LMFDB - Embedded newform 38.10.c.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,10,Mod(7,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("38.7");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	38.c (of order $3$, degree $2$, 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:	$19.5713617742$
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} - 3 x^{13} + 93094 x^{12} + 3763497 x^{11} + 6525212431 x^{10} + 244392759522 x^{9} + \cdots + 37\!\cdots\!25 $ x^14 - 3x^13 + 93094x^12 + 3763497x^11 + 6525212431x^10 + 244392759522x^9 + 198778066371639x^8 + 9216645483921129x^7 + 4530154246073222607x^6 + 142122715974381300066x^5 + 8185019559882294055671x^4 - 135327799885026117969495x^3 + 2044710563339570147369550x^2 - 9649457865335314261798875*x + 37683939484136051622500625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{6}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.2
Root			$97.2191 - 168.388i$ of defining polynomial
Character	$\chi$	$=$	38.11
Dual form			38.10.c.a.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.00000 - 13.8564i) q^{2} +(-85.2191 + 147.604i) q^{3} +(-128.000 - 221.703i) q^{4} +(-867.647 + 1502.81i) q^{5} +(1363.51 + 2361.66i) q^{6} -2874.94 q^{7} -4096.00 q^{8} +(-4683.10 - 8111.37i) q^{9} +O(q^{10})$	\(q+(8.00000 - 13.8564i) q^{2} +(-85.2191 + 147.604i) q^{3} +(-128.000 - 221.703i) q^{4} +(-867.647 + 1502.81i) q^{5} +(1363.51 + 2361.66i) q^{6} -2874.94 q^{7} -4096.00 q^{8} +(-4683.10 - 8111.37i) q^{9} +(13882.3 + 24044.9i) q^{10} +23145.6 q^{11} +43632.2 q^{12} +(-47836.2 - 82854.8i) q^{13} +(-22999.5 + 39836.3i) q^{14} +(-147880. - 256136. i) q^{15} +(-32768.0 + 56755.8i) q^{16} +(84319.5 - 146046. i) q^{17} -149859. q^{18} +(337837. - 456677. i) q^{19} +444235. q^{20} +(245000. - 424352. i) q^{21} +(185165. - 320714. i) q^{22} +(-401923. - 696152. i) q^{23} +(349058. - 604586. i) q^{24} +(-529059. - 916358. i) q^{25} -1.53076e6 q^{26} -1.75838e6 q^{27} +(367992. + 637381. i) q^{28} +(-496243. - 859518. i) q^{29} -4.73217e6 q^{30} -4.45131e6 q^{31} +(524288. + 908093. i) q^{32} +(-1.97245e6 + 3.41638e6i) q^{33} +(-1.34911e6 - 2.33673e6i) q^{34} +(2.49443e6 - 4.32048e6i) q^{35} +(-1.19887e6 + 2.07651e6i) q^{36} -5.83352e6 q^{37} +(-3.62520e6 - 8.33462e6i) q^{38} +1.63063e7 q^{39} +(3.55388e6 - 6.15550e6i) q^{40} +(9.92901e6 - 1.71975e7i) q^{41} +(-3.92000e6 - 6.78964e6i) q^{42} +(1.61200e7 - 2.79207e7i) q^{43} +(-2.96263e6 - 5.13143e6i) q^{44} +1.62531e7 q^{45} -1.28616e7 q^{46} +(2.21889e7 + 3.84322e7i) q^{47} +(-5.58492e6 - 9.67337e6i) q^{48} -3.20883e7 q^{49} -1.69299e7 q^{50} +(1.43713e7 + 2.48918e7i) q^{51} +(-1.22461e7 + 2.12108e7i) q^{52} +(3.48825e7 + 6.04183e7i) q^{53} +(-1.40670e7 + 2.43648e7i) q^{54} +(-2.00822e7 + 3.47834e7i) q^{55} +1.17758e7 q^{56} +(3.86171e7 + 8.87837e7i) q^{57} -1.58798e7 q^{58} +(1.29065e7 - 2.23547e7i) q^{59} +(-3.78573e7 + 6.55708e7i) q^{60} +(-3.82450e7 - 6.62423e7i) q^{61} +(-3.56105e7 + 6.16791e7i) q^{62} +(1.34636e7 + 2.33197e7i) q^{63} +1.67772e7 q^{64} +1.66020e8 q^{65} +(3.15591e7 + 5.46620e7i) q^{66} +(-1.78924e7 - 3.09905e7i) q^{67} -4.31716e7 q^{68} +1.37006e8 q^{69} +(-3.99109e7 - 6.91277e7i) q^{70} +(-2.44307e7 + 4.23152e7i) q^{71} +(1.91820e7 + 3.32242e7i) q^{72} +(7.43340e7 - 1.28750e8i) q^{73} +(-4.66682e7 + 8.08317e7i) q^{74} +1.80344e8 q^{75} +(-1.44490e8 - 1.64447e7i) q^{76} -6.65421e7 q^{77} +(1.30450e8 - 2.25946e8i) q^{78} +(-2.18634e8 + 3.78686e8i) q^{79} +(-5.68621e7 - 9.84880e7i) q^{80} +(2.42025e8 - 4.19199e8i) q^{81} +(-1.58864e8 - 2.75161e8i) q^{82} -4.70722e8 q^{83} -1.25440e8 q^{84} +(1.46319e8 + 2.53432e8i) q^{85} +(-2.57921e8 - 4.46732e8i) q^{86} +1.69158e8 q^{87} -9.48043e7 q^{88} +(-3.94729e8 - 6.83691e8i) q^{89} +(1.30025e8 - 2.25210e8i) q^{90} +(1.37526e8 + 2.38203e8i) q^{91} +(-1.02892e8 + 1.78215e8i) q^{92} +(3.79337e8 - 6.57030e8i) q^{93} +7.10043e8 q^{94} +(3.93174e8 + 9.03939e8i) q^{95} -1.78717e8 q^{96} +(1.11328e8 - 1.92825e8i) q^{97} +(-2.56707e8 + 4.44629e8i) q^{98} +(-1.08393e8 - 1.87742e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 112 q^{2} + 165 q^{3} - 1792 q^{4} + 909 q^{5} - 2640 q^{6} + 3692 q^{7} - 57344 q^{8} - 52286 q^{9}+O(q^{10}) $ 14 * q + 112 * q^2 + 165 * q^3 - 1792 * q^4 + 909 * q^5 - 2640 * q^6 + 3692 * q^7 - 57344 * q^8 - 52286 * q^9	\( 14 q + 112 q^{2} + 165 q^{3} - 1792 q^{4} + 909 q^{5} - 2640 q^{6} + 3692 q^{7} - 57344 q^{8} - 52286 q^{9} - 14544 q^{10} + 15656 q^{11} - 84480 q^{12} + 6423 q^{13} + 29536 q^{14} - 227715 q^{15} - 458752 q^{16} + 313667 q^{17} - 1673152 q^{18} + 1134224 q^{19} - 465408 q^{20} - 1227046 q^{21} + 125248 q^{22} + 3449345 q^{23} - 675840 q^{24} - 2398648 q^{25} + 205536 q^{26} - 1873854 q^{27} - 472576 q^{28} - 7002615 q^{29} - 7286880 q^{30} - 18666588 q^{31} + 7340032 q^{32} - 13827668 q^{33} - 5018672 q^{34} + 2584932 q^{35} - 13385216 q^{36} - 6866080 q^{37} + 22760176 q^{38} + 4568410 q^{39} - 3723264 q^{40} + 3564107 q^{41} + 19632736 q^{42} + 19837521 q^{43} - 2003968 q^{44} - 77788260 q^{45} + 110379040 q^{46} + 60353825 q^{47} + 10813440 q^{48} - 79579650 q^{49} - 76756736 q^{50} - 161350373 q^{51} + 1644288 q^{52} + 54744235 q^{53} - 14990832 q^{54} + 143199990 q^{55} - 15122432 q^{56} + 330686241 q^{57} - 224083680 q^{58} + 164456585 q^{59} - 58295040 q^{60} + 49328881 q^{61} - 149332704 q^{62} + 138012360 q^{63} + 234881024 q^{64} + 788015550 q^{65} + 221242688 q^{66} - 171522309 q^{67} - 160597504 q^{68} + 630323350 q^{69} - 41358912 q^{70} - 74596055 q^{71} + 214163456 q^{72} + 58695287 q^{73} - 54928640 q^{74} - 1115757144 q^{75} + 73801472 q^{76} - 965186644 q^{77} + 36547280 q^{78} + 121854617 q^{79} + 59572224 q^{80} - 368486747 q^{81} - 57025712 q^{82} - 732607256 q^{83} + 628247552 q^{84} + 634697565 q^{85} - 317400336 q^{86} - 2979036210 q^{87} - 64126976 q^{88} - 1652463181 q^{89} - 622306080 q^{90} - 1141270092 q^{91} + 883032320 q^{92} - 1839612746 q^{93} + 1931322400 q^{94} + 2397253503 q^{95} + 346030080 q^{96} + 248805607 q^{97} - 636637200 q^{98} + 520684712 q^{99}+O(q^{100}) \) 14 * q + 112 * q^2 + 165 * q^3 - 1792 * q^4 + 909 * q^5 - 2640 * q^6 + 3692 * q^7 - 57344 * q^8 - 52286 * q^9 - 14544 * q^10 + 15656 * q^11 - 84480 * q^12 + 6423 * q^13 + 29536 * q^14 - 227715 * q^15 - 458752 * q^16 + 313667 * q^17 - 1673152 * q^18 + 1134224 * q^19 - 465408 * q^20 - 1227046 * q^21 + 125248 * q^22 + 3449345 * q^23 - 675840 * q^24 - 2398648 * q^25 + 205536 * q^26 - 1873854 * q^27 - 472576 * q^28 - 7002615 * q^29 - 7286880 * q^30 - 18666588 * q^31 + 7340032 * q^32 - 13827668 * q^33 - 5018672 * q^34 + 2584932 * q^35 - 13385216 * q^36 - 6866080 * q^37 + 22760176 * q^38 + 4568410 * q^39 - 3723264 * q^40 + 3564107 * q^41 + 19632736 * q^42 + 19837521 * q^43 - 2003968 * q^44 - 77788260 * q^45 + 110379040 * q^46 + 60353825 * q^47 + 10813440 * q^48 - 79579650 * q^49 - 76756736 * q^50 - 161350373 * q^51 + 1644288 * q^52 + 54744235 * q^53 - 14990832 * q^54 + 143199990 * q^55 - 15122432 * q^56 + 330686241 * q^57 - 224083680 * q^58 + 164456585 * q^59 - 58295040 * q^60 + 49328881 * q^61 - 149332704 * q^62 + 138012360 * q^63 + 234881024 * q^64 + 788015550 * q^65 + 221242688 * q^66 - 171522309 * q^67 - 160597504 * q^68 + 630323350 * q^69 - 41358912 * q^70 - 74596055 * q^71 + 214163456 * q^72 + 58695287 * q^73 - 54928640 * q^74 - 1115757144 * q^75 + 73801472 * q^76 - 965186644 * q^77 + 36547280 * q^78 + 121854617 * q^79 + 59572224 * q^80 - 368486747 * q^81 - 57025712 * q^82 - 732607256 * q^83 + 628247552 * q^84 + 634697565 * q^85 - 317400336 * q^86 - 2979036210 * q^87 - 64126976 * q^88 - 1652463181 * q^89 - 622306080 * q^90 - 1141270092 * q^91 + 883032320 * q^92 - 1839612746 * q^93 + 1931322400 * q^94 + 2397253503 * q^95 + 346030080 * q^96 + 248805607 * q^97 - 636637200 * q^98 + 520684712 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	8.00000	−	13.8564i	0.353553	−	0.612372i
$2$	8.00000	−	13.8564i	0.353553	−	0.612372i
$3$	−85.2191	+	147.604i	−0.607423	+	1.05209i	0.384240	+	0.923233i	$0.374463\pi$
$3$	−85.2191	+	147.604i	−0.607423	+	1.05209i	−0.991663	+	0.128855i	$0.958870\pi$
$4$	−128.000	−	221.703i	−0.250000	−	0.433013i
$5$	−867.647	+	1502.81i	−0.620837	+	1.07532i	0.368493	+	0.929631i	$0.379874\pi$
$5$	−867.647	+	1502.81i	−0.620837	+	1.07532i	−0.989330	+	0.145691i	$0.953459\pi$
$6$	1363.51	+	2361.66i	0.429513	+	0.743939i
$7$	−2874.94			−0.452572			−0.226286	−	0.974061i	$-0.572658\pi$
$7$	−2874.94			−0.452572			−0.226286	+	0.974061i	$0.572658\pi$
$8$	−4096.00			−0.353553
$9$	−4683.10	−	8111.37i	−0.237926	−	0.412101i
$10$	13882.3	+	24044.9i	0.438998	+	0.760368i
$11$	23145.6			0.476651			0.238326	−	0.971185i	$-0.423401\pi$
$11$	23145.6			0.476651			0.238326	+	0.971185i	$0.423401\pi$
$12$	43632.2			0.607423
$13$	−47836.2	−	82854.8i	−0.464528	−	0.804586i	0.534652	−	0.845072i	$-0.320443\pi$
$13$	−47836.2	−	82854.8i	−0.464528	−	0.804586i	−0.999180	+	0.0404860i	$0.987109\pi$
$14$	−22999.5	+	39836.3i	−0.160008	+	0.277143i
$15$	−147880.	−	256136.i	−0.754222	−	1.30635i
$16$	−32768.0	+	56755.8i	−0.125000	+	0.216506i
$17$	84319.5	−	146046.i	0.244855	−	0.424100i	−0.717236	−	0.696830i	$-0.754593\pi$
$17$	84319.5	−	146046.i	0.244855	−	0.424100i	0.962091	+	0.272730i	$0.0879265\pi$
$18$	−149859.			−0.336479
$19$	337837.	−	456677.i	0.594725	−	0.803929i
$19$	337837.	−	456677.i	0.594725	−	0.803929i
$20$	444235.			0.620837
$21$	245000.	−	424352.i	0.274903	−	0.476146i
$22$	185165.	−	320714.i	0.168522	−	0.291888i
$23$	−401923.	−	696152.i	−0.299480	−	0.518715i	0.676537	−	0.736409i	$-0.263480\pi$
$23$	−401923.	−	696152.i	−0.299480	−	0.518715i	−0.976017	+	0.217694i	$0.930147\pi$
$24$	349058.	−	604586.i	0.214757	−	0.371969i
$25$	−529059.	−	916358.i	−0.270878	−	0.469175i
$26$	−1.53076e6			−0.656942
$27$	−1.75838e6			−0.636759
$28$	367992.	+	637381.i	0.113143	+	0.195969i
$29$	−496243.	−	859518.i	−0.130288	−	0.225665i	0.793500	−	0.608571i	$-0.208257\pi$
$29$	−496243.	−	859518.i	−0.130288	−	0.225665i	−0.923787	+	0.382906i	$0.874923\pi$
$30$	−4.73217e6			−1.06663
