LMFDB - Embedded newform 8.17.d.b.3.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,17,Mod(3,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 17, names="a")

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

chi := DirichletCharacter("8.3");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 17 $
Character orbit:	$[\chi]$	$=$	8.d (of order $2$, degree $1$, 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:	$12.9859635085$
Analytic rank:	$0$
Dimension:	$14$
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} - 7 x^{13} + 7894 x^{12} + 219192 x^{11} - 135772320 x^{10} + 11331786624 x^{9} + \cdots + 27\!\cdots\!20 $ x^14 - 7x^13 + 7894x^12 + 219192x^11 - 135772320x^10 + 11331786624x^9 - 652293490688x^8 + 465478371454976x^7 - 697940891942912x^6 + 5355071973862932480x^5 + 64434406660761845760x^4 - 122098039773726666915840x^3 + 21723325027733376807731200x^2 - 2811006993630615015868334080*x + 279841437428593117864520581120
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{91}\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.6
Root			$41.8643 - 116.115i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.17.d.b.3.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-107.729 + 232.229i) q^{2} +693.074 q^{3} +(-42325.1 - 50035.5i) q^{4} +333015. i q^{5} +(-74663.9 + 160952. i) q^{6} -1.01327e7i q^{7} +(1.61794e7 - 4.43887e6i) q^{8} -4.25664e7 q^{9} +O(q^{10})$	\(q+(-107.729 + 232.229i) q^{2} +693.074 q^{3} +(-42325.1 - 50035.5i) q^{4} +333015. i q^{5} +(-74663.9 + 160952. i) q^{6} -1.01327e7i q^{7} +(1.61794e7 - 4.43887e6i) q^{8} -4.25664e7 q^{9} +(-7.73360e7 - 3.58753e7i) q^{10} +3.53720e8 q^{11} +(-2.93344e7 - 3.46783e7i) q^{12} +4.13337e8i q^{13} +(2.35310e9 + 1.09158e9i) q^{14} +2.30804e8i q^{15} +(-7.12145e8 + 4.23552e9i) q^{16} +7.22096e9 q^{17} +(4.58562e9 - 9.88517e9i) q^{18} +1.17497e10 q^{19} +(1.66626e10 - 1.40949e10i) q^{20} -7.02268e9i q^{21} +(-3.81058e10 + 8.21442e10i) q^{22} -3.06432e10i q^{23} +(1.12135e10 - 3.07646e9i) q^{24} +4.16887e10 q^{25} +(-9.59889e10 - 4.45282e10i) q^{26} -5.93362e10 q^{27} +(-5.06993e11 + 4.28865e11i) q^{28} -4.93415e11i q^{29} +(-5.35995e10 - 2.48642e10i) q^{30} -8.90125e11i q^{31} +(-9.06893e11 - 6.21668e11i) q^{32} +2.45154e11 q^{33} +(-7.77905e11 + 1.67692e12i) q^{34} +3.37433e12 q^{35} +(1.80162e12 + 2.12983e12i) q^{36} -2.63407e12i q^{37} +(-1.26578e12 + 2.72862e12i) q^{38} +2.86473e11i q^{39} +(1.47821e12 + 5.38797e12i) q^{40} +1.13055e13 q^{41} +(1.63087e12 + 7.56543e11i) q^{42} -6.39851e11 q^{43} +(-1.49712e13 - 1.76986e13i) q^{44} -1.41753e13i q^{45} +(7.11626e12 + 3.30115e12i) q^{46} +9.74279e12i q^{47} +(-4.93569e11 + 2.93552e12i) q^{48} -6.94378e13 q^{49} +(-4.49107e12 + 9.68134e12i) q^{50} +5.00466e12 q^{51} +(2.06815e13 - 1.74945e13i) q^{52} +3.29935e13i q^{53} +(6.39221e12 - 1.37796e13i) q^{54} +1.17794e14i q^{55} +(-4.49775e13 - 1.63940e14i) q^{56} +8.14340e12 q^{57} +(1.14586e14 + 5.31550e13i) q^{58} -7.37981e13 q^{59} +(1.15484e13 - 9.76880e12i) q^{60} -3.01180e14i q^{61} +(2.06713e14 + 9.58920e13i) q^{62} +4.31310e14i q^{63} +(2.42068e14 - 1.43636e14i) q^{64} -1.37647e14 q^{65} +(-2.64101e13 + 5.69320e13i) q^{66} +6.34561e14 q^{67} +(-3.05628e14 - 3.61305e14i) q^{68} -2.12380e13i q^{69} +(-3.63512e14 + 7.83619e14i) q^{70} -3.99021e12i q^{71} +(-6.88696e14 + 1.88946e14i) q^{72} -7.97174e14 q^{73} +(6.11709e14 + 2.83765e14i) q^{74} +2.88933e13 q^{75} +(-4.97306e14 - 5.87902e14i) q^{76} -3.58412e15i q^{77} +(-6.65274e13 - 3.08613e13i) q^{78} +9.10605e14i q^{79} +(-1.41049e15 - 2.37155e14i) q^{80} +1.79122e15 q^{81} +(-1.21793e15 + 2.62547e15i) q^{82} +7.04053e14 q^{83} +(-3.51383e14 + 2.97235e14i) q^{84} +2.40469e15i q^{85} +(6.89303e13 - 1.48592e14i) q^{86} -3.41973e14i q^{87} +(5.72296e15 - 1.57012e15i) q^{88} -1.16467e15 q^{89} +(3.29191e15 + 1.52708e15i) q^{90} +4.18820e15 q^{91} +(-1.53325e15 + 1.29698e15i) q^{92} -6.16922e14i q^{93} +(-2.26256e15 - 1.04958e15i) q^{94} +3.91283e15i q^{95} +(-6.28544e14 - 4.30861e14i) q^{96} -3.41421e15 q^{97} +(7.48044e15 - 1.61255e16i) q^{98} -1.50566e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 350 q^{2} + 11964 q^{3} - 54220 q^{4} + 4868124 q^{6} + 10899160 q^{8} + 86397354 q^{9}+O(q^{10}) $ 14 * q - 350 * q^2 + 11964 * q^3 - 54220 * q^4 + 4868124 * q^6 + 10899160 * q^8 + 86397354 * q^9	\( 14 q - 350 q^{2} + 11964 q^{3} - 54220 q^{4} + 4868124 q^{6} + 10899160 q^{8} + 86397354 q^{9} + 87155280 q^{10} - 49140292 q^{11} + 31616184 q^{12} - 2675193504 q^{14} + 9716374544 q^{16} - 9985136356 q^{17} - 7692086106 q^{18} + 62922133180 q^{19} + 31953450720 q^{20} - 51493048676 q^{22} + 54962419344 q^{24} - 429906632050 q^{25} - 518273679696 q^{26} + 655936606584 q^{27} + 102542376000 q^{28} - 364331826720 q^{30} + 95751080800 q^{32} + 4034287537464 q^{33} + 1015818512644 q^{34} - 3057653406720 q^{35} - 9569289445092 q^{36} + 9010383442844 q^{38} - 4027933291200 q^{40} + 8719629072668 q^{41} - 6653698130880 q^{42} + 16716309178300 q^{43} - 4351929975880 q^{44} + 21043605267744 q^{46} + 46562301973344 q^{48} - 104740771400434 q^{49} - 54483696687710 q^{50} + 40911296041848 q^{51} - 73249356722400 q^{52} - 18031398151752 q^{54} + 110873799752064 q^{56} - 310730528383176 q^{57} + 256627273576560 q^{58} + 347007330293180 q^{59} - 83822619107520 q^{60} + 346701622780800 q^{62} - 332173589517760 q^{64} + 220877370432000 q^{65} + 875905832132808 q^{66} - 614258765968196 q^{67} - 12\!\cdots\!76 q^{68}+ \cdots - 18\!\cdots\!92 q^{99}+O(q^{100}) \) 14 * q - 350 * q^2 + 11964 * q^3 - 54220 * q^4 + 4868124 * q^6 + 10899160 * q^8 + 86397354 * q^9 + 87155280 * q^10 - 49140292 * q^11 + 31616184 * q^12 - 2675193504 * q^14 + 9716374544 * q^16 - 9985136356 * q^17 - 7692086106 * q^18 + 62922133180 * q^19 + 31953450720 * q^20 - 51493048676 * q^22 + 54962419344 * q^24 - 429906632050 * q^25 - 518273679696 * q^26 + 655936606584 * q^27 + 102542376000 * q^28 - 364331826720 * q^30 + 95751080800 * q^32 + 4034287537464 * q^33 + 1015818512644 * q^34 - 3057653406720 * q^35 - 9569289445092 * q^36 + 9010383442844 * q^38 - 4027933291200 * q^40 + 8719629072668 * q^41 - 6653698130880 * q^42 + 16716309178300 * q^43 - 4351929975880 * q^44 + 21043605267744 * q^46 + 46562301973344 * q^48 - 104740771400434 * q^49 - 54483696687710 * q^50 + 40911296041848 * q^51 - 73249356722400 * q^52 - 18031398151752 * q^54 + 110873799752064 * q^56 - 310730528383176 * q^57 + 256627273576560 * q^58 + 347007330293180 * q^59 - 83822619107520 * q^60 + 346701622780800 * q^62 - 332173589517760 * q^64 + 220877370432000 * q^65 + 875905832132808 * q^66 - 614258765968196 * q^67 - 1235787871965976 * q^68 - 442172390987520 * q^70 - 1312232111609976 * q^72 - 542888518370276 * q^73 + 2394643836493776 * q^74 + 2861985572983740 * q^75 - 614792000883272 * q^76 - 4928152344599520 * q^78 + 6402194304908160 * q^80 - 5344304371237818 * q^81 + 4810720063300804 * q^82 + 7362421930746044 * q^83 - 9316784627856000 * q^84 - 8963192329247716 * q^86 + 3396904358318224 * q^88 - 408131327364580 * q^89 + 14680290550241520 * q^90 - 7162887702930432 * q^91 - 9213856910218560 * q^92 - 15838781433150144 * q^94 + 48917704300183104 * q^96 + 18372136634257180 * q^97 + 34005570793293730 * q^98 - 18934692015468492 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−107.729	+	232.229i	−0.420815	+	0.907146i
$2$	−107.729	+	232.229i	−0.420815	+	0.907146i
$3$	693.074			0.105635			0.0528177	−	0.998604i	$-0.483180\pi$
$3$	693.074			0.105635			0.0528177	+	0.998604i	$0.483180\pi$
$4$	−42325.1	−	50035.5i	−0.645829	−	0.763482i
$5$			333015.i			0.852519i	0.904601	+	0.426260i	$0.140169\pi$
$5$			333015.i			0.852519i	−0.904601	+	0.426260i	$0.859831\pi$
$6$	−74663.9	+	160952.i	−0.0444530	+	0.0958267i
$7$		−	1.01327e7i		−	1.75768i	−0.477120	−	0.878838i	$-0.658319\pi$
$7$		−	1.01327e7i		−	1.75768i	0.477120	−	0.878838i	$-0.341681\pi$
$8$	1.61794e7	−	4.43887e6i	0.964365	−	0.264577i
$9$	−4.25664e7			−0.988841
$10$	−7.73360e7	−	3.58753e7i	−0.773360	−	0.358753i
$11$	3.53720e8			1.65013			0.825065	−	0.565038i	$-0.191139\pi$
$11$	3.53720e8			1.65013			0.825065	+	0.565038i	$0.191139\pi$
$12$	−2.93344e7	−	3.46783e7i	−0.0682224	−	0.0806507i
$13$			4.13337e8i			0.506707i	0.967374	+	0.253354i	$0.0815336\pi$
$13$			4.13337e8i			0.506707i	−0.967374	+	0.253354i	$0.918466\pi$
$14$	2.35310e9	+	1.09158e9i	1.59447	+	0.739657i
$15$			2.30804e8i			0.0900562i
$16$	−7.12145e8	+	4.23552e9i	−0.165809	+	0.986158i
$17$	7.22096e9			1.03515			0.517575	−	0.855638i	$-0.326835\pi$
$17$	7.22096e9			1.03515			0.517575	+	0.855638i	$0.326835\pi$
$18$	4.58562e9	−	9.88517e9i	0.416119	−	0.897024i
$19$	1.17497e10			0.691827			0.345913	−	0.938266i	$-0.387569\pi$
$19$	1.17497e10			0.691827			0.345913	+	0.938266i	$0.387569\pi$
$20$	1.66626e10	−	1.40949e10i	0.650883	−	0.550582i
$21$		−	7.02268e9i		−	0.185673i
$22$	−3.81058e10	+	8.21442e10i	−0.694400	+	1.49691i
$23$		−	3.06432e10i		−	0.391302i	−0.980674	−	0.195651i	$-0.937318\pi$
$23$		−	3.06432e10i		−	0.391302i	0.980674	−	0.195651i	$-0.0626819\pi$
$24$	1.12135e10	−	3.07646e9i	0.101871	−	0.0279487i
$25$	4.16887e10			0.273211
$26$	−9.59889e10	−	4.45282e10i	−0.459658	−	0.213230i
$27$	−5.93362e10			−0.210092
$28$	−5.06993e11	+	4.28865e11i	−1.34195	+	1.13516i
