LMFDB - Embedded newform 765.2.t.e.514.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [765,2,Mod(64,765)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("765.64"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(765, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	765.t (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$6.10855575463$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 24x^{10} + 188x^{8} + 572x^{6} + 776x^{4} + 464x^{2} + 100 $ x^12 + 24x^10 + 188x^8 + 572x^6 + 776x^4 + 464*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			514.4
Root			$1.23239i$ of defining polynomial
Character	$\chi$	$=$	765.514
Dual form			765.2.t.e.64.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.232389 q^{2} -1.94600 q^{4} +(-2.04770 + 0.898299i) q^{5} +(-1.46067 + 1.46067i) q^{7} -0.917007 q^{8} +(-0.475863 + 0.208755i) q^{10} +(0.339444 + 0.339444i) q^{11} -4.07073i q^{13} +(-0.339444 + 0.339444i) q^{14} +3.67889 q^{16} +(3.75946 + 1.69306i) q^{17} -4.00000i q^{19} +(3.98481 - 1.74809i) q^{20} +(0.0788831 + 0.0788831i) q^{22} +(5.76379 - 5.76379i) q^{23} +(3.38612 - 3.67889i) q^{25} -0.945995i q^{26} +(2.84245 - 2.84245i) q^{28} +(-0.732893 + 0.732893i) q^{29} +(-4.28544 + 4.28544i) q^{31} +2.68895 q^{32} +(0.873659 + 0.393449i) q^{34} +(1.67889 - 4.30312i) q^{35} +(0.917007 + 0.917007i) q^{37} -0.929557i q^{38} +(1.87775 - 0.823747i) q^{40} +(-7.62488 - 7.62488i) q^{41} +7.45685 q^{43} +(-0.660556 - 0.660556i) q^{44} +(1.33944 - 1.33944i) q^{46} -3.60596i q^{47} +2.73289i q^{49} +(0.786897 - 0.854934i) q^{50} +7.92163i q^{52} +6.14969 q^{53} +(-1.00000 - 0.390156i) q^{55} +(1.33944 - 1.33944i) q^{56} +(-0.170316 + 0.170316i) q^{58} -6.00000i q^{59} +(-4.00000 - 4.00000i) q^{61} +(-0.995890 + 0.995890i) q^{62} -6.73289 q^{64} +(3.65674 + 8.33563i) q^{65} -3.14118i q^{67} +(-7.31589 - 3.29468i) q^{68} +(0.390156 - 1.00000i) q^{70} +(-1.28544 + 1.28544i) q^{71} +(-8.60625 - 8.60625i) q^{73} +(0.213103 + 0.213103i) q^{74} +7.78398i q^{76} -0.991630 q^{77} +(7.23143 + 7.23143i) q^{79} +(-7.53324 + 3.30474i) q^{80} +(-1.77194 - 1.77194i) q^{82} +2.23672 q^{83} +(-9.21911 - 0.0897461i) q^{85} +1.73289 q^{86} +(-0.311272 - 0.311272i) q^{88} +9.37220 q^{89} +(5.94600 + 5.94600i) q^{91} +(-11.2163 + 11.2163i) q^{92} -0.837986i q^{94} +(3.59320 + 8.19078i) q^{95} +(11.8220 + 11.8220i) q^{97} +0.635095i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{4} - 4 q^{10} - 16 q^{11} + 16 q^{14} + 4 q^{16} + 32 q^{20} - 4 q^{29} + 4 q^{31} - 20 q^{35} + 24 q^{40} - 16 q^{41} - 28 q^{44} - 4 q^{46} + 40 q^{50} - 12 q^{55} - 4 q^{56} - 48 q^{61}+ \cdots + 36 q^{91}+O(q^{100}) $ 12 * q + 12 * q^4 - 4 * q^10 - 16 * q^11 + 16 * q^14 + 4 * q^16 + 32 * q^20 - 4 * q^29 + 4 * q^31 - 20 * q^35 + 24 * q^40 - 16 * q^41 - 28 * q^44 - 4 * q^46 + 40 * q^50 - 12 * q^55 - 4 * q^56 - 48 * q^61 - 76 * q^64 - 8 * q^65 + 40 * q^71 - 28 * q^74 - 4 * q^79 - 12 * q^80 - 52 * q^85 + 16 * q^86 + 16 * q^89 + 36 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.232389			0.164324			0.0821620	−	0.996619i	$-0.473817\pi$
$2$	0.232389			0.164324			0.0821620	+	0.996619i	$0.473817\pi$
$3$		0			0
$3$		0			0
$4$	−1.94600			−0.972998
$5$	−2.04770	+	0.898299i	−0.915757	+	0.401732i
$5$	−2.04770	+	0.898299i	−0.915757	+	0.401732i
$6$		0			0
$7$	−1.46067	+	1.46067i	−0.552081	+	0.552081i	−0.927041	−	0.374960i	$-0.877656\pi$
$7$	−1.46067	+	1.46067i	−0.552081	+	0.552081i	0.374960	+	0.927041i	$0.377656\pi$
$8$	−0.917007			−0.324211
$9$		0			0
$10$	−0.475863	+	0.208755i	−0.150481	+	0.0660142i
$11$	0.339444	+	0.339444i	0.102346	+	0.102346i	0.756426	−	0.654080i	$-0.226944\pi$
$11$	0.339444	+	0.339444i	0.102346	+	0.102346i	−0.654080	+	0.756426i	$0.726944\pi$
$12$		0			0
$13$		−	4.07073i		−	1.12902i	−0.825427	−	0.564509i	$-0.809065\pi$
$13$		−	4.07073i		−	1.12902i	0.825427	−	0.564509i	$-0.190935\pi$
$14$	−0.339444	+	0.339444i	−0.0907202	+	0.0907202i
$15$		0			0
$16$	3.67889			0.919722
$17$	3.75946	+	1.69306i	0.911803	+	0.410627i
$17$	3.75946	+	1.69306i	0.911803	+	0.410627i
$18$		0			0
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$	3.98481	−	1.74809i	0.891030	−	0.390884i
$21$		0			0
$22$	0.0788831	+	0.0788831i	0.0168179	+	0.0168179i
$23$	5.76379	−	5.76379i	1.20183	−	1.20183i	0.228226	−	0.973608i	$-0.426708\pi$
$23$	5.76379	−	5.76379i	1.20183	−	1.20183i	0.973608	−	0.228226i	$-0.0732924\pi$
$24$		0			0
$25$	3.38612	−	3.67889i	0.677223	−	0.735778i
$26$		−	0.945995i		−	0.185525i
$27$		0			0
$28$	2.84245	−	2.84245i	0.537173	−	0.537173i
$29$	−0.732893	+	0.732893i	−0.136095	+	0.136095i	−0.771872	−	0.635778i	$-0.780680\pi$
$29$	−0.732893	+	0.732893i	−0.136095	+	0.136095i	0.635778	+	0.771872i	$0.280680\pi$
$30$		0			0
$31$	−4.28544	+	4.28544i	−0.769688	+	0.769688i	−0.978051	−	0.208364i	$-0.933186\pi$
$31$	−4.28544	+	4.28544i	−0.769688	+	0.769688i	0.208364	+	0.978051i	$0.433186\pi$
$32$	2.68895			0.475343
$33$		0			0
$34$	0.873659	+	0.393449i	0.149831	+	0.0674759i
$35$	1.67889	−	4.30312i	0.283784	−	0.727361i
$36$		0			0
$37$	0.917007	+	0.917007i	0.150755	+	0.150755i	0.778455	−	0.627700i	$-0.216004\pi$
$37$	0.917007	+	0.917007i	0.150755	+	0.150755i	−0.627700	+	0.778455i	$0.716004\pi$
$38$		−	0.929557i		−	0.150794i
$39$		0			0
$40$	1.87775	−	0.823747i	0.296899	−	0.130246i
$41$	−7.62488	−	7.62488i	−1.19081	−	1.19081i	−0.976841	−	0.213965i	$-0.931362\pi$
$41$	−7.62488	−	7.62488i	−1.19081	−	1.19081i	−0.213965	−	0.976841i	$-0.568638\pi$
$42$		0			0
$43$	7.45685			1.13716			0.568580	−	0.822628i	$-0.307493\pi$
$43$	7.45685			1.13716			0.568580	+	0.822628i	$0.307493\pi$
$44$	−0.660556	−	0.660556i	−0.0995826	−	0.0995826i
$45$		0			0
$46$	1.33944	−	1.33944i	0.197490	−	0.197490i
$47$		−	3.60596i		−	0.525983i	−0.964798	−	0.262991i	$-0.915291\pi$
$47$		−	3.60596i		−	0.525983i	0.964798	−	0.262991i	$-0.0847091\pi$
$48$		0			0
$49$			2.73289i			0.390413i
$50$	0.786897	−	0.854934i	0.111284	−	0.120906i
$51$		0			0
$52$			7.92163i			1.09853i
$53$	6.14969			0.844725			0.422362	−	0.906427i	$-0.361201\pi$
$53$	6.14969			0.844725			0.422362	+	0.906427i	$0.361201\pi$
$54$		0			0
$55$	−1.00000	−	0.390156i	−0.134840	−	0.0526086i
$56$	1.33944	−	1.33944i	0.178991	−	0.178991i
$57$		0			0
$58$	−0.170316	+	0.170316i	−0.0223636	+	0.0223636i
$59$		−	6.00000i		−	0.781133i	−0.920575	−	0.390567i	$-0.872279\pi$
$59$		−	6.00000i		−	0.781133i	0.920575	−	0.390567i	$-0.127721\pi$
$60$		0			0
$61$	−4.00000	−	4.00000i	−0.512148	−	0.512148i	0.403036	−	0.915184i	$-0.367955\pi$
$61$	−4.00000	−	4.00000i	−0.512148	−	0.512148i	−0.915184	+	0.403036i	$0.867955\pi$
$62$	−0.995890	+	0.995890i	−0.126478	+	0.126478i
$63$		0			0
$64$	−6.73289			−0.841612
$65$	3.65674	+	8.33563i	0.453563	+	1.03391i
$66$		0			0
$67$		−	3.14118i		−	0.383756i	−0.981419	−	0.191878i	$-0.938542\pi$
$67$		−	3.14118i		−	0.383756i	0.981419	−	0.191878i	$-0.0614578\pi$
$68$	−7.31589	−	3.29468i	−0.887183	−	0.399539i
$69$		0			0
$70$	0.390156	−	1.00000i	0.0466325	−	0.119523i
$71$	−1.28544	+	1.28544i	−0.152554	+	0.152554i	−0.779257	−	0.626704i	$-0.784404\pi$
$71$	−1.28544	+	1.28544i	−0.152554	+	0.152554i	0.626704	+	0.779257i	$0.284404\pi$
