LMFDB - Embedded newform 5.33.c.a.2.15

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			2.15
Character	$\chi$	$=$	5.2
Dual form			5.33.c.a.3.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(84542.4 + 84542.4i) q^{2} +(5.85262e6 - 5.85262e6i) q^{3} +9.99987e9i q^{4} +(-1.33071e11 + 7.46670e10i) q^{5} +9.89589e11 q^{6} +(-4.06221e12 - 4.06221e12i) q^{7} +(-4.82306e14 + 4.82306e14i) q^{8} +1.78451e15i q^{9} +O(q^{10})$	\(q+(84542.4 + 84542.4i) q^{2} +(5.85262e6 - 5.85262e6i) q^{3} +9.99987e9i q^{4} +(-1.33071e11 + 7.46670e10i) q^{5} +9.89589e11 q^{6} +(-4.06221e12 - 4.06221e12i) q^{7} +(-4.82306e14 + 4.82306e14i) q^{8} +1.78451e15i q^{9} +(-1.75627e16 - 4.93762e15i) q^{10} -1.93753e16 q^{11} +(5.85254e16 + 5.85254e16i) q^{12} +(6.35202e17 - 6.35202e17i) q^{13} -6.86859e17i q^{14} +(-3.41817e17 + 1.21581e18i) q^{15} -3.86015e19 q^{16} +(-4.90922e19 - 4.90922e19i) q^{17} +(-1.50867e20 + 1.50867e20i) q^{18} +5.30302e17i q^{19} +(-7.46660e20 - 1.33069e21i) q^{20} -4.75492e19 q^{21} +(-1.63803e21 - 1.63803e21i) q^{22} +(-7.61780e21 + 7.61780e21i) q^{23} +5.64550e21i q^{24} +(1.21327e22 - 1.98720e22i) q^{25} +1.07403e23 q^{26} +(2.12891e22 + 2.12891e22i) q^{27} +(4.06216e22 - 4.06216e22i) q^{28} -1.82808e21i q^{29} +(-1.31686e23 + 7.38896e22i) q^{30} -1.01814e24 q^{31} +(-1.19197e24 - 1.19197e24i) q^{32} +(-1.13396e23 + 1.13396e23i) q^{33} -8.30074e24i q^{34} +(8.43877e23 + 2.37250e23i) q^{35} -1.78449e25 q^{36} +(3.94346e24 + 3.94346e24i) q^{37} +(-4.48330e22 + 4.48330e22i) q^{38} -7.43519e24i q^{39} +(2.81686e25 - 1.00193e26i) q^{40} +7.58500e25 q^{41} +(-4.01992e24 - 4.01992e24i) q^{42} +(-1.10287e26 + 1.10287e26i) q^{43} -1.93750e26i q^{44} +(-1.33244e26 - 2.37467e26i) q^{45} -1.28805e27 q^{46} +(6.32156e26 + 6.32156e26i) q^{47} +(-2.25920e26 + 2.25920e26i) q^{48} -1.07142e27i q^{49} +(2.70576e27 - 6.54298e26i) q^{50} -5.74636e26 q^{51} +(6.35194e27 + 6.35194e27i) q^{52} +(-3.02021e27 + 3.02021e27i) q^{53} +3.59966e27i q^{54} +(2.57829e27 - 1.44669e27i) q^{55} +3.91846e27 q^{56} +(3.10365e24 + 3.10365e24i) q^{57} +(1.54550e26 - 1.54550e26i) q^{58} +1.06369e28i q^{59} +(-1.21580e28 - 3.41812e27i) q^{60} -3.36099e27 q^{61} +(-8.60759e28 - 8.60759e28i) q^{62} +(7.24908e27 - 7.24908e27i) q^{63} -3.57525e28i q^{64} +(-3.70984e28 + 1.31956e29i) q^{65} -1.91736e28 q^{66} +(5.01232e28 + 5.01232e28i) q^{67} +(4.90915e29 - 4.90915e29i) q^{68} +8.91681e28i q^{69} +(5.12857e28 + 9.14010e28i) q^{70} +6.84870e28 q^{71} +(-8.60681e29 - 8.60681e29i) q^{72} +(-8.59218e29 + 8.59218e29i) q^{73} +6.66779e29i q^{74} +(-4.52951e28 - 1.87312e29i) q^{75} -5.30294e27 q^{76} +(7.87065e28 + 7.87065e28i) q^{77} +(6.28589e29 - 6.28589e29i) q^{78} +3.56643e30i q^{79} +(5.13674e30 - 2.88226e30i) q^{80} -3.05755e30 q^{81} +(6.41254e30 + 6.41254e30i) q^{82} +(-1.63821e30 + 1.63821e30i) q^{83} -4.75485e29i q^{84} +(1.01983e31 + 2.86718e30i) q^{85} -1.86478e31 q^{86} +(-1.06990e28 - 1.06990e28i) q^{87} +(9.34481e30 - 9.34481e30i) q^{88} +7.81891e30i q^{89} +(8.81125e30 - 3.13408e31i) q^{90} -5.16066e30 q^{91} +(-7.61769e31 - 7.61769e31i) q^{92} +(-5.95878e30 + 5.95878e30i) q^{93} +1.06888e32i q^{94} +(-3.95960e28 - 7.05678e28i) q^{95} -1.39523e31 q^{96} +(-3.43333e31 - 3.43333e31i) q^{97} +(9.05808e31 - 9.05808e31i) q^{98} -3.45754e31i 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 $

$2$	84542.4	+	84542.4i	1.29001	+	1.29001i	0.934775	+	0.355239i	$0.115601\pi$
$2$	84542.4	+	84542.4i	1.29001	+	1.29001i	0.355239	+	0.934775i	$0.384399\pi$
$3$	5.85262e6	−	5.85262e6i	0.135960	−	0.135960i	−0.635852	−	0.771811i	$-0.719351\pi$
$3$	5.85262e6	−	5.85262e6i	0.135960	−	0.135960i	0.771811	+	0.635852i	$0.219351\pi$
$4$			9.99987e9i			2.32828i
$5$	−1.33071e11	+	7.46670e10i	−0.872094	+	0.489338i
$5$	−1.33071e11	+	7.46670e10i	−0.872094	+	0.489338i
$6$	9.89589e11			0.350780
$7$	−4.06221e12	−	4.06221e12i	−0.122235	−	0.122235i	0.643343	−	0.765578i	$-0.277547\pi$
$7$	−4.06221e12	−	4.06221e12i	−0.122235	−	0.122235i	−0.765578	+	0.643343i	$0.777547\pi$
$8$	−4.82306e14	+	4.82306e14i	−1.71349	+	1.71349i
$9$			1.78451e15i			0.963030i
$10$	−1.75627e16	−	4.93762e15i	−1.75627	−	0.493762i
$11$	−1.93753e16			−0.421662			−0.210831	−	0.977522i	$-0.567617\pi$
$11$	−1.93753e16			−0.421662			−0.210831	+	0.977522i	$0.567617\pi$
$12$	5.85254e16	+	5.85254e16i	0.316552	+	0.316552i
$13$	6.35202e17	−	6.35202e17i	0.954593	−	0.954593i	−0.0444196	−	0.999013i	$-0.514144\pi$
$13$	6.35202e17	−	6.35202e17i	0.954593	−	0.954593i	0.999013	+	0.0444196i	$0.0141438\pi$
$14$		−	6.86859e17i		−	0.315369i
$15$	−3.41817e17	+	1.21581e18i	−0.0520395	+	0.185100i
$16$	−3.86015e19			−2.09259
$17$	−4.90922e19	−	4.90922e19i	−1.00886	−	1.00886i	−0.999960	−	0.00889669i	$-0.997168\pi$
$17$	−4.90922e19	−	4.90922e19i	−1.00886	−	1.00886i	−0.00889669	−	0.999960i	$-0.502832\pi$
$18$	−1.50867e20	+	1.50867e20i	−1.24232	+	1.24232i
$19$			5.30302e17i			0.00183851i	1.00000		0.000919254i	$0.000292608\pi$
$19$			5.30302e17i			0.00183851i	−1.00000		0.000919254i	$0.999707\pi$
$20$	−7.46660e20	−	1.33069e21i	−1.13931	−	2.03048i
$21$	−4.75492e19			−0.0332380
$22$	−1.63803e21	−	1.63803e21i	−0.543951	−	0.543951i
$23$	−7.61780e21	+	7.61780e21i	−1.24218	+	1.24218i	−0.283083	+	0.959095i	$0.591357\pi$
$23$	−7.61780e21	+	7.61780e21i	−1.24218	+	1.24218i	−0.959095	+	0.283083i	$0.908643\pi$
$24$			5.64550e21i			0.465932i
$25$	1.21327e22	−	1.98720e22i	0.521097	−	0.853497i
$26$	1.07403e23			2.46288
$27$	2.12891e22	+	2.12891e22i	0.266893	+	0.266893i
$28$	4.06216e22	−	4.06216e22i	0.284596	−	0.284596i
$29$		−	1.82808e21i		−	0.00730511i	−0.999993	−	0.00365255i	$-0.998837\pi$
$29$		−	1.82808e21i		−	0.00730511i	0.999993	−	0.00365255i	$-0.00116265\pi$
$30$	−1.31686e23	+	7.38896e22i	−0.305913	+	0.171650i
$31$	−1.01814e24			−1.39965			−0.699826	−	0.714313i	$-0.746739\pi$
$31$	−1.01814e24			−1.39965			−0.699826	+	0.714313i	$0.746739\pi$
$32$	−1.19197e24	−	1.19197e24i	−0.985977	−	0.985977i
$33$	−1.13396e23	+	1.13396e23i	−0.0573291	+	0.0573291i
$34$		−	8.30074e24i		−	2.60288i
$35$	8.43877e23	+	2.37250e23i	0.166414	+	0.0467861i
$36$	−1.78449e25			−2.24220
$37$	3.94346e24	+	3.94346e24i	0.319632	+	0.319632i	0.848626	−	0.528994i	$-0.177431\pi$
$37$	3.94346e24	+	3.94346e24i	0.319632	+	0.319632i	−0.528994	+	0.848626i	$0.677431\pi$
$38$	−4.48330e22	+	4.48330e22i	−0.00237170	+	0.00237170i
$39$		−	7.43519e24i		−	0.259572i
$40$	2.81686e25	−	1.00193e26i	0.655852	−	2.33281i
$41$	7.58500e25			1.18964			0.594818	−	0.803860i	$-0.297224\pi$
$41$	7.58500e25			1.18964			0.594818	+	0.803860i	$0.297224\pi$
$42$	−4.01992e24	−	4.01992e24i	−0.0428775	−	0.0428775i
$43$	−1.10287e26	+	1.10287e26i	−0.807286	+	0.807286i	−0.984222	−	0.176937i	$-0.943381\pi$
$43$	−1.10287e26	+	1.10287e26i	−0.807286	+	0.807286i	0.176937	+	0.984222i	$0.443381\pi$
$44$		−	1.93750e26i		−	0.981746i
$45$	−1.33244e26	−	2.37467e26i	−0.471247	−	0.839853i
$46$	−1.28805e27			−3.20486
$47$	6.32156e26	+	6.32156e26i	1.11496	+	1.11496i	0.992470	+	0.122488i	$0.0390874\pi$
$47$	6.32156e26	+	6.32156e26i	1.11496	+	1.11496i	0.122488	+	0.992470i	$0.460913\pi$
$48$	−2.25920e26	+	2.25920e26i	−0.284508	+	0.284508i
$49$		−	1.07142e27i		−	0.970117i
$50$	2.70576e27	−	6.54298e26i	1.77325	−	0.428801i
$51$	−5.74636e26			−0.274328
$52$	6.35194e27	+	6.35194e27i	2.22256	+	2.22256i
$53$	−3.02021e27	+	3.02021e27i	−0.779154	+	0.779154i	−0.979687	−	0.200533i	$-0.935733\pi$
$53$	−3.02021e27	+	3.02021e27i	−0.779154	+	0.779154i	0.200533	+	0.979687i	$0.435733\pi$
$54$			3.59966e27i			0.688592i
$55$	2.57829e27	−	1.44669e27i	0.367729	−	0.206335i
$56$	3.91846e27			0.418897
$57$	3.10365e24	+	3.10365e24i	0.000249963	+	0.000249963i
$58$	1.54550e26	−	1.54550e26i	0.00942370	−	0.00942370i
$59$			1.06369e28i			0.493380i	0.969094	+	0.246690i	$0.0793430\pi$
$59$			1.06369e28i			0.493380i	−0.969094	+	0.246690i	$0.920657\pi$
$60$	−1.21580e28	−	3.41812e27i	−0.430963	−	0.121162i
$61$	−3.36099e27			−0.0914513			−0.0457256	−	0.998954i	$-0.514560\pi$
$61$	−3.36099e27			−0.0914513			−0.0457256	+	0.998954i	$0.514560\pi$
$62$	−8.60759e28	−	8.60759e28i	−1.80557	−	1.80557i
$63$	7.24908e27	−	7.24908e27i	0.117716	−	0.117716i
$64$		−	3.57525e28i		−	0.451260i
$65$	−3.70984e28	+	1.31956e29i	−0.365377	+	1.29961i
$66$	−1.91736e28			−0.147911
$67$	5.01232e28	+	5.01232e28i	0.303978	+	0.303978i	0.842568	−	0.538590i	$-0.181043\pi$
$67$	5.01232e28	+	5.01232e28i	0.303978	+	0.303978i	−0.538590	+	0.842568i	$0.681043\pi$
$68$	4.90915e29	−	4.90915e29i	2.34890	−	2.34890i
$69$			8.91681e28i			0.337772i
$70$	5.12857e28	+	9.14010e28i	0.154322	+	0.275031i
$71$	6.84870e28			0.164238			0.0821192	−	0.996623i	$-0.473831\pi$
$71$	6.84870e28			0.164238			0.0821192	+	0.996623i	$0.473831\pi$
$72$	−8.60681e29	−	8.60681e29i	−1.65015	−	1.65015i
$73$	−8.59218e29	+	8.59218e29i	−1.32111	+	1.32111i	−0.408224	+	0.912882i	$0.633852\pi$
$73$	−8.59218e29	+	8.59218e29i	−1.32111	+	1.32111i	−0.912882	+	0.408224i	$0.866148\pi$
