LMFDB - Embedded newform 5.34.b.a.4.2

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			4.2
Root			$-78261.9i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.34.b.a.4.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-156524. i q^{2} +1.41317e8i q^{3} -1.59098e10 q^{4} +(-2.87690e11 - 1.83439e11i) q^{5} +2.21195e13 q^{6} -8.25005e13i q^{7} +1.14573e15i q^{8} -1.44114e16 q^{9} +O(q^{10})$	\(q-156524. i q^{2} +1.41317e8i q^{3} -1.59098e10 q^{4} +(-2.87690e11 - 1.83439e11i) q^{5} +2.21195e13 q^{6} -8.25005e13i q^{7} +1.14573e15i q^{8} -1.44114e16 q^{9} +(-2.87126e16 + 4.50303e16i) q^{10} -6.60805e16 q^{11} -2.24832e18i q^{12} +2.09761e18i q^{13} -1.29133e19 q^{14} +(2.59230e19 - 4.06555e19i) q^{15} +4.26697e19 q^{16} +1.67795e18i q^{17} +2.25573e21i q^{18} +3.21790e20 q^{19} +(4.57708e21 + 2.91847e21i) q^{20} +1.16587e22 q^{21} +1.03432e22i q^{22} -1.95136e22i q^{23} -1.61911e23 q^{24} +(4.91156e22 + 1.05547e23i) q^{25} +3.28326e23 q^{26} -1.25099e24i q^{27} +1.31256e24i q^{28} +6.09781e23 q^{29} +(-6.36355e24 - 4.05757e24i) q^{30} +7.68528e24 q^{31} +3.16289e24i q^{32} -9.33830e24i q^{33} +2.62639e23 q^{34} +(-1.51338e25 + 2.37345e25i) q^{35} +2.29282e26 q^{36} +7.12507e25i q^{37} -5.03677e25i q^{38} -2.96428e26 q^{39} +(2.10171e26 - 3.29614e26i) q^{40} +1.56491e26 q^{41} -1.82487e27i q^{42} -1.27423e27i q^{43} +1.05133e27 q^{44} +(4.14602e27 + 2.64362e27i) q^{45} -3.05434e27 q^{46} +5.00611e27i q^{47} +6.02996e27i q^{48} +9.24666e26 q^{49} +(1.65206e28 - 7.68776e27i) q^{50} -2.37123e26 q^{51} -3.33724e28i q^{52} +2.77023e28i q^{53} -1.95810e29 q^{54} +(1.90107e28 + 1.21217e28i) q^{55} +9.45230e28 q^{56} +4.54744e28i q^{57} -9.54452e28i q^{58} +1.46213e28 q^{59} +(-4.12429e29 + 6.46819e29i) q^{60} +2.37790e29 q^{61} -1.20293e30i q^{62} +1.18895e30i q^{63} +8.61598e29 q^{64} +(3.84783e29 - 6.03461e29i) q^{65} -1.46167e30 q^{66} -4.57295e29i q^{67} -2.66958e28i q^{68} +2.75760e30 q^{69} +(3.71502e30 + 2.36880e30i) q^{70} -2.86115e30 q^{71} -1.65116e31i q^{72} -1.51288e30i q^{73} +1.11524e31 q^{74} +(-1.49156e31 + 6.94087e30i) q^{75} -5.11960e30 q^{76} +5.45167e30i q^{77} +4.63980e31i q^{78} -1.25779e30 q^{79} +(-1.22756e31 - 7.82729e30i) q^{80} +9.66723e31 q^{81} -2.44945e31i q^{82} +1.16378e31i q^{83} -1.85487e32 q^{84} +(3.07802e29 - 4.82730e29i) q^{85} -1.99447e32 q^{86} +8.61724e31i q^{87} -7.57102e31i q^{88} -1.11905e32 q^{89} +(4.13789e32 - 6.48951e32i) q^{90} +1.73054e32 q^{91} +3.10457e32i q^{92} +1.08606e33i q^{93} +7.83575e32 q^{94} +(-9.25756e31 - 5.90288e31i) q^{95} -4.46971e32 q^{96} -4.59836e32i q^{97} -1.44732e32i q^{98} +9.52315e32 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 $

$2$		−	156524.i		−	1.68883i	−0.535691	−	0.844414i	$-0.679949\pi$
$2$		−	156524.i		−	1.68883i	0.535691	−	0.844414i	$-0.320051\pi$
$3$			1.41317e8i			1.89537i	0.319209	+	0.947684i	$0.396583\pi$
$3$			1.41317e8i			1.89537i	−0.319209	+	0.947684i	$0.603417\pi$
$4$	−1.59098e10			−1.85214
$5$	−2.87690e11	−	1.83439e11i	−0.843178	−	0.537634i
$5$	−2.87690e11	−	1.83439e11i	−0.843178	−	0.537634i
$6$	2.21195e13			3.20095
$7$		−	8.25005e13i		−	0.938294i	−0.883120	−	0.469147i	$-0.844562\pi$
$7$		−	8.25005e13i		−	0.938294i	0.883120	−	0.469147i	$-0.155438\pi$
$8$			1.14573e15i			1.43912i
$9$	−1.44114e16			−2.59242
$10$	−2.87126e16	+	4.50303e16i	−0.907971	+	1.42398i
$11$	−6.60805e16			−0.433605			−0.216802	−	0.976216i	$-0.569563\pi$
$11$	−6.60805e16			−0.433605			−0.216802	+	0.976216i	$0.569563\pi$
$12$		−	2.24832e18i		−	3.51049i
$13$			2.09761e18i			0.874297i	0.899389	+	0.437149i	$0.144012\pi$
$13$			2.09761e18i			0.874297i	−0.899389	+	0.437149i	$0.855988\pi$
$14$	−1.29133e19			−1.58462
$15$	2.59230e19	−	4.06555e19i	1.01901	−	1.59813i
$16$	4.26697e19			0.578282
$17$			1.67795e18i			0.00836320i	0.999991	+	0.00418160i	$0.00133105\pi$
$17$			1.67795e18i			0.00836320i	−0.999991	+	0.00418160i	$0.998669\pi$
$18$			2.25573e21i			4.37816i
$19$	3.21790e20			0.255940			0.127970	−	0.991778i	$-0.459154\pi$
$19$	3.21790e20			0.255940			0.127970	+	0.991778i	$0.459154\pi$
$20$	4.57708e21	+	2.91847e21i	1.56168	+	0.995773i
$21$	1.16587e22			1.77841
$22$			1.03432e22i			0.732284i
$23$		−	1.95136e22i		−	0.663481i	−0.943371	−	0.331740i	$-0.892364\pi$
$23$		−	1.95136e22i		−	0.663481i	0.943371	−	0.331740i	$-0.107636\pi$
$24$	−1.61911e23			−2.72766
$25$	4.91156e22	+	1.05547e23i	0.421900	+	0.906642i
$26$	3.28326e23			1.47654
$27$		−	1.25099e24i		−	3.01823i
$28$			1.31256e24i			1.73785i
$29$	6.09781e23			0.452488			0.226244	−	0.974071i	$-0.427355\pi$
$29$	6.09781e23			0.452488			0.226244	+	0.974071i	$0.427355\pi$
$30$	−6.36355e24	−	4.05757e24i	−2.69897	−	1.72094i
$31$	7.68528e24			1.89754			0.948772	−	0.315961i	$-0.102327\pi$
$31$	7.68528e24			1.89754			0.948772	+	0.315961i	$0.102327\pi$
$32$			3.16289e24i			0.462498i
$33$		−	9.33830e24i		−	0.821841i
$34$	2.62639e23			0.0141240
$35$	−1.51338e25	+	2.37345e25i	−0.504458	+	0.791149i
$36$	2.29282e26			4.80153
$37$			7.12507e25i			0.949425i	0.880141	+	0.474712i	$0.157448\pi$
$37$			7.12507e25i			0.949425i	−0.880141	+	0.474712i	$0.842552\pi$
$38$		−	5.03677e25i		−	0.432238i
$39$	−2.96428e26			−1.65712
$40$	2.10171e26	−	3.29614e26i	0.773718	−	1.21343i
$41$	1.56491e26			0.383314			0.191657	−	0.981462i	$-0.438614\pi$
$41$	1.56491e26			0.383314			0.191657	+	0.981462i	$0.438614\pi$
$42$		−	1.82487e27i		−	3.00343i
$43$		−	1.27423e27i		−	1.42239i	−0.702997	−	0.711193i	$-0.748155\pi$
$43$		−	1.27423e27i		−	1.42239i	0.702997	−	0.711193i	$-0.251845\pi$
$44$	1.05133e27			0.803097
$45$	4.14602e27	+	2.64362e27i	2.18587	+	1.39377i
$46$	−3.05434e27			−1.12050
$47$			5.00611e27i			1.28791i	0.765063	+	0.643955i	$0.222708\pi$
$47$			5.00611e27i			1.28791i	−0.765063	+	0.643955i	$0.777292\pi$
$48$			6.02996e27i			1.09606i
$49$	9.24666e26			0.119605
$50$	1.65206e28	−	7.68776e27i	1.53116	−	0.712516i
$51$	−2.37123e26			−0.0158513
$52$		−	3.33724e28i		−	1.61932i
$53$			2.77023e28i			0.981665i	0.871254	+	0.490833i	$0.163307\pi$
$53$			2.77023e28i			0.981665i	−0.871254	+	0.490833i	$0.836693\pi$
$54$	−1.95810e29			−5.09727
$55$	1.90107e28	+	1.21217e28i	0.365606	+	0.233121i
$56$	9.45230e28			1.35031
$57$			4.54744e28i			0.485100i
$58$		−	9.54452e28i		−	0.764174i
$59$	1.46213e28			0.0882933			0.0441466	−	0.999025i	$-0.485943\pi$
$59$	1.46213e28			0.0882933			0.0441466	+	0.999025i	$0.485943\pi$
$60$	−4.12429e29	+	6.46819e29i	−1.88736	+	2.95997i
$61$	2.37790e29			0.828421			0.414211	−	0.910181i	$-0.364058\pi$
$61$	2.37790e29			0.828421			0.414211	+	0.910181i	$0.364058\pi$
$62$		−	1.20293e30i		−	3.20463i
$63$			1.18895e30i			2.43245i
$64$	8.61598e29			1.35936
$65$	3.84783e29	−	6.03461e29i	0.470052	−	0.737189i
$66$	−1.46167e30			−1.38795
$67$		−	4.57295e29i		−	0.338814i	−0.985546	−	0.169407i	$-0.945815\pi$
$67$		−	4.57295e29i		−	0.338814i	0.985546	−	0.169407i	$-0.0541853\pi$
$68$		−	2.66958e28i		−	0.0154898i
$69$	2.75760e30			1.25754
$70$	3.71502e30	+	2.36880e30i	1.33611	+	0.851943i
$71$	−2.86115e30			−0.814288			−0.407144	−	0.913364i	$-0.633475\pi$
$71$	−2.86115e30			−0.814288			−0.407144	+	0.913364i	$0.633475\pi$
$72$		−	1.65116e31i		−	3.73080i
$73$		−	1.51288e30i		−	0.272256i	−0.990691	−	0.136128i	$-0.956534\pi$
$73$		−	1.51288e30i		−	0.272256i	0.990691	−	0.136128i	$-0.0434658\pi$
$74$	1.11524e31			1.60342
