LMFDB - Embedded newform 315.2.j.a.46.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(46,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("315.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.j (of order $3$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	315.46
Dual form			315.2.j.a.226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 2.59808i) q^{7} +(1.00000 - 1.73205i) q^{10} +(-3.00000 + 5.19615i) q^{11} -3.00000 q^{13} +(5.00000 - 1.73205i) q^{14} +(2.00000 + 3.46410i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{19} -2.00000 q^{20} +12.0000 q^{22} +(-2.00000 - 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(3.00000 + 5.19615i) q^{26} +(-4.00000 - 3.46410i) q^{28} +8.00000 q^{29} +(-0.500000 + 0.866025i) q^{31} +(4.00000 - 6.92820i) q^{32} +8.00000 q^{34} +(-2.50000 + 0.866025i) q^{35} +(-3.50000 - 6.06218i) q^{37} +(-1.00000 + 1.73205i) q^{38} +6.00000 q^{41} +1.00000 q^{43} +(-6.00000 - 10.3923i) q^{44} +(-4.00000 + 6.92820i) q^{46} +(1.00000 + 1.73205i) q^{47} +(-6.50000 - 2.59808i) q^{49} +2.00000 q^{50} +(3.00000 - 5.19615i) q^{52} +(2.00000 - 3.46410i) q^{53} -6.00000 q^{55} +(-8.00000 - 13.8564i) q^{58} +(-4.00000 + 6.92820i) q^{59} +(7.00000 + 12.1244i) q^{61} +2.00000 q^{62} -8.00000 q^{64} +(-1.50000 - 2.59808i) q^{65} +(-3.50000 + 6.06218i) q^{67} +(-4.00000 - 6.92820i) q^{68} +(4.00000 + 3.46410i) q^{70} -6.00000 q^{71} +(-0.500000 + 0.866025i) q^{73} +(-7.00000 + 12.1244i) q^{74} +2.00000 q^{76} +(-12.0000 - 10.3923i) q^{77} +(0.500000 + 0.866025i) q^{79} +(-2.00000 + 3.46410i) q^{80} +(-6.00000 - 10.3923i) q^{82} -2.00000 q^{83} -4.00000 q^{85} +(-1.00000 - 1.73205i) q^{86} +(-6.00000 - 10.3923i) q^{89} +(1.50000 - 7.79423i) q^{91} +8.00000 q^{92} +(2.00000 - 3.46410i) q^{94} +(0.500000 - 0.866025i) q^{95} -6.00000 q^{97} +(2.00000 + 13.8564i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{4} + q^{5} - q^{7} + 2 q^{10} - 6 q^{11} - 6 q^{13} + 10 q^{14} + 4 q^{16} - 4 q^{17} - q^{19} - 4 q^{20} + 24 q^{22} - 4 q^{23} - q^{25} + 6 q^{26} - 8 q^{28} + 16 q^{29} - q^{31}+ \cdots + 4 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^4 + q^5 - q^7 + 2 * q^10 - 6 * q^11 - 6 * q^13 + 10 * q^14 + 4 * q^16 - 4 * q^17 - q^19 - 4 * q^20 + 24 * q^22 - 4 * q^23 - q^25 + 6 * q^26 - 8 * q^28 + 16 * q^29 - q^31 + 8 * q^32 + 16 * q^34 - 5 * q^35 - 7 * q^37 - 2 * q^38 + 12 * q^41 + 2 * q^43 - 12 * q^44 - 8 * q^46 + 2 * q^47 - 13 * q^49 + 4 * q^50 + 6 * q^52 + 4 * q^53 - 12 * q^55 - 16 * q^58 - 8 * q^59 + 14 * q^61 + 4 * q^62 - 16 * q^64 - 3 * q^65 - 7 * q^67 - 8 * q^68 + 8 * q^70 - 12 * q^71 - q^73 - 14 * q^74 + 4 * q^76 - 24 * q^77 + q^79 - 4 * q^80 - 12 * q^82 - 4 * q^83 - 8 * q^85 - 2 * q^86 - 12 * q^89 + 3 * q^91 + 16 * q^92 + 4 * q^94 + q^95 - 12 * q^97 + 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.00000	−	1.73205i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$2$	−1.00000	−	1.73205i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$		0			0
$9$		0			0
$10$	1.00000	−	1.73205i	0.316228	−	0.547723i
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.0829925	+	0.996550i	$0.526448\pi$
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.821541	+	0.570149i	$0.806886\pi$
$12$		0			0
$13$	−3.00000			−0.832050			−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000			−0.832050			−0.416025	+	0.909353i	$0.636577\pi$
$14$	5.00000	−	1.73205i	1.33631	−	0.462910i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	−0.999853	−	0.0171533i	$-0.994540\pi$
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	0.514782	+	0.857321i	$0.327873\pi$
$18$		0			0
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−2.00000			−0.447214
$21$		0			0
$22$	12.0000			2.55841
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.00000	+	5.19615i	0.588348	+	1.01905i
$27$		0			0
$28$	−4.00000	−	3.46410i	−0.755929	−	0.654654i
$29$	8.00000			1.48556			0.742781	−	0.669534i	$-0.233506\pi$
$29$	8.00000			1.48556			0.742781	+	0.669534i	$0.233506\pi$
$30$		0			0
$31$	−0.500000	+	0.866025i	−0.0898027	+	0.155543i	−0.907428	−	0.420208i	$-0.861957\pi$
$31$	−0.500000	+	0.866025i	−0.0898027	+	0.155543i	0.817625	+	0.575751i	$0.195290\pi$
$32$	4.00000	−	6.92820i	0.707107	−	1.22474i
$33$		0			0
$34$	8.00000			1.37199
$35$	−2.50000	+	0.866025i	−0.422577	+	0.146385i
$36$		0			0
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	−0.995998	−	0.0893706i	$-0.971514\pi$
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	0.420602	−	0.907245i	$-0.361819\pi$
$38$	−1.00000	+	1.73205i	−0.162221	+	0.280976i
$39$		0			0
$40$		0			0
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$	1.00000			0.152499			0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000			0.152499			0.0762493	+	0.997089i	$0.475706\pi$
$44$	−6.00000	−	10.3923i	−0.904534	−	1.56670i
$45$		0			0
$46$	−4.00000	+	6.92820i	−0.589768	+	1.02151i
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	0.929695	−	0.368329i	$-0.120070\pi$
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	−0.783830	+	0.620975i	$0.786737\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	2.00000			0.282843
$51$		0			0
$52$	3.00000	−	5.19615i	0.416025	−	0.720577i
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	−0.695344	−	0.718677i	$-0.744748\pi$
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	0.970065	+	0.242846i	$0.0780811\pi$
$54$		0			0
$55$	−6.00000			−0.809040
$56$		0			0
$57$		0			0
$58$	−8.00000	−	13.8564i	−1.05045	−	1.81944i
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	0.478953	+	0.877841i	$0.341016\pi$
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	−0.999709	+	0.0241347i	$0.992317\pi$
$60$		0			0
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.832240	+	0.554416i	$0.187058\pi$
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.0640184	+	0.997949i	$0.479608\pi$
$62$	2.00000			0.254000
$63$		0			0
$64$	−8.00000			−1.00000
$65$	−1.50000	−	2.59808i	−0.186052	−	0.322252i
$66$		0			0
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	−0.996659	−	0.0816792i	$-0.973972\pi$
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	0.569066	+	0.822292i	$0.307305\pi$
$68$	−4.00000	−	6.92820i	−0.485071	−	0.840168i
$69$		0			0
$70$	4.00000	+	3.46410i	0.478091	+	0.414039i
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$	−0.500000	+	0.866025i	−0.0585206	+	0.101361i	−0.893801	−	0.448463i	$-0.851972\pi$
$73$	−0.500000	+	0.866025i	−0.0585206	+	0.101361i	0.835281	+	0.549823i	$0.185305\pi$
$74$	−7.00000	+	12.1244i	−0.813733	+	1.40943i
$75$		0			0
$76$	2.00000			0.229416
$77$	−12.0000	−	10.3923i	−1.36753	−	1.18431i
$78$		0			0
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	0.892781	−	0.450490i	$-0.148751\pi$
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	−0.836527	+	0.547926i	$0.815418\pi$
