LMFDB - Embedded newform 38.6.e.b.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,6,Mod(5,38)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.09458515289$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	38.17
Dual form			38.6.e.b.9.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.694593 - 3.93923i) q^{2} +(7.96877 + 6.68659i) q^{3} +(-15.0351 - 5.47232i) q^{4} +(-89.7666 + 32.6724i) q^{5} +(31.8751 - 26.7464i) q^{6} +(-116.109 - 201.107i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(-23.4057 - 132.740i) q^{9} +O(q^{10})$	\(q+(0.694593 - 3.93923i) q^{2} +(7.96877 + 6.68659i) q^{3} +(-15.0351 - 5.47232i) q^{4} +(-89.7666 + 32.6724i) q^{5} +(31.8751 - 26.7464i) q^{6} +(-116.109 - 201.107i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(-23.4057 - 132.740i) q^{9} +(66.3528 + 376.305i) q^{10} +(-172.940 + 299.541i) q^{11} +(-83.2199 - 144.141i) q^{12} +(387.869 - 325.461i) q^{13} +(-872.856 + 317.694i) q^{14} +(-933.796 - 339.874i) q^{15} +(196.107 + 164.554i) q^{16} +(-138.413 + 784.980i) q^{17} -539.153 q^{18} +(-880.656 + 1304.05i) q^{19} +1528.44 q^{20} +(419.474 - 2378.95i) q^{21} +(1059.84 + 889.309i) q^{22} +(1118.86 + 407.232i) q^{23} +(-625.609 + 227.703i) q^{24} +(4596.67 - 3857.06i) q^{25} +(-1012.65 - 1753.97i) q^{26} +(1964.97 - 3403.43i) q^{27} +(645.189 + 3659.05i) q^{28} +(-73.8636 - 418.901i) q^{29} +(-1987.45 + 3442.37i) q^{30} +(-3323.92 - 5757.21i) q^{31} +(784.430 - 658.215i) q^{32} +(-3381.02 + 1230.59i) q^{33} +(2996.07 + 1090.48i) q^{34} +(16993.4 + 14259.1i) q^{35} +(-374.491 + 2123.85i) q^{36} -7850.99 q^{37} +(4525.25 + 4374.89i) q^{38} +5267.06 q^{39} +(1061.64 - 6020.89i) q^{40} +(-12318.1 - 10336.1i) q^{41} +(-9079.88 - 3304.81i) q^{42} +(-12143.0 + 4419.71i) q^{43} +(4239.35 - 3557.23i) q^{44} +(6438.00 + 11150.9i) q^{45} +(2381.34 - 4124.59i) q^{46} +(-3679.63 - 20868.2i) q^{47} +(462.432 + 2622.58i) q^{48} +(-18559.2 + 32145.5i) q^{49} +(-12001.1 - 20786.4i) q^{50} +(-6351.82 + 5329.81i) q^{51} +(-7612.67 + 2770.78i) q^{52} +(27337.3 + 9949.97i) q^{53} +(-12042.0 - 10104.5i) q^{54} +(5737.52 - 32539.1i) q^{55} +14862.0 q^{56} +(-15737.4 + 4503.09i) q^{57} -1701.45 q^{58} +(1622.96 - 9204.26i) q^{59} +(12179.8 + 10220.1i) q^{60} +(7819.16 + 2845.94i) q^{61} +(-24987.7 + 9094.79i) q^{62} +(-23977.4 + 20119.5i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(-24184.1 + 41888.1i) q^{65} +(2499.15 + 14173.4i) q^{66} +(-2491.34 - 14129.1i) q^{67} +(6376.71 - 11044.8i) q^{68} +(6192.96 + 10726.5i) q^{69} +(67973.5 - 57036.6i) q^{70} +(29318.6 - 10671.1i) q^{71} +(8106.20 + 2950.42i) q^{72} +(1526.18 + 1280.61i) q^{73} +(-5453.24 + 30926.9i) q^{74} +62420.4 q^{75} +(20376.9 - 14787.3i) q^{76} +80319.7 q^{77} +(3658.46 - 20748.2i) q^{78} +(-7371.85 - 6185.72i) q^{79} +(-22980.3 - 8364.13i) q^{80} +(7637.48 - 2779.82i) q^{81} +(-49272.2 + 41344.3i) q^{82} +(17089.7 + 29600.3i) q^{83} +(-19325.2 + 33472.3i) q^{84} +(-13222.3 - 74987.2i) q^{85} +(8975.77 + 50904.1i) q^{86} +(2212.42 - 3832.03i) q^{87} +(-11068.1 - 19170.6i) q^{88} +(-85277.6 + 71556.4i) q^{89} +(48397.9 - 17615.4i) q^{90} +(-110488. - 40214.2i) q^{91} +(-14593.7 - 12245.5i) q^{92} +(12008.5 - 68103.6i) q^{93} -84760.6 q^{94} +(36447.1 - 145833. i) q^{95} +10652.2 q^{96} +(16843.0 - 95521.2i) q^{97} +(113738. + 95437.1i) q^{98} +(43808.9 + 15945.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 15 q^{3} + 60 q^{6} - 84 q^{7} - 960 q^{8} - 345 q^{9}+O(q^{10}) $ 30 * q + 15 * q^3 + 60 * q^6 - 84 * q^7 - 960 * q^8 - 345 * q^9	\( 30 q + 15 q^{3} + 60 q^{6} - 84 q^{7} - 960 q^{8} - 345 q^{9} - 126 q^{11} - 2610 q^{13} - 864 q^{14} - 5160 q^{15} + 1902 q^{17} + 17016 q^{18} - 2400 q^{19} + 3456 q^{20} - 6426 q^{21} + 216 q^{22} - 3306 q^{23} + 960 q^{24} - 18060 q^{25} + 456 q^{26} + 13017 q^{27} + 6048 q^{28} + 5988 q^{29} - 6840 q^{31} + 51867 q^{33} - 10752 q^{34} + 24408 q^{35} - 5520 q^{36} - 8556 q^{37} + 2772 q^{38} + 9912 q^{39} - 40527 q^{41} + 27432 q^{42} + 3678 q^{43} + 864 q^{44} - 31770 q^{45} - 15744 q^{46} - 133740 q^{47} - 7680 q^{48} - 63777 q^{49} - 107580 q^{50} + 45657 q^{51} + 5760 q^{52} - 64626 q^{53} + 1476 q^{54} + 142056 q^{55} + 10752 q^{56} + 232824 q^{57} + 117264 q^{58} + 169041 q^{59} - 56640 q^{60} + 61698 q^{61} - 101616 q^{62} - 188064 q^{63} - 61440 q^{64} - 80646 q^{65} - 173772 q^{66} - 72129 q^{67} - 65904 q^{68} - 124224 q^{69} + 97632 q^{70} + 417828 q^{71} + 44160 q^{72} + 239082 q^{73} - 116112 q^{74} - 174960 q^{75} + 6912 q^{76} + 242436 q^{77} + 336624 q^{78} - 145740 q^{79} + 14781 q^{81} - 162108 q^{82} - 201630 q^{83} - 54528 q^{84} - 46512 q^{85} - 75720 q^{86} - 376512 q^{87} - 8064 q^{88} + 416928 q^{89} + 560640 q^{90} - 380316 q^{91} + 269376 q^{92} - 205146 q^{93} + 5616 q^{94} + 708168 q^{95} + 858363 q^{97} + 308328 q^{98} - 1068531 q^{99}+O(q^{100}) \) 30 * q + 15 * q^3 + 60 * q^6 - 84 * q^7 - 960 * q^8 - 345 * q^9 - 126 * q^11 - 2610 * q^13 - 864 * q^14 - 5160 * q^15 + 1902 * q^17 + 17016 * q^18 - 2400 * q^19 + 3456 * q^20 - 6426 * q^21 + 216 * q^22 - 3306 * q^23 + 960 * q^24 - 18060 * q^25 + 456 * q^26 + 13017 * q^27 + 6048 * q^28 + 5988 * q^29 - 6840 * q^31 + 51867 * q^33 - 10752 * q^34 + 24408 * q^35 - 5520 * q^36 - 8556 * q^37 + 2772 * q^38 + 9912 * q^39 - 40527 * q^41 + 27432 * q^42 + 3678 * q^43 + 864 * q^44 - 31770 * q^45 - 15744 * q^46 - 133740 * q^47 - 7680 * q^48 - 63777 * q^49 - 107580 * q^50 + 45657 * q^51 + 5760 * q^52 - 64626 * q^53 + 1476 * q^54 + 142056 * q^55 + 10752 * q^56 + 232824 * q^57 + 117264 * q^58 + 169041 * q^59 - 56640 * q^60 + 61698 * q^61 - 101616 * q^62 - 188064 * q^63 - 61440 * q^64 - 80646 * q^65 - 173772 * q^66 - 72129 * q^67 - 65904 * q^68 - 124224 * q^69 + 97632 * q^70 + 417828 * q^71 + 44160 * q^72 + 239082 * q^73 - 116112 * q^74 - 174960 * q^75 + 6912 * q^76 + 242436 * q^77 + 336624 * q^78 - 145740 * q^79 + 14781 * q^81 - 162108 * q^82 - 201630 * q^83 - 54528 * q^84 - 46512 * q^85 - 75720 * q^86 - 376512 * q^87 - 8064 * q^88 + 416928 * q^89 + 560640 * q^90 - 380316 * q^91 + 269376 * q^92 - 205146 * q^93 + 5616 * q^94 + 708168 * q^95 + 858363 * q^97 + 308328 * q^98 - 1068531 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	0.694593	−	3.93923i	0.122788	−	0.696364i
$2$	0.694593	−	3.93923i	0.122788	−	0.696364i
$3$	7.96877	+	6.68659i	0.511197	+	0.428945i	0.861550	−	0.507672i	$-0.169494\pi$
$3$	7.96877	+	6.68659i	0.511197	+	0.428945i	−0.350353	+	0.936618i	$0.613938\pi$
$4$	−15.0351	−	5.47232i	−0.469846	−	0.171010i
$5$	−89.7666	+	32.6724i	−1.60579	+	0.584461i	−0.980602	−	0.196010i	$-0.937202\pi$
$5$	−89.7666	+	32.6724i	−1.60579	+	0.584461i	−0.625192	+	0.780471i	$0.714979\pi$
$6$	31.8751	−	26.7464i	0.361471	−	0.303310i
$7$	−116.109	−	201.107i	−0.895616	−	1.55125i	−0.833040	−	0.553212i	$-0.813402\pi$
$7$	−116.109	−	201.107i	−0.895616	−	1.55125i	−0.0625755	−	0.998040i	$-0.519931\pi$
$8$	−32.0000	+	55.4256i	−0.176777	+	0.306186i
$9$	−23.4057	−	132.740i	−0.0963198	−	0.546257i
$10$	66.3528	+	376.305i	0.209826	+	1.18998i
$11$	−172.940	+	299.541i	−0.430936	+	0.746404i	−0.996954	−	0.0779892i	$-0.975150\pi$
$11$	−172.940	+	299.541i	−0.430936	+	0.746404i	0.566018	+	0.824393i	$0.308483\pi$
$12$	−83.2199	−	144.141i	−0.166830	−	0.288958i
$13$	387.869	−	325.461i	0.636541	−	0.534122i	−0.266413	−	0.963859i	$-0.585838\pi$
$13$	387.869	−	325.461i	0.636541	−	0.534122i	0.902954	+	0.429738i	$0.141394\pi$
$14$	−872.856	+	317.694i	−1.19021	+	0.433200i
$15$	−933.796	−	339.874i	−1.07158	−	0.390023i
$16$	196.107	+	164.554i	0.191511	+	0.160697i
$17$	−138.413	+	784.980i	−0.116160	+	0.658773i	0.870010	+	0.493034i	$0.164112\pi$
$17$	−138.413	+	784.980i	−0.116160	+	0.658773i	−0.986170	+	0.165739i	$0.946999\pi$
$18$	−539.153			−0.392221
$19$	−880.656	+	1304.05i	−0.559657	+	0.828724i
$19$	−880.656	+	1304.05i	−0.559657	+	0.828724i
$20$	1528.44			0.854425
$21$	419.474	−	2378.95i	0.207566	−	1.17717i
$22$	1059.84	+	889.309i	0.466855	+	0.391738i
$23$	1118.86	+	407.232i	0.441018	+	0.160518i	0.552979	−	0.833195i	$-0.313491\pi$
$23$	1118.86	+	407.232i	0.441018	+	0.160518i	−0.111961	+	0.993713i	$0.535713\pi$
$24$	−625.609	+	227.703i	−0.221705	+	0.0806939i
$25$	4596.67	−	3857.06i	1.47093	−	1.23426i
$26$	−1012.65	−	1753.97i	−0.293784	−	0.508848i
$27$	1964.97	−	3403.43i	0.518736	−	0.898477i
$28$	645.189	+	3659.05i	0.155522	+	0.882010i
$29$	−73.8636	−	418.901i	−0.0163093	−	0.0924947i	0.975567	−	0.219704i	$-0.0705091\pi$
$29$	−73.8636	−	418.901i	−0.0163093	−	0.0924947i	−0.991876	+	0.127209i	$0.959398\pi$
$30$	−1987.45	+	3442.37i	−0.403175	+	0.698319i
$31$	−3323.92	−	5757.21i	−0.621222	−	1.07599i	−0.989258	−	0.146177i	$-0.953303\pi$
$31$	−3323.92	−	5757.21i	−0.621222	−	1.07599i	0.368036	−	0.929811i	$-0.380030\pi$
$32$	784.430	−	658.215i	0.135419	−	0.113630i
$33$	−3381.02	+	1230.59i	−0.540460	+	0.196711i
$34$	2996.07	+	1090.48i	0.444483	+	0.161779i
$35$	16993.4	+	14259.1i	2.34482	+	1.96754i
$36$	−374.491	+	2123.85i	−0.0481599	+	0.273128i
$37$	−7850.99			−0.942801			−0.471401	−	0.881919i	$-0.656251\pi$
$37$	−7850.99			−0.942801			−0.471401	+	0.881919i	$0.656251\pi$
$38$	4525.25	+	4374.89i	0.508375	+	0.491482i
$39$	5267.06			0.554507
$40$	1061.64	−	6020.89i	0.104913	−	0.594991i
$41$	−12318.1	−	10336.1i	−1.14441	−	0.960276i	−0.144838	−	0.989455i	$-0.546266\pi$
$41$	−12318.1	−	10336.1i	−1.14441	−	0.960276i	−0.999574	+	0.0291795i	$0.990711\pi$
$42$	−9079.88	−	3304.81i	−0.794249	−	0.289083i
$43$	−12143.0	+	4419.71i	−1.00151	+	0.364521i	−0.790168	−	0.612891i	$-0.790007\pi$
$43$	−12143.0	+	4419.71i	−1.00151	+	0.364521i	−0.211345	+	0.977412i	$0.567784\pi$
$44$	4239.35	−	3557.23i	0.330116	−	0.277001i
$45$	6438.00	+	11150.9i	0.473936	+	0.820881i
$46$	2381.34	−	4124.59i	0.165930	−	0.287400i
$47$	−3679.63	−	20868.2i	−0.242974	−	1.37797i	−0.825151	−	0.564912i	$-0.808910\pi$
$47$	−3679.63	−	20868.2i	−0.242974	−	1.37797i	0.582177	−	0.813062i	$-0.302201\pi$
$48$	462.432	+	2622.58i	0.0289697	+	0.164296i
$49$	−18559.2	+	32145.5i	−1.10426	+	1.91263i
