LMFDB - Embedded newform 5.24.b.a.4.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,24,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, 24, names="a")

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

chi := DirichletCharacter("5.4");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 24 $
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:	$16.7602018673$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 15644845 x^{8} + 79349217360160 x^{6} + \cdots + 34\!\cdots\!24 $ x^10 + 15644845x^8 + 79349217360160x^6 + 150324497245503837440x^4 + 76751558562242644579450880x^2 + 3490504262440921471663078375424
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{12}\cdot 5^{22} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4.7
Root			$839.925i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.24.b.a.4.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1679.85i q^{2} +330622. i q^{3} +5.56671e6 q^{4} +(-9.79539e7 + 4.82283e7i) q^{5} -5.55396e8 q^{6} +4.39640e9i q^{7} +2.34428e10i q^{8} -1.51680e10 q^{9} +O(q^{10})$	\(q+1679.85i q^{2} +330622. i q^{3} +5.56671e6 q^{4} +(-9.79539e7 + 4.82283e7i) q^{5} -5.55396e8 q^{6} +4.39640e9i q^{7} +2.34428e10i q^{8} -1.51680e10 q^{9} +(-8.10163e10 - 1.64548e11i) q^{10} -6.96897e10 q^{11} +1.84048e12i q^{12} +1.33740e12i q^{13} -7.38529e12 q^{14} +(-1.59454e13 - 3.23858e13i) q^{15} +7.31647e12 q^{16} -1.24972e14i q^{17} -2.54800e13i q^{18} -8.63652e14 q^{19} +(-5.45281e14 + 2.68473e14i) q^{20} -1.45355e15 q^{21} -1.17068e14i q^{22} -5.41138e15i q^{23} -7.75073e15 q^{24} +(7.26899e15 - 9.44830e15i) q^{25} -2.24663e15 q^{26} +2.61110e16i q^{27} +2.44735e16i q^{28} +1.26322e16 q^{29} +(5.44032e16 - 2.67858e16i) q^{30} +1.60540e17 q^{31} +2.08943e17i q^{32} -2.30410e16i q^{33} +2.09934e17 q^{34} +(-2.12031e17 - 4.30644e17i) q^{35} -8.44361e16 q^{36} +1.33010e18i q^{37} -1.45081e18i q^{38} -4.42174e17 q^{39} +(-1.13061e18 - 2.29632e18i) q^{40} -4.85637e18 q^{41} -2.44174e18i q^{42} +8.33566e18i q^{43} -3.87942e17 q^{44} +(1.48577e18 - 7.31529e17i) q^{45} +9.09030e18 q^{46} -1.44983e19i q^{47} +2.41899e18i q^{48} +8.04043e18 q^{49} +(1.58717e19 + 1.22108e19i) q^{50} +4.13184e19 q^{51} +7.44491e18i q^{52} +1.04792e20i q^{53} -4.38625e19 q^{54} +(6.82637e18 - 3.36101e18i) q^{55} -1.03064e20 q^{56} -2.85543e20i q^{57} +2.12202e19i q^{58} +1.12976e20 q^{59} +(-8.87632e19 - 1.80282e20i) q^{60} -2.79902e20 q^{61} +2.69684e20i q^{62} -6.66848e19i q^{63} -2.89619e20 q^{64} +(-6.45005e19 - 1.31003e20i) q^{65} +3.87054e19 q^{66} +1.54176e21i q^{67} -6.95681e20i q^{68} +1.78912e21 q^{69} +(7.23418e20 - 3.56180e20i) q^{70} +1.52414e21 q^{71} -3.55582e20i q^{72} -1.16861e20i q^{73} -2.23437e21 q^{74} +(3.12382e21 + 2.40329e21i) q^{75} -4.80770e21 q^{76} -3.06383e20i q^{77} -7.42787e20i q^{78} +2.27765e21 q^{79} +(-7.16676e20 + 3.52861e20i) q^{80} -1.00608e22 q^{81} -8.15797e21i q^{82} -8.52210e21i q^{83} -8.09148e21 q^{84} +(6.02717e21 + 1.22415e22i) q^{85} -1.40027e22 q^{86} +4.17649e21i q^{87} -1.63372e21i q^{88} +4.39110e22 q^{89} +(1.22886e21 + 2.49587e21i) q^{90} -5.87974e21 q^{91} -3.01236e22i q^{92} +5.30783e22i q^{93} +2.43550e22 q^{94} +(8.45981e22 - 4.16525e22i) q^{95} -6.90814e22 q^{96} +9.63106e22i q^{97} +1.35067e22i q^{98} +1.05706e21 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 41272680 q^{4} + 124761750 q^{5} - 2262077880 q^{6} - 189250631370 q^{9}+O(q^{10}) $ 10 * q - 41272680 * q^4 + 124761750 * q^5 - 2262077880 * q^6 - 189250631370 * q^9	$ 10 q - 41272680 q^{4} + 124761750 q^{5} - 2262077880 q^{6} - 189250631370 q^{9} - 992748199000 q^{10} - 1448637536280 q^{11} + 20750531044440 q^{14} - 14566613457000 q^{15} + 307971806876960 q^{16} + 887626815301400 q^{19} - 23\!\cdots\!00 q^{20}+ \cdots + 41\!\cdots\!60 q^{99}+O(q^{100}) $ 10 * q - 41272680 * q^4 + 124761750 * q^5 - 2262077880 * q^6 - 189250631370 * q^9 - 992748199000 * q^10 - 1448637536280 * q^11 + 20750531044440 * q^14 - 14566613457000 * q^15 + 307971806876960 * q^16 + 887626815301400 * q^19 - 2363707755099000 * q^20 - 781158183715080 * q^21 + 58473619965621600 * q^24 - 15436708968968750 * q^25 - 49259739315596880 * q^26 + 68538893585329500 * q^29 - 283259561673249000 * q^30 - 303703652281842880 * q^31 - 288299835336191360 * q^34 + 568057466315481000 * q^35 + 3242003939215214760 * q^36 - 8628905972055907440 * q^39 + 9426000384456940000 * q^40 - 6658832954283527580 * q^41 + 14990828914855427040 * q^44 - 8490880963475889750 * q^45 + 16736621075351903320 * q^46 + 51294362631233173870 * q^49 - 96456356624588250000 * q^50 - 117334349391643270080 * q^51 + 6367892697021344400 * q^54 + 8046234911696751000 * q^55 - 93285217288146540000 * q^56 + 461218638014732785800 * q^59 + 1248088814097510276000 * q^60 + 202894074812420701820 * q^61 - 2597882075263561124480 * q^64 + 404224351485216078000 * q^65 - 2067527591150630859360 * q^66 + 1761142984477245282360 * q^69 + 2651929720118465517000 * q^70 - 6362428274364321596880 * q^71 + 21369976437605310645840 * q^74 - 1268180400269994750000 * q^75 - 28533821601830896716000 * q^76 + 8008906997916696975200 * q^79 + 50390556129429851388000 * q^80 - 63620987817532049079390 * q^81 + 26983560053969205971040 * q^84 + 58719411820058643416000 * q^85 - 73642932902287825779480 * q^86 + 17045340818835962686500 * q^89 + 218378490181286718303000 * q^90 - 261754857315780277067280 * q^91 + 163995755653951693894840 * q^94 + 287254967024630517105000 * q^95 - 1029134712278532215134080 * q^96 + 411070875879864759534360 * 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 $

$2$			1679.85i			0.579997i	0.957027	+	0.289998i	$0.0936548\pi$
$2$			1679.85i			0.579997i	−0.957027	+	0.289998i	$0.906345\pi$
$3$			330622.i			1.07755i	0.842449	+	0.538776i	$0.181113\pi$
$3$			330622.i			1.07755i	−0.842449	+	0.538776i	$0.818887\pi$
$4$	5.56671e6			0.663604
$5$	−9.79539e7	+	4.82283e7i	−0.897153	+	0.441720i
$5$	−9.79539e7	+	4.82283e7i	−0.897153	+	0.441720i
$6$	−5.55396e8			−0.624976
$7$			4.39640e9i			0.840368i	0.907439	+	0.420184i	$0.138034\pi$
$7$			4.39640e9i			0.840368i	−0.907439	+	0.420184i	$0.861966\pi$
$8$			2.34428e10i			0.964885i
$9$	−1.51680e10			−0.161117
$10$	−8.10163e10	−	1.64548e11i	−0.256196	−	0.520346i
$11$	−6.96897e10			−0.0736466			−0.0368233	−	0.999322i	$-0.511724\pi$
$11$	−6.96897e10			−0.0736466			−0.0368233	+	0.999322i	$0.511724\pi$
$12$			1.84048e12i			0.715067i
$13$			1.33740e12i			0.206972i	0.994631	+	0.103486i	$0.0329998\pi$
$13$			1.33740e12i			0.206972i	−0.994631	+	0.103486i	$0.967000\pi$
$14$	−7.38529e12			−0.487411
$15$	−1.59454e13	−	3.23858e13i	−0.475976	−	0.966728i
$16$	7.31647e12			0.103973
$17$		−	1.24972e14i		−	0.884400i	−0.896916	−	0.442200i	$-0.854198\pi$
$17$		−	1.24972e14i		−	0.884400i	0.896916	−	0.442200i	$-0.145802\pi$
$18$		−	2.54800e13i		−	0.0934472i
$19$	−8.63652e14			−1.70088			−0.850438	−	0.526076i	$-0.823663\pi$
$19$	−8.63652e14			−1.70088			−0.850438	+	0.526076i	$0.823663\pi$
$20$	−5.45281e14	+	2.68473e14i	−0.595354	+	0.293127i
$21$	−1.45355e15			−0.905540
$22$		−	1.17068e14i		−	0.0427148i
$23$		−	5.41138e15i		−	1.18423i	−0.805852	−	0.592117i	$-0.798292\pi$
$23$		−	5.41138e15i		−	1.18423i	0.805852	−	0.592117i	$-0.201708\pi$
$24$	−7.75073e15			−1.03971
$25$	7.26899e15	−	9.44830e15i	0.609767	−	0.792580i
$26$	−2.24663e15			−0.120043
$27$			2.61110e16i			0.903940i
$28$			2.44735e16i			0.557671i
$29$	1.26322e16			0.192266			0.0961330	−	0.995368i	$-0.469353\pi$
$29$	1.26322e16			0.192266			0.0961330	+	0.995368i	$0.469353\pi$
$30$	5.44032e16	−	2.67858e16i	0.560700	−	0.276064i
$31$	1.60540e17			1.13481			0.567407	−	0.823437i	$-0.307946\pi$
$31$	1.60540e17			1.13481			0.567407	+	0.823437i	$0.307946\pi$
$32$			2.08943e17i			1.02519i
$33$		−	2.30410e16i		−	0.0793579i
$34$	2.09934e17			0.512949
$35$	−2.12031e17	−	4.30644e17i	−0.371207	−	0.753939i
$36$	−8.44361e16			−0.106918
$37$			1.33010e18i			1.22903i	0.788904	+	0.614517i	$0.210649\pi$
$37$			1.33010e18i			1.22903i	−0.788904	+	0.614517i	$0.789351\pi$
$38$		−	1.45081e18i		−	0.986502i
