LMFDB - Embedded newform 12.19.d.a.7.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,19,Mod(7,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 19, names="a")

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

chi := DirichletCharacter("12.7");

S:= CuspForms(chi, 19);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 19 $
Character orbit:	$[\chi]$	$=$	12.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$24.6463365252$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} - 332091 x^{16} - 8722796 x^{15} + 44065046710 x^{14} + 2562387593326 x^{13} + \cdots + 51\!\cdots\!09 $ x^18 - 5x^17 - 332091x^16 - 8722796x^15 + 44065046710x^14 + 2562387593326x^13 - 2939418299568910x^12 - 270086571564720600x^11 + 99892143837893471971x^10 + 13287383366374675095257x^9 - 1404426939389796697311653x^8 - 302846077765145575240351608x^7 - 3048385818268269033396834566x^6 + 2387968325606677017735731037126x^5 + 189341038803558425525784877687654x^4 + 5034939808459428548543033598246780x^3 + 5944618618967029844099743191417597x^2 - 1074790996286169638673503552568280077*x + 5142216036403070733098077860515333409
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{139}\cdot 3^{67}\cdot 13^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			7.16
Root			$309.123 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.19.d.a.7.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(421.101 + 291.236i) q^{2} -11364.0i q^{3} +(92507.4 + 245279. i) q^{4} -1.11240e6 q^{5} +(3.30960e6 - 4.78538e6i) q^{6} +6.89054e6i q^{7} +(-3.24791e7 + 1.30229e8i) q^{8} -1.29140e8 q^{9} +O(q^{10})$	\(q+(421.101 + 291.236i) q^{2} -11364.0i q^{3} +(92507.4 + 245279. i) q^{4} -1.11240e6 q^{5} +(3.30960e6 - 4.78538e6i) q^{6} +6.89054e6i q^{7} +(-3.24791e7 + 1.30229e8i) q^{8} -1.29140e8 q^{9} +(-4.68431e8 - 3.23970e8i) q^{10} -1.93042e9i q^{11} +(2.78735e9 - 1.05125e9i) q^{12} -8.31265e9 q^{13} +(-2.00677e9 + 2.90161e9i) q^{14} +1.26413e10i q^{15} +(-5.16042e10 + 4.53803e10i) q^{16} -1.99622e11 q^{17} +(-5.43810e10 - 3.76102e10i) q^{18} +2.93080e11i q^{19} +(-1.02905e11 - 2.72848e11i) q^{20} +7.83040e10 q^{21} +(5.62207e11 - 8.12900e11i) q^{22} -1.31137e12i q^{23} +(1.47992e12 + 3.69093e11i) q^{24} -2.57727e12 q^{25} +(-3.50046e12 - 2.42094e12i) q^{26} +1.46755e12i q^{27} +(-1.69011e12 + 6.37426e11i) q^{28} -1.02038e13 q^{29} +(-3.68159e12 + 5.32324e12i) q^{30} -1.94029e13i q^{31} +(-3.49469e13 + 4.08066e12i) q^{32} -2.19372e13 q^{33} +(-8.40608e13 - 5.81370e13i) q^{34} -7.66501e12i q^{35} +(-1.19464e13 - 3.16754e13i) q^{36} -1.32753e14 q^{37} +(-8.53554e13 + 1.23416e14i) q^{38} +9.44648e13i q^{39} +(3.61297e13 - 1.44866e14i) q^{40} +3.30181e14 q^{41} +(3.29739e13 + 2.28049e13i) q^{42} -1.42732e14i q^{43} +(4.73491e14 - 1.78578e14i) q^{44} +1.43655e14 q^{45} +(3.81919e14 - 5.52221e14i) q^{46} +1.39366e15i q^{47} +(5.15701e14 + 5.86430e14i) q^{48} +1.58093e15 q^{49} +(-1.08529e15 - 7.50593e14i) q^{50} +2.26850e15i q^{51} +(-7.68982e14 - 2.03892e15i) q^{52} +2.59242e15 q^{53} +(-4.27402e14 + 6.17985e14i) q^{54} +2.14739e15i q^{55} +(-8.97346e14 - 2.23799e14i) q^{56} +3.33056e15 q^{57} +(-4.29682e15 - 2.97171e15i) q^{58} +6.79409e15i q^{59} +(-3.10064e15 + 1.16941e15i) q^{60} +7.81524e15 q^{61} +(5.65083e15 - 8.17059e15i) q^{62} -8.89845e14i q^{63} +(-1.59046e16 - 8.45943e15i) q^{64} +9.24697e15 q^{65} +(-9.23779e15 - 6.38891e15i) q^{66} +3.42914e16i q^{67} +(-1.84665e16 - 4.89630e16i) q^{68} -1.49024e16 q^{69} +(2.23233e15 - 3.22774e15i) q^{70} +4.99600e15i q^{71} +(4.19436e15 - 1.68178e16i) q^{72} -2.48467e16 q^{73} +(-5.59026e16 - 3.86626e16i) q^{74} +2.92881e16i q^{75} +(-7.18864e16 + 2.71121e16i) q^{76} +1.33016e16 q^{77} +(-2.75115e16 + 3.97792e16i) q^{78} +1.86462e17i q^{79} +(5.74044e16 - 5.04809e16i) q^{80} +1.66772e16 q^{81} +(1.39039e17 + 9.61605e16i) q^{82} -3.53135e17i q^{83} +(7.24370e15 + 1.92063e16i) q^{84} +2.22059e17 q^{85} +(4.15686e16 - 6.01044e16i) q^{86} +1.15956e17i q^{87} +(2.51396e17 + 6.26983e16i) q^{88} +5.20767e17 q^{89} +(6.04933e16 + 4.18375e16i) q^{90} -5.72786e16i q^{91} +(3.21653e17 - 1.21312e17i) q^{92} -2.20495e17 q^{93} +(-4.05884e17 + 5.86871e17i) q^{94} -3.26021e17i q^{95} +(4.63725e16 + 3.97136e17i) q^{96} -1.36750e18 q^{97} +(6.65732e17 + 4.60425e17i) q^{98} +2.49294e17i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 170 q^{2} - 436932 q^{4} - 1721764 q^{5} - 6731586 q^{6} + 108558736 q^{8} - 2324522934 q^{9}+O(q^{10}) $ 18 * q - 170 * q^2 - 436932 * q^4 - 1721764 * q^5 - 6731586 * q^6 + 108558736 * q^8 - 2324522934 * q^9	$ 18 q - 170 q^{2} - 436932 q^{4} - 1721764 q^{5} - 6731586 q^{6} + 108558736 q^{8} - 2324522934 q^{9} + 1397074644 q^{10} - 6468699852 q^{12} + 1799208612 q^{13} - 48147537912 q^{14} - 119537094672 q^{16} - 282984271180 q^{17} + 21953827710 q^{18} + 491637621128 q^{20} + 254050055640 q^{21} + 272503644408 q^{22} + 4483423343232 q^{24} + 20224739695878 q^{25} - 2765456970196 q^{26} + 27756503338032 q^{28} + 1812741883820 q^{29} - 3579410315772 q^{30} + 216191588070880 q^{32} + 17014318866216 q^{33} - 275796423660708 q^{34} + 56425469699916 q^{36} + 197439381411156 q^{37} - 676030464010008 q^{38} + 19\!\cdots\!68 q^{40}+ \cdots - 37\!\cdots\!22 q^{98}+O(q^{100}) $ 18 * q - 170 * q^2 - 436932 * q^4 - 1721764 * q^5 - 6731586 * q^6 + 108558736 * q^8 - 2324522934 * q^9 + 1397074644 * q^10 - 6468699852 * q^12 + 1799208612 * q^13 - 48147537912 * q^14 - 119537094672 * q^16 - 282984271180 * q^17 + 21953827710 * q^18 + 491637621128 * q^20 + 254050055640 * q^21 + 272503644408 * q^22 + 4483423343232 * q^24 + 20224739695878 * q^25 - 2765456970196 * q^26 + 27756503338032 * q^28 + 1812741883820 * q^29 - 3579410315772 * q^30 + 216191588070880 * q^32 + 17014318866216 * q^33 - 275796423660708 * q^34 + 56425469699916 * q^36 + 197439381411156 * q^37 - 676030464010008 * q^38 + 1941137842438368 * q^40 - 204669372669676 * q^41 - 1059935698181880 * q^42 + 3599128179401424 * q^44 + 222348883607532 * q^45 - 3847169819651040 * q^46 + 1457367907812912 * q^48 - 3424095824368878 * q^49 - 10192520264009358 * q^50 + 4228291003193208 * q^52 - 14112687314785972 * q^53 + 869318113288518 * q^54 - 6591066595001856 * q^56 - 9662233004693640 * q^57 + 17584741731886020 * q^58 + 193536143011224 * q^60 + 4171094773122132 * q^61 + 77227021488187896 * q^62 - 53424456043095936 * q^64 + 35585253307254712 * q^65 + 40644920520184824 * q^66 - 91403316760947112 * q^68 + 26342656148137824 * q^69 + 264958129332427248 * q^70 - 14019292862113968 * q^72 - 83809473755653692 * q^73 + 55949505142092092 * q^74 - 129026923617832848 * q^76 - 354619239852167328 * q^77 - 34535086926497028 * q^78 + 43257628406200352 * q^80 + 300189270593998242 * q^81 - 458290372754774916 * q^82 + 324078384809786832 * q^84 + 166017223439872920 * q^85 - 975848731010420424 * q^86 + 1151342491040801280 * q^88 - 660650117825905468 * q^89 - 180418447249326972 * q^90 + 1359275349780859584 * q^92 - 447365281400937432 * q^93 - 2087066679318498384 * q^94 + 257905715132447136 * q^96 + 2412557706093917220 * q^97 - 3767017570512990122 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	421.101	+	291.236i	0.822462	+	0.568820i
$2$	421.101	+	291.236i	0.822462	+	0.568820i
$3$		−	11364.0i		−	0.577350i
$3$		−	11364.0i		−	0.577350i
$4$	92507.4	+	245279.i	0.352888	+	0.935666i
$5$	−1.11240e6			−0.569547			−0.284774	−	0.958595i	$-0.591918\pi$
$5$	−1.11240e6			−0.569547			−0.284774	+	0.958595i	$0.591918\pi$
$6$	3.30960e6	−	4.78538e6i	0.328408	−	0.474849i
$7$			6.89054e6i			0.170754i	0.996349	+	0.0853770i	$0.0272095\pi$
$7$			6.89054e6i			0.170754i	−0.996349	+	0.0853770i	$0.972791\pi$
$8$	−3.24791e7	+	1.30229e8i	−0.241989	+	0.970279i
$9$	−1.29140e8			−0.333333
$10$	−4.68431e8	−	3.23970e8i	−0.468431	−	0.323970i
$11$		−	1.93042e9i		−	0.818686i	−0.912381	−	0.409343i	$-0.865758\pi$
$11$		−	1.93042e9i		−	0.818686i	0.912381	−	0.409343i	$-0.134242\pi$
$12$	2.78735e9	−	1.05125e9i	0.540207	−	0.203740i
$13$	−8.31265e9			−0.783879			−0.391940	−	0.919991i	$-0.628196\pi$
$13$	−8.31265e9			−0.783879			−0.391940	+	0.919991i	$0.628196\pi$
$14$	−2.00677e9	+	2.90161e9i	−0.0971283	+	0.140439i
$15$			1.26413e10i			0.328828i
$16$	−5.16042e10	+	4.53803e10i	−0.750940	+	0.660370i
$17$	−1.99622e11			−1.68332			−0.841661	−	0.540006i	$-0.818422\pi$
$17$	−1.99622e11			−1.68332			−0.841661	+	0.540006i	$0.818422\pi$
$18$	−5.43810e10	−	3.76102e10i	−0.274154	−	0.189607i
$19$			2.93080e11i			0.908247i	0.890939	+	0.454123i	$0.150047\pi$
$19$			2.93080e11i			0.908247i	−0.890939	+	0.454123i	$0.849953\pi$
$20$	−1.02905e11	−	2.72848e11i	−0.200986	−	0.532906i
$21$	7.83040e10			0.0985849
$22$	5.62207e11	−	8.12900e11i	0.465685	−	0.673338i
$23$		−	1.31137e12i		−	0.728075i	−0.931384	−	0.364038i	$-0.881398\pi$
$23$		−	1.31137e12i		−	0.728075i	0.931384	−	0.364038i	$-0.118602\pi$
$24$	1.47992e12	+	3.69093e11i	0.560191	+	0.139712i
$25$	−2.57727e12			−0.675616
$26$	−3.50046e12	−	2.42094e12i	−0.644711	−	0.445886i
$27$			1.46755e12i			0.192450i
$28$	−1.69011e12	+	6.37426e11i	−0.159769	+	0.0602570i
$29$	−1.02038e13			−0.703363			−0.351682	−	0.936120i	$-0.614390\pi$
$29$	−1.02038e13			−0.703363			−0.351682	+	0.936120i	$0.614390\pi$