$50$	−12001.1	−	20786.4i	−0.678882	−	1.17586i
$51$	−6351.82	+	5329.81i	−0.341958	+	0.286937i
$52$	−7612.67	+	2770.78i	−0.390417	+	0.142100i
$53$	27337.3	+	9949.97i	1.33680	+	0.486555i	0.908803	−	0.417225i	$-0.136997\pi$
$53$	27337.3	+	9949.97i	1.33680	+	0.486555i	0.427996	+	0.903781i	$0.359220\pi$
$54$	−12042.0	−	10104.5i	−0.561973	−	0.471551i
$55$	5737.52	−	32539.1i	0.255751	−	1.45044i
$56$	14862.0			0.633296
$57$	−15737.4	+	4503.09i	−0.641572	+	0.183579i
$58$	−1701.45			−0.0664126
$59$	1622.96	−	9204.26i	0.0606985	−	0.344238i	−0.939301	−	0.343095i	$-0.888525\pi$
$59$	1622.96	−	9204.26i	0.0606985	−	0.344238i	0.999999	−	0.00114356i	$-0.000364007\pi$
$60$	12179.8	+	10220.1i	0.436779	+	0.366502i
$61$	7819.16	+	2845.94i	0.269052	+	0.0979268i	0.473023	−	0.881050i	$-0.343163\pi$
$61$	7819.16	+	2845.94i	0.269052	+	0.0979268i	−0.203971	+	0.978977i	$0.565385\pi$
$62$	−24987.7	+	9094.79i	−0.825558	+	0.300479i
$63$	−23977.4	+	20119.5i	−0.761117	+	0.638653i
$64$	−2048.00	−	3547.24i	−0.0625000	−	0.108253i
$65$	−24184.1	+	41888.1i	−0.709981	+	1.22972i
$66$	2499.15	+	14173.4i	0.0706208	+	0.400511i
$67$	−2491.34	−	14129.1i	−0.0678026	−	0.384527i	−0.999759	−	0.0219570i	$-0.993010\pi$
$67$	−2491.34	−	14129.1i	−0.0678026	−	0.384527i	0.931956	−	0.362570i	$-0.118101\pi$
$68$	6376.71	−	11044.8i	0.167234	−	0.289658i
$69$	6192.96	+	10726.5i	0.156594	+	0.271229i
$70$	67973.5	−	57036.6i	1.65804	−	1.39126i
$71$	29318.6	−	10671.1i	0.690235	−	0.251225i	0.0269990	−	0.999635i	$-0.491405\pi$
$71$	29318.6	−	10671.1i	0.690235	−	0.251225i	0.663236	+	0.748411i	$0.269183\pi$
$72$	8106.20	+	2950.42i	0.184283	+	0.0670737i
$73$	1526.18	+	1280.61i	0.0335195	+	0.0281262i	0.659394	−	0.751798i	$-0.270813\pi$
$73$	1526.18	+	1280.61i	0.0335195	+	0.0281262i	−0.625874	+	0.779924i	$0.715258\pi$
$74$	−5453.24	+	30926.9i	−0.115764	+	0.656533i
$75$	62420.4			1.28137
$76$	20376.9	−	14787.3i	0.404673	−	0.293666i
$77$	80319.7			1.54381
$78$	3658.46	−	20748.2i	0.0680867	−	0.386139i
$79$	−7371.85	−	6185.72i	−0.132895	−	0.111512i	0.573917	−	0.818913i	$-0.305423\pi$
$79$	−7371.85	−	6185.72i	−0.132895	−	0.111512i	−0.706812	+	0.707401i	$0.749868\pi$
$80$	−22980.3	−	8364.13i	−0.401448	−	0.146115i
$81$	7637.48	−	2779.82i	0.129341	−	0.0470764i
$82$	−49272.2	+	41344.3i	−0.809222	+	0.679018i
$83$	17089.7	+	29600.3i	0.272295	+	0.471629i	0.969449	−	0.245292i	$-0.0788839\pi$
$83$	17089.7	+	29600.3i	0.272295	+	0.471629i	−0.697154	+	0.716921i	$0.745551\pi$
$84$	−19325.2	+	33472.3i	−0.298831	+	0.517591i
$85$	−13222.3	−	74987.2i	−0.198499	−	1.12574i
$86$	8975.77	+	50904.1i	0.130866	+	0.742176i
$87$	2212.42	−	3832.03i	0.0313379	−	0.0542788i
$88$	−11068.1	−	19170.6i	−0.152359	−	0.263894i
$89$	−85277.6	+	71556.4i	−1.14120	+	0.957577i	−0.999477	−	0.0323300i	$-0.989707\pi$
$89$	−85277.6	+	71556.4i	−1.14120	+	0.957577i	−0.141719	+	0.989907i	$0.545263\pi$
$90$	48397.9	−	17615.4i	0.629825	−	0.229238i
$91$	−110488.	−	40214.2i	−1.39865	−	0.509068i
$92$	−14593.7	−	12245.5i	−0.179761	−	0.150837i
$93$	12008.5	−	68103.6i	0.143973	−	0.816512i
$94$	−84760.6			−0.989406
$95$	36447.1	−	145833.i	0.414337	−	1.65786i
$96$	10652.2			0.117967
$97$	16843.0	−	95521.2i	0.181756	−	1.03079i	−0.748297	−	0.663364i	$-0.769128\pi$
$97$	16843.0	−	95521.2i	0.181756	−	1.03079i	0.930053	−	0.367426i	$-0.119761\pi$
$98$	113738.	+	95437.1i	1.19630	+	1.00381i
$99$	43808.9	+	15945.1i	0.449236	+	0.163509i
$100$	−90218.4	+	32836.8i	−0.902184	+	0.328368i
$101$	−130300.	+	109334.i	−1.27098	+	1.06648i	−0.276562	+	0.960996i	$0.589195\pi$
$101$	−130300.	+	109334.i	−1.27098	+	1.06648i	−0.994421	+	0.105485i	$0.966361\pi$
$102$	16583.4	+	28723.3i	0.157824	+	0.273360i
$103$	36285.5	−	62848.3i	0.337008	−	0.583714i	−0.646861	−	0.762608i	$-0.723919\pi$
$103$	36285.5	−	62848.3i	0.337008	−	0.583714i	0.983868	+	0.178894i	$0.0572519\pi$
$104$	5627.06	+	31912.6i	0.0510150	+	0.289320i
$105$	40071.3	+	227256.i	0.354699	+	2.01160i
$106$	58183.5	−	100777.i	0.502962	−	0.871156i
$107$	34010.7	+	58908.3i	0.287181	+	0.497413i	0.973136	−	0.230232i	$-0.0739485\pi$
$107$	34010.7	+	58908.3i	0.287181	+	0.497413i	−0.685955	+	0.727644i	$0.740615\pi$
$108$	−48168.1	+	40417.9i	−0.397375	+	0.333437i
$109$	18213.7	−	6629.24i	0.146836	−	0.0534438i	−0.267557	−	0.963542i	$-0.586216\pi$
$109$	18213.7	−	6629.24i	0.146836	−	0.0534438i	0.414392	+	0.910098i	$0.363994\pi$
$110$	−124194.	−	45202.8i	−0.978629	−	0.356192i
$111$	−62562.7	−	52496.4i	−0.481957	−	0.404410i
$112$	10323.0	−	58544.8i	0.0777610	−	0.441005i
$113$	−128260.			−0.944917			−0.472458	−	0.881353i	$-0.656633\pi$
$113$	−128260.			−0.944917			−0.472458	+	0.881353i	$0.656633\pi$
$114$	6807.62	+	65121.0i	0.0490606	+	0.469309i
$115$	−113742.			−0.802001
$116$	−1181.82	+	6702.42i	−0.00815465	+	0.0462473i
$117$	−52280.1	−	43868.2i	−0.353079	−	0.296269i
$118$	−35130.4	−	12786.4i	−0.232262	−	0.0845365i
$119$	173936.	−	63307.5i	1.12596	−	0.409815i
$120$	48719.2	−	40880.3i	0.308850	−	0.259156i
$121$	20709.1	+	35869.3i	0.128588	+	0.222720i
$122$	16642.0	−	28824.7i	0.101229	−	0.175334i
$123$	−29046.6	−	164732.i	−0.173114	−	0.981780i
$124$	18470.2	+	104750.i	0.107874	+	0.611784i
$125$	−137346.	+	237891.i	−0.786215	+	1.36176i
$126$	62600.6	+	108427.i	0.351279	+	0.608433i
$127$	72717.5	−	61017.2i	0.400064	−	0.335694i	−0.420454	−	0.907314i	$-0.638129\pi$
$127$	72717.5	−	61017.2i	0.400064	−	0.335694i	0.820518	+	0.571620i	$0.193685\pi$
$128$	−15395.9	+	5603.66i	−0.0830579	+	0.0302306i
$129$	−126318.	−	45976.0i	−0.668330	−	0.243252i
$130$	148209.	+	124362.i	0.769158	+	0.645400i
$131$	46092.4	−	261403.i	0.234666	−	1.33086i	−0.608649	−	0.793440i	$-0.708288\pi$
$131$	46092.4	−	261403.i	0.234666	−	1.33086i	0.843315	−	0.537419i	$-0.180601\pi$
$132$	57568.2			0.287573
$133$	364506.	+	25693.9i	1.78680	+	0.125951i
$134$	−57388.2			−0.276096
$135$	−65190.6	+	369714.i	−0.307858	+	1.74595i
$136$	−39078.8	−	32791.0i	−0.181173	−	0.152022i
$137$	65423.5	+	23812.2i	0.297805	+	0.108392i	0.486601	−	0.873624i	$-0.338236\pi$
$137$	65423.5	+	23812.2i	0.297805	+	0.108392i	−0.188796	+	0.982016i	$0.560459\pi$
$138$	46555.8	−	16944.9i	0.208102	−	0.0757429i
$139$	283037.	−	237497.i	1.24253	−	1.04261i	0.245208	−	0.969471i	$-0.421144\pi$
$139$	283037.	−	237497.i	1.24253	−	1.04261i	0.997322	−	0.0731356i	$-0.0233006\pi$
$140$	−177466.	−	307381.i	−0.765237	−	1.32543i
$141$	110215.	−	190898.i	0.466868	−	0.808638i
$142$	−21671.4	−	122905.i	−0.0901916	−	0.511502i
$143$	30410.7	+	172468.i	0.124362	+	0.705289i
$144$	17252.9	−	29882.9i	0.0693355	−	0.120093i
$145$	20317.0	+	35190.1i	0.0802489	+	0.138995i
$146$	6104.71	−	5122.46i	0.0237019	−	0.0198882i
$147$	−362838.	+	132062.i	−1.38490	+	0.504064i
$148$	118040.	+	42963.1i	0.442972	+	0.161228i
$149$	8308.13	+	6971.35i	0.0306576	+	0.0257247i	0.657988	−	0.753029i	$-0.271408\pi$
$149$	8308.13	+	6971.35i	0.0306576	+	0.0257247i	−0.627330	+	0.778753i	$0.715852\pi$
$150$	43356.8	−	245889.i	0.157336	−	0.892298i
$151$	33593.4			0.119898			0.0599489	−	0.998201i	$-0.480906\pi$
$151$	33593.4			0.119898			0.0599489	+	0.998201i	$0.480906\pi$
$152$	−44096.8	−	90540.5i	−0.154810	−	0.317858i
$153$	107438.			0.371048
$154$	55789.5	−	316398.i	0.189562	−	1.07506i
$155$	486479.	+	408204.i	1.62643	+	1.36473i
$156$	−79190.7	−	28823.1i	−0.260533	−	0.0948262i
$157$	−537140.	+	195503.i	−1.73915	+	0.633001i	−0.999213	−	0.0396702i	$-0.987369\pi$
$157$	−537140.	+	195503.i	−1.73915	+	0.633001i	−0.739942	+	0.672671i	$0.765147\pi$
$158$	−29487.4	+	24742.9i	−0.0939710	+	0.0788510i
$159$	151313.	+	262083.i	0.474662	+	0.822139i
$160$	−48910.1	+	84714.9i	−0.151042	+	0.261613i
$161$	−48012.9	−	272295.i	−0.145980	−	0.827893i
$162$	−5645.40	−	32016.6i	−0.0169008	−	0.0958491i
$163$	−220528.	+	381966.i	−0.650123	+	1.12605i	0.332970	+	0.942937i	$0.391949\pi$
$163$	−220528.	+	381966.i	−0.650123	+	1.12605i	−0.983093	+	0.183108i	$0.941384\pi$
$164$	128641.	+	222812.i	0.373481	+	0.646888i
$165$	263297.	−	220932.i	0.752897	−	0.631755i
$166$	128473.	−	46760.3i	0.361860	−	0.131706i
$167$	30358.4	+	11049.6i	0.0842341	+	0.0306587i	0.383793	−	0.923419i	$-0.374617\pi$
$167$	30358.4	+	11049.6i	0.0842341	+	0.0306587i	−0.299559	+	0.954078i	$0.596840\pi$
$168$	118432.	+	99376.1i	0.323739	+	0.271649i
$169$	−19956.7	+	113180.i	−0.0537492	+	0.304827i
$170$	−304576.			−0.808302
$171$	193712.	+	86376.4i	0.506602	+	0.225894i
$172$	206758.			0.532894
$173$	−24329.4	+	137979.i	−0.0618040	+	0.350508i	0.938186	+	0.346130i	$0.112504\pi$
$173$	−24329.4	+	137979.i	−0.0618040	+	0.350508i	−0.999990	+	0.00437739i	$0.998607\pi$
$174$	−13558.5	−	11376.9i	−0.0339499	−	0.0284874i
$175$	−1.30940e6	−	476582.i	−3.23204	−	1.17637i
$176$	−83205.3	+	30284.2i	−0.202474	+	0.0736945i
$177$	74478.1	−	62494.6i	0.178688	−	0.149937i
$178$	222644.	+	385631.i	0.526697	+	0.912267i
$179$	−102543.	+	177610.i	−0.239208	+	0.414320i	−0.960487	−	0.278324i	$-0.910221\pi$
$179$	−102543.	+	177610.i	−0.239208	+	0.414320i	0.721279	+	0.692644i	$0.243554\pi$
$180$	−35774.3	−	202886.i	−0.0822981	−	0.466736i
$181$	−103636.	−	587749.i	−0.235133	−	1.33351i	−0.842333	−	0.538957i	$-0.818818\pi$
$181$	−103636.	−	587749.i	−0.235133	−	1.33351i	0.607200	−	0.794549i	$-0.292293\pi$
$182$	−235157.	+	407304.i	−0.526235	+	0.911465i
$183$	43279.4	+	74962.2i	0.0955331	+	0.165468i
$184$	−58374.7	+	48982.2i	−0.127110	+	0.106658i
$185$	704757.	−	256510.i	1.51394	−	0.551031i
$186$	−259935.	−	94608.5i	−0.550912	−	0.200515i
$187$	−211196.	−	177215.i	−0.441654	−	0.370591i
$188$	−58874.1	+	333892.i	−0.121487	+	0.688987i
$189$	−912605.			−1.85835
$190$	−549155.	−	244868.i	−1.10360	−	0.492094i
$191$	374224.			0.742246			0.371123	−	0.928584i	$-0.378973\pi$
$191$	374224.			0.742246			0.371123	+	0.928584i	$0.378973\pi$
$192$	7398.91	−	41961.3i	0.0144849	−	0.0821478i
$193$	141787.	+	118974.i	0.273996	+	0.229910i	0.769423	−	0.638740i	$-0.220544\pi$
$193$	141787.	+	118974.i	0.273996	+	0.229910i	−0.495427	+	0.868650i	$0.664988\pi$
$194$	−364581.	−	132697.i	−0.695488	−	0.253137i
$195$	−472806.	+	172087.i	−0.890424	+	0.324088i
$196$	454950.	−	381749.i	0.845909	−	0.709802i