$39$	−4.42174e17			−0.223023
$40$	−1.13061e18	−	2.29632e18i	−0.426209	−	0.865650i
$41$	−4.85637e18			−1.37815			−0.689076	−	0.724689i	$-0.741983\pi$
$41$	−4.85637e18			−1.37815			−0.689076	+	0.724689i	$0.741983\pi$
$42$		−	2.44174e18i		−	0.525210i
$43$			8.33566e18i			1.36789i	0.729532	+	0.683947i	$0.239738\pi$
$43$			8.33566e18i			1.36789i	−0.729532	+	0.683947i	$0.760262\pi$
$44$	−3.87942e17			−0.0488721
$45$	1.48577e18	−	7.31529e17i	0.144546	−	0.0711685i
$46$	9.09030e18			0.686852
$47$		−	1.44983e19i		−	0.855444i	−0.903910	−	0.427722i	$-0.859316\pi$
$47$		−	1.44983e19i		−	0.855444i	0.903910	−	0.427722i	$-0.140684\pi$
$48$			2.41899e18i			0.112036i
$49$	8.04043e18			0.293781
$50$	1.58717e19	+	1.22108e19i	0.459694	+	0.353663i
$51$	4.13184e19			0.952986
$52$			7.44491e18i			0.137348i
$53$			1.04792e20i			1.55294i	0.630151	+	0.776472i	$0.282993\pi$
$53$			1.04792e20i			1.55294i	−0.630151	+	0.776472i	$0.717007\pi$
$54$	−4.38625e19			−0.524282
$55$	6.82637e18	−	3.36101e18i	0.0660722	−	0.0325311i
$56$	−1.03064e20			−0.810859
$57$		−	2.85543e20i		−	1.83278i
$58$			2.12202e19i			0.111514i
$59$	1.12976e20			0.487742			0.243871	−	0.969808i	$-0.421583\pi$
$59$	1.12976e20			0.487742			0.243871	+	0.969808i	$0.421583\pi$
$60$	−8.87632e19	−	1.80282e20i	−0.315859	−	0.641524i
$61$	−2.79902e20			−0.823594			−0.411797	−	0.911276i	$-0.635099\pi$
$61$	−2.79902e20			−0.823594			−0.411797	+	0.911276i	$0.635099\pi$
$62$			2.69684e20i			0.658189i
$63$		−	6.66848e19i		−	0.135397i
$64$	−2.89619e20			−0.490633
$65$	−6.45005e19	−	1.31003e20i	−0.0914238	−	0.185686i
$66$	3.87054e19			0.0460274
$67$			1.54176e21i			1.54226i	0.636678	+	0.771130i	$0.280308\pi$
$67$			1.54176e21i			1.54226i	−0.636678	+	0.771130i	$0.719692\pi$
$68$		−	6.95681e20i		−	0.586891i
$69$	1.78912e21			1.27607
$70$	7.23418e20	−	3.56180e20i	0.437282	−	0.215299i
$71$	1.52414e21			0.782627			0.391314	−	0.920257i	$-0.372021\pi$
$71$	1.52414e21			0.782627			0.391314	+	0.920257i	$0.372021\pi$
$72$		−	3.55582e20i		−	0.155459i
$73$		−	1.16861e20i		−	0.0435969i	−0.999762	−	0.0217984i	$-0.993061\pi$
$73$		−	1.16861e20i		−	0.0435969i	0.999762	−	0.0217984i	$-0.00693921\pi$
$74$	−2.23437e21			−0.712836
$75$	3.12382e21	+	2.40329e21i	0.854046	+	0.657056i
$76$	−4.80770e21			−1.12871
$77$		−	3.06383e20i		−	0.0618902i
$78$		−	7.42787e20i		−	0.129353i
$79$	2.27765e21			0.342591			0.171296	−	0.985220i	$-0.445205\pi$
$79$	2.27765e21			0.342591			0.171296	+	0.985220i	$0.445205\pi$
$80$	−7.16676e20	+	3.52861e20i	−0.0932799	+	0.0459270i
$81$	−1.00608e22			−1.13516
$82$		−	8.15797e21i		−	0.799324i
$83$		−	8.52210e21i		−	0.726354i	−0.931720	−	0.363177i	$-0.881692\pi$
$83$		−	8.52210e21i		−	0.726354i	0.931720	−	0.363177i	$-0.118308\pi$
$84$	−8.09148e21			−0.600919
$85$	6.02717e21	+	1.22415e22i	0.390657	+	0.793442i
$86$	−1.40027e22			−0.793374
$87$			4.17649e21i			0.207177i
$88$		−	1.63372e21i		−	0.0710605i
$89$	4.39110e22			1.67721			0.838606	−	0.544738i	$-0.183371\pi$
$89$	4.39110e22			1.67721			0.838606	+	0.544738i	$0.183371\pi$
$90$	1.22886e21	+	2.49587e21i	0.0412775	+	0.0838365i
$91$	−5.87974e21			−0.173933
$92$		−	3.01236e22i		−	0.785862i
$93$			5.30783e22i			1.22282i
$94$	2.43550e22			0.496155
$95$	8.45981e22	−	4.16525e22i	1.52595	−	0.751310i
$96$	−6.90814e22			−1.10469
$97$			9.63106e22i			1.36710i	0.729906	+	0.683548i	$0.239564\pi$
$97$			9.63106e22i			1.36710i	−0.729906	+	0.683548i	$0.760436\pi$
$98$			1.35067e22i			0.170392i
$99$	1.05706e21			0.0118657
$100$	4.04644e22	−	5.25959e22i	0.404644	−	0.525959i
$101$	−1.65243e23			−1.47376			−0.736881	−	0.676022i	$-0.763702\pi$
$101$	−1.65243e23			−1.47376			−0.736881	+	0.676022i	$0.763702\pi$
$102$			6.94088e22i			0.552729i
$103$		−	1.48460e23i		−	1.05677i	−0.849005	−	0.528385i	$-0.822798\pi$
$103$		−	1.48460e23i		−	1.05677i	0.849005	−	0.528385i	$-0.177202\pi$
$104$	−3.13524e22			−0.199705
$105$	1.42381e23	−	7.01021e22i	0.812408	−	0.399995i
$106$	−1.76035e23			−0.900703
$107$		−	2.75887e23i		−	1.26712i	−0.773694	−	0.633560i	$-0.781593\pi$
$107$		−	2.75887e23i		−	1.26712i	0.773694	−	0.633560i	$-0.218407\pi$
$108$			1.45352e23i			0.599858i
$109$	6.21330e21			0.0230631			0.0115316	−	0.999934i	$-0.496329\pi$
$109$	6.21330e21			0.0230631			0.0115316	+	0.999934i	$0.496329\pi$
$110$	5.64600e21	+	1.14673e22i	0.0188680	+	0.0383217i
$111$	−4.39760e23			−1.32435
$112$			3.21661e22i			0.0873758i
$113$			2.39275e23i			0.586808i	0.955989	+	0.293404i	$0.0947880\pi$
$113$			2.39275e23i			0.586808i	−0.955989	+	0.293404i	$0.905212\pi$
$114$	4.79669e23			1.06301
$115$	2.60981e23	+	5.30065e23i	0.523100	+	1.06244i
$116$	7.03199e22			0.127588
$117$		−	2.02857e22i		−	0.0333467i
$118$			1.89784e23i			0.282889i
$119$	5.49425e23			0.743222
$120$	7.59214e23	−	3.73805e23i	0.932782	−	0.459262i
$121$	−8.90574e23			−0.994576
$122$		−	4.70194e23i		−	0.477682i
$123$		−	1.60562e24i		−	1.48503i
$124$	8.93682e23			0.753067
$125$	−2.56351e23	+	1.27607e24i	−0.196956	+	0.980412i
$126$	1.12020e23			0.0785301
$127$			1.06736e24i			0.683234i	0.939839	+	0.341617i	$0.110975\pi$
$127$			1.06736e24i			0.683234i	−0.939839	+	0.341617i	$0.889025\pi$
$128$			1.26623e24i			0.740623i
$129$	−2.75596e24			−1.47398
$130$	2.20066e23	−	1.08351e23i	0.107697	−	0.0530255i
$131$	−1.58110e24			−0.708500			−0.354250	−	0.935151i	$-0.615264\pi$
$131$	−1.58110e24			−0.708500			−0.354250	+	0.935151i	$0.615264\pi$
$132$		−	1.28262e23i		−	0.0526622i
$133$		−	3.79696e24i		−	1.42936i
$134$	−2.58993e24			−0.894506
$135$	−1.25929e24	−	2.55767e24i	−0.399288	−	0.810972i
$136$	2.92969e24			0.853344
$137$			1.42001e24i			0.380194i	0.981765	+	0.190097i	$0.0608803\pi$
$137$			1.42001e24i			0.380194i	−0.981765	+	0.190097i	$0.939120\pi$
$138$			3.00546e24i			0.740119i
$139$	3.64801e24			0.826771			0.413386	−	0.910556i	$-0.364346\pi$
$139$	3.64801e24			0.826771			0.413386	+	0.910556i	$0.364346\pi$
$140$	−1.18031e24	−	2.39727e24i	−0.246334	−	0.500317i
$141$	4.79346e24			0.921785
$142$			2.56033e24i			0.453921i
$143$		−	9.32029e22i		−	0.0152428i
$144$	−1.10976e23			−0.0167518
$145$	−1.23737e24	+	6.09230e23i	−0.172492	+	0.0849277i
$146$	1.96308e23			0.0252861
$147$			2.65835e24i			0.316565i
$148$			7.40427e24i			0.815591i
$149$	2.78024e24			0.283427			0.141713	−	0.989908i	$-0.454739\pi$
$149$	2.78024e24			0.283427			0.141713	+	0.989908i	$0.454739\pi$
$150$	−4.03717e24	+	5.24755e24i	−0.381090	+	0.495344i
$151$	1.91474e25			1.67446			0.837228	−	0.546853i	$-0.184174\pi$
$151$	1.91474e25			1.67446			0.837228	+	0.546853i	$0.184174\pi$
$152$		−	2.02465e25i		−	1.64115i
$153$			1.89557e24i			0.142492i
$154$	5.14678e23			0.0358961
$155$	−1.57256e25	+	7.74259e24i	−1.01810	+	0.501270i
$156$	−2.46146e24			−0.147999
$157$		−	2.83098e24i		−	0.158158i	−0.996868	−	0.0790789i	$-0.974802\pi$
$157$		−	2.83098e24i		−	0.158158i	0.996868	−	0.0790789i	$-0.0251979\pi$
$158$			3.82612e24i			0.198702i
$159$	−3.46466e25			−1.67338
$160$	−1.00770e25	−	2.04668e25i	−0.452846	−	0.919752i
$161$	2.37906e25			0.995193
$162$		−	1.69007e25i		−	0.658388i
$163$			9.70039e24i			0.352072i	0.984384	+	0.176036i	$0.0563275\pi$
$163$			9.70039e24i			0.352072i	−0.984384	+	0.176036i	$0.943672\pi$
$164$	−2.70340e25			−0.914547
$165$	1.11123e24	+	2.25695e24i	0.0350540	+	0.0711962i
$166$	1.43159e25			0.421283
$167$			2.84361e25i			0.780963i	0.920611	+	0.390481i	$0.127691\pi$
$167$			2.84361e25i			0.780963i	−0.920611	+	0.390481i	$0.872309\pi$
$168$		−	3.40753e25i		−	0.873742i
$169$	3.99653e25			0.957162
$170$	−2.05638e25	+	1.01247e25i	−0.460194	+	0.226580i
$171$	1.30999e25			0.274039
$172$			4.64022e25i			0.907739i
$173$		−	5.10390e25i		−	0.934054i	−0.884243	−	0.467027i	$-0.845325\pi$
$173$		−	5.10390e25i		−	0.934054i	0.884243	−	0.467027i	$-0.154675\pi$
$174$	−7.01589e24			−0.120162
$175$	4.15385e25	+	3.19574e25i	0.666059	+	0.512429i
$176$	−5.09882e23			−0.00765727
$177$			3.73526e25i			0.525567i
$178$			7.37639e25i			0.972778i
$179$	2.58674e25			0.319848			0.159924	−	0.987129i	$-0.448875\pi$
$179$	2.58674e25			0.319848			0.159924	+	0.987129i	$0.448875\pi$
