LMFDB - Embedded newform 5.33.c.a.2.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,33,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, 33, names="a")

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

chi := DirichletCharacter("5.2");

S:= CuspForms(chi, 33);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 33 $
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:	$32.4333275711$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2.5
Character	$\chi$	$=$	5.2
Dual form			5.33.c.a.3.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-39535.2 - 39535.2i) q^{2} +(4.69567e7 - 4.69567e7i) q^{3} -1.16890e9i q^{4} +(-7.61848e10 + 1.32208e11i) q^{5} -3.71289e12 q^{6} +(2.85172e13 + 2.85172e13i) q^{7} +(-2.16015e14 + 2.16015e14i) q^{8} -2.55684e15i q^{9} +O(q^{10})$	\(q+(-39535.2 - 39535.2i) q^{2} +(4.69567e7 - 4.69567e7i) q^{3} -1.16890e9i q^{4} +(-7.61848e10 + 1.32208e11i) q^{5} -3.71289e12 q^{6} +(2.85172e13 + 2.85172e13i) q^{7} +(-2.16015e14 + 2.16015e14i) q^{8} -2.55684e15i q^{9} +(8.23885e15 - 2.21489e15i) q^{10} +6.29088e16 q^{11} +(-5.48877e16 - 5.48877e16i) q^{12} +(6.68945e17 - 6.68945e17i) q^{13} -2.25487e18i q^{14} +(2.63066e18 + 9.78543e18i) q^{15} +1.20600e19 q^{16} +(9.86415e17 + 9.86415e17i) q^{17} +(-1.01085e20 + 1.01085e20i) q^{18} +3.77787e20i q^{19} +(1.54538e20 + 8.90523e19i) q^{20} +2.67814e21 q^{21} +(-2.48712e21 - 2.48712e21i) q^{22} +(5.92343e21 - 5.92343e21i) q^{23} +2.02867e22i q^{24} +(-1.16748e22 - 2.01445e22i) q^{25} -5.28938e22 q^{26} +(-3.30491e22 - 3.30491e22i) q^{27} +(3.33337e22 - 3.33337e22i) q^{28} -2.77779e19i q^{29} +(2.82865e23 - 4.90873e23i) q^{30} -3.93433e23 q^{31} +(4.50982e23 + 4.50982e23i) q^{32} +(2.95399e24 - 2.95399e24i) q^{33} -7.79962e22i q^{34} +(-5.94277e24 + 1.59762e24i) q^{35} -2.98869e24 q^{36} +(-4.19934e24 - 4.19934e24i) q^{37} +(1.49359e25 - 1.49359e25i) q^{38} -6.28229e25i q^{39} +(-1.21019e25 - 4.50160e25i) q^{40} +8.53049e25 q^{41} +(-1.05881e26 - 1.05881e26i) q^{42} +(-8.89872e25 + 8.89872e25i) q^{43} -7.35341e25i q^{44} +(3.38035e26 + 1.94792e26i) q^{45} -4.68368e26 q^{46} +(3.07295e26 + 3.07295e26i) q^{47} +(5.66299e26 - 5.66299e26i) q^{48} +5.22031e26i q^{49} +(-3.34849e26 + 1.25798e27i) q^{50} +9.26375e25 q^{51} +(-7.81929e26 - 7.81929e26i) q^{52} +(4.54942e26 - 4.54942e26i) q^{53} +2.61321e27i q^{54} +(-4.79270e27 + 8.31705e27i) q^{55} -1.23203e28 q^{56} +(1.77396e28 + 1.77396e28i) q^{57} +(-1.09821e24 + 1.09821e24i) q^{58} -1.68462e28i q^{59} +(1.14382e28 - 3.07498e27i) q^{60} -1.17239e28 q^{61} +(1.55544e28 + 1.55544e28i) q^{62} +(7.29139e28 - 7.29139e28i) q^{63} -8.74568e28i q^{64} +(3.74764e28 + 1.39403e29i) q^{65} -2.33573e29 q^{66} +(-1.91395e29 - 1.91395e29i) q^{67} +(1.15302e27 - 1.15302e27i) q^{68} -5.56289e29i q^{69} +(2.98111e29 + 1.71786e29i) q^{70} -1.41479e29 q^{71} +(5.52317e29 + 5.52317e29i) q^{72} +(5.53990e29 - 5.53990e29i) q^{73} +3.32043e29i q^{74} +(-1.49413e30 - 3.97706e29i) q^{75} +4.41595e29 q^{76} +(1.79398e30 + 1.79398e30i) q^{77} +(-2.48372e30 + 2.48372e30i) q^{78} +1.90483e30i q^{79} +(-9.18791e29 + 1.59443e30i) q^{80} +1.63413e30 q^{81} +(-3.37255e30 - 3.37255e30i) q^{82} +(2.78325e30 - 2.78325e30i) q^{83} -3.13048e30i q^{84} +(-2.05562e29 + 5.52621e28i) q^{85} +7.03626e30 q^{86} +(-1.30436e27 - 1.30436e27i) q^{87} +(-1.35893e31 + 1.35893e31i) q^{88} -2.46808e30i q^{89} +(-5.66312e30 - 2.10654e31i) q^{90} +3.81528e31 q^{91} +(-6.92389e30 - 6.92389e30i) q^{92} +(-1.84743e31 + 1.84743e31i) q^{93} -2.42979e31i q^{94} +(-4.99464e31 - 2.87816e31i) q^{95} +4.23533e31 q^{96} +(4.72097e31 + 4.72097e31i) q^{97} +(2.06386e31 - 2.06386e31i) q^{98} -1.60848e32i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{2} - 2792232 q^{3} + 229266409900 q^{5} - 645476451240 q^{6} + 21807690136848 q^{7} + 340768936037220 q^{8}+O(q^{10}) $ 30 * q - 2 * q^2 - 2792232 * q^3 + 229266409900 * q^5 - 645476451240 * q^6 + 21807690136848 * q^7 + 340768936037220 * q^8	$ 30 q - 2 q^{2} - 2792232 q^{3} + 229266409900 q^{5} - 645476451240 q^{6} + 21807690136848 q^{7} + 340768936037220 q^{8} - 17\!\cdots\!50 q^{10}+ \cdots + 12\!\cdots\!02 q^{98}+O(q^{100}) $ 30 * q - 2 * q^2 - 2792232 * q^3 + 229266409900 * q^5 - 645476451240 * q^6 + 21807690136848 * q^7 + 340768936037220 * q^8 - 17555754485145450 * q^10 - 60908362837533640 * q^11 + 444566273630869608 * q^12 + 649759187023107138 * q^13 + 6285624407445962400 * q^15 - 46108906958970522120 * q^16 - 218107661739005884502 * q^17 + 240407468159884203858 * q^18 - 3053538044199826052700 * q^20 + 4549905652154594876760 * q^21 - 11386561172247365212944 * q^22 + 13896091629970965206008 * q^23 + 35772470267692728866250 * q^25 - 23129486500762683557740 * q^26 + 176388356775702789525960 * q^27 + 59665474478272755491112 * q^28 + 1233340129583886997444800 * q^30 - 1285786827516670637255040 * q^31 + 3122517776856150857591368 * q^32 - 1644615516923295701112504 * q^33 - 818578197767771892231200 * q^35 + 31947551193266858523505980 * q^36 - 126275105375668809211002 * q^37 + 57601564734016178366855880 * q^38 + 211125410957683032210619500 * q^40 - 155417315271390260892986440 * q^41 + 797836438482097707185724336 * q^42 - 545147034084978191886568152 * q^43 + 1085165439164371861108713450 * q^45 - 3454637097270705106900721640 * q^46 + 2735203198488492729395621848 * q^47 - 3192952350241941373327314192 * q^48 + 4470181549725126255525651250 * q^50 - 6129415060408014316542923040 * q^51 + 6000870590399837156109494028 * q^52 - 11282171275183571262774628682 * q^53 - 7112951743928365540876222200 * q^55 - 47918174764291639802549158800 * q^56 + 44765351794015370451647799120 * q^57 - 29637988346430122895588672480 * q^58 + 34183609322952768706653073800 * q^60 + 50784540875895586667393303160 * q^61 - 218235799024898727529128868024 * q^62 + 213794735887989269330759842008 * q^63 - 349686192916613591890379914850 * q^65 + 1348836243659025586642346421120 * q^66 - 736483403252315334072161239752 * q^67 + 1085395947449178489054935855012 * q^68 - 363042164247863030846151545400 * q^70 + 817740403780342392034746361760 * q^71 - 951267702824572414087545605820 * q^72 - 379868722209495311437504600242 * q^73 + 104600806158947004257336610000 * q^75 - 6689750080738358201358794259600 * q^76 + 6381539826853244422672988941256 * q^77 - 9179143477318522110451614982584 * q^78 + 5875581782593356038176152810400 * q^80 - 14239669107938661073624705472070 * q^81 + 2725313872720345364461277817936 * q^82 + 4996401755555614465785455997328 * q^83 - 4438937659194362238905211673950 * q^85 + 16049932109847278395442966171960 * q^86 + 36834415428157346041110451524480 * q^87 - 47132513308908068698430156048160 * q^88 + 81433975991640870510397972968150 * q^90 - 104150500668224029090357708737840 * q^91 - 18747876848872687606754750486552 * q^92 + 112210213536624471769268225064216 * q^93 - 109796172349696400850071817591000 * q^95 + 380819283905835347723966665116960 * q^96 - 155781506757725945270376012026802 * q^97 + 125692870459469366775669291878702 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−39535.2	−	39535.2i	−0.603260	−	0.603260i	0.337916	−	0.941176i	$-0.390278\pi$
$2$	−39535.2	−	39535.2i	−0.603260	−	0.603260i	−0.941176	+	0.337916i	$0.890278\pi$
$3$	4.69567e7	−	4.69567e7i	1.09083	−	1.09083i	0.0953909	−	0.995440i	$-0.469590\pi$
$3$	4.69567e7	−	4.69567e7i	1.09083	−	1.09083i	0.995440	−	0.0953909i	$-0.0304101\pi$
$4$		−	1.16890e9i		−	0.272156i
$5$	−7.61848e10	+	1.32208e11i	−0.499284	+	0.866438i
$5$	−7.61848e10	+	1.32208e11i	−0.499284	+	0.866438i
$6$	−3.71289e12			−1.31611
$7$	2.85172e13	+	2.85172e13i	0.858100	+	0.858100i	0.991114	−	0.133014i	$-0.0424655\pi$
$7$	2.85172e13	+	2.85172e13i	0.858100	+	0.858100i	−0.133014	+	0.991114i	$0.542466\pi$
$8$	−2.16015e14	+	2.16015e14i	−0.767440	+	0.767440i
$9$		−	2.55684e15i		−	1.37982i
$10$	8.23885e15	−	2.21489e15i	0.823885	−	0.221489i
$11$	6.29088e16			1.36908			0.684540	−	0.728975i	$-0.260003\pi$
$11$	6.29088e16			1.36908			0.684540	+	0.728975i	$0.260003\pi$
$12$	−5.48877e16	−	5.48877e16i	−0.296876	−	0.296876i
$13$	6.68945e17	−	6.68945e17i	1.00530	−	1.00530i	0.00531621	−	0.999986i	$-0.498308\pi$
$13$	6.68945e17	−	6.68945e17i	1.00530	−	1.00530i	0.999986	−	0.00531621i	$-0.00169221\pi$
$14$		−	2.25487e18i		−	1.03531i
$15$	2.63066e18	+	9.78543e18i	0.400503	+	1.48977i
$16$	1.20600e19			0.653776
$17$	9.86415e17	+	9.86415e17i	0.0202711	+	0.0202711i	0.717170	−	0.696899i	$-0.245437\pi$
$17$	9.86415e17	+	9.86415e17i	0.0202711	+	0.0202711i	−0.696899	+	0.717170i	$0.745437\pi$
$18$	−1.01085e20	+	1.01085e20i	−0.832392	+	0.832392i
$19$			3.77787e20i			1.30975i	0.755736	+	0.654876i	$0.227279\pi$
$19$			3.77787e20i			1.30975i	−0.755736	+	0.654876i	$0.772721\pi$
$20$	1.54538e20	+	8.90523e19i	0.235806	+	0.135883i
$21$	2.67814e21			1.87208
$22$	−2.48712e21	−	2.48712e21i	−0.825911	−	0.825911i
$23$	5.92343e21	−	5.92343e21i	0.965890	−	0.965890i	−0.0335474	−	0.999437i	$-0.510680\pi$
$23$	5.92343e21	−	5.92343e21i	0.965890	−	0.965890i	0.999437	+	0.0335474i	$0.0106805\pi$
$24$			2.02867e22i			1.67429i
$25$	−1.16748e22	−	2.01445e22i	−0.501430	−	0.865198i
$26$	−5.28938e22			−1.21292
$27$	−3.30491e22	−	3.30491e22i	−0.414323	−	0.414323i
$28$	3.33337e22	−	3.33337e22i	0.233537	−	0.233537i
$29$		−	2.77779e19i		−	0.000111002i	−1.00000		5.55011e-5i	$-0.999982\pi$
$29$		−	2.77779e19i		−	0.000111002i	1.00000		5.55011e-5i	$-1.76665e-5\pi$
$30$	2.82865e23	−	4.90873e23i	0.657112	−	1.14033i
$31$	−3.93433e23			−0.540858			−0.270429	−	0.962740i	$-0.587166\pi$
$31$	−3.93433e23			−0.540858			−0.270429	+	0.962740i	$0.587166\pi$
$32$	4.50982e23	+	4.50982e23i	0.373044	+	0.373044i
$33$	2.95399e24	−	2.95399e24i	1.49343	−	1.49343i
$34$		−	7.79962e22i		−	0.0244574i
$35$	−5.94277e24	+	1.59762e24i	−1.17193	+	0.315055i