$30$	−3.68159e12	+	5.32324e12i	−0.187044	+	0.270449i
$31$		−	1.94029e13i		−	0.733858i	−0.930249	−	0.366929i	$-0.880409\pi$
$31$		−	1.94029e13i		−	0.733858i	0.930249	−	0.366929i	$-0.119591\pi$
$32$	−3.49469e13	+	4.08066e12i	−0.993252	+	0.115979i
$33$	−2.19372e13			−0.472668
$34$	−8.40608e13	−	5.81370e13i	−1.38447	−	0.957508i
$35$		−	7.66501e12i		−	0.0972525i
$36$	−1.19464e13	−	3.16754e13i	−0.117629	−	0.311889i
$37$	−1.32753e14			−1.02148			−0.510741	−	0.859735i	$-0.670629\pi$
$37$	−1.32753e14			−1.02148			−0.510741	+	0.859735i	$0.670629\pi$
$38$	−8.53554e13	+	1.23416e14i	−0.516629	+	0.746998i
$39$			9.44648e13i			0.452573i
$40$	3.61297e13	−	1.44866e14i	0.137824	−	0.552620i
$41$	3.30181e14			1.00855			0.504275	−	0.863543i	$-0.331760\pi$
$41$	3.30181e14			1.00855			0.504275	+	0.863543i	$0.331760\pi$
$42$	3.29739e13	+	2.28049e13i	0.0810823	+	0.0560770i
$43$		−	1.42732e14i		−	0.283991i	−0.989867	−	0.141995i	$-0.954648\pi$
$43$		−	1.42732e14i		−	0.283991i	0.989867	−	0.141995i	$-0.0453518\pi$
$44$	4.73491e14	−	1.78578e14i	0.766016	−	0.288904i
$45$	1.43655e14			0.189849
$46$	3.81919e14	−	5.52221e14i	0.414144	−	0.598814i
$47$			1.39366e15i			1.24531i	0.782498	+	0.622653i	$0.213945\pi$
$47$			1.39366e15i			1.24531i	−0.782498	+	0.622653i	$0.786055\pi$
$48$	5.15701e14	+	5.86430e14i	0.381265	+	0.433556i
$49$	1.58093e15			0.970843
$50$	−1.08529e15	−	7.50593e14i	−0.555668	−	0.384304i
$51$			2.26850e15i			0.971867i
$52$	−7.68982e14	−	2.03892e15i	−0.276621	−	0.733449i
$53$	2.59242e15			0.785637			0.392819	−	0.919616i	$-0.371500\pi$
$53$	2.59242e15			0.785637			0.392819	+	0.919616i	$0.371500\pi$
$54$	−4.27402e14	+	6.17985e14i	−0.109469	+	0.158283i
$55$			2.14739e15i			0.466280i
$56$	−8.97346e14	−	2.23799e14i	−0.165679	−	0.0413205i
$57$	3.33056e15			0.524376
$58$	−4.29682e15	−	2.97171e15i	−0.578489	−	0.400087i
$59$			6.79409e15i			0.784265i	0.919909	+	0.392133i	$0.128263\pi$
$59$			6.79409e15i			0.784265i	−0.919909	+	0.392133i	$0.871737\pi$
$60$	−3.10064e15	+	1.16941e15i	−0.307673	+	0.116039i
$61$	7.81524e15			0.668304			0.334152	−	0.942519i	$-0.391550\pi$
$61$	7.81524e15			0.668304			0.334152	+	0.942519i	$0.391550\pi$
$62$	5.65083e15	−	8.17059e15i	0.417433	−	0.603571i
$63$		−	8.89845e14i		−	0.0569180i
$64$	−1.59046e16	−	8.45943e15i	−0.882883	−	0.469593i
$65$	9.24697e15			0.446456
$66$	−9.23779e15	−	6.38891e15i	−0.388752	−	0.268863i
$67$			3.42914e16i			1.26041i	0.776429	+	0.630205i	$0.217029\pi$
$67$			3.42914e16i			1.26041i	−0.776429	+	0.630205i	$0.782971\pi$
$68$	−1.84665e16	−	4.89630e16i	−0.594024	−	1.57503i
$69$	−1.49024e16			−0.420354
$70$	2.23233e15	−	3.22774e15i	0.0553191	−	0.0799865i
$71$			4.99600e15i			0.108968i	0.998515	+	0.0544838i	$0.0173513\pi$
$71$			4.99600e15i			0.108968i	−0.998515	+	0.0544838i	$0.982649\pi$
$72$	4.19436e15	−	1.68178e16i	0.0806628	−	0.323426i
$73$	−2.48467e16			−0.422050			−0.211025	−	0.977481i	$-0.567680\pi$
$73$	−2.48467e16			−0.422050			−0.211025	+	0.977481i	$0.567680\pi$
$74$	−5.59026e16	−	3.86626e16i	−0.840130	−	0.581039i
$75$			2.92881e16i			0.390067i
$76$	−7.18864e16	+	2.71121e16i	−0.849815	+	0.320509i
$77$	1.33016e16			0.139794
$78$	−2.75115e16	+	3.97792e16i	−0.257433	+	0.372224i
$79$			1.86462e17i			1.55578i	0.628402	+	0.777889i	$0.283709\pi$
$79$			1.86462e17i			1.55578i	−0.628402	+	0.777889i	$0.716291\pi$
$80$	5.74044e16	−	5.04809e16i	0.427696	−	0.376112i
$81$	1.66772e16			0.111111
$82$	1.39039e17	+	9.61605e16i	0.829494	+	0.573683i
$83$		−	3.53135e17i		−	1.88903i	−0.328472	−	0.944514i	$-0.606534\pi$
$83$		−	3.53135e17i		−	1.88903i	0.328472	−	0.944514i	$-0.393466\pi$
$84$	7.24370e15	+	1.92063e16i	0.0347894	+	0.0922425i
$85$	2.22059e17			0.958732
$86$	4.15686e16	−	6.01044e16i	0.161540	−	0.233572i
$87$			1.15956e17i			0.406087i
$88$	2.51396e17	+	6.26983e16i	0.794354	+	0.198113i
$89$	5.20767e17			1.48639			0.743195	−	0.669074i	$-0.233309\pi$
$89$	5.20767e17			1.48639			0.743195	+	0.669074i	$0.233309\pi$
$90$	6.04933e16	+	4.18375e16i	0.156144	+	0.107990i
$91$		−	5.72786e16i		−	0.133851i
$92$	3.21653e17	−	1.21312e17i	0.681235	−	0.256929i
$93$	−2.20495e17			−0.423693
$94$	−4.05884e17	+	5.86871e17i	−0.708355	+	1.02422i
$95$		−	3.26021e17i		−	0.517289i
$96$	4.63725e16	+	3.97136e17i	0.0669606	+	0.573454i
$97$	−1.36750e18			−1.79879			−0.899395	−	0.437137i	$-0.855993\pi$
$97$	−1.36750e18			−1.79879			−0.899395	+	0.437137i	$0.855993\pi$
$98$	6.65732e17	+	4.60425e17i	0.798482	+	0.552235i
$99$			2.49294e17i			0.272895i
$100$	−2.38417e17	−	6.32151e17i	−0.238417	−	0.632151i
$101$	−1.56750e18			−1.43323			−0.716615	−	0.697469i	$-0.754309\pi$
$101$	−1.56750e18			−1.43323			−0.716615	+	0.697469i	$0.754309\pi$
$102$	−6.60668e17	+	9.55266e17i	−0.552817	+	0.799324i
$103$		−	1.58633e18i		−	1.21579i	−0.794018	−	0.607894i	$-0.792015\pi$
$103$		−	1.58633e18i		−	1.21579i	0.794018	−	0.607894i	$-0.207985\pi$
$104$	2.69988e17	−	1.08255e18i	0.189690	−	0.760582i
$105$	−8.71051e16			−0.0561487
$106$	1.09167e18	+	7.55005e17i	0.646157	+	0.446886i
$107$		−	3.10703e18i		−	1.69002i	−0.534752	−	0.845009i	$-0.679595\pi$
$107$		−	3.10703e18i		−	1.69002i	0.534752	−	0.845009i	$-0.320405\pi$
$108$	−3.59959e17	+	1.35759e17i	−0.180069	+	0.0679133i
$109$	−1.22089e18			−0.562133			−0.281066	−	0.959688i	$-0.590688\pi$
$109$	−1.22089e18			−0.562133			−0.281066	+	0.959688i	$0.590688\pi$
$110$	−6.25397e17	+	9.04268e17i	−0.265229	+	0.383498i
$111$			1.50861e18i			0.589753i
$112$	−3.12695e17	−	3.55581e17i	−0.112761	−	0.128226i
$113$	8.56895e17			0.285247			0.142624	−	0.989777i	$-0.454446\pi$
$113$	8.56895e17			0.285247			0.142624	+	0.989777i	$0.454446\pi$
$114$	1.40250e18	+	9.69977e17i	0.431280	+	0.298276i
$115$			1.45877e18i			0.414673i
$116$	−9.43926e17	−	2.50278e18i	−0.248208	−	0.658113i
$117$	1.07350e18			0.261293
$118$	−1.97868e18	+	2.86099e18i	−0.446106	+	0.645028i
$119$		−	1.37550e18i		−	0.287434i
$120$	−1.64625e18	−	4.10577e17i	−0.319055	−	0.0795727i
$121$	1.83340e18			0.329754
$122$	3.29100e18	+	2.27608e18i	0.549655	+	0.380145i
$123$		−	3.75217e18i		−	0.582286i
$124$	4.75913e18	−	1.79491e18i	0.686646	−	0.258970i
$125$	7.11041e18			0.954342
$126$	2.59155e17	−	3.74714e17i	0.0323761	−	0.0468129i
$127$			1.24556e19i			1.44921i	0.689164	+	0.724606i	$0.257978\pi$
$127$			1.24556e19i			1.44921i	−0.689164	+	0.724606i	$0.742022\pi$
$128$	−4.23375e18	−	8.19426e18i	−0.459024	−	0.888424i
$129$	−1.62200e18			−0.163962
$130$	3.89390e18	+	2.69305e18i	0.367193	+	0.253953i
$131$			1.06932e19i			0.941169i	0.882355	+	0.470584i	$0.155957\pi$
$131$			1.06932e19i			0.941169i	−0.882355	+	0.470584i	$0.844043\pi$
$132$	−2.02936e18	−	5.38075e18i	−0.166799	−	0.442260i
$133$	−2.01948e18			−0.155087
$134$	−9.98688e18	+	1.44401e19i	−0.716947	+	1.03664i
$135$		−	1.63249e18i		−	0.109609i
$136$	6.48354e18	−	2.59965e19i	0.407345	−	1.63329i
$137$	1.27765e19			0.751494			0.375747	−	0.926722i	$-0.377386\pi$
$137$	1.27765e19			0.751494			0.375747	+	0.926722i	$0.377386\pi$
$138$	−6.27543e18	−	4.34013e18i	−0.345726	−	0.239106i
$139$			1.98893e19i			1.02680i	0.858150	+	0.513399i	$0.171614\pi$
$139$			1.98893e19i			1.02680i	−0.858150	+	0.513399i	$0.828386\pi$
$140$	1.88007e18	−	7.09071e17i	0.0909958	−	0.0343192i
$141$	1.58375e19			0.718978
$142$	−1.45501e18	+	2.10382e18i	−0.0619830	+	0.0896217i
$143$			1.60469e19i			0.641751i
$144$	6.66418e18	−	5.86042e18i	0.250313	−	0.220123i
$145$	1.13507e19			0.400599
$146$	−1.04630e19	−	7.23626e18i	−0.347120	−	0.240070i
$147$		−	1.79657e19i		−	0.560517i
$148$	−1.22807e19	−	3.25617e19i	−0.360468	−	0.955765i
$149$	−3.41022e19			−0.942120			−0.471060	−	0.882101i	$-0.656128\pi$
$149$	−3.41022e19			−0.942120			−0.471060	+	0.882101i	$0.656128\pi$
$150$	−8.52973e18	+	1.23332e19i	−0.221878	+	0.320815i
$151$		−	4.13755e19i		−	1.01380i	−0.862006	−	0.506898i	$-0.830792\pi$
$151$		−	4.13755e19i		−	1.01380i	0.862006	−	0.506898i	$-0.169208\pi$
$152$	−3.81674e19	−	9.51899e18i	−0.881253	−	0.219785i
$153$	2.57792e19			0.561108
$154$	5.60132e18	+	3.87391e18i	0.114975	+	0.0795175i
$155$			2.15838e19i			0.417967i
$156$	−2.31702e19	+	8.73869e18i	−0.423457	+	0.159707i
$157$	−1.09999e20			−1.89798			−0.948989	−	0.315309i	$-0.897892\pi$
$157$	−1.09999e20			−1.89798			−0.948989	+	0.315309i	$0.897892\pi$
$158$	−5.43046e19	+	7.85195e19i	−0.884958	+	1.27957i
$159$		−	2.94602e19i		−	0.453588i
$160$	3.88749e19	−	4.53931e18i	0.565704	−	0.0660557i
$161$	9.03608e18			0.124322
$162$	7.02277e18	+	4.85699e18i	0.0913847	+	0.0632022i
$163$		−	4.39278e18i		−	0.0540818i	−0.999634	−	0.0270409i	$-0.991392\pi$
$163$		−	4.39278e18i		−	0.0540818i	0.999634	−	0.0270409i	$-0.00860843\pi$
$164$	3.05442e19	+	8.09865e19i	0.355905	+	0.943665i
$165$	2.44029e19			0.269207
$166$	1.02846e20	−	1.48705e20i	1.07452	−	1.55365i
$167$			1.85607e19i			0.183716i	0.995772	+	0.0918578i	$0.0292805\pi$
$167$			1.85607e19i			0.183716i	−0.995772	+	0.0918578i	$0.970719\pi$
$168$	−2.54325e18	+	1.01974e19i	−0.0238564	+	0.0956548i
$169$	−4.33553e19			−0.385533
$170$	9.35090e19	+	6.46714e19i	0.788521	+	0.545346i
$171$		−	3.78484e19i		−	0.302749i
$172$	3.50091e19	−	1.32037e19i	0.265721	−	0.100217i
$173$	9.23446e19			0.665268			0.332634	−	0.943056i	$-0.392063\pi$
$173$	9.23446e19			0.665268			0.332634	+	0.943056i	$0.392063\pi$