$75$	−1.49156e31	+	6.94087e30i	−1.71842	+	0.799656i
$76$	−5.11960e30			−0.474036
$77$			5.45167e30i			0.406849i
$78$			4.63980e31i			2.79858i
$79$	−1.25779e30			−0.0614837			−0.0307418	−	0.999527i	$-0.509787\pi$
$79$	−1.25779e30			−0.0614837			−0.0307418	+	0.999527i	$0.509787\pi$
$80$	−1.22756e31	−	7.82729e30i	−0.487595	−	0.310904i
$81$	9.66723e31			3.12823
$82$		−	2.44945e31i		−	0.647351i
$83$			1.16378e31i			0.251816i	0.992042	+	0.125908i	$0.0401844\pi$
$83$			1.16378e31i			0.251816i	−0.992042	+	0.125908i	$0.959816\pi$
$84$	−1.85487e32			−3.29387
$85$	3.07802e29	−	4.82730e29i	0.00449634	−	0.00705167i
$86$	−1.99447e32			−2.40217
$87$			8.61724e31i			0.857631i
$88$		−	7.57102e31i		−	0.624008i
$89$	−1.11905e32			−0.765447			−0.382724	−	0.923863i	$-0.625014\pi$
$89$	−1.11905e32			−0.765447			−0.382724	+	0.923863i	$0.625014\pi$
$90$	4.13789e32	−	6.48951e32i	2.35384	−	3.69157i
$91$	1.73054e32			0.820347
$92$			3.10457e32i			1.22886i
$93$			1.08606e33i			3.59655i
$94$	7.83575e32			2.17506
$95$	−9.25756e31	−	5.90288e31i	−0.215803	−	0.137602i
$96$	−4.46971e32			−0.876605
$97$		−	4.59836e32i		−	0.760098i	−0.924966	−	0.380049i	$-0.875907\pi$
$97$		−	4.59836e32i		−	0.760098i	0.924966	−	0.380049i	$-0.124093\pi$
$98$		−	1.44732e32i		−	0.201992i
$99$	9.52315e32			1.12409
$100$	−7.81417e32	−	1.67923e33i	−0.781417	−	1.67923i
$101$	6.62249e32			0.561977			0.280989	−	0.959711i	$-0.409338\pi$
$101$	6.62249e32			0.561977			0.280989	+	0.959711i	$0.409338\pi$
$102$			3.71154e31i			0.0267702i
$103$		−	1.81153e33i		−	1.11233i	−0.831073	−	0.556163i	$-0.812273\pi$
$103$		−	1.81153e33i		−	1.11233i	0.831073	−	0.556163i	$-0.187727\pi$
$104$	−2.40329e33			−1.25822
$105$	−3.35410e33	−	2.13866e33i	−1.49952	−	0.956135i
$106$	4.33606e33			1.65786
$107$		−	2.29623e33i		−	0.751938i	−0.926632	−	0.375969i	$-0.877310\pi$
$107$		−	2.29623e33i		−	0.751938i	0.926632	−	0.375969i	$-0.122690\pi$
$108$			1.99030e34i			5.59018i
$109$	5.83380e32			0.140739			0.0703695	−	0.997521i	$-0.477582\pi$
$109$	5.83380e32			0.140739			0.0703695	+	0.997521i	$0.477582\pi$
$110$	1.89734e33	−	2.97563e33i	0.393701	−	0.617446i
$111$	−1.00689e34			−1.79951
$112$		−	3.52027e33i		−	0.542599i
$113$			3.99672e33i			0.531997i	0.963973	+	0.265998i	$0.0857016\pi$
$113$			3.99672e33i			0.531997i	−0.963973	+	0.265998i	$0.914298\pi$
$114$	7.11782e33			0.819251
$115$	−3.57956e33	+	5.61387e33i	−0.356710	+	0.559433i
$116$	−9.70147e33			−0.838071
$117$		−	3.02295e34i		−	2.26655i
$118$		−	2.28858e33i		−	0.149112i
$119$	1.38432e32			0.00784713
$120$	4.65801e34	+	2.97007e34i	2.29990	+	1.46648i
$121$	−1.88585e34			−0.811987
$122$		−	3.72198e34i		−	1.39906i
$123$			2.21148e34i			0.726521i
$124$	−1.22271e35			−3.51452
$125$	5.23139e33	−	3.93745e34i	0.131705	−	0.991289i
$126$	1.86099e35			4.10800
$127$			6.57898e34i			1.27467i	0.770588	+	0.637334i	$0.219963\pi$
$127$			6.57898e34i			1.27467i	−0.770588	+	0.637334i	$0.780037\pi$
$128$		−	1.07692e35i		−	1.83323i
$129$	1.80070e35			2.69595
$130$	−9.44559e34	−	6.02277e34i	−1.24498	−	0.793837i
$131$	−6.23122e34			−0.723764			−0.361882	−	0.932224i	$-0.617866\pi$
$131$	−6.23122e34			−0.723764			−0.361882	+	0.932224i	$0.617866\pi$
$132$			1.48570e35i			1.52216i
$133$		−	2.65478e34i		−	0.240147i
$134$	−7.15775e34			−0.572199
$135$	−2.29481e35	+	3.59897e35i	−1.62270	+	2.54491i
$136$	−1.92247e33			−0.0120356
$137$			1.72453e35i			0.956711i	0.878166	+	0.478356i	$0.158767\pi$
$137$			1.72453e35i			0.956711i	−0.878166	+	0.478356i	$0.841233\pi$
$138$		−	4.31631e35i		−	2.12377i
$139$	4.13024e35			1.80398			0.901988	−	0.431761i	$-0.142108\pi$
$139$	4.13024e35			1.80398			0.901988	+	0.431761i	$0.142108\pi$
$140$	2.40775e35	−	3.77611e35i	0.934327	−	1.46532i
$141$	−7.07448e35			−2.44107
$142$			4.47838e35i			1.37519i
$143$		−	1.38611e35i		−	0.379099i
$144$	−6.14932e35			−1.49915
$145$	−1.75428e35	−	1.11858e35i	−0.381528	−	0.243273i
$146$	−2.36802e35			−0.459794
$147$			1.30671e35i			0.226696i
$148$		−	1.13358e36i		−	1.75847i
$149$	−3.95821e34			−0.0549446			−0.0274723	−	0.999623i	$-0.508746\pi$
$149$	−3.95821e34			−0.0549446			−0.0274723	+	0.999623i	$0.508746\pi$
$150$	1.08641e36	+	2.33465e36i	1.35048	+	2.90212i
$151$	1.67361e36			1.86438			0.932192	−	0.361965i	$-0.117894\pi$
$151$	1.67361e36			1.86438			0.932192	+	0.361965i	$0.117894\pi$
$152$			3.68683e35i			0.368327i
$153$		−	2.41817e34i		−	0.0216809i
$154$	8.53316e35			0.687097
$155$	−2.21098e36	−	1.40978e36i	−1.59997	−	1.02018i
$156$	4.71609e36			3.06921
$157$			5.41459e35i			0.317118i	0.987349	+	0.158559i	$0.0506848\pi$
$157$			5.41459e35i			0.317118i	−0.987349	+	0.158559i	$0.949315\pi$
$158$			1.96873e35i			0.103835i
$159$	−3.91480e36			−1.86062
$160$	5.80198e35	−	9.09933e35i	0.248655	−	0.389969i
$161$	−1.60988e36			−0.622540
$162$		−	1.51315e37i		−	5.28305i
$163$			4.83507e36i			1.52513i	0.646910	+	0.762566i	$0.276061\pi$
$163$			4.83507e36i			1.52513i	−0.646910	+	0.762566i	$0.723939\pi$
$164$	−2.48973e36			−0.709951
$165$	−1.71301e36	+	2.68653e36i	−0.441849	+	0.692959i
$166$	1.82160e36			0.425274
$167$			1.13436e36i			0.239843i	0.992783	+	0.119922i	$0.0382644\pi$
$167$			1.13436e36i			0.239843i	−0.992783	+	0.119922i	$0.961736\pi$
$168$			1.33577e37i			2.55934i
$169$	1.35617e36			0.235604
$170$	−7.55587e34	−	4.81783e34i	−0.0119091	−	0.00759354i
$171$	−4.63745e36			−0.663504
$172$			2.02727e37i			2.63446i
$173$		−	1.10965e37i		−	1.31046i	−0.755429	−	0.655230i	$-0.772572\pi$
$173$		−	1.10965e37i		−	1.31046i	0.755429	−	0.655230i	$-0.227428\pi$
$174$	1.34880e37			1.44839
$175$	8.70768e36	−	4.05206e36i	0.850697	−	0.395866i
$176$	−2.81964e36			−0.250746
$177$			2.06624e36i			0.167348i
$178$			1.75158e37i			1.29271i
$179$	−5.94403e36			−0.399950			−0.199975	−	0.979801i	$-0.564086\pi$
$179$	−5.94403e36			−0.399950			−0.199975	+	0.979801i	$0.564086\pi$
$180$	−6.59622e37	−	4.20593e37i	−4.04855	−	2.58146i
$181$	−2.22016e37			−1.24362			−0.621811	−	0.783168i	$-0.713603\pi$
$181$	−2.22016e37			−1.24362			−0.621811	+	0.783168i	$0.713603\pi$
$182$		−	2.70870e37i		−	1.38543i
$183$			3.36038e37i			1.57016i
$184$	2.23573e37			0.954827
$185$	1.30702e37	−	2.04981e37i	0.510443	−	0.800535i
$186$	1.69994e38			6.07395
$187$		−	1.10880e35i		−	0.00362632i
$188$		−	7.96460e37i		−	2.38539i
$189$	−1.03207e38			−2.83198
$190$	−9.23941e36	+	1.44903e37i	−0.232386	+	0.364454i
$191$	4.30473e37			0.992877			0.496438	−	0.868072i	$-0.334641\pi$
$191$	4.30473e37			0.992877			0.496438	+	0.868072i	$0.334641\pi$
$192$			1.21758e38i			2.57649i
$193$			6.65826e37i			1.29320i	0.762830	+	0.646599i	$0.223809\pi$
$193$			6.65826e37i			1.29320i	−0.762830	+	0.646599i	$0.776191\pi$
$194$	−7.19753e37			−1.28367
$195$	8.52793e37	+	5.43764e37i	1.39724	+	0.890921i
$196$	−1.47112e37			−0.221525
$197$		−	7.24256e37i		−	1.00277i	−0.865226	−	0.501383i	$-0.832825\pi$
$197$		−	7.24256e37i		−	1.00277i	0.865226	−	0.501383i	$-0.167175\pi$
$198$		−	1.49060e38i		−	1.89839i
$199$	5.94874e37			0.697187			0.348593	−	0.937274i	$-0.386659\pi$
$199$	5.94874e37			0.697187			0.348593	+	0.937274i	$0.386659\pi$
$200$	−1.20928e38	+	5.62731e37i	−1.30477	+	0.607164i
$201$	6.46235e37			0.642178
$202$		−	1.03658e38i		−	0.949082i
$203$		−	5.03072e37i		−	0.424566i
$204$	3.77257e36			0.0293589
$205$	−4.50208e37	−	2.87065e37i	−0.323202	−	0.206083i
$206$	−2.83548e38			−1.87853
