LMFDB - Embedded newform 36.5.f.a.7.4

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			7.4
Character	$\chi$	$=$	36.7
Dual form			36.5.f.a.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.28826 - 2.27757i) q^{2} +(-8.99820 + 0.179896i) q^{3} +(5.62536 + 14.9785i) q^{4} +(-2.83091 - 4.90328i) q^{5} +(29.9982 + 19.9025i) q^{6} +(45.1595 + 26.0728i) q^{7} +(15.6169 - 62.0654i) q^{8} +(80.9353 - 3.23749i) q^{9} +O(q^{10})$	\(q+(-3.28826 - 2.27757i) q^{2} +(-8.99820 + 0.179896i) q^{3} +(5.62536 + 14.9785i) q^{4} +(-2.83091 - 4.90328i) q^{5} +(29.9982 + 19.9025i) 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} +(-53.3127 - 133.768i) q^{12} +(61.0686 + 105.774i) q^{13} +(-89.1136 - 188.588i) q^{14} +(26.3552 + 43.6114i) q^{15} +(-192.711 + 168.519i) q^{16} -122.675 q^{17} +(-273.510 - 173.690i) q^{18} +593.624i q^{19} +(57.5188 - 69.9855i) q^{20} +(-411.044 - 226.484i) q^{21} +(-182.282 - 385.757i) q^{22} +(473.649 - 273.461i) q^{23} +(-129.358 + 561.286i) 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} +(12.6652 - 203.432i) q^{30} +(507.427 - 292.963i) q^{31} +(1017.50 - 115.223i) q^{32} +(-840.791 - 463.274i) q^{33} +(403.388 + 279.401i) q^{34} -295.239i q^{35} +(503.783 + 1194.08i) q^{36} +2289.29 q^{37} +(1352.02 - 1951.99i) q^{38} +(-568.535 - 940.788i) q^{39} +(-348.534 + 99.1276i) q^{40} +(1434.13 + 2483.99i) q^{41} +(835.788 + 1680.92i) 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} +(1703.73 - 1551.04i) q^{48} +(159.084 + 275.542i) q^{49} +(-2144.42 + 1013.30i) q^{50} +(1103.85 - 22.0688i) q^{51} +(-1240.80 + 1509.73i) q^{52} -4752.60 q^{53} +(2492.35 + 1513.69i) q^{54} -603.911i q^{55} +(2323.47 - 2395.66i) q^{56} +(-106.791 - 5341.55i) q^{57} +(2661.31 - 1257.55i) q^{58} +(-1864.25 + 1076.32i) q^{59} +(-504.976 + 640.091i) 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} +(1709.60 + 3438.32i) q^{66} +(3554.82 - 2052.38i) q^{67} +(-690.091 - 1837.49i) q^{68} +(-4212.79 + 2545.87i) q^{69} +(-672.427 + 970.824i) q^{70} +5031.65i q^{71} +(1063.02 - 5073.84i) q^{72} +2705.16 q^{73} +(-7527.78 - 5214.01i) q^{74} +(-2575.34 + 4673.95i) q^{75} +(-8891.60 + 3339.35i) q^{76} +(2781.03 + 4816.88i) q^{77} +(-273.215 + 4388.44i) 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} +(1080.12 - 7430.88i) q^{84} +(347.282 + 601.509i) q^{85} +(3835.74 + 8117.45i) q^{86} +(3196.09 - 5800.55i) q^{87} +(4752.65 - 4900.33i) q^{88} +3186.35 q^{89} +(-77.3677 + 1832.80i) q^{90} +6368.92i q^{91} +(6760.48 + 5556.22i) q^{92} +(-4513.23 + 2727.43i) q^{93} +(1802.68 + 3814.95i) q^{94} +(2910.71 - 1680.50i) q^{95} +(-9134.91 + 1219.85i) 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 $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−3.28826	−	2.27757i	−0.822066	−	0.569392i
$2$	−3.28826	−	2.27757i	−0.822066	−	0.569392i
$3$	−8.99820	+	0.179896i	−0.999800	+	0.0199885i
$3$	−8.99820	+	0.179896i	−0.999800	+	0.0199885i
$4$	5.62536	+	14.9785i	0.351585	+	0.936156i
$5$	−2.83091	−	4.90328i	−0.113236	−	0.196131i	0.803837	−	0.594850i	$-0.202788\pi$
$5$	−2.83091	−	4.90328i	−0.113236	−	0.196131i	−0.917073	+	0.398718i	$0.869455\pi$
$6$	29.9982	+	19.9025i	0.833283	+	0.552847i
$7$	45.1595	+	26.0728i	0.921621	+	0.532098i	0.884152	−	0.467199i	$-0.154737\pi$
$7$	45.1595	+	26.0728i	0.921621	+	0.532098i	0.0374695	+	0.999298i	$0.488070\pi$
$8$	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	$-0.188042\pi$
$11$	92.3736	+	53.3319i	0.763418	+	0.440760i	−0.0671034	+	0.997746i	$0.521376\pi$
$12$	−53.3127	−	133.768i	−0.370227	−	0.928941i
$13$	61.0686	+	105.774i	0.361352	+	0.625881i	0.988184	−	0.153274i	$-0.0489818\pi$
$13$	61.0686	+	105.774i	0.361352	+	0.625881i	−0.626831	+	0.779155i	$0.715648\pi$
$14$	−89.1136	−	188.588i	−0.454661	−	0.962184i
$15$	26.3552	+	43.6114i	0.117134	+	0.193829i
$16$	−192.711	+	168.519i	−0.752776	+	0.658277i
$17$	−122.675			−0.424481			−0.212240	−	0.977217i	$-0.568076\pi$
$17$	−122.675			−0.424481			−0.212240	+	0.977217i	$0.568076\pi$
$18$	−273.510	−	173.690i	−0.844167	−	0.536080i
$19$			593.624i			1.64439i	0.569207	+	0.822194i	$0.307250\pi$
$19$			593.624i			1.64439i	−0.569207	+	0.822194i	$0.692750\pi$
$20$	57.5188	−	69.9855i	0.143797	−	0.174964i
$21$	−411.044	−	226.484i	−0.932073	−	0.513570i
$22$	−182.282	−	385.757i	−0.376615	−	0.797018i
$23$	473.649	−	273.461i	0.895366	−	0.516940i	0.0196720	−	0.999806i	$-0.493738\pi$
$23$	473.649	−	273.461i	0.895366	−	0.516940i	0.875694	+	0.482867i	$0.160404\pi$
$24$	−129.358	+	561.286i	−0.224581	+	0.974456i
$25$	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	−0.997496	−	0.0707290i	$-0.977467\pi$
$29$	−367.933	+	637.279i	−0.437495	+	0.757763i	0.560001	+	0.828492i	$0.310801\pi$
$30$	12.6652	−	203.432i	0.0140725	−	0.226035i
$31$	507.427	−	292.963i	0.528020	−	0.304853i	−0.212190	−	0.977228i	$-0.568059\pi$
$31$	507.427	−	292.963i	0.528020	−	0.304853i	0.740210	+	0.672376i	$0.234726\pi$
$32$	1017.50	−	115.223i	0.993649	−	0.112523i
$33$	−840.791	−	463.274i	−0.772076	−	0.425412i
$34$	403.388	+	279.401i	0.348951	+	0.241696i
$35$		−	295.239i		−	0.241012i
$36$	503.783	+	1194.08i	0.388721	+	0.921355i
$37$	2289.29			1.67223			0.836117	−	0.548551i	$-0.184820\pi$
$37$	2289.29			1.67223			0.836117	+	0.548551i	$0.184820\pi$
$38$	1352.02	−	1951.99i	0.936302	−	1.35180i
$39$	−568.535	−	940.788i	−0.373791	−	0.618533i
$40$	−348.534	+	99.1276i	−0.217834	+	0.0619548i
$41$	1434.13	+	2483.99i	0.853142	+	1.47769i	0.878358	+	0.478004i	$0.158640\pi$
$41$	1434.13	+	2483.99i	0.853142	+	1.47769i	−0.0252152	+	0.999682i	$0.508027\pi$
$42$	835.788	+	1680.92i	0.473803	+	0.952904i
$43$	−1943.81	−	1122.26i	−1.05128	−	0.606955i	−0.128270	−	0.991739i	$-0.540943\pi$
$43$	−1943.81	−	1122.26i	−1.05128	−	0.606955i	−0.923007	+	0.384784i	$0.874276\pi$
$44$	−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	$-0.410075\pi$
$47$	−913.531	−	527.427i	−0.413550	−	0.238763i	−0.692314	+	0.721597i	$0.743409\pi$
$48$	1703.73	−	1551.04i	0.739467	−	0.673192i
$49$	159.084	+	275.542i	0.0662574	+	0.114761i
$50$	−2144.42	+	1013.30i	−0.857768	+	0.405321i
$51$	1103.85	−	22.0688i	0.424396	−	0.00848472i
$52$	−1240.80	+	1509.73i	−0.458876	+	0.558333i
$53$	−4752.60			−1.69192			−0.845960	−	0.533246i	$-0.820972\pi$
$53$	−4752.60			−1.69192			−0.845960	+	0.533246i	$0.820972\pi$
$54$	2492.35	+	1513.69i	0.854714	+	0.519099i
$55$		−	603.911i		−	0.199640i
$56$	2323.47	−	2395.66i	0.740902	−	0.763923i
$57$	−106.791	−	5341.55i	−0.0328688	−	1.64406i
$58$	2661.31	−	1257.55i	0.791114	−	0.373825i
$59$	−1864.25	+	1076.32i	−0.535549	+	0.309200i	−0.743273	−	0.668988i	$-0.766728\pi$
$59$	−1864.25	+	1076.32i	−0.535549	+	0.309200i	0.207724	+	0.978188i	$0.433394\pi$
$60$	−504.976	+	640.091i	−0.140271	+	0.177803i
$61$	33.1660	−	57.4451i	0.00891319	−	0.0154381i	−0.861534	−	0.507699i	$-0.830496\pi$
$61$	33.1660	−	57.4451i	0.00891319	−	0.0154381i	0.870448	+	0.492261i	$0.163829\pi$
$62$	−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
$66$	1709.60	+	3438.32i	0.392471	+	0.789331i
$67$	3554.82	−	2052.38i	0.791897	−	0.457202i	−0.0487331	−	0.998812i	$-0.515518\pi$
$67$	3554.82	−	2052.38i	0.791897	−	0.457202i	0.840630	+	0.541610i	$0.182185\pi$
$68$	−690.091	−	1837.49i	−0.149241	−	0.397380i
$69$	−4212.79	+	2545.87i	−0.884854	+	0.534733i
$70$	−672.427	+	970.824i	−0.137230	+	0.198127i
$71$			5031.65i			0.998145i	0.866560	+	0.499072i	$0.166326\pi$
$71$			5031.65i			0.998145i	−0.866560	+	0.499072i	$0.833674\pi$
$72$	1063.02	−	5073.84i	0.205058	−	0.978750i
$73$	2705.16			0.507631			0.253815	−	0.967253i	$-0.418314\pi$
$73$	2705.16			0.507631			0.253815	+	0.967253i	$0.418314\pi$
$74$	−7527.78	−	5214.01i	−1.37469	−	0.952157i
$75$	−2575.34	+	4673.95i	−0.457838	+	0.830925i
