LMFDB - Embedded newform 92.5.g.a.3.46

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			3.46
Character	$\chi$	$=$	92.3
Dual form			92.5.g.a.31.46

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.99912 + 0.0841052i) q^{2} +(14.9199 + 6.81367i) q^{3} +(15.9859 + 0.672693i) q^{4} +(-23.3579 + 26.9564i) q^{5} +(59.0932 + 28.5035i) q^{6} +(-36.5671 - 56.8995i) q^{7} +(63.8727 + 4.03467i) q^{8} +(123.132 + 142.102i) q^{9} +(-95.6780 + 105.837i) q^{10} +(118.167 + 16.9898i) q^{11} +(233.923 + 118.959i) q^{12} +(-111.441 - 71.6187i) q^{13} +(-141.451 - 230.623i) q^{14} +(-532.168 + 243.033i) q^{15} +(255.095 + 21.5071i) q^{16} +(-103.456 - 30.3775i) q^{17} +(480.469 + 578.639i) q^{18} +(-165.102 - 562.287i) q^{19} +(-391.529 + 415.209i) 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} +(-439.641 - 295.784i) q^{26} +(494.577 + 1684.38i) q^{27} +(-546.281 - 934.186i) q^{28} +(-389.800 - 114.456i) q^{29} +(-2148.64 + 927.159i) q^{30} +(-695.172 + 317.475i) q^{31} +(1018.35 + 107.464i) q^{32} +(1647.27 + 1058.64i) q^{33} +(-411.179 - 130.185i) q^{34} +(2387.94 + 343.334i) q^{35} +(1872.78 + 2354.46i) q^{36} +(-428.581 - 494.609i) q^{37} +(-612.973 - 2262.54i) q^{38} +(-1174.70 - 1827.86i) q^{39} +(-1600.69 + 1627.54i) q^{40} +(1626.13 - 1876.65i) q^{41} +(-539.031 - 4404.66i) q^{42} +(781.930 + 357.096i) q^{43} +(1877.57 + 351.087i) q^{44} -6706.68 q^{45} +(1888.36 + 954.748i) q^{46} -1212.35i q^{47} +(3659.44 + 2059.02i) q^{48} +(-902.993 + 1977.28i) q^{49} +(-314.483 - 2569.78i) q^{50} +(-1336.57 - 1158.15i) q^{51} +(-1733.30 - 1219.85i) q^{52} +(-1630.66 + 1047.96i) q^{53} +(1836.21 + 6777.61i) q^{54} +(-3218.11 + 2788.51i) q^{55} +(-2106.07 - 3781.86i) q^{56} +(1367.94 - 9514.20i) q^{57} +(-1549.23 - 490.506i) q^{58} +(-2524.27 + 3927.84i) q^{59} +(-8670.65 + 3527.11i) q^{60} +(272.561 + 596.825i) q^{61} +(-2806.78 + 1211.15i) q^{62} +(3582.96 - 12202.4i) q^{63} +(4063.44 + 515.410i) q^{64} +(4533.60 - 1331.19i) q^{65} +(6498.58 + 4372.15i) 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} +(7291.46 + 9573.25i) q^{72} +(-3633.75 + 1066.97i) q^{73} +(-1672.35 - 2014.05i) q^{74} +(2990.89 - 10186.0i) q^{75} +(-2261.06 - 9099.71i) q^{76} +(-3354.31 - 7344.91i) q^{77} +(-4544.01 - 7408.63i) q^{78} +(-2827.99 + 4400.44i) q^{79} +(-6538.23 + 6374.09i) q^{80} +(-1930.26 + 13425.3i) q^{81} +(6660.91 - 7368.18i) q^{82} +(-6894.93 + 5974.49i) q^{83} +(-1785.19 - 17660.1i) q^{84} +(3235.39 - 2079.26i) q^{85} +(3097.00 + 1493.83i) q^{86} +(-5035.90 - 4363.63i) q^{87} +(7479.08 + 1561.95i) q^{88} +(-1248.18 + 2733.14i) q^{89} +(-26820.8 - 564.066i) q^{90} +8959.82i q^{91} +(7471.48 + 3976.97i) q^{92} -12535.0 q^{93} +(101.965 - 4848.35i) q^{94} +(19013.7 + 8683.26i) q^{95} +(14461.3 + 8542.02i) q^{96} +(5762.14 - 6649.87i) q^{97} +(-3777.47 + 7831.42i) 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 $

$2$	3.99912	+	0.0841052i	0.999779	+	0.0210263i
$2$	3.99912	+	0.0841052i	0.999779	+	0.0210263i
$3$	14.9199	+	6.81367i	1.65776	+	0.757074i	0.999993	+	0.00385504i	$0.00122710\pi$
$3$	14.9199	+	6.81367i	1.65776	+	0.757074i	0.657769	+	0.753219i	$0.271500\pi$
$4$	15.9859	+	0.672693i	0.999116	+	0.0420433i
$5$	−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	$0.974441\pi$
$6$	59.0932	+	28.5035i	1.64148	+	0.791764i
$7$	−36.5671	−	56.8995i	−0.746268	−	1.16122i	−0.981905	−	0.189374i	$-0.939354\pi$
$7$	−36.5671	−	56.8995i	−0.746268	−	1.16122i	0.235637	−	0.971841i	$-0.424282\pi$
$8$	63.8727	+	4.03467i	0.998011	+	0.0630417i
$9$	123.132	+	142.102i	1.52015	+	1.75435i
$10$	−95.6780	+	105.837i	−0.956780	+	1.05837i
$11$	118.167	+	16.9898i	0.976585	+	0.140412i	0.612085	−	0.790792i	$-0.290331\pi$
$11$	118.167	+	16.9898i	0.976585	+	0.140412i	0.364500	+	0.931203i	$0.381240\pi$
$12$	233.923	+	118.959i	1.62447	+	0.826103i
$13$	−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	$0.810008\pi$
$14$	−141.451	−	230.623i	−0.721687	−	1.17665i
$15$	−532.168	+	243.033i	−2.36519	+	1.08015i
$16$	255.095	+	21.5071i	0.996465	+	0.0840122i
$17$	−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	$0.650639\pi$
$18$	480.469	+	578.639i	1.48293	+	1.78592i
$19$	−165.102	−	562.287i	−0.457348	−	1.55758i	−0.789130	−	0.614227i	$-0.789468\pi$
$19$	−165.102	−	562.287i	−0.457348	−	1.55758i	0.331782	−	0.943356i	$-0.392350\pi$
$20$	−391.529	+	415.209i	−0.978822	+	1.03802i
$21$	−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
$26$	−439.641	−	295.784i	−0.650357	−	0.437551i
$27$	494.577	+	1684.38i	0.678433	+	2.31053i
$28$	−546.281	−	934.186i	−0.696787	−	1.19156i
$29$	−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	$0.668559\pi$
$30$	−2148.64	+	927.159i	−2.38738	+	1.03018i
$31$	−695.172	+	317.475i	−0.723384	+	0.330359i	−0.742855	−	0.669452i	$-0.766529\pi$
$31$	−695.172	+	317.475i	−0.723384	+	0.330359i	0.0194711	+	0.999810i	$0.493802\pi$
$32$	1018.35	+	107.464i	0.994478	+	0.104946i
$33$	1647.27	+	1058.64i	1.51264	+	0.972117i
$34$	−411.179	−	130.185i	−0.355691	−	0.112616i
$35$	2387.94	+	343.334i	1.94934	+	0.280272i
$36$	1872.78	+	2354.46i	1.44505	+	1.81671i
$37$	−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	$0.849556\pi$
$38$	−612.973	−	2262.54i	−0.424496	−	1.56685i
$39$	−1174.70	−	1827.86i	−0.772318	−	1.20175i
$40$	−1600.69	+	1627.54i	−1.00043	+	1.01721i
$41$	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	$-0.0372391\pi$
$42$	−539.031	−	4404.66i	−0.305573	−	2.49698i
$43$	781.930	+	357.096i	0.422894	+	0.193129i	0.615483	−	0.788150i	$-0.288961\pi$
$43$	781.930	+	357.096i	0.422894	+	0.193129i	−0.192589	+	0.981280i	$0.561688\pi$
$44$	1877.57	+	351.087i	0.969818	+	0.181346i
$45$	−6706.68			−3.31194
$46$	1888.36	+	954.748i	0.892421	+	0.451204i
$47$		−	1212.35i		−	0.548825i	−0.961612	−	0.274413i	$-0.911517\pi$
$47$		−	1212.35i		−	0.548825i	0.961612	−	0.274413i	$-0.0884834\pi$
$48$	3659.44	+	2059.02i	1.58830	+	0.893670i
$49$	−902.993	+	1977.28i	−0.376090	+	0.823523i
$50$	−314.483	−	2569.78i	−0.125793	−	1.02791i
$51$	−1336.57	−	1158.15i	−0.513869	−	0.445270i
$52$	−1733.30	−	1219.85i	−0.641013	−	0.451128i
$53$	−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	$0.430312\pi$
$54$	1836.21	+	6777.61i	0.629701	+	2.32428i
$55$	−3218.11	+	2788.51i	−1.06384	+	0.921821i
$56$	−2106.07	−	3781.86i	−0.671578	−	1.20595i
$57$	1367.94	−	9514.20i	0.421033	−	2.92835i
$58$	−1549.23	−	490.506i	−0.460532	−	0.145810i
$59$	−2524.27	+	3927.84i	−0.725156	+	1.12836i	0.261446	+	0.965218i	$0.415801\pi$
$59$	−2524.27	+	3927.84i	−0.725156	+	1.12836i	−0.986602	+	0.163146i	$0.947836\pi$
$60$	−8670.65	+	3527.11i	−2.40851	+	0.979751i
$61$	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	$0.835536\pi$
$62$	−2806.78	+	1211.15i	−0.730171	+	0.315075i
$63$	3582.96	−	12202.4i	0.902736	−	3.07444i
$64$	4063.44	+	515.410i	0.992051	+	0.125833i
$65$	4533.60	−	1331.19i	1.07304	−	0.315074i
$66$	6498.58	+	4372.15i	1.49187	+	1.00371i
$67$	−2628.05	+	377.857i	−0.585443	+	0.0841740i	−0.428671	−	0.903461i	$-0.641018\pi$
$67$	−2628.05	+	377.857i	−0.585443	+	0.0841740i	−0.156772	+	0.987635i	$0.550109\pi$
$68$	−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	−0.249620	−	0.968344i	$-0.580306\pi$
$71$	−1090.45	+	156.783i	−0.216316	+	0.0311015i	0.0333049	+	0.999445i	$0.489397\pi$
$72$	7291.46	+	9573.25i	1.40653	+	1.84669i
$73$	−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	$0.524724\pi$
$74$	−1672.35	−	2014.05i	−0.305396	−	0.367795i
$75$	2990.89	−	10186.0i	0.531714	−	1.81085i
$76$	−2261.06	−	9099.71i	−0.391457	−	1.57543i
$77$	−3354.31	−	7344.91i	−0.565746	−	1.23881i
$78$	−4544.01	−	7408.63i	−0.746879	−	1.21772i
$79$	−2827.99	+	4400.44i	−0.453131	+	0.705085i	−0.990386	−	0.138335i	$-0.955825\pi$
