LMFDB - Embedded newform 525.3.f.b.449.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [525,3,Mod(449,525)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(525, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("525.449"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	525.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,56,0,-56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$14.3052138789$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			449.4
Character	$\chi$	$=$	525.449
Dual form			525.3.f.b.449.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.57278 q^{2} +(-0.176471 - 2.99481i) q^{3} +8.76473 q^{4} +(0.630492 + 10.6998i) q^{6} +2.64575i q^{7} -17.0233 q^{8} +(-8.93772 + 1.05699i) q^{9} +12.0685i q^{11} +(-1.54672 - 26.2487i) q^{12} -12.7142i q^{13} -9.45268i q^{14} +25.7616 q^{16} -22.2556 q^{17} +(31.9325 - 3.77640i) q^{18} +28.9289 q^{19} +(7.92351 - 0.466899i) q^{21} -43.1180i q^{22} +21.9101 q^{23} +(3.00412 + 50.9815i) q^{24} +45.4249i q^{26} +(4.74274 + 26.5802i) q^{27} +23.1893i q^{28} -11.4122i q^{29} -4.93977 q^{31} -23.9470 q^{32} +(36.1428 - 2.12974i) q^{33} +79.5144 q^{34} +(-78.3367 + 9.26426i) q^{36} +36.7045i q^{37} -103.356 q^{38} +(-38.0765 + 2.24369i) q^{39} -57.6874i q^{41} +(-28.3089 + 1.66812i) q^{42} +57.7493i q^{43} +105.777i q^{44} -78.2798 q^{46} +15.6773 q^{47} +(-4.54617 - 77.1508i) q^{48} -7.00000 q^{49} +(3.92747 + 66.6513i) q^{51} -111.436i q^{52} +91.2304 q^{53} +(-16.9447 - 94.9651i) q^{54} -45.0394i q^{56} +(-5.10511 - 86.6363i) q^{57} +40.7733i q^{58} -34.3101i q^{59} +71.1225 q^{61} +17.6487 q^{62} +(-2.79654 - 23.6470i) q^{63} -17.4888 q^{64} +(-129.130 + 7.60909i) q^{66} -20.1716i q^{67} -195.065 q^{68} +(-3.86649 - 65.6164i) q^{69} -69.7718i q^{71} +(152.150 - 17.9935i) q^{72} -96.8693i q^{73} -131.137i q^{74} +253.554 q^{76} -31.9302 q^{77} +(136.039 - 8.01619i) q^{78} +84.2348 q^{79} +(78.7655 - 18.8942i) q^{81} +206.104i q^{82} +20.4474 q^{83} +(69.4474 - 4.09224i) q^{84} -206.325i q^{86} +(-34.1774 + 2.01393i) q^{87} -205.446i q^{88} +1.65255i q^{89} +33.6386 q^{91} +192.036 q^{92} +(0.871726 + 14.7936i) q^{93} -56.0116 q^{94} +(4.22596 + 71.7167i) q^{96} -29.7125i q^{97} +25.0094 q^{98} +(-12.7563 - 107.865i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 56 q^{4} - 56 q^{6} - 44 q^{9} + 184 q^{16} + 32 q^{19} - 28 q^{21} - 256 q^{24} - 144 q^{31} + 352 q^{34} - 152 q^{36} - 180 q^{39} + 144 q^{46} - 224 q^{49} + 76 q^{51} - 416 q^{54} - 112 q^{61}+ \cdots + 332 q^{99}+O(q^{100}) $ 32 * q + 56 * q^4 - 56 * q^6 - 44 * q^9 + 184 * q^16 + 32 * q^19 - 28 * q^21 - 256 * q^24 - 144 * q^31 + 352 * q^34 - 152 * q^36 - 180 * q^39 + 144 * q^46 - 224 * q^49 + 76 * q^51 - 416 * q^54 - 112 * q^61 + 88 * q^64 - 520 * q^66 - 120 * q^69 + 288 * q^76 + 408 * q^79 + 916 * q^81 + 168 * q^84 - 56 * q^91 - 1968 * q^94 + 80 * q^96 + 332 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−3.57278			−1.78639			−0.893194	−	0.449671i	$-0.851541\pi$
$2$	−3.57278			−1.78639			−0.893194	+	0.449671i	$0.851541\pi$
$3$	−0.176471	−	2.99481i	−0.0588237	−	0.998268i
$3$	−0.176471	−	2.99481i	−0.0588237	−	0.998268i
$4$	8.76473			2.19118
$5$		0			0
$5$		0			0
$6$	0.630492	+	10.6998i	0.105082	+	1.78329i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	−17.0233			−2.12791
$9$	−8.93772	+	1.05699i	−0.993080	+	0.117444i
$10$		0			0
$11$			12.0685i			1.09714i	0.836106	+	0.548568i	$0.184827\pi$
$11$			12.0685i			1.09714i	−0.836106	+	0.548568i	$0.815173\pi$
$12$	−1.54672	−	26.2487i	−0.128893	−	2.18739i
$13$		−	12.7142i		−	0.978014i	−0.872280	−	0.489007i	$-0.837359\pi$
$13$		−	12.7142i		−	0.978014i	0.872280	−	0.489007i	$-0.162641\pi$
$14$		−	9.45268i		−	0.675191i
$15$		0			0
$16$	25.7616			1.61010
$17$	−22.2556			−1.30915			−0.654577	−	0.755995i	$-0.727153\pi$
$17$	−22.2556			−1.30915			−0.654577	+	0.755995i	$0.727153\pi$
$18$	31.9325	−	3.77640i	1.77403	−	0.209800i
$19$	28.9289			1.52257			0.761286	−	0.648417i	$-0.224568\pi$
$19$	28.9289			1.52257			0.761286	+	0.648417i	$0.224568\pi$
$20$		0			0
$21$	7.92351	−	0.466899i	0.377310	−	0.0222333i
$22$		−	43.1180i		−	1.95991i
$23$	21.9101			0.952612			0.476306	−	0.879280i	$-0.341975\pi$
$23$	21.9101			0.952612			0.476306	+	0.879280i	$0.341975\pi$
$24$	3.00412	+	50.9815i	0.125172	+	2.12423i
$25$		0			0
$26$			45.4249i			1.74711i
$27$	4.74274	+	26.5802i	0.175657	+	0.984451i
$28$			23.1893i			0.828189i
$29$		−	11.4122i		−	0.393525i	−0.980451	−	0.196763i	$-0.936957\pi$
$29$		−	11.4122i		−	0.393525i	0.980451	−	0.196763i	$-0.0630428\pi$
$30$		0			0
$31$	−4.93977			−0.159347			−0.0796737	−	0.996821i	$-0.525388\pi$
$31$	−4.93977			−0.159347			−0.0796737	+	0.996821i	$0.525388\pi$
$32$	−23.9470			−0.748345
$33$	36.1428	−	2.12974i	1.09524	−	0.0645376i
$34$	79.5144			2.33866
$35$		0			0
$36$	−78.3367	+	9.26426i	−2.17602	+	0.257340i
$37$			36.7045i			0.992014i	0.868319	+	0.496007i	$0.165201\pi$
$37$			36.7045i			0.992014i	−0.868319	+	0.496007i	$0.834799\pi$
$38$	−103.356			−2.71990
$39$	−38.0765	+	2.24369i	−0.976321	+	0.0575304i
$40$		0			0
$41$		−	57.6874i		−	1.40701i	−0.710691	−	0.703504i	$-0.751618\pi$
$41$		−	57.6874i		−	1.40701i	0.710691	−	0.703504i	$-0.248382\pi$
$42$	−28.3089	+	1.66812i	−0.674022	+	0.0397172i
$43$			57.7493i			1.34301i	0.741002	+	0.671503i	$0.234351\pi$
$43$			57.7493i			1.34301i	−0.741002	+	0.671503i	$0.765649\pi$
$44$			105.777i			2.40403i
$45$		0			0
$46$	−78.2798			−1.70173
$47$	15.6773			0.333561			0.166780	−	0.985994i	$-0.446663\pi$
$47$	15.6773			0.333561			0.166780	+	0.985994i	$0.446663\pi$
$48$	−4.54617	−	77.1508i	−0.0947119	−	1.60731i
$49$	−7.00000			−0.142857
$50$		0			0
$51$	3.92747	+	66.6513i	0.0770093	+	1.30689i
$52$		−	111.436i		−	2.14301i
$53$	91.2304			1.72133			0.860664	−	0.509173i	$-0.170049\pi$
$53$	91.2304			1.72133			0.860664	+	0.509173i	$0.170049\pi$
$54$	−16.9447	−	94.9651i	−0.313791	−	1.75861i
$55$		0			0
$56$		−	45.0394i		−	0.804276i
$57$	−5.10511	−	86.6363i	−0.0895633	−	1.51993i
$58$			40.7733i			0.702989i
$59$		−	34.3101i		−	0.581527i	−0.956795	−	0.290763i	$-0.906091\pi$
$59$		−	34.3101i		−	0.581527i	0.956795	−	0.290763i	$-0.0939093\pi$
$60$		0			0
$61$	71.1225			1.16594			0.582971	−	0.812493i	$-0.301890\pi$
$61$	71.1225			1.16594			0.582971	+	0.812493i	$0.301890\pi$
$62$	17.6487			0.284656
$63$	−2.79654	−	23.6470i	−0.0443895	−	0.375349i
$64$	−17.4888			−0.273263
$65$		0			0
$66$	−129.130	+	7.60909i	−1.95652	+	0.115289i
$67$		−	20.1716i		−	0.301069i	−0.988605	−	0.150534i	$-0.951901\pi$
$67$		−	20.1716i		−	0.301069i	0.988605	−	0.150534i	$-0.0480994\pi$
$68$	−195.065			−2.86860
$69$	−3.86649	−	65.6164i	−0.0560362	−	0.950963i
$70$		0			0
