LMFDB - Embedded newform 5.34.b.a.4.16

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			4.16
Root			$81004.3i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.34.b.a.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+162009. i q^{2} +1.50582e7i q^{3} -1.76568e10 q^{4} +(3.29148e11 - 8.98715e10i) q^{5} -2.43956e12 q^{6} +1.33679e14i q^{7} -1.46891e15i q^{8} +5.33231e15 q^{9} +O(q^{10})$	\(q+162009. i q^{2} +1.50582e7i q^{3} -1.76568e10 q^{4} +(3.29148e11 - 8.98715e10i) q^{5} -2.43956e12 q^{6} +1.33679e14i q^{7} -1.46891e15i q^{8} +5.33231e15 q^{9} +(1.45600e16 + 5.33248e16i) q^{10} +2.82007e17 q^{11} -2.65881e17i q^{12} +1.43267e18i q^{13} -2.16571e19 q^{14} +(1.35331e18 + 4.95639e18i) q^{15} +8.63057e19 q^{16} +2.38442e20i q^{17} +8.63880e20i q^{18} +5.86844e20 q^{19} +(-5.81171e21 + 1.58685e21i) q^{20} -2.01297e21 q^{21} +4.56875e22i q^{22} -1.73446e22i q^{23} +2.21193e22 q^{24} +(1.00262e23 - 5.91621e22i) q^{25} -2.32104e23 q^{26} +1.64005e23i q^{27} -2.36034e24i q^{28} +1.13413e23 q^{29} +(-8.02977e23 + 2.19247e23i) q^{30} +2.12133e24 q^{31} +1.36438e24i q^{32} +4.24652e24i q^{33} -3.86296e25 q^{34} +(1.20139e25 + 4.40001e25i) q^{35} -9.41517e25 q^{36} -8.11541e25i q^{37} +9.50738e25i q^{38} -2.15734e25 q^{39} +(-1.32014e26 - 4.83490e26i) q^{40} -1.96159e26 q^{41} -3.26118e26i q^{42} -8.68674e26i q^{43} -4.97935e27 q^{44} +(1.75512e27 - 4.79223e26i) q^{45} +2.80997e27 q^{46} +5.03480e27i q^{47} +1.29961e27i q^{48} -1.01390e28 q^{49} +(9.58476e27 + 1.62432e28i) q^{50} -3.59051e27 q^{51} -2.52963e28i q^{52} -7.43106e27i q^{53} -2.65702e28 q^{54} +(9.28220e28 - 2.53444e28i) q^{55} +1.96363e29 q^{56} +8.83684e27i q^{57} +1.83740e28i q^{58} -5.72962e28 q^{59} +(-2.38951e28 - 8.75141e28i) q^{60} -2.92431e29 q^{61} +3.43673e29i q^{62} +7.12817e29i q^{63} +5.20320e29 q^{64} +(1.28756e29 + 4.71559e29i) q^{65} -6.87973e29 q^{66} -8.52723e29i q^{67} -4.21013e30i q^{68} +2.61178e29 q^{69} +(-7.12839e30 + 1.94636e30i) q^{70} -1.52022e30 q^{71} -7.83271e30i q^{72} +1.66290e30i q^{73} +1.31477e31 q^{74} +(8.90876e29 + 1.50976e30i) q^{75} -1.03618e31 q^{76} +3.76983e31i q^{77} -3.49508e30i q^{78} -2.86123e31 q^{79} +(2.84073e31 - 7.75642e30i) q^{80} +2.71730e31 q^{81} -3.17794e31i q^{82} +1.27605e30i q^{83} +3.55426e31 q^{84} +(2.14291e31 + 7.84827e31i) q^{85} +1.40733e32 q^{86} +1.70781e30i q^{87} -4.14244e32i q^{88} -1.21015e32 q^{89} +(7.76382e31 + 2.84344e32i) q^{90} -1.91517e32 q^{91} +3.06250e32i q^{92} +3.19435e31i q^{93} -8.15681e32 q^{94} +(1.93159e32 - 5.27406e31i) q^{95} -2.05451e31 q^{96} +9.03160e32i q^{97} -1.64261e33i q^{98} +1.50375e33 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 $

$2$			162009.i			1.74801i	0.485920	+	0.874003i	$0.338485\pi$
$2$			162009.i			1.74801i	−0.485920	+	0.874003i	$0.661515\pi$
$3$			1.50582e7i			0.201964i	0.994888	+	0.100982i	$0.0321984\pi$
$3$			1.50582e7i			0.201964i	−0.994888	+	0.100982i	$0.967802\pi$
$4$	−1.76568e10			−2.05553
$5$	3.29148e11	−	8.98715e10i	0.964686	−	0.263401i
$5$	3.29148e11	−	8.98715e10i	0.964686	−	0.263401i
$6$	−2.43956e12			−0.353034
$7$			1.33679e14i			1.52035i	0.649716	+	0.760177i	$0.274888\pi$
$7$			1.33679e14i			1.52035i	−0.649716	+	0.760177i	$0.725112\pi$
$8$		−	1.46891e15i		−	1.84507i
$9$	5.33231e15			0.959211
$10$	1.45600e16	+	5.33248e16i	0.460426	+	1.68628i
$11$	2.82007e17			1.85046			0.925231	−	0.379403i	$-0.123871\pi$
$11$	2.82007e17			1.85046			0.925231	+	0.379403i	$0.123871\pi$
$12$		−	2.65881e17i		−	0.415141i
$13$			1.43267e18i			0.597145i	0.954387	+	0.298572i	$0.0965104\pi$
$13$			1.43267e18i			0.597145i	−0.954387	+	0.298572i	$0.903490\pi$
$14$	−2.16571e19			−2.65759
$15$	1.35331e18	+	4.95639e18i	0.0531974	+	0.194832i
$16$	8.63057e19			1.16966
$17$			2.38442e20i			1.18843i	0.804304	+	0.594217i	$0.202538\pi$
$17$			2.38442e20i			1.18843i	−0.804304	+	0.594217i	$0.797462\pi$
$18$			8.63880e20i			1.67671i
$19$	5.86844e20			0.466754			0.233377	−	0.972386i	$-0.425022\pi$
$19$	5.86844e20			0.466754			0.233377	+	0.972386i	$0.425022\pi$
$20$	−5.81171e21	+	1.58685e21i	−1.98294	+	0.541427i
$21$	−2.01297e21			−0.307056
$22$			4.56875e22i			3.23462i
$23$		−	1.73446e22i		−	0.589731i	−0.955539	−	0.294866i	$-0.904725\pi$
$23$		−	1.73446e22i		−	0.589731i	0.955539	−	0.294866i	$-0.0952749\pi$
$24$	2.21193e22			0.372636
$25$	1.00262e23	−	5.91621e22i	0.861240	−	0.508198i
$26$	−2.32104e23			−1.04381
$27$			1.64005e23i			0.395689i
$28$		−	2.36034e24i		−	3.12513i
$29$	1.13413e23			0.0841585			0.0420792	−	0.999114i	$-0.486602\pi$
$29$	1.13413e23			0.0841585			0.0420792	+	0.999114i	$0.486602\pi$
$30$	−8.02977e23	+	2.19247e23i	−0.340567	+	0.0929894i
$31$	2.12133e24			0.523769			0.261885	−	0.965099i	$-0.415656\pi$
$31$	2.12133e24			0.523769			0.261885	+	0.965099i	$0.415656\pi$
$32$			1.36438e24i			0.199507i
$33$			4.24652e24i			0.373726i
$34$	−3.86296e25			−2.07739
$35$	1.20139e25	+	4.40001e25i	0.400463	+	1.46667i
$36$	−9.41517e25			−1.97168
$37$		−	8.11541e25i		−	1.08139i	−0.841219	−	0.540695i	$-0.818161\pi$
$37$		−	8.11541e25i		−	1.08139i	0.841219	−	0.540695i	$-0.181839\pi$
$38$			9.50738e25i			0.815890i
$39$	−2.15734e25			−0.120602
$40$	−1.32014e26	−	4.83490e26i	−0.485992	−	1.77991i
$41$	−1.96159e26			−0.480478			−0.240239	−	0.970714i	$-0.577226\pi$
$41$	−1.96159e26			−0.480478			−0.240239	+	0.970714i	$0.577226\pi$
$42$		−	3.26118e26i		−	0.536736i
$43$		−	8.68674e26i		−	0.969677i	−0.874604	−	0.484838i	$-0.838878\pi$
$43$		−	8.68674e26i		−	0.969677i	0.874604	−	0.484838i	$-0.161122\pi$
$44$	−4.97935e27			−3.80367
$45$	1.75512e27	−	4.79223e26i	0.925338	−	0.252657i
$46$	2.80997e27			1.03085
$47$			5.03480e27i			1.29529i	0.761941	+	0.647646i	$0.224246\pi$
$47$			5.03480e27i			1.29529i	−0.761941	+	0.647646i	$0.775754\pi$
$48$			1.29961e27i			0.236229i
$49$	−1.01390e28			−1.31148
$50$	9.58476e27	+	1.62432e28i	0.888334	+	1.50545i
$51$	−3.59051e27			−0.240021
$52$		−	2.52963e28i		−	1.22745i
$53$		−	7.43106e27i		−	0.263329i	−0.991294	−	0.131665i	$-0.957968\pi$
$53$		−	7.43106e27i		−	0.263329i	0.991294	−	0.131665i	$-0.0420322\pi$
$54$	−2.65702e28			−0.691667
$55$	9.28220e28	−	2.53444e28i	1.78512	−	0.487413i
$56$	1.96363e29			2.80515
$57$			8.83684e27i			0.0942674i
$58$			1.83740e28i			0.147110i
$59$	−5.72962e28			−0.345993			−0.172997	−	0.984922i	$-0.555345\pi$
$59$	−5.72962e28			−0.345993			−0.172997	+	0.984922i	$0.555345\pi$
$60$	−2.38951e28	−	8.75141e28i	−0.109349	−	0.400481i
$61$	−2.92431e29			−1.01878			−0.509392	−	0.860535i	$-0.670129\pi$
$61$	−2.92431e29			−1.01878			−0.509392	+	0.860535i	$0.670129\pi$
$62$			3.43673e29i			0.915552i
$63$			7.12817e29i			1.45834i
$64$	5.20320e29			0.820920
$65$	1.28756e29	+	4.71559e29i	0.157288	+	0.576058i
$66$	−6.87973e29			−0.653276
$67$		−	8.52723e29i		−	0.631791i	−0.948794	−	0.315896i	$-0.897695\pi$
$67$		−	8.52723e29i		−	0.631791i	0.948794	−	0.315896i	$-0.102305\pi$
$68$		−	4.21013e30i		−	2.44286i
$69$	2.61178e29			0.119104
$70$	−7.12839e30	+	1.94636e30i	−2.56374	+	0.700011i
$71$	−1.52022e30			−0.432656			−0.216328	−	0.976321i	$-0.569408\pi$
$71$	−1.52022e30			−0.432656			−0.216328	+	0.976321i	$0.569408\pi$
$72$		−	7.83271e30i		−	1.76981i
$73$			1.66290e30i			0.299253i	0.988743	+	0.149627i	$0.0478071\pi$
$73$			1.66290e30i			0.299253i	−0.988743	+	0.149627i	$0.952193\pi$
$74$	1.31477e31			1.89028
