LMFDB - Embedded newform 96.6.o.a.11.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [96,6,Mod(11,96)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(96, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 5, 4])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("96.11"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 96 = 2^{5} \cdot 3 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	96.o (of order $8$, degree $4$, 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:	$15.3968467020$
Analytic rank:	$0$
Dimension:	$312$
Relative dimension:	$78$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			11.4
Character	$\chi$	$=$	96.11
Dual form			96.6.o.a.35.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.57531 + 0.957052i) q^{2} +(-15.4283 - 2.22908i) q^{3} +(30.1681 - 10.6717i) q^{4} +(-24.8298 - 10.2848i) q^{5} +(88.1506 - 2.33781i) q^{6} +(36.1711 - 36.1711i) q^{7} +(-157.983 + 88.3705i) q^{8} +(233.062 + 68.7818i) q^{9} +(148.277 + 33.5777i) q^{10} +(144.833 + 59.9918i) q^{11} +(-489.229 + 97.3987i) q^{12} +(248.339 + 599.543i) q^{13} +(-167.047 + 236.282i) q^{14} +(360.154 + 214.025i) q^{15} +(796.229 - 643.891i) q^{16} +107.893 q^{17} +(-1365.22 - 160.427i) q^{18} +(-119.020 + 49.2996i) q^{19} +(-858.824 - 45.2975i) q^{20} +(-638.685 + 477.428i) q^{21} +(-864.903 - 195.860i) q^{22} +(409.317 - 409.317i) q^{23} +(2634.39 - 1011.25i) q^{24} +(-1698.97 - 1698.97i) q^{25} +(-1958.36 - 3104.96i) q^{26} +(-3442.43 - 1580.70i) q^{27} +(705.205 - 1477.22i) q^{28} +(-1846.72 - 4458.38i) q^{29} +(-2212.80 - 848.567i) q^{30} -7053.87i q^{31} +(-3822.98 + 4351.92i) q^{32} +(-2100.79 - 1248.41i) q^{33} +(-601.535 + 103.259i) q^{34} +(-1270.13 + 526.106i) q^{35} +(7765.07 - 412.159i) q^{36} +(-3168.71 + 7649.93i) q^{37} +(616.390 - 388.769i) q^{38} +(-2495.01 - 9803.48i) q^{39} +(4831.56 - 569.391i) q^{40} +(-8471.24 - 8471.24i) q^{41} +(3103.94 - 3273.06i) q^{42} +(832.695 - 2010.30i) q^{43} +(5009.55 + 264.222i) q^{44} +(-5079.48 - 4104.84i) q^{45} +(-1890.33 + 2673.80i) q^{46} -16270.2i q^{47} +(-13719.7 + 8159.25i) q^{48} +14190.3i q^{49} +(11098.3 + 7846.27i) q^{50} +(-1664.60 - 240.502i) q^{51} +(13890.1 + 15436.9i) q^{52} +(-7905.67 + 19086.0i) q^{53} +(20705.4 + 5518.30i) q^{54} +(-2979.16 - 2979.16i) q^{55} +(-2517.96 + 8910.87i) q^{56} +(1946.16 - 495.302i) q^{57} +(14563.0 + 23089.4i) q^{58} +(7866.08 - 18990.4i) q^{59} +(13149.2 + 2613.25i) q^{60} +(-28889.5 + 11966.4i) q^{61} +(6750.92 + 39327.5i) q^{62} +(10918.0 - 5942.21i) q^{63} +(17149.3 - 27922.1i) q^{64} -17440.6i q^{65} +(12907.4 + 4949.72i) q^{66} +(3240.84 + 7824.07i) q^{67} +(3254.92 - 1151.40i) q^{68} +(-7227.45 + 5402.64i) q^{69} +(6577.87 - 4148.79i) q^{70} +(-40156.0 - 40156.0i) q^{71} +(-42898.2 + 9729.49i) q^{72} +(-12265.4 + 12265.4i) q^{73} +(10345.1 - 45683.3i) q^{74} +(22425.0 + 29999.3i) q^{75} +(-3064.49 + 2757.42i) q^{76} +(7408.73 - 3068.80i) q^{77} +(23292.9 + 52269.5i) q^{78} +5660.83 q^{79} +(-26392.5 + 7798.58i) q^{80} +(49587.1 + 32060.9i) q^{81} +(55337.2 + 39122.4i) q^{82} +(-9181.98 - 22167.3i) q^{83} +(-14172.9 + 21219.0i) q^{84} +(-2678.95 - 1109.66i) q^{85} +(-2718.57 + 12005.0i) q^{86} +(18553.6 + 72901.6i) q^{87} +(-28182.7 + 3321.28i) q^{88} +(82586.7 - 82586.7i) q^{89} +(32248.2 + 18024.4i) q^{90} +(30668.8 + 12703.4i) q^{91} +(7980.20 - 16716.4i) q^{92} +(-15723.7 + 108829. i) q^{93} +(15571.4 + 90711.1i) q^{94} +3462.27 q^{95} +(68682.8 - 58620.8i) q^{96} -111433. q^{97} +(-13580.9 - 79115.3i) q^{98} +(29628.8 + 23943.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 312 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9} + 192 q^{10} - 4 q^{12} - 8 q^{13} - 8 q^{15} - 6696 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} + 5576 q^{22} - 11024 q^{24} - 8 q^{25} + 7460 q^{27}+ \cdots + 339516 q^{99}+O(q^{100}) $ 312 * q - 4 * q^3 - 8 * q^4 - 4 * q^6 - 8 * q^7 - 4 * q^9 + 192 * q^10 - 4 * q^12 - 8 * q^13 - 8 * q^15 - 6696 * q^16 - 4 * q^18 - 8 * q^19 - 4 * q^21 + 5576 * q^22 - 11024 * q^24 - 8 * q^25 + 7460 * q^27 - 8 * q^28 + 32564 * q^30 - 8 * q^33 - 264 * q^34 + 3264 * q^36 - 8 * q^37 + 44900 * q^39 - 60136 * q^40 - 7264 * q^42 - 8 * q^43 - 4 * q^45 + 63320 * q^46 + 112368 * q^48 - 976 * q^51 - 55024 * q^52 - 115328 * q^54 - 110056 * q^55 - 4 * q^57 - 123568 * q^58 + 44648 * q^60 - 96168 * q^61 + 187432 * q^64 + 17564 * q^66 + 97848 * q^67 - 4 * q^69 - 143480 * q^70 + 179936 * q^72 - 8 * q^73 + 12496 * q^75 - 234928 * q^76 - 708428 * q^78 + 355344 * q^79 + 251552 * q^82 + 387560 * q^84 - 25008 * q^85 - 282188 * q^87 + 111632 * q^88 + 453536 * q^90 + 200104 * q^91 + 968 * q^93 - 671008 * q^94 - 911336 * q^96 - 16 * q^97 + 339516 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/96\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$65$
$\chi(n)$	$-1$	$e\left(\frac{5}{8}\right)$	$-1$

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 $

$2$	−5.57531	+	0.957052i	−0.985584	+	0.169184i
$2$	−5.57531	+	0.957052i	−0.985584	+	0.169184i
$3$	−15.4283	−	2.22908i	−0.989723	−	0.142996i
$3$	−15.4283	−	2.22908i	−0.989723	−	0.142996i
$4$	30.1681	−	10.6717i	0.942753	−	0.333491i
$5$	−24.8298	−	10.2848i	−0.444168	−	0.183981i	0.149378	−	0.988780i	$-0.452273\pi$
$5$	−24.8298	−	10.2848i	−0.444168	−	0.183981i	−0.593547	+	0.804800i	$0.702273\pi$
$6$	88.1506	−	2.33781i	0.999649	−	0.0265113i
$7$	36.1711	−	36.1711i	0.279008	−	0.279008i	−0.553705	−	0.832713i	$-0.686787\pi$
$7$	36.1711	−	36.1711i	0.279008	−	0.279008i	0.832713	+	0.553705i	$0.186787\pi$
$8$	−157.983	+	88.3705i	−0.872741	+	0.488183i
$9$	233.062	+	68.7818i	0.959104	+	0.283053i
$10$	148.277	+	33.5777i	0.468892	+	0.106182i
$11$	144.833	+	59.9918i	0.360899	+	0.149489i	0.555762	−	0.831341i	$-0.312426\pi$
$11$	144.833	+	59.9918i	0.360899	+	0.149489i	−0.194864	+	0.980830i	$0.562426\pi$
$12$	−489.229	+	97.3987i	−0.980753	+	0.195254i
$13$	248.339	+	599.543i	0.407555	+	0.983925i	0.985779	+	0.168047i	$0.0537460\pi$
$13$	248.339	+	599.543i	0.407555	+	0.983925i	−0.578224	+	0.815878i	$0.696254\pi$
$14$	−167.047	+	236.282i	−0.227782	+	0.322189i
$15$	360.154	+	214.025i	0.413295	+	0.245604i
$16$	796.229	−	643.891i	0.777567	−	0.628800i
$17$	107.893			0.0905460			0.0452730	−	0.998975i	$-0.485584\pi$
$17$	107.893			0.0905460			0.0452730	+	0.998975i	$0.485584\pi$
$18$	−1365.22	−	160.427i	−0.993166	−	0.116707i
$19$	−119.020	+	49.2996i	−0.0756371	+	0.0313299i	−0.420181	−	0.907440i	$-0.638034\pi$
$19$	−119.020	+	49.2996i	−0.0756371	+	0.0313299i	0.344544	+	0.938770i	$0.388034\pi$
$20$	−858.824	−	45.2975i	−0.480097	−	0.0253221i
$21$	−638.685	+	477.428i	−0.316037	+	0.236244i
$22$	−864.903	−	195.860i	−0.380988	−	0.0862758i
$23$	409.317	−	409.317i	0.161339	−	0.161339i	−0.621821	−	0.783160i	$-0.713607\pi$
$23$	409.317	−	409.317i	0.161339	−	0.161339i	0.783160	+	0.621821i	$0.213607\pi$
$24$	2634.39	−	1011.25i	0.933581	−	0.358367i
$25$	−1698.97	−	1698.97i	−0.543670	−	0.543670i
$26$	−1958.36	−	3104.96i	−0.568145	−	0.900789i
$27$	−3442.43	−	1580.70i	−0.908773	−	0.417292i
$28$	705.205	−	1477.22i	0.169989	−	0.356082i
$29$	−1846.72	−	4458.38i	−0.407762	−	0.984425i	−0.985725	−	0.168362i	$-0.946152\pi$
$29$	−1846.72	−	4458.38i	−0.407762	−	0.984425i	0.577963	−	0.816063i	$-0.303848\pi$
$30$	−2212.80	−	848.567i	−0.448890	−	0.172140i
$31$		−	7053.87i		−	1.31833i	−0.751999	−	0.659164i	$-0.770910\pi$
$31$		−	7053.87i		−	1.31833i	0.751999	−	0.659164i	$-0.229090\pi$
$32$	−3822.98	+	4351.92i	−0.659975	+	0.751287i
$33$	−2100.79	−	1248.41i	−0.335814	−	0.199560i
$34$	−601.535	+	103.259i	−0.0892408	+	0.0153190i
$35$	−1270.13	+	526.106i	−0.175258	+	0.0725944i
$36$	7765.07	−	412.159i	0.998594	−	0.0530040i
$37$	−3168.71	+	7649.93i	−0.380520	+	0.918657i	0.611345	+	0.791364i	$0.290629\pi$
$37$	−3168.71	+	7649.93i	−0.380520	+	0.918657i	−0.991865	+	0.127293i	$0.959371\pi$
$38$	616.390	−	388.769i	0.0692463	−	0.0436749i
$39$	−2495.01	−	9803.48i	−0.262670	−	1.03209i
$40$	4831.56	−	569.391i	0.477460	−	0.0562679i
$41$	−8471.24	−	8471.24i	−0.787023	−	0.787023i	0.193982	−	0.981005i	$-0.437860\pi$
$41$	−8471.24	−	8471.24i	−0.787023	−	0.787023i	−0.981005	+	0.193982i	$0.937860\pi$
$42$	3103.94	−	3273.06i	0.271513	−	0.286307i
$43$	832.695	−	2010.30i	0.0686775	−	0.165802i	−0.885814	−	0.464041i	$-0.846399\pi$
$43$	832.695	−	2010.30i	0.0686775	−	0.165802i	0.954491	+	0.298239i	$0.0963991\pi$
$44$	5009.55	+	264.222i	0.390092	+	0.0205749i
$45$	−5079.48	−	4104.84i	−0.373928	−	0.302180i
$46$	−1890.33	+	2673.80i	−0.131717	+	0.186310i
$47$		−	16270.2i		−	1.07435i	−0.843470	−	0.537177i	$-0.819491\pi$
$47$		−	16270.2i		−	1.07435i	0.843470	−	0.537177i	$-0.180509\pi$
$48$	−13719.7	+	8159.25i	−0.859492	+	0.511149i
$49$			14190.3i			0.844309i
$50$	11098.3	+	7846.27i	0.627813	+	0.443852i
$51$	−1664.60	−	240.502i	−0.0896155	−	0.0129477i
$52$	13890.1	+	15436.9i	0.712354	+	0.791683i
$53$	−7905.67	+	19086.0i	−0.386589	+	0.933307i	0.604069	+	0.796932i	$0.293545\pi$
$53$	−7905.67	+	19086.0i	−0.386589	+	0.933307i	−0.990657	+	0.136375i	$0.956455\pi$
$54$	20705.4	+	5518.30i	0.966271	+	0.257526i
$55$	−2979.16	−	2979.16i	−0.132797	−	0.132797i
$56$	−2517.96	+	8910.87i	−0.107295	+	0.379708i
$57$	1946.16	−	495.302i	0.0793399	−	0.0201922i
$58$	14563.0	+	23089.4i	0.568433	+	0.901247i
$59$	7866.08	−	18990.4i	0.294190	−	0.710238i	−0.705808	−	0.708403i	$-0.749416\pi$
$59$	7866.08	−	18990.4i	0.294190	−	0.710238i	0.999998	−	0.00183485i	$-0.000584051\pi$
$60$	13149.2	+	2613.25i	0.471542	+	0.0937137i
$61$	−28889.5	+	11966.4i	−0.994066	+	0.411755i	−0.819618	−	0.572911i	$-0.805814\pi$
$61$	−28889.5	+	11966.4i	−0.994066	+	0.411755i	−0.174448	+	0.984666i	$0.555814\pi$
$62$	6750.92	+	39327.5i	0.223040	+	1.29932i
