LMFDB - Embedded newform 54.26.c.b.37.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [54,26,Mod(19,54)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("54.19"); S:= CuspForms(chi, 26); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(54, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 26, names="a")

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	54.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [26] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$213.838261174$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.5
Character	$\chi$	$=$	54.37
Dual form			54.26.c.b.19.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2048.00 + 3547.24i) q^{2} +(-8.38861e6 + 1.45295e7i) q^{4} +(-1.32723e8 + 2.29884e8i) q^{5} +(1.71990e10 + 2.97895e10i) q^{7} -6.87195e10 q^{8} -1.08727e12 q^{10} +(-2.36007e12 - 4.08776e12i) q^{11} +(-7.65246e13 + 1.32545e14i) q^{13} +(-7.04470e13 + 1.22018e14i) q^{14} +(-1.40737e14 - 2.43764e14i) q^{16} -3.04534e15 q^{17} -1.34946e16 q^{19} +(-2.22673e15 - 3.85681e15i) q^{20} +(9.66685e15 - 1.67435e16i) q^{22} +(2.18045e16 - 3.77665e16i) q^{23} +(1.13781e17 + 1.97074e17i) q^{25} -6.26890e17 q^{26} -5.77102e17 q^{28} +(1.77130e18 + 3.06797e18i) q^{29} +(3.31858e18 - 5.74794e18i) q^{31} +(5.76461e17 - 9.98459e17i) q^{32} +(-6.23686e18 - 1.08026e19i) q^{34} -9.13082e18 q^{35} -4.38443e19 q^{37} +(-2.76370e19 - 4.78686e19i) q^{38} +(9.12068e18 - 1.57975e19i) q^{40} +(1.03447e19 - 1.79175e19i) q^{41} +(-4.98521e19 - 8.63463e19i) q^{43} +7.91908e19 q^{44} +1.78622e20 q^{46} +(2.23292e20 + 3.86754e20i) q^{47} +(7.89248e19 - 1.36702e20i) q^{49} +(-4.66045e20 + 8.07214e20i) q^{50} +(-1.28387e21 - 2.22373e21i) q^{52} -4.84464e21 q^{53} +1.25295e21 q^{55} +(-1.18190e21 - 2.04712e21i) q^{56} +(-7.25522e21 + 1.25664e22i) q^{58} +(-2.56635e21 + 4.44505e21i) q^{59} +(-8.18264e21 - 1.41727e22i) q^{61} +2.71858e22 q^{62} +4.72237e21 q^{64} +(-2.03132e22 - 3.51835e22i) q^{65} +(-4.45640e22 + 7.71871e22i) q^{67} +(2.55462e22 - 4.42473e22i) q^{68} +(-1.86999e22 - 3.23892e22i) q^{70} +1.00409e23 q^{71} -3.45994e23 q^{73} +(-8.97932e22 - 1.55526e23i) q^{74} +(1.13201e23 - 1.96070e23i) q^{76} +(8.11816e22 - 1.40611e23i) q^{77} +(1.58647e23 + 2.74785e23i) q^{79} +7.47166e22 q^{80} +8.47436e22 q^{82} +(8.67339e23 + 1.50228e24i) q^{83} +(4.04188e23 - 7.00075e23i) q^{85} +(2.04194e23 - 3.53675e23i) q^{86} +(1.62183e23 + 2.80909e23i) q^{88} +9.46991e23 q^{89} -5.26458e24 q^{91} +(3.65819e23 + 6.33617e23i) q^{92} +(-9.14605e23 + 1.58414e24i) q^{94} +(1.79105e24 - 3.10219e24i) q^{95} +(7.88434e23 + 1.36561e24i) q^{97} +6.46552e23 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 53248 q^{2} - 218103808 q^{4} - 49854096 q^{5} - 35213963498 q^{7} - 1786706395136 q^{8} - 408404754432 q^{10} + 1998346177329 q^{11} - 158355783504242 q^{13} + 144236394487808 q^{14} - 36\!\cdots\!28 q^{16}+ \cdots - 14\!