LMFDB - Embedded newform 272.2.v.d.145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [272,2,Mod(49,272)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(272, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("272.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 272 = 2^{4} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	272.v (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.17193093498$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			145.1
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	272.145
Dual form			272.2.v.d.257.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.41421 + 1.00000i) q^{3} +(0.707107 - 1.70711i) q^{5} +(-0.414214 - 1.00000i) q^{7} +(2.70711 + 2.70711i) q^{9} +(1.00000 - 0.414214i) q^{11} -1.41421i q^{13} +(3.41421 - 3.41421i) q^{15} +(-2.82843 + 3.00000i) q^{17} +(-3.41421 + 3.41421i) q^{19} -2.82843i q^{21} +(-3.82843 + 1.58579i) q^{23} +(1.12132 + 1.12132i) q^{25} +(0.828427 + 2.00000i) q^{27} +(-1.70711 + 4.12132i) q^{29} +(3.00000 + 1.24264i) q^{31} +2.82843 q^{33} -2.00000 q^{35} +(-3.53553 - 1.46447i) q^{37} +(1.41421 - 3.41421i) q^{39} +(-3.12132 - 7.53553i) q^{41} +(3.41421 + 3.41421i) q^{43} +(6.53553 - 2.70711i) q^{45} -10.8284i q^{47} +(4.12132 - 4.12132i) q^{49} +(-9.82843 + 4.41421i) q^{51} +(-1.00000 + 1.00000i) q^{53} -2.00000i q^{55} +(-11.6569 + 4.82843i) q^{57} +(4.24264 + 4.24264i) q^{59} +(3.53553 + 8.53553i) q^{61} +(1.58579 - 3.82843i) q^{63} +(-2.41421 - 1.00000i) q^{65} -6.82843 q^{67} -10.8284 q^{69} +(-12.0711 - 5.00000i) q^{71} +(-2.05025 + 4.94975i) q^{73} +(1.58579 + 3.82843i) q^{75} +(-0.828427 - 0.828427i) q^{77} +(3.82843 - 1.58579i) q^{79} -5.82843i q^{81} +(0.242641 - 0.242641i) q^{83} +(3.12132 + 6.94975i) q^{85} +(-8.24264 + 8.24264i) q^{87} -9.41421i q^{89} +(-1.41421 + 0.585786i) q^{91} +(6.00000 + 6.00000i) q^{93} +(3.41421 + 8.24264i) q^{95} +(2.46447 - 5.94975i) q^{97} +(3.82843 + 1.58579i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} + 4 q^{7} + 8 q^{9} + 4 q^{11} + 8 q^{15} - 8 q^{19} - 4 q^{23} - 4 q^{25} - 8 q^{27} - 4 q^{29} + 12 q^{31} - 8 q^{35} - 4 q^{41} + 8 q^{43} + 12 q^{45} + 8 q^{49} - 28 q^{51} - 4 q^{53}+ \cdots + 4 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 + 4 * q^7 + 8 * q^9 + 4 * q^11 + 8 * q^15 - 8 * q^19 - 4 * q^23 - 4 * q^25 - 8 * q^27 - 4 * q^29 + 12 * q^31 - 8 * q^35 - 4 * q^41 + 8 * q^43 + 12 * q^45 + 8 * q^49 - 28 * q^51 - 4 * q^53 - 24 * q^57 + 12 * q^63 - 4 * q^65 - 16 * q^67 - 32 * q^69 - 20 * q^71 - 28 * q^73 + 12 * q^75 + 8 * q^77 + 4 * q^79 - 16 * q^83 + 4 * q^85 - 16 * q^87 + 24 * q^93 + 8 * q^95 + 24 * q^97 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/272\mathbb{Z}\right)^\times$.

$n$	$69$	$239$	$241$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.41421	+	1.00000i	1.39385	+	0.577350i	0.948147	−	0.317832i	$-0.102955\pi$
$3$	2.41421	+	1.00000i	1.39385	+	0.577350i	0.445700	+	0.895182i	$0.352955\pi$
$4$		0			0
$5$	0.707107	−	1.70711i	0.316228	−	0.763441i	−0.683220	−	0.730213i	$-0.739421\pi$
$5$	0.707107	−	1.70711i	0.316228	−	0.763441i	0.999448	−	0.0332288i	$-0.0105790\pi$
$6$		0			0
$7$	−0.414214	−	1.00000i	−0.156558	−	0.377964i	0.826066	−	0.563574i	$-0.190574\pi$
$7$	−0.414214	−	1.00000i	−0.156558	−	0.377964i	−0.982624	+	0.185610i	$0.940574\pi$
$8$		0			0
$9$	2.70711	+	2.70711i	0.902369	+	0.902369i
$10$		0			0
$11$	1.00000	−	0.414214i	0.301511	−	0.124890i	−0.226799	−	0.973942i	$-0.572826\pi$
$11$	1.00000	−	0.414214i	0.301511	−	0.124890i	0.528310	+	0.849052i	$0.322826\pi$
$12$		0			0
$13$		−	1.41421i		−	0.392232i	−0.980581	−	0.196116i	$-0.937167\pi$
$13$		−	1.41421i		−	0.392232i	0.980581	−	0.196116i	$-0.0628330\pi$
$14$		0			0
$15$	3.41421	−	3.41421i	0.881546	−	0.881546i
$16$		0			0
$17$	−2.82843	+	3.00000i	−0.685994	+	0.727607i
$17$	−2.82843	+	3.00000i	−0.685994	+	0.727607i
$18$		0			0
$19$	−3.41421	+	3.41421i	−0.783274	+	0.783274i	−0.980382	−	0.197108i	$-0.936845\pi$
$19$	−3.41421	+	3.41421i	−0.783274	+	0.783274i	0.197108	+	0.980382i	$0.436845\pi$
$20$		0			0
$21$		−	2.82843i		−	0.617213i
$22$		0			0
$23$	−3.82843	+	1.58579i	−0.798282	+	0.330659i	−0.744268	−	0.667881i	$-0.767202\pi$
$23$	−3.82843	+	1.58579i	−0.798282	+	0.330659i	−0.0540140	+	0.998540i	$0.517202\pi$
$24$		0			0
$25$	1.12132	+	1.12132i	0.224264	+	0.224264i
$26$		0			0
$27$	0.828427	+	2.00000i	0.159431	+	0.384900i
$28$		0			0
$29$	−1.70711	+	4.12132i	−0.317002	+	0.765310i	0.682408	+	0.730971i	$0.260933\pi$
$29$	−1.70711	+	4.12132i	−0.317002	+	0.765310i	−0.999410	+	0.0343389i	$0.989067\pi$
$30$		0			0
$31$	3.00000	+	1.24264i	0.538816	+	0.223185i	0.635460	−	0.772134i	$-0.280811\pi$
$31$	3.00000	+	1.24264i	0.538816	+	0.223185i	−0.0966436	+	0.995319i	$0.530811\pi$
$32$		0			0
$33$	2.82843			0.492366
$34$		0			0
$35$	−2.00000			−0.338062
$36$		0			0
$37$	−3.53553	−	1.46447i	−0.581238	−	0.240757i	0.0726379	−	0.997358i	$-0.476858\pi$
$37$	−3.53553	−	1.46447i	−0.581238	−	0.240757i	−0.653876	+	0.756602i	$0.726858\pi$
$38$		0			0
$39$	1.41421	−	3.41421i	0.226455	−	0.546712i
$40$		0			0
$41$	−3.12132	−	7.53553i	−0.487468	−	1.17685i	−0.955990	−	0.293400i	$-0.905213\pi$
$41$	−3.12132	−	7.53553i	−0.487468	−	1.17685i	0.468521	−	0.883452i	$-0.344787\pi$
$42$		0			0
$43$	3.41421	+	3.41421i	0.520663	+	0.520663i	0.917772	−	0.397109i	$-0.129986\pi$
$43$	3.41421	+	3.41421i	0.520663	+	0.520663i	−0.397109	+	0.917772i	$0.629986\pi$
$44$		0			0
$45$	6.53553	−	2.70711i	0.974260	−	0.403552i
$46$		0			0
$47$		−	10.8284i		−	1.57949i	−0.613436	−	0.789744i	$-0.710213\pi$
$47$		−	10.8284i		−	1.57949i	0.613436	−	0.789744i	$-0.289787\pi$
$48$		0			0
$49$	4.12132	−	4.12132i	0.588760	−	0.588760i
$50$		0			0
$51$	−9.82843	+	4.41421i	−1.37626	+	0.618114i
$52$		0			0
$53$	−1.00000	+	1.00000i	−0.137361	+	0.137361i	−0.772444	−	0.635083i	$-0.780966\pi$
$53$	−1.00000	+	1.00000i	−0.137361	+	0.137361i	0.635083	+	0.772444i	$0.280966\pi$
$54$		0			0
$55$		−	2.00000i		−	0.269680i
$56$		0			0
$57$	−11.6569	+	4.82843i	−1.54399	+	0.639541i
$58$		0			0
$59$	4.24264	+	4.24264i	0.552345	+	0.552345i	0.927117	−	0.374772i	$-0.122279\pi$
$59$	4.24264	+	4.24264i	0.552345	+	0.552345i	−0.374772	+	0.927117i	$0.622279\pi$
$60$		0			0
$61$	3.53553	+	8.53553i	0.452679	+	1.09286i	0.971300	+	0.237859i	$0.0764456\pi$
$61$	3.53553	+	8.53553i	0.452679	+	1.09286i	−0.518621	+	0.855004i	$0.673554\pi$
$62$		0			0
$63$	1.58579	−	3.82843i	0.199790	−	0.482336i
$64$		0			0
$65$	−2.41421	−	1.00000i	−0.299446	−	0.124035i
$66$		0			0
$67$	−6.82843			−0.834225			−0.417113	−	0.908855i	$-0.636958\pi$
$67$	−6.82843			−0.834225			−0.417113	+	0.908855i	$0.636958\pi$
$68$		0			0
$69$	−10.8284			−1.30359
$70$		0			0
$71$	−12.0711	−	5.00000i	−1.43257	−	0.593391i	−0.474587	−	0.880209i	$-0.657403\pi$
$71$	−12.0711	−	5.00000i	−1.43257	−	0.593391i	−0.957985	+	0.286818i	$0.907403\pi$
$72$		0			0
$73$	−2.05025	+	4.94975i	−0.239964	+	0.579324i	−0.997279	−	0.0737261i	$-0.976511\pi$
