LMFDB - Embedded newform 62.6.d.a.39.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,6,Mod(33,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.33"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	62.d (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$9.94379682840$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			39.1
Character	$\chi$	$=$	62.39
Dual form			62.6.d.a.35.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.23607 - 3.80423i) q^{2} +(-6.59038 - 20.2831i) q^{3} +(-12.9443 - 9.40456i) q^{4} -48.6693 q^{5} -85.3076 q^{6} +(4.11428 + 2.98920i) q^{7} +(-51.7771 + 37.6183i) q^{8} +(-171.380 + 124.515i) q^{9} +(-60.1585 + 185.149i) q^{10} +(122.118 + 88.7240i) q^{11} +(-105.446 + 324.529i) q^{12} +(-45.6754 - 140.574i) q^{13} +(16.4571 - 11.9568i) q^{14} +(320.749 + 987.164i) q^{15} +(79.1084 + 243.470i) q^{16} +(654.300 - 475.377i) q^{17} +(261.845 + 805.876i) q^{18} +(-211.088 + 649.662i) q^{19} +(629.989 + 457.713i) q^{20} +(33.5155 - 103.150i) q^{21} +(488.472 - 354.896i) q^{22} +(-3234.00 + 2349.64i) q^{23} +(1104.25 + 802.281i) q^{24} -756.300 q^{25} -591.234 q^{26} +(-537.682 - 390.649i) q^{27} +(-25.1442 - 77.3859i) q^{28} +(-361.396 + 1112.26i) q^{29} +4151.86 q^{30} +(-4764.15 - 2435.58i) q^{31} +1024.00 q^{32} +(994.792 - 3061.66i) q^{33} +(-999.682 - 3076.70i) q^{34} +(-200.239 - 145.482i) q^{35} +3389.39 q^{36} -2513.66 q^{37} +(2210.54 + 1606.05i) q^{38} +(-2550.26 + 1852.88i) q^{39} +(2519.95 - 1830.85i) q^{40} +(-1229.36 + 3783.59i) q^{41} +(-350.979 - 255.001i) q^{42} +(186.896 - 575.205i) q^{43} +(-746.319 - 2296.93i) q^{44} +(8340.93 - 6060.04i) q^{45} +(4941.11 + 15207.2i) q^{46} +(-7186.68 - 22118.3i) q^{47} +(4416.98 - 3209.12i) q^{48} +(-5185.66 - 15959.8i) q^{49} +(-934.839 + 2877.14i) q^{50} +(-13954.2 - 10138.3i) q^{51} +(-730.806 + 2249.19i) q^{52} +(17050.4 - 12387.9i) q^{53} +(-2150.73 + 1562.59i) q^{54} +(-5943.40 - 4318.13i) q^{55} -325.474 q^{56} +14568.3 q^{57} +(3784.58 + 2749.66i) q^{58} +(1493.09 + 4595.25i) q^{59} +(5131.98 - 15794.6i) q^{60} -12951.2 q^{61} +(-15154.3 + 15113.4i) q^{62} -1077.30 q^{63} +(1265.73 - 3895.53i) q^{64} +(2222.99 + 6841.65i) q^{65} +(-10417.6 - 7568.83i) q^{66} -17689.7 q^{67} -12940.1 q^{68} +(68971.2 + 50110.5i) q^{69} +(-800.955 + 581.928i) q^{70} +(13755.8 - 9994.19i) q^{71} +(4189.52 - 12894.0i) q^{72} +(26028.1 + 18910.5i) q^{73} +(-3107.05 + 9562.51i) q^{74} +(4984.30 + 15340.1i) q^{75} +(8842.17 - 6424.21i) q^{76} +(237.214 + 730.070i) q^{77} +(3896.46 + 11992.1i) q^{78} +(-80957.9 + 58819.4i) q^{79} +(-3850.15 - 11849.5i) q^{80} +(-20287.1 + 62437.3i) q^{81} +(12874.1 + 9353.55i) q^{82} +(906.977 - 2791.39i) q^{83} +(-1403.92 + 1020.00i) q^{84} +(-31844.3 + 23136.3i) q^{85} +(-1957.20 - 1421.99i) q^{86} +24941.8 q^{87} -9660.56 q^{88} +(10569.4 + 7679.11i) q^{89} +(-12743.8 - 39221.4i) q^{90} +(232.283 - 714.894i) q^{91} +63959.1 q^{92} +(-18003.5 + 112683. i) q^{93} -93026.4 q^{94} +(10273.5 - 31618.6i) q^{95} +(-6748.55 - 20769.9i) q^{96} +(-40487.9 - 29416.2i) q^{97} -67124.5 q^{98} -31976.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - 20 q^{3} - 96 q^{4} + 120 q^{5} + 280 q^{6} - 180 q^{7} - 384 q^{8} - 200 q^{9} - 100 q^{10} + 354 q^{11} - 320 q^{12} + 39 q^{13} - 720 q^{14} + 535 q^{15} - 1536 q^{16} - 1027 q^{17}+ \cdots + 339042 q^{99}+O(q^{100}) $ 24 * q - 24 * q^2 - 20 * q^3 - 96 * q^4 + 120 * q^5 + 280 * q^6 - 180 * q^7 - 384 * q^8 - 200 * q^9 - 100 * q^10 + 354 * q^11 - 320 * q^12 + 39 * q^13 - 720 * q^14 + 535 * q^15 - 1536 * q^16 - 1027 * q^17 - 1420 * q^18 + 334 * q^19 - 560 * q^20 - 1867 * q^21 + 1416 * q^22 - 1051 * q^23 - 960 * q^24 + 4812 * q^25 + 12536 * q^26 - 5135 * q^27 + 4000 * q^28 - 1143 * q^29 + 9080 * q^30 - 8583 * q^31 + 24576 * q^32 - 24628 * q^33 - 8108 * q^34 - 7496 * q^35 + 17760 * q^36 - 25204 * q^37 - 2844 * q^38 - 20114 * q^39 - 2240 * q^40 + 19615 * q^41 + 3212 * q^42 + 22358 * q^43 - 20496 * q^44 + 6725 * q^45 - 5264 * q^46 + 4766 * q^47 - 3840 * q^48 - 12058 * q^49 + 4628 * q^50 + 6844 * q^51 + 624 * q^52 - 7393 * q^53 - 20540 * q^54 + 11861 * q^55 - 8960 * q^56 + 176704 * q^57 + 4268 * q^58 - 21070 * q^59 + 8560 * q^60 + 76556 * q^61 - 49652 * q^62 + 105854 * q^63 - 24576 * q^64 - 107146 * q^65 + 57968 * q^66 - 150906 * q^67 + 97728 * q^68 - 212560 * q^69 - 29984 * q^70 + 27475 * q^71 - 22720 * q^72 + 49671 * q^73 + 90124 * q^74 - 156002 * q^75 - 11376 * q^76 + 253908 * q^77 - 9036 * q^78 - 7162 * q^79 - 6400 * q^80 + 38329 * q^81 - 92940 * q^82 - 246088 * q^83 + 12848 * q^84 - 104879 * q^85 - 149088 * q^86 - 247668 * q^87 + 118656 * q^88 + 159253 * q^89 - 167880 * q^90 - 68566 * q^91 + 75744 * q^92 + 260391 * q^93 + 18784 * q^94 + 222814 * q^95 - 20480 * q^96 + 190 * q^97 - 144032 * q^98 + 339042 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	1.23607	−	3.80423i	0.218508	−	0.672499i
$2$	1.23607	−	3.80423i	0.218508	−	0.672499i
$3$	−6.59038	−	20.2831i	−0.422773	−	1.30116i	−0.905111	−	0.425176i	$-0.860212\pi$
$3$	−6.59038	−	20.2831i	−0.422773	−	1.30116i	0.482338	−	0.875985i	$-0.339788\pi$
$4$	−12.9443	−	9.40456i	−0.404508	−	0.293893i
$5$	−48.6693			−0.870623			−0.435311	−	0.900280i	$-0.643362\pi$
$5$	−48.6693			−0.870623			−0.435311	+	0.900280i	$0.643362\pi$
$6$	−85.3076			−0.967408
$7$	4.11428	+	2.98920i	0.0317357	+	0.0230573i	0.603540	−	0.797333i	$-0.293756\pi$
$7$	4.11428	+	2.98920i	0.0317357	+	0.0230573i	−0.571804	+	0.820390i	$0.693756\pi$
$8$	−51.7771	+	37.6183i	−0.286031	+	0.207813i
$9$	−171.380	+	124.515i	−0.705266	+	0.512406i
$10$	−60.1585	+	185.149i	−0.190238	+	0.585492i
$11$	122.118	+	88.7240i	0.304297	+	0.221085i	0.729446	−	0.684039i	$-0.239778\pi$
$11$	122.118	+	88.7240i	0.304297	+	0.221085i	−0.425148	+	0.905124i	$0.639778\pi$
$12$	−105.446	+	324.529i	−0.211386	+	0.650581i
$13$	−45.6754	−	140.574i	−0.0749590	−	0.230700i	0.906556	−	0.422086i	$-0.138702\pi$
$13$	−45.6754	−	140.574i	−0.0749590	−	0.230700i	−0.981515	+	0.191386i	$0.938702\pi$
$14$	16.4571	−	11.9568i	0.0224405	−	0.0163040i
$15$	320.749	+	987.164i	0.368076	+	1.13282i
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	654.300	−	475.377i	0.549104	−	0.398947i	−0.278351	−	0.960479i	$-0.589788\pi$
$17$	654.300	−	475.377i	0.549104	−	0.398947i	0.827455	+	0.561532i	$0.189788\pi$
$18$	261.845	+	805.876i	0.190486	+	0.586255i
$19$	−211.088	+	649.662i	−0.134147	+	0.412861i	−0.995456	−	0.0952195i	$-0.969645\pi$
$19$	−211.088	+	649.662i	−0.134147	+	0.412861i	0.861310	+	0.508080i	$0.169645\pi$
$20$	629.989	+	457.713i	0.352174	+	0.255870i
$21$	33.5155	−	103.150i	0.0165843	−	0.0510413i
$22$	488.472	−	354.896i	0.215171	−	0.156331i
$23$	−3234.00	+	2349.64i	−1.27474	+	0.926151i	−0.999381	−	0.0351916i	$-0.988796\pi$
$23$	−3234.00	+	2349.64i	−1.27474	+	0.926151i	−0.275356	+	0.961342i	$0.588796\pi$
$24$	1104.25	+	802.281i	0.391325	+	0.284314i
$25$	−756.300			−0.242016
$26$	−591.234			−0.171525
$27$	−537.682	−	390.649i	−0.141944	−	0.103128i
$28$	−25.1442	−	77.3859i	−0.00606098	−	0.0186538i
$29$	−361.396	+	1112.26i	−0.0797972	+	0.245591i	−0.982994	−	0.183635i	$-0.941214\pi$
$29$	−361.396	+	1112.26i	−0.0797972	+	0.245591i	0.903197	+	0.429226i	$0.141214\pi$
$30$	4151.86			0.842247
$31$	−4764.15	−	2435.58i	−0.890392	−	0.455195i
$31$	−4764.15	−	2435.58i	−0.890392	−	0.455195i
$32$	1024.00			0.176777
$33$	994.792	−	3061.66i	0.159018	−	0.489409i
$34$	−999.682	−	3076.70i	−0.148308	−	0.456445i
$35$	−200.239	−	145.482i	−0.0276298	−	0.0200742i
$36$	3389.39			0.435879
$37$	−2513.66			−0.301857			−0.150929	−	0.988545i	$-0.548226\pi$
$37$	−2513.66			−0.301857			−0.150929	+	0.988545i	$0.548226\pi$
$38$	2210.54	+	1606.05i	0.248336	+	0.180427i
$39$	−2550.26	+	1852.88i	−0.268487	+	0.195067i
$40$	2519.95	−	1830.85i	0.249025	−	0.180927i
$41$	−1229.36	+	3783.59i	−0.114214	+	0.351515i	−0.991782	−	0.127937i	$-0.959165\pi$
$41$	−1229.36	+	3783.59i	−0.114214	+	0.351515i	0.877568	+	0.479452i	$0.159165\pi$
$42$	−350.979	−	255.001i	−0.0307014	−	0.0223059i
$43$	186.896	−	575.205i	0.0154144	−	0.0474408i	−0.943053	−	0.332641i	$-0.892060\pi$
$43$	186.896	−	575.205i	0.0154144	−	0.0474408i	0.958468	+	0.285200i	$0.0920602\pi$
$44$	−746.319	−	2296.93i	−0.0581156	−	0.178861i
$45$	8340.93	−	6060.04i	0.614021	−	0.446112i
$46$	4941.11	+	15207.2i	0.344295	+	1.05963i
$47$	−7186.68	−	22118.3i	−0.474552	−	1.46052i	−0.846561	−	0.532292i	$-0.821331\pi$
$47$	−7186.68	−	22118.3i	−0.474552	−	1.46052i	0.372009	−	0.928229i	$-0.378669\pi$
$48$	4416.98	−	3209.12i	0.276708	−	0.201040i
$49$	−5185.66	−	15959.8i	−0.308541	−	0.949593i
$50$	−934.839	+	2877.14i	−0.0528825	+	0.162755i
$51$	−13954.2	−	10138.3i	−0.751241	−	0.545809i
$52$	−730.806	+	2249.19i	−0.0374795	+	0.115350i
$53$	17050.4	−	12387.9i	0.833770	−	0.605769i	−0.0868536	−	0.996221i	$-0.527681\pi$
$53$	17050.4	−	12387.9i	0.833770	−	0.605769i	0.920623	+	0.390452i	$0.127681\pi$
$54$	−2150.73	+	1562.59i	−0.100369	+	0.0729226i
$55$	−5943.40	−	4318.13i	−0.264928	−	0.192482i
$56$	−325.474			−0.0138690
$57$	14568.3			0.593912
$58$	3784.58	+	2749.66i	0.147723	+	0.107327i
$59$	1493.09	+	4595.25i	0.0558413	+	0.171862i	0.975087	−	0.221822i	$-0.0712004\pi$
$59$	1493.09	+	4595.25i	0.0558413	+	0.171862i	−0.919246	+	0.393684i	$0.871200\pi$
$60$	5131.98	−	15794.6i	0.184038	−	0.566410i
$61$	−12951.2			−0.445641			−0.222820	−	0.974860i	$-0.571526\pi$
