LMFDB - Embedded newform 38.10.c.a.7.3

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			7.3
Root			$5.46583 + 9.46709i$ of defining polynomial
Character	$\chi$	$=$	38.7
Dual form			38.10.c.a.11.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.00000 + 13.8564i) q^{2} +(6.53417 + 11.3175i) q^{3} +(-128.000 + 221.703i) q^{4} +(80.6193 + 139.637i) q^{5} +(-104.547 + 181.080i) q^{6} -6270.17 q^{7} -4096.00 q^{8} +(9756.11 - 16898.1i) q^{9} +O(q^{10})$	\(q+(8.00000 + 13.8564i) q^{2} +(6.53417 + 11.3175i) q^{3} +(-128.000 + 221.703i) q^{4} +(80.6193 + 139.637i) q^{5} +(-104.547 + 181.080i) q^{6} -6270.17 q^{7} -4096.00 q^{8} +(9756.11 - 16898.1i) q^{9} +(-1289.91 + 2234.19i) q^{10} -21963.9 q^{11} -3345.50 q^{12} +(-11800.4 + 20438.8i) q^{13} +(-50161.3 - 86882.0i) q^{14} +(-1053.56 + 1824.82i) q^{15} +(-32768.0 - 56755.8i) q^{16} +(-182579. - 316237. i) q^{17} +312195. q^{18} +(-133057. - 552253. i) q^{19} -41277.1 q^{20} +(-40970.4 - 70962.8i) q^{21} +(-175711. - 304340. i) q^{22} +(-574353. + 994809. i) q^{23} +(-26764.0 - 46356.6i) q^{24} +(963564. - 1.66894e6i) q^{25} -377611. q^{26} +512217. q^{27} +(802581. - 1.39011e6i) q^{28} +(3.46848e6 - 6.00759e6i) q^{29} -33713.9 q^{30} -1.02684e6 q^{31} +(524288. - 908093. i) q^{32} +(-143516. - 248577. i) q^{33} +(2.92127e6 - 5.05979e6i) q^{34} +(-505496. - 875545. i) q^{35} +(2.49756e6 + 4.32591e6i) q^{36} -1.26888e7 q^{37} +(6.58778e6 - 6.26172e6i) q^{38} -308422. q^{39} +(-330216. - 571952. i) q^{40} +(-3.30315e6 - 5.72122e6i) q^{41} +(655526. - 1.13540e6i) q^{42} +(-6.69956e6 - 1.16040e7i) q^{43} +(2.81138e6 - 4.86945e6i) q^{44} +3.14612e6 q^{45} -1.83793e7 q^{46} +(-1.72445e7 + 2.98684e7i) q^{47} +(428224. - 741705. i) q^{48} -1.03860e6 q^{49} +3.08340e7 q^{50} +(2.38601e6 - 4.13269e6i) q^{51} +(-3.02089e6 - 5.23234e6i) q^{52} +(-4.48631e7 + 7.77052e7i) q^{53} +(4.09773e6 + 7.09748e6i) q^{54} +(-1.77071e6 - 3.06696e6i) q^{55} +2.56826e7 q^{56} +(5.38072e6 - 5.11440e6i) q^{57} +1.10991e8 q^{58} +(3.01418e7 + 5.22072e7i) q^{59} +(-269712. - 467154. i) q^{60} +(-8.01600e7 + 1.38841e8i) q^{61} +(-8.21473e6 - 1.42283e7i) q^{62} +(-6.11724e7 + 1.05954e8i) q^{63} +1.67772e7 q^{64} -3.80534e6 q^{65} +(2.29625e6 - 3.97723e6i) q^{66} +(-5.27741e6 + 9.14074e6i) q^{67} +9.34806e7 q^{68} -1.50117e7 q^{69} +(8.08794e6 - 1.40087e7i) q^{70} +(4.02609e7 + 6.97339e7i) q^{71} +(-3.99610e7 + 6.92145e7i) q^{72} +(6.50245e7 + 1.12626e8i) q^{73} +(-1.01510e8 - 1.75821e8i) q^{74} +2.51844e7 q^{75} +(1.39467e8 + 4.11892e7i) q^{76} +1.37717e8 q^{77} +(-2.46738e6 - 4.27363e6i) q^{78} +(-2.84005e8 - 4.91911e8i) q^{79} +(5.28346e6 - 9.15123e6i) q^{80} +(-1.88683e8 - 3.26808e8i) q^{81} +(5.28504e7 - 9.15396e7i) q^{82} -5.01933e8 q^{83} +2.09768e7 q^{84} +(2.94388e7 - 5.09895e7i) q^{85} +(1.07193e8 - 1.85664e8i) q^{86} +9.06547e7 q^{87} +8.99640e7 q^{88} +(2.35086e8 - 4.07181e8i) q^{89} +(2.51690e7 + 4.35939e7i) q^{90} +(7.39902e7 - 1.28155e8i) q^{91} +(-1.47034e8 - 2.54671e8i) q^{92} +(-6.70956e6 - 1.16213e7i) q^{93} -5.51825e8 q^{94} +(6.63878e7 - 6.31019e7i) q^{95} +1.37032e7 q^{96} +(-1.71841e8 - 2.97637e8i) q^{97} +(-8.30883e6 - 1.43913e7i) q^{98} +(-2.14282e8 + 3.71147e8i) 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 $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	8.00000	+	13.8564i	0.353553	+	0.612372i
$2$	8.00000	+	13.8564i	0.353553	+	0.612372i
$3$	6.53417	+	11.3175i	0.0465742	+	0.0806688i	0.888373	−	0.459123i	$-0.151836\pi$
$3$	6.53417	+	11.3175i	0.0465742	+	0.0806688i	−0.841799	+	0.539792i	$0.818503\pi$
$4$	−128.000	+	221.703i	−0.250000	+	0.433013i
$5$	80.6193	+	139.637i	0.0576864	+	0.0999159i	0.893426	−	0.449209i	$-0.148294\pi$
$5$	80.6193	+	139.637i	0.0576864	+	0.0999159i	−0.835740	+	0.549125i	$0.814961\pi$
$6$	−104.547	+	181.080i	−0.0329329	+	0.0570415i
$7$	−6270.17			−0.987047			−0.493524	−	0.869732i	$-0.664291\pi$
$7$	−6270.17			−0.987047			−0.493524	+	0.869732i	$0.664291\pi$
$8$	−4096.00			−0.353553
$9$	9756.11	−	16898.1i	0.495662	−	0.858511i
$10$	−1289.91	+	2234.19i	−0.0407905	+	0.0706512i
$11$	−21963.9			−0.452316			−0.226158	−	0.974091i	$-0.572617\pi$
$11$	−21963.9			−0.452316			−0.226158	+	0.974091i	$0.572617\pi$
$12$	−3345.50			−0.0465742
$13$	−11800.4	+	20438.8i	−0.114591	+	0.198477i	−0.917616	−	0.397468i	$-0.869889\pi$
$13$	−11800.4	+	20438.8i	−0.114591	+	0.198477i	0.803025	+	0.595945i	$0.203222\pi$
$14$	−50161.3	−	86882.0i	−0.348974	−	0.604441i
$15$	−1053.56	+	1824.82i	−0.00537340	+	0.00930699i
$16$	−32768.0	−	56755.8i	−0.125000	−	0.216506i
$17$	−182579.	−	316237.i	−0.530190	−	0.918316i	−0.999380	−	0.0352187i	$-0.988787\pi$
$17$	−182579.	−	316237.i	−0.530190	−	0.918316i	0.469190	−	0.883097i	$-0.344546\pi$
$18$	312195.			0.700971
$19$	−133057.	−	552253.i	−0.234233	−	0.972181i
$19$	−133057.	−	552253.i	−0.234233	−	0.972181i
$20$	−41277.1			−0.0576864
$21$	−40970.4	−	70962.8i	−0.0459709	−	0.0796239i
$22$	−175711.	−	304340.i	−0.159918	−	0.276986i
$23$	−574353.	+	994809.i	−0.427961	+	0.741250i	−0.996692	−	0.0812737i	$-0.974101\pi$
$23$	−574353.	+	994809.i	−0.427961	+	0.741250i	0.568731	+	0.822524i	$0.307435\pi$
$24$	−26764.0	−	46356.6i	−0.0164665	−	0.0285207i
$25$	963564.	−	1.66894e6i	0.493345	−	0.854498i
$26$	−377611.			−0.162056
$27$	512217.			0.185488
$28$	802581.	−	1.39011e6i	0.246762	−	0.427404i
$29$	3.46848e6	−	6.00759e6i	0.910644	−	1.57728i	0.0974863	−	0.995237i	$-0.468920\pi$
$29$	3.46848e6	−	6.00759e6i	0.910644	−	1.57728i	0.813157	−	0.582044i	$-0.197747\pi$
$30$	−33713.9			−0.00759913
$31$	−1.02684e6			−0.199699			−0.0998494	−	0.995003i	$-0.531836\pi$
$31$	−1.02684e6			−0.199699			−0.0998494	+	0.995003i	$0.531836\pi$
$32$	524288.	−	908093.i	0.0883883	−	0.153093i
$33$	−143516.	−	248577.i	−0.0210662	−	0.0364878i
$34$	2.92127e6	−	5.05979e6i	0.374901	−	0.649348i
$35$	−505496.	−	875545.i	−0.0569393	−	0.0986217i
$36$	2.49756e6	+	4.32591e6i	0.247831	+	0.429256i
$37$	−1.26888e7			−1.11304			−0.556522	−	0.830833i	$-0.687864\pi$
$37$	−1.26888e7			−1.11304			−0.556522	+	0.830833i	$0.687864\pi$
$38$	6.58778e6	−	6.26172e6i	0.512523	−	0.487155i
$39$	−308422.			−0.0213479
$40$	−330216.	−	571952.i	−0.0203952	−	0.0353256i
$41$	−3.30315e6	−	5.72122e6i	−0.182558	−	0.316200i	0.760193	−	0.649697i	$-0.225104\pi$
$41$	−3.30315e6	−	5.72122e6i	−0.182558	−	0.316200i	−0.942751	+	0.333498i	$0.891771\pi$
$42$	655526.	−	1.13540e6i	0.0325063	−	0.0563026i
$43$	−6.69956e6	−	1.16040e7i	−0.298840	−	0.517606i	0.677031	−	0.735954i	$-0.263266\pi$
$43$	−6.69956e6	−	1.16040e7i	−0.298840	−	0.517606i	−0.975871	+	0.218349i	$0.929933\pi$
$44$	2.81138e6	−	4.86945e6i	0.113079	−	0.195859i
$45$	3.14612e6			0.114372
$46$	−1.83793e7			−0.605228
$47$	−1.72445e7	+	2.98684e7i	−0.515479	+	0.892836i	0.484360	+	0.874869i	$0.339053\pi$
$47$	−1.72445e7	+	2.98684e7i	−0.515479	+	0.892836i	−0.999839	+	0.0179669i	$0.994281\pi$
$48$	428224.	−	741705.i	0.0116435	−	0.0201672i
$49$	−1.03860e6			−0.0257376
$50$	3.08340e7			0.697695
$51$	2.38601e6	−	4.13269e6i	0.0493863	−	0.0855396i
$52$	−3.02089e6	−	5.23234e6i	−0.0572955	−	0.0992386i
$53$	−4.48631e7	+	7.77052e7i	−0.780995	+	1.35272i	0.150368	+	0.988630i	$0.451954\pi$
$53$	−4.48631e7	+	7.77052e7i	−0.780995	+	1.35272i	−0.931363	+	0.364093i	$0.881379\pi$
$54$	4.09773e6	+	7.09748e6i	0.0655801	+	0.113588i
$55$	−1.77071e6	−	3.06696e6i	−0.0260925	−	0.0451935i
$56$	2.56826e7			0.348974
$57$	5.38072e6	−	5.11440e6i	0.0675155	−	0.0641738i
$58$	1.10991e8			1.28784
$59$	3.01418e7	+	5.22072e7i	0.323844	+	0.560914i	0.981278	−	0.192598i	$-0.0616914\pi$
$59$	3.01418e7	+	5.22072e7i	0.323844	+	0.560914i	−0.657434	+	0.753512i	$0.728358\pi$
$60$	−269712.	−	467154.i	−0.00268670	−	0.00465350i
$61$	−8.01600e7	+	1.38841e8i	−0.741265	+	1.28391i	0.210655	+	0.977561i	$0.432440\pi$
$61$	−8.01600e7	+	1.38841e8i	−0.741265	+	1.28391i	−0.951920	+	0.306348i	$0.900893\pi$
$62$	−8.21473e6	−	1.42283e7i	−0.0706042	−	0.122290i
$63$	−6.11724e7	+	1.05954e8i	−0.489242	+	0.847391i
$64$	1.67772e7			0.125000
$65$	−3.80534e6			−0.0264414
$66$	2.29625e6	−	3.97723e6i	0.0148961	−	0.0258008i
$67$	−5.27741e6	+	9.14074e6i	−0.0319951	+	0.0554172i	−0.881580	−	0.472035i	$-0.843519\pi$
$67$	−5.27741e6	+	9.14074e6i	−0.0319951	+	0.0554172i	0.849584	+	0.527453i	$0.176853\pi$
$68$	9.34806e7			0.530190
$69$	−1.50117e7			−0.0797277
$70$	8.08794e6	−	1.40087e7i	0.0402621	−	0.0697361i
$71$	4.02609e7	+	6.97339e7i	0.188027	+	0.325673i	0.944592	−	0.328245i	$-0.106457\pi$
$71$	4.02609e7	+	6.97339e7i	0.188027	+	0.325673i	−0.756565	+	0.653918i	$0.773124\pi$
$72$	−3.99610e7	+	6.92145e7i	−0.175243	+	0.303530i
$73$	6.50245e7	+	1.12626e8i	0.267994	+	0.464178i	0.968344	−	0.249621i	$-0.0803061\pi$
$73$	6.50245e7	+	1.12626e8i	0.267994	+	0.464178i	−0.700350	+	0.713800i	$0.746973\pi$
$74$	−1.01510e8	−	1.75821e8i	−0.393520	−	0.681597i
$75$	2.51844e7			0.0919084
$76$	1.39467e8	+	4.11892e7i	0.479525	+	0.141619i
$77$	1.37717e8			0.446457
$78$	−2.46738e6	−	4.27363e6i	−0.00754762	−	0.0130729i
$79$	−2.84005e8	−	4.91911e8i	−0.820359	−	1.42090i	−0.905415	−	0.424528i	$-0.860440\pi$
$79$	−2.84005e8	−	4.91911e8i	−0.820359	−	1.42090i	0.0850553	−	0.996376i	$-0.472893\pi$