$79$	−2827.99	+	4400.44i	−0.453131	+	0.705085i	0.537255	+	0.843420i	$0.319461\pi$
$80$	−6538.23	+	6374.09i	−1.02160	+	0.995951i
$81$	−1930.26	+	13425.3i	−0.294203	+	2.04622i
$82$	6660.91	−	7368.18i	0.990617	−	1.09580i
$83$	−6894.93	+	5974.49i	−1.00086	+	0.867251i	−0.991156	−	0.132702i	$-0.957635\pi$
$83$	−6894.93	+	5974.49i	−1.00086	+	0.867251i	−0.00970539	+	0.999953i	$0.503089\pi$
$84$	−1785.19	−	17660.1i	−0.253003	−	2.50285i
$85$	3235.39	−	2079.26i	0.447805	−	0.287787i
$86$	3097.00	+	1493.83i	0.418739	+	0.201978i
$87$	−5035.90	−	4363.63i	−0.665332	−	0.576514i
$88$	7479.08	+	1561.95i	0.965791	+	0.201698i
$89$	−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	$0.197104\pi$
$90$	−26820.8	−	564.066i	−3.31121	−	0.0696378i
$91$			8959.82i			1.08197i
$92$	7471.48	+	3976.97i	0.882736	+	0.469869i
$93$	−12535.0			−1.44931
$94$	101.965	−	4848.35i	0.0115398	−	0.548704i
$95$	19013.7	+	8683.26i	2.10678	+	0.962135i
$96$	14461.3	+	8542.02i	1.56916	+	0.926869i
$97$	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	$0.0723965\pi$
$98$	−3777.47	+	7831.42i	−0.393323	+	0.815433i
$99$	12135.9	+	18883.8i	1.23823	+	1.92672i
$100$	−1041.52	−	10303.3i	−0.104152	−	1.03033i
$101$	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	$0.719310\pi$
$102$	−5247.70	−	4743.97i	−0.504393	−	0.455976i
$103$	13292.2	+	1911.14i	1.25292	+	0.180143i	0.736646	−	0.676279i	$-0.236409\pi$
$103$	13292.2	+	1911.14i	1.25292	+	0.180143i	0.516276	+	0.856422i	$0.327318\pi$
$104$	−6829.07	−	5024.11i	−0.631386	−	0.464507i
$105$	33288.3	+	21393.1i	3.01935	+	1.94042i
$106$	−6609.33	+	4053.77i	−0.588228	+	0.360784i
$107$	−1063.17	+	485.535i	−0.0928617	+	0.0424085i	−0.461304	−	0.887242i	$-0.652618\pi$
$107$	−1063.17	+	485.535i	−0.0928617	+	0.0424085i	0.368443	+	0.929650i	$0.379891\pi$
$108$	6773.18	+	27258.9i	0.580691	+	2.33701i
$109$	−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	$0.597514\pi$
$110$	−13104.1	+	10880.9i	−1.08299	+	0.899248i
$111$	−3024.27	−	10299.7i	−0.245456	−	0.835948i
$112$	−8104.34	−	15301.2i	−0.646073	−	1.21981i
$113$	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
$118$	−10425.2	+	15495.6i	−0.748721	+	1.11287i
$119$	2054.63	+	6997.44i	0.145091	+	0.494135i
$120$	−34971.6	+	13376.1i	−2.42858	+	0.928893i
$121$	−373.195	−	109.580i	−0.0254897	−	0.00748446i
$122$	1039.81	+	2409.70i	0.0698606	+	0.161898i
$123$	37048.5	−	16919.5i	2.44884	−	1.11835i
$124$	−11326.5	+	4607.46i	−0.736634	+	0.299653i
$125$	667.293	+	428.843i	0.0427068	+	0.0274460i
$126$	15355.0	−	48497.6i	0.967181	−	3.05478i
$127$	25927.3	+	3727.79i	1.60750	+	0.231123i	0.886809	−	0.462136i	$-0.152917\pi$
$127$	25927.3	+	3727.79i	1.60750	+	0.231123i	0.720688	+	0.693259i	$0.243826\pi$
$128$	16206.8	+	2402.94i	0.989186	+	0.146664i
$129$	9233.16	+	10655.6i	0.554844	+	0.640324i
$130$	18242.4	−	4942.27i	1.07943	−	0.292442i
$131$	−14329.1	−	22296.6i	−0.834982	−	1.29926i	−0.951991	−	0.306127i	$-0.900967\pi$
$131$	−14329.1	−	22296.6i	−0.834982	−	1.29926i	0.117008	−	0.993131i	$-0.462670\pi$
$132$	25620.9	+	18031.3i	1.47044	+	1.03485i
$133$	−25956.6	+	29955.5i	−1.46739	+	1.69345i
$134$	−10541.7	+	1290.06i	−0.587083	+	0.0718457i
$135$	−56957.0	−	26011.4i	−3.12521	−	1.42724i
$136$	−6485.48	−	2357.71i	−0.350642	−	0.127471i
$137$	−864.929			−0.0460828			−0.0230414	−	0.999735i	$-0.507335\pi$
$137$	−864.929			−0.0460828			−0.0230414	+	0.999735i	$0.507335\pi$
$138$	21668.8	+	27111.4i	1.13783	+	1.42362i
$139$			13289.3i			0.687819i	0.939003	+	0.343909i	$0.111751\pi$
$139$			13289.3i			0.687819i	−0.939003	+	0.343909i	$0.888249\pi$
$140$	37942.3	+	7094.83i	1.93583	+	0.361981i
$141$	8260.58	−	18088.2i	0.415501	−	0.909821i
$142$	−4374.01	+	535.279i	−0.216922	+	0.0265463i
$143$	−11951.8	−	10356.3i	−0.584470	−	0.506446i
$144$	28354.2	+	38897.8i	1.36739	+	1.87586i
$145$	12190.2	−	7834.17i	0.579796	−	0.372612i
$146$	−14621.5	+	3961.30i	−0.685942	+	0.185837i
$147$	−26945.0	+	23348.0i	−1.24694	+	1.08048i
$148$	−6518.52	−	8195.05i	−0.297595	−	0.374135i
$149$	−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	$0.696804\pi$
$150$	12817.6	−	40483.6i	0.569672	−	1.79927i
$151$	−1890.49	+	2941.65i	−0.0829124	+	0.129014i	−0.880233	−	0.474542i	$-0.842614\pi$
$151$	−1890.49	+	2941.65i	−0.0829124	+	0.129014i	0.797320	+	0.603556i	$0.206250\pi$
$152$	−8276.90	−	36580.9i	−0.358245	−	1.58332i
$153$	−8422.11	−	18441.8i	−0.359781	−	0.787810i
$154$	−12796.5	−	29655.2i	−0.539573	−	1.25043i
$155$	7679.77	−	26154.9i	0.319657	−	1.08865i
$156$	−17548.9	−	30010.1i	−0.721109	−	1.23316i
$157$	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	$0.217537\pi$
$158$	−11679.6	+	17360.0i	−0.467856	+	0.695402i
$159$	−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	−0.250226	−	0.968187i	$-0.580505\pi$
$163$	−5780.00	+	831.038i	−0.217547	+	0.0312785i	0.0326795	+	0.999466i	$0.489596\pi$
$164$	27257.5	−	28906.0i	1.01344	−	1.07473i
$165$	−67013.7	+	19677.0i	−2.46148	+	0.722755i
$166$	−28076.1	+	23312.8i	−1.01888	+	0.846015i
$167$	−10.6258	+	36.1882i	−0.000381003	+	0.00129758i	−0.959683	−	0.281084i	$-0.909306\pi$
$167$	−10.6258	+	36.1882i	−0.000381003	+	0.00129758i	0.959302	+	0.282381i	$0.0911243\pi$
$168$	−5653.89	−	70774.9i	−0.200322	−	2.50761i
$169$	−4574.84	−	10017.5i	−0.160178	−	0.350741i
$170$	13113.6	−	8043.08i	0.453757	−	0.278307i
$171$	59572.9	−	92697.2i	2.03731	−	3.17011i
$172$	12259.6	+	6234.48i	0.414400	+	0.210738i
$173$	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	$-0.0902253\pi$
$174$	−19772.1	−	17874.2i	−0.653063	−	0.590376i
$175$	−33084.5	+	28667.9i	−1.08031	+	0.936093i
$176$	29778.4	+	6875.45i	0.961336	+	0.221960i
$177$	−64424.7	+	41403.2i	−2.05639	+	1.32156i
$178$	−5221.50	+	10825.2i	−0.164799	+	0.341660i
$179$	25244.5	+	21874.5i	0.787882	+	0.682704i	0.952798	−	0.303604i	$-0.0981900\pi$
$179$	25244.5	+	21874.5i	0.787882	+	0.682704i	−0.164916	+	0.986308i	$0.552735\pi$
$180$	−107212.	−	4511.53i	−3.30901	−	0.139245i
$181$	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	$0.0315206\pi$
$182$	−753.567	+	35831.4i	−0.0227499	+	1.08173i
$183$			10761.7i			0.321350i
$184$	29544.8	+	16532.8i	0.872661	+	0.488326i
$185$	23343.6			0.682064
$186$	−50129.1	−	1054.26i	−1.44898	−	0.0304735i
$187$	−11709.0	−	5347.32i	−0.334840	−	0.152916i
$188$	815.542	−	19380.5i	0.0230744	−	0.548340i
$189$	77755.0	−	89734.0i	2.17673	−	2.51208i
$190$	75307.7	+	36324.5i	2.08608	+	1.00622i
$191$	5851.23	+	9104.69i	0.160391	+	0.249574i	0.912143	−	0.409873i	$-0.134427\pi$
$191$	5851.23	+	9104.69i	0.160391	+	0.249574i	−0.751751	+	0.659447i	$0.770791\pi$
$192$	57114.2	+	35376.8i	1.54932	+	0.959657i
$193$	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	$0.636230\pi$
$194$	23602.8	−	26109.0i	0.627133	−	0.693723i
$195$	76711.0	+	11029.4i	2.01738	+	0.290056i
$196$	−15765.2	+	31001.0i	−0.410381	+	0.806982i
$197$	−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	$0.865615\pi$
$198$	46944.5	+	76539.1i	1.19744	+	1.95233i
$199$	−11029.8	+	5037.16i	−0.278524	+	0.127198i	−0.549780	−	0.835310i	$-0.685288\pi$
$199$	−11029.8	+	5037.16i	−0.278524	+	0.127198i	0.271256	+	0.962507i	$0.412561\pi$
$200$	−3298.61	−	41291.7i	−0.0824652	−	1.03229i
$201$	−41784.8	−	12269.1i	−1.03425	−	0.303683i
$202$	8707.80	+	10487.0i	0.213406	+	0.257009i
$203$	7741.39	+	26364.8i	0.187857	+	0.639782i
$204$	−20587.2	−	19413.1i	−0.494694	−	0.466481i
$205$	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
$210$	131325.	+	88353.2i	2.97788	+	2.00347i
$211$	17760.0	+	60484.8i	0.398912	+	1.35857i	0.877099	+	0.480311i	$0.159476\pi$
$211$	17760.0	+	60484.8i	0.398912	+	1.35857i	−0.478187	+	0.878258i	$0.658706\pi$
$212$	−26772.4	+	15655.6i	−0.595684	+	0.348336i
$213$	−17337.6	−	5090.77i	−0.382146	−	0.112208i
$214$	−4292.59	+	1852.29i	−0.0937328	+	0.0404466i