$71$		−	69.7718i		−	0.982702i	−0.870962	−	0.491351i	$-0.836503\pi$
$71$		−	69.7718i		−	0.982702i	0.870962	−	0.491351i	$-0.163497\pi$
$72$	152.150	−	17.9935i	2.11319	−	0.249910i
$73$		−	96.8693i		−	1.32698i	−0.748186	−	0.663489i	$-0.769075\pi$
$73$		−	96.8693i		−	1.32698i	0.748186	−	0.663489i	$-0.230925\pi$
$74$		−	131.137i		−	1.77212i
$75$		0			0
$76$	253.554			3.33623
$77$	−31.9302			−0.414679
$78$	136.039	−	8.01619i	1.74409	−	0.102772i
$79$	84.2348			1.06626			0.533132	−	0.846032i	$-0.321015\pi$
$79$	84.2348			1.06626			0.533132	+	0.846032i	$0.321015\pi$
$80$		0			0
$81$	78.7655	−	18.8942i	0.972414	−	0.233262i
$82$			206.104i			2.51346i
$83$	20.4474			0.246354			0.123177	−	0.992385i	$-0.460692\pi$
$83$	20.4474			0.246354			0.123177	+	0.992385i	$0.460692\pi$
$84$	69.4474	−	4.09224i	0.826755	−	0.0487171i
$85$		0			0
$86$		−	206.325i		−	2.39913i
$87$	−34.1774	+	2.01393i	−0.392844	+	0.0231486i
$88$		−	205.446i		−	2.33461i
$89$			1.65255i			0.0185680i	0.999957	+	0.00928398i	$0.00295523\pi$
$89$			1.65255i			0.0185680i	−0.999957	+	0.00928398i	$0.997045\pi$
$90$		0			0
$91$	33.6386			0.369655
$92$	192.036			2.08735
$93$	0.871726	+	14.7936i	0.00937340	+	0.159071i
$94$	−56.0116			−0.595869
$95$		0			0
$96$	4.22596	+	71.7167i	0.0440204	+	0.747049i
$97$		−	29.7125i		−	0.306314i	−0.988202	−	0.153157i	$-0.951056\pi$
$97$		−	29.7125i		−	0.306314i	0.988202	−	0.153157i	$-0.0489440\pi$
$98$	25.0094			0.255198
$99$	−12.7563	−	107.865i	−0.128852	−	1.08954i
$100$		0			0
$101$		−	33.7684i		−	0.334341i	−0.985928	−	0.167170i	$-0.946537\pi$
$101$		−	33.7684i		−	0.334341i	0.985928	−	0.167170i	$-0.0534630\pi$
$102$	−14.0320	−	238.130i	−0.137569	−	2.33461i
$103$		−	120.360i		−	1.16855i	−0.811557	−	0.584274i	$-0.801379\pi$
$103$		−	120.360i		−	1.16855i	0.811557	−	0.584274i	$-0.198621\pi$
$104$			216.438i			2.08113i
$105$		0			0
$106$	−325.946			−3.07496
$107$	174.545			1.63126			0.815632	−	0.578570i	$-0.196389\pi$
$107$	174.545			1.63126			0.815632	+	0.578570i	$0.196389\pi$
$108$	41.5688	+	232.968i	0.384896	+	2.15711i
$109$	−25.2313			−0.231480			−0.115740	−	0.993280i	$-0.536924\pi$
$109$	−25.2313			−0.231480			−0.115740	+	0.993280i	$0.536924\pi$
$110$		0			0
$111$	109.923	−	6.47728i	0.990296	−	0.0583539i
$112$			68.1587i			0.608560i
$113$	−126.424			−1.11880			−0.559400	−	0.828898i	$-0.688969\pi$
$113$	−126.424			−1.11880			−0.559400	+	0.828898i	$0.688969\pi$
$114$	18.2394	+	309.532i	0.159995	+	2.71519i
$115$		0			0
$116$		−	100.025i		−	0.862285i
$117$	13.4388	+	113.636i	0.114862	+	0.971246i
$118$			122.582i			1.03883i
$119$		−	58.8829i		−	0.494814i
$120$		0			0
$121$	−24.6487			−0.203708
$122$	−254.105			−2.08283
$123$	−172.762	+	10.1801i	−1.40457	+	0.0827654i
$124$	−43.2957			−0.349159
$125$		0			0
$126$	9.99141	+	84.4853i	0.0792969	+	0.670519i
$127$			7.33093i			0.0577238i	0.999583	+	0.0288619i	$0.00918831\pi$
$127$			7.33093i			0.0577238i	−0.999583	+	0.0288619i	$0.990812\pi$
$128$	158.272			1.23650
$129$	172.948	−	10.1911i	1.34068	−	0.0790006i
$130$		0			0
$131$		−	96.8346i		−	0.739195i	−0.929192	−	0.369598i	$-0.879495\pi$
$131$		−	96.8346i		−	0.739195i	0.929192	−	0.369598i	$-0.120505\pi$
$132$	316.782	−	18.6666i	2.39986	−	0.141414i
$133$			76.5386i			0.575478i
$134$			72.0687i			0.537826i
$135$		0			0
$136$	378.865			2.78577
$137$	−228.866			−1.67055			−0.835277	−	0.549830i	$-0.814693\pi$
$137$	−228.866			−1.67055			−0.835277	+	0.549830i	$0.814693\pi$
$138$	13.8141	+	234.433i	0.100102	+	1.69879i
$139$	−162.799			−1.17121			−0.585606	−	0.810596i	$-0.699144\pi$
$139$	−162.799			−1.17121			−0.585606	+	0.810596i	$0.699144\pi$
$140$		0			0
$141$	−2.76660	−	46.9506i	−0.0196213	−	0.332983i
$142$			249.279i			1.75549i
$143$	153.441			1.07301
$144$	−230.249	+	27.2298i	−1.59895	+	0.189096i
$145$		0			0
$146$			346.092i			2.37050i
$147$	1.23530	+	20.9636i	0.00840338	+	0.142610i
$148$			321.705i			2.17368i
$149$		−	1.91716i		−	0.0128668i	−0.999979	−	0.00643341i	$-0.997952\pi$
$149$		−	1.91716i		−	0.0128668i	0.999979	−	0.00643341i	$-0.00204783\pi$
$150$		0			0
$151$	3.34803			0.0221724			0.0110862	−	0.999939i	$-0.496471\pi$
$151$	3.34803			0.0221724			0.0110862	+	0.999939i	$0.496471\pi$
$152$	−492.465			−3.23990
$153$	198.915	−	23.5240i	1.30009	−	0.153752i
$154$	114.080			0.740777
$155$		0			0
$156$	−333.730	+	19.6653i	−2.13930	+	0.126060i
$157$		−	3.98288i		−	0.0253687i	−0.999920	−	0.0126843i	$-0.995962\pi$
$157$		−	3.98288i		−	0.0253687i	0.999920	−	0.0126843i	$-0.00403766\pi$
$158$	−300.952			−1.90476
$159$	−16.0995	−	273.217i	−0.101255	−	1.71835i
$160$		0			0
$161$			57.9686i			0.360054i
$162$	−281.412	+	67.5048i	−1.73711	+	0.416696i
$163$		−	238.081i		−	1.46062i	−0.683116	−	0.730310i	$-0.739376\pi$
$163$		−	238.081i		−	1.46062i	0.683116	−	0.730310i	$-0.260624\pi$
$164$		−	505.614i		−	3.08301i
$165$		0			0
$166$	−73.0540			−0.440084
$167$	93.0174			0.556990			0.278495	−	0.960438i	$-0.410164\pi$
$167$	93.0174			0.556990			0.278495	+	0.960438i	$0.410164\pi$
$168$	−134.884	+	7.94816i	−0.802883	+	0.0473105i
$169$	7.34951			0.0434882
$170$		0			0
$171$	−258.558	+	30.5776i	−1.51203	+	0.178816i
$172$			506.157i			2.94277i
$173$	20.2396			0.116992			0.0584959	−	0.998288i	$-0.481370\pi$
$173$	20.2396			0.116992			0.0584959	+	0.998288i	$0.481370\pi$
$174$	122.108	−	7.19531i	0.701771	−	0.0413524i
$175$		0			0
$176$			310.903i			1.76650i
$177$	−102.752	+	6.05474i	−0.580520	+	0.0342076i
$178$		−	5.90419i		−	0.0331696i
$179$			115.119i			0.643122i	0.946889	+	0.321561i	$0.104207\pi$
$179$			115.119i			0.643122i	−0.946889	+	0.321561i	$0.895793\pi$
$180$		0			0
$181$	−35.1309			−0.194093			−0.0970467	−	0.995280i	$-0.530940\pi$
$181$	−35.1309			−0.194093			−0.0970467	+	0.995280i	$0.530940\pi$
$182$	−120.183			−0.660347
$183$	−12.5511	−	212.998i	−0.0685850	−	1.16392i
$184$	−372.982			−2.02708
$185$		0			0
$186$	−3.11448	−	52.8544i	−0.0167445	−	0.284163i
$187$		−	268.592i		−	1.43632i
$188$	137.408			0.730892
$189$	−70.3246	+	12.5481i	−0.372088	+	0.0663921i
$190$		0			0
$191$			128.664i			0.673631i	0.941571	+	0.336816i	$0.109350\pi$
$191$			128.664i			0.673631i	−0.941571	+	0.336816i	$0.890650\pi$
$192$	3.08627	+	52.3756i	0.0160743	+	0.272790i
$193$			149.261i			0.773373i	0.922211	+	0.386686i	$0.126380\pi$
$193$			149.261i			0.773373i	−0.922211	+	0.386686i	$0.873620\pi$
$194$			106.156i			0.547196i
$195$		0			0
$196$	−61.3531			−0.313026
$197$	304.740			1.54691			0.773453	−	0.633854i	$-0.218528\pi$
$197$	304.740			1.54691			0.773453	+	0.633854i	$0.218528\pi$
$198$	45.5755	+	385.377i	0.230179	+	1.94635i
$199$	98.5989			0.495472			0.247736	−	0.968828i	$-0.420313\pi$
$199$	98.5989			0.495472			0.247736	+	0.968828i	$0.420313\pi$
$200$		0			0
