LMFDB - Embedded newform 92.5.g.a.3.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [92,5,Mod(3,92)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(92, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 16])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("92.3"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	92.g (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$9.51003660371$
Analytic rank:	$0$
Dimension:	$460$
Relative dimension:	$46$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			3.4
Character	$\chi$	$=$	92.3
Dual form			92.5.g.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+(-3.81343 + 1.20738i) q^{2} +(-14.9199 - 6.81367i) q^{3} +(13.0845 - 9.20851i) q^{4} +(-23.3579 + 26.9564i) q^{5} +(65.1225 + 7.96951i) q^{6} +(36.5671 + 56.8995i) q^{7} +(-38.7785 + 50.9139i) q^{8} +(123.132 + 142.102i) q^{9} +(56.5269 - 130.998i) q^{10} +(-118.167 - 16.9898i) q^{11} +(-257.962 + 48.2364i) q^{12} +(-111.441 - 71.6187i) q^{13} +(-208.145 - 172.832i) q^{14} +(532.168 - 243.033i) q^{15} +(86.4067 - 240.977i) q^{16} +(-103.456 - 30.3775i) q^{17} +(-641.128 - 393.229i) q^{18} +(165.102 + 562.287i) q^{19} +(-57.3969 + 567.802i) q^{20} +(-157.881 - 1098.09i) q^{21} +(471.134 - 77.8827i) q^{22} +(-477.005 - 228.708i) q^{23} +(925.481 - 495.404i) q^{24} +(-92.1116 - 640.651i) q^{25} +(511.443 + 138.561i) q^{26} +(-494.577 - 1684.38i) q^{27} +(1002.42 + 407.772i) q^{28} +(-389.800 - 114.456i) q^{29} +(-1735.95 + 1569.32i) q^{30} +(695.172 - 317.475i) q^{31} +(-38.5552 + 1023.27i) q^{32} +(1647.27 + 1058.64i) q^{33} +(431.201 - 9.06856i) q^{34} +(-2387.94 - 343.334i) q^{35} +(2919.67 + 725.468i) q^{36} +(-428.581 - 494.609i) q^{37} +(-1308.50 - 1944.90i) q^{38} +(1174.70 + 1827.86i) q^{39} +(-466.673 - 2234.57i) q^{40} +(1626.13 - 1876.65i) q^{41} +(1927.88 + 3996.86i) q^{42} +(-781.930 - 357.096i) q^{43} +(-1702.60 + 865.837i) q^{44} -6706.68 q^{45} +(2095.16 + 296.236i) q^{46} +1212.35i q^{47} +(-2931.11 + 3006.59i) q^{48} +(-902.993 + 1977.28i) q^{49} +(1124.77 + 2331.86i) q^{50} +(1336.57 + 1158.15i) q^{51} +(-2117.65 + 89.1116i) q^{52} +(-1630.66 + 1047.96i) q^{53} +(3919.72 + 5826.10i) q^{54} +(3218.11 - 2788.51i) q^{55} +(-4315.00 - 344.705i) q^{56} +(1367.94 - 9514.20i) q^{57} +(1624.67 - 34.1683i) q^{58} +(2524.27 - 3927.84i) q^{59} +(4725.17 - 8080.43i) q^{60} +(272.561 + 596.825i) q^{61} +(-2267.68 + 2050.00i) q^{62} +(-3582.96 + 12202.4i) q^{63} +(-1088.45 - 3948.73i) q^{64} +(4533.60 - 1331.19i) q^{65} +(-7559.92 - 2048.15i) q^{66} +(2628.05 - 377.857i) q^{67} +(-1633.40 + 555.205i) q^{68} +(5558.50 + 6662.44i) q^{69} +(9520.76 - 1573.87i) q^{70} +(1090.45 - 156.783i) q^{71} +(-12009.9 + 758.632i) q^{72} +(-3633.75 + 1066.97i) q^{73} +(2231.55 + 1368.70i) q^{74} +(-2990.89 + 10186.0i) q^{75} +(7338.11 + 5836.88i) q^{76} +(-3354.31 - 7344.91i) q^{77} +(-6686.54 - 5552.12i) q^{78} +(2827.99 - 4400.44i) q^{79} +(4477.60 + 7957.92i) q^{80} +(-1930.26 + 13425.3i) q^{81} +(-3935.29 + 9119.83i) q^{82} +(6894.93 - 5974.49i) q^{83} +(-12177.6 - 12914.1i) q^{84} +(3235.39 - 2079.26i) q^{85} +(3412.99 + 417.672i) q^{86} +(5035.90 + 4363.63i) q^{87} +(5447.35 - 5357.49i) q^{88} +(-1248.18 + 2733.14i) q^{89} +(25575.4 - 8097.50i) q^{90} -8959.82i q^{91} +(-8347.42 + 1399.98i) q^{92} -12535.0 q^{93} +(-1463.77 - 4623.23i) q^{94} +(-19013.7 - 8683.26i) q^{95} +(7547.49 - 15004.4i) q^{96} +(5762.14 - 6649.87i) q^{97} +(1056.17 - 8630.46i) q^{98} +(-12135.9 - 18883.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 460 q - 3 q^{2} - 43 q^{4} - 18 q^{5} - 44 q^{6} + 144 q^{8} + 1116 q^{9} - 77 q^{10} - 156 q^{12} - 18 q^{13} + 253 q^{14} - 795 q^{16} - 18 q^{17} - 676 q^{18} + 113 q^{20} + 266 q^{21} - 818 q^{22} + 1006 q^{24}+ \cdots + 52545 q^{98}+O(q^{100}) $ 460 * q - 3 * q^2 - 43 * q^4 - 18 * q^5 - 44 * q^6 + 144 * q^8 + 1116 * q^9 - 77 * q^10 - 156 * q^12 - 18 * q^13 + 253 * q^14 - 795 * q^16 - 18 * q^17 - 676 * q^18 + 113 * q^20 + 266 * q^21 - 818 * q^22 + 1006 * q^24 - 4768 * q^25 + 1100 * q^26 + 499 * q^28 + 654 * q^29 - 1401 * q^30 - 2163 * q^32 - 342 * q^33 - 5959 * q^34 - 3317 * q^36 - 3666 * q^37 + 4444 * q^38 + 23023 * q^40 - 1266 * q^41 + 23419 * q^42 + 7066 * q^44 + 5464 * q^45 - 8019 * q^46 - 14166 * q^48 + 14620 * q^49 - 25358 * q^50 - 36264 * q^52 - 9138 * q^53 - 6990 * q^54 - 7592 * q^56 - 3862 * q^57 + 31769 * q^58 + 34819 * q^60 + 7534 * q^61 - 9320 * q^62 + 4562 * q^64 + 9106 * q^65 + 6490 * q^66 - 4842 * q^68 - 22 * q^69 - 4258 * q^70 - 27815 * q^72 - 18 * q^73 - 202 * q^74 + 73926 * q^76 - 56086 * q^77 - 328 * q^78 - 47488 * q^80 + 9788 * q^81 - 42110 * q^82 - 111651 * q^84 + 117026 * q^85 - 55391 * q^86 - 44639 * q^88 + 44574 * q^89 - 4626 * q^90 + 18106 * q^92 - 85004 * q^93 + 55547 * q^94 + 150069 * q^96 - 34146 * q^97 + 52545 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$-1$

Coefficient data

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

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

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

$2$	−3.81343	+	1.20738i	−0.953357	+	0.301845i
$2$	−3.81343	+	1.20738i	−0.953357	+	0.301845i
$3$	−14.9199	−	6.81367i	−1.65776	−	0.757074i	−0.999993	−	0.00385504i	$-0.998773\pi$
$3$	−14.9199	−	6.81367i	−1.65776	−	0.757074i	−0.657769	−	0.753219i	$-0.728500\pi$
$4$	13.0845	−	9.20851i	0.817779	−	0.575532i
$5$	−23.3579	+	26.9564i	−0.934315	+	1.07826i	0.0624633	+	0.998047i	$0.480104\pi$
$5$	−23.3579	+	26.9564i	−0.934315	+	1.07826i	−0.996778	+	0.0802094i	$0.974441\pi$
$6$	65.1225	+	7.96951i	1.80896	+	0.221375i
$7$	36.5671	+	56.8995i	0.746268	+	1.16122i	0.981905	+	0.189374i	$0.0606459\pi$
$7$	36.5671	+	56.8995i	0.746268	+	1.16122i	−0.235637	+	0.971841i	$0.575718\pi$
$8$	−38.7785	+	50.9139i	−0.605914	+	0.795530i
$9$	123.132	+	142.102i	1.52015	+	1.75435i
$10$	56.5269	−	130.998i	0.565269	−	1.30998i
$11$	−118.167	−	16.9898i	−0.976585	−	0.140412i	−0.364500	−	0.931203i	$-0.618760\pi$
$11$	−118.167	−	16.9898i	−0.976585	−	0.140412i	−0.612085	+	0.790792i	$0.709669\pi$
$12$	−257.962	+	48.2364i	−1.79140	+	0.334975i
$13$	−111.441	−	71.6187i	−0.659413	−	0.423779i	0.167682	−	0.985841i	$-0.446372\pi$
$13$	−111.441	−	71.6187i	−0.659413	−	0.423779i	−0.827095	+	0.562062i	$0.810008\pi$
$14$	−208.145	−	172.832i	−1.06197	−	0.881796i
$15$	532.168	−	243.033i	2.36519	−	1.08015i
$16$	86.4067	−	240.977i	0.337526	−	0.941316i
$17$	−103.456	−	30.3775i	−0.357981	−	0.105113i	0.0977968	−	0.995206i	$-0.468820\pi$
$17$	−103.456	−	30.3775i	−0.357981	−	0.105113i	−0.455777	+	0.890094i	$0.650639\pi$
$18$	−641.128	−	393.229i	−1.97879	−	1.21367i
$19$	165.102	+	562.287i	0.457348	+	1.55758i	0.789130	+	0.614227i	$0.210532\pi$
$19$	165.102	+	562.287i	0.457348	+	1.55758i	−0.331782	+	0.943356i	$0.607650\pi$
$20$	−57.3969	+	567.802i	−0.143492	+	1.41950i
$21$	−157.881	−	1098.09i	−0.358008	−	2.49000i
$22$	471.134	−	77.8827i	0.973417	−	0.160915i
$23$	−477.005	−	228.708i	−0.901711	−	0.432340i
$23$	−477.005	−	228.708i	−0.901711	−	0.432340i
$24$	925.481	−	495.404i	1.60674	−	0.860077i
$25$	−92.1116	−	640.651i	−0.147379	−	1.02504i
$26$	511.443	+	138.561i	0.756572	+	0.204972i
$27$	−494.577	−	1684.38i	−0.678433	−	2.31053i
$28$	1002.42	+	407.772i	1.27860	+	0.520117i
$29$	−389.800	−	114.456i	−0.463496	−	0.136095i	0.0416433	−	0.999133i	$-0.486741\pi$
$29$	−389.800	−	114.456i	−0.463496	−	0.136095i	−0.505139	+	0.863038i	$0.668559\pi$
$30$	−1735.95	+	1569.32i	−1.92884	+	1.74369i
$31$	695.172	−	317.475i	0.723384	−	0.330359i	−0.0194711	−	0.999810i	$-0.506198\pi$
$31$	695.172	−	317.475i	0.723384	−	0.330359i	0.742855	+	0.669452i	$0.233471\pi$
$32$	−38.5552	+	1023.27i	−0.0376516	+	0.999291i
$33$	1647.27	+	1058.64i	1.51264	+	0.972117i
$34$	431.201	−	9.06856i	0.373011	−	0.00784477i
$35$	−2387.94	−	343.334i	−1.94934	−	0.280272i
$36$	2919.67	+	725.468i	2.25283	+	0.559774i
$37$	−428.581	−	494.609i	−0.313062	−	0.361292i	0.577311	−	0.816524i	$-0.304102\pi$
$37$	−428.581	−	494.609i	−0.313062	−	0.361292i	−0.890373	+	0.455232i	$0.849556\pi$
$38$	−1308.50	−	1944.90i	−0.906164	−	1.34688i
$39$	1174.70	+	1827.86i	0.772318	+	1.20175i
$40$	−466.673	−	2234.57i	−0.291671	−	1.39661i
$41$	1626.13	−	1876.65i	0.967358	−	1.11639i	−0.0258068	−	0.999667i	$-0.508215\pi$
$41$	1626.13	−	1876.65i	0.967358	−	1.11639i	0.993164	−	0.116723i	$-0.0372391\pi$
$42$	1927.88	+	3996.86i	1.09290	+	2.26579i
$43$	−781.930	−	357.096i	−0.422894	−	0.193129i	0.192589	−	0.981280i	$-0.438312\pi$
$43$	−781.930	−	357.096i	−0.422894	−	0.193129i	−0.615483	+	0.788150i	$0.711039\pi$
$44$	−1702.60	+	865.837i	−0.879443	+	0.447230i
$45$	−6706.68			−3.31194
$46$	2095.16	+	296.236i	0.990152	+	0.139998i
$47$			1212.35i			0.548825i	0.961612	+	0.274413i	$0.0884834\pi$
$47$			1212.35i			0.548825i	−0.961612	+	0.274413i	$0.911517\pi$
$48$	−2931.11	+	3006.59i	−1.27218	+	1.30495i
$49$	−902.993	+	1977.28i	−0.376090	+	0.823523i
$50$	1124.77	+	2331.86i	0.449908	+	0.932744i
$51$	1336.57	+	1158.15i	0.513869	+	0.445270i
$52$	−2117.65	+	89.1116i	−0.783153	+	0.0329555i
$53$	−1630.66	+	1047.96i	−0.580512	+	0.373072i	−0.797697	−	0.603058i	$-0.793949\pi$
$53$	−1630.66	+	1047.96i	−0.580512	+	0.373072i	0.217185	+	0.976130i	$0.430312\pi$
$54$	3919.72	+	5826.10i	1.34421	+	1.99798i
$55$	3218.11	−	2788.51i	1.06384	−	0.921821i
$56$	−4315.00	−	344.705i	−1.37596	−	0.109919i
$57$	1367.94	−	9514.20i	0.421033	−	2.92835i
$58$	1624.67	−	34.1683i	0.482957	−	0.0101570i
$59$	2524.27	−	3927.84i	0.725156	−	1.12836i	−0.261446	−	0.965218i	$-0.584199\pi$
$59$	2524.27	−	3927.84i	0.725156	−	1.12836i	0.986602	−	0.163146i	$-0.0521642\pi$