$75$	8.90876e29	+	1.50976e30i	0.102638	+	0.173939i
$76$	−1.03618e31			−0.959426
$77$			3.76983e31i			2.81336i
$78$		−	3.49508e30i		−	0.210812i
$79$	−2.86123e31			−1.39864			−0.699319	−	0.714810i	$-0.746513\pi$
$79$	−2.86123e31			−1.39864			−0.699319	+	0.714810i	$0.746513\pi$
$80$	2.84073e31	−	7.75642e30i	1.12836	−	0.308089i
$81$	2.71730e31			0.879296
$82$		−	3.17794e31i		−	0.839879i
$83$			1.27605e30i			0.0276109i	0.999905	+	0.0138054i	$0.00439455\pi$
$83$			1.27605e30i			0.0276109i	−0.999905	+	0.0138054i	$0.995605\pi$
$84$	3.55426e31			0.631162
$85$	2.14291e31	+	7.84827e31i	0.313035	+	1.14647i
$86$	1.40733e32			1.69500
$87$			1.70781e30i			0.0169969i
$88$		−	4.14244e32i		−	3.41422i
$89$	−1.21015e32			−0.827762			−0.413881	−	0.910331i	$-0.635827\pi$
$89$	−1.21015e32			−0.827762			−0.413881	+	0.910331i	$0.635827\pi$
$90$	7.76382e31	+	2.84344e32i	0.441646	+	1.61750i
$91$	−1.91517e32			−0.907872
$92$			3.06250e32i			1.21221i
$93$			3.19435e31i			0.105782i
$94$	−8.15681e32			−2.26418
$95$	1.93159e32	−	5.27406e31i	0.450272	−	0.122943i
$96$	−2.05451e31			−0.0402933
$97$			9.03160e32i			1.49290i	0.665441	+	0.746451i	$0.268244\pi$
$97$			9.03160e32i			1.49290i	−0.665441	+	0.746451i	$0.731756\pi$
$98$		−	1.64261e33i		−	2.29247i
$99$	1.50375e33			1.77498
$100$	−1.77030e33	+	1.04461e33i	−1.77030	+	1.04461i
$101$	−1.32921e33			−1.12795			−0.563976	−	0.825791i	$-0.690729\pi$
$101$	−1.32921e33			−1.12795			−0.563976	+	0.825791i	$0.690729\pi$
$102$		−	5.81694e32i		−	0.419558i
$103$		−	2.85224e33i		−	1.75135i	−0.482905	−	0.875673i	$-0.660418\pi$
$103$		−	2.85224e33i		−	1.75135i	0.482905	−	0.875673i	$-0.339582\pi$
$104$	2.10446e33			1.10177
$105$	−6.62564e32	+	1.80908e32i	−0.296213	+	0.0808789i
$106$	1.20389e33			0.460301
$107$		−	3.50122e32i		−	0.114654i	−0.998355	−	0.0573268i	$-0.981742\pi$
$107$		−	3.50122e32i		−	0.114654i	0.998355	−	0.0573268i	$-0.0182577\pi$
$108$		−	2.89580e33i		−	0.813350i
$109$	3.72764e33			0.899285			0.449642	−	0.893209i	$-0.351551\pi$
$109$	3.72764e33			0.899285			0.449642	+	0.893209i	$0.351551\pi$
$110$	4.10601e33	+	1.50380e34i	0.852002	+	3.12039i
$111$	1.22204e33			0.218401
$112$			1.15372e34i			1.77830i
$113$		−	9.88914e33i		−	1.31633i	−0.752875	−	0.658164i	$-0.771333\pi$
$113$		−	9.88914e33i		−	1.31633i	0.752875	−	0.658164i	$-0.228667\pi$
$114$	−1.43164e33			−0.164780
$115$	−1.55878e33	−	5.70893e33i	−0.155336	−	0.568906i
$116$	−2.00252e33			−0.172990
$117$			7.63942e33i			0.572788i
$118$		−	9.28248e33i		−	0.604799i
$119$	−3.18746e34			−1.80684
$120$	7.28051e33	−	1.98789e33i	0.359477	−	0.0981526i
$121$	5.63027e34			2.42421
$122$		−	4.73764e34i		−	1.78084i
$123$		−	2.95380e33i		−	0.0970391i
$124$	−3.74560e34			−1.07662
$125$	2.76839e34	−	2.84837e34i	0.696967	−	0.717103i
$126$	−1.15482e35			−2.54919
$127$			2.44742e34i			0.474185i	0.971487	+	0.237092i	$0.0761944\pi$
$127$			2.44742e34i			0.474185i	−0.971487	+	0.237092i	$0.923806\pi$
$128$			9.60161e34i			1.63448i
$129$	1.30807e34			0.195839
$130$	−7.63966e34	+	2.08596e34i	−1.00695	+	0.274941i
$131$	−5.29429e34			−0.614939			−0.307469	−	0.951558i	$-0.599482\pi$
$131$	−5.29429e34			−0.614939			−0.307469	+	0.951558i	$0.599482\pi$
$132$		−	7.49801e34i		−	0.768204i
$133$			7.84486e34i			0.709632i
$134$	1.38148e35			1.10438
$135$	1.47394e34	+	5.39818e34i	0.104225	+	0.381716i
$136$	3.50251e35			2.19274
$137$			1.36353e35i			0.756443i	0.925715	+	0.378221i	$0.123464\pi$
$137$			1.36353e35i			0.756443i	−0.925715	+	0.378221i	$0.876536\pi$
$138$			4.23131e34i			0.208195i
$139$	1.17476e35			0.513103			0.256551	−	0.966531i	$-0.417414\pi$
$139$	1.17476e35			0.513103			0.256551	+	0.966531i	$0.417414\pi$
$140$	−2.12128e35	−	7.76903e35i	−0.823161	−	3.01477i
$141$	−7.58152e34			−0.261602
$142$		−	2.46288e35i		−	0.756286i
$143$			4.04022e35i			1.10499i
$144$	4.60209e35			1.12195
$145$	3.73298e34	−	1.01926e34i	0.0811865	−	0.0221674i
$146$	−2.69404e35			−0.523096
$147$		−	1.52676e35i		−	0.264871i
$148$			1.43292e36i			2.22282i
$149$	6.69109e35			0.928802			0.464401	−	0.885625i	$-0.346270\pi$
$149$	6.69109e35			0.928802			0.464401	+	0.885625i	$0.346270\pi$
$150$	−2.44594e35	+	1.44330e35i	−0.304047	+	0.179411i
$151$	6.65432e35			0.741283			0.370641	−	0.928776i	$-0.379138\pi$
$151$	6.65432e35			0.741283			0.370641	+	0.928776i	$0.379138\pi$
$152$		−	8.62024e35i		−	0.861192i
$153$			1.27145e36i			1.13996i
$154$	−6.10745e36			−4.91777
$155$	6.98231e35	−	1.90647e35i	0.505273	−	0.137961i
$156$	3.80918e35			0.247900
$157$		−	4.40049e35i		−	0.257725i	−0.991662	−	0.128862i	$-0.958867\pi$
$157$		−	4.40049e35i		−	0.257725i	0.991662	−	0.128862i	$-0.0411326\pi$
$158$		−	4.63543e36i		−	2.44483i
$159$	1.11899e35			0.0531829
$160$	1.22618e35	+	4.49081e35i	0.0525504	+	0.192462i
$161$	2.31860e36			0.896600
$162$			4.40226e36i			1.53701i
$163$		−	4.21573e36i		−	1.32977i	−0.746945	−	0.664886i	$-0.768480\pi$
$163$		−	4.21573e36i		−	1.32977i	0.746945	−	0.664886i	$-0.231520\pi$
$164$	3.46354e36			0.987635
$165$	3.81642e35	+	1.39773e36i	0.0984398	+	0.360529i
$166$	−2.06732e35			−0.0482640
$167$		−	5.63316e36i		−	1.19105i	−0.803337	−	0.595525i	$-0.796944\pi$
$167$		−	5.63316e36i		−	1.19105i	0.803337	−	0.595525i	$-0.203056\pi$
$168$			2.95687e36i			0.566539i
$169$	3.70360e36			0.643418
$170$	−1.27149e37	+	3.47170e36i	−2.00403	+	0.547187i
$171$	3.12924e36			0.447716
$172$			1.53380e37i			1.99320i
$173$		−	2.83870e36i		−	0.335243i	−0.985851	−	0.167621i	$-0.946391\pi$
$173$		−	2.83870e36i		−	0.335243i	0.985851	−	0.167621i	$-0.0536086\pi$
$174$	−2.76679e35			−0.0297108
$175$	7.90872e36	+	1.34028e37i	0.772642	+	1.30939i
$176$	2.43388e37			2.16441
$177$		−	8.62780e35i		−	0.0698781i
$178$		−	1.96055e37i		−	1.44693i
$179$	1.55048e37			1.04326			0.521630	−	0.853172i	$-0.325324\pi$
$179$	1.55048e37			1.04326			0.521630	+	0.853172i	$0.325324\pi$
$180$	−3.09898e37	+	8.46156e36i	−1.90206	+	0.519343i
$181$	−1.55561e36			−0.0871373			−0.0435686	−	0.999050i	$-0.513873\pi$
$181$	−1.55561e36			−0.0871373			−0.0435686	+	0.999050i	$0.513873\pi$
$182$		−	3.10274e37i		−	1.58697i
$183$		−	4.40350e36i		−	0.205757i
$184$	−2.54777e37			−1.08809
$185$	−7.29345e36	−	2.67117e37i	−0.284839	−	1.04320i
$186$	−5.17511e36			−0.184908
$187$			6.72423e37i			2.19915i
$188$		−	8.88986e37i		−	2.66251i
$189$	−2.19240e37			−0.601588
$190$	8.54443e36	+	3.12933e37i	0.214906	+	0.787078i
$191$	2.05424e37			0.473806			0.236903	−	0.971533i	$-0.423868\pi$
$191$	2.05424e37			0.473806			0.236903	+	0.971533i	$0.423868\pi$
$192$			7.83509e36i			0.165796i
$193$			6.16112e37i			1.19664i	0.801257	+	0.598321i	$0.204165\pi$
$193$			6.16112e37i			1.19664i	−0.801257	+	0.598321i	$0.795835\pi$
$194$	−1.46320e38			−2.60960
$195$	−7.10085e36	+	1.93884e36i	−0.116343	+	0.0317665i
$196$	1.79023e38			2.69578
$197$		−	2.45666e37i		−	0.340136i	−0.985432	−	0.170068i	$-0.945601\pi$
$197$		−	2.45666e37i		−	0.340136i	0.985432	−	0.170068i	$-0.0543987\pi$
$198$			2.43620e38i			3.10268i
$199$	−3.10206e37			−0.363558			−0.181779	−	0.983339i	$-0.558186\pi$
$199$	−3.10206e37			−0.363558			−0.181779	+	0.983339i	$0.558186\pi$
$200$	−8.69040e37	−	1.47276e38i	−0.937659	−	1.58904i
$201$	1.28405e37			0.127599
$202$		−	2.15343e38i		−	1.97167i
$203$			1.51610e37i			0.127951i
$204$	6.33971e37			0.493369
$205$	−6.45652e37	+	1.76291e37i	−0.463511	+	0.126558i
$206$	4.62087e38			3.06136
$207$		−	9.24866e37i		−	0.565676i