$201$	−60.4101	+	3.55971i	−0.300548	+	0.0177100i
$202$			120.647i			0.597263i
$203$	30.1939			0.148739
$204$	34.4233	+	584.180i	0.168741	+	2.86363i
$205$		0			0
$206$			430.021i			2.08748i
$207$	−195.826	+	23.1588i	−0.946020	+	0.111878i
$208$		−	327.537i		−	1.57470i
$209$			349.128i			1.67047i
$210$		0			0
$211$	255.428			1.21056			0.605280	−	0.796013i	$-0.293061\pi$
$211$	255.428			1.21056			0.605280	+	0.796013i	$0.293061\pi$
$212$	799.610			3.77175
$213$	−208.953	+	12.3127i	−0.981000	+	0.0578061i
$214$	−623.611			−2.91407
$215$		0			0
$216$	−80.7371	−	452.483i	−0.373783	−	2.09483i
$217$		−	13.0694i		−	0.0602276i
$218$	90.1459			0.413514
$219$	−290.105	+	17.0946i	−1.32468	+	0.0780577i
$220$		0			0
$221$			282.962i			1.28037i
$222$	−392.730	+	23.1419i	−1.76905	+	0.104243i
$223$		−	30.8285i		−	0.138244i	−0.997608	−	0.0691222i	$-0.977980\pi$
$223$		−	30.8285i		−	0.138244i	0.997608	−	0.0691222i	$-0.0220198\pi$
$224$		−	63.3579i		−	0.282848i
$225$		0			0
$226$	451.686			1.99861
$227$	−123.793			−0.545343			−0.272672	−	0.962107i	$-0.587907\pi$
$227$	−123.793			−0.545343			−0.272672	+	0.962107i	$0.587907\pi$
$228$	−44.7449	−	759.344i	−0.196249	−	3.33045i
$229$	38.8512			0.169656			0.0848279	−	0.996396i	$-0.472966\pi$
$229$	38.8512			0.169656			0.0848279	+	0.996396i	$0.472966\pi$
$230$		0			0
$231$	5.63476	+	95.6249i	0.0243929	+	0.413960i
$232$			194.274i			0.837388i
$233$	194.201			0.833479			0.416740	−	0.909026i	$-0.363173\pi$
$233$	194.201			0.833479			0.416740	+	0.909026i	$0.363173\pi$
$234$	−48.0138	−	405.995i	−0.205187	−	1.73502i
$235$		0			0
$236$		−	300.719i		−	1.27423i
$237$	−14.8650	−	252.267i	−0.0627215	−	1.06442i
$238$			210.375i			0.883930i
$239$			228.989i			0.958115i	0.877784	+	0.479057i	$0.159021\pi$
$239$			228.989i			0.958115i	−0.877784	+	0.479057i	$0.840979\pi$
$240$		0			0
$241$	407.123			1.68931			0.844654	−	0.535313i	$-0.179806\pi$
$241$	407.123			1.68931			0.844654	+	0.535313i	$0.179806\pi$
$242$	88.0642			0.363902
$243$	−70.4843	−	232.553i	−0.290059	−	0.957009i
$244$	623.369			2.55479
$245$		0			0
$246$	617.241	−	36.3714i	2.50911	−	0.147851i
$247$		−	367.807i		−	1.48910i
$248$	84.0912			0.339077
$249$	−3.60838	−	61.2360i	−0.0144915	−	0.245928i
$250$		0			0
$251$			164.458i			0.655211i	0.944815	+	0.327605i	$0.106242\pi$
$251$			164.458i			0.655211i	−0.944815	+	0.327605i	$0.893758\pi$
$252$	−24.5109	−	207.259i	−0.0972655	−	0.822458i
$253$			264.422i			1.04515i
$254$		−	26.1918i		−	0.103117i
$255$		0			0
$256$	−495.514			−1.93560
$257$	384.159			1.49478			0.747390	−	0.664385i	$-0.231307\pi$
$257$	384.159			1.49478			0.747390	+	0.664385i	$0.231307\pi$
$258$	−617.904	+	36.4104i	−2.39498	+	0.141126i
$259$	−97.1110			−0.374946
$260$		0			0
$261$	12.0626	+	101.999i	0.0462170	+	0.390802i
$262$			345.968i			1.32049i
$263$	198.192			0.753582			0.376791	−	0.926298i	$-0.377028\pi$
$263$	198.192			0.753582			0.376791	+	0.926298i	$0.377028\pi$
$264$	−615.270	+	36.2552i	−2.33057	+	0.137330i
$265$		0			0
$266$		−	273.455i		−	1.02803i
$267$	4.94906	−	0.291627i	0.0185358	−	0.00109224i
$268$		−	176.799i		−	0.659697i
$269$			14.3502i			0.0533465i	0.999644	+	0.0266732i	$0.00849136\pi$
$269$			14.3502i			0.0533465i	−0.999644	+	0.0266732i	$0.991509\pi$
$270$		0			0
$271$	−26.2455			−0.0968468			−0.0484234	−	0.998827i	$-0.515420\pi$
$271$	−26.2455			−0.0968468			−0.0484234	+	0.998827i	$0.515420\pi$
$272$	−573.340			−2.10787
$273$	−5.93623	−	100.741i	−0.0217444	−	0.369015i
$274$	817.686			2.98426
$275$		0			0
$276$	−33.8888	−	575.110i	−0.122785	−	2.08373i
$277$		−	21.2740i		−	0.0768014i	−0.999262	−	0.0384007i	$-0.987774\pi$
$277$		−	21.2740i		−	0.0768014i	0.999262	−	0.0384007i	$-0.0122263\pi$
$278$	581.643			2.09224
$279$	44.1503	−	5.22130i	0.158245	−	0.0187143i
$280$		0			0
$281$		−	322.063i		−	1.14613i	−0.819509	−	0.573066i	$-0.805754\pi$
$281$		−	322.063i		−	1.14613i	0.819509	−	0.573066i	$-0.194246\pi$
$282$	9.88443	+	167.744i	0.0350512	+	0.594837i
$283$		−	259.309i		−	0.916288i	−0.888878	−	0.458144i	$-0.848514\pi$
$283$		−	259.309i		−	0.916288i	0.888878	−	0.458144i	$-0.151486\pi$
$284$		−	611.531i		−	2.15328i
$285$		0			0
$286$	−548.211			−1.91682
$287$	152.626			0.531799
$288$	214.032	−	25.3119i	0.743166	−	0.0878884i
$289$	206.313			0.713886
$290$		0			0
$291$	−88.9830	+	5.24339i	−0.305784	+	0.0180185i
$292$		−	849.034i		−	2.90765i
$293$	301.196			1.02797			0.513986	−	0.857798i	$-0.328168\pi$
$293$	301.196			1.02797			0.513986	+	0.857798i	$0.328168\pi$
$294$	−4.41344	−	74.8984i	−0.0150117	−	0.254756i
$295$		0			0
$296$		−	624.832i		−	2.11092i
$297$	−320.783	+	57.2377i	−1.08008	+	0.192720i
$298$			6.84957i			0.0229851i
$299$		−	278.569i		−	0.931668i
$300$		0			0
$301$	−152.790			−0.507609
$302$	−11.9618			−0.0396084
$303$	−101.130	+	5.95915i	−0.333762	+	0.0196672i
$304$	745.252			2.45149
$305$		0			0
$306$	−710.677	+	84.0461i	−2.32247	+	0.274661i
$307$			262.697i			0.855690i	0.903852	+	0.427845i	$0.140727\pi$
$307$			262.697i			0.855690i	−0.903852	+	0.427845i	$0.859273\pi$
$308$	−279.860			−0.908636
$309$	−360.456	+	21.2401i	−1.16652	+	0.0687383i
$310$		0			0
$311$		−	248.536i		−	0.799151i	−0.916700	−	0.399575i	$-0.869158\pi$
$311$		−	248.536i		−	0.799151i	0.916700	−	0.399575i	$-0.130842\pi$
$312$	648.188	−	38.1950i	2.07753	−	0.122420i
$313$			426.733i			1.36336i	0.731648	+	0.681682i	$0.238751\pi$
$313$			426.733i			1.36336i	−0.731648	+	0.681682i	$0.761249\pi$
$314$			14.2299i			0.0453183i
$315$		0			0
$316$	738.295			2.33638
$317$	107.379			0.338735			0.169367	−	0.985553i	$-0.445828\pi$
$317$	107.379			0.338735			0.169367	+	0.985553i	$0.445828\pi$
$318$	57.5200	+	976.144i	0.180881	+	3.06964i
$319$	137.728			0.431751
$320$		0			0
$321$	−30.8022	−	522.729i	−0.0959570	−	1.62844i
$322$		−	207.109i		−	0.643195i
$323$	−643.830			−1.99328
$324$	690.359	−	165.603i	2.13074	−	0.511119i
$325$		0			0
$326$			850.610i			2.60923i
$327$	4.45260	+	75.5630i	0.0136165	+	0.231079i
$328$			982.030i			2.99399i
$329$			41.4784i			0.126074i
$330$		0			0
$331$	−451.938			−1.36537			−0.682687	−	0.730711i	$-0.739189\pi$
$331$	−451.938			−1.36537			−0.682687	+	0.730711i	$0.739189\pi$
$332$	179.216			0.539807
$333$	−38.7964	−	328.054i	−0.116506	−	0.985148i
$334$	−332.330			−0.995001
$335$		0			0
$336$	204.122	−	12.0280i	0.607506	−	0.0357977i
$337$			638.072i			1.89339i	0.322133	+	0.946695i	$0.395600\pi$
$337$			638.072i			1.89339i	−0.322133	+	0.946695i	$0.604400\pi$
$338$	−26.2582			−0.0776869
$339$	22.3103	+	378.617i	0.0658120	+	1.11686i
$340$		0			0
$341$		−	59.6156i		−	0.174826i
$342$	923.770	−	109.247i	2.70108	−	0.319435i
$343$		−	18.5203i		−	0.0539949i
$344$		−	983.084i		−	2.85780i
$345$		0			0
$346$	−72.3115			−0.208993