$63$	10918.0	−	5942.21i	0.346571	−	0.188624i
$64$	17149.3	−	27922.1i	0.523355	−	0.852115i
$65$		−	17440.6i		−	0.512011i
$66$	12907.4	+	4949.72i	0.364735	+	0.139869i
$67$	3240.84	+	7824.07i	0.0882003	+	0.212934i	0.961825	−	0.273667i	$-0.0882365\pi$
$67$	3240.84	+	7824.07i	0.0882003	+	0.212934i	−0.873624	+	0.486601i	$0.838237\pi$
$68$	3254.92	−	1151.40i	0.0853626	−	0.0301963i
$69$	−7227.45	+	5402.64i	−0.182752	+	0.136610i
$70$	6577.87	−	4148.79i	0.160450	−	0.101199i
$71$	−40156.0	−	40156.0i	−0.945377	−	0.945377i	0.0532064	−	0.998584i	$-0.483056\pi$
$71$	−40156.0	−	40156.0i	−0.945377	−	0.945377i	−0.998584	+	0.0532064i	$0.983056\pi$
$72$	−42898.2	+	9729.49i	−0.975232	+	0.221187i
$73$	−12265.4	+	12265.4i	−0.269385	+	0.269385i	−0.828852	−	0.559467i	$-0.811006\pi$
$73$	−12265.4	+	12265.4i	−0.269385	+	0.269385i	0.559467	+	0.828852i	$0.311006\pi$
$74$	10345.1	−	45683.3i	0.219612	−	0.969792i
$75$	22425.0	+	29999.3i	0.460340	+	0.615825i
$76$	−3064.49	+	2757.42i	−0.0608589	+	0.0547607i
$77$	7408.73	−	3068.80i	0.142402	−	0.0589850i
$78$	23292.9	+	52269.5i	0.433497	+	0.972775i
$79$	5660.83			0.102050			0.0510249	−	0.998697i	$-0.483751\pi$
$79$	5660.83			0.102050			0.0510249	+	0.998697i	$0.483751\pi$
$80$	−26392.5	+	7798.58i	−0.461058	+	0.136236i
$81$	49587.1	+	32060.9i	0.839762	+	0.542954i
$82$	55337.2	+	39122.4i	0.908830	+	0.642526i
$83$	−9181.98	−	22167.3i	−0.146299	−	0.353197i	0.833695	−	0.552226i	$-0.186221\pi$
$83$	−9181.98	−	22167.3i	−0.146299	−	0.353197i	−0.979994	+	0.199029i	$0.936221\pi$
$84$	−14172.9	+	21219.0i	−0.219160	+	0.328115i
$85$	−2678.95	−	1109.66i	−0.0402177	−	0.0166587i
$86$	−2718.57	+	12005.0i	−0.0396364	+	0.175031i
$87$	18553.6	+	72901.6i	0.262803	+	1.03262i
$88$	−28182.7	+	3321.28i	−0.387950	+	0.0457192i
$89$	82586.7	−	82586.7i	1.10519	−	1.10519i	0.111411	−	0.993774i	$-0.464463\pi$
$89$	82586.7	−	82586.7i	1.10519	−	1.10519i	0.993774	−	0.111411i	$-0.0355371\pi$
$90$	32248.2	+	18024.4i	0.419661	+	0.234561i
$91$	30668.8	+	12703.4i	0.388234	+	0.160812i
$92$	7980.20	−	16716.4i	0.0982979	−	0.205908i
$93$	−15723.7	+	108829.i	−0.188515	+	1.30478i
$94$	15571.4	+	90711.1i	0.181764	+	1.05887i
$95$	3462.27			0.0393597
$96$	68682.8	−	58620.8i	0.760624	−	0.649193i
$97$	−111433.			−1.20250			−0.601249	−	0.799062i	$-0.705330\pi$
$97$	−111433.			−1.20250			−0.601249	+	0.799062i	$0.705330\pi$
$98$	−13580.9	−	79115.3i	−0.142844	−	0.832138i
$99$	29628.8	+	23943.7i	0.303826	+	0.245529i
$100$	−69385.6	−	33123.8i	−0.693856	−	0.331238i
$101$	−982.146	−	406.818i	−0.00958015	−	0.00396823i	0.377888	−	0.925851i	$-0.376650\pi$
$101$	−982.146	−	406.818i	−0.00958015	−	0.00396823i	−0.387468	+	0.921883i	$0.626650\pi$
$102$	9510.80	−	252.233i	0.0905142	−	0.00240050i
$103$	62435.1	−	62435.1i	0.579877	−	0.579877i	−0.354993	−	0.934869i	$-0.615517\pi$
$103$	62435.1	−	62435.1i	0.579877	−	0.579877i	0.934869	+	0.354993i	$0.115517\pi$
$104$	−92215.3	−	72771.8i	−0.836026	−	0.659751i
$105$	20768.7	−	5285.67i	0.183838	−	0.0467872i
$106$	25810.3	−	113976.i	0.223115	−	0.985258i
$107$	−131630.	−	54523.1i	−1.11147	−	0.460385i	−0.250025	−	0.968239i	$-0.580439\pi$
$107$	−131630.	−	54523.1i	−1.11147	−	0.460385i	−0.861443	+	0.507855i	$0.830439\pi$
$108$	−120720.	−	10950.1i	−0.995911	−	0.0903355i
$109$	−66247.6	−	159936.i	−0.534077	−	1.28938i	−0.928802	−	0.370577i	$-0.879160\pi$
$109$	−66247.6	−	159936.i	−0.534077	−	1.28938i	0.394725	−	0.918799i	$-0.370840\pi$
$110$	19461.0	+	13758.5i	0.153350	+	0.108415i
$111$	65939.9	−	110962.i	0.507974	−	0.854803i
$112$	5510.24	−	52090.7i	0.0415074	−	0.392387i
$113$	−125068.			−0.921405			−0.460702	−	0.887555i	$-0.652402\pi$
$113$	−125068.			−0.921405			−0.460702	+	0.887555i	$0.652402\pi$
$114$	−10376.4	+	4624.04i	−0.0747800	+	0.0333242i
$115$	−14373.0	+	5953.49i	−0.101345	+	0.0419785i
$116$	−103291.	−	114793.i	−0.712716	−	0.792084i
$117$	16640.8	+	156812.i	0.112385	+	1.05905i
$118$	−25681.0	+	113405.i	−0.169788	+	0.749772i
$119$	3902.59	−	3902.59i	0.0252631	−	0.0252631i
$120$	−75811.8	−	1985.24i	−0.480600	−	0.0125852i
$121$	−96502.7	−	96502.7i	−0.599206	−	0.599206i
$122$	149615.	−	94365.1i	0.910073	−	0.574000i
$123$	111813.	+	149580.i	0.666394	+	0.891476i
$124$	−75276.9	−	212802.i	−0.439650	−	1.24286i
$125$	56851.5	+	137252.i	0.325437	+	0.785674i
$126$	−55184.4	+	43578.7i	−0.309663	+	0.244539i
$127$		−	359344.i		−	1.97697i	−0.151306	−	0.988487i	$-0.548348\pi$
$127$		−	359344.i		−	1.97697i	0.151306	−	0.988487i	$-0.451652\pi$
$128$	−68889.8	+	172087.i	−0.371646	+	0.928374i
$129$	−17328.2	+	29159.3i	−0.0916808	+	0.154278i
$130$	16691.6	+	97236.9i	0.0866242	+	0.504630i
$131$	−84401.4	+	34960.2i	−0.429706	+	0.177990i	−0.587044	−	0.809555i	$-0.699709\pi$
$131$	−84401.4	+	34960.2i	−0.429706	+	0.177990i	0.157339	+	0.987545i	$0.449709\pi$
$132$	−76699.7	−	15243.2i	−0.383141	−	0.0761450i
$133$	−2521.85	+	6088.29i	−0.0123621	+	0.0298446i
$134$	−25556.7	−	40520.0i	−0.122954	−	0.194943i
$135$	69217.4	+	74653.1i	0.326875	+	0.352544i
$136$	−17045.2	+	9534.53i	−0.0790233	+	0.0442030i
$137$	167574.	+	167574.i	0.762789	+	0.762789i	0.976826	−	0.214037i	$-0.0686613\pi$
$137$	167574.	+	167574.i	0.762789	+	0.762789i	−0.214037	+	0.976826i	$0.568661\pi$
$138$	35124.6	−	37038.4i	0.157005	−	0.165560i
$139$	106087.	−	256116.i	0.465720	−	1.12435i	−0.500294	−	0.865856i	$-0.666775\pi$
$139$	106087.	−	256116.i	0.465720	−	1.12435i	0.966014	−	0.258491i	$-0.0832253\pi$
$140$	−32703.0	+	29426.1i	−0.141016	+	0.126886i
$141$	−36267.5	+	251020.i	−0.153628	+	1.06331i
$142$	262314.	+	185451.i	1.09169	+	0.771806i
$143$			101732.i			0.416023i
$144$	229859.	−	95300.7i	0.923752	−	0.382992i
$145$			129694.i			0.512271i
$146$	56644.6	−	80121.7i	0.219926	−	0.311077i
$147$	31631.4	−	218932.i	0.120733	−	0.835633i
$148$	−13956.0	+	264599.i	−0.0523727	+	0.992967i
$149$	−90587.6	+	218698.i	−0.334274	+	0.807010i	0.663969	+	0.747760i	$0.268871\pi$
$149$	−90587.6	+	218698.i	−0.334274	+	0.807010i	−0.998243	+	0.0592496i	$0.981129\pi$
$150$	−153737.	−	145793.i	−0.557892	−	0.529066i
$151$	148039.	+	148039.i	0.528365	+	0.528365i	0.920085	−	0.391720i	$-0.128120\pi$
$151$	148039.	+	148039.i	0.528365	+	0.528365i	−0.391720	+	0.920085i	$0.628120\pi$
$152$	14446.5	−	18306.3i	0.0507169	−	0.0642677i
$153$	25145.7	+	7421.05i	0.0868431	+	0.0256293i
$154$	−38368.9	+	24200.0i	−0.130370	+	0.0822269i
$155$	−72547.9	+	175146.i	−0.242547	+	0.585559i
$156$	−179889.	−	269126.i	−0.591826	−	0.885410i
$157$	−88049.4	+	36471.3i	−0.285087	+	0.118087i	−0.520645	−	0.853774i	$-0.674308\pi$
$157$	−88049.4	+	36471.3i	−0.285087	+	0.118087i	0.235558	+	0.971860i	$0.424308\pi$
$158$	−31560.9	+	5417.71i	−0.100579	+	0.0172652i
$159$	164515.	−	276841.i	0.516075	−	0.868435i
$160$	139683.	−	68738.5i	0.431362	−	0.212275i
$161$		−	29610.9i		−	0.0900298i
$162$	−307147.	−	131292.i	−0.919516	−	0.393052i
$163$	11881.5	+	28684.4i	0.0350269	+	0.0845624i	0.940425	−	0.340001i	$-0.110428\pi$
$163$	11881.5	+	28684.4i	0.0350269	+	0.0845624i	−0.905398	+	0.424564i	$0.860428\pi$
$164$	−345964.	−	165159.i	−1.00443	−	0.479503i
$165$	39322.5	+	52604.1i	0.112443	+	0.150421i
$166$	72407.6	+	114802.i	0.203945	+	0.323354i
$167$	343399.	+	343399.i	0.952813	+	0.952813i	0.998936	−	0.0461227i	$-0.0146865\pi$
$167$	343399.	+	343399.i	0.952813	+	0.952813i	−0.0461227	+	0.998936i	$0.514687\pi$
$168$	58710.8	−	131867.i	0.160489	−	0.360464i
$169$	−35236.0	+	35236.0i	−0.0949009	+	0.0949009i
$170$	15998.0	+	3622.79i	0.0424563	+	0.00961436i
$171$	−31129.9	+	3303.49i	−0.0814119	+	0.00863939i
$172$	3667.44	−	69533.3i	0.00945241	−	0.179214i
$173$	312130.	−	129289.i	0.792903	−	0.328431i	0.0507932	−	0.998709i	$-0.483825\pi$
$173$	312130.	−	129289.i	0.792903	−	0.328431i	0.742110	+	0.670278i	$0.233825\pi$
$174$	−173213.	−	388692.i	−0.433717	−	0.973268i
$175$	−122907.			−0.303376
$176$	153948.	−	45489.4i	0.374622	−	0.110695i
$177$	−163691.	+	275454.i	−0.392728	+	0.660871i
$178$	−381407.	+	539486.i	−0.902274	+	1.27623i
$179$	−174737.	−	421853.i	−0.407618	−	0.984077i	−0.985763	−	0.168142i	$-0.946223\pi$
$179$	−174737.	−	421853.i	−0.407618	−	0.984077i	0.578145	−	0.815934i	$-0.303777\pi$
$180$	−197044.	−	69628.6i	−0.453296	−	0.160179i
$181$	455114.	+	188514.i	1.03258	+	0.427709i	0.833643	−	0.552304i	$-0.186251\pi$
$181$	455114.	+	188514.i	1.03258	+	0.427709i	0.198937	+	0.980012i	$0.436251\pi$
$182$	−183146.	−	41473.9i	−0.409844	−	0.0928104i
$183$	472388.	−	120224.i	1.04273	−	0.265377i
$184$	−28493.6	+	100837.i	−0.0620444	+	0.219570i
$185$	157356.	−	157356.i	0.338030	−	0.338030i
$186$	−16490.6	−	621803.i	−0.0349506	−	1.31786i
$187$	15626.4	+	6472.67i	0.0326780	+	0.0135357i
$188$	−173630.	−	490840.i	−0.358287	−	1.01285i
$189$	−181692.	+	67340.7i	−0.369982	+	0.137127i
$190$	−19303.2	+	3313.57i	−0.0387923	+	0.00665905i
$191$	709298.			1.40684			0.703421	−	0.710773i	$-0.251655\pi$
$191$	709298.			1.40684			0.703421	+	0.710773i	$0.251655\pi$
$192$	−326825.	+	392562.i	−0.639826	+	0.768520i
$193$	−786256.			−1.51939			−0.759697	−	0.650277i	$-0.774653\pi$
$193$	−786256.			−1.51939			−0.759697	+	0.650277i	$0.774653\pi$
$194$	621273.	−	106647.i	1.18516	−	0.203444i
$195$	−38876.7	+	269079.i	−0.0732154	+	0.506749i
$196$	151435.	+	428095.i	0.281570	+	0.795975i
$197$	273228.	+	113175.i	0.501603	+	0.207771i	0.619114	−	0.785301i	$-0.287492\pi$
$197$	273228.	+	113175.i	0.501603	+	0.207771i	−0.117512	+	0.993072i	$0.537492\pi$
$198$	−188105.	−	105137.i	−0.340986	−	0.190587i
$199$	−150308.	+	150308.i	−0.269060	+	0.269060i	−0.828721	−	0.559661i	$-0.810931\pi$
$199$	−150308.	+	150308.i	−0.269060	+	0.269060i	0.559661	+	0.828721i	$0.310931\pi$
$200$	418547.	+	118270.i	0.739894	+	0.209073i
$201$	−32560.0	−	127936.i	−0.0568452	−	0.223358i
$202$	5865.11	+	1328.17i	0.0101134	+	0.00229021i