$60$	4725.17	−	8080.43i	1.31255	−	2.24457i
$61$	272.561	+	596.825i	0.0732493	+	0.160394i	0.942715	−	0.333601i	$-0.108264\pi$
$61$	272.561	+	596.825i	0.0732493	+	0.160394i	−0.869465	+	0.493994i	$0.835536\pi$
$62$	−2267.68	+	2050.00i	−0.589927	+	0.533300i
$63$	−3582.96	+	12202.4i	−0.902736	+	3.07444i
$64$	−1088.45	−	3948.73i	−0.265735	−	0.964046i
$65$	4533.60	−	1331.19i	1.07304	−	0.315074i
$66$	−7559.92	−	2048.15i	−1.73552	−	0.470191i
$67$	2628.05	−	377.857i	0.585443	−	0.0841740i	0.156772	−	0.987635i	$-0.449891\pi$
$67$	2628.05	−	377.857i	0.585443	−	0.0841740i	0.428671	+	0.903461i	$0.358982\pi$
$68$	−1633.40	+	555.205i	−0.353245	+	0.120070i
$69$	5558.50	+	6662.44i	1.16751	+	1.39938i
$70$	9520.76	−	1573.87i	1.94301	−	0.321198i
$71$	1090.45	−	156.783i	0.216316	−	0.0311015i	−0.0333049	−	0.999445i	$-0.510603\pi$
$71$	1090.45	−	156.783i	0.216316	−	0.0311015i	0.249620	+	0.968344i	$0.419694\pi$
$72$	−12009.9	+	758.632i	−2.31672	+	0.146341i
$73$	−3633.75	+	1066.97i	−0.681883	+	0.200219i	−0.604288	−	0.796766i	$-0.706542\pi$
$73$	−3633.75	+	1066.97i	−0.681883	+	0.200219i	−0.0775948	+	0.996985i	$0.524724\pi$
$74$	2231.55	+	1368.70i	0.407514	+	0.249945i
$75$	−2990.89	+	10186.0i	−0.531714	+	1.81085i
$76$	7338.11	+	5836.88i	1.27045	+	1.01054i
$77$	−3354.31	−	7344.91i	−0.565746	−	1.23881i
$78$	−6686.54	−	5552.12i	−1.09904	−	0.912577i
$79$	2827.99	−	4400.44i	0.453131	−	0.705085i	−0.537255	−	0.843420i	$-0.680539\pi$
$79$	2827.99	−	4400.44i	0.453131	−	0.705085i	0.990386	+	0.138335i	$0.0441750\pi$
$80$	4477.60	+	7957.92i	0.699625	+	1.24343i
$81$	−1930.26	+	13425.3i	−0.294203	+	2.04622i
$82$	−3935.29	+	9119.83i	−0.585261	+	1.35631i
$83$	6894.93	−	5974.49i	1.00086	−	0.867251i	0.00970539	−	0.999953i	$-0.496911\pi$
$83$	6894.93	−	5974.49i	1.00086	−	0.867251i	0.991156	+	0.132702i	$0.0423652\pi$
$84$	−12177.6	−	12914.1i	−1.72584	−	1.83022i
$85$	3235.39	−	2079.26i	0.447805	−	0.287787i
$86$	3412.99	+	417.672i	0.461464	+	0.0564727i
$87$	5035.90	+	4363.63i	0.665332	+	0.576514i
$88$	5447.35	−	5357.49i	0.703429	−	0.691825i
$89$	−1248.18	+	2733.14i	−0.157579	+	0.345050i	−0.971911	−	0.235350i	$-0.924376\pi$
$89$	−1248.18	+	2733.14i	−0.157579	+	0.345050i	0.814332	+	0.580400i	$0.197104\pi$
$90$	25575.4	−	8097.50i	3.15746	−	0.999692i
$91$		−	8959.82i		−	1.08197i
$92$	−8347.42	+	1399.98i	−0.986226	+	0.165404i
$93$	−12535.0			−1.44931
$94$	−1463.77	−	4623.23i	−0.165660	−	0.523226i
$95$	−19013.7	−	8683.26i	−2.10678	−	0.962135i
$96$	7547.49	−	15004.4i	0.818955	−	1.62808i
$97$	5762.14	−	6649.87i	0.612408	−	0.706756i	−0.361839	−	0.932241i	$-0.617851\pi$
$97$	5762.14	−	6649.87i	0.612408	−	0.706756i	0.974247	+	0.225485i	$0.0723965\pi$
$98$	1056.17	−	8630.46i	0.109972	−	0.898632i
$99$	−12135.9	−	18883.8i	−1.23823	−	1.92672i
$100$	−7104.67	−	7534.36i	−0.710467	−	0.753436i
$101$	2231.60	+	2575.40i	0.218762	+	0.252465i	0.854514	−	0.519429i	$-0.173855\pi$
$101$	2231.60	+	2575.40i	0.218762	+	0.252465i	−0.635751	+	0.771894i	$0.719310\pi$
$102$	−6495.24	−	2802.76i	−0.624303	−	0.269392i
$103$	−13292.2	−	1911.14i	−1.25292	−	0.180143i	−0.516276	−	0.856422i	$-0.672682\pi$
$103$	−13292.2	−	1911.14i	−1.25292	−	0.180143i	−0.736646	+	0.676279i	$0.763591\pi$
$104$	7967.90	−	2896.62i	0.736677	−	0.267809i
$105$	33288.3	+	21393.1i	3.01935	+	1.94042i
$106$	4953.11	−	5965.15i	0.440825	−	0.530896i
$107$	1063.17	−	485.535i	0.0928617	−	0.0424085i	−0.368443	−	0.929650i	$-0.620109\pi$
$107$	1063.17	−	485.535i	0.0928617	−	0.0424085i	0.461304	+	0.887242i	$0.347382\pi$
$108$	−21981.9	−	17484.8i	−1.88459	−	1.49904i
$109$	−473.081	−	138.909i	−0.0398183	−	0.0116917i	0.261763	−	0.965132i	$-0.415696\pi$
$109$	−473.081	−	138.909i	−0.0398183	−	0.0116917i	−0.301581	+	0.953441i	$0.597514\pi$
$110$	−8905.24	+	14519.3i	−0.735971	+	1.19994i
$111$	3024.27	+	10299.7i	0.245456	+	0.835948i
$112$	16871.1	−	3895.33i	1.34496	−	0.310533i
$113$	1778.42	+	12369.2i	0.139276	+	0.968689i	0.932863	+	0.360231i	$0.117302\pi$
$113$	1778.42	+	12369.2i	0.139276	+	0.968689i	−0.793587	+	0.608457i	$0.791789\pi$
$114$	6270.73	+	37933.3i	0.482512	+	2.91885i
$115$	17307.0	−	7516.21i	1.30866	−	0.568334i
$116$	−6154.29	+	2091.89i	−0.457364	+	0.155461i
$117$	−3544.79	−	24654.6i	−0.258952	−	1.80105i
$118$	−4883.72	+	18026.3i	−0.350741	+	1.29462i
$119$	−2054.63	−	6997.44i	−0.145091	−	0.494135i
$120$	−8262.93	+	36519.2i	−0.573815	+	2.53606i
$121$	−373.195	−	109.580i	−0.0254897	−	0.00748446i
$122$	−1759.98	−	1946.86i	−0.118247	−	0.130802i
$123$	−37048.5	+	16919.5i	−2.44884	+	1.11835i
$124$	6172.49	−	10555.5i	0.401437	−	0.686491i
$125$	667.293	+	428.843i	0.0427068	+	0.0274460i
$126$	−1069.62	−	50859.1i	−0.0673731	−	3.20352i
$127$	−25927.3	−	3727.79i	−1.60750	−	0.231123i	−0.720688	−	0.693259i	$-0.756174\pi$
$127$	−25927.3	−	3727.79i	−1.60750	−	0.231123i	−0.886809	+	0.462136i	$0.847083\pi$
$128$	8918.35	+	13744.0i	0.544333	+	0.838869i
$129$	9233.16	+	10655.6i	0.554844	+	0.640324i
$130$	−15681.3	+	10550.2i	−0.927889	+	0.624270i
$131$	14329.1	+	22296.6i	0.834982	+	1.29926i	0.951991	+	0.306127i	$0.0990332\pi$
$131$	14329.1	+	22296.6i	0.834982	+	1.29926i	−0.117008	+	0.993131i	$0.537330\pi$
$132$	31302.1	−	1317.21i	1.79649	−	0.0755973i
$133$	−25956.6	+	29955.5i	−1.46739	+	1.69345i
$134$	−9565.68	+	4613.99i	−0.532729	+	0.256961i
$135$	56957.0	+	26011.4i	3.12521	+	1.42724i
$136$	5558.53	−	4089.37i	0.300526	−	0.221095i
$137$	−864.929			−0.0460828			−0.0230414	−	0.999735i	$-0.507335\pi$
$137$	−864.929			−0.0460828			−0.0230414	+	0.999735i	$0.507335\pi$
$138$	−29241.1	−	18695.5i	−1.53545	−	0.981702i
$139$		−	13289.3i		−	0.687819i	−0.939003	−	0.343909i	$-0.888249\pi$
$139$		−	13289.3i		−	0.687819i	0.939003	−	0.343909i	$-0.111751\pi$
$140$	−34406.5	+	17497.0i	−1.75543	+	0.892705i
$141$	8260.58	−	18088.2i	0.415501	−	0.909821i
$142$	−3969.04	+	1914.46i	−0.196838	+	0.0949446i
$143$	11951.8	+	10356.3i	0.584470	+	0.506446i
$144$	44882.8	−	17393.5i	2.16449	−	0.838805i
$145$	12190.2	−	7834.17i	0.579796	−	0.372612i
$146$	12568.8	−	8456.11i	0.589643	−	0.396703i
$147$	26945.0	−	23348.0i	1.24694	−	1.08048i
$148$	−10162.4	−	2525.10i	−0.463951	−	0.115281i
$149$	−5618.11	+	39074.8i	−0.253057	+	1.76005i	0.326576	+	0.945171i	$0.394105\pi$
$149$	−5618.11	+	39074.8i	−0.253057	+	1.76005i	−0.579633	+	0.814878i	$0.696804\pi$
$150$	−892.865	−	42454.8i	−0.0396829	−	1.88688i
$151$	1890.49	−	2941.65i	0.0829124	−	0.129014i	−0.797320	−	0.603556i	$-0.793750\pi$
$151$	1890.49	−	2941.65i	0.0829124	−	0.129014i	0.880233	+	0.474542i	$0.157386\pi$
$152$	−35030.7	−	13398.7i	−1.51622	−	0.579928i
$153$	−8422.11	−	18441.8i	−0.359781	−	0.787810i
$154$	21659.5	+	23959.4i	0.913286	+	1.01026i
$155$	−7679.77	+	26154.9i	−0.319657	+	1.08865i
$156$	32202.1	+	13099.4i	1.32323	+	0.538273i
$157$	26777.8	−	7862.68i	1.08637	−	0.318986i	0.310943	−	0.950429i	$-0.399355\pi$
$157$	26777.8	−	7862.68i	1.08637	−	0.318986i	0.775422	+	0.631443i	$0.217537\pi$
$158$	−5471.34	+	20195.2i	−0.219169	+	0.808973i
$159$	31469.6	−	4524.65i	1.24479	−	0.178974i
$160$	−26683.2	−	24940.8i	−1.04231	−	0.974250i
$161$	−4429.31	−	35504.6i	−0.170877	−	1.36972i
$162$	−8848.48	−	53526.9i	−0.337162	−	2.03959i
$163$	5780.00	−	831.038i	0.217547	−	0.0312785i	−0.0326795	−	0.999466i	$-0.510404\pi$
$163$	5780.00	−	831.038i	0.217547	−	0.0312785i	0.250226	+	0.968187i	$0.419495\pi$
$164$	3995.86	−	39529.2i	0.148567	−	1.46971i
$165$	−67013.7	+	19677.0i	−2.46148	+	0.722755i
$166$	−19079.9	+	31108.1i	−0.692403	+	1.12891i
$167$	10.6258	−	36.1882i	0.000381003	−	0.00129758i	−0.959302	−	0.282381i	$-0.908876\pi$
$167$	10.6258	−	36.1882i	0.000381003	−	0.00129758i	0.959683	+	0.281084i	$0.0906939\pi$
$168$	62030.4	+	34543.9i	2.19779	+	1.22392i
$169$	−4574.84	−	10017.5i	−0.160178	−	0.350741i
$170$	−9827.47	+	11835.4i	−0.340051	+	0.409531i
$171$	−59572.9	+	92697.2i	−2.03731	+	3.17011i
$172$	−13519.5	+	2528.01i	−0.456986	+	0.0854518i
$173$	3522.13	−	24497.0i	0.117683	−	0.818503i	−0.842413	−	0.538832i	$-0.818866\pi$
$173$	3522.13	−	24497.0i	0.117683	−	0.818503i	0.960096	−	0.279671i	$-0.0902253\pi$
$174$	−24472.6	−	10560.2i	−0.808317	−	0.348796i
$175$	33084.5	−	28667.9i	1.08031	−	0.936093i
$176$	−14304.6	+	27007.4i	−0.461795	+	0.871883i
$177$	−64424.7	+	41403.2i	−2.05639	+	1.32156i
$178$	1459.92	−	11929.7i	0.0460775	−	0.376520i
$179$	−25244.5	−	21874.5i	−0.787882	−	0.682704i	0.164916	−	0.986308i	$-0.447265\pi$
$179$	−25244.5	−	21874.5i	−0.787882	−	0.682704i	−0.952798	+	0.303604i	$0.901810\pi$
$180$	−87753.3	+	61758.5i	−2.70844	+	1.90613i
$181$	8803.95	−	19278.0i	0.268733	−	0.588443i	−0.726368	−	0.687306i	$-0.758793\pi$
$181$	8803.95	−	19278.0i	0.268733	−	0.588443i	0.995101	+	0.0988630i	$0.0315206\pi$
$182$	10817.9	+	34167.6i	0.326588	+	1.03151i
$183$		−	10761.7i		−	0.321350i
$184$	30142.0	−	15417.2i	0.890299	−	0.455376i
$185$	23343.6			0.682064
$186$	47801.5	−	15134.5i	1.38171	−	0.437465i
$187$	11709.0	+	5347.32i	0.334840	+	0.152916i
$188$	11164.0	+	15863.0i	0.315866	+	0.448818i
$189$	77755.0	−	89734.0i	2.17673	−	2.51208i
$190$	82991.4	+	10156.3i	2.29893	+	0.281337i
$191$	−5851.23	−	9104.69i	−0.160391	−	0.249574i	0.751751	−	0.659447i	$-0.229209\pi$
$191$	−5851.23	−	9104.69i	−0.160391	−	0.249574i	−0.912143	+	0.409873i	$0.865573\pi$
$192$	−10665.8	+	66330.9i	−0.289329	+	1.79934i
$193$	20285.0	+	23410.1i	0.544577	+	0.628475i	0.959611	−	0.281330i	$-0.0907757\pi$
$193$	20285.0	+	23410.1i	0.544577	+	0.628475i	−0.415034	+	0.909806i	$0.636230\pi$
$194$	−13944.6	+	32315.9i	−0.370512	+	0.858643i
$195$	−76711.0	−	11029.4i	−2.01738	−	0.290056i