$208$			1.23647e38i			0.698456i
$209$	1.65494e38			0.863712
$210$	−2.93087e37	−	1.07341e38i	−0.141377	−	0.517782i
$211$	−2.11768e38			−0.944494			−0.472247	−	0.881466i	$-0.656557\pi$
$211$	−2.11768e38			−0.944494			−0.472247	+	0.881466i	$0.656557\pi$
$212$			1.31209e38i			0.541280i
$213$		−	2.28918e37i		−	0.0873808i
$214$	5.67228e37			0.200415
$215$	−7.80690e37	−	2.85922e38i	−0.255414	−	0.935434i
$216$	2.40909e38			0.730073
$217$			2.83577e38i			0.796315i
$218$			6.03910e38i			1.57196i
$219$	−2.50403e37			−0.0604382
$220$	−1.63894e39	+	4.47502e38i	−3.66935	+	1.00189i
$221$	−3.41608e38			−0.709668
$222$			1.97981e38i			0.381767i
$223$		−	6.71903e38i		−	1.20303i	−0.798861	−	0.601515i	$-0.794564\pi$
$223$		−	6.71903e38i		−	1.20303i	0.798861	−	0.601515i	$-0.205436\pi$
$224$	−1.82388e38			−0.303322
$225$	5.34626e38	−	3.15471e38i	0.826111	−	0.487469i
$226$	1.60212e39			2.30095
$227$		−	1.29399e39i		−	1.72784i	−0.503631	−	0.863919i	$-0.668003\pi$
$227$		−	1.29399e39i		−	1.72784i	0.503631	−	0.863919i	$-0.331997\pi$
$228$		−	1.56031e38i		−	0.193769i
$229$	−1.37545e39			−1.58913			−0.794565	−	0.607179i	$-0.792301\pi$
$229$	−1.37545e39			−1.58913			−0.794565	+	0.607179i	$0.792301\pi$
$230$	9.24895e38	−	2.52536e38i	0.994451	−	0.271528i
$231$	−5.67670e38			−0.568196
$232$		−	1.66595e38i		−	0.155278i
$233$			7.86418e38i			0.682780i	0.939922	+	0.341390i	$0.110898\pi$
$233$			7.86418e38i			0.682780i	−0.939922	+	0.341390i	$0.889102\pi$
$234$	−1.23765e39			−1.00124
$235$	4.52485e38	+	1.65719e39i	0.341181	+	1.24955i
$236$	1.01167e39			0.711198
$237$		−	4.30850e38i		−	0.282474i
$238$		−	5.16396e39i		−	3.15837i
$239$	−1.12913e39			−0.644437			−0.322218	−	0.946665i	$-0.604429\pi$
$239$	−1.12913e39			−0.644437			−0.322218	+	0.946665i	$0.604429\pi$
$240$	1.16798e38	+	4.27764e38i	0.0622228	+	0.227887i
$241$	2.98000e39			1.48230			0.741149	−	0.671341i	$-0.234281\pi$
$241$	2.98000e39			1.48230			0.741149	+	0.671341i	$0.234281\pi$
$242$			9.12152e39i			4.23754i
$243$			1.32089e39i			0.573275i
$244$	5.16341e39			2.09413
$245$	−3.33724e39	+	9.11210e38i	−1.26516	+	0.345444i
$246$	4.78541e38			0.169625
$247$			8.40752e38i			0.278720i
$248$		−	3.11605e39i		−	0.966389i
$249$	−1.92151e37			−0.00557640
$250$	4.61461e39	+	4.48503e39i	1.25350	+	1.21830i
$251$	−3.13439e39			−0.797144			−0.398572	−	0.917137i	$-0.630494\pi$
$251$	−3.13439e39			−0.797144			−0.398572	+	0.917137i	$0.630494\pi$
$252$		−	1.25861e40i		−	2.99766i
$253$		−	4.89129e39i		−	1.09128i
$254$	−3.96503e39			−0.828878
$255$	−1.18181e39	+	3.22685e38i	−0.231545	+	0.0632216i
$256$	−1.10859e40			−2.03616
$257$			4.76577e39i			0.820798i	0.911906	+	0.410399i	$0.134611\pi$
$257$			4.76577e39i			0.820798i	−0.911906	+	0.410399i	$0.865389\pi$
$258$			2.11918e39i			0.342329i
$259$	1.08486e40			1.64410
$260$	−2.27342e39	−	8.32624e39i	−0.323310	−	1.18410i
$261$	6.04756e38			0.0807257
$262$		−	8.57721e39i		−	1.07492i
$263$			1.23745e40i			1.45632i	0.685407	+	0.728160i	$0.259624\pi$
$263$			1.23745e40i			1.45632i	−0.685407	+	0.728160i	$0.740376\pi$
$264$	6.23778e39			0.689549
$265$	−6.67841e38	−	2.44592e39i	−0.0693611	−	0.254030i
$266$	−1.27093e40			−1.24044
$267$		−	1.82228e39i		−	0.167178i
$268$			1.50564e40i			1.29866i
$269$	−4.11483e39			−0.333763			−0.166882	−	0.985977i	$-0.553370\pi$
$269$	−4.11483e39			−0.333763			−0.166882	+	0.985977i	$0.553370\pi$
$270$	−8.74552e39	+	2.38790e39i	−0.667242	+	0.182186i
$271$	−5.73521e39			−0.411676			−0.205838	−	0.978586i	$-0.565992\pi$
$271$	−5.73521e39			−0.411676			−0.205838	+	0.978586i	$0.565992\pi$
$272$			2.05789e40i			1.39006i
$273$		−	2.88391e39i		−	0.183357i
$274$	−2.20904e40			−1.32227
$275$	2.82744e40	−	1.66841e40i	1.59369	−	0.940402i
$276$	−4.61158e39			−0.244822
$277$		−	9.95302e39i		−	0.497782i	−0.968532	−	0.248891i	$-0.919934\pi$
$277$		−	9.95302e39i		−	0.497782i	0.968532	−	0.248891i	$-0.0800660\pi$
$278$			1.90321e40i			0.896907i
$279$	1.13116e40			0.502405
$280$	6.46324e40	−	1.76474e40i	2.70609	−	0.738880i
$281$	3.27698e40			1.29366			0.646829	−	0.762635i	$-0.276095\pi$
$281$	3.27698e40			1.29366			0.646829	+	0.762635i	$0.276095\pi$
$282$		−	1.22827e40i		−	0.457282i
$283$			2.13448e39i			0.0749576i	0.999297	+	0.0374788i	$0.0119327\pi$
$283$			2.13448e39i			0.0749576i	−0.999297	+	0.0374788i	$0.988067\pi$
$284$	2.68422e40			0.889336
$285$	7.94180e38	+	2.90863e39i	0.0248301	+	0.0909385i
$286$	−6.54550e40			−1.93154
$287$		−	2.62222e40i		−	0.730497i
$288$			7.27527e39i			0.191370i
$289$	−1.66001e40			−0.412378
$290$	1.65130e39	+	6.04775e39i	0.0387488	+	0.141915i
$291$	−1.36000e40			−0.301512
$292$		−	2.93615e40i		−	0.615122i
$293$			9.84017e39i			0.194844i	0.995243	+	0.0974219i	$0.0310596\pi$
$293$			9.84017e39i			0.194844i	−0.995243	+	0.0974219i	$0.968940\pi$
$294$	2.47348e40			0.462996
$295$	−1.88589e40	+	5.14930e39i	−0.333775	+	0.0911349i
$296$	−1.19208e41			−1.99523
$297$			4.62505e40i			0.732208i
$298$			1.08401e41i			1.62355i
$299$	2.48490e40			0.352155
$300$	−1.57300e40	−	2.66576e40i	−0.210974	−	0.357536i
$301$	1.16123e41			1.47425
$302$			1.07806e41i			1.29577i
$303$		−	2.00155e40i		−	0.227805i
$304$	5.06480e40			0.545944
$305$	−9.62532e40	+	2.62813e40i	−0.982806	+	0.268348i
$306$	−2.05985e41			−1.99266
$307$			2.89468e39i			0.0265349i	0.999912	+	0.0132675i	$0.00422329\pi$
$307$			2.89468e39i			0.0265349i	−0.999912	+	0.0132675i	$0.995777\pi$
$308$		−	6.65633e41i		−	5.78293i
$309$	4.29497e40			0.353708
$310$	3.08865e40	+	1.13119e41i	0.241157	+	0.883221i
$311$	−2.35932e41			−1.74679			−0.873395	−	0.487013i	$-0.838087\pi$
$311$	−2.35932e41			−1.74679			−0.873395	+	0.487013i	$0.838087\pi$
$312$			3.16895e40i			0.222518i
$313$			1.20774e41i			0.804437i	0.915544	+	0.402219i	$0.131761\pi$
$313$			1.20774e41i			0.804437i	−0.915544	+	0.402219i	$0.868239\pi$
$314$	7.12916e40			0.450505
$315$	6.40619e40	+	2.34622e41i	0.384128	+	1.40684i
$316$	5.05202e41			2.87494
$317$		−	2.94161e41i		−	1.58894i	−0.607304	−	0.794470i	$-0.707749\pi$
$317$		−	2.94161e41i		−	1.58894i	0.607304	−	0.794470i	$-0.292251\pi$
$318$			1.81285e40i			0.0929640i
$319$	3.19834e40			0.155732
$320$	1.71262e41	−	4.67619e40i	0.791930	−	0.216231i
$321$	5.27222e39			0.0231558
$322$			3.75633e41i			1.56726i
$323$			1.39928e41i			0.554707i
$324$	−4.79789e41			−1.80742
$325$	8.47595e40	+	1.43641e41i	0.303468	+	0.514285i
$326$	6.82984e41			2.32445
$327$			5.61317e40i			0.181623i
$328$			2.88140e41i			0.886513i
$329$	−6.73046e41			−1.96930
$330$	−2.26445e41	+	6.18292e40i	−0.630206	+	0.172073i
$331$	−2.83548e41			−0.750698			−0.375349	−	0.926884i	$-0.622477\pi$
$331$	−2.83548e41			−0.750698			−0.375349	+	0.926884i	$0.622477\pi$
$332$		−	2.25311e40i		−	0.0567549i
$333$		−	4.32739e41i		−	1.03728i
$334$	9.12619e41			2.08196
$335$	−7.66355e40	−	2.80672e41i	−0.166414	−	0.609481i
$336$	−1.73730e41			−0.359151
$337$		−	3.05502e41i		−	0.601341i	−0.953728	−	0.300671i	$-0.902790\pi$
$337$		−	3.05502e41i		−	0.601341i	0.953728	−	0.300671i	$-0.0972105\pi$
$338$			6.00015e41i			1.12470i
$339$	1.48913e41			0.265850
$340$	−3.78371e41	−	1.38576e42i	−0.643451	−	2.35659i
$341$	5.98229e41			0.969216
$342$			5.06963e41i			0.782610i
$343$		−	3.21903e41i		−	0.473557i
$344$	−1.27601e42			−1.78912
$345$	8.59664e40	−	2.34725e40i	0.114898	−	0.0313722i
$346$	4.59894e41			0.586006
