LMFDB - Embedded newform 306.2.g.c.217.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [306,2,Mod(55,306)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(306, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("306.55"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 306 = 2 \cdot 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	306.g (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,0,-2,-4,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$2.44342230185$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			217.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	306.217
Dual form			306.2.g.c.55.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 2.00000i) q^{5} +(1.00000 - 1.00000i) q^{7} -1.00000i q^{8} +(2.00000 - 2.00000i) q^{10} +(2.00000 - 2.00000i) q^{11} +6.00000 q^{13} +(1.00000 + 1.00000i) q^{14} +1.00000 q^{16} +(-1.00000 - 4.00000i) q^{17} -4.00000i q^{19} +(2.00000 + 2.00000i) q^{20} +(2.00000 + 2.00000i) q^{22} +(-3.00000 + 3.00000i) q^{23} +3.00000i q^{25} +6.00000i q^{26} +(-1.00000 + 1.00000i) q^{28} +(2.00000 + 2.00000i) q^{29} +(-3.00000 - 3.00000i) q^{31} +1.00000i q^{32} +(4.00000 - 1.00000i) q^{34} -4.00000 q^{35} +(-6.00000 - 6.00000i) q^{37} +4.00000 q^{38} +(-2.00000 + 2.00000i) q^{40} +(-1.00000 + 1.00000i) q^{41} +12.0000i q^{43} +(-2.00000 + 2.00000i) q^{44} +(-3.00000 - 3.00000i) q^{46} +10.0000 q^{47} +5.00000i q^{49} -3.00000 q^{50} -6.00000 q^{52} -6.00000i q^{53} -8.00000 q^{55} +(-1.00000 - 1.00000i) q^{56} +(-2.00000 + 2.00000i) q^{58} +(2.00000 - 2.00000i) q^{61} +(3.00000 - 3.00000i) q^{62} -1.00000 q^{64} +(-12.0000 - 12.0000i) q^{65} +4.00000 q^{67} +(1.00000 + 4.00000i) q^{68} -4.00000i q^{70} +(1.00000 + 1.00000i) q^{71} +(-1.00000 - 1.00000i) q^{73} +(6.00000 - 6.00000i) q^{74} +4.00000i q^{76} -4.00000i q^{77} +(-5.00000 + 5.00000i) q^{79} +(-2.00000 - 2.00000i) q^{80} +(-1.00000 - 1.00000i) q^{82} +16.0000i q^{83} +(-6.00000 + 10.0000i) q^{85} -12.0000 q^{86} +(-2.00000 - 2.00000i) q^{88} +12.0000 q^{89} +(6.00000 - 6.00000i) q^{91} +(3.00000 - 3.00000i) q^{92} +10.0000i q^{94} +(-8.00000 + 8.00000i) q^{95} +(-11.0000 - 11.0000i) q^{97} -5.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} - 4 q^{5} + 2 q^{7} + 4 q^{10} + 4 q^{11} + 12 q^{13} + 2 q^{14} + 2 q^{16} - 2 q^{17} + 4 q^{20} + 4 q^{22} - 6 q^{23} - 2 q^{28} + 4 q^{29} - 6 q^{31} + 8 q^{34} - 8 q^{35} - 12 q^{37} + 8 q^{38}+ \cdots - 10 q^{98}+O(q^{100}) $ 2 * q - 2 * q^4 - 4 * q^5 + 2 * q^7 + 4 * q^10 + 4 * q^11 + 12 * q^13 + 2 * q^14 + 2 * q^16 - 2 * q^17 + 4 * q^20 + 4 * q^22 - 6 * q^23 - 2 * q^28 + 4 * q^29 - 6 * q^31 + 8 * q^34 - 8 * q^35 - 12 * q^37 + 8 * q^38 - 4 * q^40 - 2 * q^41 - 4 * q^44 - 6 * q^46 + 20 * q^47 - 6 * q^50 - 12 * q^52 - 16 * q^55 - 2 * q^56 - 4 * q^58 + 4 * q^61 + 6 * q^62 - 2 * q^64 - 24 * q^65 + 8 * q^67 + 2 * q^68 + 2 * q^71 - 2 * q^73 + 12 * q^74 - 10 * q^79 - 4 * q^80 - 2 * q^82 - 12 * q^85 - 24 * q^86 - 4 * q^88 + 24 * q^89 + 12 * q^91 + 6 * q^92 - 16 * q^95 - 22 * q^97 - 10 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/306\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−2.00000	−	2.00000i	−0.894427	−	0.894427i	0.100509	−	0.994936i	$-0.467953\pi$
$5$	−2.00000	−	2.00000i	−0.894427	−	0.894427i	−0.994936	+	0.100509i	$0.967953\pi$
$6$		0			0
$7$	1.00000	−	1.00000i	0.377964	−	0.377964i	−0.492403	−	0.870367i	$-0.663881\pi$
$7$	1.00000	−	1.00000i	0.377964	−	0.377964i	0.870367	+	0.492403i	$0.163881\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	2.00000	−	2.00000i	0.632456	−	0.632456i
$11$	2.00000	−	2.00000i	0.603023	−	0.603023i	−0.338091	−	0.941113i	$-0.609781\pi$
$11$	2.00000	−	2.00000i	0.603023	−	0.603023i	0.941113	+	0.338091i	$0.109781\pi$
$12$		0			0
$13$	6.00000			1.66410			0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000			1.66410			0.832050	+	0.554700i	$0.187167\pi$
$14$	1.00000	+	1.00000i	0.267261	+	0.267261i
$15$		0			0
$16$	1.00000			0.250000
$17$	−1.00000	−	4.00000i	−0.242536	−	0.970143i
$17$	−1.00000	−	4.00000i	−0.242536	−	0.970143i
$18$		0			0
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$	2.00000	+	2.00000i	0.447214	+	0.447214i
$21$		0			0
$22$	2.00000	+	2.00000i	0.426401	+	0.426401i
$23$	−3.00000	+	3.00000i	−0.625543	+	0.625543i	−0.946943	−	0.321400i	$-0.895847\pi$
$23$	−3.00000	+	3.00000i	−0.625543	+	0.625543i	0.321400	+	0.946943i	$0.395847\pi$
$24$		0			0
$25$			3.00000i			0.600000i
$26$			6.00000i			1.17670i
$27$		0			0
$28$	−1.00000	+	1.00000i	−0.188982	+	0.188982i
$29$	2.00000	+	2.00000i	0.371391	+	0.371391i	0.867984	−	0.496593i	$-0.165416\pi$
$29$	2.00000	+	2.00000i	0.371391	+	0.371391i	−0.496593	+	0.867984i	$0.665416\pi$
$30$		0			0
$31$	−3.00000	−	3.00000i	−0.538816	−	0.538816i	0.384365	−	0.923181i	$-0.374420\pi$
$31$	−3.00000	−	3.00000i	−0.538816	−	0.538816i	−0.923181	+	0.384365i	$0.874420\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	4.00000	−	1.00000i	0.685994	−	0.171499i
$35$	−4.00000			−0.676123
$36$		0			0
$37$	−6.00000	−	6.00000i	−0.986394	−	0.986394i	0.0135147	−	0.999909i	$-0.495698\pi$
$37$	−6.00000	−	6.00000i	−0.986394	−	0.986394i	−0.999909	+	0.0135147i	$0.995698\pi$
$38$	4.00000			0.648886
$39$		0			0
$40$	−2.00000	+	2.00000i	−0.316228	+	0.316228i
$41$	−1.00000	+	1.00000i	−0.156174	+	0.156174i	−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−1.00000	+	1.00000i	−0.156174	+	0.156174i	0.624695	+	0.780869i	$0.285223\pi$
$42$		0			0
$43$			12.0000i			1.82998i	0.403473	+	0.914991i	$0.367803\pi$
$43$			12.0000i			1.82998i	−0.403473	+	0.914991i	$0.632197\pi$
$44$	−2.00000	+	2.00000i	−0.301511	+	0.301511i
$45$		0			0
$46$	−3.00000	−	3.00000i	−0.442326	−	0.442326i
$47$	10.0000			1.45865			0.729325	−	0.684167i	$-0.239834\pi$
$47$	10.0000			1.45865			0.729325	+	0.684167i	$0.239834\pi$
$48$		0			0
$49$			5.00000i			0.714286i
$50$	−3.00000			−0.424264
$51$		0			0
$52$	−6.00000			−0.832050
$53$		−	6.00000i		−	0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$		−	6.00000i		−	0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$		0			0
$55$	−8.00000			−1.07872
$56$	−1.00000	−	1.00000i	−0.133631	−	0.133631i
$57$		0			0
$58$	−2.00000	+	2.00000i	−0.262613	+	0.262613i
$59$		0			0		1.00000			$0$
$59$		0			0		−1.00000			$\pi$
$60$		0			0
$61$	2.00000	−	2.00000i	0.256074	−	0.256074i	−0.567381	−	0.823455i	$-0.692043\pi$
$61$	2.00000	−	2.00000i	0.256074	−	0.256074i	0.823455	+	0.567381i	$0.192043\pi$
$62$	3.00000	−	3.00000i	0.381000	−	0.381000i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−12.0000	−	12.0000i	−1.48842	−	1.48842i
$66$		0			0
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$	1.00000	+	4.00000i	0.121268	+	0.485071i
$69$		0			0
$70$		−	4.00000i		−	0.478091i
