LMFDB - Embedded newform 25.8.e.a.14.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [25,8,Mod(4,25)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("25.4"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(25, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	25.e (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:	$7.80962563710$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			14.9
Character	$\chi$	$=$	25.14
Dual form			25.8.e.a.9.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0493180 - 0.0678803i) q^{2} +(-2.30301 - 0.748293i) q^{3} +(39.5520 - 121.729i) q^{4} +(53.9059 + 274.261i) q^{5} +(0.0627853 + 0.193233i) q^{6} -911.534i q^{7} +(-20.4278 + 6.63738i) q^{8} +(-1764.58 - 1282.04i) q^{9} +(15.9584 - 17.1851i) q^{10} +(5196.92 - 3775.78i) q^{11} +(-182.177 + 250.745i) q^{12} +(5695.22 - 7838.79i) q^{13} +(-61.8752 + 44.9550i) q^{14} +(81.0819 - 671.963i) q^{15} +(-13252.7 - 9628.68i) q^{16} +(-9279.87 + 3015.21i) q^{17} +183.008i q^{18} +(-7343.10 - 22599.7i) q^{19} +(35517.5 + 4285.69i) q^{20} +(-682.094 + 2099.27i) q^{21} +(-512.603 - 166.555i) q^{22} +(54334.4 + 74784.9i) q^{23} +52.0120 q^{24} +(-72313.3 + 29568.6i) q^{25} -812.976 q^{26} +(6217.33 + 8557.43i) q^{27} +(-110960. - 36053.0i) q^{28} +(-32441.1 + 99843.4i) q^{29} +(-49.6119 + 27.6360i) q^{30} +(53556.2 + 164829. i) q^{31} +4123.78i q^{32} +(-14793.9 + 4806.84i) q^{33} +(662.338 + 481.217i) q^{34} +(249998. - 49137.0i) q^{35} +(-225853. + 164092. i) q^{36} +(294224. - 404965. i) q^{37} +(-1171.93 + 1613.02i) q^{38} +(-18981.8 + 13791.1i) q^{39} +(-2921.55 - 5244.75i) q^{40} +(-264060. - 191851. i) q^{41} +(176.139 - 57.2310i) q^{42} +448849. i q^{43} +(-254072. - 781953. i) q^{44} +(256493. - 553064. i) q^{45} +(2396.76 - 7376.48i) q^{46} +(59595.2 + 19363.6i) q^{47} +(23316.1 + 32091.9i) q^{48} -7351.23 q^{49} +(5573.47 + 3450.39i) q^{50} +23627.9 q^{51} +(-728948. - 1.00331e6i) q^{52} +(1.46477e6 + 475933. i) q^{53} +(274.255 - 844.070i) q^{54} +(1.31569e6 + 1.22178e6i) q^{55} +(6050.20 + 18620.6i) q^{56} +57542.2i q^{57} +(8377.33 - 2721.96i) q^{58} +(-2.10962e6 - 1.53273e6i) q^{59} +(-78590.1 - 36447.5i) q^{60} +(-2.04361e6 + 1.48477e6i) q^{61} +(8547.37 - 11764.4i) q^{62} +(-1.16862e6 + 1.60847e6i) q^{63} +(-1.69607e6 + 1.23227e6i) q^{64} +(2.45688e6 + 1.13942e6i) q^{65} +(1055.90 + 767.154i) q^{66} +(3.55507e6 - 1.15511e6i) q^{67} +1.24888e6i q^{68} +(-69171.6 - 212888. i) q^{69} +(-15664.8 - 14546.6i) q^{70} +(-387129. + 1.19146e6i) q^{71} +(44555.7 + 14477.0i) q^{72} +(1.72118e6 + 2.36901e6i) q^{73} -41999.7 q^{74} +(188664. - 13985.1i) q^{75} -3.04147e6 q^{76} +(-3.44175e6 - 4.73717e6i) q^{77} +(1872.29 + 608.345i) q^{78} +(855702. - 2.63358e6i) q^{79} +(1.92637e6 - 4.15376e6i) q^{80} +(1.46614e6 + 4.51232e6i) q^{81} +27386.1i q^{82} +(-799187. + 259672. i) q^{83} +(228563. + 166061. i) q^{84} +(-1.32720e6 - 2.38257e6i) q^{85} +(30468.1 - 22136.3i) q^{86} +(149424. - 205665. i) q^{87} +(-81100.1 + 111625. i) q^{88} +(3.38024e6 - 2.45588e6i) q^{89} +(-50191.9 + 9865.19i) q^{90} +(-7.14533e6 - 5.19138e6i) q^{91} +(1.12525e7 - 3.65616e6i) q^{92} -419678. i q^{93} +(-1624.70 - 5000.32i) q^{94} +(5.80239e6 - 3.23218e6i) q^{95} +(3085.80 - 9497.11i) q^{96} +(-4.86872e6 - 1.58194e6i) q^{97} +(362.547 + 499.004i) q^{98} -1.40111e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 5 q^{2} - 5 q^{3} + 893 q^{4} - 510 q^{5} + 173 q^{6} - 2510 q^{8} + 6587 q^{9} - 5805 q^{10} - 472 q^{11} + 16635 q^{12} - 5 q^{13} - 19409 q^{14} + 375 q^{15} - 42071 q^{16} + 31910 q^{17} - 48685 q^{19}+ \cdots + 57867624 q^{99}+O(q^{100}) $ 64 * q - 5 * q^2 - 5 * q^3 + 893 * q^4 - 510 * q^5 + 173 * q^6 - 2510 * q^8 + 6587 * q^9 - 5805 * q^10 - 472 * q^11 + 16635 * q^12 - 5 * q^13 - 19409 * q^14 + 375 * q^15 - 42071 * q^16 + 31910 * q^17 - 48685 * q^19 - 171405 * q^20 + 2268 * q^21 + 197230 * q^22 + 356525 * q^23 + 544720 * q^24 + 170220 * q^25 - 708942 * q^26 - 319805 * q^27 - 565125 * q^28 - 332885 * q^29 + 66235 * q^30 - 39057 * q^31 - 161110 * q^33 + 1156301 * q^34 + 337515 * q^35 + 1920669 * q^36 - 1480960 * q^37 - 2136945 * q^38 + 1307509 * q^39 - 282470 * q^40 + 1955408 * q^41 - 684355 * q^42 - 3558164 * q^44 - 1351725 * q^45 - 2982527 * q^46 + 1018980 * q^47 + 8967210 * q^48 - 3298162 * q^49 + 8550165 * q^50 - 3922092 * q^51 + 8058740 * q^52 + 316580 * q^53 - 6933535 * q^54 - 2889990 * q^55 + 480880 * q^56 - 12912030 * q^58 - 3625740 * q^59 - 10459240 * q^60 + 656223 * q^61 + 15439920 * q^62 + 16010850 * q^63 + 572908 * q^64 - 9903445 * q^65 + 8105266 * q^66 - 25482280 * q^67 - 9378031 * q^69 + 16449030 * q^70 + 2533578 * q^71 + 8757215 * q^72 + 8477055 * q^73 + 20547876 * q^74 + 28650170 * q^75 - 22436480 * q^76 + 20387770 * q^77 - 23613305 * q^78 - 5343505 * q^79 - 44517070 * q^80 + 7686054 * q^81 - 20224125 * q^83 + 10924626 * q^84 + 2795615 * q^85 + 27540603 * q^86 - 3545560 * q^87 + 36319550 * q^88 - 17844415 * q^89 - 67695745 * q^90 + 9123478 * q^91 - 88054710 * q^92 - 15200999 * q^94 + 42119295 * q^95 - 8739232 * q^96 + 41971560 * q^97 + 60378980 * q^98 + 57867624 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.0493180	−	0.0678803i	−0.00435913	−	0.00599983i	0.806832	−	0.590781i	$-0.201180\pi$
$2$	−0.0493180	−	0.0678803i	−0.00435913	−	0.00599983i	−0.811191	+	0.584781i	$0.801180\pi$
$3$	−2.30301	−	0.748293i	−0.0492460	−	0.0160010i	0.284290	−	0.958738i	$-0.408242\pi$
$3$	−2.30301	−	0.748293i	−0.0492460	−	0.0160010i	−0.333536	+	0.942737i	$0.608242\pi$
$4$	39.5520	−	121.729i	0.309000	−	0.951004i
$5$	53.9059	+	274.261i	0.192860	+	0.981226i
$5$	53.9059	+	274.261i	0.192860	+	0.981226i
$6$	0.0627853	+	0.193233i	0.000118667	+	0.000365218i
$7$		−	911.534i		−	1.00445i	−0.864736	−	0.502227i	$-0.832514\pi$
$7$		−	911.534i		−	1.00445i	0.864736	−	0.502227i	$-0.167486\pi$
$8$	−20.4278	+	6.63738i	−0.0141061	+	0.00458334i
$9$	−1764.58	−	1282.04i	−0.806848	−	0.586209i
$10$	15.9584	−	17.1851i	0.00504649	−	0.00543442i
$11$	5196.92	−	3775.78i	1.17726	−	0.855328i	0.185398	−	0.982664i	$-0.440643\pi$
$11$	5196.92	−	3775.78i	1.17726	−	0.855328i	0.991860	+	0.127336i	$0.0406425\pi$
$12$	−182.177	+	250.745i	−0.0304340	+	0.0418889i
$13$	5695.22	−	7838.79i	0.718966	−	0.989572i	−0.280591	−	0.959827i	$-0.590531\pi$
$13$	5695.22	−	7838.79i	0.718966	−	0.989572i	0.999558	−	0.0297448i	$-0.00946946\pi$
$14$	−61.8752	+	44.9550i	−0.00602655	+	0.00437855i
$15$	81.0819	−	671.963i	0.00620304	−	0.0514075i
$16$	−13252.7	−	9628.68i	−0.808884	−	0.587688i
$17$	−9279.87	+	3015.21i	−0.458111	+	0.148849i	−0.528976	−	0.848637i	$-0.677424\pi$
$17$	−9279.87	+	3015.21i	−0.458111	+	0.148849i	0.0708652	+	0.997486i	$0.477424\pi$
$18$			183.008i			0.00739632i
$19$	−7343.10	−	22599.7i	−0.245608	−	0.755902i	−0.995536	−	0.0943833i	$-0.969912\pi$
$19$	−7343.10	−	22599.7i	−0.245608	−	0.755902i	0.749928	−	0.661519i	$-0.230088\pi$
$20$	35517.5	+	4285.69i	0.992744	+	0.119789i
$21$	−682.094	+	2099.27i	−0.0160723	+	0.0494653i
$22$	−512.603	−	166.555i	−0.0102636	−	0.00333486i
$23$	54334.4	+	74784.9i	0.931167	+	1.28164i	0.959403	+	0.282040i	$0.0910110\pi$
$23$	54334.4	+	74784.9i	0.931167	+	1.28164i	−0.0282360	+	0.999601i	$0.508989\pi$
$24$	52.0120			0.000768006
$25$	−72313.3	+	29568.6i	−0.925610	+	0.378478i
$26$	−812.976			−0.00907134
$27$	6217.33	+	8557.43i	0.0607898	+	0.0836700i
$28$	−110960.	−	36053.0i	−0.955239	−	0.310376i
$29$	−32441.1	+	99843.4i	−0.247003	+	0.760197i	0.748298	+	0.663363i	$0.230872\pi$
$29$	−32441.1	+	99843.4i	−0.247003	+	0.760197i	−0.995301	+	0.0968339i	$0.969128\pi$
$30$	−49.6119	+	27.6360i	−0.000335476	+	0.000186875i
$31$	53556.2	+	164829.i	0.322882	+	0.993728i	0.972388	+	0.233371i	$0.0749758\pi$
$31$	53556.2	+	164829.i	0.322882	+	0.993728i	−0.649506	+	0.760357i	$0.725024\pi$
$32$			4123.78i			0.0222470i
$33$	−14793.9	+	4806.84i	−0.0716614	+	0.0232842i
$34$	662.338	+	481.217i	0.00289004	+	0.00209974i
$35$	249998.	−	49137.0i	0.985596	−	0.193718i
$36$	−225853.	+	164092.i	−0.806803	+	0.586177i
$37$	294224.	−	404965.i	0.954931	−	1.31435i	0.00562904	−	0.999984i	$-0.498208\pi$
$37$	294224.	−	404965.i	0.954931	−	1.31435i	0.949302	−	0.314366i	$-0.101792\pi$
$38$	−1171.93	+	1613.02i	−0.00346465	+	0.00476868i
$39$	−18981.8	+	13791.1i	−0.0512404	+	0.0372283i
$40$	−2921.55	−	5244.75i	−0.00721778	−	0.0129573i
$41$	−264060.	−	191851.i	−0.598354	−	0.434730i	0.246940	−	0.969031i	$-0.420575\pi$
$41$	−264060.	−	191851.i	−0.598354	−	0.434730i	−0.845294	+	0.534301i	$0.820575\pi$
$42$	176.139	−	57.2310i	0.000366845	−	0.000119195i
$43$			448849.i			0.860917i	0.902610	+	0.430458i	$0.141648\pi$
$43$			448849.i			0.860917i	−0.902610	+	0.430458i	$0.858352\pi$
$44$	−254072.	−	781953.i	−0.449648	−	1.38387i
$45$	256493.	−	553064.i	0.419596	−	0.904756i
$46$	2396.76	−	7376.48i	0.00363055	−	0.0111737i
$47$	59595.2	+	19363.6i	0.0837276	+	0.0272047i	0.350581	−	0.936532i	$-0.385984\pi$
$47$	59595.2	+	19363.6i	0.0837276	+	0.0272047i	−0.266854	+	0.963737i	$0.585984\pi$
$48$	23316.1	+	32091.9i	0.0304307	+	0.0418843i
$49$	−7351.23			−0.00892634
$50$	5573.47	+	3450.39i	0.00630566	+	0.00390367i
$51$	23627.9			0.0249419
$52$	−728948.	−	1.00331e6i	−0.718927	−	0.989518i
$53$	1.46477e6	+	475933.i	1.35146	+	0.439117i	0.893184	−	0.449692i	$-0.148466\pi$
$53$	1.46477e6	+	475933.i	1.35146	+	0.439117i	0.458279	+	0.888809i	$0.348466\pi$
$54$	274.255	−	844.070i	0.000237015	−	0.000729458i
$55$	1.31569e6	+	1.22178e6i	1.06632	+	0.990198i
$56$	6050.20	+	18620.6i	0.00460375	+	0.0141689i
$57$			57542.2i			0.0411552i
$58$	8377.33	−	2721.96i	0.00563777	−	0.00183182i
$59$	−2.10962e6	−	1.53273e6i	−1.33728	−	0.971590i	−0.999539	−	0.0303511i	$-0.990337\pi$
$59$	−2.10962e6	−	1.53273e6i	−1.33728	−	0.971590i	−0.337740	−	0.941239i	$-0.609663\pi$
$60$	−78590.1	−	36447.5i	−0.0469720	−	0.0217840i
$61$	−2.04361e6	+	1.48477e6i	−1.15277	+	0.837538i	−0.988847	−	0.148935i	$-0.952416\pi$
$61$	−2.04361e6	+	1.48477e6i	−1.15277	+	0.837538i	−0.163925	+	0.986473i	$0.552416\pi$