$72$		0			0
$73$	−8.60625	−	8.60625i	−1.00729	−	1.00729i	−0.999973	−	0.00731179i	$-0.997673\pi$
$73$	−8.60625	−	8.60625i	−1.00729	−	1.00729i	−0.00731179	−	0.999973i	$-0.502327\pi$
$74$	0.213103	+	0.213103i	0.0247727	+	0.0247727i
$75$		0			0
$76$			7.78398i			0.892884i
$77$	−0.991630			−0.113007
$78$		0			0
$79$	7.23143	+	7.23143i	0.813600	+	0.813600i	0.985172	−	0.171572i	$-0.0548845\pi$
$79$	7.23143	+	7.23143i	0.813600	+	0.813600i	−0.171572	+	0.985172i	$0.554885\pi$
$80$	−7.53324	+	3.30474i	−0.842242	+	0.369481i
$81$		0			0
$82$	−1.77194	−	1.77194i	−0.195678	−	0.195678i
$83$	2.23672			0.245512			0.122756	−	0.992437i	$-0.460827\pi$
$83$	2.23672			0.245512			0.122756	+	0.992437i	$0.460827\pi$
$84$		0			0
$85$	−9.21911	−	0.0897461i	−0.999953	−	0.00973434i
$86$	1.73289			0.186863
$87$		0			0
$88$	−0.311272	−	0.311272i	−0.0331818	−	0.0331818i
$89$	9.37220			0.993451			0.496726	−	0.867908i	$-0.334536\pi$
$89$	9.37220			0.993451			0.496726	+	0.867908i	$0.334536\pi$
$90$		0			0
$91$	5.94600	+	5.94600i	0.623310	+	0.623310i
$92$	−11.2163	+	11.2163i	−1.16938	+	1.16938i
$93$		0			0
$94$		−	0.837986i		−	0.0864316i
$95$	3.59320	+	8.19078i	0.368654	+	0.840357i
$96$		0			0
$97$	11.8220	+	11.8220i	1.20035	+	1.20035i	0.974061	+	0.226286i	$0.0726585\pi$
$97$	11.8220	+	11.8220i	1.20035	+	1.20035i	0.226286	+	0.974061i	$0.427342\pi$
$98$			0.635095i			0.0641543i
$99$		0			0
$100$	−6.58937	+	7.15910i	−0.658937	+	0.715910i
$101$	4.41178			0.438989			0.219494	−	0.975614i	$-0.429559\pi$
$101$	4.41178			0.438989			0.219494	+	0.975614i	$0.429559\pi$
$102$		0			0
$103$		−	17.4323i		−	1.71766i	−0.512262	−	0.858829i	$-0.671192\pi$
$103$		−	17.4323i		−	1.71766i	0.512262	−	0.858829i	$-0.328808\pi$
$104$			3.73289i			0.366040i
$105$		0			0
$106$	1.42912			0.138809
$107$	−3.68484	−	3.68484i	−0.356227	−	0.356227i	0.506193	−	0.862420i	$-0.331052\pi$
$107$	−3.68484	−	3.68484i	−0.356227	−	0.356227i	−0.862420	+	0.506193i	$0.831052\pi$
$108$		0			0
$109$	−5.73289	−	5.73289i	−0.549112	−	0.549112i	0.377072	−	0.926184i	$-0.376931\pi$
$109$	−5.73289	−	5.73289i	−0.549112	−	0.549112i	−0.926184	+	0.377072i	$0.876931\pi$
$110$	−0.232389	−	0.0906680i	−0.0221575	−	0.00864485i
$111$		0			0
$112$	−5.37364	+	5.37364i	−0.507761	+	0.507761i
$113$	2.45656	−	2.45656i	0.231094	−	0.231094i	−0.582055	−	0.813149i	$-0.697751\pi$
$113$	2.45656	−	2.45656i	0.231094	−	0.231094i	0.813149	+	0.582055i	$0.197751\pi$
$114$		0			0
$115$	−6.62488	+	16.9801i	−0.617774	+	1.58340i
$116$	1.42621	−	1.42621i	0.132420	−	0.132420i
$117$		0			0
$118$		−	1.39434i		−	0.128359i
$119$	−7.96433	+	3.01833i	−0.730089	+	0.276690i
$120$		0			0
$121$		−	10.7696i		−	0.979051i
$122$	−0.929557	−	0.929557i	−0.0841582	−	0.0841582i
$123$		0			0
$124$	8.33944	−	8.33944i	0.748904	−	0.748904i
$125$	−3.62899	+	10.5750i	−0.324587	+	0.945856i
$126$		0			0
$127$	−2.98341			−0.264735			−0.132367	−	0.991201i	$-0.542258\pi$
$127$	−2.98341			−0.264735			−0.132367	+	0.991201i	$0.542258\pi$
$128$	−6.94255			−0.613640
$129$		0			0
$130$	0.849787	+	1.93711i	0.0745312	+	0.169896i
$131$	−5.08676	+	5.08676i	−0.444432	+	0.444432i	−0.893499	−	0.449066i	$-0.851757\pi$
$131$	−5.08676	+	5.08676i	−0.444432	+	0.444432i	0.449066	+	0.893499i	$0.351757\pi$
$132$		0			0
$133$	5.84268	+	5.84268i	0.506624	+	0.506624i
$134$		−	0.729976i		−	0.0630603i
$135$		0			0
$136$	−3.44745	−	1.55255i	−0.295617	−	0.133130i
$137$		−	0.526852i		−	0.0450120i	−0.999747	−	0.0225060i	$-0.992836\pi$
$137$		−	0.526852i		−	0.0450120i	0.999747	−	0.0225060i	$-0.00716448\pi$
$138$		0			0
$139$	12.4985	−	12.4985i	1.06011	−	1.06011i	0.0620387	−	0.998074i	$-0.480240\pi$
$139$	12.4985	−	12.4985i	1.06011	−	1.06011i	0.998074	−	0.0620387i	$-0.0197602\pi$
$140$	−3.26711	+	8.37386i	−0.276121	+	0.707720i
$141$		0			0
$142$	−0.298722	+	0.298722i	−0.0250682	+	0.0250682i
$143$	1.38179	−	1.38179i	0.115551	−	0.115551i
$144$		0			0
$145$	0.842384	−	2.15910i	0.0699562	−	0.179303i
$146$	−2.00000	−	2.00000i	−0.165521	−	0.165521i
$147$		0			0
$148$	−1.78449	−	1.78449i	−0.146684	−	0.146684i
$149$	−7.32111			−0.599769			−0.299884	−	0.953976i	$-0.596948\pi$
$149$	−7.32111			−0.599769			−0.299884	+	0.953976i	$0.596948\pi$
$150$		0			0
$151$			7.46579i			0.607557i	0.952743	+	0.303778i	$0.0982483\pi$
$151$			7.46579i			0.607557i	−0.952743	+	0.303778i	$0.901752\pi$
$152$			3.66803i			0.297516i
$153$		0			0
$154$	−0.230444			−0.0185697
$155$	4.92567	−	12.6249i	0.395639	−	1.01405i
$156$		0			0
$157$		−	12.4571i		−	0.994188i	−0.867697	−	0.497094i	$-0.834400\pi$
$157$		−	12.4571i		−	0.994188i	0.867697	−	0.497094i	$-0.165600\pi$
$158$	1.68051	+	1.68051i	0.133694	+	0.133694i
$159$		0			0
$160$	−5.50615	+	2.41548i	−0.435299	+	0.190961i
$161$			16.8380i			1.32702i
$162$		0			0
$163$	6.05825	−	6.05825i	0.474519	−	0.474519i	−0.428854	−	0.903374i	$-0.641083\pi$
$163$	6.05825	−	6.05825i	0.474519	−	0.474519i	0.903374	+	0.428854i	$0.141083\pi$
$164$	14.8380	+	14.8380i	1.15865	+	1.15865i
$165$		0			0
$166$	0.519790			0.0403435
$167$	6.68080	+	6.68080i	0.516976	+	0.516976i	0.916655	−	0.399679i	$-0.130878\pi$
$167$	6.68080	+	6.68080i	0.516976	+	0.516976i	−0.399679	+	0.916655i	$0.630878\pi$
$168$		0			0
$169$	−3.57088			−0.274683
$170$	−2.14242	−	0.0208560i	−0.164316	−	0.00159959i
$171$		0			0
$172$	−14.5110			−1.10645
$173$	−11.6979	−	11.6979i	−0.889375	−	0.889375i	0.105088	−	0.994463i	$-0.466488\pi$
$173$	−11.6979	−	11.6979i	−0.889375	−	0.889375i	−0.994463	+	0.105088i	$0.966488\pi$
$174$		0			0
$175$	0.427642	+	10.3196i	0.0323267	+	0.780091i
$176$	1.24878	+	1.24878i	0.0941300	+	0.0941300i
$177$		0			0
$178$	2.17800			0.163248
$179$		−	19.5313i		−	1.45984i	−0.683534	−	0.729919i	$-0.739558\pi$
$179$		−	19.5313i		−	1.45984i	0.683534	−	0.729919i	$-0.260442\pi$
$180$		0			0
$181$	7.41178	+	7.41178i	0.550913	+	0.550913i	0.926704	−	0.375791i	$-0.122629\pi$
$181$	7.41178	+	7.41178i	0.550913	+	0.550913i	−0.375791	+	0.926704i	$0.622629\pi$
$182$	1.38179	+	1.38179i	0.102425	+	0.102425i
$183$		0			0
$184$	−5.28544	+	5.28544i	−0.389648	+	0.389648i
$185$	−2.70150	−	1.05400i	−0.198618	−	0.0774920i
$186$		0			0
$187$	0.701428	+	1.85082i	0.0512935	+	0.135346i
$188$			7.01717i			0.511780i
$189$		0			0
$190$	0.835021	+	1.90345i	0.0605788	+	0.138091i
$191$	5.32111			0.385022			0.192511	−	0.981295i	$-0.438337\pi$
$191$	5.32111			0.385022			0.192511	+	0.981295i	$0.438337\pi$
$192$		0			0
$193$	−8.82609	+	8.82609i	−0.635316	+	0.635316i	−0.949396	−	0.314081i	$-0.898304\pi$
$193$	−8.82609	+	8.82609i	−0.635316	+	0.635316i	0.314081	+	0.949396i	$0.398304\pi$
$194$	2.74732	+	2.74732i	0.197246	+	0.197246i
$195$		0			0
$196$		−	5.31820i		−	0.379871i
$197$	−0.390156	+	0.390156i	−0.0277974	+	0.0277974i	−0.720869	−	0.693071i	$-0.756257\pi$
$197$	−0.390156	+	0.390156i	−0.0277974	+	0.0277974i	0.693071	+	0.720869i	$0.256257\pi$
$198$		0			0
$199$	−12.4445	+	12.4445i	−0.882170	+	0.882170i	−0.993755	−	0.111585i	$-0.964407\pi$
$199$	−12.4445	+	12.4445i	−0.882170	+	0.882170i	0.111585	+	0.993755i	$0.464407\pi$
$200$	−3.10509	+	3.37357i	−0.219563	+	0.238547i
$201$		0			0
$202$	1.02525			0.0721364
$203$		−	2.14103i		−	0.150271i