$347$		−	1.39593e42i		−	1.69601i	−0.529989	−	0.848005i	$-0.677804\pi$
$347$		−	1.39593e42i		−	1.69601i	0.529989	−	0.848005i	$-0.322196\pi$
$348$		−	3.01544e40i		−	0.0349377i
$349$	−2.89779e41			−0.320219			−0.160109	−	0.987099i	$-0.551185\pi$
$349$	−2.89779e41			−0.320219			−0.160109	+	0.987099i	$0.551185\pi$
$350$	−2.17137e42	+	1.28128e42i	−2.28882	+	1.35058i
$351$	−2.34964e41			−0.236284
$352$			3.84763e41i			0.369181i
$353$			1.76391e42i			1.61508i	0.589815	+	0.807539i	$0.299201\pi$
$353$			1.76391e42i			1.61508i	−0.589815	+	0.807539i	$0.700799\pi$
$354$	1.39778e41			0.122147
$355$	−5.00377e41	+	1.36624e41i	−0.417378	+	0.113962i
$356$	2.13675e42			1.70149
$357$		−	4.79975e41i		−	0.364916i
$358$			2.51192e42i			1.82362i
$359$	1.86130e42			1.29050			0.645250	−	0.763971i	$-0.276753\pi$
$359$	1.86130e42			1.29050			0.645250	+	0.763971i	$0.276753\pi$
$360$	−7.03937e41	−	2.57812e42i	−0.466168	−	1.70731i
$361$	−1.23638e42			−0.782140
$362$		−	2.52022e41i		−	0.152317i
$363$			8.47819e41i			0.489603i
$364$	3.38158e42			1.86615
$365$	1.49447e41	+	5.47340e41i	0.0788235	+	0.288685i
$366$	7.13404e41			0.359665
$367$			8.65748e41i			0.417255i	0.977995	+	0.208628i	$0.0668996\pi$
$367$			8.65748e41i			0.417255i	−0.977995	+	0.208628i	$0.933100\pi$
$368$		−	1.49693e42i		−	0.689785i
$369$	−1.04598e42			−0.460880
$370$	4.32753e42	−	1.18160e42i	1.82352	−	0.497900i
$371$	9.93375e41			0.400354
$372$		−	5.64020e41i		−	0.217438i
$373$		−	3.49461e42i		−	1.28885i	−0.764667	−	0.644426i	$-0.777096\pi$
$373$		−	3.49461e42i		−	1.28885i	0.764667	−	0.644426i	$-0.222904\pi$
$374$	−1.08938e43			−3.84414
$375$	4.28915e41	+	4.16871e41i	0.144829	+	0.140762i
$376$	7.39569e42			2.38990
$377$			1.62484e41i			0.0502548i
$378$		−	3.55187e42i		−	1.05158i
$379$	1.11686e42			0.316557			0.158279	−	0.987394i	$-0.449406\pi$
$379$	1.11686e42			0.316557			0.158279	+	0.987394i	$0.449406\pi$
$380$	−3.41057e42	+	9.31232e41i	−0.925545	+	0.252713i
$381$	−3.68538e41			−0.0957680
$382$			3.32804e42i			0.828215i
$383$			6.73691e42i			1.60576i	0.596140	+	0.802880i	$0.296700\pi$
$383$			6.73691e42i			1.60576i	−0.596140	+	0.802880i	$0.703300\pi$
$384$	−1.44583e42			−0.330106
$385$	3.38801e42	+	1.24083e43i	0.741041	+	2.71401i
$386$	−9.98154e42			−2.09174
$387$		−	4.63204e42i		−	0.930125i
$388$		−	1.59469e43i		−	3.06870i
$389$	2.38206e42			0.439324			0.219662	−	0.975576i	$-0.429505\pi$
$389$	2.38206e42			0.439324			0.219662	+	0.975576i	$0.429505\pi$
$390$	−3.14108e41	−	1.15040e42i	−0.0555281	−	0.203368i
$391$	4.13567e42			0.700857
$392$			1.48934e43i			2.41976i
$393$		−	7.97227e41i		−	0.124195i
$394$	3.98000e42			0.594560
$395$	−9.41767e42	+	2.57143e42i	−1.34925	+	0.368402i
$396$	−2.65514e43			−3.64852
$397$		−	1.10200e43i		−	1.45257i	−0.687393	−	0.726286i	$-0.741245\pi$
$397$		−	1.10200e43i		−	1.45257i	0.687393	−	0.726286i	$-0.258755\pi$
$398$		−	5.02560e42i		−	0.635502i
$399$	−1.18130e42			−0.143320
$400$	8.65314e42	−	5.10602e42i	1.00736	−	0.594419i
$401$	1.04368e43			1.16596			0.582980	−	0.812487i	$-0.301887\pi$
$401$	1.04368e43			1.16596			0.582980	+	0.812487i	$0.301887\pi$
$402$			2.08027e42i			0.223044i
$403$			3.03916e42i			0.312766i
$404$	2.34696e43			2.31853
$405$	8.94394e42	−	2.44208e42i	0.848245	−	0.231607i
$406$	−2.45621e42			−0.223659
$407$		−	2.28860e43i		−	2.00107i
$408$			5.27416e42i			0.442854i
$409$	6.52594e42			0.526270			0.263135	−	0.964759i	$-0.415244\pi$
$409$	6.52594e42			0.526270			0.263135	+	0.964759i	$0.415244\pi$
$410$	−2.85606e42	−	1.04601e43i	−0.221225	−	0.810219i
$411$	−2.05324e42			−0.152774
$412$			5.03615e43i			3.59994i
$413$		−	7.65929e42i		−	0.526033i
$414$	1.49836e43			0.988806
$415$	1.14681e41	+	4.20011e41i	0.00727273	+	0.0266359i
$416$	−1.95469e42			−0.119135
$417$			1.76898e42i			0.103628i
$418$			2.68115e43i			1.50977i
$419$	−1.95597e43			−1.05884			−0.529421	−	0.848359i	$-0.677591\pi$
$419$	−1.95597e43			−1.05884			−0.529421	+	0.848359i	$0.677591\pi$
$420$	1.16988e43	−	3.19427e42i	0.608874	−	0.166249i
$421$	−3.38938e43			−1.69616			−0.848079	−	0.529871i	$-0.822241\pi$
$421$	−3.38938e43			−1.69616			−0.848079	+	0.529871i	$0.822241\pi$
$422$		−	3.43082e43i		−	1.65098i
$423$			2.68471e43i			1.24246i
$424$	−1.09156e43			−0.485859
$425$	1.41067e43	+	2.39066e43i	0.603961	+	1.02353i
$426$	3.70866e42			0.152742
$427$		−	3.90919e43i		−	1.54891i
$428$			6.18205e42i			0.235673i
$429$	−6.08385e42			−0.223169
$430$	4.63218e43	−	1.26478e43i	1.63514	−	0.446465i
$431$	3.61239e43			1.22721			0.613607	−	0.789612i	$-0.289718\pi$
$431$	3.61239e43			1.22721			0.613607	+	0.789612i	$0.289718\pi$
$432$			1.41545e43i			0.462822i
$433$		−	3.19821e42i		−	0.100660i	−0.998733	−	0.0503299i	$-0.983973\pi$
$433$		−	3.19821e42i		−	0.100660i	0.998733	−	0.0503299i	$-0.0160273\pi$
$434$	−4.59419e43			−1.39196
$435$	1.53483e41	+	5.62121e41i	0.00447701	+	0.0163967i
$436$	−6.58184e43			−1.84850
$437$		−	1.01786e43i		−	0.275260i
$438$		−	4.05674e42i		−	0.105646i
$439$	2.67557e43			0.671046			0.335523	−	0.942032i	$-0.391087\pi$
$439$	2.67557e43			0.671046			0.335523	+	0.942032i	$0.391087\pi$
$440$	−3.72287e43	−	1.36348e44i	−0.899310	−	3.29366i
$441$	−5.40644e43			−1.25798
$442$		−	5.53434e43i		−	1.24050i
$443$			3.50289e43i			0.756424i	0.925719	+	0.378212i	$0.123461\pi$
$443$			3.50289e43i			0.756424i	−0.925719	+	0.378212i	$0.876539\pi$
$444$	−2.15773e43			−0.448930
$445$	−3.98320e43	+	1.08758e43i	−0.798531	+	0.218033i
$446$	1.08854e44			2.10290
$447$			1.00756e43i			0.187584i
$448$			6.95557e43i			1.24809i
$449$	−4.00499e43			−0.692686			−0.346343	−	0.938108i	$-0.612577\pi$
$449$	−4.00499e43			−0.692686			−0.346343	+	0.938108i	$0.612577\pi$
$450$	5.11089e43	+	8.66139e43i	0.852099	+	1.44405i
$451$	−5.53180e43			−0.889107
$452$			1.74611e44i			2.70575i
$453$			1.00202e43i			0.149712i
$454$	2.09637e44			3.02027
$455$	−6.30375e43	+	1.72119e43i	−0.875812	+	0.239134i
$456$	1.29806e43			0.173930
$457$		−	5.79727e42i		−	0.0749215i	−0.999298	−	0.0374607i	$-0.988073\pi$
$457$		−	5.79727e42i		−	0.0749215i	0.999298	−	0.0374607i	$-0.0119269\pi$
$458$		−	2.22835e44i		−	2.77781i
$459$	−3.91056e43			−0.470251
$460$	2.75232e43	+	1.00802e44i	0.319296	+	1.16940i
$461$	1.20731e44			1.35131			0.675653	−	0.737220i	$-0.263862\pi$
$461$	1.20731e44			1.35131			0.675653	+	0.737220i	$0.263862\pi$
$462$		−	9.19674e43i		−	0.993211i
$463$			9.13506e43i			0.951974i	0.879452	+	0.475987i	$0.157909\pi$
$463$			9.13506e43i			0.951974i	−0.879452	+	0.475987i	$0.842091\pi$
$464$	9.78823e42			0.0984368
$465$	2.87081e42	+	1.05141e43i	0.0278632	+	0.102047i
$466$	−1.27406e44			−1.19350
$467$		−	5.31862e43i		−	0.480918i	−0.970659	−	0.240459i	$-0.922702\pi$
$467$		−	5.31862e43i		−	0.480918i	0.970659	−	0.240459i	$-0.0772979\pi$
$468$		−	1.34888e44i		−	1.17738i
$469$	1.13991e44			0.960547
$470$	−2.68480e44	+	7.33065e43i	−2.18422	+	0.596386i
$471$	6.62635e42			0.0520511
$472$			8.41632e43i			0.638380i
$473$		−	2.44972e44i		−	1.79435i
$474$	6.98014e43			0.493766
$475$	5.88379e43	−	3.47189e43i	0.401988	−	0.237204i
$476$	5.62805e44			3.71401
$477$		−	3.96247e43i		−	0.252588i
$478$		−	1.82929e44i		−	1.12648i
$479$	−1.68051e44			−0.999784			−0.499892	−	0.866088i	$-0.666627\pi$
$479$	−1.68051e44			−0.999784			−0.499892	+	0.866088i	$0.666627\pi$
$480$	−6.76237e42	+	1.84642e42i	−0.0388704	+	0.0106133i
$481$	1.16267e44			0.645746
$482$			4.82786e44i			2.59107i
