LMFDB - Embedded newform 5.34.b.a.4.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,34,Mod(4,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 34, names="a")

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

chi := DirichletCharacter("5.4");

S:= CuspForms(chi, 34);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 34 $
Character orbit:	$[\chi]$	$=$	5.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$34.4914144405$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 26286285043 x^{14} + \cdots + 16\!\cdots\!36 $ x^16 + 26286285043x^14 + 277176279803774573548x^12 + 1496006322727341104924267746816x^10 + 4376228902975645752284567792282218577920x^8 + 6785210496827316795155770011788917433647451078656x^6 + 5093319366938751307797338793282286802764384084972313509888x^4 + 1608229292592013531797229664939538769264311330074914543142623510528*x^2 + 163532475457876517394407745867705361011086521692855999713211555842344615936
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{83}\cdot 3^{26}\cdot 5^{53}\cdot 7^{4}\cdot 11^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4.9
Root			$13863.7i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.34.b.a.4.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+27727.3i q^{2} -6.45007e7i q^{3} +7.82113e9 q^{4} +(-2.89243e11 - 1.80980e11i) q^{5} +1.78843e12 q^{6} +3.09117e13i q^{7} +4.55035e14i q^{8} +1.39871e15 q^{9} +O(q^{10})$	\(q+27727.3i q^{2} -6.45007e7i q^{3} +7.82113e9 q^{4} +(-2.89243e11 - 1.80980e11i) q^{5} +1.78843e12 q^{6} +3.09117e13i q^{7} +4.55035e14i q^{8} +1.39871e15 q^{9} +(5.01809e15 - 8.01994e15i) q^{10} +1.96079e17 q^{11} -5.04469e17i q^{12} +4.53343e18i q^{13} -8.57100e17 q^{14} +(-1.16733e19 + 1.86564e19i) q^{15} +5.45661e19 q^{16} -2.94288e20i q^{17} +3.87826e19i q^{18} -6.15724e20 q^{19} +(-2.26221e21 - 1.41547e21i) q^{20} +1.99383e21 q^{21} +5.43675e21i q^{22} -1.65655e22i q^{23} +2.93501e22 q^{24} +(5.09079e22 + 1.04694e23i) q^{25} -1.25700e23 q^{26} -4.48782e23i q^{27} +2.41765e23i q^{28} +9.17408e22 q^{29} +(-5.17292e23 - 3.23670e23i) q^{30} +5.75654e24 q^{31} +5.42169e24i q^{32} -1.26472e25i q^{33} +8.15982e24 q^{34} +(5.59440e24 - 8.94100e24i) q^{35} +1.09395e25 q^{36} -9.32591e25i q^{37} -1.70724e25i q^{38} +2.92410e26 q^{39} +(8.23522e25 - 1.31616e26i) q^{40} +4.59334e26 q^{41} +5.52836e25i q^{42} -2.98860e26i q^{43} +1.53356e27 q^{44} +(-4.04569e26 - 2.53139e26i) q^{45} +4.59317e26 q^{46} -3.83658e27i q^{47} -3.51955e27i q^{48} +6.77546e27 q^{49} +(-2.90290e27 + 1.41154e27i) q^{50} -1.89818e28 q^{51} +3.54566e28i q^{52} +1.34770e28i q^{53} +1.24435e28 q^{54} +(-5.67145e28 - 3.54863e28i) q^{55} -1.40659e28 q^{56} +3.97147e28i q^{57} +2.54373e27i q^{58} -1.39545e29 q^{59} +(-9.12987e28 + 1.45914e29i) q^{60} -1.27289e29 q^{61} +1.59614e29i q^{62} +4.32367e28i q^{63} +3.18390e29 q^{64} +(8.20460e29 - 1.31126e30i) q^{65} +3.50674e29 q^{66} +1.55253e30i q^{67} -2.30166e30i q^{68} -1.06849e30 q^{69} +(2.47910e29 + 1.55118e29i) q^{70} +4.80212e30 q^{71} +6.36464e29i q^{72} -2.54238e30i q^{73} +2.58583e30 q^{74} +(6.75286e30 - 3.28360e30i) q^{75} -4.81566e30 q^{76} +6.06114e30i q^{77} +8.10774e30i q^{78} -1.90983e31 q^{79} +(-1.57829e31 - 9.87536e30i) q^{80} -2.11712e31 q^{81} +1.27361e31i q^{82} -1.69264e31i q^{83} +1.55940e31 q^{84} +(-5.32602e31 + 8.51208e31i) q^{85} +8.28660e30 q^{86} -5.91735e30i q^{87} +8.92228e31i q^{88} +8.93087e31 q^{89} +(7.01888e30 - 1.12176e31i) q^{90} -1.40136e32 q^{91} -1.29561e32i q^{92} -3.71301e32i q^{93} +1.06378e32 q^{94} +(1.78094e32 + 1.11434e32i) q^{95} +3.49703e32 q^{96} -6.99431e32i q^{97} +1.87865e32i q^{98} +2.74259e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 72851326872 q^{4} - 232168160280 q^{5} + 11001777346872 q^{6} - 27\!\cdots\!68 q^{9}+O(q^{10}) $ 16 * q - 72851326872 * q^4 - 232168160280 * q^5 + 11001777346872 * q^6 - 27535156574590368 * q^9	$ 16 q - 72851326872 q^{4} - 232168160280 q^{5} + 11001777346872 q^{6} - 27\!\cdots\!68 q^{9}+ \cdots + 34\!\cdots\!24 q^{99}+O(q^{100}) $ 16 * q - 72851326872 * q^4 - 232168160280 * q^5 + 11001777346872 * q^6 - 27535156574590368 * q^9 - 22271193818331880 * q^10 + 219974590742466912 * q^11 - 10416043581549356184 * q^14 + 9232415497377901440 * q^15 + 133171456389985196576 * q^16 - 2949217257058889591200 * q^19 + 5571772909456424216760 * q^20 + 20126160533851210892592 * q^21 - 236696360036140740492000 * q^24 + 269473151678676722148400 * q^25 + 23043234216449373353232 * q^26 + 2210824656972934579370400 * q^29 - 7438800885032297852420760 * q^30 + 4805180075928582021889472 * q^31 - 106706080442140703440064 * q^34 + 34840114703893102459924320 * q^35 + 150609707516636111776170456 * q^36 - 950668737676648885834065216 * q^39 + 967967034953888345833396000 * q^40 + 960625982433026021733974352 * q^41 - 4300041994750366563328828704 * q^44 + 5959973976670208219568382440 * q^45 + 4030532465737707969346868392 * q^46 - 48902999941413820155855454112 * q^49 + 64132734499011351066825776400 * q^50 + 37677263492556888574173469632 * q^51 - 416785644990759180210455480400 * q^54 + 208827421951347317583761567040 * q^55 + 209868986171565551575474447200 * q^56 - 204679212804521237512362904800 * q^59 - 320542648209593925139588560480 * q^60 - 62902839261738400132019069488 * q^61 + 3273202940251902417009873735808 * q^64 - 1155813780125630532662955267360 * q^65 - 2991219624550267460630717491296 * q^66 + 6899695112224183044828868241904 * q^69 - 5880904834264312779374002982280 * q^70 - 87525095316001019795902439808 * q^71 + 43140282179597200538055251968176 * q^74 - 27726088944293536006405507003200 * q^75 - 38605994956626944020944749752800 * q^76 - 10590745643822309766800662264000 * q^79 + 24913342429758171577982759437920 * q^80 + 126385893984816788804508532470336 * q^81 - 401968339664232685914350670917664 * q^84 + 174616747052458036927895334806720 * q^85 - 18805496634715830052189508032488 * q^86 - 816457769414638729740610145056800 * q^89 + 814730708455223899676092744179240 * q^90 + 572310345418666359618454810906752 * q^91 + 1084618018208246129370832376900296 * q^94 - 960346549067575215463879922304000 * q^95 - 1376269400022374885061468958478208 * q^96 + 3432482025669259323040953857901024 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$			27727.3i			0.299167i	0.988749	+	0.149583i	$0.0477932\pi$
$2$			27727.3i			0.299167i	−0.988749	+	0.149583i	$0.952207\pi$
$3$		−	6.45007e7i		−	0.865095i	−0.901611	−	0.432548i	$-0.857615\pi$
$3$		−	6.45007e7i		−	0.865095i	0.901611	−	0.432548i	$-0.142385\pi$
$4$	7.82113e9			0.910499
$5$	−2.89243e11	−	1.80980e11i	−0.847731	−	0.530426i
$5$	−2.89243e11	−	1.80980e11i	−0.847731	−	0.530426i
$6$	1.78843e12			0.258808
$7$			3.09117e13i			0.351565i	0.984429	+	0.175782i	$0.0562455\pi$
$7$			3.09117e13i			0.351565i	−0.984429	+	0.175782i	$0.943754\pi$
$8$			4.55035e14i			0.571558i
$9$	1.39871e15			0.251610
$10$	5.01809e15	−	8.01994e15i	0.158686	−	0.253613i
$11$	1.96079e17			1.28662			0.643312	−	0.765604i	$-0.277560\pi$
$11$	1.96079e17			1.28662			0.643312	+	0.765604i	$0.277560\pi$
$12$		−	5.04469e17i		−	0.787669i
$13$			4.53343e18i			1.88956i	0.327699	+	0.944782i	$0.393727\pi$
$13$			4.53343e18i			1.88956i	−0.327699	+	0.944782i	$0.606273\pi$
$14$	−8.57100e17			−0.105177
$15$	−1.16733e19	+	1.86564e19i	−0.458869	+	0.733368i
$16$	5.45661e19			0.739508
$17$		−	2.94288e20i		−	1.46678i	−0.679808	−	0.733390i	$-0.737937\pi$
$17$		−	2.94288e20i		−	1.46678i	0.679808	−	0.733390i	$-0.262063\pi$
$18$			3.87826e19i			0.0752733i
$19$	−6.15724e20			−0.489725			−0.244862	−	0.969558i	$-0.578743\pi$
$19$	−6.15724e20			−0.489725			−0.244862	+	0.969558i	$0.578743\pi$
$20$	−2.26221e21	−	1.41547e21i	−0.771858	−	0.482953i
$21$	1.99383e21			0.304137
$22$			5.43675e21i			0.384915i
$23$		−	1.65655e22i		−	0.563242i	−0.959526	−	0.281621i	$-0.909128\pi$
$23$		−	1.65655e22i		−	0.563242i	0.959526	−	0.281621i	$-0.0908720\pi$
$24$	2.93501e22			0.494452
$25$	5.09079e22	+	1.04694e23i	0.437296	+	0.899318i
$26$	−1.25700e23			−0.565295
$27$		−	4.48782e23i		−	1.08276i
$28$			2.41765e23i			0.320100i
$29$	9.17408e22			0.0680762			0.0340381	−	0.999421i	$-0.489163\pi$