$174$	−3.37705e19	+	4.88290e19i	−0.230990	+	0.333991i
$175$		−	1.77588e19i		−	0.115364i
$176$	8.76029e19	+	9.96178e19i	0.540635	+	0.614784i
$177$	7.72079e19			0.452796
$178$	2.19295e20	+	1.51666e20i	1.22250	+	0.845489i
$179$		−	2.33077e20i		−	1.23544i	−0.786397	−	0.617722i	$-0.788056\pi$
$179$		−	2.33077e20i		−	1.23544i	0.786397	−	0.617722i	$-0.211944\pi$
$180$	1.32892e19	+	3.52356e19i	0.0669954	+	0.177635i
$181$	−1.91552e20			−0.918712			−0.459356	−	0.888252i	$-0.651920\pi$
$181$	−1.91552e20			−0.918712			−0.459356	+	0.888252i	$0.651920\pi$
$182$	1.66816e19	−	2.41201e19i	0.0761369	−	0.110087i
$183$		−	8.88123e19i		−	0.385845i
$184$	1.70779e20	+	4.25923e19i	0.706436	+	0.176186i
$185$	1.47675e20			0.581782
$186$	−9.28504e19	−	6.42159e19i	−0.348472	−	0.241005i
$187$			3.85353e20i			1.37811i
$188$	−3.41836e20	+	1.28924e20i	−1.16519	+	0.439453i
$189$	−1.01122e19			−0.0328616
$190$	9.49491e19	−	1.37288e20i	0.294244	−	0.425451i
$191$		−	5.34594e20i		−	1.58024i	−0.612951	−	0.790121i	$-0.710018\pi$
$191$		−	5.34594e20i		−	1.58024i	0.612951	−	0.790121i	$-0.289982\pi$
$192$	−9.61329e19	+	1.80740e20i	−0.271120	+	0.509733i
$193$	−5.21901e20			−1.40466			−0.702332	−	0.711849i	$-0.747858\pi$
$193$	−5.21901e20			−1.40466			−0.702332	+	0.711849i	$0.747858\pi$
$194$	−5.75853e20	−	3.98264e20i	−1.47944	−	1.02319i
$195$		−	1.05082e20i		−	0.257762i
$196$	1.46248e20	+	3.87770e20i	0.342599	+	0.908385i
$197$	−1.08933e19			−0.0243760			−0.0121880	−	0.999926i	$-0.503880\pi$
$197$	−1.08933e19			−0.0243760			−0.0121880	+	0.999926i	$0.503880\pi$
$198$	−7.26035e19	+	1.04978e20i	−0.155228	+	0.224446i
$199$			8.43301e20i			1.72308i	0.507691	+	0.861539i	$0.330499\pi$
$199$			8.43301e20i			1.72308i	−0.507691	+	0.861539i	$0.669501\pi$
$200$	8.37075e19	−	3.35634e20i	0.163491	−	0.655536i
$201$	3.89687e20			0.727698
$202$	−6.60076e20	−	4.56513e20i	−1.17878	−	0.815250i
$203$		−	7.03096e19i		−	0.120102i
$204$	−5.56415e20	+	2.09853e20i	−0.909342	+	0.342960i
$205$	−3.67292e20			−0.574417
$206$	4.61995e20	−	6.68003e20i	0.691564	−	0.999939i
$207$			1.69351e20i			0.242692i
$208$	4.28968e20	−	3.77230e20i	0.588647	−	0.517650i
$209$	5.65767e20			0.743568
$210$	−3.66800e19	−	2.53681e19i	−0.0461802	−	0.0319385i
$211$		−	4.01419e18i		−	0.00484234i	−0.999997	−	0.00242117i	$-0.999229\pi$
$211$		−	4.01419e18i		−	0.00484234i	0.999997	−	0.00242117i	$-0.000770683\pi$
$212$	2.39818e20	+	6.35866e20i	0.277242	+	0.735094i
$213$	5.67745e19			0.0629125
$214$	9.04878e20	−	1.30837e21i	0.961316	−	1.38998i
$215$			1.58774e20i			0.161746i
$216$	−1.91117e20	−	4.76647e19i	−0.186730	−	0.0465707i
$217$	1.33697e20			0.125309
$218$	−5.14118e20	−	3.55568e20i	−0.462333	−	0.319752i
$219$			2.82358e20i			0.243671i
$220$	−5.26710e20	+	1.98650e20i	−0.436282	+	0.164545i
$221$	1.65938e21			1.31952
$222$	−4.39361e20	+	6.35276e20i	−0.335463	+	0.485049i
$223$			2.00619e21i			1.47105i	0.677495	+	0.735527i	$0.263065\pi$
$223$			2.00619e21i			1.47105i	−0.677495	+	0.735527i	$0.736935\pi$
$224$	−2.81179e19	−	2.40803e20i	−0.0198039	−	0.169602i
$225$	3.32829e20			0.225205
$226$	3.60839e20	+	2.49559e20i	0.234605	+	0.162254i
$227$			7.09599e20i			0.443385i	0.975117	+	0.221692i	$0.0711580\pi$
$227$			7.09599e20i			0.443385i	−0.975117	+	0.221692i	$0.928842\pi$
$228$	3.08101e20	+	8.16916e20i	0.185046	+	0.490641i
$229$	−1.35055e21			−0.779813			−0.389906	−	0.920855i	$-0.627493\pi$
$229$	−1.35055e21			−0.779813			−0.389906	+	0.920855i	$0.627493\pi$
$230$	−4.24846e20	+	6.14289e20i	−0.235874	+	0.341053i
$231$		−	1.51159e20i		−	0.0807100i
$232$	3.31410e20	−	1.32883e21i	0.170206	−	0.682459i
$233$	5.41321e20			0.267455			0.133728	−	0.991018i	$-0.457305\pi$
$233$	5.41321e20			0.267455			0.133728	+	0.991018i	$0.457305\pi$
$234$	4.52050e20	+	3.12641e20i	0.214904	+	0.148629i
$235$		−	1.55030e21i		−	0.709261i
$236$	−1.66645e21	+	6.28503e20i	−0.733810	+	0.276758i
$237$	2.11896e21			0.898229
$238$	4.00595e20	−	5.79224e20i	0.163498	−	0.236404i
$239$		−	1.27620e21i		−	0.501577i	−0.968042	−	0.250788i	$-0.919310\pi$
$239$		−	1.27620e21i		−	0.501577i	0.968042	−	0.250788i	$-0.0806898\pi$
$240$	−5.73664e20	−	6.52343e20i	−0.217148	−	0.246930i
$241$	8.53677e20			0.311272			0.155636	−	0.987814i	$-0.450257\pi$
$241$	8.53677e20			0.311272			0.155636	+	0.987814i	$0.450257\pi$
$242$	7.72047e20	+	5.33953e20i	0.271210	+	0.187571i
$243$		−	1.89519e20i		−	0.0641500i
$244$	7.22968e20	+	1.91692e21i	0.235836	+	0.625309i
$245$	−1.75863e21			−0.552941
$246$	1.09277e21	−	1.58004e21i	0.331216	−	0.478909i
$247$		−	2.43627e21i		−	0.711956i
$248$	2.52682e21	+	6.30191e20i	0.712047	+	0.177585i
$249$	−4.01302e21			−1.09063
$250$	2.99420e21	+	2.07080e21i	0.784910	+	0.542849i
$251$		−	1.76446e21i		−	0.446219i	−0.974793	−	0.223110i	$-0.928379\pi$
$251$		−	1.76446e21i		−	0.446219i	0.974793	−	0.223110i	$-0.0716208\pi$
$252$	2.18261e20	−	8.23173e19i	0.0532562	−	0.0200857i
$253$	−2.53150e21			−0.596065
$254$	−3.62752e21	+	5.24507e21i	−0.824340	+	1.19192i
$255$		−	2.52347e21i		−	0.553524i
$256$	6.03628e20	−	4.68363e21i	0.127823	−	0.991797i
$257$	−6.96487e21			−1.42402			−0.712008	−	0.702171i	$-0.752214\pi$
$257$	−6.96487e21			−1.42402			−0.712008	+	0.702171i	$0.752214\pi$
$258$	−6.83026e20	−	4.72385e20i	−0.134853	−	0.0932650i
$259$		−	9.14743e20i		−	0.174422i
$260$	8.55413e20	+	2.26809e21i	0.157549	+	0.417734i
$261$	1.31772e21			0.234454
$262$	−3.11425e21	+	4.50293e21i	−0.535356	+	0.774076i
$263$			4.80367e21i			0.797942i	0.916963	+	0.398971i	$0.130633\pi$
$263$			4.80367e21i			0.797942i	−0.916963	+	0.398971i	$0.869367\pi$
$264$	7.12503e20	−	2.85686e21i	0.114380	−	0.458620i
$265$	−2.88380e21			−0.447458
$266$	−8.50404e20	−	5.88145e20i	−0.127553	−	0.0882164i
$267$		−	5.91798e21i		−	0.858168i
$268$	−8.41097e21	+	3.17221e21i	−1.17932	+	0.444783i
$269$	−2.24134e21			−0.303904			−0.151952	−	0.988388i	$-0.548556\pi$
$269$	−2.24134e21			−0.303904			−0.151952	+	0.988388i	$0.548556\pi$
$270$	4.75441e20	−	6.87444e20i	0.0623480	−	0.0901496i
$271$		−	7.18077e21i		−	0.910851i	−0.890274	−	0.455425i	$-0.849487\pi$
$271$		−	7.18077e21i		−	0.910851i	0.890274	−	0.455425i	$-0.150513\pi$
$272$	1.03013e22	−	9.05889e21i	1.26408	−	1.11162i
$273$	−6.50914e20			−0.0772786
$274$	5.38017e21	+	3.72096e21i	0.618075	+	0.427465i
$275$			4.97521e21i			0.553117i
$276$	−1.37859e21	−	3.65526e21i	−0.148338	−	0.393311i
$277$	1.48092e22			1.54246			0.771231	−	0.636555i	$-0.219641\pi$
$277$	1.48092e22			1.54246			0.771231	+	0.636555i	$0.219641\pi$
$278$	−5.79246e21	+	8.37538e21i	−0.584063	+	0.844503i
$279$			2.50570e21i			0.244619i
$280$	9.98205e20	+	2.48953e20i	0.0943620	+	0.0235340i
$281$	−1.85996e20			−0.0170273			−0.00851365	−	0.999964i	$-0.502710\pi$
$281$	−1.85996e20			−0.0170273			−0.00851365	+	0.999964i	$0.502710\pi$
$282$	6.66920e21	+	4.61246e21i	0.591332	+	0.408969i
$283$			3.26713e21i			0.280601i	0.990109	+	0.140300i	$0.0448068\pi$
$283$			3.26713e21i			0.280601i	−0.990109	+	0.140300i	$0.955193\pi$
$284$	−1.22542e21	+	4.62167e20i	−0.101957	+	0.0384533i
$285$	−3.70490e21			−0.298657
$286$	−4.67343e21	+	6.75735e21i	−0.365041	+	0.527816i
$287$			2.27512e21i			0.172214i
$288$	4.51305e21	−	5.26977e20i	0.331084	−	0.0386597i
$289$	2.57857e22			1.83358
$290$	4.77977e21	+	3.30572e21i	0.329477	+	0.227868i
$291$			1.55402e22i			1.03853i
$292$	−2.29851e21	−	6.09439e21i	−0.148936	−	0.394898i
$293$	9.73526e21			0.611701			0.305850	−	0.952080i	$-0.401059\pi$
$293$	9.73526e21			0.611701			0.305850	+	0.952080i	$0.401059\pi$
$294$	5.23226e21	−	7.56537e21i	0.318833	−	0.461004i
$295$		−	7.55772e21i		−	0.446676i
$296$	4.31172e21	−	1.72883e22i	0.247187	−	0.991122i
$297$	2.83298e21			0.157556
$298$	−1.43605e22	−	9.93179e21i	−0.774858	−	0.535897i
$299$			1.09010e22i			0.570723i
$300$	−7.18375e21	+	2.70936e21i	−0.364972	+	0.137650i
$301$	9.83499e20			0.0484926
$302$	1.20500e22	−	1.74232e22i	0.576667	−	0.833809i
$303$			1.78131e22i			0.827475i
$304$	−1.33000e22	−	1.51242e22i	−0.599779	−	0.682039i
$305$	−8.69365e21			−0.380631
$306$	1.08556e22	+	7.50782e21i	0.461490	+	0.319169i
$307$		−	8.83551e21i		−	0.364742i	−0.983230	−	0.182371i	$-0.941623\pi$
$307$		−	8.83551e21i		−	0.364742i	0.983230	−	0.182371i	$-0.0583773\pi$
$308$	1.23050e21	+	3.26261e21i	0.0493315	+	0.130800i
$309$	−1.80270e22			−0.701935
$310$	−6.28597e21	+	9.08894e21i	−0.237748	+	0.343762i
$311$			2.29073e22i			0.841647i	0.907143	+	0.420823i	$0.138259\pi$
$311$			2.29073e22i			0.841647i	−0.907143	+	0.420823i	$0.861741\pi$
$312$	−1.23020e22	−	3.06814e21i	−0.439122	−	0.109517i
$313$	−1.87097e22			−0.648884			−0.324442	−	0.945906i	$-0.605176\pi$
$313$	−1.87097e22			−0.648884			−0.324442	+	0.945906i	$0.605176\pi$
$314$	−4.63206e22	−	3.20356e22i	−1.56102	−	1.07961i
$315$			9.89861e20i			0.0324175i
$316$	−4.57354e22	+	1.72492e22i	−1.45569	+	0.549015i
$317$	6.26918e21			0.193944			0.0969722	−	0.995287i	$-0.469084\pi$
$317$	6.26918e21			0.193944			0.0969722	+	0.995287i	$0.469084\pi$
$318$	8.57986e21	−	1.24057e22i	0.258010	−	0.373059i
$319$			1.96976e22i			0.575833i
$320$	1.76922e22	+	9.41025e21i	0.502844	+	0.267455i
$321$	−3.53082e22			−0.975732
$322$	3.80510e21	+	2.63163e21i	0.102250	+	0.0707167i
$323$		−	5.85051e22i		−	1.52887i
