LMFDB - Embedded newform 8.20.b.a.5.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,20,Mod(5,8)]

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([0, 1]))

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("8.5");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	8.b (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:	$18.3053357245$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 9 x^{17} + 847482358 x^{16} - 6779858660 x^{15} + \cdots + 11\!\cdots\!76 $ x^18 - 9x^17 + 847482358x^16 - 6779858660x^15 + 288755694526787238x^14 - 2021289743039984830x^13 + 51121850635988052944521232x^12 - 306731077539161966630890980x^11 + 5053028465804290954773516593713297x^10 - 25265139517319958838954290038554593x^9 + 277525242785226225995541366728053703523138x^8 - 1110100819550071174104182779845774739997744x^7 + 7843581170028346695466748185748667347430921666496x^6 - 23530739624732277774733733894667178736900394654048x^5 + 88699644118206331836031766951870758907094189945148981184x^4 - 177399249018514584235839520819873862547126510378177038080x^3 + 27738447216461514660719783835924541644179956872586393406592768x^2 - 27738358516840927193180104500114450400133860395870028292288768*x + 1155804113673024778339834102840085457131269774629483366903990104576
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{153}\cdot 3^{16}\cdot 5^{4}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.13
Root			$0.500000 + 5761.07i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.20.b.a.5.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(424.854 - 586.333i) q^{2} -23044.3i q^{3} +(-163286. - 498212. i) q^{4} -7.37490e6i q^{5} +(-1.35116e7 - 9.79045e6i) q^{6} +5.30965e7 q^{7} +(-3.61491e8 - 1.15928e8i) q^{8} +6.31223e8 q^{9} +O(q^{10})$	\(q+(424.854 - 586.333i) q^{2} -23044.3i q^{3} +(-163286. - 498212. i) q^{4} -7.37490e6i q^{5} +(-1.35116e7 - 9.79045e6i) q^{6} +5.30965e7 q^{7} +(-3.61491e8 - 1.15928e8i) q^{8} +6.31223e8 q^{9} +(-4.32415e9 - 3.13326e9i) q^{10} +8.12973e8i q^{11} +(-1.14809e10 + 3.76280e9i) q^{12} -1.03661e10i q^{13} +(2.25583e10 - 3.11322e10i) q^{14} -1.69949e11 q^{15} +(-2.21553e11 + 1.62702e11i) q^{16} +5.21391e11 q^{17} +(2.68178e11 - 3.70107e11i) q^{18} +1.67441e12i q^{19} +(-3.67427e12 + 1.20422e12i) q^{20} -1.22357e12i q^{21} +(4.76673e11 + 3.45395e11i) q^{22} -1.06368e13 q^{23} +(-2.67147e12 + 8.33030e12i) q^{24} -3.53156e13 q^{25} +(-6.07802e12 - 4.40410e12i) q^{26} -4.13295e13i q^{27} +(-8.66989e12 - 2.64533e13i) q^{28} +7.99511e13i q^{29} +(-7.22036e13 + 9.96468e13i) q^{30} +2.82112e14 q^{31} +(1.26965e12 + 1.99029e14i) q^{32} +1.87344e13 q^{33} +(2.21515e14 - 3.05709e14i) q^{34} -3.91581e14i q^{35} +(-1.03070e14 - 3.14483e14i) q^{36} -1.12989e15i q^{37} +(9.81761e14 + 7.11379e14i) q^{38} -2.38880e14 q^{39} +(-8.54956e14 + 2.66596e15i) q^{40} +2.42038e15 q^{41} +(-7.17419e14 - 5.19838e14i) q^{42} -2.17667e15i q^{43} +(4.05033e14 - 1.32747e14i) q^{44} -4.65521e15i q^{45} +(-4.51910e15 + 6.23672e15i) q^{46} +1.03125e15 q^{47} +(3.74935e15 + 5.10554e15i) q^{48} -8.57966e15 q^{49} +(-1.50040e16 + 2.07067e16i) q^{50} -1.20151e16i q^{51} +(-5.16454e15 + 1.69264e15i) q^{52} -1.92963e16i q^{53} +(-2.42329e16 - 1.75590e16i) q^{54} +5.99559e15 q^{55} +(-1.91939e16 - 6.15536e15i) q^{56} +3.85855e16 q^{57} +(4.68780e16 + 3.39676e16i) q^{58} +1.72226e16i q^{59} +(2.77503e16 + 8.46708e16i) q^{60} -5.82188e16i q^{61} +(1.19857e17 - 1.65412e17i) q^{62} +3.35157e16 q^{63} +(1.17237e17 + 8.38138e16i) q^{64} -7.64493e16 q^{65} +(7.95938e15 - 1.09846e16i) q^{66} +1.51600e17i q^{67} +(-8.51358e16 - 2.59764e17i) q^{68} +2.45118e17i q^{69} +(-2.29597e17 - 1.66365e17i) q^{70} +4.29045e17 q^{71} +(-2.28182e17 - 7.31764e16i) q^{72} -8.38419e17 q^{73} +(-6.62491e17 - 4.80037e17i) q^{74} +8.13823e17i q^{75} +(8.34211e17 - 2.73407e17i) q^{76} +4.31660e16i q^{77} +(-1.01489e17 + 1.40063e17i) q^{78} -1.06444e18 q^{79} +(1.19991e18 + 1.63393e18i) q^{80} -2.18762e17 q^{81} +(1.02831e18 - 1.41915e18i) q^{82} +2.96065e18i q^{83} +(-6.09597e17 + 1.99791e17i) q^{84} -3.84521e18i q^{85} +(-1.27625e18 - 9.24766e17i) q^{86} +1.84241e18 q^{87} +(9.42462e16 - 2.93883e17i) q^{88} +2.03527e18 q^{89} +(-2.72950e18 - 1.97779e18i) q^{90} -5.50405e17i q^{91} +(1.73684e18 + 5.29940e18i) q^{92} -6.50107e18i q^{93} +(4.38133e17 - 6.04659e17i) q^{94} +1.23486e19 q^{95} +(4.58647e18 - 2.92581e16i) q^{96} -1.22385e19 q^{97} +(-3.64511e18 + 5.03054e18i) q^{98} +5.13168e17i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 458 q^{2} - 412108 q^{4} - 47240948 q^{6} - 80707216 q^{7} - 173313752 q^{8} - 6198727826 q^{9}+O(q^{10}) $ 18 * q - 458 * q^2 - 412108 * q^4 - 47240948 * q^6 - 80707216 * q^7 - 173313752 * q^8 - 6198727826 * q^9	$ 18 q - 458 q^{2} - 412108 q^{4} - 47240948 q^{6} - 80707216 q^{7} - 173313752 q^{8} - 6198727826 q^{9} + 758800104 q^{10} - 9351642296 q^{12} - 122453668784 q^{14} + 156097960432 q^{15} - 696212072432 q^{16} + 14121426692 q^{17} + 1813497117770 q^{18} + 6517087595632 q^{20} - 11074654117412 q^{22} + 2177121583952 q^{23} - 36473014189168 q^{24} - 44414474211734 q^{25} + 26782030269304 q^{26} - 97002327802784 q^{28} + 327847200544208 q^{30} + 428505770260416 q^{31} + 122449430282912 q^{32} - 185380269683736 q^{33} - 478448330325748 q^{34} - 10\!\cdots\!36 q^{36}+ \cdots + 88\!\cdots\!22 q^{98}+O(q^{100}) $ 18 * q - 458 * q^2 - 412108 * q^4 - 47240948 * q^6 - 80707216 * q^7 - 173313752 * q^8 - 6198727826 * q^9 + 758800104 * q^10 - 9351642296 * q^12 - 122453668784 * q^14 + 156097960432 * q^15 - 696212072432 * q^16 + 14121426692 * q^17 + 1813497117770 * q^18 + 6517087595632 * q^20 - 11074654117412 * q^22 + 2177121583952 * q^23 - 36473014189168 * q^24 - 44414474211734 * q^25 + 26782030269304 * q^26 - 97002327802784 * q^28 + 327847200544208 * q^30 + 428505770260416 * q^31 + 122449430282912 * q^32 - 185380269683736 * q^33 - 478448330325748 * q^34 - 1053851053424436 * q^36 - 486194587539796 * q^38 + 942830575043152 * q^39 - 1697818250610976 * q^40 + 1200260021141524 * q^41 + 4964410757677984 * q^42 + 7031781193616424 * q^44 - 14917443628457488 * q^46 - 1134160959992928 * q^47 - 3197964747991392 * q^48 + 31570092936329058 * q^49 - 34734151321861826 * q^50 - 26877456911772208 * q^52 + 32102189624395064 * q^54 - 51757047863478736 * q^55 + 52858270161183424 * q^56 - 7740744140670520 * q^57 - 20470056808312424 * q^58 - 25825294995349152 * q^60 + 93766686763697984 * q^62 + 430168668665078416 * q^63 - 253721318369185216 * q^64 - 184007586011668640 * q^65 + 479551889901302712 * q^66 + 201388986348307752 * q^68 - 340698473416023872 * q^70 - 1599477989199799056 * q^71 - 115475454880420648 * q^72 - 93004298989809068 * q^73 - 93558253821761240 * q^74 - 1090379619519933176 * q^76 + 2029949680340770544 * q^78 + 1813975801025264480 * q^79 + 3057120301750869696 * q^80 + 1801762045144484330 * q^81 - 2418785089528546244 * q^82 + 141493317659087296 * q^84 + 1332333723895598620 * q^86 - 13124960835754102512 * q^87 - 3097741184498130608 * q^88 + 4470509771045743540 * q^89 - 288100905697646824 * q^90 - 2965990502259463392 * q^92 - 3533635112749329696 * q^94 + 23809730986995679856 * q^95 - 2990158800543707584 * q^96 + 8246429789464117220 * q^97 + 8841667592735478822 * q^98

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 $

$2$	424.854	−	586.333i	0.586753	−	0.809766i
$2$	424.854	−	586.333i	0.586753	−	0.809766i
$3$		−	23044.3i		−	0.675944i	−0.941156	−	0.337972i	$-0.890259\pi$
$3$		−	23044.3i		−	0.675944i	0.941156	−	0.337972i	$-0.109741\pi$
$4$	−163286.	−	498212.i	−0.311443	−	0.950265i
$5$		−	7.37490e6i		−	1.68866i	−0.535827	−	0.844328i	$-0.680000\pi$
$5$		−	7.37490e6i		−	1.68866i	0.535827	−	0.844328i	$-0.320000\pi$
$6$	−1.35116e7	−	9.79045e6i	−0.547357	−	0.396612i
$7$	5.30965e7			0.497318			0.248659	−	0.968591i	$-0.420010\pi$
$7$	5.30965e7			0.497318			0.248659	+	0.968591i	$0.420010\pi$
$8$	−3.61491e8	−	1.15928e8i	−0.952232	−	0.305375i
$9$	6.31223e8			0.543099
$10$	−4.32415e9	−	3.13326e9i	−1.36742	−	0.990823i
$11$			8.12973e8i			0.103955i	0.998648	+	0.0519775i	$0.0165524\pi$
$11$			8.12973e8i			0.103955i	−0.998648	+	0.0519775i	$0.983448\pi$
$12$	−1.14809e10	+	3.76280e9i	−0.642326	+	0.210518i
$13$		−	1.03661e10i		−	0.271116i	−0.990769	−	0.135558i	$-0.956717\pi$
$13$		−	1.03661e10i		−	0.271116i	0.990769	−	0.135558i	$-0.0432827\pi$
$14$	2.25583e10	−	3.11322e10i	0.291803	−	0.402711i
$15$	−1.69949e11			−1.14144
$16$	−2.21553e11	+	1.62702e11i	−0.806007	+	0.591906i
$17$	5.21391e11			1.06635			0.533174	−	0.846005i	$-0.320999\pi$
$17$	5.21391e11			1.06635			0.533174	+	0.846005i	$0.320999\pi$
$18$	2.68178e11	−	3.70107e11i	0.318665	−	0.439783i
$19$			1.67441e12i			1.19042i	0.803568	+	0.595212i	$0.202932\pi$
$19$			1.67441e12i			1.19042i	−0.803568	+	0.595212i	$0.797068\pi$
$20$	−3.67427e12	+	1.20422e12i	−1.60467	+	0.525919i
$21$		−	1.22357e12i		−	0.336159i
$22$	4.76673e11	+	3.45395e11i	0.0841793	+	0.0609959i
$23$	−1.06368e13			−1.23139			−0.615697	−	0.787983i	$-0.711126\pi$
$23$	−1.06368e13			−1.23139			−0.615697	+	0.787983i	$0.711126\pi$
$24$	−2.67147e12	+	8.33030e12i	−0.206416	+	0.643656i
$25$	−3.53156e13			−1.85156
$26$	−6.07802e12	−	4.40410e12i	−0.219541	−	0.159078i