$80$	5.28346e6	−	9.15123e6i	0.0144216	−	0.0249790i
$81$	−1.88683e8	−	3.26808e8i	−0.487023	−	0.843548i
$82$	5.28504e7	−	9.15396e7i	0.129088	−	0.223587i
$83$	−5.01933e8			−1.16090			−0.580449	−	0.814296i	$-0.697123\pi$
$83$	−5.01933e8			−1.16090			−0.580449	+	0.814296i	$0.697123\pi$
$84$	2.09768e7			0.0459709
$85$	2.94388e7	−	5.09895e7i	0.0611696	−	0.105949i
$86$	1.07193e8	−	1.85664e8i	0.211312	−	0.366002i
$87$	9.06547e7			0.169650
$88$	8.99640e7			0.159918
$89$	2.35086e8	−	4.07181e8i	0.397165	−	0.687911i	−0.596210	−	0.802829i	$-0.703327\pi$
$89$	2.35086e8	−	4.07181e8i	0.397165	−	0.687911i	0.993375	+	0.114918i	$0.0366606\pi$
$90$	2.51690e7	+	4.35939e7i	0.0404366	+	0.0700382i
$91$	7.39902e7	−	1.28155e8i	0.113107	−	0.195906i
$92$	−1.47034e8	−	2.54671e8i	−0.213980	−	0.370625i
$93$	−6.70956e6	−	1.16213e7i	−0.00930081	−	0.0161095i
$94$	−5.51825e8			−0.728997
$95$	6.63878e7	−	6.31019e7i	0.0836242	−	0.0794852i
$96$	1.37032e7			0.0164665
$97$	−1.71841e8	−	2.97637e8i	−0.197085	−	0.341362i	0.750497	−	0.660874i	$-0.229814\pi$
$97$	−1.71841e8	−	2.97637e8i	−0.197085	−	0.341362i	−0.947582	+	0.319512i	$0.896481\pi$
$98$	−8.30883e6	−	1.43913e7i	−0.00909961	−	0.0157610i
$99$	−2.14282e8	+	3.71147e8i	−0.224196	+	0.388318i
$100$	2.46672e8	+	4.27249e8i	0.246672	+	0.427249i
$101$	2.76782e8	−	4.79401e8i	0.264662	−	0.458408i	−0.702813	−	0.711375i	$-0.748073\pi$
$101$	2.76782e8	−	4.79401e8i	0.264662	−	0.458408i	0.967475	+	0.252966i	$0.0814062\pi$
$102$	7.63524e7			0.0698428
$103$	1.75523e9			1.53662			0.768310	−	0.640078i	$-0.221098\pi$
$103$	1.75523e9			1.53662			0.768310	+	0.640078i	$0.221098\pi$
$104$	4.83343e7	−	8.37174e7i	0.0405140	−	0.0701723i
$105$	6.60600e6	−	1.14419e7i	0.00530380	−	0.00918644i
$106$	−1.43562e9			−1.10449
$107$	6.94322e8			0.512075			0.256038	−	0.966667i	$-0.417583\pi$
$107$	6.94322e8			0.512075			0.256038	+	0.966667i	$0.417583\pi$
$108$	−6.55637e7	+	1.13560e8i	−0.0463721	+	0.0803189i
$109$	−1.86736e6	−	3.23437e6i	−0.00126710	−	0.00219467i	0.865391	−	0.501097i	$-0.167070\pi$
$109$	−1.86736e6	−	3.23437e6i	−0.00126710	−	0.00219467i	−0.866658	+	0.498902i	$0.833737\pi$
$110$	2.83314e7	−	4.90714e7i	0.0184502	−	0.0319567i
$111$	−8.29107e7	−	1.43606e8i	−0.0518391	−	0.0897879i
$112$	2.05461e8	+	3.55869e8i	0.123381	+	0.213702i
$113$	1.03662e9			0.598088			0.299044	−	0.954239i	$-0.403332\pi$
$113$	1.03662e9			0.598088			0.299044	+	0.954239i	$0.403332\pi$
$114$	1.13913e8	+	3.36422e7i	0.0631686	+	0.0186557i
$115$	−1.85216e8			−0.0987501
$116$	8.87931e8	+	1.53794e9i	0.455322	+	0.788640i
$117$	2.30251e8	+	3.98807e8i	0.113597	+	0.196755i
$118$	−4.82269e8	+	8.35315e8i	−0.228992	+	0.396626i
$119$	1.14480e9	+	1.98286e9i	0.523323	+	0.906422i
$120$	4.31538e6	−	7.47446e6i	0.00189978	−	0.00329052i
$121$	−1.87554e9			−0.795410
$122$	−2.56512e9			−1.04831
$123$	4.31667e7	−	7.47669e7i	0.0170050	−	0.0294535i
$124$	1.31436e8	−	2.27653e8i	0.0499247	−	0.0864722i
$125$	6.25646e8			0.229210
$126$	−1.95752e9			−0.691892
$127$	−1.65565e9	+	2.86767e9i	−0.564744	+	0.978166i	0.432329	+	0.901716i	$0.357692\pi$
$127$	−1.65565e9	+	2.86767e9i	−0.564744	+	0.978166i	−0.997073	+	0.0764500i	$0.975641\pi$
$128$	1.34218e8	+	2.32472e8i	0.0441942	+	0.0765466i
$129$	8.75522e7	−	1.51645e8i	0.0278364	−	0.0482141i
$130$	−3.04428e7	−	5.27284e7i	−0.00934843	−	0.0161920i
$131$	−1.43524e9	−	2.48591e9i	−0.425798	−	0.737504i	0.570696	−	0.821161i	$-0.306673\pi$
$131$	−1.43524e9	−	2.48591e9i	−0.425798	−	0.737504i	−0.996495	+	0.0836571i	$0.973340\pi$
$132$	7.34801e7			0.0210662
$133$	8.34292e8	+	3.46272e9i	0.231199	+	0.959588i
$134$	−1.68877e8			−0.0452480
$135$	4.12945e7	+	7.15242e7i	0.0107002	+	0.0185332i
$136$	7.47845e8	+	1.29531e9i	0.187451	+	0.324674i
$137$	3.00081e9	−	5.19755e9i	0.727772	−	1.26054i	−0.230051	−	0.973179i	$-0.573889\pi$
$137$	3.00081e9	−	5.19755e9i	0.727772	−	1.26054i	0.957823	−	0.287360i	$-0.0927775\pi$
$138$	−1.20094e8	−	2.08008e8i	−0.0281880	−	0.0488230i
$139$	−1.05774e9	+	1.83205e9i	−0.240331	+	0.416266i	−0.960809	−	0.277212i	$-0.910589\pi$
$139$	−1.05774e9	+	1.83205e9i	−0.240331	+	0.416266i	0.720477	+	0.693479i	$0.243923\pi$
$140$	2.58814e8			0.0569393
$141$	−4.50715e8			−0.0960320
$142$	−6.44174e8	+	1.11574e9i	−0.132955	+	0.230285i
$143$	2.59182e8	−	4.48916e8i	0.0518313	−	0.0897744i
$144$	−1.27875e9			−0.247831
$145$	1.11851e9			0.210127
$146$	−1.04039e9	+	1.80201e9i	−0.189500	+	0.328224i
$147$	−6.78642e6	−	1.17544e7i	−0.00119871	−	0.00207622i
$148$	1.62416e9	−	2.81313e9i	0.278261	−	0.481962i
$149$	1.08425e9	+	1.87797e9i	0.180215	+	0.312141i	0.941954	−	0.335743i	$-0.108987\pi$
$149$	1.08425e9	+	1.87797e9i	0.180215	+	0.312141i	−0.761739	+	0.647884i	$0.775654\pi$
$150$	2.01475e8	+	3.48965e8i	0.0324945	+	0.0562822i
$151$	8.29447e9			1.29835			0.649176	−	0.760638i	$-0.275114\pi$
$151$	8.29447e9			1.29835			0.649176	+	0.760638i	$0.275114\pi$
$152$	5.45003e8	+	2.26203e9i	0.0828138	+	0.343718i
$153$	−7.12506e9			−1.05118
$154$	1.10174e9	+	1.90827e9i	0.157846	+	0.273398i
$155$	−8.27832e7	−	1.43385e8i	−0.0115199	−	0.0199531i
$156$	3.94781e7	−	6.83780e7i	0.00533698	−	0.00924391i
$157$	−3.14377e9	−	5.44517e9i	−0.412955	−	0.715259i	0.582257	−	0.813005i	$-0.302170\pi$
$157$	−3.14377e9	−	5.44517e9i	−0.412955	−	0.715259i	−0.995211	+	0.0977464i	$0.968837\pi$
$158$	4.54408e9	−	7.87058e9i	0.580082	−	1.00473i
$159$	−1.17257e9			−0.145497
$160$	1.69071e8			0.0203952
$161$	3.60129e9	−	6.23762e9i	0.422418	−	0.731649i
$162$	3.01892e9	−	5.22893e9i	0.344377	−	0.596479i
$163$	1.29598e9			0.143798			0.0718990	−	0.997412i	$-0.477094\pi$
$163$	1.29598e9			0.143798			0.0718990	+	0.997412i	$0.477094\pi$
$164$	1.69121e9			0.182558
$165$	2.31403e7	−	4.00801e7i	0.00243047	−	0.00420970i
$166$	−4.01546e9	−	6.95499e9i	−0.410440	−	0.710902i
$167$	−1.95461e9	+	3.38549e9i	−0.194463	+	0.336819i	−0.946724	−	0.322045i	$-0.895630\pi$
$167$	−1.95461e9	+	3.38549e9i	−0.194463	+	0.336819i	0.752262	+	0.658865i	$0.228963\pi$
$168$	1.67815e8	+	2.90663e8i	0.0162532	+	0.0281513i
$169$	5.02375e9	+	8.70139e9i	0.473738	+	0.820538i
$170$	9.42043e8			0.0865068
$171$	−1.06301e10	−	3.13943e9i	−0.950728	−	0.280781i
$172$	3.43018e9			0.298840
$173$	−1.06829e10	−	1.85033e10i	−0.906736	−	1.57051i	−0.818570	−	0.574407i	$-0.805233\pi$
$173$	−1.06829e10	−	1.85033e10i	−0.906736	−	1.57051i	−0.0881663	−	0.996106i	$-0.528101\pi$
$174$	7.25237e8	+	1.25615e9i	0.0599803	+	0.103889i
$175$	−6.04171e9	+	1.04645e10i	−0.486954	+	0.843430i
$176$	7.19712e8	+	1.24658e9i	0.0565395	+	0.0979293i
$177$	−3.93904e8	+	6.82262e8i	−0.0301655	+	0.0522482i
$178$	7.52275e9			0.561677
$179$	−4.75636e9			−0.346287			−0.173143	−	0.984897i	$-0.555392\pi$
$179$	−4.75636e9			−0.346287			−0.173143	+	0.984897i	$0.555392\pi$
$180$	−4.02703e8	+	6.97503e8i	−0.0285930	+	0.0495245i
$181$	5.74786e9	−	9.95559e9i	0.398064	−	0.689467i	−0.595423	−	0.803412i	$-0.703016\pi$
$181$	5.74786e9	−	9.95559e9i	0.398064	−	0.689467i	0.993487	+	0.113946i	$0.0363490\pi$
$182$	2.36769e9			0.159957
$183$	−2.09512e9			−0.138095
$184$	2.35255e9	−	4.07474e9i	0.151307	−	0.262071i
$185$	−1.02296e9	−	1.77182e9i	−0.0642075	−	0.111211i
$186$	1.07353e8	−	1.85941e8i	0.00657666	−	0.0113911i
$187$	4.01015e9	+	6.94579e9i	0.239813	+	0.415369i
$188$	−4.41460e9	−	7.64631e9i	−0.257740	−	0.446418i
$189$	−3.21169e9			−0.183086
$190$	1.40547e9	+	4.15081e8i	0.0782402	+	0.0231069i
$191$	1.45169e10			0.789266			0.394633	−	0.918839i	$-0.370872\pi$
$191$	1.45169e10			0.789266			0.394633	+	0.918839i	$0.370872\pi$
$192$	1.09625e8	+	1.89877e8i	0.00582177	+	0.0100836i
$193$	−5.48689e9	−	9.50357e9i	−0.284655	−	0.493036i	0.687871	−	0.725833i	$-0.258546\pi$
$193$	−5.48689e9	−	9.50357e9i	−0.284655	−	0.493036i	−0.972525	+	0.232797i	$0.925212\pi$
$194$	2.74946e9	−	4.76220e9i	0.139360	−	0.241379i
$195$	−2.48648e7	−	4.30671e7i	−0.00123148	−	0.00213299i
$196$	1.32941e8	−	2.30261e8i	0.00643439	−	0.0111447i
$197$	−1.85122e10			−0.875709			−0.437855	−	0.899046i	$-0.644262\pi$
$197$	−1.85122e10			−0.875709			−0.437855	+	0.899046i	$0.644262\pi$
$198$	−6.85702e9			−0.317061
$199$	−7.03021e9	+	1.21767e10i	−0.317782	+	0.550415i	−0.980025	−	0.198875i	$-0.936271\pi$
$199$	−7.03021e9	+	1.21767e10i	−0.317782	+	0.550415i	0.662243	+	0.749289i	$0.269605\pi$
$200$	−3.94676e9	+	6.83598e9i	−0.174424	+	0.302111i
$201$	−1.37934e8			−0.00596059
$202$	8.85703e9			0.374289
$203$	−2.17480e10	+	3.76686e10i	−0.898848	+	1.55685i
$204$	6.10819e8	+	1.05797e9i	0.0246932	+	0.0427698i
$205$	5.32595e8	−	9.22481e8i	0.0210622	−	0.0364809i
$206$	1.40418e10	+	2.43212e10i	0.543277	+	0.940983i
$207$	1.12069e10	+	1.94109e10i	0.424248	+	0.734818i
$208$	1.54670e9			0.0572955
$209$	2.92246e9	+	1.21296e10i	0.105947	+	0.439733i
$210$	2.11392e8			0.00750070
$211$	1.59866e10	+	2.76896e10i	0.555245	+	0.961713i	0.997884	+	0.0650134i	$0.0207090\pi$
$211$	1.59866e10	+	2.76896e10i	0.555245	+	0.961713i	−0.442639	+	0.896700i	$0.645958\pi$
$212$	−1.14850e10	−	1.98925e10i	−0.390497	−	0.676361i
$213$	−5.26143e8	+	9.11307e8i	−0.0175144	+	0.0303359i
$214$	5.55457e9	+	9.62081e9i	0.181046	+	0.313581i