$61$	−12951.2			−0.445641			−0.222820	+	0.974860i	$0.571526\pi$
$62$	−15154.3	+	15113.4i	−0.500676	+	0.499323i
$63$	−1077.30			−0.0341968
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	2222.99	+	6841.65i	0.0652610	+	0.200853i
$66$	−10417.6	−	7568.83i	−0.294380	−	0.213879i
$67$	−17689.7			−0.481431			−0.240715	−	0.970596i	$-0.577382\pi$
$67$	−17689.7			−0.481431			−0.240715	+	0.970596i	$0.577382\pi$
$68$	−12940.1			−0.339365
$69$	68971.2	+	50110.5i	1.74400	+	1.26709i
$70$	−800.955	+	581.928i	−0.0195372	+	0.0141946i
$71$	13755.8	−	9994.19i	0.323848	−	0.235289i	−0.413968	−	0.910291i	$-0.635857\pi$
$71$	13755.8	−	9994.19i	0.323848	−	0.235289i	0.737815	+	0.675002i	$0.235857\pi$
$72$	4189.52	−	12894.0i	0.0952429	−	0.293128i
$73$	26028.1	+	18910.5i	0.571657	+	0.415333i	0.835707	−	0.549176i	$-0.185058\pi$
$73$	26028.1	+	18910.5i	0.571657	+	0.415333i	−0.264050	+	0.964509i	$0.585058\pi$
$74$	−3107.05	+	9562.51i	−0.0659582	+	0.202998i
$75$	4984.30	+	15340.1i	0.102318	+	0.314902i
$76$	8842.17	−	6424.21i	0.175600	−	0.127581i
$77$	237.214	+	730.070i	0.00455946	+	0.0140326i
$78$	3896.46	+	11992.1i	0.0725159	+	0.223181i
$79$	−80957.9	+	58819.4i	−1.45946	+	1.06036i	−0.475955	+	0.879470i	$0.657897\pi$
$79$	−80957.9	+	58819.4i	−1.45946	+	1.06036i	−0.983504	+	0.180889i	$0.942103\pi$
$80$	−3850.15	−	11849.5i	−0.0672593	−	0.207003i
$81$	−20287.1	+	62437.3i	−0.343564	+	1.05738i
$82$	12874.1	+	9353.55i	0.211437	+	0.153618i
$83$	906.977	−	2791.39i	0.0144511	−	0.0444759i	−0.943571	−	0.331170i	$-0.892556\pi$
$83$	906.977	−	2791.39i	0.0144511	−	0.0444759i	0.958022	+	0.286695i	$0.0925565\pi$
$84$	−1403.92	+	1020.00i	−0.0217092	+	0.0157726i
$85$	−31844.3	+	23136.3i	−0.478062	+	0.347333i
$86$	−1957.20	−	1421.99i	−0.0285357	−	0.0207324i
$87$	24941.8			0.353289
$88$	−9660.56			−0.132983
$89$	10569.4	+	7679.11i	0.141441	+	0.102763i	0.656256	−	0.754539i	$-0.272139\pi$
$89$	10569.4	+	7679.11i	0.141441	+	0.102763i	−0.514815	+	0.857301i	$0.672139\pi$
$90$	−12743.8	−	39221.4i	−0.165841	−	0.510407i
$91$	232.283	−	714.894i	0.00294045	−	0.00904979i
$92$	63959.1			0.787831
$93$	−18003.5	+	112683.i	−0.215849	+	1.35099i
$94$	−93026.4			−1.08589
$95$	10273.5	−	31618.6i	0.116791	−	0.359446i
$96$	−6748.55	−	20769.9i	−0.0747364	−	0.230015i
$97$	−40487.9	−	29416.2i	−0.436914	−	0.317436i	0.347494	−	0.937682i	$-0.387033\pi$
$97$	−40487.9	−	29416.2i	−0.436914	−	0.317436i	−0.784407	+	0.620246i	$0.787033\pi$
$98$	−67124.5			−0.706019
$99$	−31976.0			−0.327896
$100$	9789.76	+	7112.67i	0.0978976	+	0.0711267i
$101$	2995.86	−	2176.62i	0.0292225	−	0.0212314i	−0.573078	−	0.819501i	$-0.694251\pi$
$101$	2995.86	−	2176.62i	0.0292225	−	0.0212314i	0.602301	+	0.798269i	$0.294251\pi$
$102$	−55816.8	+	40553.3i	−0.531208	+	0.385945i
$103$	43074.8	−	132571.i	0.400065	−	1.23127i	−0.524881	−	0.851175i	$-0.675890\pi$
$103$	43074.8	−	132571.i	0.400065	−	1.23127i	0.924946	−	0.380098i	$-0.124110\pi$
$104$	7653.10	+	5560.30i	0.0693831	+	0.0504098i
$105$	−1631.18	+	5020.25i	−0.0144387	+	0.0444377i
$106$	−26050.8	−	80176.0i	−0.225193	−	0.693074i
$107$	109225.	−	79356.9i	0.922283	−	0.670078i	−0.0218084	−	0.999762i	$-0.506942\pi$
$107$	109225.	−	79356.9i	0.922283	−	0.670078i	0.944091	+	0.329685i	$0.106942\pi$
$108$	3286.02	+	10113.3i	0.0271088	+	0.0834324i
$109$	−11609.6	−	35730.8i	−0.0935949	−	0.288055i	0.893290	−	0.449481i	$-0.148391\pi$
$109$	−11609.6	−	35730.8i	−0.0935949	−	0.288055i	−0.986885	+	0.161425i	$0.948391\pi$
$110$	−23773.6	+	17272.5i	−0.187332	+	0.136105i
$111$	16565.9	+	50984.7i	0.127617	+	0.392765i
$112$	−402.307	+	1238.17i	−0.00303049	+	0.00932689i
$113$	126643.	+	92011.6i	0.933008	+	0.677870i	0.946728	−	0.322036i	$-0.104367\pi$
$113$	126643.	+	92011.6i	0.933008	+	0.677870i	−0.0137192	+	0.999906i	$0.504367\pi$
$114$	18007.4	−	55421.1i	0.129775	−	0.399405i
$115$	157397.	−	114355.i	1.10981	−	0.806328i
$116$	15138.3	−	10998.6i	0.104456	−	0.0758917i
$117$	25331.4	+	18404.3i	0.171078	+	0.124296i
$118$	19326.9			0.127779
$119$	4112.97			0.0266249
$120$	−53742.8	−	39046.4i	−0.340696	−	0.247530i
$121$	−42726.6	−	131499.i	−0.265299	−	0.816505i
$122$	−16008.5	+	49269.2i	−0.0973761	+	0.299693i
$123$	84844.9			0.505665
$124$	38762.9	+	76331.5i	0.226393	+	0.445810i
$125$	188900.			1.08133
$126$	−1331.62	+	4098.30i	−0.00747229	+	0.0229973i
$127$	−72819.7	−	224116.i	−0.400627	−	1.23300i	−0.924492	−	0.381201i	$-0.875511\pi$
$127$	−72819.7	−	224116.i	−0.400627	−	1.23300i	0.523866	−	0.851801i	$-0.324489\pi$
$128$	−13254.9	−	9630.27i	−0.0715077	−	0.0519534i
$129$	−12898.7			−0.0682449
$130$	28775.0			0.149333
$131$	92989.5	+	67560.9i	0.473430	+	0.343967i	0.798777	−	0.601628i	$-0.205481\pi$
$131$	92989.5	+	67560.9i	0.473430	+	0.343967i	−0.325346	+	0.945595i	$0.605481\pi$
$132$	−41670.4	+	30275.3i	−0.208158	+	0.151236i
$133$	−2810.44	+	2041.91i	−0.0137767	+	0.0100094i
$134$	−21865.7	+	67295.7i	−0.105197	+	0.323762i
$135$	26168.6	+	19012.6i	0.123579	+	0.0897857i
$136$	−15994.9	+	49227.3i	−0.0741540	+	0.228222i
$137$	−72293.7	−	222497.i	−0.329078	−	1.01280i	−0.969566	−	0.244830i	$-0.921268\pi$
$137$	−72293.7	−	222497.i	−0.329078	−	1.01280i	0.640488	−	0.767968i	$-0.278732\pi$
$138$	275885.	−	200442.i	1.23319	−	0.895966i
$139$	−29919.6	−	92083.2i	−0.131347	−	0.404244i	0.863657	−	0.504080i	$-0.168168\pi$
$139$	−29919.6	−	92083.2i	−0.131347	−	0.404244i	−0.995004	+	0.0998358i	$0.968168\pi$
$140$	1223.75	+	3766.32i	0.00527683	+	0.0162404i
$141$	−401265.	+	291536.i	−1.69975	+	1.23494i
$142$	−21017.0	−	64683.7i	−0.0874682	−	0.269200i
$143$	6894.52	−	21219.2i	0.0281945	−	0.0867737i
$144$	−43873.2	−	31875.7i	−0.176317	−	0.128101i
$145$	17588.9	−	54133.0i	0.0694733	−	0.213817i
$146$	104112.	−	75642.1i	0.404222	−	0.293685i
$147$	−289539.	+	210362.i	−1.10513	+	0.802924i
$148$	32537.4	+	23639.8i	0.122104	+	0.0887136i
$149$	−331064.			−1.22165			−0.610825	−	0.791766i	$-0.709162\pi$
$149$	−331064.			−1.22165			−0.610825	+	0.791766i	$0.709162\pi$
$150$	64518.2			0.234128
$151$	−407751.	−	296248.i	−1.45530	−	1.05734i	−0.984556	−	0.175068i	$-0.943986\pi$
$151$	−407751.	−	296248.i	−1.45530	−	1.05734i	−0.470744	−	0.882270i	$-0.656014\pi$
$152$	−13509.6	−	41578.4i	−0.0474280	−	0.145968i
$153$	−52942.4	+	162940.i	−0.182842	+	0.562728i
$154$	3070.56			0.0104332
$155$	231868.	+	118538.i	0.775195	+	0.396303i
$156$	50436.8			0.165934
$157$	−77897.2	+	239743.i	−0.252216	+	0.776241i	0.742150	+	0.670234i	$0.233806\pi$
$157$	−77897.2	+	239743.i	−0.252216	+	0.776241i	−0.994365	+	0.106006i	$0.966194\pi$
$158$	123693.	+	380687.i	0.394186	+	1.21318i
$159$	−363633.	−	264195.i	−1.14070	−	0.828766i
$160$	−49837.4			−0.153906
$161$	−20329.1			−0.0618093
$162$	212449.	+	154354.i	0.636016	+	0.462093i
$163$	−13212.1	+	9599.16i	−0.0389496	+	0.0282986i	−0.607090	−	0.794633i	$-0.707663\pi$
$163$	−13212.1	+	9599.16i	−0.0389496	+	0.0282986i	0.568140	+	0.822932i	$0.307663\pi$
$164$	51496.2	−	37414.2i	0.149508	−	0.108624i
$165$	−48415.8	+	149009.i	−0.138445	+	0.426090i
$166$	−9497.98	−	6900.69i	−0.0267523	−	0.0194367i
$167$	−10153.1	+	31247.9i	−0.0281713	+	0.0867022i	−0.964154	−	0.265345i	$-0.914514\pi$
$167$	−10153.1	+	31247.9i	−0.0281713	+	0.0867022i	0.935982	+	0.352047i	$0.114514\pi$
$168$	2144.99	+	6601.61i	0.00586344	+	0.0180458i
$169$	282707.	−	205399.i	0.761413	−	0.553199i
$170$	48653.8	+	149741.i	0.129120	+	0.397391i
$171$	−44716.3	−	137622.i	−0.116943	−	0.359914i
$172$	−7828.78	+	5687.94i	−0.0201778	+	0.0146600i
$173$	221855.	+	682800.i	0.563578	+	1.73452i	0.672138	+	0.740426i	$0.265376\pi$
$173$	221855.	+	682800.i	0.563578	+	1.73452i	−0.108560	+	0.994090i	$0.534624\pi$
$174$	30829.8	−	94884.4i	0.0771965	−	0.237586i
$175$	−3111.63	−	2260.73i	−0.00768055	−	0.00558025i
$176$	−11941.1	+	36750.9i	−0.0290578	+	0.0894307i
$177$	83365.9	−	60568.9i	0.200012	−	0.145317i
$178$	42277.6	−	30716.5i	0.100014	−	0.0726643i
$179$	344159.	+	250046.i	0.802835	+	0.583294i	0.911744	−	0.410758i	$-0.134736\pi$
$179$	344159.	+	250046.i	0.802835	+	0.583294i	−0.108909	+	0.994052i	$0.534736\pi$
$180$	−164959.			−0.379486
$181$	434289.			0.985332			0.492666	−	0.870218i	$-0.336022\pi$
$181$	434289.			0.985332			0.492666	+	0.870218i	$0.336022\pi$
$182$	−2432.50	−	1767.32i	−0.00544345	−	0.00395490i
$183$	85353.2	+	262690.i	0.188405	+	0.579850i
$184$	79057.8	−	243315.i	0.172147	−	0.529815i
$185$	122338.			0.262804
$186$	406418.	+	207773.i	0.861372	+	0.440359i
$187$	122079.			0.255292
$188$	−114987.	+	353893.i	−0.237276	+	0.730260i
$189$	−1044.45	−	3214.47i	−0.00212682	−	0.00654569i
$190$	−107586.	−	78165.5i	−0.216207	−	0.157084i
$191$	−841847.			−1.66974			−0.834872	−	0.550445i	$-0.814458\pi$
$191$	−841847.			−1.66974			−0.834872	+	0.550445i	$0.814458\pi$
$192$	−87355.0			−0.171015
$193$	490173.	+	356132.i	0.947232	+	0.688205i	0.950151	−	0.311791i	$-0.100929\pi$
$193$	490173.	+	356132.i	0.947232	+	0.688205i	−0.00291829	+	0.999996i	$0.500929\pi$
$194$	−161951.	+	117665.i	−0.308945	+	0.224461i
$195$	124120.	−	90178.1i	0.233751	−	0.169830i
$196$	−82970.5	+	255357.i	−0.154271	+	0.474797i
$197$	160658.	+	116725.i	0.294941	+	0.214287i	0.725408	−	0.688319i	$-0.241651\pi$
$197$	160658.	+	116725.i	0.294941	+	0.214287i	−0.430467	+	0.902606i	$0.641651\pi$
$198$	−39524.5	+	121644.i	−0.0716479	+	0.220509i
$199$	−300116.	−	923663.i	−0.537226	−	1.65341i	−0.738790	−	0.673936i	$-0.764602\pi$
$199$	−300116.	−	923663.i	−0.537226	−	1.65341i	0.201564	−	0.979475i	$-0.435398\pi$