$74$			6.66779e29i			0.824659i
$75$	−4.52951e28	−	1.87312e29i	−0.0451930	−	0.186889i
$76$	−5.30294e27			−0.00428055
$77$	7.87065e28	+	7.87065e28i	0.0515417	+	0.0515417i
$78$	6.28589e29	−	6.28589e29i	0.334852	−	0.334852i
$79$			3.56643e30i			1.54953i	0.632249	+	0.774765i	$0.282132\pi$
$79$			3.56643e30i			1.54953i	−0.632249	+	0.774765i	$0.717868\pi$
$80$	5.13674e30	−	2.88226e30i	1.82494	−	1.02398i
$81$	−3.05755e30			−0.890457
$82$	6.41254e30	+	6.41254e30i	1.53465	+	1.53465i
$83$	−1.63821e30	+	1.63821e30i	−0.322938	+	0.322938i	−0.849893	−	0.526955i	$-0.823334\pi$
$83$	−1.63821e30	+	1.63821e30i	−0.322938	+	0.322938i	0.526955	+	0.849893i	$0.323334\pi$
$84$		−	4.75485e29i		−	0.0773871i
$85$	1.01983e31	+	2.86718e30i	1.37349	+	0.386147i
$86$	−1.86478e31			−2.08282
$87$	−1.06990e28	−	1.06990e28i	−0.000993200	−	0.000993200i
$88$	9.34481e30	−	9.34481e30i	0.722516	−	0.722516i
$89$			7.81891e30i			0.504552i	0.967655	+	0.252276i	$0.0811791\pi$
$89$			7.81891e30i			0.504552i	−0.967655	+	0.252276i	$0.918821\pi$
$90$	8.81125e30	−	3.13408e31i	0.475507	−	1.69134i
$91$	−5.16066e30			−0.233369
$92$	−7.61769e31	−	7.61769e31i	−2.89213	−	2.89213i
$93$	−5.95878e30	+	5.95878e30i	−0.190296	+	0.190296i
$94$			1.06888e32i			2.87662i
$95$	−3.95960e28	−	7.05678e28i	−0.000899651	−	0.00160335i
$96$	−1.39523e31			−0.268106
$97$	−3.43333e31	−	3.43333e31i	−0.558943	−	0.558943i	0.370063	−	0.929007i	$-0.379336\pi$
$97$	−3.43333e31	−	3.43333e31i	−0.558943	−	0.558943i	−0.929007	+	0.370063i	$0.879336\pi$
$98$	9.05808e31	−	9.05808e31i	1.25147	−	1.25147i
$99$		−	3.45754e31i		−	0.406074i
$100$	1.98718e32	+	1.21326e32i	1.98718	+	1.21326i
$101$	8.46617e31			0.722013			0.361007	−	0.932563i	$-0.382433\pi$
$101$	8.46617e31			0.722013			0.361007	+	0.932563i	$0.382433\pi$
$102$	−4.85811e31	−	4.85811e31i	−0.353887	−	0.353887i
$103$	1.36234e32	−	1.36234e32i	0.848966	−	0.848966i	−0.141038	−	0.990004i	$-0.545044\pi$
$103$	1.36234e32	−	1.36234e32i	0.848966	−	0.848966i	0.990004	+	0.141038i	$0.0450439\pi$
$104$			6.12723e32i			3.27138i
$105$	6.32742e30	−	3.55036e30i	0.0289866	−	0.0162646i
$106$	−5.10672e32			−2.01024
$107$	−1.53197e32	−	1.53197e32i	−0.518930	−	0.518930i	0.398317	−	0.917248i	$-0.369594\pi$
$107$	−1.53197e32	−	1.53197e32i	−0.518930	−	0.518930i	−0.917248	+	0.398317i	$0.869594\pi$
$108$	−2.12888e32	+	2.12888e32i	−0.621400	+	0.621400i
$109$		−	2.33989e32i		−	0.589349i	−0.955598	−	0.294674i	$-0.904789\pi$
$109$		−	2.33989e32i		−	0.589349i	0.955598	−	0.294674i	$-0.0952112\pi$
$110$	3.40282e32	+	9.56677e31i	0.740552	+	0.208201i
$111$	4.61592e31			0.0869141
$112$	1.56807e32	+	1.56807e32i	0.255787	+	0.255787i
$113$	1.27505e32	−	1.27505e32i	0.180415	−	0.180415i	−0.611122	−	0.791537i	$-0.709281\pi$
$113$	1.27505e32	−	1.27505e32i	0.180415	−	0.180415i	0.791537	+	0.611122i	$0.209281\pi$
$114$			5.24781e29i			0.000644911i
$115$	4.44910e32	−	1.58251e33i	0.475452	−	1.69114i
$116$	1.82805e31			0.0170083
$117$	1.13353e33	+	1.13353e33i	0.919302	+	0.919302i
$118$	−8.99267e32	+	8.99267e32i	−0.636468	+	0.636468i
$119$			3.98846e32i			0.246635i
$120$	−4.21533e32	−	7.51253e32i	−0.227998	−	0.406337i
$121$	−1.73598e33			−0.822201
$122$	−2.84146e32	−	2.84146e32i	−0.117973	−	0.117973i
$123$	4.43921e32	−	4.43921e32i	0.161743	−	0.161743i
$124$		−	1.01813e34i		−	3.25877i
$125$	−1.30732e32	+	3.55031e33i	−0.0367978	+	0.999323i
$126$	1.22571e33			0.303710
$127$	−1.02268e33	−	1.02268e33i	−0.223297	−	0.223297i	0.586588	−	0.809885i	$-0.300471\pi$
$127$	−1.02268e33	−	1.02268e33i	−0.223297	−	0.223297i	−0.809885	+	0.586588i	$0.800471\pi$
$128$	−2.09689e33	+	2.09689e33i	−0.403846	+	0.403846i
$129$			1.29093e33i			0.219517i
$130$	−1.42922e34	+	8.01946e33i	−2.14786	+	1.20518i
$131$	9.09503e33			1.20910			0.604551	−	0.796566i	$-0.293352\pi$
$131$	9.09503e33			1.20910			0.604551	+	0.796566i	$0.293352\pi$
$132$	−1.13395e33	−	1.13395e33i	−0.133478	−	0.133478i
$133$	2.15420e30	−	2.15420e30i	0.000224729	−	0.000224729i
$134$			8.47506e33i			0.784271i
$135$	−4.42256e33	−	1.24337e33i	−0.363357	−	0.102155i
$136$	4.73549e34			3.45734
$137$	1.39497e34	+	1.39497e34i	0.905805	+	0.905805i	0.995930	−	0.0901254i	$-0.0287268\pi$
$137$	1.39497e34	+	1.39497e34i	0.905805	+	0.905805i	−0.0901254	+	0.995930i	$0.528727\pi$
$138$	−7.53849e33	+	7.53849e33i	−0.435731	+	0.435731i
$139$		−	9.38369e33i		−	0.483211i	−0.970375	−	0.241606i	$-0.922326\pi$
$139$		−	9.38369e33i		−	0.483211i	0.970375	−	0.241606i	$-0.0776740\pi$
$140$	−2.37247e33	+	8.43865e33i	−0.108931	+	0.387458i
$141$	7.39954e33			0.303179
$142$	5.79006e33	+	5.79006e33i	0.211870	+	0.211870i
$143$	−1.23072e34	+	1.23072e34i	−0.402516	+	0.402516i
$144$		−	6.88849e34i		−	2.01523i
$145$	1.36497e32	+	2.43264e32i	0.00357467	+	0.00637075i
$146$	−1.45281e35			−3.40849
$147$	−6.27064e33	−	6.27064e33i	−0.131897	−	0.131897i
$148$	−3.94341e34	+	3.94341e34i	−0.744191	+	0.744191i
$149$		−	5.90707e34i		−	1.00090i	−0.865765	−	0.500451i	$-0.833167\pi$
$149$		−	5.90707e34i		−	1.00090i	0.865765	−	0.500451i	$-0.166833\pi$
$150$	1.20064e34	−	1.96651e34i	0.182791	−	0.299390i
$151$	3.87072e34			0.529859			0.264929	−	0.964268i	$-0.414651\pi$
$151$	3.87072e34			0.529859			0.264929	+	0.964268i	$0.414651\pi$
$152$	−2.55768e32	−	2.55768e32i	−0.00315027	−	0.00315027i
$153$	8.76057e34	−	8.76057e34i	0.971560	−	0.971560i
$154$			1.33081e34i			0.132979i
$155$	1.35485e35	−	7.60214e34i	1.22063	−	0.684902i
$156$	7.43509e34			0.604356
$157$	−1.06636e34	−	1.06636e34i	−0.0782548	−	0.0782548i	0.666896	−	0.745151i	$-0.267623\pi$
$157$	−1.06636e34	−	1.06636e34i	−0.0782548	−	0.0782548i	−0.745151	+	0.666896i	$0.767623\pi$
$158$	−3.01514e35	+	3.01514e35i	−1.99892	+	1.99892i
$159$			3.53523e34i			0.211867i
$160$	2.47618e35	+	6.96161e34i	1.34234	+	0.377389i
$161$	6.18902e34			0.303674
$162$	−2.58492e35	−	2.58492e35i	−1.14870	−	1.14870i
$163$	2.93398e35	−	2.93398e35i	1.18156	−	1.18156i	0.202217	−	0.979341i	$-0.435185\pi$
$163$	2.93398e35	−	2.93398e35i	1.18156	−	1.18156i	0.979341	−	0.202217i	$-0.0648145\pi$
$164$			7.58490e35i			2.76980i
$165$	6.62279e33	−	2.35567e34i	0.0219431	−	0.0780497i
$166$	−2.76996e35			−0.833191
$167$	−6.86082e34	−	6.86082e34i	−0.187462	−	0.187462i	0.607136	−	0.794598i	$-0.292318\pi$
$167$	−6.86082e34	−	6.86082e34i	−0.187462	−	0.187462i	−0.794598	+	0.607136i	$0.792318\pi$
$168$	2.29332e34	−	2.29332e34i	0.0569531	−	0.0569531i
$169$		−	3.64185e35i		−	0.822497i
$170$	6.19792e35	+	1.10459e36i	1.27369	+	2.26996i
$171$	−9.46331e32			−0.00177054
$172$	−1.10285e36	−	1.10285e36i	−1.87958	−	1.87958i
$173$	−3.11746e34	+	3.11746e34i	−0.0484243	+	0.0484243i	−0.730904	−	0.682480i	$-0.760901\pi$
$173$	−3.11746e34	+	3.11746e34i	−0.0484243	+	0.0484243i	0.682480	+	0.730904i	$0.260901\pi$
$174$		−	1.80905e33i		−	0.00256249i
$175$	−1.30010e35	+	3.14386e34i	−0.168023	+	0.0406308i
$176$	7.47914e35			0.882366
$177$	6.22535e34	+	6.22535e34i	0.0670798	+	0.0670798i
$178$	−6.61029e35	+	6.61029e35i	−0.650880	+	0.650880i
$179$			1.80994e36i			1.62936i	0.579914	+	0.814678i	$0.303086\pi$
$179$			1.80994e36i			1.62936i	−0.579914	+	0.814678i	$0.696914\pi$
$180$	2.37464e36	−	1.33242e36i	1.95541	−	1.09719i
$181$	9.70489e35			0.731364			0.365682	−	0.930740i	$-0.380836\pi$
$181$	9.70489e35			0.731364			0.365682	+	0.930740i	$0.380836\pi$
$182$	−4.36294e35	−	4.36294e35i	−0.301049	−	0.301049i
$183$	−1.96706e34	+	1.96706e34i	−0.0124337	+	0.0124337i
$184$		−	7.34821e36i		−	4.25693i
$185$	−8.19207e35	−	2.30314e35i	−0.435157	−	0.122341i
$186$	−1.00754e36			−0.490970
$187$	9.51175e35	+	9.51175e35i	0.425397	+	0.425397i
$188$	−6.32148e36	+	6.32148e36i	−2.59593	+	2.59593i
$189$		−	1.72962e35i		−	0.0652471i
$190$	2.61843e33	−	9.31351e33i	0.000907785	−	0.00322891i
$191$	−3.26878e36			−1.04196			−0.520981	−	0.853568i	$-0.674434\pi$
$191$	−3.26878e36			−1.04196			−0.520981	+	0.853568i	$0.674434\pi$
$192$	−2.09246e35	−	2.09246e35i	−0.0613531	−	0.0613531i
$193$	−1.78102e36	+	1.78102e36i	−0.480566	+	0.480566i	−0.905312	−	0.424747i	$-0.860363\pi$
$193$	−1.78102e36	+	1.78102e36i	−0.480566	+	0.480566i	0.424747	+	0.905312i	$0.360363\pi$
$194$		−	5.80524e36i		−	1.44209i
$195$	5.55164e35	+	9.89409e35i	0.127019	+	0.226372i
$196$	1.07141e37			2.25870
$197$	3.07795e36	+	3.07795e36i	0.598139	+	0.598139i	0.939817	−	0.341678i	$-0.110995\pi$
$197$	3.07795e36	+	3.07795e36i	0.598139	+	0.598139i	−0.341678	+	0.939817i	$0.610995\pi$
$198$	2.92309e36	−	2.92309e36i	0.523841	−	0.523841i
$199$		−	3.66895e36i		−	0.606586i	−0.952897	−	0.303293i	$-0.901914\pi$
$199$		−	3.66895e36i		−	0.606586i	0.952897	−	0.303293i	$-0.0980861\pi$
$200$	3.73270e36	+	1.54361e37i	0.569565	+	2.35536i
$201$	5.86703e35			0.0826574
$202$	7.15751e36	+	7.15751e36i	0.931408	+	0.931408i
$203$	−7.42605e33	+	7.42605e33i	−0.000892937	+	0.000892937i
$204$		−	5.74628e36i		−	0.638711i
$205$	−1.00934e37	+	5.66349e36i	−1.03747	+	0.582134i
$206$	2.30351e37			2.19036
$207$	−1.35941e37	−	1.35941e37i	−1.19625	−	1.19625i
