LMFDB - Embedded newform 31.5.f.a.15.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,5,Mod(15,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.15"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	31.f (of order $10$, 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:	$3.20446885560$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			15.3
Character	$\chi$	$=$	31.15
Dual form			31.5.f.a.29.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.66939 + 2.66597i) q^{2} +(7.06689 - 9.72674i) q^{3} +(1.41276 - 4.34804i) q^{4} -44.3313 q^{5} +54.5313i q^{6} +(17.8399 - 54.9055i) q^{7} +(-16.0176 - 49.2970i) q^{8} +(-19.6382 - 60.4400i) q^{9} +(162.669 - 118.186i) q^{10} +(-130.273 - 42.3284i) q^{11} +(-32.3084 - 44.4687i) q^{12} +(23.2330 - 31.9775i) q^{13} +(80.9149 + 249.030i) q^{14} +(-313.284 + 431.199i) q^{15} +(249.377 + 181.183i) q^{16} +(285.618 - 92.8030i) q^{17} +(233.191 + 169.423i) q^{18} +(-426.218 + 309.665i) q^{19} +(-62.6297 + 192.754i) q^{20} +(-407.979 - 561.535i) q^{21} +(590.870 - 191.985i) q^{22} +(-241.680 + 78.5267i) q^{23} +(-592.693 - 192.578i) q^{24} +1340.26 q^{25} +179.276i q^{26} +(199.527 + 64.8302i) q^{27} +(-213.528 - 155.137i) q^{28} +(-114.471 - 157.556i) q^{29} -2417.44i q^{30} +(661.539 - 697.056i) q^{31} -568.749 q^{32} +(-1332.34 + 968.005i) q^{33} +(-800.635 + 1101.98i) q^{34} +(-790.866 + 2434.03i) q^{35} -290.540 q^{36} -972.281i q^{37} +(738.401 - 2272.57i) q^{38} +(-146.852 - 451.962i) q^{39} +(710.079 + 2185.40i) q^{40} +(208.081 - 151.180i) q^{41} +(2994.07 + 972.833i) q^{42} +(-1705.20 - 2347.01i) q^{43} +(-368.091 + 506.634i) q^{44} +(870.585 + 2679.39i) q^{45} +(677.469 - 932.457i) q^{46} +(-2017.16 - 1465.55i) q^{47} +(3524.65 - 1145.23i) q^{48} +(-753.907 - 547.746i) q^{49} +(-4917.95 + 3573.10i) q^{50} +(1115.76 - 3433.96i) q^{51} +(-106.217 - 146.195i) q^{52} +(1649.46 - 535.941i) q^{53} +(-904.976 + 294.045i) q^{54} +(5775.19 + 1876.47i) q^{55} -2992.43 q^{56} +6334.08i q^{57} +(840.076 + 272.957i) q^{58} +(1701.99 + 1236.56i) q^{59} +(1432.27 + 1971.36i) q^{60} -4449.01i q^{61} +(-569.115 + 4321.41i) q^{62} -3668.84 q^{63} +(-1903.08 + 1382.67i) q^{64} +(-1029.95 + 1417.60i) q^{65} +(2308.22 - 7103.98i) q^{66} -2108.33 q^{67} -1372.99i q^{68} +(-944.119 + 2905.70i) q^{69} +(-3587.06 - 11039.8i) q^{70} +(-421.584 - 1297.50i) q^{71} +(-2664.96 + 1936.20i) q^{72} +(4572.26 + 1485.62i) q^{73} +(2592.07 + 3567.68i) q^{74} +(9471.50 - 13036.4i) q^{75} +(744.293 + 2290.70i) q^{76} +(-4648.13 + 6397.60i) q^{77} +(1743.77 + 1266.93i) q^{78} +(-1997.62 + 649.066i) q^{79} +(-11055.2 - 8032.09i) q^{80} +(6205.10 - 4508.27i) q^{81} +(-360.490 + 1109.47i) q^{82} +(-488.886 - 672.894i) q^{83} +(-3017.96 + 980.594i) q^{84} +(-12661.8 + 4114.08i) q^{85} +(12514.1 + 4066.08i) q^{86} -2341.46 q^{87} +7100.08i q^{88} +(3623.07 + 1177.21i) q^{89} +(-10337.7 - 7510.76i) q^{90} +(-1341.27 - 1846.09i) q^{91} +1161.78i q^{92} +(-2105.06 - 11360.6i) q^{93} +11308.8 q^{94} +(18894.8 - 13727.9i) q^{95} +(-4019.29 + 5532.08i) q^{96} +(-2927.84 + 9010.96i) q^{97} +4226.65 q^{98} +8704.98i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} - 5 q^{3} - 79 q^{4} - 2 q^{5} - 73 q^{7} + 173 q^{8} + 62 q^{9} + 84 q^{10} + 100 q^{11} + 150 q^{12} - 260 q^{13} + 488 q^{14} - 1075 q^{15} + 777 q^{16} - 725 q^{17} - 786 q^{18} - 1581 q^{19}+ \cdots + 74456 q^{98}+O(q^{100}) $ 36 * q - 3 * q^2 - 5 * q^3 - 79 * q^4 - 2 * q^5 - 73 * q^7 + 173 * q^8 + 62 * q^9 + 84 * q^10 + 100 * q^11 + 150 * q^12 - 260 * q^13 + 488 * q^14 - 1075 * q^15 + 777 * q^16 - 725 * q^17 - 786 * q^18 - 1581 * q^19 + 827 * q^20 + 2335 * q^21 - 1030 * q^22 + 1675 * q^23 - 165 * q^24 + 1294 * q^25 - 2855 * q^27 + 352 * q^28 - 575 * q^29 + 895 * q^31 - 5470 * q^32 + 4468 * q^33 + 1815 * q^34 - 3042 * q^35 + 7808 * q^36 - 6604 * q^38 + 595 * q^39 + 1482 * q^40 - 1740 * q^41 + 3840 * q^42 - 10055 * q^43 - 5780 * q^44 + 6774 * q^45 + 16515 * q^46 + 693 * q^47 + 4710 * q^48 - 944 * q^49 - 6240 * q^50 + 12641 * q^51 + 15885 * q^52 - 10835 * q^53 - 25960 * q^54 - 14010 * q^55 - 19976 * q^56 + 4755 * q^58 - 6021 * q^59 + 35 * q^60 - 11088 * q^62 - 15564 * q^63 + 6935 * q^64 + 26645 * q^65 + 23988 * q^66 + 28596 * q^67 - 4229 * q^69 + 8041 * q^70 + 31101 * q^71 + 20690 * q^72 + 6125 * q^73 - 47295 * q^74 - 27475 * q^75 + 12511 * q^76 + 35950 * q^77 + 29801 * q^78 - 29050 * q^79 - 47358 * q^80 - 1965 * q^81 + 9198 * q^82 + 21640 * q^83 - 35875 * q^84 - 55360 * q^85 - 27935 * q^86 - 2262 * q^87 - 11645 * q^89 - 14916 * q^90 + 670 * q^91 - 36224 * q^93 - 52442 * q^94 + 73983 * q^95 + 29810 * q^96 + 55059 * q^97 + 74456 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−3.66939	+	2.66597i	−0.917347	+	0.666492i	−0.942862	−	0.333183i	$-0.891877\pi$
$2$	−3.66939	+	2.66597i	−0.917347	+	0.666492i	0.0255150	+	0.999674i	$0.491877\pi$
$3$	7.06689	−	9.72674i	0.785210	−	1.08075i	−0.209478	−	0.977813i	$-0.567176\pi$
$3$	7.06689	−	9.72674i	0.785210	−	1.08075i	0.994688	−	0.102936i	$-0.0328235\pi$
$4$	1.41276	−	4.34804i	0.0882978	−	0.271753i
$5$	−44.3313			−1.77325			−0.886626	−	0.462487i	$-0.846957\pi$
$5$	−44.3313			−1.77325			−0.886626	+	0.462487i	$0.846957\pi$
$6$			54.5313i			1.51476i
$7$	17.8399	−	54.9055i	0.364079	−	1.12052i	−0.586476	−	0.809967i	$-0.699485\pi$
$7$	17.8399	−	54.9055i	0.364079	−	1.12052i	0.950555	−	0.310555i	$-0.100515\pi$
$8$	−16.0176	−	49.2970i	−0.250274	−	0.770265i
$9$	−19.6382	−	60.4400i	−0.242446	−	0.746173i
$10$	162.669	−	118.186i	1.62669	−	1.18186i
$11$	−130.273	−	42.3284i	−1.07664	−	0.349821i	−0.283569	−	0.958952i	$-0.591519\pi$
$11$	−130.273	−	42.3284i	−1.07664	−	0.349821i	−0.793070	+	0.609130i	$0.791519\pi$
$12$	−32.3084	−	44.4687i	−0.224364	−	0.308811i
$13$	23.2330	−	31.9775i	0.137473	−	0.189216i	−0.734729	−	0.678360i	$-0.762691\pi$
$13$	23.2330	−	31.9775i	0.137473	−	0.189216i	0.872203	+	0.489144i	$0.162691\pi$
$14$	80.9149	+	249.030i	0.412831	+	1.27056i
$15$	−313.284	+	431.199i	−1.39238	+	1.91644i
$16$	249.377	+	181.183i	0.974131	+	0.707747i
$17$	285.618	−	92.8030i	0.988298	−	0.321117i	0.230118	−	0.973163i	$-0.426089\pi$
$17$	285.618	−	92.8030i	0.988298	−	0.321117i	0.758180	+	0.652045i	$0.226089\pi$
$18$	233.191	+	169.423i	0.719726	+	0.522912i
$19$	−426.218	+	309.665i	−1.18066	+	0.857799i	−0.992246	−	0.124291i	$-0.960334\pi$
$19$	−426.218	+	309.665i	−1.18066	+	0.857799i	−0.188413	+	0.982090i	$0.560334\pi$
$20$	−62.6297	+	192.754i	−0.156574	+	0.481886i
$21$	−407.979	−	561.535i	−0.925123	−	1.27332i
$22$	590.870	−	191.985i	1.22081	−	0.396664i
$23$	−241.680	+	78.5267i	−0.456862	+	0.148444i	−0.528402	−	0.848994i	$-0.677209\pi$
$23$	−241.680	+	78.5267i	−0.456862	+	0.148444i	0.0715398	+	0.997438i	$0.477209\pi$
$24$	−592.693	−	192.578i	−1.02898	−	0.334336i
$25$	1340.26			2.14442
$26$			179.276i			0.265201i
$27$	199.527	+	64.8302i	0.273699	+	0.0889303i
$28$	−213.528	−	155.137i	−0.272357	−	0.197879i
$29$	−114.471	−	157.556i	−0.136113	−	0.187343i	0.735519	−	0.677504i	$-0.236938\pi$
$29$	−114.471	−	157.556i	−0.136113	−	0.187343i	−0.871632	+	0.490160i	$0.836938\pi$
$30$		−	2417.44i		−	2.68605i
$31$	661.539	−	697.056i	0.688386	−	0.725345i
$31$	661.539	−	697.056i	0.688386	−	0.725345i
$32$	−568.749			−0.555419
$33$	−1332.34	+	968.005i	−1.22346	+	0.888894i
$34$	−800.635	+	1101.98i	−0.692590	+	0.953269i
$35$	−790.866	+	2434.03i	−0.645605	+	1.98697i
$36$	−290.540			−0.224182
$37$		−	972.281i		−	0.710212i	−0.934826	−	0.355106i	$-0.884445\pi$
$37$		−	972.281i		−	0.710212i	0.934826	−	0.355106i	$-0.115555\pi$
$38$	738.401	−	2272.57i	0.511358	−	1.57380i
$39$	−146.852	−	451.962i	−0.0965493	−	0.297148i
$40$	710.079	+	2185.40i	0.443799	+	1.36587i
$41$	208.081	−	151.180i	0.123784	−	0.0899343i	−0.524171	−	0.851613i	$-0.675625\pi$
$41$	208.081	−	151.180i	0.123784	−	0.0899343i	0.647955	+	0.761679i	$0.275625\pi$
$42$	2994.07	+	972.833i	1.69732	+	0.551492i
$43$	−1705.20	−	2347.01i	−0.922230	−	1.26934i	−0.962814	−	0.270164i	$-0.912922\pi$
$43$	−1705.20	−	2347.01i	−0.922230	−	1.26934i	0.0405846	−	0.999176i	$-0.487078\pi$
$44$	−368.091	+	506.634i	−0.190130	+	0.261691i
$45$	870.585	+	2679.39i	0.429919	+	1.32315i
$46$	677.469	−	932.457i	0.320165	−	0.440669i
$47$	−2017.16	−	1465.55i	−0.913154	−	0.663445i	0.0286565	−	0.999589i	$-0.490877\pi$
$47$	−2017.16	−	1465.55i	−0.913154	−	0.663445i	−0.941811	+	0.336144i	$0.890877\pi$
$48$	3524.65	−	1145.23i	1.52979	−	0.497060i
$49$	−753.907	−	547.746i	−0.313997	−	0.228132i
$50$	−4917.95	+	3573.10i	−1.96718	+	1.42924i
$51$	1115.76	−	3433.96i	0.428974	−	1.32025i
$52$	−106.217	−	146.195i	−0.0392813	−	0.0540661i
$53$	1649.46	−	535.941i	0.587204	−	0.190794i	−0.000321106	−	1.00000i	$-0.500102\pi$
$53$	1649.46	−	535.941i	0.587204	−	0.190794i	0.587525	+	0.809206i	$0.300102\pi$
$54$	−904.976	+	294.045i	−0.310349	+	0.100838i
$55$	5775.19	+	1876.47i	1.90915	+	0.620321i
$56$	−2992.43			−0.954218
$57$			6334.08i			1.94955i
$58$	840.076	+	272.957i	0.249725	+	0.0811407i
$59$	1701.99	+	1236.56i	0.488936	+	0.355233i	0.804775	−	0.593580i	$-0.202286\pi$
$59$	1701.99	+	1236.56i	0.488936	+	0.355233i	−0.315839	+	0.948813i	$0.602286\pi$