$29$	9.17408e22			0.0680762			0.0340381	+	0.999421i	$0.489163\pi$
$30$	−5.17292e23	−	3.23670e23i	−0.219399	−	0.137278i
$31$	5.75654e24			1.42133			0.710663	−	0.703533i	$-0.248395\pi$
$31$	5.75654e24			1.42133			0.710663	+	0.703533i	$0.248395\pi$
$32$			5.42169e24i			0.792794i
$33$		−	1.26472e25i		−	1.11305i
$34$	8.15982e24			0.438812
$35$	5.59440e24	−	8.94100e24i	0.186479	−	0.298032i
$36$	1.09395e25			0.229091
$37$		−	9.32591e25i		−	1.24269i	−0.783537	−	0.621345i	$-0.786587\pi$
$37$		−	9.32591e25i		−	1.24269i	0.783537	−	0.621345i	$-0.213413\pi$
$38$		−	1.70724e25i		−	0.146509i
$39$	2.92410e26			1.63465
$40$	8.23522e25	−	1.31616e26i	0.303169	−	0.484527i
$41$	4.59334e26			1.12511			0.562555	−	0.826760i	$-0.309818\pi$
$41$	4.59334e26			1.12511			0.562555	+	0.826760i	$0.309818\pi$
$42$			5.52836e25i			0.0909877i
$43$		−	2.98860e26i		−	0.333610i	−0.985990	−	0.166805i	$-0.946655\pi$
$43$		−	2.98860e26i		−	0.333610i	0.985990	−	0.166805i	$-0.0533450\pi$
$44$	1.53356e27			1.17147
$45$	−4.04569e26	−	2.53139e26i	−0.213298	−	0.133461i
$46$	4.59317e26			0.168503
$47$		−	3.83658e27i		−	0.987029i	−0.869738	−	0.493514i	$-0.835712\pi$
$47$		−	3.83658e27i		−	0.987029i	0.869738	−	0.493514i	$-0.164288\pi$
$48$		−	3.51955e27i		−	0.639745i
$49$	6.77546e27			0.876402
$50$	−2.90290e27	+	1.41154e27i	−0.269046	+	0.130824i
$51$	−1.89818e28			−1.26891
$52$			3.54566e28i			1.72045i
$53$			1.34770e28i			0.477575i	0.971072	+	0.238788i	$0.0767500\pi$
$53$			1.34770e28i			0.477575i	−0.971072	+	0.238788i	$0.923250\pi$
$54$	1.24435e28			0.323926
$55$	−5.67145e28	−	3.54863e28i	−1.09071	−	0.682460i
$56$	−1.40659e28			−0.200940
$57$			3.97147e28i			0.423658i
$58$			2.54373e27i			0.0203661i
$59$	−1.39545e29			−0.842667			−0.421333	−	0.906906i	$-0.638438\pi$
$59$	−1.39545e29			−0.842667			−0.421333	+	0.906906i	$0.638438\pi$
$60$	−9.12987e28	+	1.45914e29i	−0.417800	+	0.667731i
$61$	−1.27289e29			−0.443454			−0.221727	−	0.975109i	$-0.571169\pi$
$61$	−1.27289e29			−0.443454			−0.221727	+	0.975109i	$0.571169\pi$
$62$			1.59614e29i			0.425213i
$63$			4.32367e28i			0.0884572i
$64$	3.18390e29			0.502331
$65$	8.20460e29	−	1.31126e30i	1.00227	−	1.60184i
$66$	3.50674e29			0.332988
$67$			1.55253e30i			1.15029i	0.818052	+	0.575144i	$0.195054\pi$
$67$			1.55253e30i			1.15029i	−0.818052	+	0.575144i	$0.804946\pi$
$68$		−	2.30166e30i		−	1.33550i
$69$	−1.06849e30			−0.487258
$70$	2.47910e29	+	1.55118e29i	0.0891614	+	0.0557884i
$71$	4.80212e30			1.36669			0.683346	−	0.730095i	$-0.260524\pi$
$71$	4.80212e30			1.36669			0.683346	+	0.730095i	$0.260524\pi$
$72$			6.36464e29i			0.143810i
$73$		−	2.54238e30i		−	0.457523i	−0.973483	−	0.228761i	$-0.926532\pi$
$73$		−	2.54238e30i		−	0.457523i	0.973483	−	0.228761i	$-0.0734676\pi$
$74$	2.58583e30			0.371771
$75$	6.75286e30	−	3.28360e30i	0.777996	−	0.378302i
$76$	−4.81566e30			−0.445894
$77$			6.06114e30i			0.452332i
$78$			8.10774e30i			0.489034i
$79$	−1.90983e31			−0.933573			−0.466787	−	0.884370i	$-0.654588\pi$
$79$	−1.90983e31			−0.933573			−0.466787	+	0.884370i	$0.654588\pi$
$80$	−1.57829e31	−	9.87536e30i	−0.626904	−	0.392255i
$81$	−2.11712e31			−0.685082
$82$			1.27361e31i			0.336595i
$83$		−	1.69264e31i		−	0.366249i	−0.983090	−	0.183125i	$-0.941379\pi$
$83$		−	1.69264e31i		−	0.366249i	0.983090	−	0.183125i	$-0.0586212\pi$
$84$	1.55940e31			0.276917
$85$	−5.32602e31	+	8.51208e31i	−0.778019	+	1.24344i
$86$	8.28660e30			0.0998049
$87$		−	5.91735e30i		−	0.0588924i
$88$			8.92228e31i			0.735380i
$89$	8.93087e31			0.610884			0.305442	−	0.952211i	$-0.401196\pi$
$89$	8.93087e31			0.610884			0.305442	+	0.952211i	$0.401196\pi$
$90$	7.01888e30	−	1.12176e31i	0.0399270	−	0.0638115i
$91$	−1.40136e32			−0.664305
$92$		−	1.29561e32i		−	0.512831i
$93$		−	3.71301e32i		−	1.22958i
$94$	1.06378e32			0.295286
$95$	1.78094e32	+	1.11434e32i	0.415155	+	0.259763i
$96$	3.49703e32			0.685842
$97$		−	6.99431e32i		−	1.15614i	−0.815987	−	0.578071i	$-0.803806\pi$
$97$		−	6.99431e32i		−	1.15614i	0.815987	−	0.578071i	$-0.196194\pi$
$98$			1.87865e32i			0.262190i
$99$	2.74259e32			0.323728
$100$	3.98157e32	+	8.18828e32i	0.398157	+	0.818828i
$101$	9.76429e32			0.828587			0.414293	−	0.910143i	$-0.364029\pi$
$101$	9.76429e32			0.828587			0.414293	+	0.910143i	$0.364029\pi$
$102$		−	5.26314e32i		−	0.379614i
$103$			1.55055e32i			0.0952076i	0.998866	+	0.0476038i	$0.0151585\pi$
$103$			1.55055e32i			0.0952076i	−0.998866	+	0.0476038i	$0.984842\pi$
$104$	−2.06287e33			−1.08000
$105$	−5.76701e32	−	3.60843e32i	−0.257827	−	0.161322i
$106$	−3.73682e32			−0.142875
$107$			4.85223e33i			1.58895i	0.607299	+	0.794473i	$0.292253\pi$
$107$			4.85223e33i			1.58895i	−0.607299	+	0.794473i	$0.707747\pi$
$108$		−	3.50998e33i		−	0.985854i
$109$	−1.75363e33			−0.423059			−0.211530	−	0.977372i	$-0.567845\pi$
$109$	−1.75363e33			−0.423059			−0.211530	+	0.977372i	$0.567845\pi$
$110$	9.83942e32	−	1.57254e33i	0.204169	−	0.326304i
$111$	−6.01528e33			−1.07505
$112$			1.68673e33i			0.259985i
$113$			3.25949e33i			0.433866i	0.976187	+	0.216933i	$0.0696053\pi$
$113$			3.25949e33i			0.433866i	−0.976187	+	0.216933i	$0.930395\pi$
$114$	−1.10118e33			−0.126744
$115$	−2.99802e33	+	4.79145e33i	−0.298758	+	0.477477i
$116$	7.17517e32			0.0619834
$117$			6.34098e33i			0.475433i
$118$		−	3.86921e33i		−	0.252098i
$119$	9.09695e33			0.515669
$120$	−8.48932e33	−	5.31178e33i	−0.419162	−	0.262270i
$121$	1.52218e34			0.655402
$122$		−	3.52938e33i		−	0.132667i
$123$		−	2.96274e34i		−	0.973328i
$124$	4.50227e34			1.29412
$125$	4.22280e33	−	3.94954e34i	0.106313	−	0.994333i
$126$	−1.19884e33			−0.0264635
$127$			1.49443e34i			0.289543i	0.989465	+	0.144771i	$0.0462447\pi$
$127$			1.49443e34i			0.289543i	−0.989465	+	0.144771i	$0.953755\pi$
$128$			5.54001e34i			0.943075i
$129$	−1.92767e34			−0.288604
$130$	3.63579e34	+	2.27492e34i	0.479218	+	0.299847i
$131$	4.63758e33			0.0538660			0.0269330	−	0.999637i	$-0.491426\pi$
$131$	4.63758e33			0.0538660			0.0269330	+	0.999637i	$0.491426\pi$
$132$		−	9.89157e34i		−	1.01343i
$133$		−	1.90331e34i		−	0.172170i
$134$	−4.30476e34			−0.344128
$135$	−8.12204e34	+	1.29807e35i	−0.574326	+	0.917891i
$136$	1.33911e35			0.838350
$137$		−	5.85558e34i		−	0.324848i	−0.986721	−	0.162424i	$-0.948069\pi$
$137$		−	5.85558e34i		−	0.324848i	0.986721	−	0.162424i	$-0.0519312\pi$
$138$		−	2.96263e34i		−	0.145771i
$139$	−3.91943e35			−1.71190			−0.855950	−	0.517059i	$-0.827027\pi$
$139$	−3.91943e35			−1.71190			−0.855950	+	0.517059i	$0.827027\pi$
$140$	4.37545e34	−	6.99288e34i	0.169789	−	0.271358i
$141$	−2.47462e35			−0.853874
$142$			1.33150e35i			0.408869i
$143$			8.88911e35i			2.43116i
$144$	7.63224e34			0.186068
$145$	−2.65354e34	−	1.66032e34i	−0.0577103	−	0.0361094i
$146$	7.04933e34			0.136876
$147$		−	4.37022e35i		−	0.758171i
$148$		−	7.29391e35i		−	1.13147i
$149$	5.37014e35			0.745440			0.372720	−	0.927944i	$-0.378425\pi$
$149$	5.37014e35			0.745440			0.372720	+	0.927944i	$0.378425\pi$
$150$	9.10454e34	+	1.87239e35i	0.113175	+	0.232750i
$151$	2.49511e35			0.277953			0.138976	−	0.990296i	$-0.455619\pi$
$151$	2.49511e35			0.277953			0.138976	+	0.990296i	$0.455619\pi$
$152$		−	2.80176e35i		−	0.279906i
$153$		−	4.11625e35i		−	0.369057i
$154$	−1.68059e35			−0.135323
$155$	−1.66504e36	−	1.04182e36i	−1.20490	−	0.753909i
$156$	2.28697e36			1.48835
$157$			2.08550e36i			1.22142i	0.791853	+	0.610712i	$0.209117\pi$
$157$			2.08550e36i			1.22142i	−0.791853	+	0.610712i	$0.790883\pi$
$158$		−	5.29546e35i		−	0.279294i
$159$	8.69278e35			0.413148
$160$	9.81217e35	−	1.56819e36i	0.420519	−	0.672076i
$161$	5.12068e35			0.198016
$162$		−	5.87021e35i		−	0.204954i
$163$		−	4.35976e35i		−	0.137520i	−0.997633	−	0.0687601i	$-0.978096\pi$
$163$		−	4.35976e35i		−	0.137520i	0.997633	−	0.0687601i	$-0.0219043\pi$
$164$	3.59251e36			1.02441
$165$	−2.28890e36	+	3.65813e36i	−0.590393	+	0.943569i
$166$	4.69325e35			0.109570
$167$			2.81153e36i			0.594459i	0.954806	+	0.297229i	$0.0960626\pi$
$167$			2.81153e36i			0.594459i	−0.954806	+	0.297229i	$0.903937\pi$
$168$			9.07262e35i			0.173832i
$169$	−1.47959e37			−2.57045
$170$	−2.36017e36	−	1.47676e36i	−0.371994	−	0.232757i
$171$	−8.61223e35			−0.123220
$172$		−	2.33743e36i		−	0.303751i
