LMFDB - Embedded newform 3.35.b.a.2.7

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			2.7
Root			$4945.08i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.35.b.a.2.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+59341.0i q^{2} +(-8.15029e7 - 1.00172e8i) q^{3} +1.36585e10 q^{4} -7.02280e10i q^{5} +(5.94431e12 - 4.83646e12i) q^{6} +9.28487e13 q^{7} +1.82998e15i q^{8} +(-3.39173e15 + 1.63286e16i) q^{9} +O(q^{10})$	\(q+59341.0i q^{2} +(-8.15029e7 - 1.00172e8i) q^{3} +1.36585e10 q^{4} -7.02280e10i q^{5} +(5.94431e12 - 4.83646e12i) q^{6} +9.28487e13 q^{7} +1.82998e15i q^{8} +(-3.39173e15 + 1.63286e16i) q^{9} +4.16740e15 q^{10} -4.29998e17i q^{11} +(-1.11321e18 - 1.36820e18i) q^{12} -3.39144e18 q^{13} +5.50973e18i q^{14} +(-7.03489e18 + 5.72379e18i) q^{15} +1.26059e20 q^{16} -2.02536e20i q^{17} +(-9.68958e20 - 2.01269e20i) q^{18} +6.64095e21 q^{19} -9.59210e20i q^{20} +(-7.56744e21 - 9.30085e21i) q^{21} +2.55165e22 q^{22} -2.42110e23i q^{23} +(1.83313e23 - 1.49149e23i) q^{24} +5.77145e23 q^{25} -2.01251e23i q^{26} +(1.91211e24 - 9.91075e23i) q^{27} +1.26818e24 q^{28} -1.27286e25i q^{29} +(-3.39655e23 - 4.17457e23i) q^{30} -2.14060e23 q^{31} +3.89193e25i q^{32} +(-4.30738e25 + 3.50460e25i) q^{33} +1.20187e25 q^{34} -6.52058e24i q^{35} +(-4.63260e25 + 2.23025e26i) q^{36} -5.46506e26 q^{37} +3.94080e26i q^{38} +(2.76412e26 + 3.39728e26i) q^{39} +1.28516e26 q^{40} -3.09869e27i q^{41} +(5.51922e26 - 4.49059e26i) q^{42} +4.94694e27 q^{43} -5.87313e27i q^{44} +(1.14673e27 + 2.38195e26i) q^{45} +1.43671e28 q^{46} +7.73887e26i q^{47} +(-1.02742e28 - 1.26276e28i) q^{48} -4.54961e28 q^{49} +3.42483e28i q^{50} +(-2.02885e28 + 1.65073e28i) q^{51} -4.63220e28 q^{52} +2.24445e29i q^{53} +(5.88113e28 + 1.13467e29i) q^{54} -3.01979e28 q^{55} +1.69911e29i q^{56} +(-5.41256e29 - 6.65238e29i) q^{57} +7.55330e29 q^{58} -1.72696e30i q^{59} +(-9.60862e28 + 7.81784e28i) q^{60} +2.54560e30 q^{61} -1.27025e28i q^{62} +(-3.14918e29 + 1.51609e30i) q^{63} -1.43835e29 q^{64} +2.38174e29i q^{65} +(-2.07967e30 - 2.55604e30i) q^{66} +1.55798e30 q^{67} -2.76635e30i q^{68} +(-2.42527e31 + 1.97327e31i) q^{69} +3.86937e29 q^{70} +3.31673e31i q^{71} +(-2.98811e31 - 6.20680e30i) q^{72} +6.69030e31 q^{73} -3.24302e31i q^{74} +(-4.70390e31 - 5.78138e31i) q^{75} +9.07055e31 q^{76} -3.99247e31i q^{77} +(-2.01598e31 + 1.64026e31i) q^{78} +1.59249e32 q^{79} -8.85285e30i q^{80} +(-2.55121e32 - 1.10765e32i) q^{81} +1.83879e32 q^{82} +2.64046e31i q^{83} +(-1.03360e32 - 1.27036e32i) q^{84} -1.42237e31 q^{85} +2.93556e32i q^{86} +(-1.27505e33 + 1.03742e33i) q^{87} +7.86887e32 q^{88} +1.26315e33i q^{89} +(-1.41347e31 + 6.80480e31i) q^{90} -3.14891e32 q^{91} -3.30687e33i q^{92} +(1.74465e31 + 2.14428e31i) q^{93} -4.59232e31 q^{94} -4.66380e32i q^{95} +(3.89863e33 - 3.17203e33i) q^{96} -2.38063e33 q^{97} -2.69978e33i q^{98} +(7.02128e33 + 1.45844e33i) 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 $

$2$			59341.0i			0.452736i	0.974042	+	0.226368i	$0.0726852\pi$
$2$			59341.0i			0.452736i	−0.974042	+	0.226368i	$0.927315\pi$
$3$	−8.15029e7	−	1.00172e8i	−0.631120	−	0.775685i
$3$	−8.15029e7	−	1.00172e8i	−0.631120	−	0.775685i
$4$	1.36585e10			0.795030
$5$		−	7.02280e10i		−	0.0920492i	−0.998940	−	0.0460246i	$-0.985345\pi$
$5$		−	7.02280e10i		−	0.0920492i	0.998940	−	0.0460246i	$-0.0146553\pi$
$6$	5.94431e12	−	4.83646e12i	0.351181	−	0.285730i
$7$	9.28487e13			0.399125			0.199563	−	0.979885i	$-0.436048\pi$
$7$	9.28487e13			0.399125			0.199563	+	0.979885i	$0.436048\pi$
$8$			1.82998e15i			0.812674i
$9$	−3.39173e15	+	1.63286e16i	−0.203376	+	0.979101i
$10$	4.16740e15			0.0416740
$11$		−	4.29998e17i		−	0.850727i	−0.905023	−	0.425364i	$-0.860146\pi$
$11$		−	4.29998e17i		−	0.850727i	0.905023	−	0.425364i	$-0.139854\pi$
$12$	−1.11321e18	−	1.36820e18i	−0.501759	−	0.616693i
$13$	−3.39144e18			−0.392055			−0.196027	−	0.980598i	$-0.562804\pi$
$13$	−3.39144e18			−0.392055			−0.196027	+	0.980598i	$0.562804\pi$
$14$			5.50973e18i			0.180698i
$15$	−7.03489e18	+	5.72379e18i	−0.0714013	+	0.0580941i
$16$	1.26059e20			0.427104
$17$		−	2.02536e20i		−	0.244834i	−0.992479	−	0.122417i	$-0.960935\pi$
$17$		−	2.02536e20i		−	0.244834i	0.992479	−	0.122417i	$-0.0390645\pi$
$18$	−9.68958e20	−	2.01269e20i	−0.443274	−	0.0920754i
$19$	6.64095e21			1.21177			0.605883	−	0.795554i	$-0.292820\pi$
$19$	6.64095e21			1.21177			0.605883	+	0.795554i	$0.292820\pi$
$20$		−	9.59210e20i		−	0.0731819i
$21$	−7.56744e21	−	9.30085e21i	−0.251896	−	0.309596i
$22$	2.55165e22			0.385155
$23$		−	2.42110e23i		−	1.71649i	−0.513244	−	0.858243i	$-0.671556\pi$
$23$		−	2.42110e23i		−	1.71649i	0.513244	−	0.858243i	$-0.328444\pi$
$24$	1.83313e23	−	1.49149e23i	0.630380	−	0.512895i
$25$	5.77145e23			0.991527
$26$		−	2.01251e23i		−	0.177497i
$27$	1.91211e24	−	9.91075e23i	0.887829	−	0.460174i
$28$	1.26818e24			0.317317
$29$		−	1.27286e25i		−	1.75394i	−0.480541	−	0.876972i	$-0.659560\pi$
$29$		−	1.27286e25i		−	1.75394i	0.480541	−	0.876972i	$-0.340440\pi$
$30$	−3.39655e23	−	4.17457e23i	−0.0263013	−	0.0323259i
$31$	−2.14060e23			−0.00949262			−0.00474631	−	0.999989i	$-0.501511\pi$
$31$	−2.14060e23			−0.00949262			−0.00474631	+	0.999989i	$0.501511\pi$
$32$			3.89193e25i			1.00604i
$33$	−4.30738e25	+	3.50460e25i	−0.659897	+	0.536911i
$34$	1.20187e25			0.110845
$35$		−	6.52058e24i		−	0.0367392i
$36$	−4.63260e25	+	2.23025e26i	−0.161690	+	0.778415i
$37$	−5.46506e26			−1.19720			−0.598598	−	0.801050i	$-0.704275\pi$
$37$	−5.46506e26			−1.19720			−0.598598	+	0.801050i	$0.704275\pi$
$38$			3.94080e26i			0.548610i
$39$	2.76412e26	+	3.39728e26i	0.247434	+	0.304111i
$40$	1.28516e26			0.0748061
$41$		−	3.09869e27i		−	1.18537i	−0.805436	−	0.592683i	$-0.798069\pi$
$41$		−	3.09869e27i		−	1.18537i	0.805436	−	0.592683i	$-0.201931\pi$
$42$	5.51922e26	−	4.49059e26i	0.140165	−	0.114042i
$43$	4.94694e27			0.842118			0.421059	−	0.907033i	$-0.361659\pi$
$43$	4.94694e27			0.842118			0.421059	+	0.907033i	$0.361659\pi$
$44$		−	5.87313e27i		−	0.676354i
$45$	1.14673e27	+	2.38195e26i	0.0901255	+	0.0187206i
$46$	1.43671e28			0.777114
$47$			7.73887e26i			0.0290411i	0.999895	+	0.0145206i	$0.00462220\pi$
$47$			7.73887e26i			0.0290411i	−0.999895	+	0.0145206i	$0.995378\pi$
$48$	−1.02742e28	−	1.26276e28i	−0.269554	−	0.331298i
$49$	−4.54961e28			−0.840699
$50$			3.42483e28i			0.448900i
$51$	−2.02885e28	+	1.65073e28i	−0.189914	+	0.154520i
$52$	−4.63220e28			−0.311696
$53$			2.24445e29i			1.09250i	0.837623	+	0.546248i	$0.183945\pi$
$53$			2.24445e29i			1.09250i	−0.837623	+	0.546248i	$0.816055\pi$
$54$	5.88113e28	+	1.13467e29i	0.208337	+	0.401952i
$55$	−3.01979e28			−0.0783088
$56$			1.69911e29i			0.324359i
$57$	−5.41256e29	−	6.65238e29i	−0.764769	−	0.939949i
$58$	7.55330e29			0.794073
$59$		−	1.72696e30i		−	1.35768i	−0.734287	−	0.678839i	$-0.762483\pi$
$59$		−	1.72696e30i		−	1.35768i	0.734287	−	0.678839i	$-0.237517\pi$
$60$	−9.60862e28	+	7.81784e28i	−0.0567662	+	0.0461866i
$61$	2.54560e30			1.13549			0.567745	−	0.823205i	$-0.307816\pi$
$61$	2.54560e30			1.13549			0.567745	+	0.823205i	$0.307816\pi$
$62$		−	1.27025e28i		−	0.00429765i
$63$	−3.14918e29	+	1.51609e30i	−0.0811724	+	0.390784i
$64$	−1.43835e29			−0.0283664
$65$			2.38174e29i			0.0360884i
$66$	−2.07967e30	−	2.55604e30i	−0.243079	−	0.298759i
$67$	1.55798e30			0.141023			0.0705116	−	0.997511i	$-0.477537\pi$
$67$	1.55798e30			0.141023			0.0705116	+	0.997511i	$0.477537\pi$
$68$		−	2.76635e30i		−	0.194650i
$69$	−2.42527e31	+	1.97327e31i	−1.33145	+	1.08331i
$70$	3.86937e29			0.0166331
$71$			3.31673e31i			1.12026i	0.828405	+	0.560130i	$0.189249\pi$
$71$			3.31673e31i			1.12026i	−0.828405	+	0.560130i	$0.810751\pi$
$72$	−2.98811e31	−	6.20680e30i	−0.795690	−	0.165278i
$73$	6.69030e31			1.40915			0.704575	−	0.709630i	$-0.251138\pi$
$73$	6.69030e31			1.40915			0.704575	+	0.709630i	$0.251138\pi$