$27$		−	4.13295e13i		−	1.04305i
$28$	−8.66989e12	−	2.64533e13i	−0.154886	−	0.472584i
$29$			7.99511e13i			1.02340i	0.859165	+	0.511698i	$0.170983\pi$
$29$			7.99511e13i			1.02340i	−0.859165	+	0.511698i	$0.829017\pi$
$30$	−7.22036e13	+	9.96468e13i	−0.669741	+	0.924297i
$31$	2.82112e14			1.91640			0.958200	−	0.286100i	$-0.0923591\pi$
$31$	2.82112e14			1.91640			0.958200	+	0.286100i	$0.0923591\pi$
$32$	1.26965e12	+	1.99029e14i	0.00637908	+	0.999980i
$33$	1.87344e13			0.0702678
$34$	2.21515e14	−	3.05709e14i	0.625683	−	0.863493i
$35$		−	3.91581e14i		−	0.839799i
$36$	−1.03070e14	−	3.14483e14i	−0.169144	−	0.516088i
$37$		−	1.12989e15i		−	1.42928i	−0.699490	−	0.714642i	$-0.746589\pi$
$37$		−	1.12989e15i		−	1.42928i	0.699490	−	0.714642i	$-0.253411\pi$
$38$	9.81761e14	+	7.11379e14i	0.963966	+	0.698485i
$39$	−2.38880e14			−0.183259
$40$	−8.54956e14	+	2.66596e15i	−0.515672	+	1.60799i
$41$	2.42038e15			1.15461			0.577306	−	0.816528i	$-0.304104\pi$
$41$	2.42038e15			1.15461			0.577306	+	0.816528i	$0.304104\pi$
$42$	−7.17419e14	−	5.19838e14i	−0.272210	−	0.197242i
$43$		−	2.17667e15i		−	0.660453i	−0.943902	−	0.330226i	$-0.892875\pi$
$43$		−	2.17667e15i		−	0.660453i	0.943902	−	0.330226i	$-0.107125\pi$
$44$	4.05033e14	−	1.32747e14i	0.0987848	−	0.0323760i
$45$		−	4.65521e15i		−	0.917108i
$46$	−4.51910e15	+	6.23672e15i	−0.722524	+	0.997142i
$47$	1.03125e15			0.134411			0.0672057	−	0.997739i	$-0.478592\pi$
$47$	1.03125e15			0.134411			0.0672057	+	0.997739i	$0.478592\pi$
$48$	3.74935e15	+	5.10554e15i	0.400096	+	0.544816i
$49$	−8.57966e15			−0.752675
$50$	−1.50040e16	+	2.07067e16i	−1.08641	+	1.49933i
$51$		−	1.20151e16i		−	0.720792i
$52$	−5.16454e15	+	1.69264e15i	−0.257632	+	0.0844371i
$53$		−	1.92963e16i		−	0.803254i	−0.915803	−	0.401627i	$-0.868445\pi$
$53$		−	1.92963e16i		−	0.803254i	0.915803	−	0.401627i	$-0.131555\pi$
$54$	−2.42329e16	−	1.75590e16i	−0.844626	−	0.612012i
$55$	5.99559e15			0.175544
$56$	−1.91939e16	−	6.15536e15i	−0.473562	−	0.151868i
$57$	3.85855e16			0.804661
$58$	4.68780e16	+	3.39676e16i	0.828711	+	0.600480i
$59$			1.72226e16i			0.258824i	0.991591	+	0.129412i	$0.0413090\pi$
$59$			1.72226e16i			0.258824i	−0.991591	+	0.129412i	$0.958691\pi$
$60$	2.77503e16	+	8.46708e16i	0.355492	+	1.08467i
$61$		−	5.82188e16i		−	0.637427i	−0.947851	−	0.318713i	$-0.896749\pi$
$61$		−	5.82188e16i		−	0.637427i	0.947851	−	0.318713i	$-0.103251\pi$
$62$	1.19857e17	−	1.65412e17i	1.12445	−	1.55184i
$63$	3.35157e16			0.270093
$64$	1.17237e17	+	8.38138e16i	0.813493	+	0.581575i
$65$	−7.64493e16			−0.457822
$66$	7.95938e15	−	1.09846e16i	0.0412298	−	0.0569005i
$67$			1.51600e17i			0.680749i	0.940290	+	0.340375i	$0.110554\pi$
$67$			1.51600e17i			0.680749i	−0.940290	+	0.340375i	$0.889446\pi$
$68$	−8.51358e16	−	2.59764e17i	−0.332107	−	1.01331i
$69$			2.45118e17i			0.832354i
$70$	−2.29597e17	−	1.66365e17i	−0.680041	−	0.492754i
$71$	4.29045e17			1.11058			0.555288	−	0.831658i	$-0.312608\pi$
$71$	4.29045e17			1.11058			0.555288	+	0.831658i	$0.312608\pi$
$72$	−2.28182e17	−	7.31764e16i	−0.517157	−	0.165849i
$73$	−8.38419e17			−1.66684			−0.833420	−	0.552639i	$-0.813621\pi$
$73$	−8.38419e17			−1.66684			−0.833420	+	0.552639i	$0.813621\pi$
$74$	−6.62491e17	−	4.80037e17i	−1.15739	−	0.838636i
$75$			8.13823e17i			1.25155i
$76$	8.34211e17	−	2.73407e17i	1.13122	−	0.370749i
$77$			4.31660e16i			0.0516987i
$78$	−1.01489e17	+	1.40063e17i	−0.107528	+	0.148397i
$79$	−1.06444e18			−0.999223			−0.499612	−	0.866250i	$-0.666524\pi$
$79$	−1.06444e18			−0.999223			−0.499612	+	0.866250i	$0.666524\pi$
$80$	1.19991e18	+	1.63393e18i	0.999526	+	1.36107i
$81$	−2.18762e17			−0.161944
$82$	1.02831e18	−	1.41915e18i	0.677472	−	0.934966i
$83$			2.96065e18i			1.73838i	0.494475	+	0.869192i	$0.335360\pi$
$83$			2.96065e18i			1.73838i	−0.494475	+	0.869192i	$0.664640\pi$
$84$	−6.09597e17	+	1.99791e17i	−0.319440	+	0.104694i
$85$		−	3.84521e18i		−	1.80070i
$86$	−1.27625e18	−	9.24766e17i	−0.534812	−	0.387522i
$87$	1.84241e18			0.691759
$88$	9.42462e16	−	2.93883e17i	0.0317452	−	0.0989894i
$89$	2.03527e18			0.615767			0.307884	−	0.951424i	$-0.400379\pi$
$89$	2.03527e18			0.615767			0.307884	+	0.951424i	$0.400379\pi$
$90$	−2.72950e18	−	1.97779e18i	−0.742643	−	0.538115i
$91$		−	5.50405e17i		−	0.134831i
$92$	1.73684e18	+	5.29940e18i	0.383509	+	1.17015i
$93$		−	6.50107e18i		−	1.29538i
$94$	4.38133e17	−	6.04659e17i	0.0788662	−	0.108842i
$95$	1.23486e19			2.01022
$96$	4.58647e18	−	2.92581e16i	0.675931	−	0.00431190i
$97$	−1.22385e19			−1.63454			−0.817269	−	0.576257i	$-0.804513\pi$
$97$	−1.22385e19			−1.63454			−0.817269	+	0.576257i	$0.804513\pi$
$98$	−3.64511e18	+	5.03054e18i	−0.441634	+	0.609491i
$99$			5.13168e17i			0.0564579i
$100$	5.76654e18	+	1.75947e19i	0.576654	+	1.75947i
$101$		−	4.77647e18i		−	0.434564i	−0.976109	−	0.217282i	$-0.930281\pi$
$101$		−	4.77647e18i		−	0.434564i	0.976109	−	0.217282i	$-0.0697192\pi$
$102$	−7.04484e18	−	5.10466e18i	−0.583673	−	0.422927i
$103$	6.83745e18			0.516346			0.258173	−	0.966099i	$-0.416880\pi$
$103$	6.83745e18			0.516346			0.258173	+	0.966099i	$0.416880\pi$
$104$	−1.20172e18	+	3.74727e18i	−0.0827920	+	0.258166i
$105$	−9.02369e18			−0.567657
$106$	−1.13141e19	−	8.19811e18i	−0.650448	−	0.471312i
$107$		−	9.18352e17i		−	0.0482907i	−0.999708	−	0.0241453i	$-0.992314\pi$
$107$		−	9.18352e17i		−	0.0482907i	0.999708	−	0.0241453i	$-0.00768645\pi$
$108$	−2.05909e19	+	6.74852e18i	−0.991173	+	0.324850i
$109$		−	2.43225e19i		−	1.07265i	−0.844012	−	0.536324i	$-0.819813\pi$
$109$		−	2.43225e19i		−	1.07265i	0.844012	−	0.536324i	$-0.180187\pi$
$110$	2.54725e18	−	3.51542e18i	0.103001	−	0.142150i
$111$	−2.60374e19			−0.966117
$112$	−1.17637e19	+	8.63890e18i	−0.400842	+	0.294366i
$113$	−5.50211e18			−0.172300			−0.0861498	−	0.996282i	$-0.527456\pi$
$113$	−5.50211e18			−0.172300			−0.0861498	+	0.996282i	$0.527456\pi$
$114$	1.63932e19	−	2.26240e19i	0.472137	−	0.651587i
$115$			7.84455e19i			2.07940i
$116$	3.98327e19	−	1.30549e19i	0.972497	−	0.318729i
$117$		−	6.54335e18i		−	0.147243i
$118$	1.00982e19	+	7.31711e18i	0.209587	+	0.151866i
$119$	2.76840e19			0.530314
$120$	6.14351e19	+	1.97018e19i	1.08691	+	0.348566i
$121$	6.04982e19			0.989193
$122$	−3.41357e19	−	2.47345e19i	−0.516167	−	0.374012i
$123$		−	5.57758e19i		−	0.780454i
$124$	−4.60649e19	−	1.40552e20i	−0.596849	−	1.82109i
$125$			1.19784e20i			1.43799i
$126$	1.42393e19	−	1.96514e19i	0.158478	−	0.218712i
$127$	4.69956e19			0.485202			0.242601	−	0.970126i	$-0.421999\pi$
$127$	4.69956e19			0.485202			0.242601	+	0.970126i	$0.421999\pi$
$128$	9.89513e19	−	3.31311e19i	0.948259	−	0.317498i
$129$	−5.01597e19			−0.446429
$130$	−3.24798e19	+	4.48247e19i	−0.268628	+	0.370729i
$131$			5.15638e19i			0.396522i	0.980149	+	0.198261i	$0.0635294\pi$
$131$			5.15638e19i			0.396522i	−0.980149	+	0.198261i	$0.936471\pi$
$132$	−3.05905e18	−	9.33369e18i	−0.0218844	−	0.0667731i
$133$			8.89051e19i			0.592020i
$134$	8.88879e19	+	6.44077e19i	0.551248	+	0.399432i
$135$	−3.04801e20			−1.76135
$136$	−1.88478e20	−	6.04438e19i	−1.01541	−	0.325636i
$137$	−1.26213e20			−0.634247			−0.317124	−	0.948384i	$-0.602717\pi$
$137$	−1.26213e20			−0.634247			−0.317124	+	0.948384i	$0.602717\pi$
$138$	1.43721e20	+	1.04139e20i	0.674012	+	0.488386i
$139$		−	3.53665e20i		−	1.54864i	−0.632791	−	0.774322i	$-0.718091\pi$
$139$		−	3.53665e20i		−	1.54864i	0.632791	−	0.774322i	$-0.281909\pi$
$140$	−1.95091e20	+	6.39396e19i	−0.798031	+	0.261549i
$141$		−	2.37645e19i		−	0.0908546i
$142$	1.82281e20	−	2.51563e20i	0.651633	−	0.899307i
$143$	8.42739e18			0.0281839
$144$	−1.39850e20	+	1.02701e20i	−0.437742	+	0.321464i
$145$	5.89631e20			1.72816
$146$	−3.56206e20	+	4.91593e20i	−0.978023	+	1.34975i
$147$			1.97712e20i			0.508766i
$148$	−5.62924e20	+	1.84494e20i	−1.35820	+	0.445140i
$149$			3.87883e20i			0.877871i	0.898518	+	0.438936i	$0.144644\pi$
$149$			3.87883e20i			0.877871i	−0.898518	+	0.438936i	$0.855356\pi$
$150$	4.77172e20	+	3.45756e20i	1.01346	+	0.734350i
$151$	1.24861e20			0.248970			0.124485	−	0.992222i	$-0.460272\pi$
$151$	1.24861e20			0.248970			0.124485	+	0.992222i	$0.460272\pi$
$152$	1.94110e20	−	6.05284e20i	0.363525	−	1.13356i
$153$	3.29114e20			0.579133
$154$	2.53097e19	+	1.83393e19i	0.0418639	+	0.0303344i
$155$		−	2.08055e21i		−	3.23614i
$156$	3.90057e19	+	1.19013e20i	0.0570748	+	0.174145i
$157$		−	3.26809e20i		−	0.450036i	−0.974355	−	0.225018i	$-0.927756\pi$
$157$		−	3.26809e20i		−	0.450036i	0.974355	−	0.225018i	$-0.0722441\pi$
$158$	−4.52231e20	+	6.24115e20i	−0.586297	+	0.809137i
$159$	−4.44669e20			−0.542955
$160$	1.46782e21	−	9.36352e18i	1.68862	−	0.0107721i
$161$	−5.64777e20			−0.612395
$162$	−9.29420e19	+	1.28268e20i	−0.0950210	+	0.131137i
$163$			9.64660e20i			0.930234i	0.885249	+	0.465117i	$0.153988\pi$
$163$			9.64660e20i			0.930234i	−0.885249	+	0.465117i	$0.846012\pi$
$164$	−3.95213e20	−	1.20586e21i	−0.359596	−	1.09719i
$165$		−	1.38164e20i		−	0.118658i
$166$	1.73593e21	+	1.25785e21i	1.40768	+	1.02000i
$167$	6.67061e20			0.510928			0.255464	−	0.966819i	$-0.417772\pi$
$167$	6.67061e20			0.510928			0.255464	+	0.966819i	$0.417772\pi$
$168$	−1.41846e20	+	4.42309e20i	−0.102654	+	0.320102i
$169$	1.35446e21			0.926496
$170$	−2.25457e21	−	1.63365e21i	−1.45814	−	1.05656i