$215$	1.08023e9	−	1.87101e9i	0.0344780	−	0.0597177i
$216$	−2.09804e9			−0.0655801
$217$	6.43847e9			0.197112
$218$	2.98778e7	−	5.17499e7i	0.000895972	−	0.00155187i
$219$	−8.49763e8	+	1.47183e9i	−0.0249631	+	0.0432374i
$220$	9.06604e8			0.0260925
$221$	8.61801e9			0.243020
$222$	1.32657e9	−	2.29769e9i	0.0366558	−	0.0634896i
$223$	5.35679e8	+	9.27823e8i	0.0145055	+	0.0251242i	0.873187	−	0.487385i	$-0.162049\pi$
$223$	5.35679e8	+	9.27823e8i	0.0145055	+	0.0251242i	−0.858682	+	0.512510i	$0.828716\pi$
$224$	−3.28737e9	+	5.69390e9i	−0.0872435	+	0.151110i
$225$	−1.88013e10	−	3.25647e10i	−0.489064	−	0.847084i
$226$	8.29294e9	+	1.43638e10i	0.211456	+	0.366253i
$227$	9.94403e9			0.248568			0.124284	−	0.992247i	$-0.460337\pi$
$227$	9.94403e9			0.248568			0.124284	+	0.992247i	$0.460337\pi$
$228$	4.45143e8	+	1.84756e9i	0.0109092	+	0.0452785i
$229$	7.37201e10			1.77144			0.885719	−	0.464222i	$-0.153666\pi$
$229$	7.37201e10			1.77144			0.885719	+	0.464222i	$0.153666\pi$
$230$	−1.48173e9	−	2.56643e9i	−0.0349134	−	0.0604719i
$231$	8.99868e8	+	1.55862e9i	0.0207934	+	0.0360152i
$232$	−1.42069e10	+	2.46071e10i	−0.321961	+	0.557653i
$233$	−6.29987e8	−	1.09117e9i	−0.0140033	−	0.0242544i	0.858939	−	0.512078i	$-0.171124\pi$
$233$	−6.29987e8	−	1.09117e9i	−0.0140033	−	0.0242544i	−0.872942	+	0.487824i	$0.837791\pi$
$234$	−3.68402e9	+	6.38091e9i	−0.0803250	+	0.139127i
$235$	−5.56096e9			−0.118945
$236$	−1.54326e10			−0.323844
$237$	3.71148e9	−	6.42847e9i	0.0764151	−	0.132355i
$238$	−1.83169e10	+	3.17257e10i	−0.370045	+	0.640937i
$239$	−5.32484e10			−1.05564			−0.527820	−	0.849356i	$-0.676991\pi$
$239$	−5.32484e10			−1.05564			−0.527820	+	0.849356i	$0.676991\pi$
$240$	1.38092e8			0.00268670
$241$	2.54400e10	−	4.40633e10i	0.485780	−	0.841396i	−0.514086	−	0.857738i	$-0.671869\pi$
$241$	2.54400e10	−	4.40633e10i	0.485780	−	0.841396i	0.999866	+	0.0163427i	$0.00520229\pi$
$242$	−1.50043e10	−	2.59882e10i	−0.281220	−	0.487087i
$243$	7.50675e9	−	1.30021e10i	0.138110	−	0.239213i
$244$	−2.05210e10	−	3.55433e10i	−0.370632	−	0.641954i
$245$	−8.37315e7	−	1.45027e8i	−0.00148471	−	0.00257159i
$246$	1.38133e9			0.0240487
$247$	1.28575e10	+	3.79725e9i	0.219797	+	0.0649131i
$248$	4.20594e9			0.0706042
$249$	−3.27972e9	−	5.68064e9i	−0.0540679	−	0.0936483i
$250$	5.00517e9	+	8.66921e9i	0.0810380	+	0.140362i
$251$	8.97581e9	−	1.55466e10i	0.142739	−	0.247231i	−0.785788	−	0.618496i	$-0.787742\pi$
$251$	8.97581e9	−	1.55466e10i	0.142739	−	0.247231i	0.928527	+	0.371265i	$0.121076\pi$
$252$	−1.56601e10	−	2.71242e10i	−0.244621	−	0.423696i
$253$	1.26150e10	−	2.18499e10i	0.193574	−	0.335279i
$254$	−5.29808e10			−0.798669
$255$	7.69434e8			0.0113957
$256$	−2.14748e9	+	3.71955e9i	−0.0312500	+	0.0541266i
$257$	−6.19226e9	+	1.07253e10i	−0.0885422	+	0.153360i	−0.906895	−	0.421356i	$-0.861554\pi$
$257$	−6.19226e9	+	1.07253e10i	−0.0885422	+	0.153360i	0.818353	+	0.574716i	$0.194887\pi$
$258$	2.80167e9			0.0393666
$259$	7.95608e10			1.09863
$260$	4.87084e8	−	8.43654e8i	0.00661034	−	0.0114494i
$261$	−6.76778e10	−	1.17221e11i	−0.902742	−	1.56360i
$262$	2.29638e10	−	3.97745e10i	0.301085	−	0.521494i
$263$	−4.61295e10	−	7.98987e10i	−0.594536	−	1.02977i	−0.993612	−	0.112849i	$-0.964002\pi$
$263$	−4.61295e10	−	7.98987e10i	−0.594536	−	1.02977i	0.399076	−	0.916918i	$-0.369331\pi$
$264$	5.87841e8	+	1.01817e9i	0.00744804	+	0.0129004i
$265$	−1.44673e10			−0.180211
$266$	−4.13065e10	+	3.92620e10i	−0.505884	+	0.480846i
$267$	6.14437e9			0.0739906
$268$	−1.35102e9	−	2.34003e9i	−0.0159976	−	0.0277086i
$269$	−5.77223e10	−	9.99780e10i	−0.672138	−	1.16418i	−0.977297	−	0.211876i	$-0.932043\pi$
$269$	−5.77223e10	−	9.99780e10i	−0.672138	−	1.16418i	0.305158	−	0.952302i	$-0.401291\pi$
$270$	−6.60713e8	+	1.14439e9i	−0.00756616	+	0.0131050i
$271$	3.85149e10	+	6.67098e10i	0.433777	+	0.751325i	0.997195	−	0.0748477i	$-0.0238471\pi$
$271$	3.85149e10	+	6.67098e10i	0.433777	+	0.751325i	−0.563418	+	0.826172i	$0.690514\pi$
$272$	−1.19655e10	+	2.07249e10i	−0.132548	+	0.229579i
$273$	1.93386e9			0.0210714
$274$	9.60258e10			1.02923
$275$	−2.11636e10	+	3.66564e10i	−0.223148	+	0.386503i
$276$	1.92150e9	−	3.32813e9i	0.0199319	−	0.0345231i
$277$	1.11798e11			1.14098			0.570489	−	0.821306i	$-0.306754\pi$
$277$	1.11798e11			1.14098			0.570489	+	0.821306i	$0.306754\pi$
$278$	−3.38475e10			−0.339880
$279$	−1.00180e10	+	1.73516e10i	−0.0989831	+	0.171444i
$280$	2.07051e9	+	3.58623e9i	0.0201311	+	0.0348680i
$281$	6.52202e10	−	1.12965e11i	0.624028	−	1.08085i	−0.364700	−	0.931125i	$-0.618829\pi$
$281$	6.52202e10	−	1.12965e11i	0.624028	−	1.08085i	0.988728	−	0.149723i	$-0.0478381\pi$
$282$	−3.60572e9	−	6.24529e9i	−0.0339524	−	0.0588074i
$283$	8.77358e10	+	1.51963e11i	0.813089	+	1.40831i	0.910692	+	0.413086i	$0.135549\pi$
$283$	8.77358e10	+	1.51963e11i	0.813089	+	1.40831i	−0.0976034	+	0.995225i	$0.531118\pi$
$284$	−2.06136e10			−0.188027
$285$	1.14795e9	+	3.39026e8i	0.0103067	+	0.00304391i
$286$	8.29381e9			0.0733005
$287$	2.07113e10	+	3.58730e10i	0.180193	+	0.312104i
$288$	−1.02300e10	−	1.77189e10i	−0.0876214	−	0.151765i
$289$	−7.37653e9	+	1.27765e10i	−0.0622031	+	0.107739i
$290$	8.94805e9	+	1.54985e10i	0.0742912	+	0.128676i
$291$	2.24568e9	−	3.88963e9i	0.0183582	−	0.0317973i
$292$	−3.32926e10			−0.267994
$293$	−8.57908e10			−0.680043			−0.340022	−	0.940418i	$-0.610434\pi$
$293$	−8.57908e10			−0.680043			−0.340022	+	0.940418i	$0.610434\pi$
$294$	1.08583e8	−	1.88071e8i	0.000847613	−	0.00146811i
$295$	−4.86003e9	+	8.41781e9i	−0.0373628	+	0.0647143i
$296$	5.19733e10			0.393520
$297$	−1.12503e10			−0.0838994
$298$	−1.73480e10	+	3.00475e10i	−0.127431	+	0.220717i
$299$	−1.35552e10	−	2.34782e10i	−0.0980808	−	0.169881i
$300$	−3.22360e9	+	5.58344e9i	−0.0229771	+	0.0397975i
$301$	4.20074e10	+	7.27589e10i	0.294969	+	0.510901i
$302$	6.63557e10	+	1.14932e11i	0.459037	+	0.795075i
$303$	7.23417e9			0.0493057
$304$	−2.69836e10	+	2.56480e10i	−0.181204	+	0.172235i
$305$	−2.58498e10			−0.171044
$306$	−5.70005e10	−	9.87277e10i	−0.371648	−	0.643713i
$307$	9.25088e10	+	1.60230e11i	0.594375	+	1.02949i	0.993635	+	0.112649i	$0.0359337\pi$
$307$	9.25088e10	+	1.60230e11i	0.594375	+	1.02949i	−0.399260	+	0.916838i	$0.630733\pi$
$308$	−1.76278e10	+	3.05322e10i	−0.111614	+	0.193322i
$309$	1.14690e10	+	1.98648e10i	0.0715668	+	0.123957i
$310$	1.32453e9	−	2.29415e9i	0.00814581	−	0.0141090i
$311$	−1.84075e11			−1.11576			−0.557882	−	0.829921i	$-0.688386\pi$
$311$	−1.84075e11			−1.11576			−0.557882	+	0.829921i	$0.688386\pi$
$312$	1.26330e9			0.00754762
$313$	−3.16616e10	+	5.48395e10i	−0.186459	+	0.322957i	−0.944067	−	0.329753i	$-0.893035\pi$
$313$	−3.16616e10	+	5.48395e10i	−0.186459	+	0.322957i	0.757608	+	0.652710i	$0.226368\pi$
$314$	5.03003e10	−	8.71228e10i	0.292003	−	0.505764i
$315$	−1.97267e10			−0.112890
$316$	1.45411e11			0.820359
$317$	−7.60787e10	+	1.31772e11i	−0.423152	+	0.732921i	−0.996246	−	0.0865691i	$-0.972410\pi$
$317$	−7.60787e10	+	1.31772e11i	−0.423152	+	0.732921i	0.573094	+	0.819490i	$0.305743\pi$
$318$	−9.38059e9	−	1.62477e10i	−0.0514409	−	0.0890982i
$319$	−7.61813e10	+	1.31950e11i	−0.411899	+	0.713429i
$320$	1.35257e9	+	2.34271e9i	0.00721081	+	0.0124895i
$321$	4.53682e9	+	7.85800e9i	0.0238495	+	0.0413085i
$322$	1.15241e11			0.597389
$323$	−1.50349e11	+	1.42908e11i	−0.768581	+	0.730540i
$324$	9.66055e10			0.487023
$325$	2.27408e10	+	3.93882e10i	0.113066	+	0.195835i
$326$	1.03678e10	+	1.79576e10i	0.0508403	+	0.0880579i
$327$	2.44033e7	−	4.22678e7i	0.000118028	−	0.000204430i
$328$	1.35297e10	+	2.34341e10i	0.0645440	+	0.111793i
$329$	1.08126e11	−	1.87280e11i	0.508802	−	0.881271i
$330$	7.40489e8			0.00343721
$331$	−2.16904e11			−0.993210			−0.496605	−	0.867977i	$-0.665420\pi$
$331$	−2.16904e11			−0.993210			−0.496605	+	0.867977i	$0.665420\pi$
$332$	6.42474e10	−	1.11280e11i	0.290225	−	0.502684i
$333$	−1.23793e11	+	2.14416e11i	−0.551693	+	0.955560i
$334$	−6.25476e10			−0.275012
$335$	−1.70184e9			−0.00738275
$336$	−2.68503e9	+	4.65062e9i	−0.0114927	+	0.0199060i
$337$	−1.81389e11	−	3.14174e11i	−0.766082	−	1.32689i	−0.939672	−	0.342076i	$-0.888870\pi$
$337$	−1.81389e11	−	3.14174e11i	−0.766082	−	1.32689i	0.173590	−	0.984818i	$-0.444463\pi$
$338$	−8.03800e10	+	1.39222e11i	−0.334983	+	0.580208i
$339$	6.77344e9	+	1.17319e10i	0.0278555	+	0.0482471i
$340$	7.53634e9	+	1.30533e10i	0.0305848	+	0.0529744i
$341$	2.25534e10			0.0903270
$342$	−4.15399e10	−	1.72411e11i	−0.164191	−	0.681471i
$343$	2.59536e11			1.01245
$344$	2.74414e10	+	4.75299e10i	0.105656	+	0.183001i
$345$	−1.21023e9	−	2.09618e9i	−0.00459921	−	0.00796606i
$346$	1.70926e11	−	2.96053e11i	0.641159	−	1.11052i
$347$	−1.19879e11	−	2.07636e11i	−0.443874	−	0.768812i	0.554099	−	0.832451i	$-0.313063\pi$
$347$	−1.19879e11	−	2.07636e11i	−0.443874	−	0.768812i	−0.997973	+	0.0636385i	$0.979730\pi$
$348$	−1.16038e10	+	2.00984e10i	−0.0424125	+	0.0734605i
$349$	1.25323e11			0.452186			0.226093	−	0.974106i	$-0.427405\pi$
$349$	1.25323e11			0.452186			0.226093	+	0.974106i	$0.427405\pi$
$350$	−1.93335e11			−0.688658
$351$	−6.04434e9	+	1.04691e10i	−0.0212553	+	0.0368152i
$352$	−1.15154e10	+	1.99453e10i	−0.0399795	+	0.0692465i