$180$	8.27084e24	−	4.07221e24i	0.0959215	−	0.0472276i
$181$	3.14433e25			0.342156			0.171078	−	0.985257i	$-0.445275\pi$
$181$	3.14433e25			0.342156			0.171078	+	0.985257i	$0.445275\pi$
$182$		−	9.87708e24i		−	0.100881i
$183$		−	9.25420e25i		−	0.887465i
$184$	1.26858e26			1.14265
$185$	−6.41484e25	−	1.30288e26i	−0.542889	−	1.10263i
$186$	−8.91636e25			−0.709233
$187$			8.70923e24i			0.0651330i
$188$		−	8.07078e25i		−	0.567676i
$189$	−1.14794e26			−0.759642
$190$	6.99699e25	+	1.42112e26i	0.435758	+	0.885044i
$191$	−2.74302e26			−1.60822			−0.804109	−	0.594482i	$-0.797357\pi$
$191$	−2.74302e26			−1.60822			−0.804109	+	0.594482i	$0.797357\pi$
$192$		−	9.57545e25i		−	0.528683i
$193$			2.60723e26i			1.35603i	0.735046	+	0.678017i	$0.237161\pi$
$193$			2.60723e26i			1.35603i	−0.735046	+	0.678017i	$0.762839\pi$
$194$	−1.61787e26			−0.792911
$195$	4.33127e25	−	2.13253e25i	0.200086	−	0.0985138i
$196$	4.47587e25			0.194954
$197$		−	1.71647e26i		−	0.705139i	−0.935786	−	0.352569i	$-0.885308\pi$
$197$		−	1.71647e26i		−	0.705139i	0.935786	−	0.352569i	$-0.114692\pi$
$198$			1.77570e24i			0.00688207i
$199$	2.00208e26			0.732271			0.366136	−	0.930561i	$-0.380681\pi$
$199$	2.00208e26			0.732271			0.366136	+	0.930561i	$0.380681\pi$
$200$	2.21495e26	+	1.70406e26i	0.764749	+	0.588355i
$201$	−5.09742e26			−1.66186
$202$		−	2.77584e26i		−	0.854778i
$203$			5.55363e25i			0.161574i
$204$	2.30008e26			0.632405
$205$	4.75700e26	−	2.34214e26i	1.23641	−	0.608757i
$206$	2.49390e26			0.612924
$207$			8.20800e25i			0.190800i
$208$			9.78504e24i			0.0215196i
$209$	6.01876e25			0.125264
$210$	1.17761e26	+	2.39178e26i	0.231996	+	0.471194i
$211$	−1.39093e26			−0.259453			−0.129726	−	0.991550i	$-0.541410\pi$
$211$	−1.39093e26			−0.259453			−0.129726	+	0.991550i	$0.541410\pi$
$212$			5.83347e26i			1.03054i
$213$			5.03916e26i			0.843321i
$214$	4.63449e26			0.734925
$215$	−4.02014e26	−	8.16510e26i	−0.604226	−	1.22721i
$216$	−6.12115e26			−0.872198
$217$			7.05800e26i			0.953662i
$218$			1.04374e25i			0.0133765i
$219$	3.86368e25			0.0469779
$220$	3.80004e25	−	1.87098e25i	0.0438458	−	0.0215878i
$221$	1.67137e26			0.183046
$222$		−	7.38732e26i		−	0.768117i
$223$		−	1.12218e27i		−	1.10804i	−0.832503	−	0.554021i	$-0.813093\pi$
$223$		−	1.12218e27i		−	1.10804i	0.832503	−	0.554021i	$-0.186907\pi$
$224$	−9.18599e26			−0.861536
$225$	−1.10256e26	+	1.43312e26i	−0.0982437	+	0.127698i
$226$	−4.01947e26			−0.340347
$227$		−	7.05509e25i		−	0.0567813i	−0.999597	−	0.0283906i	$-0.990962\pi$
$227$		−	7.05509e25i		−	0.0567813i	0.999597	−	0.0283906i	$-0.00903824\pi$
$228$		−	1.58953e27i		−	1.21624i
$229$	1.03419e26			0.0752475			0.0376237	−	0.999292i	$-0.488021\pi$
$229$	1.03419e26			0.0752475			0.0376237	+	0.999292i	$0.488021\pi$
$230$	−8.90431e26	+	4.38410e26i	−0.616212	+	0.303396i
$231$	1.01297e26			0.0666899
$232$			2.96135e26i			0.185515i
$233$			7.93257e26i			0.472956i	0.971637	+	0.236478i	$0.0759931\pi$
$233$			7.93257e26i			0.472956i	−0.971637	+	0.236478i	$0.924007\pi$
$234$	3.40770e25			0.0193410
$235$	6.99228e26	+	1.42016e27i	0.377867	+	0.767464i
$236$	6.28907e26			0.323667
$237$			7.53044e26i			0.369160i
$238$			9.22952e26i			0.431066i
$239$	−9.35595e26			−0.416401			−0.208201	−	0.978086i	$-0.566761\pi$
$239$	−9.35595e26			−0.416401			−0.208201	+	0.978086i	$0.566761\pi$
$240$	−1.16664e26	−	2.36949e26i	−0.0494887	−	0.100514i
$241$	3.91838e27			1.58457			0.792283	−	0.610154i	$-0.208892\pi$
$241$	3.91838e27			1.58457			0.792283	+	0.610154i	$0.208892\pi$
$242$		−	1.49603e27i		−	0.576851i
$243$		−	8.68170e26i		−	0.319251i
$244$	−1.55813e27			−0.546540
$245$	−7.87591e26	+	3.87776e26i	−0.263567	+	0.129769i
$246$	2.69721e27			0.861313
$247$		−	1.15505e27i		−	0.352034i
$248$			3.76353e27i			1.09497i
$249$	2.81760e27			0.782684
$250$	−2.14360e27	−	4.30631e26i	−0.568636	−	0.114234i
$251$	5.52443e27			1.39971			0.699857	−	0.714283i	$-0.253247\pi$
$251$	5.52443e27			1.39971			0.699857	+	0.714283i	$0.253247\pi$
$252$		−	3.71215e26i		−	0.0898502i
$253$			3.77117e26i			0.0872148i
$254$	−1.79301e27			−0.396274
$255$	−4.04730e27	+	1.99272e27i	−0.854975	+	0.420953i
$256$	−4.55657e27			−0.920193
$257$		−	1.22706e27i		−	0.236938i	−0.992958	−	0.118469i	$-0.962201\pi$
$257$		−	1.22706e27i		−	0.236938i	0.992958	−	0.118469i	$-0.0377987\pi$
$258$		−	4.62959e27i		−	0.854902i
$259$	−5.84764e27			−1.03284
$260$	−3.59055e26	−	7.29258e26i	−0.0606692	−	0.123222i
$261$	−1.91606e26			−0.0309773
$262$		−	2.65602e27i		−	0.410928i
$263$		−	2.19764e27i		−	0.325437i	−0.986673	−	0.162718i	$-0.947974\pi$
$263$		−	2.19764e27i		−	0.325437i	0.986673	−	0.162718i	$-0.0520262\pi$
$264$	5.40146e26			0.0765713
$265$	−5.05394e27	−	1.02648e28i	−0.685966	−	1.39323i
$266$	6.37832e27			0.829025
$267$			1.45180e28i			1.80728i
$268$			8.58255e27i			1.02345i
$269$	6.06374e27			0.692770			0.346385	−	0.938092i	$-0.387409\pi$
$269$	6.06374e27			0.692770			0.346385	+	0.938092i	$0.387409\pi$
$270$	4.29650e27	−	2.11541e27i	0.470361	−	0.231586i
$271$	−1.49750e28			−1.57116			−0.785581	−	0.618758i	$-0.787636\pi$
$271$	−1.49750e28			−1.57116			−0.785581	+	0.618758i	$0.787636\pi$
$272$		−	9.14350e26i		−	0.0919539i
$273$		−	1.94397e27i		−	0.187422i
$274$	−2.38541e27			−0.220512
$275$	−5.06574e26	+	6.58448e26i	−0.0449073	+	0.0583708i
$276$	9.95953e27			0.846807
$277$		−	5.49488e27i		−	0.448168i	−0.974570	−	0.224084i	$-0.928061\pi$
$277$		−	5.49488e27i		−	0.448168i	0.974570	−	0.224084i	$-0.0719390\pi$
$278$			6.12810e27i			0.479525i
$279$	−2.43508e27			−0.182838
$280$	1.00955e28	−	4.97061e27i	0.727464	−	0.358172i
$281$	1.19743e28			0.828184			0.414092	−	0.910235i	$-0.364099\pi$
$281$	1.19743e28			0.828184			0.414092	+	0.910235i	$0.364099\pi$
$282$			8.05230e27i			0.534632i
$283$		−	6.93235e27i		−	0.441913i	−0.975284	−	0.220956i	$-0.929082\pi$
$283$		−	6.93235e27i		−	0.441913i	0.975284	−	0.220956i	$-0.0709178\pi$
$284$	8.48447e27			0.519354
$285$	1.37712e28	+	2.79700e28i	0.809575	+	1.64428i
$286$	1.56567e26			0.00884078
$287$		−	2.13505e28i		−	1.15816i
$288$		−	3.16926e27i		−	0.165175i
$289$	4.34967e27			0.217837
$290$	−1.02342e27	−	2.07860e27i	−0.0492578	−	0.100045i
$291$	−3.18424e28			−1.47312
$292$		−	6.50530e26i		−	0.0289311i
$293$			2.16086e27i			0.0923952i	0.998932	+	0.0461976i	$0.0147104\pi$
$293$			2.16086e27i			0.0923952i	−0.998932	+	0.0461976i	$0.985290\pi$
$294$	−4.46562e27			−0.183606
$295$	−1.10665e28	+	5.44866e27i	−0.437579	+	0.215445i
$296$	−3.11813e28			−1.18588
$297$		−	1.81966e27i		−	0.0665720i
$298$			4.67039e27i			0.164387i
$299$	7.23717e27			0.245104
$300$	1.73894e28	+	1.33784e28i	0.566748	+	0.436024i
$301$	−3.66469e28			−1.14953
$302$			3.21647e28i			0.971180i
$303$		−	5.46331e28i		−	1.58805i
$304$	−6.31888e27			−0.176845
$305$	2.74175e28	−	1.34992e28i	0.738890	−	0.363798i
$306$	−3.18428e27			−0.0826447
$307$		−	5.79971e28i		−	1.44982i	−0.688842	−	0.724912i	$-0.741881\pi$
$307$		−	5.79971e28i		−	1.44982i	0.688842	−	0.724912i	$-0.258119\pi$
$308$		−	1.70555e27i		−	0.0410706i
$309$	4.90842e28			1.13872
$310$	−1.30064e28	−	2.64166e28i	−0.290735	−	0.590496i
$311$	−3.75763e28			−0.809412			−0.404706	−	0.914447i	$-0.632626\pi$
$311$	−3.75763e28			−0.809412			−0.404706	+	0.914447i	$0.632626\pi$
$312$		−	1.03658e28i		−	0.215192i
$313$			8.49108e28i			1.69904i	0.527558	+	0.849519i	$0.323108\pi$
$313$			8.49108e28i			1.69904i	−0.527558	+	0.849519i	$0.676892\pi$
$314$	4.75562e27			0.0917311
$315$	3.21609e27	+	6.53203e27i	0.0598077	+	0.121472i
$316$	1.26790e28			0.227345
$317$			9.98488e28i			1.72648i	0.504795	+	0.863239i	$0.331568\pi$
$317$			9.98488e28i			1.72648i	−0.504795	+	0.863239i	$0.668432\pi$
$318$		−	5.82012e28i		−	0.970554i
$319$	−8.80335e26			−0.0141597
$320$	2.83693e28	−	1.39678e28i	0.440173	−	0.216722i
$321$	9.12144e28			1.36539
$322$			3.99646e28i			0.577209i
$323$			1.07932e29i			1.50425i
$324$	−5.60058e28			−0.753295
$325$	1.26361e28	+	9.72155e27i	0.164042	+	0.126205i
$326$	−1.62952e28			−0.204201
$327$			2.05426e27i			0.0248517i
$328$		−	1.13847e29i		−	1.32976i
