LMFDB - Embedded newform 5.34.b.a.4.5

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			4.5
Root			$-51228.2i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.34.b.a.4.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-102456. i q^{2} -8.77372e7i q^{3} -1.90737e9 q^{4} +(-2.51871e11 + 2.30165e11i) q^{5} -8.98924e12 q^{6} -1.11815e14i q^{7} -6.84671e14i q^{8} -2.13876e15 q^{9} +O(q^{10})$	\(q-102456. i q^{2} -8.77372e7i q^{3} -1.90737e9 q^{4} +(-2.51871e11 + 2.30165e11i) q^{5} -8.98924e12 q^{6} -1.11815e14i q^{7} -6.84671e14i q^{8} -2.13876e15 q^{9} +(2.35819e16 + 2.58058e16i) q^{10} -2.24867e17 q^{11} +1.67348e17i q^{12} +2.46334e18i q^{13} -1.14562e19 q^{14} +(2.01941e19 + 2.20985e19i) q^{15} -8.65331e19 q^{16} +3.31898e19i q^{17} +2.19130e20i q^{18} +7.93484e19 q^{19} +(4.80413e20 - 4.39011e20i) q^{20} -9.81036e21 q^{21} +2.30391e22i q^{22} +2.88111e22i q^{23} -6.00711e22 q^{24} +(1.04632e22 - 1.15944e23i) q^{25} +2.52385e23 q^{26} -3.00088e23i q^{27} +2.13273e23i q^{28} +2.32679e24 q^{29} +(2.26413e24 - 2.06901e24i) q^{30} -7.38565e24 q^{31} +2.98459e24i q^{32} +1.97292e25i q^{33} +3.40050e24 q^{34} +(2.57360e25 + 2.81631e25i) q^{35} +4.07941e24 q^{36} +1.63972e25i q^{37} -8.12975e24i q^{38} +2.16126e26 q^{39} +(1.57588e26 + 1.72449e26i) q^{40} +4.37241e26 q^{41} +1.00513e27i q^{42} -2.93769e26i q^{43} +4.28906e26 q^{44} +(5.38693e26 - 4.92269e26i) q^{45} +2.95188e27 q^{46} +6.15905e26i q^{47} +7.59218e27i q^{48} -4.77164e27 q^{49} +(-1.18792e28 - 1.07202e27i) q^{50} +2.91198e27 q^{51} -4.69850e27i q^{52} -1.66687e28i q^{53} -3.07459e28 q^{54} +(5.66377e28 - 5.17567e28i) q^{55} -7.65566e28 q^{56} -6.96181e27i q^{57} -2.38395e29i q^{58} +6.84322e28 q^{59} +(-3.85176e28 - 4.21501e28i) q^{60} -3.85377e29 q^{61} +7.56707e29i q^{62} +2.39146e29i q^{63} -4.37524e29 q^{64} +(-5.66975e29 - 6.20444e29i) q^{65} +2.02139e30 q^{66} +1.10044e30i q^{67} -6.33053e28i q^{68} +2.52780e30 q^{69} +(2.88548e30 - 2.63682e30i) q^{70} +7.46328e29 q^{71} +1.46435e30i q^{72} +6.29592e30i q^{73} +1.68000e30 q^{74} +(-1.01726e31 - 9.18008e29i) q^{75} -1.51347e29 q^{76} +2.51436e31i q^{77} -2.21435e31i q^{78} -1.61054e31 q^{79} +(2.17952e31 - 1.99169e31i) q^{80} -3.82184e31 q^{81} -4.47982e31i q^{82} +2.30501e31i q^{83} +1.87120e31 q^{84} +(-7.63914e30 - 8.35956e30i) q^{85} -3.00985e31 q^{86} -2.04146e32i q^{87} +1.53960e32i q^{88} -1.08152e32 q^{89} +(-5.04361e31 - 5.51925e31i) q^{90} +2.75439e32 q^{91} -5.49534e31i q^{92} +6.47996e32i q^{93} +6.31033e31 q^{94} +(-1.99856e31 + 1.82633e31i) q^{95} +2.61860e32 q^{96} -2.96871e32i q^{97} +4.88885e32i q^{98} +4.80938e32 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 $

$2$		−	102456.i		−	1.10546i	−0.833360	−	0.552731i	$-0.813586\pi$
$2$		−	102456.i		−	1.10546i	0.833360	−	0.552731i	$-0.186414\pi$
$3$		−	8.77372e7i		−	1.17675i	−0.808589	−	0.588374i	$-0.799768\pi$
$3$		−	8.77372e7i		−	1.17675i	0.808589	−	0.588374i	$-0.200232\pi$
$4$	−1.90737e9			−0.222047
$5$	−2.51871e11	+	2.30165e11i	−0.738200	+	0.674582i
$5$	−2.51871e11	+	2.30165e11i	−0.738200	+	0.674582i
$6$	−8.98924e12			−1.30085
$7$		−	1.11815e14i		−	1.27170i	−0.771815	−	0.635848i	$-0.780651\pi$
$7$		−	1.11815e14i		−	1.27170i	0.771815	−	0.635848i	$-0.219349\pi$
$8$		−	6.84671e14i		−	0.859997i
$9$	−2.13876e15			−0.384734
$10$	2.35819e16	+	2.58058e16i	0.745725	+	0.816052i
$11$	−2.24867e17			−1.47553			−0.737763	−	0.675060i	$-0.764118\pi$
$11$	−2.24867e17			−1.47553			−0.737763	+	0.675060i	$0.764118\pi$
$12$			1.67348e17i			0.261294i
$13$			2.46334e18i			1.02674i	0.858169	+	0.513368i	$0.171602\pi$
$13$			2.46334e18i			1.02674i	−0.858169	+	0.513368i	$0.828398\pi$
$14$	−1.14562e19			−1.40581
$15$	2.01941e19	+	2.20985e19i	0.793813	+	0.868675i
$16$	−8.65331e19			−1.17274
$17$			3.31898e19i			0.165424i	0.996574	+	0.0827118i	$0.0263581\pi$
$17$			3.31898e19i			0.165424i	−0.996574	+	0.0827118i	$0.973642\pi$
$18$			2.19130e20i			0.425309i
$19$	7.93484e19			0.0631108			0.0315554	−	0.999502i	$-0.489954\pi$
$19$	7.93484e19			0.0631108			0.0315554	+	0.999502i	$0.489954\pi$
$20$	4.80413e20	−	4.39011e20i	0.163915	−	0.149789i
$21$	−9.81036e21			−1.49646
$22$			2.30391e22i			1.63114i
$23$			2.88111e22i			0.979602i	0.871834	+	0.489801i	$0.162931\pi$
$23$			2.88111e22i			0.979602i	−0.871834	+	0.489801i	$0.837069\pi$
$24$	−6.00711e22			−1.01200
$25$	1.04632e22	−	1.15944e23i	0.0898778	−	0.995953i
$26$	2.52385e23			1.13502
$27$		−	3.00088e23i		−	0.724012i
$28$			2.13273e23i			0.282377i
$29$	2.32679e24			1.72659			0.863297	−	0.504695i	$-0.168395\pi$
$29$	2.32679e24			1.72659			0.863297	+	0.504695i	$0.168395\pi$
$30$	2.26413e24	−	2.06901e24i	0.960287	−	0.877530i
$31$	−7.38565e24			−1.82356			−0.911781	−	0.410676i	$-0.865293\pi$
$31$	−7.38565e24			−1.82356			−0.911781	+	0.410676i	$0.865293\pi$
$32$			2.98459e24i			0.436425i
$33$			1.97292e25i			1.73632i
$34$	3.40050e24			0.182869
$35$	2.57360e25	+	2.81631e25i	0.857863	+	0.938765i
$36$	4.07941e24			0.0854292
$37$			1.63972e25i			0.218495i	0.994015	+	0.109247i	$0.0348441\pi$
$37$			1.63972e25i			0.218495i	−0.994015	+	0.109247i	$0.965156\pi$
$38$		−	8.12975e24i		−	0.0697666i
$39$	2.16126e26			1.20821
$40$	1.57588e26	+	1.72449e26i	0.580139	+	0.634850i
$41$	4.37241e26			1.07100			0.535498	−	0.844537i	$-0.320124\pi$
$41$	4.37241e26			1.07100			0.535498	+	0.844537i	$0.320124\pi$
$42$			1.00513e27i			1.65429i
$43$		−	2.93769e26i		−	0.327927i	−0.986466	−	0.163963i	$-0.947572\pi$
$43$		−	2.93769e26i		−	0.327927i	0.986466	−	0.163963i	$-0.0524279\pi$
$44$	4.28906e26			0.327637
$45$	5.38693e26	−	4.92269e26i	0.284011	−	0.259535i
$46$	2.95188e27			1.08291
$47$			6.15905e26i			0.158452i	0.996857	+	0.0792262i	$0.0252449\pi$
$47$			6.15905e26i			0.158452i	−0.996857	+	0.0792262i	$0.974755\pi$
$48$			7.59218e27i			1.38002i
$49$	−4.77164e27			−0.617209
$50$	−1.18792e28	−	1.07202e27i	−1.10099	−	0.0993565i
$51$	2.91198e27			0.194662
$52$		−	4.69850e27i		−	0.227984i
$53$		−	1.66687e28i		−	0.590678i	−0.955393	−	0.295339i	$-0.904567\pi$
$53$		−	1.66687e28i		−	0.590678i	0.955393	−	0.295339i	$-0.0954326\pi$
$54$	−3.07459e28			−0.800368
$55$	5.66377e28	−	5.17567e28i	1.08923	−	0.995364i
$56$	−7.65566e28			−1.09365
$57$		−	6.96181e27i		−	0.0742655i
$58$		−	2.38395e29i		−	1.90869i
$59$	6.84322e28			0.413240			0.206620	−	0.978421i	$-0.433754\pi$
$59$	6.84322e28			0.413240			0.206620	+	0.978421i	$0.433754\pi$
$60$	−3.85176e28	−	4.21501e28i	−0.176264	−	0.192887i
$61$	−3.85377e29			−1.34259			−0.671295	−	0.741191i	$-0.734261\pi$
$61$	−3.85377e29			−1.34259			−0.671295	+	0.741191i	$0.734261\pi$
$62$			7.56707e29i			2.01588i
$63$			2.39146e29i			0.489265i
$64$	−4.37524e29			−0.690291
$65$	−5.66975e29	−	6.20444e29i	−0.692617	−	0.757936i
$66$	2.02139e30			1.91944
$67$			1.10044e30i			0.815327i	0.913132	+	0.407664i	$0.133656\pi$
$67$			1.10044e30i			0.815327i	−0.913132	+	0.407664i	$0.866344\pi$
$68$		−	6.33053e28i		−	0.0367318i
$69$	2.52780e30			1.15274
$70$	2.88548e30	−	2.63682e30i	1.03777	−	0.948336i
$71$	7.46328e29			0.212406			0.106203	−	0.994344i	$-0.466131\pi$
$71$	7.46328e29			0.212406			0.106203	+	0.994344i	$0.466131\pi$
$72$			1.46435e30i			0.330871i
$73$			6.29592e30i			1.13301i	0.824060	+	0.566503i	$0.191704\pi$
$73$			6.29592e30i			1.13301i	−0.824060	+	0.566503i	$0.808296\pi$
$74$	1.68000e30			0.241538
$75$	−1.01726e31	−	9.18008e29i	−1.17198	−	0.105763i