$215$	−27890.3	+	12737.1i	−0.603359	+	0.275545i
$216$	24794.1	+	109581.i	0.531424	+	2.34870i
$217$	43484.6	+	27945.9i	0.923456	+	0.593469i
$218$	−1880.22	−	595.302i	−0.0395636	−	0.0125263i
$219$	−61485.0	−	8840.21i	−1.28198	−	0.184321i
$220$	−53320.0	+	42411.9i	−1.10165	+	0.876278i
$221$	9353.67	+	10794.7i	0.191513	+	0.221017i
$222$	−11228.1	−	41444.1i	−0.227825	−	0.840924i
$223$	−31039.7	−	48298.7i	−0.624177	−	0.971238i	−0.999025	−	0.0441517i	$-0.985941\pi$
$223$	−31039.7	−	48298.7i	−0.624177	−	0.971238i	0.374848	−	0.927086i	$-0.377695\pi$
$224$	−31123.3	−	61873.0i	−0.620282	−	1.23312i
$225$	79696.0	−	91974.1i	1.57424	−	1.81677i
$226$	6071.80	+	49615.4i	0.118878	+	0.971403i
$227$	34094.3	+	15570.3i	0.661652	+	0.302166i	0.717793	−	0.696257i	$-0.245152\pi$
$227$	34094.3	+	15570.3i	0.661652	+	0.302166i	−0.0561411	+	0.998423i	$0.517880\pi$
$228$	28267.8	−	151172.i	0.543778	−	2.90806i
$229$	2217.79			0.0422911			0.0211455	−	0.999776i	$-0.493269\pi$
$229$	2217.79			0.0422911			0.0211455	+	0.999776i	$0.493269\pi$
$230$	−69844.7	+	28602.6i	−1.32032	+	0.540692i
$231$		−	132440.i		−	2.48196i
$232$	−24435.8	−	8883.30i	−0.453994	−	0.165044i
$233$	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	$0.0624188\pi$
$234$	−12102.5	−	98894.6i	−0.221025	−	1.80610i
$235$	32680.7	+	28318.0i	0.591774	+	0.512775i
$236$	−42994.8	+	61091.7i	−0.771955	+	1.09688i
$237$	−72176.3	+	46384.9i	−1.28498	+	0.825810i
$238$	7628.20	+	28156.4i	0.134669	+	0.497076i
$239$	69490.7	−	60214.1i	1.21655	−	1.05415i	0.219644	−	0.975580i	$-0.429510\pi$
$239$	69490.7	−	60214.1i	1.21655	−	1.05415i	0.996909	−	0.0785691i	$-0.0250351\pi$
$240$	−140980.	+	50551.1i	−2.44758	+	0.877623i
$241$	−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	$0.940488\pi$
$242$	−1483.23	−	469.611i	−0.0253267	−	0.00801876i
$243$	−43398.6	+	67529.5i	−0.734959	+	1.14362i
$244$	3955.64	+	9724.10i	0.0664411	+	0.163331i
$245$	−32208.3	−	70526.4i	−0.536582	−	1.17495i
$246$	149584.	−	64547.0i	2.47181	−	1.06661i
$247$	−21871.1	+	74486.2i	−0.358490	+	1.22091i
$248$	−45683.4	+	17473.2i	−0.742772	+	0.284098i
$249$	−143580.	+	42158.8i	−2.31576	+	0.679970i
$250$	2632.51	+	1771.12i	0.0421202	+	0.0283379i
$251$	−90830.4	+	13059.4i	−1.44173	+	0.207289i	−0.818391	−	0.574662i	$-0.805133\pi$
$251$	−90830.4	+	13059.4i	−1.44173	+	0.207289i	−0.623339	+	0.781952i	$0.714224\pi$
$252$	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
$256$	64610.9	+	10972.7i	0.985884	+	0.167430i
$257$	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	$0.406355\pi$
$258$	36028.3	+	43389.7i	0.541258	+	0.651849i
$259$	−12471.1	+	42472.5i	−0.185910	+	0.633153i
$260$	73369.0	−	18230.4i	1.08534	−	0.269681i
$261$	−31732.6	−	69484.7i	−0.465827	−	1.02002i
$262$	−55428.6	−	90371.7i	−0.807479	−	1.31653i
$263$	31757.8	−	49416.2i	0.459134	−	0.714426i	−0.532080	−	0.846694i	$-0.678589\pi$
$263$	31757.8	−	49416.2i	0.459134	−	0.714426i	0.991214	+	0.132268i	$0.0422258\pi$
$264$	100944.	+	74264.1i	1.44835	+	1.06554i
$265$	9839.44	−	68434.8i	0.140113	−	0.974508i
$266$	−106323.	+	117612.i	−1.50267	+	1.66222i
$267$	−37245.4	+	32273.3i	−0.522457	+	0.452711i
$268$	−42265.9	+	4272.49i	−0.588464	+	0.0594856i
$269$	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	$0.160598\pi$
$270$	−225590.	−	108813.i	−3.09451	−	1.49263i
$271$	−14745.9	−	12777.4i	−0.200785	−	0.173982i	0.548664	−	0.836043i	$-0.315136\pi$
$271$	−14745.9	−	12777.4i	−0.200785	−	0.173982i	−0.749450	+	0.662061i	$0.769682\pi$
$272$	−25737.9	−	9974.21i	−0.347884	−	0.134816i
$273$	−61049.3	+	133679.i	−0.819134	+	1.79365i
$274$	−3458.95	−	72.7450i	−0.0460726	−	0.000968951i
$275$		−	77268.6i		−	1.02173i
$276$	84375.6	+	110244.i	1.10764	+	1.44723i
$277$	−125721.			−1.63851			−0.819253	−	0.573432i	$-0.805612\pi$
$277$	−125721.			−1.63851			−0.819253	+	0.573432i	$0.805612\pi$
$278$	−1117.70	+	53145.6i	−0.0144623	+	0.687667i
$279$	−130712.	−	59694.2i	−1.67922	−	0.766873i
$280$	151139.	+	31564.2i	1.92779	+	0.402604i
$281$	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	$-0.00775917\pi$
$282$	34556.3	−	71641.9i	0.434540	−	0.900884i
$283$	−25578.4	−	39800.7i	−0.319374	−	0.496956i	0.644033	−	0.764998i	$-0.277260\pi$
$283$	−25578.4	−	39800.7i	−0.319374	−	0.496956i	−0.963407	+	0.268042i	$0.913624\pi$
$284$	−17537.2	+	1772.77i	−0.217432	+	0.0219794i
$285$	224517.	+	259106.i	2.76413	+	3.18998i
$286$	−46925.7	−	42421.3i	−0.573692	−	0.518623i
$287$	−166243.	−	23902.2i	−2.01828	−	0.290184i
$288$	110120.	+	157942.i	1.32765	+	1.90419i
$289$	−60481.9	−	38869.4i	−0.724152	−	0.465384i
$290$	49409.0	−	30304.5i	0.587503	−	0.360339i
$291$	131280.	−	59953.7i	1.55029	−	0.707995i
$292$	−58806.4	+	14612.0i	−0.689697	+	0.171373i
$293$	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	$0.202689\pi$
$294$	−109720.	+	91105.2i	−1.26938	+	1.05402i
$295$	−46918.9	−	159791.i	−0.539143	−	1.83615i
$296$	−25379.1	−	33321.2i	−0.289662	−	0.380310i
$297$	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
$302$	−7807.68	+	11605.0i	−0.0856068	+	0.127242i
$303$	15747.2	+	53629.9i	0.171521	+	0.584147i
$304$	−30023.6	−	146988.i	−0.324875	−	1.59050i
$305$	−22454.7	−	6593.29i	−0.241383	−	0.0708766i
$306$	−32129.9	−	74459.4i	−0.343136	−	0.795201i
$307$	154574.	−	70591.7i	1.64006	−	0.748992i	0.640247	−	0.768169i	$-0.278832\pi$
$307$	154574.	−	70591.7i	1.64006	−	0.748992i	0.999816	+	0.0191769i	$0.00610457\pi$
$308$	−48680.6	−	119671.i	−0.513162	−	1.26150i
$309$	185297.	+	119083.i	1.94066	+	1.24719i
$310$	32912.0	−	103951.i	0.342477	−	1.08169i
$311$	107519.	+	15458.9i	1.11164	+	0.159830i	0.673580	−	0.739114i	$-0.264756\pi$
$311$	107519.	+	15458.9i	1.11164	+	0.159830i	0.438063	+	0.898944i	$0.355665\pi$
$312$	−67656.1	−	121490.i	−0.695021	−	1.24805i
$313$	−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	$-0.511860\pi$
$314$	107749.	−	29191.6i	1.09283	−	0.296073i
$315$	245244.	+	381607.i	2.47159	+	3.84587i
$316$	−48167.9	+	68442.4i	−0.482374	+	0.685411i
$317$	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	$0.0121190\pi$
$318$	−126231.	+	15447.8i	−1.24828	+	0.152761i
$319$	−44116.9	−	20147.5i	−0.433534	−	0.197988i
$320$	−108807.	+	97497.0i	−1.06257	+	0.952119i
$321$	−19170.7			−0.186049
$322$	−14727.2	−	142359.i	−0.142039	−	1.37301i
$323$			63187.6i			0.605657i
$324$	−39888.0	+	213316.i	−0.379972	+	2.03205i
$325$	−35617.5	+	77991.6i	−0.337208	+	0.738382i
$326$	−23184.8	+	2837.29i	−0.218156	+	0.0266974i
$327$	−6111.82	−	5295.92i	−0.0571577	−	0.0495274i
$328$	111437.	−	113306.i	1.03581	−	1.05319i
$329$	−68982.4	+	44332.3i	−0.637304	+	0.409570i
$330$	−269651.	+	73054.4i	−2.47613	+	0.670839i
$331$	83749.9	−	72569.7i	0.764413	−	0.662368i	−0.182736	−	0.983162i	$-0.558495\pi$
$331$	83749.9	−	72569.7i	0.764413	−	0.662368i	0.947149	+	0.320794i	$0.103950\pi$
$332$	−114240.	+	90869.2i	−1.03644	+	0.824405i
$333$	17512.9	−	121805.i	0.157932	−	1.09844i
$334$	−45.5374	+	143.827i	−0.000408202	+	0.00128928i
$335$	51200.1	−	79668.8i	0.456227	−	0.709903i
$336$	−16658.0	−	283513.i	−0.147552	−	2.51127i
$337$	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	$0.668641\pi$
$338$	−17452.8	−	40445.9i	−0.152768	−	0.354031i
$339$	−57745.8	+	196664.i	−0.502482	+	1.71130i
$340$	53119.2	−	31062.3i	0.459508	−	0.268705i
$341$	−87540.1	+	25704.1i	−0.752833	+	0.221052i
$342$	246035.	−	365696.i	2.10351	−	3.12657i
$343$	−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	−0.998675	−	0.0514674i	$-0.983610\pi$
$347$	−233882.	+	33627.1i	−1.94240	+	0.279274i	−0.943721	+	0.330742i	$0.892701\pi$
$348$	−77567.8	−	73144.0i	−0.640505	−	0.603977i
$349$	−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	$0.506996\pi$
$350$	−134720.	+	111863.i	−1.09975	+	0.913171i
