LMFDB - Embedded newform 3.35.b.a.2.3

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			2.3
Root			$-12705.0i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.35.b.a.2.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-152461. i q^{2} +(6.59892e7 - 1.11007e8i) q^{3} -6.06435e9 q^{4} +1.02364e12i q^{5} +(-1.69242e13 - 1.00608e13i) q^{6} +3.85840e14 q^{7} -1.69468e15i q^{8} +(-7.96802e15 - 1.46506e16i) q^{9} +O(q^{10})$	\(q-152461. i q^{2} +(6.59892e7 - 1.11007e8i) q^{3} -6.06435e9 q^{4} +1.02364e12i q^{5} +(-1.69242e13 - 1.00608e13i) q^{6} +3.85840e14 q^{7} -1.69468e15i q^{8} +(-7.96802e15 - 1.46506e16i) q^{9} +1.56064e17 q^{10} -1.72999e17i q^{11} +(-4.00182e17 + 6.73187e17i) q^{12} +1.38475e19 q^{13} -5.88253e19i q^{14} +(1.13631e20 + 6.75491e19i) q^{15} -3.62556e20 q^{16} +1.27474e20i q^{17} +(-2.23363e21 + 1.21481e21i) q^{18} -1.48052e21 q^{19} -6.20770e21i q^{20} +(2.54613e22 - 4.28310e22i) q^{21} -2.63755e22 q^{22} -7.90513e22i q^{23} +(-1.88122e23 - 1.11831e23i) q^{24} -4.65759e23 q^{25} -2.11120e24i q^{26} +(-2.15212e24 - 8.22715e22i) q^{27} -2.33987e24 q^{28} +3.64899e23i q^{29} +(1.02986e25 - 1.73243e25i) q^{30} +6.92098e24 q^{31} +2.61612e25i q^{32} +(-1.92042e25 - 1.14161e25i) q^{33} +1.94347e25 q^{34} +3.94960e26i q^{35} +(4.83209e25 + 8.88461e25i) q^{36} +5.11756e25 q^{37} +2.25720e26i q^{38} +(9.13785e26 - 1.53717e27i) q^{39} +1.73474e27 q^{40} +2.34952e27i q^{41} +(-6.53004e27 - 3.88184e27i) q^{42} -8.17039e27 q^{43} +1.04913e27i q^{44} +(1.49969e28 - 8.15637e27i) q^{45} -1.20522e28 q^{46} -4.43275e28i q^{47} +(-2.39248e28 + 4.02464e28i) q^{48} +9.47553e28 q^{49} +7.10098e28i q^{50} +(1.41505e28 + 8.41191e27i) q^{51} -8.39760e28 q^{52} +1.03992e29i q^{53} +(-1.25432e28 + 3.28114e29i) q^{54} +1.77089e29 q^{55} -6.53874e29i q^{56} +(-9.76981e28 + 1.64348e29i) q^{57} +5.56327e28 q^{58} -8.33272e29i q^{59} +(-6.89100e29 - 4.09641e29i) q^{60} +6.58240e29 q^{61} -1.05518e30i q^{62} +(-3.07438e30 - 5.65277e30i) q^{63} -2.24012e30 q^{64} +1.41748e31i q^{65} +(-1.74050e30 + 2.92788e30i) q^{66} +1.06975e31 q^{67} -7.73046e29i q^{68} +(-8.77526e30 - 5.21653e30i) q^{69} +6.02159e31 q^{70} +5.27074e30i q^{71} +(-2.48280e31 + 1.35032e31i) q^{72} -4.83995e31 q^{73} -7.80227e30i q^{74} +(-3.07351e31 + 5.17026e31i) q^{75} +8.97837e30 q^{76} -6.67499e31i q^{77} +(-2.34358e32 - 1.39316e32i) q^{78} +2.88800e32 q^{79} -3.71127e32i q^{80} +(-1.51150e32 + 2.33472e32i) q^{81} +3.58210e32 q^{82} -3.03275e31i q^{83} +(-1.54406e32 + 2.59742e32i) q^{84} -1.30487e32 q^{85} +1.24566e33i q^{86} +(4.05064e31 + 2.40794e31i) q^{87} -2.93178e32 q^{88} +1.20701e33i q^{89} +(-1.24353e33 - 2.28643e33i) q^{90} +5.34291e33 q^{91} +4.79395e32i q^{92} +(4.56710e32 - 7.68279e32i) q^{93} -6.75820e33 q^{94} -1.51551e33i q^{95} +(2.90408e33 + 1.72636e33i) q^{96} -4.59223e33 q^{97} -1.44464e34i q^{98} +(-2.53454e33 + 1.37846e33i) 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 $

$2$		−	152461.i		−	1.16318i	−0.813481	−	0.581591i	$-0.802430\pi$
$2$		−	152461.i		−	1.16318i	0.813481	−	0.581591i	$-0.197570\pi$
$3$	6.59892e7	−	1.11007e8i	0.510989	−	0.859587i
$3$	6.59892e7	−	1.11007e8i	0.510989	−	0.859587i
$4$	−6.06435e9			−0.352992
$5$			1.02364e12i			1.34170i	0.741592	+	0.670852i	$0.234071\pi$
$5$			1.02364e12i			1.34170i	−0.741592	+	0.670852i	$0.765929\pi$
$6$	−1.69242e13	−	1.00608e13i	−0.999856	−	0.594373i
$7$	3.85840e14			1.65859			0.829297	−	0.558808i	$-0.188741\pi$
$7$	3.85840e14			1.65859			0.829297	+	0.558808i	$0.188741\pi$
$8$		−	1.69468e15i		−	0.752588i
$9$	−7.96802e15	−	1.46506e16i	−0.477780	−	0.878480i
$10$	1.56064e17			1.56064
$11$		−	1.72999e17i		−	0.342270i	−0.985248	−	0.171135i	$-0.945257\pi$
$11$		−	1.72999e17i		−	0.342270i	0.985248	−	0.171135i	$-0.0547434\pi$
$12$	−4.00182e17	+	6.73187e17i	−0.180375	+	0.303427i
$13$	1.38475e19			1.60079			0.800394	−	0.599474i	$-0.204624\pi$
$13$	1.38475e19			1.60079			0.800394	+	0.599474i	$0.204624\pi$
$14$		−	5.88253e19i		−	1.92925i
$15$	1.13631e20	+	6.75491e19i	1.15331	+	0.685596i
$16$	−3.62556e20			−1.22839
$17$			1.27474e20i			0.154095i	0.997027	+	0.0770477i	$0.0245494\pi$
$17$			1.27474e20i			0.154095i	−0.997027	+	0.0770477i	$0.975451\pi$
$18$	−2.23363e21	+	1.21481e21i	−1.02183	+	0.555745i
$19$	−1.48052e21			−0.270148			−0.135074	−	0.990836i	$-0.543127\pi$
$19$	−1.48052e21			−0.270148			−0.135074	+	0.990836i	$0.543127\pi$
$20$		−	6.20770e21i		−	0.473610i
$21$	2.54613e22	−	4.28310e22i	0.847524	−	1.42571i
$22$	−2.63755e22			−0.398122
$23$		−	7.90513e22i		−	0.560448i	−0.959935	−	0.280224i	$-0.909591\pi$
$23$		−	7.90513e22i		−	0.560448i	0.959935	−	0.280224i	$-0.0904088\pi$
$24$	−1.88122e23	−	1.11831e23i	−0.646915	−	0.384565i
$25$	−4.65759e23			−0.800167
$26$		−	2.11120e24i		−	1.86201i
$27$	−2.15212e24	−	8.22715e22i	−0.999270	−	0.0382002i
$28$	−2.33987e24			−0.585470
$29$			3.64899e23i			0.0502813i	0.999684	+	0.0251406i	$0.00800336\pi$
$29$			3.64899e23i			0.0502813i	−0.999684	+	0.0251406i	$0.991997\pi$
$30$	1.02986e25	−	1.73243e25i	0.797473	−	1.34151i
$31$	6.92098e24			0.306916			0.153458	−	0.988155i	$-0.450959\pi$
$31$	6.92098e24			0.306916			0.153458	+	0.988155i	$0.450959\pi$
$32$			2.61612e25i			0.676251i
$33$	−1.92042e25	−	1.14161e25i	−0.294211	−	0.174896i
$34$	1.94347e25			0.179241
$35$			3.94960e26i			2.22534i
$36$	4.83209e25	+	8.88461e25i	0.168652	+	0.310096i
$37$	5.11756e25			0.112107			0.0560537	−	0.998428i	$-0.482148\pi$
$37$	5.11756e25			0.112107			0.0560537	+	0.998428i	$0.482148\pi$
$38$			2.25720e26i			0.314231i
$39$	9.13785e26	−	1.53717e27i	0.817986	−	1.37602i
$40$	1.73474e27			1.00975
$41$			2.34952e27i			0.898782i	0.893335	+	0.449391i	$0.148359\pi$
$41$			2.34952e27i			0.898782i	−0.893335	+	0.449391i	$0.851641\pi$
$42$	−6.53004e27	−	3.88184e27i	−1.65836	−	0.985824i
$43$	−8.17039e27			−1.39085			−0.695423	−	0.718600i	$-0.744783\pi$
$43$	−8.17039e27			−1.39085			−0.695423	+	0.718600i	$0.744783\pi$
$44$			1.04913e27i			0.120818i
$45$	1.49969e28	−	8.15637e27i	1.17866	−	0.641039i
$46$	−1.20522e28			−0.651903
$47$		−	4.43275e28i		−	1.66345i	−0.555188	−	0.831725i	$-0.687354\pi$
$47$		−	4.43275e28i		−	1.66345i	0.555188	−	0.831725i	$-0.312646\pi$
$48$	−2.39248e28	+	4.02464e28i	−0.627693	+	1.05591i
$49$	9.47553e28			1.75094
$50$			7.10098e28i			0.930740i
$51$	1.41505e28	+	8.41191e27i	0.132458	+	0.0787411i
$52$	−8.39760e28			−0.565065
$53$			1.03992e29i			0.506187i	0.967442	+	0.253093i	$0.0814480\pi$
$53$			1.03992e29i			0.506187i	−0.967442	+	0.253093i	$0.918552\pi$
$54$	−1.25432e28	+	3.28114e29i	−0.0444337	+	1.16233i
$55$	1.77089e29			0.459224
$56$		−	6.53874e29i		−	1.24824i
$57$	−9.76981e28	+	1.64348e29i	−0.138043	+	0.232216i
$58$	5.56327e28			0.0584863
$59$		−	8.33272e29i		−	0.655093i	−0.944835	−	0.327546i	$-0.893778\pi$
$59$		−	8.33272e29i		−	0.655093i	0.944835	−	0.327546i	$-0.106222\pi$
$60$	−6.89100e29	−	4.09641e29i	−0.407109	−	0.242010i
$61$	6.58240e29			0.293614			0.146807	−	0.989165i	$-0.453100\pi$
$61$	6.58240e29			0.293614			0.146807	+	0.989165i	$0.453100\pi$
$62$		−	1.05518e30i		−	0.356999i
$63$	−3.07438e30	−	5.65277e30i	−0.792443	−	1.45704i
$64$	−2.24012e30			−0.441786
$65$			1.41748e31i			2.14778i
$66$	−1.74050e30	+	2.92788e30i	−0.203436	+	0.342220i
$67$	1.06975e31			0.968303			0.484151	−	0.874984i	$-0.339128\pi$
$67$	1.06975e31			0.968303			0.484151	+	0.874984i	$0.339128\pi$
$68$		−	7.73046e29i		−	0.0543944i
$69$	−8.77526e30	−	5.21653e30i	−0.481754	−	0.286383i
$70$	6.02159e31			2.58848
$71$			5.27074e30i			0.178025i	0.996031	+	0.0890123i	$0.0283710\pi$
$71$			5.27074e30i			0.178025i	−0.996031	+	0.0890123i	$0.971629\pi$
$72$	−2.48280e31	+	1.35032e31i	−0.661133	+	0.359572i
$73$	−4.83995e31			−1.01942			−0.509709	−	0.860347i	$-0.670247\pi$
$73$	−4.83995e31			−1.01942			−0.509709	+	0.860347i	$0.670247\pi$