$71$	1.00000	+	1.00000i	0.118678	+	0.118678i	0.763952	−	0.645273i	$-0.223257\pi$
$71$	1.00000	+	1.00000i	0.118678	+	0.118678i	−0.645273	+	0.763952i	$0.723257\pi$
$72$		0			0
$73$	−1.00000	−	1.00000i	−0.117041	−	0.117041i	0.646160	−	0.763202i	$-0.276374\pi$
$73$	−1.00000	−	1.00000i	−0.117041	−	0.117041i	−0.763202	+	0.646160i	$0.776374\pi$
$74$	6.00000	−	6.00000i	0.697486	−	0.697486i
$75$		0			0
$76$			4.00000i			0.458831i
$77$		−	4.00000i		−	0.455842i
$78$		0			0
$79$	−5.00000	+	5.00000i	−0.562544	+	0.562544i	−0.930029	−	0.367485i	$-0.880219\pi$
$79$	−5.00000	+	5.00000i	−0.562544	+	0.562544i	0.367485	+	0.930029i	$0.380219\pi$
$80$	−2.00000	−	2.00000i	−0.223607	−	0.223607i
$81$		0			0
$82$	−1.00000	−	1.00000i	−0.110432	−	0.110432i
$83$			16.0000i			1.75623i	0.478451	+	0.878114i	$0.341198\pi$
$83$			16.0000i			1.75623i	−0.478451	+	0.878114i	$0.658802\pi$
$84$		0			0
$85$	−6.00000	+	10.0000i	−0.650791	+	1.08465i
$86$	−12.0000			−1.29399
$87$		0			0
$88$	−2.00000	−	2.00000i	−0.213201	−	0.213201i
$89$	12.0000			1.27200			0.635999	−	0.771690i	$-0.280588\pi$
$89$	12.0000			1.27200			0.635999	+	0.771690i	$0.280588\pi$
$90$		0			0
$91$	6.00000	−	6.00000i	0.628971	−	0.628971i
$92$	3.00000	−	3.00000i	0.312772	−	0.312772i
$93$		0			0
$94$			10.0000i			1.03142i
$95$	−8.00000	+	8.00000i	−0.820783	+	0.820783i
$96$		0			0
$97$	−11.0000	−	11.0000i	−1.11688	−	1.11688i	−0.992196	−	0.124684i	$-0.960208\pi$
$97$	−11.0000	−	11.0000i	−1.11688	−	1.11688i	−0.124684	−	0.992196i	$-0.539792\pi$
$98$	−5.00000			−0.505076
$99$		0			0
$100$		−	3.00000i		−	0.300000i
$101$	−14.0000			−1.39305			−0.696526	−	0.717532i	$-0.745272\pi$
$101$	−14.0000			−1.39305			−0.696526	+	0.717532i	$0.745272\pi$
$102$		0			0
$103$	−2.00000			−0.197066			−0.0985329	−	0.995134i	$-0.531415\pi$
$103$	−2.00000			−0.197066			−0.0985329	+	0.995134i	$0.531415\pi$
$104$		−	6.00000i		−	0.588348i
$105$		0			0
$106$	6.00000			0.582772
$107$	14.0000	+	14.0000i	1.35343	+	1.35343i	0.881791	+	0.471640i	$0.156338\pi$
$107$	14.0000	+	14.0000i	1.35343	+	1.35343i	0.471640	+	0.881791i	$0.343662\pi$
$108$		0			0
$109$	−4.00000	+	4.00000i	−0.383131	+	0.383131i	−0.872229	−	0.489098i	$-0.837326\pi$
$109$	−4.00000	+	4.00000i	−0.383131	+	0.383131i	0.489098	+	0.872229i	$0.337326\pi$
$110$		−	8.00000i		−	0.762770i
$111$		0			0
$112$	1.00000	−	1.00000i	0.0944911	−	0.0944911i
$113$	11.0000	−	11.0000i	1.03479	−	1.03479i	0.0354205	−	0.999372i	$-0.488723\pi$
$113$	11.0000	−	11.0000i	1.03479	−	1.03479i	0.999372	−	0.0354205i	$-0.0112770\pi$
$114$		0			0
$115$	12.0000			1.11901
$116$	−2.00000	−	2.00000i	−0.185695	−	0.185695i
$117$		0			0
$118$		0			0
$119$	−5.00000	−	3.00000i	−0.458349	−	0.275010i
$120$		0			0
$121$			3.00000i			0.272727i
$122$	2.00000	+	2.00000i	0.181071	+	0.181071i
$123$		0			0
$124$	3.00000	+	3.00000i	0.269408	+	0.269408i
$125$	−4.00000	+	4.00000i	−0.357771	+	0.357771i
$126$		0			0
$127$		−	8.00000i		−	0.709885i	−0.934888	−	0.354943i	$-0.884500\pi$
$127$		−	8.00000i		−	0.709885i	0.934888	−	0.354943i	$-0.115500\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	12.0000	−	12.0000i	1.05247	−	1.05247i
$131$	14.0000	+	14.0000i	1.22319	+	1.22319i	0.966493	+	0.256693i	$0.0826328\pi$
$131$	14.0000	+	14.0000i	1.22319	+	1.22319i	0.256693	+	0.966493i	$0.417367\pi$
$132$		0			0
$133$	−4.00000	−	4.00000i	−0.346844	−	0.346844i
$134$			4.00000i			0.345547i
$135$		0			0
$136$	−4.00000	+	1.00000i	−0.342997	+	0.0857493i
$137$	−6.00000			−0.512615			−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000			−0.512615			−0.256307	+	0.966595i	$0.582506\pi$
$138$		0			0
$139$	14.0000	+	14.0000i	1.18746	+	1.18746i	0.977766	+	0.209698i	$0.0672482\pi$
$139$	14.0000	+	14.0000i	1.18746	+	1.18746i	0.209698	+	0.977766i	$0.432752\pi$
$140$	4.00000			0.338062
$141$		0			0
$142$	−1.00000	+	1.00000i	−0.0839181	+	0.0839181i
$143$	12.0000	−	12.0000i	1.00349	−	1.00349i
$144$		0			0
$145$		−	8.00000i		−	0.664364i
$146$	1.00000	−	1.00000i	0.0827606	−	0.0827606i
$147$		0			0
$148$	6.00000	+	6.00000i	0.493197	+	0.493197i
$149$	2.00000			0.163846			0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000			0.163846			0.0819232	+	0.996639i	$0.473894\pi$
$150$		0			0
$151$		−	8.00000i		−	0.651031i	−0.945537	−	0.325515i	$-0.894462\pi$
$151$		−	8.00000i		−	0.651031i	0.945537	−	0.325515i	$-0.105538\pi$
$152$	−4.00000			−0.324443
$153$		0			0
$154$	4.00000			0.322329
$155$			12.0000i			0.963863i
$156$		0			0
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$	−5.00000	−	5.00000i	−0.397779	−	0.397779i
$159$		0			0
$160$	2.00000	−	2.00000i	0.158114	−	0.158114i
$161$			6.00000i			0.472866i
$162$		0			0
$163$	12.0000	−	12.0000i	0.939913	−	0.939913i	−0.0583818	−	0.998294i	$-0.518594\pi$
$163$	12.0000	−	12.0000i	0.939913	−	0.939913i	0.998294	+	0.0583818i	$0.0185941\pi$
$164$	1.00000	−	1.00000i	0.0780869	−	0.0780869i
$165$		0			0
$166$	−16.0000			−1.24184
$167$	−11.0000	−	11.0000i	−0.851206	−	0.851206i	0.139076	−	0.990282i	$-0.455587\pi$
$167$	−11.0000	−	11.0000i	−0.851206	−	0.851206i	−0.990282	+	0.139076i	$0.955587\pi$
$168$		0			0
$169$	23.0000			1.76923
$170$	−10.0000	−	6.00000i	−0.766965	−	0.460179i
$171$		0			0
$172$		−	12.0000i		−	0.914991i
$173$	10.0000	+	10.0000i	0.760286	+	0.760286i	0.976374	−	0.216088i	$-0.0693298\pi$
$173$	10.0000	+	10.0000i	0.760286	+	0.760286i	−0.216088	+	0.976374i	$0.569330\pi$
$174$		0			0
$175$	3.00000	+	3.00000i	0.226779	+	0.226779i
$176$	2.00000	−	2.00000i	0.150756	−	0.150756i
$177$		0			0
$178$			12.0000i			0.899438i
$179$			16.0000i			1.19590i	0.801535	+	0.597948i	$0.204017\pi$
$179$			16.0000i			1.19590i	−0.801535	+	0.597948i	$0.795983\pi$
$180$		0			0
$181$	2.00000	−	2.00000i	0.148659	−	0.148659i	−0.628860	−	0.777519i	$-0.716478\pi$
$181$	2.00000	−	2.00000i	0.148659	−	0.148659i	0.777519	+	0.628860i	$0.216478\pi$
$182$	6.00000	+	6.00000i	0.444750	+	0.444750i
$183$		0			0
$184$	3.00000	+	3.00000i	0.221163	+	0.221163i
$185$			24.0000i			1.76452i
$186$		0			0
$187$	−10.0000	−	6.00000i	−0.731272	−	0.438763i
$188$	−10.0000			−0.729325
$189$		0			0
$190$	−8.00000	−	8.00000i	−0.580381	−	0.580381i
$191$	−18.0000			−1.30243			−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000			−1.30243			−0.651217	+	0.758891i	$0.725741\pi$
$192$		0			0
$193$	3.00000	−	3.00000i	0.215945	−	0.215945i	−0.590842	−	0.806787i	$-0.701204\pi$
$193$	3.00000	−	3.00000i	0.215945	−	0.215945i	0.806787	+	0.590842i	$0.201204\pi$
$194$	11.0000	−	11.0000i	0.789754	−	0.789754i
$195$		0			0
$196$		−	5.00000i		−	0.357143i
$197$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$197$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$198$		0			0
$199$	5.00000	+	5.00000i	0.354441	+	0.354441i	0.861759	−	0.507318i	$-0.169363\pi$
$199$	5.00000	+	5.00000i	0.354441	+	0.354441i	−0.507318	+	0.861759i	$0.669363\pi$