$347$	129.949			0.374493			0.187246	−	0.982313i	$-0.440044\pi$
$347$	129.949			0.374493			0.187246	+	0.982313i	$0.440044\pi$
$348$	−299.556	+	17.6515i	−0.860792	+	0.0507228i
$349$	15.1067			0.0432856			0.0216428	−	0.999766i	$-0.493110\pi$
$349$	15.1067			0.0432856			0.0216428	+	0.999766i	$0.493110\pi$
$350$		0			0
$351$	337.945	−	60.3000i	0.962807	−	0.171795i
$352$		−	289.005i		−	0.821036i
$353$	−688.966			−1.95174			−0.975872	−	0.218343i	$-0.929935\pi$
$353$	−688.966			−1.95174			−0.975872	+	0.218343i	$0.929935\pi$
$354$	367.110	−	21.6322i	1.03703	−	0.0611080i
$355$		0			0
$356$			14.4841i			0.0406858i
$357$	−176.343	+	10.3911i	−0.493957	+	0.0291068i
$358$		−	411.294i		−	1.14886i
$359$			596.806i			1.66241i	0.555965	+	0.831206i	$0.312349\pi$
$359$			596.806i			1.66241i	−0.555965	+	0.831206i	$0.687651\pi$
$360$		0			0
$361$	475.879			1.31822
$362$	125.515			0.346726
$363$	4.34978	+	73.8180i	0.0119829	+	0.203355i
$364$	294.833			0.809981
$365$		0			0
$366$	44.8421	+	760.994i	0.122519	+	2.07922i
$367$		−	653.268i		−	1.78002i	−0.455939	−	0.890011i	$-0.650696\pi$
$367$		−	653.268i		−	1.78002i	0.455939	−	0.890011i	$-0.349304\pi$
$368$	564.438			1.53380
$369$	60.9751	+	515.593i	0.165244	+	1.39727i
$370$		0			0
$371$			241.373i			0.650601i
$372$	7.64044	+	129.662i	0.0205388	+	0.348555i
$373$		−	106.838i		−	0.286430i	−0.989692	−	0.143215i	$-0.954256\pi$
$373$		−	106.838i		−	0.286430i	0.989692	−	0.143215i	$-0.0457441\pi$
$374$			959.619i			2.56583i
$375$		0			0
$376$	−266.880			−0.709788
$377$	−145.097			−0.384873
$378$	251.254	−	44.8316i	0.664693	−	0.118602i
$379$	152.839			0.403270			0.201635	−	0.979461i	$-0.435375\pi$
$379$	152.839			0.403270			0.201635	+	0.979461i	$0.435375\pi$
$380$		0			0
$381$	21.9547	−	1.29370i	0.0576239	−	0.00339553i
$382$		−	459.686i		−	1.20337i
$383$	201.860			0.527050			0.263525	−	0.964653i	$-0.415115\pi$
$383$	201.860			0.527050			0.263525	+	0.964653i	$0.415115\pi$
$384$	−27.9304	−	473.993i	−0.0727354	−	1.23436i
$385$		0			0
$386$		−	533.276i		−	1.38154i
$387$	−61.0406	−	516.147i	−0.157728	−	1.33371i
$388$		−	260.422i		−	0.671190i
$389$			414.977i			1.06678i	0.845870	+	0.533389i	$0.179082\pi$
$389$			414.977i			1.06678i	−0.845870	+	0.533389i	$0.820918\pi$
$390$		0			0
$391$	−487.623			−1.24712
$392$	119.163			0.303988
$393$	−290.001	+	17.0885i	−0.737915	+	0.0434822i
$394$	−1088.77			−2.76337
$395$		0			0
$396$	−111.806	−	945.406i	−0.282338	−	2.38739i
$397$			410.015i			1.03278i	0.856353	+	0.516391i	$0.172725\pi$
$397$			410.015i			1.03278i	−0.856353	+	0.516391i	$0.827275\pi$
$398$	−352.272			−0.885105
$399$	229.218	−	13.5068i	0.574481	−	0.0338517i
$400$		0			0
$401$			347.186i			0.865801i	0.901442	+	0.432901i	$0.142510\pi$
$401$			347.186i			0.865801i	−0.901442	+	0.432901i	$0.857490\pi$
$402$	215.832	−	12.7180i	0.536895	−	0.0316369i
$403$			62.8051i			0.155844i
$404$		−	295.971i		−	0.732602i
$405$		0			0
$406$	−107.876			−0.265705
$407$	−442.968			−1.08837
$408$	−66.8586	−	1134.63i	−0.163869	−	2.78094i
$409$	103.523			0.253112			0.126556	−	0.991959i	$-0.459608\pi$
$409$	103.523			0.253112			0.126556	+	0.991959i	$0.459608\pi$
$410$		0			0
$411$	40.3882	+	685.409i	0.0982681	+	1.66766i
$412$		−	1054.93i		−	2.56050i
$413$	90.7760			0.219797
$414$	699.643	−	82.7412i	1.68996	−	0.199858i
$415$		0			0
$416$			304.467i			0.731892i
$417$	28.7292	+	487.550i	0.0688951	+	1.16918i
$418$		−	1247.36i		−	2.98411i
$419$			85.1144i			0.203137i	0.994829	+	0.101569i	$0.0323861\pi$
$419$			85.1144i			0.203137i	−0.994829	+	0.101569i	$0.967614\pi$
$420$		0			0
$421$	−489.724			−1.16324			−0.581620	−	0.813461i	$-0.697581\pi$
$421$	−489.724			−1.16324			−0.581620	+	0.813461i	$0.697581\pi$
$422$	−912.588			−2.16253
$423$	−140.120	+	16.5708i	−0.331252	+	0.0391746i
$424$	−1553.04			−3.66284
$425$		0			0
$426$	746.542	−	43.9905i	1.75245	−	0.103264i
$427$			188.172i			0.440685i
$428$	1529.84			3.57440
$429$	−27.0779	−	459.526i	−0.0631187	−	1.07116i
$430$		0			0
$431$		−	577.191i		−	1.33919i	−0.742727	−	0.669595i	$-0.766468\pi$
$431$		−	577.191i		−	1.33919i	0.742727	−	0.669595i	$-0.233532\pi$
$432$	122.180	+	684.747i	0.282825	+	1.58506i
$433$			94.5352i			0.218326i	0.994024	+	0.109163i	$0.0348171\pi$
$433$			94.5352i			0.218326i	−0.994024	+	0.109163i	$0.965183\pi$
$434$			46.6940i			0.107590i
$435$		0			0
$436$	−221.146			−0.507215
$437$	633.834			1.45042
$438$	1036.48	−	61.0753i	2.36639	−	0.139441i
$439$	−159.446			−0.363202			−0.181601	−	0.983372i	$-0.558128\pi$
$439$	−159.446			−0.363202			−0.181601	+	0.983372i	$0.558128\pi$
$440$		0			0
$441$	62.5640	−	7.39895i	0.141869	−	0.0167777i
$442$		−	1010.96i		−	2.28724i
$443$	−129.501			−0.292326			−0.146163	−	0.989261i	$-0.546692\pi$
$443$	−129.501			−0.292326			−0.146163	+	0.989261i	$0.546692\pi$
$444$	963.444	−	56.7716i	2.16992	−	0.127864i
$445$		0			0
$446$			110.143i			0.246958i
$447$	−5.74151	+	0.338323i	−0.0128445	+	0.000756874i
$448$		−	46.2711i		−	0.103284i
$449$		−	306.203i		−	0.681967i	−0.940069	−	0.340984i	$-0.889240\pi$
$449$		−	306.203i		−	0.681967i	0.940069	−	0.340984i	$-0.110760\pi$
$450$		0			0
$451$	696.200			1.54368
$452$	−1108.08			−2.45150
$453$	−0.590830	−	10.0267i	−0.00130426	−	0.0221340i
$454$	442.284			0.974195
$455$		0			0
$456$	86.9058	+	1474.84i	0.190583	+	3.23429i
$457$			143.189i			0.313325i	0.987652	+	0.156662i	$0.0500735\pi$
$457$			143.189i			0.313325i	−0.987652	+	0.156662i	$0.949927\pi$
$458$	−138.807			−0.303071
$459$	−105.553	−	591.559i	−0.229962	−	1.28880i
$460$		0			0
$461$			743.362i			1.61250i	0.591575	+	0.806250i	$0.298506\pi$
$461$			743.362i			1.61250i	−0.591575	+	0.806250i	$0.701494\pi$
$462$	−20.1318	−	341.646i	−0.0435752	−	0.739494i
$463$		−	577.246i		−	1.24675i	−0.781923	−	0.623375i	$-0.785761\pi$
$463$		−	577.246i		−	1.24675i	0.781923	−	0.623375i	$-0.214239\pi$
$464$		−	293.997i		−	0.633614i
$465$		0			0
$466$	−693.835			−1.48892
$467$	338.396			0.724617			0.362308	−	0.932058i	$-0.381989\pi$
$467$	338.396			0.724617			0.362308	+	0.932058i	$0.381989\pi$
$468$	117.787	+	995.987i	0.251683	+	2.12818i
$469$	53.3691			0.113793
$470$		0			0
$471$	−11.9280	+	0.702863i	−0.0253247	+	0.00149228i
$472$			584.071i			1.23744i
$473$	−696.947			−1.47346
$474$	53.1093	+	901.293i	0.112045	+	1.90146i
$475$		0			0
$476$		−	516.092i		−	1.08423i
$477$	−815.392	+	96.4299i	−1.70942	+	0.202159i
$478$		−	818.128i		−	1.71156i
$479$			239.609i			0.500228i	0.968216	+	0.250114i	$0.0804681\pi$
$479$			239.609i			0.500228i	−0.968216	+	0.250114i	$0.919532\pi$
$480$		0			0
$481$	466.668			0.970203
$482$	−1454.56			−3.01776
$483$	173.605	−	10.2298i	0.359430	−	0.0211797i
$484$	−216.039			−0.446362
$485$		0			0