$62$	8547.37	−	11764.4i	0.00455472	−	0.00626903i
$63$	−1.16862e6	+	1.60847e6i	−0.588820	+	0.810441i
$64$	−1.69607e6	+	1.23227e6i	−0.808750	+	0.587591i
$65$	2.45688e6	+	1.13942e6i	1.10965	+	0.514620i
$66$	1055.90	+	767.154i	0.000452083	+	0.000328457i
$67$	3.55507e6	−	1.15511e6i	1.44406	−	0.469205i	0.520902	−	0.853617i	$-0.325596\pi$
$67$	3.55507e6	−	1.15511e6i	1.44406	−	0.469205i	0.923162	+	0.384412i	$0.125596\pi$
$68$			1.24888e6i			0.481660i
$69$	−69171.6	−	212888.i	−0.0253487	−	0.0780153i
$70$	−15664.8	−	14546.6i	−0.00545862	−	0.00506897i
$71$	−387129.	+	1.19146e6i	−0.128366	+	0.395071i	−0.994499	−	0.104742i	$-0.966598\pi$
$71$	−387129.	+	1.19146e6i	−0.128366	+	0.395071i	0.866133	+	0.499814i	$0.166598\pi$
$72$	44555.7	+	14477.0i	0.0140682	+	0.00457105i
$73$	1.72118e6	+	2.36901e6i	0.517842	+	0.712749i	0.985217	−	0.171311i	$-0.0548002\pi$
$73$	1.72118e6	+	2.36901e6i	0.517842	+	0.712749i	−0.467375	+	0.884059i	$0.654800\pi$
$74$	−41999.7			−0.0120485
$75$	188664.	−	13985.1i	0.0516387	−	0.00382783i
$76$	−3.04147e6			−0.794759
$77$	−3.44175e6	−	4.73717e6i	−0.859137	−	1.18250i
$78$	1872.29	+	608.345i	0.000446727	+	0.000145150i
$79$	855702.	−	2.63358e6i	0.195266	−	0.600968i	−0.804707	−	0.593672i	$-0.797678\pi$
$79$	855702.	−	2.63358e6i	0.195266	−	0.600968i	0.999973	−	0.00729615i	$-0.00232246\pi$
$80$	1.92637e6	−	4.15376e6i	0.420654	−	0.907039i
$81$	1.46614e6	+	4.51232e6i	0.306534	+	0.943413i
$82$			27386.1i			0.00548507i
$83$	−799187.	+	259672.i	−0.153418	+	0.0498484i	−0.384719	−	0.923034i	$-0.625702\pi$
$83$	−799187.	+	259672.i	−0.153418	+	0.0498484i	0.231301	+	0.972882i	$0.425702\pi$
$84$	228563.	+	166061.i	0.0420754	+	0.0305696i
$85$	−1.32720e6	−	2.38257e6i	−0.234406	−	0.420804i
$86$	30468.1	−	22136.3i	0.00516535	−	0.00375285i
$87$	149424.	−	205665.i	0.0243278	−	0.0334844i
$88$	−81100.1	+	111625.i	−0.0126862	+	0.0174611i
$89$	3.38024e6	−	2.45588e6i	0.508255	−	0.369269i	−0.303906	−	0.952702i	$-0.598291\pi$
$89$	3.38024e6	−	2.45588e6i	0.508255	−	0.369269i	0.812161	+	0.583433i	$0.198291\pi$
$90$	−50191.9	+	9865.19i	−0.00725746	+	0.00142645i
$91$	−7.14533e6	−	5.19138e6i	−0.993979	−	0.722168i
$92$	1.12525e7	−	3.65616e6i	1.50658	−	0.489516i
$93$		−	419678.i		−	0.0541036i
$94$	−1624.70	−	5000.32i	−0.000201756	−	0.000620940i
$95$	5.80239e6	−	3.23218e6i	0.694343	−	0.386780i
$96$	3085.80	−	9497.11i	0.000355974	−	0.00109557i
$97$	−4.86872e6	−	1.58194e6i	−0.541644	−	0.175991i	0.0254017	−	0.999677i	$-0.491914\pi$
$97$	−4.86872e6	−	1.58194e6i	−0.541644	−	0.175991i	−0.567045	+	0.823687i	$0.691914\pi$
$98$	362.547	+	499.004i	3.89111e−5	+	5.35565e-5i
$99$	−1.40111e7			−1.45127
$100$	739203.	+	9.97209e6i	0.0739203	+	0.997209i
$101$	8.89256e6			0.858820			0.429410	−	0.903110i	$-0.358722\pi$
$101$	8.89256e6			0.858820			0.429410	+	0.903110i	$0.358722\pi$
$102$	−1165.28	−	1603.87i	−0.000108725	−	0.000149647i
$103$	−1.65280e6	−	537027.i	−0.149036	−	0.0484246i	0.233549	−	0.972345i	$-0.424966\pi$
$103$	−1.65280e6	−	537027.i	−0.149036	−	0.0484246i	−0.382585	+	0.923920i	$0.624966\pi$
$104$	−64311.5	+	197930.i	−0.00560624	+	0.0172542i
$105$	−612517.	−	73908.9i	−0.0516364	−	0.00623067i
$106$	−39933.0	−	122901.i	−0.00325658	−	0.0100227i
$107$			5.62574e6i			0.443953i	0.975052	+	0.221976i	$0.0712508\pi$
$107$			5.62574e6i			0.443953i	−0.975052	+	0.221976i	$0.928749\pi$
$108$	1.28759e6	−	418364.i	0.0983546	−	0.0319574i
$109$	5.96307e6	+	4.33242e6i	0.441039	+	0.320433i	0.786048	−	0.618166i	$-0.212124\pi$
$109$	5.96307e6	+	4.33242e6i	0.441039	+	0.320433i	−0.345009	+	0.938599i	$0.612124\pi$
$110$	18047.2	−	149565.i	0.00129281	−	0.0107141i
$111$	−980633.	+	712471.i	−0.0680575	+	0.0494467i
$112$	−8.77687e6	+	1.20803e7i	−0.590305	+	0.812486i
$113$	6.08188e6	−	8.37099e6i	0.396518	−	0.545761i	−0.563348	−	0.826220i	$-0.690487\pi$
$113$	6.08188e6	−	8.37099e6i	0.396518	−	0.545761i	0.959866	+	0.280459i	$0.0904868\pi$
$114$	3905.98	−	2837.86i	0.000246924	−	0.000179401i
$115$	−1.75816e7	+	1.89332e7i	−1.07800	+	1.16086i
$116$	1.08707e7	+	7.89801e6i	0.646627	+	0.469802i
$117$	−2.00993e7	+	6.53065e6i	−1.16019	+	0.376969i
$118$			218793.i			0.0122587i
$119$	2.74847e6	+	8.45892e6i	0.149512	+	0.460151i
$120$	2803.75	+	14264.9i	0.000148117	+	0.000753587i
$121$	6.72957e6	−	2.07115e7i	0.345333	−	1.06283i
$122$	201573.	+	65495.1i	0.0100502	+	0.00326550i
$123$	464571.	+	639427.i	0.0225105	+	0.0309830i
$124$	2.21826e7			1.04481
$125$	−1.20076e7	−	1.82388e7i	−0.549885	−	0.835240i
$126$	166818.			0.00742925
$127$	1.56493e7	+	2.15394e7i	0.677926	+	0.933085i	0.999907	−	0.0136611i	$-0.00434861\pi$
$127$	1.56493e7	+	2.15394e7i	0.677926	+	0.933085i	−0.321981	+	0.946746i	$0.604349\pi$
$128$	669303.	+	217470.i	0.0282090	+	0.00916567i
$129$	335871.	−	1.03370e6i	0.0137755	−	0.0423967i
$130$	−43824.2	−	222968.i	−0.00174949	−	0.00890103i
$131$	−2.81368e6	−	8.65961e6i	−0.109351	−	0.336549i	0.881376	−	0.472416i	$-0.156618\pi$
$131$	−2.81368e6	−	8.65961e6i	−0.109351	−	0.336549i	−0.990727	+	0.135867i	$0.956618\pi$
$132$			1.99097e6i			0.0753451i
$133$	−2.06004e7	+	6.69348e6i	−0.759268	+	0.246701i
$134$	−253738.	−	184352.i	−0.00911001	−	0.00661881i
$135$	−2.01182e6	+	2.16647e6i	−0.0703753	+	0.0757852i
$136$	169554.	−	123188.i	0.00577992	−	0.00419936i
$137$	9.10219e6	−	1.25281e7i	0.302429	−	0.416258i	−0.630572	−	0.776131i	$-0.717180\pi$
$137$	9.10219e6	−	1.25281e7i	0.302429	−	0.416258i	0.933002	+	0.359872i	$0.117180\pi$
$138$	−11039.5	+	15194.6i	−0.000357580	+	0.000492167i
$139$	−3.20928e6	+	2.33168e6i	−0.101357	+	0.0736405i	−0.637310	−	0.770608i	$-0.719953\pi$
$139$	−3.20928e6	+	2.33168e6i	−0.101357	+	0.0736405i	0.535952	+	0.844248i	$0.319953\pi$
$140$	3.90655e6	−	3.23754e7i	0.120322	−	0.997165i
$141$	−122759.	−	89189.3i	−0.00368795	−	0.00267945i
$142$	99969.2	−	32482.0i	0.00292993	−	0.000951992i
$143$		−	6.22415e7i		−	1.77993i
$144$	1.10411e7	+	3.39811e7i	0.308138	+	0.948350i
$145$	−2.91319e7	−	3.51518e6i	−0.793562	−	0.0957546i
$146$	75923.7	−	233669.i	0.00201903	−	0.00621393i
$147$	16929.9	+	5500.87i	0.000439587	+	0.000142830i
$148$	−3.76586e7	−	5.18326e7i	−0.954879	−	1.31428i
$149$	6.05168e7			1.49873			0.749366	−	0.662156i	$-0.230358\pi$
$149$	6.05168e7			1.49873			0.749366	+	0.662156i	$0.230358\pi$
$150$	−10253.8	−	12116.9i	−0.000248066	−	0.000293137i
$151$	3.83877e7			0.907346			0.453673	−	0.891168i	$-0.350113\pi$
$151$	3.83877e7			0.907346			0.453673	+	0.891168i	$0.350113\pi$
$152$	300006.	+	412923.i	0.00692911	+	0.00953710i
$153$	2.02407e7	+	6.57659e6i	0.456883	+	0.148450i
$154$	−151820.	+	467255.i	−0.00334971	+	0.0103094i
$155$	−4.23192e7	+	2.35736e7i	−0.912801	+	0.508470i
$156$	928003.	+	2.85610e6i	0.0195710	+	0.0602334i
$157$			1.61559e7i			0.333182i	0.986026	+	0.166591i	$0.0532759\pi$
$157$			1.61559e7i			0.333182i	−0.986026	+	0.166591i	$0.946724\pi$
$158$	−220970.	+	71797.4i	−0.00445690	+	0.00144814i
$159$	−3.01724e6	−	2.19215e6i	−0.0595278	−	0.0432495i
$160$	−1.13099e6	+	222296.i	−0.0218293	+	0.00429054i
$161$	6.81690e7	−	4.95277e7i	1.28735	−	0.935313i
$162$	233991.	−	322060.i	0.00432410	−	0.00595161i
$163$	−1.80815e7	+	2.48871e7i	−0.327023	+	0.450109i	−0.940595	−	0.339530i	$-0.889732\pi$
$163$	−1.80815e7	+	2.48871e7i	−0.327023	+	0.450109i	0.613572	+	0.789639i	$0.289732\pi$
$164$	−3.37978e7	+	2.45555e7i	−0.598321	+	0.434706i
$165$	−2.11581e6	−	3.79829e6i	−0.0366676	−	0.0658255i
$166$	57040.9	+	41442.6i	0.000967849	+	0.000703184i
$167$	−8.14071e7	+	2.64508e7i	−1.35255	+	0.439471i	−0.893550	−	0.448963i	$-0.851793\pi$
$167$	−8.14071e7	+	2.64508e7i	−1.35255	+	0.439471i	−0.459003	+	0.888435i	$0.651793\pi$
$168$		−	47410.7i		−	0.000771426i
$169$	−9.62083e6	−	2.96099e7i	−0.153324	−	0.471881i
$170$	−96275.1	+	207594.i	−0.00150294	+	0.00324074i
$171$	−1.60163e7	+	4.92931e7i	−0.244949	+	0.753876i
$172$	5.46378e7	+	1.77529e7i	0.818735	+	0.266023i
$173$	5.60525e7	+	7.71496e7i	0.823064	+	1.13285i	0.989175	+	0.146743i	$0.0468791\pi$
$173$	5.60525e7	+	7.71496e7i	0.823064	+	1.13285i	−0.166111	+	0.986107i	$0.553121\pi$
$174$	−21329.9			−0.000306949
$175$	2.69528e7	+	6.59160e7i	0.380163	+	0.929732i
$176$	−1.05229e8			−1.45493
$177$	3.71154e6	+	5.10850e6i	0.0503093	+	0.0692448i
$178$	−333413.	−	108332.i	−0.00443110	−	0.00143975i
$179$	−86713.2	+	266876.i	−0.00113005	+	0.00347795i	−0.951620	−	0.307278i	$-0.900582\pi$
$179$	−86713.2	+	266876.i	−0.00113005	+	0.00347795i	0.950490	+	0.310755i	$0.100582\pi$
$180$	−5.71789e7	−	5.30973e7i	−0.730772	−	0.678607i
$181$	−1.67100e7	−	5.14282e7i	−0.209461	−	0.644653i	−0.999501	−	0.0315982i	$-0.989940\pi$
$181$	−1.67100e7	−	5.14282e7i	−0.209461	−	0.644653i	0.790040	−	0.613055i	$-0.210060\pi$
$182$			741056.i			0.00911173i
$183$	5.81749e6	−	1.89022e6i	0.0701709	−	0.0227999i
$184$	−1.60631e6	−	1.16705e6i	−0.0190093	−	0.0138111i
$185$	1.26926e8	+	5.88642e7i	1.47384	+	0.683519i
$186$	−28487.9	+	20697.7i	−0.000324612	+	0.000235845i
$187$	−3.68420e7	+	5.07086e7i	−0.412000	+	0.567069i
$188$	4.71422e6	−	6.48856e6i	0.0517436	−	0.0712190i
$189$	7.80038e6	−	5.66731e6i	0.0840426	−	0.0610606i
$190$	−505564.	−	234464.i	−0.00534735	−	0.00247992i
$191$	6.04846e7	+	4.39446e7i	0.628098	+	0.456340i	0.855741	−	0.517405i	$-0.173102\pi$
$191$	6.04846e7	+	4.39446e7i	0.628098	+	0.456340i	−0.227642	+	0.973745i	$0.573102\pi$
$192$	4.82817e6	−	1.56877e6i	0.0492298	−	0.0159957i
$193$		−	5.24038e7i		−	0.524701i	−0.964973	−	0.262351i	$-0.915502\pi$
$193$		−	5.24038e7i		−	0.524701i	0.964973	−	0.262351i	$-0.0844977\pi$
$194$	132732.	+	408508.i	0.00130518	+	0.00401694i
$195$	−4.80560e6	−	4.46256e6i	−0.0464116	−	0.0430986i
$196$	−290756.	+	894854.i	−0.00275824	+	0.00848899i
$197$	−2.34210e7	−	7.60994e6i	−0.218260	−	0.0709168i	0.197846	−	0.980233i	$-0.436605\pi$
$197$	−2.34210e7	−	7.60994e6i	−0.218260	−	0.0709168i	−0.416106	+	0.909316i	$0.636605\pi$
$198$	690997.	+	951076.i	0.00632627	+	0.00870737i
$199$	−5.11149e7			−0.459792			−0.229896	−	0.973215i	$-0.573839\pi$
$199$	−5.11149e7			−0.459792			−0.229896	+	0.973215i	$0.573839\pi$