$31$	−4.45131e6			−0.865685			−0.432843	−	0.901469i	$-0.642489\pi$
$31$	−4.45131e6			−0.865685			−0.432843	+	0.901469i	$0.642489\pi$
$32$	524288.	+	908093.i	0.0883883	+	0.153093i
$33$	−1.97245e6	+	3.41638e6i	−0.289529	+	0.501479i
$34$	−1.34911e6	−	2.33673e6i	−0.173138	−	0.299884i
$35$	2.49443e6	−	4.32048e6i	0.280974	−	0.486661i
$36$	−1.19887e6	+	2.07651e6i	−0.118963	+	0.206050i
$37$	−5.83352e6			−0.511709			−0.255855	−	0.966715i	$-0.582357\pi$
$37$	−5.83352e6			−0.511709			−0.255855	+	0.966715i	$0.582357\pi$
$38$	−3.62520e6	−	8.33462e6i	−0.282037	−	0.648425i
$39$	1.63063e7			1.12866
$40$	3.55388e6	−	6.15550e6i	0.219499	−	0.380184i
$41$	9.92901e6	−	1.71975e7i	0.548755	−	0.950472i	−0.449605	−	0.893227i	$-0.648435\pi$
$41$	9.92901e6	−	1.71975e7i	0.548755	−	0.950472i	0.998360	−	0.0572442i	$-0.0182314\pi$
$42$	−3.92000e6	−	6.78964e6i	−0.194386	−	0.336686i
$43$	1.61200e7	−	2.79207e7i	0.719048	−	1.24543i	−0.242329	−	0.970194i	$-0.577911\pi$
$43$	1.61200e7	−	2.79207e7i	0.719048	−	1.24543i	0.961377	−	0.275234i	$-0.0887553\pi$
$44$	−2.96263e6	−	5.13143e6i	−0.119163	−	0.206396i
$45$	1.62531e7			0.590854
$46$	−1.28616e7			−0.423529
$47$	2.21889e7	+	3.84322e7i	0.663276	+	1.14883i	0.979750	+	0.200227i	$0.0641679\pi$
$47$	2.21889e7	+	3.84322e7i	0.663276	+	1.14883i	−0.316473	+	0.948601i	$0.602499\pi$
$48$	−5.58492e6	−	9.67337e6i	−0.151856	−	0.263022i
$49$	−3.20883e7			−0.795179
$50$	−1.69299e7			−0.383080
$51$	1.43713e7	+	2.48918e7i	0.297461	+	0.515217i
$52$	−1.22461e7	+	2.12108e7i	−0.232264	+	0.402293i
$53$	3.48825e7	+	6.04183e7i	0.607248	+	1.05179i	0.991692	+	0.128637i	$0.0410601\pi$
$53$	3.48825e7	+	6.04183e7i	0.607248	+	1.05179i	−0.384443	+	0.923149i	$0.625607\pi$
$54$	−1.40670e7	+	2.43648e7i	−0.225128	+	0.389933i
$55$	−2.00822e7	+	3.47834e7i	−0.295923	+	0.512554i
$56$	1.17758e7			0.160008
$57$	3.86171e7	+	8.87837e7i	0.484554	+	1.11403i
$58$	−1.58798e7			−0.184255
$59$	1.29065e7	−	2.23547e7i	0.138667	−	0.240179i	−0.788325	−	0.615259i	$-0.789051\pi$
$59$	1.29065e7	−	2.23547e7i	0.138667	−	0.240179i	0.926992	+	0.375080i	$0.122385\pi$
$60$	−3.78573e7	+	6.55708e7i	−0.377111	+	0.653176i
$61$	−3.82450e7	−	6.62423e7i	−0.353664	−	0.612564i	0.633225	−	0.773968i	$-0.281731\pi$
$61$	−3.82450e7	−	6.62423e7i	−0.353664	−	0.612564i	−0.986888	+	0.161404i	$0.948398\pi$
$62$	−3.56105e7	+	6.16791e7i	−0.306066	+	0.530122i
$63$	1.34636e7	+	2.33197e7i	0.107679	+	0.186505i
$64$	1.67772e7			0.125000
$65$	1.66020e8			1.15359
$66$	3.15591e7	+	5.46620e7i	0.204728	+	0.354599i
$67$	−1.78924e7	−	3.09905e7i	−0.108475	−	0.187885i	0.806677	−	0.590992i	$-0.201264\pi$
$67$	−1.78924e7	−	3.09905e7i	−0.108475	−	0.187885i	−0.915153	+	0.403107i	$0.867930\pi$
$68$	−4.31716e7			−0.244855
$69$	1.37006e8			0.727645
$70$	−3.99109e7	−	6.91277e7i	−0.198678	−	0.344121i
$71$	−2.44307e7	+	4.23152e7i	−0.114097	+	0.197621i	−0.917418	−	0.397924i	$-0.869731\pi$
$71$	−2.44307e7	+	4.23152e7i	−0.114097	+	0.197621i	0.803322	+	0.595546i	$0.203064\pi$
$72$	1.91820e7	+	3.32242e7i	0.0841197	+	0.145700i
$73$	7.43340e7	−	1.28750e8i	0.306362	−	0.530635i	−0.671202	−	0.741275i	$-0.734222\pi$
$73$	7.43340e7	−	1.28750e8i	0.306362	−	0.530635i	0.977564	+	0.210640i	$0.0675549\pi$
$74$	−4.66682e7	+	8.08317e7i	−0.180916	+	0.313357i
$75$	1.80344e8			0.658151
$76$	−1.44490e8	−	1.64447e7i	−0.496793	−	0.0565412i
$77$	−6.65421e7			−0.215719
$78$	1.30450e8	−	2.25946e8i	0.399042	−	0.691161i
$79$	−2.18634e8	+	3.78686e8i	−0.631534	+	1.09385i	0.355705	+	0.934598i	$0.384241\pi$
$79$	−2.18634e8	+	3.78686e8i	−0.631534	+	1.09385i	−0.987238	+	0.159250i	$0.949092\pi$
$80$	−5.68621e7	−	9.84880e7i	−0.155209	−	0.268831i
$81$	2.42025e8	−	4.19199e8i	0.624708	−	1.08203i
$82$	−1.58864e8	−	2.75161e8i	−0.388028	−	0.672085i
$83$	−4.70722e8			−1.08871			−0.544356	−	0.838854i	$-0.683226\pi$
$83$	−4.70722e8			−1.08871			−0.544356	+	0.838854i	$0.683226\pi$
$84$	−1.25440e8			−0.274903
$85$	1.46319e8	+	2.53432e8i	0.304030	+	0.526595i
$86$	−2.57921e8	−	4.46732e8i	−0.508444	−	0.880651i
$87$	1.69158e8			0.316559
$88$	−9.48043e7			−0.168522
$89$	−3.94729e8	−	6.83691e8i	−0.666875	−	1.15506i	−0.978773	−	0.204946i	$-0.934298\pi$
$89$	−3.94729e8	−	6.83691e8i	−0.666875	−	1.15506i	0.311899	−	0.950115i	$-0.399035\pi$
$90$	1.30025e8	−	2.25210e8i	0.208899	−	0.361823i
$91$	1.37526e8	+	2.38203e8i	0.210232	+	0.364133i
$92$	−1.02892e8	+	1.78215e8i	−0.149740	+	0.259357i
$93$	3.79337e8	−	6.57030e8i	0.525838	−	0.910777i
$94$	7.10043e8			0.938014
$95$	3.93174e8	+	9.03939e8i	0.495255	+	1.13863i
$96$	−1.78717e8			−0.214757
$97$	1.11328e8	−	1.92825e8i	0.127682	−	0.221152i	−0.795096	−	0.606484i	$-0.792580\pi$
$97$	1.11328e8	−	1.92825e8i	0.127682	−	0.221152i	0.922778	+	0.385332i	$0.125913\pi$
$98$	−2.56707e8	+	4.44629e8i	−0.281138	+	0.486945i
$99$	−1.08393e8	−	1.87742e8i	−0.113408	−	0.196428i
$100$	−1.35439e8	+	2.34588e8i	−0.135439	+	0.234588i
$101$	−9.82600e8	−	1.70191e9i	−0.939573	−	1.62739i	−0.766268	−	0.642521i	$-0.777889\pi$
$101$	−9.82600e8	−	1.70191e9i	−0.939573	−	1.62739i	−0.173305	−	0.984868i	$-0.555445\pi$
$102$	4.59881e8			0.420673
$103$	−2.01936e9			−1.76785			−0.883927	−	0.467625i	$-0.845110\pi$
$103$	−2.01936e9			−1.76785			−0.883927	+	0.467625i	$0.845110\pi$
$104$	1.95937e8	+	3.39373e8i	0.164235	+	0.284464i
$105$	4.25147e8	+	7.36376e8i	0.341340	+	0.591218i
$106$	1.11624e9			0.858779
$107$	−2.17340e9			−1.60292			−0.801462	−	0.598046i	$-0.795944\pi$
$107$	−2.17340e9			−1.60292			−0.801462	+	0.598046i	$0.795944\pi$
$108$	2.25072e8	+	3.89836e8i	0.159190	+	0.275725i
$109$	1.93385e8	−	3.34953e8i	0.131221	−	0.227282i	−0.792926	−	0.609317i	$-0.791444\pi$
$109$	1.93385e8	−	3.34953e8i	0.131221	−	0.227282i	0.924148	+	0.382036i	$0.124777\pi$
$110$	3.21315e8	+	5.56534e8i	0.209249	+	0.362430i
$111$	4.97128e8	−	8.61051e8i	0.310824	−	0.538363i
$112$	9.42060e7	−	1.63170e8i	0.0565715	−	0.0979847i
$113$	4.05886e8			0.234181			0.117090	−	0.993121i	$-0.462643\pi$
$113$	4.05886e8			0.234181			0.117090	+	0.993121i	$0.462643\pi$
$114$	1.53916e9	+	1.75176e8i	0.853516	+	0.0971408i
$115$	1.39491e9			0.743714
$116$	−1.27038e8	+	2.20037e8i	−0.0651438	+	0.112832i
$117$	−4.48044e8	+	7.76035e8i	−0.221047	+	0.382865i
$118$	−2.06504e8	−	3.57676e8i	−0.0980527	−	0.169832i
$119$	−2.42414e8	+	4.19873e8i	−0.110814	+	0.191936i
$120$	6.05717e8	+	1.04913e9i	0.266658	+	0.461865i
$121$	−1.82223e9			−0.772804
$122$	−1.22384e9			−0.500156
$123$	1.69228e9	+	2.93112e9i	0.666653	+	1.15468i
$124$	5.69767e8	+	9.86866e8i	0.216421	+	0.374853i
$125$	−1.55310e9			−0.568989
$126$	4.30837e8			0.152281
$127$	8.95930e8	+	1.55180e9i	0.305603	+	0.529319i	0.977395	−	0.211420i	$-0.0678087\pi$
$127$	8.95930e8	+	1.55180e9i	0.305603	+	0.529319i	−0.671793	+	0.740739i	$0.734475\pi$
$128$	1.34218e8	−	2.32472e8i	0.0441942	−	0.0765466i
$129$	2.74747e9	+	4.75876e9i	0.873533	+	1.51300i
$130$	1.32816e9	−	2.30044e9i	0.407854	−	0.706424i
$131$	4.44908e7	−	7.70603e7i	0.0131992	−	0.0228618i	−0.859350	−	0.511387i	$-0.829132\pi$
$131$	4.44908e7	−	7.70603e7i	0.0131992	−	0.0228618i	0.872550	+	0.488526i	$0.162465\pi$
$132$	1.00989e9			0.289529
$133$	−9.71262e8	+	1.31292e9i	−0.269156	+	0.363836i
$134$	−5.72556e8			−0.153407
$135$	1.52565e9	−	2.64250e9i	0.395324	−	0.684721i
$136$	−3.45373e8	+	5.98203e8i	−0.0865691	+	0.149942i
$137$	−4.93281e8	−	8.54387e8i	−0.119633	−	0.207211i	0.799989	−	0.600014i	$-0.204839\pi$
$137$	−4.93281e8	−	8.54387e8i	−0.119633	−	0.207211i	−0.919622	+	0.392804i	$0.871505\pi$
$138$	1.09605e9	−	1.89841e9i	0.257261	−	0.445590i
$139$	1.04124e9	+	1.80348e9i	0.236584	+	0.409775i	0.959732	−	0.280918i	$-0.0906388\pi$
$139$	1.04124e9	+	1.80348e9i	0.236584	+	0.409775i	−0.723148	+	0.690693i	$0.757306\pi$
$140$	−1.27715e9			−0.280974
$141$	−7.56366e9			−1.61156
$142$	3.90891e8	+	6.77044e8i	0.0806786	+	0.139739i
$143$	−1.10720e9	−	1.91772e9i	−0.221418	−	0.383507i
$144$	6.13824e8			0.118963
$145$	1.72225e9			0.323550
$146$	−1.18934e9	−	2.06001e9i	−0.216631	−	0.375215i
$147$	2.73454e9	−	4.73636e9i	0.483010	−	0.836598i
$148$	7.46691e8	+	1.29331e9i	0.127927	+	0.221577i
$149$	2.28869e9	−	3.96412e9i	0.380407	−	0.658884i	−0.610713	−	0.791852i	$-0.709117\pi$
$149$	2.28869e9	−	3.96412e9i	0.380407	−	0.658884i	0.991120	+	0.132968i	$0.0424506\pi$
$150$	1.44275e9	−	2.49892e9i	0.232692	−	0.403034i
$151$	8.63462e9			1.35160			0.675798	−	0.737087i	$-0.263799\pi$
$151$	8.63462e9			1.35160			0.675798	+	0.737087i	$0.263799\pi$
$152$	−1.38378e9	+	1.87055e9i	−0.210267	+	0.284232i
$153$	−1.57951e9			−0.233029
$154$	−5.32337e8	+	9.22035e8i	−0.0762682	+	0.132100i
$155$	3.86216e9	−	6.68946e9i	0.537450	−	0.930891i
$156$	−2.08720e9	−	3.61514e9i	−0.282165	−	0.488725i
$157$	−5.31782e9	+	9.21074e9i	−0.698531	+	1.20989i	0.270445	+	0.962735i	$0.412829\pi$
$157$	−5.31782e9	+	9.21074e9i	−0.698531	+	1.20989i	−0.968976	+	0.247155i	$0.920504\pi$
$158$	3.49815e9	+	6.05897e9i	0.446562	+	0.773468i
$159$	−1.18906e10			−1.47543
$160$	−1.81959e9			−0.219499
$161$	1.15551e9	+	2.00140e9i	0.135536	+	0.234756i
$162$	−3.87240e9	−	6.70719e9i	−0.441736	−	0.765108i
$163$	−2.99074e9			−0.331844			−0.165922	−	0.986139i	$-0.553060\pi$
$163$	−2.99074e9			−0.331844			−0.165922	+	0.986139i	$0.553060\pi$
$164$	−5.08365e9			−0.548755
$165$	−3.42277e9	−	5.92842e9i	−0.359501	−	0.622674i
$166$	−3.76578e9	+	6.52251e9i	−0.384918	+	0.666697i
$167$	1.96674e9	+	3.40650e9i	0.195670	+	0.338910i	0.947120	−	0.320880i	$-0.103979\pi$
$167$	1.96674e9	+	3.40650e9i	0.195670	+	0.338910i	−0.751450	+	0.659790i	$0.770645\pi$
$168$	−1.00352e9	+	1.73815e9i	−0.0971928	+	0.168343i
$169$	7.25637e8	−	1.25684e9i	0.0684272	−	0.118519i
$170$	4.68221e9			0.429963
$171$	−5.28640e9	−	6.01659e8i	−0.472800	−	0.0538106i
$172$	−8.25346e9			−0.719048
$173$	3.69649e9	−	6.40251e9i	0.313749	−	0.543429i	−0.665422	−	0.746467i	$-0.731748\pi$
$173$	3.69649e9	−	6.40251e9i	0.313749	−	0.543429i	0.979171	+	0.203039i	$0.0650817\pi$
$174$	1.35326e9	−	2.34392e9i	0.111921	−	0.193852i
$175$	1.52101e9	+	2.63447e9i	0.122592	+	0.212336i
$176$	−7.58434e8	+	1.31365e9i	−0.0595814	+	0.103198i
$177$	2.19976e9	+	3.81010e9i	0.168460	+	0.291781i