$173$		−	2.92048e36i		−	0.344900i	−0.985018	−	0.172450i	$-0.944832\pi$
$173$		−	2.92048e36i		−	0.344900i	0.985018	−	0.172450i	$-0.0551683\pi$
$174$	1.64072e35			0.0176187
$175$	−3.23628e36	+	1.57365e36i	−0.316169	+	0.153738i
$176$	1.06993e37			0.951469
$177$			9.00075e36i			0.728987i
$178$			2.47629e36i			0.182756i
$179$	−1.58216e37			−1.06457			−0.532286	−	0.846565i	$-0.678667\pi$
$179$	−1.58216e37			−1.06457			−0.532286	+	0.846565i	$0.678667\pi$
$180$	−3.16418e36	−	1.97983e36i	−0.194207	−	0.121516i
$181$	3.01773e37			1.69038			0.845190	−	0.534466i	$-0.179487\pi$
$181$	3.01773e37			1.69038			0.845190	+	0.534466i	$0.179487\pi$
$182$		−	3.88560e36i		−	0.198738i
$183$			8.21023e36i			0.383630i
$184$	7.53787e36			0.321925
$185$	−1.68780e37	+	2.69746e37i	−0.659155	+	1.05347i
$186$	1.02952e37			0.367850
$187$		−	5.77037e37i		−	1.88720i
$188$		−	3.00064e37i		−	0.898689i
$189$	1.38726e37			0.380661
$190$	−3.08976e36	+	4.93807e36i	−0.0777124	+	0.124200i
$191$	5.41896e37			1.24987			0.624936	−	0.780676i	$-0.285125\pi$
$191$	5.41896e37			1.24987			0.624936	+	0.780676i	$0.285125\pi$
$192$		−	2.05364e37i		−	0.434564i
$193$			1.59025e37i			0.308865i	0.988003	+	0.154433i	$0.0493549\pi$
$193$			1.59025e37i			0.308865i	−0.988003	+	0.154433i	$0.950645\pi$
$194$	1.93933e37			0.345879
$195$	−8.45775e37	−	5.29203e37i	−1.38575	−	0.867063i
$196$	5.29917e37			0.797964
$197$			1.05989e38i			1.46747i	0.679436	+	0.733734i	$0.262224\pi$
$197$			1.05989e38i			1.46747i	−0.679436	+	0.733734i	$0.737776\pi$
$198$			7.60446e36i			0.0968485i
$199$	−4.20262e37			−0.492543			−0.246271	−	0.969201i	$-0.579205\pi$
$199$	−4.20262e37			−0.492543			−0.246271	+	0.969201i	$0.579205\pi$
$200$	−4.76396e37	+	2.31649e37i	−0.514012	+	0.249940i
$201$	1.00140e38			0.995109
$202$			2.70738e37i			0.247886i
$203$			2.83587e36i			0.0239332i
$204$	−1.48459e38			−1.15534
$205$	−1.32859e38	−	8.31302e37i	−0.953791	−	0.596788i
$206$	−4.29926e36			−0.0284829
$207$		−	2.31704e37i		−	0.141717i
$208$			2.47372e38i			1.39735i
$209$	−1.20731e38			−0.630092
$210$	1.00052e37	−	1.59904e37i	0.0482623	−	0.0771331i
$211$	2.20364e38			0.982832			0.491416	−	0.870925i	$-0.336479\pi$
$211$	2.20364e38			0.982832			0.491416	+	0.870925i	$0.336479\pi$
$212$			1.05406e38i			0.434832i
$213$		−	3.09740e38i		−	1.18232i
$214$	−1.34539e38			−0.475360
$215$	−5.40877e37	+	8.64433e37i	−0.176955	+	0.282811i
$216$	2.04211e38			0.618861
$217$			1.77945e38i			0.499688i
$218$		−	4.86236e37i		−	0.126565i
$219$	−1.63985e38			−0.395801
$220$	−4.43572e38	−	2.77543e38i	−0.993092	−	0.621379i
$221$	1.33413e39			2.77158
$222$		−	1.66788e38i		−	0.321618i
$223$		−	6.67659e35i		−	0.00119543i	−1.00000		0.000597716i	$-0.999810\pi$
$223$		−	6.67659e35i		−	0.00119543i	1.00000		0.000597716i	$-0.000190259\pi$
$224$	−1.67594e38			−0.278719
$225$	7.12057e37	+	1.46438e38i	0.110028	+	0.226277i
$226$	−9.03770e37			−0.129798
$227$		−	1.16773e39i		−	1.55925i	−0.626246	−	0.779626i	$-0.715409\pi$
$227$		−	1.16773e39i		−	1.55925i	0.626246	−	0.779626i	$-0.284591\pi$
$228$			3.10614e38i			0.385741i
$229$	8.43095e38			0.974072			0.487036	−	0.873382i	$-0.338078\pi$
$229$	8.43095e38			0.974072			0.487036	+	0.873382i	$0.338078\pi$
$230$	−1.32854e38	−	8.31270e37i	−0.142845	−	0.0893785i
$231$	3.90948e38			0.391310
$232$			4.17453e37i			0.0389095i
$233$		−	1.88168e38i		−	0.163371i	−0.996658	−	0.0816853i	$-0.973970\pi$
$233$		−	1.88168e38i		−	0.163371i	0.996658	−	0.0816853i	$-0.0260302\pi$
$234$	−1.75818e38			−0.142234
$235$	−6.94344e38	+	1.10971e39i	−0.523546	+	0.836735i
$236$	−1.09140e39			−0.767247
$237$			1.23186e39i			0.807630i
$238$			2.52234e38i			0.154271i
$239$	−2.56527e38			−0.146409			−0.0732046	−	0.997317i	$-0.523323\pi$
$239$	−2.56527e38			−0.146409			−0.0732046	+	0.997317i	$0.523323\pi$
$240$	−6.36968e38	+	1.01801e39i	−0.339338	+	0.542332i
$241$	2.87265e38			0.142890			0.0714450	−	0.997445i	$-0.477239\pi$
$241$	2.87265e38			0.142890			0.0714450	+	0.997445i	$0.477239\pi$
$242$			4.22061e38i			0.196075i
$243$		−	1.12925e39i		−	0.490100i
$244$	−9.95543e38			−0.403764
$245$	−1.95976e39	−	1.22622e39i	−0.742953	−	0.464867i
$246$	8.21489e38			0.291187
$247$		−	2.79134e39i		−	0.925366i
$248$			2.61943e39i			0.812370i
$249$	−1.09177e39			−0.316841
$250$	1.09510e39	+	1.17087e38i	0.297471	+	0.0318052i
$251$	−2.84747e39			−0.724173			−0.362087	−	0.932144i	$-0.617936\pi$
$251$	−2.84747e39			−0.724173			−0.362087	+	0.932144i	$0.617936\pi$
$252$			3.38160e38i			0.0805403i
$253$		−	3.24814e39i		−	0.724680i
$254$	−4.14364e38			−0.0866216
$255$	5.49035e39	+	3.43532e39i	1.07569	+	0.673061i
$256$	1.19885e39			0.220194
$257$			9.94184e39i			1.71226i	0.516759	+	0.856131i	$0.327138\pi$
$257$			9.94184e39i			1.71226i	−0.516759	+	0.856131i	$0.672862\pi$
$258$		−	5.34492e38i		−	0.0863408i
$259$	2.88280e39			0.436886
$260$	6.41692e39	−	1.02556e40i	0.912571	−	1.45848i
$261$	1.28319e38			0.0171287
$262$			1.28588e38i			0.0161149i
$263$		−	1.00062e40i		−	1.17761i	−0.808277	−	0.588803i	$-0.799599\pi$
$263$		−	1.00062e40i		−	1.17761i	0.808277	−	0.588803i	$-0.200401\pi$
$264$	5.75494e39			0.636174
$265$	2.43907e39	−	3.89814e39i	0.253319	−	0.404856i
$266$	5.27737e38			0.0515075
$267$		−	5.76048e39i		−	0.528473i
$268$			1.21426e40i			1.04734i
$269$	1.26431e39			0.102551			0.0512756	−	0.998685i	$-0.483671\pi$
$269$	1.26431e39			0.102551			0.0512756	+	0.998685i	$0.483671\pi$
$270$	−3.59920e39	−	2.25203e39i	−0.274602	−	0.171819i
$271$	−2.61010e40			−1.87355			−0.936773	−	0.349937i	$-0.886203\pi$
$271$	−2.61010e40			−1.87355			−0.936773	+	0.349937i	$0.886203\pi$
$272$		−	1.60581e40i		−	1.08470i
$273$			9.03889e39i			0.574687i
$274$	1.62359e39			0.0971837
$275$	9.98197e39	+	2.05284e40i	0.562635	+	1.15708i
$276$	−8.35677e39			−0.443648
$277$			1.68059e40i			0.840516i	0.907405	+	0.420258i	$0.138060\pi$
$277$			1.68059e40i			0.840516i	−0.907405	+	0.420258i	$0.861940\pi$
$278$		−	1.08675e40i		−	0.512143i
$279$	8.05176e39			0.357620
$280$	4.06847e39	+	2.54565e39i	0.170343	+	0.106584i
$281$	−3.61653e40			−1.42770			−0.713851	−	0.700298i	$-0.753051\pi$
$281$	−3.61653e40			−1.42770			−0.713851	+	0.700298i	$0.753051\pi$
$282$		−	6.86147e39i		−	0.255451i
$283$			2.73592e40i			0.960787i	0.877053	+	0.480394i	$0.159506\pi$
$283$			2.73592e40i			0.960787i	−0.877053	+	0.480394i	$0.840494\pi$
$284$	3.75580e40			1.24437
$285$	7.18756e39	−	1.14872e40i	0.224720	−	0.359148i
$286$	−2.46471e40			−0.727322
$287$			1.41988e40i			0.395549i
$288$			7.58340e39i			0.199475i
$289$	−4.63509e40			−1.15145
$290$	4.60363e38	−	7.35756e38i	0.0108027	−	0.0172650i
$291$	−4.51138e40			−1.00017
$292$		−	1.98843e40i		−	0.416574i
$293$		−	1.89832e40i		−	0.375883i	−0.982180	−	0.187942i	$-0.939818\pi$
$293$		−	1.89832e40i		−	0.375883i	0.982180	−	0.187942i	$-0.0601815\pi$
$294$	1.21175e40			0.226820
$295$	4.03624e40	+	2.52548e40i	0.714355	+	0.446973i
$296$	4.24362e40			0.710269
$297$		−	8.79967e40i		−	1.39311i
$298$			1.48900e40i			0.223011i
$299$	7.50985e40			1.06428
$300$	5.28150e40	−	2.56814e40i	0.708365	−	0.344444i
$301$	9.23829e39			0.117285
$302$			6.91829e39i			0.0831542i
$303$		−	6.29804e40i		−	0.716807i
$304$	−3.35977e40			−0.362155
$305$	3.68174e40	+	2.30367e40i	0.375929	+	0.235219i
$306$	1.14133e40			0.110409
$307$			1.00795e41i			0.923964i	0.886889	+	0.461982i	$0.152862\pi$
$307$			1.00795e41i			0.923964i	−0.886889	+	0.461982i	$0.847138\pi$
$308$			4.74050e40i			0.411848i
$309$	1.00012e40			0.0823636
$310$	2.88868e40	−	4.61671e40i	0.225544	−	0.360466i
$311$	−9.05837e40			−0.670662			−0.335331	−	0.942100i	$-0.608848\pi$
$311$	−9.05837e40			−0.670662			−0.335331	+	0.942100i	$0.608848\pi$
$312$			1.33057e41i			0.934299i
$313$		−	2.27354e41i		−	1.51433i	−0.653224	−	0.757165i	$-0.726584\pi$
$313$		−	2.27354e41i		−	1.51433i	0.653224	−	0.757165i	$-0.273416\pi$
$314$	−5.78255e40			−0.365410
$315$	7.82497e39	−	1.25059e40i	0.0469201	−	0.0749879i
$316$	−1.49371e41			−0.850018
$317$			2.78295e40i			0.150324i	0.997171	+	0.0751620i	$0.0239474\pi$
$317$			2.78295e40i			0.150324i	−0.997171	+	0.0751620i	$0.976053\pi$
$318$			2.41028e40i			0.123600i
$319$	1.79884e40			0.0875885
