LMFDB - Embedded newform 425.2.e.d.251.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(251,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.251"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.e (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
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^{2} $
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.3
Root			$0.767611i$ of defining polynomial
Character	$\chi$	$=$	425.251
Dual form			425.2.e.d.276.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.232389i q^{2} +(-1.69306 - 1.69306i) q^{3} +1.94600 q^{4} +(-0.393449 + 0.393449i) q^{6} +(1.46067 - 1.46067i) q^{7} -0.917007i q^{8} +2.73289i q^{9} +(-0.339444 + 0.339444i) q^{11} +(-3.29468 - 3.29468i) q^{12} +4.07073 q^{13} +(-0.339444 - 0.339444i) q^{14} +3.67889 q^{16} +(-1.69306 - 3.75946i) q^{17} +0.635095 q^{18} -4.00000i q^{19} -4.94600 q^{21} +(0.0788831 + 0.0788831i) q^{22} +(-5.76379 + 5.76379i) q^{23} +(-1.55255 + 1.55255i) q^{24} -0.945995i q^{26} +(-0.452229 + 0.452229i) q^{27} +(2.84245 - 2.84245i) q^{28} +(-0.732893 - 0.732893i) q^{29} +(-4.28544 - 4.28544i) q^{31} -2.68895i q^{32} +1.14940 q^{33} +(-0.873659 + 0.393449i) q^{34} +5.31820i q^{36} +(0.917007 + 0.917007i) q^{37} -0.929557 q^{38} +(-6.89199 - 6.89199i) q^{39} +(7.62488 - 7.62488i) q^{41} +1.14940i q^{42} -7.45685i q^{43} +(-0.660556 + 0.660556i) q^{44} +(1.33944 + 1.33944i) q^{46} +3.60596 q^{47} +(-6.22857 - 6.22857i) q^{48} +2.73289i q^{49} +(-3.49854 + 9.23143i) q^{51} +7.92163 q^{52} +6.14969i q^{53} +(0.105093 + 0.105093i) q^{54} +(-1.33944 - 1.33944i) q^{56} +(-6.77223 + 6.77223i) q^{57} +(-0.170316 + 0.170316i) q^{58} +6.00000i q^{59} +(-4.00000 + 4.00000i) q^{61} +(-0.995890 + 0.995890i) q^{62} +(3.99185 + 3.99185i) q^{63} +6.73289 q^{64} -0.267107i q^{66} -3.14118 q^{67} +(-3.29468 - 7.31589i) q^{68} +19.5169 q^{69} +(1.28544 + 1.28544i) q^{71} +2.50608 q^{72} +(8.60625 + 8.60625i) q^{73} +(0.213103 - 0.213103i) q^{74} -7.78398i q^{76} +0.991630i q^{77} +(-1.60162 + 1.60162i) q^{78} +(-7.23143 + 7.23143i) q^{79} +9.72998 q^{81} +(-1.77194 - 1.77194i) q^{82} +2.23672i q^{83} -9.62488 q^{84} -1.73289 q^{86} +2.48166i q^{87} +(0.311272 + 0.311272i) q^{88} +9.37220 q^{89} +(5.94600 - 5.94600i) q^{91} +(-11.2163 + 11.2163i) q^{92} +14.5110i q^{93} -0.837986i q^{94} +(-4.55255 + 4.55255i) q^{96} +(11.8220 + 11.8220i) q^{97} +0.635095 q^{98} +(-0.927664 - 0.927664i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} - 20 q^{6} + 16 q^{11} + 16 q^{14} + 4 q^{16} - 24 q^{21} + 32 q^{24} - 4 q^{29} + 4 q^{31} - 12 q^{39} + 16 q^{41} - 28 q^{44} - 4 q^{46} + 44 q^{51} - 100 q^{54} + 4 q^{56} - 48 q^{61}+ \cdots - 36 q^{99}+O(q^{100}) $ 12 * q - 12 * q^4 - 20 * q^6 + 16 * q^11 + 16 * q^14 + 4 * q^16 - 24 * q^21 + 32 * q^24 - 4 * q^29 + 4 * q^31 - 12 * q^39 + 16 * q^41 - 28 * q^44 - 4 * q^46 + 44 * q^51 - 100 * q^54 + 4 * q^56 - 48 * q^61 + 76 * q^64 + 88 * q^69 - 40 * q^71 - 28 * q^74 + 4 * q^79 - 60 * q^81 - 40 * q^84 - 16 * q^86 + 16 * q^89 + 36 * q^91 - 4 * q^96 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$		−	0.232389i		−	0.164324i	−0.996619	−	0.0821620i	$-0.973817\pi$
$2$		−	0.232389i		−	0.164324i	0.996619	−	0.0821620i	$-0.0261825\pi$
$3$	−1.69306	−	1.69306i	−0.977488	−	0.977488i	0.0222645	−	0.999752i	$-0.492912\pi$
$3$	−1.69306	−	1.69306i	−0.977488	−	0.977488i	−0.999752	+	0.0222645i	$0.992912\pi$
$4$	1.94600			0.972998
$5$		0			0
$5$		0			0
$6$	−0.393449	+	0.393449i	−0.160625	+	0.160625i
$7$	1.46067	−	1.46067i	0.552081	−	0.552081i	−0.374960	−	0.927041i	$-0.622344\pi$
$7$	1.46067	−	1.46067i	0.552081	−	0.552081i	0.927041	+	0.374960i	$0.122344\pi$
$8$		−	0.917007i		−	0.324211i
$9$			2.73289i			0.910964i
$10$		0			0
$11$	−0.339444	+	0.339444i	−0.102346	+	0.102346i	−0.756426	−	0.654080i	$-0.773056\pi$
$11$	−0.339444	+	0.339444i	−0.102346	+	0.102346i	0.654080	+	0.756426i	$0.273056\pi$
$12$	−3.29468	−	3.29468i	−0.951093	−	0.951093i
$13$	4.07073			1.12902			0.564509	−	0.825427i	$-0.309065\pi$
$13$	4.07073			1.12902			0.564509	+	0.825427i	$0.309065\pi$
$14$	−0.339444	−	0.339444i	−0.0907202	−	0.0907202i
$15$		0			0
$16$	3.67889			0.919722
$17$	−1.69306	−	3.75946i	−0.410627	−	0.911803i
$17$	−1.69306	−	3.75946i	−0.410627	−	0.911803i
$18$	0.635095			0.149693
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$		0			0
$21$	−4.94600			−1.07930
$22$	0.0788831	+	0.0788831i	0.0168179	+	0.0168179i
$23$	−5.76379	+	5.76379i	−1.20183	+	1.20183i	−0.228226	+	0.973608i	$0.573292\pi$
$23$	−5.76379	+	5.76379i	−1.20183	+	1.20183i	−0.973608	+	0.228226i	$0.926708\pi$
$24$	−1.55255	+	1.55255i	−0.316912	+	0.316912i
$25$		0			0
$26$		−	0.945995i		−	0.185525i
$27$	−0.452229	+	0.452229i	−0.0870314	+	0.0870314i
$28$	2.84245	−	2.84245i	0.537173	−	0.537173i
$29$	−0.732893	−	0.732893i	−0.136095	−	0.136095i	0.635778	−	0.771872i	$-0.280680\pi$
$29$	−0.732893	−	0.732893i	−0.136095	−	0.136095i	−0.771872	+	0.635778i	$0.780680\pi$
$30$		0			0
$31$	−4.28544	−	4.28544i	−0.769688	−	0.769688i	0.208364	−	0.978051i	$-0.433186\pi$
$31$	−4.28544	−	4.28544i	−0.769688	−	0.769688i	−0.978051	+	0.208364i	$0.933186\pi$
$32$		−	2.68895i		−	0.475343i
$33$	1.14940			0.200084
$34$	−0.873659	+	0.393449i	−0.149831	+	0.0674759i
$35$		0			0
$36$			5.31820i			0.886366i
$37$	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	$0.716004\pi$
$38$	−0.929557			−0.150794
$39$	−6.89199	−	6.89199i	−1.10360	−	1.10360i
$40$		0			0
$41$	7.62488	−	7.62488i	1.19081	−	1.19081i	0.213965	−	0.976841i	$-0.431362\pi$
$41$	7.62488	−	7.62488i	1.19081	−	1.19081i	0.976841	−	0.213965i	$-0.0686380\pi$
$42$			1.14940i			0.177356i
$43$		−	7.45685i		−	1.13716i	−0.822628	−	0.568580i	$-0.807493\pi$
$43$		−	7.45685i		−	1.13716i	0.822628	−	0.568580i	$-0.192507\pi$
$44$	−0.660556	+	0.660556i	−0.0995826	+	0.0995826i
$45$		0			0
$46$	1.33944	+	1.33944i	0.197490	+	0.197490i
$47$	3.60596			0.525983			0.262991	−	0.964798i	$-0.415291\pi$
$47$	3.60596			0.525983			0.262991	+	0.964798i	$0.415291\pi$
$48$	−6.22857	−	6.22857i	−0.899017	−	0.899017i
$49$			2.73289i			0.390413i
$50$		0			0
$51$	−3.49854	+	9.23143i	−0.489894	+	1.29266i
$52$	7.92163			1.09853
$53$			6.14969i			0.844725i	0.906427	+	0.422362i	$0.138799\pi$
$53$			6.14969i			0.844725i	−0.906427	+	0.422362i	$0.861201\pi$
$54$	0.105093	+	0.105093i	0.0143014	+	0.0143014i
$55$		0			0
$56$	−1.33944	−	1.33944i	−0.178991	−	0.178991i
$57$	−6.77223	+	6.77223i	−0.897004	+	0.897004i
$58$	−0.170316	+	0.170316i	−0.0223636	+	0.0223636i
$59$			6.00000i			0.781133i	0.920575	+	0.390567i	$0.127721\pi$
$59$			6.00000i			0.781133i	−0.920575	+	0.390567i	$0.872279\pi$
$60$		0			0
