LMFDB - Embedded newform 3.35.b.a.2.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,35,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, 35, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 35);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 35 $
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:	$21.9676962128$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 789518143 x^{8} + \cdots + 50\!\cdots\!00 $ x^10 + 789518143x^8 + 211496483076151936x^6 + 21382790524640936160081920x^4 + 613809329098098496707904510361600x^2 + 5042460246515433703013776627104481280000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{54}\cdot 3^{65}\cdot 5^{4}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.9
Root			$16987.2i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.35.b.a.2.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+203846. i q^{2} +(-1.15096e8 + 5.85668e7i) q^{3} -2.43733e10 q^{4} +1.79877e11i q^{5} +(-1.19386e13 - 2.34619e13i) q^{6} -2.97937e14 q^{7} -1.46635e15i q^{8} +(9.81704e15 - 1.34816e16i) q^{9} +O(q^{10})$	\(q+203846. i q^{2} +(-1.15096e8 + 5.85668e7i) q^{3} -2.43733e10 q^{4} +1.79877e11i q^{5} +(-1.19386e13 - 2.34619e13i) q^{6} -2.97937e14 q^{7} -1.46635e15i q^{8} +(9.81704e15 - 1.34816e16i) q^{9} -3.66671e16 q^{10} -5.45809e17i q^{11} +(2.80527e18 - 1.42747e18i) q^{12} +6.76117e18 q^{13} -6.07333e19i q^{14} +(-1.05348e19 - 2.07031e19i) q^{15} -1.19820e20 q^{16} +1.38305e21i q^{17} +(2.74817e21 + 2.00116e21i) q^{18} -8.87671e21 q^{19} -4.38419e21i q^{20} +(3.42914e22 - 1.74492e22i) q^{21} +1.11261e23 q^{22} +2.99358e22i q^{23} +(8.58794e22 + 1.68771e23i) q^{24} +5.49721e23 q^{25} +1.37824e24i q^{26} +(-3.40329e23 + 2.12663e24i) q^{27} +7.26171e24 q^{28} -3.17183e24i q^{29} +(4.22024e24 - 2.14748e24i) q^{30} +1.17602e24 q^{31} -4.96166e25i q^{32} +(3.19663e25 + 6.28205e25i) q^{33} -2.81928e26 q^{34} -5.35919e25i q^{35} +(-2.39274e26 + 3.28591e26i) q^{36} +3.74912e26 q^{37} -1.80948e27i q^{38} +(-7.78185e26 + 3.95980e26i) q^{39} +2.63762e26 q^{40} -2.13908e27i q^{41} +(3.55695e27 + 6.99016e27i) q^{42} +4.08388e27 q^{43} +1.33032e28i q^{44} +(2.42503e27 + 1.76586e27i) q^{45} -6.10229e27 q^{46} -4.95016e28i q^{47} +(1.37909e28 - 7.01750e27i) q^{48} +3.46495e28 q^{49} +1.12058e29i q^{50} +(-8.10006e28 - 1.59183e29i) q^{51} -1.64792e29 q^{52} +9.35752e28i q^{53} +(-4.33506e29 - 6.93746e28i) q^{54} +9.81784e28 q^{55} +4.36880e29i q^{56} +(1.02167e30 - 5.19881e29i) q^{57} +6.46565e29 q^{58} -6.32368e29i q^{59} +(2.56768e29 + 5.04603e29i) q^{60} +4.42775e29 q^{61} +2.39727e29i q^{62} +(-2.92486e30 + 4.01667e30i) q^{63} +8.05565e30 q^{64} +1.21618e30i q^{65} +(-1.28057e31 + 6.51620e30i) q^{66} -4.63018e30 q^{67} -3.37094e31i q^{68} +(-1.75324e30 - 3.44549e30i) q^{69} +1.09245e31 q^{70} -2.74044e30i q^{71} +(-1.97688e31 - 1.43952e31i) q^{72} -2.72565e31 q^{73} +7.64242e31i q^{74} +(-6.32707e31 + 3.21954e31i) q^{75} +2.16355e32 q^{76} +1.62617e32i q^{77} +(-8.07189e31 - 1.58630e32i) q^{78} +1.93130e32 q^{79} -2.15529e31i q^{80} +(-8.53797e31 - 2.64699e32i) q^{81} +4.36044e32 q^{82} -2.76431e32i q^{83} +(-8.35794e32 + 4.25295e32i) q^{84} -2.48778e32 q^{85} +8.32483e32i q^{86} +(1.85764e32 + 3.65065e32i) q^{87} -8.00347e32 q^{88} -2.71501e33i q^{89} +(-3.59963e32 + 4.94332e32i) q^{90} -2.01440e33 q^{91} -7.29634e32i q^{92} +(-1.35355e32 + 6.88757e31i) q^{93} +1.00907e34 q^{94} -1.59671e33i q^{95} +(2.90589e33 + 5.71068e33i) q^{96} -1.23468e33 q^{97} +7.06317e33i q^{98} +(-7.35839e33 - 5.35823e33i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 119369106 q^{3} - 55582533344 q^{4} - 9250224859872 q^{6} - 123569771565772 q^{7} + 47\!\cdots\!18 q^{9}+O(q^{10}) $ 10 * q + 119369106 * q^3 - 55582533344 * q^4 - 9250224859872 * q^6 - 123569771565772 * q^7 + 4787501147541018 * q^9	$ 10 q + 119369106 q^{3} - 55582533344 q^{4} - 9250224859872 q^{6} - 123569771565772 q^{7} + 47\!\cdots\!18 q^{9}+ \cdots + 25\!\cdots\!80 q^{99}+O(q^{100}) $ 10 * q + 119369106 * q^3 - 55582533344 * q^4 - 9250224859872 * q^6 - 123569771565772 * q^7 + 4787501147541018 * q^9 - 2611205560422720 * q^10 + 1839088058193784224 * q^12 + 3639874363106470052 * q^13 + 73840351311049043520 * q^15 - 458913568062658993664 * q^16 + 4458031837811233600320 * q^18 - 18128087575667617007644 * q^19 + 47155216574801503272132 * q^21 - 82944038352793331672640 * q^22 - 409540832361157949627904 * q^24 - 306157881917435527620230 * q^25 - 5188422304885629117270366 * q^27 + 1200257625823339935397952 * q^28 + 4536084230702466968226240 * q^30 - 16210124253435972809624620 * q^31 + 126080615773751026110338880 * q^33 - 95987113410493892068003584 * q^34 - 3778740843166378351675872 * q^36 + 1107877531995608327024550788 * q^37 - 1478567172848906073011055372 * q^39 + 1263325098820483891139005440 * q^40 - 1100302459230379163303563200 * q^42 - 9626706570211152095714911228 * q^43 + 6764773545409610284732206720 * q^45 - 27597232473865615892091763584 * q^46 - 8343379363160137604055750144 * q^48 + 123592722368423574378839845566 * q^49 - 154249157901217791265339790592 * q^51 + 364968511672502550561914224448 * q^52 - 627476296349871988055293152672 * q^54 + 613243149395194155294476807040 * q^55 - 200956522080425270978267102412 * q^57 + 911704545930429232428533728320 * q^58 - 5328764870697498499759490872320 * q^60 + 3721644688213000805892336114020 * q^61 - 17793115140162074693090527345068 * q^63 + 31237929890100178456062152876032 * q^64 - 56522434211150051720831749496640 * q^66 + 64610860820592975458220110976548 * q^67 - 75655347603668350171840261441152 * q^69 + 173956643092708582155719748059520 * q^70 - 251655858465803757687636471720960 * q^72 + 219744563327934154882825652170292 * q^73 - 496257346175691552817323610505790 * q^75 + 755138601297458545349651061598016 * q^76 - 1416035973322463045417779737274560 * q^78 + 1282143700776175332608732687725076 * q^79 - 1752271238163022185686811202609110 * q^81 + 2617087107433191584283809414490240 * q^82 - 3353754502177451840461431126935232 * q^84 + 3064318591304040683100089841123840 * q^85 - 1378895999771415686373632115051840 * q^87 + 2890193643030846777850875310341120 * q^88 - 3749676158586283582801263594857280 * q^90 + 3328617839789463835132355588364424 * q^91 - 913294458028957034010214182487068 * q^93 - 1912224205137436189468854646420224 * q^94 + 5756213457708614900907762734014464 * q^96 - 11994339580278056229821837667722092 * q^97 + 25463971047319347192017533065521280 * 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 $

$2$			203846.i			1.55522i	0.628746	+	0.777611i	$0.283568\pi$
$2$			203846.i			1.55522i	−0.628746	+	0.777611i	$0.716432\pi$
$3$	−1.15096e8	+	5.85668e7i	−0.891249	+	0.453513i
$3$	−1.15096e8	+	5.85668e7i	−0.891249	+	0.453513i
$4$	−2.43733e10			−1.41871
$5$			1.79877e11i			0.235768i	0.993027	+	0.117884i	$0.0376111\pi$
$5$			1.79877e11i			0.235768i	−0.993027	+	0.117884i	$0.962389\pi$
$6$	−1.19386e13	−	2.34619e13i	−0.705313	−	1.38609i
$7$	−2.97937e14			−1.28073			−0.640365	−	0.768070i	$-0.721217\pi$
$7$	−2.97937e14			−1.28073			−0.640365	+	0.768070i	$0.721217\pi$
$8$		−	1.46635e15i		−	0.651190i
$9$	9.81704e15	−	1.34816e16i	0.588651	−	0.808387i
$10$	−3.66671e16			−0.366671
$11$		−	5.45809e17i		−	1.07985i	−0.841712	−	0.539927i	$-0.818452\pi$
$11$		−	5.45809e17i		−	1.07985i	0.841712	−	0.539927i	$-0.181548\pi$
$12$	2.80527e18	−	1.42747e18i	1.26443	−	0.643405i
$13$	6.76117e18			0.781601			0.390800	−	0.920475i	$-0.372198\pi$
$13$	6.76117e18			0.781601			0.390800	+	0.920475i	$0.372198\pi$
$14$		−	6.07333e19i		−	1.99182i
$15$	−1.05348e19	−	2.07031e19i	−0.106924	−	0.210128i
$16$	−1.19820e20			−0.405968
$17$			1.38305e21i			1.67188i	0.548821	+	0.835940i	$0.315077\pi$
$17$			1.38305e21i			1.67188i	−0.548821	+	0.835940i	$0.684923\pi$
$18$	2.74817e21	+	2.00116e21i	1.25722	+	0.915483i
$19$	−8.87671e21			−1.61972			−0.809862	−	0.586621i	$-0.800458\pi$
$19$	−8.87671e21			−1.61972			−0.809862	+	0.586621i	$0.800458\pi$
$20$		−	4.38419e21i		−	0.334487i
$21$	3.42914e22	−	1.74492e22i	1.14145	−	0.580829i
$22$	1.11261e23			1.67941
$23$			2.99358e22i			0.212235i	0.994354	+	0.106118i	$0.0338420\pi$
$23$			2.99358e22i			0.212235i	−0.994354	+	0.106118i	$0.966158\pi$
$24$	8.58794e22	+	1.68771e23i	0.295323	+	0.580373i
$25$	5.49721e23			0.944413
$26$			1.37824e24i			1.21556i
$27$	−3.40329e23	+	2.12663e24i	−0.158021	+	0.987436i
$28$	7.26171e24			1.81699
$29$		−	3.17183e24i		−	0.437063i	−0.975830	−	0.218532i	$-0.929873\pi$
$29$		−	3.17183e24i		−	0.437063i	0.975830	−	0.218532i	$-0.0701267\pi$
$30$	4.22024e24	−	2.14748e24i	0.326796	−	0.166290i