$353$	1.78581e11			0.612137			0.306068	−	0.952010i	$-0.400986\pi$
$353$	1.78581e11			0.612137			0.306068	+	0.952010i	$0.400986\pi$
$354$	−1.26049e10			−0.0426605
$355$	−6.49161e9	+	1.12438e10i	−0.0216933	+	0.0375738i
$356$	6.01820e10	+	1.04238e11i	0.198583	+	0.343955i
$357$	−1.49607e10	+	2.59127e10i	−0.0487466	+	0.0844317i
$358$	−3.80509e10	−	6.59061e10i	−0.122431	−	0.212057i
$359$	1.31869e11	+	2.28404e11i	0.419004	+	0.725736i	0.995840	−	0.0911240i	$-0.0290460\pi$
$359$	1.31869e11	+	2.28404e11i	0.419004	+	0.725736i	−0.576835	+	0.816860i	$0.695713\pi$
$360$	−1.28865e10			−0.0404366
$361$	−2.87279e11	+	1.46963e11i	−0.890270	+	0.455433i
$362$	1.83932e11			0.562947
$363$	−1.22551e10	−	2.12264e10i	−0.0370456	−	0.0641648i
$364$	1.89415e10	+	3.28076e10i	0.0565533	+	0.0979532i
$365$	−1.04845e10	+	1.81596e10i	−0.0309192	+	0.0535536i
$366$	−1.67609e10	−	2.90308e10i	−0.0488240	−	0.0845657i
$367$	1.27150e11	−	2.20229e11i	0.365862	−	0.633692i	−0.623052	−	0.782180i	$-0.714108\pi$
$367$	1.27150e11	−	2.20229e11i	0.365862	−	0.633692i	0.988914	+	0.148489i	$0.0474408\pi$
$368$	7.52817e10			0.213980
$369$	−1.28904e11			−0.361948
$370$	1.63674e10	−	2.83491e10i	0.0454016	−	0.0786378i
$371$	2.81299e11	−	4.87225e11i	0.770879	−	1.33520i
$372$	3.43529e9			0.00930081
$373$	−3.78573e9			−0.0101265			−0.00506326	−	0.999987i	$-0.501612\pi$
$373$	−3.78573e9			−0.0101265			−0.00506326	+	0.999987i	$0.501612\pi$
$374$	−6.41624e10	+	1.11133e11i	−0.169574	+	0.293710i
$375$	4.08808e9	+	7.08076e9i	0.0106753	+	0.0184901i
$376$	7.06336e10	−	1.22341e11i	0.182249	−	0.315665i
$377$	8.18587e10	+	1.41783e11i	0.208703	+	0.361484i
$378$	−2.56935e10	−	4.45024e10i	−0.0647306	−	0.112117i
$379$	−1.02265e11			−0.254597			−0.127298	−	0.991864i	$-0.540631\pi$
$379$	−1.02265e11			−0.254597			−0.127298	+	0.991864i	$0.540631\pi$
$380$	5.49222e9	+	2.27954e10i	0.0135121	+	0.0560816i
$381$	−4.32732e10			−0.105210
$382$	1.16135e11	+	2.01152e11i	0.279048	+	0.483325i
$383$	−3.36447e11	−	5.82744e11i	−0.798956	−	1.38383i	−0.920297	−	0.391221i	$-0.872053\pi$
$383$	−3.36447e11	−	5.82744e11i	−0.798956	−	1.38383i	0.121341	−	0.992611i	$-0.461280\pi$
$384$	−1.75400e9	+	3.03802e9i	−0.00411661	+	0.00713018i
$385$	1.11027e10	+	1.92304e10i	0.0257545	+	0.0446082i
$386$	8.77902e10	−	1.52057e11i	0.201281	−	0.348629i
$387$	−2.61447e11			−0.592494
$388$	8.79826e10			0.197085
$389$	3.14991e11	−	5.45581e11i	0.697470	−	1.20805i	−0.271872	−	0.962334i	$-0.587643\pi$
$389$	3.14991e11	−	5.45581e11i	0.697470	−	1.20805i	0.969341	−	0.245719i	$-0.0790241\pi$
$390$	3.97837e8	−	6.89073e8i	0.000870791	−	0.00150825i
$391$	4.19460e11			0.907602
$392$	4.25412e9			0.00909961
$393$	1.87562e10	−	3.24867e10i	0.0396624	−	0.0686973i
$394$	−1.48098e11	−	2.56513e11i	−0.309610	−	0.536260i
$395$	4.57926e10	−	7.93150e10i	0.0946472	−	0.163934i
$396$	−5.48562e10	−	9.50137e10i	−0.112098	−	0.194159i
$397$	1.16740e11	+	2.02199e11i	0.235864	+	0.408528i	0.959523	−	0.281629i	$-0.0908747\pi$
$397$	1.16740e11	+	2.02199e11i	0.235864	+	0.408528i	−0.723660	+	0.690157i	$0.757541\pi$
$398$	−2.24967e11			−0.449412
$399$	−3.37380e10	+	3.20681e10i	−0.0666409	+	0.0633426i
$400$	−1.26296e11			−0.246672
$401$	2.58382e11	+	4.47531e11i	0.499014	+	0.864317i	0.999999	−	0.00113849i	$-0.000362394\pi$
$401$	2.58382e11	+	4.47531e11i	0.499014	+	0.864317i	−0.500986	+	0.865456i	$0.667029\pi$
$402$	−1.10347e9	−	1.91127e9i	−0.00210739	−	0.00365010i
$403$	1.21171e10	−	2.09874e10i	0.0228837	−	0.0396357i
$404$	7.08562e10	+	1.22727e11i	0.132331	+	0.229204i
$405$	3.04229e10	−	5.26940e10i	0.0561892	−	0.0973226i
$406$	−6.95935e11			−1.27116
$407$	2.78695e11			0.503447
$408$	−9.77310e9	+	1.69275e10i	−0.0174607	+	0.0302428i
$409$	−6.88817e10	+	1.19307e11i	−0.121716	+	0.210819i	−0.920445	−	0.390873i	$-0.872173\pi$
$409$	−6.88817e10	+	1.19307e11i	−0.121716	+	0.210819i	0.798728	+	0.601692i	$0.205506\pi$
$410$	1.70430e10			0.0297865
$411$	7.84312e10			0.135582
$412$	−2.24669e11	+	3.89139e11i	−0.384155	+	0.665376i
$413$	−1.88994e11	−	3.27348e11i	−0.319649	−	0.553649i
$414$	−1.79311e11	+	3.10575e11i	−0.299988	+	0.519595i
$415$	−4.04655e10	−	7.00882e10i	−0.0669681	−	0.115992i
$416$	1.23736e10	+	2.14317e10i	0.0202570	+	0.0350862i
$417$	−2.76457e10			−0.0447729
$418$	−1.44693e11	+	1.37532e11i	−0.231822	+	0.220348i
$419$	−5.16503e11			−0.818672			−0.409336	−	0.912384i	$-0.634240\pi$
$419$	−5.16503e11			−0.818672			−0.409336	+	0.912384i	$0.634240\pi$
$420$	1.69114e9	+	2.92913e9i	0.00265190	+	0.00459322i
$421$	1.44847e11	+	2.50882e11i	0.224719	+	0.389225i	0.956235	−	0.292600i	$-0.0945203\pi$
$421$	1.44847e11	+	2.50882e11i	0.224719	+	0.389225i	−0.731516	+	0.681824i	$0.761187\pi$
$422$	−2.55786e11	+	4.43034e11i	−0.392618	+	0.680034i
$423$	3.36479e11	+	5.82799e11i	0.511006	+	0.885089i
$424$	1.83759e11	−	3.18281e11i	0.276123	−	0.478260i
$425$	−7.03707e11			−1.04627
$426$	−1.68366e10			−0.0247691
$427$	5.02617e11	−	8.70557e11i	0.731663	−	1.26728i
$428$	−8.88732e10	+	1.53933e11i	−0.128019	+	0.221735i
$429$	6.77415e9			0.00965600
$430$	3.45673e10			0.0487593
$431$	2.13107e11	−	3.69113e11i	0.297475	−	0.515242i	−0.678082	−	0.734986i	$-0.737189\pi$
$431$	2.13107e11	−	3.69113e11i	0.297475	−	0.515242i	0.975558	+	0.219744i	$0.0705221\pi$
$432$	−1.67843e10	−	2.90713e10i	−0.0231861	−	0.0401594i
$433$	−5.57833e11	+	9.66196e11i	−0.762621	+	1.32090i	0.178874	+	0.983872i	$0.442755\pi$
$433$	−5.57833e11	+	9.66196e11i	−0.762621	+	1.32090i	−0.941495	+	0.337027i	$0.890579\pi$
$434$	5.15077e10	+	8.92140e10i	0.0696897	+	0.120706i
$435$	7.30851e9	+	1.26587e10i	0.00978650	+	0.0169507i
$436$	9.56089e8			0.00126710
$437$	6.25808e11	+	1.84822e11i	0.820871	+	0.242430i
$438$	−2.71924e10			−0.0353032
$439$	2.70921e11	+	4.69250e11i	0.348139	+	0.602995i	0.985919	−	0.167224i	$-0.0534803\pi$
$439$	2.70921e11	+	4.69250e11i	0.348139	+	0.602995i	−0.637780	+	0.770219i	$0.720147\pi$
$440$	7.25283e9	+	1.25623e10i	0.00922509	+	0.0159783i
$441$	−1.01327e10	+	1.75504e10i	−0.0127571	+	0.0220960i
$442$	6.89441e10	+	1.19415e11i	0.0859205	+	0.148819i
$443$	−4.04665e11	+	7.00900e11i	−0.499205	+	0.864648i	−1.00000		0.000917874i	$-0.999708\pi$
$443$	−4.04665e11	+	7.00900e11i	−0.499205	+	0.864648i	0.500795	+	0.865566i	$0.333041\pi$
$444$	4.24503e10			0.0518391
$445$	7.58098e10			0.0916442
$446$	−8.57086e9	+	1.48452e10i	−0.0102569	+	0.0177655i
$447$	−1.41693e10	+	2.45420e10i	−0.0167867	+	0.0290754i
$448$	−1.05196e11			−0.123381
$449$	1.03702e12			1.20414			0.602069	−	0.798444i	$-0.294343\pi$
$449$	1.03702e12			1.20414			0.602069	+	0.798444i	$0.294343\pi$
$450$	3.00820e11	−	5.21036e11i	0.345820	−	0.598979i
$451$	7.25500e10	+	1.25660e11i	0.0825739	+	0.143022i
$452$	−1.32687e11	+	2.29821e11i	−0.149522	+	0.258980i
$453$	5.41975e10	+	9.38728e10i	0.0604696	+	0.104736i
$454$	7.95522e10	+	1.37788e11i	0.0878822	+	0.152216i
$455$	2.38601e10			0.0260989
$456$	−2.20394e10	+	2.09486e10i	−0.0238703	+	0.0226889i
$457$	1.93958e11			0.208011			0.104005	−	0.994577i	$-0.466834\pi$
$457$	1.93958e11			0.208011			0.104005	+	0.994577i	$0.466834\pi$
$458$	5.89760e11	+	1.02150e12i	0.626298	+	1.08478i
$459$	−9.35202e10	−	1.61982e11i	−0.0983441	−	0.170337i
$460$	2.37076e10	−	4.10628e10i	0.0246875	−	0.0427601i
$461$	2.89821e11	+	5.01984e11i	0.298865	+	0.517649i	0.975877	−	0.218323i	$-0.0700586\pi$
$461$	2.89821e11	+	5.01984e11i	0.298865	+	0.517649i	−0.677012	+	0.735972i	$0.736725\pi$
$462$	−1.43979e10	+	2.49379e10i	−0.0147031	+	0.0254666i
$463$	−1.94277e12			−1.96475			−0.982374	−	0.186924i	$-0.940148\pi$
$463$	−1.94277e12			−1.96475			−0.982374	+	0.186924i	$0.940148\pi$
$464$	−4.54621e11			−0.455322
$465$	1.08184e9	−	1.87380e9i	0.00107306	−	0.00185860i
$466$	1.00798e10	−	1.74587e10i	0.00990181	−	0.0171504i
$467$	1.81323e12			1.76412			0.882058	−	0.471141i	$-0.156158\pi$
$467$	1.81323e12			1.76412			0.882058	+	0.471141i	$0.156158\pi$
$468$	−1.17889e11			−0.113597
$469$	3.30902e10	−	5.73140e10i	0.0315807	−	0.0546994i
$470$	−4.44877e10	−	7.70550e10i	−0.0420533	−	0.0728384i
$471$	4.10839e10	−	7.11594e10i	0.0384661	−	0.0666252i
$472$	−1.23461e11	−	2.13841e11i	−0.114496	−	0.198313i
$473$	1.47148e11	+	2.54868e11i	0.135170	+	0.234121i
$474$	1.18767e11			0.108067
$475$	−1.04989e12	−	3.10066e11i	−0.946284	−	0.279468i
$476$	−5.86139e11			−0.523323
$477$	8.75379e11	+	1.51620e12i	0.774218	+	1.34099i
$478$	−4.25987e11	−	7.37831e11i	−0.373225	−	0.646445i
$479$	1.08959e12	−	1.88722e12i	0.945699	−	1.63800i	0.191353	−	0.981521i	$-0.438712\pi$
$479$	1.08959e12	−	1.88722e12i	0.945699	−	1.63800i	0.754346	−	0.656477i	$-0.227954\pi$
$480$	1.10474e9	+	1.91346e9i	0.000949891	+	0.00164526i
$481$	1.49732e11	−	2.59344e11i	0.127545	−	0.220914i
$482$	8.14079e11			0.686997
$483$	9.41259e10			0.0786950
$484$	2.40069e11	−	4.15811e11i	0.198853	−	0.344423i
$485$	2.77074e10	−	4.79906e10i	0.0227383	−	0.0393839i
$486$	2.40216e11			0.195316
$487$	−6.45212e11			−0.519783			−0.259891	−	0.965638i	$-0.583687\pi$
$487$	−6.45212e11			−0.519783			−0.259891	+	0.965638i	$0.583687\pi$
$488$	3.28335e11	−	5.68693e11i	0.262077	−	0.453930i
$489$	8.46813e9	+	1.46672e10i	0.00669727	+	0.0116000i
