LMFDB - Embedded newform 3.41.b.a.2.12

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			2.12
Root			$337096. i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.41.b.a.2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.02257e6i q^{2} +(8.90215e8 - 3.37123e9i) q^{3} -2.99130e12 q^{4} +2.53853e13i q^{5} +(6.81856e15 + 1.80053e15i) q^{6} -1.01945e17 q^{7} -3.82628e18i q^{8} +(-1.05727e19 - 6.00224e18i) q^{9} +O(q^{10})$	\(q+2.02257e6i q^{2} +(8.90215e8 - 3.37123e9i) q^{3} -2.99130e12 q^{4} +2.53853e13i q^{5} +(6.81856e15 + 1.80053e15i) q^{6} -1.01945e17 q^{7} -3.82628e18i q^{8} +(-1.05727e19 - 6.00224e18i) q^{9} -5.13437e19 q^{10} -6.18638e19i q^{11} +(-2.66290e21 + 1.00843e22i) q^{12} +1.20680e22 q^{13} -2.06191e23i q^{14} +(8.55798e22 + 2.25984e22i) q^{15} +4.44997e24 q^{16} +4.09644e24i q^{17} +(1.21400e25 - 2.13841e25i) q^{18} +4.08427e25 q^{19} -7.59351e25i q^{20} +(-9.07528e25 + 3.43679e26i) q^{21} +1.25124e26 q^{22} +8.86986e26i q^{23} +(-1.28993e28 - 3.40621e27i) q^{24} +8.45053e27 q^{25} +2.44084e28i q^{26} +(-2.96469e28 + 3.02997e28i) q^{27} +3.04947e29 q^{28} -2.80705e29i q^{29} +(-4.57070e28 + 1.73092e29i) q^{30} -2.42459e29 q^{31} +4.79335e30i q^{32} +(-2.08557e29 - 5.50721e28i) q^{33} -8.28536e30 q^{34} -2.58790e30i q^{35} +(3.16261e31 + 1.79545e31i) q^{36} +1.32707e31 q^{37} +8.26074e31i q^{38} +(1.07431e31 - 4.06840e31i) q^{39} +9.71314e31 q^{40} +3.75194e31i q^{41} +(-6.95117e32 - 1.83554e32i) q^{42} +2.31440e32 q^{43} +1.85053e32i q^{44} +(1.52369e32 - 2.68392e32i) q^{45} -1.79400e33 q^{46} -1.03290e33i q^{47} +(3.96143e33 - 1.50019e34i) q^{48} +4.02593e33 q^{49} +1.70918e34i q^{50} +(1.38100e34 + 3.64671e33i) q^{51} -3.60990e34 q^{52} +1.90627e33i q^{53} +(-6.12834e34 - 5.99630e34i) q^{54} +1.57043e33 q^{55} +3.90069e35i q^{56} +(3.63588e34 - 1.37690e35i) q^{57} +5.67746e35 q^{58} -4.23888e34i q^{59} +(-2.55995e35 - 6.75985e34i) q^{60} -1.01812e35 q^{61} -4.90391e35i q^{62} +(1.07783e36 + 6.11897e35i) q^{63} -4.80213e36 q^{64} +3.06350e35i q^{65} +(1.11387e35 - 4.21822e35i) q^{66} +3.65785e36 q^{67} -1.22537e37i q^{68} +(2.99023e36 + 7.89608e35i) q^{69} +5.23423e36 q^{70} -1.23734e37i q^{71} +(-2.29662e37 + 4.04541e37i) q^{72} +3.50080e37 q^{73} +2.68411e37i q^{74} +(7.52279e36 - 2.84887e37i) q^{75} -1.22173e38 q^{76} +6.30669e36i q^{77} +(8.22864e37 + 2.17287e37i) q^{78} +7.21191e37 q^{79} +1.12964e38i q^{80} +(7.57552e37 + 1.26920e38i) q^{81} -7.58859e37 q^{82} -1.60181e38i q^{83} +(2.71468e38 - 1.02805e39i) q^{84} -1.03990e38 q^{85} +4.68104e38i q^{86} +(-9.46320e38 - 2.49888e38i) q^{87} -2.36708e38 q^{88} +9.31547e38i q^{89} +(5.42842e38 + 3.08177e38i) q^{90} -1.23027e39 q^{91} -2.65324e39i q^{92} +(-2.15840e38 + 8.17383e38i) q^{93} +2.08911e39 q^{94} +1.03681e39i q^{95} +(1.61595e40 + 4.26711e39i) q^{96} -6.46310e39 q^{97} +8.14275e39i q^{98} +(-3.71321e38 + 6.54067e38i) 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 $

$2$			2.02257e6i			1.92888i	0.264306	+	0.964439i	$0.414857\pi$
$2$			2.02257e6i			1.92888i	−0.264306	+	0.964439i	$0.585143\pi$
$3$	8.90215e8	−	3.37123e9i	0.255311	−	0.966859i
$3$	8.90215e8	−	3.37123e9i	0.255311	−	0.966859i
$4$	−2.99130e12			−2.72057
$5$			2.53853e13i			0.266185i	0.991104	+	0.133092i	$0.0424907\pi$
$5$			2.53853e13i			0.266185i	−0.991104	+	0.133092i	$0.957509\pi$
$6$	6.81856e15	+	1.80053e15i	1.86495	+	0.492464i
$7$	−1.01945e17			−1.27763			−0.638814	−	0.769361i	$-0.720575\pi$
$7$	−1.01945e17			−1.27763			−0.638814	+	0.769361i	$0.720575\pi$
$8$		−	3.82628e18i		−	3.31877i
$9$	−1.05727e19	−	6.00224e18i	−0.869632	−	0.493700i
$10$	−5.13437e19			−0.513437
$11$		−	6.18638e19i		−	0.0919566i	−0.998942	−	0.0459783i	$-0.985359\pi$
$11$		−	6.18638e19i		−	0.0919566i	0.998942	−	0.0459783i	$-0.0146405\pi$
$12$	−2.66290e21	+	1.00843e22i	−0.694591	+	2.63041i
$13$	1.20680e22			0.634992			0.317496	−	0.948260i	$-0.397158\pi$
$13$	1.20680e22			0.634992			0.317496	+	0.948260i	$0.397158\pi$
$14$		−	2.06191e23i		−	2.46439i
$15$	8.55798e22	+	2.25984e22i	0.257363	+	0.0679599i
$16$	4.44997e24			3.68093
$17$			4.09644e24i			1.00793i	0.863725	+	0.503963i	$0.168125\pi$
$17$			4.09644e24i			1.00793i	−0.863725	+	0.503963i	$0.831875\pi$
$18$	1.21400e25	−	2.13841e25i	0.952286	−	1.67741i
$19$	4.08427e25			1.08653			0.543266	−	0.839561i	$-0.317188\pi$
$19$	4.08427e25			1.08653			0.543266	+	0.839561i	$0.317188\pi$
$20$		−	7.59351e25i		−	0.724173i
$21$	−9.07528e25	+	3.43679e26i	−0.326192	+	1.23529i
$22$	1.25124e26			0.177373
$23$			8.86986e26i			0.516845i	0.966032	+	0.258422i	$0.0832026\pi$
$23$			8.86986e26i			0.516845i	−0.966032	+	0.258422i	$0.916797\pi$
$24$	−1.28993e28	−	3.40621e27i	−3.20878	−	0.847318i
$25$	8.45053e27			0.929146
$26$			2.44084e28i			1.22482i
$27$	−2.96469e28	+	3.02997e28i	−0.699365	+	0.714765i
$28$	3.04947e29			3.47587
$29$		−	2.80705e29i		−	1.58595i	−0.609253	−	0.792976i	$-0.708531\pi$
$29$		−	2.80705e29i		−	1.58595i	0.609253	−	0.792976i	$-0.291469\pi$
$30$	−4.57070e28	+	1.73092e29i	−0.131086	+	0.496422i
$31$	−2.42459e29			−0.360914			−0.180457	−	0.983583i	$-0.557758\pi$
$31$	−2.42459e29			−0.360914			−0.180457	+	0.983583i	$0.557758\pi$
$32$			4.79335e30i			3.78129i
$33$	−2.08557e29	−	5.50721e28i	−0.0889090	−	0.0234775i
$34$	−8.28536e30			−1.94416
$35$		−	2.58790e30i		−	0.340085i
$36$	3.16261e31	+	1.79545e31i	2.36590	+	1.34314i
$37$	1.32707e31			0.573932			0.286966	−	0.957941i	$-0.407353\pi$
$37$	1.32707e31			0.573932			0.286966	+	0.957941i	$0.407353\pi$
$38$			8.26074e31i			2.09579i
$39$	1.07431e31	−	4.06840e31i	0.162120	−	0.613948i
$40$	9.71314e31			0.883405
$41$			3.75194e31i			0.208247i	0.994564	+	0.104124i	$0.0332037\pi$
$41$			3.75194e31i			0.208247i	−0.994564	+	0.104124i	$0.966796\pi$
$42$	−6.95117e32	−	1.83554e32i	−2.38271	−	0.629185i
$43$	2.31440e32			0.495529			0.247764	−	0.968820i	$-0.420304\pi$
$43$	2.31440e32			0.495529			0.247764	+	0.968820i	$0.420304\pi$
$44$			1.85053e32i			0.250174i
$45$	1.52369e32	−	2.68392e32i	0.131415	−	0.231483i
$46$	−1.79400e33			−0.996930
$47$		−	1.03290e33i		−	0.373336i	−0.982423	−	0.186668i	$-0.940231\pi$
$47$		−	1.03290e33i		−	0.373336i	0.982423	−	0.186668i	$-0.0597689\pi$
$48$	3.96143e33	−	1.50019e34i	0.939781	−	3.55894i
$49$	4.02593e33			0.632332
$50$			1.70918e34i			1.79221i
$51$	1.38100e34	+	3.64671e33i	0.974521	+	0.257334i
$52$	−3.60990e34			−1.72754
$53$			1.90627e33i			0.0623255i	0.999514	+	0.0311628i	$0.00992102\pi$
$53$			1.90627e33i			0.0623255i	−0.999514	+	0.0311628i	$0.990079\pi$
$54$	−6.12834e34	−	5.99630e34i	−1.37869	−	1.34899i
$55$	1.57043e33			0.0244774
$56$			3.90069e35i			4.24015i
$57$	3.63588e34	−	1.37690e35i	0.277404	−	1.05052i
$58$	5.67746e35			3.05911
$59$		−	4.23888e34i		−	0.162260i	−0.996704	−	0.0811298i	$-0.974147\pi$
$59$		−	4.23888e34i		−	0.162260i	0.996704	−	0.0811298i	$-0.0258528\pi$
$60$	−2.55995e35	−	6.75985e34i	−0.700174	−	0.184890i
$61$	−1.01812e35			−0.200080			−0.100040	−	0.994983i	$-0.531897\pi$
$61$	−1.01812e35			−0.200080			−0.100040	+	0.994983i	$0.531897\pi$
$62$		−	4.90391e35i		−	0.696159i
$63$	1.07783e36	+	6.11897e35i	1.11107	+	0.630764i
$64$	−4.80213e36			−3.61272
$65$			3.06350e35i			0.169025i
$66$	1.11387e35	−	4.21822e35i	0.0452853	−	0.171495i
$67$	3.65785e36			1.10085			0.550427	−	0.834884i	$-0.314465\pi$
$67$	3.65785e36			1.10085			0.550427	+	0.834884i	$0.314465\pi$
$68$		−	1.22537e37i		−	2.74213i
$69$	2.99023e36	+	7.89608e35i	0.499716	+	0.131956i
$70$	5.23423e36			0.655982
$71$		−	1.23734e37i		−	1.16767i	−0.811872	−	0.583836i	$-0.801551\pi$
$71$		−	1.23734e37i		−	1.16767i	0.811872	−	0.583836i	$-0.198449\pi$
$72$	−2.29662e37	+	4.04541e37i	−1.63847	+	2.88611i
$73$	3.50080e37			1.89544			0.947720	−	0.319102i	$-0.103381\pi$
$73$	3.50080e37			1.89544			0.947720	+	0.319102i	$0.103381\pi$