$171$			1.05693e21i			0.646519i
$172$	−1.08444e21	+	3.55419e20i	−0.627605	+	0.205693i
$173$			1.05036e21i			0.575310i	0.957734	+	0.287655i	$0.0928757\pi$
$173$			1.05036e21i			0.575310i	−0.957734	+	0.287655i	$0.907124\pi$
$174$	7.82758e20	−	1.08027e21i	0.405891	−	0.560163i
$175$	−1.87514e21			−0.920812
$176$	−1.32272e20	−	1.80117e20i	−0.0615316	−	0.0837885i
$177$	3.96883e20			0.174951
$178$	8.64693e20	−	1.19335e21i	0.361303	−	0.498628i
$179$			3.05446e21i			1.21012i	0.796178	+	0.605062i	$0.206852\pi$
$179$			3.05446e21i			1.21012i	−0.796178	+	0.605062i	$0.793148\pi$
$180$	−2.31928e21	+	7.60129e20i	−0.871495	+	0.285626i
$181$			4.09335e20i			0.145926i	0.997335	+	0.0729629i	$0.0232455\pi$
$181$			4.09335e20i			0.145926i	−0.997335	+	0.0729629i	$0.976755\pi$
$182$	−3.22721e20	−	2.33842e20i	−0.109182	−	0.0791124i
$183$	−1.34161e21			−0.430865
$184$	3.84512e21	+	1.23310e21i	1.17257	+	0.376037i
$185$	−8.33280e21			−2.41357
$186$	−3.81180e21	−	2.76201e21i	−1.04895	−	0.760067i
$187$			4.23877e20i			0.110852i
$188$	−1.68389e20	−	5.13784e20i	−0.0418614	−	0.127726i
$189$		−	2.19445e21i		−	0.518727i
$190$	5.24635e21	−	7.24039e21i	1.17950	−	1.62781i
$191$	8.05271e21			1.72236			0.861182	−	0.508297i	$-0.169725\pi$
$191$	8.05271e21			1.72236			0.861182	+	0.508297i	$0.169725\pi$
$192$	1.93143e21	−	2.70163e21i	0.393112	−	0.549876i
$193$	−2.34435e20			−0.0454181			−0.0227090	−	0.999742i	$-0.507229\pi$
$193$	−2.34435e20			−0.0454181			−0.0227090	+	0.999742i	$0.507229\pi$
$194$	−5.19956e21	+	7.17581e21i	−0.959069	+	1.32359i
$195$			1.76172e21i			0.309462i
$196$	1.40094e21	+	4.27449e21i	0.234415	+	0.715241i
$197$			1.68777e21i			0.269082i	0.990908	+	0.134541i	$0.0429560\pi$
$197$			1.68777e21i			0.269082i	−0.990908	+	0.134541i	$0.957044\pi$
$198$	3.00887e20	+	2.18021e20i	0.0457177	+	0.0331268i
$199$	9.56331e21			1.38517			0.692586	−	0.721335i	$-0.256471\pi$
$199$	9.56331e21			1.38517			0.692586	+	0.721335i	$0.256471\pi$
$200$	1.27663e22	+	4.09407e21i	1.76311	+	0.565418i
$201$	3.49350e21			0.460149
$202$	−2.80060e21	−	2.02930e21i	−0.351896	−	0.254982i
$203$			4.24512e21i			0.508953i
$204$	−5.98606e21	+	1.96189e21i	−0.684944	+	0.224486i
$205$		−	1.78500e22i		−	1.94974i
$206$	2.90492e21	−	4.00902e21i	0.302967	−	0.418119i
$207$	−6.71421e21			−0.668770
$208$	1.68659e21	+	2.29665e21i	0.160475	+	0.218521i
$209$	−1.36125e21			−0.123751
$210$	−3.83376e21	+	5.29089e21i	−0.333074	+	0.459670i
$211$		−	8.14897e21i		−	0.676736i	−0.941014	−	0.338368i	$-0.890125\pi$
$211$		−	8.14897e21i		−	0.676736i	0.941014	−	0.338368i	$-0.109875\pi$
$212$	−9.61365e21	+	3.15081e21i	−0.763305	+	0.250168i
$213$		−	9.88702e21i		−	0.750687i
$214$	−5.38460e20	−	3.90166e20i	−0.0391042	−	0.0283347i
$215$	−1.60527e22			−1.11528
$216$	−4.79124e21	+	1.49403e22i	−0.318521	+	0.993225i
$217$	1.49792e22			0.953060
$218$	−1.42611e22	−	1.03335e22i	−0.868594	−	0.629379i
$219$			1.93208e22i			1.12669i
$220$	−9.78995e20	−	2.98708e21i	−0.0546720	−	0.166814i
$221$		−	5.40482e21i		−	0.289104i
$222$	−1.10621e22	+	1.52666e22i	−0.566872	+	0.782329i
$223$	1.64188e22			0.806204			0.403102	−	0.915155i	$-0.367932\pi$
$223$	1.64188e22			0.806204			0.403102	+	0.915155i	$0.367932\pi$
$224$	6.74137e19	+	1.05677e22i	0.00317243	+	0.497308i
$225$	−2.22921e22			−1.00558
$226$	−2.33760e21	+	3.22607e21i	−0.101097	+	0.139522i
$227$		−	3.07665e22i		−	1.27595i	−0.770059	−	0.637973i	$-0.779773\pi$
$227$		−	3.07665e22i		−	1.27595i	0.770059	−	0.637973i	$-0.220227\pi$
$228$	−6.30046e21	−	1.92238e22i	−0.250606	−	0.764641i
$229$			3.68234e22i			1.40503i	0.711667	+	0.702517i	$0.247941\pi$
$229$			3.68234e22i			1.40503i	−0.711667	+	0.702517i	$0.752059\pi$
$230$	4.59952e22	+	3.33279e22i	1.68383	+	1.22009i
$231$	9.94728e20			0.0349455
$232$	9.26856e21	−	2.89016e22i	0.312519	−	0.974511i
$233$	−1.13563e22			−0.367585			−0.183792	−	0.982965i	$-0.558837\pi$
$233$	−1.13563e22			−0.367585			−0.183792	+	0.982965i	$0.558837\pi$
$234$	−3.83659e21	−	2.77997e21i	−0.119232	−	0.0863952i
$235$		−	7.60539e21i		−	0.226974i
$236$	8.58053e21	−	2.81221e21i	0.245952	−	0.0806090i
$237$			2.45292e22i			0.675419i
$238$	1.17617e22	−	1.62321e22i	0.311163	−	0.429431i
$239$	−1.71615e22			−0.436289			−0.218144	−	0.975916i	$-0.570000\pi$
$239$	−1.71615e22			−0.436289			−0.218144	+	0.975916i	$0.570000\pi$
$240$	3.76528e22	−	2.76511e22i	0.920006	−	0.675624i
$241$	2.01060e22			0.472241			0.236120	−	0.971724i	$-0.424124\pi$
$241$	2.01060e22			0.472241			0.236120	+	0.971724i	$0.424124\pi$
$242$	2.57029e22	−	3.54721e22i	0.580412	−	0.801015i
$243$		−	4.29945e22i		−	0.933584i
$244$	−2.90054e22	+	9.50631e21i	−0.605724	+	0.198522i
$245$			6.32741e22i			1.27101i
$246$	−3.27032e22	−	2.36966e22i	−0.631985	−	0.457933i
$247$	1.73571e22			0.322743
$248$	−1.01981e23	−	3.27047e22i	−1.82486	−	0.585220i
$249$	6.82261e22			1.17505
$250$	7.02335e22	+	5.08909e22i	1.16443	+	0.843742i
$251$			9.14531e22i			1.45982i	0.683546	+	0.729908i	$0.260437\pi$
$251$			9.14531e22i			1.45982i	−0.683546	+	0.729908i	$0.739563\pi$
$252$	−5.47264e21	−	1.66980e22i	−0.0841185	−	0.256660i
$253$		−	8.64745e21i		−	0.128010i
$254$	1.99663e22	−	2.75551e22i	0.284693	−	0.392900i
$255$	−8.86100e22			−1.21717
$256$	2.26140e22	−	7.20944e22i	0.299294	−	0.954161i
$257$	7.33268e22			0.935186			0.467593	−	0.883944i	$-0.345121\pi$
$257$	7.33268e22			0.935186			0.467593	+	0.883944i	$0.345121\pi$
$258$	−2.13106e22	+	2.94103e22i	−0.261944	+	0.361503i
$259$		−	5.99930e22i		−	0.710809i
$260$	1.24831e22	+	3.80880e22i	0.142585	+	0.435052i
$261$			5.04670e22i			0.555806i
$262$	3.02336e22	+	2.19071e22i	0.321090	+	0.232660i
$263$	−1.28147e23			−1.31259			−0.656293	−	0.754506i	$-0.727876\pi$
$263$	−1.28147e23			−1.31259			−0.656293	+	0.754506i	$0.727876\pi$
$264$	−6.77231e21	−	2.17183e21i	−0.0669113	−	0.0214580i
$265$	−1.42308e23			−1.35642
$266$	5.21280e22	+	3.77717e22i	0.479397	+	0.347369i
$267$		−	4.69013e22i		−	0.416225i
$268$	7.55288e22	−	2.47540e22i	0.646892	−	0.212014i
$269$		−	6.95977e22i		−	0.575371i	−0.957725	−	0.287686i	$-0.907114\pi$
$269$		−	6.95977e22i		−	0.575371i	0.957725	−	0.287686i	$-0.0928858\pi$
$270$	−1.29496e23	+	1.78715e23i	−1.03348	+	1.42628i
$271$	7.81978e22			0.602541			0.301270	−	0.953539i	$-0.402589\pi$
$271$	7.81978e22			0.602541			0.301270	+	0.953539i	$0.402589\pi$
$272$	−1.15516e23	+	8.48314e22i	−0.859484	+	0.631178i
$273$	−1.26837e22			−0.0911382
$274$	−5.36221e22	+	7.40029e22i	−0.372146	+	0.513592i
$275$		−	2.87107e22i		−	0.192479i
$276$	1.22121e23	−	4.00242e22i	0.790957	−	0.259231i
$277$			4.00035e22i			0.250346i	0.992135	+	0.125173i	$0.0399485\pi$
$277$			4.00035e22i			0.250346i	−0.992135	+	0.125173i	$0.960051\pi$
$278$	−2.07366e23	−	1.50256e23i	−1.25404	−	0.908671i
$279$	1.78076e23			1.04080
$280$	−4.53951e22	+	1.41553e23i	−0.256453	+	0.799683i
$281$	8.39766e22			0.458615			0.229308	−	0.973354i	$-0.426354\pi$
$281$	8.39766e22			0.458615			0.229308	+	0.973354i	$0.426354\pi$
$282$	−1.39339e22	−	1.00964e22i	−0.0735710	−	0.0533092i
$283$		−	2.12048e23i		−	1.08259i	−0.840833	−	0.541294i	$-0.817935\pi$
$283$		−	2.12048e23i		−	1.08259i	0.840833	−	0.541294i	$-0.182065\pi$
$284$	−7.00568e22	−	2.13755e23i	−0.345881	−	1.05534i
$285$		−	2.84564e23i		−	1.35879i
$286$	3.58041e21	−	4.94126e21i	0.0165370	−	0.0228224i
$287$	1.28513e23			0.574210
$288$	8.01431e20	+	1.25632e23i	0.00346447	+	0.543088i
$289$	3.27766e22			0.137099
$290$	2.50507e23	−	3.45721e23i	1.01400	−	1.39941i
$291$			2.82026e23i			1.10486i
$292$	1.36902e23	+	4.17711e23i	0.519126	+	1.58394i
$293$		−	1.22310e23i		−	0.448974i	−0.974477	−	0.224487i	$-0.927929\pi$
$293$		−	1.22310e23i		−	0.448974i	0.974477	−	0.224487i	$-0.0720706\pi$
$294$	1.15925e23	+	8.39988e22i	0.411982	+	0.298520i
$295$	1.27015e23			0.437065
$296$	−1.30985e23	+	4.08444e23i	−0.436467	+	1.36101i
$297$	3.35998e22			0.108430
$298$	2.27429e23	+	1.64794e23i	0.710871	+	0.515093i
$299$			1.10263e23i			0.333851i
$300$	4.05457e23	−	1.32886e23i	1.18930	−	0.389786i
$301$		−	1.15573e23i		−	0.328455i
$302$	5.30478e22	−	7.32103e22i	0.146084	−	0.201607i
$303$	−1.10070e23			−0.293741
$304$	−2.72429e23	−	3.70971e23i	−0.704620	−	0.959491i
$305$	−4.29358e23			−1.07639
$306$	1.39826e23	−	1.92971e23i	0.339808	−	0.468962i
$307$			6.44871e23i			1.51935i	0.650302	+	0.759675i	$0.274642\pi$
$307$			6.44871e23i			1.51935i	−0.650302	+	0.759675i	$0.725358\pi$
$308$	2.15058e22	−	7.04839e21i	0.0491275	−	0.0161012i
$309$		−	1.57564e23i		−	0.349021i
$310$	−1.21990e24	−	8.83931e23i	−2.62052	−	1.89881i
$311$	1.39658e23			0.290966			0.145483	−	0.989361i	$-0.453526\pi$
$311$	1.39658e23			0.290966			0.145483	+	0.989361i	$0.453526\pi$
$312$	8.63531e22	+	2.76929e22i	0.174506	+	0.0559628i
$313$	−5.89594e23			−1.15580			−0.577899	−	0.816108i	$-0.696127\pi$
$313$	−5.89594e23			−1.15580			−0.577899	+	0.816108i	$0.696127\pi$
$314$	−1.91619e23	−	1.38846e23i	−0.364424	−	0.264060i
$315$		−	2.47175e23i		−	0.456094i
$316$	1.73807e23	+	5.30316e23i	0.311201	+	0.949527i
$317$			5.35459e23i			0.930386i	0.885209	+	0.465193i	$0.154015\pi$
$317$			5.35459e23i			0.930386i	−0.885209	+	0.465193i	$0.845985\pi$
$318$	−1.88919e23	+	2.60724e23i	−0.318580	+	0.439667i
$319$	−6.49981e22			−0.106387
$320$	6.18118e23	−	8.64608e23i	0.982080	−	1.37371i