$197$	−74759.7	−	129488.i	−0.137247	−	0.237718i	0.789207	−	0.614128i	$-0.210492\pi$
$197$	−74759.7	−	129488.i	−0.137247	−	0.237718i	−0.926453	+	0.376409i	$0.877159\pi$
$198$	93240.9	−	161498.i	0.169022	−	0.292755i
$199$	−53122.9	−	301275.i	−0.0950931	−	0.539300i	−0.994719	−	0.102638i	$-0.967272\pi$
$199$	−53122.9	−	301275.i	−0.0950931	−	0.539300i	0.899626	−	0.436662i	$-0.143839\pi$
$200$	66686.8	+	378199.i	0.117887	+	0.668568i
$201$	74622.6	−	129250.i	0.130281	−	0.225653i
$202$	340188.	+	589223.i	0.586598	+	1.01602i
$203$	−75667.8	+	63492.8i	−0.128876	+	0.108140i
$204$	124667.	−	45374.9i	0.209737	−	0.0763380i
$205$	1.44345e6	+	525374.i	2.39893	+	0.873141i
$206$	−222370.	−	186591.i	−0.365097	−	0.306353i
$207$	27868.4	−	158050.i	0.0452050	−	0.256370i
$208$	129620.			0.207736
$209$	−238315.	−	489314.i	−0.377386	−	0.774858i
$210$	923046.			1.44436
$211$	140609.	−	797436.i	0.217424	−	1.23308i	−0.659225	−	0.751946i	$-0.729116\pi$
$211$	140609.	−	797436.i	0.217424	−	1.23308i	0.876649	−	0.481130i	$-0.159773\pi$
$212$	−356569.	−	299197.i	−0.544884	−	0.457212i
$213$	304986.	+	111006.i	0.460608	+	0.167647i
$214$	255677.	−	93058.8i	0.381643	−	0.138907i
$215$	945637.	−	793484.i	1.39517	−	1.17069i
$216$	125758.	+	217819.i	0.183401	+	0.317660i
$217$	−771877.	+	1.33693e6i	−1.11275	+	1.92734i
$218$	−13463.0	−	76352.5i	−0.0191867	−	0.108813i
$219$	3598.81	+	20409.8i	0.00507047	+	0.0287561i
$220$	−264328.	+	457830.i	−0.368203	+	0.637746i
$221$	201794.	+	349517.i	0.277925	+	0.481380i
$222$	−250251.	+	209985.i	−0.340795	+	0.285961i
$223$	−596319.	+	217042.i	−0.803002	+	0.292269i	−0.710730	−	0.703465i	$-0.751635\pi$
$223$	−596319.	+	217042.i	−0.803002	+	0.292269i	−0.0922719	+	0.995734i	$0.529413\pi$
$224$	−223451.	−	81329.6i	−0.297552	−	0.108300i
$225$	−619577.	−	519887.i	−0.815904	−	0.684624i
$226$	−89088.1	+	505244.i	−0.116024	+	0.658006i
$227$	−93859.7			−0.120897			−0.0604484	−	0.998171i	$-0.519253\pi$
$227$	−93859.7			−0.120897			−0.0604484	+	0.998171i	$0.519253\pi$
$228$	261255.	+	18415.8i	0.332834	+	0.0234614i
$229$	176185.			0.222014			0.111007	−	0.993820i	$-0.464592\pi$
$229$	176185.			0.222014			0.111007	+	0.993820i	$0.464592\pi$
$230$	−79004.1	+	448055.i	−0.0984759	+	0.558485i
$231$	640049.	+	537065.i	0.789193	+	0.662212i
$232$	25581.5	+	9310.91i	0.0312037	+	0.0113572i
$233$	212521.	−	77351.4i	0.256456	−	0.0933423i	−0.210593	−	0.977574i	$-0.567539\pi$
$233$	212521.	−	77351.4i	0.256456	−	0.0933423i	0.467049	+	0.884232i	$0.345317\pi$
$234$	−209121.	+	175473.i	−0.249665	+	0.209493i
$235$	1.01212e6	+	1.75305e6i	1.19554	+	2.07073i
$236$	−74770.0	+	129505.i	−0.0873871	+	0.151359i
$237$	−17383.2	−	98585.2i	−0.0201029	−	0.114009i
$238$	−128568.	−	729147.i	−0.147127	−	0.834397i
$239$	171998.	−	297910.i	0.194773	−	0.337357i	−0.752053	−	0.659103i	$-0.770936\pi$
$239$	171998.	−	297910.i	0.194773	−	0.337357i	0.946826	+	0.321746i	$0.104270\pi$
$240$	−127197.	−	220311.i	−0.142544	−	0.246893i
$241$	1.21561e6	−	1.02001e6i	1.34819	−	1.13126i	0.368746	−	0.929530i	$-0.379787\pi$
$241$	1.21561e6	−	1.02001e6i	1.34819	−	1.13126i	0.979441	−	0.201732i	$-0.0646571\pi$
$242$	155682.	−	56663.6i	0.170883	−	0.0621964i
$243$	−817934.	−	297704.i	−0.888593	−	0.323421i
$244$	−101988.	−	85577.9i	−0.109666	−	0.0920211i
$245$	615728.	−	3.49197e6i	0.655351	−	3.71668i
$246$	−669092.			−0.704933
$247$	82837.8	+	792419.i	0.0863946	+	0.826442i
$248$	425462.			0.439270
$249$	−61740.9	+	350150.i	−0.0631066	+	0.357895i
$250$	841706.	+	706275.i	0.851747	+	0.714700i
$251$	−700980.	−	255136.i	−0.702298	−	0.255616i	−0.0339063	−	0.999425i	$-0.510795\pi$
$251$	−700980.	−	255136.i	−0.702298	−	0.255616i	−0.668392	+	0.743809i	$0.733017\pi$
$252$	470603.	−	171285.i	0.466824	−	0.169910i
$253$	−315478.	+	264718.i	−0.309862	+	0.260005i
$254$	−189852.	−	328833.i	−0.184642	−	0.319809i
$255$	396044.	−	685968.i	0.381411	−	0.660623i
$256$	11380.2	+	64540.4i	0.0108530	+	0.0615505i
$257$	334499.	+	1.89704e6i	0.315909	+	1.79161i	0.567079	+	0.823664i	$0.308074\pi$
$257$	334499.	+	1.89704e6i	0.315909	+	1.79161i	−0.251170	+	0.967943i	$0.580815\pi$
$258$	−268849.	+	465661.i	−0.251455	+	0.435532i
$259$	911573.	+	1.57889e6i	0.844388	+	1.46252i
$260$	592835.	−	497448.i	0.543877	−	0.456367i
$261$	−53876.3	+	19609.4i	−0.0489549	+	0.0178181i
$262$	−997710.	−	363137.i	−0.897948	−	0.326826i
$263$	−738941.	−	620045.i	−0.658750	−	0.552757i	0.250962	−	0.967997i	$-0.419253\pi$
$263$	−738941.	−	620045.i	−0.658750	−	0.552757i	−0.909712	+	0.415240i	$0.863698\pi$
$264$	39986.4	−	226774.i	0.0353104	−	0.200255i
$265$	−2.77907e6			−2.43100
$266$	354397.	−	1.41803e6i	0.307105	−	1.22880i
$267$	−1.15803e6			−0.994124
$268$	−39861.4	+	226066.i	−0.0339013	+	0.192264i
$269$	−1.23381e6	−	1.03529e6i	−1.03960	−	0.872329i	−0.0476386	−	0.998865i	$-0.515170\pi$
$269$	−1.23381e6	−	1.03529e6i	−1.03960	−	0.872329i	−0.991962	+	0.126536i	$0.959614\pi$
$270$	1.41111e6	+	513602.i	1.17802	+	0.428763i
$271$	−1.06796e6	+	388705.i	−0.883347	+	0.321512i	−0.743560	−	0.668670i	$-0.766864\pi$
$271$	−1.06796e6	+	388705.i	−0.883347	+	0.321512i	−0.139787	+	0.990182i	$0.544642\pi$
$272$	−156315.	+	131164.i	−0.128109	+	0.107496i
$273$	−611555.	−	1.05924e6i	−0.496625	−	0.860180i
$274$	139244.	−	241178.i	0.112047	−	0.194072i
$275$	360400.	+	2.04393e6i	0.287378	+	1.62980i
$276$	−34412.7	−	195164.i	−0.0271923	−	0.154215i
$277$	−324224.	+	561573.i	−0.253890	+	0.439751i	−0.964593	−	0.263741i	$-0.915044\pi$
$277$	−324224.	+	561573.i	−0.253890	+	0.439751i	0.710703	+	0.703492i	$0.248377\pi$
$278$	−738958.	−	1.27991e6i	−0.573466	−	0.993273i
$279$	−686415.	+	575971.i	−0.527930	+	0.442986i
$280$	−1.33411e6	+	485576.i	−1.01694	+	0.370137i
$281$	471559.	+	171633.i	0.356262	+	0.129669i	0.513950	−	0.857820i	$-0.328182\pi$
$281$	471559.	+	171633.i	0.356262	+	0.129669i	−0.157688	+	0.987489i	$0.550404\pi$
$282$	−675438.	−	566760.i	−0.505781	−	0.424401i
$283$	237745.	−	1.34832e6i	0.176460	−	1.00075i	−0.759986	−	0.649940i	$-0.774794\pi$
$283$	237745.	−	1.34832e6i	0.176460	−	1.00075i	0.936445	−	0.350813i	$-0.114095\pi$
$284$	−499203.			−0.367266
$285$	1.26557e6	−	918405.i	0.922938	−	0.669764i
$286$	700513.			0.506408
$287$	−648418.	+	3.67736e6i	−0.464676	+	2.63531i
$288$	−105732.	−	88719.5i	−0.0751146	−	0.0630286i
$289$	737194.	+	268317.i	0.519203	+	0.188975i
$290$	152734.	−	55590.6i	0.106645	−	0.0388156i
$291$	772929.	−	648565.i	0.535066	−	0.448974i
$292$	−15938.3	−	27605.9i	−0.0109392	−	0.0189472i
$293$	342358.	−	592981.i	0.232976	−	0.403526i	−0.725707	−	0.688004i	$-0.758487\pi$
$293$	342358.	−	592981.i	0.232976	−	0.403526i	0.958683	+	0.284478i	$0.0918203\pi$
$294$	268199.	+	1.52103e6i	0.180963	+	1.02629i
$295$	155037.	+	879261.i	0.103725	+	0.588251i
$296$	251232.	−	435146.i	0.166665	−	0.288673i
$297$	679643.	+	1.17718e6i	0.447084	+	0.774373i
$298$	33232.5	−	27885.4i	0.0216782	−	0.0181901i
$299$	566510.	−	206193.i	0.366462	−	0.133381i
$300$	−938496.	−	341585.i	−0.602046	−	0.219127i
$301$	2.29875e6	+	1.92888e6i	1.46243	+	1.22713i
$302$	23333.7	−	132332.i	0.0147220	−	0.0834925i
$303$	−1.76940e6			−1.10718
$304$	−387289.	+	110819.i	−0.240354	+	0.0687747i
$305$	−794883.			−0.489276
$306$	74625.8	−	423224.i	0.0455602	−	0.258384i
$307$	−1.09761e6	−	921003.i	−0.664663	−	0.557718i	0.246818	−	0.969062i	$-0.420615\pi$
$307$	−1.09761e6	−	921003.i	−0.664663	−	0.557718i	−0.911480	+	0.411344i	$0.865060\pi$
$308$	−1.20761e6	−	439535.i	−0.725355	−	0.264008i
$309$	709391.	−	258197.i	0.422659	−	0.153835i
$310$	1.94592e6	−	1.63282e6i	1.15006	−	0.965013i
$311$	143288.	+	248182.i	0.0840058	+	0.145502i	0.904967	−	0.425481i	$-0.139895\pi$
$311$	143288.	+	248182.i	0.0840058	+	0.145502i	−0.820961	+	0.570984i	$0.806562\pi$
$312$	−168546.	+	291930.i	−0.0980239	+	0.169782i
$313$	56655.0	+	321306.i	0.0326871	+	0.185378i	0.996780	−	0.0801883i	$-0.0255522\pi$
$313$	56655.0	+	321306.i	0.0326871	+	0.185378i	−0.964093	+	0.265566i	$0.914441\pi$
$314$	397038.	+	2.25171e6i	0.227252	+	1.28881i
$315$	1.49502e6	−	2.58945e6i	0.848929	−	1.47039i
$316$	76986.2	+	133344.i	0.0433706	+	0.0751200i
$317$	2.33170e6	−	1.95653e6i	1.30324	−	1.09355i	0.313666	−	0.949533i	$-0.398443\pi$
$317$	2.33170e6	−	1.95653e6i	1.30324	−	1.09355i	0.989575	−	0.144016i	$-0.0460018\pi$
$318$	1.13750e6	−	414018.i	0.630791	−	0.229589i
$319$	138252.	+	50319.6i	0.0760667	+	0.0276860i
$320$	299739.	+	251511.i	0.163632	+	0.137303i
$321$	−122872.	+	696842.i	−0.0665565	+	0.377461i
$322$	−1.10598e6			−0.594440
$323$	−901758.	−	871794.i	−0.480932	−	0.464951i
$324$	−130042.			−0.0688211
$325$	527583.	−	2.99207e6i	0.277065	−	1.57132i
$326$	1.35148e6	+	1.13402e6i	0.704311	+	0.590987i
$327$	189468.	+	68960.6i	0.0979864	+	0.0356641i
$328$	967061.	−	351981.i	0.496329	−	0.180649i
$329$	−3.76951e6	+	3.16300e6i	−1.91997	+	1.61105i
$330$	−687419.	−	1.19064e6i	−0.347485	−	0.601862i
$331$	1.13151e6	−	1.95983e6i	0.567660	−	0.983216i	−0.429137	−	0.903239i	$-0.641182\pi$
$331$	1.13151e6	−	1.95983e6i	0.567660	−	0.983216i	0.996797	−	0.0799763i	$-0.0254845\pi$
$332$	−94963.2	−	538563.i	−0.0472836	−	0.268158i
$333$	183758.	+	1.04214e6i	0.0908104	+	0.515012i
$334$	64613.5	−	111914.i	0.0316926	−	0.0548931i
$335$	685270.	+	1.18692e6i	0.333618	+	0.577844i
$336$	473727.	−	397504.i	0.228918	−	0.192085i
$337$	−2.19900e6	+	800372.i	−1.05475	+	0.383899i	−0.810455	−	0.585801i	$-0.800780\pi$
$337$	−2.19900e6	+	800372.i	−1.05475	+	0.383899i	−0.244299	+	0.969700i	$0.578558\pi$
$338$	431981.	+	157228.i	0.205671	+	0.0748581i
$339$	−1.02207e6	−	857619.i	−0.483038	−	0.405317i
$340$	−211556.	+	1.19980e6i	−0.0992496	+	0.562872i
$341$	2.29936e6			1.07083
$342$	474808.	−	703082.i	0.219509	−	0.325043i
$343$	4.71670e6			2.16472
$344$	143612.	−	814466.i	0.0654328	−	0.371088i
$345$	−906381.	−	760544.i	−0.409980	−	0.344014i
$346$	526632.	+	191678.i	0.236492	+	0.0860761i
$347$	1.51782e6	−	552440.i	0.676699	−	0.246298i	0.0192697	−	0.999814i	$-0.493866\pi$
$347$	1.51782e6	−	552440.i	0.676699	−	0.246298i	0.657430	+	0.753516i	$0.271644\pi$
$348$	−54234.0	+	45507.7i	−0.0240062	+	0.0201436i