$60$	1432.27	+	1971.36i	0.397854	+	0.547599i
$61$		−	4449.01i		−	1.19565i	−0.801627	−	0.597825i	$-0.796032\pi$
$61$		−	4449.01i		−	1.19565i	0.801627	−	0.597825i	$-0.203968\pi$
$62$	−569.115	+	4321.41i	−0.148053	+	1.12420i
$63$	−3668.84			−0.924373
$64$	−1903.08	+	1382.67i	−0.464618	+	0.337565i
$65$	−1029.95	+	1417.60i	−0.243775	+	0.335527i
$66$	2308.22	−	7103.98i	0.529895	−	1.63085i
$67$	−2108.33			−0.469666			−0.234833	−	0.972036i	$-0.575454\pi$
$67$	−2108.33			−0.469666			−0.234833	+	0.972036i	$0.575454\pi$
$68$		−	1372.99i		−	0.296927i
$69$	−944.119	+	2905.70i	−0.198303	+	0.610313i
$70$	−3587.06	−	11039.8i	−0.732054	−	2.25303i
$71$	−421.584	−	1297.50i	−0.0836311	−	0.257390i	0.900493	−	0.434870i	$-0.143206\pi$
$71$	−421.584	−	1297.50i	−0.0836311	−	0.257390i	−0.984124	+	0.177480i	$0.943206\pi$
$72$	−2664.96	+	1936.20i	−0.514073	+	0.373496i
$73$	4572.26	+	1485.62i	0.857996	+	0.278780i	0.704791	−	0.709415i	$-0.251041\pi$
$73$	4572.26	+	1485.62i	0.857996	+	0.278780i	0.153205	+	0.988194i	$0.451041\pi$
$74$	2592.07	+	3567.68i	0.473351	+	0.651511i
$75$	9471.50	−	13036.4i	1.68382	−	2.31758i
$76$	744.293	+	2290.70i	0.128860	+	0.396589i
$77$	−4648.13	+	6397.60i	−0.783964	+	1.07903i
$78$	1743.77	+	1266.93i	0.286616	+	0.208239i
$79$	−1997.62	+	649.066i	−0.320080	+	0.104000i	−0.464650	−	0.885494i	$-0.653820\pi$
$79$	−1997.62	+	649.066i	−0.320080	+	0.104000i	0.144570	+	0.989495i	$0.453820\pi$
$80$	−11055.2	−	8032.09i	−1.72738	−	1.25501i
$81$	6205.10	−	4508.27i	0.945756	−	0.687132i
$82$	−360.490	+	1109.47i	−0.0536124	+	0.165002i
$83$	−488.886	−	672.894i	−0.0709661	−	0.0976765i	0.772058	−	0.635552i	$-0.219227\pi$
$83$	−488.886	−	672.894i	−0.0709661	−	0.0976765i	−0.843025	+	0.537875i	$0.819227\pi$
$84$	−3017.96	+	980.594i	−0.427715	+	0.138973i
$85$	−12661.8	+	4114.08i	−1.75250	+	0.569422i
$86$	12514.1	+	4066.08i	1.69201	+	0.549767i
$87$	−2341.46			−0.309348
$88$			7100.08i			0.916849i
$89$	3623.07	+	1177.21i	0.457401	+	0.148619i	0.528650	−	0.848840i	$-0.322698\pi$
$89$	3623.07	+	1177.21i	0.457401	+	0.148619i	−0.0712490	+	0.997459i	$0.522698\pi$
$90$	−10337.7	−	7510.76i	−1.27626	−	0.927254i
$91$	−1341.27	−	1846.09i	−0.161969	−	0.222931i
$92$			1161.78i			0.137261i
$93$	−2105.06	−	11360.6i	−0.243388	−	1.31352i
$94$	11308.8			1.27986
$95$	18894.8	−	13727.9i	2.09361	−	1.52109i
$96$	−4019.29	+	5532.08i	−0.436121	+	0.600269i
$97$	−2927.84	+	9010.96i	−0.311174	+	0.957696i	0.666126	+	0.745839i	$0.267951\pi$
$97$	−2927.84	+	9010.96i	−0.311174	+	0.957696i	−0.977301	+	0.211857i	$0.932049\pi$
$98$	4226.65			0.440093
$99$			8704.98i			0.888172i
$100$	1893.48	−	5827.53i	0.189348	−	0.582753i
$101$	−1542.22	−	4746.47i	−0.151183	−	0.465295i	0.846571	−	0.532276i	$-0.178663\pi$
$101$	−1542.22	−	4746.47i	−0.151183	−	0.465295i	−0.997754	+	0.0669815i	$0.978663\pi$
$102$	5060.67	+	15575.1i	0.486415	+	1.49703i
$103$	−9244.63	+	6716.62i	−0.871395	+	0.633106i	−0.930961	−	0.365119i	$-0.881028\pi$
$103$	−9244.63	+	6716.62i	−0.871395	+	0.633106i	0.0595658	+	0.998224i	$0.481028\pi$
$104$	−1948.53	−	633.115i	−0.180152	−	0.0585350i
$105$	18086.3	+	24893.6i	1.64048	+	2.25792i
$106$	−4623.70	+	6363.98i	−0.411508	+	0.566392i
$107$	6975.70	+	21469.0i	0.609284	+	1.87518i	0.464108	+	0.885778i	$0.346375\pi$
$107$	6975.70	+	21469.0i	0.609284	+	1.87518i	0.145176	+	0.989406i	$0.453625\pi$
$108$	563.769	−	775.961i	0.0483341	−	0.0665261i
$109$	−5262.35	−	3823.32i	−0.442922	−	0.321801i	0.343873	−	0.939016i	$-0.388261\pi$
$109$	−5262.35	−	3823.32i	−0.442922	−	0.321801i	−0.786795	+	0.617215i	$0.788261\pi$
$110$	−26194.0	+	8510.96i	−2.16480	+	0.703385i
$111$	−9457.12	−	6871.00i	−0.767561	−	0.557666i
$112$	14396.8	−	10459.9i	1.14771	−	0.833858i
$113$	1402.37	−	4316.04i	0.109826	−	0.338009i	−0.881007	−	0.473103i	$-0.843134\pi$
$113$	1402.37	−	4316.04i	0.109826	−	0.338009i	0.990833	+	0.135094i	$0.0431337\pi$
$114$	−16886.5	−	23242.2i	−1.29936	−	1.78841i
$115$	10714.0	−	3481.19i	0.810132	−	0.263228i
$116$	−846.779	+	275.135i	−0.0629295	+	0.0204470i
$117$	−2388.97	−	776.224i	−0.174518	−	0.0567042i
$118$	−9541.89			−0.685283
$119$		−	17337.6i		−	1.22432i
$120$	26274.9	+	8537.22i	1.82464	+	0.592862i
$121$	3334.64	+	2422.76i	0.227760	+	0.165478i
$122$	11860.9	+	16325.2i	0.796891	+	1.09683i
$123$		−	3092.32i		−	0.204397i
$124$	−2096.23	−	3861.18i	−0.136331	−	0.251117i
$125$	−31708.6			−2.02935
$126$	13462.4	−	9781.00i	0.847971	−	0.616087i
$127$	14336.1	−	19732.0i	0.888841	−	1.22338i	−0.0850520	−	0.996377i	$-0.527106\pi$
$127$	14336.1	−	19732.0i	0.888841	−	1.22338i	0.973893	−	0.227008i	$-0.0728944\pi$
$128$	6109.04	−	18801.7i	0.372866	−	1.14756i
$129$	−34879.2			−2.09598
$130$		−	7947.55i		−	0.470269i
$131$	1957.73	−	6025.26i	0.114080	−	0.351102i	−0.877674	−	0.479258i	$-0.840906\pi$
$131$	1957.73	−	6025.26i	0.114080	−	0.351102i	0.991754	+	0.128156i	$0.0409058\pi$
$132$	2326.64	+	7160.65i	0.133531	+	0.410965i
$133$	9398.67	+	28926.1i	0.531328	+	1.63526i
$134$	7736.28	−	5620.74i	0.430847	−	0.313028i
$135$	−8845.28	−	2874.01i	−0.485338	−	0.157696i
$136$	−9149.81	−	12593.6i	−0.494691	−	0.680884i
$137$	16529.0	−	22750.2i	0.880654	−	1.21212i	−0.0955858	−	0.995421i	$-0.530472\pi$
$137$	16529.0	−	22750.2i	0.880654	−	1.21212i	0.976239	−	0.216695i	$-0.0695276\pi$
$138$	−4282.16	−	13179.1i	−0.224856	−	0.692036i
$139$	−496.838	+	683.839i	−0.0257149	+	0.0353936i	−0.821681	−	0.569948i	$-0.806963\pi$
$139$	−496.838	+	683.839i	−0.0257149	+	0.0353936i	0.795966	+	0.605341i	$0.206963\pi$
$140$	9465.98	+	6877.44i	0.482958	+	0.350890i
$141$	−28510.1	+	9263.48i	−1.43404	+	0.465946i
$142$	5006.06	+	3637.12i	0.248267	+	0.180377i
$143$	−4380.19	+	3182.40i	−0.214201	+	0.155626i
$144$	6053.41	−	18630.5i	0.291928	−	0.898461i
$145$	5074.64	+	6984.65i	0.241362	+	0.332207i
$146$	−20738.0	+	6738.19i	−0.972885	+	0.316110i
$147$	−10655.6	+	3462.20i	−0.493108	+	0.160220i
$148$	−4227.52	−	1373.60i	−0.193002	−	0.0627102i
$149$	30890.8			1.39141			0.695706	−	0.718326i	$-0.255091\pi$
$149$	30890.8			1.39141			0.695706	+	0.718326i	$0.255091\pi$
$150$			73086.4i			3.24828i
$151$	−2607.24	−	847.145i	−0.114348	−	0.0371539i	0.251284	−	0.967913i	$-0.419147\pi$
$151$	−2607.24	−	847.145i	−0.114348	−	0.0371539i	−0.365632	+	0.930759i	$0.619147\pi$
$152$	22092.5	+	16051.2i	0.956221	+	0.694735i
$153$	−11218.0	−	15440.3i	−0.479219	−	0.659588i
$154$		−	35867.0i		−	1.51236i
$155$	−29326.9	+	30901.4i	−1.22068	+	1.28622i
$156$	−2172.62			−0.0892759
$157$	−29923.3	+	21740.5i	−1.21398	+	0.882005i	−0.995586	−	0.0938571i	$-0.970080\pi$
$157$	−29923.3	+	21740.5i	−1.21398	+	0.882005i	−0.218390	+	0.975862i	$0.570080\pi$
$158$	5599.65	−	7707.26i	0.224309	−	0.308735i
$159$	6443.57	−	19831.3i	0.254878	−	0.784434i
$160$	25213.4			0.984898
$161$			14670.5i			0.565969i
$162$	−10750.0	+	33085.2i	−0.409619	+	1.26068i
$163$	12284.2	+	37806.8i	0.462350	+	1.42297i	0.862285	+	0.506424i	$0.169033\pi$
$163$	12284.2	+	37806.8i	0.462350	+	1.42297i	−0.399934	+	0.916544i	$0.630967\pi$
$164$	−363.366	−	1118.33i	−0.0135100	−	0.0415796i
$165$	59064.6	−	42912.9i	2.16950	−	1.57623i
$166$	3587.82	+	1165.75i	0.130201	+	0.0423049i
$167$	−23225.0	−	31966.5i	−0.832766	−	1.14620i	−0.987402	−	0.158232i	$-0.949420\pi$
$167$	−23225.0	−	31966.5i	−0.832766	−	1.14620i	0.154636	−	0.987972i	$-0.450580\pi$
$168$	−21147.2	+	29106.6i	−0.749262	+	1.03127i
$169$	8343.05	+	25677.3i	0.292113	+	0.899032i
$170$	35493.2	−	48852.2i	1.22814	−	1.69039i
$171$	27086.3	+	19679.4i	0.926313	+	0.673006i
$172$	−12613.9	+	4098.52i	−0.426377	+	0.138538i
$173$	−3803.07	−	2763.09i	−0.127070	−	0.0923215i	0.522435	−	0.852679i	$-0.325024\pi$
$173$	−3803.07	−	2763.09i	−0.127070	−	0.0923215i	−0.649505	+	0.760358i	$0.725024\pi$
$174$	8591.71	−	6242.25i	0.283780	−	0.206178i
$175$	23910.2	−	73587.9i	0.780740	−	2.40287i
$176$	−24818.0	−	34159.1i	−0.801202	−	1.10276i
$177$	24055.5	−	7816.10i	0.767834	−	0.249485i
$178$	−16432.9	+	5339.36i	−0.518649	+	0.168519i
$179$	−31762.5	−	10320.3i	−0.991309	−	0.322096i	−0.231921	−	0.972735i	$-0.574501\pi$
$179$	−31762.5	−	10320.3i	−0.991309	−	0.322096i	−0.759387	+	0.650639i	$0.774501\pi$
$180$	12880.0			0.397531
$181$			8513.89i			0.259879i	0.991522	+	0.129939i	$0.0414783\pi$
$181$			8513.89i			0.259879i	−0.991522	+	0.129939i	$0.958522\pi$
$182$	9843.26	+	3198.27i	0.297164	+	0.0965544i
$183$	−43274.4	−	31440.7i	−1.29220	−	0.938836i
$184$	7742.25	+	10656.3i	0.228682	+	0.314754i
$185$			43102.5i			1.25939i
$186$	38011.4	+	36074.6i	1.09872	+	1.04274i
$187$	−41136.6			−1.17637
$188$	−9222.05	+	6700.21i	−0.260923	+	0.189571i
$189$	7119.07	−	9798.56i	0.199297	−	0.274308i
$190$	−32734.3	+	100746.i	−0.906767	+	2.79074i
$191$	4394.94			0.120472			0.0602360	−	0.998184i	$-0.480815\pi$
$191$	4394.94			0.120472			0.0602360	+	0.998184i	$0.480815\pi$
$192$			28281.9i			0.767195i
$193$	1918.03	−	5903.09i	0.0514921	−	0.158476i	−0.922004	−	0.387181i	$-0.873449\pi$
$193$	1918.03	−	5903.09i	0.0514921	−	0.158476i	0.973496	+	0.228704i	$0.0734489\pi$
$194$	−13279.6	−	40870.3i	−0.352842	−	1.08594i
$195$	6510.12	+	20036.1i	0.171206	+	0.526919i