$76$	−1.51347e29			−0.0140136
$77$			2.51436e31i			1.87642i
$78$		−	2.21435e31i		−	1.33563i
$79$	−1.61054e31			−0.787273			−0.393636	−	0.919266i	$-0.628783\pi$
$79$	−1.61054e31			−0.787273			−0.393636	+	0.919266i	$0.628783\pi$
$80$	2.17952e31	−	1.99169e31i	0.865718	−	0.791111i
$81$	−3.82184e31			−1.23671
$82$		−	4.47982e31i		−	1.18394i
$83$			2.30501e31i			0.498753i	0.968407	+	0.249376i	$0.0802256\pi$
$83$			2.30501e31i			0.498753i	−0.968407	+	0.249376i	$0.919774\pi$
$84$	1.87120e31			0.332286
$85$	−7.63914e30	−	8.35956e30i	−0.111592	−	0.122116i
$86$	−3.00985e31			−0.362510
$87$		−	2.04146e32i		−	2.03177i
$88$			1.53960e32i			1.26895i
$89$	−1.08152e32			−0.739773			−0.369886	−	0.929077i	$-0.620603\pi$
$89$	−1.08152e32			−0.739773			−0.369886	+	0.929077i	$0.620603\pi$
$90$	−5.04361e31	−	5.51925e31i	−0.286906	−	0.313963i
$91$	2.75439e32			1.30569
$92$		−	5.49534e31i		−	0.217518i
$93$			6.47996e32i			2.14587i
$94$	6.31033e31			0.175163
$95$	−1.99856e31	+	1.82633e31i	−0.0465884	+	0.0425734i
$96$	2.61860e32			0.513562
$97$		−	2.96871e32i		−	0.490721i	−0.969432	−	0.245361i	$-0.921094\pi$
$97$		−	2.96871e32i		−	0.490721i	0.969432	−	0.245361i	$-0.0789064\pi$
$98$			4.88885e32i			0.682302i
$99$	4.80938e32			0.567686
$100$	−1.99571e31	+	2.21149e32i	−0.0199571	+	0.221149i
$101$	−7.27121e32			−0.617027			−0.308513	−	0.951220i	$-0.599831\pi$
$101$	−7.27121e32			−0.617027			−0.308513	+	0.951220i	$0.599831\pi$
$102$		−	2.98351e32i		−	0.215191i
$103$			1.81397e33i			1.11382i	0.830572	+	0.556912i	$0.188014\pi$
$103$			1.81397e33i			1.11382i	−0.830572	+	0.556912i	$0.811986\pi$
$104$	1.68658e33			0.882990
$105$	2.47095e33	−	2.25800e33i	1.10469	−	1.00949i
$106$	−1.70782e33			−0.652972
$107$		−	5.42390e33i		−	1.77615i	−0.459701	−	0.888074i	$-0.652043\pi$
$107$		−	5.42390e33i		−	1.77615i	0.459701	−	0.888074i	$-0.347957\pi$
$108$			5.72379e32i			0.160765i
$109$	−6.01657e33			−1.45148			−0.725741	−	0.687968i	$-0.758503\pi$
$109$	−6.01657e33			−1.45148			−0.725741	+	0.687968i	$0.758503\pi$
$110$	−5.30280e33	−	5.80289e33i	−1.10034	−	1.20411i
$111$	1.43864e33			0.257113
$112$			9.67572e33i			1.49137i
$113$			1.07074e34i			1.42524i	0.701550	+	0.712620i	$0.252492\pi$
$113$			1.07074e34i			1.42524i	−0.701550	+	0.712620i	$0.747508\pi$
$114$	−7.13282e32			−0.0820977
$115$	−6.63131e33	−	7.25668e33i	−0.660822	−	0.723142i
$116$	−4.43806e33			−0.383386
$117$		−	5.26849e33i		−	0.395020i
$118$		−	7.01131e33i		−	0.456821i
$119$	3.71112e33			0.210368
$120$	1.51302e34	−	1.38263e34i	0.747058	−	0.682677i
$121$	2.73402e34			1.17718
$122$			3.94843e34i			1.48418i
$123$		−	3.83623e34i		−	1.26029i
$124$	1.40872e34			0.404917
$125$	2.40510e34	+	3.16113e34i	0.605504	+	0.795842i
$126$	2.45020e34			0.540864
$127$			2.11841e33i			0.0410440i	0.999789	+	0.0205220i	$0.00653281\pi$
$127$			2.11841e33i			0.0410440i	−0.999789	+	0.0205220i	$0.993467\pi$
$128$			7.04645e34i			1.19952i
$129$	−2.57745e34			−0.385887
$130$	−6.35685e34	+	5.80902e34i	−0.837870	+	0.765663i
$131$	−1.12103e35			−1.30209			−0.651044	−	0.759040i	$-0.725669\pi$
$131$	−1.12103e35			−1.30209			−0.651044	+	0.759040i	$0.725669\pi$
$132$		−	3.76310e34i		−	0.385546i
$133$		−	8.87236e33i		−	0.0802577i
$134$	1.12747e35			0.901314
$135$	6.90698e34	+	7.55835e34i	0.488406	+	0.534466i
$136$	2.27241e34			0.142264
$137$		−	1.87942e35i		−	1.04264i	−0.853361	−	0.521320i	$-0.825440\pi$
$137$		−	1.87942e35i		−	1.04264i	0.853361	−	0.521320i	$-0.174560\pi$
$138$		−	2.58989e35i		−	1.27432i
$139$	−2.77030e35			−1.20999			−0.604997	−	0.796228i	$-0.706826\pi$
$139$	−2.77030e35			−1.20999			−0.604997	+	0.796228i	$0.706826\pi$
$140$	−4.90881e34	−	5.37174e34i	−0.190486	−	0.208450i
$141$	5.40378e34			0.186458
$142$		−	7.64661e34i		−	0.234807i
$143$		−	5.53924e35i		−	1.51498i
$144$	1.85074e35			0.451194
$145$	−5.86052e35	+	5.35547e35i	−1.27457	+	1.16473i
$146$	6.45057e35			1.25250
$147$			4.18651e35i			0.726300i
$148$		−	3.12755e34i		−	0.0485162i
$149$	−1.17332e36			−1.62871			−0.814354	−	0.580369i	$-0.802908\pi$
$149$	−1.17332e36			−1.62871			−0.814354	+	0.580369i	$0.802908\pi$
$150$	−9.40558e34	+	1.04225e36i	−0.116918	+	1.29559i
$151$	−2.03363e35			−0.226544			−0.113272	−	0.993564i	$-0.536133\pi$
$151$	−2.03363e35			−0.226544			−0.113272	+	0.993564i	$0.536133\pi$
$152$		−	5.43276e34i		−	0.0542751i
$153$		−	7.09850e34i		−	0.0636441i
$154$	2.57612e36			2.07431
$155$	1.86023e36	−	1.69992e36i	1.34615	−	1.23014i
$156$	−4.12233e35			−0.268279
$157$			1.48553e36i			0.870036i	0.900422	+	0.435018i	$0.143258\pi$
$157$			1.48553e36i			0.870036i	−0.900422	+	0.435018i	$0.856742\pi$
$158$			1.65010e36i			0.870300i
$159$	−1.46247e36			−0.695079
$160$	−6.86949e35	−	7.51733e35i	−0.294405	−	0.322169i
$161$	3.22151e36			1.24576
$162$			3.91571e36i			1.36714i
$163$		−	2.41405e36i		−	0.761466i	−0.924685	−	0.380733i	$-0.875672\pi$
$163$		−	2.41405e36i		−	0.761466i	0.924685	−	0.380733i	$-0.124328\pi$
$164$	−8.33982e35			−0.237812
$165$	−4.54099e36	−	4.96923e36i	−1.17129	−	1.28175i
$166$	2.36163e36			0.551352
$167$		−	6.50430e36i		−	1.37524i	−0.726071	−	0.687620i	$-0.758655\pi$
$167$		−	6.50430e36i		−	1.37524i	0.726071	−	0.687620i	$-0.241345\pi$
$168$			6.71687e36i			1.28696i
$169$	−3.11899e35			−0.0541856
$170$	−8.56490e35	+	7.82678e35i	−0.134994	+	0.123360i
$171$	−1.69707e35			−0.0242809
$172$			5.60327e35i			0.0728152i
$173$		−	5.44353e36i		−	0.642865i	−0.946933	−	0.321432i	$-0.895836\pi$
$173$		−	5.44353e36i		−	0.642865i	0.946933	−	0.321432i	$-0.104164\pi$
$174$	−2.09161e37			−2.24604
$175$	−1.29643e37	−	1.16994e36i	−1.26655	−	0.114297i
$176$	1.94585e37			1.73041
$177$		−	6.00405e36i		−	0.486279i
$178$			1.10808e37i			0.817791i
$179$	1.55767e37			1.04809			0.524047	−	0.851690i	$-0.324422\pi$
$179$	1.55767e37			1.04809			0.524047	+	0.851690i	$0.324422\pi$
$180$	−1.02749e36	+	9.38940e35i	−0.0630639	+	0.0576290i
$181$	−2.16095e37			−1.21045			−0.605227	−	0.796053i	$-0.706917\pi$
$181$	−2.16095e37			−1.21045			−0.605227	+	0.796053i	$0.706917\pi$
$182$		−	2.82204e37i		−	1.44340i
$183$			3.38119e37i			1.57989i
$184$	1.97261e37			0.842456
$185$	−3.77407e36	−	4.12998e36i	−0.147393	−	0.161293i
$186$	6.63914e37			2.37218
$187$		−	7.46330e36i		−	0.244087i
$188$		−	1.17476e36i		−	0.0351839i
$189$	−3.35543e37			−0.920723
$190$	1.87119e36	+	2.04765e36i	0.0470633	+	0.0515017i
$191$	5.39109e37			1.24344			0.621722	−	0.783238i	$-0.286433\pi$
$191$	5.39109e37			1.24344			0.621722	+	0.783238i	$0.286433\pi$
$192$			3.83871e37i			0.812298i
$193$			2.82434e37i			0.548557i	0.961650	+	0.274278i	$0.0884390\pi$
$193$			2.82434e37i			0.548557i	−0.961650	+	0.274278i	$0.911561\pi$
$194$	−3.04164e37			−0.542474
$195$	−5.44361e37	+	4.97448e37i	−0.891899	+	0.815036i
$196$	9.10130e36			0.137050
$197$			1.24116e37i			0.171844i	0.996302	+	0.0859220i	$0.0273836\pi$
$197$			1.24116e37i			0.171844i	−0.996302	+	0.0859220i	$0.972616\pi$
$198$		−	4.92751e37i		−	0.627555i
$199$	−7.16373e37			−0.839582			−0.419791	−	0.907621i	$-0.637897\pi$
$199$	−7.16373e37			−0.839582			−0.419791	+	0.907621i	$0.637897\pi$
$200$	−7.93836e37	−	7.16382e36i	−0.856517	−	0.0772947i
$201$	9.65495e37			0.959434
$202$			7.44982e37i			0.682100i
$203$		−	2.60171e38i		−	2.19570i
$204$	−5.55423e36			−0.0432241
$205$	−1.10129e38	+	1.00638e38i	−0.790608	+	0.722474i
$206$	1.85853e38			1.23129
$207$		−	6.16200e37i		−	0.376887i