$31$	1.17602e24			0.0521514			0.0260757	−	0.999660i	$-0.491699\pi$
$31$	1.17602e24			0.0521514			0.0260757	+	0.999660i	$0.491699\pi$
$32$		−	4.96166e25i		−	1.28256i
$33$	3.19663e25	+	6.28205e25i	0.489728	+	0.962420i
$34$	−2.81928e26			−2.60014
$35$		−	5.35919e25i		−	0.301955i
$36$	−2.39274e26	+	3.28591e26i	−0.835127	+	1.14687i
$37$	3.74912e26			0.821296			0.410648	−	0.911794i	$-0.365302\pi$
$37$	3.74912e26			0.821296			0.410648	+	0.911794i	$0.365302\pi$
$38$		−	1.80948e27i		−	2.51903i
$39$	−7.78185e26	+	3.95980e26i	−0.696601	+	0.354466i
$40$	2.63762e26			0.153530
$41$		−	2.13908e27i		−	0.818281i	−0.912471	−	0.409140i	$-0.865829\pi$
$41$		−	2.13908e27i		−	0.818281i	0.912471	−	0.409140i	$-0.134171\pi$
$42$	3.55695e27	+	6.99016e27i	0.903317	+	1.77521i
$43$	4.08388e27			0.695200			0.347600	−	0.937643i	$-0.386997\pi$
$43$	4.08388e27			0.695200			0.347600	+	0.937643i	$0.386997\pi$
$44$			1.33032e28i			1.53200i
$45$	2.42503e27	+	1.76586e27i	0.190592	+	0.138785i
$46$	−6.10229e27			−0.330073
$47$		−	4.95016e28i		−	1.85761i	−0.370564	−	0.928807i	$-0.620836\pi$
$47$		−	4.95016e28i		−	1.85761i	0.370564	−	0.928807i	$-0.379164\pi$
$48$	1.37909e28	−	7.01750e27i	0.361818	−	0.184112i
$49$	3.46495e28			0.640272
$50$			1.12058e29i			1.46877i
$51$	−8.10006e28	−	1.59183e29i	−0.758220	−	1.49006i
$52$	−1.64792e29			−1.10887
$53$			9.35752e28i			0.455482i	0.973722	+	0.227741i	$0.0731339\pi$
$53$			9.35752e28i			0.455482i	−0.973722	+	0.227741i	$0.926866\pi$
$54$	−4.33506e29	−	6.93746e28i	−1.53568	−	0.245757i
$55$	9.81784e28			0.254595
$56$			4.36880e29i			0.833999i
$57$	1.02167e30	−	5.19881e29i	1.44358	−	0.734566i
$58$	6.46565e29			0.679730
$59$		−	6.32368e29i		−	0.497148i	−0.968613	−	0.248574i	$-0.920038\pi$
$59$		−	6.32368e29i		−	0.497148i	0.968613	−	0.248574i	$-0.0799619\pi$
$60$	2.56768e29	+	5.04603e29i	0.151694	+	0.298111i
$61$	4.42775e29			0.197504			0.0987519	−	0.995112i	$-0.468515\pi$
$61$	4.42775e29			0.197504			0.0987519	+	0.995112i	$0.468515\pi$
$62$			2.39727e29i			0.0811069i
$63$	−2.92486e30	+	4.01667e30i	−0.753904	+	1.03533i
$64$	8.05565e30			1.58870
$65$			1.21618e30i			0.184276i
$66$	−1.28057e31	+	6.51620e30i	−1.49678	+	0.761636i
$67$	−4.63018e30			−0.419108			−0.209554	−	0.977797i	$-0.567201\pi$
$67$	−4.63018e30			−0.419108			−0.209554	+	0.977797i	$0.567201\pi$
$68$		−	3.37094e31i		−	2.37192i
$69$	−1.75324e30	−	3.44549e30i	−0.0962516	−	0.189155i
$70$	1.09245e31			0.469607
$71$		−	2.74044e30i		−	0.0925611i	−0.998928	−	0.0462805i	$-0.985263\pi$
$71$		−	2.74044e30i		−	0.0925611i	0.998928	−	0.0462805i	$-0.0147368\pi$
$72$	−1.97688e31	−	1.43952e31i	−0.526414	−	0.383324i
$73$	−2.72565e31			−0.574092			−0.287046	−	0.957917i	$-0.592673\pi$
$73$	−2.72565e31			−0.574092			−0.287046	+	0.957917i	$0.592673\pi$
$74$			7.64242e31i			1.27730i
$75$	−6.32707e31	+	3.21954e31i	−0.841708	+	0.428304i
$76$	2.16355e32			2.29792
$77$			1.62617e32i			1.38300i
$78$	−8.07189e31	−	1.58630e32i	−0.551274	−	1.08337i
$79$	1.93130e32			1.06216			0.531080	−	0.847322i	$-0.321787\pi$
$79$	1.93130e32			1.06216			0.531080	+	0.847322i	$0.321787\pi$
$80$		−	2.15529e31i		−	0.0957142i
$81$	−8.53797e31	−	2.64699e32i	−0.306979	−	0.951716i
$82$	4.36044e32			1.27261
$83$		−	2.76431e32i		−	0.656537i	−0.944584	−	0.328269i	$-0.893535\pi$
$83$		−	2.76431e32i		−	0.656537i	0.944584	−	0.328269i	$-0.106465\pi$
$84$	−8.35794e32	+	4.25295e32i	−1.61939	+	0.824029i
$85$	−2.48778e32			−0.394176
$86$			8.32483e32i			1.08119i
$87$	1.85764e32	+	3.65065e32i	0.198214	+	0.389532i
$88$	−8.00347e32			−0.703191
$89$		−	2.71501e33i		−	1.96853i	−0.176706	−	0.984264i	$-0.556544\pi$
$89$		−	2.71501e33i		−	1.96853i	0.176706	−	0.984264i	$-0.443456\pi$
$90$	−3.59963e32	+	4.94332e32i	−0.215842	+	0.296412i
$91$	−2.01440e33			−1.00102
$92$		−	7.29634e32i		−	0.301101i
$93$	−1.35355e32	+	6.88757e31i	−0.0464799	+	0.0236513i
$94$	1.00907e34			2.88900
$95$		−	1.59671e33i		−	0.381879i
$96$	2.90589e33	+	5.71068e33i	0.581658	+	1.14308i
$97$	−1.23468e33			−0.207222			−0.103611	−	0.994618i	$-0.533040\pi$
$97$	−1.23468e33			−0.207222			−0.103611	+	0.994618i	$0.533040\pi$
$98$			7.06317e33i			0.995764i
$99$	−7.35839e33	−	5.35823e33i	−0.872940	−	0.635658i
$100$	−1.33985e34			−1.33985
$101$			1.60999e34i			1.35944i	0.733473	+	0.679718i	$0.237898\pi$
$101$			1.60999e34i			1.35944i	−0.733473	+	0.679718i	$0.762102\pi$
$102$	3.24489e34	−	1.65116e34i	2.31738	−	1.17920i
$103$	−1.43441e34			−0.867841			−0.433920	−	0.900951i	$-0.642870\pi$
$103$	−1.43441e34			−0.867841			−0.433920	+	0.900951i	$0.642870\pi$
$104$		−	9.91424e33i		−	0.508971i
$105$	3.13871e33	+	6.16822e33i	0.136941	+	0.269118i
$106$	−1.90749e34			−0.708375
$107$		−	1.60322e34i		−	0.507537i	−0.967265	−	0.253768i	$-0.918330\pi$
$107$		−	1.60322e34i		−	0.507537i	0.967265	−	0.253768i	$-0.0816701\pi$
$108$	8.29493e33	−	5.18331e34i	0.224186	−	1.40089i
$109$	−5.19945e34			−1.20145			−0.600727	−	0.799454i	$-0.705122\pi$
$109$	−5.19945e34			−1.20145			−0.600727	+	0.799454i	$0.705122\pi$
$110$			2.00133e34i			0.395952i
$111$	−4.31509e34	+	2.19574e34i	−0.731980	+	0.372469i
$112$	3.56990e34			0.519935
$113$		−	1.59663e34i		−	0.199927i	−0.994991	−	0.0999633i	$-0.968127\pi$
$113$		−	1.59663e34i		−	0.199927i	0.994991	−	0.0999633i	$-0.0318725\pi$
$114$	1.05976e35	+	2.08264e35i	1.14241	+	2.24508i
$115$	−5.38475e33			−0.0500383
$116$			7.73080e34i			0.620067i
$117$	6.63747e34	−	9.11515e34i	0.460090	−	0.631836i
$118$	1.28906e35			0.773175
$119$		−	4.12061e35i		−	2.14123i
$120$	−3.03580e34	+	1.54477e34i	−0.136833	+	0.0696278i
$121$	−4.24310e34			−0.166086
$122$			9.02578e34i			0.307162i
$123$	1.25279e35	+	2.46200e35i	0.371101	+	0.729292i
$124$	−2.86635e34			−0.0739878
$125$			2.03584e35i			0.458430i
$126$	−8.18783e35	−	5.96221e35i	−1.61016	−	1.17249i
$127$	−6.17065e34			−0.106088			−0.0530442	−	0.998592i	$-0.516892\pi$
$127$	−6.17065e34			−0.106088			−0.0530442	+	0.998592i	$0.516892\pi$
$128$			7.89704e35i			1.18821i
$129$	−4.70039e35	+	2.39180e35i	−0.619596	+	0.315282i
$130$	−2.47913e35			−0.286591
$131$		−	3.37852e35i		−	0.342858i	−0.985196	−	0.171429i	$-0.945162\pi$
$131$		−	3.37852e35i		−	0.342858i	0.985196	−	0.171429i	$-0.0548385\pi$
$132$	−7.79124e35	−	1.53114e36i	−0.694784	−	1.36540i
$133$	2.64470e36			2.07443
$134$		−	9.43843e35i		−	0.651806i
$135$	−3.82532e35	−	6.12172e34i	−0.232806	−	0.0372563i
$136$	2.02803e36			1.08871
$137$			2.58108e36i			1.22335i	0.791107	+	0.611677i	$0.209505\pi$
$137$			2.58108e36i			1.22335i	−0.791107	+	0.611677i	$0.790495\pi$
$138$	7.02350e35	−	3.57392e35i	0.294177	−	0.149692i
$139$	−2.72993e36			−1.01135			−0.505673	−	0.862725i	$-0.668756\pi$
$139$	−2.72993e36			−1.01135			−0.505673	+	0.862725i	$0.668756\pi$
$140$			1.30621e36i			0.428388i
$141$	2.89915e36	+	5.69744e36i	0.842453	+	1.65560i
$142$	5.58628e35			0.143953
$143$		−	3.69031e36i		−	0.844015i
$144$	−1.17628e36	+	1.61537e36i	−0.238973	+	0.328179i
$145$	5.70539e35			0.103045
$146$		−	5.55613e36i		−	0.892841i
$147$	−3.98803e36	+	2.02931e36i	−0.570642	+	0.290372i
$148$	−9.13783e36			−1.16518
$149$		−	1.30238e37i		−	1.48105i	−0.672026	−	0.740527i	$-0.734576\pi$
$149$		−	1.30238e37i		−	1.48105i	0.672026	−	0.740527i	$-0.265424\pi$
$150$	−6.56290e36	−	1.28975e37i	−0.666108	−	1.30904i
$151$	1.53327e37			1.38998			0.694992	−	0.719017i	$-0.255408\pi$
$151$	1.53327e37			1.38998			0.694992	+	0.719017i	$0.255408\pi$
$152$			1.30164e37i			1.05475i
$153$	1.86457e37	+	1.35774e37i	1.35153	+	0.984154i
$154$	−3.31488e37			−2.15088
$155$			2.11538e35i			0.0122956i
$156$	1.89669e37	−	9.65134e36i	0.988277	−	0.502886i
$157$	−2.25738e37			−1.05514			−0.527570	−	0.849512i	$-0.676897\pi$
$157$	−2.25738e37			−1.05514			−0.527570	+	0.849512i	$0.676897\pi$
$158$			3.93688e37i			1.65189i
$159$	−5.48040e36	−	1.07701e37i	−0.206567	−	0.405948i
$160$	8.92487e36			0.302386
$161$		−	8.91899e36i		−	0.271816i
$162$	5.39579e37	−	1.74043e37i	1.48013	−	0.477421i
$163$	2.51834e37			0.622194			0.311097	−	0.950378i	$-0.399304\pi$
$163$	2.51834e37			0.622194			0.311097	+	0.950378i	$0.399304\pi$
$164$			5.21365e37i			1.16091i
$165$	−1.12999e37	+	5.74999e36i	−0.226908	+	0.115462i
$166$	5.63494e37			1.02106
$167$		−	6.73804e37i		−	1.10244i	−0.834361	−	0.551218i	$-0.814163\pi$
$167$		−	6.73804e37i		−	1.10244i	0.834361	−	0.551218i	$-0.185837\pi$
$168$	−2.55867e37	−	5.02832e37i	−0.378230	−	0.743302i
$169$	−2.91163e37			−0.389100
$170$		−	5.07123e37i		−	0.613030i
$171$	−8.71431e37	+	1.19672e38i	−0.953452	+	1.30936i
$172$	−9.95377e37			−0.986288
$173$		−	4.60014e37i		−	0.413036i	−0.978443	−	0.206518i	$-0.933787\pi$
$173$		−	4.60014e37i		−	0.413036i	0.978443	−	0.206518i	$-0.0662131\pi$