$74$			2.68411e37i			1.10705i
$75$	7.52279e36	−	2.84887e37i	0.237221	−	0.898353i
$76$	−1.22173e38			−2.95598
$77$			6.30669e36i			0.117486i
$78$	8.22864e37	+	2.17287e37i	1.18423	+	0.312711i
$79$	7.21191e37			0.804467			0.402234	−	0.915537i	$-0.368234\pi$
$79$	7.21191e37			0.804467			0.402234	+	0.915537i	$0.368234\pi$
$80$			1.12964e38i			0.979806i
$81$	7.57552e37	+	1.26920e38i	0.512521	+	0.858675i
$82$	−7.58859e37			−0.401683
$83$		−	1.60181e38i		−	0.665350i	−0.943042	−	0.332675i	$-0.892049\pi$
$83$		−	1.60181e38i		−	0.665350i	0.943042	−	0.332675i	$-0.107951\pi$
$84$	2.71468e38	−	1.02805e39i	0.887429	−	3.36068i
$85$	−1.03990e38			−0.268294
$86$			4.68104e38i			0.955814i
$87$	−9.46320e38	−	2.49888e38i	−1.53339	−	0.404911i
$88$	−2.36708e38			−0.305182
$89$			9.31547e38i			0.958087i	0.877791	+	0.479043i	$0.159016\pi$
$89$			9.31547e38i			0.958087i	−0.877791	+	0.479043i	$0.840984\pi$
$90$	5.42842e38	+	3.08177e38i	0.446502	+	0.253484i
$91$	−1.23027e39			−0.811283
$92$		−	2.65324e39i		−	1.40611i
$93$	−2.15840e38	+	8.17383e38i	−0.0921453	+	0.348953i
$94$	2.08911e39			0.720119
$95$			1.03681e39i			0.289218i
$96$	1.61595e40	+	4.26711e39i	3.65597	+	0.965405i
$97$	−6.46310e39			−1.18852			−0.594260	−	0.804273i	$-0.702555\pi$
$97$	−6.46310e39			−1.18852			−0.594260	+	0.804273i	$0.702555\pi$
$98$			8.14275e39i			1.21969i
$99$	−3.71321e38	+	6.54067e38i	−0.0453989	+	0.0799684i
$100$	−2.52781e40			−2.52781
$101$		−	2.05728e40i		−	1.68603i	−0.537887	−	0.843017i	$-0.680777\pi$
$101$		−	2.05728e40i		−	1.68603i	0.537887	−	0.843017i	$-0.319223\pi$
$102$	−7.37575e39	+	2.79318e40i	−0.496367	+	1.87973i
$103$	9.79661e39			0.542415			0.271207	−	0.962521i	$-0.412577\pi$
$103$	9.79661e39			0.542415			0.271207	+	0.962521i	$0.412577\pi$
$104$		−	4.61755e40i		−	2.10739i
$105$	−8.72441e39	−	2.30379e39i	−0.328814	−	0.0868274i
$106$	−3.85556e39			−0.120218
$107$			5.15185e40i			1.33134i	0.746248	+	0.665669i	$0.231854\pi$
$107$			5.15185e40i			1.33134i	−0.746248	+	0.665669i	$0.768146\pi$
$108$	8.86826e40	−	9.06354e40i	1.90267	−	1.94457i
$109$	8.82069e40			1.57388			0.786942	−	0.617027i	$-0.211663\pi$
$109$	8.82069e40			1.57388			0.786942	+	0.617027i	$0.211663\pi$
$110$			3.17632e39i			0.0472139i
$111$	1.18138e40	−	4.47387e40i	0.146531	−	0.554912i
$112$	−4.53651e41			−4.70285
$113$		−	7.42929e40i		−	0.644731i	−0.946615	−	0.322365i	$-0.895522\pi$
$113$		−	7.42929e40i		−	0.644731i	0.946615	−	0.322365i	$-0.104478\pi$
$114$	2.78488e41	+	7.35383e40i	2.02633	+	0.535077i
$115$	−2.25164e40			−0.137576
$116$			8.39671e41i			4.31469i
$117$	−1.27591e41	−	7.24350e40i	−0.552210	−	0.313495i
$118$	8.57344e40			0.312979
$119$		−	4.17611e41i		−	1.28775i
$120$	8.64678e40	−	3.27452e41i	0.225543	−	0.854128i
$121$	4.48765e41			0.991544
$122$		−	2.05923e41i		−	0.385930i
$123$	1.26487e41	+	3.34004e40i	0.201346	+	0.0531678i
$124$	7.25266e41			0.981891
$125$			4.45398e41i			0.513509i
$126$	−1.23761e42	+	2.18000e42i	−1.21667	+	2.14311i
$127$	−1.31824e42			−1.10642			−0.553211	−	0.833041i	$-0.686598\pi$
$127$	−1.31824e42			−1.10642			−0.553211	+	0.833041i	$0.686598\pi$
$128$		−	4.44231e42i		−	3.18720i
$129$	2.06031e41	−	7.80236e41i	0.126514	−	0.479106i
$130$	−6.19616e41			−0.326029
$131$		−	2.00843e42i		−	0.906631i	−0.891350	−	0.453315i	$-0.850241\pi$
$131$		−	2.00843e42i		−	0.906631i	0.891350	−	0.453315i	$-0.149759\pi$
$132$	6.23856e41	+	1.64737e41i	0.241883	+	0.0638722i
$133$	−4.16370e42			−1.38818
$134$			7.39827e42i			2.12341i
$135$	−7.69168e41	−	7.52596e41i	−0.190259	−	0.186160i
$136$	1.56741e43			3.34507
$137$		−	4.85421e42i		−	0.894762i	−0.894344	−	0.447381i	$-0.852357\pi$
$137$		−	4.85421e42i		−	0.894762i	0.894344	−	0.447381i	$-0.147643\pi$
$138$	−1.59704e42	+	6.04797e42i	−0.254527	+	0.963891i
$139$	−5.05668e42			−0.697541			−0.348770	−	0.937208i	$-0.613401\pi$
$139$	−5.05668e42			−0.697541			−0.348770	+	0.937208i	$0.613401\pi$
$140$			7.74119e42i			0.925224i
$141$	−3.48213e42	−	9.19500e41i	−0.360963	−	0.0953168i
$142$	2.50261e43			2.25230
$143$		−	7.46572e41i		−	0.0583917i
$144$	−4.70482e43	−	2.67097e43i	−3.20105	−	1.81727i
$145$	7.12579e42			0.422156
$146$			7.08063e43i			3.65607i
$147$	3.58395e42	−	1.35723e43i	0.161441	−	0.611376i
$148$	−3.96967e43			−1.56142
$149$		−	2.47258e43i		−	0.850010i	−0.905191	−	0.425005i	$-0.860272\pi$
$149$		−	2.47258e43i		−	0.850010i	0.905191	−	0.425005i	$-0.139728\pi$
$150$	5.76205e43	+	1.52154e43i	1.73281	+	0.457571i
$151$	1.68729e43			0.444274			0.222137	−	0.975015i	$-0.428697\pi$
$151$	1.68729e43			0.444274			0.222137	+	0.975015i	$0.428697\pi$
$152$		−	1.56275e44i		−	3.60594i
$153$	2.45878e43	−	4.33104e43i	0.497612	−	0.876524i
$154$	−1.27558e43			−0.226617
$155$		−	6.15489e42i		−	0.0960697i
$156$	−3.21358e43	+	1.21698e44i	−0.441060	+	1.67029i
$157$	6.93914e43			0.838132			0.419066	−	0.907956i	$-0.362358\pi$
$157$	6.93914e43			0.838132			0.419066	+	0.907956i	$0.362358\pi$
$158$			1.45866e44i			1.55172i
$159$	6.42646e42	+	1.69699e42i	0.0602600	+	0.0159124i
$160$	−1.21681e44			−1.00652
$161$		−	9.04236e43i		−	0.660335i
$162$	−2.56705e44	+	1.53220e44i	−1.65628	+	0.988591i
$163$	−9.38835e43			−0.535596			−0.267798	−	0.963475i	$-0.586296\pi$
$163$	−9.38835e43			−0.535596			−0.267798	+	0.963475i	$0.586296\pi$
$164$		−	1.12232e44i		−	0.566551i
$165$	1.39802e42	−	5.29429e42i	0.00624936	−	0.0236662i
$166$	3.23979e44			1.28338
$167$			2.07390e44i			0.728549i	0.931292	+	0.364275i	$0.118683\pi$
$167$			2.07390e44i			0.728549i	−0.931292	+	0.364275i	$0.881317\pi$
$168$	1.31501e45	+	3.47245e44i	4.09962	+	1.08256i
$169$	−2.15552e44			−0.596785
$170$		−	2.10327e44i		−	0.517507i
$171$	−4.31817e44	−	2.45147e44i	−0.944883	−	0.536420i
$172$	−6.92305e44			−1.34812
$173$			6.34088e44i			1.09958i	0.835302	+	0.549791i	$0.185293\pi$
$173$			6.34088e44i			1.09958i	−0.835302	+	0.549791i	$0.814707\pi$
$174$	5.05416e44	−	1.91400e45i	0.781024	−	2.95772i
$175$	−8.61488e44			−1.18710
$176$		−	2.75292e44i		−	0.338485i
$177$	−1.42902e44	−	3.77351e43i	−0.156882	−	0.0414267i
$178$	−1.88412e45			−1.84803
$179$			1.49695e45i			1.31265i	0.754479	+	0.656324i	$0.227889\pi$
$179$			1.49695e45i			1.31265i	−0.754479	+	0.656324i	$0.772111\pi$
$180$	−4.55780e44	+	8.02839e44i	−0.357524	+	0.629765i
$181$	2.56524e45			1.80118			0.900590	−	0.434670i	$-0.143135\pi$
$181$	2.56524e45			1.80118			0.900590	+	0.434670i	$0.143135\pi$
$182$		−	2.48831e45i		−	1.56487i
$183$	−9.06348e43	+	3.43233e44i	−0.0510826	+	0.193449i
$184$	3.39385e45			1.71529
$185$			3.36882e44i			0.152772i
$186$	−1.65322e45	−	4.36553e44i	−0.673087	−	0.177737i
$187$	2.53421e44			0.0926853
$188$			3.08970e45i			1.01569i
$189$	3.02235e45	−	3.08890e45i	0.893528	−	0.913203i
$190$	−2.09702e45			−0.557866
$191$			2.15834e45i			0.516954i	0.966017	+	0.258477i	$0.0832206\pi$
$191$			2.15834e45i			0.516954i	−0.966017	+	0.258477i	$0.916779\pi$
$192$	−4.27492e45	+	1.61891e46i	−0.922367	+	3.49299i
$193$	4.58141e45			0.890949			0.445475	−	0.895295i	$-0.353035\pi$
$193$	4.58141e45			0.890949			0.445475	+	0.895295i	$0.353035\pi$
$194$		−	1.30721e46i		−	2.29251i
$195$	1.03278e45	+	2.72717e44i	0.163423	+	0.0431540i
$196$	−1.20428e46			−1.72030
$197$			7.64248e45i			0.986075i	0.870008	+	0.493037i	$0.164113\pi$
$197$			7.64248e45i			0.986075i	−0.870008	+	0.493037i	$0.835887\pi$
$198$	−1.32290e45	−	7.51024e44i	−0.154249	−	0.0875690i
$199$	−5.57950e45			−0.588212			−0.294106	−	0.955773i	$-0.595022\pi$
$199$	−5.57950e45			−0.588212			−0.294106	+	0.955773i	$0.595022\pi$
$200$		−	3.23341e46i		−	3.08362i
$201$	3.25627e45	−	1.23314e46i	0.281060	−	1.06437i
$202$	4.16101e46			3.25215
$203$			2.86164e46i			2.02625i
$204$	−4.13099e46	−	1.09084e46i	−2.65125	−	0.700096i
$205$	−9.52443e44			−0.0554322
$206$			1.98144e46i			1.04625i
$207$	5.32390e45	−	9.37784e45i	0.255166	−	0.449465i
