	$-0.275915\pi$
$350$		0			0
$351$	21.9821			1.17332
$352$		0			0
$353$	−10.1196	−	17.5277i	−0.538613	−	0.932905i	−0.998979	−	0.0451760i	$-0.985615\pi$
$353$	−10.1196	−	17.5277i	−0.538613	−	0.932905i	0.460366	−	0.887729i	$-0.347718\pi$
$354$		0			0
$355$	4.17386	+	2.40978i	0.221525	+	0.127898i
$356$		0			0
$357$	13.5102	+	11.2358i	0.715038	+	0.594663i
$358$		0			0
$359$	12.5611	−	21.7564i	0.662948	−	1.14826i	−0.316889	−	0.948463i	$-0.602638\pi$
$359$	12.5611	−	21.7564i	0.662948	−	1.14826i	0.979837	−	0.199797i	$-0.0640283\pi$
$360$		0			0
$361$	12.5550	+	21.7460i	0.660791	+	1.14452i
$362$		0			0
$363$			8.32626i			0.437015i
$364$		0			0
$365$			2.56353i			0.134181i
$366$		0			0
$367$	−15.1912	−	26.3118i	−0.792972	−	1.37347i	−0.924119	−	0.382104i	$-0.875199\pi$
$367$	−15.1912	−	26.3118i	−0.792972	−	1.37347i	0.131147	−	0.991363i	$-0.458134\pi$
$368$		0			0
$369$	1.61650	−	2.79986i	0.0841515	−	0.145755i
$370$		0			0
$371$	−26.8544	+	9.90778i	−1.39421	+	0.514386i
$372$		0			0
$373$	4.86327	+	2.80781i	0.251811	+	0.145383i	0.620593	−	0.784133i	$-0.286892\pi$
$373$	4.86327	+	2.80781i	0.251811	+	0.145383i	−0.368782	+	0.929516i	$0.620225\pi$
$374$		0			0
$375$	4.20010	+	7.27479i	0.216892	+	0.375669i
$376$		0			0
$377$	32.5928			1.67861
$378$		0			0
$379$			8.07009i			0.414533i	0.978285	+	0.207266i	$0.0664566\pi$
$379$			8.07009i			0.414533i	−0.978285	+	0.207266i	$0.933543\pi$
$380$		0			0
$381$	7.23518	−	4.17723i	0.370670	−	0.214006i
$382$		0			0
$383$	−12.8166	+	22.1990i	−0.654898	+	1.13432i	0.327022	+	0.945017i	$0.393955\pi$
$383$	−12.8166	+	22.1990i	−0.654898	+	1.13432i	−0.981919	+	0.189299i	$0.939378\pi$
$384$		0			0
$385$	−3.42706	−	0.588798i	−0.174659	−	0.0300079i
$386$		0			0
$387$	−2.39691	−	1.38386i	−0.121842	−	0.0703454i
$388$		0			0
$389$	−22.9905	+	13.2736i	−1.16566	+	0.672997i	−0.952655	−	0.304053i	$-0.901660\pi$
$389$	−22.9905	+	13.2736i	−1.16566	+	0.672997i	−0.213010	+	0.977050i	$0.568327\pi$
$390$		0			0
$391$	−9.90081			−0.500705
$392$		0			0
$393$	15.8183			0.797929
$394$		0			0
$395$	−0.293506	+	0.169456i	−0.0147679	+	0.00852626i
$396$		0			0
$397$	29.5283	+	17.0482i	1.48198	+	0.855624i	0.999791	−	0.0204418i	$-0.00650729\pi$
$397$	29.5283	+	17.0482i	1.48198	+	0.855624i	0.482192	+	0.876065i	$0.339841\pi$
$398$		0			0
$399$	−27.2874	−	4.68821i	−1.36608	−	0.234704i
$400$		0			0
$401$	−9.17676	+	15.8946i	−0.458266	+	0.793739i	−0.998869	−	0.0475379i	$-0.984862\pi$
$401$	−9.17676	+	15.8946i	−0.458266	+	0.793739i	0.540604	+	0.841277i	$0.318196\pi$
$402$		0			0
$403$	2.97540	−	1.71785i	0.148215	−	0.0855721i
$404$		0			0
$405$		−	3.94738i		−	0.196147i
$406$		0			0
$407$	−0.634401			−0.0314461
$408$		0			0
$409$	−5.87455	−	10.1750i	−0.290478	−	0.503122i	0.683445	−	0.730002i	$-0.260481\pi$
$409$	−5.87455	−	10.1750i	−0.290478	−	0.503122i	−0.973923	+	0.226880i	$0.927148\pi$
$410$		0			0
$411$	−4.43441	−	2.56021i	−0.218733	−	0.126286i
$412$		0			0
$413$	9.36933	−	3.45677i	0.461035	−	0.170096i
$414$		0			0
$415$	0.302212	−	0.523446i	0.0148350	−	0.0256949i
$416$		0			0
$417$	−12.0813	−	20.9254i	−0.591623	−	1.02472i
$418$		0			0
$419$			11.0841i			0.541495i	0.962650	+	0.270748i	$0.0872709\pi$
$419$			11.0841i			0.541495i	−0.962650	+	0.270748i	$0.912729\pi$
$420$		0			0
$421$			0.137270i			0.00669012i	0.999994	+	0.00334506i	$0.00106477\pi$
$421$			0.137270i			0.00669012i	−0.999994	+	0.00334506i	$0.998935\pi$
$422$		0			0
$423$	0.672132	+	1.16417i	0.0326802	+	0.0566037i
$424$		0			0
$425$	9.90081	−	17.1487i	0.480260	−	0.831834i
$426$		0			0
$427$	−14.5176	−	12.0736i	−0.702555	−	0.584283i
$428$		0			0
$429$	−12.9397	−	7.47074i	−0.624735	−	0.360691i
$430$		0			0
$431$	6.23008	+	10.7908i	0.300092	+	0.519775i	0.976157	−	0.217067i	$-0.0696491\pi$
$431$	6.23008	+	10.7908i	0.300092	+	0.519775i	−0.676064	+	0.736843i	$0.736316\pi$
$432$		0			0
$433$	−14.1563			−0.680310			−0.340155	−	0.940369i	$-0.610480\pi$
$433$	−14.1563			−0.680310			−0.340155	+	0.940369i	$0.610480\pi$
$434$		0			0
$435$		−	7.11772i		−	0.341269i
$436$		0			0
$437$	13.5102	−	7.80014i	0.646282	−	0.373131i
$438$		0			0
$439$	−2.72948	+	4.72760i	−0.130271	+	0.225636i	−0.923781	−	0.382921i	$-0.874918\pi$
$439$	−2.72948	+	4.72760i	−0.130271	+	0.225636i	0.793510	+	0.608557i	$0.208251\pi$