$208$	−2.45197e37	+	2.45197e37i	−1.99757	+	1.99757i
$209$		−	1.02747e34i		−	0.000775229i
$210$	8.35091e35	+	2.34780e35i	0.0583747	+	0.0164116i
$211$	1.56199e37			1.01195			0.505976	−	0.862547i	$-0.331132\pi$
$211$	1.56199e37			1.01195			0.505976	+	0.862547i	$0.331132\pi$
$212$	−3.02017e37	−	3.02017e37i	−1.81409	−	1.81409i
$213$	4.00828e35	−	4.00828e35i	0.0223298	−	0.0223298i
$214$		−	2.59032e37i		−	1.33886i
$215$	6.44118e36	−	2.29107e37i	0.308994	−	1.09906i
$216$	−2.05357e37			−0.914639
$217$	4.13590e36	+	4.13590e36i	0.171086	+	0.171086i
$218$	1.97820e37	−	1.97820e37i	0.760268	−	0.760268i
$219$			1.00574e37i			0.359234i
$220$	1.44667e37	+	2.57825e37i	0.480405	+	0.856175i
$221$	−6.23669e37			−1.92610
$222$	3.90241e36	+	3.90241e36i	0.112120	+	0.112120i
$223$	−1.38056e37	+	1.38056e37i	−0.369129	+	0.369129i	−0.867160	−	0.498030i	$-0.834057\pi$
$223$	−1.38056e37	+	1.38056e37i	−0.369129	+	0.369129i	0.498030	+	0.867160i	$0.334057\pi$
$224$			9.68410e36i			0.241041i
$225$	3.54619e37	+	2.16510e37i	0.821943	+	0.501832i
$226$	2.15592e37			0.465476
$227$	1.75494e37	+	1.75494e37i	0.353060	+	0.353060i	0.861247	−	0.508187i	$-0.169684\pi$
$227$	1.75494e37	+	1.75494e37i	0.353060	+	0.353060i	−0.508187	+	0.861247i	$0.669684\pi$
$228$	−3.10361e34	+	3.10361e34i	−0.000581982	+	0.000581982i
$229$		−	1.71079e37i		−	0.299108i	−0.988754	−	0.149554i	$-0.952216\pi$
$229$		−	1.71079e37i		−	0.299108i	0.988754	−	0.149554i	$-0.0477838\pi$
$230$	1.71403e38	−	9.61751e37i	2.79494	−	1.56826i
$231$	9.21279e35			0.0140152
$232$	8.81692e35	+	8.81692e35i	0.0125173	+	0.0125173i
$233$	−1.67794e36	+	1.67794e36i	−0.0222373	+	0.0222373i	−0.718138	−	0.695901i	$-0.755005\pi$
$233$	−1.67794e36	+	1.67794e36i	−0.0222373	+	0.0222373i	0.695901	+	0.718138i	$0.255005\pi$
$234$			1.91662e38i			2.37183i
$235$	−1.31323e38	−	3.69205e37i	−1.51794	−	0.426758i
$236$	−1.06367e38			−1.14872
$237$	2.08730e37	+	2.08730e37i	0.210674	+	0.210674i
$238$	−3.37194e37	+	3.37194e37i	−0.318162	+	0.318162i
$239$			1.01699e38i			0.897330i	0.893700	+	0.448665i	$0.148100\pi$
$239$			1.01699e38i			0.897330i	−0.893700	+	0.448665i	$0.851900\pi$
$240$	1.31946e37	−	4.69321e37i	0.108897	−	0.387338i
$241$	−2.09334e37			−0.161647			−0.0808234	−	0.996728i	$-0.525755\pi$
$241$	−2.09334e37			−0.161647			−0.0808234	+	0.996728i	$0.525755\pi$
$242$	−1.46764e38	−	1.46764e38i	−1.06065	−	1.06065i
$243$	−5.73438e37	+	5.73438e37i	−0.387959	+	0.387959i
$244$		−	3.36094e37i		−	0.212924i
$245$	8.00000e37	+	1.42576e38i	0.474715	+	0.846034i
$246$	7.50603e37			0.417300
$247$	3.36849e35	+	3.36849e35i	0.00175503	+	0.00175503i
$248$	4.91054e38	−	4.91054e38i	2.39830	−	2.39830i
$249$			1.91756e37i			0.0878132i
$250$	−3.11204e38	+	2.89099e38i	−1.33661	+	1.24167i
$251$	3.44889e38			1.38963			0.694816	−	0.719187i	$-0.255486\pi$
$251$	3.44889e38			1.38963			0.694816	+	0.719187i	$0.255486\pi$
$252$	7.24898e37	+	7.24898e37i	0.274074	+	0.274074i
$253$	1.47597e38	−	1.47597e38i	0.523780	−	0.523780i
$254$		−	1.72920e38i		−	0.576112i
$255$	7.64674e37	−	4.29063e37i	0.239240	−	0.134239i
$256$	−5.08107e38			−1.49319
$257$	−1.84454e38	−	1.84454e38i	−0.509282	−	0.509282i	0.405024	−	0.914306i	$-0.367263\pi$
$257$	−1.84454e38	−	1.84454e38i	−0.509282	−	0.509282i	−0.914306	+	0.405024i	$0.867263\pi$
$258$	−1.09138e38	+	1.09138e38i	−0.283180	+	0.283180i
$259$		−	3.20384e37i		−	0.0781402i
$260$	−1.31954e39	−	3.70979e38i	−3.02586	−	0.850698i
$261$	3.26223e36			0.00703504
$262$	7.68915e38	+	7.68915e38i	1.55976	+	1.55976i
$263$	−4.14571e37	+	4.14571e37i	−0.0791237	+	0.0791237i	−0.745561	−	0.666437i	$-0.767818\pi$
$263$	−4.14571e37	+	4.14571e37i	−0.0791237	+	0.0791237i	0.666437	+	0.745561i	$0.267818\pi$
$264$		−	1.09383e38i		−	0.196466i
$265$	1.76393e38	−	6.27413e38i	0.298227	−	1.06077i
$266$	3.64242e35			0.000579808
$267$	4.57611e37	+	4.57611e37i	0.0685988	+	0.0685988i
$268$	−5.01225e38	+	5.01225e38i	−0.707743	+	0.707743i
$269$		−	1.03829e39i		−	1.38127i	−0.723201	−	0.690637i	$-0.757330\pi$
$269$		−	1.03829e39i		−	1.38127i	0.723201	−	0.690637i	$-0.242670\pi$
$270$	−2.68776e38	−	4.79011e38i	−0.336954	−	0.600517i
$271$	7.15719e38			0.845734			0.422867	−	0.906192i	$-0.361024\pi$
$271$	7.15719e38			0.845734			0.422867	+	0.906192i	$0.361024\pi$
$272$	1.89503e39	+	1.89503e39i	2.11112	+	2.11112i
$273$	−3.02034e37	+	3.02034e37i	−0.0317287	+	0.0317287i
$274$			2.35868e39i			2.33700i
$275$	−2.35075e38	+	3.85026e38i	−0.219727	+	0.359888i
$276$	−8.91669e38			−0.786427
$277$	4.40275e38	+	4.40275e38i	0.366478	+	0.366478i	0.866191	−	0.499713i	$-0.166561\pi$
$277$	4.40275e38	+	4.40275e38i	0.366478	+	0.366478i	−0.499713	+	0.866191i	$0.666561\pi$
$278$	7.93320e38	−	7.93320e38i	0.623349	−	0.623349i
$279$		−	1.81688e39i		−	1.34791i
$280$	−5.21433e38	+	2.92580e38i	−0.365317	+	0.204982i
$281$	1.10078e39			0.728452			0.364226	−	0.931311i	$-0.381333\pi$
$281$	1.10078e39			0.728452			0.364226	+	0.931311i	$0.381333\pi$
$282$	6.25575e38	+	6.25575e38i	0.391105	+	0.391105i
$283$	6.35069e38	−	6.35069e38i	0.375178	−	0.375178i	−0.494181	−	0.869359i	$-0.664532\pi$
$283$	6.35069e38	−	6.35069e38i	0.375178	−	0.375178i	0.869359	+	0.494181i	$0.164532\pi$
$284$			6.84861e38i			0.382392i
$285$	−6.44747e35	−	1.81266e35i	−0.000340307	−	9.56750e-5i
$286$	−2.08096e39			−1.03850
$287$	−3.08119e38	−	3.08119e38i	−0.145415	−	0.145415i
$288$	2.12709e39	−	2.12709e39i	0.949525	−	0.949525i
$289$			2.45217e39i			1.03559i
$290$	−9.02635e36	+	3.21059e37i	−0.00360698	+	0.0128297i
$291$	−4.01879e38			−0.151988
$292$	−8.59206e39	−	8.59206e39i	−3.07590	−	3.07590i
$293$	−2.06948e39	+	2.06948e39i	−0.701423	+	0.701423i	−0.964716	−	0.263293i	$-0.915191\pi$
$293$	−2.06948e39	+	2.06948e39i	−0.701423	+	0.701423i	0.263293	+	0.964716i	$0.415191\pi$
$294$		−	1.06027e39i		−	0.340298i
$295$	−7.94223e38	−	1.41546e39i	−0.241429	−	0.430274i
$296$	−3.80391e39			−1.09537
$297$	−4.12482e38	−	4.12482e38i	−0.112539	−	0.112539i
$298$	4.99398e39	−	4.99398e39i	1.29118	−	1.29118i
$299$			9.67768e39i			2.37155i
$300$	1.87309e39	−	4.52945e38i	0.435130	−	0.105222i
$301$	8.96015e38			0.197357
$302$	3.27240e39	+	3.27240e39i	0.683526	+	0.683526i
$303$	4.95493e38	−	4.95493e38i	0.0981647	−	0.0981647i
$304$		−	2.04704e37i		−	0.00384724i
$305$	4.47250e38	−	2.50955e38i	0.0797542	−	0.0447506i
$306$	1.48128e40			2.50665
$307$	−3.61620e39	−	3.61620e39i	−0.580816	−	0.580816i	0.354311	−	0.935128i	$-0.384715\pi$
$307$	−3.61620e39	−	3.61620e39i	−0.580816	−	0.580816i	−0.935128	+	0.354311i	$0.884715\pi$
$308$	−7.87055e38	+	7.87055e38i	−0.120003	+	0.120003i
$309$		−	1.59465e39i		−	0.230850i
$310$	1.78812e40	+	5.02718e39i	2.45816	+	0.691095i
$311$	−6.85765e39			−0.895383			−0.447692	−	0.894188i	$-0.647754\pi$
$311$	−6.85765e39			−0.895383			−0.447692	+	0.894188i	$0.647754\pi$
$312$	3.58604e39	+	3.58604e39i	0.444776	+	0.444776i
$313$	−7.78586e39	+	7.78586e39i	−0.917481	+	0.917481i	−0.996846	−	0.0793643i	$-0.974711\pi$
$313$	−7.78586e39	+	7.78586e39i	−0.917481	+	0.917481i	0.0793643	+	0.996846i	$0.474711\pi$
$314$		−	1.80306e39i		−	0.201900i
$315$	−4.23376e38	+	1.50591e39i	−0.0450564	+	0.160262i
$316$	−3.56638e40			−3.60773
$317$	4.58100e39	+	4.58100e39i	0.440567	+	0.440567i	0.892203	−	0.451635i	$-0.149159\pi$
$317$	4.58100e39	+	4.58100e39i	0.440567	+	0.440567i	−0.451635	+	0.892203i	$0.649159\pi$
$318$	−2.98877e39	+	2.98877e39i	−0.273312	+	0.273312i
$319$			3.54195e37i			0.00308029i
$320$	2.66953e39	+	4.75762e39i	0.220818	+	0.393541i
$321$	−1.79320e39			−0.141107
$322$	5.23235e39	+	5.23235e39i	0.391744	+	0.391744i
$323$	2.60337e37	−	2.60337e37i	0.00185479	−	0.00185479i
$324$		−	3.05751e40i		−	2.07323i
$325$	−4.91601e39	−	2.03295e40i	−0.317307	−	1.31218i
$326$	4.96091e40			3.04845
$327$	−1.36945e39	−	1.36945e39i	−0.0801277	−	0.0801277i
$328$	−3.65829e40	+	3.65829e40i	−2.03843	+	2.03843i
$329$		−	5.13591e39i		−	0.272573i
$330$	2.55144e39	−	1.43163e39i	0.128992	−	0.0723783i
$331$	3.21776e40			1.54991			0.774954	−	0.632017i	$-0.217773\pi$
$331$	3.21776e40			1.54991			0.774954	+	0.632017i	$0.217773\pi$
$332$	−1.63819e40	−	1.63819e40i	−0.751890	−	0.751890i
$333$	−7.03716e39	+	7.03716e39i	−0.307815	+	0.307815i
$334$		−	1.16006e40i		−	0.483657i
$335$	−1.04125e40	−	2.92740e39i	−0.413845	−	0.116349i
$336$	1.83547e39			0.0695534
$337$	−1.12808e40	−	1.12808e40i	−0.407624	−	0.407624i	0.473285	−	0.880909i	$-0.343068\pi$
$337$	−1.12808e40	−	1.12808e40i	−0.407624	−	0.407624i	−0.880909	+	0.473285i	$0.843068\pi$
$338$	3.07890e40	−	3.07890e40i	1.06103	−	1.06103i
$339$		−	1.49248e39i		−	0.0490583i
$340$	−2.86714e40	+	1.01982e41i	−0.899056	+	3.19786i
$341$	1.97267e40			0.590181
$342$	−8.00051e37	−	8.00051e37i	−0.00228402	−	0.00228402i
$343$	−8.83878e39	+	8.83878e39i	−0.240817	+	0.240817i
$344$		−	1.06384e41i		−	2.76656i
$345$	−6.65791e39	−	1.18657e40i	−0.165285	−	0.294569i
$346$	−5.27115e39			−0.124936
$347$	−2.64560e40	−	2.64560e40i	−0.598759	−	0.598759i	0.341223	−	0.939982i	$-0.389159\pi$