$36$	−2.98869e24			−0.375527
$37$	−4.19934e24	−	4.19934e24i	−0.340371	−	0.340371i	0.516136	−	0.856507i	$-0.327370\pi$
$37$	−4.19934e24	−	4.19934e24i	−0.340371	−	0.340371i	−0.856507	+	0.516136i	$0.827370\pi$
$38$	1.49359e25	−	1.49359e25i	0.790121	−	0.790121i
$39$		−	6.28229e25i		−	2.19323i
$40$	−1.21019e25	−	4.50160e25i	−0.281768	−	1.04811i
$41$	8.53049e25			1.33793			0.668964	−	0.743295i	$-0.266738\pi$
$41$	8.53049e25			1.33793			0.668964	+	0.743295i	$0.266738\pi$
$42$	−1.05881e26	−	1.05881e26i	−1.12935	−	1.12935i
$43$	−8.89872e25	+	8.89872e25i	−0.651377	+	0.651377i	−0.953324	−	0.301948i	$-0.902363\pi$
$43$	−8.89872e25	+	8.89872e25i	−0.651377	+	0.651377i	0.301948	+	0.953324i	$0.402363\pi$
$44$		−	7.35341e25i		−	0.372603i
$45$	3.38035e26	+	1.94792e26i	1.19553	+	0.688925i
$46$	−4.68368e26			−1.16536
$47$	3.07295e26	+	3.07295e26i	0.541988	+	0.541988i	0.924111	−	0.382124i	$-0.124807\pi$
$47$	3.07295e26	+	3.07295e26i	0.541988	+	0.541988i	−0.382124	+	0.924111i	$0.624807\pi$
$48$	5.66299e26	−	5.66299e26i	0.713159	−	0.713159i
$49$			5.22031e26i			0.472671i
$50$	−3.34849e26	+	1.25798e27i	−0.219447	+	0.824432i
$51$	9.26375e25			0.0442246
$52$	−7.81929e26	−	7.81929e26i	−0.273599	−	0.273599i
$53$	4.54942e26	−	4.54942e26i	0.117366	−	0.117366i	−0.645984	−	0.763351i	$-0.723553\pi$
$53$	4.54942e26	−	4.54942e26i	0.117366	−	0.117366i	0.763351	+	0.645984i	$0.223553\pi$
$54$			2.61321e27i			0.499889i
$55$	−4.79270e27	+	8.31705e27i	−0.683560	+	1.18622i
$56$	−1.23203e28			−1.31708
$57$	1.77396e28	+	1.77396e28i	1.42872	+	1.42872i
$58$	−1.09821e24	+	1.09821e24i	−6.69631e−5	+	6.69631e-5i
$59$		−	1.68462e28i		−	0.781393i	−0.920520	−	0.390696i	$-0.872234\pi$
$59$		−	1.68462e28i		−	0.781393i	0.920520	−	0.390696i	$-0.127766\pi$
$60$	1.14382e28	−	3.07498e27i	0.405450	−	0.108999i
$61$	−1.17239e28			−0.319004			−0.159502	−	0.987198i	$-0.550989\pi$
$61$	−1.17239e28			−0.319004			−0.159502	+	0.987198i	$0.550989\pi$
$62$	1.55544e28	+	1.55544e28i	0.326278	+	0.326278i
$63$	7.29139e28	−	7.29139e28i	1.18403	−	1.18403i
$64$		−	8.74568e28i		−	1.10386i
$65$	3.74764e28	+	1.39403e29i	0.369100	+	1.37296i
$66$	−2.33573e29			−1.80186
$67$	−1.91395e29	−	1.91395e29i	−1.16074	−	1.16074i	−0.984315	−	0.176422i	$-0.943548\pi$
$67$	−1.91395e29	−	1.91395e29i	−1.16074	−	1.16074i	−0.176422	−	0.984315i	$-0.556452\pi$
$68$	1.15302e27	−	1.15302e27i	0.00551689	−	0.00551689i
$69$		−	5.56289e29i		−	2.10724i
$70$	2.98111e29	+	1.71786e29i	0.897036	+	0.516916i
$71$	−1.41479e29			−0.339279			−0.169640	−	0.985506i	$-0.554260\pi$
$71$	−1.41479e29			−0.339279			−0.169640	+	0.985506i	$0.554260\pi$
$72$	5.52317e29	+	5.52317e29i	1.05893	+	1.05893i
$73$	5.53990e29	−	5.53990e29i	0.851797	−	0.851797i	−0.138558	−	0.990354i	$-0.544247\pi$
$73$	5.53990e29	−	5.53990e29i	0.851797	−	0.851797i	0.990354	+	0.138558i	$0.0442467\pi$
$74$			3.32043e29i			0.410665i
$75$	−1.49413e30	−	3.97706e29i	−1.49076	−	0.396809i
$76$	4.41595e29			0.356456
$77$	1.79398e30	+	1.79398e30i	1.17481	+	1.17481i
$78$	−2.48372e30	+	2.48372e30i	−1.32309	+	1.32309i
$79$			1.90483e30i			0.827604i	0.910367	+	0.413802i	$0.135799\pi$
$79$			1.90483e30i			0.827604i	−0.910367	+	0.413802i	$0.864201\pi$
$80$	−9.18791e29	+	1.59443e30i	−0.326420	+	0.566456i
$81$	1.63413e30			0.475910
$82$	−3.37255e30	−	3.37255e30i	−0.807117	−	0.807117i
$83$	2.78325e30	−	2.78325e30i	0.548659	−	0.548659i	−0.377394	−	0.926053i	$-0.623180\pi$
$83$	2.78325e30	−	2.78325e30i	0.548659	−	0.548659i	0.926053	+	0.377394i	$0.123180\pi$
$84$		−	3.13048e30i		−	0.509498i
$85$	−2.05562e29	+	5.52621e28i	−0.0276847	+	0.00744260i
$86$	7.03626e30			0.785898
$87$	−1.30436e27	−	1.30436e27i	−0.000121085	−	0.000121085i
$88$	−1.35893e31	+	1.35893e31i	−1.05069	+	1.05069i
$89$		−	2.46808e30i		−	0.159265i	−0.996824	−	0.0796323i	$-0.974625\pi$
$89$		−	2.46808e30i		−	0.159265i	0.996824	−	0.0796323i	$-0.0253746\pi$
$90$	−5.66312e30	−	2.10654e31i	−0.305616	−	1.13682i
$91$	3.81528e31			1.72530
$92$	−6.92389e30	−	6.92389e30i	−0.262872	−	0.262872i
$93$	−1.84743e31	+	1.84743e31i	−0.589985	+	0.589985i
$94$		−	2.42979e31i		−	0.653919i
$95$	−4.99464e31	−	2.87816e31i	−1.13482	−	0.653939i
$96$	4.23533e31			0.813855
$97$	4.72097e31	+	4.72097e31i	0.768569	+	0.768569i	0.977855	−	0.209285i	$-0.0671137\pi$
$97$	4.72097e31	+	4.72097e31i	0.768569	+	0.768569i	−0.209285	+	0.977855i	$0.567114\pi$
$98$	2.06386e31	−	2.06386e31i	0.285144	−	0.285144i
$99$		−	1.60848e32i		−	1.88909i
$100$	−2.35469e31	+	1.36467e31i	−0.235469	+	0.136467i
$101$	−7.50238e31			−0.639819			−0.319909	−	0.947448i	$-0.603652\pi$
$101$	−7.50238e31			−0.639819			−0.319909	+	0.947448i	$0.603652\pi$
$102$	−3.66245e30	−	3.66245e30i	−0.0266789	−	0.0266789i
$103$	−7.84408e30	+	7.84408e30i	−0.0488817	+	0.0488817i	−0.731125	−	0.682243i	$-0.761004\pi$
$103$	−7.84408e30	+	7.84408e30i	−0.0488817	+	0.0488817i	0.682243	+	0.731125i	$0.261004\pi$
$104$			2.89004e32i			1.54302i
$105$	−2.04034e32	+	3.54072e32i	−0.934702	+	1.62204i
$106$	−3.59725e31			−0.141604
$107$	2.98505e32	+	2.98505e32i	1.01114	+	1.01114i	0.999937	+	0.0112018i	$0.00356572\pi$
$107$	2.98505e32	+	2.98505e32i	1.01114	+	1.01114i	0.0112018	+	0.999937i	$0.496434\pi$
$108$	−3.86311e31	+	3.86311e31i	−0.112760	+	0.112760i
$109$		−	2.49847e32i		−	0.629289i	−0.949210	−	0.314644i	$-0.898115\pi$
$109$		−	2.49847e32i		−	0.629289i	0.949210	−	0.314644i	$-0.101885\pi$
$110$	5.18297e32	−	1.39336e32i	1.12796	−	0.303236i
$111$	−3.94374e32			−0.742575
$112$	3.43918e32	+	3.43918e32i	0.561005	+	0.561005i
$113$	1.36893e32	−	1.36893e32i	0.193699	−	0.193699i	−0.603593	−	0.797292i	$-0.706265\pi$
$113$	1.36893e32	−	1.36893e32i	0.193699	−	0.193699i	0.797292	+	0.603593i	$0.206265\pi$
$114$		−	1.40268e33i		−	1.72378i
$115$	3.31849e32	+	1.23440e33i	0.354630	+	1.31914i
$116$	−3.24696e28			−3.02099e−5
$117$	−1.71039e33	−	1.71039e33i	−1.38714	−	1.38714i
$118$	−6.66018e32	+	6.66018e32i	−0.471383	+	0.471383i
$119$			5.62595e31i			0.0347892i
$120$	−2.68207e33	−	1.54554e33i	−1.45067	−	0.835949i
$121$	1.84615e33			0.874379
$122$	4.63508e32	+	4.63508e32i	0.192442	+	0.192442i
$123$	4.00564e33	−	4.00564e33i	1.45945	−	1.45945i
$124$			4.59883e32i			0.147198i
$125$	3.55270e33	−	8.80412e30i	0.999997	−	0.00247814i
$126$	−5.76533e33			−1.42855
$127$	9.12962e32	+	9.12962e32i	0.199339	+	0.199339i	0.799717	−	0.600377i	$-0.204983\pi$
$127$	9.12962e32	+	9.12962e32i	0.199339	+	0.199339i	−0.600377	+	0.799717i	$0.704983\pi$
$128$	−1.52067e33	+	1.52067e33i	−0.292871	+	0.292871i
$129$			8.35709e33i			1.42108i
$130$	4.02970e33	−	6.99298e33i	0.605590	−	1.05092i
$131$	8.11479e33			1.07879			0.539394	−	0.842053i	$-0.318653\pi$
$131$	8.11479e33			1.07879			0.539394	+	0.842053i	$0.318653\pi$
$132$	−3.45292e33	−	3.45292e33i	−0.406447	−	0.406447i
$133$	−1.07734e34	+	1.07734e34i	−1.12390	+	1.12390i
$134$			1.51337e34i			1.40045i
$135$	6.88719e33	−	1.85152e33i	0.565851	−	0.152120i
$136$	−4.26161e32			−0.0311137
$137$	−1.69300e34	−	1.69300e34i	−1.09933	−	1.09933i	−0.994489	−	0.104842i	$-0.966566\pi$
$137$	−1.69300e34	−	1.69300e34i	−1.09933	−	1.09933i	−0.104842	−	0.994489i	$-0.533434\pi$
$138$	−2.19930e34	+	2.19930e34i	−1.27122	+	1.27122i
$139$			2.64534e32i			0.0136221i	0.999977	+	0.00681107i	$0.00216805\pi$
$139$			2.64534e32i			0.0136221i	−0.999977	+	0.00681107i	$0.997832\pi$
$140$	1.86746e33	+	6.94650e33i	0.0857439	+	0.318946i
$141$	2.88591e34			1.18243
$142$	5.59339e33	+	5.59339e33i	0.204673	+	0.204673i
$143$	4.20825e34	−	4.20825e34i	1.37634	−	1.37634i
$144$		−	3.08356e34i		−	0.902095i
$145$	3.67246e30	+	2.11625e30i	9.61765e−5	+	5.54217e-5i
$146$	−4.38042e34			−1.02771
$147$	2.45129e34	+	2.45129e34i	0.515605	+	0.515605i
$148$	−4.90860e33	+	4.90860e33i	−0.0926340	+	0.0926340i
$149$		−	7.97866e33i		−	0.135192i	−0.997713	−	0.0675958i	$-0.978467\pi$
$149$		−	7.97866e33i		−	0.135192i	0.997713	−	0.0675958i	$-0.0215328\pi$
$150$	4.33473e34	+	7.47941e34i	0.659936	+	1.13869i
$151$	−5.06801e34			−0.693756			−0.346878	−	0.937910i	$-0.612758\pi$
$151$	−5.06801e34			−0.693756			−0.346878	+	0.937910i	$0.612758\pi$
$152$	−8.16077e34	−	8.16077e34i	−1.00516	−	1.00516i
$153$	2.52211e33	−	2.52211e33i	0.0279705	−	0.0279705i
$154$		−	1.41851e35i		−	1.41743i
$155$	2.99736e34	−	5.20149e34i	0.270042	−	0.468620i
$156$	−7.34336e34			−0.596900
$157$	7.62382e34	+	7.62382e34i	0.559472	+	0.559472i	0.929157	−	0.369685i	$-0.120535\pi$
$157$	7.62382e34	+	7.62382e34i	0.559472	+	0.559472i	−0.369685	+	0.929157i	$0.620535\pi$
$158$	7.53079e34	−	7.53079e34i	0.499260	−	0.499260i
$159$		−	4.27252e34i		−	0.256053i
$160$	−9.39814e34	+	2.52655e34i	−0.509474	+	0.136964i
$161$	3.37839e35			1.65766
$162$	−6.46055e34	−	6.46055e34i	−0.287097	−	0.287097i
$163$	−2.81526e35	+	2.81526e35i	−1.13375	+	1.13375i	−0.144200	+	0.989549i	$0.546061\pi$
$163$	−2.81526e35	+	2.81526e35i	−1.13375	+	1.13375i	−0.989549	+	0.144200i	$0.953939\pi$
$164$		−	9.97129e34i		−	0.364124i
$165$	1.65492e35	+	6.15590e35i	0.548320	+	2.03962i
$166$	−2.20073e35			−0.661968
$167$	1.74820e35	+	1.74820e35i	0.477670	+	0.477670i	0.904386	−	0.426716i	$-0.140330\pi$
$167$	1.74820e35	+	1.74820e35i	0.477670	+	0.477670i	−0.426716	+	0.904386i	$0.640330\pi$
$168$	−5.78520e35	+	5.78520e35i	−1.43671	+	1.43671i
$169$		−	4.52195e35i		−	1.02126i
$170$	1.03117e34	+	5.94213e33i	0.0211909	+	0.0122112i
$171$	9.65941e35			1.80723
$172$	1.04017e35	+	1.04017e35i	0.177276	+	0.177276i
$173$	−4.55117e35	+	4.55117e35i	−0.706944	+	0.706944i	−0.965891	−	0.258947i	$-0.916624\pi$
$173$	−4.55117e35	+	4.55117e35i	−0.706944	+	0.706944i	0.258947	+	0.965891i	$0.416624\pi$
$174$			1.03136e32i			0.000146091i
$175$	2.41530e35	−	9.07397e35i	0.312149	−	1.17270i
$176$	7.58683e35			0.895071
$177$	−7.91041e35	−	7.91041e35i	−0.852367	−	0.852367i
$178$	−9.75761e34	+	9.75761e34i	−0.0960778	+	0.0960778i
$179$		−	1.66069e36i		−	1.49500i	−0.664262	−	0.747500i	$-0.731254\pi$