$174$	−7.44171e37	+	3.78672e37i	−0.605809	+	0.308267i
$175$	−1.63782e38			−1.20954
$176$			6.53991e37i			0.438386i
$177$	3.70358e37	+	7.27831e37i	0.225463	+	0.443083i
$178$	5.53444e38			3.06150
$179$		−	7.46180e37i		−	0.375269i	−0.982239	−	0.187634i	$-0.939918\pi$
$179$		−	7.46180e37i		−	0.375269i	0.982239	−	0.187634i	$-0.0600820\pi$
$180$	−5.91059e37	−	4.30398e37i	−0.270395	−	0.196896i
$181$	−2.13615e38			−0.889396			−0.444698	−	0.895681i	$-0.646689\pi$
$181$	−2.13615e38			−0.889396			−0.444698	+	0.895681i	$0.646689\pi$
$182$		−	4.10628e38i		−	1.55681i
$183$	−5.09616e37	+	2.59319e37i	−0.176025	+	0.0895706i
$184$	4.38964e37			0.138206
$185$			6.74379e37i			0.193635i
$186$	−1.40400e37	−	2.75916e37i	−0.0367831	−	0.0722865i
$187$	7.54880e38			1.80539
$188$			1.20652e39i			2.63542i
$189$	1.01396e38	−	6.33603e38i	0.202382	−	1.26464i
$190$	3.25484e38			0.593906
$191$			5.98739e38i			0.999242i	0.866244	+	0.499621i	$0.166527\pi$
$191$			5.98739e38i			0.999242i	−0.866244	+	0.499621i	$0.833473\pi$
$192$	−9.27173e38	+	4.71793e38i	−1.41592	+	0.720495i
$193$	−5.27026e38			−0.736814			−0.368407	−	0.929665i	$-0.620097\pi$
$193$	−5.27026e38			−0.736814			−0.368407	+	0.929665i	$0.620097\pi$
$194$		−	2.51685e38i		−	0.322276i
$195$	−7.12276e37	−	1.39977e38i	−0.0835718	−	0.164236i
$196$	−8.44524e38			−0.908361
$197$		−	1.44438e39i		−	1.42480i	−0.701772	−	0.712402i	$-0.747607\pi$
$197$		−	1.44438e39i		−	1.42480i	0.701772	−	0.712402i	$-0.252393\pi$
$198$	1.09225e39	−	1.49998e39i	0.988588	−	1.35762i
$199$	2.12251e38			0.176338			0.0881691	−	0.996106i	$-0.471898\pi$
$199$	2.12251e38			0.176338			0.0881691	+	0.996106i	$0.471898\pi$
$200$		−	8.06083e38i		−	0.614993i
$201$	5.32915e38	−	2.71175e38i	0.373530	−	0.190071i
$202$	−3.28189e39			−2.11422
$203$			9.45006e38i			0.559760i
$204$	1.97425e39	+	3.87982e39i	1.07570	+	2.11397i
$205$	3.84771e38			0.192924
$206$		−	2.92398e39i		−	1.34968i
$207$	4.03583e38	+	2.93881e38i	0.171568	+	0.124933i
$208$	−8.10127e38			−0.317305
$209$			4.84499e39i			1.74907i
$210$	−1.25737e39	+	6.39813e38i	−0.418537	+	0.212973i
$211$	2.65596e39			0.815491			0.407745	−	0.913096i	$-0.366315\pi$
$211$	2.65596e39			0.815491			0.407745	+	0.913096i	$0.366315\pi$
$212$		−	2.28074e39i		−	0.646198i
$213$	1.60499e38	+	3.15414e38i	0.0419777	+	0.0824950i
$214$	3.26809e39			0.789332
$215$			7.34595e38i			0.163906i
$216$	3.11839e39	+	4.99041e38i	0.643009	+	0.102902i
$217$	−3.50380e38			−0.0667919
$218$		−	1.05989e40i		−	1.86853i
$219$	3.13712e39	−	1.59633e39i	0.511660	−	0.260359i
$220$	−2.39293e39			−0.361197
$221$			9.35102e39i			1.30674i
$222$	−4.47592e39	−	8.79613e39i	−0.579271	−	1.13839i
$223$	−1.51320e40			−1.81432			−0.907160	−	0.420787i	$-0.861754\pi$
$223$	−1.51320e40			−1.81432			−0.907160	+	0.420787i	$0.861754\pi$
$224$			1.47826e40i			1.64261i
$225$	5.39664e39	−	7.41113e39i	0.555930	−	0.763452i
$226$	3.25466e39			0.310930
$227$		−	6.49041e38i		−	0.0575218i	−0.999586	−	0.0287609i	$-0.990844\pi$
$227$		−	6.49041e38i		−	0.0575218i	0.999586	−	0.0287609i	$-0.00915614\pi$
$228$	−2.49016e40	+	1.26712e40i	−2.04802	+	1.04214i
$229$	1.50995e40			1.15282			0.576408	−	0.817162i	$-0.304454\pi$
$229$	1.50995e40			1.15282			0.576408	+	0.817162i	$0.304454\pi$
$230$		−	1.09766e39i		−	0.0778206i
$231$	−9.52394e39	−	1.87166e40i	−0.627210	−	1.23260i
$232$	−4.65102e39			−0.284611
$233$		−	1.83862e40i		−	1.04578i	−0.852400	−	0.522891i	$-0.824853\pi$
$233$		−	1.83862e40i		−	1.04578i	0.852400	−	0.522891i	$-0.175147\pi$
$234$	1.85809e40	+	1.35302e40i	0.982645	+	0.715542i
$235$	8.90418e39			0.437966
$236$			1.54129e40i			0.705310i
$237$	−2.22285e40	+	1.13110e40i	−0.946649	+	0.481703i
$238$	8.39969e40			3.33008
$239$		−	2.31681e40i		−	0.855317i	−0.903940	−	0.427658i	$-0.859339\pi$
$239$		−	2.31681e40i		−	0.855317i	0.903940	−	0.427658i	$-0.140661\pi$
$240$	1.26228e39	+	2.48066e39i	0.0434076	+	0.0853052i
$241$	−2.31568e40			−0.741974			−0.370987	−	0.928638i	$-0.620980\pi$
$241$	−2.31568e40			−0.741974			−0.370987	+	0.928638i	$0.620980\pi$
$242$		−	8.64939e39i		−	0.258300i
$243$	2.53295e40	+	2.54654e40i	0.705211	+	0.708997i
$244$	−1.07919e40			−0.280201
$245$			6.23265e39i			0.150956i
$246$	−5.01869e40	+	2.55377e40i	−1.13421	+	0.577144i
$247$	−6.00170e40			−1.26598
$248$		−	1.72446e39i		−	0.0339605i
$249$	1.61897e40	+	3.18162e40i	0.297748	+	0.585139i
$250$	−4.14998e40			−0.712961
$251$		−	1.45158e39i		−	0.0233016i	−0.999932	−	0.0116508i	$-0.996291\pi$
$251$		−	1.45158e39i		−	0.0233016i	0.999932	−	0.0116508i	$-0.00370866\pi$
$252$	7.12885e40	−	9.78996e40i	1.06957	−	1.46883i
$253$	1.63392e40			0.229183
$254$		−	1.25786e40i		−	0.164991i
$255$	2.86334e40	−	1.45701e40i	0.351309	−	0.178764i
$256$	−2.25829e40			−0.259239
$257$			2.58352e40i			0.277555i	0.990324	+	0.138778i	$0.0443173\pi$
$257$			2.58352e40i			0.277555i	−0.990324	+	0.138778i	$0.955683\pi$
$258$	−4.87559e40	−	9.58155e40i	−0.490334	−	0.963609i
$259$	−1.11700e41			−1.05186
$260$		−	2.96422e40i		−	0.261435i
$261$	−4.27614e40	−	3.11380e40i	−0.353316	−	0.257278i
$262$	6.88698e40			0.533221
$263$		−	3.82679e40i		−	0.277707i	−0.990313	−	0.138853i	$-0.955658\pi$
$263$		−	3.82679e40i		−	0.277707i	0.990313	−	0.138853i	$-0.0443417\pi$
$264$	9.21169e40	−	4.68738e40i	0.626718	−	0.318906i
$265$	−1.68320e40			−0.107388
$266$			5.39112e41i			3.22620i
$267$	1.59009e41	+	3.12487e41i	0.892753	+	1.75445i
$268$	1.12853e41			0.594594
$269$		−	9.18662e40i		−	0.454325i	−0.973857	−	0.227163i	$-0.927055\pi$
$269$		−	9.18662e40i		−	0.454325i	0.973857	−	0.227163i	$-0.0729449\pi$
$270$	1.24789e40	−	7.79776e40i	0.0579417	−	0.362064i
$271$	5.88942e40			0.256800			0.128400	−	0.991722i	$-0.459016\pi$
$271$	5.88942e40			0.256800			0.128400	+	0.991722i	$0.459016\pi$
$272$		−	1.65717e41i		−	0.678729i
$273$	2.31850e41	−	1.17977e41i	0.892159	−	0.453976i
$274$	−5.26143e41			−1.90259
$275$		−	3.00043e41i		−	1.01983i
$276$	4.27323e40	+	8.39781e40i	0.136553	+	0.268356i
$277$	2.24409e41			0.674348			0.337174	−	0.941442i	$-0.390529\pi$
$277$	2.24409e41			0.674348			0.337174	+	0.941442i	$0.390529\pi$
$278$		−	5.56485e41i		−	1.57287i
$279$	1.15450e40	−	1.58546e40i	0.0306990	−	0.0421585i
$280$	−7.85845e40			−0.196630
$281$		−	8.35899e40i		−	0.196855i	−0.995144	−	0.0984275i	$-0.968619\pi$
$281$		−	8.35899e40i		−	0.196855i	0.995144	−	0.0984275i	$-0.0313813\pi$
$282$	−1.16140e42	+	5.90980e41i	−2.57482	+	1.31020i
$283$	4.36918e41			0.912074			0.456037	−	0.889961i	$-0.349268\pi$
$283$	4.36918e41			0.912074			0.456037	+	0.889961i	$0.349268\pi$
$284$			6.67936e40i			0.131318i
$285$	9.35144e40	+	1.83776e41i	0.173187	+	0.340349i
$286$	7.52255e41			1.31263
$287$			6.37313e41i			1.04800i
$288$	−6.68912e41	−	4.87089e41i	−1.03680	−	0.754980i
$289$	−1.22849e42			−1.79518
$290$			1.16302e41i			0.160259i
$291$	1.42107e41	−	7.23113e40i	0.184686	−	0.0939778i
$292$	6.64331e41			0.814472
$293$			2.32629e41i			0.269100i	0.990907	+	0.134550i	$0.0429590\pi$
$293$			2.32629e41i			0.269100i	−0.990907	+	0.134550i	$0.957041\pi$
$294$	−4.13667e41	−	8.12943e41i	−0.451592	−	0.887474i
$295$	1.13748e41			0.117212
$296$		−	5.49752e41i		−	0.534820i
$297$	1.16074e42	+	1.85754e41i	1.06629	+	0.170640i
$298$	2.65485e42			2.30337
$299$			2.02401e41i			0.165883i
$300$	1.54212e42	−	7.84708e41i	1.19414	−	0.607640i
$301$	−1.21674e42			−0.890364
$302$			3.12550e42i			2.16173i
$303$	−9.42917e41	−	1.85303e42i	−0.616523	−	1.21160i
$304$	1.06361e42			0.657555
$305$			7.96448e40i			0.0465651i
$306$	−2.76770e42	+	3.80085e42i	−1.53058	+	2.10192i
$307$	−3.20258e42			−1.67551			−0.837756	−	0.546044i	$-0.816133\pi$
$307$	−3.20258e42			−1.67551			−0.837756	+	0.546044i	$0.816133\pi$
$308$		−	3.96351e42i		−	1.96208i
$309$	1.65095e42	−	8.40087e41i	0.773463	−	0.393577i
$310$	−4.31212e40			−0.0191224
$311$			3.41897e42i			1.43538i	0.696360	+	0.717692i	$0.254802\pi$
$311$			3.41897e42i			1.43538i	−0.696360	+	0.717692i	$0.745198\pi$
$312$	5.80645e41	+	1.14109e42i	0.230825	+	0.453620i
$313$	4.76701e41			0.179470			0.0897350	−	0.995966i	$-0.471398\pi$
$313$	4.76701e41			0.179470			0.0897350	+	0.995966i	$0.471398\pi$
$314$		−	4.60157e42i		−	1.64097i
$315$	−7.22506e41	−	5.26114e41i	−0.244097	−	0.177746i
$316$	−4.70722e42			−1.50690
$317$		−	1.47092e42i		−	0.446254i	−0.974789	−	0.223127i	$-0.928373\pi$
$317$		−	1.47092e42i		−	0.446254i	0.974789	−	0.223127i	$-0.0716265\pi$
$318$	2.19545e42	−	1.11716e42i	0.631339	−	0.321257i
$319$	−1.73122e42			−0.471965
$320$			1.44902e42i			0.374564i
$321$	9.38952e41	+	1.84524e42i	0.230175	+	0.452342i
$322$	1.81810e42			0.422735
$323$		−	1.22769e43i		−	2.70798i