$74$		−	7.80227e30i		−	0.130401i
$75$	−3.07351e31	+	5.17026e31i	−0.408877	+	0.687814i
$76$	8.97837e30			0.0953600
$77$		−	6.67499e31i		−	0.567687i
$78$	−2.34358e32	−	1.39316e32i	−1.60056	−	0.951466i
$79$	2.88800e32			1.58831			0.794157	−	0.607713i	$-0.207913\pi$
$79$	2.88800e32			1.58831			0.794157	+	0.607713i	$0.207913\pi$
$80$		−	3.71127e32i		−	1.64813i
$81$	−1.51150e32	+	2.33472e32i	−0.543453	+	0.839440i
$82$	3.58210e32			1.04545
$83$		−	3.03275e31i		−	0.0720293i	−0.999351	−	0.0360147i	$-0.988534\pi$
$83$		−	3.03275e31i		−	0.0720293i	0.999351	−	0.0360147i	$-0.0114663\pi$
$84$	−1.54406e32	+	2.59742e32i	−0.299169	+	0.503262i
$85$	−1.30487e32			−0.206750
$86$			1.24566e33i			1.61781i
$87$	4.05064e31	+	2.40794e31i	0.0432211	+	0.0256932i
$88$	−2.93178e32			−0.257588
$89$			1.20701e33i			0.875144i	0.899183	+	0.437572i	$0.144162\pi$
$89$			1.20701e33i			0.875144i	−0.899183	+	0.437572i	$0.855838\pi$
$90$	−1.24353e33	−	2.28643e33i	−0.745645	−	1.37099i
$91$	5.34291e33			2.65506
$92$			4.79395e32i			0.197834i
$93$	4.56710e32	−	7.68279e32i	0.156831	−	0.263821i
$94$	−6.75820e33			−1.93489
$95$		−	1.51551e33i		−	0.362459i
$96$	2.90408e33	+	1.72636e33i	0.581296	+	0.345557i
$97$	−4.59223e33			−0.770734			−0.385367	−	0.922763i	$-0.625925\pi$
$97$	−4.59223e33			−0.770734			−0.385367	+	0.922763i	$0.625925\pi$
$98$		−	1.44464e34i		−	2.03666i
$99$	−2.53454e33	+	1.37846e33i	−0.300677	+	0.163530i
$100$	2.82452e33			0.282452
$101$			1.98160e34i			1.67322i	0.547799	+	0.836610i	$0.315466\pi$
$101$			1.98160e34i			1.67322i	−0.547799	+	0.836610i	$0.684534\pi$
$102$	1.28248e33	−	2.15740e33i	0.0915902	−	0.154073i
$103$	−2.20242e34			−1.33250			−0.666250	−	0.745729i	$-0.732102\pi$
$103$	−2.20242e34			−1.33250			−0.666250	+	0.745729i	$0.732102\pi$
$104$		−	2.34670e34i		−	1.20473i
$105$	4.38434e34	+	2.60631e34i	1.91287	+	1.13713i
$106$	1.58547e34			0.588787
$107$			3.23481e34i			1.02406i	0.858968	+	0.512030i	$0.171106\pi$
$107$			3.23481e34i			1.02406i	−0.858968	+	0.512030i	$0.828894\pi$
$108$	1.30512e34	+	4.98923e32i	0.352734	+	0.0134843i
$109$	3.30911e33			0.0764647			0.0382324	−	0.999269i	$-0.487827\pi$
$109$	3.30911e33			0.0764647			0.0382324	+	0.999269i	$0.487827\pi$
$110$		−	2.69990e34i		−	0.534161i
$111$	3.37704e33	−	5.68087e33i	0.0572856	−	0.0963660i
$112$	−1.39889e35			−2.03740
$113$			2.49834e34i			0.312837i	0.987691	+	0.156419i	$0.0499949\pi$
$113$			2.49834e34i			0.312837i	−0.987691	+	0.156419i	$0.950005\pi$
$114$	2.50566e34	+	1.48951e34i	0.270109	+	0.160569i
$115$	8.09199e34			0.751956
$116$		−	2.21287e33i		−	0.0177489i
$117$	−1.10337e35	−	2.02873e35i	−0.764825	−	1.40626i
$118$	−1.27041e35			−0.761992
$119$			4.91845e34i			0.255582i
$120$	1.14474e35	−	1.92568e35i	0.515971	−	0.867968i
$121$	2.25548e35			0.882851
$122$		−	1.00356e35i		−	0.341527i
$123$	2.60814e35	+	1.55043e35i	0.772581	+	0.459268i
$124$	−4.19713e34			−0.108339
$125$			1.19067e35i			0.268116i
$126$	−8.61824e35	+	4.68722e35i	−1.69480	+	0.921755i
$127$	−1.60131e34			−0.0275304			−0.0137652	−	0.999905i	$-0.504382\pi$
$127$	−1.60131e34			−0.0275304			−0.0137652	+	0.999905i	$0.504382\pi$
$128$			7.90976e35i			1.19013i
$129$	−5.39158e35	+	9.06973e35i	−0.710708	+	1.19555i
$130$	2.16110e36			2.49826
$131$		−	1.51228e36i		−	1.53469i	−0.641235	−	0.767345i	$-0.721578\pi$
$131$		−	1.51228e36i		−	1.53469i	0.641235	−	0.767345i	$-0.278422\pi$
$132$	1.16461e35	+	6.92311e34i	0.103854	+	0.0617369i
$133$	−5.71242e35			−0.448066
$134$		−	1.63095e36i		−	1.12631i
$135$	8.42162e34	−	2.20299e36i	0.0512533	−	1.34072i
$136$	2.16027e35			0.115970
$137$			3.24434e36i			1.53772i	0.639418	+	0.768860i	$0.279176\pi$
$137$			3.24434e36i			1.53772i	−0.639418	+	0.768860i	$0.720824\pi$
$138$	−7.95316e35	+	1.33788e36i	−0.333116	+	0.560368i
$139$	−1.33843e36			−0.495844			−0.247922	−	0.968780i	$-0.579748\pi$
$139$	−1.33843e36			−0.495844			−0.247922	+	0.968780i	$0.579748\pi$
$140$		−	2.39518e36i		−	0.785527i
$141$	−4.92067e36	−	2.92514e36i	−1.42988	−	0.850005i
$142$	8.03580e35			0.207075
$143$		−	2.39560e36i		−	0.547901i
$144$	2.88886e36	+	5.31165e36i	0.586899	+	1.07911i
$145$	−3.73524e35			−0.0674626
$146$			7.37901e36i			1.18577i
$147$	6.25283e36	−	1.05185e37i	0.894709	−	1.50508i
$148$	−3.10347e35			−0.0395729
$149$			7.85439e36i			0.893194i	0.894735	+	0.446597i	$0.147364\pi$
$149$			7.85439e36i			0.893194i	−0.894735	+	0.446597i	$0.852636\pi$
$150$	7.88260e36	+	4.68588e36i	0.800052	+	0.475598i
$151$	3.89814e36			0.353386			0.176693	−	0.984266i	$-0.443460\pi$
$151$	3.89814e36			0.353386			0.176693	+	0.984266i	$0.443460\pi$
$152$			2.50900e36i			0.203310i
$153$	1.86756e36	−	1.01571e36i	0.135370	−	0.0736237i
$154$	−1.01767e37			−0.660323
$155$			7.08458e36i			0.411790i
$156$	−5.54151e36	+	9.32194e36i	−0.288742	+	0.485722i
$157$	−1.71448e37			−0.801382			−0.400691	−	0.916213i	$-0.631230\pi$
$157$	−1.71448e37			−0.801382			−0.400691	+	0.916213i	$0.631230\pi$
$158$		−	4.40306e37i		−	1.84750i
$159$	1.15439e37	+	6.86236e36i	0.435111	+	0.258656i
$160$	−2.67796e37			−0.907328
$161$		−	3.05011e37i		−	0.929557i
$162$	3.55953e37	+	2.30444e37i	0.976421	+	0.632134i
$163$	−2.09833e37			−0.518424			−0.259212	−	0.965820i	$-0.583463\pi$
$163$	−2.09833e37			−0.518424			−0.259212	+	0.965820i	$0.583463\pi$
$164$		−	1.42483e37i		−	0.317262i
$165$	1.16859e37	−	1.96581e37i	0.234659	−	0.394743i
$166$	−4.62375e36			−0.0837832
$167$			3.16961e37i			0.518592i	0.965798	+	0.259296i	$0.0834905\pi$
$167$			3.16961e37i			0.518592i	−0.965798	+	0.259296i	$0.916510\pi$
$168$	−7.25847e37	−	4.31487e37i	−1.07297	−	0.637837i
$169$	1.16923e38			1.56252
$170$			1.98941e37i			0.240488i
$171$	1.17968e37	+	2.16904e37i	0.129071	+	0.237320i
$172$	4.95481e37			0.490957
$173$			1.74507e38i			1.56685i	0.621485	+	0.783426i	$0.286530\pi$
$173$			1.74507e38i			1.56685i	−0.621485	+	0.783426i	$0.713470\pi$
$174$	3.67116e36	−	6.17563e36i	0.0298859	−	0.0502740i
$175$	−1.79708e38			−1.32715
$176$			6.27219e37i			0.420440i
$177$	−9.24993e37	−	5.49870e37i	−0.563109	−	0.334745i
$178$	1.84021e38			1.01795
$179$			2.18688e38i			1.09982i	0.835222	+	0.549912i	$0.185339\pi$
$179$			2.18688e38i			1.09982i	−0.835222	+	0.549912i	$0.814661\pi$
$180$	−9.09463e37	+	4.94631e37i	−0.416057	+	0.226281i
$181$	3.38221e38			1.40820			0.704101	−	0.710099i	$-0.251350\pi$
$181$	3.38221e38			1.40820			0.704101	+	0.710099i	$0.251350\pi$
$182$		−	8.14583e38i		−	3.08832i
$183$	4.34368e37	−	7.30694e37i	0.150034	−	0.252387i
$184$	−1.33966e38			−0.421787
$185$			5.23853e37i			0.150415i
$186$	−1.17132e38	−	6.96303e37i	−0.306871	−	0.182422i
$187$	2.20529e37			0.0527422
$188$			2.68818e38i			0.587184i
$189$	−8.30374e38	−	3.17436e37i	−1.65738	−	0.0633586i
$190$	−2.31056e38			−0.421605
$191$		−	4.26269e38i		−	0.711404i	−0.934600	−	0.355702i	$-0.884242\pi$
$191$		−	4.26269e38i		−	0.711404i	0.934600	−	0.355702i	$-0.115758\pi$
$192$	−1.47824e38	+	2.48670e38i	−0.225748	+	0.379754i
$193$	4.96487e38			0.694119			0.347059	−	0.937843i	$-0.387180\pi$
$193$	4.96487e38			0.694119			0.347059	+	0.937843i	$0.387180\pi$
$194$			7.00134e38i			0.896503i
$195$	1.57351e39	+	9.35385e38i	1.84621	+	1.09749i
$196$	−5.74629e38			−0.618066
$197$		−	1.28239e39i		−	1.26501i	−0.774557	−	0.632504i	$-0.782027\pi$
$197$		−	1.28239e39i		−	1.26501i	0.774557	−	0.632504i	$-0.217973\pi$
$198$	2.10161e38	+	3.86417e38i	0.190215	+	0.349742i
$199$	−5.70997e38			−0.474385			−0.237193	−	0.971463i	$-0.576227\pi$
$199$	−5.70997e38			−0.474385			−0.237193	+	0.971463i	$0.576227\pi$
$200$			7.89311e38i			0.602197i
$201$	7.05921e38	−	1.18750e39i	0.494792	−	0.832341i
$202$	3.02116e39			1.94626
$203$			1.40792e38i			0.0833963i
$204$	−8.58137e37	−	5.10127e37i	−0.0467567	−	0.0277949i
$205$	−2.40506e39			−1.20590
$206$			3.35782e39i			1.54994i
$207$	−1.15815e39	+	6.29882e38i	−0.492343	+	0.267771i