$208$		−	2.13160e38i		−	1.20410i
$209$	−1.78429e37			−0.0931217
$210$	−2.31347e38	−	2.53164e38i	−1.11595	−	1.22119i
$211$	3.78989e38			1.69031			0.845154	−	0.534523i	$-0.179509\pi$
$211$	3.78989e38			1.69031			0.845154	+	0.534523i	$0.179509\pi$
$212$			3.17935e37i			0.131158i
$213$		−	6.54808e37i		−	0.249948i
$214$	−5.55713e38			−1.96346
$215$	6.76155e37	+	7.39921e37i	0.221213	+	0.242075i
$216$	−2.05461e38			−0.622649
$217$			8.25828e38i			2.31902i
$218$			6.16436e38i			1.60456i
$219$	5.52387e38			1.33326
$220$	−1.08029e38	+	9.87192e37i	−0.241861	+	0.221018i
$221$	−8.17576e37			−0.169846
$222$		−	1.47398e38i		−	0.284229i
$223$		−	4.51907e38i		−	0.809131i	−0.914509	−	0.404565i	$-0.867423\pi$
$223$		−	4.51907e38i		−	0.809131i	0.914509	−	0.404565i	$-0.132577\pi$
$224$	3.33722e38			0.555000
$225$	−2.23782e37	+	2.47977e38i	−0.0345791	+	0.383177i
$226$	1.09704e39			1.57555
$227$		−	9.98415e38i		−	1.33317i	−0.745431	−	0.666583i	$-0.767756\pi$
$227$		−	9.98415e38i		−	1.33317i	0.745431	−	0.666583i	$-0.232244\pi$
$228$			1.32788e37i			0.0164905i
$229$	−5.32577e38			−0.615314			−0.307657	−	0.951497i	$-0.599545\pi$
$229$	−5.32577e38			−0.615314			−0.307657	+	0.951497i	$0.599545\pi$
$230$	−7.43493e38	+	6.79419e38i	−0.799407	+	0.730514i
$231$	2.20603e39			2.20807
$232$		−	1.59309e39i		−	1.48487i
$233$			1.58065e39i			1.37234i	0.727440	+	0.686171i	$0.240710\pi$
$233$			1.58065e39i			1.37234i	−0.727440	+	0.686171i	$0.759290\pi$
$234$	−5.39790e38			−0.436680
$235$	−1.41760e38	−	1.55129e38i	−0.106889	−	0.116970i
$236$	−1.30526e38			−0.0917588
$237$			1.41305e39i			0.926421i
$238$		−	3.80228e38i		−	0.232554i
$239$	−2.18770e39			−1.24860			−0.624300	−	0.781185i	$-0.714616\pi$
$239$	−2.18770e39			−1.24860			−0.624300	+	0.781185i	$0.714616\pi$
$240$	−1.74746e39	−	1.91225e39i	−0.930938	−	1.01873i
$241$	−1.34545e39			−0.669248			−0.334624	−	0.942352i	$-0.608609\pi$
$241$	−1.34545e39			−0.669248			−0.334624	+	0.942352i	$0.608609\pi$
$242$		−	2.80117e39i		−	1.30133i
$243$			1.68497e39i			0.731288i
$244$	7.35057e38			0.298118
$245$	1.20184e39	−	1.09827e39i	0.455624	−	0.416359i
$246$	−3.93047e39			−1.39320
$247$			1.95462e38i			0.0647981i
$248$			5.05674e39i			1.56826i
$249$	2.02236e39			0.586906
$250$	3.23878e39	−	2.46417e39i	0.879774	−	0.669362i
$251$	1.33521e38			0.0339574			0.0169787	−	0.999856i	$-0.494595\pi$
$251$	1.33521e38			0.0339574			0.0169787	+	0.999856i	$0.494595\pi$
$252$		−	4.56141e38i		−	0.108640i
$253$		−	6.47866e39i		−	1.44543i
$254$	2.17045e38			0.0453726
$255$	−7.33445e38	+	6.70237e38i	−0.143699	+	0.131315i
$256$	3.46124e39			0.635729
$257$			3.02015e39i			0.520154i	0.965588	+	0.260077i	$0.0837480\pi$
$257$			3.02015e39i			0.520154i	−0.965588	+	0.260077i	$0.916252\pi$
$258$			2.64076e39i			0.426583i
$259$	1.83346e39			0.277859
$260$	1.08143e39	+	1.18342e39i	0.153794	+	0.168298i
$261$	−4.97645e39			−0.664280
$262$			1.14857e40i			1.43941i
$263$		−	5.25973e39i		−	0.619004i	−0.950899	−	0.309502i	$-0.899838\pi$
$263$		−	5.25973e39i		−	0.619004i	0.950899	−	0.309502i	$-0.100162\pi$
$264$	1.35080e40			1.49323
$265$	3.83656e39	+	4.19838e39i	0.398461	+	0.436038i
$266$	−9.09029e38			−0.0887219
$267$			9.48893e39i			0.870526i
$268$		−	2.09895e39i		−	0.181041i
$269$	−4.00271e39			−0.324670			−0.162335	−	0.986736i	$-0.551902\pi$
$269$	−4.00271e39			−0.324670			−0.162335	+	0.986736i	$0.551902\pi$
$270$	7.74401e39	−	7.07664e39i	0.590832	−	0.539914i
$271$	−1.43945e40			−1.03325			−0.516624	−	0.856212i	$-0.672812\pi$
$271$	−1.43945e40			−1.03325			−0.516624	+	0.856212i	$0.672812\pi$
$272$		−	2.87202e39i		−	0.193999i
$273$		−	2.41662e40i		−	1.53647i
$274$	−1.92559e40			−1.15260
$275$	−2.35282e39	+	2.60721e40i	−0.132617	+	1.46955i
$276$	−4.82146e39			−0.255964
$277$		−	1.51033e40i		−	0.755364i	−0.925935	−	0.377682i	$-0.876721\pi$
$277$		−	1.51033e40i		−	0.755364i	0.925935	−	0.377682i	$-0.123279\pi$
$278$			2.83835e40i			1.33760i
$279$	1.57961e40			0.701587
$280$	1.92824e40	−	1.76207e40i	0.807336	−	0.737760i
$281$	−2.79172e40			−1.10209			−0.551045	−	0.834476i	$-0.685771\pi$
$281$	−2.79172e40			−1.10209			−0.551045	+	0.834476i	$0.685771\pi$
$282$		−	5.53651e39i		−	0.206123i
$283$		−	3.85510e40i		−	1.35381i	−0.736069	−	0.676907i	$-0.763320\pi$
$283$		−	3.85510e40i		−	1.35381i	0.736069	−	0.676907i	$-0.236680\pi$
$284$	−1.42353e39			−0.0471642
$285$	1.60237e39	+	1.75348e39i	0.0500982	+	0.0548228i
$286$	−5.67530e40			−1.67475
$287$		−	4.88902e40i		−	1.36198i
$288$		−	6.38332e39i		−	0.167908i
$289$	3.91529e40			0.972635
$290$	5.48702e40	+	6.00448e40i	1.28757	+	1.40899i
$291$	−2.60467e40			−0.577455
$292$		−	1.20087e40i		−	0.251581i
$293$		−	3.74622e40i		−	0.741784i	−0.928676	−	0.370892i	$-0.879052\pi$
$293$		−	3.74622e40i		−	0.741784i	0.928676	−	0.370892i	$-0.120948\pi$
$294$	4.28934e40			0.802897
$295$	−1.72361e40	+	1.57507e40i	−0.305054	+	0.278764i
$296$	1.12267e40			0.187905
$297$			6.74799e40i			1.06830i
$298$			1.20214e41i			1.80048i
$299$	−7.09713e40			−1.00579
$300$	1.94030e40	+	1.75098e39i	0.260236	+	0.0234845i
$301$	−3.28478e40			−0.417023
$302$			2.08358e40i			0.250436i
$303$			6.37956e40i			0.726085i
$304$	−6.86626e39			−0.0740127
$305$	9.70654e40	−	8.87003e40i	0.991099	−	0.905687i
$306$	−7.27287e39			−0.0703562
$307$			1.07461e41i			0.985068i	0.870293	+	0.492534i	$0.163929\pi$
$307$			1.07461e41i			0.985068i	−0.870293	+	0.492534i	$0.836071\pi$
$308$		−	4.79582e40i		−	0.416654i
$309$	1.59153e41			1.31069
$310$	−1.74168e41	−	1.90593e41i	−1.35988	−	1.48812i
$311$	2.27431e41			1.68385			0.841924	−	0.539597i	$-0.181423\pi$
$311$	2.27431e41			1.68385			0.841924	+	0.539597i	$0.181423\pi$
$312$		−	1.47975e41i		−	1.03906i
$313$			6.49777e40i			0.432796i	0.976305	+	0.216398i	$0.0694308\pi$
$313$			6.49777e40i			0.432796i	−0.976305	+	0.216398i	$0.930569\pi$
$314$	1.52202e41			0.961792
$315$	−5.50431e40	−	6.02341e40i	−0.330049	−	0.361175i
$316$	3.07190e40			0.174812
$317$			5.13146e40i			0.277181i	0.990350	+	0.138590i	$0.0442571\pi$
$317$			5.13146e40i			0.277181i	−0.990350	+	0.138590i	$0.955743\pi$
$318$			1.49839e41i			0.768383i
$319$	−5.23219e41			−2.54764
$320$	1.10200e41	−	1.00703e41i	0.509572	−	0.465658i
$321$	−4.75878e41			−2.09008
$322$		−	3.30065e41i		−	1.37714i
$323$			2.63356e39i			0.0104400i
$324$	7.28966e40			0.274609
$325$	2.85610e41	+	2.57743e40i	1.02258	+	0.0922807i
$326$	−2.47335e41			−0.841772
$327$			5.27877e41i			1.70803i
$328$		−	2.99366e41i		−	0.921053i
$329$	6.88675e40			0.201503
$330$	−5.09129e41	+	4.65253e41i	−1.41693	+	1.29482i
$331$	3.99589e41			1.05792			0.528958	−	0.848648i	$-0.322583\pi$
$331$	3.99589e41			1.05792			0.528958	+	0.848648i	$0.322583\pi$
$332$		−	4.39652e40i		−	0.110747i
$333$		−	3.50697e40i		−	0.0840624i
$334$	−6.66407e41			−1.52028
$335$	−2.53283e41	−	2.77169e41i	−0.550005	−	0.601874i
$336$	8.48921e41			1.75497
$337$		−	5.12879e41i		−	1.00954i	−0.863255	−	0.504768i	$-0.831578\pi$
$337$		−	5.12879e41i		−	1.00954i	0.863255	−	0.504768i	$-0.168422\pi$
$338$			3.19560e40i			0.0599001i
$339$	9.39434e41			1.67715
$340$	1.45707e40	+	1.59448e40i	0.0247786	+	0.0271154i
$341$	1.66079e42			2.69072
$342$			1.73876e40i			0.0268416i
$343$		−	3.30900e41i		−	0.486793i
$344$	−2.01135e41			−0.282016
$345$	−6.36681e41	+	5.81812e41i	−0.850956	+	0.777621i
$346$	−5.57724e41			−0.710663
$347$			4.02876e41i			0.489480i	0.969589	+	0.244740i	$0.0787027\pi$