$347$	−2.64560e40	−	2.64560e40i	−0.598759	−	0.598759i	−0.939982	+	0.341223i	$0.889159\pi$
$348$	1.06989e38	−	1.06989e38i	0.00231244	−	0.00231244i
$349$			2.73612e40i			0.564845i	0.959290	+	0.282422i	$0.0911379\pi$
$349$			2.73612e40i			0.564845i	−0.959290	+	0.282422i	$0.908862\pi$
$350$	−1.36493e40	−	8.33348e39i	−0.269166	−	0.164338i
$351$	2.70458e40			0.509548
$352$	2.30948e40	+	2.30948e40i	0.415749	+	0.415749i
$353$	3.76900e39	−	3.76900e39i	0.0648382	−	0.0648382i	−0.673944	−	0.738782i	$-0.735401\pi$
$353$	3.76900e39	−	3.76900e39i	0.0648382	−	0.0648382i	0.738782	+	0.673944i	$0.235401\pi$
$354$			1.05261e40i			0.173068i
$355$	−9.11364e39	+	5.11372e39i	−0.143231	+	0.0803680i
$356$	−7.81881e40			−1.17474
$357$	2.33429e39	+	2.33429e39i	0.0335324	+	0.0335324i
$358$	−1.53017e41	+	1.53017e41i	−2.10189	+	2.10189i
$359$			8.73548e40i			1.14756i	0.819009	+	0.573780i	$0.194524\pi$
$359$			8.73548e40i			1.14756i	−0.819009	+	0.573780i	$0.805476\pi$
$360$	1.78796e41	+	5.02673e40i	2.24656	+	0.631605i
$361$	8.31982e40			0.999997
$362$	8.20475e40	+	8.20475e40i	0.943470	+	0.943470i
$363$	−1.01600e40	+	1.01600e40i	−0.111786	+	0.111786i
$364$		−	5.16059e40i		−	0.543347i
$365$	5.01818e40	−	1.78492e41i	0.505662	−	1.79860i
$366$	−3.32600e39			−0.0320793
$367$	2.42775e40	+	2.42775e40i	0.224154	+	0.224154i	0.810245	−	0.586091i	$-0.199334\pi$
$367$	2.42775e40	+	2.42775e40i	0.224154	+	0.224154i	−0.586091	+	0.810245i	$0.699334\pi$
$368$	2.94058e41	−	2.94058e41i	2.59937	−	2.59937i
$369$			1.35355e41i			1.14566i
$370$	−4.97864e40	−	8.87290e40i	−0.403537	−	0.719181i
$371$	2.45375e40			0.190479
$372$	−5.95870e40	−	5.95870e40i	−0.443062	−	0.443062i
$373$	−1.24174e41	+	1.24174e41i	−0.884484	+	0.884484i	−0.993987	−	0.109502i	$-0.965074\pi$
$373$	−1.24174e41	+	1.24174e41i	−0.884484	+	0.884484i	0.109502	+	0.993987i	$0.465074\pi$
$374$			1.60829e41i			1.09754i
$375$	2.00135e40	+	2.15437e40i	0.130865	+	0.140871i
$376$	−6.09785e41			−3.82095
$377$	−1.16120e39	−	1.16120e39i	−0.00697341	−	0.00697341i
$378$	1.46226e40	−	1.46226e40i	0.0841697	−	0.0841697i
$379$		−	1.33324e41i		−	0.735667i	−0.929892	−	0.367833i	$-0.880100\pi$
$379$		−	1.33324e41i		−	0.735667i	0.929892	−	0.367833i	$-0.119900\pi$
$380$	7.05668e38	−	3.95955e38i	0.00373304	−	0.00209463i
$381$	−1.19708e40			−0.0607187
$382$	−2.76351e41	−	2.76351e41i	−1.34415	−	1.34415i
$383$	1.21302e41	−	1.21302e41i	0.565833	−	0.565833i	−0.365125	−	0.930958i	$-0.618974\pi$
$383$	1.21302e41	−	1.21302e41i	0.565833	−	0.565833i	0.930958	+	0.365125i	$0.118974\pi$
$384$			2.45445e40i			0.109813i
$385$	−1.63503e40	−	4.59678e39i	−0.0701706	−	0.0197280i
$386$	−3.01144e41			−1.23987
$387$	−1.96808e41	−	1.96808e41i	−0.777440	−	0.777440i
$388$	3.43328e41	−	3.43328e41i	1.30137	−	1.30137i
$389$			2.36463e41i			0.860139i	0.902796	+	0.430070i	$0.141511\pi$
$389$			2.36463e41i			0.860139i	−0.902796	+	0.430070i	$0.858489\pi$
$390$	−3.67121e40	+	1.30582e41i	−0.128167	+	0.455879i
$391$	7.47949e41			2.50636
$392$	5.16754e41	+	5.16754e41i	1.66229	+	1.66229i
$393$	5.32297e40	−	5.32297e40i	0.164389	−	0.164389i
$394$			5.20435e41i			1.54322i
$395$	−2.66295e41	−	4.74588e41i	−0.758244	−	1.35134i
$396$	3.45750e41			0.945451
$397$	−1.07880e41	−	1.07880e41i	−0.283329	−	0.283329i	0.551106	−	0.834435i	$-0.314206\pi$
$397$	−1.07880e41	−	1.07880e41i	−0.283329	−	0.283329i	−0.834435	+	0.551106i	$0.814206\pi$
$398$	3.10182e41	−	3.10182e41i	0.782505	−	0.782505i
$399$		−	2.52154e37i		−	6.11082e-5i
$400$	−4.68342e41	+	7.67090e41i	−1.09044	+	1.78602i
$401$	1.19971e41			0.268391			0.134196	−	0.990955i	$-0.457155\pi$
$401$	1.19971e41			0.268391			0.134196	+	0.990955i	$0.457155\pi$
$402$	4.96013e40	+	4.96013e40i	0.106629	+	0.106629i
$403$	−6.46724e41	+	6.46724e41i	−1.33610	+	1.33610i
$404$			8.46606e41i			1.68105i
$405$	4.06871e41	−	2.28298e41i	0.776562	−	0.435734i
$406$	−1.25563e39			−0.00230380
$407$	−7.64057e40	−	7.64057e40i	−0.134777	−	0.134777i
$408$	2.77150e41	−	2.77150e41i	0.470059	−	0.470059i
$409$		−	7.26242e41i		−	1.18443i	−0.805781	−	0.592214i	$-0.798254\pi$
$409$		−	7.26242e41i		−	1.18443i	0.805781	−	0.592214i	$-0.201746\pi$
$410$	−1.33213e42	−	3.74519e41i	−2.08932	−	0.587397i
$411$	1.63284e41			0.246306
$412$	1.36232e42	+	1.36232e42i	1.97663	+	1.97663i
$413$	4.32093e40	−	4.32093e40i	0.0603081	−	0.0603081i
$414$		−	2.29855e42i		−	3.08637i
$415$	9.56780e40	−	3.40318e41i	0.123607	−	0.439659i
$416$	−1.51429e42			−1.88241
$417$	−5.49192e40	−	5.49192e40i	−0.0656972	−	0.0656972i
$418$	8.68651e38	−	8.68651e38i	0.00100006	−	0.00100006i
$419$			1.35103e42i			1.49706i	0.663099	+	0.748532i	$0.269241\pi$
$419$			1.35103e42i			1.49706i	−0.663099	+	0.748532i	$0.730759\pi$
$420$	3.55031e40	+	6.32734e40i	0.0378684	+	0.0674889i
$421$	−5.85490e41			−0.601182			−0.300591	−	0.953753i	$-0.597184\pi$
$421$	−5.85490e41			−0.601182			−0.300591	+	0.953753i	$0.597184\pi$
$422$	1.32055e42	+	1.32055e42i	1.30543	+	1.30543i
$423$	−1.12809e42	+	1.12809e42i	−1.07374	+	1.07374i
$424$		−	2.91333e42i		−	2.67015i
$425$	−1.57118e42	+	3.79939e41i	−1.38677	+	0.335344i
$426$	6.77740e40			0.0576115
$427$	1.36531e40	+	1.36531e40i	0.0111785	+	0.0111785i
$428$	1.53195e42	−	1.53195e42i	1.20821	−	1.20821i
$429$			1.44059e41i			0.109452i
$430$	2.48148e42	−	1.39237e42i	1.81642	−	1.01920i
$431$	7.83392e41			0.552513			0.276257	−	0.961084i	$-0.410906\pi$
$431$	7.83392e41			0.552513			0.276257	+	0.961084i	$0.410906\pi$
$432$	−8.21790e41	−	8.21790e41i	−0.558497	−	0.558497i
$433$	−5.60168e41	+	5.60168e41i	−0.366870	+	0.366870i	−0.866334	−	0.499465i	$-0.833530\pi$
$433$	−5.60168e41	+	5.60168e41i	−0.366870	+	0.366870i	0.499465	+	0.866334i	$0.333530\pi$
$434$			6.99318e41i			0.441407i
$435$	2.22260e39	+	6.24867e38i	0.00135217	+	0.000380154i
$436$	2.33986e42			1.37217
$437$	−4.03973e39	−	4.03973e39i	−0.00228375	−	0.00228375i
$438$	−8.50273e41	+	8.50273e41i	−0.463417	+	0.463417i
$439$			2.47115e42i			1.29857i	0.760543	+	0.649287i	$0.224933\pi$
$439$			2.47115e42i			1.29857i	−0.760543	+	0.649287i	$0.775067\pi$
$440$	−5.45775e41	+	1.94127e42i	−0.276548	+	0.983657i
$441$	1.91197e42			0.934252
$442$	−5.27265e42	−	5.27265e42i	−2.48469	−	2.48469i
$443$	1.12421e40	−	1.12421e40i	0.00510960	−	0.00510960i	−0.704547	−	0.709657i	$-0.748850\pi$
$443$	1.12421e40	−	1.12421e40i	0.00510960	−	0.00510960i	0.709657	+	0.704547i	$0.248850\pi$
$444$			4.61585e41i			0.202360i
$445$	−5.83815e41	−	1.04047e42i	−0.246896	−	0.440017i
$446$	−2.33432e42			−0.952365
$447$	−3.45718e41	−	3.45718e41i	−0.136082	−	0.136082i
$448$	−1.45234e41	+	1.45234e41i	−0.0551595	+	0.0551595i
$449$			1.14064e42i			0.418028i	0.977913	+	0.209014i	$0.0670255\pi$
$449$			1.14064e42i			0.418028i	−0.977913	+	0.209014i	$0.932975\pi$
$450$	1.16760e42	+	4.82847e42i	0.412948	+	1.70769i
$451$	−1.46962e42			−0.501625
$452$	1.27503e42	+	1.27503e42i	0.420056	+	0.420056i
$453$	2.26538e41	−	2.26538e41i	0.0720395	−	0.0720395i
$454$			2.96734e42i			0.910905i
$455$	6.86734e41	−	3.85331e41i	0.203520	−	0.114196i
$456$	−2.99382e39			−0.000856620
$457$	−2.06814e42	−	2.06814e42i	−0.571375	−	0.571375i	0.361138	−	0.932513i	$-0.382388\pi$
$457$	−2.06814e42	−	2.06814e42i	−0.571375	−	0.571375i	−0.932513	+	0.361138i	$0.882388\pi$
$458$	1.44634e42	−	1.44634e42i	0.385854	−	0.385854i
$459$		−	2.09026e42i		−	0.538514i
$460$	1.58248e43	+	4.44904e42i	3.93744	+	1.10698i
$461$	7.62382e41			0.183214			0.0916068	−	0.995795i	$-0.470800\pi$
$461$	7.62382e41			0.183214			0.0916068	+	0.995795i	$0.470800\pi$
$462$	7.78871e40	+	7.78871e40i	0.0180798	+	0.0180798i
$463$	3.25834e42	−	3.25834e42i	0.730634	−	0.730634i	−0.240111	−	0.970745i	$-0.577184\pi$
$463$	3.25834e42	−	3.25834e42i	0.730634	−	0.730634i	0.970745	+	0.240111i	$0.0771839\pi$
$464$			7.05665e40i			0.0152866i
$465$	3.48017e41	−	1.23787e42i	0.0728372	−	0.259075i
$466$	−2.83715e41			−0.0573729
$467$	3.85475e42	+	3.85475e42i	0.753228	+	0.753228i	0.975080	−	0.221852i	$-0.0712103\pi$
$467$	3.85475e42	+	3.85475e42i	0.753228	+	0.753228i	−0.221852	+	0.975080i	$0.571210\pi$
$468$	−1.13351e43	+	1.13351e43i	−2.14039	+	2.14039i
$469$		−	4.07222e41i		−	0.0743132i
$470$	−7.98100e42	−	1.42237e43i	−1.40764	−	2.50869i
$471$	−1.24820e41			−0.0212790
$472$	−5.13022e42	−	5.13022e42i	−0.845404	−	0.845404i
$473$	2.13683e42	−	2.13683e42i	0.340402	−	0.340402i
$474$			3.52930e42i			0.543544i
$475$	1.05382e40	+	6.43401e39i	0.00156916	+	0.000958041i
$476$	−3.98841e42			−0.574233
$477$	−5.38961e42	−	5.38961e42i	−0.750349	−	0.750349i
$478$	−8.59792e42	+	8.59792e42i	−1.15757	+	1.15757i
$479$		−	1.17477e43i		−	1.52963i	−0.644252	−	0.764813i	$-0.722831\pi$
$479$		−	1.17477e43i		−	1.52963i	0.644252	−	0.764813i	$-0.277169\pi$
$480$	1.85665e42	−	1.04178e42i	0.233814	−	0.131194i
$481$	5.00979e42			0.610237
$482$	−1.76976e42	−	1.76976e42i	−0.208527	−	0.208527i
$483$	3.62220e41	−	3.62220e41i	0.0412875	−	0.0412875i
$484$		−	1.73595e43i		−	1.91431i
