LMFDB - Embedded newform 25.8.e.a.14.15

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			14.15
Character	$\chi$	$=$	25.14
Dual form			25.8.e.a.9.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(11.3542 + 15.6278i) q^{2} +(-45.6000 - 14.8163i) q^{3} +(-75.7544 + 233.148i) q^{4} +(-99.3681 + 261.249i) q^{5} +(-286.207 - 880.856i) q^{6} -1166.35i q^{7} +(-2152.16 + 699.280i) q^{8} +(90.5179 + 65.7651i) q^{9} +(-5210.99 + 1413.38i) q^{10} +(-3992.39 + 2900.64i) q^{11} +(6908.81 - 9509.16i) q^{12} +(-3446.38 + 4743.54i) q^{13} +(18227.5 - 13243.1i) q^{14} +(8401.94 - 10440.7i) q^{15} +(-9978.44 - 7249.76i) q^{16} +(-6346.60 + 2062.14i) q^{17} +2161.31i q^{18} +(12597.1 + 38770.0i) q^{19} +(-53382.1 - 42958.2i) q^{20} +(-17281.1 + 53185.7i) q^{21} +(-90661.3 - 29457.6i) q^{22} +(39853.4 + 54853.5i) q^{23} +108499. q^{24} +(-58377.0 - 51919.6i) q^{25} -113262. q^{26} +(58481.6 + 80493.0i) q^{27} +(271933. + 88356.4i) q^{28} +(-25433.7 + 78276.9i) q^{29} +(258562. + 12757.6i) q^{30} +(-94157.3 - 289786. i) q^{31} +51397.0i q^{32} +(225030. - 73116.7i) q^{33} +(-104287. - 75769.3i) q^{34} +(304709. + 115898. i) q^{35} +(-22190.1 + 16122.1i) q^{36} +(-136173. + 187426. i) q^{37} +(-462859. + 637070. i) q^{38} +(227437. - 165243. i) q^{39} +(31170.2 - 631736. i) q^{40} +(-473308. - 343878. i) q^{41} +(-1.02739e6 + 333819. i) q^{42} -328323. i q^{43} +(-373838. - 1.15056e6i) q^{44} +(-26175.7 + 17112.7i) q^{45} +(-404733. + 1.24564e6i) q^{46} +(1.00932e6 + 327946. i) q^{47} +(347602. + 478433. i) q^{48} -536837. q^{49} +(148562. - 1.50181e6i) q^{50} +319959. q^{51} +(-844868. - 1.16286e6i) q^{52} +(1.26856e6 + 412181. i) q^{53} +(-593913. + 1.82788e6i) q^{54} +(-361073. - 1.33124e6i) q^{55} +(815608. + 2.51018e6i) q^{56} -1.95456e6i q^{57} +(-1.51207e6 + 491303. i) q^{58} +(492810. + 358047. i) q^{59} +(1.79774e6 + 2.74982e6i) q^{60} +(1.23139e6 - 894660. i) q^{61} +(3.45963e6 - 4.76177e6i) q^{62} +(76705.4 - 105576. i) q^{63} +(-2.08046e6 + 1.51154e6i) q^{64} +(-896783. - 1.37172e6i) q^{65} +(3.69770e6 + 2.68654e6i) q^{66} +(-1.73710e6 + 564418. i) q^{67} -1.63591e6i q^{68} +(-1.00459e6 - 3.09180e6i) q^{69} +(1.64850e6 + 6.07786e6i) q^{70} +(-866491. + 2.66678e6i) q^{71} +(-240798. - 78239.9i) q^{72} +(-666685. - 917613. i) q^{73} -4.47519e6 q^{74} +(1.89273e6 + 3.23247e6i) q^{75} -9.99345e6 q^{76} +(3.38318e6 + 4.65654e6i) q^{77} +(5.16475e6 + 1.67813e6i) q^{78} +(-1.69840e6 + 5.22714e6i) q^{79} +(2.88553e6 - 1.88646e6i) q^{80} +(-1.54977e6 - 4.76969e6i) q^{81} -1.13012e7i q^{82} +(2.02898e6 - 659256. i) q^{83} +(-1.10910e7 - 8.05811e6i) q^{84} +(91919.2 - 1.86295e6i) q^{85} +(5.13095e6 - 3.72786e6i) q^{86} +(2.31955e6 - 3.19259e6i) q^{87} +(6.56392e6 - 9.03446e6i) q^{88} +(4.82883e6 - 3.50835e6i) q^{89} +(-564639. - 214765. i) q^{90} +(5.53264e6 + 4.01970e6i) q^{91} +(-1.58080e7 + 5.13635e6i) q^{92} +1.46093e7i q^{93} +(6.33494e6 + 1.94969e7i) q^{94} +(-1.13804e7 - 561515. i) q^{95} +(761516. - 2.34370e6i) q^{96} +(468018. + 152068. i) q^{97} +(-6.09538e6 - 8.38957e6i) q^{98} -552144. 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 $

$2$	11.3542	+	15.6278i	1.00358	+	1.38131i	0.923101	+	0.384558i	$0.125646\pi$
$2$	11.3542	+	15.6278i	1.00358	+	1.38131i	0.0804821	+	0.996756i	$0.474354\pi$
$3$	−45.6000	−	14.8163i	−0.975081	−	0.316823i	−0.222216	−	0.974998i	$-0.571329\pi$
$3$	−45.6000	−	14.8163i	−0.975081	−	0.316823i	−0.752865	+	0.658175i	$0.771329\pi$
$4$	−75.7544	+	233.148i	−0.591831	+	1.82147i
$5$	−99.3681	+	261.249i	−0.355510	+	0.934672i
$5$	−99.3681	+	261.249i	−0.355510	+	0.934672i
$6$	−286.207	−	880.856i	−0.540943	−	1.66485i
$7$		−	1166.35i		−	1.28525i	−0.766182	−	0.642624i	$-0.777846\pi$
$7$		−	1166.35i		−	1.28525i	0.766182	−	0.642624i	$-0.222154\pi$
$8$	−2152.16	+	699.280i	−1.48614	+	0.482877i
$9$	90.5179	+	65.7651i	0.0413891	+	0.0300709i
$10$	−5210.99	+	1413.38i	−1.64786	+	0.446950i
$11$	−3992.39	+	2900.64i	−0.904397	+	0.657083i	−0.939592	−	0.342298i	$-0.888795\pi$
$11$	−3992.39	+	2900.64i	−0.904397	+	0.657083i	0.0351948	+	0.999380i	$0.488795\pi$
$12$	6908.81	−	9509.16i	1.15417	−	1.58857i
$13$	−3446.38	+	4743.54i	−0.435073	+	0.598826i	−0.969108	−	0.246636i	$-0.920675\pi$
$13$	−3446.38	+	4743.54i	−0.435073	+	0.598826i	0.534036	+	0.845462i	$0.320675\pi$
$14$	18227.5	−	13243.1i	1.77533	−	1.28985i
$15$	8401.94	−	10440.7i	0.642777	−	0.798747i
$16$	−9978.44	−	7249.76i	−0.609036	−	0.442490i
$17$	−6346.60	+	2062.14i	−0.313307	+	0.101800i	−0.461450	−	0.887166i	$-0.652671\pi$
$17$	−6346.60	+	2062.14i	−0.313307	+	0.101800i	0.148143	+	0.988966i	$0.452671\pi$
$18$			2161.31i			0.0873500i
$19$	12597.1	+	38770.0i	0.421342	+	1.29676i	0.906454	+	0.422305i	$0.138779\pi$
$19$	12597.1	+	38770.0i	0.421342	+	1.29676i	−0.485112	+	0.874452i	$0.661221\pi$
$20$	−53382.1	−	42958.2i	−1.49208	−	1.20072i
$21$	−17281.1	+	53185.7i	−0.407196	+	1.25322i
$22$	−90661.3	−	29457.6i	−1.81527	−	0.589818i
$23$	39853.4	+	54853.5i	0.682995	+	0.940062i	0.999965	−	0.00837343i	$-0.00266538\pi$
$23$	39853.4	+	54853.5i	0.682995	+	0.940062i	−0.316970	+	0.948436i	$0.602665\pi$
$24$	108499.			1.60209
$25$	−58377.0	−	51919.6i	−0.747225	−	0.664571i
$26$	−113262.			−1.26380
$27$	58481.6	+	80493.0i	0.571803	+	0.787019i
$28$	271933.	+	88356.4i	2.34104	+	0.760650i
$29$	−25433.7	+	78276.9i	−0.193650	+	0.595992i	0.806340	+	0.591452i	$0.201445\pi$
$29$	−25433.7	+	78276.9i	−0.193650	+	0.595992i	−0.999990	+	0.00453996i	$0.998555\pi$
$30$	258562.	+	12757.6i	1.74840	+	0.0862671i
$31$	−94157.3	−	289786.i	−0.567660	−	1.74708i	−0.659914	−	0.751341i	$-0.729407\pi$
$31$	−94157.3	−	289786.i	−0.567660	−	1.74708i	0.0922543	−	0.995735i	$-0.470593\pi$
$32$			51397.0i			0.277276i
$33$	225030.	−	73116.7i	1.09004	−	0.354175i
$34$	−104287.	−	75769.3i	−0.455047	−	0.330611i
$35$	304709.	+	115898.i	1.20129	+	0.456919i
$36$	−22190.1	+	16122.1i	−0.0792686	+	0.0575920i
$37$	−136173.	+	187426.i	−0.441962	+	0.608309i	−0.970647	−	0.240510i	$-0.922685\pi$
$37$	−136173.	+	187426.i	−0.441962	+	0.608309i	0.528685	+	0.848818i	$0.322685\pi$
$38$	−462859.	+	637070.i	−1.36838	+	1.88341i
$39$	227437.	−	165243.i	0.613953	−	0.446063i
$40$	31170.2	−	631736.i	0.0770070	−	1.56072i
$41$	−473308.	−	343878.i	−1.07251	−	0.779223i	−0.0961465	−	0.995367i	$-0.530652\pi$
$41$	−473308.	−	343878.i	−1.07251	−	0.779223i	−0.976361	+	0.216145i	$0.930652\pi$
$42$	−1.02739e6	+	333819.i	−2.13975	+	0.695246i
$43$		−	328323.i		−	0.629740i	−0.949135	−	0.314870i	$-0.898039\pi$
$43$		−	328323.i		−	0.629740i	0.949135	−	0.314870i	$-0.101961\pi$
$44$	−373838.	−	1.15056e6i	−0.661606	−	2.03621i
$45$	−26175.7	+	17112.7i	−0.0428207	+	0.0279947i
$46$	−404733.	+	1.24564e6i	−0.613078	+	1.88686i
$47$	1.00932e6	+	327946.i	1.41803	+	0.460745i	0.914975	−	0.403511i	$-0.132210\pi$
$47$	1.00932e6	+	327946.i	1.41803	+	0.460745i	0.503052	+	0.864256i	$0.332210\pi$
$48$	347602.	+	478433.i	0.453668	+	0.624420i
$49$	−536837.			−0.651863
$50$	148562.	−	1.50181e6i	0.168079	−	1.69910i
$51$	319959.			0.337752
$52$	−844868.	−	1.16286e6i	−0.833254	−	1.14688i
$53$	1.26856e6	+	412181.i	1.17043	+	0.380296i	0.828804	−	0.559539i	$-0.189022\pi$
$53$	1.26856e6	+	412181.i	1.17043	+	0.380296i	0.341628	+	0.939835i	$0.389022\pi$
$54$	−593913.	+	1.82788e6i	−0.513268	+	1.57968i
$55$	−361073.	−	1.33124e6i	−0.292635	−	1.07891i
$56$	815608.	+	2.51018e6i	0.620616	+	1.91006i
$57$		−	1.95456e6i		−	1.39793i
$58$	−1.51207e6	+	491303.i	−1.01760	+	0.330637i
$59$	492810.	+	358047.i	0.312390	+	0.226965i	0.732921	−	0.680313i	$-0.238156\pi$
$59$	492810.	+	358047.i	0.312390	+	0.226965i	−0.420531	+	0.907278i	$0.638156\pi$
$60$	1.79774e6	+	2.74982e6i	1.07448	+	1.64352i
$61$	1.23139e6	−	894660.i	0.694612	−	0.504665i	−0.183561	−	0.983008i	$-0.558762\pi$
$61$	1.23139e6	−	894660.i	0.694612	−	0.504665i	0.878173	+	0.478343i	$0.158762\pi$
$62$	3.45963e6	−	4.76177e6i	1.84357	−	2.53745i
$63$	76705.4	−	105576.i	0.0386486	−	0.0531952i
$64$	−2.08046e6	+	1.51154e6i	−0.992041	+	0.720760i
$65$	−896783.	−	1.37172e6i	−0.405033	−	0.619539i
$66$	3.69770e6	+	2.68654e6i	1.58317	+	1.15024i
$67$	−1.73710e6	+	564418.i	−0.705608	+	0.229266i	−0.639772	−	0.768565i	$-0.720971\pi$
$67$	−1.73710e6	+	564418.i	−0.705608	+	0.229266i	−0.0658355	+	0.997830i	$0.520971\pi$
$68$		−	1.63591e6i		−	0.630927i
$69$	−1.00459e6	−	3.09180e6i	−0.368142	−	1.13303i
$70$	1.64850e6	+	6.07786e6i	0.574442	+	2.11791i
$71$	−866491.	+	2.66678e6i	−0.287316	+	0.884267i	0.698379	+	0.715728i	$0.253905\pi$
$71$	−866491.	+	2.66678e6i	−0.287316	+	0.884267i	−0.985695	+	0.168539i	$0.946095\pi$
$72$	−240798.	−	78239.9i	−0.0760306	−	0.0247038i
$73$	−666685.	−	917613.i	−0.200581	−	0.276077i	0.696863	−	0.717204i	$-0.254579\pi$
$73$	−666685.	−	917613.i	−0.200581	−	0.276077i	−0.897444	+	0.441128i	$0.854579\pi$
$74$	−4.47519e6			−1.28381
$75$	1.89273e6	+	3.23247e6i	0.518053	+	0.884749i
$76$	−9.99345e6			−2.61137
$77$	3.38318e6	+	4.65654e6i	0.844514	+	1.16237i
$78$	5.16475e6	+	1.67813e6i	1.23231	+	0.400400i
$79$	−1.69840e6	+	5.22714e6i	−0.387566	+	1.19280i	0.547036	+	0.837109i	$0.315756\pi$
$79$	−1.69840e6	+	5.22714e6i	−0.387566	+	1.19280i	−0.934602	+	0.355696i	$0.884244\pi$
$80$	2.88553e6	−	1.88646e6i	0.630102	−	0.411939i
$81$	−1.54977e6	−	4.76969e6i	−0.324017	−	0.997223i
$82$		−	1.13012e7i		−	2.26348i
$83$	2.02898e6	−	659256.i	0.389497	−	0.126555i	−0.107720	−	0.994181i	$-0.534355\pi$
