LMFDB - Embedded newform 36.5.f.a.31.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,5,Mod(7,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("36.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	36.f (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.72131867102$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.19
Character	$\chi$	$=$	36.31
Dual form			36.5.f.a.7.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.61656 - 1.70894i) q^{2} +(8.99820 + 0.179896i) q^{3} +(10.1591 - 12.3610i) q^{4} +(-2.83091 + 4.90328i) q^{5} +(32.8500 - 14.7267i) q^{6} +(-45.1595 + 26.0728i) q^{7} +(15.6169 - 62.0654i) q^{8} +(80.9353 + 3.23749i) q^{9} +O(q^{10})$	\(q+(3.61656 - 1.70894i) q^{2} +(8.99820 + 0.179896i) q^{3} +(10.1591 - 12.3610i) q^{4} +(-2.83091 + 4.90328i) q^{5} +(32.8500 - 14.7267i) q^{6} +(-45.1595 + 26.0728i) q^{7} +(15.6169 - 62.0654i) q^{8} +(80.9353 + 3.23749i) q^{9} +(-1.85878 + 22.5709i) q^{10} +(-92.3736 + 53.3319i) q^{11} +(93.6371 - 109.399i) q^{12} +(61.0686 - 105.774i) q^{13} +(-118.765 + 171.469i) q^{14} +(-26.3552 + 43.6114i) q^{15} +(-49.5864 - 251.152i) q^{16} -122.675 q^{17} +(298.240 - 126.605i) q^{18} +593.624i q^{19} +(31.8498 + 84.8055i) q^{20} +(-411.044 + 226.484i) q^{21} +(-242.934 + 350.739i) q^{22} +(-473.649 - 273.461i) q^{23} +(151.689 - 555.668i) q^{24} +(296.472 + 513.504i) q^{25} +(40.0976 - 486.900i) q^{26} +(727.690 + 43.6915i) q^{27} +(-136.493 + 823.090i) q^{28} +(-367.933 - 637.279i) q^{29} +(-20.7861 + 202.763i) q^{30} +(-507.427 - 292.963i) q^{31} +(-608.535 - 823.566i) q^{32} +(-840.791 + 463.274i) q^{33} +(-443.662 + 209.644i) q^{34} -295.239i q^{35} +(862.246 - 967.547i) q^{36} +2289.29 q^{37} +(1014.47 + 2146.88i) q^{38} +(568.535 - 940.788i) q^{39} +(260.114 + 252.275i) q^{40} +(1434.13 - 2483.99i) q^{41} +(-1099.52 + 1521.54i) q^{42} +(1943.81 - 1122.26i) q^{43} +(-279.197 + 1683.63i) q^{44} +(-244.995 + 387.683i) q^{45} +(-2180.31 - 179.555i) q^{46} +(913.531 - 527.427i) q^{47} +(-401.007 - 2268.83i) q^{48} +(159.084 - 275.542i) q^{49} +(1949.76 + 1350.47i) q^{50} +(-1103.85 - 22.0688i) q^{51} +(-687.066 - 1829.43i) q^{52} -4752.60 q^{53} +(2706.40 - 1085.56i) q^{54} -603.911i q^{55} +(912.971 + 3210.02i) q^{56} +(-106.791 + 5341.55i) q^{57} +(-2419.72 - 1675.99i) q^{58} +(1864.25 + 1076.32i) q^{59} +(271.335 + 768.827i) q^{60} +(33.1660 + 57.4451i) q^{61} +(-2335.80 - 192.360i) q^{62} +(-3739.40 + 1964.01i) q^{63} +(-3608.23 - 1938.53i) q^{64} +(345.759 + 598.872i) q^{65} +(-2249.07 + 3112.32i) q^{66} +(-3554.82 - 2052.38i) q^{67} +(-1246.26 + 1516.38i) q^{68} +(-4212.79 - 2545.87i) q^{69} +(-504.545 - 1067.75i) q^{70} +5031.65i q^{71} +(1464.89 - 4972.72i) q^{72} +2705.16 q^{73} +(8279.36 - 3912.25i) q^{74} +(2575.34 + 4673.95i) q^{75} +(7337.76 + 6030.67i) q^{76} +(2781.03 - 4816.88i) q^{77} +(448.398 - 4374.01i) q^{78} +(1196.02 - 690.524i) q^{79} +(1371.84 + 467.852i) q^{80} +(6540.04 + 524.053i) q^{81} +(941.652 - 11434.4i) q^{82} +(-2605.31 + 1504.18i) q^{83} +(-1376.27 + 7381.77i) q^{84} +(347.282 - 601.509i) q^{85} +(5112.05 - 7380.57i) q^{86} +(-3196.09 - 5800.55i) q^{87} +(1867.48 + 6566.08i) q^{88} +3186.35 q^{89} +(-223.513 + 1820.76i) q^{90} +6368.92i q^{91} +(-8192.07 + 3076.64i) q^{92} +(-4513.23 - 2727.43i) q^{93} +(2402.50 - 3468.64i) q^{94} +(-2910.71 - 1680.50i) q^{95} +(-5327.56 - 7520.09i) q^{96} +(2407.03 + 4169.10i) q^{97} +(104.455 - 1268.38i) q^{98} +(-7648.94 + 4017.38i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9}+O(q^{10}) $ 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9	$ 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9} + 28 q^{10} - 228 q^{12} - 2 q^{13} + 252 q^{14} - q^{16} - 56 q^{17} + 72 q^{18} - 140 q^{20} + 138 q^{21} - 33 q^{22} - 951 q^{24} - 1752 q^{25} + 1096 q^{26} - 516 q^{28} + 526 q^{29} - 1980 q^{30} - 121 q^{32} + 2994 q^{33} + 385 q^{34} - 1005 q^{36} - 8 q^{37} + 1395 q^{38} - 2276 q^{40} - 2762 q^{41} + 3330 q^{42} + 6714 q^{44} + 4110 q^{45} + 3576 q^{46} + 2163 q^{48} + 3428 q^{49} + 6375 q^{50} + 1438 q^{52} - 10088 q^{53} - 4983 q^{54} - 7506 q^{56} + 1752 q^{57} - 4064 q^{58} - 16392 q^{60} - 2 q^{61} - 18324 q^{62} + 9026 q^{64} - 2014 q^{65} - 17358 q^{66} - 11405 q^{68} + 3354 q^{69} + 3666 q^{70} + 4083 q^{72} - 3416 q^{73} + 14620 q^{74} + 1581 q^{76} - 3942 q^{77} + 34566 q^{78} + 45520 q^{80} - 1164 q^{81} - 8486 q^{82} + 51078 q^{84} - 1252 q^{85} + 22113 q^{86} + 1995 q^{88} + 13048 q^{89} - 4692 q^{90} - 30294 q^{92} + 12090 q^{93} + 7524 q^{94} - 76164 q^{96} + 5638 q^{97} - 92938 q^{98}+O(q^{100}) $ 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9 + 28 * q^10 - 228 * q^12 - 2 * q^13 + 252 * q^14 - q^16 - 56 * q^17 + 72 * q^18 - 140 * q^20 + 138 * q^21 - 33 * q^22 - 951 * q^24 - 1752 * q^25 + 1096 * q^26 - 516 * q^28 + 526 * q^29 - 1980 * q^30 - 121 * q^32 + 2994 * q^33 + 385 * q^34 - 1005 * q^36 - 8 * q^37 + 1395 * q^38 - 2276 * q^40 - 2762 * q^41 + 3330 * q^42 + 6714 * q^44 + 4110 * q^45 + 3576 * q^46 + 2163 * q^48 + 3428 * q^49 + 6375 * q^50 + 1438 * q^52 - 10088 * q^53 - 4983 * q^54 - 7506 * q^56 + 1752 * q^57 - 4064 * q^58 - 16392 * q^60 - 2 * q^61 - 18324 * q^62 + 9026 * q^64 - 2014 * q^65 - 17358 * q^66 - 11405 * q^68 + 3354 * q^69 + 3666 * q^70 + 4083 * q^72 - 3416 * q^73 + 14620 * q^74 + 1581 * q^76 - 3942 * q^77 + 34566 * q^78 + 45520 * q^80 - 1164 * q^81 - 8486 * q^82 + 51078 * q^84 - 1252 * q^85 + 22113 * q^86 + 1995 * q^88 + 13048 * q^89 - 4692 * q^90 - 30294 * q^92 + 12090 * q^93 + 7524 * q^94 - 76164 * q^96 + 5638 * q^97 - 92938 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	3.61656	−	1.70894i	0.904141	−	0.427234i
$2$	3.61656	−	1.70894i	0.904141	−	0.427234i
$3$	8.99820	+	0.179896i	0.999800	+	0.0199885i
$3$	8.99820	+	0.179896i	0.999800	+	0.0199885i
$4$	10.1591	−	12.3610i	0.634942	−	0.772560i
$5$	−2.83091	+	4.90328i	−0.113236	+	0.196131i	−0.917073	−	0.398718i	$-0.869455\pi$
$5$	−2.83091	+	4.90328i	−0.113236	+	0.196131i	0.803837	+	0.594850i	$0.202788\pi$
$6$	32.8500	−	14.7267i	0.912500	−	0.409076i
$7$	−45.1595	+	26.0728i	−0.921621	+	0.532098i	−0.884152	−	0.467199i	$-0.845263\pi$
$7$	−45.1595	+	26.0728i	−0.921621	+	0.532098i	−0.0374695	+	0.999298i	$0.511930\pi$
$8$	15.6169	−	62.0654i	0.244014	−	0.969772i
$9$	80.9353	+	3.23749i	0.999201	+	0.0399690i
$10$	−1.85878	+	22.5709i	−0.0185878	+	0.225709i
$11$	−92.3736	+	53.3319i	−0.763418	+	0.440760i	−0.830522	−	0.556986i	$-0.811958\pi$
$11$	−92.3736	+	53.3319i	−0.763418	+	0.440760i	0.0671034	+	0.997746i	$0.478624\pi$
$12$	93.6371	−	109.399i	0.650258	−	0.759714i
$13$	61.0686	−	105.774i	0.361352	−	0.625881i	−0.626831	−	0.779155i	$-0.715648\pi$
$13$	61.0686	−	105.774i	0.361352	−	0.625881i	0.988184	+	0.153274i	$0.0489818\pi$
$14$	−118.765	+	171.469i	−0.605945	+	0.874840i
$15$	−26.3552	+	43.6114i	−0.117134	+	0.193829i
$16$	−49.5864	−	251.152i	−0.193697	−	0.981061i
$17$	−122.675			−0.424481			−0.212240	−	0.977217i	$-0.568076\pi$
$17$	−122.675			−0.424481			−0.212240	+	0.977217i	$0.568076\pi$
$18$	298.240	−	126.605i	0.920495	−	0.390755i
$19$			593.624i			1.64439i	0.569207	+	0.822194i	$0.307250\pi$
$19$			593.624i			1.64439i	−0.569207	+	0.822194i	$0.692750\pi$
$20$	31.8498	+	84.8055i	0.0796244	+	0.212014i
$21$	−411.044	+	226.484i	−0.932073	+	0.513570i
$22$	−242.934	+	350.739i	−0.501930	+	0.724667i
$23$	−473.649	−	273.461i	−0.895366	−	0.516940i	−0.0196720	−	0.999806i	$-0.506262\pi$
$23$	−473.649	−	273.461i	−0.895366	−	0.516940i	−0.875694	+	0.482867i	$0.839596\pi$
$24$	151.689	−	555.668i	0.263349	−	0.964701i
$25$	296.472	+	513.504i	0.474355	+	0.821607i
$26$	40.0976	−	486.900i	0.0593160	−	0.720266i
$27$	727.690	+	43.6915i	0.998202	+	0.0599335i
$28$	−136.493	+	823.090i	−0.174099	+	1.04986i
$29$	−367.933	−	637.279i	−0.437495	−	0.757763i	0.560001	−	0.828492i	$-0.310801\pi$
$29$	−367.933	−	637.279i	−0.437495	−	0.757763i	−0.997496	+	0.0707290i	$0.977467\pi$
$30$	−20.7861	+	202.763i	−0.0230956	+	0.225292i
$31$	−507.427	−	292.963i	−0.528020	−	0.304853i	0.212190	−	0.977228i	$-0.431941\pi$
$31$	−507.427	−	292.963i	−0.528020	−	0.304853i	−0.740210	+	0.672376i	$0.765274\pi$
$32$	−608.535	−	823.566i	−0.594272	−	0.804264i
$33$	−840.791	+	463.274i	−0.772076	+	0.425412i
$34$	−443.662	+	209.644i	−0.383791	+	0.181353i
$35$		−	295.239i		−	0.241012i
$36$	862.246	−	967.547i	0.665313	−	0.746564i
$37$	2289.29			1.67223			0.836117	−	0.548551i	$-0.184820\pi$
$37$	2289.29			1.67223			0.836117	+	0.548551i	$0.184820\pi$
$38$	1014.47	+	2146.88i	0.702539	+	1.48676i
$39$	568.535	−	940.788i	0.373791	−	0.618533i
$40$	260.114	+	252.275i	0.162571	+	0.157672i
$41$	1434.13	−	2483.99i	0.853142	−	1.47769i	−0.0252152	−	0.999682i	$-0.508027\pi$
$41$	1434.13	−	2483.99i	0.853142	−	1.47769i	0.878358	−	0.478004i	$-0.158640\pi$
$42$	−1099.52	+	1521.54i	−0.623311	+	0.862553i
$43$	1943.81	−	1122.26i	1.05128	−	0.606955i	0.128270	−	0.991739i	$-0.459057\pi$
$43$	1943.81	−	1122.26i	1.05128	−	0.606955i	0.923007	+	0.384784i	$0.125724\pi$
$44$	−279.197	+	1683.63i	−0.144213	+	0.869643i
$45$	−244.995	+	387.683i	−0.120985	+	0.191448i
$46$	−2180.31	−	179.555i	−1.03039	−	0.0848557i
$47$	913.531	−	527.427i	0.413550	−	0.238763i	−0.278764	−	0.960360i	$-0.589925\pi$
$47$	913.531	−	527.427i	0.413550	−	0.238763i	0.692314	+	0.721597i	$0.256591\pi$
$48$	−401.007	−	2268.83i	−0.174048	−	0.984737i
$49$	159.084	−	275.542i	0.0662574	−	0.114761i
$50$	1949.76	+	1350.47i	0.779902	+	0.540188i
$51$	−1103.85	−	22.0688i	−0.424396	−	0.00848472i
$52$	−687.066	−	1829.43i	−0.254092	−	0.676564i
$53$	−4752.60			−1.69192			−0.845960	−	0.533246i	$-0.820972\pi$