$200$	1.28094e6	−	1.08399e6i	0.0113220	−	0.00958122i
$201$	−9.05172e6			−0.0786221
$202$	−438563.	−	603630.i	−0.00374371	−	0.00515277i
$203$	9.10106e7	+	2.95711e7i	0.763582	+	0.248103i
$204$	934530.	−	2.87619e6i	0.00770704	−	0.0237198i
$205$	3.83828e7	−	8.27631e7i	0.311170	−	0.670963i
$206$	45059.1	+	138678.i	0.000359126	+	0.00110528i
$207$		−	2.01622e8i		−	1.57995i
$208$	−1.50955e8	+	4.90481e7i	−1.16312	+	0.377921i
$209$	−1.23493e8	−	8.97230e7i	−0.935688	−	0.679817i
$210$	25191.1	+	45222.9i	0.000187707	+	0.000336970i
$211$	−6.74368e7	+	4.89957e7i	−0.494206	+	0.359062i	−0.806800	−	0.590825i	$-0.798802\pi$
$211$	−6.74368e7	+	4.89957e7i	−0.494206	+	0.359062i	0.312593	+	0.949887i	$0.398802\pi$
$212$	1.15869e8	−	1.59480e8i	0.835204	−	1.14956i
$213$	1.78312e6	−	2.45426e6i	0.0126431	−	0.0174017i
$214$	381877.	−	277450.i	0.00266364	−	0.00193525i
$215$	−1.23102e8	+	2.41956e7i	−0.844754	+	0.166036i
$216$	−183805.	−	133542.i	−0.00124099	−	0.000901634i
$217$	1.50247e8	−	4.88183e7i	0.998153	−	0.324320i
$218$		−	618441.i		−	0.00404297i
$219$	−2.19119e6	−	6.74379e6i	−0.0140970	−	0.0433860i
$220$	2.00763e8	−	1.11834e8i	1.27117	−	0.708099i
$221$	−2.92152e7	+	8.99153e7i	−0.182069	+	0.560352i
$222$	96725.6	+	31428.1i	0.000593343	+	0.000192789i
$223$	1.31044e8	+	1.80366e8i	0.791314	+	1.08915i	0.993943	+	0.109894i	$0.0350512\pi$
$223$	1.31044e8	+	1.80366e8i	0.791314	+	1.08915i	−0.202630	+	0.979255i	$0.564949\pi$
$224$	3.75897e6			0.0223460
$225$	1.65510e8	+	4.05325e7i	0.968694	+	0.237227i
$226$	−868172.			−0.00500295
$227$	−2.77059e7	−	3.81339e7i	−0.157211	−	0.216382i	0.723145	−	0.690696i	$-0.242696\pi$
$227$	−2.77059e7	−	3.81339e7i	−0.157211	−	0.216382i	−0.880355	+	0.474315i	$0.842696\pi$
$228$	7.00452e6	+	2.27591e6i	0.0391387	+	0.0127169i
$229$	9.57994e7	−	2.94840e8i	0.527155	−	1.62242i	−0.232859	−	0.972511i	$-0.574808\pi$
$229$	9.57994e7	−	2.94840e8i	0.527155	−	1.62242i	0.760014	−	0.649907i	$-0.225192\pi$
$230$	2.15228e6	+	259703.i	0.0116641	+	0.00140744i
$231$	4.38160e6	+	1.34852e7i	0.0233879	+	0.0719805i
$232$		−	2.25490e6i		−	0.0118555i
$233$	−1.94502e8	+	6.31974e7i	−1.00734	+	0.327306i	−0.765796	−	0.643083i	$-0.777655\pi$
$233$	−1.94502e8	+	6.31974e7i	−1.00734	+	0.327306i	−0.241547	+	0.970389i	$0.577655\pi$
$234$	1.43456e6	+	1.04227e6i	0.00731919	+	0.00531770i
$235$	−2.09816e6	+	1.73885e7i	−0.0105463	+	0.0874024i
$236$	−2.70017e8	+	1.96178e8i	−1.33721	+	0.971537i
$237$	−3.94138e6	+	5.42484e6i	−0.0192322	+	0.0264709i
$238$	438645.	−	603744.i	0.00210909	−	0.00290291i
$239$	−2.02349e8	+	1.47015e8i	−0.958756	+	0.696577i	−0.952862	−	0.303405i	$-0.901876\pi$
$239$	−2.02349e8	+	1.47015e8i	−0.958756	+	0.696577i	−0.00589477	+	0.999983i	$0.501876\pi$
$240$	−7.54468e6	+	8.12465e6i	−0.0352291	+	0.0379372i
$241$	−1.75981e8	−	1.27858e8i	−0.809853	−	0.588392i	0.103935	−	0.994584i	$-0.466857\pi$
$241$	−1.75981e8	−	1.27858e8i	−0.809853	−	0.588392i	−0.913788	+	0.406192i	$0.866857\pi$
$242$	−1.73779e6	+	564642.i	−0.00788213	+	0.00256106i
$243$		−	3.46221e7i		−	0.154786i
$244$	9.99100e7	+	3.07491e8i	0.440296	+	1.35509i
$245$	−396274.	−	2.01616e6i	−0.00172153	−	0.00875876i
$246$	20492.8	−	63070.5i	8.77666e−5	−	0.000270118i
$247$	−2.18975e8	−	7.11493e7i	−0.924603	−	0.300422i
$248$	−2.18807e6	−	3.01161e6i	−0.00910918	−	0.0125377i
$249$	2.03484e6			0.00835283
$250$	−645865.	+	1.71458e6i	−0.00261428	+	0.00694014i
$251$	4.73817e7			0.189127			0.0945633	−	0.995519i	$-0.469855\pi$
$251$	4.73817e7			0.189127			0.0945633	+	0.995519i	$0.469855\pi$
$252$	1.49575e8	+	2.05873e8i	0.588787	+	0.810396i
$253$	5.64743e8	+	1.83496e8i	2.19245	+	0.712369i
$254$	690312.	−	2.12456e6i	0.00264318	−	0.00813488i
$255$	1.27368e6	+	6.48021e6i	0.00481028	+	0.0244736i
$256$	8.29055e7	+	2.55157e8i	0.308847	+	0.950533i
$257$			9.85596e7i			0.362187i	0.983466	+	0.181094i	$0.0579637\pi$
$257$			9.85596e7i			0.362187i	−0.983466	+	0.181094i	$0.942036\pi$
$258$	−86732.7	+	28181.2i	−0.000314423	+	0.000102162i
$259$	−3.69139e8	−	2.68195e8i	−1.32020	−	0.959184i
$260$	2.35874e8	−	2.54006e8i	0.832289	−	0.896268i
$261$	1.85248e8	−	1.34590e8i	0.644928	−	0.468568i
$262$	−449052.	+	618067.i	−0.00154256	+	0.00212315i
$263$	−3.33986e8	+	4.59692e8i	−1.13210	+	1.55820i	−0.348068	+	0.937469i	$0.613162\pi$
$263$	−3.33986e8	+	4.59692e8i	−1.13210	+	1.55820i	−0.784027	+	0.620727i	$0.786838\pi$
$264$	270302.	−	196386.i	0.000904141	−	0.000656897i
$265$	−5.15701e7	+	4.27385e8i	−0.170231	+	1.41078i
$266$	1.47033e6	+	1.06825e6i	0.00478992	+	0.00348008i
$267$	−9.62243e6	+	3.12652e6i	−0.0309382	+	0.0100524i
$268$		−	4.78440e8i		−	1.51829i
$269$	−8.53464e6	−	2.62669e7i	−0.0267333	−	0.0822766i	0.936800	−	0.349866i	$-0.113773\pi$
$269$	−8.53464e6	−	2.62669e7i	−0.0267333	−	0.0822766i	−0.963533	+	0.267589i	$0.913773\pi$
$270$	246279.	+	29717.1i	0.000761474	+	9.18827e-5i
$271$	9.06762e7	−	2.79073e8i	0.276758	−	0.851774i	−0.711991	−	0.702189i	$-0.752206\pi$
$271$	9.06762e7	−	2.79073e8i	0.276758	−	0.851774i	0.988749	−	0.149585i	$-0.0477939\pi$
$272$	1.52016e8	+	4.93931e7i	0.458035	+	0.148825i
$273$	1.25711e7	+	1.73026e7i	0.0373941	+	0.0514686i
$274$	−1.29931e6			−0.00381581
$275$	−2.64162e8	+	4.26705e8i	−0.765959	+	1.23727i
$276$	−2.86505e7			−0.0820257
$277$	−3.60150e8	−	4.95704e8i	−1.01813	−	1.40134i	−0.913506	−	0.406826i	$-0.866635\pi$
$277$	−3.60150e8	−	4.95704e8i	−1.01813	−	1.40134i	−0.104626	−	0.994512i	$-0.533365\pi$
$278$	316550.	+	102853.i	0.000883661	+	0.000287119i
$279$	1.16813e8	−	3.59514e8i	0.322016	−	0.991064i
$280$	−4.78076e6	+	2.66309e6i	−0.0130150	+	0.00724992i
$281$	−3.18942e7	−	9.81604e7i	−0.0857512	−	0.263915i	0.898982	−	0.437986i	$-0.144308\pi$
$281$	−3.18942e7	−	9.81604e7i	−0.0857512	−	0.263915i	−0.984733	+	0.174071i	$0.944308\pi$
$282$			12731.5i			3.38071e-5i
$283$	1.72167e7	−	5.59404e6i	0.0451541	−	0.0146715i	−0.286353	−	0.958124i	$-0.592443\pi$
$283$	1.72167e7	−	5.59404e6i	0.0451541	−	0.0146715i	0.331507	+	0.943453i	$0.392443\pi$
$284$	1.29723e8	+	9.42493e7i	0.336049	+	0.244154i
$285$	−1.57816e7	+	3.10186e6i	−0.0403825	+	0.00793716i
$286$	−4.22497e6	+	3.06962e6i	−0.0106793	+	0.00775897i
$287$	−1.74878e8	+	2.40699e8i	−0.436666	+	0.601019i
$288$	5.28685e6	−	7.27673e6i	0.0130414	−	0.0179499i
$289$	−2.54946e8	+	1.85229e8i	−0.621307	+	0.451406i
$290$	1.19811e6	+	2.15085e6i	0.00288473	+	0.00517865i
$291$	1.00289e7	+	7.28646e6i	0.0238578	+	0.0173337i
$292$	3.56452e8	−	1.15818e8i	0.837840	−	0.272231i
$293$		−	7.50220e8i		−	1.74242i	−0.490914	−	0.871208i	$-0.663337\pi$
$293$		−	7.50220e8i		−	1.74242i	0.490914	−	0.871208i	$-0.336663\pi$
$294$	−461.549	−	1420.50i	−1.05926e−6	−	3.26006e-6i
$295$	3.06647e8	−	6.61210e8i	0.695443	−	1.49955i
$296$	−3.32243e6	+	1.02254e7i	−0.00744621	+	0.0229171i
$297$	6.46220e7	+	2.09969e7i	0.143131	+	0.0465060i
$298$	−2.98457e6	−	4.10790e6i	−0.00653317	−	0.00899214i
$299$	8.95669e8			1.93775
$300$	5.75965e6	−	2.35190e7i	0.0123161	−	0.0502914i
$301$	4.09142e8			0.864750
$302$	−1.89320e6	−	2.60577e6i	−0.00395524	−	0.00544392i
$303$	−2.04796e7	−	6.65424e6i	−0.0422935	−	0.0137420i
$304$	−1.20289e8	+	3.70213e8i	−0.245567	+	0.755778i
$305$	−5.17377e8	−	4.80445e8i	−1.04414	−	0.969603i
$306$	−551807.	−	1.69829e6i	−0.00110094	−	0.00338833i
$307$			8.34641e8i			1.64632i	0.567806	+	0.823162i	$0.307792\pi$
$307$			8.34641e8i			1.64632i	−0.567806	+	0.823162i	$0.692208\pi$
$308$	−7.12777e8	+	2.31595e8i	−1.39004	+	0.451650i
$309$	3.40456e6	+	2.47356e6i	0.00656457	+	0.00476944i
$310$	3.68728e6	+	1.71004e6i	0.00702976	+	0.00326017i
$311$	1.70881e8	−	1.24152e8i	0.322131	−	0.234042i	−0.414953	−	0.909843i	$-0.636202\pi$
$311$	1.70881e8	−	1.24152e8i	0.322131	−	0.234042i	0.737084	+	0.675801i	$0.236202\pi$
$312$	296220.	−	407711.i	0.000552170	−	0.000759997i
$313$	4.41322e8	−	6.07428e8i	0.813487	−	1.11967i	−0.177288	−	0.984159i	$-0.556733\pi$
$313$	4.41322e8	−	6.07428e8i	0.813487	−	1.11967i	0.990776	−	0.135510i	$-0.0432674\pi$
$314$	1.09667e6	−	796774.i	0.00199903	−	0.00145238i
$315$	−5.04137e8	−	2.33802e8i	−0.908786	−	0.421464i
$316$	−2.86737e8	−	2.08327e8i	−0.511186	−	0.371399i
$317$	−1.34473e8	+	4.36928e7i	−0.237097	+	0.0770376i	−0.425156	−	0.905120i	$-0.639781\pi$
$317$	−1.34473e8	+	4.36928e7i	−0.237097	+	0.0770376i	0.188058	+	0.982158i	$0.439781\pi$
$318$			312924.i			0.000545687i
$319$	2.08393e8	+	6.41368e8i	0.359432	+	1.10622i
$320$	−4.29392e8	−	3.98740e8i	−0.732535	−	0.680244i
$321$	4.20970e6	−	1.29561e7i	0.00710369	−	0.0218629i
$322$	−6.72391e6	−	2.18473e6i	−0.0112234	−	0.00364672i
$323$	1.36286e8	+	1.87582e8i	0.225031	+	0.309729i
$324$	6.07267e8			0.991909
$325$	−1.80058e8	+	7.35248e8i	−0.290952	+	1.18807i
$326$	2.58109e6			0.00412611
$327$	−1.04911e7	−	1.44397e7i	−0.0165922	−	0.0228371i
$328$	6.66753e6	+	2.16641e6i	0.0104329	+	0.00338987i
$329$	1.76506e7	−	5.43230e7i	0.0273259	−	0.0841004i
$330$	−153482.	+	330946.i	−0.000235103	+	0.000506942i
$331$	−3.11940e6	−	9.60053e6i	−0.00472795	−	0.0145511i	0.948665	−	0.316284i	$-0.102435\pi$
$331$	−3.11940e6	−	9.60053e6i	−0.00472795	−	0.0145511i	−0.953393	+	0.301732i	$0.902435\pi$
$332$			1.07554e8i			0.161304i
$333$	−1.03836e9	+	3.37384e8i	−1.54097	+	0.500691i
$334$	5.81032e6	+	4.22144e6i	0.00853271	+	0.00619938i
$335$	5.08441e8	+	9.12750e8i	0.738897	+	1.32646i
$336$	2.92528e7	−	2.12534e7i	0.0420708	−	0.0305662i
$337$	−3.23715e8	+	4.45555e8i	−0.460742	+	0.634157i	−0.974662	−	0.223681i	$-0.928193\pi$
$337$	−3.23715e8	+	4.45555e8i	−0.460742	+	0.634157i	0.513920	+	0.857838i	$0.328193\pi$
$338$	−1.53545e6	+	2.11336e6i	−0.00216285	+	0.00297691i
$339$	−2.02706e7	+	1.47274e7i	−0.0282597	+	0.0205319i
$340$	−3.42520e8	+	6.73221e7i	−0.472617	+	0.0928927i
$341$	9.00685e8	+	6.54386e8i	1.23008	+	0.893704i
$342$	4.13592e6	−	1.34384e6i	0.00559089	−	0.00181659i
$343$		−	7.43987e8i		−	0.995487i
$344$	−2.97919e6	−	9.16899e6i	−0.00394587	−	0.0121441i
$345$	5.46582e7	−	3.04470e7i	0.0716620	−	0.0399188i
$346$	2.47255e6	−	7.60973e6i	0.00320907	−	0.00987649i
$347$	1.59988e8	+	5.19833e7i	0.205558	+	0.0667899i	0.409986	−	0.912092i	$-0.365533\pi$