$440$		0			0
$441$	−2.75342	+	2.35186i	−0.131115	+	0.111993i
$442$		0			0
$443$	−28.8691	−	16.6676i	−1.37161	−	0.791900i	−0.380480	−	0.924789i	$-0.624241\pi$
$443$	−28.8691	−	16.6676i	−1.37161	−	0.791900i	−0.991131	+	0.132889i	$0.957575\pi$
$444$		0			0
$445$	−3.04485	+	1.75794i	−0.144340	+	0.0833346i
$446$		0			0
$447$	11.6332			0.550232
$448$		0			0
$449$	−26.9716			−1.27287			−0.636435	−	0.771330i	$-0.719592\pi$
$449$	−26.9716			−1.27287			−0.636435	+	0.771330i	$0.719592\pi$
$450$		0			0
$451$	−12.9397	+	7.47074i	−0.609307	+	0.351783i
$452$		0			0
$453$	11.3681	+	6.56339i	0.534121	+	0.308375i
$454$		0			0
$455$	−3.68884	+	4.43555i	−0.172935	+	0.207942i
$456$		0			0
$457$	−9.54668	+	16.5353i	−0.446575	+	0.773491i	−0.998160	−	0.0606278i	$-0.980690\pi$
$457$	−9.54668	+	16.5353i	−0.446575	+	0.773491i	0.551585	+	0.834118i	$0.314023\pi$
$458$		0			0
$459$	−20.2306	+	11.6802i	−0.944285	+	0.545183i
$460$		0			0
$461$			18.9177i			0.881087i	0.897731	+	0.440543i	$0.145214\pi$
$461$			18.9177i			0.881087i	−0.897731	+	0.440543i	$0.854786\pi$
$462$		0			0
$463$	−0.860370			−0.0399848			−0.0199924	−	0.999800i	$-0.506364\pi$
$463$	−0.860370			−0.0399848			−0.0199924	+	0.999800i	$0.506364\pi$
$464$		0			0
$465$	−0.375150	−	0.649778i	−0.0173972	−	0.0301328i
$466$		0			0
$467$	16.1842	+	9.34394i	0.748914	+	0.432386i	0.825302	−	0.564692i	$-0.191005\pi$
$467$	16.1842	+	9.34394i	0.748914	+	0.432386i	−0.0763871	+	0.997078i	$0.524338\pi$
$468$		0			0
$469$	−6.64022	+	2.44987i	−0.306617	+	0.113125i
$470$		0			0
$471$	−5.62253	+	9.73852i	−0.259073	+	0.448727i
$472$		0			0
$473$	6.39558	+	11.0775i	0.294069	+	0.509342i
$474$		0			0
$475$			31.2006i			1.43158i
$476$		0			0
$477$		−	5.59660i		−	0.256251i
$478$		0			0
$479$	−9.27364	−	16.0624i	−0.423723	−	0.733911i	0.572577	−	0.819851i	$-0.305944\pi$
$479$	−9.27364	−	16.0624i	−0.423723	−	0.733911i	−0.996300	+	0.0859405i	$0.972610\pi$
$480$		0			0
$481$	−0.526255	+	0.911501i	−0.0239952	+	0.0415609i
$482$		0			0
$483$	−1.65807	+	9.65067i	−0.0754446	+	0.439120i
$484$		0			0
$485$	−6.16413	−	3.55886i	−0.279899	−	0.161600i
$486$		0			0
$487$	−11.4588	−	19.8471i	−0.519246	−	0.899360i	−0.999750	−	0.0223676i	$-0.992880\pi$
$487$	−11.4588	−	19.8471i	−0.519246	−	0.899360i	0.480504	−	0.876993i	$-0.340454\pi$
$488$		0			0
$489$	−11.5173			−0.520830
$490$		0			0
$491$		−	24.7987i		−	1.11915i	−0.828780	−	0.559575i	$-0.810964\pi$
$491$		−	24.7987i		−	1.11915i	0.828780	−	0.559575i	$-0.189036\pi$
$492$		0			0
$493$	−29.9959	+	17.3181i	−1.35095	+	0.779969i
$494$		0			0
$495$	0.339943	−	0.588798i	0.0152793	−	0.0264645i
$496$		0			0
$497$	−22.8604	−	3.92760i	−1.02543	−	0.176177i
$498$		0			0
$499$	33.9707	+	19.6130i	1.52074	+	0.877997i	0.999701	+	0.0244624i	$0.00778739\pi$
$499$	33.9707	+	19.6130i	1.52074	+	0.877997i	0.521035	+	0.853535i	$0.325546\pi$
$500$		0			0
$501$	−2.57729	+	1.48800i	−0.115145	+	0.0664788i
$502$		0			0
$503$	−7.59396			−0.338598			−0.169299	−	0.985565i	$-0.554150\pi$
$503$	−7.59396			−0.338598			−0.169299	+	0.985565i	$0.554150\pi$
$504$		0			0
$505$	−8.73240			−0.388587
$506$		0			0
$507$	−3.72852	+	2.15266i	−0.165589	+	0.0956030i
$508$		0			0
$509$	−3.79222	−	2.18944i	−0.168087	−	0.0970451i	0.413596	−	0.910460i	$-0.364272\pi$
$509$	−3.79222	−	2.18944i	−0.168087	−	0.0970451i	−0.581684	+	0.813415i	$0.697606\pi$
$510$		0			0
$511$	−4.27052	−	11.5749i	−0.188917	−	0.512046i
$512$		0			0
$513$	18.4039	−	31.8765i	0.812553	−	1.40738i
$514$		0			0
$515$	−8.94047	+	5.16178i	−0.393964	+	0.227455i
$516$		0			0
$517$		−	6.21259i		−	0.273230i
$518$		0			0
$519$	−26.0813			−1.14484
$520$		0			0
$521$	5.37827	+	9.31544i	0.235626	+	0.408117i	0.959455	−	0.281863i	$-0.0909525\pi$
$521$	5.37827	+	9.31544i	0.235626	+	0.408117i	−0.723828	+	0.689980i	$0.757619\pi$
$522$		0			0
$523$	−2.43561	−	1.40620i	−0.106502	−	0.0614889i	0.445803	−	0.895131i	$-0.352918\pi$
$523$	−2.43561	−	1.40620i	−0.106502	−	0.0614889i	−0.552305	+	0.833642i	$0.686252\pi$
$524$		0			0
$525$	−15.0574	−	12.5225i	−0.657158	−	0.546528i
$526$		0			0
$527$	−1.82555	+	3.16195i	−0.0795223	+	0.137737i
$528$		0			0
$529$	8.74135	+	15.1405i	0.380059	+	0.658281i
$530$		0			0
$531$			1.95262i			0.0847365i
$532$		0			0