$200$	3.00000			0.212132
$201$		0			0
$202$		−	14.0000i		−	0.985037i
$203$	4.00000			0.280745
$204$		0			0
$205$	4.00000			0.279372
$206$		−	2.00000i		−	0.139347i
$207$		0			0
$208$	6.00000			0.416025
$209$	−8.00000	−	8.00000i	−0.553372	−	0.553372i
$210$		0			0
$211$	−18.0000	+	18.0000i	−1.23917	+	1.23917i	−0.278831	+	0.960340i	$0.589947\pi$
$211$	−18.0000	+	18.0000i	−1.23917	+	1.23917i	−0.960340	+	0.278831i	$0.910053\pi$
$212$			6.00000i			0.412082i
$213$		0			0
$214$	−14.0000	+	14.0000i	−0.957020	+	0.957020i
$215$	24.0000	−	24.0000i	1.63679	−	1.63679i
$216$		0			0
$217$	−6.00000			−0.407307
$218$	−4.00000	−	4.00000i	−0.270914	−	0.270914i
$219$		0			0
$220$	8.00000			0.539360
$221$	−6.00000	−	24.0000i	−0.403604	−	1.61441i
$222$		0			0
$223$			22.0000i			1.47323i	0.676313	+	0.736614i	$0.263577\pi$
$223$			22.0000i			1.47323i	−0.676313	+	0.736614i	$0.736423\pi$
$224$	1.00000	+	1.00000i	0.0668153	+	0.0668153i
$225$		0			0
$226$	11.0000	+	11.0000i	0.731709	+	0.731709i
$227$	8.00000	−	8.00000i	0.530979	−	0.530979i	−0.389885	−	0.920864i	$-0.627485\pi$
$227$	8.00000	−	8.00000i	0.530979	−	0.530979i	0.920864	+	0.389885i	$0.127485\pi$
$228$		0			0
$229$		−	2.00000i		−	0.132164i	−0.997814	−	0.0660819i	$-0.978950\pi$
$229$		−	2.00000i		−	0.132164i	0.997814	−	0.0660819i	$-0.0210498\pi$
$230$			12.0000i			0.791257i
$231$		0			0
$232$	2.00000	−	2.00000i	0.131306	−	0.131306i
$233$	−15.0000	−	15.0000i	−0.982683	−	0.982683i	0.0171699	−	0.999853i	$-0.494534\pi$
$233$	−15.0000	−	15.0000i	−0.982683	−	0.982683i	−0.999853	+	0.0171699i	$0.994534\pi$
$234$		0			0
$235$	−20.0000	−	20.0000i	−1.30466	−	1.30466i
$236$		0			0
$237$		0			0
$238$	3.00000	−	5.00000i	0.194461	−	0.324102i
$239$	−22.0000			−1.42306			−0.711531	−	0.702655i	$-0.751998\pi$
$239$	−22.0000			−1.42306			−0.711531	+	0.702655i	$0.751998\pi$
$240$		0			0
$241$	9.00000	+	9.00000i	0.579741	+	0.579741i	0.934832	−	0.355091i	$-0.115550\pi$
$241$	9.00000	+	9.00000i	0.579741	+	0.579741i	−0.355091	+	0.934832i	$0.615550\pi$
$242$	−3.00000			−0.192847
$243$		0			0
$244$	−2.00000	+	2.00000i	−0.128037	+	0.128037i
$245$	10.0000	−	10.0000i	0.638877	−	0.638877i
$246$		0			0
$247$		−	24.0000i		−	1.52708i
$248$	−3.00000	+	3.00000i	−0.190500	+	0.190500i
$249$		0			0
$250$	−4.00000	−	4.00000i	−0.252982	−	0.252982i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$			12.0000i			0.754434i
$254$	8.00000			0.501965
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	8.00000i		−	0.499026i	−0.968371	−	0.249513i	$-0.919729\pi$
$257$		−	8.00000i		−	0.499026i	0.968371	−	0.249513i	$-0.0802706\pi$
$258$		0			0
$259$	−12.0000			−0.745644
$260$	12.0000	+	12.0000i	0.744208	+	0.744208i
$261$		0			0
$262$	−14.0000	+	14.0000i	−0.864923	+	0.864923i
$263$		−	2.00000i		−	0.123325i	−0.998097	−	0.0616626i	$-0.980360\pi$
$263$		−	2.00000i		−	0.123325i	0.998097	−	0.0616626i	$-0.0196403\pi$
$264$		0			0
$265$	−12.0000	+	12.0000i	−0.737154	+	0.737154i
$266$	4.00000	−	4.00000i	0.245256	−	0.245256i
$267$		0			0
$268$	−4.00000			−0.244339
$269$	−10.0000	−	10.0000i	−0.609711	−	0.609711i	0.333160	−	0.942870i	$-0.391885\pi$
$269$	−10.0000	−	10.0000i	−0.609711	−	0.609711i	−0.942870	+	0.333160i	$0.891885\pi$
$270$		0			0
$271$	−16.0000			−0.971931			−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000			−0.971931			−0.485965	+	0.873978i	$0.661532\pi$
$272$	−1.00000	−	4.00000i	−0.0606339	−	0.242536i
$273$		0			0
$274$		−	6.00000i		−	0.362473i
$275$	6.00000	+	6.00000i	0.361814	+	0.361814i
$276$		0			0
$277$	−20.0000	−	20.0000i	−1.20168	−	1.20168i	−0.973654	−	0.228029i	$-0.926772\pi$
$277$	−20.0000	−	20.0000i	−1.20168	−	1.20168i	−0.228029	−	0.973654i	$-0.573228\pi$
$278$	−14.0000	+	14.0000i	−0.839664	+	0.839664i
$279$		0			0
$280$			4.00000i			0.239046i
$281$			20.0000i			1.19310i	0.802576	+	0.596550i	$0.203462\pi$
$281$			20.0000i			1.19310i	−0.802576	+	0.596550i	$0.796538\pi$
$282$		0			0
$283$	−10.0000	+	10.0000i	−0.594438	+	0.594438i	−0.938827	−	0.344389i	$-0.888086\pi$
$283$	−10.0000	+	10.0000i	−0.594438	+	0.594438i	0.344389	+	0.938827i	$0.388086\pi$
$284$	−1.00000	−	1.00000i	−0.0593391	−	0.0593391i
$285$		0			0
$286$	12.0000	+	12.0000i	0.709575	+	0.709575i
$287$			2.00000i			0.118056i
$288$		0			0
$289$	−15.0000	+	8.00000i	−0.882353	+	0.470588i
$290$	8.00000			0.469776
$291$		0			0
$292$	1.00000	+	1.00000i	0.0585206	+	0.0585206i
$293$	30.0000			1.75262			0.876309	−	0.481749i	$-0.159998\pi$
$293$	30.0000			1.75262			0.876309	+	0.481749i	$0.159998\pi$
$294$		0			0
$295$		0			0
$296$	−6.00000	+	6.00000i	−0.348743	+	0.348743i
$297$		0			0
$298$			2.00000i			0.115857i
$299$	−18.0000	+	18.0000i	−1.04097	+	1.04097i
$300$		0			0
$301$	12.0000	+	12.0000i	0.691669	+	0.691669i
$302$	8.00000			0.460348
$303$		0			0
$304$		−	4.00000i		−	0.229416i
$305$	−8.00000			−0.458079
$306$		0			0
$307$	4.00000			0.228292			0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000			0.228292			0.114146	+	0.993464i	$0.463587\pi$
$308$			4.00000i			0.227921i
$309$		0			0
$310$	−12.0000			−0.681554
$311$	3.00000	+	3.00000i	0.170114	+	0.170114i	0.787030	−	0.616915i	$-0.211618\pi$
$311$	3.00000	+	3.00000i	0.170114	+	0.170114i	−0.616915	+	0.787030i	$0.711618\pi$
$312$		0			0
$313$	13.0000	−	13.0000i	0.734803	−	0.734803i	−0.236764	−	0.971567i	$-0.576087\pi$
$313$	13.0000	−	13.0000i	0.734803	−	0.734803i	0.971567	+	0.236764i	$0.0760868\pi$
$314$			14.0000i			0.790066i
$315$		0			0
$316$	5.00000	−	5.00000i	0.281272	−	0.281272i
$317$	−8.00000	+	8.00000i	−0.449325	+	0.449325i	−0.895130	−	0.445805i	$-0.852917\pi$
$317$	−8.00000	+	8.00000i	−0.449325	+	0.449325i	0.445805	+	0.895130i	$0.352917\pi$
$318$		0			0
$319$	8.00000			0.447914
$320$	2.00000	+	2.00000i	0.111803	+	0.111803i
$321$		0			0
$322$	−6.00000			−0.334367
$323$	−16.0000	+	4.00000i	−0.890264	+	0.222566i
$324$		0			0
$325$			18.0000i			0.998460i
$326$	12.0000	+	12.0000i	0.664619	+	0.664619i
$327$		0			0
$328$	1.00000	+	1.00000i	0.0552158	+	0.0552158i
$329$	10.0000	−	10.0000i	0.551318	−	0.551318i
$330$		0			0
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$		−	16.0000i		−	0.878114i
$333$		0			0
$334$	11.0000	−	11.0000i	0.601893	−	0.601893i
$335$	−8.00000	−	8.00000i	−0.437087	−	0.437087i
$336$		0			0
$337$	−11.0000	−	11.0000i	−0.599208	−	0.599208i	0.340894	−	0.940102i	$-0.389270\pi$
$337$	−11.0000	−	11.0000i	−0.599208	−	0.599208i	−0.940102	+	0.340894i	$0.889270\pi$
$338$			23.0000i			1.25104i
$339$		0			0
$340$	6.00000	−	10.0000i	0.325396	−	0.542326i
$341$	−12.0000			−0.649836
$342$		0			0
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$	12.0000			0.646997
$345$		0			0
$346$	−10.0000	+	10.0000i	−0.537603	+	0.537603i
$347$	20.0000	−	20.0000i	1.07366	−	1.07366i	0.0765939	−	0.997062i	$-0.475596\pi$