$324$	1.54276e21	+	4.09056e21i	0.0392097	+	0.103963i
$325$	2.14239e22			0.529601
$326$	1.27933e21	−	1.84980e21i	0.0307628	−	0.0444802i
$327$			1.38742e22i			0.324548i
$328$	−1.07240e22	+	4.29990e22i	−0.244057	+	0.978575i
$329$	−9.60307e21			−0.212641
$330$	1.02761e22	+	7.10700e21i	0.221413	+	0.153130i
$331$		−	3.48262e22i		−	0.730220i	−0.930964	−	0.365110i	$-0.881031\pi$
$331$		−	3.48262e22i		−	0.730220i	0.930964	−	0.365110i	$-0.118969\pi$
$332$	8.66167e22	−	3.26676e22i	1.76750	−	0.666615i
$333$	1.71438e22			0.340494
$334$	−5.40554e21	+	7.81592e21i	−0.104501	+	0.151099i
$335$		−	3.81457e22i		−	0.717863i
$336$	−4.04082e21	+	3.55346e21i	−0.0740314	+	0.0651025i
$337$	9.31490e22			1.66153			0.830767	−	0.556620i	$-0.187902\pi$
$337$	9.31490e22			1.66153			0.830767	+	0.556620i	$0.187902\pi$
$338$	−1.82569e22	−	1.26266e22i	−0.317086	−	0.219299i
$339$		−	9.73775e21i		−	0.164688i
$340$	2.05421e22	+	5.44663e22i	0.338325	+	0.897053i
$341$	−3.74558e22			−0.600799
$342$	1.10228e22	−	1.59380e22i	0.172210	−	0.248999i
$343$			2.21141e22i			0.336529i
$344$	1.85878e22	+	4.63581e21i	0.275550	+	0.0687226i
$345$	1.65774e22			0.239412
$346$	3.88864e22	+	2.68941e22i	0.547158	+	0.378418i
$347$		−	8.38405e21i		−	0.114945i	−0.998347	−	0.0574723i	$-0.981696\pi$
$347$		−	8.38405e21i		−	0.114945i	0.998347	−	0.0574723i	$-0.0183041\pi$
$348$	−2.84415e22	+	1.07268e22i	−0.379962	+	0.143303i
$349$	−9.45636e22			−1.23110			−0.615552	−	0.788096i	$-0.711067\pi$
$349$	−9.45636e22			−1.23110			−0.615552	+	0.788096i	$0.711067\pi$
$350$	5.17199e21	−	7.47823e21i	0.0656214	−	0.0948826i
$351$		−	1.21992e22i		−	0.150858i
$352$	7.87737e21	+	6.74622e22i	0.0949505	+	0.813161i
$353$	−3.63972e22			−0.427657			−0.213829	−	0.976871i	$-0.568593\pi$
$353$	−3.63972e22			−0.427657			−0.213829	+	0.976871i	$0.568593\pi$
$354$	3.25123e22	+	2.24857e22i	0.372407	+	0.257559i
$355$		−	5.55754e21i		−	0.0620622i
$356$	4.81748e22	+	1.27733e23i	0.524529	+	1.39076i
$357$	−1.56312e22			−0.165950
$358$	6.78805e22	−	9.81490e22i	0.702745	−	1.01611i
$359$			2.09197e22i			0.211206i	0.994408	+	0.105603i	$0.0336772\pi$
$359$			2.09197e22i			0.211206i	−0.994408	+	0.105603i	$0.966323\pi$
$360$	−4.66580e21	+	1.87080e22i	−0.0459413	+	0.184207i
$361$	1.82315e22			0.175088
$362$	−8.06626e22	−	5.57868e22i	−0.755606	−	0.522582i
$363$		−	2.08348e22i		−	0.190383i
$364$	1.40493e22	−	5.29870e21i	0.125239	−	0.0472342i
$365$	2.76394e22			0.240377
$366$	2.58653e22	−	3.73989e22i	0.219477	−	0.317343i
$367$		−	4.63663e22i		−	0.383891i	−0.981406	−	0.191945i	$-0.938520\pi$
$367$		−	4.63663e22i		−	0.383891i	0.981406	−	0.191945i	$-0.0614796\pi$
$368$	5.95105e22	+	6.76725e22i	0.480799	+	0.546741i
$369$	−4.26396e22			−0.336183
$370$	6.21859e22	+	4.30081e22i	0.478494	+	0.330929i
$371$			1.78632e22i			0.134151i
$372$	−2.03974e22	−	5.40827e22i	−0.149516	−	0.396435i
$373$	−1.52412e23			−1.09053			−0.545267	−	0.838262i	$-0.683572\pi$
$373$	−1.52412e23			−1.09053			−0.545267	+	0.838262i	$0.683572\pi$
$374$	−1.12229e23	+	1.62272e23i	−0.783898	+	1.13345i
$375$		−	8.08025e22i		−	0.550990i
$376$	−1.81495e23	−	4.52649e22i	−1.20829	−	0.301350i
$377$	8.48205e22			0.551352
$378$	−4.25825e21	−	2.94503e21i	−0.0270274	−	0.0186923i
$379$		−	1.72205e23i		−	1.06732i	−0.845700	−	0.533658i	$-0.820817\pi$
$379$		−	1.72205e23i		−	1.06732i	0.845700	−	0.533658i	$-0.179183\pi$
$380$	7.99662e22	−	3.01594e22i	0.484010	−	0.182545i
$381$	1.41545e23			0.836703
$382$	1.55693e23	−	2.25118e23i	0.898873	−	1.29969i
$383$			2.66513e23i			1.50290i	0.659793	+	0.751448i	$0.270644\pi$
$383$			2.66513e23i			1.50290i	−0.659793	+	0.751448i	$0.729356\pi$
$384$	−9.31195e22	+	4.81123e22i	−0.512932	+	0.265018i
$385$	−1.47967e22			−0.0796192
$386$	−2.19773e23	−	1.51996e23i	−1.15528	−	0.799001i
$387$			1.84324e22i			0.0946637i
$388$	−1.26504e23	−	3.35418e23i	−0.634771	−	1.68307i
$389$	−2.43790e20			−0.00119528			−0.000597639	−	1.00000i	$-0.500190\pi$
$389$	−2.43790e20			−0.00119528			−0.000597639		1.00000i	$0.500190\pi$
$390$	3.06038e22	−	4.42502e22i	0.146620	−	0.211999i
$391$			2.61779e23i			1.22559i
$392$	−5.13474e22	+	2.05883e23i	−0.234933	+	0.941989i
$393$	1.21518e23			0.543384
$394$	−4.58717e21	−	3.17251e21i	−0.0200484	−	0.0138656i
$395$		−	2.07420e23i		−	0.886089i
$396$	−6.11467e22	+	2.30616e22i	−0.255339	+	0.0963014i
$397$	1.05604e22			0.0431088			0.0215544	−	0.999768i	$-0.493138\pi$
$397$	1.05604e22			0.0431088			0.0215544	+	0.999768i	$0.493138\pi$
$398$	−2.45599e23	+	3.55115e23i	−0.980121	+	1.41717i
$399$			2.29493e22i			0.0895394i
$400$	1.32998e23	−	1.16957e23i	0.507347	−	0.446156i
$401$	8.76595e22			0.326964			0.163482	−	0.986546i	$-0.447727\pi$
$401$	8.76595e22			0.326964			0.163482	+	0.986546i	$0.447727\pi$
$402$	1.64097e23	+	1.13491e23i	0.598504	+	0.413929i
$403$			1.61290e23i			0.575256i
$404$	−1.45006e23	−	3.84476e23i	−0.505769	−	1.34102i
$405$	−1.85516e22			−0.0632830
$406$	2.04767e22	−	2.96074e22i	0.0683164	−	0.0987794i
$407$			2.56270e23i			0.836272i
$408$	−2.95423e23	−	7.36789e22i	−0.942982	−	0.235181i
$409$	−3.46605e23			−1.08224			−0.541122	−	0.840944i	$-0.682000\pi$
$409$	−3.46605e23			−1.08224			−0.541122	+	0.840944i	$0.682000\pi$
$410$	−1.54667e23	−	1.06969e23i	−0.472436	−	0.326740i
$411$		−	1.45191e23i		−	0.433875i
$412$	3.89093e23	−	1.46747e23i	1.13757	−	0.429037i
$413$	−4.68149e22			−0.133916
$414$	−4.93211e22	+	7.13139e22i	−0.138048	+	0.199605i
$415$			3.92827e23i			1.07589i
$416$	2.90502e23	−	3.39211e22i	0.778589	−	0.0909137i
$417$	2.26021e23			0.592822
$418$	2.38245e23	+	1.64772e23i	0.611557	+	0.422957i
$419$			3.28020e23i			0.824089i	0.911164	+	0.412045i	$0.135185\pi$
$419$			3.28020e23i			0.824089i	−0.911164	+	0.412045i	$0.864815\pi$
$420$	−8.05787e21	−	2.13651e22i	−0.0198142	−	0.0525364i
$421$	4.12177e23			0.992077			0.496038	−	0.868301i	$-0.334788\pi$
$421$	4.12177e23			0.992077			0.496038	+	0.868301i	$0.334788\pi$
$422$	1.16907e21	−	1.69038e21i	0.00275442	−	0.00398264i
$423$		−	1.79978e23i		−	0.415102i
$424$	−8.41995e22	+	3.37607e23i	−0.190115	+	0.762287i
$425$	5.14479e23			1.13728
$426$	2.39078e22	+	1.65348e22i	0.0517431	+	0.0357859i
$427$			5.38512e22i			0.114116i
$428$	7.62089e23	−	2.87423e23i	1.58129	−	0.596387i
$429$	1.82357e23			0.370515
$430$	−4.62408e22	+	6.68600e22i	−0.0920045	+	0.133030i
$431$		−	7.88715e23i		−	1.53683i	−0.639954	−	0.768413i	$-0.721047\pi$
$431$		−	7.88715e23i		−	1.53683i	0.639954	−	0.768413i	$-0.278953\pi$
$432$	−6.65977e22	−	7.57316e22i	−0.127088	−	0.144519i
$433$	−3.89698e23			−0.728345			−0.364173	−	0.931331i	$-0.618648\pi$
$433$	−3.89698e23			−0.728345			−0.364173	+	0.931331i	$0.618648\pi$
$434$	5.62997e22	+	3.89373e22i	0.103062	+	0.0712784i
$435$		−	1.28989e23i		−	0.231286i
$436$	−1.12942e23	−	2.99459e23i	−0.198370	−	0.525968i
$437$	3.84338e23			0.661272
$438$	−8.22328e22	+	1.18901e23i	−0.138605	+	0.200410i
$439$			6.91829e23i			1.14240i	0.820811	+	0.571200i	$0.193522\pi$
$439$			6.91829e23i			1.14240i	−0.820811	+	0.571200i	$0.806478\pi$
$440$	−2.79652e23	−	6.97454e22i	−0.452422	−	0.112834i
$441$	−2.04162e23			−0.323614
$442$	6.98768e23	+	4.83272e23i	1.08526	+	0.750570i
$443$		−	1.14875e24i		−	1.74821i	−0.485737	−	0.874105i	$-0.661449\pi$
$443$		−	1.14875e24i		−	1.74821i	0.485737	−	0.874105i	$-0.338551\pi$
$444$	−3.70030e23	+	1.39557e23i	−0.551811	+	0.208116i
$445$	−5.79299e23			−0.846570
$446$	−5.84275e23	+	8.44809e23i	−0.836765	+	1.20989i
$447$			3.87537e23i			0.543933i
$448$	5.82900e22	−	1.09591e23i	0.0801848	−	0.150756i
$449$	−6.54802e23			−0.882863			−0.441431	−	0.897295i	$-0.645529\pi$
$449$	−6.54802e23			−0.882863			−0.441431	+	0.897295i	$0.645529\pi$
$450$	1.40155e23	+	9.69318e22i	0.185223	+	0.128101i
$451$		−	6.37387e23i		−	0.825685i
$452$	7.92692e22	+	2.10179e23i	0.100660	+	0.266896i
$453$	−4.70190e23			−0.585315
$454$	−2.06661e23	+	2.98813e23i	−0.252206	+	0.364667i
$455$			6.37166e22i			0.0762342i
$456$	−1.08174e23	+	4.33734e23i	−0.126893	+	0.508791i
$457$	−9.04788e23			−1.04064			−0.520320	−	0.853971i	$-0.674187\pi$
$457$	−9.04788e23			−1.04064			−0.520320	+	0.853971i	$0.674187\pi$
$458$	−5.68716e23	−	3.93328e23i	−0.641366	−	0.443573i
$459$		−	2.92954e23i		−	0.323956i
$460$	−3.57806e23	+	1.34947e23i	−0.387996	+	0.146333i
$461$	−5.92855e23			−0.630434			−0.315217	−	0.949020i	$-0.602077\pi$
$461$	−5.92855e23			−0.630434			−0.315217	+	0.949020i	$0.602077\pi$
$462$	4.40230e22	−	6.36533e22i	0.0459095	−	0.0663809i
$463$		−	7.92010e23i		−	0.810032i	−0.914310	−	0.405016i	$-0.867266\pi$
$463$		−	7.92010e23i		−	0.810032i	0.914310	−	0.405016i	$-0.132734\pi$
$464$	5.26559e23	−	4.63051e23i	0.528184	−	0.464480i
$465$	2.45278e23			0.241313
$466$	2.27950e23	+	1.57652e23i	0.219972	+	0.152134i
$467$		−	1.82230e24i		−	1.72491i	−0.506131	−	0.862456i	$-0.668925\pi$
$467$		−	1.82230e24i		−	1.72491i	0.506131	−	0.862456i	$-0.331075\pi$
$468$	9.93064e22	+	2.63306e23i	0.0922071	+	0.244483i
$469$	−2.36286e23			−0.215220
$470$	4.51504e23	−	6.52834e23i	0.403442	−	0.583340i
$471$			1.25003e24i			1.09580i
$472$	−8.84785e23	−	2.20666e23i	−0.760956	−	0.189783i
$473$	−2.75532e23			−0.232499
$474$	8.92294e23	+	6.17116e23i	0.738759	+	0.510931i
$475$		−	7.55346e23i		−	0.613626i