$61$	−4.00000	+	4.00000i	−0.512148	+	0.512148i	−0.915184	−	0.403036i	$-0.867955\pi$
$61$	−4.00000	+	4.00000i	−0.512148	+	0.512148i	0.403036	+	0.915184i	$0.367955\pi$
$62$	−0.995890	+	0.995890i	−0.126478	+	0.126478i
$63$	3.99185	+	3.99185i	0.502926	+	0.502926i
$64$	6.73289			0.841612
$65$		0			0
$66$		−	0.267107i		−	0.0328787i
$67$	−3.14118			−0.383756			−0.191878	−	0.981419i	$-0.561458\pi$
$67$	−3.14118			−0.383756			−0.191878	+	0.981419i	$0.561458\pi$
$68$	−3.29468	−	7.31589i	−0.399539	−	0.887183i
$69$	19.5169			2.34956
$70$		0			0
$71$	1.28544	+	1.28544i	0.152554	+	0.152554i	0.779257	−	0.626704i	$-0.215596\pi$
$71$	1.28544	+	1.28544i	0.152554	+	0.152554i	−0.626704	+	0.779257i	$0.715596\pi$
$72$	2.50608			0.295345
$73$	8.60625	+	8.60625i	1.00729	+	1.00729i	0.999973	+	0.00731179i	$0.00232744\pi$
$73$	8.60625	+	8.60625i	1.00729	+	1.00729i	0.00731179	+	0.999973i	$0.497673\pi$
$74$	0.213103	−	0.213103i	0.0247727	−	0.0247727i
$75$		0			0
$76$		−	7.78398i		−	0.892884i
$77$			0.991630i			0.113007i
$78$	−1.60162	+	1.60162i	−0.181348	+	0.181348i
$79$	−7.23143	+	7.23143i	−0.813600	+	0.813600i	−0.985172	−	0.171572i	$-0.945115\pi$
$79$	−7.23143	+	7.23143i	−0.813600	+	0.813600i	0.171572	+	0.985172i	$0.445115\pi$
$80$		0			0
$81$	9.72998			1.08111
$82$	−1.77194	−	1.77194i	−0.195678	−	0.195678i
$83$			2.23672i			0.245512i	0.992437	+	0.122756i	$0.0391732\pi$
$83$			2.23672i			0.245512i	−0.992437	+	0.122756i	$0.960827\pi$
$84$	−9.62488			−1.05016
$85$		0			0
$86$	−1.73289			−0.186863
$87$			2.48166i			0.266062i
$88$	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
$93$			14.5110i			1.50472i
$94$		−	0.837986i		−	0.0864316i
$95$		0			0
$96$	−4.55255	+	4.55255i	−0.464642	+	0.464642i
$97$	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	$0.427342\pi$
$98$	0.635095			0.0641543
$99$	−0.927664	−	0.927664i	−0.0932337	−	0.0932337i
$100$		0			0
$101$	−4.41178			−0.438989			−0.219494	−	0.975614i	$-0.570441\pi$
$101$	−4.41178			−0.438989			−0.219494	+	0.975614i	$0.570441\pi$
$102$	2.14529	+	0.813024i	0.212415	+	0.0805013i
$103$	17.4323			1.71766			0.858829	−	0.512262i	$-0.171192\pi$
$103$	17.4323			1.71766			0.858829	+	0.512262i	$0.171192\pi$
$104$		−	3.73289i		−	0.366040i
$105$		0			0
$106$	1.42912			0.138809
$107$	3.68484	+	3.68484i	0.356227	+	0.356227i	0.862420	−	0.506193i	$-0.168948\pi$
$107$	3.68484	+	3.68484i	0.356227	+	0.356227i	−0.506193	+	0.862420i	$0.668948\pi$
$108$	−0.880035	+	0.880035i	−0.0846814	+	0.0846814i
$109$	5.73289	−	5.73289i	0.549112	−	0.549112i	−0.377072	−	0.926184i	$-0.623069\pi$
$109$	5.73289	−	5.73289i	0.549112	−	0.549112i	0.926184	+	0.377072i	$0.123069\pi$
$110$		0			0
$111$		−	3.10509i		−	0.294722i
$112$	5.37364	−	5.37364i	0.507761	−	0.507761i
$113$	−2.45656	+	2.45656i	−0.231094	+	0.231094i	−0.813149	−	0.582055i	$-0.802249\pi$
$113$	−2.45656	+	2.45656i	−0.231094	+	0.231094i	0.582055	+	0.813149i	$0.302249\pi$
$114$	1.57379	+	1.57379i	0.147399	+	0.147399i
$115$		0			0
$116$	−1.42621	−	1.42621i	−0.132420	−	0.132420i
$117$			11.1249i			1.02850i
$118$	1.39434			0.128359
$119$	−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
$123$	−25.8187			−2.32800
$124$	−8.33944	−	8.33944i	−0.748904	−	0.748904i
$125$		0			0
$126$	0.927664	−	0.927664i	0.0826428	−	0.0826428i
$127$		−	2.98341i		−	0.264735i	−0.991201	−	0.132367i	$-0.957742\pi$
$127$		−	2.98341i		−	0.264735i	0.991201	−	0.132367i	$-0.0422579\pi$
$128$		−	6.94255i		−	0.613640i
$129$	−12.6249	+	12.6249i	−1.11156	+	1.11156i
$130$		0			0
$131$	5.08676	+	5.08676i	0.444432	+	0.444432i	0.893499	−	0.449066i	$-0.148243\pi$
$131$	5.08676	+	5.08676i	0.444432	+	0.444432i	−0.449066	+	0.893499i	$0.648243\pi$
$132$	2.23672			0.194681
$133$	−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
$137$	0.526852			0.0450120			0.0225060	−	0.999747i	$-0.492836\pi$
$137$	0.526852			0.0450120			0.0225060	+	0.999747i	$0.492836\pi$
$138$		−	4.53551i		−	0.386089i
$139$	−12.4985	−	12.4985i	−1.06011	−	1.06011i	−0.998074	−	0.0620387i	$-0.980240\pi$
$139$	−12.4985	−	12.4985i	−1.06011	−	1.06011i	−0.0620387	−	0.998074i	$-0.519760\pi$
$140$		0			0
$141$	−6.10509	−	6.10509i	−0.514142	−	0.514142i
$142$	0.298722	−	0.298722i	0.0250682	−	0.0250682i
$143$	−1.38179	+	1.38179i	−0.115551	+	0.115551i
$144$			10.0540i			0.837834i
$145$		0			0
$146$	2.00000	−	2.00000i	0.165521	−	0.165521i
$147$	4.62695	−	4.62695i	0.381624	−	0.381624i
$148$	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	$-0.901752\pi$
$151$		−	7.46579i		−	0.607557i	0.952743	−	0.303778i	$-0.0982483\pi$
$152$	−3.66803			−0.297516
$153$	10.2742	−	4.62695i	0.830620	−	0.374066i
$154$	0.230444			0.0185697
$155$		0			0
$156$	−13.4118	−	13.4118i	−1.07380	−	1.07380i
$157$	−12.4571			−0.994188			−0.497094	−	0.867697i	$-0.665600\pi$
$157$	−12.4571			−0.994188			−0.497094	+	0.867697i	$0.665600\pi$
$158$	1.68051	+	1.68051i	0.133694	+	0.133694i
$159$	10.4118	−	10.4118i	0.825708	−	0.825708i
$160$		0			0
$161$			16.8380i			1.32702i
$162$		−	2.26114i		−	0.177652i
$163$	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	0.399679	−	0.916655i	$-0.369122\pi$
$167$	−6.68080	−	6.68080i	−0.516976	−	0.516976i	−0.916655	+	0.399679i	$0.869122\pi$
$168$			4.53551i			0.349922i
$169$	3.57088			0.274683
$170$		0			0
$171$	10.9316			0.835958
$172$		−	14.5110i		−	1.10645i
$173$	−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	$0.966488\pi$
$174$	0.576711			0.0437204
$175$		0			0
$176$	−1.24878	+	1.24878i	−0.0941300	+	0.0941300i
$177$	10.1583	−	10.1583i	0.763548	−	0.763548i
$178$		−	2.17800i		−	0.163248i
$179$			19.5313i			1.45984i	0.683534	+	0.729919i	$0.260442\pi$
$179$			19.5313i			1.45984i	−0.683534	+	0.729919i	$0.739558\pi$
$180$		0			0
$181$	7.41178	−	7.41178i	0.550913	−	0.550913i	−0.375791	−	0.926704i	$-0.622629\pi$
$181$	7.41178	−	7.41178i	0.550913	−	0.550913i	0.926704	+	0.375791i	$0.122629\pi$
$182$	−1.38179	−	1.38179i	−0.102425	−	0.102425i
$183$	13.5445			1.00124
$184$	5.28544	+	5.28544i	0.389648	+	0.389648i
$185$		0			0
$186$	3.37220			0.247262
$187$	1.85082	+	0.701428i	0.135346	+	0.0512935i
$188$	7.01717			0.511780
$189$			1.32111i			0.0960968i
$190$		0			0
$191$	−5.32111			−0.385022			−0.192511	−	0.981295i	$-0.561663\pi$
$191$	−5.32111			−0.385022			−0.192511	+	0.981295i	$0.561663\pi$
$192$	−11.3992	−	11.3992i	−0.822665	−	0.822665i
$193$	−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	$0.256257\pi$
$198$	−0.215579	+	0.215579i	−0.0153205	+	0.0153205i
$199$	12.4445	+	12.4445i	0.882170	+	0.882170i	0.993755	−	0.111585i	$-0.0355927\pi$
$199$	12.4445	+	12.4445i	0.882170	+	0.882170i	−0.111585	+	0.993755i	$0.535593\pi$
$200$		0			0
$201$	5.31820	+	5.31820i	0.375117	+	0.375117i
$202$			1.02525i			0.0721364i