$83$	2.02898e6	−	659256.i	0.389497	−	0.126555i	0.497218	+	0.867626i	$0.334355\pi$
$84$	−1.10910e7	−	8.05811e6i	−2.04171	−	1.48339i
$85$	91919.2	−	1.86295e6i	0.0162345	−	0.329030i
$86$	5.13095e6	−	3.72786e6i	0.869868	−	0.631996i
$87$	2.31955e6	−	3.19259e6i	0.377648	−	0.519788i
$88$	6.56392e6	−	9.03446e6i	1.02677	−	1.41323i
$89$	4.82883e6	−	3.50835e6i	0.726068	−	0.527519i	−0.162249	−	0.986750i	$-0.551875\pi$
$89$	4.82883e6	−	3.50835e6i	0.726068	−	0.527519i	0.888317	+	0.459231i	$0.151875\pi$
$90$	−564639.	−	214765.i	−0.0816436	−	0.0310538i
$91$	5.53264e6	+	4.01970e6i	0.769640	+	0.559176i
$92$	−1.58080e7	+	5.13635e6i	−2.11651	+	0.687697i
$93$			1.46093e7i			1.88339i
$94$	6.33494e6	+	1.94969e7i	0.786675	+	2.42114i
$95$	−1.13804e7	−	561515.i	−1.36183	−	0.0671937i
$96$	761516.	−	2.34370e6i	0.0878475	−	0.270367i
$97$	468018.	+	152068.i	0.0520669	+	0.0169176i	0.334935	−	0.942241i	$-0.391286\pi$
$97$	468018.	+	152068.i	0.0520669	+	0.0169176i	−0.282868	+	0.959159i	$0.591286\pi$
$98$	−6.09538e6	−	8.38957e6i	−0.654199	−	0.900427i
$99$	−552144.			−0.0571912
$100$	1.65273e7	−	9.67734e6i	1.65273	−	0.967734i
$101$	−1.41805e7			−1.36952			−0.684758	−	0.728770i	$-0.740092\pi$
$101$	−1.41805e7			−1.36952			−0.684758	+	0.728770i	$0.740092\pi$
$102$	3.63289e6	+	5.00024e6i	0.338962	+	0.466542i
$103$	7.59593e6	+	2.46807e6i	0.684937	+	0.222550i	0.630756	−	0.775982i	$-0.282745\pi$
$103$	7.59593e6	+	2.46807e6i	0.684937	+	0.222550i	0.0541815	+	0.998531i	$0.482745\pi$
$104$	4.10011e6	−	1.26188e7i	0.357420	−	1.10003i
$105$	−1.21775e7	−	9.79963e6i	−1.02659	−	0.826128i
$106$	7.96209e6	+	2.45048e7i	0.649317	+	1.99839i
$107$			8.81119e6i			0.695331i	0.937619	+	0.347665i	$0.113026\pi$
$107$			8.81119e6i			0.695331i	−0.937619	+	0.347665i	$0.886974\pi$
$108$	−2.31970e7	+	7.53717e6i	−1.77194	+	0.575739i
$109$	−5.11227e6	−	3.71428e6i	−0.378112	−	0.274715i	0.382455	−	0.923974i	$-0.375079\pi$
$109$	−5.11227e6	−	3.71428e6i	−0.378112	−	0.274715i	−0.760567	+	0.649260i	$0.775079\pi$
$110$	1.67046e7	−	2.07580e7i	1.19664	−	1.48700i
$111$	8.98646e6	−	6.52905e6i	0.623675	−	0.453126i
$112$	−8.45578e6	+	1.16384e7i	−0.568710	+	0.782762i
$113$	−1.02183e7	+	1.40643e7i	−0.666200	+	0.916945i	−0.999667	−	0.0258166i	$-0.991781\pi$
$113$	−1.02183e7	+	1.40643e7i	−0.666200	+	0.916945i	0.333467	+	0.942762i	$0.391781\pi$
$114$	3.05454e7	−	2.21925e7i	1.93099	−	1.40294i
$115$	−1.82906e7	+	4.96096e6i	−1.12146	+	0.304175i
$116$	−1.63234e7	−	1.18596e7i	−0.970974	−	0.705454i
$117$	−623919.	+	202723.i	−0.0360145	+	0.0117018i
$118$			1.17669e7i			0.659286i
$119$	2.40518e6	+	7.40238e6i	0.130838	+	0.402677i
$120$	−1.07814e7	+	2.83454e7i	−0.569561	+	1.49743i
$121$	1.50361e6	−	4.62762e6i	0.0771588	−	0.237470i
$122$	2.79631e7	+	9.08576e6i	1.39420	+	0.453004i
$123$	1.64878e7	+	2.26936e7i	0.798906	+	1.09960i
$124$	7.46960e7			3.51821
$125$	1.93648e7	−	1.00918e7i	0.886802	−	0.462149i
$126$	2.52085e6			0.112266
$127$	−6.45368e6	−	8.88273e6i	−0.279573	−	0.384799i	0.646020	−	0.763321i	$-0.276432\pi$
$127$	−6.45368e6	−	8.88273e6i	−0.279573	−	0.384799i	−0.925592	+	0.378522i	$0.876432\pi$
$128$	−4.09873e7	−	1.33176e7i	−1.72749	−	0.561294i
$129$	−4.86454e6	+	1.49715e7i	−0.199516	+	0.614047i
$130$	1.12546e7	−	2.95896e7i	0.449293	−	1.18124i
$131$	−1.31123e7	−	4.03556e7i	−0.509601	−	1.56839i	−0.792895	−	0.609358i	$-0.791427\pi$
$131$	−1.31123e7	−	4.03556e7i	−0.509601	−	1.56839i	0.283294	−	0.959033i	$-0.408573\pi$
$132$			5.80043e7i			2.19508i
$133$	4.52196e7	−	1.46927e7i	1.66665	−	0.541529i
$134$	−2.85441e7	−	2.07385e7i	−1.02482	−	0.744578i
$135$	−2.68399e7	+	7.27981e6i	−0.938886	+	0.254655i
$136$	1.22169e7	−	8.87610e6i	0.416462	−	0.302577i
$137$	1.30937e7	−	1.80220e7i	0.435052	−	0.598798i	−0.534051	−	0.845452i	$-0.679331\pi$
$137$	1.30937e7	−	1.80220e7i	0.435052	−	0.598798i	0.969104	+	0.246654i	$0.0793311\pi$
$138$	3.69116e7	−	5.08045e7i	1.19560	−	1.64561i
$139$	−3.96268e7	+	2.87906e7i	−1.25152	+	0.909282i	−0.998309	−	0.0581296i	$-0.981486\pi$
$139$	−3.96268e7	+	2.87906e7i	−1.25152	+	0.909282i	−0.253210	+	0.967411i	$0.581486\pi$
$140$	−5.01045e7	+	6.22624e7i	−1.54322	+	1.91769i
$141$	−4.11658e7	−	2.99087e7i	−1.23672	−	0.898527i
$142$	−5.15143e7	+	1.67380e7i	−1.50980	+	0.490562i
$143$		−	2.89348e7i		−	0.827455i
$144$	−426446.	−	1.31247e6i	−0.0119013	−	0.0366285i
$145$	−1.79224e7	−	1.44228e7i	−0.488213	−	0.392880i
$146$	6.77055e6	−	2.08376e7i	0.180048	−	0.554132i
$147$	2.44798e7	+	7.95397e6i	0.635619	+	0.206525i
$148$	−3.33823e7	−	4.59468e7i	−0.846449	−	1.16504i
$149$	−1.81489e7			−0.449466			−0.224733	−	0.974420i	$-0.572151\pi$
$149$	−1.81489e7			−0.449466			−0.224733	+	0.974420i	$0.572151\pi$
$150$	−2.90258e7	+	6.62814e7i	−0.702206	+	1.60351i
$151$	3.99960e7			0.945360			0.472680	−	0.881234i	$-0.343287\pi$
$151$	3.99960e7			0.945360			0.472680	+	0.881234i	$0.343287\pi$
$152$	−5.42222e7	−	7.46305e7i	−1.25235	−	1.72371i
$153$	−710098.	−	230725.i	−0.0160287	−	0.00520804i
$154$	−3.43580e7	+	1.05743e8i	−0.758063	+	2.33308i
$155$	8.50626e7	+	4.19704e6i	1.83475	+	0.0905278i
$156$	2.12967e7	+	6.55444e7i	0.449133	+	1.38229i
$157$			5.68720e7i			1.17287i	0.809996	+	0.586435i	$0.199469\pi$
$157$			5.68720e7i			1.17287i	−0.809996	+	0.586435i	$0.800531\pi$
$158$	−1.00973e8	+	3.28080e7i	−2.03659	+	0.661729i
$159$	−5.17394e7	−	3.75909e7i	−1.02078	−	0.741639i
$160$	−1.34274e7	−	5.10722e6i	−0.259163	−	0.0985746i
$161$	6.39785e7	−	4.64831e7i	1.20821	−	0.877818i
$162$	5.69432e7	−	7.83756e7i	1.05230	−	1.44837i
$163$	−6.03573e6	+	8.30746e6i	−0.109162	+	0.150249i	−0.860103	−	0.510121i	$-0.829601\pi$
$163$	−6.03573e6	+	8.30746e6i	−0.109162	+	0.150249i	0.750940	+	0.660370i	$0.229601\pi$
$164$	1.16030e8	−	8.43006e7i	2.05407	−	1.49237i
$165$	−3.25916e6	+	6.60544e7i	−0.0564823	+	1.14474i
$166$	3.33402e7	+	2.42231e7i	0.565706	+	0.411009i
$167$	8.49703e7	−	2.76085e7i	1.41176	−	0.458707i	0.498782	−	0.866727i	$-0.333781\pi$
$167$	8.49703e7	−	2.76085e7i	1.41176	−	0.458707i	0.912973	+	0.408020i	$0.133781\pi$
$168$		−	1.26549e8i		−	2.05909i
$169$	8.76676e6	+	2.69813e7i	0.139713	+	0.429991i
$170$	3.01575e7	−	1.97159e7i	0.470787	−	0.307784i
$171$	−1.40945e6	+	4.33784e6i	−0.0215557	+	0.0663417i
$172$	7.65478e7	+	2.48719e7i	1.14705	+	0.372700i
$173$	2.05301e6	+	2.82573e6i	0.0301461	+	0.0414925i	0.823824	−	0.566846i	$-0.191836\pi$
$173$	2.05301e6	+	2.82573e6i	0.0301461	+	0.0414925i	−0.793678	+	0.608338i	$0.791836\pi$
$174$	7.62299e7			1.09699
$175$	−6.05566e7	+	6.80882e7i	−0.854139	+	0.960370i
$176$	6.08668e7			0.841563
$177$	−1.71672e7	−	2.36286e7i	−0.232698	−	0.320281i
$178$	1.09656e8	+	3.56293e7i	1.45734	+	0.473518i
$179$	−2.70305e7	+	8.31913e7i	−0.352264	+	1.08416i	0.605315	+	0.795986i	$0.293047\pi$
$179$	−2.70305e7	+	8.31913e7i	−0.352264	+	1.08416i	−0.957579	+	0.288171i	$0.906953\pi$
$180$	−2.00688e6	−	7.39917e6i	−0.0256489	−	0.0945648i
$181$	−4.13725e6	−	1.27331e7i	−0.0518605	−	0.159610i	0.921772	−	0.387732i	$-0.126741\pi$
$181$	−4.13725e6	−	1.27331e7i	−0.0518605	−	0.159610i	−0.973633	+	0.228122i	$0.926741\pi$
$182$			1.32104e8i			1.62429i
$183$	−6.94072e7	+	2.25518e7i	−0.837193	+	0.272020i
$184$	−1.24129e8	−	9.01849e7i	−1.46896	−	1.06726i
$185$	−3.54336e7	−	5.41992e7i	−0.411447	−	0.629350i
$186$	−2.28311e8	+	1.65878e8i	−2.60155	+	1.89014i
$187$	1.93566e7	−	2.66421e7i	0.216463	−	0.297936i
$188$	−1.52920e8	+	2.10477e8i	−1.67847	+	2.31021i
$189$	9.38833e7	−	6.82102e7i	1.01151	−	0.734908i
$190$	−1.20440e8	−	1.84226e8i	−1.27390	−	1.94856i
$191$	7.04584e7	+	5.11910e7i	0.731671	+	0.531590i	0.890092	−	0.455782i	$-0.150640\pi$
$191$	7.04584e7	+	5.11910e7i	0.731671	+	0.531590i	−0.158421	+	0.987372i	$0.550640\pi$
$192$	1.17265e8	−	3.81016e7i	1.19567	−	0.388498i
$193$		−	8.67816e6i		−	0.0868915i	−0.999056	−	0.0434458i	$-0.986166\pi$
$193$		−	8.67816e6i		−	0.0868915i	0.999056	−	0.0434458i	$-0.0138336\pi$
$194$	2.93750e6	+	9.04071e6i	0.0288850	+	0.0888989i
$195$	2.05695e7	+	7.58375e7i	0.198656	+	0.732425i
$196$	4.06678e7	−	1.25163e8i	0.385793	−	1.18735i
$197$	−1.33296e8	−	4.33106e7i	−1.24218	−	0.403610i	−0.387070	−	0.922050i	$-0.626513\pi$
$197$	−1.33296e8	−	4.33106e7i	−1.24218	−	0.403610i	−0.855114	+	0.518440i	$0.826513\pi$
$198$	−6.26918e6	−	8.62879e6i	−0.0573962	−	0.0789990i
$199$	−1.87953e7			−0.169069			−0.0845344	−	0.996421i	$-0.526940\pi$
$199$	−1.87953e7			−0.169069			−0.0845344	+	0.996421i	$0.526940\pi$
$200$	1.61943e8	+	7.09176e7i	1.43139	+	0.626829i
$201$	8.75745e7			0.760661
$202$	−1.61009e8	−	2.21610e8i	−1.37442	−	1.89173i
$203$	9.12985e7	+	2.96647e7i	0.765998	+	0.248888i
$204$	−2.42383e7	+	7.45977e7i	−0.199892	+	0.615205i
$205$	1.36870e8	−	8.94807e7i	1.10961	−	0.725422i
$206$	4.76757e7	+	1.46731e8i	0.379981	+	1.16946i
$207$			7.58618e6i			0.0594466i
$208$	6.87790e7	−	2.23477e7i	0.529949	−	0.172191i
$209$	−1.62751e8	−	1.18245e8i	−1.23314	−	0.895926i
$210$	1.48799e7	−	3.01575e8i	0.110875	−	2.24713i
$211$	−1.42374e7	+	1.03441e7i	−0.104338	+	0.0758059i	−0.638731	−	0.769430i	$-0.720540\pi$
$211$	−1.42374e7	+	1.03441e7i	−0.104338	+	0.0758059i	0.534393	+	0.845236i	$0.320540\pi$
$212$	−1.92198e8	+	2.64538e8i	−1.38540	+	1.90683i
$213$	7.90240e7	−	1.08767e8i	0.560313	−	0.771204i
$214$	−1.37699e8	+	1.00044e8i	−0.960470	+	0.697822i
$215$	8.57739e7	+	3.26248e7i	0.588601	+	0.223879i
$216$	−1.82149e8	−	1.32339e8i	−1.22981	−	0.893511i