$320$	−9.20921e40	−	5.76222e40i	−0.425841	−	0.266450i
$321$	3.12973e41			1.37459
$322$			1.41983e40i			0.0592398i
$323$			1.81200e41i			0.718319i
$324$	−1.65583e41			−0.623767
$325$	−4.74625e41	+	2.30788e41i	−1.69932	+	0.826298i
$326$	1.20884e40			0.0411415
$327$			1.13111e41i			0.365987i
$328$			2.09013e41i			0.643065i
$329$	1.18595e41			0.347005
$330$	−1.01430e41	−	6.34650e40i	−0.282285	−	0.176626i
$331$	−6.40534e40			−0.169582			−0.0847911	−	0.996399i	$-0.527022\pi$
$331$	−6.40534e40			−0.169582			−0.0847911	+	0.996399i	$0.527022\pi$
$332$		−	1.32384e41i		−	0.333470i
$333$		−	1.30443e41i		−	0.312673i
$334$	−7.79564e40			−0.177842
$335$	2.80977e41	−	4.49059e41i	0.610143	−	0.975135i
$336$	1.08795e41			0.224912
$337$		−	3.19783e41i		−	0.629452i	−0.949183	−	0.314726i	$-0.898087\pi$
$337$		−	3.19783e41i		−	0.629452i	0.949183	−	0.314726i	$-0.101913\pi$
$338$		−	4.10250e41i		−	0.768994i
$339$	2.10240e41			0.375335
$340$	−4.16555e41	+	6.65741e41i	−0.708386	+	1.13215i
$341$	1.12874e42			1.82871
$342$		−	2.38794e40i		−	0.0368632i
$343$			4.48419e41i			0.659677i
$344$	1.35992e41			0.190677
$345$	3.09052e41	+	1.93374e41i	0.413063	+	0.258454i
$346$	8.09771e40			0.103183
$347$		−	1.48796e42i		−	1.80782i	−0.427721	−	0.903911i	$-0.640683\pi$
$347$		−	1.48796e42i		−	1.80782i	0.427721	−	0.903911i	$-0.359317\pi$
$348$		−	4.62804e40i		−	0.0536215i
$349$	−1.19302e42			−1.31834			−0.659172	−	0.751992i	$-0.729093\pi$
$349$	−1.19302e42			−1.31834			−0.659172	+	0.751992i	$0.729093\pi$
$350$	−4.36332e40	−	8.97335e40i	−0.0459932	−	0.0945871i
$351$	2.03452e42			2.04595
$352$			1.06308e42i			1.02003i
$353$			1.00990e42i			0.924689i	0.886701	+	0.462344i	$0.152992\pi$
$353$			1.00990e42i			0.924689i	−0.886701	+	0.462344i	$0.847008\pi$
$354$	−2.49567e41			−0.218089
$355$	−1.38898e42	−	8.69087e41i	−1.15859	−	0.724929i
$356$	6.98495e41			0.556209
$357$		−	5.86760e41i		−	0.446103i
$358$		−	4.38690e41i		−	0.318484i
$359$	−7.30004e41			−0.506136			−0.253068	−	0.967449i	$-0.581440\pi$
$359$	−7.30004e41			−0.506136			−0.253068	+	0.967449i	$0.581440\pi$
$360$	1.15187e41	−	1.84093e41i	0.0762804	−	0.121912i
$361$	−1.20165e42			−0.760170
$362$			8.36737e41i			0.505705i
$363$		−	9.81819e41i		−	0.566986i
$364$	−1.09602e42			−0.604849
$365$	−4.60119e41	+	7.35365e41i	−0.242682	+	0.387856i
$366$	−2.27648e41			−0.114769
$367$			3.74858e42i			1.80666i	0.428947	+	0.903330i	$0.358885\pi$
$367$			3.74858e42i			1.80666i	−0.428947	+	0.903330i	$0.641115\pi$
$368$		−	9.03913e41i		−	0.416522i
$369$	6.42477e41			0.283089
$370$	−7.47932e41	−	4.67982e41i	−0.315162	−	0.197197i
$371$	−4.16598e41			−0.167899
$372$		−	2.90399e42i		−	1.11953i
$373$			4.86523e42i			1.79435i	0.441673	+	0.897176i	$0.354385\pi$
$373$			4.86523e42i			1.79435i	−0.441673	+	0.897176i	$0.645615\pi$
$374$	1.59997e42			0.564586
$375$	−2.54749e42	−	2.72374e41i	−0.860193	−	0.0919707i
$376$	1.74578e42			0.564144
$377$			4.15901e41i			0.128634i
$378$			3.84651e41i			0.113881i
$379$	−1.92428e42			−0.545409			−0.272704	−	0.962098i	$-0.587918\pi$
$379$	−1.92428e42			−0.545409			−0.272704	+	0.962098i	$0.587918\pi$
$380$	1.39290e42	+	8.71537e41i	0.377998	+	0.236514i
$381$	9.63916e41			0.250482
$382$			1.50253e42i			0.373920i
$383$		−	7.09477e42i		−	1.69106i	−0.533929	−	0.845529i	$-0.679285\pi$
$383$		−	7.09477e42i		−	1.69106i	0.533929	−	0.845529i	$-0.320715\pi$
$384$	3.57335e42			0.815849
$385$	1.09694e42	−	1.75314e42i	0.239929	−	0.383456i
$386$	−4.40933e41			−0.0924021
$387$		−	4.18020e41i		−	0.0839395i
$388$		−	5.47034e42i		−	1.05267i
$389$	5.42411e42			1.00037			0.500184	−	0.865919i	$-0.333266\pi$
$389$	5.42411e42			1.00037			0.500184	+	0.865919i	$0.333266\pi$
$390$	1.46734e42	−	2.34511e42i	0.259396	−	0.414569i
$391$	−4.87502e42			−0.826152
$392$			3.08307e42i			0.500914i
$393$		−	2.99127e41i		−	0.0465993i
$394$	−2.93880e42			−0.439018
$395$	5.52406e42	+	3.45641e42i	0.791419	+	0.495192i
$396$	2.14501e42			0.294754
$397$		−	8.06392e42i		−	1.06293i	−0.847082	−	0.531463i	$-0.821643\pi$
$397$		−	8.06392e42i		−	1.06293i	0.847082	−	0.531463i	$-0.178357\pi$
$398$		−	1.16527e42i		−	0.147352i
$399$	−1.22765e42			−0.148943
$400$	2.77785e42	+	5.71276e42i	0.323384	+	0.665053i
$401$	−9.36366e42			−1.04608			−0.523038	−	0.852309i	$-0.675202\pi$
$401$	−9.36366e42			−1.04608			−0.523038	+	0.852309i	$0.675202\pi$
$402$			2.77660e42i			0.297703i
$403$			2.60969e43i			2.68569i
$404$	7.63678e42			0.754428
$405$	6.12363e42	+	3.83156e42i	0.580766	+	0.363386i
$406$	−7.86310e40			−0.00716002
$407$		−	1.82861e43i		−	1.59887i
$408$		−	8.63738e42i		−	0.725253i
$409$	−2.18606e43			−1.76290			−0.881448	−	0.472281i	$-0.843431\pi$
$409$	−2.18606e43			−1.76290			−0.881448	+	0.472281i	$0.843431\pi$
$410$	2.30498e42	−	3.68383e42i	0.178539	−	0.285342i
$411$	−3.77689e42			−0.281025
$412$			1.21270e42i			0.0866864i
$413$		−	4.31357e42i		−	0.296252i
$414$	6.42453e41			0.0423971
$415$	−3.06334e42	+	4.89586e42i	−0.194268	+	0.310481i
$416$	−2.45789e43			−1.49804
$417$			2.52806e43i			1.48096i
$418$		−	3.34754e42i		−	0.188502i
$419$	1.61908e43			0.876469			0.438235	−	0.898861i	$-0.355604\pi$
$419$	1.61908e43			0.876469			0.438235	+	0.898861i	$0.355604\pi$
$420$	−4.51046e42	−	2.82220e42i	−0.234751	−	0.146884i
$421$	−2.91687e43			−1.45970			−0.729849	−	0.683608i	$-0.760410\pi$
$421$	−2.91687e43			−1.45970			−0.729849	+	0.683608i	$0.760410\pi$
$422$			6.11009e42i			0.294031i
$423$		−	5.36629e42i		−	0.248346i
$424$	−6.13252e42			−0.272962
$425$	3.08103e43	−	1.49816e43i	1.31910	−	0.641417i
$426$	8.58828e42			0.353710
$427$		−	3.93472e42i		−	0.155903i
$428$			3.79499e43i			1.44673i
$429$	5.73354e43			2.10319
$430$	−2.39684e42	−	1.49971e42i	−0.0846077	−	0.0529392i
$431$	−1.93794e42			−0.0658362			−0.0329181	−	0.999458i	$-0.510480\pi$
$431$	−1.93794e42			−0.0658362			−0.0329181	+	0.999458i	$0.510480\pi$
$432$		−	2.44883e43i		−	0.800711i
$433$		−	4.34077e43i		−	1.36621i	−0.730322	−	0.683103i	$-0.760630\pi$
$433$		−	4.34077e43i		−	1.36621i	0.730322	−	0.683103i	$-0.239370\pi$
$434$	−4.93393e42			−0.149490
$435$	−1.07092e42	+	1.71155e42i	−0.0312381	+	0.0499249i
$436$	−1.37154e43			−0.385195
$437$			1.01998e43i			0.275833i
$438$		−	4.54687e42i		−	0.118410i
$439$	4.67712e43			1.17304			0.586522	−	0.809934i	$-0.300497\pi$
$439$	4.67712e43			1.17304			0.586522	+	0.809934i	$0.300497\pi$
$440$	1.61475e43	−	2.58071e43i	0.390065	−	0.623405i
$441$	9.47694e42			0.220511
$442$			3.69920e43i			0.829163i
$443$			1.13003e43i			0.244022i	0.992529	+	0.122011i	$0.0389343\pi$
$443$			1.13003e43i			0.244022i	−0.992529	+	0.122011i	$0.961066\pi$
$444$	−4.70463e43			−0.978828
$445$	−2.58319e43	−	1.61631e43i	−0.517865	−	0.324029i
$446$	1.85124e40			0.000357633
$447$		−	3.46378e43i		−	0.644876i
$448$			9.84198e42i			0.176602i
$449$	−4.90070e43			−0.847605			−0.423802	−	0.905755i	$-0.639305\pi$
$449$	−4.90070e43			−0.847605			−0.423802	+	0.905755i	$0.639305\pi$
$450$	−4.06032e42	+	1.97434e42i	−0.0676946	+	0.0329167i
$451$	9.00658e43			1.44759
$452$			2.54929e43i			0.395034i
$453$		−	1.60937e43i		−	0.240456i
$454$	3.23781e43			0.466476
$455$	4.05334e43	+	2.53618e43i	0.563152	+	0.352365i
$456$	−1.80716e43			−0.242145
$457$		−	1.56154e43i		−	0.201807i	−0.994896	−	0.100904i	$-0.967827\pi$
$457$		−	1.56154e43i		−	0.201807i	0.994896	−	0.100904i	$-0.0321734\pi$
$458$			2.33768e43i			0.291410i
$459$	−1.32071e44			−1.58817
$460$	−2.34479e43	+	3.74746e43i	−0.272019	+	0.434743i
$461$	−8.98487e43			−1.00565			−0.502824	−	0.864389i	$-0.667706\pi$
$461$	−8.98487e43			−1.00565			−0.502824	+	0.864389i	$0.667706\pi$
$462$			1.08399e43i			0.117067i
$463$		−	3.43299e42i		−	0.0357755i	−0.999840	−	0.0178878i	$-0.994306\pi$
$463$		−	3.43299e42i		−	0.0357755i	0.999840	−	0.0178878i	$-0.00569416\pi$
$464$	5.00594e42			0.0503429
$465$	−6.71980e43	+	1.07396e44i	−0.652203	+	1.04236i
$466$	5.21741e42			0.0488750
$467$		−	1.84417e43i		−	0.166752i	−0.996518	−	0.0833760i	$-0.973430\pi$
$467$		−	1.84417e43i		−	0.166752i	0.996518	−	0.0833760i	$-0.0265703\pi$
$468$			4.95936e43i			0.432882i
$469$	−4.79915e43			−0.404401
$470$	−3.07692e43	−	1.92523e43i	−0.250323	−	0.156628i
$471$	1.34517e44			1.05665
$472$		−	6.34978e43i		−	0.481633i