$29$		−	4.93415e11i		−	0.986345i	−0.869932	−	0.493172i	$-0.835837\pi$
$29$		−	4.93415e11i		−	0.986345i	0.869932	−	0.493172i	$-0.164163\pi$
$30$	−5.35995e10	−	2.48642e10i	−0.0816941	−	0.0378970i
$31$		−	8.90125e11i		−	1.04366i	−0.853051	−	0.521828i	$-0.825250\pi$
$31$		−	8.90125e11i		−	1.04366i	0.853051	−	0.521828i	$-0.174750\pi$
$32$	−9.06893e11	−	6.21668e11i	−0.824815	−	0.565403i
$33$	2.45154e11			0.174312
$34$	−7.77905e11	+	1.67692e12i	−0.435607	+	0.939033i
$35$	3.37433e12			1.49845
$36$	1.80162e12	+	2.12983e12i	0.638623	+	0.754962i
$37$		−	2.63407e12i		−	0.749918i	−0.927041	−	0.374959i	$-0.877657\pi$
$37$		−	2.63407e12i		−	0.749918i	0.927041	−	0.374959i	$-0.122343\pi$
$38$	−1.26578e12	+	2.72862e12i	−0.291131	+	0.627588i
$39$			2.86473e11i			0.0535262i
$40$	1.47821e12	+	5.38797e12i	0.225557	+	0.822139i
$41$	1.13055e13			1.41586			0.707928	−	0.706285i	$-0.249630\pi$
$41$	1.13055e13			1.41586			0.707928	+	0.706285i	$0.249630\pi$
$42$	1.63087e12	+	7.56543e11i	0.168432	+	0.0781339i
$43$	−6.39851e11			−0.0547433			−0.0273717	−	0.999625i	$-0.508714\pi$
$43$	−6.39851e11			−0.0547433			−0.0273717	+	0.999625i	$0.508714\pi$
$44$	−1.49712e13	−	1.76986e13i	−1.06570	−	1.25984i
$45$		−	1.41753e13i		−	0.843006i
$46$	7.11626e12	+	3.30115e12i	0.354968	+	0.164666i
$47$			9.74279e12i			0.409167i	0.978849	+	0.204584i	$0.0655840\pi$
$47$			9.74279e12i			0.409167i	−0.978849	+	0.204584i	$0.934416\pi$
$48$	−4.93569e11	+	2.93552e12i	−0.0175153	+	0.104173i
$49$	−6.94378e13			−2.08943
$50$	−4.49107e12	+	9.68134e12i	−0.114971	+	0.247842i
$51$	5.00466e12			0.109349
$52$	2.06815e13	−	1.74945e13i	0.386862	−	0.327246i
$53$			3.29935e13i			0.529933i	0.964258	+	0.264966i	$0.0853609\pi$
$53$			3.29935e13i			0.529933i	−0.964258	+	0.264966i	$0.914639\pi$
$54$	6.39221e12	−	1.37796e13i	0.0884099	−	0.190584i
$55$			1.17794e14i			1.40677i
$56$	−4.49775e13	−	1.63940e14i	−0.465041	−	1.69504i
$57$	8.14340e12			0.0730814
$58$	1.14586e14	+	5.31550e13i	0.894759	+	0.415069i
$59$	−7.37981e13			−0.502608			−0.251304	−	0.967908i	$-0.580859\pi$
$59$	−7.37981e13			−0.502608			−0.251304	+	0.967908i	$0.580859\pi$
$60$	1.15484e13	−	9.76880e12i	0.0687563	−	0.0581609i
$61$		−	3.01180e14i		−	1.57104i	−0.618837	−	0.785520i	$-0.712396\pi$
$61$		−	3.01180e14i		−	1.57104i	0.618837	−	0.785520i	$-0.287604\pi$
$62$	2.06713e14	+	9.58920e13i	0.946749	+	0.439186i
$63$			4.31310e14i			1.73806i
$64$	2.42068e14	−	1.43636e14i	0.859998	−	0.510297i
$65$	−1.37647e14			−0.431978
$66$	−2.64101e13	+	5.69320e13i	−0.0733531	+	0.158127i
$67$	6.34561e14			1.56270			0.781349	−	0.624095i	$-0.214532\pi$
$67$	6.34561e14			1.56270			0.781349	+	0.624095i	$0.214532\pi$
$68$	−3.05628e14	−	3.61305e14i	−0.668531	−	0.790319i
$69$		−	2.12380e13i		−	0.0413353i
$70$	−3.63512e14	+	7.83619e14i	−0.630572	+	1.35932i
$71$		−	3.99021e12i		−	0.00617916i	−0.999995	−	0.00308958i	$-0.999017\pi$
$71$		−	3.99021e12i		−	0.00617916i	0.999995	−	0.00308958i	$-0.000983445\pi$
$72$	−6.88696e14	+	1.88946e14i	−0.953603	+	0.261625i
$73$	−7.97174e14			−0.988486			−0.494243	−	0.869324i	$-0.664555\pi$
$73$	−7.97174e14			−0.988486			−0.494243	+	0.869324i	$0.664555\pi$
$74$	6.11709e14	+	2.83765e14i	0.680286	+	0.315577i
$75$	2.88933e13			0.0288607
$76$	−4.97306e14	−	5.87902e14i	−0.446802	−	0.528197i
$77$		−	3.58412e15i		−	2.90039i
$78$	−6.65274e13	−	3.08613e13i	−0.0485561	−	0.0225246i
$79$			9.10605e14i			0.600224i	0.953904	+	0.300112i	$0.0970240\pi$
$79$			9.10605e14i			0.600224i	−0.953904	+	0.300112i	$0.902976\pi$
$80$	−1.41049e15	−	2.37155e14i	−0.840719	−	0.141355i
$81$	1.79122e15			0.966648
$82$	−1.21793e15	+	2.62547e15i	−0.595814	+	1.28439i
$83$	7.04053e14			0.312594			0.156297	−	0.987710i	$-0.450044\pi$
$83$	7.04053e14			0.312594			0.156297	+	0.987710i	$0.450044\pi$
$84$	−3.51383e14	+	2.97235e14i	−0.141758	+	0.119913i
$85$			2.40469e15i			0.882486i
$86$	6.89303e13	−	1.48592e14i	0.0230368	−	0.0496602i
$87$		−	3.41973e14i		−	0.104193i
$88$	5.72296e15	−	1.57012e15i	1.59133	−	0.436586i
$89$	−1.16467e15			−0.295857			−0.147929	−	0.988998i	$-0.547261\pi$
$89$	−1.16467e15			−0.295857			−0.147929	+	0.988998i	$0.547261\pi$
$90$	3.29191e15	+	1.52708e15i	0.764730	+	0.354750i
$91$	4.18820e15			0.890627
$92$	−1.53325e15	+	1.29698e15i	−0.298752	+	0.252714i
$93$		−	6.16922e14i		−	0.110247i
$94$	−2.26256e15	−	1.04958e15i	−0.371174	−	0.172184i
$95$			3.91283e15i			0.589796i
$96$	−6.28544e14	−	4.30861e14i	−0.0871296	−	0.0597266i
$97$	−3.41421e15			−0.435628			−0.217814	−	0.975990i	$-0.569893\pi$
$97$	−3.41421e15			−0.435628			−0.217814	+	0.975990i	$0.569893\pi$
$98$	7.48044e15	−	1.61255e16i	0.879262	−	1.89542i
$99$	−1.50566e16			−1.63172
$100$	−1.76448e15	−	2.08592e15i	−0.176448	−	0.208592i
$101$			1.17656e16i			1.08653i	0.839561	+	0.543265i	$0.182812\pi$
$101$			1.17656e16i			1.08653i	−0.839561	+	0.543265i	$0.817188\pi$
$102$	−5.39145e14	+	1.16223e15i	−0.0460155	+	0.0991951i
$103$		−	1.11530e16i		−	0.880432i	−0.897892	−	0.440216i	$-0.854902\pi$
$103$		−	1.11530e16i		−	0.880432i	0.897892	−	0.440216i	$-0.145098\pi$
$104$	1.83475e15	+	6.68752e15i	0.134063	+	0.488650i
$105$	2.33866e15			0.158290
$106$	−7.66205e15	−	3.55434e15i	−0.480727	−	0.223004i
$107$	−1.03187e16			−0.600556			−0.300278	−	0.953852i	$-0.597079\pi$
$107$	−1.03187e16			−0.600556			−0.300278	+	0.953852i	$0.597079\pi$
$108$	2.51141e15	+	2.96892e15i	0.135684	+	0.160401i
$109$			2.45040e16i			1.22977i	0.788616	+	0.614886i	$0.210798\pi$
$109$			2.45040e16i			1.22977i	−0.788616	+	0.614886i	$0.789202\pi$
$110$	−2.73553e16	−	1.26898e16i	−1.27614	−	0.591989i
$111$		−	1.82561e15i		−	0.0792179i
$112$	4.29170e16	+	7.21592e15i	1.73335	+	0.291439i
$113$	7.23765e13			0.00272252			0.00136126	−	0.999999i	$-0.499567\pi$
$113$	7.23765e13			0.00272252			0.00136126	+	0.999999i	$0.499567\pi$
$114$	−8.77277e14	+	1.89114e15i	−0.0307537	+	0.0662955i
$115$	1.02047e16			0.333592
$116$	−2.46883e16	+	2.08838e16i	−0.753056	+	0.637010i
$117$		−	1.75942e16i		−	0.501053i
$118$	7.95017e15	−	1.71381e16i	0.211505	−	0.455939i
$119$		−	7.31675e16i		−	1.81946i
$120$	1.02451e15	+	3.73426e15i	0.0238268	+	0.0868470i
$121$	7.91681e16			1.72293
$122$	6.99428e16	+	3.24457e16i	1.42516	+	0.661117i
$123$	7.83555e15			0.149564
$124$	−4.45379e16	+	3.76746e16i	−0.796813	+	0.674024i
$125$			6.46971e16i			1.08544i
$126$	−1.00163e17	−	4.64645e16i	−1.57668	−	0.731403i
$127$			3.03618e15i			0.0448640i	0.999748	+	0.0224320i	$0.00714093\pi$
$127$			3.03618e15i			0.0448640i	−0.999748	+	0.0224320i	$0.992859\pi$
$128$	7.27884e15	+	7.16890e16i	0.101014	+	0.994885i
$129$	−4.43464e14			−0.00578283
$130$	1.48286e16	−	3.19658e16i	0.181783	−	0.391867i
$131$	4.62398e16			0.533145			0.266572	−	0.963815i	$-0.414109\pi$
$131$	4.62398e16			0.533145			0.266572	+	0.963815i	$0.414109\pi$
$132$	−1.03762e16	−	1.22664e16i	−0.112576	−	0.133084i
$133$		−	1.19056e17i		−	1.21601i
$134$	−6.83604e16	+	1.47364e17i	−0.657607	+	1.41760i
$135$		−	1.97599e16i		−	0.179107i
$136$	1.16830e17	−	3.20529e16i	0.998263	−	0.273877i
$137$	−1.83731e17			−1.48053			−0.740266	−	0.672314i	$-0.765301\pi$
$137$	−1.83731e17			−1.48053			−0.740266	+	0.672314i	$0.765301\pi$
$138$	4.93209e15	+	2.28794e15i	0.0374972	+	0.0173945i
$139$	−1.05166e17			−0.754671			−0.377336	−	0.926077i	$-0.623160\pi$
$139$	−1.05166e17			−0.754671			−0.377336	+	0.926077i	$0.623160\pi$
$140$	−1.42819e17	−	1.68836e17i	−0.967745	−	1.14404i
$141$			6.75247e15i			0.0432225i
$142$	9.26645e14	+	4.29860e14i	0.00560540	+	0.00260028i
$143$			1.46205e17i			0.836132i
$144$	3.03134e16	−	1.80291e17i	0.163959	−	0.975153i
$145$	1.64315e17			0.840878
$146$	8.58785e16	−	1.85127e17i	0.415970	−	0.896702i
$147$	−4.81255e16			−0.220717
$148$	−1.31797e17	+	1.11487e17i	−0.572549	+	0.484319i
$149$		−	5.14628e16i		−	0.211838i	−0.994375	−	0.105919i	$-0.966222\pi$
$149$		−	5.14628e16i		−	0.211838i	0.994375	−	0.105919i	$-0.0337784\pi$
$150$	−3.11264e15	+	6.70988e15i	−0.0121450	+	0.0261809i
$151$			4.76960e17i			1.76468i	0.470613	+	0.882340i	$0.344033\pi$
$151$			4.76960e17i			1.76468i	−0.470613	+	0.882340i	$0.655967\pi$
$152$	1.90102e17	−	5.21553e16i	0.667173	−	0.183041i
$153$	−3.07370e17			−1.02360
$154$	8.32339e17	+	3.86113e17i	2.63108	+	1.22053i
$155$	2.96425e17			0.889737
$156$	1.43338e16	−	1.21250e16i	0.0408663	−	0.0345688i
$157$		−	1.20209e17i		−	0.325641i	−0.986656	−	0.162821i	$-0.947941\pi$
$157$		−	1.20209e17i		−	0.325641i	0.986656	−	0.162821i	$-0.0520592\pi$
$158$	−2.11469e17	−	9.80983e16i	−0.544491	−	0.252583i
$159$			2.28669e16i			0.0559796i
$160$	2.07025e17	−	3.02009e17i	0.482017	−	0.703170i
$161$	−3.10497e17			−0.687782
$162$	−1.92966e17	+	4.15974e17i	−0.406780	+	0.876891i
$163$	3.50696e17			0.703768			0.351884	−	0.936044i	$-0.385541\pi$
$163$	3.50696e17			0.703768			0.351884	+	0.936044i	$0.385541\pi$
$164$	−4.78506e17	−	5.65677e17i	−0.914401	−	1.08098i
$165$			8.16400e16i			0.148604i
$166$	−7.58467e16	+	1.63502e17i	−0.131544	+	0.283569i
$167$			1.18444e17i			0.195786i	0.995197	+	0.0978932i	$0.0312104\pi$
$167$			1.18444e17i			0.195786i	−0.995197	+	0.0978932i	$0.968790\pi$
$168$	−3.11727e16	−	1.13622e17i	−0.0491247	−	0.179056i
$169$	4.94570e17			0.743248
$170$	−5.58440e17	−	2.59054e17i	−0.800544	−	0.371363i
$171$	−5.00141e17			−0.684107
$172$	2.70817e16	+	3.20153e16i	0.0353549	+	0.0417956i