$53$	−4752.60			−1.69192			−0.845960	+	0.533246i	$0.820972\pi$
$54$	2706.40	−	1085.56i	0.928121	−	0.372278i
$55$		−	603.911i		−	0.199640i
$56$	912.971	+	3210.02i	0.291126	+	1.02360i
$57$	−106.791	+	5341.55i	−0.0328688	+	1.64406i
$58$	−2419.72	−	1675.99i	−0.719299	−	0.498212i
$59$	1864.25	+	1076.32i	0.535549	+	0.309200i	0.743273	−	0.668988i	$-0.233272\pi$
$59$	1864.25	+	1076.32i	0.535549	+	0.309200i	−0.207724	+	0.978188i	$0.566606\pi$
$60$	271.335	+	768.827i	0.0753707	+	0.213563i
$61$	33.1660	+	57.4451i	0.00891319	+	0.0154381i	0.870448	−	0.492261i	$-0.163829\pi$
$61$	33.1660	+	57.4451i	0.00891319	+	0.0154381i	−0.861534	+	0.507699i	$0.830496\pi$
$62$	−2335.80	−	192.360i	−0.607648	−	0.0500416i
$63$	−3739.40	+	1964.01i	−0.942152	+	0.494837i
$64$	−3608.23	−	1938.53i	−0.880915	−	0.473275i
$65$	345.759	+	598.872i	0.0818365	+	0.141745i
$66$	−2249.07	+	3112.32i	−0.516315	+	0.714490i
$67$	−3554.82	−	2052.38i	−0.791897	−	0.457202i	0.0487331	−	0.998812i	$-0.484482\pi$
$67$	−3554.82	−	2052.38i	−0.791897	−	0.457202i	−0.840630	+	0.541610i	$0.817815\pi$
$68$	−1246.26	+	1516.38i	−0.269521	+	0.327937i
$69$	−4212.79	−	2545.87i	−0.884854	−	0.534733i
$70$	−504.545	−	1067.75i	−0.102968	−	0.217908i
$71$			5031.65i			0.998145i	0.866560	+	0.499072i	$0.166326\pi$
$71$			5031.65i			0.998145i	−0.866560	+	0.499072i	$0.833674\pi$
$72$	1464.89	−	4972.72i	0.282579	−	0.959244i
$73$	2705.16			0.507631			0.253815	−	0.967253i	$-0.418314\pi$
$73$	2705.16			0.507631			0.253815	+	0.967253i	$0.418314\pi$
$74$	8279.36	−	3912.25i	1.51194	−	0.714435i
$75$	2575.34	+	4673.95i	0.457838	+	0.830925i
$76$	7337.76	+	6030.67i	1.27039	+	1.04409i
$77$	2781.03	−	4816.88i	0.469055	−	0.812427i
$78$	448.398	−	4374.01i	0.0737012	−	0.718937i
$79$	1196.02	−	690.524i	0.191639	−	0.110643i	−0.401110	−	0.916030i	$-0.631376\pi$
$79$	1196.02	−	690.524i	0.191639	−	0.110643i	0.592750	+	0.805387i	$0.298042\pi$
$80$	1371.84	+	467.852i	0.214350	+	0.0731019i
$81$	6540.04	+	524.053i	0.996805	+	0.0798740i
$82$	941.652	−	11434.4i	0.140043	−	1.70053i
$83$	−2605.31	+	1504.18i	−0.378184	+	0.218345i	−0.677028	−	0.735957i	$-0.736732\pi$
$83$	−2605.31	+	1504.18i	−0.378184	+	0.218345i	0.298844	+	0.954302i	$0.403399\pi$
$84$	−1376.27	+	7381.77i	−0.195049	+	1.04617i
$85$	347.282	−	601.509i	0.0480667	−	0.0832539i
$86$	5112.05	−	7380.57i	0.691191	−	0.997914i
$87$	−3196.09	−	5800.55i	−0.422261	−	0.766356i
$88$	1867.48	+	6566.08i	0.241152	+	0.847893i
$89$	3186.35			0.402267			0.201133	−	0.979564i	$-0.435538\pi$
$89$	3186.35			0.402267			0.201133	+	0.979564i	$0.435538\pi$
$90$	−223.513	+	1820.76i	−0.0275942	+	0.224785i
$91$			6368.92i			0.769100i
$92$	−8192.07	+	3076.64i	−0.967872	+	0.363497i
$93$	−4513.23	−	2727.43i	−0.521821	−	0.315346i
$94$	2402.50	−	3468.64i	0.271899	−	0.392558i
$95$	−2910.71	−	1680.50i	−0.322516	−	0.186205i
$96$	−5327.56	−	7520.09i	−0.578077	−	0.815982i
$97$	2407.03	+	4169.10i	0.255822	+	0.443097i	0.965118	−	0.261814i	$-0.0843206\pi$
$97$	2407.03	+	4169.10i	0.255822	+	0.443097i	−0.709296	+	0.704910i	$0.750987\pi$
$98$	104.455	−	1268.38i	0.0108762	−	0.132068i
$99$	−7648.94	+	4017.38i	−0.780425	+	0.409895i
$100$	9359.28	+	1552.05i	0.935928	+	0.155205i
$101$	3510.47	+	6080.30i	0.344130	+	0.596050i	0.985195	−	0.171436i	$-0.0548407\pi$
$101$	3510.47	+	6080.30i	0.344130	+	0.596050i	−0.641066	+	0.767486i	$0.721507\pi$
$102$	−4029.87	+	1806.60i	−0.387339	+	0.173645i
$103$	1858.85	+	1073.21i	0.175214	+	0.101160i	0.585042	−	0.811003i	$-0.301078\pi$
$103$	1858.85	+	1073.21i	0.175214	+	0.101160i	−0.409828	+	0.912163i	$0.634411\pi$
$104$	−5611.20	−	5442.10i	−0.518787	−	0.503153i
$105$	53.1124	−	2656.62i	0.00481745	−	0.240963i
$106$	−17188.1	+	8121.90i	−1.52973	+	0.722846i
$107$		−	13846.7i		−	1.20943i	−0.796443	−	0.604713i	$-0.793288\pi$
$107$		−	13846.7i		−	1.20943i	0.796443	−	0.604713i	$-0.206712\pi$
$108$	7932.72	−	8551.07i	0.680103	−	0.733117i
$109$	−19384.9			−1.63159			−0.815793	−	0.578344i	$-0.803699\pi$
$109$	−19384.9			−1.63159			−0.815793	+	0.578344i	$0.803699\pi$
$110$	−1032.05	−	2184.08i	−0.0852930	−	0.180503i
$111$	20599.5	+	411.834i	1.67190	+	0.0334254i
$112$	8787.53	+	10049.0i	0.700536	+	0.801102i
$113$	−6817.20	+	11807.7i	−0.533887	+	0.924719i	0.465329	+	0.885138i	$0.345936\pi$
$113$	−6817.20	+	11807.7i	−0.533887	+	0.924719i	−0.999216	+	0.0395818i	$0.987397\pi$
$114$	8742.15	+	19500.6i	0.672680	+	1.50050i
$115$	2681.71	−	1548.29i	0.202776	−	0.117073i
$116$	−11615.2	−	1926.16i	−0.863201	−	0.143145i
$117$	5285.04	−	8363.13i	0.386079	−	0.610938i
$118$	8581.54	+	706.715i	0.616313	+	0.0507551i
$119$	5539.93	−	3198.48i	0.391211	−	0.225866i
$120$	2295.17	+	2316.82i	0.159387	+	0.160890i
$121$	−1631.91	+	2826.55i	−0.111462	+	0.193057i
$122$	218.117	+	151.076i	0.0146545	+	0.0101502i
$123$	13351.5	−	22093.5i	0.882509	−	1.46034i
$124$	−8776.30	+	3296.05i	−0.570779	+	0.214363i
$125$	−6895.78			−0.441330
$126$	−10167.4	+	13493.4i	−0.640428	+	0.849922i
$127$			15689.6i			0.972754i	0.873749	+	0.486377i	$0.161682\pi$
$127$			15689.6i			0.972754i	−0.873749	+	0.486377i	$0.838318\pi$
$128$	−16362.2	−	844.606i	−0.998670	−	0.0515506i
$129$	17692.7	−	9748.64i	1.06320	−	0.585820i
$130$	2273.89	+	1574.98i	0.134550	+	0.0931941i
$131$	−7250.25	−	4185.93i	−0.422484	−	0.243921i	0.273656	−	0.961828i	$-0.411767\pi$
$131$	−7250.25	−	4185.93i	−0.422484	−	0.243921i	−0.696140	+	0.717907i	$0.745101\pi$
$132$	−2815.15	+	15099.4i	−0.161567	+	0.866587i
$133$	−15477.5	−	26807.7i	−0.874977	−	1.51550i
$134$	−16363.6	−	1347.59i	−0.911319	−	0.0750497i
$135$	−2274.25	+	3444.38i	−0.124788	+	0.188992i
$136$	−1915.80	+	7613.87i	−0.103579	+	0.411650i
$137$	14965.1	+	25920.4i	0.797333	+	1.38102i	0.921347	+	0.388741i	$0.127090\pi$
$137$	14965.1	+	25920.4i	0.797333	+	1.38102i	−0.124014	+	0.992280i	$0.539577\pi$
$138$	−19586.5	−	2007.90i	−1.02849	−	0.105435i
$139$	−20651.8	−	11923.3i	−1.06888	−	0.617118i	−0.141005	−	0.990009i	$-0.545033\pi$
$139$	−20651.8	−	11923.3i	−1.06888	−	0.617118i	−0.927875	+	0.372891i	$0.878367\pi$
$140$	−3649.44	−	2999.36i	−0.186196	−	0.153028i
$141$	8315.02	−	4581.56i	0.418239	−	0.230449i
$142$	8598.76	+	18197.3i	0.426441	+	0.902464i
$143$			13027.6i			0.637078i
$144$	−3200.19	−	20487.6i	−0.154330	−	0.988019i
$145$	4166.34			0.198161
$146$	9783.40	−	4622.95i	0.458970	−	0.216877i
$147$	1481.04	−	2450.76i	0.0685381	−	0.113414i
$148$	23257.0	−	28297.8i	1.06177	−	1.29190i
$149$	−2636.98	+	4567.39i	−0.118778	+	0.205729i	−0.919284	−	0.393596i	$-0.871231\pi$
$149$	−2636.98	+	4567.39i	−0.118778	+	0.205729i	0.800506	+	0.599325i	$0.204564\pi$
$150$	17301.4	+	12502.6i	0.768949	+	0.555669i
$151$	28946.1	−	16712.0i	1.26951	−	0.732951i	0.294614	−	0.955616i	$-0.404809\pi$
$151$	28946.1	−	16712.0i	1.26951	−	0.732951i	0.974895	+	0.222665i	$0.0714756\pi$
$152$	36843.5	+	9270.55i	1.59468	+	0.401253i
$153$	−9928.73	−	397.158i	−0.424142	−	0.0169661i
$154$	1826.02	−	22173.2i	0.0769954	−	0.934945i
$155$	2872.96	−	1658.71i	0.119582	−	0.0690408i
$156$	−5853.25	−	16585.2i	−0.240518	−	0.681508i
$157$	−8500.73	+	14723.7i	−0.344871	+	0.597334i	−0.985330	−	0.170658i	$-0.945411\pi$
$157$	−8500.73	+	14723.7i	−0.344871	+	0.597334i	0.640459	+	0.767992i	$0.278744\pi$
$158$	3145.43	−	4541.25i	0.125999	−	0.181912i
$159$	−42764.9	−	854.976i	−1.69158	−	0.0338189i
$160$	5760.88	−	652.373i	0.225034	−	0.0254833i
$161$	28519.6			1.10025
$162$	24548.0	−	9281.23i	0.935377	−	0.353652i
$163$			30843.8i			1.16089i	0.814298	+	0.580447i	$0.197122\pi$
$163$			30843.8i			1.16089i	−0.814298	+	0.580447i	$0.802878\pi$
$164$	−16135.0	−	42962.3i	−0.599904	−	1.59735i
$165$	108.641	−	5434.12i	0.00399050	−	0.199600i
$166$	−6851.74	+	9892.27i	−0.248648	+	0.358988i
$167$	13682.1	+	7899.35i	0.490591	+	0.283243i	0.724819	−	0.688939i	$-0.241923\pi$
$167$	13682.1	+	7899.35i	0.490591	+	0.283243i	−0.234229	+	0.972181i	$0.575257\pi$
$168$	7637.63	+	29048.6i	0.270607	+	1.02922i
$169$	6821.76	+	11815.6i	0.238849	+	0.413698i
$170$	228.025	−	2768.88i	0.00789015	−	0.0958090i
$171$	−1921.85	+	48045.1i	−0.0657245	+	1.64307i
$172$	5875.12	−	35428.5i	0.198591	−	1.19756i
$173$	−23531.4	−	40757.6i	−0.786241	−	1.36181i	−0.928255	−	0.371944i	$-0.878691\pi$
$173$	−23531.4	−	40757.6i	−0.786241	−	1.36181i	0.142015	−	0.989865i	$-0.454642\pi$
$174$	−21471.6	−	15516.2i	−0.709197	−	0.512490i
$175$	−26777.0	−	15459.7i	−0.874352	−	0.504807i
$176$	17974.9	+	20555.3i	0.580284	+	0.663586i
$177$	16581.3	+	10020.4i	0.529262	+	0.319843i
$178$	11523.7	−	5445.28i	0.363706	−	0.171862i
$179$			2545.69i			0.0794511i	0.999211	+	0.0397256i	$0.0126484\pi$
$179$			2545.69i			0.0794511i	−0.999211	+	0.0397256i	$0.987352\pi$
$180$	2303.21	+	6966.87i	0.0710869	+	0.215027i
$181$	5676.58			0.173272			0.0866362	−	0.996240i	$-0.472388\pi$
$181$	5676.58			0.173272			0.0866362	+	0.996240i	$0.472388\pi$
$182$	10884.1	+	23033.6i	0.328586	+	0.695375i
$183$	288.100	+	522.869i	0.00860282	+	0.0156132i
$184$	−24369.4	+	25126.6i	−0.719795	+	0.742160i
$185$	−6480.77	+	11225.0i	−0.189358	+	0.327977i
$186$	−20983.4	−	2151.09i	−0.606526	−	0.0621775i
$187$	11331.9	−	6542.49i	0.324056	−	0.187094i
$188$	2761.12	−	16650.3i	0.0781214	−	0.471092i
$189$	−34001.2	+	16999.8i	−0.951855	+	0.475906i
$190$	−13398.6	−	1103.41i	−0.371153	−	0.0305655i
$191$	−28127.2	+	16239.2i	−0.771009	+	0.445142i	−0.833234	−	0.552920i	$-0.813513\pi$
$191$	−28127.2	+	16239.2i	−0.771009	+	0.445142i	0.0622257	+	0.998062i	$0.480180\pi$
$192$	−32118.8	−	18092.4i	−0.871279	−	0.490789i
$193$	−393.717	+	681.937i	−0.0105699	+	0.0183075i	−0.871262	−	0.490818i	$-0.836698\pi$