$200$	39159.0	−	28450.7i	0.0692240	−	0.0502942i
$201$	116582.	+	358802.i	0.203536	+	0.626419i
$202$	−4577.26	−	14087.4i	−0.00789273	−	0.0242913i
$203$	−4811.65	+	3495.87i	−0.00819509	+	0.00595408i
$204$	85280.5	+	262466.i	0.143474	+	0.441568i
$205$	59832.2	−	184145.i	0.0994375	−	0.306037i
$206$	−451085.	−	327733.i	−0.740612	−	0.538086i
$207$	261678.	−	805361.i	0.424464	−	1.30637i
$208$	30612.4	−	22241.2i	0.0490613	−	0.0356451i
$209$	−83418.3	+	60606.9i	−0.132098	+	0.0959746i
$210$	17081.9	+	12410.7i	0.0267293	+	0.0194200i
$211$	−1.01334e6			−1.56692			−0.783462	−	0.621439i	$-0.786548\pi$
$211$	−1.01334e6			−1.56692			−0.783462	+	0.621439i	$0.786548\pi$
$212$	−337208.			−0.515298
$213$	−293369.	−	213145.i	−0.443063	−	0.321904i
$214$	−166882.	−	513609.i	−0.249100	−	0.766651i
$215$	−9096.08	+	27994.8i	−0.0134202	+	0.0413030i
$216$	42535.1			0.0620317
$217$	−12320.6	−	24261.6i	−0.0177616	−	0.0349760i
$218$	−150278.			−0.214168
$219$	212029.	−	652558.i	0.298734	−	0.919409i
$220$	36322.8	+	111790.i	0.0505968	+	0.155721i
$221$	−96711.2	−	70264.8i	−0.133197	−	0.0967736i
$222$	214434.			0.292019
$223$	−839296.			−1.13019			−0.565097	−	0.825024i	$-0.691161\pi$
$223$	−839296.			−1.13019			−0.565097	+	0.825024i	$0.691161\pi$
$224$	4213.02	+	3060.94i	0.00561013	+	0.00407600i
$225$	129615.	−	94170.5i	0.170686	−	0.124010i
$226$	506573.	−	368046.i	0.659737	−	0.479327i
$227$	363179.	−	1.11775e6i	0.467795	−	1.43973i	−0.387637	−	0.921812i	$-0.626709\pi$
$227$	363179.	−	1.11775e6i	0.467795	−	1.43973i	0.855433	−	0.517914i	$-0.173291\pi$
$228$	−188576.	−	137009.i	−0.240242	−	0.174546i
$229$	304156.	−	936097.i	0.383273	−	1.17959i	−0.554452	−	0.832215i	$-0.687072\pi$
$229$	304156.	−	936097.i	0.383273	−	1.17959i	0.937725	−	0.347378i	$-0.112928\pi$
$230$	−240481.	−	740123.i	−0.299751	−	0.922538i
$231$	13244.7	−	9622.87i	0.0163310	−	0.0118652i
$232$	−23129.3	−	71184.7i	−0.0282126	−	0.0868294i
$233$	−3079.20	−	9476.80i	−0.00371576	−	0.0114359i	0.949181	−	0.314729i	$-0.101914\pi$
$233$	−3079.20	−	9476.80i	−0.00371576	−	0.0114359i	−0.952897	+	0.303293i	$0.901914\pi$
$234$	101326.	−	73617.3i	0.120970	−	0.0878902i
$235$	349771.	+	1.07648e6i	0.413156	+	1.27156i
$236$	23889.4	−	73524.0i	0.0279206	−	0.0859309i
$237$	1.72658e6	+	1.25444e6i	1.99672	+	1.45070i
$238$	5083.90	−	15646.6i	0.00581775	−	0.0179052i
$239$	−1.14137e6	+	829256.i	−1.29251	+	0.939061i	−0.999853	−	0.0171571i	$-0.994538\pi$
$239$	−1.14137e6	+	829256.i	−1.29251	+	0.939061i	−0.292654	+	0.956218i	$0.594538\pi$
$240$	−214971.	+	156186.i	−0.240909	+	0.175030i
$241$	−553660.	−	402258.i	−0.614046	−	0.446130i	0.236791	−	0.971561i	$-0.423904\pi$
$241$	−553660.	−	402258.i	−0.614046	−	0.446130i	−0.850837	+	0.525430i	$0.823904\pi$
$242$	−553065.			−0.607069
$243$	1.23862e6			1.34562
$244$	167644.	+	121800.i	0.180265	+	0.130971i
$245$	252382.	+	776753.i	0.268623	+	0.826737i
$246$	104874.	−	322769.i	0.110492	−	0.340059i
$247$	100967.			0.105302
$248$	338296.	−	53111.9i	0.349275	−	0.0548357i
$249$	−62595.3			−0.0639799
$250$	233493.	−	718619.i	0.236279	−	0.727191i
$251$	481332.	+	1.48139e6i	0.482237	+	1.48417i	0.835943	+	0.548817i	$0.184922\pi$
$251$	481332.	+	1.48139e6i	0.482237	+	1.48417i	−0.353705	+	0.935357i	$0.615078\pi$
$252$	13944.9	+	10131.6i	0.0138329	+	0.0100502i
$253$	−603399.			−0.592657
$254$	−942598.			−0.916732
$255$	679141.	+	493425.i	0.654048	+	0.475193i
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	1.09028e6	−	792131.i	1.02968	−	0.748108i	0.0614375	−	0.998111i	$-0.480432\pi$
$257$	1.09028e6	−	792131.i	1.02968	−	0.748108i	0.968245	+	0.250003i	$0.0804315\pi$
$258$	−15943.6	+	49069.4i	−0.0149121	+	0.0458946i
$259$	−10341.9	−	7513.81i	−0.00957965	−	0.00696002i
$260$	35567.8	−	109466.i	0.0326305	−	0.100426i
$261$	−76556.9	−	235618.i	−0.0695638	−	0.214095i
$262$	371958.	−	270243.i	0.334766	−	0.243221i
$263$	162982.	+	501607.i	0.145295	+	0.447172i	0.997049	−	0.0767705i	$-0.0244609\pi$
$263$	162982.	+	501607.i	0.145295	+	0.447172i	−0.851754	+	0.523942i	$0.824461\pi$
$264$	63666.7	+	195946.i	0.0562215	+	0.173032i
$265$	−829833.	+	602909.i	−0.725899	+	0.527396i
$266$	4293.97	+	13215.5i	0.00372096	+	0.0114519i
$267$	86099.9	−	264988.i	0.0739136	−	0.227483i
$268$	228981.	+	166364.i	0.194743	+	0.141489i
$269$	611251.	−	1.88124e6i	0.515038	−	1.58512i	−0.268176	−	0.963370i	$-0.586421\pi$
$269$	611251.	−	1.88124e6i	0.515038	−	1.58512i	0.783213	−	0.621753i	$-0.213579\pi$
$270$	104674.	−	76050.4i	0.0873838	−	0.0634881i
$271$	−359828.	+	261430.i	−0.297627	+	0.216238i	−0.726569	−	0.687093i	$-0.758886\pi$
$271$	−359828.	+	261430.i	−0.297627	+	0.216238i	0.428942	+	0.903332i	$0.358886\pi$
$272$	167501.	+	121696.i	0.137276	+	0.0997369i
$273$	−16031.1			−0.0130184
$274$	−935789.			−0.753012
$275$	−92357.9	−	67102.0i	−0.0736448	−	0.0535061i
$276$	−421515.	−	1.29729e6i	−0.333073	−	1.02509i
$277$	276872.	−	852125.i	0.216810	−	0.667273i	−0.782210	−	0.623015i	$-0.785908\pi$
$277$	276872.	−	852125.i	0.216810	−	0.667273i	0.999020	−	0.0442582i	$-0.0140924\pi$
$278$	−387288.			−0.300554
$279$	1.11974e6	−	175798.i	0.861208	−	0.135208i
$280$	15840.6			0.0120747
$281$	−97672.3	+	300604.i	−0.0737914	+	0.227107i	−0.981149	−	0.193253i	$-0.938096\pi$
$281$	−97672.3	+	300604.i	−0.0737914	+	0.227107i	0.907358	+	0.420360i	$0.138096\pi$
$282$	613079.	+	1.88686e6i	0.459085	+	1.41292i
$283$	−1.35723e6	−	986089.i	−1.00737	−	0.731897i	−0.0437140	−	0.999044i	$-0.513919\pi$
$283$	−1.35723e6	−	986089.i	−1.00737	−	0.731897i	−0.963656	+	0.267147i	$0.913919\pi$
$284$	−272050.			−0.200149
$285$	−709029.			−0.517073
$286$	−72200.4	−	52456.7i	−0.0521945	−	0.0379215i
$287$	−16367.8	+	11891.9i	−0.0117297	+	0.00852211i
$288$	−175493.	+	127503.i	−0.124675	+	0.0905814i
$289$	−236634.	+	728286.i	−0.166661	+	0.512929i
$290$	−184193.	−	133824.i	−0.128611	−	0.0934414i
$291$	−329820.	+	1.01508e6i	−0.228321	+	0.702698i
$292$	−159070.	−	489566.i	−0.109177	−	0.336011i
$293$	−1.24241e6	+	902661.i	−0.845463	+	0.614265i	−0.923891	−	0.382655i	$-0.875010\pi$
$293$	−1.24241e6	+	902661.i	−0.845463	+	0.614265i	0.0784283	+	0.996920i	$0.475010\pi$
$294$	442376.	+	1.36149e6i	0.298486	+	0.918644i
$295$	−72667.5	−	223648.i	−0.0486167	−	0.149627i
$296$	130150.	−	94559.3i	0.0863404	−	0.0627300i
$297$	−31000.8	−	95410.5i	−0.0203930	−	0.0627632i
$298$	−409218.	+	1.25944e6i	−0.266940	+	0.821558i
$299$	478013.	+	347297.i	0.309216	+	0.224659i
$300$	79748.9	−	245442.i	0.0511589	−	0.157451i
$301$	2488.34	−	1807.89i	0.00158305	−	0.00115015i
$302$	−1.63100e6	+	1.18499e6i	−1.02905	+	0.747651i
$303$	−63892.4	−	46420.5i	−0.0399800	−	0.0290471i
$304$	−174872.			−0.108527
$305$	630325.			0.387985
$306$	554420.	+	402810.i	0.338482	+	0.245921i
$307$	847194.	+	2.60739e6i	0.513023	+	1.57892i	0.786851	+	0.617143i	$0.211710\pi$
$307$	847194.	+	2.60739e6i	0.513023	+	1.57892i	−0.273828	+	0.961779i	$0.588290\pi$
$308$	3795.42	−	11681.1i	0.00227973	−	0.00701629i
$309$	−2.97282e6			−1.77122
$310$	737549.	−	735557.i	0.435900	−	0.434722i
$311$	2.33430e6			1.36853			0.684267	−	0.729232i	$-0.260122\pi$
$311$	2.33430e6			1.36853			0.684267	+	0.729232i	$0.260122\pi$
$312$	62343.3	−	191873.i	0.0362580	−	0.111591i
$313$	390974.	+	1.20329e6i	0.225573	+	0.694242i	0.998233	+	0.0594218i	$0.0189257\pi$
$313$	390974.	+	1.20329e6i	0.225573	+	0.694242i	−0.772660	+	0.634820i	$0.781074\pi$
$314$	815750.	+	592677.i	0.466910	+	0.339230i
$315$	52431.5			0.0297726
$316$	1.60111e6			0.901995
$317$	748352.	+	543710.i	0.418271	+	0.303892i	0.776942	−	0.629572i	$-0.216770\pi$
$317$	748352.	+	543710.i	0.418271	+	0.303892i	−0.358671	+	0.933464i	$0.616770\pi$
$318$	−1.45453e6	+	1.05678e6i	−0.806596	+	0.586026i
$319$	−142817.	+	103763.i	−0.0785785	+	0.0570906i
$320$	−61602.4	+	189593.i	−0.0336297	+	0.103501i
$321$	−2.32944e6	−	1.69244e6i	−1.26180	−	0.916748i
$322$	−25128.2	+	77336.5i	−0.0135058	+	0.0415666i
$323$	170719.	+	525420.i	0.0910493	+	0.280221i
$324$	849798.	−	617414.i	0.449731	−	0.326749i
$325$	34544.3	+	106316.i	0.0181413	+	0.0558331i
$326$	20186.3	+	62127.1i	0.0105199	+	0.0323770i
$327$	−648219.	+	470958.i	−0.335237	+	0.243564i
$328$	−78679.2	−	242150.i	−0.0403808	−	0.124279i
$329$	36548.0	−	112483.i	0.0186155	−	0.0572926i
$330$	507017.	+	368370.i	0.256294	+	0.186208i
$331$	53882.3	−	165833.i	0.0270319	−	0.0831955i	−0.936630	−	0.350319i	$-0.886073\pi$
$331$	53882.3	−	165833.i	0.0270319	−	0.0831955i	0.963662	+	0.267124i	$0.0860732\pi$
$332$	−37991.9	+	27602.8i	−0.0189167	+	0.0137438i
$333$	430789.	−	312987.i	0.212890	−	0.154673i
$334$	106324.	+	77249.2i	0.0521515	+	0.0378903i
$335$	860946.			0.419145
$336$	27765.4			0.0134170
$337$	−1.47647e6	−	1.07272e6i	−0.708191	−	0.514531i	0.174399	−	0.984675i	$-0.444202\pi$
$337$	−1.47647e6	−	1.07272e6i	−0.708191	−	0.514531i	−0.882590	+	0.470144i	$0.844202\pi$
$338$	−431939.	−	1.32937e6i	−0.205651	−	0.632928i
$339$	1.03165e6	−	3.17511e6i	0.487568	−	1.50058i
$340$	629788.			0.295459
$341$	−365695.	−	720122.i	−0.170307	−	0.335367i
$342$	−578819.			−0.267595
$343$	52784.2	−	162453.i	0.0242253	−	0.0745577i
$344$	11961.3	+	36813.1i	0.00544983	+	0.0167728i
$345$	−3.35678e6	−	2.43884e6i	−1.51836	−	1.10315i
$346$	2.87175e6			1.28961
$347$	2.10693e6			0.939348			0.469674	−	0.882840i	$-0.344371\pi$
$347$	2.10693e6			0.939348			0.469674	+	0.882840i	$0.344371\pi$
$348$	−322854.	−	234567.i	−0.142908	−	0.103829i