$207$			2.81219e38i			1.72002i
$208$			8.95043e37i			0.505591i
$209$	−2.12640e37			−0.110977
$210$	−3.34752e38	+	5.24996e38i	−1.61475	+	2.53243i
$211$	2.40911e38			1.07447			0.537237	−	0.843432i	$-0.319468\pi$
$211$	2.40911e38			1.07447			0.537237	+	0.843432i	$0.319468\pi$
$212$		−	4.40736e38i		−	1.81818i
$213$		−	4.04329e38i		−	1.54338i
$214$	−3.59414e38			−1.26989
$215$	−2.33743e38	+	3.66582e38i	−0.764723	+	1.19933i
$216$	1.43329e39			4.34359
$217$		−	6.34039e38i		−	1.78045i
$218$		−	9.13129e37i		−	0.237684i
$219$	2.13796e38			0.516026
$220$	−3.02456e38	−	1.92854e38i	−0.677154	−	0.431772i
$221$	−3.51969e36			−0.00731192
$222$			1.57603e39i			3.03906i
$223$			7.48856e38i			1.34081i	0.741994	+	0.670407i	$0.233880\pi$
$223$			7.48856e38i			1.34081i	−0.741994	+	0.670407i	$0.766120\pi$
$224$	2.60940e38			0.433959
$225$	−7.07826e38	−	1.52108e39i	−1.09374	−	2.35040i
$226$	6.25581e38			0.898451
$227$		−	5.66681e38i		−	0.756680i	−0.925667	−	0.378340i	$-0.876495\pi$
$227$		−	5.66681e38i		−	0.756680i	0.925667	−	0.378340i	$-0.123505\pi$
$228$		−	7.23486e38i		−	0.898473i
$229$	1.30369e39			1.50622			0.753110	−	0.657894i	$-0.228553\pi$
$229$	1.30369e39			1.50622			0.753110	+	0.657894i	$0.228553\pi$
$230$	8.78704e38	+	5.60286e38i	0.944785	+	0.602421i
$231$	−7.70414e38			−0.771128
$232$			6.98642e38i			0.651183i
$233$		−	8.12954e38i		−	0.705819i	−0.935658	−	0.352909i	$-0.885192\pi$
$233$		−	8.12954e38i		−	0.705819i	0.935658	−	0.352909i	$-0.114808\pi$
$234$	−4.73164e39			−3.82781
$235$	9.18316e38	−	1.44021e39i	0.692424	−	1.08594i
$236$	−2.32621e38			−0.163532
$237$		−	1.77747e38i		−	0.116534i
$238$		−	2.16679e37i		−	0.0132525i
$239$	2.20409e39			1.25795			0.628975	−	0.777426i	$-0.283475\pi$
$239$	2.20409e39			1.25795			0.628975	+	0.777426i	$0.283475\pi$
$240$	1.10613e39	−	1.73476e39i	0.589278	−	0.924173i
$241$	−1.42741e39			−0.710016			−0.355008	−	0.934863i	$-0.615522\pi$
$241$	−1.42741e39			−0.710016			−0.355008	+	0.934863i	$0.615522\pi$
$242$			2.95181e39i			1.37131i
$243$			6.70710e39i			2.91093i
$244$	−3.78318e39			−1.53435
$245$	−2.66017e38	−	1.69620e38i	−0.100848	−	0.0643038i
$246$	3.46149e39			1.22697
$247$			6.74989e38i			0.223767i
$248$			8.80524e39i			2.73079i
$249$	−1.64462e39			−0.477284
$250$	−6.16305e39	−	8.18836e38i	−1.67412	−	0.222427i
$251$	6.32196e39			1.60781			0.803906	−	0.594757i	$-0.202752\pi$
$251$	6.32196e39			1.60781			0.803906	+	0.594757i	$0.202752\pi$
$252$		−	1.89159e40i		−	4.50524i
$253$			1.28947e39i			0.287688i
$254$	1.02977e40			2.15269
$255$	6.82179e37	+	4.34976e37i	0.0133655	+	0.00852222i
$256$	−9.45522e39			−1.73665
$257$			5.44812e39i			0.938318i	0.883114	+	0.469159i	$0.155443\pi$
$257$			5.44812e39i			0.938318i	−0.883114	+	0.469159i	$0.844557\pi$
$258$		−	2.81852e40i		−	4.55299i
$259$	5.87822e39			0.890839
$260$	−6.12181e39	+	9.60092e39i	−0.870602	+	1.36538i
$261$	−8.78782e39			−1.17304
$262$			9.75334e39i			1.22231i
$263$			7.04383e39i			0.828970i	0.910056	+	0.414485i	$0.136038\pi$
$263$			7.04383e39i			0.828970i	−0.910056	+	0.414485i	$0.863962\pi$
$264$	1.06991e40			1.18273
$265$	5.08168e39	−	7.96966e39i	0.527776	−	0.827719i
$266$	−4.15536e39			−0.405566
$267$		−	1.58141e40i		−	1.45080i
$268$			7.27545e39i			0.627532i
$269$	−5.21988e39			−0.423397			−0.211699	−	0.977335i	$-0.567900\pi$
$269$	−5.21988e39			−0.423397			−0.211699	+	0.977335i	$0.567900\pi$
$270$	5.63325e40	+	3.59192e40i	4.29791	+	2.74046i
$271$	−5.71943e39			−0.410543			−0.205272	−	0.978705i	$-0.565808\pi$
$271$	−5.71943e39			−0.410543			−0.205272	+	0.978705i	$0.565808\pi$
$272$			7.15977e37i			0.00483629i
$273$			2.44554e40i			1.55486i
$274$	2.69930e40			1.61572
$275$	−3.24558e39	−	6.97460e39i	−0.182938	−	0.393125i
$276$	−4.38728e40			−2.32914
$277$		−	8.42964e39i		−	0.421592i	−0.977530	−	0.210796i	$-0.932394\pi$
$277$		−	8.42964e39i		−	0.421592i	0.977530	−	0.210796i	$-0.0676056\pi$
$278$		−	6.46480e40i		−	3.04661i
$279$	−1.10756e41			−4.91924
$280$	−2.71933e40	−	1.73392e40i	−1.13856	−	0.725975i
$281$	1.38422e40			0.546450			0.273225	−	0.961950i	$-0.411910\pi$
$281$	1.38422e40			0.546450			0.273225	+	0.961950i	$0.411910\pi$
$282$			1.10733e41i			4.12254i
$283$		−	4.63320e40i		−	1.62707i	−0.581519	−	0.813533i	$-0.697541\pi$
$283$		−	4.63320e40i		−	1.62707i	0.581519	−	0.813533i	$-0.302459\pi$
$284$	4.55202e40			1.50818
$285$	8.34177e39	−	1.30825e40i	0.260806	−	0.409026i
$286$	−2.16959e40			−0.640234
$287$		−	1.29106e40i		−	0.359661i
$288$		−	4.55819e40i		−	1.19899i
$289$	4.02517e40			0.999930
$290$	−1.75084e40	+	2.74586e40i	−0.410846	+	0.644335i
$291$	6.49827e40			1.44067
$292$			2.40696e40i			0.504256i
$293$			9.43552e40i			1.86832i	0.356861	+	0.934158i	$0.383847\pi$
$293$			9.43552e40i			1.86832i	−0.356861	+	0.934158i	$0.616153\pi$
$294$	2.04531e40			0.382850
$295$	−4.20640e39	−	2.68212e39i	−0.0744470	−	0.0474695i
$296$	−8.16338e40			−1.36633
$297$			8.26661e40i			1.30872i
$298$			6.19554e39i			0.0927921i
$299$	4.09319e40			0.580079
$300$	2.37304e41	−	1.10428e41i	3.18276	−	1.48107i
$301$	−1.05124e41			−1.33462
$302$		−	2.61960e41i		−	3.14862i
$303$			9.35870e40i			1.06515i
$304$	1.37307e40			0.148005
$305$	−6.84098e40	−	4.36199e40i	−0.698507	−	0.445387i
$306$	−3.78501e39			−0.0366154
$307$			6.36451e39i			0.0583421i	0.999574	+	0.0291710i	$0.00928674\pi$
$307$			6.36451e39i			0.0583421i	−0.999574	+	0.0291710i	$0.990713\pi$
$308$		−	8.67348e40i		−	0.753541i
$309$	2.56000e41			2.10827
$310$	−2.20664e41	+	3.46071e41i	−1.72292	+	2.70207i
$311$	−2.36303e41			−1.74954			−0.874768	−	0.484542i	$-0.838986\pi$
$311$	−2.36303e41			−1.74954			−0.874768	+	0.484542i	$0.838986\pi$
$312$		−	3.39625e41i		−	2.38478i
$313$			1.64180e41i			1.09355i	0.837279	+	0.546775i	$0.184145\pi$
$313$			1.64180e41i			1.09355i	−0.837279	+	0.546775i	$0.815855\pi$
$314$	8.47512e40			0.535558
$315$	2.18100e41	−	3.42049e41i	1.30777	−	2.05099i
$316$	2.00111e40			0.113876
$317$		−	5.69743e40i		−	0.307752i	−0.988090	−	0.153876i	$-0.950824\pi$
$317$		−	5.69743e40i		−	0.307752i	0.988090	−	0.153876i	$-0.0491757\pi$
$318$			6.12759e41i			3.14226i
$319$	−4.02946e40			−0.196201
$320$	−2.47873e41	−	1.58051e41i	−1.14619	−	0.730839i
$321$	3.24496e41			1.42520
$322$			2.51985e41i			1.05136i
$323$			5.39948e38i			0.00214047i
$324$	−1.53803e42			−5.79393
$325$	−2.21396e41	+	1.03025e41i	−0.792675	+	0.368866i
$326$	7.56804e41			2.57569
$327$			8.24416e40i			0.266752i
$328$			1.79296e41i			0.551634i
$329$	4.13006e41			1.20844
$330$	4.20506e41	+	2.68127e41i	1.17029	+	0.746208i
$331$	1.61388e40			0.0427278			0.0213639	−	0.999772i	$-0.493199\pi$
$331$	1.61388e40			0.0427278			0.0213639	+	0.999772i	$0.493199\pi$
$332$		−	1.85155e41i		−	0.466399i
$333$		−	1.02682e42i		−	2.46131i
$334$	1.77554e41			0.405054
$335$	−8.38857e40	+	1.31559e41i	−0.182158	+	0.285681i
$336$	4.97474e41			1.02842
$337$			3.76927e41i			0.741931i	0.928647	+	0.370966i	$0.120973\pi$
$337$			3.76927e41i			0.741931i	−0.928647	+	0.370966i	$0.879027\pi$
$338$		−	2.12273e41i		−	0.397895i
$339$	−5.64804e41			−1.00833
$340$	−4.89705e39	+	7.68012e39i	−0.00832785	+	0.0130607i
$341$	−5.07847e41			−0.822784
$342$			7.25871e41i			1.12054i
$343$		−	7.14096e41i		−	1.05052i
$344$	1.45992e42			2.04698
$345$	−7.93335e41	−	5.05852e41i	−1.06033	−	0.676096i
$346$	−1.73686e42			−2.21314
$347$			5.20731e41i			0.632670i	0.948648	+	0.316335i	$0.102452\pi$
