LMFDB - Embedded newform 207.4.m.a.4.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,4,Mod(4,207)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([22, 12])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("207.4"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	207.m (of order $33$, degree $20$, 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:	$12.2133953712$
Analytic rank:	$0$
Dimension:	$1400$
Relative dimension:	$70$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			4.1
Character	$\chi$	$=$	207.4
Dual form			207.4.m.a.52.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.26722 + 4.58817i) q^{2} +(-1.71615 + 4.90457i) q^{3} +(-7.76003 - 22.4211i) q^{4} +(-14.9593 + 7.71206i) q^{5} +(-16.8960 - 23.8983i) q^{6} +(12.7056 - 9.99183i) q^{7} +(84.9902 + 24.9554i) q^{8} +(-21.1097 - 16.8339i) q^{9} +(13.4911 - 93.8328i) q^{10} +(31.3146 - 2.99018i) q^{11} +(123.283 + 0.418300i) q^{12} +(-0.231798 - 0.182288i) q^{13} +(4.33206 + 90.9412i) q^{14} +(-12.1520 - 86.6040i) q^{15} +(-242.982 + 191.083i) q^{16} +(-16.4682 - 19.0053i) q^{17} +(146.207 - 41.8547i) q^{18} +(17.0858 - 19.7181i) q^{19} +(288.998 + 275.559i) q^{20} +(27.2009 + 79.4632i) q^{21} +(-88.5923 + 153.446i) q^{22} +(13.2689 - 109.503i) q^{23} +(-268.251 + 374.014i) q^{24} +(91.7979 - 128.912i) q^{25} +(1.59370 - 0.467953i) q^{26} +(118.791 - 74.6445i) q^{27} +(-322.624 - 207.338i) q^{28} +(-63.1077 + 182.338i) q^{29} +(437.057 + 227.199i) q^{30} +(199.404 - 190.132i) q^{31} +(-49.1283 - 1031.33i) q^{32} +(-39.0749 + 158.716i) q^{33} +(141.005 - 13.4643i) q^{34} +(-113.010 + 247.457i) q^{35} +(-213.624 + 603.935i) q^{36} +(-86.1380 + 55.3575i) q^{37} +(34.6468 + 142.816i) q^{38} +(1.29184 - 0.824037i) q^{39} +(-1463.85 + 282.134i) q^{40} +(14.4654 - 7.45746i) q^{41} +(-453.462 - 134.821i) q^{42} +(-267.922 - 255.464i) q^{43} +(-310.046 - 678.905i) q^{44} +(445.610 + 89.0248i) q^{45} +(459.066 + 418.651i) q^{46} +(31.8676 + 55.1963i) q^{47} +(-520.189 - 1519.65i) q^{48} +(-19.2686 + 79.4262i) q^{49} +(291.547 + 842.369i) q^{50} +(121.475 - 48.1536i) q^{51} +(-2.28834 + 6.61173i) q^{52} +(7.57407 + 52.6788i) q^{53} +(-45.6332 + 788.911i) q^{54} +(-445.384 + 286.231i) q^{55} +(1329.21 - 532.134i) q^{56} +(67.3871 + 117.638i) q^{57} +(-630.409 - 885.286i) q^{58} +(133.503 + 104.988i) q^{59} +(-1847.46 + 944.511i) q^{60} +(120.761 + 497.784i) q^{61} +(220.858 + 1536.10i) q^{62} +(-436.414 - 2.96154i) q^{63} +(2812.07 + 1807.21i) q^{64} +(4.87335 + 0.939261i) q^{65} +(-600.552 - 697.844i) q^{66} +(1042.44 + 99.5411i) q^{67} +(-298.327 + 516.717i) q^{68} +(514.295 + 253.002i) q^{69} +(-766.148 - 1327.01i) q^{70} +(-131.998 - 289.035i) q^{71} +(-1374.02 - 1957.52i) q^{72} +(152.288 - 175.750i) q^{73} +(27.4421 - 576.081i) q^{74} +(474.720 + 671.461i) q^{75} +(-574.689 - 230.071i) q^{76} +(367.995 - 350.882i) q^{77} +(-0.439915 + 8.61951i) q^{78} +(917.480 - 367.304i) q^{79} +(2161.20 - 4732.36i) q^{80} +(162.238 + 710.718i) q^{81} +(-13.0457 + 90.7351i) q^{82} +(-562.865 - 290.177i) q^{83} +(1570.57 - 1226.51i) q^{84} +(392.923 + 157.302i) q^{85} +(2047.47 - 394.618i) q^{86} +(-785.986 - 622.434i) q^{87} +(2736.06 + 527.332i) q^{88} +(-460.210 + 135.130i) q^{89} +(-1864.37 + 1753.67i) q^{90} -4.76653 q^{91} +(-2558.15 + 552.243i) q^{92} +(590.308 + 1304.29i) q^{93} +(-357.368 - 34.1245i) q^{94} +(-103.525 + 426.736i) q^{95} +(5142.55 + 1528.96i) q^{96} +(-26.0995 + 547.895i) q^{97} +(-301.466 - 347.910i) q^{98} +(-711.378 - 464.026i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1400 q - 9 q^{2} - 14 q^{3} + 263 q^{4} + 19 q^{5} - 35 q^{6} - 9 q^{7} - 74 q^{8} - 78 q^{9} - 68 q^{10} + 79 q^{11} + 54 q^{12} - 9 q^{13} + 159 q^{14} - 868 q^{15} + 1031 q^{16} - 308 q^{17} - 87 q^{18}+ \cdots + 7484 q^{99}+O(q^{100}) $ 1400 * q - 9 * q^2 - 14 * q^3 + 263 * q^4 + 19 * q^5 - 35 * q^6 - 9 * q^7 - 74 * q^8 - 78 * q^9 - 68 * q^10 + 79 * q^11 + 54 * q^12 - 9 * q^13 + 159 * q^14 - 868 * q^15 + 1031 * q^16 - 308 * q^17 - 87 * q^18 - 36 * q^19 + 119 * q^20 - 660 * q^21 - 52 * q^22 - 116 * q^23 + 2420 * q^24 + 1397 * q^25 + 432 * q^26 + 274 * q^27 - 324 * q^28 - 45 * q^29 + 768 * q^30 - 45 * q^31 + 111 * q^32 - 1664 * q^33 + 403 * q^34 - 536 * q^35 - 121 * q^36 - 180 * q^37 - 117 * q^38 - 46 * q^39 - 473 * q^40 - 333 * q^41 - 332 * q^42 - 9 * q^43 - 1908 * q^44 + 1762 * q^45 + 484 * q^46 + 216 * q^47 + 1072 * q^48 + 4615 * q^49 - 105 * q^50 + 1298 * q^51 - 708 * q^52 - 1380 * q^53 + 4116 * q^54 - 1328 * q^55 - 3971 * q^56 + 2154 * q^57 - 338 * q^58 + 1917 * q^59 + 154 * q^60 + 27 * q^61 - 3854 * q^62 - 4850 * q^63 - 5854 * q^64 + 3363 * q^65 - 2017 * q^66 + 603 * q^67 - 18454 * q^68 - 4653 * q^69 + 542 * q^70 - 5296 * q^71 - 8044 * q^72 - 36 * q^73 + 3243 * q^74 + 5140 * q^75 - 1029 * q^76 - 1661 * q^77 + 14687 * q^78 - 9 * q^79 + 10312 * q^80 - 294 * q^81 - 770 * q^82 - 2735 * q^83 + 2298 * q^84 + 241 * q^85 + 10507 * q^86 - 10268 * q^87 + 2183 * q^88 - 2980 * q^89 + 33928 * q^90 - 1452 * q^91 - 1973 * q^92 - 11406 * q^93 + 2034 * q^94 - 3339 * q^95 - 4446 * q^96 - 5193 * q^97 + 14820 * q^98 + 7484 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−3.26722	+	4.58817i	−1.15514	+	1.62216i	−0.502198	+	0.864753i	$0.667475\pi$
$2$	−3.26722	+	4.58817i	−1.15514	+	1.62216i	−0.652939	+	0.757410i	$0.726464\pi$
$3$	−1.71615	+	4.90457i	−0.330272	+	0.943886i
$3$	−1.71615	+	4.90457i	−0.330272	+	0.943886i
$4$	−7.76003	−	22.4211i	−0.970003	−	2.80264i
$5$	−14.9593	+	7.71206i	−1.33800	+	0.689787i	−0.970695	−	0.240313i	$-0.922750\pi$
$5$	−14.9593	+	7.71206i	−1.33800	+	0.689787i	−0.367306	+	0.930100i	$0.619720\pi$
$6$	−16.8960	−	23.8983i	−1.14963	−	1.62607i
$7$	12.7056	−	9.99183i	0.686040	−	0.539508i	−0.213175	−	0.977014i	$-0.568381\pi$
$7$	12.7056	−	9.99183i	0.686040	−	0.539508i	0.899215	+	0.437506i	$0.144138\pi$
$8$	84.9902	+	24.9554i	3.75607	+	1.10288i
$9$	−21.1097	−	16.8339i	−0.781840	−	0.623479i
$10$	13.4911	−	93.8328i	0.426627	−	2.96725i
$11$	31.3146	−	2.99018i	0.858337	−	0.0819613i	0.343400	−	0.939189i	$-0.388421\pi$
$11$	31.3146	−	2.99018i	0.858337	−	0.0819613i	0.514937	+	0.857228i	$0.327815\pi$
$12$	123.283	+	0.418300i	2.96574	+	0.0100627i
$13$	−0.231798	−	0.182288i	−0.00494532	−	0.00388904i	0.615683	−	0.787994i	$-0.288880\pi$
$13$	−0.231798	−	0.182288i	−0.00494532	−	0.00388904i	−0.620629	+	0.784105i	$0.713123\pi$
$14$	4.33206	+	90.9412i	0.0826994	+	1.73607i
$15$	−12.1520	−	86.6040i	−0.209176	−	1.49074i
$16$	−242.982	+	191.083i	−3.79659	+	2.98567i
$17$	−16.4682	−	19.0053i	−0.234948	−	0.271145i	0.626016	−	0.779810i	$-0.284684\pi$
$17$	−16.4682	−	19.0053i	−0.234948	−	0.271145i	−0.860964	+	0.508665i	$0.830139\pi$
$18$	146.207	−	41.8547i	1.91452	−	0.548069i
$19$	17.0858	−	19.7181i	0.206303	−	0.238087i	−0.643163	−	0.765729i	$-0.722378\pi$
$19$	17.0858	−	19.7181i	0.206303	−	0.238087i	0.849467	+	0.527642i	$0.176924\pi$
$20$	288.998	+	275.559i	3.23109	+	3.08084i
$21$	27.2009	+	79.4632i	0.282654	+	0.825728i
$22$	−88.5923	+	153.446i	−0.858543	+	1.48704i
$23$	13.2689	−	109.503i	0.120294	−	0.992738i
$23$	13.2689	−	109.503i	0.120294	−	0.992738i
$24$	−268.251	+	374.014i	−2.28152	+	3.18105i
$25$	91.7979	−	128.912i	0.734383	−	1.03130i
$26$	1.59370	−	0.467953i	0.0120212	−	0.00352974i
$27$	118.791	−	74.6445i	0.846713	−	0.532050i
$28$	−322.624	−	207.338i	−2.17751	−	1.39940i
$29$	−63.1077	+	182.338i	−0.404097	+	1.16756i	0.541072	+	0.840977i	$0.318019\pi$
$29$	−63.1077	+	182.338i	−0.404097	+	1.16756i	−0.945168	+	0.326584i	$0.894102\pi$
$30$	437.057	+	227.199i	2.65985	+	1.38269i
$31$	199.404	−	190.132i	1.15529	−	1.10157i	0.161899	−	0.986807i	$-0.448238\pi$
$31$	199.404	−	190.132i	1.15529	−	1.10157i	0.993393	−	0.114762i	$-0.0366105\pi$
$32$	−49.1283	−	1031.33i	−0.271398	−	5.69735i
$33$	−39.0749	+	158.716i	−0.206123	+	0.837242i
$34$	141.005	−	13.4643i	0.711239	−	0.0679151i
$35$	−113.010	+	247.457i	−0.545777	+	1.19508i
$36$	−213.624	+	603.935i	−0.988999	+	2.79599i
$37$	−86.1380	+	55.3575i	−0.382730	+	0.245965i	−0.717832	−	0.696216i	$-0.754865\pi$
$37$	−86.1380	+	55.3575i	−0.382730	+	0.245965i	0.335102	+	0.942182i	$0.391229\pi$
$38$	34.6468	+	142.816i	0.147907	+	0.609680i
$39$	1.29184	−	0.824037i	0.00530411	−	0.00338337i
$40$	−1463.85	+	282.134i	−5.78638	+	1.11523i
$41$	14.4654	−	7.45746i	0.0551006	−	0.0284063i	−0.430456	−	0.902612i	$-0.641647\pi$
$41$	14.4654	−	7.45746i	0.0551006	−	0.0284063i	0.485557	+	0.874205i	$0.338617\pi$
$42$	−453.462	−	134.821i	−1.66597	−	0.495319i
$43$	−267.922	−	255.464i	−0.950181	−	0.905996i	0.0454878	−	0.998965i	$-0.485516\pi$
$43$	−267.922	−	255.464i	−0.950181	−	0.905996i	−0.995669	+	0.0929689i	$0.970364\pi$
$44$	−310.046	−	678.905i	−1.06230	−	2.32611i
$45$	445.610	+	89.0248i	1.47617	+	0.294912i
$46$	459.066	+	418.651i	1.47143	+	1.34189i
$47$	31.8676	+	55.1963i	0.0989014	+	0.171302i	0.911230	−	0.411898i	$-0.135134\pi$
$47$	31.8676	+	55.1963i	0.0989014	+	0.171302i	−0.812329	+	0.583200i	$0.801800\pi$
$48$	−520.189	−	1519.65i	−1.56422	−	4.56964i
$49$	−19.2686	+	79.4262i	−0.0561766	+	0.231563i
$50$	291.547	+	842.369i	0.824618	+	2.38258i
$51$	121.475	−	48.1536i	0.333527	−	0.132213i
$52$	−2.28834	+	6.61173i	−0.00610261	+	0.0176323i
$53$	7.57407	+	52.6788i	0.0196298	+	0.136528i	0.997280	−	0.0737119i	$-0.0234845\pi$
$53$	7.57407	+	52.6788i	0.0196298	+	0.136528i	−0.977650	+	0.210240i	$0.932575\pi$
$54$	−45.6332	+	788.911i	−0.114998	+	1.98810i
$55$	−445.384	+	286.231i	−1.09192	+	0.701735i
$56$	1329.21	−	532.134i	3.17183	−	1.26981i
$57$	67.3871	+	117.638i	0.156590	+	0.273360i
$58$	−630.409	−	885.286i	−1.42719	−	2.00420i
$59$	133.503	+	104.988i	0.294587	+	0.231666i	0.754503	−	0.656297i	$-0.227878\pi$