$486$	251.825	+	830.860i	0.518158	+	1.70959i
$487$			95.6658i			0.196439i	0.995165	+	0.0982195i	$0.0313147\pi$
$487$			95.6658i			0.196439i	−0.995165	+	0.0982195i	$0.968685\pi$
$488$	−1210.74			−2.48102
$489$	−713.007	+	42.0144i	−1.45809	+	0.0859191i
$490$		0			0
$491$		−	352.470i		−	0.717861i	−0.933364	−	0.358930i	$-0.883142\pi$
$491$		−	352.470i		−	0.717861i	0.933364	−	0.358930i	$-0.116858\pi$
$492$	−1514.22	+	89.2263i	−3.07767	+	0.181354i
$493$			253.986i			0.515185i
$494$			1314.09i			2.66010i
$495$		0			0
$496$	−127.256			−0.256565
$497$	184.599			0.371426
$498$	12.8919	+	218.783i	0.0258874	+	0.439322i
$499$	317.440			0.636152			0.318076	−	0.948065i	$-0.396963\pi$
$499$	317.440			0.636152			0.318076	+	0.948065i	$0.396963\pi$
$500$		0			0
$501$	−16.4149	−	278.569i	−0.0327642	−	0.556026i
$502$		−	587.571i		−	1.17046i
$503$	244.292			0.485670			0.242835	−	0.970068i	$-0.421923\pi$
$503$	244.292			0.485670			0.242835	+	0.970068i	$0.421923\pi$
$504$	47.6064	+	402.550i	0.0944571	+	0.798710i
$505$		0			0
$506$		−	944.720i		−	1.86704i
$507$	−1.29698	−	22.0104i	−0.00255814	−	0.0434129i
$508$			64.2536i			0.126483i
$509$			4.58079i			0.00899959i	0.999990	+	0.00449979i	$0.00143233\pi$
$509$			4.58079i			0.00899959i	−0.999990	+	0.00449979i	$0.998568\pi$
$510$		0			0
$511$	256.292			0.501550
$512$	1137.27			2.22124
$513$	137.202	+	768.935i	0.267450	+	1.49890i
$514$	−1372.51			−2.67026
$515$		0			0
$516$	1515.84	−	89.3220i	2.93768	−	0.173105i
$517$			189.202i			0.365961i
$518$	346.956			0.669799
$519$	−3.57170	−	60.6136i	−0.00688189	−	0.116789i
$520$		0			0
$521$			813.583i			1.56158i	0.624794	+	0.780789i	$0.285183\pi$
$521$			813.583i			1.56158i	−0.624794	+	0.780789i	$0.714817\pi$
$522$	−43.0971	−	364.421i	−0.0825616	−	0.698124i
$523$		−	6.71882i		−	0.0128467i	−0.999979	−	0.00642335i	$-0.997955\pi$
$523$		−	6.71882i		−	0.0128467i	0.999979	−	0.00642335i	$-0.00204463\pi$
$524$		−	848.729i		−	1.61971i
$525$		0			0
$526$	−708.096			−1.34619
$527$	109.938			0.208610
$528$	931.095	−	54.8654i	1.76344	−	0.103912i
$529$	−48.9484			−0.0925301
$530$		0			0
$531$	36.2655	+	306.654i	0.0682966	+	0.577502i
$532$			670.840i			1.26098i
$533$	−733.448			−1.37607
$534$	−17.6819	+	1.04192i	−0.0331122	+	0.00195116i
$535$		0			0
$536$			343.388i			0.640649i
$537$	344.758	−	20.3151i	0.642008	−	0.0378308i
$538$		−	51.2701i		−	0.0952975i
$539$		−	84.4795i		−	0.156734i
$540$		0			0
$541$	18.1305			0.0335129			0.0167565	−	0.999860i	$-0.494666\pi$
$541$	18.1305			0.0335129			0.0167565	+	0.999860i	$0.494666\pi$
$542$	93.7692			0.173006
$543$	6.19959	+	105.210i	0.0114173	+	0.193757i
$544$	532.957			0.979699
$545$		0			0
$546$	21.2088	+	359.925i	0.0388440	+	0.659203i
$547$		−	111.345i		−	0.203556i	−0.994807	−	0.101778i	$-0.967547\pi$
$547$		−	111.345i		−	0.203556i	0.994807	−	0.101778i	$-0.0324531\pi$
$548$	−2005.95			−3.66049
$549$	−635.673	+	75.1760i	−1.15787	+	0.136933i
$550$		0			0
$551$		−	330.143i		−	0.599170i
$552$	65.8205	+	1117.01i	0.119240	+	2.02357i
$553$			222.864i			0.403010i
$554$			76.0072i			0.137197i
$555$		0			0
$556$	−1426.89			−2.56634
$557$	−100.916			−0.181177			−0.0905885	−	0.995888i	$-0.528875\pi$
$557$	−100.916			−0.181177			−0.0905885	+	0.995888i	$0.528875\pi$
$558$	−157.739	+	18.6545i	−0.282686	+	0.0334311i
$559$	734.235			1.31348
$560$		0			0
$561$	−804.381	+	47.3987i	−1.43383	+	0.0844897i
$562$			1150.66i			2.04744i
$563$	942.043			1.67326			0.836628	−	0.547772i	$-0.184524\pi$
$563$	942.043			1.67326			0.836628	+	0.547772i	$0.184524\pi$
$564$	−24.2485	−	411.509i	−0.0429938	−	0.729626i
$565$		0			0
$566$			926.455i			1.63685i
$567$	49.9894	+	208.394i	0.0881647	+	0.367538i
$568$			1187.75i			2.09110i
$569$		−	1113.81i		−	1.95749i	−0.205086	−	0.978744i	$-0.565747\pi$
$569$		−	1113.81i		−	1.95749i	0.205086	−	0.978744i	$-0.434253\pi$
$570$		0			0
$571$	−489.370			−0.857041			−0.428520	−	0.903532i	$-0.640965\pi$
$571$	−489.370			−0.857041			−0.428520	+	0.903532i	$0.640965\pi$
$572$	1344.87			2.35117
$573$	385.322	−	22.7054i	0.672465	−	0.0396255i
$574$	−545.300			−0.950000
$575$		0			0
$576$	156.310	−	18.4856i	0.271372	−	0.0320930i
$577$		−	176.145i		−	0.305277i	−0.988282	−	0.152638i	$-0.951223\pi$
$577$		−	176.145i		−	0.305277i	0.988282	−	0.152638i	$-0.0487770\pi$
$578$	−737.111			−1.27528
$579$	447.008	−	26.3402i	0.772034	−	0.0454926i
$580$		0			0
$581$			54.0988i			0.0931132i
$582$	317.916	−	18.7335i	0.546248	−	0.0321881i
$583$			1101.01i			1.88853i
$584$			1649.04i			2.82369i
$585$		0			0
$586$	−1076.11			−1.83636
$587$	−120.248			−0.204852			−0.102426	−	0.994741i	$-0.532660\pi$
$587$	−120.248			−0.204852			−0.102426	+	0.994741i	$0.532660\pi$
$588$	10.8270	+	183.741i	0.0184133	+	0.312484i
$589$	−142.902			−0.242618
$590$		0			0
$591$	−53.7779	−	912.638i	−0.0909947	−	1.54423i
$592$			945.565i			1.59724i
$593$	808.407			1.36325			0.681625	−	0.731702i	$-0.261274\pi$
$593$	808.407			1.36325			0.681625	+	0.731702i	$0.261274\pi$
$594$	1146.09	−	204.498i	1.92944	−	0.344272i
$595$		0			0
$596$		−	16.8034i		−	0.0281936i
$597$	−17.3999	−	295.285i	−0.0291455	−	0.494614i
$598$			995.264i			1.66432i
$599$			679.382i			1.13419i	0.823651	+	0.567097i	$0.191934\pi$
$599$			679.382i			1.13419i	−0.823651	+	0.567097i	$0.808066\pi$
$600$		0			0
$601$	349.965			0.582305			0.291153	−	0.956677i	$-0.405961\pi$
$601$	349.965			0.582305			0.291153	+	0.956677i	$0.405961\pi$
$602$	545.885			0.906786
$603$	21.3213	+	180.288i	0.0353586	+	0.298985i
$604$	29.3446			0.0485837
$605$		0			0
$606$	361.314	−	21.2907i	0.596228	−	0.0351332i
$607$		−	463.847i		−	0.764163i	−0.924129	−	0.382082i	$-0.875207\pi$
$607$		−	463.847i		−	0.764163i	0.924129	−	0.382082i	$-0.124793\pi$
$608$	−692.761			−1.13941
$609$	−5.32835	−	90.4249i	−0.00874935	−	0.148481i
$610$		0			0
$611$		−	199.325i		−	0.326227i
$612$	1743.43	−	206.182i	2.84874	−	0.336898i
$613$		−	137.987i		−	0.225102i	−0.993646	−	0.112551i	$-0.964098\pi$
$613$		−	137.987i		−	0.225102i	0.993646	−	0.112551i	$-0.0359022\pi$
$614$		−	938.557i		−	1.52859i
$615$		0			0
$616$	543.559			0.882400
$617$	90.3121			0.146373			0.0731864	−	0.997318i	$-0.476683\pi$
$617$	90.3121			0.146373			0.0731864	+	0.997318i	$0.476683\pi$
$618$	1287.83	−	75.8862i	2.08387	−	0.122793i
$619$	558.874			0.902866			0.451433	−	0.892305i	$-0.350913\pi$
$619$	558.874			0.902866			0.451433	+	0.892305i	$0.350913\pi$
$620$		0			0
$621$	103.914	+	582.374i	0.167333	+	0.937800i
$622$			887.963i			1.42759i
$623$	−4.37223			−0.00701803
$624$	−980.910	+	57.8008i	−1.57197	+	0.0926295i
$625$		0			0
$626$		−	1524.62i		−	2.43550i
$627$	1045.57	−	61.6110i	1.66758	−	0.0982631i
$628$		−	34.9089i		−	0.0555874i
$629$		−	816.882i		−	1.29870i
$630$		0			0