$347$			4.02876e41i			0.489480i	−0.969589	+	0.244740i	$0.921297\pi$
$348$			3.89383e41i			0.451148i
$349$	−4.84486e41			−0.535380			−0.267690	−	0.963505i	$-0.586260\pi$
$349$	−4.84486e41			−0.535380			−0.267690	+	0.963505i	$0.586260\pi$
$350$	−1.19868e41	+	1.32828e42i	−0.126351	+	1.40012i
$351$	7.39217e41			0.743369
$352$		−	6.71136e41i		−	0.643957i
$353$			1.01645e42i			0.930687i	0.885130	+	0.465344i	$0.154069\pi$
$353$			1.01645e42i			0.930687i	−0.885130	+	0.465344i	$0.845931\pi$
$354$	−6.15153e41			−0.537563
$355$	−1.87979e41	+	1.71779e41i	−0.156798	+	0.143285i
$356$	2.06286e41			0.164265
$357$		−	3.25604e41i		−	0.247550i
$358$		−	1.59593e42i		−	1.15863i
$359$	3.81937e41			0.264809			0.132405	−	0.991196i	$-0.457730\pi$
$359$	3.81937e41			0.264809			0.132405	+	0.991196i	$0.457730\pi$
$360$	−3.37042e41	−	3.68828e41i	−0.223199	−	0.244249i
$361$	−1.57447e42			−0.996017
$362$			2.21403e42i			1.33811i
$363$		−	2.39875e42i		−	1.38524i
$364$	−5.25364e41			−0.289926
$365$	−1.44910e42	−	1.58576e42i	−0.764306	−	0.836385i
$366$	3.46424e42			1.74651
$367$		−	1.28100e41i		−	0.0617391i	−0.999523	−	0.0308695i	$-0.990172\pi$
$367$		−	1.28100e41i		−	0.0617391i	0.999523	−	0.0308695i	$-0.00982764\pi$
$368$		−	2.49311e42i		−	1.14882i
$369$	−9.35155e41			−0.412049
$370$	−4.23143e41	+	3.86677e41i	−0.178303	+	0.162937i
$371$	−1.86382e42			−0.751162
$372$		−	1.23597e42i		−	0.476485i
$373$			4.95556e41i			0.182767i	0.995816	+	0.0913834i	$0.0291289\pi$
$373$			4.95556e41i			0.182767i	−0.995816	+	0.0913834i	$0.970871\pi$
$374$	−7.64662e41			−0.269829
$375$	2.77349e42	−	2.11016e42i	0.936505	−	0.712526i
$376$	4.21692e41			0.136269
$377$			5.73167e42i			1.77276i
$378$			3.43786e42i			1.01782i
$379$	−2.01391e42			−0.570813			−0.285406	−	0.958407i	$-0.592129\pi$
$379$	−2.01391e42			−0.570813			−0.285406	+	0.958407i	$0.592129\pi$
$380$	3.81200e40	−	3.48348e40i	0.0103448	−	0.00945332i
$381$	1.85864e41			0.0482984
$382$		−	5.52352e42i		−	1.37458i
$383$			6.11625e42i			1.45782i	0.684607	+	0.728912i	$0.259974\pi$
$383$			6.11625e42i			1.45782i	−0.684607	+	0.728912i	$0.740026\pi$
$384$	6.18236e42			1.41153
$385$	−5.78718e42	−	6.33295e42i	−1.26580	−	1.38517i
$386$	2.89372e42			0.606409
$387$			6.28302e41i			0.126165i
$388$			5.66244e41i			0.108963i
$389$	−8.01591e41			−0.147837			−0.0739187	−	0.997264i	$-0.523551\pi$
$389$	−8.01591e41			−0.147837			−0.0739187	+	0.997264i	$0.523551\pi$
$390$	5.09667e42	+	5.57732e42i	0.900991	+	0.985961i
$391$	−9.56233e41			−0.162049
$392$			3.26701e42i			0.530799i
$393$			9.83560e42i			1.53223i
$394$	1.27165e42			0.189967
$395$	4.05650e42	−	3.70691e42i	0.581164	−	0.531080i
$396$	−9.17327e41			−0.126053
$397$		−	6.77326e42i		−	0.892800i	−0.894834	−	0.446400i	$-0.852706\pi$
$397$		−	6.77326e42i		−	0.892800i	0.894834	−	0.446400i	$-0.147294\pi$
$398$			7.33969e42i			0.928127i
$399$	−7.78436e41			−0.0944431
$400$	−9.05409e41	+	1.00330e43i	−0.105403	+	1.16800i
$401$	−1.14344e42			−0.127741			−0.0638707	−	0.997958i	$-0.520345\pi$
$401$	−1.14344e42			−0.127741			−0.0638707	+	0.997958i	$0.520345\pi$
$402$		−	9.89212e42i		−	1.06062i
$403$		−	1.81933e43i		−	1.87232i
$404$	1.38689e42			0.137009
$405$	9.62611e42	−	8.79654e42i	0.912942	−	0.834265i
$406$	−2.66561e43			−2.42727
$407$		−	3.68719e42i		−	0.322395i
$408$		−	1.99375e42i		−	0.167409i
$409$	1.58336e43			1.27687			0.638434	−	0.769677i	$-0.279583\pi$
$409$	1.58336e43			1.27687			0.638434	+	0.769677i	$0.279583\pi$
$410$	1.03110e43	+	1.12834e43i	0.798668	+	0.873988i
$411$	−1.64895e43			−1.22692
$412$		−	3.45992e42i		−	0.247321i
$413$		−	7.65176e42i		−	0.525515i
$414$	−6.31336e42			−0.416634
$415$	−5.30535e42	−	5.80568e42i	−0.336450	−	0.368179i
$416$	−7.35205e42			−0.448093
$417$			2.43059e43i			1.42386i
$418$			1.82811e42i			0.102943i
$419$	5.87784e42			0.318190			0.159095	−	0.987263i	$-0.449142\pi$
$419$	5.87784e42			0.318190			0.159095	+	0.987263i	$0.449142\pi$
$420$	−4.71302e42	+	4.30685e42i	−0.245293	+	0.224154i
$421$	−7.76874e41			−0.0388773			−0.0194386	−	0.999811i	$-0.506188\pi$
$421$	−7.76874e41			−0.0388773			−0.0194386	+	0.999811i	$0.506188\pi$
$422$		−	3.88298e43i		−	1.86857i
$423$		−	1.31727e42i		−	0.0609621i
$424$	−1.14126e43			−0.507982
$425$	3.84816e42	+	3.47270e41i	0.164754	+	0.0148679i
$426$	−6.70892e42			−0.276309
$427$			4.30910e43i			1.70736i
$428$			1.03454e43i			0.394389i
$429$	−4.85998e43			−1.78274
$430$	7.58096e42	−	6.92763e42i	0.267605	−	0.244543i
$431$	2.29433e43			0.779438			0.389719	−	0.920934i	$-0.372572\pi$
$431$	2.29433e43			0.779438			0.389719	+	0.920934i	$0.372572\pi$
$432$			2.59675e43i			0.849080i
$433$		−	1.80460e43i		−	0.567977i	−0.958828	−	0.283988i	$-0.908342\pi$
$433$		−	1.80460e43i		−	0.567977i	0.958828	−	0.283988i	$-0.0916577\pi$
$434$	8.46113e43			2.56359
$435$	4.69874e43	+	5.14186e43i	1.37059	+	1.49985i
$436$	1.14758e43			0.322298
$437$			2.28611e42i			0.0618235i
$438$		−	5.65956e43i		−	1.47387i
$439$	1.60697e43			0.403035			0.201517	−	0.979485i	$-0.435413\pi$
$439$	1.60697e43			0.403035			0.201517	+	0.979485i	$0.435413\pi$
$440$	−3.54363e43	−	3.87782e43i	−0.856010	−	0.936738i
$441$	1.02054e43			0.237462
$442$			8.37659e42i			0.187759i
$443$		−	4.88560e43i		−	1.05501i	−0.849552	−	0.527504i	$-0.823128\pi$
$443$		−	4.88560e43i		−	1.05501i	0.849552	−	0.527504i	$-0.176872\pi$
$444$	−2.74403e42			−0.0570913
$445$	2.72403e43	−	2.48928e43i	0.546100	−	0.499038i
$446$	−4.63007e43			−0.894464
$447$			1.02944e44i			1.91658i
$448$			4.89218e43i			0.877840i
$449$	4.45262e43			0.770106			0.385053	−	0.922894i	$-0.374183\pi$
$449$	4.45262e43			0.770106			0.385053	+	0.922894i	$0.374183\pi$
$450$	2.54068e43	+	2.29279e42i	0.423588	+	0.0382259i
$451$	−9.83213e43			−1.58028
$452$		−	2.04229e43i		−	0.316471i
$453$			1.78425e43i			0.266585i
$454$	−1.02294e44			−1.47377
$455$	−6.93751e43	+	6.33964e43i	−0.963864	+	0.880798i
$456$	−4.76655e42			−0.0638681
$457$		−	5.52879e43i		−	0.714517i	−0.934006	−	0.357259i	$-0.883711\pi$
$457$		−	5.52879e43i		−	0.714517i	0.934006	−	0.357259i	$-0.116289\pi$
$458$			5.45659e43i			0.680207i
$459$	9.95984e42			0.119769
$460$	1.26484e43	+	1.38412e43i	0.146734	+	0.160572i
$461$	1.08910e44			1.21900			0.609501	−	0.792785i	$-0.291370\pi$
$461$	1.08910e44			1.21900			0.609501	+	0.792785i	$0.291370\pi$
$462$		−	2.26022e44i		−	2.44094i
$463$			7.34911e43i			0.765858i	0.923778	+	0.382929i	$0.125085\pi$
$463$			7.34911e43i			0.765858i	−0.923778	+	0.382929i	$0.874915\pi$
$464$	−2.01344e44			−2.02485
$465$	−1.49146e44	−	1.63212e44i	−1.44757	−	1.58408i
$466$	1.61947e44			1.51707
$467$		−	1.16367e44i		−	1.05220i	−0.850421	−	0.526102i	$-0.823653\pi$
$467$		−	1.16367e44i		−	1.05220i	0.850421	−	0.526102i	$-0.176347\pi$
$468$			1.00490e43i			0.0877132i
$469$	1.23046e44			1.03685
$470$	−1.58939e43	+	1.45242e43i	−0.129305	+	0.118162i
$471$	1.30336e44			1.02381
$472$		−	4.68535e43i		−	0.355385i
$473$			6.60591e43i			0.483864i
$474$	1.44775e44			1.02412
$475$	8.30234e41	−	9.19998e42i	0.00567226	−	0.0628554i
$476$	−7.07849e42			−0.0467117
$477$			3.56504e43i			0.227254i
$478$			2.24144e44i			1.38028i
$479$	−1.45527e44			−0.865783			−0.432891	−	0.901446i	$-0.642507\pi$
$479$	−1.45527e44			−0.865783			−0.432891	+	0.901446i	$0.642507\pi$
$480$	−6.59549e43	+	6.02710e43i	−0.379111	+	0.346440i
$481$	−4.03918e43			−0.224336
$482$			1.37850e44i			0.739828i