$349$	−24939.1	−	43195.8i	−0.0109602	−	0.0189836i	0.860493	−	0.509462i	$-0.170155\pi$
$349$	−24939.1	−	43195.8i	−0.0109602	−	0.0189836i	−0.871453	+	0.490478i	$0.836822\pi$
$350$	−2.78687e6	+	4.82700e6i	−1.21604	+	2.10624i
$351$	−345531.	−	1.95960e6i	−0.149699	−	0.848986i
$352$	61502.8	+	348800.i	0.0264569	+	0.150044i
$353$	−1.73342e6	+	3.00236e6i	−0.740399	+	1.28241i	0.211914	+	0.977288i	$0.432030\pi$
$353$	−1.73342e6	+	3.00236e6i	−0.740399	+	1.28241i	−0.952314	+	0.305121i	$0.901303\pi$
$354$	−194449.	−	336795.i	−0.0824701	−	0.142842i
$355$	−2.28318e6	+	1.91581e6i	−0.961544	+	0.806831i
$356$	1.67374e6	−	609190.i	0.699942	−	0.254758i
$357$	1.80937e6	+	658556.i	0.751375	+	0.273478i
$358$	628423.	+	527309.i	0.259146	+	0.217449i
$359$	517447.	−	2.93459e6i	0.211899	−	1.20174i	−0.674307	−	0.738451i	$-0.735558\pi$
$359$	517447.	−	2.93459e6i	0.211899	−	1.20174i	0.886207	−	0.463290i	$-0.153331\pi$
$360$	−824063.			−0.335123
$361$	−924990.	−	2.29684e6i	−0.373568	−	0.927603i
$362$	−2.38726e6			−0.957478
$363$	−74816.9	+	424308.i	−0.0298012	+	0.169011i
$364$	1.44113e6	+	1.20925e6i	0.570097	+	0.478368i
$365$	−178840.	−	65092.6i	−0.0702641	−	0.0255740i
$366$	325355.	−	118420.i	0.126956	−	0.0462084i
$367$	1.71469e6	−	1.43880e6i	0.664540	−	0.557615i	−0.246904	−	0.969040i	$-0.579413\pi$
$367$	1.71469e6	−	1.43880e6i	0.664540	−	0.557615i	0.911444	+	0.411425i	$0.134969\pi$
$368$	152405.	+	263974.i	0.0586653	+	0.101611i
$369$	−1.08370e6	+	1.87703e6i	−0.414328	+	0.717637i
$370$	−520935.	−	2.95437e6i	−0.197824	−	1.12192i
$371$	−1.17311e6	−	6.65301e6i	−0.442489	−	2.50948i
$372$	−553234.	+	958229.i	−0.207277	+	0.359014i
$373$	−556669.	−	964179.i	−0.207169	−	0.358827i	0.743653	−	0.668566i	$-0.233092\pi$
$373$	−556669.	−	964179.i	−0.207169	−	0.358827i	−0.950822	+	0.309739i	$0.899758\pi$
$374$	−844784.	+	708858.i	−0.312296	+	0.262048i
$375$	−2.68516e6	+	977317.i	−0.986033	+	0.358887i
$376$	1.27438e6	+	463837.i	0.464869	+	0.169198i
$377$	−164985.	−	138439.i	−0.0597850	−	0.0501655i
$378$	−633889.	+	3.59496e6i	−0.228183	+	1.29409i
$379$	3.21599e6			1.15005			0.575026	−	0.818135i	$-0.304992\pi$
$379$	3.21599e6			1.15005			0.575026	+	0.818135i	$0.304992\pi$
$380$	−1.34603e6	+	1.99316e6i	−0.478185	+	0.708083i
$381$	987467.			0.348506
$382$	259933.	−	1.47415e6i	0.0911388	−	0.516874i
$383$	376741.	+	316123.i	0.131234	+	0.110118i	0.706042	−	0.708170i	$-0.250479\pi$
$383$	376741.	+	316123.i	0.131234	+	0.110118i	−0.574808	+	0.818288i	$0.694923\pi$
$384$	−160156.	−	58292.0i	−0.0554262	−	0.0201735i
$385$	−7.21002e6	+	2.62423e6i	−2.47905	+	0.902300i
$386$	567149.	−	475894.i	0.193744	−	0.162571i
$387$	870890.	+	1.50843e6i	0.295587	+	0.511972i
$388$	−775958.	+	1.34400e6i	−0.261673	+	0.453231i
$389$	−364860.	−	2.06922e6i	−0.122251	−	0.693319i	−0.982903	−	0.184125i	$-0.941055\pi$
$389$	−364860.	−	2.06922e6i	−0.122251	−	0.693319i	0.860652	−	0.509194i	$-0.170056\pi$
$390$	349484.	+	1.98202e6i	0.116350	+	0.659853i
$391$	−474534.	+	821917.i	−0.156973	+	0.271886i
$392$	−1.18779e6	−	2.05731e6i	−0.390413	−	0.676216i
$393$	2.11519e6	−	1.77486e6i	0.690826	−	0.579672i
$394$	−562009.	+	204555.i	−0.182391	+	0.0663848i
$395$	863848.	+	314415.i	0.278577	+	0.101394i
$396$	−571414.	−	479473.i	−0.183110	−	0.153648i
$397$	−915286.	+	5.19085e6i	−0.291461	+	1.65296i	0.389786	+	0.920905i	$0.372549\pi$
$397$	−915286.	+	5.19085e6i	−0.291461	+	1.65296i	−0.681247	+	0.732053i	$0.738562\pi$
$398$	−1.22369e6			−0.387225
$399$	2.73286e6	+	2.64205e6i	0.859380	+	0.830824i
$400$	1.53614e6			0.480042
$401$	−716197.	+	4.06176e6i	−0.222419	+	1.26140i	0.645140	+	0.764065i	$0.276799\pi$
$401$	−716197.	+	4.06176e6i	−0.222419	+	1.26140i	−0.867558	+	0.497335i	$0.834312\pi$
$402$	−457314.	−	383732.i	−0.141140	−	0.118430i
$403$	−3.16299e6	−	1.15123e6i	−0.970142	−	0.353103i
$404$	2.55738e6	−	930809.i	0.779545	−	0.283731i
$405$	−594767.	+	499069.i	−0.180181	+	0.151190i
$406$	197555.	+	342175.i	0.0594802	+	0.103023i
$407$	1.35775e6	−	2.35169e6i	0.406287	−	0.703710i
$408$	−92149.8	−	522608.i	−0.0274059	−	0.155427i
$409$	−818265.	−	4.64061e6i	−0.241872	−	1.37172i	−0.827646	−	0.561250i	$-0.810321\pi$
$409$	−818265.	−	4.64061e6i	−0.241872	−	1.37172i	0.585774	−	0.810474i	$-0.300790\pi$
$410$	3.07218e6	−	5.32118e6i	0.902584	−	1.56332i
$411$	362122.	+	627214.i	0.105743	+	0.183152i
$412$	−889481.	+	746363.i	−0.258163	+	0.216624i
$413$	−2.03948e6	+	742311.i	−0.588363	+	0.214146i
$414$	−603237.	−	219560.i	−0.172977	−	0.0629583i
$415$	−2.50120e6	−	2.09875e6i	−0.712899	−	0.598193i
$416$	90032.9	−	510602.i	0.0255075	−	0.144660i
$417$	3.84350e6			1.08240
$418$	−2.09305e6	+	598905.i	−0.585922	+	0.167655i
$419$	−3.47084e6			−0.965827			−0.482914	−	0.875668i	$-0.660422\pi$
$419$	−3.47084e6			−0.965827			−0.482914	+	0.875668i	$0.660422\pi$
$420$	641141.	−	3.63609e6i	0.177350	−	1.00580i
$421$	−913302.	−	766352.i	−0.251136	−	0.210728i	0.508525	−	0.861047i	$-0.330191\pi$
$421$	−913302.	−	766352.i	−0.251136	−	0.210728i	−0.759661	+	0.650319i	$0.774635\pi$
$422$	−3.04362e6	−	1.10779e6i	−0.831972	−	0.302813i
$423$	−2.68393e6	+	976872.i	−0.729324	+	0.265452i
$424$	−1.42628e6	+	1.19679e6i	−0.385291	+	0.323298i
$425$	2.39148e6	+	4.14216e6i	0.642235	+	1.11238i
$426$	649119.	−	1.12431e6i	0.173301	−	0.300166i
$427$	−335538.	−	1.90293e6i	−0.0890578	−	0.505072i
$428$	−188989.	−	1.07181e6i	−0.0498685	−	0.282818i
$429$	−910885.	+	1.57770e6i	−0.238957	+	0.413886i
$430$	−2.46888e6	−	4.27623e6i	−0.643916	−	1.11530i
$431$	−520370.	+	436642.i	−0.134933	+	0.113222i	−0.707756	−	0.706457i	$-0.750293\pi$
$431$	−520370.	+	436642.i	−0.134933	+	0.113222i	0.572823	+	0.819679i	$0.305848\pi$
$432$	945391.	−	344094.i	0.243726	−	0.0887091i
$433$	6.71147e6	+	2.44277e6i	1.72027	+	0.626129i	0.997863	−	0.0653358i	$-0.0208118\pi$
$433$	6.71147e6	+	2.44277e6i	1.72027	+	0.626129i	0.722411	+	0.691464i	$0.243034\pi$
$434$	4.73034e6	+	3.96922e6i	1.20550	+	1.01154i
$435$	−73400.2	+	416273.i	−0.0185983	+	0.105476i
$436$	−310121.			−0.0781296
$437$	−1.51638e6	+	1.10042e6i	−0.379844	+	0.275648i
$438$	82898.8			0.0206473
$439$	280663.	−	1.59172e6i	0.0695063	−	0.394190i	−0.930130	−	0.367230i	$-0.880306\pi$
$439$	280663.	−	1.59172e6i	0.0695063	−	0.394190i	0.999637	−	0.0269599i	$-0.00858263\pi$
$440$	1.61990e6	+	1.35926e6i	0.398893	+	0.334711i
$441$	4.70140e6	+	1.71117e6i	1.15115	+	0.418983i
$442$	1.51699e6	−	552140.i	0.369341	−	0.134429i
$443$	−2.41906e6	+	2.02983e6i	−0.585649	+	0.491418i	−0.886797	−	0.462160i	$-0.847075\pi$
$443$	−2.41906e6	+	2.02983e6i	−0.585649	+	0.491418i	0.301148	+	0.953578i	$0.402630\pi$
$444$	653359.	+	1.13165e6i	0.157288	+	0.272430i
$445$	5.31717e6	−	9.20960e6i	1.27286	−	2.20466i
$446$	440781.	+	2.49979e6i	0.104927	+	0.595069i
$447$	19591.0	+	111106.i	0.00463755	+	0.0263008i
$448$	−475584.	+	823735.i	−0.111952	+	0.193907i
$449$	−739753.	−	1.28129e6i	−0.173169	−	0.299938i	0.766357	−	0.642415i	$-0.222067\pi$
$449$	−739753.	−	1.28129e6i	−0.173169	−	0.299938i	−0.939526	+	0.342477i	$0.888734\pi$
$450$	−2.47831e6	+	2.07955e6i	−0.576931	+	0.484103i
$451$	5.22636e6	−	1.90224e6i	1.20992	−	0.440376i
$452$	1.92839e6	+	701877.i	0.443966	+	0.161590i
$453$	267698.	+	224625.i	0.0612914	+	0.0514296i
$454$	−65194.3	+	369735.i	−0.0148446	+	0.0841882i
$455$	1.12320e7			2.54348
$456$	254010.	−	1.01635e6i	0.0572057	−	0.228893i
$457$	−5.30763e6			−1.18880			−0.594402	−	0.804168i	$-0.702611\pi$
$457$	−5.30763e6			−1.18880			−0.594402	+	0.804168i	$0.702611\pi$
$458$	122377.	−	694033.i	0.0272606	−	0.154602i
$459$	2.39964e6	+	2.01354e6i	0.531637	+	0.446096i
$460$	1.71011e6	+	622431.i	0.376817	+	0.137150i
$461$	1.45455e6	−	529412.i	0.318769	−	0.116022i	−0.177680	−	0.984088i	$-0.556859\pi$
$461$	1.45455e6	−	529412.i	0.318769	−	0.116022i	0.496449	+	0.868066i	$0.334637\pi$
$462$	2.56020e6	−	2.14826e6i	0.558044	−	0.468254i
$463$	−3.66099e6	−	6.34102e6i	−0.793682	−	1.37470i	−0.923673	−	0.383182i	$-0.874828\pi$
$463$	−3.66099e6	−	6.34102e6i	−0.793682	−	1.37470i	0.129991	−	0.991515i	$-0.458505\pi$
$464$	54446.5	−	94304.2i	0.0117402	−	0.0203346i
$465$	1.14714e6	+	6.50577e6i	0.246028	+	1.39530i
$466$	−157089.	−	890898.i	−0.0335106	−	0.190048i
$467$	−3.45787e6	+	5.98920e6i	−0.733696	+	1.27080i	0.221597	+	0.975138i	$0.428873\pi$
$467$	−3.45787e6	+	5.98920e6i	−0.733696	+	1.27080i	−0.955293	+	0.295661i	$0.904460\pi$
$468$	545975.	+	945656.i	0.115228	+	0.199581i
$469$	−2.55219e6	+	2.14155e6i	−0.535774	+	0.449568i
$470$	7.60867e6	−	2.76933e6i	1.58878	−	0.578269i
$471$	−5.58759e6	−	2.03372e6i	−1.16057	−	0.422414i
$472$	458217.	+	384490.i	0.0946709	+	0.0794383i
$473$	776134.	−	4.40168e6i	0.159509	−	0.904618i
$474$	−400424.			−0.0818605
$475$	981719.	+	9.39103e6i	0.199643	+	1.90976i
$476$	−2.96158e6			−0.599110
$477$	680914.	−	3.86165e6i	0.137024	−	0.777101i
$478$	−1.05407e6	−	884467.i	−0.211008	−	0.177056i
$479$	−3.03208e6	−	1.10359e6i	−0.603812	−	0.219769i	0.0219817	−	0.999758i	$-0.493002\pi$
$479$	−3.03208e6	−	1.10359e6i	−0.603812	−	0.219769i	−0.625793	+	0.779989i	$0.715225\pi$
$480$	−956208.	+	348031.i	−0.189430	+	0.0689469i
$481$	−3.04515e6	+	2.55519e6i	−0.600132	+	0.503570i
$482$	−3.17372e6	−	5.49704e6i	−0.622230	−	1.07773i
$483$	1.43812e6	−	2.49090e6i	0.280496	−	0.485834i
$484$	−115075.	−	652625.i	−0.0223290	−	0.126634i
$485$	1.60897e6	+	9.12491e6i	0.310594	+	1.76147i
$486$	−1.74085e6	+	3.01525e6i	−0.334327	+	0.579072i
$487$	2.32496e6	+	4.02695e6i	0.444215	+	0.769403i	0.997997	−	0.0632585i	$-0.0201493\pi$
$487$	2.32496e6	+	4.02695e6i	0.444215	+	0.769403i	−0.553782	+	0.832662i	$0.686816\pi$
$488$	−407951.	+	342312.i	−0.0775459	+	0.0650687i
$489$	−4.31139e6	+	1.56922e6i	−0.815353	+	0.296764i
$490$	−1.33280e7	−	4.85099e6i	−2.50769	−	0.912726i
$491$	6.31047e6	+	5.29511e6i	1.18129	+	0.991223i	0.999970	+	0.00779921i	$0.00248259\pi$
$491$	6.31047e6	+	5.29511e6i	1.18129	+	0.991223i	0.181324	+	0.983423i	$0.441962\pi$
$492$	−464746.	+	2.63571e6i	−0.0865572	+	0.490890i
$493$	339053.			0.0628275
$494$	3.17906e6	+	224091.i	0.586113	+	0.0413149i
$495$	−4.45354e6			−0.816945