$329$	6.37403e28			0.718888
$330$	−3.79134e27	+	1.86669e27i	−0.0412936	+	0.0203312i
$331$	4.20858e28			0.442704			0.221352	−	0.975194i	$-0.428953\pi$
$331$	4.20858e28			0.442704			0.221352	+	0.975194i	$0.428953\pi$
$332$		−	4.74401e28i		−	0.482011i
$333$		−	2.01750e28i		−	0.198018i
$334$	−4.77684e28			−0.452956
$335$	−7.43566e28	−	1.51022e29i	−0.681247	−	1.38364i
$336$	−1.06348e28			−0.0941519
$337$		−	7.62071e28i		−	0.652006i	−0.945369	−	0.326003i	$-0.894298\pi$
$337$		−	7.62071e28i		−	0.652006i	0.945369	−	0.326003i	$-0.105702\pi$
$338$			6.71357e28i			0.555151i
$339$	−7.91098e28			−0.632315
$340$	3.35515e28	+	6.81446e28i	0.259241	+	0.526531i
$341$	−1.11880e28			−0.0835752
$342$			2.20059e28i			0.158942i
$343$			1.55673e29i			1.08725i
$344$	−1.95412e29			−1.31986
$345$	−1.75252e29	+	8.62863e28i	−1.14483	+	0.563667i
$346$	8.57379e28			0.541748
$347$		−	2.63340e29i		−	1.60963i	−0.593523	−	0.804817i	$-0.702263\pi$
$347$		−	2.63340e29i		−	1.60963i	0.593523	−	0.804817i	$-0.297737\pi$
$348$			2.32493e28i			0.137483i
$349$	2.55895e29			1.46410			0.732048	−	0.681253i	$-0.238565\pi$
$349$	2.55895e29			1.46410			0.732048	+	0.681253i	$0.238565\pi$
$350$	−5.36836e28	+	6.97784e28i	−0.297207	+	0.386312i
$351$	−3.49208e28			−0.187091
$352$		−	1.45612e28i		−	0.0755016i
$353$		−	1.78516e29i		−	0.895918i	−0.894054	−	0.447959i	$-0.852151\pi$
$353$		−	1.78516e29i		−	0.895918i	0.894054	−	0.447959i	$-0.147849\pi$
$354$	−6.27467e28			−0.304827
$355$	−1.49296e29	+	7.35069e28i	−0.702136	+	0.345702i
$356$	2.44440e29			1.11300
$357$			1.81652e29i			0.800859i
$358$			4.34534e28i			0.185511i
$359$	−4.48846e27			−0.0185572			−0.00927858	−	0.999957i	$-0.502954\pi$
$359$	−4.48846e27			−0.0185572			−0.00927858	+	0.999957i	$0.502954\pi$
$360$	1.71491e28	+	3.48306e28i	0.0686694	+	0.139471i
$361$	4.88065e29			1.89298
$362$			5.28200e28i			0.198449i
$363$		−	2.94444e29i		−	1.07171i
$364$	−3.27308e28			−0.115423
$365$	5.63599e27	+	1.14470e28i	0.0192576	+	0.0391131i
$366$	1.55457e29			0.514727
$367$			2.69983e29i			0.866318i	0.901318	+	0.433159i	$0.142601\pi$
$367$			2.69983e29i			0.866318i	−0.901318	+	0.433159i	$0.857399\pi$
$368$		−	3.95922e28i		−	0.123129i
$369$	7.36616e28			0.222043
$370$	2.18865e29	−	1.07760e29i	0.639523	−	0.314874i
$371$	−4.60708e29			−1.30505
$372$			2.95471e29i			0.811469i
$373$			1.94234e29i			0.517217i	0.965982	+	0.258608i	$0.0832639\pi$
$373$			1.94234e29i			0.517217i	−0.965982	+	0.258608i	$0.916736\pi$
$374$	−1.46302e28			−0.0377769
$375$	−4.21897e29	−	8.47554e28i	−1.05644	−	0.212230i
$376$	3.39881e29			0.825405
$377$			1.68943e28i			0.0397938i
$378$		−	1.92837e29i		−	0.440590i
$379$	−3.51187e29			−0.778374			−0.389187	−	0.921159i	$-0.627244\pi$
$379$	−3.51187e29			−0.778374			−0.389187	+	0.921159i	$0.627244\pi$
$380$	4.70933e29	−	2.31867e29i	1.01262	−	0.498572i
$381$	−3.52894e29			−0.736219
$382$		−	4.60786e29i		−	0.932762i
$383$		−	1.42054e29i		−	0.279041i	−0.990219	−	0.139520i	$-0.955444\pi$
$383$		−	1.42054e29i		−	0.279041i	0.990219	−	0.139520i	$-0.0445561\pi$
$384$	−4.18644e29			−0.798060
$385$	1.47764e28	+	3.00114e28i	0.0273381	+	0.0555250i
$386$	−4.37976e29			−0.786496
$387$		−	1.26436e29i		−	0.220391i
$388$			5.36133e29i			0.907210i
$389$	3.24898e29			0.533736			0.266868	−	0.963733i	$-0.414011\pi$
$389$	3.24898e29			0.533736			0.266868	+	0.963733i	$0.414011\pi$
$390$	3.58233e28	+	7.27588e28i	0.0571377	+	0.116049i
$391$	−6.76268e29			−1.04734
$392$			1.88491e29i			0.283465i
$393$		−	5.22748e29i		−	0.763445i
$394$	2.88341e29			0.408978
$395$	−2.23105e29	+	1.09847e29i	−0.307357	+	0.151329i
$396$	5.88432e27			0.00787412
$397$			1.94712e29i			0.253106i	0.991960	+	0.126553i	$0.0403914\pi$
$397$			1.94712e29i			0.253106i	−0.991960	+	0.126553i	$0.959609\pi$
$398$			3.36320e29i			0.424715i
$399$	1.25536e30			1.54021
$400$	5.31833e28	−	6.91281e28i	0.0633995	−	0.0824072i
$401$	3.80076e28			0.0440262			0.0220131	−	0.999758i	$-0.492992\pi$
$401$	3.80076e28			0.0440262			0.0220131	+	0.999758i	$0.492992\pi$
$402$		−	8.56290e29i		−	0.963876i
$403$			2.14707e29i			0.234875i
$404$	−9.19861e29			−0.977994
$405$	9.85498e29	−	4.85217e29i	1.01841	−	0.501422i
$406$	−9.32926e28			−0.0937126
$407$		−	9.26941e28i		−	0.0905141i
$408$			9.68621e29i			0.919522i
$409$	1.44703e30			1.33555			0.667773	−	0.744365i	$-0.267248\pi$
$409$	1.44703e30			1.33555			0.667773	+	0.744365i	$0.267248\pi$
$410$	3.93445e29	+	7.99105e29i	0.353077	+	0.717116i
$411$	−4.69488e29			−0.409679
$412$		−	8.26433e29i		−	0.701277i
$413$			4.96690e29i			0.409883i
$414$	−1.37882e29			−0.110663
$415$	4.11006e29	+	8.34773e29i	0.320845	+	0.651651i
$416$	−2.79441e29			−0.212186
$417$			1.20611e30i			0.890888i
$418$			1.01106e29i			0.0726525i
$419$	1.27535e30			0.891597			0.445798	−	0.895133i	$-0.352920\pi$
$419$	1.27535e30			0.891597			0.445798	+	0.895133i	$0.352920\pi$
$420$	7.92592e29	−	3.90238e29i	0.539117	−	0.265438i
$421$	−2.14406e30			−1.41903			−0.709517	−	0.704688i	$-0.751087\pi$
$421$	−2.14406e30			−1.41903			−0.709517	+	0.704688i	$0.751087\pi$
$422$		−	2.33656e29i		−	0.150482i
$423$			2.19911e29i			0.137826i
$424$	−2.45663e30			−1.49841
$425$	−1.18077e30	−	9.08418e29i	−0.700958	−	0.539278i
$426$	−8.46504e29			−0.489124
$427$		−	1.23056e30i		−	0.692122i
$428$		−	1.53578e30i		−	0.840865i
$429$	3.08150e28			0.0164249
$430$	1.37161e30	−	6.75324e29i	0.711778	−	0.350449i
$431$	1.57305e30			0.794794			0.397397	−	0.917647i	$-0.369914\pi$
$431$	1.57305e30			0.794794			0.397397	+	0.917647i	$0.369914\pi$
$432$			1.91040e29i			0.0939855i
$433$		−	3.08479e30i		−	1.47779i	−0.673818	−	0.738897i	$-0.735347\pi$
$433$		−	3.08479e30i		−	1.47779i	0.673818	−	0.738897i	$-0.264653\pi$
$434$	−1.18564e30			−0.553121
$435$	−2.01425e29	−	4.09104e29i	−0.0915140	−	0.185869i
$436$	3.45877e28			0.0153048
$437$			4.67355e30i			2.01423i
$438$			6.49040e28i			0.0272470i
$439$	5.82399e29			0.238165			0.119083	−	0.992884i	$-0.462005\pi$
$439$	5.82399e29			0.238165			0.119083	+	0.992884i	$0.462005\pi$
$440$	7.87917e28	+	1.60030e29i	0.0313888	+	0.0637521i
$441$	−1.21958e29			−0.0473331
$442$			2.80765e29i			0.106166i
$443$		−	1.52664e30i		−	0.562464i	−0.959640	−	0.281232i	$-0.909257\pi$
$443$		−	1.52664e30i		−	0.562464i	0.959640	−	0.281232i	$-0.0907431\pi$
$444$	−2.44802e30			−0.878841
$445$	−4.30125e30	+	2.11775e30i	−1.50472	+	0.740858i
$446$	1.88509e30			0.642661
$447$			9.19211e29i			0.305407i
$448$		−	1.27328e30i		−	0.412313i
$449$	3.53550e30			1.11588			0.557940	−	0.829881i	$-0.311592\pi$
$449$	3.53550e30			1.11588			0.557940	+	0.829881i	$0.311592\pi$
$450$	−2.40743e29	−	1.85214e29i	−0.0740644	−	0.0569811i
$451$	3.38439e29			0.101496
$452$			1.33198e30i			0.389408i
$453$			6.33055e30i			1.80431i
$454$	1.18515e29			0.0329330
$455$	5.75943e29	−	2.83570e29i	0.156045	−	0.0768296i
$456$	6.69394e30			1.76842
$457$		−	7.32475e30i		−	1.88693i	−0.331468	−	0.943466i	$-0.607544\pi$
$457$		−	7.32475e30i		−	1.88693i	0.331468	−	0.943466i	$-0.392456\pi$
$458$			1.73728e29i			0.0436433i
$459$	3.26313e30			0.799444
$460$	1.45281e30	+	2.95072e30i	0.347131	+	0.705039i
$461$	2.03010e30			0.473103			0.236552	−	0.971619i	$-0.423983\pi$
$461$	2.03010e30			0.473103			0.236552	+	0.971619i	$0.423983\pi$
$462$			1.70164e29i			0.0386799i
$463$			9.99822e29i			0.221688i	0.993838	+	0.110844i	$0.0353553\pi$
$463$			9.99822e29i			0.221688i	−0.993838	+	0.110844i	$0.964645\pi$
$464$	9.24232e28			0.0199905
$465$	−2.55987e30	−	5.19922e30i	−0.540144	−	1.09706i
$466$	−1.33255e30			−0.274313
$467$		−	4.60056e30i		−	0.923988i	−0.886883	−	0.461994i	$-0.847134\pi$
$467$		−	4.60056e30i		−	0.923988i	0.886883	−	0.461994i	$-0.152866\pi$
$468$		−	1.12925e29i		−	0.0221290i
$469$	−6.77821e30			−1.29607
$470$	−2.38566e30	+	1.17460e30i	−0.445127	+	0.219161i
$471$	9.35986e29			0.170423
$472$			2.64849e30i			0.470615i
$473$		−	5.80909e29i		−	0.100741i
$474$	−1.26500e30			−0.214111
$475$	−6.27788e30	+	8.16004e30i	−1.03714	+	1.34808i
$476$	3.05849e30			0.493204
$477$		−	1.58949e30i		−	0.250205i
$478$		−	1.57166e30i		−	0.241511i