$533$			24.7889i			1.07372i
$534$		0			0
$535$	0.0931564	+	0.161352i	0.00402750	+	0.00697584i
$536$		0			0
$537$	−4.36620	+	7.56248i	−0.188415	+	0.326345i
$538$		0			0
$539$	16.4549	−	3.05049i	0.708762	−	0.131394i
$540$		0			0
$541$	27.0699	+	15.6288i	1.16383	+	0.671935i	0.952218	−	0.305419i	$-0.0987966\pi$
$541$	27.0699	+	15.6288i	1.16383	+	0.671935i	0.211608	+	0.977355i	$0.432130\pi$
$542$		0			0
$543$	7.86620	+	13.6247i	0.337571	+	0.584690i
$544$		0			0
$545$	−4.29055			−0.183787
$546$		0			0
$547$			29.4711i			1.26010i	0.776556	+	0.630048i	$0.216965\pi$
$547$			29.4711i			1.26010i	−0.776556	+	0.630048i	$0.783035\pi$
$548$		0			0
$549$	3.19725	−	1.84593i	0.136455	−	0.0787826i
$550$		0			0
$551$	27.2874	−	47.2632i	1.16248	−	2.01348i
$552$		0			0
$553$	1.04296	−	1.25408i	0.0443512	−	0.0533289i
$554$		0			0
$555$	0.199057	+	0.114926i	0.00844949	+	0.00487832i
$556$		0			0
$557$	−19.3751	+	11.1862i	−0.820950	+	0.473976i	−0.850744	−	0.525580i	$-0.823848\pi$
$557$	−19.3751	+	11.1862i	−0.820950	+	0.473976i	0.0297941	+	0.999556i	$0.490515\pi$
$558$		0			0
$559$	21.2213			0.897567
$560$		0			0
$561$	15.8783			0.670381
$562$		0			0
$563$	28.0528	−	16.1963i	1.18229	−	0.682593i	0.225743	−	0.974187i	$-0.427519\pi$
$563$	28.0528	−	16.1963i	1.18229	−	0.682593i	0.956542	+	0.291594i	$0.0941856\pi$
$564$		0			0
$565$	−1.19846	−	0.691928i	−0.0504194	−	0.0291097i
$566$		0			0
$567$	6.57585	+	17.8234i	0.276160	+	0.748513i
$568$		0			0
$569$	18.5288	−	32.0928i	0.776767	−	1.34540i	−0.157029	−	0.987594i	$-0.550192\pi$
$569$	18.5288	−	32.0928i	0.776767	−	1.34540i	0.933796	−	0.357806i	$-0.116475\pi$
$570$		0			0
$571$	19.4303	−	11.2181i	0.813132	−	0.469462i	−0.0349102	−	0.999390i	$-0.511115\pi$
$571$	19.4303	−	11.2181i	0.813132	−	0.469462i	0.848042	+	0.529928i	$0.177781\pi$
$572$		0			0
$573$		−	0.265356i		−	0.0110854i
$574$		0			0
$575$	11.0346			0.460175
$576$		0			0
$577$	−4.78431	−	8.28667i	−0.199173	−	0.344978i	0.749087	−	0.662471i	$-0.230492\pi$
$577$	−4.78431	−	8.28667i	−0.199173	−	0.344978i	−0.948261	+	0.317493i	$0.897159\pi$
$578$		0			0
$579$	−10.2578	−	5.92235i	−0.426300	−	0.246124i
$580$		0			0
$581$	−0.492563	+	2.86693i	−0.0204350	+	0.118940i
$582$		0			0
$583$	−12.9325	+	22.3997i	−0.535609	+	0.927703i
$584$		0			0
$585$	−0.563987	−	0.976854i	−0.0233180	−	0.0403879i
$586$		0			0
$587$		−	23.6894i		−	0.977766i	−0.872349	−	0.488883i	$-0.837405\pi$
$587$		−	23.6894i		−	0.977766i	0.872349	−	0.488883i	$-0.162595\pi$
$588$		0			0
$589$		−	5.75289i		−	0.237044i
$590$		0			0
$591$	1.06026	+	1.83643i	0.0436135	+	0.0755407i
$592$		0			0
$593$	3.72404	−	6.45023i	0.152928	−	0.264879i	−0.779375	−	0.626558i	$-0.784463\pi$
$593$	3.72404	−	6.45023i	0.152928	−	0.264879i	0.932303	+	0.361679i	$0.117796\pi$
$594$		0			0
$595$	1.03810	−	6.04219i	0.0425579	−	0.247706i
$596$		0			0
$597$	−17.4134	−	10.0536i	−0.712682	−	0.411467i
$598$		0			0
$599$	0.837627	+	1.45081i	0.0342245	+	0.0592786i	0.882630	−	0.470068i	$-0.155771\pi$
$599$	0.837627	+	1.45081i	0.0342245	+	0.0592786i	−0.848406	+	0.529346i	$0.822437\pi$
$600$		0			0
$601$	−8.27385			−0.337497			−0.168749	−	0.985659i	$-0.553973\pi$
$601$	−8.27385			−0.337497			−0.168749	+	0.985659i	$0.553973\pi$
$602$		0			0
$603$		−	1.38386i		−	0.0563550i
$604$		0			0
$605$	2.51579	−	1.45249i	0.102281	−	0.0590522i
$606$		0			0
$607$	−13.2647	+	22.9751i	−0.538397	+	0.932531i	0.460593	+	0.887611i	$0.347637\pi$
$607$	−13.2647	+	22.9751i	−0.538397	+	0.932531i	−0.998991	+	0.0449200i	$0.985697\pi$
$608$		0			0
$609$	11.8572	+	32.1383i	0.480480	+	1.30231i
$610$		0			0
$611$	−8.92620	−	5.15354i	−0.361115	−	0.208490i
$612$		0			0
$613$	27.3692	−	15.8016i	1.10543	−	0.638220i	0.167788	−	0.985823i	$-0.446338\pi$
$613$	27.3692	−	15.8016i	1.10543	−	0.638220i	0.937642	+	0.347603i	$0.113004\pi$
$614$		0			0
$615$	5.41348			0.218293
$616$		0			0
$617$	10.1113			0.407064			0.203532	−	0.979068i	$-0.434758\pi$
$617$	10.1113			0.407064			0.203532	+	0.979068i	$0.434758\pi$
$618$		0			0
$619$	4.79105	−	2.76611i	0.192568	−	0.111179i	−0.400616	−	0.916246i	$-0.631204\pi$
$619$	4.79105	−	2.76611i	0.192568	−	0.111179i	0.593184	+	0.805067i	$0.297871\pi$
$620$		0			0
$621$	−11.2737	−	6.50886i	−0.452397	−	0.261192i
$622$		0			0