$217$	−3.37993e8	+	1.09821e8i	−2.24543	+	0.729584i
$218$		−	1.22066e8i		−	0.797991i
$219$	1.68052e7	+	5.17210e7i	0.108116	+	0.332746i
$220$	3.37729e8	+	1.66637e7i	2.13840	+	0.105510i
$221$	1.20910e7	−	3.72123e7i	0.0753510	−	0.231907i
$222$	2.04069e8	+	6.63060e7i	1.25182	+	0.406741i
$223$	1.35074e8	+	1.85914e8i	0.815654	+	1.12265i	0.990426	+	0.138042i	$0.0440809\pi$
$223$	1.35074e8	+	1.85914e8i	0.815654	+	1.12265i	−0.174773	+	0.984609i	$0.555919\pi$
$224$	5.99471e7			0.356369
$225$	−1.86966e6	−	8.53882e6i	−0.0109427	−	0.0499757i
$226$	−3.35815e8			−1.93518
$227$	6.84191e7	+	9.41709e7i	0.388228	+	0.534350i	0.957741	−	0.287632i	$-0.0928681\pi$
$227$	6.84191e7	+	9.41709e7i	0.388228	+	0.534350i	−0.569513	+	0.821983i	$0.692868\pi$
$228$	4.55702e8	+	1.48066e8i	2.54629	+	0.827341i
$229$	8.77986e7	−	2.70216e8i	0.483129	−	1.48692i	−0.351543	−	0.936172i	$-0.614343\pi$
$229$	8.77986e7	−	2.70216e8i	0.483129	−	1.48692i	0.834672	−	0.550747i	$-0.185657\pi$
$230$	−2.85204e8	−	2.29513e8i	−1.54564	−	1.24383i
$231$	−8.52800e7	−	2.62465e8i	−0.455203	−	1.40097i
$232$		−	1.86250e8i		−	0.979237i
$233$	1.78471e7	−	5.79887e6i	0.0924319	−	0.0300330i	−0.262436	−	0.964949i	$-0.584526\pi$
$233$	1.78471e7	−	5.79887e6i	0.0924319	−	0.0300330i	0.354868	+	0.934916i	$0.384526\pi$
$234$	−1.02522e7	−	7.44869e6i	−0.0523074	−	0.0380036i
$235$	−1.85969e8	+	2.31095e8i	−0.934768	+	1.16159i
$236$	−1.20811e8	+	8.77740e7i	−0.598291	+	0.434684i
$237$	1.54894e8	−	2.13194e8i	0.755816	−	1.04029i
$238$	−8.83738e7	+	1.21636e8i	−0.424917	+	0.584848i
$239$	7.82191e7	−	5.68295e7i	0.370613	−	0.269266i	−0.386852	−	0.922142i	$-0.626438\pi$
$239$	7.82191e7	−	5.68295e7i	0.370613	−	0.269266i	0.757465	+	0.652876i	$0.226438\pi$
$240$	−1.59531e8	+	4.32696e7i	−0.744912	+	0.202043i
$241$	−2.47492e7	−	1.79814e7i	−0.113894	−	0.0827490i	0.529380	−	0.848385i	$-0.322425\pi$
$241$	−2.47492e7	−	1.79814e7i	−0.113894	−	0.0827490i	−0.643274	+	0.765636i	$0.722425\pi$
$242$	8.93918e7	−	2.90452e7i	0.405456	−	0.131741i
$243$			2.28644e7i			0.102221i
$244$	1.15305e8	+	3.54872e8i	0.508139	+	1.56389i
$245$	5.33445e7	−	1.40248e8i	0.231744	−	0.609278i
$246$	−1.67443e8	+	5.15337e8i	−0.717124	+	2.20708i
$247$	−2.27322e8	−	7.38613e7i	−0.959846	−	0.311873i
$248$	4.05284e8	+	5.57825e8i	1.68724	+	2.32229i
$249$	−1.02289e8			−0.419887
$250$	3.77584e8	+	1.88044e8i	1.52835	+	0.761148i
$251$	1.68168e7			0.0671250			0.0335625	−	0.999437i	$-0.489315\pi$
$251$	1.68168e7			0.0671250			0.0335625	+	0.999437i	$0.489315\pi$
$252$	1.88040e7	+	2.58816e7i	0.0740201	+	0.101880i
$253$	−3.18221e8	−	1.03396e8i	−1.23540	−	0.401405i
$254$	6.55407e7	−	2.01713e8i	0.250953	−	0.772355i
$255$	−3.17937e7	+	8.35888e7i	−0.120074	+	0.315688i
$256$	−1.55539e8	−	4.78699e8i	−0.579426	−	1.78329i
$257$			7.78631e7i			0.286132i	0.989713	+	0.143066i	$0.0456961\pi$
$257$			7.78631e7i			0.286132i	−0.989713	+	0.143066i	$0.954304\pi$
$258$	−2.89205e8	+	9.39684e7i	−1.04842	+	0.340653i
$259$	2.18605e8	+	1.58826e8i	0.781827	+	0.568031i
$260$	3.87749e8	−	1.05170e8i	1.36818	−	0.371093i
$261$	−7.45009e6	+	5.41281e6i	−0.0259370	+	0.0188443i
$262$	4.81788e8	−	6.63124e8i	1.65501	−	2.27793i
$263$	6.21676e7	−	8.55663e7i	0.210726	−	0.290040i	−0.690550	−	0.723285i	$-0.742631\pi$
$263$	6.21676e7	−	8.55663e7i	0.210726	−	0.290040i	0.901276	+	0.433245i	$0.142631\pi$
$264$	−4.33172e8	+	3.14718e8i	−1.44893	+	1.05271i
$265$	−2.33736e8	+	2.90453e8i	−0.771553	+	0.958771i
$266$	7.43049e8	+	5.39857e8i	2.42065	+	1.75870i
$267$	−2.72176e8	+	8.84353e7i	−0.875105	+	0.284339i
$268$		−	4.47759e8i		−	1.42093i
$269$	−6.66028e7	−	2.04982e8i	−0.208622	−	0.642072i	−0.999545	−	0.0301565i	$-0.990399\pi$
$269$	−6.66028e7	−	2.04982e8i	−0.208622	−	0.642072i	0.790924	−	0.611915i	$-0.209601\pi$
$270$	−4.18514e8	−	3.36792e8i	−1.29401	−	1.04133i
$271$	−1.55346e8	+	4.78107e8i	−0.474142	+	1.45926i	0.372968	+	0.927844i	$0.378340\pi$
$271$	−1.55346e8	+	4.78107e8i	−0.474142	+	1.45926i	−0.847111	+	0.531416i	$0.821660\pi$
$272$	7.82792e7	+	2.54344e7i	0.235860	+	0.0766357i
$273$	−1.92731e8	−	2.65272e8i	−0.573301	−	0.789082i
$274$	4.30313e8			1.26374
$275$	3.83664e8	+	3.79528e7i	1.11247	+	0.110047i
$276$	7.96949e8			2.28165
$277$	3.14688e8	+	4.33131e8i	0.889614	+	1.22445i	0.973664	+	0.227987i	$0.0732142\pi$
$277$	3.14688e8	+	4.33131e8i	0.889614	+	1.22445i	−0.0840506	+	0.996461i	$0.526786\pi$
$278$	−8.99865e8	−	2.92384e8i	−2.51201	−	0.816200i
$279$	1.05349e7	−	3.24231e7i	0.0290413	−	0.0893800i
$280$	−7.36828e8	−	3.63555e7i	−2.00592	−	0.0989731i
$281$	9.01889e7	+	2.77573e8i	0.242483	+	0.746285i	0.996040	+	0.0889031i	$0.0283362\pi$
$281$	9.01889e7	+	2.77573e8i	0.242483	+	0.746285i	−0.753558	+	0.657382i	$0.771664\pi$
$282$		−	9.82922e8i		−	2.61004i
$283$	4.09406e8	−	1.33024e8i	1.07375	−	0.348881i	0.281801	−	0.959473i	$-0.409068\pi$
$283$	4.09406e8	−	1.33024e8i	1.07375	−	0.348881i	0.791946	+	0.610592i	$0.209068\pi$
$284$	−5.56115e8	−	4.04041e8i	−1.44062	−	1.04667i
$285$	5.10626e8	+	1.94221e8i	1.30661	+	0.496980i
$286$	4.52187e8	−	3.28533e8i	1.14297	−	0.830420i
$287$	−4.01084e8	+	5.52045e8i	−1.00149	+	1.37844i
$288$	−3.38013e6	+	4.65235e6i	−0.00833796	+	0.0114762i
$289$	−2.95944e8	+	2.15016e8i	−0.721219	+	0.523996i
$290$	2.18997e7	−	4.43848e8i	0.0527285	−	1.06866i
$291$	−1.90885e7	−	1.38686e7i	−0.0454096	−	0.0329920i
$292$	2.64444e8	−	8.59231e7i	0.621576	−	0.201962i
$293$		−	1.14368e8i		−	0.265624i	−0.991141	−	0.132812i	$-0.957599\pi$
$293$		−	1.14368e8i		−	0.265624i	0.991141	−	0.132812i	$-0.0424006\pi$
$294$	1.53647e8	+	4.72876e8i	0.352621	+	1.08525i
$295$	−1.42509e8	+	9.31675e7i	−0.323195	+	0.211294i
$296$	1.62003e8	−	4.98594e8i	0.363080	−	1.11745i
$297$	−4.66963e8	−	1.51726e8i	−1.03427	−	0.336056i
$298$	−2.06067e8	−	2.83626e8i	−0.451077	−	0.620854i
$299$	−3.97549e8			−0.860086
$300$	−8.97027e8	+	1.96413e8i	−1.91814	+	0.419997i
$301$	−3.82940e8			−0.809372
$302$	4.54125e8	+	6.25049e8i	0.948748	+	1.30584i
$303$	6.46632e8	+	2.10103e8i	1.33539	+	0.433894i
$304$	1.55374e8	−	4.78191e8i	0.317190	−	0.976211i
$305$	1.11368e8	+	4.10601e8i	0.224755	+	0.828649i
$306$	−4.45691e6	−	1.37170e7i	−0.00889219	−	0.0273674i
$307$		−	7.10850e7i		−	0.140215i	−0.997539	−	0.0701073i	$-0.977666\pi$
$307$		−	7.10850e7i		−	0.140215i	0.997539	−	0.0701073i	$-0.0223342\pi$
$308$	−1.34195e9	+	4.36027e8i	−2.61704	+	0.850328i
$309$	−3.09807e8	−	2.25088e8i	−0.597360	−	0.434008i
$310$	9.00231e8	+	1.37699e9i	1.71628	+	2.62522i
$311$	2.04195e8	−	1.48356e8i	0.384932	−	0.279669i	−0.378444	−	0.925624i	$-0.623541\pi$
$311$	2.04195e8	−	1.48356e8i	0.384932	−	0.279669i	0.763375	+	0.645955i	$0.223541\pi$
$312$	−3.73930e8	+	5.14671e8i	−0.697027	+	0.959376i
$313$	2.69013e7	−	3.70264e7i	0.0495870	−	0.0682506i	−0.783503	−	0.621387i	$-0.786569\pi$
$313$	2.69013e7	−	3.70264e7i	0.0495870	−	0.0682506i	0.833090	+	0.553137i	$0.186569\pi$
$314$	−8.88783e8	+	6.45739e8i	−1.62010	+	1.17707i
$315$	1.99595e7	+	3.05301e7i	0.0359802	+	0.0550352i
$316$	−1.09004e9	−	7.91958e8i	−1.94328	−	1.41188i
$317$	−2.92506e8	+	9.50409e7i	−0.515736	+	0.167573i	−0.555309	−	0.831644i	$-0.687400\pi$
$317$	−2.92506e8	+	9.50409e7i	−0.515736	+	0.167573i	0.0395736	+	0.999217i	$0.487400\pi$
$318$		−	1.23539e9i		−	2.15431i
$319$	−1.25512e8	−	3.86286e8i	−0.216480	−	0.666257i
$320$	−1.88158e8	−	6.93717e8i	−0.320994	−	1.18347i
$321$	1.30550e8	−	4.01791e8i	0.220297	−	0.678004i
$322$	1.45286e9	+	4.72061e8i	2.42508	+	0.787958i
$323$	−1.59898e8	−	2.20081e8i	−0.264019	−	0.363391i
$324$	1.22945e9			2.00818
$325$	4.47472e8	−	9.79784e7i	0.723060	−	0.158321i
$326$	−1.98358e8			−0.317095
$327$	1.78087e8	+	2.45116e8i	0.281654	+	0.387664i
$328$	1.25910e9	+	4.09107e8i	1.97017	+	0.640146i
$329$	3.82501e8	−	1.17722e9i	0.592171	−	1.82252i
$330$	−1.06929e9	+	6.99064e8i	−1.63793	+	1.07082i
$331$	−2.77862e8	−	8.55170e8i	−0.421144	−	1.29615i	−0.906639	−	0.421908i	$-0.861360\pi$
$331$	−2.77862e8	−	8.55170e8i	−0.421144	−	1.29615i	0.485495	−	0.874240i	$-0.338640\pi$
$332$			5.22994e8i			0.784357i
$333$	−2.46522e7	+	8.00998e6i	−0.0365848	+	0.0118871i
$334$	1.39623e9	+	1.01442e9i	2.05043	+	1.48973i
$335$	2.51588e7	−	5.09901e8i	0.0365623	−	0.741018i
$336$	5.58022e8	−	4.05427e8i	0.802535	−	0.583076i
$337$	−4.02568e8	+	5.54087e8i	−0.572973	+	0.788630i	−0.992903	−	0.118926i	$-0.962055\pi$
$337$	−4.02568e8	+	5.54087e8i	−0.572973	+	0.788630i	0.419930	+	0.907557i	$0.362055\pi$
$338$	−3.22118e8	+	4.43357e8i	−0.453739	+	0.624519i
$339$	6.74336e8	−	4.89934e8i	0.940108	−	0.683028i
$340$	4.27381e8	+	1.62558e8i	0.589710	+	0.224301i
$341$	1.21648e9	+	8.83824e8i	1.66136	+	1.20705i
$342$	−8.37940e7	+	2.72263e7i	−0.113272	+	0.0368042i
$343$		−	3.34400e8i		−	0.447443i
$344$	2.29589e8	+	7.06604e8i	0.304087	+	0.935883i
$345$	9.07553e8	+	4.47792e7i	1.18989	+	0.0587097i
$346$	−2.08495e7	+	6.41681e7i	−0.0270601	+	0.0832823i
$347$	−4.46097e8	−	1.44946e8i	−0.573160	−	0.186231i	0.00807399	−	0.999967i	$-0.497430\pi$
$347$	−4.46097e8	−	1.44946e8i	−0.573160	−	0.186231i	−0.581234	+	0.813736i	$0.697430\pi$
$348$	5.68631e8	+	7.82653e8i	0.723274	+	0.995501i
$349$	2.85995e8			0.360138			0.180069	−	0.983654i	$-0.442368\pi$
$349$	2.85995e8			0.360138			0.180069	+	0.983654i	$0.442368\pi$
$350$	−1.75164e9	−	1.73276e8i	−2.18377	−	0.216023i
$351$	−5.83372e8			−0.720063
$352$	−1.49084e8	−	2.05197e8i	−0.182193	−	0.250768i
$353$	5.58409e8	+	1.81438e8i	0.675680	+	0.219542i	0.626703	−	0.779258i	$-0.284404\pi$