$204$		0			0
$205$	22.4629	+	8.76401i	1.56887	+	0.612105i
$206$		−	4.05109i		−	0.282253i
$207$		0			0
$208$		−	14.9758i		−	1.03838i
$209$	1.35778	−	1.35778i	0.0939193	−	0.0939193i
$210$		0			0
$211$	−9.07234	−	9.07234i	−0.624565	−	0.624565i	0.322130	−	0.946695i	$-0.395601\pi$
$211$	−9.07234	−	9.07234i	−0.624565	−	0.624565i	−0.946695	+	0.322130i	$0.895601\pi$
$212$	−11.9673			−0.821915
$213$		0			0
$214$	−0.856317	−	0.856317i	−0.0585366	−	0.0585366i
$215$	−15.2694	+	6.69848i	−1.04136	+	0.456833i
$216$		0			0
$217$		−	12.5192i		−	0.849860i
$218$	−1.33226	−	1.33226i	−0.0902322	−	0.0902322i
$219$		0			0
$220$	1.94600	+	0.759241i	0.131199	+	0.0511880i
$221$	6.89199	−	15.3038i	0.463605	−	1.02944i
$222$		0			0
$223$	−4.07073			−0.272597			−0.136298	−	0.990668i	$-0.543521\pi$
$223$	−4.07073			−0.272597			−0.136298	+	0.990668i	$0.543521\pi$
$224$	−3.92766	+	3.92766i	−0.262428	+	0.262428i
$225$		0			0
$226$	0.570878	−	0.570878i	0.0379742	−	0.0379742i
$227$	11.1542	−	11.1542i	0.740333	−	0.740333i	−0.232309	−	0.972642i	$-0.574628\pi$
$227$	11.1542	−	11.1542i	0.740333	−	0.740333i	0.972642	+	0.232309i	$0.0746281\pi$
$228$		0			0
$229$			14.9460i			0.987659i	0.869559	+	0.493830i	$0.164403\pi$
$229$			14.9460i			0.987659i	−0.869559	+	0.493830i	$0.835597\pi$
$230$	−1.53955	+	3.94600i	−0.101515	+	0.260191i
$231$		0			0
$232$	0.672068	−	0.672068i	0.0441234	−	0.0441234i
$233$	−0.514301	−	0.514301i	−0.0336930	−	0.0336930i	0.690060	−	0.723753i	$-0.257584\pi$
$233$	−0.514301	−	0.514301i	−0.0336930	−	0.0336930i	−0.723753	+	0.690060i	$0.757584\pi$
$234$		0			0
$235$	3.23923	+	7.38390i	0.211304	+	0.481673i
$236$			11.6760i			0.760041i
$237$		0			0
$238$	−1.85082	+	0.701428i	−0.119971	+	0.0454668i
$239$	9.57379			0.619277			0.309639	−	0.950854i	$-0.399792\pi$
$239$	9.57379			0.619277			0.309639	+	0.950854i	$0.399792\pi$
$240$		0			0
$241$	6.00000	−	6.00000i	0.386494	−	0.386494i	−0.486941	−	0.873435i	$-0.661887\pi$
$241$	6.00000	−	6.00000i	0.386494	−	0.386494i	0.873435	+	0.486941i	$0.161887\pi$
$242$		−	2.50273i		−	0.160882i
$243$		0			0
$244$	7.78398	+	7.78398i	0.498318	+	0.498318i
$245$	−2.45496	−	5.59613i	−0.156841	−	0.357524i
$246$		0			0
$247$	−16.2829			−1.03606
$248$	3.92978	−	3.92978i	0.249541	−	0.249541i
$249$		0			0
$250$	−0.843340	+	2.45751i	−0.0533375	+	0.155427i
$251$	6.03666			0.381031			0.190515	−	0.981684i	$-0.438984\pi$
$251$	6.03666			0.381031			0.190515	+	0.981684i	$0.438984\pi$
$252$		0			0
$253$	3.91297			0.246006
$254$	−0.693313			−0.0435023
$255$		0			0
$256$	11.8524			0.740776
$257$	−27.2752			−1.70138			−0.850689	−	0.525670i	$-0.823815\pi$
$257$	−27.2752			−1.70138			−0.850689	+	0.525670i	$0.823815\pi$
$258$		0			0
$259$	−2.67889			−0.166458
$260$	−7.11599	−	16.2211i	−0.441315	−	1.00599i
$261$		0			0
$262$	−1.18211	+	1.18211i	−0.0730309	+	0.0730309i
$263$	−12.3700			−0.762765			−0.381382	−	0.924417i	$-0.624552\pi$
$263$	−12.3700			−0.762765			−0.381382	+	0.924417i	$0.624552\pi$
$264$		0			0
$265$	−12.5927	+	5.52426i	−0.773563	+	0.339353i
$266$	1.35778	+	1.35778i	0.0832506	+	0.0832506i
$267$		0			0
$268$			6.11272i			0.373394i
$269$	−14.1958	+	14.1958i	−0.865531	+	0.865531i	−0.991974	−	0.126443i	$-0.959644\pi$
$269$	−14.1958	+	14.1958i	−0.865531	+	0.865531i	0.126443	+	0.991974i	$0.459644\pi$
$270$		0			0
$271$	−24.2102			−1.47066			−0.735332	−	0.677707i	$-0.762974\pi$
$271$	−24.2102			−1.47066			−0.735332	+	0.677707i	$0.762974\pi$
$272$	13.8306	+	6.22857i	0.838606	+	0.377663i
$273$		0			0
$274$		−	0.122435i		−	0.00739655i
$275$	2.39817	−	0.0993794i	0.144615	−	0.00599280i
$276$		0			0
$277$	4.78045	+	4.78045i	0.287230	+	0.287230i	0.835984	−	0.548754i	$-0.184898\pi$
$277$	4.78045	+	4.78045i	0.287230	+	0.287230i	−0.548754	+	0.835984i	$0.684898\pi$
$278$	2.90453	−	2.90453i	0.174202	−	0.174202i
$279$		0			0
$280$	−1.53955	+	3.94600i	−0.0920058	+	0.235818i
$281$			18.0367i			1.07598i	0.842952	+	0.537989i	$0.180816\pi$
$281$			18.0367i			1.07598i	−0.842952	+	0.537989i	$0.819184\pi$
$282$		0			0
$283$	17.8308	−	17.8308i	1.05993	−	1.05993i	0.0618440	−	0.998086i	$-0.480302\pi$
$283$	17.8308	−	17.8308i	1.05993	−	1.05993i	0.998086	−	0.0618440i	$-0.0196981\pi$
$284$	2.50146	−	2.50146i	0.148434	−	0.148434i
$285$		0			0
$286$	0.321112	−	0.321112i	0.0189878	−	0.0189878i
$287$	22.2749			1.31484
$288$		0			0
$289$	11.2671	+	12.7300i	0.662771	+	0.748822i
$290$	0.195761	−	0.501751i	0.0114955	−	0.0294639i
$291$		0			0
$292$	16.7477	+	16.7477i	0.980086	+	0.980086i
$293$			26.2584i			1.53403i	0.641627	+	0.767017i	$0.278260\pi$
$293$			26.2584i			1.53403i	−0.641627	+	0.767017i	$0.721740\pi$
$294$		0			0
$295$	5.38980	+	12.2862i	0.313806	+	0.715329i
$296$	−0.840902	−	0.840902i	−0.0488764	−	0.0488764i
$297$		0			0
$298$	−1.70135			−0.0985565
$299$	−23.4629	−	23.4629i	−1.35689	−	1.35689i
$300$		0			0
$301$	−10.8920	+	10.8920i	−0.627804	+	0.627804i
$302$			1.73497i			0.0998362i
$303$		0			0
$304$		−	14.7156i		−	0.843995i
$305$	11.7840	+	4.59759i	0.674749	+	0.263257i
$306$		0			0
$307$		−	13.9136i		−	0.794088i	−0.917800	−	0.397044i	$-0.870036\pi$
$307$		−	13.9136i		−	0.794088i	0.917800	−	0.397044i	$-0.129964\pi$
$308$	1.92971			0.109955
$309$		0			0
$310$	1.14467	−	2.93389i	0.0650130	−	0.166634i
$311$	6.18035	−	6.18035i	0.350455	−	0.350455i	−0.509824	−	0.860279i	$-0.670289\pi$
$311$	6.18035	−	6.18035i	0.350455	−	0.350455i	0.860279	+	0.509824i	$0.170289\pi$
$312$		0			0
$313$	4.91312	−	4.91312i	0.277706	−	0.277706i	−0.554487	−	0.832193i	$-0.687085\pi$
$313$	4.91312	−	4.91312i	0.277706	−	0.277706i	0.832193	+	0.554487i	$0.187085\pi$
$314$		−	2.89491i		−	0.163369i
$315$		0			0
$316$	−14.0723	−	14.0723i	−0.791631	−	0.791631i
$317$	2.98341	−	2.98341i	0.167565	−	0.167565i	−0.618343	−	0.785908i	$-0.712196\pi$
$317$	2.98341	−	2.98341i	0.167565	−	0.167565i	0.785908	+	0.618343i	$0.212196\pi$
$318$		0			0
$319$	−0.497552			−0.0278575
$320$	13.7869	−	6.04815i	0.770712	−	0.338102i
$321$		0			0
$322$			3.91297i			0.218061i
$323$	6.77223	−	15.0378i	0.376817	−	0.836728i
$324$		0			0
$325$	−14.9758	−	13.7840i	−0.830707	−	0.764598i
$326$	1.40787	−	1.40787i	0.0779749	−	0.0779749i
$327$		0			0
$328$	6.99207	+	6.99207i	0.386073	+	0.386073i
$329$	5.26711	+	5.26711i	0.290385	+	0.290385i
$330$		0			0
$331$		−	13.6760i		−	0.751699i	−0.926681	−	0.375850i	$-0.877351\pi$
$331$		−	13.6760i		−	0.751699i	0.926681	−	0.375850i	$-0.122649\pi$
$332$	−4.35265			−0.238883
$333$		0			0
$334$	1.55255	+	1.55255i	0.0849516	+	0.0849516i
$335$	2.82172	+	6.43218i	0.154167	+	0.351427i
$336$		0			0
$337$	4.58504	+	4.58504i	0.249763	+	0.249763i	0.820873	−	0.571110i	$-0.193487\pi$
$337$	4.58504	+	4.58504i	0.249763	+	0.249763i	−0.571110	+	0.820873i	$0.693487\pi$
$338$	−0.829834			−0.0451370
$339$		0			0
$340$	17.9403	+	0.174646i	0.972952	+	0.00947148i
$341$	−2.90933			−0.157549
$342$		0			0
$343$	−14.2165	−	14.2165i	−0.767621	−	0.767621i
$344$	−6.83799			−0.368679
$345$		0			0
$346$	−2.71847	−	2.71847i	−0.146146	−	0.146146i
$347$	3.53962	−	3.53962i	0.190017	−	0.190017i	−0.605686	−	0.795703i	$-0.707101\pi$
$347$	3.53962	−	3.53962i	0.190017	−	0.190017i	0.795703	+	0.605686i	$0.207101\pi$