$479$	−4.84215e30			−0.726407			−0.363203	−	0.931710i	$-0.618317\pi$
$479$	−4.84215e30			−0.726407			−0.363203	+	0.931710i	$0.618317\pi$
$480$	6.76679e30	−	3.33168e30i	0.991080	−	0.487965i
$481$	−1.77887e30			−0.254376
$482$			6.58229e30i			0.919043i
$483$			7.86570e30i			1.07237i
$484$	−4.95757e30			−0.660004
$485$	−4.64489e30	−	9.43399e30i	−0.603873	−	1.22649i
$486$	1.45840e30			0.185165
$487$		−	5.15151e30i		−	0.638781i	−0.947623	−	0.319390i	$-0.896522\pi$
$487$		−	5.15151e30i		−	0.638781i	0.947623	−	0.319390i	$-0.103478\pi$
$488$		−	6.56171e30i		−	0.794674i
$489$	−3.20717e30			−0.379376
$490$	−6.51406e29	−	1.32304e30i	−0.0752656	−	0.152868i
$491$	6.55451e30			0.739781			0.369891	−	0.929075i	$-0.379395\pi$
$491$	6.55451e30			0.739781			0.369891	+	0.929075i	$0.379395\pi$
$492$		−	8.93804e30i		−	0.985471i
$493$		−	1.57867e30i		−	0.170040i
$494$	1.94031e30			0.204179
$495$	−1.03543e29	+	5.09800e28i	−0.0106453	+	0.00524131i
$496$	1.17459e30			0.117990
$497$			6.70074e30i			0.657695i
$498$			4.73314e30i			0.453954i
$499$	1.79380e31			1.68120			0.840599	−	0.541658i	$-0.182203\pi$
$499$	1.79380e31			1.68120			0.840599	+	0.541658i	$0.182203\pi$
$500$	−1.42703e30	+	7.10350e30i	−0.130701	+	0.650605i
$501$	−9.40161e30			−0.841527
$502$			9.28021e30i			0.811830i
$503$			4.02469e30i			0.344113i	0.985087	+	0.172056i	$0.0550411\pi$
$503$			4.02469e30i			0.344113i	−0.985087	+	0.172056i	$0.944959\pi$
$504$	1.56328e30			0.130643
$505$	1.61862e31	−	7.96939e30i	1.32219	−	0.650990i
$506$	−6.33500e29			−0.0505843
$507$			1.32134e31i			1.03139i
$508$			5.94170e30i			0.453396i
$509$	3.44642e30			0.257107			0.128554	−	0.991703i	$-0.458967\pi$
$509$	3.44642e30			0.257107			0.128554	+	0.991703i	$0.458967\pi$
$510$	−3.34747e30	−	6.79886e30i	−0.244151	−	0.495883i
$511$	5.13766e29			0.0366374
$512$			2.96753e30i			0.206914i
$513$		−	2.25508e31i		−	1.53749i
$514$	2.06128e30			0.137424
$515$	7.15996e30	+	1.45422e31i	0.466797	+	0.948085i
$516$	−1.53416e31			−0.978136
$517$			1.01038e30i			0.0630005i
$518$		−	9.82316e30i		−	0.599045i
$519$	1.68746e31			1.00649
$520$	3.07109e30	−	1.51207e30i	0.179166	−	0.0882134i
$521$	−2.56471e31			−1.46354			−0.731769	−	0.681553i	$-0.761305\pi$
$521$	−2.56471e31			−1.46354			−0.731769	+	0.681553i	$0.761305\pi$
$522$		−	3.21869e29i		−	0.0179667i
$523$			3.89068e30i			0.212450i	0.994342	+	0.106225i	$0.0338763\pi$
$523$			3.89068e30i			0.212450i	−0.994342	+	0.106225i	$0.966124\pi$
$524$	−8.80154e30			−0.470163
$525$	−1.05658e31	+	1.37336e31i	−0.552169	+	0.717713i
$526$	3.69172e30			0.188752
$527$		−	2.00630e31i		−	1.00363i
$528$		−	1.68578e29i		−	0.00825110i
$529$	−8.40253e30			−0.402411
$530$	1.72433e31	−	8.48987e30i	0.808069	−	0.397858i
$531$	−1.71363e30			−0.0785834
$532$		−	2.11366e31i		−	0.948529i
$533$		−	6.49490e30i		−	0.285239i
$534$	−2.43880e31			−1.04822
$535$	1.33056e31	+	2.70242e31i	0.559712	+	1.13680i
$536$	−3.61433e31			−1.48810
$537$			8.55235e30i			0.344652i
$538$			1.01862e31i			0.401805i
$539$	−5.60335e29			−0.0216360
$540$	−7.01008e30	−	1.42378e31i	−0.264969	−	0.538164i
$541$	1.53200e31			0.566877			0.283439	−	0.958990i	$-0.408525\pi$
$541$	1.53200e31			0.566877			0.283439	+	0.958990i	$0.408525\pi$
$542$		−	2.51558e31i		−	0.911270i
$543$			1.03959e31i			0.368691i
$544$	2.61120e31			0.906677
$545$	−6.08617e29	+	2.99657e29i	−0.0206911	+	0.0101874i
$546$	3.26559e30			0.108704
$547$		−	2.71044e31i		−	0.883458i	−0.897149	−	0.441729i	$-0.854365\pi$
$547$		−	2.71044e31i		−	0.883458i	0.897149	−	0.441729i	$-0.145635\pi$
$548$			7.90480e30i			0.252298i
$549$	4.24557e30			0.132695
$550$	−1.10609e30	−	8.50968e29i	−0.0338549	−	0.0260461i
$551$	−1.09098e31			−0.327021
$552$			4.19421e31i			1.23126i
$553$			1.00135e31i			0.287903i
$554$	9.23058e30			0.259936
$555$	4.30762e31	−	2.12089e31i	1.18814	−	0.584990i
$556$	2.03074e31			0.548648
$557$			6.09979e31i			1.61428i	0.590357	+	0.807142i	$0.298987\pi$
$557$			6.09979e31i			1.61428i	−0.590357	+	0.807142i	$0.701013\pi$
$558$		−	4.09058e30i		−	0.106045i
$559$	−1.11481e31			−0.283116
$560$	−1.55132e30	−	3.15079e30i	−0.0385956	−	0.0783895i
$561$	−2.87947e30			−0.0701842
$562$			2.01150e31i			0.480344i
$563$			1.61238e31i			0.377242i	0.982050	+	0.188621i	$0.0604017\pi$
$563$			1.61238e31i			0.377242i	−0.982050	+	0.188621i	$0.939598\pi$
$564$	2.66838e31			0.611700
$565$	−1.15398e31	−	2.34379e31i	−0.259204	−	0.526456i
$566$	1.16453e31			0.256308
$567$		−	4.42314e31i		−	0.953951i
$568$			3.57303e31i			0.755145i
$569$	1.01790e31			0.210821			0.105411	−	0.994429i	$-0.466384\pi$
$569$	1.01790e31			0.210821			0.105411	+	0.994429i	$0.466384\pi$
$570$	−4.69855e31	+	2.31336e31i	−0.953680	+	0.469551i
$571$	2.76608e31			0.550237			0.275119	−	0.961410i	$-0.411283\pi$
$571$	2.76608e31			0.550237			0.275119	+	0.961410i	$0.411283\pi$
$572$		−	5.18833e29i		−	0.0101152i
$573$		−	9.06903e31i		−	1.73294i
$574$	3.58657e31			0.671726
$575$	−5.11283e31	−	3.93353e31i	−0.938601	−	0.722107i
$576$	4.39295e30			0.0790492
$577$			3.66251e31i			0.646036i	0.946393	+	0.323018i	$0.104697\pi$
$577$			3.66251e31i			0.646036i	−0.946393	+	0.323018i	$0.895303\pi$
$578$			7.30680e30i			0.126345i
$579$	−8.62010e31			−1.46120
$580$	−6.88811e30	+	3.39141e30i	−0.114466	+	0.0563583i
$581$	3.74665e31			0.610405
$582$		−	5.34905e31i		−	0.854403i
$583$		−	7.30293e30i		−	0.114369i
$584$	2.73955e30			0.0420660
$585$	9.78346e29	+	1.98707e30i	0.0147299	+	0.0299171i
$586$	−3.62992e30			−0.0535889
$587$		−	2.60978e31i		−	0.377803i	−0.981996	−	0.188901i	$-0.939507\pi$
$587$		−	2.60978e31i		−	0.377803i	0.981996	−	0.188901i	$-0.0604927\pi$
$588$			1.47982e31i			0.210073i
$589$	−1.38651e32			−1.93018
$590$	−9.15294e30	−	1.85900e31i	−0.124958	−	0.253795i
$591$	5.67503e31			0.759823
$592$			9.73162e30i			0.127787i
$593$			8.14277e31i			1.04868i	0.851509	+	0.524340i	$0.175688\pi$
$593$			8.14277e31i			1.04868i	−0.851509	+	0.524340i	$0.824312\pi$
$594$	3.05676e30			0.0386116
$595$	−5.38183e31	+	2.64978e31i	−0.666783	+	0.328296i
$596$	1.54768e31			0.188083
$597$			6.61934e31i			0.789060i
$598$			1.21574e31i			0.142159i
$599$	−3.12456e31			−0.358411			−0.179205	−	0.983812i	$-0.557353\pi$
$599$	−3.12456e31			−0.358411			−0.179205	+	0.983812i	$0.557353\pi$
$600$	−5.63400e31	+	7.32312e31i	−0.633983	+	0.824056i
$601$	2.08180e31			0.229818			0.114909	−	0.993376i	$-0.463342\pi$
$601$	2.08180e31			0.229818			0.114909	+	0.993376i	$0.463342\pi$
$602$		−	6.15612e31i		−	0.666727i
$603$		−	2.33855e31i		−	0.248484i
$604$	1.06588e32			1.11118
$605$	8.72351e31	−	4.29508e31i	0.892287	−	0.439324i
$606$	9.17754e31			0.921067
$607$		−	5.97431e31i		−	0.588325i	−0.955755	−	0.294163i	$-0.904959\pi$
$607$		−	5.97431e31i		−	0.588325i	0.955755	−	0.294163i	$-0.0950408\pi$
$608$		−	1.80454e32i		−	1.74372i
$609$	−1.83615e31			−0.174105
$610$	2.26766e31	+	4.60573e31i	0.211002	+	0.428554i
$611$	1.93900e31			0.177053
$612$			1.05521e31i			0.0945580i
$613$		−	7.40467e31i		−	0.651194i	−0.945509	−	0.325597i	$-0.894435\pi$
$613$		−	7.40467e31i		−	0.651194i	0.945509	−	0.325597i	$-0.105565\pi$
$614$	9.74265e31			0.840893
$615$	7.74365e31	+	1.57277e32i	0.655967	+	1.33230i
$616$	7.18250e30			0.0597169
$617$			6.87935e31i			0.561395i	0.959796	+	0.280697i	$0.0905657\pi$
$617$			6.87935e31i			0.561395i	−0.959796	+	0.280697i	$0.909434\pi$
$618$			8.24540e31i			0.660457i
$619$	−7.99204e31			−0.628370			−0.314185	−	0.949362i	$-0.601731\pi$
$619$	−7.99204e31			−0.628370			−0.314185	+	0.949362i	$0.601731\pi$
$620$	−8.75396e31	+	4.31008e31i	−0.675617	+	0.332645i
$621$	1.41296e32			1.07048
$622$		−	6.31226e31i		−	0.469456i
$623$			1.93050e32i			1.40948i
$624$	−3.23515e30			−0.0231885
$625$	−3.64320e31	−	1.37359e32i	−0.256368	−	0.966579i
$626$	−1.42637e32			−0.985437
$627$			1.98994e31i			0.134978i
$628$		−	1.57592e31i		−	0.104954i
$629$	1.66224e32			1.08696
$630$	−1.09728e31	+	5.40255e30i	−0.0704535	+	0.0346883i
$631$	−1.68491e32			−1.06228			−0.531141	−	0.847283i	$-0.678237\pi$
$631$	−1.68491e32			−1.06228			−0.531141	+	0.847283i	$0.678237\pi$