$203$	−228062.	−	94466.6i	−0.388431	−	0.160893i
$204$	−52784.3	+	10508.6i	−0.0888033	+	0.0176795i
$205$	123214.	+	297464.i	0.204774	+	0.494368i
$206$	−288341.	+	407848.i	−0.473411	+	0.669623i
$207$	123550.	−	67242.8i	0.200409	−	0.109074i
$208$	583775.	+	317471.i	0.935593	+	0.508798i
$209$	−20195.6			−0.0319809
$210$	−110733.	+	49345.9i	−0.173272	+	0.0772152i
$211$	−549773.	+	227724.i	−0.850115	+	0.352129i	−0.764834	−	0.644228i	$-0.777179\pi$
$211$	−549773.	+	227724.i	−0.850115	+	0.352129i	−0.0852810	+	0.996357i	$0.527179\pi$
$212$	−34819.0	+	660155.i	−0.0532080	+	1.00880i
$213$	530027.	+	709049.i	0.800477	+	1.07085i
$214$	786061.	+	178006.i	1.17333	+	0.265705i
$215$	−41351.2	+	41351.2i	−0.0610088	+	0.0610088i
$216$	683532.	−	54485.4i	0.996838	−	0.0794594i
$217$	−255146.	−	255146.i	−0.367824	−	0.367824i
$218$	522418.	+	828289.i	0.744520	+	1.18043i
$219$	216574.	−	161893.i	0.305137	−	0.228096i
$220$	−121668.	−	58082.9i	−0.169481	−	0.0809081i
$221$	26793.9	+	64686.3i	0.0369025	+	0.0890905i
$222$	−261439.	+	681754.i	−0.356031	+	0.928422i
$223$		−	493848.i		−	0.665015i	−0.943101	−	0.332507i	$-0.892105\pi$
$223$		−	493848.i		−	0.665015i	0.943101	−	0.332507i	$-0.107895\pi$
$224$	19132.2	+	295695.i	0.0254768	+	0.393753i
$225$	−279108.	−	512824.i	−0.367549	−	0.675324i
$226$	697293.	−	119697.i	0.908122	−	0.155887i
$227$	−1.24826e6	+	517045.i	−1.60783	+	0.665984i	−0.992495	−	0.122283i	$-0.960978\pi$
$227$	−1.24826e6	+	517045.i	−1.60783	+	0.665984i	−0.615333	+	0.788267i	$0.710978\pi$
$228$	53426.3	−	35711.2i	0.0680640	−	0.0454954i
$229$	298309.	−	720182.i	0.375905	−	0.907514i	−0.616820	−	0.787104i	$-0.711579\pi$
$229$	298309.	−	720182.i	0.375905	−	0.907514i	0.992724	−	0.120410i	$-0.0384208\pi$
$230$	74436.1	−	46948.2i	0.0927820	−	0.0585194i
$231$	−121144.	+	30831.5i	−0.149373	+	0.0380159i
$232$	685741.	+	541153.i	0.836450	+	0.660086i
$233$	−660135.	−	660135.i	−0.796605	−	0.796605i	0.185954	−	0.982559i	$-0.440463\pi$
$233$	−660135.	−	660135.i	−0.796605	−	0.796605i	−0.982559	+	0.185954i	$0.940463\pi$
$234$	−242855.	−	858350.i	−0.289939	−	1.02477i
$235$	−167336.	+	403984.i	−0.197660	+	0.477194i
$236$	34644.6	−	656849.i	0.0404908	−	0.767689i
$237$	−87336.8	−	12618.5i	−0.101001	−	0.0145927i
$238$	−18023.2	+	25493.1i	−0.0206248	+	0.0291730i
$239$			604453.i			0.684491i	0.939611	+	0.342245i	$0.111187\pi$
$239$			604453.i			0.684491i	−0.939611	+	0.342245i	$0.888813\pi$
$240$	424574.	−	61487.4i	0.475801	−	0.0689062i
$241$		−	1.53185e6i		−	1.69893i	−0.527647	−	0.849464i	$-0.676926\pi$
$241$		−	1.53185e6i		−	1.69893i	0.527647	−	0.849464i	$-0.323074\pi$
$242$	630390.	+	445674.i	0.691944	+	0.489192i
$243$	−693577.	−	605178.i	−0.753492	−	0.657457i
$244$	−743839.	+	669304.i	−0.799842	+	0.719696i
$245$	145945.	−	352342.i	0.155337	−	0.375016i
$246$	−766550.	−	726941.i	−0.807612	−	0.765881i
$247$	−59114.5	−	59114.5i	−0.0616526	−	0.0616526i
$248$	623354.	+	1.11439e6i	0.643585	+	1.15056i
$249$	92249.3	+	362470.i	0.0942898	+	0.370487i
$250$	−448321.	−	710810.i	−0.453669	−	0.719289i
$251$	−347196.	+	838205.i	−0.347849	+	0.839781i	0.649025	+	0.760767i	$0.275177\pi$
$251$	−347196.	+	838205.i	−0.347849	+	0.839781i	−0.996874	+	0.0790139i	$0.974823\pi$
$252$	265963.	−	295779.i	0.263827	−	0.293404i
$253$	83838.2	−	34726.9i	0.0823456	−	0.0341087i
$254$	343911.	+	2.00345e6i	0.334473	+	1.94847i
$255$	38858.0	+	23091.7i	0.0374223	+	0.0222385i
$256$	219385.	−	1.02537e6i	0.209222	−	0.977868i
$257$		−	1.39024e6i		−	1.31298i	−0.754336	−	0.656489i	$-0.772041\pi$
$257$		−	1.39024e6i		−	1.31298i	0.754336	−	0.656489i	$-0.227959\pi$
$258$	68702.9	−	179156.i	0.0642578	−	0.167565i
$259$	162091.	+	391322.i	0.150144	+	0.362480i
$260$	−186122.	−	526151.i	−0.170751	−	0.482700i
$261$	−123746.	−	1.16610e6i	−0.112442	−	1.05958i
$262$	437105.	−	275690.i	0.393398	−	0.248124i
$263$	404586.	+	404586.i	0.360680	+	0.360680i	0.864063	−	0.503384i	$-0.167912\pi$
$263$	404586.	+	404586.i	0.360680	+	0.360680i	−0.503384	+	0.864063i	$0.667912\pi$
$264$	442213.	+	11580.0i	0.390500	+	0.0102258i
$265$	392592.	−	392592.i	0.343421	−	0.343421i
$266$	8233.30	−	36357.6i	0.00713460	−	0.0315059i
$267$	−1.45826e6	+	1.09008e6i	−1.25187	+	0.935791i
$268$	181266.	+	201452.i	0.154163	+	0.171331i
$269$	−558126.	+	231183.i	−0.470274	+	0.194794i	−0.605219	−	0.796059i	$-0.706914\pi$
$269$	−558126.	+	231183.i	−0.470274	+	0.194794i	0.134945	+	0.990853i	$0.456914\pi$
$270$	−457355.	−	349970.i	−0.381807	−	0.292160i
$271$	−1.16982e6			−0.967604			−0.483802	−	0.875177i	$-0.660745\pi$
$271$	−1.16982e6			−0.967604			−0.483802	+	0.875177i	$0.660745\pi$
$272$	85907.2	−	69471.1i	0.0704057	−	0.0569353i
$273$	−444849.	−	264355.i	−0.361249	−	0.214675i
$274$	−1.09465e6	−	773898.i	−0.880844	−	0.622741i
$275$	−144143.	−	347991.i	−0.114937	−	0.277483i
$276$	−160383.	+	240117.i	−0.126732	+	0.189736i
$277$	495462.	+	205227.i	0.387981	+	0.160707i	0.568143	−	0.822930i	$-0.307662\pi$
$277$	495462.	+	205227.i	0.387981	+	0.160707i	−0.180162	+	0.983637i	$0.557662\pi$
$278$	−346350.	+	1.52946e6i	−0.268784	+	1.18693i
$279$	485178.	−	1.64399e6i	0.373156	−	1.26441i
$280$	154167.	−	195358.i	0.117516	−	0.148914i
$281$	1.86676e6	−	1.86676e6i	1.41033	−	1.41033i	0.652834	−	0.757501i	$-0.273580\pi$
$281$	1.86676e6	−	1.86676e6i	1.41033	−	1.41033i	0.757501	−	0.652834i	$-0.226420\pi$
$282$	−38036.6	−	1.43422e6i	−0.0284825	−	1.07398i
$283$	−2.25391e6	−	933602.i	−1.67290	−	0.692940i	−0.673956	−	0.738772i	$-0.735406\pi$
$283$	−2.25391e6	−	933602.i	−1.67290	−	0.692940i	−0.998949	+	0.0458320i	$0.985406\pi$
$284$	−1.63997e6	−	782898.i	−1.20653	−	0.575983i
$285$	−53416.8	−	7717.69i	−0.0389552	−	0.00562828i
$286$	−97362.7	−	567187.i	−0.0703846	−	0.410025i
$287$	−612828.			−0.439171
$288$	−1.19033e6	+	751317.i	−0.845639	+	0.533755i
$289$	−1.40822e6			−0.991801
$290$	−124124.	−	723083.i	−0.0866682	−	0.504886i
$291$	1.71922e6	+	248393.i	1.19014	+	0.171952i
$292$	−239130.	+	500915.i	−0.164126	+	0.343801i
$293$	−918340.	−	380389.i	−0.624934	−	0.258856i	0.0476648	−	0.998863i	$-0.484822\pi$
$293$	−918340.	−	380389.i	−0.624934	−	0.258856i	−0.672599	+	0.740007i	$0.734822\pi$
$294$	33174.3	+	1.25088e6i	0.0223838	+	0.844013i
$295$	−390626.	+	390626.i	−0.261340	+	0.261340i
$296$	−175427.	−	1.48858e6i	−0.116377	−	0.987513i
$297$	−403748.	−	435454.i	−0.265594	−	0.286452i
$298$	295749.	−	1.30600e6i	0.192922	−	0.851930i
$299$	347052.	+	143754.i	0.224500	+	0.0929911i
$300$	996663.	+	665708.i	0.639360	+	0.427052i
$301$	−42595.4	−	102834.i	−0.0270986	−	0.0654217i
$302$	−967045.	−	683682.i	−0.610139	−	0.431357i
$303$	14246.0	+	8465.78i	0.00891426	+	0.00529737i
$304$	−63023.4	+	115890.i	−0.0391127	+	0.0719217i
$305$	840391.			0.517288
$306$	−147297.	−	17308.9i	−0.0899273	−	0.0105673i
$307$	1.41380e6	−	585616.i	0.856136	−	0.354623i	0.0889407	−	0.996037i	$-0.471652\pi$
$307$	1.41380e6	−	585616.i	0.856136	−	0.354623i	0.767195	+	0.641414i	$0.221652\pi$
$308$	190758.	−	171644.i	0.114579	−	0.103098i
$309$	−1.10244e6	+	824091.i	−0.656837	+	0.490997i
$310$	236853.	−	1.04592e6i	0.139983	−	0.618153i
$311$	190455.	−	190455.i	0.111658	−	0.111658i	−0.649070	−	0.760729i	$-0.724842\pi$
$311$	190455.	−	190455.i	0.111658	−	0.111658i	0.760729	+	0.649070i	$0.224842\pi$
$312$	1.26051e6	+	1.32830e6i	0.733092	+	0.772519i
$313$	2.14025e6	+	2.14025e6i	1.23482	+	1.23482i	0.962091	+	0.272728i	$0.0879260\pi$
$313$	2.14025e6	+	2.14025e6i	1.23482	+	1.23482i	0.272728	+	0.962091i	$0.412074\pi$
$314$	455998.	−	287606.i	0.260999	−	0.164617i
$315$	−332207.	+	35253.6i	−0.188639	+	0.0200183i
$316$	170777.	−	60410.8i	0.0962078	−	0.0340327i
$317$	959251.	+	2.31584e6i	0.536147	+	1.29437i	0.927393	+	0.374088i	$0.122044\pi$
$317$	959251.	+	2.31584e6i	0.536147	+	1.29437i	−0.391246	+	0.920286i	$0.627956\pi$
$318$	−652270.	+	1.70092e6i	−0.361709	+	0.943228i
$319$		−	756509.i		−	0.416234i
$320$	−712987.	+	516921.i	−0.389230	+	0.282195i
$321$	1.90929e6	+	1.13461e6i	1.03421	+	0.614589i
$322$	28339.1	+	165090.i	0.0152316	+	0.0887320i
$323$	−12841.4	+	5319.06i	−0.00684864	+	0.00283680i
$324$	1.83809e6	+	438036.i	0.972759	+	0.231818i
$325$	596685.	−	1.44053e6i	0.313355	−	0.756506i
$326$	−93695.4	−	148553.i	−0.0488286	−	0.0774173i
$327$	665575.	+	2.61520e6i	0.344213	+	1.35250i
$328$	2.08692e6	+	589705.i	1.07108	+	0.302657i
$329$	−588509.	−	588509.i	−0.299753	−	0.299753i
$330$	−269580.	−	255650.i	−0.136271	−	0.129229i
$331$	−626216.	+	1.51182e6i	−0.314163	+	0.758456i	0.685379	+	0.728186i	$0.259636\pi$
$331$	−626216.	+	1.51182e6i	−0.314163	+	0.758456i	−0.999542	+	0.0302693i	$0.990364\pi$
$332$	−513566.	−	570757.i	−0.255712	−	0.284188i
$333$	−1.26468e6	+	1.56496e6i	−0.624987	+	0.773380i
$334$	−2.24320e6	−	1.58590e6i	−1.10028	−	0.777877i
$335$		−	227601.i		−	0.110806i
$336$	−201128.	+	791386.i	−0.0971906	+	0.382419i
$337$			768665.i			0.368691i	0.982862	+	0.184345i	$0.0590165\pi$
$337$			768665.i			0.368691i	−0.982862	+	0.184345i	$0.940984\pi$
$338$	162729.	−	230174.i	0.0774771	−	0.109589i
$339$	1.92958e6	+	278787.i	0.911936	+	0.131757i
$340$	−92660.8	−	4887.27i	−0.0434709	−	0.00229282i
$341$	423174.	−	1.02163e6i	0.197076	−	0.475783i
$342$	170397.	−	48210.9i	0.0787767	−	0.0222885i
$343$	1.12121e6	+	1.12121e6i	0.514577	+	0.514577i
$344$	46099.8	+	391180.i	0.0210041	+	0.178230i
$345$	235021.	−	59813.4i	0.106306	−	0.0270552i
$346$	−1.61649e6	+	1.01955e6i	−0.725908	+	0.457844i
$347$	−1.24965e6	+	3.01691e6i	−0.557138	+	1.34505i	0.354884	+	0.934910i	$0.384520\pi$
$347$	−1.24965e6	+	3.01691e6i	−0.557138	+	1.34505i	−0.912022	+	0.410140i	$0.865480\pi$
$348$	1.33771e6	+	2.00130e6i	0.592127	+	0.885860i
$349$	1.97329e6	−	817365.i	0.867218	−	0.359213i	0.0956916	−	0.995411i	$-0.469494\pi$