$76$	−8891.60	+	3339.35i	−1.53940	+	0.578143i
$77$	2781.03	+	4816.88i	0.469055	+	0.812427i
$78$	−273.215	+	4388.44i	−0.0449071	+	0.721308i
$79$	−1196.02	−	690.524i	−0.191639	−	0.110643i	0.401110	−	0.916030i	$-0.368624\pi$
$79$	−1196.02	−	690.524i	−0.191639	−	0.110643i	−0.592750	+	0.805387i	$0.701958\pi$
$80$	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	$-0.263268\pi$
$83$	2605.31	+	1504.18i	0.378184	+	0.218345i	−0.298844	+	0.954302i	$0.596601\pi$
$84$	1080.12	−	7430.88i	0.153079	−	1.05313i
$85$	347.282	+	601.509i	0.0480667	+	0.0832539i
$86$	3835.74	+	8117.45i	0.518624	+	1.09755i
$87$	3196.09	−	5800.55i	0.422261	−	0.766356i
$88$	4752.65	−	4900.33i	0.613721	−	0.632790i
$89$	3186.35			0.402267			0.201133	−	0.979564i	$-0.435538\pi$
$89$	3186.35			0.402267			0.201133	+	0.979564i	$0.435538\pi$
$90$	−77.3677	+	1832.80i	−0.00955157	+	0.226271i
$91$			6368.92i			0.769100i
$92$	6760.48	+	5556.22i	0.798734	+	0.656454i
$93$	−4513.23	+	2727.43i	−0.521821	+	0.315346i
$94$	1802.68	+	3814.95i	0.204015	+	0.431751i
$95$	2910.71	−	1680.50i	0.322516	−	0.186205i
$96$	−9134.91	+	1219.85i	−0.991201	+	0.132362i
$97$	2407.03	−	4169.10i	0.255822	−	0.443097i	−0.709296	−	0.704910i	$-0.750987\pi$
$97$	2407.03	−	4169.10i	0.255822	−	0.443097i	0.965118	+	0.261814i	$0.0843206\pi$
$98$	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	−0.641066	−	0.767486i	$-0.721507\pi$
$101$	3510.47	−	6080.30i	0.344130	−	0.596050i	0.985195	+	0.171436i	$0.0548407\pi$
$102$	−3680.03	−	2441.54i	−0.353713	−	0.234673i
$103$	−1858.85	+	1073.21i	−0.175214	+	0.101160i	−0.585042	−	0.811003i	$-0.698922\pi$
$103$	−1858.85	+	1073.21i	−0.175214	+	0.101160i	0.409828	+	0.912163i	$0.365589\pi$
$104$	7518.59	−	2138.39i	0.695136	−	0.197706i
$105$	53.1124	+	2656.62i	0.00481745	+	0.240963i
$106$	15627.8	+	10824.4i	1.39087	+	0.963366i
$107$		−	13846.7i		−	1.20943i	−0.796443	−	0.604713i	$-0.793288\pi$
$107$		−	13846.7i		−	1.20943i	0.796443	−	0.604713i	$-0.206712\pi$
$108$	−4747.95	−	10653.9i	−0.407060	−	0.913401i
$109$	−19384.9			−1.63159			−0.815793	−	0.578344i	$-0.803699\pi$
$109$	−19384.9			−1.63159			−0.815793	+	0.578344i	$0.803699\pi$
$110$	−1375.45	+	1985.82i	−0.113674	+	0.164117i
$111$	−20599.5	+	411.834i	−1.67190	+	0.0334254i
$112$	−13096.5	+	2585.71i	−1.04404	+	0.206132i
$113$	−6817.20	−	11807.7i	−0.533887	−	0.924719i	−0.999216	−	0.0395818i	$-0.987397\pi$
$113$	−6817.20	−	11807.7i	−0.533887	−	0.924719i	0.465329	−	0.885138i	$-0.345936\pi$
$114$	−11814.6	+	17807.7i	−0.909095	+	1.37024i
$115$	−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
$120$	3118.35	−	954.670i	0.216552	−	0.0662966i
$121$	−1631.91	−	2826.55i	−0.111462	−	0.193057i
$122$	−239.894	+	113.357i	−0.0161176	+	0.00761603i
$123$	−13351.5	−	22093.5i	−0.882509	−	1.46034i
$124$	7242.61	+	5952.47i	0.471034	+	0.387128i
$125$	−6895.78			−0.441330
$126$	−7822.98	−	14974.9i	−0.492755	−	0.943243i
$127$			15689.6i			0.972754i	0.873749	+	0.486377i	$0.161682\pi$
$127$			15689.6i			0.972754i	−0.873749	+	0.486377i	$0.838318\pi$
$128$	7449.66	+	14592.4i	0.454691	+	0.890649i
$129$	17692.7	+	9748.64i	1.06320	+	0.585820i
$130$	−2500.92	+	1181.76i	−0.147983	+	0.0699266i
$131$	7250.25	−	4185.93i	0.422484	−	0.243921i	−0.273656	−	0.961828i	$-0.588233\pi$
$131$	7250.25	−	4185.93i	0.422484	−	0.243921i	0.696140	+	0.717907i	$0.254899\pi$
$132$	2209.39	−	15199.9i	0.126802	−	0.872352i
$133$	−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	−0.124014	−	0.992280i	$-0.539577\pi$
$137$	14965.1	−	25920.4i	0.797333	−	1.38102i	0.921347	−	0.388741i	$-0.127090\pi$
$138$	19651.2	+	1223.44i	1.03188	+	0.0642428i
$139$	20651.8	−	11923.3i	1.06888	−	0.617118i	0.141005	−	0.990009i	$-0.454967\pi$
$139$	20651.8	−	11923.3i	1.06888	−	0.617118i	0.927875	+	0.372891i	$0.121633\pi$
$140$	4422.24	−	1660.83i	0.225624	−	0.0847361i
$141$	8315.02	+	4581.56i	0.418239	+	0.230449i
$142$	11459.9	−	16545.4i	0.568336	−	0.820541i
$143$			13027.6i			0.637078i
$144$	−15051.5	+	14263.0i	−0.725864	+	0.687839i
$145$	4166.34			0.198161
$146$	−8895.30	−	6161.20i	−0.417306	−	0.289041i
$147$	−1481.04	−	2450.76i	−0.0685381	−	0.113414i
$148$	12878.1	+	34290.1i	0.587933	+	1.56547i
$149$	−2636.98	−	4567.39i	−0.118778	−	0.205729i	0.800506	−	0.599325i	$-0.204564\pi$
$149$	−2636.98	−	4567.39i	−0.118778	−	0.205729i	−0.919284	+	0.393596i	$0.871231\pi$
$150$	19113.6	−	9503.68i	0.849495	−	0.422386i
$151$	−28946.1	−	16712.0i	−1.26951	−	0.732951i	−0.294614	−	0.955616i	$-0.595191\pi$
$151$	−28946.1	−	16712.0i	−1.26951	−	0.732951i	−0.974895	+	0.222665i	$0.928524\pi$
$152$	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
$156$	10893.4	−	13808.1i	0.447624	−	0.567393i
$157$	−8500.73	−	14723.7i	−0.344871	−	0.597334i	0.640459	−	0.767992i	$-0.278744\pi$
$157$	−8500.73	−	14723.7i	−0.344871	−	0.597334i	−0.985330	+	0.170658i	$0.945411\pi$
$158$	2360.12	+	4994.65i	0.0945410	+	0.200074i
$159$	42764.9	−	854.976i	1.69158	−	0.0338189i
$160$	−3445.41	−	4662.88i	−0.134586	−	0.182144i
$161$	28519.6			1.10025
$162$	−22698.9	−	13172.2i	−0.864919	−	0.501911i
$163$			30843.8i			1.16089i	0.814298	+	0.580447i	$0.197122\pi$
$163$			30843.8i			1.16089i	−0.814298	+	0.580447i	$0.802878\pi$
$164$	−29138.9	+	35454.5i	−1.08339	+	1.31821i
$165$	108.641	+	5434.12i	0.00399050	+	0.199600i
$166$	−5141.09	−	10879.9i	−0.186569	−	0.394829i
$167$	−13682.1	+	7899.35i	−0.490591	+	0.283243i	−0.724819	−	0.688939i	$-0.758077\pi$
$167$	−13682.1	+	7899.35i	−0.490591	+	0.283243i	0.234229	+	0.972181i	$0.424743\pi$
$168$	−20476.1	+	21974.6i	−0.725485	+	0.778580i
$169$	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	0.142015	+	0.989865i	$0.454642\pi$
$173$	−23531.4	+	40757.6i	−0.786241	+	1.36181i	−0.928255	+	0.371944i	$0.878691\pi$
$174$	−23720.7	+	11794.4i	−0.783483	+	0.389564i
$175$	26777.0	−	15459.7i	0.874352	−	0.504807i
$176$	−26788.8	+	5289.07i	−0.864825	+	0.170747i
$177$	16581.3	−	10020.4i	0.529262	−	0.319843i
$178$	−10477.6	−	7257.14i	−0.330690	−	0.229047i
$179$			2545.69i			0.0794511i	0.999211	+	0.0397256i	$0.0126484\pi$
$179$			2545.69i			0.0794511i	−0.999211	+	0.0397256i	$0.987352\pi$
$180$	4428.73	−	5850.51i	0.136689	−	0.180571i
$181$	5676.58			0.173272			0.0866362	−	0.996240i	$-0.472388\pi$
$181$	5676.58			0.173272			0.0866362	+	0.996240i	$0.472388\pi$
$182$	14505.6	−	20942.7i	0.437920	−	0.632251i
$183$	−288.100	+	522.869i	−0.00860282	+	0.0156132i
$184$	−9575.56	−	33667.8i	−0.282832	−	0.994441i
$185$	−6480.77	−	11225.0i	−0.189358	−	0.327977i
$186$	21052.6	+	1310.69i	0.608527	+	0.0378856i
$187$	−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	$-0.186487\pi$
$191$	28127.2	+	16239.2i	0.771009	+	0.445142i	−0.0622257	+	0.998062i	$0.519820\pi$
$192$	32816.3	+	16794.2i	0.890199	+	0.455572i
$193$	−393.717	−	681.937i	−0.0105699	−	0.0183075i	0.860692	−	0.509126i	$-0.170031\pi$
$193$	−393.717	−	681.937i	−0.0105699	−	0.0183075i	−0.871262	+	0.490818i	$0.836698\pi$
$194$	−17410.3	+	8226.92i	−0.462598	+	0.218592i
$195$	−3003.47	+	5450.97i	−0.0789868	+	0.143352i
$196$	−3232.29	+	3932.86i	−0.0841393	+	0.102376i
$197$	24825.9			0.639694			0.319847	−	0.947469i	$-0.396368\pi$
$197$	24825.9			0.639694			0.319847	+	0.947469i	$0.396368\pi$
$198$	−16001.9	−	30631.2i	−0.408170	−	0.781328i
$199$		−	12008.5i		−	0.303237i	−0.988439	−	0.151619i	$-0.951551\pi$
$199$		−	12008.5i		−	0.303237i	0.988439	−	0.151619i	$-0.0484485\pi$
$200$	−27240.9	−	26420.0i	−0.681022	−	0.660499i
$201$	−31617.8	+	19107.2i	−0.782600	+	0.472939i
$202$	−25391.6	+	11998.3i	−0.622283	+	0.294048i
$203$	−33231.3	+	19186.1i	−0.806409	+	0.465580i
$204$	6540.14	+	16409.9i	0.157154	+	0.394318i
$205$	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
$210$	5875.99	−	8856.64i	0.133242	−	0.200831i