$80$	−2.00000	+	3.46410i	−0.223607	+	0.387298i
$81$		0			0
$82$	−6.00000	−	10.3923i	−0.662589	−	1.14764i
$83$	−2.00000			−0.219529			−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000			−0.219529			−0.109764	+	0.993958i	$0.535010\pi$
$84$		0			0
$85$	−4.00000			−0.433861
$86$	−1.00000	−	1.73205i	−0.107833	−	0.186772i
$87$		0			0
$88$		0			0
$89$	−6.00000	−	10.3923i	−0.635999	−	1.10158i	−0.986303	−	0.164946i	$-0.947255\pi$
$89$	−6.00000	−	10.3923i	−0.635999	−	1.10158i	0.350304	−	0.936636i	$-0.386078\pi$
$90$		0			0
$91$	1.50000	−	7.79423i	0.157243	−	0.817057i
$92$	8.00000			0.834058
$93$		0			0
$94$	2.00000	−	3.46410i	0.206284	−	0.357295i
$95$	0.500000	−	0.866025i	0.0512989	−	0.0888523i
$96$		0			0
$97$	−6.00000			−0.609208			−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000			−0.609208			−0.304604	+	0.952479i	$0.598524\pi$
$98$	2.00000	+	13.8564i	0.202031	+	1.39971i
$99$		0			0
$100$	−1.00000	−	1.73205i	−0.100000	−	0.173205i
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	−0.999996	−	0.00286291i	$-0.999089\pi$
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	0.502477	+	0.864590i	$0.332422\pi$
$102$		0			0
$103$	9.50000	+	16.4545i	0.936063	+	1.62131i	0.772728	+	0.634738i	$0.218892\pi$
$103$	9.50000	+	16.4545i	0.936063	+	1.62131i	0.163335	+	0.986571i	$0.447775\pi$
$104$		0			0
$105$		0			0
$106$	−8.00000			−0.777029
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	0.995474	+	0.0950377i	$0.0302972\pi$
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	−0.415432	+	0.909624i	$0.636370\pi$
$108$		0			0
$109$	7.50000	−	12.9904i	0.718370	−	1.24425i	−0.243276	−	0.969957i	$-0.578222\pi$
$109$	7.50000	−	12.9904i	0.718370	−	1.24425i	0.961645	−	0.274296i	$-0.0884447\pi$
$110$	6.00000	+	10.3923i	0.572078	+	0.990867i
$111$		0			0
$112$	−10.0000	+	3.46410i	−0.944911	+	0.327327i
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		0			0
$115$	2.00000	−	3.46410i	0.186501	−	0.323029i
$116$	−8.00000	+	13.8564i	−0.742781	+	1.28654i
$117$		0			0
$118$	16.0000			1.47292
$119$	−8.00000	−	6.92820i	−0.733359	−	0.635107i
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$	14.0000	−	24.2487i	1.26750	−	2.19538i
$123$		0			0
$124$	−1.00000	−	1.73205i	−0.0898027	−	0.155543i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	5.00000			0.443678			0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000			0.443678			0.221839	+	0.975083i	$0.428794\pi$
$128$		0			0
$129$		0			0
$130$	−3.00000	+	5.19615i	−0.263117	+	0.455733i
$131$	1.00000	+	1.73205i	0.0873704	+	0.151330i	0.906399	−	0.422423i	$-0.138820\pi$
$131$	1.00000	+	1.73205i	0.0873704	+	0.151330i	−0.819028	+	0.573753i	$0.805487\pi$
$132$		0			0
$133$	2.50000	−	0.866025i	0.216777	−	0.0750939i
$134$	14.0000			1.20942
$135$		0			0
$136$		0			0
$137$	4.00000	−	6.92820i	0.341743	−	0.591916i	−0.643013	−	0.765855i	$-0.722316\pi$
$137$	4.00000	−	6.92820i	0.341743	−	0.591916i	0.984757	+	0.173939i	$0.0556494\pi$
$138$		0			0
$139$	21.0000			1.78120			0.890598	−	0.454791i	$-0.150286\pi$
$139$	21.0000			1.78120			0.890598	+	0.454791i	$0.150286\pi$
$140$	1.00000	−	5.19615i	0.0845154	−	0.439155i
$141$		0			0
$142$	6.00000	+	10.3923i	0.503509	+	0.872103i
$143$	9.00000	−	15.5885i	0.752618	−	1.30357i
$144$		0			0
$145$	4.00000	+	6.92820i	0.332182	+	0.575356i
$146$	2.00000			0.165521
$147$		0			0
$148$	14.0000			1.15079
$149$	−2.00000	−	3.46410i	−0.163846	−	0.283790i	0.772399	−	0.635138i	$-0.219057\pi$
$149$	−2.00000	−	3.46410i	−0.163846	−	0.283790i	−0.936245	+	0.351348i	$0.885723\pi$
$150$		0			0
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	−0.981617	−	0.190864i	$-0.938871\pi$
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	0.656101	+	0.754673i	$0.272204\pi$
$152$		0			0
$153$		0			0
$154$	−6.00000	+	31.1769i	−0.483494	+	2.51231i
$155$	−1.00000			−0.0803219
$156$		0			0
$157$	−5.00000	+	8.66025i	−0.399043	+	0.691164i	−0.993608	−	0.112884i	$-0.963991\pi$
$157$	−5.00000	+	8.66025i	−0.399043	+	0.691164i	0.594565	+	0.804048i	$0.297324\pi$
$158$	1.00000	−	1.73205i	0.0795557	−	0.137795i
$159$		0			0
$160$	8.00000			0.632456
$161$	10.0000	−	3.46410i	0.788110	−	0.273009i
$162$		0			0
$163$	6.00000	+	10.3923i	0.469956	+	0.813988i	0.999410	−	0.0343508i	$-0.0109363\pi$
$163$	6.00000	+	10.3923i	0.469956	+	0.813988i	−0.529454	+	0.848339i	$0.677603\pi$
$164$	−6.00000	+	10.3923i	−0.468521	+	0.811503i
$165$		0			0
$166$	2.00000	+	3.46410i	0.155230	+	0.268866i
$167$	10.0000			0.773823			0.386912	−	0.922117i	$-0.373542\pi$
$167$	10.0000			0.773823			0.386912	+	0.922117i	$0.373542\pi$
$168$		0			0
$169$	−4.00000			−0.307692
$170$	4.00000	+	6.92820i	0.306786	+	0.531369i
$171$		0			0
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	12.0000	+	20.7846i	0.912343	+	1.58022i	0.810745	+	0.585399i	$0.199062\pi$
$173$	12.0000	+	20.7846i	0.912343	+	1.58022i	0.101598	+	0.994826i	$0.467605\pi$
$174$		0			0
$175$	−2.00000	−	1.73205i	−0.151186	−	0.130931i
$176$	−24.0000			−1.80907
$177$		0			0
$178$	−12.0000	+	20.7846i	−0.899438	+	1.55787i
$179$	9.00000	−	15.5885i	0.672692	−	1.16514i	−0.304446	−	0.952529i	$-0.598471\pi$
$179$	9.00000	−	15.5885i	0.672692	−	1.16514i	0.977138	−	0.212607i	$-0.0681952\pi$
$180$		0			0
$181$	13.0000			0.966282			0.483141	−	0.875542i	$-0.339496\pi$
$181$	13.0000			0.966282			0.483141	+	0.875542i	$0.339496\pi$
$182$	−15.0000	+	5.19615i	−1.11187	+	0.385164i
$183$		0			0
$184$		0			0
$185$	3.50000	−	6.06218i	0.257325	−	0.445700i
$186$		0			0
$187$	−12.0000	−	20.7846i	−0.877527	−	1.51992i
$188$	−4.00000			−0.291730
$189$		0			0
$190$	−2.00000			−0.145095
$191$	5.00000	+	8.66025i	0.361787	+	0.626634i	0.988255	−	0.152813i	$-0.0488333\pi$
$191$	5.00000	+	8.66025i	0.361787	+	0.626634i	−0.626468	+	0.779447i	$0.715500\pi$
$192$		0			0
$193$	4.50000	−	7.79423i	0.323917	−	0.561041i	−0.657376	−	0.753563i	$-0.728333\pi$
$193$	4.50000	−	7.79423i	0.323917	−	0.561041i	0.981293	+	0.192522i	$0.0616668\pi$
$194$	6.00000	+	10.3923i	0.430775	+	0.746124i
$195$		0			0
$196$	11.0000	−	8.66025i	0.785714	−	0.618590i
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$		0			0
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	−0.972257	−	0.233915i	$-0.924846\pi$
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	0.688705	+	0.725042i	$0.258180\pi$
$200$		0			0
$201$		0			0
$202$	20.0000			1.40720
$203$	−4.00000	+	20.7846i	−0.280745	+	1.45879i
$204$		0			0
$205$	3.00000	+	5.19615i	0.209529	+	0.362915i
$206$	19.0000	−	32.9090i	1.32379	−	2.29288i
$207$		0			0
$208$	−6.00000	−	10.3923i	−0.416025	−	0.720577i
$209$	6.00000			0.415029
$210$		0			0
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$	4.00000	+	6.92820i	0.274721	+	0.475831i
$213$		0			0
$214$	12.0000	−	20.7846i	0.820303	−	1.42081i
$215$	0.500000	+	0.866025i	0.0340997	+	0.0590624i
$216$		0			0
$217$	−2.00000	−	1.73205i	−0.135769	−	0.117579i