$321$	−2.11627e22			−0.0326418
$322$	−2.39948e23	+	3.31148e23i	−0.359324	+	0.495897i
$323$			8.73022e23i			1.26941i
$324$	3.57207e22	+	1.08990e23i	0.0504362	+	0.153890i
$325$			3.66087e23i			0.501987i
$326$	5.65612e23	+	4.09840e23i	0.753272	+	0.545817i
$327$	−5.60495e23			−0.725050
$328$	−8.74945e23	−	2.80589e23i	−1.09946	−	0.352589i
$329$	5.47559e22			0.0668452
$330$	−8.10102e22	−	5.86996e22i	−0.0960854	−	0.0696230i
$331$		−	1.94456e23i		−	0.224107i	−0.993702	−	0.112054i	$-0.964257\pi$
$331$		−	1.94456e23i		−	0.224107i	0.993702	−	0.112054i	$-0.0357429\pi$
$332$	1.47503e24	−	4.83432e23i	1.65193	−	0.541407i
$333$		−	7.13211e23i		−	0.776243i
$334$	2.83404e23	−	3.91120e23i	0.299788	−	0.413732i
$335$	1.11803e24			1.14955
$336$	1.99077e23	+	2.71086e23i	0.198975	+	0.270947i
$337$	1.03103e24			1.00182			0.500909	−	0.865500i	$-0.332999\pi$
$337$	1.03103e24			1.00182			0.500909	+	0.865500i	$0.332999\pi$
$338$	5.75450e23	−	7.94167e23i	0.543624	−	0.750245i
$339$			1.26792e23i			0.116465i
$340$	−1.91573e24	+	6.27868e23i	−1.71114	+	0.560813i
$341$			2.29350e23i			0.199219i
$342$	6.19711e23	+	4.49039e23i	0.523529	+	0.379347i
$343$	−1.06079e24			−0.871637
$344$	−2.52336e23	+	7.86846e23i	−0.201685	+	0.628904i
$345$	1.80772e24			1.40556
$346$	6.15864e23	+	4.46252e23i	0.465867	+	0.337565i
$347$		−	1.26415e24i		−	0.930398i	−0.885206	−	0.465199i	$-0.845983\pi$
$347$		−	1.26415e24i		−	0.930398i	0.885206	−	0.465199i	$-0.154017\pi$
$348$	−3.00840e23	−	9.17914e23i	−0.215443	−	0.657354i
$349$		−	6.37817e23i		−	0.444483i	−0.974992	−	0.222241i	$-0.928663\pi$
$349$		−	6.37817e23i		−	0.444483i	0.974992	−	0.222241i	$-0.0713373\pi$
$350$	−7.96659e23	+	1.09945e24i	−0.540289	+	0.745643i
$351$	−4.28428e23			−0.282787
$352$	−1.61805e23	+	1.03219e21i	−0.103953	+	0.000663138i
$353$	−1.44725e24			−0.905073			−0.452537	−	0.891746i	$-0.649481\pi$
$353$	−1.44725e24			−0.905073			−0.452537	+	0.891746i	$0.649481\pi$
$354$	1.68617e23	−	2.32706e23i	0.102653	−	0.141669i
$355$		−	3.16416e24i		−	1.87538i
$356$	−3.32330e23	−	1.01400e24i	−0.191776	−	0.585142i
$357$		−	6.37958e23i		−	0.358463i
$358$	1.79093e24	+	1.29770e24i	0.979918	+	0.710044i
$359$	8.77525e23			0.467587			0.233793	−	0.972286i	$-0.424886\pi$
$359$	8.77525e23			0.467587			0.233793	+	0.972286i	$0.424886\pi$
$360$	−5.39668e23	+	1.68282e24i	−0.280061	+	0.873299i
$361$	−8.25221e23			−0.417111
$362$	2.40007e23	+	1.73908e23i	0.118166	+	0.0856224i
$363$		−	1.39414e24i		−	0.668640i
$364$	−2.74219e23	+	8.98733e22i	−0.128125	+	0.0419921i
$365$			6.18326e24i			2.81472i
$366$	−5.69989e23	+	7.86631e23i	−0.252811	+	0.348900i
$367$	−1.73781e24			−0.751061			−0.375531	−	0.926810i	$-0.622540\pi$
$367$	−1.73781e24			−0.751061			−0.375531	+	0.926810i	$0.622540\pi$
$368$	2.35662e24	−	1.73063e24i	0.992513	−	0.728870i
$369$	1.52780e24			0.627069
$370$	−3.54023e24	+	4.88580e24i	−1.41617	+	1.95443i
$371$		−	1.02456e24i		−	0.399473i
$372$	−3.23891e24	+	1.06153e24i	−1.23095	+	0.403436i
$373$		−	1.93757e24i		−	0.717834i	−0.933369	−	0.358917i	$-0.883146\pi$
$373$		−	1.93757e24i		−	0.717834i	0.933369	−	0.358917i	$-0.116854\pi$
$374$	2.48533e23	+	1.80086e23i	0.0897645	+	0.0650429i
$375$	2.76034e24			0.971999
$376$	−3.72789e23	−	1.19551e23i	−0.127991	−	0.0410458i
$377$	8.28785e23			0.277459
$378$	−1.28668e24	−	9.32322e23i	−0.420048	−	0.304364i
$379$			3.31679e24i			1.05595i	0.849258	+	0.527977i	$0.177049\pi$
$379$			3.31679e24i			1.05595i	−0.849258	+	0.527977i	$0.822951\pi$
$380$	−2.01635e24	−	6.15222e24i	−0.626068	−	1.91024i
$381$		−	1.08298e24i		−	0.327969i
$382$	3.42123e24	−	4.72157e24i	1.01060	−	1.39471i
$383$	−3.92182e24			−1.13005			−0.565027	−	0.825073i	$-0.691134\pi$
$383$	−3.92182e24			−1.13005			−0.565027	+	0.825073i	$0.691134\pi$
$384$	−7.63482e23	−	2.28026e24i	−0.214611	−	0.640970i
$385$	3.18345e23			0.0873013
$386$	−9.96008e22	+	1.37457e23i	−0.0266492	+	0.0367780i
$387$		−	1.37396e24i		−	0.358691i
$388$	1.99836e24	+	6.09735e24i	0.509065	+	1.55324i
$389$			1.76592e23i			0.0438986i	0.999759	+	0.0219493i	$0.00698724\pi$
$389$			1.76592e23i			0.0438986i	−0.999759	+	0.0219493i	$0.993013\pi$
$390$	1.03295e24	+	7.48473e23i	0.250592	+	0.181578i
$391$	−5.54595e24			−1.31310
$392$	3.10147e24	+	9.94622e23i	0.716721	+	0.229848i
$393$	1.18825e24			0.268027
$394$	9.89598e23	+	7.17058e23i	0.217894	+	0.157885i
$395$			7.85011e24i			1.68734i
$396$	2.55667e23	−	8.37929e22i	0.0536500	−	0.0175834i
$397$		−	1.57919e22i		−	0.00323538i	−0.999999	−	0.00161769i	$-0.999485\pi$
$397$		−	1.57919e22i		−	0.00323538i	0.999999	−	0.00161769i	$-0.000514927\pi$
$398$	4.06301e24	−	5.60729e24i	0.812754	−	1.12167i
$399$	2.04875e24			0.400172
$400$	7.82430e24	−	5.74592e24i	1.49237	−	1.09595i
$401$	2.59856e23			0.0484018			0.0242009	−	0.999707i	$-0.492296\pi$
$401$	2.59856e23			0.0484018			0.0242009	+	0.999707i	$0.492296\pi$
$402$	1.48423e24	−	2.04836e24i	0.269993	−	0.372613i
$403$		−	2.92442e24i		−	0.519567i
$404$	−2.37970e24	+	7.79930e23i	−0.412951	+	0.135342i
$405$			1.61335e24i			0.273467i
$406$	2.48906e24	+	1.80356e24i	0.412133	+	0.298630i
$407$	9.18568e23			0.148581
$408$	−1.39288e24	+	4.34335e24i	−0.220112	+	0.686362i
$409$	1.46776e23			0.0226612			0.0113306	−	0.999936i	$-0.496393\pi$
$409$	1.46776e23			0.0226612			0.0113306	+	0.999936i	$0.496393\pi$
$410$	−1.04661e25	−	7.58366e24i	−1.57884	−	1.14402i
$411$			2.90849e24i			0.428716i
$412$	−1.11646e24	−	3.40650e24i	−0.160812	−	0.490665i
$413$			9.14460e23i			0.128718i
$414$	−2.85256e24	+	3.93677e24i	−0.392402	+	0.541547i
$415$	2.18345e25			2.93553
$416$	2.06316e24	−	1.31613e22i	0.271111	−	0.00172947i
$417$	−8.14996e24			−1.04680
$418$	−5.78332e23	+	7.98145e23i	−0.0726110	+	0.100209i
$419$			7.63206e24i			0.936717i	0.883538	+	0.468359i	$0.155154\pi$
$419$			7.63206e24i			0.936717i	−0.883538	+	0.468359i	$0.844846\pi$
$420$	1.47344e24	+	4.49572e24i	0.176793	+	0.539425i
$421$		−	5.87918e24i		−	0.689663i	−0.938665	−	0.344831i	$-0.887936\pi$
$421$		−	5.87918e24i		−	0.689663i	0.938665	−	0.344831i	$-0.112064\pi$
$422$	−4.77801e24	−	3.46212e24i	−0.547998	−	0.397077i
$423$	6.50952e23			0.0729987
$424$	−2.23698e24	+	6.97544e24i	−0.245294	+	0.764885i
$425$	−1.84133e25			−1.97441
$426$	−5.79709e24	−	4.20054e24i	−0.607881	−	0.440468i
$427$		−	3.09121e24i		−	0.317004i
$428$	−4.57534e23	+	1.49954e23i	−0.0458889	+	0.0150398i
$429$		−	1.94203e23i		−	0.0190507i
$430$	−6.82006e24	+	9.41223e24i	−0.654392	+	0.903114i
$431$	−1.90683e25			−1.78969			−0.894843	−	0.446380i	$-0.852713\pi$
$431$	−1.90683e25			−1.78969			−0.894843	+	0.446380i	$0.852713\pi$
$432$	6.72440e24	+	9.15670e24i	0.617387	+	0.840705i
$433$	6.62807e24			0.595322			0.297661	−	0.954672i	$-0.403794\pi$
$433$	6.62807e24			0.595322			0.297661	+	0.954672i	$0.403794\pi$
$434$	6.36396e24	−	8.78278e24i	0.559210	−	0.771756i
$435$		−	1.35876e25i		−	1.16814i
$436$	−1.21178e25	+	3.97152e24i	−1.01930	+	0.334068i
$437$		−	1.78104e25i		−	1.46588i
$438$	1.13284e25	+	8.20851e24i	0.912357	+	0.661089i
$439$	3.89484e24			0.306956			0.153478	−	0.988152i	$-0.450953\pi$
$439$	3.89484e24			0.306956			0.153478	+	0.988152i	$0.450953\pi$
$440$	−2.16735e24	−	6.95056e23i	−0.167159	−	0.0536068i
$441$	−5.41568e24			−0.408777
$442$	−3.16903e24	−	2.29626e24i	−0.234107	−	0.169633i
$443$			1.78700e25i			1.29208i	0.763304	+	0.646039i	$0.223576\pi$
$443$			1.78700e25i			1.29208i	−0.763304	+	0.646039i	$0.776424\pi$
$444$	4.25154e24	+	1.29722e25i	0.300890	+	0.918067i
$445$		−	1.50099e25i		−	1.03982i
$446$	6.97559e24	−	9.62689e24i	0.473042	−	0.652837i
$447$	8.93847e24			0.593392
$448$	6.22485e24	+	4.45022e24i	0.404565	+	0.289228i
$449$	2.66924e25			1.69843			0.849215	−	0.528047i	$-0.177075\pi$
$449$	2.66924e25			1.69843			0.849215	+	0.528047i	$0.177075\pi$
$450$	−9.47088e24	+	1.30706e25i	−0.590026	+	0.814284i
$451$			1.96770e24i			0.120028i
$452$	8.98416e23	+	2.74122e24i	0.0536614	+	0.163730i
$453$		−	2.87733e24i		−	0.168290i
$454$	−1.80394e25	−	1.30713e25i	−1.03322	−	0.748664i
$455$	−4.05918e24			−0.227683
$456$	−1.39483e25	−	4.47313e24i	−0.766224	−	0.245723i
$457$	3.50613e25			1.88636			0.943180	−	0.332283i	$-0.107819\pi$
$457$	3.50613e25			1.88636			0.943180	+	0.332283i	$0.107819\pi$
$458$	2.15908e25	+	1.56446e25i	1.13775	+	0.824408i
$459$		−	2.15489e25i		−	1.11225i
$460$	3.90825e25	−	1.28090e25i	1.97598	−	0.647615i
$461$			2.18646e25i			1.08289i	0.840737	+	0.541443i	$0.182122\pi$
$461$			2.18646e25i			1.08289i	−0.840737	+	0.541443i	$0.817878\pi$
$462$	4.22615e23	−	5.83242e23i	0.0205043	−	0.0282976i
$463$	1.52250e25			0.723666			0.361833	−	0.932243i	$-0.382151\pi$
$463$	1.52250e25			0.723666			0.361833	+	0.932243i	$0.382151\pi$
$464$	−1.30082e25	−	1.77135e25i	−0.605754	−	0.824864i
$465$	−4.79447e25			−2.18745
$466$	−4.82479e24	+	6.65861e24i	−0.215681	+	0.297658i
$467$			3.40954e25i			1.49343i	0.665144	+	0.746715i	$0.268370\pi$
$467$			3.40954e25i			1.49343i	−0.665144	+	0.746715i	$0.731630\pi$
$468$	−3.25998e24	+	1.06844e24i	−0.139920	+	0.0458578i
$469$			8.04940e24i			0.338549i
$470$	−4.45930e24	−	3.23118e24i	−0.183796	−	0.133178i
$471$	−7.53107e24			−0.304199
$472$	1.99658e24	−	6.22583e24i	0.0790384	−	0.246461i
$473$	1.76957e24			0.0686574
$474$	1.43823e25	+	1.04213e25i	0.546932	+	0.396304i