$211$	25764.7	−	14875.2i	0.578708	−	0.334117i	−0.181912	−	0.983315i	$-0.558229\pi$
$211$	25764.7	−	14875.2i	0.578708	−	0.334117i	0.760620	+	0.649198i	$0.224895\pi$
$212$	−26735.1	−	71186.9i	−0.594854	−	1.58390i
$213$	−905.174	−	45275.8i	−0.0199514	−	0.997945i
$214$	−31536.9	+	45531.7i	−0.688638	+	0.994228i
$215$			12708.1i			0.274917i
$216$	−8652.50	+	45846.7i	−0.185453	+	0.982653i
$217$	30553.5			0.648846
$218$	63742.6	+	44150.4i	1.34127	+	0.929012i
$219$	−24341.6	+	486.649i	−0.507529	+	0.0101468i
$220$	9045.68	−	3397.22i	0.186894	−	0.0701905i
$221$	−7491.58	−	12975.8i	−0.153387	−	0.265674i
$222$	68674.5	+	45562.5i	1.39344	+	0.924489i
$223$	−45854.8	−	26474.3i	−0.922093	−	0.532371i	−0.0377910	−	0.999286i	$-0.512032\pi$
$223$	−45854.8	−	26474.3i	−0.922093	−	0.532371i	−0.884302	+	0.466915i	$0.845365\pi$
$224$	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	$-0.452329\pi$
$227$	−32593.5	−	18817.9i	−0.632528	−	0.365190i	−0.781730	+	0.623616i	$0.785663\pi$
$228$	79407.7	−	31647.7i	1.52754	−	0.608797i
$229$	28619.2	+	49569.9i	0.545741	+	0.945251i	0.998560	+	0.0536486i	$0.0170851\pi$
$229$	28619.2	+	49569.9i	0.545741	+	0.945251i	−0.452819	+	0.891603i	$0.649582\pi$
$230$	5291.85	+	11199.0i	0.100035	+	0.211701i
$231$	−25890.8	−	42843.0i	−0.485201	−	0.802889i
$232$	33807.0	+	32788.2i	0.628102	+	0.609174i
$233$	−36468.7			−0.671751			−0.335876	−	0.941906i	$-0.609032\pi$
$233$	−36468.7			−0.671751			−0.335876	+	0.941906i	$0.609032\pi$
$234$	1668.98	−	39537.2i	0.0304803	−	0.722062i
$235$			5972.39i			0.108147i
$236$	−26608.8	−	21868.9i	−0.477750	−	0.392648i
$237$	10886.3	+	5998.31i	0.193813	+	0.106790i
$238$	10932.0	+	23135.0i	0.192995	+	0.408429i
$239$	45342.6	−	26178.6i	0.793799	−	0.458300i	−0.0474993	−	0.998871i	$-0.515125\pi$
$239$	45342.6	−	26178.6i	0.793799	−	0.458300i	0.841298	+	0.540571i	$0.181792\pi$
$240$	−12428.3	−	3963.04i	−0.215769	−	0.0688027i
$241$	6755.56	−	11701.0i	0.116313	−	0.201460i	−0.801991	−	0.597336i	$-0.796226\pi$
$241$	6755.56	−	11701.0i	0.116313	−	0.201460i	0.918304	+	0.395877i	$0.129559\pi$
$242$	−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
$246$	−6416.18	+	103058.i	−0.106024	+	1.70299i
$247$	−62789.9	+	36251.8i	−1.02919	+	0.594204i
$248$	−10258.5	−	36068.9i	−0.166793	−	0.586447i
$249$	−23713.7	−	13066.2i	−0.382473	−	0.210742i
$250$	22675.1	+	15705.6i	0.362802	+	0.251290i
$251$		−	111309.i		−	1.76678i	−0.468635	−	0.883392i	$-0.655254\pi$
$251$		−	111309.i		−	1.76678i	0.468635	−	0.883392i	$-0.344746\pi$
$252$	−8382.38	+	67058.9i	−0.131998	+	1.05598i
$253$	58336.8			0.911385
$254$	35734.0	−	51591.4i	0.553879	−	0.799668i
$255$	−3233.12	−	5350.03i	−0.0497212	−	0.0822765i
$256$	8738.74	−	64950.8i	0.133343	−	0.991070i
$257$	36956.5	+	64010.6i	0.559532	+	0.969138i	0.997535	+	0.0701645i	$0.0223524\pi$
$257$	36956.5	+	64010.6i	0.559532	+	0.969138i	−0.438003	+	0.898973i	$0.644314\pi$
$258$	−35975.1	−	72352.4i	−0.540458	−	1.08696i
$259$	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	$-0.316372\pi$
$263$	6380.84	+	3683.98i	0.0922500	+	0.0532606i	−0.453165	+	0.891426i	$0.649705\pi$
$264$	−41883.8	+	44949.1i	−0.600950	+	0.644931i
$265$	13454.2	+	23303.3i	0.191587	+	0.331838i
$266$	111950.	−	52900.0i	1.58220	−	0.747639i
$267$	−28671.5	+	573.213i	−0.402186	+	0.00804069i
$268$	50738.7	+	41700.5i	0.706431	+	0.580593i
$269$	−38604.8			−0.533502			−0.266751	−	0.963765i	$-0.585950\pi$
$269$	−38604.8			−0.533502			−0.266751	+	0.963765i	$0.585950\pi$
$270$	366.457	−	16505.8i	0.00502684	−	0.226417i
$271$		−	12540.3i		−	0.170753i	−0.996349	−	0.0853767i	$-0.972791\pi$
$271$		−	12540.3i		−	0.170753i	0.996349	−	0.0853767i	$-0.0272094\pi$
$272$	23640.8	−	20673.1i	0.319539	−	0.279426i
$273$	−1145.74	−	57308.8i	−0.0153731	−	0.768946i
$274$	−108245.	+	51148.9i	−1.44180	+	0.681295i
$275$	54772.4	−	31622.8i	0.724263	−	0.418153i
$276$	−61831.7	−	48779.8i	−0.811695	−	0.640357i
$277$	46052.4	−	79765.0i	0.600195	−	1.03957i	−0.392596	−	0.919711i	$-0.628423\pi$
$277$	46052.4	−	79765.0i	0.600195	−	1.03957i	0.992791	−	0.119857i	$-0.0382436\pi$
$278$	−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	−0.927942	−	0.372723i	$-0.878424\pi$
$281$	−11148.0	+	19308.8i	−0.141183	+	0.244537i	0.786759	+	0.617260i	$0.211757\pi$
$282$	−16907.2	−	34003.4i	−0.212605	−	0.427587i
$283$	−21648.6	+	12498.8i	−0.270307	+	0.156062i	−0.629027	−	0.777383i	$-0.716547\pi$
$283$	−21648.6	+	12498.8i	−0.270307	+	0.156062i	0.358720	+	0.933445i	$0.383213\pi$
$284$	−75366.5	+	28304.8i	−0.934419	+	0.350933i
$285$	−25888.8	+	15645.1i	−0.318729	+	0.192614i
$286$	29671.3	−	42838.2i	0.362747	−	0.523720i
$287$			149568.i			1.81582i
$288$	81978.3	−	12619.7i	0.988358	−	0.152148i
$289$	−68471.9			−0.819816
$290$	−13700.0	−	9489.12i	−0.162902	−	0.112831i
$291$	−20908.9	+	37947.4i	−0.246914	+	0.448122i
$292$	15217.5	+	40519.3i	0.178475	+	0.475222i
$293$	11748.6	+	20349.1i	0.136852	+	0.237034i	0.926303	−	0.376779i	$-0.122968\pi$
$293$	11748.6	+	20349.1i	0.136852	+	0.237034i	−0.789452	+	0.613813i	$0.789635\pi$
$294$	−711.727	+	11431.9i	−0.00823416	+	0.132259i
$295$	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
$300$	−84495.9	−	12282.0i	−0.938844	−	0.136467i
$301$	−58521.0	−	101361.i	−0.645920	−	1.11877i
$302$	57119.6	+	120880.i	0.626283	+	1.32538i
$303$	−30494.1	+	55343.3i	−0.332147	+	0.602809i
$304$	−100037.	−	114398.i	−1.08246	−	1.23786i
$305$	−375.559			−0.00403719
$306$	33552.8	+	21307.4i	0.358333	+	0.227556i
$307$		−	32060.0i		−	0.340163i	−0.985430	−	0.170082i	$-0.945597\pi$
$307$		−	32060.0i		−	0.340163i	0.985430	−	0.170082i	$-0.0544031\pi$
$308$	−56505.3	+	68752.3i	−0.595646	+	0.724746i
$309$	16533.2	−	9991.34i	0.173157	−	0.104642i
$310$	5669.24	+	11997.6i	0.0589931	+	0.124845i
$311$	−61441.4	+	35473.2i	−0.635244	+	0.366758i	−0.782780	−	0.622298i	$-0.786199\pi$
$311$	−61441.4	+	35473.2i	−0.635244	+	0.366758i	0.147536	+	0.989057i	$0.452866\pi$
$312$	−67269.1	+	20594.2i	−0.691046	+	0.211561i
$313$	−59259.6	+	102641.i	−0.604882	+	1.04769i	0.387189	+	0.922001i	$0.373446\pi$
$313$	−59259.6	+	102641.i	−0.604882	+	1.04769i	−0.992070	+	0.125685i	$0.959887\pi$
$314$	−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	−0.307100	−	0.951677i	$-0.599359\pi$
$317$	67390.6	−	116724.i	0.670626	−	1.16156i	0.977727	−	0.209882i	$-0.0673080\pi$
$318$	−142570.	−	94588.6i	−1.40985	−	0.935372i
$319$	−67974.6	+	39245.2i	−0.667983	+	0.385660i
$320$	709.388	+	23180.0i	0.00692762	+	0.226367i
$321$	2490.97	+	124596.i	0.0241746	+	1.20918i
$322$	−93780.0	−	64955.4i	−0.904479	−	0.626474i
$323$		−	72822.8i		−	0.698011i
$324$	44639.6	+	95011.9i	0.425236	+	0.905082i
$325$	72420.4			0.685637
$326$	70248.8	−	101422.i	0.661003	−	0.954331i
$327$	174429.	−	3487.26i	1.63126	−	0.0326129i
$328$	176567.	−	50217.8i	1.64120	−	0.466778i
$329$	−27503.0	−	47636.7i	−0.254091	−	0.440098i
$330$	12019.3	−	18116.2i	0.110370	−	0.166357i
$331$	133143.	+	76870.2i	1.21524	+	0.701620i	0.963896	−	0.266278i	$-0.0857939\pi$
$331$	133143.	+	76870.2i	1.21524	+	0.701620i	0.251345	+	0.967898i	$0.419127\pi$
$332$	−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
$336$	117380.	−	25622.8i	1.03971	−	0.226959i
$337$	11471.8	+	19869.8i	0.101012	+	0.174958i	0.912102	−	0.409964i	$-0.134459\pi$
$337$	11471.8	+	19869.8i	0.101012	+	0.174958i	−0.811090	+	0.584922i	$0.801125\pi$
$338$	−49342.7	+	23315.9i	−0.431906	+	0.204089i
$339$	63466.7	+	105022.i	0.552264	+	0.913863i
$340$	−7056.12	+	8585.46i	−0.0610391	+	0.0742687i
$341$	62497.2			0.537467
$342$	103107.	−	162362.i	0.881524	−	1.38814i
$343$		−	108611.i		−	0.923175i
$344$	−100010.	+	103117.i	−0.845134	+	0.871393i
$345$	24409.1	+	13449.4i	0.205076	+	0.112996i
$346$	170206.	−	80427.3i	1.42174	−	0.671817i