$483$		−	2.82647e44i		−	1.46594i
$484$	−5.21479e43			−0.261389
$485$	6.83295e43	+	7.47734e43i	0.331032	+	0.362250i
$486$	1.72636e44			0.808411
$487$			2.82151e44i			1.27718i	0.769546	+	0.638591i	$0.220483\pi$
$487$			2.82151e44i			1.27718i	−0.769546	+	0.638591i	$0.779517\pi$
$488$			2.63856e44i			1.15462i
$489$	−2.11802e44			−0.896053
$490$	−1.12524e44	−	1.23136e44i	−0.460269	−	0.503675i
$491$	2.10330e44			0.831874			0.415937	−	0.909393i	$-0.363454\pi$
$491$	2.10330e44			0.831874			0.415937	+	0.909393i	$0.363454\pi$
$492$			7.31713e43i			0.279844i
$493$			7.72257e43i			0.285619i
$494$	2.00263e43			0.0716319
$495$	−1.21134e44	+	1.10695e44i	−0.419066	+	0.382951i
$496$	6.39103e44			2.13857
$497$		−	8.34508e43i		−	0.270116i
$498$		−	2.07203e44i		−	0.648802i
$499$	3.94604e44			1.19537			0.597686	−	0.801730i	$-0.296087\pi$
$499$	3.94604e44			1.19537			0.597686	+	0.801730i	$0.296087\pi$
$500$	−4.58741e43	−	6.02945e43i	−0.134451	−	0.176715i
$501$	−5.70669e44			−1.61831
$502$		−	1.36801e43i		−	0.0375386i
$503$		−	7.12742e44i		−	1.89261i	−0.323279	−	0.946304i	$-0.604785\pi$
$503$		−	7.12742e44i		−	1.89261i	0.323279	−	0.946304i	$-0.395215\pi$
$504$	1.63736e44			0.420767
$505$	1.83141e44	−	1.67358e44i	0.455489	−	0.416235i
$506$	−6.63780e44			−1.59787
$507$			2.73652e43i			0.0637627i
$508$		−	4.04060e42i		−	0.00911370i
$509$	−9.04650e44			−1.97532			−0.987659	−	0.156618i	$-0.949941\pi$
$509$	−9.04650e44			−1.97532			−0.987659	+	0.156618i	$0.949941\pi$
$510$	6.86700e43	+	7.51461e43i	0.145164	+	0.158854i
$511$	7.03980e44			1.44084
$512$			2.50660e44i			0.496741i
$513$		−	2.38115e43i		−	0.0456930i
$514$	3.09434e44			0.575011
$515$	−4.17513e44	−	4.56888e44i	−0.751365	−	0.822224i
$516$	4.91615e43			0.0856851
$517$		−	1.38497e44i		−	0.233801i
$518$		−	1.87849e44i		−	0.307162i
$519$	−4.77600e44			−0.756490
$520$	−4.24800e44	+	3.88191e44i	−0.651823	+	0.595649i
$521$	5.72183e43			0.0850575			0.0425288	−	0.999095i	$-0.486459\pi$
$521$	5.72183e43			0.0850575			0.0425288	+	0.999095i	$0.486459\pi$
$522$			5.09869e44i			0.734337i
$523$			6.60401e43i			0.0921573i	0.998938	+	0.0460787i	$0.0146725\pi$
$523$			6.60401e43i			0.0921573i	−0.998938	+	0.0460787i	$0.985328\pi$
$524$	2.13822e44			0.289125
$525$	−1.02647e44	+	1.13745e45i	−0.134499	+	1.49041i
$526$	−5.38893e44			−0.684286
$527$		−	2.45128e44i		−	0.301660i
$528$		−	1.70723e45i		−	2.03626i
$529$	3.49283e43			0.0403793
$530$	4.30151e44	−	3.93080e44i	0.482024	−	0.440483i
$531$	−1.46360e44			−0.158988
$532$			1.69229e43i			0.0178210i
$533$			1.07707e45i			1.09963i
$534$	9.72202e44			0.962334
$535$	1.24839e45	+	1.36612e45i	1.19816	+	1.31115i
$536$	7.53439e44			0.701180
$537$		−	1.36665e45i		−	1.23334i
$538$			4.10103e44i			0.358910i
$539$	1.07299e45			0.910709
$540$	−1.31742e44	−	1.44166e44i	−0.108449	−	0.118677i
$541$	−1.77379e45			−1.41628			−0.708138	−	0.706074i	$-0.750464\pi$
$541$	−1.77379e45			−1.41628			−0.708138	+	0.706074i	$0.750464\pi$
$542$			1.47481e45i			1.14222i
$543$			1.89596e45i			1.42440i
$544$	−9.90578e43			−0.0721950
$545$	1.51540e45	−	1.38481e45i	1.07148	−	0.979144i
$546$	−2.47598e45			−1.69851
$547$		−	1.16728e45i		−	0.776937i	−0.921462	−	0.388468i	$-0.873004\pi$
$547$		−	1.16728e45i		−	0.776937i	0.921462	−	0.388468i	$-0.126996\pi$
$548$			3.58475e44i			0.231515i
$549$	8.24229e44			0.516540
$550$	2.67125e45	+	2.41061e44i	1.62454	+	0.146603i
$551$	1.84627e44			0.108967
$552$		−	1.73071e45i		−	0.991357i
$553$			1.80083e45i			1.00117i
$554$	−1.54743e45			−0.835027
$555$	−3.62353e44	+	3.31126e44i	−0.189801	+	0.173444i
$556$	5.28400e44			0.268676
$557$		−	3.04688e45i		−	1.50399i	−0.659170	−	0.751994i	$-0.729092\pi$
$557$		−	3.04688e45i		−	1.50399i	0.659170	−	0.751994i	$-0.270908\pi$
$558$		−	1.61842e45i		−	0.775579i
$559$	7.23652e44			0.336694
$560$	−2.22701e45	−	2.43704e45i	−1.00605	−	1.10093i
$561$	−6.54809e44			−0.287228
$562$			2.86029e45i			1.21832i
$563$			3.49063e45i			1.44383i	0.691982	+	0.721914i	$0.256738\pi$
$563$			3.49063e45i			1.44383i	−0.691982	+	0.721914i	$0.743262\pi$
$564$	−1.03070e44			−0.0414026
$565$	−2.46446e45	−	2.69688e45i	−0.961442	−	1.05211i
$566$	−3.94979e45			−1.49659
$567$			4.27339e45i			1.57272i
$568$		−	5.10989e44i		−	0.182669i
$569$	1.15922e45			0.402543			0.201272	−	0.979535i	$-0.435493\pi$
$569$	1.15922e45			0.402543			0.201272	+	0.979535i	$0.435493\pi$
$570$	1.79655e44	−	1.64173e44i	0.0606045	−	0.0553816i
$571$	−3.31452e44			−0.108624			−0.0543119	−	0.998524i	$-0.517297\pi$
$571$	−3.31452e44			−0.108624			−0.0543119	+	0.998524i	$0.517297\pi$
$572$			1.05654e45i			0.336396i
$573$		−	4.72999e45i		−	1.46322i
$574$	−5.00911e45			−1.50562
$575$	3.34047e45	+	3.01454e44i	0.975638	+	0.0880445i
$576$	9.35759e44			0.265579
$577$		−	1.81007e45i		−	0.499224i	−0.968346	−	0.249612i	$-0.919697\pi$
$577$		−	1.81007e45i		−	0.499224i	0.968346	−	0.249612i	$-0.0803031\pi$
$578$		−	4.01147e45i		−	1.07521i
$579$	2.47800e45			0.645513
$580$	1.11782e45	−	1.02149e45i	0.283015	−	0.258625i
$581$	2.57736e45			0.634262
$582$			2.66865e45i			0.638355i
$583$			3.74825e45i			0.871561i
$584$	4.31064e45			0.974382
$585$	1.21262e45	+	1.32698e45i	0.266474	+	0.291604i
$586$	−3.83824e45			−0.820014
$587$		−	4.38043e45i		−	0.909887i	−0.890520	−	0.454944i	$-0.849659\pi$
$587$		−	4.38043e45i		−	0.909887i	0.890520	−	0.454944i	$-0.150341\pi$
$588$		−	7.98523e44i		−	0.161273i
$589$	−5.86039e44			−0.115087
$590$	1.61376e45	+	1.76595e45i	0.308164	+	0.337225i
$591$	1.08896e45			0.202217
$592$		−	1.41890e45i		−	0.256238i
$593$			4.28135e44i			0.0751932i	0.999293	+	0.0375966i	$0.0119702\pi$
$593$			4.28135e44i			0.0751932i	−0.999293	+	0.0375966i	$0.988030\pi$
$594$	6.91374e45			1.18096
$595$	−9.34726e44	+	8.54172e44i	−0.155294	+	0.141911i
$596$	2.23796e45			0.361650
$597$			6.28526e45i			0.987976i
$598$			7.27146e45i			1.11187i
$599$	−3.79121e45			−0.563944			−0.281972	−	0.959423i	$-0.590988\pi$
$599$	−3.79121e45			−0.563944			−0.281972	+	0.959423i	$0.590988\pi$
$600$	−6.28533e44	+	6.96490e45i	−0.0909563	+	1.00790i
$601$	9.56105e44			0.134610			0.0673049	−	0.997732i	$-0.478560\pi$
$601$	9.56105e44			0.134610			0.0673049	+	0.997732i	$0.478560\pi$
$602$			3.36547e45i			0.461003i
$603$		−	2.35358e45i		−	0.313685i
$604$	3.87889e44			0.0503035
$605$	−6.88621e45	+	6.29276e45i	−0.868993	+	0.794104i
$606$	6.53626e45			0.802659
$607$		−	3.04630e45i		−	0.364049i	−0.983294	−	0.182025i	$-0.941735\pi$
$607$		−	3.04630e45i		−	0.364049i	0.983294	−	0.182025i	$-0.0582650\pi$
$608$			2.36822e44i			0.0275431i
$609$	−2.28266e46			−2.58379
$610$	−9.08792e45	−	9.94497e45i	−1.00120	−	1.09562i
$611$	−1.51718e45			−0.162689
$612$			1.35395e44i			0.0141320i
$613$		−	1.50267e46i		−	1.52674i	−0.645959	−	0.763372i	$-0.723542\pi$
$613$		−	1.50267e46i		−	1.52674i	0.645959	−	0.763372i	$-0.276458\pi$
$614$	1.10100e46			1.08896
$615$	8.82968e45	+	9.66238e45i	0.850170	+	0.930346i
$616$	1.72151e46			1.61372
$617$		−	3.76624e45i		−	0.343718i	−0.985122	−	0.171859i	$-0.945023\pi$
$617$		−	3.76624e45i		−	0.343718i	0.985122	−	0.171859i	$-0.0549774\pi$
$618$		−	1.63062e46i		−	1.44892i
$619$	3.61256e45			0.312549			0.156275	−	0.987714i	$-0.450051\pi$
$619$	3.61256e45			0.312549			0.156275	+	0.987714i	$0.450051\pi$
$620$	−3.54816e45	+	3.24238e45i	−0.298910	+	0.273150i
$621$	8.64584e45			0.709244
$622$		−	2.33017e46i		−	1.86143i
$623$			1.20930e46i			0.940766i