$476$	3.37382e23	−	1.27244e23i	0.268942	−	0.101432i
$477$	−3.34785e23			−0.261879
$478$	3.71675e23	−	5.37408e23i	0.285307	−	0.412528i
$479$			2.37782e24i			1.79126i	0.444800	+	0.895630i	$0.353275\pi$
$479$			2.37782e24i			1.79126i	−0.444800	+	0.895630i	$0.646725\pi$
$480$	−5.15847e22	−	4.41773e23i	−0.0381373	−	0.326609i
$481$	1.10353e24			0.800718
$482$	3.59484e23	+	2.48621e23i	0.256009	+	0.177058i
$483$		−	1.02686e23i		−	0.0717772i
$484$	1.69603e23	+	4.49696e23i	0.116366	+	0.308539i
$485$	1.52120e24			1.02450
$486$	5.51948e22	−	7.98067e22i	0.0364898	−	0.0527610i
$487$			1.73428e24i			1.12554i	0.826615	+	0.562768i	$0.190264\pi$
$487$			1.73428e24i			1.12554i	−0.826615	+	0.562768i	$0.809736\pi$
$488$	−2.53832e23	+	1.01777e24i	−0.161722	+	0.648441i
$489$	−4.99195e22			−0.0312241
$490$	−7.40559e23	−	5.12175e23i	−0.454773	−	0.314524i
$491$			7.56114e22i			0.0455884i	0.999740	+	0.0227942i	$0.00725624\pi$
$491$			7.56114e22i			0.0455884i	−0.999740	+	0.0227942i	$0.992744\pi$
$492$	9.20329e23	−	3.47104e23i	0.544825	−	0.205482i
$493$	2.03690e24			1.18399
$494$	7.09529e23	−	1.02592e24i	0.404975	−	0.585557i
$495$		−	2.77314e23i		−	0.155427i
$496$	8.80510e23	+	1.00127e24i	0.484618	+	0.551084i
$497$	−3.44251e22			−0.0186067
$498$	−1.68989e24	−	1.16874e24i	−0.897002	−	0.620372i
$499$		−	2.14927e24i		−	1.12043i	−0.828346	−	0.560217i	$-0.810718\pi$
$499$		−	2.14927e24i		−	1.12043i	0.828346	−	0.560217i	$-0.189282\pi$
$500$	6.57765e23	+	1.74403e24i	0.336776	+	0.892945i
$501$	2.10924e23			0.106068
$502$	5.13874e23	−	7.43015e23i	0.253818	−	0.366999i
$503$			2.76285e24i			1.34043i	0.742166	+	0.670217i	$0.233799\pi$
$503$			2.76285e24i			1.34043i	−0.742166	+	0.670217i	$0.766201\pi$
$504$	1.15883e23	+	2.89014e22i	0.0552263	+	0.0137735i
$505$	1.74368e24			0.816292
$506$	−1.06602e24	−	7.37264e23i	−0.490241	−	0.339054i
$507$			4.92689e23i			0.222588i
$508$	−3.05510e24	+	1.15224e24i	−1.35598	+	0.511409i
$509$	−6.39009e23			−0.278642			−0.139321	−	0.990247i	$-0.544492\pi$
$509$	−6.39009e23			−0.278642			−0.139321	+	0.990247i	$0.544492\pi$
$510$	7.34925e23	−	1.06263e24i	0.314856	−	0.455253i
$511$		−	1.71207e23i		−	0.0720667i
$512$	1.61823e24	−	1.79648e24i	0.669284	−	0.743007i
$513$	−4.30109e23			−0.174792
$514$	−2.93291e24	−	2.02842e24i	−1.17120	−	0.810009i
$515$			1.76463e24i			0.692448i
$516$	−1.50047e23	−	3.97843e23i	−0.0578603	−	0.153414i
$517$	2.69035e24			1.01951
$518$	2.66406e23	−	3.85199e23i	0.0992147	−	0.143455i
$519$		−	1.04940e24i		−	0.384093i
$520$	−3.00334e23	+	1.20422e24i	−0.108037	+	0.433187i
$521$	−2.15213e24			−0.760903			−0.380451	−	0.924801i	$-0.624231\pi$
$521$	−2.15213e24			−0.760903			−0.380451	+	0.924801i	$0.624231\pi$
$522$	5.54892e23	+	3.83767e23i	0.192830	+	0.133362i
$523$		−	8.66926e22i		−	0.0296120i	−0.999890	−	0.0148060i	$-0.995287\pi$
$523$		−	8.66926e22i		−	0.0296120i	0.999890	−	0.0148060i	$-0.00471306\pi$
$524$	−2.62283e24	+	9.89204e23i	−0.880620	+	0.332127i
$525$	−2.01811e23			−0.0666055
$526$	−1.39900e24	+	2.02283e24i	−0.453886	+	0.656277i
$527$			3.87325e24i			1.23532i
$528$	1.13205e24	−	9.95518e23i	0.354946	−	0.312136i
$529$	1.52445e24			0.469906
$530$	−1.21437e24	−	8.39865e23i	−0.368017	−	0.254523i
$531$		−	8.77389e23i		−	0.261422i
$532$	−1.86817e23	−	4.95336e23i	−0.0547282	−	0.145109i
$533$	−2.74468e24			−0.790581
$534$	1.72353e24	−	2.49207e24i	0.488143	−	0.705811i
$535$			3.45625e24i			0.962545i
$536$	−4.46572e24	−	1.11376e24i	−1.22295	−	0.305005i
$537$	−2.64869e24			−0.713284
$538$	−9.43829e23	−	6.52758e23i	−0.249950	−	0.172867i
$539$		−	3.05186e24i		−	0.794815i
$540$	4.00417e23	−	1.51018e23i	0.102558	−	0.0386798i
$541$	7.43587e22			0.0187308			0.00936540	−	0.999956i	$-0.497019\pi$
$541$	7.43587e22			0.0187308			0.00936540	+	0.999956i	$0.497019\pi$
$542$	2.09130e24	−	3.02383e24i	0.518110	−	0.749140i
$543$			2.17679e24i			0.530419i
$544$	6.97617e24	−	8.14588e23i	1.67196	−	0.195231i
$545$	1.35812e24			0.320161
$546$	−2.74100e23	−	1.89569e23i	−0.0635587	−	0.0439576i
$547$		−	8.58196e24i		−	1.95749i	−0.205070	−	0.978747i	$-0.565742\pi$
$547$		−	8.58196e24i		−	1.95749i	0.205070	−	0.978747i	$-0.434258\pi$
$548$	1.18192e24	+	3.13380e24i	0.265193	+	0.703147i
$549$	−1.00926e24			−0.222768
$550$	−1.44896e24	+	2.09506e24i	−0.314624	+	0.454918i
$551$		−	2.99053e24i		−	0.638827i
$552$	4.84019e23	−	1.94073e24i	0.101721	−	0.407861i
$553$	−1.28483e24			−0.265655
$554$	6.23618e24	+	4.31298e24i	1.26862	+	0.877383i
$555$		−	1.67817e24i		−	0.335892i
$556$	−4.87842e24	+	1.83990e24i	−0.960740	+	0.362345i
$557$	−6.71325e24			−1.30088			−0.650438	−	0.759560i	$-0.725415\pi$
$557$	−6.71325e24			−1.30088			−0.650438	+	0.759560i	$0.725415\pi$
$558$	−7.29749e23	+	1.05515e24i	−0.139144	+	0.201190i
$559$			1.18648e24i			0.222615i
$560$	3.47840e23	+	3.95547e23i	0.0642226	+	0.0730308i
$561$	4.37915e24			0.795654
$562$	−7.83228e22	−	5.41686e22i	−0.0140043	−	0.00968546i
$563$			7.33405e22i			0.0129053i	0.999979	+	0.00645265i	$0.00205396\pi$
$563$			7.33405e22i			0.0129053i	−0.999979	+	0.00645265i	$0.997946\pi$
$564$	1.46509e24	+	3.88462e24i	0.253719	+	0.672723i
$565$	−9.53208e23			−0.162462
$566$	−9.51506e23	+	1.37579e24i	−0.159611	+	0.230783i
$567$			1.14915e23i			0.0189727i
$568$	−6.50623e23	−	1.62266e23i	−0.105729	−	0.0263689i
$569$	6.49967e24			1.03963			0.519817	−	0.854277i	$-0.326000\pi$
$569$	6.49967e24			1.03963			0.519817	+	0.854277i	$0.326000\pi$
$570$	−1.56014e24	−	1.07900e24i	−0.245634	−	0.169882i
$571$		−	5.06802e24i		−	0.785441i	−0.919658	−	0.392720i	$-0.871534\pi$
$571$		−	5.06802e24i		−	0.785441i	0.919658	−	0.392720i	$-0.128466\pi$
$572$	−3.93597e24	+	1.48446e24i	−0.600464	+	0.226466i
$573$	−6.07511e24			−0.912353
$574$	−6.62598e23	+	9.58056e23i	−0.0979587	+	0.141639i
$575$			3.37977e24i			0.491899i
$576$	2.05392e24	+	1.09245e24i	0.294294	+	0.156531i
$577$	−4.06340e24			−0.573201			−0.286600	−	0.958050i	$-0.592525\pi$
$577$	−4.06340e24			−0.573201			−0.286600	+	0.958050i	$0.592525\pi$
$578$	1.08584e25	+	7.50973e24i	1.50805	+	1.04297i
$579$			5.93088e24i			0.810983i
$580$	1.05002e24	+	2.78408e24i	0.141366	+	0.374826i
$581$	2.43329e24			0.322559
$582$	−4.52586e24	+	6.54399e24i	−0.590738	+	0.854153i
$583$		−	5.00445e24i		−	0.643190i
$584$	8.07001e23	−	3.23576e24i	0.102131	−	0.409506i
$585$	−1.19415e24			−0.148819
$586$	4.09952e24	+	2.83526e24i	0.503101	+	0.347948i
$587$		−	6.65067e24i		−	0.803752i	−0.915694	−	0.401876i	$-0.868358\pi$
$587$		−	6.65067e24i		−	0.803752i	0.915694	−	0.401876i	$-0.131642\pi$
$588$	4.40661e24	−	1.66196e24i	0.524456	−	0.197799i
$589$	5.68661e24			0.666524
$590$	2.20108e24	−	3.18256e24i	0.254078	−	0.367374i
$591$			1.23791e23i			0.0140735i
$592$	6.85064e24	−	6.02439e24i	0.767072	−	0.674556i
$593$	5.32505e24			0.587261			0.293631	−	0.955919i	$-0.405136\pi$
$593$	5.32505e24			0.587261			0.293631	+	0.955919i	$0.405136\pi$
$594$	1.19297e24	+	8.25065e23i	0.129584	+	0.0896211i
$595$			1.53010e24i			0.163707i
$596$	−3.15471e24	−	8.36456e24i	−0.332463	−	0.881509i
$597$	9.58326e24			0.994820
$598$	−3.17476e24	+	4.59042e24i	−0.324639	+	0.469398i
$599$		−	5.02953e24i		−	0.506624i	−0.967385	−	0.253312i	$-0.918480\pi$
$599$		−	5.02953e24i		−	0.506624i	0.967385	−	0.253312i	$-0.0815199\pi$
$600$	−3.81414e24	−	9.51251e23i	−0.378474	−	0.0943917i
$601$	9.01113e22			0.00880864			0.00440432	−	0.999990i	$-0.498598\pi$
$601$	9.01113e22			0.00880864			0.00440432	+	0.999990i	$0.498598\pi$
$602$	4.14152e23	+	2.86430e23i	0.0398833	+	0.0275836i
$603$		−	4.42840e24i		−	0.420137i
$604$	1.01485e25	−	3.82754e24i	0.948574	−	0.357756i
$605$	−2.03947e24			−0.187810
$606$	−5.18780e24	+	7.50109e24i	−0.470685	+	0.680567i
$607$			1.70277e25i			1.52216i	0.648661	+	0.761078i	$0.275329\pi$
$607$			1.70277e25i			1.52216i	−0.648661	+	0.761078i	$0.724671\pi$
$608$	−1.19596e24	−	1.02422e25i	−0.105338	−	0.902117i
$609$	−7.98998e23			−0.0693410
$610$	−3.66090e24	−	2.53190e24i	−0.313054	−	0.216510i
$611$		−	1.15850e25i		−	0.976170i
$612$	2.38476e24	+	6.32309e24i	0.198008	+	0.525009i
$613$	−2.20112e25			−1.80094			−0.900471	−	0.434917i	$-0.856778\pi$
$613$	−2.20112e25			−1.80094			−0.900471	+	0.434917i	$0.856778\pi$
$614$	2.57322e24	−	3.72064e24i	0.207473	−	0.299987i
$615$			4.17390e24i			0.331640i
$616$	−4.32025e23	+	1.73225e24i	−0.0338285	+	0.135639i
$617$	−1.75783e25			−1.35647			−0.678236	−	0.734845i	$-0.737255\pi$
$617$	−1.75783e25			−1.35647			−0.678236	+	0.734845i	$0.737255\pi$
$618$	−7.59118e24	−	5.25011e24i	−0.577315	−	0.399275i
$619$			1.57825e25i			1.18293i	0.806331	+	0.591465i	$0.201450\pi$
$619$			1.57825e25i			1.18293i	−0.806331	+	0.591465i	$0.798550\pi$
$620$	−5.29405e24	+	1.99666e24i	−0.391077	+	0.147495i
$621$	1.92450e24			0.140118
$622$	−6.67142e24	+	9.64626e24i	−0.478745	+	0.692222i
$623$			3.58836e24i			0.253807i
$624$	−4.28684e24	−	4.87478e24i	−0.298866	−	0.339855i
$625$	1.92191e24			0.132073
$626$	−7.87865e24	−	5.44892e24i	−0.533682	−	0.369098i
$627$		−	6.42937e24i		−	0.429299i
$628$	−1.01757e25	−	2.69804e25i	−0.669773	−	1.77587i
$629$	2.65005e25			1.71948
$630$	−2.88283e23	+	4.16831e23i	−0.0184397	+	0.0266622i
$631$			2.19061e25i			1.38134i	0.723169	+	0.690671i	$0.242685\pi$
$631$			2.19061e25i			1.38134i	−0.723169	+	0.690671i	$0.757315\pi$