$179$		−	1.66069e36i		−	1.49500i	0.664262	−	0.747500i	$-0.268746\pi$
$180$	2.27693e35	−	3.95129e35i	0.187495	−	0.325371i
$181$	−5.92307e35			−0.446365			−0.223182	−	0.974777i	$-0.571645\pi$
$181$	−5.92307e35			−0.446365			−0.223182	+	0.974777i	$0.571645\pi$
$182$	−1.50838e36	−	1.50838e36i	−1.04080	−	1.04080i
$183$	−5.50517e35	+	5.50517e35i	−0.347979	+	0.347979i
$184$			2.55910e36i			1.48253i
$185$	8.75111e35	−	2.35260e35i	0.464853	−	0.124969i
$186$	1.46077e36			0.711828
$187$	6.20542e34	+	6.20542e34i	0.0277527	+	0.0277527i
$188$	3.59197e35	−	3.59197e35i	0.147505	−	0.147505i
$189$		−	1.88493e36i		−	0.711062i
$190$	8.36756e35	+	3.11253e36i	0.290096	+	1.07909i
$191$	2.28483e36			0.728317			0.364158	−	0.931337i	$-0.381357\pi$
$191$	2.28483e36			0.728317			0.364158	+	0.931337i	$0.381357\pi$
$192$	−4.10668e36	−	4.10668e36i	−1.20412	−	1.20412i
$193$	−2.78936e36	+	2.78936e36i	−0.752640	+	0.752640i	−0.974971	−	0.222331i	$-0.928633\pi$
$193$	−2.78936e36	+	2.78936e36i	−0.752640	+	0.752640i	0.222331	+	0.974971i	$0.428633\pi$
$194$		−	3.73289e36i		−	0.927294i
$195$	8.30568e36	+	4.78614e36i	1.90030	+	1.09505i
$196$	6.10202e35			0.128640
$197$	3.43604e36	+	3.43604e36i	0.667726	+	0.667726i	0.957189	−	0.289463i	$-0.0934768\pi$
$197$	3.43604e36	+	3.43604e36i	0.667726	+	0.667726i	−0.289463	+	0.957189i	$0.593477\pi$
$198$	−6.35916e36	+	6.35916e36i	−1.13961	+	1.13961i
$199$		−	6.51209e36i		−	1.07664i	−0.842740	−	0.538321i	$-0.819059\pi$
$199$		−	6.51209e36i		−	1.07664i	0.842740	−	0.538321i	$-0.180941\pi$
$200$	6.87345e36	+	1.82957e36i	1.04881	+	0.279170i
$201$	−1.79745e37			−2.53233
$202$	2.96608e36	+	2.96608e36i	0.385977	+	0.385977i
$203$	7.92147e32	−	7.92147e32i	9.52510e−5	−	9.52510e-5i
$204$		−	1.08284e35i		−	0.0120360i
$205$	−6.49894e36	+	1.12780e37i	−0.668006	+	1.15923i
$206$	6.20235e35			0.0589767
$207$	−1.51453e37	−	1.51453e37i	−1.33276	−	1.33276i
$208$	8.06749e36	−	8.06749e36i	0.657242	−	0.657242i
$209$			2.37661e37i			1.79316i
$210$	2.20648e37	−	5.93180e36i	1.54238	−	0.414646i
$211$	2.09448e37			1.35693			0.678464	−	0.734633i	$-0.262646\pi$
$211$	2.09448e37			1.35693			0.678464	+	0.734633i	$0.262646\pi$
$212$	−5.31782e35	−	5.31782e35i	−0.0319418	−	0.0319418i
$213$	−6.64337e36	+	6.64337e36i	−0.370096	+	0.370096i
$214$		−	2.36029e37i		−	1.21996i
$215$	−4.98535e36	−	1.85443e37i	−0.239155	−	0.889600i
$216$	1.42782e37			0.635937
$217$	−1.12196e37	−	1.12196e37i	−0.464110	−	0.464110i
$218$	−9.87775e36	+	9.87775e36i	−0.379625	+	0.379625i
$219$		−	5.20270e37i		−	1.85833i
$220$	9.72180e36	+	5.60218e36i	0.322837	+	0.186035i
$221$	1.31971e36			0.0407571
$222$	1.55917e37	+	1.55917e37i	0.447966	+	0.447966i
$223$	−4.23335e37	+	4.23335e37i	−1.13190	+	1.13190i	−0.142035	+	0.989862i	$0.545365\pi$
$223$	−4.23335e37	+	4.23335e37i	−1.13190	+	1.13190i	−0.989862	+	0.142035i	$0.954635\pi$
$224$			2.57215e37i			0.640218i
$225$	−5.15062e37	+	2.98507e37i	−1.19382	+	0.691885i
$226$	−1.08242e37			−0.233701
$227$	−2.72163e37	−	2.72163e37i	−0.547540	−	0.547540i	0.378189	−	0.925729i	$-0.376547\pi$
$227$	−2.72163e37	−	2.72163e37i	−0.547540	−	0.547540i	−0.925729	+	0.378189i	$0.876547\pi$
$228$	2.07358e37	−	2.07358e37i	0.388834	−	0.388834i
$229$		−	8.21268e37i		−	1.43588i	−0.696107	−	0.717938i	$-0.745086\pi$
$229$		−	8.21268e37i		−	1.43588i	0.696107	−	0.717938i	$-0.254914\pi$
$230$	3.56825e37	−	6.19220e37i	0.581848	−	1.00972i
$231$	1.68479e38			2.56303
$232$	6.00045e33	+	6.00045e33i	8.51875e−5	+	8.51875e-5i
$233$	−8.56463e37	+	8.56463e37i	−1.13505	+	1.13505i	−0.145721	+	0.989326i	$0.546550\pi$
$233$	−8.56463e37	+	8.56463e37i	−1.13505	+	1.13505i	−0.989326	+	0.145721i	$0.953450\pi$
$234$			1.35241e38i			1.67361i
$235$	−6.40380e37	+	1.72156e37i	−0.740205	+	0.198993i
$236$	−1.96915e37			−0.212660
$237$	8.94445e37	+	8.94445e37i	0.902776	+	0.902776i
$238$	2.22423e36	−	2.22423e36i	0.0209869	−	0.0209869i
$239$			6.49375e37i			0.572966i	0.958085	+	0.286483i	$0.0924862\pi$
$239$			6.49375e37i			0.572966i	−0.958085	+	0.286483i	$0.907514\pi$
$240$	3.17259e37	+	1.18013e38i	0.261839	+	0.973977i
$241$	−4.79578e37			−0.370328			−0.185164	−	0.982708i	$-0.559282\pi$
$241$	−4.79578e37			−0.370328			−0.185164	+	0.982708i	$0.559282\pi$
$242$	−7.29878e37	−	7.29878e37i	−0.527478	−	0.527478i
$243$	1.37974e38	−	1.37974e38i	0.933461	−	0.933461i
$244$			1.37041e37i			0.0868187i
$245$	−6.90167e37	−	3.97708e37i	−0.409541	−	0.235998i
$246$	−3.16728e38			−1.76086
$247$	2.52718e38	+	2.52718e38i	1.31670	+	1.31670i
$248$	8.49874e37	−	8.49874e37i	0.415076	−	0.415076i
$249$		−	2.61384e38i		−	1.19699i
$250$	−1.40805e38	−	1.40109e38i	−0.604753	−	0.601763i
$251$	−1.70220e38			−0.685851			−0.342926	−	0.939363i	$-0.611418\pi$
$251$	−1.70220e38			−0.685851			−0.342926	+	0.939363i	$0.611418\pi$
$252$	−8.52290e37	−	8.52290e37i	−0.322240	−	0.322240i
$253$	3.72636e38	−	3.72636e38i	1.32238	−	1.32238i
$254$		−	7.21883e37i		−	0.240507i
$255$	−7.05757e36	+	1.22474e37i	−0.0220807	+	0.0383179i
$256$	−2.55384e38			−0.750506
$257$	2.03465e38	+	2.03465e38i	0.561772	+	0.561772i	0.929810	−	0.368039i	$-0.119971\pi$
$257$	2.03465e38	+	2.03465e38i	0.561772	+	0.561772i	−0.368039	+	0.929810i	$0.619971\pi$
$258$	3.30399e38	−	3.30399e38i	0.857282	−	0.857282i
$259$		−	2.39506e38i		−	0.584145i
$260$	1.62948e38	−	4.38062e37i	0.373660	−	0.100453i
$261$	−7.10237e34			−0.000153163
$262$	−3.20820e38	−	3.20820e38i	−0.650790	−	0.650790i
$263$	−5.13008e38	+	5.13008e38i	−0.979111	+	0.979111i	−0.999786	−	0.0206750i	$-0.993418\pi$
$263$	−5.13008e38	+	5.13008e38i	−0.979111	+	0.979111i	0.0206750	+	0.999786i	$0.493418\pi$
$264$			1.27621e39i			2.29224i
$265$	2.54873e37	+	9.48067e37i	0.0430914	+	0.160289i
$266$	8.51859e38			1.35601
$267$	−1.15893e38	−	1.15893e38i	−0.173731	−	0.173731i
$268$	−2.23721e38	+	2.23721e38i	−0.315901	+	0.315901i
$269$			9.62084e38i			1.27990i	0.768416	+	0.639951i	$0.221045\pi$
$269$			9.62084e38i			1.27990i	−0.768416	+	0.639951i	$0.778955\pi$
$270$	−3.45487e38	−	1.99087e38i	−0.433123	−	0.249587i
$271$	−9.79970e38			−1.15799			−0.578994	−	0.815332i	$-0.696555\pi$
$271$	−9.79970e38			−1.15799			−0.578994	+	0.815332i	$0.696555\pi$
$272$	1.18962e37	+	1.18962e37i	0.0132527	+	0.0132527i
$273$	1.79153e39	−	1.79153e39i	1.88201	−	1.88201i
$274$			1.33866e39i			1.32636i
$275$	−7.34450e38	−	1.26727e39i	−0.686498	−	1.18453i
$276$	−6.50246e38			−0.573498
$277$	1.18648e39	+	1.18648e39i	0.987607	+	0.987607i	0.999924	−	0.0123171i	$-0.00392076\pi$
$277$	1.18648e39	+	1.18648e39i	0.987607	+	0.987607i	−0.0123171	+	0.999924i	$0.503921\pi$
$278$	1.04584e37	−	1.04584e37i	0.00821769	−	0.00821769i
$279$			1.00594e39i			0.746289i
$280$	9.38618e38	−	1.62884e39i	0.657598	−	1.14117i
$281$	1.83305e39			1.21303			0.606516	−	0.795071i	$-0.292567\pi$
$281$	1.83305e39			1.21303			0.606516	+	0.795071i	$0.292567\pi$
$282$	−1.14095e39	−	1.14095e39i	−0.713315	−	0.713315i
$283$	−1.81229e39	+	1.81229e39i	−1.07064	+	1.07064i	−0.0733339	+	0.997307i	$0.523364\pi$
$283$	−1.81229e39	+	1.81229e39i	−1.07064	+	1.07064i	−0.997307	+	0.0733339i	$0.976636\pi$
$284$			1.65374e38i			0.0923368i
$285$	−3.69681e39	+	9.93830e38i	−1.95123	+	0.524559i
$286$	−3.32749e39			−1.66058
$287$	2.43266e39	+	2.43266e39i	1.14808	+	1.14808i
$288$	1.15309e39	−	1.15309e39i	0.514735	−	0.514735i
$289$		−	2.36597e39i		−	0.999178i
$290$	−6.15250e34	−	2.28858e35i	−2.45858e−5	−	9.14531e-5i
$291$	4.43362e39			1.67676
$292$	−6.47558e38	−	6.47558e38i	−0.231821	−	0.231821i
$293$	2.36618e39	−	2.36618e39i	0.801985	−	0.801985i	−0.181421	−	0.983406i	$-0.558070\pi$
$293$	2.36618e39	−	2.36618e39i	0.801985	−	0.801985i	0.983406	+	0.181421i	$0.0580696\pi$
$294$		−	1.93824e39i		−	0.622087i
$295$	2.22720e39	+	1.28342e39i	0.677029	+	0.390137i
$296$	1.81424e39			0.522429
$297$	−2.07908e39	−	2.07908e39i	−0.567242	−	0.567242i
$298$	−3.15438e38	+	3.15438e38i	−0.0815557	+	0.0815557i
$299$		−	7.92489e39i		−	1.94202i
$300$	−4.64878e38	+	1.74649e39i	−0.107994	+	0.405719i
$301$	−5.07533e39			−1.11789
$302$	2.00365e39	+	2.00365e39i	0.418515	+	0.418515i
$303$	−3.52287e39	+	3.52287e39i	−0.697934	+	0.697934i
$304$			4.55612e39i			0.856284i
$305$	8.93185e38	−	1.55000e39i	0.159274	−	0.276397i
$306$	−1.99424e38			−0.0337470
$307$	−2.91493e39	−	2.91493e39i	−0.468182	−	0.468182i	0.433143	−	0.901325i	$-0.357404\pi$
$307$	−2.91493e39	−	2.91493e39i	−0.468182	−	0.468182i	−0.901325	+	0.433143i	$0.857404\pi$
$308$	2.09699e39	−	2.09699e39i	0.319730	−	0.319730i
$309$			7.36664e38i			0.106643i
$310$	−3.24143e39	+	8.71410e38i	−0.445605	+	0.119794i
$311$	−1.21125e40			−1.58150			−0.790749	−	0.612140i	$-0.790309\pi$
$311$	−1.21125e40			−1.58150			−0.790749	+	0.612140i	$0.790309\pi$
$312$	1.35707e40	+	1.35707e40i	1.68317	+	1.68317i
$313$	−2.91575e39	+	2.91575e39i	−0.343590	+	0.343590i	−0.857715	−	0.514125i	$-0.828117\pi$
$313$	−2.91575e39	+	2.91575e39i	−0.343590	+	0.343590i	0.514125	+	0.857715i	$0.328117\pi$
$314$		−	6.02819e39i		−	0.675013i
$315$	4.08487e39	+	1.51947e40i	0.434720	+	1.61705i
$316$	2.22655e39			0.225237
$317$	−1.73245e39	−	1.73245e39i	−0.166614	−	0.166614i	0.618875	−	0.785489i	$-0.287589\pi$
$317$	−1.73245e39	−	1.73245e39i	−0.166614	−	0.166614i	−0.785489	+	0.618875i	$0.787589\pi$
$318$	−1.68915e39	+	1.68915e39i	−0.154466	+	0.154466i
$319$		−	1.74748e36i		−	0.000151971i
$320$	1.15625e40	+	6.66288e39i	0.956426	+	0.551140i
$321$	2.80336e40			2.20596
$322$	−1.33565e40	−	1.33565e40i	−0.999999	−	0.999999i
$323$	−3.72654e38	+	3.72654e38i	−0.0265501	+	0.0265501i
$324$		−	1.91013e39i		−	0.129522i
$325$	−2.12853e40	−	5.66572e39i	−1.37387	−	0.365697i
$326$	2.22604e40			1.36789
$327$	−1.17320e40	−	1.17320e40i	−0.686448	−	0.686448i
$328$	−1.84272e40	+	1.84272e40i	−1.02678	+	1.02678i
$329$			1.75264e40i			0.930159i
$330$	1.77947e40	−	3.08803e40i	0.899639	−	1.56120i