$347$			5.20731e41i			0.632670i	−0.948648	+	0.316335i	$0.897548\pi$
$348$		−	1.37098e42i		−	1.58845i
$349$	1.41921e42			1.56829			0.784146	−	0.620576i	$-0.213101\pi$
$349$	1.41921e42			1.56829			0.784146	+	0.620576i	$0.213101\pi$
$350$	−6.34244e41	−	1.36296e42i	−0.668549	−	1.43668i
$351$	2.62409e42			2.63883
$352$		−	2.09006e41i		−	0.200541i
$353$			4.94299e41i			0.452593i	0.974059	+	0.226296i	$0.0726618\pi$
$353$			4.94299e41i			0.452593i	−0.974059	+	0.226296i	$0.927338\pi$
$354$	3.23415e41			0.282623
$355$	8.23124e41	+	5.24847e41i	0.686590	+	0.437789i
$356$	1.78038e42			1.41772
$357$			1.95628e40i			0.0148732i
$358$			9.30382e41i			0.675447i
$359$	−2.23565e42			−1.55005			−0.775026	−	0.631930i	$-0.782263\pi$
$359$	−2.23565e42			−1.55005			−0.775026	+	0.631930i	$0.782263\pi$
$360$	−3.02887e42	+	4.75021e42i	−2.00581	+	3.14573i
$361$	−1.47722e42			−0.934495
$362$			3.47508e42i			2.10026i
$363$		−	2.66503e42i		−	1.53901i
$364$	−2.75324e42			−1.51940
$365$	−2.77521e41	+	4.35240e41i	−0.146374	+	0.229560i
$366$	5.25979e42			2.65174
$367$			2.99296e42i			1.44248i	0.692683	+	0.721242i	$0.256428\pi$
$367$			2.99296e42i			1.44248i	−0.692683	+	0.721242i	$0.743572\pi$
$368$		−	8.32640e41i		−	0.383679i
$369$	−2.25525e42			−0.993712
$370$	−3.20844e42	−	2.04579e42i	−1.35197	−	0.862050i
$371$	2.28545e42			0.921090
$372$		−	1.72790e43i		−	6.66131i
$373$		−	9.22162e41i		−	0.340104i	−0.985435	−	0.170052i	$-0.945606\pi$
$373$		−	9.22162e41i		−	0.340104i	0.985435	−	0.170052i	$-0.0543935\pi$
$374$	−1.73553e40			−0.00612423
$375$	5.56429e42	+	7.39284e41i	1.87886	+	0.249629i
$376$	−5.73563e42			−1.85345
$377$			1.27908e42i			0.395609i
$378$			1.61544e43i			4.78273i
$379$	−6.24555e42			−1.77021			−0.885103	−	0.465395i	$-0.845912\pi$
$379$	−6.24555e42			−1.77021			−0.885103	+	0.465395i	$0.845912\pi$
$380$	1.47286e42	+	9.39134e41i	0.399697	+	0.254858i
$381$	−9.29721e42			−2.41596
$382$		−	6.73792e42i		−	1.67680i
$383$		−	2.98883e42i		−	0.712396i	−0.934410	−	0.356198i	$-0.884073\pi$
$383$		−	2.98883e42i		−	0.712396i	0.934410	−	0.356198i	$-0.115927\pi$
$384$	1.52186e43			3.47465
$385$	1.00005e42	−	1.56839e42i	0.218736	−	0.343046i
$386$	1.04218e43			2.18399
$387$			1.83634e43i			3.68743i
$388$			7.31588e42i			1.40781i
$389$	6.88468e42			1.26974			0.634871	−	0.772618i	$-0.281053\pi$
$389$	6.88468e42			1.26974			0.634871	+	0.772618i	$0.281053\pi$
$390$	8.51120e42	−	1.33482e43i	1.50461	−	2.35971i
$391$	3.27429e40			0.00554882
$392$			1.05942e42i			0.172126i
$393$		−	8.80577e42i		−	1.37180i
$394$	−1.13363e43			−1.69350
$395$	3.61852e41	+	2.30727e41i	0.0518417	+	0.0330557i
$396$	−1.51511e43			−2.08197
$397$		−	4.83389e42i		−	0.637167i	−0.947895	−	0.318584i	$-0.896793\pi$
$397$		−	4.83389e42i		−	0.637167i	0.947895	−	0.318584i	$-0.103207\pi$
$398$		−	9.31119e42i		−	1.17743i
$399$	3.75166e42			0.455166
$400$	2.09575e42	+	4.50366e42i	0.243977	+	0.524295i
$401$	1.49185e43			1.66665			0.833324	−	0.552785i	$-0.186435\pi$
$401$	1.49185e43			1.66665			0.833324	+	0.552785i	$0.186435\pi$
$402$		−	1.01151e43i		−	1.08453i
$403$			1.61207e43i			1.65902i
$404$	−1.05362e43			−1.04086
$405$	−2.78116e43	−	1.77335e43i	−2.63766	−	1.68184i
$406$	−7.87427e42			−0.717020
$407$		−	4.70828e42i		−	0.411675i
$408$		−	2.71678e41i		−	0.0228119i
$409$	1.29234e43			1.04218			0.521090	−	0.853502i	$-0.325526\pi$
$409$	1.29234e43			1.04218			0.521090	+	0.853502i	$0.325526\pi$
$410$	−4.49325e42	+	7.04682e42i	−0.348038	+	0.545833i
$411$	−2.43705e43			−1.81332
$412$			2.88210e43i			2.06018i
$413$		−	1.20626e42i		−	0.0828450i
$414$	4.40175e43			2.90482
$415$	2.13483e42	−	3.34809e42i	0.135385	−	0.212326i
$416$	−6.63451e42			−0.404361
$417$			5.83673e43i			3.41920i
$418$			3.32833e42i			0.187421i
$419$	−1.85171e43			−1.00240			−0.501201	−	0.865331i	$-0.667108\pi$
$419$	−1.85171e43			−1.00240			−0.501201	+	0.865331i	$0.667108\pi$
$420$	5.33629e43	+	3.40256e43i	2.77732	+	1.77090i
$421$	4.22507e41			0.0211436			0.0105718	−	0.999944i	$-0.496635\pi$
$421$	4.22507e41			0.0211436			0.0105718	+	0.999944i	$0.496635\pi$
$422$		−	3.77083e43i		−	1.81460i
$423$		−	7.21452e43i		−	3.33881i
$424$	−3.17392e43			−1.41273
$425$	−1.77103e41	+	8.24136e40i	−0.00758243	+	0.00352843i
$426$	−6.32872e43			−2.60650
$427$		−	1.96178e43i		−	0.777302i
$428$			3.65324e43i			1.39270i
$429$	1.95881e43			0.718533
$430$	5.73789e43	+	3.65863e43i	2.02545	+	1.29149i
$431$	3.47380e43			1.18013			0.590064	−	0.807356i	$-0.299102\pi$
$431$	3.47380e43			1.18013			0.590064	+	0.807356i	$0.299102\pi$
$432$		−	5.33794e43i		−	1.74539i
$433$		−	1.07193e43i		−	0.337379i	−0.985669	−	0.168689i	$-0.946047\pi$
$433$		−	1.07193e43i		−	0.337379i	0.985669	−	0.168689i	$-0.0539534\pi$
$434$	−9.92423e43			−3.00688
$435$	1.58074e43	−	2.47909e43i	0.461091	−	0.723136i
$436$	−9.28144e42			−0.260668
$437$		−	6.27928e42i		−	0.169811i
$438$		−	3.34641e43i		−	0.871478i
$439$	4.72835e43			1.18589			0.592946	−	0.805242i	$-0.297965\pi$
$439$	4.72835e43			1.18589			0.592946	+	0.805242i	$0.297965\pi$
$440$	−1.38882e43	+	2.17811e43i	−0.335488	+	0.526150i
$441$	−1.33258e43			−0.310067
$442$			5.50915e41i			0.0123486i
$443$		−	3.61016e42i		−	0.0779587i	−0.999240	−	0.0389794i	$-0.987589\pi$
$443$		−	3.61016e42i		−	0.0779587i	0.999240	−	0.0389794i	$-0.0124107\pi$
$444$	1.60194e44			3.33294
$445$	3.21940e43	+	2.05278e43i	0.645408	+	0.411530i
$446$	1.17214e44			2.26440
$447$		−	5.59362e42i		−	0.104140i
$448$		−	7.10823e43i		−	1.27548i
$449$	−3.66734e43			−0.634288			−0.317144	−	0.948377i	$-0.602724\pi$
$449$	−3.66734e43			−0.634288			−0.317144	+	0.948377i	$0.602724\pi$
$450$	−2.38086e44	+	1.10792e44i	−3.96942	+	1.84714i
$451$	−1.03410e43			−0.166207
$452$		−	6.35868e43i		−	0.985332i
$453$			2.36510e44i			3.53369i
$454$	−8.86991e43			−1.27790
$455$	−4.97858e43	−	3.17448e43i	−0.691699	−	0.441047i
$456$	−5.21012e43			−0.698116
$457$			1.34942e44i			1.74393i	0.489570	+	0.871964i	$0.337154\pi$
$457$			1.34942e44i			1.74393i	−0.489570	+	0.871964i	$0.662846\pi$
$458$		−	2.04058e44i		−	2.54375i
$459$	2.09910e42			0.0252420
$460$	5.69499e43	−	8.93153e43i	0.660676	−	1.03615i
$461$	1.20751e44			1.35153			0.675765	−	0.737117i	$-0.263813\pi$
$461$	1.20751e44			1.35153			0.675765	+	0.737117i	$0.263813\pi$
$462$			1.20588e44i			1.30230i
$463$			2.45252e42i			0.0255580i	0.999918	+	0.0127790i	$0.00406779\pi$
$463$			2.45252e42i			0.0255580i	−0.999918	+	0.0127790i	$0.995932\pi$
$464$	2.60192e43			0.261666
$465$	1.99226e44	−	3.12449e44i	1.93362	−	3.03253i
$466$	−1.27247e44			−1.19201
$467$			4.50228e43i			0.407103i	0.979064	+	0.203552i	$0.0652484\pi$
$467$			4.50228e43i			0.407103i	−0.979064	+	0.203552i	$0.934752\pi$
$468$			4.80945e44i			4.19796i
$469$	−3.77270e43			−0.317907
$470$	−2.25427e44	−	1.43738e44i	−1.83396	−	1.16939i
$471$	−7.65173e43			−0.601056
$472$			1.67520e43i			0.127064i
$473$			8.42016e43i			0.616753i
$474$	−2.78216e43			−0.196806
$475$	1.58049e43	+	3.39640e43i	0.107981	+	0.232046i
$476$	−2.20242e42			−0.0145340
$477$		−	3.99229e44i		−	2.54489i
$478$		−	3.44992e44i		−	2.12446i
$479$	−8.64474e43			−0.514300			−0.257150	−	0.966372i	$-0.582783\pi$
$479$	−8.64474e43			−0.514300			−0.257150	+	0.966372i	$0.582783\pi$
$480$	1.28589e44	+	8.19919e43i	0.739134	+	0.471292i
$481$	−1.49456e44			−0.830080
$482$			2.23424e44i			1.19909i