$178$	−1.26313e10			−0.943103
$179$	1.14763e10			0.835529			0.417765	−	0.908555i	$-0.362814\pi$
$179$	1.14763e10			0.835529			0.417765	+	0.908555i	$0.362814\pi$
$180$	−2.08040e9	−	3.60336e9i	−0.147714	−	0.255847i
$181$	−1.04510e10	−	1.81016e10i	−0.723775	−	1.25362i	−0.959476	−	0.281790i	$-0.909072\pi$
$181$	−1.04510e10	−	1.81016e10i	−0.723775	−	1.25362i	0.235701	−	0.971826i	$-0.424261\pi$
$182$	4.40084e9			0.297314
$183$	1.30368e10			0.859295
$184$	1.64628e9	+	2.85144e9i	0.105882	+	0.183393i
$185$	5.06144e9	−	8.76667e9i	0.317688	−	0.550252i
$186$	−6.06939e9	−	1.05125e10i	−0.371823	−	0.644017i
$187$	1.95162e9	−	3.38031e9i	0.116710	−	0.202148i
$188$	5.68035e9	−	9.83865e9i	0.331638	−	0.574414i
$189$	5.05523e9			0.288179
$190$	1.56707e10	+	1.78353e9i	0.872365	+	0.0992860i
$191$	2.71500e10			1.47611			0.738057	−	0.674738i	$-0.235743\pi$
$191$	2.71500e10			1.47611			0.738057	+	0.674738i	$0.235743\pi$
$192$	−1.42974e9	+	2.47638e9i	−0.0759279	+	0.131511i
$193$	1.71762e10	−	2.97500e10i	0.891083	−	1.54340i	0.0525039	−	0.998621i	$-0.483280\pi$
$193$	1.71762e10	−	2.97500e10i	0.891083	−	1.54340i	0.838579	−	0.544780i	$-0.183387\pi$
$194$	−1.78124e9	−	3.08520e9i	−0.0902850	−	0.156378i
$195$	−1.41481e10	+	2.45052e10i	−0.700715	+	1.21367i
$196$	4.10731e9	+	7.11406e9i	0.198795	+	0.344322i
$197$	−3.81379e10			−1.80409			−0.902045	−	0.431641i	$-0.857935\pi$
$197$	−3.81379e10			−1.80409			−0.902045	+	0.431641i	$0.857935\pi$
$198$	−3.46858e9			−0.160383
$199$	1.12380e10	+	1.94647e10i	0.507983	+	0.879853i	0.999957	+	0.00924287i	$0.00294214\pi$
$199$	1.12380e10	+	1.94647e10i	0.507983	+	0.879853i	−0.491974	+	0.870610i	$0.663725\pi$
$200$	2.16703e9	+	3.75340e9i	0.0957700	+	0.165878i
$201$	6.09909e9			0.263562
$202$	−3.14432e10			−1.32876
$203$	1.42667e9	+	2.47106e9i	0.0589645	+	0.102130i
$204$	3.67905e9	−	6.37230e9i	0.148730	−	0.257609i
$205$	1.72297e10	+	2.98428e10i	0.681375	+	1.18018i
$206$	−1.61549e10	+	2.79811e10i	−0.625031	+	1.08259i
$207$	−3.76450e9	+	6.52030e9i	−0.142508	+	0.246832i
$208$	6.26999e9			0.232264
$209$	7.81943e9	−	1.05700e10i	0.283476	−	0.383194i
$210$	1.36047e10			0.482728
$211$	−1.38183e10	+	2.39340e10i	−0.479937	+	0.831276i	−0.999735	−	0.0230136i	$-0.992674\pi$
$211$	−1.38183e10	+	2.39340e10i	−0.479937	+	0.831276i	0.519798	+	0.854289i	$0.326007\pi$
$212$	8.92992e9	−	1.54671e10i	0.303624	−	0.525893i
$213$	−4.16393e9	−	7.21214e9i	−0.138610	−	0.240080i
$214$	−1.73872e10	+	3.01155e10i	−0.566719	+	0.981586i
$215$	2.79730e10	+	4.84507e10i	0.892824	+	1.54642i
$216$	7.20231e9			0.225128
$217$	1.27972e10			0.391785
$218$	−3.09416e9	−	5.35925e9i	−0.0927874	−	0.160712i
$219$	1.26694e10	+	2.19440e10i	0.372183	+	0.644640i
$220$	1.02821e10			0.295923
$221$	−1.61341e10			−0.454967
$222$	−7.95404e9	−	1.37768e10i	−0.219786	−	0.380680i
$223$	−1.94384e10	+	3.36683e10i	−0.526367	+	0.911694i	0.473161	+	0.880976i	$0.343113\pi$
$223$	−1.94384e10	+	3.36683e10i	−0.526367	+	0.911694i	−0.999528	+	0.0307181i	$0.990221\pi$
$224$	−1.50730e9	−	2.61071e9i	−0.0400021	−	0.0692857i
$225$	−4.95528e9	+	8.58280e9i	−0.128898	+	0.223258i
$226$	3.24709e9	−	5.62412e9i	0.0827954	−	0.143406i
$227$	−5.89117e10			−1.47260			−0.736300	−	0.676655i	$-0.763429\pi$
$227$	−5.89117e10			−1.47260			−0.736300	+	0.676655i	$0.763429\pi$
$228$	1.47406e10	−	1.99258e10i	0.361250	−	0.488325i
$229$	3.04016e10			0.730528			0.365264	−	0.930904i	$-0.380979\pi$
$229$	3.04016e10			0.730528			0.365264	+	0.930904i	$0.380979\pi$
$230$	1.11593e10	−	1.93284e10i	0.262943	−	0.455430i
$231$	5.67066e9	−	9.82188e9i	0.131033	−	0.226955i
$232$	2.03261e9	+	3.52058e9i	0.0460636	+	0.0797846i
$233$	1.73683e9	−	3.00829e9i	0.0386062	−	0.0668679i	−0.846077	−	0.533061i	$-0.821042\pi$
$233$	1.73683e9	−	3.00829e9i	0.0386062	−	0.0668679i	0.884683	+	0.466193i	$0.154375\pi$
$234$	7.16871e9	+	1.24166e10i	0.156304	+	0.270726i
$235$	−7.70083e10			−1.64715
$236$	−6.60813e9			−0.138667
$237$	−3.72637e10	−	6.45426e10i	−0.767217	−	1.32886i
$238$	3.87862e9	+	6.71796e9i	0.0783575	+	0.135719i
$239$	7.00535e10			1.38880			0.694400	−	0.719590i	$-0.255670\pi$
$239$	7.00535e10			1.38880			0.694400	+	0.719590i	$0.255670\pi$
$240$	1.93830e10			0.377111
$241$	−1.51487e10	−	2.62384e10i	−0.289267	−	0.501026i	0.684368	−	0.729137i	$-0.260078\pi$
$241$	−1.51487e10	−	2.62384e10i	−0.289267	−	0.501026i	−0.973635	+	0.228111i	$0.926745\pi$
$242$	−1.45778e10	+	2.52496e10i	−0.273227	+	0.473244i
$243$	2.39452e10	+	4.14744e10i	0.440546	+	0.763048i
$244$	−9.79072e9	+	1.69580e10i	−0.176832	+	0.306282i
$245$	2.78413e10	−	4.82226e10i	0.493677	−	0.855073i
$246$	5.41531e10			0.942790
$247$	−5.39987e10	−	6.14573e9i	−0.923097	−	0.105060i
$248$	1.82326e10			0.306066
$249$	4.01145e10	−	6.94804e10i	0.661309	−	1.14542i
$250$	−1.24248e10	+	2.15204e10i	−0.201168	+	0.348433i
$251$	−2.73020e10	−	4.72885e10i	−0.434174	−	0.752011i	0.563054	−	0.826420i	$-0.309626\pi$
$251$	−2.73020e10	−	4.72885e10i	−0.434174	−	0.752011i	−0.997228	+	0.0744093i	$0.976293\pi$
$252$	3.44669e9	−	5.96985e9i	0.0538394	−	0.0932526i
$253$	−9.30275e9	−	1.61128e10i	−0.142748	−	0.247246i
$254$	2.86698e10			0.432188
$255$	−4.98768e10			−0.738699
$256$	−2.14748e9	−	3.71955e9i	−0.0312500	−	0.0541266i
$257$	−5.94247e10	−	1.02927e11i	−0.849704	−	1.47173i	−0.881472	−	0.472236i	$-0.843447\pi$
$257$	−5.94247e10	−	1.02927e11i	−0.849704	−	1.47173i	0.0317678	−	0.999495i	$-0.489886\pi$
$258$	8.79191e10			1.23536
$259$	1.67710e10			0.231585
$260$	−2.12505e10	−	3.68070e10i	−0.288396	−	0.499517i
$261$	−4.64791e9	+	8.05042e9i	−0.0619977	+	0.107383i
$262$	−7.11852e8	−	1.23296e9i	−0.00933328	−	0.0161657i
$263$	6.34545e10	−	1.09906e11i	0.817827	−	1.41652i	−0.0894529	−	0.995991i	$-0.528512\pi$
$263$	6.34545e10	−	1.09906e11i	0.817827	−	1.41652i	0.907280	−	0.420527i	$-0.138155\pi$
$264$	8.07914e9	−	1.39935e10i	0.102364	−	0.177300i
$265$	−1.21063e11			−1.50801
$266$	1.04222e10	+	2.39615e10i	0.127642	+	0.293459i
$267$	1.34554e11			1.62030
$268$	−4.58045e9	+	7.93357e9i	−0.0542377	+	0.0939425i
$269$	−1.88151e10	+	3.25887e10i	−0.219090	+	0.379474i	−0.954530	−	0.298115i	$-0.903642\pi$
$269$	−1.88151e10	+	3.25887e10i	−0.219090	+	0.379474i	0.735440	+	0.677590i	$0.236975\pi$
$270$	−2.44104e10	−	4.22800e10i	−0.279536	−	0.484171i
$271$	−2.41203e10	+	4.17776e10i	−0.271657	+	0.470523i	−0.969286	−	0.245935i	$-0.920905\pi$
$271$	−2.41203e10	+	4.17776e10i	−0.271657	+	0.470523i	0.697629	+	0.716459i	$0.254238\pi$
$272$	5.52597e9	+	9.57125e9i	0.0612136	+	0.106025i
$273$	−4.68795e10			−0.510800
$274$	−1.57850e10			−0.169187
$275$	−1.22454e10	−	2.12096e10i	−0.129115	−	0.223633i
$276$	−1.75368e10	−	3.03746e10i	−0.181911	−	0.315080i
$277$	−9.23709e10			−0.942706			−0.471353	−	0.881945i	$-0.656234\pi$
$277$	−9.23709e10			−0.942706			−0.471353	+	0.881945i	$0.656234\pi$
$278$	3.33198e10			0.334580
$279$	2.08459e10	+	3.61062e10i	0.205969	+	0.356749i
$280$	−1.02172e10	+	1.76967e10i	−0.0993392	+	0.172061i
$281$	3.86685e10	+	6.69757e10i	0.369980	+	0.640825i	0.989562	−	0.144108i	$-0.0460311\pi$
$281$	3.86685e10	+	6.69757e10i	0.369980	+	0.640825i	−0.619582	+	0.784932i	$0.712698\pi$
$282$	−6.05093e10	+	1.04805e11i	−0.569772	+	0.986874i
$283$	−6.20030e10	+	1.07392e11i	−0.574611	+	0.995255i	0.421473	+	0.906841i	$0.361513\pi$
$283$	−6.20030e10	+	1.07392e11i	−0.574611	+	0.995255i	−0.996084	+	0.0884141i	$0.971820\pi$
$284$	1.25085e10			0.114097
$285$	−1.66931e11	−	1.89988e10i	−1.49877	−	0.170579i
$286$	−3.54303e10			−0.313132
$287$	−2.85453e10	+	4.94419e10i	−0.248351	+	0.430157i
$288$	4.91059e9	−	8.50539e9i	0.0420598	−	0.0728498i
$289$	4.50744e10	+	7.80711e10i	0.380093	+	0.658340i
$290$	1.37780e10	−	2.38643e10i	0.114392	−	0.198133i
$291$	1.89745e10	+	3.28648e10i	0.155114	+	0.268666i
$292$	−3.80590e10			−0.306362
$293$	1.27795e11			1.01300			0.506502	−	0.862239i	$-0.330938\pi$
$293$	1.27795e11			1.01300			0.506502	+	0.862239i	$0.330938\pi$
$294$	−4.37526e10	−	7.57818e10i	−0.341540	−	0.591564i
$295$	2.23966e10	+	3.87920e10i	0.172180	+	0.298224i
$296$	2.38941e10			0.180916
$297$	−4.06986e10			−0.303512
$298$	−3.66190e10	−	6.34260e10i	−0.268988	−	0.465901i
$299$	−3.84530e10	+	6.66026e10i	−0.278234	+	0.481915i
$300$	−2.30840e10	−	3.99827e10i	−0.164538	−	0.284988i
$301$	−4.63441e10	+	8.02704e10i	−0.325421	+	0.563646i
$302$	6.90769e10	−	1.19645e11i	0.477861	−	0.827680i
$303$	3.34945e11			2.28288
$304$	1.48488e10	+	3.41386e10i	0.0997151	+	0.229253i
$305$	1.32733e11			0.878271
$306$	−1.26361e10	+	2.18863e10i	−0.0823883	+	0.142701i
$307$	−8.77812e10	+	1.52041e11i	−0.564000	+	0.976876i	0.433142	+	0.901325i	$0.357405\pi$
$307$	−8.77812e10	+	1.52041e11i	−0.564000	+	0.976876i	−0.997142	+	0.0755503i	$0.975929\pi$
$308$	8.51739e9	+	1.47526e10i	0.0539298	+	0.0934091i
$309$	1.72088e11	−	2.98066e11i	1.07384	−	1.85994i
$310$	−6.17946e10	−	1.07031e11i	−0.380034	−	0.658239i
$311$	1.54711e11			0.937775			0.468888	−	0.883258i	$-0.344655\pi$
$311$	1.54711e11			0.937775			0.468888	+	0.883258i	$0.344655\pi$
$312$	−6.67904e10			−0.399042
$313$	1.47088e11	+	2.54764e11i	0.866220	+	1.50034i	0.865831	+	0.500337i	$0.166791\pi$
$313$	1.47088e11	+	2.54764e11i	0.866220	+	1.50034i	0.000389305		1.00000i	$0.499876\pi$
$314$	8.50852e10	+	1.47372e11i	0.493936	+	0.855522i
$315$	−4.67268e10			−0.267404
$316$	1.11941e11			0.631534
$317$	−1.61575e10	−	2.79856e10i	−0.0898685	−	0.155657i	0.817587	−	0.575805i	$-0.195311\pi$
$317$	−1.61575e10	−	2.79856e10i	−0.0898685	−	0.155657i	−0.907455	+	0.420148i	$0.861978\pi$
$318$	−9.51251e10	+	1.64761e11i	−0.521642	+	0.903511i
$319$	−1.14858e10	−	1.98940e10i	−0.0621018	−	0.107563i
$320$	−1.45567e10	+	2.52129e10i	−0.0776047	+	0.134415i
$321$	1.85215e11	−	3.20802e11i	0.973653	−	1.68642i
$322$	3.69762e10			0.191677
$323$	−3.82094e10	−	8.78465e10i	−0.195326	−	0.449069i
$324$	−1.23917e11			−0.624708
$325$	−5.06164e10	+	8.76702e10i	−0.251661	+	0.435890i
$326$	−2.39259e10	+	4.14409e10i	−0.117325	+	0.203212i
$327$	3.29602e10	+	5.70888e10i	0.159414	+	0.276112i
$328$	−4.06692e10	+	7.04412e10i	−0.194014	+	0.336042i
$329$	−6.37916e10	−	1.10490e11i	−0.300180	−	0.519928i