$496$	295523.	−	1.67599e6i	0.0539370	−	0.305892i
$497$	−5.55019e6	−	4.65716e6i	−1.00790	−	0.845727i
$498$	1.33644e6	+	486423.i	0.241477	+	0.0878903i
$499$	3.50496e6	−	1.27570e6i	0.630132	−	0.229349i	−0.00715690	−	0.999974i	$-0.502278\pi$
$499$	3.50496e6	−	1.27570e6i	0.630132	−	0.229349i	0.637289	+	0.770625i	$0.280056\pi$
$500$	3.36682e6	−	2.82510e6i	0.602276	−	0.505369i
$501$	168035.	+	291046.i	0.0299093	+	0.0518045i
$502$	−1.49194e6	+	2.58411e6i	−0.264235	+	0.457669i
$503$	−263345.	−	1.49351e6i	−0.0464094	−	0.263201i	0.952771	−	0.303691i	$-0.0982191\pi$
$503$	−263345.	−	1.49351e6i	−0.0464094	−	0.263201i	−0.999180	+	0.0404905i	$0.987108\pi$
$504$	−347855.	−	1.97279e6i	−0.0609990	−	0.345942i
$505$	8.12434e6	−	1.40718e7i	1.41762	−	2.45539i
$506$	823655.	+	1.42661e6i	0.143011	+	0.247702i
$507$	−915820.	+	768464.i	−0.158230	+	0.132771i
$508$	−1.42722e6	+	519465.i	−0.245376	+	0.0893094i
$509$	−1.05585e7	−	3.84299e6i	−1.80638	−	0.657468i	−0.997591	−	0.0693661i	$-0.977902\pi$
$509$	−1.05585e7	−	3.84299e6i	−1.80638	−	0.657468i	−0.808787	−	0.588102i	$-0.799875\pi$
$510$	−2.42710e6	−	2.03658e6i	−0.413201	−	0.346717i
$511$	80337.4	−	455616.i	0.0136102	−	0.0771875i
$512$	262144.			0.0441942
$513$	2.70778e6	+	5.55966e6i	0.454275	+	0.932728i
$514$	7.70520e6			1.28640
$515$	−1.20382e6	+	6.82721e6i	−0.200006	+	1.13429i
$516$	1.64760e6	+	1.38250e6i	0.272414	+	0.228582i
$517$	6.88724e6	+	2.50675e6i	1.13323	+	0.412462i
$518$	6.85278e6	−	2.49421e6i	1.12213	−	0.408421i
$519$	−1.11648e6	+	936842.i	−0.181943	+	0.152668i
$520$	−1.54778e6	−	2.68084e6i	−0.251016	−	0.434773i
$521$	−2.49978e6	+	4.32975e6i	−0.403467	+	0.698825i	−0.994142	−	0.108084i	$-0.965528\pi$
$521$	−2.49978e6	+	4.32975e6i	−0.403467	+	0.698825i	0.590675	+	0.806910i	$0.298862\pi$
$522$	39823.8	+	225852.i	0.00639685	+	0.0362783i
$523$	−851854.	−	4.83111e6i	−0.136179	−	0.772311i	−0.974031	−	0.226414i	$-0.927300\pi$
$523$	−851854.	−	4.83111e6i	−0.136179	−	0.772311i	0.837852	−	0.545897i	$-0.183811\pi$
$524$	−2.12348e6	+	3.67798e6i	−0.337847	+	0.585169i
$525$	−7.24759e6	−	1.25532e7i	−1.14761	−	1.98772i
$526$	−2.95577e6	+	2.48018e6i	−0.465806	+	0.390858i
$527$	4.97936e6	−	1.81234e6i	0.780993	−	0.284258i
$528$	−865542.	−	315032.i	−0.135115	−	0.0491778i
$529$	−3.84451e6	−	3.22593e6i	−0.597313	−	0.501205i
$530$	−1.93032e6	+	1.09474e7i	−0.298497	+	1.69286i
$531$	−1.25976e6			−0.193889
$532$	−5.33977e6	−	2.38100e6i	−0.817982	−	0.364738i
$533$	−8.14178e6			−1.24137
$534$	−804357.	+	4.56174e6i	−0.122066	+	0.692272i
$535$	−4.97770e6	−	4.17678e6i	−0.751872	−	0.630896i
$536$	862837.	+	314047.i	0.129723	+	0.0472153i
$537$	−2.00475e6	+	729671.i	−0.300003	+	0.109192i
$538$	−4.93523e6	+	4.14115e6i	−0.735109	+	0.616829i
$539$	−6.41926e6	−	1.11185e7i	−0.951728	−	1.64844i
$540$	3.00334e6	−	5.20194e6i	0.443221	−	0.767681i
$541$	665698.	+	3.77536e6i	0.0977877	+	0.554582i	0.993857	+	0.110668i	$0.0352991\pi$
$541$	665698.	+	3.77536e6i	0.0977877	+	0.554582i	−0.896070	+	0.443913i	$0.853590\pi$
$542$	789403.	+	4.47693e6i	0.115425	+	0.654609i
$543$	3.10418e6	−	5.37661e6i	0.451802	−	0.782544i
$544$	408110.	+	706867.i	0.0591261	+	0.102409i
$545$	−1.41839e6	+	1.19017e6i	−0.204552	+	0.171639i
$546$	−4.59739e6	+	1.67331e6i	−0.659978	+	0.240212i
$547$	5.48073e6	+	1.99482e6i	0.783195	+	0.285060i	0.702504	−	0.711680i	$-0.252065\pi$
$547$	5.48073e6	+	1.99482e6i	0.783195	+	0.285060i	0.0806905	+	0.996739i	$0.474287\pi$
$548$	−853339.	−	716037.i	−0.121386	−	0.101855i
$549$	194758.	−	1.10453e6i	0.0275782	−	0.156404i
$550$	8.30184e6			1.17022
$551$	611317.	+	272586.i	0.0857802	+	0.0382494i
$552$	−792698.			−0.110729
$553$	−388052.	+	2.20075e6i	−0.0539606	+	0.306026i
$554$	1.98696e6	+	1.66726e6i	0.275052	+	0.230796i
$555$	7.33123e6	+	2.66835e6i	1.01029	+	0.367714i
$556$	−5.55515e6	+	2.02191e6i	−0.762094	+	0.277380i
$557$	1.12936e6	−	947643.i	0.154239	−	0.129422i	−0.562403	−	0.826863i	$-0.690123\pi$
$557$	1.12936e6	−	947643.i	0.154239	−	0.129422i	0.716641	+	0.697442i	$0.245678\pi$
$558$	1.79210e6	+	3.10401e6i	0.243656	+	0.422025i
$559$	−3.27147e6	+	5.66635e6i	−0.442806	+	0.766962i
$560$	986134.	+	5.59265e6i	0.132882	+	0.753611i
$561$	−498012.	−	2.82436e6i	−0.0668086	−	0.378890i
$562$	1.00364e6	−	1.73836e6i	0.134041	−	0.232167i
$563$	857509.	+	1.48525e6i	0.114016	+	0.197482i	0.917386	−	0.397998i	$-0.130295\pi$
$563$	857509.	+	1.48525e6i	0.114016	+	0.197482i	−0.803370	+	0.595481i	$0.796962\pi$
$564$	−2.70175e6	+	2.26704e6i	−0.357641	+	0.300097i
$565$	1.15134e7	−	4.19054e6i	1.51734	−	0.552267i
$566$	−5.14621e6	−	1.87307e6i	−0.675222	−	0.245761i
$567$	−1.44582e6	−	1.21319e6i	−0.188868	−	0.158479i
$568$	−346743.	+	1.96647e6i	−0.0450958	+	0.255751i
$569$	1.09443e7			1.41712			0.708558	−	0.705652i	$-0.249346\pi$
$569$	1.09443e7			1.41712			0.708558	+	0.705652i	$0.249346\pi$
$570$	−2.73876e6	−	5.62327e6i	−0.353074	−	0.724940i
$571$	−7.80064e6			−1.00124			−0.500622	−	0.865666i	$-0.666895\pi$
$571$	−7.80064e6			−1.00124			−0.500622	+	0.865666i	$0.666895\pi$
$572$	486571.	−	2.75948e6i	0.0621808	−	0.352645i
$573$	2.98210e6	+	2.50228e6i	0.379434	+	0.318383i
$574$	1.40356e7	+	5.10854e6i	1.77808	+	0.647168i
$575$	6.71376e6	−	2.44361e6i	0.846830	−	0.308221i
$576$	−422927.	+	354878.i	−0.0531140	+	0.0445680i
$577$	4.00071e6	+	6.92943e6i	0.500262	+	0.866478i	1.00000		0.000302079i	$9.61547e-5\pi$
$577$	4.00071e6	+	6.92943e6i	0.500262	+	0.866478i	−0.499738	+	0.866176i	$0.666571\pi$
$578$	1.56901e6	−	2.71761e6i	0.195347	−	0.338351i
$579$	334342.	+	1.89615e6i	0.0414471	+	0.235058i
$580$	−112896.	−	640267.i	−0.0139351	−	0.0790298i
$581$	3.96855e6	−	6.87373e6i	0.487744	−	0.844797i
$582$	−2.01797e6	−	3.49523e6i	−0.246950	−	0.427729i
$583$	−7.70813e6	+	6.46789e6i	−0.939242	+	0.788118i
$584$	−119817.	+	43609.6i	−0.0145373	+	0.00529115i
$585$	6.12629e6	+	2.22979e6i	0.740130	+	0.269385i
$586$	−2.09809e6	−	1.76051e6i	−0.252395	−	0.211784i
$587$	−1.33520e6	+	7.57230e6i	−0.159938	+	0.907053i	0.794194	+	0.607665i	$0.207894\pi$
$587$	−1.33520e6	+	7.57230e6i	−0.159938	+	0.907053i	−0.954131	+	0.299388i	$0.903218\pi$
$588$	6.17799e6			0.736892
$589$	1.04349e7	+	735554.i	1.23937	+	0.0873627i
$590$	3.57130e6			0.422373
$591$	270088.	−	1.53174e6i	0.0318080	−	0.180392i
$592$	−1.53964e6	−	1.29191e6i	−0.180557	−	0.151505i
$593$	−3.64006e6	−	1.32487e6i	−0.425081	−	0.154717i	0.120616	−	0.992699i	$-0.461513\pi$
$593$	−3.64006e6	−	1.32487e6i	−0.425081	−	0.154717i	−0.545697	+	0.837982i	$0.683735\pi$
$594$	5.10924e6	−	1.85961e6i	0.594142	−	0.216250i
$595$	−1.35452e7	+	1.13658e7i	−1.56854	+	1.31616i
$596$	−86763.9	−	150280.i	−0.0100052	−	0.0173294i
$597$	1.59118e6	−	2.75600e6i	0.182719	−	0.316478i
$598$	−418747.	−	2.37483e6i	−0.0478849	−	0.271569i
$599$	−2.17516e6	−	1.23359e7i	−0.247699	−	1.40477i	−0.814140	−	0.580668i	$-0.802791\pi$
$599$	−2.17516e6	−	1.23359e7i	−0.247699	−	1.40477i	0.566442	−	0.824102i	$-0.308320\pi$
$600$	−1.99745e6	+	3.45969e6i	−0.226516	+	0.392337i
$601$	−146819.	−	254297.i	−0.0165804	−	0.0287181i	0.857616	−	0.514290i	$-0.171945\pi$
$601$	−146819.	−	254297.i	−0.0165804	−	0.0287181i	−0.874197	+	0.485572i	$0.838611\pi$
$602$	9.19502e6	−	7.71554e6i	1.03410	−	0.867711i
$603$	−1.81719e6	+	661403.i	−0.203520	+	0.0740752i
$604$	−505079.	−	183834.i	−0.0563335	−	0.0205037i
$605$	−3.03092e6	−	2.54325e6i	−0.336656	−	0.282488i
$606$	−1.22901e6	+	6.97008e6i	−0.135949	+	0.771003i
$607$	−4.13932e6			−0.455993			−0.227996	−	0.973662i	$-0.573217\pi$
$607$	−4.13932e6			−0.455993			−0.227996	+	0.973662i	$0.573217\pi$
$608$	167532.	+	1.60260e6i	0.0183797	+	0.175819i
$609$	−1.02753e6			−0.112267
$610$	−552120.	+	3.13123e6i	−0.0600771	+	0.340714i
$611$	−8.21900e6	−	6.89656e6i	−0.890668	−	0.747360i
$612$	−1.61534e6	−	587936.i	−0.174335	−	0.0634529i
$613$	−5.39286e6	+	1.96284e6i	−0.579653	+	0.210977i	−0.615173	−	0.788392i	$-0.710914\pi$
$613$	−5.39286e6	+	1.96284e6i	−0.579653	+	0.210977i	0.0355193	+	0.999369i	$0.488691\pi$
$614$	−4.39043e6	+	3.68401e6i	−0.469988	+	0.394366i
$615$	7.98959e6	+	1.38384e7i	0.851798	+	1.47536i
$616$	−2.57023e6	+	4.45177e6i	−0.272910	+	0.472695i
$617$	−2.00863e6	−	1.13915e7i	−0.212416	−	1.20467i	−0.885335	−	0.464954i	$-0.846071\pi$
$617$	−2.00863e6	−	1.13915e7i	−0.212416	−	1.20467i	0.672919	−	0.739716i	$-0.265040\pi$
$618$	−524361.	−	2.97380e6i	−0.0552280	−	0.313213i
$619$	9.23901e6	−	1.60024e7i	0.969167	−	1.67865i	0.271192	−	0.962525i	$-0.412582\pi$
$619$	9.23901e6	−	1.60024e7i	0.969167	−	1.67865i	0.697976	−	0.716122i	$-0.254084\pi$
$620$	−5.08042e6	−	8.79955e6i	−0.530788	−	0.919351i
$621$	3.58451e6	−	3.00776e6i	0.372993	−	0.312979i
$622$	1.07717e6	−	392059.i	0.111637	−	0.0406327i
$623$	2.42920e7	+	8.84158e6i	2.50752	+	0.912661i
$624$	1.03291e6	+	866714.i	0.106194	+	0.0891075i
$625$	1.30046e6	−	7.37528e6i	0.133167	−	0.755229i
$626$	1.30505e6			0.133104
$627$	1.37276e6	−	5.49275e6i	0.139453	−	0.557983i
$628$	9.14580e6			0.925385
$629$	1.08668e6	−	6.16287e6i	0.109515	−	0.621092i
$630$	−9.16203e6	−	7.68785e6i	−0.919687	−	0.771709i
$631$	−8.41706e6	−	3.06356e6i	−0.841564	−	0.306304i	−0.114968	−	0.993369i	$-0.536676\pi$
$631$	−8.41706e6	−	3.06356e6i	−0.841564	−	0.306304i	−0.726596	+	0.687065i	$0.758899\pi$
$632$	578747.	−	210647.i	0.0576363	−	0.0209779i
$633$	6.45261e6	−	5.41439e6i	0.640068	−	0.537081i
$634$	−6.08764e6	−	1.05441e7i	−0.601487	−	1.04181i
$635$	−4.53403e6	+	7.85316e6i	−0.446221	+	0.772877i
$636$	−840810.	−	4.76847e6i	−0.0824242	−	0.467451i
$637$	3.26356e6	+	1.85085e7i	0.318671	+	1.80727i
$638$	294249.	−	509655.i	0.0286196	−	0.0495706i
$639$	−2.10271e6	−	3.64199e6i	−0.203717	−	0.352848i
$640$	1.19896e6	−	1.00604e6i	0.115705	−	0.0970882i
$641$	−1.38115e7	+	5.02699e6i	−1.32769	+	0.483240i	−0.905915	−	0.423460i	$-0.860815\pi$
$641$	−1.38115e7	+	5.02699e6i	−1.32769	+	0.483240i	−0.421776	+	0.906700i	$0.638593\pi$
$642$	2.65968e6	+	968043.i	0.254678	+	0.0926952i
$643$	1.19145e7	+	9.99745e6i	1.13644	+	0.953590i	0.999317	−	0.0369630i	$-0.0117684\pi$
$643$	1.19145e7	+	9.99745e6i	1.13644	+	0.953590i	0.137128	+	0.990553i	$0.456213\pi$