$485$	7.13233e42	+	2.00520e42i	0.760964	+	0.213939i
$486$	−9.69596e42			−1.00095
$487$	9.46302e42	+	9.46302e42i	0.945293	+	0.945293i	0.998579	−	0.0532860i	$-0.0169695\pi$
$487$	9.46302e42	+	9.46302e42i	0.945293	+	0.945293i	−0.0532860	+	0.998579i	$0.516970\pi$
$488$	1.62102e42	−	1.62102e42i	0.156701	−	0.156701i
$489$		−	3.43429e42i		−	0.321288i
$490$	−5.29029e42	+	1.88171e43i	−0.479007	+	1.70379i
$491$	−8.07646e42			−0.707811			−0.353905	−	0.935281i	$-0.615147\pi$
$491$	−8.07646e42			−0.707811			−0.353905	+	0.935281i	$0.615147\pi$
$492$	4.43915e42	+	4.43915e42i	0.376581	+	0.376581i
$493$	−8.97443e40	+	8.97443e40i	−0.00736981	+	0.00736981i
$494$			5.69560e40i			0.00452802i
$495$	2.58164e42	+	4.60099e42i	0.198707	+	0.354134i
$496$	3.93017e43			2.92890
$497$	−2.78209e41	−	2.78209e41i	−0.0200756	−	0.0200756i
$498$	−1.62115e42	+	1.62115e42i	−0.113280	+	0.113280i
$499$			5.86916e42i			0.397162i	0.980085	+	0.198581i	$0.0636332\pi$
$499$			5.86916e42i			0.397162i	−0.980085	+	0.198581i	$0.936367\pi$
$500$	−3.55026e43	−	1.30730e42i	−2.32670	−	0.0856754i
$501$	−8.03076e41			−0.0509745
$502$	2.91578e43	+	2.91578e43i	1.79265	+	1.79265i
$503$	9.39744e42	−	9.39744e42i	0.559657	−	0.559657i	−0.369553	−	0.929210i	$-0.620489\pi$
$503$	9.39744e42	−	9.39744e42i	0.559657	−	0.559657i	0.929210	+	0.369553i	$0.120489\pi$
$504$			6.99254e42i			0.403410i
$505$	−1.12660e43	+	6.32144e42i	−0.629664	+	0.353308i
$506$	2.49564e43			1.35137
$507$	−2.13143e42	−	2.13143e42i	−0.111826	−	0.111826i
$508$	1.02267e43	−	1.02267e43i	0.519896	−	0.519896i
$509$			1.85122e43i			0.911957i	0.889991	+	0.455978i	$0.150711\pi$
$509$			1.85122e43i			0.911957i	−0.889991	+	0.455978i	$0.849289\pi$
$510$	1.00921e43	+	2.83733e42i	0.481793	+	0.135453i
$511$	6.98066e42			0.322970
$512$	−3.39505e43	−	3.39505e43i	−1.52239	−	1.52239i
$513$	−1.12896e40	+	1.12896e40i	−0.000490685	+	0.000490685i
$514$		−	3.11884e43i		−	1.31396i
$515$	−7.95663e42	+	2.83010e43i	−0.324948	+	1.15581i
$516$	−1.29091e43			−0.511095
$517$	−1.22482e43	−	1.22482e43i	−0.470136	−	0.470136i
$518$	2.70860e42	−	2.70860e42i	0.100802	−	0.100802i
$519$			3.64906e41i			0.0131675i
$520$	−4.57502e43	−	8.15357e43i	−1.60081	−	2.85295i
$521$	−4.40184e43			−1.49359			−0.746793	−	0.665056i	$-0.768408\pi$
$521$	−4.40184e43			−1.49359			−0.746793	+	0.665056i	$0.768408\pi$
$522$	2.75797e41	+	2.75797e41i	0.00907530	+	0.00907530i
$523$	−2.58361e43	+	2.58361e43i	−0.824516	+	0.824516i	−0.986752	−	0.162236i	$-0.948129\pi$
$523$	−2.58361e43	+	2.58361e43i	−0.824516	+	0.824516i	0.162236	+	0.986752i	$0.448129\pi$
$524$			9.09490e43i			2.81512i
$525$	−5.76902e41	+	9.44899e41i	−0.0173202	+	0.0283685i
$526$	−7.00976e42			−0.204141
$527$	4.99827e43	+	4.99827e43i	1.41205	+	1.41205i
$528$	4.37726e42	−	4.37726e42i	0.119966	−	0.119966i
$529$		−	7.84527e43i		−	2.08601i
$530$	6.79556e43	−	3.81303e43i	1.75312	−	0.983686i
$531$	−1.89816e43			−0.475140
$532$	2.15417e40	+	2.15417e40i	0.000523231	+	0.000523231i
$533$	4.81801e43	−	4.81801e43i	1.13562	−	1.13562i
$534$			7.73751e42i			0.176987i
$535$	3.18248e43	+	8.94731e42i	0.706488	+	0.198624i
$536$	−4.83494e43			−1.04173
$537$	1.05929e43	+	1.05929e43i	0.221527	+	0.221527i
$538$	8.77791e43	−	8.77791e43i	1.78186	−	1.78186i
$539$			2.07591e43i			0.409062i
$540$	1.24335e43	−	4.42250e43i	0.237845	−	0.845994i
$541$	−8.17307e43			−1.51785			−0.758926	−	0.651177i	$-0.774275\pi$
$541$	−8.17307e43			−1.51785			−0.758926	+	0.651177i	$0.774275\pi$
$542$	6.05086e43	+	6.05086e43i	1.09101	+	1.09101i
$543$	5.67990e42	−	5.67990e42i	0.0994360	−	0.0994360i
$544$			1.17033e44i			1.98942i
$545$	1.74713e43	+	3.11372e43i	0.288391	+	0.513968i
$546$	−5.10693e42			−0.0818611
$547$	−6.54115e43	−	6.54115e43i	−1.01826	−	1.01826i	−0.999830	−	0.0184255i	$-0.994135\pi$
$547$	−6.54115e43	−	6.54115e43i	−1.01826	−	1.01826i	−0.0184255	−	0.999830i	$-0.505865\pi$
$548$	−1.39495e44	+	1.39495e44i	−2.10896	+	2.10896i
$549$		−	5.99773e42i		−	0.0880703i
$550$	−5.24248e43	+	1.26772e43i	−0.747712	+	0.180809i
$551$	9.69433e38			1.34305e−5
$552$	−4.30063e43	−	4.30063e43i	−0.578771	−	0.578771i
$553$	1.44876e43	−	1.44876e43i	0.189406	−	0.189406i
$554$			7.44438e43i			0.945524i
$555$	−6.14245e42	+	3.44657e42i	−0.0757973	+	0.0425303i
$556$	9.38357e43			1.12505
$557$	−1.01533e44	−	1.01533e44i	−1.18283	−	1.18283i	−0.979007	−	0.203824i	$-0.934663\pi$
$557$	−1.01533e44	−	1.01533e44i	−1.18283	−	1.18283i	−0.203824	−	0.979007i	$-0.565337\pi$
$558$	1.53604e44	−	1.53604e44i	1.73882	−	1.73882i
$559$			1.40109e44i			1.54126i
$560$	−3.25749e43	−	9.15819e42i	−0.348237	−	0.0979042i
$561$	1.11337e43			0.115674
$562$	9.30630e43	+	9.30630e43i	0.939714	+	0.939714i
$563$	4.41398e43	−	4.41398e43i	0.433208	−	0.433208i	−0.456510	−	0.889718i	$-0.650901\pi$
$563$	4.41398e43	−	4.41398e43i	0.433208	−	0.433208i	0.889718	+	0.456510i	$0.150901\pi$
$564$			7.39944e43i			0.705884i
$565$	−7.44681e42	+	2.64877e43i	−0.0690550	+	0.245623i
$566$	1.07380e44			0.967971
$567$	1.24204e43	+	1.24204e43i	0.108845	+	0.108845i
$568$	−3.30317e43	+	3.30317e43i	−0.281422	+	0.281422i
$569$		−	2.23566e44i		−	1.85187i	−0.377689	−	0.925933i	$-0.623281\pi$
$569$		−	2.23566e44i		−	1.85187i	0.377689	−	0.925933i	$-0.376719\pi$
$570$	−3.91838e40	−	6.98331e40i	−0.000315579	−	0.000562424i
$571$	1.88532e43			0.147641			0.0738205	−	0.997272i	$-0.476481\pi$
$571$	1.88532e43			0.147641			0.0738205	+	0.997272i	$0.476481\pi$
$572$	−1.23071e44	−	1.23071e44i	−0.937168	−	0.937168i
$573$	−1.91309e43	+	1.91309e43i	−0.141665	+	0.141665i
$574$		−	5.20983e43i		−	0.375174i
$575$	5.89563e43	+	2.43806e44i	0.412900	+	1.70749i
$576$	6.38008e43			0.434576
$577$	1.36243e44	+	1.36243e44i	0.902611	+	0.902611i	0.995661	−	0.0930502i	$-0.0296617\pi$
$577$	1.36243e44	+	1.36243e44i	0.902611	+	0.902611i	−0.0930502	+	0.995661i	$0.529662\pi$
$578$	−2.07313e44	+	2.07313e44i	−1.33592	+	1.33592i
$579$			2.08473e43i			0.130675i
$580$	−2.43261e42	+	1.36495e42i	−0.0148328	+	0.00832280i
$581$	1.33095e43			0.0789485
$582$	−3.39759e43	−	3.39759e43i	−0.196066	−	0.196066i
$583$	5.85174e43	−	5.85174e43i	0.328540	−	0.328540i
$584$		−	8.28812e44i		−	4.52741i
$585$	−2.35477e44	−	6.62026e43i	−1.25157	−	0.351869i
$586$	−3.49918e44			−1.80969
$587$	1.94584e44	+	1.94584e44i	0.979259	+	0.979259i	0.999789	−	0.0205303i	$-0.00653544\pi$
$587$	1.94584e44	+	1.94584e44i	0.979259	+	0.979259i	−0.0205303	+	0.999789i	$0.506535\pi$
$588$	6.27055e43	−	6.27055e43i	0.307092	−	0.307092i
$589$		−	5.39921e41i		−	0.00257327i
$590$	5.25208e43	−	1.86812e44i	0.243612	−	0.866507i
$591$	3.60282e43			0.162646
$592$	−1.52223e44	−	1.52223e44i	−0.668858	−	0.668858i
$593$	−8.07127e43	+	8.07127e43i	−0.345197	+	0.345197i	−0.858317	−	0.513120i	$-0.828490\pi$
$593$	−8.07127e43	+	8.07127e43i	−0.345197	+	0.345197i	0.513120	+	0.858317i	$0.328490\pi$
$594$		−	6.97445e43i		−	0.290353i
$595$	−2.97806e43	−	5.30749e43i	−0.120688	−	0.215089i
$596$	5.90699e44			2.33038
$597$	−2.14730e43	−	2.14730e43i	−0.0824713	−	0.0824713i
$598$	−8.18174e44	+	8.18174e44i	−3.05933	+	3.05933i
$599$		−	6.48099e43i		−	0.235946i	−0.993017	−	0.117973i	$-0.962360\pi$
$599$		−	6.48099e43i		−	0.235946i	0.993017	−	0.117973i	$-0.0376396\pi$
$600$	1.12188e44	+	6.84954e43i	0.397672	+	0.242796i
$601$	−2.21893e44			−0.765865			−0.382933	−	0.923776i	$-0.625086\pi$
$601$	−2.21893e44			−0.765865			−0.382933	+	0.923776i	$0.625086\pi$
$602$	7.57513e43	+	7.57513e43i	0.254593	+	0.254593i
$603$	−8.94455e43	+	8.94455e43i	−0.292740	+	0.292740i
$604$			3.87067e44i			1.23366i
$605$	2.31008e44	−	1.29620e44i	0.717037	−	0.402334i
$606$	8.37803e43			0.253268
$607$	−1.45859e44	−	1.45859e44i	−0.429451	−	0.429451i	0.458990	−	0.888441i	$-0.348211\pi$
$607$	−1.45859e44	−	1.45859e44i	−0.429451	−	0.429451i	−0.888441	+	0.458990i	$0.848211\pi$
$608$	6.32105e41	−	6.32105e41i	0.00181273	−	0.00181273i
$609$			8.69236e40i			0.000242807i
$610$	5.90280e43	+	1.65953e43i	0.160613	+	0.0451552i
$611$	8.03094e44			2.12866
$612$	8.76045e44	+	8.76045e44i	2.26206	+	2.26206i
$613$	5.13025e44	−	5.13025e44i	1.29054	−	1.29054i	0.356084	−	0.934454i	$-0.384112\pi$
$613$	5.13025e44	−	5.13025e44i	1.29054	−	1.29054i	0.934454	−	0.356084i	$-0.115888\pi$
$614$		−	6.11445e44i		−	1.49852i
$615$	−2.59268e43	+	9.22193e43i	−0.0619081	+	0.220201i
$616$	−7.59212e43			−0.176633
$617$	−3.30744e44	−	3.30744e44i	−0.749772	−	0.749772i	0.224664	−	0.974436i	$-0.427872\pi$
$617$	−3.30744e44	−	3.30744e44i	−0.749772	−	0.749772i	−0.974436	+	0.224664i	$0.927872\pi$
$618$	1.34816e44	−	1.34816e44i	0.297800	−	0.297800i
$619$			7.05795e44i			1.51925i	0.650364	+	0.759623i	$0.274616\pi$
$619$			7.05795e44i			1.51925i	−0.650364	+	0.759623i	$0.725384\pi$
$620$	7.60204e44	+	1.35483e45i	1.59464	+	2.84196i
$621$	−3.24352e44			−0.663057
$622$	−5.79762e44	−	5.79762e44i	−1.15506	−	1.15506i
$623$	3.17621e43	−	3.17621e43i	0.0616738	−	0.0616738i
$624$			2.87009e44i			0.543179i
$625$	−2.47694e44	−	4.82205e44i	−0.456915	−	0.889510i
$626$	−1.31647e45			−2.36713
