LMFDB - Embedded newform 74.6.c.a.63.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [74,6,Mod(47,74)] 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("74.47"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(74, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	74.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$11.8684026662$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 993 x^{12} - 1336 x^{11} + 753233 x^{10} - 540853 x^{9} + 210096237 x^{8} + \cdots + 309997997697600 $ x^14 - x^13 + 993x^12 - 1336x^11 + 753233x^10 - 540853x^9 + 210096237x^8 + 595715192x^7 + 42924465101x^6 + 42378726071x^5 + 2501420490525x^4 - 9783756437740x^3 + 113435878155784x^2 - 189691217898720x + 309997997697600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			63.2
Root			$9.50448 - 16.4622i$ of defining polynomial
Character	$\chi$	$=$	74.63
Dual form			74.6.c.a.47.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00000 - 3.46410i) q^{2} +(-10.0045 + 17.3283i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-32.4177 + 56.1491i) q^{5} +80.0358 q^{6} +(-55.2452 + 95.6875i) q^{7} +64.0000 q^{8} +(-78.6791 - 136.276i) q^{9} +259.342 q^{10} -26.5469 q^{11} +(-160.072 - 277.252i) q^{12} +(88.6215 - 153.497i) q^{13} +441.962 q^{14} +(-648.644 - 1123.48i) q^{15} +(-128.000 - 221.703i) q^{16} +(-371.113 - 642.787i) q^{17} +(-314.717 + 545.105i) q^{18} +(16.1101 - 27.9035i) q^{19} +(-518.683 - 898.386i) q^{20} +(-1105.40 - 1914.61i) q^{21} +(53.0938 + 91.9612i) q^{22} +59.3369 q^{23} +(-640.287 + 1109.01i) q^{24} +(-539.314 - 934.119i) q^{25} -708.972 q^{26} -1713.60 q^{27} +(-883.923 - 1531.00i) q^{28} -332.478 q^{29} +(-2594.58 + 4493.94i) q^{30} -3860.10 q^{31} +(-512.000 + 886.810i) q^{32} +(265.588 - 460.012i) q^{33} +(-1484.45 + 2571.15i) q^{34} +(-3581.84 - 6203.94i) q^{35} +2517.73 q^{36} +(5050.00 - 6621.29i) q^{37} -128.881 q^{38} +(1773.22 + 3071.31i) q^{39} +(-2074.73 + 3593.54i) q^{40} +(-176.932 + 306.455i) q^{41} +(-4421.59 + 7658.43i) q^{42} +9173.56 q^{43} +(212.375 - 367.845i) q^{44} +10202.4 q^{45} +(-118.674 - 205.549i) q^{46} +19680.9 q^{47} +5122.29 q^{48} +(2299.44 + 3982.74i) q^{49} +(-2157.26 + 3736.48i) q^{50} +14851.2 q^{51} +(1417.94 + 2455.95i) q^{52} +(-13040.2 - 22586.3i) q^{53} +(3427.20 + 5936.09i) q^{54} +(860.590 - 1490.59i) q^{55} +(-3535.69 + 6124.00i) q^{56} +(322.346 + 558.321i) q^{57} +(664.956 + 1151.74i) q^{58} +(-3068.06 - 5314.03i) q^{59} +20756.6 q^{60} +(2153.51 - 3729.99i) q^{61} +(7720.19 + 13371.8i) q^{62} +17386.6 q^{63} +4096.00 q^{64} +(5745.81 + 9952.04i) q^{65} -2124.70 q^{66} +(-23938.4 + 41462.5i) q^{67} +11875.6 q^{68} +(-593.635 + 1028.21i) q^{69} +(-14327.4 + 24815.7i) q^{70} +(-35855.5 + 62103.5i) q^{71} +(-5035.46 - 8721.68i) q^{72} -34401.1 q^{73} +(-33036.8 - 4251.13i) q^{74} +21582.2 q^{75} +(257.762 + 446.457i) q^{76} +(1466.59 - 2540.21i) q^{77} +(7092.90 - 12285.3i) q^{78} +(-42369.6 + 73386.3i) q^{79} +16597.9 q^{80} +(36262.7 - 62808.9i) q^{81} +1415.46 q^{82} +(-43349.8 - 75084.0i) q^{83} +35372.8 q^{84} +48122.6 q^{85} +(-18347.1 - 31778.1i) q^{86} +(3326.27 - 5761.27i) q^{87} -1699.00 q^{88} +(-71119.1 - 123182. i) q^{89} +(-20404.8 - 35342.1i) q^{90} +(9791.83 + 16959.9i) q^{91} +(-474.695 + 822.196i) q^{92} +(38618.3 - 66888.8i) q^{93} +(-39361.8 - 68176.7i) q^{94} +(1044.51 + 1809.14i) q^{95} +(-10244.6 - 17744.1i) q^{96} -37633.6 q^{97} +(9197.75 - 15931.0i) q^{98} +(2088.69 + 3617.71i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 28 q^{2} - 8 q^{3} - 112 q^{4} + 57 q^{5} + 64 q^{6} + 188 q^{7} + 896 q^{8} - 293 q^{9} - 456 q^{10} + 704 q^{11} - 128 q^{12} - 704 q^{13} - 1504 q^{14} - 364 q^{15} - 1792 q^{16} - 561 q^{17}+ \cdots - 446840 q^{99}+O(q^{100}) $ 14 * q - 28 * q^2 - 8 * q^3 - 112 * q^4 + 57 * q^5 + 64 * q^6 + 188 * q^7 + 896 * q^8 - 293 * q^9 - 456 * q^10 + 704 * q^11 - 128 * q^12 - 704 * q^13 - 1504 * q^14 - 364 * q^15 - 1792 * q^16 - 561 * q^17 - 1172 * q^18 - 3742 * q^19 + 912 * q^20 - 506 * q^21 - 1408 * q^22 - 5700 * q^23 - 512 * q^24 - 2340 * q^25 + 5632 * q^26 + 3124 * q^27 + 3008 * q^28 - 17654 * q^29 - 1456 * q^30 + 11888 * q^31 - 7168 * q^32 + 484 * q^33 - 2244 * q^34 + 1460 * q^35 + 9376 * q^36 + 16941 * q^37 + 29936 * q^38 - 36086 * q^39 + 3648 * q^40 - 9813 * q^41 - 2024 * q^42 + 5724 * q^43 - 5632 * q^44 - 63030 * q^45 + 11400 * q^46 + 23320 * q^47 + 4096 * q^48 - 11829 * q^49 - 9360 * q^50 + 110384 * q^51 - 11264 * q^52 + 16856 * q^53 - 6248 * q^54 + 28408 * q^55 + 12032 * q^56 - 26062 * q^57 + 35308 * q^58 + 50886 * q^59 + 11648 * q^60 - 6247 * q^61 - 23776 * q^62 - 10452 * q^63 + 57344 * q^64 - 4852 * q^65 - 3872 * q^66 - 28570 * q^67 + 17952 * q^68 + 43524 * q^69 + 5840 * q^70 - 8580 * q^71 - 18752 * q^72 - 9252 * q^73 - 36336 * q^74 + 112184 * q^75 - 59872 * q^76 - 56112 * q^77 - 144344 * q^78 + 26930 * q^79 - 29184 * q^80 - 9039 * q^81 + 78504 * q^82 - 137412 * q^83 + 16192 * q^84 - 58830 * q^85 - 11448 * q^86 - 70826 * q^87 + 45056 * q^88 - 27961 * q^89 + 126060 * q^90 + 99802 * q^91 + 45600 * q^92 - 181340 * q^93 - 46640 * q^94 + 210526 * q^95 - 8192 * q^96 + 191206 * q^97 - 47316 * q^98 - 446840 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$3$	−10.0045	+	17.3283i	−0.641788	+	1.11161i	0.343246	+	0.939246i	$0.388474\pi$
$3$	−10.0045	+	17.3283i	−0.641788	+	1.11161i	−0.985033	+	0.172363i	$0.944860\pi$
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	−32.4177	+	56.1491i	−0.579905	+	1.00443i	0.415584	+	0.909555i	$0.363577\pi$
$5$	−32.4177	+	56.1491i	−0.579905	+	1.00443i	−0.995490	+	0.0948709i	$0.969756\pi$
$6$	80.0358			0.907625
$7$	−55.2452	+	95.6875i	−0.426137	+	0.738091i	−0.996526	−	0.0832837i	$-0.973459\pi$
$7$	−55.2452	+	95.6875i	−0.426137	+	0.738091i	0.570389	+	0.821375i	$0.306793\pi$
$8$	64.0000			0.353553
$9$	−78.6791	−	136.276i	−0.323782	−	0.560808i
$10$	259.342			0.820110
$11$	−26.5469			−0.0661504			−0.0330752	−	0.999453i	$-0.510530\pi$
$11$	−26.5469			−0.0661504			−0.0330752	+	0.999453i	$0.510530\pi$
$12$	−160.072	−	277.252i	−0.320894	−	0.555804i
$13$	88.6215	−	153.497i	0.145439	−	0.251908i	−0.784098	−	0.620637i	$-0.786874\pi$
$13$	88.6215	−	153.497i	0.145439	−	0.251908i	0.929537	+	0.368730i	$0.120207\pi$
$14$	441.962			0.602649
$15$	−648.644	−	1123.48i	−0.744352	−	1.28926i
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	−371.113	−	642.787i	−0.311447	−	0.539442i	0.667229	−	0.744853i	$-0.267480\pi$
$17$	−371.113	−	642.787i	−0.311447	−	0.539442i	−0.978676	+	0.205411i	$0.934147\pi$
$18$	−314.717	+	545.105i	−0.228949	+	0.396551i
$19$	16.1101	−	27.9035i	0.0102380	−	0.0177327i	−0.860861	−	0.508840i	$-0.830074\pi$
$19$	16.1101	−	27.9035i	0.0102380	−	0.0177327i	0.871099	+	0.491107i	$0.163408\pi$
$20$	−518.683	−	898.386i	−0.289953	−	0.502213i
$21$	−1105.40	−	1914.61i	−0.546979	−	0.947395i
$22$	53.0938	+	91.9612i	0.0233877	+	0.0405087i
$23$	59.3369			0.0233887			0.0116943	−	0.999932i	$-0.496277\pi$
$23$	59.3369			0.0233887			0.0116943	+	0.999932i	$0.496277\pi$
$24$	−640.287	+	1109.01i	−0.226906	+	0.393013i
$25$	−539.314	−	934.119i	−0.172580	−	0.298918i
$26$	−708.972			−0.205682
$27$	−1713.60			−0.452377
$28$	−883.923	−	1531.00i	−0.213069	−	0.369046i
$29$	−332.478			−0.0734122			−0.0367061	−	0.999326i	$-0.511687\pi$
$29$	−332.478			−0.0734122			−0.0367061	+	0.999326i	$0.511687\pi$
$30$	−2594.58	+	4493.94i	−0.526336	+	0.911641i
$31$	−3860.10			−0.721430			−0.360715	−	0.932676i	$-0.617467\pi$
$31$	−3860.10			−0.721430			−0.360715	+	0.932676i	$0.617467\pi$
$32$	−512.000	+	886.810i	−0.0883883	+	0.153093i
$33$	265.588	−	460.012i	0.0424545	−	0.0735333i
$34$	−1484.45	+	2571.15i	−0.220226	+	0.381443i
$35$	−3581.84	−	6203.94i	−0.494238	−	0.856046i
$36$	2517.73			0.323782
$37$	5050.00	−	6621.29i	0.606439	−	0.795130i
$37$	5050.00	−	6621.29i	0.606439	−	0.795130i
$38$	−128.881			−0.0144787
$39$	1773.22	+	3071.31i	0.186682	+	0.323342i
$40$	−2074.73	+	3593.54i	−0.205028	+	0.355118i
$41$	−176.932	+	306.455i	−0.0164379	+	0.0284713i	−0.874127	−	0.485697i	$-0.838566\pi$
$41$	−176.932	+	306.455i	−0.0164379	+	0.0284713i	0.857689	+	0.514168i	$0.171899\pi$
$42$	−4421.59	+	7658.43i	−0.386773	+	0.669910i
$43$	9173.56			0.756601			0.378300	−	0.925683i	$-0.376509\pi$
$43$	9173.56			0.756601			0.378300	+	0.925683i	$0.376509\pi$
$44$	212.375	−	367.845i	0.0165376	−	0.0286440i
$45$	10202.4			0.751053
$46$	−118.674	−	205.549i	−0.00826914	−	0.0143226i
$47$	19680.9			1.29957			0.649787	−	0.760117i	$-0.274858\pi$
$47$	19680.9			1.29957			0.649787	+	0.760117i	$0.274858\pi$
$48$	5122.29			0.320894
$49$	2299.44	+	3982.74i	0.136814	+	0.236969i
$50$	−2157.26	+	3736.48i	−0.122033	+	0.211367i
$51$	14851.2			0.799532
$52$	1417.94	+	2455.95i	0.0727195	+	0.125954i
$53$	−13040.2	−	22586.3i	−0.637669	−	1.10447i	−0.985943	−	0.167082i	$-0.946566\pi$
$53$	−13040.2	−	22586.3i	−0.637669	−	1.10447i	0.348274	−	0.937393i	$-0.386768\pi$
$54$	3427.20	+	5936.09i	0.159939	+	0.277023i
$55$	860.590	−	1490.59i	0.0383610	−	0.0664431i