$473$		−	5.86002e43i		−	0.429230i
$474$	−3.41561e43			−0.241616
$475$	−3.13452e43	−	6.44629e43i	−0.214154	−	0.440418i
$476$	7.11484e43			0.469516
$477$			1.88505e43i			0.120163i
$478$		−	7.11282e42i		−	0.0438007i
$479$	9.81532e43			0.583941			0.291970	−	0.956427i	$-0.405689\pi$
$479$	9.81532e43			0.583941			0.291970	+	0.956427i	$0.405689\pi$
$480$	−1.01149e44	−	6.32892e43i	−0.581410	−	0.363789i
$481$	4.22784e44			2.34814
$482$			7.96510e42i			0.0427479i
$483$		−	3.30287e43i		−	0.171303i
$484$	1.19052e44			0.596743
$485$	−1.26583e44	+	2.02306e44i	−0.613248	+	0.980097i
$486$	3.13110e43			0.146622
$487$		−	1.63587e43i		−	0.0740494i	−0.999314	−	0.0370247i	$-0.988212\pi$
$487$		−	1.63587e43i		−	0.0740494i	0.999314	−	0.0370247i	$-0.0117880\pi$
$488$		−	5.79209e43i		−	0.253459i
$489$	−2.81208e43			−0.118968
$490$	3.39999e43	−	5.43388e43i	0.139073	−	0.222267i
$491$	−2.99512e44			−1.18459			−0.592297	−	0.805719i	$-0.701779\pi$
$491$	−2.99512e44			−1.18459			−0.592297	+	0.805719i	$0.701779\pi$
$492$		−	2.31720e44i		−	0.886214i
$493$		−	2.69982e43i		−	0.0998529i
$494$	7.73965e43			0.276839
$495$	−7.93274e43	−	4.96353e43i	−0.274434	−	0.171714i
$496$	3.14112e44			1.05108
$497$			1.48442e44i			0.480481i
$498$		−	3.02718e43i		−	0.0947882i
$499$	−8.53560e43			−0.258568			−0.129284	−	0.991608i	$-0.541268\pi$
$499$	−8.53560e43			−0.258568			−0.129284	+	0.991608i	$0.541268\pi$
$500$	3.30271e43	−	3.08899e44i	0.0967977	−	0.905339i
$501$	1.81346e44			0.514263
$502$		−	7.89527e43i		−	0.216648i
$503$			1.06922e43i			0.0283918i	0.999899	+	0.0141959i	$0.00451885\pi$
$503$			1.06922e43i			0.0283918i	−0.999899	+	0.0141959i	$0.995481\pi$
$504$	−1.96742e43			−0.0505584
$505$	−2.82425e44	−	1.76714e44i	−0.702419	−	0.439504i
$506$	9.00623e43			0.216800
$507$			9.54345e44i			2.22369i
$508$			1.16881e44i			0.263629i
$509$	−5.61788e44			−1.22667			−0.613336	−	0.789822i	$-0.710173\pi$
$509$	−5.61788e44			−1.22667			−0.613336	+	0.789822i	$0.710173\pi$
$510$	−9.52523e43	+	1.52233e44i	−0.201357	+	0.321811i
$511$	7.85892e43			0.160849
$512$			5.09124e44i			1.00895i
$513$			2.76326e44i			0.530255i
$514$	−2.75661e44			−0.512252
$515$	2.80618e43	−	4.48486e43i	0.0505006	−	0.0807104i
$516$	−1.50766e44			−0.262774
$517$		−	7.52273e44i		−	1.26994i
$518$			7.99323e43i			0.130702i
$519$	−1.88373e44			−0.298371
$520$	5.96671e44	+	3.73338e44i	0.915545	+	0.572858i
$521$	−9.13138e44			−1.35742			−0.678709	−	0.734407i	$-0.737460\pi$
$521$	−9.13138e44			−1.35742			−0.678709	+	0.734407i	$0.737460\pi$
$522$			3.55795e42i			0.00512432i
$523$		−	2.09069e44i		−	0.291751i	−0.989303	−	0.145876i	$-0.953400\pi$
$523$		−	2.09069e44i		−	0.291751i	0.989303	−	0.145876i	$-0.0465999\pi$
$524$	3.62711e43			0.0490450
$525$	1.01502e44	+	2.08743e44i	0.132998	+	0.273516i
$526$	2.77446e44			0.352300
$527$		−	1.69408e45i		−	2.08477i
$528$		−	6.90110e44i		−	0.823112i
$529$	5.90590e44			0.682759
$530$	1.08085e44	+	6.76289e43i	0.121119	+	0.0757845i
$531$	−1.95184e44			−0.212023
$532$		−	1.48860e44i		−	0.156761i
$533$			2.08236e45i			2.12597i
$534$	1.59723e44			0.158101
$535$	8.78156e44	−	1.40348e45i	0.842819	−	1.34700i
$536$	−7.06457e44			−0.657456
$537$			1.02050e45i			0.920956i
$538$			3.50559e43i			0.0306799i
$539$	1.32853e45			1.12760
$540$	−6.35236e44	+	1.01524e45i	−0.522923	+	0.835739i
$541$	4.44639e44			0.355020			0.177510	−	0.984119i	$-0.443196\pi$
$541$	4.44639e44			0.355020			0.177510	+	0.984119i	$0.443196\pi$
$542$		−	7.23712e44i		−	0.560503i
$543$		−	1.94646e45i		−	1.46234i
$544$	1.59554e45			1.16285
$545$	5.07226e44	+	3.17372e44i	0.358641	+	0.224402i
$546$	−2.50624e44			−0.171927
$547$			8.21042e44i			0.546480i	0.961946	+	0.273240i	$0.0880954\pi$
$547$			8.21042e44i			0.546480i	−0.961946	+	0.273240i	$0.911905\pi$
$548$		−	4.57972e44i		−	0.295774i
$549$	−1.78041e44			−0.111577
$550$	−5.69197e44	+	2.76774e44i	−0.346161	+	0.168322i
$551$	−5.64870e43			−0.0333386
$552$		−	4.86198e44i		−	0.278496i
$553$		−	5.90362e44i		−	0.328212i
$554$	−4.65983e44			−0.251454
$555$	1.73988e45	+	1.08864e45i	0.911349	+	0.570232i
$556$	−3.06543e45			−1.55868
$557$			1.43178e44i			0.0706749i	0.999375	+	0.0353374i	$0.0112506\pi$
$557$			1.43178e44i			0.0706749i	−0.999375	+	0.0353374i	$0.988749\pi$
$558$			2.23254e44i			0.106988i
$559$	1.35486e45			0.630377
$560$	3.05264e44	−	4.87876e44i	0.137903	−	0.220397i
$561$	−3.72193e45			−1.63260
$562$		−	1.00277e45i		−	0.427121i
$563$			1.43126e45i			0.592010i	0.955186	+	0.296005i	$0.0956545\pi$
$563$			1.43126e45i			0.592010i	−0.955186	+	0.296005i	$0.904346\pi$
$564$	−1.93544e45			−0.777452
$565$	5.89902e44	−	9.42785e44i	0.230134	−	0.367801i
$566$	−7.58598e44			−0.287436
$567$		−	6.54439e44i		−	0.240851i
$568$			2.18513e45i			0.781143i
$569$	−1.75762e45			−0.610342			−0.305171	−	0.952298i	$-0.598714\pi$
$569$	−1.75762e45			−0.610342			−0.305171	+	0.952298i	$0.598714\pi$
$570$	3.18509e44	+	1.99292e44i	0.107445	+	0.0672286i
$571$	2.78038e43			0.00911189			0.00455595	−	0.999990i	$-0.498550\pi$
$571$	2.78038e43			0.00911189			0.00455595	+	0.999990i	$0.498550\pi$
$572$			6.95229e45i			2.21357i
$573$		−	3.49527e45i		−	1.08126i
$574$	−3.93695e44			−0.118335
$575$	1.73431e45	−	8.43314e44i	0.506533	−	0.246303i
$576$	4.45337e44			0.126391
$577$			3.59566e45i			0.991694i	0.868410	+	0.495847i	$0.165142\pi$
$577$			3.59566e45i			0.991694i	−0.868410	+	0.495847i	$0.834858\pi$
$578$		−	1.28519e45i		−	0.344474i
$579$	1.02572e45			0.267198
$580$	−2.07537e44	−	1.29856e44i	−0.0525452	−	0.0328776i
$581$	5.23225e44			0.128760
$582$		−	1.25089e45i		−	0.299218i
$583$			2.64256e45i			0.614460i
$584$	1.15687e45			0.261501
$585$	1.14759e45	−	1.83408e45i	0.252182	−	0.403040i
$586$	5.26352e44			0.112452
$587$		−	6.08351e45i		−	1.26365i	−0.775113	−	0.631823i	$-0.782307\pi$
$587$		−	6.08351e45i		−	1.26365i	0.775113	−	0.631823i	$-0.217693\pi$
$588$		−	3.41801e45i		−	0.690315i
$589$	−3.54444e45			−0.696058
$590$	−7.00249e44	+	1.11914e45i	−0.133719	+	0.213711i
$591$	6.83638e45			1.26950
$592$		−	5.08878e45i		−	0.918979i
$593$		−	2.13640e44i		−	0.0375215i	−0.999824	−	0.0187607i	$-0.994028\pi$
$593$		−	2.13640e44i		−	0.0375215i	0.999824	−	0.0187607i	$-0.00597208\pi$
$594$	2.43991e45			0.416771
$595$	−2.63123e45	−	1.64636e45i	−0.437148	−	0.273524i
$596$	4.20006e45			0.678722
$597$			2.71072e45i			0.426096i
$598$			2.08228e45i			0.318398i
$599$	5.45715e45			0.811751			0.405876	−	0.913928i	$-0.366967\pi$
$599$	5.45715e45			0.811751			0.405876	+	0.913928i	$0.366967\pi$
$600$	1.49415e45	+	3.07279e45i	0.216222	+	0.444669i
$601$	−8.95801e45			−1.26120			−0.630598	−	0.776110i	$-0.717190\pi$
$601$	−8.95801e45			−1.26120			−0.630598	+	0.776110i	$0.717190\pi$
$602$			2.56153e44i			0.0350879i
$603$			2.17155e45i			0.289424i
$604$	1.95146e45			0.253076
$605$	−4.40281e45	−	2.75484e45i	−0.555605	−	0.347643i
$606$	1.74628e45			0.214445
$607$		−	1.83041e45i		−	0.218744i	−0.994001	−	0.109372i	$-0.965116\pi$
$607$		−	1.83041e45i		−	0.218744i	0.994001	−	0.109372i	$-0.0348839\pi$
$608$		−	3.33827e45i		−	0.388251i
$609$	1.82915e44			0.0207045
$610$	−6.38747e44	+	1.02085e45i	−0.0703698	+	0.112466i
$611$	1.73929e46			1.86505
$612$		−	3.21937e45i		−	0.336026i
$613$			9.17673e45i			0.932374i	0.884686	+	0.466187i	$0.154373\pi$
$613$			9.17673e45i			0.932374i	−0.884686	+	0.466187i	$0.845627\pi$
$614$	−2.79477e45			−0.276419
$615$	−5.36196e45	+	8.56952e45i	−0.516279	+	0.825120i
$616$	−2.75803e45			−0.258534
$617$		−	4.72501e45i		−	0.431218i	−0.976480	−	0.215609i	$-0.930826\pi$
$617$		−	4.72501e45i		−	0.431218i	0.976480	−	0.215609i	$-0.0691737\pi$
$618$			2.77306e44i			0.0246405i
$619$	−1.89434e46			−1.63894			−0.819469	−	0.573124i	$-0.805731\pi$
$619$	−1.89434e46			−1.63894			−0.819469	+	0.573124i	$0.805731\pi$
$620$	−1.30225e46	−	8.14819e45i	−1.09706	−	0.686433i
$621$	−7.43428e45			−0.609857
$622$		−	2.51164e45i		−	0.200640i
$623$			2.76069e45i			0.214765i
$624$	1.59557e46			1.20884
$625$	−8.36930e45	+	1.06595e46i	−0.617545	+	0.786536i
$626$	6.30391e45			0.453037
$627$			7.78721e45i			0.545089i
$628$			1.63110e46i			1.11211i
$629$	−2.74450e46			−1.82275
$630$	3.46756e44	+	2.16966e44i	0.0224339	+	0.0140369i