$632$			5.33947e31i			0.330561i
$633$		−	4.59874e31i		−	0.279574i
$634$	−1.67731e32			−1.00135
$635$	−5.14771e31	−	1.04552e32i	−0.301798	−	0.612965i
$636$	−1.92868e32			−1.11046
$637$			1.07533e31i			0.0608046i
$638$		−	1.47883e30i		−	0.00821260i
$639$	−2.31183e31			−0.126094
$640$	−6.10680e31	−	1.24032e32i	−0.327148	−	0.664452i
$641$	1.95042e32			1.02627			0.513134	−	0.858309i	$-0.328484\pi$
$641$	1.95042e32			1.02627			0.513134	+	0.858309i	$0.328484\pi$
$642$			1.53227e32i			0.791920i
$643$		−	7.77114e31i		−	0.394510i	−0.980352	−	0.197255i	$-0.936797\pi$
$643$		−	7.77114e31i		−	0.394510i	0.980352	−	0.197255i	$-0.0632028\pi$
$644$	1.32435e32			0.660414
$645$	2.69956e32	−	1.32915e32i	1.32238	−	0.651084i
$646$	−1.81310e32			−0.872463
$647$		−	1.17519e32i		−	0.555534i	−0.960649	−	0.277767i	$-0.910406\pi$
$647$		−	1.17519e32i		−	0.555534i	0.960649	−	0.277767i	$-0.0895943\pi$
$648$		−	2.35855e32i		−	1.09530i
$649$	−7.87329e30			−0.0359205
$650$	−1.63307e31	+	2.12268e31i	−0.0731985	+	0.0951440i
$651$	−2.33353e32			−1.02762
$652$			5.39993e31i			0.233636i
$653$			1.99640e32i			0.848684i	0.905502	+	0.424342i	$0.139495\pi$
$653$			1.99640e32i			0.848684i	−0.905502	+	0.424342i	$0.860505\pi$
$654$	−3.45085e30			−0.0144139
$655$	1.54875e32	−	7.62538e31i	0.635633	−	0.312959i
$656$	−3.55314e31			−0.143291
$657$			1.77255e30i			0.00702419i
$658$			1.07074e32i			0.416953i
$659$	−1.51826e32			−0.580982			−0.290491	−	0.956878i	$-0.593819\pi$
$659$	−1.51826e32			−0.580982			−0.290491	+	0.956878i	$0.593819\pi$
$660$	6.18588e30	+	1.25638e31i	0.0232619	+	0.0472461i
$661$	−2.46931e32			−0.912553			−0.456276	−	0.889838i	$-0.650817\pi$
$661$	−2.46931e32			−0.912553			−0.456276	+	0.889838i	$0.650817\pi$
$662$			7.06979e31i			0.256767i
$663$			5.52592e31i			0.197242i
$664$	1.99782e32			0.700848
$665$	1.83121e32	+	3.71927e32i	0.631377	+	1.28236i
$666$	3.38910e31			0.114850
$667$		−	6.83577e31i		−	0.227688i
$668$			1.58295e32i			0.518250i
$669$	3.71018e32			1.19397
$670$	2.53694e32	−	1.24908e32i	0.802509	−	0.395121i
$671$	1.95063e31			0.0606549
$672$		−	3.03709e32i		−	0.928350i
$673$			3.87794e32i			1.16527i	0.812733	+	0.582637i	$0.197979\pi$
$673$			3.87794e32i			1.16527i	−0.812733	+	0.582637i	$0.802021\pi$
$674$	1.28016e32			0.378161
$675$	2.46704e32	+	1.89800e32i	0.716445	+	0.551193i
$676$	2.22475e32			0.635176
$677$		−	9.71351e31i		−	0.272651i	−0.990664	−	0.136325i	$-0.956471\pi$
$677$		−	9.71351e31i		−	0.272651i	0.990664	−	0.136325i	$-0.0435292\pi$
$678$		−	1.32893e32i		−	0.366741i
$679$	−4.23420e32			−1.14886
$680$	−2.86974e32	+	1.41294e32i	−0.765580	+	0.376939i
$681$	2.33257e31			0.0611847
$682$		−	1.87942e31i		−	0.0484734i
$683$		−	4.44290e32i		−	1.12675i	−0.826201	−	0.563376i	$-0.809502\pi$
$683$		−	4.44290e32i		−	1.12675i	0.826201	−	0.563376i	$-0.190498\pi$
$684$	7.29234e31			0.181854
$685$	−6.84848e31	−	1.39096e32i	−0.167939	−	0.341093i
$686$	−2.61507e32			−0.630603
$687$			3.41926e31i			0.0810830i
$688$			6.09875e31i			0.142224i
$689$	−1.40149e32			−0.321417
$690$	−1.44948e32	−	2.94396e32i	−0.326925	−	0.664000i
$691$	−2.82124e31			−0.0625811			−0.0312906	−	0.999510i	$-0.509962\pi$
$691$	−2.82124e31			−0.0625811			−0.0312906	+	0.999510i	$0.509962\pi$
$692$		−	2.84119e32i		−	0.619841i
$693$			4.64724e30i			0.00997155i
$694$	4.42371e32			0.933583
$695$	−3.57336e32	+	1.75937e32i	−0.741740	+	0.365201i
$696$	−9.79089e31			−0.199902
$697$			6.06908e32i			1.21884i
$698$			4.29865e32i			0.849171i
$699$	−2.62268e32			−0.509634
$700$	2.31233e32	+	1.77898e32i	0.441999	+	0.340050i
$701$	−8.19795e31			−0.154152			−0.0770758	−	0.997025i	$-0.524558\pi$
$701$	−8.19795e31			−0.154152			−0.0770758	+	0.997025i	$0.524558\pi$
$702$		−	5.86617e31i		−	0.108512i
$703$		−	1.14874e33i		−	2.09043i
$704$	2.01834e31			0.0361335
$705$	−4.69538e32	+	2.31181e32i	−0.826982	+	0.407171i
$706$	2.99880e32			0.519630
$707$		−	7.26475e32i		−	1.23850i
$708$			2.07931e32i			0.348768i
$709$	−6.38920e32			−1.05442			−0.527211	−	0.849734i	$-0.676762\pi$
$709$	−6.38920e32			−1.05442			−0.527211	+	0.849734i	$0.676762\pi$
$710$	−1.23481e32	−	2.50795e32i	−0.200506	−	0.407237i
$711$	−3.45476e31			−0.0551972
$712$			1.02940e33i			1.61832i
$713$		−	8.68745e32i		−	1.34389i
$714$	−3.05149e32			−0.464496
$715$	4.49502e30	+	9.12958e30i	0.00673305	+	0.0136751i
$716$	1.43996e32			0.212252
$717$		−	3.09329e32i		−	0.448694i
$718$		−	7.53995e30i		−	0.0107631i
$719$	7.83062e32			1.10005			0.550027	−	0.835147i	$-0.314618\pi$
$719$	7.83062e32			1.10005			0.550027	+	0.835147i	$0.314618\pi$
$720$	1.08706e31	−	5.35221e30i	0.0150290	−	0.00739961i
$721$	6.52688e32			0.888077
$722$			8.19877e32i			1.09792i
$723$			1.29550e33i			1.70745i
$724$	1.75036e32			0.227056
$725$	9.18235e31	−	1.19353e32i	0.117238	−	0.152386i
$726$	4.94621e32			0.621587
$727$			7.96232e32i			0.984904i	0.870340	+	0.492452i	$0.163899\pi$
$727$			7.96232e32i			0.984904i	−0.870340	+	0.492452i	$0.836101\pi$
$728$		−	1.37838e32i		−	0.167825i
$729$	−6.60122e32			−0.791148
$730$	−1.92292e31	+	9.46762e30i	−0.0226855	+	0.0111694i
$731$	1.04172e33			1.20977
$732$		−	5.15154e32i		−	0.588925i
$733$		−	1.79370e32i		−	0.201862i	−0.994893	−	0.100931i	$-0.967818\pi$
$733$		−	1.79370e32i		−	0.201862i	0.994893	−	0.100931i	$-0.0321821\pi$
$734$	−4.53532e32			−0.502462
$735$	−1.28208e32	−	2.60395e32i	−0.139833	−	0.284007i
$736$	1.13067e33			1.21406
$737$		−	1.07445e32i		−	0.113582i
$738$			1.23740e32i			0.128784i
$739$	3.97888e32			0.407709			0.203854	−	0.979001i	$-0.434653\pi$
$739$	3.97888e32			0.407709			0.203854	+	0.979001i	$0.434653\pi$
$740$	−3.57095e32	−	7.25277e32i	−0.360263	−	0.731710i
$741$	3.81885e32			0.379335
$742$		−	7.73920e32i		−	0.756922i
$743$			2.81062e32i			0.270664i	0.990800	+	0.135332i	$0.0432101\pi$
$743$			2.81062e32i			0.270664i	−0.990800	+	0.135332i	$0.956790\pi$
$744$	−1.24431e33			−1.17988
$745$	−2.72336e32	+	1.34086e32i	−0.254277	+	0.125195i
$746$	−3.26283e32			−0.299984
$747$			1.29264e32i			0.117028i
$748$			4.84817e31i			0.0432225i
$749$	1.21291e33			1.06485
$750$	1.42376e32	−	7.08724e32i	0.123093	−	0.612735i
$751$	−7.04672e31			−0.0599968			−0.0299984	−	0.999550i	$-0.509550\pi$
$751$	−7.04672e31			−0.0599968			−0.0299984	+	0.999550i	$0.509550\pi$
$752$		−	1.06076e32i		−	0.0889433i
$753$			1.82650e33i			1.50826i
$754$	−2.83799e31			−0.0230803
$755$	−1.87556e33	+	9.23444e32i	−1.50224	+	0.739641i
$756$	−6.39026e32			−0.504101
$757$		−	1.91542e33i		−	1.48820i	−0.668067	−	0.744101i	$-0.732878\pi$
$757$		−	1.91542e33i		−	1.48820i	0.668067	−	0.744101i	$-0.267122\pi$
$758$		−	5.89942e32i		−	0.451454i
$759$	−1.24683e32			−0.0939784
$760$	9.76452e32	+	1.98322e33i	0.724928	+	1.47236i
$761$	−1.56479e33			−1.14428			−0.572139	−	0.820156i	$-0.693886\pi$
$761$	−1.56479e33			−1.14428			−0.572139	+	0.820156i	$0.693886\pi$
$762$		−	5.92810e32i		−	0.427005i
$763$			2.73162e31i			0.0193815i
$764$	−1.52696e33			−1.06722
$765$	−9.14203e31	−	1.85679e32i	−0.0629414	−	0.127837i
$766$	2.38630e32			0.161843
$767$			1.51095e32i			0.100949i
$768$		−	1.50651e33i		−	0.991555i
$769$	−3.46136e32			−0.224437			−0.112218	−	0.993684i	$-0.535796\pi$
$769$	−3.46136e32			−0.224437			−0.112218	+	0.993684i	$0.535796\pi$
$770$	−5.04147e31	+	2.48221e31i	−0.0322043	+	0.0158560i
$771$	4.05694e32			0.255313
$772$			1.45137e33i			0.899869i
$773$			2.06569e32i			0.126183i	0.998008	+	0.0630915i	$0.0200960\pi$
$773$			2.06569e32i			0.126183i	−0.998008	+	0.0630915i	$0.979904\pi$
$774$	2.12393e32			0.127826
$775$	1.16697e33	−	1.51683e33i	0.691973	−	0.899432i
$776$	−2.25779e33			−1.31909
$777$		−	1.93336e33i		−	1.11294i
$778$			5.45780e32i			0.309565i
$779$	4.19421e33			2.34406
$780$	2.41109e32	−	1.18712e32i	0.132778	−	0.0653741i
$781$	−1.06217e32			−0.0576378
$782$		−	1.13603e33i		−	0.607452i
$783$			3.29839e32i			0.173797i
$784$	5.88275e31			0.0305454
$785$	1.36533e32	+	2.77305e32i	0.0698614	+	0.141892i
$786$	8.78138e32			0.442796
$787$			3.84366e33i			1.91001i	0.296590	+	0.955005i	$0.404151\pi$
