LMFDB - Embedded newform 3.43.b.b.2.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,43,Mod(2,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 43, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 43);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 43 $
Character orbit:	$[\chi]$	$=$	3.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:	$33.5183121516$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 33864221333 x^{10} + \cdots + 25\!\cdots\!00 $ x^12 + 33864221333x^10 + 431067677694832840128x^8 + 2571749156180178266268142478336x^6 + 7347696986799808047021630608244043939840x^4 + 8856020548466312086094523118699705898743155916800*x^2 + 2517175751433570113519145367463712046356978756810178560000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{73}\cdot 3^{104}\cdot 5^{6}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.12
Root			$104257. i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.43.b.b.2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.75326e6i q^{2} +(1.02269e10 + 2.19746e9i) q^{3} -9.68891e12 q^{4} -5.14242e14i q^{5} +(-8.24764e15 + 3.83843e16i) q^{6} +7.24611e17 q^{7} -1.98580e19i q^{8} +(9.97613e19 + 4.49466e19i) q^{9} +O(q^{10})$	\(q+3.75326e6i q^{2} +(1.02269e10 + 2.19746e9i) q^{3} -9.68891e12 q^{4} -5.14242e14i q^{5} +(-8.24764e15 + 3.83843e16i) q^{6} +7.24611e17 q^{7} -1.98580e19i q^{8} +(9.97613e19 + 4.49466e19i) q^{9} +1.93008e21 q^{10} +5.80883e21i q^{11} +(-9.90878e22 - 2.12910e22i) q^{12} -2.70188e23 q^{13} +2.71965e24i q^{14} +(1.13003e24 - 5.25912e24i) q^{15} +3.19198e25 q^{16} +9.64744e25i q^{17} +(-1.68696e26 + 3.74430e26i) q^{18} +4.61773e26 q^{19} +4.98245e27i q^{20} +(7.41055e27 + 1.59230e27i) q^{21} -2.18020e28 q^{22} +3.87491e28i q^{23} +(4.36371e28 - 2.03086e29i) q^{24} -3.70714e28 q^{25} -1.01409e30i q^{26} +(9.21484e29 + 6.78887e29i) q^{27} -7.02069e30 q^{28} +4.99222e30i q^{29} +(1.97388e31 + 4.24128e30i) q^{30} -6.62101e30 q^{31} +3.24671e31i q^{32} +(-1.27647e31 + 5.94065e31i) q^{33} -3.62093e32 q^{34} -3.72626e32i q^{35} +(-9.66578e32 - 4.35483e32i) q^{36} +1.25696e33 q^{37} +1.73315e33i q^{38} +(-2.76320e33 - 5.93727e32i) q^{39} -1.02118e34 q^{40} +6.68342e33i q^{41} +(-5.97633e33 + 2.78137e34i) q^{42} +1.15443e34 q^{43} -5.62812e34i q^{44} +(2.31134e34 - 5.13015e34i) q^{45} -1.45435e35 q^{46} -6.11246e34i q^{47} +(3.26442e35 + 7.01426e34i) q^{48} +2.13088e35 q^{49} -1.39139e35i q^{50} +(-2.11999e35 + 9.86637e35i) q^{51} +2.61783e36 q^{52} -1.29204e36i q^{53} +(-2.54804e36 + 3.45857e36i) q^{54} +2.98715e36 q^{55} -1.43893e37i q^{56} +(4.72252e36 + 1.01473e36i) q^{57} -1.87371e37 q^{58} -6.95742e36i q^{59} +(-1.09487e37 + 5.09551e37i) q^{60} -4.26930e37 q^{61} -2.48504e37i q^{62} +(7.22882e37 + 3.25688e37i) q^{63} +1.85273e37 q^{64} +1.38942e38i q^{65} +(-2.22968e38 - 4.79091e37i) q^{66} -1.36227e38 q^{67} -9.34731e38i q^{68} +(-8.51495e37 + 3.96284e38i) q^{69} +1.39856e39 q^{70} +7.56050e38i q^{71} +(8.92547e38 - 1.98106e39i) q^{72} +7.90940e38 q^{73} +4.71771e39i q^{74} +(-3.79127e38 - 8.14630e37i) q^{75} -4.47407e39 q^{76} +4.20914e39i q^{77} +(2.22841e39 - 1.03710e40i) q^{78} -1.56636e38 q^{79} -1.64145e40i q^{80} +(7.93213e39 + 8.96786e39i) q^{81} -2.50846e40 q^{82} +2.41146e40i q^{83} +(-7.18002e40 - 1.54277e40i) q^{84} +4.96112e40 q^{85} +4.33289e40i q^{86} +(-1.09702e40 + 5.10551e40i) q^{87} +1.15352e41 q^{88} -1.04630e41i q^{89} +(1.92548e41 + 8.67506e40i) q^{90} -1.95781e41 q^{91} -3.75436e41i q^{92} +(-6.77126e40 - 1.45494e40i) q^{93} +2.29417e41 q^{94} -2.37463e41i q^{95} +(-7.13453e40 + 3.32039e41i) q^{96} +3.83536e41 q^{97} +7.99776e41i q^{98} +(-2.61087e41 + 5.79497e41i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 16987205196 q^{3} - 34999503561888 q^{4} - 47\!\cdots\!88 q^{6}+ \cdots - 10\!\cdots\!60 q^{9}+O(q^{10}) $ 12 * q + 16987205196 * q^3 - 34999503561888 * q^4 - 47900661722006688 * q^6 - 41814621990917832 * q^7 - 10479496382139999060 * q^9	$ 12 q + 16987205196 q^{3} - 34999503561888 q^{4} - 47\!\cdots\!88 q^{6}+ \cdots - 45\!\cdots\!60 q^{99}+O(q^{100}) $ 12 * q + 16987205196 * q^3 - 34999503561888 * q^4 - 47900661722006688 * q^6 - 41814621990917832 * q^7 - 10479496382139999060 * q^9 - 1558337248111507093440 * q^10 + 49376377527162340879584 * q^12 + 104159867930333479443192 * q^13 - 448128019361693763840960 * q^15 + 30189980873605037368521216 * q^16 + 467763252053696004788775360 * q^18 + 1742192007122001281517876120 * q^19 + 9102775482298327940265250872 * q^21 - 4314702866032998614435578560 * q^22 + 213252820822149659960046027264 * q^24 - 1475565424466319180916113000660 * q^25 + 4679803843175845084152852300204 * q^27 - 12573192134196153529744555207488 * q^28 + 62452866934923176992747679887680 * q^30 - 82582711039551011868572590242696 * q^31 + 43265764437015443353441835054400 * q^33 - 263315485295738664634172504653056 * q^34 - 2405201397348598443590828900669856 * q^36 - 100843038556324004682477979351752 * q^37 - 10984759746962485956654149987757192 * q^39 + 14264689156939495925288444850785280 * q^40 - 2831182046378653470535212831685440 * q^42 - 71435403459183756447962146838987688 * q^43 + 171247471703495918987972144910848640 * q^45 - 368252835390302858087002506036095616 * q^46 + 393051873841281316858605019336751616 * q^48 + 503454865894447043110675471056528228 * q^49 - 26481340521925644924949289315966208 * q^51 + 6191863526932890484747245480405187008 * q^52 - 7762950205729260582930120693521404128 * q^54 + 7333373720922934220673629457367543680 * q^55 - 7646344343294849001862320271635263592 * q^57 - 40828097874719028971304350423217887040 * q^58 + 67409911106604936995672440638418037760 * q^60 - 86088392913854728749325031191744820616 * q^61 + 100834020234866427922563192954676937592 * q^63 - 141458640188438187587490744757105434624 * q^64 - 410927857618739095889759252898209949120 * q^66 + 637588020068292666249059312571603583128 * q^67 - 900977595682723671847728174824987261568 * q^69 + 1299257312773585175235999395827621799040 * q^70 - 1002862304292335428089280868557297904640 * q^72 + 4764698373378852277054437745609397085912 * q^73 + 10291654382848945060344626042064329363820 * q^75 - 10850719004897690517175553392098488304192 * q^76 - 1154864387471236146792590220220273542720 * q^78 - 16476824590026301016342599143867688625160 * q^79 - 29934898097734077284676557689524616295988 * q^81 + 12117774709574398821091222390193736370560 * q^82 - 115502524985324999123004799396029534507072 * q^84 + 179892388106464049414097141341403281134080 * q^85 - 108737363241821037303405571455850394882880 * q^87 + 262137413065538961600854476553505008040960 * q^88 - 246742532847586844558695609281104739341760 * q^90 + 85532425294904148246865639238250304747824 * q^91 + 153993445971229900791562733419639364858232 * q^93 + 711306705503600048406114202903471029729024 * q^94 - 1719405066055622809595776412409802129711104 * q^96 + 1090171163442244899022729083217627459542168 * q^97 - 4562402641239113129658705054315657608741760 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3\mathbb{Z}\right)^\times$.

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

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 $

$2$			3.75326e6i			1.78969i	0.446374	+	0.894847i	$0.352715\pi$
$2$			3.75326e6i			1.78969i	−0.446374	+	0.894847i	$0.647285\pi$
$3$	1.02269e10	+	2.19746e9i	0.977685	+	0.210075i
$3$	1.02269e10	+	2.19746e9i	0.977685	+	0.210075i
$4$	−9.68891e12			−2.20300
$5$		−	5.14242e14i		−	1.07844i	−0.842164	−	0.539222i	$-0.818718\pi$
$5$		−	5.14242e14i		−	1.07844i	0.842164	−	0.539222i	$-0.181282\pi$
$6$	−8.24764e15	+	3.83843e16i	−0.375970	+	1.74976i
$7$	7.24611e17			1.29732			0.648659	−	0.761079i	$-0.275330\pi$
$7$	7.24611e17			1.29732			0.648659	+	0.761079i	$0.275330\pi$
$8$		−	1.98580e19i		−	2.15301i
$9$	9.97613e19	+	4.49466e19i	0.911737	+	0.410775i
$10$	1.93008e21			1.93008
$11$			5.80883e21i			0.784950i	0.919763	+	0.392475i	$0.128381\pi$
$11$			5.80883e21i			0.784950i	−0.919763	+	0.392475i	$0.871619\pi$
$12$	−9.90878e22	−	2.12910e22i	−2.15384	−	0.462796i
$13$	−2.70188e23			−1.09359			−0.546797	−	0.837265i	$-0.684153\pi$
$13$	−2.70188e23			−1.09359			−0.546797	+	0.837265i	$0.684153\pi$
$14$			2.71965e24i			2.32180i
$15$	1.13003e24	−	5.25912e24i	0.226554	−	1.05438i
$16$	3.19198e25			1.65022
$17$			9.64744e25i			1.39632i	0.715942	+	0.698160i	$0.245997\pi$
$17$			9.64744e25i			1.39632i	−0.715942	+	0.698160i	$0.754003\pi$
$18$	−1.68696e26	+	3.74430e26i	−0.735161	+	1.63173i
$19$	4.61773e26			0.646551			0.323275	−	0.946305i	$-0.395216\pi$
$19$	4.61773e26			0.646551			0.323275	+	0.946305i	$0.395216\pi$
$20$			4.98245e27i			2.37582i
$21$	7.41055e27	+	1.59230e27i	1.26837	+	0.272534i