\cdots\!64 q^{98}+O(q^{100}) $ 26 * q + 53248 * q^2 - 218103808 * q^4 - 49854096 * q^5 - 35213963498 * q^7 - 1786706395136 * q^8 - 408404754432 * q^10 + 1998346177329 * q^11 - 158355783504242 * q^13 + 144236394487808 * q^14 - 3659174697238528 * q^16 - 3616705586624034 * q^17 - 5058456299228762 * q^19 - 836412937076736 * q^20 - 8185225942339584 * q^22 + 155570710082203362 * q^23 - 888197302847183911 * q^25 - 1297250578466750464 * q^26 + 1181584543644123136 * q^28 + 3925320594794185038 * q^29 - 6592704741949460996 * q^31 + 14987979559889010688 * q^32 - 7407013041406021632 * q^34 + 49533545961137501568 * q^35 + 78961008772462984600 * q^37 - 10359718500820504576 * q^38 + 3425947390266310656 * q^40 + 13758002834178626109 * q^41 - 191473700412044564123 * q^43 - 67053370919645872128 * q^44 + 1274435256993409941504 * q^46 - 154470707996501871078 * q^47 - 1713680737743395735817 * q^49 + 3638056152462065299456 * q^50 - 2656769184699904950272 * q^52 + 1171350014833338971736 * q^53 + 23890981280754645933408 * q^55 + 2419885145383164182528 * q^56 - 16078113156276981915648 * q^58 - 545848631253825283329 * q^59 - 10067352509024211048296 * q^61 - 54007437246049984479232 * q^62 + 122781528554610775556096 * q^64 - 12640794081283966054032 * q^65 + 79389140801664567200479 * q^67 + 30339125417599064604672 * q^68 + 101444702128409603211264 * q^70 - 415430508733527088013160 * q^71 - 539343970915021400375282 * q^73 + 161712145966004192460800 * q^74 + 42433406979360786743296 * q^76 + 327594537754607633577834 * q^77 + 611076271613290617275908 * q^79 + 28065361021061616893952 * q^80 + 112705559217591305084928 * q^82 + 400615093454630506593780 * q^83 - 1703025287061576739254000 * q^85 + 784276276887734534647808 * q^86 - 137325303643434746118144 * q^88 - 18509149037385930189952524 * q^89 + 10266453492659369810870360 * q^91 + 2610043406322503560200192 * q^92 + 632712019953671663935488 * q^94 + 16882199861176698021554184 * q^95 + 3205637813401802510221951 * q^97 - 14038472603593897867812864 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2048.00	+	3547.24i	0.353553	+	0.612372i
$2$	2048.00	+	3547.24i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−8.38861e6	+	1.45295e7i	−0.250000	+	0.433013i
$5$	−1.32723e8	+	2.29884e8i	−0.243121	+	0.421098i	−0.961602	−	0.274449i	$-0.911505\pi$
$5$	−1.32723e8	+	2.29884e8i	−0.243121	+	0.421098i	0.718481	+	0.695547i	$0.244838\pi$
$6$		0			0
$7$	1.71990e10	+	2.97895e10i	0.469653	+	0.813463i	0.999398	−	0.0346941i	$-0.0110457\pi$
$7$	1.71990e10	+	2.97895e10i	0.469653	+	0.813463i	−0.529745	+	0.848157i	$0.677712\pi$
$8$	−6.87195e10			−0.353553
$9$		0			0
$10$	−1.08727e12			−0.343825
$11$	−2.36007e12	−	4.08776e12i	−0.226734	−	0.392714i	0.730104	−	0.683336i	$-0.239471\pi$
$11$	−2.36007e12	−	4.08776e12i	−0.226734	−	0.392714i	−0.956838	+	0.290621i	$0.906138\pi$
$12$		0			0
$13$	−7.65246e13	+	1.32545e14i	−0.910981	+	1.57787i	−0.0982994	+	0.995157i	$0.531340\pi$
$13$	−7.65246e13	+	1.32545e14i	−0.910981	+	1.57787i	−0.812681	+	0.582708i	$0.801993\pi$
$14$	−7.04470e13	+	1.22018e14i	−0.332095	+	0.575205i
$15$		0			0
$16$	−1.40737e14	−	2.43764e14i	−0.125000	−	0.216506i
$17$	−3.04534e15			−1.26772			−0.633862	−	0.773446i	$-0.718531\pi$
$17$	−3.04534e15			−1.26772			−0.633862	+	0.773446i	$0.718531\pi$
$18$		0			0
$19$	−1.34946e16			−1.39875			−0.699375	−	0.714755i	$-0.746538\pi$
$19$	−1.34946e16			−1.39875			−0.699375	+	0.714755i	$0.746538\pi$
$20$	−2.22673e15	−	3.85681e15i	−0.121560	−	0.210549i
$21$		0			0
$22$	9.66685e15	−	1.67435e16i	0.160325	−	0.277691i
$23$	2.18045e16	−	3.77665e16i	0.207467	−	0.359343i	−0.743449	−	0.668792i	$-0.766811\pi$
$23$	2.18045e16	−	3.77665e16i	0.207467	−	0.359343i	0.950916	+	0.309450i	$0.100145\pi$
$24$		0			0
$25$	1.13781e17	+	1.97074e17i	0.381784	+	0.661270i
$26$	−6.26890e17			−1.28832
$27$		0			0