$490$	1.33970e9	−	2.32043e9i	0.00104985	−	0.00181839i
$491$	−1.06235e12	−	1.84005e12i	−0.824902	−	1.42877i	−0.901994	−	0.431748i	$-0.857897\pi$
$491$	−1.06235e12	−	1.84005e12i	−0.824902	−	1.42877i	0.0770927	−	0.997024i	$-0.475436\pi$
$492$	1.10507e10	+	1.91403e10i	0.00850249	+	0.0147267i
$493$	−2.53309e12			−1.93126
$494$	5.02440e10	+	2.08537e11i	0.0379589	+	0.157548i
$495$	−6.91010e10			−0.0517322
$496$	3.36475e10	+	5.82792e10i	0.0249624	+	0.0432361i
$497$	−2.52443e11	−	4.37243e11i	−0.185592	−	0.321454i
$498$	5.24755e10	−	9.08902e10i	0.0382318	−	0.0662194i
$499$	−1.67444e11	−	2.90021e11i	−0.120897	−	0.209400i	0.799224	−	0.601033i	$-0.205244\pi$
$499$	−1.67444e11	−	2.90021e11i	−0.120897	−	0.209400i	−0.920122	+	0.391632i	$0.871911\pi$
$500$	−8.00827e10	+	1.38707e11i	−0.0573025	+	0.0992509i
$501$	−5.10871e10			−0.0362278
$502$	2.87226e11			0.201863
$503$	6.01183e11	−	1.04128e12i	0.418746	−	0.725290i	−0.577067	−	0.816697i	$-0.695803\pi$
$503$	6.01183e11	−	1.04128e12i	0.418746	−	0.725290i	0.995814	+	0.0914067i	$0.0291363\pi$
$504$	2.50562e11	−	4.33987e11i	0.172973	−	0.299598i
$505$	8.92559e10			0.0610697
$506$	4.03681e11			0.273754
$507$	−6.56522e10	+	1.13713e11i	−0.0441279	+	0.0764317i
$508$	−4.23846e11	−	7.34124e11i	−0.282372	−	0.489083i
$509$	−1.22262e12	+	2.11764e12i	−0.807350	+	1.39837i	0.107343	+	0.994222i	$0.465766\pi$
$509$	−1.22262e12	+	2.11764e12i	−0.807350	+	1.39837i	−0.914693	+	0.404149i	$0.867568\pi$
$510$	6.15547e9	+	1.06616e10i	0.00402898	+	0.00697840i
$511$	−4.07715e11	−	7.06183e11i	−0.264522	−	0.458166i
$512$	−6.87195e10			−0.0441942
$513$	−6.81542e10	−	2.82873e11i	−0.0434475	−	0.180328i
$514$	−1.98152e11			−0.125218
$515$	1.41505e11	+	2.45094e11i	0.0886421	+	0.153533i
$516$	2.24134e10	+	3.88211e10i	0.0139182	+	0.0241070i
$517$	3.78757e11	−	6.56026e11i	0.233159	−	0.403844i
$518$	6.36486e11	+	1.10243e12i	0.388423	+	0.672769i
$519$	1.39608e11	−	2.41807e11i	0.0844609	−	0.146291i
$520$	1.55867e10			0.00934843
$521$	−2.85762e12			−1.69916			−0.849581	−	0.527458i	$-0.823145\pi$
$521$	−2.85762e12			−1.69916			−0.849581	+	0.527458i	$0.823145\pi$
$522$	1.08284e12	−	1.87554e12i	0.638335	−	1.10563i
$523$	9.89316e11	−	1.71355e12i	0.578199	−	1.00147i	−0.417487	−	0.908683i	$-0.637089\pi$
$523$	9.89316e11	−	1.71355e12i	0.578199	−	1.00147i	0.995686	−	0.0927872i	$-0.0295776\pi$
$524$	7.34843e11			0.425798
$525$	−1.57910e11			−0.0907180
$526$	7.38073e11	−	1.27838e12i	0.420401	−	0.728155i
$527$	1.87480e11	+	3.24725e11i	0.105878	+	0.183387i
$528$	−9.40545e9	+	1.62907e10i	−0.00526656	+	0.00912195i
$529$	2.40813e11	+	4.17100e11i	0.133699	+	0.231574i
$530$	−1.15739e11	−	2.00465e11i	−0.0637143	−	0.110356i
$531$	1.17627e12			0.642068
$532$	−8.74483e11	−	2.58263e11i	−0.473314	−	0.139785i
$533$	1.55913e11			0.0836779
$534$	4.91549e10	+	8.51389e10i	0.0261596	+	0.0453098i
$535$	5.59757e10	+	9.69528e10i	0.0295398	+	0.0511644i
$536$	2.16163e10	−	3.74405e10i	0.0113120	−	0.0195929i
$537$	−3.10789e10	−	5.38302e10i	−0.0161280	−	0.0279346i
$538$	9.23557e11	−	1.59965e12i	0.475274	−	0.823198i
$539$	2.28118e10			0.0116415
$540$	−2.11428e10			−0.0107002
$541$	7.65584e11	−	1.32603e12i	0.384242	−	0.665527i	−0.607422	−	0.794380i	$-0.707796\pi$
$541$	7.65584e11	−	1.32603e12i	0.384242	−	0.665527i	0.991664	+	0.128853i	$0.0411295\pi$
$542$	−6.16238e11	+	1.06736e12i	−0.306727	+	0.531267i
$543$	1.50230e11			0.0741579
$544$	−3.82897e11			−0.187451
$545$	3.01091e8	−	5.21504e8i	0.000146188	−	0.000253206i
$546$	1.54709e10	+	2.67964e10i	0.00744986	+	0.0129035i
$547$	−1.78877e12	+	3.09823e12i	−0.854300	+	1.47969i	0.0229922	+	0.999736i	$0.492681\pi$
$547$	−1.78877e12	+	3.09823e12i	−0.854300	+	1.47969i	−0.877293	+	0.479956i	$0.840653\pi$
$548$	7.68206e11	+	1.33057e12i	0.363886	+	0.630269i
$549$	1.56410e12	+	2.70910e12i	0.734833	+	1.27277i
$550$	−6.77235e11			−0.315578
$551$	−3.77922e12	−	1.11613e12i	−1.74670	−	0.515859i
$552$	6.14879e10			0.0281880
$553$	1.78076e12	+	3.08437e12i	0.809734	+	1.40250i
$554$	8.94388e11	+	1.54913e12i	0.403396	+	0.698703i
$555$	1.33684e10	−	2.31547e10i	0.00598082	−	0.0103591i
$556$	−2.70780e11	−	4.69005e11i	−0.120166	−	0.208133i
$557$	7.94919e11	−	1.37684e12i	0.349925	−	0.606087i	−0.636311	−	0.771432i	$-0.719541\pi$
$557$	7.94919e11	−	1.37684e12i	0.349925	−	0.606087i	0.986236	+	0.165345i	$0.0528739\pi$
$558$	−3.20575e11			−0.139983
$559$	3.16229e11			0.136977
$560$	−3.31282e10	+	5.73797e10i	−0.0142348	+	0.0246554i
$561$	−5.24061e10	+	9.07700e10i	−0.0223382	+	0.0386909i
$562$	2.08705e12			0.882509
$563$	2.81149e12			1.17937			0.589683	−	0.807635i	$-0.299253\pi$
$563$	2.81149e12			1.17937			0.589683	+	0.807635i	$0.299253\pi$
$564$	5.76915e10	−	9.99247e10i	0.0240080	−	0.0415831i
$565$	8.35713e10	+	1.44750e11i	0.0345016	+	0.0597585i
$566$	−1.40377e12	+	2.43141e12i	−0.574941	+	0.995826i
$567$	1.18307e12	+	2.04914e12i	0.480714	+	0.832622i
$568$	−1.64909e11	−	2.85630e11i	−0.0664777	−	0.115143i
$569$	−4.48030e12			−1.79185			−0.895926	−	0.444203i	$-0.853487\pi$
$569$	−4.48030e12			−1.79185			−0.895926	+	0.444203i	$0.853487\pi$
$570$	4.48589e9	+	1.86186e10i	0.00177997	+	0.00738773i
$571$	−3.86615e12			−1.52201			−0.761003	−	0.648748i	$-0.775293\pi$
$571$	−3.86615e12			−1.52201			−0.761003	+	0.648748i	$0.775293\pi$
$572$	6.63505e10	+	1.14922e11i	0.0259156	+	0.0448872i
$573$	9.48559e10	+	1.64295e11i	0.0367594	+	0.0636692i
$574$	−3.31381e11	+	5.73968e11i	−0.127416	+	0.220691i
$575$	1.10685e12	+	1.91712e12i	0.422264	+	0.731383i
$576$	1.63680e11	−	2.83503e11i	0.0619577	−	0.107314i
$577$	1.04250e12			0.391548			0.195774	−	0.980649i	$-0.437278\pi$
$577$	1.04250e12			0.391548			0.195774	+	0.980649i	$0.437278\pi$
$578$	−2.36049e11			−0.0879684
$579$	7.17046e10	−	1.24196e11i	0.0265151	−	0.0459255i
$580$	−1.43169e11	+	2.47976e11i	−0.0525318	+	0.0909877i
$581$	3.14720e12			1.14586
$582$	7.18617e10			0.0259624
$583$	9.85368e11	−	1.70671e12i	0.353256	−	0.611858i
$584$	−2.66340e11	−	4.61315e11i	−0.0947500	−	0.164112i
$585$	−3.71254e10	+	6.43030e10i	−0.0131060	+	0.0227002i
$586$	−6.86327e11	−	1.18875e12i	−0.240432	−	0.416440i
$587$	2.03326e12	+	3.52172e12i	0.706842	+	1.22429i	0.966023	+	0.258457i	$0.0832142\pi$
$587$	2.03326e12	+	3.52172e12i	0.706842	+	1.22429i	−0.259181	+	0.965829i	$0.583452\pi$
$588$	3.47465e9			0.00119871
$589$	1.36629e11	+	5.67076e11i	0.0467761	+	0.194143i
$590$	−1.55521e11			−0.0528390
$591$	−1.20962e11	−	2.09512e11i	−0.0407854	−	0.0706424i
$592$	4.15786e11	+	7.20163e11i	0.139130	+	0.240981i
$593$	1.77683e12	−	3.07757e12i	0.590066	−	1.02202i	−0.404157	−	0.914690i	$-0.632435\pi$
$593$	1.77683e12	−	3.07757e12i	0.590066	−	1.02202i	0.994223	−	0.107335i	$-0.0342317\pi$
$594$	−9.00021e10	−	1.55888e11i	−0.0296629	−	0.0513777i
$595$	−1.84586e11	+	3.19713e11i	−0.0603773	+	0.104576i
$596$	−5.55134e11			−0.180215
$597$	−1.83746e11			−0.0592017
$598$	2.16882e11	−	3.75651e11i	0.0693536	−	0.120124i
$599$	−9.11567e11	+	1.57888e12i	−0.289313	+	0.501105i	−0.973646	−	0.228065i	$-0.926760\pi$
$599$	−9.11567e11	+	1.57888e12i	−0.289313	+	0.501105i	0.684333	+	0.729170i	$0.260094\pi$
$600$	−1.03155e11			−0.0324945
$601$	−3.23422e12			−1.01119			−0.505597	−	0.862770i	$-0.668728\pi$
$601$	−3.23422e12			−1.01119			−0.505597	+	0.862770i	$0.668728\pi$
$602$	−6.72118e11	+	1.16414e12i	−0.208575	+	0.361262i
$603$	1.02974e11	+	1.78356e11i	0.0317175	+	0.0549364i
$604$	−1.06169e12	+	1.83890e12i	−0.324588	+	0.562203i
$605$	−1.51204e11	−	2.61894e11i	−0.0458844	−	0.0794741i
$606$	5.78734e10	+	1.00240e11i	0.0174322	+	0.0301934i
$607$	−3.70716e12			−1.10839			−0.554195	−	0.832387i	$-0.686974\pi$
$607$	−3.70716e12			−1.10839			−0.554195	+	0.832387i	$0.686974\pi$
$608$	−5.71258e11	−	1.68711e11i	−0.169538	−	0.0500700i
$609$	−5.68420e11			−0.167452
$610$	−2.06798e11	−	3.58185e11i	−0.0604731	−	0.104742i
$611$	−4.06983e11	−	7.04916e11i	−0.118138	−	0.204622i
$612$	9.12007e11	−	1.57964e12i	0.262795	−	0.455174i
$613$	1.25712e11	+	2.17739e11i	0.0359587	+	0.0622822i	0.883445	−	0.468536i	$-0.155218\pi$
$613$	1.25712e11	+	2.17739e11i	0.0359587	+	0.0622822i	−0.847486	+	0.530818i	$0.821885\pi$
$614$	−1.48014e12	+	2.56368e12i	−0.420286	+	0.727957i
$615$	1.39203e10			0.00392383
$616$	−5.64090e11			−0.157846
$617$	3.08127e12	−	5.33692e12i	0.855946	−	1.48254i	−0.0198182	−	0.999804i	$-0.506309\pi$
$617$	3.08127e12	−	5.33692e12i	0.855946	−	1.48254i	0.875764	−	0.482739i	$-0.160358\pi$
$618$	−1.83504e11	+	3.17838e11i	−0.0506053	+	0.0876510i
$619$	6.79713e12			1.86088			0.930438	−	0.366449i	$-0.119427\pi$
$619$	6.79713e12			1.86088			0.930438	+	0.366449i	$0.119427\pi$
$620$	4.23850e10			0.0115199
$621$	−2.94193e11	+	5.09558e11i	−0.0793818	+	0.137493i
$622$	−1.47260e12	−	2.55061e12i	−0.394482	−	0.683263i
$623$	−1.47403e12	+	2.55309e12i	−0.392021	+	0.679000i
$624$	1.01064e10	+	1.75048e10i	0.00266849	+	0.00462196i
$625$	−1.83152e12	−	3.17229e12i	−0.480122	−	0.831596i
$626$	−1.01317e12			−0.263693
$627$	−1.18181e11	+	1.12332e11i	−0.0305383	+	0.0290268i
$628$	1.60961e12			0.412955
$629$	2.31671e12	+	4.01266e12i	0.590125	+	1.02213i