$173$		−	1.57629e18i		−	1.96458i	−0.187380	−	0.982288i	$-0.559999\pi$
$173$		−	1.57629e18i		−	1.96458i	0.187380	−	0.982288i	$-0.440001\pi$
$174$	7.94163e16	+	3.68403e16i	0.0945182	+	0.0438459i
$175$		−	4.22417e17i		−	0.480216i
$176$	−2.51900e17	+	1.49819e18i	−0.273607	+	1.62729i
$177$	−5.11475e16			−0.0530932
$178$	1.25468e17	−	2.70470e17i	0.124501	−	0.268386i
$179$	−7.88205e17			−0.747851			−0.373926	−	0.927459i	$-0.621988\pi$
$179$	−7.88205e17			−0.747851			−0.373926	+	0.927459i	$0.621988\pi$
$180$	−7.09267e17	+	5.99969e17i	−0.643620	+	0.544438i
$181$			1.11046e18i			0.963993i	0.876173	+	0.481997i	$0.160088\pi$
$181$			1.11046e18i			0.963993i	−0.876173	+	0.481997i	$0.839912\pi$
$182$	−4.51189e17	+	9.72623e17i	−0.374789	+	0.807929i
$183$		−	2.08740e17i		−	0.165957i
$184$	−1.36021e17	−	4.95788e17i	−0.103529	−	0.377358i
$185$	8.77187e17			0.639320
$186$	1.43268e17	+	6.64602e16i	0.100010	+	0.0463936i
$187$	2.55420e18			1.70813
$188$	4.87486e17	−	4.12364e17i	0.312392	−	0.264252i
$189$			6.01233e17i			0.369274i
$190$	−9.08673e17	−	4.21523e17i	−0.535031	−	0.248195i
$191$		−	2.39211e18i		−	1.35056i	−0.737560	−	0.675281i	$-0.764022\pi$
$191$		−	2.39211e18i		−	1.35056i	0.737560	−	0.675281i	$-0.235978\pi$
$192$	1.67771e17	−	9.95503e16i	0.0908462	−	0.0539054i
$193$	−3.19872e17			−0.166157			−0.0830783	−	0.996543i	$-0.526475\pi$
$193$	−3.19872e17			−0.166157			−0.0830783	+	0.996543i	$0.526475\pi$
$194$	3.67808e17	−	7.92880e17i	0.183319	−	0.395179i
$195$	−9.53998e16			−0.0456321
$196$	2.93896e18	+	3.47436e18i	1.34941	+	1.59524i
$197$			1.71426e18i			0.755694i	0.925868	+	0.377847i	$0.123335\pi$
$197$			1.71426e18i			0.755694i	−0.925868	+	0.377847i	$0.876665\pi$
$198$	1.62202e18	−	3.49658e18i	0.686651	−	1.48021i
$199$		−	1.70503e17i		−	0.0693277i	−0.999399	−	0.0346638i	$-0.988964\pi$
$199$		−	1.70503e17i		−	0.0693277i	0.999399	−	0.0346638i	$-0.0110360\pi$
$200$	6.74496e17	−	1.85050e17i	0.263475	−	0.0722853i
$201$	4.39797e17			0.165076
$202$	−2.73231e18	−	1.26749e18i	−0.985642	−	0.457228i
$203$	−4.99961e18			−1.73368
$204$	−2.11822e17	−	2.50411e17i	−0.0706205	−	0.0834856i
$205$			3.76491e18i			1.20704i
$206$	2.59007e18	+	1.20150e18i	0.798680	+	0.370499i
$207$			1.30437e18i			0.386935i
$208$	−1.75069e18	−	2.94355e17i	−0.499693	−	0.0840167i
$209$	4.15610e18			1.14160
$210$	−2.51941e17	+	5.43105e17i	−0.0666107	+	0.143592i
$211$	−3.24576e18			−0.826147			−0.413073	−	0.910698i	$-0.635545\pi$
$211$	−3.24576e18			−0.826147			−0.413073	+	0.910698i	$0.635545\pi$
$212$	1.65085e18	−	1.39645e18i	0.404594	−	0.342246i
$213$		−	2.76551e15i		−	0.000652737i
$214$	1.11162e18	−	2.39630e18i	0.252723	−	0.544792i
$215$		−	2.13080e17i		−	0.0466698i
$216$	−9.60021e17	+	2.63385e17i	−0.202605	+	0.0555855i
$217$	−9.01933e18			−1.83441
$218$	−5.69054e18	−	2.63978e18i	−1.11558	−	0.517506i
$219$	−5.52501e17			−0.104419
$220$	5.89390e18	−	4.98565e18i	1.07404	−	0.908532i
$221$			2.98469e18i			0.524518i
$222$	4.23960e17	+	1.96670e17i	0.0718622	+	0.0333361i
$223$		−	2.78269e18i		−	0.455016i	−0.973776	−	0.227508i	$-0.926942\pi$
$223$		−	2.78269e18i		−	0.455016i	0.973776	−	0.227508i	$-0.0730578\pi$
$224$	−6.29914e18	+	9.18924e18i	−0.993796	+	1.44976i
$225$	−1.77454e18			−0.270162
$226$	−7.79703e15	+	1.68080e16i	−0.00114568	+	0.00246972i
$227$	1.21723e19			1.72649			0.863246	−	0.504784i	$-0.168428\pi$
$227$	1.21723e19			1.72649			0.863246	+	0.504784i	$0.168428\pi$
$228$	−3.44670e17	−	4.07459e17i	−0.0471981	−	0.0557963i
$229$		−	8.96212e18i		−	1.18502i	−0.805562	−	0.592512i	$-0.798136\pi$
$229$		−	8.96212e18i		−	1.18502i	0.805562	−	0.592512i	$-0.201864\pi$
$230$	−1.09934e18	+	2.36982e18i	−0.140381	+	0.302617i
$231$		−	2.48406e18i		−	0.306384i
$232$	−2.19020e18	−	7.98314e18i	−0.260964	−	0.951196i
$233$	9.84332e18			1.13317			0.566584	−	0.824004i	$-0.308265\pi$
$233$	9.84332e18			1.13317			0.566584	+	0.824004i	$0.308265\pi$
$234$	4.08590e18	+	1.89540e18i	0.454528	+	0.210851i
$235$	−3.24450e18			−0.348823
$236$	3.12351e18	+	3.69253e18i	0.324599	+	0.383732i
$237$			6.31116e17i			0.0634049i
$238$	1.69917e19	+	7.88224e18i	1.65052	+	0.765656i
$239$			1.41249e19i			1.32679i	0.748270	+	0.663395i	$0.230885\pi$
$239$			1.41249e19i			1.32679i	−0.748270	+	0.663395i	$0.769115\pi$
$240$	−9.77574e17	−	1.64366e17i	−0.0888096	−	0.0149321i
$241$	5.11765e18			0.449712			0.224856	−	0.974392i	$-0.427809\pi$
$241$	5.11765e18			0.449712			0.224856	+	0.974392i	$0.427809\pi$
$242$	−8.52867e18	+	1.83852e19i	−0.725034	+	1.56295i
$243$	3.79567e18			0.312204
$244$	−1.50697e19	+	1.27474e19i	−1.19946	+	1.01462i
$245$		−	2.31238e19i		−	1.78128i
$246$	−8.44113e17	+	1.81964e18i	−0.0629390	+	0.135677i
$247$			4.85657e18i			0.350554i
$248$	−3.95115e18	−	1.44017e19i	−0.276127	−	1.00647i
$249$	4.87961e17			0.0330210
$250$	−1.50246e19	−	6.96973e18i	−0.984650	−	0.456768i
$251$	2.09847e19			1.33203			0.666015	−	0.745939i	$-0.267999\pi$
$251$	2.09847e19			1.33203			0.666015	+	0.745939i	$0.267999\pi$
$252$	2.15809e19	−	1.82552e19i	1.32698	−	1.12249i
$253$		−	1.08391e19i		−	0.645699i
$254$	−7.05092e17	−	3.27084e17i	−0.0406983	−	0.0188795i
$255$			1.66663e18i			0.0932217i
$256$	−1.74324e19	−	6.03260e18i	−0.945015	−	0.327028i
$257$	−2.85157e19			−1.49837			−0.749185	−	0.662360i	$-0.769555\pi$
$257$	−2.85157e19			−1.49837			−0.749185	+	0.662360i	$0.769555\pi$
$258$	4.77738e16	−	1.02985e17i	0.00243350	−	0.00524588i
$259$	−2.66902e19			−1.31811
$260$	5.82594e18	+	6.88726e18i	0.278984	+	0.329807i
$261$			2.10029e19i			0.975338i
$262$	−4.98135e18	+	1.07382e19i	−0.224355	+	0.483640i
$263$		−	2.32632e19i		−	1.01630i	−0.861267	−	0.508152i	$-0.830329\pi$
$263$		−	2.32632e19i		−	1.01630i	0.861267	−	0.508152i	$-0.169671\pi$
$264$	3.96643e18	−	1.08821e18i	0.168100	−	0.0461190i
$265$	−1.09873e19			−0.451778
$266$	2.76482e19	+	1.28257e19i	1.10310	+	0.511715i
$267$	−8.07201e17			−0.0312530
$268$	−2.68578e19	−	3.17506e19i	−1.00924	−	1.19309i
$269$		−	1.78783e19i		−	0.652090i	−0.945354	−	0.326045i	$-0.894284\pi$
$269$		−	1.78783e19i		−	0.652090i	0.945354	−	0.326045i	$-0.105716\pi$
$270$	4.58882e18	+	2.12870e18i	0.162477	+	0.0753711i
$271$			5.77195e19i			1.98412i	0.125762	+	0.992060i	$0.459862\pi$
$271$			5.77195e19i			1.98412i	−0.125762	+	0.992060i	$0.540138\pi$
$272$	−5.14237e18	+	3.05845e19i	−0.171637	+	1.02082i
$273$	2.90273e18			0.0940817
$274$	1.97931e19	−	4.26678e19i	0.623030	−	1.34306i
$275$	1.47461e19			0.450834
$276$	−1.06266e18	+	8.98900e17i	−0.0315588	+	0.0266955i
$277$			4.25025e19i			1.22624i	0.789989	+	0.613120i	$0.210086\pi$
$277$			4.25025e19i			1.22624i	−0.789989	+	0.613120i	$0.789914\pi$
$278$	1.13294e19	−	2.44227e19i	0.317577	−	0.684597i
$279$			3.78894e19i			1.03201i
$280$	5.45945e19	−	1.49782e19i	1.44506	−	0.396456i
$281$	3.18605e19			0.819599			0.409800	−	0.912176i	$-0.365599\pi$
$281$	3.18605e19			0.819599			0.409800	+	0.912176i	$0.365599\pi$
$282$	−1.56812e18	−	7.27435e17i	−0.0392091	−	0.0181887i
$283$	−3.52370e19			−0.856460			−0.428230	−	0.903670i	$-0.640863\pi$
$283$	−3.52370e19			−0.856460			−0.428230	+	0.903670i	$0.640863\pi$
$284$	−1.99652e17	+	1.68886e17i	−0.00471767	+	0.00399068i
$285$			2.71188e18i			0.0623033i
$286$	−3.39532e19	−	1.57505e19i	−0.758495	−	0.351857i
$287$		−	1.14555e20i		−	2.48862i
$288$	3.86032e19	+	2.64621e19i	0.815611	+	0.559094i
$289$	3.48109e18			0.0715373
$290$	−1.77014e19	+	3.81588e19i	−0.353854	+	0.762799i
$291$	−2.36630e18			−0.0460178
$292$	3.37405e19	+	3.98871e19i	0.638393	+	0.754691i
$293$			3.88564e19i			0.715355i	0.933845	+	0.357678i	$0.116431\pi$
$293$			3.88564e19i			0.715355i	−0.933845	+	0.357678i	$0.883569\pi$
$294$	5.18449e18	−	1.11762e19i	0.0928812	−	0.200223i
$295$		−	2.45759e19i		−	0.428483i
$296$	−1.16923e19	−	4.26176e19i	−0.198411	−	0.723195i
$297$	−2.09884e19			−0.346679
$298$	1.19512e19	+	5.54402e18i	0.192168	+	0.0891445i
$299$	1.26660e19			0.198275
$300$	−1.22291e18	−	1.44569e18i	−0.0186391	−	0.0220346i
$301$			6.48339e18i			0.0962211i
$302$	−1.10764e20	−	5.13822e19i	−1.60082	−	0.742604i
$303$			8.15440e18i			0.114776i
$304$	−8.36748e18	+	4.97660e19i	−0.114711	+	0.682251i
$305$	1.00297e20			1.33934
$306$	3.31126e19	−	7.13804e19i	0.430746	−	0.928555i
$307$	2.98440e19			0.378225			0.189112	−	0.981955i	$-0.439439\pi$
$307$	2.98440e19			0.378225			0.189112	+	0.981955i	$0.439439\pi$
$308$	−1.79334e20	+	1.51698e20i	−2.21440	+	1.87316i
$309$		−	7.72988e18i		−	0.0930047i
$310$	−3.19335e19	+	6.88387e19i	−0.374415	+	0.807122i
$311$		−	4.84124e19i		−	0.553189i	−0.960987	−	0.276595i	$-0.910794\pi$
$311$		−	4.84124e19i		−	0.553189i	0.960987	−	0.276595i	$-0.0892059\pi$
$312$	1.27161e18	+	4.63494e18i	0.0141618	+	0.0516188i
$313$	−3.93756e19			−0.427437			−0.213719	−	0.976895i	$-0.568558\pi$
$313$	−3.93756e19			−0.427437			−0.213719	+	0.976895i	$0.568558\pi$
$314$	2.79160e19	+	1.29499e19i	0.295404	+	0.137035i
$315$	−1.43633e20			−1.48173
$316$	4.55626e19	−	3.85414e19i	0.458260	−	0.387642i
$317$		−	1.19792e19i		−	0.117477i	−0.998273	−	0.0587387i	$-0.981292\pi$
$317$		−	1.19792e19i		−	0.117477i	0.998273	−	0.0587387i	$-0.0187079\pi$
$318$	−5.31037e18	−	2.46342e18i	−0.0507817	−	0.0235571i
$319$		−	1.74531e20i		−	1.62760i
$320$	4.78330e19	+	8.06123e19i	0.435038	+	0.733165i
$321$	−7.15160e18			−0.0634400
$322$	3.34495e19	−	7.21066e19i	0.289429	−	0.623919i
$323$	8.48440e19			0.716145