$22$	−2.18020e28			−1.40482
$23$			3.87491e28i			0.981695i	0.871245	+	0.490848i	$0.163313\pi$
$23$			3.87491e28i			0.981695i	−0.871245	+	0.490848i	$0.836687\pi$
$24$	4.36371e28	−	2.03086e29i	0.452293	−	2.10496i
$25$	−3.70714e28			−0.163042
$26$		−	1.01409e30i		−	1.95720i
$27$	9.21484e29	+	6.78887e29i	0.805098	+	0.593142i
$28$	−7.02069e30			−2.85799
$29$			4.99222e30i			0.972604i	0.873791	+	0.486302i	$0.161654\pi$
$29$			4.99222e30i			0.972604i	−0.873791	+	0.486302i	$0.838346\pi$
$30$	1.97388e31	+	4.24128e30i	1.88702	+	0.405463i
$31$	−6.62101e30			−0.317928			−0.158964	−	0.987284i	$-0.550815\pi$
$31$	−6.62101e30			−0.317928			−0.158964	+	0.987284i	$0.550815\pi$
$32$			3.24671e31i			0.800377i
$33$	−1.27647e31	+	5.94065e31i	−0.164899	+	0.767435i
$34$	−3.62093e32			−2.49898
$35$		−	3.72626e32i		−	1.39908i
$36$	−9.66578e32	−	4.35483e32i	−2.00856	−	0.904938i
$37$	1.25696e33			1.46922			0.734609	−	0.678491i	$-0.237366\pi$
$37$	1.25696e33			1.46922			0.734609	+	0.678491i	$0.237366\pi$
$38$			1.73315e33i			1.15713i
$39$	−2.76320e33	−	5.93727e32i	−1.06919	−	0.229737i
$40$	−1.02118e34			−2.32190
$41$			6.68342e33i			0.904769i	0.891823	+	0.452385i	$0.149427\pi$
$41$			6.68342e33i			0.904769i	−0.891823	+	0.452385i	$0.850573\pi$
$42$	−5.97633e33	+	2.78137e34i	−0.487753	+	2.26999i
$43$	1.15443e34			0.574820			0.287410	−	0.957808i	$-0.407206\pi$
$43$	1.15443e34			0.574820			0.287410	+	0.957808i	$0.407206\pi$
$44$		−	5.62812e34i		−	1.72925i
$45$	2.31134e34	−	5.13015e34i	0.442998	−	0.983257i
$46$	−1.45435e35			−1.75693
$47$		−	6.11246e34i		−	0.470069i	−0.971987	−	0.235034i	$-0.924480\pi$
$47$		−	6.11246e34i		−	0.470069i	0.971987	−	0.235034i	$-0.0755203\pi$
$48$	3.26442e35	+	7.01426e34i	1.61339	+	0.346670i
$49$	2.13088e35			0.683033
$50$		−	1.39139e35i		−	0.291795i
$51$	−2.11999e35	+	9.86637e35i	−0.293332	+	1.36516i
$52$	2.61783e36			2.40919
$53$		−	1.29204e36i		−	0.797043i	−0.917159	−	0.398522i	$-0.869523\pi$
$53$		−	1.29204e36i		−	0.797043i	0.917159	−	0.398522i	$-0.130477\pi$
$54$	−2.54804e36	+	3.45857e36i	−1.06154	+	1.44088i
$55$	2.98715e36			0.846525
$56$		−	1.43893e37i		−	2.79313i
$57$	4.72252e36	+	1.01473e36i	0.632123	+	0.135824i
$58$	−1.87371e37			−1.74066
$59$		−	6.95742e36i		−	0.451394i	−0.974198	−	0.225697i	$-0.927534\pi$
$59$		−	6.95742e36i		−	0.451394i	0.974198	−	0.225697i	$-0.0724660\pi$
$60$	−1.09487e37	+	5.09551e37i	−0.499100	+	2.32280i
$61$	−4.26930e37			−1.37540			−0.687701	−	0.725994i	$-0.741380\pi$
$61$	−4.26930e37			−1.37540			−0.687701	+	0.725994i	$0.741380\pi$
$62$		−	2.48504e37i		−	0.568994i
$63$	7.22882e37	+	3.25688e37i	1.18281	+	0.532905i
$64$	1.85273e37			0.217788
$65$			1.38942e38i			1.17938i
$66$	−2.22968e38	−	4.79091e37i	−1.37347	−	0.295118i
$67$	−1.36227e38			−0.611917			−0.305959	−	0.952045i	$-0.598977\pi$
$67$	−1.36227e38			−0.611917			−0.305959	+	0.952045i	$0.598977\pi$
$68$		−	9.34731e38i		−	3.07609i
$69$	−8.51495e37	+	3.96284e38i	−0.206230	+	0.959789i
$70$	1.39856e39			2.50393
$71$			7.56050e38i			1.00491i	0.864605	+	0.502453i	$0.167569\pi$
$71$			7.56050e38i			1.00491i	−0.864605	+	0.502453i	$0.832431\pi$
$72$	8.92547e38	−	1.98106e39i	0.884400	−	1.96297i
$73$	7.90940e38			0.586629			0.293314	−	0.956016i	$-0.405242\pi$
$73$	7.90940e38			0.586629			0.293314	+	0.956016i	$0.405242\pi$
$74$			4.71771e39i			2.62945i
$75$	−3.79127e38	−	8.14630e37i	−0.159404	−	0.0342510i
$76$	−4.47407e39			−1.42435
$77$			4.20914e39i			1.01833i
$78$	2.22841e39	−	1.03710e40i	0.411158	−	1.91352i
$79$	−1.56636e38			−0.0221168			−0.0110584	−	0.999939i	$-0.503520\pi$
$79$	−1.56636e38			−0.0221168			−0.0110584	+	0.999939i	$0.503520\pi$
$80$		−	1.64145e40i		−	1.77967i
$81$	7.93213e39	+	8.96786e39i	0.662528	+	0.749037i
$82$	−2.50846e40			−1.61926
$83$			2.41146e40i			1.20681i	0.797433	+	0.603407i	$0.206191\pi$
$83$			2.41146e40i			1.20681i	−0.797433	+	0.603407i	$0.793809\pi$
$84$	−7.18002e40	−	1.54277e40i	−2.79422	−	0.600393i
$85$	4.96112e40			1.50585
$86$			4.33289e40i			1.02875i
$87$	−1.09702e40	+	5.10551e40i	−0.204320	+	0.950901i
$88$	1.15352e41			1.69000
$89$		−	1.04630e41i		−	1.20912i	−0.796561	−	0.604558i	$-0.793350\pi$
$89$		−	1.04630e41i		−	1.20912i	0.796561	−	0.604558i	$-0.206650\pi$
$90$	1.92548e41	+	8.67506e40i	1.75973	+	0.792830i
$91$	−1.95781e41			−1.41874
$92$		−	3.75436e41i		−	2.16268i
$93$	−6.77126e40	−	1.45494e40i	−0.310834	−	0.0667888i
$94$	2.29417e41			0.841279
$95$		−	2.37463e41i		−	0.697269i
$96$	−7.13453e40	+	3.32039e41i	−0.168139	+	0.782517i
$97$	3.83536e41			0.727109			0.363554	−	0.931573i	$-0.381563\pi$
$97$	3.83536e41			0.727109			0.363554	+	0.931573i	$0.381563\pi$
$98$			7.99776e41i			1.22242i
$99$	−2.61087e41	+	5.79497e41i	−0.322438	+	0.715668i
$100$	3.59181e41			0.359181
$101$		−	6.85959e41i		−	0.556608i	−0.960493	−	0.278304i	$-0.910228\pi$
$101$		−	6.85959e41i		−	0.556608i	0.960493	−	0.278304i	$-0.0897723\pi$
$102$	−3.70310e42	−	7.95686e41i	−2.44322	−	0.524974i
$103$	−5.84455e41			−0.314174			−0.157087	−	0.987585i	$-0.550210\pi$
$103$	−5.84455e41			−0.314174			−0.157087	+	0.987585i	$0.550210\pi$
$104$			5.36539e42i			2.35451i
$105$	8.18830e41	−	3.81082e42i	0.293913	−	1.36786i
$106$	4.84935e42			1.42646
$107$		−	6.02787e42i		−	1.45581i	−0.685678	−	0.727905i	$-0.740494\pi$
$107$		−	6.02787e42i		−	1.45581i	0.685678	−	0.727905i	$-0.259506\pi$
$108$	−8.92817e42	−	6.57767e42i	−1.77363	−	1.30669i
$109$	−6.41559e42			−1.05022			−0.525110	−	0.851034i	$-0.675976\pi$
$109$	−6.41559e42			−1.05022			−0.525110	+	0.851034i	$0.675976\pi$
$110$			1.12115e43i			1.51502i
$111$	1.28549e43	+	2.76212e42i	1.43643	+	0.308646i
$112$	2.31295e43			2.14086
$113$			9.33215e42i			0.716695i	0.933588	+	0.358347i	$0.116660\pi$
$113$			9.33215e42i			0.716695i	−0.933588	+	0.358347i	$0.883340\pi$
$114$	−3.80853e42	+	1.77248e43i	−0.243084	+	1.13131i
$115$	1.99264e43			1.05870
$116$		−	4.83692e43i		−	2.14265i
$117$	−2.69543e43	−	1.21440e43i	−0.997069	−	0.449220i
$118$	2.61130e43			0.807857
$119$			6.99065e43i			1.81147i
$120$	−1.04435e44	−	2.24400e43i	−2.27008	−	0.487773i
$121$	2.10212e43			0.383853
$122$		−	1.60238e44i		−	2.46155i
$123$	−1.46866e43	+	6.83509e43i	−0.190070	+	0.884580i
$124$	6.41504e43			0.700396
$125$		−	9.78615e43i		−	0.902613i
$126$	−1.22239e44	+	2.71316e44i	−0.953737	+	2.11687i
$127$	1.66541e43			0.110064			0.0550318	−	0.998485i	$-0.482474\pi$
$127$	1.66541e43			0.110064			0.0550318	+	0.998485i	$0.482474\pi$
$128$			2.12330e44i			1.19015i
$129$	1.18063e44	+	2.53682e43i	0.561993	+	0.120755i
$130$	−5.21486e44			−2.11073
$131$			3.25643e44i			1.12213i	0.827770	+	0.561067i	$0.189609\pi$
$131$			3.25643e44i			1.12213i	−0.827770	+	0.561067i	$0.810391\pi$
$132$	1.23676e44	−	5.75584e44i	0.363272	−	1.69066i
$133$	3.34606e44			0.838782
$134$		−	5.11296e44i		−	1.09514i
$135$	3.49112e44	−	4.73866e44i	0.639670	−	0.868253i
$136$	1.91579e45			3.00628
$137$		−	4.99119e44i		−	0.671541i	−0.941944	−	0.335770i	$-0.891003\pi$
$137$		−	4.99119e44i		−	0.671541i	0.941944	−	0.335770i	$-0.108997\pi$
$138$	−1.48736e45	−	3.19588e44i	−1.71773	−	0.369088i
$139$	−2.62476e44			−0.260483			−0.130241	−	0.991482i	$-0.541575\pi$
$139$	−2.62476e44			−0.260483			−0.130241	+	0.991482i	$0.541575\pi$
$140$			3.61034e45i			3.08219i
$141$	1.34319e44	−	6.25118e44i	0.0987497	−	0.459579i
$142$	−2.83765e45			−1.79847
$143$		−	1.56948e45i		−	0.858416i
$144$	3.18437e45	+	1.43469e45i	1.50456	+	0.677867i
$145$	2.56721e45			1.04890
$146$			2.96860e45i			1.04989i
$147$	2.17924e45	+	4.68253e44i	0.667792	+	0.143488i
$148$	−1.21786e46			−3.23669
$149$		−	7.13567e45i		−	1.64635i	−0.567785	−	0.823177i	$-0.692199\pi$
$149$		−	7.13567e45i		−	1.64635i	0.567785	−	0.823177i	$-0.307801\pi$
$150$	3.05752e44	−	1.42296e45i	0.0612988	−	0.285284i
$151$	−7.92644e43			−0.0138217			−0.00691086	−	0.999976i	$-0.502200\pi$
$151$	−7.92644e43			−0.0138217			−0.00691086	+	0.999976i	$0.502200\pi$
$152$		−	9.16987e45i		−	1.39203i
$153$	−4.33619e45	+	9.62441e45i	−0.573573	+	1.27308i
$154$	−1.57980e46			−1.82250
$155$			3.40480e45i			0.342868i
$156$	2.67723e46	+	5.75257e45i	2.35543	+	0.506111i
$157$	2.05387e46			1.58009			0.790044	−	0.613051i	$-0.210058\pi$
$157$	2.05387e46			1.58009			0.790044	+	0.613051i	$0.210058\pi$
$158$		−	5.87895e44i		−	0.0395823i
$159$	2.83920e45	−	1.32136e46i	0.167439	−	0.779257i
$160$	1.66960e46			0.863162
$161$			2.80780e46i			1.27357i
$162$	−3.36587e46	+	2.97713e46i	−1.34055	+	1.18572i
$163$	2.41150e46			0.844011			0.422006	−	0.906593i	$-0.361326\pi$
$163$	2.41150e46			0.844011			0.422006	+	0.906593i	$0.361326\pi$
$164$		−	6.47551e46i		−	1.99321i
$165$	3.05493e46	+	6.56413e45i	0.827635	+	0.177834i
$166$	−9.05084e46			−2.15983
$167$		−	1.27577e46i		−	0.268366i	−0.990957	−	0.134183i	$-0.957159\pi$