$203$	−2.14103			−0.150271
$204$	−6.80815	+	17.9643i	−0.476666	+	1.25775i
$205$		0			0
$206$		−	4.05109i		−	0.282253i
$207$	−15.7518	−	15.7518i	−1.09483	−	1.09483i
$208$	14.9758			1.03838
$209$	1.35778	+	1.35778i	0.0939193	+	0.0939193i
$210$		0			0
$211$	−9.07234	+	9.07234i	−0.624565	+	0.624565i	−0.946695	−	0.322130i	$-0.895601\pi$
$211$	−9.07234	+	9.07234i	−0.624565	+	0.624565i	0.322130	+	0.946695i	$0.395601\pi$
$212$			11.9673i			0.821915i
$213$		−	4.35265i		−	0.298238i
$214$	0.856317	−	0.856317i	0.0585366	−	0.0585366i
$215$		0			0
$216$	0.414697	+	0.414697i	0.0282165	+	0.0282165i
$217$	−12.5192			−0.849860
$218$	−1.33226	−	1.33226i	−0.0902322	−	0.0902322i
$219$		−	29.1418i		−	1.96922i
$220$		0			0
$221$	−6.89199	−	15.3038i	−0.463605	−	1.02944i
$222$	−0.721590			−0.0484300
$223$			4.07073i			0.272597i	0.990668	+	0.136298i	$0.0435206\pi$
$223$			4.07073i			0.272597i	−0.990668	+	0.136298i	$0.956479\pi$
$224$	−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	$0.0746281\pi$
$228$	−13.1787	+	13.1787i	−0.872783	+	0.872783i
$229$			14.9460i			0.987659i	0.869559	+	0.493830i	$0.164403\pi$
$229$			14.9460i			0.987659i	−0.869559	+	0.493830i	$0.835597\pi$
$230$		0			0
$231$	1.67889	−	1.67889i	0.110463	−	0.110463i
$232$	−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	$0.757584\pi$
$234$	2.58530			0.169007
$235$		0			0
$236$			11.6760i			0.760041i
$237$	24.4865			1.59057
$238$	−0.701428	+	1.85082i	−0.0454668	+	0.119971i
$239$	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	0.873435	−	0.486941i	$-0.161887\pi$
$241$	6.00000	+	6.00000i	0.386494	+	0.386494i	−0.486941	+	0.873435i	$0.661887\pi$
$242$	2.50273			0.160882
$243$	−15.1167	−	15.1167i	−0.969739	−	0.969739i
$244$	−7.78398	+	7.78398i	−0.498318	+	0.498318i
$245$		0			0
$246$			6.00000i			0.382546i
$247$		−	16.2829i		−	1.03606i
$248$	−3.92978	+	3.92978i	−0.249541	+	0.249541i
$249$	3.78690	−	3.78690i	0.239985	−	0.239985i
$250$		0			0
$251$	−6.03666			−0.381031			−0.190515	−	0.981684i	$-0.561016\pi$
$251$	−6.03666			−0.381031			−0.190515	+	0.981684i	$0.561016\pi$
$252$	7.76812	+	7.76812i	0.489346	+	0.489346i
$253$		−	3.91297i		−	0.246006i
$254$	−0.693313			−0.0435023
$255$		0			0
$256$	11.8524			0.740776
$257$			27.2752i			1.70138i	0.525670	+	0.850689i	$0.323815\pi$
$257$			27.2752i			1.70138i	−0.525670	+	0.850689i	$0.676185\pi$
$258$	2.93389	+	2.93389i	0.182656	+	0.182656i
$259$	2.67889			0.166458
$260$		0			0
$261$	2.00292	−	2.00292i	0.123977	−	0.123977i
$262$	1.18211	−	1.18211i	0.0730309	−	0.0730309i
$263$		−	12.3700i		−	0.762765i	−0.924417	−	0.381382i	$-0.875448\pi$
$263$		−	12.3700i		−	0.762765i	0.924417	−	0.381382i	$-0.124552\pi$
$264$		−	1.05400i		−	0.0648695i
$265$		0			0
$266$	−1.35778	+	1.35778i	−0.0832506	+	0.0832506i
$267$	−15.8677	−	15.8677i	−0.971086	−	0.971086i
$268$	−6.11272			−0.373394
$269$	−14.1958	−	14.1958i	−0.865531	−	0.865531i	0.126443	−	0.991974i	$-0.459644\pi$
$269$	−14.1958	−	14.1958i	−0.865531	−	0.865531i	−0.991974	+	0.126443i	$0.959644\pi$
$270$		0			0
$271$	−24.2102			−1.47066			−0.735332	−	0.677707i	$-0.762974\pi$
$271$	−24.2102			−1.47066			−0.735332	+	0.677707i	$0.762974\pi$
$272$	−6.22857	−	13.8306i	−0.377663	−	0.838606i
$273$	−20.1338			−1.21855
$274$		−	0.122435i		−	0.00739655i
$275$		0			0
$276$	37.9797			2.28611
$277$	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
$279$	11.7116	−	11.7116i	0.701158	−	0.701158i
$280$		0			0
$281$			18.0367i			1.07598i	0.842952	+	0.537989i	$0.180816\pi$
$281$			18.0367i			1.07598i	−0.842952	+	0.537989i	$0.819184\pi$
$282$	−1.41876	+	1.41876i	−0.0844858	+	0.0844858i
$283$	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
$287$		−	22.2749i		−	1.31484i
$288$	7.34861			0.433021
$289$	−11.2671	+	12.7300i	−0.662771	+	0.748822i
$290$		0			0
$291$		−	40.0308i		−	2.34665i
$292$	16.7477	+	16.7477i	0.980086	+	0.980086i
$293$	26.2584			1.53403			0.767017	−	0.641627i	$-0.221740\pi$
$293$	26.2584			1.53403			0.767017	+	0.641627i	$0.221740\pi$
$294$	−1.07525	−	1.07525i	−0.0627100	−	0.0627100i
$295$		0			0
$296$	0.840902	−	0.840902i	0.0488764	−	0.0488764i
$297$		−	0.307012i		−	0.0178147i
$298$			1.70135i			0.0985565i
$299$	−23.4629	+	23.4629i	−1.35689	+	1.35689i
$300$		0			0
$301$	−10.8920	−	10.8920i	−0.627804	−	0.627804i
$302$	−1.73497			−0.0998362
$303$	7.46940	+	7.46940i	0.429106	+	0.429106i
$304$		−	14.7156i		−	0.843995i
$305$		0			0
$306$	−1.07525	−	2.38762i	−0.0614681	−	0.136491i
$307$	−13.9136			−0.794088			−0.397044	−	0.917800i	$-0.629964\pi$
$307$	−13.9136			−0.794088			−0.397044	+	0.917800i	$0.629964\pi$
$308$			1.92971i			0.109955i
$309$	−29.5140	−	29.5140i	−1.67899	−	1.67899i
$310$		0			0
$311$	−6.18035	−	6.18035i	−0.350455	−	0.350455i	0.509824	−	0.860279i	$-0.329711\pi$
$311$	−6.18035	−	6.18035i	−0.350455	−	0.350455i	−0.860279	+	0.509824i	$0.829711\pi$
$312$	−6.32000	+	6.32000i	−0.357800	+	0.357800i
$313$	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	$0.212196\pi$
$318$	−2.41959	−	2.41959i	−0.135684	−	0.135684i
$319$	0.497552			0.0278575
$320$		0			0
$321$		−	12.4773i		−	0.696415i
$322$	3.91297			0.218061
$323$	−15.0378	+	6.77223i	−0.836728	+	0.376817i
$324$	18.9345			1.05192
$325$		0			0
$326$	−1.40787	−	1.40787i	−0.0779749	−	0.0779749i
$327$	−19.4122			−1.07350
$328$	−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	$0.122649\pi$
$331$			13.6760i			0.751699i	−0.926681	+	0.375850i	$0.877351\pi$
$332$			4.35265i			0.238883i
$333$	−2.50608	+	2.50608i	−0.137332	+	0.137332i
$334$	−1.55255	+	1.55255i	−0.0849516	+	0.0849516i
$335$		0			0
$336$	−18.1958			−0.992660
$337$	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	$0.693487\pi$
$338$		−	0.829834i		−	0.0451370i
$339$	8.31820			0.451782
$340$		0			0
$341$	2.90933			0.157549
$342$		−	2.54038i		−	0.137368i
$343$	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	$0.207101\pi$
$348$			4.82930i			0.258878i
$349$		−	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			0
$351$	−1.84090	+	1.84090i	−0.0982601	+	0.0982601i
$352$	0.912747	+	0.912747i	0.0486496	+	0.0486496i
$353$	−13.8600			−0.737693			−0.368847	−	0.929490i	$-0.620247\pi$
$353$	−13.8600			−0.737693			−0.368847	+	0.929490i	$0.620247\pi$
$354$	−2.36069	−	2.36069i	−0.125469	−	0.125469i
$355$		0			0
$356$	18.2383			0.966626
$357$	8.37386	+	18.5943i	0.443192	+	0.984114i
$358$	4.53887			0.239886
$359$			11.5024i			0.607076i	0.952819	+	0.303538i	$0.0981679\pi$
$359$			11.5024i			0.607076i	−0.952819	+	0.303538i	$0.901832\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	−1.72242	−	1.72242i	−0.0905283	−	0.0905283i
$363$	18.2335	−	18.2335i	0.957010	−	0.957010i
$364$	11.5709	−	11.5709i	0.606479	−	0.606479i
$365$		0			0