$196$	6392.60	+	34186.8i	0.166405	+	0.889912i
$197$	−35642.7	−	22906.2i	−0.918414	−	0.590229i	−0.00621693	−	0.999981i	$-0.501979\pi$
$197$	−35642.7	−	22906.2i	−0.918414	−	0.590229i	−0.912197	+	0.409752i	$0.865615\pi$
$198$	69079.1	+	57359.3i	1.76204	+	1.46310i
$199$	11029.8	−	5037.16i	0.278524	−	0.127198i	−0.271256	−	0.962507i	$-0.587439\pi$
$199$	11029.8	−	5037.16i	0.278524	−	0.127198i	0.549780	+	0.835310i	$0.314712\pi$
$200$	36190.0	+	20153.7i	0.904749	+	0.503843i
$201$	−41784.8	−	12269.1i	−1.03425	−	0.303683i
$202$	−11619.5	−	7126.72i	−0.284764	−	0.174657i
$203$	−7741.39	−	26364.8i	−0.187857	−	0.639782i
$204$	28153.1	+	2845.89i	0.676498	+	0.0683846i
$205$	12604.9	+	87669.2i	0.299939	+	2.08612i
$206$	52996.5	−	8760.80i	1.24886	−	0.206447i
$207$	−26234.8	−	95944.8i	−0.612261	−	2.23914i
$208$	−26887.7	+	20666.3i	−0.621479	+	0.477680i
$209$	−9956.47	−	69248.8i	−0.227936	−	1.58533i
$210$	−152772.	−	41389.4i	−3.46422	−	0.938536i
$211$	−17760.0	−	60484.8i	−0.398912	−	1.35857i	−0.877099	−	0.480311i	$-0.840524\pi$
$211$	−17760.0	−	60484.8i	−0.398912	−	1.35857i	0.478187	−	0.878258i	$-0.341294\pi$
$212$	−11686.1	+	28727.9i	−0.260016	+	0.639194i
$213$	−17337.6	−	5090.77i	−0.382146	−	0.112208i
$214$	−3468.11	+	3135.21i	−0.0757295	+	0.0684603i
$215$	27890.3	−	12737.1i	0.603359	−	0.275545i
$216$	104937.	+	40136.7i	2.24917	+	0.860270i
$217$	43484.6	+	27945.9i	0.923456	+	0.593469i
$218$	1971.77	−	41.4683i	0.0414901	−	0.000872576i
$219$	61485.0	+	8840.21i	1.28198	+	0.184321i
$220$	16429.3	−	66120.1i	0.339447	−	1.36612i
$221$	9353.67	+	10794.7i	0.191513	+	0.221017i
$222$	−23968.5	−	35625.8i	−0.486334	−	0.722867i
$223$	31039.7	+	48298.7i	0.624177	+	0.971238i	0.999025	+	0.0441517i	$0.0140585\pi$
$223$	31039.7	+	48298.7i	0.624177	+	0.971238i	−0.374848	+	0.927086i	$0.622305\pi$
$224$	−59633.7	+	35224.4i	−1.18849	+	0.702017i
$225$	79696.0	−	91974.1i	1.57424	−	1.81677i
$226$	−21716.2	−	45021.8i	−0.425174	−	0.881466i
$227$	−34094.3	−	15570.3i	−0.661652	−	0.302166i	0.0561411	−	0.998423i	$-0.482120\pi$
$227$	−34094.3	−	15570.3i	−0.661652	−	0.302166i	−0.717793	+	0.696257i	$0.754848\pi$
$228$	−69712.9	−	137085.i	−1.34105	−	2.63706i
$229$	2217.79			0.0422911			0.0211455	−	0.999776i	$-0.493269\pi$
$229$	2217.79			0.0422911			0.0211455	+	0.999776i	$0.493269\pi$
$230$	−56924.0	+	49558.6i	−1.07607	+	0.936836i
$231$			132440.i			2.48196i
$232$	20943.3	−	15407.8i	0.389106	−	0.286263i
$233$	10384.1	−	22738.0i	0.191274	−	0.418832i	−0.789561	−	0.613673i	$-0.789692\pi$
$233$	10384.1	−	22738.0i	0.191274	−	0.418832i	0.980835	+	0.194840i	$0.0624188\pi$
$234$	43285.2	+	89738.5i	0.790511	+	1.63888i
$235$	−32680.7	−	28318.0i	−0.591774	−	0.512775i
$236$	−3140.82	−	74638.4i	−0.0563922	−	1.34010i
$237$	−72176.3	+	46384.9i	−1.28498	+	0.825810i
$238$	16283.8	+	24203.5i	0.287476	+	0.427292i
$239$	−69490.7	+	60214.1i	−1.21655	+	1.05415i	−0.219644	+	0.975580i	$0.570490\pi$
$239$	−69490.7	+	60214.1i	−1.21655	+	1.05415i	−0.996909	+	0.0785691i	$0.974965\pi$
$240$	−12582.5	−	149240.i	−0.218446	−	2.59097i
$241$	−5353.24	+	37232.6i	−0.0921686	+	0.641046i	0.890405	+	0.455170i	$0.150422\pi$
$241$	−5353.24	+	37232.6i	−0.0921686	+	0.641046i	−0.982573	+	0.185876i	$0.940488\pi$
$242$	1555.46	−	32.7127i	0.0265600	−	0.000558581i
$243$	43398.6	−	67529.5i	0.734959	−	1.14362i
$244$	9062.18	+	5299.26i	0.152213	+	0.0890093i
$245$	−32208.3	−	70526.4i	−0.536582	−	1.17495i
$246$	120854.	−	109253.i	1.99705	−	1.80535i
$247$	21871.1	−	74486.2i	0.358490	−	1.22091i
$248$	−10793.9	+	47705.1i	−0.175499	+	0.775643i
$249$	−143580.	+	42158.8i	−2.31576	+	0.679970i
$250$	−3062.45	−	829.687i	−0.0489992	−	0.0132750i
$251$	90830.4	−	13059.4i	1.44173	−	0.207289i	0.623339	−	0.781952i	$-0.285776\pi$
$251$	90830.4	−	13059.4i	1.44173	−	0.207289i	0.818391	+	0.574662i	$0.194867\pi$
$252$	65485.2	+	192656.i	1.03120	+	3.03376i
$253$	52480.4	+	35129.9i	0.819892	+	0.548828i
$254$	103373.	−	17088.5i	1.60228	−	0.264872i
$255$	−62438.9	+	8977.37i	−0.960230	+	0.138060i
$256$	−50603.8	−	41644.0i	−0.772152	−	0.635438i
$257$	1089.22	−	319.823i	0.0164911	−	0.00484221i	−0.273477	−	0.961879i	$-0.588174\pi$
$257$	1089.22	−	319.823i	0.0164911	−	0.00484221i	0.289968	+	0.957036i	$0.406355\pi$
$258$	−48075.4	−	29486.6i	−0.722243	−	0.442981i
$259$	12471.1	−	42472.5i	0.185910	−	0.633153i
$260$	47061.6	−	59165.6i	0.696177	−	0.875231i
$261$	−31732.6	−	69484.7i	−0.465827	−	1.02002i
$262$	−81563.5	−	67725.7i	−1.18821	−	0.986622i
$263$	−31757.8	+	49416.2i	−0.459134	+	0.714426i	−0.991214	−	0.132268i	$-0.957774\pi$
$263$	−31757.8	+	49416.2i	−0.459134	+	0.714426i	0.532080	+	0.846694i	$0.321411\pi$
$264$	−117778.	+	42816.6i	−1.68988	+	0.614333i
$265$	9839.44	−	68434.8i	0.140113	−	0.974508i
$266$	62815.9	−	145573.i	0.887782	−	2.05739i
$267$	37245.4	−	32273.3i	0.522457	−	0.452711i
$268$	30907.2	−	29144.5i	0.430318	−	0.405777i
$269$	57840.9	−	37172.1i	0.799338	−	0.513704i	−0.0760614	−	0.997103i	$-0.524235\pi$
$269$	57840.9	−	37172.1i	0.799338	−	0.513704i	0.875400	+	0.483400i	$0.160598\pi$
$270$	−248607.	−	30423.9i	−3.41025	−	0.417337i
$271$	14745.9	+	12777.4i	0.200785	+	0.173982i	0.749450	−	0.662061i	$-0.230318\pi$
$271$	14745.9	+	12777.4i	0.200785	+	0.173982i	−0.548664	+	0.836043i	$0.684864\pi$
$272$	−16259.6	+	22305.8i	−0.219772	+	0.301495i
$273$	−61049.3	+	133679.i	−0.819134	+	1.79365i
$274$	3298.34	−	1044.30i	0.0439334	−	0.0139099i
$275$			77268.6i			1.02173i
$276$	134081.	+	35989.0i	1.76015	+	0.472446i
$277$	−125721.			−1.63851			−0.819253	−	0.573432i	$-0.805612\pi$
$277$	−125721.			−1.63851			−0.819253	+	0.573432i	$0.805612\pi$
$278$	16045.3	+	50678.0i	0.207615	+	0.655737i
$279$	130712.	+	59694.2i	1.67922	+	0.766873i
$280$	110081.	−	108265.i	1.40410	−	1.38093i
$281$	69608.5	−	80332.5i	0.881556	−	1.01737i	−0.118147	−	0.992996i	$-0.537695\pi$
$281$	69608.5	−	80332.5i	0.881556	−	1.01737i	0.999703	−	0.0243737i	$-0.00775917\pi$
$282$	−9661.88	+	78951.5i	−0.121496	+	0.992801i
$283$	25578.4	+	39800.7i	0.319374	+	0.496956i	0.963407	−	0.268042i	$-0.0863765\pi$
$283$	25578.4	+	39800.7i	0.319374	+	0.496956i	−0.644033	+	0.764998i	$0.722740\pi$
$284$	12824.2	−	12092.8i	0.158999	−	0.149931i
$285$	224517.	+	259106.i	2.76413	+	3.18998i
$286$	−58081.4	−	25062.7i	−0.710076	−	0.306405i
$287$	166243.	+	23902.2i	2.01828	+	0.290184i
$288$	−150157.	+	120519.i	−1.81034	+	1.45302i
$289$	−60481.9	−	38869.4i	−0.724152	−	0.465384i
$290$	−37027.7	+	44593.3i	−0.440282	+	0.530241i
$291$	−131280.	+	59953.7i	−1.55029	+	0.707995i
$292$	−37720.6	+	47422.1i	−0.442397	+	0.556180i
$293$	154689.	+	45420.8i	1.80187	+	0.529078i	0.997851	−	0.0655214i	$-0.0208711\pi$
$293$	154689.	+	45420.8i	1.80187	+	0.529078i	0.804022	+	0.594599i	$0.202689\pi$
$294$	−74563.1	+	121569.i	−0.862639	+	1.40646i
$295$	46918.9	+	159791.i	0.539143	+	1.83615i
$296$	41802.2	−	2640.54i	0.477107	−	0.0301376i
$297$	29825.4	+	207440.i	0.338122	+	2.35169i
$298$	−25753.9	−	155792.i	−0.290008	−	1.75434i
$299$	36778.1	+	59649.9i	0.411383	+	0.667217i
$300$	54664.0	+	160820.i	0.607378	+	1.78689i
$301$	−8274.36	−	57549.4i	−0.0913275	−	0.635197i
$302$	−3657.54	+	13500.3i	−0.0401029	+	0.148023i
$303$	−15747.2	−	53629.9i	−0.171521	−	0.584147i
$304$	149764.	+	8799.51i	1.62054	+	0.0952164i
$305$	−22454.7	−	6593.29i	−0.241383	−	0.0708766i
$306$	54383.4	+	60158.0i	0.580796	+	0.642466i
$307$	−154574.	+	70591.7i	−1.64006	+	0.748992i	−0.999816	−	0.0191769i	$-0.993895\pi$
$307$	−154574.	+	70591.7i	−1.64006	+	0.748992i	−0.640247	+	0.768169i	$0.721168\pi$
$308$	−111525.	−	65216.0i	−1.17563	−	0.687469i
$309$	185297.	+	119083.i	1.94066	+	1.24719i
$310$	−2292.63	−	109012.i	−0.0238567	−	1.13436i
$311$	−107519.	−	15458.9i	−1.11164	−	0.159830i	−0.438063	−	0.898944i	$-0.644335\pi$
$311$	−107519.	−	15458.9i	−1.11164	−	0.159830i	−0.673580	+	0.739114i	$0.735244\pi$
$312$	−138617.	−	11073.4i	−1.42399	−	0.113756i
$313$	−100035.	−	115446.i	−1.02108	−	1.17839i	−0.983833	−	0.179087i	$-0.942686\pi$
$313$	−100035.	−	115446.i	−1.02108	−	1.17839i	−0.0372502	−	0.999306i	$-0.511860\pi$
$314$	−92622.0	+	62314.7i	−0.939410	+	0.632021i
$315$	−245244.	−	381607.i	−2.47159	−	3.84587i
$316$	−3518.73	−	83618.9i	−0.0352380	−	0.837395i
$317$	82339.4	−	95024.7i	0.819387	−	0.945623i	−0.179888	−	0.983687i	$-0.557574\pi$
$317$	82339.4	−	95024.7i	0.819387	−	0.945623i	0.999275	+	0.0380638i	$0.0121190\pi$
$318$	−114544.	+	55250.2i	−1.13271	+	0.546361i
$319$	44116.9	+	20147.5i	0.433534	+	0.197988i
$320$	131868.	+	62893.2i	1.28777	+	0.614191i
$321$	−19170.7			−0.186049
$322$	59758.3	+	130046.i	0.576350	+	1.25426i
$323$		−	63187.6i		−	0.605657i
$324$	98370.3	+	193437.i	0.937074	+	1.84268i
$325$	−35617.5	+	77991.6i	−0.337208	+	0.738382i
$326$	−21038.2	+	10147.8i	−0.197958	+	0.0954849i
$327$	6111.82	+	5295.92i	0.0571577	+	0.0495274i
$328$	32488.8	+	155566.i	0.301986	+	1.44600i
$329$	−68982.4	+	44332.3i	−0.637304	+	0.409570i
$330$	231794.	−	155948.i	2.12851	−	1.43203i
$331$	−83749.9	+	72569.7i	−0.764413	+	0.662368i	−0.947149	−	0.320794i	$-0.896050\pi$
$331$	−83749.9	+	72569.7i	−0.764413	+	0.662368i	0.182736	+	0.983162i	$0.441505\pi$
$332$	35200.4	−	141665.i	0.319353	−	1.28525i
$333$	17512.9	−	121805.i	0.157932	−	1.09844i
$334$	3.17210	+	150.830i	2.84351e−5	+	0.00135206i
$335$	−51200.1	+	79668.8i	−0.456227	+	0.709903i
$336$	−278256.	−	56836.5i	−2.46471	−	0.503441i
$337$	54254.5	+	118801.i	0.477722	+	1.04607i	0.983083	+	0.183158i	$0.0586320\pi$
$337$	54254.5	+	118801.i	0.477722	+	1.04607i	−0.505361	+	0.862908i	$0.668641\pi$
$338$	29540.8	+	32677.5i	0.258576	+	0.286032i
$339$	57745.8	−	196664.i	0.502482	−	1.71130i