$74$		−	3.24302e31i		−	0.542014i
$75$	−4.70390e31	−	5.78138e31i	−0.625772	−	0.769113i
$76$	9.07055e31			0.963391
$77$		−	3.99247e31i		−	0.339547i
$78$	−2.01598e31	+	1.64026e31i	−0.137682	+	0.112022i
$79$	1.59249e32			0.875820			0.437910	−	0.899019i	$-0.355719\pi$
$79$	1.59249e32			0.875820			0.437910	+	0.899019i	$0.355719\pi$
$80$		−	8.85285e30i		−	0.0393146i
$81$	−2.55121e32	−	1.10765e32i	−0.917277	−	0.398251i
$82$	1.83879e32			0.536658
$83$			2.64046e31i			0.0627122i	0.999508	+	0.0313561i	$0.00998260\pi$
$83$			2.64046e31i			0.0627122i	−0.999508	+	0.0313561i	$0.990017\pi$
$84$	−1.03360e32	−	1.27036e32i	−0.200265	−	0.246138i
$85$	−1.42237e31			−0.0225368
$86$			2.93556e32i			0.381257i
$87$	−1.27505e33	+	1.03742e33i	−1.36051	+	1.10695i
$88$	7.86887e32			0.691364
$89$			1.26315e33i			0.915852i	0.888990	+	0.457926i	$0.151407\pi$
$89$			1.26315e33i			0.915852i	−0.888990	+	0.457926i	$0.848593\pi$
$90$	−1.41347e31	+	6.80480e31i	−0.00847548	+	0.0408030i
$91$	−3.14891e32			−0.156479
$92$		−	3.30687e33i		−	1.36466i
$93$	1.74465e31	+	2.14428e31i	0.00599098	+	0.00736328i
$94$	−4.59232e31			−0.0131480
$95$		−	4.66380e32i		−	0.111542i
$96$	3.89863e33	−	3.17203e33i	0.780370	−	0.634931i
$97$	−2.38063e33			−0.399551			−0.199775	−	0.979842i	$-0.564021\pi$
$97$	−2.38063e33			−0.399551			−0.199775	+	0.979842i	$0.564021\pi$
$98$		−	2.69978e33i		−	0.380615i
$99$	7.02128e33	+	1.45844e33i	0.832948	+	0.173017i
$100$	7.88294e33			0.788294
$101$			8.32061e33i			0.702574i	0.936268	+	0.351287i	$0.114256\pi$
$101$			8.32061e33i			0.702574i	−0.936268	+	0.351287i	$0.885744\pi$
$102$	−9.79560e32	−	1.20394e33i	−0.0699565	−	0.0859809i
$103$	−2.49069e34			−1.50691			−0.753455	−	0.657500i	$-0.771614\pi$
$103$	−2.49069e34			−1.50691			−0.753455	+	0.657500i	$0.771614\pi$
$104$		−	6.20626e33i		−	0.318613i
$105$	−6.53180e32	+	5.31446e32i	−0.0284980	+	0.0231868i
$106$	−1.33188e34			−0.494612
$107$			3.78732e34i			1.19897i	0.800387	+	0.599484i	$0.204627\pi$
$107$			3.78732e34i			1.19897i	−0.800387	+	0.599484i	$0.795373\pi$
$108$	2.61166e34	−	1.35366e34i	0.705851	−	0.365853i
$109$	−5.66863e34			−1.30987			−0.654935	−	0.755686i	$-0.727304\pi$
$109$	−5.66863e34			−1.30987			−0.654935	+	0.755686i	$0.727304\pi$
$110$		−	1.79197e33i		−	0.0354532i
$111$	4.45418e34	+	5.47446e34i	0.755574	+	0.928648i
$112$	1.17044e34			0.170468
$113$		−	1.20381e34i		−	0.150739i	−0.997156	−	0.0753694i	$-0.975986\pi$
$113$		−	1.20381e34i		−	0.150739i	0.997156	−	0.0753694i	$-0.0240136\pi$
$114$	3.94759e34	−	3.21187e34i	0.425549	−	0.346238i
$115$	−1.70029e34			−0.158001
$116$		−	1.73854e35i		−	1.39444i
$117$	1.15029e34	−	5.53776e34i	0.0797345	−	0.383861i
$118$	1.02479e35			0.614670
$119$		−	1.88052e34i		−	0.0977194i
$120$	−1.04744e34	−	1.28737e34i	−0.0472116	−	0.0580260i
$121$	7.05788e34			0.276263
$122$			1.51058e35i			0.514077i
$123$	−3.10402e35	+	2.52552e35i	−0.919471	+	0.748108i
$124$	−2.92374e33			−0.00754692
$125$		−	8.14098e34i		−	0.183319i
$126$	−8.99664e34	−	1.86875e34i	−0.176922	−	0.0367496i
$127$	1.67429e35			0.287851			0.143925	−	0.989589i	$-0.454028\pi$
$127$	1.67429e35			0.287851			0.143925	+	0.989589i	$0.454028\pi$
$128$			6.60093e35i			0.993197i
$129$	−4.03190e35	−	4.95546e35i	−0.531477	−	0.653219i
$130$	−1.41335e34			−0.0163385
$131$			4.29145e35i			0.435504i	0.976004	+	0.217752i	$0.0698723\pi$
$131$			4.29145e35i			0.435504i	−0.976004	+	0.217752i	$0.930128\pi$
$132$	−5.88324e35	+	4.78677e35i	−0.524638	+	0.426860i
$133$	6.16603e35			0.483646
$134$			9.24521e34i			0.0638462i
$135$	−6.96012e34	−	1.34284e35i	−0.0423587	−	0.0817240i
$136$	3.70638e35			0.198970
$137$		−	3.32309e36i		−	1.57505i	−0.616286	−	0.787523i	$-0.711363\pi$
$137$		−	3.32309e36i		−	1.57505i	0.616286	−	0.787523i	$-0.288637\pi$
$138$	−1.17096e36	−	1.43918e36i	−0.490452	−	0.602796i
$139$	5.23886e36			1.94082			0.970410	−	0.241462i	$-0.0776271\pi$
$139$	5.23886e36			1.94082			0.970410	+	0.241462i	$0.0776271\pi$
$140$		−	8.90614e34i		−	0.0292088i
$141$	7.75219e34	−	6.30740e34i	0.0225268	−	0.0183284i
$142$	−1.96818e36			−0.507182
$143$			1.45831e36i			0.333532i
$144$	−4.27558e35	+	2.05837e36i	−0.0868625	+	0.418177i
$145$	−8.93906e35			−0.161449
$146$			3.97009e36i			0.637972i
$147$	3.70806e36	+	4.55744e36i	0.530582	+	0.652118i
$148$	−7.46446e36			−0.951807
$149$		−	9.05488e36i		−	1.02971i	−0.857276	−	0.514857i	$-0.827845\pi$
$149$		−	9.05488e36i		−	1.02971i	0.857276	−	0.514857i	$-0.172155\pi$
$150$	3.43073e36	−	2.79134e36i	0.348205	−	0.283309i
$151$	−1.74694e37			−1.58369			−0.791844	−	0.610724i	$-0.790879\pi$
$151$	−1.74694e37			−1.58369			−0.791844	+	0.610724i	$0.790879\pi$
$152$			1.21528e37i			0.984771i
$153$	3.30715e36	+	6.86950e35i	0.239717	+	0.0497933i
$154$	2.36917e36			0.153725
$155$			1.50330e34i			0.000873788i
$156$	3.77538e36	+	4.64018e36i	0.196717	+	0.241778i
$157$	7.62830e36			0.356561			0.178280	−	0.983980i	$-0.442947\pi$
$157$	7.62830e36			0.356561			0.178280	+	0.983980i	$0.442947\pi$
$158$			9.44997e36i			0.396515i
$159$	2.24831e37	−	1.82929e37i	0.847434	−	0.689496i
$160$	2.73322e36			0.0926052
$161$		−	2.24796e37i		−	0.685093i
$162$	6.57289e36	−	1.51391e37i	0.180302	−	0.415284i
$163$	−1.35528e37			−0.334843			−0.167421	−	0.985885i	$-0.553544\pi$
$163$	−1.35528e37			−0.334843			−0.167421	+	0.985885i	$0.553544\pi$
$164$		−	4.23235e37i		−	0.942402i
$165$	2.46121e36	+	3.02498e36i	0.0494222	+	0.0607430i
$166$	−1.56688e36			−0.0283921
$167$			4.40587e37i			0.720861i	0.932786	+	0.360431i	$0.117370\pi$
$167$			4.40587e37i			0.720861i	−0.932786	+	0.360431i	$0.882630\pi$
$168$	1.70204e37	−	1.38483e37i	0.251600	−	0.204709i
$169$	−6.33278e37			−0.846293
$170$		−	8.44050e35i		−	0.0102032i
$171$	−2.25243e37	+	1.08438e38i	−0.246444	+	1.18644i
$172$	6.75679e37			0.669509
$173$			1.28102e38i			1.15019i	0.818085	+	0.575097i	$0.195036\pi$
$173$			1.28102e38i			1.15019i	−0.818085	+	0.575097i	$0.804964\pi$
$174$	−6.15616e37	−	7.56630e37i	−0.501155	−	0.615951i
$175$	5.35871e37			0.395743
$176$		−	5.42049e37i		−	0.363349i
$177$	−1.72993e38	+	1.40752e38i	−1.05313	+	0.856858i
$178$	−7.49566e37			−0.414639
$179$		−	1.58681e38i		−	0.798040i	−0.916942	−	0.399020i	$-0.869350\pi$
$179$		−	1.58681e38i		−	0.798040i	0.916942	−	0.399020i	$-0.130650\pi$
$180$	1.56626e37	+	3.25339e36i	0.0716525	+	0.0148834i
$181$	2.46119e38			1.02473			0.512366	−	0.858767i	$-0.328769\pi$
$181$	2.46119e38			1.02473			0.512366	+	0.858767i	$0.328769\pi$
$182$		−	1.86859e37i		−	0.0708436i
$183$	−2.07474e38	−	2.54998e38i	−0.716630	−	0.880783i
$184$	4.43057e38			1.39494
$185$			3.83800e37i			0.110201i
$186$	−1.27244e36	+	1.03529e36i	−0.00333362	+	0.00271233i
$187$	−8.70902e37			−0.208287
$188$			1.05701e37i			0.0230886i
$189$	1.77537e38	−	9.20200e37i	0.354355	−	0.183667i
$190$	2.76755e37			0.0504991
$191$		−	2.15684e38i		−	0.359957i	−0.983671	−	0.179979i	$-0.942397\pi$
$191$		−	2.15684e38i		−	0.359957i	0.983671	−	0.179979i	$-0.0576029\pi$
$192$	1.17230e37	+	1.44083e37i	0.0179026	+	0.0220034i
$193$	2.78362e37			0.0389166			0.0194583	−	0.999811i	$-0.493806\pi$
$193$	2.78362e37			0.0389166			0.0194583	+	0.999811i	$0.493806\pi$
$194$		−	1.41269e38i		−	0.180891i
$195$	2.38584e37	−	1.94119e37i	0.0279932	−	0.0227761i
$196$	−6.21409e38			−0.668381
$197$			1.32888e39i			1.31087i	0.755251	+	0.655436i	$0.227515\pi$
$197$			1.32888e39i			1.31087i	−0.755251	+	0.655436i	$0.772485\pi$
$198$	−8.65451e37	+	4.16649e38i	−0.0783311	+	0.377105i
$199$	−7.89734e38			−0.656113			−0.328057	−	0.944658i	$-0.606394\pi$
$199$	−7.89734e38			−0.656113			−0.328057	+	0.944658i	$0.606394\pi$
$200$			1.05616e39i			0.805789i
$201$	−1.26980e38	−	1.56066e38i	−0.0890025	−	0.109390i
$202$	−4.93753e38			−0.318080
$203$		−	1.18184e39i		−	0.700043i
$204$	−2.77111e38	+	2.25465e38i	−0.150987	+	0.122848i
$205$	−2.17615e38			−0.109112
$206$		−	1.47800e39i		−	0.682232i