$483$			3.49140e43i			0.181081i
$484$	−9.94127e44			−4.98303
$485$	8.11684e43	+	2.97273e44i	0.393231	+	1.44018i
$486$	−2.13995e44			−1.00209
$487$		−	2.21035e44i		−	1.00054i	−0.865870	−	0.500269i	$-0.833234\pi$
$487$		−	2.21035e44i		−	1.00054i	0.865870	−	0.500269i	$-0.166766\pi$
$488$			4.29557e44i			1.87972i
$489$	6.34814e43			0.268566
$490$	−1.47624e44	−	5.40661e44i	−0.603839	−	2.21152i
$491$	−2.22461e44			−0.879853			−0.439926	−	0.898034i	$-0.644995\pi$
$491$	−2.22461e44			−0.879853			−0.439926	+	0.898034i	$0.644995\pi$
$492$			5.21547e43i			0.199466i
$493$			2.70425e43i			0.100017i
$494$	−1.36209e44			−0.487204
$495$	4.94956e44	−	1.35144e44i	1.71230	−	0.467532i
$496$	1.83083e44			0.612632
$497$		−	2.03221e44i		−	0.657791i
$498$		−	3.11301e42i		−	0.00974758i
$499$	2.12116e44			0.642561			0.321281	−	0.946984i	$-0.395887\pi$
$499$	2.12116e44			0.642561			0.321281	+	0.946984i	$0.395887\pi$
$500$	−4.88810e44	+	5.02933e44i	−1.43263	+	1.47402i
$501$	8.48254e43			0.240549
$502$		−	5.07798e44i		−	1.39341i
$503$			2.56784e44i			0.681861i	0.940089	+	0.340930i	$0.110742\pi$
$503$			2.56784e44i			0.681861i	−0.940089	+	0.340930i	$0.889258\pi$
$504$	1.04707e45			2.69073
$505$	−4.37506e44	+	1.19458e44i	−1.08812	+	0.297103i
$506$	7.92430e44			1.90756
$507$			5.57696e43i			0.129947i
$508$		−	4.32137e44i		−	0.974698i
$509$	3.35063e44			0.731617			0.365808	−	0.930690i	$-0.380793\pi$
$509$	3.35063e44			0.731617			0.365808	+	0.930690i	$0.380793\pi$
$510$	−5.22777e43	−	1.91463e44i	−0.110512	−	0.404742i
$511$	−2.22294e44			−0.454971
$512$		−	9.71241e44i		−	1.92474i
$513$			9.62452e43i			0.184690i
$514$	−7.72095e44			−1.43476
$515$	−2.56335e44	−	9.38809e44i	−0.461306	−	1.68950i
$516$	−2.30963e44			−0.402553
$517$			1.41985e45i			2.39689i
$518$			1.75756e45i			2.87389i
$519$	4.27458e43			0.0677068
$520$	6.92680e44	−	1.89131e44i	1.06286	−	0.290207i
$521$	9.60997e44			1.42856			0.714282	−	0.699858i	$-0.246753\pi$
$521$	9.60997e44			1.42856			0.714282	+	0.699858i	$0.246753\pi$
$522$			9.79756e43i			0.141109i
$523$			2.83456e44i			0.395555i	0.980247	+	0.197778i	$0.0633724\pi$
$523$			2.83456e44i			0.395555i	−0.980247	+	0.197778i	$0.936628\pi$
$524$	9.34805e44			1.26402
$525$	−2.01823e44	+	1.19091e44i	−0.264449	+	0.156046i
$526$	−2.00477e45			−2.54566
$527$			5.05814e44i			0.622466i
$528$			3.66499e44i			0.437133i
$529$	5.64171e44			0.652217
$530$	3.96260e44	−	1.08196e44i	0.444046	−	0.121244i
$531$	−3.05521e44			−0.331881
$532$		−	1.38515e45i		−	1.45867i
$533$		−	2.81030e44i		−	0.286915i
$534$	2.95224e44			0.292228
$535$	−3.14660e43	−	1.15242e44i	−0.0301998	−	0.110605i
$536$	−1.25258e45			−1.16570
$537$			2.33476e44i			0.210701i
$538$		−	6.66637e44i		−	0.583421i
$539$	−2.85928e45			−2.42684
$540$	−2.60250e44	−	9.53148e44i	−0.214237	−	0.784627i
$541$	2.87443e43			0.0229508			0.0114754	−	0.999934i	$-0.496347\pi$
$541$	2.87443e43			0.0229508			0.0114754	+	0.999934i	$0.496347\pi$
$542$		−	9.29153e44i		−	0.719613i
$543$		−	2.34247e43i		−	0.0175986i
$544$	−3.25324e44			−0.237102
$545$	1.22695e45	−	3.35009e44i	0.867528	−	0.236872i
$546$	4.67218e44			0.320509
$547$			4.18837e44i			0.278775i	0.990238	+	0.139387i	$0.0445134\pi$
$547$			4.18837e44i			0.278775i	−0.990238	+	0.139387i	$0.955487\pi$
$548$		−	2.40757e45i		−	1.55489i
$549$	−1.55933e45			−0.977228
$550$	2.70297e45	+	4.58070e45i	1.64383	+	2.78578i
$551$	6.65561e43			0.0392813
$552$		−	3.83649e44i		−	0.219755i
$553$		−	3.82485e45i		−	2.12643i
$554$	1.61247e45			0.870125
$555$	4.02231e44	−	1.09826e44i	0.210689	−	0.0575271i
$556$	−2.07425e45			−1.05470
$557$			9.66111e44i			0.476888i	0.971156	+	0.238444i	$0.0766373\pi$
$557$			9.66111e44i			0.476888i	−0.971156	+	0.238444i	$0.923363\pi$
$558$			1.83257e45i			0.878207i
$559$	1.24452e45			0.579038
$560$	1.03687e45	+	3.79746e45i	0.468405	+	1.71550i
$561$	−1.01255e45			−0.444149
$562$			5.30899e45i			2.26132i
$563$		−	2.31505e45i		−	0.957572i	−0.877932	−	0.478786i	$-0.841077\pi$
$563$		−	2.31505e45i		−	0.957572i	0.877932	−	0.478786i	$-0.158923\pi$
$564$	1.33866e45			0.537729
$565$	−8.88752e44	−	3.25499e45i	−0.346722	−	1.26984i
$566$	−3.45804e44			−0.131026
$567$			3.63246e45i			1.33684i
$568$			2.23307e45i			0.798279i
$569$	2.87517e45			0.998416			0.499208	−	0.866482i	$-0.333624\pi$
$569$	2.87517e45			0.998416			0.499208	+	0.866482i	$0.333624\pi$
$570$	−4.71222e44	+	1.28664e44i	−0.158961	+	0.0434032i
$571$	−2.65488e45			−0.870060			−0.435030	−	0.900416i	$-0.643262\pi$
$571$	−2.65488e45			−0.870060			−0.435030	+	0.900416i	$0.643262\pi$
$572$		−	7.13374e45i		−	2.27134i
$573$			3.09332e44i			0.0956915i
$574$	4.24823e45			1.27691
$575$	−1.02614e45	−	1.73899e45i	−0.299700	−	0.507900i
$576$	2.77451e45			0.787435
$577$			2.47694e45i			0.683148i	0.939855	+	0.341574i	$0.110960\pi$
$577$			2.47694e45i			0.683148i	−0.939855	+	0.341574i	$0.889040\pi$
$578$		−	2.68935e45i		−	0.720839i
$579$	−9.27756e44			−0.241678
$580$	−6.59126e44	+	1.79970e44i	−0.166881	+	0.0455657i
$581$	−1.70581e44			−0.0419784
$582$		−	2.20331e45i		−	0.527045i
$583$		−	2.09561e45i		−	0.487281i
$584$	2.44266e45			0.552141
$585$	6.86566e44	+	2.51450e45i	0.150873	+	0.552561i
$586$	−1.59419e45			−0.340588
$587$		−	6.47352e45i		−	1.34466i	−0.740253	−	0.672328i	$-0.765294\pi$
$587$		−	6.47352e45i		−	1.34466i	0.740253	−	0.672328i	$-0.234706\pi$
$588$			2.69577e45i			0.544449i
$589$	1.24489e45			0.244472
$590$	−8.34230e44	−	3.05531e45i	−0.159304	−	0.583441i
$591$	3.69930e44			0.0686951
$592$		−	7.00406e45i		−	1.26486i
$593$			9.12580e45i			1.60276i	0.598156	+	0.801380i	$0.295900\pi$
$593$			9.12580e45i			1.60276i	−0.598156	+	0.801380i	$0.704100\pi$
$594$	−7.49297e45			−1.27990
$595$	−1.04915e46	+	2.86462e45i	−1.74304	+	0.475924i
$596$	−1.18143e46			−1.90918
$597$		−	4.67115e44i		−	0.0734256i
$598$			4.02574e45i			0.615569i
$599$	−5.76161e45			−0.857040			−0.428520	−	0.903532i	$-0.640965\pi$
$599$	−5.76161e45			−0.857040			−0.428520	+	0.903532i	$0.640965\pi$
$600$	2.21771e45	−	1.30862e45i	0.320929	−	0.189373i
$601$	1.06122e46			1.49409			0.747045	−	0.664773i	$-0.231472\pi$
$601$	1.06122e46			1.49409			0.747045	+	0.664773i	$0.231472\pi$
$602$			1.88130e46i			2.57700i
$603$		−	4.54698e45i		−	0.606021i
$604$	−1.17494e46			−1.52373
$605$	1.85319e46	−	5.06001e45i	2.33861	−	0.638540i
$606$	3.24269e45			0.398205
$607$			1.19114e46i			1.42347i	0.702449	+	0.711734i	$0.252090\pi$
$607$			1.19114e46i			1.42347i	−0.702449	+	0.711734i	$0.747910\pi$
$608$			8.00676e44i			0.0931210i
$609$	−2.28298e44			−0.0258414
$610$	−4.25779e45	−	1.55938e46i	−0.469074	−	1.71795i
$611$	−7.21319e45			−0.773477
$612$		−	2.24497e46i		−	2.34322i
$613$			1.87761e46i			1.90769i	0.300304	+	0.953843i	$0.402912\pi$
$613$			1.87761e46i			1.90769i	−0.300304	+	0.953843i	$0.597088\pi$
$614$	−4.68964e44			−0.0463832
$615$	−2.65463e44	−	9.72237e44i	−0.0255602	−	0.0936123i
$616$	5.53756e46			5.19083
$617$			9.77185e45i			0.891808i	0.895081	+	0.445904i	$0.147118\pi$
$617$			9.77185e45i			0.891808i	−0.895081	+	0.445904i	$0.852882\pi$
$618$			6.95822e45i			0.618284i
$619$	−1.04212e46			−0.901615			−0.450808	−	0.892621i	$-0.648864\pi$
$619$	−1.04212e46			−0.901615			−0.450808	+	0.892621i	$0.648864\pi$
$620$	−1.23286e46	+	3.36622e45i	−1.03860	+	0.283583i
$621$	2.84459e45			0.233350
$622$		−	3.82230e46i		−	3.05340i
$623$		−	1.61772e46i		−	1.25849i