$196$	−3446.72	+	2504.19i	−0.0897208	+	0.0651860i
$197$	59339.9	+	19280.7i	1.52903	+	0.496810i	0.948323	−	0.317306i	$-0.102778\pi$
$197$	59339.9	+	19280.7i	1.52903	+	0.496810i	0.580702	+	0.814116i	$0.302778\pi$
$198$	−23207.2	−	31942.0i	−0.591960	−	0.814763i
$199$	−6716.22	+	9244.09i	−0.169597	+	0.233431i	−0.885352	−	0.464921i	$-0.846083\pi$
$199$	−6716.22	+	9244.09i	−0.169597	+	0.233431i	0.715755	+	0.698352i	$0.246083\pi$
$200$	−21467.8	−	66071.0i	−0.536694	−	1.65177i
$201$	−14899.3	+	20507.2i	−0.368786	+	0.507591i
$202$	18312.9	+	13305.1i	0.448803	+	0.326074i
$203$	−10692.8	+	3474.31i	−0.259478	+	0.0843095i
$204$	−13354.7	−	9702.76i	−0.320903	−	0.233150i
$205$	−9224.49	+	6701.99i	−0.219500	+	0.159476i
$206$	16015.9	−	49291.8i	0.377412	−	1.16156i
$207$	9492.31	+	13065.0i	0.221529	+	0.304909i
$208$	11587.6	−	3765.03i	0.267834	−	0.0870245i
$209$	68632.5	−	22300.0i	1.57122	−	0.510520i
$210$	−132731.	−	43126.9i	−3.00977	−	0.977935i
$211$	12832.3			0.288229			0.144115	−	0.989561i	$-0.453967\pi$
$211$	12832.3			0.288229			0.144115	+	0.989561i	$0.453967\pi$
$212$		−	7929.07i		−	0.176421i
$213$	−15599.8	−	5068.67i	−0.343842	−	0.111721i
$214$	−82832.2	−	60181.1i	−1.80872	−	1.31411i
$215$	75593.9	+	104046.i	1.63535	+	2.25086i
$216$		−	10874.5i		−	0.233078i
$217$	−26470.5	−	48757.6i	−0.562137	−	1.03543i
$218$	29502.5			0.620791
$219$	46761.9	−	33974.5i	0.974998	−	0.708378i
$220$	16318.0	−	22459.7i	0.337148	−	0.464044i
$221$	3668.16	−	11289.4i	0.0751041	−	0.231147i
$222$	53019.7			1.07580
$223$		−	46927.9i		−	0.943672i	−0.881686	−	0.471836i	$-0.843591\pi$
$223$		−	46927.9i		−	0.943672i	0.881686	−	0.471836i	$-0.156409\pi$
$224$	−10146.4	+	31227.5i	−0.202217	+	0.622359i
$225$	−26320.3	−	81005.6i	−0.519908	−	1.60011i
$226$	6360.60	+	19575.9i	0.124532	+	0.383270i
$227$	−33753.8	+	24523.6i	−0.655045	+	0.475918i	−0.864986	−	0.501796i	$-0.832673\pi$
$227$	−33753.8	+	24523.6i	−0.655045	+	0.475918i	0.209941	+	0.977714i	$0.432673\pi$
$228$	27540.9	+	8948.57i	0.529795	+	0.172141i
$229$	−58241.5	−	80162.5i	−1.11061	−	1.52862i	−0.820515	−	0.571626i	$-0.806313\pi$
$229$	−58241.5	−	80162.5i	−1.11061	−	1.52862i	−0.290095	−	0.956998i	$-0.593687\pi$
$230$	−30033.1	+	41337.0i	−0.567733	+	0.781418i
$231$	29380.0	+	90422.2i	0.550589	+	1.69454i
$232$	−5933.47	+	8166.72i	−0.110238	+	0.151730i
$233$	46648.2	+	33891.9i	0.859257	+	0.624287i	0.927683	−	0.373369i	$-0.121798\pi$
$233$	46648.2	+	33891.9i	0.859257	+	0.624287i	−0.0684256	+	0.997656i	$0.521798\pi$
$234$	10835.5	−	3520.65i	0.197886	−	0.0642971i
$235$	89423.2	+	64969.8i	1.61925	+	1.17646i
$236$	7781.14	−	5653.33i	0.139707	−	0.101503i
$237$	−7803.66	+	24017.2i	−0.138932	+	0.427588i
$238$	46221.5	+	63618.5i	0.816000	+	1.12313i
$239$	33488.2	−	10881.0i	0.586268	−	0.190490i	−0.000838677	−	1.00000i	$-0.500267\pi$
$239$	33488.2	−	10881.0i	0.586268	−	0.190490i	0.587107	+	0.809510i	$0.300267\pi$
$240$	−156252.	+	50769.4i	−2.71271	+	0.881413i
$241$	−34461.7	−	11197.3i	−0.593339	−	0.192787i	−0.00307152	−	0.999995i	$-0.500978\pi$
$241$	−34461.7	−	11197.3i	−0.593339	−	0.192787i	−0.590267	+	0.807208i	$0.700978\pi$
$242$	−18695.1			−0.319225
$243$		−	75221.5i		−	1.27388i
$244$	−19344.5	−	6285.41i	−0.324921	−	0.105573i
$245$	33421.7	+	24282.3i	0.556796	+	0.404536i
$246$	8244.02	+	11346.9i	0.136229	+	0.187503i
$247$			20823.8i			0.341324i
$248$	−44959.0	−	21446.7i	−0.730993	−	0.348705i
$249$	−9999.96			−0.161287
$250$	116351.	−	84534.1i	1.86162	−	1.35255i
$251$	−18243.3	+	25109.7i	−0.289571	+	0.398561i	−0.928875	−	0.370394i	$-0.879223\pi$
$251$	−18243.3	+	25109.7i	−0.289571	+	0.398561i	0.639304	+	0.768954i	$0.279223\pi$
$252$	−5183.20	+	15952.3i	−0.0816201	+	0.251201i
$253$	34808.4			0.543805
$254$			110624.i			1.71467i
$255$	−49463.2	+	152232.i	−0.760679	+	2.34113i
$256$	16077.7	+	49482.0i	0.245326	+	0.755035i
$257$	−27869.3	−	85772.7i	−0.421948	−	1.29862i	−0.905886	−	0.423521i	$-0.860794\pi$
$257$	−27869.3	−	85772.7i	−0.421948	−	1.29862i	0.483938	−	0.875102i	$-0.339206\pi$
$258$	127986.	−	92986.9i	1.92274	−	1.39696i
$259$	−53383.6	−	17345.4i	−0.795808	−	0.258574i
$260$	4708.72	+	6481.00i	0.0696556	+	0.0958728i
$261$	−7274.67	+	10012.7i	−0.106790	+	0.146984i
$262$	8879.49	+	27328.3i	0.129356	+	0.398116i
$263$	−12165.4	+	16744.2i	−0.175879	+	0.242077i	−0.887851	−	0.460131i	$-0.847802\pi$
$263$	−12165.4	+	16744.2i	−0.175879	+	0.242077i	0.711972	+	0.702208i	$0.247802\pi$
$264$	69060.6	+	50175.5i	0.990884	+	0.719919i
$265$	−73122.6	+	23759.0i	−1.04126	+	0.338326i
$266$	−111603.	−	81084.7i	−1.57730	−	1.14598i
$267$	37054.2	−	26921.5i	0.519775	−	0.377639i
$268$	−2978.57	+	9167.11i	−0.0414705	+	0.127633i
$269$	34422.1	+	47378.0i	0.475700	+	0.654745i	0.977671	−	0.210139i	$-0.0673917\pi$
$269$	34422.1	+	47378.0i	0.475700	+	0.654745i	−0.501971	+	0.864884i	$0.667392\pi$
$270$	40118.8	−	13035.4i	0.550326	−	0.178812i
$271$	−3946.12	+	1282.17i	−0.0537318	+	0.0174585i	−0.335760	−	0.941948i	$-0.608993\pi$
$271$	−3946.12	+	1282.17i	−0.0537318	+	0.0174585i	0.282028	+	0.959406i	$0.408993\pi$
$272$	88041.1	+	28606.3i	1.19000	+	0.386655i
$273$	−27435.1			−0.368113
$274$			127545.i			1.69888i
$275$	−174601.	−	56731.2i	−2.30877	−	0.750165i
$276$	11300.3	+	8210.14i	0.148344	+	0.107779i
$277$	−5729.28	−	7885.68i	−0.0746691	−	0.102773i	0.770049	−	0.637985i	$-0.220232\pi$
$277$	−5729.28	−	7885.68i	−0.0746691	−	0.102773i	−0.844718	+	0.535212i	$0.820232\pi$
$278$		−	3833.83i		−	0.0496070i
$279$	−55121.5	−	26294.5i	−0.708129	−	0.337798i
$280$	132658.			1.69207
$281$	−28338.0	+	20588.8i	−0.358886	+	0.260746i	−0.752587	−	0.658493i	$-0.771194\pi$
$281$	−28338.0	+	20588.8i	−0.358886	+	0.260746i	0.393701	+	0.919238i	$0.371194\pi$
$282$	79918.4	−	109998.i	1.00496	−	1.38321i
$283$	42200.5	−	129880.i	0.526920	−	1.62169i	−0.233569	−	0.972340i	$-0.575040\pi$
$283$	42200.5	−	129880.i	0.526920	−	1.62169i	0.760489	−	0.649351i	$-0.224960\pi$
$284$	−6237.20			−0.0773309
$285$		−	280798.i		−	3.45704i
$286$	7588.47	−	23354.9i	0.0927731	−	0.285526i
$287$	−4588.46	−	14121.8i	−0.0557061	−	0.171446i
$288$	11169.2	+	34375.2i	0.134659	+	0.414439i
$289$	5395.42	−	3920.00i	0.0645995	−	0.0469343i
$290$	−37241.7	−	12100.6i	−0.442826	−	0.143883i
$291$	66956.6	+	92157.8i	0.790692	+	1.08829i
$292$	12919.1	−	17781.6i	0.151518	−	0.208547i
$293$	−18840.1	−	57983.9i	−0.219456	−	0.675418i	−0.998807	−	0.0488296i	$-0.984451\pi$
$293$	−18840.1	−	57983.9i	−0.219456	−	0.675418i	0.779351	−	0.626588i	$-0.215549\pi$
$294$	29869.3	−	41111.5i	0.345565	−	0.475630i
$295$	−75451.2	−	54818.5i	−0.867006	−	0.629917i
$296$	−47930.5	+	15573.6i	−0.547052	+	0.177748i
$297$	−23248.9	−	16891.3i	−0.263566	−	0.191492i
$298$	−113350.	+	82353.8i	−1.27641	+	0.927365i
$299$	−3103.87	+	9552.73i	−0.0347185	+	0.106853i
$300$	−43301.8	−	59599.9i	−0.481131	−	0.662221i
$301$	−159285.	+	51754.7i	−1.75809	+	0.571237i
$302$	11825.5	−	3842.32i	0.129659	−	0.0421289i
$303$	−57066.4	−	18542.0i	−0.621577	−	0.201963i
$304$	−162395.			−1.75722
$305$			197231.i			2.12019i
$306$	82326.6	+	26749.5i	0.879220	+	0.285676i
$307$	79454.6	+	57727.1i	0.843029	+	0.612496i	0.923215	−	0.384284i	$-0.125552\pi$
$307$	79454.6	+	57727.1i	0.843029	+	0.612496i	−0.0801865	+	0.996780i	$0.525552\pi$
$308$	21250.3	+	29248.5i	0.224008	+	0.308321i
$309$			137386.i			1.43888i
$310$	25229.6	−	191574.i	0.262535	−	1.99348i
$311$	64951.8			0.671537			0.335769	−	0.941944i	$-0.391004\pi$
$311$	64951.8			0.671537			0.335769	+	0.941944i	$0.391004\pi$
$312$	−19928.2	+	14478.7i	−0.204719	+	0.148737i
$313$	45647.4	−	62828.3i	0.465937	−	0.641308i	−0.509789	−	0.860299i	$-0.670277\pi$
$313$	45647.4	−	62828.3i	0.465937	−	0.641308i	0.975727	+	0.218992i	$0.0702767\pi$
$314$	51840.6	−	159549.i	0.525788	−	1.61821i
$315$	162644.			1.63915
$316$			9602.71i			0.0961656i
$317$	19171.4	−	59003.6i	0.190781	−	0.587164i	−0.809219	−	0.587508i	$-0.800109\pi$
$317$	19171.4	−	59003.6i	0.190781	−	0.587164i	1.00000		0.000343237i	$0.000109256\pi$
$318$	29225.6	+	89947.0i	0.289007	+	0.889473i
$319$	8243.43	+	25370.7i	0.0810078	+	0.249316i
$320$	84365.8	−	61295.4i	0.823885	−	0.598588i
$321$	258120.	+	83868.2i	2.50502	+	0.813930i
$322$	−39111.1	−	53831.8i	−0.377214	−	0.519191i
$323$	−92997.7	+	128000.i	−0.891389	+	1.22689i
$324$	−10835.8	−	33349.2i	−0.103222	−	0.317684i
$325$	31138.3	−	42858.3i	0.294801	−	0.405759i
$326$	−145867.	−	105979.i	−1.37253	−	0.997203i
$327$	−74376.9	+	24166.5i	−0.695573	+	0.226005i
$328$	−10785.6	−	7836.23i	−0.100253	−	0.0728382i
$329$	−116453.	+	84607.9i	−1.07587	+	0.781662i
$330$	−102326.	+	314928.i	−0.939637	+	2.89191i
$331$	−29720.9	−	40907.3i	−0.271273	−	0.373375i	0.651546	−	0.758609i	$-0.274121\pi$
$331$	−29720.9	−	40907.3i	−0.271273	−	0.373375i	−0.922819	+	0.385234i	$0.874121\pi$
$332$	−3616.45	+	1175.06i	−0.0328100	+	0.0106606i
$333$	−58764.7	+	19093.8i	−0.529941	+	0.172188i
$334$	170443.	+	55380.4i	1.52787	+	0.496435i
$335$	93465.0			0.832836
$336$		−	213953.i		−	1.89514i
$337$	168001.	+	54586.9i	1.47929	+	0.480650i	0.933900	−	0.357535i	$-0.116383\pi$
$337$	168001.	+	54586.9i	1.47929	+	0.480650i	0.545387	+	0.838184i	$0.316383\pi$