$207$	3.95333e39	+	8.21174e38i	1.68061	+	0.349091i
$208$	−4.27520e38			−0.167448
$209$		−	2.85559e39i		−	1.03088i
$210$	−3.15365e37	−	3.87604e37i	−0.0104975	−	0.0129021i
$211$	1.65560e38			0.0508338			0.0254169	−	0.999677i	$-0.491909\pi$
$211$	1.65560e38			0.0508338			0.0254169	+	0.999677i	$0.491909\pi$
$212$			3.06559e39i			0.868568i
$213$	3.32244e39	−	2.70324e39i	0.868969	−	0.707018i
$214$	−2.24743e39			−0.542815
$215$		−	3.47414e38i		−	0.0775163i
$216$	1.81365e39	+	3.49913e39i	0.373972	+	0.721516i
$217$	−1.98752e37			−0.00378874
$218$		−	3.36382e39i		−	0.593025i
$219$	−5.45279e39	−	6.70182e39i	−0.889342	−	1.09306i
$220$	−4.12458e38			−0.0622579
$221$			6.86890e38i			0.0959884i
$222$	−3.24860e39	+	2.64315e39i	−0.420432	+	0.342075i
$223$	4.10653e39			0.492371			0.246186	−	0.969223i	$-0.420823\pi$
$223$	4.10653e39			0.492371			0.246186	+	0.969223i	$0.420823\pi$
$224$			3.61360e39i			0.401536i
$225$	−1.95752e39	+	9.42399e39i	−0.201652	+	0.970805i
$226$	7.14354e38			0.0682448
$227$			2.12538e40i			1.88364i	0.336122	+	0.941818i	$0.390884\pi$
$227$			2.12538e40i			1.88364i	−0.336122	+	0.941818i	$0.609116\pi$
$228$	−7.39276e39	−	9.08616e39i	−0.608015	−	0.747288i
$229$	−6.56187e39			−0.500984			−0.250492	−	0.968119i	$-0.580592\pi$
$229$	−6.56187e39			−0.500984			−0.250492	+	0.968119i	$0.580592\pi$
$230$		−	1.00897e39i		−	0.0715328i
$231$	−3.99934e39	+	3.25398e39i	−0.263381	+	0.214295i
$232$	2.32931e40			1.42539
$233$		−	1.61904e40i		−	0.920888i	−0.887689	−	0.460444i	$-0.847690\pi$
$233$		−	1.61904e40i		−	0.920888i	0.887689	−	0.460444i	$-0.152310\pi$
$234$	3.28616e39	+	6.82591e38i	0.173788	+	0.0360986i
$235$	5.43485e37			0.00267322
$236$		−	2.35877e40i		−	1.07940i
$237$	−1.29792e40	−	1.59523e40i	−0.552748	−	0.679361i
$238$	1.11592e39			0.0442411
$239$		−	5.23173e39i		−	0.193144i	−0.995326	−	0.0965719i	$-0.969212\pi$
$239$		−	5.23173e39i		−	0.193144i	0.995326	−	0.0965719i	$-0.0307878\pi$
$240$	−8.86809e38	+	7.21533e38i	−0.0304957	+	0.0248122i
$241$	1.81542e40			0.581684			0.290842	−	0.956771i	$-0.406065\pi$
$241$	1.81542e40			0.581684			0.290842	+	0.956771i	$0.406065\pi$
$242$			4.18822e39i			0.125074i
$243$	9.69753e39	+	3.45836e40i	0.269994	+	0.962862i
$244$	3.47691e40			0.902749
$245$			3.19510e39i			0.0773857i
$246$	−1.49867e40	−	1.84196e40i	−0.338695	−	0.416277i
$247$	−2.25224e40			−0.475079
$248$		−	3.91725e38i		−	0.00771441i
$249$	2.64501e39	−	2.15205e39i	0.0486450	−	0.0395789i
$250$	4.83094e39			0.0829949
$251$			2.45862e40i			0.394673i	0.980336	+	0.197337i	$0.0632292\pi$
$251$			2.45862e40i			0.394673i	−0.980336	+	0.197337i	$0.936771\pi$
$252$	−4.30131e39	+	2.07076e40i	−0.0645345	+	0.310685i
$253$	−1.04107e41			−1.46026
$254$			9.93539e39i			0.130320i
$255$	1.15928e39	+	1.42482e39i	0.0142234	+	0.0174815i
$256$	−4.16416e40			−0.478022
$257$			6.45942e40i			0.693954i	0.937874	+	0.346977i	$0.112792\pi$
$257$			6.45942e40i			0.693954i	−0.937874	+	0.346977i	$0.887208\pi$
$258$	2.94062e40	−	2.39257e40i	0.295735	−	0.240619i
$259$	−5.07423e40			−0.477831
$260$			3.25310e39i			0.0286913i
$261$	2.07841e41	+	4.31721e40i	1.71729	+	0.356710i
$262$	−2.54659e40			−0.197168
$263$		−	6.64268e40i		−	0.482054i	−0.970518	−	0.241027i	$-0.922516\pi$
$263$		−	6.64268e40i		−	0.482054i	0.970518	−	0.241027i	$-0.0774842\pi$
$264$	−6.41336e40	−	7.88241e40i	−0.436334	−	0.536281i
$265$	1.57623e40			0.100564
$266$			3.65898e40i			0.218964i
$267$	1.26533e41	−	1.02950e41i	0.710413	−	0.578012i
$268$	2.12797e40			0.112118
$269$		−	1.42730e41i		−	0.705875i	−0.935647	−	0.352938i	$-0.885183\pi$
$269$		−	1.42730e41i		−	0.705875i	0.935647	−	0.352938i	$-0.114817\pi$
$270$	7.96853e39	−	4.13020e39i	0.0369994	−	0.0191773i
$271$	2.16445e40			0.0943776			0.0471888	−	0.998886i	$-0.484974\pi$
$271$	2.16445e40			0.0943776			0.0471888	+	0.998886i	$0.484974\pi$
$272$		−	2.55315e40i		−	0.104569i
$273$	2.56645e40	+	3.15433e40i	0.0987570	+	0.121378i
$274$	1.97196e41			0.713079
$275$		−	2.48171e41i		−	0.843519i
$276$	−3.31256e41	+	2.69519e41i	−1.05855	+	0.861263i
$277$	−1.40410e41			−0.421933			−0.210966	−	0.977493i	$-0.567661\pi$
$277$	−1.40410e41			−0.421933			−0.210966	+	0.977493i	$0.567661\pi$
$278$			3.10879e41i			0.878679i
$279$	7.26033e38	−	3.49530e39i	0.00193057	−	0.00929423i
$280$	1.19325e40			0.0298570
$281$			6.18152e40i			0.145575i	0.997347	+	0.0727876i	$0.0231895\pi$
$281$			6.18152e40i			0.145575i	−0.997347	+	0.0727876i	$0.976810\pi$
$282$	3.74287e39	+	4.60022e39i	0.00829794	+	0.0101987i
$283$	−2.87389e41			−0.599929			−0.299965	−	0.953950i	$-0.596975\pi$
$283$	−2.87389e41			−0.599929			−0.299965	+	0.953950i	$0.596975\pi$
$284$			4.53017e41i			0.890641i
$285$	−4.67183e40	+	3.80114e40i	−0.0865216	+	0.0703964i
$286$	−8.65376e40			−0.151002
$287$		−	2.87709e41i		−	0.473109i
$288$	−6.35499e41	−	1.32004e41i	−0.985014	−	0.204604i
$289$	6.43305e41			0.940056
$290$		−	5.30453e40i		−	0.0730938i
$291$	1.94028e41	+	2.38473e41i	0.252165	+	0.309926i
$292$	9.13796e41			1.12032
$293$			2.70381e41i			0.312771i	0.987696	+	0.156385i	$0.0499842\pi$
$293$			2.70381e41i			0.312771i	−0.987696	+	0.156385i	$0.950016\pi$
$294$	−2.70443e41	+	2.20040e41i	−0.295237	+	0.240213i
$295$	−1.21281e41			−0.124973
$296$		−	1.00009e42i		−	0.972931i
$297$	−4.26160e41	−	8.22203e41i	−0.391483	−	0.755300i
$298$	5.37326e41			0.466188
$299$			8.21102e41i			0.672957i
$300$	−6.42483e41	−	7.89651e41i	−0.497508	−	0.611468i
$301$	4.59317e41			0.336110
$302$		−	1.03665e42i		−	0.716992i
$303$	8.33494e41	−	6.78154e41i	0.544976	−	0.443408i
$304$	8.37149e41			0.517550
$305$		−	1.78773e41i		−	0.104521i
$306$	−4.07643e40	+	1.96249e41i	−0.0225432	+	0.108528i
$307$	−1.75581e42			−0.918597			−0.459298	−	0.888282i	$-0.651899\pi$
$307$	−1.75581e42			−0.918597			−0.459298	+	0.888282i	$0.651899\pi$
$308$		−	5.45312e41i		−	0.269950i
$309$	2.02999e42	+	2.49498e42i	0.951040	+	1.16889i
$310$	−8.92072e38			−0.000395595
$311$			4.41788e42i			1.85476i	0.374122	+	0.927380i	$0.377944\pi$
$311$			4.41788e42i			1.85476i	−0.374122	+	0.927380i	$0.622056\pi$
$312$	−6.21695e41	+	5.05829e41i	−0.247143	+	0.201083i
$313$	−5.05648e42			−1.90368			−0.951841	−	0.306591i	$-0.900812\pi$
$313$	−5.05648e42			−1.90368			−0.951841	+	0.306591i	$0.900812\pi$
$314$			4.52671e41i			0.161428i
$315$	1.06472e41	+	2.21161e40i	0.0359713	+	0.00747185i
$316$	2.17510e42			0.696304
$317$		−	3.28884e42i		−	0.997781i	−0.866665	−	0.498891i	$-0.833741\pi$
$317$		−	3.28884e42i		−	0.997781i	0.866665	−	0.498891i	$-0.166259\pi$
$318$	1.08552e42	+	1.33417e42i	0.312160	+	0.383664i
$319$	−5.47328e42			−1.49213
$320$			1.01012e40i			0.00261111i
$321$	3.79384e42	−	3.08677e42i	0.930021	−	0.756692i
$322$	1.33396e42			0.310166
$323$		−	1.34503e42i		−	0.296681i
$324$	−3.48457e42	−	1.51288e42i	−0.729263	−	0.316621i
$325$	−1.95735e42			−0.388733
$326$		−	8.04239e41i		−	0.151595i
$327$	4.62010e42	+	5.67839e42i	0.826684	+	1.01605i
$328$	5.67054e42			0.963317
$329$			7.18544e40i			0.0115911i
$330$	−1.79506e41	+	1.46051e41i	−0.0275005	+	0.0223752i
$331$	4.02535e42			0.585771			0.292885	−	0.956148i	$-0.405385\pi$
$331$	4.02535e42			0.585771			0.292885	+	0.956148i	$0.405385\pi$
$332$			3.60648e41i			0.0498581i
$333$	1.85360e42	−	8.92369e42i	0.243481	−	1.17218i
$334$	−2.61449e42			−0.326360
$335$		−	1.09414e41i		−	0.0129811i
$336$	−9.53942e41	−	1.17245e42i	−0.107586	−	0.132229i
$337$	2.17067e42			0.232748			0.116374	−	0.993205i	$-0.462873\pi$
$337$	2.17067e42			0.232748			0.116374	+	0.993205i	$0.462873\pi$
$338$		−	3.75794e42i		−	0.383147i
$339$	−1.20588e42	+	9.81142e41i	−0.116926	+	0.0951342i
$340$	−1.94275e41			−0.0179174
$341$			9.20451e40i			0.00807563i
$342$	−6.43479e42	−	1.33662e42i	−0.537144	−	0.111574i
$343$	−9.24894e42			−0.734669
$344$			9.05280e42i			0.684368i
$345$	1.38579e42	+	1.70322e42i	0.0997177	+	0.122559i
$346$	−7.60168e42			−0.520734