$324$	−7.58134e19	−	8.96246e19i	−0.624290	−	0.738018i
$325$			1.72315e19i			0.138438i
$326$	−3.77800e19	+	8.14419e19i	−0.296156	+	0.638421i
$327$			1.69830e19i			0.129907i
$328$	1.82916e20	−	5.01836e19i	1.36540	−	0.374603i
$329$	9.87204e19			0.719183
$330$	−1.89592e19	−	8.79497e18i	−0.134806	−	0.0625350i
$331$	1.47159e20			1.02133			0.510663	−	0.859781i	$-0.329400\pi$
$331$	1.47159e20			1.02133			0.510663	+	0.859781i	$0.329400\pi$
$332$	−2.97991e19	−	3.52277e19i	−0.201882	−	0.238660i
$333$			1.12123e20i			0.741550i
$334$	−2.75063e19	−	1.27599e19i	−0.177607	−	0.0823899i
$335$			2.11318e20i			1.33223i
$336$	2.97447e19	+	5.00116e18i	0.183103	+	0.0307862i
$337$	−1.09362e20			−0.657394			−0.328697	−	0.944435i	$-0.606610\pi$
$337$	−1.09362e20			−0.657394			−0.328697	+	0.944435i	$0.606610\pi$
$338$	−5.32793e19	+	1.14854e20i	−0.312770	+	0.674235i
$339$	5.01623e16			0.000287594
$340$	1.20320e20	−	1.01779e20i	0.673762	−	0.569935i
$341$		−	3.14855e20i		−	1.72217i
$342$	5.38796e19	−	1.16148e20i	0.287883	−	0.620585i
$343$			3.66851e20i			1.91486i
$344$	−1.03524e19	+	2.84021e18i	−0.0527925	+	0.0144838i
$345$	7.07258e18			0.0352391
$346$	3.66062e20	+	1.69812e20i	1.78216	+	0.826723i
$347$	−2.27998e20			−1.08467			−0.542333	−	0.840164i	$-0.682459\pi$
$347$	−2.27998e20			−1.08467			−0.542333	+	0.840164i	$0.682459\pi$
$348$	−1.71108e19	+	1.44740e19i	−0.0795494	+	0.0672908i
$349$			1.82625e20i			0.829767i	0.909875	+	0.414883i	$0.136178\pi$
$349$			1.82625e20i			0.829767i	−0.909875	+	0.414883i	$0.863822\pi$
$350$	9.80977e19	+	4.55064e19i	0.435627	+	0.202082i
$351$		−	2.45258e19i		−	0.106455i
$352$	−3.20786e20	−	2.19896e20i	−1.36105	−	0.932989i
$353$	−1.79298e20			−0.743667			−0.371833	−	0.928300i	$-0.621271\pi$
$353$	−1.79298e20			−0.743667			−0.371833	+	0.928300i	$0.621271\pi$
$354$	5.51006e18	−	1.18780e19i	0.0223424	−	0.0481633i
$355$	1.32880e18			0.00526785
$356$	4.92947e19	+	5.82748e19i	0.191073	+	0.225882i
$357$		−	5.07105e19i		−	0.192199i
$358$	8.49123e19	−	1.83045e20i	0.314707	−	0.678411i
$359$		−	1.77259e20i		−	0.642471i	−0.946999	−	0.321236i	$-0.895902\pi$
$359$		−	1.77259e20i		−	0.642471i	0.946999	−	0.321236i	$-0.104098\pi$
$360$	−6.29220e19	−	2.29346e20i	−0.223040	−	0.812965i
$361$	−1.50386e20			−0.521376
$362$	−2.57881e20	−	1.19628e20i	−0.874483	−	0.405663i
$363$	5.48693e19			0.182002
$364$	−1.77266e20	−	2.09559e20i	−0.575193	−	0.679978i
$365$		−	2.65471e20i		−	0.842703i
$366$	4.84755e19	+	2.24872e19i	0.150548	+	0.0698373i
$367$			4.28429e20i			1.30182i	0.759156	+	0.650909i	$0.225612\pi$
$367$			4.28429e20i			1.30182i	−0.759156	+	0.650909i	$0.774388\pi$
$368$	1.29790e20	+	2.18224e19i	0.385885	+	0.0648814i
$369$	−4.81234e20			−1.40006
$370$	−9.44982e19	+	2.03709e20i	−0.269035	+	0.579957i
$371$	3.34311e20			0.931450
$372$	−3.08680e19	+	2.61113e19i	−0.0841716	+	0.0712008i
$373$		−	2.63106e20i		−	0.702200i	−0.936338	−	0.351100i	$-0.885808\pi$
$373$		−	2.63106e20i		−	0.702200i	0.936338	−	0.351100i	$-0.114192\pi$
$374$	−2.75160e20	+	5.93160e20i	−0.718808	+	1.54953i
$375$			4.48398e19i			0.114660i
$376$	4.32469e19	+	1.57632e20i	0.108256	+	0.394586i
$377$	2.03947e20			0.499788
$378$	−1.39624e20	−	6.47700e19i	−0.334985	−	0.155396i
$379$	4.62906e19			0.108737			0.0543687	−	0.998521i	$-0.482685\pi$
$379$	4.62906e19			0.108737			0.0543687	+	0.998521i	$0.482685\pi$
$380$	1.95780e20	−	1.65611e20i	0.450298	−	0.380907i
$381$			2.10430e18i			0.00473923i
$382$	5.55519e20	+	2.57699e20i	1.22516	+	0.568337i
$383$		−	3.57193e20i		−	0.771459i	−0.922612	−	0.385729i	$-0.873950\pi$
$383$		−	3.57193e20i		−	0.771459i	0.922612	−	0.385729i	$-0.126050\pi$
$384$	5.04477e18	+	4.96858e19i	0.0106707	+	0.105095i
$385$	1.19357e21			2.47264
$386$	3.44594e19	−	7.42837e19i	0.0699212	−	0.150728i
$387$	2.72361e19			0.0541325
$388$	1.44507e20	+	1.70832e20i	0.281342	+	0.332594i
$389$			4.65383e20i			0.887592i	0.896128	+	0.443796i	$0.146368\pi$
$389$			4.65383e20i			0.887592i	−0.896128	+	0.443796i	$0.853632\pi$
$390$	1.02773e19	−	2.21546e19i	0.0192027	−	0.0413950i
$391$		−	2.21274e20i		−	0.405056i
$392$	−1.12346e21	+	3.08225e20i	−2.01497	+	0.552814i
$393$	3.20476e19			0.0563189
$394$	−3.98101e20	−	1.84675e20i	−0.685525	−	0.318007i
$395$	−3.03245e20			−0.511702
$396$	6.37271e20	+	7.53364e20i	1.05381	+	1.24579i
$397$		−	8.35637e20i		−	1.35423i	−0.735876	−	0.677117i	$-0.763229\pi$
$397$		−	8.35637e20i		−	1.35423i	0.735876	−	0.677117i	$-0.236771\pi$
$398$	3.95957e19	+	1.83680e19i	0.0628903	+	0.0291741i
$399$		−	8.25142e19i		−	0.128453i
$400$	−2.96884e19	+	1.76573e20i	−0.0453009	+	0.269429i
$401$	2.47891e20			0.370772			0.185386	−	0.982666i	$-0.440647\pi$
$401$	2.47891e20			0.370772			0.185386	+	0.982666i	$0.440647\pi$
$402$	−4.73788e19	+	1.02134e20i	−0.0694665	+	0.149748i
$403$	3.67921e20			0.528828
$404$	5.88696e20	−	4.97978e20i	0.829546	−	0.701713i
$405$			5.96503e20i			0.824086i
$406$	5.38601e20	−	1.16106e21i	0.729557	−	1.57270i
$407$		−	9.31724e20i		−	1.23746i
$408$	8.09721e19	−	2.22150e19i	0.105452	−	0.0289311i
$409$	−1.20801e21			−1.54271			−0.771356	−	0.636404i	$-0.780421\pi$
$409$	−1.20801e21			−1.54271			−0.771356	+	0.636404i	$0.780421\pi$
$410$	−8.74322e20	−	4.05588e20i	−1.09497	−	0.507943i
$411$	−1.27339e20			−0.156397
$412$	−5.58049e20	+	4.72053e20i	−0.672194	+	0.568609i
$413$			7.47771e20i			0.883422i
$414$	−3.02913e20	−	1.40518e20i	−0.351007	−	0.162828i
$415$			2.34461e20i			0.266493i
$416$	2.56958e20	−	3.74852e20i	0.286494	−	0.417939i
$417$	−7.28879e19			−0.0797199
$418$	−4.47731e20	+	9.65169e20i	−0.480404	+	1.03560i
$419$	4.01379e20			0.422515			0.211258	−	0.977430i	$-0.432244\pi$
$419$	4.01379e20			0.422515			0.211258	+	0.977430i	$0.432244\pi$
$420$	−9.89839e19	−	1.17016e20i	−0.102228	−	0.120851i
$421$			1.48548e21i			1.50526i	0.658445	+	0.752629i	$0.271214\pi$
$421$			1.48548e21i			1.50526i	−0.658445	+	0.752629i	$0.728786\pi$
$422$	3.49662e20	−	7.53762e20i	0.347655	−	0.749436i
$423$		−	4.14715e20i		−	0.404601i
$424$	1.46453e20	+	5.33813e20i	0.140208	+	0.511048i
$425$	3.01032e20			0.282815
$426$	6.42233e17	+	2.97925e17i	0.000592128	+	0.000274682i
$427$	−3.05175e21			−2.76138
$428$	4.36738e20	+	5.16300e20i	0.387857	+	0.458514i
$429$			1.01331e20i			0.0883251i
$430$	4.94835e19	+	2.29549e19i	0.0423363	+	0.0196393i
$431$			2.69096e20i			0.225990i	0.993596	+	0.112995i	$0.0360443\pi$
$431$			2.69096e20i			0.225990i	−0.993596	+	0.112995i	$0.963956\pi$
$432$	4.22559e19	−	2.51319e20i	0.0348352	−	0.207184i
$433$	−5.45318e20			−0.441313			−0.220657	−	0.975352i	$-0.570820\pi$
$433$	−5.45318e20			−0.441313			−0.220657	+	0.975352i	$0.570820\pi$
$434$	9.71641e20	−	2.09455e21i	0.771948	−	1.66408i
$435$	1.13882e20			0.0888264
$436$	1.22607e21	−	1.03713e21i	0.938908	−	0.794222i
$437$		−	3.60048e20i		−	0.270713i
$438$	5.95201e19	−	1.28307e20i	0.0439411	−	0.0947234i
$439$			3.73907e20i			0.271049i	0.990774	+	0.135524i	$0.0432719\pi$
$439$			3.73907e20i			0.271049i	−0.990774	+	0.135524i	$0.956728\pi$
$440$	5.22872e20	+	1.90583e21i	0.372198	+	1.35664i
$441$	2.95571e21			2.06611
$442$	−6.93132e20	−	3.21536e20i	−0.475815	−	0.220725i
$443$	−5.58131e20			−0.376276			−0.188138	−	0.982143i	$-0.560245\pi$
$443$	−5.58131e20			−0.376276			−0.188138	+	0.982143i	$0.560245\pi$
$444$	−9.13452e19	+	7.72689e19i	−0.0604814	+	0.0511612i
$445$		−	3.87852e20i		−	0.252224i
$446$	6.46224e20	+	2.99776e20i	0.412766	+	0.191478i
$447$		−	3.56675e19i		−	0.0223775i
$448$	−1.45541e21	−	2.45279e21i	−0.896938	−	1.51160i
$449$	−1.21177e21			−0.733582			−0.366791	−	0.930303i	$-0.619544\pi$
$449$	−1.21177e21			−0.733582			−0.366791	+	0.930303i	$0.619544\pi$
$450$	1.91168e20	−	4.12100e20i	0.113688	−	0.245077i
$451$	3.99898e21			2.33635
$452$	−3.06334e18	−	3.62140e18i	−0.00175828	−	0.00207859i
$453$			3.30568e20i			0.186413i
$454$	−1.31130e21	+	2.82676e21i	−0.726534	+	1.56618i
$455$			1.39473e21i			0.759277i
$456$	1.31755e20	−	3.61474e19i	0.0704771	−	0.0193357i
$457$	−1.97649e21			−1.03888			−0.519440	−	0.854507i	$-0.673859\pi$
$457$	−1.97649e21			−1.03888			−0.519440	+	0.854507i	$0.673859\pi$
$458$	2.08127e21	+	9.65477e20i	1.07499	+	0.498676i
$459$	−4.28464e20			−0.217477
$460$	−4.31913e20	−	5.10596e20i	−0.215444	−	0.254692i
$461$			2.21318e21i			1.08495i	0.840072	+	0.542475i	$0.182513\pi$
$461$			2.21318e21i			1.08495i	−0.840072	+	0.542475i	$0.817487\pi$
$462$	5.76872e20	+	2.67605e20i	0.277935	+	0.128931i
$463$		−	2.21006e21i		−	1.04654i	−0.852167	−	0.523270i	$-0.824712\pi$
$463$		−	2.21006e21i		−	1.04654i	0.852167	−	0.523270i	$-0.175288\pi$
$464$	2.08987e21	+	3.51383e20i	0.972692	+	0.163545i
$465$	2.05445e20			0.0939877
$466$	−1.06041e21	+	2.28591e21i	−0.476854	+	1.02795i
$467$	7.34063e20			0.324488			0.162244	−	0.986751i	$-0.448127\pi$
$467$	7.34063e20			0.324488			0.162244	+	0.986751i	$0.448127\pi$
$468$	−8.80337e20	+	7.44677e20i	−0.382545	+	0.323595i
$469$		−	6.42979e21i		−	2.74672i
$470$	3.49526e20	−	7.53468e20i	0.146790	−	0.316433i
$471$		−	8.33136e19i		−	0.0343992i
$472$	−1.19401e21	+	3.27580e20i	−0.484697	+	0.132978i
$473$	−2.26328e20			−0.0903336
$474$	−1.46564e20	−	6.79893e19i	−0.0575175	−	0.0266817i
$475$	4.89829e20			0.189015
$476$	−3.66098e21	+	3.09682e21i	−1.38913	+	1.17506i
$477$		−	1.40441e21i		−	0.524019i
$478$	−3.28022e21	−	1.52166e21i	−1.20359	−	0.558333i