$208$	−5.02049e39			−1.96639
$209$			2.56128e38i			0.0924635i
$210$	3.97360e39	−	6.68440e39i	1.32268	−	2.22502i
$211$	−4.09032e39			−1.25590			−0.627950	−	0.778254i	$-0.716106\pi$
$211$	−4.09032e39			−1.25590			−0.627950	+	0.778254i	$0.716106\pi$
$212$		−	6.30645e38i		−	0.178680i
$213$	5.85091e38	+	3.47812e38i	0.153028	+	0.0909686i
$214$	4.93182e39			1.19117
$215$		−	8.36353e39i		−	1.86610i
$216$	−1.39424e38	+	3.64715e39i	−0.0287490	+	0.752039i
$217$	2.67039e39			0.509049
$218$		−	5.04509e38i		−	0.0889423i
$219$	−3.19384e39	+	5.37269e39i	−0.520911	+	0.876278i
$220$	−1.07393e39			−0.162102
$221$			1.76519e39i			0.246674i
$222$	−8.66108e38	−	5.14866e38i	−0.112091	−	0.0666336i
$223$	2.58095e39			0.309455			0.154728	−	0.987957i	$-0.450550\pi$
$223$	2.58095e39			0.309455			0.154728	+	0.987957i	$0.450550\pi$
$224$			1.00940e40i			1.12163i
$225$	3.71118e39	+	6.82363e39i	0.382304	+	0.702931i
$226$	3.80899e39			0.363887
$227$			3.11215e38i			0.0275817i	0.999905	+	0.0137909i	$0.00438990\pi$
$227$			3.11215e38i			0.0275817i	−0.999905	+	0.0137909i	$0.995610\pi$
$228$	5.92476e38	−	9.96664e38i	0.0487279	−	0.0819702i
$229$	−5.13100e39			−0.391741			−0.195870	−	0.980630i	$-0.562753\pi$
$229$	−5.13100e39			−0.391741			−0.195870	+	0.980630i	$0.562753\pi$
$230$		−	1.23371e40i		−	0.874661i
$231$	−7.40973e39	−	4.40478e39i	−0.487976	−	0.290082i
$232$	6.18386e38			0.0378411
$233$			8.75648e39i			0.498057i	0.968496	+	0.249028i	$0.0801112\pi$
$233$			8.75648e39i			0.498057i	−0.968496	+	0.249028i	$0.919889\pi$
$234$	−3.09302e40	+	1.68221e40i	−1.63574	+	0.889630i
$235$	4.53753e40			2.23186
$236$			5.05325e39i			0.231242i
$237$	1.90577e40	−	3.20589e40i	0.811611	−	1.36529i
$238$	7.49869e39			0.297288
$239$		−	2.99075e40i		−	1.10412i	−0.833805	−	0.552059i	$-0.813842\pi$
$239$		−	2.99075e40i		−	1.10412i	0.833805	−	0.552059i	$-0.186158\pi$
$240$	−4.11977e40	−	2.44904e40i	−1.41671	−	0.842178i
$241$	−4.03421e40			−1.29261			−0.646307	−	0.763078i	$-0.723687\pi$
$241$	−4.03421e40			−1.29261			−0.646307	+	0.763078i	$0.723687\pi$
$242$		−	3.43872e40i		−	1.02692i
$243$	1.59428e40	+	3.21853e40i	0.443873	+	0.896090i
$244$	−3.99180e39			−0.103643
$245$			9.69952e40i			2.34924i
$246$	2.36380e40	−	3.97639e40i	0.534212	−	0.898652i
$247$	−2.05014e40			−0.432450
$248$		−	1.17288e40i		−	0.230981i
$249$	−3.36657e39	−	2.00129e39i	−0.0619155	−	0.0368062i
$250$	1.81531e40			0.311868
$251$			5.36851e40i			0.861789i	0.902402	+	0.430894i	$0.141802\pi$
$251$			5.36851e40i			0.861789i	−0.902402	+	0.430894i	$0.858198\pi$
$252$	1.86441e40	+	3.42804e40i	0.279726	+	0.514323i
$253$	−1.36758e40			−0.191825
$254$			2.44137e39i			0.0320229i
$255$	−8.61075e39	+	1.44850e40i	−0.105647	+	0.177720i
$256$	8.21076e40			0.942549
$257$		−	4.50642e40i		−	0.484137i	−0.970259	−	0.242069i	$-0.922174\pi$
$257$		−	4.50642e40i		−	0.484137i	0.970259	−	0.242069i	$-0.0778259\pi$
$258$	1.38278e41	+	8.22003e40i	1.39065	+	0.826682i
$259$	1.97456e40			0.185941
$260$		−	8.59610e40i		−	0.758149i
$261$	5.34597e39	−	2.90752e39i	0.0441711	−	0.0240234i
$262$	−2.30563e41			−1.78512
$263$		−	2.03857e41i		−	1.47937i	−0.672951	−	0.739687i	$-0.734974\pi$
$263$		−	2.03857e41i		−	1.47937i	0.672951	−	0.739687i	$-0.265026\pi$
$264$	−1.93466e40	+	3.25449e40i	−0.131625	+	0.221419i
$265$	−1.06450e41			−0.679152
$266$			8.70919e40i			0.521182i
$267$	1.33987e41	+	7.96495e40i	0.752263	+	0.447189i
$268$	−6.48735e40			−0.341803
$269$			9.03608e40i			0.446880i	0.974718	+	0.223440i	$0.0717287\pi$
$269$			9.03608e40i			0.446880i	−0.974718	+	0.223440i	$0.928271\pi$
$270$	−3.35870e41	−	1.28396e40i	−1.55951	−	0.0596169i
$271$	−3.36175e41			−1.46584			−0.732921	−	0.680314i	$-0.761843\pi$
$271$	−3.36175e41			−1.46584			−0.732921	+	0.680314i	$0.761843\pi$
$272$		−	4.62165e40i		−	0.189289i
$273$	3.52574e41	−	5.93101e41i	1.35671	−	2.28225i
$274$	4.94634e41			1.78865
$275$			8.05759e40i			0.273873i
$276$	5.32163e40	+	3.16349e40i	0.170055	+	0.101091i
$277$	6.72036e40			0.201947			0.100973	−	0.994889i	$-0.467804\pi$
$277$	6.72036e40			0.201947			0.100973	+	0.994889i	$0.467804\pi$
$278$			2.04058e41i			0.576757i
$279$	−5.51466e40	−	1.01396e41i	−0.146638	−	0.269619i
$280$	6.69331e41			1.67477
$281$			9.67405e40i			0.227825i	0.993491	+	0.113912i	$0.0363383\pi$
$281$			9.67405e40i			0.227825i	−0.993491	+	0.113912i	$0.963662\pi$
$282$	−4.45968e41	+	7.50209e41i	−0.988710	+	1.66321i
$283$	−4.16767e41			−0.870009			−0.435004	−	0.900428i	$-0.643253\pi$
$283$	−4.16767e41			−0.870009			−0.435004	+	0.900428i	$0.643253\pi$
$284$		−	3.19636e40i		−	0.0628412i
$285$	−1.68233e41	−	1.00008e41i	−0.311565	−	0.185212i
$286$	−3.65235e41			−0.637309
$287$			9.06540e41i			1.49071i
$288$	3.83276e41	−	2.08453e41i	0.594072	−	0.323099i
$289$	6.68077e41			0.976255
$290$			5.69477e40i			0.0784712i
$291$	−3.03038e41	+	5.09771e41i	−0.393837	+	0.662513i
$292$	2.93511e41			0.359846
$293$		−	1.70259e42i		−	1.96952i	−0.173922	−	0.984759i	$-0.555644\pi$
$293$		−	1.70259e42i		−	1.96952i	0.173922	−	0.984759i	$-0.444356\pi$
$294$	−1.60366e42	−	9.53310e41i	−1.75068	−	1.04071i
$295$	8.52970e41			0.878940
$296$		−	8.67262e40i		−	0.0843707i
$297$	−1.42329e40	+	3.72315e41i	−0.0130748	+	0.342020i
$298$	1.19748e42			1.03895
$299$		−	1.09466e42i		−	0.897159i
$300$	1.86388e41	−	3.13543e41i	0.144330	−	0.242792i
$301$	−3.15246e42			−2.30685
$302$		−	5.94312e41i		−	0.411052i
$303$	2.19972e42	+	1.30764e42i	1.43828	+	0.854998i
$304$	5.36770e41			0.331847
$305$			6.73800e41i			0.393943i
$306$	−1.54856e41	−	2.84730e41i	−0.0856377	−	0.157459i
$307$	−2.15969e42			−1.12990			−0.564949	−	0.825126i	$-0.691104\pi$
$307$	−2.15969e42			−1.12990			−0.564949	+	0.825126i	$0.691104\pi$
$308$			4.04795e41i			0.200389i
$309$	−1.45336e42	+	2.44484e42i	−0.680893	+	1.14540i
$310$	1.08012e42			0.478986
$311$		−	7.37078e40i		−	0.0309448i	−0.999880	−	0.0154724i	$-0.995075\pi$
$311$		−	7.37078e40i		−	0.0309448i	0.999880	−	0.0154724i	$-0.00492521\pi$
$312$	−2.60501e42	−	1.54857e42i	−1.03557	−	0.615606i
$313$	3.69006e42			1.38925			0.694624	−	0.719373i	$-0.255571\pi$
$313$	3.69006e42			1.38925			0.694624	+	0.719373i	$0.255571\pi$
$314$			2.61391e42i			0.932152i
$315$	5.78639e42	−	3.14705e42i	1.95492	−	1.06322i
$316$	−1.75138e42			−0.560661
$317$			5.99383e42i			1.81843i	0.416327	+	0.909215i	$0.363317\pi$
$317$			5.99383e42i			1.81843i	−0.416327	+	0.909215i	$0.636683\pi$
$318$	1.04624e42	−	1.75999e42i	0.300864	−	0.506114i
$319$	6.31272e40			0.0172098
$320$		−	2.29307e42i		−	0.592746i
$321$	3.59088e42	+	2.13463e42i	0.880268	+	0.523283i
$322$	−4.65022e42			−1.08124
$323$		−	1.88727e41i		−	0.0416286i
$324$	9.16624e41	−	1.41586e42i	0.191834	−	0.296315i
$325$	−6.44959e42			−1.28090
$326$			3.19913e42i			0.603022i
$327$	2.18366e41	−	3.67335e41i	0.0390726	−	0.0657281i
$328$	3.98169e42			0.676413
$329$		−	1.71033e43i		−	2.75899i
$330$	−2.99709e42	−	1.78164e42i	−0.459158	−	0.272951i
$331$	−6.54229e42			−0.952037			−0.476018	−	0.879435i	$-0.657920\pi$
$331$	−6.54229e42			−0.952037			−0.476018	+	0.879435i	$0.657920\pi$
$332$			1.83917e41i			0.0254258i
$333$	−4.07769e41	−	7.49752e41i	−0.0535626	−	0.0984840i
$334$	4.83240e42			0.603216
$335$			1.09504e43i			1.29918i
$336$	−9.23114e42	+	1.55286e43i	−1.04109	+	1.75132i
$337$	−1.58724e42			−0.170190			−0.0850950	−	0.996373i	$-0.527119\pi$
$337$	−1.58724e42			−0.170190			−0.0850950	+	0.996373i	$0.527119\pi$
$338$		−	1.78262e43i		−	1.81750i
$339$	2.77334e42	+	1.64864e42i	0.268911	+	0.159857i
$340$	7.91320e41			0.0729811
$341$		−	1.19732e42i		−	0.105048i
$342$	3.30693e42	−	1.79854e42i	0.276046	−	0.150133i
$343$	1.56799e43			1.24550
$344$			1.38462e43i			1.04673i
$345$	5.33984e42	−	8.98269e42i	0.384241	−	0.646371i
$346$	2.66054e43			1.82253
$347$			2.38552e42i			0.155590i	0.996969	+	0.0777951i	$0.0247880\pi$