$59$	133.503	+	104.988i	0.294587	+	0.231666i	−0.459916	+	0.887962i	$0.652120\pi$
$60$	−1847.46	+	944.511i	−3.97510	+	2.03226i
$61$	120.761	+	497.784i	0.253473	+	1.04483i	0.946188	+	0.323619i	$0.104899\pi$
$61$	120.761	+	497.784i	0.253473	+	1.04483i	−0.692714	+	0.721212i	$0.743585\pi$
$62$	220.858	+	1536.10i	0.452404	+	3.14654i
$63$	−436.414	−	2.96154i	−0.872746	−	0.00592252i
$64$	2812.07	+	1807.21i	5.49232	+	3.52970i
$65$	4.87335	+	0.939261i	0.00929946	+	0.00179232i
$66$	−600.552	−	697.844i	−1.12004	−	1.30149i
$67$	1042.44	+	99.5411i	1.90081	+	0.181506i	0.978684	−	0.205373i	$-0.0658407\pi$
$67$	1042.44	+	99.5411i	1.90081	+	0.181506i	0.922131	+	0.386879i	$0.126447\pi$
$68$	−298.327	+	516.717i	−0.532021	+	0.921487i
$69$	514.295	+	253.002i	0.897302	+	0.441418i
$70$	−766.148	−	1327.01i	−1.30817	−	2.26582i
$71$	−131.998	−	289.035i	−0.220638	−	0.483130i	0.766651	−	0.642064i	$-0.221922\pi$
$71$	−131.998	−	289.035i	−0.220638	−	0.483130i	−0.987289	+	0.158934i	$0.949194\pi$
$72$	−1374.02	−	1957.52i	−2.24902	−	3.20411i
$73$	152.288	−	175.750i	0.244164	−	0.281780i	−0.620419	−	0.784271i	$-0.713037\pi$
$73$	152.288	−	175.750i	0.244164	−	0.281780i	0.864583	+	0.502490i	$0.167583\pi$
$74$	27.4421	−	576.081i	0.0431092	−	0.904973i
$75$	474.720	+	671.461i	0.730880	+	1.03378i
$76$	−574.689	−	230.071i	−0.867386	−	0.347249i
$77$	367.995	−	350.882i	0.544635	−	0.519309i
$78$	−0.439915	+	8.61951i	−0.000638597	+	0.0125124i
$79$	917.480	−	367.304i	1.30664	−	0.523100i	0.389266	−	0.921125i	$-0.372729\pi$
$79$	917.480	−	367.304i	1.30664	−	0.523100i	0.917374	+	0.398026i	$0.130305\pi$
$80$	2161.20	−	4732.36i	3.02037	−	6.61368i
$81$	162.238	+	710.718i	0.222548	+	0.974922i
$82$	−13.0457	+	90.7351i	−0.0175690	+	0.122195i
$83$	−562.865	−	290.177i	−0.744367	−	0.383748i	0.0439364	−	0.999034i	$-0.486010\pi$
$83$	−562.865	−	290.177i	−0.744367	−	0.383748i	−0.788304	+	0.615286i	$0.789040\pi$
$84$	1570.57	−	1226.51i	2.04004	−	1.59314i
$85$	392.923	+	157.302i	0.501393	+	0.200728i
$86$	2047.47	−	394.618i	2.56726	−	0.494799i
$87$	−785.986	−	622.434i	−0.968582	−	0.767034i
$88$	2736.06	+	527.332i	3.31437	+	0.638793i
$89$	−460.210	+	135.130i	−0.548114	+	0.160941i	−0.544053	−	0.839051i	$-0.683111\pi$
$89$	−460.210	+	135.130i	−0.548114	+	0.160941i	−0.00406123	+	0.999992i	$0.501293\pi$
$90$	−1864.37	+	1753.67i	−2.18357	+	2.05393i
$91$	−4.76653			−0.00549086
$92$	−2558.15	+	552.243i	−2.89897	+	0.625818i
$93$	590.308	+	1304.29i	0.658194	+	1.45428i
$94$	−357.368	−	34.1245i	−0.392125	−	0.0374434i
$95$	−103.525	+	426.736i	−0.111805	+	0.460866i
$96$	5142.55	+	1528.96i	5.46728	+	1.62551i
$97$	−26.0995	+	547.895i	−0.0273196	+	0.573508i	0.943162	+	0.332333i	$0.107836\pi$
$97$	−26.0995	+	547.895i	−0.0273196	+	0.573508i	−0.970482	+	0.241175i	$0.922467\pi$
$98$	−301.466	−	347.910i	−0.310742	−	0.358615i
$99$	−711.378	−	464.026i	−0.722184	−	0.471075i
$100$	−3602.71	−	1057.85i	−3.60271	−	1.05785i
$101$	712.752	+	367.449i	0.702192	+	0.362005i	0.772059	−	0.635551i	$-0.219227\pi$
$101$	712.752	+	367.449i	0.702192	+	0.362005i	−0.0698665	+	0.997556i	$0.522257\pi$
$102$	−175.948	+	714.675i	−0.170798	+	0.693758i
$103$	64.3888	+	90.4213i	0.0615962	+	0.0864998i	0.844225	−	0.535989i	$-0.180061\pi$
$103$	64.3888	+	90.4213i	0.0615962	+	0.0864998i	−0.782629	+	0.622489i	$0.786122\pi$
$104$	−15.1515	−	21.2773i	−0.0142858	−	0.0200616i
$105$	−1019.73	−	978.939i	−0.947768	−	0.909854i
$106$	−266.446	−	137.362i	−0.244146	−	0.125866i
$107$	1312.51	+	385.389i	1.18585	+	0.348196i	0.814425	−	0.580269i	$-0.197052\pi$
$107$	1312.51	+	385.389i	1.18585	+	0.348196i	0.371421	+	0.928465i	$0.378871\pi$
$108$	−2595.43	−	2084.17i	−2.31246	−	1.85694i
$109$	691.046	+	797.509i	0.607249	+	0.700803i	0.973234	−	0.229818i	$-0.0738131\pi$
$109$	691.046	+	797.509i	0.607249	+	0.700803i	−0.365984	+	0.930621i	$0.619268\pi$
$110$	141.892	−	2978.68i	0.122990	−	2.58187i
$111$	−123.680	−	517.472i	−0.105758	−	0.442488i
$112$	−1177.97	+	4855.67i	−0.993821	+	4.09658i
$113$	772.920	+	73.8049i	0.643453	+	0.0614423i	0.411681	−	0.911328i	$-0.364942\pi$
$113$	772.920	+	73.8049i	0.643453	+	0.0614423i	0.231772	+	0.972770i	$0.425548\pi$
$114$	−759.912	−	75.1655i	−0.624318	−	0.0617535i
$115$	646.000	+	1740.42i	0.523825	+	1.41126i
$116$	4577.93			3.66423
$117$	1.82456	+	7.75011i	0.00144171	+	0.00612391i
$118$	−917.887	+	269.516i	−0.716088	+	0.210262i
$119$	−399.137	−	76.9273i	−0.307469	−	0.0592598i
$120$	1128.44	−	7663.75i	0.858430	−	5.83002i
$121$	−335.283	+	64.6205i	−0.251903	+	0.0485504i
$122$	−2678.47	−	1072.30i	−1.98768	−	0.795748i
$123$	11.7508	+	83.7449i	0.00861412	+	0.0613905i
$124$	−5810.35	−	2995.44i	−4.20794	−	2.16934i
$125$	−79.6561	+	554.021i	−0.0569973	+	0.396425i
$126$	1439.45	−	1992.66i	1.01775	−	1.40889i
$127$	937.321	−	2052.45i	0.654912	−	1.43406i	−0.232276	−	0.972650i	$-0.574617\pi$
$127$	937.321	−	2052.45i	0.654912	−	1.43406i	0.887188	−	0.461407i	$-0.152655\pi$
$128$	−9811.10	+	3927.77i	−6.77490	+	2.71226i
$129$	1712.73	−	875.633i	1.16898	−	0.597637i
$130$	−20.2318	+	19.2910i	−0.0136496	+	0.0130149i
$131$	2066.67	+	827.370i	1.37837	+	0.551814i	0.938197	−	0.346101i	$-0.112495\pi$
$131$	2066.67	+	827.370i	1.37837	+	0.551814i	0.440168	+	0.897915i	$0.354919\pi$
$132$	3861.82	−	355.541i	2.54643	−	0.234438i
$133$	20.0666	−	421.250i	0.0130827	−	0.274639i
$134$	−3862.60	+	4457.68i	−2.49013	+	2.87377i
$135$	−1201.36	+	2032.75i	−0.765902	+	1.29594i
$136$	−925.350	−	2026.23i	−0.583442	−	1.27756i
$137$	31.6147	+	54.7582i	0.0197155	+	0.0341482i	0.875715	−	0.482829i	$-0.160391\pi$
$137$	31.6147	+	54.7582i	0.0197155	+	0.0341482i	−0.855999	+	0.516977i	$0.827057\pi$
$138$	−2841.13	+	1533.06i	−1.75256	+	0.945671i
$139$	−104.274	+	180.608i	−0.0636290	+	0.110209i	−0.896085	−	0.443882i	$-0.853601\pi$
$139$	−104.274	+	180.608i	−0.0636290	+	0.110209i	0.832456	+	0.554091i	$0.186934\pi$
$140$	6425.24	+	613.536i	3.87880	+	0.370380i
$141$	−325.404	+	61.5721i	−0.194354	+	0.0367752i
$142$	1757.41	+	338.713i	1.03858	+	0.200170i
$143$	−7.80373	−	5.01516i	−0.00456350	−	0.00293279i
$144$	8345.95	+	56.6363i	4.82983	+	0.0327756i
$145$	−462.152	−	3214.33i	−0.264687	−	1.84094i
$146$	308.811	+	1272.94i	0.175051	+	0.721569i
$147$	−356.484	−	230.811i	−0.200016	−	0.129503i
$148$	1909.61	+	1501.73i	1.06060	+	0.834066i
$149$	−1261.78	−	1771.92i	−0.693750	−	0.974236i	−0.999753	−	0.0222052i	$-0.992931\pi$
$149$	−1261.78	−	1771.92i	−0.693750	−	0.974236i	0.306003	−	0.952030i	$-0.401008\pi$
$150$	−4631.80	−	15.7157i	−2.52123	−	0.00855453i
$151$	1624.38	−	650.305i	0.875433	−	0.350471i	0.109958	−	0.993936i	$-0.464928\pi$
$151$	1624.38	−	650.305i	0.875433	−	0.350471i	0.765475	+	0.643466i	$0.222504\pi$
$152$	1944.20	−	1249.46i	1.03747	−	0.666742i
$153$	27.7044	+	678.420i	0.0146390	+	0.358477i
$154$	407.588	+	2834.83i	0.213275	+	1.48336i
$155$	−1516.64	+	4382.05i	−0.785934	+	2.27081i
$156$	−28.5006	−	22.5700i	−0.0146274	−	0.0115836i
$157$	−224.220	−	647.841i	−0.113979	−	0.329320i	0.873555	−	0.486725i	$-0.161809\pi$
$157$	−224.220	−	647.841i	−0.113979	−	0.329320i	−0.987534	+	0.157404i	$0.949687\pi$
$158$	−1312.36	+	5409.62i	−0.660795	+	2.72383i
$159$	−271.365	−	53.2570i	−0.135350	−	0.0265632i
$160$	8688.60	+	15049.1i	4.29309	+	7.43585i
$161$	−925.546	−	1523.89i	−0.453064	−	0.745958i
$162$	−3790.96	−	1577.70i	−1.83856	−	0.765159i
$163$	−1243.32	−	2722.49i	−0.597450	−	1.30823i	−0.930834	−	0.365442i	$-0.880918\pi$
$163$	−1243.32	−	2722.49i	−0.597450	−	1.30823i	0.333384	−	0.942791i	$-0.391810\pi$
$164$	−279.457	−	266.462i	−0.133060	−	0.126873i
$165$	−639.497	−	2675.64i	−0.301726	−	1.26241i
$166$	3170.39	−	1634.45i	1.48235	−	0.764204i
$167$	2558.81	−	493.170i	1.18567	−	0.228519i	0.441967	−	0.897031i	$-0.354281\pi$
$167$	2558.81	−	493.170i	1.18567	−	0.228519i	0.743701	+	0.668512i	$0.233069\pi$
$168$	328.778	+	7432.40i	0.150987	+	3.41323i
$169$	−517.942	−	2134.99i	−0.235750	−	0.971773i
$170$	−2005.50	+	1288.85i	−0.904791	+	0.581474i
$171$	−692.610	+	128.621i	−0.309738	+	0.0575200i
$172$	−3648.69	+	7989.53i	−1.61750	+	3.54184i
$173$	−73.0540	+	6.97581i	−0.0321052	+	0.00306567i	−0.111096	−	0.993810i	$-0.535436\pi$
$173$	−73.0540	+	6.97581i	−0.0321052	+	0.00306567i	0.0789911	+	0.996875i	$0.474830\pi$
$174$	5423.83	−	1572.61i	2.36310	−	0.685168i
$175$	−121.716	−	2555.14i	−0.0525765	−	1.10372i
$176$	−7037.51	+	6710.26i	−3.01405	+	2.87389i
$177$	−744.032	+	474.601i	−0.315960	+	0.201544i
$178$	883.609	−	2553.02i	0.372075	−	1.07504i
$179$	−1135.97	−	730.043i	−0.474337	−	0.304838i	0.281542	−	0.959549i	$-0.409154\pi$
$179$	−1135.97	−	730.043i	−0.474337	−	0.304838i	−0.755879	+	0.654711i	$0.772790\pi$
$180$	−1461.91	−	10681.9i	−0.605359	−	4.42324i
$181$	1124.00	−	330.036i	0.461581	−	0.135533i	−0.0426704	−	0.999089i	$-0.513587\pi$
$181$	1124.00	−	330.036i	0.461581	−	0.135533i	0.504252	+	0.863557i	$0.331768\pi$
$182$	15.5733	−	21.8696i	0.00634269	−	0.00890707i
$183$	−2648.66	−	261.988i	−1.06992	−	0.105829i
$184$	3860.42	−	8975.56i	1.54671	−	3.59613i
$185$	861.644	−	1492.41i	0.342429	−	0.593104i
$186$	−7912.95	−	1552.96i	−3.11939	−	0.612197i
$187$	−572.524	−	545.901i	−0.223888	−	0.213477i
$188$	990.269	−	1142.83i	0.384164	−	0.443349i
$189$	763.475	−	2135.34i	0.293834	−	0.821816i
$190$	−1619.70	−	1869.23i	−0.618449	−	0.713728i
$191$	−558.543	+	439.243i	−0.211595	+	0.166400i	−0.718332	−	0.695700i	$-0.755094\pi$
$191$	−558.543	+	439.243i	−0.211595	+	0.166400i	0.506737	+	0.862101i	$0.330852\pi$
$192$	−13689.5	+	10690.6i	−5.14559	+	4.01836i
$193$	−76.0736	−	1596.98i	−0.0283725	−	0.595613i	−0.967626	−	0.252388i	$-0.918784\pi$
$193$	−76.0736	−	1596.98i	−0.0283725	−	0.595613i	0.939253	−	0.343224i	$-0.111519\pi$
$194$	−2428.56	−	1909.84i	−0.898766	−	0.706798i