$483$		−	2.27504e44i		−	1.17994i
$484$	3.00035e44			1.50391
$485$	−8.43519e43	+	1.32290e44i	−0.408654	+	0.640898i
$486$	1.04982e45			4.91605
$487$			1.47488e44i			0.667619i	0.942641	+	0.333810i	$0.108334\pi$
$487$			1.47488e44i			0.667619i	−0.942641	+	0.333810i	$0.891666\pi$
$488$			2.72442e44i			1.19220i
$489$	−6.83278e44			−2.89069
$490$	−2.65495e43	+	4.16380e43i	−0.108598	+	0.170316i
$491$	2.58382e44			1.02192			0.510962	−	0.859603i	$-0.329289\pi$
$491$	2.58382e44			1.02192			0.510962	+	0.859603i	$0.329289\pi$
$492$		−	3.51841e44i		−	1.34562i
$493$			1.02318e42i			0.00378424i
$494$	1.05652e44			0.377905
$495$	−2.73971e44	−	1.74692e44i	−0.947806	−	0.604347i
$496$	3.27929e44			1.09732
$497$			2.36046e44i			0.764041i
$498$			2.57423e44i			0.806051i
$499$	5.38007e44			1.62978			0.814891	−	0.579615i	$-0.196797\pi$
$499$	5.38007e44			1.62978			0.814891	+	0.579615i	$0.196797\pi$
$500$	−8.32301e43	+	6.26440e44i	−0.243936	+	1.83601i
$501$	−1.60304e44			−0.454592
$502$		−	9.89536e44i		−	2.71532i
$503$			3.84969e44i			1.02224i	0.859509	+	0.511121i	$0.170770\pi$
$503$			3.84969e44i			1.02224i	−0.859509	+	0.511121i	$0.829230\pi$
$504$	−1.36221e45			−3.50059
$505$	−1.90522e44	−	1.21482e44i	−0.473847	−	0.302138i
$506$	2.01833e44			0.485856
$507$			1.91650e44i			0.446557i
$508$		−	1.04670e45i		−	2.36086i
$509$	−2.11704e44			−0.462259			−0.231129	−	0.972923i	$-0.574242\pi$
$509$	−2.11704e44			−0.462259			−0.231129	+	0.972923i	$0.574242\pi$
$510$	6.80841e42	−	1.06777e43i	0.0143926	−	0.0225720i
$511$	−1.24813e44			−0.255456
$512$			5.54903e44i			1.09967i
$513$		−	4.02556e44i		−	0.772485i
$514$	8.52760e44			1.58466
$515$	−3.32306e44	+	5.21160e44i	−0.598024	+	0.937889i
$516$	−2.86487e45			−4.99327
$517$		−	3.30806e44i		−	0.558444i
$518$		−	9.20080e44i		−	1.50447i
$519$	1.56812e45			2.48381
$520$	6.91401e44	+	4.40856e44i	1.06090	+	0.676460i
$521$	8.12304e43			0.120753			0.0603763	−	0.998176i	$-0.480770\pi$
$521$	8.12304e43			0.120753			0.0603763	+	0.998176i	$0.480770\pi$
$522$			1.37550e45i			1.98106i
$523$			8.25930e44i			1.15257i	0.817250	+	0.576283i	$0.195497\pi$
$523$			8.25930e44i			1.15257i	−0.817250	+	0.576283i	$0.804503\pi$
$524$	9.91372e44			1.34051
$525$	5.72625e44	+	1.23054e45i	0.750312	+	1.61238i
$526$	1.10253e45			1.39999
$527$			1.28955e43i			0.0158695i
$528$		−	3.98463e44i		−	0.475256i
$529$	4.84224e44			0.559794
$530$	−1.24744e45	−	7.95403e44i	−1.39787	−	0.891324i
$531$	−2.10714e44			−0.228894
$532$			4.22369e44i			0.444785i
$533$			3.28256e44i			0.335130i
$534$	−2.47528e45			−2.45016
$535$	−4.21217e44	+	6.60601e44i	−0.404267	+	0.634018i
$536$	5.23935e44			0.487594
$537$		−	8.39992e44i		−	0.758053i
$538$			8.17036e44i			0.715045i
$539$	−6.11024e43			−0.0518614
$540$	3.65098e45	−	5.72588e45i	3.00547	−	4.71352i
$541$	−8.08801e44			−0.645784			−0.322892	−	0.946436i	$-0.604655\pi$
$541$	−8.08801e44			−0.645784			−0.322892	+	0.946436i	$0.604655\pi$
$542$			8.95226e44i			0.693337i
$543$		−	3.13747e45i		−	2.35712i
$544$	−5.30719e42			−0.00386796
$545$	−1.67833e44	−	1.07015e44i	−0.118668	−	0.0756661i
$546$	3.82786e45			2.62589
$547$			4.17809e43i			0.0278091i	0.999903	+	0.0139045i	$0.00442610\pi$
$547$			4.17809e43i			0.0278091i	−0.999903	+	0.0139045i	$0.995574\pi$
$548$		−	2.74368e45i		−	1.77196i
$549$	−3.42689e45			−2.14762
$550$	−1.09169e45	+	5.08011e44i	−0.663920	+	0.308950i
$551$	1.96221e44			0.115810
$552$			3.15946e45i			1.80975i
$553$			1.03768e44i			0.0576897i
$554$	−1.31944e45			−0.711997
$555$	2.89673e45	+	1.84703e45i	1.51731	+	0.967478i
$556$	−6.57111e45			−3.34122
$557$		−	2.87824e45i		−	1.42074i	−0.703826	−	0.710372i	$-0.748527\pi$
$557$		−	2.87824e45i		−	1.42074i	0.703826	−	0.710372i	$-0.251473\pi$
$558$			1.73359e46i			8.30775i
$559$	2.67283e45			1.24359
$560$	−6.45755e44	+	1.01275e45i	−0.291719	+	0.457508i
$561$	1.56692e43			0.00687322
$562$		−	2.16663e45i		−	0.922860i
$563$		−	2.38488e45i		−	0.986458i	−0.869899	−	0.493229i	$-0.835816\pi$
$563$		−	2.38488e45i		−	0.986458i	0.869899	−	0.493229i	$-0.164184\pi$
$564$	1.12553e46			4.52119
$565$	7.33153e44	−	1.14981e45i	0.286019	−	0.448568i
$566$	−7.25206e45			−2.74783
$567$		−	7.97551e45i		−	2.93520i
$568$		−	3.27810e45i		−	1.17186i
$569$	−1.87090e44			−0.0649676			−0.0324838	−	0.999472i	$-0.510342\pi$
$569$	−1.87090e44			−0.0649676			−0.0324838	+	0.999472i	$0.510342\pi$
$570$	−2.04772e45	−	1.30569e45i	−0.690775	−	0.440457i
$571$	2.83029e45			0.927546			0.463773	−	0.885954i	$-0.346495\pi$
$571$	2.83029e45			0.927546			0.463773	+	0.885954i	$0.346495\pi$
$572$			2.20527e45i			0.702145i
$573$			6.08331e45i			1.88187i
$574$	−2.02081e45			−0.607406
$575$	2.05960e45	−	9.58422e44i	0.601540	−	0.279922i
$576$	−1.24169e46			−3.52404
$577$			6.24900e45i			1.72349i	0.507339	+	0.861746i	$0.330629\pi$
$577$			6.24900e45i			1.72349i	−0.507339	+	0.861746i	$0.669371\pi$
$578$		−	6.30035e45i		−	1.68871i
$579$	−9.40925e45			−2.45109
$580$	2.79101e45	+	1.77963e45i	0.706643	+	0.450575i
$581$	9.60127e44			0.236277
$582$		−	1.01713e46i		−	2.43304i
$583$		−	1.83058e45i		−	0.425655i
$584$	1.73335e45			0.391808
$585$	−5.54528e45	+	8.69673e45i	−1.21857	+	1.91110i
$586$	1.47688e46			3.15526
$587$		−	1.52952e45i		−	0.317706i	−0.987302	−	0.158853i	$-0.949220\pi$
$587$		−	1.52952e45i		−	0.317706i	0.987302	−	0.158853i	$-0.0507796\pi$
$588$		−	2.07895e45i		−	0.419872i
$589$	2.47305e45			0.485657
$590$	−4.19815e44	+	6.58402e44i	−0.0801678	+	0.125728i
$591$	1.02350e46			1.90061
$592$			3.04025e45i			0.549036i
$593$		−	5.06259e45i		−	0.889141i	−0.895744	−	0.444570i	$-0.853356\pi$
$593$		−	5.06259e45i		−	0.889141i	0.895744	−	0.444570i	$-0.146644\pi$
$594$	1.29392e46			2.21020
$595$	−3.98254e43	−	2.53938e43i	−0.00661653	−	0.00421888i
$596$	6.29742e44			0.101765
$597$			8.40658e45i			1.32143i
$598$		−	6.40682e45i		−	0.979654i
$599$	−2.62885e44			−0.0391042			−0.0195521	−	0.999809i	$-0.506224\pi$
$599$	−2.62885e44			−0.0391042			−0.0195521	+	0.999809i	$0.506224\pi$
$600$	−7.95234e45	−	1.70892e46i	−1.15080	−	2.47301i
$601$	1.71200e45			0.241032			0.120516	−	0.992711i	$-0.461545\pi$
$601$	1.71200e45			0.241032			0.120516	+	0.992711i	$0.461545\pi$
$602$			1.64545e46i			2.25394i
$603$			6.59027e45i			0.878350i
$604$	−2.66268e46			−3.45310
$605$	5.42541e45	+	3.45939e45i	0.684650	+	0.436552i
$606$	1.46486e46			1.79886
$607$		−	6.29823e45i		−	0.752671i	−0.926483	−	0.376336i	$-0.877184\pi$
$607$		−	6.29823e45i		−	0.752671i	0.926483	−	0.376336i	$-0.122816\pi$
$608$			1.01779e45i			0.118372i
$609$	7.10926e45			0.804710
$610$	−6.82756e45	+	1.07078e46i	−0.752182	+	1.17966i
$611$	−1.05009e46			−1.12602
$612$			3.84725e44i			0.0401561i
$613$		−	6.75361e45i		−	0.686180i	−0.939302	−	0.343090i	$-0.888526\pi$
$613$		−	6.75361e45i		−	0.686180i	0.939302	−	0.343090i	$-0.111474\pi$
$614$	9.96197e44			0.0985297
$615$	4.05671e45	−	6.36220e45i	0.390602	−	0.612587i
$616$	−6.24613e45			−0.585503
$617$		−	7.99039e45i		−	0.729227i	−0.931159	−	0.364614i	$-0.881201\pi$
$617$		−	7.99039e45i		−	0.729227i	0.931159	−	0.364614i	$-0.118799\pi$
$618$		−	4.00701e46i		−	3.56050i
$619$	−1.33095e46			−1.15151			−0.575754	−	0.817623i	$-0.695291\pi$
$619$	−1.33095e46			−1.15151			−0.575754	+	0.817623i	$0.695291\pi$
$620$	3.51761e46	+	2.24293e46i	2.96337	+	1.88952i
$621$	−2.44113e46			−2.00254
$622$			3.69870e46i			2.95467i