$208$	5.37022e46			2.33736
$209$		−	2.52668e45i		−	0.0999137i
$210$	4.65959e45	−	1.76458e46i	0.167479	−	0.634242i
$211$	−4.44308e46			−1.45223			−0.726115	−	0.687573i	$-0.758676\pi$
$211$	−4.44308e46			−1.45223			−0.726115	+	0.687573i	$0.758676\pi$
$212$		−	5.70221e45i		−	0.169561i
$213$	−4.17135e46	−	1.10150e46i	−1.12897	−	0.298120i
$214$	−1.04200e47			−2.56799
$215$			5.87518e45i			0.131902i
$216$	1.15935e47	+	1.13437e47i	2.37214	+	2.32103i
$217$	2.47174e46			0.461114
$218$			1.78405e47i			3.03583i
$219$	3.11646e46	−	1.18020e47i	0.483927	−	1.83262i
$220$	−4.69763e45			−0.0665925
$221$			4.94358e46i			0.640024i
$222$	9.04874e46	+	2.38943e46i	1.07036	+	0.282641i
$223$	−2.37292e46			−0.256558			−0.128279	−	0.991738i	$-0.540945\pi$
$223$	−2.37292e46			−0.256558			−0.128279	+	0.991738i	$0.540945\pi$
$224$		−	4.88657e47i		−	4.83108i
$225$	−8.93449e46	−	5.07221e46i	−0.808015	−	0.458719i
$226$	1.50263e47			1.24361
$227$		−	2.31538e46i		−	0.175430i	−0.996146	−	0.0877151i	$-0.972043\pi$
$227$		−	2.31538e46i		−	0.175430i	0.996146	−	0.0877151i	$-0.0279565\pi$
$228$	−1.08760e47	+	4.11872e47i	−0.754695	+	2.85802i
$229$	2.26385e47			1.43925			0.719627	−	0.694361i	$-0.244313\pi$
$229$	2.26385e47			1.43925			0.719627	+	0.694361i	$0.244313\pi$
$230$		−	4.55412e46i		−	0.265367i
$231$	2.12613e46	+	5.61431e45i	0.113593	+	0.0299955i
$232$	−1.07405e48			−5.26340
$233$			3.63305e46i			0.163363i	0.996658	+	0.0816814i	$0.0260290\pi$
$233$			3.63305e46i			0.163363i	−0.996658	+	0.0816814i	$0.973971\pi$
$234$	1.46505e47	−	2.58063e47i	0.604694	−	1.06514i
$235$	2.62204e46			0.0993763
$236$			1.26797e47i			0.441438i
$237$	6.42015e46	−	2.43130e47i	0.205389	−	0.777806i
$238$	8.44649e47			2.48392
$239$		−	2.59351e47i		−	0.701343i	−0.936499	−	0.350671i	$-0.885953\pi$
$239$		−	2.59351e47i		−	0.701343i	0.936499	−	0.350671i	$-0.114047\pi$
$240$	3.80827e47	+	1.00562e47i	0.947334	+	0.250155i
$241$	−5.48377e47			−1.25527			−0.627637	−	0.778506i	$-0.715978\pi$
$241$	−5.48377e47			−1.25527			−0.627637	+	0.778506i	$0.715978\pi$
$242$			9.07662e47i			1.91257i
$243$	4.95314e47	−	1.42402e47i	0.961070	−	0.276307i
$244$	3.04551e47			0.544331
$245$			1.02200e47i			0.168317i
$246$	−6.75547e46	+	2.55829e47i	−0.102554	+	0.388371i
$247$	4.92889e47			0.689939
$248$			9.27714e47i			1.19779i
$249$	−5.40008e47	−	1.42596e47i	−0.643300	−	0.169871i
$250$	−9.00851e47			−0.990496
$251$			1.38076e48i			1.40167i	0.713325	+	0.700834i	$0.247189\pi$
$251$			1.38076e48i			1.40167i	−0.713325	+	0.700834i	$0.752811\pi$
$252$	−3.22411e48	−	1.83036e48i	−3.02273	−	1.71604i
$253$	5.48723e46			0.0475273
$254$		−	2.66624e48i		−	2.13415i
$255$	−9.25730e46	+	3.50573e47i	−0.0684985	+	0.259403i
$256$	3.70491e48			2.53500
$257$		−	2.30359e47i		−	0.145795i	−0.997339	−	0.0728976i	$-0.976775\pi$
$257$		−	2.30359e47i		−	0.145795i	0.997339	−	0.0728976i	$-0.0232246\pi$
$258$	1.57809e48	+	4.16713e47i	0.924138	+	0.244030i
$259$	−1.35288e48			−0.733272
$260$		−	9.16384e47i		−	0.459844i
$261$	−1.68486e48	+	2.96781e48i	−0.782984	+	1.37919i
$262$	4.06220e48			1.74878
$263$		−	3.16109e48i		−	1.26102i	−0.776181	−	0.630510i	$-0.782846\pi$
$263$		−	3.16109e48i		−	1.26102i	0.776181	−	0.630510i	$-0.217154\pi$
$264$	−2.10721e47	+	7.97997e47i	−0.0779165	+	0.295068i
$265$	−4.83912e46			−0.0165901
$266$		−	8.42139e48i		−	2.67763i
$267$	3.14046e48	+	8.29277e47i	0.926335	+	0.244610i
$268$	−1.09417e49			−2.99495
$269$			5.29534e48i			1.34539i	0.739920	+	0.672695i	$0.234864\pi$
$269$			5.29534e48i			1.34539i	−0.739920	+	0.672695i	$0.765136\pi$
$270$	1.52218e48	−	1.55570e48i	0.359080	−	0.366987i
$271$	−1.72966e48			−0.378944			−0.189472	−	0.981886i	$-0.560678\pi$
$271$	−1.72966e48			−0.378944			−0.189472	+	0.981886i	$0.560678\pi$
$272$			1.82290e49i			3.71010i
$273$	−1.09520e48	+	4.14752e48i	−0.207130	+	0.784396i
$274$	9.81801e48			1.72589
$275$		−	5.22782e47i		−	0.0854411i
$276$	−8.94467e48	−	2.36195e48i	−1.35951	−	0.358996i
$277$	8.78922e48			1.24267			0.621334	−	0.783546i	$-0.286591\pi$
$277$	8.78922e48			1.24267			0.621334	+	0.783546i	$0.286591\pi$
$278$		−	1.02275e49i		−	1.34547i
$279$	2.56344e48	+	1.45529e48i	0.313863	+	0.178183i
$280$	−9.90204e48			−1.12866
$281$		−	1.64666e49i		−	1.74774i	−0.486159	−	0.873871i	$-0.661602\pi$
$281$		−	1.64666e49i		−	1.74774i	0.486159	−	0.873871i	$-0.338398\pi$
$282$	1.85976e48	−	7.04287e48i	0.183855	−	0.696254i
$283$	6.58146e48			0.606168			0.303084	−	0.952964i	$-0.401984\pi$
$283$	6.58146e48			0.606168			0.303084	+	0.952964i	$0.401984\pi$
$284$			3.70124e49i			3.17673i
$285$	3.49531e48	+	9.22979e47i	0.279633	+	0.0738405i
$286$	1.51000e48			0.112630
$287$		−	3.82491e48i		−	0.266062i
$288$	2.87708e49	−	5.06787e49i	1.86682	−	3.28833i
$289$	−2.62853e47			−0.0159131
$290$			1.44124e49i			0.814287i
$291$	−5.75355e48	+	2.17886e49i	−0.303442	+	1.14913i
$292$	−1.04719e50			−5.15668
$293$		−	2.48968e49i		−	1.14496i	−0.819918	−	0.572481i	$-0.805981\pi$
$293$		−	2.48968e49i		−	1.14496i	0.819918	−	0.572481i	$-0.194019\pi$
$294$	2.74511e49	+	7.24880e48i	1.17927	+	0.311401i
$295$	1.07605e48			0.0431910
$296$		−	5.07775e49i		−	1.90475i
$297$	1.87445e48	+	1.83407e48i	0.0657273	+	0.0643112i
$298$	5.00097e49			1.63957
$299$			1.07041e49i			0.328192i
$300$	−2.25029e49	+	8.52181e49i	−0.645377	+	2.44403i
$301$	−2.35941e49			−0.633101
$302$			3.41267e49i			0.856950i
$303$	−6.93557e49	−	1.83142e49i	−1.63016	−	0.430463i
$304$	1.81749e50			3.99944
$305$		−	2.58454e48i		−	0.0532582i
$306$	8.75986e49	+	4.97307e49i	1.69071	+	0.959833i
$307$	−4.81758e49			−0.871087			−0.435544	−	0.900168i	$-0.643444\pi$
$307$	−4.81758e49			−0.871087			−0.435544	+	0.900168i	$0.643444\pi$
$308$		−	1.88652e49i		−	0.319629i
$309$	8.72109e48	−	3.30266e49i	0.138484	−	0.524438i
$310$	1.24487e49			0.185307
$311$		−	7.84856e49i		−	1.09542i	−0.836667	−	0.547712i	$-0.815499\pi$
$311$		−	7.84856e49i		−	1.09542i	0.836667	−	0.547712i	$-0.184501\pi$
$312$	−1.55668e50	−	4.11061e49i	−2.03755	−	0.538040i
$313$	1.66014e49			0.203825			0.101912	−	0.994793i	$-0.467504\pi$
$313$	1.66014e49			0.203825			0.101912	+	0.994793i	$0.467504\pi$
$314$			1.40349e50i			1.61665i
$315$	−1.55332e49	+	2.73611e49i	−0.167900	+	0.295749i
$316$	−2.15730e50			−2.18861
$317$		−	2.70229e48i		−	0.0257363i	−0.999917	−	0.0128682i	$-0.995904\pi$
$317$		−	2.70229e48i		−	0.0257363i	0.999917	−	0.0128682i	$-0.00409618\pi$
$318$	−3.43228e48	+	1.29980e49i	−0.0306931	+	0.116234i
$319$	−1.73655e49			−0.145839
$320$		−	1.21904e50i		−	0.961650i
$321$	1.73681e50	+	4.58626e49i	1.28722	+	0.339905i
$322$	1.82888e50			1.27371
$323$			1.67310e50i			1.09514i
$324$	−2.26606e50	−	3.79654e50i	−1.39435	−	2.33608i
$325$	1.01981e50			0.590000
$326$		−	1.89886e50i		−	1.03310i
$327$	7.85231e49	−	2.97366e50i	0.401830	−	1.52172i
$328$	1.43560e50			0.691124
$329$			1.05298e50i			0.476984i
$330$	1.07081e49	+	2.82761e48i	0.0456492	+	0.0120542i
$331$	4.35153e50			1.74615			0.873076	−	0.487584i	$-0.162122\pi$
$331$	4.35153e50			1.74615			0.873076	+	0.487584i	$0.162122\pi$
$332$			4.79150e50i			1.81013i
$333$	−1.40308e50	−	7.96541e49i	−0.499110	−	0.283350i
$334$	−4.19462e50			−1.40528
$335$			9.28557e49i			0.293030i
$336$	−4.03847e50	+	1.52936e51i	−1.20069	+	4.54699i
$337$	−3.26149e50			−0.913729			−0.456865	−	0.889536i	$-0.651028\pi$
$337$	−3.26149e50			−0.913729			−0.456865	+	0.889536i	$0.651028\pi$
$338$		−	4.35970e50i		−	1.15113i
$339$	−2.50458e50	−	6.61366e49i	−0.623364	−	0.164607i
$340$	3.11064e50			0.729913
$341$			1.49994e49i			0.0331884i
$342$	4.95829e50	−	8.73383e50i	1.03469	−	1.82256i
$343$	2.38640e50			0.469743
$344$		−	8.85553e50i		−	1.64454i
$345$	−2.00445e49	+	7.59081e49i	−0.0351247	+	0.133017i
$346$	−1.28249e51			−2.12096
$347$			1.21819e51i			1.90163i	0.309764	+	0.950814i	$0.399750\pi$