$347$			2.38552e42i			0.155590i	−0.996969	+	0.0777951i	$0.975212\pi$
$348$	−2.45645e41	−	1.46026e41i	−0.0152567	−	0.00906948i
$349$	−1.98294e43			−1.17295			−0.586473	−	0.809968i	$-0.699484\pi$
$349$	−1.98294e43			−1.17295			−0.586473	+	0.809968i	$0.699484\pi$
$350$			2.73984e43i			1.54372i
$351$	−2.98015e43	−	1.13925e42i	−1.59962	−	0.0611504i
$352$	4.52586e42			0.231460
$353$		−	1.66237e43i		−	0.810136i	−0.914287	−	0.405068i	$-0.867248\pi$
$353$		−	1.66237e43i		−	0.810136i	0.914287	−	0.405068i	$-0.132752\pi$
$354$	−8.38335e42	+	1.41025e43i	−0.389370	+	0.654998i
$355$	−5.39533e42			−0.238856
$356$		−	7.31971e42i		−	0.308919i
$357$	5.45983e42	+	3.24565e42i	0.219695	+	0.130600i
$358$	3.33413e43			1.27930
$359$			4.66941e43i			1.70866i	0.519728	+	0.854332i	$0.326033\pi$
$359$			4.66941e43i			1.70866i	−0.519728	+	0.854332i	$0.673967\pi$
$360$	−1.38224e43	−	2.54149e43i	−0.482438	−	0.887045i
$361$	−2.78427e43			−0.927020
$362$		−	5.15654e43i		−	1.63800i
$363$	1.48837e43	−	2.50375e43i	0.451128	−	0.758888i
$364$	−3.24013e43			−0.937213
$365$		−	4.95435e43i		−	1.36776i
$366$	−1.11402e43	−	6.62240e42i	−0.293572	−	0.174517i
$367$	4.53730e43			1.14150			0.570748	−	0.821125i	$-0.306653\pi$
$367$	4.53730e43			1.14150			0.570748	+	0.821125i	$0.306653\pi$
$368$			2.86605e43i			0.688448i
$369$	3.44218e43	−	1.87211e43i	0.789562	−	0.429420i
$370$	7.98670e42			0.174960
$371$			4.01243e43i			0.839558i
$372$	−2.76965e42	+	4.65911e42i	−0.0553599	+	0.0931265i
$373$	−2.27291e43			−0.434042			−0.217021	−	0.976167i	$-0.569634\pi$
$373$	−2.27291e43			−0.434042			−0.217021	+	0.976167i	$0.569634\pi$
$374$		−	3.36219e42i		−	0.0613487i
$375$	1.32173e43	+	7.85717e42i	0.230469	+	0.137004i
$376$	−7.51209e43			−1.25189
$377$			5.05293e42i			0.0804897i
$378$	−4.83965e42	+	1.26599e44i	−0.0736975	+	1.92784i
$379$	1.52062e43			0.221388			0.110694	−	0.993855i	$-0.464693\pi$
$379$	1.52062e43			0.221388			0.110694	+	0.993855i	$0.464693\pi$
$380$			9.19060e42i			0.127945i
$381$	−1.05669e42	+	1.77757e42i	−0.0140677	+	0.0236648i
$382$	−6.49891e43			−0.827492
$383$		−	1.86370e43i		−	0.226985i	−0.993539	−	0.113493i	$-0.963796\pi$
$383$		−	1.86370e43i		−	0.226985i	0.993539	−	0.113493i	$-0.0362038\pi$
$384$	8.78040e43	+	5.21959e43i	1.02302	+	0.608143i
$385$	6.83278e43			0.761667
$386$		−	7.56947e43i		−	0.807386i
$387$	6.51019e43	+	1.19701e44i	0.664519	+	1.22183i
$388$	2.78489e43			0.272063
$389$			7.54438e42i			0.0705473i	0.999378	+	0.0352736i	$0.0112303\pi$
$389$			7.54438e42i			0.0705473i	−0.999378	+	0.0352736i	$0.988770\pi$
$390$	1.42609e44	−	2.39898e44i	1.27658	−	2.14747i
$391$	1.00770e43			0.0863625
$392$		−	1.60580e44i		−	1.31773i
$393$	−1.67874e44	−	9.97943e43i	−1.31920	−	0.784210i
$394$	−1.95513e44			−1.47143
$395$			2.95627e44i			2.13105i
$396$	1.53703e43	−	8.35947e42i	0.106136	−	0.0577246i
$397$	−1.14501e44			−0.757482			−0.378741	−	0.925503i	$-0.623643\pi$
$397$	−1.14501e44			−0.757482			−0.378741	+	0.925503i	$0.623643\pi$
$398$			8.70545e43i			0.551796i
$399$	−3.76958e43	+	6.34120e43i	−0.228957	+	0.385152i
$400$	1.68864e44			0.982916
$401$		−	1.15906e44i		−	0.646623i	−0.946293	−	0.323311i	$-0.895204\pi$
$401$		−	1.15906e44i		−	0.646623i	0.946293	−	0.323311i	$-0.104796\pi$
$402$	−1.81047e44	−	1.07625e44i	−0.968163	−	0.575533i
$403$	9.58382e43			0.491307
$404$		−	1.20171e44i		−	0.590633i
$405$	−2.38991e44	−	1.54723e44i	−1.12628	−	0.729152i
$406$	2.14653e43			0.0970050
$407$		−	8.85334e42i		−	0.0383709i
$408$	1.42555e43	−	2.39806e43i	0.0592596	−	0.0996866i
$409$	4.73674e43			0.188879			0.0944394	−	0.995531i	$-0.469894\pi$
$409$	4.73674e43			0.188879			0.0944394	+	0.995531i	$0.469894\pi$
$410$			3.66677e44i			1.40268i
$411$	3.60145e44	+	2.14092e44i	1.32180	+	0.785758i
$412$	1.33562e44			0.470361
$413$		−	3.21510e44i		−	1.08653i
$414$	9.60322e43	+	1.76572e44i	0.311466	+	0.572684i
$415$	3.10444e43			0.0966420
$416$			3.62267e44i			1.08253i
$417$	−8.83222e43	+	1.48576e44i	−0.253371	+	0.426221i
$418$	3.90494e43			0.107552
$419$		−	5.49136e44i		−	1.45225i	−0.687562	−	0.726125i	$-0.741319\pi$
$419$		−	5.49136e44i		−	1.45225i	0.687562	−	0.726125i	$-0.258681\pi$
$420$	−2.65882e44	−	1.58056e44i	−0.675229	−	0.401396i
$421$	7.05401e44			1.72044			0.860222	−	0.509920i	$-0.170325\pi$
$421$	7.05401e44			1.72044			0.860222	+	0.509920i	$0.170325\pi$
$422$			6.23612e44i			1.46084i
$423$	−6.49423e44	+	3.53203e44i	−1.46131	+	0.794763i
$424$	1.76233e44			0.380950
$425$		−	5.93721e43i		−	0.123302i
$426$	5.30277e43	−	8.92032e43i	0.105813	−	0.177999i
$427$	2.53975e44			0.486987
$428$		−	1.96170e44i		−	0.361484i
$429$	−2.65929e44	−	1.58084e44i	−0.470969	−	0.279972i
$430$	−1.27511e45			−2.17062
$431$		−	7.55902e44i		−	1.23695i	−0.785805	−	0.618475i	$-0.787751\pi$
$431$		−	7.55902e44i		−	1.23695i	0.785805	−	0.618475i	$-0.212249\pi$
$432$	7.80265e44	+	2.98280e43i	1.22749	+	0.0469246i
$433$	−9.43548e44			−1.42715			−0.713576	−	0.700578i	$-0.752925\pi$
$433$	−9.43548e44			−1.42715			−0.713576	+	0.700578i	$0.752925\pi$
$434$		−	4.07129e44i		−	0.592116i
$435$	−2.46486e43	+	4.14639e43i	−0.0344726	+	0.0579900i
$436$	−2.00676e43			−0.0269914
$437$			1.17037e44i			0.151404i
$438$	8.19123e44	+	4.86935e44i	1.01927	+	0.605914i
$439$	1.31237e45			1.57094			0.785470	−	0.618900i	$-0.212421\pi$
$439$	1.31237e45			1.57094			0.785470	+	0.618900i	$0.212421\pi$
$440$		−	3.00108e44i		−	0.345607i
$441$	−7.55012e44	−	1.38822e45i	−0.836562	−	1.53816i
$442$	2.69122e44			0.286927
$443$			1.25341e45i			1.28597i	0.765880	+	0.642983i	$0.222303\pi$
$443$			1.25341e45i			1.28597i	−0.765880	+	0.642983i	$0.777697\pi$
$444$	−2.04796e43	+	3.44508e43i	−0.0202213	+	0.0340164i
$445$	−1.23554e45			−1.17418
$446$		−	3.93494e44i		−	0.359953i
$447$	8.71894e44	+	5.18305e44i	0.767778	+	0.456413i
$448$	−8.64328e44			−0.732744
$449$			6.98697e43i			0.0570297i	0.999593	+	0.0285148i	$0.00907778\pi$
$449$			6.98697e43i			0.0570297i	−0.999593	+	0.0285148i	$0.990922\pi$
$450$	1.04033e45	−	5.65808e44i	0.817636	−	0.444689i
$451$	4.06466e44			0.307626
$452$		−	1.51508e44i		−	0.110429i
$453$	2.57235e44	−	4.32721e44i	0.180576	−	0.303766i
$454$	4.74480e43			0.0320825
$455$			5.46921e45i			3.56230i
$456$	2.78517e44	+	1.65567e44i	0.174763	+	0.103889i
$457$	−1.04182e45			−0.629822			−0.314911	−	0.949121i	$-0.601975\pi$
$457$	−1.04182e45			−0.629822			−0.314911	+	0.949121i	$0.601975\pi$
$458$			7.82275e44i			0.455665i
$459$	1.04875e43	−	2.74339e44i	0.00588647	−	0.153983i
$460$	−4.90727e44			−0.265434
$461$		−	3.32544e45i		−	1.73354i	−0.498710	−	0.866769i	$-0.666193\pi$
$461$		−	3.32544e45i		−	1.73354i	0.498710	−	0.866769i	$-0.333807\pi$
$462$	−6.71555e44	+	1.12969e45i	−0.337418	+	0.567605i
$463$	−5.64173e44			−0.273234			−0.136617	−	0.990624i	$-0.543623\pi$
$463$	−5.64173e44			−0.273234			−0.136617	+	0.990624i	$0.543623\pi$
$464$		−	1.32296e44i		−	0.0617650i
$465$	7.86440e44	+	4.67506e44i	0.353969	+	0.210420i
$466$	1.33502e45			0.579330
$467$		−	3.89496e45i		−	1.62973i	−0.579651	−	0.814865i	$-0.696811\pi$
$467$		−	3.89496e45i		−	1.62973i	0.579651	−	0.814865i	$-0.303189\pi$
$468$	6.69123e44	+	1.23030e45i	0.269977	+	0.496398i
$469$	4.12753e45			1.60602
$470$		−	6.91795e45i		−	2.59605i
$471$	−1.13137e45	+	1.90320e45i	−0.409497	+	0.688857i
$472$	−1.41213e45			−0.493015
$473$			1.41347e45i			0.476045i
$474$	−4.88771e45	−	2.90554e45i	−1.58809	−	0.944051i
$475$	6.89563e44			0.216164
$476$		−	2.98272e44i		−	0.0902182i
$477$	1.52354e45	−	8.28612e44i	0.444675	−	0.241846i
$478$	−4.55971e45			−1.28429
$479$			5.42847e45i			1.47562i	0.675009	+	0.737809i	$0.264140\pi$
$479$			5.42847e45i			1.47562i	−0.675009	+	0.737809i	$0.735860\pi$
$480$	−1.76716e45	+	2.97273e45i	−0.463635	+	0.779927i
$481$	7.08654e44			0.179460
$482$			6.15058e45i			1.50354i
$483$	−3.38584e45	−	2.01275e45i	−0.799035	−	0.474994i