$347$	6260.87	−	3614.72i	0.0519967	−	0.0300203i	−0.473776	−	0.880645i	$-0.657109\pi$
$347$	6260.87	−	3614.72i	0.0519967	−	0.0300203i	0.525773	+	0.850625i	$0.323776\pi$
$348$	104863.	+	15242.4i	0.865890	+	0.125862i
$349$	−55282.6	+	95752.3i	−0.453877	+	0.786137i	−0.998623	−	0.0524636i	$-0.983293\pi$
$349$	−55282.6	+	95752.3i	−0.453877	+	0.786137i	0.544746	+	0.838601i	$0.316626\pi$
$350$	−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	−0.715557	−	0.698554i	$-0.753827\pi$
$353$	30801.7	−	53350.1i	0.247187	−	0.428140i	0.962744	+	0.270414i	$0.0871605\pi$
$354$	−77345.6	−	4815.37i	−0.617204	−	0.0384259i
$355$	24671.6	−	14244.1i	0.195767	−	0.113026i
$356$	17924.4	+	47726.8i	0.141431	+	0.376584i
$357$	50424.8	+	27784.0i	0.395647	+	0.218001i
$358$	5797.99	−	8370.91i	0.0452388	−	0.0653141i
$359$			84462.7i			0.655354i	0.944790	+	0.327677i	$0.106266\pi$
$359$			84462.7i			0.655354i	−0.944790	+	0.327677i	$0.893734\pi$
$360$	−27887.8	+	9151.29i	−0.215183	+	0.0706118i
$361$	−222069.			−1.70401
$362$	−18666.1	−	12928.8i	−0.142441	−	0.0986600i
$363$	15192.7	+	25140.3i	0.115298	+	0.190791i
$364$	−95396.8	+	35827.5i	−0.719998	+	0.270404i
$365$	−7658.07	−	13264.2i	−0.0574823	−	0.0995622i
$366$	2138.22	−	1063.17i	0.0159621	−	0.00793668i
$367$	−161018.	−	92963.9i	−1.19548	−	0.690212i	−0.235937	−	0.971768i	$-0.575816\pi$
$367$	−161018.	−	92963.9i	−1.19548	−	0.690212i	−0.959545	+	0.281556i	$0.909149\pi$
$368$	−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
$372$	−66241.3	−	52258.6i	−0.478678	−	0.377635i
$373$	42545.6	+	73691.2i	0.305800	+	0.529661i	0.977439	−	0.211217i	$-0.0677428\pi$
$373$	42545.6	+	73691.2i	0.305800	+	0.529661i	−0.671639	+	0.740878i	$0.734409\pi$
$374$	22361.4	+	47322.7i	0.159866	+	0.338319i
$375$	62049.6	−	1240.52i	0.441241	−	0.00882150i
$376$	−47001.5	+	48461.9i	−0.332457	+	0.342787i
$377$	−89876.5			−0.632359
$378$	73086.7	+	133340.i	0.511511	+	0.933205i
$379$		−	146982.i		−	1.02326i	−0.859206	−	0.511630i	$-0.829042\pi$
$379$		−	146982.i		−	1.02326i	0.859206	−	0.511630i	$-0.170958\pi$
$380$	41545.1	+	34144.6i	0.287708	+	0.236458i
$381$	−2822.49	−	141178.i	−0.0194439	−	0.972560i
$382$	−55503.6	−	117460.i	−0.380360	−	0.804942i
$383$	−161253.	+	93099.7i	−1.09929	+	0.634674i	−0.936034	−	0.351910i	$-0.885532\pi$
$383$	−161253.	+	93099.7i	−1.09929	+	0.634674i	−0.163254	+	0.986584i	$0.552199\pi$
$384$	−69658.6	−	129965.i	−0.472403	−	0.881383i
$385$	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	−0.0389437	−	0.999241i	$-0.512399\pi$
$389$	128002.	−	221706.i	0.845897	−	1.46514i	0.884840	−	0.465894i	$-0.154267\pi$
$390$	22291.2	−	11083.6i	0.146556	−	0.0728706i
$391$	−58104.8	+	33546.8i	−0.380066	+	0.219431i
$392$	19586.0	−	5570.52i	0.127460	−	0.0362513i
$393$	−64486.2	+	38970.2i	−0.417524	+	0.252317i
$394$	−81634.1	−	56542.7i	−0.525871	−	0.364237i
$395$			7819.24i			0.0501153i
$396$	−17146.2	+	137169.i	−0.109339	+	0.874712i
$397$	−260735.			−1.65432			−0.827159	−	0.561968i	$-0.810044\pi$
$397$	−260735.			−1.65432			−0.827159	+	0.561968i	$0.810044\pi$
$398$	−27350.2	+	39487.1i	−0.172661	+	0.249281i
$399$	134447.	−	244006.i	0.844509	−	1.53269i
$400$	29401.9	+	148919.i	0.183762	+	0.930743i
$401$	−26507.0	−	45911.4i	−0.164843	−	0.285517i	0.771756	−	0.635918i	$-0.219379\pi$
$401$	−26507.0	−	45911.4i	−0.164843	−	0.285517i	−0.936600	+	0.350401i	$0.886045\pi$
$402$	147486.	+	9182.15i	0.912637	+	0.0568189i
$403$	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
$408$	15869.0	−	68855.8i	0.0953301	−	0.413638i
$409$	−73697.8	−	127648.i	−0.440563	−	0.763078i	0.557168	−	0.830400i	$-0.311888\pi$
$409$	−73697.8	−	127648.i	−0.440563	−	0.763078i	−0.997731	+	0.0673220i	$0.978555\pi$
$410$	−58731.5	+	27752.4i	−0.349385	+	0.165095i
$411$	−129996.	+	235929.i	−0.769569	+	1.39668i
$412$	−26531.7	−	21805.6i	−0.156304	−	0.128462i
$413$	−112251.			−0.658099
$414$	−177045.	−	7473.59i	−1.03296	−	0.0436042i
$415$		−	17032.8i		−	0.0988983i
$416$	74324.7	+	100588.i	0.429483	+	0.581246i
$417$	−183684.	+	111004.i	−1.05633	+	0.638360i
$418$	228995.	−	108207.i	1.31061	−	0.619302i
$419$	201431.	−	116296.i	1.14736	−	0.662426i	0.199115	−	0.979976i	$-0.436193\pi$
$419$	201431.	−	116296.i	1.14736	−	0.662426i	0.948242	+	0.317550i	$0.102860\pi$
$420$	−39493.4	+	15740.0i	−0.223886	+	0.0892290i
$421$	34900.8	−	60449.9i	0.196911	−	0.341060i	−0.750614	−	0.660741i	$-0.770242\pi$
$421$	34900.8	−	60449.9i	0.196911	−	0.341060i	0.947525	+	0.319680i	$0.103576\pi$
$422$	−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
$426$	−100142.	+	150940.i	−0.551821	+	0.831737i
$427$	2995.51	−	1729.46i	0.0164292	−	0.00948539i
$428$	207403.	−	77892.8i	1.13221	−	0.425216i
$429$	−2343.62	−	117225.i	−0.0127342	−	0.636951i
$430$	28943.5	−	41787.5i	0.156536	−	0.226000i
$431$		−	147873.i		−	0.796037i	−0.917377	−	0.398019i	$-0.869698\pi$
$431$		−	147873.i		−	0.796037i	0.917377	−	0.398019i	$-0.130302\pi$
$432$	132871.	−	131049.i	0.711970	−	0.702210i
$433$	294850.			1.57262			0.786312	−	0.617830i	$-0.211988\pi$
$433$	294850.			1.57262			0.786312	+	0.617830i	$0.211988\pi$
$434$	−100468.	−	69587.7i	−0.533395	−	0.369448i
$435$	−37489.6	+	749.509i	−0.198122	+	0.00396094i
$436$	−109047.	−	290356.i	−0.573641	−	1.52742i
$437$	162333.	+	281169.i	0.850050	+	1.47233i
$438$	81150.0	+	53839.5i	0.423000	+	0.280642i
$439$	62468.0	+	36065.9i	0.324137	+	0.187140i	0.653235	−	0.757155i	$-0.273411\pi$
$439$	62468.0	+	36065.9i	0.324137	+	0.187140i	−0.329098	+	0.944296i	$0.606745\pi$
$440$	−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	$-0.495020\pi$
$443$	−165331.	−	95453.7i	−0.842453	−	0.486391i	−0.858097	+	0.513487i	$0.828353\pi$
$444$	−122048.	−	306232.i	−0.619106	−	1.55341i
$445$	−9020.28	−	15623.6i	−0.0455512	−	0.0788970i
$446$	90485.7	+	191492.i	0.454894	+	0.962677i
$447$	24549.7	+	40623.9i	0.122866	+	0.203314i
$448$	−112402.	−	181620.i	−0.560041	−	0.904914i
$449$	192859.			0.956639			0.478319	−	0.878186i	$-0.341246\pi$
$449$	192859.			0.956639			0.478319	+	0.878186i	$0.341246\pi$
$450$	−170279.	+	88954.5i	−0.840882	+	0.439281i
$451$			305940.i			1.50412i
$452$	138513.	−	168534.i	0.677975	−	0.824919i
$453$	263469.	+	145171.i	1.28391	+	0.707429i
$454$	64317.1	+	136112.i	0.312043	+	0.660367i
$455$	31228.6	−	18029.8i	0.150844	−	0.0870901i
$456$	−333193.	−	76790.3i	−1.60238	−	0.369298i
$457$	2962.66	−	5131.48i	0.0141857	−	0.0245703i	−0.858845	−	0.512235i	$-0.828818\pi$
$457$	2962.66	−	5131.48i	0.0141857	−	0.0245703i	0.873031	+	0.487665i	$0.162151\pi$
$458$	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	−0.975690	−	0.219156i	$-0.929670\pi$
$461$	−63341.9	+	109711.i	−0.298050	+	0.516238i	0.677640	+	0.735394i	$0.263003\pi$
$462$	−12442.1	+	199847.i	−0.0582919	+	0.936297i
$463$	−204011.	+	117786.i	−0.951682	+	0.549454i	−0.893603	−	0.448858i	$-0.851831\pi$
$463$	−204011.	+	117786.i	−0.951682	+	0.549454i	−0.0580790	+	0.998312i	$0.518498\pi$
$464$	−36488.9	−	184814.i	−0.169483	−	0.858418i
$465$	26149.9	+	14408.5i	0.120938	+	0.0666367i
$466$	119919.	+	83060.0i	0.552224	+	0.382490i
$467$		−	97776.2i		−	0.448332i	−0.974551	−	0.224166i	$-0.928034\pi$
$467$		−	97776.2i		−	0.448332i	0.974551	−	0.224166i	$-0.0719658\pi$
$468$	−95536.8	+	126208.i	−0.436193	+	0.576227i
$469$	214045.			0.973105
$470$	13602.5	−	19638.8i	0.0615778	−	0.0889036i
$471$	79140.0	+	130957.i	0.356742	+	0.590321i
$472$	37688.8	+	132514.i	0.169172	+	0.594810i
$473$	−119705.	−	207334.i	−0.535043	−	0.926721i
$474$	−22135.4	−	44518.3i	−0.0985213	−	0.198144i
$475$	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	0.999669	+	0.0257398i	$0.00819415\pi$
$479$	349162.	+	201589.i	1.52179	+	0.878608i	0.522126	+	0.852869i	$0.325139\pi$