$193$	−393.717	+	681.937i	−0.0105699	+	0.0183075i	0.860692	+	0.509126i	$0.170031\pi$
$194$	15829.9	+	10964.3i	0.420605	+	0.291326i
$195$	3003.47	+	5450.97i	0.0789868	+	0.143352i
$196$	−1789.81	−	4765.68i	−0.0465903	−	0.124055i
$197$	24825.9			0.639694			0.319847	−	0.947469i	$-0.396368\pi$
$197$	24825.9			0.639694			0.319847	+	0.947469i	$0.396368\pi$
$198$	−20797.5	+	27600.7i	−0.530493	+	0.704027i
$199$		−	12008.5i		−	0.303237i	−0.988439	−	0.151619i	$-0.951551\pi$
$199$		−	12008.5i		−	0.303237i	0.988439	−	0.151619i	$-0.0484485\pi$
$200$	36500.8	−	10381.3i	0.912520	−	0.259533i
$201$	−31617.8	−	19107.2i	−0.782600	−	0.472939i
$202$	23086.7	+	15990.7i	0.565794	+	0.391889i
$203$	33231.3	+	19186.1i	0.806409	+	0.465580i
$204$	−11486.9	+	13420.5i	−0.276022	+	0.322484i
$205$	8119.80	+	14063.9i	0.193213	+	0.334656i
$206$	8556.69	+	704.668i	0.201638	+	0.0166054i
$207$	−37449.5	−	23666.1i	−0.873989	−	0.552313i
$208$	−29593.5	−	10092.5i	−0.684020	−	0.233278i
$209$	−31659.1	−	54835.2i	−0.724780	−	1.25536i
$210$	−4347.91	−	9698.61i	−0.0985921	−	0.219923i
$211$	−25764.7	−	14875.2i	−0.578708	−	0.334117i	0.181912	−	0.983315i	$-0.441771\pi$
$211$	−25764.7	−	14875.2i	−0.578708	−	0.334117i	−0.760620	+	0.649198i	$0.775105\pi$
$212$	−48282.1	+	58746.7i	−1.07427	+	1.30711i
$213$	−905.174	+	45275.8i	−0.0199514	+	0.997945i
$214$	−23663.2	−	50077.6i	−0.516708	−	1.09349i
$215$			12708.1i			0.274917i
$216$	14076.0	−	44482.0i	0.301697	−	0.953404i
$217$	30553.5			0.648846
$218$	−70106.6	+	33127.5i	−1.47518	+	0.697069i
$219$	24341.6	+	486.649i	0.507529	+	0.0101468i
$220$	−7464.92	−	6135.18i	−0.154234	−	0.126760i
$221$	−7491.58	+	12975.8i	−0.153387	+	0.265674i
$222$	75203.1	−	33713.8i	1.52591	−	0.684071i
$223$	45854.8	−	26474.3i	0.922093	−	0.532371i	0.0377910	−	0.999286i	$-0.487968\pi$
$223$	45854.8	−	26474.3i	0.922093	−	0.532371i	0.884302	+	0.466915i	$0.154635\pi$
$224$	48953.8	+	21325.6i	0.975642	+	0.425016i
$225$	22332.6	+	42520.4i	0.441137	+	0.839910i
$226$	−4476.18	+	54353.6i	−0.0876376	+	1.06417i
$227$	32593.5	−	18817.9i	0.632528	−	0.365190i	−0.149203	−	0.988807i	$-0.547671\pi$
$227$	32593.5	−	18817.9i	0.632528	−	0.365190i	0.781730	+	0.623616i	$0.214337\pi$
$228$	64941.8	+	55585.3i	1.24926	+	1.06928i
$229$	28619.2	−	49569.9i	0.545741	−	0.945251i	−0.452819	−	0.891603i	$-0.649582\pi$
$229$	28619.2	−	49569.9i	0.545741	−	0.945251i	0.998560	−	0.0536486i	$-0.0170851\pi$
$230$	7052.66	−	10182.4i	0.133321	−	0.192483i
$231$	25890.8	−	42843.0i	0.485201	−	0.802889i
$232$	−45298.9	+	12883.6i	−0.841612	+	0.239366i
$233$	−36468.7			−0.671751			−0.335876	−	0.941906i	$-0.609032\pi$
$233$	−36468.7			−0.671751			−0.335876	+	0.941906i	$0.609032\pi$
$234$	4821.64	−	39277.6i	0.0880569	−	0.717320i
$235$			5972.39i			0.108147i
$236$	32243.4	−	12109.4i	0.578918	−	0.217420i
$237$	10886.3	−	5998.31i	0.193813	−	0.106790i
$238$	14569.5	−	21034.9i	0.257212	−	0.371353i
$239$	−45342.6	−	26178.6i	−0.793799	−	0.458300i	0.0474993	−	0.998871i	$-0.484875\pi$
$239$	−45342.6	−	26178.6i	−0.793799	−	0.458300i	−0.841298	+	0.540571i	$0.818208\pi$
$240$	12259.9	+	4456.61i	0.212846	+	0.0773718i
$241$	6755.56	+	11701.0i	0.116313	+	0.201460i	0.918304	−	0.395877i	$-0.129559\pi$
$241$	6755.56	+	11701.0i	0.116313	+	0.201460i	−0.801991	+	0.597336i	$0.796226\pi$
$242$	−1071.51	+	13011.2i	−0.0182964	+	0.222171i
$243$	58754.3	+	5892.07i	0.995009	+	0.0997827i
$244$	1047.01	+	173.627i	0.0175862	+	0.00291633i
$245$	900.705	+	1560.07i	0.0150055	+	0.0259903i
$246$	10530.2	−	102719.i	0.174006	−	1.69739i
$247$	62789.9	+	36251.8i	1.02919	+	0.594204i
$248$	−26107.3	+	26918.5i	−0.424482	+	0.437671i
$249$	−23713.7	+	13066.2i	−0.382473	+	0.210742i
$250$	−24939.0	+	11784.4i	−0.399024	+	0.188551i
$251$		−	111309.i		−	1.76678i	−0.468635	−	0.883392i	$-0.655254\pi$
$251$		−	111309.i		−	1.76678i	0.468635	−	0.883392i	$-0.344746\pi$
$252$	−13711.9	+	66175.1i	−0.215921	+	1.04206i
$253$	58336.8			0.911385
$254$	26812.4	+	56742.3i	0.415594	+	0.879507i
$255$	3233.12	−	5350.03i	0.0497212	−	0.0822765i
$256$	−60618.4	+	24907.4i	−0.924963	+	0.380057i
$257$	36956.5	−	64010.6i	0.559532	−	0.969138i	−0.438003	−	0.898973i	$-0.644314\pi$
$257$	36956.5	−	64010.6i	0.559532	−	0.969138i	0.997535	−	0.0701645i	$-0.0223524\pi$
$258$	47327.0	−	65492.2i	0.710999	−	0.983899i
$259$	−103383.	+	59688.2i	−1.54117	+	0.889793i
$260$	10915.2	+	1810.08i	0.161468	+	0.0267763i
$261$	−27715.6	−	52769.5i	−0.406858	−	0.774644i
$262$	−33374.5	−	2748.48i	−0.486197	−	0.0400397i
$263$	−6380.84	+	3683.98i	−0.0922500	+	0.0532606i	−0.545415	−	0.838166i	$-0.683628\pi$
$263$	−6380.84	+	3683.98i	−0.0922500	+	0.0532606i	0.453165	+	0.891426i	$0.350295\pi$
$264$	15622.8	+	59418.9i	0.224156	+	0.852544i
$265$	13454.2	−	23303.3i	0.191587	−	0.331838i
$266$	−101788.	−	70502.0i	−1.43858	−	0.996410i
$267$	28671.5	+	573.213i	0.402186	+	0.00804069i
$268$	−61483.1	+	23090.8i	−0.856024	+	0.321491i
$269$	−38604.8			−0.533502			−0.266751	−	0.963765i	$-0.585950\pi$
$269$	−38604.8			−0.533502			−0.266751	+	0.963765i	$0.585950\pi$
$270$	−2338.77	+	16343.4i	−0.0320818	+	0.224189i
$271$		−	12540.3i		−	0.170753i	−0.996349	−	0.0853767i	$-0.972791\pi$
$271$		−	12540.3i		−	0.170753i	0.996349	−	0.0853767i	$-0.0272094\pi$
$272$	6083.01	+	30810.0i	0.0822206	+	0.416442i
$273$	−1145.74	+	57308.8i	−0.0153731	+	0.768946i
$274$	98418.7	+	68168.3i	1.31092	+	0.907990i
$275$	−54772.4	−	31622.8i	−0.724263	−	0.418153i
$276$	−74267.4	+	26210.5i	−0.974945	+	0.344078i
$277$	46052.4	+	79765.0i	0.600195	+	1.03957i	0.992791	+	0.119857i	$0.0382436\pi$
$277$	46052.4	+	79765.0i	0.600195	+	1.03957i	−0.392596	+	0.919711i	$0.628423\pi$
$278$	−95064.9	−	7828.87i	−1.23007	−	0.101300i
$279$	−40120.3	−	25353.9i	−0.515414	−	0.325713i
$280$	−18324.1	−	4610.71i	−0.233726	−	0.0588101i
$281$	−11148.0	−	19308.8i	−0.141183	−	0.244537i	0.786759	−	0.617260i	$-0.211757\pi$
$281$	−11148.0	−	19308.8i	−0.141183	−	0.244537i	−0.927942	+	0.372723i	$0.878424\pi$
$282$	22242.2	−	30779.3i	0.279692	−	0.387044i
$283$	21648.6	+	12498.8i	0.270307	+	0.156062i	0.629027	−	0.777383i	$-0.283453\pi$
$283$	21648.6	+	12498.8i	0.270307	+	0.156062i	−0.358720	+	0.933445i	$0.616787\pi$
$284$	62196.0	+	51116.9i	0.771126	+	0.633764i
$285$	−25888.8	−	15645.1i	−0.318729	−	0.192614i
$286$	22263.4	+	47115.2i	0.272182	+	0.576009i
$287$			149568.i			1.81582i
$288$	−46585.6	−	68625.7i	−0.561652	−	0.827374i
$289$	−68471.9			−0.819816
$290$	15067.8	−	7120.01i	0.179166	−	0.0846612i
$291$	20908.9	+	37947.4i	0.246914	+	0.448122i
$292$	27482.0	−	33438.4i	0.322316	−	0.392175i
$293$	11748.6	−	20349.1i	0.136852	−	0.237034i	−0.789452	−	0.613813i	$-0.789635\pi$
$293$	11748.6	−	20349.1i	0.136852	−	0.237034i	0.926303	+	0.376779i	$0.122968\pi$
$294$	1168.08	−	11394.3i	0.0135138	−	0.131824i
$295$	−10555.0	+	6093.95i	−0.121287	+	0.0700253i
$296$	35751.5	−	142086.i	0.408048	−	1.62169i
$297$	−69549.5	+	34773.1i	−0.788462	+	0.394213i
$298$	−1731.44	+	21024.7i	−0.0194974	+	0.236754i
$299$	−57850.1	+	33399.7i	−0.647085	+	0.373595i
$300$	83937.5	+	15649.4i	0.932639	+	0.173882i
$301$	−58521.0	+	101361.i	−0.645920	+	1.11877i
$302$	76125.6	−	109907.i	0.834673	−	1.20507i
$303$	30494.1	+	55343.3i	0.332147	+	0.602809i
$304$	149090.	−	29435.7i	1.61325	−	0.318513i
$305$	−375.559			−0.00403719
$306$	−36586.6	+	15531.2i	−0.390732	+	0.165868i
$307$		−	32060.0i		−	0.340163i	−0.985430	−	0.170082i	$-0.945597\pi$
$307$		−	32060.0i		−	0.340163i	0.985430	−	0.170082i	$-0.0544031\pi$
$308$	−31288.6	−	83311.2i	−0.329826	−	0.878217i
$309$	16533.2	+	9991.34i	0.173157	+	0.104642i
$310$	7555.63	−	10908.5i	0.0786226	−	0.113512i
$311$	61441.4	+	35473.2i	0.635244	+	0.366758i	0.782780	−	0.622298i	$-0.213801\pi$
$311$	61441.4	+	35473.2i	0.635244	+	0.366758i	−0.147536	+	0.989057i	$0.547134\pi$
$312$	−49511.7	−	49978.5i	−0.508626	−	0.513422i
$313$	−59259.6	−	102641.i	−0.604882	−	1.04769i	−0.992070	−	0.125685i	$-0.959887\pi$
$313$	−59259.6	−	102641.i	−0.604882	−	1.04769i	0.387189	−	0.922001i	$-0.373446\pi$
$314$	−5581.58	+	67776.4i	−0.0566106	+	0.687415i
$315$	955.832	−	23895.3i	0.00963298	−	0.240819i
$316$	3614.95	−	21799.1i	0.0362016	−	0.218305i
$317$	67390.6	+	116724.i	0.670626	+	1.16156i	0.977727	+	0.209882i	$0.0673080\pi$
$317$	67390.6	+	116724.i	0.670626	+	1.16156i	−0.307100	+	0.951677i	$0.599359\pi$
$318$	−156123.	+	69990.4i	−1.54388	+	0.692124i
$319$	67974.6	+	39245.2i	0.667983	+	0.385660i
$320$	19719.7	−	12204.3i	0.192576	−	0.119183i
$321$	2490.97	−	124596.i	0.0241746	−	1.20918i
$322$	103143.	−	48738.2i	0.994782	−	0.470065i
$323$		−	72822.8i		−	0.698011i
$324$	72918.5	−	75517.2i	0.694621	−	0.719376i
$325$	72420.4			0.685637
$326$	52710.0	+	111548.i	0.495973	+	1.04961i
$327$	−174429.	−	3487.26i	−1.63126	−	0.0326129i
$328$	−131773.	−	127802.i	−1.22484	−	1.18793i
$329$	−27503.0	+	47636.7i	−0.254091	+	0.440098i
$330$	−8893.65	−	19838.5i	−0.0816680	−	0.182172i
$331$	−133143.	+	76870.2i	−1.21524	+	0.701620i	−0.963896	−	0.266278i	$-0.914206\pi$
$331$	−133143.	+	76870.2i	−1.21524	+	0.701620i	−0.251345	+	0.967898i	$0.580873\pi$
$332$	−7874.49	+	47485.2i	−0.0714408	+	0.430806i
$333$	185284.	+	7411.54i	1.67090	+	0.0668374i
$334$	62981.6	+	5186.72i	0.564574	+	0.0464943i
$335$	20126.8	−	11620.2i	0.179343	−	0.103544i
$336$	77264.2	+	92003.9i	0.684384	+	0.814944i
$337$	11471.8	−	19869.8i	0.101012	−	0.174958i	−0.811090	−	0.584922i	$-0.801125\pi$
$337$	11471.8	−	19869.8i	0.101012	−	0.174958i	0.912102	+	0.409964i	$0.134459\pi$
$338$	44863.5	+	31074.1i	0.392699	+	0.271997i
$339$	−63466.7	+	105022.i	−0.552264	+	0.913863i
$340$	−3907.17	−	10403.5i	−0.0337990	−	0.0899958i