$330$	−1.09529e11			−0.508411
$331$	−3.00200e11			−1.37463			−0.687314	−	0.726361i	$-0.741210\pi$
$331$	−3.00200e11			−1.37463			−0.687314	+	0.726361i	$0.741210\pi$
$332$	6.02524e10	+	1.04360e11i	0.272178	+	0.471426i
$333$	2.73190e10	+	4.73179e10i	0.121749	+	0.210876i
$334$	6.29358e10			0.276719
$335$	6.20971e10			0.269383
$336$	1.60563e10	+	2.78104e10i	0.0687257	+	0.119036i
$337$	−1.39551e11	+	2.41710e11i	−0.589385	+	1.02085i	0.404928	+	0.914349i	$0.367297\pi$
$337$	−1.39551e11	+	2.41710e11i	−0.589385	+	1.02085i	−0.994313	+	0.106497i	$0.966037\pi$
$338$	−1.16102e10	−	2.01094e10i	−0.0483854	−	0.0838059i
$339$	−3.45893e10	+	5.99104e10i	−0.142247	+	0.246379i
$340$	3.74577e10	−	6.48787e10i	0.152015	−	0.263297i
$341$	−1.03028e11			−0.412630
$342$	−5.06281e10	+	6.84373e10i	−0.200112	+	0.270505i
$343$	2.08266e11			0.812448
$344$	−6.60277e10	+	1.14363e11i	−0.254222	+	0.440325i
$345$	−1.18873e11	+	2.05894e11i	−0.451749	+	0.782453i
$346$	−5.91438e10	−	1.02440e11i	−0.221854	−	0.384262i
$347$	1.61391e11	−	2.79538e11i	0.597583	−	1.03504i	−0.395594	−	0.918425i	$-0.629461\pi$
$347$	1.61391e11	−	2.79538e11i	0.597583	−	1.03504i	0.993177	−	0.116618i	$-0.0372053\pi$
$348$	−2.16522e10	−	3.75027e10i	−0.0791398	−	0.137074i
$349$	1.94298e11			0.701059			0.350530	−	0.936552i	$-0.386002\pi$
$349$	1.94298e11			0.701059			0.350530	+	0.936552i	$0.386002\pi$
$350$	4.86724e10			0.173371
$351$	8.41141e10	+	1.45690e11i	0.295792	+	0.512327i
$352$	1.21349e10	+	2.10183e10i	0.0421304	+	0.0729720i
$353$	−3.36526e11			−1.15354			−0.576769	−	0.816907i	$-0.695687\pi$
$353$	−3.36526e11			−1.15354			−0.576769	+	0.816907i	$0.695687\pi$
$354$	7.03924e10			0.238238
$355$	−4.23945e10	−	7.34294e10i	−0.141671	−	0.245382i
$356$	−1.01051e11	+	1.75025e11i	−0.333437	+	0.577531i
$357$	−4.13166e10	−	7.15624e10i	−0.134622	−	0.233173i
$358$	9.18100e10	−	1.59020e11i	0.295404	−	0.511655i
$359$	2.20116e11	−	3.81252e11i	0.699401	−	1.21140i	−0.269273	−	0.963064i	$-0.586784\pi$
$359$	2.20116e11	−	3.81252e11i	0.699401	−	1.21140i	0.968674	−	0.248334i	$-0.0798832\pi$
$360$	−6.65728e10			−0.208899
$361$	−9.44198e10	−	3.08565e11i	−0.292604	−	0.956234i
$362$	−3.34432e11			−1.02357
$363$	1.55289e11	−	2.68968e11i	0.469419	−	0.813057i
$364$	3.52067e10	−	6.09799e10i	0.105116	−	0.182067i
$365$	1.28991e11	+	2.23420e11i	0.380402	+	0.658876i
$366$	1.04295e11	−	1.80644e11i	0.303807	−	0.526208i
$367$	1.54039e11	+	2.66804e11i	0.443235	+	0.767706i	0.997927	−	0.0643499i	$-0.0204974\pi$
$367$	1.54039e11	+	2.66804e11i	0.443235	+	0.767706i	−0.554692	+	0.832056i	$0.687164\pi$
$368$	5.26809e10			0.149740
$369$	−1.85994e11			−0.522253
$370$	−8.09830e10	−	1.40267e11i	−0.224639	−	0.389087i
$371$	−1.00285e11	−	1.73699e11i	−0.274824	−	0.476008i
$372$	−1.94220e11			−0.525838
$373$	6.47469e11			1.73192			0.865962	−	0.500109i	$-0.166707\pi$
$373$	6.47469e11			1.73192			0.865962	+	0.500109i	$0.166707\pi$
$374$	−3.12260e10	−	5.40850e10i	−0.0825266	−	0.142940i
$375$	1.32354e11	−	2.29243e11i	0.345617	−	0.598627i
$376$	−9.08855e10	−	1.57418e11i	−0.234504	−	0.406172i
$377$	−4.74768e10	+	8.22322e10i	−0.121045	+	0.209655i
$378$	4.04418e10	−	7.00473e10i	0.101887	−	0.176473i
$379$	−4.15129e11			−1.03349			−0.516746	−	0.856139i	$-0.672857\pi$
$379$	−4.15129e11			−1.03349			−0.516746	+	0.856139i	$0.672857\pi$
$380$	1.50079e11	−	2.02872e11i	0.369228	−	0.499109i
$381$	−3.05401e11			−0.742521
$382$	2.17200e11	−	3.76202e11i	0.521885	−	0.903932i
$383$	−4.15170e11	+	7.19096e11i	−0.985898	+	1.70762i	−0.348020	+	0.937487i	$0.613146\pi$
$383$	−4.15170e11	+	7.19096e11i	−0.985898	+	1.70762i	−0.637878	+	0.770138i	$0.720188\pi$
$384$	2.28758e10	+	3.96221e10i	0.0536891	+	0.0929923i
$385$	5.77351e10	−	1.00000e11i	0.133926	−	0.231967i
$386$	−2.74819e11	−	4.76000e11i	−0.630091	−	1.09135i
$387$	−3.01967e11			−0.684322
$388$	−5.69998e10			−0.127682
$389$	−1.72702e10	−	2.99128e10i	−0.0382405	−	0.0662345i	0.846272	−	0.532752i	$-0.178842\pi$
$389$	−1.72702e10	−	2.99128e10i	−0.0382405	−	0.0662345i	−0.884512	+	0.466517i	$0.845509\pi$
$390$	2.26369e11	+	3.92083e11i	0.495480	+	0.858197i
$391$	−1.35560e11			−0.293316
$392$	1.31434e11			0.281138
$393$	7.58293e9	+	1.31340e10i	0.0160351	+	0.0277735i
$394$	−3.05103e11	+	5.28454e11i	−0.637842	+	1.10478i
$395$	−3.79395e11	−	6.57131e11i	−0.784160	−	1.35820i
$396$	−2.77486e10	+	4.80621e10i	−0.0567040	+	0.0982141i
$397$	−3.16236e9	+	5.47737e9i	−0.00638931	+	0.0110666i	−0.869202	−	0.494456i	$-0.835367\pi$
$397$	−3.16236e9	+	5.47737e9i	−0.00638931	+	0.0110666i	0.862813	+	0.505523i	$0.168700\pi$
$398$	3.59615e11			0.718397
$399$	−1.11022e11	−	2.55248e11i	−0.219296	−	0.504178i
$400$	6.93449e10			0.135439
$401$	7.27688e10	−	1.26039e11i	0.140538	−	0.243420i	−0.787161	−	0.616748i	$-0.788450\pi$
$401$	7.27688e10	−	1.26039e11i	0.140538	−	0.243420i	0.927700	+	0.373328i	$0.121783\pi$
$402$	4.87927e10	−	8.45115e10i	0.0931833	−	0.161398i
$403$	2.12934e11	+	3.68812e11i	0.402135	+	0.696519i
$404$	−2.51546e11	+	4.35690e11i	−0.469787	+	0.813694i
$405$	4.19984e11	+	7.27434e11i	0.775685	+	1.34353i
$406$	4.56534e10			0.0833885
$407$	−1.35020e11			−0.243907
$408$	−5.88648e10	−	1.01957e11i	−0.105168	−	0.182157i
$409$	−7.80164e8	−	1.35128e9i	−0.00137858	−	0.00238776i	0.865335	−	0.501193i	$-0.167105\pi$
$409$	−7.80164e8	−	1.35128e9i	−0.00137858	−	0.00238776i	−0.866714	+	0.498806i	$0.833772\pi$
$410$	5.51352e11			0.963610
$411$	1.68148e11			0.290672
$412$	2.58478e11	+	4.47697e11i	0.441964	+	0.765503i
$413$	−3.71054e10	+	6.42685e10i	−0.0627570	+	0.108698i
$414$	6.02320e10	+	1.04325e11i	0.100769	+	0.174536i
$415$	4.08420e11	−	7.07405e11i	0.675913	−	1.17072i
$416$	5.01599e10	−	8.68796e10i	0.0821177	−	0.142232i
$417$	−3.54935e11			−0.574826
$418$	−8.39074e10	−	1.92910e11i	−0.134433	−	0.309073i
$419$	−4.89271e11			−0.775508			−0.387754	−	0.921763i	$-0.626749\pi$
$419$	−4.89271e11			−0.775508			−0.387754	+	0.921763i	$0.626749\pi$
$420$	1.08838e11	−	1.88512e11i	0.170670	−	0.295609i
$421$	−2.88859e11	+	5.00318e11i	−0.448143	+	0.776206i	−0.998265	−	0.0588780i	$-0.981248\pi$
$421$	−2.88859e11	+	5.00318e11i	−0.448143	+	0.776206i	0.550122	+	0.835084i	$0.314581\pi$
$422$	2.21093e11	+	3.82945e11i	0.339367	+	0.587801i
$423$	2.07825e11	−	3.59964e11i	0.315622	−	0.546673i
$424$	−1.42879e11	−	2.47473e11i	−0.214695	−	0.371862i
$425$	−1.78440e11			−0.265303
$426$	−1.33246e11			−0.196024
$427$	1.09952e11	+	1.90443e11i	0.160058	+	0.277229i
$428$	2.78195e11	+	4.81848e11i	0.400731	+	0.694086i
$429$	3.77418e11			0.537978
$430$	8.95136e11			1.26264
$431$	−1.04001e11	−	1.80135e11i	−0.145175	−	0.251450i	0.784264	−	0.620428i	$-0.213041\pi$
$431$	−1.04001e11	−	1.80135e11i	−0.145175	−	0.251450i	−0.929438	+	0.368978i	$0.879708\pi$
$432$	5.76185e10	−	9.97981e10i	0.0795948	−	0.137862i
$433$	−4.11551e11	−	7.12827e11i	−0.562636	−	0.974515i	−0.997265	−	0.0739050i	$-0.976454\pi$
$433$	−4.11551e11	−	7.12827e11i	−0.562636	−	0.974515i	0.434629	−	0.900610i	$-0.356880\pi$
$434$	1.02378e11	−	1.77324e11i	0.138517	−	0.239918i
$435$	−1.46769e11	+	2.54211e11i	−0.196532	+	0.340403i
$436$	−9.90132e10			−0.131221
$437$	−4.53701e11	−	5.16369e10i	−0.595118	−	0.0677319i
$438$	4.05420e11			0.526346
$439$	−8.79743e10	+	1.52376e11i	−0.113049	+	0.195806i	−0.916998	−	0.398892i	$-0.869395\pi$
$439$	−8.79743e10	+	1.52376e11i	−0.113049	+	0.195806i	0.803949	+	0.594698i	$0.202728\pi$
$440$	8.22566e10	−	1.42473e11i	0.104625	−	0.181215i
$441$	1.50273e11	+	2.60280e11i	0.189194	+	0.327694i
$442$	−1.29073e11	+	2.23561e11i	−0.160855	+	0.278609i
$443$	3.83287e11	+	6.63873e11i	0.472833	+	0.818970i	0.999517	−	0.0310909i	$-0.00989813\pi$
$443$	3.83287e11	+	6.63873e11i	0.472833	+	0.818970i	−0.526684	+	0.850061i	$0.676565\pi$
$444$	−2.54529e11			−0.310824
$445$	1.36994e12			1.65608
$446$	3.11014e11	+	5.38692e11i	0.372197	+	0.644665i
$447$	3.90080e11	+	6.75638e11i	0.462136	+	0.800443i
$448$	−4.82335e10			−0.0565715
$449$	−8.46127e11			−0.982487			−0.491243	−	0.871022i	$-0.663457\pi$
$449$	−8.46127e11			−0.982487			−0.491243	+	0.871022i	$0.663457\pi$
$450$	7.92845e10	+	1.37325e11i	0.0911448	+	0.157867i
$451$	2.29813e11	−	3.98047e11i	0.261565	−	0.453044i
$452$	−5.19534e10	−	8.99860e10i	−0.0585452	−	0.101403i
$453$	−7.35835e11	+	1.27450e12i	−0.820991	+	1.42200i
$454$	−4.71293e11	+	8.16304e11i	−0.520643	+	0.901780i
$455$	−4.77297e11			−0.522081
$456$	−1.58176e11	−	3.63658e11i	−0.171316	−	0.393869i
$457$	1.15959e12			1.24360			0.621799	−	0.783177i	$-0.286402\pi$
$457$	1.15959e12			1.24360			0.621799	+	0.783177i	$0.286402\pi$
$458$	2.43213e11	−	4.21257e11i	0.258281	−	0.447356i
$459$	−1.48265e11	+	2.56803e11i	−0.155913	+	0.270050i
$460$	−1.78549e11	−	3.09255e11i	−0.185929	−	0.322038i
$461$	1.76970e11	−	3.06520e11i	0.182492	−	0.316086i	−0.760236	−	0.649647i	$-0.774917\pi$
$461$	1.76970e11	−	3.06520e11i	0.182492	−	0.316086i	0.942729	+	0.333561i	$0.108250\pi$
$462$	−9.07306e10	−	1.57150e11i	−0.0926542	−	0.160482i
$463$	−1.49049e12			−1.50735			−0.753675	−	0.657247i	$-0.771721\pi$
$463$	−1.49049e12			−1.50735			−0.753675	+	0.657247i	$0.771721\pi$
$464$	6.50435e10			0.0651438
$465$	6.58260e11	+	1.14014e12i	0.652919	+	1.13089i
$466$	−2.77894e10	−	4.81326e10i	−0.0272987	−	0.0472827i
$467$	4.31394e11			0.419708			0.209854	−	0.977733i	$-0.432701\pi$
$467$	4.31394e11			0.419708			0.209854	+	0.977733i	$0.432701\pi$
$468$	2.29399e11			0.221047
$469$	5.14395e10	+	8.90959e10i	0.0490930	+	0.0850315i
$470$	−6.16067e11	+	1.06706e12i	−0.582354	+	1.00867i
$471$	−9.06361e11	−	1.56986e12i	−0.848608	−	1.46983i
$472$	−5.28650e10	+	9.15649e10i	−0.0490263	+	0.0849161i
$473$	3.73107e11	−	6.46241e11i	0.342735	−	0.593635i
$474$	−1.19244e12			−1.08501
$475$	−5.97215e11	−	6.79706e10i	−0.538282	−	0.0612632i
$476$	1.24116e11			0.110814
$477$	3.26717e11	−	5.65890e11i	0.288961	−	0.500495i
$478$	5.60428e11	−	9.70690e11i	0.491015	−	0.850462i
$479$	5.10020e10	+	8.83381e10i	0.0442667	+	0.0766723i	0.887310	−	0.461174i	$-0.152572\pi$
$479$	5.10020e10	+	8.83381e10i	0.0442667	+	0.0766723i	−0.843043	+	0.537846i	$0.819238\pi$
$480$	1.55064e11	−	2.68578e11i	0.133329	−	0.230933i