$349$	1.97329e6	−	817365.i	0.867218	−	0.359213i	0.771526	+	0.636198i	$0.219494\pi$
$350$	685245.	−	117628.i	0.299003	−	0.0513266i
$351$	92808.7	−	2.45643e6i	0.0402088	−	1.06423i
$352$	−814774.	+	400954.i	−0.350494	+	0.172480i
$353$		−	1.22333e6i		−	0.522524i	−0.965268	−	0.261262i	$-0.915861\pi$
$353$		−	1.22333e6i		−	0.522524i	0.965268	−	0.261262i	$-0.0841387\pi$
$354$	649004.	−	1.69240e6i	0.275257	−	0.717788i
$355$	584067.	+	1.41006e6i	0.245976	+	0.593838i
$356$	1.61014e6	−	3.37283e6i	0.673348	−	1.41049i
$357$	−68909.4	+	51511.0i	−0.0286159	+	0.0213909i
$358$	1.37795e6	+	2.18473e6i	0.568232	+	0.900928i
$359$	1.15160e6	+	1.15160e6i	0.471590	+	0.471590i	0.902429	−	0.430839i	$-0.141782\pi$
$359$	1.15160e6	+	1.15160e6i	0.471590	+	0.471590i	−0.430839	+	0.902429i	$0.641782\pi$
$360$	1.16522e6	+	199620.i	0.473861	+	0.0811796i
$361$	−1.73913e6	+	1.73913e6i	−0.702367	+	0.702367i
$362$	−2.71782e6	−	615458.i	−1.09006	−	0.246846i
$363$	1.27376e6	+	1.70398e6i	0.507364	+	0.678732i
$364$	1.06079e6	+	55949.8i	0.419638	+	0.0221333i
$365$	430693.	−	178399.i	0.169214	−	0.0700906i
$366$	−2.51865e6	+	1.12239e6i	−0.982800	+	0.437965i
$367$	2.27249e6			0.880718			0.440359	−	0.897822i	$-0.354851\pi$
$367$	2.27249e6			0.880718			0.440359	+	0.897822i	$0.354851\pi$
$368$	62354.6	−	589465.i	0.0240021	−	0.226902i
$369$	−1.39166e6	−	2.55700e6i	−0.532068	−	0.977606i
$370$	−726712.	+	1.02791e6i	−0.275968	+	0.390346i
$371$	404404.	+	976317.i	0.152539	+	0.368261i
$372$	687038.	+	3.45096e6i	0.257409	+	1.29295i
$373$	1.06863e6	+	442639.i	0.397698	+	0.164732i	0.572564	−	0.819860i	$-0.305949\pi$
$373$	1.06863e6	+	442639.i	0.397698	+	0.164732i	−0.174865	+	0.984592i	$0.555949\pi$
$374$	−93316.7	−	21131.8i	−0.0344969	−	0.00781193i
$375$	−571174.	−	2.24428e6i	−0.209744	−	0.824136i
$376$	1.43780e6	+	2.57041e6i	0.524481	+	0.937633i
$377$	2.21438e6	−	2.21438e6i	0.802415	−	0.802415i
$378$	948539.	−	549333.i	0.341449	−	0.197745i
$379$	−2.54729e6	−	1.05512e6i	−0.910919	−	0.377315i	−0.122511	−	0.992467i	$-0.539095\pi$
$379$	−2.54729e6	−	1.05512e6i	−0.910919	−	0.377315i	−0.788409	+	0.615152i	$0.789095\pi$
$380$	104450.	−	36948.4i	0.0371065	−	0.0131261i
$381$	−801008.	+	5.54405e6i	−0.282699	+	1.95666i
$382$	−3.95455e6	+	678835.i	−1.38656	+	0.238016i
$383$	−3.77201e6			−1.31394			−0.656970	−	0.753917i	$-0.728162\pi$
$383$	−3.77201e6			−1.31394			−0.656970	+	0.753917i	$0.728162\pi$
$384$	1.44645e6	−	2.50144e6i	0.500581	−	0.865690i
$385$	−215519.			−0.0741027
$386$	4.38362e6	−	752487.i	1.49749	−	0.257058i
$387$	332342.	−	411252.i	0.112800	−	0.139582i
$388$	−3.36172e6	+	1.18918e6i	−1.13366	+	0.401022i
$389$	−1.73803e6	−	719917.i	−0.582350	−	0.241217i	0.0720058	−	0.997404i	$-0.477060\pi$
$389$	−1.73803e6	−	719917.i	−0.582350	−	0.241217i	−0.654356	+	0.756187i	$0.727060\pi$
$390$	−40772.9	−	1.53740e6i	−0.0135741	−	0.511831i
$391$	44162.3	−	44162.3i	0.0146086	−	0.0146086i
$392$	−1.25400e6	−	2.24183e6i	−0.412177	−	0.736864i
$393$	1.38010e6	−	351237.i	0.450742	−	0.114715i
$394$	−1.63165e6	−	369491.i	−0.529523	−	0.119912i
$395$	−140557.	−	58220.7i	−0.0453273	−	0.0187752i
$396$	1.14936e6	+	406146.i	0.368315	+	0.130150i
$397$	2.03300e6	+	4.90810e6i	0.647383	+	1.56292i	0.816513	+	0.577327i	$0.195904\pi$
$397$	2.03300e6	+	4.90810e6i	0.647383	+	1.56292i	−0.169130	+	0.985594i	$0.554096\pi$
$398$	694160.	−	981865.i	0.219661	−	0.310702i
$399$	52479.1	−	88310.3i	0.0165027	−	0.0277702i
$400$	−2.44672e6	−	258818.i	−0.764600	−	0.0808806i
$401$	−562661.			−0.174737			−0.0873686	−	0.996176i	$-0.527846\pi$
$401$	−562661.			−0.174737			−0.0873686	+	0.996176i	$0.527846\pi$
$402$	303973.	+	682121.i	0.0938145	+	0.210521i
$403$	4.22910e6	−	1.75175e6i	1.29714	−	0.537291i
$404$	−33970.9	−	1791.75i	−0.0103551	−	0.000546166i
$405$	−901496.	−	1.30606e6i	−0.273103	−	0.395663i
$406$	1.36193e6	+	308413.i	0.410052	+	0.0928575i
$407$	−917866.	+	917866.i	−0.274659	+	0.274659i
$408$	284231.	−	109106.i	0.0845320	−	0.0324488i
$409$	2.49323e6	+	2.49323e6i	0.736977	+	0.736977i	0.971992	−	0.235015i	$-0.0755140\pi$
$409$	2.49323e6	+	2.49323e6i	0.736977	+	0.736977i	−0.235015	+	0.971992i	$0.575514\pi$
$410$	−971643.	−	1.54053e6i	−0.285461	−	0.452597i
$411$	−2.21183e6	−	2.95890e6i	−0.645874	−	0.864025i
$412$	1.21726e6	−	2.54984e6i	0.353297	−	0.740064i
$413$	−402378.	−	971427.i	−0.116081	−	0.280243i
$414$	−624474.	+	493143.i	−0.179066	+	0.141407i
$415$			644843.i			0.183795i
$416$	−3.55856e6	−	1.21129e6i	−1.00819	−	0.343175i
$417$	−2.20764e6	+	3.71495e6i	−0.621711	+	1.04620i
$418$	112596.	−	19328.2i	0.0315198	−	0.00541066i
$419$	707358.	−	292997.i	0.196836	−	0.0815321i	−0.282088	−	0.959389i	$-0.591027\pi$
$419$	707358.	−	292997.i	0.196836	−	0.0815321i	0.478924	+	0.877856i	$0.341027\pi$
$420$	570144.	−	381096.i	0.157711	−	0.105417i
$421$	1.12100e6	−	2.70632e6i	0.308247	−	0.744174i	−0.691515	−	0.722362i	$-0.743056\pi$
$421$	1.12100e6	−	2.70632e6i	0.308247	−	0.744174i	0.999762	−	0.0218120i	$-0.00694351\pi$
$422$	2.84721e6	−	1.79579e6i	0.778285	−	0.490879i
$423$	1.11909e6	−	3.79196e6i	0.304098	−	1.03042i
$424$	−437675.	−	3.71389e6i	−0.118233	−	1.00326i
$425$	−183306.	−	183306.i	−0.0492272	−	0.0492272i
$426$	−3.63366e6	−	3.44590e6i	−0.970108	−	0.919982i
$427$	−612125.	+	1.47780e6i	−0.162469	+	0.392235i
$428$	−4.55289e6	−	240136.i	−1.20137	−	0.0633649i
$429$	226769.	−	1.56955e6i	0.0594895	−	0.411747i
$430$	190971.	−	270121.i	0.0498076	−	0.0704511i
$431$			1.27534e6i			0.330700i	0.986235	+	0.165350i	$0.0528753\pi$
$431$			1.27534e6i			0.330700i	−0.986235	+	0.165350i	$0.947125\pi$
$432$	−3.75876e6	+	957948.i	−0.969025	+	0.246963i
$433$		−	7.16131e6i		−	1.83558i	−0.397068	−	0.917789i	$-0.629972\pi$
$433$		−	7.16131e6i		−	1.83558i	0.397068	−	0.917789i	$-0.370028\pi$
$434$	1.66671e6	+	1.17833e6i	0.424751	+	0.300291i
$435$	289098.	−	2.00095e6i	0.0732525	−	0.507006i
$436$	−3.70535e6	−	4.11799e6i	−0.933498	−	1.03745i
$437$	−28537.6	+	68895.9i	−0.00714849	+	0.0172580i
$438$	−1.05253e6	+	1.10987e6i	−0.262148	+	0.276432i
$439$	4.46100e6	+	4.46100e6i	1.10477	+	1.10477i	0.993827	+	0.110941i	$0.0353864\pi$
$439$	4.46100e6	+	4.46100e6i	1.10477	+	1.10477i	0.110941	+	0.993827i	$0.464614\pi$
$440$	733928.	+	207387.i	0.180726	+	0.0510682i
$441$	−976034.	+	3.30723e6i	−0.238984	+	0.809781i
$442$	−211293.	−	335003.i	−0.0514433	−	0.0815629i
$443$	665684.	−	1.60710e6i	0.161161	−	0.389076i	−0.822585	−	0.568642i	$-0.807469\pi$
$443$	665684.	−	1.60710e6i	0.161161	−	0.389076i	0.983746	+	0.179565i	$0.0574691\pi$
$444$	805130.	−	4.05120e6i	0.193825	−	0.975273i
$445$	−2.90000e6	+	1.20122e6i	−0.694221	+	0.287556i
$446$	472638.	+	2.75335e6i	0.112510	+	0.655428i
$447$	1.88511e6	−	3.17220e6i	0.446238	−	0.750917i
$448$	−389663.	−	1.63028e6i	−0.0917264	−	0.383767i
$449$			6.77957e6i			1.58704i	0.608547	+	0.793518i	$0.291753\pi$
$449$			6.77957e6i			1.58704i	−0.608547	+	0.793518i	$0.708247\pi$
$450$	2.04691e6	+	2.59203e6i	0.476505	+	0.603405i
$451$	−718710.	−	1.73512e6i	−0.166384	−	0.401687i
$452$	−3.77307e6	+	1.33469e6i	−0.868657	+	0.307280i
$453$	−1.95399e6	−	2.61398e6i	−0.447381	−	0.598489i
$454$	6.46458e6	−	4.07733e6i	1.47198	−	0.928403i
$455$	−630847.	−	630847.i	−0.142855	−	0.142855i
$456$	−263690.	+	250233.i	−0.0593857	+	0.0563549i
$457$	−3.29142e6	+	3.29142e6i	−0.737213	+	0.737213i	−0.972038	−	0.234825i	$-0.924548\pi$
$457$	−3.29142e6	+	3.29142e6i	−0.737213	+	0.737213i	0.234825	+	0.972038i	$0.424548\pi$
$458$	−973913.	+	4.30073e6i	−0.216949	+	0.958029i
$459$	−371412.	−	170546.i	−0.0822858	−	0.0377841i
$460$	−370072.	+	332990.i	−0.0815439	+	0.0733730i
$461$	5.39527e6	−	2.23479e6i	1.18239	−	0.489762i	0.297121	−	0.954840i	$-0.403974\pi$
$461$	5.39527e6	−	2.23479e6i	1.18239	−	0.489762i	0.885270	+	0.465078i	$0.153974\pi$
$462$	645910.	−	287837.i	0.140788	−	0.0627395i
$463$	949835.			0.205919			0.102959	−	0.994686i	$-0.467169\pi$
$463$	949835.			0.205919			0.102959	+	0.994686i	$0.467169\pi$
$464$	−4.34113e6	−	2.36081e6i	−0.936068	−	0.509056i
$465$	1.50970e6	−	2.54048e6i	0.323787	−	0.544859i
$466$	4.31224e6	+	3.04867e6i	0.919894	+	0.650348i
$467$	133336.	+	321900.i	0.0282913	+	0.0683014i	0.937394	−	0.348271i	$-0.113231\pi$
$467$	133336.	+	321900.i	0.0282913	+	0.0683014i	−0.909102	+	0.416573i	$0.863231\pi$
$468$	2.17548e6	+	4.55314e6i	0.459134	+	0.960940i
$469$	400230.	+	165781.i	0.0840189	+	0.0348018i
$470$	546314.	−	2.41249e6i	0.114077	−	0.503756i
$471$	1.43975e6	−	366418.i	0.299043	−	0.0761071i
$472$	435484.	+	3.69529e6i	0.0899739	+	0.763473i
$473$	241203.	−	241203.i	0.0495713	−	0.0495713i
$474$	499006.	−	13234.0i	0.102014	−	0.00270548i
$475$	285969.	+	118452.i	0.0581548	+	0.0240885i
$476$	76086.5	−	159381.i	0.0153918	−	0.0322418i
$477$	−3.15528e6	+	3.90446e6i	−0.634954	+	0.785714i
$478$	−578492.	−	3.37001e6i	−0.115805	−	0.674623i
$479$	−6.17017e6			−1.22874			−0.614368	−	0.789020i	$-0.710589\pi$
$479$	−6.17017e6			−1.22874			−0.614368	+	0.789020i	$0.710589\pi$
$480$	−2.30828e6	+	749150.i	−0.457284	+	0.148411i
$481$	−5.37338e6			−1.05897
$482$	1.46606e6	+	8.54056e6i	0.287432	+	1.67444i
$483$	−66005.1	+	456844.i	−0.0128739	+	0.0891046i
$484$	−3.94115e6	−	1.88145e6i	−0.764733	−	0.365073i
$485$	2.76685e6	+	1.14607e6i	0.534111	+	0.221236i
$486$	4.44609e6	+	2.71026e6i	0.853862	+	0.520500i
$487$	−6.39309e6	+	6.39309e6i	−1.22149	+	1.22149i	−0.254381	+	0.967104i	$0.581872\pi$
$487$	−6.39309e6	+	6.39309e6i	−1.22149	+	1.22149i	−0.967104	+	0.254381i	$0.918128\pi$
$488$	3.50657e6	−	4.44347e6i	0.666550	−	0.844642i
$489$	−119371.	−	469036.i	−0.0225749	−	0.0887020i
$490$	−476478.	+	2.10409e6i	−0.0896505	+	0.395890i
$491$	−2.03367e6	−	842375.i	−0.380695	−	0.157689i	0.184125	−	0.982903i	$-0.441055\pi$
$491$	−2.03367e6	−	842375.i	−0.380695	−	0.157689i	−0.564821	+	0.825214i	$0.691055\pi$