$347$	1.59988e8	+	5.19833e7i	0.205558	+	0.0667899i	−0.204428	+	0.978882i	$0.565533\pi$
$348$	−1.91252e7	−	2.63236e7i	−0.0243265	−	0.0334826i
$349$	6.86396e7			0.0864343			0.0432171	−	0.999066i	$-0.486239\pi$
$349$	6.86396e7			0.0864343			0.0432171	+	0.999066i	$0.486239\pi$
$350$	3.14515e6	−	5.08041e6i	0.00392106	−	0.00633374i
$351$	1.02489e8			0.126503
$352$	1.55705e7	+	2.14310e7i	0.0190285	+	0.0261904i
$353$	9.96525e8	+	3.23790e8i	1.20580	+	0.391789i	0.841893	−	0.539645i	$-0.181441\pi$
$353$	9.96525e8	+	3.23790e8i	1.20580	+	0.391789i	0.363911	+	0.931434i	$0.381441\pi$
$354$	163721.	−	503882.i	0.000196152	−	0.000603695i
$355$	−3.47640e8	−	4.19477e7i	−0.412411	−	0.0497633i
$356$	−1.65256e8	−	5.08606e8i	−0.194126	−	0.597457i
$357$		−	2.15376e7i		−	0.0250530i
$358$	22392.1	−	7275.65i	2.57932e−5	−	8.38071e-6i
$359$	−3.14161e8	−	2.28251e8i	−0.358362	−	0.260365i	0.394007	−	0.919108i	$-0.371089\pi$
$359$	−3.14161e8	−	2.28251e8i	−0.358362	−	0.260365i	−0.752368	+	0.658743i	$0.771089\pi$
$360$	−1.56867e6	+	1.30003e7i	−0.00177204	+	0.0146857i
$361$	2.66331e8	−	1.93501e8i	0.297952	−	0.216475i
$362$	−2.66686e6	+	3.67062e6i	−0.00295475	+	0.00406686i
$363$	−3.09965e7	+	4.26630e7i	−0.0340126	+	0.0468143i
$364$	−9.14551e8	+	6.64461e8i	−0.993924	+	0.722128i
$365$	−5.56945e8	+	5.99757e8i	−0.599497	+	0.645581i
$366$	−415216.	−	301672.i	−0.000442680	−	0.000321626i
$367$	−1.07186e9	+	3.48270e8i	−1.13190	+	0.367777i	−0.814298	−	0.580447i	$-0.802878\pi$
$367$	−1.07186e9	+	3.48270e8i	−1.13190	+	0.367777i	−0.317603	+	0.948224i	$0.602878\pi$
$368$		−	1.51427e9i		−	1.58393i
$369$	2.19993e8	+	6.77070e8i	0.227938	+	0.701522i
$370$	−2.26403e6	−	1.15189e7i	−0.00232368	−	0.0118224i
$371$	4.33829e8	−	1.33519e9i	0.441072	−	1.35748i
$372$	−5.10868e7	−	1.65991e7i	−0.0514528	−	0.0167180i
$373$	1.66418e8	+	2.29055e8i	0.166043	+	0.228538i	0.883928	−	0.467623i	$-0.154890\pi$
$373$	1.66418e8	+	2.29055e8i	0.166043	+	0.228538i	−0.717885	+	0.696162i	$0.754890\pi$
$374$	5.25909e6			0.00519828
$375$	1.40057e7	+	5.09894e7i	0.0137150	+	0.0499310i
$376$	−1.34592e6			−0.00130575
$377$	5.97893e8	+	8.22928e8i	0.574683	+	0.790983i
$378$	−769398.	−	249993.i	−0.000732706	−	0.000238071i
$379$	4.19369e8	−	1.29068e9i	0.395693	−	1.21782i	−0.532727	−	0.846287i	$-0.678833\pi$
$379$	4.19369e8	−	1.29068e9i	0.395693	−	1.21782i	0.928420	−	0.371531i	$-0.121167\pi$
$380$	−1.63953e8	−	8.34156e8i	−0.153277	−	0.779838i
$381$	−1.99227e7	−	6.13158e7i	−0.0184549	−	0.0567982i
$382$		−	6.27297e6i		−	0.00575773i
$383$	6.48700e7	−	2.10775e7i	0.0589995	−	0.0191701i	−0.279369	−	0.960184i	$-0.590125\pi$
$383$	6.48700e7	−	2.10775e7i	0.0589995	−	0.0191701i	0.338368	+	0.941014i	$0.390125\pi$
$384$	−1.37868e6	−	1.00167e6i	−0.00124252	−	0.000902745i
$385$	1.11369e9	−	1.19930e9i	0.994608	−	1.07106i
$386$	−3.55719e6	+	2.58445e6i	−0.00314812	+	0.00228724i
$387$	5.75443e8	−	7.92029e8i	0.504677	−	0.694629i
$388$	−3.85135e8	+	5.30093e8i	−0.334736	+	0.460724i
$389$	4.69367e8	−	3.41015e8i	0.404286	−	0.293731i	−0.366998	−	0.930222i	$-0.619614\pi$
$389$	4.69367e8	−	3.41015e8i	0.404286	−	0.293731i	0.771285	+	0.636490i	$0.219614\pi$
$390$	−65917.7	+	546290.i	−5.62699e−5	+	0.000466334i
$391$	−7.29709e8	−	5.30164e8i	−0.617349	−	0.448530i
$392$	150169.	−	48792.9i	0.000125916	−	4.09124e-5i
$393$			2.20486e7i			0.0183234i
$394$	638510.	+	1.96513e6i	0.000525933	+	0.00161866i
$395$	7.68416e8	+	9.27203e7i	0.627345	+	0.0756981i
$396$	−5.54166e8	+	1.70555e9i	−0.448442	+	1.38016i
$397$	−2.66117e8	−	8.64665e7i	−0.213454	−	0.0693556i	0.200338	−	0.979727i	$-0.435796\pi$
$397$	−2.66117e8	−	8.64665e7i	−0.213454	−	0.0693556i	−0.413792	+	0.910371i	$0.635796\pi$
$398$	2.52088e6	+	3.46969e6i	0.00200429	+	0.00275867i
$399$	5.24516e7			0.0413384
$400$	1.24306e9	+	3.04417e8i	0.971138	+	0.237826i
$401$	−9.54017e8			−0.738841			−0.369420	−	0.929262i	$-0.620444\pi$
$401$	−9.54017e8			−0.738841			−0.369420	+	0.929262i	$0.620444\pi$
$402$	446412.	+	614434.i	0.000342724	+	0.000471720i
$403$	1.59707e9	+	5.18921e8i	1.21551	+	0.394942i
$404$	3.51718e8	−	1.08248e9i	0.265375	−	0.816741i
$405$	−1.15852e9	+	6.45346e8i	−0.866584	+	0.482725i
$406$	−2.48116e6	−	7.63622e6i	−0.00183998	−	0.00566288i
$407$		−	3.21549e9i		−	2.36411i
$408$	−482665.	+	156827.i	−0.000351832	+	0.000114317i
$409$	−1.50946e9	−	1.09669e9i	−1.09092	−	0.792597i	−0.111363	−	0.993780i	$-0.535521\pi$
$409$	−1.50946e9	−	1.09669e9i	−1.09092	−	0.792597i	−0.979554	+	0.201183i	$0.935521\pi$
$410$	−7.51095e6	+	1.47627e6i	−0.00538210	+	0.00105785i
$411$	−3.03371e7	+	2.20412e7i	−0.0215540	+	0.0156599i
$412$	−1.30743e8	+	1.79952e8i	−0.0921040	+	0.126770i
$413$	−1.39713e9	+	1.92299e9i	−0.975917	+	1.34323i
$414$	−1.36862e7	+	9.94361e6i	−0.00947942	+	0.00688720i
$415$	−1.14299e8	−	2.05188e8i	−0.0785006	−	0.140924i
$416$	3.23255e7	+	2.34858e7i	0.0220150	+	0.0159948i
$417$	9.13578e6	−	2.96839e6i	0.00616977	−	0.00200468i
$418$			1.28077e7i			0.00857738i
$419$	4.68675e8	+	1.44243e9i	0.311260	+	0.957958i	0.977267	+	0.212013i	$0.0680019\pi$
$419$	4.68675e8	+	1.44243e9i	0.311260	+	0.957958i	−0.666007	+	0.745945i	$0.731998\pi$
$420$	−3.32231e7	+	7.16376e7i	−0.0218810	+	0.0471811i
$421$	−5.01763e8	+	1.54427e9i	−0.327726	+	1.00864i	0.642469	+	0.766312i	$0.277910\pi$
$421$	−5.01763e8	+	1.54427e9i	−0.327726	+	1.00864i	−0.970195	+	0.242326i	$0.922090\pi$
$422$	6.65169e6	+	2.16126e6i	0.00430862	+	0.00139996i
$423$	−8.03353e7	−	1.10572e8i	−0.0516077	−	0.0710320i
$424$	−3.30809e7			−0.0210764
$425$	5.81903e8	−	4.92433e8i	0.367696	−	0.311161i
$426$	−254536.			−0.000159520
$427$	1.35342e9	+	1.86282e9i	0.841268	+	1.15791i
$428$	6.84813e8	+	2.22509e8i	0.422201	+	0.137181i
$429$	−4.65749e7	+	1.43343e8i	−0.0284807	+	0.0876547i
$430$	7.71354e6	+	7.16292e6i	0.00467858	+	0.00434461i
$431$	6.17339e8	+	1.89998e9i	0.371410	+	1.14308i	0.945869	+	0.324549i	$0.105213\pi$
$431$	6.17339e8	+	1.89998e9i	0.371410	+	1.14308i	−0.574459	+	0.818533i	$0.694787\pi$
$432$		−	1.73274e8i		−	0.103405i
$433$	−2.27901e9	+	7.40496e8i	−1.34908	+	0.438344i	−0.892384	−	0.451277i	$-0.850969\pi$
$433$	−2.27901e9	+	7.40496e8i	−1.34908	+	0.438344i	−0.456700	+	0.889621i	$0.650969\pi$
$434$	−1.07237e7	−	7.79121e6i	−0.00629695	−	0.00457500i
$435$	6.44607e7	+	2.98947e7i	0.0375476	+	0.0174133i
$436$	7.63230e8	−	5.54519e8i	0.441015	−	0.320416i
$437$	1.29114e9	−	1.77710e9i	0.740094	−	1.01865i
$438$	−349706.	+	481329.i	−0.000198858	+	0.000273705i
$439$	−2.17467e9	+	1.57999e9i	−1.22678	+	0.891311i	−0.996645	−	0.0818472i	$-0.973918\pi$
$439$	−2.17467e9	+	1.57999e9i	−1.22678	+	0.891311i	−0.230139	+	0.973158i	$0.573918\pi$
$440$	−3.49861e7	−	1.62254e7i	−0.0195799	−	0.00908051i
$441$	1.29718e7	+	9.42456e6i	0.00720220	+	0.00523270i
$442$	7.54432e6	−	2.45130e6i	0.00415568	−	0.00135026i
$443$		−	1.03802e9i		−	0.567271i	−0.958932	−	0.283636i	$-0.908459\pi$
$443$		−	1.03802e9i		−	0.567271i	0.958932	−	0.283636i	$-0.0915406\pi$
$444$	4.79421e7	+	1.47551e8i	0.0259942	+	0.0800020i
$445$	8.55768e8	+	7.94680e8i	0.460358	+	0.427496i
$446$	5.78050e6	−	1.77906e7i	0.00308527	−	0.00949550i
$447$	−1.39371e8	−	4.52843e7i	−0.0738066	−	0.0239812i
$448$	1.12325e9	+	1.54603e9i	0.590208	+	0.812352i
$449$	−1.04632e9			−0.545512			−0.272756	−	0.962083i	$-0.587935\pi$
$449$	−1.04632e9			−0.545512			−0.272756	+	0.962083i	$0.587935\pi$
$450$	−5.41127e6	−	1.32339e7i	−0.00279934	−	0.00684611i
$451$	−2.09668e9			−1.07625
$452$	−7.78438e8	−	1.07143e9i	−0.396497	−	0.545731i
$453$	−8.84073e7	−	2.87253e7i	−0.0446832	−	0.0145185i
$454$	−1.22214e6	+	3.76137e6i	−0.000612953	+	0.00188648i
$455$	1.03862e9	−	2.23953e9i	0.516912	−	1.11460i
$456$	−381929.	−	1.17546e6i	−0.000188628	−	0.000580537i
$457$			7.75766e8i			0.380210i	0.981764	+	0.190105i	$0.0608829\pi$
$457$			7.75766e8i			0.380210i	−0.981764	+	0.190105i	$0.939117\pi$
$458$	−2.47385e7	+	8.03802e6i	−0.0120322	+	0.00390949i
$459$	−8.34985e7	−	6.06652e7i	−0.0403027	−	0.0292816i
$460$	1.60932e9	+	2.88903e9i	0.770884	+	1.38388i
$461$	−2.98380e9	+	2.16786e9i	−1.41846	+	1.03057i	−0.426434	+	0.904519i	$0.640230\pi$
$461$	−2.98380e9	+	2.16786e9i	−1.41846	+	1.03057i	−0.992024	+	0.126051i	$0.959770\pi$
$462$	699287.	−	962486.i	0.000329920	−	0.000454096i
$463$	1.54500e9	−	2.12651e9i	0.723427	−	0.995712i	−0.275976	−	0.961165i	$-0.589001\pi$
$463$	1.54500e9	−	2.12651e9i	0.723427	−	0.995712i	0.999403	−	0.0345474i	$-0.0109990\pi$
$464$	1.39129e9	−	1.01083e9i	0.646556	−	0.469750i
$465$	1.15101e8	−	2.26231e7i	0.0530879	−	0.0104344i
$466$	1.38823e7	+	1.00861e7i	0.00635492	+	0.00461712i
$467$	9.52309e8	−	3.09424e8i	0.432682	−	0.140587i	−0.0845747	−	0.996417i	$-0.526953\pi$
$467$	9.52309e8	−	3.09424e8i	0.432682	−	0.140587i	0.517257	+	0.855830i	$0.326953\pi$
$468$			2.70496e9i			1.21983i
$469$	−1.05292e9	−	3.24057e9i	−0.471294	−	1.45049i
$470$	1.28381e6	−	715139.i	0.000570373	−	0.000317722i
$471$	1.20893e7	−	3.72071e7i	0.00533124	−	0.0164079i
$472$	5.32681e7	+	1.73079e7i	0.0233169	+	0.00757611i
$473$	1.69476e9	+	2.33263e9i	0.736366	+	1.01352i
$474$	562621.			0.000242656
$475$	1.19925e9	+	1.41714e9i	0.513429	+	0.606714i
$476$	1.13840e9			0.483805
$477$	−1.97453e9	−	2.71771e9i	−0.833010	−	1.14654i
$478$	1.99589e7	+	6.48503e6i	0.00835869	+	0.00271590i
$479$	1.76500e8	−	5.43211e8i	0.0733788	−	0.225837i	−0.907640	−	0.419750i	$-0.862118\pi$
$479$	1.76500e8	−	5.43211e8i	0.0733788	−	0.225837i	0.981019	+	0.193913i	$0.0621179\pi$
$480$	2.77103e6	+	334364.i	0.00114366	+	0.000137999i
$481$	−1.49876e9	−	4.61272e9i	−0.614081	−	1.88995i
$482$			1.82513e7i			0.00742386i
$483$	−1.94055e8	+	6.30523e7i	−0.0783628	+	0.0254616i
$484$	−2.25501e9	−	1.63836e9i	−0.904044	−	0.656827i
$485$	1.71413e8	−	1.42058e9i	0.0682255	−	0.565416i
$486$	−2.35016e6	+	1.70749e6i	−0.000928690	+	0.000674733i
$487$	−1.32506e9	+	1.82378e9i	−0.519856	+	0.715520i	−0.985542	−	0.169430i	$-0.945807\pi$
$487$	−1.32506e9	+	1.82378e9i	−0.519856	+	0.715520i	0.465687	+	0.884950i	$0.345807\pi$
$488$	3.18914e7	−	4.38947e7i	0.0124224	−	0.0170979i