$195$	−12.9701	+	22.2898i	−0.00476310	+	0.00818567i
$196$	1930.35	−	184.326i	0.703480	−	0.0671742i
$197$	256.971	−	1787.27i	0.0929361	−	0.646384i	−0.889103	−	0.457707i	$-0.848671\pi$
$197$	256.971	−	1787.27i	0.0929361	−	0.646384i	0.982039	−	0.188677i	$-0.0604201\pi$
$198$	4453.26	−	1747.85i	1.59838	−	0.627344i
$199$	−2814.69	−	826.466i	−1.00265	−	0.294405i	−0.261108	−	0.965310i	$-0.584088\pi$
$199$	−2814.69	−	826.466i	−1.00265	−	0.294405i	−0.741544	+	0.670904i	$0.765906\pi$
$200$	11019.0	−	8665.42i	3.89580	−	3.06369i
$201$	−2277.19	+	4941.91i	−0.799107	+	1.73421i
$202$	−4014.64	+	2069.69i	−1.39836	+	0.720905i
$203$	1020.06	+	2947.28i	0.352682	+	1.01901i
$204$	−2022.30	−	2349.93i	−0.694067	−	0.806509i
$205$	−158.881	+	223.117i	−0.0541303	+	0.0760154i
$206$	−625.241			−0.211469
$207$	−2123.47	+	2088.21i	−0.713002	+	0.701162i
$208$	91.1548			0.0303868
$209$	476.076	−	668.555i	0.157564	−	0.221268i
$210$	7823.23	−	1480.29i	2.57073	−	0.486428i
$211$	1011.23	+	2921.76i	0.329934	+	0.953281i	0.980957	+	0.194223i	$0.0622187\pi$
$211$	1011.23	+	2921.76i	0.329934	+	0.953281i	−0.651024	+	0.759057i	$0.725660\pi$
$212$	1122.34	−	578.608i	0.363598	−	0.187448i
$213$	1644.12	−	151.367i	0.528890	−	0.0486925i
$214$	−6056.50	+	4762.89i	−1.93465	+	1.52142i
$215$	5978.08	+	1755.32i	1.89629	+	0.556800i
$216$	11958.8	−	3379.59i	3.76710	−	1.06459i
$217$	633.797	−	4408.16i	0.198272	−	1.37901i
$218$	−5916.91	+	564.996i	−1.83827	+	0.175534i
$219$	600.630	+	1048.52i	0.185328	+	0.323527i
$220$	9873.82	+	7764.86i	3.02588	+	2.37958i
$221$	0.352855	+	7.40734i	0.000107401	+	0.00225462i
$222$	2778.34	+	1123.23i	0.839954	+	0.339578i
$223$	2097.47	−	1649.47i	0.629853	−	0.495322i	−0.251452	−	0.967870i	$-0.580908\pi$
$223$	2097.47	−	1649.47i	0.629853	−	0.495322i	0.881305	+	0.472548i	$0.156666\pi$
$224$	−10929.1	−	12612.8i	−3.25995	−	3.76219i
$225$	−4107.92	+	1175.97i	−1.21716	+	0.348437i
$226$	−2863.93	+	3305.15i	−0.842946	+	0.972811i
$227$	−1569.60	−	1496.61i	−0.458933	−	0.437592i	0.425009	−	0.905189i	$-0.360271\pi$
$227$	−1569.60	−	1496.61i	−0.458933	−	0.437592i	−0.883941	+	0.467598i	$0.845120\pi$
$228$	2114.65	−	2423.77i	0.614237	−	0.704026i
$229$	−1650.59	+	2858.91i	−0.476306	+	0.824987i	−0.999631	−	0.0271462i	$-0.991358\pi$
$229$	−1650.59	+	2858.91i	−0.476306	+	0.824987i	0.523325	+	0.852133i	$0.324691\pi$
$230$	−10096.0	−	2722.38i	−2.89439	−	0.780472i
$231$	1089.40	+	2407.02i	0.310290	+	0.685587i
$232$	−9913.84	+	13922.0i	−2.80550	+	3.93977i
$233$	−1631.21	+	478.966i	−0.458644	+	0.134670i	−0.502890	−	0.864351i	$-0.667730\pi$
$233$	−1631.21	+	478.966i	−0.458644	+	0.134670i	0.0442456	+	0.999021i	$0.485912\pi$
$234$	−41.5200	−	16.9499i	−0.0115994	−	0.00473526i
$235$	−902.394	−	579.933i	−0.250492	−	0.160982i
$236$	1317.96	−	3808.00i	0.363525	−	1.05034i
$237$	226.938	+	5130.19i	0.0621991	+	1.40608i
$238$	1657.02	−	1579.97i	0.451298	−	0.430311i
$239$	6.22282	+	130.633i	0.00168419	+	0.0353554i	0.999553	−	0.0298967i	$-0.00951785\pi$
$239$	6.22282	+	130.633i	0.00168419	+	0.0353554i	−0.997869	+	0.0652522i	$0.979215\pi$
$240$	19501.3	+	18721.2i	5.24501	+	5.03519i
$241$	6046.40	−	577.362i	1.61611	−	0.154320i	0.752541	−	0.658546i	$-0.228828\pi$
$241$	6046.40	−	577.362i	1.61611	−	0.154320i	0.863572	+	0.504226i	$0.168222\pi$
$242$	798.954	−	1749.47i	0.212226	−	0.464710i
$243$	−3764.19	−	423.989i	−0.993716	−	0.111930i
$244$	10223.8	−	6570.41i	2.68241	−	1.72388i
$245$	−324.295	−	1336.76i	−0.0845650	−	0.348582i
$246$	−422.629	−	219.698i	−0.109536	−	0.0569409i
$247$	−7.55483	+	1.45608i	−0.00194616	+	0.000375092i
$248$	21692.2	−	11183.1i	5.55426	−	2.86342i
$249$	2389.15	−	2262.63i	0.608058	−	0.575856i
$250$	−2281.69	−	2175.58i	−0.577226	−	0.550384i
$251$	1722.54	+	3771.83i	0.433170	+	0.948510i	0.992802	+	0.119769i	$0.0382153\pi$
$251$	1722.54	+	3771.83i	0.433170	+	0.948510i	−0.559632	+	0.828741i	$0.689057\pi$
$252$	3320.18	+	9807.87i	0.829967	+	2.45174i
$253$	88.0772	−	3468.72i	0.0218868	−	0.861964i
$254$	6354.54	+	11006.4i	1.56976	+	2.71891i
$255$	−1445.81	+	1657.16i	−0.355060	+	0.406963i
$256$	7729.15	−	31860.0i	1.88700	−	7.77832i
$257$	382.772	+	1105.95i	0.0929053	+	0.268432i	0.981874	−	0.189536i	$-0.0606984\pi$
$257$	382.772	+	1105.95i	0.0929053	+	0.268432i	−0.888968	+	0.457969i	$0.848577\pi$
$258$	−1578.33	+	10719.2i	−0.380862	+	2.58662i
$259$	−541.315	+	1564.03i	−0.129868	+	0.375228i
$260$	−16.7580	−	116.555i	−0.00399727	−	0.0278016i
$261$	4401.64	−	2786.74i	1.04389	−	0.660900i
$262$	−10548.4	+	6779.03i	−2.48733	+	1.59851i
$263$	−3443.02	+	1378.38i	−0.807246	+	0.323173i	−0.738321	−	0.674449i	$-0.764381\pi$
$263$	−3443.02	+	1378.38i	−0.807246	+	0.323173i	−0.0689249	+	0.997622i	$0.521957\pi$
$264$	−7281.81	+	12514.2i	−1.69759	+	2.91741i
$265$	−519.565	−	729.627i	−0.120440	−	0.169134i
$266$	1867.21	+	1468.39i	0.430397	+	0.338468i
$267$	127.033	−	2489.04i	0.0291173	−	0.570511i
$268$	−5857.55	−	24145.2i	−1.33510	−	5.50336i
$269$	−237.269	−	1650.24i	−0.0537789	−	0.374041i	−0.998882	−	0.0472689i	$-0.984948\pi$
$269$	−237.269	−	1650.24i	−0.0537789	−	0.374041i	0.945103	−	0.326772i	$-0.105961\pi$
$270$	−5401.49	−	12153.5i	−1.21750	−	2.73940i
$271$	3301.50	+	2121.75i	0.740045	+	0.475598i	0.855557	−	0.517708i	$-0.173215\pi$
$271$	3301.50	+	2121.75i	0.740045	+	0.475598i	−0.115513	+	0.993306i	$0.536851\pi$
$272$	7633.06	+	1471.15i	1.70155	+	0.327948i
$273$	8.18006	−	23.3778i	0.00181348	−	0.00518274i
$274$	−354.532	−	33.8537i	−0.0781681	−	0.00746415i
$275$	2489.14	−	4311.33i	0.545822	−	0.945392i
$276$	1681.64	−	13494.4i	0.366750	−	2.94299i
$277$	−2284.06	−	3956.10i	−0.495436	−	0.858120i	0.504550	−	0.863382i	$-0.331658\pi$
$277$	−2284.06	−	3956.10i	−0.495436	−	0.858120i	−0.999986	+	0.00526237i	$0.998325\pi$
$278$	−487.975	−	1068.52i	−0.105276	−	0.230523i
$279$	−7410.02	+	656.861i	−1.59006	+	0.140951i
$280$	−15780.1	+	18211.3i	−3.36801	+	3.88690i
$281$	15.2647	−	320.445i	0.00324063	−	0.0680291i	−0.996668	−	0.0815689i	$-0.974007\pi$
$281$	15.2647	−	320.445i	0.00324063	−	0.0680291i	0.999908	+	0.0135398i	$0.00430998\pi$
$282$	780.663	−	1694.18i	0.164850	−	0.357754i
$283$	3407.14	+	1364.01i	0.715667	+	0.286510i	0.700778	−	0.713379i	$-0.252836\pi$
$283$	3407.14	+	1364.01i	0.715667	+	0.286510i	0.0148887	+	0.999889i	$0.495261\pi$
$284$	−5456.19	+	5202.47i	−1.14002	+	1.08701i
$285$	−1915.30	−	1240.09i	−0.398078	−	0.257742i
$286$	48.5069	−	19.4192i	0.0100289	−	0.00401498i
$287$	109.279	−	239.288i	0.0224758	−	0.0492151i
$288$	−16324.3	+	22598.1i	−3.33999	+	4.62363i
$289$	609.193	−	4237.03i	0.123996	−	0.862411i
$290$	16257.9	+	8381.51i	3.29205	+	1.69717i
$291$	−2642.40	−	1068.27i	−0.532303	−	0.215201i
$292$	−5122.27	−	2050.65i	−1.02657	−	0.410976i
$293$	7031.36	−	1355.18i	1.40197	−	0.270207i	0.568458	−	0.822712i	$-0.307540\pi$
$293$	7031.36	−	1355.18i	1.40197	−	0.270207i	0.833510	+	0.552505i	$0.186328\pi$
$294$	2223.71	−	881.498i	0.441121	−	0.174864i
$295$	−2806.79	−	540.964i	−0.553958	−	0.106767i
$296$	−8702.35	+	2555.24i	−1.70883	+	0.501758i
$297$	3496.68	−	2692.67i	0.683158	−	0.526076i
$298$	12252.4			2.38175
$299$	−23.0368	+	22.9638i	−0.00445569	+	0.00444158i
$300$	11371.1	−	15854.3i	2.18837	−	3.05117i
$301$	−5956.67	−	568.793i	−1.14065	−	0.108919i
$302$	−2323.51	+	9577.64i	−0.442725	+	1.82494i
$303$	−3025.37	+	2865.15i	−0.573606	+	0.543229i
$304$	−383.753	+	8055.96i	−0.0724004	+	1.51987i
$305$	−5645.44	−	6515.18i	−1.05986	−	1.22314i
$306$	−3203.22	−	2089.44i	−0.598419	−	0.390344i
$307$	7726.71	+	2268.77i	1.43644	+	0.421776i	0.905033	−	0.425341i	$-0.139846\pi$
$307$	7726.71	+	2268.77i	1.43644	+	0.421776i	0.531405	+	0.847118i	$0.321664\pi$
$308$	−10722.8	−	5528.00i	−1.98373	−	1.02269i
$309$	−553.979	+	160.623i	−0.101989	+	0.0295713i
$310$	−15150.4	−	21275.8i	−2.77576	−	3.89801i
$311$	1872.84	+	2630.04i	0.341476	+	0.479536i	0.949227	−	0.314591i	$-0.101867\pi$
$311$	1872.84	+	2630.04i	0.341476	+	0.479536i	−0.607751	+	0.794128i	$0.707928\pi$
$312$	130.358	−	37.7967i	0.0236541	−	0.00685838i
$313$	5181.13	+	2671.06i	0.935639	+	0.482355i	0.857441	−	0.514583i	$-0.172053\pi$
$313$	5181.13	+	2671.06i	0.935639	+	0.482355i	0.0781978	+	0.996938i	$0.475083\pi$
$314$	3704.98	+	1087.88i	0.665873	+	0.195518i
$315$	6551.29	−	3321.35i	1.17182	−	0.594085i
$316$	−15355.0	−	17720.6i	−2.73351	−	3.15463i
$317$	81.8356	−	1717.94i	0.0144995	−	0.304382i	−0.979955	−	0.199218i	$-0.936160\pi$
$317$	81.8356	−	1717.94i	0.0144995	−	0.304382i	0.994455	−	0.105165i	$-0.0335370\pi$
$318$	1130.96	−	1071.07i	0.199438	−	0.188876i
$319$	−1430.97	+	5898.54i	−0.251156	+	1.03528i
$320$	−56003.9	−	5347.72i	−9.78347	−	0.934208i
$321$	−4142.63	+	5775.94i	−0.720309	+	1.00430i
$322$	10015.8	+	732.318i	1.73342	+	0.126741i
$323$	−656.122			−0.113027
$324$	14676.1	−	9152.74i	2.51648	−	1.56940i
$325$	−44.7777	+	13.1479i	−0.00764252	+	0.00224405i
$326$	16553.5	+	3190.42i	2.81231	+	0.542027i
$327$	−5097.38	+	2020.64i	−0.862035	+	0.341718i
$328$	1415.53	−	272.820i	0.238291	−	0.0459267i
$329$	956.410	+	382.889i	0.160269	+	0.0641621i
$330$	14365.6	+	5807.77i	2.39637	+	0.968810i
$331$	2298.37	+	1184.89i	0.381662	+	0.196760i	0.638372	−	0.769728i	$-0.279608\pi$
$331$	2298.37	+	1184.89i	0.381662	+	0.196760i	−0.256710	+	0.966488i	$0.582639\pi$
$332$	−2138.25	+	14871.9i	−0.353469	+	2.45843i
$333$	2750.23	+	281.461i	0.452588	+	0.0463182i
$334$	−6097.45	+	13351.6i	−0.998915	+	2.18732i
$335$	−16361.9	+	6550.31i	−2.66849	+	1.06830i
$336$	−21793.4	−	14110.5i	−3.53848	−	2.29104i
$337$	−3276.65	+	3124.28i	−0.529646	+	0.505017i	−0.907045	−	0.421034i	$-0.861667\pi$
$337$	−3276.65	+	3124.28i	−0.529646	+	0.505017i	0.377399	+	0.926051i	$0.376819\pi$
$338$	11487.9	+	4599.06i	1.84870	+	0.740107i
$339$	−1688.42	+	3664.18i	−0.270509	+	0.587053i