$366$		−	3.14759i		−	0.164527i
$367$	−13.7349	+	13.7349i	−0.716958	+	0.716958i	−0.967981	−	0.251023i	$-0.919233\pi$
$367$	−13.7349	+	13.7349i	−0.716958	+	0.716958i	0.251023	+	0.967981i	$0.419233\pi$
$368$	−21.2043	+	21.2043i	−1.10535	+	1.10535i
$369$	20.8380	+	20.8380i	1.08478	+	1.08478i
$370$		0			0
$371$	8.98266	+	8.98266i	0.466356	+	0.466356i
$372$			28.2383i			1.46409i
$373$	−5.58922			−0.289399			−0.144699	−	0.989476i	$-0.546221\pi$
$373$	−5.58922			−0.289399			−0.144699	+	0.989476i	$0.546221\pi$
$374$	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
$378$	0.307012			0.0157910
$379$	0.393449	+	0.393449i	0.0202101	+	0.0202101i	0.717140	−	0.696930i	$-0.245451\pi$
$379$	0.393449	+	0.393449i	0.0202101	+	0.0202101i	−0.696930	+	0.717140i	$0.745451\pi$
$380$		0			0
$381$	−5.05109	+	5.05109i	−0.258775	+	0.258775i
$382$			1.23657i			0.0632684i
$383$			24.8020i			1.26732i	0.773610	+	0.633662i	$0.218449\pi$
$383$			24.8020i			1.26732i	−0.773610	+	0.633662i	$0.781551\pi$
$384$	−11.7541	+	11.7541i	−0.599826	+	0.599826i
$385$		0			0
$386$	2.05109	+	2.05109i	0.104398	+	0.104398i
$387$	20.3788			1.03591
$388$	23.0056	+	23.0056i	1.16793	+	1.16793i
$389$			8.76664i			0.444486i	0.974991	+	0.222243i	$0.0713379\pi$
$389$			8.76664i			0.444486i	−0.974991	+	0.222243i	$0.928662\pi$
$390$		0			0
$391$	31.4272	+	11.9103i	1.58934	+	0.602331i
$392$	2.50608			0.126576
$393$		−	17.2244i		−	0.868854i
$394$	0.0906680	+	0.0906680i	0.00456779	+	0.00456779i
$395$		0			0
$396$	−1.80523	−	1.80523i	−0.0907162	−	0.0907162i
$397$	−4.97519	+	4.97519i	−0.249698	+	0.249698i	−0.820847	−	0.571149i	$-0.806498\pi$
$397$	−4.97519	+	4.97519i	−0.249698	+	0.249698i	0.571149	+	0.820847i	$0.306498\pi$
$398$	2.89198	−	2.89198i	0.144962	−	0.144962i
$399$			19.7840i			0.990438i
$400$		0			0
$401$	−7.51979	+	7.51979i	−0.375520	+	0.375520i	−0.869483	−	0.493963i	$-0.835548\pi$
$401$	−7.51979	+	7.51979i	−0.375520	+	0.375520i	0.493963	+	0.869483i	$0.335548\pi$
$402$	1.23589	−	1.23589i	0.0616407	−	0.0616407i
$403$	−17.4449	−	17.4449i	−0.868992	−	0.868992i
$404$	−8.58530			−0.427135
$405$		0			0
$406$			0.497552i			0.0246931i
$407$	−0.622545			−0.0308584
$408$	8.46529	+	3.20819i	0.419094	+	0.158829i
$409$	2.53421			0.125309			0.0626544	−	0.998035i	$-0.480043\pi$
$409$	2.53421			0.125309			0.0626544	+	0.998035i	$0.480043\pi$
$410$		0			0
$411$	−0.891990	−	0.891990i	−0.0439986	−	0.0439986i
$412$	33.9232			1.67128
$413$	8.76401	+	8.76401i	0.431249	+	0.431249i
$414$	−3.66056	+	3.66056i	−0.179907	+	0.179907i
$415$		0			0
$416$		−	10.9460i		−	0.536672i
$417$			42.3215i			2.07249i
$418$	0.315533	−	0.315533i	0.0154332	−	0.0154332i
$419$	18.6403	−	18.6403i	0.910638	−	0.910638i	−0.0856842	−	0.996322i	$-0.527308\pi$
$419$	18.6403	−	18.6403i	0.910638	−	0.910638i	0.996322	+	0.0856842i	$0.0273076\pi$
$420$		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
$423$			9.85469i			0.479151i
$424$	5.63931			0.273869
$425$		0			0
$426$	−1.01151			−0.0490078
$427$			11.6854i			0.565494i
$428$	7.17068	+	7.17068i	0.346608	+	0.346608i
$429$	4.67889			0.225899
$430$		0			0
$431$	−8.01833	+	8.01833i	−0.386229	+	0.386229i	−0.873340	−	0.487111i	$-0.838051\pi$
$431$	−8.01833	+	8.01833i	−0.386229	+	0.386229i	0.487111	+	0.873340i	$0.338051\pi$
$432$	−1.66370	+	1.66370i	−0.0800447	+	0.0800447i
$433$		−	6.24538i		−	0.300134i	−0.988676	−	0.150067i	$-0.952051\pi$
$433$		−	6.24538i		−	0.300134i	0.988676	−	0.150067i	$-0.0479489\pi$
$434$			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
$438$	−6.77223			−0.323590
$439$	7.44454	+	7.44454i	0.355308	+	0.355308i	0.862080	−	0.506772i	$-0.169161\pi$
$439$	7.44454	+	7.44454i	0.355308	+	0.355308i	−0.506772	+	0.862080i	$0.669161\pi$
$440$		0			0
$441$	−7.46870			−0.355652
$442$	−3.55643	+	1.60162i	−0.169162	+	0.0761815i
$443$	−29.2669			−1.39051			−0.695257	−	0.718761i	$-0.744709\pi$
$443$	−29.2669			−1.39051			−0.695257	+	0.718761i	$0.744709\pi$
$444$		−	6.04250i		−	0.286764i
$445$		0			0
$446$	0.945995			0.0447942
$447$	12.3951	+	12.3951i	0.586267	+	0.586267i
$448$	9.83453	−	9.83453i	0.464638	−	0.464638i
$449$	23.1418	−	23.1418i	1.09213	−	1.09213i	0.0968256	−	0.995301i	$-0.469131\pi$
$449$	23.1418	−	23.1418i	1.09213	−	1.09213i	0.995301	−	0.0968256i	$-0.0308689\pi$
$450$		0			0
$451$			5.17644i			0.243749i
$452$	−4.78045	+	4.78045i	−0.224854	+	0.224854i
$453$	−12.6400	+	12.6400i	−0.593879	+	0.593879i
$454$	−2.59213	−	2.59213i	−0.121655	−	0.121655i
$455$		0			0
$456$	6.21019	+	6.21019i	0.290819	+	0.290819i
$457$		−	31.4752i		−	1.47235i	−0.676792	−	0.736174i	$-0.736631\pi$
$457$		−	31.4752i		−	1.47235i	0.676792	−	0.736174i	$-0.263369\pi$
$458$	3.47329			0.162296
$459$	2.46579	+	0.934487i	0.115093	+	0.0436181i
$460$		0			0
$461$		−	26.6442i		−	1.24094i	−0.784228	−	0.620472i	$-0.786941\pi$
$461$		−	26.6442i		−	1.24094i	0.784228	−	0.620472i	$-0.213059\pi$
$462$	−0.390156	−	0.390156i	−0.0181517	−	0.0181517i
$463$	−14.2040			−0.660115			−0.330058	−	0.943961i	$-0.607068\pi$
$463$	−14.2040			−0.660115			−0.330058	+	0.943961i	$0.607068\pi$
$464$	−2.69623	−	2.69623i	−0.125169	−	0.125169i
$465$		0			0
$466$	−0.119518	+	0.119518i	−0.00553657	+	0.00553657i
$467$		−	29.1177i		−	1.34741i	−0.739002	−	0.673703i	$-0.764703\pi$
$467$		−	29.1177i		−	1.34741i	0.739002	−	0.673703i	$-0.235297\pi$
$468$			21.6490i			1.00072i
$469$	−4.58822	+	4.58822i	−0.211864	+	0.211864i
$470$		0			0
$471$	21.0907	+	21.0907i	0.971807	+	0.971807i
$472$	5.50204			0.253252
$473$	2.53118	+	2.53118i	0.116384	+	0.116384i
$474$		−	5.69040i		−	0.261369i
$475$		0			0
$476$	−15.4985	−	5.87366i	−0.710374	−	0.269219i
$477$	−16.8064			−0.769514
$478$		−	2.22485i		−	0.101762i
$479$	1.39053	+	1.39053i	0.0635350	+	0.0635350i	0.738160	−	0.674625i	$-0.235695\pi$
$479$	1.39053	+	1.39053i	0.0635350	+	0.0635350i	−0.674625	+	0.738160i	$0.735695\pi$
$480$		0			0
$481$	3.73289	+	3.73289i	0.170205	+	0.170205i
$482$	1.39434	−	1.39434i	0.0635103	−	0.0635103i
$483$	28.5077	−	28.5077i	1.29714	−	1.29714i
$484$			20.9575i			0.952614i
$485$		0			0
$486$	−3.51297	+	3.51297i	−0.159351	+	0.159351i
$487$	−3.41883	+	3.41883i	−0.154922	+	0.154922i	−0.780312	−	0.625390i	$-0.784940\pi$
$487$	−3.41883	+	3.41883i	−0.154922	+	0.154922i	0.625390	+	0.780312i	$0.284940\pi$
$488$	3.66803	+	3.66803i	0.166044	+	0.166044i
$489$	−20.5140			−0.927673
$490$		0			0
$491$		−	16.8949i		−	0.762456i	−0.924481	−	0.381228i	$-0.875501\pi$
$491$		−	16.8949i		−	0.762456i	0.924481	−	0.381228i	$-0.124499\pi$
$492$	−50.2431			−2.26514
$493$	−1.51445	+	3.99611i	−0.0682075	+	0.179976i
$494$	−3.78398			−0.170249
$495$		0			0
$496$	−15.7656	−	15.7656i	−0.707899	−	0.707899i
$497$	3.75520			0.168444