$484$	−1.36780e45			−0.311639
$485$		−	4.70078e45i		−	1.03410i
$486$	4.90699e45	−	2.43065e45i	1.04232	−	0.516305i
$487$	2.41744e45			0.495866			0.247933	−	0.968777i	$-0.420249\pi$
$487$	2.41744e45			0.495866			0.247933	+	0.968777i	$0.420249\pi$
$488$		−	1.11551e45i		−	0.220971i
$489$	−1.38467e45	+	2.32930e45i	−0.264909	+	0.445631i
$490$	1.47879e46			2.73259
$491$			4.27144e45i			0.762410i	0.924490	+	0.381205i	$0.124491\pi$
$491$			4.27144e45i			0.762410i	−0.924490	+	0.381205i	$0.875509\pi$
$492$	−1.58167e45	−	9.40237e44i	−0.272715	−	0.162118i
$493$	−4.65151e43			−0.00774811
$494$			3.12566e45i			0.503018i
$495$	−1.41105e45	−	2.59445e45i	−0.219408	−	0.403419i
$496$	−2.50925e45			−0.377012
$497$			2.03366e45i			0.295271i
$498$	−3.05118e44	+	5.13270e44i	−0.0428123	+	0.0720190i
$499$	2.56412e45			0.347720			0.173860	−	0.984770i	$-0.444376\pi$
$499$	2.56412e45			0.347720			0.173860	+	0.984770i	$0.444376\pi$
$500$		−	7.22067e44i		−	0.0946427i
$501$	3.51849e45	+	2.09160e45i	0.445775	+	0.264995i
$502$	8.18487e45			1.00242
$503$		−	3.17803e45i		−	0.376272i	−0.982143	−	0.188136i	$-0.939755\pi$
$503$		−	3.17803e45i		−	0.376272i	0.982143	−	0.188136i	$-0.0602446\pi$
$504$	−9.57962e45	+	5.21008e45i	−1.09655	+	0.596383i
$505$	−2.02844e46			−2.24497
$506$			2.08502e45i			0.223127i
$507$	7.71567e45	−	1.29793e46i	0.798433	−	1.34312i
$508$	9.71091e43			0.00971800
$509$			3.43656e45i			0.332599i	0.986075	+	0.166300i	$0.0531819\pi$
$509$			3.43656e45i			0.332599i	−0.986075	+	0.166300i	$0.946818\pi$
$510$	2.20839e45	+	1.31280e45i	0.206720	+	0.122887i
$511$	−1.86744e46			−1.69080
$512$			1.07069e45i			0.0937723i
$513$	3.18625e45	+	1.21804e44i	0.269951	+	0.0103197i
$514$	−6.87051e45			−0.563139
$515$		−	2.25448e46i		−	1.78782i
$516$	3.26964e45	−	5.50020e45i	0.250874	−	0.422020i
$517$	−7.66862e45			−0.569348
$518$		−	3.01042e45i		−	0.216283i
$519$	1.93715e46	+	1.15156e46i	1.34685	+	0.800645i
$520$	2.40218e46			1.61640
$521$		−	1.79689e46i		−	1.17025i	−0.810942	−	0.585126i	$-0.801045\pi$
$521$		−	1.79689e46i		−	1.17025i	0.810942	−	0.585126i	$-0.198955\pi$
$522$	−4.43282e44	−	8.15050e44i	−0.0279436	−	0.0513790i
$523$	1.66544e46			1.01625			0.508126	−	0.861283i	$-0.330339\pi$
$523$	1.66544e46			1.01625			0.508126	+	0.861283i	$0.330339\pi$
$524$			9.17100e45i			0.541732i
$525$	−1.18588e46	+	1.99489e46i	−0.678161	+	1.14080i
$526$	−3.10801e46			−1.72078
$527$			8.82245e44i			0.0472943i
$528$	6.96259e45	+	4.13897e45i	0.361405	+	0.214840i
$529$	1.36460e46			0.685897
$530$			1.62295e46i			0.789977i
$531$	−1.22079e46	+	6.63953e45i	−0.575486	+	0.312990i
$532$	3.46421e45			0.158164
$533$			3.25350e46i			1.43876i
$534$	1.21434e46	−	2.04277e46i	0.520163	−	0.875018i
$535$	−3.31128e46			−1.37398
$536$		−	1.81288e46i		−	0.728733i
$537$	2.42759e46	+	1.44311e46i	0.945395	+	0.561998i
$538$	1.37765e46			0.519803
$539$		−	1.63926e46i		−	0.599292i
$540$	−5.10716e44	+	1.33597e46i	−0.0180920	+	0.473264i
$541$	1.30625e46			0.448407			0.224203	−	0.974542i	$-0.428022\pi$
$541$	1.30625e46			0.448407			0.224203	+	0.974542i	$0.428022\pi$
$542$			5.12534e46i			1.70504i
$543$	2.23190e46	−	3.75450e46i	0.719577	−	1.21047i
$544$	−3.33487e45			−0.104207
$545$			3.38733e45i			0.102593i
$546$	−9.04246e46	−	5.37537e46i	−2.65468	−	1.57810i
$547$	−1.38600e46			−0.394439			−0.197220	−	0.980359i	$-0.563191\pi$
$547$	−1.38600e46			−0.394439			−0.197220	+	0.980359i	$0.563191\pi$
$548$		−	1.96748e46i		−	0.542802i
$549$	−5.24488e45	−	9.64359e45i	−0.140283	−	0.257934i
$550$	1.22846e46			0.318564
$551$		−	5.40239e44i		−	0.0135834i
$552$	−8.84035e45	+	1.48712e46i	−0.215529	+	0.362563i
$553$	1.11430e47			2.63437
$554$		−	1.02459e46i		−	0.234900i
$555$	5.81515e45	+	3.45687e45i	0.129295	+	0.0768603i
$556$	8.11672e45			0.175029
$557$			3.13129e46i			0.654915i	0.944866	+	0.327457i	$0.106192\pi$
$557$			3.13129e46i			0.654915i	−0.944866	+	0.327457i	$0.893808\pi$
$558$	−1.54589e46	+	8.40767e45i	−0.313616	+	0.170567i
$559$	−1.13139e47			−2.22645
$560$		−	1.43195e47i		−	2.73358i
$561$	1.45525e45	−	2.44803e45i	0.0269507	−	0.0453365i
$562$	1.47491e46			0.265002
$563$		−	2.70302e46i		−	0.471202i	−0.971850	−	0.235601i	$-0.924294\pi$
$563$		−	2.70302e46i		−	0.471202i	0.971850	−	0.235601i	$-0.0757059\pi$
$564$	2.98407e46	+	1.77391e46i	0.504736	+	0.300045i
$565$	−2.55740e46			−0.419735
$566$			6.35405e46i			1.01198i
$567$	−5.83195e46	+	9.00828e46i	−0.901368	+	1.39229i
$568$	8.93221e45			0.133979
$569$			8.94656e46i			1.30241i	0.758902	+	0.651205i	$0.225736\pi$
$569$			8.94656e46i			1.30241i	−0.758902	+	0.651205i	$0.774264\pi$
$570$	−1.52472e46	+	2.56489e46i	−0.215436	+	0.362406i
$571$	8.46021e46			1.16029			0.580146	−	0.814513i	$-0.302996\pi$
$571$	8.46021e46			1.16029			0.580146	+	0.814513i	$0.302996\pi$
$572$			1.45278e46i			0.193405i
$573$	−4.73189e46	−	2.81291e46i	−0.611513	−	0.363520i
$574$	1.38212e47			1.73397
$575$			3.68188e46i			0.448453i
$576$	1.78493e46	+	3.28190e46i	0.211077	+	0.388100i
$577$	−5.10253e46			−0.585864			−0.292932	−	0.956133i	$-0.594631\pi$
$577$	−5.10253e46			−0.585864			−0.292932	+	0.956133i	$0.594631\pi$
$578$		−	1.01855e47i		−	1.13556i
$579$	3.27628e46	−	5.51137e46i	0.354687	−	0.596655i
$580$	2.26518e45			0.0238137
$581$		−	1.17016e46i		−	0.119467i
$582$	7.77199e46	+	4.62013e46i	0.770623	+	0.458104i
$583$	1.79905e46			0.173252
$584$			8.20215e46i			0.767201i
$585$	2.07669e47	−	1.12945e47i	1.88678	−	1.02617i
$586$	−2.59578e47			−2.29091
$587$		−	1.58152e46i		−	0.135589i	−0.997699	−	0.0677947i	$-0.978404\pi$
$587$		−	1.58152e46i		−	0.135589i	0.997699	−	0.0677947i	$-0.0215963\pi$
$588$	−3.79193e46	+	6.37880e46i	−0.315825	+	0.531281i
$589$	−1.02466e46			−0.0829127
$590$		−	1.30044e47i		−	1.02237i
$591$	−1.42354e47	−	8.46238e46i	−1.08738	−	0.646406i
$592$	−1.85541e46			−0.137711
$593$			5.55836e46i			0.400882i	0.979706	+	0.200441i	$0.0642375\pi$
$593$			5.55836e46i			0.400882i	−0.979706	+	0.200441i	$0.935762\pi$
$594$	5.67634e46	+	2.16995e45i	0.397831	+	0.0152083i
$595$	−5.03471e46			−0.342915
$596$		−	4.76318e46i		−	0.315290i
$597$	−3.76796e46	+	6.33848e46i	−0.242406	+	0.407776i
$598$	−1.66893e47			−1.04356
$599$		−	2.45082e47i		−	1.48955i	−0.667314	−	0.744777i	$-0.732556\pi$
$599$		−	2.45082e47i		−	1.48955i	0.667314	−	0.744777i	$-0.267444\pi$
$600$	8.76192e46	+	5.20860e46i	0.517640	+	0.307716i
$601$	−1.21199e47			−0.696039			−0.348020	−	0.937487i	$-0.613146\pi$
$601$	−1.21199e47			−0.696039			−0.348020	+	0.937487i	$0.613146\pi$
$602$			4.80626e47i			2.68329i
$603$	−8.52380e46	−	1.56725e47i	−0.462636	−	0.850634i
$604$	−2.36397e46			−0.124742
$605$			2.30880e47i			1.18452i
$606$	1.99364e47	−	3.35371e47i	0.994518	−	1.67298i
$607$	3.15310e47			1.52943			0.764716	−	0.644368i	$-0.222879\pi$
$607$	3.15310e47			1.52943			0.764716	+	0.644368i	$0.222879\pi$
$608$		−	3.87321e46i		−	0.182688i
$609$	1.56290e46	+	9.29078e45i	0.0716864	+	0.0426146i
$610$	1.02728e47			0.458228
$611$		−	6.13825e47i		−	2.66283i
$612$	−1.13256e46	+	6.15965e45i	−0.0477843	+	0.0259885i
$613$	1.64523e47			0.675149			0.337574	−	0.941299i	$-0.390394\pi$
$613$	1.64523e47			0.675149			0.337574	+	0.941299i	$0.390394\pi$
$614$			3.29267e47i			1.31428i
$615$	−1.58708e47	+	2.66979e47i	−0.616201	+	1.03657i
$616$	−1.13120e47			−0.427234
$617$			8.37926e46i			0.307863i	0.988081	+	0.153932i	$0.0491936\pi$
$617$			8.37926e46i			0.307863i	−0.988081	+	0.153932i	$0.950806\pi$
$618$	3.72742e47	+	2.21580e47i	1.33231	+	0.792002i
$619$	6.51099e46			0.226415			0.113208	−	0.993571i	$-0.463887\pi$
$619$	6.51099e46			0.226415			0.113208	+	0.993571i	$0.463887\pi$
$620$		−	4.29634e46i		−	0.145358i
$621$	−6.50366e45	+	1.70128e47i	−0.0214092	+	0.560039i
$622$	−1.12375e46			−0.0359944
$623$			4.65711e47i			1.45151i
$624$	−3.31298e47	+	5.57311e47i	−1.00480	+	1.69028i
$625$	−3.92989e47			−1.15990