$630$	−1.57814e11	−	2.73341e11i	−0.0399128	−	0.0691310i
$631$	2.56968e12	−	4.45081e12i	0.645278	−	1.11765i	−0.338960	−	0.940801i	$-0.610075\pi$
$631$	2.56968e12	−	4.45081e12i	0.645278	−	1.11765i	0.984237	−	0.176853i	$-0.0565916\pi$
$632$	1.16328e12	+	2.01487e12i	0.290041	+	0.502366i
$633$	−2.08918e11	+	3.61857e11i	−0.0517202	+	0.0895820i
$634$	−2.43452e12			−0.598427
$635$	−5.33909e11			−0.130312
$636$	1.50089e11	−	2.59963e11i	0.0363742	−	0.0630019i
$637$	1.22559e10	−	2.12278e10i	0.00294929	−	0.00510832i
$638$	−2.43780e12			−0.582513
$639$	1.57116e12			0.372792
$640$	−2.16411e10	+	3.74834e10i	−0.00509881	+	0.00883140i
$641$	−3.56878e12	−	6.18131e12i	−0.834946	−	1.44617i	−0.894074	−	0.447919i	$-0.852165\pi$
$641$	−3.56878e12	−	6.18131e12i	−0.834946	−	1.44617i	0.0591282	−	0.998250i	$-0.481168\pi$
$642$	−7.25891e10	+	1.25728e11i	−0.0168641	+	0.0292095i
$643$	−2.97125e12	−	5.14636e12i	−0.685473	−	1.18727i	−0.973288	−	0.229588i	$-0.926262\pi$
$643$	−2.97125e12	−	5.14636e12i	−0.685473	−	1.18727i	0.287815	−	0.957686i	$-0.407071\pi$
$644$	9.21931e11	+	1.59683e12i	0.211209	+	0.365824i
$645$	2.82336e10			0.00642314
$646$	−3.18298e12	−	9.40038e11i	−0.719097	−	0.212373i
$647$	5.97471e11			0.134044			0.0670221	−	0.997751i	$-0.478650\pi$
$647$	5.97471e11			0.134044			0.0670221	+	0.997751i	$0.478650\pi$
$648$	7.72844e11	+	1.33860e12i	0.172189	+	0.298239i
$649$	−6.62032e11	−	1.14667e12i	−0.146480	−	0.253710i
$650$	−3.63853e11	+	6.30211e11i	−0.0799494	+	0.138477i
$651$	4.20701e10	+	7.28675e10i	0.00918034	+	0.0159008i
$652$	−1.65885e11	+	2.87321e11i	−0.0359495	+	0.0622664i
$653$	1.55380e12			0.334415			0.167207	−	0.985922i	$-0.446525\pi$
$653$	1.55380e12			0.334415			0.167207	+	0.985922i	$0.446525\pi$
$654$	7.80907e8			0.000166917
$655$	2.31416e11	−	4.00824e11i	0.0491256	−	0.0850880i
$656$	−2.16475e11	+	3.74946e11i	−0.0456395	+	0.0790499i
$657$	2.53755e12			0.531336
$658$	3.46004e12			0.719555
$659$	3.16440e12	−	5.48091e12i	0.653593	−	1.13206i	−0.328651	−	0.944451i	$-0.606594\pi$
$659$	3.16440e12	−	5.48091e12i	0.653593	−	1.13206i	0.982244	−	0.187606i	$-0.0600727\pi$
$660$	5.92391e9	+	1.02605e10i	0.00121524	+	0.00210485i
$661$	−3.38874e11	+	5.86948e11i	−0.0690450	+	0.119589i	−0.898481	−	0.439012i	$-0.855329\pi$
$661$	−3.38874e11	+	5.86948e11i	−0.0690450	+	0.119589i	0.829436	+	0.558601i	$0.188662\pi$
$662$	−1.73523e12	−	3.00551e12i	−0.351153	−	0.608214i
$663$	5.63116e10	+	9.75345e10i	0.0113184	+	0.0196041i
$664$	2.05592e12			0.410440
$665$	−4.16262e11	+	3.95660e11i	−0.0825410	+	0.0784557i
$666$	−3.96138e12			−0.780212
$667$	3.98427e12	+	6.90096e12i	0.779439	+	1.35003i
$668$	−5.00381e11	−	8.66685e11i	−0.0972314	−	0.168410i
$669$	−7.00044e9	+	1.21251e10i	−0.00135116	+	0.00234028i
$670$	−1.36147e10	−	2.35814e10i	−0.00261019	−	0.00452099i
$671$	1.76062e12	−	3.04949e12i	0.335286	−	0.580732i
$672$	−8.59211e10			−0.0162532
$673$	3.73142e12			0.701143			0.350572	−	0.936536i	$-0.385987\pi$
$673$	3.73142e12			0.701143			0.350572	+	0.936536i	$0.385987\pi$
$674$	2.90222e12	−	5.02679e12i	0.541702	−	0.938255i
$675$	4.93553e11	−	8.54860e11i	0.0915097	−	0.158499i
$676$	−2.57216e12			−0.473738
$677$	3.01710e11			0.0552001			0.0276001	−	0.999619i	$-0.491214\pi$
$677$	3.01710e11			0.0552001			0.0276001	+	0.999619i	$0.491214\pi$
$678$	−1.08375e11	+	1.87711e11i	−0.0196968	+	0.0341158i
$679$	1.07747e12	+	1.86624e12i	0.194532	+	0.336940i
$680$	−1.20581e11	+	2.08853e11i	−0.0216267	+	0.0374586i
$681$	6.49760e10	+	1.12542e11i	0.0115769	+	0.0200517i
$682$	1.80427e11	+	3.12509e11i	0.0319354	+	0.0553138i
$683$	−1.25407e12			−0.220511			−0.110256	−	0.993903i	$-0.535167\pi$
$683$	−1.25407e12			−0.220511			−0.110256	+	0.993903i	$0.535167\pi$
$684$	2.05668e12	−	1.95488e12i	0.359264	−	0.341482i
$685$	9.67691e11			0.167930
$686$	2.07629e12	+	3.59624e12i	0.357956	+	0.619997i
$687$	4.81700e11	+	8.34328e11i	0.0825032	+	0.142900i
$688$	−4.39062e11	+	7.60479e11i	−0.0747099	+	0.129401i
$689$	−1.05880e12	−	1.83390e12i	−0.178990	−	0.310019i
$690$	1.93637e10	−	3.35389e10i	0.00325213	−	0.00563285i
$691$	−1.14277e13			−1.90681			−0.953403	−	0.301698i	$-0.902447\pi$
$691$	−1.14277e13			−1.90681			−0.953403	+	0.301698i	$0.902447\pi$
$692$	5.46963e12			0.906736
$693$	1.34358e12	−	2.32716e12i	0.221292	−	0.383289i
$694$	1.91806e12	−	3.32218e12i	0.313866	−	0.543632i
$695$	−3.41095e11			−0.0554555
$696$	−3.71321e11			−0.0599803
$697$	−1.20617e12	+	2.08915e12i	−0.193581	+	0.335292i
$698$	1.00258e12	+	1.73653e12i	0.159872	+	0.276906i
$699$	8.23289e9	−	1.42598e10i	0.00130438	−	0.00225926i
$700$	−1.54668e12	−	2.67892e12i	−0.243477	−	0.421715i
$701$	2.03827e12	+	3.53039e12i	0.318809	+	0.552193i	0.980240	−	0.197813i	$-0.0633838\pi$
$701$	2.03827e12	+	3.53039e12i	0.318809	+	0.552193i	−0.661431	+	0.750006i	$0.730050\pi$
$702$	−1.93419e11			−0.0300595
$703$	1.68834e12	+	7.00742e12i	0.260711	+	1.08208i
$704$	−3.68493e11			−0.0565395
$705$	−3.63363e10	−	6.29363e10i	−0.00553975	−	0.00959512i
$706$	1.42865e12	+	2.47449e12i	0.216423	+	0.374856i
$707$	−1.73547e12	+	3.00592e12i	−0.261234	+	0.452471i
$708$	−1.00839e11	−	1.74659e11i	−0.0150828	−	0.0261241i
$709$	3.06216e12	−	5.30382e12i	0.455114	−	0.788280i	−0.543581	−	0.839357i	$-0.682932\pi$
$709$	3.06216e12	−	5.30382e12i	0.455114	−	0.788280i	0.998695	+	0.0510764i	$0.0162652\pi$
$710$	−2.07731e11			−0.0306789
$711$	−1.10831e13			−1.62648
$712$	−9.62912e11	+	1.66781e12i	−0.140419	+	0.243213i
$713$	5.89770e11	−	1.02151e12i	0.0854633	−	0.148027i
$714$	−4.78742e11			−0.0689382
$715$	8.35801e10			0.0119599
$716$	6.08814e11	−	1.05450e12i	0.0865717	−	0.149947i
$717$	−3.47934e11	−	6.02640e11i	−0.0491656	−	0.0851573i
$718$	−2.10991e12	+	3.65447e12i	−0.296281	+	0.513173i
$719$	1.31098e12	+	2.27069e12i	0.182944	+	0.316868i	0.942882	−	0.333128i	$-0.108104\pi$
$719$	1.31098e12	+	2.27069e12i	0.182944	+	0.316868i	−0.759938	+	0.649995i	$0.774771\pi$
$720$	−1.03092e11	−	1.78561e11i	−0.0142965	−	0.0247622i
$721$	−1.10056e13			−1.51672
$722$	−4.33461e12	−	2.80495e12i	−0.593653	−	0.384157i
$723$	6.64916e11			0.0904992
$724$	1.47145e12	+	2.54863e12i	0.199032	+	0.344733i
$725$	−6.68421e12	−	1.15774e13i	−0.898522	−	1.55629i
$726$	1.96081e11	−	3.39623e11i	0.0261952	−	0.0453714i
$727$	7.04119e12	+	1.21957e13i	0.934848	+	1.61920i	0.774904	+	0.632078i	$0.217798\pi$
$727$	7.04119e12	+	1.21957e13i	0.934848	+	1.61920i	0.159944	+	0.987126i	$0.448869\pi$
$728$	−3.03064e11	+	5.24922e11i	−0.0399892	+	0.0692634i
$729$	−7.23148e12			−0.948316
$730$	−3.35503e11			−0.0437263
$731$	−2.44640e12	+	4.23730e12i	−0.316884	+	0.548859i
$732$	2.68175e11	−	4.64493e11i	0.0345238	−	0.0597970i
$733$	1.02857e13			1.31603			0.658016	−	0.753004i	$-0.271396\pi$
$733$	1.02857e13			1.31603			0.658016	+	0.753004i	$0.271396\pi$
$734$	4.06878e12			0.517407
$735$	1.09423e9	−	1.89527e9i	0.000138298	−	0.000239539i
$736$	6.02253e11	+	1.04313e12i	0.0756535	+	0.131036i
$737$	1.15912e11	−	2.00766e11i	0.0144719	−	0.0250661i
$738$	−1.03123e12	−	1.78614e12i	−0.127968	−	0.221647i
$739$	3.35517e12	+	5.81132e12i	0.413823	+	0.716762i	0.995304	−	0.0967979i	$-0.0308600\pi$
$739$	3.35517e12	+	5.81132e12i	0.413823	+	0.716762i	−0.581481	+	0.813560i	$0.697527\pi$
$740$	5.23756e11			0.0642075
$741$	4.10379e10	+	1.70327e11i	0.00500038	+	0.0207540i
$742$	9.00158e12			1.09019
$743$	−4.06653e10	−	7.04343e10i	−0.00489524	−	0.00847880i	0.863567	−	0.504233i	$-0.168225\pi$
$743$	−4.06653e10	−	7.04343e10i	−0.00489524	−	0.00847880i	−0.868463	+	0.495755i	$0.834892\pi$
$744$	2.74824e10	+	4.76008e10i	0.00328833	+	0.00569556i
$745$	−1.74822e11	+	3.02801e11i	−0.0207919	+	0.0360126i
$746$	−3.02858e10	−	5.24566e10i	−0.00358026	−	0.00620120i
$747$	−4.89691e12	+	8.48170e12i	−0.575413	+	0.996644i
$748$	−2.05320e12			−0.239813
$749$	−4.35351e12			−0.505443
$750$	−6.54093e10	+	1.13292e11i	−0.00754855	+	0.0130745i
$751$	−3.05596e12	+	5.29307e12i	−0.350564	+	0.607195i	−0.986348	−	0.164672i	$-0.947344\pi$
$751$	−3.05596e12	+	5.29307e12i	−0.350564	+	0.607195i	0.635784	+	0.771867i	$0.280677\pi$
$752$	2.26028e12			0.257740
$753$	2.34598e11			0.0265918
$754$	−1.30974e12	+	2.26853e12i	−0.147575	+	0.255608i
$755$	6.68694e11	+	1.15821e12i	0.0748973	+	0.129726i
$756$	4.11096e11	−	7.12039e11i	0.0457715	−	0.0792785i
$757$	4.91046e12	+	8.50516e12i	0.543489	+	0.941350i	0.998700	+	0.0509667i	$0.0162302\pi$
$757$	4.91046e12	+	8.50516e12i	0.543489	+	0.941350i	−0.455212	+	0.890383i	$0.650436\pi$
$758$	−8.18124e11	−	1.41703e12i	−0.0900135	−	0.155908i
$759$	3.29715e11			0.0360621
$760$	−2.71924e11	+	2.58465e11i	−0.0295656	+	0.0281023i
$761$	−2.29354e12			−0.247899			−0.123949	−	0.992289i	$-0.539556\pi$
$761$	−2.29354e12			−0.247899			−0.123949	+	0.992289i	$0.539556\pi$
$762$	−3.46186e11	−	5.99611e11i	−0.0371973	−	0.0644277i
$763$	1.17087e10	+	2.02800e10i	0.00125068	+	0.00216625i
$764$	−1.85816e12	+	3.21843e12i	−0.197317	+	0.341762i
$765$	−5.74417e11	−	9.94919e11i	−0.0606388	−	0.105030i
$766$	5.38316e12	−	9.32390e12i	0.564947	−	0.978517i
$767$	−1.42274e12			−0.148438
$768$	−5.61281e10			−0.00582177
$769$	8.33913e11	−	1.44438e12i	0.0859908	−	0.148940i	−0.819822	−	0.572618i	$-0.805928\pi$