$632$	−2.42828e25	−	6.05614e24i	−1.50954	−	0.376480i
$633$	−4.56171e22			−0.00279573
$634$	2.63995e24	+	1.82581e24i	0.159512	+	0.110319i
$635$		−	1.38556e25i		−	0.825394i
$636$	7.22597e24	−	2.72529e24i	0.424407	−	0.160066i
$637$	−1.31417e25			−0.761024
$638$	−5.73664e24	+	8.29466e24i	−0.327545	+	0.473601i
$639$		−	6.45184e23i		−	0.0363225i
$640$	4.70961e24	+	9.11527e24i	0.261436	+	0.505999i
$641$	9.43903e24			0.516660			0.258330	−	0.966057i	$-0.416828\pi$
$641$	9.43903e24			0.516660			0.258330	+	0.966057i	$0.416828\pi$
$642$	−1.48683e25	−	1.02830e25i	−0.802503	−	0.555016i
$643$		−	1.44683e24i		−	0.0770052i	−0.999259	−	0.0385026i	$-0.987741\pi$
$643$		−	1.44683e24i		−	0.0770052i	0.999259	−	0.0385026i	$-0.0122588\pi$
$644$	8.35904e23	+	2.21636e24i	0.0438716	+	0.116324i
$645$	1.80431e24			0.0933843
$646$	1.70388e25	−	2.46365e25i	0.869653	−	1.25744i
$647$			3.16838e25i			1.59477i	0.603468	+	0.797387i	$0.293785\pi$
$647$			3.16838e25i			1.59477i	−0.603468	+	0.797387i	$0.706215\pi$
$648$	−5.41661e23	+	2.17185e24i	−0.0268876	+	0.107809i
$649$	1.31154e25			0.642067
$650$	9.02163e24	+	6.23942e24i	0.435577	+	0.301248i
$651$		−	1.51933e24i		−	0.0723473i
$652$	1.07746e24	−	4.06365e23i	0.0506025	−	0.0190848i
$653$	2.39365e25			1.10877			0.554386	−	0.832260i	$-0.312953\pi$
$653$	2.39365e25			1.10877			0.554386	+	0.832260i	$0.312953\pi$
$654$	−4.04066e24	+	5.84244e24i	−0.184609	+	0.266928i
$655$		−	1.18951e25i		−	0.536040i
$656$	−1.70387e25	+	1.49837e25i	−0.757361	+	0.666016i
$657$	3.20871e24			0.140683
$658$	−4.04386e24	−	2.79676e24i	−0.174889	−	0.120954i
$659$			4.37128e24i			0.186483i	0.995644	+	0.0932416i	$0.0297229\pi$
$659$			4.37128e24i			0.186483i	−0.995644	+	0.0932416i	$0.970277\pi$
$660$	2.25745e24	+	5.98553e24i	0.0949998	+	0.251888i
$661$	−3.92498e24			−0.162939			−0.0814694	−	0.996676i	$-0.525961\pi$
$661$	−3.92498e24			−0.162939			−0.0814694	+	0.996676i	$0.525961\pi$
$662$	1.01426e25	−	1.46653e25i	0.415364	−	0.600578i
$663$		−	1.88572e25i		−	0.761826i
$664$	4.59883e25	+	1.14695e25i	1.83288	+	0.457123i
$665$	2.24646e24			0.0883292
$666$	7.21927e24	+	4.99289e24i	0.280043	+	0.193680i
$667$			1.33810e25i			0.512101i
$668$	−4.55255e24	+	1.71700e24i	−0.171896	+	0.0648310i
$669$	2.27983e25			0.849314
$670$	1.11094e25	−	1.60632e25i	0.408335	−	0.590415i
$671$		−	1.50867e25i		−	0.547131i
$672$	−2.73648e24	+	3.19532e23i	−0.0979196	+	0.0114338i
$673$	−7.74269e23			−0.0273373			−0.0136687	−	0.999907i	$-0.504351\pi$
$673$	−7.74269e23			−0.0273373			−0.0136687	+	0.999907i	$0.504351\pi$
$674$	3.92251e25	+	2.71283e25i	1.36655	+	0.945114i
$675$		−	3.78227e24i		−	0.130022i
$676$	−4.01068e24	−	1.06341e25i	−0.136050	−	0.360730i
$677$	−1.97675e25			−0.661689			−0.330844	−	0.943685i	$-0.607334\pi$
$677$	−1.97675e25			−0.661689			−0.330844	+	0.943685i	$0.607334\pi$
$678$	2.83598e24	−	4.10057e24i	0.0936777	−	0.135449i
$679$		−	9.42278e24i		−	0.307151i
$680$	−7.21227e24	+	2.89184e25i	−0.232002	+	0.930238i
$681$	8.06388e24			0.255988
$682$	−1.57726e25	−	1.09085e25i	−0.494135	−	0.341747i
$683$			3.99149e25i			1.23410i	0.786926	+	0.617048i	$0.211671\pi$
$683$			3.99149e25i			1.23410i	−0.786926	+	0.617048i	$0.788329\pi$
$684$	9.28342e24	−	3.50126e24i	0.283272	−	0.106836i
$685$	−1.42125e25			−0.428011
$686$	−6.44043e24	+	9.31228e24i	−0.191425	+	0.276783i
$687$			1.53476e25i			0.450225i
$688$	6.47721e24	+	7.36556e24i	0.187539	+	0.213260i
$689$	−2.15499e25			−0.615845
$690$	6.98077e24	+	4.82794e24i	0.196907	+	0.136182i
$691$		−	3.24094e25i		−	0.902338i	−0.892439	−	0.451169i	$-0.851007\pi$
$691$		−	3.24094e25i		−	0.902338i	0.892439	−	0.451169i	$-0.148993\pi$
$692$	8.54256e24	+	2.26502e25i	0.234765	+	0.622469i
$693$	−1.71777e24			−0.0465979
$694$	2.44173e24	−	3.53053e24i	0.0653828	−	0.0945375i
$695$		−	2.21247e25i		−	0.584810i
$696$	−1.51008e25	−	3.76614e24i	−0.394018	−	0.0982684i
$697$	−6.59113e25			−1.69771
$698$	−3.98208e25	−	2.75403e25i	−1.01254	−	0.700277i
$699$		−	6.15156e24i		−	0.154415i
$700$	4.35586e24	−	1.64282e24i	0.107942	−	0.0407106i
$701$	−5.04034e25			−1.23310			−0.616549	−	0.787317i	$-0.711470\pi$
$701$	−5.04034e25			−1.23310			−0.616549	+	0.787317i	$0.711470\pi$
$702$	3.55284e24	−	5.13709e24i	0.0858108	−	0.124075i
$703$		−	3.89074e25i		−	0.927757i
$704$	−1.63302e25	+	3.07025e25i	−0.384449	+	0.722804i
$705$	−1.76176e25			−0.409492
$706$	−1.53269e25	−	1.06002e25i	−0.351732	−	0.243260i
$707$		−	1.08009e25i		−	0.244730i
$708$	7.14230e24	+	1.89375e25i	0.159786	+	0.423665i
$709$	7.50689e25			1.65823			0.829113	−	0.559081i	$-0.188846\pi$
$709$	7.50689e25			1.65823			0.829113	+	0.559081i	$0.188846\pi$
$710$	1.61855e24	−	2.34028e24i	0.0353022	−	0.0510438i
$711$		−	2.40798e25i		−	0.518593i
$712$	−1.69141e25	+	6.78187e25i	−0.359690	+	1.44221i
$713$	−2.54445e25			−0.534304
$714$	−6.58230e24	−	4.55236e24i	−0.136488	−	0.0943958i
$715$		−	1.78505e25i		−	0.365507i
$716$	5.71690e25	−	2.15614e25i	1.15596	−	0.435973i
$717$	−1.45027e25			−0.289585
$718$	−6.09257e24	+	8.80931e24i	−0.120138	+	0.173709i
$719$		−	7.06989e23i		−	0.0137674i	−0.999976	−	0.00688372i	$-0.997809\pi$
$719$		−	7.06989e23i		−	0.0137674i	0.999976	−	0.00688372i	$-0.00219117\pi$
$720$	−7.41321e24	+	6.51911e24i	−0.142565	+	0.125371i
$721$	1.09306e25			0.207601
$722$	7.67728e24	+	5.30966e24i	0.144003	+	0.0995937i
$723$		−	9.70117e24i		−	0.179713i
$724$	−1.77200e25	−	4.69837e25i	−0.324202	−	0.859607i
$725$	2.62979e25			0.475203
$726$	6.06783e24	−	8.77353e24i	0.108294	−	0.156583i
$727$		−	7.78049e25i		−	1.37150i	−0.727835	−	0.685752i	$-0.759473\pi$
$727$		−	7.78049e25i		−	1.37150i	0.727835	−	0.685752i	$-0.240527\pi$
$728$	7.45932e24	+	1.86036e24i	0.129872	+	0.0323903i
$729$	−2.15369e24			−0.0370370
$730$	1.16390e25	+	8.04960e24i	0.197701	+	0.136731i
$731$			2.84924e25i			0.478048i
$732$	2.17838e25	−	8.21580e24i	0.361022	−	0.136160i
$733$	−4.94394e25			−0.809352			−0.404676	−	0.914460i	$-0.632616\pi$
$733$	−4.94394e25			−0.809352			−0.404676	+	0.914460i	$0.632616\pi$
$734$	1.35035e25	−	1.95249e25i	0.218365	−	0.315735i
$735$			1.99850e25i			0.319241i
$736$	5.35127e24	+	4.58285e25i	0.0844416	+	0.723162i
$737$	6.61967e25			1.03188
$738$	−1.79556e25	−	1.24182e25i	−0.276498	−	0.191228i
$739$			1.18366e26i			1.80064i	0.435231	+	0.900319i	$0.356667\pi$
$739$			1.18366e26i			1.80064i	−0.435231	+	0.900319i	$0.643333\pi$
$740$	1.36610e25	+	3.62215e25i	0.205304	+	0.544353i
$741$	−2.76857e25			−0.411048
$742$	−5.20239e24	+	7.52218e24i	−0.0763076	+	0.110334i
$743$		−	7.85790e25i		−	1.13869i	−0.822097	−	0.569347i	$-0.807196\pi$
$743$		−	7.85790e25i		−	1.13869i	0.822097	−	0.569347i	$-0.192804\pi$
$744$	7.16148e24	−	2.87147e25i	0.102529	−	0.411101i
$745$	3.79352e25			0.536582
$746$	−6.41807e25	−	4.43878e25i	−0.896923	−	0.620318i
$747$			4.56039e25i			0.629676i
$748$	−9.45191e25	+	3.56480e25i	−1.28945	+	0.486319i
$749$	2.14091e25			0.288577
$750$	2.35326e25	−	3.40260e25i	0.313414	−	0.453168i
$751$			9.88597e25i			1.30095i	0.759529	+	0.650474i	$0.225430\pi$
$751$			9.88597e25i			1.30095i	−0.759529	+	0.650474i	$0.774570\pi$
$752$	−6.32447e25	−	7.19188e25i	−0.822363	−	0.935151i
$753$	−2.00513e25			−0.257625
$754$	3.57180e25	+	2.47028e25i	0.453466	+	0.313620i
$755$			4.60260e25i			0.577405i
$756$	−9.35452e23	−	2.48031e24i	−0.0115965	−	0.0307475i
$757$	1.18242e26			1.44847			0.724236	−	0.689552i	$-0.242192\pi$
$757$	1.18242e26			1.44847			0.724236	+	0.689552i	$0.242192\pi$
$758$	5.01523e25	−	7.25157e25i	0.607111	−	0.877827i
$759$			2.87679e25i			0.344138i
$760$	4.24573e25	+	1.05889e25i	0.501915	+	0.125178i
$761$	−4.56466e25			−0.533269			−0.266635	−	0.963798i	$-0.585912\pi$
$761$	−4.56466e25			−0.533269			−0.266635	+	0.963798i	$0.585912\pi$
$762$	5.96049e25	+	4.12231e25i	0.688156	+	0.475933i
$763$		−	8.41261e24i		−	0.0959864i
$764$	1.31125e26	−	4.94539e25i	1.47858	−	0.557648i
$765$	−2.86767e25			−0.319577
$766$	−7.76180e25	+	1.12229e26i	−0.854877	+	1.23607i
$767$		−	5.64768e25i		−	0.614769i
$768$	−5.32247e25	−	6.85962e24i	−0.572614	−	0.0737988i
$769$	1.53208e26			1.62909			0.814546	−	0.580099i	$-0.196986\pi$
$769$	1.53208e26			1.62909			0.814546	+	0.580099i	$0.196986\pi$
$770$	−6.23089e24	−	4.30932e24i	−0.0654838	−	0.0452890i
$771$			7.91487e25i			0.822156i
$772$	−4.82797e25	−	1.28011e26i	−0.495689	−	1.31430i
$773$	−7.89910e25			−0.801609			−0.400804	−	0.916164i	$-0.631269\pi$
$773$	−7.89910e25			−0.801609			−0.400804	+	0.916164i	$0.631269\pi$
$774$	−5.36818e24	+	7.76190e24i	−0.0538466	+	0.0778573i
$775$			5.00066e25i			0.495806i
$776$	4.44151e25	−	1.78087e26i	0.435287	−	1.74533i
$777$	−1.03951e25			−0.100703
$778$	−1.02660e23	−	7.10003e22i	−0.000983070	−	0.000679898i
$779$			9.67694e25i			0.916012i
$780$	2.57745e25	−	9.72090e24i	0.241179	−	0.0909609i
$781$	9.64437e24			0.0892102
$782$	−7.62394e25	+	1.10235e26i	−0.697138	+	1.00800i
$783$		−	1.49745e25i		−	0.135362i
$784$	−8.15829e25	+	7.17432e25i	−0.729045	+	0.641116i
$785$	1.22362e26			1.08099
$786$	5.11712e25	+	3.53903e25i	0.446913	+	0.309088i
$787$		−	4.33840e25i		−	0.374591i	−0.982304	−	0.187295i	$-0.940028\pi$
$787$		−	4.33840e25i		−	0.374591i	0.982304	−	0.187295i	$-0.0599721\pi$
$788$	−1.00771e24	−	2.67190e24i	−0.00860200	−	0.0228078i