$348$		0			0
$349$		−	9.21310i		−	0.493166i	−0.969122	−	0.246583i	$-0.920692\pi$
$349$		−	9.21310i		−	0.493166i	0.969122	−	0.246583i	$-0.0793078\pi$
$350$	0.0993794	+	2.39817i	0.00531205	+	0.128188i
$351$		0			0
$352$	0.912747	+	0.912747i	0.0486496	+	0.0486496i
$353$		−	13.8600i		−	0.737693i	−0.929490	−	0.368847i	$-0.879753\pi$
$353$		−	13.8600i		−	0.737693i	0.929490	−	0.368847i	$-0.120247\pi$
$354$		0			0
$355$	1.47748	−	3.78690i	0.0784165	−	0.200988i
$356$	−18.2383			−0.966626
$357$		0			0
$358$		−	4.53887i		−	0.239886i
$359$		−	11.5024i		−	0.607076i	−0.952819	−	0.303538i	$-0.901832\pi$
$359$		−	11.5024i		−	0.607076i	0.952819	−	0.303538i	$-0.0981679\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	1.72242	+	1.72242i	0.0905283	+	0.0905283i
$363$		0			0
$364$	−11.5709	−	11.5709i	−0.606479	−	0.606479i
$365$	25.3540	+	9.89199i	1.32709	+	0.517770i
$366$		0			0
$367$	13.7349	−	13.7349i	0.716958	−	0.716958i	−0.251023	−	0.967981i	$-0.580767\pi$
$367$	13.7349	−	13.7349i	0.716958	−	0.716958i	0.967981	+	0.251023i	$0.0807669\pi$
$368$	21.2043	−	21.2043i	1.10535	−	1.10535i
$369$		0			0
$370$	−0.627799	−	0.244939i	−0.0326377	−	0.0127338i
$371$	−8.98266	+	8.98266i	−0.466356	+	0.466356i
$372$		0			0
$373$			5.58922i			0.289399i	0.989476	+	0.144699i	$0.0462215\pi$
$373$			5.58922i			0.289399i	−0.989476	+	0.144699i	$0.953779\pi$
$374$	0.163004	+	0.430112i	0.00842876	+	0.0222406i
$375$		0			0
$376$			3.30669i			0.170529i
$377$	2.98341	+	2.98341i	0.153653	+	0.153653i
$378$		0			0
$379$	−0.393449	+	0.393449i	−0.0202101	+	0.0202101i	−0.717140	−	0.696930i	$-0.754549\pi$
$379$	−0.393449	+	0.393449i	−0.0202101	+	0.0202101i	0.696930	+	0.717140i	$0.254549\pi$
$380$	−6.99234	−	15.9392i	−0.358700	−	0.817665i
$381$		0			0
$382$	1.23657			0.0632684
$383$	24.8020			1.26732			0.633662	−	0.773610i	$-0.281551\pi$
$383$	24.8020			1.26732			0.633662	+	0.773610i	$0.281551\pi$
$384$		0			0
$385$	2.03056	−	0.890781i	0.103487	−	0.0453984i
$386$	−2.05109	+	2.05109i	−0.104398	+	0.104398i
$387$		0			0
$388$	−23.0056	−	23.0056i	−1.16793	−	1.16793i
$389$		−	8.76664i		−	0.444486i	−0.974991	−	0.222243i	$-0.928662\pi$
$389$		−	8.76664i		−	0.444486i	0.974991	−	0.222243i	$-0.0713379\pi$
$390$		0			0
$391$	31.4272	−	11.9103i	1.58934	−	0.602331i
$392$		−	2.50608i		−	0.126576i
$393$		0			0
$394$	−0.0906680	+	0.0906680i	−0.00456779	+	0.00456779i
$395$	−21.3038	−	8.31179i	−1.07191	−	0.418211i
$396$		0			0
$397$	4.97519	−	4.97519i	0.249698	−	0.249698i	−0.571149	−	0.820847i	$-0.693502\pi$
$397$	4.97519	−	4.97519i	0.249698	−	0.249698i	0.820847	+	0.571149i	$0.193502\pi$
$398$	−2.89198	+	2.89198i	−0.144962	+	0.144962i
$399$		0			0
$400$	12.4571	−	13.5342i	0.622857	−	0.676711i
$401$	7.51979	+	7.51979i	0.375520	+	0.375520i	0.869483	−	0.493963i	$-0.164452\pi$
$401$	7.51979	+	7.51979i	0.375520	+	0.375520i	−0.493963	+	0.869483i	$0.664452\pi$
$402$		0			0
$403$	17.4449	+	17.4449i	0.868992	+	0.868992i
$404$	−8.58530			−0.427135
$405$		0			0
$406$		−	0.497552i		−	0.0246931i
$407$			0.622545i			0.0308584i
$408$		0			0
$409$	−2.53421			−0.125309			−0.0626544	−	0.998035i	$-0.519957\pi$
$409$	−2.53421			−0.125309			−0.0626544	+	0.998035i	$0.519957\pi$
$410$	5.22013	+	2.03666i	0.257804	+	0.100584i
$411$		0			0
$412$			33.9232i			1.67128i
$413$	8.76401	+	8.76401i	0.431249	+	0.431249i
$414$		0			0
$415$	−4.58012	+	2.00924i	−0.224829	+	0.0986299i
$416$		−	10.9460i		−	0.536672i
$417$		0			0
$418$	0.315533	−	0.315533i	0.0154332	−	0.0154332i
$419$	18.6403	+	18.6403i	0.910638	+	0.910638i	0.996322	−	0.0856842i	$-0.0273076\pi$
$419$	18.6403	+	18.6403i	0.910638	+	0.910638i	−0.0856842	+	0.996322i	$0.527308\pi$
$420$		0			0
$421$	−7.94308			−0.387122			−0.193561	−	0.981088i	$-0.562004\pi$
$421$	−7.94308			−0.387122			−0.193561	+	0.981088i	$0.562004\pi$
$422$	−2.10831	−	2.10831i	−0.102631	−	0.102631i
$423$		0			0
$424$	−5.63931			−0.273869
$425$	18.9585	−	8.09775i	0.919625	−	0.392798i
$426$		0			0
$427$	11.6854			0.565494
$428$	7.17068	+	7.17068i	0.346608	+	0.346608i
$429$		0			0
$430$	−3.54844	+	1.55666i	−0.171121	+	0.0750686i
$431$	8.01833	+	8.01833i	0.386229	+	0.386229i	0.873340	−	0.487111i	$-0.161949\pi$
$431$	8.01833	+	8.01833i	0.386229	+	0.386229i	−0.487111	+	0.873340i	$0.661949\pi$
$432$		0			0
$433$	6.24538			0.300134			0.150067	−	0.988676i	$-0.452051\pi$
$433$	6.24538			0.300134			0.150067	+	0.988676i	$0.452051\pi$
$434$		−	2.90933i		−	0.139652i
$435$		0			0
$436$	11.1562	+	11.1562i	0.534284	+	0.534284i
$437$	−23.0552	−	23.0552i	−1.10288	−	1.10288i
$438$		0			0
$439$	−7.44454	+	7.44454i	−0.355308	+	0.355308i	−0.862080	−	0.506772i	$-0.830839\pi$
$439$	−7.44454	+	7.44454i	−0.355308	+	0.355308i	0.506772	+	0.862080i	$0.330839\pi$
$440$	0.917007	+	0.357775i	0.0437166	+	0.0170563i
$441$		0			0
$442$	1.60162	−	3.55643i	0.0761815	−	0.169162i
$443$		−	29.2669i		−	1.39051i	−0.718761	−	0.695257i	$-0.755291\pi$
$443$		−	29.2669i		−	1.39051i	0.718761	−	0.695257i	$-0.244709\pi$
$444$		0			0
$445$	−19.1914	+	8.41904i	−0.909760	+	0.399101i
$446$	−0.945995			−0.0447942
$447$		0			0
$448$	9.83453	−	9.83453i	0.464638	−	0.464638i
$449$	23.1418	+	23.1418i	1.09213	+	1.09213i	0.995301	+	0.0968256i	$0.0308689\pi$
$449$	23.1418	+	23.1418i	1.09213	+	1.09213i	0.0968256	+	0.995301i	$0.469131\pi$
$450$		0			0
$451$		−	5.17644i		−	0.243749i
$452$	−4.78045	+	4.78045i	−0.224854	+	0.224854i
$453$		0			0
$454$	2.59213	−	2.59213i	0.121655	−	0.121655i
$455$	−17.5169	−	6.83431i	−0.821204	−	0.320397i
$456$		0			0
$457$	−31.4752			−1.47235			−0.736174	−	0.676792i	$-0.763369\pi$
$457$	−31.4752			−1.47235			−0.736174	+	0.676792i	$0.763369\pi$
$458$			3.47329i			0.162296i
$459$		0			0
$460$	12.8920	−	33.0432i	0.601092	−	1.54065i
$461$		−	26.6442i		−	1.24094i	−0.784228	−	0.620472i	$-0.786941\pi$
$461$		−	26.6442i		−	1.24094i	0.784228	−	0.620472i	$-0.213059\pi$
$462$		0			0
$463$			14.2040i			0.660115i	0.943961	+	0.330058i	$0.107068\pi$
$463$			14.2040i			0.660115i	−0.943961	+	0.330058i	$0.892932\pi$
$464$	−2.69623	+	2.69623i	−0.125169	+	0.125169i
$465$		0			0
$466$	−0.119518	−	0.119518i	−0.00553657	−	0.00553657i
$467$	29.1177			1.34741			0.673703	−	0.739002i	$-0.264703\pi$
$467$	29.1177			1.34741			0.673703	+	0.739002i	$0.264703\pi$
$468$		0			0
$469$	4.58822	+	4.58822i	0.211864	+	0.211864i
$470$	0.752762	+	1.71594i	0.0347223	+	0.0791504i
$471$		0			0
$472$			5.50204i			0.253252i
$473$	2.53118	+	2.53118i	0.116384	+	0.116384i
$474$		0			0
$475$	−14.7156	−	13.5445i	−0.675196	−	0.621463i
$476$	15.4985	−	5.87366i	0.710374	−	0.269219i
$477$		0			0
$478$	2.22485			0.101762
$479$	1.39053	−	1.39053i	0.0635350	−	0.0635350i	−0.674625	−	0.738160i	$-0.735695\pi$
$479$	1.39053	−	1.39053i	0.0635350	−	0.0635350i	0.738160	+	0.674625i	$0.235695\pi$
$480$		0			0
$481$	3.73289	−	3.73289i	0.170205	−	0.170205i
$482$	1.39434	−	1.39434i	0.0635103	−	0.0635103i
$483$		0			0
$484$			20.9575i			0.952614i
$485$	−34.8277	−	13.5882i	−1.58144	−	0.617009i
$486$		0			0
$487$	3.41883	−	3.41883i	0.154922	−	0.154922i	−0.625390	−	0.780312i	$-0.715060\pi$
$487$	3.41883	−	3.41883i	0.154922	−	0.154922i	0.780312	+	0.625390i	$0.215060\pi$