$627$	−6.01341e40	−	6.01341e40i	−0.000105400	−	0.000105400i
$628$	1.06635e44	−	1.06635e44i	0.182199	−	0.182199i
$629$		−	3.87186e44i		−	0.644926i
$630$	−1.63106e44	+	9.15200e43i	−0.264864	+	0.148617i
$631$	2.94853e44			0.466805			0.233402	−	0.972380i	$-0.425014\pi$
$631$	2.94853e44			0.466805			0.233402	+	0.972380i	$0.425014\pi$
$632$	−1.72011e45	−	1.72011e45i	−2.65511	−	2.65511i
$633$	9.14176e43	−	9.14176e43i	0.137585	−	0.137585i
$634$			7.74577e44i			1.13668i
$635$	2.12451e44	+	5.97289e43i	0.304003	+	0.0854683i
$636$	−3.53518e44			−0.493285
$637$	−6.80571e44	−	6.80571e44i	−0.926068	−	0.926068i
$638$	−2.99445e42	+	2.99445e42i	−0.00397362	+	0.00397362i
$639$			1.22216e44i			0.158166i
$640$	1.22467e44	−	4.35603e44i	0.154575	−	0.549808i
$641$	1.31960e45			1.62447			0.812236	−	0.583329i	$-0.198250\pi$
$641$	1.31960e45			1.62447			0.812236	+	0.583329i	$0.198250\pi$
$642$	−1.51602e44	−	1.51602e44i	−0.182030	−	0.182030i
$643$	−2.95984e44	+	2.95984e44i	−0.346651	+	0.346651i	−0.858860	−	0.512210i	$-0.828827\pi$
$643$	−2.95984e44	+	2.95984e44i	−0.346651	+	0.346651i	0.512210	+	0.858860i	$0.328827\pi$
$644$			6.18894e44i			0.707038i
$645$	−9.63899e43	−	1.71785e44i	−0.107418	−	0.191439i
$646$	4.40190e42			0.00478541
$647$	6.41039e44	+	6.41039e44i	0.679855	+	0.679855i	0.959967	−	0.280113i	$-0.0903718\pi$
$647$	6.41039e44	+	6.41039e44i	0.679855	+	0.679855i	−0.280113	+	0.959967i	$0.590372\pi$
$648$	1.47467e45	−	1.47467e45i	1.52579	−	1.52579i
$649$		−	2.06092e44i		−	0.208040i
$650$	1.30309e45	−	2.13432e45i	1.28340	−	2.10206i
$651$	4.84117e43			0.0465216
$652$	2.93394e45	+	2.93394e45i	2.75099	+	2.75099i
$653$	−8.98199e44	+	8.98199e44i	−0.821792	+	0.821792i	−0.986365	−	0.164573i	$-0.947375\pi$
$653$	−8.98199e44	+	8.98199e44i	−0.821792	+	0.821792i	0.164573	+	0.986365i	$0.447375\pi$
$654$		−	2.31553e44i		−	0.206732i
$655$	−1.21028e45	+	6.79098e44i	−1.05445	+	0.591659i
$656$	−2.92792e45			−2.48942
$657$	−1.53329e45	−	1.53329e45i	−1.27226	−	1.27226i
$658$	4.34202e44	−	4.34202e44i	0.351623	−	0.351623i
$659$			2.09807e45i			1.65827i	0.559052	+	0.829133i	$0.311165\pi$
$659$			2.09807e45i			1.65827i	−0.559052	+	0.829133i	$0.688835\pi$
$660$	2.35564e44	+	6.62270e43i	0.181721	+	0.0510896i
$661$	−3.92624e43			−0.0295634			−0.0147817	−	0.999891i	$-0.504705\pi$
$661$	−3.92624e43			−0.0295634			−0.0147817	+	0.999891i	$0.504705\pi$
$662$	2.72037e45	+	2.72037e45i	1.99940	+	1.99940i
$663$	−3.65010e44	+	3.65010e44i	−0.261871	+	0.261871i
$664$		−	1.58023e45i		−	1.10671i
$665$	−1.25814e41	+	4.47509e41i	−8.60166e−5	+	0.000305954i
$666$	−1.18988e45			−0.794172
$667$	1.39259e43	+	1.39259e43i	0.00907425	+	0.00907425i
$668$	6.86073e44	−	6.86073e44i	0.436463	−	0.436463i
$669$			1.61598e44i			0.100373i
$670$	−6.32808e44	−	1.12779e45i	−0.383773	−	0.683958i
$671$	6.51201e43			0.0385616
$672$	5.66773e43	+	5.66773e43i	0.0327719	+	0.0327719i
$673$	−1.35579e45	+	1.35579e45i	−0.765511	+	0.765511i	−0.977313	−	0.211802i	$-0.932067\pi$
$673$	−1.35579e45	+	1.35579e45i	−0.765511	+	0.765511i	0.211802	+	0.977313i	$0.432067\pi$
$674$		−	1.90741e45i		−	1.05168i
$675$	6.81353e44	−	1.64762e44i	0.366870	−	0.0887152i
$676$	3.64180e45			1.91500
$677$	−8.28262e43	−	8.28262e43i	−0.0425353	−	0.0425353i	0.685519	−	0.728055i	$-0.259575\pi$
$677$	−8.28262e43	−	8.28262e43i	−0.0425353	−	0.0425353i	−0.728055	+	0.685519i	$0.759575\pi$
$678$	1.26178e44	−	1.26178e44i	0.0632859	−	0.0632859i
$679$			2.78939e44i			0.136644i
$680$	−6.30156e45	+	3.53585e45i	−3.01513	+	1.69181i
$681$	2.05420e44			0.0960039
$682$	1.66774e45	+	1.66774e45i	0.761341	+	0.761341i
$683$	2.90358e44	−	2.90358e44i	0.129480	−	0.129480i	−0.639397	−	0.768877i	$-0.720816\pi$
$683$	2.90358e44	−	2.90358e44i	0.129480	−	0.129480i	0.768877	+	0.639397i	$0.220816\pi$
$684$		−	9.46318e42i		−	0.00412230i
$685$	−2.89788e45	−	8.14717e44i	−1.23319	−	0.346703i
$686$	−1.49450e45			−0.621314
$687$	−1.00126e44	−	1.00126e44i	−0.0406666	−	0.0406666i
$688$	4.25722e45	−	4.25722e45i	1.68932	−	1.68932i
$689$			3.83689e45i			1.48755i
$690$	4.40278e44	−	1.56603e45i	0.166779	−	0.593218i
$691$	4.36777e45			1.61663			0.808317	−	0.588748i	$-0.200379\pi$
$691$	4.36777e45			1.61663			0.808317	+	0.588748i	$0.200379\pi$
$692$	−3.11742e44	−	3.11742e44i	−0.112745	−	0.112745i
$693$	−1.40453e44	+	1.40453e44i	−0.0496362	+	0.0496362i
$694$		−	4.47330e45i		−	1.54481i
$695$	7.00652e44	+	1.24870e45i	0.236453	+	0.421406i
$696$	1.03204e43			0.00340369
$697$	−3.72364e45	−	3.72364e45i	−1.20017	−	1.20017i
$698$	−2.31319e45	+	2.31319e45i	−0.728658	+	0.728658i
$699$			1.96407e43i			0.00604676i
$700$	−3.14382e44	−	1.30009e45i	−0.0945996	−	0.391204i
$701$	6.04918e45			1.77913			0.889567	−	0.456806i	$-0.151006\pi$
$701$	6.04918e45			1.77913			0.889567	+	0.456806i	$0.151006\pi$
$702$	2.28651e45	+	2.28651e45i	0.657325	+	0.657325i
$703$	−2.09122e42	+	2.09122e42i	−0.000587645	+	0.000587645i
$704$			6.92714e44i			0.190279i
$705$	−9.84664e44	+	5.52501e44i	−0.264401	+	0.148357i
$706$	6.37281e44			0.167284
$707$	−3.43914e44	−	3.43914e44i	−0.0882550	−	0.0882550i
$708$	−6.22527e44	+	6.22527e44i	−0.156180	+	0.156180i
$709$		−	3.60443e45i		−	0.884091i	−0.896993	−	0.442045i	$-0.854253\pi$
$709$		−	3.60443e45i		−	0.884091i	0.896993	−	0.442045i	$-0.145747\pi$
$710$	−1.20282e45	−	3.38163e44i	−0.288447	−	0.0810947i
$711$	−6.36434e45			−1.49224
$712$	−3.77111e45	−	3.77111e45i	−0.864547	−	0.864547i
$713$	7.75598e45	−	7.75598e45i	1.73862	−	1.73862i
$714$			3.94694e44i			0.0865145i
$715$	7.18791e44	−	2.55668e45i	0.154066	−	0.547998i
$716$	−1.80992e46			−3.79359
$717$	5.95208e44	+	5.95208e44i	0.122001	+	0.122001i
$718$	−7.38518e45	+	7.38518e45i	−1.48037	+	1.48037i
$719$			1.14528e45i			0.224517i	0.993679	+	0.112258i	$0.0358084\pi$
$719$			1.14528e45i			0.224517i	−0.993679	+	0.112258i	$0.964192\pi$
$720$	5.14343e45	+	9.16658e45i	0.986126	+	1.75747i
$721$	−1.10683e45			−0.207546
$722$	7.03377e45	+	7.03377e45i	1.29001	+	1.29001i
$723$	−1.22515e44	+	1.22515e44i	−0.0219775	+	0.0219775i
$724$			9.70476e45i			1.70282i
$725$	−3.63276e43	−	2.21796e43i	−0.00623489	−	0.00380667i
$726$	−1.71790e45			−0.288412
$727$	−1.34397e45	−	1.34397e45i	−0.220719	−	0.220719i	0.588082	−	0.808801i	$-0.299883\pi$
$727$	−1.34397e45	−	1.34397e45i	−0.220719	−	0.220719i	−0.808801	+	0.588082i	$0.799883\pi$
$728$	2.48901e45	−	2.48901e45i	0.399876	−	0.399876i
$729$		−	4.99447e45i		−	0.784963i
$730$	1.93327e46	−	1.08477e46i	2.97253	−	1.66790i
$731$	1.08284e46			1.62887
$732$	−1.96703e44	−	1.96703e44i	−0.0289490	−	0.0289490i
$733$	−1.38366e45	+	1.38366e45i	−0.199235	+	0.199235i	−0.799672	−	0.600437i	$-0.794993\pi$
$733$	−1.38366e45	+	1.38366e45i	−0.199235	+	0.199235i	0.600437	+	0.799672i	$0.294993\pi$
$734$			4.10496e45i			0.578325i
$735$	1.30265e45	+	3.66231e44i	0.179569	+	0.0504844i
$736$	1.81604e46			2.44952
$737$	−9.71150e44	−	9.71150e44i	−0.128176	−	0.128176i
$738$	−1.14433e46	+	1.14433e46i	−1.47791	+	1.47791i
$739$			8.35853e45i			1.05638i	0.849127	+	0.528188i	$0.177128\pi$
$739$			8.35853e45i			1.05638i	−0.849127	+	0.528188i	$0.822872\pi$
$740$	2.30311e45	−	8.19196e45i	0.284844	−	1.01317i
$741$	3.94290e42			0.000477226
$742$	2.07446e45	+	2.07446e45i	0.245721	+	0.245721i
$743$	3.30450e45	−	3.30450e45i	0.383075	−	0.383075i	−0.489134	−	0.872209i	$-0.662687\pi$
$743$	3.30450e45	−	3.30450e45i	0.383075	−	0.383075i	0.872209	+	0.489134i	$0.162687\pi$
$744$		−	5.74791e45i		−	0.652143i
$745$	4.41063e45	+	7.86060e45i	0.489779	+	0.872882i
$746$	−2.09960e46			−2.28200
$747$	−2.92341e45	−	2.92341e45i	−0.310999	−	0.310999i
$748$	−9.51162e45	+	9.51162e45i	−0.990442	+	0.990442i
$749$			1.24464e45i			0.126862i
$750$	−1.29371e44	+	3.51334e45i	−0.0129079	+	0.350542i
$751$	3.17733e45			0.310330			0.155165	−	0.987889i	$-0.450409\pi$
$751$	3.17733e45			0.310330			0.155165	+	0.987889i	$0.450409\pi$
$752$	−2.44022e46	−	2.44022e46i	−2.33315	−	2.33315i
$753$	2.01850e45	−	2.01850e45i	0.188934	−	0.188934i
$754$		−	1.96341e44i		−	0.0179916i
$755$	−5.15080e45	+	2.89015e45i	−0.462087	+	0.259280i
$756$	1.72959e45			0.151913
$757$	−6.57529e45	−	6.57529e45i	−0.565432	−	0.565432i	0.365413	−	0.930845i	$-0.380928\pi$
$757$	−6.57529e45	−	6.57529e45i	−0.565432	−	0.565432i	−0.930845	+	0.365413i	$0.880928\pi$
$758$	1.12715e46	−	1.12715e46i	0.949021	−	0.949021i
$759$		−	1.72766e45i		−	0.142426i
$760$	5.31326e43	+	1.49379e43i	0.00428888	+	0.00120579i
$761$	−1.10400e46			−0.872601			−0.436301	−	0.899801i	$-0.643712\pi$
$761$	−1.10400e46			−0.872601			−0.436301	+	0.899801i	$0.643712\pi$
$762$	−1.01204e45	−	1.01204e45i	−0.0783280	−	0.0783280i
$763$	−9.50516e44	+	9.50516e44i	−0.0720388	+	0.0720388i
$764$		−	3.26874e46i		−	2.42598i
$765$	−5.11653e45	+	1.81990e46i	−0.371871	+	1.32271i
$766$	2.05104e46			1.45987
$767$	6.75656e45	+	6.75656e45i	0.470977	+	0.470977i
$768$	−2.97376e45	+	2.97376e45i	−0.203014	+	0.203014i
$769$			1.21763e46i			0.814127i	0.913400	+	0.407064i	$0.133447\pi$