$481$	2.79054e11	+	4.83335e11i	0.237703	+	0.411714i
$482$	−4.84759e11			−0.409086
$483$	−3.93885e11			−0.329312
$484$	2.33245e11	+	4.03993e11i	0.193201	+	0.334634i
$485$	1.93186e11	+	3.34608e11i	0.158540	+	0.274599i
$486$	7.66248e11			0.623026
$487$	−1.01885e12			−0.820788			−0.410394	−	0.911908i	$-0.634609\pi$
$487$	−1.01885e12			−0.820788			−0.410394	+	0.911908i	$0.634609\pi$
$488$	1.56652e11	+	2.71329e11i	0.125039	+	0.216574i
$489$	2.54868e11	−	4.41445e11i	0.201570	−	0.349130i
$490$	−4.45461e11	−	7.71562e11i	−0.349082	−	0.604628i
$491$	−4.92444e11	+	8.52938e11i	−0.382376	+	0.662294i	−0.991401	−	0.130857i	$-0.958227\pi$
$491$	−4.92444e11	+	8.52938e11i	−0.382376	+	0.662294i	0.609026	+	0.793150i	$0.291561\pi$
$492$	4.33225e11	−	7.50367e11i	0.333327	−	0.577339i
$493$	−1.67372e11			−0.127606
$494$	−5.17148e11	+	6.99063e11i	−0.390700	+	0.528135i
$495$	3.76188e11			0.281632
$496$	1.45860e11	−	2.52638e11i	0.108211	−	0.187426i
$497$	7.02368e10	−	1.21654e11i	0.0516370	−	0.0894380i
$498$	−6.41832e11	−	1.11169e12i	−0.467616	−	0.809935i
$499$	8.92630e11	−	1.54608e12i	0.644494	−	1.11630i	−0.339924	−	0.940453i	$-0.610401\pi$
$499$	8.92630e11	−	1.54608e12i	0.644494	−	1.11630i	0.984418	−	0.175844i	$-0.0562655\pi$
$500$	1.98797e11	+	3.44326e11i	0.142247	+	0.246380i
$501$	−6.70417e11			−0.475418
$502$	−8.73665e11			−0.614014
$503$	2.01163e11	+	3.48424e11i	0.140117	+	0.242690i	0.927541	−	0.373723i	$-0.121919\pi$
$503$	2.01163e11	+	3.48424e11i	0.140117	+	0.242690i	−0.787423	+	0.616412i	$0.788585\pi$
$504$	−5.51471e10	−	9.55176e10i	−0.0380702	−	0.0659395i
$505$	3.41020e12			2.33329
$506$	−2.97688e11			−0.201876
$507$	1.23676e11	+	2.14214e11i	0.0831286	+	0.143983i
$508$	2.29358e11	−	3.97260e11i	0.152801	−	0.264660i
$509$	−9.61783e11	−	1.66586e12i	−0.635107	−	1.10004i	−0.986492	−	0.163807i	$-0.947623\pi$
$509$	−9.61783e11	−	1.66586e12i	−0.635107	−	1.10004i	0.351385	−	0.936231i	$-0.385711\pi$
$510$	−3.99014e11	+	6.91113e11i	−0.261170	+	0.452359i
$511$	−2.13706e11	+	3.70150e11i	−0.138651	+	0.240150i
$512$	−6.87195e10			−0.0441942
$513$	−5.94045e11	+	8.03010e11i	−0.378696	+	0.511909i
$514$	−1.90159e12			−1.20166
$515$	1.75209e12	−	3.03471e12i	1.09755	−	1.90101i
$516$	7.03353e11	−	1.21824e12i	0.436767	−	0.756502i
$517$	5.13574e11	+	8.89536e11i	0.316152	+	0.547591i
$518$	1.34168e11	−	2.32386e11i	0.0818777	−	0.141816i
$519$	6.30023e11	+	1.09123e12i	0.381157	+	0.660183i
$520$	−6.80017e11			−0.407854
$521$	9.75211e11			0.579867			0.289934	−	0.957047i	$-0.406367\pi$
$521$	9.75211e11			0.579867			0.289934	+	0.957047i	$0.406367\pi$
$522$	7.43666e10	+	1.28807e11i	0.0438390	+	0.0759314i
$523$	−1.64004e12	−	2.84064e12i	−0.958512	−	1.66019i	−0.726118	−	0.687570i	$-0.758677\pi$
$523$	−1.64004e12	−	2.84064e12i	−0.958512	−	1.66019i	−0.232394	−	0.972622i	$-0.574656\pi$
$524$	−2.27793e10			−0.0131992
$525$	−5.18478e11			−0.297861
$526$	−1.01527e12	−	1.75850e12i	−0.578291	−	1.00163i
$527$	−3.75332e11	+	6.50095e11i	−0.211967	+	0.367138i
$528$	−1.29266e11	−	2.23896e11i	−0.0723823	−	0.125370i
$529$	5.77491e11	−	1.00024e12i	0.320623	−	0.555336i
$530$	−9.68502e11	+	1.67750e12i	−0.533162	+	0.923464i
$531$	−2.41770e11			−0.131971
$532$	4.15399e11	+	4.72776e10i	0.224835	+	0.0255890i
$533$	−1.89987e12			−1.01965
$534$	1.07643e12	−	1.86443e12i	0.572863	−	0.992228i
$535$	1.88574e12	−	3.26620e12i	0.995155	−	1.72366i
$536$	7.32872e10	+	1.26937e11i	0.0383519	+	0.0664274i
$537$	−9.77997e11	+	1.69394e12i	−0.507520	+	0.879050i
$538$	3.01042e11	+	5.21420e11i	0.154920	+	0.268329i
$539$	−7.42703e11			−0.379023
$540$	−7.81132e11			−0.395324
$541$	6.64104e11	+	1.15026e12i	0.333310	+	0.577310i	0.983159	−	0.182753i	$-0.0585010\pi$
$541$	6.64104e11	+	1.15026e12i	0.333310	+	0.577310i	−0.649849	+	0.760064i	$0.725168\pi$
$542$	3.85925e11	+	6.68441e11i	0.192090	+	0.332710i
$543$	3.56250e12			1.75855
$544$	1.76831e11			0.0865691
$545$	3.35580e11	+	5.81241e11i	0.162934	+	0.282210i
$546$	−3.75036e11	+	6.49582e11i	−0.180595	+	0.312800i
$547$	1.07136e12	+	1.85564e12i	0.511671	+	0.886240i	0.999908	+	0.0135291i	$0.00430657\pi$
$547$	1.07136e12	+	1.85564e12i	0.511671	+	0.886240i	−0.488238	+	0.872711i	$0.662360\pi$
$548$	−1.26280e11	+	2.18723e11i	−0.0598166	+	0.103605i
$549$	−3.58211e11	+	6.20439e11i	−0.168292	+	0.291490i
$550$	−3.91852e11			−0.182596
$551$	−5.60171e11	−	6.37545e10i	−0.258904	−	0.0294665i
$552$	−5.61178e11			−0.257261
$553$	6.28561e11	−	1.08870e12i	0.285814	−	0.495045i
$554$	−7.38967e11	+	1.27993e12i	−0.333297	+	0.577287i
$555$	8.62663e11	+	1.49418e12i	0.385942	+	0.668472i
$556$	2.66558e11	−	4.61692e11i	0.118292	−	0.204888i
$557$	−1.37256e10	−	2.37734e10i	−0.00604203	−	0.0104651i	0.862989	−	0.505223i	$-0.168590\pi$
$557$	−1.37256e10	−	2.37734e10i	−0.00604203	−	0.0104651i	−0.869031	+	0.494758i	$0.835257\pi$
$558$	6.67070e11			0.291285
$559$	−3.08449e12			−1.33607
$560$	1.63475e11	+	2.83147e11i	0.0702434	+	0.121665i
$561$	3.32631e11	+	5.76135e11i	0.141785	+	0.245579i
$562$	1.23739e12			0.523231
$563$	−1.71810e12			−0.720708			−0.360354	−	0.932816i	$-0.617344\pi$
$563$	−1.71810e12			−0.720708			−0.360354	+	0.932816i	$0.617344\pi$
$564$	9.68148e11	+	1.67688e12i	0.402890	+	0.697825i
$565$	−3.52166e11	+	6.09969e11i	−0.145388	+	0.251820i
$566$	9.92048e11	+	1.71828e12i	0.406311	+	0.703752i
$567$	−6.95807e11	+	1.20517e12i	−0.282726	+	0.489695i
$568$	1.00068e11	−	1.73323e11i	0.0403393	−	0.0698697i
$569$	−1.70081e12			−0.680224			−0.340112	−	0.940385i	$-0.610465\pi$
$569$	−1.70081e12			−0.680224			−0.340112	+	0.940385i	$0.610465\pi$
$570$	−1.59870e12	+	2.16107e12i	−0.634353	+	0.857496i
$571$	2.37377e10			0.00934495			0.00467248	−	0.999989i	$-0.498513\pi$
$571$	2.37377e10			0.00934495			0.00467248	+	0.999989i	$0.498513\pi$
$572$	−2.83442e11	+	4.90937e11i	−0.110709	+	0.191754i
$573$	−2.31370e12	+	4.00745e12i	−0.896626	+	1.55300i
$574$	4.56725e11	+	7.91071e11i	0.175611	+	0.304167i
$575$	−4.25283e11	+	7.36611e11i	−0.162245	+	0.281017i
$576$	−7.85695e10	−	1.36086e11i	−0.0297408	−	0.0515126i
$577$	−1.31790e11			−0.0494986			−0.0247493	−	0.999694i	$-0.507879\pi$
$577$	−1.31790e11			−0.0494986			−0.0247493	+	0.999694i	$0.507879\pi$
$578$	1.44238e12			0.537532
$579$	2.92747e12	+	5.07053e12i	1.08253	+	1.87500i
$580$	−2.20449e11	−	3.81828e11i	−0.0808875	−	0.140101i
$581$	1.35330e12			0.492721
$582$	6.07184e11			0.219365
$583$	8.07376e11	+	1.39842e12i	0.289446	+	0.501335i
$584$	−3.04472e11	+	5.27361e11i	−0.108315	+	0.187608i
$585$	−7.77488e11	−	1.34665e12i	−0.274468	−	0.475393i
$586$	1.02236e12	−	1.77078e12i	0.358151	−	0.620335i
$587$	1.99677e12	−	3.45850e12i	0.694155	−	1.20231i	−0.276310	−	0.961069i	$-0.589112\pi$
$587$	1.99677e12	−	3.45850e12i	0.694155	−	1.20231i	0.970465	−	0.241243i	$-0.0775550\pi$
$588$	−1.40008e12			−0.483010
$589$	−1.50382e12	+	2.03281e12i	−0.514845	+	0.695950i
$590$	7.16690e11			0.243499
$591$	3.25008e12	−	5.62930e12i	1.09585	−	1.89806i
$592$	1.91153e11	−	3.31086e11i	0.0639636	−	0.110788i
$593$	1.73999e12	+	3.01376e12i	0.577832	+	1.00083i	0.995728	+	0.0923396i	$0.0294345\pi$
$593$	1.73999e12	+	3.01376e12i	0.577832	+	1.00083i	−0.417895	+	0.908495i	$0.637232\pi$
$594$	−3.25589e11	+	5.63937e11i	−0.107308	+	0.185862i
$595$	−4.20659e11	−	7.28603e11i	−0.137595	−	0.238322i
$596$	−1.17181e12			−0.380407
$597$	−3.83076e12			−1.23424
$598$	6.15248e11	+	1.06564e12i	0.196741	+	0.340766i
$599$	−1.50016e12	−	2.59835e12i	−0.476120	−	0.824664i	0.523506	−	0.852022i	$-0.324624\pi$
$599$	−1.50016e12	−	2.59835e12i	−0.476120	−	0.824664i	−0.999626	+	0.0273584i	$0.991290\pi$
$600$	−7.38689e11			−0.232692
$601$	2.03299e12			0.635623			0.317812	−	0.948154i	$-0.397052\pi$
$601$	2.03299e12			0.635623			0.317812	+	0.948154i	$0.397052\pi$
$602$	7.41506e11	+	1.28433e12i	0.230107	+	0.398558i
$603$	−1.67584e11	+	2.90264e11i	−0.0516183	+	0.0894056i
$604$	−1.10523e12	−	1.91432e12i	−0.337899	−	0.585258i
$605$	1.58105e12	−	2.73846e12i	0.479785	−	0.831013i
$606$	2.67956e12	−	4.64114e12i	0.807118	−	1.39797i
$607$	−3.29165e12			−0.984158			−0.492079	−	0.870550i	$-0.663763\pi$
$607$	−3.29165e12			−0.984158			−0.492079	+	0.870550i	$0.663763\pi$
$608$	5.91829e11	+	6.73576e10i	0.175643	+	0.0199903i
$609$	−4.86318e11			−0.143266
$610$	1.06186e12	−	1.83920e12i	0.310516	−	0.537829i
$611$	2.12286e12	−	3.67691e12i	0.616221	−	1.06733i
$612$	2.02177e11	+	3.50181e11i	0.0582573	+	0.100905i
$613$	4.20944e10	−	7.29096e10i	0.0120407	−	0.0208551i	−0.859942	−	0.510391i	$-0.829501\pi$
$613$	4.20944e10	−	7.29096e10i	0.0120407	−	0.0208551i	0.871983	+	0.489536i	$0.162834\pi$
$614$	1.40450e12	+	2.43266e12i	0.398808	+	0.690756i
$615$	−5.87322e12			−1.65553
$616$	2.72557e11			0.0762682
$617$	2.12060e12	+	3.67298e12i	0.589081	+	1.02032i	0.994353	+	0.106122i	$0.0338435\pi$
$617$	2.12060e12	+	3.67298e12i	0.589081	+	1.02032i	−0.405272	+	0.914196i	$0.632823\pi$
$618$	−2.75341e12	−	4.76905e12i	−0.759317	−	1.31518i
$619$	5.95247e12			1.62963			0.814816	−	0.579720i	$-0.196838\pi$
$619$	5.95247e12			1.62963			0.814816	+	0.579720i	$0.196838\pi$
$620$	−1.97743e12			−0.537450
$621$	7.06733e11	+	1.22410e12i	0.190697	+	0.330296i
$622$	1.23769e12	−	2.14374e12i	0.331554	−	0.574268i
$623$	1.13482e12	+	1.96557e12i	0.301809	+	0.522748i
$624$	−5.34323e11	+	9.25475e11i	−0.141083	+	0.244362i
$625$	2.38086e12	−	4.12377e12i	0.624128	−	1.08102i
$626$	4.70682e12			1.22502
$627$	8.93814e11	+	2.05495e12i	0.230963	+	0.531003i
$628$	2.72273e12			0.698531
$629$	−4.91880e11	+	8.51961e11i	−0.125294	+	0.217016i
$630$	−3.73814e11	+	6.47465e11i	−0.0945416	+	0.163751i
$631$	6.59042e11	+	1.14149e12i	0.165494	+	0.286643i	0.936830	−	0.349784i	$-0.113745\pi$
$631$	6.59042e11	+	1.14149e12i	0.165494	+	0.286643i	−0.771337	+	0.636427i	$0.780412\pi$
$632$	8.95526e11	−	1.55110e12i	0.223281	−	0.386734i
$633$	−2.35517e12	−	4.07928e12i	−0.583050	−	1.00987i
$634$	−5.17040e11			−0.127093
$635$	−3.10940e12			−0.758919
$636$	1.52200e12	+	2.63618e12i	0.368857	+	0.638879i
$637$	1.53499e12	+	2.65867e12i	0.369383	+	0.639790i
$638$	−3.67546e11			−0.0878252
$639$	4.57646e11			0.108587