$218$	−30.0000			−2.03186
$219$		0			0
$220$	6.00000	−	10.3923i	0.404520	−	0.700649i
$221$	6.00000	−	10.3923i	0.403604	−	0.699062i
$222$		0			0
$223$	−24.0000			−1.60716			−0.803579	−	0.595198i	$-0.797074\pi$
$223$	−24.0000			−1.60716			−0.803579	+	0.595198i	$0.797074\pi$
$224$	16.0000	+	13.8564i	1.06904	+	0.925820i
$225$		0			0
$226$	−6.00000	−	10.3923i	−0.399114	−	0.691286i
$227$	−5.00000	+	8.66025i	−0.331862	+	0.574801i	−0.982877	−	0.184263i	$-0.941010\pi$
$227$	−5.00000	+	8.66025i	−0.331862	+	0.574801i	0.651015	+	0.759065i	$0.274343\pi$
$228$		0			0
$229$	−6.50000	−	11.2583i	−0.429532	−	0.743971i	0.567300	−	0.823511i	$-0.307988\pi$
$229$	−6.50000	−	11.2583i	−0.429532	−	0.743971i	−0.996832	+	0.0795401i	$0.974655\pi$
$230$	−8.00000			−0.527504
$231$		0			0
$232$		0			0
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$		0			0
$235$	−1.00000	+	1.73205i	−0.0652328	+	0.112987i
$236$	−8.00000	−	13.8564i	−0.520756	−	0.901975i
$237$		0			0
$238$	−4.00000	+	20.7846i	−0.259281	+	1.34727i
$239$	−14.0000			−0.905585			−0.452792	−	0.891616i	$-0.649572\pi$
$239$	−14.0000			−0.905585			−0.452792	+	0.891616i	$0.649572\pi$
$240$		0			0
$241$	9.00000	−	15.5885i	0.579741	−	1.00414i	−0.415768	−	0.909471i	$-0.636487\pi$
$241$	9.00000	−	15.5885i	0.579741	−	1.00414i	0.995509	−	0.0946700i	$-0.0301796\pi$
$242$	−25.0000	+	43.3013i	−1.60706	+	2.78351i
$243$		0			0
$244$	−28.0000			−1.79252
$245$	−1.00000	−	6.92820i	−0.0638877	−	0.442627i
$246$		0			0
$247$	1.50000	+	2.59808i	0.0954427	+	0.165312i
$248$		0			0
$249$		0			0
$250$	1.00000	+	1.73205i	0.0632456	+	0.109545i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	24.0000			1.50887
$254$	−5.00000	−	8.66025i	−0.313728	−	0.543393i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	−0.997374	−	0.0724199i	$-0.976928\pi$
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	0.435970	−	0.899961i	$-0.356405\pi$
$258$		0			0
$259$	17.5000	−	6.06218i	1.08740	−	0.376685i
$260$	6.00000			0.372104
$261$		0			0
$262$	2.00000	−	3.46410i	0.123560	−	0.214013i
$263$	2.00000	−	3.46410i	0.123325	−	0.213606i	−0.797752	−	0.602986i	$-0.793977\pi$
$263$	2.00000	−	3.46410i	0.123325	−	0.213606i	0.921077	+	0.389380i	$0.127311\pi$
$264$		0			0
$265$	4.00000			0.245718
$266$	−4.00000	−	3.46410i	−0.245256	−	0.212398i
$267$		0			0
$268$	−7.00000	−	12.1244i	−0.427593	−	0.740613i
$269$	−5.00000	+	8.66025i	−0.304855	+	0.528025i	−0.977229	−	0.212187i	$-0.931941\pi$
$269$	−5.00000	+	8.66025i	−0.304855	+	0.528025i	0.672374	+	0.740212i	$0.265275\pi$
$270$		0			0
$271$	12.0000	+	20.7846i	0.728948	+	1.26258i	0.957328	+	0.289003i	$0.0933238\pi$
$271$	12.0000	+	20.7846i	0.728948	+	1.26258i	−0.228380	+	0.973572i	$0.573343\pi$
$272$	−16.0000			−0.970143
$273$		0			0
$274$	−16.0000			−0.966595
$275$	−3.00000	−	5.19615i	−0.180907	−	0.313340i
$276$		0			0
$277$	3.50000	−	6.06218i	0.210295	−	0.364241i	−0.741512	−	0.670940i	$-0.765891\pi$
$277$	3.50000	−	6.06218i	0.210295	−	0.364241i	0.951807	+	0.306699i	$0.0992243\pi$
$278$	−21.0000	−	36.3731i	−1.25950	−	2.18151i
$279$		0			0
$280$		0			0
$281$	12.0000			0.715860			0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000			0.715860			0.357930	+	0.933748i	$0.383483\pi$
$282$		0			0
$283$	3.50000	−	6.06218i	0.208053	−	0.360359i	−0.743048	−	0.669238i	$-0.766621\pi$
$283$	3.50000	−	6.06218i	0.208053	−	0.360359i	0.951101	+	0.308879i	$0.0999539\pi$
$284$	6.00000	−	10.3923i	0.356034	−	0.616670i
$285$		0			0
$286$	−36.0000			−2.12872
$287$	−3.00000	+	15.5885i	−0.177084	+	0.920158i
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	8.00000	−	13.8564i	0.469776	−	0.813676i
$291$		0			0
$292$	−1.00000	−	1.73205i	−0.0585206	−	0.101361i
$293$	16.0000			0.934730			0.467365	−	0.884064i	$-0.345203\pi$
$293$	16.0000			0.934730			0.467365	+	0.884064i	$0.345203\pi$
$294$		0			0
$295$	−8.00000			−0.465778
$296$		0			0
$297$		0			0
$298$	−4.00000	+	6.92820i	−0.231714	+	0.401340i
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$		0			0
$301$	−0.500000	+	2.59808i	−0.0288195	+	0.149751i
$302$	16.0000			0.920697
$303$		0			0
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$	−7.00000	+	12.1244i	−0.400819	+	0.694239i
$306$		0			0
$307$	3.00000			0.171219			0.0856095	−	0.996329i	$-0.472716\pi$
$307$	3.00000			0.171219			0.0856095	+	0.996329i	$0.472716\pi$
$308$	30.0000	−	10.3923i	1.70941	−	0.592157i
$309$		0			0
$310$	1.00000	+	1.73205i	0.0567962	+	0.0983739i
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	−0.768345	−	0.640036i	$-0.778920\pi$
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	0.938460	+	0.345389i	$0.112253\pi$
$312$		0			0
$313$	−5.50000	−	9.52628i	−0.310878	−	0.538457i	0.667674	−	0.744453i	$-0.267290\pi$
$313$	−5.50000	−	9.52628i	−0.310878	−	0.538457i	−0.978553	+	0.205996i	$0.933957\pi$
$314$	20.0000			1.12867
$315$		0			0
$316$	−2.00000			−0.112509
$317$	10.0000	+	17.3205i	0.561656	+	0.972817i	0.997352	+	0.0727229i	$0.0231689\pi$
$317$	10.0000	+	17.3205i	0.561656	+	0.972817i	−0.435696	+	0.900094i	$0.643498\pi$
$318$		0			0
$319$	−24.0000	+	41.5692i	−1.34374	+	2.32743i
$320$	−4.00000	−	6.92820i	−0.223607	−	0.387298i
$321$		0			0
$322$	−16.0000	−	13.8564i	−0.891645	−	0.772187i
$323$	4.00000			0.222566
$324$		0			0
$325$	1.50000	−	2.59808i	0.0832050	−	0.144115i
$326$	12.0000	−	20.7846i	0.664619	−	1.15115i
$327$		0			0
$328$		0			0
$329$	−5.00000	+	1.73205i	−0.275659	+	0.0954911i
$330$		0			0
$331$	4.50000	+	7.79423i	0.247342	+	0.428410i	0.962788	−	0.270259i	$-0.0871094\pi$
$331$	4.50000	+	7.79423i	0.247342	+	0.428410i	−0.715445	+	0.698669i	$0.753776\pi$
$332$	2.00000	−	3.46410i	0.109764	−	0.190117i
$333$		0			0
$334$	−10.0000	−	17.3205i	−0.547176	−	0.947736i
$335$	−7.00000			−0.382451
$336$		0			0
$337$	25.0000			1.36184			0.680918	−	0.732359i	$-0.261581\pi$
$337$	25.0000			1.36184			0.680918	+	0.732359i	$0.261581\pi$
$338$	4.00000	+	6.92820i	0.217571	+	0.376845i
$339$		0			0
$340$	4.00000	−	6.92820i	0.216930	−	0.375735i
$341$	−3.00000	−	5.19615i	−0.162459	−	0.281387i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$		0			0
$345$		0			0
$346$	24.0000	−	41.5692i	1.29025	−	2.23478i
$347$	8.00000	−	13.8564i	0.429463	−	0.743851i	−0.567363	−	0.823468i	$-0.692036\pi$
$347$	8.00000	−	13.8564i	0.429463	−	0.743851i	0.996826	+	0.0796169i	$0.0253697\pi$
$348$		0			0
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$	−1.00000	+	5.19615i	−0.0534522	+	0.277746i
$351$		0			0
$352$	24.0000	+	41.5692i	1.27920	+	2.21565i
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	−0.999711	−	0.0240566i	$-0.992342\pi$
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	0.520689	+	0.853746i	$0.325675\pi$
$354$		0			0
$355$	−3.00000	−	5.19615i	−0.159223	−	0.275783i
$356$	24.0000			1.27200
$357$		0			0
$358$	−36.0000			−1.90266
