LMFDB - Embedded newform 5.17.c.a.3.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,17,Mod(2,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("5.2");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 17 $
Character orbit:	$[\chi]$	$=$	5.c (of order $4$, 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:	$8.11622719283$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
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} + 354217 x^{12} + 47647865256 x^{10} + \cdots + 84\!\cdots\!36 $ x^14 + 354217x^12 + 47647865256x^10 + 3062948254140560x^8 + 97982926395671183360x^6 + 1450505914836224854327296x^4 + 7749363027207208037244731392x^2 + 8484029084015876402584471207936
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{34}\cdot 3^{10}\cdot 5^{18} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.2
Root			$205.093i$ of defining polynomial
Character	$\chi$	$=$	5.3
Dual form			5.17.c.a.2.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-205.093 + 205.093i) q^{2} +(-8389.67 - 8389.67i) q^{3} -18590.3i q^{4} +(-65048.3 - 385171. i) q^{5} +3.44133e6 q^{6} +(-4.20104e6 + 4.20104e6i) q^{7} +(-9.62824e6 - 9.62824e6i) q^{8} +9.77264e7i q^{9} +O(q^{10})$	\(q+(-205.093 + 205.093i) q^{2} +(-8389.67 - 8389.67i) q^{3} -18590.3i q^{4} +(-65048.3 - 385171. i) q^{5} +3.44133e6 q^{6} +(-4.20104e6 + 4.20104e6i) q^{7} +(-9.62824e6 - 9.62824e6i) q^{8} +9.77264e7i q^{9} +(9.23368e7 + 6.56549e7i) q^{10} +1.64171e8 q^{11} +(-1.55966e8 + 1.55966e8i) q^{12} +(2.05182e8 + 2.05182e8i) q^{13} -1.72321e9i q^{14} +(-2.68572e9 + 3.77719e9i) q^{15} +5.16770e9 q^{16} +(2.00552e9 - 2.00552e9i) q^{17} +(-2.00430e10 - 2.00430e10i) q^{18} -6.44717e9i q^{19} +(-7.16044e9 + 1.20927e9i) q^{20} +7.04907e10 q^{21} +(-3.36703e10 + 3.36703e10i) q^{22} +(2.07832e10 + 2.07832e10i) q^{23} +1.61555e11i q^{24} +(-1.44125e11 + 5.01094e10i) q^{25} -8.41626e10 q^{26} +(4.58744e11 - 4.58744e11i) q^{27} +(7.80986e10 + 7.80986e10i) q^{28} +7.06157e11i q^{29} +(-2.23852e11 - 1.32550e12i) q^{30} -3.56624e11 q^{31} +(-4.28864e11 + 4.28864e11i) q^{32} +(-1.37734e12 - 1.37734e12i) q^{33} +8.22637e11i q^{34} +(1.89139e12 + 1.34485e12i) q^{35} +1.81676e12 q^{36} +(2.11875e11 - 2.11875e11i) q^{37} +(1.32227e12 + 1.32227e12i) q^{38} -3.44281e12i q^{39} +(-3.08222e12 + 4.33482e12i) q^{40} +8.10337e12 q^{41} +(-1.44571e13 + 1.44571e13i) q^{42} +(-6.40772e12 - 6.40772e12i) q^{43} -3.05199e12i q^{44} +(3.76413e13 - 6.35693e12i) q^{45} -8.52498e12 q^{46} +(-2.97346e12 + 2.97346e12i) q^{47} +(-4.33553e13 - 4.33553e13i) q^{48} -2.06454e12i q^{49} +(1.92820e13 - 3.98362e13i) q^{50} -3.36513e13 q^{51} +(3.81439e12 - 3.81439e12i) q^{52} +(8.09389e13 + 8.09389e13i) q^{53} +1.88170e14i q^{54} +(-1.06790e13 - 6.32338e13i) q^{55} +8.08972e13 q^{56} +(-5.40896e13 + 5.40896e13i) q^{57} +(-1.44828e14 - 1.44828e14i) q^{58} +1.64260e13i q^{59} +(7.02191e13 + 4.99284e13i) q^{60} +1.82780e14 q^{61} +(7.31411e13 - 7.31411e13i) q^{62} +(-4.10552e14 - 4.10552e14i) q^{63} +1.62757e14i q^{64} +(6.56832e13 - 9.23766e13i) q^{65} +5.64965e14 q^{66} +(-4.64887e14 + 4.64887e14i) q^{67} +(-3.72833e13 - 3.72833e13i) q^{68} -3.48728e14i q^{69} +(-6.63730e14 + 1.12092e14i) q^{70} -9.33424e14 q^{71} +(9.40932e14 - 9.40932e14i) q^{72} +(8.72119e14 + 8.72119e14i) q^{73} +8.69083e13i q^{74} +(1.62957e15 + 7.88763e14i) q^{75} -1.19855e14 q^{76} +(-6.89688e14 + 6.89688e14i) q^{77} +(7.06096e14 + 7.06096e14i) q^{78} -5.24106e14i q^{79} +(-3.36150e14 - 1.99045e15i) q^{80} -3.49062e15 q^{81} +(-1.66194e15 + 1.66194e15i) q^{82} +(1.59524e15 + 1.59524e15i) q^{83} -1.31044e15i q^{84} +(-9.02924e14 - 6.42013e14i) q^{85} +2.62836e15 q^{86} +(5.92442e15 - 5.92442e15i) q^{87} +(-1.58068e15 - 1.58068e15i) q^{88} -5.35714e15i q^{89} +(-6.41622e15 + 9.02374e15i) q^{90} -1.72395e15 q^{91} +(3.86366e14 - 3.86366e14i) q^{92} +(2.99196e15 + 2.99196e15i) q^{93} -1.21967e15i q^{94} +(-2.48326e15 + 4.19377e14i) q^{95} +7.19605e15 q^{96} +(-6.01491e15 + 6.01491e15i) q^{97} +(4.23424e14 + 4.23424e14i) q^{98} +1.60438e16i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 7908 q^{3} + 192880 q^{5} + 4417368 q^{6} - 386452 q^{7} - 10493340 q^{8}+O(q^{10}) $ 14 * q - 2 * q^2 + 7908 * q^3 + 192880 * q^5 + 4417368 * q^6 - 386452 * q^7 - 10493340 * q^8	\( 14 q - 2 q^{2} + 7908 q^{3} + 192880 q^{5} + 4417368 q^{6} - 386452 q^{7} - 10493340 q^{8} + 398727830 q^{10} - 539141632 q^{11} + 1973309928 q^{12} - 681358582 q^{13} + 3514452060 q^{15} - 22953579016 q^{16} + 13124182498 q^{17} - 11293583022 q^{18} - 20186820060 q^{20} + 133652286048 q^{21} - 244784660624 q^{22} + 236373052228 q^{23} + 13144083650 q^{25} + 223473840788 q^{26} + 608106053880 q^{27} - 1494176423768 q^{28} + 2252131613760 q^{30} - 1105223074952 q^{31} - 2024535639992 q^{32} - 6385551058704 q^{33} + 6956678093980 q^{35} + 12514339524924 q^{36} - 9027827087002 q^{37} - 7824802789560 q^{38} + 31912538913900 q^{40} + 39543901484288 q^{41} - 70814500818384 q^{42} - 63017457929452 q^{43} + 126481294123110 q^{45} + 44357914058008 q^{46} - 2826187575452 q^{47} - 405160526368272 q^{48} + 461109216233650 q^{50} + 208649050954008 q^{51} - 389623094881012 q^{52} - 275142037498442 q^{53} + 330504874256560 q^{55} + 865011118900080 q^{56} - 644237427525840 q^{57} - 991296507673440 q^{58} + 16\!\cdots\!80 q^{60}+ \cdots + 48\!\cdots\!02 q^{98}+O(q^{100}) \) 14 * q - 2 * q^2 + 7908 * q^3 + 192880 * q^5 + 4417368 * q^6 - 386452 * q^7 - 10493340 * q^8 + 398727830 * q^10 - 539141632 * q^11 + 1973309928 * q^12 - 681358582 * q^13 + 3514452060 * q^15 - 22953579016 * q^16 + 13124182498 * q^17 - 11293583022 * q^18 - 20186820060 * q^20 + 133652286048 * q^21 - 244784660624 * q^22 + 236373052228 * q^23 + 13144083650 * q^25 + 223473840788 * q^26 + 608106053880 * q^27 - 1494176423768 * q^28 + 2252131613760 * q^30 - 1105223074952 * q^31 - 2024535639992 * q^32 - 6385551058704 * q^33 + 6956678093980 * q^35 + 12514339524924 * q^36 - 9027827087002 * q^37 - 7824802789560 * q^38 + 31912538913900 * q^40 + 39543901484288 * q^41 - 70814500818384 * q^42 - 63017457929452 * q^43 + 126481294123110 * q^45 + 44357914058008 * q^46 - 2826187575452 * q^47 - 405160526368272 * q^48 + 461109216233650 * q^50 + 208649050954008 * q^51 - 389623094881012 * q^52 - 275142037498442 * q^53 + 330504874256560 * q^55 + 865011118900080 * q^56 - 644237427525840 * q^57 - 991296507673440 * q^58 + 1631207111049480 * q^60 + 683634528395968 * q^61 - 938995013191864 * q^62 - 1361911146729372 * q^63 + 517066464980110 * q^65 - 196778043917184 * q^66 - 181547742064252 * q^67 - 917821658187868 * q^68 + 1066699466039880 * q^70 - 1337544011098792 * q^71 + 2573199832214340 * q^72 + 778038215296478 * q^73 - 1442550824447700 * q^75 - 233750796900240 * q^76 + 1099376123524976 * q^77 + 8472064951325256 * q^78 - 14934736099860320 * q^80 + 809940307363794 * q^81 - 303814693723184 * q^82 + 13357181209550188 * q^83 - 16045734952112470 * q^85 - 20034048539985352 * q^86 + 17327533268211840 * q^87 + 22952328705949920 * q^88 - 21878453293909290 * q^90 - 24534035720748632 * q^91 + 40652972845631848 * q^92 + 15958372062212256 * q^93 - 22489885958711400 * q^95 - 27488119051061472 * q^96 - 3303551663290402 * q^97 + 48233459501789102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−205.093	+	205.093i	−0.801145	+	0.801145i	−0.983274	−	0.182130i	$-0.941701\pi$
$2$	−205.093	+	205.093i	−0.801145	+	0.801145i	0.182130	+	0.983274i	$0.441701\pi$
$3$	−8389.67	−	8389.67i	−1.27872	−	1.27872i	−0.941386	−	0.337332i	$-0.890475\pi$
$3$	−8389.67	−	8389.67i	−1.27872	−	1.27872i	−0.337332	−	0.941386i	$-0.609525\pi$
$4$		−	18590.3i		−	0.283665i
$5$	−65048.3	−	385171.i	−0.166524	−	0.986037i
$5$	−65048.3	−	385171.i	−0.166524	−	0.986037i
$6$	3.44133e6			2.04888
$7$	−4.20104e6	+	4.20104e6i	−0.728740	+	0.728740i	−0.970369	−	0.241629i	$-0.922318\pi$
$7$	−4.20104e6	+	4.20104e6i	−0.728740	+	0.728740i	0.241629	+	0.970369i	$0.422318\pi$
$8$	−9.62824e6	−	9.62824e6i	−0.573888	−	0.573888i
$9$			9.77264e7i			2.27024i
$10$	9.23368e7	+	6.56549e7i	0.923368	+	0.656549i
$11$	1.64171e8			0.765869			0.382935	−	0.923775i	$-0.374913\pi$
$11$	1.64171e8			0.765869			0.382935	+	0.923775i	$0.374913\pi$
$12$	−1.55966e8	+	1.55966e8i	−0.362728	+	0.362728i
$13$	2.05182e8	+	2.05182e8i	0.251531	+	0.251531i	0.821598	−	0.570067i	$-0.193083\pi$
$13$	2.05182e8	+	2.05182e8i	0.251531	+	0.251531i	−0.570067	+	0.821598i	$0.693083\pi$
$14$		−	1.72321e9i		−	1.16765i
$15$	−2.68572e9	+	3.77719e9i	−1.04793	+	1.47380i
$16$	5.16770e9			1.20320
$17$	2.00552e9	−	2.00552e9i	0.287499	−	0.287499i	−0.548592	−	0.836090i	$-0.684836\pi$
$17$	2.00552e9	−	2.00552e9i	0.287499	−	0.287499i	0.836090	+	0.548592i	$0.184836\pi$
$18$	−2.00430e10	−	2.00430e10i	−1.81879	−	1.81879i
$19$		−	6.44717e9i		−	0.379612i	−0.981822	−	0.189806i	$-0.939214\pi$
$19$		−	6.44717e9i		−	0.379612i	0.981822	−	0.189806i	$-0.0607859\pi$
$20$	−7.16044e9	+	1.20927e9i	−0.279705	+	0.0472370i
$21$	7.04907e10			1.86371
$22$	−3.36703e10	+	3.36703e10i	−0.613572	+	0.613572i
$23$	2.07832e10	+	2.07832e10i	0.265393	+	0.265393i	0.827241	−	0.561848i	$-0.189909\pi$
$23$	2.07832e10	+	2.07832e10i	0.265393	+	0.265393i	−0.561848	+	0.827241i	$0.689909\pi$
$24$			1.61555e11i			1.46768i
$25$	−1.44125e11	+	5.01094e10i	−0.944540	+	0.328397i
$26$	−8.41626e10			−0.403025
$27$	4.58744e11	−	4.58744e11i	1.62428	−	1.62428i
$28$	7.80986e10	+	7.80986e10i	0.206718	+	0.206718i
$29$			7.06157e11i			1.41162i	0.708402	+	0.705809i	$0.249416\pi$
$29$			7.06157e11i			1.41162i	−0.708402	+	0.705809i	$0.750584\pi$
$30$	−2.23852e11	−	1.32550e12i	−0.341186	−	2.02027i
$31$	−3.56624e11			−0.418136			−0.209068	−	0.977901i	$-0.567043\pi$
$31$	−3.56624e11			−0.418136			−0.209068	+	0.977901i	$0.567043\pi$
$32$	−4.28864e11	+	4.28864e11i	−0.390049	+	0.390049i