$347$			1.21819e51i			1.90163i	−0.309764	+	0.950814i	$0.600250\pi$
$348$	2.83072e51	+	7.47488e50i	4.17170	+	1.10159i
$349$	−2.86892e50			−0.399218			−0.199609	−	0.979876i	$-0.563967\pi$
$349$	−2.86892e50			−0.399218			−0.199609	+	0.979876i	$0.563967\pi$
$350$		−	1.74242e51i		−	2.28977i
$351$	−3.57779e50	+	3.65657e50i	−0.444091	+	0.453870i
$352$	2.96535e50			0.347714
$353$			1.23907e51i			1.37278i	0.727233	+	0.686390i	$0.240806\pi$
$353$			1.23907e51i			1.37278i	−0.727233	+	0.686390i	$0.759194\pi$
$354$	7.63221e49	−	2.89030e50i	0.0799070	−	0.302606i
$355$	3.14102e50			0.310816
$356$		−	2.78653e51i		−	2.60654i
$357$	−1.40786e51	−	3.71763e50i	−1.24508	−	0.328778i
$358$	−3.02770e51			−2.53194
$359$		−	1.57282e51i		−	1.24391i	−0.783052	−	0.621957i	$-0.786338\pi$
$359$		−	1.57282e51i		−	1.24391i	0.783052	−	0.621957i	$-0.213662\pi$
$360$	−1.02694e51	−	5.83005e50i	−0.768237	−	0.436137i
$361$	2.55119e50			0.180550
$362$			5.18840e51i			3.47426i
$363$	3.99498e50	−	1.51289e51i	0.253152	−	0.958683i
$364$	3.68010e51			2.20715
$365$			8.88690e50i			0.504537i
$366$	−6.94214e50	−	1.83316e50i	−0.373140	−	0.0985322i
$367$	−1.73705e50			−0.0884081			−0.0442040	−	0.999023i	$-0.514075\pi$
$367$	−1.73705e50			−0.0884081			−0.0442040	+	0.999023i	$0.514075\pi$
$368$			3.94706e51i			1.90247i
$369$	2.25200e50	−	3.96682e50i	0.102812	−	0.181099i
$370$	−6.81369e50			−0.294678
$371$		−	1.94334e50i		−	0.0796288i
$372$	6.45642e50	−	2.44504e51i	0.250688	−	0.949350i
$373$	3.57952e51			1.31719			0.658594	−	0.752499i	$-0.271152\pi$
$373$	3.57952e51			1.31719			0.658594	+	0.752499i	$0.271152\pi$
$374$			5.12564e50i			0.178779i
$375$	1.50154e51	+	3.96500e50i	0.496491	+	0.131105i
$376$	−3.95215e51			−1.23902
$377$		−	3.38754e51i		−	1.00707i
$378$	6.24753e51	+	6.11292e51i	1.76146	+	1.72351i
$379$	1.03807e51			0.277616			0.138808	−	0.990319i	$-0.455673\pi$
$379$	1.03807e51			0.277616			0.138808	+	0.990319i	$0.455673\pi$
$380$		−	3.10139e51i		−	0.786837i
$381$	−1.17352e51	+	4.44410e51i	−0.282482	+	1.06975i
$382$	−4.36540e51			−0.997141
$383$		−	4.88556e51i		−	1.05910i	−0.848277	−	0.529552i	$-0.822360\pi$
$383$		−	4.88556e51i		−	1.05910i	0.848277	−	0.529552i	$-0.177640\pi$
$384$	−1.49760e52	−	3.95461e51i	−3.08158	−	0.813728i
$385$	−1.60097e50			−0.0312730
$386$			9.26625e51i			1.71853i
$387$	−2.44694e51	−	1.38916e51i	−0.430928	−	0.244642i
$388$	1.93331e52			3.23345
$389$		−	5.52494e51i		−	0.877678i	−0.898566	−	0.438839i	$-0.855390\pi$
$389$		−	5.52494e51i		−	0.877678i	0.898566	−	0.438839i	$-0.144610\pi$
$390$	−5.51592e50	+	2.08887e51i	−0.0832387	+	0.315224i
$391$	−3.63349e51			−0.520941
$392$		−	1.54043e52i		−	2.09856i
$393$	−6.77087e51	−	1.78793e51i	−0.876584	−	0.231473i
$394$	−1.54575e52			−1.90202
$395$			1.83077e51i			0.214137i
$396$	1.11073e51	−	1.95651e51i	0.123511	−	0.217560i
$397$	1.08700e52			1.14926			0.574632	−	0.818412i	$-0.305145\pi$
$397$	1.08700e52			1.14926			0.574632	+	0.818412i	$0.305145\pi$
$398$		−	1.12850e52i		−	1.13459i
$399$	−3.70659e51	+	1.40368e52i	−0.354418	+	1.34218i
$400$	3.76046e52			3.42012
$401$		−	8.37891e51i		−	0.724936i	−0.931996	−	0.362468i	$-0.881934\pi$
$401$		−	8.37891e51i		−	0.724936i	0.931996	−	0.362468i	$-0.118066\pi$
$402$	2.49413e52	+	6.58605e51i	2.05304	+	0.542130i
$403$	−2.92599e51			−0.229177
$404$			6.15394e52i			4.58697i
$405$	−3.22190e51	+	1.92307e51i	−0.228566	+	0.136425i
$406$	−5.78788e52			−3.90840
$407$		−	8.20978e50i		−	0.0527768i
$408$	1.39533e52	−	5.28410e52i	0.854033	−	3.23421i
$409$	−3.47724e50			−0.0202660			−0.0101330	−	0.999949i	$-0.503225\pi$
$409$	−3.47724e50			−0.0202660			−0.0101330	+	0.999949i	$0.503225\pi$
$410$		−	1.92639e51i		−	0.106922i
$411$	−1.63647e52	−	4.32129e51i	−0.865108	−	0.228443i
$412$	−2.93046e52			−1.47568
$413$			4.32131e51i			0.207307i
$414$	1.89674e52	+	1.07680e52i	0.866963	+	0.492184i
$415$	4.06626e51			0.177106
$416$			5.78462e52i			2.40109i
$417$	−4.50153e51	+	1.70472e52i	−0.178090	+	0.674423i
$418$	5.11040e51			0.192721
$419$		−	1.97575e52i		−	0.710316i	−0.934806	−	0.355158i	$-0.884427\pi$
$419$		−	1.97575e52i		−	0.710316i	0.934806	−	0.355158i	$-0.115573\pi$
$420$	2.60973e52	+	6.89132e51i	0.894561	+	0.236220i
$421$	3.56025e52			1.16369			0.581847	−	0.813298i	$-0.302330\pi$
$421$	3.56025e52			1.16369			0.581847	+	0.813298i	$0.302330\pi$
$422$		−	8.98647e52i		−	2.80117i
$423$	−6.19969e51	+	1.09205e52i	−0.184316	+	0.324665i
$424$	7.29390e51			0.206844
$425$			3.46171e52i			0.936509i
$426$	2.22786e52	−	8.43686e52i	0.575036	−	2.17765i
$427$	1.03792e52			0.255628
$428$		−	1.54107e53i		−	3.62199i
$429$	−2.51686e51	−	6.64609e50i	−0.0564565	−	0.0149080i
$430$	−1.18830e52			−0.254423
$431$			5.78060e52i			1.18148i	0.806861	+	0.590741i	$0.201165\pi$
$431$			5.78060e52i			1.18148i	−0.806861	+	0.590741i	$0.798835\pi$
$432$	−1.31928e53	+	1.34833e53i	−2.57431	+	2.63100i
$433$	3.83783e52			0.715036			0.357518	−	0.933906i	$-0.383623\pi$
$433$	3.83783e52			0.715036			0.357518	+	0.933906i	$0.383623\pi$
$434$			4.99928e52i			0.889432i
$435$	6.34348e51	−	2.40227e52i	0.107781	−	0.408165i
$436$	−2.63853e53			−4.28186
$437$			3.62269e52i			0.561568i
$438$	2.38704e53	+	6.30328e52i	3.53491	+	0.933436i
$439$	1.12496e53			1.59165			0.795826	−	0.605526i	$-0.207037\pi$
$439$	1.12496e53			1.59165			0.795826	+	0.605526i	$0.207037\pi$
$440$		−	6.00891e51i		−	0.0812348i
$441$	−4.25650e52	−	2.41646e52i	−0.549896	−	0.312182i
$442$	−9.99877e52			−1.23453
$443$		−	1.06943e53i		−	1.26206i	−0.775759	−	0.631029i	$-0.782633\pi$
$443$		−	1.06943e53i		−	1.26206i	0.775759	−	0.631029i	$-0.217367\pi$
$444$	−3.53386e52	+	1.33827e53i	−0.398648	+	1.50968i
$445$	−2.36476e52			−0.255028
$446$		−	4.79940e52i		−	0.494868i
$447$	−8.33562e52	−	2.20112e52i	−0.821840	−	0.217017i
$448$	4.89552e53			4.61571
$449$			9.24952e52i			0.834050i	0.908895	+	0.417025i	$0.136927\pi$
$449$			9.24952e52i			0.834050i	−0.908895	+	0.417025i	$0.863073\pi$
$450$	1.02589e53	−	1.80707e53i	0.884813	−	1.55856i
$451$	2.32109e51			0.0191497
$452$			2.22232e53i			1.75403i
$453$	1.50205e52	−	5.68824e52i	0.113428	−	0.429550i
$454$	4.68302e52			0.338383
$455$		−	3.12308e52i		−	0.215951i
$456$	−5.26840e53	−	1.39119e53i	−3.48644	−	0.920638i
$457$	−3.35185e52			−0.212305			−0.106153	−	0.994350i	$-0.533853\pi$
$457$	−3.35185e52			−0.212305			−0.106153	+	0.994350i	$0.533853\pi$
$458$			4.57880e53i			2.77614i
$459$	−1.24121e53	−	1.21447e53i	−0.720430	−	0.704907i
$460$	6.73534e52			0.374285
$461$			1.67919e53i			0.893473i	0.894666	+	0.446736i	$0.147414\pi$
$461$			1.67919e53i			0.893473i	−0.894666	+	0.446736i	$0.852586\pi$
$462$	−1.13554e52	+	4.30026e52i	−0.0578577	+	0.219106i
$463$	−6.80885e52			−0.332241			−0.166121	−	0.986105i	$-0.553124\pi$
$463$	−6.80885e52			−0.332241			−0.166121	+	0.986105i	$0.553124\pi$
$464$		−	1.24913e54i		−	5.83777i
$465$	−2.07496e52	−	5.47918e51i	−0.0928859	−	0.0245277i
$466$	−7.34812e52			−0.315107
$467$			1.25479e53i			0.515508i	0.966211	+	0.257754i	$0.0829823\pi$
$467$			1.25479e53i			0.515508i	−0.966211	+	0.257754i	$0.917018\pi$
$468$	3.81664e53	+	2.16674e53i	1.50232	+	0.852886i
$469$	−3.72898e53			−1.40648
$470$			5.30328e52i			0.191685i
$471$	6.17733e52	−	2.33934e53i	0.213985	−	0.810356i
$472$	−1.62191e53			−0.538502
$473$		−	1.43177e52i		−	0.0455671i
$474$	4.91748e53	+	1.29852e53i	1.50029	+	0.396171i
$475$	3.45142e53			1.00955
$476$			1.24920e54i			3.50342i
$477$	1.14419e52	−	2.01544e52i	0.0307701	−	0.0542003i
$478$	5.24557e53			1.35280
$479$		−	4.19874e53i		−	1.03850i	−0.854621	−	0.519252i	$-0.826211\pi$
$479$		−	4.19874e53i		−	1.03850i	0.854621	−	0.519252i	$-0.173789\pi$
$480$	−1.08322e53	+	4.10214e53i	−0.256976	+	0.973164i
$481$	1.60151e53			0.364442
$482$		−	1.10913e54i		−	2.42127i
$483$	−3.04839e53	−	8.04964e52i	−0.638451	−	0.168591i