$498$	−0.880035	−	0.880035i	−0.0394353	−	0.0394353i
$499$	−3.07234	+	3.07234i	−0.137537	+	0.137537i	−0.772523	−	0.634987i	$-0.781006\pi$
$499$	−3.07234	+	3.07234i	−0.137537	+	0.137537i	0.634987	+	0.772523i	$0.281006\pi$
$500$		0			0
$501$			22.6220i			1.01067i
$502$			1.40286i			0.0626125i
$503$	8.13721	−	8.13721i	0.362820	−	0.362820i	−0.502030	−	0.864850i	$-0.667413\pi$
$503$	8.13721	−	8.13721i	0.362820	−	0.362820i	0.864850	+	0.502030i	$0.167413\pi$
$504$	3.66056	−	3.66056i	0.163054	−	0.163054i
$505$		0			0
$506$	−0.909332			−0.0404247
$507$	−6.04570	−	6.04570i	−0.268499	−	0.268499i
$508$		−	5.80570i		−	0.257586i
$509$	−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
$512$		−	16.6395i		−	0.735368i
$513$	1.80891	+	1.80891i	0.0798655	+	0.0798655i
$514$	6.33845			0.279577
$515$		0			0
$516$	−24.5680	+	24.5680i	−1.08154	+	1.08154i
$517$	−1.22402	+	1.22402i	−0.0538323	+	0.0538323i
$518$		−	0.622545i		−	0.0273531i
$519$			39.6105i			1.73871i
$520$		0			0
$521$	15.8746	−	15.8746i	0.695481	−	0.695481i	−0.267951	−	0.963432i	$-0.586347\pi$
$521$	15.8746	−	15.8746i	0.695481	−	0.695481i	0.963432	+	0.267951i	$0.0863467\pi$
$522$	−0.465456	−	0.465456i	−0.0203725	−	0.0203725i
$523$	−16.4943			−0.721243			−0.360622	−	0.932712i	$-0.617435\pi$
$523$	−16.4943			−0.721243			−0.360622	+	0.932712i	$0.617435\pi$
$524$	9.89881	+	9.89881i	0.432432	+	0.432432i
$525$		0			0
$526$	−2.87465			−0.125341
$527$	−8.85545	+	23.3664i	−0.385749	+	1.01786i
$528$	4.22850			0.184022
$529$		−	43.4426i		−	1.88881i
$530$		0			0
$531$	−16.3974			−0.711585
$532$	−11.3698	−	11.3698i	−0.492944	−	0.492944i
$533$	31.0389	−	31.0389i	1.34444	−	1.34444i
$534$	−3.68748	+	3.68748i	−0.159573	+	0.159573i
$535$		0			0
$536$			2.88048i			0.124418i
$537$	33.0676	−	33.0676i	1.42697	−	1.42697i
$538$	−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	0.486654	−	0.873595i	$-0.338217\pi$
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	−0.873595	+	0.486654i	$0.838217\pi$
$542$			5.62619i			0.241666i
$543$	−25.0972			−1.07702
$544$	−10.1090	+	4.55255i	−0.433420	+	0.195189i
$545$		0			0
$546$			4.67889i			0.200238i
$547$	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	$0.663851\pi$
$548$	1.02525			0.0437965
$549$	−10.9316	−	10.9316i	−0.466548	−	0.466548i
$550$		0			0
$551$	−2.93157	+	2.93157i	−0.124889	+	0.124889i
$552$		−	17.8971i		−	0.761752i
$553$			21.1255i			0.898346i
$554$	1.11093	−	1.11093i	0.0471987	−	0.0471987i
$555$		0			0
$556$	−24.3221	−	24.3221i	−1.03149	−	1.03149i
$557$	−38.9354			−1.64975			−0.824873	−	0.565318i	$-0.808753\pi$
$557$	−38.9354			−1.64975			−0.824873	+	0.565318i	$0.808753\pi$
$558$	−2.72166	−	2.72166i	−0.115217	−	0.115217i
$559$		−	30.3549i		−	1.28387i
$560$		0			0
$561$	−1.94600	−	4.32111i	−0.0821600	−	0.182438i
$562$	4.19153			0.176809
$563$		−	8.17844i		−	0.344680i	−0.985038	−	0.172340i	$-0.944867\pi$
$563$		−	8.17844i		−	0.344680i	0.985038	−	0.172340i	$-0.0551328\pi$
$564$	−11.8805	−	11.8805i	−0.500259	−	0.500259i
$565$		0			0
$566$	−4.14368	−	4.14368i	−0.174172	−	0.174172i
$567$	14.2123	−	14.2123i	0.596859	−	0.596859i
$568$	1.17876	−	1.17876i	0.0494595	−	0.0494595i
$569$		−	11.8920i		−	0.498538i	−0.968434	−	0.249269i	$-0.919810\pi$
$569$		−	11.8920i		−	0.498538i	0.968434	−	0.249269i	$-0.0801904\pi$
$570$		0			0
$571$	−2.80523	+	2.80523i	−0.117395	+	0.117395i	−0.763364	−	0.645969i	$-0.776454\pi$
$571$	−2.80523	+	2.80523i	−0.117395	+	0.117395i	0.645969	+	0.763364i	$0.276454\pi$
$572$	−2.68895	+	2.68895i	−0.112431	+	0.112431i
$573$	9.00895	+	9.00895i	0.376354	+	0.376354i
$574$	−5.17644			−0.216060
$575$		0			0
$576$			18.4003i			0.766678i
$577$	6.58601			0.274179			0.137090	−	0.990559i	$-0.456225\pi$
$577$	6.58601			0.274179			0.137090	+	0.990559i	$0.456225\pi$
$578$	2.95831	+	2.61836i	0.123049	+	0.108909i
$579$	29.8862			1.24203
$580$		0			0
$581$	3.26711	+	3.26711i	0.135542	+	0.135542i
$582$	−9.30274			−0.385611
$583$	−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
$587$		−	22.3369i		−	0.921944i	−0.887415	−	0.460972i	$-0.847501\pi$
$587$		−	22.3369i		−	0.921944i	0.887415	−	0.460972i	$-0.152499\pi$
$588$	9.00402	−	9.00402i	0.371319	−	0.371319i
$589$	−17.1418	+	17.1418i	−0.706314	+	0.706314i
$590$		0			0
$591$	1.32111			0.0543433
$592$	3.37357	+	3.37357i	0.138653	+	0.138653i
$593$		−	30.1344i		−	1.23747i	−0.785599	−	0.618736i	$-0.787645\pi$
$593$		−	30.1344i		−	1.23747i	0.785599	−	0.618736i	$-0.212355\pi$
$594$	−0.0713464			−0.00292738
$595$		0			0
$596$	−14.2468			−0.583574
$597$		−	42.1387i		−	1.72462i
$598$	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	−0.265017	−	0.964244i	$-0.585378\pi$
$601$	17.1418	−	17.1418i	0.699227	−	0.699227i	0.964244	+	0.265017i	$0.0853776\pi$
$602$	−2.53118	+	2.53118i	−0.103163	+	0.103163i
$603$		−	8.58450i		−	0.349588i
$604$		−	14.5284i		−	0.591151i
$605$		0			0
$606$	1.73581	−	1.73581i	0.0705124	−	0.0705124i
$607$	−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	$0.847863\pi$
$608$	−10.7558			−0.436205
$609$	3.62488	+	3.62488i	0.146888	+	0.146888i
$610$		0			0
$611$	14.6789			0.593844
$612$	19.9936	−	9.00402i	0.808192	−	0.363966i
$613$	−31.3459			−1.26605			−0.633024	−	0.774132i	$-0.718187\pi$
$613$	−31.3459			−1.26605			−0.633024	+	0.774132i	$0.718187\pi$
$614$			3.23336i			0.130488i
$615$		0			0
$616$	0.909332			0.0366380
$617$	10.9050	+	10.9050i	0.439020	+	0.439020i	0.891682	−	0.452662i	$-0.149526\pi$
$617$	10.9050	+	10.9050i	0.439020	+	0.439020i	−0.452662	+	0.891682i	$0.649526\pi$
$618$	−6.85873	+	6.85873i	−0.275899	+	0.275899i
$619$	−31.8930	+	31.8930i	−1.28189	+	1.28189i	−0.342294	+	0.939593i	$0.611204\pi$
$619$	−31.8930	+	31.8930i	−1.28189	+	1.28189i	−0.939593	+	0.342294i	$0.888796\pi$
$620$		0			0
$621$		−	5.21310i		−	0.209195i
$622$	−1.43625	+	1.43625i	−0.0575882	+	0.0575882i
$623$	13.6897	−	13.6897i	0.548466	−	0.548466i
$624$	−25.3549	−	25.3549i	−1.01501	−	1.01501i
$625$		0			0
$626$	−1.14176	−	1.14176i	−0.0456338	−	0.0456338i
$627$		−	4.59759i		−	0.183610i
$628$	−24.2415			−0.967343
$629$	1.89491	−	5.00000i	0.0755549	−	0.199363i
$630$		0			0
$631$			29.7493i			1.18430i	0.805827	+	0.592150i	$0.201721\pi$
$631$			29.7493i			1.18430i	−0.805827	+	0.592150i	$0.798279\pi$
$632$	6.63128	+	6.63128i	0.263778	+	0.263778i
$633$	30.7200			1.22101
$634$	−0.693313	−	0.693313i	−0.0275350	−	0.0275350i
$635$		0			0
$636$	20.2613	−	20.2613i	0.803412	−	0.803412i
$637$			11.1249i			0.440784i
$638$		−	0.115626i		−	0.00457767i
$639$	−3.51297	+	3.51297i	−0.138971	+	0.138971i
$640$		0			0
$641$	31.2131	+	31.2131i	1.23284	+	1.23284i	0.962867	+	0.269977i	$0.0870159\pi$
$641$	31.2131	+	31.2131i	1.23284	+	1.23284i	0.269977	+	0.962867i	$0.412984\pi$