$492$	4.96947e6	+	3.31929e6i	0.925545	+	0.618206i
$493$	−199248.	−	481027.i	−0.0369212	−	0.0891358i
$494$	386157.	+	273006.i	0.0711945	+	0.0503332i
$495$	−489419.	−	899243.i	−0.0897775	−	0.164954i
$496$	−4.54192e6	−	5.61650e6i	−0.828964	−	1.02509i
$497$	−2.90497e6			−0.527535
$498$	−861220.	−	1.93259e6i	−0.155611	−	0.349194i
$499$	8.89035e6	−	3.68251e6i	1.59833	−	0.662052i	0.607156	−	0.794583i	$-0.292310\pi$
$499$	8.89035e6	−	3.68251e6i	1.59833	−	0.662052i	0.991179	+	0.132531i	$0.0423104\pi$
$500$	3.17981e6	+	3.53392e6i	0.568822	+	0.632167i
$501$	−4.53258e6	−	6.06351e6i	−0.806773	−	1.07927i
$502$	1.13352e6	−	5.00554e6i	0.200756	−	0.886526i
$503$	3.42093e6	−	3.42093e6i	0.602872	−	0.602872i	−0.338202	−	0.941074i	$-0.609819\pi$
$503$	3.42093e6	−	3.42093e6i	0.602872	−	0.602872i	0.941074	+	0.338202i	$0.109819\pi$
$504$	−1.19975e6	+	1.90360e6i	−0.210384	+	0.333810i
$505$	20202.4	+	20202.4i	0.00352512	+	0.00352512i
$506$	−434188.	+	273851.i	−0.0753879	+	0.0475486i
$507$	622175.	−	465086.i	0.107496	−	0.0803552i
$508$	−3.83482e6	−	1.08407e7i	−0.659303	−	1.86380i
$509$	−2.60556e6	−	6.29037e6i	−0.445765	−	1.07617i	−0.973893	−	0.227008i	$-0.927106\pi$
$509$	−2.60556e6	−	6.29037e6i	−0.445765	−	1.07617i	0.528128	−	0.849165i	$-0.322894\pi$
$510$	−238745.	−	91554.1i	−0.0406452	−	0.0155866i
$511$			887302.i			0.150321i
$512$	−241810.	+	5.92671e6i	−0.0407661	+	0.999169i
$513$	487645.	+	18424.1i	0.0818107	+	0.00309096i
$514$	1.33053e6	+	7.75102e6i	0.222135	+	1.29405i
$515$	−2.19238e6	+	908114.i	−0.364249	+	0.150877i
$516$	−211578.	+	1.06460e6i	−0.0349821	+	0.176021i
$517$	976076.	−	2.35645e6i	0.160604	−	0.387733i
$518$	−1.27822e6	−	2.02661e6i	−0.209306	−	0.331853i
$519$	−5.10382e6	+	1.29893e6i	−0.831719	+	0.211674i
$520$	1.54124e6	+	2.75533e6i	0.249955	+	0.446853i
$521$	4.27180e6	+	4.27180e6i	0.689472	+	0.689472i	0.962115	−	0.272643i	$-0.0878979\pi$
$521$	4.27180e6	+	4.27180e6i	0.689472	+	0.689472i	−0.272643	+	0.962115i	$0.587898\pi$
$522$	1.80594e6	+	6.38295e6i	0.290087	+	1.02529i
$523$	3.38958e6	−	8.18317e6i	0.541866	−	1.30818i	−0.381539	−	0.924353i	$-0.624606\pi$
$523$	3.38958e6	−	8.18317e6i	0.541866	−	1.30818i	0.923405	−	0.383827i	$-0.125394\pi$
$524$	−2.17314e6	+	1.95539e6i	−0.345748	+	0.311104i
$525$	1.89624e6	+	273970.i	0.300259	+	0.0433815i
$526$	−2.64290e6	−	1.86848e6i	−0.416502	−	0.294459i
$527$		−	761061.i		−	0.119369i
$528$	−2.47655e6	+	358659.i	−0.386601	+	0.0559882i
$529$			6.10126e6i			0.947939i
$530$	−1.81309e6	+	2.56455e6i	−0.280369	+	0.396572i
$531$	3.13948e6	−	3.88490e6i	0.483194	−	0.597921i
$532$	−11107.0	+	210585.i	−0.00170145	+	0.0322588i
$533$	2.97514e6	−	7.18262e6i	0.453617	−	1.09513i
$534$	7.08700e6	−	7.47315e6i	1.07550	−	1.13410i
$535$	2.70759e6	+	2.70759e6i	0.408977	+	0.408977i
$536$	−1.20341e6	−	949677.i	−0.180927	−	0.142779i
$537$	1.75555e6	+	6.89797e6i	0.262710	+	1.03225i
$538$	2.89047e6	−	1.82307e6i	0.430539	−	0.271549i
$539$	−851302.	+	2.05522e6i	−0.126215	+	0.304710i
$540$	2.88484e6	+	1.51347e6i	0.425732	+	0.223353i
$541$	−5.01234e6	+	2.07618e6i	−0.736288	+	0.304980i	−0.719133	−	0.694872i	$-0.755461\pi$
$541$	−5.01234e6	+	2.07618e6i	−0.736288	+	0.304980i	−0.0171547	+	0.999853i	$0.505461\pi$
$542$	6.52213e6	−	1.11958e6i	0.953655	−	0.163704i
$543$	−6.60140e6	−	3.92293e6i	−0.960808	−	0.570968i
$544$	−412472.	+	469540.i	−0.0597581	+	0.0680261i
$545$			4.65252e6i			0.670960i
$546$	2.73317e6	+	1.04812e6i	0.392361	+	0.150463i
$547$	−99964.7	−	241336.i	−0.0142849	−	0.0344869i	0.916576	−	0.399860i	$-0.130941\pi$
$547$	−99964.7	−	241336.i	−0.0142849	−	0.0344869i	−0.930861	+	0.365373i	$0.880941\pi$
$548$	6.84367e6	+	3.26708e6i	0.973505	+	0.464738i
$549$	−7.55612e6	+	801851.i	−1.06996	+	0.113544i
$550$	1.13668e6	+	1.80220e6i	0.160226	+	0.254037i
$551$	439593.	+	439593.i	0.0616839	+	0.0616839i
$552$	664380.	−	1.49222e6i	0.0928044	−	0.208442i
$553$	204758.	−	204758.i	0.0284727	−	0.0284727i
$554$	−2.95877e6	−	670021.i	−0.409578	−	0.0927501i
$555$	−2.77850e6	+	2.07698e6i	−0.382893	+	0.286219i
$556$	467239.	−	8.85867e6i	0.0640992	−	1.21530i
$557$	2.73488e6	−	1.13283e6i	0.373509	−	0.154712i	−0.188029	−	0.982163i	$-0.560210\pi$
$557$	2.73488e6	−	1.13283e6i	0.373509	−	0.154712i	0.561538	+	0.827451i	$0.310210\pi$
$558$	−1.13163e6	+	9.63010e6i	−0.153858	+	1.30932i
$559$	1.41205e6			0.191127
$560$	−672562.	+	1.23673e6i	−0.0906279	+	0.166649i
$561$	−226660.	−	134695.i	−0.0304066	−	0.0180694i
$562$	−8.62117e6	+	1.21943e7i	−1.15140	+	1.62861i
$563$	−5.57012e6	−	1.34475e7i	−0.740617	−	1.78801i	−0.603356	−	0.797472i	$-0.706170\pi$
$563$	−5.57012e6	−	1.34475e7i	−0.740617	−	1.78801i	−0.137261	−	0.990535i	$-0.543830\pi$
$564$	1.58469e6	+	7.95984e6i	0.209772	+	1.05367i
$565$	3.10541e6	+	1.28630e6i	0.409259	+	0.169521i
$566$	1.34598e7	+	3.04800e6i	1.76602	+	0.399921i
$567$	2.95330e6	−	633943.i	0.385789	−	0.0828119i
$568$	9.89259e6	+	2.79537e6i	1.28659	+	0.363553i
$569$	−1.33860e6	+	1.33860e6i	−0.173328	+	0.173328i	−0.788440	−	0.615112i	$-0.789111\pi$
$569$	−1.33860e6	+	1.33860e6i	−0.173328	+	0.173328i	0.615112	+	0.788440i	$0.289111\pi$
$570$	305201.	−	8094.14i	0.0393459	−	0.00104348i
$571$	−9.72083e6	−	4.02650e6i	−1.24771	−	0.516818i	−0.341593	−	0.939848i	$-0.610966\pi$
$571$	−9.72083e6	−	4.02650e6i	−1.24771	−	0.516818i	−0.906116	+	0.423030i	$0.860966\pi$
$572$	1.08565e6	+	3.06906e6i	0.138740	+	0.392207i
$573$	−1.09432e7	−	1.58108e6i	−1.39238	−	0.201173i
$574$	3.41670e6	−	586508.i	0.432840	−	0.0743009i
$575$	−1.39083e6			−0.175431
$576$	5.91739e6	−	5.32803e6i	0.743145	−	0.669130i
$577$	−1.05550e7			−1.31983			−0.659916	−	0.751339i	$-0.729408\pi$
$577$	−1.05550e7			−1.31983			−0.659916	+	0.751339i	$0.729408\pi$
$578$	7.85124e6	−	1.34774e6i	0.977504	−	0.167797i
$579$	1.21306e7	+	1.75263e6i	1.50378	+	0.217267i
$580$	1.38406e6	+	3.91262e6i	0.170838	+	0.482945i
$581$	−1.13394e6	−	469692.i	−0.139363	−	0.0577261i
$582$	−9.82288e6	+	260509.i	−1.20207	+	0.0318798i
$583$	−2.29000e6	+	2.29000e6i	−0.279039	+	0.279039i
$584$	853823.	−	3.02162e6i	0.103594	−	0.366612i
$585$	1.19960e6	−	4.06476e6i	0.144926	−	0.491072i
$586$	5.48408e6	+	1.24189e6i	0.659720	+	0.149396i
$587$	1.34530e7	+	5.57242e6i	1.61148	+	0.667496i	0.992979	−	0.118291i	$-0.0377416\pi$
$587$	1.34530e7	+	5.57242e6i	1.61148	+	0.667496i	0.618498	+	0.785787i	$0.287742\pi$
$588$	−1.38212e6	−	6.94232e6i	−0.164855	−	0.828059i
$589$	347753.	+	839550.i	0.0413031	+	0.0997145i
$590$	1.80401e6	−	2.55171e6i	0.213358	−	0.301787i
$591$	−3.96316e6	−	2.35514e6i	−0.466738	−	0.277363i
$592$	2.40270e6	+	8.13140e6i	0.281771	+	0.953588i
$593$	−3.99218e6			−0.466201			−0.233101	−	0.972453i	$-0.574887\pi$
$593$	−3.99218e6			−0.466201			−0.233101	+	0.972453i	$0.574887\pi$
$594$	2.66777e6	+	2.04138e6i	0.310229	+	0.237388i
$595$	−137038.	+	56763.0i	−0.0158690	+	0.00657314i
$596$	−398976.	+	7.56443e6i	−0.0460077	+	0.872289i
$597$	2.65404e6	−	1.98394e6i	0.304769	−	0.227820i
$598$	−2.07250e6	−	469325.i	−0.236997	−	0.0536686i
$599$	−6.44973e6	+	6.44973e6i	−0.734470	+	0.734470i	−0.971502	−	0.237032i	$-0.923826\pi$
$599$	−6.44973e6	+	6.44973e6i	−0.734470	+	0.734470i	0.237032	+	0.971502i	$0.423826\pi$
$600$	−6.19382e6	−	2.75767e6i	−0.702394	−	0.312726i
$601$	3.50190e6	+	3.50190e6i	0.395473	+	0.395473i	0.876633	−	0.481160i	$-0.159784\pi$
$601$	3.50190e6	+	3.50190e6i	0.395473	+	0.395473i	−0.481160	+	0.876633i	$0.659784\pi$
$602$	335900.	+	532567.i	0.0377762	+	0.0598939i
$603$	217164.	+	2.04641e6i	0.0243217	+	0.229192i
$604$	6.04589e6	+	2.88623e6i	0.674323	+	0.321913i
$605$	1.40363e6	+	3.38865e6i	0.155906	+	0.376390i
$606$	−87527.8	−	33565.2i	−0.00968199	−	0.00371285i
$607$		−	400169.i		−	0.0440831i	−0.999757	−	0.0220415i	$-0.992983\pi$
$607$		−	400169.i		−	0.0440831i	0.999757	−	0.0220415i	$-0.00701661\pi$
$608$	240463.	−	706436.i	0.0263809	−	0.0775022i
$609$	3.30803e6	+	1.96583e6i	0.361432	+	0.214784i
$610$	−4.68544e6	+	804298.i	−0.509831	+	0.0875170i
$611$	9.75466e6	−	4.04051e6i	1.05708	−	0.437858i
$612$	837794.	−	44468.9i	0.0904188	−	0.00479930i
$613$	1.18244e6	−	2.85466e6i	0.127095	−	0.306834i	−0.847505	−	0.530787i	$-0.821896\pi$
$613$	1.18244e6	−	2.85466e6i	0.127095	−	0.306834i	0.974600	+	0.223953i	$0.0718963\pi$
$614$	−7.32192e6	+	4.61807e6i	−0.783797	+	0.494356i
$615$	−1.23790e6	−	4.86401e6i	−0.131977	−	0.518569i
$616$	−899263.	+	1.13953e6i	−0.0954849	+	0.120997i
$617$	4.63637e6	+	4.63637e6i	0.490304	+	0.490304i	0.908402	−	0.418098i	$-0.137303\pi$
$617$	4.63637e6	+	4.63637e6i	0.490304	+	0.490304i	−0.418098	+	0.908402i	$0.637303\pi$
$618$	5.35773e6	−	5.64965e6i	0.564299	−	0.595046i
$619$	2.19518e6	−	5.29964e6i	0.230274	−	0.555930i	−0.765936	−	0.642917i	$-0.777724\pi$
$619$	2.19518e6	−	5.29964e6i	0.230274	−	0.555930i	0.996209	+	0.0869873i	$0.0277240\pi$
$620$	−319523.	+	6.05803e6i	−0.0333828	+	0.632925i
$621$	−2.05605e6	+	762036.i	−0.213946	+	0.0792952i
$622$	−879570.	+	1.24412e6i	−0.0911580	+	0.128940i
$623$		−	5.97450e6i		−	0.616711i
$624$	−8.29896e6	−	6.19930e6i	−0.853223	−	0.637355i
$625$			3.51582e6i			0.360020i
$626$	−1.39809e7	−	9.88422e6i	−1.42593	−	1.00811i
$627$	311582.	+	45017.6i	0.0316522	+	0.00457313i
$628$	−2.26707e6	+	2.03991e6i	−0.229386	+	0.206401i
$629$	−341880.	+	825371.i	−0.0344546	+	0.0831807i
$630$	1.81841e6	−	514488.i	0.182533	−	0.0516445i
$631$	9.09111e6	+	9.09111e6i	0.908957	+	0.908957i	0.996188	−	0.0872308i	$-0.0278018\pi$
$631$	9.09111e6	+	9.09111e6i	0.908957	+	0.908957i	−0.0872308	+	0.996188i	$0.527802\pi$
$632$	−894315.	+	500250.i	−0.0890631	+	0.0498190i
$633$	8.98966e6	−	2.28789e6i	0.891731	−	0.226947i
$634$	−7.56449e6	−	1.19934e7i	−0.747406	−	1.18501i
$635$	−3.69579e6	+	8.92243e6i	−0.363725	+	0.878109i