$347$			1.81022e43i			1.18068i	0.807156	+	0.590339i	$0.201006\pi$
$347$			1.81022e43i			1.18068i	−0.807156	+	0.590339i	$0.798994\pi$
$348$	−1.74154e43	+	1.41696e43i	−1.08165	+	0.880058i
$349$	2.10481e43			1.24503			0.622517	−	0.782606i	$-0.286110\pi$
$349$	2.10481e43			1.24503			0.622517	+	0.782606i	$0.286110\pi$
$350$			3.17991e42i			0.179167i
$351$	−6.48481e42	+	3.36117e42i	−0.348078	+	0.180414i
$352$	1.67352e43			0.855865
$353$		−	2.62051e43i		−	1.27707i	−0.769591	−	0.638537i	$-0.779540\pi$
$353$		−	2.62051e43i		−	1.27707i	0.769591	−	0.638537i	$-0.220460\pi$
$354$	−8.35236e42	−	1.02656e43i	−0.387930	−	0.476790i
$355$	2.32928e42			0.103119
$356$			1.72528e43i			0.728130i
$357$	−1.88376e42	+	1.53268e42i	−0.0757995	+	0.0616726i
$358$	9.41632e42			0.361301
$359$		−	4.35627e43i		−	1.59408i	−0.603929	−	0.797038i	$-0.706399\pi$
$359$		−	4.35627e43i		−	1.59408i	0.603929	−	0.797038i	$-0.293601\pi$
$360$	−4.35891e41	+	2.09849e42i	−0.0152137	+	0.0732427i
$361$	1.40675e43			0.468376
$362$			1.46050e43i			0.463932i
$363$	−5.75238e42	−	7.07003e42i	−0.174355	−	0.214293i
$364$	−4.30094e42			−0.124406
$365$		−	4.69846e42i		−	0.129711i
$366$	1.51319e43	−	1.23117e43i	0.398762	−	0.324444i
$367$	−1.24696e43			−0.313710			−0.156855	−	0.987622i	$-0.550136\pi$
$367$	−1.24696e43			−0.313710			−0.156855	+	0.987622i	$0.550136\pi$
$368$		−	3.05201e43i		−	0.733117i
$369$	5.05974e43	+	1.05099e43i	1.16059	+	0.241075i
$370$	−2.27751e42			−0.0498919
$371$			2.08394e43i			0.436043i
$372$	2.38293e41	+	2.92877e41i	0.00476301	+	0.00585403i
$373$	−3.42301e43			−0.653669			−0.326835	−	0.945082i	$-0.605982\pi$
$373$	−3.42301e43			−0.653669			−0.326835	+	0.945082i	$0.605982\pi$
$374$		−	5.16802e42i		−	0.0942989i
$375$	−8.15499e42	+	6.63514e42i	−0.142198	+	0.115696i
$376$	−1.41620e42			−0.0236010
$377$			4.31684e43i			0.687643i
$378$	5.46056e42	+	1.05352e43i	0.0831527	+	0.160429i
$379$	−8.76035e43			−1.27542			−0.637712	−	0.770275i	$-0.720119\pi$
$379$	−8.76035e43			−1.27542			−0.637712	+	0.770275i	$0.720119\pi$
$380$		−	6.37006e42i		−	0.0886794i
$381$	−1.36459e43	−	1.67717e43i	−0.181668	−	0.223281i
$382$	1.27989e43			0.162965
$383$			1.54731e44i			1.88451i	0.334891	+	0.942257i	$0.391300\pi$
$383$			1.54731e44i			1.88451i	−0.334891	+	0.942257i	$0.608700\pi$
$384$	6.61229e43	−	5.37995e43i	0.770408	−	0.626826i
$385$	−2.80383e42			−0.0312550
$386$			1.65183e42i			0.0176190i
$387$	−1.67787e43	+	8.07768e43i	−0.171266	+	0.824518i
$388$	−3.25159e43			−0.317655
$389$		−	1.04774e44i		−	0.979740i	−0.871796	−	0.489870i	$-0.837044\pi$
$389$		−	1.04774e44i		−	0.979740i	0.871796	−	0.489870i	$-0.162956\pi$
$390$	1.15192e42	+	1.41578e42i	0.0103115	+	0.0126735i
$391$	−4.90362e43			−0.420254
$392$		−	8.32569e43i		−	0.683215i
$393$	4.29883e43	−	3.49765e43i	0.337814	−	0.274855i
$394$	−7.88571e43			−0.593479
$395$		−	1.11837e43i		−	0.0806186i
$396$	9.59002e43	+	1.99201e43i	0.662219	+	0.137554i
$397$	1.81478e44			1.20056			0.600281	−	0.799789i	$-0.295055\pi$
$397$	1.81478e44			1.20056			0.600281	+	0.799789i	$0.295055\pi$
$398$		−	4.68636e43i		−	0.297046i
$399$	−5.02549e43	−	6.17664e43i	−0.305239	−	0.375157i
$400$	7.27541e43			0.423485
$401$		−	2.03382e44i		−	1.13464i	−0.823497	−	0.567321i	$-0.807980\pi$
$401$		−	2.03382e44i		−	1.13464i	0.823497	−	0.567321i	$-0.192020\pi$
$402$	9.26113e42	−	7.53512e42i	0.0495246	−	0.0402946i
$403$	7.25970e41			0.00372163
$404$			1.13647e44i			0.558568i
$405$	−7.77879e42	+	1.79166e43i	−0.0366587	+	0.0844346i
$406$	7.01314e43			0.316935
$407$			2.34996e44i			1.01849i
$408$	−3.02081e43	−	3.71276e43i	−0.125574	−	0.154338i
$409$	2.75335e44			1.09791			0.548953	−	0.835853i	$-0.315026\pi$
$409$	2.75335e44			1.09791			0.548953	+	0.835853i	$0.315026\pi$
$410$		−	1.29135e43i		−	0.0493989i
$411$	−3.32881e44	+	2.70842e44i	−1.22174	+	0.994042i
$412$	−3.40191e44			−1.19804
$413$		−	1.60346e44i		−	0.541884i
$414$	−4.87293e43	+	2.34595e44i	−0.158046	+	0.760873i
$415$	1.85434e42			0.00577261
$416$		−	1.31992e44i		−	0.394423i
$417$	−4.26982e44	−	5.24788e44i	−1.22489	−	1.50547i
$418$	1.69454e44			0.466717
$419$			5.83277e44i			1.54254i	0.636508	+	0.771270i	$0.280378\pi$
$419$			5.83277e44i			1.54254i	−0.636508	+	0.771270i	$0.719622\pi$
$420$	−8.92147e42	+	7.25877e42i	−0.0226568	+	0.0184342i
$421$	4.16375e44			1.01552			0.507760	−	0.861498i	$-0.330474\pi$
$421$	4.16375e44			1.01552			0.507760	+	0.861498i	$0.330474\pi$
$422$			9.82447e42i			0.0230143i
$423$	−1.26365e43	−	2.62482e42i	−0.0284342	−	0.00590626i
$424$	−4.10730e44			−0.887844
$425$		−	1.16893e44i		−	0.242759i
$426$	1.60413e44	+	1.97157e44i	0.320092	+	0.393413i
$427$	2.36356e44			0.453203
$428$			5.17291e44i			0.953215i
$429$	1.46082e44	−	1.18857e44i	0.258716	−	0.210499i
$430$	2.06159e43			0.0350944
$431$		−	4.27842e44i		−	0.700116i	−0.936728	−	0.350058i	$-0.886162\pi$
$431$		−	4.27842e44i		−	0.700116i	0.936728	−	0.350058i	$-0.113838\pi$
$432$	2.41038e44	−	1.24934e44i	0.379195	−	0.196542i
$433$	5.43505e44			0.822070			0.411035	−	0.911619i	$-0.365167\pi$
$433$	5.43505e44			0.822070			0.411035	+	0.911619i	$0.365167\pi$
$434$		−	1.17941e42i		−	0.00171530i
$435$	7.28560e43	+	8.95445e43i	0.101894	+	0.125234i
$436$	−7.74251e44			−1.04139
$437$		−	1.60784e45i		−	2.07998i
$438$	3.97692e44	−	3.23574e44i	0.494866	−	0.402637i
$439$	−2.25161e44			−0.269523			−0.134762	−	0.990878i	$-0.543027\pi$
$439$	−2.25161e44			−0.269523			−0.134762	+	0.990878i	$0.543027\pi$
$440$		−	5.52615e43i		−	0.0636396i
$441$	1.54311e44	−	7.42889e44i	0.170978	−	0.823129i
$442$	−4.07607e43			−0.0434574
$443$			6.72654e44i			0.690126i	0.938579	+	0.345063i	$0.112143\pi$
$443$			6.72654e44i			0.690126i	−0.938579	+	0.345063i	$0.887857\pi$
$444$	6.08375e44	+	7.47731e44i	0.600704	+	0.738303i
$445$	8.87086e43			0.0843035
$446$			2.43686e44i			0.222914i
$447$	−9.07047e44	+	7.37999e44i	−0.798733	+	0.649872i
$448$	−1.33549e43			−0.0113218
$449$			1.26938e45i			1.03610i	0.855350	+	0.518051i	$0.173342\pi$
$449$			1.26938e45i			1.03610i	−0.855350	+	0.518051i	$0.826658\pi$
$450$	−5.59229e44	−	1.16161e44i	−0.439518	−	0.0912953i
$451$	−1.33243e45			−1.00842
$452$		−	1.64423e44i		−	0.119842i
$453$	1.42381e45	+	1.74995e45i	0.999496	+	1.22844i
$454$	−1.26122e45			−0.852790
$455$			2.21141e43i			0.0144038i
$456$	1.21737e45	−	9.90488e44i	0.763873	−	0.621508i
$457$	4.11400e44			0.248707			0.124354	−	0.992238i	$-0.460314\pi$
$457$	4.11400e44			0.248707			0.124354	+	0.992238i	$0.460314\pi$
$458$		−	3.89388e44i		−	0.226814i
$459$	−2.00729e44	−	3.87272e44i	−0.112666	−	0.217371i
$460$	−2.32235e44			−0.125616
$461$			9.22735e43i			0.0481018i	0.999711	+	0.0240509i	$0.00765638\pi$
$461$			9.22735e43i			0.0481018i	−0.999711	+	0.0240509i	$0.992344\pi$
$462$	−1.93094e44	−	2.37325e44i	−0.0970188	−	0.119242i
$463$	−1.84231e45			−0.892247			−0.446124	−	0.894971i	$-0.647196\pi$
$463$	−1.84231e45			−0.892247			−0.446124	+	0.894971i	$0.647196\pi$
$464$		−	1.60456e45i		−	0.749116i
$465$	1.50589e42	−	1.22523e42i	0.000677785	−	0.000551465i
$466$	9.60754e44			0.416919
$467$			2.67758e45i			1.12035i	0.828373	+	0.560177i	$0.189267\pi$
$467$			2.67758e45i			1.12035i	−0.828373	+	0.560177i	$0.810733\pi$
$468$	1.57112e44	−	7.56376e44i	0.0633913	−	0.305181i
$469$	1.44656e44			0.0562859
$470$			3.22509e42i			0.00121026i
$471$	−6.21728e44	−	7.64143e44i	−0.225032	−	0.276579i
$472$	3.16029e45			1.10335
$473$		−	2.12717e45i		−	0.716413i
$474$	9.46624e44	−	7.70200e44i	0.307571	−	0.250249i
$475$	3.83279e45			1.20150
$476$		−	2.56852e44i		−	0.0776899i
$477$	−3.66488e45	−	7.61258e44i	−1.06966	−	0.222187i
$478$	3.10456e44			0.0874431
$479$		−	2.29876e45i		−	0.624871i	−0.949939	−	0.312436i	$-0.898855\pi$
$479$		−	2.29876e45i		−	0.624871i	0.949939	−	0.312436i	$-0.101145\pi$
$480$	−2.22766e44	−	2.73793e44i	−0.0584450	−	0.0718325i
$481$	1.85344e45			0.469367
$482$			1.07729e45i			0.263349i