$642$	−2.89959			−0.114438
$643$	−5.36109	−	5.36109i	−0.211421	−	0.211421i	0.593450	−	0.804871i	$-0.297765\pi$
$643$	−5.36109	−	5.36109i	−0.211421	−	0.211421i	−0.804871	+	0.593450i	$0.797765\pi$
$644$			32.7666i			1.29119i
$645$		0			0
$646$	1.57379	+	3.49464i	0.0619201	+	0.137495i
$647$	10.2540			0.403128			0.201564	−	0.979475i	$-0.435398\pi$
$647$	10.2540			0.403128			0.201564	+	0.979475i	$0.435398\pi$
$648$		−	8.92246i		−	0.350507i
$649$	−2.03666	−	2.03666i	−0.0799460	−	0.0799460i
$650$		0			0
$651$	21.1958	+	21.1958i	0.830727	+	0.830727i
$652$	11.7893	−	11.7893i	0.461706	−	0.461706i
$653$	−10.1207	+	10.1207i	−0.396054	+	0.396054i	−0.876839	−	0.480785i	$-0.840352\pi$
$653$	−10.1207	+	10.1207i	−0.396054	+	0.396054i	0.480785	+	0.876839i	$0.340352\pi$
$654$			4.51120i			0.176402i
$655$		0			0
$656$	28.0511	−	28.0511i	1.09521	−	1.09521i
$657$	−23.5199	+	23.5199i	−0.917601	+	0.917601i
$658$	−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	$-0.868065\pi$
$661$		−	20.7077i		−	0.805438i	0.915324	−	0.402719i	$-0.131935\pi$
$662$	3.17815			0.123522
$663$	−14.2416	+	37.5787i	−0.553099	+	1.45944i
$664$	2.05109			0.0795977
$665$		0			0
$666$	0.582387	+	0.582387i	0.0225670	+	0.0225670i
$667$	8.44848			0.327126
$668$	−13.0008	−	13.0008i	−0.503016	−	0.503016i
$669$	6.89199	−	6.89199i	0.266460	−	0.266460i
$670$		0			0
$671$		−	2.71555i		−	0.104833i
$672$			13.2995i			0.513040i
$673$	−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	0.730628	−	0.682776i	$-0.239227\pi$
$677$	1.24509	+	1.24509i	0.0478527	+	0.0478527i	−0.682776	+	0.730628i	$0.739227\pi$
$678$		−	1.93306i		−	0.0742387i
$679$	34.5362			1.32538
$680$		0			0
$681$	−37.7696			−1.44733
$682$		−	0.676098i		−	0.0258891i
$683$	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	$0.605213\pi$
$684$	21.2728			0.813385
$685$		0			0
$686$	3.30377	−	3.30377i	0.126139	−	0.126139i
$687$	25.3044	−	25.3044i	0.965425	−	0.965425i
$688$		−	27.4329i		−	1.04587i
$689$			25.0337i			0.953710i
$690$		0			0
$691$	−18.2314	+	18.2314i	−0.693556	+	0.693556i	−0.963013	−	0.269456i	$-0.913156\pi$
$691$	−18.2314	+	18.2314i	−0.693556	+	0.693556i	0.269456	+	0.963013i	$0.413156\pi$
$692$	−22.7641	−	22.7641i	−0.865360	−	0.865360i
$693$	−2.71002			−0.102945
$694$	−0.822571	−	0.822571i	−0.0312244	−	0.0312244i
$695$		0			0
$696$	2.27570			0.0862602
$697$	−41.5748	−	15.7561i	−1.57476	−	0.596804i
$698$	−2.14103			−0.0810391
$699$			1.74148i			0.0658690i
$700$		0			0
$701$	−25.1195			−0.948751			−0.474376	−	0.880323i	$-0.657326\pi$
$701$	−25.1195			−0.948751			−0.474376	+	0.880323i	$0.657326\pi$
$702$	0.427806	+	0.427806i	0.0161465	+	0.0161465i
$703$	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
$708$	19.7681	−	19.7681i	0.742931	−	0.742931i
$709$	23.7156	+	23.7156i	0.890656	+	0.890656i	0.994585	−	0.103929i	$-0.0331413\pi$
$709$	23.7156	+	23.7156i	0.890656	+	0.890656i	−0.103929	+	0.994585i	$0.533141\pi$
$710$		0			0
$711$	−19.7627	−	19.7627i	−0.741160	−	0.741160i
$712$		−	8.59437i		−	0.322088i
$713$	49.4008			1.85007
$714$	4.32111	−	1.94600i	0.161714	−	0.0728270i
$715$		0			0
$716$			38.0078i			1.42042i
$717$	−16.2090	−	16.2090i	−0.605336	−	0.605336i
$718$	2.67305			0.0997572
$719$	−29.4812	−	29.4812i	−1.09946	−	1.09946i	−0.994473	−	0.104990i	$-0.966519\pi$
$719$	−29.4812	−	29.4812i	−1.09946	−	1.09946i	−0.104990	−	0.994473i	$-0.533481\pi$
$720$		0			0
$721$	25.4629	−	25.4629i	0.948287	−	0.948287i
$722$		−	0.697168i		−	0.0259459i
$723$		−	20.3167i		−	0.755586i
$724$	14.4233	−	14.4233i	0.536037	−	0.536037i
$725$		0			0
$726$	−4.23727	−	4.23727i	−0.157260	−	0.157260i
$727$	−12.2458			−0.454172			−0.227086	−	0.973875i	$-0.572920\pi$
$727$	−12.2458			−0.454172			−0.227086	+	0.973875i	$0.572920\pi$
$728$	−5.45252	−	5.45252i	−0.202084	−	0.202084i
$729$			21.9971i			0.814707i
$730$		0			0
$731$	−28.0337	+	12.6249i	−1.03687	+	0.466948i
$732$	26.3575			0.974200
$733$			32.8393i			1.21295i	0.795104	+	0.606473i	$0.207416\pi$
$733$			32.8393i			1.21295i	−0.795104	+	0.606473i	$0.792584\pi$
$734$	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
$738$	4.84253	−	4.84253i	0.178256	−	0.178256i
$739$			6.00000i			0.220714i	0.993892	+	0.110357i	$0.0351994\pi$
$739$			6.00000i			0.220714i	−0.993892	+	0.110357i	$0.964801\pi$
$740$		0			0
$741$	−27.5680	+	27.5680i	−1.01273	+	1.01273i
$742$	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	$0.612212\pi$
$744$	13.3067			0.487847
$745$		0			0
$746$			1.29887i			0.0475552i
$747$	−6.11272			−0.223653
$748$	3.60170	+	1.36498i	0.131691	+	0.0499085i
$749$	10.7647			0.393332
$750$		0			0
$751$	−22.6799	−	22.6799i	−0.827600	−	0.827600i	0.159584	−	0.987184i	$-0.448985\pi$
$751$	−22.6799	−	22.6799i	−0.827600	−	0.827600i	−0.987184	+	0.159584i	$0.948985\pi$
$752$	13.2659			0.483758
$753$	10.2204	+	10.2204i	0.372453	+	0.372453i
$754$	−0.693313	+	0.693313i	−0.0252490	+	0.0252490i
$755$		0			0
$756$			2.57088i			0.0935019i
$757$		−	36.2220i		−	1.31651i	−0.752794	−	0.658256i	$-0.771294\pi$
$757$		−	36.2220i		−	1.31651i	0.752794	−	0.658256i	$-0.228706\pi$
$758$	0.0914333	−	0.0914333i	0.00332101	−	0.00332101i
$759$	−6.62488	+	6.62488i	−0.240468	+	0.240468i
$760$		0			0
$761$	24.4851			0.887584			0.443792	−	0.896130i	$-0.353633\pi$
$761$	24.4851			0.887584			0.443792	+	0.896130i	$0.353633\pi$
$762$	1.17382	+	1.17382i	0.0425230	+	0.0425230i
$763$		−	16.7477i		−	0.606308i
$764$	−10.3549			−0.374626
$765$		0			0
$766$	5.76372			0.208252
$767$			24.4244i			0.881914i
$768$	−20.0668	−	20.0668i	−0.724099	−	0.724099i
$769$	5.55937			0.200476			0.100238	−	0.994963i	$-0.468040\pi$
$769$	5.55937			0.200476			0.100238	+	0.994963i	$0.468040\pi$
$770$		0			0
$771$	46.1784	−	46.1784i	1.66308	−	1.66308i
$772$	−17.1755	+	17.1755i	−0.618161	+	0.618161i
$773$		−	36.5376i		−	1.31416i	−0.753819	−	0.657082i	$-0.771790\pi$
$773$		−	36.5376i		−	1.31416i	0.753819	−	0.657082i	$-0.228210\pi$
$774$		−	4.73581i		−	0.170225i
$775$		0			0
$776$	10.8409	−	10.8409i	0.389166	−	0.389166i
$777$	−4.53551	−	4.53551i	−0.162711	−	0.162711i
$778$	2.03727			0.0730398
$779$	−30.4995	−	30.4995i	−1.09276	−	1.09276i
$780$		0			0
$781$	−0.872669			−0.0312265
$782$	2.76783	−	7.30334i	0.0989775	−	0.261167i
$783$	0.662870			0.0236890
$784$			10.0540i			0.359072i
$785$		0			0
$786$	−4.00276			−0.142774
$787$	−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
$789$	−20.9431	+	20.9431i	−0.745593	+	0.745593i
$790$		0			0
$791$			7.17644i			0.255165i
$792$	−0.850674	+	0.850674i	−0.0302274	+	0.0302274i
$793$	−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
$797$			34.7907i			1.23235i	0.787609	+	0.616175i	$0.211319\pi$