$347$	20.0000	−	20.0000i	1.07366	−	1.07366i	0.997062	−	0.0765939i	$-0.0244045\pi$
$348$		0			0
$349$			10.0000i			0.535288i	0.963518	+	0.267644i	$0.0862451\pi$
$349$			10.0000i			0.535288i	−0.963518	+	0.267644i	$0.913755\pi$
$350$	−3.00000	+	3.00000i	−0.160357	+	0.160357i
$351$		0			0
$352$	2.00000	+	2.00000i	0.106600	+	0.106600i
$353$	2.00000			0.106449			0.0532246	−	0.998583i	$-0.483050\pi$
$353$	2.00000			0.106449			0.0532246	+	0.998583i	$0.483050\pi$
$354$		0			0
$355$		−	4.00000i		−	0.212298i
$356$	−12.0000			−0.635999
$357$		0			0
$358$	−16.0000			−0.845626
$359$		−	16.0000i		−	0.844448i	−0.906492	−	0.422224i	$-0.861250\pi$
$359$		−	16.0000i		−	0.844448i	0.906492	−	0.422224i	$-0.138750\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	2.00000	+	2.00000i	0.105118	+	0.105118i
$363$		0			0
$364$	−6.00000	+	6.00000i	−0.314485	+	0.314485i
$365$			4.00000i			0.209370i
$366$		0			0
$367$	−3.00000	+	3.00000i	−0.156599	+	0.156599i	−0.781058	−	0.624459i	$-0.785320\pi$
$367$	−3.00000	+	3.00000i	−0.156599	+	0.156599i	0.624459	+	0.781058i	$0.285320\pi$
$368$	−3.00000	+	3.00000i	−0.156386	+	0.156386i
$369$		0			0
$370$	−24.0000			−1.24770
$371$	−6.00000	−	6.00000i	−0.311504	−	0.311504i
$372$		0			0
$373$	−22.0000			−1.13912			−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000			−1.13912			−0.569558	+	0.821951i	$0.692886\pi$
$374$	6.00000	−	10.0000i	0.310253	−	0.517088i
$375$		0			0
$376$		−	10.0000i		−	0.515711i
$377$	12.0000	+	12.0000i	0.618031	+	0.618031i
$378$		0			0
$379$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$379$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$380$	8.00000	−	8.00000i	0.410391	−	0.410391i
$381$		0			0
$382$		−	18.0000i		−	0.920960i
$383$		−	34.0000i		−	1.73732i	−0.495410	−	0.868659i	$-0.664982\pi$
$383$		−	34.0000i		−	1.73732i	0.495410	−	0.868659i	$-0.335018\pi$
$384$		0			0
$385$	−8.00000	+	8.00000i	−0.407718	+	0.407718i
$386$	3.00000	+	3.00000i	0.152696	+	0.152696i
$387$		0			0
$388$	11.0000	+	11.0000i	0.558440	+	0.558440i
$389$			18.0000i			0.912636i	0.889817	+	0.456318i	$0.150832\pi$
$389$			18.0000i			0.912636i	−0.889817	+	0.456318i	$0.849168\pi$
$390$		0			0
$391$	15.0000	+	9.00000i	0.758583	+	0.455150i
$392$	5.00000			0.252538
$393$		0			0
$394$		0			0
$395$	20.0000			1.00631
$396$		0			0
$397$	18.0000	−	18.0000i	0.903394	−	0.903394i	−0.0923340	−	0.995728i	$-0.529433\pi$
$397$	18.0000	−	18.0000i	0.903394	−	0.903394i	0.995728	+	0.0923340i	$0.0294327\pi$
$398$	−5.00000	+	5.00000i	−0.250627	+	0.250627i
$399$		0			0
$400$			3.00000i			0.150000i
$401$	−5.00000	+	5.00000i	−0.249688	+	0.249688i	−0.820843	−	0.571154i	$-0.806496\pi$
$401$	−5.00000	+	5.00000i	−0.249688	+	0.249688i	0.571154	+	0.820843i	$0.306496\pi$
$402$		0			0
$403$	−18.0000	−	18.0000i	−0.896644	−	0.896644i
$404$	14.0000			0.696526
$405$		0			0
$406$			4.00000i			0.198517i
$407$	−24.0000			−1.18964
$408$		0			0
$409$	24.0000			1.18672			0.593362	−	0.804936i	$-0.297800\pi$
$409$	24.0000			1.18672			0.593362	+	0.804936i	$0.297800\pi$
$410$			4.00000i			0.197546i
$411$		0			0
$412$	2.00000			0.0985329
$413$		0			0
$414$		0			0
$415$	32.0000	−	32.0000i	1.57082	−	1.57082i
$416$			6.00000i			0.294174i
$417$		0			0
$418$	8.00000	−	8.00000i	0.391293	−	0.391293i
$419$	−4.00000	+	4.00000i	−0.195413	+	0.195413i	−0.798030	−	0.602617i	$-0.794125\pi$
$419$	−4.00000	+	4.00000i	−0.195413	+	0.195413i	0.602617	+	0.798030i	$0.294125\pi$
$420$		0			0
$421$	22.0000			1.07221			0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000			1.07221			0.536107	+	0.844150i	$0.319894\pi$
$422$	−18.0000	−	18.0000i	−0.876226	−	0.876226i
$423$		0			0
$424$	−6.00000			−0.291386
$425$	12.0000	−	3.00000i	0.582086	−	0.145521i
$426$		0			0
$427$		−	4.00000i		−	0.193574i
$428$	−14.0000	−	14.0000i	−0.676716	−	0.676716i
$429$		0			0
$430$	24.0000	+	24.0000i	1.15738	+	1.15738i
$431$	11.0000	−	11.0000i	0.529851	−	0.529851i	−0.390677	−	0.920528i	$-0.627759\pi$
$431$	11.0000	−	11.0000i	0.529851	−	0.529851i	0.920528	+	0.390677i	$0.127759\pi$
$432$		0			0
$433$			8.00000i			0.384455i	0.981350	+	0.192228i	$0.0615712\pi$
$433$			8.00000i			0.384455i	−0.981350	+	0.192228i	$0.938429\pi$
$434$		−	6.00000i		−	0.288009i
$435$		0			0
$436$	4.00000	−	4.00000i	0.191565	−	0.191565i
$437$	12.0000	+	12.0000i	0.574038	+	0.574038i
$438$		0			0
$439$	29.0000	+	29.0000i	1.38409	+	1.38409i	0.837204	+	0.546890i	$0.184188\pi$
$439$	29.0000	+	29.0000i	1.38409	+	1.38409i	0.546890	+	0.837204i	$0.315812\pi$
$440$			8.00000i			0.381385i
$441$		0			0
$442$	24.0000	−	6.00000i	1.14156	−	0.285391i
$443$	−24.0000			−1.14027			−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000			−1.14027			−0.570137	+	0.821549i	$0.693110\pi$
$444$		0			0
$445$	−24.0000	−	24.0000i	−1.13771	−	1.13771i
$446$	−22.0000			−1.04173
$447$		0			0
$448$	−1.00000	+	1.00000i	−0.0472456	+	0.0472456i
$449$	−15.0000	+	15.0000i	−0.707894	+	0.707894i	−0.966092	−	0.258198i	$-0.916871\pi$
$449$	−15.0000	+	15.0000i	−0.707894	+	0.707894i	0.258198	+	0.966092i	$0.416871\pi$
$450$		0			0
$451$			4.00000i			0.188353i
$452$	−11.0000	+	11.0000i	−0.517396	+	0.517396i
$453$		0			0
$454$	8.00000	+	8.00000i	0.375459	+	0.375459i
$455$	−24.0000			−1.12514
$456$		0			0
$457$		−	8.00000i		−	0.374224i	−0.982339	−	0.187112i	$-0.940087\pi$
$457$		−	8.00000i		−	0.374224i	0.982339	−	0.187112i	$-0.0599128\pi$
$458$	2.00000			0.0934539
$459$		0			0
$460$	−12.0000			−0.559503
$461$		−	30.0000i		−	1.39724i	−0.715493	−	0.698620i	$-0.753798\pi$
$461$		−	30.0000i		−	1.39724i	0.715493	−	0.698620i	$-0.246202\pi$
$462$		0			0
$463$	18.0000			0.836531			0.418265	−	0.908325i	$-0.362638\pi$
$463$	18.0000			0.836531			0.418265	+	0.908325i	$0.362638\pi$
$464$	2.00000	+	2.00000i	0.0928477	+	0.0928477i
$465$		0			0
$466$	15.0000	−	15.0000i	0.694862	−	0.694862i
$467$		−	20.0000i		−	0.925490i	−0.886492	−	0.462745i	$-0.846865\pi$
$467$		−	20.0000i		−	0.925490i	0.886492	−	0.462745i	$-0.153135\pi$
$468$		0			0
$469$	4.00000	−	4.00000i	0.184703	−	0.184703i
$470$	20.0000	−	20.0000i	0.922531	−	0.922531i
$471$		0			0
$472$		0			0
$473$	24.0000	+	24.0000i	1.10352	+	1.10352i
$474$		0			0
$475$	12.0000			0.550598
$476$	5.00000	+	3.00000i	0.229175	+	0.137505i
$477$		0			0
$478$		−	22.0000i		−	1.00626i
$479$	−5.00000	−	5.00000i	−0.228456	−	0.228456i	0.583592	−	0.812047i	$-0.301647\pi$
$479$	−5.00000	−	5.00000i	−0.228456	−	0.228456i	−0.812047	+	0.583592i	$0.801647\pi$
$480$		0			0
$481$	−36.0000	−	36.0000i	−1.64146	−	1.64146i
$482$	−9.00000	+	9.00000i	−0.409939	+	0.409939i
$483$		0			0
$484$		−	3.00000i		−	0.136364i
$485$			44.0000i			1.99794i
$486$		0			0
$487$	−21.0000	+	21.0000i	−0.951601	+	0.951601i	−0.998882	−	0.0472808i	$-0.984944\pi$