$640$	2.32907e11	+	4.03407e11i	0.0548748	+	0.0950459i
$641$	1.53165e12	−	2.65290e12i	0.358343	−	0.620669i	−0.629341	−	0.777129i	$-0.716675\pi$
$641$	1.53165e12	−	2.65290e12i	0.358343	−	0.620669i	0.987684	+	0.156460i	$0.0500084\pi$
$642$	−2.96345e12	−	5.13284e12i	−0.688477	−	1.19248i
$643$	−1.97243e12	+	3.41635e12i	−0.455043	+	0.788158i	−0.998691	−	0.0511555i	$-0.983710\pi$
$643$	−1.97243e12	+	3.41635e12i	−0.455043	+	0.788158i	0.543647	+	0.839314i	$0.317043\pi$
$644$	2.95810e11	−	5.12357e11i	0.0677682	−	0.117378i
$645$	−9.53534e12			−2.16929
$646$	−1.52291e12	−	1.73326e11i	−0.344055	−	0.0391578i
$647$	−6.75296e12			−1.51504			−0.757521	−	0.652811i	$-0.773590\pi$
$647$	−6.75296e12			−1.51504			−0.757521	+	0.652811i	$0.773590\pi$
$648$	−9.91334e11	+	1.71704e12i	−0.220868	+	0.382554i
$649$	2.98728e11	−	5.17413e11i	0.0660960	−	0.114482i
$650$	8.09863e11	+	1.40272e12i	0.177951	+	0.308221i
$651$	−1.09057e12	+	1.88892e12i	−0.237979	+	0.412192i
$652$	3.82815e11	+	6.63055e11i	0.0829611	+	0.143693i
$653$	−3.80084e12			−0.818033			−0.409016	−	0.912527i	$-0.634128\pi$
$653$	−3.80084e12			−0.818033			−0.409016	+	0.912527i	$0.634128\pi$
$654$	1.05473e12			0.225445
$655$	7.72046e10	+	1.33722e11i	0.0163892	+	0.0283869i
$656$	6.50708e11	+	1.12706e12i	0.137189	+	0.237618i
$657$	−1.39246e12			−0.291566
$658$	−2.04133e12			−0.424519
$659$	2.31936e12	+	4.01724e12i	0.479053	+	0.829744i	0.999711	−	0.0240212i	$-0.00764693\pi$
$659$	2.31936e12	+	4.01724e12i	0.479053	+	0.829744i	−0.520659	+	0.853765i	$0.674314\pi$
$660$	−8.76230e11	+	1.51767e12i	−0.179751	+	0.311337i
$661$	−3.98934e12	−	6.90975e12i	−0.812821	−	1.40785i	−0.910882	−	0.412667i	$-0.864597\pi$
$661$	−3.98934e12	−	6.90975e12i	−0.812821	−	1.40785i	0.0980609	−	0.995180i	$-0.468736\pi$
$662$	−2.40160e12	+	4.15970e12i	−0.486004	+	0.841784i
$663$	1.37494e12	−	2.38146e12i	0.276358	−	0.478666i
$664$	1.92808e12			0.384918
$665$	−1.13035e12	−	2.59877e12i	−0.224139	−	0.515312i
$666$	8.74208e11			0.172179
$667$	−3.98903e11	+	6.90921e11i	−0.0780371	+	0.135164i
$668$	5.03486e11	−	8.72064e11i	0.0978349	−	0.169455i
$669$	−3.31305e12	−	5.73836e12i	−0.639455	−	1.10757i
$670$	4.96777e11	−	8.60442e11i	0.0952411	−	0.164962i
$671$	−8.85203e11	−	1.53322e12i	−0.168574	−	0.291979i
$672$	5.13802e11			0.0971928
$673$	−7.58083e12			−1.42445			−0.712227	−	0.701949i	$-0.752314\pi$
$673$	−7.58083e12			−1.42445			−0.712227	+	0.701949i	$0.752314\pi$
$674$	2.23282e12	+	3.86736e12i	0.416758	+	0.721847i
$675$	9.30285e11	+	1.61130e12i	0.172484	+	0.298751i
$676$	−3.71526e11			−0.0684272
$677$	8.45656e12			1.54719			0.773597	−	0.633678i	$-0.218456\pi$
$677$	8.45656e12			1.54719			0.773597	+	0.633678i	$0.218456\pi$
$678$	5.53428e11	+	9.58566e11i	0.100584	+	0.174216i
$679$	−3.20060e11	+	5.54361e11i	−0.0577854	+	0.100087i
$680$	−5.99323e11	−	1.03806e12i	−0.107491	−	0.186179i
$681$	5.02040e12	−	8.69559e12i	0.894492	−	1.54931i
$682$	−8.24225e11	+	1.42760e12i	−0.145887	+	0.252683i
$683$	−4.76125e11			−0.0837197			−0.0418598	−	0.999123i	$-0.513328\pi$
$683$	−4.76125e11			−0.0837197			−0.0418598	+	0.999123i	$0.513328\pi$
$684$	5.43270e11	+	1.24902e12i	0.0948994	+	0.218181i
$685$	1.71197e12			0.297091
$686$	1.66613e12	−	2.88582e12i	0.287244	−	0.497520i
$687$	−2.59080e12	+	4.48740e12i	−0.443740	+	0.768580i
$688$	1.05644e12	+	1.82981e12i	0.179762	+	0.311357i
$689$	3.33730e12	−	5.78037e12i	0.564168	−	0.977168i
$690$	1.90197e12	+	3.29431e12i	0.319435	+	0.553278i
$691$	1.88713e12			0.314884			0.157442	−	0.987528i	$-0.449675\pi$
$691$	1.88713e12			0.314884			0.157442	+	0.987528i	$0.449675\pi$
$692$	−1.89260e12			−0.313749
$693$	3.11624e11	+	5.39748e11i	0.0513252	+	0.0888979i
$694$	−2.58226e12	−	4.47261e12i	−0.422555	−	0.731886i
$695$	−3.61372e12			−0.587521
$696$	−6.92869e11			−0.111921
$697$	−1.67442e12	−	2.90018e12i	−0.268730	−	0.465455i
$698$	1.55439e12	−	2.69228e12i	0.247862	−	0.429309i
$699$	2.96023e11	+	5.12727e11i	0.0469006	+	0.0812342i
$700$	3.89380e11	−	6.74425e11i	0.0612960	−	0.106168i
$701$	2.06306e12	−	3.57332e12i	0.322686	−	0.558909i	−0.658355	−	0.752707i	$-0.728747\pi$
$701$	2.06306e12	−	3.57332e12i	0.322686	−	0.558909i	0.981041	+	0.193798i	$0.0620808\pi$
$702$	2.69165e12			0.418313
$703$	−1.97078e12	+	2.66403e12i	−0.304326	+	0.411378i
$704$	3.88318e11			0.0595814
$705$	6.56259e12	−	1.13667e13i	1.00052	−	1.73294i
$706$	−2.69221e12	+	4.66304e12i	−0.407837	+	0.706395i
$707$	2.82492e12	+	4.89290e12i	0.425225	+	0.736511i
$708$	5.63139e11	−	9.75386e11i	0.0842299	−	0.145890i
$709$	3.47949e12	+	6.02666e12i	0.517140	+	0.895713i	0.999802	+	0.0199059i	$0.00633665\pi$
$709$	3.47949e12	+	6.02666e12i	0.517140	+	0.895713i	−0.482662	+	0.875807i	$0.660330\pi$
$710$	−1.35662e12			−0.200353
$711$	4.09555e12			0.601034
$712$	1.61681e12	+	2.80040e12i	0.235776	+	0.408376i
$713$	1.78909e12	+	3.09879e12i	0.259256	+	0.449044i
$714$	−1.32213e12			−0.190385
$715$	3.84262e12			0.549858
$716$	−1.46896e12	−	2.54431e12i	−0.208882	−	0.361795i
$717$	−5.96990e12	+	1.03402e13i	−0.843589	+	1.46114i
$718$	−3.52185e12	−	6.10003e12i	−0.494551	−	0.856588i
$719$	−3.57616e12	+	6.19409e12i	−0.499042	+	0.864366i	−0.999999	−	0.00110597i	$-0.999648\pi$
$719$	−3.57616e12	+	6.19409e12i	−0.499042	+	0.864366i	0.500957	+	0.865472i	$0.332981\pi$
$720$	−5.32582e11	+	9.22460e11i	−0.0738568	+	0.127924i
$721$	5.80554e12			0.800081
$722$	−5.03096e12	−	1.16020e12i	−0.689022	−	0.158897i
$723$	5.16384e12			0.702831
$724$	−2.67545e12	+	4.63402e12i	−0.361888	+	0.626808i
$725$	−5.25084e11	+	9.09472e11i	−0.0705842	+	0.122255i
$726$	−2.48462e12	−	4.30349e12i	−0.331929	−	0.574918i
$727$	−3.65386e12	+	6.32867e12i	−0.485118	+	0.840248i	−0.999854	−	0.0171003i	$-0.994557\pi$
$727$	−3.65386e12	+	6.32867e12i	−0.485118	+	0.840248i	0.514736	+	0.857349i	$0.327890\pi$
$728$	−5.63308e11	−	9.75678e11i	−0.0743284	−	0.128741i
$729$	1.36518e12			0.179026
$730$	4.12772e12			0.537970
$731$	−2.71847e12	−	4.70853e12i	−0.352124	−	0.609897i
$732$	−1.66871e12	−	2.89030e12i	−0.214824	−	0.372086i
$733$	3.18256e12			0.407201			0.203600	−	0.979054i	$-0.434736\pi$
$733$	3.18256e12			0.407201			0.203600	+	0.979054i	$0.434736\pi$
$734$	4.92926e12			0.626829
$735$	4.74523e12	+	8.21898e12i	0.599742	+	1.03878i
$736$	4.21447e11	−	7.29968e11i	0.0529411	−	0.0916967i
$737$	−4.14129e11	−	7.17293e11i	−0.0517050	−	0.0895556i
$738$	−1.48795e12	+	2.57721e12i	−0.184644	+	0.319813i
$739$	−2.52544e12	+	4.37420e12i	−0.311486	+	0.539509i	−0.978684	−	0.205371i	$-0.934160\pi$
$739$	−2.52544e12	+	4.37420e12i	−0.311486	+	0.539509i	0.667199	+	0.744880i	$0.267493\pi$
$740$	−2.59146e12			−0.317688
$741$	5.50886e12	−	7.44669e12i	0.671243	−	0.907363i
$742$	−3.20913e12			−0.388659
$743$	3.20763e12	−	5.55578e12i	0.386131	−	0.668799i	−0.605794	−	0.795621i	$-0.707145\pi$
$743$	3.20763e12	−	5.55578e12i	0.386131	−	0.668799i	0.991925	+	0.126822i	$0.0404778\pi$
$744$	−1.55376e12	+	2.69120e12i	−0.185912	+	0.322008i
$745$	3.97155e12	+	6.87892e12i	0.472342	+	0.818120i
$746$	5.17975e12	−	8.97159e12i	0.612328	−	1.06058i
$747$	2.20444e12	+	3.81820e12i	0.259033	+	0.448659i
$748$	−9.99231e11			−0.116710
$749$	6.24840e12			0.725438
$750$	−2.11766e12	−	3.66789e12i	−0.244388	−	0.423293i
$751$	6.01186e12	+	1.04128e13i	0.689650	+	1.19451i	0.971951	+	0.235183i	$0.0755690\pi$
$751$	6.01186e12	+	1.04128e13i	0.689650	+	1.19451i	−0.282301	+	0.959326i	$0.591098\pi$
$752$	−2.90834e12			−0.331638
$753$	9.30663e12			1.05491
$754$	7.59629e11	+	1.31572e12i	0.0855914	+	0.148249i
$755$	−7.49180e12	+	1.29762e13i	−0.839121	+	1.45340i
$756$	−6.47069e11	−	1.12076e12i	−0.0720448	−	0.124785i
$757$	−5.84034e12	+	1.01158e13i	−0.646408	+	1.11961i	0.337567	+	0.941302i	$0.390396\pi$
$757$	−5.84034e12	+	1.01158e13i	−0.646408	+	1.11961i	−0.983974	+	0.178309i	$0.942937\pi$
$758$	−3.32103e12	+	5.75220e12i	−0.365395	+	0.632882i
$759$	3.17109e12			0.346833
$760$	−1.61044e12	−	3.70253e12i	−0.175099	−	0.402567i
$761$	−1.24898e13			−1.34997			−0.674984	−	0.737832i	$-0.735849\pi$
$761$	−1.24898e13			−1.34997			−0.674984	+	0.737832i	$0.735849\pi$
$762$	−2.44321e12	+	4.23177e12i	−0.262521	+	0.454699i
$763$	−5.55971e11	+	9.62969e11i	−0.0593870	+	0.102861i
$764$	−3.47520e12	−	6.01923e12i	−0.369029	−	0.639176i
$765$	1.37046e12	−	2.37370e12i	0.144673	−	0.250582i
$766$	6.64273e12	+	1.15055e13i	0.697135	+	1.20747i
$767$	−2.46959e12			−0.257660
$768$	7.32027e11			0.0759279
$769$	−5.82084e12	−	1.00820e13i	−0.600229	−	1.03963i	−0.992786	−	0.119899i	$-0.961743\pi$
$769$	−5.82084e12	−	1.00820e13i	−0.600229	−	1.03963i	0.392557	−	0.919728i	$-0.371591\pi$
$770$	−9.23761e11	−	1.60000e12i	−0.0947003	−	0.164026i
$771$	2.02565e13			2.06452
$772$	−8.79419e12			−0.891083
$773$	−5.51201e12	−	9.54708e12i	−0.555268	−	0.961752i	−0.997883	−	0.0650400i	$-0.979282\pi$
$773$	−5.51201e12	−	9.54708e12i	−0.555268	−	0.961752i	0.442615	−	0.896712i	$-0.354051\pi$
$774$	−2.41574e12	+	4.18418e12i	−0.241944	+	0.419060i
$775$	2.35501e12	+	4.07899e12i	0.234495	+	0.406158i
$776$	−4.55998e11	+	7.89812e11i	−0.0451425	+	0.0781891i
$777$	−1.42921e12	+	2.47547e12i	−0.140670	+	0.243648i
$778$	−5.52646e11			−0.0540803
$779$	−4.49933e12	−	1.03443e13i	−0.437753	−	1.00643i
$780$	7.24381e12			0.700715
$781$	−5.65463e11	+	9.79410e11i	−0.0543844	+	0.0941965i
$782$	−1.08448e12	+	1.87837e12i	−0.103703	+	0.179619i
$783$	8.72582e11	+	1.51136e12i	0.0829618	+	0.143694i
$784$	1.05147e12	−	1.82120e12i	0.0993973	−	0.172161i
$785$	−9.22798e12	−	1.59833e13i	−0.867348	−	1.50229i
$786$	2.42654e11			0.0226770
$787$	−3.35754e12			−0.311986			−0.155993	−	0.987758i	$-0.549858\pi$
$787$	−3.35754e12			−0.311986			−0.155993	+	0.987758i	$0.549858\pi$
$788$	4.88165e12	+	8.45526e12i	0.451023	+	0.781194i
$789$	1.08151e13	+	1.87323e13i	0.993535	+	1.72085i
$790$	−1.21406e13			−1.10897
$791$	−1.16690e12			−0.105984
$792$	4.43978e11	+	7.68993e11i	0.0400957	+	0.0694479i
$793$	−3.65900e12	+	6.33757e12i	−0.328574	+	0.569106i
$794$	5.05978e10	+	8.76379e10i	0.00451793	+	0.00782528i
$795$	1.03169e13	−	1.78693e13i	0.916001	−	1.58656i
$796$	2.87692e12	−	4.98298e12i	0.253992	−	0.439926i