$769$			1.21763e46i			0.814127i	−0.913400	+	0.407064i	$0.866553\pi$
$770$	−9.93674e44	−	1.77092e45i	−0.0650717	−	0.115970i
$771$	−2.15908e45			−0.138484
$772$	−1.78100e46	−	1.78100e46i	−1.11889	−	1.11889i
$773$	1.53073e46	−	1.53073e46i	0.941945	−	0.941945i	−0.0564602	−	0.998405i	$-0.517981\pi$
$773$	1.53073e46	−	1.53073e46i	0.941945	−	0.941945i	0.998405	+	0.0564602i	$0.0179814\pi$
$774$		−	3.32772e46i		−	2.00582i
$775$	−1.23528e46	+	2.02325e46i	−0.729355	+	1.19460i
$776$	3.31183e46			1.91549
$777$	−1.87508e44	−	1.87508e44i	−0.0106239	−	0.0106239i
$778$	−1.99911e46	+	1.99911e46i	−1.10959	+	1.10959i
$779$			4.02234e43i			0.00218715i
$780$	−9.89396e45	+	5.55156e45i	−0.527056	+	0.295734i
$781$	−1.32695e45			−0.0692532
$782$	6.32334e46	+	6.32334e46i	3.23324	+	3.23324i
$783$	3.89181e43	−	3.89181e43i	0.00194968	−	0.00194968i
$784$			4.13586e46i			2.03006i
$785$	2.21524e45	+	6.22800e44i	0.106539	+	0.0299526i
$786$	9.00034e45			0.424129
$787$	−1.93360e46	−	1.93360e46i	−0.892832	−	0.892832i	0.101957	−	0.994789i	$-0.467490\pi$
$787$	−1.93360e46	−	1.93360e46i	−0.892832	−	0.892832i	−0.994789	+	0.101957i	$0.967490\pi$
$788$	−3.07791e46	+	3.07791e46i	−1.39263	+	1.39263i
$789$			4.85265e44i			0.0215153i
$790$	1.76097e46	−	6.26360e46i	0.765099	−	2.72139i
$791$	−1.03591e45			−0.0441059
$792$	1.66759e46	+	1.66759e46i	0.695805	+	0.695805i
$793$	−2.13491e45	+	2.13491e45i	−0.0872988	+	0.0872988i
$794$		−	1.82408e46i		−	0.730997i
$795$	−2.63965e45	−	4.70437e45i	−0.103675	−	0.184768i
$796$	3.66890e46			1.41230
$797$	2.24556e46	+	2.24556e46i	0.847209	+	0.847209i	0.989784	−	0.142575i	$-0.0455381\pi$
$797$	2.24556e46	+	2.24556e46i	0.847209	+	0.847209i	−0.142575	+	0.989784i	$0.545538\pi$
$798$	2.13177e42	−	2.13177e42i	7.88305e−5	−	7.88305e-5i
$799$		−	6.20679e46i		−	2.24967i
$800$	−3.81488e46	+	9.22502e45i	−1.35532	+	0.327739i
$801$	−1.39530e46			−0.485899
$802$	1.01427e46	+	1.01427e46i	0.346228	+	0.346228i
$803$	1.66476e46	−	1.66476e46i	0.557061	−	0.557061i
$804$			5.86696e45i			0.192449i
$805$	−8.23580e45	+	4.62116e45i	−0.264833	+	0.148599i
$806$	−1.09351e47			−3.44717
$807$	−6.07669e45	−	6.07669e45i	−0.187798	−	0.187798i
$808$	−4.08328e46	+	4.08328e46i	−1.23717	+	1.23717i
$809$			1.62226e46i			0.481886i	0.970539	+	0.240943i	$0.0774567\pi$
$809$			1.62226e46i			0.481886i	−0.970539	+	0.240943i	$0.922543\pi$
$810$	5.36987e46	+	1.50970e46i	1.56388	+	0.439673i
$811$	−4.01951e46			−1.14773			−0.573864	−	0.818950i	$-0.694556\pi$
$811$	−4.01951e46			−1.14773			−0.573864	+	0.818950i	$0.694556\pi$
$812$	−7.42595e43	−	7.42595e43i	−0.00207900	−	0.00207900i
$813$	4.18883e45	−	4.18883e45i	0.114986	−	0.114986i
$814$		−	1.29190e46i		−	0.347728i
$815$	−1.71356e46	+	6.09498e46i	−0.452249	+	1.60861i
$816$	2.21818e46			0.574055
$817$	−5.84851e43	−	5.84851e43i	−0.00148420	−	0.00148420i
$818$	6.13982e46	−	6.13982e46i	1.52793	−	1.52793i
$819$		−	9.20926e45i		−	0.224741i
$820$	−5.66342e46	−	1.00933e47i	−1.35537	−	2.41553i
$821$	4.45189e46			1.04485			0.522425	−	0.852685i	$-0.325027\pi$
$821$	4.45189e46			1.04485			0.522425	+	0.852685i	$0.325027\pi$
$822$	1.38044e46	+	1.38044e46i	0.317738	+	0.317738i
$823$	5.55851e46	−	5.55851e46i	1.25476	−	1.25476i	0.301200	−	0.953561i	$-0.402613\pi$
$823$	5.55851e46	−	5.55851e46i	1.25476	−	1.25476i	0.953561	−	0.301200i	$-0.0973873\pi$
$824$			1.31413e47i			2.90940i
$825$	8.77605e44	+	3.62922e45i	0.0190562	+	0.0788043i
$826$	7.30603e45			0.155597
$827$	−6.54928e46	−	6.54928e46i	−1.36806	−	1.36806i	−0.863201	−	0.504861i	$-0.831544\pi$
$827$	−6.54928e46	−	6.54928e46i	−1.36806	−	1.36806i	−0.504861	−	0.863201i	$-0.668456\pi$
$828$	1.35939e47	−	1.35939e47i	2.78521	−	2.78521i
$829$			7.35096e46i			1.47731i	0.674084	+	0.738655i	$0.264539\pi$
$829$			7.35096e46i			1.47731i	−0.674084	+	0.738655i	$0.735461\pi$
$830$	3.68602e46	−	2.06825e46i	0.726621	−	0.407712i
$831$	5.15352e45			0.0996525
$832$	−2.27100e46	−	2.27100e46i	−0.430769	−	0.430769i
$833$	−5.25986e46	+	5.25986e46i	−0.978710	+	0.978710i
$834$		−	9.28600e45i		−	0.169501i
$835$	1.42525e46	+	4.00700e45i	0.255216	+	0.0717523i
$836$	1.02746e44			0.00180495
$837$	−2.16753e46	−	2.16753e46i	−0.373557	−	0.373557i
$838$	−1.14219e47	+	1.14219e47i	−1.93123	+	1.93123i
$839$		−	2.82921e46i		−	0.469326i	−0.972077	−	0.234663i	$-0.924601\pi$
$839$		−	2.82921e46i		−	0.469326i	0.972077	−	0.234663i	$-0.0753986\pi$
$840$	−1.33939e45	+	4.76411e45i	−0.0217992	+	0.0775377i
$841$	6.26200e46			0.999947
$842$	−4.94987e46	−	4.94987e46i	−0.775533	−	0.775533i
$843$	6.44247e45	−	6.44247e45i	0.0990402	−	0.0990402i
$844$			1.56197e47i			2.35610i
$845$	2.71926e46	+	4.84624e46i	0.402479	+	0.717295i
$846$	−1.90743e47			−2.77028
$847$	7.05191e45	+	7.05191e45i	0.100501	+	0.100501i
$848$	1.16585e47	−	1.16585e47i	1.63045	−	1.63045i
$849$		−	7.43363e45i		−	0.102018i
$850$	−1.64953e47	−	1.00711e47i	−2.22155	−	1.35635i
$851$	−6.00810e46			−0.794079
$852$	4.00823e45	+	4.00823e45i	0.0519899	+	0.0519899i
$853$	−1.04164e46	+	1.04164e46i	−0.132597	+	0.132597i	−0.770290	−	0.637693i	$-0.779889\pi$
$853$	−1.04164e46	+	1.04164e46i	−0.132597	+	0.132597i	0.637693	+	0.770290i	$0.279889\pi$
$854$			2.30853e45i			0.0288409i
$855$	1.25929e44	−	7.06597e43i	0.00154408	−	0.000866391i
$856$	1.47775e47			1.77837
$857$	5.70463e46	+	5.70463e46i	0.673805	+	0.673805i	0.958591	−	0.284786i	$-0.0919226\pi$
$857$	5.70463e46	+	5.70463e46i	0.673805	+	0.673805i	−0.284786	+	0.958591i	$0.591923\pi$
$858$	−1.21791e46	+	1.21791e46i	−0.141195	+	0.141195i
$859$			8.45121e46i			0.961675i	0.876810	+	0.480837i	$0.159667\pi$
$859$			8.45121e46i			0.961675i	−0.876810	+	0.480837i	$0.840333\pi$
$860$	2.29104e47	+	6.44109e46i	2.55892	+	0.719423i
$861$	−3.60661e45			−0.0395411
$862$	6.62298e46	+	6.62298e46i	0.712750	+	0.712750i
$863$	3.59185e46	−	3.59185e46i	0.379442	−	0.379442i	−0.491459	−	0.870901i	$-0.663536\pi$
$863$	3.59185e46	−	3.59185e46i	0.379442	−	0.379442i	0.870901	+	0.491459i	$0.163536\pi$
$864$		−	5.07521e46i		−	0.526301i
$865$	1.82072e45	−	6.47615e45i	0.0185347	−	0.0659264i
$866$	−9.47159e46			−0.946534
$867$	1.43516e46	+	1.43516e46i	0.140798	+	0.140798i
$868$	−4.13584e46	+	4.13584e46i	−0.398335	+	0.398335i
$869$		−	6.91005e46i		−	0.653379i
$870$	1.35076e44	+	2.40732e44i	0.00125392	+	0.00223473i
$871$	6.36767e46			0.580350
$872$	1.12854e47	+	1.12854e47i	1.00985	+	1.00985i
$873$	6.12683e46	−	6.12683e46i	0.538279	−	0.538279i
$874$		−	6.83057e44i		−	0.00589215i
$875$	1.49532e46	−	1.38911e46i	0.126650	−	0.117654i
$876$	−1.00572e47			−0.836396
$877$	−2.58708e44	−	2.58708e44i	−0.00211260	−	0.00211260i	0.706050	−	0.708162i	$-0.250476\pi$
$877$	−2.58708e44	−	2.58708e44i	−0.00211260	−	0.00211260i	−0.708162	+	0.706050i	$0.750476\pi$
$878$	−2.08917e47	+	2.08917e47i	−1.67518	+	1.67518i
$879$			2.42238e46i			0.190730i
$880$	−9.95257e46	+	5.58445e46i	−0.769507	+	0.431775i
$881$	5.70576e46			0.433211			0.216605	−	0.976259i	$-0.430502\pi$
$881$	5.70576e46			0.433211			0.216605	+	0.976259i	$0.430502\pi$
$882$	1.61643e47	+	1.61643e47i	1.20520	+	1.20520i
$883$	−3.54385e46	+	3.54385e46i	−0.259480	+	0.259480i	−0.824842	−	0.565363i	$-0.808736\pi$
$883$	−3.54385e46	+	3.54385e46i	−0.259480	+	0.259480i	0.565363	+	0.824842i	$0.308736\pi$
$884$		−	6.23661e47i		−	4.48448i
$885$	−1.29324e46	−	3.63586e45i	−0.0913246	−	0.0256753i
$886$	1.90086e45			0.0131829
$887$	−1.55571e47	−	1.55571e47i	−1.05962	−	1.05962i	−0.998106	−	0.0615166i	$-0.980406\pi$
$887$	−1.55571e47	−	1.55571e47i	−1.05962	−	1.05962i	−0.0615166	−	0.998106i	$-0.519594\pi$
$888$	−2.22628e46	+	2.22628e46i	−0.148927	+	0.148927i
$889$			8.30873e45i			0.0545892i
$890$	3.86068e46	−	1.37321e47i	0.249129	−	0.886129i
$891$	5.92408e46			0.375472
$892$	−1.38054e47	−	1.38054e47i	−0.859435	−	0.859435i
$893$	−3.35233e44	+	3.35233e44i	−0.00204986	+	0.00204986i
$894$		−	5.84557e46i		−	0.351097i
$895$	−1.35143e47	−	2.40851e47i	−0.797305	−	1.42095i
$896$	1.70360e46			0.0987278
$897$	5.66398e46	+	5.66398e46i	0.322435	+	0.322435i
$898$	−9.64321e46	+	9.64321e46i	−0.539263	+	0.539263i
$899$			1.86124e45i			0.0102246i
$900$	−2.16508e47	+	3.54614e47i	−1.16840	+	1.91371i
$901$	2.96538e47			1.57211
$902$	−1.24245e47	−	1.24245e47i	−0.647103	−	0.647103i
$903$	5.24404e45	−	5.24404e45i	0.0268325	−	0.0268325i
$904$			1.22993e47i			0.618280i
$905$	−1.29144e47	+	7.24635e46i	−0.637818	+	0.357884i
$906$	3.83042e46			0.185864
$907$	−1.54419e47	−	1.54419e47i	−0.736180	−	0.736180i	0.235656	−	0.971836i	$-0.424276\pi$
$907$	−1.54419e47	−	1.54419e47i	−0.736180	−	0.736180i	−0.971836	+	0.235656i	$0.924276\pi$
$908$	−1.75492e47	+	1.75492e47i	−0.822021	+	0.822021i
$909$			1.51080e47i			0.695320i
$910$	9.06349e46	+	2.54814e46i	0.409858	+	0.115229i
$911$	1.17212e47			0.520807			0.260403	−	0.965500i	$-0.416144\pi$
$911$	1.17212e47			0.520807			0.260403	+	0.965500i	$0.416144\pi$
$912$	−1.19806e44	−	1.19806e44i	−0.000523070	−	0.000523070i
$913$	3.17407e46	−	3.17407e46i	0.136171	−	0.136171i