$338$	−99068.6	−	71977.6i	−0.867167	−	0.630034i
$339$	−32070.6	−	44141.5i	−0.279067	−	0.384103i
$340$			60866.4i			0.526526i
$341$	−115686.	+	62806.0i	−0.994884	+	0.540122i
$342$	−151855.			−1.29830
$343$	68615.9	−	49852.3i	0.583225	−	0.423738i
$344$	−88387.3	+	121655.i	−0.746918	+	1.02804i
$345$	41854.0	−	128813.i	0.351641	−	1.08224i
$346$	21321.2			0.178099
$347$			6006.11i			0.0498809i	0.999689	+	0.0249404i	$0.00793961\pi$
$347$			6006.11i			0.0498809i	−0.999689	+	0.0249404i	$0.992060\pi$
$348$	−3307.93	+	10180.7i	−0.0273148	+	0.0840662i
$349$	35717.2	+	109926.i	0.293243	+	0.902508i	0.983806	+	0.179236i	$0.0573626\pi$
$349$	35717.2	+	109926.i	0.293243	+	0.902508i	−0.690563	+	0.723272i	$0.742637\pi$
$350$	108447.	+	333767.i	0.885284	+	2.72463i
$351$	6708.71	−	4874.16i	0.0544533	−	0.0395627i
$352$	74092.9	+	24074.2i	0.597986	+	0.194297i
$353$	92725.3	+	127625.i	0.744130	+	1.02421i	0.998370	+	0.0570658i	$0.0181745\pi$
$353$	92725.3	+	127625.i	0.744130	+	1.02421i	−0.254241	+	0.967141i	$0.581826\pi$
$354$	−67431.5	+	92811.5i	−0.538091	+	0.740619i
$355$	18689.4	+	57520.0i	0.148299	+	0.456418i
$356$	10237.1	−	14090.2i	0.0807750	−	0.111177i
$357$	−168638.	−	122523.i	−1.32318	−	0.961349i
$358$	144063.	−	46808.8i	1.12405	−	0.365226i
$359$	14119.4	+	10258.3i	0.109553	+	0.0795952i	0.641213	−	0.767363i	$-0.278431\pi$
$359$	14119.4	+	10258.3i	0.109553	+	0.0795952i	−0.531660	+	0.846958i	$0.678431\pi$
$360$	118141.	−	85834.4i	0.911581	−	0.662303i
$361$	45497.6	−	140027.i	0.349119	−	1.07448i
$362$	−22697.7	−	31240.8i	−0.173207	−	0.238399i
$363$	47131.0	−	15313.8i	0.357679	−	0.116217i
$364$	−9921.79	+	3223.79i	−0.0748837	+	0.0243312i
$365$	−202694.	−	65859.4i	−1.52144	−	0.494347i
$366$	242610.			1.81112
$367$			52194.1i			0.387516i	0.981049	+	0.193758i	$0.0620677\pi$
$367$			52194.1i			0.387516i	−0.981049	+	0.193758i	$0.937932\pi$
$368$	−74497.3	−	24205.6i	−0.550104	−	0.178740i
$369$	−13223.6	−	9607.53i	−0.0971176	−	0.0705600i
$370$	−114910.	−	158160.i	−0.839370	−	1.15529i
$371$		−	100125.i		−	0.727439i
$372$	−52370.5	−	6897.01i	−0.378443	−	0.0498397i
$373$	168132.			1.20846			0.604232	−	0.796809i	$-0.293480\pi$
$373$	168132.			1.20846			0.604232	+	0.796809i	$0.293480\pi$
$374$	150946.	−	109669.i	1.07914	−	0.784044i
$375$	−224081.	+	308421.i	−1.59347	+	2.19322i
$376$	−39937.3	+	122914.i	−0.282490	+	0.869414i
$377$	−7697.73			−0.0541602
$378$			54934.0i			0.384465i
$379$	36139.2	−	111225.i	0.251594	−	0.774325i	−0.742888	−	0.669416i	$-0.766545\pi$
$379$	36139.2	−	111225.i	0.251594	−	0.774325i	0.994482	−	0.104910i	$-0.0334554\pi$
$380$	−32995.5	−	101550.i	−0.228500	−	0.703252i
$381$	−90616.0	−	278887.i	−0.624245	−	1.92123i
$382$	−16126.8	+	11716.8i	−0.110515	+	0.0802936i
$383$	−138299.	−	44936.2i	−0.942807	−	0.306337i	−0.203018	−	0.979175i	$-0.565075\pi$
$383$	−138299.	−	44936.2i	−0.942807	−	0.306337i	−0.739789	+	0.672839i	$0.765075\pi$
$384$	−139707.	−	192290.i	−0.947450	−	1.30405i
$385$	206057.	−	283614.i	1.39017	−	1.91340i
$386$	8699.44	+	26774.1i	0.0583871	+	0.179697i
$387$	−108366.	+	149153.i	−0.723557	+	0.995890i
$388$	35043.7	+	25460.7i	0.232780	+	0.169125i
$389$	198043.	−	64348.1i	1.30876	−	0.425242i	0.430140	−	0.902762i	$-0.358464\pi$
$389$	198043.	−	64348.1i	1.30876	−	0.425242i	0.878621	+	0.477520i	$0.158464\pi$
$390$	−77303.7	−	56164.4i	−0.508243	−	0.369260i
$391$	−61740.8	+	44857.3i	−0.403848	+	0.293413i
$392$	−14926.5	+	45938.9i	−0.0971370	+	0.298957i
$393$	−44771.1	−	61622.2i	−0.289876	−	0.398981i
$394$	−269143.	+	87449.9i	−1.73377	+	0.563335i
$395$	88557.1	−	28773.9i	0.567582	−	0.184419i
$396$	37849.6	+	12298.1i	0.241363	+	0.0784237i
$397$	−128235.			−0.813628			−0.406814	−	0.913511i	$-0.633360\pi$
$397$	−128235.			−0.813628			−0.406814	+	0.913511i	$0.633360\pi$
$398$		−	51825.4i		−	0.327172i
$399$	347776.	+	112999.i	2.18451	+	0.709790i
$400$	334232.	+	242834.i	2.08895	+	1.51771i
$401$	118099.	+	162549.i	0.734442	+	1.01087i	0.998919	+	0.0464809i	$0.0148007\pi$
$401$	118099.	+	162549.i	0.734442	+	1.01087i	−0.264477	+	0.964392i	$0.585199\pi$
$402$		−	114970.i		−	0.711430i
$403$	−6920.56	−	37349.0i	−0.0426119	−	0.229969i
$404$	−22816.6			−0.139794
$405$	−275080.	+	199858.i	−1.67706	+	1.21846i
$406$	29973.7	−	41255.3i	0.181840	−	0.250281i
$407$	−41155.1	+	126662.i	−0.248447	+	0.764642i
$408$	−187156.			−1.12430
$409$			144457.i			0.863557i	0.901980	+	0.431778i	$0.142114\pi$
$409$			144457.i			0.863557i	−0.901980	+	0.431778i	$0.857886\pi$
$410$	15981.0	−	49184.4i	0.0950683	−	0.292590i
$411$	−104477.	−	321546.i	−0.618495	−	1.90353i
$412$	16143.7	+	49685.0i	0.0951059	+	0.292706i
$413$	98257.5	−	71388.2i	0.576057	−	0.418530i
$414$	−69662.0	−	22634.5i	−0.406439	−	0.132060i
$415$	21672.9	+	29830.2i	0.125841	+	0.173205i
$416$	−13213.7	+	18187.2i	−0.0763553	+	0.105094i
$417$	3140.42	+	9665.23i	0.0180599	+	0.0555827i
$418$	−192388.	+	264799.i	−1.10110	+	1.51553i
$419$	−23499.8	−	17073.6i	−0.133856	−	0.0972519i	0.518843	−	0.854870i	$-0.326363\pi$
$419$	−23499.8	−	17073.6i	−0.133856	−	0.0972519i	−0.652698	+	0.757618i	$0.726363\pi$
$420$	133790.	−	43471.0i	0.758447	−	0.246434i
$421$	−66539.4	−	48343.7i	−0.375418	−	0.272757i	0.384036	−	0.923318i	$-0.374534\pi$
$421$	−66539.4	−	48343.7i	−0.375418	−	0.272757i	−0.759454	+	0.650561i	$0.774534\pi$
$422$	−47086.6	+	34210.4i	−0.264407	+	0.192103i
$423$	−48964.7	+	150698.i	−0.273654	+	0.842221i
$424$	−52840.5	−	72728.8i	−0.293924	−	0.404552i
$425$	382804.	−	124380.i	2.11933	−	0.688612i
$426$	70754.6	−	22989.5i	0.389884	−	0.126681i
$427$	−244275.	−	79369.9i	−1.33975	−	0.435312i
$428$	103203.			0.563385
$429$			65094.7i			0.353696i
$430$	−554767.	−	180255.i	−3.00036	−	0.974876i
$431$	−83480.9	−	60652.4i	−0.449400	−	0.326508i	0.339959	−	0.940440i	$-0.389587\pi$
$431$	−83480.9	−	60652.4i	−0.449400	−	0.326508i	−0.789359	+	0.613932i	$0.789587\pi$
$432$	38011.3	+	52318.1i	0.203679	+	0.280340i
$433$		−	4645.68i		−	0.0247784i	−0.999923	−	0.0123892i	$-0.996056\pi$
$433$		−	4645.68i		−	0.0247784i	0.999923	−	0.0123892i	$-0.00394371\pi$
$434$	227117.	+	108341.i	1.20578	+	0.575193i
$435$	103800.			0.548552
$436$	−24058.4	+	17479.5i	−0.126559	+	0.0919508i
$437$	78691.4	−	108309.i	0.412064	−	0.567157i
$438$	−81012.7	+	249331.i	−0.422284	+	1.29966i
$439$	249346.			1.29382			0.646909	−	0.762567i	$-0.276061\pi$
$439$	249346.			1.29382			0.646909	+	0.762567i	$0.276061\pi$
$440$		−	314756.i		−	1.62580i
$441$	−18300.4	+	56322.9i	−0.0940988	+	0.289606i
$442$	16637.4	+	51204.5i	0.0851608	+	0.262098i
$443$	−104456.	−	321482.i	−0.532262	−	1.63814i	−0.749491	−	0.662015i	$-0.769702\pi$
$443$	−104456.	−	321482.i	−0.532262	−	1.63814i	0.217228	−	0.976121i	$-0.430298\pi$
$444$	−43236.1	+	31412.9i	−0.219321	+	0.159346i
$445$	−160615.	−	52187.1i	−0.811087	−	0.263538i
$446$	125108.	+	172197.i	0.628950	+	0.865675i
$447$	218302.	−	300466.i	1.09255	−	1.50377i
$448$	41965.3	+	129156.i	0.209091	+	0.643515i
$449$	67905.5	−	93463.9i	0.336831	−	0.463608i	−0.606681	−	0.794945i	$-0.707500\pi$
$449$	67905.5	−	93463.9i	0.336831	−	0.463608i	0.943513	+	0.331337i	$0.107500\pi$
$450$	312538.	+	227072.i	1.54340	+	1.12134i
$451$	−33506.6	+	10886.9i	−0.164732	+	0.0535245i
$452$	−16785.1	−	12195.1i	−0.0821576	−	0.0596910i
$453$	−26665.1	+	19373.3i	−0.129941	+	0.0944077i
$454$	58476.8	−	179973.i	0.283708	−	0.873165i
$455$	59460.1	+	81839.8i	0.287212	+	0.395313i
$456$	312251.	−	101457.i	1.50167	−	0.487922i
$457$	141760.	−	46060.6i	0.678768	−	0.220545i	0.0507123	−	0.998713i	$-0.483851\pi$
$457$	141760.	−	46060.6i	0.678768	−	0.220545i	0.628056	+	0.778168i	$0.283851\pi$
$458$	427421.	+	138878.i	2.03763	+	0.662066i
$459$	63004.9			0.299053
$460$		−	51503.0i		−	0.243398i
$461$	−20089.9	−	6527.61i	−0.0945314	−	0.0307151i	0.261369	−	0.965239i	$-0.415826\pi$
$461$	−20089.9	−	6527.61i	−0.0945314	−	0.0307151i	−0.355901	+	0.934524i	$0.615826\pi$
$462$	−348869.	−	253468.i	−1.63448	−	1.18752i
$463$	103734.	+	142778.i	0.483904	+	0.666037i	0.979249	−	0.202659i	$-0.0649583\pi$
$463$	103734.	+	142778.i	0.483904	+	0.666037i	−0.495345	+	0.868696i	$0.664958\pi$
$464$		−	60031.0i		−	0.278830i
$465$	93320.1	+	503632.i	0.431588	+	2.32920i
$466$	−261525.			−1.20432
$467$	−202605.	+	147201.i	−0.929001	+	0.674959i	−0.945748	−	0.324901i	$-0.894669\pi$
$467$	−202605.	+	147201.i	−0.929001	+	0.674959i	0.0167467	+	0.999860i	$0.494669\pi$
$468$	−6750.11	+	9290.73i	−0.0308190	+	0.0424188i
$469$	−37612.4	+	115759.i	−0.170996	+	0.526271i
$470$	−501336.			−2.26952
$471$			444694.i			2.00456i
$472$	33697.2	−	103709.i	0.151255	−	0.465516i
$473$	122797.	+	377931.i	0.548866	+	1.68924i
$474$	−35394.4	−	108933.i	−0.157535	−	0.484844i
$475$	−571245.	+	415033.i	−2.53183	+	1.83948i
$476$	−75384.7	−	24494.0i	−0.332713	−	0.108105i
$477$	−64784.6	−	89168.3i	−0.284731	−	0.391899i
$478$	−93872.9	+	129205.i	−0.410851	+	0.565488i
$479$	23346.8	+	71854.1i	0.101755	+	0.313170i	0.988955	−	0.148215i	$-0.0473527\pi$
$479$	23346.8	+	71854.1i	0.101755	+	0.313170i	−0.887200	+	0.461385i	$0.847353\pi$
$480$	178180.	−	245244.i	0.773352	−	1.06443i
$481$	−31091.1	−	22589.0i	−0.134383	−	0.0976352i