$488$	3.66803	+	3.66803i	0.166044	+	0.166044i
$489$		0			0
$490$	−0.570505	−	1.30048i	−0.0257728	−	0.0587498i
$491$		−	16.8949i		−	0.762456i	−0.924481	−	0.381228i	$-0.875501\pi$
$491$		−	16.8949i		−	0.762456i	0.924481	−	0.381228i	$-0.124499\pi$
$492$		0			0
$493$	−3.99611	+	1.51445i	−0.179976	+	0.0682075i
$494$	−3.78398			−0.170249
$495$		0			0
$496$	−15.7656	+	15.7656i	−0.707899	+	0.707899i
$497$		−	3.75520i		−	0.168444i
$498$		0			0
$499$	3.07234	+	3.07234i	0.137537	+	0.137537i	0.772523	−	0.634987i	$-0.218994\pi$
$499$	3.07234	+	3.07234i	0.137537	+	0.137537i	−0.634987	+	0.772523i	$0.718994\pi$
$500$	7.06201	−	20.5789i	0.315822	−	0.920315i
$501$		0			0
$502$	1.40286			0.0626125
$503$	−8.13721	+	8.13721i	−0.362820	+	0.362820i	−0.864850	−	0.502030i	$-0.832587\pi$
$503$	−8.13721	+	8.13721i	−0.362820	+	0.362820i	0.502030	+	0.864850i	$0.332587\pi$
$504$		0			0
$505$	−9.03398	+	3.96310i	−0.402007	+	0.176356i
$506$	0.909332			0.0404247
$507$		0			0
$508$	5.80570			0.257586
$509$	−34.8177			−1.54327			−0.771634	−	0.636066i	$-0.780560\pi$
$509$	−34.8177			−1.54327			−0.771634	+	0.636066i	$0.780560\pi$
$510$		0			0
$511$	25.1418			1.11221
$512$	16.6395			0.735368
$513$		0			0
$514$	−6.33845			−0.279577
$515$	15.6595	+	35.6961i	0.690038	+	1.57296i
$516$		0			0
$517$	1.22402	−	1.22402i	0.0538323	−	0.0538323i
$518$	−0.622545			−0.0273531
$519$		0			0
$520$	−3.35325	−	7.64383i	−0.147050	−	0.335204i
$521$	−15.8746	−	15.8746i	−0.695481	−	0.695481i	0.267951	−	0.963432i	$-0.413653\pi$
$521$	−15.8746	−	15.8746i	−0.695481	−	0.695481i	−0.963432	+	0.267951i	$0.913653\pi$
$522$		0			0
$523$			16.4943i			0.721243i	0.932712	+	0.360622i	$0.117435\pi$
$523$			16.4943i			0.721243i	−0.932712	+	0.360622i	$0.882565\pi$
$524$	9.89881	−	9.89881i	0.432432	−	0.432432i
$525$		0			0
$526$	−2.87465			−0.125341
$527$	−23.3664	+	8.85545i	−1.01786	+	0.385749i
$528$		0			0
$529$		−	43.4426i		−	1.88881i
$530$	−2.92641	+	1.28378i	−0.127115	+	0.0557638i
$531$		0			0
$532$	−11.3698	−	11.3698i	−0.492944	−	0.492944i
$533$	−31.0389	+	31.0389i	−1.34444	+	1.34444i
$534$		0			0
$535$	10.8555	+	4.23534i	0.469325	+	0.183110i
$536$			2.88048i			0.124418i
$537$		0			0
$538$	−3.29894	+	3.29894i	−0.142228	+	0.142228i
$539$	−0.927664	+	0.927664i	−0.0399573	+	0.0399573i
$540$		0			0
$541$	−9.00000	+	9.00000i	−0.386940	+	0.386940i	−0.873595	−	0.486654i	$-0.838217\pi$
$541$	−9.00000	+	9.00000i	−0.386940	+	0.386940i	0.486654	+	0.873595i	$0.338217\pi$
$542$	−5.62619			−0.241666
$543$		0			0
$544$	10.1090	+	4.55255i	0.433420	+	0.195189i
$545$	16.8891	+	6.58937i	0.723448	+	0.282257i
$546$		0			0
$547$	8.84290	+	8.84290i	0.378095	+	0.378095i	0.870415	−	0.492320i	$-0.163851\pi$
$547$	8.84290	+	8.84290i	0.378095	+	0.378095i	−0.492320	+	0.870415i	$0.663851\pi$
$548$			1.02525i			0.0437965i
$549$		0			0
$550$	0.557310	−	0.0230947i	0.0237638	−	0.000984762i
$551$	2.93157	+	2.93157i	0.124889	+	0.124889i
$552$		0			0
$553$	−21.1255			−0.898346
$554$	1.11093	+	1.11093i	0.0471987	+	0.0471987i
$555$		0			0
$556$	−24.3221	+	24.3221i	−1.03149	+	1.03149i
$557$			38.9354i			1.64975i	0.565318	+	0.824873i	$0.308753\pi$
$557$			38.9354i			1.64975i	−0.565318	+	0.824873i	$0.691247\pi$
$558$		0			0
$559$		−	30.3549i		−	1.28387i
$560$	6.17644	−	15.8307i	0.261002	−	0.668970i
$561$		0			0
$562$			4.19153i			0.176809i
$563$	−8.17844			−0.344680			−0.172340	−	0.985038i	$-0.555133\pi$
$563$	−8.17844			−0.344680			−0.172340	+	0.985038i	$0.555133\pi$
$564$		0			0
$565$	−2.82356	+	7.23701i	−0.118788	+	0.304463i
$566$	4.14368	−	4.14368i	0.174172	−	0.174172i
$567$		0			0
$568$	1.17876	−	1.17876i	0.0494595	−	0.0494595i
$569$			11.8920i			0.498538i	0.968434	+	0.249269i	$0.0801904\pi$
$569$			11.8920i			0.498538i	−0.968434	+	0.249269i	$0.919810\pi$
$570$		0			0
$571$	−2.80523	−	2.80523i	−0.117395	−	0.117395i	0.645969	−	0.763364i	$-0.276454\pi$
$571$	−2.80523	−	2.80523i	−0.117395	−	0.117395i	−0.763364	+	0.645969i	$0.776454\pi$
$572$	−2.68895	+	2.68895i	−0.112431	+	0.112431i
$573$		0			0
$574$	5.17644			0.216060
$575$	−1.68747	−	40.7212i	−0.0703725	−	1.69819i
$576$		0			0
$577$			6.58601i			0.274179i	0.990559	+	0.137090i	$0.0437749\pi$
$577$			6.58601i			0.274179i	−0.990559	+	0.137090i	$0.956225\pi$
$578$	2.61836	+	2.95831i	0.108909	+	0.123049i
$579$		0			0
$580$	−1.63928	+	4.20159i	−0.0680672	+	0.174462i
$581$	−3.26711	+	3.26711i	−0.135542	+	0.135542i
$582$		0			0
$583$	2.08747	+	2.08747i	0.0864543	+	0.0864543i
$584$	7.89199	+	7.89199i	0.326573	+	0.326573i
$585$		0			0
$586$			6.10218i			0.252079i
$587$	22.3369			0.921944			0.460972	−	0.887415i	$-0.347501\pi$
$587$	22.3369			0.921944			0.460972	+	0.887415i	$0.347501\pi$
$588$		0			0
$589$	17.1418	+	17.1418i	0.706314	+	0.706314i
$590$	1.25253	+	2.85518i	0.0515659	+	0.117546i
$591$		0			0
$592$	3.37357	+	3.37357i	0.138653	+	0.138653i
$593$	−30.1344			−1.23747			−0.618736	−	0.785599i	$-0.712355\pi$
$593$	−30.1344			−1.23747			−0.618736	+	0.785599i	$0.712355\pi$
$594$		0			0
$595$	13.5972	−	13.3350i	0.557429	−	0.546681i
$596$	14.2468			0.583574
$597$		0			0
$598$	−5.45252	−	5.45252i	−0.222970	−	0.222970i
$599$	8.88907			0.363198			0.181599	−	0.983373i	$-0.441873\pi$
$599$	8.88907			0.363198			0.181599	+	0.983373i	$0.441873\pi$
$600$		0			0
$601$	17.1418	+	17.1418i	0.699227	+	0.699227i	0.964244	−	0.265017i	$-0.0853776\pi$
$601$	17.1418	+	17.1418i	0.699227	+	0.699227i	−0.265017	+	0.964244i	$0.585378\pi$
$602$	−2.53118	+	2.53118i	−0.103163	+	0.103163i
$603$		0			0
$604$		−	14.5284i		−	0.591151i
$605$	9.67429	+	22.0528i	0.393316	+	0.896573i
$606$		0			0
$607$	−10.5442	−	10.5442i	−0.427978	−	0.427978i	0.459961	−	0.887939i	$-0.347863\pi$
$607$	−10.5442	−	10.5442i	−0.427978	−	0.427978i	−0.887939	+	0.459961i	$0.847863\pi$
$608$		−	10.7558i		−	0.436205i
$609$		0			0
$610$	2.73847	+	1.06843i	0.110877	+	0.0432595i
$611$	−14.6789			−0.593844
$612$		0			0
$613$			31.3459i			1.26605i	0.774132	+	0.633024i	$0.218187\pi$
$613$			31.3459i			1.26605i	−0.774132	+	0.633024i	$0.781813\pi$
$614$		−	3.23336i		−	0.130488i
$615$		0			0
$616$	0.909332			0.0366380
$617$	−10.9050	−	10.9050i	−0.439020	−	0.439020i	0.452662	−	0.891682i	$-0.350474\pi$
$617$	−10.9050	−	10.9050i	−0.439020	−	0.439020i	−0.891682	+	0.452662i	$0.850474\pi$
$618$		0			0
$619$	31.8930	+	31.8930i	1.28189	+	1.28189i	0.939593	+	0.342294i	$0.111204\pi$
$619$	31.8930	+	31.8930i	1.28189	+	1.28189i	0.342294	+	0.939593i	$0.388796\pi$
$620$	−9.58533	+	24.5680i	−0.384956	+	0.986673i
$621$		0			0
$622$	1.43625	−	1.43625i	0.0575882	−	0.0575882i
$623$	−13.6897	+	13.6897i	−0.548466	+	0.548466i
$624$		0			0
$625$	−2.06843	−	24.9143i	−0.0827372	−	0.996571i
$626$	1.14176	−	1.14176i	0.0456338	−	0.0456338i
$627$		0			0
$628$			24.2415i			0.967343i
$629$	1.89491	+	5.00000i	0.0755549	+	0.199363i
$630$		0			0
$631$		−	29.7493i		−	1.18430i	−0.805827	−	0.592150i	$-0.798279\pi$
$631$		−	29.7493i		−	1.18430i	0.805827	−	0.592150i	$-0.201721\pi$
$632$	−6.63128	−	6.63128i	−0.263778	−	0.263778i
$633$		0			0
$634$	0.693313	−	0.693313i	0.0275350	−	0.0275350i
$635$	6.10912	−	2.68000i	0.242433	−	0.106352i
$636$		0			0
$637$	11.1249			0.440784