$340$	477.809	−	10030.4i	0.0762142	−	1.59993i
$341$	5675.74	−	6550.15i	0.901345	−	1.04021i
$342$	1672.77	−	3598.05i	0.264483	−	0.568889i
$343$	2851.94	+	6244.87i	0.448951	+	0.983065i
$344$	−16395.6	−	28398.0i	−2.56974	−	4.45092i
$345$	−9644.66	+	181.539i	−1.50508	+	0.0283297i
$346$	206.677	−	357.976i	0.0321128	−	0.0556211i
$347$	2652.56	+	253.289i	0.410365	+	0.0391851i	0.298198	−	0.954504i	$-0.403615\pi$
$347$	2652.56	+	253.289i	0.410365	+	0.0391851i	0.112168	+	0.993689i	$0.464221\pi$
$348$	−7856.40	+	22452.8i	−1.21019	+	3.45861i
$349$	−3315.38	−	638.988i	−0.508506	−	0.0980064i	−0.0714558	−	0.997444i	$-0.522764\pi$
$349$	−3315.38	−	638.988i	−0.508506	−	0.0980064i	−0.437050	+	0.899437i	$0.643977\pi$
$350$	12121.1	+	7789.75i	1.85114	+	1.18966i
$351$	−41.1422	−	4.35163i	−0.00625643	−	0.000661746i
$352$	−4622.30	−	32148.8i	−0.699913	−	4.86800i
$353$	−1249.17	−	5149.13i	−0.188347	−	0.776376i	−0.985087	−	0.172055i	$-0.944959\pi$
$353$	−1249.17	−	5149.13i	−0.188347	−	0.776376i	0.796741	−	0.604321i	$-0.206556\pi$
$354$	253.367	−	4964.37i	0.0380404	−	0.745349i
$355$	4203.66	+	3305.79i	0.628470	+	0.494235i
$356$	6601.00	+	9269.81i	0.982732	+	1.38005i
$357$	1062.27	−	1825.58i	0.157483	−	0.270644i
$358$	7061.03	−	2826.81i	1.04242	−	0.417323i
$359$	−394.502	+	253.531i	−0.0579973	+	0.0372726i	−0.569318	−	0.822117i	$-0.692793\pi$
$359$	−394.502	+	253.531i	−0.0579973	+	0.0372726i	0.511321	+	0.859390i	$0.329156\pi$
$360$	35650.9	+	18686.6i	5.21935	+	2.73575i
$361$	879.259	+	6115.38i	0.128191	+	0.891585i
$362$	−2158.09	+	6235.40i	−0.313334	+	0.905319i
$363$	258.459	−	1755.32i	0.0373707	−	0.253803i
$364$	36.9884	+	106.871i	0.00532615	+	0.0153889i
$365$	−922.732	+	3803.55i	−0.132323	+	0.545444i
$366$	9855.80	−	11296.5i	1.40757	−	1.61333i
$367$	−5383.40	−	9324.32i	−0.765698	−	1.32623i	−0.939877	−	0.341513i	$-0.889061\pi$
$367$	−5383.40	−	9324.32i	−0.765698	−	1.32623i	0.174179	−	0.984714i	$-0.444273\pi$
$368$	17700.1	+	29142.8i	2.50729	+	4.12818i
$369$	−430.899	−	86.0858i	−0.0607906	−	0.0121448i
$370$	4032.25	+	8829.40i	0.566559	+	1.24059i
$371$	622.591	+	593.639i	0.0871249	+	0.0830734i
$372$	24662.8	−	23356.7i	3.43738	−	3.25534i
$373$	3008.11	−	1550.79i	0.417571	−	0.215273i	−0.236620	−	0.971602i	$-0.576040\pi$
$373$	3008.11	−	1550.79i	0.417571	−	0.215273i	0.654191	+	0.756329i	$0.273009\pi$
$374$	4375.25	−	843.260i	0.604916	−	0.116588i
$375$	−2580.53	−	1341.46i	−0.355355	−	0.184727i
$376$	1330.99	+	5486.41i	0.182555	+	0.752500i
$377$	47.8662	−	30.7617i	0.00653908	−	0.00420241i
$378$	7302.87	+	10479.6i	0.993701	+	1.42596i
$379$	−430.673	+	943.043i	−0.0583699	+	0.127812i	−0.936569	−	0.350482i	$-0.886018\pi$
$379$	−430.673	+	943.043i	−0.0583699	+	0.127812i	0.878199	+	0.478295i	$0.158745\pi$
$380$	10371.3	−	990.336i	1.40009	−	0.133693i
$381$	8457.80	+	8119.46i	1.13729	+	1.09179i
$382$	−190.438	−	3997.79i	−0.0255070	−	0.535458i
$383$	4853.45	−	4627.76i	0.647519	−	0.617409i	−0.293420	−	0.955984i	$-0.594793\pi$
$383$	4853.45	−	4627.76i	0.647519	−	0.617409i	0.940939	+	0.338575i	$0.109945\pi$
$384$	−2426.77	−	54859.9i	−0.322501	−	7.29051i
$385$	−2798.92	+	8086.96i	−0.370510	+	1.07052i
$386$	7575.77	+	4868.65i	0.998955	+	0.641989i
$387$	1355.30	+	9902.94i	0.178021	+	1.30076i
$388$	12487.0	−	3666.50i	1.63384	−	0.479738i
$389$	2137.80	−	3002.12i	0.278639	−	0.391294i	−0.651412	−	0.758724i	$-0.725823\pi$
$389$	2137.80	−	3002.12i	0.278639	−	0.391294i	0.930051	+	0.367430i	$0.119762\pi$
$390$	−59.8933	−	132.334i	−0.00777645	−	0.0171821i
$391$	−2299.66	+	1551.14i	−0.297439	+	0.200625i
$392$	−3619.75	+	6269.60i	−0.466391	+	0.807812i
$393$	−7604.61	+	8716.25i	−0.976085	+	1.11877i
$394$	7360.72	+	7018.43i	0.941187	+	0.897420i
$395$	−10892.2	+	12570.3i	−1.38746	+	1.60121i
$396$	−4883.67	+	19550.8i	−0.619732	+	2.48097i
$397$	8482.27	+	9789.06i	1.07233	+	1.23753i	0.970084	+	0.242769i	$0.0780558\pi$
$397$	8482.27	+	9789.06i	1.07233	+	1.23753i	0.102241	+	0.994760i	$0.467399\pi$
$398$	12988.2	−	10214.0i	1.63577	−	1.28639i
$399$	2031.62	+	821.345i	0.254907	+	0.103054i
$400$	2327.70	+	48864.3i	0.290962	+	6.10804i
$401$	−6826.07	−	5368.08i	−0.850069	−	0.668502i	0.0949622	−	0.995481i	$-0.469727\pi$
$401$	−6826.07	−	5368.08i	−0.850069	−	0.668502i	−0.945032	+	0.326979i	$0.893969\pi$
$402$	−15234.2	−	26594.4i	−1.89008	−	3.29953i
$403$	−80.8802	+	7.72312i	−0.00999734	+	0.000954630i
$404$	2707.65	−	18832.1i	0.333442	−	2.31914i
$405$	−7908.06	−	9380.66i	−0.970259	−	1.15094i
$406$	−16855.4	−	4949.19i	−2.06039	−	0.604985i
$407$	−2531.85	+	1991.07i	−0.308351	+	0.242490i
$408$	11525.9	−	1061.13i	1.39857	−	0.128760i
$409$	−7355.11	+	3791.82i	−0.889210	+	0.458420i	−0.841385	−	0.540436i	$-0.818259\pi$
$409$	−7355.11	+	3791.82i	−0.889210	+	0.458420i	−0.0478250	+	0.998856i	$0.515229\pi$
$410$	−504.599	−	1457.94i	−0.0607814	−	0.175616i
$411$	−322.821	+	61.0834i	−0.0387435	+	0.00733095i
$412$	1527.69	−	2145.34i	0.182679	−	0.256537i
$413$	2745.26			0.327084
$414$	−2643.21	−	16565.5i	−0.313784	−	1.96654i
$415$	10657.9			1.26067
$416$	−176.611	+	248.016i	−0.0208151	+	0.0292307i
$417$	−706.857	−	821.371i	−0.0830094	−	0.0964574i
$418$	1512.00	+	4368.63i	0.176924	+	0.511189i
$419$	6806.78	−	3509.14i	0.793635	−	0.409147i	−0.0132085	−	0.999913i	$-0.504205\pi$
$419$	6806.78	−	3509.14i	0.793635	−	0.409147i	0.806843	+	0.590766i	$0.201174\pi$
$420$	−14035.8	+	30460.1i	−1.63066	+	3.53881i
$421$	−8630.48	+	6787.09i	−0.999107	+	0.785706i	−0.976824	−	0.214045i	$-0.931336\pi$
$421$	−8630.48	+	6787.09i	−0.999107	+	0.785706i	−0.0222831	+	0.999752i	$0.507094\pi$
$422$	−16709.4	−	4906.34i	−1.92750	−	0.565964i
$423$	256.455	−	1701.63i	0.0294782	−	0.195594i
$424$	−670.898	+	4666.20i	−0.0768436	+	0.534459i
$425$	−3961.76	+	378.302i	−0.452173	+	0.0431773i
$426$	−4677.22	+	8038.07i	−0.531953	+	0.914192i
$427$	6508.11	+	5118.04i	0.737587	+	0.580045i
$428$	−1544.29	−	32418.7i	−0.174407	−	3.66125i
$429$	37.9895	−	29.6673i	0.00427541	−	0.00333881i
$430$	−27585.4	+	21693.4i	−3.09369	+	2.43291i
$431$	−4996.85	−	5766.67i	−0.558445	−	0.644479i	0.404385	−	0.914589i	$-0.367486\pi$
$431$	−4996.85	−	5766.67i	−0.558445	−	0.644479i	−0.962830	+	0.270109i	$0.912940\pi$
$432$	−14600.7	+	40836.1i	−1.62610	+	4.54799i
$433$	−5453.86	+	6294.09i	−0.605302	+	0.698555i	−0.972847	−	0.231450i	$-0.925653\pi$
$433$	−5453.86	+	6294.09i	−0.605302	+	0.698555i	0.367545	+	0.930006i	$0.380198\pi$
$434$	18154.6	+	17310.4i	2.00795	+	1.91457i
$435$	16558.1	+	3249.61i	1.82505	+	0.358177i
$436$	12518.5	−	21682.7i	1.37506	−	2.38168i
$437$	−1932.48	−	2132.59i	−0.211541	−	0.233446i
$438$	−6773.18	−	669.959i	−0.738893	−	0.0730865i
$439$	9522.96	−	13373.1i	1.03532	−	1.45391i	0.150136	−	0.988665i	$-0.452029\pi$
$439$	9522.96	−	13373.1i	1.03532	−	1.45391i	0.885185	−	0.465240i	$-0.154032\pi$
$440$	−44996.3	+	13212.1i	−4.87526	+	1.43151i
$441$	1743.81	−	1352.30i	0.188296	−	0.146021i
$442$	−35.1390	−	22.5825i	−0.00378143	−	0.00243018i
$443$	−4715.17	+	13623.6i	−0.505699	+	1.46112i	0.346573	+	0.938023i	$0.387345\pi$
$443$	−4715.17	+	13623.6i	−0.505699	+	1.46112i	−0.852272	+	0.523098i	$0.824776\pi$
$444$	−10642.5	+	6788.63i	−1.13755	+	0.725617i
$445$	5842.29	−	5570.61i	0.622362	−	0.593421i
$446$	715.145	+	15012.7i	0.0759263	+	1.59389i
$447$	10855.9	−	3147.61i	1.14869	−	0.333058i
$448$	53786.4	−	5135.98i	5.67225	−	0.541634i
$449$	−1637.38	+	3585.36i	−0.172100	+	0.376846i	−0.975953	−	0.217982i	$-0.930053\pi$
$449$	−1637.38	+	3585.36i	−0.172100	+	0.376846i	0.803853	+	0.594828i	$0.202780\pi$
$450$	8025.92	−	22690.0i	0.840767	−	2.37693i
$451$	430.681	−	276.782i	0.0449667	−	0.0288983i
$452$	−4343.09	−	17902.5i	−0.451951	−	1.86297i
$453$	401.790	+	9082.93i	0.0416727	+	0.942060i
$454$	11994.9	−	2311.83i	1.23998	−	0.238986i
$455$	71.3040	−	36.7598i	0.00734677	−	0.00378752i
$456$	2791.55	+	11679.7i	0.286680	+	1.19946i
$457$	116.820	+	111.388i	0.0119576	+	0.0114015i	0.696034	−	0.718009i	$-0.254946\pi$
$457$	116.820	+	111.388i	0.0119576	+	0.0114015i	−0.684077	+	0.729410i	$0.739795\pi$
$458$	−7724.31	−	16913.9i	−0.788064	−	1.72562i
$459$	−3374.91	−	1028.39i	−0.343196	−	0.104578i
$460$	34009.2	−	27989.8i	3.44715	−	2.83702i
$461$	−355.359	−	615.499i	−0.0359017	−	0.0621836i	0.847516	−	0.530769i	$-0.178097\pi$
$461$	−355.359	−	615.499i	−0.0359017	−	0.0621836i	−0.883418	+	0.468586i	$0.844764\pi$
$462$	−14603.1	−	2865.95i	−1.47056	−	0.288606i
$463$	−2792.48	+	11510.8i	−0.280297	+	1.15540i	0.641312	+	0.767280i	$0.278391\pi$
$463$	−2792.48	+	11510.8i	−0.280297	+	1.15540i	−0.921609	+	0.388120i	$0.873125\pi$
$464$	−19507.6	−	56363.6i	−1.95176	−	5.63925i
$465$	−18889.3	−	14958.7i	−1.88381	−	1.49182i
$466$	3131.94	−	9049.15i	0.311340	−	0.899558i
$467$	−2275.71	−	15827.9i	−0.225498	−	1.56837i	−0.716735	−	0.697345i	$-0.754364\pi$
$467$	−2275.71	−	15827.9i	−0.225498	−	1.56837i	0.491238	−	0.871026i	$-0.336545\pi$
$468$	159.607	−	101.050i	0.0157647	−	0.00998082i
$469$	14239.5	−	9151.17i	1.40196	−	0.900984i
$470$	5609.15	−	2245.57i	0.550491	−	0.220384i
$471$	3562.18	+	12.0865i	0.348485	+	0.00118241i
$472$	8726.44	+	12254.6i	0.850990	+	1.19505i
$473$	−9153.77	−	7198.61i	−0.889833	−	0.699772i
$474$	−24279.7	−	15720.2i	−2.35275	−	1.52332i
$475$	−973.459	−	4012.65i	−0.0940324	−	0.387607i
$476$	1372.51	+	9546.05i	0.132162	+	0.919207i
$477$	726.905	−	1239.53i	0.0697751	−	0.118982i
$478$	−619.698	−	398.256i	−0.0592977	−	0.0381083i
$479$	9747.42	+	1878.66i	0.929793	+	0.179203i	0.631593	−	0.775300i	$-0.282402\pi$
$479$	9747.42	+	1878.66i	0.929793	+	0.179203i	0.298200	+	0.954503i	$0.403614\pi$
$480$	−88720.3	+	16787.4i	−8.43648	+	1.59633i
$481$	30.0576	+	2.87015i	0.00284929	+	0.000272074i
$482$	−17105.9	+	29628.3i	−1.61650	+	2.79986i