$482$	156305.	−	50786.6i	0.672789	−	0.218602i
$483$	142696.	+	103675.i	0.611671	+	0.444405i
$484$	15245.3	−	11076.4i	0.0650797	−	0.0472832i
$485$	129795.	−	399468.i	0.551791	−	1.69824i
$486$	200538.	+	276017.i	0.849032	+	1.16859i
$487$	−335299.	+	108945.i	−1.41376	+	0.459357i	−0.913613	−	0.406586i	$-0.866719\pi$
$487$	−335299.	+	108945.i	−1.41376	+	0.459357i	−0.500143	+	0.865943i	$0.666719\pi$
$488$	−219323.	+	71262.3i	−0.920967	+	0.299240i
$489$	454548.	+	147692.i	1.90091	+	0.617644i
$490$	−187373.			−0.780396
$491$		−	442719.i		−	1.83639i	−0.396128	−	0.918195i	$-0.629646\pi$
$491$		−	442719.i		−	1.83639i	0.396128	−	0.918195i	$-0.370354\pi$
$492$	−13445.5	−	4368.72i	−0.0555453	−	0.0180478i
$493$	−47316.6	−	34377.5i	−0.194679	−	0.141443i
$494$	−55515.6	−	76410.7i	−0.227489	−	0.313112i
$495$		−	385903.i		−	1.57495i
$496$	291268.	−	53970.3i	1.18394	−	0.219377i
$497$	−78761.2			−0.318859
$498$	36693.8	−	26659.6i	0.147956	−	0.107497i
$499$	19092.0	−	26278.0i	0.0766746	−	0.105534i	−0.768957	−	0.639300i	$-0.779224\pi$
$499$	19092.0	−	26278.0i	0.0766746	−	0.105534i	0.845632	+	0.533767i	$0.179224\pi$
$500$	−44796.8	+	137870.i	−0.179187	+	0.551481i
$501$	−475058.			−1.89265
$502$		−	140773.i		−	0.558615i
$503$	64303.3	−	197905.i	0.254154	−	0.782206i	−0.739841	−	0.672782i	$-0.765099\pi$
$503$	64303.3	−	197905.i	0.254154	−	0.782206i	0.993995	−	0.109424i	$-0.0349007\pi$
$504$	58765.8	+	180862.i	0.231347	+	0.712012i
$505$	68368.7	+	210417.i	0.268086	+	0.825085i
$506$	−127726.	+	92798.1i	−0.498858	+	0.362442i
$507$	308715.	+	100308.i	1.20100	+	0.390228i
$508$	−65541.9	−	90210.7i	−0.253975	−	0.349567i
$509$	−143303.	+	197240.i	−0.553120	+	0.761305i	−0.990431	−	0.138006i	$-0.955931\pi$
$509$	−143303.	+	197240.i	−0.553120	+	0.761305i	0.437311	+	0.899310i	$0.355931\pi$
$510$	−224346.	−	690466.i	−0.862537	−	2.65462i
$511$	163137.	−	224539.i	0.624758	−	0.859905i
$512$	64986.0	+	47215.1i	0.247902	+	0.180111i
$513$	−105118.	+	34154.8i	−0.399430	+	0.129783i
$514$	330930.	+	240435.i	1.25259	+	0.910063i
$515$	409827.	−	297756.i	1.54520	−	1.12266i
$516$	−49276.2	+	151656.i	−0.185071	+	0.569589i
$517$	200747.	+	276305.i	0.751050	+	1.03373i
$518$	242127.	−	78672.0i	0.902370	−	0.293198i
$519$	−53751.7	+	17465.0i	−0.199553	+	0.0648386i
$520$	86380.8	+	28066.8i	0.319456	+	0.103797i
$521$	−351391.			−1.29454			−0.647270	−	0.762261i	$-0.724089\pi$
$521$	−351391.			−1.29454			−0.647270	+	0.762261i	$0.724089\pi$
$522$		−	56134.6i		−	0.206011i
$523$	263690.	+	85678.1i	0.964029	+	0.313232i	0.748403	−	0.663244i	$-0.230821\pi$
$523$	263690.	+	85678.1i	0.964029	+	0.313232i	0.215626	+	0.976476i	$0.430821\pi$
$524$	−23432.3	−	17024.6i	−0.0853399	−	0.0620031i
$525$	−546800.	−	752606.i	−1.98386	−	2.73054i
$526$		−	93873.5i		−	0.339290i
$527$	124259.	−	260485.i	0.447410	−	0.937909i
$528$	−507643.			−1.82092
$529$	−174153.	+	126530.i	−0.622329	+	0.452149i
$530$	204975.	−	282123.i	0.729707	−	1.00435i
$531$	41314.2	−	127152.i	0.146524	−	0.450956i
$532$	139050.			0.491301
$533$		−	10166.3i		−	0.0357854i
$534$	−64194.7	+	197571.i	−0.225121	+	0.692852i
$535$	−309242.	−	951748.i	−1.08041	−	3.32517i
$536$	33770.3	+	103934.i	0.117545	+	0.361767i
$537$	−324845.	+	236014.i	−1.12649	+	0.818443i
$538$	−252616.	−	82080.1i	−0.872765	−	0.283578i
$539$	75028.8	+	103268.i	0.258256	+	0.355459i
$540$	−24992.6	+	34399.4i	−0.0857085	+	0.117968i
$541$	35293.9	+	108624.i	0.120588	+	0.371133i	0.993072	−	0.117511i	$-0.0374916\pi$
$541$	35293.9	+	108624.i	0.120588	+	0.371133i	−0.872483	+	0.488644i	$0.837492\pi$
$542$	11061.6	−	15225.0i	0.0376548	−	0.0518274i
$543$	82812.4	+	60166.7i	0.280864	+	0.204059i
$544$	−162445.	+	52781.6i	−0.548920	+	0.178355i
$545$	233287.	+	169493.i	0.785411	+	0.570635i
$546$	100670.	−	73141.0i	0.337687	−	0.245344i
$547$	85738.4	−	263876.i	0.286550	−	0.881910i	−0.699380	−	0.714750i	$-0.746540\pi$
$547$	85738.4	−	263876.i	0.286550	−	0.881910i	0.985930	−	0.167160i	$-0.0534597\pi$
$548$	−75567.3	−	104009.i	−0.251636	−	0.346347i
$549$	−268899.	+	87370.4i	−0.892162	+	0.289881i
$550$	791922.	−	257311.i	2.61792	−	0.850615i
$551$	97579.1	+	31705.4i	0.321406	+	0.104431i
$552$	158365.			0.519733
$553$			121260.i			0.396521i
$554$	42045.9	+	13661.6i	0.136995	+	0.0445124i
$555$	419246.	+	304600.i	1.36108	+	0.988882i
$556$	2271.45	+	3126.38i	0.00734772	+	0.0101133i
$557$			474101.i			1.52813i	0.645138	+	0.764066i	$0.276800\pi$
$557$			474101.i			1.52813i	−0.645138	+	0.764066i	$0.723200\pi$
$558$	272363.	−	50467.2i	0.874740	−	0.162084i
$559$	−114668.			−0.366961
$560$	−638230.	+	463702.i	−2.03517	+	1.47864i
$561$	−290708.	+	400125.i	−0.923701	+	1.27137i
$562$	49094.2	−	151096.i	0.155438	−	0.478389i
$563$	−277189.			−0.874499			−0.437250	−	0.899340i	$-0.644047\pi$
$563$	−277189.			−0.874499			−0.437250	+	0.899340i	$0.644047\pi$
$564$			137050.i			0.430845i
$565$	−62168.8	+	191336.i	−0.194749	+	0.599376i
$566$	191405.	+	589084.i	0.597476	+	1.83884i
$567$	−136831.	−	421122.i	−0.425616	−	1.30991i
$568$	−57210.2	+	41565.7i	−0.177328	+	0.128836i
$569$	−385699.	−	125321.i	−1.19131	−	0.387080i	−0.354753	−	0.934960i	$-0.615435\pi$
$569$	−385699.	−	125321.i	−1.19131	−	0.387080i	−0.836557	+	0.547880i	$0.815435\pi$
$570$	748599.	+	1.03036e6i	2.30409	+	3.17131i
$571$	−36529.2	+	50278.2i	−0.112039	+	0.154208i	−0.861354	−	0.508006i	$-0.830383\pi$
$571$	−36529.2	+	50278.2i	−0.112039	+	0.154208i	0.749315	+	0.662214i	$0.230383\pi$
$572$	7649.01	+	23541.2i	0.0233783	+	0.0719511i
$573$	31058.6	−	42748.5i	0.0945959	−	0.130200i
$574$	54485.1	+	39585.8i	0.165369	+	0.120148i
$575$	−323915.	+	105246.i	−0.979706	+	0.318326i
$576$	120941.	+	87869.0i	0.364527	+	0.264844i
$577$	226587.	−	164625.i	0.680585	−	0.494474i	−0.192967	−	0.981205i	$-0.561811\pi$
$577$	226587.	−	164625.i	0.680585	−	0.494474i	0.873552	+	0.486731i	$0.161811\pi$
$578$	−9347.30	+	28768.0i	−0.0279789	+	0.0861101i
$579$	−43863.3	−	60372.6i	−0.130841	−	0.180087i
$580$	37538.8	−	12197.1i	0.111590	−	0.0362577i
$581$	−45667.3	+	14838.2i	−0.135286	+	0.0439571i
$582$	−491380.	−	159659.i	−1.45068	−	0.471354i
$583$	−237566.			−0.698951
$584$		−	249195.i		−	0.730656i
$585$	105906.	+	34411.0i	0.309464	+	0.100551i
$586$	223715.	+	162538.i	0.651478	+	0.473327i
$587$	−13197.8	−	18165.2i	−0.0383024	−	0.0527187i	0.789436	−	0.613833i	$-0.210373\pi$
$587$	−13197.8	−	18165.2i	−0.0383024	−	0.0527187i	−0.827739	+	0.561114i	$0.810373\pi$
$588$			51222.1i			0.148150i
$589$	−66105.5	+	501953.i	−0.190549	+	1.44688i
$590$	423004.			1.21518
$591$	606887.	−	440929.i	1.73753	−	1.26239i
$592$	176161.	−	242465.i	0.502651	−	0.691839i
$593$	−10072.8	+	31000.9i	−0.0286445	+	0.0881586i	−0.964357	−	0.264606i	$-0.914758\pi$
$593$	−10072.8	+	31000.9i	−0.0286445	+	0.0881586i	0.935712	+	0.352764i	$0.114758\pi$
$594$	130341.			0.369409
$595$			768599.i			2.17103i
$596$	43641.4	−	134314.i	0.122859	−	0.378120i
$597$	42452.0	+	130654.i	0.119110	+	0.366584i
$598$	−14078.0	−	43327.5i	−0.0393675	−	0.121161i
$599$	105974.	−	76994.8i	0.295357	−	0.214589i	−0.430231	−	0.902719i	$-0.641568\pi$
$599$	105974.	−	76994.8i	0.295357	−	0.214589i	0.725588	+	0.688130i	$0.241568\pi$
$600$	−794366.	−	258105.i	−2.20657	−	0.716958i
$601$	−321398.	−	442367.i	−0.889805	−	1.22471i	−0.973608	−	0.228229i	$-0.926707\pi$
$601$	−321398.	−	442367.i	−0.889805	−	1.22471i	0.0838030	−	0.996482i	$-0.473293\pi$
$602$	446501.	−	614555.i	1.23205	−	1.69577i
$603$	41403.7	+	127428.i	0.113869	+	0.350452i
$604$	−7366.85	+	10139.6i	−0.0201933	+	0.0277937i
$605$	−147829.	−	107404.i	−0.403876	−	0.293433i
$606$	258831.	−	84099.3i	0.704809	−	0.229006i
$607$	262631.	+	190813.i	0.712801	+	0.517881i	0.884076	−	0.467343i	$-0.154789\pi$
$607$	262631.	+	190813.i	0.712801	+	0.517881i	−0.171275	+	0.985223i	$0.554789\pi$
$608$	242411.	−	176122.i	0.655761	−	0.476438i
$609$	−41771.3	+	128559.i	−0.112627	+	0.346631i
$610$	−525810.	−	723716.i	−1.41309	−	1.94495i
$611$	−93729.2	+	30454.5i	−0.251069	+	0.0815771i
$612$	−82983.5	+	26963.0i	−0.221559	+	0.0719888i
$613$	423515.	+	137608.i	1.12706	+	0.366205i	0.812459	−	0.583018i	$-0.198128\pi$
$613$	423515.	+	137608.i	1.12706	+	0.366205i	0.314604	+	0.949223i	$0.398128\pi$
$614$	−445449.			−1.18157
$615$			137086.i			0.362447i
$616$	389834.	+	126665.i	1.02735	+	0.333806i
$617$	187270.	+	136060.i	0.491923	+	0.357403i	0.805924	−	0.592020i	$-0.201669\pi$
$617$	187270.	+	136060.i	0.491923	+	0.357403i	−0.314000	+	0.949423i	$0.601669\pi$
$618$	−366266.	−	504122.i	−0.959002	−	1.31995i
$619$		−	155689.i		−	0.406327i	−0.979145	−	0.203163i	$-0.934878\pi$
$619$		−	155689.i		−	0.406327i	0.979145	−	0.203163i	$-0.0651223\pi$
$620$	92928.6	+	171171.i	0.241750	+	0.445294i
$621$	−53312.6			−0.138244
$622$	−238333.	+	173159.i	−0.616033	+	0.447574i
$623$	129270.	−	177925.i	0.333060	−	0.458418i
$624$	45266.6	−	139316.i	0.116254	−	0.357794i
$625$	568018.			1.45413
$626$			352236.i			0.898845i
$627$	268111.	−	825162.i	0.681993	−	2.09896i
$628$	52254.2	+	160822.i	0.132496	+	0.407780i
$629$	−90230.5	−	277701.i	−0.228062	−	0.701901i
$630$	−596805.	+	433604.i	−1.50367	+	1.09248i