$480$	31841.3	+	41337.7i	0.138200	+	0.179417i
$481$	139803.	+	242147.i	0.604266	+	1.04662i
$482$	−48863.8	+	23089.6i	−0.210326	+	0.0993855i
$483$	−256625.	+	5130.57i	−1.10003	+	0.0219923i
$484$	33157.4	−	40344.0i	0.141543	−	0.172222i
$485$	−27256.3			−0.115873
$486$	206619.	+	114442.i	0.874779	+	0.484523i
$487$		−	195207.i		−	0.823071i	−0.911394	−	0.411536i	$-0.864993\pi$
$487$		−	195207.i		−	0.823071i	0.911394	−	0.411536i	$-0.135007\pi$
$488$	−3047.41	−	2955.57i	−0.0127965	−	0.0124109i
$489$	−5548.68	−	277538.i	−0.0232045	−	1.16066i
$490$	−6514.92	+	3078.49i	−0.0271342	+	0.0128217i
$491$	65937.1	−	38068.8i	0.273506	−	0.157909i	−0.356974	−	0.934114i	$-0.616191\pi$
$491$	65937.1	−	38068.8i	0.273506	−	0.157909i	0.630480	+	0.776206i	$0.282858\pi$
$492$	255820.	−	324269.i	1.05683	−	1.33960i
$493$	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
$498$	48217.8	+	96974.8i	0.194423	+	0.391021i
$499$	12618.3	−	7285.17i	0.0506757	−	0.0292576i	−0.474448	−	0.880283i	$-0.657352\pi$
$499$	12618.3	−	7285.17i	0.0506757	−	0.0292576i	0.525124	+	0.851026i	$0.324019\pi$
$500$	−38791.2	−	103288.i	−0.155165	−	0.413153i
$501$	121693.	−	73541.3i	0.484831	−	0.292992i
$502$	−253514.	+	366014.i	−1.00599	+	1.45241i
$503$			280154.i			1.10729i	0.832753	+	0.553645i	$0.186764\pi$
$503$			280154.i			1.10729i	−0.832753	+	0.553645i	$0.813236\pi$
$504$	180295.	−	201416.i	0.709777	−	0.792926i
$505$	−39751.2			−0.155872
$506$	−191827.	−	132866.i	−0.749219	−	0.518935i
$507$	−59258.0	+	107547.i	−0.230532	+	0.418390i
$508$	−235006.	+	88259.4i	−0.910650	+	0.342006i
$509$	−101505.	−	175811.i	−0.391787	−	0.678595i	0.600899	−	0.799325i	$-0.294810\pi$
$509$	−101505.	−	175811.i	−0.391787	−	0.678595i	−0.992685	+	0.120731i	$0.961476\pi$
$510$	−1553.71	+	24956.0i	−0.00597349	+	0.0959476i
$511$	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
$516$	−46492.1	+	319850.i	−0.174614	+	1.20129i
$517$	−56257.4	−	97440.7i	−0.210474	−	0.364552i
$518$	−204007.	−	431732.i	−0.760300	−	1.60900i
$519$	204408.	−	370978.i	0.758863	−	1.37725i
$520$	−31769.6	−	30812.2i	−0.117491	−	0.113950i
$521$	−30822.1			−0.113550			−0.0567749	−	0.998387i	$-0.518082\pi$
$521$	−30822.1			−0.113550			−0.0567749	+	0.998387i	$0.518082\pi$
$522$	211322.	−	110396.i	0.775540	−	0.405146i
$523$		−	94412.3i		−	0.345164i	−0.984995	−	0.172582i	$-0.944789\pi$
$523$		−	94412.3i		−	0.345164i	0.984995	−	0.172582i	$-0.0552109\pi$
$524$	103484.	+	85050.4i	0.376887	+	0.309752i
$525$	−238164.	+	143927.i	−0.864087	+	0.522183i
$526$	−12591.4	−	26646.7i	−0.0455095	−	0.0963101i
$527$	−62248.6	+	35939.3i	−0.224134	+	0.129404i
$528$	240100.	−	52411.4i	0.861239	−	0.188000i
$529$	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
$534$	95584.9	+	63416.3i	0.335202	+	0.222392i
$535$	−67894.3	+	39198.8i	−0.237206	+	0.136951i
$536$	−71866.5	−	252683.i	−0.250148	−	0.879523i
$537$	−457.961	−	22906.7i	−0.00158811	−	0.0794352i
$538$	126943.	+	87925.0i	0.438574	+	0.303772i
$539$			33937.0i			0.116814i
$540$	−38798.1	+	53440.8i	−0.133052	+	0.183267i
$541$	166561.			0.569087			0.284544	−	0.958663i	$-0.408158\pi$
$541$	166561.			0.569087			0.284544	+	0.958663i	$0.408158\pi$
$542$	−28561.4	+	41235.8i	−0.0972257	+	0.140371i
$543$	−51079.0	+	1021.20i	−0.173238	+	0.00346345i
$544$	−124821.	+	14135.0i	−0.421785	+	0.0477637i
$545$	54876.8	+	95049.4i	0.184755	+	0.320005i
$546$	−126757.	+	191056.i	−0.425194	+	0.640878i
$547$	−256245.	−	147943.i	−0.856410	−	0.494448i	0.00639865	−	0.999980i	$-0.497963\pi$
$547$	−256245.	−	147943.i	−0.856410	−	0.494448i	−0.862808	+	0.505531i	$0.831297\pi$
$548$	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
$552$	92219.6	+	301227.i	0.302653	+	0.988589i
$553$	−36007.8	−	62367.3i	−0.117746	−	0.203942i
$554$	−333103.	+	157401.i	−1.08532	+	0.512847i
$555$	60334.6	+	99839.1i	0.195876	+	0.324127i
$556$	294768.	+	242260.i	0.953521	+	0.783669i
$557$	−30600.2			−0.0986312			−0.0493156	−	0.998783i	$-0.515704\pi$
$557$	−30600.2			−0.0986312			−0.0493156	+	0.998783i	$0.515704\pi$
$558$	−189671.	−	8006.58i	−0.609163	−	0.0257145i
$559$		−	274139.i		−	0.877298i
$560$	49753.4	+	56895.7i	0.158652	+	0.181428i
$561$	103144.	+	56832.1i	0.327731	+	0.180579i
$562$	80634.7	−	38102.3i	0.255299	−	0.120637i
$563$	−210267.	+	121398.i	−0.663369	+	0.382996i	−0.793559	−	0.608493i	$-0.791774\pi$
$563$	−210267.	+	121398.i	−0.663369	+	0.382996i	0.130191	+	0.991489i	$0.458441\pi$
$564$	−21849.8	+	150319.i	−0.0686894	+	0.472560i
$565$	−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	−0.998884	−	0.0472242i	$-0.984962\pi$
$569$	−148459.	+	257138.i	−0.458545	+	0.794223i	0.540339	+	0.841447i	$0.318296\pi$
$570$	120762.	+	7518.39i	0.371690	+	0.0231406i
$571$	228446.	−	131893.i	0.700665	−	0.404529i	−0.106930	−	0.994267i	$-0.534102\pi$
$571$	228446.	−	131893.i	0.700665	−	0.404529i	0.807595	+	0.589737i	$0.200769\pi$
$572$	−195134.	+	73285.1i	−0.596405	+	0.223987i
$573$	−256015.	−	141064.i	−0.779752	−	0.429642i
$574$	340650.	−	491818.i	1.03392	−	1.49273i
$575$		−	324294.i		−	0.980852i
$576$	−298309.	−	145214.i	−0.899127	−	0.437688i
$577$	350367.			1.05238			0.526188	−	0.850368i	$-0.323621\pi$
$577$	350367.			1.05238			0.526188	+	0.850368i	$0.323621\pi$
$578$	225154.	+	155949.i	0.673943	+	0.466797i
$579$	3665.42	+	6065.38i	0.0109337	+	0.0180926i
$580$	23437.2	+	62405.5i	0.0696705	+	0.185510i
$581$	78436.3	+	135856.i	0.232362	+	0.402463i
$582$	155182.	−	77159.5i	0.458137	−	0.227795i
$583$	−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	$-0.336515\pi$
$587$	−5965.76	−	3444.33i	−0.0173137	−	0.00999606i	−0.508632	+	0.860984i	$0.669849\pi$
$588$	28377.3	−	35970.2i	0.0820761	−	0.104037i
$589$	173910.	+	301221.i	0.501296	+	0.868270i
$590$	−20828.3	−	44078.3i	−0.0598344	−	0.126625i
$591$	−223388.	+	4466.08i	−0.639566	+	0.0127865i
$592$	−441170.	+	385788.i	−1.25882	+	1.10079i
$593$	544416.			1.54818			0.774090	−	0.633076i	$-0.218208\pi$
$593$	544416.			1.54818			0.774090	+	0.633076i	$0.218208\pi$
$594$	149499.	+	272747.i	0.423706	+	0.773013i
$595$			36218.4i			0.102305i
$596$	53578.6	−	65191.2i	0.150834	−	0.183526i
$597$	2160.28	+	108055.i	0.00606125	+	0.303177i
$598$	−114156.	−	241585.i	−0.319225	−	0.675565i
$599$	−122771.	+	70881.9i	−0.342170	+	0.197552i	−0.661231	−	0.750182i	$-0.729966\pi$
$599$	−122771.	+	70881.9i	−0.342170	+	0.197552i	0.319061	+	0.947734i	$0.396633\pi$
$600$	249872.	+	232832.i	0.694089	+	0.646755i
$601$	265380.	−	459652.i	0.734715	−	1.27256i	−0.220133	−	0.975470i	$-0.570649\pi$
$601$	265380.	−	459652.i	0.734715	−	1.27256i	0.954848	−	0.297094i	$-0.0960176\pi$
$602$	−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
$606$	226321.	−	112531.i	0.616281	−	0.306427i
$607$	35215.7	−	20331.8i	0.0955782	−	0.0551821i	−0.451449	−	0.892297i	$-0.649093\pi$
$607$	35215.7	−	20331.8i	0.0955782	−	0.0551821i	0.547027	+	0.837115i	$0.315759\pi$
$608$	68399.3	+	604011.i	0.185031	+	1.63395i
$609$	295570.	−	178619.i	0.796942	−	0.481606i
$610$	1234.94	+	855.362i	0.00331883	+	0.00229874i
$611$		−	128837.i		−	0.345110i
$612$	−61801.5	−	146483.i	−0.165005	−	0.391098i
$613$	−498556.			−1.32676			−0.663382	−	0.748281i	$-0.730879\pi$
$613$	−498556.			−1.32676			−0.663382	+	0.748281i	$0.730879\pi$
$614$	−73018.9	+	105422.i	−0.193686	+	0.279636i
$615$	−70533.5	+	128011.i	−0.186486	+	0.338451i
$616$	342393.	−	97381.0i	0.902325	−	0.256633i
$617$	45030.4	+	77995.0i	0.118287	+	0.204879i	0.919089	−	0.394050i	$-0.128926\pi$
$617$	45030.4	+	77995.0i	0.118287	+	0.204879i	−0.800802	+	0.598929i	$0.795593\pi$
$618$	−77121.6	−	4801.43i	−0.201929	−	0.0125717i
$619$	−149379.	−	86244.1i	−0.389860	−	0.225086i	0.292240	−	0.956345i	$-0.405600\pi$
$619$	−149379.	−	86244.1i	−0.389860	−	0.225086i	−0.682099	+	0.731259i	$0.738933\pi$