$787$			3.84366e33i			1.91001i	−0.296590	+	0.955005i	$0.595849\pi$
$788$		−	9.55509e32i		−	0.467932i
$789$	7.26591e32			0.350675
$790$	−1.84527e32	−	3.74783e32i	−0.0877705	−	0.178266i
$791$	−1.05195e33			−0.493134
$792$			2.47804e31i			0.0114490i
$793$		−	3.74341e32i		−	0.170461i
$794$	−3.27088e32			−0.146801
$795$	3.39377e33	−	1.67095e33i	1.50128	−	0.739164i
$796$	1.11450e33			0.485938
$797$			3.79572e33i			1.63126i	0.578574	+	0.815630i	$0.303610\pi$
$797$			3.79572e33i			1.63126i	−0.578574	+	0.815630i	$0.696390\pi$
$798$			2.10882e33i			0.893317i
$799$	−1.81188e33			−0.756555
$800$	1.97416e33	+	1.51881e33i	0.812545	+	0.625127i
$801$	−6.66044e32			−0.270227
$802$			6.38472e31i			0.0255350i
$803$			8.14398e30i			0.00321076i
$804$	−2.83758e33			−1.10282
$805$	−2.33038e33	+	1.14738e33i	−0.892840	+	0.439596i
$806$	−3.60675e32			−0.136227
$807$			2.00481e33i			0.746495i
$808$		−	3.87377e33i		−	1.42201i
$809$	3.97696e33			1.43927			0.719636	−	0.694352i	$-0.244309\pi$
$809$	3.97696e33			1.43927			0.719636	+	0.694352i	$0.244309\pi$
$810$	8.15092e32	+	1.65549e33i	0.290823	+	0.590675i
$811$	−3.14424e33			−1.10605			−0.553026	−	0.833164i	$-0.686527\pi$
$811$	−3.14424e33			−1.10605			−0.553026	+	0.833164i	$0.686527\pi$
$812$			3.09154e32i			0.107221i
$813$		−	4.95108e33i		−	1.69301i
$814$	1.55712e32			0.0524979
$815$	−4.67833e32	−	9.50191e32i	−0.155517	−	0.315863i
$816$	3.02305e32			0.0990851
$817$		−	7.19911e33i		−	2.32662i
$818$			2.43079e33i			0.774612i
$819$	8.91841e31			0.0280235
$820$	2.64808e33	−	1.30380e33i	0.820488	−	0.403973i
$821$	−5.38964e33			−1.64670			−0.823348	−	0.567537i	$-0.807896\pi$
$821$	−5.38964e33			−1.64670			−0.823348	+	0.567537i	$0.807896\pi$
$822$		−	7.88670e32i		−	0.237613i
$823$			1.47866e33i			0.439310i	0.975578	+	0.219655i	$0.0704932\pi$
$823$			1.47866e33i			0.439310i	−0.975578	+	0.219655i	$0.929507\pi$
$824$	3.48032e33			1.01966
$825$	−2.17698e32	−	1.67485e32i	−0.0628976	−	0.0483899i
$826$	−8.34364e32			−0.237731
$827$			7.62144e32i			0.214153i	0.994251	+	0.107076i	$0.0341489\pi$
$827$			7.62144e32i			0.214153i	−0.994251	+	0.107076i	$0.965851\pi$
$828$			4.56916e32i			0.126616i
$829$	−6.30600e33			−1.72336			−0.861681	−	0.507450i	$-0.830588\pi$
$829$	−6.30600e33			−1.72336			−0.861681	+	0.507450i	$0.830588\pi$
$830$	−1.40229e33	+	6.90429e32i	−0.377956	+	0.186089i
$831$	1.81673e33			0.482924
$832$		−	3.87336e32i		−	0.101548i
$833$		−	1.00483e33i		−	0.259820i
$834$	−2.02609e33			−0.516712
$835$	−1.37142e33	−	2.78542e33i	−0.344967	−	0.700643i
$836$	3.35047e32			0.0831254
$837$			4.19186e33i			1.02580i
$838$			2.14240e33i			0.517123i
$839$	5.93385e33			1.41278			0.706390	−	0.707823i	$-0.250323\pi$
$839$	5.93385e33			1.41278			0.706390	+	0.707823i	$0.250323\pi$
$840$	1.64339e33	+	3.33781e33i	0.385949	+	0.783880i
$841$	−4.15715e33			−0.963034
$842$		−	3.60170e33i		−	0.823035i
$843$			3.95897e33i			0.892411i
$844$	−7.74293e32			−0.172174
$845$	−3.91475e33	+	1.92746e33i	−0.858721	+	0.422798i
$846$	−3.69417e32			−0.0799389
$847$		−	3.91532e33i		−	0.835810i
$848$			7.66708e32i			0.161465i
$849$	2.29199e33			0.476184
$850$	1.52601e33	−	1.98351e33i	0.312780	−	0.406554i
$851$	7.19766e33			1.45546
$852$			2.80516e33i			0.559631i
$853$			4.82522e33i			0.949737i	0.880057	+	0.474869i	$0.157504\pi$
$853$			4.82522e33i			0.949737i	−0.880057	+	0.474869i	$0.842496\pi$
$854$	2.06716e33			0.401429
$855$	−1.28319e33	+	6.31786e32i	−0.245855	+	0.121049i
$856$	6.46757e33			1.22262
$857$		−	7.21886e33i		−	1.34645i	−0.739439	−	0.673224i	$-0.764909\pi$
$857$		−	7.21886e33i		−	1.34645i	0.739439	−	0.673224i	$-0.235091\pi$
$858$			5.17645e31i			0.00952639i
$859$	7.78226e31			0.0141314			0.00706569	−	0.999975i	$-0.497751\pi$
$859$	7.78226e31			0.0141314			0.00706569	+	0.999975i	$0.497751\pi$
$860$	−2.23790e33	−	4.54527e33i	−0.400966	−	0.814381i
$861$	7.05896e33			1.24797
$862$			2.64249e33i			0.460978i
$863$		−	3.55415e33i		−	0.611804i	−0.952063	−	0.305902i	$-0.901042\pi$
$863$		−	3.55415e33i		−	0.611804i	0.952063	−	0.305902i	$-0.0989580\pi$
$864$	−5.45571e33			−0.926709
$865$	2.46152e33	+	4.99947e33i	0.412590	+	0.837989i
$866$	5.18198e33			0.857117
$867$			1.43810e33i			0.234730i
$868$			3.92898e33i			0.632854i
$869$	−1.58729e32			−0.0252307
$870$	6.87233e32	−	3.38364e32i	0.107803	−	0.0530778i
$871$	−2.06195e33			−0.319205
$872$			1.45658e32i			0.0222532i
$873$		−	1.46084e33i		−	0.220262i
$874$	−7.85086e33			−1.16825
$875$	−5.61010e33	−	1.12702e33i	−0.823907	−	0.165516i
$876$	2.15080e32			0.0311747
$877$			5.12341e33i			0.732931i	0.930432	+	0.366466i	$0.119432\pi$
$877$			5.12341e33i			0.732931i	−0.930432	+	0.366466i	$0.880568\pi$
$878$			9.78344e32i			0.138135i
$879$	−7.14429e32			−0.0995605
$880$	4.99449e31	−	2.45907e31i	0.00686974	−	0.00338237i
$881$	−1.65535e33			−0.224734			−0.112367	−	0.993667i	$-0.535843\pi$
$881$	−1.65535e33			−0.224734			−0.112367	+	0.993667i	$0.535843\pi$
$882$		−	2.04871e32i		−	0.0274531i
$883$		−	1.26608e34i		−	1.67460i	−0.546742	−	0.837301i	$-0.684132\pi$
$883$		−	1.26608e34i		−	1.67460i	0.546742	−	0.837301i	$-0.315868\pi$
$884$	9.30403e32			0.121470
$885$	−1.80145e33	−	3.65883e33i	−0.232153	−	0.471514i
$886$	2.56453e33			0.326228
$887$			1.33275e34i			1.67350i	0.547586	+	0.836750i	$0.315547\pi$
$887$			1.33275e34i			1.67350i	−0.547586	+	0.836750i	$0.684453\pi$
$888$		−	1.03092e34i		−	1.27784i
$889$	−4.69255e33			−0.574168
$890$	−3.55751e33	−	7.22546e33i	−0.429695	−	0.872731i
$891$	7.01136e32			0.0836005
$892$		−	6.24685e33i		−	0.735301i
$893$			1.25215e34i			1.45500i
$894$	−1.54414e33			−0.177135
$895$	−2.53381e33	+	1.24754e33i	−0.286952	+	0.141283i
$896$	−5.56684e33			−0.622396
$897$			2.39277e33i			0.264112i
$898$			5.93911e33i			0.647207i
$899$	2.02798e33			0.218186
$900$	−6.13765e32	+	7.97777e32i	−0.0651949	+	0.0847408i
$901$	1.30960e34			1.37342
$902$			5.68526e32i			0.0588675i
$903$		−	1.21163e34i		−	1.23868i
$904$	−5.60929e33			−0.566202
$905$	−3.07999e33	+	1.51646e33i	−0.306966	+	0.151137i
$906$	−1.06344e34			−1.04650
$907$		−	5.73573e33i		−	0.557321i	−0.960390	−	0.278660i	$-0.910110\pi$
$907$		−	5.73573e33i		−	0.557321i	0.960390	−	0.278660i	$-0.0898904\pi$
$908$		−	3.92736e32i		−	0.0376803i
$909$	2.50641e33			0.237448
$910$	4.76355e32	+	9.67499e32i	0.0445610	+	0.0905054i
$911$	4.55477e32			0.0420731			0.0210366	−	0.999779i	$-0.493303\pi$
$911$	4.55477e32			0.0420731			0.0210366	+	0.999779i	$0.493303\pi$
$912$		−	2.08916e33i		−	0.190560i
$913$			5.93902e32i			0.0534935i
$914$	1.23045e34			1.09442
$915$	4.46314e33	+	9.06484e33i	0.392011	+	0.796192i
$916$	5.75703e32			0.0499345
$917$		−	6.95115e33i		−	0.595401i
$918$			5.48157e33i			0.463675i
$919$	−1.20040e33			−0.100276			−0.0501379	−	0.998742i	$-0.515966\pi$
$919$	−1.20040e33			−0.100276			−0.0501379	+	0.998742i	$0.515966\pi$
$920$	−1.24262e34	+	6.11815e33i	−1.02513	+	0.504731i
$921$	1.91751e34			1.56226
$922$			3.41026e33i			0.274398i
$923$			2.03839e33i			0.161982i
$924$	5.63893e32			0.0442556
$925$	1.25672e34	+	9.66848e33i	0.974108	+	0.749425i
$926$	−1.67955e33			−0.128578
$927$			2.25184e33i			0.170263i
$928$			2.63942e33i			0.197109i
$929$	2.02680e34			1.49496			0.747482	−	0.664282i	$-0.231263\pi$
$929$	2.02680e34			1.49496			0.747482	+	0.664282i	$0.231263\pi$
$930$	8.73392e33	−	4.30021e33i	0.636290	−	0.313282i
$931$	−6.94413e33			−0.499685
$932$			4.41583e33i			0.313855i
$933$		−	1.24236e34i		−	0.872182i
$934$	7.72825e33			0.535910
$935$	−4.20031e32	−	8.53103e32i	−0.0287705	−	0.0584343i
$936$	4.75555e32			0.0321758
$937$		−	2.00964e34i		−	1.34311i	−0.740953	−	0.671557i	$-0.765626\pi$
$937$		−	2.00964e34i		−	1.34311i	0.740953	−	0.671557i	$-0.234374\pi$
$938$		−	1.13864e34i		−	0.751714i
$939$	−2.80734e34			−1.83080
$940$	3.89240e33	+	7.90564e33i	0.250754	+	0.509292i
$941$	−2.37748e34			−1.51299			−0.756495	−	0.654000i	$-0.773090\pi$
$941$	−2.37748e34			−1.51299			−0.756495	+	0.654000i	$0.773090\pi$
$942$			1.57232e33i			0.0988449i
$943$			2.62796e34i			1.63206i
$944$	8.26589e32			0.0507121
$945$	1.12445e34	−	5.53633e33i	0.681515	−	0.335549i