$769$	8.33913e11	−	1.44438e12i	0.0859908	−	0.148940i	0.905813	+	0.423678i	$0.139261\pi$
$770$	−1.77643e11	+	3.07686e11i	−0.0182112	+	0.0315427i
$771$	−1.61845e11			−0.0164951
$772$	2.80929e12			0.284655
$773$	1.32631e12	−	2.29723e12i	0.133609	−	0.231418i	−0.791456	−	0.611226i	$-0.790677\pi$
$773$	1.32631e12	−	2.29723e12i	0.133609	−	0.231418i	0.925065	+	0.379808i	$0.124010\pi$
$774$	−2.09157e12	−	3.62271e12i	−0.209478	−	0.362827i
$775$	−9.89427e11	+	1.71374e12i	−0.0985204	+	0.170642i
$776$	7.03861e11	+	1.21912e12i	0.0696801	+	0.120690i
$777$	5.19864e11	+	9.00431e11i	0.0511676	+	0.0886249i
$778$	1.00797e13			0.986371
$779$	−2.72005e12	+	2.58543e12i	−0.264642	+	0.251544i
$780$	1.27308e10			0.00123148
$781$	−8.84285e11	−	1.53163e12i	−0.0850477	−	0.147307i
$782$	3.35568e12	+	5.81221e12i	0.320886	+	0.555791i
$783$	1.77661e12	−	3.07719e12i	0.168914	−	0.292567i
$784$	3.40330e10	+	5.89468e10i	0.00321720	+	0.00557235i
$785$	5.06897e11	−	8.77971e11i	0.0476438	−	0.0825215i
$786$	6.00199e11			0.0560911
$787$	−1.22421e12			−0.113755			−0.0568773	−	0.998381i	$-0.518114\pi$
$787$	−1.22421e12			−0.113755			−0.0568773	+	0.998381i	$0.518114\pi$
$788$	2.36956e12	−	4.10420e12i	0.218927	−	0.379193i
$789$	6.02837e11	−	1.04414e12i	0.0553801	−	0.0959211i
$790$	1.46536e12			0.133851
$791$	−6.49976e12			−0.590342
$792$	8.77699e11	−	1.52022e12i	0.0792652	−	0.137291i
$793$	−1.89183e12	−	3.27675e12i	−0.169884	−	0.294248i
$794$	−1.86784e12	+	3.23519e12i	−0.166781	+	0.288873i
$795$	−9.45321e10	−	1.63734e11i	−0.00839319	−	0.0145374i
$796$	−1.79973e12	−	3.11723e12i	−0.158891	−	0.275207i
$797$	1.62623e13			1.42764			0.713821	−	0.700328i	$-0.246963\pi$
$797$	1.62623e13			1.42764			0.713821	+	0.700328i	$0.246963\pi$
$798$	−7.14253e11	−	2.10942e11i	−0.0623504	−	0.0184141i
$799$	1.25940e13			1.09321
$800$	−1.01037e12	−	1.75001e12i	−0.0872118	−	0.151055i
$801$	−4.58705e12	−	7.94500e12i	−0.393719	−	0.681942i
$802$	−4.13411e12	+	7.16049e12i	−0.352856	+	0.611164i
$803$	−1.42819e12	−	2.47370e12i	−0.121218	−	0.209955i
$804$	1.76556e10	−	3.05803e10i	0.00149015	−	0.00258101i
$805$	1.16133e12			0.0974711
$806$	3.87747e11			0.0323624
$807$	7.54336e11	−	1.30655e12i	0.0626086	−	0.108441i
$808$	−1.13370e12	+	1.96363e12i	−0.0935722	+	0.162072i
$809$	−8.21942e12			−0.674641			−0.337320	−	0.941390i	$-0.609521\pi$
$809$	−8.21942e12			−0.674641			−0.337320	+	0.941390i	$0.609521\pi$
$810$	9.73533e11			0.0794636
$811$	−6.76839e12	+	1.17232e13i	−0.549403	+	0.951595i	0.448912	+	0.893576i	$0.351812\pi$
$811$	−6.76839e12	+	1.17232e13i	−0.549403	+	0.951595i	−0.998315	+	0.0580187i	$0.981522\pi$
$812$	−5.56748e12	−	9.64316e12i	−0.449424	−	0.778425i
$813$	−5.03326e11	+	8.71787e11i	−0.0404056	+	0.0699846i
$814$	2.22956e12	+	3.86171e12i	0.177996	+	0.308297i
$815$	1.04481e11	+	1.80966e11i	0.00829519	+	0.0143677i
$816$	−3.12739e11			−0.0246932
$817$	−5.51691e12	+	5.24385e12i	−0.433208	+	0.411766i
$818$	−2.20421e12			−0.172133
$819$	−1.44371e12	−	2.50059e12i	−0.112125	−	0.194207i
$820$	1.36344e11	+	2.36155e11i	0.0105311	+	0.0182404i
$821$	1.98981e12	−	3.44645e12i	0.152851	−	0.264745i	−0.779424	−	0.626497i	$-0.784488\pi$
$821$	1.98981e12	−	3.44645e12i	0.152851	−	0.264745i	0.932274	+	0.361752i	$0.117821\pi$
$822$	6.27449e11	+	1.08677e12i	0.0479353	+	0.0830264i
$823$	7.52520e12	−	1.30340e13i	0.571766	−	0.990328i	−0.424618	−	0.905372i	$-0.639592\pi$
$823$	7.52520e12	−	1.30340e13i	0.571766	−	0.990328i	0.996385	−	0.0849558i	$-0.0270749\pi$
$824$	−7.18942e12			−0.543277
$825$	−5.53146e11			−0.0415717
$826$	3.02391e12	−	5.23757e12i	0.226026	−	0.391489i
$827$	1.32075e13	−	2.28761e13i	0.981855	−	1.70062i	0.326701	−	0.945128i	$-0.394063\pi$
$827$	1.32075e13	−	2.28761e13i	0.981855	−	1.70062i	0.655154	−	0.755495i	$-0.272604\pi$
$828$	−5.73794e12			−0.424248
$829$	4.41276e12			0.324500			0.162250	−	0.986750i	$-0.448125\pi$
$829$	4.41276e12			0.324500			0.162250	+	0.986750i	$0.448125\pi$
$830$	6.47447e11	−	1.12141e12i	0.0473536	−	0.0820189i
$831$	7.30511e11	+	1.26528e12i	0.0531401	+	0.0920413i
$832$	−1.97977e11	+	3.42907e11i	−0.0143239	+	0.0248097i
$833$	1.89628e11	+	3.28445e11i	0.0136458	+	0.0236352i
$834$	−2.21166e11	−	3.83070e11i	−0.0158296	−	0.0274177i
$835$	−6.30317e11			−0.0448715
$836$	−3.06324e12	−	9.04675e11i	−0.216897	−	0.0640567i
$837$	−5.25965e11			−0.0370418
$838$	−4.13203e12	−	7.15688e12i	−0.289444	−	0.501332i
$839$	−1.89531e12	−	3.28277e12i	−0.132054	−	0.228724i	0.792414	−	0.609983i	$-0.208824\pi$
$839$	−1.89531e12	−	3.28277e12i	−0.132054	−	0.228724i	−0.924468	+	0.381259i	$0.875490\pi$
$840$	−2.70582e10	+	4.68661e10i	−0.00187518	+	0.00324790i
$841$	−1.68072e13	−	2.91109e13i	−1.15854	−	2.00666i
$842$	−2.31755e12	+	4.01411e12i	−0.158900	+	0.275223i
$843$	1.70464e12			0.116254
$844$	−8.18514e12			−0.555245
$845$	−8.10022e11	+	1.40300e12i	−0.0546565	+	0.0946678i
$846$	−5.38366e12	+	9.32478e12i	−0.361336	+	0.625853i
$847$	1.17599e13			0.785108
$848$	5.88030e12			0.390497
$849$	−1.14656e12	+	1.98590e12i	−0.0757379	+	0.131182i
$850$	−5.62966e12	−	9.75086e12i	−0.369911	−	0.640704i
$851$	7.28785e12	−	1.26229e13i	0.476339	−	0.825043i
$852$	−1.34693e11	−	2.33295e11i	−0.00875721	−	0.0151679i
$853$	7.48734e12	+	1.29684e13i	0.484236	+	0.838721i	0.999836	−	0.0181085i	$-0.00576444\pi$
$853$	7.48734e12	+	1.29684e13i	0.484236	+	0.838721i	−0.515600	+	0.856829i	$0.672431\pi$
$854$	1.60837e13			1.03473
$855$	−4.18615e11	−	1.73745e12i	−0.0267897	−	0.111190i
$856$	−2.84394e12			−0.181046
$857$	−1.63352e12	−	2.82934e12i	−0.103445	−	0.179173i	0.809657	−	0.586904i	$-0.199653\pi$
$857$	−1.63352e12	−	2.82934e12i	−0.103445	−	0.179173i	−0.913102	+	0.407731i	$0.866320\pi$
$858$	5.41932e10	+	9.38654e10i	0.00341391	+	0.00591307i
$859$	1.08178e13	−	1.87370e13i	0.677907	−	1.17417i	−0.297703	−	0.954659i	$-0.596221\pi$
$859$	1.08178e13	−	1.87370e13i	0.677907	−	1.17417i	0.975610	−	0.219511i	$-0.0704461\pi$
$860$	2.76538e11	+	4.78978e11i	0.0172390	+	0.0298588i
$861$	−2.70662e11	+	4.68801e11i	−0.0167847	+	0.0290720i
$862$	6.81943e12			0.420693
$863$	−1.59630e13			−0.979640			−0.489820	−	0.871824i	$-0.662937\pi$
$863$	−1.59630e13			−0.979640			−0.489820	+	0.871824i	$0.662937\pi$
$864$	2.68549e11	−	4.65141e11i	0.0163950	−	0.0283970i
$865$	1.72249e12	−	2.98344e12i	0.104613	−	0.181195i
$866$	−1.78507e13			−1.07851
$867$	−1.92798e11			−0.0115882
$868$	−8.24124e11	+	1.42742e12i	−0.0492781	+	0.0853521i
$869$	6.23785e12	+	1.08043e13i	0.371062	+	0.642698i
$870$	−1.16936e11	+	2.02539e11i	−0.00692010	+	0.0119860i
$871$	−1.24551e11	−	2.15728e11i	−0.00733271	−	0.0127006i
$872$	7.64872e9	+	1.32480e10i	0.000447986	+	0.000775934i
$873$	−6.70600e12			−0.390750
$874$	2.44550e12	+	1.01500e13i	0.141764	+	0.588391i
$875$	−3.92291e12			−0.226241
$876$	−2.17539e11	−	3.76789e11i	−0.0124816	−	0.0216187i
$877$	8.62917e12	+	1.49462e13i	0.492573	+	0.853162i	0.999963	−	0.00855464i	$-0.00272306\pi$
$877$	8.62917e12	+	1.49462e13i	0.492573	+	0.853162i	−0.507390	+	0.861716i	$0.669390\pi$
$878$	−4.33474e12	+	7.50800e12i	−0.246172	+	0.426382i
$879$	−5.60572e11	−	9.70940e11i	−0.0316724	−	0.0548583i
$880$	−1.16045e11	+	2.00996e11i	−0.00652313	+	0.0112984i
$881$	−1.70890e13			−0.955709			−0.477855	−	0.878439i	$-0.658585\pi$
$881$	−1.70890e13			−0.955709			−0.477855	+	0.878439i	$0.658585\pi$
$882$	−3.24247e11			−0.0180413
$883$	−7.99292e12	+	1.38441e13i	−0.442469	+	0.766378i	−0.997872	−	0.0652029i	$-0.979231\pi$
$883$	−7.99292e12	+	1.38441e13i	−0.442469	+	0.766378i	0.555403	+	0.831581i	$0.312564\pi$
$884$	−1.10311e12	+	1.91063e12i	−0.0607550	+	0.105231i
$885$	−1.27025e11			−0.00696057
$886$	−1.29493e13			−0.705982
$887$	−1.29046e13	+	2.23515e13i	−0.699986	+	1.21241i	0.268484	+	0.963284i	$0.413477\pi$
$887$	−1.29046e13	+	2.23515e13i	−0.699986	+	1.21241i	−0.968471	+	0.249128i	$0.919856\pi$
$888$	3.39602e11	+	5.88208e11i	0.0183279	+	0.0317448i
$889$	1.03812e13	−	1.79808e13i	0.557429	−	0.965496i
$890$	6.06478e11	+	1.05045e12i	0.0324011	+	0.0561204i
$891$	4.14420e12	+	7.17797e12i	0.220288	+	0.381550i
$892$	−2.74267e11			−0.0145055
$893$	1.87894e13	+	5.54913e12i	0.988740	+	0.292007i
$894$	−4.53418e11			−0.0237400
$895$	−3.83454e11	−	6.64162e11i	−0.0199761	−	0.0345996i
$896$	−8.41568e11	−	1.45764e12i	−0.0436217	−	0.0755551i
$897$	1.77143e11	−	3.06822e11i	0.00913606	−	0.0158241i
$898$	8.29612e12	+	1.43693e13i	0.425727	+	0.737381i
$899$	−3.56158e12	+	6.16884e12i	−0.181854	+	0.314981i
$900$	9.62625e12			0.489064
$901$	3.27643e13			1.65630
$902$	−1.16080e12	+	2.01056e12i	−0.0583886	+	0.101132i
$903$	−5.48967e11	+	9.50839e11i	−0.0274759	+	0.0475896i
$904$	−4.24598e12			−0.211456
$905$	1.85355e12			0.0918515
$906$	−8.67160e11	+	1.50197e12i	−0.0427585	+	0.0740599i
$907$	4.74686e12	+	8.22181e12i	0.232902	+	0.403399i	0.958661	−	0.284551i	$-0.0918444\pi$
$907$	4.74686e12	+	8.22181e12i	0.232902	+	0.403399i	−0.725759	+	0.687949i	$0.758511\pi$
$908$	−1.27284e12	+	2.20462e12i	−0.0621421	+	0.107633i
$909$	−5.40064e12	−	9.35417e12i	−0.262366	−	0.454431i
$910$	1.90881e11	+	3.30616e11i	0.00922735	+	0.0159822i
$911$	−8.09195e12			−0.389243			−0.194621	−	0.980878i	$-0.562348\pi$