$623$	10.8197	−	13.0099i	0.433483	−	0.521230i
$624$		0			0
$625$	−10.2791	+	17.8039i	−0.411163	+	0.712155i
$626$		0			0
$627$	−21.6668	+	12.5094i	−0.865290	+	0.499576i
$628$		0			0
$629$		−	1.11850i		−	0.0445975i
$630$		0			0
$631$	−35.5582			−1.41555			−0.707774	−	0.706439i	$-0.750300\pi$
$631$	−35.5582			−1.41555			−0.707774	+	0.706439i	$0.750300\pi$
$632$		0			0
$633$	6.66781	+	11.5490i	0.265022	+	0.459031i
$634$		0			0
$635$	−2.52431	−	1.45741i	−0.100174	−	0.0578357i
$636$		0			0
$637$	9.26693	−	26.1727i	0.367169	−	1.03700i
$638$		0			0
$639$	2.26760	−	3.92760i	0.0897050	−	0.155374i
$640$		0			0
$641$	−4.73300	−	8.19779i	−0.186942	−	0.323793i	0.757287	−	0.653082i	$-0.226524\pi$
$641$	−4.73300	−	8.19779i	−0.186942	−	0.323793i	−0.944229	+	0.329289i	$0.893191\pi$
$642$		0			0
$643$		−	13.0085i		−	0.513007i	−0.966543	−	0.256503i	$-0.917430\pi$
$643$		−	13.0085i		−	0.513007i	0.966543	−	0.256503i	$-0.0825705\pi$
$644$		0			0
$645$		−	4.63439i		−	0.182479i
$646$		0			0
$647$	13.7610	+	23.8347i	0.540999	+	0.937039i	0.998847	+	0.0480078i	$0.0152872\pi$
$647$	13.7610	+	23.8347i	0.540999	+	0.937039i	−0.457848	+	0.889031i	$0.651379\pi$
$648$		0			0
$649$	4.51207	−	7.81514i	0.177114	−	0.306771i
$650$		0			0
$651$	2.77634	+	2.30896i	0.108813	+	0.0904951i
$652$		0			0
$653$	30.4390	+	17.5740i	1.19117	+	0.687723i	0.958572	−	0.284850i	$-0.0919439\pi$
$653$	30.4390	+	17.5740i	1.19117	+	0.687723i	0.232598	+	0.972573i	$0.425277\pi$
$654$		0			0
$655$	−2.75946	−	4.77952i	−0.107821	−	0.186751i
$656$		0			0
$657$	2.41228			0.0941121
$658$		0			0
$659$			3.86719i			0.150644i	0.997159	+	0.0753222i	$0.0239985\pi$
$659$			3.86719i			0.150644i	−0.997159	+	0.0753222i	$0.976001\pi$
$660$		0			0
$661$	14.4295	−	8.33085i	0.561241	−	0.324033i	−0.192403	−	0.981316i	$-0.561628\pi$
$661$	14.4295	−	8.33085i	0.561241	−	0.324033i	0.753643	+	0.657284i	$0.228295\pi$
$662$		0			0
$663$	13.1715	−	22.8138i	0.511540	−	0.886013i
$664$		0			0
$665$	3.34366	+	9.06278i	0.129662	+	0.351439i
$666$		0			0
$667$	−16.7154	−	9.65067i	−0.647225	−	0.373675i
$668$		0			0
$669$	7.91664	−	4.57068i	0.306075	−	0.176713i
$670$		0			0
$671$	−17.0622			−0.658679
$672$		0			0
$673$	−3.95795			−0.152568			−0.0762838	−	0.997086i	$-0.524306\pi$
$673$	−3.95795			−0.152568			−0.0762838	+	0.997086i	$0.524306\pi$
$674$		0			0
$675$	22.5474	−	13.0177i	0.867848	−	0.501053i
$676$		0			0
$677$	−35.6839	−	20.6021i	−1.37144	−	0.791804i	−0.380334	−	0.924849i	$-0.624191\pi$
$677$	−35.6839	−	20.6021i	−1.37144	−	0.791804i	−0.991110	+	0.133045i	$0.957524\pi$
$678$		0			0
$679$	33.7612	+	5.80045i	1.29564	+	0.222601i
$680$		0			0
$681$	−8.99940	+	15.5874i	−0.344858	+	0.597311i
$682$		0			0
$683$	−28.6643	+	16.5493i	−1.09681	+	0.633242i	−0.935381	−	0.353642i	$-0.884943\pi$
$683$	−28.6643	+	16.5493i	−1.09681	+	0.633242i	−0.161427	+	0.986885i	$0.551610\pi$
$684$		0			0
$685$			1.78648i			0.0682580i
$686$		0			0
$687$	29.1580			1.11245
$688$		0			0
$689$	21.4558	+	37.1626i	0.817402	+	1.41578i
$690$		0			0
$691$	−12.9010	−	7.44840i	−0.490777	−	0.283350i	0.234120	−	0.972208i	$-0.424779\pi$
$691$	−12.9010	−	7.44840i	−0.490777	−	0.283350i	−0.724897	+	0.688857i	$0.758113\pi$
$692$		0			0
$693$	−0.554060	+	3.22487i	−0.0210470	+	0.122503i
$694$		0			0
$695$	−4.21509	+	7.30075i	−0.159888	+	0.276933i
$696$		0			0
$697$	−13.1715	−	22.8138i	−0.498907	−	0.864133i
$698$		0			0
$699$		−	17.4131i		−	0.658623i
$700$		0			0
$701$		−	32.5746i		−	1.23032i	−0.788401	−	0.615162i	$-0.789090\pi$
$701$		−	32.5746i		−	1.23032i	0.788401	−	0.615162i	$-0.210910\pi$
$702$		0			0
$703$	0.881187	+	1.52626i	0.0332346	+	0.0575640i
$704$		0			0
$705$	−1.12545	+	1.94934i	−0.0423869	+	0.0734162i
$706$		0			0
$707$	39.4289	−	14.5471i	1.48288	−	0.547100i
$708$		0			0
$709$	9.95635	+	5.74830i	0.373918	+	0.215882i	0.675169	−	0.737663i	$-0.264071\pi$
$709$	9.95635	+	5.74830i	0.373918	+	0.215882i	−0.301251	+	0.953545i	$0.597404\pi$
$710$		0			0
$711$	0.159458	+	0.276190i	0.00598016	+	0.0103579i
$712$		0			0
$713$	−2.03461			−0.0761967
$714$		0			0
$715$			5.21300i			0.194955i
$716$		0			0
$717$	30.8536	−	17.8133i	1.15225	−	0.665251i
$718$		0			0
$719$	−13.4887	+	23.3632i	−0.503045	+	0.871299i	0.496949	+	0.867780i	$0.334454\pi$