$340$	23186.5	−	56999.1i	0.200575	−	0.493072i
$341$	−87540.1	+	25704.1i	−0.752833	+	0.221052i
$342$	115256.	−	425421.i	0.985399	−	3.63720i
$343$	15216.5	−	2187.81i	0.129338	−	0.0185960i
$344$	48503.2	−	25963.5i	0.409877	−	0.219405i
$345$	−309430.	−	5783.17i	−2.59971	−	0.0485879i
$346$	16145.7	+	97670.0i	0.134867	+	0.815848i
$347$	233882.	−	33627.1i	1.94240	−	0.279274i	0.943721	−	0.330742i	$-0.107299\pi$
$347$	233882.	−	33627.1i	1.94240	−	0.279274i	0.998675	+	0.0514674i	$0.0163898\pi$
$348$	106075.	+	10722.7i	0.875897	+	0.0885411i
$349$	−70763.5	+	20778.0i	−0.580976	+	0.170590i	−0.558999	−	0.829168i	$-0.688814\pi$
$349$	−70763.5	+	20778.0i	−0.580976	+	0.170590i	−0.0219774	+	0.999758i	$0.506996\pi$
$350$	−91552.3	+	149268.i	−0.747365	+	1.21852i
$351$	−65516.7	+	223129.i	−0.531787	+	1.81110i
$352$	21941.2	−	120262.i	0.177082	−	0.970606i
$353$	−89369.3	−	195691.i	−0.717198	−	1.57044i	−0.817790	−	0.575516i	$-0.804801\pi$
$353$	−89369.3	−	195691.i	−0.717198	−	1.57044i	0.100592	−	0.994928i	$-0.467926\pi$
$354$	195689.	−	235673.i	1.56157	−	1.88063i
$355$	−21244.2	+	33056.6i	−0.168571	+	0.262302i
$356$	8836.32	+	47255.6i	0.0697223	+	0.372866i
$357$	−17023.4	+	118400.i	−0.133570	+	0.929002i
$358$	122679.	+	52937.1i	0.957203	+	0.413042i
$359$	−10782.8	+	9343.36i	−0.0836649	+	0.0724961i	−0.695689	−	0.718343i	$-0.744901\pi$
$359$	−10782.8	+	9343.36i	−0.0836649	+	0.0724961i	0.612024	+	0.790839i	$0.290355\pi$
$360$	260075.	−	341463.i	2.00675	−	2.63475i
$361$	−179275.	+	115213.i	−1.37564	+	0.884073i
$362$	−10297.4	+	84144.9i	−0.0785799	+	0.642112i
$363$	4821.38	+	4177.75i	0.0365896	+	0.0317051i
$364$	−82506.6	−	117235.i	−0.622710	−	0.884816i
$365$	56115.1	−	122875.i	0.421206	−	0.922312i
$366$	12993.4	+	41038.9i	0.0969977	+	0.306361i
$367$		−	158610.i		−	1.17760i	−0.808279	−	0.588800i	$-0.799601\pi$
$367$		−	158610.i		−	1.17760i	0.808279	−	0.588800i	$-0.200399\pi$
$368$	−96329.8	+	95185.3i	−0.711320	+	0.702868i
$369$	466905.			3.42907
$370$	−89019.3	+	28184.6i	−0.650251	+	0.205878i
$371$	−119257.	−	54462.8i	−0.866435	−	0.395688i
$372$	−164014.	+	115429.i	−1.18521	+	0.834121i
$373$	7244.38	−	8360.46i	0.0520695	−	0.0600914i	−0.729117	−	0.684389i	$-0.760069\pi$
$373$	7244.38	−	8360.46i	0.0520695	−	0.0600914i	0.781187	+	0.624297i	$0.214615\pi$
$374$	−51107.7	−	6254.42i	−0.365379	−	0.0447140i
$375$	−7033.92	−	10945.0i	−0.0500190	−	0.0778311i
$376$	−61725.7	−	47013.3i	−0.436607	−	0.332541i
$377$	35242.5	+	40672.0i	0.247961	+	0.286163i
$378$	−188170.	+	436074.i	−1.31694	+	3.05194i
$379$	5229.96	+	751.955i	0.0364099	+	0.00523496i	0.160496	−	0.987037i	$-0.448691\pi$
$379$	5229.96	+	751.955i	0.0364099	+	0.00523496i	−0.124086	+	0.992271i	$0.539600\pi$
$380$	−328744.	+	61471.9i	−2.27662	+	0.425706i
$381$	361432.	+	232278.i	2.48987	+	1.60014i
$382$	33306.1	+	27655.4i	0.228243	+	0.189519i
$383$	2741.97	−	1252.22i	0.0186924	−	0.00853654i	−0.406047	−	0.913852i	$-0.633093\pi$
$383$	2741.97	−	1252.22i	0.0186924	−	0.00853654i	0.424739	+	0.905316i	$0.360366\pi$
$384$	−39413.2	−	265826.i	−0.267288	−	1.80275i
$385$	276342.	+	81141.3i	1.86434	+	0.547420i
$386$	−105620.	−	64781.0i	−0.708879	−	0.434784i
$387$	−45536.8	−	155084.i	−0.304047	−	1.03549i
$388$	14159.2	−	140071.i	0.0940537	−	0.930431i
$389$	−7291.27	−	50711.9i	−0.0481842	−	0.335128i	−0.999627	−	0.0273033i	$-0.991308\pi$
$389$	−7291.27	−	50711.9i	−0.0481842	−	0.335128i	0.951443	−	0.307825i	$-0.0996011\pi$
$390$	305848.	−	50559.5i	2.01084	−	0.332410i
$391$	42401.6	+	38151.5i	0.277350	+	0.249551i
$392$	−65654.2	−	122651.i	−0.427258	−	0.798175i
$393$	−61867.2	−	430296.i	−0.400567	−	2.78600i
$394$	163577.	+	44316.8i	1.05373	+	0.285480i
$395$	52564.2	+	179017.i	0.336896	+	1.14736i
$396$	−332683.	−	135331.i	−2.12148	−	0.862992i
$397$	−103018.	−	30248.7i	−0.653628	−	0.191923i	−0.0619281	−	0.998081i	$-0.519725\pi$
$397$	−103018.	−	30248.7i	−0.653628	−	0.191923i	−0.591700	+	0.806158i	$0.701543\pi$
$398$	−35979.8	+	32526.1i	−0.227139	+	0.205336i
$399$	591375.	−	270072.i	3.71464	−	1.69642i
$400$	−162341.	−	33159.7i	−1.01463	−	0.207248i
$401$	−54380.1	−	34948.0i	−0.338183	−	0.217337i	0.360516	−	0.932753i	$-0.382601\pi$
$401$	−54380.1	−	34948.0i	−0.338183	−	0.217337i	−0.698699	+	0.715416i	$0.746237\pi$
$402$	174157.	−	3662.68i	1.07768	−	0.0226645i
$403$	−100208.	−	14407.7i	−0.617008	−	0.0887124i
$404$	52914.8	+	13148.1i	0.324201	+	0.0805562i
$405$	−316810.	−	365619.i	−1.93148	−	2.22904i
$406$	61353.5	+	91193.3i	0.372209	+	0.553237i
$407$	42240.8	+	65727.9i	0.255002	+	0.396790i
$408$	−110796.	+	23138.9i	−0.665586	+	0.139002i
$409$	−113741.	+	131264.i	−0.679938	+	0.784691i	−0.985897	−	0.167354i	$-0.946478\pi$
$409$	−113741.	+	131264.i	−0.679938	+	0.784691i	0.305959	+	0.952045i	$0.401023\pi$
$410$	−153918.	−	319101.i	−0.915633	−	1.89828i
$411$	12904.6	+	5893.34i	0.0763944	+	0.0348881i
$412$	−191521.	+	97395.6i	−1.12829	+	0.573779i
$413$	315797.			1.85143
$414$	215886.	+	334203.i	1.25958	+	1.94989i
$415$			325414.i			1.88947i
$416$	77582.2	−	111273.i	0.448307	−	0.642990i
$417$	−90549.2	+	198275.i	−0.520730	+	1.14024i
$418$	121578.	+	252054.i	0.695828	+	1.44258i
$419$	−90641.8	−	78541.6i	−0.516298	−	0.447375i	0.357324	−	0.933981i	$-0.383689\pi$
$419$	−90641.8	−	78541.6i	−0.516298	−	0.447375i	−0.873622	+	0.486606i	$0.838235\pi$
$420$	632559.	−	26618.4i	3.58593	−	0.150898i
$421$	−285933.	+	183758.i	−1.61325	+	1.03677i	−0.653099	+	0.757272i	$0.726532\pi$
$421$	−285933.	+	183758.i	−1.61325	+	1.03677i	−0.960146	+	0.279498i	$0.909832\pi$
$422$	140754.	+	209212.i	0.790382	+	1.17479i
$423$	−172278.	+	149280.i	−0.962831	+	0.834297i
$424$	9878.76	−	123662.i	0.0549504	−	0.687865i
$425$	−9931.85	+	69077.5i	−0.0549860	+	0.382436i
$426$	72262.1	−	1519.74i	0.398191	−	0.00837433i
$427$	−23992.3	+	37332.7i	−0.131588	+	0.204755i
$428$	9440.01	−	16143.2i	0.0515329	−	0.0881257i
$429$	−107755.	−	235950.i	−0.585494	−	1.28205i
$430$	−90979.0	+	82245.9i	−0.492044	+	0.444813i
$431$	−30876.9	+	105157.i	−0.166219	+	0.566089i	0.833685	+	0.552240i	$0.186227\pi$
$431$	−30876.9	+	105157.i	−0.166219	+	0.566089i	−0.999904	+	0.0138491i	$0.995592\pi$
$432$	−448631.	−	26359.6i	−2.40393	−	0.141245i
$433$	179025.	−	52566.6i	0.954858	−	0.280372i	0.233050	−	0.972465i	$-0.425129\pi$
$433$	179025.	−	52566.6i	0.954858	−	0.280372i	0.721808	+	0.692093i	$0.243311\pi$
$434$	−199567.	−	54067.1i	−1.05952	−	0.287047i
$435$	−235256.	+	33824.7i	−1.24326	+	0.178754i
$436$	−7469.15	+	2538.82i	−0.0392915	+	0.0133554i
$437$	49844.9	−	305974.i	0.261011	−	1.60222i
$438$	−245142.	+	40524.2i	−1.27782	+	0.211235i
$439$	166587.	−	23951.5i	0.864393	−	0.124281i	0.304165	−	0.952619i	$-0.401623\pi$
$439$	166587.	−	23951.5i	0.864393	−	0.124281i	0.560228	+	0.828339i	$0.310714\pi$
$440$	17180.3	+	271981.i	0.0887412	+	1.40486i
$441$	−392163.	+	115150.i	−2.01646	+	0.592086i
$442$	−48702.9	−	29871.4i	−0.249293	−	0.152901i
$443$	66366.3	−	226023.i	0.338174	−	1.15171i	−0.598386	−	0.801208i	$-0.704191\pi$
$443$	66366.3	−	226023.i	0.338174	−	1.15171i	0.936560	−	0.350507i	$-0.113991\pi$
$444$	134416.	+	106917.i	0.681844	+	0.542353i
$445$	−44520.7	−	97486.8i	−0.224824	−	0.492295i
$446$	−176682.	−	146707.i	−0.888226	−	0.737532i
$447$	350065.	−	544711.i	1.75200	−	2.72616i
$448$	184880.	−	206326.i	0.921155	−	1.02801i
$449$	−21848.9	+	151963.i	−0.108377	+	0.753779i	0.861071	+	0.508484i	$0.169794\pi$
$449$	−21848.9	+	151963.i	−0.108377	+	0.753779i	−0.969448	+	0.245295i	$0.921115\pi$
$450$	−192867.	+	446960.i	−0.952431	+	2.20721i
$451$	−224038.	+	194130.i	−1.10146	+	0.954422i
$452$	137171.	+	145468.i	0.671408	+	0.712016i
$453$	−48249.2	+	31007.9i	−0.235122	+	0.151104i
$454$	148815.	+	18211.6i	0.721998	+	0.0883562i
$455$	241525.	+	209282.i	1.16665	+	1.01090i
$456$	431359.	+	438594.i	2.07448	+	2.10927i
$457$	98368.4	−	215397.i	0.471003	−	1.03135i	−0.513838	−	0.857887i	$-0.671777\pi$
$457$	98368.4	−	215397.i	0.471003	−	1.03135i	0.984840	−	0.173464i	$-0.0554961\pi$
$458$	−8457.37	+	2677.71i	−0.0403185	+	0.0127653i
$459$			189284.i			0.898437i
$460$	157239.	−	257717.i	0.743097	−	1.21794i
$461$	−226910.			−1.06771			−0.533853	−	0.845577i	$-0.679256\pi$
$461$	−226910.			−1.06771			−0.533853	+	0.845577i	$0.679256\pi$
$462$	−159905.	−	505051.i	−0.749168	−	2.36620i
$463$	−229087.	−	104621.i	−1.06866	−	0.488040i	−0.198139	−	0.980174i	$-0.563490\pi$
$463$	−229087.	−	104621.i	−1.06866	−	0.488040i	−0.870519	+	0.492134i	$0.836217\pi$
$464$	−61262.5	+	84043.1i	−0.284550	+	0.390361i
$465$	292792.	−	337900.i	1.35411	−	1.56272i
$466$	−12145.6	+	99247.3i	−0.0559304	+	0.457032i
$467$	−113312.	−	176317.i	−0.519569	−	0.808465i	0.477985	−	0.878368i	$-0.341367\pi$
$467$	−113312.	−	176317.i	−0.519569	−	0.808465i	−0.997554	+	0.0699030i	$0.977731\pi$
$468$	−273414.	−	289950.i	−1.24833	−	1.32383i
$469$	117600.	+	135718.i	0.534641	+	0.617009i
$470$	158816.	+	68530.7i	0.718951	+	0.310234i
$471$	−453095.	−	65145.2i	−2.04243	−	0.293657i
$472$	102094.	+	280836.i	0.458265	+	1.26058i
$473$	86331.2	+	55481.7i	0.385874	+	0.247986i
$474$	219235.	−	264030.i	0.975783	−	1.17516i
$475$	345022.	−	157566.i	1.52918	−	0.698354i
$476$	−91319.8	−	72637.7i	−0.403043	−	0.320589i
$477$	−349704.	−	102682.i	−1.53697	−	0.451294i
$478$	192297.	−	313524.i	0.841620	−	1.37219i
$479$	−41958.5	−	142898.i	−0.182873	−	0.622808i	−0.998991	−	0.0449219i	$-0.985696\pi$
$479$	−41958.5	−	142898.i	−0.182873	−	0.622808i	0.816118	−	0.577886i	$-0.196122\pi$
$480$	228172.	+	553924.i	0.990328	+	2.40418i
$481$	12338.2	+	85814.1i	0.0533288	+	0.370910i
$482$	−24539.7	−	148447.i	−0.105627	−	0.638967i