$636$	2.00874e6	−	1.01074e7i	0.196916	−	0.990827i
$637$	−8.50770e6	+	3.52401e6i	−0.830737	+	0.344103i
$638$	724018.	+	4.21777e6i	0.0704203	+	0.410234i
$639$	−6.59686e6	−	1.21209e7i	−0.639124	−	1.17431i
$640$	3.48040e6	−	3.56436e6i	0.335876	−	0.343979i
$641$			5.87479e6i			0.564739i	0.959306	+	0.282369i	$0.0911204\pi$
$641$			5.87479e6i			0.564739i	−0.959306	+	0.282369i	$0.908880\pi$
$642$	−1.17308e7	−	4.49852e6i	−1.12328	−	0.430757i
$643$	−6.52972e6	−	1.57641e7i	−0.622826	−	1.50364i	−0.848370	−	0.529403i	$-0.822416\pi$
$643$	−6.52972e6	−	1.57641e7i	−0.622826	−	1.50364i	0.225544	−	0.974233i	$-0.427584\pi$
$644$	−315999.	−	893303.i	−0.0300241	−	0.0848759i
$645$	730153.	−	545802.i	0.0691058	−	0.0516578i
$646$	66503.9	−	41945.3i	0.00626997	−	0.00395459i
$647$	7.62741e6	+	7.62741e6i	0.716335	+	0.716335i	0.967853	−	0.251518i	$-0.0809297\pi$
$647$	7.62741e6	+	7.62741e6i	0.716335	+	0.716335i	−0.251518	+	0.967853i	$0.580930\pi$
$648$	−1.06672e7	−	683036.i	−0.997956	−	0.0639008i
$649$	2.27853e6	−	2.27853e6i	0.212346	−	0.212346i
$650$	−1.94805e6	+	8.60243e6i	−0.180849	+	0.798616i
$651$	3.36772e6	+	4.50520e6i	0.311446	+	0.416641i
$652$	664554.	+	738559.i	0.0612225	+	0.0680403i
$653$	−141212.	+	58492.1i	−0.0129596	+	0.00536802i	−0.389154	−	0.921173i	$-0.627233\pi$
$653$	−141212.	+	58492.1i	−0.0129596	+	0.00536802i	0.376194	+	0.926541i	$0.377233\pi$
$654$	−6.21367e6	−	1.39436e7i	−0.568072	−	1.27476i
$655$	2.45523e6			0.223608
$656$	−1.21996e7	−	1.29049e6i	−1.10684	−	0.117084i
$657$	−3.70223e6	+	2.01496e6i	−0.334618	+	0.182118i
$658$	3.84435e6	+	2.71789e6i	0.346145	+	0.244718i
$659$	1.49155e6	+	3.60092e6i	0.133790	+	0.322998i	0.976550	−	0.215292i	$-0.0690704\pi$
$659$	1.49155e6	+	3.60092e6i	0.133790	+	0.322998i	−0.842759	+	0.538290i	$0.819070\pi$
$660$	1.74766e6	+	1.16733e6i	0.156170	+	0.104312i
$661$	1.29694e7	+	5.37210e6i	1.15456	+	0.478234i	0.876060	−	0.482202i	$-0.160163\pi$
$661$	1.29694e7	+	5.37210e6i	1.15456	+	0.478234i	0.278499	+	0.960436i	$0.410163\pi$
$662$	2.04446e6	−	9.02818e6i	0.181315	−	0.800673i
$663$	−269193.	−	1.05772e6i	−0.0237837	−	0.0934519i
$664$	3.40953e6	+	2.69064e6i	0.300106	+	0.236829i
$665$	125234.	−	125234.i	0.0109817	−	0.0109817i
$666$	5.55324e6	−	9.93551e6i	0.485133	−	0.867970i
$667$	−2.58079e6	−	1.06900e6i	−0.224614	−	0.0930383i
$668$	1.40243e7	+	6.69504e6i	1.21602	+	0.580513i
$669$	−1.10083e6	+	7.61922e6i	−0.0950943	+	0.658180i
$670$	217826.	+	1.26895e6i	0.0187466	+	0.109209i
$671$	−4.90203e6			−0.420310
$672$	363953.	−	4.60471e6i	0.0310901	−	0.393350i
$673$	3.39950e6			0.289319			0.144660	−	0.989481i	$-0.453791\pi$
$673$	3.39950e6			0.289319			0.144660	+	0.989481i	$0.453791\pi$
$674$	−735652.	−	4.28554e6i	−0.0623767	−	0.363376i
$675$	3.16302e6	+	8.53413e6i	0.267204	+	0.720941i
$676$	−686975.	+	1.43903e6i	−0.0578195	+	0.121117i
$677$	−2.07252e6	−	858465.i	−0.173791	−	0.0719864i	0.294092	−	0.955777i	$-0.404983\pi$
$677$	−2.07252e6	−	858465.i	−0.173791	−	0.0719864i	−0.467882	+	0.883791i	$0.654983\pi$
$678$	−1.10248e7	+	292386.i	−0.921081	+	0.0244277i
$679$	−4.03065e6	+	4.03065e6i	−0.335506	+	0.335506i
$680$	521290.	−	61433.1i	0.0432321	−	0.00509483i
$681$	2.04110e7	−	5.19464e6i	1.68654	−	0.429227i
$682$	−1.38157e6	+	6.10092e6i	−0.113740	+	0.502267i
$683$	1.63551e7	+	6.77449e6i	1.34153	+	0.555680i	0.933922	−	0.357477i	$-0.116363\pi$
$683$	1.63551e7	+	6.77449e6i	1.34153	+	0.555680i	0.407608	+	0.913157i	$0.366363\pi$
$684$	−903878.	+	431870.i	−0.0738702	+	0.0352950i
$685$	−2.43735e6	−	5.88428e6i	−0.198468	−	0.479145i
$686$	−7.32412e6	−	5.17802e6i	−0.594217	−	0.420100i
$687$	−6.20773e6	+	1.04462e7i	−0.501812	+	0.844435i
$688$	−631400.	−	2.13683e6i	−0.0508550	−	0.172107i
$689$	−1.34062e7			−1.07586
$690$	−1.25307e6	+	558405.i	−0.100197	+	0.0446505i
$691$	−6.98180e6	+	2.89196e6i	−0.556253	+	0.230408i	−0.643058	−	0.765818i	$-0.722334\pi$
$691$	−6.98180e6	+	2.89196e6i	−0.556253	+	0.230408i	0.0868046	+	0.996225i	$0.472334\pi$
$692$	8.03664e6	−	7.23135e6i	0.637983	−	0.574056i
$693$	1.93777e6	−	205635.i	0.153274	−	0.0162654i
$694$	4.07982e6	−	1.80162e7i	0.321545	−	1.41992i
$695$	−5.26822e6	+	5.26822e6i	−0.413716	+	0.413716i
$696$	−9.37351e6	−	9.87763e6i	−0.733464	−	0.772911i
$697$	−913985.	−	913985.i	−0.0712618	−	0.0712618i
$698$	−1.02195e7	+	6.44561e6i	−0.793943	+	0.500755i
$699$	8.71324e6	+	1.16562e7i	0.674507	+	0.902330i
$700$	−3.70787e6	+	1.31163e6i	−0.286009	+	0.101173i
$701$	−965914.	−	2.33192e6i	−0.0742409	−	0.179233i	0.882402	−	0.470496i	$-0.155925\pi$
$701$	−965914.	−	2.33192e6i	−0.0742409	−	0.179233i	−0.956643	+	0.291262i	$0.905925\pi$
$702$	1.83350e6	+	1.37842e7i	0.140423	+	1.05569i
$703$		−	1.06671e6i		−	0.0814062i
$704$	4.15888e6	−	3.01522e6i	0.316260	−	0.229291i
$705$	3.48221e6	−	5.85977e6i	0.263866	−	0.444025i
$706$	1.17079e6	+	6.82043e6i	0.0884029	+	0.514992i
$707$	−50240.3	+	20810.2i	−0.00378010	+	0.00156577i
$708$	−1.99868e6	+	1.00568e7i	−0.149851	+	0.754010i
$709$	9.75737e6	−	2.35564e7i	0.728983	−	1.75992i	0.0830246	−	0.996547i	$-0.473542\pi$
$709$	9.75737e6	−	2.35564e7i	0.728983	−	1.75992i	0.645958	−	0.763373i	$-0.276458\pi$
$710$	−4.60586e6	−	7.30255e6i	−0.342898	−	0.543662i
$711$	1.31933e6	+	389362.i	0.0978765	+	0.0288855i
$712$	−5.74907e6	+	2.03455e7i	−0.425009	+	1.50407i
$713$	−2.88727e6	−	2.88727e6i	−0.212698	−	0.212698i
$714$	334892.	−	353140.i	0.0245844	−	0.0259239i
$715$	1.04629e6	−	2.52598e6i	0.0765401	−	0.184784i
$716$	−9.77339e6	−	1.08618e7i	−0.712464	−	0.791804i
$717$	1.34738e6	−	9.32565e6i	0.0978793	−	0.677456i
$718$	−7.52265e6	−	5.31837e6i	−0.544577	−	0.385006i
$719$		−	9.53025e6i		−	0.687515i	−0.939058	−	0.343758i	$-0.888300\pi$
$719$		−	9.53025e6i		−	0.687515i	0.939058	−	0.343758i	$-0.111700\pi$
$720$	−6.68750e6	+	2233.59i	−0.480764	+	0.000160573i
$721$		−	4.51669e6i		−	0.323580i
$722$	8.03175e6	−	1.13606e7i	0.573413	−	0.811072i
$723$	−3.41463e6	+	2.36338e7i	−0.242939	+	1.68147i
$724$	1.57417e7	+	830275.i	1.11610	+	0.0588675i
$725$	−4.43713e6	+	1.07122e7i	−0.313514	+	0.756890i
$726$	−8.73238e6	−	8.28117e6i	−0.614881	−	0.583109i
$727$	1.37661e6	+	1.37661e6i	0.0965998	+	0.0965998i	0.753755	−	0.657155i	$-0.228240\pi$
$727$	1.37661e6	+	1.37661e6i	0.0965998	+	0.0965998i	−0.657155	+	0.753755i	$0.728240\pi$
$728$	−5.96776e6	+	703291.i	−0.417333	+	0.0491820i
$729$	9.35169e6	+	1.08829e7i	0.651735	+	0.758446i
$730$	−2.23051e6	+	1.40682e6i	−0.154916	+	0.0977086i
$731$	89841.6	−	216897.i	0.00621848	−	0.0150127i
$732$	1.29681e7	−	8.66812e6i	0.894536	−	0.597926i
$733$	7.61953e6	−	3.15611e6i	0.523803	−	0.216966i	−0.105083	−	0.994463i	$-0.533511\pi$
$733$	7.61953e6	−	3.15611e6i	0.523803	−	0.216966i	0.628887	+	0.777497i	$0.283511\pi$
$734$	−1.26698e7	+	2.17489e6i	−0.868022	+	0.149004i
$735$	−3.03707e6	+	5.11070e6i	−0.207366	+	0.348949i
$736$	216502.	+	3.34613e6i	0.0147322	+	0.227692i
$737$			1.32761e6i			0.0900328i
$738$	1.02061e7	+	1.29241e7i	0.689794	+	0.873496i
$739$	−1.19820e6	−	2.89272e6i	−0.0807085	−	0.194848i	0.878374	−	0.477974i	$-0.158629\pi$
$739$	−1.19820e6	−	2.89272e6i	−0.0807085	−	0.194848i	−0.959083	+	0.283126i	$0.908629\pi$
$740$	3.06788e6	−	6.42641e6i	0.205949	−	0.431409i
$741$	780262.	+	1.04380e6i	0.0522030	+	0.0698351i
$742$	−3.18906e6	−	5.05623e6i	−0.212644	−	0.337145i
$743$	−1.73624e7	−	1.73624e7i	−1.15382	−	1.15382i	−0.985781	−	0.168037i	$-0.946257\pi$
$743$	−1.73624e7	−	1.73624e7i	−1.15382	−	1.15382i	−0.168037	−	0.985781i	$-0.553743\pi$
$744$	−7.13320e6	−	1.85826e7i	−0.472446	−	1.23077i
$745$	4.49854e6	−	4.49854e6i	0.296948	−	0.296948i
$746$	−6.38155e6	−	1.44512e6i	−0.419835	−	0.0950730i
$747$	−615271.	−	5.79791e6i	−0.0403427	−	0.380163i
$748$	540494.	+	28507.6i	0.0353213	+	0.00186298i
$749$	−6.73337e6	+	2.78905e6i	−0.438559	+	0.181657i
$750$	5.33236e6	+	1.19659e7i	0.346152	+	0.776770i
$751$	−5.25682e6			−0.340113			−0.170057	−	0.985434i	$-0.554395\pi$
$751$	−5.25682e6			−0.340113			−0.170057	+	0.985434i	$0.554395\pi$
$752$	−1.04762e7	−	1.29548e7i	−0.675553	−	0.835382i
$753$	7.22506e6	−	1.21581e7i	0.464359	−	0.781410i
$754$	−1.02266e7	+	1.44651e7i	−0.655091	+	0.926603i
$755$	−2.15322e6	−	5.19833e6i	−0.137474	−	0.331892i
$756$	−4.76266e6	+	3.97050e6i	−0.303071	+	0.252663i
$757$	−692985.	−	287044.i	−0.0439526	−	0.0182058i	0.360599	−	0.932721i	$-0.382572\pi$
$757$	−692985.	−	287044.i	−0.0439526	−	0.0182058i	−0.404551	+	0.914515i	$0.632572\pi$
$758$	1.52117e7	+	3.44474e6i	0.961624	+	0.217763i
$759$	−1.37089e6	+	348893.i	−0.0863768	+	0.0219831i
$760$	−546980.	+	305963.i	−0.0343509	+	0.0192147i
$761$	7.56116e6	−	7.56116e6i	0.473290	−	0.473290i	−0.429688	−	0.902977i	$-0.641376\pi$
$761$	7.56116e6	−	7.56116e6i	0.473290	−	0.473290i	0.902977	+	0.429688i	$0.141376\pi$
$762$	−840079.	−	3.16764e7i	−0.0524122	−	1.97628i
$763$	−8.18130e6	−	3.38881e6i	−0.508758	−	0.210734i
$764$	2.13982e7	−	7.56943e6i	1.32630	−	0.469169i
$765$	−548038.	−	442882.i	−0.0338577	−	0.0273612i
$766$	2.10301e7	−	3.61000e6i	1.29500	−	0.222298i
$767$	1.33390e7			0.818720
$768$	−5.67037e6	+	1.53306e7i	−0.346903	+	0.937901i
$769$	−1.96831e6			−0.120026			−0.0600132	−	0.998198i	$-0.519114\pi$
$769$	−1.96831e6			−0.120026			−0.0600132	+	0.998198i	$0.519114\pi$
$770$	1.20159e6	−	206263.i	0.0730344	−	0.0125370i
$771$	−3.09896e6	+	2.14490e7i	−0.187750	+	1.29948i
$772$	−2.37198e7	+	8.39069e6i	−1.43241	+	0.506704i
$773$	−3.67580e6	−	1.52257e6i	−0.221260	−	0.0916489i	0.269300	−	0.963056i	$-0.413208\pi$
$773$	−3.67580e6	−	1.52257e6i	−0.221260	−	0.0916489i	−0.490560	+	0.871407i	$0.663208\pi$
$774$	−1.45932e6	+	2.61092e6i	−0.0875585	+	0.156654i
$775$	−1.19843e7	+	1.19843e7i	−0.716735	+	0.716735i
$776$	1.76045e7	−	9.84738e6i	1.04947	−	0.587039i
$777$	−1.62849e6	−	6.39873e6i	−0.0967681	−	0.380225i