$73$	−2.05025	+	4.94975i	−0.239964	+	0.579324i	0.757315	+	0.653050i	$0.226511\pi$
$74$		0			0
$75$	1.58579	+	3.82843i	0.183111	+	0.442069i
$76$		0			0
$77$	−0.828427	−	0.828427i	−0.0944080	−	0.0944080i
$78$		0			0
$79$	3.82843	−	1.58579i	0.430732	−	0.178415i	−0.156775	−	0.987634i	$-0.550110\pi$
$79$	3.82843	−	1.58579i	0.430732	−	0.178415i	0.587506	+	0.809219i	$0.300110\pi$
$80$		0			0
$81$		−	5.82843i		−	0.647603i
$82$		0			0
$83$	0.242641	−	0.242641i	0.0266333	−	0.0266333i	−0.693665	−	0.720298i	$-0.744005\pi$
$83$	0.242641	−	0.242641i	0.0266333	−	0.0266333i	0.720298	+	0.693665i	$0.244005\pi$
$84$		0			0
$85$	3.12132	+	6.94975i	0.338555	+	0.753806i
$86$		0			0
$87$	−8.24264	+	8.24264i	−0.883704	+	0.883704i
$88$		0			0
$89$		−	9.41421i		−	0.997905i	−0.866629	−	0.498952i	$-0.833718\pi$
$89$		−	9.41421i		−	0.997905i	0.866629	−	0.498952i	$-0.166282\pi$
$90$		0			0
$91$	−1.41421	+	0.585786i	−0.148250	+	0.0614071i
$92$		0			0
$93$	6.00000	+	6.00000i	0.622171	+	0.622171i
$94$		0			0
$95$	3.41421	+	8.24264i	0.350291	+	0.845677i
$96$		0			0
$97$	2.46447	−	5.94975i	0.250229	−	0.604105i	−0.747994	−	0.663706i	$-0.768983\pi$
$97$	2.46447	−	5.94975i	0.250229	−	0.604105i	0.998222	+	0.0596005i	$0.0189827\pi$
$98$		0			0
$99$	3.82843	+	1.58579i	0.384771	+	0.159378i
$100$		0			0
$101$	−13.4142			−1.33476			−0.667382	−	0.744715i	$-0.732585\pi$
$101$	−13.4142			−1.33476			−0.667382	+	0.744715i	$0.732585\pi$
$102$		0			0
$103$	4.48528			0.441948			0.220974	−	0.975280i	$-0.429076\pi$
$103$	4.48528			0.441948			0.220974	+	0.975280i	$0.429076\pi$
$104$		0			0
$105$	−4.82843	−	2.00000i	−0.471206	−	0.195180i
$106$		0			0
$107$	2.41421	−	5.82843i	0.233391	−	0.563455i	−0.763181	−	0.646184i	$-0.776364\pi$
$107$	2.41421	−	5.82843i	0.233391	−	0.563455i	0.996572	+	0.0827292i	$0.0263636\pi$
$108$		0			0
$109$	1.63604	+	3.94975i	0.156704	+	0.378317i	0.982660	−	0.185418i	$-0.0593639\pi$
$109$	1.63604	+	3.94975i	0.156704	+	0.378317i	−0.825956	+	0.563735i	$0.809364\pi$
$110$		0			0
$111$	−7.07107	−	7.07107i	−0.671156	−	0.671156i
$112$		0			0
$113$	14.9497	−	6.19239i	1.40635	−	0.582531i	0.454961	−	0.890511i	$-0.349653\pi$
$113$	14.9497	−	6.19239i	1.40635	−	0.582531i	0.951393	+	0.307980i	$0.0996531\pi$
$114$		0			0
$115$			7.65685i			0.714005i
$116$		0			0
$117$	3.82843	−	3.82843i	0.353938	−	0.353938i
$118$		0			0
$119$	4.17157	+	1.58579i	0.382407	+	0.145369i
$120$		0			0
$121$	−6.94975	+	6.94975i	−0.631795	+	0.631795i
$122$		0			0
$123$		−	21.3137i		−	1.92179i
$124$		0			0
$125$	11.2426	−	4.65685i	1.00557	−	0.416522i
$126$		0			0
$127$	12.2426	+	12.2426i	1.08636	+	1.08636i	0.995900	+	0.0904585i	$0.0288332\pi$
$127$	12.2426	+	12.2426i	1.08636	+	1.08636i	0.0904585	+	0.995900i	$0.471167\pi$
$128$		0			0
$129$	4.82843	+	11.6569i	0.425119	+	1.02633i
$130$		0			0
$131$	−0.0710678	+	0.171573i	−0.00620922	+	0.0149904i	−0.926954	−	0.375176i	$-0.877582\pi$
$131$	−0.0710678	+	0.171573i	−0.00620922	+	0.0149904i	0.920745	+	0.390166i	$0.127582\pi$
$132$		0			0
$133$	4.82843	+	2.00000i	0.418678	+	0.173422i
$134$		0			0
$135$	4.00000			0.344265
$136$		0			0
$137$	8.72792			0.745677			0.372838	−	0.927896i	$-0.378385\pi$
$137$	8.72792			0.745677			0.372838	+	0.927896i	$0.378385\pi$
$138$		0			0
$139$	13.8284	+	5.72792i	1.17291	+	0.485836i	0.882154	−	0.470961i	$-0.156093\pi$
$139$	13.8284	+	5.72792i	1.17291	+	0.485836i	0.290758	+	0.956797i	$0.406093\pi$
$140$		0			0
$141$	10.8284	−	26.1421i	0.911918	−	2.20156i
$142$		0			0
$143$	−0.585786	−	1.41421i	−0.0489859	−	0.118262i
$144$		0			0
$145$	5.82843	+	5.82843i	0.484025	+	0.484025i
$146$		0			0
$147$	14.0711	−	5.82843i	1.16056	−	0.480721i
$148$		0			0
$149$			16.9706i			1.39028i	0.718873	+	0.695141i	$0.244658\pi$
$149$			16.9706i			1.39028i	−0.718873	+	0.695141i	$0.755342\pi$
$150$		0			0
$151$	9.07107	−	9.07107i	0.738193	−	0.738193i	−0.234035	−	0.972228i	$-0.575193\pi$
$151$	9.07107	−	9.07107i	0.738193	−	0.738193i	0.972228	+	0.234035i	$0.0751931\pi$
$152$		0			0
$153$	−15.7782	+	0.464466i	−1.27559	+	0.0375499i
$154$		0			0
$155$	4.24264	−	4.24264i	0.340777	−	0.340777i
$156$		0			0
$157$		−	1.65685i		−	0.132231i	−0.997812	−	0.0661157i	$-0.978939\pi$
$157$		−	1.65685i		−	0.132231i	0.997812	−	0.0661157i	$-0.0210606\pi$
$158$		0			0
$159$	−3.41421	+	1.41421i	−0.270765	+	0.112154i
$160$		0			0
$161$	3.17157	+	3.17157i	0.249955	+	0.249955i
$162$		0			0
$163$	2.17157	+	5.24264i	0.170091	+	0.410635i	0.985822	−	0.167796i	$-0.0536650\pi$
$163$	2.17157	+	5.24264i	0.170091	+	0.410635i	−0.815731	+	0.578431i	$0.803665\pi$
$164$		0			0
$165$	2.00000	−	4.82843i	0.155700	−	0.375893i
$166$		0			0
$167$	−9.24264	−	3.82843i	−0.715217	−	0.296253i	−0.00475555	−	0.999989i	$-0.501514\pi$
$167$	−9.24264	−	3.82843i	−0.715217	−	0.296253i	−0.710461	+	0.703736i	$0.751514\pi$
$168$		0			0
$169$	11.0000			0.846154
$170$		0			0
$171$	−18.4853			−1.41360
$172$		0			0
$173$	−3.12132	−	1.29289i	−0.237310	−	0.0982969i	0.260859	−	0.965377i	$-0.415994\pi$
$173$	−3.12132	−	1.29289i	−0.237310	−	0.0982969i	−0.498169	+	0.867080i	$0.665994\pi$
$174$		0			0
$175$	0.656854	−	1.58579i	0.0496535	−	0.119874i
$176$		0			0
$177$	6.00000	+	14.4853i	0.450988	+	1.08878i
$178$		0			0
$179$	−4.24264	−	4.24264i	−0.317110	−	0.317110i	0.530546	−	0.847656i	$-0.321987\pi$
$179$	−4.24264	−	4.24264i	−0.317110	−	0.317110i	−0.847656	+	0.530546i	$0.821987\pi$
$180$		0			0
$181$	−11.5355	+	4.77817i	−0.857429	+	0.355159i	−0.767702	−	0.640807i	$-0.778600\pi$
$181$	−11.5355	+	4.77817i	−0.857429	+	0.355159i	−0.0897278	+	0.995966i	$0.528600\pi$
$182$		0			0
$183$			24.1421i			1.78464i
$184$		0			0
$185$	−5.00000	+	5.00000i	−0.367607	+	0.367607i
$186$		0			0
$187$	−1.58579	+	4.17157i	−0.115964	+	0.305056i
$188$		0			0
$189$	1.65685	−	1.65685i	0.120518	−	0.120518i
$190$		0			0
$191$			20.0000i			1.44715i	0.690246	+	0.723575i	$0.257502\pi$
$191$			20.0000i			1.44715i	−0.690246	+	0.723575i	$0.742498\pi$
$192$		0			0
$193$	5.12132	−	2.12132i	0.368641	−	0.152696i	−0.190670	−	0.981654i	$-0.561066\pi$
$193$	5.12132	−	2.12132i	0.368641	−	0.152696i	0.559310	+	0.828958i	$0.311066\pi$
$194$		0			0
$195$	−4.82843	−	4.82843i	−0.345771	−	0.345771i
$196$		0			0
$197$	−5.70711	−	13.7782i	−0.406615	−	0.981654i	−0.986022	−	0.166616i	$-0.946716\pi$
$197$	−5.70711	−	13.7782i	−0.406615	−	0.981654i	0.579407	−	0.815038i	$-0.303284\pi$
$198$		0			0
$199$	0.656854	−	1.58579i	0.0465632	−	0.112413i	−0.898887	−	0.438181i	$-0.855623\pi$
$199$	0.656854	−	1.58579i	0.0465632	−	0.112413i	0.945450	+	0.325768i	$0.105623\pi$
$200$		0			0
$201$	−16.4853	−	6.82843i	−1.16278	−	0.481640i
$202$		0			0
$203$	4.82843			0.338889
$204$		0			0
$205$	−15.0711			−1.05261
$206$		0			0
$207$	−14.6569	−	6.07107i	−1.01872	−	0.421968i
$208$		0			0
$209$	−2.00000	+	4.82843i	−0.138343	+	0.333989i
$210$		0			0
$211$	−5.72792	−	13.8284i	−0.394326	−	0.951988i	−0.988986	−	0.148010i	$-0.952713\pi$