$479$			2.73260e21i			0.986036i	0.870019	+	0.493018i	$0.164106\pi$
$479$			2.73260e21i			0.986036i	−0.870019	+	0.493018i	$0.835894\pi$
$480$	1.43483e20	−	2.09315e20i	0.0509181	−	0.0742796i
$481$	1.08876e21			0.379989
$482$	−5.51318e20	+	1.18847e21i	−0.189245	+	0.407954i
$483$	−2.15197e20			−0.0726541
$484$	−3.35079e21	−	3.96122e21i	−1.11272	−	1.31542i
$485$		−	1.13698e21i		−	0.371382i
$486$	−4.08903e20	+	8.81467e20i	−0.131380	+	0.283215i
$487$			4.11313e21i			1.29999i	0.759937	+	0.649996i	$0.225230\pi$
$487$			4.11313e21i			1.29999i	−0.759937	+	0.649996i	$0.774770\pi$
$488$	−1.33690e21	−	4.87289e21i	−0.415661	−	1.51505i
$489$	2.43058e20			0.0743428
$490$	5.37004e21	+	2.49110e21i	1.61588	+	0.749588i
$491$	−2.95568e21			−0.874995			−0.437497	−	0.899220i	$-0.644135\pi$
$491$	−2.95568e21			−0.874995			−0.437497	+	0.899220i	$0.644135\pi$
$492$	−3.31640e20	−	3.92056e20i	−0.0965931	−	0.114190i
$493$		−	3.56293e21i		−	1.02102i
$494$	−1.12784e21	−	5.23192e20i	−0.318003	−	0.147518i
$495$		−	5.01407e21i		−	1.39107i
$496$	3.77014e21	+	6.33898e20i	1.02921	+	0.173048i
$497$	−4.04314e19			−0.0108610
$498$	−5.25674e19	+	1.13319e20i	−0.0138957	+	0.0299549i
$499$	3.95981e21			1.03008			0.515039	−	0.857167i	$-0.327777\pi$
$499$	3.95981e21			1.03008			0.515039	+	0.857167i	$0.327777\pi$
$500$	3.23715e21	−	2.73831e21i	0.828711	−	0.701007i
$501$			8.20906e19i			0.0206820i
$502$	−2.26066e21	+	4.87327e21i	−0.560538	+	1.20835i
$503$			9.69646e20i			0.236630i	0.992976	+	0.118315i	$0.0377492\pi$
$503$			9.69646e20i			0.236630i	−0.992976	+	0.118315i	$0.962251\pi$
$504$	1.91453e21	+	6.97832e21i	0.459851	+	1.67613i
$505$	−3.91811e21			−0.926288
$506$	2.51716e21	+	1.16768e21i	0.585743	+	0.271720i
$507$	3.42773e20			0.0785133
$508$	1.51917e20	−	1.28507e20i	0.0342529	−	0.0289745i
$509$			7.70210e21i			1.70949i	0.519046	+	0.854746i	$0.326287\pi$
$509$			7.70210e21i			1.70949i	−0.519046	+	0.854746i	$0.673713\pi$
$510$	−3.87040e20	−	1.79544e20i	−0.0845658	−	0.0392291i
$511$			8.07749e21i			1.73744i
$512$	3.27892e21	−	3.39844e21i	0.694339	−	0.719648i
$513$	−6.97181e20			−0.145347
$514$	3.07196e21	−	6.62219e21i	0.630537	−	1.35924i
$515$	3.71413e21			0.750585
$516$	1.87696e19	+	2.21890e19i	0.00373472	+	0.00441509i
$517$			3.44622e21i			0.675179i
$518$	2.87529e21	−	6.19824e21i	0.554682	−	1.19572i
$519$		−	1.09249e21i		−	0.207529i
$520$	−2.22705e21	+	6.10998e20i	−0.416584	+	0.114291i
$521$	6.21683e20			0.114516			0.0572581	−	0.998359i	$-0.481764\pi$
$521$	6.21683e20			0.114516			0.0572581	+	0.998359i	$0.481764\pi$
$522$	−4.87749e21	−	2.26262e21i	−0.884775	−	0.410437i
$523$	−6.21034e21			−1.10943			−0.554717	−	0.832039i	$-0.687174\pi$
$523$	−6.21034e21			−1.10943			−0.554717	+	0.832039i	$0.687174\pi$
$524$	−1.95710e21	−	2.31363e21i	−0.344321	−	0.407046i
$525$		−	2.92766e20i		−	0.0507278i
$526$	5.40240e21	+	2.50611e21i	0.921936	+	0.427676i
$527$		−	6.42756e21i		−	1.08034i
$528$	−1.74585e20	+	1.03835e21i	−0.0289025	+	0.171899i
$529$	5.19360e21			0.846883
$530$	1.18365e21	−	2.55158e21i	0.190115	−	0.409829i
$531$	3.14132e21			0.496999
$532$	−5.95701e21	+	5.03903e21i	−0.928400	+	0.785333i
$533$			4.67298e21i			0.717424i
$534$	8.69587e19	−	1.87456e20i	0.0131517	−	0.0283510i
$535$		−	3.43628e21i		−	0.511986i
$536$	1.02668e22	−	2.81673e21i	1.50701	−	0.413454i
$537$	−5.46284e20			−0.0789995
$538$	4.15186e21	+	1.92600e21i	0.591541	+	0.274409i
$539$	−2.45615e22			−3.44783
$540$	−9.88695e20	+	8.36337e20i	−0.136745	+	0.115673i
$541$		−	9.49735e21i		−	1.29427i	−0.762376	−	0.647134i	$-0.775967\pi$
$541$		−	9.49735e21i		−	1.29427i	0.762376	−	0.647134i	$-0.224033\pi$
$542$	−1.34042e22	−	6.21804e21i	−1.79989	−	0.834948i
$543$			7.69630e20i			0.101832i
$544$	−6.54864e21	−	4.48904e21i	−0.853808	−	0.585278i
$545$	−8.16020e21			−1.04840
$546$	−3.12707e20	+	6.74099e20i	−0.0395910	+	0.0853459i
$547$	1.37046e22			1.70988			0.854942	−	0.518723i	$-0.173592\pi$
$547$	1.37046e22			1.70988			0.854942	+	0.518723i	$0.173592\pi$
$548$	7.77643e21	+	9.19308e21i	0.956171	+	1.13036i
$549$			1.28201e22i			1.55351i
$550$	−1.58858e21	+	3.42448e21i	−0.189718	+	0.408972i
$551$		−	5.79748e21i		−	0.682380i
$552$	−9.42727e19	−	3.43617e20i	−0.0109364	−	0.0398623i
$553$	9.22685e21			1.05500
$554$	−9.87032e21	−	4.57873e21i	−1.11238	−	0.516021i
$555$	6.07955e20			0.0675348
$556$	4.45117e21	+	5.26205e21i	0.487389	+	0.576178i
$557$			2.12963e21i			0.229859i	0.993374	+	0.114930i	$0.0366643\pi$
$557$			2.12963e21i			0.229859i	−0.993374	+	0.114930i	$0.963336\pi$
$558$	−8.79904e21	−	4.08177e21i	−0.936185	−	0.434286i
$559$		−	2.64474e20i		−	0.0277388i
$560$	−2.40301e21	+	1.42920e22i	−0.248457	+	1.47771i
$561$	1.77025e21			0.180439
$562$	−3.43229e21	+	7.39894e21i	−0.344900	+	0.743497i
$563$	8.66720e21			0.858641			0.429321	−	0.903152i	$-0.358753\pi$
$563$	8.66720e21			0.858641			0.429321	+	0.903152i	$0.358753\pi$
$564$	3.37864e20	−	2.85799e20i	0.0329996	−	0.0279144i
$565$			2.41025e19i			0.00232100i
$566$	3.79603e21	−	8.18306e21i	0.360411	−	0.776934i
$567$		−	1.81498e22i		−	1.69905i
$568$	−1.77120e19	−	6.45591e19i	−0.00163486	−	0.00595896i
$569$	9.09704e21			0.827946			0.413973	−	0.910289i	$-0.364141\pi$
$569$	9.09704e21			0.827946			0.413973	+	0.910289i	$0.364141\pi$
$570$	−6.29778e20	−	2.92147e20i	−0.0565182	−	0.0262182i
$571$	−2.09893e21			−0.185741			−0.0928706	−	0.995678i	$-0.529604\pi$
$571$	−2.09893e21			−0.185741			−0.0928706	+	0.995678i	$0.529604\pi$
$572$	7.31547e21	−	6.18815e21i	0.638372	−	0.539999i
$573$		−	1.65791e21i		−	0.142667i
$574$	2.66030e22	+	1.23408e22i	2.25754	+	1.04725i
$575$		−	1.27748e21i		−	0.106908i
$576$	−1.03040e22	+	6.11406e21i	−0.850401	+	0.504603i
$577$	6.48518e20			0.0527856			0.0263928	−	0.999652i	$-0.491598\pi$
$577$	6.48518e20			0.0527856			0.0263928	+	0.999652i	$0.491598\pi$
$578$	−3.75013e20	+	8.08412e20i	−0.0301040	+	0.0648948i
$579$	−2.21695e20			−0.0175520
$580$	−6.95464e21	−	8.22159e21i	−0.543064	−	0.641995i
$581$		−	7.13393e21i		−	0.549439i
$582$	2.54918e20	−	5.49524e20i	0.0193650	−	0.0417448i
$583$			1.16704e22i			0.874458i
$584$	−1.28978e22	+	3.53855e21i	−0.953261	+	0.261531i
$585$	5.85915e21			0.427157
$586$	−9.02360e21	−	4.18595e21i	−0.648932	−	0.301032i
$587$	−1.68575e20			−0.0119588			−0.00597941	−	0.999982i	$-0.501903\pi$
$587$	−1.68575e20			−0.0119588			−0.00597941	+	0.999982i	$0.501903\pi$
$588$	2.03691e21	+	2.40798e21i	0.142546	+	0.168514i
$589$		−	1.04587e22i		−	0.722030i
$590$	5.70725e21	+	2.64753e21i	0.388697	+	0.180312i
$591$			1.18811e21i			0.0798280i
$592$	1.11567e22	+	1.87584e21i	0.739538	+	0.124343i
$593$	1.22211e21			0.0799229			0.0399614	−	0.999201i	$-0.487276\pi$
$593$	1.22211e21			0.0799229			0.0399614	+	0.999201i	$0.487276\pi$
$594$	2.26105e21	−	4.87412e21i	0.145888	−	0.314489i
$595$	2.43659e22			1.55112
$596$	−2.57497e21	+	2.17817e21i	−0.161734	+	0.136811i
$597$		−	1.18171e20i		−	0.00732345i
$598$	−1.36449e21	+	2.94141e21i	−0.0834373	+	0.179865i
$599$			7.33813e21i			0.442763i	0.975187	+	0.221381i	$0.0710565\pi$
$599$			7.33813e21i			0.442763i	−0.975187	+	0.221381i	$0.928943\pi$
$600$	4.67475e20	−	1.28254e20i	0.0278323	−	0.00763589i
$601$	−2.74475e22			−1.61253			−0.806265	−	0.591555i	$-0.798514\pi$
$601$	−2.74475e22			−1.61253			−0.806265	+	0.591555i	$0.798514\pi$
$602$	−1.50563e21	−	6.98447e20i	−0.0872866	−	0.0404913i
$603$	−2.70110e22			−1.54526
$604$	2.38649e22	−	2.01873e22i	1.34730	−	1.13968i
$605$			2.63642e22i			1.46883i
$606$	−1.89369e21	−	8.78463e20i	−0.104119	−	0.0482995i
$607$			1.66048e22i			0.901000i	0.892776	+	0.450500i	$0.148754\pi$
$607$			1.66048e22i			0.901000i	−0.892776	+	0.450500i	$0.851246\pi$
$608$	−1.06557e22	−	7.30440e21i	−0.570629	−	0.391161i
$609$	−3.46510e21			−0.183137
$610$	−1.08049e22	+	2.32920e22i	−0.563615	+	1.21498i
$611$	−4.02705e21			−0.207328
$612$	1.30095e22	+	1.53794e22i	0.661071	+	0.781500i
$613$		−	2.36056e22i		−	1.18394i	−0.805959	−	0.591971i	$-0.798350\pi$
$613$		−	2.36056e22i		−	1.18394i	0.805959	−	0.591971i	$-0.201650\pi$
$614$	−3.21505e21	+	6.93065e21i	−0.159163	+	0.343105i
$615$			2.60936e21i			0.127507i
$616$	−1.59094e22	−	5.79888e22i	−0.767378	−	2.79704i
$617$	−8.65344e21			−0.412010			−0.206005	−	0.978551i	$-0.566046\pi$
$617$	−8.65344e21			−0.412010			−0.206005	+	0.978551i	$0.566046\pi$
$618$	1.79511e21	+	8.32730e20i	0.0843689	+	0.0391378i
$619$	−7.33205e21			−0.340173			−0.170087	−	0.985429i	$-0.554405\pi$
$619$	−7.33205e21			−0.340173			−0.170087	+	0.985429i	$0.554405\pi$
$620$	−1.25462e22	−	1.48318e22i	−0.574618	−	0.679298i
$621$			1.81825e21i			0.0822094i
$622$	1.12428e22	+	5.21541e21i	0.501824	+	0.232790i
$623$			1.18012e22i			0.520021i
$624$	−1.21336e21	−	2.04010e20i	−0.0527853	−	0.00887513i
$625$	−1.51839e22			−0.652145
$626$	4.24188e21	−	9.14417e21i	0.179872	−	0.387748i
$627$	2.88048e21			0.120594
$628$	−6.01472e21	+	5.08785e21i	−0.248621	+	0.210309i
$629$		−	1.90205e22i		−	0.776279i
$630$	1.54734e22	−	3.33558e22i	0.623535	−	1.34415i
$631$			3.76900e22i			1.49965i	0.661634	+	0.749827i	$0.269863\pi$
$631$			3.76900e22i			1.49965i	−0.661634	+	0.749827i	$0.730137\pi$
$632$	4.04205e21	+	1.47330e22i	0.158805	+	0.578835i
$633$	−2.24955e21			−0.0872703
$634$	2.78193e21	+	1.29051e21i	0.106569	+	0.0494363i
$635$	−1.01110e21			−0.0382475
$636$	1.14416e21	−	9.67843e20i	0.0427394	−	0.0361533i