$623$			9.23223e45i			0.718214i
$624$	−1.26485e46			−0.958281
$625$	−8.72784e45	+	1.03680e46i	−0.644001	+	0.765025i
$626$	2.56981e46			1.84682
$627$		−	3.00497e45i		−	0.210342i
$628$		−	8.61448e45i		−	0.587347i
$629$	−1.19555e44			−0.00794023
$630$	−5.35388e46	−	3.41378e46i	−3.46377	−	2.20860i
$631$	−8.15430e45			−0.513928			−0.256964	−	0.966421i	$-0.582722\pi$
$631$	−8.15430e45			−0.513928			−0.256964	+	0.966421i	$0.582722\pi$
$632$		−	1.44108e45i		−	0.0884823i
$633$			3.40448e46i			2.03652i
$634$	−8.91784e45			−0.519741
$635$	1.20684e46	−	1.89270e46i	0.685304	−	1.07477i
$636$	6.22835e46			3.44612
$637$			1.93959e45i			0.104570i
$638$			6.30707e45i			0.331349i
$639$	4.12333e46			2.11098
$640$	−1.97548e46	+	3.09818e46i	−0.985607	+	1.54574i
$641$	−3.31956e46			−1.61407			−0.807036	−	0.590502i	$-0.798930\pi$
$641$	−3.31956e46			−1.61407			−0.807036	+	0.590502i	$0.798930\pi$
$642$		−	5.07913e46i		−	2.40692i
$643$			1.19701e46i			0.552860i	0.961034	+	0.276430i	$0.0891514\pi$
$643$			1.19701e46i			0.552860i	−0.961034	+	0.276430i	$0.910849\pi$
$644$	2.56128e46			1.15303
$645$	−5.18043e46	−	3.30319e46i	−2.27316	−	1.44943i
$646$	8.45147e43			0.00361489
$647$		−	1.55116e46i		−	0.646749i	−0.946271	−	0.323374i	$-0.895183\pi$
$647$		−	1.55116e46i		−	0.646749i	0.946271	−	0.323374i	$-0.104817\pi$
$648$			1.10760e47i			4.50190i
$649$	−9.66183e44			−0.0382844
$650$	1.61259e46	+	3.46538e46i	0.622951	+	1.33869i
$651$	8.96006e46			3.37462
$652$		−	7.69248e46i		−	2.82476i
$653$		−	1.78651e46i		−	0.639643i	−0.947478	−	0.319821i	$-0.896377\pi$
$653$		−	1.78651e46i		−	0.639643i	0.947478	−	0.319821i	$-0.103623\pi$
$654$	1.29041e46			0.450499
$655$	1.79266e46	+	1.14305e46i	0.610262	+	0.389120i
$656$	6.67741e45			0.221664
$657$			2.18028e46i			0.705803i
$658$		−	6.46453e46i		−	2.04084i
$659$	−2.58870e46			−0.797024			−0.398512	−	0.917163i	$-0.630473\pi$
$659$	−2.58870e46			−0.797024			−0.398512	+	0.917163i	$0.630473\pi$
$660$	2.72535e46	−	4.27421e46i	0.818367	−	1.28346i
$661$	3.44323e45			0.100842			0.0504211	−	0.998728i	$-0.483944\pi$
$661$	3.44323e45			0.100842			0.0504211	+	0.998728i	$0.483944\pi$
$662$		−	2.52611e45i		−	0.0721599i
$663$		−	4.97391e44i		−	0.0138588i
$664$	−1.33338e46			−0.362393
$665$	−4.86990e45	+	7.63753e45i	−0.129111	+	0.202486i
$666$	−1.60722e47			−4.15673
$667$		−	1.18990e46i		−	0.300217i
$668$		−	1.80473e46i		−	0.444224i
$669$	−1.05826e47			−2.54134
$670$	2.05921e46	+	1.31301e46i	0.482466	+	0.307634i
$671$	−1.57133e46			−0.359207
$672$			3.68753e46i			0.822513i
$673$			4.91861e46i			1.07052i	0.844688	+	0.535259i	$0.179786\pi$
$673$			4.91861e46i			1.07052i	−0.844688	+	0.535259i	$0.820214\pi$
$674$	5.89980e46			1.25299
$675$	1.32038e47	−	6.14432e46i	2.73645	−	1.27339i
$676$	−2.15763e46			−0.436372
$677$		−	1.43105e46i		−	0.282450i	−0.989978	−	0.141225i	$-0.954896\pi$
$677$		−	1.43105e46i		−	0.282450i	0.989978	−	0.141225i	$-0.0451041\pi$
$678$			8.84052e46i			1.70290i
$679$	−3.79367e46			−0.713195
$680$	5.53077e44	+	3.52657e44i	0.0101482	+	0.00647076i
$681$	8.00817e46			1.43419
$682$			7.94902e46i			1.38954i
$683$		−	4.72458e46i		−	0.806161i	−0.915165	−	0.403081i	$-0.867939\pi$
$683$		−	4.72458e46i		−	0.806161i	0.915165	−	0.403081i	$-0.132061\pi$
$684$	7.37807e46			1.22890
$685$	3.16346e46	−	4.96129e46i	0.514360	−	0.806678i
$686$	−1.11773e47			−1.77414
$687$			1.84233e47i			2.85484i
$688$		−	5.43709e46i		−	0.822541i
$689$	−5.81085e46			−0.858267
$690$	−7.91779e46	+	1.24176e47i	−1.14181	+	1.79072i
$691$	8.79095e46			1.23779			0.618896	−	0.785473i	$-0.287580\pi$
$691$	8.79095e46			1.23779			0.618896	+	0.785473i	$0.287580\pi$
$692$			1.76542e47i			2.42716i
$693$		−	7.85664e46i		−	1.05472i
$694$	8.15068e46			1.06847
$695$	−1.18823e47	−	7.57646e46i	−1.52107	−	0.969879i
$696$	−9.87300e46			−1.23423
$697$			2.62584e44i			0.00320573i
$698$		−	2.22140e47i		−	2.64858i
$699$	1.14884e47			1.33779
$700$	−1.38537e47	+	6.44673e46i	−1.57561	+	0.733199i
$701$	−8.85277e46			−0.983404			−0.491702	−	0.870763i	$-0.663625\pi$
$701$	−8.85277e46			−0.983404			−0.491702	+	0.870763i	$0.663625\pi$
$702$		−	4.10732e47i		−	4.45653i
$703$			2.29277e46i			0.242996i
$704$	−5.69349e46			−0.589426
$705$	2.03526e47	+	1.29774e47i	2.05825	+	1.31240i
$706$	7.73696e46			0.764351
$707$		−	5.46358e46i		−	0.527299i
$708$		−	3.28734e46i		−	0.309953i
$709$	1.72675e46			0.159062			0.0795310	−	0.996832i	$-0.474658\pi$
$709$	1.72675e46			0.159062			0.0795310	+	0.996832i	$0.474658\pi$
$710$	8.21510e46	−	1.28839e47i	0.739350	−	1.15953i
$711$	1.81265e46			0.159392
$712$		−	1.28213e47i		−	1.10157i
$713$		−	1.49968e47i		−	1.25898i
$714$	3.06204e45			0.0251183
$715$	−2.54267e46	+	3.98770e46i	−0.203817	+	0.319648i
$716$	9.45681e46			0.740764
$717$			3.11475e47i			2.38428i
$718$			3.49933e47i			2.61777i
$719$	9.89920e46			0.723725			0.361862	−	0.932232i	$-0.382141\pi$
$719$	9.89920e46			0.723725			0.361862	+	0.932232i	$0.382141\pi$
$720$	1.76910e47	+	1.12802e47i	1.26405	+	0.805995i
$721$	−1.49452e47			−1.04369
$722$			2.31220e47i			1.57820i
$723$		−	2.01718e47i		−	1.34574i
$724$	3.53222e47			2.30336
$725$	2.99498e46	+	6.43606e46i	0.190904	+	0.410245i
$726$	−4.17141e47			−2.59913
$727$			1.89327e46i			0.115318i	0.998336	+	0.0576588i	$0.0183635\pi$
$727$			1.89327e46i			0.115318i	−0.998336	+	0.0576588i	$0.981636\pi$
$728$			1.98272e47i			1.18058i
$729$	−4.10420e47			−2.38905
$730$	6.81255e46	+	4.34387e46i	0.387688	+	0.247201i
$731$	2.13809e45			0.0118957
$732$		−	5.34628e47i		−	2.90816i
$733$		−	1.41763e47i		−	0.753957i	−0.926222	−	0.376979i	$-0.876963\pi$
$733$		−	1.41763e47i		−	0.753957i	0.926222	−	0.376979i	$-0.123037\pi$
$734$	4.68469e47			2.43611
$735$	2.39702e46	−	3.75927e46i	0.121879	−	0.191145i
$736$	6.17195e46			0.306859
$737$			3.02183e46i			0.146912i
$738$			3.53001e47i			1.67821i
$739$	8.34826e46			0.388117			0.194058	−	0.980990i	$-0.437835\pi$
$739$	8.34826e46			0.388117			0.194058	+	0.980990i	$0.437835\pi$
$740$	−2.07943e47	+	3.26120e47i	−0.945412	+	1.48270i
$741$	−9.53874e46			−0.424122
$742$		−	3.57727e47i		−	1.55556i
$743$		−	2.83798e47i		−	1.20696i	−0.797377	−	0.603482i	$-0.793780\pi$
$743$		−	2.83798e47i		−	1.20696i	0.797377	−	0.603482i	$-0.206220\pi$
$744$	−1.24433e48			−5.17585
$745$	1.13874e46	+	7.26090e45i	0.0463281	+	0.0295401i
$746$	−1.44340e47			−0.574377
$747$		−	1.67718e47i		−	0.652814i
$748$			1.76407e45i			0.00671646i
$749$	−1.89440e47			−0.705539
$750$	1.15716e47	−	8.70944e47i	0.421581	−	3.17307i
$751$	1.17772e47			0.419744			0.209872	−	0.977729i	$-0.432695\pi$
$751$	1.17772e47			0.419744			0.209872	+	0.977729i	$0.432695\pi$
$752$			2.13609e47i			0.744776i
$753$			8.93400e47i			3.04740i
$754$	2.00207e47			0.668115
$755$	−4.81481e47	−	3.07006e47i	−1.57201	−	1.00236i
$756$	1.64200e48			5.24523
$757$		−	3.05444e47i		−	0.954662i	−0.878723	−	0.477331i	$-0.841604\pi$
$757$		−	3.05444e47i		−	0.954662i	0.878723	−	0.477331i	$-0.158396\pi$
$758$			9.77578e47i			2.98957i
$759$	−1.82224e47			−0.545276
$760$	6.76309e46	−	1.06066e47i	0.198025	−	0.310566i
$761$	6.05608e47			1.73518			0.867591	−	0.497279i	$-0.165667\pi$
$761$	6.05608e47			1.73518			0.867591	+	0.497279i	$0.165667\pi$
$762$			1.45523e48i			4.08015i
$763$		−	4.81291e46i		−	0.132055i
$764$	−6.84872e47			−1.83895
$765$	−4.43587e45	+	6.95683e45i	−0.0116564	+	0.0182809i
$766$	−4.67823e47			−1.20311