$211$	−5.72792	−	13.8284i	−0.394326	−	0.951988i	0.594659	−	0.803978i	$-0.297287\pi$
$212$		0			0
$213$	−24.1421	−	24.1421i	−1.65419	−	1.65419i
$214$		0			0
$215$	8.24264	−	3.41421i	0.562143	−	0.232847i
$216$		0			0
$217$		−	3.51472i		−	0.238595i
$218$		0			0
$219$	−9.89949	+	9.89949i	−0.668946	+	0.668946i
$220$		0			0
$221$	4.24264	+	4.00000i	0.285391	+	0.269069i
$222$		0			0
$223$	−0.585786	+	0.585786i	−0.0392272	+	0.0392272i	−0.726448	−	0.687221i	$-0.758830\pi$
$223$	−0.585786	+	0.585786i	−0.0392272	+	0.0392272i	0.687221	+	0.726448i	$0.258830\pi$
$224$		0			0
$225$			6.07107i			0.404738i
$226$		0			0
$227$	4.65685	−	1.92893i	0.309086	−	0.128028i	−0.222748	−	0.974876i	$-0.571503\pi$
$227$	4.65685	−	1.92893i	0.309086	−	0.128028i	0.531835	+	0.846848i	$0.321503\pi$
$228$		0			0
$229$	16.1421	+	16.1421i	1.06670	+	1.06670i	0.997610	+	0.0690921i	$0.0220102\pi$
$229$	16.1421	+	16.1421i	1.06670	+	1.06670i	0.0690921	+	0.997610i	$0.477990\pi$
$230$		0			0
$231$	−1.17157	−	2.82843i	−0.0770838	−	0.186097i
$232$		0			0
$233$	3.87868	−	9.36396i	0.254101	−	0.613453i	−0.744427	−	0.667704i	$-0.767277\pi$
$233$	3.87868	−	9.36396i	0.254101	−	0.613453i	0.998527	+	0.0542508i	$0.0172771\pi$
$234$		0			0
$235$	−18.4853	−	7.65685i	−1.20585	−	0.499478i
$236$		0			0
$237$	10.8284			0.703382
$238$		0			0
$239$	−9.17157			−0.593260			−0.296630	−	0.954993i	$-0.595863\pi$
$239$	−9.17157			−0.593260			−0.296630	+	0.954993i	$0.595863\pi$
$240$		0			0
$241$	11.3640	+	4.70711i	0.732017	+	0.303211i	0.717381	−	0.696681i	$-0.245341\pi$
$241$	11.3640	+	4.70711i	0.732017	+	0.303211i	0.0146365	+	0.999893i	$0.495341\pi$
$242$		0			0
$243$	8.31371	−	20.0711i	0.533325	−	1.28756i
$244$		0			0
$245$	−4.12132	−	9.94975i	−0.263301	−	0.635666i
$246$		0			0
$247$	4.82843	+	4.82843i	0.307225	+	0.307225i
$248$		0			0
$249$	0.828427	−	0.343146i	0.0524994	−	0.0217460i
$250$		0			0
$251$		−	3.51472i		−	0.221847i	−0.993829	−	0.110924i	$-0.964619\pi$
$251$		−	3.51472i		−	0.221847i	0.993829	−	0.110924i	$-0.0353809\pi$
$252$		0			0
$253$	−3.17157	+	3.17157i	−0.199395	+	0.199395i
$254$		0			0
$255$	0.585786	+	19.8995i	0.0366834	+	1.24615i
$256$		0			0
$257$	−15.6569	+	15.6569i	−0.976648	+	0.976648i	−0.999733	−	0.0230858i	$-0.992651\pi$
$257$	−15.6569	+	15.6569i	−0.976648	+	0.976648i	0.0230858	+	0.999733i	$0.492651\pi$
$258$		0			0
$259$			4.14214i			0.257380i
$260$		0			0
$261$	−15.7782	+	6.53553i	−0.976644	+	0.404539i
$262$		0			0
$263$	4.58579	+	4.58579i	0.282772	+	0.282772i	0.834213	−	0.551442i	$-0.185922\pi$
$263$	4.58579	+	4.58579i	0.282772	+	0.282772i	−0.551442	+	0.834213i	$0.685922\pi$
$264$		0			0
$265$	1.00000	+	2.41421i	0.0614295	+	0.148304i
$266$		0			0
$267$	9.41421	−	22.7279i	0.576141	−	1.39093i
$268$		0			0
$269$	5.87868	+	2.43503i	0.358429	+	0.148466i	0.554629	−	0.832098i	$-0.312860\pi$
$269$	5.87868	+	2.43503i	0.358429	+	0.148466i	−0.196200	+	0.980564i	$0.562860\pi$
$270$		0			0
$271$	6.14214			0.373108			0.186554	−	0.982445i	$-0.440268\pi$
$271$	6.14214			0.373108			0.186554	+	0.982445i	$0.440268\pi$
$272$		0			0
$273$	−4.00000			−0.242091
$274$		0			0
$275$	1.58579	+	0.656854i	0.0956265	+	0.0396098i
$276$		0			0
$277$	8.43503	−	20.3640i	0.506812	−	1.22355i	−0.438897	−	0.898537i	$-0.644631\pi$
$277$	8.43503	−	20.3640i	0.506812	−	1.22355i	0.945709	−	0.325015i	$-0.105369\pi$
$278$		0			0
$279$	4.75736	+	11.4853i	0.284816	+	0.687606i
$280$		0			0
$281$	−12.6569	−	12.6569i	−0.755045	−	0.755045i	0.220371	−	0.975416i	$-0.429273\pi$
$281$	−12.6569	−	12.6569i	−0.755045	−	0.755045i	−0.975416	+	0.220371i	$0.929273\pi$
$282$		0			0
$283$	−21.1421	+	8.75736i	−1.25677	+	0.520571i	−0.908917	−	0.416978i	$-0.863089\pi$
$283$	−21.1421	+	8.75736i	−1.25677	+	0.520571i	−0.347853	+	0.937549i	$0.613089\pi$
$284$		0			0
$285$			23.3137i			1.38098i
$286$		0			0
$287$	−6.24264	+	6.24264i	−0.368491	+	0.368491i
$288$		0			0
$289$	−1.00000	−	16.9706i	−0.0588235	−	0.998268i
$290$		0			0
$291$	11.8995	−	11.8995i	0.697561	−	0.697561i
$292$		0			0
$293$			23.6569i			1.38205i	0.722832	+	0.691024i	$0.242840\pi$
$293$			23.6569i			1.38205i	−0.722832	+	0.691024i	$0.757160\pi$
$294$		0			0
$295$	10.2426	−	4.24264i	0.596350	−	0.247016i
$296$		0			0
$297$	1.65685	+	1.65685i	0.0961404	+	0.0961404i
$298$		0			0
$299$	2.24264	+	5.41421i	0.129695	+	0.313112i
$300$		0			0
$301$	2.00000	−	4.82843i	0.115278	−	0.278306i
$302$		0			0
$303$	−32.3848	−	13.4142i	−1.86046	−	0.770626i
$304$		0			0
$305$	17.0711			0.977486
$306$		0			0
$307$	−2.14214			−0.122258			−0.0611291	−	0.998130i	$-0.519470\pi$
$307$	−2.14214			−0.122258			−0.0611291	+	0.998130i	$0.519470\pi$
$308$		0			0
$309$	10.8284	+	4.48528i	0.616008	+	0.255159i
$310$		0			0
$311$	1.72792	−	4.17157i	0.0979815	−	0.236548i	−0.867287	−	0.497809i	$-0.834138\pi$
$311$	1.72792	−	4.17157i	0.0979815	−	0.236548i	0.965268	+	0.261261i	$0.0841382\pi$
$312$		0			0
$313$	−4.87868	−	11.7782i	−0.275759	−	0.665742i	0.723950	−	0.689852i	$-0.242325\pi$
$313$	−4.87868	−	11.7782i	−0.275759	−	0.665742i	−0.999709	+	0.0241106i	$0.992325\pi$
$314$		0			0
$315$	−5.41421	−	5.41421i	−0.305056	−	0.305056i
$316$		0			0
$317$	−5.36396	+	2.22183i	−0.301270	+	0.124790i	−0.528198	−	0.849122i	$-0.677132\pi$
$317$	−5.36396	+	2.22183i	−0.301270	+	0.124790i	0.226927	+	0.973912i	$0.427132\pi$
$318$		0			0
$319$			4.82843i			0.270340i
$320$		0			0
$321$	11.6569	−	11.6569i	0.650622	−	0.650622i
$322$		0			0
$323$	−0.585786	−	19.8995i	−0.0325940	−	1.10724i
$324$		0			0
$325$	1.58579	−	1.58579i	0.0879636	−	0.0879636i
$326$		0			0
$327$			11.1716i			0.617789i
$328$		0			0
$329$	−10.8284	+	4.48528i	−0.596991	+	0.247282i
$330$		0			0
$331$	12.5858	+	12.5858i	0.691777	+	0.691777i	0.962623	−	0.270845i	$-0.0873032\pi$
$331$	12.5858	+	12.5858i	0.691777	+	0.691777i	−0.270845	+	0.962623i	$0.587303\pi$
$332$		0			0
$333$	−5.60660	−	13.5355i	−0.307240	−	0.741743i
$334$		0			0
$335$	−4.82843	+	11.6569i	−0.263805	+	0.636882i
$336$		0			0
$337$	−31.8492	−	13.1924i	−1.73494	−	0.718635i	−0.999141	−	0.0414336i	$-0.986808\pi$
$337$	−31.8492	−	13.1924i	−1.73494	−	0.718635i	−0.735798	−	0.677202i	$-0.763192\pi$
$338$		0			0
$339$	42.2843			2.29657
$340$		0			0
$341$	3.51472			0.190333
$342$		0			0
$343$	−12.8284	−	5.31371i	−0.692670	−	0.286913i
$344$		0			0
$345$	−7.65685	+	18.4853i	−0.412231	+	0.995214i
$346$		0			0
$347$	1.48528	+	3.58579i	0.0797341	+	0.192495i	0.958719	−	0.284354i	$-0.0917790\pi$
$347$	1.48528	+	3.58579i	0.0797341	+	0.192495i	−0.878985	+	0.476849i	$0.841779\pi$
$348$		0			0
$349$	3.00000	+	3.00000i	0.160586	+	0.160586i	0.782826	−	0.622240i	$-0.213777\pi$
$349$	3.00000	+	3.00000i	0.160586	+	0.160586i	−0.622240	+	0.782826i	$0.713777\pi$
$350$		0			0
$351$	2.82843	−	1.17157i	0.150970	−	0.0625339i
$352$		0			0
$353$		−	14.0000i		−	0.745145i	−0.928003	−	0.372572i	$-0.878476\pi$
$353$		−	14.0000i		−	0.745145i	0.928003	−	0.372572i	$-0.121524\pi$
$354$		0			0
$355$	−17.0711	+	17.0711i	−0.906038	+	0.906038i