$483$	−2.25183e45	+	1.83216e45i	−0.531416	+	0.432375i
$484$	9.64002e44			0.219638
$485$			1.67187e44i			0.0367784i
$486$	−2.05223e45	+	5.75461e44i	−0.435922	+	0.122236i
$487$	−2.07776e45			−0.426189			−0.213094	−	0.977032i	$-0.568354\pi$
$487$	−2.07776e45			−0.426189			−0.213094	+	0.977032i	$0.568354\pi$
$488$			4.65840e45i			0.922783i
$489$	1.10460e45	+	1.35762e45i	0.211326	+	0.259733i
$490$	−1.89600e44			−0.0350353
$491$			9.25292e44i			0.165156i	0.996585	+	0.0825778i	$0.0263153\pi$
$491$			9.25292e44i			0.165156i	−0.996585	+	0.0825778i	$0.973685\pi$
$492$	−4.23964e45	+	3.44949e45i	−0.731007	+	0.594768i
$493$	−2.57801e45			−0.429425
$494$		−	1.33650e45i		−	0.215085i
$495$	1.02423e44	−	4.93090e44i	0.0159261	−	0.0766722i
$496$	−2.69841e43			−0.00405433
$497$			3.07954e45i			0.447124i
$498$	1.27705e44	+	1.56957e44i	0.0179188	+	0.0220233i
$499$	−7.06560e44			−0.0958164			−0.0479082	−	0.998852i	$-0.515255\pi$
$499$	−7.06560e44			−0.0958164			−0.0479082	+	0.998852i	$0.515255\pi$
$500$		−	1.11194e45i		−	0.145744i
$501$	4.41345e45	−	3.59091e45i	0.559161	−	0.454950i
$502$	−1.45897e45			−0.178683
$503$		−	4.21132e45i		−	0.498612i	−0.968425	−	0.249306i	$-0.919797\pi$
$503$		−	4.21132e45i		−	0.498612i	0.968425	−	0.249306i	$-0.0802025\pi$
$504$	−2.77442e45	−	5.76294e44i	−0.317580	−	0.0659667i
$505$	5.84340e44			0.0646714
$506$		−	6.17780e45i		−	0.661112i
$507$	5.16140e45	+	6.34369e45i	0.534112	+	0.656457i
$508$	2.28683e45			0.228850
$509$		−	5.60335e45i		−	0.542307i	−0.962536	−	0.271154i	$-0.912595\pi$
$509$		−	5.60335e45i		−	0.542307i	0.962536	−	0.271154i	$-0.0874052\pi$
$510$	−8.45503e43	+	6.87925e43i	−0.00791448	+	0.00643944i
$511$	6.21186e45			0.562427
$512$			8.86925e45i			0.776779i
$513$	1.26982e46	−	6.58167e45i	1.07584	−	0.557623i
$514$	−3.83308e45			−0.314178
$515$			1.74916e45i			0.138710i
$516$	−5.50698e45	−	6.76842e45i	−0.422540	−	0.519329i
$517$	3.32769e44			0.0247061
$518$		−	3.01110e45i		−	0.216331i
$519$	1.28322e46	−	1.04407e46i	0.892189	−	0.725910i
$520$	−4.35854e44			−0.0293281
$521$		−	1.22702e45i		−	0.0799120i	−0.999201	−	0.0399560i	$-0.987278\pi$
$521$		−	1.22702e45i		−	0.0799120i	0.999201	−	0.0399560i	$-0.0127218\pi$
$522$	−2.56188e45	+	1.23335e46i	−0.161495	+	0.777478i
$523$	−2.10978e46			−1.28739			−0.643694	−	0.765283i	$-0.722599\pi$
$523$	−2.10978e46			−1.28739			−0.643694	+	0.765283i	$0.722599\pi$
$524$			5.86148e45i			0.346239i
$525$	−4.36751e45	−	5.36794e45i	−0.249761	−	0.306972i
$526$	3.94183e45			0.218243
$527$			4.33549e43i			0.00232411i
$528$	−5.42983e45	+	4.41786e45i	−0.281844	+	0.229317i
$529$	−3.87223e46			−1.94632
$530$			9.35352e44i			0.0455287i
$531$	2.81988e46	+	5.85737e45i	1.32930	+	0.276119i
$532$	8.42188e45			0.384513
$533$			1.05090e46i			0.464729i
$534$	6.10918e45	+	7.50857e45i	0.261687	+	0.321629i
$535$	2.65976e45			0.110364
$536$			2.85107e45i			0.114606i
$537$	−1.58955e46	+	1.29330e46i	−0.619028	+	0.503659i
$538$	8.46976e45			0.319575
$539$			1.95632e46i			0.715206i
$540$	−9.50649e44	−	1.83412e45i	−0.0336765	−	0.0649730i
$541$	−1.41707e45			−0.0486448			−0.0243224	−	0.999704i	$-0.507743\pi$
$541$	−1.41707e45			−0.0486448			−0.0243224	+	0.999704i	$0.507743\pi$
$542$			1.28440e45i			0.0427281i
$543$	−2.00594e46	−	2.46543e46i	−0.646728	−	0.794869i
$544$	7.88257e45			0.246313
$545$			3.98097e45i			0.120572i
$546$	−1.87181e45	+	1.52296e45i	−0.0549524	+	0.0447108i
$547$	2.85727e46			0.813142			0.406571	−	0.913619i	$-0.366724\pi$
$547$	2.85727e46			0.813142			0.406571	+	0.913619i	$0.366724\pi$
$548$		−	4.53885e46i		−	1.25221i
$549$	−8.63400e45	+	4.15662e46i	−0.230931	+	1.11176i
$550$	1.47267e46			0.381891
$551$		−	8.45302e46i		−	2.12537i
$552$	−3.61104e46	−	4.43820e46i	−0.880377	−	1.08204i
$553$	1.47860e46			0.349562
$554$		−	8.33209e45i		−	0.191024i
$555$	3.84461e45	−	3.12808e45i	0.0854813	−	0.0695500i
$556$	7.15551e46			1.54301
$557$			5.61155e46i			1.17367i	0.809708	+	0.586833i	$0.199625\pi$
$557$			5.61155e46i			1.17367i	−0.809708	+	0.586833i	$0.800375\pi$
$558$	2.07415e44	+	4.30835e43i	0.00420783	+	0.000874037i
$559$	−1.67772e46			−0.330156
$560$		−	8.21976e44i		−	0.0156914i
$561$	7.09810e45	+	8.72401e45i	0.131454	+	0.161565i
$562$	−3.66817e45			−0.0659071
$563$			5.23971e46i			0.913408i	0.889619	+	0.456704i	$0.150970\pi$
$563$			5.23971e46i			0.913408i	−0.889619	+	0.456704i	$0.849030\pi$
$564$	1.05883e45	−	8.61497e44i	0.0179095	−	0.0145717i
$565$	−8.45413e44			−0.0138754
$566$		−	1.70539e46i		−	0.271609i
$567$	−2.36876e46	−	1.02844e46i	−0.366108	−	0.158952i
$568$	−6.06956e46			−0.910407
$569$			1.00624e47i			1.46486i	0.680845	+	0.732428i	$0.261613\pi$
$569$			1.00624e47i			1.46486i	−0.680845	+	0.732428i	$0.738387\pi$
$570$	−2.25563e45	−	2.77231e45i	−0.0318710	−	0.0391714i
$571$	5.05451e46			0.693210			0.346605	−	0.938011i	$-0.387334\pi$
$571$	5.05451e46			0.693210			0.346605	+	0.938011i	$0.387334\pi$
$572$			1.99184e46i			0.265168i
$573$	−2.16055e46	+	1.75789e46i	−0.279214	+	0.227176i
$574$	1.70729e46			0.214194
$575$		−	1.39733e47i		−	1.70194i
$576$	4.87850e44	−	2.34863e45i	0.00576904	−	0.0277736i
$577$	−1.47714e47			−1.69603			−0.848014	−	0.529974i	$-0.822202\pi$
$577$	−1.47714e47			−1.69603			−0.848014	+	0.529974i	$0.822202\pi$
$578$			3.81744e46i			0.425597i
$579$	−2.26873e45	−	2.78841e45i	−0.0245611	−	0.0301871i
$580$	−1.22094e46			−0.128357
$581$			2.45163e45i			0.0250300i
$582$	−1.41512e46	+	1.15138e46i	−0.140315	+	0.114164i
$583$	9.65108e46			0.929417
$584$			1.22431e47i			1.14518i
$585$	−3.88906e45	−	8.07823e44i	−0.0353341	−	0.00733950i
$586$	−1.60447e46			−0.141602
$587$		−	1.80084e46i		−	0.154393i	−0.997016	−	0.0771965i	$-0.975403\pi$
$587$		−	1.80084e46i		−	0.154393i	0.997016	−	0.0771965i	$-0.0245969\pi$
$588$	5.06466e46	+	6.22479e46i	0.421829	+	0.518454i
$589$	−1.42156e45			−0.0115028
$590$		−	7.19691e45i		−	0.0565799i
$591$	1.33117e47	−	1.08308e47i	1.01682	−	0.827317i
$592$	−6.88918e46			−0.511327
$593$		−	1.47533e47i		−	1.06405i	−0.846730	−	0.532023i	$-0.821432\pi$
$593$		−	1.47533e47i		−	1.06405i	0.846730	−	0.532023i	$-0.178568\pi$
$594$	4.87903e46	−	2.52887e46i	0.341951	−	0.177238i
$595$	−1.32065e45			−0.00899500
$596$		−	1.23676e47i		−	0.818653i
$597$	6.43656e46	+	7.91094e46i	0.414086	+	0.508937i
$598$	−4.87250e46			−0.304672
$599$		−	1.07056e47i		−	0.650659i	−0.945601	−	0.325329i	$-0.894525\pi$
$599$		−	1.07056e47i		−	0.650659i	0.945601	−	0.325329i	$-0.105475\pi$
$600$	1.05798e47	−	8.60804e46i	0.625038	−	0.508549i
$601$	2.00635e47			1.15223			0.576117	−	0.817367i	$-0.304567\pi$
$601$	2.00635e47			1.15223			0.576117	+	0.817367i	$0.304567\pi$
$602$			2.72563e46i			0.152169i
$603$	−5.28426e45	+	2.54397e46i	−0.0286807	+	0.138076i
$604$	−2.38606e47			−1.25908
$605$		−	4.95661e45i		−	0.0254298i
$606$	4.02423e46	+	4.94603e46i	0.200747	+	0.246730i
$607$	−1.25171e47			−0.607149			−0.303574	−	0.952808i	$-0.598180\pi$
$607$	−1.25171e47			−0.607149			−0.303574	+	0.952808i	$0.598180\pi$
$608$			2.58461e47i			1.21908i
$609$	−1.18387e47	+	9.63231e46i	−0.543013	+	0.441811i
$610$	1.06085e46			0.0473204
$611$		−	2.62459e45i		−	0.0113857i
$612$	4.51707e46	+	9.38272e45i	0.190582	+	0.0395872i
$613$	−2.69700e47			−1.10676			−0.553380	−	0.832929i	$-0.686662\pi$
$613$	−2.69700e47			−1.10676			−0.553380	+	0.832929i	$0.686662\pi$
$614$		−	1.04191e47i		−	0.415882i
$615$	1.77362e46	+	2.17989e46i	0.0688628	+	0.0846366i
$616$	7.30614e46			0.275941
$617$			3.34049e47i			1.22733i	0.789565	+	0.613667i	$0.210306\pi$
$617$			3.34049e47i			1.22733i	−0.789565	+	0.613667i	$0.789694\pi$
$618$	−1.48054e47	+	1.20461e47i	−0.529197	+	0.430570i
$619$	3.90603e47			1.35830			0.679149	−	0.734001i	$-0.262349\pi$
$619$	3.90603e47			1.35830			0.679149	+	0.734001i	$0.262349\pi$
$620$			2.05328e44i			0.000694688i
$621$	−2.39949e47	−	4.62942e47i	−0.789882	−	1.52394i
$622$	−2.62161e47			−0.839716
$623$			1.17282e47i			0.365539i