$475$		−	5.91328e25i		−	2.20414i
$476$	−4.52041e24	−	1.37925e25i	−0.165163	−	0.503939i
$477$		−	1.21803e25i		−	0.436247i
$478$	−7.29112e24	+	1.00623e25i	−0.255994	+	0.353292i
$479$	−1.65943e25			−0.571177			−0.285589	−	0.958352i	$-0.592189\pi$
$479$	−1.65943e25			−0.571177			−0.285589	+	0.958352i	$0.592189\pi$
$480$	−2.15775e23	−	3.38248e25i	−0.00728132	−	1.14141i
$481$	−1.17126e25			−0.387502
$482$	8.54211e24	−	1.17888e25i	0.277088	−	0.382404i
$483$			1.30149e25i			0.413945i
$484$	−9.87849e24	−	3.01409e25i	−0.308077	−	0.939996i
$485$			9.02573e25i			2.76017i
$486$	−2.52091e25	−	1.82664e25i	−0.755985	−	0.547783i
$487$	−4.18125e25			−1.22965			−0.614824	−	0.788664i	$-0.710773\pi$
$487$	−4.18125e25			−1.22965			−0.614824	+	0.788664i	$0.710773\pi$
$488$	−6.74919e24	+	2.10456e25i	−0.194654	+	0.606978i
$489$	2.22299e25			0.628786
$490$	3.70997e25	+	2.68823e25i	1.02922	+	0.745768i
$491$			1.21005e25i			0.329253i	0.986356	+	0.164626i	$0.0526419\pi$
$491$			1.21005e25i			0.329253i	−0.986356	+	0.164626i	$0.947358\pi$
$492$	−2.77882e25	+	9.10739e24i	−0.741638	+	0.243067i
$493$			4.16858e25i			1.09130i
$494$	7.37426e24	−	1.01771e25i	0.189370	−	0.261347i
$495$	3.78456e24			0.0953380
$496$	−6.25030e25	+	4.59002e25i	−1.54463	+	1.13433i
$497$	2.27807e25			0.552309
$498$	2.89861e25	−	4.00032e25i	0.689464	−	0.951517i
$499$			2.17124e25i			0.506703i	0.967374	+	0.253351i	$0.0815329\pi$
$499$			2.17124e25i			0.506703i	−0.967374	+	0.253351i	$0.918467\pi$
$500$	5.96780e25	−	1.95591e25i	1.36647	−	0.447850i
$501$		−	1.53719e25i		−	0.345359i
$502$	5.36220e25	+	3.88542e25i	1.18211	+	0.856550i
$503$	−9.72377e24			−0.210348			−0.105174	−	0.994454i	$-0.533540\pi$
$503$	−9.72377e24			−0.210348			−0.105174	+	0.994454i	$0.533540\pi$
$504$	−1.21156e25	−	3.88541e24i	−0.257191	−	0.0824795i
$505$	−3.52260e25			−0.733830
$506$	−5.07029e24	−	3.67391e24i	−0.103658	−	0.0751100i
$507$		−	3.12126e25i		−	0.626260i
$508$	−7.67372e24	−	2.34138e25i	−0.151113	−	0.461070i
$509$		−	7.14540e25i		−	1.38104i	−0.723311	−	0.690522i	$-0.757381\pi$
$509$		−	7.14540e25i		−	1.38104i	0.723311	−	0.690522i	$-0.242619\pi$
$510$	−3.76463e25	+	5.19550e25i	−0.714177	+	0.985623i
$511$	−4.45171e25			−0.828950
$512$	−3.26637e25	−	4.38890e25i	−0.597036	−	0.802215i
$513$	6.92025e25			1.24167
$514$	3.11532e25	−	4.29939e25i	0.548723	−	0.757282i
$515$		−	5.04255e25i		−	0.871930i
$516$	8.19036e24	+	2.49902e25i	0.139037	+	0.424226i
$517$			8.38382e23i			0.0139727i
$518$	−3.51759e25	−	2.54883e25i	−0.575589	−	0.417069i
$519$	2.42049e25			0.388878
$520$	2.76357e25	+	8.86260e24i	0.435953	+	0.139807i
$521$	−2.53391e25			−0.392494			−0.196247	−	0.980554i	$-0.562875\pi$
$521$	−2.53391e25			−0.392494			−0.196247	+	0.980554i	$0.562875\pi$
$522$	2.95905e25	+	2.14411e25i	0.450073	+	0.326120i
$523$		−	2.71691e25i		−	0.405798i	−0.979200	−	0.202899i	$-0.934964\pi$
$523$		−	2.71691e25i		−	0.405798i	0.979200	−	0.202899i	$-0.0650362\pi$
$524$	2.56897e25	−	8.41963e24i	0.376801	−	0.123494i
$525$			4.32111e25i			0.622418i
$526$	−5.44437e25	+	7.51367e25i	−0.770163	+	1.06289i
$527$	1.47091e26			2.04355
$528$	−4.15066e24	+	3.04812e24i	−0.0566364	+	0.0415920i
$529$	3.85265e25			0.516333
$530$	−6.04603e25	+	8.34401e25i	−0.795883	+	1.09838i
$531$			1.08713e25i			0.140567i
$532$	4.42936e25	−	1.45169e25i	0.562575	−	0.184380i
$533$		−	2.50900e25i		−	0.313034i
$534$	−2.74998e25	−	1.99262e25i	−0.337045	−	0.244221i
$535$	−6.77275e24			−0.0815463
$536$	1.75746e25	−	5.48019e25i	0.207884	−	0.648232i
$537$	7.03877e25			0.817977
$538$	−4.08074e25	−	2.95689e25i	−0.465916	−	0.337600i
$539$		−	6.97503e24i		−	0.0782444i
$540$	4.97697e25	+	1.51856e26i	0.548560	+	1.67375i
$541$		−	1.69248e26i		−	1.83295i	−0.400095	−	0.916474i	$-0.631023\pi$
$541$		−	1.69248e26i		−	1.83295i	0.400095	−	0.916474i	$-0.368977\pi$
$542$	3.32227e25	−	4.58500e25i	0.353542	−	0.487917i
$543$	9.43282e24			0.0986378
$544$	6.61983e23	+	1.03772e26i	0.00680232	+	1.06633i
$545$	−1.79376e26			−1.81133
$546$	−5.38872e24	+	7.43687e24i	−0.0534756	+	0.0738006i
$547$			1.60559e25i			0.156586i	0.996930	+	0.0782932i	$0.0249470\pi$
$547$			1.60559e25i			0.156586i	−0.996930	+	0.0782932i	$0.975053\pi$
$548$	2.06088e25	+	6.28809e25i	0.197532	+	0.602703i
$549$		−	3.67491e25i		−	0.346186i
$550$	−1.68340e25	−	1.21978e25i	−0.155863	−	0.112937i
$551$	−1.33871e26			−1.21828
$552$	2.84160e25	−	8.86079e25i	0.254180	−	0.792595i
$553$	−5.65178e25			−0.496932
$554$	2.34554e25	+	1.69957e25i	0.202721	+	0.146891i
$555$			1.92023e26i			1.63144i
$556$	−1.76200e26	+	5.77485e25i	−1.47162	+	0.482314i
$557$			1.81361e25i			0.148909i	0.997224	+	0.0744544i	$0.0237215\pi$
$557$			1.81361e25i			0.148909i	−0.997224	+	0.0744544i	$0.976278\pi$
$558$	7.56563e25	−	1.04412e26i	0.610689	−	0.842801i
$559$	−2.25636e25			−0.179059
$560$	6.37110e25	+	8.67561e25i	0.497082	+	0.676883i
$561$	9.76794e24			0.0749300
$562$	3.56778e25	−	4.92383e25i	0.269094	−	0.371371i
$563$		−	7.15020e25i		−	0.530260i	−0.964213	−	0.265130i	$-0.914585\pi$
$563$		−	7.15020e25i		−	0.530260i	0.964213	−	0.265130i	$-0.0854148\pi$
$564$	−1.18398e25	+	3.88040e24i	−0.0863359	+	0.0282960i
$565$			4.05775e25i			0.290955i
$566$	−1.24331e26	−	9.00895e25i	−0.876643	−	0.635211i
$567$	−1.16155e25			−0.0805376
$568$	−1.55096e26	−	4.97382e25i	−1.05753	−	0.339142i
$569$	−8.69099e25			−0.582778			−0.291389	−	0.956605i	$-0.594117\pi$
$569$	−8.69099e25			−0.582778			−0.291389	+	0.956605i	$0.594117\pi$
$570$	−1.66849e26	−	1.20898e26i	−1.10031	−	0.797276i
$571$			2.62084e26i			1.69980i	0.526946	+	0.849899i	$0.323337\pi$
$571$			2.62084e26i			1.69980i	−0.526946	+	0.849899i	$0.676663\pi$
$572$	−1.37607e24	−	4.19863e24i	−0.00877767	−	0.0267822i
$573$		−	1.85569e26i		−	1.16422i
$574$	5.45995e25	−	7.53517e25i	0.336919	−	0.464976i
$575$	3.75646e26			2.28000
$576$	7.40025e25	+	5.29052e25i	0.441807	+	0.315853i
$577$	3.26333e25			0.191642			0.0958210	−	0.995399i	$-0.469452\pi$
$577$	3.26333e25			0.191642			0.0958210	+	0.995399i	$0.469452\pi$
$578$	1.39253e25	−	1.92180e25i	0.0804433	−	0.111018i
$579$			5.40239e24i			0.0307001i
$580$	−9.62784e25	−	2.93762e26i	−0.538224	−	1.64221i
$581$			1.57200e26i			0.864530i
$582$	1.65361e26	+	1.19820e26i	0.894676	+	0.648277i
$583$	1.56874e25			0.0835024
$584$	3.03081e26	+	9.71962e25i	1.58722	+	0.509011i
$585$	−4.82566e25			−0.248643
$586$	−7.17146e25	−	5.19641e25i	−0.363564	−	0.263436i
$587$			6.88215e24i			0.0343291i	0.999853	+	0.0171645i	$0.00546391\pi$
$587$			6.88215e24i			0.0343291i	−0.999853	+	0.0171645i	$0.994536\pi$
$588$	9.85026e25	−	3.22835e25i	0.483463	−	0.158452i
$589$			4.72371e26i			2.28133i
$590$	5.39629e25	−	7.44732e25i	0.256449	−	0.353921i
$591$	3.88935e25			0.181885
$592$	1.83835e26	+	2.50330e26i	0.846002	+	1.15201i
$593$	−2.74812e25			−0.124456			−0.0622281	−	0.998062i	$-0.519821\pi$
$593$	−2.74812e25			−0.124456			−0.0622281	+	0.998062i	$0.519821\pi$
$594$	1.42750e25	−	1.97007e25i	0.0636217	−	0.0878031i
$595$		−	2.04167e26i		−	0.895518i
$596$	1.93248e26	−	6.33357e25i	0.834210	−	0.273407i
$597$		−	2.20379e26i		−	0.936300i
$598$	6.46508e25	+	4.68456e25i	0.270341	+	0.195888i
$599$	−2.05361e26			−0.845207			−0.422604	−	0.906315i	$-0.638884\pi$
$599$	−2.05361e26			−0.845207			−0.422604	+	0.906315i	$0.638884\pi$
$600$	9.43448e25	−	2.94190e26i	0.382191	−	1.19177i
$601$	−1.15717e26			−0.461414			−0.230707	−	0.973023i	$-0.574104\pi$
$601$	−1.15717e26			−0.461414			−0.230707	+	0.973023i	$0.574104\pi$
$602$	−6.77645e25	−	4.91018e25i	−0.265972	−	0.192722i
$603$			9.56932e25i			0.369715i
$604$	−2.03880e25	−	6.22074e25i	−0.0775398	−	0.236587i
$605$		−	4.46168e26i		−	1.67041i
$606$	−4.67638e25	+	6.45379e25i	−0.172354	+	0.237862i
$607$	−2.75446e25			−0.0999411			−0.0499705	−	0.998751i	$-0.515913\pi$
$607$	−2.75446e25			−0.0999411			−0.0499705	+	0.998751i	$0.515913\pi$
$608$	−3.33255e26	+	2.12591e24i	−1.19040	+	0.00759382i
$609$	9.78257e25			0.344024
$610$	−1.82415e26	+	2.51747e26i	−0.631577	+	0.871627i
$611$		−	1.06901e25i		−	0.0364411i
$612$	−5.37397e25	−	1.63969e26i	−0.180367	−	0.550330i
$613$			2.06636e26i			0.682860i	0.939907	+	0.341430i	$0.110911\pi$
$613$			2.06636e26i			0.682860i	−0.939907	+	0.341430i	$0.889089\pi$
$614$	3.78109e26	+	2.73976e26i	1.23032	+	0.891483i
$615$	−4.11341e26			−1.31792
$616$	5.00414e24	−	1.56041e25i	0.0157875	−	0.0492292i
$617$	5.57410e26			1.73167			0.865837	−	0.500327i	$-0.166787\pi$
$617$	5.57410e26			1.73167			0.865837	+	0.500327i	$0.166787\pi$
$618$	−9.23850e25	−	6.69417e25i	−0.282625	−	0.204789i
$619$		−	2.05924e26i		−	0.620363i	−0.950677	−	0.310182i	$-0.899610\pi$
$619$		−	2.05924e26i		−	0.620363i	0.950677	−	0.310182i	$-0.100390\pi$
$620$	−1.03656e27	+	3.39724e26i	−3.07519	+	1.00787i
$621$			4.39615e26i			1.28441i
$622$	5.93344e25	−	8.18863e25i	0.170725	−	0.235615i
$623$	1.08066e26			0.306232
$624$	5.29247e25	−	3.88663e25i	0.147708	−	0.108472i
$625$	2.09804e26			0.576706
$626$	−2.50492e26	+	3.45699e26i	−0.678167	+	0.935926i
$627$			3.13690e25i			0.0836486i
$628$	−1.62820e26	+	5.33632e25i	−0.427653	+	0.140160i
$629$		−	5.89114e26i		−	1.52412i
$630$	−1.44927e26	−	1.05013e26i	−0.369330	−	0.267614i
$631$	−5.57503e26			−1.39948			−0.699742	−	0.714396i	$-0.746702\pi$
$631$	−5.57503e26			−1.39948			−0.699742	+	0.714396i	$0.746702\pi$