$767$			3.06698e46i			0.0771946i
$768$		−	1.33618e48i		−	3.29159i
$769$	1.20494e47			0.290523			0.145261	−	0.989393i	$-0.453598\pi$
$769$	1.20494e47			0.290523			0.145261	+	0.989393i	$0.453598\pi$
$770$	−2.45490e47	−	1.56532e47i	−0.579346	−	0.369407i
$771$	−7.69912e47			−1.77846
$772$		−	1.05931e48i		−	2.39518i
$773$			7.97009e46i			0.176401i	0.996103	+	0.0882006i	$0.0281117\pi$
$773$			7.97009e46i			0.176401i	−0.996103	+	0.0882006i	$0.971888\pi$
$774$	2.87432e48			6.22743
$775$	3.77467e47	+	8.11159e47i	0.800574	+	1.72039i
$776$	5.26847e47			1.09387
$777$			8.30692e47i			1.68847i
$778$		−	1.07762e48i		−	2.14438i
$779$	5.03571e46			0.0981053
$780$	−1.35677e48	−	8.65116e47i	−2.58789	−	1.65011i
$781$	1.89066e47			0.353079
$782$		−	5.12504e45i		−	0.00937100i
$783$		−	7.62830e47i		−	1.36571i
$784$	3.94553e46			0.0691655
$785$	9.93246e46	−	1.55772e47i	0.170493	−	0.267387i
$786$	−1.37831e48			−2.31673
$787$			3.17048e47i			0.521846i	0.965360	+	0.260923i	$0.0840269\pi$
$787$			3.17048e47i			0.521846i	−0.965360	+	0.260923i	$0.915973\pi$
$788$			1.15227e48i			1.85726i
$789$	−9.95413e47			−1.57120
$790$	3.61143e46	−	5.66385e46i	0.0558254	−	0.0875517i
$791$	3.29731e47			0.499169
$792$			1.09109e48i			1.61769i
$793$			4.98790e47i			0.724286i
$794$	−7.56619e47			−1.07607
$795$	1.12625e48	+	7.18127e47i	1.56883	+	1.00033i
$796$	−9.46430e47			−1.29129
$797$		−	9.38509e47i		−	1.25423i	−0.778928	−	0.627113i	$-0.784236\pi$
$797$		−	9.38509e47i		−	1.25423i	0.778928	−	0.627113i	$-0.215764\pi$
$798$		−	5.87223e47i		−	0.768698i
$799$	−8.40001e45			−0.0107710
$800$	−3.33834e47	+	1.55347e47i	−0.419321	+	0.195128i
$801$	1.61271e48			1.98436
$802$		−	2.33510e48i		−	2.81468i
$803$			9.99719e46i			0.118052i
$804$	−1.02814e48			−1.18940
$805$	4.63147e47	+	2.95315e47i	0.524912	+	0.334698i
$806$	2.52328e48			2.80180
$807$		−	7.37658e47i		−	0.802494i
$808$			7.58756e47i			0.808751i
$809$	−8.66728e47			−0.905174			−0.452587	−	0.891720i	$-0.649499\pi$
$809$	−8.66728e47			−0.905174			−0.452587	+	0.891720i	$0.649499\pi$
$810$	−2.77571e48	+	4.35318e48i	−2.84034	+	4.45455i
$811$	6.53424e47			0.655166			0.327583	−	0.944822i	$-0.393766\pi$
$811$	6.53424e47			0.655166			0.327583	+	0.944822i	$0.393766\pi$
$812$			8.00376e47i			0.786356i
$813$		−	8.08252e47i		−	0.778131i
$814$	−7.36958e47			−0.695249
$815$	8.86941e47	−	1.39100e48i	0.819963	−	1.28596i
$816$	−1.01180e46			−0.00916655
$817$		−	4.10033e47i		−	0.364045i
$818$		−	2.02282e48i		−	1.76006i
$819$	−2.49395e48			−2.12669
$820$	7.16270e47	+	4.56713e47i	0.598616	+	0.381694i
$821$	−2.16299e48			−1.77171			−0.885854	−	0.463964i	$-0.846427\pi$
$821$	−2.16299e48			−1.77171			−0.885854	+	0.463964i	$0.846427\pi$
$822$			3.81456e48i			3.06239i
$823$			2.29757e48i			1.80789i	0.427652	+	0.903943i	$0.359341\pi$
$823$			2.29757e48i			1.80789i	−0.427652	+	0.903943i	$0.640659\pi$
$824$	2.07552e48			1.60077
$825$	9.85630e47	−	4.58656e47i	0.745116	−	0.346735i
$826$	−1.88809e47			−0.139911
$827$			5.54431e47i			0.402723i	0.979517	+	0.201361i	$0.0645366\pi$
$827$			5.54431e47i			0.402723i	−0.979517	+	0.201361i	$0.935463\pi$
$828$		−	4.47413e48i		−	3.18572i
$829$	−1.01376e48			−0.707595			−0.353798	−	0.935322i	$-0.615110\pi$
$829$	−1.01376e48			−0.707595			−0.353798	+	0.935322i	$0.615110\pi$
$830$	−5.24055e47	−	3.34152e47i	−0.358582	−	0.228642i
$831$	1.19125e48			0.799073
$832$			1.80730e48i			1.18849i
$833$			1.55155e45i			0.00100028i
$834$	9.13587e48			5.77444
$835$	2.08085e47	−	3.26343e47i	0.128948	−	0.202231i
$836$	3.38306e47			0.205544
$837$		−	9.61422e48i		−	5.72722i
$838$			2.89837e48i			1.69289i
$839$	−2.04969e48			−1.17386			−0.586930	−	0.809638i	$-0.699664\pi$
$839$	−2.04969e48			−1.17386			−0.586930	+	0.809638i	$0.699664\pi$
$840$	2.45032e48	−	3.84288e48i	1.37599	−	2.15798i
$841$	−1.44424e48			−0.795255
$842$		−	6.61323e46i		−	0.0357079i
$843$			1.95614e48i			1.03572i
$844$	−3.83283e48			−1.99007
$845$	−3.90156e47	−	2.48774e47i	−0.198657	−	0.126669i
$846$	−1.12924e49			−5.63867
$847$			1.55584e48i			0.761882i
$848$			1.18205e48i			0.567680i
$849$	6.54750e48			3.08389
$850$	1.28997e46	+	2.77208e46i	0.00595891	+	0.0128054i
$851$	1.39036e48			0.629925
$852$			6.43278e48i			2.85855i
$853$		−	4.38159e47i		−	0.190973i	−0.995431	−	0.0954867i	$-0.969559\pi$
$853$		−	4.38159e47i		−	0.190973i	0.995431	−	0.0954867i	$-0.0304407\pi$
$854$	−3.07065e48			−1.31273
$855$	1.33415e48	+	8.50689e47i	0.559452	+	0.356722i
$856$	2.63085e48			1.08213
$857$			2.70397e48i			1.09098i	0.838116	+	0.545492i	$0.183657\pi$
$857$			2.70397e48i			1.09098i	−0.838116	+	0.545492i	$0.816343\pi$
$858$		−	3.06600e48i		−	1.21348i
$859$	1.02774e48			0.399023			0.199511	−	0.979896i	$-0.436065\pi$
$859$	1.02774e48			0.399023			0.199511	+	0.979896i	$0.436065\pi$
$860$	3.71880e48	−	5.83224e48i	1.41637	−	2.22132i
$861$	1.82448e48			0.681690
$862$		−	5.43732e48i		−	1.99303i
$863$			4.88051e47i			0.175504i	0.996142	+	0.0877520i	$0.0279683\pi$
$863$			4.88051e47i			0.175504i	−0.996142	+	0.0877520i	$0.972032\pi$
$864$	3.95675e48			1.39593
$865$	−2.03552e48	+	3.19234e48i	−0.704548	+	1.10495i
$866$	−1.67783e48			−0.569774
$867$			5.68825e48i			1.89524i
$868$			1.00874e49i			3.29765i
$869$	8.31152e46			0.0266596
$870$	−3.88037e48	−	2.47423e48i	−1.22125	−	0.778704i
$871$	9.59225e47			0.296225
$872$			6.68395e47i			0.202540i
$873$			6.62690e48i			1.97049i
$874$	−9.82856e47			−0.286782
$875$	−3.24842e48	−	4.31592e47i	−0.930120	−	0.123578i
$876$	−3.40144e48			−0.955752
$877$		−	6.43951e48i		−	1.77566i	−0.460172	−	0.887830i	$-0.652212\pi$
$877$		−	6.43951e48i		−	1.77566i	0.460172	−	0.887830i	$-0.347788\pi$
$878$		−	7.40099e48i		−	2.00277i
$879$	−1.33340e49			−3.54115
$880$	8.11181e47	+	5.17231e47i	0.211424	+	0.134810i
$881$	5.01387e48			1.28254			0.641269	−	0.767316i	$-0.278408\pi$
$881$	5.01387e48			1.28254			0.641269	+	0.767316i	$0.278408\pi$
$882$			2.08580e48i			0.523650i
$883$			2.49431e48i			0.614608i	0.951611	+	0.307304i	$0.0994268\pi$
$883$			2.49431e48i			0.614608i	−0.951611	+	0.307304i	$0.900573\pi$
$884$	5.59974e46			0.0135427
$885$	3.79029e47	−	5.94436e47i	0.0899721	−	0.141105i
$886$	−5.65076e47			−0.131659
$887$		−	1.33184e48i		−	0.304587i	−0.988335	−	0.152293i	$-0.951334\pi$
$887$		−	1.33184e48i		−	0.304587i	0.988335	−	0.152293i	$-0.0486659\pi$
$888$		−	1.15362e49i		−	2.58971i
$889$	5.42769e48			1.19601
$890$	3.21309e48	−	5.03913e48i	0.695004	−	1.08998i
$891$	−6.38815e48			−1.35642
$892$		−	1.19141e49i		−	2.48337i
$893$			1.61091e48i			0.329627i
$894$	−8.75535e47			−0.175875
$895$	1.71004e48	+	1.09037e48i	0.337229	+	0.215027i
$896$	−8.88460e48			−1.72011
$897$			5.78437e48i			1.09946i
$898$			5.74026e48i			1.07120i
$899$	4.68634e48			0.858616
$900$	1.12613e49	+	2.42001e49i	2.02576	+	4.35327i
$901$	−4.64831e46			−0.00820986
$902$			1.61861e48i			0.280695i
$903$		−	1.48559e49i		−	2.52959i
$904$	−4.57914e48			−0.765606
$905$	6.38718e48	+	4.07264e48i	1.04859	+	0.668613i
$906$	3.70194e49			5.96780
$907$		−	8.30771e48i		−	1.31511i	−0.753408	−	0.657554i	$-0.771591\pi$
$907$		−	8.30771e48i		−	1.31511i	0.753408	−	0.657554i	$-0.228409\pi$
$908$			9.01577e48i			1.40148i
$909$	−9.54396e48			−1.45688
$910$	−4.96881e48	+	7.79266e48i	−0.744852	+	1.16816i
$911$	−8.81483e48			−1.29766			−0.648830	−	0.760934i	$-0.724741\pi$