$356$		0			0
$357$	8.48528	+	8.00000i	0.449089	+	0.423405i
$358$		0			0
$359$	−16.3848	+	16.3848i	−0.864755	+	0.864755i	−0.991886	−	0.127131i	$-0.959423\pi$
$359$	−16.3848	+	16.3848i	−0.864755	+	0.864755i	0.127131	+	0.991886i	$0.459423\pi$
$360$		0			0
$361$		−	4.31371i		−	0.227037i
$362$		0			0
$363$	−23.7279	+	9.82843i	−1.24539	+	0.515859i
$364$		0			0
$365$	7.00000	+	7.00000i	0.366397	+	0.366397i
$366$		0			0
$367$	−10.0711	−	24.3137i	−0.525705	−	1.26917i	−0.934313	−	0.356455i	$-0.883985\pi$
$367$	−10.0711	−	24.3137i	−0.525705	−	1.26917i	0.408607	−	0.912710i	$-0.366015\pi$
$368$		0			0
$369$	11.9497	−	28.8492i	0.622079	−	1.50183i
$370$		0			0
$371$	1.41421	+	0.585786i	0.0734223	+	0.0304125i
$372$		0			0
$373$	−19.5563			−1.01259			−0.506295	−	0.862361i	$-0.668985\pi$
$373$	−19.5563			−1.01259			−0.506295	+	0.862361i	$0.668985\pi$
$374$		0			0
$375$	31.7990			1.64209
$376$		0			0
$377$	5.82843	+	2.41421i	0.300179	+	0.124338i
$378$		0			0
$379$	−0.414214	+	1.00000i	−0.0212767	+	0.0513665i	−0.934161	−	0.356852i	$-0.883850\pi$
$379$	−0.414214	+	1.00000i	−0.0212767	+	0.0513665i	0.912884	+	0.408219i	$0.133850\pi$
$380$		0			0
$381$	17.3137	+	41.7990i	0.887008	+	2.14143i
$382$		0			0
$383$	−3.89949	−	3.89949i	−0.199255	−	0.199255i	0.600426	−	0.799681i	$-0.294998\pi$
$383$	−3.89949	−	3.89949i	−0.199255	−	0.199255i	−0.799681	+	0.600426i	$0.794998\pi$
$384$		0			0
$385$	−2.00000	+	0.828427i	−0.101929	+	0.0422206i
$386$		0			0
$387$			18.4853i			0.939660i
$388$		0			0
$389$	−11.4142	+	11.4142i	−0.578724	+	0.578724i	−0.934551	−	0.355828i	$-0.884199\pi$
$389$	−11.4142	+	11.4142i	−0.578724	+	0.578724i	0.355828	+	0.934551i	$0.384199\pi$
$390$		0			0
$391$	6.07107	−	15.9706i	0.307027	−	0.807666i
$392$		0			0
$393$	−0.343146	+	0.343146i	−0.0173094	+	0.0173094i
$394$		0			0
$395$		−	7.65685i		−	0.385258i
$396$		0			0
$397$	25.1924	−	10.4350i	1.26437	−	0.523719i	0.353122	−	0.935577i	$-0.385120\pi$
$397$	25.1924	−	10.4350i	1.26437	−	0.523719i	0.911248	+	0.411858i	$0.135120\pi$
$398$		0			0
$399$	9.65685	+	9.65685i	0.483447	+	0.483447i
$400$		0			0
$401$	6.53553	+	15.7782i	0.326369	+	0.787924i	0.998856	+	0.0478157i	$0.0152260\pi$
$401$	6.53553	+	15.7782i	0.326369	+	0.787924i	−0.672487	+	0.740109i	$0.734774\pi$
$402$		0			0
$403$	1.75736	−	4.24264i	0.0875403	−	0.211341i
$404$		0			0
$405$	−9.94975	−	4.12132i	−0.494407	−	0.204790i
$406$		0			0
$407$	−4.14214			−0.205318
$408$		0			0
$409$	19.3137			0.955001			0.477501	−	0.878631i	$-0.341543\pi$
$409$	19.3137			0.955001			0.477501	+	0.878631i	$0.341543\pi$
$410$		0			0
$411$	21.0711	+	8.72792i	1.03936	+	0.430517i
$412$		0			0
$413$	2.48528	−	6.00000i	0.122293	−	0.295241i
$414$		0			0
$415$	−0.242641	−	0.585786i	−0.0119108	−	0.0287551i
$416$		0			0
$417$	27.6569	+	27.6569i	1.35436	+	1.35436i
$418$		0			0
$419$	24.8995	−	10.3137i	1.21642	−	0.503858i	0.320150	−	0.947367i	$-0.396267\pi$
$419$	24.8995	−	10.3137i	1.21642	−	0.503858i	0.896270	+	0.443509i	$0.146267\pi$
$420$		0			0
$421$			17.4142i			0.848717i	0.905494	+	0.424358i	$0.139500\pi$
$421$			17.4142i			0.848717i	−0.905494	+	0.424358i	$0.860500\pi$
$422$		0			0
$423$	29.3137	−	29.3137i	1.42528	−	1.42528i
$424$		0			0
$425$	−6.53553	+	0.192388i	−0.317020	+	0.00933220i
$426$		0			0
$427$	7.07107	−	7.07107i	0.342193	−	0.342193i
$428$		0			0
$429$		−	4.00000i		−	0.193122i
$430$		0			0
$431$	36.7990	−	15.2426i	1.77254	−	0.734212i	0.778200	−	0.628017i	$-0.216133\pi$
$431$	36.7990	−	15.2426i	1.77254	−	0.734212i	0.994345	−	0.106195i	$-0.0338669\pi$
$432$		0			0
$433$	−10.7279	−	10.7279i	−0.515551	−	0.515551i	0.400671	−	0.916222i	$-0.368777\pi$
$433$	−10.7279	−	10.7279i	−0.515551	−	0.515551i	−0.916222	+	0.400671i	$0.868777\pi$
$434$		0			0
$435$	8.24264	+	19.8995i	0.395204	+	0.954108i
$436$		0			0
$437$	7.65685	−	18.4853i	0.366277	−	0.884271i
$438$		0			0
$439$	−10.0711	−	4.17157i	−0.480666	−	0.199098i	0.129176	−	0.991622i	$-0.458767\pi$
$439$	−10.0711	−	4.17157i	−0.480666	−	0.199098i	−0.609841	+	0.792523i	$0.708767\pi$
$440$		0			0
$441$	22.3137			1.06256
$442$		0			0
$443$	−15.7990			−0.750633			−0.375316	−	0.926897i	$-0.622466\pi$
$443$	−15.7990			−0.750633			−0.375316	+	0.926897i	$0.622466\pi$
$444$		0			0
$445$	−16.0711	−	6.65685i	−0.761842	−	0.315565i
$446$		0			0
$447$	−16.9706	+	40.9706i	−0.802680	+	1.93784i
$448$		0			0
$449$	−7.19239	−	17.3640i	−0.339430	−	0.819456i	−0.997771	−	0.0667361i	$-0.978741\pi$
$449$	−7.19239	−	17.3640i	−0.339430	−	0.819456i	0.658341	−	0.752720i	$-0.271259\pi$
$450$		0			0
$451$	−6.24264	−	6.24264i	−0.293954	−	0.293954i
$452$		0			0
$453$	30.9706	−	12.8284i	1.45512	−	0.602732i
$454$		0			0
$455$			2.82843i			0.132599i
$456$		0			0
$457$	−13.3137	+	13.3137i	−0.622789	+	0.622789i	−0.946244	−	0.323455i	$-0.895156\pi$
$457$	−13.3137	+	13.3137i	−0.622789	+	0.622789i	0.323455	+	0.946244i	$0.395156\pi$
$458$		0			0
$459$	−8.34315	−	3.17157i	−0.389425	−	0.148036i
$460$		0			0
$461$	17.0000	−	17.0000i	0.791769	−	0.791769i	−0.190013	−	0.981782i	$-0.560853\pi$
$461$	17.0000	−	17.0000i	0.791769	−	0.791769i	0.981782	+	0.190013i	$0.0608529\pi$
$462$		0			0
$463$		−	30.6274i		−	1.42338i	−0.702495	−	0.711688i	$-0.747931\pi$
$463$		−	30.6274i		−	1.42338i	0.702495	−	0.711688i	$-0.252069\pi$
$464$		0			0
$465$	14.4853	−	6.00000i	0.671739	−	0.278243i
$466$		0			0
$467$	−8.92893	−	8.92893i	−0.413182	−	0.413182i	0.469664	−	0.882845i	$-0.344375\pi$
$467$	−8.92893	−	8.92893i	−0.413182	−	0.413182i	−0.882845	+	0.469664i	$0.844375\pi$
$468$		0			0
$469$	2.82843	+	6.82843i	0.130605	+	0.315307i
$470$		0			0
$471$	1.65685	−	4.00000i	0.0763438	−	0.184310i
$472$		0			0
$473$	4.82843	+	2.00000i	0.222011	+	0.0919601i
$474$		0			0
$475$	−7.65685			−0.351321
$476$		0			0
$477$	−5.41421			−0.247900
$478$		0			0
$479$	31.9706	+	13.2426i	1.46077	+	0.605072i	0.964733	−	0.263229i	$-0.0847874\pi$
$479$	31.9706	+	13.2426i	1.46077	+	0.605072i	0.496039	+	0.868300i	$0.334787\pi$
$480$		0			0
$481$	−2.07107	+	5.00000i	−0.0944326	+	0.227980i
$482$		0			0
$483$	4.48528	+	10.8284i	0.204087	+	0.492710i
$484$		0			0
$485$	−8.41421	−	8.41421i	−0.382070	−	0.382070i
$486$		0			0
$487$	4.07107	−	1.68629i	0.184478	−	0.0764132i	−0.288533	−	0.957470i	$-0.593167\pi$
$487$	4.07107	−	1.68629i	0.184478	−	0.0764132i	0.473010	+	0.881057i	$0.343167\pi$
$488$		0			0
$489$			14.8284i			0.670565i
$490$		0			0
$491$	−17.7574	+	17.7574i	−0.801378	+	0.801378i	−0.983311	−	0.181933i	$-0.941765\pi$
$491$	−17.7574	+	17.7574i	−0.801378	+	0.801378i	0.181933	+	0.983311i	$0.441765\pi$
$492$		0			0
$493$	−7.53553	−	16.7782i	−0.339383	−	0.755651i
$494$		0			0
$495$	5.41421	−	5.41421i	0.243351	−	0.243351i
$496$		0			0
$497$			14.1421i			0.634361i
$498$		0			0
$499$	−34.2132	+	14.1716i	−1.53159	+	0.634407i	−0.979873	−	0.199622i	$-0.936028\pi$
$499$	−34.2132	+	14.1716i	−1.53159	+	0.634407i	−0.551720	+	0.834029i	$0.686028\pi$
$500$		0			0
$501$	−18.4853	−	18.4853i	−0.825861	−	0.825861i