$331$	−3.29585e40			−1.58752			−0.793761	−	0.608230i	$-0.791880\pi$
$331$	−3.29585e40			−1.58752			−0.793761	+	0.608230i	$0.791880\pi$
$332$	−3.25334e39	−	3.25334e39i	−0.149321	−	0.149321i
$333$	−1.07370e40	+	1.07370e40i	−0.469652	+	0.469652i
$334$		−	1.38231e40i		−	0.576318i
$335$	3.98853e40	−	1.07226e40i	1.58524	−	0.426169i
$336$	3.22985e40			1.22392
$337$	−2.99278e40	−	2.99278e40i	−1.08143	−	1.08143i	−0.996377	−	0.0850487i	$-0.972895\pi$
$337$	−2.99278e40	−	2.99278e40i	−1.08143	−	1.08143i	−0.0850487	−	0.996377i	$-0.527105\pi$
$338$	−1.78776e40	+	1.78776e40i	−0.616088	+	0.616088i
$339$		−	1.28561e40i		−	0.422585i
$340$	6.45959e37	+	2.40281e38i	0.00202555	+	0.00753454i
$341$	−2.47504e40			−0.740478
$342$	−3.81887e40	−	3.81887e40i	−1.09023	−	1.09023i
$343$	1.66083e40	−	1.66083e40i	0.452501	−	0.452501i
$344$		−	3.84452e40i		−	0.999785i
$345$	7.35458e40	+	4.23807e40i	1.82580	+	1.05211i
$346$	3.59863e40			0.852942
$347$	4.29749e40	+	4.29749e40i	0.972619	+	0.972619i	0.999635	−	0.0270159i	$-0.00860047\pi$
$347$	4.29749e40	+	4.29749e40i	0.972619	+	0.972619i	−0.0270159	+	0.999635i	$0.508600\pi$
$348$	−1.52466e36	+	1.52466e36i	−3.29539e−5	+	3.29539e-5i
$349$			2.89824e40i			0.598311i	0.954204	+	0.299156i	$0.0967049\pi$
$349$			2.89824e40i			0.598311i	−0.954204	+	0.299156i	$0.903295\pi$
$350$	−4.54231e40	+	2.63252e40i	−0.895752	+	0.519138i
$351$	−4.42160e40			−0.833040
$352$	2.83708e40	+	2.83708e40i	0.510727	+	0.510727i
$353$	3.40782e39	−	3.40782e39i	0.0586248	−	0.0586248i	−0.677187	−	0.735811i	$-0.736801\pi$
$353$	3.40782e39	−	3.40782e39i	0.0586248	−	0.0586248i	0.735811	+	0.677187i	$0.236801\pi$
$354$			6.25480e40i			1.02840i
$355$	1.07785e40	−	1.87046e40i	0.169397	−	0.293965i
$356$	−2.88494e39			−0.0433447
$357$	2.64176e39	+	2.64176e39i	0.0379492	+	0.0379492i
$358$	−6.56559e40	+	6.56559e40i	−0.901873	+	0.901873i
$359$			5.42658e39i			0.0712877i	0.999365	+	0.0356439i	$0.0113482\pi$
$359$			5.42658e39i			0.0712877i	−0.999365	+	0.0356439i	$0.988652\pi$
$360$	−1.15099e41	+	3.09425e40i	−1.44621	+	0.388791i
$361$	−5.95244e40			−0.715451
$362$	2.34170e40	+	2.34170e40i	0.269274	+	0.269274i
$363$	8.66889e40	−	8.66889e40i	0.953800	−	0.953800i
$364$		−	4.45968e40i		−	0.469550i
$365$	3.10363e40	+	1.15447e41i	0.312740	+	1.16332i
$366$	4.35296e40			0.419844
$367$	1.06545e40	+	1.06545e40i	0.0983731	+	0.0983731i	0.754581	−	0.656207i	$-0.227840\pi$
$367$	1.06545e40	+	1.06545e40i	0.0983731	+	0.0983731i	−0.656207	+	0.754581i	$0.727840\pi$
$368$	7.14367e40	−	7.14367e40i	0.631475	−	0.631475i
$369$		−	2.18111e41i		−	1.84610i
$370$	−4.38988e40	−	2.52966e40i	−0.355815	−	0.205038i
$371$	2.59473e40			0.201424
$372$	2.15946e40	+	2.15946e40i	0.160568	+	0.160568i
$373$	−7.61669e40	+	7.61669e40i	−0.542531	+	0.542531i	−0.924270	−	0.381739i	$-0.875325\pi$
$373$	−7.61669e40	+	7.61669e40i	−0.542531	+	0.542531i	0.381739	+	0.924270i	$0.375325\pi$
$374$		−	4.90665e39i		−	0.0334842i
$375$	1.66410e41	−	1.67237e41i	1.08812	−	1.09353i
$376$	−1.32761e41			−0.831886
$377$	−1.85819e37	−	1.85819e37i	−0.000111591	−	0.000111591i
$378$	−7.45213e40	+	7.45213e40i	−0.428955	+	0.428955i
$379$			1.33071e40i			0.0734272i	0.999326	+	0.0367136i	$0.0116889\pi$
$379$			1.33071e40i			0.0734272i	−0.999326	+	0.0367136i	$0.988311\pi$
$380$	−3.36428e40	+	5.83824e40i	−0.177973	+	0.308847i
$381$	8.57394e40			0.434891
$382$	−9.03313e40	−	9.03313e40i	−0.439364	−	0.439364i
$383$	1.44371e41	−	1.44371e41i	0.673443	−	0.673443i	−0.285065	−	0.958508i	$-0.592015\pi$
$383$	1.44371e41	−	1.44371e41i	0.673443	−	0.673443i	0.958508	+	0.285065i	$0.0920153\pi$
$384$			1.42811e41i			0.638944i
$385$	−3.73853e41	+	1.00505e41i	−1.60446	+	0.431335i
$386$	2.20556e41			0.908075
$387$	2.27526e41	+	2.27526e41i	0.898785	+	0.898785i
$388$	5.51834e40	−	5.51834e40i	0.209171	−	0.209171i
$389$			2.16396e41i			0.787146i	0.919293	+	0.393573i	$0.128761\pi$
$389$			2.16396e41i			0.787146i	−0.919293	+	0.393573i	$0.871239\pi$
$390$	−1.39146e41	−	5.17588e41i	−0.485776	−	1.80697i
$391$	1.16859e40			0.0391592
$392$	−1.12767e41	−	1.12767e41i	−0.362747	−	0.362747i
$393$	3.81043e41	−	3.81043e41i	1.17678	−	1.17678i
$394$		−	2.71689e41i		−	0.805624i
$395$	−2.51834e41	−	1.45119e41i	−0.717068	−	0.413210i
$396$	−1.88015e41			−0.514126
$397$	−2.96206e40	−	2.96206e40i	−0.0777938	−	0.0777938i	0.667139	−	0.744933i	$-0.267519\pi$
$397$	−2.96206e40	−	2.96206e40i	−0.0777938	−	0.0777938i	−0.744933	+	0.667139i	$0.767519\pi$
$398$	−2.57457e41	+	2.57457e41i	−0.649494	+	0.649494i
$399$			1.01177e42i			2.45197i
$400$	−1.40799e41	−	2.42943e41i	−0.327823	−	0.565646i
$401$	2.99873e41			0.670853			0.335427	−	0.942066i	$-0.391120\pi$
$401$	2.99873e41			0.670853			0.335427	+	0.942066i	$0.391120\pi$
$402$	7.10628e41	+	7.10628e41i	1.52765	+	1.52765i
$403$	−2.63185e41	+	2.63185e41i	−0.543726	+	0.543726i
$404$			8.76953e40i			0.174130i
$405$	−1.24495e41	+	2.16044e41i	−0.237615	+	0.412347i
$406$	−6.26355e37			−0.000114922
$407$	−2.64175e41	−	2.64175e41i	−0.465996	−	0.465996i
$408$	−2.00111e40	+	2.00111e40i	−0.0339398	+	0.0339398i
$409$			3.93446e40i			0.0641670i	0.999485	+	0.0320835i	$0.0102143\pi$
$409$			3.93446e40i			0.0641670i	−0.999485	+	0.0320835i	$0.989786\pi$
$410$	7.02815e41	−	1.88941e41i	1.10230	−	0.296336i
$411$	−1.58995e42			−2.39837
$412$	9.16894e39	+	9.16894e39i	0.0133034	+	0.0133034i
$413$	4.80406e41	−	4.80406e41i	0.670513	−	0.670513i
$414$			1.19754e42i			1.60800i
$415$	1.55927e41	+	5.80009e41i	0.201442	+	0.749316i
$416$	6.03364e41			0.750043
$417$	1.24217e40	+	1.24217e40i	0.0148595	+	0.0148595i
$418$	9.39599e41	−	9.39599e41i	1.08174	−	1.08174i
$419$		−	7.00287e41i		−	0.775982i	−0.921663	−	0.387991i	$-0.873169\pi$
$419$		−	7.00287e41i		−	0.775982i	0.921663	−	0.387991i	$-0.126831\pi$
$420$	4.13875e41	+	2.38495e41i	0.441449	+	0.254385i
$421$	−9.56131e41			−0.981756			−0.490878	−	0.871228i	$-0.663324\pi$
$421$	−9.56131e41			−0.981756			−0.490878	+	0.871228i	$0.663324\pi$
$422$	−8.28058e41	−	8.28058e41i	−0.818580	−	0.818580i
$423$	7.85704e41	−	7.85704e41i	0.747848	−	0.747848i
$424$			1.96549e41i			0.180143i
$425$	8.35457e39	−	3.13870e40i	0.00737397	−	0.0277030i
$426$	5.25294e41			0.446528
$427$	−3.34333e41	−	3.34333e41i	−0.273737	−	0.273737i
$428$	3.48922e41	−	3.48922e41i	0.275187	−	0.275187i
$429$		−	3.95211e42i		−	3.00271i
$430$	−5.36055e41	+	9.30249e41i	−0.392387	+	0.680932i
$431$	−1.48305e42			−1.04597			−0.522987	−	0.852341i	$-0.675182\pi$
$431$	−1.48305e42			−1.04597			−0.522987	+	0.852341i	$0.675182\pi$
$432$	−3.98573e41	−	3.98573e41i	−0.270875	−	0.270875i
$433$	−1.27440e41	+	1.27440e41i	−0.0834641	+	0.0834641i	−0.747606	−	0.664142i	$-0.768797\pi$
$433$	−1.27440e41	+	1.27440e41i	−0.0834641	+	0.0834641i	0.664142	+	0.747606i	$0.268797\pi$
$434$			8.87138e41i			0.559958i
$435$	2.71819e38	−	7.30743e37i	0.000165368	−	4.44567e-5i
$436$	−2.92046e41			−0.171265
$437$	2.23779e42	+	2.23779e42i	1.26508	+	1.26508i
$438$	−2.05690e42	+	2.05690e42i	−1.12106	+	1.12106i
$439$			2.12587e42i			1.11713i	0.829460	+	0.558566i	$0.188648\pi$
$439$			2.12587e42i			1.11713i	−0.829460	+	0.558566i	$0.811352\pi$
$440$	−7.61314e41	−	2.83190e42i	−0.385764	−	1.43495i
$441$	1.33475e42			0.652203
$442$	−5.21752e40	−	5.21752e40i	−0.0245871	−	0.0245871i
$443$	−2.43354e42	+	2.43354e42i	−1.10606	+	1.10606i	−0.112396	+	0.993663i	$0.535853\pi$
$443$	−2.43354e42	+	2.43354e42i	−1.10606	+	1.10606i	−0.993663	+	0.112396i	$0.964147\pi$
$444$			4.60983e41i			0.202096i
$445$	3.26300e41	+	1.88030e41i	0.137993	+	0.0795183i
$446$	3.34733e42			1.36566
$447$	−3.74652e41	−	3.74652e41i	−0.147471	−	0.147471i
$448$	2.49402e42	−	2.49402e42i	0.947222	−	0.947222i
$449$		−	3.20066e42i		−	1.17300i	−0.809950	−	0.586499i	$-0.800506\pi$
$449$		−	3.20066e42i		−	1.17300i	0.809950	−	0.586499i	$-0.199494\pi$
$450$	3.21646e42	+	8.56156e41i	1.13757	+	0.302798i
$451$	5.36644e42			1.83173
$452$	−1.60014e41	−	1.60014e41i	−0.0527162	−	0.0527162i
$453$	−2.37977e42	+	2.37977e42i	−0.756770	+	0.756770i
$454$			2.15201e42i			0.660617i
$455$	−2.90666e42	+	5.04411e42i	−0.861415	+	1.49487i
$456$	−7.66405e42			−2.19291
$457$	1.65118e42	+	1.65118e42i	0.456180	+	0.456180i	0.897399	−	0.441219i	$-0.145454\pi$
$457$	1.65118e42	+	1.65118e42i	0.456180	+	0.456180i	−0.441219	+	0.897399i	$0.645454\pi$
$458$	−3.24690e42	+	3.24690e42i	−0.866206	+	0.866206i
$459$		−	6.52002e40i		−	0.0167976i
$460$	1.44289e42	−	3.87898e41i	0.359011	−	0.0965145i
$461$	2.76608e42			0.664738			0.332369	−	0.943150i	$-0.392152\pi$
$461$	2.76608e42			0.664738			0.332369	+	0.943150i	$0.392152\pi$
$462$	−6.66085e42	−	6.66085e42i	−1.54617	−	1.54617i
$463$	−2.83244e42	+	2.83244e42i	−0.635134	+	0.635134i	−0.949351	−	0.314217i	$-0.898258\pi$
$463$	−2.83244e42	+	2.83244e42i	−0.635134	+	0.635134i	0.314217	+	0.949351i	$0.398258\pi$
$464$		−	3.35002e38i		−	7.25705e-5i
$465$	−1.03499e42	−	3.84991e42i	−0.216615	−	0.805755i
$466$	6.77209e42			1.36946
$467$	−3.50143e42	−	3.50143e42i	−0.684187	−	0.684187i	0.276754	−	0.960941i	$-0.410741\pi$
$467$	−3.50143e42	−	3.50143e42i	−0.684187	−	0.684187i	−0.960941	+	0.276754i	$0.910741\pi$
$468$	−1.99927e42	+	1.99927e42i	−0.377518	+	0.377518i
$469$		−	1.09161e43i		−	1.99206i
$470$	3.21238e42	+	1.85113e42i	0.566580	+	0.326491i
$471$	7.15978e42			1.22058
$472$	3.63903e42	+	3.63903e42i	0.599672	+	0.599672i
$473$	−5.59808e42	+	5.59808e42i	−0.891786	+	0.891786i
$474$		−	7.07242e42i		−	1.08922i
$475$	7.61031e42	−	4.41060e42i	1.13320	−	0.656749i
$476$	6.57617e40			0.00946808
$477$	−1.16322e42	−	1.16322e42i	−0.161944	−	0.161944i
$478$	2.56732e42	−	2.56732e42i	0.345647	−	0.345647i
$479$		−	2.15369e41i		−	0.0280424i	−0.999902	−	0.0140212i	$-0.995537\pi$
$479$		−	2.15369e41i		−	0.0280424i	0.999902	−	0.0140212i	$-0.00446323\pi$
$480$	−3.22667e42	+	5.59944e42i	−0.406345	+	0.705155i
$481$	−5.61825e42			−0.684352
