LMFDB - Embedded newform 3.41.b.a.2.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,41,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, 41, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 41);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 41 $
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:	$30.4026855589$
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} + 249659905422 x^{10} + \cdots + 12\!\cdots\!00 $ x^12 + 249659905422x^10 + 21357900831219724160448x^8 + 757005714875983264074654770397184x^6 + 10196659004511185116272142565764285511761920x^4 + 42071301184141474816096210166597335428414342325862400*x^2 + 12606130133749306378798090199763505554693706712963960799232000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{63}\cdot 3^{98}\cdot 5^{6}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.2
Root			$-245022. i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.41.b.a.2.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.47013e6i q^{2} +(1.53875e9 - 3.12889e9i) q^{3} -1.06178e12 q^{4} -3.18557e13i q^{5} +(-4.59988e15 - 2.26216e15i) q^{6} +7.85404e14 q^{7} -5.54756e16i q^{8} +(-7.42219e18 - 9.62912e18i) q^{9} +O(q^{10})$	\(q-1.47013e6i q^{2} +(1.53875e9 - 3.12889e9i) q^{3} -1.06178e12 q^{4} -3.18557e13i q^{5} +(-4.59988e15 - 2.26216e15i) q^{6} +7.85404e14 q^{7} -5.54756e16i q^{8} +(-7.42219e18 - 9.62912e18i) q^{9} -4.68322e19 q^{10} +8.83914e20i q^{11} +(-1.63380e21 + 3.32218e21i) q^{12} -1.50265e22 q^{13} -1.15465e21i q^{14} +(-9.96730e22 - 4.90179e22i) q^{15} -1.24899e24 q^{16} +2.97100e24i q^{17} +(-1.41561e25 + 1.09116e25i) q^{18} -6.09769e25 q^{19} +3.38237e25i q^{20} +(1.20854e24 - 2.45744e24i) q^{21} +1.29947e27 q^{22} -1.99164e27i q^{23} +(-1.73577e26 - 8.53628e25i) q^{24} +8.08016e27 q^{25} +2.20910e28i q^{26} +(-4.15493e28 + 8.40642e27i) q^{27} -8.33924e26 q^{28} +8.61658e28i q^{29} +(-7.20628e28 + 1.46532e29i) q^{30} +3.82717e29 q^{31} +1.77519e30i q^{32} +(2.76567e30 + 1.36012e30i) q^{33} +4.36777e30 q^{34} -2.50196e28i q^{35} +(7.88071e30 + 1.02240e31i) q^{36} -1.30186e31 q^{37} +8.96441e31i q^{38} +(-2.31220e31 + 4.70163e31i) q^{39} -1.76722e30 q^{40} -1.97826e32i q^{41} +(-3.61276e30 - 1.77671e30i) q^{42} +8.12325e32 q^{43} -9.38519e32i q^{44} +(-3.06743e32 + 2.36439e32i) q^{45} -2.92797e33 q^{46} -4.06950e33i q^{47} +(-1.92188e33 + 3.90795e33i) q^{48} -6.36619e33 q^{49} -1.18789e34i q^{50} +(9.29593e33 + 4.57162e33i) q^{51} +1.59548e34 q^{52} -2.48872e34i q^{53} +(1.23586e34 + 6.10829e34i) q^{54} +2.81577e34 q^{55} -4.35708e31i q^{56} +(-9.38279e34 + 1.90790e35i) q^{57} +1.26675e35 q^{58} +1.16497e35i q^{59} +(1.05830e35 + 5.20460e34i) q^{60} -5.58865e35 q^{61} -5.62644e35i q^{62} +(-5.82942e33 - 7.56275e33i) q^{63} +1.23648e36 q^{64} +4.78682e35i q^{65} +(1.99955e36 - 4.06589e36i) q^{66} -4.40203e36 q^{67} -3.15454e36i q^{68} +(-6.23160e36 - 3.06462e36i) q^{69} -3.67822e34 q^{70} +1.87733e37i q^{71} +(-5.34181e35 + 4.11750e35i) q^{72} +8.39273e35 q^{73} +1.91391e37i q^{74} +(1.24333e37 - 2.52819e37i) q^{75} +6.47438e37 q^{76} +6.94230e35i q^{77} +(6.91202e37 + 3.39924e37i) q^{78} -8.62105e37 q^{79} +3.97876e37i q^{80} +(-3.76310e37 + 1.42938e38i) q^{81} -2.90830e38 q^{82} -1.72703e38i q^{83} +(-1.28320e36 + 2.60925e36i) q^{84} +9.46435e37 q^{85} -1.19423e39i q^{86} +(2.69603e38 + 1.32587e38i) q^{87} +4.90356e37 q^{88} -3.16586e38i q^{89} +(3.47597e38 + 4.50952e38i) q^{90} -1.18019e37 q^{91} +2.11467e39i q^{92} +(5.88904e38 - 1.19748e39i) q^{93} -5.98270e39 q^{94} +1.94246e39i q^{95} +(5.55436e39 + 2.73156e39i) q^{96} +2.49823e39 q^{97} +9.35914e39i q^{98} +(8.51131e39 - 6.56057e39i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 372082572 q^{3} - 4781373657072 q^{4} + 84\!\cdots\!52 q^{6}+ \cdots - 23\!\cdots\!20 q^{9}+O(q^{10}) $ 12 * q - 372082572 * q^3 - 4781373657072 * q^4 + 8471862485327952 * q^6 - 94341749124766584 * q^7 - 23605502262041939220 * q^9	$ 12 q - 372082572 q^{3} - 4781373657072 q^{4} + 84\!\cdots\!52 q^{6}+ \cdots + 54\!\cdots\!80 q^{99}+O(q^{100}) $ 12 * q - 372082572 * q^3 - 4781373657072 * q^4 + 8471862485327952 * q^6 - 94341749124766584 * q^7 - 23605502262041939220 * q^9 - 129384136354706290080 * q^10 - 4708039830028985428272 * q^12 + 704368845864154901976 * q^13 + 320935800901459838631840 * q^15 + 6054431850962872672227456 * q^16 + 10227710367381761273509920 * q^18 + 37616619688417835612151720 * q^19 - 179163719456723608834234728 * q^21 + 846315150249292772829325920 * q^22 - 18213480358094369517645250944 * q^24 + 8842265325510151276196474700 * q^25 - 70717074113738779393083858252 * q^27 + 469404222007499612173589889696 * q^28 - 207809636542026559976510503200 * q^30 - 914600368399753689553849145016 * q^31 + 157344642221562801276041757600 * q^33 - 14575908480758621487300381842304 * q^34 + 41100171486790863962401658870544 * q^36 + 5673106137824212681873457220696 * q^37 - 9206461430638842876438079090008 * q^39 + 50495897877443363581635475618560 * q^40 - 939238658319640212873301303645920 * q^42 + 1012654832326802922602871229857576 * q^43 + 196109968512215856818385626472000 * q^45 - 3082500781506234684371181468390336 * q^46 + 6532128822166367998693520969705088 * q^48 + 8498166150175390075155260408801892 * q^49 + 27565453699222767413826960590504832 * q^51 - 57328509042562386918101767400001504 * q^52 - 102847607224782098537542351912875792 * q^54 - 9637639495259752880102706884884800 * q^55 - 40307213604482059940636368892395464 * q^57 + 772129436848561910287203884295052320 * q^58 - 114385571579949295944121547557720320 * q^60 - 494443282701607071691140418439862696 * q^61 + 1379291076525018665154441723571240776 * q^63 - 6231783699524672226208093043936541696 * q^64 + 2652084094607847915810184973553481440 * q^66 + 5401062423529881431761320436868275176 * q^67 + 7110274695178254111533494284632123328 * q^69 + 516103243900107216646679160954379200 * q^70 - 27544975046740790141119542770107057920 * q^72 + 30000154498324943042431295514883418136 * q^73 + 43820294796704764666539599709819928500 * q^75 - 215478934792040263381331019050660960352 * q^76 + 234946633516471169601955850003339878560 * q^78 - 128704557118405295534397879672035334840 * q^79 + 473157359902659920298963194247360443532 * q^81 - 639159997421964256448917103585883414720 * q^82 + 1283288903941350744781821238287455403552 * q^84 - 1077142486191382871466217243736209678080 * q^85 + 1076668306862385320797179121273520148960 * q^87 - 2918662713596496795370587920448329114880 * q^88 + 6571793457940570799819318674019816438880 * q^90 - 9859184204686878150356379414618151910256 * q^91 + 11506410044121210986218054652959643683416 * q^93 - 16857264118330945289191940748512432348544 * q^94 + 53068562519213731340201280418423192237056 * q^96 - 41841010071967618660163746722085070705064 * q^97 + 54341076855402233475300783474292013590080 * 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 $

$2$		−	1.47013e6i		−	1.40203i	−0.713148	−	0.701014i	$-0.752731\pi$
$2$		−	1.47013e6i		−	1.40203i	0.713148	−	0.701014i	$-0.247269\pi$
$3$	1.53875e9	−	3.12889e9i	0.441308	−	0.897356i
$3$	1.53875e9	−	3.12889e9i	0.441308	−	0.897356i
$4$	−1.06178e12			−0.965680
$5$		−	3.18557e13i		−	0.334032i	−0.985954	−	0.167016i	$-0.946587\pi$
$5$		−	3.18557e13i		−	0.334032i	0.985954	−	0.167016i	$-0.0534131\pi$
$6$	−4.59988e15	−	2.26216e15i	−1.25812	−	0.618726i
$7$	7.85404e14			0.00984311			0.00492156	−	0.999988i	$-0.498433\pi$
$7$	7.85404e14			0.00984311			0.00492156	+	0.999988i	$0.498433\pi$
$8$		−	5.54756e16i		−	0.0481174i
$9$	−7.42219e18	−	9.62912e18i	−0.610495	−	0.792020i
$10$	−4.68322e19			−0.468322
$11$			8.83914e20i			1.31388i	0.753942	+	0.656941i	$0.228150\pi$
$11$			8.83914e20i			1.31388i	−0.753942	+	0.656941i	$0.771850\pi$
$12$	−1.63380e21	+	3.32218e21i	−0.426162	+	0.866559i
$13$	−1.50265e22			−0.790664			−0.395332	−	0.918538i	$-0.629370\pi$
$13$	−1.50265e22			−0.790664			−0.395332	+	0.918538i	$0.629370\pi$
$14$		−	1.15465e21i		−	0.0138003i
$15$	−9.96730e22	−	4.90179e22i	−0.299745	−	0.147411i
$16$	−1.24899e24			−1.03314
$17$			2.97100e24i			0.731012i	0.930809	+	0.365506i	$0.119104\pi$
$17$			2.97100e24i			0.731012i	−0.930809	+	0.365506i	$0.880896\pi$
$18$	−1.41561e25	+	1.09116e25i	−1.11043	+	0.855930i
$19$	−6.09769e25			−1.62216			−0.811079	−	0.584936i	$-0.801119\pi$
$19$	−6.09769e25			−1.62216			−0.811079	+	0.584936i	$0.801119\pi$
$20$			3.38237e25i			0.322568i
$21$	1.20854e24	−	2.45744e24i	0.00434384	−	0.00883277i
$22$	1.29947e27			1.84210
$23$		−	1.99164e27i		−	1.16052i	−0.814431	−	0.580261i	$-0.802951\pi$
$23$		−	1.99164e27i		−	1.16052i	0.814431	−	0.580261i	$-0.197049\pi$
$24$	−1.73577e26	−	8.53628e25i	−0.0431784	−	0.0212346i
$25$	8.08016e27			0.888423
$26$			2.20910e28i			1.10853i