$624$	−1.86191e45			−0.141063
$625$	6.55222e45	−	1.18634e46i	0.483469	−	0.875362i
$626$	−1.95664e46			−1.40616
$627$			2.49205e45i			0.174438i
$628$			7.76986e45i			0.529760i
$629$	1.93506e46			1.28516
$630$	−3.80108e46	+	1.03786e46i	−2.45917	+	0.671458i
$631$	1.47410e46			0.929056			0.464528	−	0.885558i	$-0.346224\pi$
$631$	1.47410e46			0.929056			0.464528	+	0.885558i	$0.346224\pi$
$632$			4.20290e46i			2.58058i
$633$		−	3.18884e45i		−	0.190753i
$634$	4.76566e46			2.77748
$635$	2.19954e45	+	8.05564e45i	0.124901	+	0.457439i
$636$	−1.97577e45			−0.109319
$637$		−	1.45258e46i		−	0.783142i
$638$			5.18158e45i			0.272221i
$639$	−8.10627e45			−0.415008
$640$	8.62912e45	+	3.16035e46i	0.430523	+	1.57676i
$641$	−2.92413e45			−0.142180			−0.0710902	−	0.997470i	$-0.522648\pi$
$641$	−2.92413e45			−0.142180			−0.0710902	+	0.997470i	$0.522648\pi$
$642$			8.54145e44i			0.0404766i
$643$			6.54844e45i			0.302452i	0.988499	+	0.151226i	$0.0483222\pi$
$643$			6.54844e45i			0.302452i	−0.988499	+	0.151226i	$0.951678\pi$
$644$	−4.09391e46			−1.84299
$645$	4.30548e45	−	1.17558e45i	0.188924	−	0.0515843i
$646$	−2.26696e46			−0.969632
$647$		−	2.24177e46i		−	0.934696i	−0.884074	−	0.467348i	$-0.845210\pi$
$647$		−	2.24177e46i		−	0.934696i	0.884074	−	0.467348i	$-0.154790\pi$
$648$		−	3.99148e46i		−	1.62236i
$649$	−1.61579e46			−0.640248
$650$	−2.32711e46	+	1.37318e46i	−0.898973	+	0.530464i
$651$	−4.27016e45			−0.160827
$652$			7.44364e46i			2.73338i
$653$		−	4.25379e46i		−	1.52303i	−0.648148	−	0.761515i	$-0.724456\pi$
$653$		−	4.25379e46i		−	1.52303i	0.648148	−	0.761515i	$-0.275544\pi$
$654$	−9.09382e45			−0.317478
$655$	−1.74261e46	+	4.75806e45i	−0.593223	+	0.161975i
$656$	−1.69296e46			−0.561996
$657$			8.86709e45i			0.287047i
$658$		−	1.09039e47i		−	3.44235i
$659$	1.43240e46			0.441017			0.220509	−	0.975385i	$-0.429228\pi$
$659$	1.43240e46			0.441017			0.220509	+	0.975385i	$0.429228\pi$
$660$	−6.73858e45	−	2.46796e46i	−0.202345	−	0.741076i
$661$	5.54323e46			1.62345			0.811725	−	0.584040i	$-0.198529\pi$
$661$	5.54323e46			1.62345			0.811725	+	0.584040i	$0.198529\pi$
$662$		−	4.59372e46i		−	1.31222i
$663$		−	5.14401e45i		−	0.143327i
$664$	1.87441e45			0.0509439
$665$	7.05030e45	+	2.58212e46i	0.186918	+	0.684573i
$666$	7.01074e46			1.81317
$667$		−	1.96711e45i		−	0.0496309i
$668$			9.94637e46i			2.44823i
$669$	1.01177e46			0.242968
$670$	4.54713e46	−	1.24156e46i	1.06538	−	0.290893i
$671$	−8.24677e46			−1.88522
$672$		−	2.74644e45i		−	0.0612600i
$673$			7.20788e46i			1.56877i	0.620275	+	0.784385i	$0.287021\pi$
$673$			7.20788e46i			1.56877i	−0.620275	+	0.784385i	$0.712979\pi$
$674$	4.94940e46			1.05115
$675$	9.70286e45	+	1.64434e46i	0.201089	+	0.340783i
$676$	−6.53938e46			−1.32256
$677$		−	6.09779e46i		−	1.20354i	−0.798670	−	0.601769i	$-0.794463\pi$
$677$		−	6.09779e46i		−	1.20354i	0.798670	−	0.601769i	$-0.205537\pi$
$678$			2.41252e46i			0.464708i
$679$	−1.20733e47			−2.26974
$680$	1.15284e47	−	3.14776e46i	2.11531	−	0.577570i
$681$	1.94851e46			0.348960
$682$			9.69183e46i			1.69420i
$683$		−	2.92500e46i		−	0.499095i	−0.968363	−	0.249548i	$-0.919718\pi$
$683$		−	2.92500e46i		−	0.499095i	0.968363	−	0.249548i	$-0.0802819\pi$
$684$	−5.52524e46			−0.920291
$685$	1.22543e46	+	4.48804e46i	0.199248	+	0.729730i
$686$	5.21510e46			0.827780
$687$		−	2.07119e46i		−	0.320947i
$688$		−	7.49715e46i		−	1.13419i
$689$	1.06462e46			0.157246
$690$	3.80275e45	+	1.39273e46i	0.0548387	+	0.200843i
$691$	−5.05530e46			−0.711803			−0.355901	−	0.934524i	$-0.615826\pi$
$691$	−5.05530e46			−0.711803			−0.355901	+	0.934524i	$0.615826\pi$
$692$			5.01225e46i			0.689100i
$693$			2.01019e47i			2.69860i
$694$	2.26153e47			2.96464
$695$	3.86670e46	−	1.05577e46i	0.494983	−	0.135152i
$696$	2.50862e45			0.0313605
$697$		−	4.67724e46i		−	0.571017i
$698$		−	4.69466e46i		−	0.559744i
$699$	−1.18421e46			−0.137897
$700$	−1.39643e47	−	2.36652e47i	−1.58818	−	2.69149i
$701$	7.87167e45			0.0874419			0.0437209	−	0.999044i	$-0.486079\pi$
$701$	7.87167e45			0.0874419			0.0437209	+	0.999044i	$0.486079\pi$
$702$		−	3.80662e46i		−	0.413026i
$703$		−	4.76248e46i		−	0.504743i
$704$	1.46734e47			1.51908
$705$	−2.49544e46	+	6.81363e45i	−0.252364	+	0.0689061i
$706$	−2.85768e47			−2.82317
$707$		−	1.77687e47i		−	1.71489i
$708$			1.52340e46i			0.143636i
$709$	−6.37039e46			−0.586818			−0.293409	−	0.955987i	$-0.594790\pi$
$709$	−6.37039e46			−0.586818			−0.293409	+	0.955987i	$0.594790\pi$
$710$	−2.21343e46	−	8.10653e46i	−0.199206	−	0.729579i
$711$	−1.52570e47			−1.34159
$712$			1.77761e47i			1.52727i
$713$		−	3.67935e46i		−	0.308883i
$714$	7.77601e46			0.637876
$715$	3.63100e46	+	1.32983e47i	0.291056	+	1.06597i
$716$	−2.73766e47			−2.14445
$717$		−	1.70028e46i		−	0.130153i
$718$			3.01547e47i			2.25580i
$719$	−1.38244e47			−1.01070			−0.505349	−	0.862915i	$-0.668636\pi$
$719$	−1.38244e47			−1.01070			−0.505349	+	0.862915i	$0.668636\pi$
$720$	1.51477e47	−	4.13597e46i	1.08233	−	0.295523i
$721$	3.81284e47			2.66267
$722$		−	2.00305e47i		−	1.36719i
$723$			4.48736e46i			0.299370i
$724$	2.74671e46			0.179113
$725$	1.13710e46	−	6.70978e45i	0.0724806	−	0.0427692i
$726$	−1.37354e47			−0.855829
$727$			9.54196e46i			0.581192i	0.956846	+	0.290596i	$0.0938536\pi$
$727$			9.54196e46i			0.581192i	−0.956846	+	0.290596i	$0.906146\pi$
$728$			2.81322e47i			1.67508i
$729$	1.31166e47			0.763515
$730$	−8.86737e46	+	2.42117e46i	−0.504624	+	0.137784i
$731$	2.07128e47			1.15240
$732$			7.77518e46i			0.422939i
$733$		−	1.90546e47i		−	1.01341i	−0.862120	−	0.506704i	$-0.830864\pi$
$733$		−	1.90546e47i		−	1.01341i	0.862120	−	0.506704i	$-0.169136\pi$
$734$	−1.40259e47			−0.729364
$735$	−1.37212e46	−	5.02529e46i	−0.0697672	−	0.255517i
$736$	2.36645e46			0.117656
$737$		−	2.40474e47i		−	1.16911i
$738$		−	1.69457e47i		−	0.805620i
$739$	−3.12949e47			−1.45492			−0.727462	−	0.686148i	$-0.759300\pi$
$739$	−3.12949e47			−1.45492			−0.727462	+	0.686148i	$0.759300\pi$
$740$	1.28779e47	+	4.71644e47i	0.585494	+	2.14433i
$741$	−1.26602e46			−0.0562913
$742$			1.60935e47i			0.699821i
$743$		−	1.30046e47i		−	0.553074i	−0.961003	−	0.276537i	$-0.910813\pi$
$743$		−	1.30046e47i		−	0.553074i	0.961003	−	0.276537i	$-0.0891868\pi$
$744$	4.69222e46			0.195175
$745$	2.20236e47	−	6.01338e46i	0.896003	−	0.244647i
$746$	5.66157e47			2.25292
$747$			6.80432e45i			0.0264847i
$748$		−	1.18729e48i		−	4.52042i
$749$	4.68039e46			0.174314
$750$	−6.75366e46	+	6.94878e46i	−0.246053	+	0.253162i
$751$	−1.13850e47			−0.405766			−0.202883	−	0.979203i	$-0.565031\pi$
$751$	−1.13850e47			−0.405766			−0.202883	+	0.979203i	$0.565031\pi$
$752$			4.34532e47i			1.51505i
$753$		−	4.71984e46i		−	0.160994i
$754$	−2.63237e46			−0.0878457
$755$	2.19026e47	−	5.98034e46i	0.715105	−	0.195254i
$756$	3.87108e47			1.23658
$757$			5.43917e47i			1.70001i	0.526778	+	0.850003i	$0.323400\pi$
$757$			5.43917e47i			1.70001i	−0.526778	+	0.850003i	$0.676600\pi$
$758$			1.80941e47i			0.553344i
$759$	7.36541e46			0.220398
$760$	−7.74714e46	−	2.83734e47i	−0.226839	−	0.830781i
$761$	3.05470e46			0.0875230			0.0437615	−	0.999042i	$-0.486066\pi$
$761$	3.05470e46			0.0875230			0.0437615	+	0.999042i	$0.486066\pi$
$762$		−	5.97064e46i		−	0.167403i
$763$			4.98307e47i			1.36723i
$764$	−3.62713e47			−0.973920
$765$	1.14267e47	+	4.18494e47i	0.300266	+	1.09970i
$766$	−1.09144e48			−2.80688