$484$	−1.34239e54			−2.69756
$485$		−	1.64068e53i		−	0.316366i
$486$	2.88019e53	+	1.00181e54i	0.532962	+	1.85379i
$487$	2.61724e53			0.464799			0.232399	−	0.972620i	$-0.425342\pi$
$487$	2.61724e53			0.464799			0.232399	+	0.972620i	$0.425342\pi$
$488$			3.89562e53i			0.664019i
$489$	−8.35764e52	+	3.16503e53i	−0.136744	+	0.517845i
$490$	−2.06707e53			−0.324663
$491$		−	5.97285e53i		−	0.900640i	−0.892867	−	0.450320i	$-0.851310\pi$
$491$		−	5.97285e53i		−	0.900640i	0.892867	−	0.450320i	$-0.148690\pi$
$492$	−3.78359e53	−	9.99104e52i	−0.547775	−	0.144647i
$493$	1.14989e54			1.59852
$494$			9.96906e53i			1.33081i
$495$	−1.66037e52	−	9.42611e51i	−0.0212864	−	0.0120845i
$496$	−1.07893e54			−1.32850
$497$			1.26140e54i			1.49185i
$498$	2.88411e53	−	1.09221e54i	0.327661	−	1.24085i
$499$	2.43723e53			0.266003			0.133001	−	0.991116i	$-0.457539\pi$
$499$	2.43723e53			0.266003			0.133001	+	0.991116i	$0.457539\pi$
$500$		−	1.33232e54i		−	1.39704i
$501$	6.99160e53	+	1.84622e53i	0.704404	+	0.186007i
$502$	−2.79270e54			−2.70365
$503$		−	1.07655e54i		−	1.00156i	−0.865575	−	0.500779i	$-0.833047\pi$
$503$		−	1.07655e54i		−	1.00156i	0.865575	−	0.500779i	$-0.166953\pi$
$504$	2.34129e54	−	4.12408e54i	2.09336	−	3.68737i
$505$	5.22248e53			0.448796
$506$			1.10983e53i			0.0916743i
$507$	−1.91888e53	+	7.26675e53i	−0.152366	+	0.577007i
$508$	3.94325e54			3.01010
$509$			1.06927e54i			0.784752i	0.919805	+	0.392376i	$0.128347\pi$
$509$			1.06927e54i			0.784752i	−0.919805	+	0.392376i	$0.871653\pi$
$510$	−7.09059e53	−	1.87236e53i	−0.500356	−	0.132125i
$511$	−3.56888e54			−2.42167
$512$			2.60909e54i			1.70251i
$513$	−1.21086e54	+	1.23752e54i	−0.759882	+	0.776614i
$514$	4.65919e53			0.281221
$515$			2.48690e53i			0.144382i
$516$	−6.16300e53	+	2.33392e54i	−0.344190	+	1.30344i
$517$	−6.38989e52			−0.0343307
$518$		−	2.73631e54i		−	1.41439i
$519$	2.13766e54	+	5.64474e53i	1.06314	+	0.280735i
$520$	1.17218e54			0.560955
$521$		−	1.70691e54i		−	0.786061i	−0.919525	−	0.393030i	$-0.871427\pi$
$521$		−	1.70691e54i		−	0.786061i	0.919525	−	0.393030i	$-0.128573\pi$
$522$	−6.00261e54	−	3.40775e54i	−2.66030	−	1.51028i
$523$	−3.30169e54			−1.40832			−0.704162	−	0.710039i	$-0.748677\pi$
$523$	−3.30169e54			−1.40832			−0.704162	+	0.710039i	$0.748677\pi$
$524$			6.00780e54i			2.46655i
$525$	−7.66909e53	+	2.90427e54i	−0.303080	+	1.14776i
$526$	6.39354e54			2.43235
$527$		−	9.93217e53i		−	0.363774i
$528$	−9.28071e53	−	2.45069e53i	−0.327268	−	0.0864191i
$529$	2.15845e54			0.732872
$530$		−	9.78748e52i		−	0.0320003i
$531$	−2.54427e53	+	4.48164e53i	−0.0801075	+	0.141106i
$532$	1.24549e55			3.77665
$533$			4.52784e53i			0.132235i
$534$	−1.67728e54	+	6.35181e54i	−0.471823	+	1.78679i
$535$	−1.30782e54			−0.354381
$536$		−	1.39959e55i		−	3.65348i
$537$	5.04658e54	+	1.33261e54i	1.26914	+	0.335133i
$538$	−1.07102e55			−2.59509
$539$		−	2.49059e53i		−	0.0581471i
$540$	2.30081e54	+	2.25124e54i	0.517614	+	0.506461i
$541$	6.10923e53			0.132447			0.0662234	−	0.997805i	$-0.478905\pi$
$541$	6.10923e53			0.132447			0.0662234	+	0.997805i	$0.478905\pi$
$542$		−	3.49837e54i		−	0.730936i
$543$	2.28362e54	−	8.64802e54i	0.459861	−	1.74149i
$544$	−1.96357e55			−3.81126
$545$			2.23916e54i			0.418943i
$546$	−8.38867e54	−	2.21513e54i	−1.51300	−	0.399528i
$547$	6.34621e54			1.10349			0.551744	−	0.834013i	$-0.313962\pi$
$547$	6.34621e54			1.10349			0.551744	+	0.834013i	$0.313962\pi$
$548$			1.45204e55i			2.43426i
$549$	1.07643e54	+	6.11102e53i	0.173996	+	0.0987794i
$550$	1.05737e54			0.164805
$551$		−	1.14647e55i		−	1.72319i
$552$	3.02126e54	−	1.14415e55i	0.437932	−	1.65844i
$553$	−7.35216e54			−1.02781
$554$			1.77769e55i			2.39695i
$555$	1.13571e54	+	2.99898e53i	0.147709	+	0.0390044i
$556$	1.51260e55			1.89771
$557$			1.10626e55i			1.33892i	0.742848	+	0.669461i	$0.233475\pi$
$557$			1.10626e55i			1.33892i	−0.742848	+	0.669461i	$0.766525\pi$
$558$	−2.94344e54	+	5.18475e54i	−0.343693	+	0.605402i
$559$	2.79301e54			0.314657
$560$		−	1.15161e55i		−	1.25183i
$561$	2.25599e53	−	8.54341e53i	0.0236636	−	0.0896136i
$562$	3.33049e55			3.37118
$563$		−	1.77066e55i		−	1.72969i	−0.502039	−	0.864845i	$-0.667417\pi$
$563$		−	1.77066e55i		−	1.72969i	0.502039	−	0.864845i	$-0.332583\pi$
$564$	1.04161e55	+	2.75050e54i	0.982025	+	0.259316i
$565$	1.88595e54			0.171617
$566$			1.33115e55i			1.16922i
$567$	−7.72284e54	−	1.29388e55i	−0.654811	−	1.09707i
$568$	−4.73439e55			−3.87523
$569$			2.13371e55i			1.68613i	0.537814	+	0.843063i	$0.319250\pi$
$569$			2.13371e55i			1.68613i	−0.537814	+	0.843063i	$0.680750\pi$
$570$	−1.86679e54	+	7.06952e54i	−0.142429	+	0.539378i
$571$	−2.16126e55			−1.59215			−0.796075	−	0.605197i	$-0.793094\pi$
$571$	−2.16126e55			−1.59215			−0.796075	+	0.605197i	$0.793094\pi$
$572$			2.23322e54i			0.158859i
$573$	7.27625e54	+	1.92138e54i	0.499822	+	0.131984i
$574$	7.73617e54			0.513202
$575$			7.49550e54i			0.480224i
$576$	5.07714e55	+	2.88235e55i	3.14174	+	1.78360i
$577$	−2.34534e55			−1.40181			−0.700905	−	0.713255i	$-0.747220\pi$
$577$	−2.34534e55			−1.40181			−0.700905	+	0.713255i	$0.747220\pi$
$578$		−	5.31640e53i		−	0.0306945i
$579$	4.07844e54	−	1.54450e55i	0.227469	−	0.861422i
$580$	−2.13153e55			−1.14850
$581$			1.63297e55i			0.850070i
$582$	−4.40691e55	−	1.16370e55i	−2.21653	−	0.585303i
$583$	1.17929e53			0.00573124
$584$		−	1.33950e56i		−	6.29053i
$585$	1.83879e54	−	3.23895e54i	0.0834476	−	0.146990i
$586$	5.03556e55			2.20849
$587$		−	1.47942e55i		−	0.627089i	−0.949573	−	0.313545i	$-0.898483\pi$
$587$		−	1.47942e55i		−	0.627089i	0.949573	−	0.313545i	$-0.101517\pi$
$588$	−1.07206e55	+	4.05989e55i	−0.439212	+	1.66329i
$589$	−9.90266e54			−0.392144
$590$			2.17640e54i			0.0833102i
$591$	2.57646e55	+	6.80345e54i	0.953395	+	0.251756i
$592$	5.90543e55			2.11260
$593$			7.41967e54i			0.256620i	0.991734	+	0.128310i	$0.0409553\pi$
$593$			7.41967e54i			0.256620i	−0.991734	+	0.128310i	$0.959045\pi$
$594$	−3.70954e54	+	3.79122e54i	−0.124048	+	0.126780i
$595$	1.06012e55			0.342780
$596$			7.39621e55i			2.31251i
$597$	−4.96696e54	+	1.88098e55i	−0.150177	+	0.568718i
$598$	−2.16499e55			−0.633042
$599$			2.10034e55i			0.593955i	0.954885	+	0.296977i	$0.0959786\pi$
$599$			2.10034e55i			0.593955i	−0.954885	+	0.296977i	$0.904021\pi$
$600$	−1.09006e56	−	2.87843e55i	−2.98142	−	0.787282i
$601$	4.57949e55			1.21151			0.605756	−	0.795651i	$-0.292871\pi$
$601$	4.57949e55			1.21151			0.605756	+	0.795651i	$0.292871\pi$
$602$		−	4.77208e55i		−	1.22117i
$603$	−3.86733e55	−	2.19553e55i	−0.957338	−	0.543491i
$604$	−5.04719e55			−1.20868
$605$			1.13921e55i			0.263934i
$606$	3.70419e55	−	1.40277e56i	0.830311	−	3.14437i
$607$	1.81638e55			0.393943			0.196972	−	0.980409i	$-0.436889\pi$
$607$	1.81638e55			0.393943			0.196972	+	0.980409i	$0.436889\pi$
$608$			1.95773e56i			4.10849i
$609$	9.64724e55	+	2.54747e55i	1.95910	+	0.517325i
$610$	5.22743e54			0.102729
$611$		−	1.24650e55i		−	0.237065i
$612$	−7.35494e55	+	1.29554e56i	−1.35379	+	2.38465i
$613$	−1.77971e55			−0.317058			−0.158529	−	0.987354i	$-0.550675\pi$
$613$	−1.77971e55			−0.317058			−0.158529	+	0.987354i	$0.550675\pi$
$614$		−	9.74392e55i		−	1.68022i
$615$	−8.47879e53	+	3.21090e54i	−0.0141525	+	0.0535951i
$616$	2.41311e55			0.389909
$617$			4.89792e55i			0.766141i	0.923719	+	0.383071i	$0.125133\pi$
$617$			4.89792e55i			0.766141i	−0.923719	+	0.383071i	$0.874867\pi$
$618$	6.67988e55	+	1.76391e55i	1.01158	+	0.267120i
$619$	−6.33953e55			−0.929488			−0.464744	−	0.885445i	$-0.653854\pi$
$619$	−6.33953e55			−0.929488			−0.464744	+	0.885445i	$0.653854\pi$
$620$			1.84111e55i			0.261364i
$621$	−2.68754e55	−	2.62964e55i	−0.369422	−	0.361463i
$622$	1.58743e56			2.11294
$623$		−	9.49664e55i		−	1.22408i
$624$	4.78065e55	−	1.81042e56i	0.596754	−	2.25990i
$625$	6.55506e55			0.792458