$489$	6.02647e7	−	4.37849e7i	0.0233068	−	0.0169334i
$490$	−117314.	+	126332.i	−4.50467e−5	+	4.85095e-5i
$491$	1.93963e9	+	1.40922e9i	0.739492	+	0.537272i	0.892552	−	0.450945i	$-0.148913\pi$
$491$	1.93963e9	+	1.40922e9i	0.739492	+	0.537272i	−0.153060	+	0.988217i	$0.548913\pi$
$492$	9.62113e7	−	3.12609e7i	0.0364207	−	0.0118338i
$493$		−	1.02435e9i		−	0.385021i
$494$	5.96977e6	+	1.83730e7i	0.00222799	+	0.00685704i
$495$	−7.55279e8	−	3.84269e9i	−0.279891	−	1.42402i
$496$	8.77320e8	−	2.70011e9i	0.322829	−	0.993564i
$497$	1.08606e9	+	3.52881e8i	0.396831	+	0.128938i
$498$	−100354.	−	138126.i	−3.64111e−5	−	5.01156e-5i
$499$	8.38764e8			0.302195			0.151098	−	0.988519i	$-0.451719\pi$
$499$	8.38764e8			0.302195			0.151098	+	0.988519i	$0.451719\pi$
$500$	−2.69511e9	+	7.40289e8i	−0.964232	+	0.264854i
$501$	2.07274e8			0.0736399
$502$	−2.33677e6	−	3.21629e6i	−0.000824428	−	0.00113473i
$503$	−8.54719e8	−	2.77715e8i	−0.299458	−	0.0972997i	0.155435	−	0.987846i	$-0.450322\pi$
$503$	−8.54719e8	−	2.77715e8i	−0.299458	−	0.0972997i	−0.454892	+	0.890547i	$0.650322\pi$
$504$	1.31963e7	−	4.06141e7i	0.00459140	−	0.0141309i
$505$	4.79361e8	+	2.43888e9i	0.165632	+	0.842696i
$506$	−1.53962e7	−	4.73846e7i	−0.00528307	−	0.0162596i
$507$			7.53910e7i			0.0256916i
$508$	3.24093e9	−	1.05304e9i	1.09685	−	0.356387i
$509$	2.85582e9	+	2.07488e9i	0.959884	+	0.697397i	0.953124	−	0.302580i	$-0.0978481\pi$
$509$	2.85582e9	+	2.07488e9i	0.959884	+	0.697397i	0.00676042	+	0.999977i	$0.497848\pi$
$510$	377064.	−	406049.i	0.000125869	−	0.000135545i
$511$	2.15943e9	−	1.56892e9i	0.715923	−	0.520148i
$512$	6.61789e7	−	9.10874e7i	0.0217909	−	0.0299926i
$513$	1.47741e8	−	2.03348e8i	0.0483159	−	0.0665012i
$514$	6.69026e6	−	4.86076e6i	0.00217306	−	0.00157882i
$515$	5.81900e7	−	4.82248e8i	0.0187726	−	0.155577i
$516$	−1.12547e8	−	8.17701e7i	−0.0360628	−	0.0262012i
$517$	3.82824e8	−	1.24387e8i	0.121838	−	0.0395875i
$518$			3.82841e7i			0.0121022i
$519$	−7.13589e7	−	2.19620e8i	−0.0224059	−	0.0689582i
$520$	−5.77514e7	−	6.96852e6i	−0.0180115	−	0.00217335i
$521$	−8.74848e8	+	2.69251e9i	−0.271020	+	0.834112i	0.719226	+	0.694777i	$0.244497\pi$
$521$	−8.74848e8	+	2.69251e9i	−0.271020	+	0.834112i	−0.990245	+	0.139336i	$0.955503\pi$
$522$	−1.82721e7	−	5.93696e6i	−0.00562266	−	0.00182691i
$523$	−3.27665e9	−	4.50992e9i	−1.00155	−	1.37852i	−0.924367	−	0.381504i	$-0.875406\pi$
$523$	−3.27665e9	−	4.50992e9i	−1.00155	−	1.37852i	−0.0771864	−	0.997017i	$-0.524594\pi$
$524$	−1.16541e9			−0.353849
$525$	−1.27479e7	−	1.71974e8i	−0.00384488	−	0.0518686i
$526$	4.76756e7			0.0142839
$527$	−9.93989e8	−	1.36811e9i	−0.295831	−	0.407177i
$528$	2.42344e8	+	7.87423e7i	0.0716496	+	0.0232804i
$529$	−1.58840e9	+	4.88860e9i	−0.466515	+	1.43579i
$530$	3.15544e7	−	1.75772e7i	0.00920649	−	0.00512842i
$531$	1.75757e9	+	5.40923e9i	0.509426	+	1.56785i
$532$			2.77240e9i			0.798298i
$533$	−3.00775e9	+	9.77278e8i	−0.860393	+	0.279559i
$534$	686788.	+	498981.i	0.000195177	+	0.000141804i
$535$	−1.54292e9	+	3.03261e8i	−0.435618	+	0.0856205i
$536$	−6.49552e7	+	4.71927e7i	−0.0182195	+	0.0132373i
$537$	399402.	−	549730.i	0.000111301	−	0.000153193i
$538$	−1.36210e6	+	1.87477e6i	−0.000377112	+	0.000519050i
$539$	−3.82037e7	+	2.77566e7i	−0.0105086	+	0.00763495i
$540$	1.84150e8	+	3.30584e8i	0.0503260	+	0.0903449i
$541$	−3.77984e9	−	2.74622e9i	−1.02632	−	0.745666i	−0.0587523	−	0.998273i	$-0.518712\pi$
$541$	−3.77984e9	−	2.74622e9i	−1.02632	−	0.745666i	−0.967569	+	0.252606i	$0.918712\pi$
$542$	−2.34155e7	+	7.60816e6i	−0.00631693	+	0.00205249i
$543$			1.30944e8i			0.0350982i
$544$	−1.24341e7	−	3.82682e7i	−0.00331145	−	0.0101916i
$545$	−8.66770e8	+	1.86898e9i	−0.229359	+	0.494558i
$546$	554527.	−	1.70666e6i	0.000145797	−	0.000448717i
$547$	3.25671e9	+	1.05817e9i	0.850792	+	0.276439i	0.701778	−	0.712396i	$-0.252390\pi$
$547$	3.25671e9	+	1.05817e9i	0.850792	+	0.276439i	0.149014	+	0.988835i	$0.452390\pi$
$548$	−1.16502e9	−	1.60351e9i	−0.302413	−	0.416236i
$549$	5.50964e9			1.42108
$550$	4.19928e7	−	3.11281e6i	0.0107623	−	0.000797780i
$551$	2.49465e9			0.635300
$552$	2.82604e6	+	3.88971e6i	0.000715141	+	0.000984308i
$553$	−2.40060e9	−	7.80001e8i	−0.603645	−	0.196136i
$554$	−1.58867e7	+	4.88942e7i	−0.00396962	+	0.0122172i
$555$	−2.48265e8	−	2.30543e8i	−0.0616439	−	0.0572435i
$556$	1.56898e8	+	4.82883e8i	0.0387130	+	0.119146i
$557$			5.48068e9i			1.34382i	0.740632	+	0.671911i	$0.234526\pi$
$557$			5.48068e9i			1.34382i	−0.740632	+	0.671911i	$0.765474\pi$
$558$	−3.01650e7	+	9.80119e6i	−0.00734993	+	0.00238814i
$559$	3.51844e9	+	2.55629e9i	0.851939	+	0.618970i
$560$	−3.78629e9	−	1.75595e9i	−0.911078	−	0.422528i
$561$	1.22792e8	−	8.92138e7i	0.0293630	−	0.0213335i
$562$	−5.09020e6	+	7.00606e6i	−0.00120964	+	0.00166493i
$563$	−2.26567e9	+	3.11843e9i	−0.535079	+	0.736473i	−0.987894	−	0.155132i	$-0.950420\pi$
$563$	−2.26567e9	+	3.11843e9i	−0.535079	+	0.736473i	0.452815	+	0.891604i	$0.350420\pi$
$564$	−1.57122e7	+	1.14156e7i	−0.00368774	+	0.00267930i
$565$	2.62369e9	+	1.21678e9i	0.611987	+	0.283819i
$566$	−1.22882e6	−	892788.i	−0.000284859	−	0.000206962i
$567$	4.11313e9	−	1.33644e9i	0.947615	−	0.307899i
$568$		−	2.69084e7i		−	0.00616125i
$569$	9.10529e8	+	2.80232e9i	0.207205	+	0.637712i	0.999616	+	0.0277239i	$0.00882591\pi$
$569$	9.10529e8	+	2.80232e9i	0.207205	+	0.637712i	−0.792410	+	0.609988i	$0.791174\pi$
$570$	988871.	+	918282.i	0.000223654	+	0.000207689i
$571$	1.15400e9	−	3.55166e9i	0.259407	−	0.798372i	−0.733523	−	0.679665i	$-0.762125\pi$
$571$	1.15400e9	−	3.55166e9i	0.259407	−	0.798372i	0.992929	−	0.118707i	$-0.0378749\pi$
$572$	−7.57656e9	−	2.46177e9i	−1.69272	−	0.549999i
$573$	−1.06413e8	−	1.46465e8i	−0.0236295	−	0.0325232i
$574$	2.49634e7			0.00550950
$575$	−6.14038e9	−	3.80135e9i	−1.34697	−	0.833874i
$576$	4.57266e9			0.996990
$577$	2.43932e9	+	3.35744e9i	0.528633	+	0.727601i	0.986921	−	0.161203i	$-0.0515373\pi$
$577$	2.43932e9	+	3.35744e9i	0.528633	+	0.727601i	−0.458288	+	0.888803i	$0.651537\pi$
$578$	2.51469e7	+	8.17072e6i	0.00541672	+	0.00176000i
$579$	−3.92134e7	+	1.20686e8i	−0.00839575	+	0.0258394i
$580$	−1.58012e9	+	3.40715e9i	−0.336274	+	0.725093i
$581$	2.36699e8	+	7.28486e8i	0.0500704	+	0.154101i
$582$		−	1.04012e6i		−	0.000218702i
$583$	9.40931e9	−	3.05727e9i	1.96661	−	0.638990i
$584$	−5.08839e7	−	3.69694e7i	−0.0105715	−	0.00768063i
$585$	−2.87457e9	−	5.16041e9i	−0.593647	−	1.06571i
$586$	−5.09252e7	+	3.69993e7i	−0.0104542	+	0.00759542i
$587$	−3.61793e9	+	4.97965e9i	−0.738289	+	1.01617i	0.260426	+	0.965494i	$0.416137\pi$
$587$	−3.61793e9	+	4.97965e9i	−0.738289	+	1.01617i	−0.998715	+	0.0506739i	$0.983863\pi$
$588$	1.33923e6	−	1.84329e6i	0.000271665	−	0.000373914i
$589$	3.33182e9	−	2.42071e9i	0.671859	−	0.488134i
$590$	−6.00064e7	+	1.17942e7i	−0.0120286	+	0.00236422i
$591$	4.82443e7	+	3.50515e7i	0.00961368	+	0.00698474i
$592$	−7.79855e9	+	2.53390e9i	−1.54486	+	0.501954i
$593$		−	1.83862e9i		−	0.362076i	−0.983476	−	0.181038i	$-0.942054\pi$
$593$		−	1.83862e9i		−	0.362076i	0.983476	−	0.181038i	$-0.0579458\pi$
$594$	−1.76174e6	−	5.42209e6i	−0.000344897	−	0.00106149i
$595$	−2.17179e9	+	1.20978e9i	−0.422678	+	0.235450i
$596$	2.39356e9	−	7.36662e9i	0.463108	−	1.42530i
$597$	1.17718e8	+	3.82489e7i	0.0226429	+	0.00735713i
$598$	−4.41726e7	−	6.07984e7i	−0.00844693	−	0.0116262i
$599$	−3.22955e9			−0.613971			−0.306986	−	0.951714i	$-0.599320\pi$
$599$	−3.22955e9			−0.613971			−0.306986	+	0.951714i	$0.599320\pi$
$600$	−3.76116e6	+	1.53792e6i	−0.000710874	+	0.000290673i
$601$	4.17382e8			0.0784284			0.0392142	−	0.999231i	$-0.487515\pi$
$601$	4.17382e8			0.0784284			0.0392142	+	0.999231i	$0.487515\pi$
$602$	−2.01780e7	−	2.77727e7i	−0.00376956	−	0.00518836i
$603$	−7.75409e9	−	2.51946e9i	−1.44019	−	0.467947i
$604$	1.51831e9	−	4.67288e9i	0.280370	−	0.862890i
$605$	6.04312e9	+	7.29188e8i	1.10947	+	0.133874i
$606$	558322.	+	1.71834e6i	0.000101913	+	0.000313657i
$607$		−	1.22046e9i		−	0.221494i	−0.993849	−	0.110747i	$-0.964676\pi$
$607$		−	1.22046e9i		−	0.221494i	0.993849	−	0.110747i	$-0.0353244\pi$
$608$	9.31964e7	−	3.02813e7i	0.0168165	−	0.00546402i
$609$	−1.87470e8	−	1.36205e8i	−0.0336335	−	0.0244362i
$610$	−7.09678e6	+	5.88143e7i	−0.00126592	+	0.0104913i
$611$	4.91195e8	−	3.56874e8i	0.0871184	−	0.0632952i
$612$	1.60112e9	−	2.20375e9i	0.282354	−	0.388626i
$613$	5.81666e9	−	8.00594e9i	1.01991	−	1.40379i	0.107642	−	0.994190i	$-0.465670\pi$
$613$	5.81666e9	−	8.00594e9i	1.01991	−	1.40379i	0.912267	−	0.409595i	$-0.134330\pi$
$614$	5.66557e7	−	4.11628e7i	0.00987767	−	0.00717655i
$615$	−1.50327e8	+	1.61883e8i	−0.0260600	+	0.0280632i
$616$	1.01750e8	+	7.39255e7i	0.0175388	+	0.0127427i
$617$	5.73547e9	−	1.86357e9i	0.983039	−	0.319409i	0.226971	−	0.973902i	$-0.427118\pi$
$617$	5.73547e9	−	1.86357e9i	0.983039	−	0.319409i	0.756068	+	0.654493i	$0.227118\pi$
$618$		−	353093.i		−	6.01769e-5i
$619$	1.25834e9	+	3.87278e9i	0.213246	+	0.656304i	0.999273	+	0.0381125i	$0.0121345\pi$
$619$	1.25834e9	+	3.87278e9i	0.213246	+	0.656304i	−0.786027	+	0.618192i	$0.787865\pi$
$620$	1.19577e9	+	6.08384e9i	0.201502	+	1.02520i
$621$	−3.02151e8	+	9.29925e8i	−0.0506295	+	0.155822i
$622$	−1.68550e7	−	5.47652e6i	−0.00280842	−	0.000912511i
$623$	−2.23862e9	−	3.08120e9i	−0.370914	−	0.510519i
$624$	3.84352e8			0.0633261
$625$	4.35491e9	−	4.27640e9i	0.713509	−	0.700646i
$626$	−6.29976e7			−0.0102639
$627$	2.17267e8	+	2.99042e8i	0.0352011	+	0.0484502i
$628$	1.96663e9	+	6.38996e8i	0.316857	+	0.102953i
$629$	−1.50931e9	+	4.64517e9i	−0.241824	+	0.744259i
$630$	8.99245e6	+	4.57516e7i	0.00143280	+	0.00728978i
$631$	−2.83574e9	−	8.72750e9i	−0.449328	−	1.38289i	−0.877667	−	0.479271i	$-0.840901\pi$
$631$	−2.83574e9	−	8.72750e9i	−0.449328	−	1.38289i	0.428339	−	0.903618i	$-0.359099\pi$
$632$			5.94778e7i			0.00937227i
$633$	1.91971e8	−	6.23750e7i	0.0300830	−	0.00977457i
$634$	9.59780e6	+	6.97321e6i	0.00149575	+	0.00108673i
$635$	−5.06384e9	+	5.45310e9i	−0.784823	+	0.845153i
$636$	−3.86186e8	+	2.80580e8i	−0.0595246	+	0.0432471i
$637$	−4.18668e7	+	5.76247e7i	−0.00641774	+	0.00883326i