$789$	5.45889e25			0.460692
$790$	6.04082e25	−	8.73448e25i	0.504025	−	0.728775i
$791$			5.90447e24i			0.0487071i
$792$	−3.24653e25	−	8.09687e24i	−0.264785	−	0.0660375i
$793$	−6.49654e25			−0.523870
$794$	4.44699e24	+	3.07557e24i	0.0354554	+	0.0245212i
$795$			3.27714e25i			0.258340i
$796$	−2.06844e26	+	7.80116e25i	−1.61223	+	0.608053i
$797$	1.59217e25			0.122706			0.0613528	−	0.998116i	$-0.480459\pi$
$797$	1.59217e25			0.122706			0.0613528	+	0.998116i	$0.480459\pi$
$798$	−6.68367e24	+	9.66398e24i	−0.0509318	+	0.0736427i
$799$		−	2.78205e26i		−	2.09625i
$800$	9.00677e25	−	1.05170e25i	0.671057	−	0.0783574i
$801$	−6.72519e25			−0.495464
$802$	3.69135e25	+	2.55296e25i	0.268915	+	0.185984i
$803$			4.79646e25i			0.345526i
$804$	3.60489e25	+	9.55821e25i	0.256796	+	0.680882i
$805$	−1.00517e25			−0.0708071
$806$	−4.69734e25	+	6.79192e25i	−0.327217	+	0.473127i
$807$			2.54705e25i			0.175459i
$808$	5.09111e25	−	2.04134e26i	0.346825	−	1.39063i
$809$	1.91039e25			0.128702			0.0643510	−	0.997927i	$-0.479502\pi$
$809$	1.91039e25			0.128702			0.0643510	+	0.997927i	$0.479502\pi$
$810$	−7.81211e24	−	5.40290e24i	−0.0520479	−	0.0359966i
$811$			3.38451e25i			0.223001i	0.993764	+	0.111501i	$0.0355657\pi$
$811$			3.38451e25i			0.223001i	−0.993764	+	0.111501i	$0.964434\pi$
$812$	1.72455e25	−	6.50416e24i	0.112375	−	0.0423825i
$813$	−8.16021e25			−0.525880
$814$	−7.46349e25	+	1.07915e26i	−0.475688	+	0.687802i
$815$			4.88651e24i			0.0308021i
$816$	−1.02945e26	−	1.17064e26i	−0.641792	−	0.729814i
$817$	4.18318e25			0.257934
$818$	−1.45956e26	−	1.00944e26i	−0.890105	−	0.615602i
$819$			7.39697e24i			0.0446168i
$820$	−3.39773e25	−	9.00891e25i	−0.202705	−	0.537462i
$821$	−2.03212e26			−1.19912			−0.599559	−	0.800331i	$-0.704657\pi$
$821$	−2.03212e26			−1.19912			−0.599559	+	0.800331i	$0.704657\pi$
$822$	4.22850e25	−	6.11402e25i	0.246797	−	0.356846i
$823$		−	1.31651e26i		−	0.760020i	−0.924982	−	0.380010i	$-0.875921\pi$
$823$		−	1.31651e26i		−	0.760020i	0.924982	−	0.380010i	$-0.124079\pi$
$824$	2.06585e26	+	5.15226e25i	1.17965	+	0.294207i
$825$	5.65382e25			0.319342
$826$	−1.97138e25	−	1.36342e25i	−0.110141	−	0.0761743i
$827$		−	9.01008e25i		−	0.497942i	−0.968511	−	0.248971i	$-0.919908\pi$
$827$		−	9.01008e25i		−	0.497942i	0.968511	−	0.248971i	$-0.0800925\pi$
$828$	−4.15383e25	+	1.56662e25i	−0.227078	+	0.0856430i
$829$	−1.52392e26			−0.824083			−0.412041	−	0.911165i	$-0.635184\pi$
$829$	−1.52392e26			−0.824083			−0.412041	+	0.911165i	$0.635184\pi$
$830$	−1.14405e26	+	1.65419e26i	−0.611988	+	0.884879i
$831$		−	1.68292e26i		−	0.890541i
$832$	1.32209e26	+	7.03203e25i	0.692074	+	0.368104i
$833$	−3.15589e26			−1.63424
$834$	9.51776e25	+	6.58255e25i	0.487574	+	0.337209i
$835$		−	2.06469e25i		−	0.104635i
$836$	5.23376e25	+	1.38771e26i	0.262396	+	0.695731i
$837$	2.84747e25			0.141231
$838$	−9.55312e25	+	1.38129e26i	−0.468758	+	0.677782i
$839$			8.67062e24i			0.0420913i	0.999779	+	0.0210457i	$0.00669954\pi$
$839$			8.67062e24i			0.0420913i	−0.999779	+	0.0210457i	$0.993300\pi$
$840$	2.82910e24	−	1.13436e25i	0.0135873	−	0.0544799i
$841$	−1.06340e26			−0.505280
$842$	1.73568e26	+	1.20041e26i	0.815945	+	0.564313i
$843$			2.11365e24i			0.00983071i
$844$	9.84596e23	−	3.71342e23i	0.00453081	−	0.00170880i
$845$	4.82283e25			0.219579
$846$	5.24159e25	−	7.57887e25i	0.236118	−	0.341406i
$847$			1.26331e25i			0.0563068i
$848$	−1.33780e26	+	1.17645e26i	−0.589967	+	0.518811i
$849$	3.71276e25			0.162005
$850$	2.16647e26	+	1.49835e26i	0.935369	+	0.646907i
$851$			1.74090e26i			0.743715i
$852$	5.25206e24	+	1.39256e25i	0.0222010	+	0.0588650i
$853$	2.69544e25			0.112743			0.0563713	−	0.998410i	$-0.482047\pi$
$853$	2.69544e25			0.112743			0.0563713	+	0.998410i	$0.482047\pi$
$854$	−1.56834e25	+	2.26768e25i	−0.0649112	+	0.0938557i
$855$			4.21024e25i			0.172430i
$856$	4.04624e26	+	1.00914e26i	1.63979	+	0.408965i
$857$	2.46852e26			0.989940			0.494970	−	0.868910i	$-0.335179\pi$
$857$	2.46852e26			0.989940			0.494970	+	0.868910i	$0.335179\pi$
$858$	7.67905e25	+	5.31088e25i	0.304735	+	0.210756i
$859$			2.58714e26i			1.01597i	0.861366	+	0.507985i	$0.169610\pi$
$859$			2.58714e26i			1.01597i	−0.861366	+	0.507985i	$0.830390\pi$
$860$	−3.89440e25	+	1.46878e25i	−0.151340	+	0.0570783i
$861$	2.58545e25			0.0994277
$862$	2.29702e26	−	3.32128e26i	0.874177	−	1.26398i
$863$		−	3.80793e26i		−	1.43414i	−0.697001	−	0.717070i	$-0.745483\pi$
$863$		−	3.80793e26i		−	1.43414i	0.697001	−	0.717070i	$-0.254517\pi$
$864$	−5.98856e24	−	5.12863e25i	−0.0223202	−	0.191151i
$865$	−1.02724e26			−0.378902
$866$	−1.64102e26	−	1.13494e26i	−0.599036	−	0.414297i
$867$		−	2.93029e26i		−	1.05862i
$868$	1.23679e25	+	3.27930e25i	0.0442201	+	0.117248i
$869$	3.59951e26			1.27369
$870$	3.75662e25	−	5.43173e25i	0.131560	−	0.190224i
$871$		−	2.85052e26i		−	0.988010i
$872$	3.96535e25	−	1.58995e26i	0.136030	−	0.545426i
$873$	1.76599e26			0.599597
$874$	1.61845e26	+	1.11933e26i	0.543871	+	0.376145i
$875$			4.89945e25i			0.162958i
$876$	−6.92565e25	+	2.61202e25i	−0.227994	+	0.0859884i
$877$	3.63510e26			1.18446			0.592230	−	0.805769i	$-0.298248\pi$
$877$	3.63510e26			1.18446			0.592230	+	0.805769i	$0.298248\pi$
$878$	−2.01485e26	+	2.91329e26i	−0.649819	+	0.939580i
$879$		−	1.10631e26i		−	0.353166i
$880$	−9.74492e25	−	1.10814e26i	−0.307917	−	0.350149i
$881$	5.39626e25			0.168775			0.0843877	−	0.996433i	$-0.473107\pi$
$881$	5.39626e25			0.168775			0.0843877	+	0.996433i	$0.473107\pi$
$882$	−8.59728e25	−	5.94593e25i	−0.266161	−	0.184078i
$883$			5.31505e26i			1.62878i	0.580321	+	0.814388i	$0.302927\pi$
$883$			5.31505e26i			1.62878i	−0.580321	+	0.814388i	$0.697073\pi$
$884$	1.53505e26	+	4.07013e26i	0.465643	+	1.23463i
$885$	−8.58858e25			−0.257889
$886$	3.34558e26	−	4.83741e26i	0.994417	−	1.43784i
$887$			3.01263e26i			0.886408i	0.896421	+	0.443204i	$0.146158\pi$
$887$			3.01263e26i			0.886408i	−0.896421	+	0.443204i	$0.853842\pi$
$888$	−1.96464e26	−	4.89983e25i	−0.572225	−	0.142713i
$889$	−8.58259e25			−0.247459
$890$	−2.43943e26	−	1.68713e26i	−0.696272	−	0.481546i
$891$		−	3.21939e25i		−	0.0909651i
$892$	−4.92077e26	+	1.85588e26i	−1.37642	+	0.519117i
$893$	−4.08454e26			−1.13105
$894$	−1.12865e26	+	1.63192e26i	−0.309400	+	0.447365i
$895$			2.59275e26i			0.703644i
$896$	5.64629e25	−	2.91728e25i	0.151702	−	0.0783802i
$897$	1.23879e26			0.329507
$898$	−2.75738e26	−	1.90702e26i	−0.726121	−	0.502190i
$899$			1.97983e26i			0.516169i
$900$	3.07892e25	+	8.16360e25i	0.0794722	+	0.210717i
$901$	−5.17503e26			−1.32248
$902$	1.85630e26	−	2.68404e26i	0.469666	−	0.679095i
$903$		−	1.11765e25i		−	0.0279972i
$904$	−2.78312e25	+	1.11592e26i	−0.0690266	+	0.276770i
$905$	2.13082e26			0.523250
$906$	−1.97997e26	−	1.36936e26i	−0.481400	−	0.332939i
$907$		−	3.23084e26i		−	0.777767i	−0.921287	−	0.388883i	$-0.872861\pi$
$907$		−	3.23084e26i		−	0.777767i	0.921287	−	0.388883i	$-0.127139\pi$
$908$	−1.74050e26	+	6.56432e25i	−0.414860	+	0.156465i
$909$	2.02427e26			0.477743
$910$	−1.85565e25	+	2.68311e25i	−0.0433635	+	0.0626997i
$911$		−	1.31106e26i		−	0.303360i	−0.988430	−	0.151680i	$-0.951532\pi$
$911$		−	1.31106e26i		−	0.303360i	0.988430	−	0.151680i	$-0.0484683\pi$
$912$	−1.71871e26	+	1.51142e26i	−0.393775	+	0.346282i
$913$	−6.81699e26			−1.54652
$914$	−3.81007e26	−	2.63507e26i	−0.855888	−	0.591937i
$915$			9.87946e25i			0.219757i
$916$	−1.24936e26	−	3.31261e26i	−0.275186	−	0.729644i
$917$	−7.36822e25			−0.160708
$918$	8.53188e25	−	1.23363e26i	0.184272	−	0.266441i
$919$			4.00429e26i			0.856419i	0.903679	+	0.428210i	$0.140856\pi$
$919$			4.00429e26i			0.856419i	−0.903679	+	0.428210i	$0.859144\pi$
$920$	−1.89974e26	−	4.73796e25i	−0.402349	−	0.100346i
$921$	−1.00407e26			−0.210584
$922$	−2.49651e26	−	1.72660e26i	−0.518508	−	0.358604i
$923$		−	4.15300e25i		−	0.0854175i
$924$	3.70763e25	−	1.39834e25i	0.0755176	−	0.0284816i
$925$	3.42142e26			0.690129
$926$	2.30662e26	−	3.33516e26i	0.460762	−	0.666220i
$927$			2.04859e26i			0.405263i
$928$	3.56591e26	−	4.16382e25i	0.698617	−	0.0815755i
$929$	5.73834e26			1.11338			0.556692	−	0.830719i	$-0.312071\pi$
$929$	5.73834e26			1.11338			0.556692	+	0.830719i	$0.312071\pi$
$930$	1.03287e26	+	7.14336e25i	0.198471	+	0.137264i
$931$			4.63340e26i			0.881765i
$932$	5.00762e25	+	1.32775e26i	0.0943817	+	0.250249i
$933$	2.60318e26			0.485925
$934$	5.30718e26	−	7.67370e26i	0.981165	−	1.41868i
$935$		−	4.28666e26i		−	0.784900i
$936$	−3.48663e25	+	1.39800e26i	−0.0632299	+	0.253527i
$937$	−2.86120e26			−0.513916			−0.256958	−	0.966423i	$-0.582720\pi$
$937$	−2.86120e26			−0.513916			−0.256958	+	0.966423i	$0.582720\pi$
$938$	−9.95003e25	−	6.88150e25i	−0.177010	−	0.122421i
$939$			2.12616e26i			0.374633i
$940$	3.80257e26	−	1.43415e26i	0.663631	−	0.250289i
$941$	2.24889e26			0.388741			0.194371	−	0.980928i	$-0.437734\pi$
$941$	2.24889e26			0.388741			0.194371	+	0.980928i	$0.437734\pi$
$942$	−3.64052e26	+	5.26386e26i	−0.623312	+	0.901252i
$943$		−	4.32991e26i		−	0.734300i
$944$	−3.08317e26	−	3.50604e26i	−0.517905	−	0.588936i
$945$	1.12488e25			0.0187162
$946$	−1.16027e26	−	8.02448e25i	−0.191222	−	0.132250i
$947$			1.37675e26i			0.224753i	0.993666	+	0.112376i	$0.0358462\pi$
$947$			1.37675e26i			0.224753i	−0.993666	+	0.112376i	$0.964154\pi$