$483$	9062.40	−	1924.19i	0.853733	−	0.181271i
$484$	4050.67	+	7015.97i	0.380416	+	0.658900i
$485$	−3834.97	−	8397.41i	−0.359045	−	0.786199i
$486$	14243.8	−	15885.5i	1.32945	−	1.48268i
$487$	−1793.16	+	2069.42i	−0.166850	+	0.192555i	−0.833017	−	0.553247i	$-0.813388\pi$
$487$	−1793.16	+	2069.42i	−0.166850	+	0.192555i	0.666167	+	0.745803i	$0.267934\pi$
$488$	−2158.88	+	45320.4i	−0.200262	+	4.20401i
$489$	15486.4	−	1425.76i	1.43214	−	0.131851i
$490$	7192.83	+	2879.57i	0.663141	+	0.265481i
$491$	764.849	−	729.282i	0.0702997	−	0.0670306i	−0.654115	−	0.756395i	$-0.726959\pi$
$491$	764.849	−	729.282i	0.0702997	−	0.0670306i	0.724415	+	0.689365i	$0.242110\pi$
$492$	1786.47	−	913.330i	0.163700	−	0.0836912i
$493$	4504.65	−	1803.39i	0.411520	−	0.164748i
$494$	18.0026	−	39.4202i	0.00163963	−	0.00359028i
$495$	14220.3	+	1455.32i	1.29122	+	0.132145i
$496$	−12120.7	+	84301.3i	−1.09725	+	7.63154i
$497$	−4565.11	−	2353.48i	−0.412019	−	0.212410i
$498$	2575.42	+	18354.4i	0.231742	+	1.65156i
$499$	11153.6	+	4465.21i	1.00061	+	0.400582i	0.813379	−	0.581735i	$-0.197626\pi$
$499$	11153.6	+	4465.21i	1.00061	+	0.400582i	0.187227	+	0.982317i	$0.440050\pi$
$500$	13039.9	−	2513.23i	1.16632	−	0.224791i
$501$	−1972.50	+	13396.2i	−0.175898	+	1.19461i
$502$	−22933.7	−	4420.11i	−2.03901	−	0.392987i
$503$	−4681.71	+	1374.68i	−0.415005	+	0.121856i	−0.482568	−	0.875859i	$-0.660296\pi$
$503$	−4681.71	+	1374.68i	−0.415005	+	0.121856i	0.0675631	+	0.997715i	$0.478478\pi$
$504$	−37017.0	−	11142.6i	−3.27156	−	0.984781i
$505$	−13496.1			−1.18924
$506$	15627.3	+	11737.2i	1.37296	+	1.03119i
$507$	11360.1	+	1123.66i	0.995104	+	0.0984292i
$508$	−53291.8	−	5088.75i	−4.65441	−	0.444443i
$509$	586.367	−	2417.04i	0.0510614	−	0.210478i	−0.940566	−	0.339611i	$-0.889704\pi$
$509$	586.367	−	2417.04i	0.0510614	−	0.210478i	0.991627	+	0.129134i	$0.0412196\pi$
$510$	−2879.56	−	12048.0i	−0.250017	−	1.04606i
$511$	178.856	−	3754.65i	0.0154836	−	0.325041i
$512$	65561.1	+	75661.6i	5.65902	+	6.53086i
$513$	557.787	−	3617.69i	0.0480057	−	0.311355i
$514$	−6324.88	−	1857.15i	−0.542759	−	0.159369i
$515$	−1660.55	−	856.071i	−0.142082	−	0.0732485i
$516$	−32923.5	−	31606.5i	−2.80887	−	2.69651i
$517$	1162.97	+	1633.16i	0.0989309	+	0.138929i
$518$	−5407.43	−	7593.67i	−0.458666	−	0.644106i
$519$	91.1580	−	370.270i	0.00770981	−	0.0313161i
$520$	390.747	+	201.444i	0.0329527	+	0.0169883i
$521$	−2093.94	−	614.837i	−0.176079	−	0.0517015i	0.192504	−	0.981296i	$-0.438339\pi$
$521$	−2093.94	−	614.837i	−0.176079	−	0.0517015i	−0.368584	+	0.929595i	$0.620157\pi$
$522$	−1595.10	+	29300.4i	−0.133746	+	2.45679i
$523$	−13966.5	−	16118.2i	−1.16771	−	1.34761i	−0.926118	−	0.377234i	$-0.876875\pi$
$523$	−13966.5	−	16118.2i	−1.16771	−	1.34761i	−0.241594	−	0.970378i	$-0.577670\pi$
$524$	2513.15	−	52757.5i	0.209518	−	4.39832i
$525$	12740.8	+	3788.03i	1.05915	+	0.314901i
$526$	4924.88	−	20300.6i	0.408241	−	1.68279i
$527$	−6897.33	−	658.616i	−0.570119	−	0.0544397i
$528$	−20833.5	−	46031.8i	−1.71717	−	3.79408i
$529$	−11814.9	−	2905.98i	−0.971059	−	0.238841i
$530$	5045.19			0.413488
$531$	−1050.85	−	4463.65i	−0.0858812	−	0.364794i
$532$	−9600.62	+	2819.00i	−0.782405	+	0.229735i
$533$	−4.71246	−	0.908253i	−0.000382963	−	7.38101e-5i
$534$	11005.1	+	8715.08i	0.891828	+	0.706252i
$535$	−22606.4	+	4357.03i	−1.82684	+	0.352095i
$536$	86113.3	+	34474.6i	6.93942	+	2.77812i
$537$	5530.04	−	4318.59i	0.444393	−	0.347040i
$538$	8346.79	+	4303.07i	0.668877	+	0.344830i
$539$	−365.890	+	2544.82i	−0.0292393	+	0.203364i
$540$	54899.1	+	11161.7i	4.37497	+	0.889485i
$541$	69.6403	−	152.491i	0.00553432	−	0.0121185i	−0.906845	−	0.421465i	$-0.861516\pi$
$541$	69.6403	−	152.491i	0.00553432	−	0.0121185i	0.912379	+	0.409347i	$0.134243\pi$
$542$	−20521.7	+	8215.64i	−1.62635	+	0.651093i
$543$	−310.261	+	6079.13i	−0.0245204	+	0.480443i
$544$	−18791.7	+	17917.8i	−1.48104	+	1.41217i
$545$	−16488.0	−	6600.80i	−1.29591	−	0.518802i
$546$	80.5352	+	113.912i	0.00631243	+	0.00892854i
$547$	−373.371	+	7838.02i	−0.0291850	+	0.612668i	0.936142	+	0.351623i	$0.114370\pi$
$547$	−373.371	+	7838.02i	−0.0291850	+	0.612668i	−0.965327	+	0.261045i	$0.915933\pi$
$548$	982.410	−	1133.76i	0.0765811	−	0.0883793i
$549$	5830.43	−	12540.9i	0.453254	−	0.974926i
$550$	11648.5	+	25506.7i	0.903080	+	1.97747i
$551$	2517.11	+	4359.76i	0.194614	+	0.337081i
$552$	37396.3	+	34337.1i	2.88350	+	2.64762i
$553$	7987.14	−	13834.1i	0.614191	−	1.06381i
$554$	25613.8	+	2445.82i	1.96431	+	0.187569i
$555$	5840.93	+	6787.19i	0.446727	+	0.519099i
$556$	4858.61	+	936.421i	0.370595	+	0.0714264i
$557$	−13372.7	−	8594.14i	−1.01727	−	0.653762i	−0.0780074	−	0.996953i	$-0.524856\pi$
$557$	−13372.7	−	8594.14i	−1.01727	−	0.653762i	−0.939266	+	0.343191i	$0.888492\pi$
$558$	21196.4	−	36144.6i	1.60809	−	2.74215i
$559$	15.5359	+	108.055i	0.00117549	+	0.00817573i
$560$	−19825.5	−	81722.0i	−1.49604	−	6.16676i
$561$	3659.95	−	1871.14i	0.275442	−	0.140819i
$562$	1420.39	+	1117.00i	0.106611	+	0.0838397i
$563$	−12575.5	−	17659.8i	−0.941372	−	1.32197i	−0.946744	−	0.321986i	$-0.895649\pi$
$563$	−12575.5	−	17659.8i	−0.941372	−	1.32197i	0.00537228	−	0.999986i	$-0.498290\pi$
$564$	3905.66	+	6818.11i	0.291592	+	0.509033i
$565$	−12131.5	+	4856.73i	−0.903323	+	0.361636i
$566$	−17390.2	+	11176.0i	−1.29146	+	0.829970i
$567$	9162.70	+	7409.08i	0.678655	+	0.548769i
$568$	−4005.56	−	27859.3i	−0.295897	−	2.05801i
$569$	−8475.73	+	24489.0i	−0.624466	+	1.80427i	−0.0308532	+	0.999524i	$0.509822\pi$
$569$	−8475.73	+	24489.0i	−0.624466	+	1.80427i	−0.593612	+	0.804751i	$0.702299\pi$
$570$	11947.4	−	4736.06i	0.877935	−	0.348020i
$571$	−4405.16	−	12727.9i	−0.322855	−	0.932829i	−0.983306	−	0.181960i	$-0.941756\pi$
$571$	−4405.16	−	12727.9i	−0.322855	−	0.932829i	0.660451	−	0.750869i	$-0.270365\pi$
$572$	−51.8882	+	213.886i	−0.00379293	+	0.0156347i
$573$	−1195.76	−	3493.22i	−0.0871789	−	0.254679i
$574$	740.855	+	1283.20i	0.0538723	+	0.0933095i
$575$	−12898.2	−	11762.7i	−0.935466	−	0.853109i
$576$	−28939.5	−	85487.7i	−2.09342	−	6.18401i
$577$	−2084.59	−	4564.62i	−0.150403	−	0.329337i	0.819401	−	0.573220i	$-0.194306\pi$
$577$	−2084.59	−	4564.62i	−0.150403	−	0.329337i	−0.969805	+	0.243883i	$0.921579\pi$
$578$	17449.8	+	16638.4i	1.25574	+	1.19735i
$579$	7963.07	+	2367.54i	0.571561	+	0.169934i
$580$	−68482.7	+	35305.3i	−4.90274	+	2.52754i
$581$	−10051.0	+	1937.16i	−0.717701	+	0.138326i
$582$	13534.7	−	8633.50i	0.963974	−	0.614897i
$583$	394.698	+	1626.97i	0.0280390	+	0.115578i
$584$	17328.9	−	11136.6i	1.22787	−	0.789103i
$585$	−87.0634	−	101.865i	−0.00615321	−	0.00719932i
$586$	−16755.2	+	36688.8i	−1.18115	+	2.58635i
$587$	8344.25	−	796.780i	0.586719	−	0.0560249i	0.202525	−	0.979277i	$-0.435085\pi$
$587$	8344.25	−	796.780i	0.586719	−	0.0560249i	0.384194	+	0.923252i	$0.374479\pi$
$588$	−2408.72	+	9783.87i	−0.168935	+	0.686191i
$589$	−342.046	−	7180.44i	−0.0239283	−	0.502317i
$590$	11652.4	−	11110.6i	0.813090	−	0.775279i
$591$	8324.80	+	4327.55i	0.579419	+	0.301204i
$592$	10352.1	−	29910.4i	0.718696	−	2.07654i
$593$	−5072.13	−	3259.66i	−0.351243	−	0.225730i	0.353107	−	0.935583i	$-0.385125\pi$
$593$	−5072.13	−	3259.66i	−0.351243	−	0.225730i	−0.704350	+	0.709853i	$0.748762\pi$
$594$	930.004	+	24840.9i	0.0642399	+	1.71588i
$595$	6564.07	−	1927.39i	0.452270	−	0.132799i
$596$	−29937.0	+	42040.6i	−2.05749	+	2.88934i
$597$	8883.88	−	12386.5i	0.609033	−	0.849155i
$598$	−30.0956	−	180.725i	−0.00205803	−	0.0123585i
$599$	11859.8	−	20541.7i	0.808976	−	1.40119i	−0.104597	−	0.994515i	$-0.533355\pi$
$599$	11859.8	−	20541.7i	0.808976	−	1.40119i	0.913574	−	0.406673i	$-0.133311\pi$
$600$	23590.0	+	68914.5i	1.60510	+	4.68904i
$601$	18595.1	+	17730.4i	1.26208	+	1.20339i	0.968932	+	0.247326i	$0.0795518\pi$
$601$	18595.1	+	17730.4i	1.26208	+	1.20339i	0.293149	+	0.956067i	$0.405297\pi$
$602$	22071.5	−	25471.9i	1.49430	−	1.72451i
$603$	−20330.0	−	19649.7i	−1.37297	−	1.32703i
$604$	−27185.8	−	31374.1i	−1.83142	−	2.11357i
$605$	4517.25	−	3552.40i	0.303557	−	0.238720i
$606$	−3261.24	−	23242.0i	−0.218612	−	1.55799i
$607$	−574.970	−	12070.1i	−0.0384469	−	0.807101i	−0.932943	−	0.360025i	$-0.882768\pi$
$607$	−574.970	−	12070.1i	−0.0384469	−	0.807101i	0.894496	−	0.447076i	$-0.147535\pi$
$608$	−21175.3	−	16652.4i	−1.41245	−	1.11076i
$609$	−16205.7	−	54.9860i	−1.07831	−	0.00365869i
$610$	48337.7	−	4615.69i	3.20842	−	0.306367i
$611$	2.67477	−	18.6035i	0.000177103	−	0.00123178i
$612$	14996.0	−	5885.72i	0.990483	−	0.388752i
$613$	−8466.38	−	2485.95i	−0.557837	−	0.163796i	−0.00935209	−	0.999956i	$-0.502977\pi$
$613$	−8466.38	−	2485.95i	−0.557837	−	0.163796i	−0.548485	+	0.836161i	$0.684795\pi$
$614$	−35654.4	+	28038.9i	−2.34347	+	1.84293i
$615$	−821.630	−	1162.14i	−0.0538721	−	0.0761986i
$616$	40032.4	−	20638.1i	2.61843	−	1.34989i
$617$	−675.724	−	1952.38i	−0.0440902	−	0.127390i	0.920807	−	0.390019i	$-0.127532\pi$
$617$	−675.724	−	1952.38i	−0.0440902	−	0.127390i	−0.964897	+	0.262629i	$0.915410\pi$
$618$	1073.00	−	3066.54i	0.0698423	−	0.199602i
$619$	−5957.66	+	8366.36i	−0.386847	+	0.543251i	−0.961378	−	0.275232i	$-0.911245\pi$
$619$	−5957.66	+	8366.36i	−0.386847	+	0.543251i	0.574530	+	0.818483i	$0.305185\pi$
$620$	110020.			7.12661
$621$	−6597.59	−	13998.4i	−0.426332	−	0.904567i
$622$	−18186.1			−1.17234
$623$	−4497.07	+	6315.25i	−0.289199	+	0.406124i
$624$	−156.435	+	447.076i	−0.0100359	+	0.0286816i
$625$	3389.05	+	9792.01i	0.216899	+	0.626689i
$626$	−29183.2	+	15045.0i	−1.86325	+	0.960572i
$627$	2461.96	+	3482.29i	0.156812	+	0.221801i
$628$	−12785.4	+	10054.5i	−0.812407	+	0.638884i
$629$	2470.62	+	725.440i	0.156614	+	0.0459860i
$630$	−6165.60	+	40910.0i	−0.389910	+	2.58713i
$631$	1736.87	−	12080.2i	0.109578	−	0.762133i	−0.858740	−	0.512412i	$-0.828752\pi$