$946$	9.75840e32			0.0584293
$947$			3.92535e33i			0.232196i	0.993238	+	0.116098i	$0.0370386\pi$
$947$			3.92535e33i			0.232196i	−0.993238	+	0.116098i	$0.962961\pi$
$948$			4.19198e33i			0.244976i
$949$	1.56289e32			0.00902335
$950$	−1.37076e34	−	1.05459e34i	−0.781882	−	0.601537i
$951$	−3.30122e34			−1.86037
$952$			1.28801e34i			0.717123i
$953$			1.27592e34i			0.701866i	0.936401	+	0.350933i	$0.114135\pi$
$953$			1.27592e34i			0.701866i	−0.936401	+	0.350933i	$0.885865\pi$
$954$	2.67011e33			0.145118
$955$	2.68689e34	−	1.32291e34i	1.44282	−	0.710382i
$956$	−5.20818e33			−0.276325
$957$		−	2.91058e32i		−	0.0152578i
$958$		−	8.13409e33i		−	0.421314i
$959$	−6.24294e33			−0.319503
$960$	4.61807e33	+	9.37952e33i	0.233530	+	0.474309i
$961$	5.75993e33			0.287805
$962$		−	2.98824e33i		−	0.147537i
$963$			4.18466e33i			0.204154i
$964$	2.18125e34			1.05152
$965$	−1.25742e34	−	2.55389e34i	−0.598987	−	1.21657i
$966$	−1.32132e34			−0.621972
$967$		−	2.84876e34i		−	1.32511i	−0.749015	−	0.662553i	$-0.769473\pi$
$967$		−	2.84876e34i		−	1.32511i	0.749015	−	0.662553i	$-0.230527\pi$
$968$		−	2.08776e34i		−	0.959652i
$969$	−3.56847e34			−1.62091
$970$	1.58477e34	−	7.80273e33i	0.711363	−	0.350245i
$971$	−1.28129e34			−0.568363			−0.284182	−	0.958770i	$-0.591722\pi$
$971$	−1.28129e34			−0.568363			−0.284182	+	0.958770i	$0.591722\pi$
$972$		−	4.83285e33i		−	0.211856i
$973$			1.60381e34i			0.694792i
$974$	8.65377e33			0.370491
$975$	−3.21416e33	+	4.17779e33i	−0.135992	+	0.176764i
$976$	−2.04790e33			−0.0856317
$977$			1.93721e34i			0.800552i	0.916395	+	0.400276i	$0.131086\pi$
$977$			1.93721e34i			0.800552i	−0.916395	+	0.400276i	$0.868914\pi$
$978$		−	5.38756e33i		−	0.220037i
$979$	−3.06014e33			−0.123521
$980$	−4.38429e33	+	2.15864e33i	−0.174904	+	0.0861152i
$981$	−9.42436e31			−0.00371585
$982$			1.10106e34i			0.429071i
$983$		−	1.33081e34i		−	0.512568i	−0.966601	−	0.256284i	$-0.917502\pi$
$983$		−	1.33081e34i		−	0.512568i	0.966601	−	0.256284i	$-0.0824983\pi$
$984$	3.76404e34			1.43288
$985$	8.27824e33	+	1.68135e34i	0.311474	+	0.632617i
$986$	2.65193e33			0.0986227
$987$			2.10740e34i			0.774639i
$988$		−	6.42981e33i		−	0.233611i
$989$	4.51074e34			1.61991
$990$	−8.56388e31	−	1.73936e32i	−0.00303994	−	0.00617427i
$991$	1.64929e34			0.578696			0.289348	−	0.957224i	$-0.406562\pi$
$991$	1.64929e34			0.578696			0.289348	+	0.957224i	$0.406562\pi$
$992$			3.35439e34i			1.16340i
$993$			1.39145e34i			0.477037i
$994$	−1.12562e34			−0.381461
$995$	−1.96112e34	+	9.65571e33i	−0.656959	+	0.323459i
$996$	1.56847e34			0.519392
$997$			3.35048e34i			1.09676i	0.836228	+	0.548382i	$0.184756\pi$
$997$			3.35048e34i			1.09676i	−0.836228	+	0.548382i	$0.815244\pi$
$998$			3.01332e34i			0.975089i
$999$	−3.47301e34			−1.11097

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.24.b.a.4.7	yes	10
3.2	odd	2		45.24.b.b.19.4		10
5.2	odd	4		25.24.a.f.1.4		10
5.3	odd	4		25.24.a.f.1.7		10
5.4	even	2	inner	5.24.b.a.4.4	✓	10
15.14	odd	2		45.24.b.b.19.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.24.b.a.4.4	✓	10	5.4	even	2	inner
5.24.b.a.4.7	yes	10	1.1	even	1	trivial
25.24.a.f.1.4		10	5.2	odd	4
25.24.a.f.1.7		10	5.3	odd	4
45.24.b.b.19.4		10	3.2	odd	2
45.24.b.b.19.7		10	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	5.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1679.85i q^{2} +330622. i q^{3} +5.56671e6 q^{4} +(-9.79539e7 + 4.82283e7i) q^{5} -5.55396e8 q^{6} +4.39640e9i q^{7} +2.34428e10i q^{8} -1.51680e10 q^{9} +O(q^{10})\)	\(q+1679.85i q^{2} +330622. i q^{3} +5.56671e6 q^{4} +(-9.79539e7 + 4.82283e7i) q^{5} -5.55396e8 q^{6} +4.39640e9i q^{7} +2.34428e10i q^{8} -1.51680e10 q^{9} +(-8.10163e10 - 1.64548e11i) q^{10} -6.96897e10 q^{11} +1.84048e12i q^{12} +1.33740e12i q^{13} -7.38529e12 q^{14} +(-1.59454e13 - 3.23858e13i) q^{15} +7.31647e12 q^{16} -1.24972e14i q^{17} -2.54800e13i q^{18} -8.63652e14 q^{19} +(-5.45281e14 + 2.68473e14i) q^{20} -1.45355e15 q^{21} -1.17068e14i q^{22} -5.41138e15i q^{23} -7.75073e15 q^{24} +(7.26899e15 - 9.44830e15i) q^{25} -2.24663e15 q^{26} +2.61110e16i q^{27} +2.44735e16i q^{28} +1.26322e16 q^{29} +(5.44032e16 - 2.67858e16i) q^{30} +1.60540e17 q^{31} +2.08943e17i q^{32} -2.30410e16i q^{33} +2.09934e17 q^{34} +(-2.12031e17 - 4.30644e17i) q^{35} -8.44361e16 q^{36} +1.33010e18i q^{37} -1.45081e18i q^{38} -4.42174e17 q^{39} +(-1.13061e18 - 2.29632e18i) q^{40} -4.85637e18 q^{41} -2.44174e18i q^{42} +8.33566e18i q^{43} -3.87942e17 q^{44} +(1.48577e18 - 7.31529e17i) q^{45} +9.09030e18 q^{46} -1.44983e19i q^{47} +2.41899e18i q^{48} +8.04043e18 q^{49} +(1.58717e19 + 1.22108e19i) q^{50} +4.13184e19 q^{51} +7.44491e18i q^{52} +1.04792e20i q^{53} -4.38625e19 q^{54} +(6.82637e18 - 3.36101e18i) q^{55} -1.03064e20 q^{56} -2.85543e20i q^{57} +2.12202e19i q^{58} +1.12976e20 q^{59} +(-8.87632e19 - 1.80282e20i) q^{60} -2.79902e20 q^{61} +2.69684e20i q^{62} -6.66848e19i q^{63} -2.89619e20 q^{64} +(-6.45005e19 - 1.31003e20i) q^{65} +3.87054e19 q^{66} +1.54176e21i q^{67} -6.95681e20i q^{68} +1.78912e21 q^{69} +(7.23418e20 - 3.56180e20i) q^{70} +1.52414e21 q^{71} -3.55582e20i q^{72} -1.16861e20i q^{73} -2.23437e21 q^{74} +(3.12382e21 + 2.40329e21i) q^{75} -4.80770e21 q^{76} -3.06383e20i q^{77} -7.42787e20i q^{78} +2.27765e21 q^{79} +(-7.16676e20 + 3.52861e20i) q^{80} -1.00608e22 q^{81} -8.15797e21i q^{82} -8.52210e21i q^{83} -8.09148e21 q^{84} +(6.02717e21 + 1.22415e22i) q^{85} -1.40027e22 q^{86} +4.17649e21i q^{87} -1.63372e21i q^{88} +4.39110e22 q^{89} +(1.22886e21 + 2.49587e21i) q^{90} -5.87974e21 q^{91} -3.01236e22i q^{92} +5.30783e22i q^{93} +2.43550e22 q^{94} +(8.45981e22 - 4.16525e22i) q^{95} -6.90814e22 q^{96} +9.63106e22i q^{97} +1.35067e22i q^{98} +1.05706e21 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 41272680 q^{4} + 124761750 q^{5} - 2262077880 q^{6} - 189250631370 q^{9}+O(q^{10}) \) 10 * q - 41272680 * q^4 + 124761750 * q^5 - 2262077880 * q^6 - 189250631370 * q^9	\( 10 q - 41272680 q^{4} + 124761750 q^{5} - 2262077880 q^{6} - 189250631370 q^{9} - 992748199000 q^{10} - 1448637536280 q^{11} + 20750531044440 q^{14} - 14566613457000 q^{15} + 307971806876960 q^{16} + 887626815301400 q^{19} - 23\!\cdots\!00 q^{20}+ \cdots + 41\!\cdots\!60 q^{99}+O(q^{100}) \) 10 * q - 41272680 * q^4 + 124761750 * q^5 - 2262077880 * q^6 - 189250631370 * q^9 - 992748199000 * q^10 - 1448637536280 * q^11 + 20750531044440 * q^14 - 14566613457000 * q^15 + 307971806876960 * q^16 + 887626815301400 * q^19 - 2363707755099000 * q^20 - 781158183715080 * q^21 + 58473619965621600 * q^24 - 15436708968968750 * q^25 - 49259739315596880 * q^26 + 68538893585329500 * q^29 - 283259561673249000 * q^30 - 303703652281842880 * q^31 - 288299835336191360 * q^34 + 568057466315481000 * q^35 + 3242003939215214760 * q^36 - 8628905972055907440 * q^39 + 9426000384456940000 * q^40 - 6658832954283527580 * q^41 + 14990828914855427040 * q^44 - 8490880963475889750 * q^45 + 16736621075351903320 * q^46 + 51294362631233173870 * q^49 - 96456356624588250000 * q^50 - 117334349391643270080 * q^51 + 6367892697021344400 * q^54 + 8046234911696751000 * q^55 - 93285217288146540000 * q^56 + 461218638014732785800 * q^59 + 1248088814097510276000 * q^60 + 202894074812420701820 * q^61 - 2597882075263561124480 * q^64 + 404224351485216078000 * q^65 - 2067527591150630859360 * q^66 + 1761142984477245282360 * q^69 + 2651929720118465517000 * q^70 - 6362428274364321596880 * q^71 + 21369976437605310645840 * q^74 - 1268180400269994750000 * q^75 - 28533821601830896716000 * q^76 + 8008906997916696975200 * q^79 + 50390556129429851388000 * q^80 - 63620987817532049079390 * q^81 + 26983560053969205971040 * q^84 + 58719411820058643416000 * q^85 - 73642932902287825779480 * q^86 + 17045340818835962686500 * q^89 + 218378490181286718303000 * q^90 - 261754857315780277067280 * q^91 + 163995755653951693894840 * q^94 + 287254967024630517105000 * q^95 - 1029134712278532215134080 * q^96 + 411070875879864759534360 * q^99

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