$911$	−8.09195e12			−0.389243			−0.194621	+	0.980878i	$0.562348\pi$
$912$	−4.66587e11	−	1.37798e11i	−0.0223335	−	0.00659580i
$913$	1.10244e13			0.525093
$914$	1.55167e12	+	2.68757e12i	0.0735429	+	0.127380i
$915$	−1.68907e11	−	2.92555e11i	−0.00796622	−	0.0137979i
$916$	−9.43617e12	+	1.63439e13i	−0.442860	+	0.767055i
$917$	8.99920e12	+	1.55871e13i	0.420283	+	0.727951i
$918$	1.49632e12	−	2.59171e12i	0.0695398	−	0.120446i
$919$	2.06975e13			0.957192			0.478596	−	0.878035i	$-0.341146\pi$
$919$	2.06975e13			0.957192			0.478596	+	0.878035i	$0.341146\pi$
$920$	7.58644e11			0.0349134
$921$	−1.20894e12	+	2.09394e12i	−0.0553650	+	0.0958950i
$922$	−4.63713e12	+	8.03174e12i	−0.211329	+	0.366033i
$923$	−1.90037e12			−0.0861849
$924$	−4.60733e11			−0.0207934
$925$	−1.22264e13	+	2.11768e13i	−0.549114	+	0.951093i
$926$	−1.55422e13	−	2.69198e13i	−0.694644	−	1.20316i
$927$	1.71242e13	−	2.96600e13i	0.761643	−	1.31921i
$928$	−3.63697e12	−	6.29941e12i	−0.160981	−	0.278827i
$929$	9.92733e12	+	1.71946e13i	0.437282	+	0.757395i	0.997479	−	0.0709649i	$-0.0226078\pi$
$929$	9.92733e12	+	1.71946e13i	0.437282	+	0.757395i	−0.560197	+	0.828360i	$0.689275\pi$
$930$	3.46189e10			0.00151754
$931$	1.38194e11	+	5.73572e11i	0.00602859	+	0.0250216i
$932$	3.22553e11			0.0140033
$933$	−1.20278e12	−	2.08327e12i	−0.0519657	−	0.0900073i
$934$	1.45058e13	+	2.51249e13i	0.623709	+	1.08030i
$935$	−6.46591e11	+	1.11993e12i	−0.0276680	+	0.0479223i
$936$	−9.43109e11	−	1.63351e12i	−0.0401625	−	0.0695635i
$937$	−1.00126e13	+	1.73423e13i	−0.424343	+	0.734984i	−0.996359	−	0.0852585i	$-0.972828\pi$
$937$	−1.00126e13	+	1.73423e13i	−0.424343	+	0.734984i	0.572015	+	0.820243i	$0.306162\pi$
$938$	1.05889e12			0.0446619
$939$	−8.27530e11			−0.0347367
$940$	7.11804e11	−	1.23288e12i	0.0297362	−	0.0515045i
$941$	−1.15846e13	+	2.00651e13i	−0.481645	+	0.834234i	−0.999778	−	0.0210662i	$-0.993294\pi$
$941$	−1.15846e13	+	2.00651e13i	−0.481645	+	0.834234i	0.518133	+	0.855300i	$0.326627\pi$
$942$	1.31468e12			0.0543992
$943$	7.58870e12			0.312511
$944$	1.97538e12	−	3.42145e12i	0.0809610	−	0.140229i
$945$	−2.58924e11	−	4.48469e11i	−0.0105616	−	0.0182932i
$946$	−2.35437e12	+	4.07789e12i	−0.0955796	+	0.165549i
$947$	4.13389e12	+	7.16011e12i	0.167026	+	0.289297i	0.937373	−	0.348328i	$-0.113250\pi$
$947$	4.13389e12	+	7.16011e12i	0.167026	+	0.289297i	−0.770347	+	0.637625i	$0.779917\pi$
$948$	9.50138e11	+	1.64569e12i	0.0382076	+	0.0661774i
$949$	−3.06925e12			−0.122838
$950$	−4.10270e12	−	1.70282e13i	−0.163423	−	0.678285i
$951$	−1.98845e12			−0.0788318
$952$	−4.68911e12	−	8.12178e12i	−0.185023	−	0.320468i
$953$	−5.01067e12	−	8.67873e12i	−0.196778	−	0.340830i	0.750704	−	0.660639i	$-0.229715\pi$
$953$	−5.01067e12	−	8.67873e12i	−0.196778	−	0.340830i	−0.947482	+	0.319809i	$0.896381\pi$
$954$	−1.40061e13	+	2.42592e13i	−0.547455	+	0.948220i
$955$	1.17034e12	+	2.02709e12i	0.0455300	+	0.0788602i
$956$	6.81580e12	−	1.18053e13i	0.263910	−	0.457106i
$957$	−1.99113e12			−0.0767353
$958$	3.48668e13			1.33742
$959$	−1.88156e13	+	3.25895e13i	−0.718346	+	1.24421i
$960$	−1.76758e10	+	3.06154e10i	−0.000671674	+	0.00116337i
$961$	−2.53852e13			−0.960120
$962$	4.79143e12			0.180375
$963$	6.77388e12	−	1.17327e13i	0.253816	−	0.439622i
$964$	6.51263e12	+	1.12802e13i	0.242890	+	0.420698i
$965$	8.84698e11	−	1.53234e12i	0.0328414	−	0.0568830i
$966$	7.53007e11	+	1.30425e12i	0.0278229	+	0.0481906i
$967$	−1.65820e13	−	2.87209e13i	−0.609843	−	1.05628i	−0.991266	−	0.131879i	$-0.957899\pi$
$967$	−1.65820e13	−	2.87209e13i	−0.609843	−	1.05628i	0.381423	−	0.924401i	$-0.375434\pi$
$968$	7.68219e12			0.281220
$969$	−2.59977e12	−	7.67796e11i	−0.0947279	−	0.0279762i
$970$	8.86637e11			0.0321568
$971$	−1.23354e13	−	2.13655e13i	−0.445314	−	0.771307i	0.552760	−	0.833341i	$-0.313575\pi$
$971$	−1.23354e13	−	2.13655e13i	−0.445314	−	0.771307i	−0.998074	+	0.0620336i	$0.980241\pi$
$972$	1.92173e12	+	3.32853e12i	0.0690548	+	0.119606i
$973$	6.63218e12	−	1.14873e13i	0.237218	−	0.410874i
$974$	−5.16170e12	−	8.94032e12i	−0.183771	−	0.318301i
$975$	−2.97185e11	+	5.14739e11i	−0.0105319	+	0.0182417i
$976$	1.05067e13			0.370632
$977$	−2.08255e13			−0.731256			−0.365628	−	0.930761i	$-0.619146\pi$
$977$	−2.08255e13			−0.731256			−0.365628	+	0.930761i	$0.619146\pi$
$978$	−1.35490e11	+	2.34676e11i	−0.00473569	+	0.00820245i
$979$	−5.16340e12	+	8.94327e12i	−0.179644	+	0.311153i
$980$	4.28705e10			0.00148471
$981$	−7.28728e10			−0.00251220
$982$	1.69977e13	−	2.94408e13i	0.583294	−	1.01029i
$983$	−5.35501e12	−	9.27514e12i	−0.182923	−	0.316833i	0.759951	−	0.649980i	$-0.225223\pi$
$983$	−5.35501e12	−	9.27514e12i	−0.182923	−	0.316833i	−0.942875	+	0.333147i	$0.891889\pi$
$984$	−1.76811e11	+	3.06245e11i	−0.00601217	+	0.0104134i
$985$	−1.49244e12	−	2.58498e12i	−0.0505166	−	0.0874973i
$986$	−2.02647e13	−	3.50996e13i	−0.682802	−	1.18265i
$987$	2.82606e12			0.0947882
$988$	−2.48762e12	+	2.36450e12i	−0.0830574	+	0.0789465i
$989$	1.53917e13			0.511567
$990$	−5.52808e11	−	9.57492e11i	−0.0182901	−	0.0316794i
$991$	−2.83683e13	−	4.91354e13i	−0.934334	−	1.61831i	−0.775817	−	0.630958i	$-0.782662\pi$
$991$	−2.83683e13	−	4.91354e13i	−0.934334	−	1.61831i	−0.158517	−	0.987356i	$-0.550671\pi$
$992$	−5.38360e11	+	9.32468e11i	−0.0176511	+	0.0305725i
$993$	−1.41729e12	−	2.45481e12i	−0.0462579	−	0.0801211i
$994$	4.03908e12	−	6.99589e12i	0.131233	−	0.227303i
$995$	−2.26708e12			−0.0733269
$996$	1.67922e12			0.0540679
$997$	−1.89609e13	+	3.28413e13i	−0.607760	+	1.05267i	0.383849	+	0.923396i	$0.374598\pi$
$997$	−1.89609e13	+	3.28413e13i	−0.607760	+	1.05267i	−0.991609	+	0.129275i	$0.958735\pi$
$998$	2.67910e12	−	4.64034e12i	0.0854873	−	0.148068i
$999$	−6.49941e12			−0.206457

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.c.a.7.3	✓	14
19.11	even	3	inner	38.10.c.a.11.3	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.c.a.7.3	✓	14	1.1	even	1	trivial
38.10.c.a.11.3	yes	14	19.11	even	3	inner

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)

\(f(q)\)	\(=\)	\(q+(8.00000 + 13.8564i) q^{2} +(6.53417 + 11.3175i) q^{3} +(-128.000 + 221.703i) q^{4} +(80.6193 + 139.637i) q^{5} +(-104.547 + 181.080i) q^{6} -6270.17 q^{7} -4096.00 q^{8} +(9756.11 - 16898.1i) q^{9} +O(q^{10})\)	\(q+(8.00000 + 13.8564i) q^{2} +(6.53417 + 11.3175i) q^{3} +(-128.000 + 221.703i) q^{4} +(80.6193 + 139.637i) q^{5} +(-104.547 + 181.080i) q^{6} -6270.17 q^{7} -4096.00 q^{8} +(9756.11 - 16898.1i) q^{9} +(-1289.91 + 2234.19i) q^{10} -21963.9 q^{11} -3345.50 q^{12} +(-11800.4 + 20438.8i) q^{13} +(-50161.3 - 86882.0i) q^{14} +(-1053.56 + 1824.82i) q^{15} +(-32768.0 - 56755.8i) q^{16} +(-182579. - 316237. i) q^{17} +312195. q^{18} +(-133057. - 552253. i) q^{19} -41277.1 q^{20} +(-40970.4 - 70962.8i) q^{21} +(-175711. - 304340. i) q^{22} +(-574353. + 994809. i) q^{23} +(-26764.0 - 46356.6i) q^{24} +(963564. - 1.66894e6i) q^{25} -377611. q^{26} +512217. q^{27} +(802581. - 1.39011e6i) q^{28} +(3.46848e6 - 6.00759e6i) q^{29} -33713.9 q^{30} -1.02684e6 q^{31} +(524288. - 908093. i) q^{32} +(-143516. - 248577. i) q^{33} +(2.92127e6 - 5.05979e6i) q^{34} +(-505496. - 875545. i) q^{35} +(2.49756e6 + 4.32591e6i) q^{36} -1.26888e7 q^{37} +(6.58778e6 - 6.26172e6i) q^{38} -308422. q^{39} +(-330216. - 571952. i) q^{40} +(-3.30315e6 - 5.72122e6i) q^{41} +(655526. - 1.13540e6i) q^{42} +(-6.69956e6 - 1.16040e7i) q^{43} +(2.81138e6 - 4.86945e6i) q^{44} +3.14612e6 q^{45} -1.83793e7 q^{46} +(-1.72445e7 + 2.98684e7i) q^{47} +(428224. - 741705. i) q^{48} -1.03860e6 q^{49} +3.08340e7 q^{50} +(2.38601e6 - 4.13269e6i) q^{51} +(-3.02089e6 - 5.23234e6i) q^{52} +(-4.48631e7 + 7.77052e7i) q^{53} +(4.09773e6 + 7.09748e6i) q^{54} +(-1.77071e6 - 3.06696e6i) q^{55} +2.56826e7 q^{56} +(5.38072e6 - 5.11440e6i) q^{57} +1.10991e8 q^{58} +(3.01418e7 + 5.22072e7i) q^{59} +(-269712. - 467154. i) q^{60} +(-8.01600e7 + 1.38841e8i) q^{61} +(-8.21473e6 - 1.42283e7i) q^{62} +(-6.11724e7 + 1.05954e8i) q^{63} +1.67772e7 q^{64} -3.80534e6 q^{65} +(2.29625e6 - 3.97723e6i) q^{66} +(-5.27741e6 + 9.14074e6i) q^{67} +9.34806e7 q^{68} -1.50117e7 q^{69} +(8.08794e6 - 1.40087e7i) q^{70} +(4.02609e7 + 6.97339e7i) q^{71} +(-3.99610e7 + 6.92145e7i) q^{72} +(6.50245e7 + 1.12626e8i) q^{73} +(-1.01510e8 - 1.75821e8i) q^{74} +2.51844e7 q^{75} +(1.39467e8 + 4.11892e7i) q^{76} +1.37717e8 q^{77} +(-2.46738e6 - 4.27363e6i) q^{78} +(-2.84005e8 - 4.91911e8i) q^{79} +(5.28346e6 - 9.15123e6i) q^{80} +(-1.88683e8 - 3.26808e8i) q^{81} +(5.28504e7 - 9.15396e7i) q^{82} -5.01933e8 q^{83} +2.09768e7 q^{84} +(2.94388e7 - 5.09895e7i) q^{85} +(1.07193e8 - 1.85664e8i) q^{86} +9.06547e7 q^{87} +8.99640e7 q^{88} +(2.35086e8 - 4.07181e8i) q^{89} +(2.51690e7 + 4.35939e7i) q^{90} +(7.39902e7 - 1.28155e8i) q^{91} +(-1.47034e8 - 2.54671e8i) q^{92} +(-6.70956e6 - 1.16213e7i) q^{93} -5.51825e8 q^{94} +(6.63878e7 - 6.31019e7i) q^{95} +1.37032e7 q^{96} +(-1.71841e8 - 2.97637e8i) q^{97} +(-8.30883e6 - 1.43913e7i) q^{98} +(-2.14282e8 + 3.71147e8i) 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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