$620$	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
$624$	268103.	+	85490.9i	0.688546	+	0.219559i
$625$	−165774.	−	287128.i	−0.424380	−	0.735049i
$626$	428633.	−	202542.i	1.09380	−	0.516852i
$627$	275011.	−	499114.i	0.699543	−	1.26959i
$628$	172719.	−	210154.i	0.437946	−	0.532867i
$629$	−280838.			−0.709831
$630$	−51280.1	+	80750.9i	−0.129201	+	0.203454i
$631$			210621.i			0.528985i	0.964388	+	0.264492i	$0.0852044\pi$
$631$			210621.i			0.528985i	−0.964388	+	0.264492i	$0.914796\pi$
$632$	−61535.7	+	63447.8i	−0.154061	+	0.158848i
$633$	−229160.	+	138485.i	−0.571914	+	0.345618i
$634$	−487445.	+	230332.i	−1.21268	+	0.573029i
$635$	76930.2	−	44415.7i	0.190787	−	0.110151i
$636$	253374.	+	635744.i	0.626395	+	1.57169i
$637$	−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	−0.431746	−	0.901995i	$-0.642102\pi$
$641$	232262.	−	402289.i	0.565278	−	0.979089i	0.997024	−	0.0770943i	$-0.0245642\pi$
$642$	275584.	−	415377.i	0.668627	−	1.00779i
$643$	361978.	−	208988.i	0.875509	−	0.505476i	0.00633423	−	0.999980i	$-0.497984\pi$
$643$	361978.	−	208988.i	0.875509	−	0.505476i	0.869175	+	0.494504i	$0.164650\pi$
$644$	160433.	+	427181.i	0.386832	+	1.03001i
$645$	−2286.13	−	114350.i	−0.00549518	−	0.274863i
$646$	−165859.	+	239461.i	−0.397442	+	0.573811i
$647$			825841.i			1.97282i	0.164299	+	0.986411i	$0.447464\pi$
$647$			825841.i			1.97282i	−0.164299	+	0.986411i	$0.552536\pi$
$648$	69609.3	−	414094.i	0.165774	−	0.986164i
$649$	−229610.			−0.545131
$650$	−238138.	−	164943.i	−0.563639	−	0.390397i
$651$	−274927.	+	5496.46i	−0.648717	+	0.0129694i
$652$	−461993.	+	173507.i	−1.08678	+	0.408153i
$653$	−164273.	−	284529.i	−0.385247	−	0.667267i	0.606557	−	0.795040i	$-0.292550\pi$
$653$	−164273.	−	284529.i	−0.385247	−	0.667267i	−0.991803	+	0.127773i	$0.959217\pi$
$654$	−581511.	−	385807.i	−1.35957	−	0.902016i
$655$	−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	$-0.271613\pi$
$659$	144939.	+	83680.3i	0.333744	+	0.192687i	−0.323758	+	0.946140i	$0.604946\pi$
$660$	−80783.7	+	32196.2i	−0.185454	+	0.0739122i
$661$	152616.	+	264339.i	0.349300	+	0.605005i	0.986125	−	0.166003i	$-0.0530862\pi$
$661$	152616.	+	264339.i	0.349300	+	0.605005i	−0.636826	+	0.771008i	$0.719753\pi$
$662$	−262732.	−	556012.i	−0.599512	−	1.26873i
$663$	69745.1	+	115411.i	0.158667	+	0.262555i
$664$	134044.	−	138209.i	0.304027	−	0.313473i
$665$	175261.			0.396317
$666$	−626143.	−	397626.i	−1.41164	−	0.896451i
$667$			402461.i			0.904633i
$668$	−195287.	−	160500.i	−0.437644	−	0.359685i
$669$	417373.	+	229972.i	0.932550	+	0.513833i
$670$	39716.3	+	84050.4i	0.0884748	+	0.187236i
$671$	6127.32	−	3537.61i	0.0136090	−	0.00785715i
$672$	−444332.	−	183085.i	−0.983942	−	0.405429i
$673$	−403032.	+	698073.i	−0.889836	+	1.54124i	−0.0497671	+	0.998761i	$0.515848\pi$
$673$	−403032.	+	698073.i	−0.889836	+	1.54124i	−0.840069	+	0.542480i	$0.817485\pi$
$674$	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	−0.594136	−	0.804365i	$-0.702506\pi$
$677$	183117.	−	317169.i	0.399533	−	0.692011i	0.993668	+	0.112354i	$0.0358390\pi$
$678$	30499.5	−	489890.i	0.0663489	−	1.06571i
$679$	217400.	−	125516.i	0.471542	−	0.272245i
$680$	42756.4	−	12160.5i	0.0924662	−	0.0262986i
$681$	296668.	+	163464.i	0.639701	+	0.352474i
$682$	−205507.	−	142342.i	−0.441833	−	0.306029i
$683$		−	398332.i		−	0.853894i	−0.904277	−	0.426947i	$-0.859589\pi$
$683$		−	398332.i		−	0.853894i	0.904277	−	0.426947i	$-0.140411\pi$
$684$	−708833.	+	299058.i	−1.51507	+	0.639209i
$685$	−169460.			−0.361148
$686$	−247368.	+	357140.i	−0.525649	+	0.758911i
$687$	−266439.	−	440892.i	−0.564526	−	0.934154i
$688$	563715.	−	111298.i	1.19092	−	0.235130i
$689$	−290235.	−	502701.i	−0.611379	−	1.05894i
$690$	−49631.8	−	99818.5i	−0.104246	−	0.209659i
$691$	304679.	+	175906.i	0.638096	+	0.368405i	0.783881	−	0.620912i	$-0.213237\pi$
$691$	304679.	+	175906.i	0.638096	+	0.368405i	−0.145785	+	0.989316i	$0.546571\pi$
$692$	−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
$696$	−310101.	−	288953.i	−0.640153	−	0.596498i
$697$	−175932.	−	304723.i	−0.362143	−	0.627249i
$698$	399866.	−	188949.i	0.820737	−	0.387823i
$699$	328153.	−	6560.58i	0.671617	−	0.0134273i
$700$	382194.	+	314113.i	0.779987	+	0.641047i
$701$	−620142.			−1.26199			−0.630994	−	0.775788i	$-0.717353\pi$
$701$	−620142.			−1.26199			−0.630994	+	0.775788i	$0.717353\pi$
$702$	−7905.23	+	356064.i	−0.0160413	+	0.722527i
$703$			1.35898e6i			2.74980i
$704$	−229919.	−	371503.i	−0.463906	−	0.749579i
$705$	−1074.41	−	53740.8i	−0.00216168	−	0.108125i
$706$	−222793.	+	105276.i	−0.446984	+	0.211213i
$707$	317061.	−	183055.i	0.634314	−	0.366222i
$708$	243365.	+	191994.i	0.485503	+	0.383020i
$709$	−157448.	+	272708.i	−0.313217	+	0.542508i	−0.979057	−	0.203587i	$-0.934740\pi$
$709$	−157448.	+	272708.i	−0.313217	+	0.542508i	0.665840	+	0.746095i	$0.268073\pi$
$710$	−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
$714$	−102530.	−	206207.i	−0.201120	−	0.404489i
$715$	63878.0	−	36880.0i	0.124951	−	0.0721404i
$716$	−38130.7	+	14320.4i	−0.0743786	+	0.0279338i
$717$	−403292.	+	243717.i	−0.784480	+	0.474075i
$718$	192370.	−	277736.i	0.373154	−	0.538745i
$719$		−	361941.i		−	0.700132i	−0.936725	−	0.350066i	$-0.886159\pi$
$719$		−	361941.i		−	0.700132i	0.936725	−	0.350066i	$-0.113841\pi$
$720$	112545.	+	33424.4i	0.217101	+	0.0644761i
$721$	−111926.			−0.215308
$722$	730221.	+	505777.i	1.40081	+	0.970252i
$723$	−58682.9	+	106503.i	−0.112263	+	0.203744i
$724$	31932.8	+	85026.6i	0.0609200	+	0.162210i
$725$	218164.	+	377870.i	0.415056	+	0.718897i
$726$	7301.02	−	117271.i	0.0138519	−	0.222493i
$727$	−267542.	−	154465.i	−0.506200	−	0.292255i	0.225070	−	0.974343i	$-0.427739\pi$
$727$	−267542.	−	154465.i	−0.506200	−	0.292255i	−0.731270	+	0.682088i	$0.761072\pi$
$728$	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
$732$	−9452.46	−	1373.97i	−0.0176410	−	0.00256422i
$733$	−441272.	−	764305.i	−0.821293	−	1.42252i	−0.904719	−	0.426008i	$-0.859920\pi$
$733$	−441272.	−	764305.i	−0.821293	−	1.42252i	0.0834259	−	0.996514i	$-0.473414\pi$
$734$	317739.	+	672420.i	0.589764	+	1.24810i
$735$	−7824.08	+	14199.8i	−0.0144830	+	0.0262850i
$736$	450427.	−	332821.i	0.831512	−	0.614406i
$737$	437829.			0.806065
$738$	39194.3	−	928491.i	0.0719632	−	1.70477i
$739$			396910.i			0.726781i	0.931637	+	0.363390i	$0.118381\pi$
$739$			396910.i			0.726781i	−0.931637	+	0.363390i	$0.881619\pi$
$740$	131677.	−	160217.i	0.240462	−	0.292580i
$741$	558475.	−	337496.i	1.01711	−	0.614657i
$742$	423522.	+	896284.i	0.769250	+	1.62794i
$743$	831366.	−	479989.i	1.50596	−	0.869469i	0.505988	−	0.862541i	$-0.331128\pi$
$743$	831366.	−	479989.i	1.50596	−	0.869469i	0.999976	−	0.00692819i	$-0.00220533\pi$
$744$	98796.3	+	322709.i	0.178482	+	0.582996i
$745$	−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
$750$	−206861.	−	137243.i	−0.367753	−	0.243988i
$751$	572212.	−	330367.i	1.01456	−	0.585756i	0.102036	−	0.994781i	$-0.467464\pi$
$751$	572212.	−	330367.i	1.01456	−	0.585756i	0.912523	+	0.409025i	$0.134131\pi$
$752$	264929.	−	52306.4i	0.468482	−	0.0924952i
$753$	20024.1	+	1.00158e6i	0.0353153	+	1.76643i
$754$	295538.	+	204700.i	0.519841	+	0.360060i
$755$			189241.i			0.331987i
$756$	63362.7	−	604917.i	0.110864	−	1.05841i
$757$	326842.			0.570356			0.285178	−	0.958475i	$-0.407947\pi$
$757$	326842.			0.570356			0.285178	+	0.958475i	$0.407947\pi$
$758$	−334762.	+	483316.i	−0.582636	+	0.841187i
$759$	−524927.	+	10494.6i	−0.911203	+	0.0182172i
$760$	−58844.6	−	206898.i	−0.101878	−	0.358203i
$761$	−164813.	−	285464.i	−0.284591	−	0.492927i	0.687919	−	0.725788i	$-0.258525\pi$
$761$	−164813.	−	285464.i	−0.284591	−	0.492927i	−0.972510	+	0.232861i	$0.925191\pi$