$33$	−1.37734e12	−	1.37734e12i	−0.979331	−	0.979331i
$34$			8.22637e11i			0.460656i
$35$	1.89139e12	+	1.34485e12i	0.839917	+	0.597212i
$36$	1.81676e12			0.643989
$37$	2.11875e11	−	2.11875e11i	0.0603207	−	0.0603207i	−0.676303	−	0.736624i	$-0.736419\pi$
$37$	2.11875e11	−	2.11875e11i	0.0603207	−	0.0603207i	0.736624	+	0.676303i	$0.236419\pi$
$38$	1.32227e12	+	1.32227e12i	0.304124	+	0.304124i
$39$		−	3.44281e12i		−	0.643274i
$40$	−3.08222e12	+	4.33482e12i	−0.470309	+	0.661440i
$41$	8.10337e12			1.01483			0.507417	−	0.861701i	$-0.330600\pi$
$41$	8.10337e12			1.01483			0.507417	+	0.861701i	$0.330600\pi$
$42$	−1.44571e13	+	1.44571e13i	−1.49310	+	1.49310i
$43$	−6.40772e12	−	6.40772e12i	−0.548221	−	0.548221i	0.377705	−	0.925926i	$-0.376713\pi$
$43$	−6.40772e12	−	6.40772e12i	−0.548221	−	0.548221i	−0.925926	+	0.377705i	$0.876713\pi$
$44$		−	3.05199e12i		−	0.217251i
$45$	3.76413e13	−	6.35693e12i	2.23854	−	0.378048i
$46$	−8.52498e12			−0.425237
$47$	−2.97346e12	+	2.97346e12i	−0.124876	+	0.124876i	−0.766783	−	0.641907i	$-0.778144\pi$
$47$	−2.97346e12	+	2.97346e12i	−0.124876	+	0.124876i	0.641907	+	0.766783i	$0.278144\pi$
$48$	−4.33553e13	−	4.33553e13i	−1.53855	−	1.53855i
$49$		−	2.06454e12i		−	0.0621235i
$50$	1.92820e13	−	3.98362e13i	0.493620	−	1.01981i
$51$	−3.36513e13			−0.735260
$52$	3.81439e12	−	3.81439e12i	0.0713506	−	0.0713506i
$53$	8.09389e13	+	8.09389e13i	1.30002	+	1.30002i	0.928374	+	0.371648i	$0.121207\pi$
$53$	8.09389e13	+	8.09389e13i	1.30002	+	1.30002i	0.371648	+	0.928374i	$0.378793\pi$
$54$			1.88170e14i			2.60256i
$55$	−1.06790e13	−	6.32338e13i	−0.127535	−	0.755176i
$56$	8.08972e13			0.836429
$57$	−5.40896e13	+	5.40896e13i	−0.485417	+	0.485417i
$58$	−1.44828e14	−	1.44828e14i	−1.13091	−	1.13091i
$59$			1.64260e13i			0.111871i	0.998434	+	0.0559353i	$0.0178140\pi$
$59$			1.64260e13i			0.111871i	−0.998434	+	0.0559353i	$0.982186\pi$
$60$	7.02191e13	+	4.99284e13i	0.418066	+	0.297261i
$61$	1.82780e14			0.953431			0.476715	−	0.879058i	$-0.341827\pi$
$61$	1.82780e14			0.953431			0.476715	+	0.879058i	$0.341827\pi$
$62$	7.31411e13	−	7.31411e13i	0.334987	−	0.334987i
$63$	−4.10552e14	−	4.10552e14i	−1.65441	−	1.65441i
$64$			1.62757e14i			0.578228i
$65$	6.56832e13	−	9.23766e13i	0.206133	−	0.289905i
$66$	5.64965e14			1.56917
$67$	−4.64887e14	+	4.64887e14i	−1.14485	+	1.14485i	−0.157302	+	0.987551i	$0.550279\pi$
$67$	−4.64887e14	+	4.64887e14i	−1.14485	+	1.14485i	−0.987551	+	0.157302i	$0.949721\pi$
$68$	−3.72833e13	−	3.72833e13i	−0.0815535	−	0.0815535i
$69$		−	3.48728e14i		−	0.678726i
$70$	−6.63730e14	+	1.12092e14i	−1.15135	+	0.194442i
$71$	−9.33424e14			−1.44548			−0.722740	−	0.691120i	$-0.757118\pi$
$71$	−9.33424e14			−1.44548			−0.722740	+	0.691120i	$0.757118\pi$
$72$	9.40932e14	−	9.40932e14i	1.30286	−	1.30286i
$73$	8.72119e14	+	8.72119e14i	1.08142	+	1.08142i	0.996378	+	0.0850387i	$0.0271014\pi$
$73$	8.72119e14	+	8.72119e14i	1.08142	+	1.08142i	0.0850387	+	0.996378i	$0.472899\pi$
$74$			8.69083e13i			0.0966512i
$75$	1.62957e15	+	7.88763e14i	1.62773	+	0.787873i
$76$	−1.19855e14			−0.107683
$77$	−6.89688e14	+	6.89688e14i	−0.558119	+	0.558119i
$78$	7.06096e14	+	7.06096e14i	0.515356	+	0.515356i
$79$		−	5.24106e14i		−	0.345463i	−0.984969	−	0.172732i	$-0.944741\pi$
$79$		−	5.24106e14i		−	0.345463i	0.984969	−	0.172732i	$-0.0552594\pi$
$80$	−3.36150e14	−	1.99045e15i	−0.200361	−	1.18640i
$81$	−3.49062e15			−1.88375
$82$	−1.66194e15	+	1.66194e15i	−0.813029	+	0.813029i
$83$	1.59524e15	+	1.59524e15i	0.708273	+	0.708273i	0.966172	−	0.257899i	$-0.0830303\pi$
$83$	1.59524e15	+	1.59524e15i	0.708273	+	0.708273i	−0.257899	+	0.966172i	$0.583030\pi$
$84$		−	1.31044e15i		−	0.528669i
$85$	−9.02924e14	−	6.42013e14i	−0.331360	−	0.235609i
$86$	2.62836e15			0.878409
$87$	5.92442e15	−	5.92442e15i	1.80506	−	1.80506i
$88$	−1.58068e15	−	1.58068e15i	−0.439523	−	0.439523i
$89$		−	5.35714e15i		−	1.36086i	−0.732814	−	0.680429i	$-0.761793\pi$
$89$		−	5.35714e15i		−	1.36086i	0.732814	−	0.680429i	$-0.238207\pi$
$90$	−6.41622e15	+	9.02374e15i	−1.49052	+	2.09627i
$91$	−1.72395e15			−0.366601
$92$	3.86366e14	−	3.86366e14i	0.0752829	−	0.0752829i
$93$	2.99196e15	+	2.99196e15i	0.534677	+	0.534677i
$94$		−	1.21967e15i		−	0.200088i
$95$	−2.48326e15	+	4.19377e14i	−0.374312	+	0.0632144i
$96$	7.19605e15			0.997526
$97$	−6.01491e15	+	6.01491e15i	−0.767459	+	0.767459i	−0.977659	−	0.210199i	$-0.932589\pi$
$97$	−6.01491e15	+	6.01491e15i	−0.767459	+	0.767459i	0.210199	+	0.977659i	$0.432589\pi$
$98$	4.23424e14	+	4.23424e14i	0.0497699	+	0.0497699i
$99$			1.60438e16i			1.73871i
$100$	9.31549e14	+	2.67933e15i	0.0931549	+	0.267933i
$101$	1.15160e16			1.06348			0.531741	−	0.846907i	$-0.321538\pi$
$101$	1.15160e16			1.06348			0.531741	+	0.846907i	$0.321538\pi$
$102$	6.90165e15	−	6.90165e15i	0.589049	−	0.589049i
$103$	−2.07551e15	−	2.07551e15i	−0.163843	−	0.163843i	0.620424	−	0.784267i	$-0.286961\pi$
$103$	−2.07551e15	−	2.07551e15i	−0.163843	−	0.163843i	−0.784267	+	0.620424i	$0.786961\pi$
$104$		−	3.95107e15i		−	0.288701i
$105$	−4.58530e15	−	2.71510e16i	−0.310351	−	1.83768i
$106$	−3.32000e16			−2.08301
$107$	1.43252e16	−	1.43252e16i	0.833737	−	0.833737i	−0.154289	−	0.988026i	$-0.549309\pi$
$107$	1.43252e16	−	1.43252e16i	0.833737	−	0.833737i	0.988026	+	0.154289i	$0.0493086\pi$
$108$	−8.52819e15	−	8.52819e15i	−0.460752	−	0.460752i
$109$			5.29140e15i			0.265558i	0.991146	+	0.132779i	$0.0423900\pi$
$109$			5.29140e15i			0.265558i	−0.991146	+	0.132779i	$0.957610\pi$
$110$	1.51590e16	+	1.07786e16i	0.707179	+	0.502831i
$111$	−3.55513e15			−0.154266
$112$	−2.17097e16	+	2.17097e16i	−0.876819	+	0.876819i
$113$	2.07985e16	+	2.07985e16i	0.782355	+	0.782355i	0.980228	−	0.197872i	$-0.0634032\pi$
$113$	2.07985e16	+	2.07985e16i	0.782355	+	0.782355i	−0.197872	+	0.980228i	$0.563403\pi$
$114$		−	2.21868e16i		−	0.777779i
$115$	6.65317e15	−	9.35700e15i	0.217493	−	0.305882i
$116$	1.31277e16			0.400428
$117$	−2.00516e16	+	2.00516e16i	−0.571035	+	0.571035i
$118$	−3.36886e15	−	3.36886e15i	−0.0896245	−	0.0896245i
$119$			1.68506e16i			0.419024i
$120$	6.22264e16	−	1.05089e16i	1.44719	−	0.244403i
$121$	−1.89977e16			−0.413444
$122$	−3.74868e16	+	3.74868e16i	−0.763836	+	0.763836i
$123$	−6.79846e16	−	6.79846e16i	−1.29769	−	1.29769i
$124$			6.62975e15i			0.118611i
$125$	2.86758e16	+	5.22534e16i	0.481100	+	0.876666i
$126$	1.68403e17			2.65085
$127$	1.08046e16	−	1.08046e16i	0.159653	−	0.159653i	−0.622760	−	0.782413i	$-0.713989\pi$
$127$	1.08046e16	−	1.08046e16i	0.159653	−	0.159653i	0.782413	+	0.622760i	$0.213989\pi$
$128$	−6.14863e16	−	6.14863e16i	−0.853293	−	0.853293i
$129$			1.07517e17i			1.40204i
$130$	5.47463e15	+	3.24170e16i	0.0671132	+	0.397398i
$131$	−7.45216e16			−0.859235			−0.429617	−	0.903011i	$-0.641352\pi$
$131$	−7.45216e16			−0.859235			−0.429617	+	0.903011i	$0.641352\pi$
$132$	−2.56051e16	+	2.56051e16i	−0.277802	+	0.277802i
$133$	2.70848e16	+	2.70848e16i	0.276639	+	0.276639i
$134$		−	1.90690e17i		−	1.83438i
$135$	−2.06535e17	−	1.46854e17i	−1.87208	−	1.33112i
$136$	−3.86193e16			−0.329984
$137$	4.14270e16	−	4.14270e16i	0.333825	−	0.333825i	−0.520212	−	0.854037i	$-0.674147\pi$
$137$	4.14270e16	−	4.14270e16i	0.333825	−	0.333825i	0.854037	+	0.520212i	$0.174147\pi$
$138$	7.15218e16	+	7.15218e16i	0.543758	+	0.543758i
$139$		−	6.38336e15i		−	0.0458069i	−0.999738	−	0.0229034i	$-0.992709\pi$
$139$		−	6.38336e15i		−	0.0458069i	0.999738	−	0.0229034i	$-0.00729103\pi$
$140$	2.50011e16	−	3.51615e16i	0.169409	−	0.238256i
$141$	4.98927e16			0.319363
$142$	1.91439e17	−	1.91439e17i	1.15804	−	1.15804i
$143$	3.36848e16	+	3.36848e16i	0.192640	+	0.192640i
$144$			5.05021e17i			2.73155i
$145$	2.71991e17	−	4.59343e16i	1.39191	−	0.235068i
$146$	−3.57731e17			−1.73274
$147$	−1.73208e16	+	1.73208e16i	−0.0794384	+	0.0794384i
$148$	−3.93882e15	−	3.93882e15i	−0.0171109	−	0.0171109i
$149$			3.04050e16i			0.125157i	0.998040	+	0.0625785i	$0.0199324\pi$
$149$			3.04050e16i			0.125157i	−0.998040	+	0.0625785i	$0.980068\pi$
$150$	−4.95982e17	+	1.72443e17i	−1.93525	+	0.672845i
$151$	3.56867e17			1.32035			0.660177	−	0.751110i	$-0.270481\pi$
$151$	3.56867e17			1.32035			0.660177	+	0.751110i	$0.270481\pi$
$152$	−6.20749e16	+	6.20749e16i	−0.217855	+	0.217855i
$153$	1.95992e17	+	1.95992e17i	0.652691	+	0.652691i
$154$		−	2.82901e17i		−	0.894269i
$155$	2.31978e16	+	1.37361e17i	0.0696294	+	0.412297i
$156$	−6.40029e16			−0.182475
$157$	−2.02512e17	+	2.02512e17i	−0.548596	+	0.548596i	−0.926035	−	0.377438i	$-0.876805\pi$
$157$	−2.02512e17	+	2.02512e17i	−0.548596	+	0.548596i	0.377438	+	0.926035i	$0.376805\pi$
$158$	1.07490e17	+	1.07490e17i	0.276766	+	0.276766i
$159$		−	1.35810e18i		−	3.32472i
$160$	1.93083e17	+	1.37289e17i	0.449555	+	0.319651i
$161$	−1.74622e17			−0.386805
$162$	7.15902e17	−	7.15902e17i	1.50915	−	1.50915i
$163$	2.72951e17	+	2.72951e17i	0.547751	+	0.547751i	0.925790	−	0.378039i	$-0.123401\pi$
$163$	2.72951e17	+	2.72951e17i	0.547751	+	0.547751i	−0.378039	+	0.925790i	$0.623401\pi$
$164$		−	1.50644e17i		−	0.287873i
$165$	−4.40917e17	+	6.20104e17i	−0.802575	+	1.12874i
$166$	−6.54344e17			−1.13486
$167$	−7.50989e17	+	7.50989e17i	−1.24137	+	1.24137i	−0.281938	+	0.959433i	$0.590977\pi$
$167$	−7.50989e17	+	7.50989e17i	−1.24137	+	1.24137i	−0.959433	+	0.281938i	$0.909023\pi$
$168$	−6.78701e17	−	6.78701e17i	−1.06956	−	1.06956i
$169$		−	5.81218e17i		−	0.873464i
$170$	3.16856e17	−	5.35111e16i	0.454224	−	0.0767101i
$171$	6.30058e17			0.861811
$172$	−1.19121e17	+	1.19121e17i	−0.155511	+	0.155511i
$173$	3.71537e17	+	3.71537e17i	0.463056	+	0.463056i	0.899656	−	0.436600i	$-0.143817\pi$
$173$	3.71537e17	+	3.71537e17i	0.463056	+	0.463056i	−0.436600	+	0.899656i	$0.643817\pi$
$174$			2.43012e18i			2.89223i
$175$	3.94965e17	−	8.15988e17i	0.449008	−	0.927640i
$176$	8.48386e17			0.921493
$177$	1.37809e17	−	1.37809e17i	0.143051	−	0.143051i