$167$		−	1.27577e46i		−	0.268366i	0.990957	−	0.134183i	$-0.0428409\pi$
$168$	3.16199e46	−	1.47159e47i	0.586768	−	2.73080i
$169$	1.19607e46			0.195946
$170$			1.86204e47i			2.69501i
$171$	4.60670e46	+	2.07551e46i	0.589484	+	0.265587i
$172$	−1.11852e47			−1.26633
$173$		−	8.07502e44i		−	0.00809423i	−0.999992	−	0.00404711i	$-0.998712\pi$
$173$		−	8.07502e44i		−	0.00809423i	0.999992	−	0.00404711i	$-0.00128824\pi$
$174$	−1.91623e47	−	4.11740e46i	−1.70182	−	0.365670i
$175$	−2.68624e46			−0.211517
$176$			1.85417e47i			1.29534i
$177$	1.52887e46	−	7.11531e46i	0.0948267	−	0.441322i
$178$	3.92705e47			2.16395
$179$			6.10839e45i			0.0299236i	0.999888	+	0.0149618i	$0.00476266\pi$
$179$			6.10839e45i			0.0299236i	−0.999888	+	0.0149618i	$0.995237\pi$
$180$	−2.23944e47	+	4.97055e47i	−0.975925	+	2.16612i
$181$	1.05779e47			0.410346			0.205173	−	0.978726i	$-0.434224\pi$
$181$	1.05779e47			0.410346			0.205173	+	0.978726i	$0.434224\pi$
$182$		−	7.34818e47i		−	2.53911i
$183$	−4.36618e47	−	9.38161e46i	−1.34471	−	0.288938i
$184$	7.69478e47			2.11360
$185$		−	6.46383e47i		−	1.58447i
$186$	5.46077e46	−	2.54143e47i	0.119531	−	0.556297i
$187$	−5.60403e47			−1.09604
$188$			5.92231e47i			1.03556i
$189$	6.67718e47	+	4.91929e47i	1.04447	+	0.769493i
$190$	8.91260e47			1.24790
$191$		−	6.70025e46i		−	0.0840215i	−0.999117	−	0.0420107i	$-0.986624\pi$
$191$		−	6.70025e46i		−	0.0840215i	0.999117	−	0.0420107i	$-0.0133764\pi$
$192$	1.89478e47	+	4.07130e46i	0.212928	+	0.0457517i
$193$	−2.34629e47			−0.236416			−0.118208	−	0.992989i	$-0.537715\pi$
$193$	−2.34629e47			−0.236416			−0.118208	+	0.992989i	$0.537715\pi$
$194$			1.43951e48i			1.30130i
$195$	−3.05320e47	+	1.42095e48i	−0.247758	+	1.15306i
$196$	−2.06459e48			−1.50472
$197$		−	2.09534e48i		−	1.37235i	−0.727439	−	0.686173i	$-0.759289\pi$
$197$		−	2.09534e48i		−	1.37235i	0.727439	−	0.686173i	$-0.240711\pi$
$198$	−2.17500e48	−	9.79927e47i	−1.28083	−	0.577065i
$199$	−6.04782e47			−0.320394			−0.160197	−	0.987085i	$-0.551213\pi$
$199$	−6.04782e47			−0.320394			−0.160197	+	0.987085i	$0.551213\pi$
$200$			7.36163e47i			0.351030i
$201$	−1.39319e48	−	2.99354e47i	−0.598263	−	0.128549i
$202$	2.57458e48			0.996158
$203$			3.61742e48i			1.26178i
$204$	2.05403e48	−	9.55944e48i	0.646211	−	3.00745i
$205$	3.43690e48			0.975743
$206$		−	2.19361e48i		−	0.562274i
$207$	−1.74164e48	+	3.86566e48i	−0.403256	+	0.895048i
$208$	−8.62436e48			−1.80467
$209$			2.68236e48i			0.507510i
$210$	1.43030e49	+	3.07328e48i	2.44806	+	0.526014i
$211$	−1.12281e49			−1.73930			−0.869652	−	0.493665i	$-0.835657\pi$
$211$	−1.12281e49			−1.73930			−0.869652	+	0.493665i	$0.835657\pi$
$212$			1.25184e49i			1.75589i
$213$	−1.66139e48	+	7.73208e48i	−0.211106	+	0.982482i
$214$	2.26242e49			2.60545
$215$		−	5.93659e48i		−	0.619911i
$216$	1.34813e49	−	1.82988e49i	1.27704	−	1.73338i
$217$	−4.79766e48			−0.412454
$218$		−	2.40794e49i		−	1.87957i
$219$	8.08889e48	+	1.73806e48i	0.573538	+	0.123236i
$220$	−2.89422e49			−1.86490
$221$		−	2.60662e49i		−	1.52701i
$222$	−1.03670e49	+	4.82477e49i	−0.552382	+	2.57077i
$223$	−1.04880e49			−0.508500			−0.254250	−	0.967139i	$-0.581829\pi$
$223$	−1.04880e49			−0.508500			−0.254250	+	0.967139i	$0.581829\pi$
$224$			2.35261e49i			1.03834i
$225$	−3.69829e48	−	1.66623e48i	−0.148651	−	0.0669735i
$226$	−3.50260e49			−1.28266
$227$		−	4.72205e49i		−	1.57611i	−0.615602	−	0.788057i	$-0.711087\pi$
$227$		−	4.72205e49i		−	1.57611i	0.615602	−	0.788057i	$-0.288913\pi$
$228$	−4.57560e49	−	9.83159e48i	−1.39257	−	0.299221i
$229$	5.59139e49			1.55230			0.776148	−	0.630550i	$-0.217171\pi$
$229$	5.59139e49			1.55230			0.776148	+	0.630550i	$0.217171\pi$
$230$			7.47890e49i			1.89475i
$231$	−9.24943e48	+	4.30466e49i	−0.213926	+	0.995606i
$232$	9.91354e49			2.09402
$233$			3.55371e49i			0.685817i	0.939369	+	0.342908i	$0.111412\pi$
$233$			3.55371e49i			0.685817i	−0.939369	+	0.342908i	$0.888588\pi$
$234$	4.55797e49	−	1.01167e50i	0.803967	−	1.78445i
$235$	−3.14329e49			−0.506943
$236$			6.74098e49i			0.994423i
$237$	−1.60190e48	−	3.44201e47i	−0.0216233	−	0.00464619i
$238$	−2.62377e50			−3.24198
$239$		−	1.54845e50i		−	1.75203i	−0.482283	−	0.876015i	$-0.660192\pi$
$239$		−	1.54845e50i		−	1.75203i	0.482283	−	0.876015i	$-0.339808\pi$
$240$	3.60703e49	−	1.67870e50i	0.373864	−	1.73995i
$241$	1.92291e50			1.82642			0.913210	−	0.407488i	$-0.133595\pi$
$241$	1.92291e50			1.82642			0.913210	+	0.407488i	$0.133595\pi$
$242$			7.88980e49i			0.686979i
$243$	6.14149e49	+	1.09144e50i	0.490390	+	0.871503i
$244$	4.13648e50			3.03001
$245$		−	1.09579e50i		−	0.736613i
$246$	−2.56539e50	−	5.51224e49i	−1.58313	−	0.340166i
$247$	−1.24765e50			−0.707063
$248$			1.31480e50i			0.684501i
$249$	−5.29909e49	+	2.46619e50i	−0.253522	+	1.17988i
$250$	3.67299e50			1.61540
$251$			4.15830e50i			1.68177i	0.541212	+	0.840886i	$0.317966\pi$
$251$			4.15830e50i			1.68177i	−0.541212	+	0.840886i	$0.682034\pi$
$252$	−7.00394e50	−	3.15556e50i	−2.60574	−	1.17399i
$253$	−2.25087e50			−0.770582
$254$			6.25073e49i			0.196980i
$255$	5.07371e50	+	1.09019e50i	1.47225	+	0.316342i
$256$	−7.15445e50			−1.91222
$257$		−	5.11943e50i		−	1.26074i	−0.776294	−	0.630371i	$-0.782903\pi$
$257$		−	5.11943e50i		−	1.26074i	0.776294	−	0.630371i	$-0.217097\pi$
$258$	−9.52136e49	+	4.43122e50i	−0.216115	+	1.00579i
$259$	9.10810e50			1.90604
$260$		−	1.34620e51i		−	2.59817i
$261$	−2.24383e50	+	4.98031e50i	−0.399521	+	0.886759i
$262$	−1.22222e51			−2.00828
$263$		−	5.17583e50i		−	0.785071i	−0.919737	−	0.392536i	$-0.871598\pi$
$263$		−	5.17583e50i		−	0.785071i	0.919737	−	0.392536i	$-0.128402\pi$
$264$	1.17969e51	+	2.53480e50i	1.65229	+	0.355027i
$265$	−6.64420e50			−0.859566
$266$			1.25586e51i			1.50116i
$267$	2.29921e50	−	1.07005e51i	0.254005	−	1.18213i
$268$	1.31989e51			1.34806
$269$		−	4.39733e50i		−	0.415328i	−0.978200	−	0.207664i	$-0.933414\pi$
$269$		−	4.39733e50i		−	0.415328i	0.978200	−	0.207664i	$-0.0665861\pi$
$270$	1.77854e51	+	1.31031e51i	1.55391	+	1.14481i
$271$	−4.50806e50			−0.364447			−0.182224	−	0.983257i	$-0.558330\pi$
$271$	−4.50806e50			−0.364447			−0.182224	+	0.983257i	$0.558330\pi$
$272$			3.07945e51i			2.30423i
$273$	−2.00224e51	−	4.30222e50i	−1.38708	−	0.298042i
$274$	1.87332e51			1.20185
$275$		−	2.15342e50i		−	0.127980i
$276$	8.25006e50	−	3.83956e51i	0.454325	−	2.11442i
$277$	1.80963e51			0.923667			0.461834	−	0.886967i	$-0.347192\pi$
$277$	1.80963e51			0.923667			0.461834	+	0.886967i	$0.347192\pi$
$278$		−	9.85140e50i		−	0.466184i
$279$	−6.60521e50	−	2.97592e50i	−0.289867	−	0.130597i
$280$	−7.39959e51			−3.01224
$281$			2.73994e51i			1.03492i	0.855706	+	0.517462i	$0.173123\pi$
$281$			2.73994e51i			1.03492i	−0.855706	+	0.517462i	$0.826877\pi$
$282$	2.34623e51	+	5.04134e50i	0.822506	+	0.176732i
$283$	−3.95811e51			−1.28817			−0.644084	−	0.764955i	$-0.722761\pi$
$283$	−3.95811e51			−1.28817			−0.644084	+	0.764955i	$0.722761\pi$
$284$		−	7.32530e51i		−	2.21381i
$285$	5.21815e50	−	2.42852e51i	0.146479	−	0.681709i
$286$	5.89065e51			1.53630
$287$			4.84288e51i			1.17377i
$288$	−1.45929e51	+	3.23897e51i	−0.328775	+	0.729733i
$289$	−4.53361e51			−0.949707
$290$			9.63541e51i			1.87721i
$291$	3.92239e51	+	8.42804e50i	0.710883	+	0.152747i
$292$	−7.66334e51			−1.29234
$293$			2.96723e51i			0.465726i	0.972510	+	0.232863i	$0.0748094\pi$
$293$			2.96723e51i			0.465726i	−0.972510	+	0.232863i	$0.925191\pi$
$294$	−1.75747e51	+	8.17925e51i	−0.256800	+	1.19514i
$295$	−3.57780e51			−0.486804
$296$		−	2.49607e52i		−	3.16323i
$297$	−3.94354e51	+	5.35274e51i	−0.465587	+	0.631962i
$298$	2.67820e52			2.94647
$299$		−	1.04695e52i		−	1.07358i
$300$	3.67333e51	+	7.89287e50i	0.351166	+	0.0754551i
$301$	8.36516e51			0.745724
$302$		−	2.97500e50i		−	0.0247367i
$303$	1.50737e51	−	7.01526e51i	0.116930	−	0.544188i
$304$	1.47397e52			1.06695
$305$			2.19545e52i			1.48329i
$306$	−3.61229e52	−	1.62748e52i	−2.27842	−	1.02652i
$307$	8.53677e51			0.502791			0.251395	−	0.967884i	$-0.419111\pi$
$307$	8.53677e51			0.502791			0.251395	+	0.967884i	$0.419111\pi$
$308$		−	4.07820e52i		−	2.24338i
$309$	−5.97719e51	−	1.28432e51i	−0.307163	−	0.0660000i
$310$	−1.27791e52			−0.613628
$311$			3.00572e52i			1.34890i	0.738320	+	0.674450i	$0.235619\pi$
$311$			3.00572e52i			1.34890i	−0.738320	+	0.674450i	$0.764381\pi$
$312$	−1.17902e52	+	5.48714e52i	−0.494624	+	2.30197i
$313$	5.27239e51			0.206812			0.103406	−	0.994639i	$-0.467026\pi$
$313$	5.27239e51			0.206812			0.103406	+	0.994639i	$0.467026\pi$
$314$			7.70872e52i			2.82787i
$315$	1.67482e52	−	3.71736e52i	0.574709	−	1.27560i
$316$	1.51763e51			0.0487233
$317$		−	5.15943e52i		−	1.55009i	−0.631906	−	0.775045i	$-0.717727\pi$
$317$		−	5.15943e52i		−	1.55009i	0.631906	−	0.775045i	$-0.282273\pi$