$341$	62497.2			0.537467
$342$	75155.6	+	177043.i	0.642553	+	1.51365i
$343$		−	108611.i		−	0.923175i
$344$	−39297.3	−	138170.i	−0.332082	−	1.16760i
$345$	24409.1	−	13449.4i	0.205076	−	0.112996i
$346$	−154755.	−	107189.i	−1.29268	−	0.895358i
$347$	−6260.87	−	3614.72i	−0.0519967	−	0.0300203i	0.473776	−	0.880645i	$-0.342891\pi$
$347$	−6260.87	−	3614.72i	−0.0519967	−	0.0300203i	−0.525773	+	0.850625i	$0.676224\pi$
$348$	−104170.	−	19421.5i	−0.860167	−	0.160370i
$349$	−55282.6	−	95752.3i	−0.453877	−	0.786137i	0.544746	−	0.838601i	$-0.316626\pi$
$349$	−55282.6	−	95752.3i	−0.453877	−	0.786137i	−0.998623	+	0.0524636i	$0.983293\pi$
$350$	−123260.	−	10150.9i	−1.00621	−	0.0828641i
$351$	49060.4	−	74302.3i	0.398214	−	0.603098i
$352$	100135.	+	43621.5i	0.808165	+	0.352059i
$353$	30801.7	+	53350.1i	0.247187	+	0.428140i	0.962744	−	0.270414i	$-0.0871605\pi$
$353$	30801.7	+	53350.1i	0.247187	+	0.428140i	−0.715557	+	0.698554i	$0.753827\pi$
$354$	77091.3	+	7902.95i	0.615175	+	0.0630642i
$355$	−24671.6	−	14244.1i	−0.195767	−	0.113026i
$356$	32370.4	−	39386.4i	0.255416	−	0.310775i
$357$	50424.8	−	27784.0i	0.395647	−	0.218001i
$358$	4350.43	+	9206.66i	0.0339442	+	0.0718350i
$359$			84462.7i			0.655354i	0.944790	+	0.327677i	$0.106266\pi$
$359$			84462.7i			0.655354i	−0.944790	+	0.327677i	$0.893734\pi$
$360$	20235.7	+	21260.1i	0.156139	+	0.164044i
$361$	−222069.			−1.70401
$362$	20529.7	−	9700.91i	0.156663	−	0.0740279i
$363$	−15192.7	+	25140.3i	−0.115298	+	0.190791i
$364$	78725.9	+	64702.3i	0.594176	+	0.488334i
$365$	−7658.07	+	13264.2i	−0.0574823	+	0.0995622i
$366$	1935.48	+	1398.65i	0.0144486	+	0.0104411i
$367$	161018.	−	92963.9i	1.19548	−	0.690212i	0.235937	−	0.971768i	$-0.424184\pi$
$367$	161018.	−	92963.9i	1.19548	−	0.690212i	0.959545	+	0.281556i	$0.0908507\pi$
$368$	−45193.7	+	132518.i	−0.333720	+	0.978538i
$369$	124114.	−	196399.i	0.911522	−	1.44241i
$370$	−4255.27	+	51671.2i	−0.0310831	+	0.377438i
$371$	214625.	−	123914.i	1.55931	−	0.900268i
$372$	−79563.9	+	28079.7i	−0.574950	+	0.202911i
$373$	42545.6	−	73691.2i	0.305800	−	0.529661i	−0.671639	−	0.740878i	$-0.734409\pi$
$373$	42545.6	−	73691.2i	0.305800	−	0.529661i	0.977439	+	0.211217i	$0.0677428\pi$
$374$	29801.9	−	43026.9i	0.213060	−	0.307607i
$375$	−62049.6	−	1240.52i	−0.441241	−	0.00882150i
$376$	−18468.5	−	64935.4i	−0.130634	−	0.459310i
$377$	−89876.5			−0.632359
$378$	−93916.0	+	119587.i	−0.657288	+	0.836951i
$379$		−	146982.i		−	1.02326i	−0.859206	−	0.511630i	$-0.829042\pi$
$379$		−	146982.i		−	1.02326i	0.859206	−	0.511630i	$-0.170958\pi$
$380$	−50342.6	+	18906.8i	−0.348633	+	0.130934i
$381$	−2822.49	+	141178.i	−0.0194439	+	0.972560i
$382$	−73971.9	+	106798.i	−0.506921	+	0.731872i
$383$	161253.	+	93099.7i	1.09929	+	0.634674i	0.936034	−	0.351910i	$-0.114468\pi$
$383$	161253.	+	93099.7i	1.09929	+	0.634674i	0.163254	+	0.986584i	$0.447801\pi$
$384$	−147079.	−	10543.4i	−0.997440	−	0.0715022i
$385$	15745.7	+	27272.3i	0.106228	+	0.183993i
$386$	−258.515	+	3139.11i	−0.00173504	+	0.0210684i
$387$	160956.	−	84537.3i	1.07470	−	0.564452i
$388$	75987.2	+	12601.0i	0.504751	+	0.0837030i
$389$	128002.	+	221706.i	0.845897	+	1.46514i	0.884840	+	0.465894i	$0.154267\pi$
$389$	128002.	+	221706.i	0.845897	+	1.46514i	−0.0389437	+	0.999241i	$0.512399\pi$
$390$	20177.6	+	14581.1i	0.132660	+	0.0958649i
$391$	58104.8	+	33546.8i	0.380066	+	0.219431i
$392$	−14617.2	−	14176.7i	−0.0951245	−	0.0922579i
$393$	−64486.2	−	38970.2i	−0.417524	−	0.252317i
$394$	89784.4	−	42425.9i	0.578374	−	0.273299i
$395$			7819.24i			0.0501153i
$396$	−28047.6	+	135361.i	−0.178857	+	0.863184i
$397$	−260735.			−1.65432			−0.827159	−	0.561968i	$-0.810044\pi$
$397$	−260735.			−1.65432			−0.827159	+	0.561968i	$0.810044\pi$
$398$	−20521.7	−	43429.5i	−0.129553	−	0.274169i
$399$	−134447.	−	244006.i	−0.844509	−	1.53269i
$400$	114267.	−	99922.3i	0.714166	−	0.624514i
$401$	−26507.0	+	45911.4i	−0.164843	+	0.285517i	−0.936600	−	0.350401i	$-0.886045\pi$
$401$	−26507.0	+	45911.4i	−0.164843	+	0.285517i	0.771756	+	0.635918i	$0.219379\pi$
$402$	−147001.	−	15069.7i	−0.909636	−	0.0932506i
$403$	−61975.7	+	35781.7i	−0.381603	+	0.220318i
$404$	110821.	+	18377.6i	0.678986	+	0.112597i
$405$	−21083.8	+	30584.1i	−0.128540	+	0.186460i
$406$	152971.	+	12597.6i	0.928019	+	0.0764251i
$407$	−211470.	+	122092.i	−1.27661	+	0.737053i
$408$	−18608.5	+	68166.5i	−0.111787	+	0.409497i
$409$	−73697.8	+	127648.i	−0.440563	+	0.763078i	−0.997731	−	0.0673220i	$-0.978555\pi$
$409$	−73697.8	+	127648.i	−0.440563	+	0.763078i	0.557168	+	0.830400i	$0.311888\pi$
$410$	53400.1	+	36986.8i	0.317668	+	0.220028i
$411$	129996.	+	235929.i	0.769569	+	1.39668i
$412$	32150.1	−	12074.4i	0.189403	−	0.0711328i
$413$	−112251.			−0.658099
$414$	−175883.	−	21591.0i	−1.02618	−	0.125972i
$415$		−	17032.8i		−	0.0988983i
$416$	−124274.	+	14073.0i	−0.718115	+	0.0813206i
$417$	−183684.	−	111004.i	−1.05633	−	0.638360i
$418$	−208207.	−	144212.i	−1.19163	−	0.825368i
$419$	−201431.	−	116296.i	−1.14736	−	0.662426i	−0.199115	−	0.979976i	$-0.563807\pi$
$419$	−201431.	−	116296.i	−1.14736	−	0.662426i	−0.948242	+	0.317550i	$0.897140\pi$
$420$	−32298.8	−	27645.3i	−0.183100	−	0.156720i
$421$	34900.8	+	60449.9i	0.196911	+	0.341060i	0.947525	−	0.319680i	$-0.103576\pi$
$421$	34900.8	+	60449.9i	0.196911	+	0.341060i	−0.750614	+	0.660741i	$0.770242\pi$
$422$	−118600.	−	9767.08i	−0.665980	−	0.0548454i
$423$	75644.4	−	39729.9i	0.422762	−	0.222043i
$424$	−74220.8	+	294972.i	−0.412852	+	1.64078i
$425$	−36369.7	−	62994.1i	−0.201355	−	0.348756i
$426$	74099.8	+	165290.i	0.408317	+	0.910807i
$427$	−2995.51	−	1729.46i	−0.0164292	−	0.00948539i
$428$	−171159.	−	140670.i	−0.934354	−	0.767916i
$429$	−2343.62	+	117225.i	−0.0127342	+	0.636951i
$430$	21717.3	+	45959.5i	0.117454	+	0.248564i
$431$		−	147873.i		−	0.796037i	−0.917377	−	0.398019i	$-0.869698\pi$
$431$		−	147873.i		−	0.796037i	0.917377	−	0.398019i	$-0.130302\pi$
$432$	−25110.3	−	184927.i	−0.134550	−	0.990907i
$433$	294850.			1.57262			0.786312	−	0.617830i	$-0.211988\pi$
$433$	294850.			1.57262			0.786312	+	0.617830i	$0.211988\pi$
$434$	110499.	−	52214.0i	0.586649	−	0.277209i
$435$	37489.6	+	749.509i	0.198122	+	0.00396094i
$436$	−196932.	+	239615.i	−1.03596	+	1.26050i
$437$	162333.	−	281169.i	0.850050	−	1.47233i
$438$	88864.7	−	39838.3i	0.463213	−	0.207660i
$439$	−62468.0	+	36065.9i	−0.324137	+	0.187140i	−0.653235	−	0.757155i	$-0.726589\pi$
$439$	−62468.0	+	36065.9i	−0.324137	+	0.187140i	0.329098	+	0.944296i	$0.393255\pi$
$440$	−37482.0	−	9431.20i	−0.193605	−	0.0487149i
$441$	13767.6	−	21786.0i	0.0707914	−	0.112021i
$442$	−4918.98	+	59730.5i	−0.0251785	+	0.305739i
$443$	165331.	−	95453.7i	0.842453	−	0.486391i	−0.0156440	−	0.999878i	$-0.504980\pi$
$443$	165331.	−	95453.7i	0.842453	−	0.486391i	0.858097	+	0.513487i	$0.171647\pi$
$444$	214362.	−	250445.i	1.08738	−	1.27042i
$445$	−9020.28	+	15623.6i	−0.0455512	+	0.0788970i
$446$	120594.	−	174109.i	0.606255	−	0.875288i
$447$	−24549.7	+	40623.9i	−0.122866	+	0.203314i
$448$	213489.	−	6533.50i	1.06370	−	0.0325529i
$449$	192859.			0.956639			0.478319	−	0.878186i	$-0.341246\pi$
$449$	192859.			0.956639			0.478319	+	0.878186i	$0.341246\pi$
$450$	153432.	+	115613.i	0.757688	+	0.570928i
$451$			305940.i			1.50412i
$452$	76698.5	+	204223.i	0.375414	+	0.999603i
$453$	263469.	−	145171.i	1.28391	−	0.707429i
$454$	85718.0	−	123756.i	0.415873	−	0.600421i
$455$	−31228.6	−	18029.8i	−0.150844	−	0.0870901i
$456$	329858.	+	90046.3i	1.58634	+	0.433048i
$457$	2962.66	+	5131.48i	0.0141857	+	0.0245703i	0.873031	−	0.487665i	$-0.162151\pi$
$457$	2962.66	+	5131.48i	0.0141857	+	0.0245703i	−0.858845	+	0.512235i	$0.828818\pi$
$458$	18791.4	−	228181.i	0.0895834	−	1.08780i
$459$	−89269.3	−	5359.85i	−0.423718	−	0.0254406i
$460$	8105.41	−	48877.7i	0.0383053	−	0.230991i
$461$	−63341.9	−	109711.i	−0.298050	−	0.516238i	0.677640	−	0.735394i	$-0.263003\pi$
$461$	−63341.9	−	109711.i	−0.298050	−	0.516238i	−0.975690	+	0.219156i	$0.929670\pi$
$462$	20419.8	−	199190.i	0.0956682	−	0.933219i
$463$	204011.	+	117786.i	0.951682	+	0.549454i	0.893603	−	0.448858i	$-0.148169\pi$
$463$	204011.	+	117786.i	0.951682	+	0.549454i	0.0580790	+	0.998312i	$0.481502\pi$
$464$	−141809.	+	124007.i	−0.658671	+	0.575985i
$465$	26149.9	−	14408.5i	0.120938	−	0.0666367i
$466$	−131891.	+	62322.7i	−0.607358	+	0.286995i
$467$		−	97776.2i		−	0.448332i	−0.974551	−	0.224166i	$-0.928034\pi$
$467$		−	97776.2i		−	0.448332i	0.974551	−	0.224166i	$-0.0719658\pi$
$468$	−49685.1	−	150290.i	−0.226848	−	0.686180i
$469$	214045.			0.973105
$470$	10206.4	+	21599.5i	0.0462039	+	0.0977798i
$471$	−79140.0	+	130957.i	−0.356742	+	0.590321i
$472$	95916.2	−	98896.5i	0.430534	−	0.443912i
$473$	−119705.	+	207334.i	−0.535043	+	0.926721i
$474$	29120.2	−	40297.2i	0.129610	−	0.179357i
$475$	−304829.	+	175993.i	−1.35104	+	0.780024i
$476$	16744.3	−	100972.i	0.0739015	−	0.445645i
$477$	−384653.	−	15386.5i	−1.69057	−	0.0676243i
$478$	−208722.	−	17188.8i	−0.913508	−	0.0752300i
$479$	−349162.	+	201589.i	−1.52179	+	0.878608i	−0.522126	+	0.852869i	$0.674861\pi$
$479$	−349162.	+	201589.i	−1.52179	+	0.878608i	−0.999669	+	0.0257398i	$0.991806\pi$
$480$	51954.9	−	4833.82i	0.225499	−	0.0209801i
$481$	139803.	−	242147.i	0.604266	−	1.04662i
$482$	44428.1	+	30772.5i	0.191233	+	0.132455i
$483$	256625.	+	5130.57i	1.10003	+	0.0219923i
$484$	18360.2	+	48887.1i	0.0783766	+	0.208691i
$485$	−27256.3			−0.115873
$486$	222558.	−	79098.3i	0.942259	−	0.334884i
$487$		−	195207.i		−	0.823071i	−0.911394	−	0.411536i	$-0.864993\pi$
$487$		−	195207.i		−	0.823071i	0.911394	−	0.411536i	$-0.135007\pi$