$719$	−13.4887	+	23.3632i	−0.503045	+	0.871299i	−0.999994	+	0.00351948i	$0.998880\pi$
$720$		0			0
$721$	31.7695	−	38.2004i	1.18316	−	1.42266i
$722$		0			0
$723$	−19.0077	−	10.9741i	−0.706906	−	0.408132i
$724$		0			0
$725$	33.4309	−	19.3013i	1.24159	−	0.716833i
$726$		0			0
$727$	27.0230			1.00223			0.501113	−	0.865382i	$-0.332924\pi$
$727$	27.0230			1.00223			0.501113	+	0.865382i	$0.332924\pi$
$728$		0			0
$729$	−29.9117			−1.10784
$730$		0			0
$731$	−19.5305	+	11.2759i	−0.722361	+	0.417055i
$732$		0			0
$733$	−17.9059	−	10.3380i	−0.661371	−	0.381843i	0.131428	−	0.991326i	$-0.458044\pi$
$733$	−17.9059	−	10.3380i	−0.661371	−	0.381843i	−0.792799	+	0.609483i	$0.791377\pi$
$734$		0			0
$735$	−5.71569	−	2.02375i	−0.210826	−	0.0746470i
$736$		0			0
$737$	−3.19779	+	5.53873i	−0.117792	+	0.204022i
$738$		0			0
$739$	9.30563	−	5.37261i	0.342313	−	0.197635i	−0.318981	−	0.947761i	$-0.603341\pi$
$739$	9.30563	−	5.37261i	0.342313	−	0.197635i	0.661294	+	0.750126i	$0.270007\pi$
$740$		0			0
$741$			41.5076i			1.52482i
$742$		0			0
$743$	−11.8708			−0.435498			−0.217749	−	0.976005i	$-0.569871\pi$
$743$	−11.8708			−0.435498			−0.217749	+	0.976005i	$0.569871\pi$
$744$		0			0
$745$	−2.02938	−	3.51499i	−0.0743507	−	0.128779i
$746$		0			0
$747$	−0.492563	−	0.284382i	−0.0180219	−	0.0104050i
$748$		0			0
$749$	−0.689416	−	0.573355i	−0.0251907	−	0.0209499i
$750$		0			0
$751$	8.53229	−	14.7784i	0.311348	−	0.539270i	−0.667307	−	0.744783i	$-0.732553\pi$
$751$	8.53229	−	14.7784i	0.311348	−	0.539270i	0.978654	+	0.205513i	$0.0658863\pi$
$752$		0			0
$753$	0.556233	+	0.963424i	0.0202703	+	0.0351091i
$754$		0			0
$755$		−	4.57986i		−	0.166678i
$756$		0			0
$757$			46.3272i			1.68379i	0.539641	+	0.841895i	$0.318560\pi$
$757$			46.3272i			1.68379i	−0.539641	+	0.841895i	$0.681440\pi$
$758$		0			0
$759$	4.42415	+	7.66285i	0.160586	+	0.278144i
$760$		0			0
$761$	7.30474	−	12.6522i	0.264796	−	0.458641i	−0.702714	−	0.711473i	$-0.748029\pi$
$761$	7.30474	−	12.6522i	0.264796	−	0.458641i	0.967510	+	0.252832i	$0.0813619\pi$
$762$		0			0
$763$	19.3729	−	7.14753i	0.701346	−	0.258758i
$764$		0			0
$765$	1.03810	+	0.599347i	0.0375326	+	0.0216694i
$766$		0			0
$767$	−7.48582	−	12.9658i	−0.270297	−	0.468169i
$768$		0			0
$769$	49.3177			1.77844			0.889221	−	0.457477i	$-0.151247\pi$
$769$	49.3177			1.77844			0.889221	+	0.457477i	$0.151247\pi$
$770$		0			0
$771$			32.7480i			1.17939i
$772$		0			0
$773$	−0.902744	+	0.521200i	−0.0324695	+	0.0187462i	−0.516147	−	0.856500i	$-0.672634\pi$
$773$	−0.902744	+	0.521200i	−0.0324695	+	0.0187462i	0.483677	+	0.875246i	$0.339301\pi$
$774$		0			0
$775$	2.03461	−	3.52404i	0.0730853	−	0.126587i
$776$		0			0
$777$	−1.09024	−	0.187313i	−0.0391122	−	0.00671981i
$778$		0			0
$779$	35.9467	+	20.7538i	1.28792	+	0.743583i
$780$		0			0
$781$	−18.1517	+	10.4799i	−0.649517	+	0.374999i
$782$		0			0
$783$	−45.5403			−1.62748
$784$		0			0
$785$	3.92334			0.140030
$786$		0			0
$787$	−34.8899	+	20.1437i	−1.24369	+	0.718045i	−0.969844	−	0.243728i	$-0.921629\pi$
$787$	−34.8899	+	20.1437i	−1.24369	+	0.718045i	−0.273847	+	0.961773i	$0.588296\pi$
$788$		0			0
$789$	−31.0834	−	17.9460i	−1.10660	−	0.638895i
$790$		0			0
$791$	6.56399	+	1.12775i	0.233388	+	0.0400981i
$792$		0			0
$793$	−14.1536	+	24.5148i	−0.502610	+	0.870546i
$794$		0			0
$795$	8.11570	−	4.68560i	0.287834	−	0.166181i
$796$		0			0
$797$			32.2902i			1.14378i	0.820331	+	0.571889i	$0.193789\pi$
$797$			32.2902i			1.14378i	−0.820331	+	0.571889i	$0.806211\pi$
$798$		0			0
$799$	10.9533			0.387501
$800$		0			0
$801$	1.65423	+	2.86521i	0.0584493	+	0.101237i
$802$		0			0
$803$	−9.65489	−	5.57425i	−0.340714	−	0.196711i
$804$		0			0
$805$	3.20521	−	1.18254i	0.112969	−	0.0416792i
$806$		0			0
$807$	2.35956	−	4.08688i	0.0830605	−	0.143865i
$808$		0			0
$809$	−20.8131	−	36.0493i	−0.731749	−	1.26743i	−0.956135	−	0.292926i	$-0.905371\pi$
$809$	−20.8131	−	36.0493i	−0.731749	−	1.26743i	0.224386	−	0.974500i	$-0.427962\pi$
$810$		0			0
$811$		−	18.7227i		−	0.657444i	−0.944427	−	0.328722i	$-0.893382\pi$
$811$		−	18.7227i		−	0.657444i	0.944427	−	0.328722i	$-0.106618\pi$
$812$		0			0
$813$			39.6831i			1.39175i
$814$		0			0
$815$	2.00916	+	3.47997i	0.0703778	+	0.121898i
$816$		0			0
$817$	17.7670	−	30.7734i	0.621589	−	1.07662i