$631$	1736.87	−	12080.2i	0.109578	−	0.762133i	0.968318	−	0.249721i	$-0.0803389\pi$
$632$	87143.0	−	8321.15i	5.48475	−	0.523730i
$633$	−16065.4	−	54.5099i	−1.00876	−	0.00342271i
$634$	7614.83	+	5988.37i	0.477009	+	0.375124i
$635$	1806.92	+	37931.9i	0.112922	+	2.37052i
$636$	911.722	+	6497.59i	0.0568429	+	0.405104i
$637$	18.9448	−	14.8984i	0.00117837	−	0.000926681i
$638$	−22388.2	−	25837.4i	−1.38927	−	1.60331i
$639$	−2079.16	+	8323.49i	−0.128718	+	0.515293i
$640$	116476.	−	134420.i	7.19394	−	8.30224i
$641$	4067.95	+	3878.78i	0.250662	+	0.239006i	0.804984	−	0.593297i	$-0.202174\pi$
$641$	4067.95	+	3878.78i	0.250662	+	0.239006i	−0.554322	+	0.832302i	$0.687022\pi$
$642$	−12966.1	−	37878.4i	−0.797088	−	2.32857i
$643$	9006.42	−	15599.6i	0.552377	−	0.956745i	−0.445725	−	0.895170i	$-0.647054\pi$
$643$	9006.42	−	15599.6i	0.552377	−	0.956745i	0.998102	−	0.0615756i	$-0.0196125\pi$
$644$	−26985.0	+	32577.2i	−1.65118	+	1.99336i
$645$	−18868.4	+	26307.6i	−1.15185	+	1.60598i
$646$	2143.69	−	3010.40i	0.130561	−	0.183348i
$647$	8929.33	−	2621.89i	0.542579	−	0.159315i	0.00105257	−	0.999999i	$-0.499665\pi$
$647$	8929.33	−	2621.89i	0.542579	−	0.159315i	0.541526	+	0.840684i	$0.317847\pi$
$648$	−3947.62	+	64452.8i	−0.239317	+	3.90732i
$649$	4494.53	+	2888.46i	0.271843	+	0.174703i
$650$	85.9737	−	248.405i	0.00518795	−	0.0149896i
$651$	20532.4	+	10673.5i	1.23614	+	0.642595i
$652$	−51393.1	+	49003.3i	−3.08698	+	2.94343i
$653$	−723.612	−	15190.5i	−0.0433647	−	0.910336i	−0.910816	−	0.412814i	$-0.864546\pi$
$653$	−723.612	−	15190.5i	−0.0433647	−	0.910336i	0.867451	−	0.497523i	$-0.165757\pi$
$654$	7383.21	−	29989.5i	0.441447	−	1.79309i
$655$	−37296.7	+	3561.40i	−2.22489	+	0.212451i
$656$	−2089.85	+	4576.13i	−0.124382	+	0.272360i
$657$	−6173.32	+	1146.42i	−0.366581	+	0.0680761i
$658$	−4881.56	+	3137.19i	−0.289214	+	0.185867i
$659$	−387.323	−	1596.57i	−0.0228952	−	0.0943754i	0.959218	−	0.282669i	$-0.0912196\pi$
$659$	−387.323	−	1596.57i	−0.0228952	−	0.0943754i	−0.982113	+	0.188293i	$0.939704\pi$
$660$	−55028.2	+	35101.2i	−3.24541	+	2.07017i
$661$	4818.98	−	928.783i	0.283565	−	0.0546528i	−0.0454853	−	0.998965i	$-0.514483\pi$
$661$	4818.98	−	928.783i	0.283565	−	0.0546528i	0.329051	+	0.944312i	$0.393271\pi$
$662$	−12945.8	+	6674.01i	−0.760049	+	0.391832i
$663$	−36.9354	−	10.9815i	−0.00216358	−	0.000643265i
$664$	−40596.6	−	38708.7i	−2.37267	−	2.26234i
$665$	2948.52	+	6456.36i	0.171938	+	0.376492i
$666$	−10277.0	+	11698.9i	−0.597936	+	0.680667i
$667$	19129.2	+	9329.91i	1.11047	+	0.541613i
$668$	−30913.9	−	53544.4i	−1.79056	−	3.10134i
$669$	4490.38	+	13117.9i	0.259504	+	0.758100i
$670$	23403.9	−	96472.4i	1.34951	−	5.56277i
$671$	5270.05	+	15226.8i	0.303201	+	0.876042i
$672$	80616.4	−	31957.0i	4.62775	−	1.83448i
$673$	−8711.53	+	25170.3i	−0.498967	+	1.44167i	0.361600	+	0.932333i	$0.382231\pi$
$673$	−8711.53	+	25170.3i	−0.498967	+	1.44167i	−0.860567	+	0.509337i	$0.829891\pi$
$674$	−3629.19	−	25241.6i	−0.207405	−	1.44254i
$675$	1282.14	−	22165.7i	0.0731104	−	1.26394i
$676$	−43849.5	+	28180.4i	−2.49485	+	1.60334i
$677$	16584.8	−	6639.56i	0.941516	−	0.376926i	0.150423	−	0.988622i	$-0.451937\pi$
$677$	16584.8	−	6639.56i	0.941516	−	0.376926i	0.791093	+	0.611696i	$0.209512\pi$
$678$	−11295.4	−	19718.5i	−0.639821	−	1.11694i
$679$	5142.86	+	7222.14i	0.290670	+	0.408189i
$680$	29469.0	+	23174.7i	1.66189	+	1.30693i
$681$	10033.9	−	5129.80i	0.564609	−	0.288656i
$682$	11509.3	+	47442.1i	0.646209	+	2.66371i
$683$	−3383.08	−	23529.9i	−0.189532	−	1.31822i	−0.833224	−	0.552936i	$-0.813507\pi$
$683$	−3383.08	−	23529.9i	−0.189532	−	1.31822i	0.643692	−	0.765285i	$-0.277402\pi$
$684$	8258.51	+	14531.0i	0.461655	+	0.812290i
$685$	−895.232	−	575.330i	−0.0499344	−	0.0320909i
$686$	−37970.4	−	7318.20i	−2.11329	−	0.407304i
$687$	−11189.1	−	13001.8i	−0.621382	−	0.722049i
$688$	113915.	+	10877.6i	6.31246	+	0.602767i
$689$	7.84706	−	13.5915i	0.000433888	−	0.000751517i
$690$	30678.3	−	44844.5i	1.69261	−	2.47420i
$691$	13539.2	+	23450.6i	0.745378	+	1.29103i	0.950018	+	0.312195i	$0.101064\pi$
$691$	13539.2	+	23450.6i	0.745378	+	1.29103i	−0.204640	+	0.978837i	$0.565602\pi$
$692$	723.307	+	1583.82i	0.0397341	+	0.0870055i
$693$	−13675.0	+	1212.22i	−0.749596	+	0.0664478i
$694$	−9828.62	+	11342.8i	−0.537593	+	0.620415i
$695$	167.009	−	3505.94i	0.00911511	−	0.191350i
$696$	−51268.1	−	72515.4i	−2.79211	−	3.94927i
$697$	−379.951	−	152.109i	−0.0206480	−	0.00826622i
$698$	13763.9	−	13123.8i	0.746376	−	0.711668i
$699$	450.268	−	8822.36i	0.0243644	−	0.477385i
$700$	−56344.6	+	22557.0i	−3.04232	+	1.21796i
$701$	9703.87	−	21248.5i	0.522839	−	1.14486i	−0.445514	−	0.895275i	$-0.646979\pi$
$701$	9703.87	−	21248.5i	0.522839	−	1.14486i	0.968353	−	0.249583i	$-0.0802935\pi$
$702$	154.387	−	174.550i	0.00830050	−	0.00938454i
$703$	−380.194	+	2644.31i	−0.0203973	+	0.141866i
$704$	93462.7	+	48183.4i	5.00356	+	2.57952i
$705$	4392.97	−	3430.61i	0.234679	−	0.183268i
$706$	27706.4	+	11092.0i	1.47697	+	0.591292i
$707$	12727.5	−	2453.02i	0.677037	−	0.130488i
$708$	16414.8	+	12999.1i	0.871336	+	0.690024i
$709$	5518.95	+	1063.69i	0.292339	+	0.0563438i	0.333312	−	0.942816i	$-0.391834\pi$
$709$	5518.95	+	1063.69i	0.292339	+	0.0563438i	−0.0409731	+	0.999160i	$0.513046\pi$
$710$	−28901.8	+	8486.34i	−1.52770	+	0.448573i
$711$	−25550.9	−	7691.13i	−1.34773	−	0.405682i
$712$	−42485.6			−2.23626
$713$	−18174.1	−	24358.2i	−0.954595	−	1.27942i
$714$	4905.38	+	10838.4i	0.257114	+	0.568093i
$715$	155.416	+	14.8404i	0.00812897	+	0.000776223i
$716$	−7553.24	+	31134.9i	−0.394243	+	1.62509i
$717$	−651.379	−	193.665i	−0.0339277	−	0.0100872i
$718$	125.682	−	2638.38i	0.00653259	−	0.137136i
$719$	−9258.63	−	10685.0i	−0.480234	−	0.554220i	0.462996	−	0.886361i	$-0.346775\pi$
$719$	−9258.63	−	10685.0i	−0.480234	−	0.554220i	−0.943230	+	0.332141i	$0.892229\pi$
$720$	−125286.	+	63517.2i	−6.48493	+	3.28771i
$721$	1721.57	+	505.500i	0.0889248	+	0.0261107i
$722$	−30931.2	−	15946.1i	−1.59437	−	0.821957i
$723$	−7544.80	+	30645.9i	−0.388097	+	1.57639i
$724$	−16122.0	−	22640.2i	−0.827584	−	1.16218i
$725$	17712.4	+	24873.6i	0.907340	+	1.27418i
$726$	7209.26	+	6920.87i	0.368541	+	0.353798i
$727$	−8202.00	−	4228.42i	−0.418425	−	0.215713i	0.236139	−	0.971719i	$-0.424118\pi$
$727$	−8202.00	−	4228.42i	−0.418425	−	0.215713i	−0.654565	+	0.756006i	$0.727148\pi$
$728$	−405.108	−	118.951i	−0.0206241	−	0.00605577i
$729$	8539.39	−	17734.1i	0.433846	−	0.900987i
$730$	−14436.6	−	16660.7i	−0.731947	−	0.844712i
$731$	−442.964	+	9298.97i	−0.0224126	+	0.470499i
$732$	14679.6	+	61419.0i	0.741221	+	3.10124i
$733$	5910.95	−	24365.3i	0.297853	−	1.22777i	−0.604443	−	0.796648i	$-0.706604\pi$
$733$	5910.95	−	24365.3i	0.297853	−	1.22777i	0.902296	−	0.431117i	$-0.141880\pi$
$734$	60370.3	+	5764.66i	3.03584	+	0.289888i
$735$	7112.78	+	703.550i	0.356951	+	0.0353072i
$736$	−113586.	−	8304.95i	−5.68862	−	0.415930i
$737$	32941.3			1.64642
$738$	1802.82	−	1695.78i	0.0899224	−	0.0845833i
$739$	10844.9	−	3184.35i	0.539833	−	0.158509i	−0.000438803	−	1.00000i	$-0.500140\pi$
$739$	10844.9	−	3184.35i	0.539833	−	0.158509i	0.540272	+	0.841491i	$0.318321\pi$
$740$	−40147.9	−	7737.87i	−1.99441	−	0.384392i
$741$	5.82377	−	39.5521i	0.000288720	−	0.00196084i
$742$	−4757.86	+	917.003i	−0.235400	+	0.0453696i
$743$	−17054.7	−	6827.68i	−0.842096	−	0.337124i	−0.0898083	−	0.995959i	$-0.528625\pi$
$743$	−17054.7	−	6827.68i	−0.842096	−	0.337124i	−0.752288	+	0.658835i	$0.771050\pi$
$744$	17621.4	+	125583.i	0.868323	+	6.18830i
$745$	32540.4	+	16775.8i	1.60025	+	0.824988i
$746$	−2712.88	+	18868.5i	−0.133144	+	0.926038i
$747$	6997.09	+	15600.8i	0.342718	+	0.764127i
$748$	−7796.91	+	17072.8i	−0.381127	+	0.834552i
$749$	20527.1	−	8217.80i	1.00139	−	0.400897i
$750$	14586.0	−	7457.08i	0.710141	−	0.363059i
$751$	1819.56	−	1734.95i	0.0884112	−	0.0842999i	−0.644585	−	0.764533i	$-0.722970\pi$
$751$	1819.56	−	1734.95i	0.0884112	−	0.0842999i	0.732996	+	0.680233i	$0.238121\pi$
$752$	−18290.3	−	7322.34i	−0.886941	−	0.355078i
$753$	−21455.4	+	1975.30i	−1.03835	+	0.0955963i
$754$	−15.2494	+	320.123i	−0.000736537	+	0.0154618i
$755$	−19284.5	+	22255.5i	−0.929581	+	1.07279i
$756$	−53801.3	−	547.660i	−2.58827	−	0.0263468i
$757$	6183.90	+	13540.9i	0.296906	+	0.650133i	0.998019	−	0.0629170i	$-0.0200403\pi$
$757$	6183.90	+	13540.9i	0.296906	+	0.650133i	−0.701113	+	0.713050i	$0.747313\pi$
$758$	−2919.74	−	5057.13i	−0.139907	−	0.242326i
$759$	16861.5	+	6384.82i	0.806367	+	0.305342i
$760$	−19448.0	+	33684.9i	−0.928227	+	1.60774i
$761$	8661.76	+	827.098i	0.412600	+	0.0393985i	0.299292	−	0.954161i	$-0.403249\pi$
$761$	8661.76	+	827.098i	0.412600	+	0.0393985i	0.113308	+	0.993560i	$0.463855\pi$
$762$	−64887.0	+	12277.7i	−3.08479	+	0.583695i
$763$	16748.7	+	3228.06i	0.794686	+	0.153163i
$764$	14182.6	+	9114.62i	0.671609	+	0.431617i
$765$	−5646.45	−	9935.04i	−0.266860	−	0.469545i
$766$	5375.64	+	37388.4i	0.253564	+	1.76357i
$767$	−11.8077	−	48.6720i	−0.000555869	−	0.00229132i
$768$	142995.	+	92584.6i	6.71862	+	4.35008i
$769$	22353.1	+	17578.6i	1.04821	+	0.824320i	0.984804	−	0.173668i	$-0.0555618\pi$
$769$	22353.1	+	17578.6i	1.04821	+	0.824320i	0.0634042	+	0.997988i	$0.479804\pi$
$770$	−27959.6	−	39263.8i	−1.30857	−	1.83762i
$771$	−6081.09	−	20.6331i	−0.284054	−	0.000963793i
$772$	−35215.8	+	14098.3i	−1.64177	+	0.657264i
$773$	−2526.62	+	1623.76i	−0.117563	+	0.0755533i	−0.598101	−	0.801421i	$-0.704078\pi$
$773$	−2526.62	+	1623.76i	−0.117563	+	0.0755533i	0.480538	+	0.876974i	$0.340441\pi$
$774$	−49864.5	−	26136.7i	−2.31569	−	1.21378i
$775$	−6205.37	−	43159.3i	−0.287617	−	2.00042i
$776$	−15891.1	+	45914.4i	−0.735127	+	2.12401i
$777$	−6741.92	−	5339.02i	−0.311280	−	0.246508i