$28$	−5.77102e17			−0.469653
$29$	1.77130e18	+	3.06797e18i	0.929642	+	1.61019i	0.783920	+	0.620862i	$0.213217\pi$
$29$	1.77130e18	+	3.06797e18i	0.929642	+	1.61019i	0.145723	+	0.989325i	$0.453449\pi$
$30$		0			0
$31$	3.31858e18	−	5.74794e18i	0.756712	−	1.31066i	−0.187807	−	0.982206i	$-0.560138\pi$
$31$	3.31858e18	−	5.74794e18i	0.756712	−	1.31066i	0.944519	−	0.328457i	$-0.106529\pi$
$32$	5.76461e17	−	9.98459e17i	0.0883883	−	0.153093i
$33$		0			0
$34$	−6.23686e18	−	1.08026e19i	−0.448208	−	0.776319i
$35$	−9.13082e18			−0.456730
$36$		0			0
$37$	−4.38443e19			−1.09494			−0.547472	−	0.836824i	$-0.684410\pi$
$37$	−4.38443e19			−1.09494			−0.547472	+	0.836824i	$0.684410\pi$
$38$	−2.76370e19	−	4.78686e19i	−0.494533	−	0.856556i
$39$		0			0
$40$	9.12068e18	−	1.57975e19i	0.0859562	−	0.148881i
$41$	1.03447e19	−	1.79175e19i	0.0716010	−	0.124017i	−0.828002	−	0.560725i	$-0.810523\pi$
$41$	1.03447e19	−	1.79175e19i	0.0716010	−	0.124017i	0.899603	+	0.436708i	$0.143856\pi$
$42$		0			0
$43$	−4.98521e19	−	8.63463e19i	−0.190251	−	0.329525i	0.755082	−	0.655630i	$-0.227597\pi$
$43$	−4.98521e19	−	8.63463e19i	−0.190251	−	0.329525i	−0.945333	+	0.326105i	$0.894264\pi$
$44$	7.91908e19			0.226734
$45$		0			0
$46$	1.78622e20			0.293402
$47$	2.23292e20	+	3.86754e20i	0.280318	+	0.485524i	0.971463	−	0.237191i	$-0.0762269\pi$
$47$	2.23292e20	+	3.86754e20i	0.280318	+	0.485524i	−0.691145	+	0.722716i	$0.742894\pi$
$48$		0			0
$49$	7.89248e19	−	1.36702e20i	0.0588521	−	0.101935i
$50$	−4.66045e20	+	8.07214e20i	−0.269962	+	0.467589i
$51$		0			0
$52$	−1.28387e21	−	2.22373e21i	−0.455490	−	0.788933i
$53$	−4.84464e21			−1.35461			−0.677303	−	0.735705i	$-0.736851\pi$
$53$	−4.84464e21			−1.35461			−0.677303	+	0.735705i	$0.736851\pi$
$54$		0			0
$55$	1.25295e21			0.220495
$56$	−1.18190e21	−	2.04712e21i	−0.166047	−	0.287603i
$57$		0			0
$58$	−7.25522e21	+	1.25664e22i	−0.657356	+	1.13857i
$59$	−2.56635e21	+	4.44505e21i	−0.187787	+	0.325257i	−0.944512	−	0.328476i	$-0.893465\pi$
$59$	−2.56635e21	+	4.44505e21i	−0.187787	+	0.325257i	0.756725	+	0.653733i	$0.226798\pi$
$60$		0			0
$61$	−8.18264e21	−	1.41727e22i	−0.394703	−	0.683646i	0.598360	−	0.801227i	$-0.295819\pi$
$61$	−8.18264e21	−	1.41727e22i	−0.394703	−	0.683646i	−0.993063	+	0.117582i	$0.962486\pi$
$62$	2.71858e22			1.07015
$63$		0			0
$64$	4.72237e21			0.125000
$65$	−2.03132e22	−	3.51835e22i	−0.442957	−	0.767224i
$66$		0			0
$67$	−4.45640e22	+	7.71871e22i	−0.665348	+	1.15242i	0.313842	+	0.949475i	$0.398384\pi$
$67$	−4.45640e22	+	7.71871e22i	−0.665348	+	1.15242i	−0.979191	+	0.202942i	$0.934950\pi$
$68$	2.55462e22	−	4.42473e22i	0.316931	−	0.548941i
$69$		0			0
$70$	−1.86999e22	−	3.23892e22i	−0.161478	−	0.279689i
$71$	1.00409e23			0.726179			0.363089	−	0.931754i	$-0.381722\pi$
$71$	1.00409e23			0.726179			0.363089	+	0.931754i	$0.381722\pi$
$72$		0			0
$73$	−3.45994e23			−1.76820			−0.884102	−	0.467294i	$-0.845229\pi$
$73$	−3.45994e23			−1.76820			−0.884102	+	0.467294i	$0.845229\pi$
$74$	−8.97932e22	−	1.55526e23i	−0.387121	−	0.670514i
$75$		0			0
$76$	1.13201e23	−	1.96070e23i	0.349688	−	0.605677i
$77$	8.11816e22	−	1.40611e23i	0.212972	−	0.368879i
$78$		0			0
$79$	1.58647e23	+	2.74785e23i	0.302060	+	0.523184i	0.976602	−	0.215053i	$-0.0689923\pi$
$79$	1.58647e23	+	2.74785e23i	0.302060	+	0.523184i	−0.674542	+	0.738236i	$0.735659\pi$
$80$	7.47166e22			0.121560
$81$		0			0