$626$			3.35775e55i			0.393153i
$627$	−8.51803e54	−	2.24929e54i	−0.0966024	−	0.0255091i
$628$	−2.07570e56			−2.28020
$629$			5.43628e55i			0.578481i
$630$	−5.53399e55	−	3.14171e55i	−0.570463	−	0.323858i
$631$	−1.01805e55			−0.101668			−0.0508338	−	0.998707i	$-0.516188\pi$
$631$	−1.01805e55			−0.101668			−0.0508338	+	0.998707i	$0.516188\pi$
$632$		−	2.75948e56i		−	2.66984i
$633$	−3.95530e55	+	1.49787e56i	−0.370770	+	1.40410i
$634$	5.46558e54			0.0496422
$635$		−	3.34640e55i		−	0.294512i
$636$	−1.92234e55	−	5.07619e54i	−0.163941	−	0.0432908i
$637$	4.85850e55			0.401526
$638$		−	3.51229e55i		−	0.281305i
$639$	−7.42679e55	+	1.30820e56i	−0.576479	+	1.01545i
$640$	1.12770e56			0.848384
$641$		−	5.58788e55i		−	0.407462i	−0.979027	−	0.203731i	$-0.934693\pi$
$641$		−	5.58788e55i		−	0.407462i	0.979027	−	0.203731i	$-0.0653067\pi$
$642$	−9.27605e55	+	3.51282e56i	−0.655635	+	2.48288i
$643$	−1.60963e56			−1.10282			−0.551411	−	0.834234i	$-0.685910\pi$
$643$	−1.60963e56			−1.10282			−0.551411	+	0.834234i	$0.685910\pi$
$644$			2.70484e56i			1.79649i
$645$	1.98066e55	+	5.23017e54i	0.127531	+	0.0336761i
$646$	−3.38396e56			−2.11240
$647$		−	3.12995e56i		−	1.89431i	−0.320775	−	0.947155i	$-0.603943\pi$
$647$		−	3.12995e56i		−	1.89431i	0.320775	−	0.947155i	$-0.396057\pi$
$648$	4.85630e56	−	2.89860e56i	2.84974	−	1.70094i
$649$	−2.62233e54			−0.0149208
$650$			2.06264e56i			1.13804i
$651$	2.20038e55	−	8.33280e55i	0.117727	−	0.445832i
$652$	2.80833e56			1.45712
$653$		−	1.86047e56i		−	0.936180i	−0.883681	−	0.468090i	$-0.844942\pi$
$653$		−	1.86047e56i		−	0.936180i	0.883681	−	0.468090i	$-0.155058\pi$
$654$	6.01444e56	+	1.58819e56i	2.93522	+	0.775081i
$655$	5.09846e55			0.241331
$656$			1.66960e56i			0.766542i
$657$	−3.70129e56	−	2.10126e56i	−1.64834	−	0.935779i
$658$	−2.12974e56			−0.920044
$659$			2.26325e56i			0.948471i	0.880398	+	0.474235i	$0.157275\pi$
$659$			2.26325e56i			0.948471i	−0.880398	+	0.474235i	$0.842725\pi$
$660$	−4.18190e54	+	1.58368e55i	−0.0170018	+	0.0643856i
$661$	8.83208e55			0.348364			0.174182	−	0.984713i	$-0.444272\pi$
$661$	8.83208e55			0.348364			0.174182	+	0.984713i	$0.444272\pi$
$662$			8.80129e56i			3.36811i
$663$	1.66660e56	+	4.40085e55i	0.618813	+	0.163405i
$664$	−6.12899e56			−2.20814
$665$		−	1.05697e56i		−	0.369513i
$666$	1.61106e56	−	2.83783e56i	0.546548	−	0.962722i
$667$	2.48981e56			0.819690
$668$		−	6.20366e56i		−	1.98207i
$669$	−2.11241e55	+	7.99964e55i	−0.0655020	+	0.248055i
$670$	−1.87808e56			−0.565219
$671$			6.29850e54i			0.0183987i
$672$	−1.64738e57	−	4.35010e56i	−4.67097	−	1.23343i
$673$	1.12011e56			0.308291			0.154146	−	0.988048i	$-0.450738\pi$
$673$	1.12011e56			0.308291			0.154146	+	0.988048i	$0.450738\pi$
$674$		−	6.59660e56i		−	1.76247i
$675$	−2.50532e56	+	2.56049e56i	−0.649812	+	0.664121i
$676$	6.44780e56			1.62360
$677$			2.34608e56i			0.573548i	0.957998	+	0.286774i	$0.0925829\pi$
$677$			2.34608e56i			0.573548i	−0.957998	+	0.286774i	$0.907417\pi$
$678$	1.33766e56	−	5.06571e56i	0.317507	−	1.20239i
$679$	6.58880e56			1.51849
$680$			3.97893e56i			0.890406i
$681$	−7.80566e55	−	2.06118e55i	−0.169616	−	0.0447893i
$682$	−3.03374e55			−0.0640164
$683$		−	1.00258e55i		−	0.0205450i	−0.999947	−	0.0102725i	$-0.996730\pi$
$683$		−	1.00258e55i		−	0.0205450i	0.999947	−	0.0102725i	$-0.00326989\pi$
$684$	1.29169e57	+	7.33309e56i	2.57062	+	1.45937i
$685$	1.23226e56			0.238172
$686$			4.82667e56i			0.906077i
$687$	2.01531e56	−	7.63194e56i	0.367457	−	1.39155i
$688$	1.02990e57			1.82400
$689$			2.30048e55i			0.0395762i
$690$	−1.53530e56	−	4.05414e55i	−0.256573	−	0.0677512i
$691$	−6.80947e56			−1.10548			−0.552742	−	0.833352i	$-0.686419\pi$
$691$	−6.80947e56			−1.10548			−0.552742	+	0.833352i	$0.686419\pi$
$692$		−	1.89675e57i		−	2.99149i
$693$	3.78542e55	−	6.66787e55i	0.0580029	−	0.102170i
$694$	−2.46388e57			−3.66801
$695$		−	1.28366e56i		−	0.185675i
$696$	−9.56139e56	+	3.62088e57i	−1.34381	+	5.08897i
$697$	−1.53696e56			−0.209898
$698$		−	5.80261e56i		−	0.770043i
$699$	1.22478e56	+	3.23420e55i	0.157949	+	0.0417083i
$700$	2.57697e57			3.22959
$701$			9.31909e56i			1.13505i	0.823358	+	0.567523i	$0.192098\pi$
$701$			9.31909e56i			1.13505i	−0.823358	+	0.567523i	$0.807902\pi$
$702$	−7.39568e56	−	7.23634e56i	−0.875460	−	0.856597i
$703$	5.42013e56			0.623595
$704$			2.97078e56i			0.332213i
$705$	2.33418e55	−	8.83951e55i	0.0253719	−	0.0960829i
$706$	−2.50611e57			−2.64793
$707$			2.09729e57i			2.15412i
$708$	4.27463e56	+	1.12877e56i	0.426809	+	0.112704i
$709$	−3.00365e56			−0.291558			−0.145779	−	0.989317i	$-0.546569\pi$
$709$	−3.00365e56			−0.291558			−0.145779	+	0.989317i	$0.546569\pi$
$710$			6.35295e56i			0.599527i
$711$	−7.62493e56	−	4.32876e56i	−0.699591	−	0.397165i
$712$	3.56436e57			3.17967
$713$		−	2.15057e56i		−	0.186536i
$714$	7.51919e56	−	2.84751e57i	0.634172	−	2.40160i
$715$	1.89520e55			0.0155430
$716$		−	4.47784e57i		−	3.57115i
$717$	−8.74332e56	−	2.30878e56i	−0.678100	−	0.179061i
$718$	3.18115e57			2.39936
$719$			1.41687e57i			1.03933i	0.854371	+	0.519664i	$0.173943\pi$
$719$			1.41687e57i			1.03933i	−0.854371	+	0.519664i	$0.826057\pi$
$720$	6.78036e56	−	1.19433e57i	0.483730	−	0.852071i
$721$	−9.98713e56			−0.693004
$722$			5.15996e56i			0.348259i
$723$	−4.88174e56	+	1.84871e57i	−0.320485	+	1.21367i
$724$	−7.67341e57			−4.90023
$725$		−	2.37210e57i		−	1.47358i
$726$	3.05993e57	+	8.08014e56i	1.84918	+	0.488300i
$727$	1.54182e57			0.906452			0.453226	−	0.891396i	$-0.350273\pi$
$727$	1.54182e57			0.906452			0.453226	+	0.891396i	$0.350273\pi$
$728$			4.70735e57i			2.69246i
$729$	−3.91349e55	−	1.79658e57i	−0.0217778	−	0.999763i
$730$	−1.79744e57			−0.973190
$731$			9.48079e56i			0.499456i
$732$	2.71116e56	−	1.02671e57i	0.138974	−	0.526292i
$733$	1.12747e57			0.562375			0.281187	−	0.959653i	$-0.409272\pi$
$733$	1.12747e57			0.562375			0.281187	+	0.959653i	$0.409272\pi$
$734$		−	3.51332e56i		−	0.170528i
$735$	3.44539e56	+	9.09797e55i	0.162739	+	0.0429732i
$736$	−4.25164e57			−1.95434
$737$		−	2.26288e56i		−	0.101231i
$738$	8.02318e56	+	4.55485e56i	0.349317	+	0.198311i
$739$	−2.39948e56			−0.101678			−0.0508391	−	0.998707i	$-0.516190\pi$
$739$	−2.39948e56			−0.101678			−0.0508391	+	0.998707i	$0.516190\pi$
$740$		−	1.00771e57i		−	0.415627i
$741$	4.38777e56	−	1.66164e57i	0.176149	−	0.667073i
$742$	3.93055e56			0.153594
$743$		−	2.31392e56i		−	0.0880183i	−0.999031	−	0.0440091i	$-0.985987\pi$
$743$		−	2.31392e56i		−	0.0880183i	0.999031	−	0.0440091i	$-0.0140131\pi$
$744$	3.12754e57	+	8.25865e56i	1.15809	+	0.305809i
$745$	6.27672e56			0.226260
$746$			7.23984e57i			2.54069i
$747$	−9.61447e56	+	1.69355e57i	−0.328483	+	0.578610i
$748$	−7.58058e56			−0.252157
$749$		−	5.25205e57i		−	1.70095i
$750$	−8.01951e56	+	3.03697e57i	−0.252885	+	0.957670i
$751$	4.70972e57			1.44609			0.723047	−	0.690799i	$-0.242741\pi$
$751$	4.70972e57			1.44609			0.723047	+	0.690799i	$0.242741\pi$
$752$		−	4.59636e57i		−	1.37422i
$753$	4.65487e57	+	1.22918e57i	1.35522	+	0.357861i
$754$	6.85156e57			1.94251
$755$			4.28324e56i			0.118259i
$756$	−9.04073e57	+	9.23981e57i	−2.43090	+	2.48443i
$757$	−2.09698e56			−0.0549133			−0.0274567	−	0.999623i	$-0.508741\pi$
$757$	−2.09698e56			−0.0549133			−0.0274567	+	0.999623i	$0.508741\pi$
$758$			2.09958e57i			0.535487i
$759$	4.88481e55	−	1.84987e56i	0.0121342	−	0.0459522i
$760$	3.96711e57			0.959847
$761$		−	5.33392e57i		−	1.25705i	−0.777789	−	0.628526i	$-0.783659\pi$
$761$		−	5.33392e57i		−	1.25705i	0.777789	−	0.628526i	$-0.216341\pi$
$762$	−8.98852e57	−	2.37353e57i	−2.06342	−	0.544873i
$763$	−8.99223e57			−2.01084
$764$		−	6.45623e57i		−	1.40641i
$765$	1.09945e57	+	6.24170e56i	0.233317	+	0.132457i
$766$	9.88141e57			2.04288
$767$		−	5.11547e56i		−	0.103034i
$768$	3.29817e57	−	1.24901e58i	0.647215	−	2.45099i