$818$		0			0
$819$	4.17386	+	3.47120i	0.145846	+	0.121294i
$820$		0			0
$821$	−16.2308	−	9.37088i	−0.566460	−	0.327046i	0.189274	−	0.981924i	$-0.439386\pi$
$821$	−16.2308	−	9.37088i	−0.566460	−	0.327046i	−0.755734	+	0.654878i	$0.772720\pi$
$822$		0			0
$823$	−10.2211	−	17.7035i	−0.356286	−	0.617106i	0.631051	−	0.775741i	$-0.282624\pi$
$823$	−10.2211	−	17.7035i	−0.356286	−	0.617106i	−0.987337	+	0.158636i	$0.949291\pi$
$824$		0			0
$825$	−17.6966			−0.616116
$826$		0			0
$827$			48.6254i			1.69087i	0.534079	+	0.845435i	$0.320659\pi$
$827$			48.6254i			1.69087i	−0.534079	+	0.845435i	$0.679341\pi$
$828$		0			0
$829$	−6.06173	+	3.49974i	−0.210532	+	0.121551i	−0.601559	−	0.798829i	$-0.705453\pi$
$829$	−6.06173	+	3.49974i	−0.210532	+	0.121551i	0.391026	+	0.920379i	$0.372120\pi$
$830$		0			0
$831$	7.44085	−	12.8879i	0.258120	−	0.447078i
$832$		0			0
$833$	5.37827	+	29.0113i	0.186346	+	1.00518i
$834$		0			0
$835$	0.899200	+	0.519154i	0.0311181	+	0.0179660i
$836$		0			0
$837$	−4.15738	+	2.40026i	−0.143700	+	0.0829653i
$838$		0			0
$839$	−40.1867			−1.38740			−0.693700	−	0.720264i	$-0.744021\pi$
$839$	−40.1867			−1.38740			−0.693700	+	0.720264i	$0.744021\pi$
$840$		0			0
$841$	−38.5224			−1.32836
$842$		0			0
$843$	36.6281	−	21.1473i	1.26154	−	0.728350i
$844$		0			0
$845$	1.30086	+	0.751051i	0.0447509	+	0.0258369i
$846$		0			0
$847$	−8.93974	+	10.7494i	−0.307173	+	0.369352i
$848$		0			0
$849$	−10.2278	+	17.7150i	−0.351016	+	0.607978i
$850$		0			0
$851$	0.539788	−	0.311647i	0.0185037	−	0.0106831i
$852$		0			0
$853$		−	30.8071i		−	1.05482i	−0.849612	−	0.527408i	$-0.823164\pi$
$853$		−	30.8071i		−	1.05482i	0.849612	−	0.527408i	$-0.176836\pi$
$854$		0			0
$855$	−1.88873			−0.0645933
$856$		0			0
$857$	−6.84889	−	11.8626i	−0.233954	−	0.405220i	0.725014	−	0.688734i	$-0.241833\pi$
$857$	−6.84889	−	11.8626i	−0.233954	−	0.405220i	−0.958968	+	0.283514i	$0.908500\pi$
$858$		0			0
$859$	−7.52869	−	4.34669i	−0.256876	−	0.148307i	0.366033	−	0.930602i	$-0.380716\pi$
$859$	−7.52869	−	4.34669i	−0.256876	−	0.148307i	−0.622908	+	0.782295i	$0.714049\pi$
$860$		0			0
$861$	−24.4432	+	9.01819i	−0.833022	+	0.307339i
$862$		0			0
$863$	−0.296174	+	0.512989i	−0.0100819	+	0.0174623i	−0.871022	−	0.491243i	$-0.836543\pi$
$863$	−0.296174	+	0.512989i	−0.0100819	+	0.0174623i	0.860940	+	0.508706i	$0.169876\pi$
$864$		0			0
$865$	4.54981	+	7.88049i	0.154698	+	0.267945i
$866$		0			0
$867$			1.20854i			0.0410440i
$868$		0			0
$869$		−	1.47389i		−	0.0499984i
$870$		0			0
$871$	5.30533	+	9.18911i	0.179764	+	0.311361i
$872$		0			0
$873$	−3.34889	+	5.80045i	−0.113343	+	0.196316i
$874$		0			0
$875$	−2.38839	+	13.9015i	−0.0807422	+	0.469955i
$876$		0			0
$877$	−13.2310	−	7.63892i	−0.446779	−	0.257948i	0.259690	−	0.965692i	$-0.416380\pi$
$877$	−13.2310	−	7.63892i	−0.446779	−	0.257948i	−0.706469	+	0.707744i	$0.749713\pi$
$878$		0			0
$879$	−7.53401	−	13.0493i	−0.254116	−	0.440142i
$880$		0			0
$881$	−43.1280			−1.45302			−0.726509	−	0.687157i	$-0.758859\pi$
$881$	−43.1280			−1.45302			−0.726509	+	0.687157i	$0.758859\pi$
$882$		0			0
$883$		−	20.2255i		−	0.680642i	−0.940309	−	0.340321i	$-0.889464\pi$
$883$		−	20.2255i		−	0.680642i	0.940309	−	0.340321i	$-0.110536\pi$
$884$		0			0
$885$	−2.83152	+	1.63478i	−0.0951805	+	0.0549525i
$886$		0			0
$887$	10.7820	−	18.6750i	0.362024	−	0.627044i	−0.626270	−	0.779606i	$-0.715419\pi$
$887$	10.7820	−	18.6750i	0.362024	−	0.627044i	0.988294	+	0.152563i	$0.0487525\pi$
$888$		0			0
$889$	13.8258	+	2.37538i	0.463701	+	0.0796678i
$890$		0			0
$891$	14.8668	+	8.58338i	0.498058	+	0.287554i
$892$		0			0
$893$	−14.9465	+	8.62934i	−0.500164	+	0.288770i
$894$		0			0
$895$	3.04668			0.101839
$896$		0			0
$897$	14.6799			0.490147
$898$		0			0
$899$	−6.16413	+	3.55886i	−0.205585	+	0.118695i
$900$		0			0
$901$	−39.4926	−	22.8011i	−1.31569	−	0.759614i
$902$		0			0
$903$	7.72032	+	20.9254i	0.256916	+	0.696354i
$904$		0			0
$905$	2.74447	−	4.75356i	0.0912293	−	0.158014i
$906$		0			0
$907$	−27.3384	+	15.7838i	−0.907757	+	0.524094i	−0.879709	−	0.475513i	$-0.842263\pi$
$907$	−27.3384	+	15.7838i	−0.907757	+	0.524094i	−0.0280482	+	0.999607i	$0.508929\pi$
$908$		0			0
$909$			8.21720i			0.272547i
$910$		0			0