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	−0.986865	−	0.161546i	$-0.948352\pi$
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	0.353529	−	0.935423i	$-0.384981\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	−13.0000	−	22.5167i	−0.683265	−	1.18345i
$363$		0			0
$364$	12.0000	+	10.3923i	0.628971	+	0.544705i
$365$	−1.00000			−0.0523424
$366$		0			0
$367$	−9.50000	+	16.4545i	−0.495896	+	0.858917i	−0.999989	−	0.00473247i	$-0.998494\pi$
$367$	−9.50000	+	16.4545i	−0.495896	+	0.858917i	0.504093	+	0.863649i	$0.331827\pi$
$368$	8.00000	−	13.8564i	0.417029	−	0.722315i
$369$		0			0
$370$	−14.0000			−0.727825
$371$	8.00000	+	6.92820i	0.415339	+	0.359694i
$372$		0			0
$373$	−5.50000	−	9.52628i	−0.284779	−	0.493252i	0.687776	−	0.725923i	$-0.258587\pi$
$373$	−5.50000	−	9.52628i	−0.284779	−	0.493252i	−0.972556	+	0.232671i	$0.925254\pi$
$374$	−24.0000	+	41.5692i	−1.24101	+	2.14949i
$375$		0			0
$376$		0			0
$377$	−24.0000			−1.23606
$378$		0			0
$379$	11.0000			0.565032			0.282516	−	0.959263i	$-0.408831\pi$
$379$	11.0000			0.565032			0.282516	+	0.959263i	$0.408831\pi$
$380$	1.00000	+	1.73205i	0.0512989	+	0.0888523i
$381$		0			0
$382$	10.0000	−	17.3205i	0.511645	−	0.886194i
$383$	14.0000	+	24.2487i	0.715367	+	1.23905i	0.962818	+	0.270151i	$0.0870736\pi$
$383$	14.0000	+	24.2487i	0.715367	+	1.23905i	−0.247451	+	0.968900i	$0.579593\pi$
$384$		0			0
$385$	3.00000	−	15.5885i	0.152894	−	0.794461i
$386$	−18.0000			−0.916176
$387$		0			0
$388$	6.00000	−	10.3923i	0.304604	−	0.527589i
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	−0.779895	−	0.625910i	$-0.784728\pi$
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	0.932002	+	0.362454i	$0.118061\pi$
$390$		0			0
$391$	16.0000			0.809155
$392$		0			0
$393$		0			0
$394$	12.0000	+	20.7846i	0.604551	+	1.04711i
$395$	−0.500000	+	0.866025i	−0.0251577	+	0.0435745i
$396$		0			0
$397$	18.5000	+	32.0429i	0.928488	+	1.60819i	0.785853	+	0.618414i	$0.212224\pi$
$397$	18.5000	+	32.0429i	0.928488	+	1.60819i	0.142636	+	0.989775i	$0.454442\pi$
$398$	16.0000			0.802008
$399$		0			0
$400$	−4.00000			−0.200000
$401$	−6.00000	−	10.3923i	−0.299626	−	0.518967i	0.676425	−	0.736512i	$-0.263528\pi$
$401$	−6.00000	−	10.3923i	−0.299626	−	0.518967i	−0.976050	+	0.217545i	$0.930195\pi$
$402$		0			0
$403$	1.50000	−	2.59808i	0.0747203	−	0.129419i
$404$	−10.0000	−	17.3205i	−0.497519	−	0.861727i
$405$		0			0
$406$	40.0000	−	13.8564i	1.98517	−	0.687682i
$407$	42.0000			2.08186
$408$		0			0
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	−0.921192	−	0.389109i	$-0.872783\pi$
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	0.797574	+	0.603220i	$0.206116\pi$
$410$	6.00000	−	10.3923i	0.296319	−	0.513239i
$411$		0			0
$412$	−38.0000			−1.87213
$413$	−16.0000	−	13.8564i	−0.787309	−	0.681829i
$414$		0			0
$415$	−1.00000	−	1.73205i	−0.0490881	−	0.0850230i
$416$	−12.0000	+	20.7846i	−0.588348	+	1.01905i
$417$		0			0
$418$	−6.00000	−	10.3923i	−0.293470	−	0.508304i
$419$	−6.00000			−0.293119			−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000			−0.293119			−0.146560	+	0.989202i	$0.546820\pi$
$420$		0			0
$421$	1.00000			0.0487370			0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000			0.0487370			0.0243685	+	0.999703i	$0.492242\pi$
$422$	20.0000	+	34.6410i	0.973585	+	1.68630i
$423$		0			0
$424$		0			0
$425$	−2.00000	−	3.46410i	−0.0970143	−	0.168034i
$426$		0			0
$427$	−35.0000	+	12.1244i	−1.69377	+	0.586739i
$428$	−24.0000			−1.16008
$429$		0			0
$430$	1.00000	−	1.73205i	0.0482243	−	0.0835269i
$431$	−1.00000	+	1.73205i	−0.0481683	+	0.0834300i	−0.889104	−	0.457705i	$-0.848672\pi$
$431$	−1.00000	+	1.73205i	−0.0481683	+	0.0834300i	0.840936	+	0.541135i	$0.182005\pi$
$432$		0			0
$433$	−5.00000			−0.240285			−0.120142	−	0.992757i	$-0.538335\pi$
$433$	−5.00000			−0.240285			−0.120142	+	0.992757i	$0.538335\pi$
$434$	−1.00000	+	5.19615i	−0.0480015	+	0.249423i
$435$		0			0
$436$	15.0000	+	25.9808i	0.718370	+	1.24425i
$437$	−2.00000	+	3.46410i	−0.0956730	+	0.165710i
$438$		0			0
$439$	−8.00000	−	13.8564i	−0.381819	−	0.661330i	0.609503	−	0.792784i	$-0.291369\pi$
$439$	−8.00000	−	13.8564i	−0.381819	−	0.661330i	−0.991322	+	0.131453i	$0.958036\pi$
$440$		0			0
$441$		0			0
$442$	−24.0000			−1.14156
$443$	−18.0000	−	31.1769i	−0.855206	−	1.48126i	−0.876454	−	0.481486i	$-0.840097\pi$
$443$	−18.0000	−	31.1769i	−0.855206	−	1.48126i	0.0212481	−	0.999774i	$-0.493236\pi$
$444$		0			0
$445$	6.00000	−	10.3923i	0.284427	−	0.492642i
$446$	24.0000	+	41.5692i	1.13643	+	1.96836i
$447$		0			0
$448$	4.00000	−	20.7846i	0.188982	−	0.981981i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$	−18.0000	+	31.1769i	−0.847587	+	1.46806i
$452$	−6.00000	+	10.3923i	−0.282216	+	0.488813i
$453$		0			0
$454$	20.0000			0.938647
$455$	7.50000	−	2.59808i	0.351605	−	0.121800i
$456$		0			0
$457$	7.50000	+	12.9904i	0.350835	+	0.607664i	0.986396	−	0.164386i	$-0.0525644\pi$
$457$	7.50000	+	12.9904i	0.350835	+	0.607664i	−0.635561	+	0.772051i	$0.719231\pi$
$458$	−13.0000	+	22.5167i	−0.607450	+	1.05213i
$459$		0			0
$460$	4.00000	+	6.92820i	0.186501	+	0.323029i
$461$	8.00000			0.372597			0.186299	−	0.982493i	$-0.440351\pi$
$461$	8.00000			0.372597			0.186299	+	0.982493i	$0.440351\pi$
$462$		0			0
$463$	3.00000			0.139422			0.0697109	−	0.997567i	$-0.477792\pi$
$463$	3.00000			0.139422			0.0697109	+	0.997567i	$0.477792\pi$
$464$	16.0000	+	27.7128i	0.742781	+	1.28654i
$465$		0			0
$466$	6.00000	−	10.3923i	0.277945	−	0.481414i
$467$	11.0000	+	19.0526i	0.509019	+	0.881647i	0.999945	+	0.0104461i	$0.00332515\pi$
$467$	11.0000	+	19.0526i	0.509019	+	0.881647i	−0.490926	+	0.871201i	$0.663342\pi$
$468$		0			0
$469$	−14.0000	−	12.1244i	−0.646460	−	0.559851i
$470$	4.00000			0.184506
$471$		0			0
$472$		0			0
$473$	−3.00000	+	5.19615i	−0.137940	+	0.238919i
$474$		0			0
$475$	1.00000			0.0458831
$476$	20.0000	−	6.92820i	0.916698	−	0.317554i
$477$		0			0
$478$	14.0000	+	24.2487i	0.640345	+	1.10911i
$479$	−2.00000	+	3.46410i	−0.0913823	+	0.158279i	−0.908093	−	0.418769i	$-0.862462\pi$
$479$	−2.00000	+	3.46410i	−0.0913823	+	0.158279i	0.816711	+	0.577047i	$0.195795\pi$
$480$		0			0
$481$	10.5000	+	18.1865i	0.478759	+	0.829235i
$482$	−36.0000			−1.63976
$483$		0			0
$484$	50.0000			2.27273
$485$	−3.00000	−	5.19615i	−0.136223	−	0.235945i
$486$		0			0
$487$	6.50000	−	11.2583i	0.294543	−	0.510164i	−0.680335	−	0.732901i	$-0.738166\pi$
$487$	6.50000	−	11.2583i	0.294543	−	0.510164i	0.974879	+	0.222737i	$0.0714992\pi$
$488$		0			0
$489$		0			0
$490$	−11.0000	+	8.66025i	−0.496929	+	0.391230i
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$		0			0
$493$	−16.0000	+	27.7128i	−0.720604	+	1.24812i
$494$	3.00000	−	5.19615i	0.134976	−	0.233786i
$495$		0			0
$496$	−4.00000			−0.179605
$497$	3.00000	−	15.5885i	0.134568	−	0.699238i
$498$		0			0
$499$	−14.5000	−	25.1147i	−0.649109	−	1.12429i	−0.983336	−	0.181797i	$-0.941809\pi$