$488$	4083.30	−	1161.35i	0.0171464	−	0.00487665i
$489$	−5548.68	+	277538.i	−0.0232045	+	1.16066i
$490$	5923.51	+	4102.83i	0.0246710	+	0.0170880i
$491$	−65937.1	−	38068.8i	−0.273506	−	0.157909i	0.356974	−	0.934114i	$-0.383809\pi$
$491$	−65937.1	−	38068.8i	−0.273506	−	0.157909i	−0.630480	+	0.776206i	$0.717142\pi$
$492$	−137458.	−	389486.i	−0.567856	−	1.60902i
$493$	45136.2	+	78178.1i	0.185708	+	0.321656i
$494$	289036.	+	23802.9i	1.18440	+	0.0975386i
$495$	1955.15	−	48877.7i	0.00797941	−	0.199481i
$496$	−48416.8	+	141968.i	−0.196803	+	0.577069i
$497$	−131189.	−	227226.i	−0.531111	−	0.919912i
$498$	−63432.9	+	87780.0i	−0.255774	+	0.353946i
$499$	−12618.3	−	7285.17i	−0.0506757	−	0.0292576i	0.474448	−	0.880283i	$-0.342648\pi$
$499$	−12618.3	−	7285.17i	−0.0506757	−	0.0292576i	−0.525124	+	0.851026i	$0.675981\pi$
$500$	−70054.7	+	85238.4i	−0.280219	+	0.340953i
$501$	121693.	+	73541.3i	0.484831	+	0.292992i
$502$	−190220.	−	402557.i	−0.754830	−	1.59742i
$503$			280154.i			1.10729i	0.832753	+	0.553645i	$0.186764\pi$
$503$			280154.i			1.10729i	−0.832753	+	0.553645i	$0.813236\pi$
$504$	63499.2	+	262759.i	0.249981	+	1.03442i
$505$	−39751.2			−0.155872
$506$	210979.	−	99693.9i	0.824020	−	0.389375i
$507$	59258.0	+	107547.i	0.230532	+	0.418390i
$508$	193938.	+	159391.i	0.751511	+	0.617643i
$509$	−101505.	+	175811.i	−0.391787	+	0.678595i	−0.992685	−	0.120731i	$-0.961476\pi$
$509$	−101505.	+	175811.i	−0.391787	+	0.678595i	0.600899	+	0.799325i	$0.294810\pi$
$510$	2549.93	−	24873.9i	0.00980364	−	0.0956321i
$511$	−122164.	+	70531.3i	−0.467843	+	0.270110i
$512$	−176665.	+	193672.i	−0.673924	+	0.738801i
$513$	−25936.3	+	431974.i	−0.0985539	+	1.64143i
$514$	24265.7	−	294655.i	0.0918472	−	1.11529i
$515$	−10524.5	+	6076.30i	−0.0396813	+	0.0229100i
$516$	59239.0	−	317736.i	0.222489	−	1.19335i
$517$	−56257.4	+	97440.7i	−0.210474	+	0.364552i
$518$	−271888.	+	392541.i	−1.01328	+	1.46294i
$519$	−204408.	−	370978.i	−0.758863	−	1.37725i
$520$	42568.9	−	12107.2i	0.157429	−	0.0447750i
$521$	−30822.1			−0.113550			−0.0567749	−	0.998387i	$-0.518082\pi$
$521$	−30822.1			−0.113550			−0.0567749	+	0.998387i	$0.518082\pi$
$522$	−190415.	−	143480.i	−0.698811	−	0.526564i
$523$		−	94412.3i		−	0.345164i	−0.984995	−	0.172582i	$-0.944789\pi$
$523$		−	94412.3i		−	0.345164i	0.984995	−	0.172582i	$-0.0552109\pi$
$524$	−125398.	+	47094.8i	−0.456697	+	0.171518i
$525$	−238164.	−	143927.i	−0.864087	−	0.522183i
$526$	−16781.0	+	24227.8i	−0.0606523	+	0.0875674i
$527$	62248.6	+	35939.3i	0.224134	+	0.129404i
$528$	158044.	+	188194.i	0.566904	+	0.675053i
$529$	9641.45	+	16699.5i	0.0344533	+	0.0596749i
$530$	8834.03	−	107270.i	0.0314490	−	0.381881i
$531$	147399.	+	93148.0i	0.522763	+	0.330358i
$532$	−488606.	−	81025.8i	−1.72638	−	0.286286i
$533$	−175161.	−	303387.i	−0.616570	−	1.06793i
$534$	104672.	−	46924.6i	0.367068	−	0.164558i
$535$	67894.3	+	39198.8i	0.237206	+	0.136951i
$536$	−182897.	+	188580.i	−0.636615	+	0.656396i
$537$	−457.961	+	22906.7i	−0.00158811	+	0.0794352i
$538$	−139617.	+	65973.1i	−0.482361	+	0.227930i
$539$			33937.0i			0.116814i
$540$	19471.5	+	63103.6i	0.0667746	+	0.216405i
$541$	166561.			0.569087			0.284544	−	0.958663i	$-0.408158\pi$
$541$	166561.			0.569087			0.284544	+	0.958663i	$0.408158\pi$
$542$	−21430.6	−	45352.8i	−0.0729517	−	0.154385i
$543$	51079.0	+	1021.20i	0.173238	+	0.00346345i
$544$	74651.9	+	101031.i	0.252257	+	0.341395i
$545$	54876.8	−	95049.4i	0.184755	−	0.320005i
$546$	93793.4	+	209219.i	0.314621	+	0.701804i
$547$	256245.	−	147943.i	0.856410	−	0.494448i	−0.00639865	−	0.999980i	$-0.502037\pi$
$547$	256245.	−	147943.i	0.856410	−	0.494448i	0.862808	+	0.505531i	$0.168703\pi$
$548$	472433.	+	78343.7i	1.57318	+	0.260881i
$549$	2498.32	+	4756.71i	0.00828902	+	0.0157820i
$550$	−252129.	−	20763.6i	−0.833485	−	0.0686399i
$551$	378304.	−	218414.i	1.24606	−	0.719411i
$552$	−223801.	+	221710.i	−0.734486	+	0.727624i
$553$	−36007.8	+	62367.3i	−0.117746	+	0.203942i
$554$	302865.	+	209775.i	0.986800	+	0.683492i
$555$	−60334.6	+	99839.1i	−0.195876	+	0.324127i
$556$	−357187.	+	134146.i	−1.15544	+	0.433939i
$557$	−30600.2			−0.0986312			−0.0493156	−	0.998783i	$-0.515704\pi$
$557$	−30600.2			−0.0986312			−0.0493156	+	0.998783i	$0.515704\pi$
$558$	−188426.	−	23130.8i	−0.605162	−	0.0742886i
$559$		−	274139.i		−	0.877298i
$560$	−74149.8	+	14639.8i	−0.236447	+	0.0466832i
$561$	103144.	−	56832.1i	0.327731	−	0.180579i
$562$	−73314.9	−	50780.5i	−0.232124	−	0.160777i
$563$	210267.	+	121398.i	0.663369	+	0.382996i	0.793559	−	0.608493i	$-0.208226\pi$
$563$	210267.	+	121398.i	0.663369	+	0.382996i	−0.130191	+	0.991489i	$0.541559\pi$
$564$	27840.5	−	149326.i	0.0875222	−	0.469437i
$565$	−38597.8	−	66853.3i	−0.120911	−	0.209424i
$566$	99653.3	+	8206.73i	0.311070	+	0.0256175i
$567$	−309008.	+	146851.i	−0.961178	+	0.456785i
$568$	312291.	+	78578.6i	0.967973	+	0.243561i
$569$	−148459.	−	257138.i	−0.458545	−	0.794223i	0.540339	−	0.841447i	$-0.318296\pi$
$569$	−148459.	−	257138.i	−0.458545	−	0.794223i	−0.998884	+	0.0472242i	$0.984962\pi$
$570$	−120365.	−	12339.1i	−0.370468	−	0.0379782i
$571$	−228446.	−	131893.i	−0.700665	−	0.404529i	0.106930	−	0.994267i	$-0.465898\pi$
$571$	−228446.	−	131893.i	−0.700665	−	0.404529i	−0.807595	+	0.589737i	$0.799231\pi$
$572$	161034.	+	132349.i	0.492181	+	0.404508i
$573$	−256015.	+	141064.i	−0.779752	+	0.429642i
$574$	255601.	+	540921.i	0.775781	+	1.64176i
$575$		−	324294.i		−	0.980852i
$576$	−285757.	−	168577.i	−0.861295	−	0.508106i
$577$	350367.			1.05238			0.526188	−	0.850368i	$-0.323621\pi$
$577$	350367.			1.05238			0.526188	+	0.850368i	$0.323621\pi$
$578$	−247633.	+	117014.i	−0.741229	+	0.350253i
$579$	−3665.42	+	6065.38i	−0.0109337	+	0.0180926i
$580$	42326.2	−	51499.9i	0.125821	−	0.153091i
$581$	78436.3	−	135856.i	0.232362	−	0.402463i
$582$	140468.	+	101507.i	0.414698	+	0.299675i
$583$	439015.	−	253466.i	1.29164	−	0.745730i
$584$	42246.2	−	167897.i	0.123869	−	0.492286i
$585$	26045.3	+	49589.3i	0.0761057	+	0.144903i
$586$	7714.12	−	93671.5i	0.0224642	−	0.272780i
$587$	5965.76	−	3444.33i	0.0173137	−	0.00999606i	−0.491318	−	0.870980i	$-0.663485\pi$
$587$	5965.76	−	3444.33i	0.0173137	−	0.00999606i	0.508632	+	0.860984i	$0.330151\pi$
$588$	−15247.8	−	43204.5i	−0.0441013	−	0.124961i
$589$	173910.	−	301221.i	0.501296	−	0.868270i
$590$	−27758.8	+	40077.0i	−0.0797437	+	0.115131i
$591$	223388.	+	4466.08i	0.639566	+	0.0127865i
$592$	−113517.	−	574959.i	−0.323906	−	1.64056i
$593$	544416.			1.54818			0.774090	−	0.633076i	$-0.218208\pi$
$593$	544416.			1.54818			0.774090	+	0.633076i	$0.218208\pi$
$594$	−192105.	+	244615.i	−0.544460	+	0.693282i
$595$			36218.4i			0.102305i
$596$	29668.0	+	78996.0i	0.0835209	+	0.222389i
$597$	2160.28	−	108055.i	0.00606125	−	0.303177i
$598$	−152140.	+	219654.i	−0.425444	+	0.614239i
$599$	122771.	+	70881.9i	0.342170	+	0.197552i	0.661231	−	0.750182i	$-0.270034\pi$
$599$	122771.	+	70881.9i	0.342170	+	0.197552i	−0.319061	+	0.947734i	$0.603367\pi$
$600$	330309.	−	86846.8i	0.917526	−	0.241241i
$601$	265380.	+	459652.i	0.734715	+	1.27256i	0.954848	+	0.297094i	$0.0960176\pi$
$601$	265380.	+	459652.i	0.734715	+	1.27256i	−0.220133	+	0.975470i	$0.570649\pi$
$602$	−38424.9	+	466588.i	−0.106028	+	1.28748i
$603$	−281066.	−	177619.i	−0.772990	−	0.488488i
$604$	87488.8	−	527580.i	0.239816	−	1.44615i
$605$	−9239.58	−	16003.4i	−0.0252430	−	0.0437222i
$606$	204862.	+	148040.i	0.557848	+	0.403120i
$607$	−35215.7	−	20331.8i	−0.0955782	−	0.0551821i	0.451449	−	0.892297i	$-0.350907\pi$
$607$	−35215.7	−	20331.8i	−0.0955782	−	0.0551821i	−0.547027	+	0.837115i	$0.684241\pi$
$608$	488889.	−	361241.i	1.32252	−	0.977214i
$609$	295570.	+	178619.i	0.796942	+	0.481606i
$610$	−1358.23	+	641.807i	−0.00365019	+	0.00172482i
$611$		−	128837.i		−	0.345110i
$612$	−105776.	+	118694.i	−0.282413	+	0.316902i
$613$	−498556.			−1.32676			−0.663382	−	0.748281i	$-0.730879\pi$
$613$	−498556.			−1.32676			−0.663382	+	0.748281i	$0.730879\pi$
$614$	−54788.5	−	115947.i	−0.145329	−	0.307555i
$615$	70533.5	+	128011.i	0.186486	+	0.338451i
$616$	−255531.	−	247830.i	−0.673413	−	0.653120i
$617$	45030.4	−	77995.0i	0.118287	−	0.204879i	−0.800802	−	0.598929i	$-0.795593\pi$
$617$	45030.4	−	77995.0i	0.118287	−	0.204879i	0.919089	+	0.394050i	$0.128926\pi$
$618$	76868.1	+	7880.06i	0.201265	+	0.0206325i
$619$	149379.	−	86244.1i	0.389860	−	0.225086i	−0.292240	−	0.956345i	$-0.594400\pi$
$619$	149379.	−	86244.1i	0.389860	−	0.225086i	0.682099	+	0.731259i	$0.261067\pi$
$620$	8683.45	−	52363.5i	0.0225896	−	0.136221i
$621$	−332721.	−	219689.i	−0.862774	−	0.569673i
$622$	282828.	+	23291.7i	0.731042	+	0.0602034i
$623$	−143894.	+	83077.2i	−0.370738	+	0.214045i
$624$	−264472.	−	96138.4i	−0.679221	−	0.246904i
$625$	−165774.	+	287128.i	−0.424380	+	0.735049i
$626$	−389723.	−	269936.i	−0.994505	−	0.688830i
$627$	−275011.	−	499114.i	−0.699543	−	1.26959i
$628$	95639.3	+	254656.i	0.242503	+	0.645706i
$629$	−280838.			−0.709831
$630$	−37378.6	−	88052.2i	−0.0941765	−	0.221850i
$631$			210621.i			0.528985i	0.964388	+	0.264492i	$0.0852044\pi$
$631$			210621.i			0.528985i	−0.964388	+	0.264492i	$0.914796\pi$
$632$	−24179.5	−	85015.4i	−0.0605359	−	0.212845i
$633$	−229160.	−	138485.i	−0.571914	−	0.345618i
$634$	443196.	+	306973.i	1.10260	+	0.763699i
$635$	−76930.2	−	44415.7i	−0.190787	−	0.110151i
$636$	−445020.	+	519929.i	−1.10018	+	1.28538i
$637$	−19430.1	−	33653.9i	−0.0478846	−	0.0829385i
$638$	312902.	+	25768.4i	0.768718	+	0.0633061i
$639$	−16289.9	+	407238.i	−0.0398948	+	0.997347i
$640$	50461.3	−	77837.5i	0.123196	−	0.190033i
$641$	232262.	+	402289.i	0.565278	+	0.979089i	0.997024	+	0.0770943i	$0.0245642\pi$