$631$	−308417.	−	100211.i	−0.774603	−	0.251684i	−0.105069	−	0.994465i	$-0.533506\pi$
$631$	−308417.	−	100211.i	−0.774603	−	0.251684i	−0.669534	+	0.742781i	$0.733506\pi$
$632$	63994.0	+	88080.1i	0.160216	+	0.220518i
$633$	90684.2	−	124816.i	0.226321	−	0.311504i
$634$	86954.2	+	267617.i	0.216328	+	0.665788i
$635$	−635539.	+	874744.i	−1.57614	+	2.16937i
$636$	−77124.0	−	56033.9i	−0.190667	−	0.138528i
$637$	−35031.0	+	11382.3i	−0.0863325	+	0.0280511i
$638$	−97885.7	−	71118.1i	−0.240479	−	0.174719i
$639$	−70142.0	+	50961.2i	−0.171782	+	0.124807i
$640$	−270822.	+	833503.i	−0.661185	+	2.03492i
$641$	−109135.	−	150211.i	−0.265612	−	0.365583i	0.655291	−	0.755377i	$-0.272546\pi$
$641$	−109135.	−	150211.i	−0.265612	−	0.365583i	−0.920902	+	0.389794i	$0.872546\pi$
$642$	−1.17073e6	+	380394.i	−2.84045	+	0.922918i
$643$	542497.	−	176268.i	1.31212	−	0.426335i	0.432341	−	0.901710i	$-0.357688\pi$
$643$	542497.	−	176268.i	1.31212	−	0.426335i	0.879783	+	0.475375i	$0.157688\pi$
$644$	63787.9	+	20726.0i	0.153804	+	0.0499738i
$645$	1.54624e6			3.71670
$646$		−	717612.i		−	1.71959i
$647$	−136059.	−	44208.2i	−0.325026	−	0.105607i	0.141959	−	0.989873i	$-0.454660\pi$
$647$	−136059.	−	44208.2i	−0.325026	−	0.105607i	−0.466985	+	0.884265i	$0.654660\pi$
$648$	−321635.	−	233681.i	−0.765972	−	0.556511i
$649$	−169382.	−	233134.i	−0.402139	−	0.553497i
$650$			240277.i			0.568704i
$651$	−661316.	−	87093.0i	−1.56044	−	0.205505i
$652$	181740.			0.427520
$653$	302928.	−	220090.i	0.710416	−	0.516148i	−0.172892	−	0.984941i	$-0.555311\pi$
$653$	302928.	−	220090.i	0.710416	−	0.516148i	0.883308	+	0.468793i	$0.155311\pi$
$654$	208491.	−	286963.i	0.487451	−	0.670919i
$655$	−86788.5	+	267108.i	−0.202293	+	0.622592i
$656$	79281.9			0.184233
$657$		−	305522.i		−	0.707803i
$658$	201749.	−	620918.i	0.465971	−	1.43411i
$659$	31487.6	+	96908.8i	0.0725051	+	0.223148i	0.980742	−	0.195309i	$-0.0625711\pi$
$659$	31487.6	+	96908.8i	0.0725051	+	0.223148i	−0.908237	+	0.418457i	$0.862571\pi$
$660$	−103143.	−	317441.i	−0.236783	−	0.728745i
$661$	440258.	−	319866.i	1.00764	−	0.732092i	0.0439260	−	0.999035i	$-0.486013\pi$
$661$	440258.	−	319866.i	1.00764	−	0.732092i	0.963712	+	0.266943i	$0.0860134\pi$
$662$	218115.	+	70870.0i	0.497703	+	0.161713i
$663$	−83886.9	−	115460.i	−0.190839	−	0.262667i
$664$	−25340.9	+	34878.7i	−0.0574758	+	0.0791087i
$665$	−416655.	−	1.28233e6i	−0.942179	−	2.89973i
$666$	164727.	−	226727.i	0.371378	−	0.511158i
$667$	40037.7	+	29089.1i	0.0899947	+	0.0653850i
$668$	−171803.	+	55822.2i	−0.385015	+	0.125099i
$669$	−456455.	−	331634.i	−1.01987	−	0.740981i
$670$	−342959.	+	249175.i	−0.764000	+	0.555078i
$671$	−188320.	+	579588.i	−0.418264	+	1.28728i
$672$	232038.	+	319373.i	0.513831	+	0.707228i
$673$	232649.	−	75592.1i	0.513654	−	0.166896i	−0.0407096	−	0.999171i	$-0.512962\pi$
$673$	232649.	−	75592.1i	0.513654	−	0.166896i	0.554363	+	0.832275i	$0.312962\pi$
$674$	−761989.	+	247585.i	−1.67737	+	0.545010i
$675$	267419.	+	86889.6i	0.586927	+	0.190704i
$676$	123433.			0.270107
$677$			92063.4i			0.200867i	0.994944	+	0.100434i	$0.0320230\pi$
$677$			92063.4i			0.200867i	−0.994944	+	0.100434i	$0.967977\pi$
$678$	235359.	+	76472.9i	0.512003	+	0.166360i
$679$	442520.	+	321509.i	0.959827	+	0.697355i
$680$	405623.	+	558292.i	0.877212	+	1.20738i
$681$			501620.i			1.08164i
$682$	257059.	−	538875.i	0.552667	−	1.15856i
$683$	287906.			0.617177			0.308588	−	0.951196i	$-0.400143\pi$
$683$	287906.			0.617177			0.308588	+	0.951196i	$0.400143\pi$
$684$	123833.	−	89970.2i	0.264683	−	0.192303i
$685$	−732752.	+	1.00855e6i	−1.56162	+	2.14939i
$686$	−118874.	+	365855.i	−0.252602	+	0.777430i
$687$	−1.19131e6			−2.52412
$688$		−	894246.i		−	1.88921i
$689$	21183.8	−	65197.0i	0.0446236	−	0.137337i
$690$	189834.	+	584248.i	0.398727	+	1.22715i
$691$	130004.	+	400110.i	0.272270	+	0.837960i	0.989929	+	0.141566i	$0.0452137\pi$
$691$	130004.	+	400110.i	0.272270	+	0.837960i	−0.717659	+	0.696395i	$0.754786\pi$
$692$	−17386.9	+	12632.3i	−0.0363086	+	0.0263797i
$693$	477952.	+	155296.i	0.995216	+	0.323365i
$694$	−16012.1	−	22038.7i	−0.0332452	−	0.0457581i
$695$	22025.5	−	30315.5i	0.0455990	−	0.0627617i
$696$	37504.4	+	115427.i	0.0774219	+	0.238280i
$697$	45401.7	−	62490.1i	0.0934560	−	0.128631i
$698$	−424121.	−	308142.i	−0.870520	−	0.632469i
$699$	659316.	−	214225.i	1.34939	−	0.438445i
$700$	−286184.	−	207925.i	−0.584049	−	0.424337i
$701$	−309855.	+	225123.i	−0.630554	+	0.458125i	−0.856592	−	0.515994i	$-0.827423\pi$
$701$	−309855.	+	225123.i	−0.630554	+	0.458125i	0.226038	+	0.974119i	$0.427423\pi$
$702$	−11622.5	+	35770.4i	−0.0235844	+	0.0725854i
$703$	301082.	+	414403.i	0.609219	+	0.838518i
$704$	306446.	−	99570.4i	0.618314	−	0.200902i
$705$	1.26389e6	−	410662.i	2.54291	−	0.826240i
$706$	−680490.	−	221105.i	−1.36525	−	0.443597i
$707$	−288121.			−0.576415
$708$		−	115637.i		−	0.230690i
$709$	−432000.	−	140365.i	−0.859393	−	0.279234i	−0.154018	−	0.988068i	$-0.549221\pi$
$709$	−432000.	−	140365.i	−0.859393	−	0.279234i	−0.705375	+	0.708834i	$0.749221\pi$
$710$	−221925.	−	161238.i	−0.440240	−	0.319853i
$711$	78459.1	+	107990.i	0.155204	+	0.213621i
$712$		−	197462.i		−	0.389515i
$713$	−105143.	+	220413.i	−0.206825	+	0.433569i
$714$	945443.			1.85455
$715$	194180.	−	141080.i	0.379832	−	0.275964i
$716$	−89745.9	+	123525.i	−0.175061	+	0.240950i
$717$	130821.	−	402626.i	0.254472	−	0.783183i
$718$	−79157.7			−0.153548
$719$			241622.i			0.467389i	0.972310	+	0.233695i	$0.0750816\pi$
$719$			241622.i			0.467389i	−0.972310	+	0.233695i	$0.924918\pi$
$720$	−268356.	+	825914.i	−0.517661	+	1.59320i
$721$	203856.	+	627405.i	0.392151	+	1.20692i
$722$	206360.	+	635109.i	0.395868	+	1.21836i
$723$	−352450.	+	256070.i	−0.674251	+	0.489872i
$724$	37018.7	+	12028.1i	0.0706227	+	0.0229467i
$725$	−153421.	−	211166.i	−0.291883	−	0.401743i
$726$	−132116.	+	181842.i	−0.250658	+	0.345002i
$727$	46745.7	+	143868.i	0.0884448	+	0.272205i	0.985490	−	0.169734i	$-0.0542908\pi$
$727$	46745.7	+	143868.i	0.0884448	+	0.272205i	−0.897045	+	0.441939i	$0.854291\pi$
$728$	−69523.1	+	95690.3i	−0.131180	+	0.180553i
$729$	−229047.	−	166412.i	−0.430992	−	0.313134i
$730$	919343.	−	298713.i	1.72517	−	0.560542i
$731$	−704846.	−	512101.i	−1.31905	−	0.958342i
$732$	−197842.	+	143741.i	−0.369229	+	0.268261i
$733$	285264.	−	877953.i	0.530933	−	1.63404i	−0.221345	−	0.975196i	$-0.571045\pi$
$733$	285264.	−	877953.i	0.530933	−	1.63404i	0.752277	−	0.658847i	$-0.228955\pi$
$734$	−139148.	−	191521.i	−0.258276	−	0.355487i
$735$	472375.	−	153484.i	0.874404	−	0.284111i
$736$	137455.	−	44662.0i	0.253750	−	0.0824484i
$737$	274659.	+	89242.2i	0.505661	+	0.164299i
$738$	74136.0			0.136118
$739$		−	826025.i		−	1.51253i	−0.654265	−	0.756266i	$-0.727022\pi$
$739$		−	826025.i		−	1.51253i	0.654265	−	0.756266i	$-0.272978\pi$
$740$	187411.	+	60893.6i	0.342241	+	0.111201i
$741$	202548.	+	147160.i	0.368885	+	0.268011i
$742$	266931.	+	367399.i	0.484832	+	0.667314i
$743$			763429.i			1.38290i	0.722424	+	0.691451i	$0.243028\pi$
$743$			763429.i			1.38290i	−0.722424	+	0.691451i	$0.756972\pi$
$744$	−526327.	+	285743.i	−0.950845	+	0.516214i
$745$	−1.36943e6			−2.46733
$746$	−616943.	+	448235.i	−1.10858	+	0.805431i
$747$	−31068.9	+	42762.7i	−0.0556781	+	0.0766344i
$748$	−58116.4	+	178864.i	−0.103871	+	0.319683i
$749$	1.30321e6			2.32301
$750$		−	1.72911e6i		−	3.07398i
$751$	−230097.	+	708166.i	−0.407973	+	1.25561i	0.510415	+	0.859928i	$0.329492\pi$
$751$	−230097.	+	708166.i	−0.407973	+	1.25561i	−0.918387	+	0.395682i	$0.870508\pi$
$752$	−237500.	−	730951.i	−0.419980	−	1.29256i
$753$	115312.	+	354895.i	0.203370	+	0.625907i
$754$	28246.0	−	20521.9i	0.0496837	−	0.0360973i
$755$	115583.	+	37555.0i	0.202768	+	0.0658832i
$756$	−32547.0	−	44797.1i	−0.0569465	−	0.0783802i
$757$	−211029.	+	290456.i	−0.368256	+	0.506861i	−0.952426	−	0.304770i	$-0.901420\pi$
$757$	−211029.	+	290456.i	−0.368256	+	0.506861i	0.584170	+	0.811632i	$0.301420\pi$
$758$	163913.	+	504473.i	0.285283	+	0.878010i
$759$	245987.	−	338572.i	0.427001	−	0.587716i
$760$	−979391.	−	711569.i	−1.69562	−	1.23194i
$761$	563868.	−	183212.i	0.973662	−	0.316362i	0.221368	−	0.975190i	$-0.428948\pi$
$761$	563868.	−	183212.i	0.973662	−	0.316362i	0.752293	+	0.658828i	$0.228948\pi$
$762$	1.07601e6	+	781767.i	1.85313	+	1.34638i
$763$	−303801.	+	220725.i	−0.521844	+	0.379142i
$764$	6209.02	−	19109.4i	0.0106374	−	0.0327386i
$765$	497310.	+	684488.i	0.849775	+	1.16962i
$766$	627273.	−	203813.i	1.06905	−	0.347356i
$767$	79084.4	−	25696.1i	0.134431	−	0.0436793i
$768$	594918.	+	193300.i	1.00864	+	0.327726i
$769$	−1.11172e6			−1.87994			−0.939969	−	0.341260i	$-0.889146\pi$
$769$	−1.11172e6			−1.87994			−0.939969	+	0.341260i	$0.889146\pi$
$770$			1.59003e6i			2.68179i
$771$	−1.03124e6	−	335070.i	−1.73480	−	0.563672i
$772$	−22957.1	−	16679.3i	−0.0385197	−	0.0279862i
$773$	−546718.	−	752493.i	−0.914965	−	1.25934i	−0.965443	−	0.260616i	$-0.916074\pi$
$773$	−546718.	−	752493.i	−0.914965	−	1.25934i	0.0504779	−	0.998725i	$-0.483926\pi$
$774$		−	836203.i		−	1.39582i
$775$	886637.	−	934240.i	1.47619	−	1.55545i
$776$	491110.			0.815559