$631$	−699.239			−1.10814			−0.554072	−	0.832469i	$-0.686927\pi$
$631$	−699.239			−1.10814			−0.554072	+	0.832469i	$0.686927\pi$
$632$	−1433.95			−2.26892
$633$	−45.0757	−	764.958i	−0.0712096	−	1.20846i
$634$	−383.641			−0.605112
$635$		0			0
$636$	−141.108	−	2394.68i	−0.221868	−	3.76521i
$637$			88.9993i			0.139716i
$638$	−492.073			−0.771274
$639$	73.7483	+	623.601i	0.115412	+	0.975901i
$640$		0			0
$641$		−	773.823i		−	1.20721i	−0.797283	−	0.603606i	$-0.793730\pi$
$641$		−	773.823i		−	1.20721i	0.797283	−	0.603606i	$-0.206270\pi$
$642$	110.049	+	1867.59i	0.171416	+	2.90903i
$643$			93.1342i			0.144843i	0.997374	+	0.0724216i	$0.0230727\pi$
$643$			93.1342i			0.144843i	−0.997374	+	0.0724216i	$0.976927\pi$
$644$			508.079i			0.788943i
$645$		0			0
$646$	2300.26			3.56077
$647$	−1130.06			−1.74662			−0.873311	−	0.487164i	$-0.838031\pi$
$647$	−1130.06			−1.74662			−0.873311	+	0.487164i	$0.838031\pi$
$648$	−1340.85	+	321.642i	−2.06921	+	0.496361i
$649$	414.071			0.638014
$650$		0			0
$651$	−39.1403	+	2.30637i	−0.0601234	+	0.00354281i
$652$		−	2086.72i		−	3.20049i
$653$	482.760			0.739296			0.369648	−	0.929172i	$-0.379478\pi$
$653$	482.760			0.739296			0.369648	+	0.929172i	$0.379478\pi$
$654$	−15.9082	−	269.970i	−0.0243244	−	0.412797i
$655$		0			0
$656$		−	1486.12i		−	2.26542i
$657$	102.390	+	865.791i	0.155845	+	1.31779i
$658$		−	148.193i		−	0.225217i
$659$		−	39.2039i		−	0.0594901i	−0.999558	−	0.0297450i	$-0.990530\pi$
$659$		−	39.2039i		−	0.0594901i	0.999558	−	0.0297450i	$-0.00946953\pi$
$660$		0			0
$661$	−638.260			−0.965598			−0.482799	−	0.875731i	$-0.660380\pi$
$661$	−638.260			−0.965598			−0.482799	+	0.875731i	$0.660380\pi$
$662$	1614.67			2.43909
$663$	847.417	−	49.9346i	1.27815	−	0.0753162i
$664$	−348.083			−0.524221
$665$		0			0
$666$	138.611	+	1172.06i	0.208124	+	1.75986i
$667$		−	250.043i		−	0.374877i
$668$	815.272			1.22047
$669$	−92.3253	+	5.44033i	−0.138005	+	0.00813204i
$670$		0			0
$671$			858.342i			1.27920i
$672$	−189.745	+	11.1808i	−0.282358	+	0.0166382i
$673$			233.289i			0.346641i	0.984866	+	0.173320i	$0.0554496\pi$
$673$			233.289i			0.346641i	−0.984866	+	0.173320i	$0.944550\pi$
$674$		−	2279.69i		−	3.38233i
$675$		0			0
$676$	64.4165			0.0952906
$677$	−550.920			−0.813766			−0.406883	−	0.913480i	$-0.633384\pi$
$677$	−550.920			−0.813766			−0.406883	+	0.913480i	$0.633384\pi$
$678$	−79.7096	−	1352.71i	−0.117566	−	1.99515i
$679$	78.6118			0.115776
$680$		0			0
$681$	21.8459	+	370.736i	0.0320791	+	0.544399i
$682$			212.993i			0.312307i
$683$	117.573			0.172142			0.0860712	−	0.996289i	$-0.472569\pi$
$683$	117.573			0.172142			0.0860712	+	0.996289i	$0.472569\pi$
$684$	−2266.19	+	268.004i	−3.31314	+	0.391819i
$685$		0			0
$686$			66.1687i			0.0964559i
$687$	−6.85611	−	116.352i	−0.00997978	−	0.169362i
$688$			1487.71i			2.16237i
$689$		−	1159.92i		−	1.68348i
$690$		0			0
$691$	831.462			1.20327			0.601637	−	0.798770i	$-0.294515\pi$
$691$	831.462			1.20327			0.601637	+	0.798770i	$0.294515\pi$
$692$	177.394			0.256350
$693$	285.383	−	33.7500i	0.411809	−	0.0487014i
$694$	−464.278			−0.668989
$695$		0			0
$696$	581.813	−	34.2837i	0.835938	−	0.0492582i
$697$			1283.87i			1.84199i
$698$	−53.9727			−0.0773248
$699$	−34.2708	−	581.593i	−0.0490283	−	0.832036i
$700$		0			0
$701$		−	1265.38i		−	1.80510i	−0.430583	−	0.902551i	$-0.641692\pi$
$701$		−	1265.38i		−	1.80510i	0.430583	−	0.902551i	$-0.358308\pi$
$702$	−1207.40	+	215.438i	−1.71995	+	0.306892i
$703$			1061.82i			1.51041i
$704$		−	211.064i		−	0.299807i
$705$		0			0
$706$	2461.52			3.48657
$707$	89.3429			0.126369
$708$	−900.594	+	53.0681i	−1.27202	+	0.0749550i
$709$	−404.244			−0.570161			−0.285080	−	0.958504i	$-0.592020\pi$
$709$	−404.244			−0.570161			−0.285080	+	0.958504i	$0.592020\pi$
$710$		0			0
$711$	−752.867	+	89.0356i	−1.05888	+	0.125226i
$712$		−	28.1319i		−	0.0395110i
$713$	−108.231			−0.151796
$714$	630.033	−	37.1252i	0.882399	−	0.0519960i
$715$		0			0
$716$			1008.98i			1.40920i
$717$	685.779	−	40.4100i	0.956456	−	0.0563598i
$718$		−	2132.25i		−	2.96971i
$719$			790.437i			1.09936i	0.835377	+	0.549678i	$0.185250\pi$
$719$			790.437i			1.09936i	−0.835377	+	0.549678i	$0.814750\pi$
$720$		0			0
$721$	318.444			0.441670
$722$	−1700.21			−2.35486
$723$	−71.8454	−	1219.25i	−0.0993713	−	1.68638i
$724$	−307.913			−0.425294
$725$		0			0
$726$	−15.5408	−	263.735i	−0.0214060	−	0.363272i
$727$		−	951.432i		−	1.30871i	−0.756188	−	0.654355i	$-0.772940\pi$
$727$		−	951.432i		−	1.30871i	0.756188	−	0.654355i	$-0.227060\pi$
$728$	−572.640			−0.786593
$729$	−684.013	+	252.126i	−0.938289	+	0.345851i
$730$		0			0
$731$		−	1285.25i		−	1.75820i
$732$	−110.007	−	1866.87i	−0.150282	−	2.55037i
$733$			920.746i			1.25613i	0.778159	+	0.628067i	$0.216154\pi$
$733$			920.746i			1.25613i	−0.778159	+	0.628067i	$0.783846\pi$
$734$			2333.98i			3.17981i
$735$		0			0
$736$	−524.682			−0.712883
$737$	243.441			0.330314
$738$	−217.850	−	1842.10i	−0.295190	−	2.49607i
$739$	312.768			0.423231			0.211615	−	0.977353i	$-0.432128\pi$
$739$	312.768			0.423231			0.211615	+	0.977353i	$0.432128\pi$
$740$		0			0
$741$	−1101.51	+	64.9073i	−1.48652	+	0.0875941i
$742$		−	862.372i		−	1.16223i
$743$	−1116.08			−1.50212			−0.751060	−	0.660234i	$-0.770457\pi$
$743$	−1116.08			−1.50212			−0.751060	+	0.660234i	$0.770457\pi$
$744$	−14.8397	−	251.837i	−0.0199458	−	0.338490i
$745$		0			0
$746$			381.710i			0.511676i
$747$	−182.753	+	21.6128i	−0.244649	+	0.0289328i
$748$		−	2354.14i		−	3.14724i
$749$			461.804i			0.616560i
$750$		0			0
$751$	−1419.71			−1.89043			−0.945215	−	0.326448i	$-0.894148\pi$
$751$	−1419.71			−1.89043			−0.945215	+	0.326448i	$0.894148\pi$
$752$	403.873			0.537065
$753$	492.519	−	29.0221i	0.654076	−	0.0385419i
$754$	518.400			0.687533
$755$		0			0
$756$	−616.376	+	109.981i	−0.815312	+	0.145477i
$757$		−	822.074i		−	1.08596i	−0.839745	−	0.542981i	$-0.817295\pi$
$757$		−	822.074i		−	1.08596i	0.839745	−	0.542981i	$-0.182705\pi$
$758$	−546.060			−0.720396
$759$	791.892	−	46.6628i	1.04334	−	0.0614793i
$760$		0			0
$761$			1366.47i			1.79562i	0.440380	+	0.897812i	$0.354844\pi$
$761$			1366.47i			1.79562i	−0.440380	+	0.897812i	$0.645156\pi$
$762$	−78.4392	+	4.62209i	−0.102939	+	0.00606573i
$763$		−	66.7559i		−	0.0874913i
$764$			1127.70i			1.47605i
$765$		0			0
$766$	−721.201			−0.941516
$767$	−436.225			−0.568742
$768$	87.4440	+	1483.97i	0.113859	+	1.93225i
$769$	−117.440			−0.152718			−0.0763591	−	0.997080i	$-0.524330\pi$
$769$	−117.440			−0.152718			−0.0763591	+	0.997080i	$0.524330\pi$
$770$		0			0
$771$	−67.7929	−	1150.48i	−0.0879285	−	1.49219i
$772$			1308.23i			1.69460i
$773$	−306.116			−0.396011			−0.198005	−	0.980201i	$-0.563446\pi$