$631$	1.47344e46			0.928639			0.464319	−	0.885668i	$-0.346299\pi$
$631$	1.47344e46			0.928639			0.464319	+	0.885668i	$0.346299\pi$
$632$		−	8.69041e45i		−	0.533591i
$633$		−	1.42136e46i		−	0.850244i
$634$	−7.71639e44			−0.0449719
$635$	2.70461e45	−	4.32252e45i	0.153581	−	0.245455i
$636$	6.79873e45			0.376171
$637$			3.07161e46i			1.65602i
$638$			4.98772e44i			0.0262036i
$639$	6.71680e45			0.343873
$640$	1.00263e46	−	1.60241e46i	0.500232	−	0.799474i
$641$	1.80612e46			0.878189			0.439095	−	0.898441i	$-0.355299\pi$
$641$	1.80612e46			0.878189			0.439095	+	0.898441i	$0.355299\pi$
$642$			8.67790e45i			0.411232i
$643$		−	3.87997e46i		−	1.79204i	−0.444013	−	0.896020i	$-0.646446\pi$
$643$		−	3.87997e46i		−	1.79204i	0.444013	−	0.896020i	$-0.353554\pi$
$644$	4.00495e45			0.180293
$645$	5.57566e45	+	3.48870e45i	0.244659	+	0.153083i
$646$	−5.02420e45			−0.214897
$647$		−	1.26941e46i		−	0.529277i	−0.964348	−	0.264638i	$-0.914747\pi$
$647$		−	1.26941e46i		−	0.529277i	0.964348	−	0.264638i	$-0.0852526\pi$
$648$		−	9.63364e45i		−	0.391564i
$649$	−2.73618e46			−1.08420
$650$	−6.39912e45	−	1.31601e46i	−0.247201	−	0.508380i
$651$	1.14776e46			0.432278
$652$		−	3.40982e45i		−	0.125212i
$653$			3.71297e46i			1.32940i	0.747112	+	0.664698i	$0.231440\pi$
$653$			3.71297e46i			1.32940i	−0.747112	+	0.664698i	$0.768560\pi$
$654$	−3.13626e45			−0.109491
$655$	−1.34139e45	−	8.39308e44i	−0.0456639	−	0.0285720i
$656$	2.50641e46			0.832028
$657$		−	3.55606e45i		−	0.115117i
$658$			3.28833e45i			0.103812i
$659$	4.60623e46			1.41820			0.709098	−	0.705110i	$-0.249102\pi$
$659$	4.60623e46			1.41820			0.709098	+	0.705110i	$0.249102\pi$
$660$	−1.79017e46	+	2.86107e46i	−0.537552	+	0.859119i
$661$	3.33859e45			0.0977775			0.0488888	−	0.998804i	$-0.484432\pi$
$661$	3.33859e45			0.0977775			0.0488888	+	0.998804i	$0.484432\pi$
$662$		−	1.77603e45i		−	0.0507333i
$663$		−	8.60526e46i		−	2.39768i
$664$	7.70212e45			0.209333
$665$	−3.44461e45	+	5.50519e45i	−0.0913235	+	0.145954i
$666$	3.61683e45			0.0935414
$667$		−	1.51973e45i		−	0.0383434i
$668$			2.19894e46i			0.541254i
$669$	−4.30645e43			−0.00103416
$670$	1.24512e46	+	7.79075e45i	0.291728	+	0.182534i
$671$	−2.49587e46			−0.570558
$672$			1.08099e46i			0.241118i
$673$			8.45139e46i			1.83941i	0.392606	+	0.919707i	$0.371574\pi$
$673$			8.45139e46i			1.83941i	−0.392606	+	0.919707i	$0.628426\pi$
$674$	8.86674e45			0.188311
$675$	4.69849e46	−	2.28465e46i	0.973747	−	0.473487i
$676$	−1.15720e47			−2.34040
$677$			1.49073e46i			0.294230i	0.989119	+	0.147115i	$0.0469987\pi$
$677$			1.49073e46i			0.294230i	−0.989119	+	0.147115i	$0.953001\pi$
$678$			5.82938e45i			0.112288i
$679$	2.16206e46			0.406459
$680$	−3.87329e46	−	2.42353e46i	−0.710695	−	0.444683i
$681$	−7.53195e46			−1.34890
$682$			3.12969e46i			0.547090i
$683$			2.90497e45i			0.0495678i	0.999693	+	0.0247839i	$0.00788977\pi$
$683$			2.90497e45i			0.0495678i	−0.999693	+	0.0247839i	$0.992110\pi$
$684$	−6.73574e45			−0.112191
$685$	−1.05974e46	+	1.69369e46i	−0.172308	+	0.275384i
$686$	−1.24335e46			−0.197353
$687$		−	5.43803e46i		−	0.842665i
$688$		−	1.63076e46i		−	0.246707i
$689$	−6.10971e46			−0.902410
$690$	−5.36176e45	+	8.56919e45i	−0.0773209	+	0.123575i
$691$	3.48577e46			0.490807			0.245403	−	0.969421i	$-0.421080\pi$
$691$	3.48577e46			0.490807			0.245403	+	0.969421i	$0.421080\pi$
$692$		−	2.28414e46i		−	0.314031i
$693$			8.47781e45i			0.113811i
$694$	4.12572e46			0.540840
$695$	1.13367e47	+	7.09337e46i	1.45123	+	0.908037i
$696$	2.69260e45			0.0336604
$697$		−	1.35176e47i		−	1.65029i
$698$		−	3.30793e46i		−	0.394404i
$699$	−1.21370e46			−0.141331
$700$	−2.53114e46	+	1.23077e46i	−0.287871	+	0.139978i
$701$	1.80849e46			0.200895			0.100447	−	0.994942i	$-0.467973\pi$
$701$	1.80849e46			0.200895			0.100447	+	0.994942i	$0.467973\pi$
$702$			5.64118e46i			0.612080i
$703$			5.74219e46i			0.608576i
$704$	6.24296e46			0.646311
$705$	7.15768e46	+	4.47857e46i	0.723856	+	0.452917i
$706$	−2.80018e46			−0.276636
$707$			3.01831e46i			0.291302i
$708$			7.03960e46i			0.663742i
$709$	1.69160e46			0.155824			0.0779121	−	0.996960i	$-0.475175\pi$
$709$	1.69160e46			0.155824			0.0779121	+	0.996960i	$0.475175\pi$
$710$	2.40975e46	−	3.85127e46i	0.216875	−	0.346611i
$711$	−2.67131e46			−0.234896
$712$			4.06386e46i			0.349155i
$713$		−	9.53599e46i		−	0.800550i
$714$	1.62693e46			0.133459
$715$	1.60875e47	−	2.57111e47i	1.28955	−	2.06097i
$716$	−1.23743e47			−0.969292
$717$			1.65462e46i			0.126658i
$718$		−	2.02411e46i		−	0.151419i
$719$	−3.49896e46			−0.255807			−0.127904	−	0.991787i	$-0.540825\pi$
$719$	−3.49896e46			−0.255807			−0.127904	+	0.991787i	$0.540825\pi$
$720$	−2.20757e46	−	1.38128e46i	−0.157735	−	0.0986952i
$721$	−4.79302e45			−0.0334716
$722$		−	3.33187e46i		−	0.227417i
$723$		−	1.85288e46i		−	0.123613i
$724$	2.36021e47			1.53909
$725$	4.67033e45	+	9.60474e45i	0.0297694	+	0.0612222i
$726$	2.72232e46			0.169623
$727$		−	1.04633e46i		−	0.0637311i	−0.999492	−	0.0318655i	$-0.989855\pi$
$727$		−	1.04633e46i		−	0.0637311i	0.999492	−	0.0318655i	$-0.0101448\pi$
$728$		−	6.37669e46i		−	0.379688i
$729$	−1.90529e47			−1.10907
$730$	−2.03897e46	−	1.27579e46i	−0.116034	−	0.0726024i
$731$	−8.79510e46			−0.489332
$732$			6.42132e46i			0.349295i
$733$		−	3.33329e46i		−	0.177279i	−0.996064	−	0.0886395i	$-0.971748\pi$
$733$		−	3.33329e46i		−	0.177279i	0.996064	−	0.0886395i	$-0.0282519\pi$
$734$	−1.03938e47			−0.540492
$735$	−7.90922e46	+	1.26406e47i	−0.402154	+	0.642725i
$736$	8.98130e46			0.446535
$737$			3.04419e47i			1.47999i
$738$			1.78142e46i			0.0846908i
$739$	4.78197e46			0.222317			0.111159	−	0.993803i	$-0.464544\pi$
$739$	4.78197e46			0.222317			0.111159	+	0.993803i	$0.464544\pi$
$740$	−1.32005e47	+	2.10971e47i	−0.600161	+	0.959181i
$741$	−1.80044e47			−0.800530
$742$		−	1.15511e46i		−	0.0502297i
$743$			3.94781e47i			1.67896i	0.543388	+	0.839482i	$0.317141\pi$
$743$			3.94781e47i			1.67896i	−0.543388	+	0.839482i	$0.682859\pi$
$744$	1.68955e47			0.702777
$745$	−1.55328e47	−	9.71888e46i	−0.631932	−	0.395401i
$746$	−1.34900e47			−0.536810
$747$		−	2.36753e46i		−	0.0921520i
$748$		−	4.51308e47i		−	1.71829i
$749$	−1.49991e47			−0.558618
$750$	7.55220e45	−	7.06350e46i	0.0275146	−	0.257341i
$751$	4.15026e47			1.47916			0.739582	−	0.673067i	$-0.235023\pi$
$751$	4.15026e47			1.47916			0.739582	+	0.673067i	$0.235023\pi$
$752$		−	2.09347e47i		−	0.729916i
$753$			1.83664e47i			0.626479i
$754$	−1.15318e46			−0.0384831
$755$	−7.21695e46	−	4.51565e46i	−0.235629	−	0.147433i
$756$	1.08500e47			0.346592
$757$			1.09180e47i			0.341240i	0.985337	+	0.170620i	$0.0545771\pi$
$757$			1.09180e47i			0.341240i	−0.985337	+	0.170620i	$0.945423\pi$
$758$		−	5.33553e46i		−	0.163168i
$759$	−2.09508e47			−0.626918
$760$	−5.07062e46	+	8.10390e46i	−0.148469	+	0.237285i
$761$	−1.59076e47			−0.455784			−0.227892	−	0.973686i	$-0.573183\pi$
$761$	−1.59076e47			−0.455784			−0.227892	+	0.973686i	$0.573183\pi$
$762$			2.67268e46i			0.0749359i
$763$		−	5.42078e46i		−	0.148733i
$764$	4.23824e47			1.13801
$765$	−7.44958e46	+	1.19060e47i	−0.195757	+	0.312861i
$766$	1.96719e47			0.505908
$767$		−	6.32617e47i		−	1.59227i
$768$		−	7.73268e46i		−	0.190489i
$769$	−4.86716e47			−1.17352			−0.586761	−	0.809760i	$-0.699597\pi$
$769$	−4.86716e47			−1.17352			−0.586761	+	0.809760i	$0.699597\pi$
$770$	4.86100e46	+	3.04153e46i	0.114717	+	0.0717787i
$771$	6.41256e47			1.48127
$772$			1.24375e47i			0.281221i
$773$		−	1.81874e47i		−	0.402540i	−0.979536	−	0.201270i	$-0.935493\pi$
$773$		−	1.81874e47i		−	0.402540i	0.979536	−	0.201270i	$-0.0645068\pi$
$774$	1.15906e46			0.0251119
$775$	2.93053e47	+	6.02677e47i	0.621540	+	1.27822i
$776$	3.18265e47			0.660802
$777$		−	1.85943e47i		−	0.377948i
$778$			1.50396e47i			0.299277i
$779$	−2.82823e47			−0.550994
$780$	−6.61492e47	−	4.13896e47i	−1.26172	−	0.789461i
$781$	9.41595e47			1.75842
$782$		−	1.35171e47i		−	0.247157i
$783$		−	4.11716e46i		−	0.0737104i
$784$	3.69710e47			0.648107
$785$	3.77434e47	−	6.03218e47i	0.647876	−	1.03544i
$786$	8.29400e45			0.0139409
$787$		−	7.92430e46i		−	0.130430i	−0.997871	−	0.0652150i	$-0.979227\pi$
$787$		−	7.92430e46i		−	0.130430i	0.997871	−	0.0652150i	$-0.0207733\pi$