$353$	5.58409e8	+	1.81438e8i	0.675680	+	0.219542i	0.0489769	+	0.998800i	$0.484404\pi$
$354$	1.74342e8	−	5.36570e8i	0.208877	−	0.642858i
$355$	−6.10593e8	−	4.91363e8i	−0.724357	−	0.582912i
$356$	4.52161e8	+	1.39161e9i	0.531151	+	1.63471i
$357$		−	3.73185e8i		−	0.434095i
$358$	−1.60701e9	+	5.22148e8i	−1.85109	+	0.601455i
$359$	1.30254e9	+	9.46350e8i	1.48580	+	1.07950i	0.975630	+	0.219423i	$0.0704176\pi$
$359$	1.30254e9	+	9.46350e8i	1.48580	+	1.07950i	0.510170	+	0.860073i	$0.329582\pi$
$360$	4.43677e7	−	5.51335e7i	0.0501196	−	0.0622812i
$361$	−6.21270e8	+	4.51379e8i	−0.695033	+	0.504971i
$362$	1.52015e8	−	2.09231e8i	0.168425	−	0.231818i
$363$	−1.37129e8	+	1.88742e8i	−0.150472	+	0.207107i
$364$	−1.35631e9	+	9.85415e8i	−1.47402	+	1.07094i
$365$	3.05973e8	−	8.29892e7i	0.329350	−	0.0893299i
$366$	−1.14050e9	−	8.28622e8i	−1.21594	−	0.883431i
$367$	1.15592e9	−	3.75582e8i	1.22067	−	0.396619i	0.373343	−	0.927694i	$-0.378212\pi$
$367$	1.15592e9	−	3.75582e8i	1.22067	−	0.396619i	0.847325	+	0.531075i	$0.178212\pi$
$368$		−	8.36279e8i		−	0.874750i
$369$	−2.02277e7	−	6.22543e7i	−0.0209582	−	0.0645026i
$370$	4.44692e8	−	1.16914e9i	0.456408	−	1.19994i
$371$	4.80748e8	−	1.47959e9i	0.488775	−	1.50429i
$372$	−3.40614e9	−	1.10672e9i	−3.43054	−	1.11465i
$373$	−4.29544e8	−	5.91216e8i	−0.428575	−	0.589883i	0.539051	−	0.842273i	$-0.318783\pi$
$373$	−4.29544e8	−	5.91216e8i	−0.428575	−	0.589883i	−0.967625	+	0.252391i	$0.918783\pi$
$374$	6.36136e8			0.628781
$375$	−1.03256e9	+	1.73270e8i	−1.01112	+	0.169673i
$376$	−2.40154e9			−2.32987
$377$	−2.83655e8	−	3.90418e8i	−0.272644	−	0.375262i
$378$	2.13195e9	+	6.92712e8i	2.03028	+	0.659677i
$379$	6.01024e7	−	1.84976e8i	0.0567094	−	0.174533i	−0.918690	−	0.394980i	$-0.870751\pi$
$379$	6.01024e7	−	1.84976e8i	0.0567094	−	0.174533i	0.975399	+	0.220447i	$0.0707515\pi$
$380$	9.93031e8	−	2.61078e9i	0.928368	−	2.44077i
$381$	1.62678e8	+	5.00673e8i	0.150693	+	0.463785i
$382$			1.68234e9i			1.54416i
$383$	−7.37645e8	+	2.39675e8i	−0.670890	+	0.217985i	−0.624603	−	0.780943i	$-0.714739\pi$
$383$	−7.37645e8	+	2.39675e8i	−0.670890	+	0.217985i	−0.0462876	+	0.998928i	$0.514739\pi$
$384$	1.67170e9	+	1.21456e9i	1.50661	+	1.09461i
$385$	−1.55270e9	+	4.21139e8i	−1.38667	+	0.376108i
$386$	1.35620e8	−	9.85340e7i	0.120024	−	0.0872028i
$387$	2.15922e7	−	2.97191e7i	0.0189369	−	0.0260644i
$388$	−7.09089e7	+	9.75977e7i	−0.0616297	+	0.0848259i
$389$	−2.34075e8	+	1.70065e8i	−0.201619	+	0.146485i	−0.684014	−	0.729469i	$-0.739767\pi$
$389$	−2.34075e8	+	1.70065e8i	−0.201619	+	0.146485i	0.482395	+	0.875954i	$0.339767\pi$
$390$	−9.51621e8	+	1.18253e9i	−0.812340	+	1.00946i
$391$	−3.66049e8	−	2.65950e8i	−0.309685	−	0.224999i
$392$	1.15536e9	−	3.75399e8i	0.968760	−	0.314769i
$393$			2.03449e9i			1.69076i
$394$	−8.36630e8	−	2.57488e9i	−0.689123	−	2.12090i
$395$	−1.19682e9	−	9.63117e8i	−0.977098	−	0.786301i
$396$	4.18274e7	−	1.28731e8i	0.0338476	−	0.104172i
$397$	7.04556e8	+	2.28924e8i	0.565131	+	0.183622i	0.577628	−	0.816300i	$-0.303978\pi$
$397$	7.04556e8	+	2.28924e8i	0.565131	+	0.183622i	−0.0124977	+	0.999922i	$0.503978\pi$
$398$	−2.13407e8	−	2.93729e8i	−0.169675	−	0.233537i
$399$	−2.27971e9			−1.79669
$400$	2.06106e8	+	9.41296e8i	0.161020	+	0.735387i
$401$	1.54153e9			1.19384			0.596922	−	0.802299i	$-0.296390\pi$
$401$	1.54153e9			1.19384			0.596922	+	0.802299i	$0.296390\pi$
$402$	9.94342e8	+	1.36859e9i	0.763387	+	1.05071i
$403$	1.69911e9	+	5.52076e8i	1.29317	+	0.420176i
$404$	1.07424e9	−	3.30616e9i	0.810523	−	2.49453i
$405$	1.40007e9	+	6.90804e7i	1.04727	+	0.0516728i
$406$	5.73033e8	+	1.76361e9i	0.424950	+	1.30786i
$407$		−	1.14327e9i		−	0.840558i
$408$	−6.88603e8	+	2.23741e8i	−0.501947	+	0.163093i
$409$	−3.91794e8	−	2.84655e8i	−0.283156	−	0.205725i	0.437137	−	0.899395i	$-0.355993\pi$
$409$	−3.91794e8	−	2.84655e8i	−0.283156	−	0.205725i	−0.720293	+	0.693670i	$0.755993\pi$
$410$	2.95244e9	+	1.12298e9i	2.11562	+	0.804692i
$411$	−8.64094e8	+	6.27801e8i	−0.613924	+	0.446042i
$412$	−1.15085e9	+	1.58401e9i	−0.810735	+	1.11588i
$413$	4.17609e8	−	5.74790e8i	0.291706	−	0.401499i
$414$	−1.18555e8	+	8.61354e7i	−0.0821144	+	0.0596596i
$415$	−2.93862e7	+	5.95578e8i	−0.0201825	+	0.409044i
$416$	−2.43804e8	−	1.77134e8i	−0.166040	−	0.120635i
$417$	2.23356e9	−	7.25726e8i	1.50841	−	0.490113i
$418$		−	3.88602e9i		−	2.60249i
$419$	7.56143e8	+	2.32717e9i	0.502174	+	1.54553i	0.805469	+	0.592637i	$0.201913\pi$
$419$	7.56143e8	+	2.32717e9i	0.502174	+	1.54553i	−0.303295	+	0.952897i	$0.598087\pi$
$420$	3.20727e9	−	2.09680e9i	2.11233	−	1.38097i
$421$	1.48274e8	−	4.56341e8i	0.0968452	−	0.298059i	−0.890885	−	0.454229i	$-0.849915\pi$
$421$	1.48274e8	−	4.56341e8i	0.0968452	−	0.298059i	0.987730	+	0.156170i	$0.0499148\pi$
$422$	−3.23310e8	−	1.05050e8i	−0.209423	−	0.0680458i
$423$	6.97937e7	+	9.60628e7i	0.0448358	+	0.0617112i
$424$	−3.01838e9			−1.92306
$425$	4.77561e8	+	2.09132e8i	0.301764	+	0.132148i
$426$	2.59705e9			1.62759
$427$	−1.04349e9	−	1.43624e9i	−0.648620	−	0.892749i
$428$	−2.05431e9	−	6.67487e8i	−1.26652	−	0.411519i
$429$	−4.28708e8	+	1.31943e9i	−0.262157	+	0.806836i
$430$	4.64045e8	+	1.71089e9i	0.281463	+	1.03772i
$431$	−3.16446e8	−	9.73920e8i	−0.190383	−	0.585939i	0.809616	−	0.586960i	$-0.199675\pi$
$431$	−3.16446e8	−	9.73920e8i	−0.190383	−	0.585939i	−0.999999	+	0.00102021i	$0.999675\pi$
$432$		−	1.22717e9i		−	0.732340i
$433$	−1.18446e9	+	3.84853e8i	−0.701151	+	0.227818i	−0.637832	−	0.770175i	$-0.720169\pi$
$433$	−1.18446e9	+	3.84853e8i	−0.701151	+	0.227818i	−0.0633192	+	0.997993i	$0.520169\pi$
$434$	−5.55391e9	−	4.03515e9i	−3.26126	−	2.36944i
$435$	6.03572e8	+	9.23223e8i	0.351574	+	0.537767i
$436$	1.25325e9	−	9.10542e8i	0.724163	−	0.526135i
$437$	−1.62463e9	+	2.23611e9i	−0.931258	+	1.28177i
$438$	−6.17475e8	+	8.49881e8i	−0.351123	+	0.483280i
$439$	−2.37671e9	+	1.72678e9i	−1.34076	+	0.974119i	−0.341345	+	0.939938i	$0.610882\pi$
$439$	−2.37671e9	+	1.72678e9i	−1.34076	+	0.974119i	−0.999416	+	0.0341812i	$0.989118\pi$
$440$	1.70800e9	+	2.61255e9i	0.955879	+	1.46211i
$441$	−4.85934e7	−	3.53052e7i	−0.0269800	−	0.0196021i
$442$	7.18829e8	−	2.33562e8i	0.395957	−	0.128654i
$443$			1.17463e9i			0.641932i	0.947091	+	0.320966i	$0.104008\pi$
$443$			1.17463e9i			0.641932i	−0.947091	+	0.320966i	$0.895992\pi$
$444$	8.41471e8	+	2.58978e9i	0.456245	+	1.40418i
$445$	4.36721e8	+	1.61015e9i	0.234933	+	0.866174i
$446$	−1.37175e9	+	4.22182e9i	−0.732157	+	2.25335i
$447$	8.27588e8	+	2.68900e8i	0.438266	+	0.142401i
$448$	1.76299e9	+	2.42655e9i	0.926356	+	1.27502i
$449$	−5.09638e8			−0.265705			−0.132852	−	0.991136i	$-0.542414\pi$
$449$	−5.09638e8			−0.265705			−0.132852	+	0.991136i	$0.542414\pi$
$450$	1.12214e8	−	1.26171e8i	0.0580503	−	0.0652701i
$451$	2.88710e9			1.48199
$452$	−2.50498e9	−	3.44781e9i	−1.27591	−	1.75614i
$453$	−1.82382e9	−	5.92595e8i	−0.921803	−	0.299512i
$454$	−6.94834e8	+	2.13848e9i	−0.348486	+	1.07253i
$455$	−1.59991e9	+	1.04597e9i	−0.796261	+	0.520568i
$456$	1.36678e9	+	4.20653e9i	0.675030	+	2.07753i
$457$		−	6.17481e8i		−	0.302634i	−0.988485	−	0.151317i	$-0.951649\pi$
$457$		−	6.17481e8i		−	0.302634i	0.988485	−	0.151317i	$-0.0483513\pi$
$458$	5.21977e9	−	1.69601e9i	2.53876	−	0.824894i
$459$	−5.37147e8	−	3.90260e8i	−0.259268	−	0.188369i
$460$	2.28951e8	−	4.64022e9i	0.109671	−	2.22273i
$461$	−1.94238e9	+	1.41122e9i	−0.923381	+	0.670875i	−0.944363	−	0.328905i	$-0.893321\pi$
$461$	−1.94238e9	+	1.41122e9i	−0.923381	+	0.670875i	0.0209825	+	0.999780i	$0.493321\pi$
$462$	3.13345e9	−	4.31283e9i	1.47835	−	2.03477i
$463$	2.28298e9	−	3.14225e9i	1.06898	−	1.47132i	0.197867	−	0.980229i	$-0.436599\pi$
$463$	2.28298e9	−	3.14225e9i	1.06898	−	1.47132i	0.871109	−	0.491090i	$-0.163401\pi$
$464$	8.21277e8	−	5.96693e8i	0.381660	−	0.277292i
$465$	−3.81667e9	−	1.45170e9i	−1.76035	−	0.669564i
$466$	2.93264e8	+	2.13069e8i	0.134248	+	0.0975369i
$467$	3.57611e9	−	1.16195e9i	1.62481	−	0.527932i	0.651737	−	0.758445i	$-0.274040\pi$
$467$	3.57611e9	−	1.16195e9i	1.62481	−	0.527932i	0.973069	+	0.230513i	$0.0740404\pi$
$468$		−	1.60823e8i		−	0.0725248i
$469$	6.58311e8	+	2.02607e9i	0.294663	+	0.906881i
$470$	−5.72305e9	−	2.82378e8i	−2.54264	−	0.125455i
$471$	8.42635e8	−	2.59336e9i	0.371592	−	1.14364i
$472$	−1.31098e9	−	4.25964e8i	−0.573852	−	0.186456i
$473$	9.52347e8	+	1.31079e9i	0.413791	+	0.569535i
$474$	5.09045e9			2.19549
$475$	1.27754e9	−	2.91732e9i	0.546950	−	1.24898i
$476$	−1.90805e9			−0.810898
$477$	8.77205e7	+	1.20737e8i	0.0370072	+	0.0509361i
$478$	1.77624e9	+	5.77135e8i	0.743881	+	0.241702i
$479$	4.00597e8	−	1.23291e9i	0.166546	−	0.512575i	−0.832601	−	0.553873i	$-0.813149\pi$
$479$	4.00597e8	−	1.23291e9i	0.166546	−	0.512575i	0.999147	+	0.0412980i	$0.0131493\pi$
$480$	5.36620e8	+	4.31835e8i	0.221474	+	0.178227i
$481$	−4.19758e8	−	1.29188e9i	−0.171985	−	0.529317i
$482$		−	5.90940e8i		−	0.240369i
$483$	−3.60613e9	+	1.17170e9i	−1.45622	+	0.473154i
$484$	9.65017e8	+	7.01126e8i	0.386880	+	0.281085i
$485$	−8.62338e7	+	1.07159e8i	−0.0343227	+	0.0426511i
$486$	−3.57321e8	+	2.59609e8i	−0.141199	+	0.102587i
$487$	1.19180e8	−	1.64037e8i	0.0467574	−	0.0643560i	−0.784998	−	0.619498i	$-0.787336\pi$
$487$	1.19180e8	−	1.64037e8i	0.0467574	−	0.0643560i	0.831756	+	0.555142i	$0.187336\pi$
$488$	−2.02454e9	+	2.78654e9i	−0.788601	+	1.08542i
$489$	3.98316e8	−	2.89393e8i	0.154045	−	0.111920i
$490$	2.79745e9	−	7.58756e8i	1.07418	−	0.291350i