$56$	−3535.69	+	6124.00i	−0.150662	+	0.260955i
$57$	322.346	+	558.321i	0.0131412	+	0.0227613i
$58$	664.956	+	1151.74i	0.0259551	+	0.0449556i
$59$	−3068.06	−	5314.03i	−0.114745	−	0.198744i	0.802933	−	0.596070i	$-0.203272\pi$
$59$	−3068.06	−	5314.03i	−0.114745	−	0.198744i	−0.917678	+	0.397325i	$0.869938\pi$
$60$	20756.6			0.744352
$61$	2153.51	−	3729.99i	0.0741008	−	0.128346i	−0.826594	−	0.562799i	$-0.809725\pi$
$61$	2153.51	−	3729.99i	0.0741008	−	0.128346i	0.900695	+	0.434452i	$0.143058\pi$
$62$	7720.19	+	13371.8i	0.255064	+	0.441784i
$63$	17386.6			0.551903
$64$	4096.00			0.125000
$65$	5745.81	+	9952.04i	0.168682	+	0.292165i
$66$	−2124.70			−0.0600397
$67$	−23938.4	+	41462.5i	−0.651490	+	1.12841i	0.331272	+	0.943535i	$0.392522\pi$
$67$	−23938.4	+	41462.5i	−0.651490	+	1.12841i	−0.982761	+	0.184878i	$0.940811\pi$
$68$	11875.6			0.311447
$69$	−593.635	+	1028.21i	−0.0150105	+	0.0259990i
$70$	−14327.4	+	24815.7i	−0.349479	+	0.605316i
$71$	−35855.5	+	62103.5i	−0.844131	+	1.46208i	0.0422426	+	0.999107i	$0.486550\pi$
$71$	−35855.5	+	62103.5i	−0.844131	+	1.46208i	−0.886374	+	0.462971i	$0.846784\pi$
$72$	−5035.46	−	8721.68i	−0.114474	−	0.198275i
$73$	−34401.1			−0.755553			−0.377777	−	0.925897i	$-0.623311\pi$
$73$	−34401.1			−0.755553			−0.377777	+	0.925897i	$0.623311\pi$
$74$	−33036.8	−	4251.13i	−0.701324	−	0.0902453i
$75$	21582.2			0.443040
$76$	257.762	+	446.457i	0.00511899	+	0.00886636i
$77$	1466.59	−	2540.21i	0.0281891	−	0.0488250i
$78$	7092.90	−	12285.3i	0.132004	−	0.228638i
$79$	−42369.6	+	73386.3i	−0.763813	+	1.32296i	0.177059	+	0.984200i	$0.443342\pi$
$79$	−42369.6	+	73386.3i	−0.763813	+	1.32296i	−0.940872	+	0.338762i	$0.889992\pi$
$80$	16597.9			0.289953
$81$	36262.7	−	62808.9i	0.614112	−	1.06367i
$82$	1415.46			0.0232467
$83$	−43349.8	−	75084.0i	−0.690703	−	1.19633i	−0.971608	−	0.236598i	$-0.923968\pi$
$83$	−43349.8	−	75084.0i	−0.690703	−	1.19633i	0.280904	−	0.959736i	$-0.409366\pi$
$84$	35372.8			0.546979
$85$	48122.6			0.722439
$86$	−18347.1	−	31778.1i	−0.267499	−	0.463322i
$87$	3326.27	−	5761.27i	0.0471150	−	0.0816056i
$88$	−1699.00			−0.0233877
$89$	−71119.1	−	123182.i	−0.951724	−	1.64843i	−0.741693	−	0.670739i	$-0.765977\pi$
$89$	−71119.1	−	123182.i	−0.951724	−	1.64843i	−0.210031	−	0.977695i	$-0.567356\pi$
$90$	−20404.8	−	35342.1i	−0.265537	−	0.459924i
$91$	9791.83	+	16959.9i	0.123954	+	0.214694i
$92$	−474.695	+	822.196i	−0.00584716	+	0.0101276i
$93$	38618.3	−	66888.8i	0.463005	−	0.801947i
$94$	−39361.8	−	68176.7i	−0.459468	−	0.795823i
$95$	1044.51	+	1809.14i	0.0118741	+	0.0205666i
$96$	−10244.6	−	17744.1i	−0.113453	−	0.196506i
$97$	−37633.6			−0.406113			−0.203056	−	0.979167i	$-0.565087\pi$
$97$	−37633.6			−0.406113			−0.203056	+	0.979167i	$0.565087\pi$
$98$	9197.75	−	15931.0i	0.0967423	−	0.167563i
$99$	2088.69	+	3617.71i	0.0214183	+	0.0370976i
$100$	17258.0			0.172580
$101$	−169975.			−1.65798			−0.828992	−	0.559260i	$-0.811085\pi$
$101$	−169975.			−1.65798			−0.828992	+	0.559260i	$0.811085\pi$
$102$	−29702.4	−	51446.0i	−0.282677	−	0.489611i
$103$	117451.			1.09085			0.545423	−	0.838161i	$-0.316369\pi$
$103$	117451.			1.09085			0.545423	+	0.838161i	$0.316369\pi$
$104$	5671.78	−	9823.81i	0.0514205	−	0.0890628i
$105$	143338.			1.26878
$106$	−52160.9	+	90345.3i	−0.450900	+	0.780981i
$107$	−39766.7	+	68878.0i	−0.335784	+	0.581596i	−0.983635	−	0.180172i	$-0.942335\pi$
$107$	−39766.7	+	68878.0i	−0.335784	+	0.581596i	0.647851	+	0.761767i	$0.275668\pi$
$108$	13708.8	−	23744.4i	0.113094	−	0.195885i
$109$	34352.5	+	59500.3i	0.276944	+	0.479682i	0.970624	−	0.240602i	$-0.0773449\pi$
$109$	34352.5	+	59500.3i	0.276944	+	0.479682i	−0.693679	+	0.720284i	$0.744012\pi$
$110$	−6884.72			−0.0542506
$111$	64212.9	+	153750.i	0.494669	+	1.18443i
$112$	28285.5			0.213069
$113$	−2656.17	−	4600.62i	−0.0195686	−	0.0338938i	0.856075	−	0.516851i	$-0.172896\pi$
$113$	−2656.17	−	4600.62i	−0.0195686	−	0.0338938i	−0.875644	+	0.482957i	$0.839563\pi$
$114$	1289.39	−	2233.28i	0.00929225	−	0.0160946i
$115$	−1923.57	+	3331.71i	−0.0135632	+	0.0234922i
$116$	2659.83	−	4606.95i	0.0183530	−	0.0317884i
$117$	−27890.7			−0.188362
$118$	−12272.2	+	21256.1i	−0.0811369	+	0.140533i
$119$	82008.9			0.530877
$120$	−41513.2	−	71903.0i	−0.263168	−	0.455821i
$121$	−160346.			−0.995624
$122$	−17228.1			−0.104794
$123$	−3540.22	−	6131.85i	−0.0210993	−	0.0365450i
$124$	30880.8	−	53487.1i	0.180357	−	0.312388i
$125$	−132677.			−0.759489
$126$	−34773.2	−	60228.9i	−0.195127	−	0.337970i
$127$	65112.5	+	112778.i	0.358224	+	0.620463i	0.987664	−	0.156587i	$-0.0500490\pi$
$127$	65112.5	+	112778.i	0.358224	+	0.620463i	−0.629440	+	0.777049i	$0.716716\pi$
$128$	−8192.00	−	14189.0i	−0.0441942	−	0.0765466i
$129$	−91776.7	+	158962.i	−0.485577	+	0.841044i
$130$	22983.2	−	39808.2i	0.119276	−	0.206592i
$131$	−97105.3	−	168191.i	−0.494384	−	0.856299i	0.505595	−	0.862771i	$-0.331273\pi$
$131$	−97105.3	−	168191.i	−0.494384	−	0.856299i	−0.999979	+	0.00647240i	$0.997940\pi$
$132$	4249.41	+	7360.19i	0.0212272	+	0.0367667i
$133$	1780.01	+	3083.07i	0.00872557	+	0.0151131i
$134$	191507.			0.921346
$135$	55551.0	−	96217.2i	0.262336	−	0.454379i
$136$	−23751.3	−	41138.4i	−0.110113	−	0.190722i
$137$	56831.8			0.258696			0.129348	−	0.991599i	$-0.458712\pi$
$137$	56831.8			0.258696			0.129348	+	0.991599i	$0.458712\pi$
$138$	4749.08			0.0212281
$139$	108831.	+	188502.i	0.477768	+	0.827519i	0.999675	−	0.0254834i	$-0.00811249\pi$
$139$	108831.	+	188502.i	0.477768	+	0.827519i	−0.521907	+	0.853002i	$0.674779\pi$
$140$	114619.			0.494238
$141$	−196897.	+	341036.i	−0.834050	+	1.44462i
$142$	286844.			1.19378
$143$	−2352.63	+	4074.87i	−0.00962084	+	0.0166638i
$144$	−20141.9	+	34886.7i	−0.0809456	+	0.140202i
$145$	10778.2	−	18668.3i	0.0425721	−	0.0737371i
$146$	68802.2	+	119169.i	0.267128	+	0.462680i
$147$	−92018.7			−0.351223
$148$	51347.3	+	122945.i	0.192692	+	0.461378i
$149$	84536.6			0.311946			0.155973	−	0.987761i	$-0.450149\pi$
$149$	84536.6			0.311946			0.155973	+	0.987761i	$0.450149\pi$
$150$	−43164.4	−	74763.0i	−0.156638	−	0.271305i
$151$	−116202.	+	201268.i	−0.414736	+	0.718344i	−0.995401	−	0.0957989i	$-0.969459\pi$
$151$	−116202.	+	201268.i	−0.414736	+	0.718344i	0.580665	+	0.814143i	$0.302793\pi$
$152$	1031.05	−	1785.83i	0.00361967	−	0.00626946i
$153$	−58397.8	+	101148.i	−0.201682	+	0.349324i
$154$	−11732.7			−0.0398654
$155$	125135.	−	216741.i	0.418361	−	0.724622i
$156$	−56743.2			−0.186682
$157$	−18323.3	−	31736.9i	−0.0593274	−	0.102758i	0.834836	−	0.550498i	$-0.185562\pi$
$157$	−18323.3	−	31736.9i	−0.0593274	−	0.102758i	−0.894164	+	0.447740i	$0.852229\pi$
$158$	338957.			1.08019
$159$	521842.			1.63699
$160$	−33195.7	−	57496.7i	−0.102514	−	0.177559i
$161$	−3278.08	+	5677.80i	−0.00996678	+	0.0172630i
$162$	−290102.			−0.868486
$163$	−117524.	−	203558.i	−0.346464	−	0.600094i	0.639154	−	0.769078i	$-0.279284\pi$
$163$	−117524.	−	203558.i	−0.346464	−	0.600094i	−0.985619	+	0.168985i	$0.945951\pi$
$164$	−2830.91	−	4903.28i	−0.00821895	−	0.0142356i
$165$	17219.5	+	29825.0i	0.0492392	+	0.0852847i
$166$	−173399.	+	300336.i	−0.488401	+	0.845936i
$167$	282793.	−	489812.i	0.784652	−	1.35906i	−0.144554	−	0.989497i	$-0.546175\pi$
$167$	282793.	−	489812.i	0.784652	−	1.35906i	0.929207	−	0.369561i	$-0.120492\pi$
$168$	−70745.5	−	122535.i	−0.193386	−	0.334955i
$169$	169939.	+	294343.i	0.457695	+	0.792751i
$170$	−96245.1	−	166701.i	−0.255421	−	0.442402i
$171$	−5070.12			−0.0132595
$172$	−73388.5	+	127113.i	−0.189150	+	0.327618i
$173$	−354520.	−	614047.i	−0.900587	−	1.55986i	−0.826734	−	0.562592i	$-0.809804\pi$
$173$	−354520.	−	614047.i	−0.900587	−	1.55986i	−0.0738522	−	0.997269i	$-0.523529\pi$
$174$	−26610.2			−0.0666307
$175$	119178.			0.294172
$176$	3398.00	+	5885.52i	0.00826880	+	0.0143220i
$177$	122777.			0.294567
$178$	−284476.	+	492727.i	−0.672970	+	1.16562i
$179$	650535.			1.51753			0.758766	−	0.651363i	$-0.225803\pi$
$179$	650535.			1.51753			0.758766	+	0.651363i	$0.225803\pi$
$180$	−81619.1	+	141368.i	−0.187763	+	0.325215i
$181$	−72003.2	+	124713.i	−0.163364	+	0.282954i	−0.936073	−	0.351806i	$-0.885568\pi$
$181$	−72003.2	+	124713.i	−0.163364	+	0.282954i	0.772709	+	0.634760i	$0.218901\pi$
$182$	39167.3	−	67839.8i	0.0876487	−	0.151812i
$183$	43089.5	+	74633.2i	0.0951139	+	0.164742i
$184$	3797.56			0.00826914
$185$	208070.	+	498200.i	0.446972	+	1.07022i
$186$	−308946.			−0.654787
$187$	9851.91	+	17064.0i	0.0206023	+	0.0356843i
$188$	−157447.	+	272707.i	−0.324893	+	0.562732i
$189$	94668.2	−	163970.i	0.192775	−	0.333895i
$190$	4178.02	−	7236.55i	0.00839628	−	0.0145428i
$191$	577983.			1.14639			0.573194	−	0.819420i	$-0.305704\pi$
$191$	577983.			1.14639			0.573194	+	0.819420i	$0.305704\pi$
$192$	−40978.3	+	70976.6i	−0.0802234	+	0.138951i
$193$	−53262.4			−0.102926			−0.0514632	−	0.998675i	$-0.516388\pi$
$193$	−53262.4			−0.102926			−0.0514632	+	0.998675i	$0.516388\pi$
$194$	75267.3	+	130367.i	0.143583	+	0.248692i
$195$	−229935.			−0.433031
$196$	−73582.0			−0.136814