$638$	−0.115626			−0.00457767
$639$		0			0
$640$	14.2162	−	6.23649i	0.561946	−	0.246519i
$641$	−31.2131	+	31.2131i	−1.23284	+	1.23284i	−0.269977	+	0.962867i	$0.587016\pi$
$641$	−31.2131	+	31.2131i	−1.23284	+	1.23284i	−0.962867	+	0.269977i	$0.912984\pi$
$642$		0			0
$643$	5.36109	+	5.36109i	0.211421	+	0.211421i	0.804871	−	0.593450i	$-0.202235\pi$
$643$	5.36109	+	5.36109i	0.211421	+	0.211421i	−0.593450	+	0.804871i	$0.702235\pi$
$644$		−	32.7666i		−	1.29119i
$645$		0			0
$646$	1.57379	−	3.49464i	0.0619201	−	0.137495i
$647$		−	10.2540i		−	0.403128i	−0.979475	−	0.201564i	$-0.935398\pi$
$647$		−	10.2540i		−	0.403128i	0.979475	−	0.201564i	$-0.0646024\pi$
$648$		0			0
$649$	2.03666	−	2.03666i	0.0799460	−	0.0799460i
$650$	−3.48021	−	3.20325i	−0.136505	−	0.125642i
$651$		0			0
$652$	−11.7893	+	11.7893i	−0.461706	+	0.461706i
$653$	10.1207	−	10.1207i	0.396054	−	0.396054i	−0.480785	−	0.876839i	$-0.659648\pi$
$653$	10.1207	−	10.1207i	0.396054	−	0.396054i	0.876839	+	0.480785i	$0.159648\pi$
$654$		0			0
$655$	5.84671	−	14.9856i	0.228450	−	0.585535i
$656$	−28.0511	−	28.0511i	−1.09521	−	1.09521i
$657$		0			0
$658$	1.22402	+	1.22402i	0.0477172	+	0.0477172i
$659$	43.9653			1.71265			0.856323	−	0.516441i	$-0.172743\pi$
$659$	43.9653			1.71265			0.856323	+	0.516441i	$0.172743\pi$
$660$		0			0
$661$			20.7077i			0.805438i	0.915324	+	0.402719i	$0.131935\pi$
$661$			20.7077i			0.805438i	−0.915324	+	0.402719i	$0.868065\pi$
$662$		−	3.17815i		−	0.123522i
$663$		0			0
$664$	−2.05109			−0.0795977
$665$	−17.2125	−	6.71555i	−0.667472	−	0.260418i
$666$		0			0
$667$			8.44848i			0.327126i
$668$	−13.0008	−	13.0008i	−0.503016	−	0.503016i
$669$		0			0
$670$	0.655737	+	1.49477i	0.0253333	+	0.0577480i
$671$		−	2.71555i		−	0.104833i
$672$		0			0
$673$	−32.7151	+	32.7151i	−1.26108	+	1.26108i	−0.310503	+	0.950572i	$0.600497\pi$
$673$	−32.7151	+	32.7151i	−1.26108	+	1.26108i	−0.950572	+	0.310503i	$0.899503\pi$
$674$	1.06551	+	1.06551i	0.0410420	+	0.0410420i
$675$		0			0
$676$	6.94891			0.267266
$677$	−1.24509	−	1.24509i	−0.0478527	−	0.0478527i	0.682776	−	0.730628i	$-0.260773\pi$
$677$	−1.24509	−	1.24509i	−0.0478527	−	0.0478527i	−0.730628	+	0.682776i	$0.760773\pi$
$678$		0			0
$679$	−34.5362			−1.32538
$680$	8.45399	+	0.0822978i	0.324196	+	0.00315598i
$681$		0			0
$682$	−0.676098			−0.0258891
$683$	16.2377	+	16.2377i	0.621317	+	0.621317i	0.945868	−	0.324551i	$-0.105213\pi$
$683$	16.2377	+	16.2377i	0.621317	+	0.621317i	−0.324551	+	0.945868i	$0.605213\pi$
$684$		0			0
$685$	0.473270	+	1.07883i	0.0180827	+	0.0412200i
$686$	−3.30377	−	3.30377i	−0.126139	−	0.126139i
$687$		0			0
$688$	27.4329			1.04587
$689$		−	25.0337i		−	0.953710i
$690$		0			0
$691$	−18.2314	−	18.2314i	−0.693556	−	0.693556i	0.269456	−	0.963013i	$-0.413156\pi$
$691$	−18.2314	−	18.2314i	−0.693556	−	0.693556i	−0.963013	+	0.269456i	$0.913156\pi$
$692$	22.7641	+	22.7641i	0.865360	+	0.865360i
$693$		0			0
$694$	0.822571	−	0.822571i	0.0312244	−	0.0312244i
$695$	−14.3658	+	36.8206i	−0.544925	+	1.39669i
$696$		0			0
$697$	−15.7561	−	41.5748i	−0.596804	−	1.57476i
$698$		−	2.14103i		−	0.0810391i
$699$		0			0
$700$	−0.832189	−	20.0820i	−0.0314538	−	0.759027i
$701$	25.1195			0.948751			0.474376	−	0.880323i	$-0.342674\pi$
$701$	25.1195			0.948751			0.474376	+	0.880323i	$0.342674\pi$
$702$		0			0
$703$	3.66803	−	3.66803i	0.138342	−	0.138342i
$704$	−2.28544	−	2.28544i	−0.0861357	−	0.0861357i
$705$		0			0
$706$		−	3.22092i		−	0.121221i
$707$	−6.44415	+	6.44415i	−0.242357	+	0.242357i
$708$		0			0
$709$	−23.7156	+	23.7156i	−0.890656	+	0.890656i	−0.994585	−	0.103929i	$-0.966859\pi$
$709$	−23.7156	+	23.7156i	−0.890656	+	0.890656i	0.103929	+	0.994585i	$0.466859\pi$
$710$	0.343350	−	0.880035i	0.0128857	−	0.0330271i
$711$		0			0
$712$	−8.59437			−0.322088
$713$			49.4008i			1.85007i
$714$		0			0
$715$	−1.58822	+	4.07073i	−0.0593961	+	0.152237i
$716$			38.0078i			1.42042i
$717$		0			0
$718$		−	2.67305i		−	0.0997572i
$719$	−29.4812	+	29.4812i	−1.09946	+	1.09946i	−0.104990	+	0.994473i	$0.533481\pi$
$719$	−29.4812	+	29.4812i	−1.09946	+	1.09946i	−0.994473	+	0.104990i	$0.966519\pi$
$720$		0			0
$721$	25.4629	+	25.4629i	0.948287	+	0.948287i
$722$	0.697168			0.0259459
$723$		0			0
$724$	−14.4233	−	14.4233i	−0.536037	−	0.536037i
$725$	0.214570	+	5.17789i	0.00796892	+	0.192302i
$726$		0			0
$727$		−	12.2458i		−	0.454172i	−0.973875	−	0.227086i	$-0.927080\pi$
$727$		−	12.2458i		−	0.454172i	0.973875	−	0.227086i	$-0.0729199\pi$
$728$	−5.45252	−	5.45252i	−0.202084	−	0.202084i
$729$		0			0
$730$	5.89199	+	2.29879i	0.218072	+	0.0850821i
$731$	28.0337	+	12.6249i	1.03687	+	0.466948i
$732$		0			0
$733$	−32.8393			−1.21295			−0.606473	−	0.795104i	$-0.707416\pi$
$733$	−32.8393			−1.21295			−0.606473	+	0.795104i	$0.707416\pi$
$734$	3.19185	−	3.19185i	0.117814	−	0.117814i
$735$		0			0
$736$	15.4985	−	15.4985i	0.571284	−	0.571284i
$737$	1.06625	−	1.06625i	0.0392759	−	0.0392759i
$738$		0			0
$739$			6.00000i			0.220714i	0.993892	+	0.110357i	$0.0351994\pi$
$739$			6.00000i			0.220714i	−0.993892	+	0.110357i	$0.964801\pi$
$740$	5.25710	+	2.05109i	0.193255	+	0.0753995i
$741$		0			0
$742$	−2.08747	+	2.08747i	−0.0766336	+	0.0766336i
$743$	16.1704	+	16.1704i	0.593236	+	0.593236i	0.938504	−	0.345268i	$-0.112212\pi$
$743$	16.1704	+	16.1704i	0.593236	+	0.593236i	−0.345268	+	0.938504i	$0.612212\pi$
$744$		0			0
$745$	14.9914	−	6.57655i	0.549243	−	0.240946i
$746$			1.29887i			0.0475552i
$747$		0			0
$748$	−1.36498	−	3.60170i	−0.0499085	−	0.131691i
$749$	10.7647			0.393332
$750$		0			0
$751$	−22.6799	+	22.6799i	−0.827600	+	0.827600i	−0.987184	−	0.159584i	$-0.948985\pi$
$751$	−22.6799	+	22.6799i	−0.827600	+	0.827600i	0.159584	+	0.987184i	$0.448985\pi$
$752$		−	13.2659i		−	0.483758i
$753$		0			0
$754$	0.693313	+	0.693313i	0.0252490	+	0.0252490i
$755$	−6.70651	−	15.2877i	−0.244075	−	0.556375i
$756$		0			0
$757$	−36.2220			−1.31651			−0.658256	−	0.752794i	$-0.728706\pi$
$757$	−36.2220			−1.31651			−0.658256	+	0.752794i	$0.728706\pi$
$758$	−0.0914333	+	0.0914333i	−0.00332101	+	0.00332101i
$759$		0			0
$760$	−3.29499	−	7.51101i	−0.119522	−	0.272453i
$761$	−24.4851			−0.887584			−0.443792	−	0.896130i	$-0.646367\pi$
$761$	−24.4851			−0.887584			−0.443792	+	0.896130i	$0.646367\pi$
$762$		0			0
$763$	16.7477			0.606308
$764$	−10.3549			−0.374626
$765$		0			0
$766$	5.76372			0.208252
$767$	−24.4244			−0.881914
$768$		0			0
$769$	−5.55937			−0.200476			−0.100238	−	0.994963i	$-0.531960\pi$
$769$	−5.55937			−0.200476			−0.100238	+	0.994963i	$0.531960\pi$
$770$	0.471880	−	0.207008i	0.0170054	−	0.00746005i
$771$		0			0
$772$	17.1755	−	17.1755i	0.618161	−	0.618161i
$773$	−36.5376			−1.31416			−0.657082	−	0.753819i	$-0.728210\pi$
$773$	−36.5376			−1.31416			−0.657082	+	0.753819i	$0.728210\pi$
$774$		0			0
$775$	1.25465	+	30.2766i	0.0450685	+	1.08757i
$776$	−10.8409	−	10.8409i	−0.389166	−	0.389166i
$777$		0			0
$778$		−	2.03727i		−	0.0730398i
$779$	−30.4995	+	30.4995i	−1.09276	+	1.09276i
$780$		0			0
$781$	−0.872669			−0.0312265
$782$	7.30334	−	2.76783i	0.261167	−	0.0989775i
$783$		0			0
$784$			10.0540i			0.359072i
$785$	11.1902	+	25.5084i	0.399397	+	0.910435i