$351$	65516.7	−	223129.i	0.531787	−	1.81110i
$352$	118509.	+	30000.2i	0.956457	+	0.242125i
$353$	−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	$-0.467926\pi$
$354$	−261124.	+	160158.i	−2.08372	+	1.27803i
$355$	21244.2	−	33056.6i	0.168571	−	0.262302i
$356$	−21791.8	+	42851.9i	−0.171947	+	0.338119i
$357$	−17023.4	+	118400.i	−0.133570	+	0.929002i
$358$	99116.0	+	89601.9i	0.773353	+	0.699119i
$359$	10782.8	−	9343.36i	0.0836649	−	0.0724961i	−0.612024	−	0.790839i	$-0.709645\pi$
$359$	10782.8	−	9343.36i	0.0836649	−	0.0724961i	0.695689	+	0.718343i	$0.255099\pi$
$360$	−428373.	−	27059.2i	−3.30535	−	0.208790i
$361$	−179275.	+	115213.i	−1.37564	+	0.884073i
$362$	36829.4	−	76354.4i	0.281046	−	0.582662i
$363$	−4821.38	−	4177.75i	−0.0365896	−	0.0317051i
$364$	−6027.21	+	143230.i	−0.0454897	+	1.08102i
$365$	56115.1	−	122875.i	0.421206	−	0.922312i
$366$	−905.113	+	43037.2i	−0.00675679	+	0.321279i
$367$			158610.i			1.17760i	0.808279	+	0.588800i	$0.200399\pi$
$367$			158610.i			1.17760i	−0.808279	+	0.588800i	$0.799601\pi$
$368$	116763.	+	68601.3i	0.862201	+	0.506567i
$369$	466905.			3.42907
$370$	93353.9	+	1963.32i	0.681913	+	0.0143413i
$371$	119257.	+	54462.8i	0.866435	+	0.395688i
$372$	−200383.	−	8432.23i	−1.44802	−	0.0609335i
$373$	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	$0.214615\pi$
$374$	−46375.9	−	22369.3i	−0.331550	−	0.159923i
$375$	7033.92	+	10945.0i	0.0500190	+	0.0778311i
$376$	4891.45	−	77436.4i	0.0345989	−	0.547733i
$377$	35242.5	+	40672.0i	0.247961	+	0.286163i
$378$	318498.	−	352317.i	2.22907	−	2.46576i
$379$	−5229.96	−	751.955i	−0.0364099	−	0.00523496i	0.124086	−	0.992271i	$-0.460400\pi$
$379$	−5229.96	−	751.955i	−0.0364099	−	0.00523496i	−0.160496	+	0.987037i	$0.551309\pi$
$380$	298109.	+	151600.i	2.06447	+	1.04986i
$381$	361432.	+	232278.i	2.48987	+	1.60014i
$382$	22634.0	+	36902.8i	0.155108	+	0.252891i
$383$	−2741.97	+	1252.22i	−0.0186924	+	0.00853654i	−0.424739	−	0.905316i	$-0.639634\pi$
$383$	−2741.97	+	1252.22i	−0.0186924	+	0.00853654i	0.406047	+	0.913852i	$0.366907\pi$
$384$	225431.	+	146280.i	1.52880	+	0.992022i
$385$	276342.	+	81141.3i	1.86434	+	0.547420i
$386$	79153.0	+	95325.7i	0.531242	+	0.639787i
$387$	45536.8	+	155084.i	0.304047	+	1.03549i
$388$	96586.1	−	102428.i	0.641580	−	0.680383i
$389$	−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
$394$	−140613.	−	94602.2i	−0.905801	−	0.609409i
$395$	−52564.2	−	179017.i	−0.336896	−	1.14736i
$396$	181299.	+	310037.i	1.15613	+	1.97707i
$397$	−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	$0.701543\pi$
$398$	−44533.3	+	19216.5i	−0.281137	+	0.121313i
$399$	−591375.	+	270072.i	−3.71464	+	1.69642i
$400$	−9718.66	−	165408.i	−0.0607416	−	1.03380i
$401$	−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	$0.746237\pi$
$402$	−166070.	−	52579.9i	−1.02764	−	0.325363i
$403$	100208.	+	14407.7i	0.617008	+	0.0887124i
$404$	33941.5	+	42671.1i	0.207955	+	0.261440i
$405$	−316810.	−	365619.i	−1.93148	−	2.22904i
$406$	28741.3	+	106087.i	0.174363	+	0.643590i
$407$	−42240.8	−	65727.9i	−0.255002	−	0.396790i
$408$	−80697.7	−	79366.6i	−0.484776	−	0.476779i
$409$	−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	$0.401023\pi$
$410$	43035.1	+	351659.i	0.256009	+	2.09197i
$411$	−12904.6	−	5893.34i	−0.0763944	−	0.0348881i
$412$	211202.	+	39492.7i	1.24424	+	0.232661i
$413$	315797.			1.85143
$414$	96846.5	+	385901.i	0.565045	+	2.25152i
$415$		−	325414.i		−	1.88947i
$416$	−105789.	−	84908.5i	−0.611298	−	0.490642i
$417$	−90549.2	+	198275.i	−0.520730	+	1.14024i
$418$	−33992.9	−	277771.i	−0.194552	−	1.58977i
$419$	90641.8	+	78541.6i	0.516298	+	0.447375i	0.873622	−	0.486606i	$-0.161765\pi$
$419$	90641.8	+	78541.6i	0.516298	+	0.447375i	−0.357324	+	0.933981i	$0.616311\pi$
$420$	517751.	+	364380.i	2.93510	+	2.06565i
$421$	−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	$0.909832\pi$
$422$	65937.0	+	243380.i	0.370258	+	1.36666i
$423$	172278.	−	149280.i	0.962831	−	0.834297i
$424$	−108383.	+	60356.9i	−0.602877	+	0.335734i
$425$	−9931.85	+	69077.5i	−0.0549860	+	0.382436i
$426$	−68906.8	−	21816.8i	−0.379702	−	0.120218i
$427$	23992.3	−	37332.7i	0.131588	−	0.204755i
$428$	−17322.3	+	7046.50i	−0.0945626	+	0.0384668i
$429$	−107755.	−	235950.i	−0.585494	−	1.28205i
$430$	−112608.	+	48591.2i	−0.609019	+	0.262797i
$431$	30876.9	−	105157.i	0.166219	−	0.566089i	−0.833685	−	0.552240i	$-0.813773\pi$
$431$	30876.9	−	105157.i	0.166219	−	0.566089i	0.999904	−	0.0138491i	$-0.00440844\pi$
$432$	89938.1	+	440313.i	0.481922	+	2.35936i
$433$	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	$0.243311\pi$
$434$	171550.	+	115416.i	0.910773	+	0.612755i
$435$	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	−0.560228	−	0.828339i	$-0.689286\pi$
$439$	−166587.	+	23951.5i	−0.864393	+	0.124281i	−0.304165	+	0.952619i	$0.598377\pi$
$440$	−216800.	+	165126.i	−1.11983	+	0.852921i
$441$	−392163.	+	115150.i	−2.01646	+	0.592086i
$442$	36498.5	+	43956.0i	0.186823	+	0.224995i
$443$	−66366.3	+	226023.i	−0.338174	+	1.15171i	0.598386	+	0.801208i	$0.295809\pi$
$443$	−66366.3	+	226023.i	−0.338174	+	1.15171i	−0.936560	+	0.350507i	$0.886009\pi$
$444$	−41417.0	−	166684.i	−0.210093	−	0.845528i
$445$	−44520.7	−	97486.8i	−0.224824	−	0.492295i
$446$	−120069.	−	195763.i	−0.603617	−	0.984147i
$447$	−350065.	+	544711.i	−1.75200	+	2.72616i
$448$	−119262.	−	250055.i	−0.594217	−	1.24589i
$449$	−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	$0.921115\pi$
$450$	326449.	−	361112.i	1.61209	−	1.78327i
$451$	224038.	−	194130.i	1.10146	−	0.954422i
$452$	20108.9	+	198928.i	0.0984264	+	0.973688i
$453$	−48249.2	+	31007.9i	−0.235122	+	0.151104i
$454$	135037.	+	65135.0i	0.655152	+	0.316012i
$455$	−241525.	−	209282.i	−1.16665	−	1.01090i
$456$	125760.	−	602179.i	0.604803	−	2.89598i
$457$	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	$-0.0554961\pi$
$458$	8869.19	+	186.527i	0.0422817	+	0.000889225i
$459$		−	189284.i		−	0.898437i
$460$	−281723.	+	108511.i	−1.33139	+	0.512811i
$461$	−226910.			−1.06771			−0.533853	−	0.845577i	$-0.679256\pi$
$461$	−226910.			−1.06771			−0.533853	+	0.845577i	$0.679256\pi$
$462$	11138.9	−	529643.i	0.0521865	−	2.48142i
$463$	229087.	+	104621.i	1.06866	+	0.488040i	0.870519	−	0.492134i	$-0.163783\pi$
$463$	229087.	+	104621.i	1.06866	+	0.488040i	0.198139	+	0.980174i	$0.436510\pi$
$464$	−96974.4	−	37580.5i	−0.450424	−	0.174553i
$465$	292792.	−	337900.i	1.35411	−	1.56272i
$466$	43439.6	−	90058.5i	0.200039	−	0.414718i
$467$	113312.	+	176317.i	0.519569	+	0.808465i	0.997554	−	0.0699030i	$-0.0222690\pi$
$467$	113312.	+	176317.i	0.519569	+	0.808465i	−0.477985	+	0.878368i	$0.658633\pi$
$468$	−40081.6	−	396509.i	−0.183001	−	1.81034i
$469$	117600.	+	135718.i	0.534641	+	0.617009i
$470$	128312.	+	115996.i	0.580862	+	0.525105i
$471$	453095.	+	65145.2i	2.04243	+	0.293657i
$472$	−177079.	+	240697.i	−0.794847	+	1.08040i
$473$	86331.2	+	55481.7i	0.385874	+	0.247986i
$474$	−292543.	+	179428.i	−1.30206	+	0.798608i
$475$	−345022.	+	157566.i	−1.52918	+	0.698354i
$476$	28137.9	+	113242.i	0.124188	+	0.499798i
$477$	−349704.	−	102682.i	−1.53697	−	0.451294i
$478$	282966.	−	234958.i	1.23845	−	1.02834i
$479$	41958.5	+	142898.i	0.182873	+	0.622808i	0.998991	+	0.0449219i	$0.0143039\pi$
$479$	41958.5	+	142898.i	0.182873	+	0.622808i	−0.816118	+	0.577886i	$0.803878\pi$
$480$	−568048.	+	190303.i	−2.46549	+	0.825966i
$481$	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
$486$	−179236.	+	266408.i	−0.758842	+	1.12791i
$487$	80671.5	+	274742.i	0.340144	+	1.15842i	0.935017	+	0.354603i	$0.115384\pi$
$487$	80671.5	+	274742.i	0.340144	+	1.15842i	−0.594873	+	0.803819i	$0.702798\pi$
$488$	15001.2	+	39220.5i	0.0629921	+	0.164692i
$489$	−91899.2	−	26984.0i	−0.384321	−	0.112847i