$178$	1.09871e18	+	1.09871e18i	1.09024	+	1.09024i
$179$		−	3.73578e16i		−	0.0354451i	−0.999843	−	0.0177226i	$-0.994358\pi$
$179$		−	3.73578e16i		−	0.0354451i	0.999843	−	0.0177226i	$-0.00564157\pi$
$180$	−1.18177e17	−	6.99764e17i	−0.107239	−	0.634997i
$181$	−1.00561e18			−0.872976			−0.436488	−	0.899710i	$-0.643778\pi$
$181$	−1.00561e18			−0.872976			−0.436488	+	0.899710i	$0.643778\pi$
$182$	3.53570e17	−	3.53570e17i	0.293701	−	0.293701i
$183$	−1.53346e18	−	1.53346e18i	−1.21917	−	1.21917i
$184$		−	4.00211e17i		−	0.304612i
$185$	−9.53903e16	−	6.78261e16i	−0.0695233	−	0.0494337i
$186$	−1.22726e18			−0.856708
$187$	3.29248e17	−	3.29248e17i	0.220186	−	0.220186i
$188$	5.52776e16	+	5.52776e16i	0.0354231	+	0.0354231i
$189$			3.85440e18i			2.36735i
$190$	4.23288e17	−	5.95311e17i	0.249234	−	0.350522i
$191$	1.08836e18			0.614479			0.307240	−	0.951632i	$-0.400595\pi$
$191$	1.08836e18			0.614479			0.307240	+	0.951632i	$0.400595\pi$
$192$	1.36547e18	−	1.36547e18i	0.739390	−	0.739390i
$193$	−8.02796e16	−	8.02796e16i	−0.0417010	−	0.0417010i	0.685949	−	0.727650i	$-0.259387\pi$
$193$	−8.02796e16	−	8.02796e16i	−0.0417010	−	0.0417010i	−0.727650	+	0.685949i	$0.759387\pi$
$194$		−	2.46723e18i		−	1.22969i
$195$	−1.32607e18	+	2.23949e17i	−0.634292	+	0.107120i
$196$	−3.83805e16			−0.0176223
$197$	−2.15636e18	+	2.15636e18i	−0.950584	+	0.950584i	−0.998835	−	0.0482510i	$-0.984635\pi$
$197$	−2.15636e18	+	2.15636e18i	−0.950584	+	0.950584i	0.0482510	+	0.998835i	$0.484635\pi$
$198$	−3.29048e18	−	3.29048e18i	−1.39296	−	1.39296i
$199$			2.98808e15i			0.00121497i	1.00000		0.000607487i	$0.000193369\pi$
$199$			2.98808e15i			0.00121497i	−1.00000		0.000607487i	$0.999807\pi$
$200$	1.87014e18	+	9.05208e17i	0.730523	+	0.353597i
$201$	7.80050e18			2.92789
$202$	−2.36185e18	+	2.36185e18i	−0.852003	+	0.852003i
$203$	−2.96659e18	−	2.96659e18i	−1.02870	−	1.02870i
$204$			6.25588e17i			0.208568i
$205$	−5.27110e17	−	3.12118e18i	−0.168994	−	1.00066i
$206$	8.51345e17			0.262523
$207$	−2.03107e18	+	2.03107e18i	−0.602506	+	0.602506i
$208$	1.06032e18	+	1.06032e18i	0.302642	+	0.302642i
$209$		−	1.05844e18i		−	0.290733i
$210$	6.50888e18	+	4.62806e18i	1.72089	+	1.22361i
$211$	−4.84744e18			−1.23382			−0.616911	−	0.787033i	$-0.711616\pi$
$211$	−4.84744e18			−1.23382			−0.616911	+	0.787033i	$0.711616\pi$
$212$	1.50468e18	−	1.50468e18i	0.368771	−	0.368771i
$213$	7.83112e18	+	7.83112e18i	1.84836	+	1.84836i
$214$			5.87598e18i			1.33589i
$215$	−2.05126e18	+	2.88488e18i	−0.449275	+	0.631858i
$216$	−8.83379e18			−1.86431
$217$	1.49819e18	−	1.49819e18i	0.304712	−	0.304712i
$218$	−1.08523e18	−	1.08523e18i	−0.212750	−	0.212750i
$219$		−	1.46336e19i		−	2.76565i
$220$	−1.17554e18	+	1.98526e17i	−0.214217	+	0.0361774i
$221$	8.22992e17			0.144630
$222$	7.29132e17	−	7.29132e17i	0.123590	−	0.123590i
$223$	1.97065e18	+	1.97065e18i	0.322233	+	0.322233i	0.849623	−	0.527390i	$-0.176829\pi$
$223$	1.97065e18	+	1.97065e18i	0.322233	+	0.322233i	−0.527390	+	0.849623i	$0.676829\pi$
$224$		−	3.60335e18i		−	0.568489i
$225$	−4.89701e18	−	1.40848e19i	−0.745540	−	2.14433i
$226$	−8.53125e18			−1.25356
$227$	1.91079e18	−	1.91079e18i	0.271023	−	0.271023i	−0.558489	−	0.829512i	$-0.688619\pi$
$227$	1.91079e18	−	1.91079e18i	0.271023	−	0.271023i	0.829512	+	0.558489i	$0.188619\pi$
$228$	1.00554e18	+	1.00554e18i	0.137696	+	0.137696i
$229$			1.33935e19i			1.77097i	0.464670	+	0.885484i	$0.346173\pi$
$229$			1.33935e19i			1.77097i	−0.464670	+	0.885484i	$0.653827\pi$
$230$	5.54535e17	+	3.28357e18i	0.0708119	+	0.419299i
$231$	1.15725e19			1.42735
$232$	6.79905e18	−	6.79905e18i	0.810110	−	0.810110i
$233$	−7.42725e16	−	7.42725e16i	−0.00855028	−	0.00855028i	0.702819	−	0.711369i	$-0.251925\pi$
$233$	−7.42725e16	−	7.42725e16i	−0.00855028	−	0.00855028i	−0.711369	+	0.702819i	$0.751925\pi$
$234$		−	8.22490e18i		−	0.914964i
$235$	1.33871e18	+	9.51873e17i	0.143927	+	0.102338i
$236$	3.05364e17			0.0317338
$237$	−4.39707e18	+	4.39707e18i	−0.441750	+	0.441750i
$238$	−3.45593e18	−	3.45593e18i	−0.335699	−	0.335699i
$239$			1.44443e19i			1.35679i	0.734698	+	0.678395i	$0.237324\pi$
$239$			1.44443e19i			1.35679i	−0.734698	+	0.678395i	$0.762676\pi$
$240$	−1.38790e19	+	1.95194e19i	−1.26087	+	1.77328i
$241$	−1.87129e19			−1.64439			−0.822197	−	0.569204i	$-0.807252\pi$
$241$	−1.87129e19			−1.64439			−0.822197	+	0.569204i	$0.807252\pi$
$242$	3.89629e18	−	3.89629e18i	0.331229	−	0.331229i
$243$	9.53773e18	+	9.53773e18i	0.784503	+	0.784503i
$244$		−	3.39793e18i		−	0.270455i
$245$	−7.95203e17	+	1.34295e17i	−0.0612561	+	0.0103450i
$246$	2.78863e19			2.07927
$247$	1.32284e18	−	1.32284e18i	0.0954842	−	0.0954842i
$248$	3.43366e18	+	3.43366e18i	0.239963	+	0.239963i
$249$		−	2.67670e19i		−	1.81136i
$250$	−1.65980e19	−	4.83560e18i	−1.08777	−	0.316906i
$251$	2.03016e19			1.28866			0.644332	−	0.764746i	$-0.277135\pi$
$251$	2.03016e19			1.28866			0.644332	+	0.764746i	$0.277135\pi$
$252$	−7.63229e18	+	7.63229e18i	−0.469300	+	0.469300i
$253$	3.41200e18	+	3.41200e18i	0.203256	+	0.203256i
$254$			4.43188e18i			0.255810i
$255$	2.18896e18	+	1.29615e19i	0.122438	+	0.724994i
$256$	1.45544e19			0.788995
$257$	1.09517e19	−	1.09517e19i	0.575464	−	0.575464i	−0.358186	−	0.933650i	$-0.616605\pi$
$257$	1.09517e19	−	1.09517e19i	0.575464	−	0.575464i	0.933650	+	0.358186i	$0.116605\pi$
$258$	−2.20510e19	−	2.20510e19i	−1.12324	−	1.12324i
$259$			1.78019e18i			0.0879162i
$260$	−1.71731e18	−	1.22107e18i	−0.0822360	−	0.0584728i
$261$	−6.90102e19			−3.20471
$262$	1.52839e19	−	1.52839e19i	0.688371	−	0.688371i
$263$	−1.37565e19	−	1.37565e19i	−0.600982	−	0.600982i	0.339591	−	0.940573i	$-0.389711\pi$
$263$	−1.37565e19	−	1.37565e19i	−0.600982	−	0.600982i	−0.940573	+	0.339591i	$0.889711\pi$
$264$			2.65227e19i			1.12405i
$265$	2.59104e19	−	3.64403e19i	1.06539	−	1.49835i
$266$	−1.11098e19			−0.443255
$267$	−4.49446e19	+	4.49446e19i	−1.74015	+	1.74015i
$268$	8.64240e18	+	8.64240e18i	0.324755	+	0.324755i
$269$		−	5.10593e18i		−	0.186233i	−0.995655	−	0.0931166i	$-0.970317\pi$
$269$		−	5.10593e18i		−	0.186233i	0.995655	−	0.0931166i	$-0.0296829\pi$
$270$	7.24778e19	−	1.22402e19i	2.56622	−	0.433388i
$271$	2.35874e19			0.810823			0.405411	−	0.914134i	$-0.367128\pi$
$271$	2.35874e19			0.810823			0.405411	+	0.914134i	$0.367128\pi$
$272$	1.03639e19	−	1.03639e19i	0.345918	−	0.345918i
$273$	1.44634e19	+	1.44634e19i	0.468780	+	0.468780i
$274$			1.69928e19i			0.534885i
$275$	−2.36612e19	+	8.22650e18i	−0.723394	+	0.251509i
$276$	−6.48297e18			−0.192531
$277$	−9.51102e18	+	9.51102e18i	−0.274403	+	0.274403i	−0.830870	−	0.556467i	$-0.812157\pi$
$277$	−9.51102e18	+	9.51102e18i	−0.274403	+	0.274403i	0.556467	+	0.830870i	$0.312157\pi$
$278$	1.30918e18	+	1.30918e18i	0.0366979	+	0.0366979i
$279$		−	3.48516e19i		−	0.949268i
$280$	−5.26222e18	−	3.11592e19i	−0.139285	−	0.824751i
$281$	1.83084e18			0.0470977			0.0235488	−	0.999723i	$-0.492503\pi$
$281$	1.83084e18			0.0470977			0.0235488	+	0.999723i	$0.492503\pi$
$282$	−1.02326e19	+	1.02326e19i	−0.255856	+	0.255856i
$283$	2.69341e19	+	2.69341e19i	0.654652	+	0.654652i	0.954110	−	0.299458i	$-0.0968057\pi$
$283$	2.69341e19	+	2.69341e19i	0.654652	+	0.654652i	−0.299458	+	0.954110i	$0.596806\pi$
$284$			1.73526e19i			0.410033i
$285$	2.43522e19	+	1.73153e19i	0.559473	+	0.397806i
$286$	−1.38170e19			−0.308665
$287$	−3.40426e19	+	3.40426e19i	−0.739550	+	0.739550i
$288$	−4.19113e19	−	4.19113e19i	−0.885505	−	0.885505i
$289$			4.06170e19i			0.834689i
$290$	−4.63627e19	+	6.52043e19i	−0.926797	+	1.30344i
$291$	1.00926e20			1.96273
$292$	1.62130e19	−	1.62130e19i	0.306760	−	0.306760i
$293$	−5.35018e19	−	5.35018e19i	−0.984980	−	0.984980i	0.0149093	−	0.999889i	$-0.495254\pi$
$293$	−5.35018e19	−	5.35018e19i	−0.984980	−	0.984980i	−0.999889	+	0.0149093i	$0.995254\pi$
$294$		−	7.10477e18i		−	0.127283i
$295$	6.32682e18	−	1.06848e18i	0.110309	−	0.0186291i
$296$	−4.07997e18			−0.0692346
$297$	7.53124e19	−	7.53124e19i	1.24398	−	1.24398i
$298$	−6.23586e18	−	6.23586e18i	−0.100269	−	0.100269i
$299$			8.52866e18i			0.133509i
$300$	1.46633e19	−	3.02941e19i	0.223492	−	0.461730i
$301$	5.38382e19			0.799021
$302$	−7.31909e19	+	7.31909e19i	−1.05779	+	1.05779i
$303$	−9.66153e19	−	9.66153e19i	−1.35989	−	1.35989i
$304$		−	3.33170e19i		−	0.456749i
$305$	−1.18895e19	−	7.04014e19i	−0.158769	−	0.940118i
$306$	−8.03933e19			−1.04580
$307$	3.51466e19	−	3.51466e19i	0.445427	−	0.445427i	−0.448404	−	0.893831i	$-0.648007\pi$
$307$	3.51466e19	−	3.51466e19i	0.445427	−	0.445427i	0.893831	+	0.448404i	$0.148007\pi$
$308$	1.28215e19	+	1.28215e19i	0.158319	+	0.158319i
$309$			3.48257e19i			0.419017i
$310$	−3.29295e19	−	2.34141e19i	−0.386093	−	0.274527i
$311$	8.59958e19			0.982639			0.491319	−	0.870979i	$-0.336515\pi$
$311$	8.59958e19			0.982639			0.491319	+	0.870979i	$0.336515\pi$
$312$	−3.31482e19	+	3.31482e19i	−0.369167	+	0.369167i
$313$	8.90456e19	+	8.90456e19i	0.966624	+	0.966624i	0.999461	−	0.0328366i	$-0.0104541\pi$
$313$	8.90456e19	+	8.90456e19i	0.966624	+	0.966624i	−0.0328366	+	0.999461i	$0.510454\pi$
$314$		−	8.30675e19i		−	0.879010i
$315$	−1.31427e20	+	1.84839e20i	−1.35582	+	1.90681i
$316$	−9.74328e18			−0.0979961
$317$	1.12978e20	−	1.12978e20i	1.10795	−	1.10795i	0.114529	−	0.993420i	$-0.463464\pi$
$317$	1.12978e20	−	1.12978e20i	1.10795	−	1.10795i	0.993420	−	0.114529i	$-0.0365357\pi$
$318$	2.78537e20	+	2.78537e20i	2.66358	+	2.66358i
$319$			1.15930e20i			1.08112i
$320$	6.26891e19	−	1.05870e19i	0.570154	−	0.0962885i
$321$	−2.40367e20			−2.13223
$322$	3.58138e19	−	3.58138e19i	0.309887	−	0.309887i
$323$	−1.29299e19	−	1.29299e19i	−0.109138	−	0.109138i
$324$			6.48917e19i			0.534354i
$325$	−3.98534e19	−	1.92903e19i	−0.320183	−	0.154979i
$326$	−1.11961e20			−0.877656
$327$	4.43931e19	−	4.43931e19i	0.339573	−	0.339573i
$328$	−7.80212e19	−	7.80212e19i	−0.582400	−	0.582400i