$778$	6789.57	+	19617.2i	0.312876	+	0.903997i
$779$	100.107	−	412.648i	0.00460426	−	0.0189790i
$780$	600.410	+	117.834i	0.0275617	+	0.00540914i
$781$	−4997.74	−	8656.34i	−0.228980	−	0.396604i
$782$	396.598	−	15619.1i	0.0181359	−	0.714244i
$783$	6113.91	+	26370.6i	0.279047	+	1.20359i
$784$	−10495.1	−	22981.0i	−0.478093	−	1.04688i
$785$	8350.36	+	7962.05i	0.379665	+	0.362010i
$786$	−15145.7	−	63369.1i	−0.687315	−	2.87570i
$787$	−12135.6	+	6256.32i	−0.549665	+	0.283372i	−0.710604	−	0.703592i	$-0.751578\pi$
$787$	−12135.6	+	6256.32i	−0.549665	+	0.283372i	0.160939	+	0.986964i	$0.448548\pi$
$788$	−42066.7	+	8107.69i	−1.90173	+	0.366529i
$789$	−851.628	−	19252.0i	−0.0384268	−	0.868683i
$790$	−22087.3	−	91045.1i	−0.994723	−	4.10030i
$791$	10557.9	−	6785.14i	0.474583	−	0.304996i
$792$	−48880.2	−	57190.4i	−2.19304	−	2.56587i
$793$	62.7478	−	137.398i	0.00280988	−	0.00615279i
$794$	−72627.3	+	6935.07i	−3.24616	+	0.309970i
$795$	4470.16	−	1296.10i	0.199422	−	0.0578212i
$796$	3311.73	+	69521.8i	0.147464	+	3.09565i
$797$	12758.1	−	12164.9i	0.567022	−	0.540655i	−0.351416	−	0.936220i	$-0.614300\pi$
$797$	12758.1	−	12164.9i	0.567022	−	0.540655i	0.918438	+	0.395565i	$0.129451\pi$
$798$	−10406.2	+	6637.88i	−0.461624	+	0.294459i
$799$	524.221	−	1514.64i	0.0232110	−	0.0670638i
$800$	−137461.	−	88340.7i	−6.07497	−	3.90414i
$801$	11989.7	+	4894.59i	0.528881	+	0.215908i
$802$	46932.0	−	13780.5i	2.06637	−	0.606740i
$803$	4243.32	−	5958.91i	0.186480	−	0.261875i
$804$	128474.	+	12707.8i	5.63549	+	0.557426i
$805$	25597.8	+	15658.4i	1.12075	+	0.685575i
$806$	228.818	−	396.325i	0.00999973	−	0.0173200i
$807$	8500.91	+	1668.35i	0.370813	+	0.0727742i
$808$	51407.1	+	49016.6i	2.23824	+	2.13415i
$809$	10531.4	−	12153.9i	0.457683	−	0.528195i	−0.479262	−	0.877672i	$-0.659095\pi$
$809$	10531.4	−	12153.9i	0.457683	−	0.528195i	0.936945	+	0.349478i	$0.113641\pi$
$810$	68877.4	−	5634.84i	2.98779	−	0.244430i
$811$	19046.2	+	21980.5i	0.824663	+	0.951712i	0.999459	−	0.0328927i	$-0.0104720\pi$
$811$	19046.2	+	21980.5i	0.824663	+	0.951712i	−0.174796	+	0.984605i	$0.555927\pi$
$812$	58165.6	−	45741.9i	2.51381	−	1.97688i
$813$	−16072.1	+	12551.2i	−0.693326	+	0.541441i
$814$	−863.248	−	18121.8i	−0.0371705	−	0.780306i
$815$	39595.2	+	31138.0i	1.70179	+	1.33830i
$816$	−20314.8	+	34912.2i	−0.871521	+	1.49776i
$817$	−9614.94	+	918.116i	−0.411731	+	0.0393155i
$818$	6633.25	−	46135.2i	0.283528	−	1.97198i
$819$	100.620	+	80.2394i	0.00429297	+	0.00342343i
$820$	6235.45	+	1830.89i	0.265550	+	0.0779726i
$821$	14899.9	−	11717.4i	0.633384	−	0.498099i	−0.249077	−	0.968484i	$-0.580127\pi$
$821$	14899.9	−	11717.4i	0.633384	−	0.498099i	0.882461	+	0.470385i	$0.155885\pi$
$822$	774.467	−	1680.73i	0.0328621	−	0.0713165i
$823$	−10453.0	+	5388.90i	−0.442733	+	0.228245i	−0.665154	−	0.746706i	$-0.731634\pi$
$823$	−10453.0	+	5388.90i	−0.442733	+	0.228245i	0.222422	+	0.974951i	$0.428604\pi$
$824$	3215.92	+	9291.78i	0.135961	+	0.392833i
$825$	16873.5	+	19607.1i	0.712072	+	0.827430i
$826$	−8969.39	+	12595.7i	−0.377827	+	0.530583i
$827$	−39187.0			−1.64772			−0.823861	−	0.566792i	$-0.808184\pi$
$827$	−39187.0			−1.64772			−0.823861	+	0.566792i	$0.808184\pi$
$828$	63298.2	+	31406.1i	2.65672	+	1.31816i
$829$	−46588.9			−1.95187			−0.975934	−	0.218064i	$-0.930026\pi$
$829$	−46588.9			−1.95187			−0.975934	+	0.218064i	$0.930026\pi$
$830$	−34821.8	+	48900.4i	−1.45625	+	2.04501i
$831$	23322.8	−	4413.08i	0.973596	−	0.184221i
$832$	−322.399	−	931.512i	−0.0134341	−	0.0388154i
$833$	1826.84	−	941.800i	0.0759858	−	0.0391734i
$834$	6078.05	−	559.579i	0.252357	−	0.0232334i
$835$	−34474.7	+	27111.2i	−1.42880	+	1.12362i
$836$	−18684.1	−	5486.15i	−0.772971	−	0.226965i
$837$	9495.06	−	37470.3i	0.392111	−	1.54739i
$838$	−6138.73	+	42695.8i	−0.253054	+	1.76003i
$839$	−28998.3	+	2769.00i	−1.19324	+	0.113941i	−0.672714	−	0.739903i	$-0.734872\pi$
$839$	−28998.3	+	2769.00i	−1.19324	+	0.113941i	−0.520530	+	0.853844i	$0.674265\pi$
$840$	−62237.4	−	108648.i	−2.55642	−	4.46275i
$841$	−10093.4	−	7937.53i	−0.413850	−	0.325455i
$842$	−2942.61	−	61773.0i	−0.120438	−	2.52831i
$843$	1545.45	+	624.798i	0.0631414	+	0.0255269i
$844$	57662.0	−	45345.9i	2.35167	−	1.84937i
$845$	24213.2	+	27943.5i	0.985750	+	1.13762i
$846$	6969.48	+	6736.27i	0.283234	+	0.273756i
$847$	−3614.31	+	4171.14i	−0.146622	+	0.169211i
$848$	−11906.4	−	11352.7i	−0.482155	−	0.459734i
$849$	−12537.1	+	14369.7i	−0.506797	+	0.580881i
$850$	11208.2	−	19413.2i	0.452281	−	0.783374i
$851$	4918.86	+	10166.9i	0.198139	+	0.409538i
$852$	−16152.3	−	35688.5i	−0.649492	−	1.43506i
$853$	17857.8	−	25077.8i	0.716812	−	1.00662i	−0.282072	−	0.959393i	$-0.591022\pi$
$853$	17857.8	−	25077.8i	0.716812	−	1.00662i	0.998884	−	0.0472283i	$-0.0150388\pi$
$854$	−44745.9	+	13138.6i	−1.79294	+	0.526455i
$855$	9369.03	−	7265.54i	0.374753	−	0.290615i
$856$	101933.	+	65508.6i	4.07010	+	2.61570i
$857$	−4191.28	+	12109.9i	−0.167061	+	0.482692i	−0.997193	−	0.0748757i	$-0.976144\pi$
$857$	−4191.28	+	12109.9i	−0.167061	+	0.482692i	0.830132	+	0.557567i	$0.188265\pi$
$858$	11.9981	+	271.232i	0.000477401	+	0.0107922i
$859$	−4189.73	+	3994.90i	−0.166417	+	0.158678i	−0.768711	−	0.639596i	$-0.779102\pi$
$859$	−4189.73	+	3994.90i	−0.166417	+	0.158678i	0.602295	+	0.798274i	$0.294253\pi$
$860$	−7033.76	−	147657.i	−0.278894	−	5.85471i
$861$	986.067	+	946.621i	0.0390303	+	0.0374689i
$862$	42784.2	−	4085.40i	1.69053	−	0.161426i
$863$	−5405.18	+	11835.7i	−0.213203	+	0.466850i	−0.985774	−	0.168079i	$-0.946244\pi$
$863$	−5405.18	+	11835.7i	−0.213203	+	0.466850i	0.772570	+	0.634930i	$0.218971\pi$
$864$	−82819.1	−	118845.i	−3.26107	−	4.67962i
$865$	1039.04	−	667.750i	0.0408421	−	0.0262476i
$866$	−11059.4	−	45587.4i	−0.433964	−	1.78883i
$867$	19735.3	+	10259.2i	0.773065	+	0.401869i
$868$	−103754.	+	19997.0i	−4.05719	+	0.781960i
$869$	27632.2	−	14245.4i	1.07866	−	0.556090i
$870$	−69008.6	+	65354.0i	−2.68921	+	2.54679i
$871$	−223.491	−	213.098i	−0.00869425	−	0.00828995i
$872$	38830.0	+	85025.8i	1.50797	+	3.30199i
$873$	9774.18	−	11126.5i	0.378930	−	0.431359i
$874$	16098.5	−	1898.92i	0.623045	−	0.0734918i
$875$	4523.60	+	7835.10i	0.174772	+	0.302714i
$876$	18848.1	−	21603.3i	0.726962	−	0.833230i
$877$	−7503.68	+	30930.6i	−0.288918	+	1.19094i	0.623548	+	0.781785i	$0.285691\pi$
$877$	−7503.68	+	30930.6i	−0.288918	+	1.19094i	−0.912466	+	0.409152i	$0.865825\pi$
$878$	30244.6	+	87385.9i	1.16253	+	3.35892i
$879$	−5420.25	+	36811.5i	−0.207987	+	1.41254i
$880$	53526.4	−	154654.i	2.05043	−	5.92432i
$881$	−4607.06	−	32042.8i	−0.176181	−	1.22537i	−0.865499	−	0.500910i	$-0.832999\pi$
$881$	−4607.06	−	32042.8i	−0.176181	−	1.22537i	0.689318	−	0.724459i	$-0.257910\pi$
$882$	507.155	+	12419.1i	0.0193615	+	0.474120i
$883$	−4921.88	+	3163.10i	−0.187581	+	0.120551i	−0.631061	−	0.775733i	$-0.717380\pi$
$883$	−4921.88	+	3163.10i	−0.187581	+	0.120551i	0.443480	+	0.896284i	$0.353744\pi$
$884$	163.343	−	65.3925i	0.00621472	−	0.00248800i
$885$	7470.05	−	12837.7i	0.283732	−	0.487611i
$886$	−47101.9	−	66145.3i	−1.78603	−	2.50812i
$887$	−2321.32	−	1825.51i	−0.0878719	−	0.0691033i	0.573257	−	0.819376i	$-0.305680\pi$
$887$	−2321.32	−	1825.51i	−0.0878719	−	0.0691033i	−0.661129	+	0.750273i	$0.729922\pi$
$888$	2402.14	−	47066.5i	0.0907776	−	1.77866i
$889$	−8598.43	−	35443.2i	−0.324389	−	1.33715i
$890$	6470.87	+	45005.9i	0.243712	+	1.69506i
$891$	7205.59	+	21770.7i	0.270927	+	0.818571i
$892$	−53259.4	−	34227.8i	−1.99917	−	1.28479i
$893$	1632.85	+	314.706i	0.0611884	+	0.0117931i
$894$	−21026.8	+	60092.6i	−0.786625	+	2.24810i
$895$	22623.5	+	2160.28i	0.844937	+	0.0806817i
$896$	−85410.7	+	147936.i	−3.18457	+	5.51583i
$897$	−73.0933	−	152.395i	−0.00272075	−	0.00567260i
$898$	−11100.6	−	19226.8i	−0.412507	−	0.714482i
$899$	22084.2	+	48357.7i	0.819299	+	1.79401i
$900$	58244.3	+	82978.6i	2.15719	+	3.07328i
$901$	876.446	−	1011.47i	0.0324069	−	0.0373996i
$902$	−137.208	+	2880.34i	−0.00506487	+	0.106325i
$903$	13012.2	−	28238.8i	0.479534	−	1.04067i
$904$	63848.8	+	25561.2i	2.34909	+	0.940435i
$905$	−14269.0	+	13605.5i	−0.524108	+	0.499736i
$906$	−42986.7	−	27832.4i	−1.57631	−	1.02061i
$907$	33055.2	−	13233.3i	1.21012	−	0.484460i	0.323179	−	0.946338i	$-0.395249\pi$
$907$	33055.2	−	13233.3i	1.21012	−	0.484460i	0.886943	+	0.461878i	$0.152824\pi$
$908$	−21375.5	+	46805.8i	−0.781245	+	1.71069i
$909$	−8860.35	−	19755.1i	−0.323300	−	0.720832i
$910$	−64.3058	+	447.257i	−0.00234255	+	0.0162928i
$911$	45478.9	+	23446.0i	1.65399	+	0.852690i	0.994927	+	0.100600i	$0.0320762\pi$
$911$	45478.9	+	23446.0i	1.65399	+	0.852690i	0.659061	+	0.752090i	$0.270954\pi$
$912$	−38852.5	−	15707.4i	−1.41067	−	0.570310i
$913$	−18493.6	−	7403.72i	−0.670371	−	0.268376i
$914$	−892.744	+	172.062i	−0.0323078	+	0.00622682i
$915$	41642.6	−	16507.5i	1.50455	−	0.596415i
$916$	76908.6	+	14822.9i	2.77416	+	0.534676i
$917$	34525.3	−	10137.5i	1.24332	−	0.365072i
$918$	15745.0	−	12124.7i	0.566081	−	0.435919i
$919$	−49826.7			−1.78850			−0.894250	−	0.447567i	$-0.852291\pi$
$919$	−49826.7			−1.78850			−0.894250	+	0.447567i	$0.852291\pi$
$920$	11470.8	+	164040.i	0.411068	+	5.87852i
$921$	−24387.5	+	34002.7i	−0.872525	+	1.21653i
$922$	3985.05	+	380.526i	0.142343	+	0.0135921i
$923$	−22.0908	+	91.0594i	−0.000787787	+	0.00324730i
$924$	45514.4	−	43104.0i	1.62047	−	1.53465i
$925$	−771.031	+	16185.9i	−0.0274068	+	0.575341i
$926$	−43689.7	−	50420.6i	−1.55047	−	1.78933i
$927$	162.920	−	2992.68i	0.00577239	−	0.106033i
$928$	191151.	+	56126.9i	6.76167	+	1.98540i
$929$	13179.1	+	6794.32i	0.465440	+	0.239951i	0.674961	−	0.737853i	$-0.264160\pi$
$929$	13179.1	+	6794.32i	0.465440	+	0.239951i	−0.209521	+	0.977804i	$0.567191\pi$
$930$	130349.	−	37793.9i	4.59603	−	1.33259i