$914$		−	3.49691e47i		−	1.47416i
$915$	1.14884e45	−	4.08633e45i	0.00475908	−	0.0169276i
$916$	1.71076e47			0.696406
$917$	−3.69460e46	−	3.69460e46i	−0.147794	−	0.147794i
$918$	1.76715e47	−	1.76715e47i	0.694690	−	0.694690i
$919$		−	1.69436e47i		−	0.654573i	−0.944925	−	0.327287i	$-0.893866\pi$
$919$		−	1.69436e47i		−	0.654573i	0.944925	−	0.327287i	$-0.106134\pi$
$920$	5.48669e47	+	9.77834e47i	2.08308	+	3.71245i
$921$	−4.23285e46			−0.157935
$922$	6.44536e46	+	6.44536e46i	0.236348	+	0.236348i
$923$	4.35031e46	−	4.35031e46i	0.156781	−	0.156781i
$924$			9.21266e45i			0.0326312i
$925$	1.26210e47	−	3.05196e46i	0.439364	−	0.106246i
$926$	5.50935e47			1.88506
$927$	2.43112e47	+	2.43112e47i	0.817580	+	0.817580i
$928$	−2.17902e45	+	2.17902e45i	−0.00720267	+	0.00720267i
$929$			1.45277e47i			0.472005i	0.971752	+	0.236003i	$0.0758374\pi$
$929$			1.45277e47i			0.472005i	−0.971752	+	0.236003i	$0.924163\pi$
$930$	1.34074e47	−	7.52299e46i	0.428172	−	0.240250i
$931$	5.68178e44			0.00178357
$932$	−1.67792e46	−	1.67792e46i	−0.0517746	−	0.0517746i
$933$	−4.01352e46	+	4.01352e46i	−0.121736	+	0.121736i
$934$			6.51780e47i			1.94335i
$935$	−1.97595e47	−	5.55525e46i	−0.579149	−	0.162824i
$936$	−1.09341e48			−3.15044
$937$	−2.91188e47	−	2.91188e47i	−0.824783	−	0.824783i	0.162007	−	0.986790i	$-0.448203\pi$
$937$	−2.91188e47	−	2.91188e47i	−0.824783	−	0.824783i	−0.986790	+	0.162007i	$0.948203\pi$
$938$	3.44275e46	−	3.44275e46i	0.0958651	−	0.0958651i
$939$			9.11354e46i			0.249481i
$940$	3.69200e47	−	1.31321e48i	0.993610	−	3.53418i
$941$	−3.92460e47			−1.03839			−0.519196	−	0.854655i	$-0.673768\pi$
$941$	−3.92460e47			−1.03839			−0.519196	+	0.854655i	$0.673768\pi$
$942$	−1.05526e46	−	1.05526e46i	−0.0274502	−	0.0274502i
$943$	−5.77810e47	+	5.77810e47i	−1.47774	+	1.47774i
$944$		−	4.10599e47i		−	1.03244i
$945$	1.29145e46	+	2.30162e46i	0.0319279	+	0.0569016i
$946$	3.61306e47			0.878247
$947$	−2.40052e47	−	2.40052e47i	−0.573728	−	0.573728i	0.359440	−	0.933168i	$-0.382968\pi$
$947$	−2.40052e47	−	2.40052e47i	−0.573728	−	0.573728i	−0.933168	+	0.359440i	$0.882968\pi$
$948$	−2.08727e47	+	2.08727e47i	−0.490506	+	0.490506i
$949$			1.09155e48i			2.52224i
$950$	3.46975e44	+	1.43487e45i	0.000788353	+	0.00326013i
$951$	5.36217e46			0.119799
$952$	−1.92366e47	−	1.92366e47i	−0.422607	−	0.422607i
$953$	−4.68847e47	+	4.68847e47i	−1.01285	+	1.01285i	−0.0129331	+	0.999916i	$0.504117\pi$
$953$	−4.68847e47	+	4.68847e47i	−1.01285	+	1.01285i	−0.999916	+	0.0129331i	$0.995883\pi$
$954$		−	9.11301e47i		−	1.93592i
$955$	4.34980e47	−	2.44070e47i	0.908690	−	0.509872i
$956$	−1.01698e48			−2.08923
$957$	2.07297e44	+	2.07297e44i	0.000418795	+	0.000418795i
$958$	9.93181e47	−	9.93181e47i	1.97324	−	1.97324i
$959$		−	1.13333e47i		−	0.221441i
$960$	4.34683e46	+	1.22208e46i	0.0835281	+	0.0234833i
$961$	5.07463e47			0.959025
$962$	4.23540e47	+	4.23540e47i	0.787214	+	0.787214i
$963$	2.73382e47	−	2.73382e47i	0.499745	−	0.499745i
$964$		−	2.09331e47i		−	0.376358i
$965$	1.04019e47	−	3.69986e47i	0.183940	−	0.654258i
$966$	6.12459e46			0.106523
$967$	4.83138e47	+	4.83138e47i	0.826510	+	0.826510i	0.987032	−	0.160522i	$-0.0513179\pi$
$967$	4.83138e47	+	4.83138e47i	0.826510	+	0.826510i	−0.160522	+	0.987032i	$0.551318\pi$
$968$	8.37271e47	−	8.37271e47i	1.40884	−	1.40884i
$969$		−	3.04730e44i		−	0.000504354i
$970$	4.33460e47	+	7.72509e47i	0.705669	+	1.25764i
$971$	−1.04183e48			−1.66835			−0.834176	−	0.551498i	$-0.814056\pi$
$971$	−1.04183e48			−1.66835			−0.834176	+	0.551498i	$0.814056\pi$
$972$	−5.73430e47	−	5.73430e47i	−0.903276	−	0.903276i
$973$	−3.81186e46	+	3.81186e46i	−0.0590651	+	0.0590651i
$974$			1.60005e48i			2.43888i
$975$	−1.47752e47	−	9.02093e46i	−0.221544	−	0.135263i
$976$	1.29739e47			0.191370
$977$	2.78721e47	+	2.78721e47i	0.404443	+	0.404443i	0.879795	−	0.475352i	$-0.157679\pi$
$977$	2.78721e47	+	2.78721e47i	0.404443	+	0.404443i	−0.475352	+	0.879795i	$0.657679\pi$
$978$	2.90343e47	−	2.90343e47i	0.414467	−	0.414467i
$979$		−	1.51494e47i		−	0.212751i
$980$	−1.42574e48	+	7.99990e47i	−1.96980	+	1.10527i
$981$	4.17557e47			0.567561
$982$	−6.82803e47	−	6.82803e47i	−0.913086	−	0.913086i
$983$	−3.09325e47	+	3.09325e47i	−0.406967	+	0.406967i	−0.880680	−	0.473713i	$-0.842914\pi$
$983$	−3.09325e47	+	3.09325e47i	−0.406967	+	0.406967i	0.473713	+	0.880680i	$0.342914\pi$
$984$			4.28212e47i			0.554290i
$985$	−6.39408e47	−	1.79765e47i	−0.814326	−	0.228942i
$986$	−1.51744e46			−0.0190143
$987$	−3.00585e46	−	3.00585e46i	−0.0370589	−	0.0370589i
$988$	−3.36844e45	+	3.36844e45i	−0.00408619	+	0.00408619i
$989$		−	1.68028e48i		−	2.00559i
$990$	−1.70720e47	+	6.07237e47i	−0.200504	+	0.713174i
$991$	1.34300e48			1.55202			0.776010	−	0.630720i	$-0.217240\pi$
$991$	1.34300e48			1.55202			0.776010	+	0.630720i	$0.217240\pi$
$992$	1.21359e48	+	1.21359e48i	1.38002	+	1.38002i
$993$	1.88323e47	−	1.88323e47i	0.210725	−	0.210725i
$994$		−	4.70409e46i		−	0.0517957i
$995$	2.73949e47	+	4.88231e47i	0.296825	+	0.529000i
$996$	−1.91754e47			−0.204453
$997$	−2.55318e47	−	2.55318e47i	−0.267891	−	0.267891i	0.560359	−	0.828250i	$-0.310663\pi$
$997$	−2.55318e47	−	2.55318e47i	−0.267891	−	0.267891i	−0.828250	+	0.560359i	$0.810663\pi$
$998$	−4.96193e47	+	4.96193e47i	−0.512344	+	0.512344i
$999$			1.67905e47i			0.170615i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.33.c.a.2.15	✓	30
5.2	odd	4		25.33.c.b.18.1		30
5.3	odd	4	inner	5.33.c.a.3.15	yes	30
5.4	even	2		25.33.c.b.7.1		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.33.c.a.2.15	✓	30	1.1	even	1	trivial
5.33.c.a.3.15	yes	30	5.3	odd	4	inner
25.33.c.b.7.1		30	5.4	even	2
25.33.c.b.18.1		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)

\(f(q)\)	\(=\)	\(q+(84542.4 + 84542.4i) q^{2} +(5.85262e6 - 5.85262e6i) q^{3} +9.99987e9i q^{4} +(-1.33071e11 + 7.46670e10i) q^{5} +9.89589e11 q^{6} +(-4.06221e12 - 4.06221e12i) q^{7} +(-4.82306e14 + 4.82306e14i) q^{8} +1.78451e15i q^{9} +O(q^{10})\)	\(q+(84542.4 + 84542.4i) q^{2} +(5.85262e6 - 5.85262e6i) q^{3} +9.99987e9i q^{4} +(-1.33071e11 + 7.46670e10i) q^{5} +9.89589e11 q^{6} +(-4.06221e12 - 4.06221e12i) q^{7} +(-4.82306e14 + 4.82306e14i) q^{8} +1.78451e15i q^{9} +(-1.75627e16 - 4.93762e15i) q^{10} -1.93753e16 q^{11} +(5.85254e16 + 5.85254e16i) q^{12} +(6.35202e17 - 6.35202e17i) q^{13} -6.86859e17i q^{14} +(-3.41817e17 + 1.21581e18i) q^{15} -3.86015e19 q^{16} +(-4.90922e19 - 4.90922e19i) q^{17} +(-1.50867e20 + 1.50867e20i) q^{18} +5.30302e17i q^{19} +(-7.46660e20 - 1.33069e21i) q^{20} -4.75492e19 q^{21} +(-1.63803e21 - 1.63803e21i) q^{22} +(-7.61780e21 + 7.61780e21i) q^{23} +5.64550e21i q^{24} +(1.21327e22 - 1.98720e22i) q^{25} +1.07403e23 q^{26} +(2.12891e22 + 2.12891e22i) q^{27} +(4.06216e22 - 4.06216e22i) q^{28} -1.82808e21i q^{29} +(-1.31686e23 + 7.38896e22i) q^{30} -1.01814e24 q^{31} +(-1.19197e24 - 1.19197e24i) q^{32} +(-1.13396e23 + 1.13396e23i) q^{33} -8.30074e24i q^{34} +(8.43877e23 + 2.37250e23i) q^{35} -1.78449e25 q^{36} +(3.94346e24 + 3.94346e24i) q^{37} +(-4.48330e22 + 4.48330e22i) q^{38} -7.43519e24i q^{39} +(2.81686e25 - 1.00193e26i) q^{40} +7.58500e25 q^{41} +(-4.01992e24 - 4.01992e24i) q^{42} +(-1.10287e26 + 1.10287e26i) q^{43} -1.93750e26i q^{44} +(-1.33244e26 - 2.37467e26i) q^{45} -1.28805e27 q^{46} +(6.32156e26 + 6.32156e26i) q^{47} +(-2.25920e26 + 2.25920e26i) q^{48} -1.07142e27i q^{49} +(2.70576e27 - 6.54298e26i) q^{50} -5.74636e26 q^{51} +(6.35194e27 + 6.35194e27i) q^{52} +(-3.02021e27 + 3.02021e27i) q^{53} +3.59966e27i q^{54} +(2.57829e27 - 1.44669e27i) q^{55} +3.91846e27 q^{56} +(3.10365e24 + 3.10365e24i) q^{57} +(1.54550e26 - 1.54550e26i) q^{58} +1.06369e28i q^{59} +(-1.21580e28 - 3.41812e27i) q^{60} -3.36099e27 q^{61} +(-8.60759e28 - 8.60759e28i) q^{62} +(7.24908e27 - 7.24908e27i) q^{63} -3.57525e28i q^{64} +(-3.70984e28 + 1.31956e29i) q^{65} -1.91736e28 q^{66} +(5.01232e28 + 5.01232e28i) q^{67} +(4.90915e29 - 4.90915e29i) q^{68} +8.91681e28i q^{69} +(5.12857e28 + 9.14010e28i) q^{70} +6.84870e28 q^{71} +(-8.60681e29 - 8.60681e29i) q^{72} +(-8.59218e29 + 8.59218e29i) q^{73} +6.66779e29i q^{74} +(-4.52951e28 - 1.87312e29i) q^{75} -5.30294e27 q^{76} +(7.87065e28 + 7.87065e28i) q^{77} +(6.28589e29 - 6.28589e29i) q^{78} +3.56643e30i q^{79} +(5.13674e30 - 2.88226e30i) q^{80} -3.05755e30 q^{81} +(6.41254e30 + 6.41254e30i) q^{82} +(-1.63821e30 + 1.63821e30i) q^{83} -4.75485e29i q^{84} +(1.01983e31 + 2.86718e30i) q^{85} -1.86478e31 q^{86} +(-1.06990e28 - 1.06990e28i) q^{87} +(9.34481e30 - 9.34481e30i) q^{88} +7.81891e30i q^{89} +(8.81125e30 - 3.13408e31i) q^{90} -5.16066e30 q^{91} +(-7.61769e31 - 7.61769e31i) q^{92} +(-5.95878e30 + 5.95878e30i) q^{93} +1.06888e32i q^{94} +(-3.95960e28 - 7.05678e28i) q^{95} -1.39523e31 q^{96} +(-3.43333e31 - 3.43333e31i) q^{97} +(9.05808e31 - 9.05808e31i) q^{98} -3.45754e31i 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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