$483$	−175832.	+	559903.i	−0.753707	+	2.40004i
$484$	−5892.13	+	2002.77i	−0.0251525	+	0.00854951i
$485$	44665.2	+	310653.i	0.189883	+	1.32067i
$486$	−83963.6	+	309917.i	−0.355483	+	1.31212i
$487$	−80671.5	−	274742.i	−0.340144	−	1.15842i	−0.935017	−	0.354603i	$-0.884616\pi$
$487$	−80671.5	−	274742.i	−0.340144	−	1.15842i	0.594873	−	0.803819i	$-0.297202\pi$
$488$	−40956.2	−	9266.85i	−0.171981	−	0.0389128i
$489$	−91899.2	−	26984.0i	−0.384321	−	0.112847i
$490$	207976.	+	230060.i	0.866207	+	0.958183i
$491$	−375837.	+	171639.i	−1.55896	+	0.711955i	−0.993607	−	0.112892i	$-0.963989\pi$
$491$	−375837.	+	171639.i	−1.55896	+	0.711955i	−0.565357	+	0.824847i	$0.691261\pi$
$492$	−328957.	+	562544.i	−1.35897	+	2.32395i
$493$	36850.4	+	23682.3i	0.151617	+	0.0974385i
$494$	6529.15	+	310455.i	0.0267549	+	1.27217i
$495$	792507.	+	113945.i	3.23439	+	0.465035i
$496$	−16436.5	−	194952.i	−0.0668107	−	0.792438i
$497$	48795.4	+	56312.8i	0.197545	+	0.227979i
$498$	496629.	−	334125.i	2.00250	−	1.34726i
$499$	−44227.1	−	68818.8i	−0.177618	−	0.276379i	0.741017	−	0.671486i	$-0.234344\pi$
$499$	−44227.1	−	68818.8i	−0.177618	−	0.276379i	−0.918635	+	0.395107i	$0.870708\pi$
$500$	12680.2	−	533.588i	0.0507207	−	0.00213435i
$501$	−405.110	+	467.521i	−0.00161398	+	0.00186263i
$502$	−330608.	+	159468.i	−1.31191	+	0.632800i
$503$	−200566.	−	91595.4i	−0.792722	−	0.362024i	−0.0224572	−	0.999748i	$-0.507149\pi$
$503$	−200566.	−	91595.4i	−0.792722	−	0.362024i	−0.770265	+	0.637724i	$0.779876\pi$
$504$	−482332.	−	655615.i	−1.89883	−	2.58100i
$505$	−121549.			−0.476615
$506$	−242546.	−	70601.7i	−0.947310	−	0.275749i
$507$			180631.i			0.702711i
$508$	−373573.	+	189976.i	−1.44760	+	0.736158i
$509$	−66066.5	+	144665.i	−0.255003	+	0.558379i	−0.993229	−	0.116175i	$-0.962937\pi$
$509$	−66066.5	+	144665.i	−0.255003	+	0.558379i	0.738226	+	0.674554i	$0.235664\pi$
$510$	227267.	−	109622.i	0.873769	−	0.421461i
$511$	−193586.	−	167743.i	−0.741364	−	0.642396i
$512$	243254.	+	97708.6i	0.927940	+	0.372729i
$513$	865448.	−	556189.i	3.28856	−	2.11343i
$514$	−3767.51	+	2534.72i	−0.0142603	+	0.00959410i
$515$	361996.	−	313671.i	1.36486	−	1.18266i
$516$	218933.	+	54399.7i	0.822267	+	0.204313i
$517$	20597.7	−	143260.i	0.0770615	−	0.535974i
$518$	3722.96	+	177023.i	0.0138749	+	0.659737i
$519$	−219464.	+	341493.i	−0.814758	+	1.26779i
$520$	−108031.	+	282445.i	−0.399521	+	1.04454i
$521$	−165192.	−	361720.i	−0.608574	−	1.33259i	−0.923545	−	0.383489i	$-0.874722\pi$
$521$	−165192.	−	361720.i	−0.608574	−	1.33259i	0.314972	−	0.949101i	$-0.398005\pi$
$522$	204904.	+	226662.i	0.751986	+	0.831834i
$523$	−103431.	+	352255.i	−0.378137	+	1.28782i	0.522275	+	0.852777i	$0.325084\pi$
$523$	−103431.	+	352255.i	−0.378137	+	1.28782i	−0.900412	+	0.435039i	$0.856735\pi$
$524$	392807.	+	159789.i	1.43060	+	0.581947i
$525$	−688949.	+	202294.i	−2.49959	+	0.733945i
$526$	61442.2	−	226789.i	0.222073	−	0.819691i
$527$	−81564.1	+	11727.2i	−0.293682	+	0.0422252i
$528$	397442.	−	305481.i	1.42563	−	1.09576i
$529$	175226.	+	218190.i	0.626164	+	0.779692i
$530$	45104.8	+	272851.i	0.160572	+	0.971347i
$531$	868973.	−	124939.i	3.08189	−	0.443109i
$532$	−63782.7	+	630973.i	−0.225361	+	2.22940i
$533$	−315620.	+	92674.5i	−1.11099	+	0.326217i
$534$	−103067.	+	168041.i	−0.361439	+	0.589296i
$535$	−11745.2	+	40000.4i	−0.0410348	+	0.139752i
$536$	−82673.8	+	148457.i	−0.287765	+	0.516740i
$537$	227599.	+	498372.i	0.789263	+	1.72825i
$538$	−175691.	+	211589.i	−0.606996	+	0.731019i
$539$	140297.	−	218307.i	0.482916	−	0.751433i
$540$	984779.	−	184144.i	3.37716	−	0.631495i
$541$	49156.2	−	341889.i	0.167951	−	1.16813i	−0.715159	−	0.698962i	$-0.753646\pi$
$541$	49156.2	−	341889.i	0.167951	−	1.16813i	0.883110	−	0.469166i	$-0.155445\pi$
$542$	−71659.5	−	30921.8i	−0.243936	−	0.105261i
$543$	−262707.	+	227637.i	−0.890990	+	0.772047i
$544$	35073.3	−	104693.i	0.118517	−	0.353769i
$545$	14794.6	−	9507.94i	0.0498094	−	0.0320106i
$546$	71405.4	−	583486.i	0.239522	−	1.95724i
$547$	149051.	+	129154.i	0.498151	+	0.431651i	0.867349	−	0.497700i	$-0.165822\pi$
$547$	149051.	+	129154.i	0.498151	+	0.431651i	−0.369198	+	0.929351i	$0.620367\pi$
$548$	−11317.1	+	7964.70i	−0.0376856	+	0.0265221i
$549$	−51249.1	+	112220.i	−0.170036	+	0.372328i
$550$	−93292.5	−	294658.i	−0.308405	−	0.974077i
$551$		−	238077.i		−	0.784176i
$552$	−554762.	+	24645.4i	−1.82066	+	0.0808830i
$553$	353794.			1.15691
$554$	479428.	−	151793.i	1.56208	−	0.494575i
$555$	−348284.	−	159056.i	−1.13070	−	0.516373i
$556$	−122375.	−	173884.i	−0.395862	−	0.562484i
$557$	127709.	−	147384.i	0.411634	−	0.475051i	−0.511636	−	0.859202i	$-0.670960\pi$
$557$	127709.	−	147384.i	0.411634	−	0.475051i	0.923270	+	0.384151i	$0.125506\pi$
$558$	−570534.	−	69820.5i	−1.83237	−	0.224241i
$559$	61564.3	+	95795.9i	0.197018	+	0.306565i
$560$	−289069.	+	545772.i	−0.921777	+	1.74034i
$561$	−138262.	−	159563.i	−0.439315	−	0.506997i
$562$	−168455.	+	390386.i	−0.533350	+	1.23601i
$563$	258414.	+	37154.3i	0.815265	+	0.117217i	0.537319	−	0.843379i	$-0.319437\pi$
$563$	258414.	+	37154.3i	0.815265	+	0.117217i	0.277946	+	0.960597i	$0.410346\pi$
$564$	−58479.6	−	312742.i	−0.183843	−	0.983167i
$565$	−374969.	−	240978.i	−1.17462	−	0.754884i
$566$	−145596.	−	120894.i	−0.454481	−	0.377375i
$567$	−834476.	+	381092.i	−2.59566	+	1.18540i
$568$	−34303.5	+	61598.7i	−0.106327	+	0.190930i
$569$	−348862.	−	102435.i	−1.07753	−	0.316391i	−0.305640	−	0.952147i	$-0.598870\pi$
$569$	−348862.	−	102435.i	−1.07753	−	0.316391i	−0.771890	+	0.635756i	$0.780689\pi$
$570$	−1.16902e6	−	717006.i	−3.59809	−	2.20685i
$571$	−21596.5	−	73550.8i	−0.0662385	−	0.225587i	0.919721	−	0.392573i	$-0.128415\pi$
$571$	−21596.5	−	73550.8i	−0.0662385	−	0.225587i	−0.985959	+	0.166985i	$0.946597\pi$
$572$	251749.	+	25448.4i	0.769443	+	0.0777801i
$573$	25263.1	+	175709.i	0.0769446	+	0.535162i
$574$	−662817.	+	109570.i	−2.01173	+	0.332557i
$575$	−102584.	+	326660.i	−0.310274	+	0.988008i
$576$	427100.	−	640888.i	1.28731	−	1.93169i
$577$	−4660.48	−	32414.4i	−0.0139984	−	0.0973612i	0.981624	−	0.190823i	$-0.0611157\pi$
$577$	−4660.48	−	32414.4i	−0.0139984	−	0.0973612i	−0.995623	+	0.0934620i	$0.970207\pi$
$578$	277573.	+	75200.9i	0.830849	+	0.225096i
$579$	−143140.	−	487490.i	−0.426976	−	1.45415i
$580$	87361.4	−	214760.i	0.259695	−	0.638406i
$581$	592074.	+	173849.i	1.75398	+	0.515014i
$582$	428241.	−	387134.i	1.26428	−	1.14292i
$583$	210494.	−	96129.6i	0.619303	−	0.282826i
$584$	86588.1	−	226384.i	0.253882	−	0.663773i
$585$	747398.	+	480323.i	2.18394	+	1.40353i
$586$	−644736.	+	13559.4i	−1.87753	+	0.0394862i
$587$	−40356.1	−	5802.33i	−0.117120	−	0.0168394i	0.0835053	−	0.996507i	$-0.473388\pi$
$587$	−40356.1	−	5802.33i	−0.117120	−	0.0168394i	−0.200626	+	0.979668i	$0.564298\pi$
$588$	137561.	−	553620.i	0.397870	−	1.60124i
$589$	293287.	+	338471.i	0.845399	+	0.975642i
$590$	−371850.	−	552703.i	−1.06823	−	1.58777i
$591$	375709.	+	584615.i	1.07566	+	1.67377i
$592$	−156222.	+	60540.7i	−0.445757	+	0.172744i
$593$	−200391.	+	231264.i	−0.569862	+	0.657655i	−0.965394	−	0.260797i	$-0.916015\pi$
$593$	−200391.	+	231264.i	−0.569862	+	0.657655i	0.395532	+	0.918452i	$0.370560\pi$
$594$	−364196.	−	755048.i	−1.03220	−	2.13994i
$595$	236618.	+	108060.i	0.668365	+	0.305232i
$596$	286311.	+	563008.i	0.806019	+	1.58497i
$597$	−198885.			−0.558025
$598$	−212271.	−	183065.i	−0.593591	−	0.511922i
$599$		−	587616.i		−	1.63772i	−0.573993	−	0.818860i	$-0.694606\pi$
$599$		−	587616.i		−	1.63772i	0.573993	−	0.818860i	$-0.305394\pi$
$600$	−402628.	−	547277.i	−1.11841	−	1.52021i
$601$	−210716.	+	461404.i	−0.583376	+	1.27742i	0.355987	+	0.934491i	$0.384145\pi$
$601$	−210716.	+	461404.i	−0.583376	+	1.27742i	−0.939363	+	0.342925i	$0.888582\pi$
$602$	101038.	+	209470.i	0.278799	+	0.578002i
$603$	377293.	+	326926.i	1.03763	+	0.899114i
$604$	−2352.24	−	55898.5i	−0.00644774	−	0.153224i
$605$	11670.9	−	7500.45i	0.0318856	−	0.0204916i
$606$	124802.	+	185501.i	0.339842	+	0.505128i
$607$	−33415.2	+	28954.4i	−0.0906914	+	0.0785846i	−0.699027	−	0.715096i	$-0.746383\pi$
$607$	−33415.2	+	28954.4i	−0.0906914	+	0.0785846i	0.608335	+	0.793680i	$0.291838\pi$
$608$	−581740.	+	147266.i	−1.57370	+	0.398378i
$609$	−64140.3	+	446106.i	−0.172940	+	1.20283i
$610$	93590.0	−	1968.29i	0.251518	−	0.00528967i
$611$	86827.2	−	135106.i	0.232581	−	0.361903i
$612$	−280021.	−	163747.i	−0.747631	−	0.437189i
$613$	−242958.	−	532003.i	−0.646561	−	1.41577i	−0.894532	−	0.447004i	$-0.852491\pi$
$613$	−242958.	−	532003.i	−0.646561	−	1.41577i	0.247971	−	0.968768i	$-0.420236\pi$
$614$	504227.	−	455826.i	1.33749	−	1.20910i
$615$	409285.	−	1.39390e6i	1.08212	−	3.68537i
$616$	504033.	+	114044.i	1.32830	+	0.300545i
$617$	685774.	−	201361.i	1.80140	−	0.528939i	0.803597	−	0.595174i	$-0.202917\pi$
$617$	685774.	−	201361.i	1.80140	−	0.528939i	0.997804	+	0.0662348i	$0.0210986\pi$
$618$	−850393.	−	230391.i	−2.22660	−	0.603237i
$619$	−143116.	+	20576.9i	−0.373513	+	0.0537030i	−0.326515	−	0.945192i	$-0.605874\pi$
$619$	−143116.	+	20576.9i	−0.373513	+	0.0537030i	−0.0469976	+	0.998895i	$0.514965\pi$
$620$	140362.	+	412942.i	0.365145	+	1.07425i
$621$	−149314.	+	916569.i	−0.387185	+	2.37674i
$622$	428681.	−	70864.9i	1.10804	−	0.183168i
$623$	−201157.	+	28922.0i	−0.518273	+	0.0745164i
$624$	541974.	−	125135.i	1.39190	−	0.321373i
$625$	360991.	−	105997.i	0.924138	−	0.271351i
$626$	520862.	+	319465.i	1.32915	+	0.815221i
$627$	−323289.	+	1.10102e6i	−0.822349	+	2.80066i
$628$	277970.	−	349463.i	0.704821	−	0.886097i
$629$	29314.5	+	64189.7i	0.0740936	+	0.162242i
$630$	1.39596e6	+	1.15913e6i	3.51717	+	2.92045i