$27$	−4.15493e28	+	8.40642e27i	−0.980140	+	0.198306i
$28$	−8.33924e26			−0.00950530
$29$			8.61658e28i			0.486827i	0.969923	+	0.243414i	$0.0782673\pi$
$29$			8.61658e28i			0.486827i	−0.969923	+	0.243414i	$0.921733\pi$
$30$	−7.20628e28	+	1.46532e29i	−0.206674	+	0.420251i
$31$	3.82717e29			0.569696			0.284848	−	0.958573i	$-0.408057\pi$
$31$	3.82717e29			0.569696			0.284848	+	0.958573i	$0.408057\pi$
$32$			1.77519e30i			1.40038i
$33$	2.76567e30	+	1.36012e30i	1.17902	+	0.579826i
$34$	4.36777e30			1.02490
$35$		−	2.50196e28i		−	0.00328791i
$36$	7.88071e30	+	1.02240e31i	0.589543	+	0.764838i
$37$	−1.30186e31			−0.563030			−0.281515	−	0.959557i	$-0.590837\pi$
$37$	−1.30186e31			−0.563030			−0.281515	+	0.959557i	$0.590837\pi$
$38$			8.96441e31i			2.27431i
$39$	−2.31220e31	+	4.70163e31i	−0.348926	+	0.709507i
$40$	−1.76722e30			−0.0160727
$41$		−	1.97826e32i		−	1.09801i	−0.835820	−	0.549004i	$-0.815007\pi$
$41$		−	1.97826e32i		−	1.09801i	0.835820	−	0.549004i	$-0.184993\pi$
$42$	−3.61276e30	−	1.77671e30i	−0.0123838	−	0.00609019i
$43$	8.12325e32			1.73925			0.869623	−	0.493717i	$-0.164362\pi$
$43$	8.12325e32			1.73925			0.869623	+	0.493717i	$0.164362\pi$
$44$		−	9.38519e32i		−	1.26879i
$45$	−3.06743e32	+	2.36439e32i	−0.264560	+	0.203925i
$46$	−2.92797e33			−1.62708
$47$		−	4.06950e33i		−	1.47090i	−0.677577	−	0.735452i	$-0.736970\pi$
$47$		−	4.06950e33i		−	1.47090i	0.677577	−	0.735452i	$-0.263030\pi$
$48$	−1.92188e33	+	3.90795e33i	−0.455934	+	0.927096i
$49$	−6.36619e33			−0.999903
$50$		−	1.18789e34i		−	1.24559i
$51$	9.29593e33	+	4.57162e33i	0.655978	+	0.322601i
$52$	1.59548e34			0.763528
$53$		−	2.48872e34i		−	0.813690i	−0.913497	−	0.406845i	$-0.866629\pi$
$53$		−	2.48872e34i		−	0.813690i	0.913497	−	0.406845i	$-0.133371\pi$
$54$	1.23586e34	+	6.10829e34i	0.278030	+	1.37418i
$55$	2.81577e34			0.438878
$56$		−	4.35708e31i		−	0.000473625i
$57$	−9.38279e34	+	1.90790e35i	−0.715871	+	1.45565i
$58$	1.26675e35			0.682545
$59$			1.16497e35i			0.445938i	0.974826	+	0.222969i	$0.0715748\pi$
$59$			1.16497e35i			0.445938i	−0.974826	+	0.222969i	$0.928425\pi$
$60$	1.05830e35	+	5.20460e34i	0.289458	+	0.142352i
$61$	−5.58865e35			−1.09827			−0.549136	−	0.835733i	$-0.685043\pi$
$61$	−5.58865e35			−1.09827			−0.549136	+	0.835733i	$0.685043\pi$
$62$		−	5.62644e35i		−	0.798730i
$63$	−5.82942e33	−	7.56275e33i	−0.00600917	−	0.00779595i
$64$	1.23648e36			0.930223
$65$			4.78682e35i			0.264107i
$66$	1.99955e36	−	4.06589e36i	0.812932	−	1.65302i
$67$	−4.40203e36			−1.32482			−0.662410	−	0.749141i	$-0.730466\pi$
$67$	−4.40203e36			−1.32482			−0.662410	+	0.749141i	$0.730466\pi$
$68$		−	3.15454e36i		−	0.705924i
$69$	−6.23160e36	−	3.06462e36i	−1.04140	−	0.512148i
$70$	−3.67822e34			−0.00460974
$71$			1.87733e37i			1.77163i	0.464039	+	0.885815i	$0.346400\pi$
$71$			1.87733e37i			1.77163i	−0.464039	+	0.885815i	$0.653600\pi$
$72$	−5.34181e35	+	4.11750e35i	−0.0381100	+	0.0293754i
$73$	8.39273e35			0.0454408			0.0227204	−	0.999742i	$-0.492767\pi$
$73$	8.39273e35			0.0454408			0.0227204	+	0.999742i	$0.492767\pi$
$74$			1.91391e37i			0.789383i
$75$	1.24333e37	−	2.52819e37i	0.392068	−	0.797231i
$76$	6.47438e37			1.56649
$77$			6.94230e35i			0.0129327i
$78$	6.91202e37	+	3.39924e37i	0.994748	+	0.489204i
$79$	−8.62105e37			−0.961653			−0.480827	−	0.876816i	$-0.659663\pi$
$79$	−8.62105e37			−0.961653			−0.480827	+	0.876816i	$0.659663\pi$
$80$			3.97876e37i			0.345102i
$81$	−3.76310e37	+	1.42938e38i	−0.254593	+	0.967048i
$82$	−2.90830e38			−1.53944
$83$		−	1.72703e38i		−	0.717363i	−0.933460	−	0.358682i	$-0.883226\pi$
$83$		−	1.72703e38i		−	0.717363i	0.933460	−	0.358682i	$-0.116774\pi$
$84$	−1.28320e36	+	2.60925e36i	−0.00419476	+	0.00852963i
$85$	9.46435e37			0.244181
$86$		−	1.19423e39i		−	2.43847i
$87$	2.69603e38	+	1.32587e38i	0.436857	+	0.214841i
$88$	4.90356e37			0.0632206
$89$		−	3.16586e38i		−	0.325605i	−0.986659	−	0.162803i	$-0.947947\pi$
$89$		−	3.16586e38i		−	0.325605i	0.986659	−	0.162803i	$-0.0520534\pi$
$90$	3.47597e38	+	4.50952e38i	0.285908	+	0.370920i
$91$	−1.18019e37			−0.00778259
$92$			2.11467e39i			1.12069i
$93$	5.88904e38	−	1.19748e39i	0.251412	−	0.511220i
$94$	−5.98270e39			−2.06225
$95$			1.94246e39i			0.541852i
$96$	5.55436e39	+	2.73156e39i	1.25664	+	0.617997i
$97$	2.49823e39			0.459408			0.229704	−	0.973261i	$-0.426224\pi$
$97$	2.49823e39			0.459408			0.229704	+	0.973261i	$0.426224\pi$
$98$			9.35914e39i			1.40189i
$99$	8.51131e39	−	6.56057e39i	1.04062	−	0.802118i
$100$	−8.57932e39			−0.857932
$101$		−	1.38822e39i		−	0.113771i	−0.998381	−	0.0568855i	$-0.981883\pi$
$101$		−	1.38822e39i		−	0.113771i	0.998381	−	0.0568855i	$-0.0181170\pi$
$102$	6.72088e39	−	1.36662e40i	0.452296	−	0.919699i
$103$	−5.22898e38			−0.0289516			−0.0144758	−	0.999895i	$-0.504608\pi$
$103$	−5.22898e38			−0.0289516			−0.0144758	+	0.999895i	$0.504608\pi$
$104$			8.33606e38i			0.0380447i
$105$	−7.82836e37	−	3.84989e37i	−0.00295043	−	0.00145098i
$106$	−3.65875e40			−1.14081
$107$		−	2.81098e40i		−	0.726411i	−0.931709	−	0.363206i	$-0.881682\pi$
$107$		−	2.81098e40i		−	0.726411i	0.931709	−	0.363206i	$-0.118318\pi$
$108$	4.41160e40	−	8.92574e39i	0.946502	−	0.191500i
$109$	−9.91057e40			−1.76835			−0.884176	−	0.467154i	$-0.845279\pi$
$109$	−9.91057e40			−1.76835			−0.884176	+	0.467154i	$0.845279\pi$
$110$		−	4.13956e40i		−	0.615319i
$111$	−2.00324e40	+	4.07339e40i	−0.248470	+	0.505238i
$112$	−9.80964e38			−0.0101693
$113$		−	4.74724e39i		−	0.0411977i	−0.999788	−	0.0205988i	$-0.993443\pi$
$113$		−	4.74724e39i		−	0.0411977i	0.999788	−	0.0205988i	$-0.00655728\pi$
$114$	2.80486e41	+	1.37939e41i	2.04087	+	1.00367i
$115$	−6.34451e40			−0.387651
$116$		−	9.14888e40i		−	0.470120i
$117$	1.11530e41	+	1.44692e41i	0.482696	+	0.626222i
$118$	1.71266e41			0.625217
$119$			2.33344e39i			0.00719543i
$120$	−2.71930e39	+	5.52942e39i	−0.00709303	+	0.0144230i
$121$	−3.28711e41			−0.726284
$122$			8.21605e41i			1.53981i
$123$	−6.18974e41	−	3.04403e41i	−0.985304	−	0.484560i
$124$	−4.06360e41			−0.550145
$125$		−	5.47126e41i		−	0.630793i
$126$	−1.11182e40	+	8.57002e39i	−0.0109301	+	0.00842502i
$127$	8.29339e41			0.696078			0.348039	−	0.937480i	$-0.386848\pi$
$127$	8.29339e41			0.696078			0.348039	+	0.937480i	$0.386848\pi$
$128$			1.34053e41i			0.0961781i
$129$	1.24996e42	−	2.54167e42i	0.767543	−	1.56072i
$130$	7.03725e41			0.370285
$131$		−	3.01248e42i		−	1.35987i	−0.733272	−	0.679935i	$-0.762008\pi$
$131$		−	3.01248e42i		−	1.35987i	0.733272	−	0.679935i	$-0.237992\pi$
$132$	−2.93652e42	−	1.44414e42i	−1.13856	−	0.559927i
$133$	−4.78915e40			−0.0159671
$134$			6.47156e42i			1.85743i
$135$	2.67793e41	+	1.32358e42i	0.0662405	+	0.327398i
$136$	1.64818e41			0.0351744
$137$			1.97127e42i			0.363359i	0.983358	+	0.181679i	$0.0581533\pi$
$137$			1.97127e42i			0.363359i	−0.983358	+	0.181679i	$0.941847\pi$
$138$	−4.50540e42	+	9.16128e42i	−0.718045	+	1.46007i
$139$	2.34490e42			0.323466			0.161733	−	0.986835i	$-0.448292\pi$
$139$	2.34490e42			0.323466			0.161733	+	0.986835i	$0.448292\pi$
$140$			2.65653e40i			0.00317507i
$141$	−1.27330e43	−	6.26193e42i	−1.31992	−	0.649121i
$142$	2.75992e43			2.48387
$143$		−	1.32822e43i		−	1.03884i
$144$	9.27026e42	+	1.20267e43i	0.630728	+	0.818270i
$145$	2.74488e42			0.162616
$146$		−	1.23384e42i		−	0.0637093i
$147$	−9.79594e42	+	1.99191e43i	−0.441265	+	0.897269i
$148$	1.38229e43			0.543707
$149$		−	2.99713e43i		−	1.03034i	−0.857088	−	0.515170i	$-0.827729\pi$
$149$		−	2.99713e43i		−	1.03034i	0.857088	−	0.515170i	$-0.172271\pi$
$150$	−3.71677e43	−	1.82786e43i	−1.11774	−	0.549690i
$151$	−7.32154e43			−1.92781			−0.963904	−	0.266252i	$-0.914215\pi$
$151$	−7.32154e43			−1.92781			−0.963904	+	0.266252i	$0.914215\pi$
$152$			3.38273e42i			0.0780541i
$153$	2.86081e43	−	2.20513e43i	0.578976	−	0.446279i
$154$	1.02061e42			0.0181320
$155$		−	1.21917e43i		−	0.190297i
$156$	2.45504e43	−	4.99208e43i	0.336951	−	0.685156i
$157$	2.98232e43			0.360214			0.180107	−	0.983647i	$-0.442356\pi$
$157$	2.98232e43			0.360214			0.180107	+	0.983647i	$0.442356\pi$
$158$			1.26741e44i			1.34826i
$159$	−7.78692e43	−	3.82951e43i	−0.730169	−	0.359088i
$160$	5.65499e43			0.467770
$161$		−	1.56424e42i		−	0.0114231i
$162$	2.10138e44	+	5.53226e43i	1.35583	+	0.356946i
$163$	6.16652e43			0.351794			0.175897	−	0.984409i	$-0.443717\pi$
$163$	6.16652e43			0.351794			0.175897	+	0.984409i	$0.443717\pi$
$164$			2.10047e44i			1.06032i
$165$	4.33276e43	−	8.81023e43i	0.193680	−	0.393830i
$166$	−2.53897e44			−1.00576
$167$			1.03723e44i			0.364373i	0.983264	+	0.182186i	$0.0583174\pi$
$167$			1.03723e44i			0.364373i	−0.983264	+	0.182186i	$0.941683\pi$
$168$	−1.36328e41	−	6.70443e40i	−0.000425010	−	0.000209014i
$169$	−1.35392e44			−0.374851
$170$		−	1.39138e44i		−	0.342349i