$197$	−411369.	−	712512.i	−0.755207	−	1.30806i	−0.945271	−	0.326286i	$-0.894203\pi$
$197$	−411369.	−	712512.i	−0.755207	−	1.30806i	0.190064	−	0.981772i	$-0.439130\pi$
$198$	8354.75	−	14470.9i	0.0151450	−	0.0262320i
$199$	−629744.			−1.12728			−0.563639	−	0.826021i	$-0.690599\pi$
$199$	−629744.			−1.12728			−0.563639	+	0.826021i	$0.690599\pi$
$200$	−34516.1	−	59783.6i	−0.0610164	−	0.105684i
$201$	−478982.	−	829621.i	−0.836236	−	1.44840i
$202$	339949.	+	588809.i	0.586186	+	1.01530i
$203$	18367.8	−	31814.0i	0.0312837	−	0.0541849i
$204$	−118809.	+	205784.i	−0.199883	+	0.346207i
$205$	−11471.4	−	19869.1i	−0.0190649	−	0.0330213i
$206$	−234902.	−	406862.i	−0.385672	−	0.668004i
$207$	−4668.58	−	8086.21i	−0.00757284	−	0.0131165i
$208$	−45374.2			−0.0727195
$209$	−427.674	+	740.753i	−0.000677247	+	0.00117303i
$210$	−286676.	−	496537.i	−0.448583	−	0.776969i
$211$	−937782.			−1.45009			−0.725046	−	0.688700i	$-0.758182\pi$
$211$	−937782.			−1.45009			−0.725046	+	0.688700i	$0.758182\pi$
$212$	417287.			0.637669
$213$	−717431.	−	1.24263e6i	−1.08351	−	1.87669i
$214$	318134.			0.474871
$215$	−297386.	+	515087.i	−0.438757	+	0.759949i
$216$	−109670.			−0.159939
$217$	213252.	−	369363.i	0.307428	−	0.532481i
$218$	137410.	−	238001.i	0.195829	−	0.339186i
$219$	344165.	−	596111.i	0.484905	−	0.839880i
$220$	13769.4	+	23849.4i	0.0191805	+	0.0332216i
$221$	−131555.			−0.181186
$222$	404181.	−	529940.i	0.550419	−	0.721680i
$223$	438727.			0.590788			0.295394	−	0.955375i	$-0.404549\pi$
$223$	438727.			0.590788			0.295394	+	0.955375i	$0.404549\pi$
$224$	−56571.1	−	97984.0i	−0.0753311	−	0.130477i
$225$	−84865.5	+	146991.i	−0.111757	+	0.193569i
$226$	−10624.7	+	18402.5i	−0.0138371	+	0.0239665i
$227$	−335717.	+	581479.i	−0.432423	+	0.748979i	−0.997081	−	0.0763459i	$-0.975675\pi$
$227$	−335717.	+	581479.i	−0.432423	+	0.748979i	0.564658	+	0.825325i	$0.309008\pi$
$228$	−10315.1			−0.0131412
$229$	474130.	−	821218.i	0.597460	−	1.03483i	−0.395734	−	0.918365i	$-0.629510\pi$
$229$	474130.	−	821218.i	0.597460	−	1.03483i	0.993195	−	0.116467i	$-0.0371568\pi$
$230$	15388.5			0.0191813
$231$	29344.9	+	50826.9i	0.0361829	+	0.0626706i
$232$	−21278.6			−0.0259551
$233$	−437606.			−0.528072			−0.264036	−	0.964513i	$-0.585054\pi$
$233$	−437606.			−0.528072			−0.264036	+	0.964513i	$0.585054\pi$
$234$	55781.3	+	96616.1i	0.0665962	+	0.115348i
$235$	−638010.	+	1.10507e6i	−0.753629	+	1.30532i
$236$	98177.8			0.114745
$237$	−847772.	−	1.46838e6i	−0.980411	−	1.69812i
$238$	−164018.	−	284087.i	−0.187693	−	0.325094i
$239$	524149.	+	907852.i	0.593554	+	1.02806i	0.993749	+	0.111635i	$0.0356088\pi$
$239$	524149.	+	907852.i	0.593554	+	1.02806i	−0.400196	+	0.916430i	$0.631058\pi$
$240$	−166053.	+	287612.i	−0.186088	+	0.322314i
$241$	−318322.	+	551350.i	−0.353040	+	0.611484i	−0.986781	−	0.162062i	$-0.948185\pi$
$241$	−318322.	+	551350.i	−0.353040	+	0.611484i	0.633740	+	0.773546i	$0.281519\pi$
$242$	320693.	+	555456.i	0.352006	+	0.609693i
$243$	517377.	+	896122.i	0.562071	+	0.973535i
$244$	34456.2	+	59679.9i	0.0370504	+	0.0641731i
$245$	−298170.			−0.317357
$246$	−14160.9	+	24527.4i	−0.0149194	+	0.0258412i
$247$	−2855.41	−	4945.71i	−0.00297801	−	0.00515806i
$248$	−247046.			−0.255064
$249$	1.73477e6			1.77314
$250$	265355.	+	459608.i	0.268520	+	0.465090i
$251$	−729523.			−0.730894			−0.365447	−	0.930832i	$-0.619084\pi$
$251$	−729523.			−0.730894			−0.365447	+	0.930832i	$0.619084\pi$
$252$	−139093.	+	240915.i	−0.137976	+	0.238981i
$253$	−1575.21			−0.00154717
$254$	260450.	−	451113.i	0.253303	−	0.438733i
$255$	−481441.	+	833881.i	−0.463653	+	0.803070i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	638290.	+	1.10555e6i	0.602817	+	1.04411i	0.992392	+	0.123115i	$0.0392884\pi$
$257$	638290.	+	1.10555e6i	0.602817	+	1.04411i	−0.389575	+	0.920995i	$0.627378\pi$
$258$	734213.			0.686710
$259$	354586.	+	849016.i	0.328453	+	0.786442i
$260$	−183866.			−0.168682
$261$	26159.1	+	45308.9i	0.0237696	+	0.0411701i
$262$	−388421.	+	672765.i	−0.349582	+	0.605495i
$263$	−62479.3	+	108217.i	−0.0556989	+	0.0964734i	−0.892530	−	0.450987i	$-0.851072\pi$
$263$	−62479.3	+	108217.i	−0.0556989	+	0.0964734i	0.836832	+	0.547461i	$0.184405\pi$
$264$	16997.6	−	29440.8i	0.0150099	−	0.0259980i
$265$	1.69093e6			1.47915
$266$	7120.05	−	12332.3i	0.00616991	−	0.0106866i
$267$	2.84604e6			2.44322
$268$	−383014.	−	663400.i	−0.325745	−	0.564207i
$269$	−1.22179e6			−1.02947			−0.514737	−	0.857348i	$-0.672111\pi$
$269$	−1.22179e6			−1.02947			−0.514737	+	0.857348i	$0.672111\pi$
$270$	−444408.			−0.370999
$271$	165402.	+	286485.i	0.136810	+	0.236962i	0.926287	−	0.376818i	$-0.122982\pi$
$271$	165402.	+	286485.i	0.136810	+	0.236962i	−0.789477	+	0.613780i	$0.789648\pi$
$272$	−95005.0	+	164554.i	−0.0778618	+	0.134861i
$273$	−391848.			−0.318208
$274$	−113664.	−	196871.i	−0.0914629	−	0.158418i
$275$	14317.1	+	24798.0i	0.0114163	+	0.0197735i
$276$	−9498.16	−	16451.3i	−0.00750527	−	0.0129995i
$277$	162432.	−	281341.i	0.127196	−	0.220310i	−0.795393	−	0.606094i	$-0.792736\pi$
$277$	162432.	−	281341.i	0.127196	−	0.220310i	0.922589	+	0.385784i	$0.126069\pi$
$278$	435326.	−	754006.i	0.337833	−	0.585144i
$279$	303709.	+	526040.i	0.233586	+	0.404583i
$280$	−229238.	−	397052.i	−0.174740	−	0.302658i
$281$	−7572.97	−	13116.8i	−0.00572138	−	0.00990971i	0.863151	−	0.504947i	$-0.168488\pi$
$281$	−7572.97	−	13116.8i	−0.00572138	−	0.00990971i	−0.868872	+	0.495037i	$0.835155\pi$
$282$	1.57518e6			1.17952
$283$	−566403.	+	981038.i	−0.420397	+	0.728148i	−0.995978	−	0.0895961i	$-0.971442\pi$
$283$	−566403.	+	981038.i	−0.420397	+	0.728148i	0.575582	+	0.817744i	$0.304776\pi$
$284$	−573688.	−	993657.i	−0.422066	−	0.731039i
$285$	−41798.9			−0.0304827
$286$	18821.0			0.0136059
$287$	−19549.3	−	33860.3i	−0.0140096	−	0.0242653i
$288$	161135.			0.114474
$289$	434478.	−	752538.i	0.306001	−	0.530010i
$290$	−86225.4			−0.0602061
$291$	376505.	−	652125.i	0.260638	−	0.451439i
$292$	275209.	−	476676.i	0.188888	−	0.327164i
$293$	380145.	−	658431.i	0.258691	−	0.448065i	−0.707201	−	0.707013i	$-0.750042\pi$
$293$	380145.	−	658431.i	0.258691	−	0.448065i	0.965891	+	0.258947i	$0.0833756\pi$
$294$	184037.	+	318762.i	0.124176	+	0.215079i
$295$	397837.			0.266165
$296$	323200.	−	423763.i	0.214408	−	0.281121i
$297$	45490.8			0.0299249
$298$	−169073.	−	292843.i	−0.110290	−	0.191027i
$299$	5258.53	−	9108.04i	0.00340162	−	0.00589178i
$300$	−172658.	+	299052.i	−0.110760	+	0.191842i
$301$	−506795.	+	877795.i	−0.322416	+	0.558440i
$302$	929617.			0.586525
$303$	1.70051e6	−	2.94536e6i	1.06407	−	1.84303i
$304$	−8248.38			−0.00511899
$305$	139624.	+	241835.i	0.0859429	+	0.148857i
$306$	467182.			0.285222
$307$	−2.38915e6			−1.44677			−0.723383	−	0.690447i	$-0.757414\pi$
$307$	−2.38915e6			−1.44677			−0.723383	+	0.690447i	$0.757414\pi$
$308$	23465.4	+	40643.3i	0.0140946	+	0.0244125i
$309$	−1.17503e6	+	2.03522e6i	−0.700091	+	1.21259i
$310$	−1.00108e6			−0.591652
$311$	−176002.	−	304844.i	−0.103185	−	0.178721i	0.809810	−	0.586692i	$-0.199570\pi$
$311$	−176002.	−	304844.i	−0.103185	−	0.178721i	−0.912995	+	0.407970i	$0.866237\pi$
$312$	113486.	+	196564.i	0.0660020	+	0.114319i
$313$	1.07430e6	+	1.86074e6i	0.619817	+	1.07356i	0.989519	+	0.144405i	$0.0461267\pi$
$313$	1.07430e6	+	1.86074e6i	0.619817	+	1.07356i	−0.369701	+	0.929151i	$0.620540\pi$
$314$	−73293.3	+	126948.i	−0.0419508	+	0.0726609i
$315$	−563633.	+	976241.i	−0.320051	+	0.554345i
$316$	−677914.	−	1.17418e6i	−0.381906	−	0.661481i
$317$	636088.	+	1.10174e6i	0.355524	+	0.615785i	0.987207	−	0.159441i	$-0.0509691\pi$
$317$	636088.	+	1.10174e6i	0.355524	+	0.615785i	−0.631684	+	0.775226i	$0.717636\pi$
$318$	−1.04368e6	−	1.80771e6i	−0.578764	−	1.00245i
$319$	8826.27			0.00485624
$320$	−132783.	+	229987.i	−0.0724882	+	0.125553i
$321$	−795691.	−	1.37818e6i	−0.431004	−	0.746522i
$322$	26224.6			0.0140951
$323$	−23914.7			−0.0127544
$324$	580203.	+	1.00494e6i	0.307056	+	0.531837i
$325$	−191179.			−0.100400
$326$	−470097.	+	814232.i	−0.244987	+	0.424330i
$327$	−1.37472e6			−0.710958
$328$	−11323.6	+	19613.1i	−0.00581168	+	0.0100661i
$329$	−1.08728e6	+	1.88322e6i	−0.553796	+	0.959203i
$330$	68878.0	−	119300.i	0.0348173	−	0.0603054i
$331$	1.33302e6	+	2.30886e6i	0.668754	+	1.15832i	0.978253	+	0.207416i	$0.0665054\pi$
$331$	1.33302e6	+	2.30886e6i	0.668754	+	1.15832i	−0.309499	+	0.950900i	$0.600161\pi$
$332$	1.38719e6			0.690703
$333$	−1.29965e6	−	167237.i	−0.642269	−	0.0826462i
$334$	−2.26234e6			−1.10967
$335$	−1.55205e6	−	2.68824e6i	−0.755605	−	1.30875i
$336$	−282982.	+	490139.i	−0.136745	+	0.236849i
$337$	−57170.0	+	99021.3i	−0.0274216	+	0.0474956i	−0.879411	−	0.476064i	$-0.842063\pi$
$337$	−57170.0	+	99021.3i	−0.0274216	+	0.0474956i	0.851989	+	0.523560i	$0.175396\pi$
$338$	679756.	−	1.17737e6i	0.323639	−	0.560560i
$339$	106294.			0.0502355
$340$	−384981.	+	666806.i	−0.180610	+	0.312825i
$341$	102474.			0.0477228
$342$	10140.2	+	17563.4i	0.00468795	+	0.00811977i
$343$	−2.36514e6			−1.08548
$344$	587108.			0.267499
$345$	−38488.5	−	66664.1i	−0.0174094	−	0.0301540i