$632$	3.84785e26	+	1.23398e26i	0.951493	+	0.305137i
$633$	−1.87787e26			−0.457436
$634$	3.13958e26	+	2.27492e26i	0.753396	+	0.545907i
$635$		−	3.46588e26i		−	0.819338i
$636$	7.26081e25	+	2.21540e26i	0.169099	+	0.515951i
$637$			8.89380e25i			0.204062i
$638$	−2.76147e25	+	3.81106e25i	−0.0624230	+	0.0861487i
$639$	2.70823e26			0.603153
$640$	−2.44339e26	−	7.29756e26i	−0.536145	−	1.60128i
$641$	7.78879e25			0.168391			0.0841955	−	0.996449i	$-0.473168\pi$
$641$	7.78879e25			0.168391			0.0841955	+	0.996449i	$0.473168\pi$
$642$	−8.99108e24	+	1.24084e25i	−0.0191527	+	0.0264322i
$643$		−	6.65702e26i		−	1.39725i	−0.715486	−	0.698627i	$-0.753794\pi$
$643$		−	6.65702e26i		−	1.39725i	0.715486	−	0.698627i	$-0.246206\pi$
$644$	9.22201e25	+	2.81379e26i	0.190726	+	0.581937i
$645$			3.69923e26i			0.753865i
$646$	5.11882e26	+	3.70907e26i	1.02792	+	0.744828i
$647$	3.44957e26			0.682614			0.341307	−	0.939952i	$-0.389130\pi$
$647$	3.44957e26			0.682614			0.341307	+	0.939952i	$0.389130\pi$
$648$	7.90806e25	+	2.53606e25i	0.154208	+	0.0494535i
$649$	−1.40015e25			−0.0269061
$650$	2.14649e26	+	1.55534e26i	0.406492	+	0.294542i
$651$		−	3.45184e26i		−	0.644215i
$652$	4.80606e26	−	1.57515e26i	0.883968	−	0.289715i
$653$			6.00601e26i			1.08871i	0.838856	+	0.544354i	$0.183225\pi$
$653$			6.00601e26i			1.08871i	−0.838856	+	0.544354i	$0.816775\pi$
$654$	−2.38129e26	+	3.28637e26i	−0.425425	+	0.587121i
$655$	3.80278e26			0.669589
$656$	−5.36243e26	+	3.93800e26i	−0.930626	+	0.683423i
$657$	−5.29230e26			−0.905260
$658$	2.32633e25	−	3.21052e25i	0.0392216	−	0.0541290i
$659$			2.01544e26i			0.334933i	0.985878	+	0.167466i	$0.0535585\pi$
$659$			2.01544e26i			0.334933i	−0.985878	+	0.167466i	$0.946441\pi$
$660$	−6.88351e25	+	2.25602e25i	−0.112757	+	0.0369552i
$661$			3.42807e26i			0.553523i	0.960939	+	0.276761i	$0.0892611\pi$
$661$			3.42807e26i			0.553523i	−0.960939	+	0.276761i	$0.910739\pi$
$662$	−1.14016e26	−	8.26156e25i	−0.181475	−	0.131496i
$663$	−1.24550e26			−0.195418
$664$	3.43222e26	−	1.07025e27i	0.530858	−	1.65535i
$665$	6.55666e26			0.999717
$666$	−4.18180e26	−	3.03011e26i	−0.628576	−	0.455463i
$667$		−	8.50426e26i		−	1.26020i
$668$	−1.08922e26	−	3.32338e26i	−0.159125	−	0.485517i
$669$		−	3.78359e26i		−	0.544949i
$670$	4.75000e26	−	6.55539e26i	0.674502	−	0.930868i
$671$	4.73304e25			0.0662637
$672$	2.43525e26	−	1.55350e24i	0.336152	−	0.00214439i
$673$	9.95640e25			0.135506			0.0677531	−	0.997702i	$-0.478417\pi$
$673$	9.95640e25			0.135506			0.0677531	+	0.997702i	$0.478417\pi$
$674$	4.38039e26	−	6.04530e26i	0.587820	−	0.811239i
$675$			1.45958e27i			1.93126i
$676$	−2.21164e26	−	6.74811e26i	−0.288550	−	0.880417i
$677$		−	8.97633e26i		−	1.15480i	−0.816462	−	0.577400i	$-0.804067\pi$
$677$		−	8.97633e26i		−	1.15480i	0.816462	−	0.577400i	$-0.195933\pi$
$678$	7.43424e25	+	5.38682e25i	0.0943093	+	0.0683361i
$679$	−6.49818e26			−0.812885
$680$	−4.45767e26	+	1.39001e27i	−0.549887	+	1.71468i
$681$	−7.08991e26			−0.862468
$682$	1.34475e26	+	9.74402e25i	0.161321	+	0.116893i
$683$			6.48900e26i			0.767681i	0.923399	+	0.383841i	$0.125399\pi$
$683$			6.48900e26i			0.767681i	−0.923399	+	0.383841i	$0.874601\pi$
$684$	5.26573e26	−	1.72581e26i	0.614364	−	0.201354i
$685$			9.30808e26i			1.07103i
$686$	−4.50681e26	+	6.21977e26i	−0.511435	+	0.705822i
$687$	8.48569e26			0.949725
$688$	3.54148e26	+	4.82248e26i	0.390926	+	0.532329i
$689$	−2.00028e26			−0.217775
$690$	7.68017e26	−	1.05993e27i	0.824716	−	1.13817i
$691$			1.77349e27i			1.87840i	0.343372	+	0.939200i	$0.388431\pi$
$691$			1.77349e27i			1.87840i	−0.343372	+	0.939200i	$0.611569\pi$
$692$	5.23305e26	−	1.71510e26i	0.546697	−	0.179176i
$693$			2.72474e25i			0.0280775i
$694$	−7.41214e26	−	5.37080e26i	−0.753405	−	0.545914i
$695$	−2.60825e27			−2.61513
$696$	−6.66017e26	−	2.13587e26i	−0.658715	−	0.211245i
$697$	1.26196e27			1.23122
$698$	−3.73974e26	−	2.70979e26i	−0.359927	−	0.260801i
$699$			2.61699e26i			0.248467i
$700$	3.06183e26	+	9.34216e26i	0.286780	+	0.875016i
$701$		−	1.23835e27i		−	1.14425i	−0.820166	−	0.572125i	$-0.806119\pi$
$701$		−	1.23835e27i		−	1.14425i	0.820166	−	0.572125i	$-0.193881\pi$
$702$	−1.82019e26	+	2.51202e26i	−0.165926	+	0.228992i
$703$	1.89189e27			1.70146
$704$	−6.81384e25	+	9.53102e25i	−0.0604577	+	0.0845667i
$705$	−1.75261e26			−0.153422
$706$	−6.14870e26	+	8.48571e26i	−0.531054	+	0.732898i
$707$		−	2.53614e26i		−	0.216117i
$708$	−6.48053e25	−	1.97732e26i	−0.0544872	−	0.166250i
$709$			4.11828e26i			0.341646i	0.985302	+	0.170823i	$0.0546427\pi$
$709$			4.11828e26i			0.341646i	−0.985302	+	0.170823i	$0.945357\pi$
$710$	−1.85525e27	−	1.34431e27i	−1.51862	−	1.10038i
$711$	−6.71897e26			−0.542677
$712$	−7.35732e26	−	2.35944e26i	−0.586354	−	0.188040i
$713$	−3.00078e27			−2.35984
$714$	−3.74056e26	−	2.71039e26i	−0.290271	−	0.210329i
$715$		−	6.21512e25i		−	0.0475929i
$716$	1.52177e27	−	4.98749e26i	1.14994	−	0.376885i
$717$			3.95473e26i			0.294907i
$718$	3.72820e26	−	5.14522e26i	0.274358	−	0.378636i
$719$	2.65339e27			1.92698			0.963488	−	0.267753i	$-0.0862811\pi$
$719$	2.65339e27			1.92698			0.963488	+	0.267753i	$0.0862811\pi$
$720$	7.57411e26	+	1.03138e27i	0.542842	+	0.739195i
$721$	3.63044e26			0.256788
$722$	−3.50599e26	+	4.83855e26i	−0.244741	+	0.337763i
$723$		−	4.63327e26i		−	0.319208i
$724$	2.03936e26	−	6.68385e25i	0.138668	−	0.0454476i
$725$		−	2.82353e27i		−	1.89488i
$726$	−8.17428e26	−	5.92305e26i	−0.541442	−	0.392326i
$727$	−5.35591e26			−0.350152			−0.175076	−	0.984555i	$-0.556017\pi$
$727$	−5.35591e26			−0.350152			−0.175076	+	0.984555i	$0.556017\pi$
$728$	−6.38073e25	+	1.98967e26i	−0.0411739	+	0.128390i
$729$	−1.24504e27			−0.792995
$730$	3.62545e27	+	2.62698e27i	2.27927	+	1.65154i
$731$		−	1.13490e27i		−	0.704273i
$732$	2.19066e26	+	6.68407e26i	0.134190	+	0.409436i
$733$		−	3.45816e26i		−	0.209102i	−0.994520	−	0.104551i	$-0.966659\pi$
$733$		−	3.45816e26i		−	0.209102i	0.994520	−	0.104551i	$-0.0333405\pi$
$734$	−7.38317e26	+	1.01894e27i	−0.440687	+	0.608184i
$735$	1.45811e27			0.859131
$736$	−1.35050e25	−	2.11703e27i	−0.00785517	−	1.23137i
$737$	−1.23246e26			−0.0707674
$738$	6.49092e26	−	8.95799e26i	0.367935	−	0.507780i
$739$		−	6.39162e26i		−	0.357675i	−0.983879	−	0.178838i	$-0.942766\pi$
$739$		−	6.39162e26i		−	0.357675i	0.983879	−	0.178838i	$-0.0572337\pi$
$740$	1.36063e27	+	4.15151e27i	0.751689	+	2.29353i
$741$		−	3.99983e26i		−	0.218157i
$742$	−6.00737e26	−	4.35291e26i	−0.323480	−	0.234392i
$743$	1.77477e27			0.943514			0.471757	−	0.881729i	$-0.343620\pi$
$743$	1.77477e27			0.943514			0.471757	+	0.881729i	$0.343620\pi$
$744$	−7.53655e26	+	2.35008e27i	−0.395576	+	1.23350i
$745$	2.86060e27			1.48242
$746$	−1.13606e27	−	8.23186e26i	−0.581278	−	0.421191i
$747$			1.86883e27i			0.944115i
$748$	2.11181e26	−	6.92131e25i	0.105339	−	0.0345242i
$749$		−	4.87612e25i		−	0.0240158i
$750$	1.17274e27	−	1.61848e27i	0.570323	−	0.787092i
$751$	−1.12256e27			−0.539050			−0.269525	−	0.962993i	$-0.586867\pi$
$751$	−1.12256e27			−0.539050			−0.269525	+	0.962993i	$0.586867\pi$
$752$	−2.28478e26	+	1.67787e26i	−0.108336	+	0.0795589i
$753$	2.10747e27			0.986754
$754$	3.52113e26	−	4.85944e26i	0.162800	−	0.224677i
$755$		−	9.20838e26i		−	0.420424i
$756$	−1.09330e27	+	3.58323e26i	−0.492928	+	0.161554i
$757$			1.11106e27i			0.494684i	0.968928	+	0.247342i	$0.0795571\pi$
$757$			1.11106e27i			0.494684i	−0.968928	+	0.247342i	$0.920443\pi$
$758$	1.94474e27	+	1.40915e27i	0.855076	+	0.619584i
$759$	−1.99274e26			−0.0865275
$760$	−4.46391e27	−	1.43155e27i	−1.91419	−	0.613869i
$761$	5.48843e26			0.232431			0.116215	−	0.993224i	$-0.462924\pi$
$761$	5.48843e26			0.232431			0.116215	+	0.993224i	$0.462924\pi$
$762$	−6.34987e26	−	4.60109e26i	−0.265578	−	0.192437i
$763$		−	1.29144e27i		−	0.533447i
$764$	−1.31489e27	−	4.01196e27i	−0.536418	−	1.63670i
$765$		−	2.42719e27i		−	0.977956i
$766$	−1.66620e27	+	2.29949e27i	−0.663062	+	0.915079i
$767$	1.78532e26			0.0701715
$768$	−1.66136e27	−	5.21123e26i	−0.644960	−	0.202306i
$769$	−1.02318e27			−0.392331			−0.196166	−	0.980571i	$-0.562849\pi$
$769$	−1.02318e27			−0.392331			−0.196166	+	0.980571i	$0.562849\pi$
$770$	1.35250e26	−	1.86656e26i	0.0512243	−	0.0706937i
$771$		−	1.68976e27i		−	0.632134i
$772$	3.82799e25	+	1.16799e26i	0.0141451	+	0.0431592i
$773$			4.21302e27i			1.53776i	0.639393	+	0.768880i	$0.279186\pi$
$773$			4.21302e27i			1.53776i	−0.639393	+	0.768880i	$0.720814\pi$
$774$	−8.05601e26	−	5.83734e26i	−0.290456	−	0.210463i
$775$	−9.96298e27			−3.54832
$776$	4.42409e27	+	1.41878e27i	1.55646	+	0.499146i
$777$	−1.38249e27			−0.480467
$778$	1.03542e26	+	7.50260e25i	0.0355476	+	0.0257576i
$779$			4.05270e27i			1.37448i
$780$	8.77709e26	−	2.87663e26i	0.294071	−	0.0963797i
$781$			3.48802e26i			0.115450i
$782$	−2.35622e27	+	3.25177e27i	−0.770463	+	1.06330i
$783$	3.30434e27			1.06745
$784$	1.90085e27	−	1.39593e27i	0.606661	−	0.445513i
$785$	−2.41018e27			−0.759956
$786$	5.04833e26	−	6.96710e26i	0.157266	−	0.217039i
$787$		−	4.46480e27i		−	1.37417i	−0.726575	−	0.687087i	$-0.758889\pi$
$787$		−	4.46480e27i		−	1.37417i	0.726575	−	0.687087i	$-0.241111\pi$
$788$	8.40870e26	−	2.75589e26i	0.255699	−	0.0838037i
$789$			2.95305e27i			0.887235i
$790$	4.60278e27	+	3.33515e27i	1.36635	+	0.990053i