$788$			8.28955e47i			1.33613i
$789$	−6.45408e47			−1.01874
$790$	−9.58371e46	+	1.53168e47i	−0.148145	+	0.236766i
$791$	−1.00756e47			−0.152532
$792$			1.24797e47i			0.185029i
$793$		−	5.77055e47i		−	0.837934i
$794$	2.23591e47			0.317992
$795$	−2.51433e47	−	1.57322e47i	−0.350239	−	0.219145i
$796$	−3.28692e47			−0.448460
$797$			1.23720e48i			1.65340i	0.562641	+	0.826701i	$0.309785\pi$
$797$			1.23720e48i			1.65340i	−0.562641	+	0.826701i	$0.690215\pi$
$798$		−	3.40394e46i		−	0.0445589i
$799$	−1.12906e48			−1.44776
$800$	−5.67621e47	+	2.76007e47i	−0.712974	+	0.346685i
$801$	1.24917e47			0.153704
$802$		−	2.59629e47i		−	0.312951i
$803$		−	4.98507e47i		−	0.588660i
$804$	7.83204e47			0.906046
$805$	−1.48112e47	−	9.26739e46i	−0.167864	−	0.105033i
$806$	−7.23597e47			−0.803468
$807$		−	8.15488e46i		−	0.0887165i
$808$			4.44309e47i			0.473585i
$809$	1.21597e47			0.126991			0.0634956	−	0.997982i	$-0.479775\pi$
$809$	1.21597e47			0.126991			0.0634956	+	0.997982i	$0.479775\pi$
$810$	−1.06239e47	+	1.69792e47i	−0.108713	+	0.173746i
$811$	2.95931e47			0.296720			0.148360	−	0.988933i	$-0.452601\pi$
$811$	2.95931e47			0.296720			0.148360	+	0.988933i	$0.452601\pi$
$812$			2.21797e46i			0.0217912i
$813$			1.68354e48i			1.62080i
$814$	5.07026e47			0.478330
$815$	−7.89028e46	+	1.26103e47i	−0.0729444	+	0.116580i
$816$	−1.03576e48			−0.938366
$817$			1.84016e47i			0.163377i
$818$		−	6.06135e47i		−	0.527400i
$819$	−1.96011e47			−0.167146
$820$	−1.03911e48	−	6.50172e47i	−0.868426	−	0.543375i
$821$	7.27375e47			0.595794			0.297897	−	0.954598i	$-0.403715\pi$
$821$	7.27375e47			0.595794			0.297897	+	0.954598i	$0.403715\pi$
$822$		−	1.04723e47i		−	0.0840732i
$823$		−	6.72010e47i		−	0.528784i	−0.964415	−	0.264392i	$-0.914829\pi$
$823$		−	6.72010e47i		−	0.528784i	0.964415	−	0.264392i	$-0.0851713\pi$
$824$	−7.05554e46			−0.0544166
$825$	1.32409e48	−	6.43845e47i	1.00099	−	0.486733i
$826$	1.19604e47			0.0886287
$827$			8.31356e47i			0.603874i	0.953328	+	0.301937i	$0.0976332\pi$
$827$			8.31356e47i			0.603874i	−0.953328	+	0.301937i	$0.902367\pi$
$828$		−	1.81219e47i		−	0.129033i
$829$	1.01391e48			0.707702			0.353851	−	0.935302i	$-0.384872\pi$
$829$	1.01391e48			0.707702			0.353851	+	0.935302i	$0.384872\pi$
$830$	−1.35749e47	−	8.49384e46i	−0.0928856	−	0.0581186i
$831$	1.08399e48			0.727127
$832$			1.44340e48i			0.949186i
$833$		−	1.99394e48i		−	1.28549i
$834$	−7.00963e47			−0.443053
$835$	5.08831e47	−	8.13217e47i	0.315317	−	0.503941i
$836$	−9.44250e47			−0.573698
$837$		−	2.58343e48i		−	1.53896i
$838$			4.48928e47i			0.262210i
$839$	1.56484e47			0.0896186			0.0448093	−	0.998996i	$-0.485732\pi$
$839$	1.56484e47			0.0896186			0.0448093	+	0.998996i	$0.485732\pi$
$840$	1.64196e47	−	2.62419e47i	0.0922051	−	0.147363i
$841$	−1.80766e48			−0.995366
$842$		−	8.08771e47i		−	0.436693i
$843$			2.33269e48i			1.23510i
$844$	1.72349e48			0.894868
$845$	4.27960e48	+	2.67775e48i	2.17905	+	1.36344i
$846$	1.48793e47			0.0742969
$847$			4.70533e47i			0.230416i
$848$			7.35388e47i			0.353171i
$849$	1.76469e48			0.831173
$850$	4.15399e47	+	8.54287e47i	0.191891	+	0.394631i
$851$	−1.54488e48			−0.699934
$852$		−	2.42252e48i		−	1.07650i
$853$		−	2.34435e48i		−	1.02179i	−0.859642	−	0.510896i	$-0.829314\pi$
$853$		−	2.34435e48i		−	1.02179i	0.859642	−	0.510896i	$-0.170686\pi$
$854$	1.09099e47			0.0466409
$855$	2.49103e47	+	1.55864e47i	0.104457	+	0.0653589i
$856$	−2.20794e48			−0.908175
$857$		−	1.46847e48i		−	0.592489i	−0.955112	−	0.296245i	$-0.904266\pi$
$857$		−	1.46847e48i		−	0.592489i	0.955112	−	0.296245i	$-0.0957343\pi$
$858$			1.58976e48i			0.629203i
$859$	−4.47736e48			−1.73834			−0.869170	−	0.494513i	$-0.835346\pi$
$859$	−4.47736e48			−1.73834			−0.869170	+	0.494513i	$0.835346\pi$
$860$	−4.23027e47	+	6.76084e47i	−0.161118	+	0.257500i
$861$	9.15834e47			0.342188
$862$		−	5.37338e46i		−	0.0196960i
$863$		−	3.32539e48i		−	1.19581i	−0.801565	−	0.597907i	$-0.795999\pi$
$863$		−	3.32539e48i		−	1.19581i	0.801565	−	0.597907i	$-0.204001\pi$
$864$	2.43316e48			0.858407
$865$	−5.28548e47	+	8.44728e47i	−0.182944	+	0.292382i
$866$	1.20358e48			0.408724
$867$			2.98967e48i			0.996111i
$868$			1.39173e48i			0.454966i
$869$	−3.74478e48			−1.20116
$870$	−4.74568e46	−	2.96938e46i	−0.0149359	−	0.00934540i
$871$	−7.03830e48			−2.17354
$872$		−	7.97964e47i		−	0.241803i
$873$		−	9.78304e47i		−	0.290897i
$874$	−2.82812e47			−0.0825201
$875$	1.22087e48	+	1.30534e47i	0.349573	+	0.0373759i
$876$	−1.28255e48			−0.360376
$877$			6.37678e48i			1.75836i	0.476487	+	0.879181i	$0.341910\pi$
$877$			6.37678e48i			1.75836i	−0.476487	+	0.879181i	$0.658090\pi$
$878$			1.29684e48i			0.350935i
$879$	−1.22443e48			−0.325175
$880$	−3.09469e48	−	1.93635e48i	−0.806590	−	0.504685i
$881$	2.27415e48			0.581724			0.290862	−	0.956765i	$-0.406058\pi$
$881$	2.27415e48			0.581724			0.290862	+	0.956765i	$0.406058\pi$
$882$			2.62770e47i			0.0659697i
$883$			4.10071e48i			1.01043i	0.862993	+	0.505216i	$0.168587\pi$
$883$			4.10071e48i			1.01043i	−0.862993	+	0.505216i	$0.831413\pi$
$884$	1.04344e49			2.52352
$885$	1.62895e48	−	2.60341e48i	0.386674	−	0.617985i
$886$	−3.13327e47			−0.0730032
$887$		−	2.02235e48i		−	0.462504i	−0.972894	−	0.231252i	$-0.925718\pi$
$887$		−	2.02235e48i		−	0.462504i	0.972894	−	0.231252i	$-0.0742822\pi$
$888$		−	2.73716e48i		−	0.614450i
$889$	−4.61953e47			−0.101793
$890$	4.48159e47	−	7.16251e47i	0.0969387	−	0.154928i
$891$	−4.15123e48			−0.881444
$892$		−	5.22185e45i		−	0.00108844i
$893$			2.36228e48i			0.483372i
$894$	9.60415e47			0.192926
$895$	4.57629e48	+	2.86339e48i	0.902471	+	0.564677i
$896$	−1.71251e48			−0.331552
$897$		−	4.84391e48i		−	0.920705i
$898$		−	1.35883e48i		−	0.253575i
$899$	5.28110e47			0.0967585
$900$	5.56909e47	+	1.14531e48i	0.100180	+	0.206025i
$901$	3.96612e48			0.700499
$902$			2.49728e48i			0.433072i
$903$		−	5.95876e47i		−	0.101463i
$904$	−1.48318e48			−0.247979
$905$	−8.72859e48	−	5.46149e48i	−1.43299	−	0.896622i
$906$	4.46235e47			0.0719363
$907$			7.98241e47i			0.126361i	0.998002	+	0.0631806i	$0.0201244\pi$
$907$			7.98241e47i			0.126361i	−0.998002	+	0.0631806i	$0.979876\pi$
$908$		−	9.13298e48i		−	1.41970i
$909$	1.36575e48			0.208481
$910$	−7.03216e47	+	1.12388e48i	−0.105416	+	0.168476i
$911$	8.71761e48			1.28335			0.641674	−	0.766978i	$-0.278240\pi$
$911$	8.71761e48			1.28335			0.641674	+	0.766978i	$0.278240\pi$
$912$			2.16707e48i			0.313299i
$913$		−	3.31892e48i		−	0.471226i
$914$	4.32974e47			0.0603740
$915$	1.48589e48	−	2.37475e48i	0.203487	−	0.325215i
$916$	6.59396e48			0.886892
$917$			1.43356e47i			0.0189374i
$918$		−	3.66198e48i		−	0.475129i
$919$	−5.61506e48			−0.715563			−0.357782	−	0.933805i	$-0.616467\pi$
$919$	−5.61506e48			−0.715563			−0.357782	+	0.933805i	$0.616467\pi$
$920$	−2.18028e48	−	1.36420e48i	−0.272906	−	0.170758i
$921$	6.50134e48			0.799317
$922$		−	2.49126e48i		−	0.300857i
$923$			2.17701e49i			2.58245i
$924$	3.05765e48			0.356288
$925$	9.76370e48	−	4.74763e48i	1.11757	−	0.543423i
$926$	9.51876e46			0.0107028
$927$			2.16878e47i			0.0239552i
$928$			4.97390e47i			0.0539704i
$929$	−1.39756e49			−1.48974			−0.744871	−	0.667209i	$-0.767489\pi$
$929$	−1.39756e49			−1.48974			−0.744871	+	0.667209i	$0.767489\pi$
$930$	−2.97781e48	−	1.86322e48i	−0.311838	−	0.195117i
$931$	−4.17182e48			−0.429196
$932$		−	1.47169e48i		−	0.148749i
$933$			5.84271e48i			0.580186i
$934$	5.11338e47			0.0498867
$935$	−1.04432e49	+	1.66904e49i	−1.00102	+	1.59983i
$936$	−2.88537e48			−0.271738
$937$			1.20423e48i			0.111431i	0.998447	+	0.0557156i	$0.0177440\pi$
$937$			1.20423e48i			0.111431i	−0.998447	+	0.0557156i	$0.982256\pi$
$938$		−	1.33068e48i		−	0.120983i
$939$	−1.46645e49			−1.31004
$940$	−5.43056e48	+	8.67915e48i	−0.476688	+	0.761847i
$941$	1.31236e49			1.13194			0.565971	−	0.824425i	$-0.308502\pi$
$941$	1.31236e49			1.13194			0.565971	+	0.824425i	$0.308502\pi$
$942$			3.72979e48i			0.316114i
$943$		−	7.60909e48i		−	0.633709i
$944$	−7.61442e48			−0.623159
$945$	−4.01256e48	−	2.51066e48i	−0.322698	−	0.201913i
$946$	1.62483e48			0.128411
$947$		−	2.09928e49i		−	1.63041i	−0.579175	−	0.815203i	$-0.696625\pi$
$947$		−	2.09928e49i		−	1.63041i	0.579175	−	0.815203i	$-0.303375\pi$