$502$		0			0
$503$	−5.72792	−	13.8284i	−0.255395	−	0.616579i	0.743228	−	0.669039i	$-0.233294\pi$
$503$	−5.72792	−	13.8284i	−0.255395	−	0.616579i	−0.998623	+	0.0524595i	$0.983294\pi$
$504$		0			0
$505$	−9.48528	+	22.8995i	−0.422089	+	1.01901i
$506$		0			0
$507$	26.5563	+	11.0000i	1.17941	+	0.488527i
$508$		0			0
$509$	−3.02944			−0.134277			−0.0671387	−	0.997744i	$-0.521387\pi$
$509$	−3.02944			−0.134277			−0.0671387	+	0.997744i	$0.521387\pi$
$510$		0			0
$511$	5.79899			0.256532
$512$		0			0
$513$	−9.65685	−	4.00000i	−0.426361	−	0.176604i
$514$		0			0
$515$	3.17157	−	7.65685i	0.139756	−	0.337401i
$516$		0			0
$517$	−4.48528	−	10.8284i	−0.197262	−	0.476234i
$518$		0			0
$519$	−6.24264	−	6.24264i	−0.274022	−	0.274022i
$520$		0			0
$521$	2.87868	−	1.19239i	0.126117	−	0.0522395i	−0.318732	−	0.947845i	$-0.603257\pi$
$521$	2.87868	−	1.19239i	0.126117	−	0.0522395i	0.444850	+	0.895605i	$0.353257\pi$
$522$		0			0
$523$		−	6.82843i		−	0.298586i	−0.988793	−	0.149293i	$-0.952300\pi$
$523$		−	6.82843i		−	0.298586i	0.988793	−	0.149293i	$-0.0476998\pi$
$524$		0			0
$525$	3.17157	−	3.17157i	0.138419	−	0.138419i
$526$		0			0
$527$	−12.2132	+	5.48528i	−0.532015	+	0.238943i
$528$		0			0
$529$	−4.12132	+	4.12132i	−0.179188	+	0.179188i
$530$		0			0
$531$			22.9706i			0.996838i
$532$		0			0
$533$	−10.6569	+	4.41421i	−0.461600	+	0.191201i
$534$		0			0
$535$	−8.24264	−	8.24264i	−0.356360	−	0.356360i
$536$		0			0
$537$	−6.00000	−	14.4853i	−0.258919	−	0.625086i
$538$		0			0
$539$	2.41421	−	5.82843i	0.103988	−	0.251048i
$540$		0			0
$541$	−16.9497	−	7.02082i	−0.728727	−	0.301848i	−0.0126980	−	0.999919i	$-0.504042\pi$
$541$	−16.9497	−	7.02082i	−0.728727	−	0.301848i	−0.716029	+	0.698071i	$0.754042\pi$
$542$		0			0
$543$	−32.6274			−1.40018
$544$		0			0
$545$	7.89949			0.338377
$546$		0			0
$547$	−22.8995	−	9.48528i	−0.979112	−	0.405561i	−0.165015	−	0.986291i	$-0.552767\pi$
$547$	−22.8995	−	9.48528i	−0.979112	−	0.405561i	−0.814096	+	0.580730i	$0.802767\pi$
$548$		0			0
$549$	−13.5355	+	32.6777i	−0.577683	+	1.39465i
$550$		0			0
$551$	−8.24264	−	19.8995i	−0.351148	−	0.847747i
$552$		0			0
$553$	−3.17157	−	3.17157i	−0.134869	−	0.134869i
$554$		0			0
$555$	−17.0711	+	7.07107i	−0.724626	+	0.300150i
$556$		0			0
$557$		−	28.2426i		−	1.19668i	−0.801243	−	0.598340i	$-0.795827\pi$
$557$		−	28.2426i		−	1.19668i	0.801243	−	0.598340i	$-0.204173\pi$
$558$		0			0
$559$	4.82843	−	4.82843i	0.204221	−	0.204221i
$560$		0			0
$561$	−8.00000	+	8.48528i	−0.337760	+	0.358249i
$562$		0			0
$563$	−27.4142	+	27.4142i	−1.15537	+	1.15537i	−0.169912	+	0.985459i	$0.554348\pi$
$563$	−27.4142	+	27.4142i	−1.15537	+	1.15537i	−0.985459	+	0.169912i	$0.945652\pi$
$564$		0			0
$565$		−	29.8995i		−	1.25788i
$566$		0			0
$567$	−5.82843	+	2.41421i	−0.244771	+	0.101387i
$568$		0			0
$569$	25.4853	+	25.4853i	1.06840	+	1.06840i	0.997482	+	0.0709163i	$0.0225923\pi$
$569$	25.4853	+	25.4853i	1.06840	+	1.06840i	0.0709163	+	0.997482i	$0.477408\pi$
$570$		0			0
$571$	18.0711	+	43.6274i	0.756251	+	1.82575i	0.520295	+	0.853987i	$0.325822\pi$
$571$	18.0711	+	43.6274i	0.756251	+	1.82575i	0.235956	+	0.971764i	$0.424178\pi$
$572$		0			0
$573$	−20.0000	+	48.2843i	−0.835512	+	2.01710i
$574$		0			0
$575$	−6.07107	−	2.51472i	−0.253181	−	0.104871i
$576$		0			0
$577$	−12.9289			−0.538238			−0.269119	−	0.963107i	$-0.586733\pi$
$577$	−12.9289			−0.538238			−0.269119	+	0.963107i	$0.586733\pi$
$578$		0			0
$579$	14.4853			0.601988
$580$		0			0
$581$	−0.343146	−	0.142136i	−0.0142361	−	0.00589678i
$582$		0			0
$583$	−0.585786	+	1.41421i	−0.0242608	+	0.0585707i
$584$		0			0
$585$	−3.82843	−	9.24264i	−0.158286	−	0.382136i
$586$		0			0
$587$	16.0416	+	16.0416i	0.662109	+	0.662109i	0.955877	−	0.293768i	$-0.0949093\pi$
$587$	16.0416	+	16.0416i	0.662109	+	0.662109i	−0.293768	+	0.955877i	$0.594909\pi$
$588$		0			0
$589$	−14.4853	+	6.00000i	−0.596856	+	0.247226i
$590$		0			0
$591$		−	38.9706i		−	1.60303i
$592$		0			0
$593$	−19.1421	+	19.1421i	−0.786073	+	0.786073i	−0.980848	−	0.194775i	$-0.937602\pi$
$593$	−19.1421	+	19.1421i	−0.786073	+	0.786073i	0.194775	+	0.980848i	$0.437602\pi$
$594$		0			0
$595$	5.65685	−	6.00000i	0.231908	−	0.245976i
$596$		0			0
$597$	3.17157	−	3.17157i	0.129804	−	0.129804i
$598$		0			0
$599$			34.6274i			1.41484i	0.706794	+	0.707419i	$0.250141\pi$
$599$			34.6274i			1.41484i	−0.706794	+	0.707419i	$0.749859\pi$
$600$		0			0
$601$	−18.7782	+	7.77817i	−0.765978	+	0.317278i	−0.731242	−	0.682118i	$-0.761059\pi$
$601$	−18.7782	+	7.77817i	−0.765978	+	0.317278i	−0.0347358	+	0.999397i	$0.511059\pi$
$602$		0			0
$603$	−18.4853	−	18.4853i	−0.752779	−	0.752779i
$604$		0			0
$605$	6.94975	+	16.7782i	0.282547	+	0.682130i
$606$		0			0
$607$	13.1421	−	31.7279i	0.533423	−	1.28780i	−0.395820	−	0.918328i	$-0.629540\pi$
$607$	13.1421	−	31.7279i	0.533423	−	1.28780i	0.929243	−	0.369469i	$-0.120460\pi$
$608$		0			0
$609$	11.6569	+	4.82843i	0.472360	+	0.195658i
$610$		0			0
$611$	−15.3137			−0.619526
$612$		0			0
$613$	−17.3137			−0.699294			−0.349647	−	0.936881i	$-0.613698\pi$
$613$	−17.3137			−0.699294			−0.349647	+	0.936881i	$0.613698\pi$
$614$		0			0
$615$	−36.3848	−	15.0711i	−1.46718	−	0.607724i
$616$		0			0
$617$	−1.29289	+	3.12132i	−0.0520499	+	0.125660i	−0.947766	−	0.318968i	$-0.896664\pi$
$617$	−1.29289	+	3.12132i	−0.0520499	+	0.125660i	0.895716	+	0.444627i	$0.146664\pi$
$618$		0			0
$619$	−3.68629	−	8.89949i	−0.148165	−	0.357701i	0.832320	−	0.554295i	$-0.187012\pi$
$619$	−3.68629	−	8.89949i	−0.148165	−	0.357701i	−0.980485	+	0.196594i	$0.937012\pi$
$620$		0			0
$621$	−6.34315	−	6.34315i	−0.254542	−	0.254542i
$622$		0			0
$623$	−9.41421	+	3.89949i	−0.377173	+	0.156230i
$624$		0			0
$625$		−	14.5563i		−	0.582254i
$626$		0			0
$627$	−9.65685	+	9.65685i	−0.385658	+	0.385658i
$628$		0			0
$629$	14.3934	−	6.46447i	0.573902	−	0.257755i
$630$		0			0
$631$	−4.72792	+	4.72792i	−0.188216	+	0.188216i	−0.794924	−	0.606709i	$-0.792489\pi$
$631$	−4.72792	+	4.72792i	−0.188216	+	0.188216i	0.606709	+	0.794924i	$0.292489\pi$
$632$		0			0
$633$		−	39.1127i		−	1.55459i
$634$		0			0
$635$	29.5563	−	12.2426i	1.17291	−	0.485834i
$636$		0			0
$637$	−5.82843	−	5.82843i	−0.230931	−	0.230931i
$638$		0			0
$639$	−19.1421	−	46.2132i	−0.757251	−	1.82817i
$640$		0			0
$641$	−5.73654	+	13.8492i	−0.226580	+	0.547012i	−0.995757	−	0.0920237i	$-0.970666\pi$
$641$	−5.73654	+	13.8492i	−0.226580	+	0.547012i	0.769177	+	0.639036i	$0.220666\pi$
$642$		0			0
$643$	37.0416	+	15.3431i	1.46078	+	0.605075i	0.964735	−	0.263223i	$-0.0847854\pi$
$643$	37.0416	+	15.3431i	1.46078	+	0.605075i	0.496044	+	0.868297i	$0.334785\pi$
$644$		0			0
$645$	23.3137			0.917976
$646$		0			0
$647$	−2.82843			−0.111197			−0.0555985	−	0.998453i	$-0.517707\pi$
$647$	−2.82843			−0.111197			−0.0555985	+	0.998453i	$0.517707\pi$
$648$		0			0
$649$	6.00000	+	2.48528i	0.235521	+	0.0975558i
$650$		0			0
$651$	3.51472	−	8.48528i	0.137753	−	0.332564i
$652$		0			0