$911$	−8.81483e48			−1.29766			−0.648830	+	0.760934i	$0.724741\pi$
$912$			1.94038e48i			0.280525i
$913$		−	7.69034e47i		−	0.109189i
$914$	2.11216e49			2.94519
$915$	6.16424e48	−	9.66746e48i	0.844173	−	1.32393i
$916$	−2.07414e49			−2.78973
$917$			5.14079e48i			0.679103i
$918$		−	3.28560e47i		−	0.0426295i
$919$	−6.75725e48			−0.861121			−0.430560	−	0.902562i	$-0.641684\pi$
$919$	−6.75725e48			−0.861121			−0.430560	+	0.902562i	$0.641684\pi$
$920$	−6.43196e48	−	4.10119e48i	−0.805089	−	0.513347i
$921$	−8.99413e47			−0.110580
$922$		−	1.89004e49i		−	2.28250i
$923$		−	6.00157e48i		−	0.711930i
$924$	1.22571e49			1.42824
$925$	−7.52030e48	+	3.49952e48i	−0.860789	+	0.400562i
$926$	3.83878e47			0.0431630
$927$			2.61068e49i			2.88362i
$928$			1.92867e48i			0.209275i
$929$	−1.55034e48			−0.165260			−0.0826301	−	0.996580i	$-0.526332\pi$
$929$	−1.55034e48			−0.165260			−0.0826301	+	0.996580i	$0.526332\pi$
$930$	−4.89057e49	−	3.11836e49i	−5.12142	−	3.26556i
$931$	2.97548e47			0.0306117
$932$			1.29339e49i			1.30728i
$933$		−	3.33936e49i		−	3.31602i
$934$	7.04714e48			0.687527
$935$	−2.03397e46	+	3.18990e46i	−0.00194963	+	0.00305764i
$936$	3.46348e49			3.26183
$937$		−	4.89952e48i		−	0.453368i	−0.973968	−	0.226684i	$-0.927212\pi$
$937$		−	4.89952e48i		−	0.453368i	0.973968	−	0.226684i	$-0.0727884\pi$
$938$			5.90518e48i			0.536891i
$939$	−2.32014e49			−2.07268
$940$	−1.46102e49	+	2.29133e49i	−1.28247	+	2.01131i
$941$	5.26418e48			0.454048			0.227024	−	0.973889i	$-0.427100\pi$
$941$	5.26418e48			0.454048			0.227024	+	0.973889i	$0.427100\pi$
$942$			1.19768e49i			1.01508i
$943$		−	3.05370e48i		−	0.254321i
$944$	6.23887e47			0.0510585
$945$	2.96917e49	+	1.89323e49i	2.38787	+	1.52257i
$946$	1.31796e49			1.04159
$947$			1.52352e49i			1.18324i	0.806216	+	0.591622i	$0.201512\pi$
$947$			1.52352e49i			1.18324i	−0.806216	+	0.591622i	$0.798488\pi$
$948$			2.82791e48i			0.215838i
$949$	3.17343e48			0.238033
$950$	5.31617e48	−	2.47384e48i	0.391886	−	0.182361i
$951$	8.05144e48			0.583304
$952$			1.58605e47i			0.0112930i
$953$			1.93617e49i			1.35491i	0.735563	+	0.677456i	$0.236918\pi$
$953$			1.93617e49i			1.35491i	−0.735563	+	0.677456i	$0.763082\pi$
$954$	−6.24889e49			−4.29788
$955$	−1.23843e49	−	7.89655e48i	−0.837172	−	0.533804i
$956$	−3.50665e49			−2.32990
$957$		−	5.69432e48i		−	0.371873i
$958$			1.35311e49i			0.868564i
$959$	1.42274e49			0.897676
$960$	2.23353e49	−	3.50287e49i	1.38521	−	2.17244i
$961$	4.26601e49			2.60067
$962$			2.33934e49i			1.40186i
$963$			3.30919e49i			1.94934i
$964$	2.27098e49			1.31505
$965$	1.22138e49	−	1.91551e49i	0.695267	−	1.09040i
$966$	−3.56097e49			−1.99272
$967$			6.10302e48i			0.335744i	0.985809	+	0.167872i	$0.0536895\pi$
$967$			6.10302e48i			0.335744i	−0.985809	+	0.167872i	$0.946310\pi$
$968$		−	2.16067e49i		−	1.16854i
$969$	−7.63038e46			−0.00405699
$970$	2.07066e49	+	1.32031e49i	1.08237	+	0.690147i
$971$	−1.37276e48			−0.0705467			−0.0352734	−	0.999378i	$-0.511230\pi$
$971$	−1.37276e48			−0.0705467			−0.0352734	+	0.999378i	$0.511230\pi$
$972$		−	1.06708e50i		−	5.39144i
$973$		−	3.40746e49i		−	1.69266i
$974$	2.30854e49			1.12749
$975$	−1.45592e49	−	3.12871e49i	−0.699137	−	1.50241i
$976$	1.01464e49			0.479061
$977$		−	2.36526e49i		−	1.09804i	−0.835809	−	0.549021i	$-0.815001\pi$
$977$		−	2.36526e49i		−	1.09804i	0.835809	−	0.549021i	$-0.184999\pi$
$978$			1.06949e50i			4.88187i
$979$	7.39475e48			0.331901
$980$	4.23227e48	+	2.69861e48i	0.186785	+	0.119100i
$981$	−8.40735e48			−0.364855
$982$		−	4.04430e49i		−	1.72585i
$983$		−	4.75948e48i		−	0.199722i	−0.995001	−	0.0998612i	$-0.968160\pi$
$983$		−	4.75948e48i		−	0.199722i	0.995001	−	0.0998612i	$-0.0318399\pi$
$984$	−2.53375e49			−1.04555
$985$	−1.32857e49	+	2.08361e49i	−0.539121	+	0.845510i
$986$	1.60152e47			0.00639094
$987$			5.83648e49i			2.29044i
$988$		−	1.07389e49i		−	0.414449i
$989$	−2.48648e49			−0.943726
$990$	−2.73434e49	+	4.28830e49i	−1.02064	+	1.60068i
$991$	6.42977e48			0.236037			0.118018	−	0.993011i	$-0.462346\pi$
$991$	6.42977e48			0.236037			0.118018	+	0.993011i	$0.462346\pi$
$992$			2.43077e49i			0.877611i
$993$			2.28069e48i			0.0809849i
$994$	3.69469e49			1.29033
$995$	−1.71139e49	−	1.09123e49i	−0.587853	−	0.374831i
$996$	2.61656e49			0.883997
$997$		−	1.85552e49i		−	0.616589i	−0.951291	−	0.308295i	$-0.900242\pi$
$997$		−	1.85552e49i		−	0.616589i	0.951291	−	0.308295i	$-0.0997583\pi$
$998$		−	8.42110e49i		−	2.75242i
$999$	8.91340e49			2.86558

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.34.b.a.4.2	✓	16
5.2	odd	4		25.34.a.f.1.15		16
5.3	odd	4		25.34.a.f.1.2		16
5.4	even	2	inner	5.34.b.a.4.15	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.b.a.4.2	✓	16	1.1	even	1	trivial
5.34.b.a.4.15	yes	16	5.4	even	2	inner
25.34.a.f.1.2		16	5.3	odd	4
25.34.a.f.1.15		16	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-156524. i q^{2} +1.41317e8i q^{3} -1.59098e10 q^{4} +(-2.87690e11 - 1.83439e11i) q^{5} +2.21195e13 q^{6} -8.25005e13i q^{7} +1.14573e15i q^{8} -1.44114e16 q^{9} +O(q^{10})\)	\(q-156524. i q^{2} +1.41317e8i q^{3} -1.59098e10 q^{4} +(-2.87690e11 - 1.83439e11i) q^{5} +2.21195e13 q^{6} -8.25005e13i q^{7} +1.14573e15i q^{8} -1.44114e16 q^{9} +(-2.87126e16 + 4.50303e16i) q^{10} -6.60805e16 q^{11} -2.24832e18i q^{12} +2.09761e18i q^{13} -1.29133e19 q^{14} +(2.59230e19 - 4.06555e19i) q^{15} +4.26697e19 q^{16} +1.67795e18i q^{17} +2.25573e21i q^{18} +3.21790e20 q^{19} +(4.57708e21 + 2.91847e21i) q^{20} +1.16587e22 q^{21} +1.03432e22i q^{22} -1.95136e22i q^{23} -1.61911e23 q^{24} +(4.91156e22 + 1.05547e23i) q^{25} +3.28326e23 q^{26} -1.25099e24i q^{27} +1.31256e24i q^{28} +6.09781e23 q^{29} +(-6.36355e24 - 4.05757e24i) q^{30} +7.68528e24 q^{31} +3.16289e24i q^{32} -9.33830e24i q^{33} +2.62639e23 q^{34} +(-1.51338e25 + 2.37345e25i) q^{35} +2.29282e26 q^{36} +7.12507e25i q^{37} -5.03677e25i q^{38} -2.96428e26 q^{39} +(2.10171e26 - 3.29614e26i) q^{40} +1.56491e26 q^{41} -1.82487e27i q^{42} -1.27423e27i q^{43} +1.05133e27 q^{44} +(4.14602e27 + 2.64362e27i) q^{45} -3.05434e27 q^{46} +5.00611e27i q^{47} +6.02996e27i q^{48} +9.24666e26 q^{49} +(1.65206e28 - 7.68776e27i) q^{50} -2.37123e26 q^{51} -3.33724e28i q^{52} +2.77023e28i q^{53} -1.95810e29 q^{54} +(1.90107e28 + 1.21217e28i) q^{55} +9.45230e28 q^{56} +4.54744e28i q^{57} -9.54452e28i q^{58} +1.46213e28 q^{59} +(-4.12429e29 + 6.46819e29i) q^{60} +2.37790e29 q^{61} -1.20293e30i q^{62} +1.18895e30i q^{63} +8.61598e29 q^{64} +(3.84783e29 - 6.03461e29i) q^{65} -1.46167e30 q^{66} -4.57295e29i q^{67} -2.66958e28i q^{68} +2.75760e30 q^{69} +(3.71502e30 + 2.36880e30i) q^{70} -2.86115e30 q^{71} -1.65116e31i q^{72} -1.51288e30i q^{73} +1.11524e31 q^{74} +(-1.49156e31 + 6.94087e30i) q^{75} -5.11960e30 q^{76} +5.45167e30i q^{77} +4.63980e31i q^{78} -1.25779e30 q^{79} +(-1.22756e31 - 7.82729e30i) q^{80} +9.66723e31 q^{81} -2.44945e31i q^{82} +1.16378e31i q^{83} -1.85487e32 q^{84} +(3.07802e29 - 4.82730e29i) q^{85} -1.99447e32 q^{86} +8.61724e31i q^{87} -7.57102e31i q^{88} -1.11905e32 q^{89} +(4.13789e32 - 6.48951e32i) q^{90} +1.73054e32 q^{91} +3.10457e32i q^{92} +1.08606e33i q^{93} +7.83575e32 q^{94} +(-9.25756e31 - 5.90288e31i) q^{95} -4.46971e32 q^{96} -4.59836e32i q^{97} -1.44732e32i q^{98} +9.52315e32 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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