$490$	−122873.	−	284752.i	−0.511759	−	1.18597i
$491$	375837.	−	171639.i	1.55896	−	0.711955i	0.565357	−	0.824847i	$-0.308739\pi$
$491$	375837.	−	171639.i	1.55896	−	0.711955i	0.993607	+	0.112892i	$0.0360113\pi$
$492$	603633.	−	245550.i	2.49369	−	1.01440i
$493$	36850.4	+	23682.3i	0.151617	+	0.0974385i
$494$	−93729.8	+	296039.i	−0.384082	+	1.21310i
$495$	−792507.	−	113945.i	−3.23439	−	0.465035i
$496$	−184163.	+	66035.0i	−0.748581	+	0.268418i
$497$	48795.4	+	56312.8i	0.197545	+	0.227979i
$498$	−577737.	+	156522.i	−2.32955	+	0.631127i
$499$	44227.1	+	68818.8i	0.177618	+	0.276379i	0.918635	−	0.395107i	$-0.129292\pi$
$499$	44227.1	+	68818.8i	0.177618	+	0.276379i	−0.741017	+	0.671486i	$0.765656\pi$
$500$	10378.8	+	7304.31i	0.0415151	+	0.0292172i
$501$	−405.110	+	467.521i	−0.00161398	+	0.00186263i
$502$	−364340.	+	44586.9i	−1.44577	+	0.176929i
$503$	200566.	+	91595.4i	0.792722	+	0.362024i	0.770265	−	0.637724i	$-0.220124\pi$
$503$	200566.	+	91595.4i	0.792722	+	0.362024i	0.0224572	+	0.999748i	$0.492851\pi$
$504$	278086.	−	764947.i	1.09476	−	3.01141i
$505$	−121549.			−0.476615
$506$	206921.	+	144903.i	0.808170	+	0.565946i
$507$		−	180631.i		−	0.702711i
$508$	411963.	+	77033.0i	1.59636	+	0.298503i
$509$	−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	$0.235664\pi$
$510$	250456.	−	30650.1i	0.962921	−	0.117840i
$511$	193586.	+	167743.i	0.741364	+	0.642396i
$512$	257464.	+	49315.3i	0.982145	+	0.188123i
$513$	865448.	−	556189.i	3.28856	−	2.11343i
$514$	4382.81	−	1187.40i	0.0165892	−	0.00449440i
$515$	−361996.	+	313671.i	−1.36486	+	1.18266i
$516$	140432.	+	176550.i	0.527432	+	0.663085i
$517$	20597.7	−	143260.i	0.0770615	−	0.535974i
$518$	−53445.4	+	168804.i	−0.199182	+	0.629104i
$519$	219464.	−	341493.i	0.814758	−	1.26779i
$520$	294944.	−	66734.9i	1.09077	−	0.246801i
$521$	−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	$-0.398005\pi$
$522$	−121058.	−	280546.i	−0.444277	−	1.02959i
$523$	103431.	−	352255.i	0.378137	−	1.28782i	−0.522275	−	0.852777i	$-0.674916\pi$
$523$	103431.	−	352255.i	0.378137	−	1.28782i	0.900412	−	0.435039i	$-0.143265\pi$
$524$	−214065.	−	366069.i	−0.779619	−	1.33321i
$525$	−688949.	+	202294.i	−2.49959	+	0.733945i
$526$	131159.	−	194950.i	0.474054	−	0.704615i
$527$	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
$532$	−435089.	+	461403.i	−1.53729	+	1.63026i
$533$	−315620.	+	92674.5i	−1.11099	+	0.326217i
$534$	−151663.	+	125932.i	−0.531860	+	0.441626i
$535$	11745.2	−	40000.4i	0.0410348	−	0.139752i
$536$	−169385.	+	13531.4i	−0.589585	+	0.0470992i
$537$	227599.	+	498372.i	0.789263	+	1.72825i
$538$	234439.	−	143791.i	0.809963	−	0.496783i
$539$	−140297.	+	218307.i	−0.482916	+	0.751433i
$540$	−893009.	−	454129.i	−3.06244	−	1.55737i
$541$	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	$-0.155445\pi$
$542$	−57895.9	−	52338.4i	−0.197083	−	0.178165i
$543$	262707.	−	227637.i	0.890990	−	0.772047i
$544$	−102090.	−	42052.7i	−0.344973	−	0.142101i
$545$	14794.6	−	9507.94i	0.0498094	−	0.0320106i
$546$	−255386.	+	529464.i	−0.856667	+	1.77603i
$547$	−149051.	−	129154.i	−0.498151	−	0.431651i	0.369198	−	0.929351i	$-0.379633\pi$
$547$	−149051.	−	129154.i	−0.498151	−	0.431651i	−0.867349	+	0.497700i	$0.834178\pi$
$548$	−13826.6	−	581.831i	−0.0460421	−	0.00193747i
$549$	−51249.1	+	112220.i	−0.170036	+	0.372328i
$550$	6498.69	−	309006.i	0.0214833	−	1.02151i
$551$			238077.i			0.784176i
$552$	328156.	+	447975.i	1.07697	+	1.47020i
$553$	353794.			1.15691
$554$	−502773.	−	10573.8i	−1.63814	−	0.0344517i
$555$	348284.	+	159056.i	1.13070	+	0.516373i
$556$	−8939.64	+	212442.i	−0.0289182	+	0.687211i
$557$	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	$0.125506\pi$
$558$	−517712.	−	249718.i	−1.66272	−	0.802012i
$559$	−61564.3	−	95795.9i	−0.197018	−	0.306565i
$560$	601767.	+	138940.i	1.91890	+	0.443050i
$561$	−138262.	−	159563.i	−0.439315	−	0.506997i
$562$	285129.	−	315405.i	0.902753	−	0.998609i
$563$	−258414.	−	37154.3i	−0.815265	−	0.117217i	−0.277946	−	0.960597i	$-0.589654\pi$
$563$	−258414.	−	37154.3i	−0.815265	−	0.117217i	−0.537319	+	0.843379i	$0.680563\pi$
$564$	144220.	−	283598.i	0.453386	−	0.891548i
$565$	−374969.	−	240978.i	−1.17462	−	0.754884i
$566$	−98943.4	−	161319.i	−0.308854	−	0.503561i
$567$	834476.	−	381092.i	2.59566	−	1.18540i
$568$	−70282.3	+	5614.53i	−0.217846	+	0.0174027i
$569$	−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	$0.780689\pi$
$570$	876076.	+	1.05508e6i	2.69645	+	3.24739i
$571$	21596.5	+	73550.8i	0.0662385	+	0.225587i	0.985959	−	0.166985i	$-0.0534033\pi$
$571$	21596.5	+	73550.8i	0.0662385	+	0.225587i	−0.919721	+	0.392573i	$0.871585\pi$
$572$	−184093.	−	173594.i	−0.562660	−	0.530571i
$573$	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	$0.970207\pi$
$578$	−238605.	−	160530.i	−0.714207	−	0.480508i
$579$	143140.	+	487490.i	0.426976	+	1.45415i
$580$	200141.	−	117036.i	0.594949	−	0.347906i
$581$	592074.	+	173849.i	1.75398	+	0.515014i
$582$	530048.	−	228721.i	1.56484	−	0.675242i
$583$	−210494.	+	96129.6i	−0.619303	+	0.282826i
$584$	−236402.	+	53489.0i	−0.693148	+	0.156833i
$585$	747398.	+	480323.i	2.18394	+	1.40353i
$586$	614799.	+	194653.i	1.79035	+	0.566848i
$587$	40356.1	+	5802.33i	0.117120	+	0.0168394i	0.200626	−	0.979668i	$-0.435702\pi$
$587$	40356.1	+	5802.33i	0.117120	+	0.0168394i	−0.0835053	+	0.996507i	$0.526612\pi$
$588$	−446445.	+	355112.i	−1.29126	+	1.02710i
$589$	293287.	+	338471.i	0.845399	+	0.975642i
$590$	−174195.	−	642969.i	−0.500416	−	1.84708i
$591$	−375709.	−	584615.i	−1.07566	−	1.67377i
$592$	−98691.3	−	135390.i	−0.281602	−	0.386316i
$593$	−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	$0.370560\pi$
$594$	101828.	+	832086.i	0.288600	+	2.35828i
$595$	−236618.	−	108060.i	−0.668365	−	0.305232i
$596$	−116096.	+	620865.i	−0.326831	+	1.74785i
$597$	−198885.			−0.558025
$598$	−142063.	−	241640.i	−0.397263	−	0.675719i
$599$			587616.i			1.63772i	0.573993	+	0.818860i	$0.305394\pi$
$599$			587616.i			1.63772i	−0.573993	+	0.818860i	$0.694606\pi$
$600$	232133.	−	638542.i	0.644815	−	1.77373i
$601$	−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	$0.888582\pi$
$602$	−28249.9	−	230843.i	−0.0779515	−	0.636976i
$603$	−377293.	−	326926.i	−1.03763	−	0.899114i
$604$	−32199.9	+	45753.1i	−0.0882633	+	0.125414i
$605$	11670.9	−	7500.45i	0.0318856	−	0.0204916i
$606$	58464.2	+	215797.i	0.159201	+	0.587624i
$607$	33415.2	−	28954.4i	0.0906914	−	0.0785846i	−0.608335	−	0.793680i	$-0.708162\pi$
$607$	33415.2	−	28954.4i	0.0906914	−	0.0785846i	0.699027	+	0.715096i	$0.253617\pi$
$608$	−107706.	−	590345.i	−0.291361	−	1.59698i
$609$	−64140.3	+	446106.i	−0.172940	+	1.20283i
$610$	−89244.4	−	28255.9i	−0.239840	−	0.0759363i
$611$	−86827.2	+	135106.i	−0.232581	+	0.361903i
$612$	−122229.	−	300474.i	−0.326341	−	0.802240i
$613$	−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	$-0.420236\pi$
$614$	624098.	−	269304.i	1.65545	−	0.714342i
$615$	−409285.	+	1.39390e6i	−1.08212	+	3.68537i
$616$	−184614.	−	482672.i	−0.486524	−	1.27201i
$617$	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	$0.0210986\pi$
$618$	731007.	+	491811.i	1.91401	+	1.28772i
$619$	143116.	−	20576.9i	0.373513	−	0.0537030i	0.0469976	−	0.998895i	$-0.485035\pi$
$619$	143116.	−	20576.9i	0.373513	−	0.0537030i	0.326515	+	0.945192i	$0.394126\pi$
$620$	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
$624$	−260347.	−	491543.i	−0.668626	−	1.26239i
$625$	360991.	−	105997.i	0.924138	−	0.271351i
$626$	−390340.	−	470095.i	−0.996080	−	1.19960i
$627$	323289.	−	1.10102e6i	0.822349	−	2.80066i
$628$	433355.	−	107678.i	1.09882	−	0.273029i
$629$	29314.5	+	64189.7i	0.0740936	+	0.162242i
$630$	948663.	+	1.54672e6i	2.39018	+	3.89699i
$631$	206584.	−	321451.i	0.518845	−	0.807339i	−0.478655	−	0.878003i	$-0.658876\pi$