$797$	−1.23113e13			−1.08079			−0.540396	−	0.841411i	$-0.681726\pi$
$797$	−1.23113e13			−1.08079			−0.540396	+	0.841411i	$0.681726\pi$
$798$	−4.42499e12	−	5.03619e11i	−0.386278	−	0.0439632i
$799$	7.48382e12			0.649625
$800$	5.54759e11	−	9.60871e11i	0.0478850	−	0.0829392i
$801$	−3.69712e12	+	6.40359e12i	−0.317334	+	0.549639i
$802$	−1.16430e12	−	2.01663e12i	−0.0993757	−	0.172124i
$803$	1.72050e12	−	2.98000e12i	0.146028	−	0.252928i
$804$	−7.80684e11	−	1.35218e12i	−0.0658905	−	0.114126i
$805$	−4.01028e12			−0.336584
$806$	6.81388e12			0.568705
$807$	−3.20682e12	−	5.55437e12i	−0.266160	−	0.461003i
$808$	4.02473e12	+	6.97104e12i	0.332189	+	0.575369i
$809$	3.97478e11			0.0326245			0.0163123	−	0.999867i	$-0.494807\pi$
$809$	3.97478e11			0.0326245			0.0163123	+	0.999867i	$0.494807\pi$
$810$	1.34395e13			1.09698
$811$	−6.86378e12	−	1.18884e13i	−0.557146	−	0.965006i	−0.997733	−	0.0672957i	$-0.978563\pi$
$811$	−6.86378e12	−	1.18884e13i	−0.557146	−	0.965006i	0.440587	−	0.897710i	$-0.354770\pi$
$812$	3.65227e11	−	6.32592e11i	0.0294823	−	0.0510648i
$813$	−4.11102e12	−	7.12050e12i	−0.330021	−	0.571614i
$814$	−1.08016e12	+	1.87089e12i	−0.0862341	+	0.149362i
$815$	2.59491e12	−	4.49451e12i	0.206022	−	0.356840i
$816$	−1.88367e12			−0.148730
$817$	−7.30480e12	−	1.67943e13i	−0.573600	−	1.31875i
$818$	−2.49652e10			−0.00194960
$819$	1.28810e12	−	2.23106e12i	0.100040	−	0.173274i
$820$	4.41081e12	−	7.63976e12i	0.340688	−	0.590088i
$821$	6.28898e12	+	1.08928e13i	0.483099	+	0.836752i	0.999812	−	0.0194067i	$-0.00617775\pi$
$821$	6.28898e12	+	1.08928e13i	0.483099	+	0.836752i	−0.516713	+	0.856159i	$0.672844\pi$
$822$	1.34518e12	−	2.32993e12i	0.102768	−	0.177999i
$823$	−3.23628e12	−	5.60540e12i	−0.245893	−	0.425900i	0.716489	−	0.697598i	$-0.245748\pi$
$823$	−3.23628e12	−	5.60540e12i	−0.245893	−	0.425900i	−0.962382	+	0.271699i	$0.912415\pi$
$824$	8.27130e12			0.625031
$825$	4.17416e12			0.313709
$826$	5.93687e11	+	1.02830e12i	0.0443759	+	0.0768613i
$827$	1.11094e12	+	1.92420e12i	0.0825874	+	0.143046i	0.904361	−	0.426769i	$-0.140348\pi$
$827$	1.11094e12	+	1.92420e12i	0.0825874	+	0.143046i	−0.821773	+	0.569815i	$0.807015\pi$
$828$	1.92742e12			0.142508
$829$	−1.61427e13			−1.18708			−0.593540	−	0.804805i	$-0.702270\pi$
$829$	−1.61427e13			−1.18708			−0.593540	+	0.804805i	$0.702270\pi$
$830$	−6.53473e12	−	1.13185e13i	−0.477943	−	0.827821i
$831$	7.87177e12	−	1.36343e13i	0.572621	−	0.991809i
$832$	−8.02559e11	−	1.39007e12i	−0.0580660	−	0.100573i
$833$	−2.70567e12	+	4.68636e12i	−0.194703	+	0.337236i
$834$	−2.83948e12	+	4.91813e12i	−0.203232	+	0.352008i
$835$	−6.82576e12			−0.485916
$836$	−3.34429e12	−	3.80622e11i	−0.236797	−	0.0269505i
$837$	7.82707e12			0.551233
$838$	−3.91417e12	+	6.77954e12i	−0.274183	+	0.474900i
$839$	2.79930e12	−	4.84852e12i	0.195038	−	0.337816i	−0.751875	−	0.659306i	$-0.770850\pi$
$839$	2.79930e12	−	4.84852e12i	0.195038	−	0.337816i	0.946913	+	0.321490i	$0.104184\pi$
$840$	−1.74140e12	−	3.01620e12i	−0.120682	−	0.209027i
$841$	6.76106e12	−	1.17105e13i	0.466050	−	0.807223i
$842$	4.62174e12	+	8.00509e12i	0.316885	+	0.548861i
$843$	−1.31812e13			−0.898939
$844$	7.07498e12			0.479937
$845$	1.25919e12	+	2.18099e12i	0.0849644	+	0.147163i
$846$	−3.32521e12	−	5.75943e12i	−0.223178	−	0.386556i
$847$	5.23880e12			0.349749
$848$	−4.57212e12			−0.303624
$849$	−1.05677e13	−	1.83038e13i	−0.698064	−	1.20908i
$850$	−1.42752e12	+	2.47254e12i	−0.0937988	+	0.162464i
$851$	2.34463e12	+	4.06102e12i	0.153247	+	0.265431i
$852$	−1.06597e12	+	1.84631e12i	−0.0693051	+	0.120040i
$853$	−4.31646e12	+	7.47633e12i	−0.279163	+	0.483524i	−0.971177	−	0.238360i	$-0.923390\pi$
$853$	−4.31646e12	+	7.47633e12i	−0.279163	+	0.483524i	0.692014	+	0.721884i	$0.256723\pi$
$854$	3.51847e12			0.226357
$855$	5.49091e12	−	7.42242e12i	0.351396	−	0.475005i
$856$	8.90225e12			0.566719
$857$	−1.35098e13	+	2.33996e13i	−0.855529	+	1.48182i	0.0206251	+	0.999787i	$0.493434\pi$
$857$	−1.35098e13	+	2.33996e13i	−0.855529	+	1.48182i	−0.876154	+	0.482032i	$0.839899\pi$
$858$	3.01934e12	−	5.22965e12i	0.190204	−	0.329443i
$859$	9.35676e11	+	1.62064e12i	0.0586349	+	0.101559i	0.893853	−	0.448360i	$-0.147992\pi$
$859$	9.35676e11	+	1.62064e12i	0.0586349	+	0.101559i	−0.835218	+	0.549919i	$0.814659\pi$
$860$	7.16109e12	−	1.24034e13i	0.446412	−	0.773208i
$861$	−4.86521e12	−	8.42680e12i	−0.301709	−	0.522575i
$862$	−3.32804e12			−0.205308
$863$	−3.63482e12			−0.223067			−0.111533	−	0.993761i	$-0.535576\pi$
$863$	−3.63482e12			−0.223067			−0.111533	+	0.993761i	$0.535576\pi$
$864$	−9.21896e11	−	1.59677e12i	−0.0562820	−	0.0974834i
$865$	6.41449e12	+	1.11102e13i	0.389574	+	0.674762i
$866$	−1.31696e13			−0.795688
$867$	−1.53648e13			−0.923508
$868$	−1.63805e12	−	2.83718e12i	−0.0979462	−	0.169648i
$869$	−5.06042e12	+	8.76490e12i	−0.301021	+	0.521384i
$870$	2.34830e12	+	4.06738e12i	0.138969	+	0.240701i
$871$	−1.71181e12	+	2.96494e12i	−0.100780	+	0.174556i
$872$	−7.92105e11	+	1.37197e12i	−0.0463937	+	0.0803562i
$873$	−2.08544e12			−0.121516
$874$	−4.34511e12	+	5.87357e12i	−0.251883	+	0.340487i
$875$	4.46507e12			0.257509
$876$	3.24336e12	−	5.61766e12i	0.186091	−	0.322320i
$877$	−1.67499e13	+	2.90117e13i	−0.956124	+	1.65606i	−0.224349	+	0.974509i	$0.572026\pi$
$877$	−1.67499e13	+	2.90117e13i	−0.956124	+	1.65606i	−0.731775	+	0.681546i	$0.761308\pi$
$878$	1.40759e12	+	2.43801e12i	0.0799374	+	0.138456i
$879$	−1.08906e13	+	1.88631e13i	−0.615322	+	1.06577i
$880$	−1.31611e12	−	2.27956e12i	−0.0739807	−	0.128138i
$881$	3.16714e13			1.77123			0.885617	−	0.464416i	$-0.153736\pi$
$881$	3.16714e13			1.77123			0.885617	+	0.464416i	$0.153736\pi$
$882$	4.80874e12			0.267561
$883$	−3.40712e12	−	5.90130e12i	−0.188610	−	0.326682i	0.756177	−	0.654367i	$-0.227065\pi$
$883$	−3.40712e12	−	5.90130e12i	−0.188610	−	0.326682i	−0.944787	+	0.327685i	$0.893731\pi$
$884$	2.06517e12	+	3.57698e12i	0.113742	+	0.197007i
$885$	−7.63447e12			−0.418344
$886$	1.22652e13			0.668687
$887$	−7.17650e12	−	1.24301e13i	−0.389275	−	0.674244i	0.603077	−	0.797683i	$-0.293941\pi$
$887$	−7.17650e12	−	1.24301e13i	−0.389275	−	0.674244i	−0.992352	+	0.123439i	$0.960608\pi$
$888$	−2.03624e12	+	3.52686e12i	−0.109893	+	0.190340i
$889$	−2.57574e12	−	4.46132e12i	−0.138307	−	0.239555i
$890$	1.09595e13	−	1.89825e13i	0.585514	−	1.01414i
$891$	5.60180e12	−	9.70261e12i	0.297768	−	0.515749i
$892$	9.95246e12			0.526367
$893$	2.50473e13	+	2.85070e12i	1.31804	+	0.150010i
$894$	1.24826e13			0.653559
$895$	−9.95734e12	+	1.72466e13i	−0.518728	+	0.898463i
$896$	−3.85868e11	+	6.68343e11i	−0.0200010	+	0.0346428i
$897$	−6.55387e12	−	1.13516e13i	−0.338012	−	0.585453i
$898$	−6.76901e12	+	1.17243e13i	−0.347362	+	0.601648i
$899$	2.20893e12	+	3.82598e12i	0.112788	+	0.195355i
$900$	2.53710e12			0.128898
$901$	1.17651e13			0.594750
$902$	−3.67700e12	−	6.36875e12i	−0.184954	−	0.320350i
$903$	−7.89882e12	−	1.36812e13i	−0.395337	−	0.684743i
$904$	−1.66251e12			−0.0827954
$905$	3.62711e13			1.79739
$906$	1.17734e13	+	2.03921e13i	0.580528	+	1.00550i
$907$	7.39395e12	−	1.28067e13i	0.362780	−	0.628354i	−0.625637	−	0.780114i	$-0.715161\pi$
$907$	7.39395e12	−	1.28067e13i	0.362780	−	0.628354i	0.988417	+	0.151761i	$0.0484943\pi$
$908$	7.54070e12	+	1.30609e13i	0.368150	+	0.637655i
$909$	−9.20324e12	+	1.59405e13i	−0.447099	+	0.774397i
$910$	−3.81838e12	+	6.61362e12i	−0.184583	+	0.319708i
$911$	3.00970e13			1.44774			0.723870	−	0.689936i	$-0.242361\pi$
$911$	3.00970e13			1.44774			0.723870	+	0.689936i	$0.242361\pi$
$912$	−6.30440e12	−	7.17519e11i	−0.301764	−	0.0343445i
$913$	−1.08951e13			−0.518936
$914$	9.27669e12	−	1.60677e13i	0.439678	−	0.761545i
$915$	−1.13114e13	+	1.95919e13i	−0.533482	+	0.924019i
$916$	−3.89141e12	−	6.74012e12i	−0.182632	−	0.316328i
$917$	−1.27908e11	+	2.21544e11i	−0.00597361	+	0.0103466i
$918$	2.37225e12	+	4.10885e12i	0.110247	+	0.190954i
$919$	5.79846e12			0.268159			0.134080	−	0.990971i	$-0.457192\pi$
$919$	5.79846e12			0.268159			0.134080	+	0.990971i	$0.457192\pi$
$920$	−5.71355e12			−0.262943
$921$	−1.49613e13	−	2.59137e13i	−0.685173	−	1.18675i
$922$	−2.83151e12	−	4.90433e12i	−0.129042	−	0.223507i
$923$	4.67469e12			0.212005
$924$	−2.90338e12			−0.131033
$925$	3.08628e12	+	5.34559e12i	0.138611	+	0.240081i
$926$	−1.19239e13	+	2.06528e13i	−0.532929	+	0.923060i
$927$	9.45688e12	+	1.63798e13i	0.420619	+	0.728534i
$928$	5.20348e11	−	9.01270e11i	0.0230318	−	0.0398923i
$929$	1.40093e13	−	2.42649e13i	0.617087	−	1.06883i	−0.372927	−	0.927861i	$-0.621646\pi$
$929$	1.40093e13	−	2.42649e13i	0.617087	−	1.06883i	0.990014	−	0.140966i	$-0.0450208\pi$
$930$	2.10643e13			0.923367
$931$	−1.08406e13	+	1.46540e13i	−0.472913	+	0.639267i
$932$	−8.89259e11			−0.0386062
$933$	−1.31843e13	+	2.28359e13i	−0.569627	+	0.986622i
$934$	3.45115e12	−	5.97757e12i	0.148389	−	0.257018i
$935$	3.38664e12	+	5.86583e12i	0.144916	+	0.251002i
$936$	1.83519e12	−	3.17864e12i	0.0781519	−	0.135363i
$937$	1.93766e13	+	3.35612e13i	0.821200	+	1.42236i	0.904789	+	0.425860i	$0.140028\pi$
$937$	1.93766e13	+	3.35612e13i	0.821200	+	1.42236i	−0.0835894	+	0.996500i	$0.526638\pi$
$938$	1.64607e12			0.0694279
$939$	−5.01389e13			−2.10465
$940$	9.85707e12	+	1.70729e13i	0.411787	+	0.713236i
$941$	−9.92646e12	−	1.71931e13i	−0.412706	−	0.714828i	0.582478	−	0.812846i	$-0.302083\pi$
$941$	−9.92646e12	−	1.71931e13i	−0.412706	−	0.714828i	−0.995185	+	0.0980179i	$0.968750\pi$
$942$	−2.90035e13			−1.20011
$943$	−1.59628e13			−0.657365
$944$	8.45841e11	+	1.46504e12i	0.0346669	+	0.0600448i
$945$	−4.38615e12	+	7.59704e12i	−0.178912	+	0.309885i
$946$	−5.96972e12	−	1.03399e13i	−0.242350	−	0.419763i
$947$	−8.44863e12	+	1.46335e13i	−0.341359	+	0.591251i	−0.984685	−	0.174341i	$-0.944221\pi$
$947$	−8.44863e12	+	1.46335e13i	−0.341359	+	0.591251i	0.643326	+	0.765592i	$0.277554\pi$
$948$	−9.53950e12	+	1.65229e13i	−0.383608	+	0.664429i
$949$	−1.42234e13			−0.569255
$950$	−5.71955e12	+	7.73149e12i	−0.227827	+	0.307969i
$951$	5.50771e12			0.218353
$952$	9.92926e11	−	1.71980e12i	0.0391788	−	0.0678596i
$953$	6.90013e12	−	1.19514e13i	0.270981	−	0.469353i	−0.698132	−	0.715969i	$-0.745985\pi$