$346$	−1.41808e6	+	2.45619e6i	−0.636811	+	1.10299i
$347$	−2.33778e6			−1.04227			−0.521134	−	0.853475i	$-0.674491\pi$
$347$	−2.33778e6			−1.04227			−0.521134	+	0.853475i	$0.674491\pi$
$348$	53220.3	+	92180.3i	0.0235575	+	0.0408028i
$349$	794712.	+	1.37648e6i	0.349258	+	0.604932i	0.986118	−	0.166047i	$-0.0531005\pi$
$349$	794712.	+	1.37648e6i	0.349258	+	0.604932i	−0.636860	+	0.770979i	$0.719767\pi$
$350$	−238356.	−	412845.i	−0.104005	−	0.180143i
$351$	−151862.	+	263033.i	−0.0657932	+	0.113957i
$352$	13592.0	−	23542.1i	0.00584692	−	0.0101272i
$353$	−570251.	−	987704.i	−0.243573	−	0.421881i	0.718156	−	0.695882i	$-0.244986\pi$
$353$	−570251.	−	987704.i	−0.243573	−	0.421881i	−0.961729	+	0.274001i	$0.911653\pi$
$354$	−245555.	−	425313.i	−0.104145	−	0.180385i
$355$	−2.32471e6	−	4.02651e6i	−0.979032	−	1.69573i
$356$	2.27581e6			0.951724
$357$	−820456.	+	1.42107e6i	−0.340710	+	0.590127i
$358$	−1.30107e6	−	2.25352e6i	−0.536529	−	0.929295i
$359$	690429.			0.282737			0.141369	−	0.989957i	$-0.454850\pi$
$359$	690429.			0.282737			0.141369	+	0.989957i	$0.454850\pi$
$360$	652953.			0.265537
$361$	1.23753e6	+	2.14347e6i	0.499790	+	0.865662i
$362$	576026.			0.231031
$363$	1.60418e6	−	2.77852e6i	0.638979	−	1.10674i
$364$	−313338.			−0.123954
$365$	1.11520e6	−	1.93159e6i	0.438149	−	0.758897i
$366$	172358.	−	298533.i	0.0672557	−	0.116490i
$367$	1.09388e6	−	1.89465e6i	0.423939	−	0.734283i	−0.572382	−	0.819987i	$-0.693981\pi$
$367$	1.09388e6	−	1.89465e6i	0.423939	−	0.734283i	0.996321	+	0.0857040i	$0.0273139\pi$
$368$	−7595.12	−	13155.1i	−0.00292358	−	0.00506379i
$369$	55683.4			0.0212892
$370$	1.30967e6	−	1.71718e6i	0.497346	−	0.652094i
$371$	2.88164e6			1.08694
$372$	617892.	+	1.07022e6i	0.231502	+	0.400974i
$373$	2.52923e6	−	4.38076e6i	0.941275	−	1.63034i	0.178233	−	0.983988i	$-0.442962\pi$
$373$	2.52923e6	−	4.38076e6i	0.941275	−	1.63034i	0.763043	−	0.646348i	$-0.223705\pi$
$374$	39407.7	−	68256.1i	0.0145681	−	0.0252326i
$375$	1.32737e6	−	2.29907e6i	0.487431	−	0.844255i
$376$	1.25958e6			0.459468
$377$	−29464.7	+	51034.4i	−0.0106770	+	0.0184931i
$378$	−757346.			−0.272624
$379$	−352699.	−	610893.i	−0.126127	−	0.218458i	0.796046	−	0.605236i	$-0.206921\pi$
$379$	−352699.	−	610893.i	−0.126127	−	0.218458i	−0.922173	+	0.386778i	$0.873588\pi$
$380$	−33424.2			−0.0118741
$381$	−2.60567e6			−0.919615
$382$	−1.15597e6	−	2.00219e6i	−0.405309	−	0.702016i
$383$	−871897.	+	1.51017e6i	−0.303716	+	0.526052i	−0.976975	−	0.213355i	$-0.931561\pi$
$383$	−871897.	+	1.51017e6i	−0.303716	+	0.526052i	0.673258	+	0.739407i	$0.264894\pi$
$384$	327827.			0.113453
$385$	95086.9	+	164695.i	0.0326941	+	0.0566278i
$386$	106525.	+	184506.i	0.0363900	+	0.0630293i
$387$	−721768.	−	1.25014e6i	−0.244974	−	0.424308i
$388$	301069.	−	521467.i	0.101528	−	0.175852i
$389$	−1.10667e6	+	1.91681e6i	−0.370804	+	0.642251i	−0.989689	−	0.143230i	$-0.954251\pi$
$389$	−1.10667e6	+	1.91681e6i	−0.370804	+	0.642251i	0.618885	+	0.785481i	$0.287585\pi$
$390$	459871.	+	796520.i	0.153100	+	0.265176i
$391$	−22020.7	−	38141.0i	−0.00728433	−	0.0126168i
$392$	147164.	+	254896.i	0.0483712	+	0.0837813i
$393$	3.88595e6			1.26916
$394$	−1.64548e6	+	2.85005e6i	−0.534012	+	0.924936i
$395$	−2.74705e6	−	4.75803e6i	−0.885878	−	1.53439i
$396$	−66838.0			−0.0214183
$397$	−2.74654e6			−0.874600			−0.437300	−	0.899316i	$-0.644065\pi$
$397$	−2.74654e6			−0.874600			−0.437300	+	0.899316i	$0.644065\pi$
$398$	1.25949e6	+	2.18150e6i	0.398553	+	0.690315i
$399$	−71232.4			−0.0223999
$400$	−138064.	+	239135.i	−0.0431451	+	0.0747295i
$401$	−2.24461e6			−0.697076			−0.348538	−	0.937295i	$-0.613322\pi$
$401$	−2.24461e6			−0.697076			−0.348538	+	0.937295i	$0.613322\pi$
$402$	−1.91593e6	+	3.31848e6i	−0.591308	+	1.02418i
$403$	−342088.	+	592513.i	−0.104924	+	0.181734i
$404$	1.35980e6	−	2.35524e6i	0.414496	−	0.717928i
$405$	2.35111e6	+	4.07224e6i	0.712254	+	1.23366i
$406$	−146943.			−0.0442418
$407$	−134062.	+	175775.i	−0.0401161	+	0.0525982i
$408$	950476.			0.282677
$409$	165235.	+	286195.i	0.0488419	+	0.0845967i	0.889413	−	0.457105i	$-0.151114\pi$
$409$	165235.	+	286195.i	0.0488419	+	0.0845967i	−0.840571	+	0.541702i	$0.817780\pi$
$410$	−45885.8	+	79476.5i	−0.0134809	+	0.0233496i
$411$	−568572.	+	984796.i	−0.166028	+	0.287569i
$412$	−939607.	+	1.62745e6i	−0.272711	+	0.472350i
$413$	677982.			0.195588
$414$	−18674.3	+	32344.8i	−0.00535480	+	0.00927479i
$415$	5.62120e6			1.60217
$416$	90748.5	+	157181.i	0.0257102	+	0.0445314i
$417$	−4.35521e6			−1.22650
$418$	3421.39			0.000957771
$419$	2.24326e6	+	3.88544e6i	0.624229	+	1.08120i	0.988689	+	0.149978i	$0.0479201\pi$
$419$	2.24326e6	+	3.88544e6i	0.624229	+	1.08120i	−0.364460	+	0.931219i	$0.618747\pi$
$420$	−1.14670e6	+	1.98615e6i	−0.317196	+	0.549400i
$421$	6.88738e6			1.89386			0.946932	−	0.321435i	$-0.104165\pi$
$421$	6.88738e6			1.89386			0.946932	+	0.321435i	$0.104165\pi$
$422$	1.87556e6	+	3.24857e6i	0.512685	+	0.887997i
$423$	−1.54848e6	−	2.68204e6i	−0.420779	−	0.728811i
$424$	−834574.	−	1.44552e6i	−0.225450	−	0.390491i
$425$	−400293.	+	693328.i	−0.107499	+	0.186194i
$426$	−2.86972e6	+	4.97051e6i	−0.766154	+	1.32702i
$427$	237942.	+	412128.i	0.0631542	+	0.109386i
$428$	−636268.	−	1.10205e6i	−0.167892	−	0.290798i
$429$	−47073.6	−	81533.9i	−0.0123491	−	0.0213892i
$430$	2.37909e6			0.620496
$431$	138293.	−	239531.i	0.0358598	−	0.0621110i	−0.847538	−	0.530734i	$-0.821916\pi$
$431$	138293.	−	239531.i	0.0358598	−	0.0621110i	0.883398	+	0.468623i	$0.155250\pi$
$432$	219341.	+	379910.i	0.0565471	+	0.0979425i
$433$	2.43955e6			0.625302			0.312651	−	0.949868i	$-0.398783\pi$
$433$	2.43955e6			0.625302			0.312651	+	0.949868i	$0.398783\pi$
$434$	−1.70601e6			−0.434769
$435$	215660.	+	373534.i	0.0546445	+	0.0946471i
$436$	−1.09928e6			−0.276944
$437$	955.924	−	1655.71i	0.000239453	−	0.000414744i
$438$	−2.75332e6			−0.685759
$439$	−992401.	+	1.71889e6i	−0.245768	+	0.425683i	−0.962347	−	0.271823i	$-0.912374\pi$
$439$	−992401.	+	1.71889e6i	−0.245768	+	0.425683i	0.716579	+	0.697506i	$0.245707\pi$
$440$	55077.7	−	95397.4i	0.0135626	−	0.0234912i
$441$	361836.	−	626718.i	0.0885961	−	0.153453i
$442$	263109.	+	455718.i	0.0640590	+	0.110953i
$443$	−1.31565e6			−0.318516			−0.159258	−	0.987237i	$-0.550910\pi$
$443$	−1.31565e6			−0.318516			−0.159258	+	0.987237i	$0.550910\pi$
$444$	−2.64413e6	−	340242.i	−0.636539	−	0.0819089i
$445$	9.22206e6			2.20764
$446$	−877453.	−	1.51979e6i	−0.208875	−	0.361782i
$447$	−845745.	+	1.46487e6i	−0.200203	+	0.346762i
$448$	−226284.	+	391936.i	−0.0532671	+	0.0922614i
$449$	−1.68792e6	+	2.92356e6i	−0.395126	+	0.684378i	−0.993117	−	0.117125i	$-0.962632\pi$
$449$	−1.68792e6	+	2.92356e6i	−0.395126	+	0.684378i	0.597992	+	0.801502i	$0.295966\pi$
$450$	678924.			0.158048
$451$	4697.00	−	8135.43i	0.00108737	−	0.00188339i
$452$	84997.4			0.0195686
$453$	−2.32508e6	−	4.02716e6i	−0.532345	−	0.922048i
$454$	2.68574e6			0.611539
$455$	−1.26971e6			−0.287526
$456$	20630.2	+	35732.5i	0.00464612	+	0.00804732i
$457$	1.26430e6	−	2.18984e6i	0.283179	−	0.490480i	−0.688987	−	0.724773i	$-0.741944\pi$
$457$	1.26430e6	−	2.18984e6i	0.283179	−	0.490480i	0.972166	+	0.234294i	$0.0752777\pi$
$458$	−3.79304e6			−0.844937
$459$	635940.	+	1.10148e6i	0.140891	+	0.244031i
$460$	−30777.1	−	53307.4i	−0.00678160	−	0.0117461i
$461$	4.14355e6	+	7.17684e6i	0.908072	+	1.57283i	0.816739	+	0.577007i	$0.195779\pi$
$461$	4.14355e6	+	7.17684e6i	0.908072	+	1.57283i	0.0913330	+	0.995820i	$0.470887\pi$
$462$	117380.	−	203308.i	0.0255851	−	0.0443148i
$463$	2.40058e6	−	4.15792e6i	0.520431	−	0.901414i	−0.479286	−	0.877659i	$-0.659104\pi$
$463$	2.40058e6	−	4.15792e6i	0.520431	−	0.901414i	0.999718	−	0.0237550i	$-0.00756217\pi$
$464$	42557.2	+	73711.2i	0.00917652	+	0.0158942i
$465$	2.50383e6	+	4.33676e6i	0.536998	+	0.930107i
$466$	875211.	+	1.51591e6i	0.186702	+	0.323377i
$467$	−4.03321e6			−0.855773			−0.427886	−	0.903832i	$-0.640742\pi$
$467$	−4.03321e6			−0.855773			−0.427886	+	0.903832i	$0.640742\pi$
$468$	223125.	−	386464.i	0.0470906	−	0.0815633i
$469$	−2.64496e6	−	4.58121e6i	−0.555248	−	0.961718i
$470$	5.10408e6			1.06579
$471$	733261.			0.152302
$472$	−196356.	−	340098.i	−0.0405685	−	0.0702666i
$473$	−243530.			−0.0500494
$474$	−3.39109e6	+	5.87354e6i	−0.693255	+	1.20075i
$475$	−34753.6			−0.00706751
$476$	−656071.	+	1.13635e6i	−0.132719	+	0.229876i
$477$	−2.05199e6	+	3.55414e6i	−0.412932	+	0.715219i
$478$	2.09660e6	−	3.63141e6i	0.419706	−	0.726952i
$479$	−1.74125e6	−	3.01593e6i	−0.346755	−	0.600597i	0.638916	−	0.769276i	$-0.279383\pi$
$479$	−1.74125e6	−	3.01593e6i	−0.346755	−	0.600597i	−0.985671	+	0.168680i	$0.946050\pi$
$480$	1.32842e6			0.263168
$481$	−568810.	−	1.36195e6i	−0.112100	−	0.268410i
$482$	2.54658e6			0.499274
$483$	−65590.9	−	113607.i	−0.0127931	−	0.0221583i
$484$	1.28277e6	−	2.22182e6i	0.248906	−	0.431118i
$485$	1.22000e6	−	2.11309e6i	0.235507	−	0.407910i
$486$	2.06951e6	−	3.58449e6i	0.397444	−	0.688393i
$487$	−3.33940e6			−0.638038			−0.319019	−	0.947748i	$-0.603353\pi$