$948$	1.96019e26	+	5.19736e26i	0.316974	+	0.840442i
$949$	2.06542e26			0.330836
$950$	2.19984e26	−	3.18077e26i	0.349043	−	0.504684i
$951$		−	7.12429e25i		−	0.111974i
$952$	1.79130e26	+	4.46751e25i	0.278891	+	0.0695557i
$953$	−1.28353e26			−0.197957			−0.0989783	−	0.995090i	$-0.531557\pi$
$953$	−1.28353e26			−0.197957			−0.0989783	+	0.995090i	$0.531557\pi$
$954$	−1.40978e26	−	9.75014e25i	−0.215386	−	0.148962i
$955$			5.94680e26i			0.900022i
$956$	3.13025e26	−	1.18058e26i	0.469308	−	0.177000i
$957$	2.23843e26			0.332458
$958$	−6.92505e26	+	1.00130e27i	−1.01890	+	1.47324i
$959$			8.80367e25i			0.128321i
$960$	1.06938e26	−	2.01054e26i	0.154415	−	0.290317i
$961$	3.22580e26			0.461452
$962$	4.64698e26	+	3.21388e26i	0.658560	+	0.455464i
$963$			4.01242e26i			0.563339i
$964$	7.89714e25	+	2.09389e26i	0.109844	+	0.291247i
$965$	5.80561e26			0.800023
$966$	2.99058e25	−	4.32411e25i	0.0408283	−	0.0590340i
$967$		−	2.57155e26i		−	0.347821i	−0.984761	−	0.173911i	$-0.944360\pi$
$967$		−	2.57155e26i		−	0.347821i	0.984761	−	0.173911i	$-0.0556404\pi$
$968$	−5.95474e25	+	2.38762e26i	−0.0797966	+	0.319953i
$969$	−6.64851e26			−0.882695
$970$	6.40578e26	+	4.43027e26i	0.842609	+	0.582754i
$971$		−	9.88662e26i		−	1.28847i	−0.764827	−	0.644236i	$-0.777176\pi$
$971$		−	9.88662e26i		−	1.28847i	0.764827	−	0.644236i	$-0.222824\pi$
$972$	4.64851e25	−	1.75319e25i	0.0600230	−	0.0226378i
$973$	−1.37048e26			−0.175330
$974$	−5.05085e26	+	7.30308e26i	−0.640227	+	0.925710i
$975$		−	2.43461e26i		−	0.305766i
$976$	−4.03300e26	+	3.54658e26i	−0.501857	+	0.441328i
$977$	−2.57330e26			−0.317277			−0.158639	−	0.987337i	$-0.550710\pi$
$977$	−2.57330e26			−0.317277			−0.158639	+	0.987337i	$0.550710\pi$
$978$	−2.10211e25	−	1.45383e25i	−0.0256807	−	0.0177609i
$979$		−	1.00530e27i		−	1.21689i
$980$	−1.62686e26	−	4.31354e26i	−0.195126	−	0.517368i
$981$	1.57666e26			0.187378
$982$	−2.20207e25	+	3.18400e25i	−0.0259316	+	0.0374947i
$983$		−	5.04156e26i		−	0.588279i	−0.955763	−	0.294139i	$-0.904967\pi$
$983$		−	5.04156e26i		−	0.588279i	0.955763	−	0.294139i	$-0.0950330\pi$
$984$	4.88640e26	+	1.21867e26i	0.564980	+	0.140907i
$985$	1.21177e25			0.0138833
$986$	8.57739e26	+	5.93218e26i	0.973785	+	0.673476i
$987$			1.09129e26i			0.122768i
$988$	5.97566e26	−	2.25373e26i	0.666153	−	0.251240i
$989$	−1.87175e26			−0.206767
$990$	8.07639e25	−	1.16777e26i	0.0884098	−	0.127833i
$991$			1.73325e27i			1.88017i	0.340937	+	0.940086i	$0.389256\pi$
$991$			1.73325e27i			1.88017i	−0.340937	+	0.940086i	$0.610744\pi$
$992$	7.91767e25	+	6.78073e26i	0.0851123	+	0.728906i
$993$	−3.95764e26			−0.421593
$994$	−1.44964e25	−	1.00258e25i	−0.0153033	−	0.0105838i
$995$		−	9.38086e26i		−	0.981374i
$996$	−3.71234e26	−	9.84311e26i	−0.384870	−	1.02047i
$997$	−1.00418e27			−1.03170			−0.515852	−	0.856678i	$-0.672525\pi$
$997$	−1.00418e27			−1.03170			−0.515852	+	0.856678i	$0.672525\pi$
$998$	6.25945e26	−	9.05059e26i	0.637325	−	0.921514i
$999$		−	1.94822e26i		−	0.196584i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.19.d.a.7.16	yes	18
3.2	odd	2		36.19.d.e.19.3		18
4.3	odd	2	inner	12.19.d.a.7.15	✓	18
12.11	even	2		36.19.d.e.19.4		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.19.d.a.7.15	✓	18	4.3	odd	2	inner
12.19.d.a.7.16	yes	18	1.1	even	1	trivial
36.19.d.e.19.3		18	3.2	odd	2
36.19.d.e.19.4		18	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	12.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(421.101 + 291.236i) q^{2} -11364.0i q^{3} +(92507.4 + 245279. i) q^{4} -1.11240e6 q^{5} +(3.30960e6 - 4.78538e6i) q^{6} +6.89054e6i q^{7} +(-3.24791e7 + 1.30229e8i) q^{8} -1.29140e8 q^{9} +O(q^{10})\)	\(q+(421.101 + 291.236i) q^{2} -11364.0i q^{3} +(92507.4 + 245279. i) q^{4} -1.11240e6 q^{5} +(3.30960e6 - 4.78538e6i) q^{6} +6.89054e6i q^{7} +(-3.24791e7 + 1.30229e8i) q^{8} -1.29140e8 q^{9} +(-4.68431e8 - 3.23970e8i) q^{10} -1.93042e9i q^{11} +(2.78735e9 - 1.05125e9i) q^{12} -8.31265e9 q^{13} +(-2.00677e9 + 2.90161e9i) q^{14} +1.26413e10i q^{15} +(-5.16042e10 + 4.53803e10i) q^{16} -1.99622e11 q^{17} +(-5.43810e10 - 3.76102e10i) q^{18} +2.93080e11i q^{19} +(-1.02905e11 - 2.72848e11i) q^{20} +7.83040e10 q^{21} +(5.62207e11 - 8.12900e11i) q^{22} -1.31137e12i q^{23} +(1.47992e12 + 3.69093e11i) q^{24} -2.57727e12 q^{25} +(-3.50046e12 - 2.42094e12i) q^{26} +1.46755e12i q^{27} +(-1.69011e12 + 6.37426e11i) q^{28} -1.02038e13 q^{29} +(-3.68159e12 + 5.32324e12i) q^{30} -1.94029e13i q^{31} +(-3.49469e13 + 4.08066e12i) q^{32} -2.19372e13 q^{33} +(-8.40608e13 - 5.81370e13i) q^{34} -7.66501e12i q^{35} +(-1.19464e13 - 3.16754e13i) q^{36} -1.32753e14 q^{37} +(-8.53554e13 + 1.23416e14i) q^{38} +9.44648e13i q^{39} +(3.61297e13 - 1.44866e14i) q^{40} +3.30181e14 q^{41} +(3.29739e13 + 2.28049e13i) q^{42} -1.42732e14i q^{43} +(4.73491e14 - 1.78578e14i) q^{44} +1.43655e14 q^{45} +(3.81919e14 - 5.52221e14i) q^{46} +1.39366e15i q^{47} +(5.15701e14 + 5.86430e14i) q^{48} +1.58093e15 q^{49} +(-1.08529e15 - 7.50593e14i) q^{50} +2.26850e15i q^{51} +(-7.68982e14 - 2.03892e15i) q^{52} +2.59242e15 q^{53} +(-4.27402e14 + 6.17985e14i) q^{54} +2.14739e15i q^{55} +(-8.97346e14 - 2.23799e14i) q^{56} +3.33056e15 q^{57} +(-4.29682e15 - 2.97171e15i) q^{58} +6.79409e15i q^{59} +(-3.10064e15 + 1.16941e15i) q^{60} +7.81524e15 q^{61} +(5.65083e15 - 8.17059e15i) q^{62} -8.89845e14i q^{63} +(-1.59046e16 - 8.45943e15i) q^{64} +9.24697e15 q^{65} +(-9.23779e15 - 6.38891e15i) q^{66} +3.42914e16i q^{67} +(-1.84665e16 - 4.89630e16i) q^{68} -1.49024e16 q^{69} +(2.23233e15 - 3.22774e15i) q^{70} +4.99600e15i q^{71} +(4.19436e15 - 1.68178e16i) q^{72} -2.48467e16 q^{73} +(-5.59026e16 - 3.86626e16i) q^{74} +2.92881e16i q^{75} +(-7.18864e16 + 2.71121e16i) q^{76} +1.33016e16 q^{77} +(-2.75115e16 + 3.97792e16i) q^{78} +1.86462e17i q^{79} +(5.74044e16 - 5.04809e16i) q^{80} +1.66772e16 q^{81} +(1.39039e17 + 9.61605e16i) q^{82} -3.53135e17i q^{83} +(7.24370e15 + 1.92063e16i) q^{84} +2.22059e17 q^{85} +(4.15686e16 - 6.01044e16i) q^{86} +1.15956e17i q^{87} +(2.51396e17 + 6.26983e16i) q^{88} +5.20767e17 q^{89} +(6.04933e16 + 4.18375e16i) q^{90} -5.72786e16i q^{91} +(3.21653e17 - 1.21312e17i) q^{92} -2.20495e17 q^{93} +(-4.05884e17 + 5.86871e17i) q^{94} -3.26021e17i q^{95} +(4.63725e16 + 3.97136e17i) q^{96} -1.36750e18 q^{97} +(6.65732e17 + 4.60425e17i) q^{98} +2.49294e17i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 170 q^{2} - 436932 q^{4} - 1721764 q^{5} - 6731586 q^{6} + 108558736 q^{8} - 2324522934 q^{9}+O(q^{10}) \) 18 * q - 170 * q^2 - 436932 * q^4 - 1721764 * q^5 - 6731586 * q^6 + 108558736 * q^8 - 2324522934 * q^9	\( 18 q - 170 q^{2} - 436932 q^{4} - 1721764 q^{5} - 6731586 q^{6} + 108558736 q^{8} - 2324522934 q^{9} + 1397074644 q^{10} - 6468699852 q^{12} + 1799208612 q^{13} - 48147537912 q^{14} - 119537094672 q^{16} - 282984271180 q^{17} + 21953827710 q^{18} + 491637621128 q^{20} + 254050055640 q^{21} + 272503644408 q^{22} + 4483423343232 q^{24} + 20224739695878 q^{25} - 2765456970196 q^{26} + 27756503338032 q^{28} + 1812741883820 q^{29} - 3579410315772 q^{30} + 216191588070880 q^{32} + 17014318866216 q^{33} - 275796423660708 q^{34} + 56425469699916 q^{36} + 197439381411156 q^{37} - 676030464010008 q^{38} + 19\!\cdots\!68 q^{40}+ \cdots - 37\!\cdots\!22 q^{98}+O(q^{100}) \) 18 * q - 170 * q^2 - 436932 * q^4 - 1721764 * q^5 - 6731586 * q^6 + 108558736 * q^8 - 2324522934 * q^9 + 1397074644 * q^10 - 6468699852 * q^12 + 1799208612 * q^13 - 48147537912 * q^14 - 119537094672 * q^16 - 282984271180 * q^17 + 21953827710 * q^18 + 491637621128 * q^20 + 254050055640 * q^21 + 272503644408 * q^22 + 4483423343232 * q^24 + 20224739695878 * q^25 - 2765456970196 * q^26 + 27756503338032 * q^28 + 1812741883820 * q^29 - 3579410315772 * q^30 + 216191588070880 * q^32 + 17014318866216 * q^33 - 275796423660708 * q^34 + 56425469699916 * q^36 + 197439381411156 * q^37 - 676030464010008 * q^38 + 1941137842438368 * q^40 - 204669372669676 * q^41 - 1059935698181880 * q^42 + 3599128179401424 * q^44 + 222348883607532 * q^45 - 3847169819651040 * q^46 + 1457367907812912 * q^48 - 3424095824368878 * q^49 - 10192520264009358 * q^50 + 4228291003193208 * q^52 - 14112687314785972 * q^53 + 869318113288518 * q^54 - 6591066595001856 * q^56 - 9662233004693640 * q^57 + 17584741731886020 * q^58 + 193536143011224 * q^60 + 4171094773122132 * q^61 + 77227021488187896 * q^62 - 53424456043095936 * q^64 + 35585253307254712 * q^65 + 40644920520184824 * q^66 - 91403316760947112 * q^68 + 26342656148137824 * q^69 + 264958129332427248 * q^70 - 14019292862113968 * q^72 - 83809473755653692 * q^73 + 55949505142092092 * q^74 - 129026923617832848 * q^76 - 354619239852167328 * q^77 - 34535086926497028 * q^78 + 43257628406200352 * q^80 + 300189270593998242 * q^81 - 458290372754774916 * q^82 + 324078384809786832 * q^84 + 166017223439872920 * q^85 - 975848731010420424 * q^86 + 1151342491040801280 * q^88 - 660650117825905468 * q^89 - 180418447249326972 * q^90 + 1359275349780859584 * q^92 - 447365281400937432 * q^93 - 2087066679318498384 * q^94 + 257905715132447136 * q^96 + 2412557706093917220 * q^97 - 3767017570512990122 * q^98

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