$491$	5.63976e8	+	4.09753e8i	0.215018	+	0.156220i	0.690081	−	0.723732i	$-0.257575\pi$
$491$	5.63976e8	+	4.09753e8i	0.215018	+	0.156220i	−0.475063	+	0.879952i	$0.657575\pi$
$492$	−6.53999e9	+	2.12497e9i	−2.47571	+	0.804406i
$493$		−	5.49240e8i		−	0.206442i
$494$	−1.42678e9	−	4.39117e9i	−0.532491	−	1.63884i
$495$	5.48656e7	−	1.44247e8i	0.0203321	−	0.0534551i
$496$	−1.16134e9	+	3.57423e9i	−0.427340	+	1.31522i
$497$	3.11041e9	+	1.01063e9i	1.13650	+	0.369272i
$498$	−1.16142e9	−	1.59855e9i	−0.421392	−	0.579996i
$499$	4.45992e8			0.160685			0.0803425	−	0.996767i	$-0.474399\pi$
$499$	4.45992e8			0.160685			0.0803425	+	0.996767i	$0.474399\pi$
$500$	8.85909e8	+	5.27935e9i	0.316952	+	1.88880i
$501$	−4.28370e9			−1.52190
$502$	1.90942e8	+	2.62809e8i	0.0673655	+	0.0927206i
$503$	−2.19199e9	−	7.12221e8i	−0.767982	−	0.249532i	−0.101281	−	0.994858i	$-0.532294\pi$
$503$	−2.19199e9	−	7.12221e8i	−0.767982	−	0.249532i	−0.666701	+	0.745325i	$0.732294\pi$
$504$	−9.12553e7	+	2.80855e8i	−0.0317506	+	0.0977182i
$505$	1.40909e9	−	3.70464e9i	0.486877	−	1.28005i
$506$	−1.99730e9	−	6.14707e9i	−0.685358	−	2.10931i
$507$		−	1.36024e9i		−	0.463540i
$508$	2.55989e9	−	8.31758e8i	0.866359	−	0.281497i
$509$	−1.32451e8	−	9.62316e7i	−0.0445189	−	0.0323449i	0.565303	−	0.824883i	$-0.308759\pi$
$509$	−1.32451e8	−	9.62316e7i	−0.0445189	−	0.0323449i	−0.609822	+	0.792538i	$0.708759\pi$
$510$	−1.66730e9	+	4.52223e8i	−0.556568	+	0.150958i
$511$	−1.07026e9	+	7.77591e8i	−0.354827	+	0.257797i
$512$	2.47253e9	−	3.40315e9i	0.814137	−	1.12056i
$513$	−2.38402e9	+	3.28132e9i	−0.779648	+	1.07309i
$514$	−1.21683e9	+	8.84077e8i	−0.395238	+	0.287157i
$515$	−1.39957e9	+	1.73918e9i	−0.451513	+	0.561073i
$516$	−3.12207e9	−	2.26832e9i	−1.00039	−	0.726825i
$517$	−4.98084e9	+	1.61837e9i	−1.58521	+	0.515065i
$518$			5.21966e9i			1.65002i
$519$	−5.17505e7	−	1.59272e8i	−0.0162491	−	0.0500095i
$520$	2.88924e9	+	2.32506e9i	0.901098	+	0.725141i
$521$	−2.12648e8	+	6.54463e8i	−0.0658763	+	0.202746i	−0.978577	−	0.205883i	$-0.933993\pi$
$521$	−2.12648e8	+	6.54463e8i	−0.0658763	+	0.202746i	0.912700	+	0.408630i	$0.133993\pi$
$522$	−1.69180e8	−	5.49700e7i	−0.0520599	−	0.0169153i
$523$	−6.97747e8	−	9.60366e8i	−0.213276	−	0.293549i	0.688953	−	0.724806i	$-0.258070\pi$
$523$	−6.97747e8	−	9.60366e8i	−0.213276	−	0.293549i	−0.902229	+	0.431256i	$0.858070\pi$
$524$	1.04022e10			3.15837
$525$	3.77020e9	−	2.20759e9i	1.13712	−	0.665827i
$526$	2.04308e9			0.612118
$527$	1.19516e9	+	1.64499e9i	0.355703	+	0.489584i
$528$	−2.77553e9	−	9.01824e8i	−0.820592	−	0.266626i
$529$	−3.68462e8	+	1.13401e9i	−0.108218	+	0.333059i
$530$	−7.19303e9	−	3.54908e8i	−2.09868	−	0.103550i
$531$	2.10611e7	+	6.48194e7i	0.00610450	+	0.0187877i
$532$			1.16559e10i			3.35625i
$533$	3.26240e9	−	1.06002e9i	0.933237	−	0.303227i
$534$	−4.47240e9	−	3.24939e9i	−1.27100	−	0.923437i
$535$	−2.30191e9	−	8.75552e8i	−0.649907	−	0.247197i
$536$	3.34384e9	−	2.42944e9i	0.937925	−	0.681443i
$537$	2.46518e9	−	3.39303e9i	0.686972	−	0.945536i
$538$	2.44719e9	−	3.36827e9i	0.677533	−	0.932544i
$539$	2.14327e9	−	1.55717e9i	0.589543	−	0.428328i
$540$	3.35968e8	−	6.80916e9i	0.0918162	−	1.86087i
$541$	3.97151e9	+	2.88547e9i	1.07836	+	0.783477i	0.977397	−	0.211413i	$-0.0678066\pi$
$541$	3.97151e9	+	2.88547e9i	1.07836	+	0.783477i	0.100966	+	0.994890i	$0.467807\pi$
$542$	−9.23560e9	+	3.00083e9i	−2.49154	+	0.809550i
$543$			6.41930e8i			0.172063i
$544$	−1.05988e8	−	3.26196e8i	−0.0282266	−	0.0868726i
$545$	1.47835e9	−	9.66493e8i	0.391191	−	0.255747i
$546$	1.95729e9	−	6.02393e9i	0.514614	−	1.58382i
$547$	3.33366e9	+	1.08317e9i	0.870895	+	0.282971i	0.710172	−	0.704029i	$-0.248617\pi$
$547$	3.33366e9	+	1.08317e9i	0.870895	+	0.282971i	0.160723	+	0.987000i	$0.448617\pi$
$548$	3.20988e9	+	4.41802e9i	0.833215	+	1.14682i
$549$	1.70301e8			0.0439251
$550$	3.76310e9	+	6.42674e9i	0.964442	+	1.64711i
$551$	−3.35519e9			−0.854450
$552$	4.32407e9	+	5.95157e9i	1.09422	+	1.50607i
$553$	6.09669e9	+	1.98094e9i	1.53305	+	0.498118i
$554$	−3.19583e9	+	9.83576e9i	−0.798546	+	2.45767i
$555$	8.12738e8	+	2.99648e9i	0.201802	+	0.744023i
$556$	−3.71056e9	−	1.14199e10i	−0.915541	−	2.81775i
$557$			8.42430e8i			0.206557i	0.994652	+	0.103279i	$0.0329333\pi$
$557$			8.42430e8i			0.206557i	−0.994652	+	0.103279i	$0.967067\pi$
$558$	6.26317e8	−	2.03503e8i	0.152607	−	0.0495851i
$559$	1.55741e9	+	1.13153e9i	0.377105	+	0.273983i
$560$	−2.20028e9	−	3.36555e9i	−0.529444	−	0.809837i
$561$	−1.27740e9	+	9.28086e8i	−0.305462	+	0.221931i
$562$	−3.31382e9	+	4.56108e9i	−0.787502	+	1.08390i
$563$	3.46026e9	−	4.76264e9i	0.817202	−	1.12478i	−0.172970	−	0.984927i	$-0.555336\pi$
$563$	3.46026e9	−	4.76264e9i	0.817202	−	1.12478i	0.990172	−	0.139855i	$-0.0446636\pi$
$564$	1.00917e10	−	7.33202e9i	2.36857	−	1.72086i
$565$	−2.65891e9	−	4.06706e9i	−0.620203	−	0.948662i
$566$	6.72737e9	+	4.88772e9i	1.55951	+	1.13305i
$567$	−5.56314e9	+	1.80757e9i	−1.28168	+	0.416443i
$568$		−	6.34527e9i		−	1.45288i
$569$	1.42294e9	+	4.37935e9i	0.323812	+	0.996590i	0.971974	+	0.235088i	$0.0755378\pi$
$569$	1.42294e9	+	4.37935e9i	0.323812	+	0.996590i	−0.648162	+	0.761502i	$0.724462\pi$
$570$	2.76254e9	+	1.01852e10i	0.624807	+	2.30360i
$571$	−9.10034e8	+	2.80080e9i	−0.204565	+	0.629586i	0.795166	+	0.606392i	$0.207384\pi$
$571$	−9.10034e8	+	2.80080e9i	−0.204565	+	0.629586i	−0.999731	+	0.0231945i	$0.992616\pi$
$572$	6.74609e9	+	2.19194e9i	1.50718	+	0.489714i
$573$	−2.45444e9	−	3.37825e9i	−0.545019	−	0.750154i
$574$	−1.31812e10			−2.90914
$575$	5.21452e8	−	5.27135e9i	0.114387	−	1.15634i
$576$	−2.87726e8			−0.0627336
$577$	−1.59944e9	−	2.20144e9i	−0.346620	−	0.477081i	0.599741	−	0.800195i	$-0.295270\pi$
$577$	−1.59944e9	−	2.20144e9i	−0.346620	−	0.477081i	−0.946360	+	0.323113i	$0.895270\pi$
$578$	−6.72044e9	−	2.18360e9i	−1.44761	−	0.470356i
$579$	−1.28579e8	+	3.95725e8i	−0.0275292	+	0.0847263i
$580$	4.72034e9	−	3.08600e9i	1.00456	−	0.656746i
$581$	−7.68925e8	−	2.36651e9i	−0.162655	−	0.500601i
$582$		−	4.55780e8i		−	0.0958351i
$583$	−6.26019e9	+	2.03406e9i	−1.30842	+	0.425132i
$584$	2.07648e9	+	1.50865e9i	0.431403	+	0.313433i
$585$	9.03635e6	−	1.83142e8i	0.00186615	−	0.0378219i
$586$	1.78731e9	−	1.29856e9i	0.366910	−	0.266575i
$587$	−4.79014e8	+	6.59306e8i	−0.0977496	+	0.134541i	−0.855090	−	0.518479i	$-0.826498\pi$
$587$	−4.79014e8	+	6.59306e8i	−0.0977496	+	0.134541i	0.757341	+	0.653020i	$0.226498\pi$
$588$	−3.70890e9	+	5.10487e9i	−0.752359	+	1.03553i
$589$	1.00489e10	−	7.30096e9i	2.02636	−	1.47223i
$590$	−3.07408e9	−	1.16925e9i	−0.616217	−	0.234383i
$591$	5.43661e9	+	3.94993e9i	1.08336	+	0.787105i
$592$	2.71759e9	−	8.82998e8i	0.538341	−	0.174918i
$593$			6.22588e9i			1.22605i	0.790062	+	0.613026i	$0.210048\pi$
$593$			6.22588e9i			1.22605i	−0.790062	+	0.613026i	$0.789952\pi$
$594$	−2.93088e9	−	9.02033e9i	−0.573781	−	1.76591i
$595$	−2.17286e9	−	1.07210e8i	−0.422885	−	0.0208654i
$596$	1.37486e9	−	4.23137e9i	0.266008	−	0.818689i
$597$	8.57066e8	+	2.78478e8i	0.164856	+	0.0535649i
$598$	−4.51387e9	−	6.21281e9i	−0.863168	−	1.18805i
$599$	5.27144e9			1.00216			0.501078	−	0.865402i	$-0.332937\pi$
$599$	5.27144e9			1.00216			0.501078	+	0.865402i	$0.332937\pi$
$600$	−6.33387e9	−	5.63325e9i	−1.19712	−	1.06471i
$601$	3.72132e9			0.699256			0.349628	−	0.936889i	$-0.386308\pi$
$601$	3.72132e9			0.699256			0.349628	+	0.936889i	$0.386308\pi$
$602$	−4.34800e9	−	5.98451e9i	−0.812272	−	1.11800i
$603$	−1.94358e8	−	6.31507e7i	−0.0360987	−	0.0117292i
$604$	−3.02987e9	+	9.32499e9i	−0.559494	+	1.72194i
$605$	1.05955e9	+	8.52654e8i	0.194526	+	0.156541i
$606$	4.05857e9	+	1.24910e10i	0.740830	+	2.28004i
$607$		−	7.03533e9i		−	1.27680i	−0.769703	−	0.638402i	$-0.779596\pi$
$607$		−	7.03533e9i		−	1.27680i	0.769703	−	0.638402i	$-0.220404\pi$
$608$	−1.99266e9	+	6.47456e8i	−0.359560	+	0.116828i
$609$	−3.72369e9	−	2.70542e9i	−0.668056	−	0.485371i
$610$	−5.15228e9	+	6.40249e9i	−0.919063	+	1.14208i
$611$	−5.03411e9	+	3.65750e9i	−0.892850	+	0.648694i
$612$	1.07586e8	−	1.48080e8i	0.0189726	−	0.0261135i
$613$	−4.90033e9	+	6.74472e9i	−0.859238	+	1.18264i	0.122513	+	0.992467i	$0.460905\pi$
$613$	−4.90033e9	+	6.74472e9i	−0.859238	+	1.18264i	−0.981751	+	0.190173i	$0.939095\pi$
$614$	1.11090e9	−	8.07116e8i	0.193680	−	0.140717i
$615$	−7.56703e9	+	2.05241e9i	−1.31179	+	0.355797i
$616$	−1.05374e10	−	7.65585e9i	−1.81635	−	1.31966i
$617$	9.02366e9	−	2.93196e9i	1.54662	−	0.502528i	0.593429	−	0.804886i	$-0.297774\pi$
$617$	9.02366e9	−	2.93196e9i	1.54662	−	0.502528i	0.953195	+	0.302358i	$0.0977737\pi$
$618$		−	7.39730e9i		−	1.26070i
$619$	1.87932e8	+	5.78395e8i	0.0318481	+	0.0980182i	0.965717	−	0.259597i	$-0.0835898\pi$
$619$	1.87932e8	+	5.78395e8i	0.0318481	+	0.0980182i	−0.933869	+	0.357616i	$0.883590\pi$
$620$	−7.42240e9	+	1.95142e10i	−1.25076	+	3.28837i
$621$	−2.08463e9	+	6.41584e9i	−0.349308	+	1.07506i
$622$	4.63696e9	+	1.50664e9i	0.772622	+	0.251040i
$623$	−4.09198e9	−	5.63213e9i	−0.677993	−	0.933178i
$624$	−3.46744e9			−0.571298
$625$	7.12221e8	+	6.06182e9i	0.116690	+	0.993168i
$626$	8.84085e8			0.144040
$627$	5.66948e9	+	7.80337e9i	0.918558	+	1.26429i
$628$	−1.32596e10	−	4.30831e9i	−2.13635	−	0.694141i
$629$	4.77738e8	−	1.47033e9i	0.0765442	−	0.235579i
$630$	−2.50492e8	+	6.58569e8i	−0.0399119	+	0.104932i
$631$	−1.38385e9	−	4.25905e9i	−0.219274	−	0.674855i	−0.998823	−	0.0485135i	$-0.984552\pi$