$641$	232262.	+	402289.i	0.565278	+	0.979089i	−0.431746	+	0.901995i	$0.642102\pi$
$642$	−203917.	−	454865.i	−0.494748	−	1.10360i
$643$	−361978.	−	208988.i	−0.875509	−	0.505476i	−0.00633423	−	0.999980i	$-0.502016\pi$
$643$	−361978.	−	208988.i	−0.875509	−	0.505476i	−0.869175	+	0.494504i	$0.835350\pi$
$644$	289733.	−	352530.i	0.698596	−	0.850010i
$645$	−2286.13	+	114350.i	−0.00549518	+	0.274863i
$646$	−124450.	−	263368.i	−0.298214	−	0.631101i
$647$			825841.i			1.97282i	0.164299	+	0.986411i	$0.447464\pi$
$647$			825841.i			1.97282i	−0.164299	+	0.986411i	$0.552536\pi$
$648$	134660.	−	397726.i	0.320694	−	0.947183i
$649$	−229610.			−0.545131
$650$	261913.	−	123762.i	0.619913	−	0.292928i
$651$	274927.	+	5496.46i	0.648717	+	0.0129694i
$652$	381258.	+	313344.i	0.896859	+	0.737100i
$653$	−164273.	+	284529.i	−0.385247	+	0.667267i	−0.991803	−	0.127773i	$-0.959217\pi$
$653$	−164273.	+	284529.i	−0.385247	+	0.667267i	0.606557	+	0.795040i	$0.292550\pi$
$654$	−636793.	+	285476.i	−1.48882	+	0.667443i
$655$	41049.6	−	23700.0i	0.0956811	−	0.0552415i
$656$	−694972.	−	237013.i	−1.61495	−	0.550762i
$657$	218943.	+	8757.93i	0.507225	+	0.0202895i
$658$	−18058.5	+	219282.i	−0.0417090	+	0.506467i
$659$	−144939.	+	83680.3i	−0.333744	+	0.192687i	−0.657502	−	0.753453i	$-0.728387\pi$
$659$	−144939.	+	83680.3i	−0.333744	+	0.192687i	0.323758	+	0.946140i	$0.395054\pi$
$660$	−66067.2	−	56548.5i	−0.151669	−	0.129818i
$661$	152616.	−	264339.i	0.349300	−	0.605005i	−0.636826	−	0.771008i	$-0.719753\pi$
$661$	152616.	−	264339.i	0.349300	−	0.605005i	0.986125	+	0.166003i	$0.0530862\pi$
$662$	−350154.	+	505539.i	−0.798994	+	1.15356i
$663$	−69745.1	+	115411.i	−0.158667	+	0.262555i
$664$	52670.6	+	185190.i	0.119463	+	0.420032i
$665$	175261.			0.396317
$666$	682758.	−	289834.i	1.53928	−	0.653434i
$667$			402461.i			0.904633i
$668$	236641.	−	88873.4i	0.530318	−	0.199168i
$669$	417373.	−	229972.i	0.932550	−	0.513833i
$670$	52931.6	−	76420.5i	0.117914	−	0.170240i
$671$	−6127.32	−	3537.61i	−0.0136090	−	0.00785715i
$672$	436660.	+	200699.i	0.966951	+	0.444433i
$673$	−403032.	−	698073.i	−0.889836	−	1.54124i	−0.840069	−	0.542480i	$-0.817485\pi$
$673$	−403032.	−	698073.i	−0.889836	−	1.54124i	−0.0497671	−	0.998761i	$-0.515848\pi$
$674$	7532.41	−	91465.0i	0.0165811	−	0.201342i
$675$	193304.	+	386625.i	0.424261	+	0.848560i
$676$	215355.	+	35712.5i	0.471262	+	0.0781496i
$677$	183117.	+	317169.i	0.399533	+	0.692011i	0.993668	−	0.112354i	$-0.0358390\pi$
$677$	183117.	+	317169.i	0.399533	+	0.692011i	−0.594136	+	0.804365i	$0.702506\pi$
$678$	−50055.6	+	488280.i	−0.108891	+	1.06221i
$679$	−217400.	−	125516.i	−0.471542	−	0.272245i
$680$	−31909.5	−	30947.9i	−0.0690084	−	0.0669288i
$681$	296668.	−	163464.i	0.639701	−	0.352474i
$682$	226025.	−	106804.i	0.485946	−	0.229624i
$683$		−	398332.i		−	0.853894i	−0.904277	−	0.426947i	$-0.859589\pi$
$683$		−	398332.i		−	0.853894i	0.904277	−	0.426947i	$-0.140411\pi$
$684$	574360.	+	511850.i	1.22764	+	1.09403i
$685$	−169460.			−0.361148
$686$	−185609.	−	392797.i	−0.394412	−	0.834680i
$687$	266439.	−	440892.i	0.564526	−	0.934154i
$688$	−378244.	−	432543.i	−0.799089	−	0.913802i
$689$	−290235.	+	502701.i	−0.611379	+	1.05894i
$690$	65293.0	−	90354.1i	0.137141	−	0.189780i
$691$	−304679.	+	175906.i	−0.638096	+	0.368405i	−0.783881	−	0.620912i	$-0.786763\pi$
$691$	−304679.	+	175906.i	−0.638096	+	0.368405i	0.145785	+	0.989316i	$0.453429\pi$
$692$	−742860.	−	123189.i	−1.55130	−	0.257252i
$693$	240678.	−	380852.i	0.501152	−	0.793030i
$694$	−28820.2	−	2373.42i	−0.0598381	−	0.00492784i
$695$	116927.	−	67507.8i	0.242072	−	0.139760i
$696$	−409926.	+	107780.i	−0.846228	+	0.222495i
$697$	−175932.	+	304723.i	−0.362143	+	0.627249i
$698$	−363568.	−	251820.i	−0.746233	−	0.516868i
$699$	−328153.	−	6560.58i	−0.671617	−	0.0134273i
$700$	−463127.	+	173933.i	−0.945156	+	0.354965i
$701$	−620142.			−1.26199			−0.630994	−	0.775788i	$-0.717353\pi$
$701$	−620142.			−1.26199			−0.630994	+	0.775788i	$0.717353\pi$
$702$	50452.0	−	352560.i	0.102377	−	0.715417i
$703$			1.35898e6i			2.74980i
$704$	436691.	−	13364.3i	0.881107	−	0.0269650i
$705$	−1074.41	+	53740.8i	−0.00216168	+	0.108125i
$706$	202568.	+	140306.i	0.406408	+	0.281493i
$707$	−317061.	−	183055.i	−0.634314	−	0.366222i
$708$	292311.	−	103163.i	0.583148	−	0.205805i
$709$	−157448.	−	272708.i	−0.313217	−	0.542508i	0.665840	−	0.746095i	$-0.268073\pi$
$709$	−157448.	−	272708.i	−0.313217	−	0.542508i	−0.979057	+	0.203587i	$0.934740\pi$
$710$	−113569.	−	9352.70i	−0.225290	−	0.0185533i
$711$	99035.9	−	52015.6i	0.195909	−	0.102895i
$712$	49760.9	−	197762.i	0.0981585	−	0.390107i
$713$	160228.	+	277523.i	0.315181	+	0.545909i
$714$	134884.	−	186655.i	0.264584	−	0.366137i
$715$	−63878.0	−	36880.0i	−0.124951	−	0.0721404i
$716$	31467.2	+	25861.9i	0.0613807	+	0.0504469i
$717$	−403292.	−	243717.i	−0.784480	−	0.474075i
$718$	144341.	+	305465.i	0.279990	+	0.592533i
$719$		−	361941.i		−	0.700132i	−0.936725	−	0.350066i	$-0.886159\pi$
$719$		−	361941.i		−	0.700132i	0.936725	−	0.350066i	$-0.113841\pi$
$720$	109516.	+	42307.0i	0.211257	+	0.0816108i
$721$	−111926.			−0.215308
$722$	−803126.	+	379501.i	−1.54067	+	0.728013i
$723$	58682.9	+	106503.i	0.112263	+	0.203744i
$724$	57668.8	−	70167.9i	0.110018	−	0.133863i
$725$	218164.	−	377870.i	0.415056	−	0.718897i
$726$	−11982.4	+	116885.i	−0.0227337	+	0.221761i
$727$	267542.	−	154465.i	0.506200	−	0.292255i	−0.225070	−	0.974343i	$-0.572261\pi$
$727$	267542.	−	154465.i	0.506200	−	0.292255i	0.731270	+	0.682088i	$0.238928\pi$
$728$	395289.	+	99462.6i	0.745852	+	0.187671i
$729$	527623.	+	63587.7i	0.992816	+	0.119651i
$730$	−5028.29	+	61057.9i	−0.00943572	+	0.114577i
$731$	−238457.	+	137673.i	−0.446247	+	0.257641i
$732$	9389.99	+	1750.68i	0.0175244	+	0.00326727i
$733$	−441272.	+	764305.i	−0.821293	+	1.42252i	0.0834259	+	0.996514i	$0.473414\pi$
$733$	−441272.	+	764305.i	−0.821293	+	1.42252i	−0.904719	+	0.426008i	$0.859920\pi$
$734$	423464.	−	611380.i	0.786002	−	1.13480i
$735$	7824.08	+	14199.8i	0.0144830	+	0.0262850i
$736$	63018.1	+	556492.i	0.116335	+	1.02731i
$737$	437829.			0.806065
$738$	113231.	−	922394.i	0.207900	−	1.69357i
$739$			396910.i			0.726781i	0.931637	+	0.363390i	$0.118381\pi$
$739$			396910.i			0.726781i	−0.931637	+	0.363390i	$0.881619\pi$
$740$	72913.3	+	194144.i	0.133151	+	0.354537i
$741$	558475.	+	337496.i	1.01711	+	0.614657i
$742$	564444.	−	814923.i	1.02521	−	1.48016i
$743$	−831366.	−	479989.i	−1.50596	−	0.869469i	−0.999976	−	0.00692819i	$-0.997795\pi$
$743$	−831366.	−	479989.i	−1.50596	−	0.869469i	−0.505988	−	0.862541i	$-0.668872\pi$
$744$	−239761.	+	237522.i	−0.433145	+	0.429099i
$745$	−14930.1	−	25859.7i	−0.0268999	−	0.0465920i
$746$	27935.5	−	339217.i	0.0501971	−	0.609536i
$747$	−215731.	+	113306.i	−0.386609	+	0.203055i
$748$	34250.5	−	206539.i	0.0612158	−	0.369147i
$749$	361023.	+	625310.i	0.643534	+	1.11463i
$750$	−226526.	+	101552.i	−0.402713	+	0.180537i
$751$	−572212.	−	330367.i	−1.01456	−	0.585756i	−0.102036	−	0.994781i	$-0.532536\pi$
$751$	−572212.	−	330367.i	−1.01456	−	0.585756i	−0.912523	+	0.409025i	$0.865869\pi$
$752$	−177763.	−	203282.i	−0.314344	−	0.359470i
$753$	20024.1	−	1.00158e6i	0.0353153	−	1.76643i
$754$	−325044.	+	153593.i	−0.571742	+	0.270165i
$755$			189241.i			0.331987i
$756$	−135287.	+	592990.i	−0.236707	+	1.03754i
$757$	326842.			0.570356			0.285178	−	0.958475i	$-0.407947\pi$
$757$	326842.			0.570356			0.285178	+	0.958475i	$0.407947\pi$
$758$	−251183.	−	531570.i	−0.437171	−	0.925171i
$759$	524927.	+	10494.6i	0.911203	+	0.0182172i
$760$	−149757.	+	154410.i	−0.259274	+	0.267330i
$761$	−164813.	+	285464.i	−0.284591	+	0.492927i	−0.972510	−	0.232861i	$-0.925191\pi$
$761$	−164813.	+	285464.i	−0.284591	+	0.492927i	0.687919	+	0.725788i	$0.258525\pi$
$762$	231056.	+	515402.i	0.397931	+	0.887638i
$763$	875410.	−	505418.i	1.50370	−	0.868164i
$764$	−85013.7	+	512654.i	−0.145647	+	0.878290i
$765$	30054.7	−	47559.0i	0.0513558	−	0.0812662i
$766$	742285.	+	61129.3i	1.26507	+	0.104182i
$767$	227694.	−	131459.i	0.387044	−	0.223460i
$768$	−549937.	+	213217.i	−0.932375	+	0.361492i
$769$	299738.	−	519162.i	0.506862	−	0.877910i	−0.493107	−	0.869969i	$-0.664139\pi$
$769$	299738.	−	519162.i	0.506862	−	0.877910i	0.999968	−	0.00794129i	$-0.00252782\pi$
$770$	103552.	+	71723.7i	0.174653	+	0.120971i
$771$	344058.	−	569332.i	0.578792	−	0.957760i
$772$	4429.60	+	11794.6i	0.00743241	+	0.0197901i
$773$	−58555.0			−0.0979952			−0.0489976	−	0.998799i	$-0.515603\pi$
$773$	−58555.0			−0.0979952			−0.0489976	+	0.998799i	$0.515603\pi$
$774$	437639.	−	580799.i	0.730524	−	0.969491i
$775$		−	347422.i		−	0.578433i
$776$	296347.	−	84285.0i	0.492127	−	0.139967i
$777$	−940999.	+	518488.i	−1.55864	+	0.858810i
$778$	841808.	+	583066.i	1.39077	+	0.963294i
$779$	1.47456e6	+	851336.i	2.42989	+	1.40290i
$780$	97891.8	+	18251.0i	0.160900	+	0.0299984i
$781$	−268347.	−	464791.i	−0.439942	−	0.762002i
$782$	267469.	+	22026.9i	0.437381	+	0.0360196i
$783$	−239897.	−	479817.i	−0.391293	−	0.782621i
$784$	−77091.2	−	26291.1i	−0.125422	−	0.0427737i
$785$	−48129.6	−	83362.8i	−0.0781039	−	0.135280i
$786$	−299816.	−	30735.4i	−0.485299	−	0.0497500i
$787$	553254.	+	319421.i	0.893254	+	0.515720i	0.875005	−	0.484113i	$-0.160858\pi$
$787$	553254.	+	319421.i	0.893254	+	0.515720i	0.0182482	+	0.999833i	$0.494191\pi$
$788$	252208.	−	306872.i	0.406169	−	0.494202i
$789$	−58078.8	+	32001.3i	−0.0932962	+	0.0514060i
$790$	13362.6	+	28278.8i	0.0214110	+	0.0453113i
$791$		−	710975.i		−	1.13632i
$792$	129887.	+	537474.i	0.207070	+	0.856854i
$793$	8101.59			0.0128832