$482$	1.89602e42	+	1.89602e42i	0.223404	+	0.223404i
$483$	1.58638e43	−	1.58638e43i	1.80823	−	1.80823i
$484$		−	2.15796e42i		−	0.237967i
$485$	−9.83815e42	+	2.64484e42i	−1.04965	+	0.282183i
$486$	−1.09096e43			−1.12624
$487$	5.13317e42	+	5.13317e42i	0.512770	+	0.512770i	0.915374	−	0.402604i	$-0.131895\pi$
$487$	5.13317e42	+	5.13317e42i	0.512770	+	0.512770i	−0.402604	+	0.915374i	$0.631895\pi$
$488$	2.53255e42	−	2.53255e42i	0.244816	−	0.244816i
$489$			2.64390e43i			2.47345i
$490$	1.15624e42	+	4.30094e42i	0.104692	+	0.389427i
$491$	−1.66880e43			−1.46251			−0.731256	−	0.682103i	$-0.761066\pi$
$491$	−1.66880e43			−1.46251			−0.731256	+	0.682103i	$0.761066\pi$
$492$	−4.68219e42	−	4.68219e42i	−0.397198	−	0.397198i
$493$	2.74005e37	−	2.74005e37i	2.25013e−6	−	2.25013e-6i
$494$		−	1.99826e43i		−	1.58862i
$495$	2.12654e43	+	1.22542e43i	1.63678	+	0.943193i
$496$	−4.74481e42			−0.353600
$497$	−4.03457e42	−	4.03457e42i	−0.291136	−	0.291136i
$498$	−1.03339e43	+	1.03339e43i	−0.722095	+	0.722095i
$499$		−	9.79318e41i		−	0.0662697i	−0.999451	−	0.0331348i	$-0.989451\pi$
$499$		−	9.79318e41i		−	0.0662697i	0.999451	−	0.0331348i	$-0.0105491\pi$
$500$	−1.02911e40	−	4.15275e42i	−0.000674439	−	0.272155i
$501$	1.64179e43			1.04211
$502$	6.72967e42	+	6.72967e42i	0.413747	+	0.413747i
$503$	9.12414e41	−	9.12414e41i	0.0543381	−	0.0543381i	−0.679416	−	0.733754i	$-0.737767\pi$
$503$	9.12414e41	−	9.12414e41i	0.0543381	−	0.0543381i	0.733754	+	0.679416i	$0.237767\pi$
$504$			3.15010e43i			1.81734i
$505$	5.71567e42	−	9.91874e42i	0.319452	−	0.554363i
$506$	−2.94645e43			−1.59548
$507$	−2.12336e43	−	2.12336e43i	−1.11403	−	1.11403i
$508$	1.06716e42	−	1.06716e42i	0.0542514	−	0.0542514i
$509$			7.86389e42i			0.387394i	0.981061	+	0.193697i	$0.0620479\pi$
$509$			7.86389e42i			0.387394i	−0.981061	+	0.193697i	$0.937952\pi$
$510$	7.63227e41	−	2.05182e41i	0.0364360	−	0.00979527i
$511$	3.15964e43			1.46185
$512$	1.66279e43	+	1.66279e43i	0.745621	+	0.745621i
$513$	1.24855e43	−	1.24855e43i	0.542661	−	0.542661i
$514$		−	1.60881e43i		−	0.677788i
$515$	−4.39450e41	−	1.63465e42i	−0.0179471	−	0.0667589i
$516$	9.76859e42			0.386756
$517$	1.93316e43	+	1.93316e43i	0.742024	+	0.742024i
$518$	−9.46894e42	+	9.46894e42i	−0.352391	+	0.352391i
$519$			4.27415e43i			1.54231i
$520$	−3.82087e43	−	2.20177e43i	−1.33693	−	0.770405i
$521$	−2.00091e43			−0.678930			−0.339465	−	0.940619i	$-0.610246\pi$
$521$	−2.00091e43			−0.678930			−0.339465	+	0.940619i	$0.610246\pi$
$522$	2.80794e39	+	2.80794e39i	9.23973e−5	+	9.23973e-5i
$523$	−2.61260e43	+	2.61260e43i	−0.833771	+	0.833771i	−0.988030	−	0.154260i	$-0.950701\pi$
$523$	−2.61260e43	+	2.61260e43i	−0.833771	+	0.833771i	0.154260	+	0.988030i	$0.450701\pi$
$524$		−	9.48537e42i		−	0.293598i
$525$	−3.12669e43	−	5.39498e43i	−0.938719	−	1.61972i
$526$	4.05638e43			1.18132
$527$	−3.88088e41	−	3.88088e41i	−0.0109638	−	0.0109638i
$528$	3.56252e43	−	3.56252e43i	0.976371	−	0.976371i
$529$		−	3.25650e43i		−	0.865886i
$530$	2.74056e42	−	4.75585e42i	0.0707009	−	0.122691i
$531$	−4.30730e43			−1.07818
$532$	1.25930e43	+	1.25930e43i	0.305875	+	0.305875i
$533$	5.70643e43	−	5.70643e43i	1.34502	−	1.34502i
$534$			9.16370e42i			0.209609i
$535$	−6.22062e43	+	1.67232e43i	−1.38094	+	0.371243i
$536$	8.26884e43			1.78159
$537$	−7.79807e43	−	7.79807e43i	−1.63079	−	1.63079i
$538$	3.80362e43	−	3.80362e43i	0.772113	−	0.772113i
$539$			3.28404e43i			0.647125i
$540$	−2.16424e42	−	8.05044e42i	−0.0414004	−	0.153999i
$541$	−8.85705e42			−0.164488			−0.0822438	−	0.996612i	$-0.526209\pi$
$541$	−8.85705e42			−0.164488			−0.0822438	+	0.996612i	$0.526209\pi$
$542$	3.87433e43	+	3.87433e43i	0.698568	+	0.698568i
$543$	−2.78128e43	+	2.78128e43i	−0.486908	+	0.486908i
$544$			8.89711e41i			0.0151240i
$545$	3.30318e43	+	1.90345e43i	0.545240	+	0.314194i
$546$	−1.41657e44			−2.27068
$547$	5.56967e43	+	5.56967e43i	0.867026	+	0.867026i	0.992142	−	0.125116i	$-0.0399302\pi$
$547$	5.56967e43	+	5.56967e43i	0.867026	+	0.867026i	−0.125116	+	0.992142i	$0.539930\pi$
$548$	−1.97895e43	+	1.97895e43i	−0.299189	+	0.299189i
$549$			2.99762e43i			0.440169i
$550$	−2.10650e43	+	7.91383e43i	−0.300440	+	1.12871i
$551$	1.04941e40			0.000145385
$552$	1.20167e44	+	1.20167e44i	1.61718	+	1.61718i
$553$	−5.43204e43	+	5.43204e43i	−0.710167	+	0.710167i
$554$		−	9.38155e43i		−	1.19157i
$555$	3.00453e43	−	5.21394e43i	0.370756	−	0.643395i
$556$	3.09214e41			0.00370734
$557$	9.98545e42	+	9.98545e42i	0.116328	+	0.116328i	0.762875	−	0.646547i	$-0.223787\pi$
$557$	9.98545e42	+	9.98545e42i	0.116328	+	0.116328i	−0.646547	+	0.762875i	$0.723787\pi$
$558$	3.97702e43	−	3.97702e43i	0.450206	−	0.450206i
$559$			1.19055e44i			1.30966i
$560$	−7.16700e43	+	1.92674e43i	−0.766177	+	0.205975i
$561$	5.82772e42			0.0605470
$562$	−7.24699e43	−	7.24699e43i	−0.731773	−	0.731773i
$563$	−3.53624e43	+	3.53624e43i	−0.347062	+	0.347062i	−0.859014	−	0.511952i	$-0.828923\pi$
$563$	−3.53624e43	+	3.53624e43i	−0.347062	+	0.347062i	0.511952	+	0.859014i	$0.328923\pi$
$564$		−	3.37334e43i		−	0.321806i
$565$	7.66920e42	+	2.85276e43i	0.0711172	+	0.264539i
$566$	1.43298e44			1.29175
$567$	4.66006e43	+	4.66006e43i	0.408379	+	0.408379i
$568$	3.05615e43	−	3.05615e43i	0.260377	−	0.260377i
$569$		−	2.03561e44i		−	1.68616i	−0.537787	−	0.843080i	$-0.680740\pi$
$569$		−	2.03561e44i		−	1.68616i	0.537787	−	0.843080i	$-0.319260\pi$
$570$	1.85445e44	+	1.06863e44i	1.49355	+	0.860655i
$571$	−9.39789e43			−0.735957			−0.367979	−	0.929834i	$-0.619950\pi$
$571$	−9.39789e43			−0.735957			−0.367979	+	0.929834i	$0.619950\pi$
$572$	−4.91903e43	−	4.91903e43i	−0.374578	−	0.374578i
$573$	1.07288e44	−	1.07288e44i	0.794470	−	0.794470i
$574$		−	1.92351e44i		−	1.38518i
$575$	−1.88479e44	−	5.01693e43i	−1.32001	−	0.351360i
$576$	−2.23613e44			−1.52313
$577$	−1.19785e44	−	1.19785e44i	−0.793578	−	0.793578i	0.188496	−	0.982074i	$-0.439639\pi$
$577$	−1.19785e44	−	1.19785e44i	−0.793578	−	0.793578i	−0.982074	+	0.188496i	$0.939639\pi$
$578$	−9.35390e43	+	9.35390e43i	−0.602764	+	0.602764i
$579$			2.61958e44i			1.64201i
$580$	2.47369e39	−	4.29274e39i	1.50833e−5	−	2.61750e-5i
$581$	1.58741e44			0.941609
$582$	−1.75284e44	−	1.75284e44i	−1.01152	−	1.01152i
$583$	2.86199e43	−	2.86199e43i	0.160683	−	0.160683i
$584$			2.39340e44i			1.30741i
$585$	3.56432e44	−	9.58213e43i	1.89445	−	0.509293i
$586$	−1.87095e44			−0.967610
$587$	1.61244e44	+	1.61244e44i	0.811471	+	0.811471i	0.984854	−	0.173384i	$-0.0554700\pi$
$587$	1.61244e44	+	1.61244e44i	0.811471	+	0.811471i	−0.173384	+	0.984854i	$0.555470\pi$
$588$	2.86531e43	−	2.86531e43i	0.140325	−	0.140325i
$589$		−	1.48634e44i		−	0.708390i
$590$	−3.73124e43	−	1.38793e44i	−0.173070	−	0.643778i
$591$	3.22690e44			1.45675
$592$	−5.06441e43	−	5.06441e43i	−0.222527	−	0.222527i
$593$	9.91752e43	−	9.91752e43i	0.424158	−	0.424158i	−0.462474	−	0.886633i	$-0.653038\pi$
$593$	9.91752e43	−	9.91752e43i	0.424158	−	0.424158i	0.886633	+	0.462474i	$0.153038\pi$
$594$			1.64394e44i			0.684388i
$595$	−7.43796e42	−	4.28612e42i	−0.0301427	−	0.0173697i
$596$	−9.32626e42			−0.0367932
$597$	−3.05786e44	−	3.05786e44i	−1.17443	−	1.17443i
$598$	−3.13312e44	+	3.13312e44i	−1.17154	+	1.17154i
$599$		−	1.31082e44i		−	0.477216i	−0.971116	−	0.238608i	$-0.923309\pi$
$599$		−	1.31082e44i		−	0.477216i	0.971116	−	0.238608i	$-0.0766911\pi$
$600$	4.08665e44	−	2.36844e44i	1.44860	−	0.839542i
$601$	3.67921e44			1.26988			0.634940	−	0.772561i	$-0.281025\pi$
$601$	3.67921e44			1.26988			0.634940	+	0.772561i	$0.281025\pi$
$602$	2.00654e44	+	2.00654e44i	0.674379	+	0.674379i
$603$	−4.89366e44	+	4.89366e44i	−1.60161	+	1.60161i
$604$			5.92400e43i			0.188809i
$605$	−1.40648e44	+	2.44075e44i	−0.436564	+	0.757596i
$606$	2.78555e44			0.842071
$607$	−3.15598e44	−	3.15598e44i	−0.929213	−	0.929213i	0.0684420	−	0.997655i	$-0.478197\pi$
$607$	−3.15598e44	−	3.15598e44i	−0.929213	−	0.929213i	−0.997655	+	0.0684420i	$0.978197\pi$
$608$	−1.70375e44	+	1.70375e44i	−0.488595	+	0.488595i
$609$		−	7.43932e40i		−	0.000207805i
$610$	−9.65917e43	+	2.59672e43i	−0.262823	+	0.0706558i
$611$	4.11126e44			1.08972
$612$	−2.94809e42	−	2.94809e42i	−0.00761233	−	0.00761233i
$613$	−7.90423e43	+	7.90423e43i	−0.198835	+	0.198835i	−0.799500	−	0.600666i	$-0.794902\pi$
$613$	−7.90423e43	+	7.90423e43i	−0.198835	+	0.198835i	0.600666	+	0.799500i	$0.294902\pi$
$614$			2.30485e44i			0.564870i
$615$	2.24409e44	+	8.34746e44i	0.535843	+	1.99321i
$616$	−7.75055e44			−1.80319
$617$	−3.84469e44	−	3.84469e44i	−0.871563	−	0.871563i	0.121080	−	0.992643i	$-0.461364\pi$
$617$	−3.84469e44	−	3.84469e44i	−0.871563	−	0.871563i	−0.992643	+	0.121080i	$0.961364\pi$
$618$	2.91242e43	−	2.91242e43i	0.0643336	−	0.0643336i
$619$		−	7.77858e44i		−	1.67436i	−0.546924	−	0.837182i	$-0.684201\pi$
$619$		−	7.77858e44i		−	1.67436i	0.546924	−	0.837182i	$-0.315799\pi$
$620$	−6.08002e43	−	3.50361e43i	−0.127538	−	0.0734934i
$621$	−3.91528e44			−0.800381
$622$	4.78872e44	+	4.78872e44i	0.954054	+	0.954054i
$623$	7.03827e43	−	7.03827e43i	0.136665	−	0.136665i
$624$		−	7.57646e44i		−	1.43388i
$625$	−2.69498e44	+	4.70366e44i	−0.497136	+	0.867673i
$626$	2.30550e44			0.414548
$627$	1.11598e45	+	1.11598e45i	1.95603	+	1.95603i
$628$	8.91148e43	−	8.91148e43i	0.152263	−	0.152263i
$629$		−	8.28457e42i		−	0.0137994i
$630$	4.39231e44	−	7.62223e44i	0.713253	−	1.23775i
$631$	−1.02238e44			−0.161861			−0.0809306	−	0.996720i	$-0.525789\pi$
$631$	−1.02238e44			−0.161861			−0.0809306	+	0.996720i	$0.525789\pi$
$632$	−4.11472e44	−	4.11472e44i	−0.635137	−	0.635137i
$633$	9.83499e44	−	9.83499e44i	1.48018	−	1.48018i
$634$			1.36986e44i			0.201024i
$635$	−1.90255e44	+	5.11471e43i	−0.272242	+	0.0731882i
$636$	−4.99414e43			−0.0696863
$637$	3.49210e44	+	3.49210e44i	0.475178	+	0.475178i
$638$	−6.90868e40	+	6.90868e40i	−9.16779e−5	+	9.16779e-5i
$639$			3.61738e44i			0.468146i