$797$			34.7907i			1.23235i	−0.787609	+	0.616175i	$0.788681\pi$
$798$	4.59759			0.162753
$799$	−6.10509	−	13.5565i	−0.215983	−	0.479593i
$800$		0			0
$801$			25.6132i			0.904999i
$802$	1.74752	+	1.74752i	0.0617070	+	0.0617070i
$803$	−5.84268			−0.206184
$804$	10.3492	+	10.3492i	0.364988	+	0.364988i
$805$		0			0
$806$	−4.05400	+	4.05400i	−0.142796	+	0.142796i
$807$			48.0685i			1.69209i
$808$			4.04563i			0.142325i
$809$	13.3549	−	13.3549i	0.469532	−	0.469532i	−0.432231	−	0.901763i	$-0.642274\pi$
$809$	13.3549	−	13.3549i	0.469532	−	0.469532i	0.901763	+	0.432231i	$0.142274\pi$
$810$		0			0
$811$	−9.28544	−	9.28544i	−0.326056	−	0.326056i	0.525029	−	0.851085i	$-0.324055\pi$
$811$	−9.28544	−	9.28544i	−0.326056	−	0.326056i	−0.851085	+	0.525029i	$0.824055\pi$
$812$	−4.16643			−0.146213
$813$	40.9893	+	40.9893i	1.43756	+	1.43756i
$814$			0.144673i			0.00507078i
$815$		0			0
$816$	−12.8707	+	33.9614i	−0.450566	+	1.18889i
$817$	−29.8274			−1.04353
$818$		−	0.588924i		−	0.0205913i
$819$	16.2498	+	16.2498i	0.567813	+	0.567813i
$820$		0			0
$821$	−27.8206	−	27.8206i	−0.970947	−	0.970947i	0.0286425	−	0.999590i	$-0.490882\pi$
$821$	−27.8206	−	27.8206i	−0.970947	−	0.970947i	−0.999590	+	0.0286425i	$0.990882\pi$
$822$	−0.207289	+	0.207289i	−0.00723004	+	0.00723004i
$823$	−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	$0.0493071\pi$
$828$	−30.6530	−	30.6530i	−1.06526	−	1.06526i
$829$	8.18134			0.284150			0.142075	−	0.989856i	$-0.454623\pi$
$829$	8.18134			0.284150			0.142075	+	0.989856i	$0.454623\pi$
$830$		0			0
$831$		−	16.1872i		−	0.561527i
$832$	27.4078			0.950195
$833$	10.2742	−	4.62695i	0.355980	−	0.160314i
$834$	9.83507			0.340561
$835$		0			0
$836$	2.64222	+	2.64222i	0.0913832	+	0.0913832i
$837$	3.87600			0.133974
$838$	−4.33181	−	4.33181i	−0.149640	−	0.149640i
$839$	−15.5381	+	15.5381i	−0.536436	+	0.536436i	−0.922480	−	0.386045i	$-0.873841\pi$
$839$	−15.5381	+	15.5381i	−0.536436	+	0.536436i	0.386045	+	0.922480i	$0.373841\pi$
$840$		0			0
$841$		−	27.9257i		−	0.962956i
$842$			1.84589i			0.0636135i
$843$	30.5371	−	30.5371i	1.05175	−	1.05175i
$844$	−17.6547	+	17.6547i	−0.607701	+	0.607701i
$845$		0			0
$846$	2.29012			0.0787361
$847$	15.7308	+	15.7308i	0.540515	+	0.540515i
$848$			22.6240i			0.776912i
$849$	−60.3771			−2.07214
$850$		0			0
$851$	−10.5709			−0.362365
$852$		−	8.47023i		−	0.290185i
$853$	−26.1383	−	26.1383i	−0.894959	−	0.894959i	0.100026	−	0.994985i	$-0.468107\pi$
$853$	−26.1383	−	26.1383i	−0.894959	−	0.894959i	−0.994985	+	0.100026i	$0.968107\pi$
$854$	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	$0.332600\pi$
$858$		−	1.08732i		−	0.0371206i
$859$		−	40.2180i		−	1.37222i	−0.727498	−	0.686110i	$-0.759317\pi$
$859$		−	40.2180i		−	1.37222i	0.727498	−	0.686110i	$-0.240683\pi$
$860$		0			0
$861$	−37.7126	+	37.7126i	−1.28524	+	1.28524i
$862$	1.86337	+	1.86337i	0.0634668	+	0.0634668i
$863$	12.3865			0.421643			0.210822	−	0.977525i	$-0.432386\pi$
$863$	12.3865			0.421643			0.210822	+	0.977525i	$0.432386\pi$
$864$	1.21602	+	1.21602i	0.0413698	+	0.0413698i
$865$		0			0
$866$	−1.45136			−0.0493192
$867$	40.6285	−	2.47672i	1.37981	−	0.0841139i
$868$	−24.3623			−0.826911
$869$		−	4.90933i		−	0.166538i
$870$		0			0
$871$	−12.7869			−0.433267
$872$	−5.25710	−	5.25710i	−0.178028	−	0.178028i
$873$	−32.3084	+	32.3084i	−1.09347	+	1.09347i
$874$	5.35778	−	5.35778i	0.181229	−	0.181229i
$875$		0			0
$876$		−	56.7097i		−	1.91604i
$877$	−31.9433	+	31.9433i	−1.07865	+	1.07865i	−0.0820188	+	0.996631i	$0.526137\pi$
$877$	−31.9433	+	31.9433i	−1.07865	+	1.07865i	−0.996631	+	0.0820188i	$0.973863\pi$
$878$	1.73003	−	1.73003i	0.0583857	−	0.0583857i
$879$	−44.4570	−	44.4570i	−1.49950	−	1.49950i
$880$		0			0
$881$	−12.0367	−	12.0367i	−0.405525	−	0.405525i	0.474649	−	0.880175i	$-0.342575\pi$
$881$	−12.0367	−	12.0367i	−0.405525	−	0.405525i	−0.880175	+	0.474649i	$0.842575\pi$
$882$			1.73565i			0.0584423i
$883$	−13.3497			−0.449254			−0.224627	−	0.974445i	$-0.572116\pi$
$883$	−13.3497			−0.449254			−0.224627	+	0.974445i	$0.572116\pi$
$884$	−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	$0.0187799\pi$
$887$	31.4868	+	31.4868i	1.05722	+	1.05722i	0.0589646	+	0.998260i	$0.481220\pi$
$888$	−2.84739			−0.0955522
$889$	−4.35778	−	4.35778i	−0.146155	−	0.146155i
$890$		0			0
$891$	−3.30278	+	3.30278i	−0.110647	+	0.110647i
$892$			7.92163i			0.265236i
$893$		−	14.4238i		−	0.482675i
$894$	2.88048	−	2.88048i	0.0963377	−	0.0963377i
$895$		0			0
$896$	−10.1408	−	10.1408i	−0.338779	−	0.338779i
$897$	79.4480			2.65269
$898$	−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
$902$	1.20295			0.0400538
$903$			36.8815i			1.22734i
$904$	2.25268	+	2.25268i	0.0749231	+	0.0749231i
$905$		0			0
$906$	2.93740	+	2.93740i	0.0975887	+	0.0975887i
$907$	−23.2958	+	23.2958i	−0.773526	+	0.773526i	−0.978721	−	0.205195i	$-0.934217\pi$
$907$	−23.2958	+	23.2958i	−0.773526	+	0.773526i	0.205195	+	0.978721i	$0.434217\pi$
$908$	21.7061	−	21.7061i	0.720342	−	0.720342i
$909$		−	12.0569i		−	0.399903i
$910$		0			0
$911$	25.1630	−	25.1630i	0.833688	−	0.833688i	−0.154332	−	0.988019i	$-0.549322\pi$
$911$	25.1630	−	25.1630i	0.833688	−	0.833688i	0.988019	+	0.154332i	$0.0493224\pi$
$912$	−24.9143	+	24.9143i	−0.824994	+	0.824994i
$913$	−0.759241	−	0.759241i	−0.0251272	−	0.0251272i
$914$	−7.31450			−0.241942
$915$		0			0
$916$			29.0848i			0.960990i
$917$	14.8601			0.490725
$918$	0.217165	−	0.573022i	0.00716750	−	0.0189125i
$919$	−28.5997			−0.943418			−0.471709	−	0.881754i	$-0.656363\pi$
$919$	−28.5997			−0.943418			−0.471709	+	0.881754i	$0.656363\pi$
$920$		0			0
$921$	23.5565	+	23.5565i	0.776212	+	0.776212i
$922$	−6.19183			−0.203917
$923$	5.23268	+	5.23268i	0.172236	+	0.172236i
$924$	3.26711	−	3.26711i	0.107480	−	0.107480i
$925$		0			0
$926$			3.30085i			0.108473i
$927$			47.6407i			1.56473i
$928$	−1.97071	+	1.97071i	−0.0646917	+	0.0646917i
$929$	8.98266	−	8.98266i	0.294711	−	0.294711i	−0.544227	−	0.838938i	$-0.683177\pi$
$929$	8.98266	−	8.98266i	0.294711	−	0.294711i	0.838938	+	0.544227i	$0.183177\pi$
$930$		0			0
$931$	10.9316			0.358268
$932$	−1.00083	−	1.00083i	−0.0327832	−	0.0327832i
$933$			20.9274i			0.685131i
$934$	−6.76664			−0.221411
$935$		0			0
$936$	10.2016			0.333450
$937$			30.7655i			1.00506i	0.864558	+	0.502532i	$0.167598\pi$
$937$			30.7655i			1.00506i	−0.864558	+	0.502532i	$0.832402\pi$
$938$	1.06625	+	1.06625i	0.0348144	+	0.0348144i
$939$	−16.6364			−0.542908
$940$		0			0
$941$	−27.7522	+	27.7522i	−0.904696	+	0.904696i	−0.995838	−	0.0911416i	$-0.970948\pi$
$941$	−27.7522	+	27.7522i	−0.904696	+	0.904696i	0.0911416	+	0.995838i	$0.470948\pi$
$942$	4.90125	−	4.90125i	0.159691	−	0.159691i
$943$			87.8965i			2.86230i