$624$	−1.87021e46			−1.41692
$625$	−1.33336e46	−	2.42628e45i	−0.983844	−	0.179028i
$626$	6.65738e45			0.478440
$627$			1.56548e45i			0.109581i
$628$		−	2.83346e45i		−	0.193189i
$629$	−5.44219e44			−0.0361442
$630$	−6.17136e45	+	5.63952e45i	−0.399266	+	0.364857i
$631$	−1.19160e46			−0.751008			−0.375504	−	0.926821i	$-0.622530\pi$
$631$	−1.19160e46			−0.751008			−0.375504	+	0.926821i	$0.622530\pi$
$632$			1.10269e46i			0.677052i
$633$		−	3.32514e46i		−	1.98907i
$634$	5.25750e45			0.306413
$635$	−4.87585e44	−	5.33568e44i	−0.0276875	−	0.0302986i
$636$	2.78947e45			0.154340
$637$		−	1.17542e46i		−	0.633711i
$638$			5.36071e46i			2.81632i
$639$	−1.59622e45			−0.0817200
$640$	−1.62185e46	−	1.77480e46i	−0.809172	−	0.885482i
$641$	1.22124e45			0.0593806			0.0296903	−	0.999559i	$-0.490548\pi$
$641$	1.22124e45			0.0593806			0.0296903	+	0.999559i	$0.490548\pi$
$642$			4.87567e46i			2.31050i
$643$			2.16557e46i			1.00021i	0.865965	+	0.500105i	$0.166705\pi$
$643$			2.16557e46i			1.00021i	−0.865965	+	0.500105i	$0.833295\pi$
$644$	−6.14462e45			−0.276617
$645$	6.49186e45	−	5.93239e45i	0.284861	−	0.260312i
$646$	2.69825e44			0.0115410
$647$			1.30233e45i			0.0543002i	0.999631	+	0.0271501i	$0.00864321\pi$
$647$			1.30233e45i			0.0543002i	−0.999631	+	0.0271501i	$0.991357\pi$
$648$			2.61670e46i			1.06357i
$649$	−1.53882e46			−0.609747
$650$	2.64074e45	−	2.92625e46i	0.102013	−	1.13042i
$651$	7.24559e46			2.72890
$652$			4.60449e45i			0.169081i
$653$		−	1.93235e46i		−	0.691861i	−0.938260	−	0.345930i	$-0.887563\pi$
$653$		−	1.93235e46i		−	0.691861i	0.938260	−	0.345930i	$-0.112437\pi$
$654$	5.40844e46			1.88816
$655$	2.82355e46	−	2.58022e46i	0.961201	−	0.878366i
$656$	−3.78358e46			−1.25600
$657$		−	1.34655e46i		−	0.435906i
$658$		−	7.05591e45i		−	0.222754i
$659$	1.11486e46			0.343249			0.171625	−	0.985162i	$-0.445098\pi$
$659$	1.11486e46			0.343249			0.171625	+	0.985162i	$0.445098\pi$
$660$	8.66135e45	+	9.47817e45i	0.260082	+	0.284610i
$661$	−5.28685e46			−1.54836			−0.774182	−	0.632963i	$-0.781839\pi$
$661$	−5.28685e46			−1.54836			−0.774182	+	0.632963i	$0.781839\pi$
$662$		−	4.09404e46i		−	1.16949i
$663$			7.17319e45i			0.199866i
$664$	1.57818e46			0.428926
$665$	2.04211e45	+	2.23469e45i	0.0541404	+	0.0592462i
$666$	−3.59311e45			−0.0929279
$667$			6.70373e46i			1.69138i
$668$			1.24061e46i			0.305368i
$669$	−3.96491e46			−0.952143
$670$	−2.83978e46	+	2.59505e46i	−0.665350	+	0.608010i
$671$	8.66586e46			1.98103
$672$		−	2.92799e46i		−	0.653095i
$673$			3.85972e46i			0.840054i	0.907512	+	0.420027i	$0.137979\pi$
$673$			3.85972e46i			0.840054i	−0.907512	+	0.420027i	$0.862021\pi$
$674$	−5.25478e46			−1.11600
$675$	−3.47934e46	−	3.13986e45i	−0.721082	−	0.0650726i
$676$	5.94908e44			0.0120318
$677$			2.19045e46i			0.432335i	0.976356	+	0.216167i	$0.0693557\pi$
$677$			2.19045e46i			0.432335i	−0.976356	+	0.216167i	$0.930644\pi$
$678$		−	9.62510e46i		−	1.85402i
$679$	−3.31947e46			−0.624048
$680$	−5.72355e45	+	5.23030e45i	−0.105019	+	0.0959686i
$681$	−8.75981e46			−1.56880
$682$		−	1.70159e47i		−	2.97449i
$683$			8.23915e44i			0.0140586i	0.999975	+	0.00702928i	$0.00223751\pi$
$683$			8.23915e44i			0.0140586i	−0.999975	+	0.00702928i	$0.997762\pi$
$684$	3.23695e44			0.00539151
$685$	4.32577e46	+	4.73372e46i	0.703346	+	0.769677i
$686$	−3.39029e46			−0.538131
$687$			4.67268e46i			0.724069i
$688$			2.54208e46i			0.384573i
$689$	4.10607e46			0.606470
$690$	5.96104e46	+	6.52320e46i	0.859631	+	0.940700i
$691$	−6.11797e46			−0.861430			−0.430715	−	0.902488i	$-0.641739\pi$
$691$	−6.11797e46			−0.861430			−0.430715	+	0.902488i	$0.641739\pi$
$692$			1.03828e46i			0.142746i
$693$		−	5.37761e46i		−	0.721924i
$694$	4.12772e46			0.541102
$695$	6.97761e46	−	6.37628e46i	0.893218	−	0.816241i
$696$	−1.39773e47			−1.74731
$697$			1.45119e46i			0.177168i
$698$			4.96387e46i			0.591842i
$699$	1.38682e47			1.61490
$700$	2.47278e46	+	2.23151e45i	0.281234	+	0.0253794i
$701$	−9.95653e46			−1.10601			−0.553007	−	0.833177i	$-0.686520\pi$
$701$	−9.95653e46			−1.10601			−0.553007	+	0.833177i	$0.686520\pi$
$702$		−	7.57375e46i		−	0.821766i
$703$			1.30109e45i			0.0137894i
$704$	9.83848e46			1.01854
$705$	−1.36106e46	+	1.24376e46i	−0.137644	+	0.125782i
$706$	1.04142e47			1.02884
$707$			8.13032e46i			0.784670i
$708$			1.14520e46i			0.107977i
$709$	−1.13327e47			−1.04393			−0.521964	−	0.852967i	$-0.674801\pi$
$709$	−1.13327e47			−1.04393			−0.521964	+	0.852967i	$0.674801\pi$
$710$	1.75998e46	+	1.92596e46i	0.158397	+	0.173335i
$711$	3.44457e46			0.302891
$712$			7.40484e46i			0.636203i
$713$		−	2.12788e47i		−	1.78637i
$714$	−3.33602e46			−0.273658
$715$	1.27494e47	+	1.39518e47i	1.02198	+	1.11835i
$716$	−2.97105e46			−0.232726
$717$			1.91943e47i			1.46929i
$718$		−	3.91319e46i		−	0.292737i
$719$	5.42492e46			0.396613			0.198306	−	0.980140i	$-0.436456\pi$
$719$	5.42492e46			0.396613			0.198306	+	0.980140i	$0.436456\pi$
$720$	−4.66148e46	+	4.25976e46i	−0.333072	+	0.304368i
$721$	2.02830e47			1.41644
$722$			1.61315e47i			1.10106i
$723$			1.18046e47i			0.787536i
$724$	4.12173e46			0.268778
$725$	2.43456e46	−	2.69778e47i	0.155183	−	1.71961i
$726$	−2.45767e47			−1.53133
$727$		−	1.08635e47i		−	0.661687i	−0.943686	−	0.330843i	$-0.892667\pi$
$727$		−	1.08635e47i		−	0.661687i	0.943686	−	0.330843i	$-0.107333\pi$
$728$		−	1.88585e47i		−	1.12289i
$729$	−6.46237e46			−0.376173
$730$	−1.62472e47	+	1.48470e47i	−0.924592	+	0.844911i
$731$	9.75013e45			0.0542468
$732$		−	6.44918e46i		−	0.350810i
$733$			1.51370e47i			0.805054i	0.915408	+	0.402527i	$0.131868\pi$
$733$			1.51370e47i			0.805054i	−0.915408	+	0.402527i	$0.868132\pi$
$734$	−1.31247e46			−0.0682502
$735$	−9.63589e46	−	1.05446e47i	−0.489949	−	0.536154i
$736$	−8.59891e46			−0.427523
$737$		−	2.47453e47i		−	1.20304i
$738$			9.58126e46i			0.455504i
$739$	−2.57207e47			−1.19578			−0.597888	−	0.801580i	$-0.703993\pi$
$739$	−2.57207e47			−1.19578			−0.597888	+	0.801580i	$0.703993\pi$
$740$	7.19855e45	+	7.87742e45i	0.0327281	+	0.0358146i
$741$	1.71493e46			0.0762510
$742$			1.90960e47i			0.830382i
$743$			1.84386e46i			0.0784173i	0.999231	+	0.0392087i	$0.0124837\pi$
$743$			1.84386e46i			0.0784173i	−0.999231	+	0.0392087i	$0.987516\pi$
$744$	4.43664e47			1.84545
$745$	2.95526e47	−	2.70058e47i	1.20231	−	1.09870i
$746$	5.07729e46			0.202042
$747$		−	4.92988e46i		−	0.191887i
$748$			1.42353e46i			0.0541988i
$749$	−6.06474e47			−2.25872
$750$	−2.16200e47	−	2.84161e47i	−0.787670	−	1.03527i
$751$	−4.41078e46			−0.157201			−0.0786007	−	0.996906i	$-0.525045\pi$
$751$	−4.41078e46			−0.157201			−0.0786007	+	0.996906i	$0.525045\pi$
$752$		−	5.32961e46i		−	0.185824i
$753$		−	1.17148e46i		−	0.0399593i
$754$	5.87246e47			1.95972
$755$	5.12213e46	−	4.68071e46i	0.167235	−	0.152822i
$756$	6.40006e46			0.204444
$757$		−	4.65678e47i		−	1.45547i	−0.685857	−	0.727736i	$-0.740573\pi$
$757$		−	4.65678e47i		−	1.45547i	0.685857	−	0.727736i	$-0.259427\pi$
$758$			2.06338e47i			0.631012i
$759$	−5.68420e47			−1.70091
$760$	1.25043e46	+	1.36836e46i	0.0366130	+	0.0400659i
$761$	1.32920e47			0.380841			0.190420	−	0.981703i	$-0.439015\pi$
$761$	1.32920e47			0.380841			0.190420	+	0.981703i	$0.439015\pi$
$762$		−	1.90429e46i		−	0.0533920i
$763$			6.72744e47i			1.84584i
$764$	−1.02828e47			−0.276103
$765$	1.63383e46	+	1.78791e46i	0.0429332	+	0.0469821i
$766$	6.26648e47			1.61157