$329$		−	2.49833e19i		−	0.182004i
$330$	−3.67500e19	−	2.17608e20i	−0.261304	−	1.54726i
$331$	−1.30193e20			−0.903571			−0.451786	−	0.892126i	$-0.649213\pi$
$331$	−1.30193e20			−0.903571			−0.451786	+	0.892126i	$0.649213\pi$
$332$	2.96559e19	−	2.96559e19i	0.200912	−	0.200912i
$333$	2.07058e19	+	2.07058e19i	0.136942	+	0.136942i
$334$		−	3.08045e20i		−	1.98904i
$335$	2.09301e20	+	1.48821e20i	1.31951	+	0.938222i
$336$	3.64275e20			2.24241
$337$	−2.26807e20	+	2.26807e20i	−1.36338	+	1.36338i	−0.493814	+	0.869567i	$0.664398\pi$
$337$	−2.26807e20	+	2.26807e20i	−1.36338	+	1.36338i	−0.869567	+	0.493814i	$0.835602\pi$
$338$	1.19204e20	+	1.19204e20i	0.699771	+	0.699771i
$339$		−	3.48985e20i		−	2.00082i
$340$	−1.19352e19	+	1.67856e19i	−0.0668342	+	0.0939954i
$341$	−5.85473e19			−0.320237
$342$	−1.29221e20	+	1.29221e20i	−0.690435	+	0.690435i
$343$	−1.30940e20	−	1.30940e20i	−0.683468	−	0.683468i
$344$			1.23390e20i			0.629235i
$345$	−1.34320e20	+	2.26842e19i	−0.669249	+	0.113024i
$346$	−1.52399e20			−0.741949
$347$	1.77227e20	−	1.77227e20i	0.843127	−	0.843127i	−0.146137	−	0.989264i	$-0.546684\pi$
$347$	1.77227e20	−	1.77227e20i	0.843127	−	0.843127i	0.989264	+	0.146137i	$0.0466840\pi$
$348$	−1.10137e20	−	1.10137e20i	−0.512034	−	0.512034i
$349$			1.60963e19i			0.0731345i	0.999331	+	0.0365673i	$0.0116423\pi$
$349$			1.60963e19i			0.0731345i	−0.999331	+	0.0365673i	$0.988358\pi$
$350$	8.63489e19	+	2.48358e20i	0.383453	+	1.10289i
$351$	1.88252e20			0.817112
$352$	−7.04069e19	+	7.04069e19i	−0.298727	+	0.298727i
$353$	−1.04889e20	−	1.04889e20i	−0.435043	−	0.435043i	0.455297	−	0.890340i	$-0.349533\pi$
$353$	−1.04889e20	−	1.04889e20i	−0.435043	−	0.435043i	−0.890340	+	0.455297i	$0.849533\pi$
$354$			5.65272e19i			0.229209i
$355$	6.07176e19	+	3.59528e20i	0.240707	+	1.42530i
$356$	−9.95908e19			−0.386029
$357$	1.41371e20	−	1.41371e20i	0.535813	−	0.535813i
$358$	7.66182e18	+	7.66182e18i	0.0283967	+	0.0283967i
$359$			1.73787e20i			0.629884i	0.949111	+	0.314942i	$0.101985\pi$
$359$			1.73787e20i			0.629884i	−0.949111	+	0.314942i	$0.898015\pi$
$360$	−4.23626e20	−	3.01214e20i	−1.50163	−	1.06771i
$361$	2.46875e20			0.855895
$362$	2.06244e20	−	2.06244e20i	0.699380	−	0.699380i
$363$	1.59384e20	+	1.59384e20i	0.528679	+	0.528679i
$364$			3.20488e19i			0.103992i
$365$	2.79185e20	−	3.92645e20i	0.886236	−	1.24640i
$366$	6.29004e20			1.95346
$367$	−3.77293e20	+	3.77293e20i	−1.14644	+	1.14644i	−0.159189	+	0.987248i	$0.550888\pi$
$367$	−3.77293e20	+	3.77293e20i	−1.14644	+	1.14644i	−0.987248	+	0.159189i	$0.949112\pi$
$368$	1.07401e20	+	1.07401e20i	0.319321	+	0.319321i
$369$			7.91913e20i			2.30392i
$370$	3.34745e19	−	5.65323e18i	0.0953017	−	0.0160947i
$371$	−6.80056e20			−1.89476
$372$	5.56214e19	−	5.56214e19i	0.151670	−	0.151670i
$373$	1.39094e19	+	1.39094e19i	0.0371225	+	0.0371225i	0.725424	−	0.688302i	$-0.241644\pi$
$373$	1.39094e19	+	1.39094e19i	0.0371225	+	0.0371225i	−0.688302	+	0.725424i	$0.741644\pi$
$374$			1.35053e20i			0.352802i
$375$	1.97808e20	−	6.78969e20i	0.505817	−	1.73620i
$376$	5.72584e19			0.143330
$377$	−1.44890e20	+	1.44890e20i	−0.355066	+	0.355066i
$378$	−7.90511e20	−	7.90511e20i	−1.89659	−	1.89659i
$379$		−	4.00950e20i		−	0.941838i	−0.882177	−	0.470919i	$-0.843922\pi$
$379$		−	4.00950e20i		−	0.941838i	0.882177	−	0.470919i	$-0.156078\pi$
$380$	7.79635e18	+	4.61646e19i	0.0179317	+	0.106179i
$381$	−1.81293e20			−0.408302
$382$	−2.23216e20	+	2.23216e20i	−0.492287	+	0.492287i
$383$	−3.49429e20	−	3.49429e20i	−0.754690	−	0.754690i	0.220661	−	0.975351i	$-0.429179\pi$
$383$	−3.49429e20	−	3.49429e20i	−0.754690	−	0.754690i	−0.975351	+	0.220661i	$0.929179\pi$
$384$			1.03170e21i			2.18224i
$385$	3.10511e20	+	2.20785e20i	0.643267	+	0.457387i
$386$	3.29296e19			0.0668171
$387$	6.26203e20	−	6.26203e20i	1.24459	−	1.24459i
$388$	1.11819e20	+	1.11819e20i	0.217702	+	0.217702i
$389$		−	2.59773e20i		−	0.495448i	−0.968831	−	0.247724i	$-0.920317\pi$
$389$		−	2.59773e20i		−	0.495448i	0.968831	−	0.247724i	$-0.0796825\pi$
$390$	2.26037e20	−	3.17898e20i	0.422341	−	0.593979i
$391$	8.33623e19			0.152600
$392$	−1.98779e19	+	1.98779e19i	−0.0356519	+	0.0356519i
$393$	6.25212e20	+	6.25212e20i	1.09872	+	1.09872i
$394$		−	8.84507e20i		−	1.52311i
$395$	−2.01870e20	+	3.40922e19i	−0.340640	+	0.0575278i
$396$	2.98259e20			0.493211
$397$	4.77777e20	−	4.77777e20i	0.774286	−	0.774286i	−0.204567	−	0.978853i	$-0.565579\pi$
$397$	4.77777e20	−	4.77777e20i	0.774286	−	0.774286i	0.978853	+	0.204567i	$0.0655786\pi$
$398$	−6.12834e17	−	6.12834e17i	−0.000973370	−	0.000973370i
$399$		−	4.54465e20i		−	0.707485i
$400$	−7.44797e20	+	2.58950e20i	−1.13647	+	0.395127i
$401$	−6.26940e20			−0.937715			−0.468858	−	0.883274i	$-0.655334\pi$
$401$	−6.26940e20			−0.937715			−0.468858	+	0.883274i	$0.655334\pi$
$402$	−1.59983e21	+	1.59983e21i	−2.34566	+	2.34566i
$403$	−7.31727e19	−	7.31727e19i	−0.105174	−	0.105174i
$404$		−	2.14086e20i		−	0.301673i
$405$	2.27059e20	+	1.34449e21i	0.313688	+	1.85744i
$406$	1.21686e21			1.64828
$407$	3.47837e19	−	3.47837e19i	0.0461978	−	0.0461978i
$408$	3.24003e20	+	3.24003e20i	0.421956	+	0.421956i
$409$			3.68560e20i			0.470675i	0.971914	+	0.235338i	$0.0756196\pi$
$409$			3.68560e20i			0.470675i	−0.971914	+	0.235338i	$0.924380\pi$
$410$	7.48239e20	+	5.32026e20i	0.937065	+	0.666288i
$411$	−6.95118e20			−0.853737
$412$	−3.85843e19	+	3.85843e19i	−0.0464765	+	0.0464765i
$413$	−6.90063e19	−	6.90063e19i	−0.0815245	−	0.0815245i
$414$		−	8.33115e20i		−	0.965389i
$415$	5.10671e20	−	7.18206e20i	0.580439	−	0.816327i
$416$	−1.75990e20			−0.196219
$417$	−5.35543e19	+	5.35543e19i	−0.0585741	+	0.0585741i
$418$	2.17078e20	+	2.17078e20i	0.232919	+	0.232919i
$419$			6.43195e20i			0.677065i	0.940955	+	0.338532i	$0.109930\pi$
$419$			6.43195e20i			0.677065i	−0.940955	+	0.338532i	$0.890070\pi$
$420$	−5.04744e20	+	8.52420e19i	−0.521287	+	0.0880358i
$421$	1.79685e21			1.82077			0.910385	−	0.413761i	$-0.135785\pi$
$421$	1.79685e21			1.82077			0.910385	+	0.413761i	$0.135785\pi$
$422$	9.94175e20	−	9.94175e20i	0.988470	−	0.988470i
$423$	−2.90586e20	−	2.90586e20i	−0.283499	−	0.283499i
$424$		−	1.55860e21i		−	1.49213i
$425$	−1.88551e20	+	3.89542e20i	−0.177140	+	0.365968i
$426$	−3.21222e21			−2.96161
$427$	−7.67864e20	+	7.67864e20i	−0.694803	+	0.694803i
$428$	−2.66309e20	−	2.66309e20i	−0.236502	−	0.236502i
$429$		−	5.65209e20i		−	0.492664i
$430$	−1.70970e20	−	1.01237e21i	−0.146276	−	0.866144i
$431$	−4.54811e20			−0.381955			−0.190978	−	0.981594i	$-0.561166\pi$
$431$	−4.54811e20			−0.381955			−0.190978	+	0.981594i	$0.561166\pi$
$432$	2.37065e21	−	2.37065e21i	1.95433	−	1.95433i
$433$	−9.99119e19	−	9.99119e19i	−0.0808563	−	0.0808563i	0.665522	−	0.746378i	$-0.268209\pi$
$433$	−9.99119e19	−	9.99119e19i	−0.0808563	−	0.0808563i	−0.746378	+	0.665522i	$0.768209\pi$
$434$			6.14538e20i			0.488237i
$435$	−2.66729e21	−	1.89654e21i	−2.08044	−	1.47927i
$436$	9.83688e19			0.0753296
$437$	1.33993e20	−	1.33993e20i	0.100747	−	0.100747i
$438$	3.00125e21	+	3.00125e21i	2.21569	+	2.21569i
$439$			2.16981e21i			1.57291i	0.617645	+	0.786457i	$0.288087\pi$
$439$			2.16981e21i			1.57291i	−0.617645	+	0.786457i	$0.711913\pi$
$440$	−5.06010e20	+	7.11650e20i	−0.360195	+	0.506577i
$441$	2.01760e20			0.141035
$442$	−1.68790e20	+	1.68790e20i	−0.115869	+	0.115869i
$443$	1.77138e21	+	1.77138e21i	1.19421	+	1.19421i	0.975873	+	0.218339i	$0.0700637\pi$
$443$	1.77138e21	+	1.77138e21i	1.19421	+	1.19421i	0.218339	+	0.975873i	$0.429936\pi$
$444$			6.60909e19i			0.0437600i
$445$	−2.06341e21	+	3.48473e20i	−1.34186	+	0.226615i
$446$	−8.08333e20			−0.516311
$447$	2.55088e20	−	2.55088e20i	0.160040	−	0.160040i
$448$	−6.83747e20	−	6.83747e20i	−0.421378	−	0.421378i
$449$			1.16424e20i			0.0704812i	0.999379	+	0.0352406i	$0.0112198\pi$
$449$			1.16424e20i			0.0704812i	−0.999379	+	0.0352406i	$0.988780\pi$
$450$	3.89305e21	+	1.88436e21i	2.31520	+	1.12063i
$451$	1.33034e21			0.777230
$452$	3.86650e20	−	3.86650e20i	0.221927	−	0.221927i
$453$	−2.99399e21	−	2.99399e21i	−1.68836	−	1.68836i
$454$			7.83780e20i			0.434258i
$455$	1.12140e20	+	6.64016e20i	0.0610477	+	0.361483i
$456$	1.04158e21			0.557150
$457$	−3.43991e20	+	3.43991e20i	−0.180808	+	0.180808i	−0.791708	−	0.610900i	$-0.790808\pi$
$457$	−3.43991e20	+	3.43991e20i	−0.180808	+	0.180808i	0.610900	+	0.791708i	$0.290808\pi$
$458$	−2.74692e21	−	2.74692e21i	−1.41880	−	1.41880i
$459$		−	1.84004e21i		−	0.933956i
$460$	−1.73949e20	−	1.23684e20i	−0.0867681	−	0.0616954i
$461$	4.62167e20			0.226565			0.113282	−	0.993563i	$-0.463864\pi$
$461$	4.62167e20			0.226565			0.113282	+	0.993563i	$0.463864\pi$
$462$	−2.37344e21	+	2.37344e21i	−1.14352	+	1.14352i
$463$	2.13884e21	+	2.13884e21i	1.01282	+	1.01282i	0.999917	+	0.0129003i	$0.00410640\pi$
$463$	2.13884e21	+	2.13884e21i	1.01282	+	1.01282i	0.0129003	+	0.999917i	$0.495894\pi$
$464$			3.64921e21i			1.69846i
$465$	9.57793e20	−	1.34704e21i	0.438176	−	0.616248i
$466$	3.04655e19			0.0137000
$467$	1.63587e21	−	1.63587e21i	0.723124	−	0.723124i	−0.246117	−	0.969240i	$-0.579155\pi$
$467$	1.63587e21	−	1.63587e21i	0.723124	−	0.723124i	0.969240	+	0.246117i	$0.0791546\pi$
$468$	3.72766e20	+	3.72766e20i	0.161983	+	0.161983i
$469$		−	3.90602e21i		−	1.66860i
$470$	−4.69782e20	+	7.93376e19i	−0.197294	+	0.0333193i
$471$	3.39801e21			1.40300
$472$	1.58153e20	−	1.58153e20i	0.0642011	−	0.0642011i
$473$	−1.05196e21	−	1.05196e21i	−0.419866	−	0.419866i
$474$		−	1.80362e21i		−	0.707812i
$475$	3.23064e20	+	9.29200e20i	0.124664	+	0.358559i
$476$	3.13257e20			0.118863
$477$	−7.90987e21	+	7.90987e21i	−2.95136	+	2.95136i
$478$	−2.96242e21	−	2.96242e21i	−1.08698	−	1.08698i
$479$			1.27046e21i			0.458434i	0.973375	+	0.229217i	$0.0736166\pi$
$479$			1.27046e21i			0.458434i	−0.973375	+	0.229217i	$0.926383\pi$
$480$	−4.68090e20	−	2.77171e21i	−0.166112	−	0.983598i