$911$	−15.6873			−0.519744			−0.259872	−	0.965643i	$-0.583680\pi$
$911$	−15.6873			−0.519744			−0.259872	+	0.965643i	$0.583680\pi$
$912$		0			0
$913$	1.31429	+	2.27641i	0.0434965	+	0.0753382i
$914$		0			0
$915$	5.35363	+	3.09092i	0.176986	+	0.102183i
$916$		0			0
$917$	20.4217	+	16.9838i	0.674385	+	0.560855i
$918$		0			0
$919$	7.79407	−	13.4997i	0.257103	−	0.445315i	−0.708362	−	0.705849i	$-0.750566\pi$
$919$	7.79407	−	13.4997i	0.257103	−	0.445315i	0.965464	+	0.260535i	$0.0838988\pi$
$920$		0			0
$921$	−9.62857	−	16.6772i	−0.317272	−	0.549532i
$922$		0			0
$923$			34.7735i			1.14458i
$924$		0			0
$925$			1.24659i			0.0409875i
$926$		0			0
$927$	4.85725	+	8.41300i	0.159533	+	0.276319i
$928$		0			0
$929$	−20.6926	+	35.8406i	−0.678901	+	1.17589i	0.296411	+	0.955060i	$0.404210\pi$
$929$	−20.6926	+	35.8406i	−0.678901	+	1.17589i	−0.975312	+	0.220830i	$0.929123\pi$
$930$		0			0
$931$	−30.1949	−	35.3505i	−0.989599	−	1.15857i
$932$		0			0
$933$	43.5061	+	25.1183i	1.42433	+	0.822335i
$934$		0			0
$935$	−2.76992	−	4.79764i	−0.0905860	−	0.156900i
$936$		0			0
$937$	−23.9308			−0.781785			−0.390892	−	0.920436i	$-0.627834\pi$
$937$	−23.9308			−0.781785			−0.390892	+	0.920436i	$0.627834\pi$
$938$		0			0
$939$			33.9137i			1.10673i
$940$		0			0
$941$	33.3285	−	19.2422i	1.08648	−	0.627278i	0.153841	−	0.988096i	$-0.450836\pi$
$941$	33.3285	−	19.2422i	1.08648	−	0.627278i	0.932636	+	0.360818i	$0.117502\pi$
$942$		0			0
$943$	7.33994	−	12.7132i	0.239021	−	0.413997i
$944$		0			0
$945$	5.15423	−	6.19757i	0.167667	−	0.201607i
$946$		0			0
$947$	−8.36198	−	4.82779i	−0.271728	−	0.156882i	0.357945	−	0.933743i	$-0.383478\pi$
$947$	−8.36198	−	4.82779i	−0.271728	−	0.156882i	−0.629673	+	0.776861i	$0.716811\pi$
$948$		0			0
$949$	−16.0181	+	9.24804i	−0.519969	+	0.300204i
$950$		0			0
$951$	−36.4757			−1.18280
$952$		0			0
$953$	−19.3777			−0.627704			−0.313852	−	0.949472i	$-0.601620\pi$
$953$	−19.3777			−0.627704			−0.313852	+	0.949472i	$0.601620\pi$
$954$		0			0
$955$	−0.0801777	+	0.0462906i	−0.00259449	+	0.00149793i
$956$		0			0
$957$	26.8071	+	15.4771i	0.866552	+	0.500304i
$958$		0			0
$959$	−2.97606	−	8.06641i	−0.0961020	−	0.260478i
$960$		0			0
$961$	15.1249	−	26.1970i	0.487898	−	0.845065i
$962$		0			0
$963$	0.151832	−	0.0876603i	0.00489272	−	0.00282481i
$964$		0			0
$965$			4.13255i			0.133031i
$966$		0			0
$967$	−34.8845			−1.12181			−0.560905	−	0.827880i	$-0.689547\pi$
$967$	−34.8845			−1.12181			−0.560905	+	0.827880i	$0.689547\pi$
$968$		0			0
$969$	−22.0550	−	38.2004i	−0.708510	−	1.22717i
$970$		0			0
$971$	−38.4767	−	22.2146i	−1.23478	−	0.712899i	−0.266755	−	0.963764i	$-0.585952\pi$
$971$	−38.4767	−	22.2146i	−1.23478	−	0.712899i	−0.968022	+	0.250865i	$0.919285\pi$
$972$		0			0
$973$	6.87002	−	39.9865i	0.220243	−	1.28191i
$974$		0			0
$975$	−14.6799	+	25.4263i	−0.470133	+	0.814294i
$976$		0			0
$977$	13.5436	+	23.4581i	0.433297	+	0.750492i	0.997155	−	0.0753795i	$-0.0240168\pi$
$977$	13.5436	+	23.4581i	0.433297	+	0.750492i	−0.563858	+	0.825872i	$0.690684\pi$
$978$		0			0
$979$		−	15.2902i		−	0.488678i
$980$		0			0
$981$			4.03742i			0.128905i
$982$		0			0
$983$	12.5444	+	21.7275i	0.400103	+	0.692999i	0.993738	−	0.111736i	$-0.0356410\pi$
$983$	12.5444	+	21.7275i	0.400103	+	0.692999i	−0.593635	+	0.804735i	$0.702308\pi$
$984$		0			0
$985$	0.369920	−	0.640721i	0.0117866	−	0.0204151i
$986$		0			0
$987$	1.83433	−	10.6766i	0.0583873	−	0.339839i
$988$		0			0
$989$	−10.8835	−	6.28360i	−0.346076	−	0.199807i
$990$		0			0
$991$	8.81972	+	15.2762i	0.280168	+	0.485265i	0.971426	−	0.237343i	$-0.0762766\pi$
$991$	8.81972	+	15.2762i	0.280168	+	0.485265i	−0.691258	+	0.722608i	$0.742943\pi$
$992$		0			0
$993$	46.5068			1.47585
$994$		0			0
$995$			7.01530i			0.222400i
$996$		0			0
$997$	−26.5529	+	15.3303i	−0.840939	+	0.485516i	−0.857583	−	0.514345i	$-0.828035\pi$
$997$	−26.5529	+	15.3303i	−0.840939	+	0.485516i	0.0166442	+	0.999861i	$0.494702\pi$
$998$		0			0
$999$	0.735311	−	1.27360i	0.0232642	−	0.0402948i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.t.a.177.5		12
3.2	odd	2		2016.2.cr.c.1297.4		12
4.3	odd	2		56.2.p.a.37.6	yes	12
7.2	even	3		1568.2.b.f.785.5		6
7.3	odd	6		1568.2.t.g.753.5		12
7.4	even	3	inner	224.2.t.a.81.2		12
7.5	odd	6		1568.2.b.e.785.2		6