$638$	3.32588e7	−	4.57768e7i	0.00507030	−	0.00697867i
$639$	2.21062e9	−	1.60611e9i	0.335167	−	0.243513i
$640$	−2.35641e7	+	1.95287e8i	−0.00355321	+	0.0294471i
$641$	2.95361e9	+	2.14592e9i	0.442945	+	0.321818i	0.786804	−	0.617203i	$-0.211734\pi$
$641$	2.95361e9	+	2.14592e9i	0.442945	+	0.321818i	−0.343859	+	0.939021i	$0.611734\pi$
$642$	−1.08708e6	+	353214.i	−0.000162140	+	5.26824e-5i
$643$			1.11169e10i			1.64909i	0.565797	+	0.824545i	$0.308569\pi$
$643$			1.11169e10i			1.64909i	−0.565797	+	0.824545i	$0.691431\pi$
$644$	−3.33271e9	−	1.02570e10i	−0.491696	−	1.51329i
$645$	3.01610e8	+	3.63936e7i	0.0442575	+	0.00534030i
$646$	6.01176e6	−	1.85023e7i	0.000877380	−	0.00270030i
$647$	2.55648e9	+	8.30652e8i	0.371089	+	0.120574i	0.488624	−	0.872495i	$-0.337499\pi$
$647$	2.55648e9	+	8.30652e8i	0.371089	+	0.120574i	−0.117535	+	0.993069i	$0.537499\pi$
$648$	−5.98999e7	−	8.24452e7i	−0.00864796	−	0.0119029i
$649$	−1.67508e10			−2.40535
$650$	5.87890e7	−	2.40386e7i	0.00839652	−	0.00343330i
$651$	−3.82551e8			−0.0543445
$652$	2.31431e9	+	3.18537e9i	0.327005	+	0.450084i
$653$	−3.98083e9	−	1.29345e9i	−0.559471	−	0.181783i	0.0156120	−	0.999878i	$-0.495030\pi$
$653$	−3.98083e9	−	1.29345e9i	−0.559471	−	0.181783i	−0.575083	+	0.818095i	$0.695030\pi$
$654$	−462775.	+	1.42428e6i	−6.46916e−5	+	0.000199100i
$655$	2.22332e9	−	1.23849e9i	0.309142	−	0.172205i
$656$	1.65225e9	+	5.08509e9i	0.228513	+	0.703292i
$657$		−	6.38692e9i		−	0.878644i
$658$	−4.55796e6	+	1.48097e6i	−0.000623706	+	0.000202654i
$659$	1.08171e10	+	7.85910e9i	1.47236	+	1.06973i	0.979923	+	0.199379i	$0.0638924\pi$
$659$	1.08171e10	+	7.85910e9i	1.47236	+	1.06973i	0.492433	+	0.870350i	$0.336108\pi$
$660$	−5.46044e8	+	1.07325e8i	−0.0739306	+	0.0145310i
$661$	4.33266e8	−	3.14786e8i	0.0583511	−	0.0423946i	−0.558227	−	0.829688i	$-0.688518\pi$
$661$	4.33266e8	−	3.14786e8i	0.0583511	−	0.0423946i	0.616578	+	0.787293i	$0.288518\pi$
$662$	−497845.	+	685224.i	−6.66946e−5	+	9.17973e-5i
$663$	1.34566e8	−	1.85214e8i	0.0179324	−	0.0246818i
$664$	1.46021e7	−	1.06090e7i	0.00193565	−	0.00140633i
$665$	−2.94625e9	−	5.28908e9i	−0.388502	−	0.697436i
$666$	7.41116e7	+	5.38452e7i	0.00972135	+	0.00706297i
$667$	−9.22944e9	+	2.99883e9i	−1.20430	+	0.391301i
$668$			1.09557e10i			1.42208i
$669$	−1.66828e8	−	5.13443e8i	−0.0215416	−	0.0662981i
$670$	3.68825e7	−	7.95281e7i	0.00473760	−	0.0102155i
$671$	−5.01431e9	+	1.54325e10i	−0.640741	+	1.97200i
$672$	−8.65694e6	−	2.81281e6i	−0.00110045	−	0.000357559i
$673$	5.35513e8	+	7.37070e8i	0.0677200	+	0.0932086i	0.841534	−	0.540205i	$-0.181653\pi$
$673$	5.35513e8	+	7.37070e8i	0.0677200	+	0.0932086i	−0.773814	+	0.633413i	$0.781653\pi$
$674$	4.62094e7			0.00581327
$675$	−7.02627e8	−	4.34978e8i	−0.0879350	−	0.0544383i
$676$	−3.98489e9			−0.496138
$677$	−2.99071e9	−	4.11635e9i	−0.370436	−	0.509862i	0.582583	−	0.812771i	$-0.302042\pi$
$677$	−2.99071e9	−	4.11635e9i	−0.370436	−	0.509862i	−0.953019	+	0.302909i	$0.902042\pi$
$678$	1.99941e6	+	649647.i	0.000246375	+	8.00522e-5i
$679$	−1.44199e9	+	4.43800e9i	−0.176774	+	0.544056i
$680$	4.29257e7	+	3.98615e7i	0.00523523	+	0.00486152i
$681$	3.52716e7	+	1.08555e8i	0.00427967	+	0.0131715i
$682$		−	9.34118e7i		−	0.0112760i
$683$	5.50432e9	−	1.78846e9i	0.661045	−	0.214787i	0.0407671	−	0.999169i	$-0.487020\pi$
$683$	5.50432e9	−	1.78846e9i	0.661045	−	0.214787i	0.620278	+	0.784382i	$0.287020\pi$
$684$	5.36690e9	+	3.89928e9i	0.641250	+	0.465895i
$685$	3.92663e9	+	1.82104e9i	0.466770	+	0.216472i
$686$	−5.05021e7	+	3.66919e7i	−0.00597276	+	0.00433946i
$687$	−4.41254e8	+	6.07334e8i	−0.0519206	+	0.0714626i
$688$	4.32183e9	−	5.94849e9i	0.505951	−	0.696381i
$689$	1.20729e10	−	8.77149e9i	1.40619	−	1.02166i
$690$	−4.76239e6	−	2.20864e6i	−0.000551890	−	0.000255948i
$691$	1.52696e9	+	1.10940e9i	0.176058	+	0.127913i	0.672324	−	0.740257i	$-0.265296\pi$
$691$	1.52696e9	+	1.10940e9i	0.176058	+	0.127913i	−0.496267	+	0.868170i	$0.665296\pi$
$692$	1.16083e10	−	3.77177e9i	1.33167	−	0.432687i
$693$			1.27716e10i			1.45773i
$694$	−4.36164e6	−	1.34238e7i	−0.000495327	−	0.00152446i
$695$	−8.12488e8	−	7.54489e8i	−0.0918058	−	0.0852523i
$696$	−1.68733e6	+	5.19306e6i	−0.000189700	+	0.000583836i
$697$	3.02891e9	+	9.84152e8i	0.338822	+	0.110090i
$698$	−3.38517e6	−	4.65928e6i	−0.000376779	−	0.000518591i
$699$	4.95229e8			0.0548449
$700$	9.08990e9	−	6.73809e8i	1.00165	−	0.0742495i
$701$	−1.38946e10			−1.52347			−0.761735	−	0.647888i	$-0.775652\pi$
$701$	−1.38946e10			−1.52347			−0.761735	+	0.647888i	$0.775652\pi$
$702$	−5.05455e6	−	6.95699e6i	−0.000551445	−	0.000758999i
$703$	−1.13126e10	−	3.67569e9i	−1.22806	−	0.399020i
$704$	−4.16157e9	+	1.28080e10i	−0.449524	+	1.38349i
$705$	1.78437e7	−	3.84757e7i	0.00191789	−	0.00413547i
$706$	−2.71675e7	−	8.36131e7i	−0.00290559	−	0.00894248i
$707$		−	8.10587e9i		−	0.862644i
$708$	7.68649e8	−	2.49749e8i	0.0813977	−	0.0264477i
$709$	−1.51262e10	−	1.09898e10i	−1.59393	−	1.15806i	−0.898049	−	0.439896i	$-0.855015\pi$
$709$	−1.51262e10	−	1.09898e10i	−1.59393	−	1.15806i	−0.695878	−	0.718160i	$-0.744985\pi$
$710$	1.42975e7	+	2.56667e7i	0.00149918	+	0.00269132i
$711$	−4.88631e9	+	3.55011e9i	−0.509844	+	0.370423i
$712$	−5.27500e7	+	7.26041e7i	−0.00547700	+	0.00753844i
$713$	−9.41677e9	+	1.29611e10i	−0.972946	+	1.33915i
$714$	−1.46198e6	+	1.06219e6i	−0.000150314	+	0.000109209i
$715$	1.70704e10	−	3.35518e9i	1.74652	−	0.343277i
$716$	2.90567e7	+	2.11109e7i	0.00295836	+	0.00214937i
$717$	5.76022e8	−	1.87161e8i	0.0583609	−	0.0189626i
$718$			3.25822e7i			0.00328507i
$719$	−4.97862e9	−	1.53226e10i	−0.499526	−	1.53738i	−0.809783	−	0.586729i	$-0.800415\pi$
$719$	−4.97862e9	−	1.53226e10i	−0.499526	−	1.53738i	0.310258	−	0.950652i	$-0.399585\pi$
$720$	−8.72451e9	+	4.85993e9i	−0.871119	+	0.485251i
$721$	−4.89519e8	+	1.50658e9i	−0.0486402	+	0.149699i
$722$	−2.62698e7	−	8.53557e6i	−0.00259762	−	0.000844019i
$723$	3.09611e8	+	4.26143e8i	0.0304672	+	0.0419344i
$724$	−6.92120e9			−0.677792
$725$	−6.06304e8	−	8.17924e9i	−0.0590891	−	0.797131i
$726$	4.42467e6			0.000429143
$727$	−4.59593e8	−	6.32576e8i	−0.0443612	−	0.0610580i	0.786260	−	0.617896i	$-0.212015\pi$
$727$	−4.59593e8	−	6.32576e8i	−0.0443612	−	0.0610580i	−0.830621	+	0.556838i	$0.812015\pi$
$728$	1.80420e8	+	5.86221e7i	0.0173311	+	0.00563121i
$729$	3.18054e9	−	9.78870e9i	0.304057	−	0.935791i
$730$	6.81791e7	+	8.22678e6i	0.00648666	+	0.000782708i
$731$	−1.35338e9	−	4.16527e9i	−0.128147	−	0.394395i
$732$		−	7.82917e8i		−	0.0737780i
$733$	1.96639e10	−	6.38919e9i	1.84419	−	0.599214i	0.846417	−	0.532521i	$-0.178755\pi$
$733$	1.96639e10	−	6.38919e9i	1.84419	−	0.599214i	0.997774	−	0.0666926i	$-0.0212447\pi$
$734$	7.65028e7	+	5.55826e7i	0.00714071	+	0.00518803i
$735$	−596052.	+	4.93975e6i	−5.53705e−5	+	0.000458880i
$736$	−3.08397e8	+	2.24063e8i	−0.0285126	+	0.0207156i
$737$	1.41140e10	−	1.94262e10i	1.29871	−	1.78752i
$738$	3.51101e7	−	4.83249e7i	0.00321540	−	0.00442562i
$739$	−1.57497e10	+	1.14428e10i	−1.43554	+	1.04298i	−0.446591	+	0.894738i	$0.647362\pi$
$739$	−1.57497e10	+	1.14428e10i	−1.43554	+	1.04298i	−0.988951	+	0.148244i	$0.952638\pi$
$740$	1.21856e10	−	1.31224e10i	1.10545	−	1.19042i
$741$	4.51061e8	+	3.27715e8i	0.0407260	+	0.0295892i
$742$	−1.12029e8	+	3.64003e7i	−0.0100673	+	0.00327108i
$743$		−	1.74705e9i		−	0.156259i	−0.996943	−	0.0781295i	$-0.975105\pi$
$743$		−	1.74705e9i		−	0.156259i	0.996943	−	0.0781295i	$-0.0248948\pi$
$744$	2.78556e6	+	8.57309e6i	0.000247975	+	0.000763189i
$745$	3.26221e9	+	1.65974e10i	0.289045	+	1.47060i
$746$	7.34093e6	−	2.25931e7i	0.000647389	−	0.00199246i
$747$	1.74314e9	+	5.66379e8i	0.153006	+	0.0497147i
$748$	4.71551e9	+	6.49034e9i	0.411977	+	0.567038i
$749$	5.12806e9			0.445930
$750$	2.77044e6	−	3.46540e6i	0.000239792	−	0.000299943i
$751$	2.13683e9			0.184090			0.0920449	−	0.995755i	$-0.470660\pi$
$751$	2.13683e9			0.184090			0.0920449	+	0.995755i	$0.470660\pi$
$752$	−6.03353e8	−	8.30445e8i	−0.0517380	−	0.0712112i
$753$	−1.09121e8	−	3.54554e7i	−0.00931374	−	0.00302622i
$754$	2.63738e7	−	8.11703e7i	0.00224065	−	0.00689600i
$755$	2.06932e9	+	1.05283e10i	0.174990	+	0.890312i
$756$	−3.81353e8	−	1.17368e9i	−0.0320997	−	0.0987926i
$757$		−	4.24925e9i		−	0.356021i	−0.984029	−	0.178011i	$-0.943034\pi$
$757$		−	4.24925e9i		−	0.356021i	0.984029	−	0.178011i	$-0.0569662\pi$
$758$	−1.08294e8	+	3.51870e7i	−0.00903159	+	0.00293454i
$759$	−1.16330e9	−	8.45186e8i	−0.0965707	−	0.0701627i
$760$	−9.70766e7	+	1.04539e8i	−0.00802171	+	0.00863835i
$761$	1.13894e10	−	8.27486e9i	0.936814	−	0.680635i	−0.0108376	−	0.999941i	$-0.503450\pi$
$761$	1.13894e10	−	8.27486e9i	0.936814	−	0.680635i	0.947652	+	0.319306i	$0.103450\pi$
$762$	−3.17959e6	+	4.37633e6i	−0.000260333	+	0.000358317i
$763$	3.94915e9	−	5.43554e9i	0.321860	−	0.443003i
$764$	7.74160e9	−	5.62460e9i	0.628064	−	0.456315i
$765$	−7.12612e8	+	5.90574e9i	−0.0575491	+	0.476935i
$766$	−4.63000e6	−	3.36390e6i	−0.000372204	−	0.000270422i
$767$	−2.40295e10	+	7.80765e9i	−1.92292	+	0.624794i
$768$		−	6.49666e8i		−	0.0517519i
$769$	−4.71457e9	−	1.45100e10i	−0.373852	−	1.15060i	−0.944250	−	0.329230i	$-0.893211\pi$
$769$	−4.71457e9	−	1.45100e10i	−0.373852	−	1.15060i	0.570398	−	0.821369i	$-0.306789\pi$
$770$	−1.36334e8	−	1.64506e7i	−0.0107618	−	0.00129857i
$771$	7.37514e7	−	2.26984e8i	0.00579536	−	0.0178363i
$772$	−6.37903e9	−	2.07267e9i	−0.498993	−	0.162133i
$773$	−5.92834e9	−	8.15966e9i	−0.461641	−	0.635395i	0.513207	−	0.858265i	$-0.328457\pi$
$773$	−5.92834e9	−	8.15966e9i	−0.461641	−	0.635395i	−0.974848	+	0.222870i	$0.928457\pi$
$774$	−8.21429e7			−0.00636761
$775$	−8.74658e9	−	1.03357e10i	−0.674967	−	0.797601i
$776$	1.09957e8			0.00844708
$777$	6.49442e8	+	8.93880e8i	0.0496669	+	0.0683606i
$778$	−4.62965e7	−	1.50426e7i	−0.00352468	−	0.00114524i
$779$	−2.39675e9	+	7.37645e9i	−0.181653	+	0.559070i
$780$	−7.33292e8	+	4.08476e8i	−0.0553281	+	0.0308202i
$781$	2.48682e9	+	7.65364e9i	0.186795	+	0.574896i
$782$			7.56795e7i			0.00565920i
$783$	−1.05610e9	+	3.43147e8i	−0.0786210	+	0.0255455i