$637$		−	2.87012e22i		−	1.05873i
$638$	4.05312e22	+	1.88020e22i	1.47647	+	0.684917i
$639$			1.69849e20i			0.00611020i
$640$	−2.38735e22	+	2.42397e21i	−0.848159	+	0.0861166i
$641$	2.49051e22			0.873825			0.436912	−	0.899504i	$-0.356072\pi$
$641$	2.49051e22			0.873825			0.436912	+	0.899504i	$0.356072\pi$
$642$	7.70432e20	−	1.66081e21i	0.0266965	−	0.0575493i
$643$	3.27108e22			1.11945			0.559723	−	0.828680i	$-0.310908\pi$
$643$	3.27108e22			1.11945			0.559723	+	0.828680i	$0.310908\pi$
$644$	1.31418e22	+	1.55359e22i	0.444190	+	0.525109i
$645$		−	1.47680e20i		−	0.00492998i
$646$	−9.14013e21	+	1.97033e22i	−0.301365	+	0.649649i
$647$		−	3.34257e22i		−	1.08855i	−0.838908	−	0.544273i	$-0.816806\pi$
$647$		−	3.34257e22i		−	1.08855i	0.838908	−	0.544273i	$-0.183194\pi$
$648$	2.89808e22	−	7.95098e21i	0.932201	−	0.255753i
$649$	−2.61039e22			−0.829368
$650$	−4.00165e21	−	1.85632e21i	−0.125583	−	0.0582568i
$651$	−6.25106e21			−0.193779
$652$	−1.48432e22	−	1.75472e22i	−0.454514	−	0.537314i
$653$			5.02261e22i			1.51923i	0.650372	+	0.759616i	$0.274613\pi$
$653$			5.02261e22i			1.51923i	−0.650372	+	0.759616i	$0.725387\pi$
$654$	−3.94396e21	−	1.82956e21i	−0.117845	−	0.0546670i
$655$			1.53985e22i			0.454516i
$656$	−8.05116e21	+	4.78846e22i	−0.234762	+	1.39626i
$657$	3.39328e22			0.977456
$658$	−1.06350e22	+	2.29258e22i	−0.302643	+	0.652405i
$659$	4.93070e22			1.38620			0.693098	−	0.720843i	$-0.256245\pi$
$659$	4.93070e22			1.38620			0.693098	+	0.720843i	$0.256245\pi$
$660$	4.08490e21	−	3.45542e21i	0.113457	−	0.0959730i
$661$			6.39611e21i			0.175511i	0.996142	+	0.0877554i	$0.0279694\pi$
$661$			6.39611e21i			0.175511i	−0.996142	+	0.0877554i	$0.972031\pi$
$662$	−1.58533e22	+	3.41748e22i	−0.429789	+	0.926492i
$663$			2.06861e21i			0.0554077i
$664$	1.13911e22	−	3.12520e21i	0.301455	−	0.0827052i
$665$	3.96473e22			1.03667
$666$	−2.60382e22	−	1.20789e22i	−0.672695	−	0.312056i
$667$	−1.51198e22			−0.385959
$668$	5.92643e21	−	5.01317e21i	0.149479	−	0.126445i
$669$		−	1.92861e21i		−	0.0480658i
$670$	−4.90744e22	−	2.27651e22i	−1.20853	−	0.560622i
$671$		−	1.06533e23i		−	2.59242i
$672$	−4.36577e21	+	6.36882e21i	−0.104980	+	0.153146i
$673$	−3.23731e22			−0.769242			−0.384621	−	0.923075i	$-0.625668\pi$
$673$	−3.23731e22			−0.769242			−0.384621	+	0.923075i	$0.625668\pi$
$674$	1.17814e22	−	2.53970e22i	0.276641	−	0.596353i
$675$	−2.47365e21			−0.0573994
$676$	−2.09327e22	−	2.47461e22i	−0.480011	−	0.567456i
$677$		−	6.51909e22i		−	1.47733i	−0.674072	−	0.738666i	$-0.735456\pi$
$677$		−	6.51909e22i		−	1.47733i	0.674072	−	0.738666i	$-0.264544\pi$
$678$	−5.40391e18	+	1.16492e19i	−0.000121024	+	0.000260890i
$679$			3.45950e22i			0.765694i
$680$	1.06741e22	+	3.89063e22i	0.233485	+	0.851038i
$681$	8.43627e21			0.182379
$682$	7.31186e22	+	3.39189e22i	1.56226	+	0.724715i
$683$	−5.47847e22			−1.15689			−0.578447	−	0.815720i	$-0.696341\pi$
$683$	−5.47847e22			−1.15689			−0.578447	+	0.815720i	$0.696341\pi$
$684$	2.11685e22	+	2.50249e22i	0.441816	+	0.522303i
$685$		−	6.11852e22i		−	1.26218i
$686$	−8.51937e22	−	3.95204e22i	−1.73706	−	0.805802i
$687$		−	6.21141e21i		−	0.125180i
$688$	4.55667e20	−	2.71010e21i	0.00907695	−	0.0539856i
$689$	−1.36374e22			−0.268521
$690$	−7.61920e20	+	1.64246e21i	−0.0148292	+	0.0319671i
$691$	−8.52041e22			−1.63922			−0.819608	−	0.572924i	$-0.805809\pi$
$691$	−8.52041e22			−1.63922			−0.819608	+	0.572924i	$0.805809\pi$
$692$	−7.88708e22	+	6.67168e22i	−1.49992	+	1.26878i
$693$			1.52563e23i			2.86803i
$694$	2.45620e22	−	5.29480e22i	0.456444	−	0.983951i
$695$		−	3.50219e22i		−	0.643372i
$696$	−1.51797e21	−	5.53290e21i	−0.0275670	−	0.100480i
$697$	8.16366e22			1.46562
$698$	−4.24108e22	−	1.96739e22i	−0.752720	−	0.349178i
$699$	6.82215e21			0.119703
$700$	−2.11359e22	+	1.78788e22i	−0.366637	+	0.310138i
$701$			2.82304e22i			0.484142i	0.970258	+	0.242071i	$0.0778268\pi$
$701$			2.82304e22i			0.484142i	−0.970258	+	0.242071i	$0.922173\pi$
$702$	5.69562e21	+	2.64213e21i	0.0965703	+	0.0447979i
$703$		−	3.09495e22i		−	0.518814i
$704$	8.56243e22	−	5.08069e22i	1.41911	−	0.842057i
$705$	−2.24868e21			−0.0368480
$706$	1.93156e22	−	4.16383e22i	0.312946	−	0.674614i
$707$	1.19216e23			1.90977
$708$	2.16482e21	+	2.55919e21i	0.0342891	+	0.0405357i
$709$			9.31234e22i			1.45844i	0.684279	+	0.729220i	$0.260117\pi$
$709$			9.31234e22i			1.45844i	−0.684279	+	0.729220i	$0.739883\pi$
$710$	−1.43150e20	+	3.08587e20i	−0.00221679	+	0.00477871i
$711$		−	3.87611e22i		−	0.593526i
$712$	−1.88436e22	+	5.16981e21i	−0.285314	+	0.0782770i
$713$	−2.72763e22			−0.408385
$714$	1.17765e22	+	5.46297e21i	0.174353	+	0.0808804i
$715$	−4.86886e22			−0.712819
$716$	3.33608e22	+	3.94383e22i	0.482984	+	0.570971i
$717$			9.78959e21i			0.140156i
$718$	4.11649e22	+	1.90959e22i	0.582816	+	0.270362i
$719$			6.77334e22i			0.948357i	0.880429	+	0.474178i	$0.157255\pi$
$719$			6.77334e22i			0.948357i	−0.880429	+	0.474178i	$0.842745\pi$
$720$	6.00395e22	+	1.00948e22i	0.831337	+	0.139778i
$721$	−1.13010e23			−1.54751
$722$	1.62009e22	−	3.49241e22i	0.219403	−	0.472964i
$723$	3.54691e21			0.0475054
$724$	5.55624e22	−	4.70003e22i	0.735991	−	0.622575i
$725$		−	2.05698e22i		−	0.269480i
$726$	−5.91100e21	+	1.27423e22i	−0.0765892	+	0.165103i
$727$			7.07899e22i			0.907186i	0.891209	+	0.453593i	$0.149858\pi$
$727$			7.07899e22i			0.907186i	−0.891209	+	0.453593i	$0.850142\pi$
$728$	6.77623e22	−	1.85908e22i	0.858889	−	0.235639i
$729$	−7.44754e22			−0.933668
$730$	6.16503e22	+	2.85989e22i	0.764455	+	0.354622i
$731$	−4.62034e21			−0.0566676
$732$	−1.04444e22	+	8.83492e21i	−0.126705	+	0.107180i
$733$		−	9.03253e22i		−	1.08387i	−0.840420	−	0.541936i	$-0.817692\pi$
$733$		−	9.03253e22i		−	1.08387i	0.840420	−	0.541936i	$-0.182308\pi$
$734$	−9.94938e22	−	4.61541e22i	−1.18094	−	0.547824i
$735$		−	1.60265e22i		−	0.188166i
$736$	−1.90499e22	+	2.77901e22i	−0.221243	+	0.322751i
$737$	2.24457e23			2.57865
$738$	5.18427e22	−	1.11757e23i	0.589165	−	1.27006i
$739$	−3.00022e22			−0.337286			−0.168643	−	0.985677i	$-0.553938\pi$
$739$	−3.00022e22			−0.337286			−0.168643	+	0.985677i	$0.553938\pi$
$740$	−3.71270e22	−	4.38905e22i	−0.412891	−	0.488109i
$741$			3.36596e21i			0.0370309i
$742$	−3.60149e22	+	7.76369e22i	−0.391968	+	0.844962i
$743$		−	5.17319e22i		−	0.556990i	−0.960438	−	0.278495i	$-0.910164\pi$
$743$		−	5.17319e22i		−	0.556990i	0.960438	−	0.278495i	$-0.0898356\pi$
$744$	−2.73843e21	−	9.98140e21i	−0.0291688	−	0.106318i
$745$	1.71379e22			0.180596
$746$	6.11011e22	+	2.83441e22i	0.636998	+	0.295496i
$747$	−2.99690e22			−0.309106
$748$	−1.08107e23	−	1.27801e23i	−1.10316	−	1.30413i
$749$			1.04556e23i			1.05558i
$750$	−1.04131e22	−	4.83054e21i	−0.104014	−	0.0482509i
$751$			1.53690e23i			1.51889i	0.650572	+	0.759445i	$0.274529\pi$
$751$			1.53690e23i			1.51889i	−0.650572	+	0.759445i	$0.725471\pi$
$752$	−4.12658e22	−	6.93828e21i	−0.403503	−	0.0678436i
$753$	1.45440e22			0.140709
$754$	−2.19709e22	+	4.73624e22i	−0.210318	+	0.453381i
$755$	−1.58835e23			−1.50442
$756$	3.00830e22	−	2.54472e22i	0.281934	−	0.238488i
$757$		−	7.98884e22i		−	0.740827i	−0.928867	−	0.370414i	$-0.879216\pi$
$757$		−	7.98884e22i		−	0.740827i	0.928867	−	0.370414i	$-0.120784\pi$
$758$	−4.98682e21	+	1.07500e22i	−0.0457583	+	0.0986407i
$759$		−	7.51231e21i		−	0.0682086i
$760$	1.73685e22	+	6.33070e22i	0.156046	+	0.568778i
$761$	−1.36540e23			−1.21390			−0.606951	−	0.794739i	$-0.707608\pi$
$761$	−1.36540e23			−1.21390			−0.606951	+	0.794739i	$0.707608\pi$
$762$	−4.88680e20	−	2.26693e20i	−0.00429917	−	0.00199434i
$763$	2.48290e23			2.16154
$764$	−1.19691e23	+	1.01246e23i	−1.03113	+	0.872233i
$765$		−	1.02359e23i		−	0.872639i
$766$	8.29508e22	+	3.84799e22i	0.699826	+	0.324642i
$767$		−	3.05035e22i		−	0.254675i
$768$	−1.20820e22	−	4.18104e21i	−0.0998270	−	0.0345457i
$769$	−1.49662e23			−1.22377			−0.611887	−	0.790945i	$-0.709589\pi$
$769$	−1.49662e23			−1.22377			−0.611887	+	0.790945i	$0.709589\pi$
$770$	−1.28581e23	+	2.77182e23i	−1.04053	+	2.24305i
$771$	−1.97635e22			−0.158281
$772$	1.35386e22	+	1.60050e22i	0.107309	+	0.126858i
$773$		−	2.33581e23i		−	1.83232i	−0.400809	−	0.916162i	$-0.631271\pi$
$773$		−	2.33581e23i		−	1.83232i	0.400809	−	0.916162i	$-0.368729\pi$
$774$	−2.93411e21	+	6.32504e21i	−0.0227798	+	0.0491061i
$775$		−	3.71082e22i		−	0.285138i
$776$	−5.52397e22	+	1.51552e22i	−0.420105	+	0.115257i
$777$	−1.84982e22			−0.139239
$778$	−1.08076e23	−	5.01350e22i	−0.805176	−	0.373512i
$779$	1.32836e23			0.979527
$780$	4.03780e21	+	4.77338e21i	0.0294705	+	0.0348393i
$781$		−	1.41142e21i		−	0.0101964i
$782$	5.13863e22	+	2.38375e22i	0.367445	+	0.170454i
$783$			2.92774e22i			0.207223i
$784$	4.94497e22	−	2.94105e23i	0.346446	−	2.06050i
$785$	4.00314e22			0.277615
$786$	−3.45244e21	+	7.44239e21i	−0.0236999	+	0.0510895i
$787$	2.27015e23			1.54261			0.771306	−	0.636464i	$-0.219604\pi$
$787$	2.27015e23			1.54261			0.771306	+	0.636464i	$0.219604\pi$
$788$	8.57737e22	−	7.25560e22i	0.576959	−	0.488049i
$789$		−	1.61231e22i		−	0.107358i
$790$	3.26682e22	−	7.04225e22i	0.215332	−	0.464189i
$791$		−	7.33367e20i		−	0.00478530i
$792$	−2.43606e23	+	6.68341e22i	−1.57357	+	0.431715i
$793$	1.24489e23			0.796057
$794$	1.94060e23	+	9.00220e22i	1.22849	+	0.569882i
$795$	−7.61502e21			−0.0477237
$796$	−8.53119e21	+	7.21654e21i	−0.0529304	+	0.0447738i