$769$	−7.65032e57			−1.46269			−0.731346	−	0.682007i	$-0.761107\pi$
$769$	−7.65032e57			−1.46269			−0.731346	+	0.682007i	$0.761107\pi$
$770$		−	3.23809e56i		−	0.0603218i
$771$	−7.76594e56	−	2.05069e56i	−0.140963	−	0.0372231i
$772$	−1.37044e58			−2.42389
$773$		−	2.90279e57i		−	0.500294i	−0.968208	−	0.250147i	$-0.919521\pi$
$773$		−	2.90279e57i		−	0.500294i	0.968208	−	0.250147i	$-0.0804790\pi$
$774$	2.80967e57	−	4.94913e57i	0.471885	−	0.831207i
$775$	−2.04890e57			−0.335342
$776$			2.47296e58i			3.94442i
$777$	−1.20436e57	+	4.56088e57i	−0.187212	+	0.708970i
$778$	1.11746e58			1.69293
$779$			1.53239e57i			0.226267i
$780$	−3.08934e57	−	8.15779e56i	−0.444605	−	0.117403i
$781$	−7.65463e56			−0.107375
$782$		−	7.34900e57i		−	1.00483i
$783$	8.50527e57	+	8.32202e57i	1.13358	+	1.10916i
$784$	1.79153e58			2.32757
$785$			1.76152e57i			0.223098i
$786$	3.61623e57	−	1.36946e58i	0.446483	−	1.69082i
$787$	−2.28721e57			−0.275303			−0.137652	−	0.990481i	$-0.543955\pi$
$787$	−2.28721e57			−0.275303			−0.137652	+	0.990481i	$0.543955\pi$
$788$		−	2.28609e58i		−	2.68268i
$789$	−1.06568e58	−	2.81405e57i	−1.21923	−	0.321952i
$790$	−3.70286e57			−0.413044
$791$			7.57377e57i			0.823726i
$792$	2.50264e57	+	1.42078e57i	0.265397	+	0.150668i
$793$	−1.22867e57			−0.127049
$794$			2.19854e58i			2.21679i
$795$	−4.30786e55	+	1.63138e56i	−0.00423564	+	0.0160403i
$796$	1.66900e58			1.60027
$797$			4.77942e56i			0.0446898i	0.999750	+	0.0223449i	$0.00711320\pi$
$797$			4.77942e56i			0.0446898i	−0.999750	+	0.0223449i	$0.992887\pi$
$798$	−2.83904e58	−	7.49685e57i	−2.58889	−	0.683630i
$799$	4.23120e57			0.376295
$800$			4.05064e58i			3.51337i
$801$	5.59137e57	−	9.84897e57i	0.473007	−	0.833183i
$802$	1.69470e58			1.39831
$803$		−	2.16573e57i		−	0.174298i
$804$	−9.74047e57	+	3.68870e58i	−0.764643	+	2.89569i
$805$	2.29543e57			0.175771
$806$		−	5.91803e57i		−	0.442055i
$807$	1.78518e58	+	4.71399e57i	1.30080	+	0.343493i
$808$	−7.87173e58			−5.59556
$809$		−	1.21173e58i		−	0.840304i	−0.907454	−	0.420152i	$-0.861977\pi$
$809$		−	1.21173e58i		−	0.840304i	0.907454	−	0.420152i	$-0.138023\pi$
$810$	−3.88955e57	−	6.51653e57i	−0.263148	−	0.440876i
$811$	−2.24915e57			−0.148457			−0.0742287	−	0.997241i	$-0.523649\pi$
$811$	−2.24915e57			−0.148457			−0.0742287	+	0.997241i	$0.523649\pi$
$812$		−	8.56001e58i		−	5.51257i
$813$	−1.53977e57	+	5.83108e57i	−0.0967486	+	0.366385i
$814$	1.66049e57			0.101800
$815$		−	2.38326e57i		−	0.142567i
$816$	6.14542e58	+	1.62277e58i	3.58714	+	0.947229i
$817$	9.45262e57			0.538408
$818$		−	7.03298e56i		−	0.0390907i
$819$	1.30073e58	+	7.38437e57i	0.705518	+	0.400530i
$820$	2.84904e57			0.150807
$821$			2.88890e58i			1.49234i	0.665753	+	0.746172i	$0.268110\pi$
$821$			2.88890e58i			1.49234i	−0.665753	+	0.746172i	$0.731890\pi$
$822$	8.74014e57	−	3.30987e58i	0.440638	−	1.66869i
$823$	1.65769e58			0.815653			0.407826	−	0.913059i	$-0.366287\pi$
$823$	1.65769e58			0.815653			0.407826	+	0.913059i	$0.366287\pi$
$824$		−	3.74846e58i		−	1.80015i
$825$	−1.76242e57	−	4.65388e56i	−0.0826094	−	0.0218141i
$826$	−8.74018e57			−0.399870
$827$			2.16857e58i			0.968420i	0.874952	+	0.484210i	$0.160893\pi$
$827$			2.16857e58i			0.968420i	−0.874952	+	0.484210i	$0.839107\pi$
$828$	−1.59254e58	+	2.80519e58i	−0.694197	+	1.22280i
$829$	−1.17567e57			−0.0500260			−0.0250130	−	0.999687i	$-0.507963\pi$
$829$	−1.17567e57			−0.0500260			−0.0250130	+	0.999687i	$0.507963\pi$
$830$			8.22431e57i			0.341616i
$831$	7.82430e57	−	2.96305e58i	0.317267	−	1.20148i
$832$	−5.79520e58			−2.29405
$833$			1.64920e58i			0.637343i
$834$	−3.44793e58	−	9.10469e57i	−1.30088	−	0.343514i
$835$	−5.26467e57			−0.193929
$836$			7.55806e57i			0.271822i
$837$	7.18814e57	−	7.34643e57i	0.252411	−	0.257969i
$838$	3.99610e58			1.37011
$839$		−	1.62527e58i		−	0.544109i	−0.962282	−	0.272055i	$-0.912297\pi$
$839$		−	1.62527e58i		−	0.544109i	0.962282	−	0.272055i	$-0.0877031\pi$
$840$	−8.81494e57	+	3.33820e58i	−0.288160	+	1.09126i
$841$	−4.74681e58			−1.51524
$842$			7.20088e58i			2.24462i
$843$	−5.55126e58	−	1.46588e58i	−1.68982	−	0.446218i
$844$	1.32906e59			3.95089
$845$		−	5.47186e57i		−	0.158855i
$846$	−2.20876e58	−	1.25393e58i	−0.626239	−	0.355523i
$847$	−4.57493e58			−1.26682
$848$			8.48282e57i			0.229416i
$849$	5.85891e57	−	2.21876e58i	0.154762	−	0.586079i
$850$	−7.00157e58			−1.80641
$851$			1.17710e58i			0.296634i
$852$	1.24777e59	+	3.29490e58i	3.07145	+	0.811055i
$853$	2.75227e58			0.661774			0.330887	−	0.943670i	$-0.392652\pi$
$853$	2.75227e58			0.661774			0.330887	+	0.943670i	$0.392652\pi$
$854$			2.09928e58i			0.493075i
$855$	6.22315e57	−	1.09618e58i	0.142787	−	0.251513i
$856$	1.97124e59			4.41840
$857$			3.46477e58i			0.758678i	0.925258	+	0.379339i	$0.123849\pi$
$857$			3.46477e58i			0.758678i	−0.925258	+	0.379339i	$0.876151\pi$
$858$	1.34422e57	−	5.09055e57i	0.0287558	−	0.108898i
$859$	−3.09959e57			−0.0647799			−0.0323900	−	0.999475i	$-0.510312\pi$
$859$	−3.09959e57			−0.0647799			−0.0323900	+	0.999475i	$0.510312\pi$
$860$		−	1.75744e58i		−	0.358849i
$861$	−1.28946e58	−	3.40499e57i	−0.257245	−	0.0679287i
$862$	−1.16917e59			−2.27894
$863$		−	3.99818e58i		−	0.761459i	−0.924686	−	0.380729i	$-0.875673\pi$
$863$		−	3.99818e58i		−	0.761459i	0.924686	−	0.380729i	$-0.124327\pi$
$864$	−1.45237e59	−	1.42108e59i	−2.70273	−	2.64450i
$865$	−1.60965e58			−0.292692
$866$			7.76230e58i			1.37922i
$867$	−2.33995e56	+	8.86137e56i	−0.00406280	+	0.0153858i
$868$	−7.39371e58			−1.25449
$869$		−	4.46156e57i		−	0.0739760i
$870$	4.85876e58	+	1.28302e58i	0.787300	+	0.207896i
$871$	4.41429e58			0.699033
$872$		−	3.37504e59i		−	5.22335i
$873$	6.83325e58	+	3.87931e58i	1.03358	+	0.586772i
$874$	−7.32716e58			−1.08320
$875$		−	4.54060e58i		−	0.656073i
$876$	−9.32227e58	+	3.53033e59i	−1.31656	+	4.98578i
$877$	3.39066e58			0.468050			0.234025	−	0.972231i	$-0.424810\pi$
$877$	3.39066e58			0.468050			0.234025	+	0.972231i	$0.424810\pi$
$878$			2.27532e59i			3.07010i
$879$	−8.39328e58	−	2.21635e58i	−1.10702	−	0.292322i
$880$	6.98837e57			0.0900996
$881$		−	3.64124e58i		−	0.458914i	−0.973319	−	0.229457i	$-0.926305\pi$
$881$		−	3.64124e58i		−	0.458914i	0.973319	−	0.229457i	$-0.0736950\pi$
$882$	4.88747e58	−	8.60909e58i	0.602161	−	1.06068i
$883$	1.02015e58			0.122871			0.0614357	−	0.998111i	$-0.480432\pi$
$883$	1.02015e58			0.122871			0.0614357	+	0.998111i	$0.480432\pi$
$884$		−	1.47877e59i		−	1.74123i
$885$	9.57918e56	−	3.62762e57i	0.0110271	−	0.0417596i
$886$	2.16301e59			2.43436
$887$		−	3.63573e58i		−	0.400055i	−0.979790	−	0.200027i	$-0.935897\pi$
$887$		−	3.63573e58i		−	0.400055i	0.979790	−	0.200027i	$-0.0641031\pi$
$888$	−1.71183e59	−	4.52029e58i	−1.84162	−	0.486303i
$889$	1.34388e59			1.41360
$890$		−	4.78291e58i		−	0.491918i
$891$	7.85173e57	−	4.68650e57i	0.0789608	−	0.0471297i
$892$	7.09810e58			0.697983
$893$		−	4.21863e58i		−	0.405641i
$894$	4.45194e58	−	1.68594e59i	0.418599	−	1.58523i
$895$	−3.80007e58			−0.349407
$896$			4.52870e59i			4.07206i
$897$	3.60861e58	+	9.52899e57i	0.317316	+	0.0837911i
$898$	−1.87078e59			−1.60878
$899$			6.80593e58i			0.572392i
$900$	2.67257e59	+	1.51725e59i	2.19826	+	1.24798i
$901$	−7.80890e57			−0.0628195
$902$			4.69459e57i			0.0369374i
$903$	−2.10038e58	+	7.95410e58i	−0.161638	+	0.612119i
$904$	−2.84265e59			−2.13971
$905$			6.51196e58i			0.479446i
$906$	1.15049e59	+	3.03801e58i	0.828550	+	0.218789i
$907$	1.26422e58			0.0890591			0.0445296	−	0.999008i	$-0.485821\pi$
$907$	1.26422e58			0.0890591			0.0445296	+	0.999008i	$0.485821\pi$
$908$			6.92598e58i			0.477270i
$909$	−1.23483e59	+	2.17510e59i	−0.832395	+	1.46623i
$910$	6.31666e58			0.416543
$911$		−	2.56648e59i		−	1.65566i	−0.560980	−	0.827829i	$-0.689576\pi$
$911$		−	2.56648e59i		−	1.65566i	0.560980	−	0.827829i	$-0.310424\pi$