$631$	−206584.	+	321451.i	−0.518845	+	0.807339i	−0.997500	−	0.0706643i	$-0.977488\pi$
$631$	−206584.	+	321451.i	−0.518845	+	0.807339i	0.478655	+	0.878003i	$0.341124\pi$
$632$	114378.	+	314626.i	0.286358	+	0.787700i
$633$	−147148.	+	1.02344e6i	−0.367237	+	2.55419i
$634$	−199264.	+	461785.i	−0.495737	+	1.14884i
$635$	706095.	−	611835.i	1.75112	−	1.51735i
$636$	370098.	−	348991.i	0.914962	−	0.862780i
$637$	242240.	−	155678.i	0.596991	−	0.383663i
$638$	−192562.	−	23565.2i	−0.473074	−	0.0578936i
$639$	156548.	+	135650.i	0.383395	+	0.332214i
$640$	−578804.	−	80624.5i	−1.41309	−	0.196837i
$641$	134284.	−	294040.i	0.326819	−	0.715633i	−0.672891	−	0.739742i	$-0.734948\pi$
$641$	134284.	−	294040.i	0.326819	−	0.715633i	0.999709	+	0.0241089i	$0.00767485\pi$
$642$	73106.0	−	23146.3i	0.177371	−	0.0561579i
$643$			74128.0i			0.179292i	0.995974	+	0.0896458i	$0.0285735\pi$
$643$			74128.0i			0.179292i	−0.995974	+	0.0896458i	$0.971426\pi$
$644$	−384899.	−	423771.i	−0.928058	−	1.02178i
$645$	−502905.			−1.20883
$646$	76291.4	+	240962.i	0.182815	+	0.577408i
$647$	16356.2	+	7469.62i	0.0390727	+	0.0178439i	0.434856	−	0.900500i	$-0.356799\pi$
$647$	16356.2	+	7469.62i	0.0390727	+	0.0178439i	−0.395783	+	0.918344i	$0.629527\pi$
$648$	−608680.	−	618890.i	−1.44957	−	1.47388i
$649$	−365018.	+	421253.i	−0.866612	+	1.00012i
$650$	41659.6	−	340419.i	0.0986025	−	0.805726i
$651$	−458370.	−	713238.i	−1.08157	−	1.68295i
$652$	67975.6	−	64098.9i	0.159903	−	0.150784i
$653$	331673.	+	382771.i	0.777829	+	0.897663i	0.996951	−	0.0780350i	$-0.0248646\pi$
$653$	331673.	+	382771.i	0.777829	+	0.897663i	−0.219122	+	0.975698i	$0.570319\pi$
$654$	−29701.2	−	12816.3i	−0.0694413	−	0.0299646i
$655$	−935734.	−	134538.i	−2.18107	−	0.313591i
$656$	−311721.	−	554015.i	−0.724368	−	1.28740i
$657$	−599051.	−	384986.i	−1.38782	−	0.891897i
$658$	209534.	−	252346.i	0.483952	−	0.582834i
$659$	−513478.	+	234498.i	−1.18236	+	0.539967i	−0.906901	−	0.421344i	$-0.861558\pi$
$659$	−513478.	+	234498.i	−1.18236	+	0.539967i	−0.275463	+	0.961312i	$0.588831\pi$
$660$	−695643.	+	874560.i	−1.59698	+	2.00771i
$661$	526312.	+	154539.i	1.20459	+	0.353701i	0.821607	−	0.570054i	$-0.193078\pi$
$661$	526312.	+	154539.i	1.20459	+	0.353701i	0.382986	+	0.923754i	$0.374896\pi$
$662$	231755.	−	377857.i	0.528826	−	0.862207i
$663$	−66003.8	−	224788.i	−0.150156	−	0.511383i
$664$	36809.5	+	582730.i	0.0834880	+	1.32170i
$665$	−201202.	−	1.39939e6i	−0.454977	−	3.16444i
$666$	80280.4	+	485638.i	0.180993	+	1.09488i
$667$	159760.	+	143746.i	0.359100	+	0.323106i
$668$	−194.206	−	571.351i	−0.000435221	−	0.00128041i
$669$	−134016.	−	932104.i	−0.299437	−	2.08263i
$670$	99057.2	−	365629.i	0.220667	−	0.814501i
$671$	−22067.7	−	75155.6i	−0.0490131	−	0.166923i
$672$	1.12973e6	−	119219.i	2.50171	−	0.264002i
$673$	303400.	+	89086.3i	0.669863	+	0.196689i	0.598942	−	0.800793i	$-0.295588\pi$
$673$	303400.	+	89086.3i	0.669863	+	0.196689i	0.0709208	+	0.997482i	$0.477406\pi$
$674$	−350333.	−	387532.i	−0.771190	−	0.853077i
$675$	−1.03354e6	+	472002.i	−2.26840	+	1.03594i
$676$	−152106.	−	88946.3i	−0.332853	−	0.194641i
$677$	−320047.	−	205681.i	−0.698290	−	0.448764i	0.142734	−	0.989761i	$-0.454411\pi$
$677$	−320047.	−	205681.i	−0.698290	−	0.448764i	−0.841024	+	0.540997i	$0.818047\pi$
$678$	17238.8	+	819685.i	0.0375013	+	1.78315i
$679$	589079.	+	84696.8i	1.27772	+	0.183708i
$680$	−19600.4	+	245357.i	−0.0423885	+	0.530616i
$681$	402590.	+	464614.i	0.868099	+	1.00184i
$682$	302793.	−	203715.i	0.650995	−	0.437980i
$683$	−321199.	−	499796.i	−0.688546	−	1.07140i	−0.992913	−	0.118844i	$-0.962081\pi$
$683$	−321199.	−	499796.i	−0.688546	−	1.07140i	0.304366	−	0.952555i	$-0.401555\pi$
$684$	74123.6	+	1.76147e6i	0.158432	+	3.76498i
$685$	20202.9	−	23315.4i	0.0430559	−	0.0496891i
$686$	−55385.6	+	26715.2i	−0.117692	+	0.0567688i
$687$	−33089.1	−	15111.3i	−0.0701085	−	0.0320175i
$688$	−153616.	+	157572.i	−0.324533	+	0.332891i
$689$	256776.			0.540898
$690$	1.18697e6	−	351546.i	2.49312	−	0.738387i
$691$		−	594067.i		−	1.24417i	−0.782950	−	0.622084i	$-0.786286\pi$
$691$		−	594067.i		−	1.24417i	0.782950	−	0.622084i	$-0.213714\pi$
$692$	−179495.	−	352964.i	−0.374836	−	0.737085i
$693$	630704.	−	1.38105e6i	1.31329	−	2.87570i
$694$	−851291.	+	410619.i	−1.76750	+	0.852550i
$695$	358233.	+	310411.i	0.741645	+	0.642639i
$696$	−417454.	+	87182.1i	−0.861768	+	0.179974i
$697$	−225241.	+	144754.i	−0.463642	+	0.297965i
$698$	244765.	−	164674.i	0.502386	−	0.337998i
$699$	−309858.	+	268494.i	−0.634175	+	0.549516i
$700$	168905.	−	679762.i	0.344703	−	1.38727i
$701$	−46397.8	+	322704.i	−0.0944195	+	0.656702i	0.886563	+	0.462607i	$0.153086\pi$
$701$	−46397.8	+	322704.i	−0.0944195	+	0.656702i	−0.980983	+	0.194095i	$0.937823\pi$
$702$	−19558.6	−	929991.i	−0.0396884	−	1.88714i
$703$	207353.	−	322647.i	0.419565	−	0.652856i
$704$	61530.7	+	485102.i	0.124150	+	0.978785i
$705$	294642.	+	645177.i	0.592812	+	1.29808i
$706$	577077.	+	638353.i	1.15778	+	1.28071i
$707$	−64936.0	+	221152.i	−0.129911	+	0.442437i
$708$	−461701.	+	1.13499e6i	−0.921073	+	2.26426i
$709$	−627662.	+	184298.i	−1.24863	+	0.366631i	−0.838251	−	0.545285i	$-0.816422\pi$
$709$	−627662.	+	184298.i	−1.24863	+	0.366631i	−0.410378	+	0.911915i	$0.634603\pi$
$710$	41101.4	−	151709.i	0.0815342	−	0.300950i
$711$	973529.	−	139972.i	1.92579	−	0.276887i
$712$	−90752.1	−	169537.i	−0.179018	−	0.334429i
$713$	−404210.	−	7554.57i	−0.795111	−	0.0148604i
$714$	−78036.7	−	472065.i	−0.153074	−	0.925988i
$715$	−558338.	+	80276.9i	−1.09216	+	0.157029i
$716$	−531743.	−	53751.9i	−1.03723	−	0.104850i
$717$	1.44707e6	−	424898.i	2.81482	−	0.826507i
$718$	29838.5	−	48649.2i	0.0578800	−	0.0943685i
$719$	−157257.	+	535568.i	−0.304195	+	1.03599i	0.655557	+	0.755145i	$0.272434\pi$
$719$	−157257.	+	535568.i	−0.304195	+	1.03599i	−0.959752	+	0.280848i	$0.909384\pi$
$720$	−579502.	+	1.61615e6i	−1.11787	+	3.11758i
$721$	−377316.	−	826208.i	−0.725830	−	1.58935i
$722$	544547.	−	655811.i	1.04463	−	1.25807i
$723$	333560.	−	519030.i	0.638113	−	0.992924i
$724$	−62326.3	−	333313.i	−0.118903	−	0.635881i
$725$	−37420.9	+	260268.i	−0.0711932	+	0.495160i
$726$	−23430.1	−	10110.3i	−0.0444530	−	0.0191819i
$727$	336112.	−	291242.i	0.635938	−	0.551043i	−0.276111	−	0.961126i	$-0.589046\pi$
$727$	336112.	−	291242.i	0.635938	−	0.551043i	0.912048	+	0.410083i	$0.134500\pi$
$728$	456180.	+	347449.i	0.860742	+	0.655583i
$729$	−183398.	+	117863.i	−0.345096	+	0.221780i
$730$	−65634.3	+	536327.i	−0.123164	+	1.00643i
$731$	70048.0	+	60697.0i	0.131087	+	0.113588i
$732$	−99099.0	−	140811.i	−0.184947	−	0.262793i
$733$	173094.	−	379023.i	0.322162	−	0.705436i	−0.677382	−	0.735631i	$-0.736886\pi$
$733$	173094.	−	379023.i	0.322162	−	0.705436i	0.999544	+	0.0301953i	$0.00961292\pi$
$734$	191502.	+	604847.i	0.355452	+	1.12267i
$735$			1.27170e6i			2.35402i
$736$	252422.	−	479289.i	0.465985	−	0.884793i
$737$	−316968.			−0.583554
$738$	−1.78051e6	+	563732.i	−3.26913	+	1.03505i
$739$	170470.	+	77850.9i	0.312146	+	0.142553i	0.565328	−	0.824866i	$-0.308750\pi$
$739$	170470.	+	77850.9i	0.312146	+	0.142553i	−0.253181	+	0.967419i	$0.581477\pi$
$740$	305439.	−	214960.i	0.557778	−	0.392550i
$741$	−833838.	+	962301.i	−1.51861	+	1.75257i
$742$	520535.	+	63701.7i	0.945458	+	0.115703i
$743$	99515.2	+	154849.i	0.180265	+	0.280498i	0.919613	−	0.392826i	$-0.128502\pi$
$743$	99515.2	+	154849.i	0.180265	+	0.280498i	−0.739348	+	0.673324i	$0.764866\pi$
$744$	486090.	−	638208.i	0.878155	−	1.15297i
$745$	−922091.	−	1.06415e6i	−1.66135	−	1.91730i
$746$	−17531.7	+	40628.7i	−0.0315026	+	0.0730055i
$747$	1.69798e6	+	244132.i	3.04292	+	0.437506i
$748$	202447.	−	37855.6i	0.361833	−	0.0676592i
$749$	66503.9	+	42739.5i	0.118545	+	0.0761843i
$750$	40038.1	+	33245.3i	0.0711789	+	0.0591028i
$751$	83303.6	−	38043.5i	0.147701	−	0.0674528i	−0.340193	−	0.940356i	$-0.610492\pi$
$751$	83303.6	−	38043.5i	0.147701	−	0.0674528i	0.487894	+	0.872903i	$0.337765\pi$
$752$	292149.	+	104756.i	0.516618	+	0.185243i
$753$	−1.44416e6	−	424044.i	−2.54698	−	0.747860i
$754$	−183501.	−	112549.i	−0.322772	−	0.197969i
$755$	35138.7	+	119671.i	0.0616442	+	0.209941i
$756$	191066.	−	1.89013e6i	0.334303	−	3.30710i
$757$	132827.	+	923833.i	0.231790	+	1.61214i	0.690352	+	0.723474i	$0.257456\pi$
$757$	132827.	+	923833.i	0.231790	+	1.61214i	−0.458561	+	0.888663i	$0.651635\pi$
$758$	−20852.0	+	3447.02i	−0.0362918	+	0.00599937i
$759$	−543637.	−	881718.i	−0.943681	−	1.53054i
$760$	1.17942e6	−	631337.i	2.04194	−	1.09304i
$761$	−24891.4	−	173124.i	−0.0429814	−	0.298942i	−0.999961	−	0.00878814i	$-0.997203\pi$
$761$	−24891.4	−	173124.i	−0.0429814	−	0.298942i	0.956980	−	0.290154i	$-0.0937065\pi$
$762$	−1.65874e6	−	449391.i	−2.85673	−	0.773953i
$763$	−9395.34	−	31997.6i	−0.0161385	−	0.0549627i
$764$	−160401.	−	65249.0i	−0.274802	−	0.111786i
$765$	693849.	+	203732.i	1.18561	+	0.348126i
$766$	−8944.41	+	8085.84i	−0.0152438	+	0.0137806i
$767$	−562613.	+	256937.i	−0.956355	+	0.436752i
$768$	471252.	+	966121.i	0.798971	+	1.63798i
$769$	−211180.	−	135717.i	−0.357109	−	0.229500i	0.349768	−	0.936836i	$-0.386260\pi$
$769$	−211180.	−	135717.i	−0.357109	−	0.229500i	−0.706877	+	0.707336i	$0.749897\pi$
$770$	−1.15178e6	+	24223.0i	−1.94262	+	0.0408551i
$771$	−18430.2	−	2649.86i	−0.0310042	−	0.00445773i
$772$	480990.	+	119514.i	0.807052	+	0.200533i
$773$	−185248.	−	213787.i	−0.310023	−	0.357785i	0.579260	−	0.815143i	$-0.303342\pi$
$773$	−185248.	−	213787.i	−0.310023	−	0.357785i	−0.889283	+	0.457357i	$0.848796\pi$
$774$	360897.	+	536422.i	0.602422	+	0.895415i