$171$	4.52582e44	+	5.87154e44i	0.990319	+	1.28478i
$172$	−8.62508e44			−1.67955
$173$		−	4.64474e44i		−	0.805451i	−0.915321	−	0.402726i	$-0.868063\pi$
$173$		−	4.64474e44i		−	0.805451i	0.915321	−	0.402726i	$-0.131937\pi$
$174$	1.94921e44	−	3.96352e44i	0.301213	−	0.612486i
$175$	6.34619e42			0.00874485
$176$		−	1.10400e45i		−	1.35743i
$177$	3.64506e44	+	1.79259e44i	0.400165	+	0.196796i
$178$	−4.65423e44			−0.456507
$179$		−	7.06105e44i		−	0.619168i	−0.950872	−	0.309584i	$-0.899810\pi$
$179$		−	7.06105e44i		−	0.619168i	0.950872	−	0.309584i	$-0.100190\pi$
$180$	3.25692e44	−	2.51046e44i	0.255480	−	0.196926i
$181$	1.48674e45			1.04391			0.521955	−	0.852973i	$-0.325203\pi$
$181$	1.48674e45			1.04391			0.521955	+	0.852973i	$0.325203\pi$
$182$			1.73504e43i			0.0109114i
$183$	−8.59951e44	+	1.74862e45i	−0.484676	+	0.985541i
$184$	−1.10487e44			−0.0558413
$185$			4.14719e44i			0.188070i
$186$	−1.76045e45	−	8.65766e44i	−0.716745	−	0.352486i
$187$	−2.62611e45			−0.960463
$188$			4.32090e45i			1.42042i
$189$	−3.26330e43	+	6.60244e42i	−0.00964763	+	0.00195195i
$190$	2.85568e45			0.759692
$191$			7.76747e45i			1.86043i	0.367020	+	0.930213i	$0.380378\pi$
$191$			7.76747e45i			1.86043i	−0.367020	+	0.930213i	$0.619622\pi$
$192$	1.90263e45	−	3.86880e45i	0.410515	−	0.834741i
$193$	5.76691e45			1.12149			0.560747	−	0.827987i	$-0.310514\pi$
$193$	5.76691e45			1.12149			0.560747	+	0.827987i	$0.310514\pi$
$194$		−	3.67273e45i		−	0.644102i
$195$	1.49774e45	+	7.36569e44i	0.236998	+	0.116552i
$196$	6.75947e45			0.965587
$197$		−	6.43416e45i		−	0.830170i	−0.909783	−	0.415085i	$-0.863752\pi$
$197$		−	6.43416e45i		−	0.830170i	0.909783	−	0.415085i	$-0.136248\pi$
$198$	−9.64491e45	−	1.25127e46i	−1.12459	−	1.45898i
$199$	−4.76778e45			−0.502638			−0.251319	−	0.967904i	$-0.580864\pi$
$199$	−4.76778e45			−0.502638			−0.251319	+	0.967904i	$0.580864\pi$
$200$		−	4.48252e44i		−	0.0427486i
$201$	−6.77360e45	+	1.37734e46i	−0.584654	+	1.18883i
$202$	−2.04087e45			−0.159510
$203$			6.76750e43i			0.00479190i
$204$	−9.87020e45	−	4.85403e45i	−0.633465	−	0.311530i
$205$	−6.30188e45			−0.366769
$206$			7.68729e44i			0.0405909i
$207$	−1.91777e46	+	1.47823e46i	−0.919157	+	0.708493i
$208$	1.87680e46			0.816868
$209$		−	5.38983e46i		−	2.13132i
$210$	−5.65984e43	+	1.15087e44i	−0.00203432	+	0.00413658i
$211$	4.75899e46			1.55548			0.777742	−	0.628583i	$-0.216365\pi$
$211$	4.75899e46			1.55548			0.777742	+	0.628583i	$0.216365\pi$
$212$			2.64247e46i			0.785764i
$213$	5.87394e46	+	2.88873e46i	1.58978	+	0.781834i
$214$	−4.13252e46			−1.01845
$215$		−	2.58772e46i		−	0.580963i
$216$	4.66351e44	+	2.30497e45i	0.00954197	+	0.0471618i
$217$	3.00587e44			0.00560759
$218$			1.45698e47i			2.47928i
$219$	1.29143e45	−	2.62599e45i	0.0200534	−	0.0407766i
$220$	−2.98972e46			−0.423816
$221$		−	4.46439e46i		−	0.577985i
$222$	5.98842e46	+	2.94503e46i	0.708358	+	0.348361i
$223$	−1.24456e47			−1.34561			−0.672804	−	0.739821i	$-0.734910\pi$
$223$	−1.24456e47			−1.34561			−0.672804	+	0.739821i	$0.734910\pi$
$224$			1.39424e45i			0.0137841i
$225$	−5.99725e46	−	7.78048e46i	−0.542377	−	0.703649i
$226$	−6.97908e45			−0.0577603
$227$		−	9.40746e46i		−	0.712780i	−0.934337	−	0.356390i	$-0.884008\pi$
$227$		−	9.40746e46i		−	0.712780i	0.934337	−	0.356390i	$-0.115992\pi$
$228$	9.96243e46	−	2.02576e47i	0.691303	−	1.40570i
$229$	4.05603e45			0.0257864			0.0128932	−	0.999917i	$-0.495896\pi$
$229$	4.05603e45			0.0257864			0.0128932	+	0.999917i	$0.495896\pi$
$230$			9.32726e46i			0.543498i
$231$	2.17217e45	+	1.06824e45i	0.0116052	+	0.00570729i
$232$	4.78010e45			0.0234249
$233$			8.72200e46i			0.392191i	0.980585	+	0.196095i	$0.0628263\pi$
$233$			8.72200e46i			0.392191i	−0.980585	+	0.196095i	$0.937174\pi$
$234$	2.12717e47	−	1.63964e47i	0.877980	−	0.676753i
$235$	−1.29637e47			−0.491328
$236$		−	1.23694e47i		−	0.430633i
$237$	−1.32656e47	+	2.69743e47i	−0.424385	+	0.862945i
$238$	3.43046e45			0.0100882
$239$		−	3.37265e47i		−	0.912039i	−0.889970	−	0.456020i	$-0.849275\pi$
$239$		−	3.37265e47i		−	0.912039i	0.889970	−	0.456020i	$-0.150725\pi$
$240$	1.24491e47	+	6.12230e46i	0.309679	+	0.152296i
$241$	−7.05542e47			−1.61503			−0.807517	−	0.589844i	$-0.799189\pi$
$241$	−7.05542e47			−1.61503			−0.807517	+	0.589844i	$0.799189\pi$
$242$			4.83248e47i			1.01827i
$243$	3.89333e47	+	3.37689e47i	0.755433	+	0.655226i
$244$	5.93389e47			1.06058
$245$			2.02800e47i			0.333999i
$246$	−4.47513e47	+	9.09973e47i	−0.679366	+	1.38142i
$247$	9.16271e47			1.28258
$248$		−	2.12314e46i		−	0.0274123i
$249$	−5.40370e47	−	2.65747e47i	−0.643730	−	0.316578i
$250$	−8.04347e47			−0.884389
$251$		−	1.12398e48i		−	1.14100i	−0.821298	−	0.570499i	$-0.806750\pi$
$251$		−	1.12398e48i		−	1.14100i	0.821298	−	0.570499i	$-0.193250\pi$
$252$	6.18954e45	+	8.02995e45i	0.00580293	+	0.00752839i
$253$	1.76043e48			1.52479
$254$		−	1.21924e48i		−	0.975920i
$255$	1.45632e47	−	2.96129e47i	0.107759	−	0.219117i
$256$	1.55660e48			1.06507
$257$			1.62765e48i			1.03015i	0.857146	+	0.515073i	$0.172235\pi$
$257$			1.62765e48i			1.03015i	−0.857146	+	0.515073i	$0.827765\pi$
$258$	−3.73659e48	−	1.83761e48i	−2.18817	−	1.07612i
$259$	−1.02249e46			−0.00554197
$260$		−	5.08253e47i		−	0.255043i
$261$	8.29701e47	−	6.39539e47i	0.385577	−	0.297206i
$262$	−4.42874e48			−1.90658
$263$			1.72240e48i			0.687098i	0.939135	+	0.343549i	$0.111629\pi$
$263$			1.72240e48i			0.687098i	−0.939135	+	0.343549i	$0.888371\pi$
$264$	7.54534e46	−	1.53427e47i	0.0278997	−	0.0567313i
$265$	−7.92801e47			−0.271798
$266$			7.04068e46i			0.0223863i
$267$	−9.90561e47	−	4.87145e47i	−0.292184	−	0.143692i
$268$	4.67397e48			1.27935
$269$			3.60605e48i			0.916192i	0.888903	+	0.458096i	$0.151468\pi$
$269$			3.60605e48i			0.916192i	−0.888903	+	0.458096i	$0.848532\pi$
$270$	1.94584e48	−	3.93691e47i	0.459021	−	0.0928710i
$271$	4.48842e48			0.983349			0.491674	−	0.870779i	$-0.336385\pi$
$271$	4.48842e48			0.983349			0.491674	+	0.870779i	$0.336385\pi$
$272$		−	3.71076e48i		−	0.755239i
$273$	−1.81601e46	+	3.69268e46i	−0.00343452	+	0.00698375i
$274$	2.89803e48			0.509439
$275$			7.14216e48i			1.16728i
$276$	6.61657e48	+	3.25394e48i	1.00566	+	0.494571i
$277$	−4.95445e48			−0.700488			−0.350244	−	0.936659i	$-0.613901\pi$
$277$	−4.95445e48			−0.700488			−0.350244	+	0.936659i	$0.613901\pi$
$278$		−	3.44731e48i		−	0.453508i
$279$	−2.84060e48	−	3.68522e48i	−0.347797	−	0.451211i
$280$	−1.38798e45			−0.000158206
$281$			3.18401e48i			0.337947i	0.985621	+	0.168973i	$0.0540452\pi$
$281$			3.18401e48i			0.337947i	−0.985621	+	0.168973i	$0.945955\pi$
$282$	−9.20586e48	+	1.87192e49i	−0.910085	+	1.85057i
$283$	−1.24165e49			−1.14359			−0.571794	−	0.820397i	$-0.693752\pi$
$283$	−1.24165e49			−1.14359			−0.571794	+	0.820397i	$0.693752\pi$
$284$		−	1.99330e49i		−	1.71083i
$285$	6.07775e48	+	2.98896e48i	0.486234	+	0.239124i
$286$	−1.95265e49			−1.45648
$287$		−	1.55373e47i		−	0.0108078i
$288$	1.70935e49	−	1.31758e49i	1.10913	−	0.854922i
$289$	7.69112e48			0.465621
$290$		−	4.03533e48i		−	0.227992i
$291$	3.84415e48	−	7.81669e48i	0.202740	−	0.412252i
$292$	−8.91120e47			−0.0438813
$293$		−	3.17462e49i		−	1.45996i	−0.683471	−	0.729978i	$-0.739530\pi$
$293$		−	3.17462e49i		−	1.45996i	0.683471	−	0.729978i	$-0.260470\pi$
$294$	2.92837e49	+	1.44013e49i	1.25800	+	0.618666i
$295$	3.71110e48			0.148957
$296$			7.22217e47i			0.0270915i
$297$	−7.43055e48	−	3.67260e49i	−0.260551	−	1.28779i
$298$	−4.40618e49			−1.44457
$299$			2.99274e49i			0.917583i
$300$	−1.32014e49	+	2.68437e49i	−0.378612	+	0.769870i
$301$	6.38004e47			0.0171196
$302$			1.07636e50i			2.70284i
$303$	−4.34359e48	−	2.13612e48i	−0.102093	−	0.0502080i
$304$	7.61596e49			1.67592
$305$			1.78031e49i			0.366858i
$306$	−3.24184e49	−	4.20577e49i	−0.625695	−	0.811741i
$307$	−1.26028e49			−0.227877			−0.113939	−	0.993488i	$-0.536347\pi$
$307$	−1.26028e49			−0.227877			−0.113939	+	0.993488i	$0.536347\pi$
$308$		−	7.37117e47i		−	0.0124888i
$309$	−8.04607e47	+	1.63609e48i	−0.0127766	+	0.0259799i
$310$	−1.79234e49			−0.266801
$311$		−	4.17051e49i		−	0.582079i	−0.956711	−	0.291039i	$-0.905999\pi$
$311$		−	4.17051e49i		−	0.582079i	0.956711	−	0.291039i	$-0.0940011\pi$
$312$	2.60826e48	+	1.28271e48i	0.0341396	+	0.0167894i
$313$	8.98638e49			1.10331			0.551656	−	0.834072i	$-0.313996\pi$
$313$	8.98638e49			1.10331			0.551656	+	0.834072i	$0.313996\pi$
$314$		−	4.38440e49i		−	0.505030i
$315$	−2.40917e47	+	1.85701e47i	−0.00260409	+	0.00200725i
$316$	9.15363e49			0.928649
$317$		−	3.17725e49i		−	0.302598i	−0.988488	−	0.151299i	$-0.951654\pi$
$317$		−	3.17725e49i		−	0.302598i	0.988488	−	0.151299i	$-0.0483456\pi$
$318$	−5.62988e49	+	1.14478e50i	−0.503451	+	1.02372i
$319$	−7.61631e49			−0.639633
$320$		−	3.93889e49i		−	0.310724i