$786$		0			0
$787$	−11.3490	−	11.3490i	−0.404547	−	0.404547i	0.475285	−	0.879832i	$-0.342345\pi$
$787$	−11.3490	−	11.3490i	−0.404547	−	0.404547i	−0.879832	+	0.475285i	$0.842345\pi$
$788$	0.759241	−	0.759241i	0.0270468	−	0.0270468i
$789$		0			0
$790$	−4.95077	−	1.93157i	−0.176140	−	0.0687222i
$791$			7.17644i			0.255165i
$792$		0			0
$793$	−16.2829	+	16.2829i	−0.578224	+	0.578224i
$794$	1.15618	−	1.15618i	0.0410313	−	0.0410313i
$795$		0			0
$796$	24.2170	−	24.2170i	0.858349	−	0.858349i
$797$	−34.7907			−1.23235			−0.616175	−	0.787609i	$-0.711319\pi$
$797$	−34.7907			−1.23235			−0.616175	+	0.787609i	$0.711319\pi$
$798$		0			0
$799$	6.10509	−	13.5565i	0.215983	−	0.479593i
$800$	9.10509	−	9.89234i	0.321914	−	0.349747i
$801$		0			0
$802$	1.74752	+	1.74752i	0.0617070	+	0.0617070i
$803$		−	5.84268i		−	0.206184i
$804$		0			0
$805$	−15.1256	−	34.4791i	−0.533106	−	1.21523i
$806$	4.05400	+	4.05400i	0.142796	+	0.142796i
$807$		0			0
$808$	−4.04563			−0.142325
$809$	13.3549	+	13.3549i	0.469532	+	0.469532i	0.901763	−	0.432231i	$-0.142274\pi$
$809$	13.3549	+	13.3549i	0.469532	+	0.469532i	−0.432231	+	0.901763i	$0.642274\pi$
$810$		0			0
$811$	−9.28544	+	9.28544i	−0.326056	+	0.326056i	−0.851085	−	0.525029i	$-0.824055\pi$
$811$	−9.28544	+	9.28544i	−0.326056	+	0.326056i	0.525029	+	0.851085i	$0.324055\pi$
$812$			4.16643i			0.146213i
$813$		0			0
$814$			0.144673i			0.00507078i
$815$	−6.96334	+	17.8476i	−0.243915	+	0.625174i
$816$		0			0
$817$		−	29.8274i		−	1.04353i
$818$	−0.588924			−0.0205913
$819$		0			0
$820$	−43.7126	−	17.0547i	−1.52651	−	0.595577i
$821$	27.8206	−	27.8206i	0.970947	−	0.970947i	−0.0286425	−	0.999590i	$-0.509118\pi$
$821$	27.8206	−	27.8206i	0.970947	−	0.970947i	0.999590	+	0.0286425i	$0.00911845\pi$
$822$		0			0
$823$	−28.4414	+	28.4414i	−0.991403	+	0.991403i	−0.999963	−	0.00855996i	$-0.997275\pi$
$823$	−28.4414	+	28.4414i	−0.991403	+	0.991403i	0.00855996	+	0.999963i	$0.497275\pi$
$824$			15.9856i			0.556884i
$825$		0			0
$826$	2.03666	+	2.03666i	0.0708646	+	0.0708646i
$827$	23.9764	−	23.9764i	0.833742	−	0.833742i	−0.154284	−	0.988027i	$-0.549307\pi$
$827$	23.9764	−	23.9764i	0.833742	−	0.833742i	0.988027	+	0.154284i	$0.0493071\pi$
$828$		0			0
$829$	−8.18134			−0.284150			−0.142075	−	0.989856i	$-0.545377\pi$
$829$	−8.18134			−0.284150			−0.142075	+	0.989856i	$0.545377\pi$
$830$	−1.06437	+	0.466927i	−0.0369449	+	0.0162073i
$831$		0			0
$832$			27.4078i			0.950195i
$833$	−4.62695	+	10.2742i	−0.160314	+	0.355980i
$834$		0			0
$835$	−19.6816	−	7.67889i	−0.681110	−	0.265739i
$836$	−2.64222	+	2.64222i	−0.0913832	+	0.0913832i
$837$		0			0
$838$	4.33181	+	4.33181i	0.149640	+	0.149640i
$839$	−15.5381	−	15.5381i	−0.536436	−	0.536436i	0.386045	−	0.922480i	$-0.373841\pi$
$839$	−15.5381	−	15.5381i	−0.536436	−	0.536436i	−0.922480	+	0.386045i	$0.873841\pi$
$840$		0			0
$841$			27.9257i			0.962956i
$842$	−1.84589			−0.0636135
$843$		0			0
$844$	17.6547	+	17.6547i	0.607701	+	0.607701i
$845$	7.31207	−	3.20772i	0.251543	−	0.110349i
$846$		0			0
$847$	15.7308	+	15.7308i	0.540515	+	0.540515i
$848$	22.6240			0.776912
$849$		0			0
$850$	4.40576	−	1.88183i	0.151116	−	0.0645462i
$851$	10.5709			0.362365
$852$		0			0
$853$	26.1383	+	26.1383i	0.894959	+	0.894959i	0.994985	−	0.100026i	$-0.0318927\pi$
$853$	26.1383	+	26.1383i	0.894959	+	0.894959i	−0.100026	+	0.994985i	$0.531893\pi$
$854$	2.71555			0.0929242
$855$		0			0
$856$	3.37902	+	3.37902i	0.115493	+	0.115493i
$857$	−10.6231	+	10.6231i	−0.362879	+	0.362879i	−0.864872	−	0.501993i	$-0.832600\pi$
$857$	−10.6231	+	10.6231i	−0.362879	+	0.362879i	0.501993	+	0.864872i	$0.332600\pi$
$858$		0			0
$859$		−	40.2180i		−	1.37222i	−0.727498	−	0.686110i	$-0.759317\pi$
$859$		−	40.2180i		−	1.37222i	0.727498	−	0.686110i	$-0.240683\pi$
$860$	29.7141	−	13.0352i	1.01324	−	0.444497i
$861$		0			0
$862$	1.86337	+	1.86337i	0.0634668	+	0.0634668i
$863$			12.3865i			0.421643i	0.977525	+	0.210822i	$0.0676139\pi$
$863$			12.3865i			0.421643i	−0.977525	+	0.210822i	$0.932386\pi$
$864$		0			0
$865$	34.4620	+	13.4455i	1.17174	+	0.457162i
$866$	1.45136			0.0493192
$867$		0			0
$868$			24.3623i			0.826911i
$869$			4.90933i			0.166538i
$870$		0			0
$871$	−12.7869			−0.433267
$872$	5.25710	+	5.25710i	0.178028	+	0.178028i
$873$		0			0
$874$	−5.35778	−	5.35778i	−0.181229	−	0.181229i
$875$	−10.1458	−	20.7473i	−0.342991	−	0.701387i
$876$		0			0
$877$	31.9433	−	31.9433i	1.07865	−	1.07865i	0.0820188	−	0.996631i	$-0.473863\pi$
$877$	31.9433	−	31.9433i	1.07865	−	1.07865i	0.996631	−	0.0820188i	$-0.0261368\pi$
$878$	−1.73003	+	1.73003i	−0.0583857	+	0.0583857i
$879$		0			0
$880$	−3.67889	−	1.43534i	−0.124015	−	0.0483853i
$881$	12.0367	−	12.0367i	0.405525	−	0.405525i	−0.474649	−	0.880175i	$-0.657425\pi$
$881$	12.0367	−	12.0367i	0.405525	−	0.405525i	0.880175	+	0.474649i	$0.157425\pi$
$882$		0			0
$883$			13.3497i			0.449254i	0.974445	+	0.224627i	$0.0721164\pi$
$883$			13.3497i			0.449254i	−0.974445	+	0.224627i	$0.927884\pi$
$884$	−13.4118	+	29.7811i	−0.451087	+	1.00165i
$885$		0			0
$886$		−	6.80132i		−	0.228495i
$887$	−31.4868	−	31.4868i	−1.05722	−	1.05722i	−0.998260	−	0.0589646i	$-0.981220\pi$
$887$	−31.4868	−	31.4868i	−1.05722	−	1.05722i	−0.0589646	−	0.998260i	$-0.518780\pi$
$888$		0			0
$889$	4.35778	−	4.35778i	0.146155	−	0.146155i
$890$	−4.45988	+	1.95650i	−0.149496	+	0.0655819i
$891$		0			0
$892$	7.92163			0.265236
$893$	−14.4238			−0.482675
$894$		0			0
$895$	17.5450	+	39.9942i	0.586463	+	1.33686i
$896$	10.1408	−	10.1408i	0.338779	−	0.338779i
$897$		0			0
$898$	5.37790	+	5.37790i	0.179463	+	0.179463i
$899$		−	6.28153i		−	0.209501i
$900$		0			0
$901$	23.1195	+	10.4118i	0.770223	+	0.346867i
$902$		−	1.20295i		−	0.0400538i
$903$		0			0
$904$	−2.25268	+	2.25268i	−0.0749231	+	0.0749231i
$905$	−21.8351	−	8.51907i	−0.725822	−	0.283184i
$906$		0			0
$907$	23.2958	−	23.2958i	0.773526	−	0.773526i	−0.205195	−	0.978721i	$-0.565783\pi$
$907$	23.2958	−	23.2958i	0.773526	−	0.773526i	0.978721	+	0.205195i	$0.0657829\pi$
$908$	−21.7061	+	21.7061i	−0.720342	+	0.720342i
$909$		0			0
$910$	−4.07073	−	1.58822i	−0.134944	−	0.0526490i
$911$	−25.1630	−	25.1630i	−0.833688	−	0.833688i	0.154332	−	0.988019i	$-0.450678\pi$
$911$	−25.1630	−	25.1630i	−0.833688	−	0.833688i	−0.988019	+	0.154332i	$0.950678\pi$
$912$		0			0
$913$	0.759241	+	0.759241i	0.0251272	+	0.0251272i
$914$	−7.31450			−0.241942
$915$		0			0
$916$		−	29.0848i		−	0.960990i
$917$		−	14.8601i		−	0.490725i
$918$		0			0
$919$	28.5997			0.943418			0.471709	−	0.881754i	$-0.343637\pi$
$919$	28.5997			0.943418			0.471709	+	0.881754i	$0.343637\pi$
$920$	6.07507	−	15.5709i	0.200289	−	0.513357i
$921$		0			0
$922$		−	6.19183i		−	0.203917i
$923$	5.23268	+	5.23268i	0.172236	+	0.172236i
$924$		0			0
$925$	6.47866	−	0.268473i	0.213017	−	0.00882735i
$926$			3.30085i			0.108473i
$927$		0			0
$928$	−1.97071	+	1.97071i	−0.0646917	+	0.0646917i
$929$	8.98266	+	8.98266i	0.294711	+	0.294711i	0.838938	−	0.544227i	$-0.183177\pi$
$929$	8.98266	+	8.98266i	0.294711	+	0.294711i	−0.544227	+	0.838938i	$0.683177\pi$
$930$		0			0
$931$	10.9316			0.358268
$932$	1.00083	+	1.00083i	0.0327832	+	0.0327832i