$640$	−8.51928e43	−	3.16897e44i	−0.107528	−	0.399980i
$641$	−3.10298e44			−0.381989			−0.190995	−	0.981591i	$-0.561171\pi$
$641$	−3.10298e44			−0.381989			−0.190995	+	0.981591i	$0.561171\pi$
$642$	−1.10831e45	−	1.10831e45i	−1.33077	−	1.33077i
$643$	−8.25926e43	+	8.25926e43i	−0.0967310	+	0.0967310i	−0.753816	−	0.657085i	$-0.771789\pi$
$643$	−8.25926e43	+	8.25926e43i	−0.0967310	+	0.0967310i	0.657085	+	0.753816i	$0.271789\pi$
$644$		−	3.94900e44i		−	0.451142i
$645$	−1.10487e45	−	6.36683e44i	−1.23128	−	0.709525i
$646$	2.94660e43			0.0320332
$647$	5.97296e44	+	5.97296e44i	0.633463	+	0.633463i	0.948935	−	0.315472i	$-0.102163\pi$
$647$	5.97296e44	+	5.97296e44i	0.633463	+	0.633463i	−0.315472	+	0.948935i	$0.602163\pi$
$648$	−3.52996e44	+	3.52996e44i	−0.365233	+	0.365233i
$649$		−	1.05977e45i		−	1.06979i
$650$	6.17526e44	+	1.06552e45i	0.608193	+	1.04941i
$651$	−1.05367e45			−1.01253
$652$	3.29075e44	+	3.29075e44i	0.308556	+	0.308556i
$653$	−3.68464e44	+	3.68464e44i	−0.337120	+	0.337120i	−0.855282	−	0.518163i	$-0.826616\pi$
$653$	−3.68464e44	+	3.68464e44i	−0.337120	+	0.337120i	0.518163	+	0.855282i	$0.326616\pi$
$654$			9.27653e44i			0.828212i
$655$	−6.18223e44	+	1.07284e45i	−0.538622	+	0.934703i
$656$	1.02878e45			0.874704
$657$	−1.41646e45	−	1.41646e45i	−1.17533	−	1.17533i
$658$	6.92909e44	−	6.92909e44i	0.561128	−	0.561128i
$659$		−	1.44815e45i		−	1.14458i	−0.820050	−	0.572291i	$-0.806055\pi$
$659$		−	1.44815e45i		−	1.14458i	0.820050	−	0.572291i	$-0.193945\pi$
$660$	7.19563e44	−	1.93444e44i	0.555093	−	0.149228i
$661$	1.61686e45			1.21744			0.608722	−	0.793384i	$-0.291683\pi$
$661$	1.61686e45			1.21744			0.608722	+	0.793384i	$0.291683\pi$
$662$	1.30302e45	+	1.30302e45i	0.957688	+	0.957688i
$663$	6.19694e43	−	6.19694e43i	0.0444591	−	0.0444591i
$664$			1.20245e45i			0.842126i
$665$	−6.03561e44	−	2.24510e45i	−0.412643	−	1.53493i
$666$	8.48982e44			0.566645
$667$	−1.64540e41	−	1.64540e41i	−0.000107216	−	0.000107216i
$668$	2.04347e44	−	2.04347e44i	0.130000	−	0.130000i
$669$			3.97569e45i			2.46942i
$670$	−2.00079e45	−	1.15296e45i	−1.21340	−	0.699223i
$671$	−7.37539e44			−0.436742
$672$	1.20780e45	+	1.20780e45i	0.698369	+	0.698369i
$673$	−2.46534e44	+	2.46534e44i	−0.139199	+	0.139199i	−0.773273	−	0.634074i	$-0.781382\pi$
$673$	−2.46534e44	+	2.46534e44i	−0.139199	+	0.139199i	0.634074	+	0.773273i	$0.281382\pi$
$674$			2.36641e45i			1.30476i
$675$	−2.79914e44	+	1.05160e45i	−0.150718	+	0.566226i
$676$	−5.28570e44			−0.277943
$677$	2.18968e44	+	2.18968e44i	0.112451	+	0.112451i	0.761093	−	0.648643i	$-0.224663\pi$
$677$	2.18968e44	+	2.18968e44i	0.112451	+	0.112451i	−0.648643	+	0.761093i	$0.724663\pi$
$678$	−5.08269e44	+	5.08269e44i	−0.254929	+	0.254929i
$679$			2.69257e45i			1.31902i
$680$	3.24670e43	−	5.63419e43i	0.0155346	−	0.0269581i
$681$	−2.55598e45			−1.19455
$682$	9.78512e44	+	9.78512e44i	0.446700	+	0.446700i
$683$	1.73095e45	−	1.73095e45i	0.771886	−	0.771886i	−0.206550	−	0.978436i	$-0.566223\pi$
$683$	1.73095e45	−	1.73095e45i	0.771886	−	0.771886i	0.978436	+	0.206550i	$0.0662235\pi$
$684$		−	1.12909e45i		−	0.491847i
$685$	3.52809e45	−	9.48474e44i	1.50138	−	0.403623i
$686$	−1.31323e45			−0.545951
$687$	−3.85640e45	−	3.85640e45i	−1.56630	−	1.56630i
$688$	−1.07319e45	+	1.07319e45i	−0.425854	+	0.425854i
$689$		−	6.08662e44i		−	0.235977i
$690$	−1.23212e45	−	4.58318e45i	−0.466731	−	1.73613i
$691$	1.12336e45			0.415785			0.207892	−	0.978152i	$-0.433340\pi$
$691$	1.12336e45			0.415785			0.207892	+	0.978152i	$0.433340\pi$
$692$	5.31986e44	+	5.31986e44i	0.192399	+	0.192399i
$693$	4.58693e45	−	4.58693e45i	1.62103	−	1.62103i
$694$		−	3.39804e45i		−	1.17348i
$695$	−3.49736e43	−	2.01535e43i	−0.0118027	−	0.00680132i
$696$	5.63522e41			0.000185850
$697$	8.41460e43	+	8.41460e43i	0.0271212	+	0.0271212i
$698$	1.14582e45	−	1.14582e45i	0.360937	−	0.360937i
$699$			8.04333e45i			2.47629i
$700$	−1.06066e45	−	2.82324e44i	−0.319158	−	0.0849532i
$701$	−3.92745e45			−1.15511			−0.577554	−	0.816352i	$-0.695993\pi$
$701$	−3.92745e45			−1.15511			−0.577554	+	0.816352i	$0.695993\pi$
$702$	1.74809e45	+	1.74809e45i	0.502540	+	0.502540i
$703$	1.58645e45	−	1.58645e45i	0.445802	−	0.445802i
$704$		−	5.50181e45i		−	1.51127i
$705$	−2.19862e45	+	3.81540e45i	−0.590371	+	1.02451i
$706$	−2.69458e44			−0.0707319
$707$	−2.13947e45	−	2.13947e45i	−0.549028	−	0.549028i
$708$	−9.24648e44	+	9.24648e44i	−0.231977	+	0.231977i
$709$		−	7.48151e45i		−	1.83506i	−0.397671	−	0.917528i	$-0.630181\pi$
$709$		−	7.48151e45i		−	1.83506i	0.397671	−	0.917528i	$-0.369819\pi$
$710$	−1.16562e45	+	3.13360e44i	−0.279527	+	0.0751466i
$711$	4.87035e45			1.14195
$712$	5.33143e44	+	5.33143e44i	0.122226	+	0.122226i
$713$	−2.33047e45	+	2.33047e45i	−0.522409	+	0.522409i
$714$		−	2.08885e44i		−	0.0457864i
$715$	2.35760e45	+	8.76970e45i	0.505328	+	1.87970i
$716$	−1.94119e45			−0.406873
$717$	3.04925e45	+	3.04925e45i	0.625009	+	0.625009i
$718$	2.14541e44	−	2.14541e44i	0.0430050	−	0.0430050i
$719$			1.61834e45i			0.317254i	0.987339	+	0.158627i	$0.0507067\pi$
$719$			1.61834e45i			0.317254i	−0.987339	+	0.158627i	$0.949293\pi$
$720$	4.07671e45	+	2.34920e45i	0.781610	+	0.450402i
$721$	−4.47382e44			−0.0838908
$722$	2.35331e45	+	2.35331e45i	0.431603	+	0.431603i
$723$	−2.25194e45	+	2.25194e45i	−0.403965	+	0.403965i
$724$			6.92348e44i			0.121481i
$725$	−5.59571e41	+	3.24302e41i	−9.60389e−5	+	5.56598e-5i
$726$	−6.85453e45			−1.15078
$727$	3.84402e45	+	3.84402e45i	0.631299	+	0.631299i	0.948394	−	0.317095i	$-0.102707\pi$
$727$	3.84402e45	+	3.84402e45i	0.631299	+	0.631299i	−0.317095	+	0.948394i	$0.602707\pi$
$728$	−8.24159e45	+	8.24159e45i	−1.32406	+	1.32406i
$729$		−	9.92952e45i		−	1.56059i
$730$	3.33721e45	−	5.79127e45i	0.513119	−	0.890446i
$731$	−1.75556e44			−0.0264082
$732$	6.43499e44	+	6.43499e44i	0.0947045	+	0.0947045i
$733$	8.30891e45	−	8.30891e45i	1.19641	−	1.19641i	0.221178	−	0.975233i	$-0.429010\pi$
$733$	8.30891e45	−	8.30891e45i	1.19641	−	1.19641i	0.975233	−	0.221178i	$-0.0709903\pi$
$734$		−	8.42456e44i		−	0.118689i
$735$	−5.10830e45	+	1.37329e45i	−0.704173	+	0.189306i
$736$	5.34272e45			0.720638
$737$	−1.20404e46	−	1.20404e46i	−1.58914	−	1.58914i
$738$	−8.62307e45	+	8.62307e45i	−1.11368	+	1.11368i
$739$			1.31493e46i			1.66185i	0.556384	+	0.830925i	$0.312188\pi$
$739$			1.31493e46i			1.66185i	−0.556384	+	0.830925i	$0.687812\pi$
$740$	−2.74996e44	−	1.02292e45i	−0.0340109	−	0.126512i
$741$	2.37336e46			2.87259
$742$	−1.02583e45	−	1.02583e45i	−0.121511	−	0.121511i
$743$	−2.01767e45	+	2.01767e45i	−0.233899	+	0.233899i	−0.814318	−	0.580419i	$-0.802889\pi$
$743$	−2.01767e45	+	2.01767e45i	−0.233899	+	0.233899i	0.580419	+	0.814318i	$0.302889\pi$
$744$		−	7.98146e45i		−	0.905556i
$745$	1.05484e45	+	6.07853e44i	0.117135	+	0.0674991i
$746$	6.02255e45			0.654574
$747$	−7.11633e45	−	7.11633e45i	−0.757053	−	0.757053i
$748$	7.25351e43	−	7.25351e43i	0.00755306	−	0.00755306i
$749$			1.70250e46i			1.73532i
$750$	−1.31908e46	+	3.26887e43i	−1.31610	+	0.00326150i
$751$	−1.37535e46			−1.34330			−0.671651	−	0.740867i	$-0.734415\pi$
$751$	−1.37535e46			−1.34330			−0.671651	+	0.740867i	$0.734415\pi$
$752$	3.70599e45	+	3.70599e45i	0.354338	+	0.354338i
$753$	−7.99295e45	+	7.99295e45i	−0.748148	+	0.748148i
$754$			1.46928e42i			0.000134636i
$755$	3.86105e45	−	6.70032e45i	0.346381	−	0.601096i
$756$	−2.20330e45			−0.193520
$757$	8.00852e45	+	8.00852e45i	0.688681	+	0.688681i	0.961940	−	0.273259i	$-0.0881016\pi$
$757$	8.00852e45	+	8.00852e45i	0.688681	+	0.688681i	−0.273259	+	0.961940i	$0.588102\pi$
$758$	5.26100e44	−	5.26100e44i	0.0442957	−	0.0442957i
$759$		−	3.49955e46i		−	2.88499i
$760$	1.70064e46	−	4.57192e45i	1.37276	−	0.369047i
$761$	2.20783e46			1.74506			0.872530	−	0.488560i	$-0.162478\pi$
$761$	2.20783e46			1.74506			0.872530	+	0.488560i	$0.162478\pi$
$762$	−3.38973e45	−	3.38973e45i	−0.262352	−	0.262352i
$763$	7.12493e45	−	7.12493e45i	0.539993	−	0.539993i
$764$		−	2.67074e45i		−	0.198215i
$765$	1.41296e44	+	5.25588e44i	0.0102695	+	0.0382000i
$766$	−1.14155e46			−0.812522
$767$	−1.12692e46	−	1.12692e46i	−0.785536	−	0.785536i
$768$	−1.19920e46	+	1.19920e46i	−0.818675	+	0.818675i
$769$		−	1.38404e46i		−	0.925394i	−0.886517	−	0.462697i	$-0.846882\pi$
$769$		−	1.38404e46i		−	0.925394i	0.886517	−	0.462697i	$-0.153118\pi$
$770$	1.87538e46	+	1.08069e46i	1.22811	+	0.707700i
$771$	1.91081e46			1.22560
$772$	3.26048e45	+	3.26048e45i	0.204835	+	0.204835i
$773$	−1.26312e46	+	1.26312e46i	−0.777272	+	0.777272i	−0.979366	−	0.202094i	$-0.935225\pi$
$773$	−1.26312e46	+	1.26312e46i	−0.777272	+	0.777272i	0.202094	+	0.979366i	$0.435225\pi$
$774$		−	1.79906e46i		−	1.08440i
$775$	4.59326e45	+	7.92549e45i	0.271202	+	0.467949i
$776$	−2.03960e46			−1.17966
$777$	−1.12464e46	−	1.12464e46i	−0.637204	−	0.637204i
$778$	8.55526e45	−	8.55526e45i	0.474853	−	0.474853i
$779$			3.22271e46i			1.75235i
$780$	5.59452e45	−	9.70851e45i	0.298023	−	0.517177i
$781$	−8.90026e45			−0.464500
$782$	−4.62005e44	−	4.62005e44i	−0.0236232	−	0.0236232i
$783$	−9.18035e41	+	9.18035e41i	−4.59908e−5	+	4.59908e-5i
$784$			6.29572e45i			0.309021i
$785$	−1.58875e46	+	4.27111e45i	−0.764083	+	0.205412i
$786$	−3.01293e46			−1.41980
$787$	−1.68108e46	−	1.68108e46i	−0.776234	−	0.776234i	0.202954	−	0.979188i	$-0.434946\pi$
$787$	−1.68108e46	−	1.68108e46i	−0.776234	−	0.776234i	−0.979188	+	0.202954i	$0.934946\pi$
$788$	4.01638e45	−	4.01638e45i	0.181725	−	0.181725i
$789$			4.81783e46i			2.13609i
$790$	4.21899e45	+	1.56936e46i	0.183305	+	0.681851i
$791$	7.80762e45			0.332426
$792$	3.47456e46	+	3.47456e46i	1.44976	+	1.44976i
$793$	−7.84266e45	+	7.84266e45i	−0.320695	+	0.320695i
$794$			2.34211e45i			0.0938598i
$795$	5.64861e45	+	3.25501e45i	0.221854	+	0.127843i
$796$	−7.61198e45			−0.293014
$797$	−1.80369e45	−	1.80369e45i	−0.0680502	−	0.0680502i	0.672263	−	0.740313i	$-0.265323\pi$