$321$	−8.79524e49	−	4.32539e49i	−0.651849	−	0.320571i
$322$	−2.29964e48			−0.0160156
$323$		−	1.81162e50i		−	1.18582i
$324$	3.99557e49	−	1.51769e50i	0.245855	−	0.933859i
$325$	−1.21417e50			−0.702444
$326$		−	9.06560e49i		−	0.493224i
$327$	−1.52498e50	+	3.10090e50i	−0.780388	+	1.58684i
$328$	−1.09745e49			−0.0528333
$329$		−	3.19620e48i		−	0.0144783i
$330$	−1.29522e50	−	6.36973e49i	−0.552160	−	0.271545i
$331$	2.81121e50			1.12806			0.564031	−	0.825754i	$-0.309250\pi$
$331$	2.81121e50			1.12806			0.564031	+	0.825754i	$0.309250\pi$
$332$			1.83373e50i			0.692744i
$333$	9.66269e49	+	1.25358e50i	0.343727	+	0.445931i
$334$	1.52487e50			0.510861
$335$			1.40230e50i			0.442532i
$336$	−1.50945e48	+	3.06932e48i	−0.00448781	+	0.00912551i
$337$	2.00107e50			0.560613			0.280307	−	0.959910i	$-0.409564\pi$
$337$	2.00107e50			0.560613			0.280307	+	0.959910i	$0.409564\pi$
$338$			1.99044e50i			0.525551i
$339$	−1.48536e49	−	7.30480e48i	−0.0369690	−	0.0181809i
$340$	−1.00490e50			−0.235801
$341$			3.38288e50i			0.748513i
$342$	8.63193e50	−	6.65355e50i	1.80130	−	1.38845i
$343$	−1.00005e49			−0.0196853
$344$		−	4.50642e49i		−	0.0836880i
$345$	−9.76258e49	+	1.98512e50i	−0.171074	+	0.347861i
$346$	−6.82838e50			−1.12926
$347$			2.08623e49i			0.0325666i	0.999867	+	0.0162833i	$0.00518337\pi$
$347$			2.08623e49i			0.0325666i	−0.999867	+	0.0162833i	$0.994817\pi$
$348$	−2.86258e50	−	1.40778e50i	−0.421864	−	0.207467i
$349$	−5.22713e50			−0.727369			−0.363684	−	0.931522i	$-0.618481\pi$
$349$	−5.22713e50			−0.727369			−0.363684	+	0.931522i	$0.618481\pi$
$350$		−	9.32974e48i		−	0.0122605i
$351$	6.24342e50	−	1.26319e50i	0.774961	−	0.156793i
$352$	−1.56911e51			−1.83993
$353$			4.45127e50i			0.493162i	0.969122	+	0.246581i	$0.0793071\pi$
$353$			4.45127e50i			0.493162i	−0.969122	+	0.246581i	$0.920693\pi$
$354$	2.63535e50	−	5.35871e50i	0.275913	−	0.561042i
$355$	5.98037e50			0.591781
$356$			3.36143e50i			0.314430i
$357$	7.30106e48	+	3.59057e48i	0.00645686	+	0.00317540i
$358$	−1.03807e51			−0.868091
$359$		−	2.36020e51i		−	1.86663i	−0.359054	−	0.933317i	$-0.616900\pi$
$359$		−	2.36020e51i		−	1.86663i	0.359054	−	0.933317i	$-0.383100\pi$
$360$	1.31166e49	+	1.70167e49i	0.00981232	+	0.0127299i
$361$	2.30517e51			1.63140
$362$		−	2.18570e51i		−	1.46359i
$363$	−5.05802e50	+	1.02850e51i	−0.320515	+	0.651735i
$364$	1.25310e49			0.00751549
$365$		−	2.67357e49i		−	0.0151787i
$366$	2.57071e51	+	1.26424e51i	1.38176	+	0.679529i
$367$	7.49900e50			0.381665			0.190832	−	0.981623i	$-0.438881\pi$
$367$	7.49900e50			0.381665			0.190832	+	0.981623i	$0.438881\pi$
$368$			2.48754e51i			1.19898i
$369$	−1.90489e51	+	1.46830e51i	−0.869645	+	0.670328i
$370$	6.09691e50			0.263679
$371$		−	1.95465e49i		−	0.00800924i
$372$	−6.25284e50	+	1.27145e51i	−0.242783	+	0.493675i
$373$	−3.43410e51			−1.26368			−0.631838	−	0.775100i	$-0.717699\pi$
$373$	−3.43410e51			−1.26368			−0.631838	+	0.775100i	$0.717699\pi$
$374$			3.86073e51i			1.34660i
$375$	−1.71189e51	−	8.41887e50i	−0.566046	−	0.278374i
$376$	−2.25758e50			−0.0707760
$377$		−	1.29477e51i		−	0.384917i
$378$	9.70646e48	+	4.79748e49i	0.00273668	+	0.0135262i
$379$	−6.62305e50			−0.177123			−0.0885613	−	0.996071i	$-0.528227\pi$
$379$	−6.62305e50			−0.177123			−0.0885613	+	0.996071i	$0.528227\pi$
$380$		−	2.06246e51i		−	0.523256i
$381$	1.27614e51	−	2.59491e51i	0.307185	−	0.624629i
$382$	1.14192e52			2.60837
$383$			5.12395e51i			1.11078i	0.831589	+	0.555391i	$0.187432\pi$
$383$			5.12395e51i			1.11078i	−0.831589	+	0.555391i	$0.812568\pi$
$384$	4.19436e50	+	2.06273e50i	0.0863060	+	0.0424442i
$385$	2.21152e49			0.00431993
$386$		−	8.47813e51i		−	1.57237i
$387$	−6.02923e51	−	7.82198e51i	−1.06180	−	1.37752i
$388$	−2.65257e51			−0.443641
$389$			2.31289e51i			0.367420i	0.982980	+	0.183710i	$0.0588107\pi$
$389$			2.31289e51i			0.367420i	−0.982980	+	0.183710i	$0.941189\pi$
$390$	1.08285e51	−	2.20188e51i	0.163410	−	0.332277i
$391$	5.91716e51			0.848356
$392$			3.53168e50i			0.0481127i
$393$	−9.42569e51	−	4.63543e51i	−1.22029	−	0.600122i
$394$	−9.45906e51			−1.16392
$395$			2.74630e51i			0.321223i
$396$	−9.03711e51	+	6.96586e51i	−1.00491	+	0.774589i
$397$	1.17777e52			1.24523			0.622616	−	0.782528i	$-0.286070\pi$
$397$	1.17777e52			1.24523			0.622616	+	0.782528i	$0.286070\pi$
$398$			7.00927e51i			0.704712i
$399$	−7.36928e49	+	1.49847e50i	−0.00704640	+	0.0143282i
$400$	−1.00921e52			−0.917867
$401$		−	4.24297e51i		−	0.367098i	−0.983011	−	0.183549i	$-0.941241\pi$
$401$		−	4.24297e51i		−	0.367098i	0.983011	−	0.183549i	$-0.0587587\pi$
$402$	2.02488e52	+	9.95809e51i	1.66678	+	0.819700i
$403$	−5.75091e51			−0.450438
$404$			1.47398e51i			0.109866i
$405$	4.55341e51	+	1.19876e51i	0.323025	+	0.0850420i
$406$	9.94912e49			0.00671837
$407$		−	1.15074e52i		−	0.739754i
$408$	2.53613e50	−	5.15697e50i	0.0155227	−	0.0315640i
$409$	2.21554e52			1.29126			0.645630	−	0.763651i	$-0.276595\pi$
$409$	2.21554e52			1.29126			0.645630	+	0.763651i	$0.276595\pi$
$410$			9.26460e51i			0.514221i
$411$	6.16789e51	+	3.03329e51i	0.326062	+	0.160353i
$412$	5.55201e50			0.0279580
$413$			9.14972e49i			0.00438942i
$414$	2.17319e52	+	2.81938e52i	0.993326	+	1.28868i
$415$	−5.50160e51			−0.239622
$416$		−	2.66749e52i		−	1.10723i
$417$	3.60820e51	−	7.33692e51i	0.142748	−	0.290264i
$418$	−7.92376e52			−2.98817
$419$			3.58632e52i			1.28934i	0.764460	+	0.644672i	$0.223006\pi$
$419$			3.58632e52i			1.28934i	−0.764460	+	0.644672i	$0.776994\pi$
$420$	8.31197e49	+	4.08772e49i	0.00284917	+	0.00140118i
$421$	2.87166e52			0.938621			0.469311	−	0.883033i	$-0.344502\pi$
$421$	2.87166e52			0.938621			0.469311	+	0.883033i	$0.344502\pi$
$422$		−	6.99634e52i		−	2.18083i
$423$	−3.91857e52	+	3.02046e52i	−1.16499	+	0.897978i
$424$	−1.38063e51			−0.0391526
$425$			2.40062e52i			0.649448i
$426$	4.24681e52	−	8.63547e52i	1.09615	−	2.22892i
$427$	−4.38935e50			−0.0108104
$428$			2.98464e52i			0.701481i
$429$	−4.15584e52	−	2.04379e52i	−0.932208	−	0.458448i
$430$	−3.80429e52			−0.814526
$431$		−	2.54987e52i		−	0.521162i	−0.965452	−	0.260581i	$-0.916086\pi$
$431$		−	2.54987e52i		−	0.521162i	0.965452	−	0.260581i	$-0.0839141\pi$
$432$	5.18947e52	−	1.04996e52i	1.01262	−	0.204878i
$433$	−5.65399e52			−1.05341			−0.526705	−	0.850048i	$-0.676573\pi$
$433$	−5.65399e52			−1.05341			−0.526705	+	0.850048i	$0.676573\pi$
$434$		−	4.41903e50i		−	0.00786199i
$435$	4.22367e51	−	8.58840e51i	0.0717636	−	0.145924i
$436$	1.05228e53			1.70766
$437$			1.21444e53i			1.88255i
$438$	−3.86055e51	−	1.89857e51i	−0.0571699	−	0.0281154i
$439$	7.68897e52			1.08787			0.543936	−	0.839127i	$-0.316933\pi$
$439$	7.68897e52			1.08787			0.543936	+	0.839127i	$0.316933\pi$
$440$		−	1.56207e51i		−	0.0211177i
$441$	4.72511e52	+	6.13008e52i	0.610436	+	0.791944i
$442$	−6.56324e52			−0.810350
$443$		−	7.92880e52i		−	0.935692i	−0.883810	−	0.467846i	$-0.845030\pi$
$443$		−	7.92880e52i		−	0.935692i	0.883810	−	0.467846i	$-0.154970\pi$
$444$	2.12699e52	−	4.32503e52i	0.239942	−	0.487898i
$445$	−1.00851e52			−0.108762
$446$			1.82967e53i			1.88658i
$447$	−9.37769e52	−	4.61183e52i	−0.924582	−	0.454697i
$448$	9.71135e50			0.00915629
$449$		−	1.28592e53i		−	1.15955i	−0.814777	−	0.579774i	$-0.803141\pi$
$449$		−	1.28592e53i		−	1.15955i	0.814777	−	0.579774i	$-0.196859\pi$
$450$	−1.14383e53	+	8.81674e52i	−0.986535	+	0.760428i
$451$	1.74861e53			1.44265
$452$			5.04051e51i			0.0397838i
$453$	−1.12660e53	+	2.29083e53i	−0.850756	+	1.72993i
$454$	−1.38302e53			−0.999336
$455$			3.75959e50i			0.00259963i
$456$	1.05842e52	+	5.20516e51i	0.0700423	+	0.0344459i
$457$	2.32780e53			1.47442			0.737209	−	0.675665i	$-0.236143\pi$
$457$	2.32780e53			1.47442			0.737209	+	0.675665i	$0.236143\pi$
$458$		−	5.96290e51i		−	0.0361533i
$459$	−2.49755e52	−	1.23443e53i	−0.144964	−	0.716494i
$460$	6.73645e52			0.374347
$461$		−	3.68046e53i		−	1.95832i	−0.203089	−	0.979160i	$-0.565098\pi$
$461$		−	3.68046e53i		−	1.95832i	0.203089	−	0.979160i	$-0.434902\pi$
$462$	1.57046e51	−	3.19337e51i	0.00800178	−	0.0162708i
$463$	−9.46582e52			−0.461890			−0.230945	−	0.972967i	$-0.574182\pi$
$463$	−9.46582e52			−0.461890			−0.230945	+	0.972967i	$0.574182\pi$
$464$		−	1.07620e53i		−	0.502962i
$465$	−3.81465e52	−	1.87600e52i	−0.170764	−	0.0839794i
$466$	1.28225e53			0.549862
$467$		−	3.32159e53i		−	1.36461i	−0.731068	−	0.682304i	$-0.760978\pi$
$467$		−	3.32159e53i		−	1.36461i	0.731068	−	0.682304i	$-0.239022\pi$
$468$	−1.18420e53	−	1.53631e53i	−0.466130	−	0.604730i
$469$	−3.45737e51			−0.0130404
$470$			1.90584e53i			0.688856i
$471$	4.58903e52	−	9.33134e52i	0.158965	−	0.323240i
$472$	6.46274e51			0.0214574
$473$			7.18025e53i			2.28516i
$474$	3.96558e53	+	1.95022e53i	1.20987	+	0.595000i
$475$	−4.92703e53			−1.44116
$476$		−	2.47759e51i		−	0.00694849i