$631$	−1.38385e9	−	4.25905e9i	−0.219274	−	0.674855i	0.779549	−	0.626341i	$-0.215448\pi$
$632$		−	1.24373e10i		−	1.95982i
$633$	8.02487e8	−	2.60744e8i	0.125755	−	0.0408603i
$634$	−4.80646e9	−	3.49210e9i	−0.749054	−	0.544219i
$635$	2.96189e9	−	8.03357e8i	0.459051	−	0.124509i
$636$	1.26837e10	−	9.21527e9i	1.95500	−	1.42039i
$637$	1.85015e9	−	2.54651e9i	0.283608	−	0.390352i
$638$	4.61170e9	−	6.34746e9i	0.703054	−	0.967671i
$639$	−2.53814e8	+	1.84407e8i	−0.0384825	+	0.0279592i
$640$	7.55204e9	−	9.38455e9i	1.13877	−	1.41509i
$641$	−2.85721e9	−	2.07588e9i	−0.428488	−	0.311315i	0.352556	−	0.935791i	$-0.385313\pi$
$641$	−2.85721e9	−	2.07588e9i	−0.428488	−	0.311315i	−0.781044	+	0.624476i	$0.785313\pi$
$642$	7.76139e9	−	2.52183e9i	1.15762	−	0.376134i
$643$		−	8.75492e9i		−	1.29871i	−0.760483	−	0.649357i	$-0.775038\pi$
$643$		−	8.75492e9i		−	1.29871i	0.760483	−	0.649357i	$-0.224962\pi$
$644$	5.99080e9	+	1.84378e10i	0.883861	+	2.72024i
$645$	−3.42791e9	−	2.75855e9i	−0.503003	−	0.404782i
$646$	1.62385e9	−	4.99771e9i	0.236992	−	0.729385i
$647$	−1.08828e10	−	3.53605e9i	−1.57971	−	0.513278i	−0.617727	−	0.786393i	$-0.711946\pi$
$647$	−1.08828e10	−	3.53605e9i	−1.57971	−	0.513278i	−0.961982	+	0.273114i	$0.911946\pi$
$648$	6.67069e9	+	9.18142e9i	0.963071	+	1.32555i
$649$	−3.00606e9			−0.431659
$650$	6.61189e9	+	5.88052e9i	0.944341	+	0.839884i
$651$	1.70396e10			2.42062
$652$	−1.47964e9	−	2.03655e9i	−0.209068	−	0.287758i
$653$	2.21248e9	+	7.18879e8i	0.310945	+	0.101032i	0.460332	−	0.887747i	$-0.347730\pi$
$653$	2.21248e9	+	7.18879e8i	0.310945	+	0.101032i	−0.149388	+	0.988779i	$0.547730\pi$
$654$	−1.80858e9	+	5.56622e9i	−0.252822	+	0.778106i
$655$	1.18458e10	+	5.84479e8i	1.64710	+	0.0812689i
$656$	2.22984e9	+	6.86274e9i	0.308397	+	0.949149i
$657$		−	1.26905e8i		−	0.0174582i
$658$	2.27403e10	−	7.38878e9i	3.11176	−	1.01107i
$659$	1.00530e10	+	7.30390e9i	1.36834	+	0.994159i	0.997864	+	0.0653184i	$0.0208063\pi$
$659$	1.00530e10	+	7.30390e9i	1.36834	+	0.994159i	0.370479	+	0.928841i	$0.379194\pi$
$660$	−1.51536e10	−	5.76378e9i	−2.05169	−	0.780375i
$661$	−1.16236e10	+	8.44507e9i	−1.56544	+	1.13736i	−0.634079	+	0.773268i	$0.718621\pi$
$661$	−1.16236e10	+	8.44507e9i	−1.56544	+	1.13736i	−0.931363	+	0.364092i	$0.881379\pi$
$662$	1.02095e10	−	1.40522e10i	1.36773	−	1.88252i
$663$	−1.10270e9	+	1.51774e9i	−0.146947	+	0.202255i
$664$	−3.90569e9	+	2.83765e9i	−0.517737	+	0.376158i
$665$	−6.54925e8	+	1.32735e10i	−0.0863606	+	1.75030i
$666$	−4.05085e8	−	2.94312e8i	−0.0531357	−	0.0386054i
$667$	−5.30738e9	+	1.72447e9i	−0.692531	+	0.225017i
$668$			2.19021e10i			2.84295i
$669$	−3.40483e9	−	1.04790e10i	−0.439647	−	1.35309i
$670$	8.25428e9	−	5.39636e9i	1.06027	−	0.693169i
$671$	−2.32112e9	+	7.14367e9i	−0.296598	+	0.912835i
$672$	−2.73359e9	−	8.88196e8i	−0.347489	−	0.112906i
$673$	−7.18966e9	−	9.89571e9i	−0.909191	−	1.25139i	−0.967442	−	0.253093i	$-0.918552\pi$
$673$	−7.18966e9	−	9.89571e9i	−0.909191	−	1.25139i	0.0582506	−	0.998302i	$-0.481448\pi$
$674$	−1.32300e10			−1.66437
$675$	7.65190e8	−	7.73528e9i	0.0957648	−	0.968084i
$676$	−6.95476e9			−0.865902
$677$	−6.67083e9	−	9.18161e9i	−0.826266	−	1.13726i	−0.988607	−	0.150522i	$-0.951904\pi$
$677$	−6.67083e9	−	9.18161e9i	−0.826266	−	1.13726i	0.162341	−	0.986735i	$-0.448096\pi$
$678$	1.53132e10	+	4.97555e9i	1.88695	+	0.613108i
$679$	1.77365e8	−	5.45875e8i	0.0217433	−	0.0669189i
$680$	1.10490e9	+	4.07366e9i	0.134754	+	0.496825i
$681$	−1.72465e9	−	5.30792e9i	−0.209259	−	0.644034i
$682$			2.90460e10i			3.50624i
$683$	7.49767e9	−	2.43614e9i	0.900438	−	0.292570i	0.178020	−	0.984027i	$-0.443031\pi$
$683$	7.49767e9	−	2.43614e9i	0.900438	−	0.292570i	0.722418	+	0.691457i	$0.243031\pi$
$684$	−9.04586e8	−	6.57221e8i	−0.108082	−	0.0785262i
$685$	3.40712e9	+	5.21153e9i	0.405015	+	0.619510i
$686$	5.22593e9	−	3.79686e9i	0.618058	−	0.449046i
$687$	−8.00724e9	+	1.10210e10i	−0.942180	+	1.29680i
$688$	−2.38026e9	+	3.27615e9i	−0.278654	+	0.383534i
$689$	−6.32714e9	+	4.59694e9i	−0.736954	+	0.535428i
$690$	9.60478e9	+	1.46915e10i	1.11305	+	1.70253i
$691$	2.47964e9	+	1.80156e9i	0.285900	+	0.207719i	0.721487	−	0.692428i	$-0.243459\pi$
$691$	2.47964e9	+	1.80156e9i	0.285900	+	0.207719i	−0.435587	+	0.900147i	$0.643459\pi$
$692$	−8.14339e8	+	2.64595e8i	−0.0934187	+	0.0303536i
$693$			6.43995e8i			0.0735049i
$694$	−2.79991e9	−	8.61725e9i	−0.317970	−	0.978612i
$695$	−3.58386e9	−	1.32133e10i	−0.404953	−	1.49302i
$696$	−2.75954e9	+	8.49300e9i	−0.310245	+	0.954836i
$697$	3.71302e9	+	1.20643e9i	0.415349	+	0.134955i
$698$	3.24725e9	+	4.46946e9i	0.361428	+	0.497464i
$699$	−8.99746e8			−0.0996437
$700$	−1.12872e10	−	1.92766e10i	−1.24378	−	2.12416i
$701$	−1.36182e10			−1.49316			−0.746578	−	0.665298i	$-0.768305\pi$
$701$	−1.36182e10			−1.49316			−0.746578	+	0.665298i	$0.768305\pi$
$702$	−6.62375e9	−	9.11680e9i	−0.722643	−	0.994633i
$703$	−8.98191e9	−	2.91840e9i	−0.975046	−	0.316812i
$704$	3.92157e9	−	1.20694e10i	0.423600	−	1.30371i
$705$	1.19042e10	−	7.78256e9i	1.27949	−	0.836489i
$706$	3.50484e9	+	1.07868e10i	0.374845	+	1.15365i
$707$			1.65395e10i			1.76017i
$708$	6.80945e9	−	2.21253e9i	0.721100	−	0.234300i
$709$	−9.25229e9	−	6.72218e9i	−0.974961	−	0.708351i	−0.0183843	−	0.999831i	$-0.505852\pi$
$709$	−9.25229e9	−	6.72218e9i	−0.974961	−	0.708351i	−0.956577	+	0.291480i	$0.905852\pi$
$710$	7.46092e8	−	1.51213e10i	0.0782327	−	1.58556i
$711$	−4.97499e8	+	3.61454e8i	−0.0519097	+	0.0377146i
$712$	−7.93912e9	+	1.09273e10i	−0.824313	+	1.13457i
$713$	1.21433e10	−	1.67138e10i	1.25465	−	1.72688i
$714$	5.83205e9	−	4.23723e9i	0.599622	−	0.435651i
$715$	7.55918e9	+	2.87520e9i	0.773399	+	0.294169i
$716$	−1.73482e10	−	1.26042e10i	−1.76628	−	1.28328i
$717$	−4.40880e9	+	1.43251e9i	−0.446687	+	0.145137i
$718$			3.11009e10i			3.13572i
$719$	−1.54279e9	−	4.74821e9i	−0.154794	−	0.476408i	0.843346	−	0.537371i	$-0.180583\pi$
$719$	−1.54279e9	−	4.74821e9i	−0.154794	−	0.476408i	−0.998140	+	0.0609635i	$0.980583\pi$
$720$	3.85256e8	+	1.90087e7i	0.0384667	+	0.00189797i
$721$	2.87864e9	−	8.85954e9i	0.286031	−	0.880314i
$722$	−1.41081e10	−	4.58400e9i	−1.39505	−	0.453278i
$723$	8.62147e8	+	1.18664e9i	0.0848393	+	0.116771i
$724$	3.28212e9			0.321418
$725$	5.54885e9	−	3.24906e9i	0.540779	−	0.316646i
$726$	−4.50661e9			−0.437091
$727$	4.99893e9	+	6.88044e9i	0.482511	+	0.664119i	0.978985	−	0.203933i	$-0.0653723\pi$
$727$	4.99893e9	+	6.88044e9i	0.482511	+	0.664119i	−0.496474	+	0.868051i	$0.665372\pi$
$728$	−1.47180e10	−	4.78218e9i	−1.41381	−	0.459374i
$729$	−3.05057e9	+	9.38869e9i	−0.291632	+	0.897550i
$730$	4.77103e9	+	3.83939e9i	0.453923	+	0.365286i
$731$	6.77046e8	+	2.08373e9i	0.0641073	+	0.197302i
$732$		−	1.78905e10i		−	1.68591i
$733$	−1.75086e10	+	5.68889e9i	−1.64205	+	0.533536i	−0.976996	−	0.213256i	$-0.931593\pi$
$733$	−1.75086e10	+	5.68889e9i	−1.64205	+	0.533536i	−0.665058	+	0.746792i	$0.731593\pi$
$734$	1.89941e10	+	1.38001e10i	1.77290	+	1.28808i
$735$	−4.51048e9	+	5.60495e9i	−0.419002	+	0.520674i
$736$	−2.81930e9	+	2.04834e9i	−0.260657	+	0.189378i
$737$	5.29801e9	−	7.29209e9i	0.487503	−	0.670990i
$738$	7.43227e8	−	1.02296e9i	0.0680651	−	0.0936835i
$739$	−3.32831e9	+	2.41816e9i	−0.303367	+	0.220409i	−0.729045	−	0.684466i	$-0.760036\pi$
$739$	−3.32831e9	+	2.41816e9i	−0.303367	+	0.220409i	0.425678	+	0.904875i	$0.360036\pi$
$740$	1.53207e10	−	4.15544e9i	1.38985	−	0.376970i
$741$	9.27152e9	+	6.73616e9i	0.837119	+	0.608203i
$742$	2.85813e10	−	9.28661e9i	2.56843	−	0.834533i
$743$			1.11822e10i			1.00015i	0.865981	+	0.500076i	$0.166695\pi$
$743$			1.11822e10i			1.00015i	−0.865981	+	0.500076i	$0.833305\pi$
$744$	−1.02160e10	−	3.14417e10i	−0.909444	−	2.79898i
$745$	1.80342e9	−	4.74137e9i	0.159790	−	0.420104i
$746$	4.36225e9	−	1.34256e10i	0.384702	−	1.18399i
$747$	2.27015e8	+	7.37617e7i	0.0199266	+	0.00647454i
$748$	4.74520e9	+	6.53121e9i	0.414571	+	0.570609i
$749$	1.02770e10			0.893673
$750$	−1.44317e10	−	1.41692e10i	−1.24912	−	1.22640i
$751$	−2.63947e9			−0.227393			−0.113696	−	0.993516i	$-0.536269\pi$
$751$	−2.63947e9			−0.227393			−0.113696	+	0.993516i	$0.536269\pi$
$752$	−7.69386e9	−	1.05897e10i	−0.659754	−	0.908073i
$753$	−7.66844e8	−	2.49163e8i	−0.0654523	−	0.0212667i
$754$	2.88067e9	−	8.86580e9i	0.244734	−	0.753214i
$755$	−3.97433e9	+	1.04489e10i	−0.336085	+	0.883602i
$756$	8.79101e9	+	2.70559e10i	0.739967	+	2.27738i
$757$		−	1.51053e10i		−	1.26559i	−0.774318	−	0.632797i	$-0.781907\pi$
$757$		−	1.51053e10i		−	1.26559i	0.774318	−	0.632797i	$-0.218093\pi$
$758$	3.57319e9	−	1.16100e9i	0.297998	−	0.0968254i
$759$	1.29789e10	+	9.42974e9i	1.07744	+	0.782805i
$760$	2.48851e10	−	6.74960e9i	2.05632	−	0.557739i
$761$	−3.15415e9	+	2.29163e9i	−0.259440	+	0.188494i	−0.709900	−	0.704302i	$-0.751260\pi$
$761$	−3.15415e9	+	2.29163e9i	−0.259440	+	0.188494i	0.450460	+	0.892796i	$0.351260\pi$
$762$	−5.97731e9	+	8.22706e9i	−0.489399	+	0.673601i
$763$	−4.33216e9	+	5.96271e9i	−0.353077	+	0.485968i
$764$	−1.72726e10	+	1.25493e10i	−1.40130	+	1.01810i
$765$	1.30838e8	−	1.62586e8i	0.0105662	−	0.0131301i
$766$	−1.21210e10	−	8.80642e9i	−0.974400	−	0.707943i
$767$	−3.39682e9	+	1.10369e9i	−0.271825	+	0.0883212i
$768$			2.41332e10i			1.92243i
$769$	3.88321e9	+	1.19513e10i	0.307927	+	0.947703i	0.978569	+	0.205921i	$0.0660191\pi$
$769$	3.88321e9	+	1.19513e10i	0.307927	+	0.947703i	−0.670641	+	0.741782i	$0.733981\pi$