$767$			1.68572e47i			0.424288i
$768$		−	3.03679e47i		−	0.748092i
$769$	2.70521e47			0.652253			0.326127	−	0.945326i	$-0.394256\pi$
$769$	2.70521e47			0.652253			0.326127	+	0.945326i	$0.394256\pi$
$770$	−6.48851e47	+	5.92934e47i	−1.53126	+	1.39929i
$771$	2.64980e47			0.612090
$772$		−	5.38707e46i		−	0.121806i
$773$			6.16100e47i			1.36361i	0.731535	+	0.681804i	$0.238804\pi$
$773$			6.16100e47i			1.36361i	−0.731535	+	0.681804i	$0.761196\pi$
$774$	6.43736e46			0.139470
$775$	−7.72772e46	+	8.56323e47i	−0.163898	+	1.81618i
$776$	−2.03259e47			−0.422019
$777$		−	1.60862e47i		−	0.326970i
$778$			8.21281e46i			0.163429i
$779$	3.46944e46			0.0675914
$780$	1.03830e47	−	9.48818e46i	0.198044	−	0.180977i
$781$	−1.67825e47			−0.313411
$782$			9.79721e46i			0.179139i
$783$		−	6.98241e47i		−	1.25008i
$784$	4.12905e47			0.723828
$785$	−3.41918e47	−	3.74163e47i	−0.586911	−	0.642261i
$786$	1.00772e48			1.69382
$787$		−	9.09975e46i		−	0.149777i	−0.997192	−	0.0748887i	$-0.976140\pi$
$787$		−	9.09975e46i		−	0.149777i	0.997192	−	0.0748887i	$-0.0238602\pi$
$788$		−	2.36735e46i		−	0.0381575i
$789$	−4.61474e47			−0.728412
$790$	−3.79797e47	−	4.15614e47i	−0.587089	−	0.642455i
$791$	1.19725e48			1.81247
$792$		−	3.29284e47i		−	0.488208i
$793$		−	9.49313e47i		−	1.37848i
$794$	−6.93963e47			−0.986957
$795$	3.68354e47	−	3.36610e47i	0.513107	−	0.468888i
$796$	1.36639e47			0.186427
$797$			9.51335e47i			1.27137i	0.771950	+	0.635684i	$0.219282\pi$
$797$			9.51335e47i			1.27137i	−0.771950	+	0.635684i	$0.780718\pi$
$798$			7.97557e46i			0.104403i
$799$	−2.04417e46			−0.0262117
$800$	3.46046e47	+	3.12282e46i	0.434659	+	0.0392249i
$801$	2.31311e47			0.284616
$802$			1.17153e47i			0.141213i
$803$		−	1.41575e48i		−	1.67178i
$804$	−1.84156e47			−0.213040
$805$	−8.11407e47	+	7.41481e47i	−0.919617	+	0.840365i
$806$	−1.86402e48			−2.06978
$807$			3.51187e47i			0.382054i
$808$			4.97839e47i			0.530642i
$809$	−6.61127e46			−0.0690453			−0.0345227	−	0.999404i	$-0.510991\pi$
$809$	−6.61127e46			−0.0690453			−0.0345227	+	0.999404i	$0.510991\pi$
$810$	−9.01262e47	−	9.86257e47i	−0.922249	−	1.00922i
$811$	−1.12294e48			−1.12593			−0.562966	−	0.826480i	$-0.690340\pi$
$811$	−1.12294e48			−1.12593			−0.562966	+	0.826480i	$0.690340\pi$
$812$			4.96242e47i			0.487550i
$813$			1.26294e48i			1.21587i
$814$	−3.77776e47			−0.356395
$815$	5.55630e47	+	6.08030e47i	0.513671	+	0.562114i
$816$	−2.51983e47			−0.228288
$817$		−	2.33101e46i		−	0.0206957i
$818$		−	1.62226e48i		−	1.41153i
$819$	−5.89097e47			−0.502346
$820$	2.10056e47	−	1.91954e47i	0.175552	−	0.160423i
$821$	1.43390e48			1.17451			0.587257	−	0.809401i	$-0.300208\pi$
$821$	1.43390e48			1.17451			0.587257	+	0.809401i	$0.300208\pi$
$822$			1.68946e48i			1.35632i
$823$		−	1.07892e48i		−	0.848970i	−0.905435	−	0.424485i	$-0.860455\pi$
$823$		−	1.07892e48i		−	0.848970i	0.905435	−	0.424485i	$-0.139545\pi$
$824$	1.24197e48			0.957885
$825$	2.28749e48	+	2.06430e47i	1.72929	+	0.156057i
$826$	−7.83971e47			−0.580938
$827$		−	1.67232e48i		−	1.21473i	−0.794424	−	0.607364i	$-0.792227\pi$
$827$		−	1.67232e48i		−	1.21473i	0.794424	−	0.607364i	$-0.207773\pi$
$828$			1.17532e47i			0.0836867i
$829$	−3.48680e47			−0.243376			−0.121688	−	0.992568i	$-0.538831\pi$
$829$	−3.48680e47			−0.243376			−0.121688	+	0.992568i	$0.538831\pi$
$830$	−5.94828e47	+	5.43566e47i	−0.407008	+	0.371932i
$831$	−1.32512e48			−0.888873
$832$		−	1.07777e48i		−	0.708746i
$833$		−	1.58370e47i		−	0.102101i
$834$	2.49029e48			1.57402
$835$	1.49706e48	+	1.63825e48i	0.927713	+	1.01520i
$836$	3.40330e46			0.0206774
$837$			2.21634e48i			1.32028i
$838$		−	6.02222e47i		−	0.351747i
$839$	1.43688e48			0.822900			0.411450	−	0.911432i	$-0.365022\pi$
$839$	1.43688e48			0.822900			0.411450	+	0.911432i	$0.365022\pi$
$840$	−1.54599e48	−	1.69179e48i	−0.868157	−	0.950030i
$841$	3.59788e48			1.98113
$842$			7.95957e46i			0.0429774i
$843$			2.44937e48i			1.29688i
$844$	−7.22873e47			−0.375328
$845$	7.85585e46	−	7.17884e46i	0.0399998	−	0.0365526i
$846$	−1.34963e47			−0.0673913
$847$		−	3.05704e48i		−	1.49701i
$848$			1.44240e48i			0.692713i
$849$	−3.38235e48			−1.59310
$850$	3.55800e46	−	3.94269e47i	0.0164359	−	0.182129i
$851$	−4.72420e47			−0.214038
$852$			1.24896e47i			0.0555004i
$853$			3.06470e48i			1.33576i	0.744269	+	0.667880i	$0.232798\pi$
$853$			3.06470e48i			1.33576i	−0.744269	+	0.667880i	$0.767202\pi$
$854$	4.41494e48			1.88743
$855$	4.27444e46	−	3.90607e46i	0.0179242	−	0.0163795i
$856$	−3.71358e48			−1.52748
$857$		−	3.52656e47i		−	0.142288i	−0.997466	−	0.0711439i	$-0.977335\pi$
$857$		−	3.52656e47i		−	0.142288i	0.997466	−	0.0711439i	$-0.0226650\pi$
$858$			4.97935e48i			1.97076i
$859$	−3.49821e48			−1.35819			−0.679093	−	0.734052i	$-0.737627\pi$
$859$	−3.49821e48			−1.35819			−0.679093	+	0.734052i	$0.737627\pi$
$860$	−1.28968e47	−	1.41130e47i	−0.0491198	−	0.0537522i
$861$	−4.28949e48			−1.60271
$862$		−	2.35069e48i		−	0.861639i
$863$		−	2.18223e48i		−	0.784733i	−0.919809	−	0.392366i	$-0.871657\pi$
$863$		−	2.18223e48i		−	0.784733i	0.919809	−	0.392366i	$-0.128343\pi$
$864$	8.95638e47			0.315977
$865$	1.25291e48	+	1.37107e48i	0.433665	+	0.474563i
$866$	−1.84893e48			−0.627877
$867$		−	3.43517e48i		−	1.14455i
$868$		−	1.57516e48i		−	0.514932i
$869$	3.62158e48			1.16164
$870$	5.26816e48	−	4.81416e48i	1.65803	−	1.51514i
$871$	−2.71075e48			−0.837125
$872$			4.11937e48i			1.24827i
$873$			6.34937e47i			0.188797i
$874$	2.34227e47			0.0683436
$875$	3.53462e48	−	2.68926e48i	1.01207	−	0.770017i
$876$	−1.05361e48			−0.296047
$877$		−	5.47361e48i		−	1.50932i	−0.656117	−	0.754659i	$-0.727802\pi$
$877$		−	5.47361e48i		−	1.50932i	0.656117	−	0.754659i	$-0.272198\pi$
$878$		−	1.64644e48i		−	0.445540i
$879$	−3.28683e48			−0.872892
$880$	−4.90103e48	+	4.47867e48i	−1.27739	+	1.16731i
$881$	−1.58161e48			−0.404572			−0.202286	−	0.979326i	$-0.564837\pi$
$881$	−1.58161e48			−0.404572			−0.202286	+	0.979326i	$0.564837\pi$
$882$		−	1.04561e48i		−	0.262505i
$883$		−	2.91205e48i		−	0.717542i	−0.933426	−	0.358771i	$-0.883196\pi$
$883$		−	2.91205e48i		−	0.717542i	0.933426	−	0.358771i	$-0.116804\pi$
$884$	1.55942e47			0.0377139
$885$	1.38192e48	+	1.51225e48i	0.328035	+	0.358971i
$886$	−5.00561e48			−1.16627
$887$			5.31827e48i			1.21627i	0.793833	+	0.608136i	$0.208082\pi$
$887$			5.31827e48i			1.21627i	−0.793833	+	0.608136i	$0.791918\pi$
$888$		−	9.84998e47i		−	0.221117i
$889$	2.36871e47			0.0521954
$890$	−2.55042e48	−	2.79095e48i	−0.551667	−	0.603693i
$891$	8.59406e48			1.82480
$892$			8.61955e47i			0.179665i
$893$			4.88710e46i			0.0100001i
$894$	1.05473e49			2.11870
$895$	−3.92332e48	+	3.58521e48i	−0.773702	+	0.707025i
$896$	7.87900e48			1.52542
$897$			6.22683e48i			1.18356i
$898$		−	4.56199e48i		−	0.851324i
$899$	−1.71849e49			−3.14855
$900$	4.26835e46	−	4.72984e47i	0.00767819	−	0.0850835i
$901$	5.53232e47			0.0977120
$902$			1.00736e49i			1.74694i
$903$			2.88198e48i			0.490730i
$904$	7.33102e48			1.22570
$905$	5.44281e48	−	4.97375e48i	0.893556	−	0.816550i
$906$	1.82808e48			0.294700
$907$		−	3.23851e48i		−	0.512654i	−0.966590	−	0.256327i	$-0.917488\pi$
$907$		−	3.23851e48i		−	0.512654i	0.966590	−	0.256327i	$-0.0825124\pi$
$908$			1.90435e48i			0.296026i
$909$	1.55514e48			0.237391
$910$	6.49536e48	+	7.10792e48i	0.973690	+	1.06552i
$911$	−5.41124e48			−0.796605			−0.398303	−	0.917254i	$-0.630401\pi$