$624$	3.48442e46	+	4.28256e46i	0.105680	+	0.129887i
$625$	3.30225e47			0.974653
$626$		−	3.00056e47i		−	0.861865i
$627$	−2.86051e47	+	2.32739e47i	−0.799640	+	0.650610i
$628$	1.04191e47			0.283477
$629$			1.10687e47i			0.293114i
$630$	−1.31239e45	+	6.31816e45i	−0.00338278	+	0.0162855i
$631$	1.28189e47			0.321626			0.160813	−	0.986985i	$-0.448588\pi$
$631$	1.28189e47			0.321626			0.160813	+	0.986985i	$0.448588\pi$
$632$			2.91422e47i			0.711757i
$633$	−1.34936e46	−	1.65845e46i	−0.0320822	−	0.0394310i
$634$	1.95163e47			0.451731
$635$		−	1.17582e46i		−	0.0264964i
$636$	3.07086e47	−	2.49854e47i	0.673736	−	0.548171i
$637$	1.54297e47			0.329600
$638$		−	3.24790e47i		−	0.675540i
$639$	−5.41578e47	−	1.12495e47i	−1.09685	−	0.227834i
$640$	4.63570e46			0.0914230
$641$		−	8.48593e47i		−	1.62972i	−0.579658	−	0.814860i	$-0.696814\pi$
$641$		−	8.48593e47i		−	1.62972i	0.579658	−	0.814860i	$-0.303186\pi$
$642$	1.83172e47	+	2.25130e47i	0.342582	+	0.421054i
$643$	4.94226e47			0.900200			0.450100	−	0.892978i	$-0.351388\pi$
$643$	4.94226e47			0.900200			0.450100	+	0.892978i	$0.351388\pi$
$644$		−	3.07038e47i		−	0.544669i
$645$	−3.48012e46	+	2.83152e46i	−0.0601283	+	0.0489221i
$646$	7.98156e46			0.134318
$647$			6.83223e47i			1.11993i	0.828517	+	0.559963i	$0.189185\pi$
$647$			6.83223e47i			1.11993i	−0.828517	+	0.559963i	$0.810815\pi$
$648$	2.02697e47	−	4.66866e47i	0.323648	−	0.745447i
$649$	−7.42587e47			−1.15501
$650$		−	1.16151e47i		−	0.175993i
$651$	1.61988e45	+	1.99094e45i	0.00239115	+	0.00293887i
$652$	−1.85112e47			−0.266210
$653$			3.05006e47i			0.427350i	0.976905	+	0.213675i	$0.0685434\pi$
$653$			3.05006e47i			0.427350i	−0.976905	+	0.213675i	$0.931457\pi$
$654$	−3.36961e47	+	2.74161e47i	−0.460001	+	0.374270i
$655$	3.01380e46			0.0400878
$656$		−	3.90617e47i		−	0.506274i
$657$	−2.26917e47	+	1.09243e48i	−0.286587	+	1.37970i
$658$	−4.26391e45			−0.00524768
$659$			9.00545e47i			1.08007i	0.841641	+	0.540037i	$0.181590\pi$
$659$			9.00545e47i			1.08007i	−0.841641	+	0.540037i	$0.818410\pi$
$660$	3.36165e46	+	4.13168e46i	0.0392922	+	0.0482925i
$661$	1.19164e48			1.35744			0.678718	−	0.734399i	$-0.262536\pi$
$661$	1.19164e48			1.35744			0.678718	+	0.734399i	$0.262536\pi$
$662$			2.38868e47i			0.265199i
$663$	6.88072e46	−	5.59835e46i	0.0744568	−	0.0605801i
$664$	−4.83199e46			−0.0509646
$665$		−	4.33028e46i		−	0.0445193i
$666$	5.29541e47	+	1.09995e47i	0.530686	+	0.110232i
$667$	−3.08173e48			−3.01062
$668$			6.01776e47i			0.573106i
$669$	−3.34694e47	−	4.11360e47i	−0.310745	−	0.381925i
$670$	6.49273e45			0.00587700
$671$		−	1.09460e48i		−	0.965992i
$672$	3.61982e47	−	2.94519e47i	0.311465	−	0.253417i
$673$	6.79634e47			0.570189			0.285094	−	0.958499i	$-0.407975\pi$
$673$	6.79634e47			0.570189			0.285094	+	0.958499i	$0.407975\pi$
$674$			1.28810e47i			0.105373i
$675$	1.10356e48	−	5.71993e47i	0.880306	−	0.456275i
$676$	−8.64964e47			−0.672829
$677$			2.45156e47i			0.185966i	0.995668	+	0.0929832i	$0.0296403\pi$
$677$			2.45156e47i			0.185966i	−0.995668	+	0.0929832i	$0.970360\pi$
$678$	−5.82219e46	−	7.15583e46i	−0.0430707	−	0.0529365i
$679$	−2.21038e47			−0.159471
$680$		−	2.60291e46i		−	0.0183151i
$681$	2.12904e48	−	1.73225e48i	1.46111	−	1.18880i
$682$	−5.46205e45			−0.00365612
$683$		−	8.30387e47i		−	0.542161i	−0.962557	−	0.271081i	$-0.912619\pi$
$683$		−	8.30387e47i		−	0.542161i	0.962557	−	0.271081i	$-0.0873810\pi$
$684$	−3.07649e47	+	1.48110e48i	−0.195930	+	0.943257i
$685$	−2.33374e47			−0.144982
$686$		−	5.48841e47i		−	0.332611i
$687$	5.34811e47	+	6.57316e47i	0.316181	+	0.388606i
$688$	6.23605e47			0.359672
$689$		−	7.61192e47i		−	0.428319i
$690$	−1.01071e47	+	8.22340e46i	−0.0554869	+	0.0451458i
$691$	2.70369e48			1.44820			0.724101	−	0.689694i	$-0.242255\pi$
$691$	2.70369e48			1.44820			0.724101	+	0.689694i	$0.242255\pi$
$692$			1.74968e48i			0.914439i
$693$	6.51916e47	+	1.35414e47i	0.332450	+	0.0690555i
$694$	−1.07420e48			−0.534535
$695$		−	3.67915e47i		−	0.178651i
$696$	−1.89846e48	−	2.33332e48i	−0.899589	−	1.10565i
$697$	−6.27598e47			−0.290218
$698$			1.24902e48i			0.563672i
$699$	−1.62183e48	+	1.31956e48i	−0.714320	+	0.581191i
$700$	7.31921e47			0.314628
$701$		−	1.19862e48i		−	0.502893i	−0.967871	−	0.251446i	$-0.919094\pi$
$701$		−	1.19862e48i		−	0.502893i	0.967871	−	0.251446i	$-0.0809062\pi$
$702$	−1.99455e47	−	3.84815e47i	−0.0816797	−	0.157587i
$703$	−3.62931e48			−1.45072
$704$			6.18487e46i			0.0241321i
$705$	−4.42956e45	−	5.44421e45i	−0.00168712	−	0.00207357i
$706$	1.55504e48			0.578177
$707$			7.72558e47i			0.280415i
$708$	−2.36283e48	+	1.92246e48i	−0.837271	+	0.681228i
$709$	3.87201e48			1.33952			0.669762	−	0.742576i	$-0.266396\pi$
$709$	3.87201e48			1.33952			0.669762	+	0.742576i	$0.266396\pi$
$710$			1.38222e47i			0.0466857i
$711$	−5.40129e47	+	2.60031e48i	−0.178121	+	0.857516i
$712$	−2.31154e48			−0.744289
$713$			5.18260e46i			0.0162939i
$714$	−9.09509e46	−	1.11784e47i	−0.0279214	−	0.0343171i
$715$	1.02414e47			0.0307014
$716$		−	2.16735e48i		−	0.634466i
$717$	−5.24074e47	+	4.26401e47i	−0.149819	+	0.121897i
$718$	2.58505e48			0.721695
$719$			5.80826e48i			1.58363i	0.610758	+	0.791817i	$0.290865\pi$
$719$			5.80826e48i			1.58363i	−0.610758	+	0.791817i	$0.709135\pi$
$720$	1.44555e47	+	3.00265e46i	0.0384929	+	0.00799563i
$721$	−2.31257e48			−0.601445
$722$			8.34780e47i			0.212051i
$723$	−1.47962e48	−	1.81854e48i	−0.367112	−	0.451203i
$724$	3.36163e48			0.814692
$725$		−	7.34626e48i		−	1.73908i
$726$	4.19543e47	−	3.41352e47i	0.0970183	−	0.0789368i
$727$	3.69442e48			0.834567			0.417284	−	0.908776i	$-0.362982\pi$
$727$	3.69442e48			0.834567			0.417284	+	0.908776i	$0.362982\pi$
$728$		−	5.76244e47i		−	0.127166i
$729$	2.67394e48	−	3.79009e48i	0.576479	−	0.817112i
$730$	2.78811e47			0.0587249
$731$		−	1.00194e48i		−	0.206179i
$732$	−2.83379e48	−	3.48290e48i	−0.569743	−	0.700249i
$733$	−6.37033e47			−0.125139			−0.0625697	−	0.998041i	$-0.519930\pi$
$733$	−6.37033e47			−0.125139			−0.0625697	+	0.998041i	$0.519930\pi$
$734$		−	7.39957e47i		−	0.142028i
$735$	3.20060e47	−	2.60410e47i	0.0600270	−	0.0488397i
$736$	9.42276e48			1.72685
$737$		−	6.69928e47i		−	0.119972i
$738$	−6.23669e47	+	3.00250e48i	−0.109143	+	0.525442i
$739$	−1.03580e49			−1.77142			−0.885711	−	0.464237i	$-0.846328\pi$
$739$	−1.03580e49			−1.77142			−0.885711	+	0.464237i	$0.846328\pi$
$740$			5.24214e47i			0.0876131i
$741$	1.83564e48	+	2.25611e48i	0.299832	+	0.368512i
$742$	−1.23663e48			−0.197412
$743$			7.24435e48i			1.13029i	0.824992	+	0.565145i	$0.191180\pi$
$743$			7.24435e48i			1.13029i	−0.824992	+	0.565145i	$0.808820\pi$
$744$	−3.92399e46	+	3.19267e46i	−0.00598395	+	0.00486871i
$745$	−6.35906e47			−0.0947843
$746$		−	2.03125e48i		−	0.295939i
$747$	−4.31152e47	−	8.95574e46i	−0.0614016	−	0.0127541i
$748$	−1.18952e48			−0.165594
$749$			3.51647e48i			0.478538i
$750$	−3.93735e47	−	4.83925e47i	−0.0523797	−	0.0643779i
$751$	2.80502e47			0.0364801			0.0182401	−	0.999834i	$-0.494194\pi$
$751$	2.80502e47			0.0364801			0.0182401	+	0.999834i	$0.494194\pi$
$752$			9.75552e46i			0.0124036i
$753$	2.46285e48	−	2.00385e48i	0.306142	−	0.249086i
$754$	−2.56165e48			−0.311320
$755$			1.22684e48i			0.145777i
$756$	2.42489e48	−	1.25686e48i	0.281723	−	0.146021i
$757$	−1.36490e49			−1.55049			−0.775246	−	0.631659i	$-0.782374\pi$
$757$	−1.36490e49			−1.55049			−0.775246	+	0.631659i	$0.782374\pi$
$758$		−	5.19848e48i		−	0.577430i
$759$	8.48501e48	+	1.04286e49i	0.921599	+	1.13270i
$760$	8.53467e47			0.0906474
$761$			7.76384e48i			0.806375i	0.915117	+	0.403188i	$0.132098\pi$
$761$			7.76384e48i			0.806375i	−0.915117	+	0.403188i	$0.867902\pi$
$762$	9.95249e47	−	8.09763e47i	0.101087	−	0.0822477i
$763$	−5.26325e48			−0.522802
$764$		−	2.94593e48i		−	0.286177i
$765$	4.82431e46	−	2.32254e47i	0.00458343	−	0.0220658i
$766$	−9.18191e48			−0.853187