$477$	−2.39642e53	+	1.84718e53i	−0.644459	+	0.496753i
$478$	−4.95824e53			−1.27870
$479$		−	2.50146e53i		−	0.618705i	−0.950947	−	0.309353i	$-0.899888\pi$
$479$		−	2.50146e53i		−	0.618705i	0.950947	−	0.309353i	$-0.100112\pi$
$480$	8.70159e52	−	1.76938e53i	0.206431	−	0.419756i
$481$	1.95625e53			0.445167
$482$			1.03724e54i			2.26432i
$483$	−4.89433e51	−	2.40697e51i	−0.0102506	−	0.00504113i
$484$	3.49017e53			0.701358
$485$		−	7.95831e52i		−	0.153457i
$486$	4.96447e53	−	5.72371e53i	0.918645	−	1.05914i
$487$	3.98927e53			0.708457			0.354229	−	0.935159i	$-0.384743\pi$
$487$	3.98927e53			0.708457			0.354229	+	0.935159i	$0.384743\pi$
$488$			3.10034e52i			0.0528460i
$489$	9.48871e52	−	1.92943e53i	0.155249	−	0.315684i
$490$	2.98142e53			0.468276
$491$			4.07385e53i			0.614292i	0.951662	+	0.307146i	$0.0993740\pi$
$491$			4.07385e53i			0.614292i	−0.951662	+	0.307146i	$0.900626\pi$
$492$	6.57212e53	+	3.23208e53i	0.951488	+	0.467930i
$493$	−2.55999e53			−0.355877
$494$		−	1.34704e54i		−	1.79821i
$495$	−2.08992e53	−	2.71134e53i	−0.267933	−	0.347600i
$496$	−4.78010e53			−0.588577
$497$			1.47446e52i			0.0174384i
$498$	−3.90683e53	+	7.94415e53i	−0.443851	+	0.902527i
$499$	−7.38488e53			−0.805995			−0.402998	−	0.915201i	$-0.632032\pi$
$499$	−7.38488e53			−0.805995			−0.402998	+	0.915201i	$0.632032\pi$
$500$			5.80925e53i			0.609144i
$501$	3.24538e53	+	1.59603e53i	0.326972	+	0.160801i
$502$	−1.65240e54			−1.59971
$503$		−	8.34228e53i		−	0.776114i	−0.921635	−	0.388057i	$-0.873146\pi$
$503$		−	8.34228e53i		−	0.776114i	0.921635	−	0.388057i	$-0.126854\pi$
$504$	−4.19548e50	+	3.23391e50i	−0.000375121	+	0.000289146i
$505$	−4.42228e52			−0.0380031
$506$		−	2.58807e54i		−	2.13779i
$507$	−2.08334e53	+	4.23626e53i	−0.165425	+	0.336375i
$508$	−8.80573e53			−0.672188
$509$			2.04133e54i			1.49816i	0.662480	+	0.749080i	$0.269504\pi$
$509$			2.04133e54i			1.49816i	−0.662480	+	0.749080i	$0.730496\pi$
$510$	−4.35348e53	−	2.14099e53i	−0.307209	−	0.151081i
$511$	6.59169e50			0.000447279
$512$		−	2.14101e54i		−	1.39707i
$513$	2.53355e54	−	5.12597e53i	1.58994	−	0.321684i
$514$	2.39286e54			1.44429
$515$			1.66573e52i			0.00967075i
$516$	−1.32718e54	+	2.69869e54i	−0.741201	+	1.50716i
$517$	3.59709e54			1.93259
$518$			1.50320e52i			0.00776999i
$519$	−1.45329e54	−	7.14707e53i	−0.722776	−	0.355452i
$520$	2.65551e52			0.0127081
$521$			2.09664e54i			0.965539i	0.875747	+	0.482770i	$0.160369\pi$
$521$			2.09664e54i			0.965539i	−0.875747	+	0.482770i	$0.839631\pi$
$522$	−9.40207e53	−	1.21977e54i	−0.416690	−	0.540590i
$523$	−7.49003e53			−0.319484			−0.159742	−	0.987159i	$-0.551066\pi$
$523$	−7.49003e53			−0.319484			−0.159742	+	0.987159i	$0.551066\pi$
$524$			3.19858e54i			1.31320i
$525$	9.76517e51	−	1.98565e52i	0.00385917	−	0.00784724i
$526$	2.53215e54			0.963330
$527$			1.13705e54i			0.416455i
$528$	−3.45429e54	−	1.69878e54i	−1.21809	−	0.599043i
$529$	−1.02143e54			−0.346812
$530$			1.16552e54i			0.381068i
$531$	1.12176e54	−	8.64662e53i	0.353192	−	0.272243i
$532$	5.08501e52			0.0154191
$533$			2.97263e54i			0.868155i
$534$	−7.16168e53	+	1.45626e54i	−0.201460	+	0.409649i
$535$	−8.95460e53			−0.242644
$536$			2.44205e53i			0.0637469i
$537$	−2.20932e54	−	1.08652e54i	−0.555614	−	0.273244i
$538$	5.30137e54			1.28453
$539$		−	5.62716e54i		−	1.31375i
$540$	−2.84336e53	−	1.40535e54i	−0.0639671	−	0.316162i
$541$	−2.63120e54			−0.570438			−0.285219	−	0.958462i	$-0.592066\pi$
$541$	−2.63120e54			−0.570438			−0.285219	+	0.958462i	$0.592066\pi$
$542$		−	6.59857e54i		−	1.37868i
$543$	2.28771e54	−	4.65183e54i	0.460686	−	0.936758i
$544$	−5.27408e54			−1.02369
$545$			3.15709e54i			0.590686i
$546$	5.42873e52	+	2.66978e52i	0.00979141	+	0.00481529i
$547$	−4.02299e54			−0.699523			−0.349762	−	0.936839i	$-0.613737\pi$
$547$	−4.02299e54			−0.699523			−0.349762	+	0.936839i	$0.613737\pi$
$548$		−	2.09305e54i		−	0.350888i
$549$	4.14800e54	+	5.38137e54i	0.670489	+	0.869854i
$550$	1.04999e55			1.63656
$551$		−	5.25412e54i		−	0.789711i
$552$	−1.70012e53	+	3.45702e53i	−0.0246432	+	0.0501095i
$553$	−6.77101e52			−0.00946566
$554$			7.28370e54i			0.982103i
$555$	1.29761e54	+	6.38147e53i	0.168766	+	0.0829967i
$556$	−2.48976e54			−0.312364
$557$		−	3.05699e54i		−	0.369991i	−0.982739	−	0.184995i	$-0.940773\pi$
$557$		−	3.05699e54i		−	0.369991i	0.982739	−	0.184995i	$-0.0592270\pi$
$558$	−5.41777e54	+	4.17605e54i	−0.632610	+	0.487620i
$559$	−1.22064e55			−1.37516
$560$			3.12493e52i			0.00339688i
$561$	−4.04091e54	+	8.21680e54i	−0.423860	+	0.861877i
$562$	4.68092e54			0.473811
$563$		−	1.63777e55i		−	1.59988i	−0.600083	−	0.799938i	$-0.704866\pi$
$563$		−	1.63777e55i		−	1.59988i	0.600083	−	0.799938i	$-0.295134\pi$
$564$	1.35196e55	+	6.64877e54i	1.27462	+	0.626843i
$565$	−1.51227e53			−0.0137613
$566$			1.82539e55i			1.60334i
$567$	−2.95556e52	+	1.12264e53i	−0.00250598	+	0.00951877i
$568$	1.04146e54			0.0852462
$569$			1.09842e55i			0.868010i	0.900910	+	0.434005i	$0.142900\pi$
$569$			1.09842e55i			0.868010i	−0.900910	+	0.434005i	$0.857100\pi$
$570$	4.39416e54	−	8.93509e54i	0.335258	−	0.681714i
$571$	−1.49352e55			−1.10024			−0.550120	−	0.835085i	$-0.685418\pi$
$571$	−1.49352e55			−1.10024			−0.550120	+	0.835085i	$0.685418\pi$
$572$			1.41027e55i			1.00319i
$573$	2.43035e55	+	1.19522e55i	1.66946	+	0.821021i
$574$	−2.28419e53			−0.0151528
$575$		−	1.60927e55i		−	1.03103i
$576$	−9.17738e54	−	1.19062e55i	−0.567896	−	0.736755i
$577$	7.87830e54			0.470887			0.235443	−	0.971888i	$-0.424346\pi$
$577$	7.87830e54			0.470887			0.235443	+	0.971888i	$0.424346\pi$
$578$		−	1.13070e55i		−	0.652814i
$579$	8.87381e54	−	1.80440e55i	0.494925	−	1.00638i
$580$	−2.91445e54			−0.157035
$581$		−	1.35642e53i		−	0.00706109i
$582$	−1.14916e55	−	5.65140e54i	−0.577989	−	0.284247i
$583$	2.19981e55			1.06909
$584$		−	4.65592e52i		−	0.00218649i
$585$	4.60928e54	−	3.55287e54i	0.209178	−	0.161236i
$586$	−4.66711e55			−2.04690
$587$		−	2.21712e54i		−	0.0939782i	−0.998895	−	0.0469891i	$-0.985037\pi$
$587$		−	2.21712e54i		−	0.0939782i	0.998895	−	0.0469891i	$-0.0149626\pi$
$588$	1.04011e55	−	2.11496e55i	0.426121	−	0.866475i
$589$	−2.33369e55			−0.924138
$590$		−	5.45580e54i		−	0.208842i
$591$	−2.01317e55	−	9.90053e54i	−0.744958	−	0.366361i
$592$	1.62602e55			0.581690
$593$			4.82567e55i			1.66903i	0.550987	+	0.834514i	$0.314251\pi$
$593$			4.82567e55i			1.66903i	−0.550987	+	0.834514i	$0.685749\pi$
$594$	−5.39920e55	+	1.09239e55i	−1.80551	+	0.365299i
$595$	7.43334e52			0.00240350
$596$			3.18229e55i			0.994979i
$597$	−7.33641e54	+	1.49179e55i	−0.221818	+	0.451045i
$598$	4.39972e55			1.28648
$599$		−	6.29039e55i		−	1.77886i	−0.457075	−	0.889428i	$-0.651103\pi$
$599$		−	6.29039e55i		−	1.77886i	0.457075	−	0.889428i	$-0.348897\pi$
$600$	−1.40253e54	−	6.89745e53i	−0.0383607	−	0.0188653i
$601$	1.93988e55			0.513198			0.256599	−	0.966518i	$-0.417398\pi$
$601$	1.93988e55			0.513198			0.256599	+	0.966518i	$0.417398\pi$
$602$		−	9.37950e53i		−	0.0240021i
$603$	3.26727e55	+	4.23877e55i	0.808796	+	1.04928i
$604$	7.77384e55			1.86164
$605$			1.04713e55i			0.242602i
$606$	−3.14038e54	+	6.38564e54i	−0.0703930	+	0.143137i
$607$	−1.78014e55			−0.386082			−0.193041	−	0.981191i	$-0.561835\pi$
$607$	−1.78014e55			−0.386082			−0.193041	+	0.981191i	$0.561835\pi$
$608$		−	1.08245e56i		−	2.27163i
$609$	2.11747e53	+	1.04135e53i	0.00430004	+	0.00211470i
$610$	2.61728e55			0.514345
$611$			6.11505e55i			1.16299i
$612$	−3.03754e55	+	2.34136e55i	−0.559106	+	0.430963i
$613$	2.54745e55			0.453833			0.226916	−	0.973914i	$-0.427136\pi$
$613$	2.54745e55			0.453833			0.226916	+	0.973914i	$0.427136\pi$
$614$			1.85278e55i			0.319490i
$615$	−9.69700e54	+	1.97179e55i	−0.161858	+	0.329123i
$616$	3.85128e52			0.000622287
$617$			5.04493e55i			0.789137i	0.918867	+	0.394568i	$0.129106\pi$
$617$			5.04493e55i			0.789137i	−0.918867	+	0.394568i	$0.870894\pi$
$618$	2.40526e54	+	1.18288e54i	0.0364245	+	0.0179131i
$619$	−1.10845e56			−1.62519			−0.812595	−	0.582829i	$-0.801946\pi$
$619$	−1.10845e56			−1.62519			−0.812595	+	0.582829i	$0.801946\pi$
$620$			1.29449e55i			0.183766i
$621$	1.67425e55	+	8.27511e55i	0.230139	+	1.13747i
$622$	−6.13121e55			−0.816090
$623$		−	2.48648e53i		−	0.00320497i
$624$	2.88792e55	−	5.87230e55i	0.360490	−	0.733021i
$625$	5.60595e55			0.677718
$626$		−	1.32112e56i		−	1.54687i
$627$	−1.68642e56	−	8.29358e55i	−1.91256	−	0.940570i
$628$	−3.16656e55			−0.347852
$629$		−	3.86784e55i		−	0.411582i
$630$	2.73004e53	+	3.54180e53i	0.00281422	+	0.00365101i
$631$	6.65827e55			0.664927			0.332464	−	0.943116i	$-0.392120\pi$
$631$	6.65827e55			0.664927			0.332464	+	0.943116i	$0.392120\pi$
$632$			4.78258e54i			0.0462723i
$633$	7.32288e55	−	1.48903e56i	0.686448	−	1.39582i
$634$	−4.67098e55			−0.424251
$635$		−	2.64192e55i		−	0.232512i