$324$	2.08098e42	+	6.45159e42i	0.435515	+	1.35021i
$325$	3.71676e42			0.738154
$326$			5.13354e42i			0.967649i
$327$	5.98437e42	−	3.04515e42i	1.07080	−	0.544875i
$328$	−3.13665e42			−0.532857
$329$			1.47484e43i			2.37910i
$330$	−1.17211e42	−	2.30345e42i	−0.179569	−	0.352892i
$331$	−1.30392e43			−1.89746			−0.948732	−	0.316081i	$-0.897633\pi$
$331$	−1.30392e43			−1.89746			−0.948732	+	0.316081i	$0.897633\pi$
$332$			6.73754e42i			0.931438i
$333$	3.68053e42	−	5.05442e42i	0.483457	−	0.663925i
$334$	1.37352e43			1.71453
$335$		−	8.32861e41i		−	0.0988123i
$336$	−4.10881e42	+	2.09077e42i	−0.463392	+	0.235798i
$337$	3.57010e42			0.382800			0.191400	−	0.981512i	$-0.438697\pi$
$337$	3.57010e42			0.382800			0.191400	+	0.981512i	$0.438697\pi$
$338$		−	5.93523e42i		−	0.605137i
$339$	9.35095e41	+	1.83766e42i	0.0906694	+	0.178184i
$340$	6.06354e42			0.559222
$341$		−	6.41882e41i		−	0.0563159i
$342$	−2.43947e43	−	1.77638e43i	−2.03635	−	1.48283i
$343$	5.80006e42			0.460715
$344$		−	5.98840e42i		−	0.452707i
$345$	6.19764e41	−	3.15368e41i	0.0445966	−	0.0226930i
$346$	9.37720e42			0.642362
$347$			2.26027e43i			1.47421i	0.675777	+	0.737106i	$0.263808\pi$
$347$			2.26027e43i			1.47421i	−0.675777	+	0.737106i	$0.736192\pi$
$348$	−4.52768e42	−	8.89785e42i	−0.281209	−	0.552634i
$349$	−1.34307e43			−0.794450			−0.397225	−	0.917721i	$-0.630027\pi$
$349$	−1.34307e43			−0.794450			−0.397225	+	0.917721i	$0.630027\pi$
$350$		−	3.33863e43i		−	1.88110i
$351$	−2.30102e42	+	1.43785e43i	−0.123509	+	0.771781i
$352$	−2.70812e43			−1.38498
$353$		−	1.97828e43i		−	0.964088i	−0.876147	−	0.482044i	$-0.839895\pi$
$353$		−	1.97828e43i		−	0.964088i	0.876147	−	0.482044i	$-0.160105\pi$
$354$	−1.48365e43	+	7.54959e42i	−0.689092	+	0.350645i
$355$	4.92941e41			0.0218229
$356$			6.61738e43i			2.79277i
$357$	2.41331e43	+	4.74266e43i	0.971076	+	1.90837i
$358$	1.52106e43			0.583626
$359$		−	3.01626e43i		−	1.10373i	−0.833933	−	0.551865i	$-0.813916\pi$
$359$		−	3.01626e43i		−	1.10373i	0.833933	−	0.551865i	$-0.186084\pi$
$360$	2.58937e42	−	3.55594e42i	0.0903755	−	0.124112i
$361$	4.87614e43			1.62350
$362$		−	4.35445e43i		−	1.38321i
$363$	4.88364e42	−	2.48505e42i	0.148024	−	0.0753221i
$364$	4.90977e43			1.42016
$365$		−	4.90281e42i		−	0.135353i
$366$	−5.28611e42	−	1.03883e43i	−0.139302	−	0.273758i
$367$	−3.90052e43			−0.981295			−0.490648	−	0.871358i	$-0.663240\pi$
$367$	−3.90052e43			−0.981295			−0.490648	+	0.871358i	$0.663240\pi$
$368$		−	3.58692e42i		−	0.0861607i
$369$	−2.88383e43	−	2.09995e43i	−0.661488	−	0.481682i
$370$	−1.37469e43			−0.301146
$371$		−	2.78795e43i		−	0.583350i
$372$	3.29905e42	−	1.67873e42i	0.0659416	−	0.0335544i
$373$	4.80844e43			0.918236			0.459118	−	0.888375i	$-0.348166\pi$
$373$	4.80844e43			0.918236			0.459118	+	0.888375i	$0.348166\pi$
$374$			1.53879e44i			2.80778i
$375$	−1.19233e43	−	2.34317e43i	−0.207904	−	0.408576i
$376$	−7.25866e43			−1.20966
$377$		−	2.14453e43i		−	0.341609i
$378$	1.29157e44	+	2.06693e43i	1.96679	+	0.314749i
$379$	−1.06583e44			−1.55175			−0.775875	−	0.630886i	$-0.782691\pi$
$379$	−1.06583e44			−1.55175			−0.775875	+	0.630886i	$0.782691\pi$
$380$			3.89172e43i			0.541776i
$381$	7.10218e42	−	3.61395e42i	0.0945512	−	0.0481125i
$382$	−1.22051e44			−1.55404
$383$			1.75688e42i			0.0213975i	0.999943	+	0.0106988i	$0.00340559\pi$
$383$			1.75688e42i			0.0213975i	−0.999943	+	0.0106988i	$0.996594\pi$
$384$	−4.62504e43	−	9.08918e43i	−0.538871	−	1.05899i
$385$	−2.92510e43			−0.326068
$386$		−	1.07432e44i		−	1.14591i
$387$	4.00917e43	−	5.50574e43i	0.409230	−	0.561990i
$388$	3.00932e43			0.293988
$389$			5.10095e41i			0.00476988i	0.999997	+	0.00238494i	$0.000759151\pi$
$389$			5.10095e41i			0.00476988i	−0.999997	+	0.00238494i	$0.999241\pi$
$390$	2.85338e43	−	1.45195e43i	0.255424	−	0.129973i
$391$	−4.14026e43			−0.354832
$392$		−	5.08084e43i		−	0.416939i
$393$	1.97869e43	+	3.88855e43i	0.155491	+	0.305572i
$394$	2.94431e44			2.21589
$395$			3.47396e43i			0.250423i
$396$	1.79348e44	+	1.30598e44i	1.23845	+	0.901815i
$397$	7.73555e43			0.511744			0.255872	−	0.966711i	$-0.417637\pi$
$397$	7.73555e43			0.511744			0.255872	+	0.966711i	$0.417637\pi$
$398$			4.32664e43i			0.274245i
$399$	−3.04395e44	+	1.54892e44i	−1.84883	+	0.940782i
$400$	−6.58678e43			−0.383401
$401$			2.78483e44i			1.55362i	0.629737	+	0.776808i	$0.283163\pi$
$401$			2.78483e44i			1.55362i	−0.629737	+	0.776808i	$0.716837\pi$
$402$	5.52778e43	+	1.08633e44i	0.295603	+	0.580921i
$403$	7.95127e42			0.0407615
$404$		−	3.92407e44i		−	1.92865i
$405$	4.76132e43	−	1.53578e43i	0.224384	−	0.0723759i
$406$	−1.92636e44			−0.870551
$407$		−	2.04630e44i		−	0.886880i
$408$	−2.33418e44	+	1.18775e44i	−0.970314	+	0.493745i
$409$	2.45834e44			0.980271			0.490136	−	0.871646i	$-0.336947\pi$
$409$	2.45834e44			0.980271			0.490136	+	0.871646i	$0.336947\pi$
$410$			7.84341e43i			0.300040i
$411$	−1.51166e44	−	2.97073e44i	−0.554808	−	1.09031i
$412$	3.49613e44			1.23122
$413$			1.88406e44i			0.636713i
$414$	−5.99065e43	+	8.22688e43i	−0.194298	+	0.266827i
$415$	4.97235e43			0.154790
$416$		−	3.35466e44i		−	1.00245i
$417$	3.14204e44	−	1.59883e44i	0.901362	−	0.458659i
$418$	−9.87632e44			−2.72018
$419$		−	3.06939e44i		−	0.811733i	−0.913932	−	0.405866i	$-0.866970\pi$
$419$		−	3.06939e44i		−	0.811733i	0.913932	−	0.405866i	$-0.133030\pi$
$420$	−7.65006e43	−	1.50340e44i	−0.194280	−	0.381800i
$421$	5.45542e44			1.33055			0.665277	−	0.746596i	$-0.268313\pi$
$421$	5.45542e44			1.33055			0.665277	+	0.746596i	$0.268313\pi$
$422$			5.41406e44i			1.26827i
$423$	−6.67361e44	−	4.85959e44i	−1.50167	−	1.09349i
$424$	1.37214e44			0.296605
$425$			7.60290e44i			1.57895i
$426$	−6.42959e43	+	3.27170e43i	−0.128298	+	0.0652846i
$427$	−1.31919e44			−0.252949
$428$			3.90756e44i			0.720049i
$429$	2.16130e44	+	4.24740e44i	0.382772	+	0.752228i
$430$	−1.49744e44			−0.254910
$431$		−	1.40207e44i		−	0.229433i	−0.993398	−	0.114717i	$-0.963404\pi$
$431$		−	1.40207e44i		−	0.229433i	0.993398	−	0.114717i	$-0.0365960\pi$
$432$	4.07783e43	−	2.54814e44i	0.0641513	−	0.400867i
$433$	1.02287e45			1.54712			0.773560	−	0.633723i	$-0.218474\pi$
$433$	1.02287e45			1.54712			0.773560	+	0.633723i	$0.218474\pi$
$434$		−	7.14235e43i		−	0.103876i
$435$	−6.56668e43	+	3.34146e43i	−0.0918392	+	0.0467325i
$436$	1.26728e45			1.70452
$437$		−	2.65732e44i		−	0.343763i
$438$	3.25405e44	+	6.39489e44i	0.404915	+	0.795744i
$439$	−4.46827e44			−0.534863			−0.267432	−	0.963577i	$-0.586175\pi$
$439$	−4.46827e44			−0.534863			−0.267432	+	0.963577i	$0.586175\pi$
$440$		−	1.43964e44i		−	0.165790i
$441$	3.40156e44	−	4.67132e44i	0.376897	−	0.517587i
$442$	−1.90617e45			−2.03227
$443$			4.00047e44i			0.410438i	0.978716	+	0.205219i	$0.0657907\pi$
$443$			4.00047e44i			0.410438i	−0.978716	+	0.205219i	$0.934209\pi$
$444$	1.05173e45	−	5.35174e44i	1.03847	−	0.528426i
$445$	4.88367e44			0.464116
$446$		−	3.08460e45i		−	2.82167i
$447$	7.62762e44	+	1.49899e45i	0.671678	+	1.31999i
$448$	−2.40008e45			−2.03469
$449$			3.21986e44i			0.262814i	0.991328	+	0.131407i	$0.0419495\pi$
$449$			3.21986e44i			0.262814i	−0.991328	+	0.131407i	$0.958051\pi$
$450$	1.51073e45	+	1.10008e45i	1.18734	+	0.864594i
$451$	−1.16753e45			−0.883624
$452$			3.89151e44i			0.283638i
$453$	−1.76473e45	+	8.97986e44i	−1.23882	+	0.630376i
$454$	1.32304e44			0.0894591
$455$		−	3.62344e44i		−	0.236008i
$456$	−7.62327e44	−	1.49813e45i	−0.478342	−	0.940044i
$457$	−1.13640e45			−0.686996			−0.343498	−	0.939153i	$-0.611612\pi$
$457$	−1.13640e45			−0.686996			−0.343498	+	0.939153i	$0.611612\pi$
$458$			3.07797e45i			1.79288i
$459$	−2.94123e45	−	4.70690e44i	−1.65087	−	0.264192i
$460$	1.31244e44			0.0709900
$461$		−	1.29866e45i		−	0.676985i	−0.940969	−	0.338493i	$-0.890083\pi$
$461$		−	1.29866e45i		−	0.676985i	0.940969	−	0.338493i	$-0.109917\pi$
$462$	3.81529e45	−	1.94142e45i	1.91697	−	0.975451i
$463$	1.91002e45			0.925042			0.462521	−	0.886608i	$-0.346945\pi$
$463$	1.91002e45			0.925042			0.462521	+	0.886608i	$0.346945\pi$
$464$			3.80050e44i			0.177433i
$465$	−1.23891e43	−	2.43472e43i	−0.00557623	−	0.0109585i
$466$	3.74795e45			1.62642
$467$		−	2.71525e45i		−	1.13612i	−0.822988	−	0.568058i	$-0.807695\pi$
$467$		−	2.71525e45i		−	1.13612i	0.822988	−	0.568058i	$-0.192305\pi$
$468$	−1.61777e45	+	2.22166e45i	−0.652736	+	0.896393i
$469$	1.37950e45			0.536765
$470$			1.81508e45i			0.681134i
$471$	2.59815e45	−	1.32207e45i	0.940392	−	0.478520i
$472$	−9.27273e44			−0.323738
$473$		−	2.22902e45i		−	0.750714i
$474$	−2.30570e45	−	4.53120e45i	−0.749155	−	1.47225i
$475$	−4.87971e45			−1.52969
$476$			1.00433e46i			3.03779i
$477$	1.26155e45	+	9.18632e44i	0.368206	+	0.268120i