$933$		0			0
$934$	6.76664			0.221411
$935$	−3.09891	−	3.15983i	−0.101345	−	0.103338i
$936$		0			0
$937$	30.7655			1.00506			0.502532	−	0.864558i	$-0.332402\pi$
$937$	30.7655			1.00506			0.502532	+	0.864558i	$0.332402\pi$
$938$	1.06625	+	1.06625i	0.0348144	+	0.0348144i
$939$		0			0
$940$	−6.30352	−	14.3690i	−0.205598	−	0.468666i
$941$	27.7522	+	27.7522i	0.904696	+	0.904696i	0.995838	−	0.0911416i	$-0.0290516\pi$
$941$	27.7522	+	27.7522i	0.904696	+	0.904696i	−0.0911416	+	0.995838i	$0.529052\pi$
$942$		0			0
$943$	−87.8965			−2.86230
$944$		−	22.0733i		−	0.718426i
$945$		0			0
$946$	0.588220	+	0.588220i	0.0191247	+	0.0191247i
$947$	−2.52289	−	2.52289i	−0.0819830	−	0.0819830i	0.664926	−	0.746909i	$-0.268463\pi$
$947$	−2.52289	−	2.52289i	−0.0819830	−	0.0819830i	−0.746909	+	0.664926i	$0.768463\pi$
$948$		0			0
$949$	−35.0337	+	35.0337i	−1.13724	+	1.13724i
$950$	−3.41974	−	3.14759i	−0.110951	−	0.102121i
$951$		0			0
$952$	7.30334	−	2.76783i	0.236703	−	0.0897059i
$953$			53.8491i			1.74434i	0.489200	+	0.872172i	$0.337289\pi$
$953$			53.8491i			1.74434i	−0.489200	+	0.872172i	$0.662711\pi$
$954$		0			0
$955$	−10.8960	+	4.77995i	−0.352587	+	0.154676i
$956$	−18.6306			−0.602555
$957$		0			0
$958$	0.323145	−	0.323145i	0.0104403	−	0.0104403i
$959$	0.769556	+	0.769556i	0.0248503	+	0.0248503i
$960$		0			0
$961$		−	5.72998i		−	0.184838i
$962$	0.867484	−	0.867484i	0.0279688	−	0.0279688i
$963$		0			0
$964$	−11.6760	+	11.6760i	−0.376058	+	0.376058i
$965$	10.1447	−	26.0016i	0.326569	−	0.837021i
$966$		0			0
$967$	14.6688			0.471716			0.235858	−	0.971788i	$-0.424210\pi$
$967$	14.6688			0.471716			0.235858	+	0.971788i	$0.424210\pi$
$968$			9.87576i			0.317419i
$969$		0			0
$970$	−8.09358	−	3.15776i	−0.259869	−	0.101389i
$971$			14.2468i			0.457203i	0.973520	+	0.228602i	$0.0734153\pi$
$971$			14.2468i			0.457203i	−0.973520	+	0.228602i	$0.926585\pi$
$972$		0			0
$973$			36.5125i			1.17054i
$974$	0.794499	−	0.794499i	0.0254574	−	0.0254574i
$975$		0			0
$976$	−14.7156	−	14.7156i	−0.471033	−	0.471033i
$977$	20.9141			0.669103			0.334551	−	0.942378i	$-0.391415\pi$
$977$	20.9141			0.669103			0.334551	+	0.942378i	$0.391415\pi$
$978$		0			0
$979$	3.18134	+	3.18134i	0.101676	+	0.101676i
$980$	4.77733	+	10.8900i	0.152606	+	0.347870i
$981$		0			0
$982$		−	3.92620i		−	0.125290i
$983$	−12.3036	−	12.3036i	−0.392425	−	0.392425i	0.483126	−	0.875551i	$-0.339501\pi$
$983$	−12.3036	−	12.3036i	−0.392425	−	0.392425i	−0.875551	+	0.483126i	$0.839501\pi$
$984$		0			0
$985$	0.448443	−	1.14940i	0.0142886	−	0.0366228i
$986$	−0.928654	+	0.351942i	−0.0295744	+	0.0112081i
$987$		0			0
$988$	31.6865			1.00808
$989$	42.9797	−	42.9797i	1.36668	−	1.36668i
$990$		0			0
$991$	3.73190	−	3.73190i	0.118548	−	0.118548i	−0.645344	−	0.763892i	$-0.723286\pi$
$991$	3.73190	−	3.73190i	0.118548	−	0.118548i	0.763892	+	0.645344i	$0.223286\pi$
$992$	−11.5233	+	11.5233i	−0.365866	+	0.365866i
$993$		0			0
$994$		−	0.872669i		−	0.0276794i
$995$	14.3037	−	36.6615i	0.453458	−	1.16225i
$996$		0			0
$997$	−18.1295	+	18.1295i	−0.574167	+	0.574167i	−0.933290	−	0.359123i	$-0.883076\pi$
$997$	−18.1295	+	18.1295i	−0.574167	+	0.574167i	0.359123	+	0.933290i	$0.383076\pi$
$998$	0.713978	+	0.713978i	0.0226006	+	0.0226006i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.2.t.e.514.4		12
3.2	odd	2		85.2.j.c.4.3	✓	12
5.4	even	2	inner	765.2.t.e.514.3		12
15.2	even	4		425.2.e.d.276.3		12
15.8	even	4		425.2.e.d.276.4		12
15.14	odd	2		85.2.j.c.4.4	yes	12
17.13	even	4	inner	765.2.t.e.64.3		12
51.8	odd	8		1445.2.b.f.579.7		12
51.26	odd	8		1445.2.b.f.579.8		12
51.47	odd	4		85.2.j.c.64.4	yes	12
85.64	even	4	inner	765.2.t.e.64.4		12
255.8	even	8		7225.2.a.bp.1.8		12
255.47	even	4		425.2.e.d.251.4		12
255.59	odd	8		1445.2.b.f.579.6		12
255.77	even	8		7225.2.a.bp.1.6		12
255.98	even	4		425.2.e.d.251.3		12
255.128	even	8		7225.2.a.bp.1.7		12
255.149	odd	4		85.2.j.c.64.3	yes	12
255.179	odd	8		1445.2.b.f.579.5		12
255.212	even	8		7225.2.a.bp.1.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.j.c.4.3	✓	12	3.2	odd	2
85.2.j.c.4.4	yes	12	15.14	odd	2
85.2.j.c.64.3	yes	12	255.149	odd	4
85.2.j.c.64.4	yes	12	51.47	odd	4
425.2.e.d.251.3		12	255.98	even	4
425.2.e.d.251.4		12	255.47	even	4
425.2.e.d.276.3		12	15.2	even	4
425.2.e.d.276.4		12	15.8	even	4
765.2.t.e.64.3		12	17.13	even	4	inner
765.2.t.e.64.4		12	85.64	even	4	inner
765.2.t.e.514.3		12	5.4	even	2	inner
765.2.t.e.514.4		12	1.1	even	1	trivial
1445.2.b.f.579.5		12	255.179	odd	8
1445.2.b.f.579.6		12	255.59	odd	8
1445.2.b.f.579.7		12	51.8	odd	8
1445.2.b.f.579.8		12	51.26	odd	8
7225.2.a.bp.1.5		12	255.212	even	8
7225.2.a.bp.1.6		12	255.77	even	8
7225.2.a.bp.1.7		12	255.128	even	8
7225.2.a.bp.1.8		12	255.8	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.232389 q^{2} -1.94600 q^{4} +(-2.04770 + 0.898299i) q^{5} +(-1.46067 + 1.46067i) q^{7} -0.917007 q^{8} +(-0.475863 + 0.208755i) q^{10} +(0.339444 + 0.339444i) q^{11} -4.07073i q^{13} +(-0.339444 + 0.339444i) q^{14} +3.67889 q^{16} +(3.75946 + 1.69306i) q^{17} -4.00000i q^{19} +(3.98481 - 1.74809i) q^{20} +(0.0788831 + 0.0788831i) q^{22} +(5.76379 - 5.76379i) q^{23} +(3.38612 - 3.67889i) q^{25} -0.945995i q^{26} +(2.84245 - 2.84245i) q^{28} +(-0.732893 + 0.732893i) q^{29} +(-4.28544 + 4.28544i) q^{31} +2.68895 q^{32} +(0.873659 + 0.393449i) q^{34} +(1.67889 - 4.30312i) q^{35} +(0.917007 + 0.917007i) q^{37} -0.929557i q^{38} +(1.87775 - 0.823747i) q^{40} +(-7.62488 - 7.62488i) q^{41} +7.45685 q^{43} +(-0.660556 - 0.660556i) q^{44} +(1.33944 - 1.33944i) q^{46} -3.60596i q^{47} +2.73289i q^{49} +(0.786897 - 0.854934i) q^{50} +7.92163i q^{52} +6.14969 q^{53} +(-1.00000 - 0.390156i) q^{55} +(1.33944 - 1.33944i) q^{56} +(-0.170316 + 0.170316i) q^{58} -6.00000i q^{59} +(-4.00000 - 4.00000i) q^{61} +(-0.995890 + 0.995890i) q^{62} -6.73289 q^{64} +(3.65674 + 8.33563i) q^{65} -3.14118i q^{67} +(-7.31589 - 3.29468i) q^{68} +(0.390156 - 1.00000i) q^{70} +(-1.28544 + 1.28544i) q^{71} +(-8.60625 - 8.60625i) q^{73} +(0.213103 + 0.213103i) q^{74} +7.78398i q^{76} -0.991630 q^{77} +(7.23143 + 7.23143i) q^{79} +(-7.53324 + 3.30474i) q^{80} +(-1.77194 - 1.77194i) q^{82} +2.23672 q^{83} +(-9.21911 - 0.0897461i) q^{85} +1.73289 q^{86} +(-0.311272 - 0.311272i) q^{88} +9.37220 q^{89} +(5.94600 + 5.94600i) q^{91} +(-11.2163 + 11.2163i) q^{92} -0.837986i q^{94} +(3.59320 + 8.19078i) q^{95} +(11.8220 + 11.8220i) q^{97} +0.635095i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{4} - 4 q^{10} - 16 q^{11} + 16 q^{14} + 4 q^{16} + 32 q^{20} - 4 q^{29} + 4 q^{31} - 20 q^{35} + 24 q^{40} - 16 q^{41} - 28 q^{44} - 4 q^{46} + 40 q^{50} - 12 q^{55} - 4 q^{56} - 48 q^{61}+ \cdots + 36 q^{91}+O(q^{100}) \) 12 * q + 12 * q^4 - 4 * q^10 - 16 * q^11 + 16 * q^14 + 4 * q^16 + 32 * q^20 - 4 * q^29 + 4 * q^31 - 20 * q^35 + 24 * q^40 - 16 * q^41 - 28 * q^44 - 4 * q^46 + 40 * q^50 - 12 * q^55 - 4 * q^56 - 48 * q^61 - 76 * q^64 - 8 * q^65 + 40 * q^71 - 28 * q^74 - 4 * q^79 - 12 * q^80 - 52 * q^85 + 16 * q^86 + 16 * q^89 + 36 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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