$487$	−21.0000	+	21.0000i	−0.951601	+	0.951601i	0.0472808	+	0.998882i	$0.484944\pi$
$488$	−2.00000	−	2.00000i	−0.0905357	−	0.0905357i
$489$		0			0
$490$	10.0000	+	10.0000i	0.451754	+	0.451754i
$491$		−	8.00000i		−	0.361035i	−0.983572	−	0.180517i	$-0.942223\pi$
$491$		−	8.00000i		−	0.361035i	0.983572	−	0.180517i	$-0.0577772\pi$
$492$		0			0
$493$	6.00000	−	10.0000i	0.270226	−	0.450377i
$494$	24.0000			1.07981
$495$		0			0
$496$	−3.00000	−	3.00000i	−0.134704	−	0.134704i
$497$	2.00000			0.0897123
$498$		0			0
$499$	−6.00000	+	6.00000i	−0.268597	+	0.268597i	−0.828535	−	0.559938i	$-0.810825\pi$
$499$	−6.00000	+	6.00000i	−0.268597	+	0.268597i	0.559938	+	0.828535i	$0.310825\pi$
$500$	4.00000	−	4.00000i	0.178885	−	0.178885i
$501$		0			0
$502$		0			0
$503$	27.0000	−	27.0000i	1.20387	−	1.20387i	0.230891	−	0.972980i	$-0.425836\pi$
$503$	27.0000	−	27.0000i	1.20387	−	1.20387i	0.972980	−	0.230891i	$-0.0741640\pi$
$504$		0			0
$505$	28.0000	+	28.0000i	1.24598	+	1.24598i
$506$	−12.0000			−0.533465
$507$		0			0
$508$			8.00000i			0.354943i
$509$	−14.0000			−0.620539			−0.310270	−	0.950649i	$-0.600419\pi$
$509$	−14.0000			−0.620539			−0.310270	+	0.950649i	$0.600419\pi$
$510$		0			0
$511$	−2.00000			−0.0884748
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	8.00000			0.352865
$515$	4.00000	+	4.00000i	0.176261	+	0.176261i
$516$		0			0
$517$	20.0000	−	20.0000i	0.879599	−	0.879599i
$518$		−	12.0000i		−	0.527250i
$519$		0			0
$520$	−12.0000	+	12.0000i	−0.526235	+	0.526235i
$521$	−1.00000	+	1.00000i	−0.0438108	+	0.0438108i	−0.728673	−	0.684862i	$-0.759862\pi$
$521$	−1.00000	+	1.00000i	−0.0438108	+	0.0438108i	0.684862	+	0.728673i	$0.259862\pi$
$522$		0			0
$523$	12.0000			0.524723			0.262362	−	0.964970i	$-0.415499\pi$
$523$	12.0000			0.524723			0.262362	+	0.964970i	$0.415499\pi$
$524$	−14.0000	−	14.0000i	−0.611593	−	0.611593i
$525$		0			0
$526$	2.00000			0.0872041
$527$	−9.00000	+	15.0000i	−0.392046	+	0.653410i
$528$		0			0
$529$			5.00000i			0.217391i
$530$	−12.0000	−	12.0000i	−0.521247	−	0.521247i
$531$		0			0
$532$	4.00000	+	4.00000i	0.173422	+	0.173422i
$533$	−6.00000	+	6.00000i	−0.259889	+	0.259889i
$534$		0			0
$535$		−	56.0000i		−	2.42109i
$536$		−	4.00000i		−	0.172774i
$537$		0			0
$538$	10.0000	−	10.0000i	0.431131	−	0.431131i
$539$	10.0000	+	10.0000i	0.430730	+	0.430730i
$540$		0			0
$541$	6.00000	+	6.00000i	0.257960	+	0.257960i	0.824224	−	0.566264i	$-0.191612\pi$
$541$	6.00000	+	6.00000i	0.257960	+	0.257960i	−0.566264	+	0.824224i	$0.691612\pi$
$542$		−	16.0000i		−	0.687259i
$543$		0			0
$544$	4.00000	−	1.00000i	0.171499	−	0.0428746i
$545$	16.0000			0.685365
$546$		0			0
$547$	−2.00000	−	2.00000i	−0.0855138	−	0.0855138i	0.663056	−	0.748570i	$-0.269259\pi$
$547$	−2.00000	−	2.00000i	−0.0855138	−	0.0855138i	−0.748570	+	0.663056i	$0.769259\pi$
$548$	6.00000			0.256307
$549$		0			0
$550$	−6.00000	+	6.00000i	−0.255841	+	0.255841i
$551$	8.00000	−	8.00000i	0.340811	−	0.340811i
$552$		0			0
$553$			10.0000i			0.425243i
$554$	20.0000	−	20.0000i	0.849719	−	0.849719i
$555$		0			0
$556$	−14.0000	−	14.0000i	−0.593732	−	0.593732i
$557$	18.0000			0.762684			0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000			0.762684			0.381342	+	0.924434i	$0.375462\pi$
$558$		0			0
$559$			72.0000i			3.04528i
$560$	−4.00000			−0.169031
$561$		0			0
$562$	−20.0000			−0.843649
$563$			36.0000i			1.51722i	0.651546	+	0.758610i	$0.274121\pi$
$563$			36.0000i			1.51722i	−0.651546	+	0.758610i	$0.725879\pi$
$564$		0			0
$565$	−44.0000			−1.85109
$566$	−10.0000	−	10.0000i	−0.420331	−	0.420331i
$567$		0			0
$568$	1.00000	−	1.00000i	0.0419591	−	0.0419591i
$569$			10.0000i			0.419222i	0.977785	+	0.209611i	$0.0672197\pi$
$569$			10.0000i			0.419222i	−0.977785	+	0.209611i	$0.932780\pi$
$570$		0			0
$571$	16.0000	−	16.0000i	0.669579	−	0.669579i	−0.288039	−	0.957619i	$-0.593003\pi$
$571$	16.0000	−	16.0000i	0.669579	−	0.669579i	0.957619	+	0.288039i	$0.0930034\pi$
$572$	−12.0000	+	12.0000i	−0.501745	+	0.501745i
$573$		0			0
$574$	−2.00000			−0.0834784
$575$	−9.00000	−	9.00000i	−0.375326	−	0.375326i
$576$		0			0
$577$	−32.0000			−1.33218			−0.666089	−	0.745873i	$-0.732033\pi$
$577$	−32.0000			−1.33218			−0.666089	+	0.745873i	$0.732033\pi$
$578$	−8.00000	−	15.0000i	−0.332756	−	0.623918i
$579$		0			0
$580$			8.00000i			0.332182i
$581$	16.0000	+	16.0000i	0.663792	+	0.663792i
$582$		0			0
$583$	−12.0000	−	12.0000i	−0.496989	−	0.496989i
$584$	−1.00000	+	1.00000i	−0.0413803	+	0.0413803i
$585$		0			0
$586$			30.0000i			1.23929i
$587$			28.0000i			1.15568i	0.816149	+	0.577842i	$0.196105\pi$
$587$			28.0000i			1.15568i	−0.816149	+	0.577842i	$0.803895\pi$
$588$		0			0
$589$	−12.0000	+	12.0000i	−0.494451	+	0.494451i
$590$		0			0
$591$		0			0
$592$	−6.00000	−	6.00000i	−0.246598	−	0.246598i
$593$			18.0000i			0.739171i	0.929197	+	0.369586i	$0.120500\pi$
$593$			18.0000i			0.739171i	−0.929197	+	0.369586i	$0.879500\pi$
$594$		0			0
$595$	4.00000	+	16.0000i	0.163984	+	0.655936i
$596$	−2.00000			−0.0819232
$597$		0			0
$598$	−18.0000	−	18.0000i	−0.736075	−	0.736075i
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$		0			0
$601$	−5.00000	+	5.00000i	−0.203954	+	0.203954i	−0.801692	−	0.597738i	$-0.796066\pi$
$601$	−5.00000	+	5.00000i	−0.203954	+	0.203954i	0.597738	+	0.801692i	$0.296066\pi$
$602$	−12.0000	+	12.0000i	−0.489083	+	0.489083i
$603$		0			0
$604$			8.00000i			0.325515i
$605$	6.00000	−	6.00000i	0.243935	−	0.243935i
$606$		0			0
$607$	−15.0000	−	15.0000i	−0.608831	−	0.608831i	0.333809	−	0.942641i	$-0.391666\pi$
$607$	−15.0000	−	15.0000i	−0.608831	−	0.608831i	−0.942641	+	0.333809i	$0.891666\pi$
$608$	4.00000			0.162221
$609$		0			0
$610$		−	8.00000i		−	0.323911i
$611$	60.0000			2.42734
$612$		0			0
$613$	18.0000			0.727013			0.363507	−	0.931592i	$-0.381579\pi$
$613$	18.0000			0.727013			0.363507	+	0.931592i	$0.381579\pi$
$614$			4.00000i			0.161427i
$615$		0			0
$616$	−4.00000			−0.161165
$617$	−17.0000	−	17.0000i	−0.684394	−	0.684394i	0.276593	−	0.960987i	$-0.410795\pi$
$617$	−17.0000	−	17.0000i	−0.684394	−	0.684394i	−0.960987	+	0.276593i	$0.910795\pi$
$618$		0			0
$619$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$619$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$620$		−	12.0000i		−	0.481932i
$621$		0			0
$622$	−3.00000	+	3.00000i	−0.120289	+	0.120289i
$623$	12.0000	−	12.0000i	0.480770	−	0.480770i
$624$		0			0
$625$	31.0000			1.24000
$626$	13.0000	+	13.0000i	0.519584	+	0.519584i
$627$		0			0
$628$	−14.0000			−0.558661
$629$	−18.0000	+	30.0000i	−0.717707	+	1.19618i
$630$		0			0
$631$			30.0000i			1.19428i	0.802137	+	0.597141i	$0.203697\pi$
$631$			30.0000i			1.19428i	−0.802137	+	0.597141i	$0.796303\pi$
$632$	5.00000	+	5.00000i	0.198889	+	0.198889i
$633$		0			0
$634$	−8.00000	−	8.00000i	−0.317721	−	0.317721i