$791$	−2.92143e26			−0.0856876
$792$	5.94904e25	−	1.85506e26i	0.0172408	−	0.0537611i
$793$	−6.03505e26			−0.172817
$794$	−9.25933e24	−	6.70927e24i	−0.00261990	−	0.00189837i
$795$			3.27939e27i			0.916864i
$796$	−1.56155e27	−	4.76456e27i	−0.431402	−	1.31628i
$797$			3.11016e27i			0.849042i	0.905418	+	0.424521i	$0.139558\pi$
$797$			3.11016e27i			0.849042i	−0.905418	+	0.424521i	$0.860442\pi$
$798$	8.70421e26	−	1.20125e27i	0.234802	−	0.324046i
$799$	5.37687e26			0.143329
$800$	−4.48384e25	−	7.02883e27i	−0.0118112	−	1.85152i
$801$	1.28471e27			0.334423
$802$	1.10401e26	−	1.52362e26i	0.0283999	−	0.0391941i
$803$		−	6.81612e26i		−	0.173277i
$804$	−5.70439e26	−	1.74051e27i	−0.143310	−	0.437263i
$805$			4.16518e27i			1.03412i
$806$	−1.71468e27	−	1.24245e27i	−0.420728	−	0.304857i
$807$	−1.60383e27			−0.388919
$808$	−5.53726e26	+	1.72665e27i	−0.132705	+	0.413806i
$809$	7.90445e27			1.87224			0.936118	−	0.351686i	$-0.114392\pi$
$809$	7.90445e27			1.87224			0.936118	+	0.351686i	$0.114392\pi$
$810$	9.45960e26	+	6.85438e26i	0.221445	+	0.160458i
$811$		−	2.25871e27i		−	0.522593i	−0.965259	−	0.261296i	$-0.915850\pi$
$811$		−	2.25871e27i		−	0.522593i	0.965259	−	0.261296i	$-0.0841500\pi$
$812$	2.11497e27	−	6.93168e26i	0.483640	−	0.158510i
$813$		−	1.80201e27i		−	0.407284i
$814$	3.90257e26	−	5.38587e26i	0.0871805	−	0.120316i
$815$	7.11427e27			1.57084
$816$	1.95488e27	+	2.66198e27i	0.426641	+	0.580963i
$817$	3.64463e27			0.786219
$818$	6.23584e25	−	8.60596e25i	0.0132965	−	0.0183503i
$819$		−	3.47429e26i		−	0.0732266i
$820$	−8.89311e27	+	2.91466e27i	−1.85277	+	0.607233i
$821$		−	9.36979e26i		−	0.192961i	−0.995335	−	0.0964806i	$-0.969241\pi$
$821$		−	9.36979e26i		−	0.192961i	0.995335	−	0.0964806i	$-0.0307586\pi$
$822$	1.70534e27	+	1.23568e27i	0.347160	+	0.251550i
$823$	−7.47754e27			−1.50474			−0.752368	−	0.658743i	$-0.771088\pi$
$823$	−7.47754e27			−1.50474			−0.752368	+	0.658743i	$0.771088\pi$
$824$	−2.47168e27	−	7.92651e26i	−0.491681	−	0.157679i
$825$	−6.61616e26			−0.130105
$826$	5.36179e26	+	3.88512e26i	0.104232	+	0.0755256i
$827$			8.79290e26i			0.168978i	0.996424	+	0.0844889i	$0.0269258\pi$
$827$			8.79290e26i			0.168978i	−0.996424	+	0.0844889i	$0.973074\pi$
$828$	1.09633e27	+	3.34510e27i	0.208283	+	0.635508i
$829$			6.19276e27i			1.16310i	0.813511	+	0.581549i	$0.197553\pi$
$829$			6.19276e27i			1.16310i	−0.813511	+	0.581549i	$0.802447\pi$
$830$	9.27649e27	−	1.28023e28i	1.72243	−	2.37709i
$831$	9.21851e26			0.169220
$832$	8.68826e26	−	1.21529e27i	0.157674	−	0.220551i
$833$	−4.47336e27			−0.802614
$834$	−3.46254e27	+	4.77859e27i	−0.614211	+	0.847661i
$835$		−	4.91951e27i		−	0.862781i
$836$	2.22272e26	+	6.78191e26i	0.0385413	+	0.117596i
$837$		−	1.16596e28i		−	1.99890i
$838$	4.47493e27	+	3.24251e27i	0.758522	+	0.549621i
$839$	−4.04517e27			−0.677951			−0.338975	−	0.940795i	$-0.610080\pi$
$839$	−4.04517e27			−0.677951			−0.338975	+	0.940795i	$0.610080\pi$
$840$	3.26199e27	+	1.04610e27i	0.540541	+	0.173348i
$841$	−2.88922e26			−0.0473390
$842$	−3.44716e27	−	2.49780e27i	−0.558466	−	0.404662i
$843$		−	1.93518e27i		−	0.309998i
$844$	−4.05992e27	+	1.33061e27i	−0.643079	+	0.210765i
$845$		−	9.98903e27i		−	1.56453i
$846$	2.76560e26	−	3.81675e26i	0.0428322	−	0.0591119i
$847$	3.21224e27			0.491944
$848$	3.13954e27	+	4.27516e27i	0.475451	+	0.647429i
$849$	−4.88649e27			−0.731769
$850$	−7.82296e27	+	1.07963e28i	−1.15849	+	1.59881i
$851$			1.20184e28i			1.76001i
$852$	−4.92583e27	+	1.61441e27i	−0.713352	+	0.233796i
$853$			9.99086e27i			1.43083i	0.698701	+	0.715413i	$0.253762\pi$
$853$			9.99086e27i			1.43083i	−0.698701	+	0.715413i	$0.746238\pi$
$854$	−1.81248e27	−	1.31332e27i	−0.256699	−	0.186003i
$855$	7.79472e27			1.09175
$856$	−1.06463e26	+	3.31976e26i	−0.0147467	+	0.0459839i
$857$	−7.95258e27			−1.08941			−0.544703	−	0.838629i	$-0.683358\pi$
$857$	−7.95258e27			−1.08941			−0.544703	+	0.838629i	$0.683358\pi$
$858$	−1.13868e26	−	8.25080e25i	−0.0154266	−	0.0111781i
$859$		−	1.08517e28i		−	1.45400i	−0.686640	−	0.726998i	$-0.740915\pi$
$859$		−	1.08517e28i		−	1.45400i	0.686640	−	0.726998i	$-0.259085\pi$
$860$	2.62118e27	+	7.99766e27i	0.347345	+	1.05981i
$861$		−	2.96150e27i		−	0.388134i
$862$	−8.10123e27	+	1.11804e28i	−1.05010	+	1.44923i
$863$	7.24244e27			0.928501			0.464250	−	0.885704i	$-0.346324\pi$
$863$	7.24244e27			0.928501			0.464250	+	0.885704i	$0.346324\pi$
$864$	8.22577e27	−	5.24739e25i	1.04303	−	0.00665370i
$865$	7.74633e27			0.971501
$866$	2.81596e27	−	3.88626e27i	0.349307	−	0.482072i
$867$		−	7.55314e26i		−	0.0926714i
$868$	−2.44588e27	−	7.46281e27i	−0.296824	−	0.905659i
$869$		−	8.65358e26i		−	0.103874i
$870$	−7.96688e27	−	5.77276e27i	−0.945922	−	0.685410i
$871$	1.57150e27			0.184562
$872$	−2.81966e27	+	8.79238e27i	−0.327559	+	1.02141i
$873$	−7.72520e27			−0.887716
$874$	−1.04428e28	−	7.56681e27i	−1.18702	−	0.860111i
$875$			6.36012e27i			0.715136i
$876$	9.62584e27	−	3.15480e27i	1.07066	−	0.350900i
$877$		−	1.15489e28i		−	1.27070i	−0.772224	−	0.635350i	$-0.780856\pi$
$877$		−	1.15489e28i		−	1.27070i	0.772224	−	0.635350i	$-0.219144\pi$
$878$	1.65474e27	−	2.28367e27i	0.180107	−	0.248563i
$879$	−2.81855e27			−0.303481
$880$	−1.32834e27	+	9.75495e26i	−0.141490	+	0.103906i
$881$	8.19582e26			0.0863617			0.0431809	−	0.999067i	$-0.486251\pi$
$881$	8.19582e26			0.0863617			0.0431809	+	0.999067i	$0.486251\pi$
$882$	−2.30088e27	+	3.17540e27i	−0.239851	+	0.331014i
$883$			4.66342e27i			0.480926i	0.970658	+	0.240463i	$0.0772992\pi$
$883$			4.66342e27i			0.480926i	−0.970658	+	0.240463i	$0.922701\pi$
$884$	−2.69275e27	+	8.82530e26i	−0.274726	+	0.0900394i
$885$		−	2.92697e27i		−	0.295432i
$886$	1.04778e28	+	7.59214e27i	1.04628	+	0.758130i
$887$	−1.92404e28			−1.90081			−0.950407	−	0.311009i	$-0.899333\pi$
$887$	−1.92404e28			−1.90081			−0.950407	+	0.311009i	$0.899333\pi$
$888$	9.41230e27	+	3.01846e27i	0.919968	+	0.295028i
$889$	2.49530e27			0.241299
$890$	−8.80081e27	−	6.37702e27i	−0.842010	−	0.610117i
$891$		−	1.77848e26i		−	0.0168349i
$892$	−2.68095e27	−	8.18005e27i	−0.251086	−	0.766107i
$893$			1.72674e27i			0.160007i
$894$	3.79755e27	−	5.24092e27i	0.348174	−	0.480509i
$895$	2.25263e28			2.04348
$896$	5.25396e27	−	1.75914e27i	0.471586	−	0.157898i
$897$	2.54092e27			0.225665
$898$	1.13404e28	−	1.56507e28i	0.996559	−	1.37533i
$899$			2.25552e28i			1.96123i
$900$	3.63997e27	+	1.11062e28i	0.313180	+	0.955567i
$901$		−	1.00609e28i		−	0.856549i
$902$	1.15373e27	+	8.35986e26i	0.0971945	+	0.0704266i
$903$	−2.66330e27			−0.222017
$904$	1.98896e27	+	6.37848e26i	0.164069	+	0.0526159i
$905$	3.01880e27			0.246419
$906$	−1.68708e27	−	1.22245e27i	−0.136275	−	0.0987444i
$907$		−	2.50336e27i		−	0.200103i	−0.994982	−	0.100052i	$-0.968099\pi$
$907$		−	2.50336e27i		−	0.200103i	0.994982	−	0.100052i	$-0.0319008\pi$
$908$	−1.53282e28	+	5.02372e27i	−1.21249	+	0.397384i
$909$		−	3.01502e27i		−	0.236012i
$910$	−1.72456e27	+	2.38004e27i	−0.133594	+	0.184370i
$911$	1.70782e27			0.130923			0.0654616	−	0.997855i	$-0.479148\pi$
$911$	1.70782e27			0.130923			0.0654616	+	0.997855i	$0.479148\pi$
$912$	−8.54875e27	+	6.27793e27i	−0.648562	+	0.476284i
$913$	−2.40693e27			−0.180714
$914$	1.48960e28	−	2.05576e28i	1.10683	−	1.52751i
$915$			9.89424e27i			0.727582i
$916$	1.83459e28	−	6.01274e27i	1.33516	−	0.437588i
$917$			2.73785e27i			0.197198i
$918$	−1.26348e28	−	9.15513e27i	−0.900666	−	0.652618i
$919$	−3.74442e27			−0.264172			−0.132086	−	0.991238i	$-0.542168\pi$
$919$	−3.74442e27			−0.264172			−0.132086	+	0.991238i	$0.542168\pi$
$920$	9.09401e27	−	2.83574e28i	0.634996	−	1.98007i
$921$	1.48606e28			1.02700
$922$	1.28199e28	+	9.28927e27i	0.876884	+	0.635386i
$923$		−	4.44754e27i		−	0.301095i
$924$	−1.62425e26	−	4.95586e26i	−0.0108835	−	0.0332074i
$925$			3.99027e28i			2.64640i
$926$	6.46841e27	−	8.92693e27i	0.424613	−	0.586000i
$927$	4.31596e27			0.280427
$928$	−1.59126e28	+	1.01510e26i	−1.02337	+	0.00652833i
$929$	−2.37867e28			−1.51421			−0.757104	−	0.653294i	$-0.773387\pi$
$929$	−2.37867e28			−1.51421			−0.757104	+	0.653294i	$0.773387\pi$
$930$	−2.03695e28	+	2.81116e28i	−1.28349	+	1.77132i
$931$		−	1.43659e28i		−	0.896003i
$932$	1.85433e27	+	5.65787e27i	0.114482	+	0.349303i
$933$		−	3.21832e27i		−	0.196677i
$934$	1.99913e28	+	1.44856e28i	1.20933	+	0.876274i
$935$	3.12605e27			0.187191
$936$	−7.58557e26	+	2.36536e27i	−0.0449643	+	0.140210i
$937$	−1.43366e28			−0.841243			−0.420621	−	0.907236i	$-0.638188\pi$
$937$	−1.43366e28			−0.841243			−0.420621	+	0.907236i	$0.638188\pi$
$938$	4.71963e27	+	3.41982e27i	0.274145	+	0.198644i
$939$			1.35868e28i			0.781255i
$940$	−3.78910e27	+	1.24185e27i	−0.215686	+	0.0706896i
$941$			3.81829e27i			0.215163i	0.994196	+	0.107581i	$0.0343106\pi$
$941$			3.81829e27i			0.215163i	−0.994196	+	0.107581i	$0.965689\pi$
$942$	−3.19961e27	+	4.41572e27i	−0.178490	+	0.246330i
$943$	−2.57451e28			−1.42178
$944$	−2.80215e27	−	3.81573e27i	−0.153200	−	0.208614i
$945$	−1.61839e28			−0.875951
$946$	7.51810e26	−	1.03756e27i	0.0402849	−	0.0555964i
$947$		−	1.04528e28i		−	0.554509i	−0.960797	−	0.277254i	$-0.910576\pi$
$947$		−	1.04528e28i		−	0.554509i	0.960797	−	0.277254i	$-0.0894245\pi$
$948$	1.22207e28	−	4.00526e27i	0.641827	−	0.210354i