$778$	1.03791e7	+	2.35037e6i	0.614765	+	0.139215i
$779$	1.42587e6	+	590617.i	0.0841856	+	0.0348708i
$780$	1.69870e6	+	8.53248e6i	0.0999722	+	0.502156i
$781$	−3.40689e6	−	8.22495e6i	−0.199862	−	0.482509i
$782$	−203953.	+	288484.i	−0.0119265	+	0.0168696i
$783$	−690153.	+	1.82668e7i	−0.0402292	+	1.06477i
$784$	9.13701e6	+	1.12987e7i	0.530901	+	0.656507i
$785$	2.56135e6			0.148352
$786$	−7.35830e6	+	3.27908e6i	−0.424836	+	0.189319i
$787$	−8.97196e6	+	3.71631e6i	−0.516358	+	0.213882i	−0.625616	−	0.780131i	$-0.715152\pi$
$787$	−8.97196e6	+	3.71631e6i	−0.516358	+	0.213882i	0.109259	+	0.994013i	$0.465152\pi$
$788$	9.45054e6	+	498457.i	0.542177	+	0.0285964i
$789$	−5.34020e6	−	7.14391e6i	−0.305397	−	0.408549i
$790$	839369.	+	190078.i	0.0478504	+	0.0108359i
$791$	−4.52385e6	+	4.52385e6i	−0.257079	+	0.257079i
$792$	−6.79676e6	−	1.16439e6i	−0.385025	−	0.0659606i
$793$	−1.43488e7	−	1.43488e7i	−0.810273	−	0.810273i
$794$	−1.60319e7	−	2.54185e7i	−0.902473	−	1.43086i
$795$	−6.93213e6	+	5.18189e6i	−0.388999	+	0.290784i
$796$	−2.93046e6	+	6.13855e6i	−0.163928	+	0.343386i
$797$	−5.99290e6	−	1.44681e7i	−0.334188	−	0.806802i	−0.998251	−	0.0591245i	$-0.981169\pi$
$797$	−5.99290e6	−	1.44681e7i	−0.334188	−	0.806802i	0.664062	−	0.747677i	$-0.268831\pi$
$798$	−208070.	+	542582.i	−0.0115665	+	0.0301619i
$799$		−	1.75543e6i		−	0.0972784i
$800$	1.38889e7	−	898646.i	0.767261	−	0.0496437i
$801$	2.49283e7	−	1.35674e7i	1.37281	−	0.747163i
$802$	3.13701e6	−	538495.i	0.172218	−	0.0295628i
$803$	−2.51225e6	+	1.04061e6i	−0.137491	+	0.0569506i
$804$	−2.34757e6	−	3.51211e6i	−0.128079	−	0.191615i
$805$	−304542.	+	735231.i	−0.0165637	+	0.0399884i
$806$	−2.19020e7	+	1.38140e7i	−1.18754	+	0.749001i
$807$	9.12623e6	−	2.32265e6i	0.493296	−	0.125545i
$808$	191113.	−	22522.4i	0.0102982	−	0.00121363i
$809$	4533.03	+	4533.03i	0.000243510	+	0.000243510i	0.707229	−	0.706985i	$-0.249945\pi$
$809$	4533.03	+	4533.03i	0.000243510	+	0.000243510i	−0.706985	+	0.707229i	$0.749945\pi$
$810$	6.27609e6	+	6.41890e6i	0.336106	+	0.343754i
$811$	−4.68862e6	+	1.13193e7i	−0.250318	+	0.604322i	−0.998230	−	0.0594765i	$-0.981057\pi$
$811$	−4.68862e6	+	1.13193e7i	−0.250318	+	0.604322i	0.747911	+	0.663799i	$0.231057\pi$
$812$	−7.88833e6	−	416060.i	−0.419851	−	0.0221445i
$813$	1.80484e7	+	2.60764e6i	0.957660	+	0.138363i
$814$	4.23894e6	−	5.99583e6i	0.224231	−	0.317167i
$815$		−	834427.i		−	0.0440042i
$816$	−1.48026e6	+	880323.i	−0.0778236	+	0.0462825i
$817$			280317.i			0.0146925i
$818$	−1.62867e7	−	1.15144e7i	−0.851038	−	0.601668i
$819$	6.27398e6	+	5.07015e6i	0.326839	+	0.264126i
$820$	6.89158e6	+	7.65903e6i	0.357918	+	0.397777i
$821$	−5.78870e6	+	1.39752e7i	−0.299725	+	0.723601i	0.700228	+	0.713919i	$0.253082\pi$
$821$	−5.78870e6	+	1.39752e7i	−0.299725	+	0.723601i	−0.999953	+	0.00968125i	$0.996918\pi$
$822$	1.51635e7	+	1.43800e7i	0.782743	+	0.742298i
$823$	8.69418e6	+	8.69418e6i	0.447434	+	0.447434i	0.894501	−	0.447067i	$-0.147531\pi$
$823$	8.69418e6	+	8.69418e6i	0.447434	+	0.447434i	−0.447067	+	0.894501i	$0.647531\pi$
$824$	−4.34626e6	+	1.53811e7i	−0.222997	+	0.789168i
$825$	1.44817e6	+	5.69020e6i	0.0740771	+	0.291067i
$826$	3.17309e6	+	5.03091e6i	0.161820	+	0.256564i
$827$	8.22256e6	−	1.98510e7i	0.418064	−	1.00930i	−0.564843	−	0.825198i	$-0.691063\pi$
$827$	8.22256e6	−	1.98510e7i	0.418064	−	1.00930i	0.982908	−	0.184099i	$-0.0589366\pi$
$828$	3.00967e6	−	3.34708e6i	0.152561	−	0.169664i
$829$	1.95867e7	−	8.11306e6i	0.989860	−	0.410014i	0.171791	−	0.985133i	$-0.445045\pi$
$829$	1.95867e7	−	8.11306e6i	0.989860	−	0.410014i	0.818069	+	0.575120i	$0.195045\pi$
$830$	−617148.	−	3.59520e6i	−0.0310953	−	0.181146i
$831$	−7.18665e6	−	4.27072e6i	−0.361014	−	0.214535i
$832$	2.09993e7	+	3.34761e6i	1.05171	+	0.167659i
$833$			1.53103e6i			0.0764489i
$834$	8.75287e6	−	2.28248e7i	0.435748	−	1.13630i
$835$	−4.99472e6	−	1.20583e7i	−0.247910	−	0.598509i
$836$	−609262.	+	215521.i	−0.0301501	+	0.0106653i
$837$	−1.11500e7	+	2.42824e7i	−0.550127	+	1.19806i
$838$	−3.66333e6	+	2.31053e6i	−0.180205	+	0.113658i
$839$	1.58746e7	+	1.58746e7i	0.778571	+	0.778571i	0.979588	−	0.201017i	$-0.0644246\pi$
$839$	1.58746e7	+	1.58746e7i	0.778571	+	0.778571i	−0.201017	+	0.979588i	$0.564425\pi$
$840$	−2.81400e6	+	2.67038e6i	−0.137602	+	0.130580i
$841$	−1.96323e6	+	1.96323e6i	−0.0957151	+	0.0957151i
$842$	−3.65981e6	+	1.61614e7i	−0.177901	+	0.785597i
$843$	−3.29620e7	+	2.46397e7i	−1.59751	+	1.19417i
$844$	−1.41554e7	+	1.27370e7i	−0.684016	+	0.615476i
$845$	1.23730e6	−	512506.i	0.0596119	−	0.0246920i
$846$	−2.61017e6	+	2.22124e7i	−0.125384	+	1.06701i
$847$	−6.98121e6			−0.334366
$848$	5.99456e6	+	2.02872e7i	0.286265	+	0.968796i
$849$	3.26929e7	+	1.94280e7i	1.55663	+	0.925037i
$850$	1.19742e6	+	846555.i	0.0568460	+	0.0401891i
$851$	1.83424e6	+	4.42825e6i	0.0868225	+	0.209608i
$852$	2.35567e7	+	1.57344e7i	1.11177	+	0.742592i
$853$	8.48263e6	+	3.51362e6i	0.399170	+	0.165342i	0.573232	−	0.819393i	$-0.305689\pi$
$853$	8.48263e6	+	3.51362e6i	0.399170	+	0.165342i	−0.174062	+	0.984735i	$0.555689\pi$
$854$	1.99845e6	−	8.82503e6i	0.0937669	−	0.414068i
$855$	806925.	+	238141.i	0.0377501	+	0.0111409i
$856$	2.56136e7	−	3.01852e6i	1.19478	−	0.140802i
$857$	−1.70753e6	+	1.70753e6i	−0.0794177	+	0.0794177i	−0.745700	−	0.666282i	$-0.767885\pi$
$857$	−1.70753e6	+	1.70753e6i	−0.0794177	+	0.0794177i	0.666282	+	0.745700i	$0.267885\pi$
$858$	237830.	+	8.96773e6i	0.0110293	+	0.415876i
$859$	6.53048e6	+	2.70501e6i	0.301969	+	0.125080i	0.528523	−	0.848919i	$-0.322746\pi$
$859$	6.53048e6	+	2.70501e6i	0.301969	+	0.125080i	−0.226554	+	0.973999i	$0.572746\pi$
$860$	−806200.	+	1.68878e6i	−0.0371704	+	0.0778621i
$861$	9.45487e6	+	1.36604e6i	0.434658	+	0.0627996i
$862$	−1.22057e6	−	7.11043e6i	−0.0559492	−	0.325932i
$863$	3.11983e7			1.42595			0.712974	−	0.701191i	$-0.247348\pi$
$863$	3.11983e7			1.42595			0.712974	+	0.701191i	$0.247348\pi$
$864$	2.00394e7	−	8.93818e6i	0.913273	−	0.407347i
$865$	−9.07983e6			−0.412608
$866$	6.85375e6	+	3.99265e7i	0.310551	+	1.80912i
$867$	2.17263e7	+	3.13903e6i	0.981609	+	0.141823i
$868$	−1.04201e7	−	4.97443e6i	−0.469433	−	0.224101i
$869$	819875.	+	339603.i	0.0368297	+	0.0152554i
$870$	303200.	+	1.14326e7i	0.0135810	+	0.512090i
$871$	−3.88604e6	+	3.88604e6i	−0.173565	+	0.173565i
$872$	2.45996e7	+	1.94128e7i	1.09556	+	0.864565i
$873$	−2.59708e7	−	7.66455e6i	−1.15332	−	0.340370i
$874$	93169.1	−	411428.i	0.00412566	−	0.0182186i
$875$	7.02092e6	+	2.90816e6i	0.310009	+	0.128410i
$876$	4.80594e6	−	7.19521e6i	0.211601	−	0.316798i
$877$	9.05193e6	+	2.18533e7i	0.397413	+	0.959440i	0.988277	+	0.152669i	$0.0487869\pi$
$877$	9.05193e6	+	2.18533e7i	0.397413	+	0.959440i	−0.590864	+	0.806771i	$0.701213\pi$
$878$	−2.91409e7	−	2.06020e7i	−1.27575	−	0.901932i
$879$	1.33205e7	+	7.91579e6i	0.581497	+	0.345559i
$880$	−4.29035e6	−	453841.i	−0.186761	−	0.0197559i
$881$	−1.41647e7			−0.614846			−0.307423	−	0.951573i	$-0.599467\pi$
$881$	−1.41647e7			−0.614846			−0.307423	+	0.951573i	$0.599467\pi$
$882$	2.27651e6	−	1.93729e7i	0.0985365	−	0.838540i
$883$	3.25103e6	−	1.34662e6i	0.140320	−	0.0581223i	−0.311419	−	0.950273i	$-0.600804\pi$
$883$	3.25103e6	−	1.34662e6i	0.140320	−	0.0581223i	0.451738	+	0.892151i	$0.350804\pi$
$884$	1.49864e6	+	1.66553e6i	0.0645009	+	0.0716837i
$885$	6.89741e6	−	5.15594e6i	0.296025	−	0.221284i
$886$	−2.17331e6	+	9.59719e6i	−0.0930118	+	0.410733i
$887$	1.57093e7	−	1.57093e7i	0.670421	−	0.670421i	−0.287392	−	0.957813i	$-0.592788\pi$
$887$	1.57093e7	−	1.57093e7i	0.670421	−	0.670421i	0.957813	+	0.287392i	$0.0927882\pi$
$888$	−611642.	+	2.33572e7i	−0.0260295	+	0.994006i
$889$	−1.29979e7	−	1.29979e7i	−0.551591	−	0.551591i
$890$	1.50188e7	−	9.47262e6i	0.635564	−	0.400862i
$891$	5.25846e6	+	7.61829e6i	0.221904	+	0.321487i
$892$	−5.27021e6	−	1.48985e7i	−0.221776	−	0.626945i
$893$	802112.	+	1.93647e6i	0.0336594	+	0.0812610i
$894$	−7.47408e6	+	1.94901e7i	−0.312762	+	0.815588i
$895$			1.22717e7i			0.512089i
$896$	3.73276e6	+	8.71639e6i	0.155332	+	0.362716i
$897$	−5.03397e6	−	2.99148e6i	−0.208896	−	0.124138i
$898$	−6.48840e6	−	3.77982e7i	−0.268502	−	1.56416i
$899$	−3.14489e7	+	1.30265e7i	−1.29779	+	0.537564i
$900$	−1.38929e7	−	1.24924e7i	−0.571723	−	0.514089i
$901$	−852964.	+	2.05924e6i	−0.0350041	+	0.0845073i
$902$	5.66763e6	+	8.98598e6i	0.231945	+	0.367747i
$903$	427946.	+	1.68150e6i	0.0174650	+	0.0686243i
$904$	1.97586e7	−	1.10523e7i	0.804148	−	0.449814i
$905$	−9.36153e6	−	9.36153e6i	−0.379949	−	0.379949i
$906$	1.33958e7	+	1.27037e7i	0.542187	+	0.514172i
$907$	6.24659e6	−	1.50806e7i	0.252130	−	0.608696i	−0.746246	−	0.665671i	$-0.768146\pi$
$907$	6.24659e6	−	1.50806e7i	0.252130	−	0.608696i	0.998376	+	0.0569749i	$0.0181455\pi$
$908$	−3.21398e7	+	2.89193e7i	−1.29369	+	1.16406i
$909$	−200920.	−	162368.i	−0.00806515	−	0.00651763i
$910$	4.12092e6	+	2.91341e6i	0.164964	+	0.116627i
$911$		−	3.17820e7i		−	1.26878i	−0.773015	−	0.634388i	$-0.781252\pi$
$911$		−	3.17820e7i		−	1.26878i	0.773015	−	0.634388i	$-0.218748\pi$
$912$	1.23067e6	−	1.64749e6i	0.0489953	−	0.0655897i
$913$		−	3.76139e6i		−	0.149338i
$914$	1.52006e7	−	2.15007e7i	0.601861	−	0.851311i
$915$	−1.29658e7	−	1.87330e6i	−0.511972	−	0.0739700i
$916$	1.31384e6	−	2.49100e7i	0.0517375	−	0.980923i
$917$	−1.78834e6	+	4.31743e6i	−0.0702307	+	0.169552i
$918$	2.23396e6	+	595384.i	0.0874921	+	0.0233180i
$919$	−3.47231e7	−	3.47231e7i	−1.35622	−	1.35622i	−0.878529	−	0.477689i	$-0.841475\pi$
$919$	−3.47231e7	−	3.47231e7i	−1.35622	−	1.35622i	−0.477689	−	0.878529i	$-0.658525\pi$
$920$	1.74458e6	−	2.21070e6i	0.0679549	−	0.0861113i
$921$	−2.31179e7	+	5.88355e6i	−0.898047	+	0.228555i
$922$	−2.79415e7	+	1.76232e7i	−1.08249	+	0.682744i
$923$	1.41030e7	−	3.40476e7i	0.544887	−	1.31547i