$948$			9.63451e48i			0.735347i
$949$	1.15257e49			0.864519
$950$	1.78738e48	−	8.69120e47i	0.131758	−	0.0640679i
$951$	1.79503e48			0.130045
$952$			4.13943e48i			0.294734i
$953$		−	1.57940e49i		−	1.10524i	−0.833432	−	0.552622i	$-0.813627\pi$
$953$		−	1.57940e49i		−	1.10524i	0.833432	−	0.552622i	$-0.186373\pi$
$954$	−5.22674e47			−0.0359487
$955$	−1.56740e49	−	9.80722e48i	−1.05955	−	0.662965i
$956$	−2.00633e48			−0.133305
$957$		−	1.16027e48i		−	0.0757724i
$958$			2.72153e48i			0.174696i
$959$	1.81006e48			0.114205
$960$	−3.71667e48	+	5.94001e48i	−0.230504	+	0.368393i
$961$	1.67343e49			1.02017
$962$			1.17227e49i			0.702486i
$963$			6.78689e48i			0.399795i
$964$	2.24674e48			0.130101
$965$	2.87803e48	−	4.59968e48i	0.163830	−	0.261835i
$966$	9.15799e47			0.0512481
$967$			3.32626e48i			0.182987i	0.995806	+	0.0914933i	$0.0291640\pi$
$967$			3.32626e48i			0.182987i	−0.995806	+	0.0914933i	$0.970836\pi$
$968$			6.92646e48i			0.374600i
$969$	1.16875e49			0.621414
$970$	−5.60939e48	−	3.50980e48i	−0.293212	−	0.183463i
$971$	1.28962e49			0.662743			0.331371	−	0.943500i	$-0.392489\pi$
$971$	1.28962e49			0.662743			0.331371	+	0.943500i	$0.392489\pi$
$972$		−	8.83198e48i		−	0.446236i
$973$		−	1.21156e49i		−	0.601844i
$974$	4.53584e47			0.0221531
$975$	1.48860e49	+	3.06136e49i	0.714827	+	1.47007i
$976$	−6.94566e48			−0.327938
$977$			2.39192e48i			0.111042i	0.998458	+	0.0555208i	$0.0176819\pi$
$977$			2.39192e48i			0.111042i	−0.998458	+	0.0555208i	$0.982318\pi$
$978$		−	7.79714e47i		−	0.0355913i
$979$	1.75116e49			0.785978
$980$	−1.53275e49	−	9.59044e48i	−0.676458	−	0.423261i
$981$	−2.45283e48			−0.106446
$982$		−	8.30467e48i		−	0.354391i
$983$		−	2.85699e49i		−	1.19888i	−0.800420	−	0.599440i	$-0.795390\pi$
$983$		−	2.85699e49i		−	1.19888i	0.800420	−	0.599440i	$-0.204610\pi$
$984$	1.34815e49			0.556313
$985$	1.91819e49	−	3.06567e49i	0.778384	−	1.24402i
$986$	7.48588e47			0.0298727
$987$		−	7.64949e48i		−	0.300192i
$988$		−	2.18315e49i		−	0.842545i
$989$	−4.95076e48			−0.187903
$990$	1.37625e48	−	2.19954e48i	0.0513710	−	0.0821015i
$991$	2.21432e48			0.0812876			0.0406438	−	0.999174i	$-0.487059\pi$
$991$	2.21432e48			0.0812876			0.0406438	+	0.999174i	$0.487059\pi$
$992$			3.12102e49i			1.12682i
$993$			4.13149e48i			0.146705i
$994$	−4.11590e48			−0.143744
$995$	1.21558e49	+	7.60589e48i	0.417544	+	0.261258i
$996$	−8.53886e48			−0.288483
$997$			4.21638e49i			1.40110i	0.713603	+	0.700551i	$0.247062\pi$
$997$			4.21638e49i			1.40110i	−0.713603	+	0.700551i	$0.752938\pi$
$998$		−	2.36669e48i		−	0.0773550i
$999$	−4.18530e49			−1.34554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.34.b.a.4.9	yes	16
5.2	odd	4		25.34.a.f.1.8		16
5.3	odd	4		25.34.a.f.1.9		16
5.4	even	2	inner	5.34.b.a.4.8	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.b.a.4.8	✓	16	5.4	even	2	inner
5.34.b.a.4.9	yes	16	1.1	even	1	trivial
25.34.a.f.1.8		16	5.2	odd	4
25.34.a.f.1.9		16	5.3	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:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	5.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+27727.3i q^{2} -6.45007e7i q^{3} +7.82113e9 q^{4} +(-2.89243e11 - 1.80980e11i) q^{5} +1.78843e12 q^{6} +3.09117e13i q^{7} +4.55035e14i q^{8} +1.39871e15 q^{9} +O(q^{10})\)	\(q+27727.3i q^{2} -6.45007e7i q^{3} +7.82113e9 q^{4} +(-2.89243e11 - 1.80980e11i) q^{5} +1.78843e12 q^{6} +3.09117e13i q^{7} +4.55035e14i q^{8} +1.39871e15 q^{9} +(5.01809e15 - 8.01994e15i) q^{10} +1.96079e17 q^{11} -5.04469e17i q^{12} +4.53343e18i q^{13} -8.57100e17 q^{14} +(-1.16733e19 + 1.86564e19i) q^{15} +5.45661e19 q^{16} -2.94288e20i q^{17} +3.87826e19i q^{18} -6.15724e20 q^{19} +(-2.26221e21 - 1.41547e21i) q^{20} +1.99383e21 q^{21} +5.43675e21i q^{22} -1.65655e22i q^{23} +2.93501e22 q^{24} +(5.09079e22 + 1.04694e23i) q^{25} -1.25700e23 q^{26} -4.48782e23i q^{27} +2.41765e23i q^{28} +9.17408e22 q^{29} +(-5.17292e23 - 3.23670e23i) q^{30} +5.75654e24 q^{31} +5.42169e24i q^{32} -1.26472e25i q^{33} +8.15982e24 q^{34} +(5.59440e24 - 8.94100e24i) q^{35} +1.09395e25 q^{36} -9.32591e25i q^{37} -1.70724e25i q^{38} +2.92410e26 q^{39} +(8.23522e25 - 1.31616e26i) q^{40} +4.59334e26 q^{41} +5.52836e25i q^{42} -2.98860e26i q^{43} +1.53356e27 q^{44} +(-4.04569e26 - 2.53139e26i) q^{45} +4.59317e26 q^{46} -3.83658e27i q^{47} -3.51955e27i q^{48} +6.77546e27 q^{49} +(-2.90290e27 + 1.41154e27i) q^{50} -1.89818e28 q^{51} +3.54566e28i q^{52} +1.34770e28i q^{53} +1.24435e28 q^{54} +(-5.67145e28 - 3.54863e28i) q^{55} -1.40659e28 q^{56} +3.97147e28i q^{57} +2.54373e27i q^{58} -1.39545e29 q^{59} +(-9.12987e28 + 1.45914e29i) q^{60} -1.27289e29 q^{61} +1.59614e29i q^{62} +4.32367e28i q^{63} +3.18390e29 q^{64} +(8.20460e29 - 1.31126e30i) q^{65} +3.50674e29 q^{66} +1.55253e30i q^{67} -2.30166e30i q^{68} -1.06849e30 q^{69} +(2.47910e29 + 1.55118e29i) q^{70} +4.80212e30 q^{71} +6.36464e29i q^{72} -2.54238e30i q^{73} +2.58583e30 q^{74} +(6.75286e30 - 3.28360e30i) q^{75} -4.81566e30 q^{76} +6.06114e30i q^{77} +8.10774e30i q^{78} -1.90983e31 q^{79} +(-1.57829e31 - 9.87536e30i) q^{80} -2.11712e31 q^{81} +1.27361e31i q^{82} -1.69264e31i q^{83} +1.55940e31 q^{84} +(-5.32602e31 + 8.51208e31i) q^{85} +8.28660e30 q^{86} -5.91735e30i q^{87} +8.92228e31i q^{88} +8.93087e31 q^{89} +(7.01888e30 - 1.12176e31i) q^{90} -1.40136e32 q^{91} -1.29561e32i q^{92} -3.71301e32i q^{93} +1.06378e32 q^{94} +(1.78094e32 + 1.11434e32i) q^{95} +3.49703e32 q^{96} -6.99431e32i q^{97} +1.87865e32i q^{98} +2.74259e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 72851326872 q^{4} - 232168160280 q^{5} + 11001777346872 q^{6} - 27\!\cdots\!68 q^{9}+O(q^{10}) \) 16 * q - 72851326872 * q^4 - 232168160280 * q^5 + 11001777346872 * q^6 - 27535156574590368 * q^9	\( 16 q - 72851326872 q^{4} - 232168160280 q^{5} + 11001777346872 q^{6} - 27\!\cdots\!68 q^{9}+ \cdots + 34\!\cdots\!24 q^{99}+O(q^{100}) \) 16 * q - 72851326872 * q^4 - 232168160280 * q^5 + 11001777346872 * q^6 - 27535156574590368 * q^9 - 22271193818331880 * q^10 + 219974590742466912 * q^11 - 10416043581549356184 * q^14 + 9232415497377901440 * q^15 + 133171456389985196576 * q^16 - 2949217257058889591200 * q^19 + 5571772909456424216760 * q^20 + 20126160533851210892592 * q^21 - 236696360036140740492000 * q^24 + 269473151678676722148400 * q^25 + 23043234216449373353232 * q^26 + 2210824656972934579370400 * q^29 - 7438800885032297852420760 * q^30 + 4805180075928582021889472 * q^31 - 106706080442140703440064 * q^34 + 34840114703893102459924320 * q^35 + 150609707516636111776170456 * q^36 - 950668737676648885834065216 * q^39 + 967967034953888345833396000 * q^40 + 960625982433026021733974352 * q^41 - 4300041994750366563328828704 * q^44 + 5959973976670208219568382440 * q^45 + 4030532465737707969346868392 * q^46 - 48902999941413820155855454112 * q^49 + 64132734499011351066825776400 * q^50 + 37677263492556888574173469632 * q^51 - 416785644990759180210455480400 * q^54 + 208827421951347317583761567040 * q^55 + 209868986171565551575474447200 * q^56 - 204679212804521237512362904800 * q^59 - 320542648209593925139588560480 * q^60 - 62902839261738400132019069488 * q^61 + 3273202940251902417009873735808 * q^64 - 1155813780125630532662955267360 * q^65 - 2991219624550267460630717491296 * q^66 + 6899695112224183044828868241904 * q^69 - 5880904834264312779374002982280 * q^70 - 87525095316001019795902439808 * q^71 + 43140282179597200538055251968176 * q^74 - 27726088944293536006405507003200 * q^75 - 38605994956626944020944749752800 * q^76 - 10590745643822309766800662264000 * q^79 + 24913342429758171577982759437920 * q^80 + 126385893984816788804508532470336 * q^81 - 401968339664232685914350670917664 * q^84 + 174616747052458036927895334806720 * q^85 - 18805496634715830052189508032488 * q^86 - 816457769414638729740610145056800 * q^89 + 814730708455223899676092744179240 * q^90 + 572310345418666359618454810906752 * q^91 + 1084618018208246129370832376900296 * q^94 - 960346549067575215463879922304000 * q^95 - 1376269400022374885061468958478208 * q^96 + 3432482025669259323040953857901024 * q^99

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