$911$	−5.41124e48			−0.796605			−0.398303	+	0.917254i	$0.630401\pi$
$912$			6.02427e47i			0.0870943i
$913$		−	5.18323e48i		−	0.735923i
$914$	−5.66460e48			−0.789872
$915$	−7.78232e48	−	8.51625e48i	−1.06576	−	1.16627i
$916$	1.01582e48			0.136629
$917$			1.25348e49i			1.65586i
$918$		−	1.02045e48i		−	0.132400i
$919$	4.23316e48			0.539459			0.269730	−	0.962936i	$-0.413066\pi$
$919$	4.23316e48			0.539459			0.269730	+	0.962936i	$0.413066\pi$
$920$	−4.96844e48	+	4.54026e48i	−0.621900	+	0.568305i
$921$	9.42830e48			1.15918
$922$		−	1.11586e49i		−	1.34756i
$923$			1.83846e48i			0.218085i
$924$	−4.20772e48			−0.490297
$925$	1.90116e48	+	1.71566e47i	0.217610	+	0.0196378i
$926$	7.52963e48			0.846627
$927$		−	3.87965e48i		−	0.428526i
$928$			6.94451e48i			0.753529i
$929$	1.09693e49			1.16929			0.584644	−	0.811290i	$-0.301234\pi$
$929$	1.09693e49			1.16929			0.584644	+	0.811290i	$0.301234\pi$
$930$	−1.67221e49	+	1.52810e49i	−1.75114	+	1.60023i
$931$	−3.78622e47			−0.0389526
$932$		−	3.01488e48i		−	0.304725i
$933$		−	1.99541e49i		−	1.98146i
$934$	−1.19225e49			−1.16317
$935$	1.71779e48	+	1.87979e48i	0.164657	+	0.180185i
$936$	−3.60718e48			−0.339717
$937$		−	8.82160e48i		−	0.816289i	−0.912917	−	0.408145i	$-0.866176\pi$
$937$		−	8.82160e48i		−	0.816289i	0.912917	−	0.408145i	$-0.133824\pi$
$938$		−	1.26068e49i		−	1.14620i
$939$	5.70097e48			0.509291
$940$	2.70389e47	+	2.95888e47i	0.0237345	+	0.0259728i
$941$	−7.63482e48			−0.658522			−0.329261	−	0.944239i	$-0.606800\pi$
$941$	−7.63482e48			−0.658522			−0.329261	+	0.944239i	$0.606800\pi$
$942$		−	1.33538e49i		−	1.13179i
$943$			1.25974e49i			1.04915i
$944$	−5.92165e48			−0.484624
$945$	8.45138e48	−	7.72305e48i	0.679678	−	0.621103i
$946$	6.76817e48			0.534894
$947$		−	1.62448e49i		−	1.26165i	−0.775924	−	0.630827i	$-0.782716\pi$
$947$		−	1.62448e49i		−	1.26165i	0.775924	−	0.630827i	$-0.217284\pi$
$948$		−	2.69520e48i		−	0.205709i
$949$	−1.55090e49			−1.16330
$950$	−9.42597e47	−	8.50628e46i	−0.0694843	−	0.00627047i
$951$	4.50220e48			0.326172
$952$		−	2.54090e48i		−	0.180916i
$953$			9.94250e48i			0.695766i	0.937538	+	0.347883i	$0.113099\pi$
$953$			9.94250e48i			0.695766i	−0.937538	+	0.347883i	$0.886901\pi$
$954$	3.65262e48			0.251221
$955$	−1.35786e49	+	1.24084e49i	−0.917910	+	0.838805i
$956$	4.17277e48			0.277248
$957$			4.59058e49i			2.99792i
$958$			1.49102e49i			0.957090i
$959$	−2.10148e49			−1.32592
$960$	−8.83538e48	−	9.66862e48i	−0.547962	−	0.599638i
$961$	3.81443e49			2.32538
$962$			4.13840e48i			0.247995i
$963$			1.16004e49i			0.683345i
$964$	2.56628e48			0.148605
$965$	−6.50065e48	−	7.11371e48i	−0.370047	−	0.404944i
$966$	−2.89589e49			−1.62054
$967$		−	2.72293e49i		−	1.49796i	−0.662593	−	0.748980i	$-0.730544\pi$
$967$		−	2.72293e49i		−	1.49796i	0.662593	−	0.748980i	$-0.269456\pi$
$968$		−	1.87190e49i		−	1.01237i
$969$	2.31061e47			0.0122853
$970$	7.66101e48	−	7.00079e48i	0.400454	−	0.365943i
$971$	3.20196e48			0.164550			0.0822751	−	0.996610i	$-0.473781\pi$
$971$	3.20196e48			0.164550			0.0822751	+	0.996610i	$0.473781\pi$
$972$		−	3.21386e48i		−	0.162380i
$973$			3.09762e49i			1.53874i
$974$	2.89081e49			1.41188
$975$	2.26136e48	−	2.50586e49i	0.108591	−	1.20332i
$976$	3.33478e49			1.57451
$977$			2.56729e49i			1.19183i	0.803047	+	0.595915i	$0.203211\pi$
$977$			2.56729e49i			1.19183i	−0.803047	+	0.595915i	$0.796789\pi$
$978$			2.17005e49i			0.990553i
$979$	2.43198e49			1.09155
$980$	−2.29236e48	+	2.09480e48i	−0.101170	+	0.0924513i
$981$	1.28680e49			0.558435
$982$		−	2.15497e49i		−	0.919606i
$983$			2.12937e49i			0.893548i	0.894647	+	0.446774i	$0.147427\pi$
$983$			2.12937e49i			0.893548i	−0.894647	+	0.446774i	$0.852573\pi$
$984$	−2.62656e49			−1.08385
$985$	−2.85672e48	−	3.12612e48i	−0.115923	−	0.126855i
$986$	7.91226e48			0.315742
$987$		−	6.04224e48i		−	0.237118i
$988$		−	3.72818e47i		−	0.0143882i
$989$	8.46380e48			0.321238
$990$	1.13414e49	+	1.24110e49i	0.423338	+	0.463261i
$991$	−1.22972e49			−0.451432			−0.225716	−	0.974193i	$-0.572472\pi$
$991$	−1.22972e49			−0.451432			−0.225716	+	0.974193i	$0.572472\pi$
$992$		−	2.20431e49i		−	0.795849i
$993$		−	3.50588e49i		−	1.24490i
$994$	−8.55007e48			−0.298603
$995$	1.80434e49	−	1.64884e49i	0.619779	−	0.566367i
$996$	−3.85739e48			−0.130321
$997$			4.53447e49i			1.50680i	0.657562	+	0.753401i	$0.271588\pi$
$997$			4.53447e49i			1.50680i	−0.657562	+	0.753401i	$0.728412\pi$
$998$		−	4.04297e49i		−	1.32144i
$999$	4.92059e48			0.158193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.34.b.a.4.5	✓	16
5.2	odd	4		25.34.a.f.1.12		16
5.3	odd	4		25.34.a.f.1.5		16
5.4	even	2	inner	5.34.b.a.4.12	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.b.a.4.5	✓	16	1.1	even	1	trivial
5.34.b.a.4.12	yes	16	5.4	even	2	inner
25.34.a.f.1.5		16	5.3	odd	4
25.34.a.f.1.12		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)

\(f(q)\)	\(=\)	\(q-102456. i q^{2} -8.77372e7i q^{3} -1.90737e9 q^{4} +(-2.51871e11 + 2.30165e11i) q^{5} -8.98924e12 q^{6} -1.11815e14i q^{7} -6.84671e14i q^{8} -2.13876e15 q^{9} +O(q^{10})\)	\(q-102456. i q^{2} -8.77372e7i q^{3} -1.90737e9 q^{4} +(-2.51871e11 + 2.30165e11i) q^{5} -8.98924e12 q^{6} -1.11815e14i q^{7} -6.84671e14i q^{8} -2.13876e15 q^{9} +(2.35819e16 + 2.58058e16i) q^{10} -2.24867e17 q^{11} +1.67348e17i q^{12} +2.46334e18i q^{13} -1.14562e19 q^{14} +(2.01941e19 + 2.20985e19i) q^{15} -8.65331e19 q^{16} +3.31898e19i q^{17} +2.19130e20i q^{18} +7.93484e19 q^{19} +(4.80413e20 - 4.39011e20i) q^{20} -9.81036e21 q^{21} +2.30391e22i q^{22} +2.88111e22i q^{23} -6.00711e22 q^{24} +(1.04632e22 - 1.15944e23i) q^{25} +2.52385e23 q^{26} -3.00088e23i q^{27} +2.13273e23i q^{28} +2.32679e24 q^{29} +(2.26413e24 - 2.06901e24i) q^{30} -7.38565e24 q^{31} +2.98459e24i q^{32} +1.97292e25i q^{33} +3.40050e24 q^{34} +(2.57360e25 + 2.81631e25i) q^{35} +4.07941e24 q^{36} +1.63972e25i q^{37} -8.12975e24i q^{38} +2.16126e26 q^{39} +(1.57588e26 + 1.72449e26i) q^{40} +4.37241e26 q^{41} +1.00513e27i q^{42} -2.93769e26i q^{43} +4.28906e26 q^{44} +(5.38693e26 - 4.92269e26i) q^{45} +2.95188e27 q^{46} +6.15905e26i q^{47} +7.59218e27i q^{48} -4.77164e27 q^{49} +(-1.18792e28 - 1.07202e27i) q^{50} +2.91198e27 q^{51} -4.69850e27i q^{52} -1.66687e28i q^{53} -3.07459e28 q^{54} +(5.66377e28 - 5.17567e28i) q^{55} -7.65566e28 q^{56} -6.96181e27i q^{57} -2.38395e29i q^{58} +6.84322e28 q^{59} +(-3.85176e28 - 4.21501e28i) q^{60} -3.85377e29 q^{61} +7.56707e29i q^{62} +2.39146e29i q^{63} -4.37524e29 q^{64} +(-5.66975e29 - 6.20444e29i) q^{65} +2.02139e30 q^{66} +1.10044e30i q^{67} -6.33053e28i q^{68} +2.52780e30 q^{69} +(2.88548e30 - 2.63682e30i) q^{70} +7.46328e29 q^{71} +1.46435e30i q^{72} +6.29592e30i q^{73} +1.68000e30 q^{74} +(-1.01726e31 - 9.18008e29i) q^{75} -1.51347e29 q^{76} +2.51436e31i q^{77} -2.21435e31i q^{78} -1.61054e31 q^{79} +(2.17952e31 - 1.99169e31i) q^{80} -3.82184e31 q^{81} -4.47982e31i q^{82} +2.30501e31i q^{83} +1.87120e31 q^{84} +(-7.63914e30 - 8.35956e30i) q^{85} -3.00985e31 q^{86} -2.04146e32i q^{87} +1.53960e32i q^{88} -1.08152e32 q^{89} +(-5.04361e31 - 5.51925e31i) q^{90} +2.75439e32 q^{91} -5.49534e31i q^{92} +6.47996e32i q^{93} +6.31033e31 q^{94} +(-1.99856e31 + 1.82633e31i) q^{95} +2.61860e32 q^{96} -2.96871e32i q^{97} +4.88885e32i q^{98} +4.80938e32 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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