$912$	1.61795e59	−	6.12716e59i	1.02110	−	3.86690i
$913$	−9.90943e57			−0.0611833
$914$		−	6.77938e58i		−	0.409511i
$915$	−8.71308e57	−	2.30080e57i	−0.0514932	−	0.0135974i
$916$	−6.77184e59			−3.91559
$917$			2.04749e59i			1.15834i
$918$	2.45635e59	−	2.51044e59i	1.35968	−	1.38962i
$919$	6.32460e58			0.342549			0.171275	−	0.985223i	$-0.445211\pi$
$919$	6.32460e58			0.342549			0.171275	+	0.985223i	$0.445211\pi$
$920$			8.61541e58i			0.456583i
$921$	−4.28868e58	+	1.62412e59i	−0.222398	+	0.842218i
$922$	−3.39629e59			−1.72340
$923$		−	1.49322e59i		−	0.741462i
$924$	−6.35988e58	−	1.67941e58i	−0.309037	−	0.0816049i
$925$	1.12145e59			0.533267
$926$		−	1.37714e59i		−	0.640853i
$927$	−1.03577e59	−	5.88016e58i	−0.471701	−	0.267790i
$928$	1.34552e60			5.99694
$929$			3.20109e59i			1.39632i	0.715944	+	0.698158i	$0.245996\pi$
$929$			3.20109e59i			1.39632i	−0.715944	+	0.698158i	$0.754004\pi$
$930$	1.10820e58	−	4.19675e58i	0.0473109	−	0.179165i
$931$	1.64430e59			0.687048
$932$		−	1.08675e59i		−	0.444440i
$933$	−2.64593e59	−	6.98691e58i	−1.05912	−	0.279674i
$934$	−2.53792e59			−0.994351
$935$			6.43319e57i			0.0246714i
$936$	−2.77156e59	+	4.88200e59i	−1.04042	+	1.83265i
$937$	−2.66392e59			−0.978880			−0.489440	−	0.872037i	$-0.662799\pi$
$937$	−2.66392e59			−0.978880			−0.489440	+	0.872037i	$0.662799\pi$
$938$		−	7.54215e59i		−	2.71293i
$939$	1.47788e58	−	5.59670e58i	0.0520388	−	0.197070i
$940$	−7.84331e58			−0.270360
$941$		−	1.45567e58i		−	0.0491214i	−0.999698	−	0.0245607i	$-0.992181\pi$
$941$		−	1.45567e58i		−	0.0491214i	0.999698	−	0.0245607i	$-0.00781871\pi$
$942$	4.73150e59	+	1.24941e59i	1.56308	+	0.412750i
$943$	−3.32792e58			−0.107631
$944$		−	1.88629e59i		−	0.597266i
$945$	7.84127e58	+	7.67233e58i	0.243081	+	0.237843i
$946$	2.89587e58			0.0878934
$947$		−	2.75989e59i		−	0.820147i	−0.912052	−	0.410073i	$-0.865503\pi$
$947$		−	2.75989e59i		−	0.820147i	0.912052	−	0.410073i	$-0.134497\pi$
$948$	−1.92046e59	+	7.27274e59i	−0.558776	+	2.11608i
$949$	4.22477e59			1.20359
$950$			6.98076e59i			1.94729i
$951$	−9.11004e57	−	2.40562e57i	−0.0248834	−	0.00657077i
$952$	−1.59789e60			−4.27375
$953$		−	1.83048e59i		−	0.479410i	−0.970846	−	0.239705i	$-0.922949\pi$
$953$		−	1.83048e59i		−	0.479410i	0.970846	−	0.239705i	$-0.0770507\pi$
$954$	4.07637e58	+	2.31420e58i	0.104546	+	0.0593517i
$955$	−5.47901e58			−0.137605
$956$			7.75797e59i			1.90805i
$957$	−1.54590e58	+	5.85429e58i	−0.0372342	+	0.141005i
$958$	8.49226e59			2.00315
$959$			4.94862e59i			1.14317i
$960$	−4.10965e59	−	1.08520e59i	−0.929780	−	0.245520i
$961$	−3.92516e59			−0.869741
$962$			3.23918e59i			0.702965i
$963$	3.09226e59	−	5.44690e59i	0.657281	−	1.15777i
$964$	1.64036e60			3.41506
$965$			1.16301e59i			0.237157i
$966$	1.62810e59	−	6.16559e59i	0.325191	−	1.23149i
$967$	−5.12589e58			−0.100286			−0.0501429	−	0.998742i	$-0.515968\pi$
$967$	−5.12589e58			−0.100286			−0.0501429	+	0.998742i	$0.515968\pi$
$968$		−	1.71710e60i		−	3.29070i
$969$	5.64039e59	+	1.48942e59i	1.05885	+	0.279602i
$970$	3.31840e59			0.610231
$971$		−	7.83460e59i		−	1.41134i	−0.708540	−	0.705671i	$-0.750646\pi$
$971$		−	7.83460e59i		−	1.41134i	0.708540	−	0.705671i	$-0.249354\pi$
$972$	−1.48163e60	+	4.25967e59i	−2.61466	+	0.751711i
$973$	5.15502e59			0.891197
$974$			5.29357e59i			0.896540i
$975$	9.07850e58	−	3.43801e59i	0.150634	−	0.570447i
$976$	−4.53061e59			−0.736480
$977$		−	2.36714e59i		−	0.376992i	−0.982074	−	0.188496i	$-0.939639\pi$
$977$		−	2.36714e59i		−	0.376992i	0.982074	−	0.188496i	$-0.0603613\pi$
$978$	−6.40150e59	−	1.69040e59i	−0.998860	−	0.263761i
$979$	5.76290e58			0.0881023
$980$		−	3.05710e59i		−	0.457918i
$981$	−9.32585e59	−	5.29439e59i	−1.36870	−	0.777026i
$982$	1.20805e60			1.73723
$983$			1.21390e60i			1.71046i	0.518247	+	0.855231i	$0.326585\pi$
$983$			1.21390e60i			1.71046i	−0.518247	+	0.855231i	$0.673415\pi$
$984$	1.27799e59	−	4.83973e59i	0.176452	−	0.668219i
$985$	−1.94007e59			−0.262478
$986$			2.32574e60i			3.08335i
$987$	3.54985e59	+	9.37383e58i	0.461177	+	0.121779i
$988$	−1.47438e60			−1.87703
$989$			2.05284e59i			0.256111i
$990$	1.90650e58	−	3.35823e58i	0.0233095	−	0.0410588i
$991$	−1.27420e60			−1.52673			−0.763367	−	0.645965i	$-0.776455\pi$
$991$	−1.27420e60			−1.52673			−0.763367	+	0.645965i	$0.776455\pi$
$992$		−	1.16219e60i		−	1.36472i
$993$	3.87380e59	−	1.46700e60i	0.445812	−	1.68828i
$994$	−2.55128e60			−2.87760
$995$		−	1.41638e59i		−	0.156573i
$996$	1.61532e60	+	4.26547e59i	1.75014	+	0.462147i
$997$	9.49442e59			1.00824			0.504122	−	0.863633i	$-0.331816\pi$
$997$	9.49442e59			1.00824			0.504122	+	0.863633i	$0.331816\pi$
$998$			4.92949e59i			0.513087i
$999$	−3.93436e59	+	4.02100e59i	−0.401388	+	0.410227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.41.b.a.2.12	yes	12
3.2	odd	2	inner	3.41.b.a.2.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.41.b.a.2.1	✓	12	3.2	odd	2	inner
3.41.b.a.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:	\( k \)	\(=\)	\( 41 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.02257e6i q^{2} +(8.90215e8 - 3.37123e9i) q^{3} -2.99130e12 q^{4} +2.53853e13i q^{5} +(6.81856e15 + 1.80053e15i) q^{6} -1.01945e17 q^{7} -3.82628e18i q^{8} +(-1.05727e19 - 6.00224e18i) q^{9} +O(q^{10})\)	\(q+2.02257e6i q^{2} +(8.90215e8 - 3.37123e9i) q^{3} -2.99130e12 q^{4} +2.53853e13i q^{5} +(6.81856e15 + 1.80053e15i) q^{6} -1.01945e17 q^{7} -3.82628e18i q^{8} +(-1.05727e19 - 6.00224e18i) q^{9} -5.13437e19 q^{10} -6.18638e19i q^{11} +(-2.66290e21 + 1.00843e22i) q^{12} +1.20680e22 q^{13} -2.06191e23i q^{14} +(8.55798e22 + 2.25984e22i) q^{15} +4.44997e24 q^{16} +4.09644e24i q^{17} +(1.21400e25 - 2.13841e25i) q^{18} +4.08427e25 q^{19} -7.59351e25i q^{20} +(-9.07528e25 + 3.43679e26i) q^{21} +1.25124e26 q^{22} +8.86986e26i q^{23} +(-1.28993e28 - 3.40621e27i) q^{24} +8.45053e27 q^{25} +2.44084e28i q^{26} +(-2.96469e28 + 3.02997e28i) q^{27} +3.04947e29 q^{28} -2.80705e29i q^{29} +(-4.57070e28 + 1.73092e29i) q^{30} -2.42459e29 q^{31} +4.79335e30i q^{32} +(-2.08557e29 - 5.50721e28i) q^{33} -8.28536e30 q^{34} -2.58790e30i q^{35} +(3.16261e31 + 1.79545e31i) q^{36} +1.32707e31 q^{37} +8.26074e31i q^{38} +(1.07431e31 - 4.06840e31i) q^{39} +9.71314e31 q^{40} +3.75194e31i q^{41} +(-6.95117e32 - 1.83554e32i) q^{42} +2.31440e32 q^{43} +1.85053e32i q^{44} +(1.52369e32 - 2.68392e32i) q^{45} -1.79400e33 q^{46} -1.03290e33i q^{47} +(3.96143e33 - 1.50019e34i) q^{48} +4.02593e33 q^{49} +1.70918e34i q^{50} +(1.38100e34 + 3.64671e33i) q^{51} -3.60990e34 q^{52} +1.90627e33i q^{53} +(-6.12834e34 - 5.99630e34i) q^{54} +1.57043e33 q^{55} +3.90069e35i q^{56} +(3.63588e34 - 1.37690e35i) q^{57} +5.67746e35 q^{58} -4.23888e34i q^{59} +(-2.55995e35 - 6.75985e34i) q^{60} -1.01812e35 q^{61} -4.90391e35i q^{62} +(1.07783e36 + 6.11897e35i) q^{63} -4.80213e36 q^{64} +3.06350e35i q^{65} +(1.11387e35 - 4.21822e35i) q^{66} +3.65785e36 q^{67} -1.22537e37i q^{68} +(2.99023e36 + 7.89608e35i) q^{69} +5.23423e36 q^{70} -1.23734e37i q^{71} +(-2.29662e37 + 4.04541e37i) q^{72} +3.50080e37 q^{73} +2.68411e37i q^{74} +(7.52279e36 - 2.84887e37i) q^{75} -1.22173e38 q^{76} +6.30669e36i q^{77} +(8.22864e37 + 2.17287e37i) q^{78} +7.21191e37 q^{79} +1.12964e38i q^{80} +(7.57552e37 + 1.26920e38i) q^{81} -7.58859e37 q^{82} -1.60181e38i q^{83} +(2.71468e38 - 1.02805e39i) q^{84} -1.03990e38 q^{85} +4.68104e38i q^{86} +(-9.46320e38 - 2.49888e38i) q^{87} -2.36708e38 q^{88} +9.31547e38i q^{89} +(5.42842e38 + 3.08177e38i) q^{90} -1.23027e39 q^{91} -2.65324e39i q^{92} +(-2.15840e38 + 8.17383e38i) q^{93} +2.08911e39 q^{94} +1.03681e39i q^{95} +(1.61595e40 + 4.26711e39i) q^{96} -6.46310e39 q^{97} +8.14275e39i q^{98} +(-3.71321e38 + 6.54067e38i) 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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