$349$	−380527.	+	276469.i	−0.167233	+	0.121502i	−0.668254	−	0.743933i	$-0.732958\pi$
$349$	−380527.	+	276469.i	−0.167233	+	0.121502i	0.501021	+	0.865435i	$0.332958\pi$
$350$	−12446.5	+	9042.92i	−0.00543097	+	0.00394583i
$351$	−30356.4	+	93427.3i	−0.0131517	+	0.0404768i
$352$	125049.	+	90853.3i	0.0537927	+	0.0390827i
$353$	467649.	−	1.43928e6i	0.199749	−	0.614763i	−0.800140	−	0.599814i	$-0.795241\pi$
$353$	467649.	−	1.43928e6i	0.199749	−	0.614763i	0.999888	−	0.0149491i	$-0.00475862\pi$
$354$	−127372.	−	392010.i	−0.0540213	−	0.166260i
$355$	−669486.	+	486410.i	−0.281949	+	0.204848i
$356$	−64594.4	−	198801.i	−0.0270128	−	0.0831369i
$357$	−27106.0	−	83423.7i	−0.0112563	−	0.0346433i
$358$	1.37664e6	−	1.00018e6i	0.567690	−	0.412451i
$359$	−246358.	−	758212.i	−0.100886	−	0.310495i	0.887857	−	0.460120i	$-0.152194\pi$
$359$	−246358.	−	758212.i	−0.100886	−	0.310495i	−0.988743	+	0.149625i	$0.952194\pi$
$360$	−203901.	+	627542.i	−0.0829207	+	0.255204i
$361$	1.62570e6	+	1.18114e6i	0.656558	+	0.477018i
$362$	536811.	−	1.65213e6i	0.215303	−	0.662634i
$363$	−2.38562e6	+	1.73326e6i	−0.950244	+	0.690393i
$364$	−9730.01	+	7069.26i	−0.00384910	+	0.00279654i
$365$	−1.26677e6	−	920362.i	−0.497697	−	0.361598i
$366$	1.10483e6			0.431116
$367$	−620479.			−0.240471			−0.120235	−	0.992745i	$-0.538365\pi$
$367$	−620479.			−0.240471			−0.120235	+	0.992745i	$0.538365\pi$
$368$	−827904.	−	601508.i	−0.318684	−	0.231538i
$369$	−260424.	−	801504.i	−0.0995671	−	0.306436i
$370$	151218.	−	465401.i	0.0574247	−	0.176735i
$371$	107180.			0.0404277
$372$	1.29278e6	−	1.28929e6i	0.484358	−	0.483050i
$373$	−147719.			−0.0549751			−0.0274875	−	0.999622i	$-0.508751\pi$
$373$	−147719.			−0.0549751			−0.0274875	+	0.999622i	$0.508751\pi$
$374$	150898.	−	464417.i	0.0557834	−	0.171684i
$375$	−1.24492e6	−	3.83148e6i	−0.457156	−	1.40698i
$376$	1.20416e6	+	874872.i	0.439252	+	0.319136i
$377$	172862.			0.0626393
$378$	−13519.6			−0.00486669
$379$	2.38308e6	+	1.73141e6i	0.852196	+	0.619157i	0.925751	−	0.378134i	$-0.123434\pi$
$379$	2.38308e6	+	1.73141e6i	0.852196	+	0.619157i	−0.0735543	+	0.997291i	$0.523434\pi$
$380$	−430342.	+	312662.i	−0.152882	+	0.111075i
$381$	−4.06586e6	+	2.95402e6i	−1.43496	+	1.04256i
$382$	−1.04058e6	+	3.20258e6i	−0.364852	+	1.12290i
$383$	−706519.	−	513316.i	−0.246109	−	0.178809i	0.457892	−	0.889008i	$-0.348605\pi$
$383$	−706519.	−	513316.i	−0.246109	−	0.178809i	−0.704001	+	0.710199i	$0.748605\pi$
$384$	−107977.	+	332318.i	−0.0373682	+	0.115007i
$385$	−11545.0	−	35532.0i	−0.00396957	−	0.0122171i
$386$	1.96069e6	−	1.42453e6i	0.669794	−	0.486634i
$387$	39591.4	+	121850.i	0.0134377	+	0.0413568i
$388$	247440.	+	761541.i	0.0834431	+	0.256811i
$389$	1.85230e6	−	1.34577e6i	0.620636	−	0.450918i	−0.232508	−	0.972595i	$-0.574693\pi$
$389$	1.85230e6	−	1.34577e6i	0.620636	−	0.450918i	0.853143	+	0.521676i	$0.174693\pi$
$390$	−189638.	−	583645.i	−0.0631340	−	0.194307i
$391$	−999043.	+	3.07474e6i	−0.330478	+	1.01711i
$392$	868878.	+	631277.i	0.285591	+	0.207494i
$393$	757507.	−	2.33137e6i	0.247403	−	0.761429i
$394$	642630.	−	466898.i	0.208555	−	0.151524i
$395$	3.94017e6	−	2.86270e6i	1.27064	−	0.923172i
$396$	413906.	+	300720.i	0.132637	+	0.0963662i
$397$	1.73868e6			0.553659			0.276829	−	0.960919i	$-0.410716\pi$
$397$	1.73868e6			0.553659			0.276829	+	0.960919i	$0.410716\pi$
$398$	−3.88479e6			−1.22930
$399$	59938.0	+	43547.5i	0.0188482	+	0.0136940i
$400$	−59829.7	−	184137.i	−0.0186968	−	0.0575427i
$401$	1.82086e6	−	5.60404e6i	0.565479	−	1.74037i	−0.101045	−	0.994882i	$-0.532219\pi$
$401$	1.82086e6	−	5.60404e6i	0.565479	−	1.74037i	0.666524	−	0.745484i	$-0.267781\pi$
$402$	1.50907e6			0.465740
$403$	−124775.	+	780963.i	−0.0382706	+	0.239534i
$404$	−59249.3			−0.0180605
$405$	987359.	−	3.03878e6i	0.299115	−	0.920580i
$406$	7351.54	+	22625.7i	0.00221342	+	0.00681220i
$407$	−306963.	−	223021.i	−0.0918543	−	0.0667361i
$408$	1.10389e6			0.328304
$409$	4.01253e6			1.18607			0.593035	−	0.805177i	$-0.297930\pi$
$409$	4.01253e6			1.18607			0.593035	+	0.805177i	$0.297930\pi$
$410$	−626571.	−	455230.i	−0.184082	−	0.133743i
$411$	−4.03649e6	+	2.93268e6i	−1.17869	+	0.856367i
$412$	−1.80434e6	+	1.31093e6i	−0.523692	+	0.380484i
$413$	−7593.13	+	23369.3i	−0.00219051	+	0.00674171i
$414$	−2.74032e6	−	1.99096e6i	−0.785780	−	0.570903i
$415$	−44141.9	+	135855.i	−0.0125815	+	0.0387217i
$416$	−46771.6	−	143948.i	−0.0132510	−	0.0407824i
$417$	−1.67055e6	+	1.21373e6i	−0.470457	+	0.341807i
$418$	127452.	+	392256.i	0.0356784	+	0.109807i
$419$	−914523.	−	2.81461e6i	−0.254484	−	0.783220i	−0.993931	−	0.110005i	$-0.964913\pi$
$419$	−914523.	−	2.81461e6i	−0.254484	−	0.783220i	0.739447	−	0.673214i	$-0.235087\pi$
$420$	68327.6	−	49642.9i	0.0189005	−	0.0137320i
$421$	2.03692e6	+	6.26900e6i	0.560105	+	1.72383i	0.682066	+	0.731291i	$0.261082\pi$
$421$	2.03692e6	+	6.26900e6i	0.560105	+	1.72383i	−0.121961	+	0.992535i	$0.538918\pi$
$422$	−1.25255e6	+	3.85497e6i	−0.342386	+	1.05375i
$423$	3.98571e6	+	2.89579e6i	1.08307	+	0.786893i
$424$	−416812.	+	1.28282e6i	−0.112597	+	0.346537i
$425$	−494847.	+	359528.i	−0.132892	+	0.0965517i
$426$	−1.17348e6	+	852580.i	−0.313293	+	0.227621i
$427$	−53284.7	−	38713.6i	−0.0141427	−	0.0102753i
$428$	−2.16016e6			−0.570002
$429$	−475828.			−0.124826
$430$	95255.3	+	69207.1i	0.0248438	+	0.0180501i
$431$	2.08062e6	+	6.40349e6i	0.539510	+	1.66044i	0.733697	+	0.679477i	$0.237793\pi$
$431$	2.08062e6	+	6.40349e6i	0.539510	+	1.66044i	−0.194187	+	0.980965i	$0.562207\pi$
$432$	52576.3	−	161813.i	0.0135544	−	0.0417162i
$433$	−1.88631e6			−0.483496			−0.241748	−	0.970339i	$-0.577721\pi$
$433$	−1.88631e6			−0.483496			−0.241748	+	0.970339i	$0.577721\pi$
$434$	−107526.	+	16881.4i	−0.0274024	+	0.00430213i
$435$	−1.21390e6			−0.307582
$436$	−185754.	+	571692.i	−0.0467974	+	0.144028i
$437$	−843813.	−	2.59699e6i	−0.211370	−	0.650529i
$438$	−2.22040e6	−	1.61321e6i	−0.553025	−	0.401796i
$439$	−508116.			−0.125835			−0.0629175	−	0.998019i	$-0.520040\pi$
$439$	−508116.			−0.125835			−0.0629175	+	0.998019i	$0.520040\pi$
$440$	470172.			0.115778
$441$	2.87595e6	+	2.08950e6i	0.704181	+	0.511617i
$442$	−386845.	+	281059.i	−0.0941848	+	0.0684293i
$443$	−4.67218e6	+	3.39454e6i	−1.13112	+	0.821810i	−0.985858	−	0.167583i	$-0.946404\pi$
$443$	−4.67218e6	+	3.39454e6i	−1.13112	+	0.821810i	−0.145266	+	0.989393i	$0.546404\pi$
$444$	265055.	−	815755.i	0.0638085	−	0.196382i
$445$	−514405.	−	373737.i	−0.123142	−	0.0894677i
$446$	−1.03743e6	+	3.19287e6i	−0.246957	+	0.760054i
$447$	2.18184e6	+	6.71501e6i	0.516480	+	1.58956i
$448$	16852.1	−	12243.7i	0.00396696	−	0.00288217i
$449$	−2.14756e6	−	6.60950e6i	−0.502723	−	1.54722i	−0.804565	−	0.593864i	$-0.797602\pi$
$449$	−2.14756e6	−	6.60950e6i	−0.502723	−	1.54722i	0.301842	−	0.953358i	$-0.402398\pi$
$450$	−198033.	−	609484.i	−0.0461007	−	0.141883i
$451$	−485822.	+	352971.i	−0.112470	+	0.0817141i
$452$	−773974.	−	2.38205e6i	−0.178189	−	0.548409i
$453$	−3.32160e6	+	1.02228e7i	−0.760505	+	2.34059i
$454$	−3.80326e6	−	2.76323e6i	−0.865997	−	0.629183i
$455$	−11305.1	+	34793.4i	−0.00256003	+	0.00787895i
$456$	−754305.	+	548034.i	−0.169877	+	0.123423i
$457$	4.67728e6	−	3.39824e6i	1.04762	−	0.761139i	0.0758603	−	0.997118i	$-0.475830\pi$
$457$	4.67728e6	−	3.39824e6i	1.04762	−	0.761139i	0.971758	+	0.235979i	$0.0758297\pi$
$458$	−3.18517e6	−	2.31416e6i	−0.709526	−	0.515501i
$459$	−537511.			−0.119085
$460$	−3.11285e6			−0.685903
$461$	2.06324e6	+	1.49903e6i	0.452166	+	0.328518i	0.790451	−	0.612526i	$-0.209846\pi$
$461$	2.06324e6	+	1.49903e6i	0.452166	+	0.328518i	−0.338284	+	0.941044i	$0.609846\pi$
$462$	−20236.2	−	62280.5i	−0.00441086	−	0.0135752i
$463$	−670787.	+	2.06447e6i	−0.145423	+	0.447565i	−0.997065	−	0.0765583i	$-0.975607\pi$
$463$	−670787.	+	2.06447e6i	−0.145423	+	0.447565i	0.851642	+	0.524123i	$0.175607\pi$
$464$	−299392.			−0.0645573
$465$	876217.	−	5.48420e6i	0.187923	−	1.17620i
$466$	−39858.0			−0.00850258
$467$	1.65998e6	−	5.10891e6i	0.352218	−	1.08402i	−0.605387	−	0.795932i	$-0.706982\pi$
$467$	1.65998e6	−	5.10891e6i	0.352218	−	1.08402i	0.957605	−	0.288085i	$-0.0930185\pi$
$468$	−154812.	−	476461.i	−0.0326730	−	0.100557i
$469$	−72780.4	−	52878.0i	−0.0152786	−	0.0111005i
$470$	4.52753e6			0.945402
$471$	5.37610e6			1.11664
$472$	−250173.	−	181761.i	−0.0516875	−	0.0375532i
$473$	73857.8	−	53660.8i	0.0151790	−	0.0110282i
$474$	6.90633e6	−	5.01774e6i	1.41189	−	1.02580i
$475$	159646.	−	491340.i	0.0324656	−	0.0999190i
$476$	−53239.3	−	38680.6i	−0.0107700	−	0.00782486i
$477$	−1.37963e6	+	4.24606e6i	−0.277630	+	0.854457i
$478$	1.74386e6	+	5.36706e6i	0.349094	+	1.07440i
$479$	1.15141e6	−	836551.i	0.229294	−	0.166592i	−0.467206	−	0.884148i	$-0.654739\pi$
$479$	1.15141e6	−	836551.i	0.229294	−	0.166592i	0.696500	+	0.717557i	$0.254739\pi$
$480$	328447.	+	1.01086e6i	0.0650672	+	0.200256i
$481$	114812.	+	353355.i	0.0226269	+	0.0696384i
$482$	−2.21464e6	+	1.60903e6i	−0.434196	+	0.315462i
$483$	133976.	+	412337.i	0.0261313	+	0.0804238i
$484$	−683626.	+	2.10398e6i	−0.132649	+	0.408253i
$485$	1.97052e6	+	1.43166e6i	0.380387	+	0.276367i
$486$	1.53102e6	−	4.71200e6i	0.294029	−	0.904928i
$487$	−1.00663e6	+	731361.i	−0.192331	+	0.139736i	−0.679783	−	0.733413i	$-0.737926\pi$
$487$	−1.00663e6	+	731361.i	−0.192331	+	0.139736i	0.487453	+	0.873149i	$0.337926\pi$
$488$	670575.	−	487201.i	0.127467	−	0.0926101i
$489$	281774.	+	204720.i	0.0532878	+	0.0387159i