$626$		−	5.62589e47i		−	1.61595i
$627$	2.84321e46	+	1.69017e46i	0.0794804	+	0.0472479i
$628$	1.03972e47			0.282881
$629$			6.52356e45i			0.0172752i
$630$	−4.79801e47	−	8.82196e47i	−1.23672	−	2.27392i
$631$	−2.80194e47			−0.703007			−0.351503	−	0.936187i	$-0.614329\pi$
$631$	−2.80194e47			−0.703007			−0.351503	+	0.936187i	$0.614329\pi$
$632$		−	4.89423e47i		−	1.19535i
$633$	−2.69917e47	+	4.54055e47i	−0.641751	+	1.07956i
$634$	9.13822e47			2.11516
$635$		−	1.63916e46i		−	0.0369376i
$636$	−7.00061e46	−	4.16157e46i	−0.153591	−	0.0913034i
$637$	1.31212e48			2.80288
$638$		−	9.62440e45i		−	0.0200181i
$639$	7.72194e46	−	4.19974e46i	0.156391	−	0.0850566i
$640$	−8.09673e47			−1.59680
$641$		−	6.22146e47i		−	1.19483i	−0.801932	−	0.597415i	$-0.796195\pi$
$641$		−	6.22146e47i		−	1.19483i	0.801932	−	0.597415i	$-0.203805\pi$
$642$	3.25447e47	−	5.47467e47i	0.608674	−	1.02391i
$643$	−5.82492e47			−1.06097			−0.530485	−	0.847694i	$-0.677990\pi$
$643$	−5.82492e47			−1.06097			−0.530485	+	0.847694i	$0.677990\pi$
$644$			1.84969e47i			0.328126i
$645$	−9.28412e47	−	5.51903e47i	−1.60408	−	0.953559i
$646$	−2.87735e46			−0.0484216
$647$			8.75871e47i			1.43571i	0.696192	+	0.717856i	$0.254876\pi$
$647$			8.75871e47i			1.43571i	−0.696192	+	0.717856i	$0.745124\pi$
$648$	3.95660e47	+	2.56150e47i	0.631753	+	0.408996i
$649$	−1.44155e47			−0.224218
$650$			9.83308e47i			1.48992i
$651$	1.76217e47	−	2.96433e47i	0.260118	−	0.437572i
$652$	1.27250e47			0.182999
$653$		−	9.18179e46i		−	0.128648i	−0.997929	−	0.0643240i	$-0.979511\pi$
$653$		−	9.18179e46i		−	0.128648i	0.997929	−	0.0643240i	$-0.0204891\pi$
$654$	−5.60041e46	−	3.32922e46i	−0.0764537	−	0.0454486i
$655$	1.54803e48			2.05910
$656$		−	8.51835e47i		−	1.10405i
$657$	3.85648e47	+	7.09079e47i	0.487057	+	0.895537i
$658$	−2.60758e48			−3.20921
$659$			7.25700e47i			0.870372i	0.900341	+	0.435186i	$0.143317\pi$
$659$			7.25700e47i			0.870372i	−0.900341	+	0.435186i	$0.856683\pi$
$660$	−7.08676e46	+	1.19214e47i	−0.0828325	+	0.139341i
$661$	9.27198e47			1.05620			0.528102	−	0.849181i	$-0.322904\pi$
$661$	9.27198e47			1.05620			0.528102	+	0.849181i	$0.322904\pi$
$662$			9.97441e47i			1.10739i
$663$	1.95949e47	+	1.16484e47i	0.212038	+	0.126048i
$664$	−5.13954e46			−0.0542084
$665$		−	5.84745e47i		−	0.601172i
$666$	−1.14308e47	+	6.21686e46i	−0.114555	+	0.0623031i
$667$	2.88457e46			0.0281801
$668$		−	1.92216e47i		−	0.183059i
$669$	1.70315e47	−	2.86505e47i	0.158128	−	0.266004i
$670$	1.66950e48			1.51118
$671$		−	1.13875e47i		−	0.100495i
$672$	1.12051e48	+	6.66097e47i	0.964135	+	0.573139i
$673$	−1.33897e48			−1.12335			−0.561675	−	0.827358i	$-0.689843\pi$
$673$	−1.33897e48			−1.12335			−0.561675	+	0.827358i	$0.689843\pi$
$674$			2.41991e47i			0.197962i
$675$	1.00237e48	+	3.83186e46i	0.799583	+	0.0305665i
$676$	−7.09063e47			−0.551558
$677$		−	2.31873e48i		−	1.75891i	−0.475982	−	0.879455i	$-0.657907\pi$
$677$		−	2.31873e48i		−	1.75891i	0.475982	−	0.879455i	$-0.342093\pi$
$678$	2.51352e47	−	4.22825e47i	0.185942	−	0.312792i
$679$	−1.77187e48			−1.27833
$680$			2.21134e47i			0.155598i
$681$	3.45471e46	+	2.05368e46i	0.0237089	+	0.0140940i
$682$	−1.82545e47			−0.122190
$683$			6.23821e47i			0.407294i	0.979044	+	0.203647i	$0.0652795\pi$
$683$			6.23821e47i			0.407294i	−0.979044	+	0.203647i	$0.934720\pi$
$684$	−7.15398e46	−	1.31538e47i	−0.0455611	−	0.0837718i
$685$	−3.32103e48			−2.06316
$686$		−	2.39056e48i		−	1.44874i
$687$	−3.38591e47	+	5.69578e47i	−0.200175	+	0.336735i
$688$	2.96223e48			1.70850
$689$			1.44003e48i			0.810298i
$690$	−1.36951e48	−	8.14115e47i	−0.751847	−	0.446942i
$691$	4.68962e47			0.251195			0.125597	−	0.992081i	$-0.459915\pi$
$691$	4.68962e47			0.251195			0.125597	+	0.992081i	$0.459915\pi$
$692$		−	1.05827e48i		−	0.553086i
$693$	−9.77924e47	+	5.31865e47i	−0.498701	+	0.271229i
$694$	3.63698e47			0.180980
$695$		−	1.37007e48i		−	0.665275i
$696$	4.08068e46	−	6.86453e46i	0.0193364	−	0.0325277i
$697$	−2.99503e47			−0.138498
$698$			3.02321e48i			1.36435i
$699$	9.72032e47	+	5.77833e47i	0.428123	+	0.254502i
$700$	1.08981e48			0.468474
$701$		−	2.16901e48i		−	0.910031i	−0.890484	−	0.455015i	$-0.849634\pi$
$701$		−	2.16901e48i		−	0.910031i	0.890484	−	0.455015i	$-0.150366\pi$
$702$	−1.73691e47	+	4.54355e48i	−0.0711290	+	1.86065i
$703$	−7.57664e46			−0.0302856
$704$			3.87539e47i			0.151210i
$705$	2.99428e48	−	5.03699e48i	1.14045	−	1.91847i
$706$	−2.53446e48			−0.942335
$707$			7.64581e48i			2.77519i
$708$	5.60948e47	+	3.33460e47i	0.198773	+	0.118162i
$709$	4.60929e48			1.59459			0.797293	−	0.603593i	$-0.206265\pi$
$709$	4.60929e48			1.59459			0.797293	+	0.603593i	$0.206265\pi$
$710$			8.22576e47i			0.277833i
$711$	−2.30116e48	−	4.23108e48i	−0.758864	−	1.39530i
$712$	2.04549e48			0.658623
$713$		−	5.47113e47i		−	0.172010i
$714$	4.94833e47	−	8.32409e47i	0.151911	−	0.255545i
$715$	2.45223e48			0.735121
$716$		−	1.32620e48i		−	0.388229i
$717$	−3.31994e48	−	1.97357e48i	−0.949085	−	0.564192i
$718$	7.11901e48			1.98749
$719$			1.37100e47i			0.0373805i	0.999825	+	0.0186903i	$0.00594964\pi$
$719$			1.37100e47i			0.0373805i	−0.999825	+	0.0186903i	$0.994050\pi$
$720$	−5.43721e48	+	2.95714e48i	−1.44785	+	0.787445i
$721$	−8.49781e48			−2.21008
$722$			4.24492e48i			1.07829i
$723$	−2.66214e48	+	4.47826e48i	−0.660512	+	1.11111i
$724$	−2.05109e48			−0.497084
$725$		−	1.69955e47i		−	0.0402334i
$726$	−3.81722e48	−	2.26918e48i	−0.882724	−	0.524743i
$727$	3.40746e48			0.769743			0.384871	−	0.922970i	$-0.374246\pi$
$727$	3.40746e48			0.769743			0.384871	+	0.922970i	$0.374246\pi$
$728$		−	9.05451e48i		−	1.99817i
$729$	4.62486e48	+	3.54116e47i	0.997081	+	0.0763446i
$730$	−7.55344e48			−1.59095
$731$		−	1.04151e48i		−	0.214323i
$732$	−2.63416e47	+	4.43119e47i	−0.0529607	+	0.0890905i
$733$	4.68908e48			0.921129			0.460565	−	0.887626i	$-0.347647\pi$
$733$	4.68908e48			0.921129			0.460565	+	0.887626i	$0.347647\pi$
$734$		−	6.91759e48i		−	1.32777i
$735$	1.07672e49	+	6.40064e48i	2.01937	+	1.20043i
$736$	2.06807e48			0.379004
$737$		−	1.85066e48i		−	0.331421i
$738$	−2.85422e48	−	5.24797e48i	−0.499493	−	0.918403i
$739$	−2.77151e48			−0.473981			−0.236990	−	0.971512i	$-0.576161\pi$
$739$	−2.77151e48			−0.473981			−0.236990	+	0.971512i	$0.576161\pi$
$740$		−	3.17683e47i		−	0.0530951i
$741$	−1.35287e48	+	2.27581e48i	−0.220977	+	0.371728i
$742$	6.11737e48			0.976559
$743$		−	9.77186e48i		−	1.52464i	−0.647201	−	0.762320i	$-0.724060\pi$
$743$		−	9.77186e48i		−	1.52464i	0.647201	−	0.762320i	$-0.275940\pi$
$744$	−1.30199e48	−	7.73977e47i	−0.198548	−	0.118029i
$745$	−8.04005e48			−1.19840
$746$			3.46529e48i			0.504869i
$747$	−4.44315e47	+	2.41650e47i	−0.0632763	+	0.0344142i
$748$	−1.33736e47			−0.0186175
$749$			1.24812e49i			1.69850i
$750$	1.19791e48	−	2.01512e48i	0.159361	−	0.268077i
$751$	2.00552e48			0.260825			0.130412	−	0.991460i	$-0.458370\pi$
$751$	2.00552e48			0.260825			0.130412	+	0.991460i	$0.458370\pi$
$752$			1.60712e49i			2.04336i
$753$	5.95944e48	+	3.54264e48i	0.740783	+	0.440365i
$754$	7.70372e47			0.0936241
$755$			3.99028e48i			0.474139i
$756$	5.03568e48	+	1.92504e47i	0.585043	+	0.0223650i
$757$	−1.08018e49			−1.22707			−0.613533	−	0.789669i	$-0.710252\pi$
$757$	−1.08018e49			−1.22707			−0.613533	+	0.789669i	$0.710252\pi$
$758$		−	2.31834e48i		−	0.257514i
$759$	−9.02456e47	+	1.51811e48i	−0.0980203	+	0.164890i
$760$	−2.56831e48			−0.272782
$761$		−	4.26841e46i		−	0.00443330i	−0.999998	−	0.00221665i	$-0.999294\pi$
$761$		−	4.26841e46i		−	0.00443330i	0.999998	−	0.00221665i	$-0.000705582\pi$
$762$	2.71010e47	+	1.61104e47i	0.0275264	+	0.0163633i
$763$	1.27679e48			0.126824
$764$			2.58504e48i			0.251119i
$765$	1.03972e48	+	1.91171e48i	0.0987811	+	0.181626i
$766$	−2.84141e48			−0.264025
$767$		−	1.15387e49i		−	1.04866i
$768$	5.41822e48	−	9.11454e48i	0.481633	−	0.810203i