$318$	4.95940e52	+	1.06563e52i	1.39463	+	0.299664i
$319$	−2.89990e52			−0.763446
$320$		−	9.52753e51i		−	0.234872i
$321$	1.32460e52	−	6.16467e52i	0.305830	−	1.42332i
$322$	−1.05384e53			−2.27930
$323$			4.45492e52i			0.902791i
$324$	−7.68537e52	−	8.68887e52i	−1.45955	−	1.65013i
$325$	1.00163e52			0.178301
$326$			9.05100e52i			1.51052i
$327$	−6.56118e52	−	1.40980e52i	−1.02678	−	0.220625i
$328$	1.32719e53			1.94797
$329$		−	4.42916e52i		−	0.609828i
$330$	−2.46369e52	+	1.14660e53i	−0.318268	+	1.48121i
$331$	7.26343e52			0.880550			0.440275	−	0.897863i	$-0.354881\pi$
$331$	7.26343e52			0.880550			0.440275	+	0.897863i	$0.354881\pi$
$332$		−	2.33644e53i		−	2.65861i
$333$	1.25396e53	+	5.64961e52i	1.33954	+	0.603517i
$334$	4.78830e52			0.480292
$335$			7.00537e52i			0.659919i
$336$	2.36544e53	+	5.08261e52i	2.09308	+	0.449741i
$337$	9.67459e52			0.804275			0.402137	−	0.915579i	$-0.368267\pi$
$337$	9.67459e52			0.804275			0.402137	+	0.915579i	$0.368267\pi$
$338$			4.48917e52i			0.350683i
$339$	−2.05070e52	+	9.54392e52i	−0.150560	+	0.700702i
$340$	−4.80678e53			−3.31740
$341$		−	3.84603e52i		−	0.249558i
$342$	−7.78992e52	+	1.72902e53i	−0.475319	+	1.05500i
$343$	−7.16533e52			−0.411206
$344$		−	2.29247e53i		−	1.23759i
$345$	2.03786e53	+	4.37875e52i	1.03508	+	0.222407i
$346$	3.03076e51			0.0144862
$347$			5.77439e52i			0.259769i	0.991529	+	0.129884i	$0.0414606\pi$
$347$			5.77439e52i			0.259769i	−0.991529	+	0.129884i	$0.958539\pi$
$348$	1.06289e53	−	4.94668e53i	0.450117	−	2.09484i
$349$	−2.86857e53			−1.14375			−0.571875	−	0.820341i	$-0.693784\pi$
$349$	−2.86857e53			−1.14375			−0.571875	+	0.820341i	$0.693784\pi$
$350$		−	1.00821e53i		−	0.378551i
$351$	−2.48974e53	−	1.83427e53i	−0.880450	−	0.648656i
$352$	−1.88596e53			−0.628256
$353$		−	7.09859e52i		−	0.222794i	−0.993776	−	0.111397i	$-0.964467\pi$
$353$		−	7.09859e52i		−	0.222794i	0.993776	−	0.111397i	$-0.0355325\pi$
$354$	2.67056e53	+	5.73823e52i	0.789830	+	0.169711i
$355$	3.88793e53			1.08373
$356$			1.01375e54i			2.66368i
$357$	−1.53617e53	+	7.14929e53i	−0.380545	+	1.77105i
$358$	−2.29264e52			−0.0535540
$359$		−	1.69674e53i		−	0.373793i	−0.982380	−	0.186896i	$-0.940157\pi$
$359$		−	1.69674e53i		−	0.373793i	0.982380	−	0.186896i	$-0.0598429\pi$
$360$	−1.01874e54	−	4.58985e53i	−2.11696	−	0.953776i
$361$	−2.96861e53			−0.581972
$362$			3.97017e53i			0.734393i
$363$	2.14982e53	+	4.61932e52i	0.375287	+	0.0806379i
$364$	1.89691e54			3.12548
$365$		−	4.06735e53i		−	0.632646i
$366$	3.52116e53	−	1.63874e54i	0.517110	−	2.40662i
$367$	−7.62830e53			−1.05789			−0.528945	−	0.848656i	$-0.677412\pi$
$367$	−7.62830e53			−1.05789			−0.528945	+	0.848656i	$0.677412\pi$
$368$			1.23686e54i			1.62001i
$369$	−3.00397e53	+	6.66747e53i	−0.371656	+	0.824912i
$370$	2.42604e54			2.83571
$371$		−	9.36225e53i		−	1.03402i
$372$	6.56061e53	+	1.40968e53i	0.684767	+	0.147136i
$373$	−1.96577e54			−1.93931			−0.969656	−	0.244473i	$-0.921385\pi$
$373$	−1.96577e54			−1.93931			−0.969656	+	0.244473i	$0.921385\pi$
$374$		−	2.10334e54i		−	1.96158i
$375$	2.15047e53	−	1.00082e54i	0.189616	−	0.882471i
$376$	−1.21381e54			−1.01206
$377$		−	1.34884e54i		−	1.06363i
$378$	−1.84634e54	+	2.50612e54i	−1.37716	+	1.86928i
$379$	1.43891e54			1.01534			0.507670	−	0.861552i	$-0.330507\pi$
$379$	1.43891e54			1.01534			0.507670	+	0.861552i	$0.330507\pi$
$380$			2.30076e54i			1.53608i
$381$	1.70321e53	+	3.65968e52i	0.107608	+	0.0231216i
$382$	2.51478e53			0.150373
$383$			1.88455e54i			1.06668i	0.845901	+	0.533340i	$0.179063\pi$
$383$			1.88455e54i			1.06668i	−0.845901	+	0.533340i	$0.820937\pi$
$384$	−4.66586e53	+	2.17148e54i	−0.250021	+	1.16359i
$385$	2.16452e54			1.09821
$386$		−	8.80623e53i		−	0.423113i
$387$	1.15168e54	+	5.18878e53i	0.524084	+	0.236121i
$388$	−3.71604e54			−1.60182
$389$		−	7.46859e53i		−	0.304998i	−0.988304	−	0.152499i	$-0.951268\pi$
$389$		−	7.46859e53i		−	0.304998i	0.988304	−	0.152499i	$-0.0487321\pi$
$390$	−5.33320e54	−	1.14594e54i	−2.06363	−	0.443411i
$391$	−3.73829e54			−1.37076
$392$		−	4.23150e54i		−	1.47057i
$393$	−7.15588e53	+	3.33033e54i	−0.235733	+	1.09709i
$394$	7.86435e54			2.45608
$395$			8.05487e52i			0.0238517i
$396$	2.52965e54	−	5.61469e54i	0.710331	−	1.57662i
$397$	−3.44358e53			−0.0917084			−0.0458542	−	0.998948i	$-0.514601\pi$
$397$	−3.44358e53			−0.0917084			−0.0458542	+	0.998948i	$0.514601\pi$
$398$		−	2.26991e54i		−	0.573407i
$399$	3.42199e54	+	7.35283e53i	0.820064	+	0.176207i
$400$	−1.18331e54			−0.269054
$401$			3.13021e54i			0.675370i	0.941259	+	0.337685i	$0.109644\pi$
$401$			3.13021e54i			0.675370i	−0.941259	+	0.337685i	$0.890356\pi$
$402$	1.12355e54	−	5.22899e54i	0.230063	−	1.07071i
$403$	1.78892e54			0.347684
$404$			6.64620e54i			1.22621i
$405$	4.61165e54	−	4.07904e54i	0.807794	−	0.714500i
$406$	−1.35771e55			−2.25819
$407$			7.30148e54i			1.15326i
$408$	1.95926e55	+	4.20986e54i	2.93920	+	0.631545i
$409$	−7.57120e54			−1.07889			−0.539443	−	0.842022i	$-0.681365\pi$
$409$	−7.57120e54			−1.07889			−0.539443	+	0.842022i	$0.681365\pi$
$410$			1.28996e55i			1.74628i
$411$	1.09679e54	−	5.10446e54i	0.141074	−	0.656555i
$412$	5.66273e54			0.692125
$413$		−	5.04143e54i		−	0.585602i
$414$	−1.45088e55	−	6.53682e54i	−1.60186	−	0.721704i
$415$	1.24008e55			1.30148
$416$		−	8.77224e54i		−	0.875287i
$417$	−2.68432e54	−	5.76781e53i	−0.254670	−	0.0547209i
$418$	−1.00676e55			−0.908288
$419$		−	5.92571e54i		−	0.508447i	−0.967146	−	0.254223i	$-0.918180\pi$
$419$		−	5.92571e54i		−	0.508447i	0.967146	−	0.254223i	$-0.0818199\pi$
$420$	−7.93357e54	+	3.69227e55i	−0.647491	+	3.01341i
$421$	1.70784e55			1.32594			0.662968	−	0.748648i	$-0.269297\pi$
$421$	1.70784e55			1.32594			0.662968	+	0.748648i	$0.269297\pi$
$422$		−	4.21421e55i		−	3.11282i
$423$	2.74734e54	−	6.09788e54i	0.193092	−	0.428579i
$424$	−2.56572e55			−1.71604
$425$		−	3.57644e54i		−	0.227658i
$426$	−2.90205e55	−	6.23563e54i	−1.75834	−	0.377814i
$427$	−3.09358e55			−1.78433
$428$			5.84035e55i			3.20715i
$429$	3.44886e54	−	1.60509e55i	0.180332	−	0.839261i
$430$	2.22816e55			1.10945
$431$		−	6.55253e54i		−	0.310732i	−0.987857	−	0.155366i	$-0.950344\pi$
$431$		−	6.55253e54i		−	0.310732i	0.987857	−	0.155366i	$-0.0496557\pi$
$432$	2.94136e55	+	2.16700e55i	1.32859	+	0.978812i
$433$	4.18498e54			0.180073			0.0900364	−	0.995938i	$-0.471302\pi$
$433$	4.18498e54			0.180073			0.0900364	+	0.995938i	$0.471302\pi$
$434$		−	1.80069e55i		−	0.738166i
$435$	2.62547e55	+	5.64135e54i	1.02549	+	0.220348i
$436$	6.21601e55			2.31364
$437$			1.78933e55i			0.634716i
$438$	−6.52338e54	+	3.03597e55i	−0.220555	+	1.02646i
$439$	−4.80865e55			−1.54977			−0.774887	−	0.632100i	$-0.782193\pi$
$439$	−4.80865e55			−1.54977			−0.774887	+	0.632100i	$0.782193\pi$
$440$		−	5.93186e55i		−	1.82257i
$441$	2.12580e55	+	9.57758e54i	0.622747	+	0.280573i
$442$	9.78333e55			2.73287
$443$			2.85134e55i			0.759574i	0.925074	+	0.379787i	$0.124003\pi$
$443$			2.85134e55i			0.759574i	−0.925074	+	0.379787i	$0.875997\pi$
$444$	−1.24550e56	−	2.67620e55i	−3.16446	−	0.679948i
$445$	−5.38054e55			−1.30396
$446$		−	3.93642e55i		−	0.910059i
$447$	1.56804e55	−	7.29761e55i	0.345858	−	1.60962i
$448$	1.34251e55			0.282540
$449$			8.34240e55i			1.67540i	0.546133	+	0.837698i	$0.316099\pi$
$449$			8.34240e55i			1.67540i	−0.546133	+	0.837698i	$0.683901\pi$
$450$	6.25380e54	−	1.38807e55i	0.119862	−	0.266040i
$451$	−3.88229e55			−0.710199
$452$		−	9.04183e55i		−	1.57888i
$453$	−8.10632e53	−	1.74180e53i	−0.0135133	−	0.00290360i
$454$	1.77231e56			2.82076
$455$			1.00679e56i			1.53003i
$456$	2.01504e55	−	9.37796e55i	0.292430	−	1.36096i
$457$	2.64725e55			0.366906			0.183453	−	0.983028i	$-0.441273\pi$
$457$	2.64725e55			0.366906			0.183453	+	0.983028i	$0.441273\pi$
$458$			2.09859e56i			2.77814i
$459$	−6.54952e55	+	8.88996e55i	−0.828215	+	1.12417i
$460$	−1.93065e56			−2.33233
$461$		−	1.49317e56i		−	1.72342i	−0.507405	−	0.861708i	$-0.669395\pi$
$461$		−	1.49317e56i		−	1.72342i	0.507405	−	0.861708i	$-0.330605\pi$
$462$	−1.61565e56	−	3.47155e55i	−1.78183	−	0.382862i
$463$	4.17276e55			0.439767			0.219883	−	0.975526i	$-0.429432\pi$
$463$	4.17276e55			0.439767			0.219883	+	0.975526i	$0.429432\pi$
$464$			1.59351e56i			1.60501i
$465$	−7.48192e54	+	3.48207e55i	−0.0720280	+	0.335217i
$466$	−1.33380e56			−1.22740
$467$		−	1.06470e56i		−	0.936644i	−0.883558	−	0.468322i	$-0.844859\pi$
$467$		−	1.06470e56i		−	0.936644i	0.883558	−	0.468322i	$-0.155141\pi$
$468$	2.61158e56	+	1.17662e56i	2.19655	+	0.989634i
$469$	−9.87117e55			−0.793851
$470$		−	1.17976e56i		−	0.907272i
$471$	2.10048e56	+	4.51331e55i	1.54483	+	0.331937i
$472$	−1.38160e56			−0.971854
$473$			6.70591e55i			0.451205i