$797$	−1.80369e45	−	1.80369e45i	−0.0680502	−	0.0680502i	−0.740313	+	0.672263i	$0.765323\pi$
$798$	4.00005e46	−	4.00005e46i	1.47917	−	1.47917i
$799$			6.06240e44i			0.0219733i
$800$	3.81965e45	−	1.43499e46i	0.135701	−	0.509812i
$801$	−6.31049e45			−0.219757
$802$	−1.18556e46	−	1.18556e46i	−0.404699	−	0.404699i
$803$	3.48508e46	−	3.48508e46i	1.16618	−	1.16618i
$804$			2.10104e46i			0.689189i
$805$	−2.57382e46	+	4.46650e46i	−0.827644	+	1.43626i
$806$	2.08101e46			0.656015
$807$	4.51763e46	+	4.51763e46i	1.39616	+	1.39616i
$808$	1.62063e46	−	1.62063e46i	0.491023	−	0.491023i
$809$		−	2.60290e46i		−	0.773181i	−0.922251	−	0.386590i	$-0.873653\pi$
$809$		−	2.60290e46i		−	0.773181i	0.922251	−	0.386590i	$-0.126347\pi$
$810$	1.34633e46	−	3.61941e45i	0.392095	−	0.105409i
$811$	−6.35697e46			−1.81517			−0.907584	−	0.419871i	$-0.862075\pi$
$811$	−6.35697e46			−1.81517			−0.907584	+	0.419871i	$0.862075\pi$
$812$	−9.25941e41	−	9.25941e41i	−2.59231e−5	−	2.59231e-5i
$813$	−4.60162e46	+	4.60162e46i	−1.26317	+	1.26317i
$814$			2.08885e46i			0.562233i
$815$	−1.57720e46	−	5.86679e46i	−0.416260	−	1.54839i
$816$	1.11721e45			0.0289130
$817$	−3.36182e46	−	3.36182e46i	−0.853142	−	0.853142i
$818$	1.55550e45	−	1.55550e45i	0.0387094	−	0.0387094i
$819$		−	9.75507e46i		−	2.38061i
$820$	1.31828e46	+	7.59660e45i	0.315491	+	0.181802i
$821$	3.29602e46			0.773569			0.386785	−	0.922170i	$-0.373586\pi$
$821$	3.29602e46			0.773569			0.386785	+	0.922170i	$0.373586\pi$
$822$	6.28592e46	+	6.28592e46i	1.44684	+	1.44684i
$823$	1.46966e46	−	1.46966e46i	0.331756	−	0.331756i	−0.521497	−	0.853253i	$-0.674626\pi$
$823$	1.46966e46	−	1.46966e46i	0.331756	−	0.331756i	0.853253	+	0.521497i	$0.174626\pi$
$824$		−	3.38888e45i		−	0.0750276i
$825$	−9.39939e46	−	2.50192e46i	−2.04097	−	0.543264i
$826$	−3.79859e46			−0.808987
$827$	−3.35463e46	−	3.35463e46i	−0.700739	−	0.700739i	0.263830	−	0.964569i	$-0.415014\pi$
$827$	−3.35463e46	−	3.35463e46i	−0.700739	−	0.700739i	−0.964569	+	0.263830i	$0.915014\pi$
$828$	−1.77033e46	+	1.77033e46i	−0.362717	+	0.362717i
$829$			3.75145e46i			0.753923i	0.926229	+	0.376961i	$0.123031\pi$
$829$			3.75145e46i			0.753923i	−0.926229	+	0.376961i	$0.876969\pi$
$830$	1.67662e46	−	2.90954e46i	0.330510	−	0.573554i
$831$	1.11426e47			2.15462
$832$	−5.85038e46	−	5.85038e46i	−1.10971	−	1.10971i
$833$	−5.14939e44	+	5.14939e44i	−0.00958156	+	0.00958156i
$834$		−	9.82186e44i		−	0.0179282i
$835$	−3.64312e46	+	9.79398e45i	−0.652364	+	0.175378i
$836$	2.77802e46			0.488017
$837$	1.30026e46	+	1.30026e46i	0.224090	+	0.224090i
$838$	−2.76860e46	+	2.76860e46i	−0.468119	+	0.468119i
$839$			4.26224e46i			0.707044i	0.935426	+	0.353522i	$0.115016\pi$
$839$			4.26224e46i			0.707044i	−0.935426	+	0.353522i	$0.884984\pi$
$840$	−3.24105e46	−	1.20559e47i	−0.527494	−	1.96215i
$841$	6.26233e46			1.00000
$842$	3.78008e46	+	3.78008e46i	0.592254	+	0.592254i
$843$	8.60738e46	−	8.60738e46i	1.32321	−	1.32321i
$844$		−	2.44824e46i		−	0.369296i
$845$	5.97837e46	+	3.44503e46i	0.884863	+	0.509901i
$846$	−6.21260e46			−0.902292
$847$	5.26469e46	+	5.26469e46i	0.750305	+	0.750305i
$848$	5.48662e45	−	5.48662e45i	0.0767311	−	0.0767311i
$849$			1.70198e47i			2.33578i
$850$	−1.57119e45	+	9.10593e44i	−0.0211605	+	0.0122637i
$851$	−4.97489e46			−0.657522
$852$	7.76543e45	+	7.76543e45i	0.100724	+	0.100724i
$853$	3.51606e46	−	3.51606e46i	0.447581	−	0.447581i	−0.446969	−	0.894550i	$-0.647496\pi$
$853$	3.51606e46	−	3.51606e46i	0.447581	−	0.447581i	0.894550	+	0.446969i	$0.147496\pi$
$854$			2.64359e46i			0.330269i
$855$	−7.35900e46	+	1.27705e47i	−0.902320	+	1.56585i
$856$	−1.28963e47			−1.55198
$857$	2.08023e46	+	2.08023e46i	0.245707	+	0.245707i	0.819206	−	0.573499i	$-0.194414\pi$
$857$	2.08023e46	+	2.08023e46i	0.245707	+	0.245707i	−0.573499	+	0.819206i	$0.694414\pi$
$858$	−1.56248e47	+	1.56248e47i	−1.81141	+	1.81141i
$859$		−	5.96305e46i		−	0.678544i	−0.940688	−	0.339272i	$-0.889819\pi$
$859$		−	5.96305e46i		−	0.678544i	0.940688	−	0.339272i	$-0.110181\pi$
$860$	−2.16764e46	+	5.82737e45i	−0.242110	+	0.0650875i
$861$	2.28459e47			2.50471
$862$	5.86329e46	+	5.86329e46i	0.630993	+	0.630993i
$863$	1.98909e46	−	1.98909e46i	0.210127	−	0.210127i	−0.594194	−	0.804322i	$-0.702529\pi$
$863$	1.98909e46	−	1.98909e46i	0.210127	−	0.210127i	0.804322	+	0.594194i	$0.202529\pi$
$864$		−	2.98091e46i		−	0.309121i
$865$	−2.54971e46	−	9.48430e46i	−0.259557	−	0.965490i
$866$	1.00767e46			0.100701
$867$	−1.11098e47	−	1.11098e47i	−1.08993	−	1.08993i
$868$	−1.31146e46	+	1.31146e46i	−0.126310	+	0.126310i
$869$			1.19831e47i			1.13306i
$870$	−1.36354e43	−	7.85741e42i	−0.000126579	−	7.29409e-5i
$871$	−2.56065e47			−2.33378
$872$	5.39707e46	+	5.39707e46i	0.482942	+	0.482942i
$873$	1.20708e47	−	1.20708e47i	1.06049	−	1.06049i
$874$		−	1.76943e47i		−	1.52634i
$875$	1.01564e47	+	1.01062e47i	0.860224	+	0.855971i
$876$	−6.08144e46			−0.505756
$877$	8.41422e46	+	8.41422e46i	0.687101	+	0.687101i	0.961590	−	0.274490i	$-0.0885089\pi$
$877$	8.41422e46	+	8.41422e46i	0.687101	+	0.687101i	−0.274490	+	0.961590i	$0.588509\pi$
$878$	8.40468e46	−	8.40468e46i	0.673921	−	0.673921i
$879$		−	2.22216e47i		−	1.74966i
$880$	−5.78001e46	+	1.00304e47i	−0.446895	+	0.775524i
$881$	−1.37730e47			−1.04572			−0.522859	−	0.852419i	$-0.675134\pi$
$881$	−1.37730e47			−1.04572			−0.522859	+	0.852419i	$0.675134\pi$
$882$	−5.27697e46	−	5.27697e46i	−0.393448	−	0.393448i
$883$	1.33961e46	−	1.33961e46i	0.0980858	−	0.0980858i	−0.656361	−	0.754447i	$-0.727905\pi$
$883$	1.33961e46	−	1.33961e46i	0.0980858	−	0.0980858i	0.754447	+	0.656361i	$0.227905\pi$
$884$		−	1.54261e45i		−	0.0110923i
$885$	1.64847e47	−	4.43167e46i	1.16410	−	0.312950i
$886$	1.92421e47			1.33448
$887$	−8.50711e46	−	8.50711e46i	−0.579434	−	0.579434i	0.355313	−	0.934747i	$-0.384374\pi$
$887$	−8.50711e46	−	8.50711e46i	−0.579434	−	0.579434i	−0.934747	+	0.355313i	$0.884374\pi$
$888$	8.51907e46	−	8.51907e46i	0.569882	−	0.569882i
$889$			5.20702e46i			0.342106i
$890$	−5.46652e45	−	2.03341e46i	−0.0352753	−	0.131216i
$891$	1.02801e47			0.651559
$892$	4.94837e46	+	4.94837e46i	0.308052	+	0.308052i
$893$	−1.16092e47	+	1.16092e47i	−0.709870	+	0.709870i
$894$			2.96239e46i			0.177927i
$895$	2.19557e47	+	1.26520e47i	1.29533	+	0.746430i
$896$	−8.67305e46			−0.502624
$897$	−3.72127e47	−	3.72127e47i	−2.11842	−	2.11842i
$898$	−1.26539e47	+	1.26539e47i	−0.707623	+	0.707623i
$899$			1.09287e43i			6.00364e-5i
$900$	3.48925e46	+	6.02056e46i	0.188300	+	0.324905i
$901$	8.97523e44			0.00475827
$902$	−2.12163e47	−	2.12163e47i	−1.10501	−	1.10501i
$903$	−2.38321e47	+	2.38321e47i	−1.21943	+	1.21943i
$904$			5.91420e46i			0.297304i
$905$	4.51248e46	−	7.83078e46i	0.222863	−	0.386747i
$906$	1.88170e47			0.913058
$907$	5.21733e46	+	5.21733e46i	0.248732	+	0.248732i	0.820450	−	0.571718i	$-0.193723\pi$
$907$	5.21733e46	+	5.21733e46i	0.248732	+	0.248732i	−0.571718	+	0.820450i	$0.693723\pi$
$908$	−3.18132e46	+	3.18132e46i	−0.149016	+	0.149016i
$909$			1.91824e47i			0.882837i
$910$	3.14336e47	−	8.45043e46i	1.42145	−	0.382135i
$911$	9.62130e46			0.427504			0.213752	−	0.976888i	$-0.431432\pi$
$911$	9.62130e46			0.427504			0.213752	+	0.976888i	$0.431432\pi$
$912$	2.13940e47	+	2.13940e47i	0.934061	+	0.934061i
$913$	1.75091e47	−	1.75091e47i	0.751158	−	0.751158i
$914$		−	1.30560e47i		−	0.550390i
$915$	−3.08417e46	−	1.14724e47i	−0.127762	−	0.475243i
$916$	−9.59980e46			−0.390782
$917$	2.31411e47	+	2.31411e47i	0.925708	+	0.925708i
$918$	−2.57771e45	+	2.57771e45i	−0.0101333	+	0.0101333i
$919$		−	2.47961e47i		−	0.957934i	−0.877833	−	0.478967i	$-0.841011\pi$
$919$		−	2.47961e47i		−	0.957934i	0.877833	−	0.478967i	$-0.158989\pi$
$920$	−3.38333e47	−	1.94964e47i	−1.28452	−	0.740202i
$921$	−2.73751e47			−1.02141
$922$	−1.09358e47	−	1.09358e47i	−0.401009	−	0.401009i
$923$	−9.46414e46	+	9.46414e46i	−0.341078	+	0.341078i
$924$		−	1.96935e47i		−	0.697544i
$925$	−3.55668e46	+	1.33620e47i	−0.123816	+	0.465161i
$926$	2.23963e47			0.766302
$927$	2.00561e46	+	2.00561e46i	0.0674481	+	0.0674481i
$928$	1.25273e43	−	1.25273e43i	4.14087e−5	−	4.14087e-5i
$929$			2.99823e47i			0.974123i	0.873368	+	0.487062i	$0.161931\pi$
$929$			2.99823e47i			0.974123i	−0.873368	+	0.487062i	$0.838069\pi$
$930$	−1.11288e47	+	1.93125e47i	−0.355404	+	0.616755i
$931$	−1.97217e47			−0.619083
$932$	1.00112e47	+	1.00112e47i	0.308909	+	0.308909i
$933$	−5.68765e47	+	5.68765e47i	−1.72515	+	1.72515i
$934$			2.76859e47i			0.825485i
$935$	−1.29316e46	+	3.47648e45i	−0.0379025	+	0.0101895i
$936$	7.38938e47			2.12909
$937$	−3.46305e46	−	3.46305e46i	−0.0980900	−	0.0980900i	0.656359	−	0.754449i	$-0.272096\pi$
$937$	−3.46305e46	−	3.46305e46i	−0.0980900	−	0.0980900i	−0.754449	+	0.656359i	$0.772096\pi$
$938$	−4.31570e47	+	4.31570e47i	−1.20173	+	1.20173i
$939$			2.73828e47i			0.749598i
$940$	2.01234e46	+	7.48540e46i	0.0541570	+	0.201451i
$941$	3.57451e47			0.945763			0.472881	−	0.881126i	$-0.343214\pi$
$941$	3.57451e47			0.945763			0.472881	+	0.881126i	$0.343214\pi$
$942$	−2.83064e47	−	2.83064e47i	−0.736325	−	0.736325i
$943$	5.05297e47	−	5.05297e47i	1.29229	−	1.29229i
$944$		−	2.03166e47i		−	0.510856i
$945$	2.49203e47	+	1.43603e47i	0.616091	+	0.355022i
$946$	4.42643e47			1.07596
$947$	−1.27440e47	−	1.27440e47i	−0.304583	−	0.304583i	0.538221	−	0.842804i	$-0.319097\pi$
$947$	−1.27440e47	−	1.27440e47i	−0.304583	−	0.304583i	−0.842804	+	0.538221i	$0.819097\pi$
$948$	1.04552e47	−	1.04552e47i	0.245696	−	0.245696i
$949$		−	7.41177e47i		−	1.71263i
$950$	−4.75249e47	−	1.26502e47i	−1.07980	−	0.287421i
$951$	−1.62700e47			−0.363496
$952$	−1.21529e46	−	1.21529e46i	−0.0266986	−	0.0266986i
$953$	−9.30380e46	+	9.30380e46i	−0.200990	+	0.200990i	−0.800424	−	0.599434i	$-0.795392\pi$
$953$	−9.30380e46	+	9.30380e46i	−0.200990	+	0.200990i	0.599434	+	0.800424i	$0.295392\pi$