$490$	3.26690e6			0.614676
$491$	−1.01827e7			−1.90615			−0.953075	−	0.302733i	$-0.902101\pi$
$491$	−1.01827e7			−1.90615			−0.953075	+	0.302733i	$0.902101\pi$
$492$	−1.09825e6	−	797929.i	−0.204546	−	0.148611i
$493$	292282.	+	899552.i	0.0541608	+	0.166690i
$494$	124803.	−	384103.i	0.0230094	−	0.0708158i
$495$	1.55625e6			0.285474
$496$	216107.	−	1.35260e6i	0.0394425	−	0.246869i
$497$	86469.8			0.0157027
$498$	−77372.0	+	238127.i	−0.0139801	+	0.0430264i
$499$	−403551.	−	1.24200e6i	−0.0725516	−	0.223291i	0.908205	−	0.418526i	$-0.137453\pi$
$499$	−403551.	−	1.24200e6i	−0.0725516	−	0.223291i	−0.980756	+	0.195235i	$0.937453\pi$
$500$	−2.44517e6	−	1.77652e6i	−0.437406	−	0.317794i
$501$	700717.			0.124724
$502$	6.23050e6			1.10348
$503$	4.41142e6	+	3.20509e6i	0.777426	+	0.564833i	0.904205	−	0.427098i	$-0.140464\pi$
$503$	4.41142e6	+	3.20509e6i	0.777426	+	0.564833i	−0.126780	+	0.991931i	$0.540464\pi$
$504$	55779.6	−	40526.2i	0.00978135	−	0.00710657i
$505$	−145806.	+	105934.i	−0.0254418	+	0.0184845i
$506$	−745842.	+	2.29547e6i	−0.129500	+	0.398561i
$507$	−6.02928e6	−	4.38052e6i	−1.04171	−	0.756844i
$508$	−1.16512e6	+	3.58586e6i	−0.200313	+	0.616501i
$509$	2.07463e6	+	6.38505e6i	0.354933	+	1.09237i	0.956049	+	0.293208i	$0.0947230\pi$
$509$	2.07463e6	+	6.38505e6i	0.354933	+	1.09237i	−0.601116	+	0.799162i	$0.705277\pi$
$510$	2.71656e6	−	1.97370e6i	0.462482	−	0.336012i
$511$	50559.5	+	155606.i	0.00856546	+	0.0263618i
$512$	81007.0	+	249314.i	0.0136568	+	0.0420312i
$513$	367288.	−	266850.i	0.0616188	−	0.0447687i
$514$	−1.66579e6	−	5.12678e6i	−0.278108	−	0.855928i
$515$	−2.09642e6	+	6.45212e6i	−0.348306	+	1.07197i
$516$	166964.	+	121306.i	0.0276056	+	0.0200567i
$517$	1.08480e6	−	3.33868e6i	0.178494	−	0.549349i
$518$	−41367.5	+	30055.2i	−0.00677384	+	0.00492148i
$519$	1.23872e7	−	8.99982e6i	2.01862	−	1.46661i
$520$	−372471.	−	270616.i	−0.0604065	−	0.0438879i
$521$	3.66334e6			0.591266			0.295633	−	0.955302i	$-0.404469\pi$
$521$	3.66334e6			0.591266			0.295633	+	0.955302i	$0.404469\pi$
$522$	−990974.			−0.159179
$523$	2.69024e6	+	1.95458e6i	0.430068	+	0.312463i	0.781676	−	0.623685i	$-0.214365\pi$
$523$	2.69024e6	+	1.95458e6i	0.430068	+	0.312463i	−0.351608	+	0.936147i	$0.614365\pi$
$524$	−568301.	−	1.74905e6i	−0.0904171	−	0.278275i
$525$	−25347.8	+	78012.5i	−0.00401367	+	0.0123528i
$526$	2.10968e6			0.332470
$527$	−4.27500e6	+	671168.i	−0.670517	+	0.105270i
$528$	824119.			0.128649
$529$	2.94902e6	−	9.07615e6i	0.458182	−	1.41014i
$530$	1.26787e6	+	3.90211e6i	0.196059	+	0.603406i
$531$	−828061.	−	601621.i	−0.127446	−	0.0925949i
$532$	55582.4			0.00851448
$533$	588027.			0.0896560
$534$	−901650.	−	655087.i	−0.136831	−	0.0994136i
$535$	−5.31592e6	+	3.86224e6i	−0.802960	+	0.583385i
$536$	915922.	−	665456.i	0.137704	−	0.100048i
$537$	2.80357e6	−	8.62850e6i	0.419542	−	1.29122i
$538$	−6.40111e6	−	4.65068e6i	−0.953453	−	0.692724i
$539$	782755.	−	2.40907e6i	0.116052	−	0.357172i
$540$	−159928.	−	492208.i	−0.0236016	−	0.0726381i
$541$	−5.60863e6	+	4.07491e6i	−0.823879	+	0.598583i	−0.917821	−	0.396994i	$-0.870053\pi$
$541$	−5.60863e6	+	4.07491e6i	−0.823879	+	0.598583i	0.0939416	+	0.995578i	$0.470053\pi$
$542$	549768.	+	1.69201e6i	0.0803862	+	0.247403i
$543$	−2.86213e6	−	8.80873e6i	−0.416572	−	1.28208i
$544$	670003.	−	486786.i	0.0970688	−	0.0705246i
$545$	565032.	+	1.73899e6i	0.0814858	+	0.250788i
$546$	−19815.5	+	60985.9i	−0.00284462	+	0.00875484i
$547$	−5.61531e6	−	4.07976e6i	−0.802427	−	0.582997i	0.109198	−	0.994020i	$-0.465172\pi$
$547$	−5.61531e6	−	4.07976e6i	−0.802427	−	0.582997i	−0.911625	+	0.411023i	$0.865172\pi$
$548$	−1.15670e6	+	3.55995e6i	−0.164539	+	0.506399i
$549$	2.21957e6	−	1.61261e6i	0.314295	−	0.228349i
$550$	−369432.	+	268408.i	−0.0520748	+	0.0378345i
$551$	−646308.	−	469570.i	−0.0906902	−	0.0658903i
$552$	−5.45620e6			−0.762154
$553$	−508906.			−0.0707660
$554$	−2.89944e6	−	2.10657e6i	−0.401365	−	0.291609i
$555$	−806252.	−	2.48139e6i	−0.111106	−	0.341950i
$556$	−478714.	+	1.47333e6i	−0.0656734	+	0.202122i
$557$	−6.63035e6			−0.905520			−0.452760	−	0.891632i	$-0.649561\pi$
$557$	−6.63035e6			−0.905520			−0.452760	+	0.891632i	$0.649561\pi$
$558$	715304.	−	4.47706e6i	0.0972534	−	0.608705i
$559$	−89395.6			−0.0121000
$560$	19580.0	−	60261.1i	0.00263841	−	0.00812020i
$561$	−804548.	−	2.47614e6i	−0.107931	−	0.332176i
$562$	1.02284e6	+	743135.i	0.136605	+	0.0992492i
$563$	1.28387e6			0.170707			0.0853535	−	0.996351i	$-0.472798\pi$
$563$	1.28387e6			0.170707			0.0853535	+	0.996351i	$0.472798\pi$
$564$	7.93586e6			1.05050
$565$	−6.16363e6	−	4.47814e6i	−0.812298	−	0.590169i
$566$	−5.42894e6	+	3.94436e6i	−0.712318	+	0.517529i
$567$	−270104.	+	196242.i	−0.0352837	+	0.0256351i
$568$	−336272.	+	1.03494e6i	−0.0437341	+	0.134600i
$569$	−7.68295e6	−	5.58199e6i	−0.994827	−	0.722784i	−0.0338540	−	0.999427i	$-0.510778\pi$
$569$	−7.68295e6	−	5.58199e6i	−0.994827	−	0.722784i	−0.960973	+	0.276643i	$0.910778\pi$
$570$	−876408.	+	2.69731e6i	−0.112985	+	0.347731i
$571$	−1.51619e6	−	4.66634e6i	−0.194609	−	0.598944i	−0.999981	−	0.00617478i	$-0.998034\pi$
$571$	−1.51619e6	−	4.66634e6i	−0.194609	−	0.598944i	0.805372	−	0.592770i	$-0.201966\pi$
$572$	−288802.	+	209827.i	−0.0369071	+	0.0268145i
$573$	5.54809e6	+	1.70753e7i	0.705922	+	2.17261i
$574$	25007.8	+	76966.1i	0.00316808	+	0.00975034i
$575$	2.44588e6	−	1.77703e6i	0.308507	−	0.224143i
$576$	268129.	+	825217.i	0.0336735	+	0.103636i
$577$	−528575.	+	1.62679e6i	−0.0660948	+	0.203419i	−0.978650	−	0.205535i	$-0.934106\pi$
$577$	−528575.	+	1.62679e6i	−0.0660948	+	0.203419i	0.912555	+	0.408954i	$0.134106\pi$
$578$	2.47807e6	+	1.80042e6i	0.308527	+	0.224158i
$579$	3.99303e6	−	1.22893e7i	0.495001	−	1.52346i
$580$	−736772.	+	535296.i	−0.0909417	+	0.0660730i
$581$	12075.6	−	8773.41i	0.00148411	−	0.00107827i
$582$	3.45392e6	+	2.50942e6i	0.422674	+	0.307090i
$583$	3.18127e6			0.387640
$584$	−2.05904e6			−0.249823
$585$	−1.23286e6	−	895726.i	−0.148944	−	0.108215i
$586$	1.89823e6	+	5.84215e6i	0.228352	+	0.702794i
$587$	370693.	−	1.14088e6i	0.0444038	−	0.136661i	−0.926397	−	0.376549i	$-0.877111\pi$
$587$	370693.	−	1.14088e6i	0.0444038	−	0.136661i	0.970801	+	0.239888i	$0.0771107\pi$
$588$	5.72624e6			0.683008
$589$	2.58796e6	−	2.58097e6i	0.307375	−	0.306545i
$590$	−940628.			−0.111247
$591$	1.30874e6	−	4.02789e6i	0.154129	−	0.474361i
$592$	−198851.	−	612001.i	−0.0233197	−	0.0717708i
$593$	1.74776e6	+	1.26982e6i	0.204101	+	0.148288i	0.685141	−	0.728411i	$-0.259741\pi$
$593$	1.74776e6	+	1.26982e6i	0.204101	+	0.148288i	−0.481040	+	0.876699i	$0.659741\pi$
$594$	−401282.			−0.0466642
$595$	−200175.			−0.0231802
$596$	4.28539e6	+	3.11352e6i	0.494168	+	0.359034i
$597$	−1.67569e7	+	1.21746e7i	−1.92423	+	1.39803i
$598$	1.91205e6	−	1.38919e6i	0.218649	−	0.158858i
$599$	1.75856e6	−	5.41229e6i	0.200258	−	0.616331i	−0.799617	−	0.600511i	$-0.794964\pi$
$599$	1.75856e6	−	5.41229e6i	0.200258	−	0.616331i	0.999875	−	0.0158202i	$-0.00503595\pi$
$600$	−835141.	−	606765.i	−0.0947069	−	0.0688086i
$601$	1.08047e6	−	3.32536e6i	0.122019	−	0.375536i	−0.871327	−	0.490703i	$-0.836740\pi$
$601$	1.08047e6	−	3.32536e6i	0.122019	−	0.375536i	0.993346	+	0.115166i	$0.0367401\pi$
$602$	−3801.85	−	11700.9i	−0.000427566	−	0.00131591i
$603$	3.03166e6	−	2.20263e6i	0.339537	−	0.246688i
$604$	2.49195e6	+	7.66944e6i	0.277938	+	0.855404i
$605$	2.07947e6	+	6.39996e6i	0.230975	+	0.710868i
$606$	−255569.	+	185682.i	−0.0282701	+	0.0205394i
$607$	4.39479e6	+	1.35258e7i	0.484134	+	1.49001i	0.833231	+	0.552926i	$0.186489\pi$
$607$	4.39479e6	+	1.35258e7i	0.484134	+	1.49001i	−0.349096	+	0.937087i	$0.613511\pi$
$608$	−216154.	+	665254.i	−0.0237140	+	0.0729842i
$609$	102618.	+	74556.0i	0.0112119	+	0.00814591i
$610$	779124.	−	2.39790e6i	0.0847778	−	0.260919i
$611$	−2.78102e6	+	2.02053e6i	−0.301370	+	0.218958i
$612$	2.21768e6	−	1.61124e6i	0.239343	−	0.173893i
$613$	8.80471e6	+	6.39700e6i	0.946377	+	0.687583i	0.949947	−	0.312411i	$-0.101137\pi$
$613$	8.80471e6	+	6.39700e6i	0.946377	+	0.687583i	−0.00357048	+	0.999994i	$0.501137\pi$
$614$	1.09663e7			1.17392
$615$	−4.12934e6			−0.440243
$616$	−39746.2	−	28877.3i	−0.00422030	−	0.00306623i
$617$	264438.	+	813857.i	0.0279648	+	0.0860667i	0.964065	−	0.265667i	$-0.0855922\pi$
$617$	264438.	+	813857.i	0.0279648	+	0.0860667i	−0.936100	+	0.351734i	$0.885592\pi$
$618$	−3.67461e6	+	1.13093e7i	−0.387026	+	1.19114i
$619$	−2.72915e6			−0.286287			−0.143143	−	0.989702i	$-0.545721\pi$
$619$	−2.72915e6			−0.286287			−0.143143	+	0.989702i	$0.545721\pi$
$620$	−1.88656e6	−	3.71500e6i	−0.197103	−	0.388132i
$621$	2.65675e6			0.276453
$622$	2.88535e6	−	8.88020e6i	0.299036	−	0.920337i
$623$	20531.0	+	63188.0i	0.00211929	+	0.00652250i
$624$	−652868.	−	474336.i	−0.0671218	−	0.0487669i
$625$	−6.83020e6			−0.699412
$626$	5.06087e6			0.516166
$627$	1.77905e6	+	1.29256e6i	0.180726	+	0.131305i
$628$	3.26300e6	−	2.37071e6i	0.330155	−	0.239872i
$629$	−1.64468e6	+	1.19493e6i	−0.165751	+	0.120425i
$630$	64808.9	−	199461.i	0.00650554	−	0.0200220i
$631$	−9.24565e6	−	6.71736e6i	−0.924409	−	0.671622i	0.0202085	−	0.999796i	$-0.493567\pi$
$631$	−9.24565e6	−	6.71736e6i	−0.924409	−	0.671622i	−0.944618	+	0.328173i	$0.893567\pi$
$632$	1.97908e6	−	6.09099e6i	0.197093	−	0.606590i
$633$	6.67828e6	+	2.05536e7i	0.662453	+	2.03882i
$634$	2.99341e6	−	2.17484e6i	0.295762	−	0.214884i
$635$	3.54408e6	+	1.09076e7i	0.348795	+	1.07348i