$82$	8.47436e22			0.101259
$83$	8.67339e23	+	1.50228e24i	0.890662	+	1.54267i	0.839083	+	0.544003i	$0.183092\pi$
$83$	8.67339e23	+	1.50228e24i	0.890662	+	1.54267i	0.0515784	+	0.998669i	$0.483575\pi$
$84$		0			0
$85$	4.04188e23	−	7.00075e23i	0.308210	−	0.533836i
$86$	2.04194e23	−	3.53675e23i	0.134528	−	0.233009i
$87$		0			0
$88$	1.62183e23	+	2.80909e23i	0.0801625	+	0.138846i
$89$	9.46991e23			0.406416			0.203208	−	0.979136i	$-0.434863\pi$
$89$	9.46991e23			0.406416			0.203208	+	0.979136i	$0.434863\pi$
$90$		0			0
$91$	−5.26458e24			−1.71138
$92$	3.65819e23	+	6.33617e23i	0.103733	+	0.179671i
$93$		0			0
$94$	−9.14605e23	+	1.58414e24i	−0.198215	+	0.343318i
$95$	1.79105e24	−	3.10219e24i	0.340065	−	0.589011i
$96$		0			0
$97$	7.88434e23	+	1.36561e24i	0.115377	+	0.199839i	0.917930	−	0.396742i	$-0.129859\pi$
$97$	7.88434e23	+	1.36561e24i	0.115377	+	0.199839i	−0.802553	+	0.596580i	$0.796526\pi$
$98$	6.46552e23			0.0832295
$99$		0			0
$100$	−3.81784e24			−0.381784
$101$	−4.23384e24	−	7.33323e24i	−0.373867	−	0.647557i	0.616290	−	0.787520i	$-0.288635\pi$
$101$	−4.23384e24	−	7.33323e24i	−0.373867	−	0.647557i	−0.990157	+	0.139963i	$0.955302\pi$
$102$		0			0
$103$	6.13560e24	−	1.06272e25i	0.424025	−	0.734433i	−0.572304	−	0.820042i	$-0.693950\pi$
$103$	6.13560e24	−	1.06272e25i	0.424025	−	0.734433i	0.996329	+	0.0856089i	$0.0272835\pi$
$104$	5.25873e24	−	9.10839e24i	0.322080	−	0.557860i
$105$		0			0
$106$	−9.92181e24	−	1.71851e25i	−0.478925	−	0.829523i
$107$	9.32764e24			0.400382			0.200191	−	0.979757i	$-0.435844\pi$
$107$	9.32764e24			0.400382			0.200191	+	0.979757i	$0.435844\pi$
$108$		0			0
$109$	1.87852e25			0.639711			0.319856	−	0.947466i	$-0.396366\pi$
$109$	1.87852e25			0.639711			0.319856	+	0.947466i	$0.396366\pi$
$110$	2.56603e24	+	4.44450e24i	0.0779567	+	0.135025i
$111$		0			0
$112$	4.84108e24	−	8.38500e24i	0.117413	−	0.203366i
$113$	−2.40021e25	+	4.15728e25i	−0.520917	+	0.902254i	0.478787	+	0.877931i	$0.341077\pi$
$113$	−2.40021e25	+	4.15728e25i	−0.520917	+	0.902254i	−0.999704	+	0.0243235i	$0.992257\pi$
$114$		0			0
$115$	5.78793e24	+	1.00250e25i	0.100879	+	0.174727i
$116$	−5.94348e25			−0.929642
$117$		0			0
$118$	−2.10235e25			−0.265571
$119$	−5.23768e25	−	9.07193e25i	−0.595390	−	1.03125i
$120$		0			0
$121$	4.30337e25	−	7.45365e25i	0.397184	−	0.687942i
$122$	3.35161e25	−	5.80516e25i	0.279097	−	0.483410i
$123$		0			0
$124$	5.56765e25	+	9.64345e25i	0.378356	+	0.655332i
$125$	−1.39515e26			−0.857521
$126$		0			0
$127$	1.71215e26			0.862970			0.431485	−	0.902120i	$-0.357990\pi$
$127$	1.71215e26			0.862970			0.431485	+	0.902120i	$0.357990\pi$
$128$	9.67141e24	+	1.67514e25i	0.0441942	+	0.0765466i
$129$		0			0
$130$	8.32029e25	−	1.44112e26i	0.313218	−	0.542509i
$131$	−6.13452e25	+	1.06253e26i	−0.209841	+	0.363454i	−0.951664	−	0.307141i	$-0.900628\pi$
$131$	−6.13452e25	+	1.06253e26i	−0.209841	+	0.363454i	0.741824	+	0.670595i	$0.233961\pi$
$132$		0			0
$133$	−2.32093e26	−	4.01998e26i	−0.656927	−	1.13783i
$134$	−3.65068e26			−0.940945
$135$		0			0
$136$	2.09274e26			0.448208
$137$	−3.33562e26	−	5.77747e26i	−0.651883	−	1.12909i	−0.982665	−	0.185388i	$-0.940646\pi$
$137$	−3.33562e26	−	5.77747e26i	−0.651883	−	1.12909i	0.330782	−	0.943707i	$-0.392687\pi$
$138$		0			0
$139$	2.83147e26	−	4.90426e26i	0.461666	−	0.799628i	−0.537379	−	0.843341i	$-0.680585\pi$