$631$	206584.	−	321451.i	0.518845	−	0.807339i	0.997500	+	0.0706643i	$0.0225119\pi$
$632$	−198386.	+	269658.i	−0.496679	+	0.675116i
$633$	−147148.	+	1.02344e6i	−0.367237	+	2.55419i
$634$	337277.	−	373090.i	0.839089	−	0.928186i
$635$	−706095.	+	611835.i	−1.75112	+	1.51735i
$636$	−506113.	+	51161.0i	−1.25122	+	0.126481i
$637$	242240.	−	155678.i	0.596991	−	0.383663i
$638$	−174734.	−	84282.6i	−0.429275	−	0.207060i
$639$	−156548.	−	135650.i	−0.383395	−	0.332214i
$640$	−443332.	+	380750.i	−1.08235	+	0.929567i
$641$	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	$0.00767485\pi$
$642$	−76665.7	−	1612.35i	−0.186008	−	0.00391192i
$643$		−	74128.0i		−	0.179292i	−0.995974	−	0.0896458i	$-0.971426\pi$
$643$		−	74128.0i		−	0.179292i	0.995974	−	0.0896458i	$-0.0285735\pi$
$644$	−46922.7	−	570550.i	−0.113139	−	1.37569i
$645$	−502905.			−1.20883
$646$	−5314.41	+	252695.i	−0.0127347	+	0.605524i
$647$	−16356.2	−	7469.62i	−0.0390727	−	0.0178439i	0.395783	−	0.918344i	$-0.370473\pi$
$647$	−16356.2	−	7469.62i	−0.0390727	−	0.0178439i	−0.434856	+	0.900500i	$0.643201\pi$
$648$	−177458.	+	849721.i	−0.422615	+	2.02361i
$649$	−365018.	+	421253.i	−0.866612	+	1.00012i
$650$	−148998.	+	308902.i	−0.352658	+	0.731128i
$651$	458370.	+	713238.i	1.08157	+	1.68295i
$652$	−92957.3	+	9396.70i	−0.218669	+	0.0221045i
$653$	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	$0.570319\pi$
$654$	−23996.4	−	21693.0i	−0.0561037	−	0.0507183i
$655$	935734.	+	134538.i	2.18107	+	0.313591i
$656$	455179.	−	443751.i	1.05773	−	1.03117i
$657$	−599051.	−	384986.i	−1.38782	−	0.891897i
$658$	−279597.	+	171488.i	−0.645775	+	0.396080i
$659$	513478.	−	234498.i	1.18236	−	0.539967i	0.275463	−	0.961312i	$-0.411169\pi$
$659$	513478.	−	234498.i	1.18236	−	0.539967i	0.906901	+	0.421344i	$0.138442\pi$
$660$	−1.08451e6	+	269474.i	−2.48969	+	0.618627i
$661$	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	$0.374896\pi$
$662$	341029.	−	283171.i	0.778171	−	0.646149i
$663$	66003.8	+	224788.i	0.150156	+	0.511383i
$664$	−464503.	+	353788.i	−1.05354	+	0.802430i
$665$	−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
$670$	211455.	−	314299.i	0.471053	−	0.700153i
$671$	22067.7	+	75155.6i	0.0490131	+	0.166923i
$672$	−42772.4	−	1.13520e6i	−0.0947164	−	2.51382i
$673$	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	$0.477406\pi$
$674$	206978.	+	479661.i	0.455622	+	1.05588i
$675$	1.03354e6	−	472002.i	2.26840	−	1.03594i
$676$	−66394.0	−	163216.i	−0.145290	−	0.357165i
$677$	−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	$0.818047\pi$
$678$	−247472.	+	781625.i	−0.538353	+	1.70035i
$679$	−589079.	−	84696.8i	−1.27772	−	0.183708i
$680$	215042.	−	119754.i	0.465057	−	0.258984i
$681$	402590.	+	464614.i	0.868099	+	1.00184i
$682$	−352245.	+	95431.1i	−0.757314	+	0.205173i
$683$	321199.	+	499796.i	0.688546	+	1.07140i	0.992913	+	0.118844i	$0.0379189\pi$
$683$	321199.	+	499796.i	0.688546	+	1.07140i	−0.304366	+	0.952555i	$0.598445\pi$
$684$	1.01468e6	−	1.44177e6i	2.16879	−	3.08165i
$685$	20202.9	−	23315.4i	0.0430559	−	0.0496891i
$686$	−61036.6	+	7469.50i	−0.129701	+	0.0158724i
$687$	33089.1	+	15111.3i	0.0701085	+	0.0320175i
$688$	191786.	+	107910.i	0.405173	+	0.227975i
$689$	256776.			0.540898
$690$	−1.23696e6	−	49152.3i	−2.59811	−	0.103239i
$691$			594067.i			1.24417i	0.782950	+	0.622084i	$0.213714\pi$
$691$			594067.i			1.24417i	−0.782950	+	0.622084i	$0.786286\pi$
$692$	72783.3	−	389236.i	0.151992	−	0.812832i
$693$	630704.	−	1.38105e6i	1.31329	−	2.87570i
$694$	−938149.	+	114808.i	−1.94784	+	0.238371i
$695$	−358233.	−	310411.i	−0.741645	−	0.642639i
$696$	−304051.	−	299035.i	−0.627664	−	0.617311i
$697$	−225241.	+	144754.i	−0.463642	+	0.297965i
$698$	−284739.	+	77142.2i	−0.584435	+	0.158337i
$699$	309858.	−	268494.i	0.634175	−	0.549516i
$700$	−548168.	+	436024.i	−1.11871	+	0.889846i
$701$	−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	$0.937823\pi$
$702$	280775.	−	886810.i	0.569750	−	1.79952i
$703$	−207353.	+	322647.i	−0.419565	+	0.652856i
$704$	471407.	+	129942.i	0.951154	+	0.262182i
$705$	294642.	+	645177.i	0.592812	+	1.29808i
$706$	−340940.	−	790109.i	−0.684019	−	1.58518i
$707$	64936.0	−	221152.i	0.129911	−	0.442437i
$708$	−1.05774e6	+	618528.i	−2.11014	+	1.23394i
$709$	−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	$0.634603\pi$
$710$	87738.3	−	130411.i	0.174049	−	0.258700i
$711$	−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
$716$	388840.	+	366664.i	0.758482	+	0.715225i
$717$	1.44707e6	−	424898.i	2.81482	−	0.826507i
$718$	43907.6	−	36458.3i	0.0851707	−	0.0707209i
$719$	157257.	−	535568.i	0.304195	−	1.03599i	−0.655557	−	0.755145i	$-0.727566\pi$
$719$	157257.	−	535568.i	0.304195	−	1.03599i	0.959752	−	0.280848i	$-0.0906156\pi$
$720$	−1.71084e6	−	144241.i	−3.30023	−	0.278243i
$721$	−377316.	−	826208.i	−0.725830	−	1.58935i
$722$	−726633.	+	445673.i	−1.39393	+	0.854953i
$723$	−333560.	+	519030.i	−0.638113	+	0.992924i
$724$	153707.	−	302252.i	0.293235	−	0.576624i
$725$	−37420.9	+	260268.i	−0.0711932	+	0.495160i
$726$	−18929.9	−	17112.8i	−0.0359149	−	0.0324674i
$727$	−336112.	+	291242.i	−0.635938	+	0.551043i	−0.912048	−	0.410083i	$-0.865500\pi$
$727$	−336112.	+	291242.i	−0.635938	+	0.551043i	0.276111	+	0.961126i	$0.410954\pi$
$728$	−36149.9	+	572288.i	−0.0682094	+	1.07982i
$729$	−183398.	+	117863.i	−0.345096	+	0.221780i
$730$	234745.	−	486672.i	0.440505	−	0.913251i
$731$	−70048.0	−	60697.0i	−0.131087	−	0.113588i
$732$	−7239.30	+	172035.i	−0.0135106	+	0.321066i
$733$	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	$0.00961292\pi$
$734$	−13339.9	+	634298.i	−0.0247605	+	1.17734i
$735$		−	1.27170e6i		−	2.35402i
$736$	461178.	+	284165.i	0.851359	+	0.524583i
$737$	−316968.			−0.583554
$738$	1.86721e6	+	39269.2i	3.42831	+	0.0721006i
$739$	−170470.	−	77850.9i	−0.312146	−	0.142553i	0.253181	−	0.967419i	$-0.418523\pi$
$739$	−170470.	−	77850.9i	−0.312146	−	0.142553i	−0.565328	+	0.824866i	$0.691250\pi$
$740$	373168.	+	15703.1i	0.681461	+	0.0286762i
$741$	−833838.	+	962301.i	−1.51861	+	1.75257i
$742$	472342.	+	227833.i	0.857923	+	0.413818i
$743$	−99515.2	−	154849.i	−0.180265	−	0.280498i	0.739348	−	0.673324i	$-0.235134\pi$
$743$	−99515.2	−	154849.i	−0.180265	−	0.280498i	−0.919613	+	0.392826i	$0.871498\pi$
$744$	−800647.	−	50574.7i	−1.44642	−	0.0913666i
$745$	−922091.	−	1.06415e6i	−1.66135	−	1.91730i
$746$	29674.3	−	32825.2i	0.0533215	−	0.0589833i
$747$	−1.69798e6	−	244132.i	−3.04292	−	0.437506i
$748$	−183581.	−	93358.1i	−0.328114	−	0.166859i
$749$	66503.9	+	42739.5i	0.118545	+	0.0761843i
$750$	27208.9	+	44361.9i	0.0483714	+	0.0788656i
$751$	−83303.6	+	38043.5i	−0.147701	+	0.0674528i	−0.487894	−	0.872903i	$-0.662235\pi$
$751$	−83303.6	+	38043.5i	−0.147701	+	0.0674528i	0.340193	+	0.940356i	$0.389508\pi$
$752$	26074.3	−	309266.i	0.0461080	−	0.546885i
$753$	−1.44416e6	−	424044.i	−2.54698	−	0.747860i
$754$	137518.	+	165616.i	0.241890	+	0.291313i
$755$	−35138.7	−	119671.i	−0.0616442	−	0.209941i
$756$	1.30334e6	−	1.38217e6i	2.28042	−	2.41834i
$757$	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	$-0.0937065\pi$
$762$	1.42587e6	+	959306.i	2.45568	+	1.65214i
$763$	9395.34	+	31997.6i	0.0161385	+	0.0549627i
$764$	87412.2	+	149482.i	0.149756	+	0.256096i
$765$	693849.	+	203732.i	1.18561	+	0.348126i
$766$	−11070.8	+	4777.14i	−0.0188678	+	0.00814162i
$767$	562613.	−	256937.i	0.956355	−	0.436752i
$768$	889221.	+	603949.i	1.50760	+	1.02395i
$769$	−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	$0.749897\pi$
$770$	1.09830e6	+	347735.i	1.85242	+	0.586499i
$771$	18430.2	+	2649.86i	0.0310042	+	0.00445773i
$772$	308524.	+	387876.i	0.517672	+	0.650816i
$773$	−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	$0.848796\pi$