$794$	−942966.	+	445580.i	−1.49574	+	0.706781i
$795$	125256.	−	207268.i	0.198182	−	0.327942i
$796$	−148436.	−	121995.i	−0.234269	−	0.192538i
$797$	587628.	−	1.01780e6i	0.925095	−	1.60231i	0.133686	−	0.991024i	$-0.457319\pi$
$797$	587628.	−	1.01780e6i	0.925095	−	1.60231i	0.791409	−	0.611287i	$-0.209348\pi$
$798$	−903226.	−	652702.i	−1.41837	−	1.02497i
$799$	−112067.	+	64702.1i	−0.175544	+	0.101350i
$800$	242492.	−	556649.i	0.378893	−	0.869765i
$801$	257888.	+	10315.8i	0.401945	+	0.0160782i
$802$	−17404.5	+	211340.i	−0.0270591	+	0.328574i
$803$	−249886.	+	144272.i	−0.387535	+	0.223743i
$804$	−557391.	+	196715.i	−0.862279	+	0.304316i
$805$	−80736.4	+	139840.i	−0.124588	+	0.215793i
$806$	−162991.	+	235319.i	−0.250895	+	0.362233i
$807$	−347373.	−	6944.85i	−0.533396	−	0.0106639i
$808$	432199.	−	122923.i	0.662005	−	0.188283i
$809$	−215543.			−0.329334			−0.164667	−	0.986349i	$-0.552655\pi$
$809$	−215543.			−0.329334			−0.164667	+	0.986349i	$0.552655\pi$
$810$	−23984.8	+	146640.i	−0.0365566	+	0.223503i
$811$		−	1.05773e6i		−	1.60817i	−0.594512	−	0.804087i	$-0.702655\pi$
$811$		−	1.05773e6i		−	1.60817i	0.594512	−	0.804087i	$-0.297345\pi$
$812$	574758.	−	215858.i	0.871712	−	0.327382i
$813$	2255.95	−	112840.i	0.00341310	−	0.170719i
$814$	−556146.	+	802942.i	−0.839345	+	1.21181i
$815$	−151236.	−	87315.9i	−0.227687	−	0.131455i
$816$	49193.5	+	278329.i	0.0738801	+	0.418002i
$817$	666201.	+	1.15389e6i	0.998070	+	1.72871i
$818$	−48390.0	+	587594.i	−0.0723185	+	0.878153i
$819$	−20619.3	+	515470.i	−0.0307401	+	0.768486i
$820$	256333.	+	42507.8i	0.381221	+	0.0632180i
$821$	37925.7	+	65689.3i	0.0562662	+	0.0974559i	0.892787	−	0.450480i	$-0.148747\pi$
$821$	37925.7	+	65689.3i	0.0562662	+	0.0974559i	−0.836520	+	0.547936i	$0.815414\pi$
$822$	873328.	+	631097.i	1.29251	+	0.934012i
$823$	−569508.	−	328806.i	−0.840815	−	0.485445i	0.0167265	−	0.999860i	$-0.494676\pi$
$823$	−569508.	−	328806.i	−0.840815	−	0.485445i	−0.857541	+	0.514416i	$0.828009\pi$
$824$	95638.4	−	98610.1i	0.140857	−	0.145234i
$825$	−487164.	−	294402.i	−0.715760	−	0.432547i
$826$	−405964.	+	191830.i	−0.595014	+	0.281162i
$827$			669017.i			0.978196i	0.872229	+	0.489098i	$0.162674\pi$
$827$			669017.i			0.978196i	−0.872229	+	0.489098i	$0.837326\pi$
$828$	−672988.	+	222487.i	−0.981627	+	0.324521i
$829$	−637042.			−0.926955			−0.463478	−	0.886109i	$-0.653399\pi$
$829$	−637042.			−0.926955			−0.463478	+	0.886109i	$0.653399\pi$
$830$	−29107.9	−	61600.1i	−0.0422527	−	0.0894180i
$831$	400039.	+	726026.i	0.579296	+	1.05136i
$832$	−425395.	+	263273.i	−0.614534	+	0.380328i
$833$	−19515.6	+	33802.1i	−0.0281250	+	0.0487139i
$834$	−854005.	−	87547.5i	−1.22780	−	0.125867i
$835$	−77465.4	+	44724.7i	−0.111105	+	0.0641467i
$836$	−999443.	−	165738.i	−1.43003	−	0.237143i
$837$	−356450.	−	235357.i	−0.508800	−	0.335951i
$838$	−927231.	−	76360.1i	−1.32038	−	0.108737i
$839$	872716.	−	503863.i	1.23979	−	0.715795i	0.270741	−	0.962652i	$-0.412731\pi$
$839$	872716.	−	503863.i	1.23979	−	0.715795i	0.969052	+	0.246858i	$0.0793980\pi$
$840$	−164055.	−	44784.6i	−0.232504	−	0.0634702i
$841$	82891.1	−	143572.i	0.117197	−	0.202991i
$842$	229526.	+	158978.i	0.323748	+	0.224240i
$843$	−96838.1	−	175750.i	−0.136267	−	0.247310i
$844$	−445617.	+	167357.i	−0.625572	+	0.234941i
$845$	−77247.2			−0.108186
$846$	205677.	−	272957.i	0.287372	−	0.381377i
$847$		−	170194.i		−	0.237234i
$848$	235664.	+	1.19362e6i	0.327720	+	1.65988i
$849$	192550.	+	116361.i	0.267133	+	0.161434i
$850$	−239186.	−	165669.i	−0.331054	−	0.229299i
$851$	−1.08432e6	−	626031.i	−1.49726	−	0.864444i
$852$	550456.	+	471149.i	0.758304	+	0.649051i
$853$	96790.1	+	167645.i	0.133025	+	0.230406i	0.924841	−	0.380353i	$-0.124198\pi$
$853$	96790.1	+	167645.i	0.133025	+	0.230406i	−0.791816	+	0.610759i	$0.790864\pi$
$854$	−13789.0	−	1135.56i	−0.0189068	−	0.00155703i
$855$	−230138.	−	145435.i	−0.314816	−	0.198946i
$856$	−859402.	−	216242.i	−1.17287	−	0.295116i
$857$	−461864.	−	799972.i	−0.628858	−	1.08921i	−0.987781	−	0.155847i	$-0.950189\pi$
$857$	−461864.	−	799972.i	−0.628858	−	1.08921i	0.358923	−	0.933367i	$-0.383144\pi$
$858$	191854.	+	427957.i	0.260614	+	0.581334i
$859$	628431.	+	362825.i	0.851670	+	0.491712i	0.861214	−	0.508243i	$-0.169705\pi$
$859$	628431.	+	362825.i	0.851670	+	0.491712i	−0.00954418	+	0.999954i	$0.503038\pi$
$860$	157084.	+	129102.i	0.212390	+	0.174557i
$861$	−26906.6	+	1.34584e6i	−0.0362955	+	1.81546i
$862$	−252705.	−	534791.i	−0.340094	−	0.719730i
$863$			444700.i			0.597097i	0.954394	+	0.298549i	$0.0965025\pi$
$863$			444700.i			0.597097i	−0.954394	+	0.298549i	$0.903497\pi$
$864$	−406841.	−	625888.i	−0.545001	−	0.838435i
$865$	266461.			0.356124
$866$	1.06634e6	−	503879.i	1.42187	−	0.671878i
$867$	−616124.	−	12317.8i	−0.819652	−	0.0163869i
$868$	310396.	−	377671.i	0.411980	−	0.501272i
$869$	−73653.9	+	127572.i	−0.0975341	+	0.168934i
$870$	136864.	−	61356.6i	0.180822	−	0.0810630i
$871$	−434176.	+	250672.i	−0.572308	+	0.330422i
$872$	−302731.	+	1.20313e6i	−0.398129	+	1.58227i
$873$	181316.	+	345220.i	0.237907	+	0.452968i
$874$	106588.	−	1.29428e6i	0.139536	−	1.69436i
$875$	311409.	−	179792.i	0.406739	−	0.234831i
$876$	253304.	−	295942.i	0.330091	−	0.385654i
$877$	288301.	−	499353.i	0.374841	−	0.649244i	−0.615462	−	0.788167i	$-0.711031\pi$
$877$	288301.	−	499353.i	0.374841	−	0.649244i	0.990303	+	0.138922i	$0.0443638\pi$
$878$	−164285.	+	237188.i	−0.213113	+	0.307684i
$879$	109377.	−	180992.i	0.141562	−	0.234251i
$880$	−151673.	+	29945.8i	−0.195859	+	0.0386696i
$881$	−1.16458e6			−1.50044			−0.750219	−	0.661190i	$-0.770052\pi$
$881$	−1.16458e6			−1.50044			−0.750219	+	0.661190i	$0.770052\pi$
$882$	12560.4	−	102318.i	0.0161461	−	0.131528i
$883$		−	12142.2i		−	0.0155731i	−0.999970	−	0.00778655i	$-0.997521\pi$
$883$		−	12142.2i		−	0.0155731i	0.999970	−	0.00778655i	$-0.00247856\pi$
$884$	84285.7	+	224425.i	0.107857	+	0.287189i
$885$	−96072.6	+	52935.8i	−0.122663	+	0.0675869i
$886$	434805.	−	627754.i	0.553894	−	0.799691i
$887$	1.12130e6	+	647385.i	1.42520	+	0.822840i	0.996737	−	0.0807193i	$-0.0257217\pi$
$887$	1.12130e6	+	647385.i	1.42520	+	0.822840i	0.428464	+	0.903559i	$0.359055\pi$
$888$	347260.	−	1.27208e6i	0.440381	−	1.61320i
$889$	−409071.	−	708532.i	−0.517601	−	0.896511i
$890$	−5922.72	+	71918.8i	−0.00747723	+	0.0907951i
$891$	−632076.	+	300384.i	−0.796184	+	0.378374i
$892$	138595.	−	835763.i	0.174188	−	1.05040i
$893$	313094.	+	542294.i	0.392619	+	0.680036i
$894$	−19362.1	+	188873.i	−0.0242258	+	0.236317i
$895$	−12482.2	−	7206.63i	−0.0155828	−	0.00899676i
$896$	760930.	−	388467.i	0.947826	−	0.483881i
$897$	−526555.	+	290131.i	−0.654423	+	0.360586i
$898$	697488.	−	329584.i	0.864937	−	0.408709i
$899$			431164.i			0.533485i
$900$	752472.	+	155916.i	0.928977	+	0.192489i
$901$	583026.			0.718188
$902$	522832.	+	1.10645e6i	0.642613	+	1.35994i
$903$	−544818.	+	901541.i	−0.668153	+	1.10563i
$904$	626389.	+	607512.i	0.766491	+	0.743393i
$905$	−16069.9	+	27833.8i	−0.0196207	+	0.0339841i
$906$	704765.	−	975271.i	0.858594	−	1.18814i
$907$	593065.	−	342406.i	0.720921	−	0.416224i	−0.0941708	−	0.995556i	$-0.530020\pi$
$907$	593065.	−	342406.i	0.720921	−	0.416224i	0.815091	+	0.579332i	$0.196687\pi$
$908$	98513.1	−	594059.i	0.119487	−	0.720540i
$909$	264436.	+	503476.i	0.320031	+	0.609328i
$910$	−143752.	−	11838.4i	−0.173593	−	0.0142958i
$911$	−621519.	+	358834.i	−0.748890	+	0.432372i	−0.825293	−	0.564705i	$-0.808990\pi$
$911$	−621519.	+	358834.i	−0.748890	+	0.432372i	0.0764028	+	0.997077i	$0.475657\pi$
$912$	1.34684e6	−	238047.i	1.61929	−	0.286203i
$913$	160441.	−	277893.i	0.192475	−	0.333377i
$914$	19484.0	+	13495.3i	0.0233231	+	0.0161544i
$915$	−3379.36	−	67.5617i	−0.00403638	−	8.06972e-5i
$916$	−321987.	−	857345.i	−0.383749	−	1.02180i
$917$	436556.			0.519160
$918$	−332008.	+	133171.i	−0.393970	+	0.158025i
$919$		−	441444.i		−	0.522691i	−0.965245	−	0.261345i	$-0.915834\pi$
$919$		−	441444.i		−	0.522691i	0.965245	−	0.261345i	$-0.0841661\pi$
$920$	−54215.1	−	190621.i	−0.0640538	−	0.225214i
$921$	5767.48	−	288483.i	0.00679934	−	0.340095i
$922$	−416570.	−	288531.i	−0.490034	−	0.339415i
$923$	532217.	+	307275.i	0.624720	+	0.360682i
$924$	−266554.	−	755280.i	−0.312206	−	0.884635i
$925$	678710.	+	1.17556e6i	0.793232	+	1.37392i
$926$	939108.	+	77338.2i	1.09520	+	0.0901929i
$927$	146972.	+	92878.3i	0.171031	+	0.108082i
$928$	−300941.	+	690823.i	−0.349451	+	0.802179i
$929$	−633285.	−	1.09688e6i	−0.733783	−	1.27095i	−0.955255	−	0.295783i	$-0.904420\pi$
$929$	−633285.	−	1.09688e6i	−0.733783	−	1.27095i	0.221472	−	0.975167i	$-0.428914\pi$
$930$	69949.5	−	96797.8i	0.0808758	−	0.111918i
$931$	163568.	+	94436.2i	0.188712	+	0.108953i
$932$	−370488.	+	450788.i	−0.426523	+	0.518968i
$933$	546481.	+	330248.i	0.627786	+	0.379382i
$934$	−167093.	−	353614.i	−0.191543	−	0.405355i
$935$			74084.8i			0.0847434i
$936$	−436525.	−	458624.i	−0.498262	−	0.523486i
$937$	377258.			0.429694			0.214847	−	0.976648i	$-0.431075\pi$
$937$	377258.			0.429694			0.214847	+	0.976648i	$0.431075\pi$
$938$	774108.	−	365790.i	0.879825	−	0.415744i
$939$	−514766.	−	934242.i	−0.583819	−	1.05957i
$940$	73824.5	+	60674.0i	0.0835497	+	0.0686668i
$941$	645770.	−	1.11851e6i	0.729288	−	1.26316i	−0.227897	−	0.973685i	$-0.573185\pi$
$941$	645770.	−	1.11851e6i	0.729288	−	1.26316i	0.957185	−	0.289478i	$-0.0934817\pi$
$942$	−62416.9	+	608861.i	−0.0703397	+	0.686146i
$943$	−1.35855e6	+	784359.i	−1.52775	+	0.882046i
$944$	177879.	−	521580.i	0.199610	−	0.585298i
$945$	12899.4	−	214842.i	0.0144447	−	0.240578i
$946$	−78598.0	+	954405.i	−0.0878273	+	1.06647i