$635$	−16.0000	+	16.0000i	−0.634941	+	0.634941i
$636$		0			0
$637$			30.0000i			1.18864i
$638$			8.00000i			0.316723i
$639$		0			0
$640$	−2.00000	+	2.00000i	−0.0790569	+	0.0790569i
$641$	19.0000	+	19.0000i	0.750455	+	0.750455i	0.974564	−	0.224109i	$-0.0719472\pi$
$641$	19.0000	+	19.0000i	0.750455	+	0.750455i	−0.224109	+	0.974564i	$0.571947\pi$
$642$		0			0
$643$	−8.00000	−	8.00000i	−0.315489	−	0.315489i	0.531542	−	0.847032i	$-0.321613\pi$
$643$	−8.00000	−	8.00000i	−0.315489	−	0.315489i	−0.847032	+	0.531542i	$0.821613\pi$
$644$		−	6.00000i		−	0.236433i
$645$		0			0
$646$	−4.00000	−	16.0000i	−0.157378	−	0.629512i
$647$	−18.0000			−0.707653			−0.353827	−	0.935311i	$-0.615120\pi$
$647$	−18.0000			−0.707653			−0.353827	+	0.935311i	$0.615120\pi$
$648$		0			0
$649$		0			0
$650$	−18.0000			−0.706018
$651$		0			0
$652$	−12.0000	+	12.0000i	−0.469956	+	0.469956i
$653$	−14.0000	+	14.0000i	−0.547862	+	0.547862i	−0.925822	−	0.377960i	$-0.876626\pi$
$653$	−14.0000	+	14.0000i	−0.547862	+	0.547862i	0.377960	+	0.925822i	$0.376626\pi$
$654$		0			0
$655$		−	56.0000i		−	2.18810i
$656$	−1.00000	+	1.00000i	−0.0390434	+	0.0390434i
$657$		0			0
$658$	10.0000	+	10.0000i	0.389841	+	0.389841i
$659$	−4.00000			−0.155818			−0.0779089	−	0.996960i	$-0.524824\pi$
$659$	−4.00000			−0.155818			−0.0779089	+	0.996960i	$0.524824\pi$
$660$		0			0
$661$			2.00000i			0.0777910i	0.999243	+	0.0388955i	$0.0123839\pi$
$661$			2.00000i			0.0777910i	−0.999243	+	0.0388955i	$0.987616\pi$
$662$		0			0
$663$		0			0
$664$	16.0000			0.620920
$665$			16.0000i			0.620453i
$666$		0			0
$667$	−12.0000			−0.464642
$668$	11.0000	+	11.0000i	0.425603	+	0.425603i
$669$		0			0
$670$	8.00000	−	8.00000i	0.309067	−	0.309067i
$671$		−	8.00000i		−	0.308837i
$672$		0			0
$673$	−21.0000	+	21.0000i	−0.809491	+	0.809491i	−0.984557	−	0.175066i	$-0.943986\pi$
$673$	−21.0000	+	21.0000i	−0.809491	+	0.809491i	0.175066	+	0.984557i	$0.443986\pi$
$674$	11.0000	−	11.0000i	0.423704	−	0.423704i
$675$		0			0
$676$	−23.0000			−0.884615
$677$	24.0000	+	24.0000i	0.922395	+	0.922395i	0.997198	−	0.0748034i	$-0.0238329\pi$
$677$	24.0000	+	24.0000i	0.922395	+	0.922395i	−0.0748034	+	0.997198i	$0.523833\pi$
$678$		0			0
$679$	−22.0000			−0.844283
$680$	10.0000	+	6.00000i	0.383482	+	0.230089i
$681$		0			0
$682$		−	12.0000i		−	0.459504i
$683$	−20.0000	−	20.0000i	−0.765279	−	0.765279i	0.211993	−	0.977271i	$-0.432005\pi$
$683$	−20.0000	−	20.0000i	−0.765279	−	0.765279i	−0.977271	+	0.211993i	$0.932005\pi$
$684$		0			0
$685$	12.0000	+	12.0000i	0.458496	+	0.458496i
$686$	−12.0000	+	12.0000i	−0.458162	+	0.458162i
$687$		0			0
$688$			12.0000i			0.457496i
$689$		−	36.0000i		−	1.37149i
$690$		0			0
$691$	−14.0000	+	14.0000i	−0.532585	+	0.532585i	−0.921341	−	0.388756i	$-0.872905\pi$
$691$	−14.0000	+	14.0000i	−0.532585	+	0.532585i	0.388756	+	0.921341i	$0.372905\pi$
$692$	−10.0000	−	10.0000i	−0.380143	−	0.380143i
$693$		0			0
$694$	20.0000	+	20.0000i	0.759190	+	0.759190i
$695$		−	56.0000i		−	2.12420i
$696$		0			0
$697$	5.00000	+	3.00000i	0.189389	+	0.113633i
$698$	−10.0000			−0.378506
$699$		0			0
$700$	−3.00000	−	3.00000i	−0.113389	−	0.113389i
$701$	−6.00000			−0.226617			−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000			−0.226617			−0.113308	+	0.993560i	$0.536145\pi$
$702$		0			0
$703$	−24.0000	+	24.0000i	−0.905177	+	0.905177i
$704$	−2.00000	+	2.00000i	−0.0753778	+	0.0753778i
$705$		0			0
$706$			2.00000i			0.0752710i
$707$	−14.0000	+	14.0000i	−0.526524	+	0.526524i
$708$		0			0
$709$	−4.00000	−	4.00000i	−0.150223	−	0.150223i	0.627995	−	0.778218i	$-0.283876\pi$
$709$	−4.00000	−	4.00000i	−0.150223	−	0.150223i	−0.778218	+	0.627995i	$0.783876\pi$
$710$	4.00000			0.150117
$711$		0			0
$712$		−	12.0000i		−	0.449719i
$713$	18.0000			0.674105
$714$		0			0
$715$	−48.0000			−1.79510
$716$		−	16.0000i		−	0.597948i
$717$		0			0
$718$	16.0000			0.597115
$719$	−19.0000	−	19.0000i	−0.708580	−	0.708580i	0.257656	−	0.966237i	$-0.417050\pi$
$719$	−19.0000	−	19.0000i	−0.708580	−	0.708580i	−0.966237	+	0.257656i	$0.917050\pi$
$720$		0			0
$721$	−2.00000	+	2.00000i	−0.0744839	+	0.0744839i
$722$			3.00000i			0.111648i
$723$		0			0
$724$	−2.00000	+	2.00000i	−0.0743294	+	0.0743294i
$725$	−6.00000	+	6.00000i	−0.222834	+	0.222834i
$726$		0			0
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$	−6.00000	−	6.00000i	−0.222375	−	0.222375i
$729$		0			0
$730$	−4.00000			−0.148047
$731$	48.0000	−	12.0000i	1.77534	−	0.443836i
$732$		0			0
$733$		−	10.0000i		−	0.369358i	−0.982799	−	0.184679i	$-0.940875\pi$
$733$		−	10.0000i		−	0.369358i	0.982799	−	0.184679i	$-0.0591246\pi$
$734$	−3.00000	−	3.00000i	−0.110732	−	0.110732i
$735$		0			0
$736$	−3.00000	−	3.00000i	−0.110581	−	0.110581i
$737$	8.00000	−	8.00000i	0.294684	−	0.294684i
$738$		0			0
$739$		−	36.0000i		−	1.32428i	−0.749380	−	0.662141i	$-0.769648\pi$
$739$		−	36.0000i		−	1.32428i	0.749380	−	0.662141i	$-0.230352\pi$
$740$		−	24.0000i		−	0.882258i
$741$		0			0
$742$	6.00000	−	6.00000i	0.220267	−	0.220267i
$743$	−9.00000	−	9.00000i	−0.330178	−	0.330178i	0.522476	−	0.852654i	$-0.325008\pi$
$743$	−9.00000	−	9.00000i	−0.330178	−	0.330178i	−0.852654	+	0.522476i	$0.825008\pi$
$744$		0			0
$745$	−4.00000	−	4.00000i	−0.146549	−	0.146549i
$746$		−	22.0000i		−	0.805477i
$747$		0			0
$748$	10.0000	+	6.00000i	0.365636	+	0.219382i
$749$	28.0000			1.02310
$750$		0			0
$751$	9.00000	+	9.00000i	0.328415	+	0.328415i	0.851983	−	0.523569i	$-0.175400\pi$
$751$	9.00000	+	9.00000i	0.328415	+	0.328415i	−0.523569	+	0.851983i	$0.675400\pi$
$752$	10.0000			0.364662
$753$		0			0
$754$	−12.0000	+	12.0000i	−0.437014	+	0.437014i
$755$	−16.0000	+	16.0000i	−0.582300	+	0.582300i
$756$		0			0
$757$		−	2.00000i		−	0.0726912i	−0.999339	−	0.0363456i	$-0.988428\pi$
$757$		−	2.00000i		−	0.0726912i	0.999339	−	0.0363456i	$-0.0115717\pi$
$758$		0			0
$759$		0			0
$760$	8.00000	+	8.00000i	0.290191	+	0.290191i
$761$	−10.0000			−0.362500			−0.181250	−	0.983437i	$-0.558014\pi$
$761$	−10.0000			−0.362500			−0.181250	+	0.983437i	$0.558014\pi$
$762$		0			0
$763$			8.00000i			0.289619i
$764$	18.0000			0.651217
$765$		0			0
$766$	34.0000			1.22847
$767$		0			0
$768$		0			0
$769$	−4.00000			−0.144244			−0.0721218	−	0.997396i	$-0.522977\pi$
$769$	−4.00000			−0.144244			−0.0721218	+	0.997396i	$0.522977\pi$
$770$	−8.00000	−	8.00000i	−0.288300	−	0.288300i
$771$		0			0
$772$	−3.00000	+	3.00000i	−0.107972	+	0.107972i
$773$		−	14.0000i		−	0.503545i	−0.967786	−	0.251773i	$-0.918987\pi$
$773$		−	14.0000i		−	0.503545i	0.967786	−	0.251773i	$-0.0810135\pi$
$774$		0			0
$775$	9.00000	−	9.00000i	0.323290	−	0.323290i
$776$	−11.0000	+	11.0000i	−0.394877	+	0.394877i
$777$		0			0
$778$	−18.0000			−0.645331
$779$	4.00000	+	4.00000i	0.143315	+	0.143315i
$780$		0			0