$499$	−14.5000	−	25.1147i	−0.649109	−	1.12429i	0.334227	−	0.942493i	$-0.391525\pi$
$500$	1.00000	−	1.73205i	0.0447214	−	0.0774597i
$501$		0			0
$502$	12.0000	+	20.7846i	0.535586	+	0.927663i
$503$	2.00000			0.0891756			0.0445878	−	0.999005i	$-0.485803\pi$
$503$	2.00000			0.0891756			0.0445878	+	0.999005i	$0.485803\pi$
$504$		0			0
$505$	−10.0000			−0.444994
$506$	−24.0000	−	41.5692i	−1.06693	−	1.84798i
$507$		0			0
$508$	−5.00000	+	8.66025i	−0.221839	+	0.384237i
$509$	5.00000	+	8.66025i	0.221621	+	0.383859i	0.955300	−	0.295637i	$-0.0955319\pi$
$509$	5.00000	+	8.66025i	0.221621	+	0.383859i	−0.733679	+	0.679496i	$0.762199\pi$
$510$		0			0
$511$	−2.00000	−	1.73205i	−0.0884748	−	0.0766214i
$512$	32.0000			1.41421
$513$		0			0
$514$	−18.0000	+	31.1769i	−0.793946	+	1.37515i
$515$	−9.50000	+	16.4545i	−0.418620	+	0.725071i
$516$		0			0
$517$	−12.0000			−0.527759
$518$	−28.0000	−	24.2487i	−1.23025	−	1.06543i
$519$		0			0
$520$		0			0
$521$	2.00000	−	3.46410i	0.0876216	−	0.151765i	−0.818884	−	0.573959i	$-0.805407\pi$
$521$	2.00000	−	3.46410i	0.0876216	−	0.151765i	0.906505	+	0.422194i	$0.138740\pi$
$522$		0			0
$523$	−5.50000	−	9.52628i	−0.240498	−	0.416555i	0.720358	−	0.693602i	$-0.243977\pi$
$523$	−5.50000	−	9.52628i	−0.240498	−	0.416555i	−0.960856	+	0.277047i	$0.910644\pi$
$524$	−4.00000			−0.174741
$525$		0			0
$526$	−8.00000			−0.348817
$527$	−2.00000	−	3.46410i	−0.0871214	−	0.150899i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	−4.00000	−	6.92820i	−0.173749	−	0.300942i
$531$		0			0
$532$	−1.00000	+	5.19615i	−0.0433555	+	0.225282i
$533$	−18.0000			−0.779667
$534$		0			0
$535$	−6.00000	+	10.3923i	−0.259403	+	0.449299i
$536$		0			0
$537$		0			0
$538$	20.0000			0.862261
$539$	33.0000	−	25.9808i	1.42141	−	1.11907i
$540$		0			0
$541$	1.50000	+	2.59808i	0.0644900	+	0.111700i	0.896468	−	0.443109i	$-0.146125\pi$
$541$	1.50000	+	2.59808i	0.0644900	+	0.111700i	−0.831978	+	0.554809i	$0.812791\pi$
$542$	24.0000	−	41.5692i	1.03089	−	1.78555i
$543$		0			0
$544$	16.0000	+	27.7128i	0.685994	+	1.18818i
$545$	15.0000			0.642529
$546$		0			0
$547$	36.0000			1.53925			0.769624	−	0.638497i	$-0.220443\pi$
$547$	36.0000			1.53925			0.769624	+	0.638497i	$0.220443\pi$
$548$	8.00000	+	13.8564i	0.341743	+	0.591916i
$549$		0			0
$550$	−6.00000	+	10.3923i	−0.255841	+	0.443129i
$551$	−4.00000	−	6.92820i	−0.170406	−	0.295151i
$552$		0			0
$553$	−2.50000	+	0.866025i	−0.106311	+	0.0368271i
$554$	−14.0000			−0.594803
$555$		0			0
$556$	−21.0000	+	36.3731i	−0.890598	+	1.54256i
$557$	−5.00000	+	8.66025i	−0.211857	+	0.366947i	−0.952296	−	0.305177i	$-0.901284\pi$
$557$	−5.00000	+	8.66025i	−0.211857	+	0.366947i	0.740439	+	0.672124i	$0.234618\pi$
$558$		0			0
$559$	−3.00000			−0.126886
$560$	−8.00000	−	6.92820i	−0.338062	−	0.292770i
$561$		0			0
$562$	−12.0000	−	20.7846i	−0.506189	−	0.876746i
$563$	−13.0000	+	22.5167i	−0.547885	+	0.948964i	0.450535	+	0.892759i	$0.351233\pi$
$563$	−13.0000	+	22.5167i	−0.547885	+	0.948964i	−0.998419	+	0.0562051i	$0.982100\pi$
$564$		0			0
$565$	3.00000	+	5.19615i	0.126211	+	0.218604i
$566$	−14.0000			−0.588464
$567$		0			0
$568$		0			0
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	0.990668	−	0.136295i	$-0.0435194\pi$
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	−0.613369	+	0.789797i	$0.710186\pi$
$570$		0			0
$571$	1.50000	−	2.59808i	0.0627730	−	0.108726i	−0.832931	−	0.553377i	$-0.813339\pi$
$571$	1.50000	−	2.59808i	0.0627730	−	0.108726i	0.895704	+	0.444651i	$0.146672\pi$
$572$	18.0000	+	31.1769i	0.752618	+	1.30357i
$573$		0			0
$574$	30.0000	−	10.3923i	1.25218	−	0.433766i
$575$	4.00000			0.166812
$576$		0			0
$577$	14.5000	−	25.1147i	0.603643	−	1.04554i	−0.388621	−	0.921397i	$-0.627049\pi$
$577$	14.5000	−	25.1147i	0.603643	−	1.04554i	0.992264	−	0.124143i	$-0.0396180\pi$
$578$	1.00000	−	1.73205i	0.0415945	−	0.0720438i
$579$		0			0
$580$	−16.0000			−0.664364
$581$	1.00000	−	5.19615i	0.0414870	−	0.215573i
$582$		0			0
$583$	12.0000	+	20.7846i	0.496989	+	0.860811i
$584$		0			0
$585$		0			0
$586$	−16.0000	−	27.7128i	−0.660954	−	1.14481i
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	1.00000			0.0412043
$590$	8.00000	+	13.8564i	0.329355	+	0.570459i
$591$		0			0
$592$	14.0000	−	24.2487i	0.575396	−	0.996616i
$593$	−9.00000	−	15.5885i	−0.369586	−	0.640141i	0.619915	−	0.784669i	$-0.287167\pi$
$593$	−9.00000	−	15.5885i	−0.369586	−	0.640141i	−0.989501	+	0.144528i	$0.953834\pi$
$594$		0			0
$595$	2.00000	−	10.3923i	0.0819920	−	0.426043i
$596$	8.00000			0.327693
$597$		0			0
$598$	12.0000	−	20.7846i	0.490716	−	0.849946i
$599$	−2.00000	+	3.46410i	−0.0817178	+	0.141539i	−0.903988	−	0.427558i	$-0.859374\pi$
$599$	−2.00000	+	3.46410i	−0.0817178	+	0.141539i	0.822270	+	0.569097i	$0.192707\pi$
$600$		0			0
$601$	−33.0000			−1.34610			−0.673049	−	0.739598i	$-0.735016\pi$
$601$	−33.0000			−1.34610			−0.673049	+	0.739598i	$0.735016\pi$
$602$	5.00000	−	1.73205i	0.203785	−	0.0705931i
$603$		0			0
$604$	−8.00000	−	13.8564i	−0.325515	−	0.563809i
$605$	12.5000	−	21.6506i	0.508197	−	0.880223i
$606$		0			0
$607$	−17.5000	−	30.3109i	−0.710303	−	1.23028i	−0.964743	−	0.263193i	$-0.915225\pi$
$607$	−17.5000	−	30.3109i	−0.710303	−	1.23028i	0.254440	−	0.967088i	$-0.418109\pi$
$608$	−8.00000			−0.324443
$609$		0			0
$610$	28.0000			1.13369
$611$	−3.00000	−	5.19615i	−0.121367	−	0.210214i
$612$		0			0
$613$	15.0000	−	25.9808i	0.605844	−	1.04935i	−0.386073	−	0.922468i	$-0.626169\pi$
$613$	15.0000	−	25.9808i	0.605844	−	1.04935i	0.991917	−	0.126885i	$-0.0404979\pi$
$614$	−3.00000	−	5.19615i	−0.121070	−	0.209700i
$615$		0			0
$616$		0			0
$617$	−18.0000			−0.724653			−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000			−0.724653			−0.362326	+	0.932051i	$0.618017\pi$
$618$		0			0
$619$	−1.50000	+	2.59808i	−0.0602901	+	0.104425i	−0.894595	−	0.446878i	$-0.852536\pi$
$619$	−1.50000	+	2.59808i	−0.0602901	+	0.104425i	0.834305	+	0.551303i	$0.185869\pi$
$620$	1.00000	−	1.73205i	0.0401610	−	0.0695608i
$621$		0			0
$622$	−12.0000			−0.481156
$623$	30.0000	−	10.3923i	1.20192	−	0.416359i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−11.0000	+	19.0526i	−0.439648	+	0.761493i
$627$		0			0
$628$	−10.0000	−	17.3205i	−0.399043	−	0.691164i
$629$	28.0000			1.11643
$630$		0			0
$631$	24.0000			0.955425			0.477712	−	0.878516i	$-0.341466\pi$
$631$	24.0000			0.955425			0.477712	+	0.878516i	$0.341466\pi$
$632$		0			0
$633$		0			0
$634$	20.0000	−	34.6410i	0.794301	−	1.37577i
$635$	2.50000	+	4.33013i	0.0992095	+	0.171836i
$636$		0			0
$637$	19.5000	+	7.79423i	0.772618	+	0.308819i
$638$	96.0000			3.80068
$639$		0			0
$640$		0			0
$641$	6.00000	−	10.3923i	0.236986	−	0.410471i	−0.722862	−	0.690992i	$-0.757174\pi$
$641$	6.00000	−	10.3923i	0.236986	−	0.410471i	0.959848	+	0.280521i	$0.0905072\pi$
$642$		0			0
$643$	1.00000			0.0394362			0.0197181	−	0.999806i	$-0.493723\pi$