$947$	−1.02088e6	+	589403.i	−1.13834	+	0.657222i	−0.946019	−	0.324110i	$-0.894935\pi$
$947$	−1.02088e6	+	589403.i	−1.13834	+	0.657222i	−0.192322	+	0.981332i	$0.561602\pi$
$948$	36449.6	−	195502.i	0.0405579	−	0.217538i
$949$	165200.	−	286136.i	0.183434	−	0.317716i
$950$	−801672.	+	1.15742e6i	−0.888279	+	1.28246i
$951$	585396.	+	1.06243e6i	0.647275	+	1.17473i
$952$	−111999.	−	393788.i	−0.123577	−	0.434499i
$953$	613396.			0.675391			0.337695	−	0.941255i	$-0.390353\pi$
$953$	613396.			0.675391			0.337695	+	0.941255i	$0.390353\pi$
$954$	−1.41742e6	+	601702.i	−1.55740	+	0.661126i
$955$		−	183887.i		−	0.201625i
$956$	−784231.	+	294528.i	−0.858081	+	0.322263i
$957$	604589.	+	365364.i	0.660141	+	0.398935i
$958$	−918265.	+	1.32575e6i	−1.00055	+	1.44455i
$959$	−1.35163e6	−	780367.i	−1.46968	−	0.848519i
$960$	179638.	−	106269.i	0.194919	−	0.115310i
$961$	−290105.	−	502477.i	−0.314130	−	0.544089i
$962$	91795.0	−	1.11465e6i	0.0991903	−	1.20445i
$963$	44828.6	−	1.12069e6i	0.0483395	−	1.20846i
$964$	213265.	+	35365.9i	0.229491	+	0.0380567i
$965$	−2229.15	−	3861.01i	−0.00239379	−	0.00414616i
$966$	936869.	−	420001.i	1.00398	−	0.450087i
$967$	41063.4	+	23708.0i	0.0439139	+	0.0253537i	0.521796	−	0.853070i	$-0.325262\pi$
$967$	41063.4	+	23708.0i	0.0439139	+	0.0253537i	−0.477882	+	0.878424i	$0.658595\pi$
$968$	149946.	+	145427.i	0.160023	+	0.155201i
$969$	13100.6	−	655275.i	0.0139522	−	0.697872i
$970$	−98574.2	+	46579.3i	−0.104766	+	0.0495051i
$971$			746340.i			0.791586i	0.918340	+	0.395793i	$0.129530\pi$
$971$			746340.i			0.791586i	−0.918340	+	0.395793i	$0.870470\pi$
$972$	669721.	−	666401.i	0.708861	−	0.705348i
$973$	1.24350e6			1.31347
$974$	−333596.	−	705978.i	−0.351644	−	0.744172i
$975$	651654.	+	13028.2i	0.685500	+	0.0137048i
$976$	12782.9	−	11178.2i	0.0134193	−	0.0117347i
$977$	143356.	−	248299.i	0.150185	−	0.260128i	−0.781111	−	0.624393i	$-0.785346\pi$
$977$	143356.	−	248299.i	0.150185	−	0.260128i	0.931295	+	0.364265i	$0.118680\pi$
$978$	454228.	+	1.01322e6i	0.474894	+	1.05932i
$979$	−294335.	+	169934.i	−0.307098	+	0.177303i
$980$	28434.2	+	4715.26i	0.0296067	+	0.00490969i
$981$	−1.56892e6	−	62758.2i	−1.63028	−	0.0652128i
$982$	−303523.	−	24996.0i	−0.314752	−	0.0259208i
$983$	504643.	−	291356.i	0.522249	−	0.301521i	−0.215605	−	0.976481i	$-0.569172\pi$
$983$	504643.	−	291356.i	0.522249	−	0.301521i	0.737854	+	0.674960i	$0.235839\pi$
$984$	−1.16273e6	−	1.17370e6i	−1.20085	−	1.21217i
$985$	−70279.8	+	121728.i	−0.0724366	+	0.125464i
$986$	296839.	+	205601.i	0.305329	+	0.211481i
$987$	−256048.	+	423697.i	−0.262837	+	0.434931i
$988$	1.08599e6	−	407859.i	1.11253	−	0.417826i
$989$	−1.22758e6			−1.25504
$990$	−76458.0	−	180111.i	−0.0780104	−	0.183768i
$991$			918794.i			0.935558i	0.883845	+	0.467779i	$0.154946\pi$
$991$			918794.i			0.935558i	−0.883845	+	0.467779i	$0.845054\pi$
$992$	67512.3	+	596178.i	0.0686056	+	0.605833i
$993$	−1.21188e6	+	667741.i	−1.22902	+	0.677189i
$994$	−862770.	−	597585.i	−0.873217	−	0.604821i
$995$	58881.0	+	33995.0i	0.0594742	+	0.0343375i
$996$	−79398.7	+	425865.i	−0.0800377	+	0.429292i
$997$	697626.	+	1.20832e6i	0.701830	+	1.21561i	0.967823	+	0.251631i	$0.0809668\pi$
$997$	697626.	+	1.20832e6i	0.701830	+	1.21561i	−0.265993	+	0.963975i	$0.585700\pi$
$998$	−58084.7	−	4783.45i	−0.0583178	−	0.00480264i
$999$	1.66589e6	+	100022.i	1.66923	+	0.100223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.5.f.a.31.19	yes	44
3.2	odd	2		108.5.f.a.91.4		44
4.3	odd	2	inner	36.5.f.a.31.4	yes	44
9.2	odd	6		108.5.f.a.19.19		44
9.4	even	3		324.5.d.f.163.12		22
9.5	odd	6		324.5.d.e.163.11		22
9.7	even	3	inner	36.5.f.a.7.4	✓	44
12.11	even	2		108.5.f.a.91.19		44
36.7	odd	6	inner	36.5.f.a.7.19	yes	44
36.11	even	6		108.5.f.a.19.4		44
36.23	even	6		324.5.d.e.163.12		22
36.31	odd	6		324.5.d.f.163.11		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.4	✓	44	9.7	even	3	inner
36.5.f.a.7.19	yes	44	36.7	odd	6	inner
36.5.f.a.31.4	yes	44	4.3	odd	2	inner
36.5.f.a.31.19	yes	44	1.1	even	1	trivial
108.5.f.a.19.4		44	36.11	even	6
108.5.f.a.19.19		44	9.2	odd	6
108.5.f.a.91.4		44	3.2	odd	2
108.5.f.a.91.19		44	12.11	even	2
324.5.d.e.163.11		22	9.5	odd	6
324.5.d.e.163.12		22	36.23	even	6
324.5.d.f.163.11		22	36.31	odd	6
324.5.d.f.163.12		22	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	36.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.61656 - 1.70894i) q^{2} +(8.99820 + 0.179896i) q^{3} +(10.1591 - 12.3610i) q^{4} +(-2.83091 + 4.90328i) q^{5} +(32.8500 - 14.7267i) q^{6} +(-45.1595 + 26.0728i) q^{7} +(15.6169 - 62.0654i) q^{8} +(80.9353 + 3.23749i) q^{9} +O(q^{10})\)	\(q+(3.61656 - 1.70894i) q^{2} +(8.99820 + 0.179896i) q^{3} +(10.1591 - 12.3610i) q^{4} +(-2.83091 + 4.90328i) q^{5} +(32.8500 - 14.7267i) q^{6} +(-45.1595 + 26.0728i) q^{7} +(15.6169 - 62.0654i) q^{8} +(80.9353 + 3.23749i) q^{9} +(-1.85878 + 22.5709i) q^{10} +(-92.3736 + 53.3319i) q^{11} +(93.6371 - 109.399i) q^{12} +(61.0686 - 105.774i) q^{13} +(-118.765 + 171.469i) q^{14} +(-26.3552 + 43.6114i) q^{15} +(-49.5864 - 251.152i) q^{16} -122.675 q^{17} +(298.240 - 126.605i) q^{18} +593.624i q^{19} +(31.8498 + 84.8055i) q^{20} +(-411.044 + 226.484i) q^{21} +(-242.934 + 350.739i) q^{22} +(-473.649 - 273.461i) q^{23} +(151.689 - 555.668i) q^{24} +(296.472 + 513.504i) q^{25} +(40.0976 - 486.900i) q^{26} +(727.690 + 43.6915i) q^{27} +(-136.493 + 823.090i) q^{28} +(-367.933 - 637.279i) q^{29} +(-20.7861 + 202.763i) q^{30} +(-507.427 - 292.963i) q^{31} +(-608.535 - 823.566i) q^{32} +(-840.791 + 463.274i) q^{33} +(-443.662 + 209.644i) q^{34} -295.239i q^{35} +(862.246 - 967.547i) q^{36} +2289.29 q^{37} +(1014.47 + 2146.88i) q^{38} +(568.535 - 940.788i) q^{39} +(260.114 + 252.275i) q^{40} +(1434.13 - 2483.99i) q^{41} +(-1099.52 + 1521.54i) q^{42} +(1943.81 - 1122.26i) q^{43} +(-279.197 + 1683.63i) q^{44} +(-244.995 + 387.683i) q^{45} +(-2180.31 - 179.555i) q^{46} +(913.531 - 527.427i) q^{47} +(-401.007 - 2268.83i) q^{48} +(159.084 - 275.542i) q^{49} +(1949.76 + 1350.47i) q^{50} +(-1103.85 - 22.0688i) q^{51} +(-687.066 - 1829.43i) q^{52} -4752.60 q^{53} +(2706.40 - 1085.56i) q^{54} -603.911i q^{55} +(912.971 + 3210.02i) q^{56} +(-106.791 + 5341.55i) q^{57} +(-2419.72 - 1675.99i) q^{58} +(1864.25 + 1076.32i) q^{59} +(271.335 + 768.827i) q^{60} +(33.1660 + 57.4451i) q^{61} +(-2335.80 - 192.360i) q^{62} +(-3739.40 + 1964.01i) q^{63} +(-3608.23 - 1938.53i) q^{64} +(345.759 + 598.872i) q^{65} +(-2249.07 + 3112.32i) q^{66} +(-3554.82 - 2052.38i) q^{67} +(-1246.26 + 1516.38i) q^{68} +(-4212.79 - 2545.87i) q^{69} +(-504.545 - 1067.75i) q^{70} +5031.65i q^{71} +(1464.89 - 4972.72i) q^{72} +2705.16 q^{73} +(8279.36 - 3912.25i) q^{74} +(2575.34 + 4673.95i) q^{75} +(7337.76 + 6030.67i) q^{76} +(2781.03 - 4816.88i) q^{77} +(448.398 - 4374.01i) q^{78} +(1196.02 - 690.524i) q^{79} +(1371.84 + 467.852i) q^{80} +(6540.04 + 524.053i) q^{81} +(941.652 - 11434.4i) q^{82} +(-2605.31 + 1504.18i) q^{83} +(-1376.27 + 7381.77i) q^{84} +(347.282 - 601.509i) q^{85} +(5112.05 - 7380.57i) q^{86} +(-3196.09 - 5800.55i) q^{87} +(1867.48 + 6566.08i) q^{88} +3186.35 q^{89} +(-223.513 + 1820.76i) q^{90} +6368.92i q^{91} +(-8192.07 + 3076.64i) q^{92} +(-4513.23 - 2727.43i) q^{93} +(2402.50 - 3468.64i) q^{94} +(-2910.71 - 1680.50i) q^{95} +(-5327.56 - 7520.09i) q^{96} +(2407.03 + 4169.10i) q^{97} +(104.455 - 1268.38i) q^{98} +(-7648.94 + 4017.38i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9}+O(q^{10}) \) 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9	\( 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9} + 28 q^{10} - 228 q^{12} - 2 q^{13} + 252 q^{14} - q^{16} - 56 q^{17} + 72 q^{18} - 140 q^{20} + 138 q^{21} - 33 q^{22} - 951 q^{24} - 1752 q^{25} + 1096 q^{26} - 516 q^{28} + 526 q^{29} - 1980 q^{30} - 121 q^{32} + 2994 q^{33} + 385 q^{34} - 1005 q^{36} - 8 q^{37} + 1395 q^{38} - 2276 q^{40} - 2762 q^{41} + 3330 q^{42} + 6714 q^{44} + 4110 q^{45} + 3576 q^{46} + 2163 q^{48} + 3428 q^{49} + 6375 q^{50} + 1438 q^{52} - 10088 q^{53} - 4983 q^{54} - 7506 q^{56} + 1752 q^{57} - 4064 q^{58} - 16392 q^{60} - 2 q^{61} - 18324 q^{62} + 9026 q^{64} - 2014 q^{65} - 17358 q^{66} - 11405 q^{68} + 3354 q^{69} + 3666 q^{70} + 4083 q^{72} - 3416 q^{73} + 14620 q^{74} + 1581 q^{76} - 3942 q^{77} + 34566 q^{78} + 45520 q^{80} - 1164 q^{81} - 8486 q^{82} + 51078 q^{84} - 1252 q^{85} + 22113 q^{86} + 1995 q^{88} + 13048 q^{89} - 4692 q^{90} - 30294 q^{92} + 12090 q^{93} + 7524 q^{94} - 76164 q^{96} + 5638 q^{97} - 92938 q^{98}+O(q^{100}) \) 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9 + 28 * q^10 - 228 * q^12 - 2 * q^13 + 252 * q^14 - q^16 - 56 * q^17 + 72 * q^18 - 140 * q^20 + 138 * q^21 - 33 * q^22 - 951 * q^24 - 1752 * q^25 + 1096 * q^26 - 516 * q^28 + 526 * q^29 - 1980 * q^30 - 121 * q^32 + 2994 * q^33 + 385 * q^34 - 1005 * q^36 - 8 * q^37 + 1395 * q^38 - 2276 * q^40 - 2762 * q^41 + 3330 * q^42 + 6714 * q^44 + 4110 * q^45 + 3576 * q^46 + 2163 * q^48 + 3428 * q^49 + 6375 * q^50 + 1438 * q^52 - 10088 * q^53 - 4983 * q^54 - 7506 * q^56 + 1752 * q^57 - 4064 * q^58 - 16392 * q^60 - 2 * q^61 - 18324 * q^62 + 9026 * q^64 - 2014 * q^65 - 17358 * q^66 - 11405 * q^68 + 3354 * q^69 + 3666 * q^70 + 4083 * q^72 - 3416 * q^73 + 14620 * q^74 + 1581 * q^76 - 3942 * q^77 + 34566 * q^78 + 45520 * q^80 - 1164 * q^81 - 8486 * q^82 + 51078 * q^84 - 1252 * q^85 + 22113 * q^86 + 1995 * q^88 + 13048 * q^89 - 4692 * q^90 - 30294 * q^92 + 12090 * q^93 + 7524 * q^94 - 76164 * q^96 + 5638 * q^97 - 92938 * q^98

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