$784$	9.74239e7	+	7.07826e7i	0.00722037	+	0.00524591i
$785$	−4.43092e9	+	8.70896e8i	−0.326927	+	0.0642573i
$786$	1.49667e6	−	1.08739e6i	0.000109938	−	7.98743e-5i
$787$	−1.05241e10	+	1.44852e10i	−0.769617	+	1.05929i	0.226736	+	0.973956i	$0.427195\pi$
$787$	−1.05241e10	+	1.44852e10i	−0.769617	+	1.05929i	−0.996353	+	0.0853304i	$0.972805\pi$
$788$	−1.85269e9	+	2.55001e9i	−0.134884	+	0.185652i
$789$	1.11316e9	−	8.08756e8i	0.0806839	−	0.0586203i
$790$	−3.16028e7	−	5.67331e7i	−0.00228050	−	0.00409394i
$791$	−7.63044e9	−	5.54384e9i	−0.548191	−	0.398284i
$792$	2.86215e8	−	9.29968e7i	0.0204717	−	0.00665166i
$793$			2.44755e10i			1.74291i
$794$	7.25495e6	+	2.23284e7i	0.000514355	+	0.00158302i
$795$	4.38576e8	−	9.45682e8i	0.0309571	−	0.0667514i
$796$	−2.02169e9	+	6.22214e9i	−0.142076	+	0.437264i
$797$	1.51148e10	+	4.91110e9i	1.05754	+	0.343617i	0.785625	−	0.618703i	$-0.212342\pi$
$797$	1.51148e10	+	4.91110e9i	1.05754	+	0.343617i	0.271919	+	0.962320i	$0.412342\pi$
$798$	−2.58681e6	−	3.56044e6i	−0.000180200	−	0.000248024i
$799$	−6.11421e8			−0.0424059
$800$	−1.21934e8	−	2.98204e8i	−0.00841998	−	0.0205920i
$801$	−9.11322e9			−0.626554
$802$	4.70502e7	+	6.47590e7i	0.00322071	+	0.00443292i
$803$	1.78897e10	+	5.81272e9i	1.21927	+	0.396164i
$804$	−3.58014e8	+	1.10185e9i	−0.0242942	+	0.0747700i
$805$	1.72582e10	+	1.60263e10i	1.16603	+	1.08280i
$806$	−4.35399e7	−	1.34002e8i	−0.00292897	−	0.00901444i
$807$			6.68794e7i			0.00447955i
$808$	−1.81655e8	+	5.90233e7i	−0.0121146	+	0.00393626i
$809$	6.25825e9	+	4.54689e9i	0.415559	+	0.301922i	0.775849	−	0.630919i	$-0.217322\pi$
$809$	6.25825e9	+	4.54689e9i	0.415559	+	0.301922i	−0.360289	+	0.932841i	$0.617322\pi$
$810$	1.00942e8	+	4.68136e7i	0.00667383	+	0.00309510i
$811$	−3.43374e9	+	2.49476e9i	−0.226045	+	0.164231i	−0.695043	−	0.718968i	$-0.744615\pi$
$811$	−3.43374e9	+	2.49476e9i	−0.226045	+	0.164231i	0.468999	+	0.883199i	$0.344615\pi$
$812$	7.19930e9	−	9.90899e9i	0.471894	−	0.649506i
$813$	−4.17656e8	+	5.74854e8i	−0.0272585	+	0.0375181i
$814$	−2.18269e8	+	1.58582e8i	−0.0141842	+	0.0103055i
$815$	−7.80026e9	−	3.61750e9i	−0.504728	−	0.234076i
$816$	−3.13134e8	−	2.27506e8i	−0.0201751	−	0.0146581i
$817$	1.01439e10	−	3.29595e9i	0.650769	−	0.211448i
$818$			1.56550e8i			0.0100004i
$819$	5.95291e9	+	1.83212e10i	0.378648	+	1.16536i
$820$	−8.55652e9	−	7.94573e9i	−0.541937	−	0.503252i
$821$	2.17339e9	−	6.68899e9i	0.137068	−	0.421852i	−0.858838	−	0.512247i	$-0.828813\pi$
$821$	2.17339e9	−	6.68899e9i	0.137068	−	0.421852i	0.995906	+	0.0903957i	$0.0288132\pi$
$822$	2.99233e6	+	972267.i	0.000187914	+	6.10568e-5i
$823$	−3.08604e9	−	4.24757e9i	−0.192976	−	0.265608i	0.701554	−	0.712616i	$-0.252490\pi$
$823$	−3.08604e9	−	4.24757e9i	−0.192976	−	0.265608i	−0.894530	+	0.447008i	$0.852490\pi$
$824$	3.73275e7			0.00232425
$825$	9.27668e8	−	7.85035e8i	0.0575180	−	0.0486743i
$826$	1.99437e8			0.0123133
$827$	8.11120e9	+	1.11641e10i	0.498673	+	0.686365i	0.981958	−	0.189098i	$-0.0605565\pi$
$827$	8.11120e9	+	1.11641e10i	0.498673	+	0.686365i	−0.483285	+	0.875463i	$0.660556\pi$
$828$	−2.45432e10	−	7.97457e9i	−1.50254	−	0.488204i
$829$	−2.25015e9	+	6.92526e9i	−0.137174	+	0.422178i	−0.995922	−	0.0902204i	$-0.971243\pi$
$829$	−2.25015e9	+	6.92526e9i	−0.137174	+	0.422178i	0.858748	+	0.512398i	$0.171243\pi$
$830$	−8.29126e6	+	1.78781e7i	−0.000503323	+	0.00108529i
$831$	4.58497e8	+	1.41111e9i	0.0277161	+	0.0853015i
$832$			2.03132e10i			1.22277i
$833$	6.82184e7	−	2.21655e7i	0.00408926	−	0.00132868i
$834$	−652054.	−	473745.i	−3.89226e−5	−	2.82789e-5i
$835$	−1.16427e10	−	2.09009e10i	−0.692074	−	1.24240i
$836$	−1.58063e10	+	1.14839e10i	−0.935636	+	0.679779i
$837$	−1.07753e9	+	1.48310e9i	−0.0635173	+	0.0874241i
$838$	7.47988e7	−	1.02952e8i	0.00439077	−	0.00604337i
$839$	7.21117e9	−	5.23922e9i	0.421540	−	0.306267i	−0.356717	−	0.934212i	$-0.616104\pi$
$839$	7.21117e9	−	5.23922e9i	0.421540	−	0.306267i	0.778257	+	0.627946i	$0.216104\pi$
$840$	1.30029e7	−	2.55572e6i	0.000756943	−	0.000148777i
$841$	5.03917e9	+	3.66117e9i	0.292128	+	0.212243i
$842$	1.29571e8	−	4.21003e7i	0.00748026	−	0.00243048i
$843$			2.49930e8i			0.0143689i
$844$	3.29691e9	+	1.01469e10i	0.188760	+	0.580942i
$845$	7.60221e9	−	4.23476e9i	0.433453	−	0.241452i
$846$	−3.54369e6	+	1.09064e7i	−0.000201215	+	0.000619276i
$847$	−1.88792e10	−	6.13423e9i	−1.06756	−	0.346871i
$848$	−1.48296e10	−	2.04112e10i	−0.835112	−	1.14943i
$849$	−4.38362e7			−0.00245842
$850$	−6.21248e7	−	1.52140e7i	−0.00346975	−	0.000849722i
$851$	4.62717e10			2.57372
$852$	−2.28227e8	−	3.14128e8i	−0.0126424	−	0.0174007i
$853$	−1.80979e10	−	5.88038e9i	−0.998407	−	0.324402i	−0.236178	−	0.971710i	$-0.575895\pi$
$853$	−1.80979e10	−	5.88038e9i	−0.998407	−	0.324402i	−0.762229	+	0.647308i	$0.775895\pi$
$854$	5.97011e7	−	1.83741e8i	0.00328004	−	0.0100949i
$855$	−1.43825e10	−	1.73546e9i	−0.786963	−	0.0949583i
$856$	−3.73402e7	−	1.14921e8i	−0.00203478	−	0.00626242i
$857$		−	3.35750e9i		−	0.182215i	−0.995841	−	0.0911074i	$-0.970959\pi$
$857$		−	3.35750e9i		−	0.182215i	0.995841	−	0.0911074i	$-0.0290406\pi$
$858$	1.20271e7	−	3.90785e6i	0.000650064	−	0.000211219i
$859$	2.68231e10	+	1.94881e10i	1.44389	+	1.04905i	0.987212	+	0.159412i	$0.0509597\pi$
$859$	2.68231e10	+	1.94881e10i	1.44389	+	1.04905i	0.456675	+	0.889634i	$0.349040\pi$
$860$	−1.92363e9	+	1.59420e10i	−0.103128	+	0.854670i
$861$	5.82860e8	−	4.23472e8i	0.0311210	−	0.0226107i
$862$	9.85251e7	−	1.35608e8i	0.00523928	−	0.00721125i
$863$	1.67082e10	−	2.29968e10i	0.884894	−	1.21795i	−0.0901466	−	0.995929i	$-0.528734\pi$
$863$	1.67082e10	−	2.29968e10i	0.884894	−	1.21795i	0.975041	−	0.222024i	$-0.0712664\pi$
$864$	−3.52890e7	+	2.56389e7i	−0.00186140	+	0.00135239i
$865$	−1.81376e10	+	1.95318e10i	−0.952847	+	1.02609i
$866$	1.62661e8	+	1.18180e8i	0.00851082	+	0.00618348i
$867$	7.25750e8	−	2.35810e8i	0.0378199	−	0.0122884i
$868$		−	2.02202e10i		−	1.04946i
$869$	−5.49681e9	−	1.69174e10i	−0.284146	−	0.874512i
$870$	−1.14981e6	−	5.84996e6i	−5.91980e−5	−	0.000301186i
$871$	1.11922e10	−	3.44461e10i	0.573921	−	1.76635i
$872$	−1.50568e8	−	4.89225e7i	−0.00768998	−	0.00249862i
$873$	6.56311e9	+	9.03335e9i	0.333857	+	0.459514i
$874$	−1.84306e8			−0.00933791
$875$	−1.66253e10	+	1.09454e10i	−0.838960	+	0.552334i
$876$	−9.07578e8			−0.0456163
$877$	−8.52683e9	−	1.17362e10i	−0.426864	−	0.587527i	0.540366	−	0.841430i	$-0.318286\pi$
$877$	−8.52683e9	−	1.17362e10i	−0.426864	−	0.587527i	−0.967230	+	0.253903i	$0.918286\pi$
$878$	2.14501e8	+	6.96955e7i	0.0106954	+	0.00347515i
$879$	−5.61384e8	+	1.72776e9i	−0.0278804	+	0.0858071i
$880$	−5.67248e9	−	2.88603e10i	−0.280597	−	1.42762i
$881$	−2.87298e9	−	8.84212e9i	−0.141552	−	0.435653i	0.854999	−	0.518629i	$-0.173557\pi$
$881$	−2.87298e9	−	8.84212e9i	−0.141552	−	0.435653i	−0.996552	+	0.0829762i	$0.973557\pi$
$882$		−	1.34533e6i		−	6.60220e-5i
$883$	7.82278e9	−	2.54178e9i	0.382383	−	0.124244i	−0.111517	−	0.993763i	$-0.535571\pi$
$883$	7.82278e9	−	2.54178e9i	0.382383	−	0.124244i	0.493900	+	0.869519i	$0.335571\pi$
$884$	9.78974e9	+	7.11266e9i	0.476637	+	0.346297i
$885$	−1.20099e9	+	1.29331e9i	−0.0582422	+	0.0627193i
$886$	−7.04609e7	+	5.11928e7i	−0.00340353	+	0.00247281i
$887$	−1.76106e10	+	2.42389e10i	−0.847308	+	1.16622i	0.137141	+	0.990552i	$0.456209\pi$
$887$	−1.76106e10	+	2.42389e10i	−0.847308	+	1.16622i	−0.984449	+	0.175668i	$0.943791\pi$
$888$	1.53032e7	−	2.10630e7i	0.000733392	−	0.00100943i
$889$	1.96339e10	−	1.42649e10i	0.937240	−	0.680945i
$890$	1.17384e7	−	9.72819e7i	0.000558143	−	0.00462559i
$891$	2.46569e10	+	1.79143e10i	1.16780	+	0.848454i
$892$	2.71387e10	−	8.81790e9i	1.28030	−	0.415995i
$893$		−	1.48902e9i		−	0.0699716i
$894$	3.79957e6	+	1.16939e7i	0.000177850	+	0.000547365i
$895$	−7.78680e7	−	9.39588e6i	−0.00363060	−	0.000438083i
$896$	1.98231e8	−	6.10093e8i	0.00920648	−	0.0283346i
$897$	−2.06273e9	−	6.70223e8i	−0.0954267	−	0.0310060i
$898$	5.16026e7	+	7.10248e7i	0.00237796	+	0.00327298i
$899$	−1.81945e10			−0.835182
$900$	1.14802e10	−	1.85442e10i	0.524931	−	0.847929i
$901$	−1.50279e10			−0.684482
$902$	1.03404e8	+	1.42324e8i	0.00469153	+	0.00645734i
$903$	−9.42257e8	−	3.06158e8i	−0.0425855	−	0.0138369i
$904$	−6.86777e7	+	2.11368e8i	−0.00309191	+	0.00951591i
$905$	1.32040e10	−	7.35520e9i	0.592155	−	0.329856i
$906$	2.41019e6	+	7.41779e6i	0.000107672	+	0.000331380i
$907$			1.31844e10i			0.586726i	0.956001	+	0.293363i	$0.0947745\pi$
$907$			1.31844e10i			0.586726i	−0.956001	+	0.293363i	$0.905225\pi$
$908$	−5.73781e9	+	1.86433e9i	−0.254358	+	0.0826460i
$909$	−1.56916e10	−	1.14006e10i	−0.692937	−	0.503448i
$910$	−2.03243e8	+	3.99473e7i	−0.00894067	+	0.00175728i
$911$	2.99677e10	−	2.17728e10i	1.31323	−	0.954115i	0.313236	−	0.949675i	$-0.398587\pi$
$911$	2.99677e10	−	2.17728e10i	1.31323	−	0.954115i	0.999990	−	0.00443946i	$-0.00141313\pi$
$912$	5.54055e8	−	7.62592e8i	0.0241864	−	0.0332897i
$913$	−3.17285e9	+	4.36705e9i	−0.137975	+	0.189907i
$914$	5.26593e7	−	3.82592e7i	0.00228120	−	0.00165739i
$915$	8.32011e8	+	1.49362e9i	0.0359050	+	0.0644564i
$916$	−3.21014e10	−	2.33230e10i	−1.38003	−	1.00265i
$917$	−7.89353e9	+	2.56476e9i	−0.338048	+	0.109838i
$918$			8.65979e6i			0.000369452i
$919$	2.30602e9	+	7.09721e9i	0.0980075	+	0.301636i	0.988026	−	0.154289i	$-0.0493086\pi$
$919$	2.30602e9	+	7.09721e9i	0.0980075	+	0.301636i	−0.890018	+	0.455925i	$0.849309\pi$
$920$	2.33487e8	−	5.03458e8i	0.00988565	−	0.0213160i
$921$	6.24556e8	−	1.92219e9i	0.0263428	−	0.0810749i
$922$	2.94310e8	+	9.56271e7i	0.0123665	+	0.00401812i
$923$	7.13483e9	+	9.82025e9i	0.298660	+	0.411071i
$924$	1.81483e9			0.0756806
$925$	−9.30209e9	+	3.79841e10i	−0.386442	+	1.57800i
$926$	−2.20544e8			−0.00912762
$927$	2.22800e9	+	3.06658e9i	0.0918621	+	0.126437i
$928$	−4.11732e8	−	1.33780e8i	−0.0169121	−	0.00549507i
$929$	3.57310e9	−	1.09969e10i	0.146215	−	0.450002i	−0.850951	−	0.525246i	$-0.823973\pi$
$929$	3.57310e9	−	1.09969e10i	0.146215	−	0.450002i	0.997165	+	0.0752436i	$0.0239734\pi$
$930$	−7.21223e6	−	6.69740e6i	−0.000294022	−	0.000273033i