$636$	2.22233e6	+	6.83963e6i	0.217854	+	0.670486i
$637$	−2.00668e6	+	1.45794e6i	−0.195943	+	0.142361i
$638$	218205.	+	671567.i	0.0212233	+	0.0653187i
$639$	−1.11305e6	+	3.42560e6i	−0.107835	+	0.331883i
$640$	645108.	+	468699.i	0.0622562	+	0.0452318i
$641$	−352592.	+	1.08517e6i	−0.0338944	+	0.104316i	−0.966572	−	0.256394i	$-0.917466\pi$
$641$	−352592.	+	1.08517e6i	−0.0338944	+	0.104316i	0.932678	+	0.360710i	$0.117466\pi$
$642$	−9.31776e6	+	6.76975e6i	−0.892224	+	0.648239i
$643$	9.01790e6	−	6.55188e6i	0.860157	−	0.624941i	−0.0677706	−	0.997701i	$-0.521589\pi$
$643$	9.01790e6	−	6.55188e6i	0.860157	−	0.624941i	0.927928	+	0.372760i	$0.121589\pi$
$644$	263145.	+	191186.i	0.0250024	+	0.0181653i
$645$	627769.			0.0594156
$646$	2.20984e6			0.208343
$647$	−3.83680e6	−	2.78760e6i	−0.360337	−	0.261800i	0.392856	−	0.919600i	$-0.371487\pi$
$647$	−3.83680e6	−	2.78760e6i	−0.360337	−	0.261800i	−0.753193	+	0.657800i	$0.771487\pi$
$648$	−1.29838e6	−	3.99599e6i	−0.121468	−	0.373841i
$649$	−225376.	+	693636.i	−0.0210037	+	0.0646427i
$650$	447151.			0.0415117
$651$	−410903.	+	409793.i	−0.0380003	+	0.0378976i
$652$	261297.			0.0240722
$653$	−574570.	+	1.76834e6i	−0.0527303	+	0.162287i	−0.973954	−	0.226747i	$-0.927191\pi$
$653$	−574570.	+	1.76834e6i	−0.0527303	+	0.162287i	0.921223	+	0.389034i	$0.127191\pi$
$654$	990390.	+	3.04811e6i	0.0905444	+	0.278667i
$655$	−4.52573e6	−	3.28814e6i	−0.412179	−	0.299466i
$656$	−1.01845e6			−0.0924013
$657$	−6.81532e6			−0.615989
$658$	−382736.	−	278074.i	−0.0344615	−	0.0250378i
$659$	−943775.	+	685693.i	−0.0846554	+	0.0615058i	−0.629308	−	0.777156i	$-0.716662\pi$
$659$	−943775.	+	685693.i	−0.0846554	+	0.0615058i	0.544652	+	0.838662i	$0.316662\pi$
$660$	2.02807e6	−	1.47348e6i	0.181227	−	0.131669i
$661$	2.16953e6	−	6.67712e6i	0.193135	−	0.594409i	−0.806858	−	0.590745i	$-0.798834\pi$
$661$	2.16953e6	−	6.67712e6i	0.193135	−	0.594409i	0.999993	−	0.00366358i	$-0.00116616\pi$
$662$	−564263.	−	409961.i	−0.0500422	−	0.0363578i
$663$	−787824.	+	2.42467e6i	−0.0696058	+	0.214225i
$664$	58046.5	+	178649.i	0.00510924	+	0.0157246i
$665$	136782.	−	99378.1i	0.0119943	−	0.00871438i
$666$	−658188.	−	2.02569e6i	−0.0574995	−	0.176965i
$667$	−1.44466e6	−	4.44620e6i	−0.125733	−	0.386968i
$668$	425297.	−	308997.i	0.0368767	−	0.0267925i
$669$	5.53128e6	+	1.70235e7i	0.477816	+	1.47057i
$670$	1.06419e6	−	3.27523e6i	0.0915865	−	0.281874i
$671$	−1.58157e6	−	1.14908e6i	−0.135607	−	0.0985245i
$672$	34319.9	−	105626.i	0.00293172	−	0.00902291i
$673$	1.42486e6	−	1.03522e6i	0.121265	−	0.0881041i	−0.525500	−	0.850794i	$-0.676122\pi$
$673$	1.42486e6	−	1.03522e6i	0.121265	−	0.0881041i	0.646765	+	0.762690i	$0.276122\pi$
$674$	−5.90589e6	+	4.29088e6i	−0.500767	+	0.363828i
$675$	406649.	+	295448.i	0.0343526	+	0.0249587i
$676$	−5.59113e6			−0.470579
$677$	−9.92643e6			−0.832380			−0.416190	−	0.909278i	$-0.636635\pi$
$677$	−9.92643e6			−0.832380			−0.416190	+	0.909278i	$0.636635\pi$
$678$	−1.08036e7	−	7.84929e6i	−0.902600	−	0.655777i
$679$	−78647.6	−	242052.i	−0.00654653	−	0.0201481i
$680$	778461.	−	2.39586e6i	0.0645601	−	0.198696i
$681$	−2.50649e7			−2.07109
$682$	−3.19153e6	+	501065.i	−0.262747	+	0.0412509i
$683$	−1.72694e6			−0.141653			−0.0708264	−	0.997489i	$-0.522564\pi$
$683$	−1.72694e6			−0.141653			−0.0708264	+	0.997489i	$0.522564\pi$
$684$	−715460.	+	2.20196e6i	−0.0584716	+	0.179957i
$685$	3.51848e6	+	1.08288e7i	0.286503	+	0.881765i
$686$	−552763.	−	401606.i	−0.0448465	−	0.0325829i
$687$	−2.09915e7			−1.69688
$688$	154831.			0.0124705
$689$	−2.52020e6	−	1.83103e6i	−0.202249	−	0.146943i
$690$	−1.34271e7	+	9.75538e6i	−1.07364	+	0.780048i
$691$	1.34935e7	−	9.80363e6i	1.07506	−	0.781073i	0.0982410	−	0.995163i	$-0.468678\pi$
$691$	1.34935e7	−	9.80363e6i	1.07506	−	0.781073i	0.976814	+	0.214089i	$0.0686784\pi$
$692$	3.54968e6	−	1.09248e7i	0.281789	−	0.867258i
$693$	−131558.	−	95582.5i	−0.0104060	−	0.00756041i
$694$	2.60431e6	−	8.01524e6i	0.205255	−	0.631710i
$695$	1.45617e6	+	4.48162e6i	0.114354	+	0.351944i
$696$	−1.29142e6	+	938268.i	−0.101052	+	0.0734182i
$697$	994259.	+	3.06001e6i	0.0775206	+	0.238584i
$698$	581393.	+	1.78934e6i	0.0451680	+	0.139013i
$699$	−171926.	+	124911.i	−0.0133091	+	0.00966961i
$700$	19016.6	+	58527.0i	0.00146686	+	0.00451452i
$701$	3.03315e6	−	9.33509e6i	0.233131	−	0.717502i	−0.764233	−	0.644940i	$-0.776882\pi$
$701$	3.03315e6	−	9.33509e6i	0.233131	−	0.717502i	0.997364	−	0.0725623i	$-0.0231176\pi$
$702$	317896.	+	230965.i	0.0243468	+	0.0176890i
$703$	530603.	−	1.63303e6i	0.0404931	−	0.124625i
$704$	500196.	−	363413.i	0.0380372	−	0.0276356i
$705$	1.95293e7	−	1.41889e7i	1.47984	−	1.07516i
$706$	−4.89729e6	−	3.55809e6i	−0.369780	−	0.268661i
$707$	18832.1			0.00141694
$708$	−1.64873e6			−0.123614
$709$	−1.46700e7	−	1.06584e7i	−1.09601	−	0.796300i	−0.115608	−	0.993295i	$-0.536882\pi$
$709$	−1.46700e7	−	1.06584e7i	−1.09601	−	0.796300i	−0.980405	+	0.196995i	$0.936882\pi$
$710$	1.02288e6	+	3.14811e6i	0.0761518	+	0.234371i
$711$	6.55067e6	−	2.01609e7i	0.485973	−	1.49567i
$712$	−836127.			−0.0618119
$713$	2.11300e7	−	3.31738e6i	1.55659	−	0.244383i
$714$	−350867.			−0.0257571
$715$	−335552.	+	1.03272e6i	−0.0245468	+	0.0755472i
$716$	−2.10331e6	−	6.47333e6i	−0.153328	−	0.471895i
$717$	2.43420e7	+	1.76855e7i	1.76831	+	1.28475i
$718$	−3.18893e6			−0.230852
$719$	1.43496e7			1.03518			0.517592	−	0.855628i	$-0.326829\pi$
$719$	1.43496e7			1.03518			0.517592	+	0.855628i	$0.326829\pi$
$720$	2.13528e6	+	1.55137e6i	0.153505	+	0.111528i
$721$	573501.	−	416673.i	0.0410862	−	0.0298509i
$722$	6.50281e6	−	4.72457e6i	0.464257	−	0.337302i
$723$	−4.51020e6	+	1.38810e7i	−0.320886	+	0.987584i
$724$	−5.62156e6	−	4.08430e6i	−0.398575	−	0.289582i
$725$	273324.	−	841204.i	0.0193122	−	0.0594369i
$726$	3.64491e6	+	1.12179e7i	0.256652	+	0.789894i
$727$	9.39104e6	−	6.82299e6i	0.658988	−	0.478783i	−0.207333	−	0.978270i	$-0.566478\pi$
$727$	9.39104e6	−	6.82299e6i	0.658988	−	0.478783i	0.866321	+	0.499487i	$0.166478\pi$
$728$	14866.1	+	45753.2i	0.00103961	+	0.00319958i
$729$	−3.23321e6	−	9.95080e6i	−0.225328	−	0.693488i
$730$	−5.06708e6	+	3.68145e6i	−0.351925	+	0.255689i
$731$	−151154.	−	465203.i	−0.0104622	−	0.0321995i
$732$	1.36565e6	−	4.20304e6i	0.0942024	−	0.289925i
$733$	1.21832e7	+	8.85159e6i	0.837530	+	0.608501i	0.921680	−	0.387952i	$-0.126817\pi$
$733$	1.21832e7	+	8.85159e6i	0.837530	+	0.608501i	−0.0841496	+	0.996453i	$0.526817\pi$
$734$	−766955.	+	2.36044e6i	−0.0525448	+	0.161716i
$735$	1.40917e7	−	1.02382e7i	0.962152	−	0.699044i
$736$	−3.31162e6	+	2.40603e6i	−0.225344	+	0.163722i
$737$	−2.16023e6	−	1.56950e6i	−0.146498	−	0.106437i
$738$	−3.37100e6			−0.227834
$739$	−1.29206e7			−0.870302			−0.435151	−	0.900357i	$-0.643305\pi$
$739$	−1.29206e7			−0.870302			−0.435151	+	0.900357i	$0.643305\pi$
$740$	−1.58357e6	−	1.15053e6i	−0.106306	−	0.0772361i
$741$	−665413.	−	2.04793e6i	−0.0445190	−	0.137015i
$742$	132482.	−	407737.i	0.00883378	−	0.0271876i
$743$	−1.15437e7			−0.767135			−0.383567	−	0.923513i	$-0.625305\pi$
$743$	−1.15437e7			−0.767135			−0.383567	+	0.923513i	$0.625305\pi$
$744$	−3.30677e6	−	6.51166e6i	−0.219014	−	0.431280i
$745$	1.61127e7			1.06360
$746$	−182591.	+	561958.i	−0.0120125	+	0.0369706i
$747$	192131.	+	591319.i	0.0125978	+	0.0387722i
$748$	−1.58023e6	−	1.14810e6i	−0.103268	−	0.0750285i
$749$	686597.			0.0447195
$750$	−1.61146e7			−1.04608
$751$	2.21724e6	+	1.61092e6i	0.143454	+	0.104226i	0.657198	−	0.753718i	$-0.271742\pi$
$751$	2.21724e6	+	1.61092e6i	0.143454	+	0.104226i	−0.513743	+	0.857944i	$0.671742\pi$
$752$	4.81663e6	−	3.49949e6i	0.310598	−	0.225663i
$753$	2.68750e7	−	1.95258e7i	1.72727	−	1.25494i
$754$	213670.	−	657607.i	0.0136872	−	0.0421248i
$755$	1.98450e7	+	1.44182e7i	1.26702	+	0.920542i
$756$	−16711.1	+	51431.6i	−0.00106341	+	0.00327284i
$757$	−5.96390e6	−	1.83550e7i	−0.378260	−	1.16417i	−0.941253	−	0.337703i	$-0.890350\pi$
$757$	−5.96390e6	−	1.83550e7i	−0.378260	−	1.16417i	0.562992	−	0.826462i	$-0.309650\pi$
$758$	9.53230e6	−	6.92562e6i	0.602594	−	0.437810i
$759$	3.97663e6	+	1.22388e7i	0.250559	+	0.771142i
$760$	657504.	+	2.02359e6i	0.0412919	+	0.127083i
$761$	−1.28372e7	+	9.32677e6i	−0.803542	+	0.583808i	−0.911951	−	0.410299i	$-0.865424\pi$
$761$	−1.28372e7	+	9.32677e6i	−0.803542	+	0.583808i	0.108409	+	0.994106i	$0.465424\pi$
$762$	6.21208e6	+	1.91188e7i	0.387569	+	1.19282i
$763$	59041.0	−	181710.i	0.00367149	−	0.0112997i
$764$	1.08971e7	+	7.91720e6i	0.675425	+	0.490725i
$765$	2.57667e6	−	7.93017e6i	0.159186	−	0.489924i
$766$	−2.82608e6	+	2.05327e6i	−0.174025	+	0.126437i
$767$	577777.	−	419780.i	0.0354627	−	0.0257652i
$768$	1.13075e6	+	821536.i	0.0691771	+	0.0502601i
$769$	−5.16580e6			−0.315008			−0.157504	−	0.987518i	$-0.550345\pi$
$769$	−5.16580e6			−0.315008			−0.157504	+	0.987518i	$0.550345\pi$
$770$	−149442.			−0.00908335
$771$	−2.32522e7	−	1.68937e7i	−1.40873	−	1.02350i
$772$	−2.99567e6	−	9.21974e6i	−0.180905	−	0.556769i
$773$	−3.16638e6	+	9.74510e6i	−0.190596	+	0.586594i	−1.00000		0.000658467i	$-0.999790\pi$
$773$	−3.16638e6	+	9.74510e6i	−0.190596	+	0.586594i	0.809404	+	0.587252i	$0.199790\pi$
$774$	512482.			0.0307486
$775$	3.60313e6	+	1.84203e6i	0.215489	+	0.110165i
$776$	3.20293e6			0.190938
$777$	−84246.5	+	259284.i	−0.00500610	+	0.0154072i
$778$	−2.83006e6	−	8.71003e6i	−0.167628	−	0.515906i
$779$	−2.19855e6	−	1.59734e6i	−0.129805	−	0.0943092i
$780$	−2.45472e6			−0.144466