$636$	8.26797e55	+	4.06608e55i	0.705110	+	0.346764i
$637$	9.56618e55			0.790587
$638$			1.11970e56i			0.896783i
$639$	1.80770e56	−	1.39339e56i	1.40317	−	1.08157i
$640$	4.27035e54			0.0321266
$641$			9.15350e55i			0.667462i	0.942668	+	0.333731i	$0.108308\pi$
$641$			9.15350e55i			0.667462i	−0.942668	+	0.333731i	$0.891692\pi$
$642$	−6.35889e55	+	1.29302e56i	−0.449449	+	0.913911i
$643$	5.36382e54			0.0367498			0.0183749	−	0.999831i	$-0.494151\pi$
$643$	5.36382e54			0.0367498			0.0183749	+	0.999831i	$0.494151\pi$
$644$			1.66087e54i			0.0110311i
$645$	−8.09669e55	−	3.98185e55i	−0.521331	−	0.256384i
$646$	−2.66333e56			−1.66255
$647$			7.57259e55i			0.458309i	0.973390	+	0.229155i	$0.0735962\pi$
$647$			7.57259e55i			0.458309i	−0.973390	+	0.229155i	$0.926404\pi$
$648$	7.92959e54	+	2.08760e54i	0.0465319	+	0.0122503i
$649$	−1.02973e56			−0.585909
$650$			1.78499e56i			0.984845i
$651$	4.62527e53	−	9.40503e53i	0.00247467	−	0.00503200i
$652$	−6.54747e55			−0.339720
$653$		−	1.47287e56i		−	0.741140i	−0.928804	−	0.370570i	$-0.879162\pi$
$653$		−	1.47287e56i		−	0.741140i	0.928804	−	0.370570i	$-0.120838\pi$
$654$	4.55874e56	+	2.24193e56i	2.22479	+	1.09412i
$655$	−9.59647e55			−0.454240
$656$			2.47083e56i			1.13440i
$657$	−6.22924e54	−	8.08146e54i	−0.0277414	−	0.0359900i
$658$	−4.69884e54			−0.0202989
$659$			3.56702e55i			0.149485i	0.997203	+	0.0747425i	$0.0238135\pi$
$659$			3.56702e55i			0.149485i	−0.997203	+	0.0747425i	$0.976187\pi$
$660$	−4.60042e55	+	9.35450e55i	−0.187033	+	0.380314i
$661$	1.95144e56			0.769707			0.384854	−	0.922978i	$-0.374252\pi$
$661$	1.95144e56			0.769707			0.384854	+	0.922978i	$0.374252\pi$
$662$		−	4.13285e56i		−	1.58157i
$663$	−1.39686e56	−	6.86956e55i	−0.518658	−	0.255069i
$664$	−9.58083e54			−0.0345177
$665$			1.52562e54i			0.00533351i
$666$	1.84293e56	−	1.42054e56i	0.625208	−	0.481914i
$667$	1.71611e56			0.564974
$668$		−	1.10131e56i		−	0.351868i
$669$	−1.91506e56	+	3.89408e56i	−0.593827	+	1.20749i
$670$	2.06157e56			0.620442
$671$		−	4.93988e56i		−	1.44300i
$672$	4.36242e54	+	2.14538e54i	0.0123692	+	0.00608301i
$673$	−3.95837e56			−1.08947			−0.544735	−	0.838609i	$-0.683370\pi$
$673$	−3.95837e56			−1.08947			−0.544735	+	0.838609i	$0.683370\pi$
$674$		−	2.94183e56i		−	0.785995i
$675$	−3.35725e56	+	6.79252e55i	−0.870779	+	0.176180i
$676$	1.43756e56			0.361986
$677$		−	1.03199e56i		−	0.252292i	−0.992012	−	0.126146i	$-0.959739\pi$
$677$		−	1.03199e56i		−	0.252292i	0.992012	−	0.126146i	$-0.0402607\pi$
$678$	−1.07390e55	+	2.18367e55i	−0.0254901	+	0.0518315i
$679$	1.96212e54			0.00452200
$680$		−	5.25040e54i		−	0.0117494i
$681$	−2.94349e56	−	1.44757e56i	−0.639617	−	0.314555i
$682$	4.97329e56			1.04944
$683$			6.20211e56i			1.27094i	0.772125	+	0.635471i	$0.219194\pi$
$683$			6.20211e56i			1.27094i	−0.772125	+	0.635471i	$0.780806\pi$
$684$	−4.80541e56	−	6.23426e56i	−0.956331	−	1.24069i
$685$	6.27964e55			0.121373
$686$			1.47021e55i			0.0275993i
$687$	6.24120e54	−	1.26909e55i	0.0113798	−	0.0231396i
$688$	−1.01459e57			−1.79689
$689$			3.73969e56i			0.643355i
$690$	2.91839e56	+	1.43523e56i	0.487711	+	0.239850i
$691$	7.95190e56			1.29095			0.645476	−	0.763780i	$-0.276659\pi$
$691$	7.95190e56			1.29095			0.645476	+	0.763780i	$0.276659\pi$
$692$			4.93167e56i			0.777808i
$693$	6.68482e54	−	5.15270e54i	0.0102429	−	0.00789533i
$694$	3.06703e55			0.0456593
$695$		−	7.46985e55i		−	0.108048i
$696$	7.35536e54	−	1.49564e55i	0.0103376	−	0.0210204i
$697$	5.87740e56			0.802657
$698$			7.68457e56i			1.01979i
$699$	2.72901e56	+	1.34209e56i	0.351935	+	0.173077i
$700$	−6.73824e54			−0.00844472
$701$		−	3.53553e56i		−	0.430620i	−0.976546	−	0.215310i	$-0.930924\pi$
$701$		−	3.53553e56i		−	0.430620i	0.976546	−	0.215310i	$-0.0690762\pi$
$702$	−1.85706e56	−	9.17865e56i	−0.219829	−	1.08652i
$703$	7.93837e56			0.913324
$704$			1.09294e57i			1.22220i
$705$	−1.99478e56	+	4.05619e56i	−0.216827	+	0.440896i
$706$	6.54395e56			0.691426
$707$		−	1.09031e54i		−	0.00111986i
$708$	−3.87023e56	−	1.90333e56i	−0.386431	−	0.190042i
$709$	5.27547e55			0.0512079			0.0256039	−	0.999672i	$-0.491849\pi$
$709$	5.27547e55			0.0512079			0.0256039	+	0.999672i	$0.491849\pi$
$710$		−	8.79193e56i		−	0.829693i
$711$	6.39871e56	+	8.30131e56i	0.587084	+	0.761649i
$712$	−1.75628e55			−0.0156673
$713$		−	7.62233e56i		−	0.661145i
$714$	5.27861e54	−	1.07335e55i	0.00445200	−	0.00905270i
$715$	−4.23113e56			−0.347005
$716$			7.49726e56i			0.597919i
$717$	−1.05526e57	−	5.18965e56i	−0.818424	−	0.402490i
$718$	−3.46980e57			−2.61707
$719$		−	1.10786e57i		−	0.812660i	−0.913726	−	0.406330i	$-0.866808\pi$
$719$		−	1.10786e57i		−	0.812660i	0.913726	−	0.406330i	$-0.133192\pi$
$720$	3.83119e56	−	2.95311e56i	0.273328	−	0.210683i
$721$	−4.10686e53			−0.000284974
$722$		−	3.38891e57i		−	2.28726i
$723$	−1.08565e57	+	2.20756e57i	−0.712728	+	1.44926i
$724$	−1.57858e57			−1.00808
$725$			6.96233e56i			0.432509i
$726$	1.51203e57	+	7.43596e56i	0.913750	+	0.449371i
$727$	2.26670e57			1.33262			0.666308	−	0.745677i	$-0.267874\pi$
$727$	2.26670e57			1.33262			0.666308	+	0.745677i	$0.267874\pi$
$728$			6.54718e53i			0.000374478i
$729$	1.65567e57	−	6.98562e56i	0.921349	−	0.388735i
$730$	−3.93050e55			−0.0212809
$731$			2.41342e57i			1.27141i
$732$	9.13075e56	−	1.85665e57i	0.468042	−	0.951717i
$733$	−2.19626e57			−1.09548			−0.547740	−	0.836648i	$-0.684512\pi$
$733$	−2.19626e57			−1.09548			−0.547740	+	0.836648i	$0.684512\pi$
$734$		−	1.10245e57i		−	0.535104i
$735$	6.34537e56	+	3.12057e56i	0.299716	+	0.147397i
$736$	3.53553e57			1.62517
$737$		−	3.89101e57i		−	1.74066i
$738$	2.15859e57	+	2.80043e57i	0.939818	+	1.21927i
$739$	−3.97320e57			−1.68365			−0.841824	−	0.539752i	$-0.818518\pi$
$739$	−3.97320e57			−1.68365			−0.841824	+	0.539752i	$0.818518\pi$
$740$		−	4.40339e56i		−	0.181615i
$741$	1.40991e57	−	2.86691e57i	0.566013	−	1.15093i
$742$	−2.87360e55			−0.0112292
$743$			2.93565e57i			1.11668i	0.829613	+	0.558339i	$0.188561\pi$
$743$			2.93565e57i			1.11668i	−0.829613	+	0.558339i	$0.811439\pi$
$744$	−6.64307e55	−	3.26698e55i	−0.0245986	−	0.0120973i
$745$	−9.54759e56			−0.344166
$746$			5.04857e57i			1.77171i
$747$	−1.66298e57	+	1.28184e57i	−0.568166	+	0.437947i
$748$	2.78834e57			0.927500
$749$		−	2.20776e55i		−	0.00715015i
$750$	−1.23769e57	+	2.51671e57i	−0.390288	+	0.793612i
$751$	−3.66179e56			−0.112433			−0.0562166	−	0.998419i	$-0.517904\pi$
$751$	−3.66179e56			−0.112433			−0.0562166	+	0.998419i	$0.517904\pi$
$752$			5.08277e57i			1.51965i
$753$	−3.51681e57	−	1.72952e57i	−1.02388	−	0.503531i
$754$	−1.90349e57			−0.539664
$755$			2.33233e57i			0.643949i
$756$	3.46489e55	−	7.01032e54i	0.00931652	−	0.00188496i
$757$	1.69184e57			0.443039			0.221520	−	0.975156i	$-0.428898\pi$
$757$	1.69184e57			0.443039			0.221520	+	0.975156i	$0.428898\pi$
$758$			9.73676e56i			0.248331i
$759$	2.70886e57	−	5.50820e57i	0.672901	−	1.36828i
$760$	1.07759e56			0.0260725
$761$		−	1.28568e57i		−	0.302999i	−0.988457	−	0.151499i	$-0.951590\pi$
$761$		−	1.28568e57i		−	0.302999i	0.988457	−	0.151499i	$-0.0484102\pi$
$762$	−3.81486e57	−	1.87610e57i	−0.875747	−	0.430681i
$763$	−7.78380e55			−0.0174061
$764$		−	8.24732e57i		−	1.79658i
$765$	−7.02462e56	−	9.11333e56i	−0.149071	−	0.193396i
$766$	7.53288e57			1.55735
$767$		−	1.75055e57i		−	0.352587i
$768$	2.39521e57	−	4.87042e57i	0.470023	−	0.955744i
$769$	3.55428e57			0.679555			0.339777	−	0.940506i	$-0.389648\pi$
$769$	3.55428e57			0.679555			0.339777	+	0.940506i	$0.389648\pi$
$770$		−	3.25123e55i		−	0.00605665i
$771$	5.09273e57	+	2.50454e57i	0.924407	+	0.454611i
$772$	−6.12317e57			−1.08301
$773$		−	9.17318e57i		−	1.58099i	−0.612466	−	0.790497i	$-0.709822\pi$
$773$		−	9.17318e57i		−	1.58099i	0.612466	−	0.790497i	$-0.290178\pi$
$774$	−1.14993e58	+	8.86377e57i	−1.93132	+	1.48867i
$775$	3.09241e57			0.506131
$776$		−	1.38591e56i		−	0.0221055i
$777$	−1.57335e55	+	3.19926e55i	−0.00244571	+	0.00497312i
$778$	3.40025e57			0.515133
$779$			1.20628e58i			1.78114i
$780$	−1.59027e57	−	7.82072e56i	−0.228864	−	0.112552i
$781$	−1.65940e58			−2.32771
$782$		−	8.69900e57i		−	1.18942i
$783$	−7.24346e56	−	3.58013e57i	−0.0965408	−	0.477159i
$784$	7.95132e57			1.03304
$785$		−	9.50040e56i		−	0.120323i
$786$	−6.81470e57	+	1.38570e58i	−0.841387	+	1.71088i
$787$	−1.58399e57			−0.190659			−0.0953297	−	0.995446i	$-0.530391\pi$
$787$	−1.58399e57			−0.190659			−0.0953297	+	0.995446i	$0.530391\pi$
$788$			6.83164e57i			0.801679i
$789$	5.38919e57	+	2.65033e57i	0.616572	+	0.303222i
$790$	4.03743e57			0.450363
$791$		−	3.72851e54i		−	0.000405513i
$792$	−3.63952e56	−	4.72170e56i	−0.0385958	−	0.0500720i
$793$	8.39780e57			0.868364
$794$		−	1.73148e58i		−	1.74585i
$795$	−1.21992e57	+	2.48058e57i	−0.119947	+	0.243900i
$796$	5.06232e57			0.485387