$643$	1.00000			0.0394362			0.0197181	+	0.999806i	$0.493723\pi$
$644$	−4.00000	+	20.7846i	−0.157622	+	0.819028i
$645$		0			0
$646$	−4.00000	−	6.92820i	−0.157378	−	0.272587i
$647$	15.0000	−	25.9808i	0.589711	−	1.02141i	−0.404559	−	0.914512i	$-0.632575\pi$
$647$	15.0000	−	25.9808i	0.589711	−	1.02141i	0.994270	−	0.106897i	$-0.0340916\pi$
$648$		0			0
$649$	−24.0000	−	41.5692i	−0.942082	−	1.63173i
$650$	−6.00000			−0.235339
$651$		0			0
$652$	−24.0000			−0.939913
$653$	7.00000	+	12.1244i	0.273931	+	0.474463i	0.969865	−	0.243643i	$-0.0783426\pi$
$653$	7.00000	+	12.1244i	0.273931	+	0.474463i	−0.695934	+	0.718106i	$0.745009\pi$
$654$		0			0
$655$	−1.00000	+	1.73205i	−0.0390732	+	0.0676768i
$656$	12.0000	+	20.7846i	0.468521	+	0.811503i
$657$		0			0
$658$	8.00000	+	6.92820i	0.311872	+	0.270089i
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$		0			0
$661$	−11.5000	+	19.9186i	−0.447298	+	0.774743i	−0.998209	−	0.0598209i	$-0.980947\pi$
$661$	−11.5000	+	19.9186i	−0.447298	+	0.774743i	0.550911	+	0.834564i	$0.314280\pi$
$662$	9.00000	−	15.5885i	0.349795	−	0.605863i
$663$		0			0
$664$		0			0
$665$	2.00000	+	1.73205i	0.0775567	+	0.0671660i
$666$		0			0
$667$	−16.0000	−	27.7128i	−0.619522	−	1.07304i
$668$	−10.0000	+	17.3205i	−0.386912	+	0.670151i
$669$		0			0
$670$	7.00000	+	12.1244i	0.270434	+	0.468405i
$671$	−84.0000			−3.24278
$672$		0			0
$673$	−37.0000			−1.42625			−0.713123	−	0.701039i	$-0.752720\pi$
$673$	−37.0000			−1.42625			−0.713123	+	0.701039i	$0.752720\pi$
$674$	−25.0000	−	43.3013i	−0.962964	−	1.66790i
$675$		0			0
$676$	4.00000	−	6.92820i	0.153846	−	0.266469i
$677$	8.00000	+	13.8564i	0.307465	+	0.532545i	0.977807	−	0.209507i	$-0.0671860\pi$
$677$	8.00000	+	13.8564i	0.307465	+	0.532545i	−0.670342	+	0.742052i	$0.733853\pi$
$678$		0			0
$679$	3.00000	−	15.5885i	0.115129	−	0.598230i
$680$		0			0
$681$		0			0
$682$	−6.00000	+	10.3923i	−0.229752	+	0.397942i
$683$	−24.0000	+	41.5692i	−0.918334	+	1.59060i	−0.116390	+	0.993204i	$0.537132\pi$
$683$	−24.0000	+	41.5692i	−0.918334	+	1.59060i	−0.801945	+	0.597398i	$0.796201\pi$
$684$		0			0
$685$	8.00000			0.305664
$686$	−37.0000	−	1.73205i	−1.41267	−	0.0661300i
$687$		0			0
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$		0			0
$691$	−13.5000	−	23.3827i	−0.513564	−	0.889519i	−0.999876	−	0.0157341i	$-0.994991\pi$
$691$	−13.5000	−	23.3827i	−0.513564	−	0.889519i	0.486312	−	0.873785i	$-0.338342\pi$
$692$	−48.0000			−1.82469
$693$		0			0
$694$	−32.0000			−1.21470
$695$	10.5000	+	18.1865i	0.398288	+	0.689855i
$696$		0			0
$697$	−12.0000	+	20.7846i	−0.454532	+	0.787273i
$698$	−2.00000	−	3.46410i	−0.0757011	−	0.131118i
$699$		0			0
$700$	5.00000	−	1.73205i	0.188982	−	0.0654654i
$701$	44.0000			1.66186			0.830929	−	0.556379i	$-0.187810\pi$
$701$	44.0000			1.66186			0.830929	+	0.556379i	$0.187810\pi$
$702$		0			0
$703$	−3.50000	+	6.06218i	−0.132005	+	0.228639i
$704$	24.0000	−	41.5692i	0.904534	−	1.56670i
$705$		0			0
$706$	36.0000			1.35488
$707$	−20.0000	−	17.3205i	−0.752177	−	0.651405i
$708$		0			0
$709$	13.0000	+	22.5167i	0.488225	+	0.845631i	0.999908	−	0.0135434i	$-0.00431112\pi$
$709$	13.0000	+	22.5167i	0.488225	+	0.845631i	−0.511683	+	0.859174i	$0.670978\pi$
$710$	−6.00000	+	10.3923i	−0.225176	+	0.390016i
$711$		0			0
$712$		0			0
$713$	4.00000			0.149801
$714$		0			0
$715$	18.0000			0.673162
$716$	18.0000	+	31.1769i	0.672692	+	1.16514i
$717$		0			0
$718$	−24.0000	+	41.5692i	−0.895672	+	1.55135i
$719$	−17.0000	−	29.4449i	−0.633993	−	1.09811i	−0.986728	−	0.162385i	$-0.948081\pi$
$719$	−17.0000	−	29.4449i	−0.633993	−	1.09811i	0.352735	−	0.935723i	$-0.385252\pi$
$720$		0			0
$721$	−47.5000	+	16.4545i	−1.76899	+	0.612797i
$722$	−36.0000			−1.33978
$723$		0			0
$724$	−13.0000	+	22.5167i	−0.483141	+	0.836825i
$725$	−4.00000	+	6.92820i	−0.148556	+	0.257307i
$726$		0			0
$727$	7.00000			0.259616			0.129808	−	0.991539i	$-0.458564\pi$
$727$	7.00000			0.259616			0.129808	+	0.991539i	$0.458564\pi$
$728$		0			0
$729$		0			0
$730$	1.00000	+	1.73205i	0.0370117	+	0.0641061i
$731$	−2.00000	+	3.46410i	−0.0739727	+	0.128124i
$732$		0			0
$733$	21.5000	+	37.2391i	0.794121	+	1.37546i	0.923396	+	0.383849i	$0.125402\pi$
$733$	21.5000	+	37.2391i	0.794121	+	1.37546i	−0.129275	+	0.991609i	$0.541265\pi$
$734$	38.0000			1.40261
$735$		0			0
$736$	−32.0000			−1.17954
$737$	−21.0000	−	36.3731i	−0.773545	−	1.33982i
$738$		0			0
$739$	−20.5000	+	35.5070i	−0.754105	+	1.30615i	0.191714	+	0.981451i	$0.438596\pi$
$739$	−20.5000	+	35.5070i	−0.754105	+	1.30615i	−0.945818	+	0.324697i	$0.894738\pi$
$740$	7.00000	+	12.1244i	0.257325	+	0.445700i
$741$		0			0
$742$	4.00000	−	20.7846i	0.146845	−	0.763027i
$743$	−6.00000			−0.220119			−0.110059	−	0.993925i	$-0.535104\pi$
$743$	−6.00000			−0.220119			−0.110059	+	0.993925i	$0.535104\pi$
$744$		0			0
$745$	2.00000	−	3.46410i	0.0732743	−	0.126915i
$746$	−11.0000	+	19.0526i	−0.402739	+	0.697564i
$747$		0			0
$748$	48.0000			1.75505
$749$	−30.0000	+	10.3923i	−1.09618	+	0.379727i
$750$		0			0
$751$	−14.5000	−	25.1147i	−0.529113	−	0.916450i	−0.999424	−	0.0339490i	$-0.989192\pi$
$751$	−14.5000	−	25.1147i	−0.529113	−	0.916450i	0.470311	−	0.882501i	$-0.344142\pi$
$752$	−4.00000	+	6.92820i	−0.145865	+	0.252646i
$753$		0			0
$754$	24.0000	+	41.5692i	0.874028	+	1.51386i
$755$	−8.00000			−0.291150
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	−11.0000	−	19.0526i	−0.399538	−	0.692020i
$759$		0			0
$760$		0			0
$761$	−6.00000	−	10.3923i	−0.217500	−	0.376721i	0.736543	−	0.676391i	$-0.236457\pi$
$761$	−6.00000	−	10.3923i	−0.217500	−	0.376721i	−0.954043	+	0.299670i	$0.903123\pi$
$762$		0			0
$763$	30.0000	+	25.9808i	1.08607	+	0.940567i
$764$	−20.0000			−0.723575
$765$		0			0
$766$	28.0000	−	48.4974i	1.01168	−	1.75228i
$767$	12.0000	−	20.7846i	0.433295	−	0.750489i
$768$		0			0
$769$	−49.0000			−1.76699			−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−49.0000			−1.76699			−0.883493	+	0.468445i	$0.844814\pi$
$770$	−30.0000	+	10.3923i	−1.08112	+	0.374513i
$771$		0			0
$772$	9.00000	+	15.5885i	0.323917	+	0.561041i
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	−0.657542	−	0.753418i	$-0.728404\pi$
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	0.981250	+	0.192740i	$0.0617373\pi$
$774$		0			0
$775$	−0.500000	−	0.866025i	−0.0179605	−	0.0311086i
$776$		0			0
$777$		0			0
$778$	−12.0000			−0.430221
$779$	−3.00000	−	5.19615i	−0.107486	−	0.186171i
$780$		0			0
$781$	18.0000	−	31.1769i	0.644091	−	1.11560i
$782$	−16.0000	−	27.7128i	−0.572159	−	0.991008i
$783$		0			0
$784$	−4.00000	−	27.7128i	−0.142857	−	0.989743i
$785$	−10.0000			−0.356915
$786$		0			0
$787$	16.0000	−	27.7128i	0.570338	−	0.987855i	−0.426193	−	0.904632i	$-0.640145\pi$
$787$	16.0000	−	27.7128i	0.570338	−	0.987855i	0.996531	−	0.0832226i	$-0.0265213\pi$
$788$	12.0000	−	20.7846i	0.427482	−	0.740421i