$767$		−	8.20863e46i		−	0.206608i
$768$		−	1.66934e47i		−	0.411231i
$769$	−1.42016e46			−0.0342415			−0.0171208	−	0.999853i	$-0.505450\pi$
$769$	−1.42016e46			−0.0342415			−0.0171208	+	0.999853i	$0.505450\pi$
$770$	−2.01026e48	+	5.48886e47i	−4.74411	+	1.29534i
$771$	−7.17640e46			−0.165771
$772$		−	1.08786e48i		−	2.45973i
$773$		−	1.83451e47i		−	0.406029i	−0.979176	−	0.203015i	$-0.934926\pi$
$773$		−	1.83451e47i		−	0.406029i	0.979176	−	0.203015i	$-0.0650739\pi$
$774$	7.50430e47			1.62586
$775$	2.12688e47	−	1.25502e47i	0.451091	−	0.266179i
$776$	1.32667e48			2.75450
$777$			1.63361e47i			0.332048i
$778$			3.85915e47i			0.767941i
$779$	−1.15115e47			−0.224265
$780$	1.25378e47	−	3.42337e46i	0.239145	−	0.0652969i
$781$	−4.28712e47			−0.800614
$782$			6.70014e47i			1.22510i
$783$			1.86004e46i			0.0333006i
$784$	−8.75055e47			−1.53398
$785$	−3.95478e46	−	1.44841e47i	−0.0678849	−	0.248624i
$786$	1.29158e47			0.217094
$787$			1.26346e47i			0.207959i	0.994579	+	0.103980i	$0.0331577\pi$
$787$			1.26346e47i			0.207959i	−0.994579	+	0.103980i	$0.966842\pi$
$788$			4.33768e47i			0.699158i
$789$	−1.86338e47			−0.294124
$790$	−4.16593e47	−	1.52574e48i	−0.643970	−	2.35849i
$791$	1.32197e48			2.00128
$792$		−	2.20888e48i		−	3.27496i
$793$		−	4.18957e47i		−	0.608361i
$794$	1.78533e48			2.53910
$795$	3.68312e46	−	1.00565e46i	0.0513048	−	0.0140084i
$796$	5.47725e47			0.747303
$797$			6.98979e47i			0.934118i	0.884226	+	0.467059i	$0.154686\pi$
$797$			6.98979e47i			0.934118i	−0.884226	+	0.467059i	$0.845314\pi$
$798$		−	1.91380e47i		−	0.250524i
$799$	−1.20051e48			−1.53937
$800$	8.07193e46	+	1.36794e47i	0.101389	+	0.171824i
$801$	−6.45291e47			−0.793998
$802$			1.69084e48i			2.03810i
$803$			4.68949e47i			0.553757i
$804$	−2.26722e47			−0.262283
$805$	7.63163e47	−	2.08376e47i	0.864938	−	0.236165i
$806$	−4.92369e47			−0.546717
$807$		−	6.19620e46i		−	0.0674081i
$808$			1.95249e48i			2.08114i
$809$	−1.36317e48			−1.42364			−0.711818	−	0.702364i	$-0.752128\pi$
$809$	−1.36317e48			−1.42364			−0.711818	+	0.702364i	$0.752128\pi$
$810$	3.95638e47	+	1.44900e48i	0.404851	+	1.48274i
$811$	6.10621e47			0.612248			0.306124	−	0.951992i	$-0.400968\pi$
$811$	6.10621e47			0.612248			0.306124	+	0.951992i	$0.400968\pi$
$812$		−	2.67695e47i		−	0.263006i
$813$		−	8.63621e46i		−	0.0831437i
$814$	3.70773e48			3.49789
$815$	−3.78874e47	−	1.38760e48i	−0.350263	−	1.28281i
$816$	−3.09882e47			−0.280743
$817$		−	5.09776e47i		−	0.452601i
$818$			1.05726e48i			0.919922i
$819$	−1.02123e48			−0.870840
$820$	1.14002e48	−	3.11273e47i	0.952758	−	0.260144i
$821$	8.40767e47			0.688674			0.344337	−	0.938846i	$-0.388104\pi$
$821$	8.40767e47			0.688674			0.344337	+	0.938846i	$0.388104\pi$
$822$		−	3.32642e47i		−	0.267050i
$823$			8.92715e47i			0.702450i	0.936291	+	0.351225i	$0.114235\pi$
$823$			8.92715e47i			0.702450i	−0.936291	+	0.351225i	$0.885765\pi$
$824$	−4.18970e48			−3.23135
$825$	2.51233e47	+	4.25763e47i	0.189927	+	0.321868i
$826$	1.24087e48			0.919508
$827$		−	2.30578e48i		−	1.67485i	−0.546550	−	0.837426i	$-0.684059\pi$
$827$		−	2.30578e48i		−	1.67485i	0.546550	−	0.837426i	$-0.315941\pi$
$828$			1.63302e48i			1.16276i
$829$	−6.85395e47			−0.478400			−0.239200	−	0.970970i	$-0.576885\pi$
$829$	−6.85395e47			−0.478400			−0.239200	+	0.970970i	$0.576885\pi$
$830$	−6.80453e46	+	1.85793e46i	−0.0465596	+	0.0127128i
$831$	1.49875e47			0.100534
$832$			7.45444e47i			0.490208i
$833$		−	2.41757e48i		−	1.55861i
$834$	−2.86590e47			−0.181143
$835$	−5.06260e47	−	1.85414e48i	−0.313724	−	1.14899i
$836$	−2.92210e48			−1.77538
$837$			3.47908e47i			0.207250i
$838$		−	3.16884e48i		−	1.85086i
$839$	1.53456e48			0.878841			0.439420	−	0.898282i	$-0.355184\pi$
$839$	1.53456e48			0.878841			0.439420	+	0.898282i	$0.355184\pi$
$840$	2.65739e47	+	9.73250e47i	0.149227	+	0.546532i
$841$	−1.80321e48			−0.992917
$842$		−	5.49109e48i		−	2.96489i
$843$			4.93455e47i			0.261272i
$844$	3.73914e48			1.94143
$845$	1.21903e48	−	3.32848e47i	0.620697	−	0.169477i
$846$	−4.34946e48			−2.17182
$847$			7.52648e48i			3.68566i
$848$		−	6.41342e47i		−	0.308005i
$849$	−3.21415e46			−0.0151387
$850$	−3.87307e48	+	2.28541e48i	−1.78913	+	1.05573i
$851$	−1.40758e48			−0.637729
$852$			4.04196e47i			0.179614i
$853$		−	1.76958e48i		−	0.771278i	−0.922650	−	0.385639i	$-0.873981\pi$
$853$		−	1.76958e48i		−	0.771278i	0.922650	−	0.385639i	$-0.126019\pi$
$854$	6.33322e48			2.70751
$855$	1.02998e48	−	2.81229e47i	0.431905	−	0.117929i
$856$	−5.14300e47			−0.211543
$857$			3.25318e48i			1.31258i	0.754510	+	0.656288i	$0.227875\pi$
$857$			3.25318e48i			1.31258i	−0.754510	+	0.656288i	$0.772125\pi$
$858$		−	9.85636e47i		−	0.390100i
$859$	1.29796e48			0.503934			0.251967	−	0.967736i	$-0.418922\pi$
$859$	1.29796e48			0.503934			0.251967	+	0.967736i	$0.418922\pi$
$860$	1.37845e48	+	5.04848e48i	0.525009	+	1.92281i
$861$	3.94860e47			0.147534
$862$			5.85239e48i			2.14518i
$863$		−	4.45924e48i		−	1.60355i	−0.597626	−	0.801775i	$-0.703889\pi$
$863$		−	4.45924e48i		−	1.60355i	0.597626	−	0.801775i	$-0.296111\pi$
$864$	−2.23764e47			−0.0789430
$865$	−2.55119e47	−	9.34353e47i	−0.0883032	−	0.323404i
$866$	5.18137e47			0.175954
$867$		−	2.49967e47i		−	0.0832853i
$868$		−	5.00707e48i		−	1.63685i
$869$	−8.06886e48			−2.58813
$870$	−9.10684e46	+	2.48656e46i	−0.0286616	+	0.00782584i
$871$	1.22167e48			0.377271
$872$		−	5.47559e48i		−	1.65924i
$873$			4.81593e48i			1.43201i
$874$	1.64901e48			0.481156
$875$	3.80767e48	+	3.70075e48i	1.09025	+	1.05964i
$876$	4.42132e47			0.124232
$877$		−	3.25524e48i		−	0.897615i	−0.893628	−	0.448808i	$-0.851849\pi$
$877$		−	3.25524e48i		−	0.897615i	0.893628	−	0.448808i	$-0.148151\pi$
$878$			4.33466e48i			1.17299i
$879$	−1.48175e47			−0.0393514
$880$	8.01106e48	−	2.18736e48i	2.08798	−	0.570108i
$881$	2.55040e48			0.652387			0.326193	−	0.945303i	$-0.394234\pi$
$881$	2.55040e48			0.652387			0.326193	+	0.945303i	$0.394234\pi$
$882$		−	8.75890e48i		−	2.19896i
$883$			7.29440e47i			0.179737i	0.995954	+	0.0898686i	$0.0286447\pi$
$883$			7.29440e47i			0.179737i	−0.995954	+	0.0898686i	$0.971355\pi$
$884$	6.03171e48			1.45874
$885$	−7.75393e46	−	2.83982e47i	−0.0184059	−	0.0674104i
$886$	−5.67498e48			−1.32223
$887$			7.19151e47i			0.164468i	0.996613	+	0.0822338i	$0.0262054\pi$
$887$			7.19151e47i			0.164468i	−0.996613	+	0.0822338i	$0.973795\pi$
$888$		−	1.79507e48i		−	0.402965i
$889$	−3.27168e48			−0.720929
$890$	−1.76198e48	−	6.45312e48i	−0.381123	−	1.39584i
$891$	7.66298e48			1.62710
$892$			1.18637e49i			2.47286i
$893$			2.95464e48i			0.604583i
$894$	−1.63233e48			−0.327898
$895$	5.10339e48	−	1.39344e48i	1.00642	−	0.274795i
$896$	−1.28353e49			−2.48499
$897$			3.74181e47i			0.0711225i
$898$		−	6.48842e48i		−	1.21082i
$899$	2.40587e47			0.0440796
$900$	−9.43979e48	+	5.57021e48i	−1.69809	+	1.00201i
$901$	1.77188e48			0.312950
$902$		−	8.96200e48i		−	1.55416i
$903$			1.74861e48i			0.297745i
$904$	−1.45263e49			−2.42871
$905$	−5.12026e47	+	1.39805e47i	−0.0840602	+	0.0229520i
$906$	−1.62336e48			−0.261698
$907$			3.79462e48i			0.600686i	0.953831	+	0.300343i	$0.0971012\pi$
$907$			3.79462e48i			0.600686i	−0.953831	+	0.300343i	$0.902899\pi$
$908$			2.28477e49i			3.55161i
$909$	−7.08775e48			−1.08194
$910$	−2.78848e48	−	1.02126e49i	−0.418008	−	1.53092i
$911$	5.16241e47			0.0759974			0.0379987	−	0.999278i	$-0.487902\pi$