$770$	−2.42112e10	−	1.94835e10i	−1.91116	−	1.53797i
$771$	1.15365e9	−	3.55056e9i	0.0906531	−	0.279002i
$772$	2.02330e9	+	6.57409e8i	0.158270	+	0.0514251i
$773$	1.10837e10	+	1.52554e10i	0.863093	+	1.18795i	0.980823	+	0.194900i	$0.0624381\pi$
$773$	1.10837e10	+	1.52554e10i	0.863093	+	1.18795i	−0.117730	+	0.993046i	$0.537562\pi$
$774$	7.09606e8			0.0550078
$775$	−9.54898e9	+	2.18055e10i	−0.736887	+	1.68271i
$776$	−1.11359e9			−0.0855479
$777$	−7.61517e9	−	1.04814e10i	−0.582380	−	0.801577i
$778$	−5.31549e9	−	1.72711e9i	−0.404683	−	0.131489i
$779$	7.36985e9	−	2.26821e10i	0.558570	−	1.71910i
$780$	−1.92396e10	−	9.49293e8i	−1.45166	−	0.0716258i
$781$	−4.27602e9	−	1.31602e10i	−0.321189	−	0.988519i
$782$		−	8.74019e9i		−	0.653578i
$783$	−7.78815e9	+	2.53052e9i	−0.579786	+	0.188384i
$784$	5.35680e9	+	3.89194e9i	0.397008	+	0.288443i
$785$	−1.48577e10	−	5.65126e9i	−1.09625	−	0.416967i
$786$	−3.17946e10	+	2.31001e10i	−2.33547	+	1.69682i
$787$	−8.13118e9	+	1.11916e10i	−0.594623	+	0.818429i	−0.995203	−	0.0978332i	$-0.968809\pi$
$787$	−8.13118e9	+	1.11916e10i	−0.594623	+	0.818429i	0.400580	+	0.916262i	$0.368809\pi$
$788$	2.01956e10	−	2.77968e10i	1.47033	−	2.02373i
$789$	−4.10262e9	+	2.98073e9i	−0.297367	+	0.216049i
$790$	1.46241e9	−	2.96391e10i	0.105530	−	2.13880i
$791$	1.64039e10	+	1.19182e10i	1.17850	+	0.856232i
$792$	1.18830e9	−	3.86104e8i	0.0849943	−	0.0276163i
$793$			8.92450e9i			0.635518i
$794$	4.42213e9	+	1.36099e10i	0.313516	+	0.964903i
$795$	1.49618e10	−	9.78153e9i	1.05609	−	0.690434i
$796$	1.42383e9	−	4.38209e9i	0.100060	−	0.307954i
$797$	8.22606e8	+	2.67281e8i	0.0575556	+	0.0187010i	0.337653	−	0.941271i	$-0.390367\pi$
$797$	8.22606e8	+	2.67281e8i	0.0575556	+	0.0187010i	−0.280098	+	0.959972i	$0.590367\pi$
$798$	−2.58843e10	−	3.56267e10i	−1.80313	−	2.48180i
$799$	−7.08199e9			−0.491181
$800$	2.66851e9	−	3.00040e9i	0.184270	−	0.207188i
$801$	6.67823e8			0.0459143
$802$	1.75029e10	+	2.40907e10i	1.19812	+	1.64907i
$803$	5.32334e9	+	1.72966e9i	0.362810	+	0.117884i
$804$	−6.63415e9	+	2.04178e10i	−0.450183	+	1.38552i
$805$	5.78624e9	+	2.13333e10i	0.390940	+	1.44136i
$806$	1.06644e10	+	3.28218e10i	0.717407	+	2.20795i
$807$			1.03340e10i			0.692168i
$808$	3.05188e10	−	9.91615e9i	2.03530	−	0.661308i
$809$	−1.91580e10	−	1.39191e10i	−1.27212	−	0.924252i	−0.272838	−	0.962060i	$-0.587962\pi$
$809$	−1.91580e10	−	1.39191e10i	−1.27212	−	0.924252i	−0.999285	+	0.0378081i	$0.987962\pi$
$810$	1.48172e10	+	2.26644e10i	0.979644	+	1.49846i
$811$	1.59480e10	−	1.15869e10i	1.04986	−	0.762771i	0.0776775	−	0.996979i	$-0.475250\pi$
$811$	1.59480e10	−	1.15869e10i	1.04986	−	0.762771i	0.972187	+	0.234208i	$0.0752495\pi$
$812$	−1.38325e10	+	1.90388e10i	−0.906683	+	1.24794i
$813$	1.41676e10	−	1.95000e10i	0.924655	−	1.27268i
$814$	1.78667e10	−	1.29809e10i	1.16107	−	0.843570i
$815$	−1.57056e9	−	2.40232e9i	−0.101625	−	0.155446i
$816$	−3.19269e9	−	2.31962e9i	−0.205703	−	0.149452i
$817$	1.27291e10	−	4.13593e9i	0.816620	−	0.265336i
$818$		−	9.35491e9i		−	0.597589i
$819$	2.36447e8	+	7.27710e8i	0.0150397	+	0.0462876i
$820$	1.04938e10	+	3.86894e10i	0.664635	+	2.45044i
$821$	2.28049e8	−	7.01864e8i	0.0143823	−	0.0442641i	−0.943608	−	0.331065i	$-0.892592\pi$
$821$	2.28049e8	−	7.01864e8i	0.0143823	−	0.0442641i	0.957990	+	0.286801i	$0.0925919\pi$
$822$	−1.96223e10	−	6.37567e9i	−1.23225	−	0.400382i
$823$	−1.32224e9	−	1.81991e9i	−0.0826819	−	0.113802i	0.765673	−	0.643231i	$-0.222406\pi$
$823$	−1.32224e9	−	1.81991e9i	−0.0826819	−	0.113802i	−0.848354	+	0.529429i	$0.822406\pi$
$824$	−1.80735e10			−1.12538
$825$	−1.69328e10	−	7.41515e9i	−1.04988	−	0.459760i
$826$	1.37243e10			0.847347
$827$	−6.55664e8	−	9.02444e8i	−0.0403099	−	0.0554818i	0.788386	−	0.615181i	$-0.210917\pi$
$827$	−6.55664e8	−	9.02444e8i	−0.0403099	−	0.0554818i	−0.828696	+	0.559699i	$0.810917\pi$
$828$	−1.76870e9	−	5.74687e8i	−0.108280	−	0.0351824i
$829$	−4.96458e9	+	1.52794e10i	−0.302651	+	0.931464i	0.677892	+	0.735161i	$0.262894\pi$
$829$	−4.96458e9	+	1.52794e10i	−0.302651	+	0.931464i	−0.980543	+	0.196303i	$0.937106\pi$
$830$	−9.64122e9	+	6.30310e9i	−0.585273	+	0.382631i
$831$	−7.93237e9	−	2.44133e10i	−0.479512	−	1.47579i
$832$		−	1.50781e10i		−	0.907643i
$833$	3.40709e9	−	1.10703e9i	0.204233	−	0.0663594i
$834$	3.67018e10	+	2.66654e10i	2.19082	+	1.59172i
$835$	−1.23064e9	+	2.49418e10i	−0.0731525	+	1.48260i
$836$	3.98978e10	−	2.89874e10i	2.36171	−	1.71588i
$837$	1.78193e10	−	2.45262e10i	1.05039	−	1.44574i
$838$	−2.77830e10	+	3.82401e10i	−1.63089	+	2.24473i
$839$	−1.26030e10	+	9.15659e9i	−0.736726	+	0.535263i	−0.891684	−	0.452658i	$-0.850476\pi$
$839$	−1.26030e10	+	9.15659e9i	−0.736726	+	0.535263i	0.154958	+	0.987921i	$0.450476\pi$
$840$	3.30607e10	+	1.25749e10i	1.92457	+	0.732027i
$841$	8.47505e9	+	6.15748e9i	0.491311	+	0.356958i
$842$	8.81514e9	−	2.86421e9i	0.508905	−	0.165353i
$843$		−	1.39936e10i		−	0.804512i
$844$	−1.33316e9	−	4.10303e9i	−0.0763277	−	0.234913i
$845$	−7.91997e9	−	3.90776e8i	−0.451570	−	0.0222807i
$846$	−7.08793e8	+	2.18144e9i	−0.0402461	+	0.123865i
$847$	−5.39745e9	−	1.75374e9i	−0.305208	−	0.0991682i
$848$	−9.67005e9	−	1.33097e10i	−0.544557	−	0.749519i
$849$	−2.06399e10			−1.15752
$850$	2.15407e9	+	9.83775e9i	0.120308	+	0.549452i
$851$	−1.57079e10			−0.873706
$852$	1.93724e10	+	2.66639e10i	1.07311	+	1.47702i
$853$	2.63712e10	+	8.56851e9i	1.45482	+	0.472698i	0.926482	−	0.376339i	$-0.122817\pi$
$853$	2.63712e10	+	8.56851e9i	1.45482	+	0.472698i	0.528333	+	0.849037i	$0.322817\pi$
$854$	1.05972e10	−	3.26148e10i	0.582222	−	1.79190i
$855$	−9.93201e8	−	7.99260e8i	−0.0543445	−	0.0437327i
$856$	−6.16149e9	−	1.89631e10i	−0.335759	−	1.03336i
$857$		−	1.62107e10i		−	0.879771i	−0.898054	−	0.439885i	$-0.855019\pi$
$857$		−	1.62107e10i		−	0.879771i	0.898054	−	0.439885i	$-0.144981\pi$
$858$	−2.54874e10	+	8.28135e9i	−1.37759	+	0.447606i
$859$	1.58682e10	+	1.15289e10i	0.854184	+	0.620601i	0.926296	−	0.376796i	$-0.122974\pi$
$859$	1.58682e10	+	1.15289e10i	0.854184	+	0.620601i	−0.0721127	+	0.997396i	$0.522974\pi$
$860$	−1.41042e10	+	1.75266e10i	−0.756141	+	0.939619i
$861$	2.64687e10	−	1.92306e10i	1.41326	−	1.02679i
$862$	1.16272e10	−	1.60035e10i	0.618301	−	0.851018i
$863$	−1.39369e9	+	1.91825e9i	−0.0738124	+	0.101594i	−0.844327	−	0.535828i	$-0.819999\pi$
$863$	−1.39369e9	+	1.91825e9i	−0.0738124	+	0.101594i	0.770515	+	0.637422i	$0.219999\pi$
$864$	−4.13710e9	+	3.00578e9i	−0.218222	+	0.158547i
$865$	−9.42223e8	+	2.55560e8i	−0.0494991	+	0.0134257i
$866$	−1.94630e10	−	1.41407e10i	−1.01835	−	0.739876i
$867$	1.66808e10	−	5.41992e9i	0.869261	−	0.282440i
$868$		−	8.71219e10i		−	4.52177i
$869$	−8.38139e9	−	2.57953e10i	−0.433258	−	1.33343i
$870$	−7.57483e9	+	1.99150e10i	−0.389992	+	1.02533i
$871$	3.30937e9	−	1.01852e10i	0.169700	−	0.522283i
$872$	1.35998e10	+	4.41883e9i	0.694582	+	0.225683i
$873$	3.23632e7	+	4.45442e7i	0.00164627	+	0.00226590i
$874$	−5.33920e10			−2.70512
$875$	−1.17706e10	−	2.25861e10i	−0.593976	−	1.13976i
$876$	−1.33317e10			−0.670073
$877$	1.09541e10	+	1.50770e10i	0.548376	+	0.754775i	0.989791	−	0.142528i	$-0.0455231\pi$
$877$	1.09541e10	+	1.50770e10i	0.548376	+	0.754775i	−0.441414	+	0.897303i	$0.645523\pi$
$878$	−5.39716e10	−	1.75364e10i	−2.69113	−	0.874401i
$879$	−1.69451e9	+	5.21517e9i	−0.0841557	+	0.259005i
$880$	−6.04822e9	+	1.59014e10i	−0.299184	+	0.786585i
$881$	−6.49512e9	−	1.99899e10i	−0.320016	−	0.984908i	−0.973640	−	0.228089i	$-0.926752\pi$
$881$	−6.49512e9	−	1.99899e10i	−0.320016	−	0.984908i	0.653624	−	0.756819i	$-0.273248\pi$
$882$		−	1.16027e9i		−	0.0569402i
$883$	1.62641e10	−	5.28454e9i	0.795002	−	0.258312i	0.116769	−	0.993159i	$-0.462746\pi$
$883$	1.62641e10	−	5.28454e9i	0.795002	−	0.258312i	0.678233	+	0.734847i	$0.262746\pi$
$884$	7.76002e9	+	5.63798e9i	0.377816	+	0.274499i
$885$	7.87881e9	−	2.13698e9i	0.382084	−	0.103633i
$886$	−1.83569e10	+	1.33371e10i	−0.886709	+	0.644232i
$887$	−6.21708e9	+	8.55708e9i	−0.299126	+	0.411712i	−0.931952	−	0.362583i	$-0.881895\pi$
$887$	−6.21708e9	+	8.55708e9i	−0.299126	+	0.411712i	0.632826	+	0.774294i	$0.281895\pi$
$888$	−1.47747e10	+	2.03356e10i	−0.708065	+	0.974568i
$889$	−1.03604e10	+	7.52727e9i	−0.494562	+	0.359320i
$890$	−2.02044e10	+	2.51070e10i	−0.960683	+	1.19379i
$891$	2.00224e10	+	1.45472e10i	0.948298	+	0.688979i
$892$	−5.35779e10	+	1.74085e10i	−2.52760	+	0.821268i
$893$			4.32624e10i			2.03297i
$894$	5.19433e9	+	1.59865e10i	0.243136	+	0.748295i
$895$	−1.90477e10	−	1.53283e10i	−0.888099	−	0.714681i
$896$	−1.55330e10	+	4.78057e10i	−0.721402	+	2.22025i
$897$	1.81283e10	+	5.89023e9i	0.838654	+	0.272495i
$898$	−5.78656e9	−	7.96451e9i	−0.266657	−	0.367022i
$899$	2.50783e10			1.15117
$900$	2.13245e9	+	2.10946e8i	0.0975055	+	0.00964544i
$901$	−8.90103e9			−0.405418
$902$	3.27809e10	+	4.51190e10i	1.48730	+	2.04709i
$903$	1.74621e10	+	5.67378e9i	0.789203	+	0.256428i
$904$	1.21566e10	−	3.74141e10i	0.547295	−	1.68440i
$905$	3.73763e9	+	1.84417e8i	0.167620	+	0.00827048i
$906$	−1.14472e10	−	3.52307e10i	−0.511386	−	1.57388i
$907$		−	3.48613e10i		−	1.55138i	−0.631115	−	0.775690i	$-0.717402\pi$
$907$		−	3.48613e10i		−	1.55138i	0.631115	−	0.775690i	$-0.282598\pi$
$908$	−2.71388e10	+	8.81793e9i	−1.20307	+	0.390901i
$909$	−1.28359e9	−	9.32584e8i	−0.0566830	−	0.0411826i
$910$	−3.45119e10	−	1.31269e10i	−1.51818	−	0.577453i
$911$	6.29367e8	−	4.57262e8i	0.0275797	−	0.0200378i	−0.573910	−	0.818918i	$-0.694574\pi$