$954$			9.19759e46i			0.195389i
$955$	−1.74069e47	+	3.02073e47i	−0.363637	+	0.631041i
$956$	7.59054e46			0.155936
$957$	−8.20557e43	−	8.20557e43i	−0.000165774	−	0.000165774i
$958$	−8.51466e45	+	8.51466e45i	−0.0169168	+	0.0169168i
$959$		−	9.65593e47i		−	1.88667i
$960$	8.55803e47	−	2.30069e47i	1.64450	−	0.442099i
$961$	−3.74355e47			−0.707473
$962$	2.22119e47	+	2.22119e47i	0.412842	+	0.412842i
$963$	7.63229e47	−	7.63229e47i	1.39519	−	1.39519i
$964$			5.60578e46i			0.100787i
$965$	−1.56269e47	−	5.81282e47i	−0.276335	−	1.02790i
$966$	−1.25436e48			−2.18166
$967$	3.22631e47	+	3.22631e47i	0.551928	+	0.551928i	0.926997	−	0.375069i	$-0.122381\pi$
$967$	3.22631e47	+	3.22631e47i	0.551928	+	0.551928i	−0.375069	+	0.926997i	$0.622381\pi$
$968$	−3.98795e47	+	3.98795e47i	−0.671034	+	0.671034i
$969$			3.49972e46i			0.0579233i
$970$	4.93518e47	+	2.84389e47i	0.803443	+	0.462983i
$971$	−4.89239e47			−0.783454			−0.391727	−	0.920081i	$-0.628122\pi$
$971$	−4.89239e47			−0.783454			−0.391727	+	0.920081i	$0.628122\pi$
$972$	−1.61277e47	−	1.61277e47i	−0.254047	−	0.254047i
$973$	−7.54378e45	+	7.54378e45i	−0.0116892	+	0.0116892i
$974$		−	4.05882e47i		−	0.618666i
$975$	−1.26553e48	+	7.33446e47i	−1.89758	+	1.09975i
$976$	−1.41391e47			−0.208557
$977$	−8.39845e46	−	8.39845e46i	−0.121867	−	0.121867i	0.643543	−	0.765410i	$-0.277464\pi$
$977$	−8.39845e46	−	8.39845e46i	−0.121867	−	0.121867i	−0.765410	+	0.643543i	$0.777464\pi$
$978$	1.04527e48	−	1.04527e48i	1.49214	−	1.49214i
$979$		−	1.55264e47i		−	0.218046i
$980$	−4.64881e46	+	8.06736e46i	−0.0642281	+	0.111459i
$981$	−6.38819e47			−0.868308
$982$	6.59763e47	+	6.59763e47i	0.882275	+	0.882275i
$983$	8.80136e47	−	8.80136e47i	1.15796	−	1.15796i	0.173046	−	0.984914i	$-0.444639\pi$
$983$	8.80136e47	−	8.80136e47i	1.15796	−	1.15796i	0.984914	−	0.173046i	$-0.0553609\pi$
$984$			1.73056e48i			2.24008i
$985$	−7.16045e47	+	1.92498e47i	−0.911928	+	0.245158i
$986$	−2.16657e42			−2.71483e−6
$987$	8.22980e47	+	8.22980e47i	1.01465	+	1.01465i
$988$	2.95403e47	−	2.95403e47i	0.358346	−	0.358346i
$989$			1.05422e48i			1.25832i
$990$	−3.56260e47	−	1.32520e48i	−0.418412	−	1.55639i
$991$	7.10636e47			0.821237			0.410619	−	0.911807i	$-0.365313\pi$
$991$	7.10636e47			0.821237			0.410619	+	0.911807i	$0.365313\pi$
$992$	−1.77431e47	−	1.77431e47i	−0.201764	−	0.201764i
$993$	−1.54762e48	+	1.54762e48i	−1.73172	+	1.73172i
$994$			3.19015e47i			0.351261i
$995$	8.60950e47	+	4.96122e47i	0.932843	+	0.537550i
$996$	−3.05532e47			−0.325767
$997$	3.03618e47	+	3.03618e47i	0.318570	+	0.318570i	0.848218	−	0.529648i	$-0.177676\pi$
$997$	3.03618e47	+	3.03618e47i	0.318570	+	0.318570i	−0.529648	+	0.848218i	$0.677676\pi$
$998$	−3.87176e46	+	3.87176e46i	−0.0399778	+	0.0399778i
$999$			2.77569e47i			0.282048i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.33.c.a.2.5	✓	30
5.2	odd	4		25.33.c.b.18.11		30
5.3	odd	4	inner	5.33.c.a.3.5	yes	30
5.4	even	2		25.33.c.b.7.11		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.33.c.a.2.5	✓	30	1.1	even	1	trivial
5.33.c.a.3.5	yes	30	5.3	odd	4	inner
25.33.c.b.7.11		30	5.4	even	2
25.33.c.b.18.11		30	5.2	odd	4

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:	\( k \)	\(=\)	\( 33 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-39535.2 - 39535.2i) q^{2} +(4.69567e7 - 4.69567e7i) q^{3} -1.16890e9i q^{4} +(-7.61848e10 + 1.32208e11i) q^{5} -3.71289e12 q^{6} +(2.85172e13 + 2.85172e13i) q^{7} +(-2.16015e14 + 2.16015e14i) q^{8} -2.55684e15i q^{9} +O(q^{10})\)	\(q+(-39535.2 - 39535.2i) q^{2} +(4.69567e7 - 4.69567e7i) q^{3} -1.16890e9i q^{4} +(-7.61848e10 + 1.32208e11i) q^{5} -3.71289e12 q^{6} +(2.85172e13 + 2.85172e13i) q^{7} +(-2.16015e14 + 2.16015e14i) q^{8} -2.55684e15i q^{9} +(8.23885e15 - 2.21489e15i) q^{10} +6.29088e16 q^{11} +(-5.48877e16 - 5.48877e16i) q^{12} +(6.68945e17 - 6.68945e17i) q^{13} -2.25487e18i q^{14} +(2.63066e18 + 9.78543e18i) q^{15} +1.20600e19 q^{16} +(9.86415e17 + 9.86415e17i) q^{17} +(-1.01085e20 + 1.01085e20i) q^{18} +3.77787e20i q^{19} +(1.54538e20 + 8.90523e19i) q^{20} +2.67814e21 q^{21} +(-2.48712e21 - 2.48712e21i) q^{22} +(5.92343e21 - 5.92343e21i) q^{23} +2.02867e22i q^{24} +(-1.16748e22 - 2.01445e22i) q^{25} -5.28938e22 q^{26} +(-3.30491e22 - 3.30491e22i) q^{27} +(3.33337e22 - 3.33337e22i) q^{28} -2.77779e19i q^{29} +(2.82865e23 - 4.90873e23i) q^{30} -3.93433e23 q^{31} +(4.50982e23 + 4.50982e23i) q^{32} +(2.95399e24 - 2.95399e24i) q^{33} -7.79962e22i q^{34} +(-5.94277e24 + 1.59762e24i) q^{35} -2.98869e24 q^{36} +(-4.19934e24 - 4.19934e24i) q^{37} +(1.49359e25 - 1.49359e25i) q^{38} -6.28229e25i q^{39} +(-1.21019e25 - 4.50160e25i) q^{40} +8.53049e25 q^{41} +(-1.05881e26 - 1.05881e26i) q^{42} +(-8.89872e25 + 8.89872e25i) q^{43} -7.35341e25i q^{44} +(3.38035e26 + 1.94792e26i) q^{45} -4.68368e26 q^{46} +(3.07295e26 + 3.07295e26i) q^{47} +(5.66299e26 - 5.66299e26i) q^{48} +5.22031e26i q^{49} +(-3.34849e26 + 1.25798e27i) q^{50} +9.26375e25 q^{51} +(-7.81929e26 - 7.81929e26i) q^{52} +(4.54942e26 - 4.54942e26i) q^{53} +2.61321e27i q^{54} +(-4.79270e27 + 8.31705e27i) q^{55} -1.23203e28 q^{56} +(1.77396e28 + 1.77396e28i) q^{57} +(-1.09821e24 + 1.09821e24i) q^{58} -1.68462e28i q^{59} +(1.14382e28 - 3.07498e27i) q^{60} -1.17239e28 q^{61} +(1.55544e28 + 1.55544e28i) q^{62} +(7.29139e28 - 7.29139e28i) q^{63} -8.74568e28i q^{64} +(3.74764e28 + 1.39403e29i) q^{65} -2.33573e29 q^{66} +(-1.91395e29 - 1.91395e29i) q^{67} +(1.15302e27 - 1.15302e27i) q^{68} -5.56289e29i q^{69} +(2.98111e29 + 1.71786e29i) q^{70} -1.41479e29 q^{71} +(5.52317e29 + 5.52317e29i) q^{72} +(5.53990e29 - 5.53990e29i) q^{73} +3.32043e29i q^{74} +(-1.49413e30 - 3.97706e29i) q^{75} +4.41595e29 q^{76} +(1.79398e30 + 1.79398e30i) q^{77} +(-2.48372e30 + 2.48372e30i) q^{78} +1.90483e30i q^{79} +(-9.18791e29 + 1.59443e30i) q^{80} +1.63413e30 q^{81} +(-3.37255e30 - 3.37255e30i) q^{82} +(2.78325e30 - 2.78325e30i) q^{83} -3.13048e30i q^{84} +(-2.05562e29 + 5.52621e28i) q^{85} +7.03626e30 q^{86} +(-1.30436e27 - 1.30436e27i) q^{87} +(-1.35893e31 + 1.35893e31i) q^{88} -2.46808e30i q^{89} +(-5.66312e30 - 2.10654e31i) q^{90} +3.81528e31 q^{91} +(-6.92389e30 - 6.92389e30i) q^{92} +(-1.84743e31 + 1.84743e31i) q^{93} -2.42979e31i q^{94} +(-4.99464e31 - 2.87816e31i) q^{95} +4.23533e31 q^{96} +(4.72097e31 + 4.72097e31i) q^{97} +(2.06386e31 - 2.06386e31i) q^{98} -1.60848e32i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{2} - 2792232 q^{3} + 229266409900 q^{5} - 645476451240 q^{6} + 21807690136848 q^{7} + 340768936037220 q^{8}+O(q^{10}) \) 30 * q - 2 * q^2 - 2792232 * q^3 + 229266409900 * q^5 - 645476451240 * q^6 + 21807690136848 * q^7 + 340768936037220 * q^8	\( 30 q - 2 q^{2} - 2792232 q^{3} + 229266409900 q^{5} - 645476451240 q^{6} + 21807690136848 q^{7} + 340768936037220 q^{8} - 17\!\cdots\!50 q^{10}+ \cdots + 12\!\cdots\!02 q^{98}+O(q^{100}) \) 30 * q - 2 * q^2 - 2792232 * q^3 + 229266409900 * q^5 - 645476451240 * q^6 + 21807690136848 * q^7 + 340768936037220 * q^8 - 17555754485145450 * q^10 - 60908362837533640 * q^11 + 444566273630869608 * q^12 + 649759187023107138 * q^13 + 6285624407445962400 * q^15 - 46108906958970522120 * q^16 - 218107661739005884502 * q^17 + 240407468159884203858 * q^18 - 3053538044199826052700 * q^20 + 4549905652154594876760 * q^21 - 11386561172247365212944 * q^22 + 13896091629970965206008 * q^23 + 35772470267692728866250 * q^25 - 23129486500762683557740 * q^26 + 176388356775702789525960 * q^27 + 59665474478272755491112 * q^28 + 1233340129583886997444800 * q^30 - 1285786827516670637255040 * q^31 + 3122517776856150857591368 * q^32 - 1644615516923295701112504 * q^33 - 818578197767771892231200 * q^35 + 31947551193266858523505980 * q^36 - 126275105375668809211002 * q^37 + 57601564734016178366855880 * q^38 + 211125410957683032210619500 * q^40 - 155417315271390260892986440 * q^41 + 797836438482097707185724336 * q^42 - 545147034084978191886568152 * q^43 + 1085165439164371861108713450 * q^45 - 3454637097270705106900721640 * q^46 + 2735203198488492729395621848 * q^47 - 3192952350241941373327314192 * q^48 + 4470181549725126255525651250 * q^50 - 6129415060408014316542923040 * q^51 + 6000870590399837156109494028 * q^52 - 11282171275183571262774628682 * q^53 - 7112951743928365540876222200 * q^55 - 47918174764291639802549158800 * q^56 + 44765351794015370451647799120 * q^57 - 29637988346430122895588672480 * q^58 + 34183609322952768706653073800 * q^60 + 50784540875895586667393303160 * q^61 - 218235799024898727529128868024 * q^62 + 213794735887989269330759842008 * q^63 - 349686192916613591890379914850 * q^65 + 1348836243659025586642346421120 * q^66 - 736483403252315334072161239752 * q^67 + 1085395947449178489054935855012 * q^68 - 363042164247863030846151545400 * q^70 + 817740403780342392034746361760 * q^71 - 951267702824572414087545605820 * q^72 - 379868722209495311437504600242 * q^73 + 104600806158947004257336610000 * q^75 - 6689750080738358201358794259600 * q^76 + 6381539826853244422672988941256 * q^77 - 9179143477318522110451614982584 * q^78 + 5875581782593356038176152810400 * q^80 - 14239669107938661073624705472070 * q^81 + 2725313872720345364461277817936 * q^82 + 4996401755555614465785455997328 * q^83 - 4438937659194362238905211673950 * q^85 + 16049932109847278395442966171960 * q^86 + 36834415428157346041110451524480 * q^87 - 47132513308908068698430156048160 * q^88 + 81433975991640870510397972968150 * q^90 - 104150500668224029090357708737840 * q^91 - 18747876848872687606754750486552 * q^92 + 112210213536624471769268225064216 * q^93 - 109796172349696400850071817591000 * q^95 + 380819283905835347723966665116960 * q^96 - 155781506757725945270376012026802 * q^97 + 125692870459469366775669291878702 * q^98

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