$139$	2.83147e26	−	4.90426e26i	0.461666	−	0.799628i	0.999044	+	0.0437129i	$0.0139187\pi$
$140$	7.65949e25	−	1.32666e26i	0.114182	−	0.197770i
$141$		0			0
$142$	2.05638e26	+	3.56175e26i	0.256743	+	0.444692i
$143$	7.22414e26			0.826201
$144$		0			0
$145$	−9.40369e26			−0.904062
$146$	−7.08595e26	−	1.22732e27i	−0.625154	−	1.08280i
$147$		0			0
$148$	3.67793e26	−	6.37036e26i	0.273736	−	0.474125i
$149$	−5.55749e26	+	9.62585e26i	−0.380233	+	0.658583i	−0.991095	−	0.133154i	$-0.957490\pi$
$149$	−5.55749e26	+	9.62585e26i	−0.380233	+	0.658583i	0.610862	+	0.791737i	$0.290823\pi$
$150$		0			0
$151$	−3.78651e26	−	6.55843e26i	−0.219294	−	0.379829i	0.735298	−	0.677744i	$-0.237042\pi$
$151$	−3.78651e26	−	6.55843e26i	−0.219294	−	0.379829i	−0.954592	+	0.297915i	$0.903709\pi$
$152$	9.27342e26			0.494533
$153$		0			0
$154$	6.65039e26			0.301188
$155$	8.80905e26	+	1.52577e27i	0.367945	+	0.637299i
$156$		0			0
$157$	−4.05457e26	+	7.02271e26i	−0.144278	+	0.249896i	−0.929103	−	0.369821i	$-0.879419\pi$
$157$	−4.05457e26	+	7.02271e26i	−0.144278	+	0.249896i	0.784826	+	0.619717i	$0.212752\pi$
$158$	−6.49819e26	+	1.12552e27i	−0.213589	+	0.369947i
$159$		0			0
$160$	1.53020e26	+	2.65038e26i	0.0429781	+	0.0744403i
$161$	1.50006e27			0.389749
$162$		0			0
$163$	4.58614e27			1.02118			0.510590	−	0.859824i	$-0.329427\pi$
$163$	4.58614e27			1.02118			0.510590	+	0.859824i	$0.329427\pi$
$164$	1.73555e26	+	3.00606e26i	0.0358005	+	0.0620083i
$165$		0			0
$166$	−3.55262e27	+	6.15332e27i	−0.629793	+	1.09083i
$167$	3.98366e27	−	6.89990e27i	0.655129	−	1.13472i	−0.326733	−	0.945117i	$-0.605948\pi$
$167$	3.98366e27	−	6.89990e27i	0.655129	−	1.13472i	0.981862	−	0.189599i	$-0.0607189\pi$
$168$		0			0
$169$	−8.18383e27	−	1.41748e28i	−1.15977	−	2.00878i
$170$	3.31111e27			0.435875
$171$		0			0
$172$	1.67276e27			0.190251
$173$	4.54830e27	+	7.87788e27i	0.481141	+	0.833361i	0.999766	−	0.0216410i	$-0.00688909\pi$
$173$	4.54830e27	+	7.87788e27i	0.481141	+	0.833361i	−0.518625	+	0.855002i	$0.673556\pi$
$174$		0			0
$175$	−3.91382e27	+	6.77894e27i	−0.358612	+	0.621135i
$176$	−6.64301e26	+	1.15060e27i	−0.0566834	+	0.0981786i
$177$		0			0
$178$	1.93944e27	+	3.35921e27i	0.143690	+	0.248878i
$179$	1.04876e28			0.724459			0.362229	−	0.932089i	$-0.382016\pi$
$179$	1.04876e28			0.724459			0.362229	+	0.932089i	$0.382016\pi$
$180$		0			0
$181$	−1.06095e28			−0.637839			−0.318920	−	0.947782i	$-0.603320\pi$
$181$	−1.06095e28			−0.637839			−0.318920	+	0.947782i	$0.603320\pi$
$182$	−1.07819e28	−	1.86747e28i	−0.605064	−	1.04800i
$183$		0			0
$184$	−1.49839e27	+	2.59529e27i	−0.0733505	+	0.127047i
$185$	5.81917e27	−	1.00791e28i	0.266204	−	0.461079i
$186$		0			0
$187$	7.18722e27	+	1.24486e28i	0.287436	+	0.497854i
$188$	−7.49245e27			−0.280318
$189$		0			0
$190$	1.46723e28			0.480925
$191$	1.98703e28	+	3.44164e28i	0.609941	+	1.05645i	0.991250	+	0.132002i	$0.0421404\pi$
$191$	1.98703e28	+	3.44164e28i	0.609941	+	1.05645i	−0.381308	+	0.924448i	$0.624526\pi$
$192$		0			0
$193$	2.01477e27	−	3.48968e27i	0.0542948	−	0.0940414i	−0.837601	−	0.546283i	$-0.816042\pi$
$193$	2.01477e27	−	3.48968e27i	0.0542948	−	0.0940414i	0.891895	+	0.452242i	$0.149376\pi$
$194$	−3.22943e27	+	5.59353e27i	−0.0815837	+	0.141307i
$195$		0			0
$196$	1.32414e27	+	2.29347e27i	0.0294261	+	0.0509675i
$197$	1.57433e28			0.328298			0.164149	−	0.986436i	$-0.447512\pi$
$197$	1.57433e28			0.328298			0.164149	+	0.986436i	$0.447512\pi$