$767$			5.85686e48i			0.532285i
$768$	3.39391e48	+	4.17133e48i	0.301689	+	0.370795i
$769$	5.80555e48			0.504772			0.252386	−	0.967627i	$-0.418785\pi$
$769$	5.80555e48			0.504772			0.252386	+	0.967627i	$0.418785\pi$
$770$		−	1.66382e47i		−	0.0141503i
$771$	6.47054e48	−	5.26462e48i	0.538290	−	0.437968i
$772$	3.80201e47			0.0309399
$773$		−	1.08914e49i		−	0.867027i	−0.901147	−	0.433514i	$-0.857274\pi$
$773$		−	1.08914e49i		−	0.867027i	0.901147	−	0.433514i	$-0.142726\pi$
$774$	−4.79337e48	−	9.95664e47i	−0.373289	−	0.0775384i
$775$	−1.23543e47			−0.00941218
$776$		−	4.35650e48i		−	0.324705i
$777$	4.13565e48	+	5.08297e48i	0.301569	+	0.370647i
$778$	6.21740e48			0.443563
$779$		−	2.05782e49i		−	1.43639i
$780$	3.25870e47	−	2.65137e47i	0.0222555	−	0.0181077i
$781$	1.42619e49			0.953036
$782$		−	2.90985e48i		−	0.190264i
$783$	−1.26150e49	−	2.43386e49i	−0.807120	−	1.55720i
$784$	−5.73518e48			−0.359066
$785$		−	5.35720e47i		−	0.0328211i
$786$	2.07554e48	+	2.55097e48i	0.124437	+	0.152940i
$787$	2.74794e49			1.61227			0.806134	−	0.591733i	$-0.201556\pi$
$787$	2.74794e49			1.61227			0.806134	+	0.591733i	$0.201556\pi$
$788$			1.81505e49i			1.04218i
$789$	−6.65411e48	+	5.41398e48i	−0.373922	+	0.304234i
$790$	6.63652e47			0.0364989
$791$		−	1.11772e48i		−	0.0601636i
$792$	−2.66891e48	+	1.28488e49i	−0.140607	+	0.676915i
$793$	−8.63325e48			−0.445174
$794$			1.07691e49i			0.543537i
$795$	−1.28468e48	−	1.57895e48i	−0.0634676	−	0.0780057i
$796$	−1.07866e49			−0.521630
$797$			2.00720e49i			0.950166i	0.879941	+	0.475083i	$0.157582\pi$
$797$			2.00720e49i			0.950166i	−0.879941	+	0.475083i	$0.842418\pi$
$798$	3.66528e48	−	2.98218e48i	0.169847	−	0.138192i
$799$	1.56740e47			0.00711026
$800$			2.24620e49i			0.997515i
$801$	−2.06255e49	−	4.28427e48i	−0.896711	−	0.186262i
$802$	1.20689e49			0.513693
$803$		−	2.87681e49i		−	1.19880i
$804$	−1.73436e48	−	2.13163e48i	−0.0707597	−	0.0869681i
$805$	−1.57870e48			−0.0630623
$806$			4.30798e46i			0.00168491i
$807$	−1.42976e49	+	1.16329e49i	−0.547537	+	0.445492i
$808$	−1.52266e49			−0.570964
$809$			4.63516e48i			0.170192i	0.996373	+	0.0850962i	$0.0271198\pi$
$809$			4.63516e48i			0.170192i	−0.996373	+	0.0850962i	$0.972880\pi$
$810$	−1.06319e48	−	4.61601e47i	−0.0382266	−	0.0165967i
$811$	1.73482e48			0.0610803			0.0305401	−	0.999534i	$-0.490277\pi$
$811$	1.73482e48			0.0610803			0.0305401	+	0.999534i	$0.490277\pi$
$812$		−	1.61421e49i		−	0.556556i
$813$	−1.76409e48	−	2.16817e48i	−0.0595636	−	0.0732074i
$814$	−1.39449e49			−0.461106
$815$			9.51789e47i			0.0308220i
$816$	−2.55754e48	+	2.08089e48i	−0.0811130	+	0.0659958i
$817$	3.28524e49			1.02045
$818$			1.63387e49i			0.497062i
$819$	1.06803e48	−	5.14174e48i	0.0318240	−	0.153209i
$820$	−2.97229e48			−0.0867474
$821$			4.40139e49i			1.25822i	0.777316	+	0.629110i	$0.216580\pi$
$821$			4.40139e49i			1.25822i	−0.777316	+	0.629110i	$0.783420\pi$
$822$	−1.60720e49	−	1.97535e49i	−0.450038	−	0.553125i
$823$	5.14454e49			1.41107			0.705536	−	0.708674i	$-0.250706\pi$
$823$	5.14454e49			1.41107			0.705536	+	0.708674i	$0.250706\pi$
$824$		−	4.55792e49i		−	1.22463i
$825$	−2.48598e49	+	2.02266e49i	−0.654305	+	0.532361i
$826$	9.51506e48			0.245330
$827$		−	4.78194e49i		−	1.20784i	−0.797044	−	0.603921i	$-0.793604\pi$
$827$		−	4.78194e49i		−	1.20784i	0.797044	−	0.603921i	$-0.206396\pi$
$828$	5.39967e49	+	1.12160e49i	1.33614	+	0.277538i
$829$	2.02582e48			0.0491105			0.0245553	−	0.999698i	$-0.492183\pi$
$829$	2.02582e48			0.0491105			0.0245553	+	0.999698i	$0.492183\pi$
$830$			1.10039e47i			0.00261347i
$831$	1.14439e49	+	1.40652e49i	0.266290	+	0.327287i
$832$	4.87807e47			0.0111212
$833$			9.21462e48i			0.205832i
$834$	3.11414e49	−	2.53376e49i	0.681578	−	0.554552i
$835$	3.09415e48			0.0663547
$836$		−	3.90031e49i		−	0.819583i
$837$	−4.09306e47	+	2.12149e47i	−0.00842782	+	0.00436826i
$838$	−3.46122e49			−0.698363
$839$		−	4.42360e49i		−	0.874626i	−0.899309	−	0.437313i	$-0.855930\pi$
$839$		−	4.42360e49i		−	0.874626i	0.899309	−	0.437313i	$-0.144070\pi$
$840$	−9.72536e47	−	1.19531e48i	−0.0188433	−	0.0231596i
$841$	−1.09352e50			−2.07632
$842$			2.47081e49i			0.459762i
$843$	6.19216e48	−	5.03812e48i	0.112921	−	0.0918754i
$844$	2.26130e48			0.0404144
$845$			4.44739e48i			0.0779006i
$846$	1.55759e47	−	7.49863e47i	0.00267398	−	0.0128732i
$847$	6.55315e48			0.110264
$848$			2.82933e49i			0.466609i
$849$	2.34230e49	+	2.87883e49i	0.378627	+	0.465356i
$850$	6.93654e48			0.109906
$851$			1.32315e50i			2.05497i
$852$	4.53797e49	−	3.69222e49i	0.690857	−	0.562101i
$853$	−4.34259e49			−0.648060			−0.324030	−	0.946047i	$-0.605038\pi$
$853$	−4.34259e49			−0.648060			−0.324030	+	0.946047i	$0.605038\pi$
$854$			1.40256e49i			0.205181i
$855$	7.61536e48	+	1.58184e48i	0.109211	+	0.0226850i
$856$	−6.93071e49			−0.974370
$857$		−	2.04116e49i		−	0.281322i	−0.990058	−	0.140661i	$-0.955077\pi$
$857$		−	2.04116e49i		−	0.281322i	0.990058	−	0.140661i	$-0.0449227\pi$
$858$	7.05306e48	+	8.66865e48i	0.0953002	+	0.117130i
$859$	−7.79113e48			−0.103209			−0.0516044	−	0.998668i	$-0.516433\pi$
$859$	−7.79113e48			−0.103209			−0.0516044	+	0.998668i	$0.516433\pi$
$860$		−	4.74516e48i		−	0.0616278i
$861$	−2.88204e49	+	2.34491e49i	−0.366984	+	0.298589i
$862$	2.53886e49			0.316968
$863$			2.44891e49i			0.299770i	0.988703	+	0.149885i	$0.0478904\pi$
$863$			2.44891e49i			0.299770i	−0.988703	+	0.149885i	$0.952110\pi$
$864$	3.85719e49	+	7.44180e49i	0.462953	+	0.893191i
$865$	8.99632e48			0.105874
$866$			3.22521e49i			0.372181i
$867$	−5.24313e49	−	6.44413e49i	−0.593288	−	0.729188i
$868$	−2.71465e47			−0.00301216
$869$		−	6.84765e49i		−	0.745084i
$870$	−5.31366e48	+	4.32335e48i	−0.0566978	+	0.0461310i
$871$	−5.28380e48			−0.0552888
$872$		−	1.03735e50i		−	1.06450i
$873$	8.07446e48	−	3.88724e49i	0.0812590	−	0.391201i
$874$	9.54109e49			0.941681
$875$		−	7.55879e48i		−	0.0731670i
$876$	−7.44770e49	−	9.15369e49i	−0.707054	−	0.869013i
$877$	3.04549e49			0.283572			0.141786	−	0.989897i	$-0.454715\pi$
$877$	3.04549e49			0.283572			0.141786	+	0.989897i	$0.454715\pi$
$878$		−	1.33613e49i		−	0.122023i
$879$	2.70846e49	−	2.20368e49i	0.242612	−	0.197396i
$880$	−3.80670e48			−0.0334460
$881$			8.06966e49i			0.695448i	0.937597	+	0.347724i	$0.113045\pi$
$881$			8.06966e49i			0.695448i	−0.937597	+	0.347724i	$0.886955\pi$
$882$	4.40838e49	+	9.15694e48i	0.372660	+	0.0774077i
$883$	1.62572e50			1.34808			0.674038	−	0.738696i	$-0.264558\pi$
$883$	1.62572e50			1.34808			0.674038	+	0.738696i	$0.264558\pi$
$884$			9.38190e48i			0.0763137i
$885$	9.88472e48	+	1.21489e49i	0.0788731	+	0.0969400i
$886$	−3.99160e49			−0.312445
$887$		−	1.67845e50i		−	1.28887i	−0.764661	−	0.644433i	$-0.777093\pi$
$887$		−	1.67845e50i		−	1.28887i	0.764661	−	0.644433i	$-0.222907\pi$
$888$	−1.00182e50	+	8.15106e49i	−0.754688	+	0.614036i
$889$	1.55455e49			0.114888
$890$			5.26405e48i			0.0381672i
$891$	−4.76286e49	+	1.09701e50i	−0.338803	+	0.780352i
$892$	5.60892e49			0.391450
$893$			5.13934e48i			0.0351911i
$894$	−4.37936e49	−	5.38250e49i	−0.294220	−	0.361615i
$895$	−1.11439e49			−0.0734590
$896$			6.12887e49i			0.396410i
$897$	8.22516e49	−	6.69222e49i	0.522003	−	0.424716i
$898$	−7.53260e49			−0.469080
$899$			2.72469e48i			0.0166495i
$900$	−2.67368e49	+	1.28718e50i	−0.160320	+	0.771819i
$901$	4.54583e49			0.267480
$902$		−	7.90676e49i		−	0.456549i
$903$	−3.74357e49	−	4.60108e49i	−0.212126	−	0.260716i
$904$	2.20295e49			0.122502
$905$		−	1.72845e49i		−	0.0943257i
$906$	−1.03843e50	+	8.44900e49i	−0.556160	+	0.452508i
$907$	−3.53266e48			−0.0185685			−0.00928427	−	0.999957i	$-0.502955\pi$
$907$	−3.53266e48			−0.0185685			−0.00928427	+	0.999957i	$0.502955\pi$
$908$			2.90295e50i			1.49755i
$909$	−1.35864e50	−	2.82213e49i	−0.687891	−	0.142886i
$910$	−1.31227e48			−0.00652110
$911$			8.54930e49i			0.416983i	0.978024	+	0.208491i	$0.0668553\pi$