$797$			5.79622e57i			0.541974i	0.962583	+	0.270987i	$0.0873500\pi$
$797$			5.79622e57i			0.541974i	−0.962583	+	0.270987i	$0.912650\pi$
$798$	2.20295e56	+	1.08338e56i	0.0200885	+	0.00987925i
$799$	1.20905e58			1.07525
$800$			1.43438e58i			1.24413i
$801$	−3.04844e57	+	2.34976e57i	−0.257886	+	0.198780i
$802$	−6.23773e57			−0.514682
$803$			7.41845e56i			0.0597038i
$804$	7.19205e57	−	1.46243e58i	0.564588	−	1.14803i
$805$	−4.98300e55			−0.00381569
$806$			8.45459e57i			0.631527i
$807$	1.12829e58	+	5.54880e57i	0.822150	+	0.404323i
$808$	−7.70124e55			−0.00547436
$809$			7.60503e57i			0.527389i	0.964606	+	0.263694i	$0.0849410\pi$
$809$			7.60503e57i			0.527389i	−0.964606	+	0.263694i	$0.915059\pi$
$810$	1.76234e57	−	6.69411e57i	0.119231	−	0.452890i
$811$	−1.24011e57			−0.0818548			−0.0409274	−	0.999162i	$-0.513031\pi$
$811$	−1.24011e57			−0.0818548			−0.0409274	+	0.999162i	$0.513031\pi$
$812$		−	7.18557e55i		−	0.00462744i
$813$	6.90654e57	−	1.40438e58i	0.433960	−	0.882414i
$814$	−1.69173e58			−1.03716
$815$		−	1.96439e57i		−	0.117510i
$816$	−1.16105e58	−	5.70991e57i	−0.677718	−	0.333293i
$817$	−4.95331e58			−2.82133
$818$		−	3.25714e58i		−	1.81038i
$819$	8.75960e55	+	1.13642e56i	0.00475123	+	0.00616397i
$820$	6.69119e57			0.354182
$821$			2.11936e58i			1.09482i	0.836865	+	0.547409i	$0.184386\pi$
$821$			2.11936e58i			1.09482i	−0.836865	+	0.547409i	$0.815614\pi$
$822$	4.45933e57	−	9.06761e57i	0.224819	−	0.457148i
$823$	−1.61545e58			−0.794874			−0.397437	−	0.917630i	$-0.630100\pi$
$823$	−1.61545e58			−0.794874			−0.397437	+	0.917630i	$0.630100\pi$
$824$			2.90081e55i			0.00139308i
$825$	2.23470e58	+	1.09900e58i	1.04747	+	0.515131i
$826$	1.34513e56			0.00615408
$827$		−	9.15034e57i		−	0.408627i	−0.978906	−	0.204313i	$-0.934504\pi$
$827$		−	9.15034e57i		−	0.408627i	0.978906	−	0.204313i	$-0.0654962\pi$
$828$	2.03624e58	−	1.56955e58i	0.887612	−	0.684177i
$829$	1.73502e58			0.738269			0.369135	−	0.929376i	$-0.379654\pi$
$829$	1.73502e58			0.738269			0.369135	+	0.929376i	$0.379654\pi$
$830$			8.08808e57i			0.335957i
$831$	−7.62364e57	+	1.55019e58i	−0.309131	+	0.628587i
$832$	−1.85800e58			−0.735493
$833$		−	1.89140e58i		−	0.730941i
$834$	−1.07862e58	−	5.30454e57i	−0.406958	−	0.200137i
$835$	3.30418e57			0.121712
$836$			5.72280e58i			2.05818i
$837$	−1.59016e58	+	3.21728e57i	−0.558382	+	0.112974i
$838$	5.27236e58			1.80769
$839$		−	3.59646e58i		−	1.20403i	−0.798486	−	0.602014i	$-0.794365\pi$
$839$		−	3.59646e58i		−	1.20403i	0.798486	−	0.602014i	$-0.205635\pi$
$840$	−2.13575e54	+	4.34283e54i	−6.98175e−5	+	0.000141967i
$841$	2.39025e58			0.762999
$842$		−	4.22171e58i		−	1.31597i
$843$	9.96241e57	+	4.89939e57i	0.303259	+	0.149139i
$844$	−5.05298e58			−1.50210
$845$			4.31301e57i			0.125212i
$846$	4.44048e58	+	5.76082e58i	1.25899	+	1.63334i
$847$	−2.58171e56			−0.00714890
$848$			3.10839e58i			0.840657i
$849$	−1.91058e58	+	3.88497e58i	−0.504674	+	1.02621i
$850$	3.52922e58			0.910543
$851$			2.59284e58i			0.653409i
$852$	−6.23681e58	−	3.06718e58i	−1.53522	−	0.755002i
$853$	6.51802e58			1.56724			0.783619	−	0.621242i	$-0.213371\pi$
$853$	6.51802e58			1.56724			0.783619	+	0.621242i	$0.213371\pi$
$854$			6.45292e56i			0.0151565i
$855$	1.87042e58	−	1.44173e58i	0.429158	−	0.330798i
$856$	−1.55941e57			−0.0349530
$857$		−	6.66361e58i		−	1.45913i	−0.683913	−	0.729564i	$-0.739723\pi$
$857$		−	6.66361e58i		−	1.45913i	0.683913	−	0.729564i	$-0.260277\pi$
$858$	−3.00464e58	+	6.10963e58i	−0.642756	+	1.30698i
$859$	−8.25379e58			−1.72500			−0.862502	−	0.506053i	$-0.831104\pi$
$859$	−8.25379e58			−1.72500			−0.862502	+	0.506053i	$0.831104\pi$
$860$			2.74758e58i			0.561025i
$861$	−4.86145e56	−	2.39080e56i	−0.00969845	−	0.00476957i
$862$	−3.74865e58			−0.730683
$863$		−	3.26696e58i		−	0.622197i	−0.950378	−	0.311098i	$-0.899303\pi$
$863$		−	3.26696e58i		−	0.622197i	0.950378	−	0.311098i	$-0.100697\pi$
$864$	−1.49230e58	−	7.37577e58i	−0.277703	−	1.37256i
$865$	−1.47962e58			−0.269046
$866$			8.31212e58i			1.47691i
$867$	1.18347e58	−	2.40647e58i	0.205482	−	0.417828i
$868$	−3.19157e56			−0.00541513
$869$		−	7.62027e58i		−	1.26350i
$870$	−1.26261e58	−	6.20935e57i	−0.204590	−	0.100615i
$871$	6.61473e58			1.04749
$872$			5.49795e57i			0.0850885i
$873$	−1.85424e58	−	2.40558e58i	−0.280466	−	0.363860i
$874$	1.78538e59			2.63939
$875$		−	4.29715e56i		−	0.00620897i
$876$	−1.37121e57	+	2.78821e57i	−0.0193652	+	0.0393771i
$877$	−1.90902e58			−0.263524			−0.131762	−	0.991281i	$-0.542063\pi$
$877$	−1.90902e58			−0.263524			−0.131762	+	0.991281i	$0.542063\pi$
$878$		−	1.13038e59i		−	1.52523i
$879$	−9.93303e58	−	4.88494e58i	−1.31010	−	0.644290i
$880$	−3.51688e58			−0.453423
$881$			1.22884e59i			1.54874i	0.632733	+	0.774370i	$0.281933\pi$
$881$			1.22884e59i			1.54874i	−0.632733	+	0.774370i	$0.718067\pi$
$882$	9.01203e58	−	6.94653e58i	1.11033	−	0.855847i
$883$	2.29805e58			0.276787			0.138393	−	0.990377i	$-0.455806\pi$
$883$	2.29805e58			0.276787			0.138393	+	0.990377i	$0.455806\pi$
$884$			4.74018e58i			0.558148i
$885$	5.71043e57	−	1.16116e58i	0.0657361	−	0.133668i
$886$	−1.16564e59			−1.31187
$887$		−	1.96194e58i		−	0.215881i	−0.994157	−	0.107940i	$-0.965574\pi$
$887$		−	1.96194e58i		−	0.215881i	0.994157	−	0.107940i	$-0.0344255\pi$
$888$	2.25974e57	+	1.11131e57i	0.0243108	+	0.0119557i
$889$	6.51366e56			0.00685157
$890$			1.48264e58i			0.152488i
$891$	−1.26345e59	−	3.32626e58i	−1.27059	−	0.334504i
$892$	1.32144e59			1.29943
$893$			2.48146e59i			2.38604i
$894$	−6.77999e58	+	1.37864e59i	−0.637498	+	1.29629i
$895$	−2.24935e58			−0.206822
$896$			1.05286e56i			0.000946692i
$897$	9.36394e58	+	4.60507e58i	0.823398	+	0.404937i
$898$	−1.89048e59			−1.62572
$899$			3.29771e58i			0.277344i
$900$	6.36774e58	+	8.26113e58i	0.523763	+	0.679500i
$901$	7.39399e58			0.594817
$902$		−	2.57068e59i		−	2.02264i
$903$	9.81725e56	−	1.99624e57i	0.00755501	−	0.0153624i
$904$	−2.63356e56			−0.00198233
$905$		−	4.73612e58i		−	0.348699i
$906$	3.36782e59	+	1.65625e59i	2.42541	+	1.19278i
$907$	−1.32909e59			−0.936284			−0.468142	−	0.883653i	$-0.655076\pi$
$907$	−1.32909e59			−0.936284			−0.468142	+	0.883653i	$0.655076\pi$
$908$			9.98862e58i			0.688317i
$909$	−1.33673e58	+	1.03036e58i	−0.0901089	+	0.0694565i
$910$	5.52709e56			0.00364476
$911$		−	9.58216e56i		−	0.00618153i	−0.999995	−	0.00309077i	$-0.999016\pi$
$911$		−	9.58216e56i		−	0.00618153i	0.999995	−	0.00309077i	$-0.000983823\pi$
$912$	1.17190e59	−	2.38295e59i	0.739597	−	1.50390i
$913$	1.52655e59			0.942530
$914$		−	3.42217e59i		−	2.06717i
$915$	5.57037e58	+	2.73944e58i	0.329202	+	0.161897i
$916$	−4.30660e57			−0.0249015
$917$		−	2.36601e57i		−	0.0133854i
$918$	−1.81477e59	+	3.67173e58i	−1.00454	+	0.203244i
$919$	8.88524e58			0.481237			0.240619	−	0.970620i	$-0.422650\pi$
$919$	8.88524e58			0.481237			0.240619	+	0.970620i	$0.422650\pi$
$920$			3.51965e57i			0.0186528i
$921$	−1.93926e58	+	3.94329e58i	−0.100564	+	0.204487i
$922$	−5.41076e59			−2.74562
$923$		−	2.82097e59i		−	1.40076i
$924$	−2.30635e57	−	1.13423e57i	−0.0112069	−	0.00551142i
$925$	−1.05193e59			−0.500209
$926$			1.39160e59i			0.647582i
$927$	3.88105e57	+	5.03505e57i	0.0176748	+	0.0229302i
$928$	−1.52960e59			−0.681741
$929$			3.17122e59i			1.38329i	0.722239	+	0.691643i	$0.243113\pi$
$929$			3.17122e59i			1.38329i	−0.722239	+	0.691643i	$0.756887\pi$
$930$	−2.75796e58	+	5.60804e58i	−0.117741	+	0.239416i
$931$	3.88190e59			1.62200
$932$		−	9.26081e58i		−	0.378731i
$933$	−1.30491e59	−	6.41736e58i	−0.522332	−	0.256876i
$934$	−4.88317e59			−1.91322
$935$			8.36567e58i			0.320825i
$936$	8.02689e57	−	6.18718e57i	0.0301322	−	0.0232261i
$937$	3.88543e59			1.42773			0.713866	−	0.700282i	$-0.246942\pi$
$937$	3.88543e59			1.42773			0.713866	+	0.700282i	$0.246942\pi$
$938$			5.08279e57i			0.0182829i
$939$	1.38278e59	−	2.81174e59i	0.486900	−	0.990063i
$940$	1.37646e59			0.474466
$941$			1.95897e59i			0.661051i	0.943797	+	0.330525i	$0.107226\pi$
$941$			1.95897e59i			0.661051i	−0.943797	+	0.330525i	$0.892774\pi$
$942$	−1.37183e59	−	6.74648e58i	−0.453192	−	0.222874i
$943$	−3.93997e59			−1.27426
$944$		−	1.45504e59i		−	0.460717i
$945$	2.10326e56	+	1.03955e57i	0.000652013	+	0.00322261i
$946$	1.05559e60			3.20386
$947$		−	4.05743e59i		−	1.20573i	−0.797842	−	0.602866i	$-0.794025\pi$
$947$		−	4.05743e59i		−	1.20573i	0.797842	−	0.602866i	$-0.205975\pi$
$948$	1.40851e59	−	2.86407e59i	0.409820	−	0.833329i
$949$	−1.26114e58			−0.0359284
$950$			7.24338e59i			2.02055i
$951$	−9.94125e58	−	4.88898e58i	−0.271538	−	0.133539i
$952$	1.29449e56			0.000346226
$953$			4.59879e59i			1.20444i	0.798330	+	0.602220i	$0.205717\pi$
$953$			4.59879e59i			1.20444i	−0.798330	+	0.602220i	$0.794283\pi$
$954$	2.71559e59	+	3.52305e59i	0.696461	+	0.903549i