$769$	8.73163e48			0.759185			0.379592	−	0.925154i	$-0.376064\pi$
$769$	8.73163e48			0.759185			0.379592	+	0.925154i	$0.376064\pi$
$770$		−	1.04173e49i		−	0.885957i
$771$	−5.00245e48	−	2.97375e48i	−0.416158	−	0.247389i
$772$	−3.01087e48			−0.245018
$773$			5.82809e48i			0.463954i	0.972721	+	0.231977i	$0.0745194\pi$
$773$			5.82809e48i			0.463954i	−0.972721	+	0.231977i	$0.925481\pi$
$774$	1.82497e49	−	9.92547e48i	1.42121	−	0.772956i
$775$	−3.22351e48			−0.245584
$776$			7.78236e48i			0.580045i
$777$	1.30300e48	−	2.19190e48i	0.0950136	−	0.159832i
$778$	1.15022e48			0.0820593
$779$		−	3.47851e48i		−	0.242804i
$780$	−9.54229e48	−	5.67250e48i	−0.651695	−	0.387406i
$781$	9.11834e47			0.0609324
$782$		−	1.53634e48i		−	0.100455i
$783$	3.00207e46	−	7.85307e47i	0.00192075	−	0.0502446i
$784$	−3.43541e49			−2.15083
$785$		−	1.75501e49i		−	1.07522i
$786$	−1.52147e49	+	2.55942e49i	−0.912178	+	1.53447i
$787$	−8.45539e48			−0.496093			−0.248046	−	0.968748i	$-0.579789\pi$
$787$	−8.45539e48			−0.496093			−0.248046	+	0.968748i	$0.579789\pi$
$788$			7.77685e48i			0.446537i
$789$	−2.26296e49	−	1.34524e49i	−1.27165	−	0.755944i
$790$	4.50714e49			2.47879
$791$			9.63960e48i			0.518870i
$792$	2.33605e48	+	4.29522e48i	0.123070	+	0.226286i
$793$	9.11497e48			0.470015
$794$			1.74569e49i			0.881089i
$795$	−7.02457e48	+	1.18168e49i	−0.347039	+	0.583790i
$796$	3.46272e48			0.167454
$797$		−	2.91743e49i		−	1.38105i	−0.723310	−	0.690523i	$-0.757380\pi$
$797$		−	2.91743e49i		−	1.38105i	0.723310	−	0.690523i	$-0.242620\pi$
$798$	9.66782e48	+	5.74713e48i	0.448002	+	0.266319i
$799$	5.65060e48			0.256330
$800$		−	1.21848e49i		−	0.541114i
$801$	1.76833e49	−	9.61746e48i	0.768796	−	0.418126i
$802$	−1.76711e49			−0.752139
$803$			8.37307e48i			0.348916i
$804$	−4.28095e48	+	7.20142e48i	−0.174658	+	0.293809i
$805$	3.12221e49			1.24719
$806$		−	1.46115e49i		−	0.571479i
$807$	1.00307e49	+	5.96284e48i	0.384132	+	0.228351i
$808$	3.35818e49			1.25925
$809$			3.97284e49i			1.45873i	0.684123	+	0.729367i	$0.260185\pi$
$809$			3.97284e49i			1.45873i	−0.684123	+	0.729367i	$0.739815\pi$
$810$	−2.35891e49	+	3.64367e49i	−0.848136	+	1.31007i
$811$	4.03893e48			0.142204			0.0711021	−	0.997469i	$-0.477348\pi$
$811$	4.03893e48			0.142204			0.0711021	+	0.997469i	$0.477348\pi$
$812$		−	8.53814e47i		−	0.0294382i
$813$	−2.21839e49	+	3.73178e49i	−0.749029	+	1.26002i
$814$	−1.34979e48			−0.0446324
$815$		−	2.14794e49i		−	0.695572i
$816$	−5.13036e48	−	3.04979e48i	−0.162710	−	0.0967246i
$817$	1.20964e49			0.375735
$818$		−	7.22165e48i		−	0.219700i
$819$	−4.25724e49	−	7.82766e49i	−1.26853	−	2.33241i
$820$	1.45851e49			0.425672
$821$		−	4.77655e48i		−	0.136546i	−0.997667	−	0.0682732i	$-0.978251\pi$
$821$		−	4.77655e48i		−	0.136546i	0.997667	−	0.0682732i	$-0.0217490\pi$
$822$	3.26405e49	−	5.49080e49i	0.913979	−	1.53750i
$823$	−6.21566e49			−1.70487			−0.852433	−	0.522837i	$-0.824874\pi$
$823$	−6.21566e49			−1.70487			−0.852433	+	0.522837i	$0.824874\pi$
$824$			3.73239e49i			1.00282i
$825$	8.94450e48	+	5.31714e48i	0.235418	+	0.139946i
$826$	−4.90175e49			−1.26384
$827$			1.65744e49i			0.418643i	0.977847	+	0.209322i	$0.0671256\pi$
$827$			1.65744e49i			0.418643i	−0.977847	+	0.209322i	$0.932874\pi$
$828$	7.02340e48	−	3.81983e48i	0.173793	−	0.0945209i
$829$	4.95736e49			1.20178			0.600888	−	0.799333i	$-0.294814\pi$
$829$	4.95736e49			1.20178			0.600888	+	0.799333i	$0.294814\pi$
$830$		−	4.73305e48i		−	0.112412i
$831$	4.43471e48	−	7.46008e48i	0.103193	−	0.173591i
$832$	−3.10201e49			−0.707206
$833$			1.20788e49i			0.269811i
$834$	2.26519e49	+	1.34656e49i	0.495772	+	0.294716i
$835$	−3.24453e49			−0.695796
$836$		−	1.55325e48i		−	0.0326388i
$837$	−1.48948e49	−	5.69399e47i	−0.306692	−	0.0117242i
$838$	−8.37216e49			−1.68923
$839$		−	1.37895e49i		−	0.272644i	−0.990665	−	0.136322i	$-0.956472\pi$
$839$		−	1.37895e49i		−	0.272644i	0.990665	−	0.136322i	$-0.0435282\pi$
$840$	4.41686e49	−	7.43005e49i	0.855787	−	1.43961i
$841$	5.25330e49			0.997472
$842$		−	1.07546e50i		−	2.00119i
$843$	1.07389e49	+	6.38383e48i	0.195835	+	0.116416i
$844$	2.48051e49			0.443322
$845$			1.19687e50i			2.09644i
$846$	5.38495e49	+	9.90114e49i	0.924454	+	1.69977i
$847$	8.70254e49			1.46429
$848$		−	3.77030e49i		−	0.621794i
$849$	−2.75021e49	+	4.62641e49i	−0.444565	+	0.747848i
$850$	−9.05190e48			−0.143423
$851$		−	4.04550e48i		−	0.0628304i
$852$	−3.54819e48	−	2.10926e48i	−0.0540175	−	0.0321112i
$853$	−7.48674e49			−1.11727			−0.558636	−	0.829413i	$-0.688675\pi$
$853$	−7.48674e49			−1.11727			−0.558636	+	0.829413i	$0.688675\pi$
$854$		−	3.87212e49i		−	0.566455i
$855$	−2.22031e49	+	1.20756e49i	−0.318412	+	0.173175i
$856$	5.48197e49			0.770695
$857$			3.87435e49i			0.533980i	0.963699	+	0.266990i	$0.0860291\pi$
$857$			3.87435e49i			0.533980i	−0.963699	+	0.266990i	$0.913971\pi$
$858$	−2.41016e49	+	4.05437e49i	−0.325658	+	0.547822i
$859$	2.79699e49			0.370517			0.185258	−	0.982690i	$-0.440688\pi$
$859$	2.79699e49			0.370517			0.185258	+	0.982690i	$0.440688\pi$
$860$			5.07193e49i			0.658719i
$861$	1.00632e50	+	5.98219e49i	1.28140	+	0.761739i
$862$	−1.15245e50			−1.43880
$863$		−	7.65151e49i		−	0.936620i	−0.883564	−	0.468310i	$-0.844863\pi$
$863$		−	7.65151e49i		−	0.936620i	0.883564	−	0.468310i	$-0.155137\pi$
$864$	2.15232e48	−	5.63021e49i	0.0258329	−	0.675757i
$865$	−1.78632e50			−2.10225
$866$			1.43854e50i			1.66004i
$867$	4.40859e49	−	7.41614e49i	0.498856	−	0.839176i
$868$	−1.61942e49			−0.179690
$869$		−	4.99621e49i		−	0.543632i
$870$	6.32161e48	+	3.75794e48i	0.0674528	+	0.0400980i
$871$	1.48134e50			1.55005
$872$		−	5.60788e48i		−	0.0575464i
$873$	3.65910e49	+	6.72788e49i	0.368241	+	0.677074i
$874$	1.78435e49			0.176110
$875$			4.59409e49i			0.444696i
$876$	1.93686e49	−	3.25819e49i	0.183877	−	0.309319i
$877$	6.30507e49			0.587079			0.293540	−	0.955947i	$-0.405167\pi$
$877$	6.30507e49			0.587079			0.293540	+	0.955947i	$0.405167\pi$
$878$		−	2.00085e50i		−	1.82729i
$879$	−1.89000e50	−	1.12353e50i	−1.69297	−	1.00640i
$880$	−6.42046e49			−0.564106
$881$		−	1.77640e50i		−	1.53092i	−0.643486	−	0.765458i	$-0.722512\pi$
$881$		−	1.77640e50i		−	1.53092i	0.643486	−	0.765458i	$-0.277488\pi$
$882$	−2.11649e50	+	1.15110e50i	−1.78916	+	0.973074i
$883$	1.09287e50			0.906224			0.453112	−	0.891454i	$-0.350314\pi$
$883$	1.09287e50			0.906224			0.453112	+	0.891454i	$0.350314\pi$
$884$		−	1.07047e49i		−	0.0870739i
$885$	5.62868e49	−	9.46858e49i	0.449129	−	0.755526i
$886$	1.91095e50			1.49581
$887$		−	5.66030e49i		−	0.434648i	−0.976100	−	0.217324i	$-0.930267\pi$
$887$		−	5.66030e49i		−	0.434648i	0.976100	−	0.217324i	$-0.0697328\pi$
$888$	−9.62724e48	−	5.72300e48i	−0.0725239	−	0.0431125i
$889$	−6.17850e48			−0.0456618
$890$			1.88371e50i			1.36579i
$891$	4.03905e49	+	2.61488e49i	0.287315	+	0.186007i
$892$	−1.56518e49			−0.109235
$893$			6.56276e49i			0.449378i
$894$	7.90211e49	−	1.32929e50i	0.530891	−	0.893065i
$895$	−2.23857e50			−1.47564
$896$			3.05190e50i			1.97394i
$897$	−1.21515e50	−	7.22359e49i	−0.771187	−	0.458439i
$898$	1.06524e49			0.0663359
$899$			2.52546e48i			0.0154321i
$900$	−2.25059e49	−	4.13809e49i	−0.134950	−	0.248129i
$901$	−1.32563e49			−0.0780010
$902$		−	6.19700e49i		−	0.357825i
$903$	−2.08029e50	+	3.49946e50i	−1.17878	+	1.98294i
$904$	4.23389e49			0.235438
$905$			3.46216e50i			1.88939i
$906$	−6.59729e49	−	3.92182e49i	−0.353335	−	0.210043i
$907$	−1.16227e50			−0.610920			−0.305460	−	0.952205i	$-0.598810\pi$
$907$	−1.16227e50			−0.610920			−0.305460	+	0.952205i	$0.598810\pi$
$908$		−	1.88732e48i		−	0.00973611i
$909$	2.90316e50	−	1.57895e50i	1.46989	−	0.799431i
$910$	8.33838e50			4.14360
$911$		−	1.95445e50i		−	0.953262i	−0.879103	−	0.476631i	$-0.841858\pi$
$911$		−	1.95445e50i		−	0.953262i	0.879103	−	0.476631i	$-0.158142\pi$