$949$			8.69117e27i			0.451907i
$950$	−3.46715e28	−	2.51228e28i	−1.78484	−	1.29328i
$951$	1.23393e28			0.628889
$952$	−1.00075e28	−	3.20935e27i	−0.504982	−	0.161944i
$953$	−1.43987e28			−0.719349			−0.359675	−	0.933078i	$-0.617112\pi$
$953$	−1.43987e28			−0.719349			−0.359675	+	0.933078i	$0.617112\pi$
$954$	−7.14170e27	−	5.17484e27i	−0.353258	−	0.255969i
$955$		−	5.93879e28i		−	2.90848i
$956$	2.80222e27	+	8.55005e27i	0.135879	+	0.414590i
$957$			1.49783e27i			0.0719118i
$958$	−7.05015e27	+	9.72978e27i	−0.335140	+	0.462520i
$959$	−6.70146e27			−0.315423
$960$	−1.99243e28	−	1.42441e28i	−0.928551	−	0.663831i
$961$	5.79167e28			2.67259
$962$	−4.97614e27	+	6.86747e27i	−0.227368	+	0.313786i
$963$		−	5.79685e26i		−	0.0262266i
$964$	−3.28302e27	−	1.00170e28i	−0.147076	−	0.448754i
$965$			1.72894e27i			0.0766954i
$966$	7.63106e27	+	5.52943e27i	0.335198	+	0.242883i
$967$	−1.33691e28			−0.581500			−0.290750	−	0.956799i	$-0.593905\pi$
$967$	−1.33691e28			−0.581500			−0.290750	+	0.956799i	$0.593905\pi$
$968$	−2.18696e28	−	7.01342e27i	−0.941942	−	0.302075i
$969$	2.01181e28			0.858049
$970$	5.29209e28	+	3.83462e28i	2.23509	+	1.61954i
$971$			3.44674e28i			1.44154i	0.693176	+	0.720768i	$0.256211\pi$
$971$			3.44674e28i			1.44154i	−0.693176	+	0.720768i	$0.743789\pi$
$972$	−2.14204e28	+	7.02039e27i	−0.887152	+	0.290758i
$973$		−	1.87784e28i		−	0.770169i
$974$	−1.77642e28	+	2.45161e28i	−0.721499	+	0.995728i
$975$	8.43621e27			0.339315
$976$	9.47232e27	+	1.28986e28i	0.377297	+	0.513770i
$977$	3.40684e28			1.34386			0.671930	−	0.740615i	$-0.265466\pi$
$977$	3.40684e28			1.34386			0.671930	+	0.740615i	$0.265466\pi$
$978$	9.44446e27	−	1.30341e28i	0.368942	−	0.509170i
$979$			1.65462e27i			0.0640121i
$980$	3.15240e28	−	1.03318e28i	1.20779	−	0.395846i
$981$		−	1.53530e28i		−	0.582554i
$982$	7.09494e27	+	5.14096e27i	0.266618	+	0.193190i
$983$	1.47311e28			0.548246			0.274123	−	0.961695i	$-0.411612\pi$
$983$	1.47311e28			0.548246			0.274123	+	0.961695i	$0.411612\pi$
$984$	−6.46597e27	+	2.01625e28i	−0.238331	+	0.743173i
$985$	1.24472e28			0.454387
$986$	2.44418e28	+	1.77104e28i	0.883695	+	0.640321i
$987$		−	1.26181e27i		−	0.0451836i
$988$	−2.83417e27	−	8.64755e27i	−0.100516	−	0.306692i
$989$			2.31528e28i			0.813278i
$990$	1.60789e27	−	2.21901e27i	0.0559398	−	0.0772015i
$991$	−3.41639e28			−1.17725			−0.588623	−	0.808407i	$-0.700330\pi$
$991$	−3.41639e28			−1.17725			−0.588623	+	0.808407i	$0.700330\pi$
$992$	3.58183e26	+	5.61485e28i	0.0122249	+	1.91636i
$993$	−4.48110e27			−0.151484
$994$	9.67850e27	−	1.33571e28i	0.324069	−	0.447241i
$995$		−	7.05284e28i		−	2.33908i
$996$	−1.11403e28	−	3.39911e28i	−0.365961	−	1.11661i
$997$		−	2.85756e28i		−	0.929805i	−0.885362	−	0.464902i	$-0.846089\pi$
$997$		−	2.85756e28i		−	0.929805i	0.885362	−	0.464902i	$-0.153911\pi$
$998$	1.27307e28	+	9.22462e27i	0.410311	+	0.297309i
$999$	−4.66977e28			−1.49081

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.20.b.a.5.13	✓	18
3.2	odd	2		72.20.d.b.37.6		18
4.3	odd	2		32.20.b.a.17.12		18
8.3	odd	2		32.20.b.a.17.7		18
8.5	even	2	inner	8.20.b.a.5.14	yes	18
24.5	odd	2		72.20.d.b.37.5		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.20.b.a.5.13	✓	18	1.1	even	1	trivial
8.20.b.a.5.14	yes	18	8.5	even	2	inner
32.20.b.a.17.7		18	8.3	odd	2
32.20.b.a.17.12		18	4.3	odd	2
72.20.d.b.37.5		18	24.5	odd	2
72.20.d.b.37.6		18	3.2	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:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(424.854 - 586.333i) q^{2} -23044.3i q^{3} +(-163286. - 498212. i) q^{4} -7.37490e6i q^{5} +(-1.35116e7 - 9.79045e6i) q^{6} +5.30965e7 q^{7} +(-3.61491e8 - 1.15928e8i) q^{8} +6.31223e8 q^{9} +O(q^{10})\)	\(q+(424.854 - 586.333i) q^{2} -23044.3i q^{3} +(-163286. - 498212. i) q^{4} -7.37490e6i q^{5} +(-1.35116e7 - 9.79045e6i) q^{6} +5.30965e7 q^{7} +(-3.61491e8 - 1.15928e8i) q^{8} +6.31223e8 q^{9} +(-4.32415e9 - 3.13326e9i) q^{10} +8.12973e8i q^{11} +(-1.14809e10 + 3.76280e9i) q^{12} -1.03661e10i q^{13} +(2.25583e10 - 3.11322e10i) q^{14} -1.69949e11 q^{15} +(-2.21553e11 + 1.62702e11i) q^{16} +5.21391e11 q^{17} +(2.68178e11 - 3.70107e11i) q^{18} +1.67441e12i q^{19} +(-3.67427e12 + 1.20422e12i) q^{20} -1.22357e12i q^{21} +(4.76673e11 + 3.45395e11i) q^{22} -1.06368e13 q^{23} +(-2.67147e12 + 8.33030e12i) q^{24} -3.53156e13 q^{25} +(-6.07802e12 - 4.40410e12i) q^{26} -4.13295e13i q^{27} +(-8.66989e12 - 2.64533e13i) q^{28} +7.99511e13i q^{29} +(-7.22036e13 + 9.96468e13i) q^{30} +2.82112e14 q^{31} +(1.26965e12 + 1.99029e14i) q^{32} +1.87344e13 q^{33} +(2.21515e14 - 3.05709e14i) q^{34} -3.91581e14i q^{35} +(-1.03070e14 - 3.14483e14i) q^{36} -1.12989e15i q^{37} +(9.81761e14 + 7.11379e14i) q^{38} -2.38880e14 q^{39} +(-8.54956e14 + 2.66596e15i) q^{40} +2.42038e15 q^{41} +(-7.17419e14 - 5.19838e14i) q^{42} -2.17667e15i q^{43} +(4.05033e14 - 1.32747e14i) q^{44} -4.65521e15i q^{45} +(-4.51910e15 + 6.23672e15i) q^{46} +1.03125e15 q^{47} +(3.74935e15 + 5.10554e15i) q^{48} -8.57966e15 q^{49} +(-1.50040e16 + 2.07067e16i) q^{50} -1.20151e16i q^{51} +(-5.16454e15 + 1.69264e15i) q^{52} -1.92963e16i q^{53} +(-2.42329e16 - 1.75590e16i) q^{54} +5.99559e15 q^{55} +(-1.91939e16 - 6.15536e15i) q^{56} +3.85855e16 q^{57} +(4.68780e16 + 3.39676e16i) q^{58} +1.72226e16i q^{59} +(2.77503e16 + 8.46708e16i) q^{60} -5.82188e16i q^{61} +(1.19857e17 - 1.65412e17i) q^{62} +3.35157e16 q^{63} +(1.17237e17 + 8.38138e16i) q^{64} -7.64493e16 q^{65} +(7.95938e15 - 1.09846e16i) q^{66} +1.51600e17i q^{67} +(-8.51358e16 - 2.59764e17i) q^{68} +2.45118e17i q^{69} +(-2.29597e17 - 1.66365e17i) q^{70} +4.29045e17 q^{71} +(-2.28182e17 - 7.31764e16i) q^{72} -8.38419e17 q^{73} +(-6.62491e17 - 4.80037e17i) q^{74} +8.13823e17i q^{75} +(8.34211e17 - 2.73407e17i) q^{76} +4.31660e16i q^{77} +(-1.01489e17 + 1.40063e17i) q^{78} -1.06444e18 q^{79} +(1.19991e18 + 1.63393e18i) q^{80} -2.18762e17 q^{81} +(1.02831e18 - 1.41915e18i) q^{82} +2.96065e18i q^{83} +(-6.09597e17 + 1.99791e17i) q^{84} -3.84521e18i q^{85} +(-1.27625e18 - 9.24766e17i) q^{86} +1.84241e18 q^{87} +(9.42462e16 - 2.93883e17i) q^{88} +2.03527e18 q^{89} +(-2.72950e18 - 1.97779e18i) q^{90} -5.50405e17i q^{91} +(1.73684e18 + 5.29940e18i) q^{92} -6.50107e18i q^{93} +(4.38133e17 - 6.04659e17i) q^{94} +1.23486e19 q^{95} +(4.58647e18 - 2.92581e16i) q^{96} -1.22385e19 q^{97} +(-3.64511e18 + 5.03054e18i) q^{98} +5.13168e17i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 458 q^{2} - 412108 q^{4} - 47240948 q^{6} - 80707216 q^{7} - 173313752 q^{8} - 6198727826 q^{9}+O(q^{10}) \) 18 * q - 458 * q^2 - 412108 * q^4 - 47240948 * q^6 - 80707216 * q^7 - 173313752 * q^8 - 6198727826 * q^9	\( 18 q - 458 q^{2} - 412108 q^{4} - 47240948 q^{6} - 80707216 q^{7} - 173313752 q^{8} - 6198727826 q^{9} + 758800104 q^{10} - 9351642296 q^{12} - 122453668784 q^{14} + 156097960432 q^{15} - 696212072432 q^{16} + 14121426692 q^{17} + 1813497117770 q^{18} + 6517087595632 q^{20} - 11074654117412 q^{22} + 2177121583952 q^{23} - 36473014189168 q^{24} - 44414474211734 q^{25} + 26782030269304 q^{26} - 97002327802784 q^{28} + 327847200544208 q^{30} + 428505770260416 q^{31} + 122449430282912 q^{32} - 185380269683736 q^{33} - 478448330325748 q^{34} - 10\!\cdots\!36 q^{36}+ \cdots + 88\!\cdots\!22 q^{98}+O(q^{100}) \) 18 * q - 458 * q^2 - 412108 * q^4 - 47240948 * q^6 - 80707216 * q^7 - 173313752 * q^8 - 6198727826 * q^9 + 758800104 * q^10 - 9351642296 * q^12 - 122453668784 * q^14 + 156097960432 * q^15 - 696212072432 * q^16 + 14121426692 * q^17 + 1813497117770 * q^18 + 6517087595632 * q^20 - 11074654117412 * q^22 + 2177121583952 * q^23 - 36473014189168 * q^24 - 44414474211734 * q^25 + 26782030269304 * q^26 - 97002327802784 * q^28 + 327847200544208 * q^30 + 428505770260416 * q^31 + 122449430282912 * q^32 - 185380269683736 * q^33 - 478448330325748 * q^34 - 1053851053424436 * q^36 - 486194587539796 * q^38 + 942830575043152 * q^39 - 1697818250610976 * q^40 + 1200260021141524 * q^41 + 4964410757677984 * q^42 + 7031781193616424 * q^44 - 14917443628457488 * q^46 - 1134160959992928 * q^47 - 3197964747991392 * q^48 + 31570092936329058 * q^49 - 34734151321861826 * q^50 - 26877456911772208 * q^52 + 32102189624395064 * q^54 - 51757047863478736 * q^55 + 52858270161183424 * q^56 - 7740744140670520 * q^57 - 20470056808312424 * q^58 - 25825294995349152 * q^60 + 93766686763697984 * q^62 + 430168668665078416 * q^63 - 253721318369185216 * q^64 - 184007586011668640 * q^65 + 479551889901302712 * q^66 + 201388986348307752 * q^68 - 340698473416023872 * q^70 - 1599477989199799056 * q^71 - 115475454880420648 * q^72 - 93004298989809068 * q^73 - 93558253821761240 * q^74 - 1090379619519933176 * q^76 + 2029949680340770544 * q^78 + 1813975801025264480 * q^79 + 3057120301750869696 * q^80 + 1801762045144484330 * q^81 - 2418785089528546244 * q^82 + 141493317659087296 * q^84 + 1332333723895598620 * q^86 - 13124960835754102512 * q^87 - 3097741184498130608 * q^88 + 4470509771045743540 * q^89 - 288100905697646824 * q^90 - 2965990502259463392 * q^92 - 3533635112749329696 * q^94 + 23809730986995679856 * q^95 - 2990158800543707584 * q^96 + 8246429789464117220 * q^97 + 8841667592735478822 * q^98

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