$644$	−768206.	+	4.35671e6i	−0.0729899	+	0.413946i
$645$	1.28413e7			1.21537
$646$	−4.06055e6	+	2.94669e6i	−0.382828	+	0.277813i
$647$	−5.91558e6			−0.555567			−0.277784	−	0.960644i	$-0.589600\pi$
$647$	−5.91558e6			−0.555567			−0.277784	+	0.960644i	$0.589600\pi$
$648$	−90326.3	+	512266.i	−0.00845039	+	0.0479246i
$649$	2.47637e6	+	2.07793e6i	0.230783	+	0.193650i
$650$	−1.14200e7	−	4.15654e6i	−1.06019	−	0.385877i
$651$	−1.50904e7	+	5.49246e6i	−1.39556	+	0.507943i
$652$	5.40590e6	−	4.53609e6i	0.498023	−	0.417891i
$653$	−636886.	−	1.10312e6i	−0.0584492	−	0.101237i	0.835320	−	0.549764i	$-0.185282\pi$
$653$	−636886.	−	1.10312e6i	−0.0584492	−	0.101237i	−0.893769	+	0.448527i	$0.851949\pi$
$654$	403255.	−	698457.i	0.0368668	−	0.0638551i
$655$	4.40309e6	+	2.49712e7i	0.401010	+	2.27424i
$656$	−714823.	−	4.05396e6i	−0.0648543	−	0.367807i
$657$	134268.	−	232559.i	0.0121355	−	0.0210194i
$658$	9.84149e6	+	1.70460e7i	0.886128	+	1.53482i
$659$	−5.34741e6	+	4.48701e6i	−0.479656	+	0.402480i	−0.850302	−	0.526295i	$-0.823581\pi$
$659$	−5.34741e6	+	4.48701e6i	−0.479656	+	0.402480i	0.370646	+	0.928774i	$0.379136\pi$
$660$	−5.16770e6	+	1.88089e6i	−0.461782	+	0.168075i
$661$	9.67765e6	+	3.52238e6i	0.861522	+	0.313568i	0.734729	−	0.678361i	$-0.237309\pi$
$661$	9.67765e6	+	3.52238e6i	0.861522	+	0.313568i	0.126793	+	0.991929i	$0.459532\pi$
$662$	−6.93429e6	−	5.81856e6i	−0.614975	−	0.516025i
$663$	−729030.	+	4.13454e6i	−0.0644112	+	0.365294i
$664$	−2.18749e6			−0.192542
$665$	−3.35599e7	+	9.60282e6i	−2.94284	+	0.842063i
$666$	4.23288e6			0.369786
$667$	87947.0	−	498772.i	0.00765432	−	0.0434098i
$668$	−395975.	−	332262.i	−0.0343341	−	0.0288098i
$669$	−6.20320e6	−	2.25778e6i	−0.535859	−	0.195037i
$670$	5.15155e6	−	1.87501e6i	0.443354	−	0.161368i
$671$	−2.20472e6	+	1.84998e6i	−0.189037	+	0.158621i
$672$	−1.23681e6	−	2.14222e6i	−0.105653	−	0.182996i
$673$	2.74181e6	−	4.74896e6i	0.233346	−	0.404167i	−0.725445	−	0.688280i	$-0.758366\pi$
$673$	2.74181e6	−	4.74896e6i	0.233346	−	0.404167i	0.958791	+	0.284114i	$0.0916993\pi$
$674$	1.62544e6	+	9.21832e6i	0.137823	+	0.781631i
$675$	−4.09492e6	−	2.32234e7i	−0.345928	−	1.96186i
$676$	919409.	−	1.59246e6i	0.0773823	−	0.134030i
$677$	−2.49656e6	−	4.32417e6i	−0.209349	−	0.362603i	0.742161	−	0.670222i	$-0.233801\pi$
$677$	−2.49656e6	−	4.32417e6i	−0.209349	−	0.362603i	−0.951510	+	0.307619i	$0.900468\pi$
$678$	−4.08828e6	+	3.43048e6i	−0.341560	+	0.286603i
$679$	−2.11656e7	+	7.70366e6i	−1.76180	+	0.641243i
$680$	4.57933e6	+	1.66674e6i	0.379778	+	0.138228i
$681$	−747947.	−	627602.i	−0.0618021	−	0.0518581i
$682$	1.59712e6	−	9.05769e6i	0.131485	−	0.745687i
$683$	−6.96239e6			−0.571093			−0.285546	−	0.958365i	$-0.592175\pi$
$683$	−6.96239e6			−0.571093			−0.285546	+	0.958365i	$0.592175\pi$
$684$	−2.43980e6	−	2.35873e6i	−0.199395	−	0.192770i
$685$	−6.65084e6			−0.541565
$686$	3.27618e6	−	1.85802e7i	0.265802	−	1.50744i
$687$	1.40398e6	+	1.17808e6i	0.113493	+	0.0952317i
$688$	−3.10862e6	−	1.13144e6i	−0.250378	−	0.0911302i
$689$	1.38416e7	−	5.03794e6i	1.11081	−	0.404301i
$690$	−3.62552e6	+	3.04218e6i	−0.289900	+	0.243255i
$691$	−4.64760e6	−	8.04988e6i	−0.370283	−	0.641349i	0.619326	−	0.785134i	$-0.287406\pi$
$691$	−4.64760e6	−	8.04988e6i	−0.370283	−	0.641349i	−0.989609	+	0.143785i	$0.954073\pi$
$692$	1.12086e6	−	1.94139e6i	0.0889787	−	0.154116i
$693$	−1.87994e6	−	1.06617e7i	−0.148700	−	0.843319i
$694$	−1.12193e6	−	6.36275e6i	−0.0884230	−	0.501472i
$695$	−1.76477e7	+	3.05668e7i	−1.38588	+	2.40042i
$696$	141595.	+	245250.i	0.0110796	+	0.0191905i
$697$	9.81859e6	−	8.23877e6i	0.765538	−	0.642363i
$698$	−187481.	+	68237.4i	−0.0145652	+	0.00530132i
$699$	2.21075e6	+	804647.i	0.171138	+	0.0622892i
$700$	1.70789e7	+	1.43309e7i	1.31739	+	1.10542i
$701$	−1.33748e6	+	7.58521e6i	−0.102800	+	0.583005i	0.889277	+	0.457369i	$0.151208\pi$
$701$	−1.33748e6	+	7.58521e6i	−0.102800	+	0.583005i	−0.992076	+	0.125636i	$0.959903\pi$
$702$	−7.95933e6			−0.609585
$703$	6.91402e6	−	1.02381e7i	0.527645	−	0.781322i
$704$	1.41672e6			0.107734
$705$	−3.65654e6	+	2.07373e7i	−0.277075	+	1.57137i
$706$	1.06230e7	+	8.91375e6i	0.802112	+	0.673052i
$707$	3.71169e7	+	1.35094e7i	2.79269	+	1.01646i
$708$	−1.46178e6	+	532043.i	−0.109597	+	0.0398899i
$709$	393148.	−	329890.i	0.0293724	−	0.0246464i	−0.627983	−	0.778227i	$-0.716119\pi$
$709$	393148.	−	329890.i	0.0293724	−	0.0246464i	0.657356	+	0.753580i	$0.271675\pi$
$710$	5.96096e6	+	1.03247e7i	0.443782	+	0.768654i
$711$	−648551.	+	1.12332e6i	−0.0481139	+	0.0833357i
$712$	−1.23718e6	−	7.01637e6i	−0.0914601	−	0.518696i
$713$	−1.37449e6	−	7.79512e6i	−0.101255	−	0.574248i
$714$	3.85098e6	−	6.67009e6i	0.282700	−	0.489651i
$715$	−8.36479e6	−	1.44882e7i	−0.611913	−	1.05986i
$716$	2.51369e6	−	2.10924e6i	0.183244	−	0.153760i
$717$	3.36262e6	−	1.22389e6i	0.244275	−	0.0889089i
$718$	−1.12006e7	−	4.07669e6i	−0.810831	−	0.295118i
$719$	2.91565e6	+	2.44652e6i	0.210336	+	0.176493i	0.741869	−	0.670545i	$-0.233940\pi$
$719$	2.91565e6	+	2.44652e6i	0.210336	+	0.176493i	−0.531533	+	0.847037i	$0.678384\pi$
$720$	−572388.	+	3.24618e6i	−0.0411490	+	0.233368i
$721$	−1.68523e7			−1.20732
$722$	−9.69026e6	+	2.04839e6i	−0.691819	+	0.146241i
$723$	1.65073e7			1.17444
$724$	−1.65817e6	+	9.40398e6i	−0.117567	+	0.666753i
$725$	−1.95526e6	−	1.64066e6i	−0.138152	−	0.115924i
$726$	1.61948e6	+	589442.i	0.114034	+	0.0415049i
$727$	2.29036e7	−	8.33621e6i	1.60719	−	0.584969i	0.626307	−	0.779576i	$-0.284565\pi$
$727$	2.29036e7	−	8.33621e6i	1.60719	−	0.584969i	0.980881	+	0.194607i	$0.0623433\pi$
$728$	5.76450e6	−	4.83699e6i	0.403119	−	0.338257i
$729$	−5.51481e6	−	9.55194e6i	−0.384337	−	0.665691i
$730$	−380636.	+	659281.i	−0.0264364	+	0.0457892i
$731$	−1.78862e6	−	1.01438e7i	−0.123801	−	0.702112i
$732$	−240493.	−	1.36390e6i	−0.0165892	−	0.0940818i
$733$	−2.23280e6	+	3.86732e6i	−0.153493	+	0.265858i	−0.932509	−	0.361146i	$-0.882386\pi$
$733$	−2.23280e6	+	3.86732e6i	−0.153493	+	0.265858i	0.779016	+	0.627004i	$0.215719\pi$
$734$	−4.47674e6	−	7.75395e6i	−0.306706	−	0.531230i
$735$	2.82560e7	−	2.37096e7i	1.92927	−	1.61885i
$736$	1.14571e6	−	417006.i	0.0779618	−	0.0283758i
$737$	4.66309e6	+	1.69723e6i	0.316231	+	0.115099i
$738$	6.64131e6	+	5.57272e6i	0.448862	+	0.376640i
$739$	−354973.	+	2.01315e6i	−0.0239102	+	0.135602i	−0.994426	−	0.105435i	$-0.966376\pi$
$739$	−354973.	+	2.01315e6i	−0.0239102	+	0.135602i	0.970516	+	0.241037i	$0.0774875\pi$
$740$	−1.19998e7			−0.805553
$741$	−4.63847e6	+	6.86851e6i	−0.310334	+	0.459533i
$742$	−2.70226e7			−1.80184
$743$	3.30782e6	−	1.87596e7i	0.219821	−	1.24667i	−0.652520	−	0.757771i	$-0.726288\pi$
$743$	3.30782e6	−	1.87596e7i	0.219821	−	1.24667i	0.872341	−	0.488897i	$-0.162601\pi$
$744$	3.39041e6	+	2.84489e6i	0.224554	+	0.188423i
$745$	−973563.	−	354348.i	−0.0642648	−	0.0233905i
$746$	−4.18478e6	+	1.52314e6i	−0.275312	+	0.100206i
$747$	3.52916e6	−	2.96131e6i	0.231403	−	0.194170i
$748$	2.20557e6	+	3.82017e6i	0.144134	+	0.249648i
$749$	7.89792e6	−	1.36796e7i	0.514408	−	0.890981i
$750$	1.98479e6	+	1.12563e7i	0.128843	+	0.730705i
$751$	1.88974e6	+	1.07173e7i	0.122265	+	0.693400i	0.982895	+	0.184168i	$0.0589592\pi$
$751$	1.88974e6	+	1.07173e7i	0.122265	+	0.693400i	−0.860630	+	0.509231i	$0.829930\pi$
$752$	2.71234e6	−	4.69791e6i	0.174904	−	0.302942i
$753$	−3.87996e6	−	6.72029e6i	−0.249368	−	0.431917i
$754$	−659941.	+	553756.i	−0.0422743	+	0.0354724i
$755$	−3.01556e6	+	1.09757e6i	−0.192531	+	0.0700756i
$756$	1.37211e7	+	4.99407e6i	0.873140	+	0.317797i
$757$	1.72203e6	+	1.44495e6i	0.109220	+	0.0916462i	0.695762	−	0.718272i	$-0.255067\pi$
$757$	1.72203e6	+	1.44495e6i	0.109220	+	0.0916462i	−0.586542	+	0.809919i	$0.699511\pi$
$758$	2.23381e6	−	1.26685e7i	0.141212	−	0.800854i
$759$	−4.28403e6			−0.269928
$760$	6.91659e6	+	6.68676e6i	0.434368	+	0.419935i
$761$	1.37969e7			0.863614			0.431807	−	0.901966i	$-0.357876\pi$
$761$	1.37969e7			0.863614			0.431807	+	0.901966i	$0.357876\pi$
$762$	685887.	−	3.88986e6i	0.0427923	−	0.242687i
$763$	−3.44796e6	−	2.89319e6i	−0.214413	−	0.179914i
$764$	−5.62649e6	−	2.04787e6i	−0.348742	−	0.126932i
$765$	−9.64436e6	+	3.51026e6i	−0.595826	+	0.216863i
$766$	1.50696e6	−	1.26449e6i	0.0927963	−	0.0778653i
$767$	−2.36613e6	−	4.09826e6i	−0.145228	−	0.251542i
$768$	−340869.	+	590402.i	−0.0208538	+	0.0361198i
$769$	5.48798e6	+	3.11239e7i	0.334654	+	1.89792i	0.430618	+	0.902534i	$0.358296\pi$
$769$	5.48798e6	+	3.11239e7i	0.334654	+	1.89792i	−0.0959632	+	0.995385i	$0.530593\pi$
$770$	5.32943e6	+	3.02247e7i	0.323932	+	1.83711i
$771$	−1.00192e7	+	1.73537e7i	−0.607009	+	1.05137i
$772$	−1.48072e6	−	2.56468e6i	−0.0894190	−	0.154878i
$773$	−1.63710e7	+	1.37369e7i	−0.985432	+	0.826875i	−0.984900	−	0.173124i	$-0.944614\pi$
$773$	−1.63710e7	+	1.37369e7i	−0.985432	+	0.826875i	−0.000531857		1.00000i	$0.500169\pi$
$774$	6.54695e6	−	2.38290e6i	0.392814	−	0.142973i
$775$	−3.74849e7	−	1.36434e7i	−2.24183	−	0.815958i
$776$	4.75535e6	+	3.99021e6i	0.283484	+	0.237871i
$777$	−3.29328e6	+	1.86771e7i	−0.195693	+	1.10983i
$778$	−8.40458e6			−0.497814
$779$	2.43267e7	−	6.96083e6i	1.43628	−	0.410977i
$780$	8.05040e6			0.473785
$781$	−1.87392e6	+	1.06276e7i	−0.109932	+	0.623456i
$782$	2.90811e6	+	2.44020e6i	0.170057	+	0.142695i
$783$	−1.57084e6	−	571739.i	−0.0915646	−	0.0333268i
$784$	−8.92926e6	+	3.24999e6i	−0.518831	+	0.188839i
$785$	4.18297e7	−	3.50993e7i	2.42276	−	2.03294i
$786$	−5.52238e6	−	9.56504e6i	−0.318838	−	0.552243i
$787$	9.56345e6	−	1.65644e7i	0.550399	−	0.953320i	−0.447846	−	0.894111i	$-0.647809\pi$
$787$	9.56345e6	−	1.65644e7i	0.550399	−	0.953320i	0.998246	−	0.0592091i	$-0.0188579\pi$
$788$	415420.	+	2.35597e6i	0.0238326	+	0.135162i
$789$	−1.74246e6	−	9.88200e6i	−0.0996486	−	0.565135i
$790$	1.83858e6	−	3.18451e6i	0.104813	−	0.181541i
$791$	1.48921e7	+	2.57939e7i	0.846282	+	1.46580i
$792$	−2.28565e6	+	1.91789e6i	−0.129478	+	0.108645i
$793$	3.95905e6	−	1.44098e6i	0.223567	−	0.0813718i
$794$	1.98122e7	+	7.21105e6i	1.11527	+	0.405926i
$795$	−2.21458e7	−	1.85825e7i	−1.24272	−	1.04276i
$796$	−849966.	+	4.82040e6i	−0.0475466	+	0.269650i