$911$			8.54930e49i			0.416983i	−0.978024	+	0.208491i	$0.933145\pi$
$912$	−6.82301e49	−	8.38590e49i	−0.326636	−	0.401456i
$913$	1.13539e49			0.0533510
$914$			2.44129e49i			0.112599i
$915$	−1.79080e49	+	1.45705e49i	−0.0810754	+	0.0659653i
$916$	−8.96254e49			−0.398298
$917$			3.98455e49i			0.173820i
$918$	2.29811e49	−	1.19114e49i	0.0984114	−	0.0510081i
$919$	1.23165e50			0.517755			0.258877	−	0.965910i	$-0.416647\pi$
$919$	1.23165e50			0.517755			0.258877	+	0.965910i	$0.416647\pi$
$920$		−	3.11150e49i		−	0.128404i
$921$	1.43104e50	+	1.75883e50i	0.579745	+	0.712542i
$922$	−5.47560e48			−0.0217774
$923$		−	1.12485e50i		−	0.439203i
$924$	−5.46251e49	+	4.44445e49i	−0.209396	+	0.170371i
$925$	−3.15413e50			−1.18705
$926$		−	1.09324e50i		−	0.403952i
$927$	8.44776e49	−	4.06696e50i	0.306469	−	1.47542i
$928$	4.95389e50			1.76454
$929$		−	5.13378e49i		−	0.179544i	−0.995962	−	0.0897719i	$-0.971386\pi$
$929$		−	5.13378e49i		−	0.179544i	0.995962	−	0.0897719i	$-0.0286138\pi$
$930$	7.27064e46	+	8.93607e46i	0.000249668	+	0.000306857i
$931$	−3.02137e50			−1.01873
$932$		−	2.21137e50i		−	0.732134i
$933$	4.42549e50	−	3.60070e50i	1.43871	−	1.17058i
$934$	−1.58890e50			−0.507225
$935$			6.11617e48i			0.0191727i
$936$	1.01340e50	+	2.10500e49i	0.311954	+	0.0647981i
$937$	3.26326e50			0.986459			0.493230	−	0.869899i	$-0.335816\pi$
$937$	3.26326e50			0.986459			0.493230	+	0.869899i	$0.335816\pi$
$938$			8.58406e48i			0.0254826i
$939$	4.12118e50	+	5.06518e50i	1.20145	+	1.47666i
$940$	7.42320e47			0.00212529
$941$			1.68484e50i			0.473733i	0.971542	+	0.236867i	$0.0761205\pi$
$941$			1.68484e50i			0.473733i	−0.971542	+	0.236867i	$0.923880\pi$
$942$	4.53450e49	−	3.68940e49i	0.125217	−	0.101880i
$943$	−7.50225e50			−2.03466
$944$		−	2.17698e50i		−	0.579869i
$945$	−6.46238e48	−	1.24681e49i	−0.0169064	−	0.0326181i
$946$	1.26228e50			0.324346
$947$			4.39633e50i			1.10953i	0.832006	+	0.554767i	$0.187192\pi$
$947$			4.39633e50i			1.10953i	−0.832006	+	0.554767i	$0.812808\pi$
$948$	−1.77277e50	−	2.17884e50i	−0.439451	−	0.540113i
$949$	−2.26897e50			−0.552464
$950$			2.27441e50i			0.543961i
$951$	−3.29450e50	+	2.68050e50i	−0.773964	+	0.629719i
$952$	3.44132e49			0.0794140
$953$		−	3.80976e50i		−	0.863611i	−0.901967	−	0.431806i	$-0.857877\pi$
$953$		−	3.80976e50i		−	0.863611i	0.901967	−	0.431806i	$-0.142123\pi$
$954$	4.51738e49	−	2.17478e50i	0.100592	−	0.484275i
$955$	−1.51471e49			−0.0331338
$956$		−	7.14577e49i		−	0.153555i
$957$	4.46088e50	+	5.48270e50i	0.941712	+	1.15742i
$958$	1.36411e50			0.282902
$959$		−	3.08545e50i		−	0.628640i
$960$	1.01186e48	−	8.23280e47i	0.00202540	−	0.00164792i
$961$	−5.08462e50			−0.999910
$962$			1.09985e50i			0.212499i
$963$	−6.18417e50	−	1.28456e50i	−1.17391	−	0.243841i
$964$	2.47959e50			0.462456
$965$		−	1.95488e48i		−	0.00358225i
$966$	−1.08722e50	−	1.33626e50i	−0.195752	−	0.240591i
$967$	−2.39194e50			−0.423156			−0.211578	−	0.977361i	$-0.567860\pi$
$967$	−2.39194e50			−0.423156			−0.211578	+	0.977361i	$0.567860\pi$
$968$			1.29158e50i			0.224512i
$969$	−1.34735e50	+	1.09624e50i	−0.230131	+	0.187241i
$970$	−9.92103e48			−0.0166509
$971$			1.12489e51i			1.85516i	0.373624	+	0.927580i	$0.378115\pi$
$971$			1.12489e51i			1.85516i	−0.373624	+	0.927580i	$0.621885\pi$
$972$	1.32454e50	+	4.72361e50i	0.214654	+	0.765504i
$973$	4.86421e50			0.774630
$974$		−	1.23296e50i		−	0.192951i
$975$	1.59530e50	+	1.96072e50i	0.245337	+	0.301535i
$976$	3.20895e50			0.484972
$977$		−	5.75994e50i		−	0.855481i	−0.903902	−	0.427740i	$-0.859310\pi$
$977$		−	5.75994e50i		−	0.855481i	0.903902	−	0.427740i	$-0.140690\pi$
$978$	−8.05623e49	+	6.55478e49i	−0.117590	+	0.0956748i
$979$	5.43152e50			0.779140
$980$			4.36403e49i			0.0615240i
$981$	1.92265e50	−	9.25611e50i	0.266396	−	1.28249i
$982$	−5.49077e49			−0.0747719
$983$		−	5.12551e49i		−	0.0686004i	−0.999412	−	0.0343002i	$-0.989080\pi$
$983$		−	5.12551e49i		−	0.0686004i	0.999412	−	0.0343002i	$-0.0109202\pi$
$984$	−4.62165e50	−	5.68030e50i	−0.607968	−	0.747231i
$985$	9.33247e49			0.120665
$986$		−	1.52982e50i		−	0.194416i
$987$	7.19780e48	−	5.85634e48i	0.00899101	−	0.00731534i
$988$	−3.07622e50			−0.377702
$989$		−	1.19771e51i		−	1.44548i
$990$	2.92605e49	+	6.07789e48i	0.0347122	+	0.00721032i
$991$	1.33032e51			1.55133			0.775667	−	0.631142i	$-0.217414\pi$
$991$	1.33032e51			1.55133			0.775667	+	0.631142i	$0.217414\pi$
$992$		−	8.33104e48i		−	0.00954995i
$993$	−3.28078e50	−	4.03228e50i	−0.369691	−	0.454374i
$994$	−1.82743e50			−0.202429
$995$			5.54615e49i			0.0603947i
$996$	3.61269e49	−	2.93939e49i	0.0386742	−	0.0314665i
$997$	1.39115e50			0.146405			0.0732023	−	0.997317i	$-0.476678\pi$
$997$	1.39115e50			0.146405			0.0732023	+	0.997317i	$0.476678\pi$
$998$		−	4.19280e49i		−	0.0433795i
$999$	−1.04498e51	+	5.41628e50i	−1.06291	+	0.550919i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.35.b.a.2.7	yes	10
3.2	odd	2	inner	3.35.b.a.2.4	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.35.b.a.2.4	✓	10	3.2	odd	2	inner
3.35.b.a.2.7	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)

\(f(q)\)	\(=\)	\(q+59341.0i q^{2} +(-8.15029e7 - 1.00172e8i) q^{3} +1.36585e10 q^{4} -7.02280e10i q^{5} +(5.94431e12 - 4.83646e12i) q^{6} +9.28487e13 q^{7} +1.82998e15i q^{8} +(-3.39173e15 + 1.63286e16i) q^{9} +O(q^{10})\)	\(q+59341.0i q^{2} +(-8.15029e7 - 1.00172e8i) q^{3} +1.36585e10 q^{4} -7.02280e10i q^{5} +(5.94431e12 - 4.83646e12i) q^{6} +9.28487e13 q^{7} +1.82998e15i q^{8} +(-3.39173e15 + 1.63286e16i) q^{9} +4.16740e15 q^{10} -4.29998e17i q^{11} +(-1.11321e18 - 1.36820e18i) q^{12} -3.39144e18 q^{13} +5.50973e18i q^{14} +(-7.03489e18 + 5.72379e18i) q^{15} +1.26059e20 q^{16} -2.02536e20i q^{17} +(-9.68958e20 - 2.01269e20i) q^{18} +6.64095e21 q^{19} -9.59210e20i q^{20} +(-7.56744e21 - 9.30085e21i) q^{21} +2.55165e22 q^{22} -2.42110e23i q^{23} +(1.83313e23 - 1.49149e23i) q^{24} +5.77145e23 q^{25} -2.01251e23i q^{26} +(1.91211e24 - 9.91075e23i) q^{27} +1.26818e24 q^{28} -1.27286e25i q^{29} +(-3.39655e23 - 4.17457e23i) q^{30} -2.14060e23 q^{31} +3.89193e25i q^{32} +(-4.30738e25 + 3.50460e25i) q^{33} +1.20187e25 q^{34} -6.52058e24i q^{35} +(-4.63260e25 + 2.23025e26i) q^{36} -5.46506e26 q^{37} +3.94080e26i q^{38} +(2.76412e26 + 3.39728e26i) q^{39} +1.28516e26 q^{40} -3.09869e27i q^{41} +(5.51922e26 - 4.49059e26i) q^{42} +4.94694e27 q^{43} -5.87313e27i q^{44} +(1.14673e27 + 2.38195e26i) q^{45} +1.43671e28 q^{46} +7.73887e26i q^{47} +(-1.02742e28 - 1.26276e28i) q^{48} -4.54961e28 q^{49} +3.42483e28i q^{50} +(-2.02885e28 + 1.65073e28i) q^{51} -4.63220e28 q^{52} +2.24445e29i q^{53} +(5.88113e28 + 1.13467e29i) q^{54} -3.01979e28 q^{55} +1.69911e29i q^{56} +(-5.41256e29 - 6.65238e29i) q^{57} +7.55330e29 q^{58} -1.72696e30i q^{59} +(-9.60862e28 + 7.81784e28i) q^{60} +2.54560e30 q^{61} -1.27025e28i q^{62} +(-3.14918e29 + 1.51609e30i) q^{63} -1.43835e29 q^{64} +2.38174e29i q^{65} +(-2.07967e30 - 2.55604e30i) q^{66} +1.55798e30 q^{67} -2.76635e30i q^{68} +(-2.42527e31 + 1.97327e31i) q^{69} +3.86937e29 q^{70} +3.31673e31i q^{71} +(-2.98811e31 - 6.20680e30i) q^{72} +6.69030e31 q^{73} -3.24302e31i q^{74} +(-4.70390e31 - 5.78138e31i) q^{75} +9.07055e31 q^{76} -3.99247e31i q^{77} +(-2.01598e31 + 1.64026e31i) q^{78} +1.59249e32 q^{79} -8.85285e30i q^{80} +(-2.55121e32 - 1.10765e32i) q^{81} +1.83879e32 q^{82} +2.64046e31i q^{83} +(-1.03360e32 - 1.27036e32i) q^{84} -1.42237e31 q^{85} +2.93556e32i q^{86} +(-1.27505e33 + 1.03742e33i) q^{87} +7.86887e32 q^{88} +1.26315e33i q^{89} +(-1.41347e31 + 6.80480e31i) q^{90} -3.14891e32 q^{91} -3.30687e33i q^{92} +(1.74465e31 + 2.14428e31i) q^{93} -4.59232e31 q^{94} -4.66380e32i q^{95} +(3.89863e33 - 3.17203e33i) q^{96} -2.38063e33 q^{97} -2.69978e33i q^{98} +(7.02128e33 + 1.45844e33i) 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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