$474$	1.29187e54	−	6.01236e54i	0.00831525	−	0.0386990i
$475$	−1.71186e55			−0.105415
$476$		−	6.77317e56i		−	3.99067i
$477$	5.80726e55	−	1.28895e56i	0.327405	−	0.726694i
$478$	5.81174e56			3.13560
$479$		−	2.60939e56i		−	1.34739i	−0.739010	−	0.673694i	$-0.764707\pi$
$479$		−	2.60939e56i		−	1.34739i	0.739010	−	0.673694i	$-0.235293\pi$
$480$	1.70749e56	+	3.66887e55i	0.843901	+	0.181329i
$481$	−3.39616e56			−1.60673
$482$			7.21718e56i			3.26873i
$483$	−6.17003e55	+	2.87152e56i	−0.267546	+	1.24515i
$484$	−2.03672e56			−0.845628
$485$		−	1.97230e56i		−	0.784146i
$486$	−4.09646e56	+	2.30506e56i	−1.55972	+	0.877648i
$487$	2.29921e56			0.838438			0.419219	−	0.907885i	$-0.362304\pi$
$487$	2.29921e56			0.838438			0.419219	+	0.907885i	$0.362304\pi$
$488$			8.47795e56i			2.96125i
$489$	2.46623e56	+	5.29918e55i	0.825178	+	0.177306i
$490$	4.11278e56			1.31831
$491$		−	5.52415e56i		−	1.69650i	−0.529595	−	0.848251i	$-0.677656\pi$
$491$		−	5.52415e56i		−	1.69650i	0.529595	−	0.848251i	$-0.322344\pi$
$492$	1.42297e56	−	6.62246e56i	0.418724	−	1.94873i
$493$	−4.81622e56			−1.35807
$494$		−	4.68277e56i		−	1.26543i
$495$	2.98002e56	+	1.34262e56i	0.771808	+	0.347731i
$496$	−2.11342e56			−0.524650
$497$			5.47843e56i			1.30368i
$498$	−9.25623e56	−	1.98889e56i	−2.11163	−	0.453726i
$499$	6.53739e56			1.42986			0.714929	−	0.699198i	$-0.246459\pi$
$499$	6.53739e56			1.42986			0.714929	+	0.699198i	$0.246459\pi$
$500$			9.48171e56i			1.98846i
$501$	2.80346e55	−	1.30472e56i	0.0563770	−	0.262377i
$502$	−1.56072e57			−3.00986
$503$		−	1.45999e56i		−	0.270036i	−0.990843	−	0.135018i	$-0.956891\pi$
$503$		−	1.45999e56i		−	0.270036i	0.990843	−	0.135018i	$-0.0431092\pi$
$504$	6.46750e56	−	1.43550e57i	1.14735	−	2.54660i
$505$	−3.52749e56			−0.600271
$506$		−	8.44809e56i		−	1.37911i
$507$	1.22321e56	+	2.62832e55i	0.191573	+	0.0411634i
$508$	−1.61360e56			−0.242470
$509$			8.80675e56i			1.26982i	0.772586	+	0.634910i	$0.218963\pi$
$509$			8.80675e56i			1.26982i	−0.772586	+	0.634910i	$0.781037\pi$
$510$	−4.09175e56	+	1.90429e57i	−0.566155	+	2.63488i
$511$	5.73124e56			0.761044
$512$		−	1.75141e57i		−	2.23213i
$513$	4.25516e56	+	3.13491e56i	0.520537	+	0.383496i
$514$	1.92145e57			2.25634
$515$			3.00552e56i			0.338819i
$516$	−1.14390e57	−	2.45790e56i	−1.23807	−	0.266024i
$517$	3.55063e56			0.368981
$518$			3.41850e57i			3.41123i
$519$	1.77445e54	−	8.25827e54i	0.00170040	−	0.00791361i
$520$	2.75911e57			2.53921
$521$		−	3.72877e56i		−	0.329590i	−0.986328	−	0.164795i	$-0.947304\pi$
$521$		−	3.72877e56i		−	0.329590i	0.986328	−	0.164795i	$-0.0526962\pi$
$522$	−1.86924e57	−	8.42168e56i	−1.58703	−	0.715020i
$523$	−7.07575e56			−0.577081			−0.288540	−	0.957468i	$-0.593170\pi$
$523$	−7.07575e56			−0.577081			−0.288540	+	0.957468i	$0.593170\pi$
$524$		−	3.15513e57i		−	2.47206i
$525$	−2.74720e56	−	5.90290e55i	−0.206797	−	0.0444345i
$526$	1.94262e57			1.40504
$527$		−	6.38758e56i		−	0.443929i
$528$	−4.07446e56	+	1.89625e57i	−0.272118	+	1.26643i
$529$	5.65154e55			0.0362742
$530$		−	2.49374e57i		−	1.53836i
$531$	3.12712e56	−	6.94082e56i	0.185421	−	0.411553i
$532$	−3.24196e57			−1.84784
$533$		−	1.80578e57i		−	0.989450i
$534$	4.01617e57	+	8.62953e56i	2.11566	+	0.454591i
$535$	−3.09979e57			−1.57001
$536$			2.70519e57i			1.31746i
$537$	−1.34229e55	+	6.24701e55i	−0.00628619	+	0.0292558i
$538$	1.65043e57			0.743310
$539$			1.23779e57i			0.536147i
$540$	−3.38252e57	+	4.59124e57i	−1.40919	+	1.91276i
$541$	−4.09025e57			−1.63911			−0.819554	−	0.573002i	$-0.805779\pi$
$541$	−4.09025e57			−1.63911			−0.819554	+	0.573002i	$0.805779\pi$
$542$		−	1.69199e57i		−	0.652249i
$543$	1.08180e57	+	2.32445e56i	0.401189	+	0.0862034i
$544$	−3.13225e57			−1.11758
$545$			3.29917e57i			1.13260i
$546$	1.61473e57	−	7.51494e57i	0.533403	−	2.48245i
$547$	4.71343e57			1.49832			0.749158	−	0.662392i	$-0.230459\pi$
$547$	4.71343e57			1.49832			0.749158	+	0.662392i	$0.230459\pi$
$548$			4.83592e57i			1.47941i
$549$	−4.25911e57	−	1.91890e57i	−1.25400	−	0.564980i
$550$	8.08233e56			0.229045
$551$			2.30527e57i			0.628838i
$552$	7.86940e57	+	1.69090e57i	2.06643	+	0.444014i
$553$	−1.13500e56			−0.0286925
$554$			6.79202e57i			1.65308i
$555$	1.42040e57	−	6.61052e57i	0.332858	−	1.54911i
$556$	2.54311e57			0.573844
$557$		−	5.99960e57i		−	1.30366i	−0.758366	−	0.651829i	$-0.774002\pi$
$557$		−	5.99960e57i		−	1.30366i	0.758366	−	0.651829i	$-0.225998\pi$
$558$	1.11694e57	−	2.47911e57i	0.233728	−	0.518772i
$559$	−3.11914e57			−0.628619
$560$		−	1.18942e58i		−	2.30879i
$561$	−5.73121e57	−	1.23146e57i	−1.07158	−	0.230251i
$562$	−1.02837e58			−1.85220
$563$			6.67422e57i			1.15804i	0.815313	+	0.579021i	$0.196565\pi$
$563$			6.67422e57i			1.15804i	−0.815313	+	0.579021i	$0.803435\pi$
$564$	−1.30140e57	+	6.05671e57i	−0.217546	+	1.01245i
$565$	4.79898e57			0.772915
$566$		−	1.48558e58i		−	2.30543i
$567$	5.74771e57	+	6.49821e57i	0.859510	+	0.971739i
$568$	1.50136e58			2.16357
$569$			6.97280e57i			0.968389i	0.874961	+	0.484194i	$0.160887\pi$
$569$			6.97280e57i			0.968389i	−0.874961	+	0.484194i	$0.839113\pi$
$570$	9.11486e57	+	1.95851e57i	1.22005	+	0.262152i
$571$	8.05857e57			1.03968			0.519840	−	0.854263i	$-0.325991\pi$
$571$	8.05857e57			1.03968			0.519840	+	0.854263i	$0.325991\pi$
$572$			1.52065e58i			1.89109i
$573$	1.47235e56	−	6.85230e56i	0.0176508	−	0.0821466i
$574$	−1.81766e58			−2.10069
$575$		−	1.43648e57i		−	0.160057i
$576$	1.84831e57	+	8.32739e56i	0.198565	+	0.0894616i
$577$	−2.72612e57			−0.282392			−0.141196	−	0.989982i	$-0.545095\pi$
$577$	−2.72612e57			−0.282392			−0.141196	+	0.989982i	$0.545095\pi$
$578$		−	1.70158e58i		−	1.69968i
$579$	−2.39953e57	−	5.15587e56i	−0.231141	−	0.0496652i
$580$	−2.48735e58			−2.31073
$581$			1.74737e58i			1.56562i
$582$	−3.16326e57	+	1.47218e58i	−0.273371	+	1.27226i
$583$	7.50522e57			0.625639
$584$		−	1.57065e58i		−	1.26301i
$585$	−6.24497e57	+	1.38611e58i	−0.484459	+	1.07528i
$586$	−1.11368e58			−0.833507
$587$		−	1.30204e58i		−	0.940206i	−0.882611	−	0.470103i	$-0.844217\pi$
$587$		−	1.30204e58i		−	0.940206i	0.882611	−	0.470103i	$-0.155783\pi$
$588$	−2.11145e58	−	4.53686e57i	−1.47115	−	0.316105i
$589$	−3.05740e57			−0.205557
$590$		−	1.34284e58i		−	0.871229i
$591$	4.60442e57	−	2.14289e58i	0.288296	−	1.34172i
$592$	4.01220e58			2.42453
$593$		−	2.47365e58i		−	1.44275i	−0.692547	−	0.721373i	$-0.743511\pi$
$593$		−	2.47365e58i		−	1.44275i	0.692547	−	0.721373i	$-0.256489\pi$
$594$	−2.00902e58	−	1.48011e58i	−1.13102	−	0.833258i
$595$	3.59489e58			1.95357
$596$			6.91369e58i			3.62692i
$597$	−6.18507e57	−	1.32899e57i	−0.313245	−	0.0673068i
$598$	3.92949e58			1.92137
$599$		−	1.19346e58i		−	0.563434i	−0.959498	−	0.281717i	$-0.909096\pi$
$599$		−	1.19346e58i		−	0.563434i	0.959498	−	0.281717i	$-0.0909039\pi$
$600$	−1.61769e57	+	7.52869e57i	−0.0737426	+	0.343197i
$601$	−2.72028e58			−1.19743			−0.598715	−	0.800962i	$-0.704322\pi$
$601$	−2.72028e58			−1.19743			−0.598715	+	0.800962i	$0.704322\pi$
$602$			3.13966e58i			1.33462i
$603$	−1.35902e58	−	6.12294e57i	−0.557908	−	0.251360i
$604$	7.67985e56			0.0304493
$605$		−	1.08100e58i		−	0.413964i
$606$	2.63301e58	+	5.65754e57i	0.973929	+	0.209268i
$607$	3.19838e58			1.14279			0.571396	−	0.820675i	$-0.306402\pi$
$607$	3.19838e58			1.14279			0.571396	+	0.820675i	$0.306402\pi$
$608$			1.49924e58i			0.517484i
$609$	−7.94914e57	+	3.69951e58i	−0.265068	+	1.23362i
$610$	−8.24010e58			−2.65464
$611$			1.65151e58i			0.514064i
$612$	4.20130e58	−	9.32500e58i	1.26358	−	2.80459i
$613$	−3.27172e58			−0.950836			−0.475418	−	0.879760i	$-0.657703\pi$
$613$	−3.27172e58			−0.950836			−0.475418	+	0.879760i	$0.657703\pi$
$614$			3.20407e58i			0.899842i
$615$	3.51489e58	+	7.55245e57i	0.953970	+	0.204979i
$616$	8.35851e58			2.19247
$617$		−	5.56508e58i		−	1.41086i	−0.708781	−	0.705429i	$-0.750754\pi$
$617$		−	5.56508e58i		−	1.41086i	0.708781	−	0.705429i	$-0.249246\pi$
$618$	4.82038e57	−	2.24339e58i	0.118120	−	0.549727i
$619$	8.02722e58			1.90135			0.950674	−	0.310193i	$-0.100394\pi$
$619$	8.02722e58			1.90135			0.950674	+	0.310193i	$0.100394\pi$
$620$		−	3.29888e58i		−	0.755338i
$621$	−2.63062e58	+	3.57067e58i	−0.582284	+	0.790361i
$622$	−1.12812e59			−2.41412
$623$		−	7.58164e58i		−	1.56861i
$624$	−8.82007e58	−	1.89517e58i	−1.76440	−	0.379115i
$625$	−5.87536e58			−1.13646
$626$			1.97886e58i			0.370131i
$627$	−5.89438e57	+	2.74323e58i	−0.106615	+	0.496185i
$628$	−1.98998e59			−3.48094
$629$			1.21265e59i			2.05150i
$630$	1.39522e59	+	6.28605e58i	2.28293	+	1.02855i
$631$	8.71597e58			1.37943			0.689714	−	0.724082i	$-0.257736\pi$
$631$	8.71597e58			1.37943			0.689714	+	0.724082i	$0.257736\pi$
$632$			3.11047e57i			0.0476176i
$633$	−1.14829e59	−	2.46734e58i	−1.70049	−	0.365385i
$634$	1.93647e59			2.77419