$198$		0			0
$199$	−8.51081e27			−0.156425			−0.0782127	−	0.996937i	$-0.524921\pi$
$199$	−8.51081e27			−0.156425			−0.0782127	+	0.996937i	$0.524921\pi$
$200$	−7.81894e27	−	1.35428e28i	−0.134981	−	0.233794i
$201$		0			0
$202$	1.73418e28	−	3.00369e28i	0.264364	−	0.457892i
$203$	−6.09289e28	+	1.05532e29i	−0.873219	+	1.51246i
$204$		0			0
$205$	2.74596e27	+	4.75615e27i	0.0348154	+	0.0603020i
$206$	5.02628e28			0.599662
$207$		0			0
$208$	4.30795e28			0.455490
$209$	3.18482e28	+	5.51627e28i	0.317144	+	0.549309i
$210$		0			0
$211$	1.02857e29	−	1.78154e29i	0.909294	−	1.57494i	0.0942462	−	0.995549i	$-0.469956\pi$
$211$	1.02857e29	−	1.78154e29i	0.909294	−	1.57494i	0.815048	−	0.579394i	$-0.196711\pi$
$212$	4.06397e28	−	7.03901e28i	0.338651	−	0.586561i
$213$		0			0
$214$	1.91030e28	+	3.30874e28i	0.141556	+	0.245183i
$215$	2.64661e28			0.185016
$216$		0			0
$217$	2.28304e29			1.42157
$218$	3.84720e28	+	6.66355e28i	0.226172	+	0.391742i
$219$		0			0
$220$	−1.05105e28	+	1.82047e28i	−0.0551237	+	0.0954771i
$221$	2.33044e29	−	4.03644e29i	1.15487	−	2.00030i
$222$		0			0
$223$	−1.75459e29	−	3.03903e29i	−0.776898	−	1.34563i	−0.933722	−	0.358000i	$-0.883459\pi$
$223$	−1.75459e29	−	3.03903e29i	−0.776898	−	1.34563i	0.156824	−	0.987627i	$-0.449874\pi$
$224$	3.96581e28			0.166047
$225$		0			0
$226$	−1.96625e29			−0.736688
$227$	7.43757e27	+	1.28823e28i	0.0263699	+	0.0456740i	0.878909	−	0.476989i	$-0.158272\pi$
$227$	7.43757e27	+	1.28823e28i	0.0263699	+	0.0456740i	−0.852539	+	0.522663i	$0.824939\pi$
$228$		0			0
$229$	−1.92922e29	+	3.34151e29i	−0.612968	+	1.06169i	0.377769	+	0.925900i	$0.376691\pi$
$229$	−1.92922e29	+	3.34151e29i	−0.612968	+	1.06169i	−0.990737	+	0.135792i	$0.956642\pi$
$230$	−2.37074e28	+	4.10624e28i	−0.0713322	+	0.123551i
$231$		0			0
$232$	−1.21722e29	−	2.10829e29i	−0.328678	−	0.569287i
$233$	3.90887e29			1.00024			0.500118	−	0.865957i	$-0.333290\pi$
$233$	3.90887e29			1.00024			0.500118	+	0.865957i	$0.333290\pi$
$234$		0			0
$235$	−1.18544e29			−0.272604
$236$	−4.30562e28	−	7.45756e28i	−0.0938936	−	0.162628i
$237$		0			0
$238$	2.14535e29	−	3.71586e29i	0.421005	−	0.729201i
$239$	3.63162e29	−	6.29015e29i	0.676280	−	1.17135i	−0.299813	−	0.953998i	$-0.596924\pi$
$239$	3.63162e29	−	6.29015e29i	0.676280	−	1.17135i	0.976093	−	0.217354i	$-0.0697425\pi$
$240$		0			0
$241$	−1.38816e29	−	2.40436e29i	−0.232930	−	0.403446i	0.725739	−	0.687970i	$-0.241498\pi$
$241$	−1.38816e29	−	2.40436e29i	−0.232930	−	0.403446i	−0.958669	+	0.284524i	$0.908165\pi$
$242$	3.52532e29			0.561702
$243$		0			0
$244$	2.74564e29			0.394703
$245$	2.09503e28	+	3.62870e28i	0.0286164	+	0.0495650i
$246$		0			0
$247$	1.03267e30	−	1.78864e30i	1.27423	−	2.20704i
$248$	−2.28051e29	+	3.94996e29i	−0.267538	+	0.463389i
$249$		0			0
$250$	−2.85726e29	−	4.94892e29i	−0.303179	−	0.525122i
$251$	−1.12542e29			−0.113604			−0.0568020	−	0.998385i	$-0.518090\pi$
$251$	−1.12542e29			−0.113604			−0.0568020	+	0.998385i	$0.518090\pi$
$252$		0			0
$253$	−2.05841e29			−0.188159
$254$	3.50649e29	+	6.07341e29i	0.305106	+	0.528459i
$255$		0			0
$256$	−3.96141e28	+	6.86136e28i	−0.0312500	+	0.0541266i
$257$	6.96320e29	−	1.20606e30i	0.523173	−	0.906161i	−0.476464	−	0.879194i	$-0.658082\pi$
$257$	6.96320e29	−	1.20606e30i	0.523173	−	0.906161i	0.999636	−	0.0269673i	$-0.00858501\pi$
$258$		0			0
$259$	−7.54078e29	−	1.30610e30i	−0.514244	−	0.890696i