$797$	−8.28296e6			−0.461891			−0.230946	−	0.972967i	$-0.574182\pi$
$797$	−8.28296e6			−0.461891			−0.230946	+	0.972967i	$0.574182\pi$
$798$	1.23059e7	−	8.93022e6i	0.684078	−	0.496426i
$799$	1.68904e7			0.935996
$800$	1.06699e6	−	6.05119e6i	0.0589433	−	0.334284i
$801$	1.14944e7	+	9.64496e6i	0.633003	+	0.531152i
$802$	1.55027e7	+	5.64253e6i	0.851084	+	0.309769i
$803$	−647533.	+	235683.i	−0.0354383	+	0.0128985i
$804$	−1.82925e6	+	1.53493e6i	−0.0998008	+	0.0837428i
$805$	1.32065e7	+	2.28743e7i	0.718285	+	1.24411i
$806$	−6.73197e6	+	1.16601e7i	−0.365010	+	0.632215i
$807$	−2.90938e6	−	1.64999e7i	−0.157260	−	0.891863i
$808$	−1.89034e6	−	1.07206e7i	−0.101862	−	0.577686i
$809$	4.45829e6	−	7.72198e6i	0.239495	−	0.414818i	−0.721074	−	0.692858i	$-0.756351\pi$
$809$	4.45829e6	−	7.72198e6i	0.239495	−	0.414818i	0.960570	+	0.278040i	$0.0896847\pi$
$810$	1.55283e6	+	2.68958e6i	0.0831593	+	0.144036i
$811$	−1.16553e7	+	9.77996e6i	−0.622259	+	0.522137i	−0.898513	−	0.438947i	$-0.855351\pi$
$811$	−1.16553e7	+	9.77996e6i	−0.622259	+	0.522137i	0.276254	+	0.961085i	$0.410907\pi$
$812$	1.48513e6	−	540541.i	0.0790447	−	0.0287699i
$813$	−1.11094e7	−	4.04350e6i	−0.589475	−	0.214551i
$814$	−8.32077e6	−	6.98195e6i	−0.440152	−	0.369331i
$815$	7.31633e6	−	4.14930e7i	0.385833	−	2.18817i
$816$	−2.12268e6			−0.111599
$817$	4.93032e6	−	1.97274e7i	0.258417	−	1.03398i
$818$	−1.88488e7			−0.984918
$819$	−2.75201e6	+	1.56074e7i	−0.143364	+	0.813058i
$820$	−1.88274e7	−	1.57981e7i	−0.977814	−	0.820484i
$821$	−2.10404e7	−	7.65807e6i	−1.08942	−	0.396517i	−0.266015	−	0.963969i	$-0.585707\pi$
$821$	−2.10404e7	−	7.65807e6i	−1.08942	−	0.396517i	−0.823406	+	0.567452i	$0.807929\pi$
$822$	2.72227e6	−	990825.i	0.140524	−	0.0511467i
$823$	−1.61287e7	+	1.35336e7i	−0.830042	+	0.696488i	−0.955301	−	0.295636i	$-0.904468\pi$
$823$	−1.61287e7	+	1.35336e7i	−0.830042	+	0.696488i	0.125258	+	0.992124i	$0.460024\pi$
$824$	2.32227e6	+	4.02229e6i	0.119150	+	0.206374i
$825$	−1.07950e7	+	1.86975e7i	−0.552188	+	0.956418i
$826$	1.50753e6	+	8.54960e6i	0.0768802	+	0.436009i
$827$	3.88156e6	+	2.20134e7i	0.197352	+	1.11924i	0.909029	+	0.416733i	$0.136825\pi$
$827$	3.88156e6	+	2.20134e7i	0.197352	+	1.11924i	−0.711677	+	0.702507i	$0.752064\pi$
$828$	−1.28390e6	+	2.22379e6i	−0.0650813	+	0.112724i
$829$	1.52088e7	+	2.63424e7i	0.768613	+	1.33128i	0.938315	+	0.345782i	$0.112386\pi$
$829$	1.52088e7	+	2.63424e7i	0.768613	+	1.33128i	−0.169702	+	0.985495i	$0.554280\pi$
$830$	−1.00048e7	+	8.39502e6i	−0.504096	+	0.422986i
$831$	−6.33868e6	+	2.30709e6i	−0.318417	+	0.115894i
$832$	−1.94884e6	−	709321.i	−0.0976042	−	0.0355250i
$833$	−2.26647e7	−	1.90180e7i	−1.13172	−	0.949624i
$834$	2.66967e6	−	1.51404e7i	0.132905	−	0.753743i
$835$	−3.08619e6			−0.153181
$836$	905405.	+	8.66102e6i	0.0448051	+	0.428601i
$837$	−2.61256e7			−1.28900
$838$	−2.41082e6	+	1.36724e7i	−0.118592	+	0.672568i
$839$	−1.84756e7	−	1.55029e7i	−0.906137	−	0.760339i	0.0652431	−	0.997869i	$-0.479218\pi$
$839$	−1.84756e7	−	1.55029e7i	−0.906137	−	0.760339i	−0.971380	+	0.237530i	$0.923662\pi$
$840$	−1.38781e7	−	5.05120e6i	−0.678627	−	0.247000i
$841$	1.91042e7	−	6.95334e6i	0.931403	−	0.339003i
$842$	−3.65321e6	+	3.06541e6i	−0.177580	+	0.149007i
$843$	2.61010e6	+	4.52083e6i	0.126499	+	0.219103i
$844$	−6.47790e6	+	1.12201e7i	−0.313024	+	0.542174i
$845$	−1.90642e6	−	1.08118e7i	−0.0918493	−	0.520904i
$846$	1.98388e6	+	1.12512e7i	0.0952994	+	0.540470i
$847$	4.80905e6	−	8.32952e6i	0.230330	−	0.398943i
$848$	3.72375e6	+	6.44972e6i	0.177824	+	0.308000i
$849$	1.09102e7	−	9.15475e6i	0.519474	−	0.435890i
$850$	1.79780e7	−	6.54347e6i	0.853483	−	0.310642i
$851$	−8.78417e6	−	3.19718e6i	−0.415793	−	0.151336i
$852$	−3.97803e6	−	3.33796e6i	−0.187745	−	0.157537i
$853$	2.86665e6	−	1.62576e7i	0.134897	−	0.765040i	−0.840034	−	0.542534i	$-0.817465\pi$
$853$	2.86665e6	−	1.62576e7i	0.134897	−	0.765040i	0.974931	−	0.222506i	$-0.0714237\pi$
$854$	−7.72914e6			−0.362649
$855$	−2.02110e7	−	1.42467e6i	−0.945525	−	0.0666498i
$856$	−4.35337e6			−0.203068
$857$	−1.97103e6	+	1.11783e7i	−0.0916729	+	0.519903i	0.904043	+	0.427441i	$0.140585\pi$
$857$	−1.97103e6	+	1.11783e7i	−0.0916729	+	0.519903i	−0.995716	+	0.0924619i	$0.970526\pi$
$858$	5.58222e6	+	4.68404e6i	0.258874	+	0.217221i
$859$	−1.88814e7	−	6.87228e6i	−0.873075	−	0.317773i	−0.133664	−	0.991027i	$-0.542674\pi$
$859$	−1.88814e7	−	6.87228e6i	−0.873075	−	0.317773i	−0.739412	+	0.673253i	$0.764896\pi$
$860$	−1.85599e7	+	6.75526e6i	−0.855717	+	0.311456i
$861$	−2.97561e7	+	2.49684e7i	−1.36794	+	1.14784i
$862$	1.35859e6	+	2.35314e6i	0.0622759	+	0.107865i
$863$	−9.86687e6	+	1.70899e7i	−0.450975	+	0.781111i	−0.998447	−	0.0557126i	$-0.982257\pi$
$863$	−9.86687e6	+	1.70899e7i	−0.450975	+	0.781111i	0.547472	+	0.836824i	$0.315590\pi$
$864$	−698805.	−	3.96312e6i	−0.0318472	−	0.180615i
$865$	−2.32413e6	−	1.31808e7i	−0.105614	−	0.598965i
$866$	1.42844e7	−	2.47413e7i	0.647242	−	1.12106i
$867$	4.08041e6	+	7.06748e6i	0.184355	+	0.319313i
$868$	1.89213e7	−	1.58769e7i	0.852418	−	0.715264i
$869$	3.12776e6	−	1.13841e6i	0.140502	−	0.0511387i
$870$	1.58881e6	+	578280.i	0.0711663	+	0.0259024i
$871$	−5.56478e6	−	4.66940e6i	−0.248544	−	0.208553i
$872$	−215408.	+	1.22164e6i	−0.00959336	+	0.0544067i
$873$	−1.30737e7			−0.580583
$874$	3.28154e6	+	6.73772e6i	0.145311	+	0.298356i
$875$	6.37887e7			2.81659
$876$	57580.9	−	326558.i	0.00253524	−	0.0143780i
$877$	1.41008e7	+	1.18320e7i	0.619078	+	0.519468i	0.897514	−	0.440987i	$-0.145371\pi$
$877$	1.41008e7	+	1.18320e7i	0.619078	+	0.519468i	−0.278436	+	0.960455i	$0.589816\pi$
$878$	−6.07520e6	−	2.21119e6i	−0.265965	−	0.0968034i
$879$	6.69319e6	−	2.43612e6i	0.292187	−	0.106347i
$880$	6.47960e6	−	5.43703e6i	0.282060	−	0.236676i
$881$	−7.11552e6	−	1.23244e7i	−0.308864	−	0.534968i	0.669250	−	0.743037i	$-0.266615\pi$
$881$	−7.11552e6	−	1.23244e7i	−0.308864	−	0.534968i	−0.978114	+	0.208069i	$0.933282\pi$
$882$	1.00063e7	−	1.73313e7i	0.433112	−	0.750172i
$883$	1.84436e6	+	1.04599e7i	0.0796056	+	0.451466i	0.998391	+	0.0567079i	$0.0180604\pi$
$883$	1.84436e6	+	1.04599e7i	0.0796056	+	0.451466i	−0.918785	+	0.394758i	$0.870829\pi$
$884$	−1.12132e6	−	6.35930e6i	−0.0482611	−	0.273702i
$885$	−4.64380e6	+	8.04330e6i	−0.199304	+	0.345204i
$886$	6.31572e6	+	1.09391e7i	0.270295	+	0.468165i
$887$	3.66970e6	−	3.07925e6i	0.156611	−	0.131412i	−0.561115	−	0.827738i	$-0.689628\pi$
$887$	3.66970e6	−	3.07925e6i	0.156611	−	0.131412i	0.717726	+	0.696326i	$0.245183\pi$
$888$	4.91165e6	−	1.78770e6i	0.209024	−	0.0760783i
$889$	−2.07142e7	−	7.53934e6i	−0.879050	−	0.319948i
$890$	−3.25855e7	−	2.73425e7i	−1.37895	−	1.15708i
$891$	−488157.	+	2.76848e6i	−0.0205999	+	0.116828i
$892$	1.01534e7			0.427268
$893$	3.04537e7	+	1.35793e7i	1.27794	+	0.569835i
$894$	451281.			0.0188844
$895$	3.40202e6	−	1.92938e7i	0.141964	−	0.805120i
$896$	2.91455e6	+	2.44559e6i	0.121283	+	0.101769i
$897$	5.89311e6	+	2.14492e6i	0.244548	+	0.0890081i
$898$	−5.56112e6	+	2.02408e6i	−0.230129	+	0.0837601i
$899$	−2.16618e6	+	1.81764e6i	−0.0893915	+	0.0750084i
$900$	6.47040e6	+	1.12071e7i	0.266272	+	0.461196i
$901$	−1.15944e7	+	2.00820e7i	−0.475812	+	0.824130i
$902$	−3.86317e6	−	2.19091e7i	−0.158098	−	0.896620i
$903$	5.42059e6	+	3.07417e7i	0.221221	+	1.25461i
$904$	4.10430e6	−	7.10886e6i	0.167039	−	0.289320i
$905$	2.85062e7	+	4.93742e7i	1.15696	+	2.00391i
$906$	1.07079e6	−	898501.i	0.0433396	−	0.0363662i
$907$	3.63735e7	−	1.32389e7i	1.46814	−	0.534358i	0.520543	−	0.853835i	$-0.325729\pi$
$907$	3.63735e7	−	1.32389e7i	1.46814	−	0.534358i	0.947594	+	0.319477i	$0.103507\pi$
$908$	1.41119e6	+	513631.i	0.0568029	+	0.0206746i
$909$	1.75628e7	+	1.47370e7i	0.704993	+	0.591560i
$910$	7.80166e6	−	4.42454e7i	0.312308	−	1.77119i
$911$	2.75114e7			1.09829			0.549146	−	0.835727i	$-0.314953\pi$
$911$	2.75114e7			1.09829			0.549146	+	0.835727i	$0.314953\pi$
$912$	−3.82722e6	−	1.70656e6i	−0.152369	−	0.0679413i
$913$	−1.18220e7			−0.469368
$914$	−3.68664e6	+	2.09080e7i	−0.145971	+	0.827841i
$915$	−6.33424e6	−	5.31506e6i	−0.250116	−	0.209872i
$916$	−2.64895e6	−	964140.i	−0.104312	−	0.0379666i
$917$	−5.79217e7	+	2.10818e7i	−2.27467	+	0.827912i
$918$	9.59857e6	−	8.05416e6i	0.375924	−	0.315438i
$919$	6.61702e6	+	1.14610e7i	0.258448	+	0.447645i	0.965826	−	0.259190i	$-0.0834555\pi$
$919$	6.61702e6	+	1.14610e7i	0.258448	+	0.447645i	−0.707378	+	0.706835i	$0.750122\pi$
$920$	3.63973e6	−	6.30420e6i	0.141775	−	0.245562i
$921$	−2.58822e6	−	1.46785e7i	−0.100543	−	0.570208i
$922$	−1.07516e6	−	6.09753e6i	−0.0416529	−	0.236225i
$923$	7.89874e6	−	1.36810e7i	0.305178	−	0.528584i
$924$	−6.68420e6	−	1.15774e7i	−0.257555	−	0.446098i
$925$	−3.60884e7	+	3.02818e7i	−1.38680	+	1.16366i
$926$	−2.75217e7	+	1.00171e7i	−1.05474	+	0.383895i
$927$	−9.19179e6	−	3.34554e6i	−0.351318	−	0.127869i
$928$	−333668.	−	279981.i	−0.0127187	−	0.0106723i
$929$	−3.36976e6	+	1.91109e7i	−0.128103	+	0.726509i	0.851313	+	0.524658i	$0.175807\pi$
$929$	−3.36976e6	+	1.91109e7i	−0.128103	+	0.726509i	−0.979416	+	0.201851i	$0.935304\pi$
$930$	2.64245e7			1.00184
$931$	−2.55751e7	−	5.25113e7i	−0.967036	−	1.98554i
$932$	−3.61857e6			−0.136457
$933$	−517664.	+	2.93582e6i	−0.0194690	+	0.110414i
$934$	2.11910e7	+	1.77814e7i	0.794850	+	0.666958i
$935$	2.47484e7	+	9.00767e6i	0.925801	+	0.336964i
$936$	4.10439e6	−	1.49388e6i	0.153129	−	0.0557346i
$937$	3.60598e7	−	3.02577e7i	1.34176	−	1.12587i	0.360587	−	0.932726i	$-0.382577\pi$
$937$	3.60598e7	−	3.02577e7i	1.34176	−	1.12587i	0.981171	−	0.193142i	$-0.0618679\pi$
$938$	6.66331e6	+	1.15412e7i	0.247276	+	0.428295i
$939$	−1.69697e6	+	2.93924e6i	−0.0628074	+	0.108786i
$940$	−5.62410e6	−	3.18959e7i	−0.207603	−	1.17738i
$941$	8.70964e6	+	4.93948e7i	0.320646	+	1.81847i	0.538653	+	0.842527i	$0.318933\pi$
$941$	8.70964e6	+	4.93948e7i	0.320646	+	1.81847i	−0.218007	+	0.975947i	$0.569956\pi$
$942$	−1.18924e7	+	2.05982e7i	−0.436658	+	0.756314i
$943$	−9.57301e6	−	1.65809e7i	−0.350566	−	0.607198i
$944$	1.83287e6	−	1.53796e6i	0.0669424	−	0.0561714i
$945$	8.19214e7	−	2.98170e7i	2.98413	−	1.08614i