$653$	−6.77817	−	16.3640i	−0.265250	−	0.640371i	0.733997	−	0.679152i	$-0.237652\pi$
$653$	−6.77817	−	16.3640i	−0.265250	−	0.640371i	−0.999248	+	0.0387812i	$0.987652\pi$
$654$		0			0
$655$	0.242641	+	0.242641i	0.00948076	+	0.00948076i
$656$		0			0
$657$	−18.9497	+	7.84924i	−0.739300	+	0.306228i
$658$		0			0
$659$		−	8.48528i		−	0.330540i	−0.986248	−	0.165270i	$-0.947151\pi$
$659$		−	8.48528i		−	0.330540i	0.986248	−	0.165270i	$-0.0528495\pi$
$660$		0			0
$661$	29.1421	−	29.1421i	1.13350	−	1.13350i	0.143906	−	0.989591i	$-0.454034\pi$
$661$	29.1421	−	29.1421i	1.13350	−	1.13350i	0.989591	−	0.143906i	$-0.0459664\pi$
$662$		0			0
$663$	6.24264	+	13.8995i	0.242444	+	0.539812i
$664$		0			0
$665$	6.82843	−	6.82843i	0.264795	−	0.264795i
$666$		0			0
$667$		−	18.4853i		−	0.715753i
$668$		0			0
$669$	−2.00000	+	0.828427i	−0.0773245	+	0.0320288i
$670$		0			0
$671$	7.07107	+	7.07107i	0.272976	+	0.272976i
$672$		0			0
$673$	−0.121320	−	0.292893i	−0.00467656	−	0.0112902i	0.921524	−	0.388321i	$-0.126945\pi$
$673$	−0.121320	−	0.292893i	−0.00467656	−	0.0112902i	−0.926201	+	0.377031i	$0.876945\pi$
$674$		0			0
$675$	−1.31371	+	3.17157i	−0.0505647	+	0.122074i
$676$		0			0
$677$	40.5772	+	16.8076i	1.55951	+	0.645969i	0.985004	−	0.172533i	$-0.0551952\pi$
$677$	40.5772	+	16.8076i	1.55951	+	0.645969i	0.574503	+	0.818502i	$0.305195\pi$
$678$		0			0
$679$	−6.97056			−0.267506
$680$		0			0
$681$	13.1716			0.504736
$682$		0			0
$683$	28.8995	+	11.9706i	1.10581	+	0.458041i	0.859492	−	0.511149i	$-0.170780\pi$
$683$	28.8995	+	11.9706i	1.10581	+	0.458041i	0.246316	+	0.969190i	$0.420780\pi$
$684$		0			0
$685$	6.17157	−	14.8995i	0.235804	−	0.569280i
$686$		0			0
$687$	22.8284	+	55.1127i	0.870959	+	2.10268i
$688$		0			0
$689$	1.41421	+	1.41421i	0.0538772	+	0.0538772i
$690$		0			0
$691$	−37.6274	+	15.5858i	−1.43141	+	0.592911i	−0.957700	−	0.287767i	$-0.907087\pi$
$691$	−37.6274	+	15.5858i	−1.43141	+	0.592911i	−0.473714	+	0.880679i	$0.657087\pi$
$692$		0			0
$693$		−	4.48528i		−	0.170382i
$694$		0			0
$695$	19.5563	−	19.5563i	0.741815	−	0.741815i
$696$		0			0
$697$	31.4350	+	11.9497i	1.19069	+	0.452629i
$698$		0			0
$699$	18.7279	−	18.7279i	0.708355	−	0.708355i
$700$		0			0
$701$			21.6985i			0.819540i	0.912189	+	0.409770i	$0.134391\pi$
$701$			21.6985i			0.819540i	−0.912189	+	0.409770i	$0.865609\pi$
$702$		0			0
$703$	17.0711	−	7.07107i	0.643848	−	0.266690i
$704$		0			0
$705$	−36.9706	−	36.9706i	−1.39239	−	1.39239i
$706$		0			0
$707$	5.55635	+	13.4142i	0.208968	+	0.504493i
$708$		0			0
$709$	−4.43503	+	10.7071i	−0.166561	+	0.402114i	−0.985017	−	0.172455i	$-0.944830\pi$
$709$	−4.43503	+	10.7071i	−0.166561	+	0.402114i	0.818456	+	0.574569i	$0.194830\pi$
$710$		0			0
$711$	14.6569	+	6.07107i	0.549675	+	0.227683i
$712$		0			0
$713$	−13.4558			−0.503925
$714$		0			0
$715$	−2.82843			−0.105777
$716$		0			0
$717$	−22.1421	−	9.17157i	−0.826913	−	0.342519i
$718$		0			0
$719$	−5.38478	+	13.0000i	−0.200818	+	0.484818i	−0.991920	−	0.126867i	$-0.959508\pi$
$719$	−5.38478	+	13.0000i	−0.200818	+	0.484818i	0.791102	+	0.611685i	$0.209508\pi$
$720$		0			0
$721$	−1.85786	−	4.48528i	−0.0691905	−	0.167041i
$722$		0			0
$723$	22.7279	+	22.7279i	0.845261	+	0.845261i
$724$		0			0
$725$	−6.53553	+	2.70711i	−0.242724	+	0.100539i
$726$		0			0
$727$		−	19.1127i		−	0.708851i	−0.935084	−	0.354425i	$-0.884676\pi$
$727$		−	19.1127i		−	0.708851i	0.935084	−	0.354425i	$-0.115324\pi$
$728$		0			0
$729$	27.7782	−	27.7782i	1.02882	−	1.02882i
$730$		0			0
$731$	−19.8995	+	0.585786i	−0.736009	+	0.0216661i
$732$		0			0
$733$	−8.51472	+	8.51472i	−0.314498	+	0.314498i	−0.846649	−	0.532151i	$-0.821384\pi$
$733$	−8.51472	+	8.51472i	−0.314498	+	0.314498i	0.532151	+	0.846649i	$0.321384\pi$
$734$		0			0
$735$		−	28.1421i		−	1.03804i
$736$		0			0
$737$	−6.82843	+	2.82843i	−0.251528	+	0.104186i
$738$		0			0
$739$	−24.2426	−	24.2426i	−0.891780	−	0.891780i	0.102911	−	0.994691i	$-0.467184\pi$
$739$	−24.2426	−	24.2426i	−0.891780	−	0.891780i	−0.994691	+	0.102911i	$0.967184\pi$
$740$		0			0
$741$	6.82843	+	16.4853i	0.250849	+	0.605602i
$742$		0			0
$743$	−18.8579	+	45.5269i	−0.691828	+	1.67022i	0.0492371	+	0.998787i	$0.484321\pi$
$743$	−18.8579	+	45.5269i	−0.691828	+	1.67022i	−0.741065	+	0.671433i	$0.765679\pi$
$744$		0			0
$745$	28.9706	+	12.0000i	1.06140	+	0.439646i
$746$		0			0
$747$	1.31371			0.0480661
$748$		0			0
$749$	−6.82843			−0.249505
$750$		0			0
$751$	24.2132	+	10.0294i	0.883552	+	0.365979i	0.777873	−	0.628421i	$-0.216298\pi$
$751$	24.2132	+	10.0294i	0.883552	+	0.365979i	0.105679	+	0.994400i	$0.466298\pi$
$752$		0			0
$753$	3.51472	−	8.48528i	0.128083	−	0.309221i
$754$		0			0
$755$	−9.07107	−	21.8995i	−0.330130	−	0.797004i
$756$		0			0
$757$	37.7990	+	37.7990i	1.37383	+	1.37383i	0.854692	+	0.519136i	$0.173746\pi$
$757$	37.7990	+	37.7990i	1.37383	+	1.37383i	0.519136	+	0.854692i	$0.326254\pi$
$758$		0			0
$759$	−10.8284	+	4.48528i	−0.393047	+	0.162805i
$760$		0			0
$761$		−	21.6985i		−	0.786569i	−0.919417	−	0.393285i	$-0.871339\pi$
$761$		−	21.6985i		−	0.786569i	0.919417	−	0.393285i	$-0.128661\pi$
$762$		0			0
$763$	3.27208	−	3.27208i	0.118457	−	0.118457i
$764$		0			0
$765$	−10.3640	+	27.2635i	−0.374710	+	0.985712i
$766$		0			0
$767$	6.00000	−	6.00000i	0.216647	−	0.216647i
$768$		0			0
$769$			12.7279i			0.458981i	0.973311	+	0.229490i	$0.0737059\pi$
$769$			12.7279i			0.458981i	−0.973311	+	0.229490i	$0.926294\pi$
$770$		0			0
$771$	−53.4558	+	22.1421i	−1.92517	+	0.797430i
$772$		0			0
$773$	−3.41421	−	3.41421i	−0.122801	−	0.122801i	0.643036	−	0.765836i	$-0.277675\pi$
$773$	−3.41421	−	3.41421i	−0.122801	−	0.122801i	−0.765836	+	0.643036i	$0.777675\pi$
$774$		0			0
$775$	1.97056	+	4.75736i	0.0707847	+	0.170889i
$776$		0			0
$777$	−4.14214	+	10.0000i	−0.148598	+	0.358748i
$778$		0			0
$779$	36.3848	+	15.0711i	1.30362	+	0.539977i
$780$		0			0
$781$	−14.1421			−0.506045
$782$		0			0
$783$	−9.65685			−0.345108
$784$		0			0
$785$	−2.82843	−	1.17157i	−0.100951	−	0.0418152i
$786$		0			0
$787$	19.0000	−	45.8701i	0.677277	−	1.63509i	−0.0916786	−	0.995789i	$-0.529223\pi$
$787$	19.0000	−	45.8701i	0.677277	−	1.63509i	0.768955	−	0.639302i	$-0.220777\pi$
$788$		0			0
$789$	6.48528	+	15.6569i	0.230882	+	0.557399i
$790$		0			0
$791$	−12.3848	−	12.3848i	−0.440352	−	0.440352i
$792$		0			0
$793$	12.0711	−	5.00000i	0.428656	−	0.177555i
$794$		0			0
$795$			6.82843i			0.242179i
$796$		0			0
$797$	−12.1716	+	12.1716i	−0.431139	+	0.431139i	−0.889016	−	0.457877i	$-0.848610\pi$
$797$	−12.1716	+	12.1716i	−0.431139	+	0.431139i	0.457877	+	0.889016i	$0.348610\pi$
$798$		0			0
$799$	32.4853	+	30.6274i	1.14925	+	1.08352i
$800$		0			0
$801$	25.4853	−	25.4853i	0.900478	−	0.900478i
$802$		0			0
$803$			5.79899i			0.204642i
$804$		0			0
$805$	7.65685	−	3.17157i	0.269869	−	0.111783i
$806$		0			0
$807$	11.7574	+	11.7574i	0.413879	+	0.413879i
$808$		0			0
$809$	−11.3934	−	27.5061i	−0.400571	−	0.967063i	−0.987528	−	0.157445i	$-0.949674\pi$