$912$	3.54211e49	−	5.95854e49i	0.169570	−	0.285251i
$913$	−5.24664e48			−0.0246535
$914$			1.58837e50i			0.732598i
$915$	7.47967e49	+	4.44636e49i	0.338629	+	0.201301i
$916$	3.11162e49			0.138281
$917$		−	5.83498e50i		−	2.54543i
$918$	−4.18259e49	−	1.59892e48i	−0.179110	−	0.00684703i
$919$	−1.28916e50			−0.541931			−0.270965	−	0.962589i	$-0.587343\pi$
$919$	−1.28916e50			−0.541931			−0.270965	+	0.962589i	$0.587343\pi$
$920$		−	1.37133e50i		−	0.565913i
$921$	−1.42516e50	+	2.39741e50i	−0.577365	+	0.971245i
$922$	−5.06998e50			−2.01642
$923$			7.29865e49i			0.284980i
$924$	4.49352e49	+	2.67121e49i	0.172251	+	0.102396i
$925$	−2.38355e49			−0.0897046
$926$			8.60141e49i			0.317821i
$927$	1.75489e50	+	3.22667e50i	0.636642	+	1.17057i
$928$	−9.54618e48			−0.0340028
$929$		−	1.47009e50i		−	0.514136i	−0.966393	−	0.257068i	$-0.917244\pi$
$929$		−	1.47009e50i		−	0.514136i	0.966393	−	0.257068i	$-0.0827564\pi$
$930$	7.12763e49	−	1.19901e50i	0.244757	−	0.411730i
$931$	−1.40287e50			−0.473012
$932$		−	5.31023e49i		−	0.175810i
$933$	−8.18210e48	−	4.86392e48i	−0.0265997	−	0.0158124i
$934$	−5.93827e50			−1.89567
$935$			2.25742e49i			0.0707643i
$936$	−3.43805e50	+	1.86986e50i	−1.05833	+	0.575598i
$937$	2.71376e50			0.820347			0.410174	−	0.912007i	$-0.365468\pi$
$937$	2.71376e50			0.820347			0.410174	+	0.912007i	$0.365468\pi$
$938$		−	6.29285e50i		−	1.86810i
$939$	2.43504e50	−	4.09624e50i	0.709891	−	1.19418i
$940$	−2.75172e50			−0.787826
$941$			3.06534e50i			0.861896i	0.902377	+	0.430948i	$0.141821\pi$
$941$			3.06534e50i			0.861896i	−0.902377	+	0.430948i	$0.858179\pi$
$942$	2.90163e50	+	1.72490e50i	0.801266	+	0.476320i
$943$	1.85733e50			0.503721
$944$			3.02108e50i			0.804708i
$945$	3.24940e49	−	8.50003e50i	0.0850084	−	2.22372i
$946$	2.15499e50			0.553726
$947$			1.74769e50i			0.441076i	0.975378	+	0.220538i	$0.0707814\pi$
$947$			1.74769e50i			0.441076i	−0.975378	+	0.220538i	$0.929219\pi$
$948$	−1.15572e50	+	1.94416e50i	−0.286492	+	0.481937i
$949$	−6.70211e50			−1.63187
$950$		−	1.05131e50i		−	0.251438i
$951$	6.65358e50	+	3.95528e50i	1.56310	+	0.929198i
$952$	8.33519e49			0.192348
$953$		−	1.31002e50i		−	0.296960i	−0.988915	−	0.148480i	$-0.952562\pi$
$953$		−	1.31002e50i		−	0.296960i	0.988915	−	0.148480i	$-0.0474381\pi$
$954$	−1.26331e50	−	2.32280e50i	−0.281311	−	0.517237i
$955$	4.36345e50			0.954492
$956$			1.81369e50i			0.389744i
$957$	4.16571e48	−	7.00757e48i	0.00879400	−	0.0147933i
$958$	8.27628e50			1.71641
$959$			1.25180e51i			2.55045i
$960$	−2.54548e50	−	1.51318e50i	−0.509517	−	0.302887i
$961$	−4.60608e50			−0.905803
$962$		−	1.08042e50i		−	0.208745i
$963$	4.73919e50	−	2.57751e50i	0.899615	−	0.489275i
$964$	2.44649e50			0.456282
$965$			5.08223e50i			0.931301i
$966$	−3.06864e50	+	5.16208e50i	−0.552504	+	0.929423i
$967$	1.62356e49			0.0287222			0.0143611	−	0.999897i	$-0.495429\pi$
$967$	1.62356e49			0.0287222			0.0143611	+	0.999897i	$0.495429\pi$
$968$		−	3.82231e50i		−	0.664424i
$969$	−2.09501e49	−	1.24540e49i	−0.0357834	−	0.0212718i
$970$	−7.16684e50			−1.20284
$971$			2.34528e49i			0.0386784i	0.999813	+	0.0193392i	$0.00615624\pi$
$971$			2.34528e49i			0.0386784i	−0.999813	+	0.0193392i	$0.993844\pi$
$972$	−9.66829e49	−	1.95183e50i	−0.156683	−	0.316312i
$973$	−5.16420e50			−0.822404
$974$		−	3.68565e50i		−	0.576782i
$975$	−4.25603e50	+	7.15951e50i	−0.654525	+	1.10104i
$976$	−2.38649e50			−0.360673
$977$		−	5.14409e50i		−	0.764013i	−0.924160	−	0.382006i	$-0.875233\pi$
$977$		−	5.14409e50i		−	0.764013i	0.924160	−	0.382006i	$-0.124767\pi$
$978$	3.55127e50	+	2.11108e50i	0.518350	+	0.308138i
$979$	2.08811e50			0.299535
$980$		−	5.88213e50i		−	0.829261i
$981$	−2.63671e49	−	4.84804e49i	−0.0365333	−	0.0671727i
$982$	6.51226e50			0.886822
$983$		−	5.13651e50i		−	0.687478i	−0.939065	−	0.343739i	$-0.888307\pi$
$983$		−	5.13651e50i		−	0.687478i	0.939065	−	0.343739i	$-0.111693\pi$
$984$	2.62748e50	−	4.41996e50i	0.345640	−	0.581436i
$985$	1.31270e51			1.69727
$986$			7.09171e48i			0.00901246i
$987$	−1.89859e51	−	1.12863e51i	−2.37159	−	1.40981i
$988$	1.24328e50			0.152651
$989$			6.45880e50i			0.779498i
$990$	−3.95551e50	+	2.15129e50i	−0.469250	+	0.255212i
$991$	7.10378e50			0.828395			0.414197	−	0.910187i	$-0.364062\pi$
$991$	7.10378e50			0.828395			0.414197	+	0.910187i	$0.364062\pi$
$992$			1.81061e50i			0.207552i
$993$	−4.31721e50	+	7.26241e50i	−0.486481	+	0.818359i
$994$	3.10053e50			0.343453
$995$		−	5.84494e50i		−	0.636484i
$996$	2.04161e49	+	1.21365e49i	0.0218556	+	0.0129923i
$997$	−1.30591e51			−1.37434			−0.687170	−	0.726496i	$-0.741147\pi$
$997$	−1.30591e51			−1.37434			−0.687170	+	0.726496i	$0.741147\pi$
$998$		−	3.90928e50i		−	0.404461i
$999$	−1.10136e50	−	4.21029e48i	−0.112025	−	0.00428252i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.35.b.a.2.3	✓	10
3.2	odd	2	inner	3.35.b.a.2.8	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.35.b.a.2.3	✓	10	1.1	even	1	trivial
3.35.b.a.2.8	yes	10	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 35 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-152461. i q^{2} +(6.59892e7 - 1.11007e8i) q^{3} -6.06435e9 q^{4} +1.02364e12i q^{5} +(-1.69242e13 - 1.00608e13i) q^{6} +3.85840e14 q^{7} -1.69468e15i q^{8} +(-7.96802e15 - 1.46506e16i) q^{9} +O(q^{10})\)	\(q-152461. i q^{2} +(6.59892e7 - 1.11007e8i) q^{3} -6.06435e9 q^{4} +1.02364e12i q^{5} +(-1.69242e13 - 1.00608e13i) q^{6} +3.85840e14 q^{7} -1.69468e15i q^{8} +(-7.96802e15 - 1.46506e16i) q^{9} +1.56064e17 q^{10} -1.72999e17i q^{11} +(-4.00182e17 + 6.73187e17i) q^{12} +1.38475e19 q^{13} -5.88253e19i q^{14} +(1.13631e20 + 6.75491e19i) q^{15} -3.62556e20 q^{16} +1.27474e20i q^{17} +(-2.23363e21 + 1.21481e21i) q^{18} -1.48052e21 q^{19} -6.20770e21i q^{20} +(2.54613e22 - 4.28310e22i) q^{21} -2.63755e22 q^{22} -7.90513e22i q^{23} +(-1.88122e23 - 1.11831e23i) q^{24} -4.65759e23 q^{25} -2.11120e24i q^{26} +(-2.15212e24 - 8.22715e22i) q^{27} -2.33987e24 q^{28} +3.64899e23i q^{29} +(1.02986e25 - 1.73243e25i) q^{30} +6.92098e24 q^{31} +2.61612e25i q^{32} +(-1.92042e25 - 1.14161e25i) q^{33} +1.94347e25 q^{34} +3.94960e26i q^{35} +(4.83209e25 + 8.88461e25i) q^{36} +5.11756e25 q^{37} +2.25720e26i q^{38} +(9.13785e26 - 1.53717e27i) q^{39} +1.73474e27 q^{40} +2.34952e27i q^{41} +(-6.53004e27 - 3.88184e27i) q^{42} -8.17039e27 q^{43} +1.04913e27i q^{44} +(1.49969e28 - 8.15637e27i) q^{45} -1.20522e28 q^{46} -4.43275e28i q^{47} +(-2.39248e28 + 4.02464e28i) q^{48} +9.47553e28 q^{49} +7.10098e28i q^{50} +(1.41505e28 + 8.41191e27i) q^{51} -8.39760e28 q^{52} +1.03992e29i q^{53} +(-1.25432e28 + 3.28114e29i) q^{54} +1.77089e29 q^{55} -6.53874e29i q^{56} +(-9.76981e28 + 1.64348e29i) q^{57} +5.56327e28 q^{58} -8.33272e29i q^{59} +(-6.89100e29 - 4.09641e29i) q^{60} +6.58240e29 q^{61} -1.05518e30i q^{62} +(-3.07438e30 - 5.65277e30i) q^{63} -2.24012e30 q^{64} +1.41748e31i q^{65} +(-1.74050e30 + 2.92788e30i) q^{66} +1.06975e31 q^{67} -7.73046e29i q^{68} +(-8.77526e30 - 5.21653e30i) q^{69} +6.02159e31 q^{70} +5.27074e30i q^{71} +(-2.48280e31 + 1.35032e31i) q^{72} -4.83995e31 q^{73} -7.80227e30i q^{74} +(-3.07351e31 + 5.17026e31i) q^{75} +8.97837e30 q^{76} -6.67499e31i q^{77} +(-2.34358e32 - 1.39316e32i) q^{78} +2.88800e32 q^{79} -3.71127e32i q^{80} +(-1.51150e32 + 2.33472e32i) q^{81} +3.58210e32 q^{82} -3.03275e31i q^{83} +(-1.54406e32 + 2.59742e32i) q^{84} -1.30487e32 q^{85} +1.24566e33i q^{86} +(4.05064e31 + 2.40794e31i) q^{87} -2.93178e32 q^{88} +1.20701e33i q^{89} +(-1.24353e33 - 2.28643e33i) q^{90} +5.34291e33 q^{91} +4.79395e32i q^{92} +(4.56710e32 - 7.68279e32i) q^{93} -6.75820e33 q^{94} -1.51551e33i q^{95} +(2.90408e33 + 1.72636e33i) q^{96} -4.59223e33 q^{97} -1.44464e34i q^{98} +(-2.53454e33 + 1.37846e33i) 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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