$953$	6.90013e12	−	1.19514e13i	0.270981	−	0.469353i	0.969113	+	0.246616i	$0.0793186\pi$
$954$	−5.22747e12	−	9.05425e12i	−0.204326	−	0.353903i
$955$	−2.35566e13	+	4.08013e13i	−0.916427	+	1.58730i
$956$	−8.96685e12	−	1.55310e13i	−0.347200	−	0.601368i
$957$	3.91525e12			0.150888
$958$	1.63206e12			0.0626026
$959$	1.41815e12	+	2.45631e12i	0.0541426	+	0.0937778i
$960$	−2.48102e12	−	4.29725e12i	−0.0942778	−	0.163294i
$961$	−6.62548e12			−0.250589
$962$	8.92972e12			0.336163
$963$	1.01783e13	+	1.76293e13i	0.381378	+	0.660566i
$964$	−3.87807e12	+	6.71702e12i	−0.144634	+	0.250513i
$965$	2.98057e13	+	5.16249e13i	1.10644	+	1.91640i
$966$	−3.15108e12	+	5.45783e12i	−0.116429	+	0.201661i
$967$	2.14519e13	−	3.71557e13i	0.788943	−	1.36649i	−0.137672	−	0.990478i	$-0.543962\pi$
$967$	2.14519e13	−	3.71557e13i	0.788943	−	1.36649i	0.926615	−	0.376012i	$-0.122705\pi$
$968$	7.46386e12			0.273227
$969$	1.62227e13	+	1.84634e12i	0.591105	+	0.0672752i
$970$	6.18196e12			0.224209
$971$	1.08228e13	−	1.87456e13i	0.390709	−	0.676727i	−0.601835	−	0.798621i	$-0.705563\pi$
$971$	1.08228e13	−	1.87456e13i	0.390709	−	0.676727i	0.992543	+	0.121894i	$0.0388967\pi$
$972$	6.12998e12	−	1.06174e13i	0.220273	−	0.381524i
$973$	−2.99351e12	−	5.18491e12i	−0.107071	−	0.185453i
$974$	−8.15082e12	+	1.41176e13i	−0.290192	+	0.502628i
$975$	−8.62698e12	−	1.49424e13i	−0.305730	−	0.529540i
$976$	5.01285e12			0.176832
$977$	2.57363e13			0.903692			0.451846	−	0.892096i	$-0.350766\pi$
$977$	2.57363e13			0.903692			0.451846	+	0.892096i	$0.350766\pi$
$978$	−4.07789e12	−	7.06312e12i	−0.142532	−	0.246872i
$979$	−9.13623e12	−	1.58244e13i	−0.317867	−	0.550561i
$980$	−1.42548e13			−0.493677
$981$	−3.62257e12			−0.124884
$982$	7.87910e12	+	1.36470e13i	0.270380	+	0.468313i
$983$	2.09067e13	−	3.62114e13i	0.714158	−	1.23696i	−0.249126	−	0.968471i	$-0.580143\pi$
$983$	2.09067e13	−	3.62114e13i	0.714158	−	1.23696i	0.963283	−	0.268486i	$-0.0865235\pi$
$984$	−6.93159e12	−	1.20059e13i	−0.235698	−	0.408240i
$985$	3.30902e13	−	5.73139e13i	1.12005	−	1.93998i
$986$	−1.33898e12	+	2.31917e12i	−0.0451156	+	0.0781424i
$987$	2.17451e13			0.729346
$988$	5.54931e12	+	1.27583e13i	0.185282	+	0.425978i
$989$	−2.59161e13			−0.861363
$990$	3.00950e12	−	5.21261e12i	0.0995718	−	0.172463i
$991$	1.09738e13	−	1.90072e13i	0.361431	−	0.626017i	−0.626765	−	0.779208i	$-0.715622\pi$
$991$	1.09738e13	−	1.90072e13i	0.361431	−	0.626017i	0.988197	+	0.153191i	$0.0489549\pi$
$992$	−2.33377e12	−	4.04220e12i	−0.0765165	−	0.132530i
$993$	2.55828e13	−	4.43107e13i	0.834981	−	1.44623i
$994$	−1.12379e12	−	1.94646e12i	−0.0365129	−	0.0632422i
$995$	−3.90024e13			−1.26150
$996$	−2.05386e13			−0.661309
$997$	−8.71186e12	−	1.50894e13i	−0.279243	−	0.483663i	0.691954	−	0.721942i	$-0.256750\pi$
$997$	−8.71186e12	−	1.50894e13i	−0.279243	−	0.483663i	−0.971197	+	0.238279i	$0.923417\pi$
$998$	−1.42821e13	−	2.47373e13i	−0.455726	−	0.789341i
$999$	1.02575e13			0.325835

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.c.a.11.2	yes	14
19.7	even	3	inner	38.10.c.a.7.2	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.c.a.7.2	✓	14	19.7	even	3	inner
38.10.c.a.11.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(8.00000 - 13.8564i) q^{2} +(-85.2191 + 147.604i) q^{3} +(-128.000 - 221.703i) q^{4} +(-867.647 + 1502.81i) q^{5} +(1363.51 + 2361.66i) q^{6} -2874.94 q^{7} -4096.00 q^{8} +(-4683.10 - 8111.37i) q^{9} +O(q^{10})\)	\(q+(8.00000 - 13.8564i) q^{2} +(-85.2191 + 147.604i) q^{3} +(-128.000 - 221.703i) q^{4} +(-867.647 + 1502.81i) q^{5} +(1363.51 + 2361.66i) q^{6} -2874.94 q^{7} -4096.00 q^{8} +(-4683.10 - 8111.37i) q^{9} +(13882.3 + 24044.9i) q^{10} +23145.6 q^{11} +43632.2 q^{12} +(-47836.2 - 82854.8i) q^{13} +(-22999.5 + 39836.3i) q^{14} +(-147880. - 256136. i) q^{15} +(-32768.0 + 56755.8i) q^{16} +(84319.5 - 146046. i) q^{17} -149859. q^{18} +(337837. - 456677. i) q^{19} +444235. q^{20} +(245000. - 424352. i) q^{21} +(185165. - 320714. i) q^{22} +(-401923. - 696152. i) q^{23} +(349058. - 604586. i) q^{24} +(-529059. - 916358. i) q^{25} -1.53076e6 q^{26} -1.75838e6 q^{27} +(367992. + 637381. i) q^{28} +(-496243. - 859518. i) q^{29} -4.73217e6 q^{30} -4.45131e6 q^{31} +(524288. + 908093. i) q^{32} +(-1.97245e6 + 3.41638e6i) q^{33} +(-1.34911e6 - 2.33673e6i) q^{34} +(2.49443e6 - 4.32048e6i) q^{35} +(-1.19887e6 + 2.07651e6i) q^{36} -5.83352e6 q^{37} +(-3.62520e6 - 8.33462e6i) q^{38} +1.63063e7 q^{39} +(3.55388e6 - 6.15550e6i) q^{40} +(9.92901e6 - 1.71975e7i) q^{41} +(-3.92000e6 - 6.78964e6i) q^{42} +(1.61200e7 - 2.79207e7i) q^{43} +(-2.96263e6 - 5.13143e6i) q^{44} +1.62531e7 q^{45} -1.28616e7 q^{46} +(2.21889e7 + 3.84322e7i) q^{47} +(-5.58492e6 - 9.67337e6i) q^{48} -3.20883e7 q^{49} -1.69299e7 q^{50} +(1.43713e7 + 2.48918e7i) q^{51} +(-1.22461e7 + 2.12108e7i) q^{52} +(3.48825e7 + 6.04183e7i) q^{53} +(-1.40670e7 + 2.43648e7i) q^{54} +(-2.00822e7 + 3.47834e7i) q^{55} +1.17758e7 q^{56} +(3.86171e7 + 8.87837e7i) q^{57} -1.58798e7 q^{58} +(1.29065e7 - 2.23547e7i) q^{59} +(-3.78573e7 + 6.55708e7i) q^{60} +(-3.82450e7 - 6.62423e7i) q^{61} +(-3.56105e7 + 6.16791e7i) q^{62} +(1.34636e7 + 2.33197e7i) q^{63} +1.67772e7 q^{64} +1.66020e8 q^{65} +(3.15591e7 + 5.46620e7i) q^{66} +(-1.78924e7 - 3.09905e7i) q^{67} -4.31716e7 q^{68} +1.37006e8 q^{69} +(-3.99109e7 - 6.91277e7i) q^{70} +(-2.44307e7 + 4.23152e7i) q^{71} +(1.91820e7 + 3.32242e7i) q^{72} +(7.43340e7 - 1.28750e8i) q^{73} +(-4.66682e7 + 8.08317e7i) q^{74} +1.80344e8 q^{75} +(-1.44490e8 - 1.64447e7i) q^{76} -6.65421e7 q^{77} +(1.30450e8 - 2.25946e8i) q^{78} +(-2.18634e8 + 3.78686e8i) q^{79} +(-5.68621e7 - 9.84880e7i) q^{80} +(2.42025e8 - 4.19199e8i) q^{81} +(-1.58864e8 - 2.75161e8i) q^{82} -4.70722e8 q^{83} -1.25440e8 q^{84} +(1.46319e8 + 2.53432e8i) q^{85} +(-2.57921e8 - 4.46732e8i) q^{86} +1.69158e8 q^{87} -9.48043e7 q^{88} +(-3.94729e8 - 6.83691e8i) q^{89} +(1.30025e8 - 2.25210e8i) q^{90} +(1.37526e8 + 2.38203e8i) q^{91} +(-1.02892e8 + 1.78215e8i) q^{92} +(3.79337e8 - 6.57030e8i) q^{93} +7.10043e8 q^{94} +(3.93174e8 + 9.03939e8i) q^{95} -1.78717e8 q^{96} +(1.11328e8 - 1.92825e8i) q^{97} +(-2.56707e8 + 4.44629e8i) q^{98} +(-1.08393e8 - 1.87742e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 112 q^{2} + 165 q^{3} - 1792 q^{4} + 909 q^{5} - 2640 q^{6} + 3692 q^{7} - 57344 q^{8} - 52286 q^{9}+O(q^{10}) \) 14 * q + 112 * q^2 + 165 * q^3 - 1792 * q^4 + 909 * q^5 - 2640 * q^6 + 3692 * q^7 - 57344 * q^8 - 52286 * q^9	\( 14 q + 112 q^{2} + 165 q^{3} - 1792 q^{4} + 909 q^{5} - 2640 q^{6} + 3692 q^{7} - 57344 q^{8} - 52286 q^{9} - 14544 q^{10} + 15656 q^{11} - 84480 q^{12} + 6423 q^{13} + 29536 q^{14} - 227715 q^{15} - 458752 q^{16} + 313667 q^{17} - 1673152 q^{18} + 1134224 q^{19} - 465408 q^{20} - 1227046 q^{21} + 125248 q^{22} + 3449345 q^{23} - 675840 q^{24} - 2398648 q^{25} + 205536 q^{26} - 1873854 q^{27} - 472576 q^{28} - 7002615 q^{29} - 7286880 q^{30} - 18666588 q^{31} + 7340032 q^{32} - 13827668 q^{33} - 5018672 q^{34} + 2584932 q^{35} - 13385216 q^{36} - 6866080 q^{37} + 22760176 q^{38} + 4568410 q^{39} - 3723264 q^{40} + 3564107 q^{41} + 19632736 q^{42} + 19837521 q^{43} - 2003968 q^{44} - 77788260 q^{45} + 110379040 q^{46} + 60353825 q^{47} + 10813440 q^{48} - 79579650 q^{49} - 76756736 q^{50} - 161350373 q^{51} + 1644288 q^{52} + 54744235 q^{53} - 14990832 q^{54} + 143199990 q^{55} - 15122432 q^{56} + 330686241 q^{57} - 224083680 q^{58} + 164456585 q^{59} - 58295040 q^{60} + 49328881 q^{61} - 149332704 q^{62} + 138012360 q^{63} + 234881024 q^{64} + 788015550 q^{65} + 221242688 q^{66} - 171522309 q^{67} - 160597504 q^{68} + 630323350 q^{69} - 41358912 q^{70} - 74596055 q^{71} + 214163456 q^{72} + 58695287 q^{73} - 54928640 q^{74} - 1115757144 q^{75} + 73801472 q^{76} - 965186644 q^{77} + 36547280 q^{78} + 121854617 q^{79} + 59572224 q^{80} - 368486747 q^{81} - 57025712 q^{82} - 732607256 q^{83} + 628247552 q^{84} + 634697565 q^{85} - 317400336 q^{86} - 2979036210 q^{87} - 64126976 q^{88} - 1652463181 q^{89} - 622306080 q^{90} - 1141270092 q^{91} + 883032320 q^{92} - 1839612746 q^{93} + 1931322400 q^{94} + 2397253503 q^{95} + 346030080 q^{96} + 248805607 q^{97} - 636637200 q^{98} + 520684712 q^{99}+O(q^{100}) \) 14 * q + 112 * q^2 + 165 * q^3 - 1792 * q^4 + 909 * q^5 - 2640 * q^6 + 3692 * q^7 - 57344 * q^8 - 52286 * q^9 - 14544 * q^10 + 15656 * q^11 - 84480 * q^12 + 6423 * q^13 + 29536 * q^14 - 227715 * q^15 - 458752 * q^16 + 313667 * q^17 - 1673152 * q^18 + 1134224 * q^19 - 465408 * q^20 - 1227046 * q^21 + 125248 * q^22 + 3449345 * q^23 - 675840 * q^24 - 2398648 * q^25 + 205536 * q^26 - 1873854 * q^27 - 472576 * q^28 - 7002615 * q^29 - 7286880 * q^30 - 18666588 * q^31 + 7340032 * q^32 - 13827668 * q^33 - 5018672 * q^34 + 2584932 * q^35 - 13385216 * q^36 - 6866080 * q^37 + 22760176 * q^38 + 4568410 * q^39 - 3723264 * q^40 + 3564107 * q^41 + 19632736 * q^42 + 19837521 * q^43 - 2003968 * q^44 - 77788260 * q^45 + 110379040 * q^46 + 60353825 * q^47 + 10813440 * q^48 - 79579650 * q^49 - 76756736 * q^50 - 161350373 * q^51 + 1644288 * q^52 + 54744235 * q^53 - 14990832 * q^54 + 143199990 * q^55 - 15122432 * q^56 + 330686241 * q^57 - 224083680 * q^58 + 164456585 * q^59 - 58295040 * q^60 + 49328881 * q^61 - 149332704 * q^62 + 138012360 * q^63 + 234881024 * q^64 + 788015550 * q^65 + 221242688 * q^66 - 171522309 * q^67 - 160597504 * q^68 + 630323350 * q^69 - 41358912 * q^70 - 74596055 * q^71 + 214163456 * q^72 + 58695287 * q^73 - 54928640 * q^74 - 1115757144 * q^75 + 73801472 * q^76 - 965186644 * q^77 + 36547280 * q^78 + 121854617 * q^79 + 59572224 * q^80 - 368486747 * q^81 - 57025712 * q^82 - 732607256 * q^83 + 628247552 * q^84 + 634697565 * q^85 - 317400336 * q^86 - 2979036210 * q^87 - 64126976 * q^88 - 1652463181 * q^89 - 622306080 * q^90 - 1141270092 * q^91 + 883032320 * q^92 - 1839612746 * q^93 + 1931322400 * q^94 + 2397253503 * q^95 + 346030080 * q^96 + 248805607 * q^97 - 636637200 * q^98 + 520684712 * q^99

Introduction

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