$481$	8.69458e19			0.0303450
$482$	3.83789e21	−	3.83789e21i	1.31740	−	1.31740i
$483$	1.46502e21	+	1.46502e21i	0.494615	+	0.494615i
$484$			3.53172e20i			0.117280i
$485$	2.70803e21	+	1.92551e21i	0.884544	+	0.628943i
$486$	−3.91224e21			−1.25700
$487$	1.92045e21	−	1.92045e21i	0.606975	−	0.606975i	−0.335180	−	0.942154i	$-0.608797\pi$
$487$	1.92045e21	−	1.92045e21i	0.606975	−	0.606975i	0.942154	+	0.335180i	$0.108797\pi$
$488$	−1.75985e21	−	1.75985e21i	−0.547162	−	0.547162i
$489$		−	4.57993e21i		−	1.40084i
$490$	1.35548e20	−	1.90633e20i	0.0407871	−	0.0573628i
$491$	−6.48441e21			−1.91963			−0.959817	−	0.280626i	$-0.909458\pi$
$491$	−6.48441e21			−1.91963			−0.959817	+	0.280626i	$0.909458\pi$
$492$	−1.26385e21	+	1.26385e21i	−0.368109	+	0.368109i
$493$	1.41621e21	+	1.41621e21i	0.405839	+	0.405839i
$494$			5.42610e20i			0.152993i
$495$	6.17961e21	−	1.04362e21i	1.71443	−	0.289536i
$496$	−1.84293e21			−0.503100
$497$	3.92135e21	−	3.92135e21i	1.05338	−	1.05338i
$498$	5.48973e21	+	5.48973e21i	1.45116	+	1.45116i
$499$			6.75223e21i			1.75648i	0.478222	+	0.878239i	$0.341281\pi$
$499$			6.75223e21i			1.75648i	−0.478222	+	0.878239i	$0.658719\pi$
$500$	9.71406e20	−	5.33091e20i	0.248680	−	0.136471i
$501$	1.26011e22			3.17473
$502$	−4.16371e21	+	4.16371e21i	−1.03241	+	1.03241i
$503$	−3.30609e21	−	3.30609e21i	−0.806810	−	0.806810i	0.177340	−	0.984150i	$-0.443251\pi$
$503$	−3.30609e21	−	3.30609e21i	−0.806810	−	0.806810i	−0.984150	+	0.177340i	$0.943251\pi$
$504$			7.90579e21i			1.89889i
$505$	−7.49095e20	−	4.43562e21i	−0.177095	−	1.04863i
$506$	−1.39955e21			−0.325676
$507$	−4.87622e21	+	4.87622e21i	−1.11691	+	1.11691i
$508$	−2.00860e20	−	2.00860e20i	−0.0452881	−	0.0452881i
$509$		−	5.72220e20i		−	0.127005i	−0.997982	−	0.0635025i	$-0.979773\pi$
$509$		−	5.72220e20i		−	0.127005i	0.997982	−	0.0635025i	$-0.0202271\pi$
$510$	−3.10726e21	−	2.20937e21i	−0.678915	−	0.482734i
$511$	−7.32761e21			−1.57614
$512$	1.04456e21	−	1.04456e21i	0.221194	−	0.221194i
$513$	−2.95760e21	−	2.95760e21i	−0.616596	−	0.616596i
$514$			4.49225e21i			0.922060i
$515$	−6.64417e20	+	9.34434e20i	−0.134271	+	0.188839i
$516$	1.99878e21			0.397711
$517$	−4.88156e20	+	4.88156e20i	−0.0956388	+	0.0956388i
$518$	−3.65105e20	−	3.65105e20i	−0.0704336	−	0.0704336i
$519$		−	6.23415e21i		−	1.18424i
$520$	−1.52184e21	+	2.57010e20i	−0.284670	+	0.0480755i
$521$	1.84497e21			0.339850			0.169925	−	0.985457i	$-0.445648\pi$
$521$	1.84497e21			0.339850			0.169925	+	0.985457i	$0.445648\pi$
$522$	1.41535e22	−	1.41535e22i	2.56744	−	2.56744i
$523$	4.05226e21	+	4.05226e21i	0.723908	+	0.723908i	0.969399	−	0.245491i	$-0.0789491\pi$
$523$	4.05226e21	+	4.05226e21i	0.723908	+	0.723908i	−0.245491	+	0.969399i	$0.578949\pi$
$524$			1.38538e21i			0.243735i
$525$	−1.01595e22	+	3.53224e21i	−1.76034	+	0.612035i
$526$	5.64272e21			0.962947
$527$	−7.15217e20	+	7.15217e20i	−0.120213	+	0.120213i
$528$	−7.11768e21	−	7.11768e21i	−1.17833	−	1.17833i
$529$		−	5.26873e21i		−	0.859133i
$530$	2.15960e21	+	1.27877e22i	0.346870	+	2.05393i
$531$	−1.60525e21			−0.253973
$532$	5.03515e20	−	5.03515e20i	0.0784728	−	0.0784728i
$533$	1.66266e21	+	1.66266e21i	0.255262	+	0.255262i
$534$		−	1.84357e22i		−	2.78823i
$535$	−6.44946e21	−	4.58581e21i	−0.960933	−	0.683259i
$536$	8.95209e21			1.31403
$537$	−3.13419e20	+	3.13419e20i	−0.0453243	+	0.0453243i
$538$	1.04719e21	+	1.04719e21i	0.149200	+	0.149200i
$539$		−	3.38938e20i		−	0.0475784i
$540$	−2.73007e21	+	3.83955e21i	−0.377592	+	0.531044i
$541$	−7.88758e21			−1.07489			−0.537447	−	0.843298i	$-0.680611\pi$
$541$	−7.88758e21			−1.07489			−0.537447	+	0.843298i	$0.680611\pi$
$542$	−4.83761e21	+	4.83761e21i	−0.649586	+	0.649586i
$543$	8.43676e21	+	8.43676e21i	1.11629	+	1.11629i
$544$			1.72019e21i			0.224277i
$545$	2.03809e21	−	3.44197e20i	0.261850	−	0.0442216i
$546$	−5.93268e21			−0.751120
$547$	−4.00434e21	+	4.00434e21i	−0.499612	+	0.499612i	−0.911317	−	0.411705i	$-0.864933\pi$
$547$	−4.00434e21	+	4.00434e21i	−0.499612	+	0.499612i	0.411705	+	0.911317i	$0.364933\pi$
$548$	−7.70141e20	−	7.70141e20i	−0.0946947	−	0.0946947i
$549$			1.78624e22i			2.16452i
$550$	3.16554e21	−	6.53994e21i	0.378048	−	0.781038i
$551$	4.55271e21			0.535868
$552$	−3.35764e21	+	3.35764e21i	−0.389512	+	0.389512i
$553$	2.20179e21	+	2.20179e21i	0.251753	+	0.251753i
$554$		−	3.90129e21i		−	0.439673i
$555$	2.31255e20	+	1.36933e21i	0.0256890	+	0.152112i
$556$	−1.18669e20			−0.0129938
$557$	4.28151e21	−	4.28151e21i	0.462120	−	0.462120i	−0.437230	−	0.899350i	$-0.644040\pi$
$557$	4.28151e21	−	4.28151e21i	0.462120	−	0.462120i	0.899350	+	0.437230i	$0.144040\pi$
$558$	7.14781e21	+	7.14781e21i	0.760501	+	0.760501i
$559$		−	2.62949e21i		−	0.275789i
$560$	9.77413e21	+	6.94977e21i	1.01059	+	0.718566i
$561$	−5.52457e21			−0.563113
$562$	−3.75492e20	+	3.75492e20i	−0.0377320	+	0.0377320i
$563$	−3.98308e20	−	3.98308e20i	−0.0394596	−	0.0394596i	0.687102	−	0.726561i	$-0.258883\pi$
$563$	−3.98308e20	−	3.98308e20i	−0.0394596	−	0.0394596i	−0.726561	+	0.687102i	$0.758883\pi$
$564$		−	9.27521e20i		−	0.0905922i
$565$	6.65806e21	−	9.36388e21i	0.641151	−	0.901712i
$566$	−1.10480e22			−1.04894
$567$	1.46642e22	−	1.46642e22i	1.37276	−	1.37276i
$568$	8.98723e21	+	8.98723e21i	0.829543	+	0.829543i
$569$			1.52419e20i			0.0138720i	0.999976	+	0.00693602i	$0.00220782\pi$
$569$			1.52419e20i			0.0138720i	−0.999976	+	0.00693602i	$0.997792\pi$
$570$	−8.54571e21	+	1.44321e21i	−0.766919	+	0.129518i
$571$	−5.36852e21			−0.475079			−0.237539	−	0.971378i	$-0.576341\pi$
$571$	−5.36852e21			−0.475079			−0.237539	+	0.971378i	$0.576341\pi$
$572$	6.26211e20	−	6.26211e20i	0.0546453	−	0.0546453i
$573$	−9.13101e21	−	9.13101e21i	−0.785745	−	0.785745i
$574$		−	1.39638e22i		−	1.18497i
$575$	−4.03682e21	−	1.95395e21i	−0.337829	−	0.163520i
$576$	−1.59056e22			−1.31272
$577$	4.04216e21	−	4.04216e21i	0.329008	−	0.329008i	−0.523201	−	0.852209i	$-0.675262\pi$
$577$	4.04216e21	−	4.04216e21i	0.329008	−	0.329008i	0.852209	+	0.523201i	$0.175262\pi$
$578$	−8.33025e21	−	8.33025e21i	−0.668707	−	0.668707i
$579$			1.34704e21i			0.106648i
$580$	−8.53932e20	−	5.05640e21i	−0.0666806	−	0.394837i
$581$	−1.34033e22			−1.03229
$582$	−2.06993e22	+	2.06993e22i	−1.57243	+	1.57243i
$583$	1.32878e22	+	1.32878e22i	0.995646	+	0.995646i
$584$		−	1.67939e22i		−	1.24122i
$585$	9.02763e21	+	6.41898e21i	0.658153	+	0.467971i
$586$	2.19457e22			1.57822
$587$	−3.87474e21	+	3.87474e21i	−0.274877	+	0.274877i	−0.831060	−	0.556183i	$-0.812265\pi$
$587$	−3.87474e21	+	3.87474e21i	−0.274877	+	0.274877i	0.556183	+	0.831060i	$0.312265\pi$
$588$	3.22000e20	+	3.22000e20i	0.0225339	+	0.0225339i
$589$			2.29922e21i			0.158729i
$590$	−1.07845e21	+	1.51672e21i	−0.0734485	+	0.103298i
$591$	3.61822e22			2.43106
$592$	1.09491e21	−	1.09491e21i	0.0725778	−	0.0725778i
$593$	−9.11572e21	−	9.11572e21i	−0.596147	−	0.596147i	0.343138	−	0.939285i	$-0.388510\pi$
$593$	−9.11572e21	−	9.11572e21i	−0.596147	−	0.596147i	−0.939285	+	0.343138i	$0.888510\pi$
$594$			3.08921e22i			1.99322i
$595$	6.49034e21	−	1.09610e21i	0.413173	−	0.0697773i
$596$	5.65238e20			0.0355027
$597$	2.50690e19	−	2.50690e19i	0.00155361	−	0.00155361i
$598$	−1.74917e21	−	1.74917e21i	−0.106960	−	0.106960i
$599$			3.16467e21i			0.190948i	0.995432	+	0.0954738i	$0.0304366\pi$
$599$			3.16467e21i			0.190948i	−0.995432	+	0.0954738i	$0.969563\pi$
$600$	−8.09544e21	−	2.32842e22i	−0.481982	−	1.38628i
$601$	−7.86522e21			−0.462078			−0.231039	−	0.972944i	$-0.574212\pi$
$601$	−7.86522e21			−0.462078			−0.231039	+	0.972944i	$0.574212\pi$
$602$	−1.10418e22	+	1.10418e22i	−0.640132	+	0.640132i
$603$	−4.54318e22	−	4.54318e22i	−2.59909	−	2.59909i
$604$		−	6.63426e21i		−	0.374539i
$605$	1.23576e21	+	7.31735e21i	0.0688482	+	0.407672i
$606$	3.96302e22			2.17894
$607$	6.11512e21	−	6.11512e21i	0.331815	−	0.331815i	−0.521461	−	0.853275i	$-0.674613\pi$
$607$	6.11512e21	−	6.11512e21i	0.331815	−	0.331815i	0.853275	+	0.521461i	$0.174613\pi$
$608$	2.76496e21	+	2.76496e21i	0.148067	+	0.148067i
$609$			4.97775e22i			2.63084i
$610$	1.68773e22	+	1.20004e22i	0.880367	+	0.625974i
$611$	−1.22020e21			−0.0628204
$612$	3.64356e21	−	3.64356e21i	0.185146	−	0.185146i
$613$	−4.37072e21	−	4.37072e21i	−0.219214	−	0.219214i	0.588953	−	0.808167i	$-0.299540\pi$
$613$	−4.37072e21	−	4.37072e21i	−0.219214	−	0.219214i	−0.808167	+	0.588953i	$0.799540\pi$
$614$			1.44167e22i			0.713703i
$615$	−2.17634e22	+	3.06080e22i	−1.06347	+	1.49566i
$616$	1.32810e22			0.640596
$617$	1.49877e22	−	1.49877e22i	0.713598	−	0.713598i	−0.253688	−	0.967286i	$-0.581644\pi$
$617$	1.49877e22	−	1.49877e22i	0.713598	−	0.713598i	0.967286	+	0.253688i	$0.0816437\pi$
$618$	−7.14250e21	−	7.14250e21i	−0.335693	−	0.335693i
$619$		−	1.80952e22i		−	0.839535i	−0.907632	−	0.419768i	$-0.862112\pi$
$619$		−	1.80952e22i		−	0.839535i	0.907632	−	0.419768i	$-0.137888\pi$
$620$	2.55359e21	−	4.31254e20i	0.116955	−	0.0197515i
$621$	1.90683e22			0.862144
$622$	−1.76371e22	+	1.76371e22i	−0.787236	+	0.787236i
$623$	2.25056e22	+	2.25056e22i	0.991712	+	0.991712i
$624$		−	1.77914e22i		−	0.773987i
$625$	1.82612e22	−	1.44441e22i	0.784311	−	0.620368i
$626$	−3.65253e22			−1.54881
$627$	−8.87994e21	+	8.87994e21i	−0.371766	+	0.371766i
$628$	3.76475e21	+	3.76475e21i	0.155618	+	0.155618i
$629$		−	8.49841e20i		−	0.0346843i
$630$	−1.09543e22	−	6.48639e22i	−0.441429	−	2.61384i
$631$	−3.13976e22			−1.24929			−0.624643	−	0.780910i	$-0.714756\pi$
$631$	−3.13976e22			−1.24929			−0.624643	+	0.780910i	$0.714756\pi$
$632$	−5.04621e21	+	5.04621e21i	−0.198257	+	0.198257i
$633$	4.06684e22	+	4.06684e22i	1.57771	+	1.57771i
$634$			4.63420e22i			1.77525i
$635$	−4.86442e21	−	3.45878e21i	−0.184010	−	0.130838i
$636$	−2.52475e22			−0.943109
$637$	4.23606e20	−	4.23606e20i	0.0156260	−	0.0156260i
$638$	−2.37765e22	−	2.37765e22i	−0.866130	−	0.866130i