$931$	5.39808e7	+	1.66136e8i	0.00219238	+	0.00674744i
$932$			2.61760e10i			1.05913i
$933$	−4.86442e8	+	1.58055e8i	−0.0196086	+	0.00637121i
$934$	−6.79698e7	−	4.93829e7i	−0.00272962	−	0.00198318i
$935$	−1.58934e10	−	7.37082e9i	−0.635881	−	0.294900i
$936$	3.67237e8	−	2.66813e8i	0.0146380	−	0.0106351i
$937$	−2.48514e10	+	3.42051e10i	−0.986876	+	1.35832i	−0.0538351	+	0.998550i	$0.517145\pi$
$937$	−2.48514e10	+	3.42051e10i	−0.986876	+	1.35832i	−0.933041	+	0.359769i	$0.882855\pi$
$938$	−1.68043e8	+	2.31291e8i	−0.00664829	+	0.00915058i
$939$	−1.47090e9	+	1.06867e9i	−0.0579769	+	0.0421227i
$940$	2.03368e9	+	9.43154e8i	0.0798612	+	0.0370370i
$941$	−1.40239e10	−	1.01890e10i	−0.548664	−	0.398627i	0.278629	−	0.960399i	$-0.410120\pi$
$941$	−1.40239e10	−	1.01890e10i	−0.548664	−	0.398627i	−0.827292	+	0.561771i	$0.810120\pi$
$942$	−3.12185e6	+	1.01435e6i	−0.000121684	+	3.95376e-5i
$943$		−	3.01717e10i		−	1.17168i
$944$	1.32001e10	+	4.06257e10i	0.510711	+	1.57181i
$945$	1.97481e9	+	1.83384e9i	0.0761226	+	0.0706887i
$946$	7.47580e7	−	2.30082e8i	0.00287104	−	0.00883614i
$947$	−1.38060e10	−	4.48585e9i	−0.528256	−	0.171641i	0.0327331	−	0.999464i	$-0.489579\pi$
$947$	−1.38060e10	−	4.48585e9i	−0.528256	−	0.171641i	−0.560989	+	0.827823i	$0.689579\pi$
$948$	5.04469e8	+	6.94342e8i	0.0192311	+	0.0264694i
$949$	2.83727e10			1.07763
$950$	3.70514e7	−	1.51295e8i	0.00140208	−	0.00572524i
$951$	3.42387e8			0.0129088
$952$	−1.12290e8	−	1.54554e8i	−0.00421806	−	0.00580566i
$953$	2.24671e10	+	7.30000e9i	0.840856	+	0.273211i	0.697611	−	0.716477i	$-0.254246\pi$
$953$	2.24671e10	+	7.30000e9i	0.840856	+	0.273211i	0.143245	+	0.989687i	$0.454246\pi$
$954$	−8.70993e7	+	2.68064e8i	−0.00324785	+	0.00999584i
$955$	−8.79182e9	+	1.89574e10i	−0.326638	+	0.704316i
$956$	9.89263e9	+	3.04464e10i	0.366192	+	1.12702i
$957$		−	1.63302e9i		−	0.0602280i
$958$	−4.55780e7	+	1.48092e7i	−0.00167485	+	0.000544192i
$959$	−1.14198e10	−	8.29696e9i	−0.418112	−	0.303776i
$960$	6.90518e8	+	1.23961e9i	0.0251899	+	0.0452206i
$961$	−2.04215e9	+	1.48371e9i	−0.0742258	+	0.0539282i
$962$	−2.39197e8	+	3.29227e8i	−0.00866250	+	0.0119229i
$963$	7.21242e9	−	9.92705e9i	0.260249	−	0.358202i
$964$	−2.25243e10	+	1.63649e10i	−0.809808	+	0.588360i
$965$	1.43723e10	−	2.82487e9i	0.514851	−	0.101194i
$966$	1.38504e7	+	1.00629e7i	0.000494359	+	0.000359173i
$967$	2.27754e10	−	7.40017e9i	0.809978	−	0.263178i	0.125389	−	0.992108i	$-0.459982\pi$
$967$	2.27754e10	−	7.40017e9i	0.809978	−	0.263178i	0.684588	+	0.728930i	$0.259982\pi$
$968$			4.67756e8i			0.0165751i
$969$	−1.73502e8	−	5.33984e8i	−0.00612592	−	0.0188536i
$970$	−1.04883e8	+	5.84244e7i	−0.00368981	+	0.00205538i
$971$	−1.20640e10	+	3.71292e10i	−0.422887	+	1.30151i	0.482116	+	0.876107i	$0.339868\pi$
$971$	−1.20640e10	+	3.71292e10i	−0.422887	+	1.30151i	−0.905003	+	0.425405i	$0.860132\pi$
$972$	−4.21450e9	−	1.36937e9i	−0.147202	−	0.0478289i
$973$	2.12540e9	+	2.92537e9i	0.0739684	+	0.101809i
$974$	1.89148e8			0.00655912
$975$	9.64857e8	−	1.55855e9i	0.0333385	−	0.0538523i
$976$	4.13798e10			1.42467
$977$	−1.91675e10	−	2.63818e10i	−0.657560	−	0.905053i	0.341838	−	0.939759i	$-0.388951\pi$
$977$	−1.91675e10	−	2.63818e10i	−0.657560	−	0.905053i	−0.999398	+	0.0347058i	$0.988951\pi$
$978$	−5.94427e6	−	1.93141e6i	−0.000203195	−	6.60220e-5i
$979$	8.29392e9	−	2.55261e10i	0.282501	−	0.869450i
$980$	−2.61097e8	−	3.15051e7i	−0.00886157	−	0.00106927i
$981$	−4.96795e9	−	1.52898e10i	−0.168010	−	0.517082i
$982$		−	2.01163e8i		−	0.00677887i
$983$	−4.64896e10	+	1.51054e10i	−1.56106	+	0.507218i	−0.957090	−	0.289792i	$-0.906414\pi$
$983$	−4.64896e10	+	1.51054e10i	−1.56106	+	0.507218i	−0.603966	+	0.797010i	$0.706414\pi$
$984$	−1.37343e7	−	9.97853e6i	−0.000459539	−	0.000333875i
$985$	8.24581e8	−	6.83368e9i	0.0274920	−	0.227839i
$986$	−6.95333e7	+	5.05189e7i	−0.00231006	+	0.00167836i
$987$	−8.12991e7	+	1.11899e8i	−0.00269138	+	0.00370437i
$988$	−1.73218e10	+	2.38414e10i	−0.571405	+	0.786471i
$989$	−3.35672e10	+	2.43880e10i	−1.10339	+	0.801657i
$990$	−2.23594e8	+	2.40782e8i	−0.00732382	+	0.00788681i
$991$	2.45275e10	+	1.78202e10i	0.800562	+	0.581642i	0.911079	−	0.412232i	$-0.135251\pi$
$991$	2.45275e10	+	1.78202e10i	0.800562	+	0.581642i	−0.110517	+	0.993874i	$0.535251\pi$
$992$	−6.79719e8	+	2.20854e8i	−0.0221074	+	0.00718314i
$993$			2.44443e7i			0.000792238i
$994$	−2.96084e7	−	9.11253e7i	−0.000956231	−	0.00294298i
$995$	−2.75539e9	−	1.40188e10i	−0.0886753	−	0.451160i
$996$	8.04822e7	−	2.47699e8i	0.00258102	−	0.00794357i
$997$	5.15202e10	+	1.67399e10i	1.64644	+	0.534959i	0.977963	−	0.208778i	$-0.0669485\pi$
$997$	5.15202e10	+	1.67399e10i	1.64644	+	0.534959i	0.668472	+	0.743737i	$0.266949\pi$
$998$	−4.13661e7	−	5.69356e7i	−0.00131731	−	0.00181312i
$999$	5.29474e9			0.168022

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.8.e.a.14.9	yes	64
25.3	odd	20		625.8.a.g.1.33		64
25.9	even	10	inner	25.8.e.a.9.9	✓	64
25.22	odd	20		625.8.a.g.1.32		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.8.e.a.9.9	✓	64	25.9	even	10	inner
25.8.e.a.14.9	yes	64	1.1	even	1	trivial
625.8.a.g.1.32		64	25.22	odd	20
625.8.a.g.1.33		64	25.3	odd	20

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	25.e (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0493180 - 0.0678803i) q^{2} +(-2.30301 - 0.748293i) q^{3} +(39.5520 - 121.729i) q^{4} +(53.9059 + 274.261i) q^{5} +(0.0627853 + 0.193233i) q^{6} -911.534i q^{7} +(-20.4278 + 6.63738i) q^{8} +(-1764.58 - 1282.04i) q^{9} +(15.9584 - 17.1851i) q^{10} +(5196.92 - 3775.78i) q^{11} +(-182.177 + 250.745i) q^{12} +(5695.22 - 7838.79i) q^{13} +(-61.8752 + 44.9550i) q^{14} +(81.0819 - 671.963i) q^{15} +(-13252.7 - 9628.68i) q^{16} +(-9279.87 + 3015.21i) q^{17} +183.008i q^{18} +(-7343.10 - 22599.7i) q^{19} +(35517.5 + 4285.69i) q^{20} +(-682.094 + 2099.27i) q^{21} +(-512.603 - 166.555i) q^{22} +(54334.4 + 74784.9i) q^{23} +52.0120 q^{24} +(-72313.3 + 29568.6i) q^{25} -812.976 q^{26} +(6217.33 + 8557.43i) q^{27} +(-110960. - 36053.0i) q^{28} +(-32441.1 + 99843.4i) q^{29} +(-49.6119 + 27.6360i) q^{30} +(53556.2 + 164829. i) q^{31} +4123.78i q^{32} +(-14793.9 + 4806.84i) q^{33} +(662.338 + 481.217i) q^{34} +(249998. - 49137.0i) q^{35} +(-225853. + 164092. i) q^{36} +(294224. - 404965. i) q^{37} +(-1171.93 + 1613.02i) q^{38} +(-18981.8 + 13791.1i) q^{39} +(-2921.55 - 5244.75i) q^{40} +(-264060. - 191851. i) q^{41} +(176.139 - 57.2310i) q^{42} +448849. i q^{43} +(-254072. - 781953. i) q^{44} +(256493. - 553064. i) q^{45} +(2396.76 - 7376.48i) q^{46} +(59595.2 + 19363.6i) q^{47} +(23316.1 + 32091.9i) q^{48} -7351.23 q^{49} +(5573.47 + 3450.39i) q^{50} +23627.9 q^{51} +(-728948. - 1.00331e6i) q^{52} +(1.46477e6 + 475933. i) q^{53} +(274.255 - 844.070i) q^{54} +(1.31569e6 + 1.22178e6i) q^{55} +(6050.20 + 18620.6i) q^{56} +57542.2i q^{57} +(8377.33 - 2721.96i) q^{58} +(-2.10962e6 - 1.53273e6i) q^{59} +(-78590.1 - 36447.5i) q^{60} +(-2.04361e6 + 1.48477e6i) q^{61} +(8547.37 - 11764.4i) q^{62} +(-1.16862e6 + 1.60847e6i) q^{63} +(-1.69607e6 + 1.23227e6i) q^{64} +(2.45688e6 + 1.13942e6i) q^{65} +(1055.90 + 767.154i) q^{66} +(3.55507e6 - 1.15511e6i) q^{67} +1.24888e6i q^{68} +(-69171.6 - 212888. i) q^{69} +(-15664.8 - 14546.6i) q^{70} +(-387129. + 1.19146e6i) q^{71} +(44555.7 + 14477.0i) q^{72} +(1.72118e6 + 2.36901e6i) q^{73} -41999.7 q^{74} +(188664. - 13985.1i) q^{75} -3.04147e6 q^{76} +(-3.44175e6 - 4.73717e6i) q^{77} +(1872.29 + 608.345i) q^{78} +(855702. - 2.63358e6i) q^{79} +(1.92637e6 - 4.15376e6i) q^{80} +(1.46614e6 + 4.51232e6i) q^{81} +27386.1i q^{82} +(-799187. + 259672. i) q^{83} +(228563. + 166061. i) q^{84} +(-1.32720e6 - 2.38257e6i) q^{85} +(30468.1 - 22136.3i) q^{86} +(149424. - 205665. i) q^{87} +(-81100.1 + 111625. i) q^{88} +(3.38024e6 - 2.45588e6i) q^{89} +(-50191.9 + 9865.19i) q^{90} +(-7.14533e6 - 5.19138e6i) q^{91} +(1.12525e7 - 3.65616e6i) q^{92} -419678. i q^{93} +(-1624.70 - 5000.32i) q^{94} +(5.80239e6 - 3.23218e6i) q^{95} +(3085.80 - 9497.11i) q^{96} +(-4.86872e6 - 1.58194e6i) q^{97} +(362.547 + 499.004i) q^{98} -1.40111e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 5 q^{2} - 5 q^{3} + 893 q^{4} - 510 q^{5} + 173 q^{6} - 2510 q^{8} + 6587 q^{9} - 5805 q^{10} - 472 q^{11} + 16635 q^{12} - 5 q^{13} - 19409 q^{14} + 375 q^{15} - 42071 q^{16} + 31910 q^{17} - 48685 q^{19}+ \cdots + 57867624 q^{99}+O(q^{100}) \) 64 * q - 5 * q^2 - 5 * q^3 + 893 * q^4 - 510 * q^5 + 173 * q^6 - 2510 * q^8 + 6587 * q^9 - 5805 * q^10 - 472 * q^11 + 16635 * q^12 - 5 * q^13 - 19409 * q^14 + 375 * q^15 - 42071 * q^16 + 31910 * q^17 - 48685 * q^19 - 171405 * q^20 + 2268 * q^21 + 197230 * q^22 + 356525 * q^23 + 544720 * q^24 + 170220 * q^25 - 708942 * q^26 - 319805 * q^27 - 565125 * q^28 - 332885 * q^29 + 66235 * q^30 - 39057 * q^31 - 161110 * q^33 + 1156301 * q^34 + 337515 * q^35 + 1920669 * q^36 - 1480960 * q^37 - 2136945 * q^38 + 1307509 * q^39 - 282470 * q^40 + 1955408 * q^41 - 684355 * q^42 - 3558164 * q^44 - 1351725 * q^45 - 2982527 * q^46 + 1018980 * q^47 + 8967210 * q^48 - 3298162 * q^49 + 8550165 * q^50 - 3922092 * q^51 + 8058740 * q^52 + 316580 * q^53 - 6933535 * q^54 - 2889990 * q^55 + 480880 * q^56 - 12912030 * q^58 - 3625740 * q^59 - 10459240 * q^60 + 656223 * q^61 + 15439920 * q^62 + 16010850 * q^63 + 572908 * q^64 - 9903445 * q^65 + 8105266 * q^66 - 25482280 * q^67 - 9378031 * q^69 + 16449030 * q^70 + 2533578 * q^71 + 8757215 * q^72 + 8477055 * q^73 + 20547876 * q^74 + 28650170 * q^75 - 22436480 * q^76 + 20387770 * q^77 - 23613305 * q^78 - 5343505 * q^79 - 44517070 * q^80 + 7686054 * q^81 - 20224125 * q^83 + 10924626 * q^84 + 2795615 * q^85 + 27540603 * q^86 - 3545560 * q^87 + 36319550 * q^88 - 17844415 * q^89 - 67695745 * q^90 + 9123478 * q^91 - 88054710 * q^92 - 15200999 * q^94 + 42119295 * q^95 - 8739232 * q^96 + 41971560 * q^97 + 60378980 * q^98 + 57867624 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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