$777$	−545970.	+	396670.i	−0.904330	+	0.657034i
$778$	−555147.	+	764095.i	−0.917168	+	1.26237i
$779$	−41872.7	+	128871.i	−0.0690011	+	0.212363i
$780$	96315.0			0.158309
$781$			186875.i			0.306372i
$782$	106963.	−	329198.i	0.174912	−	0.538323i
$783$	−12625.6	−	38857.7i	−0.0205935	−	0.0633802i
$784$	−88765.1	−	273191.i	−0.144414	−	0.444461i
$785$	1.32654e6	−	963786.i	2.15268	−	1.56402i
$786$	328565.	+	106757.i	0.531835	+	0.172804i
$787$	216560.	+	298069.i	0.349646	+	0.481247i	0.947228	−	0.320561i	$-0.103872\pi$
$787$	216560.	+	298069.i	0.349646	+	0.481247i	−0.597581	+	0.801808i	$0.703872\pi$
$788$	167667.	−	230773.i	0.270019	−	0.371649i
$789$	76895.1	+	236659.i	0.123522	+	0.380162i
$790$	−248240.	+	341673.i	−0.397757	+	0.547465i
$791$	−211957.	−	153995.i	−0.338761	−	0.246125i
$792$	429129.	−	139432.i	0.684128	−	0.222287i
$793$	−142268.	−	103364.i	−0.226236	−	0.164370i
$794$	470545.	−	341871.i	0.746380	−	0.542277i
$795$	−285652.	+	879146.i	−0.451963	+	1.39100i
$796$	30705.3	+	42262.2i	0.0484603	+	0.0666999i
$797$	−842985.	+	273902.i	−1.32710	+	0.431201i	−0.884927	−	0.465730i	$-0.845792\pi$
$797$	−842985.	+	273902.i	−1.32710	+	0.431201i	−0.442172	+	0.896930i	$0.645792\pi$
$798$	−1.57738e6	+	512522.i	−2.47702	+	0.804834i
$799$	−712144.	−	231390.i	−1.11551	−	0.362452i
$800$	−762274.			−1.19105
$801$		−	242097.i		−	0.377332i
$802$	−866703.	−	281609.i	−1.34748	−	0.437822i
$803$	−532760.	−	387073.i	−0.826229	−	0.600291i
$804$	68116.8	+	93754.8i	0.105376	+	0.145038i
$805$		−	650362.i		−	1.00361i
$806$	124966.	+	118598.i	0.192362	+	0.182561i
$807$	704091.			1.08114
$808$	−209284.	+	152054.i	−0.320563	+	0.232903i
$809$	−111728.	+	153780.i	−0.170712	+	0.234965i	−0.885797	−	0.464072i	$-0.846388\pi$
$809$	−111728.	+	153780.i	−0.170712	+	0.234965i	0.715085	+	0.699037i	$0.246388\pi$
$810$	476563.	−	1.46671e6i	0.726357	−	2.23550i
$811$	−75506.3			−0.114800			−0.0574000	−	0.998351i	$-0.518281\pi$
$811$	−75506.3			−0.114800			−0.0574000	+	0.998351i	$0.518281\pi$
$812$			51401.2i			0.0779582i
$813$	−15415.4	+	47443.9i	−0.0233225	+	0.0717792i
$814$	−186663.	−	574491.i	−0.281715	−	0.867031i
$815$	−544574.	−	1.67603e6i	−0.819863	−	2.52328i
$816$	900422.	−	654195.i	1.35228	−	0.982487i
$817$	1.45358e6	+	472295.i	2.17768	+	0.707570i
$818$	−385117.	−	530068.i	−0.575554	−	0.792182i
$819$	−85238.0	+	117320.i	−0.127077	+	0.174906i
$820$	16108.5	+	49576.8i	0.0239567	+	0.0737312i
$821$	−14548.7	+	20024.6i	−0.0215843	+	0.0297082i	−0.819673	−	0.572832i	$-0.805845\pi$
$821$	−14548.7	+	20024.6i	−0.0215843	+	0.0297082i	0.798088	+	0.602540i	$0.205845\pi$
$822$	1.24060e6	+	901347.i	1.83606	+	1.33398i
$823$	−556483.	+	180812.i	−0.821585	+	0.266949i	−0.689497	−	0.724289i	$-0.742168\pi$
$823$	−556483.	+	180812.i	−0.821585	+	0.266949i	−0.132088	+	0.991238i	$0.542168\pi$
$824$	479185.	+	348148.i	0.705747	+	0.512755i
$825$	−1.78569e6	+	1.29738e6i	−2.62361	+	1.90616i
$826$	−170226.	+	523903.i	−0.249498	+	0.767875i
$827$	779950.	+	1.07351e6i	1.14040	+	1.56962i	0.766618	+	0.642103i	$0.221938\pi$
$827$	779950.	+	1.07351e6i	1.14040	+	1.56962i	0.373778	+	0.927518i	$0.378062\pi$
$828$	70217.8	−	22815.1i	0.102420	−	0.0332784i
$829$	−1.22942e6	+	399461.i	−1.78891	+	0.581254i	−0.999470	−	0.0325680i	$-0.989631\pi$
$829$	−1.22942e6	+	399461.i	−1.78891	+	0.581254i	−0.789445	+	0.613822i	$0.789631\pi$
$830$	−159053.	−	51679.4i	−0.230880	−	0.0750173i
$831$	−117190.			−0.169703
$832$			92979.0i			0.134319i
$833$	−266162.	−	86481.3i	−0.383580	−	0.124633i
$834$	−37290.6	−	27093.2i	−0.0536127	−	0.0389519i
$835$	1.02959e6	+	1.41712e6i	1.47670	+	2.03251i
$836$		−	329922.i		−	0.472061i
$837$	177185.	−	96193.7i	0.252916	−	0.137308i
$838$	131748.			0.187610
$839$	925445.	−	672375.i	1.31470	−	0.955186i	0.314718	−	0.949185i	$-0.398090\pi$
$839$	925445.	−	672375.i	1.31470	−	0.955186i	0.999982	−	0.00600062i	$-0.00191007\pi$
$840$	937481.	−	1.29033e6i	1.32863	−	1.82870i
$841$	206842.	−	636593.i	0.292446	−	0.900057i
$842$	373042.			0.526179
$843$			421135.i			0.592606i
$844$	18129.0	−	55795.2i	0.0254500	−	0.0783271i
$845$	−369858.	−	1.13831e6i	−0.517991	−	1.59421i
$846$	−222085.	−	683507.i	−0.310298	−	0.954998i
$847$	192512.	−	139868.i	0.268344	−	0.194963i
$848$	508441.	+	165202.i	0.707048	+	0.229734i
$849$	−965080.	−	1.32832e6i	−1.33890	−	1.84284i
$850$	−1.07306e6	+	1.47694e6i	−1.48521	+	2.04421i
$851$	76350.0	+	234981.i	0.105426	+	0.324469i
$852$	−44077.6	+	60667.6i	−0.0607210	+	0.0835753i
$853$	486.603	+	353.538i	0.000668770	+	0.000485890i	0.588120	−	0.808774i	$-0.299868\pi$
$853$	486.603	+	353.538i	0.000668770	+	0.000485890i	−0.587451	+	0.809260i	$0.699868\pi$
$854$	1.10794e6	−	359991.i	1.51915	−	0.493601i
$855$	−1.20077e6	−	872412.i	−1.64259	−	1.19341i
$856$	946622.	−	687761.i	1.29190	−	0.938621i
$857$	−225068.	+	692690.i	−0.306445	+	0.943142i	0.672689	+	0.739926i	$0.265139\pi$
$857$	−225068.	+	692690.i	−0.306445	+	0.943142i	−0.979134	+	0.203216i	$0.934861\pi$
$858$	−173540.	−	238858.i	−0.235736	−	0.324463i
$859$	575476.	−	186984.i	0.779904	−	0.253406i	0.108105	−	0.994139i	$-0.465522\pi$
$859$	575476.	−	186984.i	0.779904	−	0.253406i	0.671799	+	0.740733i	$0.265522\pi$
$860$	559193.	−	181693.i	0.756075	−	0.245664i
$861$	−169785.	−	55166.6i	−0.229031	−	0.0744166i
$862$	468021.			0.629870
$863$		−	463281.i		−	0.622047i	−0.950402	−	0.311023i	$-0.899328\pi$
$863$		−	463281.i		−	0.622047i	0.950402	−	0.311023i	$-0.100672\pi$
$864$	−113481.	−	36872.1i	−0.152018	−	0.0493936i
$865$	168595.	+	122491.i	0.225327	+	0.163709i
$866$	12385.2	+	17046.8i	0.0165146	+	0.0227304i
$867$		−	80182.0i		−	0.106669i
$868$	−249396.	+	46211.7i	−0.331017	+	0.0613356i
$869$	287710.			0.380992
$870$	−380882.	+	276727.i	−0.503213	+	0.365606i
$871$	−48982.8	+	67419.0i	−0.0645665	+	0.0888682i
$872$	−104188.	+	320658.i	−0.137020	+	0.421706i
$873$	602120.			0.790050
$874$			607219.i			0.794918i
$875$	−565678.	+	1.74098e6i	−0.738845	+	2.27393i
$876$	−81659.0	−	251321.i	−0.106413	−	0.327507i
$877$	271471.	+	835502.i	0.352959	+	1.08630i	0.957183	+	0.289482i	$0.0934831\pi$
$877$	271471.	+	835502.i	0.352959	+	1.08630i	−0.604224	+	0.796814i	$0.706517\pi$
$878$	−914947.	+	664748.i	−1.18688	+	0.862319i
$879$	−697136.	−	226513.i	−0.902276	−	0.293167i
$880$	1.10022e6	+	1.51432e6i	1.42073	+	1.95547i
$881$	231905.	−	319189.i	0.298784	−	0.411241i	−0.633058	−	0.774104i	$-0.718201\pi$
$881$	231905.	−	319189.i	0.298784	−	0.411241i	0.931843	+	0.362863i	$0.118201\pi$
$882$	−83003.7	−	255459.i	−0.106699	−	0.328386i
$883$	849328.	−	1.16900e6i	1.08932	−	1.49931i	0.240483	−	0.970653i	$-0.422694\pi$
$883$	849328.	−	1.16900e6i	1.08932	−	1.49931i	0.848833	−	0.528661i	$-0.177306\pi$
$884$	−43904.7	−	31898.6i	−0.0561832	−	0.0408195i
$885$	−1.06641e6	+	346498.i	−1.36156	+	0.442399i
$886$	1.24035e6	+	901168.i	1.58007	+	1.14799i
$887$	−766679.	+	557025.i	−0.974465	+	0.707990i	−0.956465	−	0.291848i	$-0.905730\pi$
$887$	−766679.	+	557025.i	−0.974465	+	0.707990i	−0.0180003	+	0.999838i	$0.505730\pi$
$888$	−187240.	+	576264.i	−0.237450	+	0.730795i
$889$	−827640.	−	1.13915e6i	−1.04722	−	1.44137i
$890$	728490.	−	236701.i	0.919695	−	0.298827i
$891$	−999187.	+	324656.i	−1.25861	+	0.408947i
$892$	−204044.	−	66298.0i	−0.256445	−	0.0833242i
$893$	1.31358e6			1.64723
$894$			1.68451e6i			2.10765i
$895$	1.40807e6	+	457511.i	1.75784	+	0.571157i
$896$	−923332.	−	670840.i	−1.15012	−	0.835609i
$897$	70982.2	+	97698.6i	0.0882195	+	0.121424i
$898$			523989.i			0.649785i
$899$	−185552.	−	24436.6i	−0.229587	−	0.0302357i
$900$	−389400.			−0.480741
$901$	421378.	−	306149.i	0.519066	−	0.377123i
$902$	93924.4	−	129276.i	0.115442	−	0.158893i
$903$	−622242.	+	1.91506e6i	−0.763104	+	2.34859i
$904$	−235230.			−0.287843
$905$		−	377432.i		−	0.460830i
$906$	46195.9	−	142176.i	0.0562791	−	0.173209i
$907$	−280949.	−	864671.i	−0.341517	−	1.05108i	−0.963422	−	0.267988i	$-0.913641\pi$
$907$	−280949.	−	864671.i	−0.341517	−	1.05108i	0.621905	−	0.783093i	$-0.286359\pi$
$908$	58943.4	+	181409.i	0.0714930	+	0.220033i
$909$	−256590.	+	186424.i	−0.310537	+	0.225618i
$910$	−436364.	−	141783.i	−0.526946	−	0.171215i
$911$	421296.	+	579864.i	0.507633	+	0.698697i	0.983518	−	0.180810i	$-0.0578720\pi$
$911$	421296.	+	579864.i	0.507633	+	0.698697i	−0.475885	+	0.879508i	$0.657872\pi$
$912$	−1.14763e6	+	1.57958e6i	−1.37979	+	1.89911i
$913$	35206.3	+	108354.i	0.0422356	+	0.129988i
$914$	−397377.	+	546942.i	−0.475675	+	0.654710i
$915$	1.91841e6	+	1.39381e6i	2.29139	+	1.66479i
$916$	−430832.	+	139986.i	−0.513472	+	0.166837i
$917$	−295895.	−	214980.i	−0.351883	−	0.255658i
$918$	−231189.	+	167969.i	−0.274336	+	0.199317i
$919$	98047.3	−	301758.i	0.116093	−	0.357296i	−0.876081	−	0.482164i	$-0.839851\pi$
$919$	98047.3	−	301758.i	0.116093	−	0.357296i	0.992173	+	0.124868i	$0.0398508\pi$
$920$	−343224.	−	472408.i	−0.405511	−	0.558138i
$921$	1.12299e6	−	364883.i	1.32391	−	0.430164i
$922$	91120.1	−	29606.7i	0.107190	−	0.0348280i
$923$	−51285.5	−	16663.7i	−0.0601993	−	0.0195599i
$924$	434667.			0.509111
$925$		−	1.30311e6i		−	1.52300i
$926$	−761282.	−	247355.i	−0.887817	−	0.288469i
$927$	587500.	+	426844.i	0.683673	+	0.496718i