$639$		−	9.12202e22i		−	3.28159i
$640$	−1.96831e22	+	2.76823e22i	−0.699286	+	0.983473i
$641$	−2.34798e22			−0.823818			−0.411909	−	0.911225i	$-0.635138\pi$
$641$	−2.34798e22			−0.823818			−0.411909	+	0.911225i	$0.635138\pi$
$642$	4.92975e22	−	4.92975e22i	1.70822	−	1.70822i
$643$	−3.89742e22	−	3.89742e22i	−1.33380	−	1.33380i	−0.901945	−	0.431851i	$-0.857861\pi$
$643$	−3.89742e22	−	3.89742e22i	−1.33380	−	1.33380i	−0.431851	−	0.901945i	$-0.642139\pi$
$644$			3.24628e21i			0.109723i
$645$	4.14125e22	−	6.99381e21i	1.38246	−	0.233473i
$646$	5.30368e21			0.174871
$647$	1.28050e22	−	1.28050e22i	0.417009	−	0.417009i	−0.467162	−	0.884172i	$-0.654724\pi$
$647$	1.28050e22	−	1.28050e22i	0.417009	−	0.417009i	0.884172	+	0.467162i	$0.154724\pi$
$648$	3.36085e22	+	3.36085e22i	1.08106	+	1.08106i
$649$			2.69667e21i			0.0856782i
$650$	1.21300e22	−	4.21734e21i	0.380673	−	0.132352i
$651$	−2.51387e22			−0.779282
$652$	5.07424e21	−	5.07424e21i	0.155378	−	0.155378i
$653$	2.14869e22	+	2.14869e22i	0.649933	+	0.649933i	0.952977	−	0.303043i	$-0.0980027\pi$
$653$	2.14869e22	+	2.14869e22i	0.649933	+	0.649933i	−0.303043	+	0.952977i	$0.598003\pi$
$654$			1.82094e22i			0.544095i
$655$	4.84750e21	+	2.87036e22i	0.143083	+	0.847238i
$656$	4.18758e22			1.22105
$657$	−8.52290e22	+	8.52290e22i	−2.45507	+	2.45507i
$658$	5.12389e21	+	5.12389e21i	0.145812	+	0.145812i
$659$			5.49699e22i			1.54540i	0.634770	+	0.772701i	$0.281095\pi$
$659$			5.49699e22i			1.54540i	−0.634770	+	0.772701i	$0.718905\pi$
$660$	1.15279e22	+	8.19679e21i	0.320184	+	0.227663i
$661$	1.34327e22			0.368598			0.184299	−	0.982870i	$-0.440999\pi$
$661$	1.34327e22			0.368598			0.184299	+	0.982870i	$0.440999\pi$
$662$	2.67016e22	−	2.67016e22i	0.723891	−	0.723891i
$663$	−6.90463e21	−	6.90463e21i	−0.184941	−	0.184941i
$664$		−	3.07186e22i		−	0.812938i
$665$	8.67046e21	−	1.21941e22i	0.226709	−	0.318843i
$666$	−8.49323e21			−0.219421
$667$	−1.46762e22	+	1.46762e22i	−0.374634	+	0.374634i
$668$	1.39611e22	+	1.39611e22i	0.352134	+	0.352134i
$669$		−	3.30662e22i		−	0.824091i
$670$	−7.34484e22	+	1.24041e22i	−1.80877	+	0.305468i
$671$	3.00071e22			0.730203
$672$	−3.02309e22	+	3.02309e22i	−0.726937	+	0.726937i
$673$	−3.34007e21	−	3.34007e21i	−0.0793660	−	0.0793660i	0.666309	−	0.745675i	$-0.267873\pi$
$673$	−3.34007e21	−	3.34007e21i	−0.0793660	−	0.0793660i	−0.745675	+	0.666309i	$0.767873\pi$
$674$		−	9.30331e22i		−	2.18453i
$675$	−4.31292e22	+	8.91040e22i	−1.00079	+	2.06760i
$676$	−1.08050e22			−0.247772
$677$	1.70858e22	−	1.70858e22i	0.387192	−	0.387192i	−0.486492	−	0.873685i	$-0.661724\pi$
$677$	1.70858e22	−	1.70858e22i	0.387192	−	0.387192i	0.873685	+	0.486492i	$0.161724\pi$
$678$	7.15743e22	+	7.15743e22i	1.60295	+	1.60295i
$679$		−	5.05378e22i		−	1.11856i
$680$	2.51212e21	+	1.48750e22i	0.0549501	+	0.325377i
$681$	−3.20618e22			−0.693125
$682$	1.20076e22	−	1.20076e22i	0.256556	−	0.256556i
$683$	2.42001e21	+	2.42001e21i	0.0511036	+	0.0511036i	0.732197	−	0.681093i	$-0.238495\pi$
$683$	2.42001e21	+	2.42001e21i	0.0511036	+	0.0511036i	−0.681093	+	0.732197i	$0.738495\pi$
$684$		−	1.17130e22i		−	0.244466i
$685$	−1.86512e22	−	1.32617e22i	−0.384754	−	0.273574i
$686$	5.37096e22			1.09511
$687$	1.12367e23	−	1.12367e23i	2.26457	−	2.26457i
$688$	−3.31132e22	−	3.31132e22i	−0.659619	−	0.659619i
$689$			3.32143e22i			0.653991i
$690$	2.28957e22	−	3.22005e22i	0.445617	−	0.626714i
$691$	1.46583e22			0.282006			0.141003	−	0.990009i	$-0.454967\pi$
$691$	1.46583e22			0.282006			0.141003	+	0.990009i	$0.454967\pi$
$692$	6.90699e21	−	6.90699e21i	0.131353	−	0.131353i
$693$	−6.74007e22	−	6.74007e22i	−1.26706	−	1.26706i
$694$			7.26959e22i			1.35093i
$695$	−2.45868e21	+	4.15226e20i	−0.0451673	+	0.00762793i
$696$	−1.14084e23			−2.07181
$697$	1.62515e22	−	1.62515e22i	0.291763	−	0.291763i
$698$	−3.30124e21	−	3.30124e21i	−0.0585913	−	0.0585913i
$699$			1.24624e21i			0.0218668i
$700$	−1.51695e22	−	7.34251e21i	−0.263139	−	0.127368i
$701$	1.28395e22			0.220193			0.110097	−	0.993921i	$-0.464884\pi$
$701$	1.28395e22			0.220193			0.110097	+	0.993921i	$0.464884\pi$
$702$	−3.86091e22	+	3.86091e22i	−0.654625	+	0.654625i
$703$	−1.36600e21	−	1.36600e21i	−0.0228985	−	0.0228985i
$704$			2.67199e22i			0.442847i
$705$	−3.24544e21	−	1.92172e22i	−0.0531814	−	0.314904i
$706$	4.30240e22			0.697065
$707$	−4.83791e22	+	4.83791e22i	−0.775001	+	0.775001i
$708$	−2.56191e21	−	2.56191e21i	−0.0405786	−	0.0405786i
$709$			6.08168e22i			0.952475i	0.879317	+	0.476238i	$0.158000\pi$
$709$			6.08168e22i			0.952475i	−0.879317	+	0.476238i	$0.842000\pi$
$710$	−8.61894e22	−	6.12839e22i	−1.33471	−	0.949029i
$711$	5.12189e22			0.784285
$712$	−5.15798e22	+	5.15798e22i	−0.780980	+	0.780980i
$713$	−7.41179e21	−	7.41179e21i	−0.110970	−	0.110970i
$714$			5.79882e22i			0.858527i
$715$	1.07833e22	−	1.51656e22i	0.157871	−	0.222029i
$716$	−6.94492e20			−0.0100546
$717$	1.21183e23	−	1.21183e23i	1.73495	−	1.73495i
$718$	−3.56424e22	−	3.56424e22i	−0.504629	−	0.504629i
$719$			6.77987e22i			0.949271i	0.880182	+	0.474636i	$0.157420\pi$
$719$			6.77987e22i			0.949271i	−0.880182	+	0.474636i	$0.842580\pi$
$720$	1.94519e23	−	3.28507e22i	2.69341	−	0.454867i
$721$	1.74386e22			0.238797
$722$	−5.06324e22	+	5.06324e22i	−0.685695	+	0.685695i
$723$	1.56995e23	+	1.56995e23i	2.10272	+	2.10272i
$724$			1.86947e22i			0.247633i
$725$	−3.53851e22	−	1.01775e23i	−0.463571	−	1.33333i
$726$	−6.53771e22			−0.847096
$727$	7.18487e20	−	7.18487e20i	0.00920754	−	0.00920754i	−0.702488	−	0.711696i	$-0.747928\pi$
$727$	7.18487e20	−	7.18487e20i	0.00920754	−	0.00920754i	0.711696	+	0.702488i	$0.247928\pi$
$728$	1.65986e22	+	1.65986e22i	0.210388	+	0.210388i
$729$		−	9.77695e21i		−	0.122570i
$730$	2.32698e22	+	1.37788e23i	0.288542	+	1.70855i
$731$	−2.57016e22			−0.315226
$732$	−2.85075e22	+	2.85075e22i	−0.345836	+	0.345836i
$733$	6.44423e21	+	6.44423e21i	0.0773284	+	0.0773284i	0.744713	−	0.667385i	$-0.232586\pi$
$733$	6.44423e21	+	6.44423e21i	0.0773284	+	0.0773284i	−0.667385	+	0.744713i	$0.732586\pi$
$734$		−	1.54760e23i		−	1.83692i
$735$	7.79818e21	+	5.54479e21i	0.0915576	+	0.0651009i
$736$	−1.78263e22			−0.207033
$737$	−7.63210e22	+	7.63210e22i	−0.876807	+	0.876807i
$738$	−1.62416e23	−	1.62416e23i	−1.84577	−	1.84577i
$739$		−	1.15905e22i		−	0.130301i	−0.997875	−	0.0651504i	$-0.979247\pi$
$739$		−	1.15905e22i		−	0.130301i	0.997875	−	0.0651504i	$-0.0207527\pi$
$740$	−1.26091e21	+	1.77333e21i	−0.0140226	+	0.0197214i
$741$	−2.21964e22			−0.244195
$742$	1.39475e23	−	1.39475e23i	1.51797	−	1.51797i
$743$	5.70430e21	+	5.70430e21i	0.0614175	+	0.0614175i	0.737148	−	0.675731i	$-0.236172\pi$
$743$	5.70430e21	+	5.70430e21i	0.0614175	+	0.0614175i	−0.675731	+	0.737148i	$0.736172\pi$
$744$		−	5.76146e22i		−	0.613690i
$745$	1.17111e22	−	1.97779e21i	0.123409	−	0.0208416i
$746$	−5.70544e21			−0.0594811
$747$	−1.55897e23	+	1.55897e23i	−1.60795	+	1.60795i
$748$	−6.12082e21	−	6.12082e21i	−0.0624593	−	0.0624593i
$749$			1.20361e23i			1.21515i
$750$	9.86827e22	+	1.79821e23i	0.985714	+	1.79618i
$751$	1.29022e23			1.27510			0.637548	−	0.770411i	$-0.279949\pi$
$751$	1.29022e23			1.27510			0.637548	+	0.770411i	$0.279949\pi$
$752$	−1.53660e22	+	1.53660e22i	−0.150251	+	0.150251i
$753$	−1.70323e23	−	1.70323e23i	−1.64784	−	1.64784i
$754$		−	5.94320e22i		−	0.568918i
$755$	−2.32136e22	−	1.37455e23i	−0.219870	−	1.30192i
$756$	7.16545e22			0.671536
$757$	−9.53976e22	+	9.53976e22i	−0.884648	+	0.884648i	−0.994003	−	0.109355i	$-0.965122\pi$
$757$	−9.53976e22	+	9.53976e22i	−0.884648	+	0.884648i	0.109355	+	0.994003i	$0.465122\pi$
$758$	8.22320e22	+	8.22320e22i	0.754548	+	0.754548i
$759$		−	5.72510e22i		−	0.519815i
$760$	2.79473e22	+	1.98716e22i	0.251091	+	0.178535i
$761$	5.54160e22			0.492672			0.246336	−	0.969184i	$-0.420773\pi$
$761$	5.54160e22			0.492672			0.246336	+	0.969184i	$0.420773\pi$
$762$	3.71820e22	−	3.71820e22i	0.327109	−	0.327109i
$763$	−2.22294e22	−	2.22294e22i	−0.193522	−	0.193522i
$764$		−	2.02330e22i		−	0.174306i
$765$	6.27416e22	−	8.82395e22i	0.534889	−	0.752266i
$766$	1.43331e23			1.20923
$767$	−3.37031e21	+	3.37031e21i	−0.0281389	+	0.0281389i
$768$	−1.22106e23	−	1.22106e23i	−1.00890	−	1.00890i
$769$		−	1.66871e23i		−	1.36449i	−0.731125	−	0.682244i	$-0.761004\pi$
$769$		−	1.66871e23i		−	1.36449i	0.731125	−	0.682244i	$-0.238996\pi$
$770$	−1.08965e23	+	1.84022e22i	−0.881782	+	0.148917i
$771$	−1.83763e23			−1.47171
$772$	−1.49242e21	+	1.49242e21i	−0.0118291	+	0.0118291i
$773$	−5.54790e22	−	5.54790e22i	−0.435204	−	0.435204i	0.455190	−	0.890394i	$-0.349571\pi$
$773$	−5.54790e22	−	5.54790e22i	−0.435204	−	0.435204i	−0.890394	+	0.455190i	$0.849571\pi$
$774$			2.56860e23i			1.99420i
$775$	5.13986e22	−	1.78702e22i	0.394946	−	0.137314i
$776$	1.15826e23			0.880871
$777$	1.49352e22	−	1.49352e22i	0.112420	−	0.112420i
$778$	5.32777e22	+	5.32777e22i	0.396925	+	0.396925i
$779$		−	5.22438e22i		−	0.385243i
$780$	4.16328e21	+	2.46520e22i	0.0303863	+	0.179927i
$781$	−1.53241e23			−1.10705
$782$	−1.70970e22	+	1.70970e22i	−0.122255	+	0.122255i
$783$	3.23945e23	+	3.23945e23i	2.29286	+	2.29286i
$784$		−	1.06690e22i		−	0.0747469i
$785$	9.11746e22	+	6.48286e22i	0.632291	+	0.449582i
$786$	−2.56453e23			−1.76047
$787$	1.39803e23	−	1.39803e23i	0.949986	−	0.949986i	−0.0488216	−	0.998808i	$-0.515547\pi$
$787$	1.39803e23	−	1.39803e23i	0.949986	−	0.949986i	0.998808	+	0.0488216i	$0.0155466\pi$
$788$	4.00873e22	+	4.00873e22i	0.269648	+	0.269648i
$789$			2.30825e23i			1.53697i
$790$	3.44101e22	−	4.83942e22i	0.226814	−	0.318990i
$791$	−1.74751e23			−1.14027
$792$	1.54474e23	−	1.54474e23i	0.997822	−	0.997822i
$793$	3.75030e22	+	3.75030e22i	0.239817	+	0.239817i
$794$			1.95978e23i			1.24063i
$795$	−5.23101e23	+	8.83422e22i	−3.27830	+	0.553645i
$796$	5.55493e19			0.000344646
$797$	−3.21700e22	+	3.21700e22i	−0.197599	+	0.197599i	−0.798970	−	0.601371i	$-0.794621\pi$