$775$	−267424.	−	416119.i	−0.445242	−	0.692811i
$776$	115123.	+	551245.i	0.191179	+	0.915422i
$777$	−475460.	+	548710.i	−0.787539	+	0.908868i
$778$	89033.3	+	184583.i	0.147093	+	0.304953i
$779$	1.32370e6	+	604512.i	2.18129	+	0.996161i
$780$	−1.10529e6	+	562080.i	−1.81671	+	0.923866i
$781$	−131518.			−0.215618
$782$	−207759.	−	94293.3i	−0.339740	−	0.154194i
$783$			713177.i			1.16325i
$784$	398454.	+	388450.i	0.648255	+	0.631980i
$785$	−413523.	+	905489.i	−0.671059	+	1.46941i
$786$	755456.	+	1.56620e6i	1.22282	+	2.53515i
$787$	−170821.	−	148017.i	−0.275798	−	0.238981i	0.505968	−	0.862552i	$-0.331135\pi$
$787$	−170821.	−	148017.i	−0.275798	−	0.238981i	−0.781766	+	0.623572i	$0.785681\pi$
$788$	−677298.	+	28501.0i	−1.09076	+	0.0458995i
$789$	810528.	−	520895.i	1.30201	−	0.836750i
$790$	−416592.	−	619204.i	−0.667508	−	0.992156i
$791$	−638769.	+	553497.i	−1.02092	+	0.884631i
$792$	1.43206e6	+	114400.i	2.28302	+	0.182380i
$793$	12369.4	−	86031.1i	0.0196699	−	0.136807i
$794$	429372.	−	9030.10i	0.681072	−	0.0143236i
$795$	−613096.	+	953995.i	−0.970049	+	1.50943i
$796$	97934.9	−	167477.i	0.154565	−	0.264319i
$797$	420322.	+	920378.i	0.661707	+	1.44894i	0.880923	+	0.473260i	$0.156923\pi$
$797$	420322.	+	920378.i	0.661707	+	1.44894i	−0.219215	+	0.975677i	$0.570350\pi$
$798$	−1.92909e6	+	1.74391e6i	−3.02933	+	2.73854i
$799$	36828.3	−	125426.i	0.0576884	−	0.196469i
$800$	659112.	−	69555.0i	1.02986	−	0.108680i
$801$	−542077.	+	159168.i	−0.844881	+	0.248080i
$802$	249570.	+	67614.2i	0.388011	+	0.105121i
$803$	447516.	−	64343.2i	0.694029	−	0.0997864i
$804$	−659712.	+	224241.i	−1.02057	+	0.346898i
$805$	1.06053e6	+	709912.i	1.63656	+	1.09550i
$806$	399530.	−	66046.0i	0.615007	−	0.101666i
$807$	−1.11626e6	+	160494.i	−1.71402	+	0.246440i
$808$	−217662.	+	13749.1i	−0.333395	+	0.0210597i
$809$	223887.	−	65739.1i	0.342083	−	0.100445i	−0.106179	−	0.994347i	$-0.533862\pi$
$809$	223887.	−	65739.1i	0.342083	−	0.100445i	0.448261	+	0.893903i	$0.352043\pi$
$810$	1.64957e6	+	1.01175e6i	2.51421	+	1.54207i
$811$	143624.	−	489139.i	0.218367	−	0.743688i	−0.775327	−	0.631560i	$-0.782415\pi$
$811$	143624.	−	489139.i	0.218367	−	0.743688i	0.993694	−	0.112128i	$-0.0357668\pi$
$812$	−344072.	−	273682.i	−0.521840	−	0.415083i
$813$	−132946.	−	291110.i	−0.201137	−	0.440430i
$814$	−240441.	−	199648.i	−0.362877	−	0.301312i
$815$	−112607.	+	175219.i	−0.169531	+	0.263795i
$816$	394575.	−	222011.i	0.592584	−	0.333423i
$817$	71691.7	−	498627.i	0.107405	−	0.747019i
$818$	275257.	−	637893.i	0.411369	−	0.953326i
$819$	1.27321e6	−	1.10324e6i	1.89816	−	1.64476i
$820$	972231.	+	1.03103e6i	1.44591	+	1.53336i
$821$	974059.	−	625990.i	1.44510	−	0.928712i	0.445665	−	0.895200i	$-0.352967\pi$
$821$	974059.	−	625990.i	1.44510	−	0.928712i	0.999438	−	0.0335121i	$-0.0106692\pi$
$822$	−56326.3	−	6893.06i	−0.0833619	−	0.0102016i
$823$	304737.	+	264056.i	0.449910	+	0.389849i	0.850133	−	0.526569i	$-0.176522\pi$
$823$	304737.	+	264056.i	0.449910	+	0.389849i	−0.400223	+	0.916418i	$0.631067\pi$
$824$	612757.	−	602649.i	0.902473	−	0.887586i
$825$	526483.	−	1.15284e6i	0.773528	−	1.69379i
$826$	−1.20427e6	+	381287.i	−1.76508	+	0.558846i
$827$			67482.4i			0.0986687i	0.998782	+	0.0493344i	$0.0157100\pi$
$827$			67482.4i			0.0986687i	−0.998782	+	0.0493344i	$0.984290\pi$
$828$	−1.22678e6	−	1.01380e6i	−1.78939	−	1.47874i
$829$	91076.9			0.132525			0.0662627	−	0.997802i	$-0.478892\pi$
$829$	91076.9			0.132525			0.0662627	+	0.997802i	$0.478892\pi$
$830$	−392898.	−	1.24094e6i	−0.570327	−	1.80134i
$831$	1.87574e6	+	856621.i	2.71625	+	1.24047i
$832$	−161505.	+	518004.i	−0.233313	+	0.748318i
$833$	153485.	−	177131.i	0.221196	−	0.255273i
$834$	105910.	−	865435.i	0.152266	−	1.24424i
$835$	727.307	+	1131.71i	0.00104315	+	0.00162317i
$836$	−767953.	−	814399.i	−1.09881	−	1.16527i
$837$	−878563.	−	1.01392e6i	−1.25407	−	1.44727i
$838$	440485.	+	190074.i	0.627254	+	0.270666i
$839$	−800193.	−	115050.i	−1.13677	−	0.163442i	−0.451870	−	0.892084i	$-0.649243\pi$
$839$	−800193.	−	115050.i	−1.13677	−	0.163442i	−0.684895	+	0.728641i	$0.740152\pi$
$840$	−2.38008e6	+	865246.i	−3.37313	+	1.22626i
$841$	−456159.	−	293155.i	−0.644947	−	0.414482i
$842$	868520.	−	1.04598e6i	1.22506	−	1.47536i
$843$	−1.58591e6	+	724260.i	−2.23163	+	1.01915i
$844$	−789355.	−	627869.i	−1.10812	−	0.881423i
$845$	376895.	+	110666.i	0.527845	+	0.154989i
$846$	476733.	−	777274.i	0.666093	−	1.08601i
$847$	−7411.62	−	25241.7i	−0.0103311	−	0.0351845i
$848$	111634.	+	483502.i	0.155241	+	0.672367i
$849$	−110437.	−	768103.i	−0.153214	−	1.06562i
$850$	−45528.4	−	275414.i	−0.0630151	−	0.381195i
$851$	91314.3	+	333951.i	0.126090	+	0.461130i
$852$	−273731.	+	93043.2i	−0.377090	+	0.128176i
$853$	195025.	+	1.35643e6i	0.268035	+	1.86422i	0.467054	+	0.884229i	$0.345315\pi$
$853$	195025.	+	1.35643e6i	0.268035	+	1.86422i	−0.199019	+	0.979996i	$0.563776\pi$
$854$	46418.1	−	171334.i	0.0636461	−	0.234924i
$855$	−1.10729e6	−	3.77108e6i	−1.51471	−	5.15862i
$856$	−16507.8	+	72958.6i	−0.0225290	+	0.0995702i
$857$	−226579.	−	66529.5i	−0.308501	−	0.0905842i	0.123817	−	0.992305i	$-0.460486\pi$
$857$	−226579.	−	66529.5i	−0.308501	−	0.0905842i	−0.432319	+	0.901721i	$0.642304\pi$
$858$	695798.	+	769679.i	0.945166	+	1.04553i
$859$	1.14678e6	−	523717.i	1.55415	−	0.709759i	0.561137	−	0.827723i	$-0.310364\pi$
$859$	1.14678e6	−	523717.i	1.55415	−	0.709759i	0.993018	+	0.117965i	$0.0376369\pi$
$860$	247640.	−	423485.i	0.334829	−	0.572587i
$861$	−2.31747e6	−	1.48935e6i	−3.12613	−	2.00904i
$862$	−9217.64	−	438290.i	−0.0124052	−	0.589857i
$863$	7861.61	+	1130.33i	0.0105558	+	0.00151769i	0.147591	−	0.989049i	$-0.452848\pi$
$863$	7861.61	+	1130.33i	0.0105558	+	0.00151769i	−0.137035	+	0.990566i	$0.543757\pi$
$864$	1.74265e6	−	441147.i	2.33444	−	0.590957i
$865$	578081.	+	667142.i	0.772604	+	0.891632i
$866$	−619233.	+	416611.i	−0.825692	+	0.555513i
$867$	637538.	+	992029.i	0.848141	+	1.31973i
$868$	826313.	−	34771.6i	1.09674	−	0.0461515i
$869$	−408937.	+	471938.i	−0.541523	+	0.624951i
$870$	856292.	−	413031.i	1.13131	−	0.545688i
$871$	−319934.	−	146109.i	−0.421720	−	0.192593i
$872$	25417.8	−	18699.7i	0.0334275	−	0.0245924i
$873$	1.65447e6			2.17085
$874$	179347.	+	1.22699e6i	0.234785	+	1.60627i
$875$			53650.2i			0.0700738i
$876$	885904.	−	450516.i	1.15446	−	0.587086i
$877$	19669.6	−	43070.4i	0.0255739	−	0.0559990i	−0.896414	−	0.443218i	$-0.853837\pi$
$877$	19669.6	−	43070.4i	0.0255739	−	0.0559990i	0.921988	+	0.387219i	$0.126564\pi$
$878$	−606348.	+	292471.i	−0.786561	+	0.379397i
$879$	−1.99846e6	−	1.73167e6i	−2.58653	−	2.24124i
$880$	−393900.	−	1.01644e6i	−0.508652	−	1.31255i
$881$	−320192.	+	205775.i	−0.412533	+	0.265119i	−0.730404	−	0.683015i	$-0.760668\pi$
$881$	−320192.	+	205775.i	−0.412533	+	0.265119i	0.317871	+	0.948134i	$0.397032\pi$
$882$	1.35646e6	−	912604.i	1.74369	−	1.17313i
$883$	497112.	−	430750.i	0.637577	−	0.552464i	−0.274961	−	0.961455i	$-0.588665\pi$
$883$	497112.	−	430750.i	0.637577	−	0.552464i	0.912538	+	0.408992i	$0.134119\pi$
$884$	221791.	+	55109.7i	0.283818	+	0.0705218i
$885$	388741.	−	2.70375e6i	0.496333	−	3.45207i
$886$	19812.2	+	942051.i	0.0252386	+	1.20007i
$887$	767.738	−	1194.62i	0.000975812	−	0.00151839i	−0.840765	−	0.541400i	$-0.817895\pi$
$887$	767.738	−	1194.62i	0.000975812	−	0.00151839i	0.841741	+	0.539881i	$0.181531\pi$
$888$	−641675.	−	245430.i	−0.813747	−	0.311245i
$889$	−735978.	−	1.61157e6i	−0.931240	−	2.03913i
$890$	287480.	+	318006.i	0.362934	+	0.401471i
$891$	456186.	−	1.55363e6i	0.574628	−	1.95700i
$892$	850897.	+	346134.i	1.06942	+	0.435025i
$893$	−681692.	+	200163.i	−0.854840	+	0.251004i
$894$	−677273.	+	2.49988e6i	−0.847401	+	3.12783i
$895$	1.17932e6	−	169560.i	1.47226	−	0.211679i
$896$	−455911.	+	1.01003e6i	−0.567889	+	1.25811i
$897$	−142289.	−	1.14056e6i	−0.176842	−	1.41753i
$898$	−100157.	−	605878.i	−0.124202	−	0.751334i
$899$	−307315.	+	44185.2i	−0.380246	+	0.0546711i
$900$	195836.	−	1.93731e6i	0.241772	−	2.39174i
$901$	200537.	−	58882.8i	0.247027	−	0.0725336i
$902$	619965.	−	1.01080e6i	0.761999	−	1.24238i
$903$	−268671.	+	915008.i	−0.329492	+	1.12215i
$904$	−698728.	−	389112.i	−0.855010	−	0.476144i
$905$	314023.	+	687615.i	0.383411	+	0.839554i
$906$	146557.	−	176502.i	0.178546	−	0.215027i
$907$	−484872.	+	754476.i	−0.589404	+	0.917130i	0.410582	+	0.911824i	$0.365325\pi$
$907$	−484872.	+	754476.i	−0.589404	+	0.917130i	−0.999986	+	0.00530634i	$0.998311\pi$
$908$	−589485.	+	110228.i	−0.714992	+	0.133696i
$909$	−91188.4	+	634230.i	−0.110360	+	0.767571i
$910$	−1.17372e6	−	506471.i	−1.41737	−	0.611606i
$911$	577149.	−	500102.i	0.695426	−	0.602590i	−0.233719	−	0.972304i	$-0.575090\pi$
$911$	577149.	−	500102.i	0.695426	−	0.602590i	0.929146	+	0.369714i	$0.120544\pi$
$912$	−2.17450e6	−	1.15173e6i	−2.61439	−	1.38472i
$913$	−916258.	+	588843.i	−1.09920	+	0.706412i
$914$	−115055.	+	940168.i	−0.137725	+	1.12542i
$915$	290096.	+	251370.i	0.346497	+	0.300242i
$916$	29018.6	−	20422.5i	0.0345848	−	0.0243399i
$917$	−744689.	+	1.63064e6i	−0.885598	+	1.93919i
$918$	−228537.	−	721819.i	−0.271188	−	0.856531i
$919$		−	333207.i		−	0.394532i	−0.980350	−	0.197266i	$-0.936794\pi$
$919$		−	333207.i		−	0.394532i	0.980350	−	0.197266i	$-0.0632063\pi$
$920$	−288459.	+	1.17263e6i	−0.340807	+	1.38544i
$921$	2.78722e6			3.28588
$922$	865305.	−	273966.i	1.01790	−	0.322282i
$923$	−132749.	−	60624.4i	−0.155822	−	0.0711613i
$924$	1.21958e6	+	1.73291e6i	1.42845	+	2.02970i
$925$	−277394.	+	320130.i	−0.324201	+	0.374148i
$926$	999924.	+	122368.i	1.16612	+	0.142707i
$927$	−1.36513e6	−	2.12418e6i	−1.58860	−	2.47191i