$928$	65105.2	+	89609.7i	0.0755997	+	0.104054i
$929$			1.61395e6i			1.87007i	0.354557	+	0.935034i	$0.384632\pi$
$929$			1.61395e6i			1.87007i	−0.354557	+	0.935034i	$0.615368\pi$
$930$	−1.68509e6	−	1.59923e6i	−1.94831	−	1.84904i
$931$	490947.			0.566415
$932$	213266.	−	154947.i	0.245522	−	0.178382i
$933$	459007.	−	631769.i	0.527298	−	0.725763i
$934$	351003.	−	1.08028e6i	0.402362	−	1.23834i
$935$	1.82364e6			2.08601
$936$			130202.i			0.148616i
$937$	280684.	−	863856.i	0.319697	−	0.983925i	−0.654081	−	0.756424i	$-0.726945\pi$
$937$	280684.	−	863856.i	0.319697	−	0.983925i	0.973778	−	0.227501i	$-0.0730555\pi$
$938$	−170595.	−	525038.i	−0.193893	−	0.596740i
$939$	−288529.	−	888001.i	−0.327234	−	1.00712i
$940$	408825.	−	297029.i	0.462681	−	0.336158i
$941$	738474.	+	239945.i	0.833981	+	0.270977i	0.694721	−	0.719279i	$-0.255528\pi$
$941$	738474.	+	239945.i	0.833981	+	0.270977i	0.139260	+	0.990256i	$0.455528\pi$
$942$	−1.18554e6	−	1.63176e6i	−1.33602	−	1.83888i
$943$	−38417.4	+	52877.0i	−0.0432021	+	0.0594626i
$944$	200392.	+	616743.i	0.224872	+	0.692086i
$945$	−315598.	+	434383.i	−0.353403	+	0.486417i
$946$	−1.45814e6	−	1.05940e6i	−1.62936	−	1.18380i
$947$	−1.48652e6	+	482999.i	−1.65756	+	0.538575i	−0.980359	−	0.197220i	$-0.936809\pi$
$947$	−1.48652e6	+	482999.i	−1.65756	+	0.538575i	−0.677204	+	0.735795i	$0.736809\pi$
$948$	93403.1	+	67861.3i	0.103931	+	0.0755102i
$949$	153734.	−	111694.i	0.170701	−	0.124022i
$950$	989653.	−	3.04584e6i	1.09657	−	3.37489i
$951$	−438430.	−	603447.i	−0.484774	−	0.667234i
$952$	−854692.	+	277706.i	−0.943052	+	0.306416i
$953$	1.60202e6	−	520527.i	1.76393	−	0.573136i	0.766335	−	0.642441i	$-0.222078\pi$
$953$	1.60202e6	−	520527.i	1.76393	−	0.573136i	0.997595	+	0.0693054i	$0.0220783\pi$
$954$	475440.	+	154480.i	0.522395	+	0.169736i
$955$	−194833.			−0.213627
$956$		−	160980.i		−	0.176140i
$957$	305029.	+	99110.0i	0.333056	+	0.108217i
$958$	−277229.	−	201419.i	−0.302070	−	0.219467i
$959$	−954237.	−	1.31339e6i	−1.03757	−	1.42810i
$960$		−	1.25377e6i		−	1.36043i
$961$	−48253.5	−	922260.i	−0.0522495	−	0.998634i
$962$	174307.			0.188349
$963$	1.16060e6	−	843223.i	1.25149	−	0.909263i
$964$	−97372.6	+	134022.i	−0.104781	+	0.144219i
$965$	−85028.7	+	261691.i	−0.0913084	+	0.281019i
$966$	−800001.			−0.857307
$967$			1.05191e6i			1.12493i	0.826821	+	0.562465i	$0.190147\pi$
$967$			1.05191e6i			1.12493i	−0.826821	+	0.562465i	$0.809853\pi$
$968$	66021.8	−	203194.i	0.0704590	−	0.216851i
$969$	587822.	+	1.80913e6i	0.626034	+	1.92673i
$970$	588700.	+	1.81183e6i	0.625677	+	1.92564i
$971$	−1.15381e6	+	838295.i	−1.22376	+	0.889116i	−0.996407	−	0.0846959i	$-0.973008\pi$
$971$	−1.15381e6	+	838295.i	−1.22376	+	0.889116i	−0.227356	+	0.973812i	$0.573008\pi$
$972$	−327066.	−	106270.i	−0.346181	−	0.112481i
$973$	28683.0	+	39478.8i	0.0302970	+	0.0417002i
$974$	939898.	−	1.29366e6i	0.990747	−	1.36365i
$975$	−196820.	−	605749.i	−0.207043	−	0.637212i
$976$	806087.	−	1.10948e6i	0.846218	−	1.16472i
$977$	−288184.	−	209378.i	−0.301912	−	0.219352i	0.426506	−	0.904485i	$-0.359744\pi$
$977$	−288184.	−	209378.i	−0.301912	−	0.219352i	−0.728418	+	0.685133i	$0.759744\pi$
$978$	−2.06166e6	+	669872.i	−2.15545	+	0.700349i
$979$	−422160.	−	306718.i	−0.440466	−	0.320017i
$980$	152797.	−	111014.i	0.159098	−	0.115591i
$981$	−127739.	+	393140.i	−0.132735	+	0.408516i
$982$	1.18027e6	+	1.62451e6i	1.22394	+	1.68461i
$983$	193016.	−	62714.8i	0.199750	−	0.0649027i	−0.207433	−	0.978249i	$-0.566511\pi$
$983$	193016.	−	62714.8i	0.199750	−	0.0649027i	0.407183	+	0.913346i	$0.366511\pi$
$984$	−152442.	+	49531.4i	−0.157440	+	0.0511552i
$985$	−2.63062e6	−	854739.i	−2.71135	−	0.880970i
$986$	265272.			0.272859
$987$			1.73062e6i			1.77651i
$988$	90542.8	+	29419.2i	0.0927556	+	0.0301381i
$989$	596417.	+	433322.i	0.609758	+	0.443015i
$990$	1.02880e6	+	1.41603e6i	1.04969	+	1.44478i
$991$		−	97021.9i		−	0.0987921i	−0.998779	−	0.0493961i	$-0.984270\pi$
$991$		−	97021.9i		−	0.0987921i	0.998779	−	0.0493961i	$-0.0157297\pi$
$992$	−376250.	+	396450.i	−0.382343	+	0.402870i
$993$	−607930.			−0.616531
$994$	289005.	−	209975.i	0.292505	−	0.212517i
$995$	297739.	−	409803.i	0.300739	−	0.413932i
$996$	−14127.6	+	43480.3i	−0.0142413	+	0.0438302i
$997$	−979724.			−0.985629			−0.492815	−	0.870134i	$-0.664032\pi$
$997$	−979724.			−0.985629			−0.492815	+	0.870134i	$0.664032\pi$
$998$			147323.i			0.147914i
$999$	63033.1	−	193996.i	0.0631594	−	0.194385i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.5.f.a.15.3	✓	36
31.29	odd	10	inner	31.5.f.a.29.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.5.f.a.15.3	✓	36	1.1	even	1	trivial
31.5.f.a.29.3	yes	36	31.29	odd	10	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:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	31.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.66939 + 2.66597i) q^{2} +(7.06689 - 9.72674i) q^{3} +(1.41276 - 4.34804i) q^{4} -44.3313 q^{5} +54.5313i q^{6} +(17.8399 - 54.9055i) q^{7} +(-16.0176 - 49.2970i) q^{8} +(-19.6382 - 60.4400i) q^{9} +(162.669 - 118.186i) q^{10} +(-130.273 - 42.3284i) q^{11} +(-32.3084 - 44.4687i) q^{12} +(23.2330 - 31.9775i) q^{13} +(80.9149 + 249.030i) q^{14} +(-313.284 + 431.199i) q^{15} +(249.377 + 181.183i) q^{16} +(285.618 - 92.8030i) q^{17} +(233.191 + 169.423i) q^{18} +(-426.218 + 309.665i) q^{19} +(-62.6297 + 192.754i) q^{20} +(-407.979 - 561.535i) q^{21} +(590.870 - 191.985i) q^{22} +(-241.680 + 78.5267i) q^{23} +(-592.693 - 192.578i) q^{24} +1340.26 q^{25} +179.276i q^{26} +(199.527 + 64.8302i) q^{27} +(-213.528 - 155.137i) q^{28} +(-114.471 - 157.556i) q^{29} -2417.44i q^{30} +(661.539 - 697.056i) q^{31} -568.749 q^{32} +(-1332.34 + 968.005i) q^{33} +(-800.635 + 1101.98i) q^{34} +(-790.866 + 2434.03i) q^{35} -290.540 q^{36} -972.281i q^{37} +(738.401 - 2272.57i) q^{38} +(-146.852 - 451.962i) q^{39} +(710.079 + 2185.40i) q^{40} +(208.081 - 151.180i) q^{41} +(2994.07 + 972.833i) q^{42} +(-1705.20 - 2347.01i) q^{43} +(-368.091 + 506.634i) q^{44} +(870.585 + 2679.39i) q^{45} +(677.469 - 932.457i) q^{46} +(-2017.16 - 1465.55i) q^{47} +(3524.65 - 1145.23i) q^{48} +(-753.907 - 547.746i) q^{49} +(-4917.95 + 3573.10i) q^{50} +(1115.76 - 3433.96i) q^{51} +(-106.217 - 146.195i) q^{52} +(1649.46 - 535.941i) q^{53} +(-904.976 + 294.045i) q^{54} +(5775.19 + 1876.47i) q^{55} -2992.43 q^{56} +6334.08i q^{57} +(840.076 + 272.957i) q^{58} +(1701.99 + 1236.56i) q^{59} +(1432.27 + 1971.36i) q^{60} -4449.01i q^{61} +(-569.115 + 4321.41i) q^{62} -3668.84 q^{63} +(-1903.08 + 1382.67i) q^{64} +(-1029.95 + 1417.60i) q^{65} +(2308.22 - 7103.98i) q^{66} -2108.33 q^{67} -1372.99i q^{68} +(-944.119 + 2905.70i) q^{69} +(-3587.06 - 11039.8i) q^{70} +(-421.584 - 1297.50i) q^{71} +(-2664.96 + 1936.20i) q^{72} +(4572.26 + 1485.62i) q^{73} +(2592.07 + 3567.68i) q^{74} +(9471.50 - 13036.4i) q^{75} +(744.293 + 2290.70i) q^{76} +(-4648.13 + 6397.60i) q^{77} +(1743.77 + 1266.93i) q^{78} +(-1997.62 + 649.066i) q^{79} +(-11055.2 - 8032.09i) q^{80} +(6205.10 - 4508.27i) q^{81} +(-360.490 + 1109.47i) q^{82} +(-488.886 - 672.894i) q^{83} +(-3017.96 + 980.594i) q^{84} +(-12661.8 + 4114.08i) q^{85} +(12514.1 + 4066.08i) q^{86} -2341.46 q^{87} +7100.08i q^{88} +(3623.07 + 1177.21i) q^{89} +(-10337.7 - 7510.76i) q^{90} +(-1341.27 - 1846.09i) q^{91} +1161.78i q^{92} +(-2105.06 - 11360.6i) q^{93} +11308.8 q^{94} +(18894.8 - 13727.9i) q^{95} +(-4019.29 + 5532.08i) q^{96} +(-2927.84 + 9010.96i) q^{97} +4226.65 q^{98} +8704.98i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} - 5 q^{3} - 79 q^{4} - 2 q^{5} - 73 q^{7} + 173 q^{8} + 62 q^{9} + 84 q^{10} + 100 q^{11} + 150 q^{12} - 260 q^{13} + 488 q^{14} - 1075 q^{15} + 777 q^{16} - 725 q^{17} - 786 q^{18} - 1581 q^{19}+ \cdots + 74456 q^{98}+O(q^{100}) \) 36 * q - 3 * q^2 - 5 * q^3 - 79 * q^4 - 2 * q^5 - 73 * q^7 + 173 * q^8 + 62 * q^9 + 84 * q^10 + 100 * q^11 + 150 * q^12 - 260 * q^13 + 488 * q^14 - 1075 * q^15 + 777 * q^16 - 725 * q^17 - 786 * q^18 - 1581 * q^19 + 827 * q^20 + 2335 * q^21 - 1030 * q^22 + 1675 * q^23 - 165 * q^24 + 1294 * q^25 - 2855 * q^27 + 352 * q^28 - 575 * q^29 + 895 * q^31 - 5470 * q^32 + 4468 * q^33 + 1815 * q^34 - 3042 * q^35 + 7808 * q^36 - 6604 * q^38 + 595 * q^39 + 1482 * q^40 - 1740 * q^41 + 3840 * q^42 - 10055 * q^43 - 5780 * q^44 + 6774 * q^45 + 16515 * q^46 + 693 * q^47 + 4710 * q^48 - 944 * q^49 - 6240 * q^50 + 12641 * q^51 + 15885 * q^52 - 10835 * q^53 - 25960 * q^54 - 14010 * q^55 - 19976 * q^56 + 4755 * q^58 - 6021 * q^59 + 35 * q^60 - 11088 * q^62 - 15564 * q^63 + 6935 * q^64 + 26645 * q^65 + 23988 * q^66 + 28596 * q^67 - 4229 * q^69 + 8041 * q^70 + 31101 * q^71 + 20690 * q^72 + 6125 * q^73 - 47295 * q^74 - 27475 * q^75 + 12511 * q^76 + 35950 * q^77 + 29801 * q^78 - 29050 * q^79 - 47358 * q^80 - 1965 * q^81 + 9198 * q^82 + 21640 * q^83 - 35875 * q^84 - 55360 * q^85 - 27935 * q^86 - 2262 * q^87 - 11645 * q^89 - 14916 * q^90 + 670 * q^91 - 36224 * q^93 - 52442 * q^94 + 73983 * q^95 + 29810 * q^96 + 55059 * q^97 + 74456 * q^98

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