$797$	−3.21700e22	+	3.21700e22i	−0.197599	+	0.197599i	0.601371	+	0.798970i	$0.294621\pi$
$798$	9.32077e22	+	9.32077e22i	0.566798	+	0.566798i
$799$			1.19267e22i			0.0718035i
$800$	4.03200e22	−	8.33002e22i	0.240326	−	0.496508i
$801$	5.23534e23			3.08947
$802$	1.28581e23	−	1.28581e23i	0.751246	−	0.751246i
$803$	1.43177e23	+	1.43177e23i	0.828223	+	0.828223i
$804$		−	1.45014e23i		−	0.830540i
$805$	1.13589e22	+	6.72594e22i	0.0644122	+	0.381404i
$806$	3.00144e22			0.168519
$807$	−4.28371e22	+	4.28371e22i	−0.238140	+	0.238140i
$808$	−1.10879e23	−	1.10879e23i	−0.610319	−	0.610319i
$809$		−	2.99113e23i		−	1.63022i	−0.579304	−	0.815111i	$-0.696676\pi$
$809$		−	2.99113e23i		−	1.63022i	0.579304	−	0.815111i	$-0.303324\pi$
$810$	−3.22313e23	−	2.29176e23i	−1.73939	−	1.23677i
$811$	−3.25551e23			−1.73961			−0.869805	−	0.493395i	$-0.835756\pi$
$811$	−3.25551e23			−1.73961			−0.869805	+	0.493395i	$0.835756\pi$
$812$	−5.51499e22	+	5.51499e22i	−0.291807	+	0.291807i
$813$	−1.97891e23	−	1.97891e23i	−1.03681	−	1.03681i
$814$			1.42678e22i			0.0740222i
$815$	8.73777e22	−	1.22888e23i	0.448890	−	0.631317i
$816$	−1.73900e23			−0.884664
$817$	−4.13117e22	+	4.13117e22i	−0.208112	+	0.208112i
$818$	−7.55890e22	−	7.55890e22i	−0.377079	−	0.377079i
$819$		−	1.68475e23i		−	0.832272i
$820$	−5.80237e22	+	9.79914e21i	−0.283854	+	0.0479377i
$821$	1.90901e23			0.924833			0.462417	−	0.886663i	$-0.346982\pi$
$821$	1.90901e23			0.924833			0.462417	+	0.886663i	$0.346982\pi$
$822$	1.42564e23	−	1.42564e23i	0.683967	−	0.683967i
$823$	2.51605e22	+	2.51605e22i	0.119542	+	0.119542i	0.764347	−	0.644805i	$-0.223061\pi$
$823$	2.51605e22	+	2.51605e22i	0.119542	+	0.119542i	−0.644805	+	0.764347i	$0.723061\pi$
$824$			3.99670e22i			0.188054i
$825$	2.67527e23	+	1.29492e23i	1.24663	+	0.603408i
$826$	2.83054e22			0.130626
$827$	1.54768e23	−	1.54768e23i	0.707356	−	0.707356i	−0.258622	−	0.965979i	$-0.583269\pi$
$827$	1.54768e23	−	1.54768e23i	0.707356	−	0.707356i	0.965979	+	0.258622i	$0.0832685\pi$
$828$	3.77581e22	+	3.77581e22i	0.170910	+	0.170910i
$829$			2.15416e23i			0.965699i	0.875703	+	0.482850i	$0.160398\pi$
$829$			2.15416e23i			0.965699i	−0.875703	+	0.482850i	$0.839602\pi$
$830$	4.25639e22	+	2.52034e23i	0.188981	+	1.11901i
$831$	1.59589e23			0.701769
$832$	−3.33947e22	+	3.33947e22i	−0.145442	+	0.145442i
$833$	−4.14049e21	−	4.14049e21i	−0.0178604	−	0.0178604i
$834$		−	2.19672e22i		−	0.0938527i
$835$	3.38109e23	+	2.40408e23i	1.43076	+	1.01732i
$836$	−1.96767e22			−0.0824710
$837$	−1.63599e23	+	1.63599e23i	−0.679168	+	0.679168i
$838$	−1.31915e23	−	1.31915e23i	−0.542427	−	0.542427i
$839$		−	3.64639e23i		−	1.48514i	−0.669768	−	0.742570i	$-0.733606\pi$
$839$		−	3.64639e23i		−	1.48514i	0.669768	−	0.742570i	$-0.266394\pi$
$840$	−2.17267e23	+	3.05564e23i	−0.876517	+	1.23273i
$841$	−2.48412e23			−0.992667
$842$	−3.68522e23	+	3.68522e23i	−1.45870	+	1.45870i
$843$	−1.53601e22	−	1.53601e22i	−0.0602246	−	0.0602246i
$844$			9.01153e22i			0.349993i
$845$	−2.23868e23	+	3.78072e22i	−0.861269	+	0.145452i
$846$	1.19194e23			0.454247
$847$	7.98099e22	−	7.98099e22i	0.301293	−	0.301293i
$848$	4.18268e23	+	4.18268e23i	1.56419	+	1.56419i
$849$		−	4.51936e23i		−	1.67423i
$850$	−4.12218e22	−	1.18563e23i	−0.151278	−	0.435108i
$851$	8.80689e21			0.0320174
$852$	1.45583e23	−	1.45583e23i	0.524317	−	0.524317i
$853$	1.64311e23	+	1.64311e23i	0.586239	+	0.586239i	0.936611	−	0.350372i	$-0.113945\pi$
$853$	1.64311e23	+	1.64311e23i	0.586239	+	0.586239i	−0.350372	+	0.936611i	$0.613945\pi$
$854$		−	3.14967e23i		−	1.11328i
$855$	−4.09842e22	−	2.42680e23i	−0.143512	−	0.849778i
$856$	−2.75852e23			−0.956943
$857$	−3.83573e23	+	3.83573e23i	−1.31826	+	1.31826i	−0.403112	+	0.915151i	$0.632071\pi$
$857$	−3.83573e23	+	3.83573e23i	−1.31826	+	1.31826i	−0.915151	+	0.403112i	$0.867929\pi$
$858$	1.15920e23	+	1.15920e23i	0.394695	+	0.394695i
$859$			3.27610e23i			1.10513i	0.833471	+	0.552563i	$0.186350\pi$
$859$			3.27610e23i			1.10513i	−0.833471	+	0.552563i	$0.813650\pi$
$860$	5.36308e22	+	3.81335e22i	0.179236	+	0.127444i
$861$	5.71212e23			1.89135
$862$	9.32785e22	−	9.32785e22i	0.306001	−	0.306001i
$863$	−8.85315e22	−	8.85315e22i	−0.287748	−	0.287748i	0.548441	−	0.836189i	$-0.315221\pi$
$863$	−8.85315e22	−	8.85315e22i	−0.287748	−	0.287748i	−0.836189	+	0.548441i	$0.815221\pi$
$864$			3.93477e23i			1.26710i
$865$	1.18937e23	−	1.67273e23i	0.379481	−	0.533700i
$866$	4.09825e22			0.129555
$867$	3.40763e23	−	3.40763e23i	1.06733	−	1.06733i
$868$	−2.78518e22	−	2.78518e22i	−0.0864363	−	0.0864363i
$869$		−	8.60429e22i		−	0.264580i
$870$	9.36010e23	−	1.58075e23i	2.85185	−	0.481625i
$871$	−1.90773e23			−0.575931
$872$	5.09469e22	−	5.09469e22i	0.152400	−	0.152400i
$873$	−5.87815e23	−	5.87815e23i	−1.74232	−	1.74232i
$874$			5.49620e22i			0.161425i
$875$	−3.39987e23	−	9.90503e22i	−0.989458	−	0.288265i
$876$	−2.72043e23			−0.784520
$877$	−4.18588e23	+	4.18588e23i	−1.19616	+	1.19616i	−0.220855	+	0.975307i	$0.570885\pi$
$877$	−4.18588e23	+	4.18588e23i	−1.19616	+	1.19616i	−0.975307	+	0.220855i	$0.929115\pi$
$878$	−4.45012e23	−	4.45012e23i	−1.26013	−	1.26013i
$879$			8.97724e23i			2.51902i
$880$	−5.51860e22	−	3.26774e23i	−0.153450	−	0.908627i
$881$	2.22044e23			0.611831			0.305915	−	0.952059i	$-0.401038\pi$
$881$	2.22044e23			0.611831			0.305915	+	0.952059i	$0.401038\pi$
$882$	−4.13797e22	+	4.13797e22i	−0.112990	+	0.112990i
$883$	2.91787e23	+	2.91787e23i	0.789552	+	0.789552i	0.981421	−	0.191869i	$-0.0614548\pi$
$883$	2.91787e23	+	2.91787e23i	0.789552	+	0.789552i	−0.191869	+	0.981421i	$0.561455\pi$
$884$		−	1.52997e22i		−	0.0410264i
$885$	−6.20441e22	−	4.41157e22i	−0.164875	−	0.117232i
$886$	−7.26594e23			−1.91347
$887$	2.49372e23	−	2.49372e23i	0.650817	−	0.650817i	−0.302373	−	0.953190i	$-0.597779\pi$
$887$	2.49372e23	−	2.49372e23i	0.650817	−	0.650817i	0.953190	+	0.302373i	$0.0977788\pi$
$888$	3.42296e22	+	3.42296e22i	0.0885315	+	0.0885315i
$889$			9.07808e22i			0.232691i
$890$	3.51723e23	−	4.94661e23i	0.893470	−	1.25657i
$891$	−5.73058e23			−1.44270
$892$	3.66350e22	−	3.66350e22i	0.0914065	−	0.0914065i
$893$	1.91704e22	+	1.91704e22i	0.0474045	+	0.0474045i
$894$			1.04634e23i			0.256431i
$895$	−1.43891e22	+	2.43006e21i	−0.0349502	+	0.00590245i
$896$	5.16612e23			1.24366
$897$	7.15526e22	−	7.15526e22i	0.170721	−	0.170721i
$898$	−2.38778e22	−	2.38778e22i	−0.0564656	−	0.0564656i
$899$		−	2.51833e23i		−	0.590248i
$900$	−2.61841e23	+	9.10369e22i	−0.608273	+	0.211484i
$901$	3.24650e23			0.747509
$902$	−2.72843e23	+	2.72843e23i	−0.622674	+	0.622674i
$903$	−4.51684e23	−	4.51684e23i	−1.02172	−	1.02172i
$904$		−	4.00505e23i		−	0.897968i
$905$	6.54134e22	+	3.87333e23i	0.145371	+	0.860787i
$906$	1.22809e24			2.70524
$907$	2.13376e23	−	2.13376e23i	0.465895	−	0.465895i	−0.434687	−	0.900582i	$-0.643141\pi$
$907$	2.13376e23	−	2.13376e23i	0.465895	−	0.465895i	0.900582	+	0.434687i	$0.143141\pi$
$908$	−3.55222e22	−	3.55222e22i	−0.0768800	−	0.0768800i
$909$			1.12542e24i			2.41436i
$910$	−1.59184e23	−	1.13186e23i	−0.338508	−	0.240692i
$911$	6.96622e23			1.46842			0.734210	−	0.678923i	$-0.237553\pi$
$911$	6.96622e23			1.46842			0.734210	+	0.678923i	$0.237553\pi$
$912$	−2.79519e23	+	2.79519e23i	−0.584053	+	0.584053i
$913$	2.61891e23	+	2.61891e23i	0.542444	+	0.542444i
$914$		−	1.41100e23i		−	0.289707i
$915$	−4.90895e23	+	6.90393e23i	−0.999126	+	1.40517i
$916$	2.48990e23			0.502363
$917$	3.13068e23	−	3.13068e23i	0.626159	−	0.626159i
$918$	3.77380e23	+	3.77380e23i	0.748234	+	0.748234i
$919$		−	6.98454e23i		−	1.37282i	−0.727215	−	0.686410i	$-0.759186\pi$
$919$		−	6.98454e23i		−	1.37282i	0.727215	−	0.686410i	$-0.240814\pi$
$920$	−1.54150e23	+	2.60330e22i	−0.300359	+	0.0507250i
$921$	−5.89737e23			−1.13915
$922$	−9.47873e22	+	9.47873e22i	−0.181511	+	0.181511i
$923$	−1.91521e23	−	1.91521e23i	−0.363583	−	0.363583i
$924$		−	2.15137e23i		−	0.404891i
$925$	−1.99196e22	+	4.11535e22i	−0.0371662	+	0.0767844i
$926$	−8.77324e23			−1.62283
$927$	2.02832e23	−	2.02832e23i	0.371962	−	0.371962i
$928$	−3.02845e23	−	3.02845e23i	−0.550601	−	0.550601i
$929$			9.29131e23i			1.67476i	0.546625	+	0.837378i	$0.315912\pi$
$929$			9.29131e23i			1.67476i	−0.546625	+	0.837378i	$0.684088\pi$
$930$	7.98311e22	+	4.72705e23i	0.142662	+	0.844746i
$931$	−1.33105e22			−0.0235828
$932$	−1.38075e21	+	1.38075e21i	−0.00242542	+	0.00242542i
$933$	−7.21476e23	−	7.21476e23i	−1.25652	−	1.25652i
$934$			6.71009e23i			1.15865i
$935$	−1.48234e23	−	1.05400e23i	−0.253778	−	0.180446i
$936$	3.86124e23			0.655420
$937$	−9.84369e22	+	9.84369e22i	−0.165669	+	0.165669i	−0.785073	−	0.619404i	$-0.787374\pi$
$937$	−9.84369e22	+	9.84369e22i	−0.165669	+	0.165669i	0.619404	+	0.785073i	$0.287374\pi$
$938$	8.01098e23	+	8.01098e23i	1.33679	+	1.33679i
$939$		−	1.49413e24i		−	2.47208i
$940$	1.76956e22	−	2.48870e22i	0.0290297	−	0.0408272i
$941$	4.34393e23			0.706588			0.353294	−	0.935512i	$-0.385062\pi$
$941$	4.34393e23			0.706588			0.353294	+	0.935512i	$0.385062\pi$
$942$	−6.96909e23	+	6.96909e23i	−1.12401	+	1.12401i
$943$	1.68414e23	+	1.68414e23i	0.269330	+	0.269330i
$944$			8.48847e22i			0.134603i
$945$	1.48460e24	−	2.50722e23i	2.33430	−	0.394220i
$946$	4.31500e23			0.672746
$947$	−1.13312e23	+	1.13312e23i	−0.175177	+	0.175177i	−0.789250	−	0.614072i	$-0.789530\pi$
$947$	−1.13312e23	+	1.13312e23i	−0.175177	+	0.175177i	0.614072	+	0.789250i	$0.289530\pi$
$948$	8.17429e22	+	8.17429e22i	0.125309	+	0.125309i
$949$			3.57885e23i			0.544019i
$950$	−2.56831e23	−	1.24314e23i	−0.387131	−	0.187384i
$951$	−1.89569e24			−2.83351
$952$	1.62241e23	−	1.62241e23i	0.240472	−	0.240472i
$953$	−2.80484e22	−	2.80484e22i	−0.0412254	−	0.0412254i	0.686194	−	0.727419i	$-0.259280\pi$
$953$	−2.80484e22	−	2.80484e22i	−0.0412254	−	0.0412254i	−0.727419	+	0.686194i	$0.759280\pi$