$762$	−312261.	+	470658.i	−0.537784	+	0.810580i
$763$	−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
$768$	−66948.6	+	586012.i	−0.113506	+	0.993537i
$769$	299738.	+	519162.i	0.506862	+	0.877910i	0.999968	+	0.00794129i	$0.00252782\pi$
$769$	299738.	+	519162.i	0.506862	+	0.877910i	−0.493107	+	0.869969i	$0.664139\pi$
$770$	−113890.	+	53816.7i	−0.192091	+	0.0907686i
$771$	−344058.	−	569332.i	−0.578792	−	0.957760i
$772$	7999.60	−	9733.43i	0.0134225	−	0.0163317i
$773$	−58555.0			−0.0979952			−0.0489976	−	0.998799i	$-0.515603\pi$
$773$	−58555.0			−0.0979952			−0.0489976	+	0.998799i	$0.515603\pi$
$774$	336727.	+	644570.i	0.562077	+	1.07594i
$775$		−	347422.i		−	0.578433i
$776$	−221166.	−	214501.i	−0.367279	−	0.356211i
$777$	−940999.	−	518488.i	−1.55864	−	0.858810i
$778$	−925854.	+	437494.i	−1.52962	+	0.722792i
$779$	−1.47456e6	+	851336.i	−2.42989	+	1.40290i
$780$	−98543.0	−	14323.8i	−0.161971	−	0.0235434i
$781$	−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
$786$	300805.	+	18727.5i	0.486900	+	0.0303134i
$787$	−553254.	+	319421.i	−0.893254	+	0.515720i	−0.875005	−	0.484113i	$-0.839142\pi$
$787$	−553254.	+	319421.i	−0.893254	+	0.515720i	−0.0182482	+	0.999833i	$0.505809\pi$
$788$	139655.	+	371855.i	0.224907	+	0.598854i
$789$	−58078.8	−	32001.3i	−0.0932962	−	0.0514060i
$790$	17808.9	−	25711.7i	0.0285353	−	0.0411981i
$791$		−	710975.i		−	1.13632i
$792$	368793.	−	411996.i	0.587938	−	0.656814i
$793$	8101.59			0.0128832
$794$	857367.	+	593843.i	1.35996	+	0.941955i
$795$	−125256.	−	207268.i	−0.198182	−	0.327942i
$796$	179869.	−	67552.1i	0.283877	−	0.106614i
$797$	587628.	+	1.01780e6i	0.925095	+	1.60231i	0.791409	+	0.611287i	$0.209348\pi$
$797$	587628.	+	1.01780e6i	0.925095	+	1.60231i	0.133686	+	0.991024i	$0.457319\pi$
$798$	−997836.	+	496144.i	−1.56694	+	0.779116i
$799$	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
$804$	−464059.	−	366102.i	−0.717895	−	0.566357i
$805$	−80736.4	−	139840.i	−0.124588	−	0.215793i
$806$	−122297.	−	258814.i	−0.188255	−	0.398398i
$807$	347373.	−	6944.85i	0.533396	−	0.0106639i
$808$	−322554.	−	312834.i	−0.494060	−	0.479171i
$809$	−215543.			−0.329334			−0.164667	−	0.986349i	$-0.552655\pi$
$809$	−215543.			−0.329334			−0.164667	+	0.986349i	$0.552655\pi$
$810$	−328.123	+	148588.i	−0.000500111	+	0.226472i
$811$		−	1.05773e6i		−	1.60817i	−0.594512	−	0.804087i	$-0.702655\pi$
$811$		−	1.05773e6i		−	1.60817i	0.594512	−	0.804087i	$-0.297345\pi$
$812$	−474317.	−	389826.i	−0.719377	−	0.591233i
$813$	2255.95	+	112840.i	0.00341310	+	0.170719i
$814$	−417295.	−	883108.i	−0.629788	−	1.33280i
$815$	151236.	−	87315.9i	0.227687	−	0.131455i
$816$	−209005.	+	190273.i	−0.313890	+	0.285757i
$817$	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	−0.836520	−	0.547936i	$-0.815414\pi$
$821$	37925.7	−	65689.3i	0.0562662	−	0.0974559i	0.892787	+	0.450480i	$0.148747\pi$
$822$	964807.	−	479721.i	1.42790	−	0.709979i
$823$	569508.	−	328806.i	0.840815	−	0.485445i	−0.0167265	−	0.999860i	$-0.505324\pi$
$823$	569508.	−	328806.i	0.840815	−	0.485445i	0.857541	+	0.514416i	$0.171991\pi$
$824$	37579.6	+	132130.i	0.0553475	+	0.194602i
$825$	−487164.	+	294402.i	−0.715760	+	0.432547i
$826$	369112.	+	255660.i	0.541000	+	0.374716i
$827$			669017.i			0.978196i	0.872229	+	0.489098i	$0.162674\pi$
$827$			669017.i			0.978196i	−0.872229	+	0.489098i	$0.837326\pi$
$828$	565150.	+	427808.i	0.824333	+	0.624005i
$829$	−637042.			−0.926955			−0.463478	−	0.886109i	$-0.653399\pi$
$829$	−637042.			−0.926955			−0.463478	+	0.886109i	$0.653399\pi$
$830$	−38793.3	+	56008.2i	−0.0563119	+	0.0813010i
$831$	−400039.	+	726026.i	−0.579296	+	1.05136i
$832$	−15303.0	−	500039.i	−0.0221070	−	0.722367i
$833$	−19515.6	−	33802.1i	−0.0281250	−	0.0487139i
$834$	856821.	+	53343.9i	1.23185	+	0.0766925i
$835$	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	$-0.587269\pi$
$839$	−872716.	−	503863.i	−1.23979	−	0.715795i	−0.969052	+	0.246858i	$0.920602\pi$
$840$	165714.	+	38191.7i	0.234855	+	0.0541265i
$841$	82891.1	+	143572.i	0.117197	+	0.202991i
$842$	−252442.	+	119286.i	−0.356071	+	0.168254i
$843$	96838.1	−	175750.i	0.136267	−	0.247310i
$844$	367744.	+	302237.i	0.516251	+	0.424290i
$845$	−77247.2			−0.108186
$846$	158251.	+	302928.i	0.221109	+	0.423251i
$847$		−	170194.i		−	0.237234i
$848$	915877.	−	800904.i	1.27364	−	1.11375i
$849$	192550.	−	116361.i	0.267133	−	0.161434i
$850$	263067.	−	124307.i	0.364106	−	0.172051i
$851$	1.08432e6	−	626031.i	1.49726	−	0.864444i
$852$	673071.	−	268251.i	0.927218	−	0.369540i
$853$	96790.1	−	167645.i	0.133025	−	0.230406i	−0.791816	−	0.610759i	$-0.790864\pi$
$853$	96790.1	−	167645.i	0.133025	−	0.230406i	0.924841	+	0.380353i	$0.124198\pi$
$854$	−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	0.358923	+	0.933367i	$0.383144\pi$
$857$	−461864.	+	799972.i	−0.628858	+	1.08921i	−0.987781	+	0.155847i	$0.950189\pi$
$858$	−259282.	+	390805.i	−0.352207	+	0.530867i
$859$	−628431.	+	362825.i	−0.851670	+	0.491712i	−0.861214	−	0.508243i	$-0.830295\pi$
$859$	−628431.	+	362825.i	−0.851670	+	0.491712i	0.00954418	+	0.999954i	$0.496962\pi$
$860$	−190348.	+	71487.4i	−0.257366	+	0.0966569i
$861$	−26906.6	−	1.34584e6i	−0.0362955	−	1.81546i
$862$	−336790.	+	486244.i	−0.453257	+	0.654395i
$863$			444700.i			0.597097i	0.954394	+	0.298549i	$0.0965025\pi$
$863$			444700.i			0.597097i	−0.954394	+	0.298549i	$0.903497\pi$
$864$	−735387.	+	128303.i	−0.985119	+	0.171873i
$865$	266461.			0.356124
$866$	−969543.	−	671540.i	−1.29280	−	0.895439i
$867$	616124.	−	12317.8i	0.819652	−	0.0163869i
$868$	171875.	+	457646.i	0.228125	+	0.607421i
$869$	−73653.9	−	127572.i	−0.0975341	−	0.168934i
$870$	124983.	+	82920.5i	0.165124	+	0.109553i
$871$	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
$876$	−144220.	−	361863.i	−0.187939	−	0.471559i
$877$	288301.	+	499353.i	0.374841	+	0.649244i	0.990303	−	0.138922i	$-0.0443638\pi$
$877$	288301.	+	499353.i	0.374841	+	0.649244i	−0.615462	+	0.788167i	$0.711031\pi$
$878$	−123269.	−	260869.i	−0.159906	−	0.338403i
$879$	−109377.	−	180992.i	−0.141562	−	0.234251i
$880$	101770.	+	116380.i	0.131419	+	0.150284i
$881$	−1.16458e6			−1.50044			−0.750219	−	0.661190i	$-0.770052\pi$
$881$	−1.16458e6			−1.50044			−0.750219	+	0.661190i	$0.770052\pi$
$882$	4347.71	−	102995.i	0.00558886	−	0.132397i
$883$		−	12142.2i		−	0.0155731i	−0.999970	−	0.00778655i	$-0.997521\pi$
$883$		−	12142.2i		−	0.0155731i	0.999970	−	0.00778655i	$-0.00247856\pi$
$884$	152215.	−	185206.i	0.194784	−	0.237001i
$885$	−96072.6	−	52935.8i	−0.122663	−	0.0675869i
$886$	326248.	+	690429.i	0.415605	+	0.879532i
$887$	−1.12130e6	+	647385.i	−1.42520	+	0.822840i	−0.996737	−	0.0807193i	$-0.974278\pi$
$887$	−1.12130e6	+	647385.i	−1.42520	+	0.822840i	−0.428464	+	0.903559i	$0.640945\pi$
$888$	−296139.	+	1.28495e6i	−0.375551	+	1.62952i
$889$	−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
$894$	11797.6	−	189496.i	0.0147611	−	0.237096i
$895$	12482.2	−	7206.63i	0.0155828	−	0.00899676i
$896$	−44042.5	+	853218.i	−0.0548600	+	1.06278i
$897$	−526555.	−	290131.i	−0.654423	−	0.360586i
$898$	−634173.	−	439250.i	−0.786420	−	0.544703i
$899$			431164.i			0.533485i
$900$	762521.	+	95315.4i	0.941384	+	0.117673i
$901$	583026.			0.718188
$902$	696800.	−	1.00601e6i	0.856436	−	1.23649i
$903$	544818.	+	901541.i	0.668153	+	1.10563i
$904$	−839316.	+	238712.i	−1.02704	+	0.292104i
$905$	−16069.9	−	27833.8i	−0.0196207	−	0.0339841i
$906$	−535719.	−	1.07743e6i	−0.652651	−	1.31260i
$907$	−593065.	−	342406.i	−0.720921	−	0.416224i	0.0941708	−	0.995556i	$-0.469980\pi$
$907$	−593065.	−	342406.i	−0.720921	−	0.416224i	−0.815091	+	0.579332i	$0.803313\pi$
$908$	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	$-0.191010\pi$