$260$	6.81598e29			0.442957
$261$		0			0
$262$	−5.02540e29			−0.296759
$263$	−7.47940e29	−	1.29547e30i	−0.421133	−	0.729424i	0.574917	−	0.818212i	$-0.305034\pi$
$263$	−7.47940e29	−	1.29547e30i	−0.421133	−	0.729424i	−0.996051	+	0.0887872i	$0.971701\pi$
$264$		0			0
$265$	6.42996e29	−	1.11370e30i	0.329333	−	0.570421i
$266$	9.50655e29	−	1.64658e30i	0.464518	−	0.804568i
$267$		0			0
$268$	−7.47660e29	−	1.29498e30i	−0.332674	−	0.576209i
$269$	1.83919e30			0.781130			0.390565	−	0.920575i	$-0.372280\pi$
$269$	1.83919e30			0.781130			0.390565	+	0.920575i	$0.372280\pi$
$270$		0			0
$271$	4.56536e30			1.76750			0.883749	−	0.467961i	$-0.155011\pi$
$271$	4.56536e30			1.76750			0.883749	+	0.467961i	$0.155011\pi$
$272$	4.28594e29	+	7.42346e29i	0.158466	+	0.274470i
$273$		0			0
$274$	1.36627e30	−	2.36645e30i	0.460951	−	0.798390i
$275$	5.37060e29	−	9.30216e29i	0.173127	−	0.299865i
$276$		0			0
$277$	−1.50581e28	−	2.60814e28i	−0.00443376	−	0.00767950i	0.863800	−	0.503835i	$-0.168078\pi$
$277$	−1.50581e28	−	2.60814e28i	−0.00443376	−	0.00767950i	−0.868234	+	0.496155i	$0.834745\pi$
$278$	2.31954e30			0.652894
$279$		0			0
$280$	6.27465e29			0.161478
$281$	2.79701e30	+	4.84457e30i	0.688439	+	1.19241i	0.972343	+	0.233558i	$0.0750369\pi$
$281$	2.79701e30	+	4.84457e30i	0.688439	+	1.19241i	−0.283904	+	0.958853i	$0.591630\pi$
$282$		0			0
$283$	3.70023e29	−	6.40898e29i	0.0833485	−	0.144364i	−0.821338	−	0.570442i	$-0.806772\pi$
$283$	3.70023e29	−	6.40898e29i	0.0833485	−	0.144364i	0.904686	+	0.426078i	$0.140105\pi$
$284$	−8.42292e29	+	1.45889e30i	−0.181545	+	0.314445i
$285$		0			0
$286$	1.47950e30	+	2.56257e30i	0.292106	+	0.505942i
$287$	7.11672e29			0.134510
$288$		0			0
$289$	3.50349e30			0.607124
$290$	−1.92588e30	−	3.33571e30i	−0.319634	−	0.553623i
$291$		0			0
$292$	2.90240e30	−	5.02711e30i	0.442051	−	0.765655i
$293$	5.90145e29	−	1.02216e30i	0.0861219	−	0.149168i	−0.819747	−	0.572726i	$-0.805886\pi$
$293$	5.90145e29	−	1.02216e30i	0.0861219	−	0.149168i	0.905869	+	0.423559i	$0.139219\pi$
$294$		0			0
$295$	−6.81230e29	−	1.17992e30i	−0.0913100	−	0.158154i
$296$	3.01296e30			0.387121
$297$		0			0
$298$	−4.55269e30			−0.537731
$299$	3.33716e30	+	5.78013e30i	0.377996	+	0.654709i
$300$		0			0
$301$	1.71481e30	−	2.97014e30i	0.178704	−	0.309525i
$302$	1.55096e30	−	2.68633e30i	0.155065	−	0.268580i
$303$		0			0
$304$	1.89920e30	+	3.28951e30i	0.174844	+	0.302838i
$305$	4.34411e30			0.383842
$306$		0			0
$307$	−1.44737e31			−1.17855			−0.589276	−	0.807932i	$-0.700587\pi$
$307$	−1.44737e31			−1.17855			−0.589276	+	0.807932i	$0.700587\pi$
$308$	1.36200e30	+	2.35905e30i	0.106486	+	0.184440i
$309$		0			0
$310$	−3.60819e30	+	6.24956e30i	−0.260176	+	0.450639i
$311$	5.85692e30	−	1.01445e31i	0.405662	−	0.702627i	−0.588736	−	0.808325i	$-0.700374\pi$
$311$	5.85692e30	−	1.01445e31i	0.405662	−	0.702627i	0.994398	+	0.105698i	$0.0337078\pi$
$312$		0			0
$313$	−3.19904e30	−	5.54090e30i	−0.204511	−	0.354223i	0.745466	−	0.666544i	$-0.232227\pi$
$313$	−3.19904e30	−	5.54090e30i	−0.204511	−	0.354223i	−0.949977	+	0.312321i	$0.898894\pi$
$314$	−3.32150e30			−0.204039
$315$		0			0
$316$	−5.32331e30			−0.302060
$317$	8.22057e29	+	1.42384e30i	0.0448396	+	0.0776644i	0.887574	−	0.460665i	$-0.152389\pi$
$317$	8.22057e29	+	1.42384e30i	0.0448396	+	0.0776644i	−0.842735	+	0.538329i	$0.819056\pi$
$318$		0			0