$773$	−306.116			−0.396011			−0.198005	+	0.980201i	$0.563446\pi$
$774$	218.084	+	1844.08i	0.281763	+	2.38253i
$775$		0			0
$776$			505.804i			0.651810i
$777$	17.1373	+	290.828i	0.0220557	+	0.374297i
$778$		−	1482.62i		−	1.90568i
$779$		−	1668.83i		−	2.14227i
$780$		0			0
$781$	842.041			1.07816
$782$	1742.17			2.22783
$783$	303.339	−	54.1252i	0.387406	−	0.0691254i
$784$	−180.331			−0.230014
$785$		0			0
$786$	1036.11	−	61.0534i	1.31820	−	0.0776761i
$787$			279.568i			0.355232i	0.984100	+	0.177616i	$0.0568386\pi$
$787$			279.568i			0.355232i	−0.984100	+	0.177616i	$0.943161\pi$
$788$	2670.97			3.38955
$789$	−34.9752	−	593.546i	−0.0443285	−	0.752277i
$790$		0			0
$791$		−	334.488i		−	0.422867i
$792$	217.155	+	1836.22i	0.274185	+	2.31845i
$793$		−	904.264i		−	1.14031i
$794$		−	1464.89i		−	1.84495i
$795$		0			0
$796$	864.193			1.08567
$797$	−327.577			−0.411013			−0.205507	−	0.978656i	$-0.565884\pi$
$797$	−327.577			−0.411013			−0.205507	+	0.978656i	$0.565884\pi$
$798$	−818.945	+	48.2569i	−1.02625	+	0.0604723i
$799$	−348.909			−0.436682
$800$		0			0
$801$	−1.74673	−	14.7700i	−0.00218069	−	0.0184395i
$802$		−	1240.42i		−	1.54666i
$803$	1169.07			1.45588
$804$	−529.478	+	31.1999i	−0.658555	+	0.0388058i
$805$		0			0
$806$		−	224.389i		−	0.278398i
$807$	42.9761	−	2.53240i	0.0532541	−	0.00313804i
$808$			574.851i			0.711449i
$809$		−	219.021i		−	0.270731i	−0.990796	−	0.135365i	$-0.956779\pi$
$809$		−	219.021i		−	0.270731i	0.990796	−	0.135365i	$-0.0432208\pi$
$810$		0			0
$811$	57.9161			0.0714132			0.0357066	−	0.999362i	$-0.488632\pi$
$811$	57.9161			0.0714132			0.0357066	+	0.999362i	$0.488632\pi$
$812$	264.642			0.325913
$813$	4.63157	+	78.6001i	0.00569688	+	0.0966791i
$814$	1582.63			1.94426
$815$		0			0
$816$	101.178	+	1717.04i	0.123992	+	2.10422i
$817$			1670.62i			2.04482i
$818$	−369.863			−0.452156
$819$	−300.652	+	35.5557i	−0.367096	+	0.0434136i
$820$		0			0
$821$		−	1385.60i		−	1.68770i	−0.536577	−	0.843851i	$-0.680283\pi$
$821$		−	1385.60i		−	1.68770i	0.536577	−	0.843851i	$-0.319717\pi$
$822$	−144.298	−	2448.81i	−0.175545	−	2.97909i
$823$			1414.41i			1.71861i	0.511468	+	0.859303i	$0.329102\pi$
$823$			1414.41i			1.71861i	−0.511468	+	0.859303i	$0.670898\pi$
$824$			2048.93i			2.48657i
$825$		0			0
$826$	−324.322			−0.392642
$827$	−305.144			−0.368977			−0.184488	−	0.982835i	$-0.559063\pi$
$827$	−305.144			−0.368977			−0.184488	+	0.982835i	$0.559063\pi$
$828$	−1716.36	+	202.981i	−2.07290	+	0.245146i
$829$	−517.903			−0.624732			−0.312366	−	0.949962i	$-0.601122\pi$
$829$	−517.903			−0.624732			−0.312366	+	0.949962i	$0.601122\pi$
$830$		0			0
$831$	−63.7114	+	3.75424i	−0.0766684	+	0.00451774i
$832$			222.356i			0.267255i
$833$	155.789			0.187022
$834$	−102.643	−	1741.91i	−0.123073	−	2.08862i
$835$		0			0
$836$			3060.01i			3.66030i
$837$	−23.4280	−	131.300i	−0.0279905	−	0.156870i
$838$		−	304.095i		−	0.362882i
$839$			3.40272i			0.00405569i	0.999998	+	0.00202784i	$0.000645483\pi$
$839$			3.40272i			0.00405569i	−0.999998	+	0.00202784i	$0.999355\pi$
$840$		0			0
$841$	710.761			0.845138
$842$	1749.67			2.07800
$843$	−964.517	+	56.8349i	−1.14415	+	0.0674198i
$844$	2238.76			2.65256
$845$		0			0
$846$	500.616	−	59.2039i	0.591745	−	0.0699810i
$847$		−	65.2143i		−	0.0769944i
$848$	2350.24			2.77151
$849$	−776.581	+	45.7606i	−0.914701	+	0.0538994i
$850$		0			0
$851$			804.199i			0.945004i
$852$	−1831.42	+	107.918i	−2.14955	+	0.126664i
$853$			639.114i			0.749255i	0.927175	+	0.374627i	$0.122229\pi$
$853$			639.114i			0.749255i	−0.927175	+	0.374627i	$0.877771\pi$
$854$		−	672.298i		−	0.787234i
$855$		0			0
$856$	−2971.34			−3.47119
$857$	724.119			0.844946			0.422473	−	0.906375i	$-0.361162\pi$
$857$	724.119			0.844946			0.422473	+	0.906375i	$0.361162\pi$
$858$	96.7433	+	1641.78i	0.112754	+	1.91350i
$859$	952.638			1.10901			0.554504	−	0.832181i	$-0.312908\pi$
$859$	952.638			1.10901			0.554504	+	0.832181i	$0.312908\pi$
$860$		0			0
$861$	−26.9341	−	457.086i	−0.0312824	−	0.530878i
$862$			2062.17i			2.39231i
$863$	1609.84			1.86540			0.932698	−	0.360659i	$-0.117448\pi$
$863$	1609.84			1.86540			0.932698	+	0.360659i	$0.117448\pi$
$864$	−113.574	−	636.517i	−0.131452	−	0.736709i
$865$		0			0
$866$		−	337.753i		−	0.390015i
$867$	−36.4083	−	617.868i	−0.0419934	−	0.712650i
$868$		−	114.550i		−	0.131970i
$869$			1016.59i			1.16984i
$870$		0			0
$871$	−256.466			−0.294450
$872$	429.521			0.492570
$873$	31.4059	+	265.562i	0.0359746	+	0.304194i
$874$	−2264.55			−2.59101
$875$		0			0
$876$	−2542.69	+	149.830i	−2.90261	+	0.171039i
$877$		−	740.088i		−	0.843886i	−0.906622	−	0.421943i	$-0.861348\pi$
$877$		−	740.088i		−	0.843886i	0.906622	−	0.421943i	$-0.138652\pi$
$878$	569.664			0.648820
$879$	−53.1524	−	902.023i	−0.0604691	−	1.02619i
$880$		0			0
$881$			81.0232i			0.0919673i	0.998942	+	0.0459836i	$0.0146422\pi$
$881$			81.0232i			0.0919673i	−0.998942	+	0.0459836i	$0.985358\pi$
$882$	−223.527	+	26.4348i	−0.253432	+	0.0299714i
$883$			783.824i			0.887682i	0.896105	+	0.443841i	$0.146385\pi$
$883$			783.824i			0.887682i	−0.896105	+	0.443841i	$0.853615\pi$
$884$			2480.09i			2.80553i
$885$		0			0
$886$	462.676			0.522208
$887$	−1320.12			−1.48830			−0.744150	−	0.668012i	$-0.767145\pi$
$887$	−1320.12			−1.48830			−0.744150	+	0.668012i	$0.767145\pi$
$888$	−1871.25	+	110.265i	−2.10726	+	0.124172i
$889$	−19.3958			−0.0218176
$890$		0			0
$891$	228.025	+	950.582i	0.255920	+	1.06687i
$892$		−	270.203i		−	0.302918i
$893$	453.528			0.507870
$894$	20.5131	−	1.20875i	0.0229453	−	0.00135207i
$895$		0			0
$896$			418.748i			0.467352i
$897$	−834.259	+	49.1593i	−0.930055	+	0.0548042i
$898$			1094.00i			1.21826i
$899$			56.3738i			0.0627072i
$900$		0			0
$901$	−2030.39			−2.25349
$902$	−2487.37			−2.75761
$903$	26.9631	+	457.577i	0.0298594	+	0.506730i
$904$	2152.16			2.38071
$905$		0			0
$906$	2.11090	+	35.8231i	0.00232991	+	0.0395399i
$907$		−	1149.97i		−	1.26788i	−0.773381	−	0.633942i	$-0.781436\pi$
$907$		−	1149.97i		−	1.26788i	0.773381	−	0.633942i	$-0.218564\pi$
$908$	−1085.01			−1.19495
$909$	35.6930	+	301.813i	0.0392662	+	0.332027i
$910$		0			0
$911$			1275.15i			1.39972i	0.714280	+	0.699860i	$0.246754\pi$
$911$			1275.15i			1.39972i	−0.714280	+	0.699860i	$0.753246\pi$
$912$	−131.515	−	2231.89i	−0.144206	−	2.44724i
$913$			246.770i			0.270284i
$914$		−	511.584i		−	0.559720i
$915$		0			0
$916$	340.520			0.371747
$917$	256.200			0.279390
$918$	377.116	+	2113.51i	0.410801	+	2.30230i
$919$	228.393			0.248523			0.124262	−	0.992249i	$-0.460344\pi$
$919$	228.393			0.248523			0.124262	+	0.992249i	$0.460344\pi$
$920$		0			0
$921$	786.726	−	46.3584i	0.854209	−	0.0503349i
$922$		−	2655.87i		−	2.88055i
$923$	−887.092			−0.961096