$635$		−	8.56426e57i		−	0.118697i
$636$	−2.75087e58	+	1.28025e59i	−0.368868	+	1.71671i
$637$	−5.75739e58			−0.746961
$638$		−	1.08841e59i		−	1.36633i
$639$	−3.39819e58	+	7.54246e58i	−0.412790	+	0.916210i
$640$	1.09189e59			1.28351
$641$		−	7.65162e57i		−	0.0870432i	−0.999052	−	0.0435216i	$-0.986142\pi$
$641$		−	7.65162e57i		−	0.0870432i	0.999052	−	0.0435216i	$-0.0138577\pi$
$642$	2.31376e59	+	4.97157e58i	2.54731	+	0.547341i
$643$	−1.02721e59			−1.09453			−0.547265	−	0.836959i	$-0.684331\pi$
$643$	−1.02721e59			−1.09453			−0.547265	+	0.836959i	$0.684331\pi$
$644$		−	2.72045e59i		−	2.80568i
$645$	1.30454e58	−	6.07131e58i	0.130228	−	0.606078i
$646$	−1.67205e59			−1.61572
$647$			1.70616e59i			1.59599i	0.602666	+	0.797994i	$0.294105\pi$
$647$			1.70616e59i			1.59599i	−0.602666	+	0.797994i	$0.705895\pi$
$648$	1.78083e59	−	1.57516e59i	1.61268	−	1.42643i
$649$	4.04145e58			0.354322
$650$			3.75936e58i			0.319105i
$651$	−4.90654e58	−	1.05427e58i	−0.403250	−	0.0866463i
$652$	−2.33648e59			−1.85936
$653$		−	2.62640e58i		−	0.202388i	−0.994867	−	0.101194i	$-0.967734\pi$
$653$		−	2.62640e58i		−	0.202388i	0.994867	−	0.101194i	$-0.0322663\pi$
$654$	5.29135e58	−	2.46258e59i	0.394851	−	1.83763i
$655$	1.67460e59			1.21016
$656$			2.13334e59i			1.49307i
$657$	7.89052e58	+	3.55500e58i	0.534851	+	0.240972i
$658$	1.66238e59			1.09141
$659$			3.75568e58i			0.238833i	0.992844	+	0.119417i	$0.0381024\pi$
$659$			3.75568e58i			0.238833i	−0.992844	+	0.119417i	$0.961898\pi$
$660$	−2.95990e59	−	6.35993e58i	−1.82328	−	0.391769i
$661$	−9.80098e58			−0.584843			−0.292421	−	0.956290i	$-0.594461\pi$
$661$	−9.80098e58			−0.584843			−0.292421	+	0.956290i	$0.594461\pi$
$662$			2.72615e59i			1.57591i
$663$	5.72795e58	−	2.66578e59i	0.320786	−	1.49293i
$664$	4.78867e59			2.59828
$665$		−	1.72068e59i		−	0.904579i
$666$	−2.12045e59	+	4.70645e59i	−1.08011	+	2.39737i
$667$	−1.93444e59			−0.954801
$668$			1.23608e59i			0.591210i
$669$	−1.07260e59	−	2.30470e58i	−0.497153	−	0.106823i
$670$	−2.62930e59			−1.18105
$671$		−	2.47996e59i		−	1.07962i
$672$	−5.16976e58	+	2.40600e59i	−0.218130	+	1.01517i
$673$	1.25195e59			0.512003			0.256001	−	0.966676i	$-0.417595\pi$
$673$	1.25195e59			0.512003			0.256001	+	0.966676i	$0.417595\pi$
$674$			3.63112e59i			1.43941i
$675$	−3.41607e58	−	2.51673e58i	−0.131265	−	0.0967069i
$676$	−1.15886e59			−0.431669
$677$			4.16483e59i			1.50395i	0.659189	+	0.751977i	$0.270900\pi$
$677$			4.16483e59i			1.50395i	−0.659189	+	0.751977i	$0.729100\pi$
$678$	−3.58208e59	−	7.69681e58i	−1.25404	−	0.269456i
$679$	2.77914e59			0.943291
$680$		−	9.85178e59i		−	3.24211i
$681$	1.03765e59	−	4.82921e59i	0.331103	−	1.54094i
$682$	1.44352e59			0.446632
$683$		−	2.02654e59i		−	0.608025i	−0.952668	−	0.304012i	$-0.901674\pi$
$683$		−	2.02654e59i		−	0.608025i	0.952668	−	0.304012i	$-0.0983264\pi$
$684$	−4.46339e59	−	2.01094e59i	−1.29863	−	0.585088i
$685$	−2.56668e59			−0.724219
$686$		−	2.68934e59i		−	0.735933i
$687$	5.71828e59	+	1.22869e59i	1.51766	+	0.326099i
$688$	3.68494e59			0.948577
$689$			3.49093e59i			0.871641i
$690$	−1.64346e59	+	7.64862e59i	−0.398041	+	1.85247i
$691$	4.07236e59			0.956768			0.478384	−	0.878151i	$-0.341223\pi$
$691$	4.07236e59			0.956768			0.478384	+	0.878151i	$0.341223\pi$
$692$			7.82381e57i			0.0178316i
$693$	−1.89187e59	+	4.19910e59i	−0.418304	+	0.928449i
$694$	−2.16728e59			−0.464906
$695$			1.34976e59i			0.280916i
$696$	1.01385e60	+	2.17846e59i	2.04729	+	0.439902i
$697$	−6.44779e59			−1.26335
$698$		−	1.07665e60i		−	2.04696i
$699$	−7.80914e58	+	3.63436e59i	−0.144073	+	0.670513i
$700$	2.60267e59			0.465973
$701$			6.37311e59i			1.10732i	0.832743	+	0.553660i	$0.186769\pi$
$701$			6.37311e59i			1.10732i	−0.832743	+	0.553660i	$0.813231\pi$
$702$	6.88450e59	−	9.34464e59i	1.16089	−	1.57574i
$703$	5.80431e59			0.949924
$704$			1.07622e59i			0.170952i
$705$	−3.21462e59	−	6.90725e58i	−0.495631	−	0.106496i
$706$	2.66429e59			0.398733
$707$		−	4.97054e59i		−	0.722098i
$708$	−1.48130e59	+	6.89396e59i	−0.208903	+	0.972232i
$709$	9.41879e59			1.28951			0.644754	−	0.764390i	$-0.276960\pi$
$709$	9.41879e59			1.28951			0.644754	+	0.764390i	$0.276960\pi$
$710$			1.45924e60i			1.93955i
$711$	−1.56262e58	−	7.04024e57i	−0.0201647	−	0.00908502i
$712$	−2.07775e60			−2.60323
$713$		−	2.56558e59i		−	0.312108i
$714$	−2.68331e60	−	5.76563e59i	−3.16963	−	0.681058i
$715$	−8.07091e59			−0.925754
$716$		−	5.91836e58i		−	0.0659217i
$717$	3.40266e59	−	1.58359e60i	0.368058	−	1.71293i
$718$	6.36829e59			0.668975
$719$			3.75591e59i			0.383185i	0.981475	+	0.191592i	$0.0613652\pi$
$719$			3.75591e59i			0.383185i	−0.981475	+	0.191592i	$0.938635\pi$
$720$	7.37776e59	−	1.63754e60i	0.731042	−	1.62259i
$721$	−4.23503e59			−0.407583
$722$		−	1.11420e60i		−	1.04155i
$723$	1.96655e60	+	4.22552e59i	1.78566	+	0.383686i
$724$	−1.02488e60			−0.903993
$725$		−	1.85069e59i		−	0.158575i
$726$	−1.73375e59	+	8.06884e59i	−0.144317	+	0.671649i
$727$	−2.28875e60			−1.85087			−0.925435	−	0.378905i	$-0.876301\pi$
$727$	−2.28875e60			−1.85087			−0.925435	+	0.378905i	$0.876301\pi$
$728$			3.88782e60i			3.05455i
$729$	3.88246e59	+	1.25117e60i	0.296366	+	0.955074i
$730$	1.52658e60			1.13224
$731$			1.11373e60i			0.802632i
$732$	4.23035e60	+	9.08975e59i	2.96240	+	0.636531i
$733$	−4.64225e58			−0.0315897			−0.0157948	−	0.999875i	$-0.505028\pi$
$733$	−4.64225e58			−0.0315897			−0.0157948	+	0.999875i	$0.505028\pi$
$734$		−	2.86310e60i		−	1.89330i
$735$	2.40795e59	−	1.12066e60i	0.154744	−	0.720176i
$736$	−1.25807e60			−0.785726
$737$		−	7.91320e59i		−	0.480325i
$738$	−2.50247e60	−	1.12747e60i	−1.47634	−	0.665151i
$739$	−7.61542e59			−0.436677			−0.218339	−	0.975873i	$-0.570064\pi$
$739$	−7.61542e59			−0.436677			−0.218339	+	0.975873i	$0.570064\pi$
$740$			6.26275e60i			3.49059i
$741$	−1.27597e60	−	2.74167e59i	−0.691285	−	0.148536i
$742$	3.51389e60			1.85058
$743$		−	3.20623e60i		−	1.64146i	−0.571319	−	0.820728i	$-0.693568\pi$
$743$		−	3.20623e60i		−	1.64146i	0.571319	−	0.820728i	$-0.306432\pi$
$744$	−2.88922e59	+	1.34464e60i	−0.143797	+	0.669226i
$745$	−3.66946e60			−1.77550
$746$		−	7.37805e60i		−	3.47077i
$747$	−1.08387e60	+	2.40571e60i	−0.495729	+	1.10030i
$748$	5.42970e60			2.41458
$749$		−	4.36787e60i		−	1.88865i
$750$	3.75635e60	+	8.07126e59i	1.57935	+	0.339355i
$751$	3.65531e60			1.49447			0.747233	−	0.664563i	$-0.231382\pi$
$751$	3.65531e60			1.49447			0.747233	+	0.664563i	$0.231382\pi$
$752$		−	1.95109e60i		−	0.775715i
$753$	−9.13769e59	+	4.25266e60i	−0.353299	+	1.64424i
$754$	5.06254e60			1.90358
$755$			4.07611e58i			0.0149060i
$756$	−6.46946e60	−	4.76626e60i	−2.30097	−	1.69520i
$757$	−4.13891e59			−0.143177			−0.0715884	−	0.997434i	$-0.522807\pi$
$757$	−4.13891e59			−0.143177			−0.0715884	+	0.997434i	$0.522807\pi$
$758$			5.40061e60i			1.81715i
$759$	−2.30195e60	−	4.94619e59i	−0.753387	−	0.161880i
$760$	−4.71553e60			−1.50122
$761$			3.07895e60i			0.953508i	0.879037	+	0.476754i	$0.158187\pi$
$761$			3.07895e60i			0.953508i	−0.879037	+	0.476754i	$0.841813\pi$
$762$	−1.37357e59	+	6.39258e59i	−0.0413806	+	0.192585i
$763$	−4.64881e60			−1.36247
$764$			6.49181e59i			0.185100i
$765$	4.94928e60	+	2.22985e60i	1.37294	+	0.618566i
$766$	−7.07322e60			−1.90903
$767$			1.87981e60i			0.493642i
$768$	−7.31681e60	−	1.57216e60i	−1.86955	−	0.401709i
$769$	6.16064e60			1.53170			0.765848	−	0.643021i	$-0.222319\pi$
$769$	6.16064e60			1.53170			0.765848	+	0.643021i	$0.222319\pi$
$770$			8.12400e60i			1.96546i
$771$	1.12497e60	−	5.23561e60i	0.264850	−	1.23261i
$772$	2.27330e60			0.520826
$773$			3.23420e60i			0.721104i	0.932739	+	0.360552i	$0.117412\pi$
$773$			3.23420e60i			0.721104i	−0.932739	+	0.360552i	$0.882588\pi$
$774$	−1.94749e60	+	4.32255e60i	−0.422585	+	0.937950i
$775$	2.45450e59			0.0518356
$776$		−	7.61624e60i		−	1.56547i
$777$	9.31479e60	+	2.00147e60i	1.86351	+	0.400412i
$778$	2.80316e60			0.545853
$779$			3.08622e60i			0.584979i
$780$	2.95821e60	−	1.37675e61i	0.545812	−	2.54020i
$781$	−4.39177e60			−0.788801
$782$		−	1.40308e61i		−	2.45324i
$783$	−3.38915e60	+	4.60025e60i	−0.576892	+	0.783042i
$784$	6.80174e60			1.12715
$785$		−	1.05619e61i		−	1.70404i
$786$	−1.24996e61	−	2.68579e60i	−1.96346	−	0.421889i
$787$	−6.93462e60			−1.06060			−0.530302	−	0.847809i	$-0.677922\pi$
$787$	−6.93462e60			−1.06060			−0.530302	+	0.847809i	$0.677922\pi$
$788$			2.03015e61i			3.02328i
$789$	1.13737e60	−	5.29328e60i	0.164924	−	0.767553i
$790$	−3.02320e59			−0.0426873
$791$			6.76218e60i			0.929781i
$792$	1.15076e61	+	5.18465e60i	1.54084	+	0.694210i
$793$	1.15351e61			1.50413
$794$		−	1.29246e60i		−	0.164130i
$795$	−6.79498e60	−	1.46004e60i	−0.840385	−	0.180574i
$796$	5.85968e60			0.705829