$797$			6.18875e22i			0.380134i	0.981771	+	0.190067i	$0.0608705\pi$
$797$			6.18875e22i			0.380134i	−0.981771	+	0.190067i	$0.939130\pi$
$798$	1.91622e22	+	8.88915e21i	0.116526	+	0.0540551i
$799$			7.03523e22i			0.423550i
$800$	−3.78072e22	−	2.59165e22i	−0.225348	−	0.154474i
$801$	4.95757e22			0.292556
$802$	−2.67050e22	+	5.75677e22i	−0.156026	+	0.336344i
$803$	−2.81977e23			−1.63113
$804$	−1.86145e22	−	2.20055e22i	−0.106611	−	0.126033i
$805$		−	1.03400e23i		−	0.586347i
$806$	−3.96357e22	+	8.54422e22i	−0.222539	+	0.479725i
$807$		−	1.23910e22i		−	0.0688837i
$808$	5.22257e22	+	1.90359e23i	0.287471	+	1.04781i
$809$	1.54179e23			0.840306			0.420153	−	0.907453i	$-0.361976\pi$
$809$	1.54179e23			0.840306			0.420153	+	0.907453i	$0.361976\pi$
$810$	−1.38526e23	−	6.42605e22i	−0.747567	−	0.346788i
$811$	1.07728e23			0.575654			0.287827	−	0.957682i	$-0.407067\pi$
$811$	1.07728e23			0.575654			0.287827	+	0.957682i	$0.407067\pi$
$812$	2.11609e23	+	2.50158e23i	1.11966	+	1.32363i
$813$			4.00038e22i			0.209593i
$814$	2.16374e23	+	1.00373e23i	1.12256	+	0.520743i
$815$			1.16787e23i			0.599976i
$816$	−3.56404e21	+	2.11973e22i	−0.0181310	+	0.107835i
$817$	−7.51805e21			−0.0378729
$818$	1.30138e23	−	2.80536e23i	0.649196	−	1.39947i
$819$	−1.78276e23			−0.880689
$820$	1.88379e23	−	1.59350e23i	0.921557	−	0.779545i
$821$			1.47976e22i			0.0716879i	0.999357	+	0.0358439i	$0.0114119\pi$
$821$			1.47976e22i			0.0716879i	−0.999357	+	0.0358439i	$0.988588\pi$
$822$	1.37181e22	−	2.95719e22i	0.0658140	−	0.141875i
$823$			1.12690e23i			0.535409i	0.963501	+	0.267704i	$0.0862650\pi$
$823$			1.12690e23i			0.535409i	−0.963501	+	0.267704i	$0.913735\pi$
$824$	−4.95069e22	−	1.80449e23i	−0.232942	−	0.849057i
$825$	1.02201e22			0.0476240
$826$	−1.73654e23	−	8.05564e22i	−0.801393	−	0.371757i
$827$	2.62013e22			0.119751			0.0598754	−	0.998206i	$-0.480930\pi$
$827$	2.62013e22			0.119751			0.0598754	+	0.998206i	$0.480930\pi$
$828$	6.52649e22	−	5.52076e22i	0.295418	−	0.249894i
$829$			2.05806e23i			0.922619i	0.887239	+	0.461310i	$0.152620\pi$
$829$			2.05806e23i			0.922619i	−0.887239	+	0.461310i	$0.847380\pi$
$830$	−5.44487e22	−	2.52581e22i	−0.241748	−	0.112144i
$831$			2.94573e22i			0.129534i
$832$	5.93700e22	+	1.00056e23i	0.258571	+	0.435767i
$833$	−5.01407e23			−2.16287
$834$	7.85212e21	−	1.69267e22i	0.0335474	−	0.0723177i
$835$	−3.94438e22			−0.166912
$836$	−1.75907e23	−	2.07953e23i	−0.737281	−	0.871594i
$837$			5.28166e22i			0.219264i
$838$	−4.32400e22	+	9.32121e22i	−0.177801	+	0.383283i
$839$			6.28571e22i			0.256011i	0.991773	+	0.128005i	$0.0408575\pi$
$839$			6.28571e22i			0.256011i	−0.991773	+	0.128005i	$0.959142\pi$
$840$	3.78380e22	−	1.03810e22i	0.152649	−	0.0418798i
$841$	6.78767e21			0.0271239
$842$	−3.44973e23	−	1.60029e23i	−1.36549	−	0.633435i
$843$	2.20817e22			0.0865787
$844$	1.37377e23	+	1.62404e23i	0.533550	+	0.630748i
$845$			1.64699e23i			0.633633i
$846$	9.63091e22	+	4.46767e22i	0.367033	+	0.170262i
$847$		−	8.02183e23i		−	3.02835i
$848$	−1.39744e23	−	2.34961e22i	−0.522597	−	0.0878677i
$849$	−2.44218e22			−0.0904724
$850$	−3.24298e22	+	6.99086e22i	−0.119013	+	0.256554i
$851$	−8.07165e22			−0.293444
$852$	−1.38374e20	+	1.17050e20i	−0.000498353	+	0.000421557i
$853$			3.85176e23i			1.37426i	0.726537	+	0.687128i	$0.241129\pi$
$853$			3.85176e23i			1.37426i	−0.726537	+	0.687128i	$0.758871\pi$
$854$	3.28761e23	−	7.08706e23i	1.16203	−	2.50497i
$855$		−	1.66555e23i		−	0.583214i
$856$	−1.66949e23	+	4.58032e22i	−0.579155	+	0.158893i
$857$	−1.24791e23			−0.428882			−0.214441	−	0.976737i	$-0.568793\pi$
$857$	−1.24791e23			−0.428882			−0.214441	+	0.976737i	$0.568793\pi$
$858$	−2.35321e22	−	1.09163e22i	−0.0801238	−	0.0371686i
$859$	−5.24837e23			−1.77043			−0.885215	−	0.465182i	$-0.845989\pi$
$859$	−5.24837e23			−1.77043			−0.885215	+	0.465182i	$0.845989\pi$
$860$	−1.06616e22	+	9.01864e21i	−0.0356315	+	0.0301407i
$861$		−	7.93949e22i		−	0.262886i
$862$	−6.24919e22	−	2.89893e22i	−0.205006	−	0.0950998i
$863$			2.70794e23i			0.880143i	0.897963	+	0.440072i	$0.145047\pi$
$863$			2.70794e23i			0.880143i	−0.897963	+	0.440072i	$0.854953\pi$
$864$	5.38116e22	+	3.68874e22i	0.173287	+	0.118787i
$865$	5.24930e23			1.67484
$866$	5.87464e22	−	1.26639e23i	0.185711	−	0.400336i
$867$	2.41265e21			0.00755687
$868$	3.81744e23	+	4.51287e23i	1.18472	+	1.40054i
$869$			3.22099e23i			0.990447i
$870$	−1.22684e22	+	2.64468e22i	−0.0373795	+	0.0805786i
$871$			2.62287e23i			0.791830i
$872$	1.08770e23	+	3.96458e23i	0.325369	+	1.18595i
$873$	1.45330e23			0.430767
$874$	8.36138e22	+	3.87875e22i	0.245576	+	0.113920i
$875$	6.55553e23			1.90785
$876$	2.33846e22	+	2.76447e22i	0.0674369	+	0.0797221i
$877$		−	4.90854e23i		−	1.40267i	−0.712832	−	0.701335i	$-0.752588\pi$
$877$		−	4.90854e23i		−	1.40267i	0.712832	−	0.701335i	$-0.247412\pi$
$878$	−8.68323e22	−	4.02805e22i	−0.245881	−	0.114062i
$879$			2.69303e22i			0.0755668i
$880$	−4.98919e23	−	8.38865e22i	−1.38729	−	0.233255i
$881$	3.81347e23			1.05078			0.525391	−	0.850861i	$-0.323919\pi$
$881$	3.81347e23			1.05078			0.525391	+	0.850861i	$0.323919\pi$
$882$	−3.18415e23	+	6.86404e23i	−0.869451	+	1.87427i
$883$	−5.61332e23			−1.51892			−0.759459	−	0.650555i	$-0.774536\pi$
$883$	−5.61332e23			−1.51892			−0.759459	+	0.650555i	$0.774536\pi$
$884$	1.49340e23	−	1.26327e23i	0.400460	−	0.338749i
$885$		−	1.70329e22i		−	0.0452629i
$886$	6.01267e22	−	1.29615e23i	0.158343	−	0.341337i
$887$		−	5.20176e23i		−	1.35757i	−0.734338	−	0.678783i	$-0.762507\pi$
$887$		−	5.20176e23i		−	1.35757i	0.734338	−	0.678783i	$-0.237493\pi$
$888$	−8.10362e21	−	2.95371e22i	−0.0209592	−	0.0763949i
$889$	3.07646e22			0.0788565
$890$	9.00708e22	+	4.17828e22i	0.228804	+	0.106140i
$891$	6.33590e23			1.59509
$892$	−1.39234e23	+	1.17778e23i	−0.347396	+	0.293863i
$893$			1.14475e23i			0.283073i
$894$	8.28304e21	+	3.84241e21i	0.0202997	+	0.00941681i
$895$		−	2.62485e23i		−	0.637558i
$896$	7.26400e23	−	7.37540e22i	1.74869	−	0.177550i
$897$	8.77845e21			0.0209449
$898$	1.30542e23	−	2.81408e23i	0.308703	−	0.665467i
$899$	−4.39202e23			−1.02941
$900$	7.51074e22	+	8.87899e22i	0.174479	+	0.206264i
$901$			2.38244e23i			0.548560i
$902$	−4.30805e23	+	9.28682e23i	−0.983170	+	2.11941i
$903$			4.49347e21i			0.0101643i
$904$	1.17101e21	−	3.21270e20i	0.00262550	−	0.000720315i
$905$	−3.69800e23			−0.821823
$906$	−7.67676e22	−	3.56117e22i	−0.169104	−	0.0784452i
$907$	8.15171e23			1.77988			0.889940	−	0.456079i	$-0.150746\pi$
$907$	8.15171e23			1.77988			0.889940	+	0.456079i	$0.150746\pi$
$908$	−5.15192e23	−	6.09046e23i	−1.11502	−	1.31815i
$909$		−	5.00817e23i		−	1.07441i
$910$	−3.23898e23	−	1.50253e23i	−0.688775	−	0.319515i
$911$		−	2.57950e23i		−	0.543736i	−0.962335	−	0.271868i	$-0.912359\pi$
$911$		−	2.57950e23i		−	0.543736i	0.962335	−	0.271868i	$-0.0876414\pi$
$912$	−5.79928e21	+	3.44915e22i	−0.0121176	+	0.0720698i
$913$	2.49038e23			0.515821
$914$	2.12925e23	−	4.58999e23i	0.437176	−	0.942416i
$915$	6.95135e22			0.141482
$916$	−4.48424e23	+	3.79322e23i	−0.904744	+	0.765323i
$917$		−	4.68532e23i		−	0.937096i
$918$	4.61579e22	−	9.95020e22i	0.0915175	−	0.197283i
$919$			3.42269e23i			0.672733i	0.941731	+	0.336367i	$0.109198\pi$
$919$			3.42269e23i			0.672733i	−0.941731	+	0.336367i	$0.890802\pi$
$920$	1.65105e23	−	4.52971e22i	0.321705	−	0.0882609i
$921$	2.06841e22			0.0399539
$922$	−5.13966e23	−	2.38423e23i	−0.984208	−	0.456563i
$923$	1.64930e21			0.00313102
$924$	−1.24291e23	+	1.05138e23i	−0.233919	+	0.197872i
$925$		−	1.09811e23i		−	0.204886i
$926$	5.13240e23	+	2.38087e23i	0.949365	+	0.440400i
$927$			4.74745e23i			0.870607i
$928$	−3.06740e23	+	4.47475e23i	−0.557683	+	0.813552i
$929$	−8.15669e23			−1.47024			−0.735120	−	0.677937i	$-0.762874\pi$
$929$	−8.15669e23			−1.47024			−0.735120	+	0.677937i	$0.762874\pi$
$930$	−2.21323e22	+	4.77103e22i	−0.0395514	+	0.0852606i
$931$	−8.15872e23			−1.44552
$932$	−4.16619e23	−	4.92516e23i	−0.731833	−	0.865153i
$933$		−	3.35534e22i		−	0.0584363i
$934$	−7.90797e22	+	1.70471e23i	−0.136549	+	0.294358i
$935$			8.50587e23i			1.45622i
$936$	−7.80984e22	−	2.84663e23i	−0.132567	−	0.483198i
$937$	−2.39983e23			−0.403890			−0.201945	−	0.979397i	$-0.564726\pi$
$937$	−2.39983e23			−0.403890			−0.201945	+	0.979397i	$0.564726\pi$
$938$	1.49319e24	+	6.92672e23i	2.49167	+	1.15586i
$939$	−2.72902e22			−0.0451525
$940$	1.37324e23	+	1.62340e23i	0.225280	+	0.266320i
$941$			2.14117e23i			0.348285i	0.984720	+	0.174143i	$0.0557154\pi$
$941$			2.14117e23i			0.348285i	−0.984720	+	0.174143i	$0.944285\pi$
$942$	1.93479e22	+	8.97526e21i	0.0312051	+	0.0144757i
$943$		−	3.46437e23i		−	0.554027i
$944$	5.25549e22	−	3.12573e23i	0.0833370	−	0.495651i
$945$	−2.00220e23			−0.314813
$946$	2.43820e22	−	5.25601e22i	0.0380138	−	0.0819458i
$947$	−3.68376e23			−0.569497			−0.284749	−	0.958602i	$-0.591910\pi$
$947$	−3.68376e23			−0.569497			−0.284749	+	0.958602i	$0.591910\pi$
$948$	3.15782e22	−	2.67120e22i	0.0484085	−	0.0409487i
$949$		−	3.29501e23i		−	0.500873i
$950$	−5.27686e22	+	1.13753e23i	−0.0795402	+	0.171464i
$951$		−	8.30248e21i		−	0.0124098i
$952$	−3.24781e23	−	1.18380e24i	−0.481387	−	1.75462i
$953$	2.04167e23			0.300084			0.150042	−	0.988680i	$-0.452059\pi$
$953$	2.04167e23			0.300084			0.150042	+	0.988680i	$0.452059\pi$