$924$	49.3872	+	838.126i	0.0534493	+	0.907063i
$925$		0			0
$926$			2062.37i			2.22718i
$927$	127.220	+	1075.75i	0.137239	+	1.16046i
$928$			273.289i			0.294493i
$929$			71.5997i			0.0770718i	0.999257	+	0.0385359i	$0.0122694\pi$
$929$			71.5997i			0.0770718i	−0.999257	+	0.0385359i	$0.987731\pi$
$930$		0			0
$931$	−202.502			−0.217510
$932$	1702.12			1.82630
$933$	−744.317	+	43.8594i	−0.797767	+	0.0470090i
$934$	−1209.01			−1.29445
$935$		0			0
$936$	−228.773	−	1934.46i	−0.244415	−	2.06673i
$937$		−	606.742i		−	0.647536i	−0.946136	−	0.323768i	$-0.895050\pi$
$937$		−	606.742i		−	0.647536i	0.946136	−	0.323768i	$-0.104950\pi$
$938$	−190.676			−0.203279
$939$	1277.98	−	75.3060i	1.36100	−	0.0801981i
$940$		0			0
$941$		−	1043.93i		−	1.10938i	−0.832056	−	0.554692i	$-0.812836\pi$
$941$		−	1043.93i		−	1.10938i	0.832056	−	0.554692i	$-0.187164\pi$
$942$	42.6159	−	2.51117i	0.0452398	−	0.00266579i
$943$		−	1263.93i		−	1.34033i
$944$		−	883.881i		−	0.936315i
$945$		0			0
$946$	2490.04			2.63217
$947$	−1057.69			−1.11688			−0.558440	−	0.829545i	$-0.688600\pi$
$947$	−1057.69			−1.11688			−0.558440	+	0.829545i	$0.688600\pi$
$948$	−130.288	−	2211.05i	−0.137434	−	2.33233i
$949$	−1231.61			−1.29780
$950$		0			0
$951$	−18.9493	−	321.579i	−0.0199256	−	0.338148i
$952$			1002.38i			1.05292i
$953$	278.572			0.292311			0.146155	−	0.989262i	$-0.453310\pi$
$953$	278.572			0.292311			0.146155	+	0.989262i	$0.453310\pi$
$954$	2913.21	−	344.523i	3.05368	−	0.361135i
$955$		0			0
$956$			2007.03i			2.09940i
$957$	−24.3051	−	412.470i	−0.0253972	−	0.431003i
$958$		−	856.070i		−	0.893601i
$959$		−	605.522i		−	0.631410i
$960$		0			0
$961$	−936.599			−0.974608
$962$	−1667.30			−1.73316
$963$	−1560.04	+	184.493i	−1.61998	+	0.191582i
$964$	3568.32			3.70158
$965$		0			0
$966$	−620.251	+	36.5487i	−0.642082	+	0.0378351i
$967$		−	717.616i		−	0.742105i	−0.928612	−	0.371053i	$-0.878997\pi$
$967$		−	717.616i		−	0.742105i	0.928612	−	0.371053i	$-0.121003\pi$
$968$	419.602			0.433473
$969$	113.617	+	1928.15i	0.117252	+	1.98983i
$970$		0			0
$971$			1566.83i			1.61363i	0.590806	+	0.806814i	$0.298810\pi$
$971$			1566.83i			1.61363i	−0.590806	+	0.806814i	$0.701190\pi$
$972$	−617.776	−	2038.27i	−0.635572	−	2.09698i
$973$		−	430.725i		−	0.442677i
$974$		−	341.792i		−	0.350916i
$975$		0			0
$976$	1832.23			1.87728
$977$	−727.568			−0.744696			−0.372348	−	0.928093i	$-0.621447\pi$
$977$	−727.568			−0.744696			−0.372348	+	0.928093i	$0.621447\pi$
$978$	2547.41	−	150.108i	2.60472	−	0.153485i
$979$	−19.9438			−0.0203716
$980$		0			0
$981$	225.511	−	26.6694i	0.229878	−	0.0271859i
$982$			1259.30i			1.28238i
$983$	−686.673			−0.698549			−0.349274	−	0.937021i	$-0.613572\pi$
$983$	−686.673			−0.698549			−0.349274	+	0.937021i	$0.613572\pi$
$984$	2940.99	−	173.300i	2.98881	−	0.176118i
$985$		0			0
$986$		−	907.436i		−	0.920321i
$987$	124.220	−	7.31973i	0.125856	−	0.00741614i
$988$		−	3223.73i		−	3.26288i
$989$			1265.29i			1.27936i
$990$		0			0
$991$	468.764			0.473022			0.236511	−	0.971629i	$-0.423996\pi$
$991$	468.764			0.473022			0.236511	+	0.971629i	$0.423996\pi$
$992$	118.293			0.119247
$993$	79.7541	+	1353.47i	0.0803163	+	1.36301i
$994$	−659.531			−0.663512
$995$		0			0
$996$	−31.6264	−	536.717i	−0.0317535	−	0.538873i
$997$			1860.83i			1.86643i	0.359323	+	0.933213i	$0.383008\pi$
$997$			1860.83i			1.86643i	−0.359323	+	0.933213i	$0.616992\pi$
$998$	−1134.14			−1.13641
$999$	−975.613	+	174.080i	−0.976589	+	0.174254i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.f.b.449.4		32
3.2	odd	2	inner	525.3.f.b.449.29		32
5.2	odd	4		105.3.c.a.71.2	✓	16
5.3	odd	4		525.3.c.b.176.15		16
5.4	even	2	inner	525.3.f.b.449.30		32
15.2	even	4		105.3.c.a.71.15	yes	16
15.8	even	4		525.3.c.b.176.2		16
15.14	odd	2	inner	525.3.f.b.449.3		32
20.7	even	4		1680.3.l.a.1121.15		16
60.47	odd	4		1680.3.l.a.1121.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.c.a.71.2	✓	16	5.2	odd	4
105.3.c.a.71.15	yes	16	15.2	even	4
525.3.c.b.176.2		16	15.8	even	4
525.3.c.b.176.15		16	5.3	odd	4
525.3.f.b.449.3		32	15.14	odd	2	inner
525.3.f.b.449.4		32	1.1	even	1	trivial
525.3.f.b.449.29		32	3.2	odd	2	inner
525.3.f.b.449.30		32	5.4	even	2	inner
1680.3.l.a.1121.15		16	20.7	even	4
1680.3.l.a.1121.16		16	60.47	odd	4

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-3.57278 q^{2} +(-0.176471 - 2.99481i) q^{3} +8.76473 q^{4} +(0.630492 + 10.6998i) q^{6} +2.64575i q^{7} -17.0233 q^{8} +(-8.93772 + 1.05699i) q^{9} +12.0685i q^{11} +(-1.54672 - 26.2487i) q^{12} -12.7142i q^{13} -9.45268i q^{14} +25.7616 q^{16} -22.2556 q^{17} +(31.9325 - 3.77640i) q^{18} +28.9289 q^{19} +(7.92351 - 0.466899i) q^{21} -43.1180i q^{22} +21.9101 q^{23} +(3.00412 + 50.9815i) q^{24} +45.4249i q^{26} +(4.74274 + 26.5802i) q^{27} +23.1893i q^{28} -11.4122i q^{29} -4.93977 q^{31} -23.9470 q^{32} +(36.1428 - 2.12974i) q^{33} +79.5144 q^{34} +(-78.3367 + 9.26426i) q^{36} +36.7045i q^{37} -103.356 q^{38} +(-38.0765 + 2.24369i) q^{39} -57.6874i q^{41} +(-28.3089 + 1.66812i) q^{42} +57.7493i q^{43} +105.777i q^{44} -78.2798 q^{46} +15.6773 q^{47} +(-4.54617 - 77.1508i) q^{48} -7.00000 q^{49} +(3.92747 + 66.6513i) q^{51} -111.436i q^{52} +91.2304 q^{53} +(-16.9447 - 94.9651i) q^{54} -45.0394i q^{56} +(-5.10511 - 86.6363i) q^{57} +40.7733i q^{58} -34.3101i q^{59} +71.1225 q^{61} +17.6487 q^{62} +(-2.79654 - 23.6470i) q^{63} -17.4888 q^{64} +(-129.130 + 7.60909i) q^{66} -20.1716i q^{67} -195.065 q^{68} +(-3.86649 - 65.6164i) q^{69} -69.7718i q^{71} +(152.150 - 17.9935i) q^{72} -96.8693i q^{73} -131.137i q^{74} +253.554 q^{76} -31.9302 q^{77} +(136.039 - 8.01619i) q^{78} +84.2348 q^{79} +(78.7655 - 18.8942i) q^{81} +206.104i q^{82} +20.4474 q^{83} +(69.4474 - 4.09224i) q^{84} -206.325i q^{86} +(-34.1774 + 2.01393i) q^{87} -205.446i q^{88} +1.65255i q^{89} +33.6386 q^{91} +192.036 q^{92} +(0.871726 + 14.7936i) q^{93} -56.0116 q^{94} +(4.22596 + 71.7167i) q^{96} -29.7125i q^{97} +25.0094 q^{98} +(-12.7563 - 107.865i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 56 q^{4} - 56 q^{6} - 44 q^{9} + 184 q^{16} + 32 q^{19} - 28 q^{21} - 256 q^{24} - 144 q^{31} + 352 q^{34} - 152 q^{36} - 180 q^{39} + 144 q^{46} - 224 q^{49} + 76 q^{51} - 416 q^{54} - 112 q^{61}+ \cdots + 332 q^{99}+O(q^{100}) \) 32 * q + 56 * q^4 - 56 * q^6 - 44 * q^9 + 184 * q^16 + 32 * q^19 - 28 * q^21 - 256 * q^24 - 144 * q^31 + 352 * q^34 - 152 * q^36 - 180 * q^39 + 144 * q^46 - 224 * q^49 + 76 * q^51 - 416 * q^54 - 112 * q^61 + 88 * q^64 - 520 * q^66 - 120 * q^69 + 288 * q^76 + 408 * q^79 + 916 * q^81 + 168 * q^84 - 56 * q^91 - 1968 * q^94 + 80 * q^96 + 332 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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