$478$	4.72273e45			1.33021
$479$			4.10305e45i			1.11533i	0.830066	+	0.557665i	$0.188303\pi$
$479$			4.10305e45i			1.11533i	−0.830066	+	0.557665i	$0.811697\pi$
$480$	−1.02722e45	+	5.22701e44i	−0.269502	+	0.137136i
$481$	2.53484e45			0.641926
$482$		−	4.72042e45i		−	1.15393i
$483$	5.22356e44	+	1.02654e45i	0.123272	+	0.242256i
$484$	1.03418e45			0.235628
$485$		−	2.22090e44i		−	0.0488562i
$486$	−5.19103e45	+	5.16331e45i	−1.10265	+	1.09676i
$487$	−2.80093e45			−0.574527			−0.287263	−	0.957852i	$-0.592746\pi$
$487$	−2.80093e45			−0.574527			−0.287263	+	0.957852i	$0.592746\pi$
$488$		−	6.49262e44i		−	0.128613i
$489$	−2.89852e45	+	1.47491e45i	−0.554530	+	0.282173i
$490$	−1.27050e45			−0.234769
$491$		−	1.01670e46i		−	1.81471i	−0.420365	−	0.907355i	$-0.638098\pi$
$491$		−	1.01670e46i		−	1.81471i	0.420365	−	0.907355i	$-0.361902\pi$
$492$	−3.05347e45	−	6.00071e45i	−0.526486	−	1.03466i
$493$	4.38679e45			0.730717
$494$		−	1.22342e46i		−	1.96887i
$495$	9.63821e44	−	1.32360e45i	0.149868	−	0.205811i
$496$	−1.40911e44			−0.0211718
$497$			8.16479e44i			0.118546i
$498$	−6.48559e45	+	3.30020e45i	−0.910020	+	0.463065i
$499$	−8.61330e44			−0.116805			−0.0584023	−	0.998293i	$-0.518601\pi$
$499$	−8.61330e44			−0.116805			−0.0584023	+	0.998293i	$0.518601\pi$
$500$		−	4.96201e45i		−	0.650381i
$501$	3.94625e45	+	7.75522e45i	0.499970	+	0.982546i
$502$	2.95898e44			0.0362392
$503$			1.60755e46i			1.90331i	0.307173	+	0.951654i	$0.400617\pi$
$503$			1.60755e46i			1.90331i	−0.307173	+	0.951654i	$0.599383\pi$
$504$	5.88985e45	+	4.28887e45i	0.674194	+	0.490935i
$505$	−2.89599e45			−0.320512
$506$			3.33069e45i			0.356431i
$507$	3.35117e45	−	1.70525e45i	0.346785	−	0.176462i
$508$	1.50399e45			0.150509
$509$			7.93372e45i			0.767847i	0.923365	+	0.383923i	$0.125427\pi$
$509$			7.93372e45i			0.767847i	−0.923365	+	0.383923i	$0.874573\pi$
$510$	2.97006e45	+	5.83679e45i	0.278018	+	0.546363i
$511$	8.12073e45			0.735258
$512$			8.96357e45i			0.785040i
$513$	3.02100e45	−	1.88775e46i	0.255950	−	1.59937i
$514$	−5.26641e45			−0.431660
$515$		−	2.58017e45i		−	0.204609i
$516$	1.14564e46	−	5.82960e45i	0.879029	−	0.447295i
$517$	−2.70184e46			−2.00595
$518$		−	2.27696e46i		−	1.63587i
$519$	2.69416e45	+	5.29459e45i	0.187317	+	0.368118i
$520$	1.78334e45			0.119999
$521$			1.97184e46i			1.28419i	0.766623	+	0.642097i	$0.221936\pi$
$521$			1.97184e46i			1.28419i	−0.766623	+	0.642097i	$0.778064\pi$
$522$	6.34736e45	−	8.71674e45i	0.400124	−	0.549485i
$523$	6.08625e45			0.371382			0.185691	−	0.982608i	$-0.440548\pi$
$523$	6.08625e45			0.371382			0.185691	+	0.982608i	$0.440548\pi$
$524$			8.23457e45i			0.486418i
$525$	1.88507e46	−	9.59220e45i	1.07800	−	0.548542i
$526$	7.80075e45			0.431895
$527$			1.62649e45i			0.0871908i
$528$	−3.83022e45	−	7.52718e45i	−0.198814	−	0.390711i
$529$	1.89990e46			0.954956
$530$		−	3.43113e45i		−	0.167012i
$531$	−8.52534e45	−	6.20798e45i	−0.401888	−	0.292647i
$532$	−6.44601e46			−2.94302
$533$		−	1.44627e46i		−	0.639569i
$534$	−6.36992e46	+	3.24134e46i	−2.72856	+	1.38843i
$535$	2.88381e45			0.119661
$536$			6.78946e45i			0.272919i
$537$	4.37014e45	+	8.58824e45i	0.170189	+	0.334458i
$538$	1.87265e46			0.706576
$539$		−	1.89120e46i		−	0.691400i
$540$	9.32356e45	+	1.49206e45i	0.330284	+	0.0528559i
$541$	−4.44680e46			−1.52649			−0.763245	−	0.646109i	$-0.776395\pi$
$541$	−4.44680e46			−1.52649			−0.763245	+	0.646109i	$0.776395\pi$
$542$			1.20054e46i			0.399381i
$543$	2.45862e46	−	1.25107e46i	0.792674	−	0.403353i
$544$	6.86221e46			2.14429
$545$		−	9.35260e45i		−	0.283264i
$546$	2.40492e46	+	4.72617e46i	0.706033	+	1.38750i
$547$	−6.87329e45			−0.195605			−0.0978026	−	0.995206i	$-0.531181\pi$
$547$	−6.87329e45			−0.195605			−0.0978026	+	0.995206i	$0.531181\pi$
$548$		−	6.29095e46i		−	1.73559i
$549$	4.34674e45	−	5.96932e45i	0.116261	−	0.159660i
$550$	6.11625e46			1.58606
$551$			2.81554e46i			0.707922i
$552$	−5.05230e45	+	2.57087e45i	−0.123176	+	0.0626781i
$553$	−5.75406e46			−1.36034
$554$			4.57449e46i			1.04876i
$555$	−3.94962e45	−	7.76184e45i	−0.0878162	−	0.172577i
$556$	6.65374e46			1.43481
$557$		−	7.61000e46i		−	1.59164i	−0.605530	−	0.795822i	$-0.707039\pi$
$557$		−	7.61000e46i		−	1.59164i	0.605530	−	0.795822i	$-0.292961\pi$
$558$	3.23190e45	+	2.35341e45i	0.0655658	+	0.0477437i
$559$	2.76118e46			0.543369
$560$			6.42141e45i			0.122584i
$561$	−8.68837e46	+	4.42109e46i	−1.60905	+	0.818767i
$562$	1.70395e46			0.306153
$563$			7.61164e46i			1.32689i	0.748225	+	0.663446i	$0.230907\pi$
$563$			7.61164e46i			1.32689i	−0.748225	+	0.663446i	$0.769093\pi$
$564$	−7.06618e46	−	1.38865e47i	−1.19520	−	2.34882i
$565$	2.87196e45			0.0471363
$566$			8.90639e46i			1.41848i
$567$	2.54378e46	+	7.88637e46i	0.393158	+	1.21889i
$568$	−4.01844e45			−0.0602749
$569$		−	5.50884e46i		−	0.801958i	−0.916087	−	0.400979i	$-0.868670\pi$
$569$		−	5.50884e46i		−	0.801958i	0.916087	−	0.400979i	$-0.131330\pi$
$570$	−3.74619e46	+	1.90625e46i	−0.529319	+	0.269344i
$571$	5.77202e46			0.791615			0.395808	−	0.918333i	$-0.370465\pi$
$571$	5.77202e46			0.791615			0.395808	+	0.918333i	$0.370465\pi$
$572$			8.99450e46i			1.19741i
$573$	−3.50662e46	−	6.89126e46i	−0.453170	−	0.890574i
$574$	−1.29914e47			−1.62987
$575$			1.64563e46i			0.200438i
$576$	7.90826e46	−	1.08603e47i	0.935188	−	1.28428i
$577$	−8.48789e46			−0.974565			−0.487283	−	0.873244i	$-0.662012\pi$
$577$	−8.48789e46			−0.974565			−0.487283	+	0.873244i	$0.662012\pi$
$578$		−	2.50423e47i		−	2.79191i
$579$	6.06587e46	−	3.08662e46i	0.656685	−	0.334155i
$580$	−1.39059e46			−0.146192
$581$			8.23591e46i			0.840848i
$582$	1.47404e46	+	2.89679e46i	0.146156	+	0.287228i
$583$	5.10742e46			0.491854
$584$			3.99676e46i			0.373843i
$585$	1.63960e46	+	1.19393e46i	0.148967	+	0.108475i
$586$	−4.74205e46			−0.418511
$587$		−	1.53943e46i		−	0.131982i	−0.997820	−	0.0659908i	$-0.978979\pi$
$587$		−	1.53943e46i		−	0.131982i	0.997820	−	0.0659908i	$-0.0210208\pi$
$588$	9.72014e46	−	4.94610e46i	0.809576	−	0.411954i
$589$	−1.04392e46			−0.0844708
$590$			2.31871e46i			0.182290i
$591$	8.45926e46	+	1.66242e47i	0.646168	+	1.26986i
$592$	−4.49221e46			−0.333420
$593$		−	1.56245e47i		−	1.12687i	−0.826159	−	0.563437i	$-0.809479\pi$
$593$		−	1.56245e47i		−	1.12687i	0.826159	−	0.563437i	$-0.190521\pi$
$594$	−3.78653e46	+	2.36611e47i	−0.265382	+	1.65831i
$595$	7.41201e46			0.504833
$596$			3.17433e47i			2.10119i
$597$	−2.44292e46	+	1.24308e46i	−0.157161	+	0.0799717i
$598$	−4.12586e46			−0.257985
$599$		−	1.40577e47i		−	0.854394i	−0.904159	−	0.427197i	$-0.859501\pi$
$599$		−	1.40577e47i		−	0.854394i	0.904159	−	0.427197i	$-0.140499\pi$
$600$	4.72097e46	+	9.27771e46i	0.278907	+	0.548112i
$601$	1.86614e47			1.07171			0.535856	−	0.844309i	$-0.319989\pi$
$601$	1.86614e47			1.07171			0.535856	+	0.844309i	$0.319989\pi$
$602$		−	2.48028e47i		−	1.38471i
$603$	−4.54547e46	+	6.24223e46i	−0.246708	+	0.338802i
$604$	−3.73708e47			−1.97199
$605$		−	7.63235e45i		−	0.0391577i
$606$	3.77733e47	−	1.92210e47i	1.88430	−	0.958829i
$607$	2.36509e47			1.14720			0.573600	−	0.819135i	$-0.305546\pi$
$607$	2.36509e47			1.14720			0.573600	+	0.819135i	$0.305546\pi$
$608$			4.40432e47i			2.07739i
$609$	−5.53460e46	−	1.08767e47i	−0.253859	−	0.498886i
$610$	−1.62353e46			−0.0724190
$611$		−	3.34689e47i		−	1.45191i
$612$	−4.54457e47	−	3.30927e47i	−1.91743	−	1.39623i
$613$	−8.98395e46			−0.368671			−0.184336	−	0.982863i	$-0.559013\pi$
$613$	−8.98395e46			−0.368671			−0.184336	+	0.982863i	$0.559013\pi$
$614$		−	6.52833e47i		−	2.60579i
$615$	−4.42857e46	+	2.25348e46i	−0.171944	+	0.0874938i
$616$	2.38453e47			0.900598
$617$			3.23338e47i			1.18798i	0.804472	+	0.593990i	$0.202448\pi$
$617$			3.23338e47i			1.18798i	−0.804472	+	0.593990i	$0.797552\pi$
$618$	1.71248e47	+	3.36539e47i	0.612100	+	1.20291i
$619$	−4.05876e47			−1.41141			−0.705703	−	0.708507i	$-0.749369\pi$
$619$	−4.05876e47			−1.41141			−0.705703	+	0.708507i	$0.749369\pi$
$620$		−	5.15589e45i		−	0.0174439i
$621$	−6.36625e46	−	1.01880e46i	−0.209569	−	0.0335376i
$622$	−6.96943e47			−2.23234
$623$			8.08902e47i			2.52115i
$624$	9.32424e46	−	4.74465e46i	0.282798	−	0.143902i
$625$	2.83360e47			0.836330
$626$			9.71735e46i			0.279116i
$627$	−2.83756e47	−	5.57640e47i	−0.793225	−	1.55885i
$628$	5.50197e47			1.49694
$629$			5.18520e47i			1.37311i
$630$	1.07246e47	−	1.47280e47i	0.276435	−	0.379624i
$631$	3.21525e47			0.806705			0.403353	−	0.915045i	$-0.367845\pi$
$631$	3.21525e47			0.806705			0.403353	+	0.915045i	$0.367845\pi$
$632$		−	2.83196e47i		−	0.691668i
$633$	−3.05690e47	+	1.55551e47i	−0.726806	+	0.369836i
$634$	2.99842e47			0.694024
$635$		−	1.10996e46i		−	0.0250122i