$911$	621519.	+	358834.i	0.748890	+	0.432372i	−0.0764028	+	0.997077i	$0.524343\pi$
$912$	920732.	+	1.01138e6i	1.10699	+	1.21597i
$913$	160441.	+	277893.i	0.192475	+	0.333377i
$914$	−21429.3	+	10126.0i	−0.0256517	+	0.0121212i
$915$	3379.36	−	67.5617i	0.00403638	−	8.06972e-5i
$916$	−581489.	+	707521.i	−0.693028	+	0.843235i
$917$	436556.			0.519160
$918$	−305748.	−	185692.i	−0.362810	−	0.220348i
$919$		−	441444.i		−	0.522691i	−0.965245	−	0.261345i	$-0.915834\pi$
$919$		−	441444.i		−	0.522691i	0.965245	−	0.261345i	$-0.0841661\pi$
$920$	−137975.	+	142262.i	−0.163014	+	0.168079i
$921$	5767.48	+	288483.i	0.00679934	+	0.340095i
$922$	458160.	−	216495.i	0.538959	−	0.254674i
$923$	−532217.	+	307275.i	−0.624720	+	0.360682i
$924$	496078.	−	628812.i	0.581040	−	0.736507i
$925$	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	0.221472	+	0.975167i	$0.428914\pi$
$929$	−633285.	+	1.09688e6i	−0.733783	+	1.27095i	−0.955255	+	0.295783i	$0.904420\pi$
$930$	−53171.3	−	106937.i	−0.0614768	−	0.123641i
$931$	−163568.	+	94436.2i	−0.188712	+	0.108953i
$932$	−205150.	−	546246.i	−0.236178	−	0.628864i
$933$	546481.	−	330248.i	0.627786	−	0.379382i
$934$	−222692.	+	321514.i	−0.255277	+	0.368558i
$935$			74084.8i			0.0847434i
$936$	601597.	−	197412.i	0.686679	−	0.225332i
$937$	377258.			0.429694			0.214847	−	0.976648i	$-0.431075\pi$
$937$	377258.			0.429694			0.214847	+	0.976648i	$0.431075\pi$
$938$	−703837.	−	487503.i	−0.799957	−	0.554079i
$939$	514766.	−	934242.i	0.583819	−	1.05957i
$940$	−89457.5	+	33596.9i	−0.101242	+	0.0380227i
$941$	645770.	+	1.11851e6i	0.729288	+	1.26316i	0.957185	+	0.289478i	$0.0934817\pi$
$941$	645770.	+	1.11851e6i	0.729288	+	1.26316i	−0.227897	+	0.973685i	$0.573185\pi$
$942$	38031.5	−	610869.i	0.0428589	−	0.688409i
$943$	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	$-0.105065\pi$
$947$	1.02088e6	+	589403.i	1.13834	+	0.657222i	0.192322	+	0.981332i	$0.438398\pi$
$948$	−28606.5	+	196803.i	−0.0318308	+	0.218985i
$949$	165200.	+	286136.i	0.183434	+	0.317716i
$950$	−601521.	−	1.27298e6i	−0.666506	−	1.41050i
$951$	−585396.	+	1.06243e6i	−0.647275	+	1.17473i
$952$	−285031.	+	293888.i	−0.314499	+	0.324271i
$953$	613396.			0.675391			0.337695	−	0.941255i	$-0.390353\pi$
$953$	613396.			0.675391			0.337695	+	0.941255i	$0.390353\pi$
$954$	1.29989e6	+	825480.i	1.42826	+	0.907005i
$955$		−	183887.i		−	0.201625i
$956$	647184.	+	531900.i	0.708128	+	0.581988i
$957$	604589.	−	365364.i	0.660141	−	0.398935i
$958$	−689005.	−	1.45812e6i	−0.750743	−	1.58877i
$959$	1.35163e6	−	780367.i	1.46968	−	0.848519i
$960$	−10553.2	−	208450.i	−0.0114510	−	0.226183i
$961$	−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
$966$	855537.	+	567611.i	0.916821	+	0.608270i
$967$	−41063.4	+	23708.0i	−0.0439139	+	0.0253537i	−0.521796	−	0.853070i	$-0.674738\pi$
$967$	−41063.4	+	23708.0i	−0.0439139	+	0.0253537i	0.477882	+	0.878424i	$0.341405\pi$
$968$	−200916.	+	57143.3i	−0.214420	+	0.0609838i
$969$	13100.6	+	655275.i	0.0139522	+	0.697872i
$970$	89626.0	+	62078.1i	0.0952556	+	0.0659774i
$971$			746340.i			0.791586i	0.918340	+	0.395793i	$0.129530\pi$
$971$			746340.i			0.791586i	−0.918340	+	0.395793i	$0.870470\pi$
$972$	−418769.	−	846906.i	−0.443243	−	0.896402i
$973$	1.24350e6			1.31347
$974$	−444597.	+	641892.i	−0.468650	+	0.676619i
$975$	−651654.	+	13028.2i	−0.685500	+	0.0137048i
$976$	3289.16	+	16659.4i	0.00345291	+	0.0174888i
$977$	143356.	+	248299.i	0.150185	+	0.260128i	0.931295	−	0.364265i	$-0.118680\pi$
$977$	143356.	+	248299.i	0.150185	+	0.260128i	−0.781111	+	0.624393i	$0.785346\pi$
$978$	−613867.	+	925257.i	−0.641796	+	0.967353i
$979$	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	$-0.430828\pi$
$983$	−504643.	−	291356.i	−0.522249	−	0.301521i	−0.737854	+	0.674960i	$0.764161\pi$
$984$	−1.57975e6	+	483634.i	−1.63154	+	0.499490i
$985$	−70279.8	−	121728.i	−0.0724366	−	0.125464i
$986$	−326476.	+	154270.i	−0.335813	+	0.158682i
$987$	256048.	+	423697.i	0.262837	+	0.434931i
$988$	−896213.	−	736569.i	−0.918116	−	0.754570i
$989$	−1.22758e6			−1.25504
$990$	−104893.	+	165176.i	−0.107023	+	0.168530i
$991$			918794.i			0.935558i	0.883845	+	0.467779i	$0.154946\pi$
$991$			918794.i			0.935558i	−0.883845	+	0.467779i	$0.845054\pi$
$992$	482550.	−	356557.i	0.490364	−	0.362331i
$993$	−1.21188e6	−	667741.i	−1.22902	−	0.677189i
$994$	948909.	−	448388.i	0.960399	−	0.453818i
$995$	−58881.0	+	33995.0i	−0.0594742	+	0.0343375i
$996$	62313.9	−	428698.i	0.0628154	−	0.432148i
$997$	697626.	−	1.20832e6i	0.701830	−	1.21561i	−0.265993	−	0.963975i	$-0.585700\pi$
$997$	697626.	−	1.20832e6i	0.701830	−	1.21561i	0.967823	−	0.251631i	$-0.0809668\pi$
$998$	−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.7.4	✓	44
3.2	odd	2		108.5.f.a.19.19		44
4.3	odd	2	inner	36.5.f.a.7.19	yes	44
9.2	odd	6		324.5.d.e.163.11		22
9.4	even	3	inner	36.5.f.a.31.19	yes	44
9.5	odd	6		108.5.f.a.91.4		44
9.7	even	3		324.5.d.f.163.12		22
12.11	even	2		108.5.f.a.19.4		44
36.7	odd	6		324.5.d.f.163.11		22
36.11	even	6		324.5.d.e.163.12		22
36.23	even	6		108.5.f.a.91.19		44
36.31	odd	6	inner	36.5.f.a.31.4	yes	44

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

\(f(q)\)	\(=\)	\(q+(-3.28826 - 2.27757i) q^{2} +(-8.99820 + 0.179896i) q^{3} +(5.62536 + 14.9785i) q^{4} +(-2.83091 - 4.90328i) q^{5} +(29.9982 + 19.9025i) q^{6} +(45.1595 + 26.0728i) q^{7} +(15.6169 - 62.0654i) q^{8} +(80.9353 - 3.23749i) q^{9} +O(q^{10})\)	\(q+(-3.28826 - 2.27757i) q^{2} +(-8.99820 + 0.179896i) q^{3} +(5.62536 + 14.9785i) q^{4} +(-2.83091 - 4.90328i) q^{5} +(29.9982 + 19.9025i) 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} +(-53.3127 - 133.768i) q^{12} +(61.0686 + 105.774i) q^{13} +(-89.1136 - 188.588i) q^{14} +(26.3552 + 43.6114i) q^{15} +(-192.711 + 168.519i) q^{16} -122.675 q^{17} +(-273.510 - 173.690i) q^{18} +593.624i q^{19} +(57.5188 - 69.9855i) q^{20} +(-411.044 - 226.484i) q^{21} +(-182.282 - 385.757i) q^{22} +(473.649 - 273.461i) q^{23} +(-129.358 + 561.286i) 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} +(12.6652 - 203.432i) q^{30} +(507.427 - 292.963i) q^{31} +(1017.50 - 115.223i) q^{32} +(-840.791 - 463.274i) q^{33} +(403.388 + 279.401i) q^{34} -295.239i q^{35} +(503.783 + 1194.08i) q^{36} +2289.29 q^{37} +(1352.02 - 1951.99i) q^{38} +(-568.535 - 940.788i) q^{39} +(-348.534 + 99.1276i) q^{40} +(1434.13 + 2483.99i) q^{41} +(835.788 + 1680.92i) 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} +(1703.73 - 1551.04i) q^{48} +(159.084 + 275.542i) q^{49} +(-2144.42 + 1013.30i) q^{50} +(1103.85 - 22.0688i) q^{51} +(-1240.80 + 1509.73i) q^{52} -4752.60 q^{53} +(2492.35 + 1513.69i) q^{54} -603.911i q^{55} +(2323.47 - 2395.66i) q^{56} +(-106.791 - 5341.55i) q^{57} +(2661.31 - 1257.55i) q^{58} +(-1864.25 + 1076.32i) q^{59} +(-504.976 + 640.091i) 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} +(1709.60 + 3438.32i) q^{66} +(3554.82 - 2052.38i) q^{67} +(-690.091 - 1837.49i) q^{68} +(-4212.79 + 2545.87i) q^{69} +(-672.427 + 970.824i) q^{70} +5031.65i q^{71} +(1063.02 - 5073.84i) q^{72} +2705.16 q^{73} +(-7527.78 - 5214.01i) q^{74} +(-2575.34 + 4673.95i) q^{75} +(-8891.60 + 3339.35i) q^{76} +(2781.03 + 4816.88i) q^{77} +(-273.215 + 4388.44i) 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} +(1080.12 - 7430.88i) q^{84} +(347.282 + 601.509i) q^{85} +(3835.74 + 8117.45i) q^{86} +(3196.09 - 5800.55i) q^{87} +(4752.65 - 4900.33i) q^{88} +3186.35 q^{89} +(-77.3677 + 1832.80i) q^{90} +6368.92i q^{91} +(6760.48 + 5556.22i) q^{92} +(-4513.23 + 2727.43i) q^{93} +(1802.68 + 3814.95i) q^{94} +(2910.71 - 1680.50i) q^{95} +(-9134.91 + 1219.85i) 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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