$781$	2.56656e6			0.150565
$782$	1.04621e7	+	7.60117e6i	0.611790	+	0.444492i
$783$	628819.	−	456864.i	0.0366540	−	0.0266307i
$784$	3.47551e6	−	2.52511e6i	0.201943	−	0.146720i
$785$	3.79120e6	−	1.16681e7i	0.219585	−	0.675813i
$786$	−7.93272e6	−	5.76346e6i	−0.458000	−	0.332757i
$787$	−3.79263e6	+	1.16725e7i	−0.218275	+	0.671780i	0.780630	+	0.624993i	$0.214898\pi$
$787$	−3.79263e6	+	1.16725e7i	−0.218275	+	0.671780i	−0.998905	+	0.0467872i	$0.985102\pi$
$788$	−981852.	−	3.02183e6i	−0.0563288	−	0.173362i
$789$	9.10003e6	−	6.61156e6i	0.520415	−	0.378104i
$790$	−6.02004e6	−	1.85278e7i	−0.343187	−	1.05622i
$791$	246004.	+	757122.i	0.0139798	+	0.0430254i
$792$	1.65562e6	−	1.20288e6i	0.0937883	−	0.0681412i
$793$	591550.	+	1.82060e6i	0.0334048	+	0.102809i
$794$	2.14912e6	−	6.61431e6i	0.120979	−	0.372335i
$795$	1.76978e7	+	1.28582e7i	0.993118	+	0.721542i
$796$	−4.80186e6	+	1.47786e7i	−0.268613	+	0.826706i
$797$	−5.02462e6	+	3.65060e6i	−0.280193	+	0.203572i	−0.719002	−	0.695008i	$-0.755401\pi$
$797$	−5.02462e6	+	3.65060e6i	−0.280193	+	0.203572i	0.438809	+	0.898581i	$0.355401\pi$
$798$	239752.	−	174190.i	0.0133277	−	0.00968314i
$799$	−1.52168e7	−	1.10556e7i	−0.843250	−	0.612657i
$800$	−774451.			−0.0427828
$801$	−2.76754e6			−0.152410
$802$	−1.90683e7	−	1.38540e7i	−1.04683	−	0.760568i
$803$	1.50068e6	+	4.61863e6i	0.0821298	+	0.252769i
$804$	1.86531e6	−	5.74084e6i	0.101768	−	0.313210i
$805$	989403.			0.0538125
$806$	2.81673e6	+	1.44000e6i	0.152724	+	0.0780771i
$807$	−4.21857e7			−2.28024
$808$	−73236.2	+	225398.i	−0.00394637	+	0.0121457i
$809$	4.26900e6	+	1.31386e7i	0.229327	+	0.705795i	0.997824	+	0.0659412i	$0.0210050\pi$
$809$	4.26900e6	+	1.31386e7i	0.229327	+	0.705795i	−0.768497	+	0.639853i	$0.778995\pi$
$810$	−1.03398e7	−	7.51228e6i	−0.553730	−	0.402308i
$811$	−2.61118e7			−1.39407			−0.697035	−	0.717037i	$-0.745498\pi$
$811$	−2.61118e7			−1.39407			−0.697035	+	0.717037i	$0.745498\pi$
$812$	95160.4			0.00506484
$813$	7.67402e6	+	5.57550e6i	0.407189	+	0.295840i
$814$	−1.22785e6	+	892086.i	−0.0649508	+	0.0471895i
$815$	643024.	−	467184.i	0.0339104	−	0.0246374i
$816$	1.36449e6	−	4.19946e6i	0.0717372	−	0.220784i
$817$	334238.	+	242838.i	0.0175186	+	0.0127280i
$818$	4.95976e6	−	1.52646e7i	0.259166	−	0.797630i
$819$	49206.2	+	151441.i	0.00256336	+	0.00788921i
$820$	−2.50628e6	+	1.82092e6i	−0.130165	+	0.0945707i
$821$	7.23436e6	+	2.22651e7i	0.374578	+	1.15283i	0.943763	+	0.330623i	$0.107259\pi$
$821$	7.23436e6	+	2.22651e7i	0.374578	+	1.15283i	−0.569185	+	0.822210i	$0.692741\pi$
$822$	6.16720e6	+	1.89807e7i	0.318353	+	0.979789i
$823$	8.19127e6	−	5.95131e6i	0.421553	−	0.306276i	−0.356710	−	0.934215i	$-0.616101\pi$
$823$	8.19127e6	−	5.95131e6i	0.421553	−	0.306276i	0.778262	+	0.627939i	$0.216101\pi$
$824$	2.75679e6	+	8.48452e6i	0.141444	+	0.435321i
$825$	−752362.	+	2.31553e6i	−0.0384850	+	0.118445i
$826$	79516.3	+	57772.0i	0.00405514	+	0.00294623i
$827$	892623.	−	2.74721e6i	0.0453841	−	0.139678i	−0.925797	−	0.378022i	$-0.876604\pi$
$827$	892623.	−	2.74721e6i	0.0453841	−	0.139678i	0.971181	+	0.238344i	$0.0766045\pi$
$828$	−1.09613e7	+	7.96385e6i	−0.555630	+	0.403689i
$829$	−1.45055e7	+	1.05389e7i	−0.733073	+	0.532609i	−0.890534	−	0.454916i	$-0.849669\pi$
$829$	−1.45055e7	+	1.05389e7i	−0.733073	+	0.532609i	0.157461	+	0.987525i	$0.449669\pi$
$830$	462260.	+	335852.i	0.0232912	+	0.0169220i
$831$	−1.91084e7			−0.959891
$832$	−605424.			−0.0303215
$833$	−1.09799e7	−	7.97736e6i	−0.548259	−	0.398334i
$834$	2.55237e6	+	7.85540e6i	0.127066	+	0.391069i
$835$	494143.	−	1.52082e6i	0.0245265	−	0.0754849i
$836$	1.64977e6			0.0816409
$837$	1.61014e6	+	3.17067e6i	0.0794421	+	0.156436i
$838$	−1.18378e7			−0.582321
$839$	−8.51628e6	+	2.62104e7i	−0.417681	+	1.28549i	0.492149	+	0.870511i	$0.336211\pi$
$839$	−8.51628e6	+	2.62104e7i	−0.417681	+	1.28549i	−0.909831	+	0.414980i	$0.863789\pi$
$840$	−104395.	−	321296.i	−0.00510485	−	0.0157111i
$841$	1.54873e7	+	1.12522e7i	0.755070	+	0.548590i
$842$	2.63665e7			1.28166
$843$	6.74089e6			0.326699
$844$	1.31169e7	+	9.53000e6i	0.633834	+	0.460508i
$845$	−1.37592e7	+	9.99662e6i	−0.662904	+	0.481628i
$846$	1.59428e7	−	1.15831e7i	0.765843	−	0.556417i
$847$	217287.	−	668741.i	0.0104070	−	0.0320295i
$848$	4.36491e6	+	3.17130e6i	0.208442	+	0.151442i
$849$	−1.10562e7	+	3.40276e7i	−0.526427	+	1.62018i
$850$	756059.	+	2.32691e6i	0.0358929	+	0.110467i
$851$	8.12916e6	−	5.90618e6i	0.384788	−	0.279565i
$852$	1.79291e6	+	5.51802e6i	0.0846175	+	0.260426i
$853$	−2.87319e6	−	8.84275e6i	−0.135204	−	0.416117i	0.860417	−	0.509590i	$-0.170203\pi$
$853$	−2.87319e6	−	8.84275e6i	−0.135204	−	0.416117i	−0.995622	+	0.0934735i	$0.970203\pi$
$854$	−213139.	+	154855.i	−0.0100004	+	0.00726573i
$855$	2.17631e6	+	6.69799e6i	0.101813	+	0.313350i
$856$	−2.67010e6	+	8.21774e6i	−0.124550	+	0.383326i
$857$	1.95123e7	+	1.41765e7i	0.907519	+	0.659351i	0.940386	−	0.340108i	$-0.110464\pi$
$857$	1.95123e7	+	1.41765e7i	0.907519	+	0.659351i	−0.0328669	+	0.999460i	$0.510464\pi$
$858$	−588155.	+	1.81016e6i	−0.0272756	+	0.0839456i
$859$	1.83647e7	−	1.33428e7i	0.849184	−	0.616969i	−0.0757367	−	0.997128i	$-0.524131\pi$
$859$	1.83647e7	−	1.33428e7i	0.849184	−	0.616969i	0.924921	+	0.380159i	$0.124131\pi$
$860$	381021.	−	276828.i	0.0175672	−	0.0127633i
$861$	349075.	+	253618.i	0.0160476	+	0.0116593i
$862$	2.69321e7			1.23453
$863$	−4.01479e7			−1.83500			−0.917500	−	0.397736i	$-0.869796\pi$
$863$	−4.01479e7			−1.83500			−0.917500	+	0.397736i	$0.869796\pi$
$864$	−550586.	−	400024.i	−0.0250923	−	0.0182306i
$865$	−1.07975e7	−	3.32314e7i	−0.490664	−	1.51011i
$866$	−2.33161e6	+	7.17594e6i	−0.105648	+	0.325150i
$867$	1.63314e7			0.737863
$868$	−68688.6	+	429919.i	−0.00309446	+	0.0193681i
$869$	−1.51051e7			−0.678539
$870$	−1.50046e6	+	4.61796e6i	−0.0672090	+	0.206848i
$871$	807984.	+	2.48672e6i	0.0360876	+	0.111066i
$872$	1.94524e6	+	1.41330e6i	0.0866328	+	0.0629424i
$873$	1.06015e7			0.470797
$874$	−1.09225e7			−0.483666
$875$	777187.	+	564660.i	0.0343167	+	0.0249325i
$876$	−8.88158e6	+	6.45285e6i	−0.391048	+	0.284113i
$877$	−2.84739e7	+	2.06875e7i	−1.25011	+	0.908259i	−0.998228	−	0.0594994i	$-0.981050\pi$
$877$	−2.84739e7	+	2.06875e7i	−1.25011	+	0.908259i	−0.251882	+	0.967758i	$0.581050\pi$
$878$	−628066.	+	1.93299e6i	−0.0274960	+	0.0846238i
$879$	2.64967e7	+	1.92510e7i	1.15670	+	0.840389i
$880$	581165.	−	1.78864e6i	0.0252984	−	0.0778604i
$881$	−1.18528e7	−	3.64792e7i	−0.514495	−	1.58345i	−0.784199	−	0.620509i	$-0.786926\pi$
$881$	−1.18528e7	−	3.64792e7i	−0.514495	−	1.58345i	0.269704	−	0.962943i	$-0.413074\pi$
$882$	1.15038e7	−	8.35799e6i	0.497931	−	0.361768i
$883$	1.25525e7	+	3.86327e7i	0.541787	+	1.66745i	0.728508	+	0.685037i	$0.240214\pi$
$883$	1.25525e7	+	3.86327e7i	0.541787	+	1.66745i	−0.186721	+	0.982413i	$0.559786\pi$
$884$	591046.	+	1.81905e6i	0.0254385	+	0.0782915i
$885$	−4.05736e6	+	2.94784e6i	−0.174135	+	0.126516i
$886$	7.13846e6	+	2.19699e7i	0.305506	+	0.940251i
$887$	8.95346e6	−	2.75559e7i	0.382104	−	1.17600i	−0.556455	−	0.830878i	$-0.687839\pi$
$887$	8.95346e6	−	2.75559e7i	0.382104	−	1.17600i	0.938559	−	0.345119i	$-0.112161\pi$
$888$	−2.77569e6	−	2.01666e6i	−0.118124	−	0.0858222i
$889$	370326.	−	1.13975e6i	0.0157156	−	0.0483676i
$890$	−2.05762e6	+	1.49495e6i	−0.0870743	+	0.0632632i
$891$	−8.01711e6	+	5.82477e6i	−0.338317	+	0.245802i
$892$	1.08641e7	+	7.89322e6i	0.457173	+	0.332156i
$893$	1.58865e7			0.666651
$894$	2.82423e7			1.18183
$895$	−1.67500e7	−	1.21696e7i	−0.698966	−	0.507829i
$896$	−25747.7	−	79243.2i	−0.00107144	−	0.00329755i
$897$	3.89397e6	−	1.19844e7i	0.161589	−	0.497319i
$898$	−2.77986e7			−1.15035
$899$	4.43074e6	−	4.41877e6i	0.182842	−	0.182349i
$900$	−2.56340e6			−0.105490
$901$	5.26720e6	−	1.62108e7i	0.216156	−	0.665261i
$902$	742271.	+	2.28447e6i	0.0303771	+	0.0934910i
$903$	−53068.6	−	38556.6i	−0.00216580	−	0.00157355i
$904$	−1.00185e7			−0.407740
$905$	−2.11366e7			−0.857853
$906$	3.47843e7	+	2.52723e7i	1.40787	+	1.02288i
$907$	3.88797e6	−	2.82477e6i	0.156929	−	0.114016i	−0.506550	−	0.862211i	$-0.669079\pi$
$907$	3.88797e6	−	2.82477e6i	0.156929	−	0.114016i	0.663479	+	0.748195i	$0.269079\pi$
$908$	−1.52130e7	+	1.10529e7i	−0.612352	+	0.444900i
$909$	−242408.	+	746056.i	−0.00973056	+	0.0299476i
$910$	118388.	+	86014.0i	0.00473920	+	0.00344323i
$911$	−837064.	+	2.57622e6i	−0.0334167	+	0.102846i	−0.966374	−	0.257142i	$-0.917219\pi$
$911$	−837064.	+	2.57622e6i	−0.0334167	+	0.102846i	0.932957	+	0.359988i	$0.117219\pi$
$912$	1.15247e6	+	3.54695e6i	0.0458822	+	0.141211i
$913$	358421.	−	260408.i	0.0142304	−	0.0103390i
$914$	−7.14625e6	−	2.19939e7i	−0.282952	−	0.870837i
$915$	−4.15408e6	−	1.27849e7i	−0.164030	−	0.504831i
$916$	−1.27407e7	+	9.25664e6i	−0.501711	+	0.364514i
$917$	180632.	+	555928.i	0.00709367	+	0.0218321i
$918$	−664400.	+	2.04481e6i	−0.0260209	+	0.0800842i
$919$	−9.69956e6	−	7.04714e6i	−0.378846	−	0.275248i	0.382023	−	0.924153i	$-0.375227\pi$
$919$	−9.69956e6	−	7.04714e6i	−0.378846	−	0.275248i	−0.760870	+	0.648905i	$0.775227\pi$
$920$	−3.84769e6	+	1.18420e7i	−0.149875	+	0.461269i
$921$	4.73027e7	−	3.43674e7i	1.83754	−	1.33505i
$922$	8.25298e6	−	5.99614e6i	0.319730	−	0.232297i
$923$	−2.03323e6	−	1.47723e6i	−0.0785565	−	0.0570746i
$924$	−261942.			−0.0100931
$925$	1.90108e6			0.0730543
$926$	7.02457e6	+	5.10365e6i	0.269211	+	0.195593i
$927$	9.12484e6	+	2.80834e7i	0.348759	+	1.07337i