$931$	1236.91	+	1737.00i	0.0435427	+	0.0611472i
$932$	23397.2	+	32856.7i	0.822318	+	1.15478i
$933$	−16113.3	+	4671.96i	−0.565408	+	0.163937i
$934$	80056.5	+	41272.0i	2.80463	+	1.44589i
$935$	12774.6	+	3750.96i	0.446817	+	0.131197i
$936$	−38.3372	+	704.216i	−0.00133877	+	0.0245919i
$937$	25838.2	+	29818.8i	0.900849	+	1.03964i	0.999011	+	0.0444649i	$0.0141583\pi$
$937$	25838.2	+	29818.8i	0.900849	+	1.03964i	−0.0981618	+	0.995170i	$0.531296\pi$
$938$	−4536.46	+	95232.1i	−0.157911	+	3.31497i
$939$	−21992.0	+	20827.3i	−0.764304	+	0.723827i
$940$	−6000.16	+	24733.0i	−0.208195	+	0.858193i
$941$	−23782.5	−	2270.96i	−0.823899	−	0.0786728i	−0.325414	−	0.945572i	$-0.605504\pi$
$941$	−23782.5	−	2270.96i	−0.823899	−	0.0786728i	−0.498484	+	0.866899i	$0.666110\pi$
$942$	−11693.9	+	16304.4i	−0.404466	+	0.563933i
$943$	−624.674	−	1682.96i	−0.0215718	−	0.0581176i
$944$	−52500.3			−1.81010
$945$	5046.82	+	37831.2i	0.173728	+	1.30227i
$946$	62935.8	−	18479.6i	2.16302	−	0.635121i
$947$	−34019.4	−	6556.70i	−1.16735	−	0.224989i	−0.431488	−	0.902119i	$-0.642011\pi$
$947$	−34019.4	−	6556.70i	−1.16735	−	0.224989i	−0.735863	+	0.677130i	$0.763223\pi$
$948$	113264.	−	44898.6i	3.88041	−	1.53823i
$949$	−67.3371	+	12.9782i	−0.00230333	+	0.000443930i
$950$	21591.2	+	8643.83i	0.737381	+	0.295203i
$951$	8285.33	+	3349.61i	0.282513	+	0.114215i
$952$	−32003.0	−	16498.7i	−1.08952	−	0.561686i
$953$	−5615.94	+	39059.7i	−0.190890	+	1.32767i	0.638769	+	0.769399i	$0.279444\pi$
$953$	−5615.94	+	39059.7i	−0.190890	+	1.32767i	−0.829659	+	0.558270i	$0.811465\pi$
$954$	3312.24	+	7385.00i	0.112408	+	0.250627i
$955$	4967.94	−	10878.3i	0.168334	−	0.368600i
$956$	2880.65	−	1153.24i	0.0974549	−	0.0390151i
$957$	−26474.1	−	17141.0i	−0.894237	−	0.578988i
$958$	−40466.6	+	38584.8i	−1.36473	+	1.30127i
$959$	948.819	+	379.850i	0.0319489	+	0.0127904i
$960$	122339.	−	265498.i	4.11300	−	8.92593i
$961$	2194.53	−	46068.8i	0.0736642	−	1.54640i
$962$	−111.374	+	128.532i	−0.00373267	+	0.00430773i
$963$	−21219.2	−	30230.2i	−0.710049	−	1.01158i
$964$	−59865.3	−	131087.i	−2.00014	−	4.37969i
$965$	13454.0	+	23303.1i	0.448809	+	0.777359i
$966$	−20780.3	+	47866.6i	−0.692128	+	1.59429i
$967$	2182.98	−	3781.03i	0.0725955	−	0.125739i	−0.827443	−	0.561550i	$-0.810205\pi$
$967$	2182.98	−	3781.03i	0.0725955	−	0.125739i	0.900038	+	0.435811i	$0.143538\pi$
$968$	−30108.4	−	2875.01i	−0.999712	−	0.0954609i
$969$	1126.00	−	3218.00i	0.0373296	−	0.106684i
$970$	51058.4	+	9840.71i	1.69009	+	0.325738i
$971$	13654.7	+	8775.32i	0.451286	+	0.290024i	0.746473	−	0.665415i	$-0.231746\pi$
$971$	13654.7	+	8775.32i	0.451286	+	0.290024i	−0.295187	+	0.955440i	$0.595382\pi$
$972$	19703.9	+	87687.6i	0.650209	+	2.89360i
$973$	479.736	+	3336.64i	0.0158064	+	0.109936i
$974$	−3636.19	−	14988.6i	−0.119621	−	0.493086i
$975$	12.3601	−	242.179i	0.000405990	−	0.00795481i
$976$	−124461.	−	97877.1i	−4.08186	−	3.21001i
$977$	−31325.9	−	43991.1i	−1.02580	−	1.44053i	−0.893360	−	0.449341i	$-0.851659\pi$
$977$	−31325.9	−	43991.1i	−1.02580	−	1.44053i	−0.132438	−	0.991191i	$-0.542281\pi$
$978$	−44055.8	+	75712.4i	−1.44044	+	2.47548i
$979$	−14007.2	+	5607.65i	−0.457276	+	0.183066i
$980$	−27455.2	+	17644.4i	−0.894921	+	0.575131i
$981$	−1162.54	−	28468.2i	−0.0378360	−	0.926523i
$982$	847.139	+	5891.98i	0.0275288	+	0.191467i
$983$	−11589.1	+	33484.6i	−0.376029	+	1.08646i	0.585243	+	0.810858i	$0.300999\pi$
$983$	−11589.1	+	33484.6i	−0.376029	+	1.08646i	−0.961271	+	0.275605i	$0.911122\pi$
$984$	−1091.18	+	7410.75i	−0.0353512	+	0.240087i
$985$	9939.43	+	28718.1i	0.321519	+	0.928969i
$986$	−6443.43	+	26560.2i	−0.208114	+	0.857858i
$987$	−3519.25	+	4033.69i	−0.113494	+	0.130085i
$988$	91.2726	+	158.089i	0.00293904	+	0.00509056i
$989$	−31529.1	+	25948.6i	−1.01372	+	0.834295i
$990$	−53138.2	+	60490.4i	−1.70590	+	1.94193i
$991$	−24452.7	−	53543.8i	−0.783819	−	1.71632i	−0.693553	−	0.720405i	$-0.743956\pi$
$991$	−24452.7	−	53543.8i	−0.783819	−	1.71632i	−0.0902654	−	0.995918i	$-0.528772\pi$
$992$	−205885.	−	196311.i	−6.58957	−	6.28314i
$993$	−9755.74	+	9239.09i	−0.311771	+	0.295260i
$994$	25713.4	−	13256.2i	0.820502	−	0.422998i
$995$	48479.5	−	9343.66i	1.54463	−	0.297702i
$996$	−69270.6	−	36009.5i	−2.20374	−	1.14559i
$997$	−9328.85	−	38454.0i	−0.296337	−	1.22152i	−0.904073	−	0.427377i	$-0.859438\pi$
$997$	−9328.85	−	38454.0i	−0.296337	−	1.22152i	0.607737	−	0.794139i	$-0.292078\pi$
$998$	−56928.3	+	36585.6i	−1.80565	+	1.16042i
$999$	−6100.24	+	13005.7i	−0.193196	+	0.411893i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.m.a.4.1	✓	1400
9.7	even	3	inner	207.4.m.a.142.70	yes	1400
23.6	even	11	inner	207.4.m.a.121.70	yes	1400
207.52	even	33	inner	207.4.m.a.52.1	yes	1400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.4.m.a.4.1	✓	1400	1.1	even	1	trivial
207.4.m.a.52.1	yes	1400	207.52	even	33	inner
207.4.m.a.121.70	yes	1400	23.6	even	11	inner
207.4.m.a.142.70	yes	1400	9.7	even	3	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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	207.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.26722 + 4.58817i) q^{2} +(-1.71615 + 4.90457i) q^{3} +(-7.76003 - 22.4211i) q^{4} +(-14.9593 + 7.71206i) q^{5} +(-16.8960 - 23.8983i) q^{6} +(12.7056 - 9.99183i) q^{7} +(84.9902 + 24.9554i) q^{8} +(-21.1097 - 16.8339i) q^{9} +(13.4911 - 93.8328i) q^{10} +(31.3146 - 2.99018i) q^{11} +(123.283 + 0.418300i) q^{12} +(-0.231798 - 0.182288i) q^{13} +(4.33206 + 90.9412i) q^{14} +(-12.1520 - 86.6040i) q^{15} +(-242.982 + 191.083i) q^{16} +(-16.4682 - 19.0053i) q^{17} +(146.207 - 41.8547i) q^{18} +(17.0858 - 19.7181i) q^{19} +(288.998 + 275.559i) q^{20} +(27.2009 + 79.4632i) q^{21} +(-88.5923 + 153.446i) q^{22} +(13.2689 - 109.503i) q^{23} +(-268.251 + 374.014i) q^{24} +(91.7979 - 128.912i) q^{25} +(1.59370 - 0.467953i) q^{26} +(118.791 - 74.6445i) q^{27} +(-322.624 - 207.338i) q^{28} +(-63.1077 + 182.338i) q^{29} +(437.057 + 227.199i) q^{30} +(199.404 - 190.132i) q^{31} +(-49.1283 - 1031.33i) q^{32} +(-39.0749 + 158.716i) q^{33} +(141.005 - 13.4643i) q^{34} +(-113.010 + 247.457i) q^{35} +(-213.624 + 603.935i) q^{36} +(-86.1380 + 55.3575i) q^{37} +(34.6468 + 142.816i) q^{38} +(1.29184 - 0.824037i) q^{39} +(-1463.85 + 282.134i) q^{40} +(14.4654 - 7.45746i) q^{41} +(-453.462 - 134.821i) q^{42} +(-267.922 - 255.464i) q^{43} +(-310.046 - 678.905i) q^{44} +(445.610 + 89.0248i) q^{45} +(459.066 + 418.651i) q^{46} +(31.8676 + 55.1963i) q^{47} +(-520.189 - 1519.65i) q^{48} +(-19.2686 + 79.4262i) q^{49} +(291.547 + 842.369i) q^{50} +(121.475 - 48.1536i) q^{51} +(-2.28834 + 6.61173i) q^{52} +(7.57407 + 52.6788i) q^{53} +(-45.6332 + 788.911i) q^{54} +(-445.384 + 286.231i) q^{55} +(1329.21 - 532.134i) q^{56} +(67.3871 + 117.638i) q^{57} +(-630.409 - 885.286i) q^{58} +(133.503 + 104.988i) q^{59} +(-1847.46 + 944.511i) q^{60} +(120.761 + 497.784i) q^{61} +(220.858 + 1536.10i) q^{62} +(-436.414 - 2.96154i) q^{63} +(2812.07 + 1807.21i) q^{64} +(4.87335 + 0.939261i) q^{65} +(-600.552 - 697.844i) q^{66} +(1042.44 + 99.5411i) q^{67} +(-298.327 + 516.717i) q^{68} +(514.295 + 253.002i) q^{69} +(-766.148 - 1327.01i) q^{70} +(-131.998 - 289.035i) q^{71} +(-1374.02 - 1957.52i) q^{72} +(152.288 - 175.750i) q^{73} +(27.4421 - 576.081i) q^{74} +(474.720 + 671.461i) q^{75} +(-574.689 - 230.071i) q^{76} +(367.995 - 350.882i) q^{77} +(-0.439915 + 8.61951i) q^{78} +(917.480 - 367.304i) q^{79} +(2161.20 - 4732.36i) q^{80} +(162.238 + 710.718i) q^{81} +(-13.0457 + 90.7351i) q^{82} +(-562.865 - 290.177i) q^{83} +(1570.57 - 1226.51i) q^{84} +(392.923 + 157.302i) q^{85} +(2047.47 - 394.618i) q^{86} +(-785.986 - 622.434i) q^{87} +(2736.06 + 527.332i) q^{88} +(-460.210 + 135.130i) q^{89} +(-1864.37 + 1753.67i) q^{90} -4.76653 q^{91} +(-2558.15 + 552.243i) q^{92} +(590.308 + 1304.29i) q^{93} +(-357.368 - 34.1245i) q^{94} +(-103.525 + 426.736i) q^{95} +(5142.55 + 1528.96i) q^{96} +(-26.0995 + 547.895i) q^{97} +(-301.466 - 347.910i) q^{98} +(-711.378 - 464.026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1400 q - 9 q^{2} - 14 q^{3} + 263 q^{4} + 19 q^{5} - 35 q^{6} - 9 q^{7} - 74 q^{8} - 78 q^{9} - 68 q^{10} + 79 q^{11} + 54 q^{12} - 9 q^{13} + 159 q^{14} - 868 q^{15} + 1031 q^{16} - 308 q^{17} - 87 q^{18}+ \cdots + 7484 q^{99}+O(q^{100}) \) 1400 * q - 9 * q^2 - 14 * q^3 + 263 * q^4 + 19 * q^5 - 35 * q^6 - 9 * q^7 - 74 * q^8 - 78 * q^9 - 68 * q^10 + 79 * q^11 + 54 * q^12 - 9 * q^13 + 159 * q^14 - 868 * q^15 + 1031 * q^16 - 308 * q^17 - 87 * q^18 - 36 * q^19 + 119 * q^20 - 660 * q^21 - 52 * q^22 - 116 * q^23 + 2420 * q^24 + 1397 * q^25 + 432 * q^26 + 274 * q^27 - 324 * q^28 - 45 * q^29 + 768 * q^30 - 45 * q^31 + 111 * q^32 - 1664 * q^33 + 403 * q^34 - 536 * q^35 - 121 * q^36 - 180 * q^37 - 117 * q^38 - 46 * q^39 - 473 * q^40 - 333 * q^41 - 332 * q^42 - 9 * q^43 - 1908 * q^44 + 1762 * q^45 + 484 * q^46 + 216 * q^47 + 1072 * q^48 + 4615 * q^49 - 105 * q^50 + 1298 * q^51 - 708 * q^52 - 1380 * q^53 + 4116 * q^54 - 1328 * q^55 - 3971 * q^56 + 2154 * q^57 - 338 * q^58 + 1917 * q^59 + 154 * q^60 + 27 * q^61 - 3854 * q^62 - 4850 * q^63 - 5854 * q^64 + 3363 * q^65 - 2017 * q^66 + 603 * q^67 - 18454 * q^68 - 4653 * q^69 + 542 * q^70 - 5296 * q^71 - 8044 * q^72 - 36 * q^73 + 3243 * q^74 + 5140 * q^75 - 1029 * q^76 - 1661 * q^77 + 14687 * q^78 - 9 * q^79 + 10312 * q^80 - 294 * q^81 - 770 * q^82 - 2735 * q^83 + 2298 * q^84 + 241 * q^85 + 10507 * q^86 - 10268 * q^87 + 2183 * q^88 - 2980 * q^89 + 33928 * q^90 - 1452 * q^91 - 1973 * q^92 - 11406 * q^93 + 2034 * q^94 - 3339 * q^95 - 4446 * q^96 - 5193 * q^97 + 14820 * q^98 + 7484 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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