$774$	169064.	+	624029.i	0.282207	+	1.04165i
$775$	267424.	+	416119.i	0.445242	+	0.692811i
$776$	394874.	−	401497.i	0.655745	−	0.666743i
$777$	−475460.	+	548710.i	−0.787539	+	0.908868i
$778$	−24893.5	−	203416.i	−0.0411270	−	0.336067i
$779$	−1.32370e6	−	604512.i	−2.18129	−	0.996161i
$780$	1.21887e6	+	227917.i	2.00340	+	0.374617i
$781$	−131518.			−0.215618
$782$	−166360.	−	156139.i	−0.272042	−	0.255327i
$783$		−	713177.i		−	1.16325i
$784$	−272874.	+	484973.i	−0.443947	+	0.789015i
$785$	−413523.	+	905489.i	−0.671059	+	1.46941i
$786$	−211224.	−	1.72601e6i	−0.341899	−	2.79381i
$787$	170821.	+	148017.i	0.275798	+	0.238981i	0.781766	−	0.623572i	$-0.214319\pi$
$787$	170821.	+	148017.i	0.275798	+	0.238981i	−0.505968	+	0.862552i	$0.668865\pi$
$788$	−554371.	−	390152.i	−0.892787	−	0.628320i
$789$	810528.	−	520895.i	1.30201	−	0.836750i
$790$	−195154.	−	720332.i	−0.312697	−	1.15419i
$791$	638769.	−	553497.i	1.02092	−	0.884631i
$792$	698960.	+	1.25512e6i	1.11430	+	2.00095i
$793$	12369.4	−	86031.1i	0.0196699	−	0.136807i
$794$	−409436.	−	129632.i	−0.649448	−	0.205624i
$795$	613096.	−	953995.i	0.970049	−	1.50943i
$796$	−179710.	+	73103.6i	−0.283626	+	0.115375i
$797$	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	$0.570350\pi$
$798$	−2.38769e6	+	1.03031e6i	−3.74949	+	1.61794i
$799$	−36828.3	+	125426.i	−0.0576884	+	0.196469i
$800$	−24954.4	−	662302.i	−0.0389913	−	1.03485i
$801$	−542077.	+	159168.i	−0.844881	+	0.248080i
$802$	−214533.	−	144335.i	−0.333538	−	0.224400i
$803$	−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
$808$	132147.	+	173501.i	0.202411	+	0.265754i
$809$	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	$0.352043\pi$
$810$	−1.23621e6	−	1.48880e6i	−1.88418	−	2.26916i
$811$	−143624.	+	489139.i	−0.218367	+	0.743688i	0.775327	+	0.631560i	$0.217585\pi$
$811$	−143624.	+	489139.i	−0.218367	+	0.743688i	−0.993694	+	0.112128i	$0.964233\pi$
$812$	106017.	+	426671.i	0.160792	+	0.647114i
$813$	−132946.	−	291110.i	−0.201137	−	0.440430i
$814$	−163398.	−	266406.i	−0.246602	−	0.402064i
$815$	112607.	−	175219.i	0.169531	−	0.263795i
$816$	−316044.	−	324183.i	−0.474644	−	0.486867i
$817$	71691.7	−	498627.i	0.107405	−	0.747019i
$818$	−465902.	+	515373.i	−0.696287	+	0.770221i
$819$	−1.27321e6	+	1.10324e6i	−1.89816	+	1.64476i
$820$	142526.	+	1.40995e6i	0.211966	+	2.09689i
$821$	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	$-0.0106692\pi$
$822$	−51111.4	−	24653.5i	−0.0756439	−	0.0364867i
$823$	−304737.	−	264056.i	−0.449910	−	0.389849i	0.400223	−	0.916418i	$-0.368933\pi$
$823$	−304737.	−	264056.i	−0.449910	−	0.389849i	−0.850133	+	0.526569i	$0.823478\pi$
$824$	841301.	+	175699.i	1.23907	+	0.258771i
$825$	526483.	−	1.15284e6i	0.773528	−	1.69379i
$826$	1.26291e6	+	26560.2i	1.85102	+	0.0389288i
$827$		−	67482.4i		−	0.0986687i	−0.998782	−	0.0493344i	$-0.984290\pi$
$827$		−	67482.4i		−	0.0986687i	0.998782	−	0.0493344i	$-0.0157100\pi$
$828$	354844.	+	1.55141e6i	0.517579	+	2.26290i
$829$	91076.9			0.132525			0.0662627	−	0.997802i	$-0.478892\pi$
$829$	91076.9			0.132525			0.0662627	+	0.997802i	$0.478892\pi$
$830$	27369.0	−	1.30137e6i	0.0397286	−	1.88905i
$831$	−1.87574e6	−	856621.i	−2.71625	−	1.24047i
$832$	−415921.	−	348456.i	−0.600847	−	0.503386i
$833$	153485.	−	177131.i	0.221196	−	0.255273i
$834$	−378793.	+	785310.i	−0.544590	+	1.12904i
$835$	−727.307	−	1131.71i	−0.00104315	−	0.00162317i
$836$	−112580.	−	1.11370e6i	−0.161082	−	1.59351i
$837$	−878563.	−	1.01392e6i	−1.25407	−	1.44727i
$838$	355881.	+	321720.i	0.506777	+	0.458132i
$839$	800193.	+	115050.i	1.13677	+	0.163442i	0.684895	−	0.728641i	$-0.259848\pi$
$839$	800193.	+	115050.i	1.13677	+	0.163442i	0.451870	+	0.892084i	$0.350757\pi$
$840$	2.03990e6	+	1.50074e6i	2.89102	+	2.12690i
$841$	−456159.	−	293155.i	−0.644947	−	0.414482i
$842$	−1.15894e6	+	710822.i	−1.63469	+	1.00262i
$843$	1.58591e6	−	724260.i	2.23163	−	1.01915i
$844$	243220.	+	978849.i	0.341440	+	1.37414i
$845$	376895.	+	110666.i	0.527845	+	0.154989i
$846$	701516.	−	582499.i	0.980160	−	0.813868i
$847$	7411.62	+	25241.7i	0.0103311	+	0.0351845i
$848$	−438511.	+	232259.i	−0.609802	+	0.322983i
$849$	−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	$0.563776\pi$
$854$	99087.8	−	147280.i	0.135864	−	0.201943i
$855$	1.10729e6	+	3.77108e6i	1.51471	+	5.15862i
$856$	−69866.7	+	26722.9i	−0.0953505	+	0.0364700i
$857$	−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	$0.642304\pi$
$858$	−411080.	−	952656.i	−0.558408	−	1.29408i
$859$	−1.14678e6	+	523717.i	−1.55415	+	0.709759i	−0.993018	−	0.117965i	$-0.962363\pi$
$859$	−1.14678e6	+	523717.i	−1.55415	+	0.709759i	−0.561137	+	0.827723i	$0.689636\pi$
$860$	−454418.	+	184851.i	−0.614410	+	0.249934i
$861$	−2.31747e6	−	1.48935e6i	−3.12613	−	2.00904i
$862$	132325.	−	417939.i	0.178085	−	0.562469i
$863$	−7861.61	−	1130.33i	−0.0105558	−	0.00151769i	0.137035	−	0.990566i	$-0.456243\pi$
$863$	−7861.61	−	1130.33i	−0.0105558	−	0.00151769i	−0.147591	+	0.989049i	$0.547152\pi$
$864$	322640.	+	1.76843e6i	0.432206	+	2.36897i
$865$	578081.	+	667142.i	0.772604	+	0.891632i
$866$	720365.	−	195163.i	0.960542	−	0.260233i
$867$	−637538.	−	992029.i	−0.848141	−	1.31973i
$868$	676340.	+	475990.i	0.897688	+	0.631769i
$869$	−408937.	+	471938.i	−0.541523	+	0.624951i
$870$	943660.	−	115483.i	1.24674	−	0.152573i
$871$	319934.	+	146109.i	0.421720	+	0.192593i
$872$	−29656.5	−	10781.2i	−0.0390020	−	0.0141786i
$873$	1.65447e6			2.17085
$874$	225070.	−	1.21943e6i	0.294642	−	1.59638i
$875$		−	53650.2i		−	0.0700738i
$876$	−976944.	−	182679.i	−1.27310	−	0.238056i
$877$	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	$0.126564\pi$
$878$	−668214.	+	81774.2i	−0.866815	+	0.106078i
$879$	1.99846e6	+	1.73167e6i	2.58653	+	2.24124i
$880$	−880896.	+	642122.i	−1.13752	+	0.829187i
$881$	−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	$0.397032\pi$
$882$	−1.57799e6	+	427513.i	−2.02846	+	0.549557i
$883$	−497112.	+	430750.i	−0.637577	+	0.552464i	−0.912538	−	0.408992i	$-0.865881\pi$
$883$	−497112.	+	430750.i	−0.637577	+	0.552464i	0.274961	+	0.961455i	$0.411335\pi$
$884$	142265.	+	178855.i	0.182051	+	0.228874i
$885$	388741.	−	2.70375e6i	0.496333	−	3.45207i
$886$	−284416.	+	898310.i	−0.362315	+	1.14435i
$887$	−767.738	+	1194.62i	−0.000975812	+	0.00151839i	−0.841741	−	0.539881i	$-0.818469\pi$
$887$	−767.738	+	1194.62i	−0.000975812	+	0.00151839i	0.840765	+	0.541400i	$0.182105\pi$
$888$	−151612.	−	670072.i	−0.192269	−	0.849759i
$889$	−735978.	−	1.61157e6i	−0.931240	−	2.03913i
$890$	−169844.	−	393605.i	−0.214423	−	0.496914i
$891$	−456186.	+	1.55363e6i	−0.574628	+	1.95700i
$892$	−463706.	−	792976.i	−0.582791	−	0.996622i
$893$	−681692.	+	200163.i	−0.854840	+	0.251004i
$894$	−1.44576e6	+	2.14892e6i	−1.80893	+	2.68872i
$895$	−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
$900$	1.33588e6	−	1.41667e6i	1.64923	−	1.74898i
$901$	200537.	−	58882.8i	0.247027	−	0.0725336i
$902$	912283.	−	757507.i	1.12129	−	0.931051i
$903$	268671.	−	915008.i	0.329492	−	1.12215i
$904$	63686.9	+	797228.i	0.0779316	+	0.975542i
$905$	314023.	+	687615.i	0.383411	+	0.839554i
$906$	−195562.	+	119946.i	−0.238248	+	0.146127i
$907$	484872.	−	754476.i	0.589404	−	0.917130i	−0.410582	−	0.911824i	$-0.634675\pi$
$907$	484872.	−	754476.i	0.589404	−	0.917130i	0.999986	−	0.00530634i	$-0.00168907\pi$
$908$	534552.	+	271840.i	0.648363	+	0.329717i
$909$	−91188.4	+	634230.i	−0.110360	+	0.767571i
$910$	−948283.	−	857258.i	−1.14513	−	1.03521i
$911$	−577149.	+	500102.i	−0.695426	+	0.602590i	−0.929146	−	0.369714i	$-0.879456\pi$
$911$	−577149.	+	500102.i	−0.695426	+	0.602590i	0.233719	+	0.972304i	$0.424910\pi$
$912$	553577.	−	2.39760e6i	0.665561	−	2.88262i
$913$	−916258.	+	588843.i	−1.09920	+	0.706412i