$487$	−3.33940e6			−0.638038			−0.319019	+	0.947748i	$0.603353\pi$
$488$	137825.	−	238719.i	0.0261986	−	0.0453773i
$489$	4.70308e6			0.889426
$490$	596340.	+	1.03289e6i	0.112203	+	0.194341i
$491$	−8.36824e6			−1.56650			−0.783250	−	0.621707i	$-0.786440\pi$
$491$	−8.36824e6			−1.56650			−0.783250	+	0.621707i	$0.786440\pi$
$492$	113287.			0.0210993
$493$	123387.	+	213713.i	0.0228640	+	0.0396016i
$494$	−11421.6	+	19782.8i	−0.00210577	+	0.00364730i
$495$	−270842.			−0.0496824
$496$	494092.	+	855793.i	0.0901787	+	0.156194i
$497$	−3.96169e6	−	6.86184e6i	−0.719431	−	1.24609i
$498$	−3.46954e6	−	6.00941e6i	−0.626900	−	1.08582i
$499$	−2.18144e6	+	3.77837e6i	−0.392186	+	0.679287i	−0.992738	−	0.120300i	$-0.961614\pi$
$499$	−2.18144e6	+	3.77837e6i	−0.392186	+	0.679287i	0.600551	+	0.799586i	$0.294948\pi$
$500$	1.06142e6	−	1.83843e6i	0.189872	−	0.328869i
$501$	5.65839e6	+	9.80062e6i	1.00716	+	1.74445i
$502$	1.45905e6	+	2.52714e6i	0.258410	+	0.447579i
$503$	−1.18916e6	−	2.05968e6i	−0.209565	−	0.362977i	0.742012	−	0.670386i	$-0.233871\pi$
$503$	−1.18916e6	−	2.05968e6i	−0.209565	−	0.362977i	−0.951578	+	0.307409i	$0.900538\pi$
$504$	1.11274e6			0.195127
$505$	5.51018e6	−	9.54392e6i	0.961474	−	1.66532i
$506$	3150.42	+	5456.69i	0.000547007	+	0.000947443i
$507$	−6.80060e6			−1.17497
$508$	−2.08360e6			−0.358224
$509$	−1.06730e6	−	1.84861e6i	−0.182596	−	0.316266i	0.760168	−	0.649727i	$-0.225117\pi$
$509$	−1.06730e6	−	1.84861e6i	−0.182596	−	0.316266i	−0.942764	+	0.333461i	$0.891783\pi$
$510$	3.85153e6			0.655704
$511$	1.90050e6	−	3.29175e6i	0.321969	−	0.557667i
$512$	262144.			0.0441942
$513$	−27606.3	+	47815.5i	−0.00463143	+	0.00802187i
$514$	2.55316e6	−	4.42221e6i	0.426256	−	0.738297i
$515$	−3.80749e6	+	6.59476e6i	−0.632587	+	1.09567i
$516$	−1.46843e6	−	2.54339e6i	−0.242788	−	0.420522i
$517$	−522468.			−0.0859672
$518$	2.23190e6	−	2.92636e6i	0.365470	−	0.479184i
$519$	1.41871e7			2.31194
$520$	367732.	+	636930.i	0.0596380	+	0.103296i
$521$	−2.02888e6	+	3.51412e6i	−0.327462	+	0.567181i	−0.982008	−	0.188842i	$-0.939527\pi$
$521$	−2.02888e6	+	3.51412e6i	−0.327462	+	0.567181i	0.654545	+	0.756023i	$0.272860\pi$
$522$	104636.	−	181236.i	0.0168076	−	0.0291117i
$523$	2.51729e6	−	4.36008e6i	0.402420	−	0.697011i	−0.591598	−	0.806233i	$-0.701503\pi$
$523$	2.51729e6	−	4.36008e6i	0.402420	−	0.697011i	0.994017	+	0.109222i	$0.0348359\pi$
$524$	3.10737e6			0.494384
$525$	−1.19231e6	+	2.06515e6i	−0.188796	+	0.327004i
$526$	499835.			0.0787702
$527$	1.43253e6	+	2.48122e6i	0.224687	+	0.389170i
$528$	−135981.			−0.0212272
$529$	−6.43282e6			−0.999453
$530$	−3.38187e6	−	5.85757e6i	−0.522958	−	0.905791i
$531$	−482784.	+	836207.i	−0.0743048	+	0.128700i
$532$	−56960.4			−0.00872557
$533$	31360.0	+	54317.0i	0.00478143	+	0.00828167i
$534$	−5.69207e6	−	9.85896e6i	−0.863808	−	1.49616i
$535$	−2.57829e6	−	4.46573e6i	−0.389446	−	0.674541i
$536$	−1.53206e6	+	2.65360e6i	−0.230336	+	0.398954i
$537$	−6.50826e6	+	1.12726e7i	−0.973933	+	1.68690i
$538$	2.44358e6	+	4.23240e6i	0.363974	+	0.630422i
$539$	−61043.0	−	105730.i	−0.00905031	−	0.0156756i
$540$	888816.	+	1.53947e6i	0.131168	+	0.227189i
$541$	−4.52167e6			−0.664210			−0.332105	−	0.943242i	$-0.607759\pi$
$541$	−4.52167e6			−0.664210			−0.332105	+	0.943242i	$0.607759\pi$
$542$	661609.	−	1.14594e6i	0.0967393	−	0.167557i
$543$	−1.44071e6	−	2.49538e6i	−0.209690	−	0.363193i
$544$	760040.			0.110113
$545$	−4.45452e6			−0.642406
$546$	783697.	+	1.35740e6i	0.112504	+	0.194862i
$547$	−516857.			−0.0738588			−0.0369294	−	0.999318i	$-0.511758\pi$
$547$	−516857.			−0.0738588			−0.0369294	+	0.999318i	$0.511758\pi$
$548$	−454654.	+	787484.i	−0.0646740	+	0.112019i
$549$	−677746.			−0.0959701
$550$	57268.5	−	99191.9i	0.00807252	−	0.0139820i
$551$	−5356.26	+	9277.32i	−0.000751593	+	0.00130180i
$552$	−37992.6	+	65805.2i	−0.00530703	+	0.00919205i
$553$	−4.68144e6	−	8.10848e6i	−0.650978	−	1.12753i
$554$	−1.29946e6			−0.179882
$555$	−1.07146e7	−	1.37873e6i	−1.47653	−	0.189998i
$556$	−3.48261e6			−0.477768
$557$	3.98017e6	+	6.89385e6i	0.543580	+	0.941508i	0.998695	+	0.0510752i	$0.0162648\pi$
$557$	3.98017e6	+	6.89385e6i	0.543580	+	0.941508i	−0.455115	+	0.890433i	$0.650402\pi$
$558$	1.21484e6	−	2.10416e6i	0.165170	−	0.286084i
$559$	812975.	−	1.40811e6i	0.110039	−	0.190594i
$560$	−916952.	+	1.58821e6i	−0.123560	+	0.214012i
$561$	−394253.			−0.0528893
$562$	−30291.9	+	52467.1i	−0.00404562	+	0.00700723i
$563$	465924.			0.0619503			0.0309752	−	0.999520i	$-0.490139\pi$
$563$	465924.			0.0619503			0.0309752	+	0.999520i	$0.490139\pi$
$564$	−3.15036e6	−	5.45658e6i	−0.417025	−	0.722308i
$565$	344428.			0.0453917
$566$	4.53122e6			0.594531
$567$	4.00668e6	+	6.93978e6i	0.523392	+	0.906542i
$568$	−2.29475e6	+	3.97463e6i	−0.298445	+	0.516923i
$569$	−1.21610e6			−0.157467			−0.0787335	−	0.996896i	$-0.525088\pi$
$569$	−1.21610e6			−0.157467			−0.0787335	+	0.996896i	$0.525088\pi$
$570$	83597.8	+	144796.i	0.0107772	+	0.0186667i
$571$	−535965.	−	928319.i	−0.0687933	−	0.119154i	0.829577	−	0.558392i	$-0.188582\pi$
$571$	−535965.	−	928319.i	−0.0687933	−	0.119154i	−0.898370	+	0.439239i	$0.855248\pi$
$572$	−37642.0	−	65197.9i	−0.00481042	−	0.00833190i
$573$	−5.78241e6	+	1.00154e7i	−0.735737	+	1.27433i
$574$	−78197.1	+	135441.i	−0.00990629	+	0.0171582i
$575$	−32001.2	−	55427.7i	−0.00403643	−	0.00699129i
$576$	−322270.	−	558188.i	−0.0404728	−	0.0701010i
$577$	−2.73419e6	−	4.73576e6i	−0.341893	−	0.592175i	0.642892	−	0.765957i	$-0.277735\pi$
$577$	−2.73419e6	−	4.73576e6i	−0.341893	−	0.592175i	−0.984784	+	0.173782i	$0.944401\pi$
$578$	−3.47583e6			−0.432751
$579$	532862.	−	922944.i	0.0660569	−	0.114414i
$580$	172451.	+	298694.i	0.0212861	+	0.0368685i
$581$	9.57947e6			1.17734
$582$	−3.01204e6			−0.368598
$583$	346177.	+	599597.i	0.0421820	+	0.0730614i
$584$	−2.20167e6			−0.267128
$585$	904151.	−	1.56604e6i	0.109232	−	0.189196i
$586$	−3.04116e6			−0.365844
$587$	−3.91159e6	+	6.77507e6i	−0.468552	+	0.811556i	−0.999354	−	0.0359397i	$-0.988558\pi$
$587$	−3.91159e6	+	6.77507e6i	−0.468552	+	0.811556i	0.530802	+	0.847496i	$0.321891\pi$
$588$	736149.	−	1.27505e6i	0.0878057	−	0.152084i
$589$	−62186.6	+	107710.i	−0.00738599	+	0.0127929i
$590$	−795675.	−	1.37815e6i	−0.0941035	−	0.162992i
$591$	1.64621e7			1.93873
$592$	−2.11436e6	−	272072.i	−0.247956	−	0.0319065i
$593$	4.90773e6			0.573118			0.286559	−	0.958063i	$-0.407489\pi$
$593$	4.90773e6			0.573118			0.286559	+	0.958063i	$0.407489\pi$
$594$	−90981.6	−	157585.i	−0.0105800	−	0.0183252i
$595$	−2.65854e6	+	4.60473e6i	−0.307858	+	0.533226i
$596$	−676293.	+	1.17137e6i	−0.0779865	+	0.135077i
$597$	6.30026e6	−	1.09124e7i	0.723474	−	1.25309i
$598$	−42068.2			−0.00481062
$599$	−4.68705e6	+	8.11821e6i	−0.533744	+	0.924471i	0.465479	+	0.885059i	$0.345882\pi$
$599$	−4.68705e6	+	8.11821e6i	−0.533744	+	0.924471i	−0.999223	+	0.0394125i	$0.987451\pi$
$600$	1.38126e6			0.156638
$601$	−1.58550e6	−	2.74617e6i	−0.179053	−	0.310128i	0.762504	−	0.646984i	$-0.223970\pi$
$601$	−1.58550e6	−	2.74617e6i	−0.179053	−	0.310128i	−0.941556	+	0.336856i	$0.890637\pi$
$602$	4.05436e6			0.455965
$603$	7.53380e6			0.843764
$604$	−1.85923e6	−	3.22029e6i	−0.207368	−	0.359172i
$605$	5.19806e6	−	9.00330e6i	0.577368	−	1.00003i
$606$	−1.36041e7			−1.50483
$607$	−3.59976e6	−	6.23497e6i	−0.396554	−	0.686852i	0.596744	−	0.802431i	$-0.296461\pi$
$607$	−3.59976e6	−	6.23497e6i	−0.396554	−	0.686852i	−0.993298	+	0.115580i	$0.963127\pi$
$608$	16496.8	+	28573.2i	0.00180984	+	0.00313473i
$609$	367521.	+	636565.i	0.0401549	+	0.0695504i
$610$	558495.	−	967342.i	0.0607708	−	0.105258i
$611$	1.74415e6	−	3.02096e6i	0.189009	−	0.327373i
$612$	−934364.	−	1.61837e6i	−0.100841	−	0.174662i
$613$	7.54214e6	+	1.30634e7i	0.810669	+	1.40412i	0.912397	+	0.409307i	$0.134230\pi$
$613$	7.54214e6	+	1.30634e7i	0.810669	+	1.40412i	−0.101728	+	0.994812i	$0.532437\pi$
$614$	4.77831e6	+	8.27627e6i	0.511509	+	0.885960i
$615$	459063.			0.0489424
$616$	93861.7	−	162573.i	0.00996636	−	0.0172622i
$617$	−364734.	−	631737.i	−0.0385712	−	0.0668072i	0.846095	−	0.533032i	$-0.178947\pi$
$617$	−364734.	−	631737.i	−0.0385712	−	0.0668072i	−0.884667	+	0.466224i	$0.845614\pi$
$618$	9.40028e6			0.990078
$619$	−1.74198e7			−1.82732			−0.913662	−	0.406474i	$-0.866758\pi$
$619$	−1.74198e7			−1.82732			−0.913662	+	0.406474i	$0.866758\pi$
$620$	2.00217e6	+	3.46786e6i	0.209180	+	0.362311i
$621$	−101680.			−0.0105805
$622$	−704007.	+	1.21938e6i	−0.0729627	+	0.126375i
$623$	1.57159e7			1.62226
$624$	453945.	−	786257.i	0.0466705	−	0.0808356i
$625$	5.98645e6	−	1.03688e7i	0.613012	−	1.06177i
$626$	4.29719e6	−	7.44295e6i	0.438277	−	0.759118i
$627$	−8557.30	−	14821.7i	−0.000869297	−	0.00150567i
$628$	586346.			0.0593274
$629$	−6.13020e6	−	788825.i	−0.617800	−	0.0794976i
$630$	4.50906e6			0.452621
$631$	3.65417e6	+	6.32921e6i	0.365356	+	0.632814i	0.988833	−	0.149027i	$-0.0476141\pi$
$631$	3.65417e6	+	6.32921e6i	0.365356	+	0.632814i	−0.623478	+	0.781841i	$0.714281\pi$
$632$	−2.71166e6	+	4.69673e6i	−0.270049	+	0.467738i
$633$	9.38202e6	−	1.62501e7i	0.930651	−	1.61194i