$928$	132148.	−	394459.i	0.153450	−	0.458043i
$929$	351304.	+	405427.i	0.407054	+	0.469766i	0.921850	−	0.387547i	$-0.126678\pi$
$929$	351304.	+	405427.i	0.407054	+	0.469766i	−0.514796	+	0.857313i	$0.672132\pi$
$930$	−708567.	+	1.64207e6i	−0.819248	+	1.89856i
$931$	−1.26088e6	−	181288.i	−1.45471	−	0.209156i
$932$	−73512.7	−	393137.i	−0.0846312	−	0.452597i
$933$	1.49884e6	+	963245.i	1.72184	+	1.10656i
$934$	644990.	+	535563.i	0.739366	+	0.613927i
$935$	−417642.	+	190731.i	−0.477728	+	0.218171i
$936$	1.39272e6	+	775589.i	1.58969	+	0.885278i
$937$	65913.8	+	19354.0i	0.0750753	+	0.0220441i	0.319055	−	0.947736i	$-0.396635\pi$
$937$	65913.8	+	19354.0i	0.0750753	+	0.0220441i	−0.243979	+	0.969780i	$0.578453\pi$
$938$	−612323.	−	375562.i	−0.695945	−	0.426851i
$939$	705890.	+	2.40404e6i	0.800582	+	2.72653i
$940$	−688377.	−	69585.4i	−0.779059	−	0.0787522i
$941$	101150.	+	703511.i	0.114231	+	0.794496i	0.963725	+	0.266897i	$0.0859984\pi$
$941$	101150.	+	703511.i	0.114231	+	0.794496i	−0.849494	+	0.527599i	$0.823093\pi$
$942$	1.80650e6	−	298631.i	2.03580	−	0.336537i
$943$	−1.20488e6	+	523264.i	−1.35494	+	0.588433i
$944$	−728404.	−	947681.i	−0.817388	−	1.06345i
$945$	602717.	+	4.19199e6i	0.674916	+	4.69415i
$946$	−396205.	−	107341.i	−0.442729	−	0.119945i
$947$	448781.	+	1.52841e6i	0.500420	+	1.70427i	0.691220	+	0.722644i	$0.257074\pi$
$947$	448781.	+	1.52841e6i	0.500420	+	1.70427i	−0.190800	+	0.981629i	$0.561108\pi$
$948$	−517253.	+	1.27156e6i	−0.575554	+	1.41488i
$949$	481363.	+	141341.i	0.534491	+	0.156941i
$950$	−1.12547e6	+	1.01744e6i	−1.24706	+	1.12736i
$951$	−1.87596e6	+	856722.i	−2.07426	+	0.947281i
$952$	435943.	+	166741.i	0.481012	+	0.183979i
$953$	−1.01854e6	−	654578.i	−1.12149	−	0.720735i	−0.157720	−	0.987484i	$-0.550414\pi$
$953$	−1.01854e6	−	654578.i	−1.12149	−	0.720735i	−0.963766	+	0.266749i	$0.914051\pi$
$954$	1.45755e6	−	30653.6i	1.60150	−	0.0336810i
$955$	382102.	+	54938.0i	0.418960	+	0.0602374i
$956$	−354768.	+	1.42777e6i	−0.388176	+	1.56223i
$957$	−520939.	−	601195.i	−0.568804	−	0.656435i
$958$	332537.	+	494270.i	0.362334	+	0.538559i
$959$	−31627.9	−	49214.0i	−0.0343901	−	0.0535121i
$960$	−1.53891e6	−	1.83686e6i	−1.66983	−	1.99312i
$961$	−222303.	+	256551.i	−0.240713	+	0.277797i
$962$	−150661.	−	312349.i	−0.162799	−	0.337513i
$963$	199907.	+	91294.3i	0.215563	+	0.0984444i
$964$	272813.	+	536464.i	0.293569	+	0.577281i
$965$	−1.10487e6			−1.18646
$966$	−5493.70	−	2.34744e6i	−0.00588722	−	2.51560i
$967$			1.66138e6i			1.77671i	0.459157	+	0.888355i	$0.348152\pi$
$967$			1.66138e6i			1.77671i	−0.459157	+	0.888355i	$0.651848\pi$
$968$	20051.1	−	14751.5i	0.0213987	−	0.0157429i
$969$	−430540.	+	942750.i	−0.458528	+	1.00404i
$970$	−545404.	−	1.13073e6i	−0.579662	−	1.20175i
$971$	−47289.9	−	40977.0i	−0.0501569	−	0.0434612i	0.629422	−	0.777064i	$-0.283292\pi$
$971$	−47289.9	−	40977.0i	−0.0501569	−	0.0434612i	−0.679579	+	0.733603i	$0.737837\pi$
$972$	−53998.7	−	1.28322e6i	−0.0571546	−	1.35822i
$973$	756158.	−	485953.i	0.798706	−	0.513297i
$974$	639353.	+	950308.i	0.673942	+	1.00172i
$975$	1.06282e6	−	920937.i	1.11802	−	0.968770i
$976$	167372.	−	14111.2i	0.175705	−	0.0148137i
$977$	−117954.	+	820391.i	−0.123573	+	0.859473i	0.829882	+	0.557939i	$0.188408\pi$
$977$	−117954.	+	820391.i	−0.123573	+	0.859473i	−0.953456	+	0.301534i	$0.902501\pi$
$978$	383031.	−	8055.50i	0.400457	−	0.00842199i
$979$	193929.	−	301760.i	0.202338	−	0.314844i
$980$	−1.07087e6	−	626210.i	−1.11503	−	0.652031i
$981$	−38512.2	−	84330.0i	−0.0400185	−	0.0876283i
$982$	1.22599e6	−	1.10831e6i	1.27135	−	1.14931i
$983$	48319.4	−	164561.i	0.0500051	−	0.170302i	−0.930705	−	0.365772i	$-0.880805\pi$
$983$	48319.4	−	164561.i	0.0500051	−	0.170302i	0.980710	+	0.195470i	$0.0626232\pi$
$984$	575249.	−	2.54240e6i	0.594108	−	2.62575i
$985$	1.45001e6	−	425760.i	1.49451	−	0.438827i
$986$	−169120.	−	45818.4i	−0.173957	−	0.0471288i
$987$	1.33127e6	−	191408.i	1.36657	−	0.196484i
$988$	−399735.	−	1.17601e6i	−0.409504	−	1.20475i
$989$	291314.	+	349170.i	0.297830	+	0.356981i
$990$	−3.15974e6	+	522334.i	−3.22390	+	0.532940i
$991$	1.12475e6	−	161715.i	1.14527	−	0.164665i	0.456556	−	0.889695i	$-0.349083\pi$
$991$	1.12475e6	−	161715.i	1.14527	−	0.164665i	0.688718	+	0.725029i	$0.258174\pi$
$992$	298061.	+	723592.i	0.302888	+	0.735310i
$993$	1.74400e6	−	512085.i	1.76868	−	0.519330i
$994$	−254069.	−	155830.i	−0.257145	−	0.157717i
$995$	−121850.	+	414982.i	−0.123078	+	0.419164i
$996$	−1.49044e6	+	1.87378e6i	−1.50244	+	1.88886i
$997$	746585.	+	1.63479e6i	0.751085	+	1.64465i	0.764405	+	0.644736i	$0.223033\pi$
$997$	746585.	+	1.63479e6i	0.751085	+	1.64465i	−0.0133201	+	0.999911i	$0.504240\pi$
$998$	251747.	+	209037.i	0.252757	+	0.209875i
$999$	−621141.	+	966515.i	−0.622385	+	0.968451i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.5.g.a.3.4	✓	460
4.3	odd	2	inner	92.5.g.a.3.46	yes	460
23.8	even	11	inner	92.5.g.a.31.46	yes	460
92.31	odd	22	inner	92.5.g.a.31.4	yes	460

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.5.g.a.3.4	✓	460	1.1	even	1	trivial
92.5.g.a.3.46	yes	460	4.3	odd	2	inner
92.5.g.a.31.4	yes	460	92.31	odd	22	inner
92.5.g.a.31.46	yes	460	23.8	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	92.g (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.81343 + 1.20738i) q^{2} +(-14.9199 - 6.81367i) q^{3} +(13.0845 - 9.20851i) q^{4} +(-23.3579 + 26.9564i) q^{5} +(65.1225 + 7.96951i) q^{6} +(36.5671 + 56.8995i) q^{7} +(-38.7785 + 50.9139i) q^{8} +(123.132 + 142.102i) q^{9} +(56.5269 - 130.998i) q^{10} +(-118.167 - 16.9898i) q^{11} +(-257.962 + 48.2364i) q^{12} +(-111.441 - 71.6187i) q^{13} +(-208.145 - 172.832i) q^{14} +(532.168 - 243.033i) q^{15} +(86.4067 - 240.977i) q^{16} +(-103.456 - 30.3775i) q^{17} +(-641.128 - 393.229i) q^{18} +(165.102 + 562.287i) q^{19} +(-57.3969 + 567.802i) q^{20} +(-157.881 - 1098.09i) q^{21} +(471.134 - 77.8827i) q^{22} +(-477.005 - 228.708i) q^{23} +(925.481 - 495.404i) q^{24} +(-92.1116 - 640.651i) q^{25} +(511.443 + 138.561i) q^{26} +(-494.577 - 1684.38i) q^{27} +(1002.42 + 407.772i) q^{28} +(-389.800 - 114.456i) q^{29} +(-1735.95 + 1569.32i) q^{30} +(695.172 - 317.475i) q^{31} +(-38.5552 + 1023.27i) q^{32} +(1647.27 + 1058.64i) q^{33} +(431.201 - 9.06856i) q^{34} +(-2387.94 - 343.334i) q^{35} +(2919.67 + 725.468i) q^{36} +(-428.581 - 494.609i) q^{37} +(-1308.50 - 1944.90i) q^{38} +(1174.70 + 1827.86i) q^{39} +(-466.673 - 2234.57i) q^{40} +(1626.13 - 1876.65i) q^{41} +(1927.88 + 3996.86i) q^{42} +(-781.930 - 357.096i) q^{43} +(-1702.60 + 865.837i) q^{44} -6706.68 q^{45} +(2095.16 + 296.236i) q^{46} +1212.35i q^{47} +(-2931.11 + 3006.59i) q^{48} +(-902.993 + 1977.28i) q^{49} +(1124.77 + 2331.86i) q^{50} +(1336.57 + 1158.15i) q^{51} +(-2117.65 + 89.1116i) q^{52} +(-1630.66 + 1047.96i) q^{53} +(3919.72 + 5826.10i) q^{54} +(3218.11 - 2788.51i) q^{55} +(-4315.00 - 344.705i) q^{56} +(1367.94 - 9514.20i) q^{57} +(1624.67 - 34.1683i) q^{58} +(2524.27 - 3927.84i) q^{59} +(4725.17 - 8080.43i) q^{60} +(272.561 + 596.825i) q^{61} +(-2267.68 + 2050.00i) q^{62} +(-3582.96 + 12202.4i) q^{63} +(-1088.45 - 3948.73i) q^{64} +(4533.60 - 1331.19i) q^{65} +(-7559.92 - 2048.15i) q^{66} +(2628.05 - 377.857i) q^{67} +(-1633.40 + 555.205i) q^{68} +(5558.50 + 6662.44i) q^{69} +(9520.76 - 1573.87i) q^{70} +(1090.45 - 156.783i) q^{71} +(-12009.9 + 758.632i) q^{72} +(-3633.75 + 1066.97i) q^{73} +(2231.55 + 1368.70i) q^{74} +(-2990.89 + 10186.0i) q^{75} +(7338.11 + 5836.88i) q^{76} +(-3354.31 - 7344.91i) q^{77} +(-6686.54 - 5552.12i) q^{78} +(2827.99 - 4400.44i) q^{79} +(4477.60 + 7957.92i) q^{80} +(-1930.26 + 13425.3i) q^{81} +(-3935.29 + 9119.83i) q^{82} +(6894.93 - 5974.49i) q^{83} +(-12177.6 - 12914.1i) q^{84} +(3235.39 - 2079.26i) q^{85} +(3412.99 + 417.672i) q^{86} +(5035.90 + 4363.63i) q^{87} +(5447.35 - 5357.49i) q^{88} +(-1248.18 + 2733.14i) q^{89} +(25575.4 - 8097.50i) q^{90} -8959.82i q^{91} +(-8347.42 + 1399.98i) q^{92} -12535.0 q^{93} +(-1463.77 - 4623.23i) q^{94} +(-19013.7 - 8683.26i) q^{95} +(7547.49 - 15004.4i) q^{96} +(5762.14 - 6649.87i) q^{97} +(1056.17 - 8630.46i) q^{98} +(-12135.9 - 18883.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 460 q - 3 q^{2} - 43 q^{4} - 18 q^{5} - 44 q^{6} + 144 q^{8} + 1116 q^{9} - 77 q^{10} - 156 q^{12} - 18 q^{13} + 253 q^{14} - 795 q^{16} - 18 q^{17} - 676 q^{18} + 113 q^{20} + 266 q^{21} - 818 q^{22} + 1006 q^{24}+ \cdots + 52545 q^{98}+O(q^{100}) \) 460 * q - 3 * q^2 - 43 * q^4 - 18 * q^5 - 44 * q^6 + 144 * q^8 + 1116 * q^9 - 77 * q^10 - 156 * q^12 - 18 * q^13 + 253 * q^14 - 795 * q^16 - 18 * q^17 - 676 * q^18 + 113 * q^20 + 266 * q^21 - 818 * q^22 + 1006 * q^24 - 4768 * q^25 + 1100 * q^26 + 499 * q^28 + 654 * q^29 - 1401 * q^30 - 2163 * q^32 - 342 * q^33 - 5959 * q^34 - 3317 * q^36 - 3666 * q^37 + 4444 * q^38 + 23023 * q^40 - 1266 * q^41 + 23419 * q^42 + 7066 * q^44 + 5464 * q^45 - 8019 * q^46 - 14166 * q^48 + 14620 * q^49 - 25358 * q^50 - 36264 * q^52 - 9138 * q^53 - 6990 * q^54 - 7592 * q^56 - 3862 * q^57 + 31769 * q^58 + 34819 * q^60 + 7534 * q^61 - 9320 * q^62 + 4562 * q^64 + 9106 * q^65 + 6490 * q^66 - 4842 * q^68 - 22 * q^69 - 4258 * q^70 - 27815 * q^72 - 18 * q^73 - 202 * q^74 + 73926 * q^76 - 56086 * q^77 - 328 * q^78 - 47488 * q^80 + 9788 * q^81 - 42110 * q^82 - 111651 * q^84 + 117026 * q^85 - 55391 * q^86 - 44639 * q^88 + 44574 * q^89 - 4626 * q^90 + 18106 * q^92 - 85004 * q^93 + 55547 * q^94 + 150069 * q^96 - 34146 * q^97 + 52545 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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