$955$	2.47439e59			0.621441
$956$			3.58100e59i			0.880738i
$957$	−1.17196e59	+	2.38306e59i	−0.282275	+	0.573979i
$958$	−3.67748e59			−0.867442
$959$			1.54825e57i			0.00357658i
$960$	−1.23244e59	−	6.06096e58i	−0.278830	−	0.137125i
$961$	−3.04830e59			−0.675446
$962$		−	2.87595e59i		−	0.624137i
$963$	−2.70673e59	+	2.08636e59i	−0.575333	+	0.443470i
$964$	7.49128e59			1.55961
$965$		−	1.83709e59i		−	0.374615i
$966$	−3.53856e57	+	7.19531e57i	−0.00706780	+	0.0143717i
$967$	−6.05101e59			−1.18386			−0.591928	−	0.805991i	$-0.701633\pi$
$967$	−6.05101e59			−1.18386			−0.591928	+	0.805991i	$0.701633\pi$
$968$			1.82354e58i			0.0349469i
$969$	−5.66837e59	−	2.78763e59i	−1.06410	−	0.523310i
$970$	−1.16998e59			−0.215151
$971$		−	4.08611e59i		−	0.736081i	−0.929810	−	0.368040i	$-0.880029\pi$
$971$		−	4.08611e59i		−	0.736081i	0.929810	−	0.368040i	$-0.119971\pi$
$972$	−4.13385e59	−	3.58550e59i	−0.729506	−	0.632739i
$973$	1.84169e57			0.00318391
$974$		−	5.86475e59i		−	0.993277i
$975$	−1.86830e59	+	3.79899e59i	−0.309994	+	0.630342i
$976$	6.98018e59			1.13467
$977$		−	5.00416e59i		−	0.796966i	−0.917176	−	0.398483i	$-0.869537\pi$
$977$		−	5.00416e59i		−	0.796966i	0.917176	−	0.398483i	$-0.130463\pi$
$978$	−2.83652e59	−	1.39497e59i	−0.442598	−	0.217664i
$979$	2.79835e59			0.427807
$980$		−	2.15328e59i		−	0.322537i
$981$	7.35581e59	+	9.54301e59i	1.07957	+	1.40057i
$982$	5.98909e59			0.861254
$983$		−	3.00318e59i		−	0.423167i	−0.977360	−	0.211583i	$-0.932138\pi$
$983$		−	3.00318e59i		−	0.423167i	0.977360	−	0.211583i	$-0.0678620\pi$
$984$	−1.68870e58	+	3.43379e58i	−0.0233158	+	0.0474103i
$985$	−2.04965e59			−0.277303
$986$			3.76352e59i			0.498949i
$987$	−1.00006e58	−	4.91814e57i	−0.0129922	−	0.00638937i
$988$	−9.72875e59			−1.23856
$989$		−	1.61786e60i		−	2.01843i
$990$	−3.98603e59	+	3.07246e59i	−0.487345	+	0.375649i
$991$	8.35257e58			0.100080			0.0500400	−	0.998747i	$-0.484065\pi$
$991$	8.35257e58			0.100080			0.0500400	+	0.998747i	$0.484065\pi$
$992$			6.79394e59i			0.797789i
$993$	4.32573e59	−	8.79595e59i	0.497823	−	1.01227i
$994$	2.16765e58			0.0244490
$995$			1.51881e59i			0.167897i
$996$	5.73752e59	+	2.82164e59i	0.621637	+	0.305713i
$997$	6.98796e58			0.0742074			0.0371037	−	0.999311i	$-0.488187\pi$
$997$	6.98796e58			0.0742074			0.0371037	+	0.999311i	$0.488187\pi$
$998$			1.08567e60i			1.13003i
$999$	5.40915e59	−	1.09440e59i	0.551848	−	0.111652i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.41.b.a.2.2	✓	12
3.2	odd	2	inner	3.41.b.a.2.11	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.41.b.a.2.2	✓	12	1.1	even	1	trivial
3.41.b.a.2.11	yes	12	3.2	odd	2	inner

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:	\( k \)	\(=\)	\( 41 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.47013e6i q^{2} +(1.53875e9 - 3.12889e9i) q^{3} -1.06178e12 q^{4} -3.18557e13i q^{5} +(-4.59988e15 - 2.26216e15i) q^{6} +7.85404e14 q^{7} -5.54756e16i q^{8} +(-7.42219e18 - 9.62912e18i) q^{9} +O(q^{10})\)	\(q-1.47013e6i q^{2} +(1.53875e9 - 3.12889e9i) q^{3} -1.06178e12 q^{4} -3.18557e13i q^{5} +(-4.59988e15 - 2.26216e15i) q^{6} +7.85404e14 q^{7} -5.54756e16i q^{8} +(-7.42219e18 - 9.62912e18i) q^{9} -4.68322e19 q^{10} +8.83914e20i q^{11} +(-1.63380e21 + 3.32218e21i) q^{12} -1.50265e22 q^{13} -1.15465e21i q^{14} +(-9.96730e22 - 4.90179e22i) q^{15} -1.24899e24 q^{16} +2.97100e24i q^{17} +(-1.41561e25 + 1.09116e25i) q^{18} -6.09769e25 q^{19} +3.38237e25i q^{20} +(1.20854e24 - 2.45744e24i) q^{21} +1.29947e27 q^{22} -1.99164e27i q^{23} +(-1.73577e26 - 8.53628e25i) q^{24} +8.08016e27 q^{25} +2.20910e28i q^{26} +(-4.15493e28 + 8.40642e27i) q^{27} -8.33924e26 q^{28} +8.61658e28i q^{29} +(-7.20628e28 + 1.46532e29i) q^{30} +3.82717e29 q^{31} +1.77519e30i q^{32} +(2.76567e30 + 1.36012e30i) q^{33} +4.36777e30 q^{34} -2.50196e28i q^{35} +(7.88071e30 + 1.02240e31i) q^{36} -1.30186e31 q^{37} +8.96441e31i q^{38} +(-2.31220e31 + 4.70163e31i) q^{39} -1.76722e30 q^{40} -1.97826e32i q^{41} +(-3.61276e30 - 1.77671e30i) q^{42} +8.12325e32 q^{43} -9.38519e32i q^{44} +(-3.06743e32 + 2.36439e32i) q^{45} -2.92797e33 q^{46} -4.06950e33i q^{47} +(-1.92188e33 + 3.90795e33i) q^{48} -6.36619e33 q^{49} -1.18789e34i q^{50} +(9.29593e33 + 4.57162e33i) q^{51} +1.59548e34 q^{52} -2.48872e34i q^{53} +(1.23586e34 + 6.10829e34i) q^{54} +2.81577e34 q^{55} -4.35708e31i q^{56} +(-9.38279e34 + 1.90790e35i) q^{57} +1.26675e35 q^{58} +1.16497e35i q^{59} +(1.05830e35 + 5.20460e34i) q^{60} -5.58865e35 q^{61} -5.62644e35i q^{62} +(-5.82942e33 - 7.56275e33i) q^{63} +1.23648e36 q^{64} +4.78682e35i q^{65} +(1.99955e36 - 4.06589e36i) q^{66} -4.40203e36 q^{67} -3.15454e36i q^{68} +(-6.23160e36 - 3.06462e36i) q^{69} -3.67822e34 q^{70} +1.87733e37i q^{71} +(-5.34181e35 + 4.11750e35i) q^{72} +8.39273e35 q^{73} +1.91391e37i q^{74} +(1.24333e37 - 2.52819e37i) q^{75} +6.47438e37 q^{76} +6.94230e35i q^{77} +(6.91202e37 + 3.39924e37i) q^{78} -8.62105e37 q^{79} +3.97876e37i q^{80} +(-3.76310e37 + 1.42938e38i) q^{81} -2.90830e38 q^{82} -1.72703e38i q^{83} +(-1.28320e36 + 2.60925e36i) q^{84} +9.46435e37 q^{85} -1.19423e39i q^{86} +(2.69603e38 + 1.32587e38i) q^{87} +4.90356e37 q^{88} -3.16586e38i q^{89} +(3.47597e38 + 4.50952e38i) q^{90} -1.18019e37 q^{91} +2.11467e39i q^{92} +(5.88904e38 - 1.19748e39i) q^{93} -5.98270e39 q^{94} +1.94246e39i q^{95} +(5.55436e39 + 2.73156e39i) q^{96} +2.49823e39 q^{97} +9.35914e39i q^{98} +(8.51131e39 - 6.56057e39i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 372082572 q^{3} - 4781373657072 q^{4} + 84\!\cdots\!52 q^{6}+ \cdots - 23\!\cdots\!20 q^{9}+O(q^{10}) \) 12 * q - 372082572 * q^3 - 4781373657072 * q^4 + 8471862485327952 * q^6 - 94341749124766584 * q^7 - 23605502262041939220 * q^9	\( 12 q - 372082572 q^{3} - 4781373657072 q^{4} + 84\!\cdots\!52 q^{6}+ \cdots + 54\!\cdots\!80 q^{99}+O(q^{100}) \) 12 * q - 372082572 * q^3 - 4781373657072 * q^4 + 8471862485327952 * q^6 - 94341749124766584 * q^7 - 23605502262041939220 * q^9 - 129384136354706290080 * q^10 - 4708039830028985428272 * q^12 + 704368845864154901976 * q^13 + 320935800901459838631840 * q^15 + 6054431850962872672227456 * q^16 + 10227710367381761273509920 * q^18 + 37616619688417835612151720 * q^19 - 179163719456723608834234728 * q^21 + 846315150249292772829325920 * q^22 - 18213480358094369517645250944 * q^24 + 8842265325510151276196474700 * q^25 - 70717074113738779393083858252 * q^27 + 469404222007499612173589889696 * q^28 - 207809636542026559976510503200 * q^30 - 914600368399753689553849145016 * q^31 + 157344642221562801276041757600 * q^33 - 14575908480758621487300381842304 * q^34 + 41100171486790863962401658870544 * q^36 + 5673106137824212681873457220696 * q^37 - 9206461430638842876438079090008 * q^39 + 50495897877443363581635475618560 * q^40 - 939238658319640212873301303645920 * q^42 + 1012654832326802922602871229857576 * q^43 + 196109968512215856818385626472000 * q^45 - 3082500781506234684371181468390336 * q^46 + 6532128822166367998693520969705088 * q^48 + 8498166150175390075155260408801892 * q^49 + 27565453699222767413826960590504832 * q^51 - 57328509042562386918101767400001504 * q^52 - 102847607224782098537542351912875792 * q^54 - 9637639495259752880102706884884800 * q^55 - 40307213604482059940636368892395464 * q^57 + 772129436848561910287203884295052320 * q^58 - 114385571579949295944121547557720320 * q^60 - 494443282701607071691140418439862696 * q^61 + 1379291076525018665154441723571240776 * q^63 - 6231783699524672226208093043936541696 * q^64 + 2652084094607847915810184973553481440 * q^66 + 5401062423529881431761320436868275176 * q^67 + 7110274695178254111533494284632123328 * q^69 + 516103243900107216646679160954379200 * q^70 - 27544975046740790141119542770107057920 * q^72 + 30000154498324943042431295514883418136 * q^73 + 43820294796704764666539599709819928500 * q^75 - 215478934792040263381331019050660960352 * q^76 + 234946633516471169601955850003339878560 * q^78 - 128704557118405295534397879672035334840 * q^79 + 473157359902659920298963194247360443532 * q^81 - 639159997421964256448917103585883414720 * q^82 + 1283288903941350744781821238287455403552 * q^84 - 1077142486191382871466217243736209678080 * q^85 + 1076668306862385320797179121273520148960 * q^87 - 2918662713596496795370587920448329114880 * q^88 + 6571793457940570799819318674019816438880 * q^90 - 9859184204686878150356379414618151910256 * q^91 + 11506410044121210986218054652959643683416 * q^93 - 16857264118330945289191940748512432348544 * q^94 + 53068562519213731340201280418423192237056 * q^96 - 41841010071967618660163746722085070705064 * q^97 + 54341076855402233475300783474292013590080 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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