$634$	2.54435e6	−	4.40694e6i	0.251393	−	0.435426i
$635$	−8.44319e6			−0.830945
$636$	−4.17474e6	+	7.23086e6i	−0.409248	+	0.708838i
$637$	815119.			0.0795925
$638$	−17652.5	−	30575.1i	−0.00171694	−	0.00297383i
$639$	1.12843e7			1.09326
$640$	1.06226e6			0.102514
$641$	7.79246e6	+	1.34969e7i	0.749082	+	1.29745i	0.948263	+	0.317485i	$0.102838\pi$
$641$	7.79246e6	+	1.34969e7i	0.749082	+	1.29745i	−0.199181	+	0.979963i	$0.563828\pi$
$642$	−3.18276e6	+	5.51271e6i	−0.304766	+	0.527870i
$643$	−1.16617e7			−1.11234			−0.556168	−	0.831070i	$-0.687729\pi$
$643$	−1.16617e7			−1.11234			−0.556168	+	0.831070i	$0.687729\pi$
$644$	−52449.3	−	90844.8i	−0.00498339	−	0.00863148i
$645$	−5.95038e6	−	1.03064e7i	−0.563177	−	0.975452i
$646$	47829.4	+	82843.0i	0.00450935	+	0.00781042i
$647$	−9.48925e6	+	1.64359e7i	−0.891192	+	1.54359i	−0.0527436	+	0.998608i	$0.516797\pi$
$647$	−9.48925e6	+	1.64359e7i	−0.891192	+	1.54359i	−0.838448	+	0.544981i	$0.816537\pi$
$648$	2.32081e6	−	4.01977e6i	0.217121	−	0.376065i
$649$	81447.5	+	141071.i	0.00759042	+	0.0131470i
$650$	382359.	+	662265.i	0.0354967	+	0.0614820i
$651$	4.26695e6	+	7.39057e6i	0.394607	+	0.683479i
$652$	3.76078e6			0.346464
$653$	−2.89503e6	+	5.01434e6i	−0.265687	+	0.460184i	−0.967743	−	0.251938i	$-0.918932\pi$
$653$	−2.89503e6	+	5.01434e6i	−0.265687	+	0.460184i	0.702056	+	0.712121i	$0.252265\pi$
$654$	2.74943e6	+	4.76216e6i	0.251361	+	0.435371i
$655$	1.25917e7			1.14678
$656$	90589.1			0.00821895
$657$	2.70665e6	+	4.68805e6i	0.244635	+	0.423720i
$658$	8.69821e6			0.783186
$659$	4.69820e6	−	8.13751e6i	0.421422	−	0.729925i	−0.574656	−	0.818395i	$-0.694864\pi$
$659$	4.69820e6	−	8.13751e6i	0.421422	−	0.729925i	0.996079	+	0.0884697i	$0.0281977\pi$
$660$	−551024.			−0.0492392
$661$	−5.36965e6	+	9.30050e6i	−0.478016	+	0.827948i	−0.999682	−	0.0252019i	$-0.991977\pi$
$661$	−5.36965e6	+	9.30050e6i	−0.478016	+	0.827948i	0.521667	+	0.853149i	$0.325310\pi$
$662$	5.33208e6	−	9.23543e6i	0.472881	−	0.819053i
$663$	1.31613e6	−	2.27961e6i	0.116283	−	0.201408i
$664$	−2.77439e6	−	4.80538e6i	−0.244201	−	0.422968i
$665$	−230816.			−0.0202400
$666$	2.01998e6	+	4.83661e6i	0.176466	+	0.422528i
$667$	−19728.2			−0.00171701
$668$	4.52469e6	+	7.83699e6i	0.392326	+	0.679529i
$669$	−4.38923e6	+	7.60237e6i	−0.379161	+	0.656725i
$670$	−6.20822e6	+	1.07529e7i	−0.534293	+	0.925423i
$671$	−57169.1	+	99019.8i	−0.00490179	+	0.00849015i
$672$	2.26386e6			0.193386
$673$	−7.77396e6	+	1.34649e7i	−0.661614	+	1.14595i	0.318578	+	0.947897i	$0.396795\pi$
$673$	−7.77396e6	+	1.34649e7i	−0.661614	+	1.14595i	−0.980192	+	0.198052i	$0.936539\pi$
$674$	457360.			0.0387800
$675$	924169.	+	1.60071e6i	0.0780714	+	0.135224i
$676$	−5.43805e6			−0.457695
$677$	1.00615e7			0.843705			0.421852	−	0.906665i	$-0.361380\pi$
$677$	1.00615e7			0.843705			0.421852	+	0.906665i	$0.361380\pi$
$678$	−212589.	−	368214.i	−0.0177609	−	0.0307629i
$679$	2.07908e6	−	3.60107e6i	0.173060	−	0.299748i
$680$	3.07984e6			0.255421
$681$	−6.71735e6	−	1.16348e7i	−0.555048	−	0.961371i
$682$	−204947.	−	354979.i	−0.0168726	−	0.0292241i
$683$	−794804.	−	1.37664e6i	−0.0651941	−	0.112919i	0.831586	−	0.555396i	$-0.187433\pi$
$683$	−794804.	−	1.37664e6i	−0.0651941	−	0.112919i	−0.896780	+	0.442477i	$0.854100\pi$
$684$	40561.0	−	70253.6i	0.00331488	−	0.00574154i
$685$	−1.84236e6	+	3.19105e6i	−0.150019	+	0.259841i
$686$	4.73029e6	+	8.19310e6i	0.383775	+	0.664719i
$687$	9.48685e6	+	1.64317e7i	0.766885	+	1.32828i
$688$	−1.17422e6	−	2.03380e6i	−0.0945751	−	0.163809i
$689$	−4.62258e6			−0.370968
$690$	−153954.	+	266656.i	−0.0123103	+	0.0213221i
$691$	−317507.	−	549938.i	−0.0252964	−	0.0438146i	0.853100	−	0.521747i	$-0.174720\pi$
$691$	−317507.	−	549938.i	−0.0252964	−	0.0438146i	−0.878396	+	0.477933i	$0.841386\pi$
$692$	1.13446e7			0.900587
$693$	−461560.			−0.0365086
$694$	4.67555e6	+	8.09830e6i	0.368497	+	0.638256i
$695$	−1.41123e7			−1.10824
$696$	212881.	−	368721.i	0.0166577	−	0.0288519i
$697$	262647.			0.0204782
$698$	3.17885e6	−	5.50592e6i	0.246962	−	0.427752i
$699$	4.37802e6	−	7.58295e6i	0.338910	−	0.587009i
$700$	−953424.	+	1.65138e6i	−0.0735430	+	0.127380i
$701$	−7.99879e6	−	1.38543e7i	−0.614793	−	1.06485i	−0.990421	−	0.138082i	$-0.955906\pi$
$701$	−7.99879e6	−	1.38543e7i	−0.614793	−	1.06485i	0.375627	−	0.926771i	$-0.377427\pi$
$702$	1.21490e6			0.0930457
$703$	−103401.	−	247582.i	−0.00789111	−	0.0188943i
$704$	−108736.			−0.00826880
$705$	−1.27659e7	−	2.21112e7i	−0.967340	−	1.67548i
$706$	−2.28100e6	+	3.95082e6i	−0.172232	+	0.298315i
$707$	9.39028e6	−	1.62644e7i	0.706529	−	1.22374i
$708$	−982218.	+	1.70125e6i	−0.0736419	+	0.127551i
$709$	1.53555e6			0.114723			0.0573613	−	0.998353i	$-0.481731\pi$
$709$	1.53555e6			0.114723			0.0573613	+	0.998353i	$0.481731\pi$
$710$	−9.29882e6	+	1.61060e7i	−0.692280	+	1.19906i
$711$	1.33344e7			0.989237
$712$	−4.55162e6	−	7.88364e6i	−0.336485	−	0.582809i
$713$	−229046.			−0.0168733
$714$	6.56365e6			0.481837
$715$	−152534.	−	264196.i	−0.0111584	−	0.0193268i
$716$	−5.20428e6	+	9.01407e6i	−0.379383	+	0.657111i
$717$	−2.09753e7			−1.52374
$718$	−1.38086e6	−	2.39172e6i	−0.0999627	−	0.173141i
$719$	−436073.	−	755300.i	−0.0314584	−	0.0544876i	0.849868	−	0.526996i	$-0.176682\pi$
$719$	−436073.	−	755300.i	−0.0314584	−	0.0544876i	−0.881326	+	0.472509i	$0.843349\pi$
$720$	−1.30591e6	−	2.26189e6i	−0.0938816	−	0.162608i
$721$	−6.48860e6	+	1.12386e7i	−0.464850	+	0.805143i
$722$	4.95012e6	−	8.57386e6i	0.353405	−	0.612116i
$723$	−6.36929e6	−	1.10319e7i	−0.453154	−	0.784885i
$724$	−1.15205e6	−	1.99541e6i	−0.0816819	−	0.141477i
$725$	179310.	+	310574.i	0.0126695	+	0.0219442i
$726$	−1.28334e7			−0.903653
$727$	421281.	−	729679.i	0.0295621	−	0.0512031i	−0.850866	−	0.525383i	$-0.823922\pi$
$727$	421281.	−	729679.i	0.0295621	−	0.0512031i	0.880428	+	0.474180i	$0.157255\pi$
$728$	626677.	+	1.08544e6i	0.0438243	+	0.0759060i
$729$	−3.08065e6			−0.214696
$730$	−8.92163e6			−0.619637
$731$	−3.40443e6	−	5.89665e6i	−0.235641	−	0.408142i
$732$	−1.37886e6			−0.0951139
$733$	1.38140e7	−	2.39266e7i	0.949641	−	1.64483i	0.203461	−	0.979083i	$-0.434781\pi$
$733$	1.38140e7	−	2.39266e7i	0.949641	−	1.64483i	0.746180	−	0.665744i	$-0.231886\pi$
$734$	−8.75101e6			−0.599540
$735$	2.98303e6	−	5.16677e6i	0.203676	−	0.352777i
$736$	−30380.5	+	52620.6i	−0.00206728	+	0.00358064i
$737$	635490.	−	1.10070e6i	0.0430963	−	0.0746450i
$738$	−111367.	−	192893.i	−0.00752688	−	0.0130369i
$739$	3.58086e6			0.241199			0.120600	−	0.992701i	$-0.461518\pi$
$739$	3.58086e6			0.241199			0.120600	+	0.992701i	$0.461518\pi$
$740$	−8.56782e6	−	1.10249e6i	−0.575163	−	0.0740111i
$741$	114267.			0.00764499
$742$	−5.76327e6	−	9.98228e6i	−0.384290	−	0.665610i
$743$	9.51175e6	−	1.64748e7i	0.632104	−	1.09484i	−0.355017	−	0.934860i	$-0.615525\pi$
$743$	9.51175e6	−	1.64748e7i	0.632104	−	1.09484i	0.987121	−	0.159976i	$-0.0511418\pi$
$744$	2.47157e6	−	4.28088e6i	0.163697	−	0.283531i
$745$	−2.74048e6	+	4.74665e6i	−0.180899	+	0.313326i
$746$	−2.02339e7			−1.33116
$747$	−6.82145e6	+	1.18151e7i	−0.447275	+	0.774704i
$748$	−315261.			−0.0206023
$749$	−4.39384e6	−	7.61036e6i	−0.286180	−	0.495679i
$750$	−1.06189e7			−0.689331
$751$	2.47352e7			1.60035			0.800175	−	0.599766i	$-0.204740\pi$
$751$	2.47352e7			1.60035			0.800175	+	0.599766i	$0.204740\pi$
$752$	−2.51916e6	−	4.36331e6i	−0.162447	−	0.281366i
$753$	7.29849e6	−	1.26414e7i	0.469079	−	0.812468i
$754$	235718.			0.0150996
$755$	−7.53401e6	−	1.30493e7i	−0.481015	−	0.833143i
$756$	1.51469e6	+	2.62352e6i	0.0963873	+	0.166948i
$757$	3.70412e6	+	6.41573e6i	0.234934	+	0.406917i	0.959253	−	0.282547i	$-0.0911793\pi$
$757$	3.70412e6	+	6.41573e6i	0.234934	+	0.406917i	−0.724320	+	0.689464i	$0.757846\pi$
$758$	−1.41080e6	+	2.44357e6i	−0.0891849	+	0.154473i
$759$	15759.2	−	27295.7i	0.000992953	−	0.00171985i
$760$	66848.3	+	115785.i	0.00419814	+	0.00727139i
$761$	1.06035e7	+	1.83658e7i	0.663723	+	1.14960i	0.979630	+	0.200812i	$0.0643581\pi$
$761$	1.06035e7	+	1.83658e7i	0.663723	+	1.14960i	−0.315907	+	0.948790i	$0.602309\pi$
$762$	5.21133e6	+	9.02629e6i	0.325133	+	0.563147i
$763$	−7.59125e6			−0.472065
$764$	−4.62386e6	+	8.00876e6i	−0.286597	+	0.496400i
$765$	−3.78624e6	−	6.55796e6i	−0.233913	−	0.405150i
$766$	6.97518e6			0.429520
$767$	−1.08758e6			−0.0667535
$768$	−655653.	−	1.13563e6i	−0.0401117	−	0.0694755i
$769$	−1.31558e7			−0.802235			−0.401117	−	0.916027i	$-0.631378\pi$
$769$	−1.31558e7			−0.802235			−0.401117	+	0.916027i	$0.631378\pi$
$770$	380348.	−	658781.i	0.0231182	−	0.0400419i
$771$	−2.55430e7			−1.54752
$772$	426099.	−	738025.i	0.0257316	−	0.0445685i
$773$	1.02681e7	−	1.77848e7i	0.618074	−	1.07054i	−0.371763	−	0.928328i	$-0.621247\pi$
$773$	1.02681e7	−	1.77848e7i	0.618074	−	1.07054i	0.989837	−	0.142208i	$-0.0454201\pi$
$774$	−2.88707e6	+	5.00055e6i	−0.173223	+	0.300031i
$775$	2.08180e6	+	3.60579e6i	0.124505	+	0.215648i
$776$	−2.40855e6			−0.143583
$777$	−1.82594e7	−	2.34959e6i	−1.08501	−	0.139618i
$778$	8.85337e6			0.524396
$779$	5700.79	+	9874.05i	0.000336582	+	0.000582977i