$789$		0			0
$790$	2.00000			0.0711568
$791$	−3.00000	+	15.5885i	−0.106668	+	0.554262i
$792$		0			0
$793$	−21.0000	−	36.3731i	−0.745732	−	1.29165i
$794$	37.0000	−	64.0859i	1.31308	−	2.27432i
$795$		0			0
$796$	−8.00000	−	13.8564i	−0.283552	−	0.491127i
$797$	36.0000			1.27519			0.637593	−	0.770374i	$-0.279930\pi$
$797$	36.0000			1.27519			0.637593	+	0.770374i	$0.279930\pi$
$798$		0			0
$799$	−8.00000			−0.283020
$800$	4.00000	+	6.92820i	0.141421	+	0.244949i
$801$		0			0
$802$	−12.0000	+	20.7846i	−0.423735	+	0.733930i
$803$	−3.00000	−	5.19615i	−0.105868	−	0.183368i
$804$		0			0
$805$	8.00000	+	6.92820i	0.281963	+	0.244187i
$806$	−6.00000			−0.211341
$807$		0			0
$808$		0			0
$809$	−21.0000	+	36.3731i	−0.738321	+	1.27881i	0.214930	+	0.976629i	$0.431048\pi$
$809$	−21.0000	+	36.3731i	−0.738321	+	1.27881i	−0.953251	+	0.302180i	$0.902286\pi$
$810$		0			0
$811$	−48.0000			−1.68551			−0.842754	−	0.538299i	$-0.819067\pi$
$811$	−48.0000			−1.68551			−0.842754	+	0.538299i	$0.819067\pi$
$812$	−32.0000	−	27.7128i	−1.12298	−	0.972529i
$813$		0			0
$814$	−42.0000	−	72.7461i	−1.47210	−	2.54975i
$815$	−6.00000	+	10.3923i	−0.210171	+	0.364027i
$816$		0			0
$817$	−0.500000	−	0.866025i	−0.0174928	−	0.0302984i
$818$	10.0000			0.349642
$819$		0			0
$820$	−12.0000			−0.419058
$821$	27.0000	+	46.7654i	0.942306	+	1.63212i	0.761056	+	0.648686i	$0.224681\pi$
$821$	27.0000	+	46.7654i	0.942306	+	1.63212i	0.181250	+	0.983437i	$0.441986\pi$
$822$		0			0
$823$	−4.00000	+	6.92820i	−0.139431	+	0.241502i	−0.927281	−	0.374365i	$-0.877861\pi$
$823$	−4.00000	+	6.92820i	−0.139431	+	0.241502i	0.787850	+	0.615867i	$0.211194\pi$
$824$		0			0
$825$		0			0
$826$	−8.00000	+	41.5692i	−0.278356	+	1.44638i
$827$	30.0000			1.04320			0.521601	−	0.853189i	$-0.325335\pi$
$827$	30.0000			1.04320			0.521601	+	0.853189i	$0.325335\pi$
$828$		0			0
$829$	−28.5000	+	49.3634i	−0.989846	+	1.71446i	−0.371822	+	0.928304i	$0.621267\pi$
$829$	−28.5000	+	49.3634i	−0.989846	+	1.71446i	−0.618024	+	0.786159i	$0.712066\pi$
$830$	−2.00000	+	3.46410i	−0.0694210	+	0.120241i
$831$		0			0
$832$	24.0000			0.832050
$833$	22.0000	−	17.3205i	0.762255	−	0.600120i
$834$		0			0
$835$	5.00000	+	8.66025i	0.173032	+	0.299700i
$836$	−6.00000	+	10.3923i	−0.207514	+	0.359425i
$837$		0			0
$838$	6.00000	+	10.3923i	0.207267	+	0.358996i
$839$	−24.0000			−0.828572			−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000			−0.828572			−0.414286	+	0.910147i	$0.635969\pi$
$840$		0			0
$841$	35.0000			1.20690
$842$	−1.00000	−	1.73205i	−0.0344623	−	0.0596904i
$843$		0			0
$844$	20.0000	−	34.6410i	0.688428	−	1.19239i
$845$	−2.00000	−	3.46410i	−0.0688021	−	0.119169i
$846$		0			0
$847$	62.5000	−	21.6506i	2.14753	−	0.743925i
$848$	16.0000			0.549442
$849$		0			0
$850$	−4.00000	+	6.92820i	−0.137199	+	0.237635i
$851$	−14.0000	+	24.2487i	−0.479914	+	0.831235i
$852$		0			0
$853$	−9.00000			−0.308154			−0.154077	−	0.988059i	$-0.549240\pi$
$853$	−9.00000			−0.308154			−0.154077	+	0.988059i	$0.549240\pi$
$854$	56.0000	+	48.4974i	1.91628	+	1.65955i
$855$		0			0
$856$		0			0
$857$	−6.00000	+	10.3923i	−0.204956	+	0.354994i	−0.950119	−	0.311888i	$-0.899038\pi$
$857$	−6.00000	+	10.3923i	−0.204956	+	0.354994i	0.745163	+	0.666883i	$0.232372\pi$
$858$		0			0
$859$	20.0000	+	34.6410i	0.682391	+	1.18194i	0.974249	+	0.225475i	$0.0723932\pi$
$859$	20.0000	+	34.6410i	0.682391	+	1.18194i	−0.291858	+	0.956462i	$0.594273\pi$
$860$	−2.00000			−0.0681994
$861$		0			0
$862$	4.00000			0.136241
$863$	−3.00000	−	5.19615i	−0.102121	−	0.176879i	0.810437	−	0.585826i	$-0.199230\pi$
$863$	−3.00000	−	5.19615i	−0.102121	−	0.176879i	−0.912558	+	0.408946i	$0.865896\pi$
$864$		0			0
$865$	−12.0000	+	20.7846i	−0.408012	+	0.706698i
$866$	5.00000	+	8.66025i	0.169907	+	0.294287i
$867$		0			0
$868$	5.00000	−	1.73205i	0.169711	−	0.0587896i
$869$	−6.00000			−0.203536
$870$		0			0
$871$	10.5000	−	18.1865i	0.355779	−	0.616227i
$872$		0			0
$873$		0			0
$874$	8.00000			0.270604
$875$	0.500000	−	2.59808i	0.0169031	−	0.0878310i
$876$		0			0
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	0.989788	−	0.142548i	$-0.0455296\pi$
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	−0.618344	+	0.785907i	$0.712196\pi$
$878$	−16.0000	+	27.7128i	−0.539974	+	0.935262i
$879$		0			0
$880$	−12.0000	−	20.7846i	−0.404520	−	0.700649i
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$	7.00000			0.235569			0.117784	−	0.993039i	$-0.462421\pi$
$883$	7.00000			0.235569			0.117784	+	0.993039i	$0.462421\pi$
$884$	12.0000	+	20.7846i	0.403604	+	0.699062i
$885$		0			0
$886$	−36.0000	+	62.3538i	−1.20944	+	2.09482i
$887$	5.00000	+	8.66025i	0.167884	+	0.290783i	0.937676	−	0.347512i	$-0.112973\pi$
$887$	5.00000	+	8.66025i	0.167884	+	0.290783i	−0.769792	+	0.638295i	$0.779640\pi$
$888$		0			0
$889$	−2.50000	+	12.9904i	−0.0838473	+	0.435683i
$890$	−24.0000			−0.804482
$891$		0			0
$892$	24.0000	−	41.5692i	0.803579	−	1.39184i
$893$	1.00000	−	1.73205i	0.0334637	−	0.0579609i
$894$		0			0
$895$	18.0000			0.601674
$896$		0			0
$897$		0			0
$898$	30.0000	+	51.9615i	1.00111	+	1.73398i
$899$	−4.00000	+	6.92820i	−0.133407	+	0.231069i
$900$		0			0
$901$	8.00000	+	13.8564i	0.266519	+	0.461624i
$902$	72.0000			2.39734
$903$		0			0
$904$		0			0
$905$	6.50000	+	11.2583i	0.216067	+	0.374240i
$906$		0			0
$907$	−15.5000	+	26.8468i	−0.514669	+	0.891433i	0.485186	+	0.874411i	$0.338752\pi$
$907$	−15.5000	+	26.8468i	−0.514669	+	0.891433i	−0.999855	+	0.0170220i	$0.994581\pi$
$908$	−10.0000	−	17.3205i	−0.331862	−	0.574801i
$909$		0			0
$910$	−12.0000	−	10.3923i	−0.397796	−	0.344502i
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$		0			0
$913$	6.00000	−	10.3923i	0.198571	−	0.343935i
$914$	15.0000	−	25.9808i	0.496156	−	0.859367i
$915$		0			0
$916$	26.0000			0.859064
$917$	−5.00000	+	1.73205i	−0.165115	+	0.0571974i
$918$		0			0
$919$	4.50000	+	7.79423i	0.148441	+	0.257108i	0.930652	−	0.365907i	$-0.119241\pi$
$919$	4.50000	+	7.79423i	0.148441	+	0.257108i	−0.782210	+	0.623015i	$0.785908\pi$
$920$		0			0
$921$		0			0
$922$	−8.00000	−	13.8564i	−0.263466	−	0.456336i
$923$	18.0000			0.592477
$924$		0			0
$925$	7.00000			0.230159
$926$	−3.00000	−	5.19615i	−0.0985861	−	0.170756i
$927$		0			0
$928$	32.0000	−	55.4256i	1.05045	−	1.81944i
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	0.728046	−	0.685529i	$-0.240429\pi$
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	−0.957708	+	0.287742i	$0.907096\pi$
$930$		0			0
$931$	1.00000	+	6.92820i	0.0327737	+	0.227063i
$932$	−12.0000			−0.393073
$933$		0			0
$934$	22.0000	−	38.1051i	0.719862	−	1.24684i
$935$	12.0000	−	20.7846i	0.392442	−	0.679729i
$936$		0			0
$937$	−29.0000			−0.947389			−0.473694	−	0.880689i	$-0.657080\pi$
$937$	−29.0000			−0.947389			−0.473694	+	0.880689i	$0.657080\pi$
$938$	−7.00000	+	36.3731i	−0.228558	+	1.18762i