$954$	3.26146e23	+	1.51295e23i	0.475362	+	0.220515i
$955$	7.96610e23			1.15138
$956$	7.06747e23	−	5.97837e23i	1.01298	−	0.856879i
$957$		−	1.20963e23i		−	0.171932i
$958$	−6.34591e23	−	2.94380e23i	−0.894479	−	0.414939i
$959$			1.86168e24i			2.60230i
$960$	3.31518e22	+	5.58703e22i	0.0459554	+	0.0774481i
$961$	−6.48999e22			−0.0892189
$962$	−1.17291e23	+	2.52842e23i	−0.159905	+	0.344706i
$963$	4.39228e23			0.593855
$964$	−2.16605e23	−	2.56064e23i	−0.290437	−	0.343347i
$965$		−	1.06522e23i		−	0.141652i
$966$	2.31829e22	−	4.99752e22i	0.0305739	−	0.0659079i
$967$		−	7.59082e23i		−	0.992834i	−0.868084	−	0.496417i	$-0.834649\pi$
$967$		−	7.59082e23i		−	0.992834i	0.868084	−	0.496417i	$-0.165351\pi$
$968$	1.28089e24	−	3.51416e23i	1.66153	−	0.455847i
$969$	5.88032e22			0.0756503
$970$	2.64041e23	+	1.22486e23i	0.336897	+	0.156283i
$971$	4.96151e22			0.0627856			0.0313928	−	0.999507i	$-0.490006\pi$
$971$	4.96151e22			0.0627856			0.0313928	+	0.999507i	$0.490006\pi$
$972$	−1.60652e23	−	1.89919e23i	−0.201631	−	0.238362i
$973$			1.06561e24i			1.32647i
$974$	−9.55191e23	−	4.43102e23i	−1.17928	−	0.547057i
$975$			1.19427e22i			0.0146239i
$976$	1.27565e24	+	2.14484e23i	1.54929	+	0.260493i
$977$	2.99474e22			0.0360747			0.0180374	−	0.999837i	$-0.494258\pi$
$977$	2.99474e22			0.0360747			0.0180374	+	0.999837i	$0.494258\pi$
$978$	−2.61843e22	+	5.64452e22i	−0.0312846	+	0.0674398i
$979$	−4.11967e23			−0.488203
$980$	−1.15701e24	+	9.78718e23i	−1.35997	+	1.15040i
$981$		−	1.04304e24i		−	1.21605i
$982$	3.18412e23	−	6.86396e23i	0.368211	−	0.793749i
$983$			4.49793e23i			0.515923i	0.966155	+	0.257961i	$0.0830507\pi$
$983$			4.49793e23i			0.515923i	−0.966155	+	0.257961i	$0.916949\pi$
$984$	1.26774e23	−	3.47809e22i	0.144235	−	0.0395713i
$985$	−5.70874e23			−0.644244
$986$	8.27418e23	+	3.83830e23i	0.926211	+	0.429659i
$987$	6.84205e22			0.0759712
$988$	2.43001e23	−	2.05555e23i	0.267641	−	0.226398i
$989$			1.96071e22i			0.0214212i
$990$	1.16441e24	+	5.40159e23i	1.26190	+	0.585383i
$991$		−	8.85854e23i		−	0.952298i	−0.879365	−	0.476149i	$-0.842032\pi$
$991$		−	8.85854e23i		−	0.952298i	0.879365	−	0.476149i	$-0.157968\pi$
$992$	−5.53362e23	+	8.07249e23i	−0.590087	+	0.860823i
$993$	1.01992e23			0.107888
$994$	4.35563e21	−	9.38937e21i	0.00457046	−	0.00985248i
$995$	5.67800e22			0.0591032
$996$	−2.06530e22	−	2.44154e22i	−0.0213259	−	0.0252109i
$997$			2.97306e23i			0.304539i	0.988339	+	0.152269i	$0.0486581\pi$
$997$			2.97306e23i			0.304539i	−0.988339	+	0.152269i	$0.951342\pi$
$998$	−4.26585e23	+	9.19585e23i	−0.433472	+	0.934432i
$999$			1.56296e23i			0.157552i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.17.d.b.3.6	yes	14
3.2	odd	2		72.17.b.b.19.9		14
4.3	odd	2		32.17.d.b.15.8		14
8.3	odd	2	inner	8.17.d.b.3.5	✓	14
8.5	even	2		32.17.d.b.15.7		14
24.11	even	2		72.17.b.b.19.10		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.17.d.b.3.5	✓	14	8.3	odd	2	inner
8.17.d.b.3.6	yes	14	1.1	even	1	trivial
32.17.d.b.15.7		14	8.5	even	2
32.17.d.b.15.8		14	4.3	odd	2
72.17.b.b.19.9		14	3.2	odd	2
72.17.b.b.19.10		14	24.11	even	2

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:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-107.729 + 232.229i) q^{2} +693.074 q^{3} +(-42325.1 - 50035.5i) q^{4} +333015. i q^{5} +(-74663.9 + 160952. i) q^{6} -1.01327e7i q^{7} +(1.61794e7 - 4.43887e6i) q^{8} -4.25664e7 q^{9} +O(q^{10})\)	\(q+(-107.729 + 232.229i) q^{2} +693.074 q^{3} +(-42325.1 - 50035.5i) q^{4} +333015. i q^{5} +(-74663.9 + 160952. i) q^{6} -1.01327e7i q^{7} +(1.61794e7 - 4.43887e6i) q^{8} -4.25664e7 q^{9} +(-7.73360e7 - 3.58753e7i) q^{10} +3.53720e8 q^{11} +(-2.93344e7 - 3.46783e7i) q^{12} +4.13337e8i q^{13} +(2.35310e9 + 1.09158e9i) q^{14} +2.30804e8i q^{15} +(-7.12145e8 + 4.23552e9i) q^{16} +7.22096e9 q^{17} +(4.58562e9 - 9.88517e9i) q^{18} +1.17497e10 q^{19} +(1.66626e10 - 1.40949e10i) q^{20} -7.02268e9i q^{21} +(-3.81058e10 + 8.21442e10i) q^{22} -3.06432e10i q^{23} +(1.12135e10 - 3.07646e9i) q^{24} +4.16887e10 q^{25} +(-9.59889e10 - 4.45282e10i) q^{26} -5.93362e10 q^{27} +(-5.06993e11 + 4.28865e11i) q^{28} -4.93415e11i q^{29} +(-5.35995e10 - 2.48642e10i) q^{30} -8.90125e11i q^{31} +(-9.06893e11 - 6.21668e11i) q^{32} +2.45154e11 q^{33} +(-7.77905e11 + 1.67692e12i) q^{34} +3.37433e12 q^{35} +(1.80162e12 + 2.12983e12i) q^{36} -2.63407e12i q^{37} +(-1.26578e12 + 2.72862e12i) q^{38} +2.86473e11i q^{39} +(1.47821e12 + 5.38797e12i) q^{40} +1.13055e13 q^{41} +(1.63087e12 + 7.56543e11i) q^{42} -6.39851e11 q^{43} +(-1.49712e13 - 1.76986e13i) q^{44} -1.41753e13i q^{45} +(7.11626e12 + 3.30115e12i) q^{46} +9.74279e12i q^{47} +(-4.93569e11 + 2.93552e12i) q^{48} -6.94378e13 q^{49} +(-4.49107e12 + 9.68134e12i) q^{50} +5.00466e12 q^{51} +(2.06815e13 - 1.74945e13i) q^{52} +3.29935e13i q^{53} +(6.39221e12 - 1.37796e13i) q^{54} +1.17794e14i q^{55} +(-4.49775e13 - 1.63940e14i) q^{56} +8.14340e12 q^{57} +(1.14586e14 + 5.31550e13i) q^{58} -7.37981e13 q^{59} +(1.15484e13 - 9.76880e12i) q^{60} -3.01180e14i q^{61} +(2.06713e14 + 9.58920e13i) q^{62} +4.31310e14i q^{63} +(2.42068e14 - 1.43636e14i) q^{64} -1.37647e14 q^{65} +(-2.64101e13 + 5.69320e13i) q^{66} +6.34561e14 q^{67} +(-3.05628e14 - 3.61305e14i) q^{68} -2.12380e13i q^{69} +(-3.63512e14 + 7.83619e14i) q^{70} -3.99021e12i q^{71} +(-6.88696e14 + 1.88946e14i) q^{72} -7.97174e14 q^{73} +(6.11709e14 + 2.83765e14i) q^{74} +2.88933e13 q^{75} +(-4.97306e14 - 5.87902e14i) q^{76} -3.58412e15i q^{77} +(-6.65274e13 - 3.08613e13i) q^{78} +9.10605e14i q^{79} +(-1.41049e15 - 2.37155e14i) q^{80} +1.79122e15 q^{81} +(-1.21793e15 + 2.62547e15i) q^{82} +7.04053e14 q^{83} +(-3.51383e14 + 2.97235e14i) q^{84} +2.40469e15i q^{85} +(6.89303e13 - 1.48592e14i) q^{86} -3.41973e14i q^{87} +(5.72296e15 - 1.57012e15i) q^{88} -1.16467e15 q^{89} +(3.29191e15 + 1.52708e15i) q^{90} +4.18820e15 q^{91} +(-1.53325e15 + 1.29698e15i) q^{92} -6.16922e14i q^{93} +(-2.26256e15 - 1.04958e15i) q^{94} +3.91283e15i q^{95} +(-6.28544e14 - 4.30861e14i) q^{96} -3.41421e15 q^{97} +(7.48044e15 - 1.61255e16i) q^{98} -1.50566e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 350 q^{2} + 11964 q^{3} - 54220 q^{4} + 4868124 q^{6} + 10899160 q^{8} + 86397354 q^{9}+O(q^{10}) \) 14 * q - 350 * q^2 + 11964 * q^3 - 54220 * q^4 + 4868124 * q^6 + 10899160 * q^8 + 86397354 * q^9	\( 14 q - 350 q^{2} + 11964 q^{3} - 54220 q^{4} + 4868124 q^{6} + 10899160 q^{8} + 86397354 q^{9} + 87155280 q^{10} - 49140292 q^{11} + 31616184 q^{12} - 2675193504 q^{14} + 9716374544 q^{16} - 9985136356 q^{17} - 7692086106 q^{18} + 62922133180 q^{19} + 31953450720 q^{20} - 51493048676 q^{22} + 54962419344 q^{24} - 429906632050 q^{25} - 518273679696 q^{26} + 655936606584 q^{27} + 102542376000 q^{28} - 364331826720 q^{30} + 95751080800 q^{32} + 4034287537464 q^{33} + 1015818512644 q^{34} - 3057653406720 q^{35} - 9569289445092 q^{36} + 9010383442844 q^{38} - 4027933291200 q^{40} + 8719629072668 q^{41} - 6653698130880 q^{42} + 16716309178300 q^{43} - 4351929975880 q^{44} + 21043605267744 q^{46} + 46562301973344 q^{48} - 104740771400434 q^{49} - 54483696687710 q^{50} + 40911296041848 q^{51} - 73249356722400 q^{52} - 18031398151752 q^{54} + 110873799752064 q^{56} - 310730528383176 q^{57} + 256627273576560 q^{58} + 347007330293180 q^{59} - 83822619107520 q^{60} + 346701622780800 q^{62} - 332173589517760 q^{64} + 220877370432000 q^{65} + 875905832132808 q^{66} - 614258765968196 q^{67} - 12\!\cdots\!76 q^{68}+ \cdots - 18\!\cdots\!92 q^{99}+O(q^{100}) \) 14 * q - 350 * q^2 + 11964 * q^3 - 54220 * q^4 + 4868124 * q^6 + 10899160 * q^8 + 86397354 * q^9 + 87155280 * q^10 - 49140292 * q^11 + 31616184 * q^12 - 2675193504 * q^14 + 9716374544 * q^16 - 9985136356 * q^17 - 7692086106 * q^18 + 62922133180 * q^19 + 31953450720 * q^20 - 51493048676 * q^22 + 54962419344 * q^24 - 429906632050 * q^25 - 518273679696 * q^26 + 655936606584 * q^27 + 102542376000 * q^28 - 364331826720 * q^30 + 95751080800 * q^32 + 4034287537464 * q^33 + 1015818512644 * q^34 - 3057653406720 * q^35 - 9569289445092 * q^36 + 9010383442844 * q^38 - 4027933291200 * q^40 + 8719629072668 * q^41 - 6653698130880 * q^42 + 16716309178300 * q^43 - 4351929975880 * q^44 + 21043605267744 * q^46 + 46562301973344 * q^48 - 104740771400434 * q^49 - 54483696687710 * q^50 + 40911296041848 * q^51 - 73249356722400 * q^52 - 18031398151752 * q^54 + 110873799752064 * q^56 - 310730528383176 * q^57 + 256627273576560 * q^58 + 347007330293180 * q^59 - 83822619107520 * q^60 + 346701622780800 * q^62 - 332173589517760 * q^64 + 220877370432000 * q^65 + 875905832132808 * q^66 - 614258765968196 * q^67 - 1235787871965976 * q^68 - 442172390987520 * q^70 - 1312232111609976 * q^72 - 542888518370276 * q^73 + 2394643836493776 * q^74 + 2861985572983740 * q^75 - 614792000883272 * q^76 - 4928152344599520 * q^78 + 6402194304908160 * q^80 - 5344304371237818 * q^81 + 4810720063300804 * q^82 + 7362421930746044 * q^83 - 9316784627856000 * q^84 - 8963192329247716 * q^86 + 3396904358318224 * q^88 - 408131327364580 * q^89 + 14680290550241520 * q^90 - 7162887702930432 * q^91 - 9213856910218560 * q^92 - 15838781433150144 * q^94 + 48917704300183104 * q^96 + 18372136634257180 * q^97 + 34005570793293730 * q^98 - 18934692015468492 * q^99

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