$780$	1.83948e6	−	3.18608e6i	0.108258	−	0.187508i
$781$	951853.	−	1.64866e6i	0.0558396	−	0.0967170i
$782$	−88082.9	+	152564.i	−0.00515080	+	0.00892145i
$783$	569735.			0.0332100
$784$	588656.	−	1.01958e6i	0.0342036	−	0.0592423i
$785$	2.37600e6			0.137617
$786$	−7.77190e6	−	1.34613e7i	−0.448715	−	0.777198i
$787$	2.94592e7			1.69545			0.847724	−	0.530437i	$-0.177972\pi$
$787$	2.94592e7			1.69545			0.847724	+	0.530437i	$0.177972\pi$
$788$	1.31638e7			0.755207
$789$	−1.25015e6	−	2.16532e6i	−0.0714938	−	0.123831i
$790$	−1.09882e7	+	1.90321e7i	−0.626410	+	1.08497i
$791$	586962.			0.0333556
$792$	133676.	+	231534.i	0.00757252	+	0.0131160i
$793$	−381695.	−	661115.i	−0.0215543	−	0.0373331i
$794$	5.49308e6	+	9.51429e6i	0.309218	+	0.535581i
$795$	−1.69169e7	+	2.93010e7i	−0.949300	+	1.64424i
$796$	5.03795e6	−	8.72599e6i	0.281820	−	0.488126i
$797$	7.66031e6	+	1.32680e7i	0.427170	+	0.739880i	0.996620	−	0.0821457i	$-0.0261773\pi$
$797$	7.66031e6	+	1.32680e7i	0.427170	+	0.739880i	−0.569450	+	0.822026i	$0.692844\pi$
$798$	142465.	+	246756.i	0.00791954	+	0.0137171i
$799$	−7.30385e6	−	1.26506e7i	−0.404748	−	0.701045i
$800$	1.10452e6			0.0610164
$801$	−1.11912e7	+	1.93837e7i	−0.616303	+	1.06747i
$802$	4.48922e6	+	7.77556e6i	0.246454	+	0.426870i
$803$	913243.			0.0499801
$804$	1.53274e7			0.836236
$805$	−212536.	−	368122.i	−0.0115596	−	0.0200218i
$806$	2.73670e6			0.148385
$807$	1.22234e7	−	2.11715e7i	0.660704	−	1.14437i
$808$	−1.08784e7			−0.586186
$809$	−3.79590e6	+	6.57469e6i	−0.203912	+	0.353187i	−0.949786	−	0.312901i	$-0.898699\pi$
$809$	−3.79590e6	+	6.57469e6i	−0.203912	+	0.353187i	0.745873	+	0.666088i	$0.232032\pi$
$810$	9.40443e6	−	1.62890e7i	0.503640	−	0.872329i
$811$	−1.35074e7	+	2.33955e7i	−0.721140	+	1.24905i	0.239403	+	0.970920i	$0.423048\pi$
$811$	−1.35074e7	+	2.33955e7i	−0.721140	+	1.24905i	−0.960543	+	0.278132i	$0.910285\pi$
$812$	293885.	+	509024.i	0.0156418	+	0.0270924i
$813$	−6.61905e6			−0.351212
$814$	877025.	+	112854.i	0.0463929	+	0.00596976i
$815$	1.52395e7			0.803666
$816$	−1.90095e6	−	3.29254e6i	−0.0999414	−	0.173104i
$817$	147787.	−	255975.i	0.00774607	−	0.0134166i
$818$	660938.	−	1.14478e6i	0.0345364	−	0.0598189i
$819$	1.54083e6	−	2.66879e6i	0.0802682	−	0.139029i
$820$	367086.			0.0190649
$821$	−2.13912e6	+	3.70507e6i	−0.110759	+	0.191840i	−0.916076	−	0.401004i	$-0.868661\pi$
$821$	−2.13912e6	+	3.70507e6i	−0.110759	+	0.191840i	0.805318	+	0.592844i	$0.201995\pi$
$822$	4.54858e6			0.234799
$823$	5.94935e6	+	1.03046e7i	0.306175	+	0.530311i	0.977522	−	0.210832i	$-0.0676174\pi$
$823$	5.94935e6	+	1.03046e7i	0.306175	+	0.530311i	−0.671347	+	0.741143i	$0.734284\pi$
$824$	7.51686e6			0.385672
$825$	−572941.			−0.0293073
$826$	−1.35596e6	−	2.34860e6i	−0.0691509	−	0.119773i
$827$	−6.52542e6	+	1.13024e7i	−0.331776	+	0.574652i	−0.982860	−	0.184353i	$-0.940981\pi$
$827$	−6.52542e6	+	1.13024e7i	−0.331776	+	0.574652i	0.651084	+	0.759005i	$0.274314\pi$
$828$	149394.			0.00757284
$829$	1.58422e6	+	2.74394e6i	0.0800623	+	0.138672i	0.903277	−	0.429059i	$-0.141155\pi$
$829$	1.58422e6	+	2.74394e6i	0.0800623	+	0.138672i	−0.823214	+	0.567731i	$0.807821\pi$
$830$	−1.12424e7	−	1.94724e7i	−0.566453	−	0.981125i
$831$	3.25010e6	+	5.62934e6i	0.163265	+	0.282784i
$832$	362994.	−	628724.i	0.0181799	−	0.0314885i
$833$	1.70670e6	−	2.95610e6i	0.0852208	−	0.147607i
$834$	8.71041e6	+	1.50869e7i	0.433634	+	0.751077i
$835$	1.83350e7	+	3.17571e7i	0.910048	+	1.57625i
$836$	−6842.78	−	11852.0i	−0.000338623	−	0.000586513i
$837$	6.61467e6			0.326358
$838$	8.97303e6	−	1.55417e7i	0.441397	−	0.764521i
$839$	−9.14767e6	−	1.58442e7i	−0.448648	−	0.777081i	0.549651	−	0.835395i	$-0.314761\pi$
$839$	−9.14767e6	−	1.58442e7i	−0.448648	−	0.777081i	−0.998298	+	0.0583140i	$0.981428\pi$
$840$	9.17363e6			0.448583
$841$	−2.04006e7			−0.994611
$842$	−1.37748e7	−	2.38586e7i	−0.669582	−	1.15975i
$843$	303054.			0.0146876
$844$	7.50226e6	−	1.29943e7i	0.362523	−	0.627908i
$845$	−2.20361e7			−1.06168
$846$	−6.19391e6	+	1.07282e7i	−0.297536	+	0.515347i
$847$	8.85836e6	−	1.53431e7i	0.424272	−	0.734861i
$848$	−3.33830e6	+	5.78210e6i	−0.159417	+	0.276119i
$849$	−1.13331e7	−	1.96296e7i	−0.539611	−	0.934633i
$850$	3.20235e6			0.152027
$851$	299651.	−	392887.i	0.0141838	−	0.0185970i
$852$	2.29578e7			1.08351
$853$	−130486.	−	226008.i	−0.00614031	−	0.0106353i	0.862939	−	0.505308i	$-0.168621\pi$
$853$	−130486.	−	226008.i	−0.00614031	−	0.0106353i	−0.869079	+	0.494673i	$0.835288\pi$
$854$	951769.	−	1.64851e6i	0.0446567	−	0.0773478i
$855$	164362.	−	284683.i	0.00768927	−	0.0133182i
$856$	−2.54507e6	+	4.40819e6i	−0.118718	+	0.205625i
$857$	2.63157e7			1.22395			0.611974	−	0.790878i	$-0.290376\pi$
$857$	2.63157e7			1.22395			0.611974	+	0.790878i	$0.290376\pi$
$858$	−188295.	+	326136.i	−0.00873211	+	0.0151245i
$859$	1.99705e7			0.923436			0.461718	−	0.887027i	$-0.347233\pi$
$859$	1.99705e7			0.923436			0.461718	+	0.887027i	$0.347233\pi$
$860$	−4.75817e6	−	8.24139e6i	−0.219378	−	0.379975i
$861$	782321.			0.0359648
$862$	−1.10635e6			−0.0507135
$863$	3.49174e6	+	6.04786e6i	0.159593	+	0.276424i	0.934722	−	0.355380i	$-0.115648\pi$
$863$	3.49174e6	+	6.04786e6i	0.159593	+	0.276424i	−0.775129	+	0.631803i	$0.782315\pi$
$864$	877364.	−	1.51964e6i	0.0399848	−	0.0692558i
$865$	4.59709e7			2.08902
$866$	−4.87910e6	−	8.45085e6i	−0.221078	−	0.382918i
$867$	8.69345e6	+	1.50575e7i	0.392776	+	0.680307i
$868$	3.41203e6	+	5.90981e6i	0.153714	+	0.266240i
$869$	1.12478e6	−	1.94818e6i	0.0505265	−	0.0875144i
$870$	862640.	−	1.49414e6i	0.0386395	−	0.0669256i
$871$	4.24291e6	+	7.34894e6i	0.189504	+	0.328231i
$872$	2.19856e6	+	3.80802e6i	0.0979146	+	0.169593i
$873$	2.96098e6	+	5.12857e6i	0.131492	+	0.227751i
$874$	−7647.39			−0.000338637
$875$	7.32978e6	−	1.26956e7i	0.323647	−	0.560572i
$876$	5.50664e6	+	9.53778e6i	0.242452	+	0.419940i
$877$	−3.58601e7			−1.57439			−0.787194	−	0.616705i	$-0.788467\pi$
$877$	−3.58601e7			−1.57439			−0.787194	+	0.616705i	$0.788467\pi$
$878$	7.93921e6			0.347569
$879$	7.60631e6	+	1.31745e7i	0.332049	+	0.575126i
$880$	−440622.			−0.0191805
$881$	−1.27198e7	+	2.20314e7i	−0.552130	+	0.956317i	0.445991	+	0.895038i	$0.352851\pi$
$881$	−1.27198e7	+	2.20314e7i	−0.552130	+	0.956317i	−0.998121	+	0.0612794i	$0.980482\pi$
$882$	−2.89468e6			−0.125294
$883$	−7.07103e6	+	1.22474e7i	−0.305198	+	0.528618i	−0.977305	−	0.211836i	$-0.932056\pi$
$883$	−7.07103e6	+	1.22474e7i	−0.305198	+	0.528618i	0.672108	+	0.740453i	$0.265389\pi$
$884$	1.05244e6	−	1.82287e6i	0.0452966	−	0.0784559i
$885$	−3.98016e6	+	6.89383e6i	−0.170821	+	0.295871i
$886$	2.63130e6	+	4.55755e6i	0.112612	+	0.195050i
$887$	2.74830e7			1.17288			0.586441	−	0.809992i	$-0.300529\pi$
$887$	2.74830e7			1.17288			0.586441	+	0.809992i	$0.300529\pi$
$888$	4.10962e6	+	9.84002e6i	0.174892	+	0.418758i
$889$	−1.43886e7			−0.610611
$890$	−1.84441e7	−	3.19462e7i	−0.780518	−	1.35190i
$891$	−962663.	+	1.66738e6i	−0.0406238	+	0.0703624i
$892$	−3.50981e6	+	6.07917e6i	−0.147697	+	0.255819i
$893$	317062.	−	549167.i	0.0133050	−	0.0230450i
$894$	6.76596e6			0.283130
$895$	−2.10888e7	+	3.65269e7i	−0.880025	+	1.52425i
$896$	1.81027e6			0.0753311
$897$	105218.	+	182242.i	0.00436624	+	0.00756255i
$898$	1.35033e7			0.558792
$899$	1.28340e6			0.0529617
$900$	−1.35785e6	−	2.35186e6i	−0.0558785	−	0.0967845i
$901$	−9.67880e6	+	1.67642e7i	−0.397200	+	0.687971i
$902$	−37576.0			−0.00153778
$903$	−1.01404e7	−	1.75638e7i	−0.413845	−	0.716800i
$904$	−169995.	−	294440.i	−0.00691854	−	0.0119833i
$905$	−4.66836e6	−	8.08583e6i	−0.189471	−	0.328173i
$906$	−9.30034e6	+	1.61087e7i	−0.376425	+	0.651987i
$907$	−1.47912e7	+	2.56192e7i	−0.597017	+	1.03406i	0.396242	+	0.918146i	$0.370314\pi$
$907$	−1.47912e7	+	2.56192e7i	−0.597017	+	1.03406i	−0.993259	+	0.115917i	$0.963019\pi$
$908$	−5.37148e6	−	9.30367e6i	−0.216212	−	0.374490i
$909$	1.33735e7	+	2.31635e7i	0.536826	+	0.929811i
$910$	2.53943e6	+	4.39842e6i	0.101656	+	0.176073i
$911$	1.81644e7			0.725147			0.362573	−	0.931955i	$-0.381898\pi$
$911$	1.81644e7			0.725147			0.362573	+	0.931955i	$0.381898\pi$
$912$	82520.7	−	142930.i	0.00328531	−	0.00569032i
$913$	1.15080e6	+	1.99325e6i	0.0456903	+	0.0791379i
$914$	−1.01144e7			−0.400475
$915$	−5.58745e6			−0.220628
$916$	7.58609e6	+	1.31395e7i	0.298730	+	0.517416i
$917$	2.14584e7			0.842702
$918$	2.54376e6	−	4.40592e6i	0.0996253	−	0.172556i
$919$	−3.53634e7			−1.38123			−0.690614	−	0.723224i	$-0.742660\pi$
$919$	−3.53634e7			−1.38123			−0.690614	+	0.723224i	$0.742660\pi$
$920$	−123108.	+	213230.i	−0.00479532	+	0.00830573i
$921$	2.39022e7	−	4.13999e7i	0.928516	−	1.60824i
$922$	1.65742e7	−	2.87074e7i	0.642104	−	1.11216i
$923$	6.35514e6	+	1.10074e7i	0.245539	+	0.425286i
$924$	−939037.			−0.0361829
$925$	−8.90861e6	−	1.14635e6i	−0.342338	−	0.0440516i
$926$	−1.92046e7			−0.736001
$927$	−9.24093e6	−	1.60058e7i	−0.353197	−	0.611755i
$928$	170229.	−	294845.i	0.00648878	−	0.0112389i
$929$	2.45259e7	−	4.24801e7i	0.932363	−	1.61490i	0.153094	−	0.988212i	$-0.451076\pi$