$924$	−3.32567e6	+	2.22295e6i	−0.128144	+	0.0856543i
$925$	1.83805e7	−	7.61346e6i	0.706323	−	0.292569i
$926$	−5.29562e6	+	909041.i	−0.202950	+	0.0348382i
$927$	1.88457e7	−	1.02569e7i	0.720298	−	0.392027i
$928$	2.64625e7	+	9.00754e6i	1.00870	+	0.343349i
$929$		−	1.77522e7i		−	0.674859i	−0.941351	−	0.337430i	$-0.890443\pi$
$929$		−	1.77522e7i		−	0.674859i	0.941351	−	0.337430i	$-0.109557\pi$
$930$	−5.98568e6	+	1.56088e7i	−0.226937	+	0.591784i
$931$	−699577.	−	1.68893e6i	−0.0264522	−	0.0638611i
$932$	−2.69598e7	−	1.28702e7i	−1.01666	−	0.485341i
$933$	−3.36293e6	+	2.51385e6i	−0.126478	+	0.0945443i
$934$	−1.05146e6	−	1.66708e6i	−0.0394390	−	0.0625303i
$935$	−321430.	−	321430.i	−0.0120242	−	0.0120242i
$936$	−1.64865e7	−	2.33031e7i	−0.615092	−	0.869409i
$937$	−3.16457e7	+	3.16457e7i	−1.17751	+	1.17751i	−0.197139	+	0.980376i	$0.563165\pi$
$937$	−3.16457e7	+	3.16457e7i	−1.17751	+	1.17751i	−0.980376	+	0.197139i	$0.936835\pi$
$938$	−2.39006e6	−	541237.i	−0.0886957	−	0.0200854i
$939$	−2.82495e7	−	3.77911e7i	−1.04556	−	1.39870i
$940$	−736998.	+	1.39732e7i	−0.0272049	+	0.515794i
$941$	−3.70306e7	+	1.53386e7i	−1.36329	+	0.564692i	−0.939960	−	0.341285i	$-0.889138\pi$
$941$	−3.70306e7	+	1.53386e7i	−1.36329	+	0.564692i	−0.423327	+	0.905977i	$0.639138\pi$
$942$	−7.67635e6	+	3.42081e6i	−0.281856	+	0.125603i
$943$	−6.93484e6			−0.253955
$944$	−5.96454e6	−	2.01856e7i	−0.217845	−	0.737244i
$945$	5.20395e6	+	196615.i	0.189563	+	0.00716205i
$946$	−1.11394e6	+	1.57563e6i	−0.0404700	+	0.0572434i
$947$	−1.07581e7	−	2.59724e7i	−0.389818	−	0.941104i	−0.989978	−	0.141224i	$-0.954896\pi$
$947$	−1.07581e7	−	2.59724e7i	−0.389818	−	0.941104i	0.600160	−	0.799880i	$-0.295104\pi$
$948$	−2.76945e6	+	551358.i	−0.100086	+	0.0199257i
$949$	−1.03996e7	−	4.30765e6i	−0.374844	−	0.155265i
$950$	−1.70773e6	−	386721.i	−0.0613919	−	0.0139024i
$951$	−9.63738e6	−	3.78676e7i	−0.345547	−	1.35774i
$952$	−271669.	+	961418.i	−0.00971512	+	0.0343811i
$953$	1.66544e7	−	1.66544e7i	0.594015	−	0.594015i	−0.344699	−	0.938713i	$-0.612019\pi$
$953$	1.66544e7	−	1.66544e7i	0.594015	−	0.594015i	0.938713	+	0.344699i	$0.112019\pi$
$954$	1.38549e7	−	2.47883e7i	0.492870	−	0.881812i
$955$	−1.76117e7	−	7.29501e6i	−0.624875	−	0.258832i
$956$	6.45054e6	+	1.82352e7i	0.228271	+	0.645306i
$957$	−1.68632e6	+	1.16716e7i	−0.0595197	+	0.411956i
$958$	3.44006e7	−	5.90518e6i	1.21102	−	0.207883i
$959$	1.21226e7			0.425648
$960$	1.21524e7	−	6.38589e6i	0.425583	−	0.223637i
$961$	−2.11280e7			−0.737988
$962$	2.99582e7	−	5.14260e6i	1.04371	−	0.179162i
$963$	−2.69279e7	−	2.17611e7i	−0.935700	−	0.756161i
$964$	−1.63475e7	−	4.62131e7i	−0.566577	−	1.60167i
$965$	1.95225e7	+	8.08650e6i	0.674867	+	0.279539i
$966$	−69224.6	−	2.61022e6i	−0.00238681	−	0.0899981i
$967$	2.39521e7	−	2.39521e7i	0.823716	−	0.823716i	−0.162923	−	0.986639i	$-0.552092\pi$
$967$	2.39521e7	−	2.39521e7i	0.823716	−	0.823716i	0.986639	+	0.162923i	$0.0520922\pi$
$968$	2.37738e7	+	6.71780e6i	0.815474	+	0.230430i
$969$	209976.	−	53439.4i	0.00718391	−	0.00182832i
$970$	−1.65229e7	−	3.74166e6i	−0.563842	−	0.127684i
$971$	−4.14200e7	−	1.71567e7i	−1.40981	−	0.583964i	−0.457534	−	0.889192i	$-0.651267\pi$
$971$	−4.14200e7	−	1.71567e7i	−1.40981	−	0.583964i	−0.952279	+	0.305228i	$0.901267\pi$
$972$	−2.73822e7	−	1.08554e7i	−0.929613	−	0.368536i
$973$	−5.42673e6	−	1.31013e7i	−0.183762	−	0.443641i
$974$	2.95249e7	−	4.17619e7i	0.997221	−	1.41053i
$975$	−1.24169e7	+	2.08947e7i	−0.418312	+	0.703923i
$976$	−1.52976e7	+	2.81297e7i	−0.514041	+	0.945236i
$977$	−4.25055e7			−1.42465			−0.712327	−	0.701848i	$-0.752358\pi$
$977$	−4.25055e7			−1.42465			−0.712327	+	0.701848i	$0.752358\pi$
$978$	1.11442e6	+	2.50077e6i	0.0372564	+	0.0836040i
$979$	1.69158e7	−	7.00676e6i	0.564074	−	0.233647i
$980$	642786.	−	1.21870e7i	0.0213797	−	0.405350i
$981$	−4.43915e6	−	4.18317e7i	−0.147274	−	1.38782i
$982$	1.21446e7	+	2.75017e6i	0.401886	+	0.0910083i
$983$	−8.56707e6	+	8.56707e6i	−0.282780	+	0.282780i	−0.834217	−	0.551437i	$-0.814080\pi$
$983$	−8.56707e6	+	8.56707e6i	−0.282780	+	0.282780i	0.551437	+	0.834217i	$0.314080\pi$
$984$	−3.08831e7	−	1.37500e7i	−1.01679	−	0.452706i
$985$	−5.62021e6	−	5.62021e6i	−0.184570	−	0.184570i
$986$	1.57124e6	+	2.49118e6i	0.0514694	+	0.0816043i
$987$	7.76783e6	+	1.03915e7i	0.253809	+	0.339536i
$988$	−2.41422e6	−	1.15252e6i	−0.0786838	−	0.0375626i
$989$	−482015.	−	1.16369e6i	−0.0156700	−	0.0378308i
$990$	3.58928e6	+	4.54516e6i	0.116391	+	0.147388i
$991$			4.74245e7i			1.53398i	0.641661	+	0.766989i	$0.278246\pi$
$991$			4.74245e7i			1.53398i	−0.641661	+	0.766989i	$0.721754\pi$
$992$	3.06979e7	+	2.69668e7i	0.990443	+	0.870064i
$993$	1.30314e7	−	2.19289e7i	0.419390	−	0.705737i
$994$	1.61961e7	−	2.78021e6i	0.519930	−	0.0892507i
$995$	5.27800e6	−	2.18622e6i	0.169010	−	0.0700061i
$996$	6.65116e6	+	9.95056e6i	0.212446	+	0.317833i
$997$	−1.27050e7	+	3.06727e7i	−0.404797	+	0.977268i	0.581687	+	0.813413i	$0.302393\pi$
$997$	−1.27050e7	+	3.06727e7i	−0.404797	+	0.977268i	−0.986484	+	0.163855i	$0.947607\pi$
$998$	−4.60421e7	+	2.90396e7i	−1.46328	+	0.922921i
$999$	2.30003e7	−	2.13256e7i	0.729154	−	0.676062i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	96.6.o.a.11.4	✓	312
3.2	odd	2	inner	96.6.o.a.11.75	yes	312
32.3	odd	8	inner	96.6.o.a.35.75	yes	312
96.35	even	8	inner	96.6.o.a.35.4	yes	312

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.6.o.a.11.4	✓	312	1.1	even	1	trivial
96.6.o.a.11.75	yes	312	3.2	odd	2	inner
96.6.o.a.35.4	yes	312	96.35	even	8	inner
96.6.o.a.35.75	yes	312	32.3	odd	8	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:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	96.o (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.57531 + 0.957052i) q^{2} +(-15.4283 - 2.22908i) q^{3} +(30.1681 - 10.6717i) q^{4} +(-24.8298 - 10.2848i) q^{5} +(88.1506 - 2.33781i) q^{6} +(36.1711 - 36.1711i) q^{7} +(-157.983 + 88.3705i) q^{8} +(233.062 + 68.7818i) q^{9} +(148.277 + 33.5777i) q^{10} +(144.833 + 59.9918i) q^{11} +(-489.229 + 97.3987i) q^{12} +(248.339 + 599.543i) q^{13} +(-167.047 + 236.282i) q^{14} +(360.154 + 214.025i) q^{15} +(796.229 - 643.891i) q^{16} +107.893 q^{17} +(-1365.22 - 160.427i) q^{18} +(-119.020 + 49.2996i) q^{19} +(-858.824 - 45.2975i) q^{20} +(-638.685 + 477.428i) q^{21} +(-864.903 - 195.860i) q^{22} +(409.317 - 409.317i) q^{23} +(2634.39 - 1011.25i) q^{24} +(-1698.97 - 1698.97i) q^{25} +(-1958.36 - 3104.96i) q^{26} +(-3442.43 - 1580.70i) q^{27} +(705.205 - 1477.22i) q^{28} +(-1846.72 - 4458.38i) q^{29} +(-2212.80 - 848.567i) q^{30} -7053.87i q^{31} +(-3822.98 + 4351.92i) q^{32} +(-2100.79 - 1248.41i) q^{33} +(-601.535 + 103.259i) q^{34} +(-1270.13 + 526.106i) q^{35} +(7765.07 - 412.159i) q^{36} +(-3168.71 + 7649.93i) q^{37} +(616.390 - 388.769i) q^{38} +(-2495.01 - 9803.48i) q^{39} +(4831.56 - 569.391i) q^{40} +(-8471.24 - 8471.24i) q^{41} +(3103.94 - 3273.06i) q^{42} +(832.695 - 2010.30i) q^{43} +(5009.55 + 264.222i) q^{44} +(-5079.48 - 4104.84i) q^{45} +(-1890.33 + 2673.80i) q^{46} -16270.2i q^{47} +(-13719.7 + 8159.25i) q^{48} +14190.3i q^{49} +(11098.3 + 7846.27i) q^{50} +(-1664.60 - 240.502i) q^{51} +(13890.1 + 15436.9i) q^{52} +(-7905.67 + 19086.0i) q^{53} +(20705.4 + 5518.30i) q^{54} +(-2979.16 - 2979.16i) q^{55} +(-2517.96 + 8910.87i) q^{56} +(1946.16 - 495.302i) q^{57} +(14563.0 + 23089.4i) q^{58} +(7866.08 - 18990.4i) q^{59} +(13149.2 + 2613.25i) q^{60} +(-28889.5 + 11966.4i) q^{61} +(6750.92 + 39327.5i) q^{62} +(10918.0 - 5942.21i) q^{63} +(17149.3 - 27922.1i) q^{64} -17440.6i q^{65} +(12907.4 + 4949.72i) q^{66} +(3240.84 + 7824.07i) q^{67} +(3254.92 - 1151.40i) q^{68} +(-7227.45 + 5402.64i) q^{69} +(6577.87 - 4148.79i) q^{70} +(-40156.0 - 40156.0i) q^{71} +(-42898.2 + 9729.49i) q^{72} +(-12265.4 + 12265.4i) q^{73} +(10345.1 - 45683.3i) q^{74} +(22425.0 + 29999.3i) q^{75} +(-3064.49 + 2757.42i) q^{76} +(7408.73 - 3068.80i) q^{77} +(23292.9 + 52269.5i) q^{78} +5660.83 q^{79} +(-26392.5 + 7798.58i) q^{80} +(49587.1 + 32060.9i) q^{81} +(55337.2 + 39122.4i) q^{82} +(-9181.98 - 22167.3i) q^{83} +(-14172.9 + 21219.0i) q^{84} +(-2678.95 - 1109.66i) q^{85} +(-2718.57 + 12005.0i) q^{86} +(18553.6 + 72901.6i) q^{87} +(-28182.7 + 3321.28i) q^{88} +(82586.7 - 82586.7i) q^{89} +(32248.2 + 18024.4i) q^{90} +(30668.8 + 12703.4i) q^{91} +(7980.20 - 16716.4i) q^{92} +(-15723.7 + 108829. i) q^{93} +(15571.4 + 90711.1i) q^{94} +3462.27 q^{95} +(68682.8 - 58620.8i) q^{96} -111433. q^{97} +(-13580.9 - 79115.3i) q^{98} +(29628.8 + 23943.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 312 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9} + 192 q^{10} - 4 q^{12} - 8 q^{13} - 8 q^{15} - 6696 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} + 5576 q^{22} - 11024 q^{24} - 8 q^{25} + 7460 q^{27}+ \cdots + 339516 q^{99}+O(q^{100}) \) 312 * q - 4 * q^3 - 8 * q^4 - 4 * q^6 - 8 * q^7 - 4 * q^9 + 192 * q^10 - 4 * q^12 - 8 * q^13 - 8 * q^15 - 6696 * q^16 - 4 * q^18 - 8 * q^19 - 4 * q^21 + 5576 * q^22 - 11024 * q^24 - 8 * q^25 + 7460 * q^27 - 8 * q^28 + 32564 * q^30 - 8 * q^33 - 264 * q^34 + 3264 * q^36 - 8 * q^37 + 44900 * q^39 - 60136 * q^40 - 7264 * q^42 - 8 * q^43 - 4 * q^45 + 63320 * q^46 + 112368 * q^48 - 976 * q^51 - 55024 * q^52 - 115328 * q^54 - 110056 * q^55 - 4 * q^57 - 123568 * q^58 + 44648 * q^60 - 96168 * q^61 + 187432 * q^64 + 17564 * q^66 + 97848 * q^67 - 4 * q^69 - 143480 * q^70 + 179936 * q^72 - 8 * q^73 + 12496 * q^75 - 234928 * q^76 - 708428 * q^78 + 355344 * q^79 + 251552 * q^82 + 387560 * q^84 - 25008 * q^85 - 282188 * q^87 + 111632 * q^88 + 453536 * q^90 + 200104 * q^91 + 968 * q^93 - 671008 * q^94 - 911336 * q^96 - 16 * q^97 + 339516 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more