$954$		−	3.24452e24i		−	4.72893i
$955$	−7.07962e22	−	4.19206e23i	−0.102325	−	0.605899i
$956$	2.68523e23			0.384874
$957$	9.72618e23	−	9.72618e23i	1.38244	−	1.38244i
$958$	−2.60563e23	−	2.60563e23i	−0.367272	−	0.367272i
$959$			3.48073e23i			0.486544i
$960$	−6.14763e23	−	4.37119e23i	−0.852192	−	0.605941i
$961$	−6.00242e23			−0.825163
$962$	−1.78320e22	+	1.78320e22i	−0.0243108	+	0.0243108i
$963$	1.39995e24	+	1.39995e24i	1.89278	+	1.89278i
$964$			3.47879e23i			0.466458i
$965$	−2.56993e22	+	3.61434e22i	−0.0341746	+	0.0480630i
$966$	−6.00932e23			−0.792516
$967$	−5.82229e23	+	5.82229e23i	−0.761522	+	0.761522i	−0.976597	−	0.215076i	$-0.931000\pi$
$967$	−5.82229e23	+	5.82229e23i	−0.761522	+	0.761522i	0.215076	+	0.976597i	$0.431000\pi$
$968$	1.82914e23	+	1.82914e23i	0.237271	+	0.237271i
$969$			2.16956e23i			0.279114i
$970$	−9.50306e23	+	1.60489e23i	−1.21252	+	0.204773i
$971$	−1.12801e24			−1.42745			−0.713725	−	0.700426i	$-0.752993\pi$
$971$	−1.12801e24			−1.42745			−0.713725	+	0.700426i	$0.752993\pi$
$972$	1.77309e23	−	1.77309e23i	0.222536	−	0.222536i
$973$	2.68167e22	+	2.68167e22i	0.0333813	+	0.0333813i
$974$			7.87741e23i			0.972549i
$975$	1.72517e23	+	4.96196e23i	0.211249	+	0.607598i
$976$	9.44551e23			1.14717
$977$	1.13897e23	−	1.13897e23i	0.137201	−	0.137201i	−0.635171	−	0.772372i	$-0.719070\pi$
$977$	1.13897e23	−	1.13897e23i	0.137201	−	0.137201i	0.772372	+	0.635171i	$0.219070\pi$
$978$	9.39312e23	+	9.39312e23i	1.12227	+	1.12227i
$979$		−	8.79486e23i		−	1.04224i
$980$	2.49659e21	+	1.47831e22i	0.00293453	+	0.0173762i
$981$	−5.17110e23			−0.602879
$982$	1.32991e24	−	1.32991e24i	1.53791	−	1.53791i
$983$	4.75523e22	+	4.75523e22i	0.0545435	+	0.0545435i	0.733852	−	0.679309i	$-0.237720\pi$
$983$	4.75523e22	+	4.75523e22i	0.0545435	+	0.0545435i	−0.679309	+	0.733852i	$0.737720\pi$
$984$			1.30914e24i			1.48945i
$985$	9.70833e23	+	6.90298e23i	1.09561	+	0.779017i
$986$	−5.80911e23			−0.650271
$987$	−2.09601e23	+	2.09601e23i	−0.232732	+	0.232732i
$988$	−2.45920e22	−	2.45920e22i	−0.0270856	−	0.0270856i
$989$		−	2.66346e23i		−	0.290988i
$990$	−1.05336e24	+	1.48144e24i	−1.14155	+	1.60547i
$991$	1.14875e24			1.23492			0.617458	−	0.786604i	$-0.288162\pi$
$991$	1.14875e24			1.23492			0.617458	+	0.786604i	$0.288162\pi$
$992$	1.52943e23	−	1.52943e23i	0.163093	−	0.163093i
$993$	1.09227e24	+	1.09227e24i	1.15541	+	1.15541i
$994$			1.60848e24i			1.68782i
$995$	1.15092e21	−	1.94369e20i	0.00119801	−	0.000202322i
$996$	−4.97607e23			−0.513821
$997$	8.65451e23	−	8.65451e23i	0.886505	−	0.886505i	−0.107681	−	0.994186i	$-0.534342\pi$
$997$	8.65451e23	−	8.65451e23i	0.886505	−	0.886505i	0.994186	+	0.107681i	$0.0343425\pi$
$998$	−1.38483e24	−	1.38483e24i	−1.40719	−	1.40719i
$999$		−	1.94393e23i		−	0.195955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.17.c.a.3.2	yes	14
3.2	odd	2		45.17.g.a.28.6		14
4.3	odd	2		80.17.p.c.33.7		14
5.2	odd	4	inner	5.17.c.a.2.2	✓	14
5.3	odd	4		25.17.c.b.7.6		14
5.4	even	2		25.17.c.b.18.6		14
15.2	even	4		45.17.g.a.37.6		14
20.7	even	4		80.17.p.c.17.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.17.c.a.2.2	✓	14	5.2	odd	4	inner
5.17.c.a.3.2	yes	14	1.1	even	1	trivial
25.17.c.b.7.6		14	5.3	odd	4
25.17.c.b.18.6		14	5.4	even	2
45.17.g.a.28.6		14	3.2	odd	2
45.17.g.a.37.6		14	15.2	even	4
80.17.p.c.17.7		14	20.7	even	4
80.17.p.c.33.7		14	4.3	odd	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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-205.093 + 205.093i) q^{2} +(-8389.67 - 8389.67i) q^{3} -18590.3i q^{4} +(-65048.3 - 385171. i) q^{5} +3.44133e6 q^{6} +(-4.20104e6 + 4.20104e6i) q^{7} +(-9.62824e6 - 9.62824e6i) q^{8} +9.77264e7i q^{9} +O(q^{10})\)	\(q+(-205.093 + 205.093i) q^{2} +(-8389.67 - 8389.67i) q^{3} -18590.3i q^{4} +(-65048.3 - 385171. i) q^{5} +3.44133e6 q^{6} +(-4.20104e6 + 4.20104e6i) q^{7} +(-9.62824e6 - 9.62824e6i) q^{8} +9.77264e7i q^{9} +(9.23368e7 + 6.56549e7i) q^{10} +1.64171e8 q^{11} +(-1.55966e8 + 1.55966e8i) q^{12} +(2.05182e8 + 2.05182e8i) q^{13} -1.72321e9i q^{14} +(-2.68572e9 + 3.77719e9i) q^{15} +5.16770e9 q^{16} +(2.00552e9 - 2.00552e9i) q^{17} +(-2.00430e10 - 2.00430e10i) q^{18} -6.44717e9i q^{19} +(-7.16044e9 + 1.20927e9i) q^{20} +7.04907e10 q^{21} +(-3.36703e10 + 3.36703e10i) q^{22} +(2.07832e10 + 2.07832e10i) q^{23} +1.61555e11i q^{24} +(-1.44125e11 + 5.01094e10i) q^{25} -8.41626e10 q^{26} +(4.58744e11 - 4.58744e11i) q^{27} +(7.80986e10 + 7.80986e10i) q^{28} +7.06157e11i q^{29} +(-2.23852e11 - 1.32550e12i) q^{30} -3.56624e11 q^{31} +(-4.28864e11 + 4.28864e11i) q^{32} +(-1.37734e12 - 1.37734e12i) q^{33} +8.22637e11i q^{34} +(1.89139e12 + 1.34485e12i) q^{35} +1.81676e12 q^{36} +(2.11875e11 - 2.11875e11i) q^{37} +(1.32227e12 + 1.32227e12i) q^{38} -3.44281e12i q^{39} +(-3.08222e12 + 4.33482e12i) q^{40} +8.10337e12 q^{41} +(-1.44571e13 + 1.44571e13i) q^{42} +(-6.40772e12 - 6.40772e12i) q^{43} -3.05199e12i q^{44} +(3.76413e13 - 6.35693e12i) q^{45} -8.52498e12 q^{46} +(-2.97346e12 + 2.97346e12i) q^{47} +(-4.33553e13 - 4.33553e13i) q^{48} -2.06454e12i q^{49} +(1.92820e13 - 3.98362e13i) q^{50} -3.36513e13 q^{51} +(3.81439e12 - 3.81439e12i) q^{52} +(8.09389e13 + 8.09389e13i) q^{53} +1.88170e14i q^{54} +(-1.06790e13 - 6.32338e13i) q^{55} +8.08972e13 q^{56} +(-5.40896e13 + 5.40896e13i) q^{57} +(-1.44828e14 - 1.44828e14i) q^{58} +1.64260e13i q^{59} +(7.02191e13 + 4.99284e13i) q^{60} +1.82780e14 q^{61} +(7.31411e13 - 7.31411e13i) q^{62} +(-4.10552e14 - 4.10552e14i) q^{63} +1.62757e14i q^{64} +(6.56832e13 - 9.23766e13i) q^{65} +5.64965e14 q^{66} +(-4.64887e14 + 4.64887e14i) q^{67} +(-3.72833e13 - 3.72833e13i) q^{68} -3.48728e14i q^{69} +(-6.63730e14 + 1.12092e14i) q^{70} -9.33424e14 q^{71} +(9.40932e14 - 9.40932e14i) q^{72} +(8.72119e14 + 8.72119e14i) q^{73} +8.69083e13i q^{74} +(1.62957e15 + 7.88763e14i) q^{75} -1.19855e14 q^{76} +(-6.89688e14 + 6.89688e14i) q^{77} +(7.06096e14 + 7.06096e14i) q^{78} -5.24106e14i q^{79} +(-3.36150e14 - 1.99045e15i) q^{80} -3.49062e15 q^{81} +(-1.66194e15 + 1.66194e15i) q^{82} +(1.59524e15 + 1.59524e15i) q^{83} -1.31044e15i q^{84} +(-9.02924e14 - 6.42013e14i) q^{85} +2.62836e15 q^{86} +(5.92442e15 - 5.92442e15i) q^{87} +(-1.58068e15 - 1.58068e15i) q^{88} -5.35714e15i q^{89} +(-6.41622e15 + 9.02374e15i) q^{90} -1.72395e15 q^{91} +(3.86366e14 - 3.86366e14i) q^{92} +(2.99196e15 + 2.99196e15i) q^{93} -1.21967e15i q^{94} +(-2.48326e15 + 4.19377e14i) q^{95} +7.19605e15 q^{96} +(-6.01491e15 + 6.01491e15i) q^{97} +(4.23424e14 + 4.23424e14i) q^{98} +1.60438e16i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 7908 q^{3} + 192880 q^{5} + 4417368 q^{6} - 386452 q^{7} - 10493340 q^{8}+O(q^{10}) \) 14 * q - 2 * q^2 + 7908 * q^3 + 192880 * q^5 + 4417368 * q^6 - 386452 * q^7 - 10493340 * q^8	\( 14 q - 2 q^{2} + 7908 q^{3} + 192880 q^{5} + 4417368 q^{6} - 386452 q^{7} - 10493340 q^{8} + 398727830 q^{10} - 539141632 q^{11} + 1973309928 q^{12} - 681358582 q^{13} + 3514452060 q^{15} - 22953579016 q^{16} + 13124182498 q^{17} - 11293583022 q^{18} - 20186820060 q^{20} + 133652286048 q^{21} - 244784660624 q^{22} + 236373052228 q^{23} + 13144083650 q^{25} + 223473840788 q^{26} + 608106053880 q^{27} - 1494176423768 q^{28} + 2252131613760 q^{30} - 1105223074952 q^{31} - 2024535639992 q^{32} - 6385551058704 q^{33} + 6956678093980 q^{35} + 12514339524924 q^{36} - 9027827087002 q^{37} - 7824802789560 q^{38} + 31912538913900 q^{40} + 39543901484288 q^{41} - 70814500818384 q^{42} - 63017457929452 q^{43} + 126481294123110 q^{45} + 44357914058008 q^{46} - 2826187575452 q^{47} - 405160526368272 q^{48} + 461109216233650 q^{50} + 208649050954008 q^{51} - 389623094881012 q^{52} - 275142037498442 q^{53} + 330504874256560 q^{55} + 865011118900080 q^{56} - 644237427525840 q^{57} - 991296507673440 q^{58} + 16\!\cdots\!80 q^{60}+ \cdots + 48\!\cdots\!02 q^{98}+O(q^{100}) \) 14 * q - 2 * q^2 + 7908 * q^3 + 192880 * q^5 + 4417368 * q^6 - 386452 * q^7 - 10493340 * q^8 + 398727830 * q^10 - 539141632 * q^11 + 1973309928 * q^12 - 681358582 * q^13 + 3514452060 * q^15 - 22953579016 * q^16 + 13124182498 * q^17 - 11293583022 * q^18 - 20186820060 * q^20 + 133652286048 * q^21 - 244784660624 * q^22 + 236373052228 * q^23 + 13144083650 * q^25 + 223473840788 * q^26 + 608106053880 * q^27 - 1494176423768 * q^28 + 2252131613760 * q^30 - 1105223074952 * q^31 - 2024535639992 * q^32 - 6385551058704 * q^33 + 6956678093980 * q^35 + 12514339524924 * q^36 - 9027827087002 * q^37 - 7824802789560 * q^38 + 31912538913900 * q^40 + 39543901484288 * q^41 - 70814500818384 * q^42 - 63017457929452 * q^43 + 126481294123110 * q^45 + 44357914058008 * q^46 - 2826187575452 * q^47 - 405160526368272 * q^48 + 461109216233650 * q^50 + 208649050954008 * q^51 - 389623094881012 * q^52 - 275142037498442 * q^53 + 330504874256560 * q^55 + 865011118900080 * q^56 - 644237427525840 * q^57 - 991296507673440 * q^58 + 1631207111049480 * q^60 + 683634528395968 * q^61 - 938995013191864 * q^62 - 1361911146729372 * q^63 + 517066464980110 * q^65 - 196778043917184 * q^66 - 181547742064252 * q^67 - 917821658187868 * q^68 + 1066699466039880 * q^70 - 1337544011098792 * q^71 + 2573199832214340 * q^72 + 778038215296478 * q^73 - 1442550824447700 * q^75 - 233750796900240 * q^76 + 1099376123524976 * q^77 + 8472064951325256 * q^78 - 14934736099860320 * q^80 + 809940307363794 * q^81 - 303814693723184 * q^82 + 13357181209550188 * q^83 - 16045734952112470 * q^85 - 20034048539985352 * q^86 + 17327533268211840 * q^87 + 22952328705949920 * q^88 - 21878453293909290 * q^90 - 24534035720748632 * q^91 + 40652972845631848 * q^92 + 15958372062212256 * q^93 - 22489885958711400 * q^95 - 27488119051061472 * q^96 - 3303551663290402 * q^97 + 48233459501789102 * q^98

Introduction

L-functions

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