$914$	411503.	−	853123.i	0.492584	−	1.02122i
$915$	−290096.	−	251370.i	−0.346497	−	0.300242i
$916$	35453.2	+	1491.89i	0.0422537	+	0.00177806i
$917$	−744689.	+	1.63064e6i	−0.885598	+	1.93919i
$918$	15919.7	−	756967.i	0.0188908	−	0.898238i
$919$			333207.i			0.394532i	0.980350	+	0.197266i	$0.0632063\pi$
$919$			333207.i			0.394532i	−0.980350	+	0.197266i	$0.936794\pi$
$920$	−1.13577e6	+	410253.i	−1.34188	+	0.484703i
$921$	2.78722e6			3.28588
$922$	−907439.	−	19084.3i	−1.06747	−	0.0224499i
$923$	132749.	+	60624.4i	0.155822	+	0.0711613i
$924$	89091.5	−	2.11717e6i	0.104350	−	2.47977i
$925$	−277394.	+	320130.i	−0.324201	+	0.374148i
$926$	907347.	+	437657.i	1.05816	+	0.510402i
$927$	1.36513e6	+	2.12418e6i	1.58860	+	2.47191i
$928$	−384651.	−	158445.i	−0.446654	−	0.183985i
$929$	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	$0.672132\pi$
$930$	1.19933e6	−	1.32667e6i	1.38667	−	1.53391i
$931$	1.26088e6	+	181288.i	1.45471	+	0.209156i
$932$	181294.	−	356501.i	0.208714	−	0.410420i
$933$	1.49884e6	+	963245.i	1.72184	+	1.10656i
$934$	438320.	+	714644.i	0.502455	+	0.819211i
$935$	417642.	−	190731.i	0.477728	−	0.218171i
$936$	−126942.	−	1.58906e6i	−0.144896	−	1.81379i
$937$	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	$0.578453\pi$
$938$	458882.	+	552642.i	0.521550	+	0.628114i
$939$	−705890.	−	2.40404e6i	−0.800582	−	2.72653i
$940$	503380.	+	474672.i	0.569692	+	0.537202i
$941$	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
$946$	340582.	+	229139.i	0.380575	+	0.256045i
$947$	−448781.	−	1.52841e6i	−0.500420	−	1.70427i	−0.691220	−	0.722644i	$-0.742926\pi$
$947$	−448781.	−	1.52841e6i	−0.500420	−	1.70427i	0.190800	−	0.981629i	$-0.438892\pi$
$948$	−1.18500e6	+	692950.i	−1.31857	+	0.771054i
$949$	481363.	+	141341.i	0.534491	+	0.156941i
$950$	−1.39303e6	+	601107.i	−1.54353	+	0.666047i
$951$	1.87596e6	−	856722.i	2.07426	−	0.947281i
$952$	103003.	+	455235.i	0.113651	+	0.502299i
$953$	−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	$0.914051\pi$
$954$	−1.38987e6	−	440051.i	−1.52714	−	0.483511i
$955$	−382102.	−	54938.0i	−0.418960	−	0.0602374i
$956$	1.15137e6	−	915827.i	1.25980	−	1.00207i
$957$	−520939.	−	601195.i	−0.568804	−	0.656435i
$958$	155779.	+	574993.i	0.169737	+	0.626515i
$959$	31627.9	+	49214.0i	0.0343901	+	0.0535121i
$960$	−2.28770e6	+	713266.i	−2.48231	+	0.773943i
$961$	−222303.	+	256551.i	−0.240713	+	0.277797i
$962$	42124.5	+	344218.i	0.0455182	+	0.371949i
$963$	−199907.	−	91294.3i	−0.215563	−	0.0984444i
$964$	−110622.	+	591594.i	−0.119039	+	0.636605i
$965$	−1.10487e6			−1.18646
$966$	750262.	−	2.22433e6i	0.804005	−	2.38366i
$967$		−	1.66138e6i		−	1.77671i	−0.459157	−	0.888355i	$-0.651848\pi$
$967$		−	1.66138e6i		−	1.77671i	0.459157	−	0.888355i	$-0.348152\pi$
$968$	−23394.9	−	8504.89i	−0.0249672	−	0.00907649i
$969$	−430540.	+	942750.i	−0.458528	+	1.00404i
$970$	152494.	+	1.24610e6i	0.162072	+	1.32437i
$971$	47289.9	+	40977.0i	0.0501569	+	0.0434612i	0.679579	−	0.733603i	$-0.262163\pi$
$971$	47289.9	+	40977.0i	0.0501569	+	0.0434612i	−0.629422	+	0.777064i	$0.716708\pi$
$972$	−739190.	+	1.05032e6i	−0.782390	+	1.11171i
$973$	756158.	−	485953.i	0.798706	−	0.513297i
$974$	299507.	+	1.10551e6i	0.315711	+	1.16532i
$975$	−1.06282e6	+	920937.i	−1.11802	+	0.968770i
$976$	56692.9	+	158109.i	0.0595153	+	0.165980i
$977$	−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	$0.902501\pi$
$978$	−365246.	−	115641.i	−0.381863	−	0.120903i
$979$	−193929.	+	301760.i	−0.202338	+	0.314844i
$980$	−467435.	−	1.14909e6i	−0.486709	−	1.19647i
$981$	−38512.2	−	84330.0i	−0.0400185	−	0.0876283i
$982$	1.51745e6	−	654794.i	1.57359	−	0.679018i
$983$	−48319.4	+	164561.i	−0.0500051	+	0.170302i	−0.980710	−	0.195470i	$-0.937377\pi$
$983$	−48319.4	+	164561.i	−0.0500051	+	0.170302i	0.930705	+	0.365772i	$0.119195\pi$
$984$	2.43465e6	−	931214.i	2.51447	−	0.961744i
$985$	1.45001e6	−	425760.i	1.49451	−	0.438827i
$986$	145377.	+	97807.7i	0.149535	+	0.100605i
$987$	−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	−0.688718	−	0.725029i	$-0.741826\pi$
$991$	−1.12475e6	+	161715.i	−1.14527	+	0.164665i	−0.456556	+	0.889695i	$0.650917\pi$
$992$	−742043.	+	248593.i	−0.754059	+	0.252618i
$993$	1.74400e6	−	512085.i	1.76868	−	0.519330i
$994$	190402.	+	229305.i	0.192708	+	0.232082i
$995$	121850.	−	414982.i	0.123078	−	0.419164i
$996$	−2.32360e6	+	577359.i	−2.34230	+	0.582006i
$997$	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	$0.504240\pi$
$998$	171081.	+	278934.i	0.171768	+	0.280053i
$999$	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.3.46	yes	460
4.3	odd	2	inner	92.5.g.a.3.4	✓	460
23.8	even	11	inner	92.5.g.a.31.4	yes	460
92.31	odd	22	inner	92.5.g.a.31.46	yes	460

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.5.g.a.3.4	✓	460	4.3	odd	2	inner
92.5.g.a.3.46	yes	460	1.1	even	1	trivial
92.5.g.a.31.4	yes	460	23.8	even	11	inner
92.5.g.a.31.46	yes	460	92.31	odd	22	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+(3.99912 + 0.0841052i) q^{2} +(14.9199 + 6.81367i) q^{3} +(15.9859 + 0.672693i) q^{4} +(-23.3579 + 26.9564i) q^{5} +(59.0932 + 28.5035i) q^{6} +(-36.5671 - 56.8995i) q^{7} +(63.8727 + 4.03467i) q^{8} +(123.132 + 142.102i) q^{9} +(-95.6780 + 105.837i) q^{10} +(118.167 + 16.9898i) q^{11} +(233.923 + 118.959i) q^{12} +(-111.441 - 71.6187i) q^{13} +(-141.451 - 230.623i) q^{14} +(-532.168 + 243.033i) q^{15} +(255.095 + 21.5071i) q^{16} +(-103.456 - 30.3775i) q^{17} +(480.469 + 578.639i) q^{18} +(-165.102 - 562.287i) q^{19} +(-391.529 + 415.209i) 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} +(-439.641 - 295.784i) q^{26} +(494.577 + 1684.38i) q^{27} +(-546.281 - 934.186i) q^{28} +(-389.800 - 114.456i) q^{29} +(-2148.64 + 927.159i) q^{30} +(-695.172 + 317.475i) q^{31} +(1018.35 + 107.464i) q^{32} +(1647.27 + 1058.64i) q^{33} +(-411.179 - 130.185i) q^{34} +(2387.94 + 343.334i) q^{35} +(1872.78 + 2354.46i) q^{36} +(-428.581 - 494.609i) q^{37} +(-612.973 - 2262.54i) q^{38} +(-1174.70 - 1827.86i) q^{39} +(-1600.69 + 1627.54i) q^{40} +(1626.13 - 1876.65i) q^{41} +(-539.031 - 4404.66i) q^{42} +(781.930 + 357.096i) q^{43} +(1877.57 + 351.087i) q^{44} -6706.68 q^{45} +(1888.36 + 954.748i) q^{46} -1212.35i q^{47} +(3659.44 + 2059.02i) q^{48} +(-902.993 + 1977.28i) q^{49} +(-314.483 - 2569.78i) q^{50} +(-1336.57 - 1158.15i) q^{51} +(-1733.30 - 1219.85i) q^{52} +(-1630.66 + 1047.96i) q^{53} +(1836.21 + 6777.61i) q^{54} +(-3218.11 + 2788.51i) q^{55} +(-2106.07 - 3781.86i) q^{56} +(1367.94 - 9514.20i) q^{57} +(-1549.23 - 490.506i) q^{58} +(-2524.27 + 3927.84i) q^{59} +(-8670.65 + 3527.11i) q^{60} +(272.561 + 596.825i) q^{61} +(-2806.78 + 1211.15i) q^{62} +(3582.96 - 12202.4i) q^{63} +(4063.44 + 515.410i) q^{64} +(4533.60 - 1331.19i) q^{65} +(6498.58 + 4372.15i) 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} +(7291.46 + 9573.25i) q^{72} +(-3633.75 + 1066.97i) q^{73} +(-1672.35 - 2014.05i) q^{74} +(2990.89 - 10186.0i) q^{75} +(-2261.06 - 9099.71i) q^{76} +(-3354.31 - 7344.91i) q^{77} +(-4544.01 - 7408.63i) q^{78} +(-2827.99 + 4400.44i) q^{79} +(-6538.23 + 6374.09i) q^{80} +(-1930.26 + 13425.3i) q^{81} +(6660.91 - 7368.18i) q^{82} +(-6894.93 + 5974.49i) q^{83} +(-1785.19 - 17660.1i) q^{84} +(3235.39 - 2079.26i) q^{85} +(3097.00 + 1493.83i) q^{86} +(-5035.90 - 4363.63i) q^{87} +(7479.08 + 1561.95i) q^{88} +(-1248.18 + 2733.14i) q^{89} +(-26820.8 - 564.066i) q^{90} +8959.82i q^{91} +(7471.48 + 3976.97i) q^{92} -12535.0 q^{93} +(101.965 - 4848.35i) q^{94} +(19013.7 + 8683.26i) q^{95} +(14461.3 + 8542.02i) q^{96} +(5762.14 - 6649.87i) q^{97} +(-3777.47 + 7831.42i) 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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