$636$	1.33575e47	+	2.62504e47i	0.293059	+	0.575923i
$637$	2.34272e47			0.500437
$638$		−	3.52901e47i		−	0.734009i
$639$	−3.69456e46	−	2.69030e46i	−0.0748252	−	0.0544862i
$640$	−1.42049e47			−0.280143
$641$		−	8.34203e47i		−	1.60208i	−0.598608	−	0.801042i	$-0.704279\pi$
$641$		−	8.34203e47i		−	1.60208i	0.598608	−	0.801042i	$-0.295721\pi$
$642$	−3.76144e47	+	1.91402e47i	−0.703492	+	0.357973i
$643$	−2.61463e47			−0.476237			−0.238119	−	0.971236i	$-0.576531\pi$
$643$	−2.61463e47			−0.476237			−0.238119	+	0.971236i	$0.576531\pi$
$644$			2.17385e47i			0.385629i
$645$	−4.30229e46	−	8.45491e46i	−0.0743335	−	0.146081i
$646$	2.50260e48			4.21151
$647$		−	2.68818e47i		−	0.440642i	−0.975427	−	0.220321i	$-0.929289\pi$
$647$		−	2.68818e47i		−	0.440642i	0.975427	−	0.220321i	$-0.0707105\pi$
$648$	−3.88142e47	+	1.25196e47i	−0.619748	+	0.199902i
$649$	−3.45152e47			−0.536847
$650$			7.57646e47i			1.14799i
$651$	4.03273e46	−	2.05206e46i	0.0595282	−	0.0302910i
$652$	−6.13803e47			−0.882714
$653$		−	1.04474e47i		−	0.146381i	−0.997318	−	0.0731907i	$-0.976682\pi$
$653$		−	1.04474e47i		−	0.146381i	0.997318	−	0.0731907i	$-0.0233182\pi$
$654$	6.20742e47	+	1.21989e48i	0.847402	+	1.66532i
$655$	6.07718e46			0.0808350
$656$			2.56306e47i			0.332196i
$657$	−2.67578e47	+	3.67462e47i	−0.337940	+	0.464089i
$658$	−3.00639e48			−3.70003
$659$		−	3.02504e47i		−	0.362810i	−0.983408	−	0.181405i	$-0.941936\pi$
$659$		−	3.02504e47i		−	0.362810i	0.983408	−	0.181405i	$-0.0580645\pi$
$660$	2.75417e47	−	1.40146e47i	0.321917	−	0.163808i
$661$	−8.00100e47			−0.911422			−0.455711	−	0.890128i	$-0.650615\pi$
$661$	−8.00100e47			−0.911422			−0.455711	+	0.890128i	$0.650615\pi$
$662$		−	2.65798e48i		−	2.95098i
$663$	−5.47659e47	−	1.07627e48i	−0.592625	−	1.16463i
$664$	−4.05345e47			−0.427531
$665$			4.75720e47i			0.489084i
$666$	1.03032e48	+	7.50260e47i	1.03255	+	0.751882i
$667$	9.49514e46			0.0927603
$668$			1.64228e48i			1.56404i
$669$	1.74163e48	−	8.86233e47i	1.61701	−	0.822818i
$670$	1.69775e47			0.153675
$671$		−	2.41670e47i		−	0.213275i
$672$	−8.65771e47	−	1.70142e48i	−0.744947	−	1.46398i
$673$	1.44286e48			1.21051			0.605255	−	0.796032i	$-0.293071\pi$
$673$	1.44286e48			1.21051			0.605255	+	0.796032i	$0.293071\pi$
$674$			7.27750e47i			0.595339i
$675$	−1.87086e47	+	1.16906e48i	−0.149237	+	0.932548i
$676$	7.09659e47			0.552021
$677$		−	4.98678e47i		−	0.378280i	−0.981950	−	0.189140i	$-0.939430\pi$
$677$		−	4.98678e47i		−	0.378280i	0.981950	−	0.189140i	$-0.0605699\pi$
$678$	−3.74599e47	+	1.90615e47i	−0.277116	+	0.141011i
$679$	3.67857e47			0.265395
$680$			3.64795e47i			0.256683i
$681$	3.80122e46	+	7.47020e46i	0.0260869	+	0.0512662i
$682$	1.30845e47			0.0875836
$683$			1.74664e48i			1.14039i	0.821511	+	0.570193i	$0.193132\pi$
$683$			1.74664e48i			1.14039i	−0.821511	+	0.570193i	$0.806868\pi$
$684$	2.12396e48	−	2.91681e48i	1.35267	−	1.85761i
$685$	−4.64277e47			−0.288428
$686$			1.18232e48i			0.716514i
$687$	−1.73790e48	+	8.84330e47i	−1.02745	+	0.522817i
$688$	−4.89333e47			−0.282229
$689$			6.32678e47i			0.356005i
$690$	6.42864e46	+	1.26336e47i	0.0352927	+	0.0693576i
$691$	−5.10678e47			−0.273540			−0.136770	−	0.990603i	$-0.543672\pi$
$691$	−5.10678e47			−0.273540			−0.136770	+	0.990603i	$0.543672\pi$
$692$			1.12121e48i			0.585979i
$693$	2.19234e48	+	1.59642e48i	1.11800	+	0.814106i
$694$	−4.60748e48			−2.29273
$695$		−	4.91051e47i		−	0.238443i
$696$	5.35314e47	−	2.72395e47i	0.253660	−	0.129075i
$697$	2.95845e48			1.36807
$698$		−	2.73779e48i		−	1.23554i
$699$	1.07682e48	+	2.11618e48i	0.474276	+	0.932053i
$700$	3.99191e48			1.71599
$701$			1.07393e48i			0.450579i	0.974292	+	0.225289i	$0.0723328\pi$
$701$			1.07393e48i			0.450579i	−0.974292	+	0.225289i	$0.927667\pi$
$702$	−2.93101e48	−	4.69053e47i	−1.20029	−	0.192084i
$703$	−3.32798e48			−1.33027
$704$		−	4.39685e48i		−	1.71556i
$705$	−1.02484e48	+	5.21489e47i	−0.390337	+	0.198623i
$706$	4.03263e48			1.49937
$707$		−	4.79675e48i		−	1.74107i
$708$	−9.02683e47	−	1.77396e48i	−0.319867	−	0.628607i
$709$	−3.47364e48			−1.20171			−0.600854	−	0.799359i	$-0.705173\pi$
$709$	−3.47364e48			−1.20171			−0.600854	+	0.799359i	$0.705173\pi$
$710$			1.00484e47i			0.0339395i
$711$	1.89597e48	−	2.60371e48i	0.625241	−	0.858636i
$712$	−3.98116e48			−1.28189
$713$			3.52051e46i			0.0110684i
$714$	−9.66772e48	+	4.91943e48i	−2.96794	+	1.51024i
$715$	6.63801e47			0.198992
$716$			1.81869e48i			0.532398i
$717$	1.35688e48	+	2.66656e48i	0.387898	+	0.762301i
$718$	6.14852e48			1.71654
$719$		−	3.13338e48i		−	0.854321i	−0.904176	−	0.427161i	$-0.859514\pi$
$719$		−	3.13338e48i		−	0.854321i	0.904176	−	0.427161i	$-0.140486\pi$
$720$	−2.90568e47	−	2.11586e47i	−0.0773741	−	0.0563423i
$721$	4.27363e48			1.11147
$722$			9.93981e48i			2.52491i
$723$	2.66526e48	−	1.35622e48i	0.661284	−	0.336495i
$724$	5.20649e48			1.26180
$725$		−	1.74362e48i		−	0.412768i
$726$	5.06567e47	+	9.95511e47i	0.117142	+	0.230210i
$727$	−6.94524e48			−1.56893			−0.784463	−	0.620176i	$-0.787061\pi$
$727$	−6.94524e48			−1.56893			−0.784463	+	0.620176i	$0.787061\pi$
$728$			2.95382e48i			0.651855i
$729$	−4.40675e48	−	1.44751e48i	−0.950059	−	0.312071i
$730$	9.99418e47			0.210503
$731$			5.64820e48i			1.16229i
$732$	1.24210e48	−	6.32045e47i	0.249729	−	0.127075i
$733$	5.31469e48			1.04402			0.522012	−	0.852938i	$-0.325182\pi$
$733$	5.31469e48			1.04402			0.522012	+	0.852938i	$0.325182\pi$
$734$		−	7.95106e48i		−	1.52613i
$735$	−3.65026e47	−	7.17353e47i	−0.0684603	−	0.134539i
$736$	1.48531e48			0.272205
$737$			2.52719e48i			0.452576i
$738$	4.28066e48	−	5.87857e48i	0.749122	−	1.02876i
$739$	−4.01720e48			−0.687017			−0.343509	−	0.939150i	$-0.611615\pi$
$739$	−4.01720e48			−0.687017			−0.343509	+	0.939150i	$0.611615\pi$
$740$		−	1.64368e48i		−	0.274713i
$741$	6.90772e48	−	3.51500e48i	1.12830	−	0.574138i
$742$	5.68313e48			0.907238
$743$		−	6.75695e48i		−	1.05424i	−0.849790	−	0.527121i	$-0.823271\pi$
$743$		−	6.75695e48i		−	1.05424i	0.849790	−	0.527121i	$-0.176729\pi$
$744$	1.00996e47	+	1.98478e47i	0.0154015	+	0.0302672i
$745$	2.34268e48			0.349185
$746$			9.80181e48i			1.42806i
$747$	−3.72674e48	−	2.71374e48i	−0.530736	−	0.386472i
$748$	−1.83989e49			−2.56133
$749$			4.77657e48i			0.650018i
$750$	4.77646e48	−	2.43051e48i	0.635426	−	0.323337i
$751$	−1.38155e49			−1.79675			−0.898377	−	0.439226i	$-0.855253\pi$
$751$	−1.38155e49			−1.79675			−0.898377	+	0.439226i	$0.855253\pi$
$752$			5.93130e48i			0.754131i
$753$	8.50142e46	+	1.67071e47i	0.0105676	+	0.0207676i
$754$	4.37154e48			0.531277
$755$			2.75799e48i			0.327714i
$756$	−2.47137e48	+	1.54430e49i	−0.287122	+	1.79416i
$757$	−9.82606e48			−1.11622			−0.558109	−	0.829767i	$-0.688473\pi$
$757$	−9.82606e48			−1.11622			−0.558109	+	0.829767i	$0.688473\pi$
$758$		−	2.17265e49i		−	2.41332i
$759$	−1.88058e48	+	9.56937e47i	−0.204260	+	0.103938i
$760$	−2.34134e48			−0.248676
$761$			8.35952e48i			0.868245i	0.900854	+	0.434122i	$0.142941\pi$
$761$			8.35952e48i			0.868245i	−0.900854	+	0.434122i	$0.857059\pi$
$762$	7.36689e47	+	1.44775e48i	0.0748255	+	0.147048i
$763$	1.54911e49			1.53874
$764$		−	1.45933e49i		−	1.41764i
$765$	−2.44226e48	+	3.35393e48i	−0.232032	+	0.318647i
$766$	−3.58133e47			−0.0332779
$767$		−	4.27555e48i		−	0.388571i
$768$	2.59920e48	−	1.32261e48i	0.231047	−	0.117568i
$769$	−7.58017e48			−0.659069			−0.329535	−	0.944144i	$-0.606892\pi$
$769$	−7.58017e48			−0.659069			−0.329535	+	0.944144i	$0.606892\pi$
$770$		−	5.96269e48i		−	0.507107i
$771$	−1.51309e48	−	2.97353e48i	−0.125875	−	0.247371i
$772$	1.28454e49			1.04533
$773$		−	6.23870e48i		−	0.496641i	−0.968678	−	0.248320i	$-0.920121\pi$
$773$		−	6.23870e48i		−	0.496641i	0.968678	−	0.248320i	$-0.0798786\pi$
$774$	1.12232e49	+	8.17252e48i	0.874019	+	0.636443i
$775$	6.46482e47			0.0492524
$776$			1.81047e48i			0.134941i
$777$	1.28562e49	−	6.54192e48i	0.937469	−	0.477032i
$778$	−1.03981e47			−0.00741822
$779$			1.89880e49i			1.32539i
$780$	1.73605e48	+	3.41171e48i	0.118564	+	0.233004i
$781$	−1.49576e48			−0.0999525
$782$		−	8.43976e48i		−	0.551842i
$783$	6.74533e48	+	1.07946e48i	0.431572	+	0.0690651i
$784$	−4.15173e48			−0.259930
$785$		−	4.06049e48i		−	0.248768i
$786$	−7.92665e48	+	4.03348e48i	−0.475233	+	0.241823i
$787$	3.06475e48			0.179814			0.0899071	−	0.995950i	$-0.471343\pi$
$787$	3.06475e48			0.179814			0.0899071	+	0.995950i	$0.471343\pi$
$788$			3.52043e49i			2.02139i
$789$	2.24123e48	+	4.40448e48i	0.125944	+	0.247506i
$790$	−7.08153e48			−0.389463
$791$			4.75695e48i			0.256052i
$792$	−7.85705e48	+	1.07900e49i	−0.413934	+	0.568450i
$793$	2.99367e48			0.154369
$794$			1.57686e49i			0.795875i