$911$	6.29367e8	−	4.57262e8i	0.0275797	−	0.0200378i	0.601490	+	0.798881i	$0.294574\pi$
$912$	−1.41701e10	+	1.95034e10i	−0.618572	+	0.851392i
$913$	−6.18822e9	+	8.51736e9i	−0.269103	+	0.370388i
$914$	9.64986e9	−	7.01103e9i	0.418032	−	0.303718i
$915$	1.00524e9	−	2.03735e10i	0.0433806	−	0.879207i
$916$	5.63493e10	+	4.09401e10i	2.42245	+	1.76001i
$917$	−4.70689e10	+	1.52936e10i	−2.01577	+	0.654964i
$918$		−	1.28255e10i		−	0.547174i
$919$	−3.59697e9	−	1.10703e10i	−0.152874	−	0.470496i	0.845066	−	0.534663i	$-0.179561\pi$
$919$	−3.59697e9	−	1.10703e10i	−0.152874	−	0.470496i	−0.997939	+	0.0641661i	$0.979561\pi$
$920$	3.58952e10	−	2.34670e10i	1.51977	−	0.993575i
$921$	−1.05322e9	+	3.24148e9i	−0.0444232	+	0.136721i
$922$	−4.41085e10	−	1.43317e10i	−1.85338	−	0.602199i
$923$	−9.66373e9	−	1.33010e10i	−0.404519	−	0.556773i
$924$	6.76535e10			2.82123
$925$	1.76805e10	−	3.87131e9i	0.734509	−	0.160828i
$926$	7.50278e10			3.10516
$927$	5.25255e8	+	7.22952e8i	0.0216566	+	0.0298078i
$928$	−4.02320e9	−	1.30722e9i	−0.165255	−	0.0536944i
$929$	5.14601e9	−	1.58378e10i	0.210579	−	0.648096i	−0.788859	−	0.614574i	$-0.789328\pi$
$929$	5.14601e9	−	1.58378e10i	0.210579	−	0.648096i	0.999438	−	0.0335216i	$-0.0106722\pi$
$930$	−2.06486e10	−	7.61291e10i	−0.841781	−	3.10356i
$931$	−6.76262e9	−	2.08132e10i	−0.274657	−	0.845308i
$932$			4.60031e9i			0.186136i
$933$	−1.15094e10	+	3.73963e9i	−0.463945	+	0.150745i
$934$	5.87627e10	+	4.26936e10i	2.35987	+	1.71454i
$935$	5.03679e9	+	7.70427e9i	0.201518	+	0.308241i
$936$	1.20101e9	−	8.72588e8i	0.0478721	−	0.0347811i
$937$	−8.88507e9	+	1.22293e10i	−0.352836	+	0.485637i	−0.948135	−	0.317867i	$-0.897033\pi$
$937$	−8.88507e9	+	1.22293e10i	−0.352836	+	0.485637i	0.595300	+	0.803504i	$0.297033\pi$
$938$	−2.41884e10	+	3.32925e10i	−0.956968	+	1.31715i
$939$	−1.77530e9	+	1.28983e9i	−0.0699747	+	0.0508396i
$940$	−3.97914e10	−	6.08649e10i	−1.56258	−	2.39012i
$941$	−1.54534e10	−	1.12276e10i	−0.604589	−	0.439260i	0.242916	−	0.970047i	$-0.421896\pi$
$941$	−1.54534e10	−	1.12276e10i	−0.604589	−	0.439260i	−0.847505	+	0.530788i	$0.821896\pi$
$942$	5.00960e10	−	1.62772e10i	1.95265	−	0.634455i
$943$		−	3.96673e10i		−	1.54043i
$944$	−2.32171e9	−	7.14550e9i	−0.0898270	−	0.276459i
$945$	8.49084e9	+	3.13048e10i	0.327295	+	1.20670i
$946$	−9.67161e9	+	2.97661e10i	−0.371432	+	1.14315i
$947$	3.87736e10	+	1.25983e10i	1.48358	+	0.482044i	0.935180	−	0.354173i	$-0.115237\pi$
$947$	3.87736e10	+	1.25983e10i	1.48358	+	0.482044i	0.548399	+	0.836217i	$0.315237\pi$
$948$	3.79718e10	+	5.22637e10i	1.44754	+	1.99237i
$949$	6.65039e9			0.252589
$950$	6.00967e10	−	1.31588e10i	2.27414	−	0.497947i
$951$	1.47464e10			0.555975
$952$	−1.03527e10	−	1.42492e10i	−0.388887	−	0.535257i
$953$	2.04801e10	+	6.65437e9i	0.766489	+	0.249047i	0.666061	−	0.745897i	$-0.267979\pi$
$953$	2.04801e10	+	6.65437e9i	0.766489	+	0.249047i	0.100428	+	0.994944i	$0.467979\pi$
$954$	−8.90849e8	+	2.74175e9i	−0.0332189	+	0.102237i
$955$	−2.03749e10	+	1.33204e10i	−0.756979	+	0.494887i
$956$	7.32425e9	+	2.25417e10i	0.271119	+	0.834420i
$957$			1.94743e10i			0.718240i
$958$	2.38161e10	−	7.73833e9i	0.875169	−	0.284360i
$959$	−2.10200e10	−	1.52719e10i	−0.769604	−	0.559150i
$960$	−1.69837e9	+	3.44213e10i	−0.0619559	+	1.25568i
$961$	−5.28524e10	+	3.83995e10i	−1.92102	+	1.39570i
$962$	1.54232e10	−	2.12283e10i	0.558551	−	0.768779i
$963$	−5.79469e8	+	7.97571e8i	−0.0209092	+	0.0287791i
$964$	6.06718e9	−	4.40807e9i	0.218131	−	0.158481i
$965$	2.26716e9	+	8.62333e8i	0.0812151	+	0.0308908i
$966$	−5.92560e10	−	4.30520e10i	−2.11501	−	1.53665i
$967$	−4.21928e10	+	1.37093e10i	−1.50053	+	0.487553i	−0.940173	−	0.340697i	$-0.889337\pi$
$967$	−4.21928e10	+	1.37093e10i	−1.50053	+	0.487553i	−0.560360	+	0.828249i	$0.689337\pi$
$968$			1.10108e10i			0.390173i
$969$	4.03057e9	+	1.24048e10i	0.142309	+	0.437982i
$970$	−2.65377e9	−	1.30939e8i	−0.0933603	−	0.00460645i
$971$	7.72539e9	−	2.37763e10i	0.270803	−	0.833445i	−0.719497	−	0.694496i	$-0.755627\pi$
$971$	7.72539e9	−	2.37763e10i	0.270803	−	0.833445i	0.990299	−	0.138950i	$-0.0443726\pi$
$972$	−5.33080e9	−	1.73208e9i	−0.186192	−	0.0604974i
$973$	3.35800e10	+	4.62189e10i	1.16865	+	1.60851i
$974$	3.91672e9			0.135821
$975$	−2.18564e10	−	2.16208e9i	−0.755201	−	0.0747060i
$976$	−1.87735e10			−0.646353
$977$	7.88517e9	+	1.08530e10i	0.270508	+	0.372322i	0.922561	−	0.385851i	$-0.126092\pi$
$977$	7.88517e9	+	1.08530e10i	0.270508	+	0.372322i	−0.652053	+	0.758173i	$0.726092\pi$
$978$	9.04515e9	+	2.93895e9i	0.309193	+	0.100463i
$979$	−9.10212e9	+	2.80135e10i	−0.310030	+	0.954173i
$980$	2.86575e10	+	2.30616e10i	0.972629	+	0.782705i
$981$	−2.18482e8	−	6.72418e8i	−0.00738880	−	0.0227404i
$982$			1.34661e10i			0.453787i
$983$	9.82130e9	−	3.19113e9i	0.329786	−	0.107154i	−0.139444	−	0.990230i	$-0.544532\pi$
$983$	9.82130e9	−	3.19113e9i	0.329786	−	0.107154i	0.469230	+	0.883076i	$0.344532\pi$
$984$	−5.13537e10	−	3.73106e10i	−1.71826	−	1.24839i
$985$	2.45602e10	−	3.05198e10i	0.818852	−	1.01755i
$986$	8.58340e9	−	6.23621e9i	0.285161	−	0.207182i
$987$	−3.48842e10	+	4.80139e10i	−1.15483	+	1.58949i
$988$	3.44413e10	−	4.74043e10i	1.13613	−	1.56375i
$989$	1.80096e10	−	1.30848e10i	0.591995	−	0.430109i
$990$	2.87722e9	−	7.80390e8i	0.0942431	−	0.0255616i
$991$	−2.55089e10	−	1.85333e10i	−0.832597	−	0.604917i	0.0876962	−	0.996147i	$-0.472050\pi$
$991$	−2.55089e10	−	1.85333e10i	−0.832597	−	0.604917i	−0.920293	+	0.391230i	$0.872050\pi$
$992$	1.48941e10	−	4.83940e9i	0.484423	−	0.157399i
$993$			4.31127e10i			1.39728i
$994$	1.95224e10	+	6.00838e10i	0.630495	+	1.94046i
$995$	1.86765e9	−	4.91025e9i	0.0601057	−	0.158024i
$996$	7.74887e9	−	2.38486e10i	0.248502	−	0.764812i
$997$	3.16668e10	+	1.02892e10i	1.01198	+	0.328812i	0.767642	−	0.640879i	$-0.221430\pi$
$997$	3.16668e10	+	1.02892e10i	1.01198	+	0.328812i	0.244336	+	0.969691i	$0.421430\pi$
$998$	5.06391e9	+	6.96987e9i	0.161261	+	0.221956i
$999$	−2.30501e10			−0.731465

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.8.e.a.14.15	yes	64
25.3	odd	20		625.8.a.g.1.5		64
25.9	even	10	inner	25.8.e.a.9.15	✓	64
25.22	odd	20		625.8.a.g.1.60		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.8.e.a.9.15	✓	64	25.9	even	10	inner
25.8.e.a.14.15	yes	64	1.1	even	1	trivial
625.8.a.g.1.5		64	25.3	odd	20
625.8.a.g.1.60		64	25.22	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+(11.3542 + 15.6278i) q^{2} +(-45.6000 - 14.8163i) q^{3} +(-75.7544 + 233.148i) q^{4} +(-99.3681 + 261.249i) q^{5} +(-286.207 - 880.856i) q^{6} -1166.35i q^{7} +(-2152.16 + 699.280i) q^{8} +(90.5179 + 65.7651i) q^{9} +(-5210.99 + 1413.38i) q^{10} +(-3992.39 + 2900.64i) q^{11} +(6908.81 - 9509.16i) q^{12} +(-3446.38 + 4743.54i) q^{13} +(18227.5 - 13243.1i) q^{14} +(8401.94 - 10440.7i) q^{15} +(-9978.44 - 7249.76i) q^{16} +(-6346.60 + 2062.14i) q^{17} +2161.31i q^{18} +(12597.1 + 38770.0i) q^{19} +(-53382.1 - 42958.2i) q^{20} +(-17281.1 + 53185.7i) q^{21} +(-90661.3 - 29457.6i) q^{22} +(39853.4 + 54853.5i) q^{23} +108499. q^{24} +(-58377.0 - 51919.6i) q^{25} -113262. q^{26} +(58481.6 + 80493.0i) q^{27} +(271933. + 88356.4i) q^{28} +(-25433.7 + 78276.9i) q^{29} +(258562. + 12757.6i) q^{30} +(-94157.3 - 289786. i) q^{31} +51397.0i q^{32} +(225030. - 73116.7i) q^{33} +(-104287. - 75769.3i) q^{34} +(304709. + 115898. i) q^{35} +(-22190.1 + 16122.1i) q^{36} +(-136173. + 187426. i) q^{37} +(-462859. + 637070. i) q^{38} +(227437. - 165243. i) q^{39} +(31170.2 - 631736. i) q^{40} +(-473308. - 343878. i) q^{41} +(-1.02739e6 + 333819. i) q^{42} -328323. i q^{43} +(-373838. - 1.15056e6i) q^{44} +(-26175.7 + 17112.7i) q^{45} +(-404733. + 1.24564e6i) q^{46} +(1.00932e6 + 327946. i) q^{47} +(347602. + 478433. i) q^{48} -536837. q^{49} +(148562. - 1.50181e6i) q^{50} +319959. q^{51} +(-844868. - 1.16286e6i) q^{52} +(1.26856e6 + 412181. i) q^{53} +(-593913. + 1.82788e6i) q^{54} +(-361073. - 1.33124e6i) q^{55} +(815608. + 2.51018e6i) q^{56} -1.95456e6i q^{57} +(-1.51207e6 + 491303. i) q^{58} +(492810. + 358047. i) q^{59} +(1.79774e6 + 2.74982e6i) q^{60} +(1.23139e6 - 894660. i) q^{61} +(3.45963e6 - 4.76177e6i) q^{62} +(76705.4 - 105576. i) q^{63} +(-2.08046e6 + 1.51154e6i) q^{64} +(-896783. - 1.37172e6i) q^{65} +(3.69770e6 + 2.68654e6i) q^{66} +(-1.73710e6 + 564418. i) q^{67} -1.63591e6i q^{68} +(-1.00459e6 - 3.09180e6i) q^{69} +(1.64850e6 + 6.07786e6i) q^{70} +(-866491. + 2.66678e6i) q^{71} +(-240798. - 78239.9i) q^{72} +(-666685. - 917613. i) q^{73} -4.47519e6 q^{74} +(1.89273e6 + 3.23247e6i) q^{75} -9.99345e6 q^{76} +(3.38318e6 + 4.65654e6i) q^{77} +(5.16475e6 + 1.67813e6i) q^{78} +(-1.69840e6 + 5.22714e6i) q^{79} +(2.88553e6 - 1.88646e6i) q^{80} +(-1.54977e6 - 4.76969e6i) q^{81} -1.13012e7i q^{82} +(2.02898e6 - 659256. i) q^{83} +(-1.10910e7 - 8.05811e6i) q^{84} +(91919.2 - 1.86295e6i) q^{85} +(5.13095e6 - 3.72786e6i) q^{86} +(2.31955e6 - 3.19259e6i) q^{87} +(6.56392e6 - 9.03446e6i) q^{88} +(4.82883e6 - 3.50835e6i) q^{89} +(-564639. - 214765. i) q^{90} +(5.53264e6 + 4.01970e6i) q^{91} +(-1.58080e7 + 5.13635e6i) q^{92} +1.46093e7i q^{93} +(6.33494e6 + 1.94969e7i) q^{94} +(-1.13804e7 - 561515. i) q^{95} +(761516. - 2.34370e6i) q^{96} +(468018. + 152068. i) q^{97} +(-6.09538e6 - 8.38957e6i) q^{98} -552144. 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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