$781$	4.00000			0.143131
$782$	−9.00000	+	15.0000i	−0.321839	+	0.536399i
$783$		0			0
$784$			5.00000i			0.178571i
$785$	−28.0000	−	28.0000i	−0.999363	−	0.999363i
$786$		0			0
$787$	18.0000	+	18.0000i	0.641631	+	0.641631i	0.950956	−	0.309326i	$-0.100103\pi$
$787$	18.0000	+	18.0000i	0.641631	+	0.641631i	−0.309326	+	0.950956i	$0.600103\pi$
$788$		0			0
$789$		0			0
$790$			20.0000i			0.711568i
$791$		−	22.0000i		−	0.782230i
$792$		0			0
$793$	12.0000	−	12.0000i	0.426132	−	0.426132i
$794$	18.0000	+	18.0000i	0.638796	+	0.638796i
$795$		0			0
$796$	−5.00000	−	5.00000i	−0.177220	−	0.177220i
$797$		−	42.0000i		−	1.48772i	−0.668338	−	0.743858i	$-0.732994\pi$
$797$		−	42.0000i		−	1.48772i	0.668338	−	0.743858i	$-0.267006\pi$
$798$		0			0
$799$	−10.0000	−	40.0000i	−0.353775	−	1.41510i
$800$	−3.00000			−0.106066
$801$		0			0
$802$	−5.00000	−	5.00000i	−0.176556	−	0.176556i
$803$	−4.00000			−0.141157
$804$		0			0
$805$	12.0000	−	12.0000i	0.422944	−	0.422944i
$806$	18.0000	−	18.0000i	0.634023	−	0.634023i
$807$		0			0
$808$			14.0000i			0.492518i
$809$	−17.0000	+	17.0000i	−0.597688	+	0.597688i	−0.939697	−	0.342009i	$-0.888893\pi$
$809$	−17.0000	+	17.0000i	−0.597688	+	0.597688i	0.342009	+	0.939697i	$0.388893\pi$
$810$		0			0
$811$	−4.00000	−	4.00000i	−0.140459	−	0.140459i	0.633381	−	0.773840i	$-0.281667\pi$
$811$	−4.00000	−	4.00000i	−0.140459	−	0.140459i	−0.773840	+	0.633381i	$0.781667\pi$
$812$	−4.00000			−0.140372
$813$		0			0
$814$		−	24.0000i		−	0.841200i
$815$	−48.0000			−1.68137
$816$		0			0
$817$	48.0000			1.67931
$818$			24.0000i			0.839140i
$819$		0			0
$820$	−4.00000			−0.139686
$821$	28.0000	+	28.0000i	0.977207	+	0.977207i	0.999746	−	0.0225392i	$-0.00717506\pi$
$821$	28.0000	+	28.0000i	0.977207	+	0.977207i	−0.0225392	+	0.999746i	$0.507175\pi$
$822$		0			0
$823$	−21.0000	+	21.0000i	−0.732014	+	0.732014i	−0.971018	−	0.239004i	$-0.923179\pi$
$823$	−21.0000	+	21.0000i	−0.732014	+	0.732014i	0.239004	+	0.971018i	$0.423179\pi$
$824$			2.00000i			0.0696733i
$825$		0			0
$826$		0			0
$827$	−38.0000	+	38.0000i	−1.32139	+	1.32139i	−0.408737	+	0.912652i	$0.634031\pi$
$827$	−38.0000	+	38.0000i	−1.32139	+	1.32139i	−0.912652	+	0.408737i	$0.865969\pi$
$828$		0			0
$829$	−10.0000			−0.347314			−0.173657	−	0.984806i	$-0.555558\pi$
$829$	−10.0000			−0.347314			−0.173657	+	0.984806i	$0.555558\pi$
$830$	32.0000	+	32.0000i	1.11074	+	1.11074i
$831$		0			0
$832$	−6.00000			−0.208013
$833$	20.0000	−	5.00000i	0.692959	−	0.173240i
$834$		0			0
$835$			44.0000i			1.52268i
$836$	8.00000	+	8.00000i	0.276686	+	0.276686i
$837$		0			0
$838$	−4.00000	−	4.00000i	−0.138178	−	0.138178i
$839$	−7.00000	+	7.00000i	−0.241667	+	0.241667i	−0.817539	−	0.575873i	$-0.804662\pi$
$839$	−7.00000	+	7.00000i	−0.241667	+	0.241667i	0.575873	+	0.817539i	$0.304662\pi$
$840$		0			0
$841$		−	21.0000i		−	0.724138i
$842$			22.0000i			0.758170i
$843$		0			0
$844$	18.0000	−	18.0000i	0.619586	−	0.619586i
$845$	−46.0000	−	46.0000i	−1.58245	−	1.58245i
$846$		0			0
$847$	3.00000	+	3.00000i	0.103081	+	0.103081i
$848$		−	6.00000i		−	0.206041i
$849$		0			0
$850$	3.00000	+	12.0000i	0.102899	+	0.411597i
$851$	36.0000			1.23406
$852$		0			0
$853$	28.0000	+	28.0000i	0.958702	+	0.958702i	0.999180	−	0.0404787i	$-0.0128883\pi$
$853$	28.0000	+	28.0000i	0.958702	+	0.958702i	−0.0404787	+	0.999180i	$0.512888\pi$
$854$	4.00000			0.136877
$855$		0			0
$856$	14.0000	−	14.0000i	0.478510	−	0.478510i
$857$	−9.00000	+	9.00000i	−0.307434	+	0.307434i	−0.843913	−	0.536479i	$-0.819754\pi$
$857$	−9.00000	+	9.00000i	−0.307434	+	0.307434i	0.536479	+	0.843913i	$0.319754\pi$
$858$		0			0
$859$		0			0		1.00000			$0$
$859$		0			0		−1.00000			$\pi$
$860$	−24.0000	+	24.0000i	−0.818393	+	0.818393i
$861$		0			0
$862$	11.0000	+	11.0000i	0.374661	+	0.374661i
$863$	40.0000			1.36162			0.680808	−	0.732462i	$-0.261629\pi$
$863$	40.0000			1.36162			0.680808	+	0.732462i	$0.261629\pi$
$864$		0			0
$865$		−	40.0000i		−	1.36004i
$866$	−8.00000			−0.271851
$867$		0			0
$868$	6.00000			0.203653
$869$			20.0000i			0.678454i
$870$		0			0
$871$	24.0000			0.813209
$872$	4.00000	+	4.00000i	0.135457	+	0.135457i
$873$		0			0
$874$	−12.0000	+	12.0000i	−0.405906	+	0.405906i
$875$			8.00000i			0.270449i
$876$		0			0
$877$	−20.0000	+	20.0000i	−0.675352	+	0.675352i	−0.958945	−	0.283593i	$-0.908474\pi$
$877$	−20.0000	+	20.0000i	−0.675352	+	0.675352i	0.283593	+	0.958945i	$0.408474\pi$
$878$	−29.0000	+	29.0000i	−0.978703	+	0.978703i
$879$		0			0
$880$	−8.00000			−0.269680
$881$	−11.0000	−	11.0000i	−0.370599	−	0.370599i	0.497096	−	0.867696i	$-0.334400\pi$
$881$	−11.0000	−	11.0000i	−0.370599	−	0.370599i	−0.867696	+	0.497096i	$0.834400\pi$
$882$		0			0
$883$	48.0000			1.61533			0.807664	−	0.589643i	$-0.200731\pi$
$883$	48.0000			1.61533			0.807664	+	0.589643i	$0.200731\pi$
$884$	6.00000	+	24.0000i	0.201802	+	0.807207i
$885$		0			0
$886$		−	24.0000i		−	0.806296i
$887$	7.00000	+	7.00000i	0.235037	+	0.235037i	0.814791	−	0.579754i	$-0.196851\pi$
$887$	7.00000	+	7.00000i	0.235037	+	0.235037i	−0.579754	+	0.814791i	$0.696851\pi$
$888$		0			0
$889$	−8.00000	−	8.00000i	−0.268311	−	0.268311i
$890$	24.0000	−	24.0000i	0.804482	−	0.804482i
$891$		0			0
$892$		−	22.0000i		−	0.736614i
$893$		−	40.0000i		−	1.33855i
$894$		0			0
$895$	32.0000	−	32.0000i	1.06964	−	1.06964i
$896$	−1.00000	−	1.00000i	−0.0334077	−	0.0334077i
$897$		0			0
$898$	−15.0000	−	15.0000i	−0.500556	−	0.500556i
$899$		−	12.0000i		−	0.400222i
$900$		0			0
$901$	−24.0000	+	6.00000i	−0.799556	+	0.199889i
$902$	−4.00000			−0.133185
$903$		0			0
$904$	−11.0000	−	11.0000i	−0.365855	−	0.365855i
$905$	−8.00000			−0.265929
$906$		0			0
$907$	38.0000	−	38.0000i	1.26177	−	1.26177i	0.311534	−	0.950235i	$-0.399157\pi$
$907$	38.0000	−	38.0000i	1.26177	−	1.26177i	0.950235	−	0.311534i	$-0.100843\pi$
$908$	−8.00000	+	8.00000i	−0.265489	+	0.265489i
$909$		0			0
$910$		−	24.0000i		−	0.795592i
$911$	19.0000	−	19.0000i	0.629498	−	0.629498i	−0.318444	−	0.947942i	$-0.603160\pi$
$911$	19.0000	−	19.0000i	0.629498	−	0.629498i	0.947942	+	0.318444i	$0.103160\pi$
$912$		0			0
$913$	32.0000	+	32.0000i	1.05905	+	1.05905i
$914$	8.00000			0.264616
$915$		0			0
$916$			2.00000i			0.0660819i
$917$	28.0000			0.924641
$918$		0			0
$919$	−16.0000			−0.527791			−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000			−0.527791			−0.263896	+	0.964551i	$0.585007\pi$
$920$		−	12.0000i		−	0.395628i
$921$		0			0
$922$	30.0000			0.987997
$923$	6.00000	+	6.00000i	0.197492	+	0.197492i
$924$		0			0
$925$	18.0000	−	18.0000i	0.591836	−	0.591836i
$926$			18.0000i			0.591517i
$927$		0			0
$928$	−2.00000	+	2.00000i	−0.0656532	+	0.0656532i
$929$	−13.0000	+	13.0000i	−0.426516	+	0.426516i	−0.887440	−	0.460924i	$-0.847518\pi$
$929$	−13.0000	+	13.0000i	−0.426516	+	0.426516i	0.460924	+	0.887440i	$0.347518\pi$