$795$	1.93730e48	−	9.85796e47i	0.0957095	−	0.0487019i
$796$	−5.17324e48			−0.250173
$797$		−	5.47474e48i		−	0.259162i	−0.991569	−	0.129581i	$-0.958637\pi$
$797$		−	5.47474e48i		−	0.259162i	0.991569	−	0.129581i	$-0.0413633\pi$
$798$	−3.15740e49	−	6.20497e49i	−1.46312	−	2.87535i
$799$	6.84630e49			3.10571
$800$		−	2.72753e49i		−	1.21127i
$801$	−3.66027e49	−	2.66534e49i	−1.59133	−	1.15878i
$802$	−5.67676e49			−2.41622
$803$			1.48769e49i			0.619936i
$804$	−1.29889e49	+	6.60942e48i	−0.529931	+	0.269656i
$805$	1.60432e48			0.0640856
$806$			1.62083e48i			0.0633932i
$807$	5.38031e48	+	1.05734e49i	0.206043	+	0.404917i
$808$	2.36080e49			0.885252
$809$		−	2.65490e49i		−	0.974818i	−0.873174	−	0.487409i	$-0.837942\pi$
$809$		−	2.65490e49i		−	0.974818i	0.873174	−	0.487409i	$-0.162058\pi$
$810$	3.13063e48	+	9.70576e48i	0.112561	+	0.348967i
$811$	1.59289e49			0.560832			0.280416	−	0.959879i	$-0.409528\pi$
$811$	1.59289e49			0.560832			0.280416	+	0.959879i	$0.409528\pi$
$812$		−	2.30329e49i		−	0.794139i
$813$	−6.77850e48	+	3.44925e48i	−0.228873	+	0.116462i
$814$	4.17131e49			1.37929
$815$			4.52991e48i			0.146693i
$816$	9.70553e48	+	1.90734e49i	0.307813	+	0.604917i
$817$	−3.62515e49			−1.12603
$818$			5.01123e49i			1.52454i
$819$	−1.97755e49	+	2.71574e49i	−0.589252	+	0.809212i
$820$	−9.37815e48			−0.273704
$821$		−	3.21505e49i		−	0.919082i	−0.888156	−	0.459541i	$-0.848014\pi$
$821$		−	3.21505e49i		−	0.919082i	0.888156	−	0.459541i	$-0.151986\pi$
$822$	6.05570e49	−	3.08145e49i	1.69568	−	0.862848i
$823$	−1.30350e49			−0.357532			−0.178766	−	0.983892i	$-0.557210\pi$
$823$	−1.30350e49			−0.357532			−0.178766	+	0.983892i	$0.557210\pi$
$824$			2.10334e49i			0.565129i
$825$	1.75725e49	+	3.45338e49i	0.462506	+	0.908922i
$826$	−3.84058e49			−0.990229
$827$		−	1.13125e49i		−	0.285736i	−0.989742	−	0.142868i	$-0.954367\pi$
$827$		−	1.13125e49i		−	0.285736i	0.989742	−	0.142868i	$-0.0456325\pi$
$828$	−9.83665e48	−	7.16285e48i	−0.243406	−	0.177243i
$829$	−2.88791e49			−0.700094			−0.350047	−	0.936732i	$-0.613834\pi$
$829$	−2.88791e49			−0.700094			−0.350047	+	0.936732i	$0.613834\pi$
$830$			1.01359e49i			0.240733i
$831$	−2.58286e49	+	1.31429e49i	−0.601013	+	0.305826i
$832$	5.44656e49			1.24173
$833$			4.79219e49i			1.07046i
$834$	3.25916e49	+	6.40493e49i	0.713317	+	1.40182i
$835$	1.21202e49			0.259919
$836$		−	1.18088e50i		−	2.48142i
$837$	−4.00233e47	+	2.50096e48i	−0.00824100	+	0.0514961i
$838$	6.25682e49			1.26242
$839$		−	8.09012e49i		−	1.59956i	−0.600290	−	0.799782i	$-0.704948\pi$
$839$		−	8.09012e49i		−	1.59956i	0.600290	−	0.799782i	$-0.295052\pi$
$840$	9.04477e48	−	4.60244e48i	0.175247	−	0.0891745i
$841$	4.26057e49			0.808976
$842$			1.11207e50i			2.06931i
$843$	4.89559e48	+	9.62088e48i	0.0892764	+	0.175447i
$844$	−6.47344e49			−1.15695
$845$		−	5.23734e48i		−	0.0917374i
$846$	9.90608e49	−	1.36039e50i	1.70061	−	2.33543i
$847$	1.26418e49			0.212711
$848$		−	1.12122e49i		−	0.184911i
$849$	−5.02875e49	+	2.55889e49i	−0.812885	+	0.413638i
$850$	−1.54982e50			−2.45561
$851$			1.12233e49i			0.174308i
$852$	−3.91188e48	−	7.68768e48i	−0.0595543	−	0.117037i
$853$	−8.15421e49			−1.21688			−0.608441	−	0.793599i	$-0.708205\pi$
$853$	−8.15421e49			−1.21688			−0.608441	+	0.793599i	$0.708205\pi$
$854$		−	2.68911e49i		−	0.393392i
$855$	−2.15263e49	−	1.56750e49i	−0.308706	−	0.224794i
$856$	−2.35088e49			−0.330503
$857$		−	1.28860e48i		−	0.0177600i	−0.999961	−	0.00888001i	$-0.997173\pi$
$857$		−	1.28860e48i		−	0.0177600i	0.999961	−	0.00888001i	$-0.00282663\pi$
$858$	−8.65816e49	+	4.40571e49i	−1.16988	+	0.595295i
$859$	−3.27445e48			−0.0433764			−0.0216882	−	0.999765i	$-0.506904\pi$
$859$	−3.27445e48			−0.0433764			−0.0216882	+	0.999765i	$0.506904\pi$
$860$		−	1.79045e49i		−	0.232535i
$861$	−3.73254e49	−	7.33522e49i	−0.475281	−	0.934027i
$862$	2.85806e49			0.356819
$863$			1.42272e50i			1.74155i	0.491683	+	0.870774i	$0.336382\pi$
$863$			1.42272e50i			1.74155i	−0.491683	+	0.870774i	$0.663618\pi$
$864$	1.05516e50	+	1.68860e49i	1.26645	+	0.202671i
$865$	8.27458e48			0.0973806
$866$			2.08507e50i			2.40611i
$867$	1.41395e50	−	7.19488e49i	1.59996	−	0.814140i
$868$	8.53991e48			0.0947584
$869$		−	1.05412e50i		−	1.14698i
$870$	−6.81143e48	−	1.33859e49i	−0.0726794	−	0.142830i
$871$	−3.13054e49			−0.327575
$872$			7.62422e49i			0.782375i
$873$	−1.21209e49	+	1.66455e49i	−0.121981	+	0.167515i
$874$	5.41683e49			0.534627
$875$		−	6.06552e49i		−	0.587126i
$876$	−7.64619e49	+	3.89077e49i	−0.725898	+	0.369374i
$877$	1.15072e50			1.07146			0.535732	−	0.844388i	$-0.320036\pi$
$877$	1.15072e50			1.07146			0.535732	+	0.844388i	$0.320036\pi$
$878$		−	9.10839e49i		−	0.831831i
$879$	−1.36243e49	−	2.67747e49i	−0.122041	−	0.239836i
$880$	−1.17638e49			−0.103357
$881$		−	1.73656e50i		−	1.49658i	−0.663373	−	0.748289i	$-0.730876\pi$
$881$		−	1.73656e50i		−	1.49658i	0.663373	−	0.748289i	$-0.269124\pi$
$882$	9.52230e49	+	6.93394e49i	0.804963	+	0.586158i
$883$	1.12242e50			0.930729			0.465364	−	0.885119i	$-0.345923\pi$
$883$	1.12242e50			0.930729			0.465364	+	0.885119i	$0.345923\pi$
$884$		−	2.27915e50i		−	1.85389i
$885$	−1.30920e49	+	6.66187e48i	−0.104465	+	0.0531570i
$886$	−8.15480e49			−0.638322
$887$			7.41162e49i			0.569130i	0.958657	+	0.284565i	$0.0918492\pi$
$887$			7.41162e49i			0.569130i	−0.958657	+	0.284565i	$0.908151\pi$
$888$	3.21972e49	+	6.32743e49i	0.242548	+	0.476658i
$889$	1.83847e49			0.135871
$890$			9.95517e49i			0.721803i
$891$	−1.44475e50	+	4.66010e49i	−1.02771	+	0.331493i
$892$	3.68817e50			2.57400
$893$			4.39411e50i			3.00882i
$894$	−3.05563e50	+	1.55486e50i	−2.05287	+	1.04461i
$895$	1.34220e49			0.0884763
$896$		−	2.35282e50i		−	1.52178i
$897$	−1.18540e49	−	2.32956e49i	−0.0752303	−	0.147843i
$898$	−6.56355e49			−0.408734
$899$		−	3.73014e48i		−	0.0227934i
$900$	−1.31534e50	+	1.80634e50i	−0.788705	+	1.08312i
$901$	−1.29419e50			−0.761511
$902$		−	2.37997e50i		−	1.37423i
$903$	1.40042e50	−	7.12606e49i	0.793536	−	0.403792i
$904$	−2.34122e49			−0.130190
$905$		−	3.84243e49i		−	0.209691i
$906$	−1.83051e50	−	3.59733e50i	−0.980375	−	1.92664i
$907$	−8.59889e49			−0.451979			−0.225990	−	0.974130i	$-0.572562\pi$
$907$	−8.59889e49			−0.451979			−0.225990	+	0.974130i	$0.572562\pi$
$908$			1.58193e49i			0.0816068i
$909$	2.17052e50	+	1.58053e50i	1.09895	+	0.800234i
$910$	7.38624e49			0.367045
$911$			4.93285e49i			0.240594i	0.992738	+	0.120297i	$0.0383847\pi$
$911$			4.93285e49i			0.240594i	−0.992738	+	0.120297i	$0.961615\pi$
$912$	−1.22418e50	+	6.22923e49i	−0.586046	+	0.298210i
$913$	−1.50879e50			−0.708965
$914$		−	2.31650e50i		−	1.06843i
$915$	−4.66454e48	−	9.16681e48i	−0.0211179	−	0.0415011i
$916$	−3.68025e50			−1.63551
$917$			1.00659e50i			0.439109i
$918$	9.59483e49	−	5.99559e50i	0.410877	−	2.56747i
$919$	1.25993e50			0.529643			0.264822	−	0.964297i	$-0.414687\pi$
$919$	1.25993e50			0.529643			0.264822	+	0.964297i	$0.414687\pi$
$920$			7.89593e48i			0.0325845i
$921$	3.68605e50	−	1.87565e50i	1.49330	−	0.759867i
$922$	2.64726e50			1.05286
$923$		−	1.85286e49i		−	0.0723458i
$924$	2.32130e50	+	4.56184e50i	0.889831	+	1.74871i
$925$	2.06097e50			0.775643
$926$			3.89350e50i			1.43865i
$927$	−1.40817e50	+	1.93381e50i	−0.510856	+	0.701551i
$928$	−1.57376e50			−0.560560
$929$			1.62540e50i			0.568452i	0.958757	+	0.284226i	$0.0917366\pi$
$929$			1.62540e50i			0.568452i	−0.958757	+	0.284226i	$0.908263\pi$
$930$	4.96309e48	−	2.52547e48i	0.0170428	−	0.00867227i
$931$	−3.07574e50			−1.03706
$932$			4.48132e50i			1.48366i
$933$	−2.00238e50	−	3.93510e50i	−0.650966	−	1.27929i
$934$	5.53493e50			1.76691
$935$			1.35785e50i			0.425652i
$936$	−1.33660e50	−	9.73286e49i	−0.411445	−	0.299606i
$937$	−1.89835e50			−0.573856			−0.286928	−	0.957952i	$-0.592634\pi$
$937$	−1.89835e50			−0.573856			−0.286928	+	0.957952i	$0.592634\pi$
$938$			2.81206e50i			0.834788i
$939$	−5.48664e49	+	2.79188e49i	−0.159953	+	0.0813921i
$940$	−2.17024e50			−0.621348
$941$		−	3.83489e50i		−	1.07827i	−0.842218	−	0.539137i	$-0.818750\pi$
$941$		−	3.83489e50i		−	1.07827i	0.842218	−	0.539137i	$-0.181250\pi$
$942$	2.69499e50	+	5.29623e50i	0.744204	+	1.46252i
$943$	6.40352e49			0.173668
$944$			7.57706e49i			0.201826i
$945$	1.13970e50	+	1.82389e49i	0.298161	+	0.0477152i
$946$	4.54377e50			1.16753
$947$		−	5.14482e50i		−	1.29844i	−0.760602	−	0.649218i	$-0.775096\pi$
$947$		−	5.14482e50i		−	1.29844i	0.760602	−	0.649218i	$-0.224904\pi$
$948$	5.41782e50	−	2.75687e50i	1.34302	−	0.683398i
$949$	−1.84286e50			−0.448711
$950$		−	9.94710e50i		−	2.37900i
$951$	8.61472e49	+	1.69297e50i	0.202382	+	0.397724i
$952$	−6.04226e50			−1.39435