$911$	5.16241e47			0.0759974			0.0379987	+	0.999278i	$0.487902\pi$
$912$			7.62669e47i			0.110261i
$913$			3.59856e47i			0.0510929i
$914$	9.39208e47			0.130963
$915$	−3.95749e47	−	1.44940e48i	−0.0541966	−	0.198491i
$916$	2.42861e49			3.26650
$917$		−	7.07735e48i		−	0.934925i
$918$		−	6.33544e48i		−	0.822002i
$919$	1.41530e49			1.80361			0.901806	−	0.432141i	$-0.142242\pi$
$919$	1.41530e49			1.80361			0.901806	+	0.432141i	$0.142242\pi$
$920$	−8.38593e48	+	2.28972e48i	−1.04967	+	0.286604i
$921$	−4.35888e46			−0.00535909
$922$			1.95595e49i			2.36209i
$923$		−	2.17796e48i		−	0.258358i
$924$	1.00233e49			1.16794
$925$	−4.80125e48	−	8.13664e48i	−0.549561	−	0.931336i
$926$	−1.47996e49			−1.66406
$927$		−	1.52090e49i		−	1.67991i
$928$			1.54739e47i			0.0167902i
$929$	3.30086e48			0.351859			0.175929	−	0.984403i	$-0.443707\pi$
$929$	3.30086e48			0.351859			0.175929	+	0.984403i	$0.443707\pi$
$930$	−1.70338e48	+	4.65095e47i	−0.178378	+	0.0487050i
$931$	−5.95003e48			−0.612138
$932$		−	1.38856e49i		−	1.40347i
$933$		−	3.55272e48i		−	0.352788i
$934$	8.61663e48			0.840647
$935$	6.04317e48	+	2.21327e49i	0.579259	+	2.12149i
$936$	1.12217e49			1.05683
$937$		−	1.77391e49i		−	1.64146i	−0.571318	−	0.820729i	$-0.693568\pi$
$937$		−	1.77391e49i		−	1.64146i	0.571318	−	0.820729i	$-0.306432\pi$
$938$			1.84675e49i			1.67904i
$939$	−1.81864e48			−0.162467
$940$	−7.98946e48	−	2.92608e49i	−0.701306	−	2.56848i
$941$	−7.81290e48			−0.673882			−0.336941	−	0.941526i	$-0.609392\pi$
$941$	−7.81290e48			−0.673882			−0.336941	+	0.941526i	$0.609392\pi$
$942$			1.07353e48i			0.0909856i
$943$			3.40228e48i			0.283353i
$944$	−4.94499e48			−0.404695
$945$	−7.21623e48	+	1.97034e48i	−0.580344	+	0.158459i
$946$	3.96875e49			3.13654
$947$			4.67824e48i			0.363336i	0.983360	+	0.181668i	$0.0581496\pi$
$947$			4.67824e48i			0.363336i	−0.983360	+	0.181668i	$0.941850\pi$
$948$			7.60745e48i			0.580633i
$949$	−2.38238e48			−0.178697
$950$	5.62476e48	+	9.53224e48i	0.414634	+	0.702677i
$951$	4.42954e48			0.320908
$952$			4.68211e49i			3.33374i
$953$			5.74579e48i			0.402084i	0.979583	+	0.201042i	$0.0644328\pi$
$953$			5.74579e48i			0.402084i	−0.979583	+	0.201042i	$0.935567\pi$
$954$	6.41954e48			0.441526
$955$	6.76148e48	−	1.84618e48i	0.457074	−	0.124801i
$956$	1.99369e49			1.32466
$957$			4.81613e47i			0.0314522i
$958$		−	2.72258e49i		−	1.74763i
$959$	−1.82275e49			−1.15006
$960$	7.04152e47	+	2.57891e48i	0.0436708	+	0.159941i
$961$	−1.19034e49			−0.725666
$962$			1.88362e49i			1.12877i
$963$		−	1.86696e48i		−	0.109977i
$964$	−5.26174e49			−3.04690
$965$	5.53709e48	+	2.02792e49i	0.315196	+	1.15438i
$966$	−5.65637e48			−0.316530
$967$			7.95661e48i			0.437715i	0.975757	+	0.218857i	$0.0702330\pi$
$967$			7.95661e48i			0.437715i	−0.975757	+	0.218857i	$0.929767\pi$
$968$		−	8.27039e49i		−	4.47283i
$969$	−2.10707e48			−0.112031
$970$	−4.81608e49	+	1.31500e49i	−2.51745	+	0.687371i
$971$	8.39693e48			0.431522			0.215761	−	0.976446i	$-0.430777\pi$
$971$	8.39693e48			0.431522			0.215761	+	0.976446i	$0.430777\pi$
$972$		−	2.33227e49i		−	1.17838i
$973$			1.57040e49i			0.780098i
$974$	3.58096e49			1.74895
$975$	−2.16298e48	+	1.27633e48i	−0.103867	+	0.0612895i
$976$	−2.52385e49			−1.19163
$977$		−	3.91342e48i		−	0.181675i	−0.995866	−	0.0908377i	$-0.971046\pi$
$977$		−	3.91342e48i		−	0.181675i	0.995866	−	0.0908377i	$-0.0289544\pi$
$978$			1.02845e49i			0.469454i
$979$	−3.41272e49			−1.53174
$980$	5.89251e49	−	1.60891e49i	2.60058	−	0.710070i
$981$	1.98770e49			0.862604
$982$		−	3.60406e49i		−	1.53799i
$983$		−	1.84117e49i		−	0.772612i	−0.922371	−	0.386306i	$-0.873751\pi$
$983$		−	1.84117e49i		−	0.772612i	0.922371	−	0.386306i	$-0.126249\pi$
$984$	−4.33888e48			−0.179043
$985$	−2.20784e48	−	8.08605e48i	−0.0895921	−	0.328125i
$986$	−4.38112e48			−0.174830
$987$		−	1.01349e49i		−	0.397728i
$988$		−	1.48450e49i		−	0.572916i
$989$	−1.50668e49			−0.571849
$990$	2.18945e49	+	8.01871e49i	0.817249	+	2.99312i
$991$	4.75733e47			0.0174642			0.00873208	−	0.999962i	$-0.497220\pi$
$991$	4.75733e47			0.0174642			0.00873208	+	0.999962i	$0.497220\pi$
$992$			2.89429e48i			0.104496i
$993$		−	4.26973e48i		−	0.151614i
$994$	3.29235e49			1.14982
$995$	−1.02104e49	+	2.78787e48i	−0.350720	+	0.0957616i
$996$	3.39278e47			0.0114624
$997$			2.41124e49i			0.801254i	0.916241	+	0.400627i	$0.131208\pi$
$997$			2.41124e49i			0.801254i	−0.916241	+	0.400627i	$0.868792\pi$
$998$			3.43646e49i			1.12320i
$999$	1.33097e49			0.427894

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.34.b.a.4.16	yes	16
5.2	odd	4		25.34.a.f.1.1		16
5.3	odd	4		25.34.a.f.1.16		16
5.4	even	2	inner	5.34.b.a.4.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.b.a.4.1	✓	16	5.4	even	2	inner
5.34.b.a.4.16	yes	16	1.1	even	1	trivial
25.34.a.f.1.1		16	5.2	odd	4
25.34.a.f.1.16		16	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+162009. i q^{2} +1.50582e7i q^{3} -1.76568e10 q^{4} +(3.29148e11 - 8.98715e10i) q^{5} -2.43956e12 q^{6} +1.33679e14i q^{7} -1.46891e15i q^{8} +5.33231e15 q^{9} +O(q^{10})\)	\(q+162009. i q^{2} +1.50582e7i q^{3} -1.76568e10 q^{4} +(3.29148e11 - 8.98715e10i) q^{5} -2.43956e12 q^{6} +1.33679e14i q^{7} -1.46891e15i q^{8} +5.33231e15 q^{9} +(1.45600e16 + 5.33248e16i) q^{10} +2.82007e17 q^{11} -2.65881e17i q^{12} +1.43267e18i q^{13} -2.16571e19 q^{14} +(1.35331e18 + 4.95639e18i) q^{15} +8.63057e19 q^{16} +2.38442e20i q^{17} +8.63880e20i q^{18} +5.86844e20 q^{19} +(-5.81171e21 + 1.58685e21i) q^{20} -2.01297e21 q^{21} +4.56875e22i q^{22} -1.73446e22i q^{23} +2.21193e22 q^{24} +(1.00262e23 - 5.91621e22i) q^{25} -2.32104e23 q^{26} +1.64005e23i q^{27} -2.36034e24i q^{28} +1.13413e23 q^{29} +(-8.02977e23 + 2.19247e23i) q^{30} +2.12133e24 q^{31} +1.36438e24i q^{32} +4.24652e24i q^{33} -3.86296e25 q^{34} +(1.20139e25 + 4.40001e25i) q^{35} -9.41517e25 q^{36} -8.11541e25i q^{37} +9.50738e25i q^{38} -2.15734e25 q^{39} +(-1.32014e26 - 4.83490e26i) q^{40} -1.96159e26 q^{41} -3.26118e26i q^{42} -8.68674e26i q^{43} -4.97935e27 q^{44} +(1.75512e27 - 4.79223e26i) q^{45} +2.80997e27 q^{46} +5.03480e27i q^{47} +1.29961e27i q^{48} -1.01390e28 q^{49} +(9.58476e27 + 1.62432e28i) q^{50} -3.59051e27 q^{51} -2.52963e28i q^{52} -7.43106e27i q^{53} -2.65702e28 q^{54} +(9.28220e28 - 2.53444e28i) q^{55} +1.96363e29 q^{56} +8.83684e27i q^{57} +1.83740e28i q^{58} -5.72962e28 q^{59} +(-2.38951e28 - 8.75141e28i) q^{60} -2.92431e29 q^{61} +3.43673e29i q^{62} +7.12817e29i q^{63} +5.20320e29 q^{64} +(1.28756e29 + 4.71559e29i) q^{65} -6.87973e29 q^{66} -8.52723e29i q^{67} -4.21013e30i q^{68} +2.61178e29 q^{69} +(-7.12839e30 + 1.94636e30i) q^{70} -1.52022e30 q^{71} -7.83271e30i q^{72} +1.66290e30i q^{73} +1.31477e31 q^{74} +(8.90876e29 + 1.50976e30i) q^{75} -1.03618e31 q^{76} +3.76983e31i q^{77} -3.49508e30i q^{78} -2.86123e31 q^{79} +(2.84073e31 - 7.75642e30i) q^{80} +2.71730e31 q^{81} -3.17794e31i q^{82} +1.27605e30i q^{83} +3.55426e31 q^{84} +(2.14291e31 + 7.84827e31i) q^{85} +1.40733e32 q^{86} +1.70781e30i q^{87} -4.14244e32i q^{88} -1.21015e32 q^{89} +(7.76382e31 + 2.84344e32i) q^{90} -1.91517e32 q^{91} +3.06250e32i q^{92} +3.19435e31i q^{93} -8.15681e32 q^{94} +(1.93159e32 - 5.27406e31i) q^{95} -2.05451e31 q^{96} +9.03160e32i q^{97} -1.64261e33i q^{98} +1.50375e33 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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