$797$		−	3.79547e60i		−	0.445288i	−0.974900	−	0.222644i	$-0.928531\pi$
$797$		−	3.79547e60i		−	0.445288i	0.974900	−	0.222644i	$-0.0714688\pi$
$798$	−2.75971e60	+	1.28436e61i	−0.315357	+	1.46766i
$799$	5.89696e60			0.656366
$800$		−	1.20360e60i		−	0.130495i
$801$	4.70277e60	−	1.04381e61i	0.496674	−	1.10239i
$802$	−1.17485e61			−1.20870
$803$			4.59443e60i			0.460475i
$804$	1.34984e61	+	2.90041e60i	1.31797	+	0.283193i
$805$	1.44389e61			1.37348
$806$			6.71427e60i			0.622248i
$807$	9.66296e59	−	4.49712e60i	0.0872501	−	0.406060i
$808$	−1.36218e61			−1.19838
$809$			1.00290e61i			0.859683i	0.902904	+	0.429842i	$0.141431\pi$
$809$			1.00290e61i			0.859683i	−0.902904	+	0.429842i	$0.858569\pi$
$810$	1.53097e61	+	1.73087e61i	1.27874	+	1.44570i
$811$	−2.23570e61			−1.81960			−0.909800	−	0.415047i	$-0.863765\pi$
$811$	−2.23570e61			−1.81960			−0.909800	+	0.415047i	$0.863765\pi$
$812$		−	3.50489e61i		−	2.77970i
$813$	−4.61037e60	−	9.90629e59i	−0.356315	−	0.0765613i
$814$	−2.74044e61			−2.06399
$815$		−	1.24010e61i		−	0.910219i
$816$	−6.76696e60	+	3.14933e61i	−0.484061	+	2.25281i
$817$	5.33086e60			0.371650
$818$		−	2.84167e61i		−	1.93087i
$819$	−1.95314e61	−	8.79970e60i	−1.29352	−	0.582782i
$820$	−3.32998e61			−2.14956
$821$		−	1.21036e61i		−	0.761566i	−0.924664	−	0.380783i	$-0.875655\pi$
$821$		−	1.21036e61i		−	0.761566i	0.924664	−	0.380783i	$-0.124345\pi$
$822$	1.91584e61	+	4.11655e60i	1.17503	+	0.252479i
$823$	4.76830e60			0.285080			0.142540	−	0.989789i	$-0.454473\pi$
$823$	4.76830e60			0.285080			0.142540	+	0.989789i	$0.454473\pi$
$824$			1.16061e61i			0.676417i
$825$	4.73204e59	−	2.20228e60i	0.0268854	−	0.125124i
$826$	1.89218e61			1.04805
$827$			2.41842e61i			1.30592i	0.757394	+	0.652958i	$0.226472\pi$
$827$			2.41842e61i			1.30592i	−0.757394	+	0.652958i	$0.773528\pi$
$828$	1.68746e61	−	3.74540e61i	0.888373	−	1.97179i
$829$	1.24242e61			0.637710			0.318855	−	0.947803i	$-0.396702\pi$
$829$	1.24242e61			0.637710			0.318855	+	0.947803i	$0.396702\pi$
$830$			4.65432e61i			2.32925i
$831$	1.85070e61	+	3.97660e60i	0.903056	+	0.194039i
$832$	−5.00586e60			−0.238171
$833$			2.05576e61i			0.953733i
$834$	2.16481e60	−	1.00750e61i	0.0979337	−	0.455781i
$835$	−6.56056e60			−0.289417
$836$		−	2.59891e61i		−	1.11805i
$837$	−6.10116e60	−	4.49492e60i	−0.255963	−	0.188576i
$838$	2.22407e61			0.909964
$839$		−	8.63752e60i		−	0.344658i	−0.985039	−	0.172329i	$-0.944871\pi$
$839$		−	8.63752e60i		−	0.344658i	0.985039	−	0.172329i	$-0.0551291\pi$
$840$	−7.56751e61	−	1.62603e61i	−2.94502	−	0.632796i
$841$	1.42378e60			0.0540415
$842$			6.40995e61i			2.37302i
$843$	−6.02091e60	+	2.80212e61i	−0.217412	+	1.01183i
$844$	1.08788e62			3.83169
$845$		−	6.15070e60i		−	0.211317i
$846$	2.28869e61	+	1.03115e61i	0.767025	+	0.345576i
$847$	1.52322e61			0.497979
$848$		−	4.12416e61i		−	1.31529i
$849$	−4.04793e61	−	8.69778e60i	−1.25942	−	0.270612i
$850$	1.34233e61			0.407439
$851$			4.87061e61i			1.44232i
$852$	1.60971e61	−	7.49154e61i	0.465066	−	2.16441i
$853$	1.30531e61			0.367946			0.183973	−	0.982931i	$-0.441104\pi$
$853$	1.30531e61			0.367946			0.183973	+	0.982931i	$0.441104\pi$
$854$		−	1.16110e62i		−	3.19341i
$855$	1.06731e61	−	2.36896e61i	0.286420	−	0.635726i
$856$	−1.19701e62			−3.13437
$857$			2.13574e61i			0.545695i	0.962057	+	0.272848i	$0.0879655\pi$
$857$			2.13574e61i			0.545695i	−0.962057	+	0.272848i	$0.912034\pi$
$858$	6.02433e61	+	1.29445e61i	1.50202	+	0.322739i
$859$	−7.92701e61			−1.92865			−0.964324	−	0.264724i	$-0.914719\pi$
$859$	−7.92701e61			−1.92865			−0.964324	+	0.264724i	$0.914719\pi$
$860$			5.75191e61i			1.36567i
$861$	−1.06420e61	+	4.95279e61i	−0.246581	+	1.14758i
$862$	2.45933e61			0.556115
$863$		−	6.53731e61i		−	1.44269i	−0.692577	−	0.721344i	$-0.743525\pi$
$863$		−	6.53731e61i		−	1.44269i	0.692577	−	0.721344i	$-0.256475\pi$
$864$	−2.20415e61	+	2.99180e61i	−0.474737	+	0.644382i
$865$	−4.15252e59			−0.00872917
$866$			1.57073e61i			0.322275i
$867$	−4.63650e61	−	9.96243e60i	−0.928515	−	0.199510i
$868$	4.64841e61			0.908636
$869$		−	9.09871e59i		−	0.0173606i
$870$	−2.11734e61	+	9.85407e61i	−0.394355	+	1.83532i
$871$	3.68069e61			0.669189
$872$			1.27401e62i			2.26113i
$873$	3.82620e61	+	1.72386e61i	0.662932	+	0.298678i
$874$	−6.71580e61			−1.13595
$875$		−	7.09115e61i		−	1.17098i
$876$	−7.83725e61	−	1.68399e61i	−1.26351	−	0.271489i
$877$	5.89907e61			0.928522			0.464261	−	0.885698i	$-0.346320\pi$
$877$	5.89907e61			0.928522			0.464261	+	0.885698i	$0.346320\pi$
$878$		−	1.80481e62i		−	2.77362i
$879$	−6.52036e60	+	3.03456e61i	−0.0978375	+	0.455334i
$880$	9.53492e61			1.39695
$881$		−	3.46249e61i		−	0.495330i	−0.968846	−	0.247665i	$-0.920337\pi$
$881$		−	3.46249e61i		−	0.495330i	0.968846	−	0.247665i	$-0.0796633\pi$
$882$	−3.59472e61	+	7.97867e61i	−0.502139	+	1.11453i
$883$	2.64433e59			0.00360696			0.00180348	−	0.999998i	$-0.499426\pi$
$883$	2.64433e59			0.00360696			0.00180348	+	0.999998i	$0.499426\pi$
$884$			2.52553e62i			3.36400i
$885$	−3.65899e61	−	7.86207e60i	−0.475941	−	0.102265i
$886$	−1.07018e62			−1.35941
$887$		−	3.59415e61i		−	0.445862i	−0.974834	−	0.222931i	$-0.928437\pi$
$887$		−	3.59415e61i		−	0.445862i	0.974834	−	0.222931i	$-0.0715625\pi$
$888$	5.48502e61	−	2.55272e62i	0.664517	−	3.09265i
$889$	1.20678e61			0.142787
$890$		−	2.01945e62i		−	2.33369i
$891$	−5.20927e61	+	4.60764e61i	−0.587957	+	0.520052i
$892$	1.01617e62			1.12023
$893$		−	2.82257e61i		−	0.303923i
$894$	2.73898e62	+	5.88524e61i	2.88072	+	0.618980i
$895$	3.14119e60			0.0322709
$896$			1.53857e62i			1.54400i
$897$	2.30064e61	−	1.07071e62i	0.225531	−	1.04962i
$898$	−3.13112e62			−2.99845
$899$		−	3.30536e61i		−	0.309218i
$900$	3.58324e61	+	1.61440e61i	0.327479	+	0.147543i
$901$	1.24649e62			1.11293
$902$		−	1.45712e62i		−	1.27104i
$903$	8.55500e61	+	1.83821e61i	0.729083	+	0.156658i
$904$	1.85317e62			1.54305
$905$		−	5.43961e61i		−	0.442535i
$906$	6.53744e59	−	3.04251e60i	0.00519656	−	0.0241847i
$907$	1.24353e62			0.965834			0.482917	−	0.875666i	$-0.339577\pi$
$907$	1.24353e62			0.965834			0.482917	+	0.875666i	$0.339577\pi$
$908$			4.57515e62i			3.47218i
$909$	3.08315e61	−	6.84322e61i	0.228641	−	0.507480i
$910$	−3.77875e62			−2.73828
$911$			1.51904e62i			1.07568i	0.843047	+	0.537840i	$0.180759\pi$
$911$			1.51904e62i			1.07568i	−0.843047	+	0.537840i	$0.819241\pi$
$912$	1.50742e62	+	3.23899e61i	1.04314	+	0.224139i
$913$	−1.40078e62			−0.947289
$914$			9.93581e61i			0.656649i
$915$	−4.82442e61	+	2.24527e62i	−0.311603	+	1.45019i
$916$	−5.41745e62			−3.41971
$917$			2.35965e62i			1.45576i
$918$	−3.33663e62	−	2.45820e62i	−2.01193	−	1.48225i
$919$	8.87370e61			0.522972			0.261486	−	0.965207i	$-0.415787\pi$
$919$	8.87370e61			0.522972			0.261486	+	0.965207i	$0.415787\pi$
$920$		−	3.95698e62i		−	2.27939i
$921$	8.73049e61	+	1.87592e61i	0.491571	+	0.105624i
$922$	5.60426e62			3.08439
$923$		−	2.04276e62i		−	1.09896i
$924$	8.96168e61	−	4.17075e62i	0.471279	−	2.19332i
$925$	−4.65974e61			−0.239544
$926$			1.56614e62i			0.787047i
$927$	−5.83060e61	−	2.62693e61i	−0.286444	−	0.129055i
$928$	−1.62083e62			−0.778450
$929$		−	1.48660e62i		−	0.698012i	−0.937120	−	0.349006i	$-0.886519\pi$
$929$		−	1.48660e62i		−	0.698012i	0.937120	−	0.349006i	$-0.113481\pi$
$930$	−1.30691e62	−	2.80816e61i	−0.599935	−	0.128908i
$931$	9.83983e61			0.441616
$932$		−	3.44316e62i		−	1.51086i
$933$	−6.60494e61	+	3.07393e62i	−0.283370	+	1.31880i
$934$	3.99611e62			1.67631
$935$			2.88183e62i			1.18202i
$936$	−2.41156e62	+	5.35258e62i	−0.967174	+	2.14670i
$937$	−1.79061e62			−0.702214			−0.351107	−	0.936335i	$-0.614195\pi$
$937$	−1.79061e62			−0.702214			−0.351107	+	0.936335i	$0.614195\pi$
$938$		−	3.70491e62i		−	1.42075i
$939$	5.39204e61	+	1.15859e61i	0.202197	+	0.0434461i
$940$	3.04550e62			1.11680
$941$		−	1.27200e62i		−	0.456148i	−0.973644	−	0.228074i	$-0.926757\pi$
$941$		−	1.27200e62i		−	0.456148i	0.973644	−	0.228074i	$-0.0732429\pi$
$942$	−1.69396e62	+	7.88366e62i	−0.594065	+	2.76477i
$943$	−2.58976e62			−0.888208
$944$		−	2.22080e62i		−	0.744898i
$945$	2.52971e62	−	3.43369e62i	0.829855	−	1.12640i
$946$	−2.51690e62			−0.807519
$947$			9.15420e61i			0.287257i	0.989632	+	0.143628i	$0.0458770\pi$
$947$			9.15420e61i			0.287257i	−0.989632	+	0.143628i	$0.954123\pi$
$948$	1.55207e61	+	3.33493e60i	0.0476361	+	0.0102356i
$949$	−2.13702e62			−0.641533
$950$		−	6.42504e61i		−	0.188660i
$951$	1.13376e62	−	5.27651e62i	0.325635	−	1.51550i
$952$	1.38820e63			3.90010
$953$			1.84564e62i			0.507220i	0.967307	+	0.253610i	$0.0816180\pi$
$953$			1.84564e62i			0.507220i	−0.967307	+	0.253610i	$0.918382\pi$
$954$	4.83778e62	+	2.17962e62i	1.30056	+	0.585955i
$955$	−3.44555e61			−0.0906125
$956$			1.50028e63i			3.85973i