$809$	−11.3934	−	27.5061i	−0.400571	−	0.967063i	0.586957	−	0.809618i	$-0.300326\pi$
$810$		0			0
$811$	−16.9411	+	40.8995i	−0.594883	+	1.43618i	0.283853	+	0.958868i	$0.408387\pi$
$811$	−16.9411	+	40.8995i	−0.594883	+	1.43618i	−0.878736	+	0.477308i	$0.841613\pi$
$812$		0			0
$813$	14.8284	+	6.14214i	0.520056	+	0.215414i
$814$		0			0
$815$	10.4853			0.367283
$816$		0			0
$817$	−23.3137			−0.815643
$818$		0			0
$819$	−5.41421	−	2.24264i	−0.189188	−	0.0783642i
$820$		0			0
$821$	−5.50610	+	13.2929i	−0.192164	+	0.463925i	−0.990368	−	0.138463i	$-0.955784\pi$
$821$	−5.50610	+	13.2929i	−0.192164	+	0.463925i	0.798204	+	0.602388i	$0.205784\pi$
$822$		0			0
$823$	−9.00000	−	21.7279i	−0.313720	−	0.757388i	−0.999561	−	0.0296358i	$-0.990565\pi$
$823$	−9.00000	−	21.7279i	−0.313720	−	0.757388i	0.685840	−	0.727752i	$-0.259435\pi$
$824$		0			0
$825$	3.17157	+	3.17157i	0.110420	+	0.110420i
$826$		0			0
$827$	32.0711	−	13.2843i	1.11522	−	0.461939i	0.252488	−	0.967600i	$-0.418751\pi$
$827$	32.0711	−	13.2843i	1.11522	−	0.461939i	0.862732	+	0.505661i	$0.168751\pi$
$828$		0			0
$829$		−	13.9411i		−	0.484195i	−0.970252	−	0.242098i	$-0.922165\pi$
$829$		−	13.9411i		−	0.484195i	0.970252	−	0.242098i	$-0.0778354\pi$
$830$		0			0
$831$	40.7279	−	40.7279i	1.41284	−	1.41284i
$832$		0			0
$833$	0.707107	+	24.0208i	0.0244998	+	0.832272i
$834$		0			0
$835$	−13.0711	+	13.0711i	−0.452343	+	0.452343i
$836$		0			0
$837$			7.02944i			0.242973i
$838$		0			0
$839$	3.58579	−	1.48528i	0.123795	−	0.0512776i	−0.319926	−	0.947443i	$-0.603658\pi$
$839$	3.58579	−	1.48528i	0.123795	−	0.0512776i	0.443721	+	0.896165i	$0.353658\pi$
$840$		0			0
$841$	6.43503	+	6.43503i	0.221898	+	0.221898i
$842$		0			0
$843$	−17.8995	−	43.2132i	−0.616491	−	1.48834i
$844$		0			0
$845$	7.77817	−	18.7782i	0.267577	−	0.645989i
$846$		0			0
$847$	9.82843	+	4.07107i	0.337709	+	0.139884i
$848$		0			0
$849$	−59.7990			−2.05230
$850$		0			0
$851$	15.8579			0.543601
$852$		0			0
$853$	39.3345	+	16.2929i	1.34679	+	0.557858i	0.935397	−	0.353601i	$-0.115043\pi$
$853$	39.3345	+	16.2929i	1.34679	+	0.557858i	0.411392	+	0.911459i	$0.365043\pi$
$854$		0			0
$855$	−13.0711	+	31.5563i	−0.447021	+	1.07920i
$856$		0			0
$857$	−1.46447	−	3.53553i	−0.0500252	−	0.120772i	0.896891	−	0.442251i	$-0.145820\pi$
$857$	−1.46447	−	3.53553i	−0.0500252	−	0.120772i	−0.946917	+	0.321479i	$0.895820\pi$
$858$		0			0
$859$	0.727922	+	0.727922i	0.0248364	+	0.0248364i	0.719416	−	0.694580i	$-0.244410\pi$
$859$	0.727922	+	0.727922i	0.0248364	+	0.0248364i	−0.694580	+	0.719416i	$0.744410\pi$
$860$		0			0
$861$	−21.3137	+	8.82843i	−0.726369	+	0.300872i
$862$		0			0
$863$		−	34.6274i		−	1.17873i	−0.807867	−	0.589365i	$-0.799378\pi$
$863$		−	34.6274i		−	1.17873i	0.807867	−	0.589365i	$-0.200622\pi$
$864$		0			0
$865$	−4.41421	+	4.41421i	−0.150088	+	0.150088i
$866$		0			0
$867$	14.5563	−	41.9706i	0.494360	−	1.42540i
$868$		0			0
$869$	3.17157	−	3.17157i	0.107588	−	0.107588i
$870$		0			0
$871$			9.65685i			0.327210i
$872$		0			0
$873$	22.7782	−	9.43503i	0.770924	−	0.319327i
$874$		0			0
$875$	−9.31371	−	9.31371i	−0.314861	−	0.314861i
$876$		0			0
$877$	−14.4056	−	34.7782i	−0.486442	−	1.17438i	−0.956498	−	0.291739i	$-0.905766\pi$
$877$	−14.4056	−	34.7782i	−0.486442	−	1.17438i	0.470056	−	0.882637i	$-0.344234\pi$
$878$		0			0
$879$	−23.6569	+	57.1127i	−0.797926	+	1.92636i
$880$		0			0
$881$	17.1213	+	7.09188i	0.576832	+	0.238932i	0.651974	−	0.758241i	$-0.273941\pi$
$881$	17.1213	+	7.09188i	0.576832	+	0.238932i	−0.0751422	+	0.997173i	$0.523941\pi$
$882$		0			0
$883$	−8.00000			−0.269221			−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000			−0.269221			−0.134611	+	0.990899i	$0.542978\pi$
$884$		0			0
$885$	28.9706			0.973835
$886$		0			0
$887$	−45.1421	−	18.6985i	−1.51572	−	0.627834i	−0.538995	−	0.842309i	$-0.681196\pi$
$887$	−45.1421	−	18.6985i	−1.51572	−	0.627834i	−0.976729	+	0.214475i	$0.931196\pi$
$888$		0			0
$889$	7.17157	−	17.3137i	0.240527	−	0.580683i
$890$		0			0
$891$	−2.41421	−	5.82843i	−0.0808792	−	0.195260i
$892$		0			0
$893$	36.9706	+	36.9706i	1.23717	+	1.23717i
$894$		0			0
$895$	−10.2426	+	4.24264i	−0.342374	+	0.141816i
$896$		0			0
$897$			15.3137i			0.511310i
$898$		0			0
$899$	−10.2426	+	10.2426i	−0.341611	+	0.341611i
$900$		0			0
$901$	−0.171573	−	5.82843i	−0.00571592	−	0.194173i
$902$		0			0
$903$	9.65685	−	9.65685i	0.321360	−	0.321360i
$904$		0			0
$905$			23.0711i			0.766908i
$906$		0			0
$907$	23.1421	−	9.58579i	0.768422	−	0.318291i	0.0361889	−	0.999345i	$-0.488478\pi$
$907$	23.1421	−	9.58579i	0.768422	−	0.318291i	0.732233	+	0.681054i	$0.238478\pi$
$908$		0			0
$909$	−36.3137	−	36.3137i	−1.20445	−	1.20445i
$910$		0			0
$911$	3.24264	+	7.82843i	0.107433	+	0.259367i	0.968449	−	0.249211i	$-0.0801712\pi$
$911$	3.24264	+	7.82843i	0.107433	+	0.259367i	−0.861016	+	0.508578i	$0.830171\pi$
$912$		0			0
$913$	0.142136	−	0.343146i	0.00470400	−	0.0113565i
$914$		0			0
$915$	41.2132	+	17.0711i	1.36247	+	0.564352i
$916$		0			0
$917$	0.201010			0.00663794
$918$		0			0
$919$	3.31371			0.109309			0.0546546	−	0.998505i	$-0.482594\pi$
$919$	3.31371			0.109309			0.0546546	+	0.998505i	$0.482594\pi$
$920$		0			0
$921$	−5.17157	−	2.14214i	−0.170409	−	0.0705858i
$922$		0			0
$923$	−7.07107	+	17.0711i	−0.232747	+	0.561901i
$924$		0			0
$925$	−2.32233	−	5.60660i	−0.0763578	−	0.184344i
$926$		0			0
$927$	12.1421	+	12.1421i	0.398800	+	0.398800i
$928$		0			0
$929$	19.3640	−	8.02082i	0.635311	−	0.263154i	−0.0416968	−	0.999130i	$-0.513276\pi$
$929$	19.3640	−	8.02082i	0.635311	−	0.263154i	0.677008	+	0.735976i	$0.263276\pi$
$930$		0			0
$931$			28.1421i			0.922321i
$932$		0			0
$933$	8.34315	−	8.34315i	0.273142	−	0.273142i
$934$		0			0
$935$	6.00000	+	5.65685i	0.196221	+	0.184999i
$936$		0			0
$937$	2.51472	−	2.51472i	0.0821523	−	0.0821523i	−0.664837	−	0.746989i	$-0.731499\pi$
$937$	2.51472	−	2.51472i	0.0821523	−	0.0821523i	0.746989	+	0.664837i	$0.231499\pi$
$938$		0			0
$939$		−	33.3137i		−	1.08715i
$940$		0			0
$941$	17.2635	−	7.15076i	0.562773	−	0.233108i	−0.0831158	−	0.996540i	$-0.526487\pi$
$941$	17.2635	−	7.15076i	0.562773	−	0.233108i	0.645888	+	0.763432i	$0.276487\pi$
$942$		0			0
$943$	23.8995	+	23.8995i	0.778275	+	0.778275i
$944$		0			0
$945$	−1.65685	−	4.00000i	−0.0538975	−	0.130120i
$946$		0			0
$947$	−5.68629	+	13.7279i	−0.184780	+	0.446098i	−0.988940	−	0.148315i	$-0.952615\pi$
$947$	−5.68629	+	13.7279i	−0.184780	+	0.446098i	0.804161	+	0.594412i	$0.202615\pi$
$948$		0			0
$949$	7.00000	+	2.89949i	0.227230	+	0.0941216i
$950$		0			0
$951$	−15.1716			−0.491972
$952$		0			0
$953$	−9.69848			−0.314165			−0.157082	−	0.987586i	$-0.550209\pi$
$953$	−9.69848			−0.314165			−0.157082	+	0.987586i	$0.550209\pi$
$954$		0			0
$955$	34.1421	+	14.1421i	1.10481	+	0.457629i
$956$		0			0
$957$	−4.82843	+	11.6569i	−0.156081	+	0.376813i
$958$		0			0
$959$	−3.61522	−	8.72792i	−0.116742	−	0.281839i
$960$		0			0
$961$	−14.4645	−	14.4645i	−0.466596	−	0.466596i