7.6	odd	2		1568.2.t.g.177.2		12
8.3	odd	2		56.2.p.a.37.3	✓	12
8.5	even	2	inner	224.2.t.a.177.2		12
12.11	even	2		504.2.cj.c.37.1		12
21.11	odd	6		2016.2.cr.c.1873.3		12
24.5	odd	2		2016.2.cr.c.1297.3		12
24.11	even	2		504.2.cj.c.37.4		12
28.3	even	6		392.2.p.g.165.3		12
28.11	odd	6		56.2.p.a.53.3	yes	12
28.19	even	6		392.2.b.f.197.1		6
28.23	odd	6		392.2.b.e.197.1		6
28.27	even	2		392.2.p.g.373.6		12
56.3	even	6		392.2.p.g.165.6		12
56.5	odd	6		1568.2.b.e.785.5		6
56.11	odd	6		56.2.p.a.53.6	yes	12
56.13	odd	2		1568.2.t.g.177.5		12
56.19	even	6		392.2.b.f.197.2		6
56.27	even	2		392.2.p.g.373.3		12
56.37	even	6		1568.2.b.f.785.2		6
56.45	odd	6		1568.2.t.g.753.2		12
56.51	odd	6		392.2.b.e.197.2		6
56.53	even	6	inner	224.2.t.a.81.5		12
84.11	even	6		504.2.cj.c.109.4		12
168.11	even	6		504.2.cj.c.109.1		12
168.53	odd	6		2016.2.cr.c.1873.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.p.a.37.3	✓	12	8.3	odd	2
56.2.p.a.37.6	yes	12	4.3	odd	2
56.2.p.a.53.3	yes	12	28.11	odd	6
56.2.p.a.53.6	yes	12	56.11	odd	6
224.2.t.a.81.2		12	7.4	even	3	inner
224.2.t.a.81.5		12	56.53	even	6	inner
224.2.t.a.177.2		12	8.5	even	2	inner
224.2.t.a.177.5		12	1.1	even	1	trivial
392.2.b.e.197.1		6	28.23	odd	6
392.2.b.e.197.2		6	56.51	odd	6
392.2.b.f.197.1		6	28.19	even	6
392.2.b.f.197.2		6	56.19	even	6
392.2.p.g.165.3		12	28.3	even	6
392.2.p.g.165.6		12	56.3	even	6
392.2.p.g.373.3		12	56.27	even	2
392.2.p.g.373.6		12	28.27	even	2
504.2.cj.c.37.1		12	12.11	even	2
504.2.cj.c.37.4		12	24.11	even	2
504.2.cj.c.109.1		12	168.11	even	6
504.2.cj.c.109.4		12	84.11	even	6
1568.2.b.e.785.2		6	7.5	odd	6
1568.2.b.e.785.5		6	56.5	odd	6
1568.2.b.f.785.2		6	56.37	even	6
1568.2.b.f.785.5		6	7.2	even	3
1568.2.t.g.177.2		12	7.6	odd	2
1568.2.t.g.177.5		12	56.13	odd	2
1568.2.t.g.753.2		12	56.45	odd	6
1568.2.t.g.753.5		12	7.3	odd	6
2016.2.cr.c.1297.3		12	24.5	odd	2
2016.2.cr.c.1297.4		12	3.2	odd	2
2016.2.cr.c.1873.3		12	21.11	odd	6
2016.2.cr.c.1873.4		12	168.53	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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36456 - 0.787829i) q^{3} +(-0.476087 - 0.274869i) q^{5} +(2.60755 + 0.447998i) q^{7} +(-0.258652 + 0.447998i) q^{9} +O(q^{10})\)	\(q+(1.36456 - 0.787829i) q^{3} +(-0.476087 - 0.274869i) q^{5} +(2.60755 + 0.447998i) q^{7} +(-0.258652 + 0.447998i) q^{9} +(2.07045 - 1.19538i) q^{11} -3.96641i q^{13} -0.866198 q^{15} +(2.10755 + 3.65038i) q^{17} +(-5.75174 - 3.32077i) q^{19} +(3.91110 - 1.44298i) q^{21} +(-1.17445 + 2.03420i) q^{23} +(-2.34889 - 4.06840i) q^{25} +5.54207i q^{27} +8.21720i q^{29} +(0.433099 + 0.750150i) q^{31} +(1.88350 - 3.26232i) q^{33} +(-1.11828 - 0.930019i) q^{35} +(-0.229805 - 0.132678i) q^{37} +(-3.12485 - 5.41240i) q^{39} -6.24970 q^{41} +5.35027i q^{43} +(0.246282 - 0.142191i) q^{45} +(1.29930 - 2.25045i) q^{47} +(6.59859 + 2.33635i) q^{49} +(5.75174 + 3.32077i) q^{51} +(-9.36933 + 5.40939i) q^{53} -1.31429 q^{55} -10.4648 q^{57} +(3.26891 - 1.88730i) q^{59} +(-6.18061 - 3.56837i) q^{61} +(-0.875150 + 1.05230i) q^{63} +(-1.09024 + 1.88835i) q^{65} +(-2.31673 + 1.33757i) q^{67} +3.70105i q^{69} -8.76700 q^{71} +(-2.33159 - 4.03843i) q^{73} +(-6.41041 - 3.70105i) q^{75} +(5.93432 - 2.18944i) q^{77} +(0.308249 - 0.533903i) q^{79} +(3.59024 + 6.21848i) q^{81} +1.09948i q^{83} -2.31720i q^{85} +(6.47374 + 11.2129i) q^{87} +(3.19779 - 5.53873i) q^{89} +(1.77694 - 10.3426i) q^{91} +(1.18198 + 0.682416i) q^{93} +(1.82555 + 3.16195i) q^{95} +12.9475 q^{97} +1.23675i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{7}+O(q^{10}) \) 12 * q + 4 * q^7	\( 12 q + 4 q^{7} + 20 q^{15} - 2 q^{17} - 2 q^{23} - 4 q^{25} - 10 q^{31} - 14 q^{33} - 4 q^{39} - 8 q^{41} - 30 q^{47} - 12 q^{49} - 4 q^{55} - 4 q^{57} - 44 q^{63} + 8 q^{65} - 32 q^{71} - 10 q^{73} + 22 q^{79} + 22 q^{81} + 20 q^{87} - 10 q^{89} + 34 q^{95} + 40 q^{97}+O(q^{100}) \) 12 * q + 4 * q^7 + 20 * q^15 - 2 * q^17 - 2 * q^23 - 4 * q^25 - 10 * q^31 - 14 * q^33 - 4 * q^39 - 8 * q^41 - 30 * q^47 - 12 * q^49 - 4 * q^55 - 4 * q^57 - 44 * q^63 + 8 * q^65 - 32 * q^71 - 10 * q^73 + 22 * q^79 + 22 * q^81 + 20 * q^87 - 10 * q^89 + 34 * q^95 + 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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