$957$	−2.96571e62	−	6.37241e61i	−0.746410	−	0.160381i
$958$	9.79370e62			2.41141
$959$		−	3.61668e62i		−	0.871202i
$960$	2.09364e61	−	9.74374e61i	0.0493407	−	0.229631i
$961$	−3.89864e62			−0.898922
$962$		−	1.27467e63i		−	2.87555i
$963$	2.70932e62	−	6.01349e62i	0.598010	−	1.32732i
$964$	−1.86309e63			−4.02361
$965$			1.20656e62i			0.254962i
$966$	−1.07776e63	−	2.31577e62i	−2.22844	−	0.478825i
$967$	1.81165e62			0.366538			0.183269	−	0.983063i	$-0.441332\pi$
$967$	1.81165e62			0.366538			0.183269	+	0.983063i	$0.441332\pi$
$968$		−	4.17438e62i		−	0.826437i
$969$	−9.78952e61	+	4.55602e62i	−0.189654	+	0.882646i
$970$	7.40256e62			1.40338
$971$			3.31204e62i			0.614457i	0.951636	+	0.307228i	$0.0994016\pi$
$971$			3.31204e62i			0.614457i	−0.951636	+	0.307228i	$0.900598\pi$
$972$	−5.95043e62	−	1.05749e63i	−1.08033	−	1.91992i
$973$	−1.90193e62			−0.337929
$974$			8.62955e62i			1.50055i
$975$	1.02436e62	+	2.20103e61i	0.174323	+	0.0374567i
$976$	−1.36275e63			−2.26971
$977$			5.30049e62i			0.864033i	0.901866	+	0.432016i	$0.142198\pi$
$977$			5.30049e62i			0.864033i	−0.901866	+	0.432016i	$0.857802\pi$
$978$	−1.98892e62	+	9.25640e62i	−0.317323	+	1.47681i
$979$	6.07780e62			0.949095
$980$			1.06170e63i			1.62276i
$981$	−6.40028e62	−	2.88359e62i	−0.957524	−	0.431404i
$982$	2.07336e63			3.03622
$983$			1.81769e62i			0.260552i	0.991478	+	0.130276i	$0.0415864\pi$
$983$			1.81769e62i			0.260552i	−0.991478	+	0.130276i	$0.958414\pi$
$984$	1.35731e63	+	2.91645e62i	1.90450	+	0.409221i
$985$	−1.07751e63			−1.48000
$986$		−	1.80765e63i		−	2.43052i
$987$	9.73291e61	−	4.52967e62i	0.128110	−	0.596220i
$988$	1.20884e63			1.55766
$989$			4.47333e62i			0.564298i
$990$	−5.03920e62	+	1.11848e63i	−0.622332	+	1.38130i
$991$	−3.13176e62			−0.378653			−0.189326	−	0.981914i	$-0.560630\pi$
$991$	−3.13176e62			−0.378653			−0.189326	+	0.981914i	$0.560630\pi$
$992$		−	2.14965e62i		−	0.254462i
$993$	7.42826e62	+	1.59611e62i	0.860901	+	0.184982i
$994$	−2.05620e63			−2.33319
$995$			3.11005e62i			0.345527i
$996$	5.13424e62	−	2.38946e63i	0.558509	−	2.59929i
$997$	−3.77697e62			−0.402295			−0.201148	−	0.979561i	$-0.564467\pi$
$997$	−3.77697e62			−0.402295			−0.201148	+	0.979561i	$0.564467\pi$
$998$			2.45365e63i			2.55901i
$999$	1.15827e63	+	8.53335e62i	1.18286	+	0.871454i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.43.b.b.2.12	yes	12
3.2	odd	2	inner	3.43.b.b.2.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.43.b.b.2.1	✓	12	3.2	odd	2	inner
3.43.b.b.2.12	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 43 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.75326e6i q^{2} +(1.02269e10 + 2.19746e9i) q^{3} -9.68891e12 q^{4} -5.14242e14i q^{5} +(-8.24764e15 + 3.83843e16i) q^{6} +7.24611e17 q^{7} -1.98580e19i q^{8} +(9.97613e19 + 4.49466e19i) q^{9} +O(q^{10})\)	\(q+3.75326e6i q^{2} +(1.02269e10 + 2.19746e9i) q^{3} -9.68891e12 q^{4} -5.14242e14i q^{5} +(-8.24764e15 + 3.83843e16i) q^{6} +7.24611e17 q^{7} -1.98580e19i q^{8} +(9.97613e19 + 4.49466e19i) q^{9} +1.93008e21 q^{10} +5.80883e21i q^{11} +(-9.90878e22 - 2.12910e22i) q^{12} -2.70188e23 q^{13} +2.71965e24i q^{14} +(1.13003e24 - 5.25912e24i) q^{15} +3.19198e25 q^{16} +9.64744e25i q^{17} +(-1.68696e26 + 3.74430e26i) q^{18} +4.61773e26 q^{19} +4.98245e27i q^{20} +(7.41055e27 + 1.59230e27i) q^{21} -2.18020e28 q^{22} +3.87491e28i q^{23} +(4.36371e28 - 2.03086e29i) q^{24} -3.70714e28 q^{25} -1.01409e30i q^{26} +(9.21484e29 + 6.78887e29i) q^{27} -7.02069e30 q^{28} +4.99222e30i q^{29} +(1.97388e31 + 4.24128e30i) q^{30} -6.62101e30 q^{31} +3.24671e31i q^{32} +(-1.27647e31 + 5.94065e31i) q^{33} -3.62093e32 q^{34} -3.72626e32i q^{35} +(-9.66578e32 - 4.35483e32i) q^{36} +1.25696e33 q^{37} +1.73315e33i q^{38} +(-2.76320e33 - 5.93727e32i) q^{39} -1.02118e34 q^{40} +6.68342e33i q^{41} +(-5.97633e33 + 2.78137e34i) q^{42} +1.15443e34 q^{43} -5.62812e34i q^{44} +(2.31134e34 - 5.13015e34i) q^{45} -1.45435e35 q^{46} -6.11246e34i q^{47} +(3.26442e35 + 7.01426e34i) q^{48} +2.13088e35 q^{49} -1.39139e35i q^{50} +(-2.11999e35 + 9.86637e35i) q^{51} +2.61783e36 q^{52} -1.29204e36i q^{53} +(-2.54804e36 + 3.45857e36i) q^{54} +2.98715e36 q^{55} -1.43893e37i q^{56} +(4.72252e36 + 1.01473e36i) q^{57} -1.87371e37 q^{58} -6.95742e36i q^{59} +(-1.09487e37 + 5.09551e37i) q^{60} -4.26930e37 q^{61} -2.48504e37i q^{62} +(7.22882e37 + 3.25688e37i) q^{63} +1.85273e37 q^{64} +1.38942e38i q^{65} +(-2.22968e38 - 4.79091e37i) q^{66} -1.36227e38 q^{67} -9.34731e38i q^{68} +(-8.51495e37 + 3.96284e38i) q^{69} +1.39856e39 q^{70} +7.56050e38i q^{71} +(8.92547e38 - 1.98106e39i) q^{72} +7.90940e38 q^{73} +4.71771e39i q^{74} +(-3.79127e38 - 8.14630e37i) q^{75} -4.47407e39 q^{76} +4.20914e39i q^{77} +(2.22841e39 - 1.03710e40i) q^{78} -1.56636e38 q^{79} -1.64145e40i q^{80} +(7.93213e39 + 8.96786e39i) q^{81} -2.50846e40 q^{82} +2.41146e40i q^{83} +(-7.18002e40 - 1.54277e40i) q^{84} +4.96112e40 q^{85} +4.33289e40i q^{86} +(-1.09702e40 + 5.10551e40i) q^{87} +1.15352e41 q^{88} -1.04630e41i q^{89} +(1.92548e41 + 8.67506e40i) q^{90} -1.95781e41 q^{91} -3.75436e41i q^{92} +(-6.77126e40 - 1.45494e40i) q^{93} +2.29417e41 q^{94} -2.37463e41i q^{95} +(-7.13453e40 + 3.32039e41i) q^{96} +3.83536e41 q^{97} +7.99776e41i q^{98} +(-2.61087e41 + 5.79497e41i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 16987205196 q^{3} - 34999503561888 q^{4} - 47\!\cdots\!88 q^{6}+ \cdots - 10\!\cdots\!60 q^{9}+O(q^{10}) \) 12 * q + 16987205196 * q^3 - 34999503561888 * q^4 - 47900661722006688 * q^6 - 41814621990917832 * q^7 - 10479496382139999060 * q^9	\( 12 q + 16987205196 q^{3} - 34999503561888 q^{4} - 47\!\cdots\!88 q^{6}+ \cdots - 45\!\cdots\!60 q^{99}+O(q^{100}) \) 12 * q + 16987205196 * q^3 - 34999503561888 * q^4 - 47900661722006688 * q^6 - 41814621990917832 * q^7 - 10479496382139999060 * q^9 - 1558337248111507093440 * q^10 + 49376377527162340879584 * q^12 + 104159867930333479443192 * q^13 - 448128019361693763840960 * q^15 + 30189980873605037368521216 * q^16 + 467763252053696004788775360 * q^18 + 1742192007122001281517876120 * q^19 + 9102775482298327940265250872 * q^21 - 4314702866032998614435578560 * q^22 + 213252820822149659960046027264 * q^24 - 1475565424466319180916113000660 * q^25 + 4679803843175845084152852300204 * q^27 - 12573192134196153529744555207488 * q^28 + 62452866934923176992747679887680 * q^30 - 82582711039551011868572590242696 * q^31 + 43265764437015443353441835054400 * q^33 - 263315485295738664634172504653056 * q^34 - 2405201397348598443590828900669856 * q^36 - 100843038556324004682477979351752 * q^37 - 10984759746962485956654149987757192 * q^39 + 14264689156939495925288444850785280 * q^40 - 2831182046378653470535212831685440 * q^42 - 71435403459183756447962146838987688 * q^43 + 171247471703495918987972144910848640 * q^45 - 368252835390302858087002506036095616 * q^46 + 393051873841281316858605019336751616 * q^48 + 503454865894447043110675471056528228 * q^49 - 26481340521925644924949289315966208 * q^51 + 6191863526932890484747245480405187008 * q^52 - 7762950205729260582930120693521404128 * q^54 + 7333373720922934220673629457367543680 * q^55 - 7646344343294849001862320271635263592 * q^57 - 40828097874719028971304350423217887040 * q^58 + 67409911106604936995672440638418037760 * q^60 - 86088392913854728749325031191744820616 * q^61 + 100834020234866427922563192954676937592 * q^63 - 141458640188438187587490744757105434624 * q^64 - 410927857618739095889759252898209949120 * q^66 + 637588020068292666249059312571603583128 * q^67 - 900977595682723671847728174824987261568 * q^69 + 1299257312773585175235999395827621799040 * q^70 - 1002862304292335428089280868557297904640 * q^72 + 4764698373378852277054437745609397085912 * q^73 + 10291654382848945060344626042064329363820 * q^75 - 10850719004897690517175553392098488304192 * q^76 - 1154864387471236146792590220220273542720 * q^78 - 16476824590026301016342599143867688625160 * q^79 - 29934898097734077284676557689524616295988 * q^81 + 12117774709574398821091222390193736370560 * q^82 - 115502524985324999123004799396029534507072 * q^84 + 179892388106464049414097141341403281134080 * q^85 - 108737363241821037303405571455850394882880 * q^87 + 262137413065538961600854476553505008040960 * q^88 - 246742532847586844558695609281104739341760 * q^90 + 85532425294904148246865639238250304747824 * q^91 + 153993445971229900791562733419639364858232 * q^93 + 711306705503600048406114202903471029729024 * q^94 - 1719405066055622809595776412409802129711104 * q^96 + 1090171163442244899022729083217627459542168 * q^97 - 4562402641239113129658705054315657608741760 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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