$962$		0			0
$963$	22.3137	−	9.24264i	0.719049	−	0.297840i
$964$		0			0
$965$		−	10.2426i		−	0.329722i
$966$		0			0
$967$	−22.8701	+	22.8701i	−0.735451	+	0.735451i	−0.971694	−	0.236243i	$-0.924084\pi$
$967$	−22.8701	+	22.8701i	−0.735451	+	0.735451i	0.236243	+	0.971694i	$0.424084\pi$
$968$		0			0
$969$	18.4853	−	48.6274i	0.593833	−	1.56214i
$970$		0			0
$971$	39.4142	−	39.4142i	1.26486	−	1.26486i	0.316155	−	0.948708i	$-0.397608\pi$
$971$	39.4142	−	39.4142i	1.26486	−	1.26486i	0.948708	−	0.316155i	$-0.102392\pi$
$972$		0			0
$973$		−	16.2010i		−	0.519381i
$974$		0			0
$975$	5.41421	−	2.24264i	0.173394	−	0.0718220i
$976$		0			0
$977$	1.14214	+	1.14214i	0.0365402	+	0.0365402i	0.725141	−	0.688601i	$-0.241775\pi$
$977$	1.14214	+	1.14214i	0.0365402	+	0.0365402i	−0.688601	+	0.725141i	$0.741775\pi$
$978$		0			0
$979$	−3.89949	−	9.41421i	−0.124628	−	0.300880i
$980$		0			0
$981$	−6.26346	+	15.1213i	−0.199977	+	0.482787i
$982$		0			0
$983$	21.7279	+	9.00000i	0.693013	+	0.287055i	0.701255	−	0.712911i	$-0.252623\pi$
$983$	21.7279	+	9.00000i	0.693013	+	0.287055i	−0.00824183	+	0.999966i	$0.502623\pi$
$984$		0			0
$985$	−27.5563			−0.878018
$986$		0			0
$987$	−30.6274			−0.974881
$988$		0			0
$989$	−18.4853	−	7.65685i	−0.587798	−	0.243474i
$990$		0			0
$991$	−12.2721	+	29.6274i	−0.389835	+	0.941146i	0.600139	+	0.799896i	$0.295112\pi$
$991$	−12.2721	+	29.6274i	−0.389835	+	0.941146i	−0.989974	+	0.141250i	$0.954888\pi$
$992$		0			0
$993$	17.7990	+	42.9706i	0.564834	+	1.36363i
$994$		0			0
$995$	−2.24264	−	2.24264i	−0.0710965	−	0.0710965i
$996$		0			0
$997$	−7.12132	+	2.94975i	−0.225534	+	0.0934194i	−0.492589	−	0.870262i	$-0.663950\pi$
$997$	−7.12132	+	2.94975i	−0.225534	+	0.0934194i	0.267055	+	0.963681i	$0.413950\pi$
$998$		0			0
$999$		−	8.28427i		−	0.262103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.2.v.d.145.1		4
4.3	odd	2		17.2.d.a.9.1	yes	4
12.11	even	2		153.2.l.c.145.1		4
17.2	even	8	inner	272.2.v.d.257.1		4
17.6	odd	16		4624.2.a.bp.1.4		4
17.11	odd	16		4624.2.a.bp.1.1		4
20.3	even	4		425.2.n.b.349.1		4
20.7	even	4		425.2.n.a.349.1		4
20.19	odd	2		425.2.m.a.26.1		4
28.3	even	6		833.2.v.a.128.1		8
28.11	odd	6		833.2.v.b.128.1		8
28.19	even	6		833.2.v.a.655.1		8
28.23	odd	6		833.2.v.b.655.1		8
28.27	even	2		833.2.l.a.638.1		4
68.3	even	16		289.2.c.c.251.3		8
68.7	even	16		289.2.b.b.288.4		4
68.11	even	16		289.2.a.f.1.2		4
68.15	odd	8		289.2.d.a.155.1		4
68.19	odd	8		17.2.d.a.2.1	✓	4
68.23	even	16		289.2.a.f.1.1		4
68.27	even	16		289.2.b.b.288.3		4
68.31	even	16		289.2.c.c.251.4		8
68.39	even	16		289.2.c.c.38.2		8
68.43	odd	8		289.2.d.b.134.1		4
68.47	odd	4		289.2.d.c.110.1		4
68.55	odd	4		289.2.d.b.110.1		4
68.59	odd	8		289.2.d.c.134.1		4
68.63	even	16		289.2.c.c.38.1		8
68.67	odd	2		289.2.d.a.179.1		4
204.11	odd	16		2601.2.a.bb.1.3		4
204.23	odd	16		2601.2.a.bb.1.4		4
204.155	even	8		153.2.l.c.19.1		4
340.19	odd	8		425.2.m.a.376.1		4
340.79	even	16		7225.2.a.u.1.3		4
340.87	even	8		425.2.n.b.274.1		4
340.159	even	16		7225.2.a.u.1.4		4
340.223	even	8		425.2.n.a.274.1		4
476.19	even	24		833.2.v.a.410.1		8
476.87	even	24		833.2.v.a.716.1		8
476.223	even	8		833.2.l.a.393.1		4
476.291	odd	24		833.2.v.b.716.1		8
476.359	odd	24		833.2.v.b.410.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.2.d.a.2.1	✓	4	68.19	odd	8
17.2.d.a.9.1	yes	4	4.3	odd	2
153.2.l.c.19.1		4	204.155	even	8
153.2.l.c.145.1		4	12.11	even	2
272.2.v.d.145.1		4	1.1	even	1	trivial
272.2.v.d.257.1		4	17.2	even	8	inner
289.2.a.f.1.1		4	68.23	even	16
289.2.a.f.1.2		4	68.11	even	16
289.2.b.b.288.3		4	68.27	even	16
289.2.b.b.288.4		4	68.7	even	16
289.2.c.c.38.1		8	68.63	even	16
289.2.c.c.38.2		8	68.39	even	16
289.2.c.c.251.3		8	68.3	even	16
289.2.c.c.251.4		8	68.31	even	16
289.2.d.a.155.1		4	68.15	odd	8
289.2.d.a.179.1		4	68.67	odd	2
289.2.d.b.110.1		4	68.55	odd	4
289.2.d.b.134.1		4	68.43	odd	8
289.2.d.c.110.1		4	68.47	odd	4
289.2.d.c.134.1		4	68.59	odd	8
425.2.m.a.26.1		4	20.19	odd	2
425.2.m.a.376.1		4	340.19	odd	8
425.2.n.a.274.1		4	340.223	even	8
425.2.n.a.349.1		4	20.7	even	4
425.2.n.b.274.1		4	340.87	even	8
425.2.n.b.349.1		4	20.3	even	4
833.2.l.a.393.1		4	476.223	even	8
833.2.l.a.638.1		4	28.27	even	2
833.2.v.a.128.1		8	28.3	even	6
833.2.v.a.410.1		8	476.19	even	24
833.2.v.a.655.1		8	28.19	even	6
833.2.v.a.716.1		8	476.87	even	24
833.2.v.b.128.1		8	28.11	odd	6
833.2.v.b.410.1		8	476.359	odd	24
833.2.v.b.655.1		8	28.23	odd	6
833.2.v.b.716.1		8	476.291	odd	24
2601.2.a.bb.1.3		4	204.11	odd	16
2601.2.a.bb.1.4		4	204.23	odd	16
4624.2.a.bp.1.1		4	17.11	odd	16
4624.2.a.bp.1.4		4	17.6	odd	16
7225.2.a.u.1.3		4	340.79	even	16
7225.2.a.u.1.4		4	340.159	even	16

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:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	272.v (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.41421 + 1.00000i) q^{3} +(0.707107 - 1.70711i) q^{5} +(-0.414214 - 1.00000i) q^{7} +(2.70711 + 2.70711i) q^{9} +(1.00000 - 0.414214i) q^{11} -1.41421i q^{13} +(3.41421 - 3.41421i) q^{15} +(-2.82843 + 3.00000i) q^{17} +(-3.41421 + 3.41421i) q^{19} -2.82843i q^{21} +(-3.82843 + 1.58579i) q^{23} +(1.12132 + 1.12132i) q^{25} +(0.828427 + 2.00000i) q^{27} +(-1.70711 + 4.12132i) q^{29} +(3.00000 + 1.24264i) q^{31} +2.82843 q^{33} -2.00000 q^{35} +(-3.53553 - 1.46447i) q^{37} +(1.41421 - 3.41421i) q^{39} +(-3.12132 - 7.53553i) q^{41} +(3.41421 + 3.41421i) q^{43} +(6.53553 - 2.70711i) q^{45} -10.8284i q^{47} +(4.12132 - 4.12132i) q^{49} +(-9.82843 + 4.41421i) q^{51} +(-1.00000 + 1.00000i) q^{53} -2.00000i q^{55} +(-11.6569 + 4.82843i) q^{57} +(4.24264 + 4.24264i) q^{59} +(3.53553 + 8.53553i) q^{61} +(1.58579 - 3.82843i) q^{63} +(-2.41421 - 1.00000i) q^{65} -6.82843 q^{67} -10.8284 q^{69} +(-12.0711 - 5.00000i) q^{71} +(-2.05025 + 4.94975i) q^{73} +(1.58579 + 3.82843i) q^{75} +(-0.828427 - 0.828427i) q^{77} +(3.82843 - 1.58579i) q^{79} -5.82843i q^{81} +(0.242641 - 0.242641i) q^{83} +(3.12132 + 6.94975i) q^{85} +(-8.24264 + 8.24264i) q^{87} -9.41421i q^{89} +(-1.41421 + 0.585786i) q^{91} +(6.00000 + 6.00000i) q^{93} +(3.41421 + 8.24264i) q^{95} +(2.46447 - 5.94975i) q^{97} +(3.82843 + 1.58579i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} + 4 q^{7} + 8 q^{9} + 4 q^{11} + 8 q^{15} - 8 q^{19} - 4 q^{23} - 4 q^{25} - 8 q^{27} - 4 q^{29} + 12 q^{31} - 8 q^{35} - 4 q^{41} + 8 q^{43} + 12 q^{45} + 8 q^{49} - 28 q^{51} - 4 q^{53}+ \cdots + 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 + 4 * q^7 + 8 * q^9 + 4 * q^11 + 8 * q^15 - 8 * q^19 - 4 * q^23 - 4 * q^25 - 8 * q^27 - 4 * q^29 + 12 * q^31 - 8 * q^35 - 4 * q^41 + 8 * q^43 + 12 * q^45 + 8 * q^49 - 28 * q^51 - 4 * q^53 - 24 * q^57 + 12 * q^63 - 4 * q^65 - 16 * q^67 - 32 * q^69 - 20 * q^71 - 28 * q^73 + 12 * q^75 + 8 * q^77 + 4 * q^79 - 16 * q^83 + 4 * q^85 - 16 * q^87 + 24 * q^93 + 8 * q^95 + 24 * q^97 + 4 * q^99

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