$928$	−370069.	+	1.13896e6i	−0.0141063	+	0.0434147i
$929$	−4.50230e7			−1.71157			−0.855786	−	0.517329i	$-0.826926\pi$
$929$	−4.50230e7			−1.71157			−0.855786	+	0.517329i	$0.826926\pi$
$930$	−1.97801e7	−	1.01122e7i	−0.749930	−	0.383387i
$931$	1.14631e7			0.433440
$932$	−49267.2	+	151629.i	−0.00185788	+	0.00571797i
$933$	−1.53839e7	−	4.73468e7i	−0.578579	−	1.78068i
$934$	−1.73836e7	−	1.26299e7i	−0.652037	−	0.473733i
$935$	−5.94151e6			−0.222263
$936$	−2.00392e6			−0.0747639
$937$	−2.45315e6	−	1.78232e6i	−0.0912799	−	0.0663187i	0.541209	−	0.840888i	$-0.317967\pi$
$937$	−2.45315e6	−	1.78232e6i	−0.0912799	−	0.0663187i	−0.632489	+	0.774569i	$0.717967\pi$
$938$	−291122.	+	211512.i	−0.0108036	+	0.00784925i
$939$	2.18299e7	−	1.58603e7i	0.807954	−	0.587013i
$940$	5.59633e6	−	1.72237e7i	0.206578	−	0.635781i
$941$	−1.88049e7	−	1.36626e7i	−0.692305	−	0.502989i	0.185112	−	0.982717i	$-0.440735\pi$
$941$	−1.88049e7	−	1.36626e7i	−0.692305	−	0.502989i	−0.877417	+	0.479728i	$0.840735\pi$
$942$	6.64522e6	−	2.04519e7i	0.243996	−	0.750942i
$943$	−4.91431e6	−	1.51247e7i	−0.179963	−	0.553869i
$944$	−1.00069e6	+	727045.i	−0.0365486	+	0.0265541i
$945$	50832.4	+	156446.i	0.00185166	+	0.00569882i
$946$	−112845.	−	347300.i	−0.00409971	−	0.0126176i
$947$	1.49647e7	−	1.08725e7i	0.542241	−	0.393961i	−0.282675	−	0.959216i	$-0.591222\pi$
$947$	1.49647e7	−	1.08725e7i	0.542241	−	0.393961i	0.824917	+	0.565254i	$0.191222\pi$
$948$	−1.05519e7	−	3.24755e7i	−0.381339	−	1.17364i
$949$	1.46949e6	−	4.52263e6i	0.0529665	−	0.163014i
$950$	−1.67183e6	−	1.21466e6i	−0.0601013	−	0.0436662i
$951$	6.09619e6	−	1.87622e7i	0.218579	−	0.672715i
$952$	−212957.	+	154723.i	−0.00761553	+	0.00553301i
$953$	−1.85729e7	+	1.34940e7i	−0.662442	+	0.481292i	−0.867487	−	0.497460i	$-0.834266\pi$
$953$	−1.85729e7	+	1.34940e7i	−0.662442	+	0.481292i	0.205045	+	0.978753i	$0.434266\pi$
$954$	1.44477e7	+	1.04968e7i	0.513957	+	0.373411i
$955$	4.09721e7			1.45372
$956$	2.25730e7			0.798813
$957$	3.04585e6	+	2.21294e6i	0.107505	+	0.0781069i
$958$	−1.75920e6	−	5.41427e6i	−0.0619302	−	0.190601i
$959$	367651.	−	1.13151e6i	0.0129089	−	0.0397295i
$960$	4.25151e6			0.148890
$961$	1.67651e7	+	2.32069e7i	0.585595	+	0.810604i
$962$	1.48616e6			0.0517759
$963$	−8.83792e6	+	2.72003e7i	−0.307103	+	0.945166i
$964$	3.38367e6	+	1.04139e7i	0.117272	+	0.360927i
$965$	−2.38564e7	−	1.73327e7i	−0.824682	−	0.599167i
$966$	1.73423e6			0.0597948
$967$	1.74261e6			0.0599286			0.0299643	−	0.999551i	$-0.490461\pi$
$967$	1.74261e6			0.0599286			0.0299643	+	0.999551i	$0.490461\pi$
$968$	7.15902e6	+	5.20133e6i	0.245564	+	0.178413i
$969$	9.53205e6	−	6.92544e6i	0.326119	−	0.236940i
$970$	7.88206e6	−	5.72665e6i	0.268974	−	0.195421i
$971$	1.31589e6	−	4.04988e6i	0.0447889	−	0.137846i	−0.926161	−	0.377127i	$-0.876912\pi$
$971$	1.31589e6	−	4.04988e6i	0.0447889	−	0.137846i	0.970950	+	0.239281i	$0.0769119\pi$
$972$	−1.60330e7	−	1.16487e7i	−0.544315	−	0.395468i
$973$	152157.	−	468291.i	0.00515241	−	0.0158575i
$974$	1.53800e6	+	4.73347e6i	0.0519467	+	0.159876i
$975$	1.92877e6	−	1.40133e6i	0.0649782	−	0.0472095i
$976$	−1.02455e6	−	3.15323e6i	−0.0344276	−	0.105957i
$977$	−1.72663e7	−	5.31401e7i	−0.578711	−	1.78109i	−0.623179	−	0.782080i	$-0.714159\pi$
$977$	−1.72663e7	−	5.31401e7i	−0.578711	−	1.78109i	0.0444672	−	0.999011i	$-0.485841\pi$
$978$	1.12709e6	−	818882.i	0.0376802	−	0.0273763i
$979$	609392.	+	1.87552e6i	0.0203208	+	0.0625409i
$980$	4.03812e6	−	1.24280e7i	0.134312	−	0.413369i
$981$	6.43866e6	+	4.67796e6i	0.213611	+	0.155197i
$982$	−1.25865e7	+	3.87371e7i	−0.416509	+	1.28188i
$983$	−4.61942e6	+	3.35620e6i	−0.152477	+	0.110781i	−0.661408	−	0.750026i	$-0.730041\pi$
$983$	−4.61942e6	+	3.35620e6i	−0.152477	+	0.110781i	0.508931	+	0.860807i	$0.330041\pi$
$984$	−4.39302e6	+	3.19172e6i	−0.144636	+	0.105084i
$985$	−7.81909e6	−	5.68090e6i	−0.256783	−	0.186563i
$986$	3.78338e6			0.123933
$987$	−2.52238e6			−0.0824170
$988$	−1.30695e6	−	949554.i	−0.0425958	−	0.0309476i
$989$	747105.	+	2.29935e6i	0.0242879	+	0.0747506i
$990$	1.92363e6	−	5.92032e6i	0.0623783	−	0.191981i
$991$	1.66270e7			0.537812			0.268906	−	0.963166i	$-0.413338\pi$
$991$	1.66270e7			0.537812			0.268906	+	0.963166i	$0.413338\pi$
$992$	−4.87849e6	−	2.49403e6i	−0.157401	−	0.0804679i
$993$	−3.71870e6			−0.119679
$994$	106883.	−	328951.i	0.00343116	−	0.0105600i
$995$	1.46064e7	+	4.49540e7i	0.467721	+	1.43950i
$996$	810251.	+	588681.i	0.0258804	+	0.0188032i
$997$	4.11148e7			1.30997			0.654983	−	0.755644i	$-0.272676\pi$
$997$	4.11148e7			1.30997			0.654983	+	0.755644i	$0.272676\pi$
$998$	−5.22367e6			−0.166016
$999$	1.35155e6	+	981956.i	0.0428467	+	0.0311299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.6.d.a.39.1	yes	24
31.4	even	5	inner	62.6.d.a.35.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.6.d.a.35.1	✓	24	31.4	even	5	inner
62.6.d.a.39.1	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	62.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23607 - 3.80423i) q^{2} +(-6.59038 - 20.2831i) q^{3} +(-12.9443 - 9.40456i) q^{4} -48.6693 q^{5} -85.3076 q^{6} +(4.11428 + 2.98920i) q^{7} +(-51.7771 + 37.6183i) q^{8} +(-171.380 + 124.515i) q^{9} +(-60.1585 + 185.149i) q^{10} +(122.118 + 88.7240i) q^{11} +(-105.446 + 324.529i) q^{12} +(-45.6754 - 140.574i) q^{13} +(16.4571 - 11.9568i) q^{14} +(320.749 + 987.164i) q^{15} +(79.1084 + 243.470i) q^{16} +(654.300 - 475.377i) q^{17} +(261.845 + 805.876i) q^{18} +(-211.088 + 649.662i) q^{19} +(629.989 + 457.713i) q^{20} +(33.5155 - 103.150i) q^{21} +(488.472 - 354.896i) q^{22} +(-3234.00 + 2349.64i) q^{23} +(1104.25 + 802.281i) q^{24} -756.300 q^{25} -591.234 q^{26} +(-537.682 - 390.649i) q^{27} +(-25.1442 - 77.3859i) q^{28} +(-361.396 + 1112.26i) q^{29} +4151.86 q^{30} +(-4764.15 - 2435.58i) q^{31} +1024.00 q^{32} +(994.792 - 3061.66i) q^{33} +(-999.682 - 3076.70i) q^{34} +(-200.239 - 145.482i) q^{35} +3389.39 q^{36} -2513.66 q^{37} +(2210.54 + 1606.05i) q^{38} +(-2550.26 + 1852.88i) q^{39} +(2519.95 - 1830.85i) q^{40} +(-1229.36 + 3783.59i) q^{41} +(-350.979 - 255.001i) q^{42} +(186.896 - 575.205i) q^{43} +(-746.319 - 2296.93i) q^{44} +(8340.93 - 6060.04i) q^{45} +(4941.11 + 15207.2i) q^{46} +(-7186.68 - 22118.3i) q^{47} +(4416.98 - 3209.12i) q^{48} +(-5185.66 - 15959.8i) q^{49} +(-934.839 + 2877.14i) q^{50} +(-13954.2 - 10138.3i) q^{51} +(-730.806 + 2249.19i) q^{52} +(17050.4 - 12387.9i) q^{53} +(-2150.73 + 1562.59i) q^{54} +(-5943.40 - 4318.13i) q^{55} -325.474 q^{56} +14568.3 q^{57} +(3784.58 + 2749.66i) q^{58} +(1493.09 + 4595.25i) q^{59} +(5131.98 - 15794.6i) q^{60} -12951.2 q^{61} +(-15154.3 + 15113.4i) q^{62} -1077.30 q^{63} +(1265.73 - 3895.53i) q^{64} +(2222.99 + 6841.65i) q^{65} +(-10417.6 - 7568.83i) q^{66} -17689.7 q^{67} -12940.1 q^{68} +(68971.2 + 50110.5i) q^{69} +(-800.955 + 581.928i) q^{70} +(13755.8 - 9994.19i) q^{71} +(4189.52 - 12894.0i) q^{72} +(26028.1 + 18910.5i) q^{73} +(-3107.05 + 9562.51i) q^{74} +(4984.30 + 15340.1i) q^{75} +(8842.17 - 6424.21i) q^{76} +(237.214 + 730.070i) q^{77} +(3896.46 + 11992.1i) q^{78} +(-80957.9 + 58819.4i) q^{79} +(-3850.15 - 11849.5i) q^{80} +(-20287.1 + 62437.3i) q^{81} +(12874.1 + 9353.55i) q^{82} +(906.977 - 2791.39i) q^{83} +(-1403.92 + 1020.00i) q^{84} +(-31844.3 + 23136.3i) q^{85} +(-1957.20 - 1421.99i) q^{86} +24941.8 q^{87} -9660.56 q^{88} +(10569.4 + 7679.11i) q^{89} +(-12743.8 - 39221.4i) q^{90} +(232.283 - 714.894i) q^{91} +63959.1 q^{92} +(-18003.5 + 112683. i) q^{93} -93026.4 q^{94} +(10273.5 - 31618.6i) q^{95} +(-6748.55 - 20769.9i) q^{96} +(-40487.9 - 29416.2i) q^{97} -67124.5 q^{98} -31976.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - 20 q^{3} - 96 q^{4} + 120 q^{5} + 280 q^{6} - 180 q^{7} - 384 q^{8} - 200 q^{9} - 100 q^{10} + 354 q^{11} - 320 q^{12} + 39 q^{13} - 720 q^{14} + 535 q^{15} - 1536 q^{16} - 1027 q^{17}+ \cdots + 339042 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 20 * q^3 - 96 * q^4 + 120 * q^5 + 280 * q^6 - 180 * q^7 - 384 * q^8 - 200 * q^9 - 100 * q^10 + 354 * q^11 - 320 * q^12 + 39 * q^13 - 720 * q^14 + 535 * q^15 - 1536 * q^16 - 1027 * q^17 - 1420 * q^18 + 334 * q^19 - 560 * q^20 - 1867 * q^21 + 1416 * q^22 - 1051 * q^23 - 960 * q^24 + 4812 * q^25 + 12536 * q^26 - 5135 * q^27 + 4000 * q^28 - 1143 * q^29 + 9080 * q^30 - 8583 * q^31 + 24576 * q^32 - 24628 * q^33 - 8108 * q^34 - 7496 * q^35 + 17760 * q^36 - 25204 * q^37 - 2844 * q^38 - 20114 * q^39 - 2240 * q^40 + 19615 * q^41 + 3212 * q^42 + 22358 * q^43 - 20496 * q^44 + 6725 * q^45 - 5264 * q^46 + 4766 * q^47 - 3840 * q^48 - 12058 * q^49 + 4628 * q^50 + 6844 * q^51 + 624 * q^52 - 7393 * q^53 - 20540 * q^54 + 11861 * q^55 - 8960 * q^56 + 176704 * q^57 + 4268 * q^58 - 21070 * q^59 + 8560 * q^60 + 76556 * q^61 - 49652 * q^62 + 105854 * q^63 - 24576 * q^64 - 107146 * q^65 + 57968 * q^66 - 150906 * q^67 + 97728 * q^68 - 212560 * q^69 - 29984 * q^70 + 27475 * q^71 - 22720 * q^72 + 49671 * q^73 + 90124 * q^74 - 156002 * q^75 - 11376 * q^76 + 253908 * q^77 - 9036 * q^78 - 7162 * q^79 - 6400 * q^80 + 38329 * q^81 - 92940 * q^82 - 246088 * q^83 + 12848 * q^84 - 104879 * q^85 - 149088 * q^86 - 247668 * q^87 + 118656 * q^88 + 159253 * q^89 - 167880 * q^90 - 68566 * q^91 + 75744 * q^92 + 260391 * q^93 + 18784 * q^94 + 222814 * q^95 - 20480 * q^96 + 190 * q^97 - 144032 * q^98 + 339042 * q^99

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