$944$			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	0.746909	−	0.664926i	$-0.231537\pi$
$947$	2.52289	+	2.52289i	0.0819830	+	0.0819830i	−0.664926	+	0.746909i	$0.731537\pi$
$948$	47.6506			1.54762
$949$	35.0337	+	35.0337i	1.13724	+	1.13724i
$950$		0			0
$951$	−10.1022			−0.327586
$952$	−2.76783	+	7.30334i	−0.0897059	+	0.236703i
$953$	53.8491			1.74434			0.872172	−	0.489200i	$-0.162711\pi$
$953$	53.8491			1.74434			0.872172	+	0.489200i	$0.162711\pi$
$954$			3.90564i			0.126450i
$955$		0			0
$956$	18.6306			0.602555
$957$	−0.842384	−	0.842384i	−0.0272304	−	0.0272304i
$958$	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
$963$	−10.0703	+	10.0703i	−0.324510	+	0.324510i
$964$	11.6760	+	11.6760i	0.376058	+	0.376058i
$965$		0			0
$966$	−6.62488	−	6.62488i	−0.213152	−	0.213152i
$967$			14.6688i			0.471716i	0.971788	+	0.235858i	$0.0757900\pi$
$967$			14.6688i			0.471716i	−0.971788	+	0.235858i	$0.924210\pi$
$968$	9.87576			0.317419
$969$	36.9257	+	13.9942i	1.18623	+	0.449557i
$970$		0			0
$971$			14.2468i			0.457203i	0.973520	+	0.228602i	$0.0734153\pi$
$971$			14.2468i			0.457203i	−0.973520	+	0.228602i	$0.926585\pi$
$972$	−29.4171	−	29.4171i	−0.943553	−	0.943553i
$973$	−36.5125			−1.17054
$974$	0.794499	+	0.794499i	0.0254574	+	0.0254574i
$975$		0			0
$976$	−14.7156	+	14.7156i	−0.471033	+	0.471033i
$977$		−	20.9141i		−	0.669103i	−0.942378	−	0.334551i	$-0.891415\pi$
$977$		−	20.9141i		−	0.669103i	0.942378	−	0.334551i	$-0.108585\pi$
$978$			4.76722i			0.152439i
$979$	−3.18134	+	3.18134i	−0.101676	+	0.101676i
$980$		0			0
$981$	15.6674	+	15.6674i	0.500221	+	0.500221i
$982$	−3.92620			−0.125290
$983$	−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	$0.839501\pi$
$984$			23.6760i			0.754762i
$985$		0			0
$986$	0.928654	+	0.351942i	0.0295744	+	0.0112081i
$987$	−17.8350			−0.567696
$988$		−	31.6865i		−	1.00808i
$989$	42.9797	+	42.9797i	1.36668	+	1.36668i
$990$		0			0
$991$	3.73190	+	3.73190i	0.118548	+	0.118548i	0.763892	−	0.645344i	$-0.223286\pi$
$991$	3.73190	+	3.73190i	0.118548	+	0.118548i	−0.645344	+	0.763892i	$0.723286\pi$
$992$	−11.5233	+	11.5233i	−0.365866	+	0.365866i
$993$	23.1542	−	23.1542i	0.734777	−	0.734777i
$994$		−	0.872669i		−	0.0276794i
$995$		0			0
$996$	7.36928	−	7.36928i	0.233505	−	0.233505i
$997$	18.1295	−	18.1295i	0.574167	−	0.574167i	−0.359123	−	0.933290i	$-0.616924\pi$
$997$	18.1295	−	18.1295i	0.574167	−	0.574167i	0.933290	+	0.359123i	$0.116924\pi$
$998$	0.713978	+	0.713978i	0.0226006	+	0.0226006i
$999$	−0.829394			−0.0262409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.e.d.251.3		12
5.2	odd	4		85.2.j.c.64.4	yes	12
5.3	odd	4		85.2.j.c.64.3	yes	12
5.4	even	2	inner	425.2.e.d.251.4		12
15.2	even	4		765.2.t.e.64.3		12
15.8	even	4		765.2.t.e.64.4		12
17.2	even	8		7225.2.a.bp.1.7		12
17.4	even	4	inner	425.2.e.d.276.4		12
17.15	even	8		7225.2.a.bp.1.8		12
85.2	odd	8		1445.2.b.f.579.8		12
85.4	even	4	inner	425.2.e.d.276.3		12
85.19	even	8		7225.2.a.bp.1.6		12
85.32	odd	8		1445.2.b.f.579.7		12
85.38	odd	4		85.2.j.c.4.4	yes	12
85.49	even	8		7225.2.a.bp.1.5		12
85.53	odd	8		1445.2.b.f.579.5		12
85.72	odd	4		85.2.j.c.4.3	✓	12
85.83	odd	8		1445.2.b.f.579.6		12
255.38	even	4		765.2.t.e.514.3		12
255.242	even	4		765.2.t.e.514.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.j.c.4.3	✓	12	85.72	odd	4
85.2.j.c.4.4	yes	12	85.38	odd	4
85.2.j.c.64.3	yes	12	5.3	odd	4
85.2.j.c.64.4	yes	12	5.2	odd	4
425.2.e.d.251.3		12	1.1	even	1	trivial
425.2.e.d.251.4		12	5.4	even	2	inner
425.2.e.d.276.3		12	85.4	even	4	inner
425.2.e.d.276.4		12	17.4	even	4	inner
765.2.t.e.64.3		12	15.2	even	4
765.2.t.e.64.4		12	15.8	even	4
765.2.t.e.514.3		12	255.38	even	4
765.2.t.e.514.4		12	255.242	even	4
1445.2.b.f.579.5		12	85.53	odd	8
1445.2.b.f.579.6		12	85.83	odd	8
1445.2.b.f.579.7		12	85.32	odd	8
1445.2.b.f.579.8		12	85.2	odd	8
7225.2.a.bp.1.5		12	85.49	even	8
7225.2.a.bp.1.6		12	85.19	even	8
7225.2.a.bp.1.7		12	17.2	even	8
7225.2.a.bp.1.8		12	17.15	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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.232389i q^{2} +(-1.69306 - 1.69306i) q^{3} +1.94600 q^{4} +(-0.393449 + 0.393449i) q^{6} +(1.46067 - 1.46067i) q^{7} -0.917007i q^{8} +2.73289i q^{9} +(-0.339444 + 0.339444i) q^{11} +(-3.29468 - 3.29468i) q^{12} +4.07073 q^{13} +(-0.339444 - 0.339444i) q^{14} +3.67889 q^{16} +(-1.69306 - 3.75946i) q^{17} +0.635095 q^{18} -4.00000i q^{19} -4.94600 q^{21} +(0.0788831 + 0.0788831i) q^{22} +(-5.76379 + 5.76379i) q^{23} +(-1.55255 + 1.55255i) q^{24} -0.945995i q^{26} +(-0.452229 + 0.452229i) q^{27} +(2.84245 - 2.84245i) q^{28} +(-0.732893 - 0.732893i) q^{29} +(-4.28544 - 4.28544i) q^{31} -2.68895i q^{32} +1.14940 q^{33} +(-0.873659 + 0.393449i) q^{34} +5.31820i q^{36} +(0.917007 + 0.917007i) q^{37} -0.929557 q^{38} +(-6.89199 - 6.89199i) q^{39} +(7.62488 - 7.62488i) q^{41} +1.14940i q^{42} -7.45685i q^{43} +(-0.660556 + 0.660556i) q^{44} +(1.33944 + 1.33944i) q^{46} +3.60596 q^{47} +(-6.22857 - 6.22857i) q^{48} +2.73289i q^{49} +(-3.49854 + 9.23143i) q^{51} +7.92163 q^{52} +6.14969i q^{53} +(0.105093 + 0.105093i) q^{54} +(-1.33944 - 1.33944i) q^{56} +(-6.77223 + 6.77223i) q^{57} +(-0.170316 + 0.170316i) q^{58} +6.00000i q^{59} +(-4.00000 + 4.00000i) q^{61} +(-0.995890 + 0.995890i) q^{62} +(3.99185 + 3.99185i) q^{63} +6.73289 q^{64} -0.267107i q^{66} -3.14118 q^{67} +(-3.29468 - 7.31589i) q^{68} +19.5169 q^{69} +(1.28544 + 1.28544i) q^{71} +2.50608 q^{72} +(8.60625 + 8.60625i) q^{73} +(0.213103 - 0.213103i) q^{74} -7.78398i q^{76} +0.991630i q^{77} +(-1.60162 + 1.60162i) q^{78} +(-7.23143 + 7.23143i) q^{79} +9.72998 q^{81} +(-1.77194 - 1.77194i) q^{82} +2.23672i q^{83} -9.62488 q^{84} -1.73289 q^{86} +2.48166i q^{87} +(0.311272 + 0.311272i) q^{88} +9.37220 q^{89} +(5.94600 - 5.94600i) q^{91} +(-11.2163 + 11.2163i) q^{92} +14.5110i q^{93} -0.837986i q^{94} +(-4.55255 + 4.55255i) q^{96} +(11.8220 + 11.8220i) q^{97} +0.635095 q^{98} +(-0.927664 - 0.927664i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} - 20 q^{6} + 16 q^{11} + 16 q^{14} + 4 q^{16} - 24 q^{21} + 32 q^{24} - 4 q^{29} + 4 q^{31} - 12 q^{39} + 16 q^{41} - 28 q^{44} - 4 q^{46} + 44 q^{51} - 100 q^{54} + 4 q^{56} - 48 q^{61}+ \cdots - 36 q^{99}+O(q^{100}) \) 12 * q - 12 * q^4 - 20 * q^6 + 16 * q^11 + 16 * q^14 + 4 * q^16 - 24 * q^21 + 32 * q^24 - 4 * q^29 + 4 * q^31 - 12 * q^39 + 16 * q^41 - 28 * q^44 - 4 * q^46 + 44 * q^51 - 100 * q^54 + 4 * q^56 - 48 * q^61 + 76 * q^64 + 88 * q^69 - 40 * q^71 - 28 * q^74 + 4 * q^79 - 60 * q^81 - 40 * q^84 - 16 * q^86 + 16 * q^89 + 36 * q^91 - 4 * q^96 - 36 * q^99

Introduction

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