$930$		0			0
$931$	20.0000			0.655474
$932$	15.0000	+	15.0000i	0.491341	+	0.491341i
$933$		0			0
$934$	20.0000			0.654420
$935$	8.00000	+	32.0000i	0.261628	+	1.04651i
$936$		0			0
$937$		−	26.0000i		−	0.849383i	−0.905338	−	0.424691i	$-0.860383\pi$
$937$		−	26.0000i		−	0.849383i	0.905338	−	0.424691i	$-0.139617\pi$
$938$	4.00000	+	4.00000i	0.130605	+	0.130605i
$939$		0			0
$940$	20.0000	+	20.0000i	0.652328	+	0.652328i
$941$	−12.0000	+	12.0000i	−0.391189	+	0.391189i	−0.875111	−	0.483922i	$-0.839212\pi$
$941$	−12.0000	+	12.0000i	−0.391189	+	0.391189i	0.483922	+	0.875111i	$0.339212\pi$
$942$		0			0
$943$		−	6.00000i		−	0.195387i
$944$		0			0
$945$		0			0
$946$	−24.0000	+	24.0000i	−0.780307	+	0.780307i
$947$	−6.00000	−	6.00000i	−0.194974	−	0.194974i	0.602868	−	0.797841i	$-0.294025\pi$
$947$	−6.00000	−	6.00000i	−0.194974	−	0.194974i	−0.797841	+	0.602868i	$0.794025\pi$
$948$		0			0
$949$	−6.00000	−	6.00000i	−0.194768	−	0.194768i
$950$			12.0000i			0.389331i
$951$		0			0
$952$	−3.00000	+	5.00000i	−0.0972306	+	0.162051i
$953$	16.0000			0.518291			0.259145	−	0.965838i	$-0.416559\pi$
$953$	16.0000			0.518291			0.259145	+	0.965838i	$0.416559\pi$
$954$		0			0
$955$	36.0000	+	36.0000i	1.16493	+	1.16493i
$956$	22.0000			0.711531
$957$		0			0
$958$	5.00000	−	5.00000i	0.161543	−	0.161543i
$959$	−6.00000	+	6.00000i	−0.193750	+	0.193750i
$960$		0			0
$961$		−	13.0000i		−	0.419355i
$962$	36.0000	−	36.0000i	1.16069	−	1.16069i
$963$		0			0
$964$	−9.00000	−	9.00000i	−0.289870	−	0.289870i
$965$	−12.0000			−0.386294
$966$		0			0
$967$			22.0000i			0.707472i	0.935345	+	0.353736i	$0.115089\pi$
$967$			22.0000i			0.707472i	−0.935345	+	0.353736i	$0.884911\pi$
$968$	3.00000			0.0964237
$969$		0			0
$970$	−44.0000			−1.41275
$971$		−	12.0000i		−	0.385098i	−0.981287	−	0.192549i	$-0.938325\pi$
$971$		−	12.0000i		−	0.385098i	0.981287	−	0.192549i	$-0.0616755\pi$
$972$		0			0
$973$	28.0000			0.897639
$974$	−21.0000	−	21.0000i	−0.672883	−	0.672883i
$975$		0			0
$976$	2.00000	−	2.00000i	0.0640184	−	0.0640184i
$977$		−	34.0000i		−	1.08776i	−0.839164	−	0.543878i	$-0.816955\pi$
$977$		−	34.0000i		−	1.08776i	0.839164	−	0.543878i	$-0.183045\pi$
$978$		0			0
$979$	24.0000	−	24.0000i	0.767043	−	0.767043i
$980$	−10.0000	+	10.0000i	−0.319438	+	0.319438i
$981$		0			0
$982$	8.00000			0.255290
$983$	25.0000	+	25.0000i	0.797376	+	0.797376i	0.982681	−	0.185305i	$-0.0593273\pi$
$983$	25.0000	+	25.0000i	0.797376	+	0.797376i	−0.185305	+	0.982681i	$0.559327\pi$
$984$		0			0
$985$		0			0
$986$	10.0000	+	6.00000i	0.318465	+	0.191079i
$987$		0			0
$988$			24.0000i			0.763542i
$989$	−36.0000	−	36.0000i	−1.14473	−	1.14473i
$990$		0			0
$991$	−11.0000	−	11.0000i	−0.349427	−	0.349427i	0.510469	−	0.859896i	$-0.329472\pi$
$991$	−11.0000	−	11.0000i	−0.349427	−	0.349427i	−0.859896	+	0.510469i	$0.829472\pi$
$992$	3.00000	−	3.00000i	0.0952501	−	0.0952501i
$993$		0			0
$994$			2.00000i			0.0634361i
$995$		−	20.0000i		−	0.634043i
$996$		0			0
$997$	−30.0000	+	30.0000i	−0.950110	+	0.950110i	−0.998813	−	0.0487037i	$-0.984491\pi$
$997$	−30.0000	+	30.0000i	−0.950110	+	0.950110i	0.0487037	+	0.998813i	$0.484491\pi$
$998$	−6.00000	−	6.00000i	−0.189927	−	0.189927i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	306.2.g.c.217.1	yes	2
3.2	odd	2		306.2.g.f.217.1	yes	2
4.3	odd	2		2448.2.be.b.1441.1		2
12.11	even	2		2448.2.be.l.1441.1		2
17.2	even	8		5202.2.a.r.1.2		2
17.4	even	4	inner	306.2.g.c.55.1	✓	2
17.15	even	8		5202.2.a.r.1.1		2
51.2	odd	8		5202.2.a.ba.1.1		2
51.32	odd	8		5202.2.a.ba.1.2		2
51.38	odd	4		306.2.g.f.55.1	yes	2
68.55	odd	4		2448.2.be.b.1585.1		2
204.191	even	4		2448.2.be.l.1585.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
306.2.g.c.55.1	✓	2	17.4	even	4	inner
306.2.g.c.217.1	yes	2	1.1	even	1	trivial
306.2.g.f.55.1	yes	2	51.38	odd	4
306.2.g.f.217.1	yes	2	3.2	odd	2
2448.2.be.b.1441.1		2	4.3	odd	2
2448.2.be.b.1585.1		2	68.55	odd	4
2448.2.be.l.1441.1		2	12.11	even	2
2448.2.be.l.1585.1		2	204.191	even	4
5202.2.a.r.1.1		2	17.15	even	8
5202.2.a.r.1.2		2	17.2	even	8
5202.2.a.ba.1.1		2	51.2	odd	8
5202.2.a.ba.1.2		2	51.32	odd	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 306 = 2 \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	306.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 2.00000i) q^{5} +(1.00000 - 1.00000i) q^{7} -1.00000i q^{8} +(2.00000 - 2.00000i) q^{10} +(2.00000 - 2.00000i) q^{11} +6.00000 q^{13} +(1.00000 + 1.00000i) q^{14} +1.00000 q^{16} +(-1.00000 - 4.00000i) q^{17} -4.00000i q^{19} +(2.00000 + 2.00000i) q^{20} +(2.00000 + 2.00000i) q^{22} +(-3.00000 + 3.00000i) q^{23} +3.00000i q^{25} +6.00000i q^{26} +(-1.00000 + 1.00000i) q^{28} +(2.00000 + 2.00000i) q^{29} +(-3.00000 - 3.00000i) q^{31} +1.00000i q^{32} +(4.00000 - 1.00000i) q^{34} -4.00000 q^{35} +(-6.00000 - 6.00000i) q^{37} +4.00000 q^{38} +(-2.00000 + 2.00000i) q^{40} +(-1.00000 + 1.00000i) q^{41} +12.0000i q^{43} +(-2.00000 + 2.00000i) q^{44} +(-3.00000 - 3.00000i) q^{46} +10.0000 q^{47} +5.00000i q^{49} -3.00000 q^{50} -6.00000 q^{52} -6.00000i q^{53} -8.00000 q^{55} +(-1.00000 - 1.00000i) q^{56} +(-2.00000 + 2.00000i) q^{58} +(2.00000 - 2.00000i) q^{61} +(3.00000 - 3.00000i) q^{62} -1.00000 q^{64} +(-12.0000 - 12.0000i) q^{65} +4.00000 q^{67} +(1.00000 + 4.00000i) q^{68} -4.00000i q^{70} +(1.00000 + 1.00000i) q^{71} +(-1.00000 - 1.00000i) q^{73} +(6.00000 - 6.00000i) q^{74} +4.00000i q^{76} -4.00000i q^{77} +(-5.00000 + 5.00000i) q^{79} +(-2.00000 - 2.00000i) q^{80} +(-1.00000 - 1.00000i) q^{82} +16.0000i q^{83} +(-6.00000 + 10.0000i) q^{85} -12.0000 q^{86} +(-2.00000 - 2.00000i) q^{88} +12.0000 q^{89} +(6.00000 - 6.00000i) q^{91} +(3.00000 - 3.00000i) q^{92} +10.0000i q^{94} +(-8.00000 + 8.00000i) q^{95} +(-11.0000 - 11.0000i) q^{97} -5.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} - 4 q^{5} + 2 q^{7} + 4 q^{10} + 4 q^{11} + 12 q^{13} + 2 q^{14} + 2 q^{16} - 2 q^{17} + 4 q^{20} + 4 q^{22} - 6 q^{23} - 2 q^{28} + 4 q^{29} - 6 q^{31} + 8 q^{34} - 8 q^{35} - 12 q^{37} + 8 q^{38}+ \cdots - 10 q^{98}+O(q^{100}) \) 2 * q - 2 * q^4 - 4 * q^5 + 2 * q^7 + 4 * q^10 + 4 * q^11 + 12 * q^13 + 2 * q^14 + 2 * q^16 - 2 * q^17 + 4 * q^20 + 4 * q^22 - 6 * q^23 - 2 * q^28 + 4 * q^29 - 6 * q^31 + 8 * q^34 - 8 * q^35 - 12 * q^37 + 8 * q^38 - 4 * q^40 - 2 * q^41 - 4 * q^44 - 6 * q^46 + 20 * q^47 - 6 * q^50 - 12 * q^52 - 16 * q^55 - 2 * q^56 - 4 * q^58 + 4 * q^61 + 6 * q^62 - 2 * q^64 - 24 * q^65 + 8 * q^67 + 2 * q^68 + 2 * q^71 - 2 * q^73 + 12 * q^74 - 10 * q^79 - 4 * q^80 - 2 * q^82 - 12 * q^85 - 24 * q^86 - 4 * q^88 + 24 * q^89 + 12 * q^91 + 6 * q^92 - 16 * q^95 - 22 * q^97 - 10 * q^98

Introduction

L-functions

Modular forms

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