$946$	−1.68001e7	−	6.11474e6i	−0.610358	−	0.222152i
$947$	1.42187e7	+	1.19309e7i	0.515212	+	0.432314i	0.862959	−	0.505274i	$-0.168609\pi$
$947$	1.42187e7	+	1.19309e7i	0.515212	+	0.432314i	−0.347747	+	0.937588i	$0.613053\pi$
$948$	−278132.	+	1.57736e6i	−0.0100515	+	0.0570047i
$949$	1.00875e6			0.0363594
$950$	3.76753e7	+	2.65572e6i	1.35440	+	0.0954715i
$951$	3.16633e7			1.13529
$952$	−2.05709e6	+	1.16664e7i	−0.0735634	+	0.417199i
$953$	2.76003e7	+	2.31594e7i	0.984423	+	0.826029i	0.984751	−	0.173971i	$-0.0556600\pi$
$953$	2.76003e7	+	2.31594e7i	0.984423	+	0.826029i	−0.000328086		1.00000i	$0.500104\pi$
$954$	−1.47390e7	−	5.36455e6i	−0.524320	−	0.190837i
$955$	−3.35928e7	+	1.22268e7i	−1.19189	+	0.433814i
$956$	−4.21626e6	+	3.53787e6i	−0.149205	+	0.125198i
$957$	765231.	+	1.32542e6i	0.0270093	+	0.0467814i
$958$	−6.45334e6	+	1.11775e7i	−0.227180	+	0.393488i
$959$	−2.80747e6	−	1.59219e7i	−0.0985754	−	0.559049i
$960$	706800.	+	4.00846e6i	0.0247525	+	0.140378i
$961$	−7.78236e6	+	1.34795e7i	−0.271834	+	0.470830i
$962$	7.95033e6	+	1.37704e7i	0.276980	+	0.479743i
$963$	7.02346e6	−	5.89338e6i	0.244054	−	0.204785i
$964$	−2.38586e7	+	8.68381e6i	−0.826898	+	0.300966i
$965$	−1.66149e7	−	6.04733e6i	−0.574354	−	0.209048i
$966$	−8.81331e6	−	7.39524e6i	−0.303876	−	0.254982i
$967$	2.13457e6	−	1.21057e7i	0.0734081	−	0.416318i	−0.925853	−	0.377884i	$-0.876652\pi$
$967$	2.13457e6	−	1.21057e7i	0.0734081	−	0.416318i	0.999261	−	0.0384342i	$-0.0122370\pi$
$968$	−2.65077e6			−0.0909251
$969$	−1.35657e6	−	1.29768e7i	−0.0464123	−	0.443975i
$970$	3.70627e7			1.26476
$971$	3.01764e6	−	1.71139e7i	0.102712	−	0.582507i	−0.889398	−	0.457134i	$-0.848876\pi$
$971$	3.01764e6	−	1.71139e7i	0.102712	−	0.582507i	0.992110	−	0.125373i	$-0.0400128\pi$
$972$	1.06686e7	+	8.95200e6i	0.362194	+	0.303917i
$973$	−8.06255e7	−	2.93453e7i	−2.73017	−	0.993702i
$974$	1.74780e7	−	6.36147e6i	0.590329	−	0.214862i
$975$	2.42109e7	−	2.03154e7i	0.815643	−	0.684406i
$976$	1.06509e6	+	1.84478e6i	0.0357898	+	0.0619898i
$977$	7.70501e6	−	1.33455e7i	0.258248	−	0.447299i	−0.707525	−	0.706689i	$-0.750188\pi$
$977$	7.70501e6	−	1.33455e7i	0.258248	−	0.447299i	0.965773	+	0.259390i	$0.0835215\pi$
$978$	3.18685e6	+	1.80735e7i	0.106541	+	0.604221i
$979$	−6.68615e6	−	3.79191e7i	−0.222956	−	1.26445i
$980$	−2.83667e7	+	4.91326e7i	−0.943504	+	1.63420i
$981$	−1.30627e6	−	2.26253e6i	−0.0433372	−	0.0750623i
$982$	2.52419e7	−	2.11804e7i	0.835300	−	0.700900i
$983$	−5.12985e7	+	1.86711e7i	−1.69325	+	0.616293i	−0.995029	−	0.0995895i	$-0.968247\pi$
$983$	−5.12985e7	+	1.86711e7i	−1.69325	+	0.616293i	−0.698221	+	0.715882i	$0.746025\pi$
$984$	1.00598e7	+	3.66148e6i	0.331210	+	0.120551i
$985$	1.09416e7	+	9.18108e6i	0.359327	+	0.301511i
$986$	235504.	−	1.33561e6i	0.00771445	−	0.0437508i
$987$	−5.11880e7			−1.67254
$988$	3.09090e6	−	1.23674e7i	0.100738	−	0.403075i
$989$	−1.53862e7			−0.500197
$990$	−3.09340e6	+	1.75435e7i	−0.100311	+	0.568891i
$991$	3.29276e7	+	2.76295e7i	1.06506	+	0.893694i	0.994596	−	0.103820i	$-0.0331066\pi$
$991$	3.29276e7	+	2.76295e7i	1.06506	+	0.893694i	0.0704670	+	0.997514i	$0.477551\pi$
$992$	−6.39686e6	−	2.32827e6i	−0.206390	−	0.0751196i
$993$	2.21213e7	−	8.05151e6i	0.711932	−	0.259122i
$994$	−2.22008e7	+	1.86286e7i	−0.712692	+	0.598019i
$995$	1.46120e7	+	2.53088e7i	0.467900	+	0.810426i
$996$	2.84441e6	−	4.92667e6i	0.0908540	−	0.157364i
$997$	−9.24600e6	−	5.24366e7i	−0.294588	−	1.67069i	−0.668870	−	0.743379i	$-0.733222\pi$
$997$	−9.24600e6	−	5.24366e7i	−0.294588	−	1.67069i	0.374282	−	0.927315i	$-0.377889\pi$
$998$	−2.59076e6	−	1.46929e7i	−0.0823381	−	0.466963i
$999$	−1.54270e7	+	2.67203e7i	−0.489065	+	0.847085i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.6.e.b.17.4	yes	30
19.3	odd	18		722.6.a.q.1.6		15
19.9	even	9	inner	38.6.e.b.9.4	✓	30
19.16	even	9		722.6.a.r.1.10		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.b.9.4	✓	30	19.9	even	9	inner
38.6.e.b.17.4	yes	30	1.1	even	1	trivial
722.6.a.q.1.6		15	19.3	odd	18
722.6.a.r.1.10		15	19.16	even	9

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.694593 - 3.93923i) q^{2} +(7.96877 + 6.68659i) q^{3} +(-15.0351 - 5.47232i) q^{4} +(-89.7666 + 32.6724i) q^{5} +(31.8751 - 26.7464i) q^{6} +(-116.109 - 201.107i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(-23.4057 - 132.740i) q^{9} +O(q^{10})\)	\(q+(0.694593 - 3.93923i) q^{2} +(7.96877 + 6.68659i) q^{3} +(-15.0351 - 5.47232i) q^{4} +(-89.7666 + 32.6724i) q^{5} +(31.8751 - 26.7464i) q^{6} +(-116.109 - 201.107i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(-23.4057 - 132.740i) q^{9} +(66.3528 + 376.305i) q^{10} +(-172.940 + 299.541i) q^{11} +(-83.2199 - 144.141i) q^{12} +(387.869 - 325.461i) q^{13} +(-872.856 + 317.694i) q^{14} +(-933.796 - 339.874i) q^{15} +(196.107 + 164.554i) q^{16} +(-138.413 + 784.980i) q^{17} -539.153 q^{18} +(-880.656 + 1304.05i) q^{19} +1528.44 q^{20} +(419.474 - 2378.95i) q^{21} +(1059.84 + 889.309i) q^{22} +(1118.86 + 407.232i) q^{23} +(-625.609 + 227.703i) q^{24} +(4596.67 - 3857.06i) q^{25} +(-1012.65 - 1753.97i) q^{26} +(1964.97 - 3403.43i) q^{27} +(645.189 + 3659.05i) q^{28} +(-73.8636 - 418.901i) q^{29} +(-1987.45 + 3442.37i) q^{30} +(-3323.92 - 5757.21i) q^{31} +(784.430 - 658.215i) q^{32} +(-3381.02 + 1230.59i) q^{33} +(2996.07 + 1090.48i) q^{34} +(16993.4 + 14259.1i) q^{35} +(-374.491 + 2123.85i) q^{36} -7850.99 q^{37} +(4525.25 + 4374.89i) q^{38} +5267.06 q^{39} +(1061.64 - 6020.89i) q^{40} +(-12318.1 - 10336.1i) q^{41} +(-9079.88 - 3304.81i) q^{42} +(-12143.0 + 4419.71i) q^{43} +(4239.35 - 3557.23i) q^{44} +(6438.00 + 11150.9i) q^{45} +(2381.34 - 4124.59i) q^{46} +(-3679.63 - 20868.2i) q^{47} +(462.432 + 2622.58i) q^{48} +(-18559.2 + 32145.5i) q^{49} +(-12001.1 - 20786.4i) q^{50} +(-6351.82 + 5329.81i) q^{51} +(-7612.67 + 2770.78i) q^{52} +(27337.3 + 9949.97i) q^{53} +(-12042.0 - 10104.5i) q^{54} +(5737.52 - 32539.1i) q^{55} +14862.0 q^{56} +(-15737.4 + 4503.09i) q^{57} -1701.45 q^{58} +(1622.96 - 9204.26i) q^{59} +(12179.8 + 10220.1i) q^{60} +(7819.16 + 2845.94i) q^{61} +(-24987.7 + 9094.79i) q^{62} +(-23977.4 + 20119.5i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(-24184.1 + 41888.1i) q^{65} +(2499.15 + 14173.4i) q^{66} +(-2491.34 - 14129.1i) q^{67} +(6376.71 - 11044.8i) q^{68} +(6192.96 + 10726.5i) q^{69} +(67973.5 - 57036.6i) q^{70} +(29318.6 - 10671.1i) q^{71} +(8106.20 + 2950.42i) q^{72} +(1526.18 + 1280.61i) q^{73} +(-5453.24 + 30926.9i) q^{74} +62420.4 q^{75} +(20376.9 - 14787.3i) q^{76} +80319.7 q^{77} +(3658.46 - 20748.2i) q^{78} +(-7371.85 - 6185.72i) q^{79} +(-22980.3 - 8364.13i) q^{80} +(7637.48 - 2779.82i) q^{81} +(-49272.2 + 41344.3i) q^{82} +(17089.7 + 29600.3i) q^{83} +(-19325.2 + 33472.3i) q^{84} +(-13222.3 - 74987.2i) q^{85} +(8975.77 + 50904.1i) q^{86} +(2212.42 - 3832.03i) q^{87} +(-11068.1 - 19170.6i) q^{88} +(-85277.6 + 71556.4i) q^{89} +(48397.9 - 17615.4i) q^{90} +(-110488. - 40214.2i) q^{91} +(-14593.7 - 12245.5i) q^{92} +(12008.5 - 68103.6i) q^{93} -84760.6 q^{94} +(36447.1 - 145833. i) q^{95} +10652.2 q^{96} +(16843.0 - 95521.2i) q^{97} +(113738. + 95437.1i) q^{98} +(43808.9 + 15945.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 15 q^{3} + 60 q^{6} - 84 q^{7} - 960 q^{8} - 345 q^{9}+O(q^{10}) \) 30 * q + 15 * q^3 + 60 * q^6 - 84 * q^7 - 960 * q^8 - 345 * q^9	\( 30 q + 15 q^{3} + 60 q^{6} - 84 q^{7} - 960 q^{8} - 345 q^{9} - 126 q^{11} - 2610 q^{13} - 864 q^{14} - 5160 q^{15} + 1902 q^{17} + 17016 q^{18} - 2400 q^{19} + 3456 q^{20} - 6426 q^{21} + 216 q^{22} - 3306 q^{23} + 960 q^{24} - 18060 q^{25} + 456 q^{26} + 13017 q^{27} + 6048 q^{28} + 5988 q^{29} - 6840 q^{31} + 51867 q^{33} - 10752 q^{34} + 24408 q^{35} - 5520 q^{36} - 8556 q^{37} + 2772 q^{38} + 9912 q^{39} - 40527 q^{41} + 27432 q^{42} + 3678 q^{43} + 864 q^{44} - 31770 q^{45} - 15744 q^{46} - 133740 q^{47} - 7680 q^{48} - 63777 q^{49} - 107580 q^{50} + 45657 q^{51} + 5760 q^{52} - 64626 q^{53} + 1476 q^{54} + 142056 q^{55} + 10752 q^{56} + 232824 q^{57} + 117264 q^{58} + 169041 q^{59} - 56640 q^{60} + 61698 q^{61} - 101616 q^{62} - 188064 q^{63} - 61440 q^{64} - 80646 q^{65} - 173772 q^{66} - 72129 q^{67} - 65904 q^{68} - 124224 q^{69} + 97632 q^{70} + 417828 q^{71} + 44160 q^{72} + 239082 q^{73} - 116112 q^{74} - 174960 q^{75} + 6912 q^{76} + 242436 q^{77} + 336624 q^{78} - 145740 q^{79} + 14781 q^{81} - 162108 q^{82} - 201630 q^{83} - 54528 q^{84} - 46512 q^{85} - 75720 q^{86} - 376512 q^{87} - 8064 q^{88} + 416928 q^{89} + 560640 q^{90} - 380316 q^{91} + 269376 q^{92} - 205146 q^{93} + 5616 q^{94} + 708168 q^{95} + 858363 q^{97} + 308328 q^{98} - 1068531 q^{99}+O(q^{100}) \) 30 * q + 15 * q^3 + 60 * q^6 - 84 * q^7 - 960 * q^8 - 345 * q^9 - 126 * q^11 - 2610 * q^13 - 864 * q^14 - 5160 * q^15 + 1902 * q^17 + 17016 * q^18 - 2400 * q^19 + 3456 * q^20 - 6426 * q^21 + 216 * q^22 - 3306 * q^23 + 960 * q^24 - 18060 * q^25 + 456 * q^26 + 13017 * q^27 + 6048 * q^28 + 5988 * q^29 - 6840 * q^31 + 51867 * q^33 - 10752 * q^34 + 24408 * q^35 - 5520 * q^36 - 8556 * q^37 + 2772 * q^38 + 9912 * q^39 - 40527 * q^41 + 27432 * q^42 + 3678 * q^43 + 864 * q^44 - 31770 * q^45 - 15744 * q^46 - 133740 * q^47 - 7680 * q^48 - 63777 * q^49 - 107580 * q^50 + 45657 * q^51 + 5760 * q^52 - 64626 * q^53 + 1476 * q^54 + 142056 * q^55 + 10752 * q^56 + 232824 * q^57 + 117264 * q^58 + 169041 * q^59 - 56640 * q^60 + 61698 * q^61 - 101616 * q^62 - 188064 * q^63 - 61440 * q^64 - 80646 * q^65 - 173772 * q^66 - 72129 * q^67 - 65904 * q^68 - 124224 * q^69 + 97632 * q^70 + 417828 * q^71 + 44160 * q^72 + 239082 * q^73 - 116112 * q^74 - 174960 * q^75 + 6912 * q^76 + 242436 * q^77 + 336624 * q^78 - 145740 * q^79 + 14781 * q^81 - 162108 * q^82 - 201630 * q^83 - 54528 * q^84 - 46512 * q^85 - 75720 * q^86 - 376512 * q^87 - 8064 * q^88 + 416928 * q^89 + 560640 * q^90 - 380316 * q^91 + 269376 * q^92 - 205146 * q^93 + 5616 * q^94 + 708168 * q^95 + 858363 * q^97 + 308328 * q^98 - 1068531 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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