$939$		0			0
$940$	−2.00000	−	3.46410i	−0.0652328	−	0.112987i
$941$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$941$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$942$		0			0
$943$	−12.0000	−	20.7846i	−0.390774	−	0.676840i
$944$	−32.0000			−1.04151
$945$		0			0
$946$	12.0000			0.390154
$947$	13.0000	+	22.5167i	0.422443	+	0.731693i	0.996178	−	0.0873481i	$-0.0278392\pi$
$947$	13.0000	+	22.5167i	0.422443	+	0.731693i	−0.573735	+	0.819041i	$0.694506\pi$
$948$		0			0
$949$	1.50000	−	2.59808i	0.0486921	−	0.0843371i
$950$	−1.00000	−	1.73205i	−0.0324443	−	0.0561951i
$951$		0			0
$952$		0			0
$953$	−4.00000			−0.129573			−0.0647864	−	0.997899i	$-0.520637\pi$
$953$	−4.00000			−0.129573			−0.0647864	+	0.997899i	$0.520637\pi$
$954$		0			0
$955$	−5.00000	+	8.66025i	−0.161796	+	0.280239i
$956$	14.0000	−	24.2487i	0.452792	−	0.784259i
$957$		0			0
$958$	8.00000			0.258468
$959$	16.0000	+	13.8564i	0.516667	+	0.447447i
$960$		0			0
$961$	15.0000	+	25.9808i	0.483871	+	0.838089i
$962$	21.0000	−	36.3731i	0.677067	−	1.17271i
$963$		0			0
$964$	18.0000	+	31.1769i	0.579741	+	1.00414i
$965$	9.00000			0.289720
$966$		0			0
$967$	55.0000			1.76868			0.884340	−	0.466843i	$-0.154609\pi$
$967$	55.0000			1.76868			0.884340	+	0.466843i	$0.154609\pi$
$968$		0			0
$969$		0			0
$970$	−6.00000	+	10.3923i	−0.192648	+	0.333677i
$971$	−26.0000	−	45.0333i	−0.834380	−	1.44519i	−0.894534	−	0.446999i	$-0.852493\pi$
$971$	−26.0000	−	45.0333i	−0.834380	−	1.44519i	0.0601548	−	0.998189i	$-0.480841\pi$
$972$		0			0
$973$	−10.5000	+	54.5596i	−0.336615	+	1.74910i
$974$	−26.0000			−0.833094
$975$		0			0
$976$	−28.0000	+	48.4974i	−0.896258	+	1.55236i
$977$	−11.0000	+	19.0526i	−0.351921	+	0.609545i	−0.986586	−	0.163242i	$-0.947805\pi$
$977$	−11.0000	+	19.0526i	−0.351921	+	0.609545i	0.634665	+	0.772787i	$0.281138\pi$
$978$		0			0
$979$	72.0000			2.30113
$980$	13.0000	+	5.19615i	0.415270	+	0.165985i
$981$		0			0
$982$	−12.0000	−	20.7846i	−0.382935	−	0.663264i
$983$	16.0000	−	27.7128i	0.510321	−	0.883901i	−0.489608	−	0.871943i	$-0.662860\pi$
$983$	16.0000	−	27.7128i	0.510321	−	0.883901i	0.999928	−	0.0119587i	$-0.00380665\pi$
$984$		0			0
$985$	−6.00000	−	10.3923i	−0.191176	−	0.331126i
$986$	64.0000			2.03818
$987$		0			0
$988$	−6.00000			−0.190885
$989$	−2.00000	−	3.46410i	−0.0635963	−	0.110152i
$990$		0			0
$991$	7.50000	−	12.9904i	0.238245	−	0.412653i	−0.721966	−	0.691929i	$-0.756761\pi$
$991$	7.50000	−	12.9904i	0.238245	−	0.412653i	0.960211	+	0.279276i	$0.0900944\pi$
$992$	4.00000	+	6.92820i	0.127000	+	0.219971i
$993$		0			0
$994$	−30.0000	+	10.3923i	−0.951542	+	0.329624i
$995$	−8.00000			−0.253617
$996$		0			0
$997$	12.5000	−	21.6506i	0.395879	−	0.685682i	−0.597334	−	0.801993i	$-0.703773\pi$
$997$	12.5000	−	21.6506i	0.395879	−	0.685682i	0.993213	+	0.116310i	$0.0371066\pi$
$998$	−29.0000	+	50.2295i	−0.917979	+	1.58999i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.j.a.46.1		2
3.2	odd	2		105.2.i.b.46.1	yes	2
7.2	even	3	inner	315.2.j.a.226.1		2
7.3	odd	6		2205.2.a.m.1.1		1
7.4	even	3		2205.2.a.k.1.1		1
12.11	even	2		1680.2.bg.l.1201.1		2
15.2	even	4		525.2.r.d.424.1		4
15.8	even	4		525.2.r.d.424.2		4
15.14	odd	2		525.2.i.a.151.1		2
21.2	odd	6		105.2.i.b.16.1	✓	2
21.5	even	6		735.2.i.f.226.1		2
21.11	odd	6		735.2.a.b.1.1		1
21.17	even	6		735.2.a.a.1.1		1
21.20	even	2		735.2.i.f.361.1		2
84.23	even	6		1680.2.bg.l.961.1		2
105.2	even	12		525.2.r.d.499.2		4
105.23	even	12		525.2.r.d.499.1		4
105.44	odd	6		525.2.i.a.226.1		2
105.59	even	6		3675.2.a.p.1.1		1
105.74	odd	6		3675.2.a.o.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.i.b.16.1	✓	2	21.2	odd	6
105.2.i.b.46.1	yes	2	3.2	odd	2
315.2.j.a.46.1		2	1.1	even	1	trivial
315.2.j.a.226.1		2	7.2	even	3	inner
525.2.i.a.151.1		2	15.14	odd	2
525.2.i.a.226.1		2	105.44	odd	6
525.2.r.d.424.1		4	15.2	even	4
525.2.r.d.424.2		4	15.8	even	4
525.2.r.d.499.1		4	105.23	even	12
525.2.r.d.499.2		4	105.2	even	12
735.2.a.a.1.1		1	21.17	even	6
735.2.a.b.1.1		1	21.11	odd	6
735.2.i.f.226.1		2	21.5	even	6
735.2.i.f.361.1		2	21.20	even	2
1680.2.bg.l.961.1		2	84.23	even	6
1680.2.bg.l.1201.1		2	12.11	even	2
2205.2.a.k.1.1		1	7.4	even	3
2205.2.a.m.1.1		1	7.3	odd	6
3675.2.a.o.1.1		1	105.74	odd	6
3675.2.a.p.1.1		1	105.59	even	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 2.59808i) q^{7} +(1.00000 - 1.73205i) q^{10} +(-3.00000 + 5.19615i) q^{11} -3.00000 q^{13} +(5.00000 - 1.73205i) q^{14} +(2.00000 + 3.46410i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{19} -2.00000 q^{20} +12.0000 q^{22} +(-2.00000 - 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(3.00000 + 5.19615i) q^{26} +(-4.00000 - 3.46410i) q^{28} +8.00000 q^{29} +(-0.500000 + 0.866025i) q^{31} +(4.00000 - 6.92820i) q^{32} +8.00000 q^{34} +(-2.50000 + 0.866025i) q^{35} +(-3.50000 - 6.06218i) q^{37} +(-1.00000 + 1.73205i) q^{38} +6.00000 q^{41} +1.00000 q^{43} +(-6.00000 - 10.3923i) q^{44} +(-4.00000 + 6.92820i) q^{46} +(1.00000 + 1.73205i) q^{47} +(-6.50000 - 2.59808i) q^{49} +2.00000 q^{50} +(3.00000 - 5.19615i) q^{52} +(2.00000 - 3.46410i) q^{53} -6.00000 q^{55} +(-8.00000 - 13.8564i) q^{58} +(-4.00000 + 6.92820i) q^{59} +(7.00000 + 12.1244i) q^{61} +2.00000 q^{62} -8.00000 q^{64} +(-1.50000 - 2.59808i) q^{65} +(-3.50000 + 6.06218i) q^{67} +(-4.00000 - 6.92820i) q^{68} +(4.00000 + 3.46410i) q^{70} -6.00000 q^{71} +(-0.500000 + 0.866025i) q^{73} +(-7.00000 + 12.1244i) q^{74} +2.00000 q^{76} +(-12.0000 - 10.3923i) q^{77} +(0.500000 + 0.866025i) q^{79} +(-2.00000 + 3.46410i) q^{80} +(-6.00000 - 10.3923i) q^{82} -2.00000 q^{83} -4.00000 q^{85} +(-1.00000 - 1.73205i) q^{86} +(-6.00000 - 10.3923i) q^{89} +(1.50000 - 7.79423i) q^{91} +8.00000 q^{92} +(2.00000 - 3.46410i) q^{94} +(0.500000 - 0.866025i) q^{95} -6.00000 q^{97} +(2.00000 + 13.8564i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{4} + q^{5} - q^{7} + 2 q^{10} - 6 q^{11} - 6 q^{13} + 10 q^{14} + 4 q^{16} - 4 q^{17} - q^{19} - 4 q^{20} + 24 q^{22} - 4 q^{23} - q^{25} + 6 q^{26} - 8 q^{28} + 16 q^{29} - q^{31}+ \cdots + 4 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^4 + q^5 - q^7 + 2 * q^10 - 6 * q^11 - 6 * q^13 + 10 * q^14 + 4 * q^16 - 4 * q^17 - q^19 - 4 * q^20 + 24 * q^22 - 4 * q^23 - q^25 + 6 * q^26 - 8 * q^28 + 16 * q^29 - q^31 + 8 * q^32 + 16 * q^34 - 5 * q^35 - 7 * q^37 - 2 * q^38 + 12 * q^41 + 2 * q^43 - 12 * q^44 - 8 * q^46 + 2 * q^47 - 13 * q^49 + 4 * q^50 + 6 * q^52 + 4 * q^53 - 12 * q^55 - 16 * q^58 - 8 * q^59 + 14 * q^61 + 4 * q^62 - 16 * q^64 - 3 * q^65 - 7 * q^67 - 8 * q^68 + 8 * q^70 - 12 * q^71 - q^73 - 14 * q^74 + 4 * q^76 - 24 * q^77 + q^79 - 4 * q^80 - 12 * q^82 - 4 * q^83 - 8 * q^85 - 2 * q^86 - 12 * q^89 + 3 * q^91 + 16 * q^92 + 4 * q^94 + q^95 - 12 * q^97 + 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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