$953$		−	2.02536e50i		−	0.459116i	−0.973295	−	0.229558i	$-0.926272\pi$
$953$		−	2.02536e50i		−	0.459116i	0.973295	−	0.229558i	$-0.0737281\pi$
$954$	−1.87259e50	+	2.57161e50i	−0.416986	+	0.572641i
$955$	−1.07699e50			−0.235589
$956$			5.64684e50i			1.21345i
$957$	1.99256e50	−	1.01392e50i	0.420638	−	0.214042i
$958$	−8.36391e50			−1.73458
$959$		−	7.69000e50i		−	1.56679i
$960$	−8.48646e49	−	1.66777e50i	−0.169870	−	0.333830i
$961$	−5.07125e50			−0.997280
$962$			5.16717e50i			0.998336i
$963$	−2.16139e50	−	1.57388e50i	−0.410286	−	0.298762i
$964$	5.64407e50			1.05265
$965$		−	9.47998e49i		−	0.173717i
$966$	−2.09256e50	+	1.06480e50i	−0.376762	+	0.191716i
$967$	3.17102e49			0.0560983			0.0280491	−	0.999607i	$-0.491071\pi$
$967$	3.17102e49			0.0560983			0.0280491	+	0.999607i	$0.491071\pi$
$968$			6.22187e49i			0.108153i
$969$	7.19019e50	+	1.41302e51i	1.22811	+	2.41349i
$970$	4.52722e49			0.0759823
$971$			2.74349e50i			0.452456i	0.974074	+	0.226228i	$0.0726395\pi$
$971$			2.74349e50i			0.452456i	−0.974074	+	0.226228i	$0.927361\pi$
$972$	−6.17362e50	−	6.20677e50i	−1.00049	−	1.00586i
$973$	8.13348e50			1.29526
$974$		−	5.70959e50i		−	0.893516i
$975$	−4.27784e50	+	2.17679e50i	−0.657880	+	0.334763i
$976$	−5.30535e49			−0.0801801
$977$			3.91008e50i			0.580735i	0.956915	+	0.290367i	$0.0937775\pi$
$977$			3.91008e50i			0.580735i	−0.956915	+	0.290367i	$0.906222\pi$
$978$	−3.00655e50	−	5.90851e50i	−0.438842	−	0.862417i
$979$	−1.48188e51			−2.12572
$980$		−	1.51910e50i		−	0.214162i
$981$	−5.10433e50	+	7.00970e50i	−0.707237	+	0.971240i
$982$	2.07250e51			2.82228
$983$			5.78758e50i			0.774618i	0.921950	+	0.387309i	$0.126595\pi$
$983$			5.78758e50i			0.774618i	−0.921950	+	0.387309i	$0.873405\pi$
$984$	3.61016e50	−	1.83703e50i	0.474908	−	0.241658i
$985$	2.59810e50			0.335923
$986$			8.94230e50i			1.13643i
$987$	−8.63764e50	−	1.69748e51i	−1.07896	−	2.12037i
$988$	1.46281e51			1.79606
$989$			1.22254e50i			0.147546i
$990$	2.69811e50	+	1.96471e50i	0.320082	+	0.233077i
$991$	5.62137e50			0.655526			0.327763	−	0.944760i	$-0.393705\pi$
$991$	5.62137e50			0.655526			0.327763	+	0.944760i	$0.393705\pi$
$992$		−	5.83501e49i		−	0.0668872i
$993$	1.50076e51	−	7.63661e50i	1.69111	−	0.860525i
$994$	−1.66436e50			−0.184365
$995$			3.81789e49i			0.0415749i
$996$	−3.94596e50	−	7.75464e50i	−0.422419	−	0.830143i
$997$	4.10467e50			0.431977			0.215988	−	0.976396i	$-0.430703\pi$
$997$	4.10467e50			0.431977			0.215988	+	0.976396i	$0.430703\pi$
$998$		−	1.75579e50i		−	0.181657i
$999$	−1.27593e50	+	7.97300e50i	−0.129782	+	0.810977i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.35.b.a.2.9	yes	10
3.2	odd	2	inner	3.35.b.a.2.2	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.35.b.a.2.2	✓	10	3.2	odd	2	inner
3.35.b.a.2.9	yes	10	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:	\( k \)	\(=\)	\( 35 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+203846. i q^{2} +(-1.15096e8 + 5.85668e7i) q^{3} -2.43733e10 q^{4} +1.79877e11i q^{5} +(-1.19386e13 - 2.34619e13i) q^{6} -2.97937e14 q^{7} -1.46635e15i q^{8} +(9.81704e15 - 1.34816e16i) q^{9} +O(q^{10})\)	\(q+203846. i q^{2} +(-1.15096e8 + 5.85668e7i) q^{3} -2.43733e10 q^{4} +1.79877e11i q^{5} +(-1.19386e13 - 2.34619e13i) q^{6} -2.97937e14 q^{7} -1.46635e15i q^{8} +(9.81704e15 - 1.34816e16i) q^{9} -3.66671e16 q^{10} -5.45809e17i q^{11} +(2.80527e18 - 1.42747e18i) q^{12} +6.76117e18 q^{13} -6.07333e19i q^{14} +(-1.05348e19 - 2.07031e19i) q^{15} -1.19820e20 q^{16} +1.38305e21i q^{17} +(2.74817e21 + 2.00116e21i) q^{18} -8.87671e21 q^{19} -4.38419e21i q^{20} +(3.42914e22 - 1.74492e22i) q^{21} +1.11261e23 q^{22} +2.99358e22i q^{23} +(8.58794e22 + 1.68771e23i) q^{24} +5.49721e23 q^{25} +1.37824e24i q^{26} +(-3.40329e23 + 2.12663e24i) q^{27} +7.26171e24 q^{28} -3.17183e24i q^{29} +(4.22024e24 - 2.14748e24i) q^{30} +1.17602e24 q^{31} -4.96166e25i q^{32} +(3.19663e25 + 6.28205e25i) q^{33} -2.81928e26 q^{34} -5.35919e25i q^{35} +(-2.39274e26 + 3.28591e26i) q^{36} +3.74912e26 q^{37} -1.80948e27i q^{38} +(-7.78185e26 + 3.95980e26i) q^{39} +2.63762e26 q^{40} -2.13908e27i q^{41} +(3.55695e27 + 6.99016e27i) q^{42} +4.08388e27 q^{43} +1.33032e28i q^{44} +(2.42503e27 + 1.76586e27i) q^{45} -6.10229e27 q^{46} -4.95016e28i q^{47} +(1.37909e28 - 7.01750e27i) q^{48} +3.46495e28 q^{49} +1.12058e29i q^{50} +(-8.10006e28 - 1.59183e29i) q^{51} -1.64792e29 q^{52} +9.35752e28i q^{53} +(-4.33506e29 - 6.93746e28i) q^{54} +9.81784e28 q^{55} +4.36880e29i q^{56} +(1.02167e30 - 5.19881e29i) q^{57} +6.46565e29 q^{58} -6.32368e29i q^{59} +(2.56768e29 + 5.04603e29i) q^{60} +4.42775e29 q^{61} +2.39727e29i q^{62} +(-2.92486e30 + 4.01667e30i) q^{63} +8.05565e30 q^{64} +1.21618e30i q^{65} +(-1.28057e31 + 6.51620e30i) q^{66} -4.63018e30 q^{67} -3.37094e31i q^{68} +(-1.75324e30 - 3.44549e30i) q^{69} +1.09245e31 q^{70} -2.74044e30i q^{71} +(-1.97688e31 - 1.43952e31i) q^{72} -2.72565e31 q^{73} +7.64242e31i q^{74} +(-6.32707e31 + 3.21954e31i) q^{75} +2.16355e32 q^{76} +1.62617e32i q^{77} +(-8.07189e31 - 1.58630e32i) q^{78} +1.93130e32 q^{79} -2.15529e31i q^{80} +(-8.53797e31 - 2.64699e32i) q^{81} +4.36044e32 q^{82} -2.76431e32i q^{83} +(-8.35794e32 + 4.25295e32i) q^{84} -2.48778e32 q^{85} +8.32483e32i q^{86} +(1.85764e32 + 3.65065e32i) q^{87} -8.00347e32 q^{88} -2.71501e33i q^{89} +(-3.59963e32 + 4.94332e32i) q^{90} -2.01440e33 q^{91} -7.29634e32i q^{92} +(-1.35355e32 + 6.88757e31i) q^{93} +1.00907e34 q^{94} -1.59671e33i q^{95} +(2.90589e33 + 5.71068e33i) q^{96} -1.23468e33 q^{97} +7.06317e33i q^{98} +(-7.35839e33 - 5.35823e33i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 119369106 q^{3} - 55582533344 q^{4} - 9250224859872 q^{6} - 123569771565772 q^{7} + 47\!\cdots\!18 q^{9}+O(q^{10}) \) 10 * q + 119369106 * q^3 - 55582533344 * q^4 - 9250224859872 * q^6 - 123569771565772 * q^7 + 4787501147541018 * q^9	\( 10 q + 119369106 q^{3} - 55582533344 q^{4} - 9250224859872 q^{6} - 123569771565772 q^{7} + 47\!\cdots\!18 q^{9}+ \cdots + 25\!\cdots\!80 q^{99}+O(q^{100}) \) 10 * q + 119369106 * q^3 - 55582533344 * q^4 - 9250224859872 * q^6 - 123569771565772 * q^7 + 4787501147541018 * q^9 - 2611205560422720 * q^10 + 1839088058193784224 * q^12 + 3639874363106470052 * q^13 + 73840351311049043520 * q^15 - 458913568062658993664 * q^16 + 4458031837811233600320 * q^18 - 18128087575667617007644 * q^19 + 47155216574801503272132 * q^21 - 82944038352793331672640 * q^22 - 409540832361157949627904 * q^24 - 306157881917435527620230 * q^25 - 5188422304885629117270366 * q^27 + 1200257625823339935397952 * q^28 + 4536084230702466968226240 * q^30 - 16210124253435972809624620 * q^31 + 126080615773751026110338880 * q^33 - 95987113410493892068003584 * q^34 - 3778740843166378351675872 * q^36 + 1107877531995608327024550788 * q^37 - 1478567172848906073011055372 * q^39 + 1263325098820483891139005440 * q^40 - 1100302459230379163303563200 * q^42 - 9626706570211152095714911228 * q^43 + 6764773545409610284732206720 * q^45 - 27597232473865615892091763584 * q^46 - 8343379363160137604055750144 * q^48 + 123592722368423574378839845566 * q^49 - 154249157901217791265339790592 * q^51 + 364968511672502550561914224448 * q^52 - 627476296349871988055293152672 * q^54 + 613243149395194155294476807040 * q^55 - 200956522080425270978267102412 * q^57 + 911704545930429232428533728320 * q^58 - 5328764870697498499759490872320 * q^60 + 3721644688213000805892336114020 * q^61 - 17793115140162074693090527345068 * q^63 + 31237929890100178456062152876032 * q^64 - 56522434211150051720831749496640 * q^66 + 64610860820592975458220110976548 * q^67 - 75655347603668350171840261441152 * q^69 + 173956643092708582155719748059520 * q^70 - 251655858465803757687636471720960 * q^72 + 219744563327934154882825652170292 * q^73 - 496257346175691552817323610505790 * q^75 + 755138601297458545349651061598016 * q^76 - 1416035973322463045417779737274560 * q^78 + 1282143700776175332608732687725076 * q^79 - 1752271238163022185686811202609110 * q^81 + 2617087107433191584283809414490240 * q^82 - 3353754502177451840461431126935232 * q^84 + 3064318591304040683100089841123840 * q^85 - 1378895999771415686373632115051840 * q^87 + 2890193643030846777850875310341120 * q^88 - 3749676158586283582801263594857280 * q^90 + 3328617839789463835132355588364424 * q^91 - 913294458028957034010214182487068 * q^93 - 1912224205137436189468854646420224 * q^94 + 5756213457708614900907762734014464 * q^96 - 11994339580278056229821837667722092 * q^97 + 25463971047319347192017533065521280 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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