$929$	2.45259e7	−	4.24801e7i	0.932363	−	1.61490i	0.779269	−	0.626689i	$-0.215590\pi$
$930$	1.00153e7	−	1.73470e7i	0.379715	−	0.657685i
$931$	148177.			0.00560281
$932$	3.50084e6	−	6.06364e6i	0.132018	−	0.228662i
$933$	7.04322e6			0.264891
$934$	8.06642e6	+	1.39714e7i	0.302561	+	0.524052i
$935$	−1.27751e6			−0.0477896
$936$	−1.78500e6			−0.0665962
$937$	1.43046e7	+	2.47763e7i	0.532263	+	0.921907i	0.999290	+	0.0376642i	$0.0119917\pi$
$937$	1.43046e7	+	2.47763e7i	0.532263	+	0.921907i	−0.467027	+	0.884243i	$0.654675\pi$
$938$	−1.05798e7	+	1.83248e7i	−0.392620	+	0.680037i
$939$	−4.29911e7			−1.59116
$940$	−1.02082e7	−	1.76811e7i	−0.376815	−	0.652662i
$941$	−7.11059e6	−	1.23159e7i	−0.261777	−	0.453411i	0.704937	−	0.709270i	$-0.250975\pi$
$941$	−7.11059e6	−	1.23159e7i	−0.261777	−	0.453411i	−0.966714	+	0.255859i	$0.917642\pi$
$942$	−1.46652e6	−	2.54009e6i	−0.0538470	−	0.0932657i
$943$	−10498.6	+	18184.1i	−0.000384461	+	0.000665905i
$944$	−785423.	+	1.36039e6i	−0.0286862	+	0.0496860i
$945$	6.13785e6	+	1.06311e7i	0.223582	+	0.387255i
$946$	487059.	+	843612.i	0.0176951	+	0.0306489i
$947$	6.88113e6	+	1.19185e7i	0.249336	+	0.431863i	0.963342	−	0.268277i	$-0.0864543\pi$
$947$	6.88113e6	+	1.19185e7i	0.249336	+	0.431863i	−0.714006	+	0.700140i	$0.753121\pi$
$948$	2.71287e7			0.980411
$949$	−3.04868e6	+	5.28047e6i	−0.109887	+	0.190330i
$950$	69507.3	+	120390.i	0.00249874	+	0.00432795i
$951$	−2.54549e7			−0.912683
$952$	5.24857e6			0.187693
$953$	−1.36453e7	−	2.36343e7i	−0.486686	−	0.842966i	0.513196	−	0.858271i	$-0.328461\pi$
$953$	−1.36453e7	−	2.36343e7i	−0.486686	−	0.842966i	−0.999883	+	0.0153055i	$0.995128\pi$
$954$	1.64159e7			0.583974
$955$	−1.87369e7	+	3.24532e7i	−0.664796	+	1.15146i
$956$	−1.67728e7			−0.593554
$957$	−88302.2	+	152944.i	−0.00311668	+	0.00539824i
$958$	−6.96500e6	+	1.20637e7i	−0.245193	+	0.424686i
$959$	−3.13968e6	+	5.43809e6i	−0.110240	+	0.190941i
$960$	−2.65685e6	−	4.60179e6i	−0.0930440	−	0.161157i
$961$	−1.37288e7			−0.479539
$962$	−3.58031e6	+	4.69431e6i	−0.124733	+	0.163544i
$963$	1.25152e7			0.434884
$964$	−5.09316e6	−	8.82160e6i	−0.176520	−	0.305742i
$965$	1.72664e6	−	2.99063e6i	0.0596876	−	0.103382i
$966$	−262364.	+	454427.i	−0.00904609	+	0.0156683i
$967$	−4.27149e6	+	7.39843e6i	−0.146897	+	0.254433i	−0.930079	−	0.367359i	$-0.880262\pi$
$967$	−4.27149e6	+	7.39843e6i	−0.146897	+	0.254433i	0.783182	+	0.621792i	$0.213595\pi$
$968$	−1.02622e7			−0.352006
$969$	239254.	−	414400.i	0.00818559	−	0.0141779i
$970$	−9.75996e6			−0.333057
$971$	1.18170e7	+	2.04676e7i	0.402215	+	0.696657i	0.993993	−	0.109444i	$-0.0349071\pi$
$971$	1.18170e7	+	2.04676e7i	0.402215	+	0.696657i	−0.591778	+	0.806101i	$0.701574\pi$
$972$	−1.65560e7			−0.562071
$973$	−2.40497e7			−0.814379
$974$	6.67881e6	+	1.15680e7i	0.225580	+	0.390717i
$975$	1.91265e6	−	3.31281e6i	0.0644353	−	0.111605i
$976$	−1.10260e6			−0.0370504
$977$	1.49320e7	+	2.58629e7i	0.500473	+	0.866845i	1.00000		0.000546747i	$0.000174035\pi$
$977$	1.49320e7	+	2.58629e7i	0.500473	+	0.866845i	−0.499526	+	0.866299i	$0.666493\pi$
$978$	−9.40615e6	−	1.62919e7i	−0.314460	−	0.544660i
$979$	1.88799e6	+	3.27010e6i	0.0629569	+	0.109045i
$980$	2.38536e6	−	4.13156e6i	0.0793393	−	0.137420i
$981$	5.40565e6	−	9.36287e6i	0.179339	−	0.310625i
$982$	1.67365e7	+	2.89884e7i	0.553842	+	0.959282i
$983$	3.47158e6	+	6.01296e6i	0.114589	+	0.198474i	0.917615	−	0.397469i	$-0.130111\pi$
$983$	3.47158e6	+	6.01296e6i	0.114589	+	0.198474i	−0.803026	+	0.595944i	$0.796778\pi$
$984$	−226574.	−	392438.i	−0.00745972	−	0.0129206i
$985$	5.33426e7			1.75180
$986$	493548.	−	854851.i	0.0161673	−	0.0280026i
$987$	−2.17553e7	−	3.76812e7i	−0.710839	−	1.23121i
$988$	91373.0			0.00297801
$989$	544331.			0.0176959
$990$	541684.	+	938224.i	0.0175654	+	0.0304241i
$991$	6.07990e7			1.96658			0.983292	−	0.182034i	$-0.0582682\pi$
$991$	6.07990e7			1.96658			0.983292	+	0.182034i	$0.0582682\pi$
$992$	1.97637e6	−	3.42317e6i	0.0637660	−	0.110446i
$993$	−5.33446e7			−1.71679
$994$	−1.58468e7	+	2.74474e7i	−0.508715	+	0.881120i
$995$	2.04149e7	−	3.53596e7i	0.653715	−	1.13227i
$996$	−1.38781e7	+	2.40376e7i	−0.443285	+	0.767792i
$997$	−2.29824e7	−	3.98067e7i	−0.732246	−	1.26829i	−0.955921	−	0.293624i	$-0.905139\pi$
$997$	−2.29824e7	−	3.98067e7i	−0.732246	−	1.26829i	0.223675	−	0.974664i	$-0.428195\pi$
$998$	1.74515e7			0.554635
$999$	−8.65368e6	+	1.13463e7i	−0.274339	+	0.359699i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.c.a.63.2	yes	14
37.10	even	3	inner	74.6.c.a.47.2	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.c.a.47.2	✓	14	37.10	even	3	inner
74.6.c.a.63.2	yes	14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	74.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 3.46410i) q^{2} +(-10.0045 + 17.3283i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-32.4177 + 56.1491i) q^{5} +80.0358 q^{6} +(-55.2452 + 95.6875i) q^{7} +64.0000 q^{8} +(-78.6791 - 136.276i) q^{9} +259.342 q^{10} -26.5469 q^{11} +(-160.072 - 277.252i) q^{12} +(88.6215 - 153.497i) q^{13} +441.962 q^{14} +(-648.644 - 1123.48i) q^{15} +(-128.000 - 221.703i) q^{16} +(-371.113 - 642.787i) q^{17} +(-314.717 + 545.105i) q^{18} +(16.1101 - 27.9035i) q^{19} +(-518.683 - 898.386i) q^{20} +(-1105.40 - 1914.61i) q^{21} +(53.0938 + 91.9612i) q^{22} +59.3369 q^{23} +(-640.287 + 1109.01i) q^{24} +(-539.314 - 934.119i) q^{25} -708.972 q^{26} -1713.60 q^{27} +(-883.923 - 1531.00i) q^{28} -332.478 q^{29} +(-2594.58 + 4493.94i) q^{30} -3860.10 q^{31} +(-512.000 + 886.810i) q^{32} +(265.588 - 460.012i) q^{33} +(-1484.45 + 2571.15i) q^{34} +(-3581.84 - 6203.94i) q^{35} +2517.73 q^{36} +(5050.00 - 6621.29i) q^{37} -128.881 q^{38} +(1773.22 + 3071.31i) q^{39} +(-2074.73 + 3593.54i) q^{40} +(-176.932 + 306.455i) q^{41} +(-4421.59 + 7658.43i) q^{42} +9173.56 q^{43} +(212.375 - 367.845i) q^{44} +10202.4 q^{45} +(-118.674 - 205.549i) q^{46} +19680.9 q^{47} +5122.29 q^{48} +(2299.44 + 3982.74i) q^{49} +(-2157.26 + 3736.48i) q^{50} +14851.2 q^{51} +(1417.94 + 2455.95i) q^{52} +(-13040.2 - 22586.3i) q^{53} +(3427.20 + 5936.09i) q^{54} +(860.590 - 1490.59i) q^{55} +(-3535.69 + 6124.00i) q^{56} +(322.346 + 558.321i) q^{57} +(664.956 + 1151.74i) q^{58} +(-3068.06 - 5314.03i) q^{59} +20756.6 q^{60} +(2153.51 - 3729.99i) q^{61} +(7720.19 + 13371.8i) q^{62} +17386.6 q^{63} +4096.00 q^{64} +(5745.81 + 9952.04i) q^{65} -2124.70 q^{66} +(-23938.4 + 41462.5i) q^{67} +11875.6 q^{68} +(-593.635 + 1028.21i) q^{69} +(-14327.4 + 24815.7i) q^{70} +(-35855.5 + 62103.5i) q^{71} +(-5035.46 - 8721.68i) q^{72} -34401.1 q^{73} +(-33036.8 - 4251.13i) q^{74} +21582.2 q^{75} +(257.762 + 446.457i) q^{76} +(1466.59 - 2540.21i) q^{77} +(7092.90 - 12285.3i) q^{78} +(-42369.6 + 73386.3i) q^{79} +16597.9 q^{80} +(36262.7 - 62808.9i) q^{81} +1415.46 q^{82} +(-43349.8 - 75084.0i) q^{83} +35372.8 q^{84} +48122.6 q^{85} +(-18347.1 - 31778.1i) q^{86} +(3326.27 - 5761.27i) q^{87} -1699.00 q^{88} +(-71119.1 - 123182. i) q^{89} +(-20404.8 - 35342.1i) q^{90} +(9791.83 + 16959.9i) q^{91} +(-474.695 + 822.196i) q^{92} +(38618.3 - 66888.8i) q^{93} +(-39361.8 - 68176.7i) q^{94} +(1044.51 + 1809.14i) q^{95} +(-10244.6 - 17744.1i) q^{96} -37633.6 q^{97} +(9197.75 - 15931.0i) q^{98} +(2088.69 + 3617.71i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 28 q^{2} - 8 q^{3} - 112 q^{4} + 57 q^{5} + 64 q^{6} + 188 q^{7} + 896 q^{8} - 293 q^{9} - 456 q^{10} + 704 q^{11} - 128 q^{12} - 704 q^{13} - 1504 q^{14} - 364 q^{15} - 1792 q^{16} - 561 q^{17}+ \cdots - 446840 q^{99}+O(q^{100}) \) 14 * q - 28 * q^2 - 8 * q^3 - 112 * q^4 + 57 * q^5 + 64 * q^6 + 188 * q^7 + 896 * q^8 - 293 * q^9 - 456 * q^10 + 704 * q^11 - 128 * q^12 - 704 * q^13 - 1504 * q^14 - 364 * q^15 - 1792 * q^16 - 561 * q^17 - 1172 * q^18 - 3742 * q^19 + 912 * q^20 - 506 * q^21 - 1408 * q^22 - 5700 * q^23 - 512 * q^24 - 2340 * q^25 + 5632 * q^26 + 3124 * q^27 + 3008 * q^28 - 17654 * q^29 - 1456 * q^30 + 11888 * q^31 - 7168 * q^32 + 484 * q^33 - 2244 * q^34 + 1460 * q^35 + 9376 * q^36 + 16941 * q^37 + 29936 * q^38 - 36086 * q^39 + 3648 * q^40 - 9813 * q^41 - 2024 * q^42 + 5724 * q^43 - 5632 * q^44 - 63030 * q^45 + 11400 * q^46 + 23320 * q^47 + 4096 * q^48 - 11829 * q^49 - 9360 * q^50 + 110384 * q^51 - 11264 * q^52 + 16856 * q^53 - 6248 * q^54 + 28408 * q^55 + 12032 * q^56 - 26062 * q^57 + 35308 * q^58 + 50886 * q^59 + 11648 * q^60 - 6247 * q^61 - 23776 * q^62 - 10452 * q^63 + 57344 * q^64 - 4852 * q^65 - 3872 * q^66 - 28570 * q^67 + 17952 * q^68 + 43524 * q^69 + 5840 * q^70 - 8580 * q^71 - 18752 * q^72 - 9252 * q^73 - 36336 * q^74 + 112184 * q^75 - 59872 * q^76 - 56112 * q^77 - 144344 * q^78 + 26930 * q^79 - 29184 * q^80 - 9039 * q^81 + 78504 * q^82 - 137412 * q^83 + 16192 * q^84 - 58830 * q^85 - 11448 * q^86 - 70826 * q^87 + 45056 * q^88 - 27961 * q^89 + 126060 * q^90 + 99802 * q^91 + 45600 * q^92 - 181340 * q^93 - 46640 * q^94 + 210526 * q^95 - 8192 * q^96 + 191206 * q^97 - 47316 * q^98 - 446840 * q^99

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