$319$	8.36076e30	−	1.44813e31i	0.421563	−	0.730168i
$320$	−6.26768e29	+	1.08559e30i	−0.0303901	+	0.0526372i
$321$		0			0
$322$	3.07212e30	+	5.32107e30i	0.137797	+	0.238672i
$323$	4.10957e31			1.77323
$324$		0			0
$325$	−3.48281e31			−1.39119
$326$	9.39242e30	+	1.62682e31i	0.361042	+	0.625343i
$327$		0			0
$328$	−7.10881e29	+	1.23128e30i	−0.0253148	+	0.0438465i
$329$	−7.68080e30	+	1.33035e31i	−0.263304	+	0.456056i
$330$		0			0
$331$	−1.48237e30	−	2.56754e30i	−0.0471093	−	0.0815958i	0.841509	−	0.540243i	$-0.181668\pi$
$331$	−1.48237e30	−	2.56754e30i	−0.0471093	−	0.0815958i	−0.888619	+	0.458647i	$0.848334\pi$
$332$	−2.91031e31			−0.890662
$333$		0			0
$334$	3.26342e31			0.926492
$335$	−1.18294e31	−	2.04891e31i	−0.323520	−	0.560354i
$336$		0			0
$337$	−1.64567e31	+	2.85038e31i	−0.417800	+	0.723651i	−0.995718	−	0.0924441i	$-0.970532\pi$
$337$	−1.64567e31	+	2.85038e31i	−0.417800	+	0.723651i	0.577918	+	0.816095i	$0.303865\pi$
$338$	3.35210e31	−	5.80600e31i	0.820083	−	1.42043i
$339$		0			0
$340$	6.78115e30	+	1.17453e31i	0.154105	+	0.266918i
$341$	−3.13283e31			−0.686289
$342$		0			0
$343$	5.15597e31			1.04987
$344$	3.42581e30	+	5.93367e30i	0.0672640	+	0.116505i
$345$		0			0
$346$	−1.86298e31	+	3.22678e31i	−0.340218	+	0.589275i
$347$	−2.48515e31	+	4.30441e31i	−0.437759	+	0.758220i	−0.997516	−	0.0704362i	$-0.977561\pi$
$347$	−2.48515e31	+	4.30441e31i	−0.437759	+	0.758220i	0.559758	+	0.828656i	$0.310894\pi$
$348$		0			0
$349$	−1.48658e31	−	2.57483e31i	−0.243709	−	0.422116i	0.718059	−	0.695982i	$-0.245031\pi$
$349$	−1.48658e31	−	2.57483e31i	−0.243709	−	0.422116i	−0.961768	+	0.273866i	$0.911697\pi$
$350$	−3.20620e31			−0.507154
$351$		0			0
$352$	−5.44195e30			−0.0801625
$353$	3.99075e31	+	6.91218e31i	0.567376	+	0.982724i	0.996824	+	0.0796324i	$0.0253746\pi$
$353$	3.99075e31	+	6.91218e31i	0.567376	+	0.982724i	−0.429448	+	0.903091i	$0.641292\pi$
$354$		0			0
$355$	−1.33266e31	+	2.30824e31i	−0.176549	+	0.305792i
$356$	−7.94394e30	+	1.37593e31i	−0.101604	+	0.175983i
$357$		0			0
$358$	2.14786e31	+	3.72021e31i	0.256135	+	0.443639i
$359$	−1.48192e32			−1.70665			−0.853324	−	0.521380i	$-0.825417\pi$
$359$	−1.48192e32			−1.70665			−0.853324	+	0.521380i	$0.825417\pi$
$360$		0			0
$361$	8.90279e31			0.956502
$362$	−2.17282e31	−	3.76343e31i	−0.225510	−	0.390595i
$363$		0			0
$364$	4.41625e31	−	7.64917e31i	0.427845	−	0.741049i
$365$	4.59214e31	−	7.95383e31i	0.429887	−	0.744587i
$366$		0			0
$367$	−4.12223e31	−	7.13991e31i	−0.360418	−	0.624262i	0.627612	−	0.778526i	$-0.284032\pi$
$367$	−4.12223e31	−	7.13991e31i	−0.360418	−	0.624262i	−0.988030	+	0.154265i	$0.950699\pi$
$368$	−1.22748e31			−0.103733
$369$		0			0
$370$	4.76706e31			0.376469
$371$	−8.33228e31	−	1.44319e32i	−0.636194	−	1.10192i
$372$		0			0
$373$	−5.32861e31	+	9.22942e31i	−0.380411	+	0.658891i	−0.991121	−	0.132963i	$-0.957551\pi$
$373$	−5.32861e31	+	9.22942e31i	−0.380411	+	0.658891i	0.610710	+	0.791854i	$0.290884\pi$
$374$	−2.94389e31	+	5.09896e31i	−0.203248	+	0.352036i
$375$		0			0
$376$	−1.53445e31	−	2.65775e31i	−0.0991073	−	0.171659i
$377$	−5.42191e32			−3.38755
$378$		0			0
$379$	−1.49459e32			−0.874044			−0.437022	−	0.899451i	$-0.643967\pi$
$379$	−1.49459e32			−0.874044			−0.437022	+	0.899451i	$0.643967\pi$
$380$	3.00488e31	+	5.20461e31i	0.170033	+	0.294505i
$381$		0			0
$382$	−8.13889e31	+	1.40970e32i	−0.431294	+	0.747023i
$383$	−1.00039e32	+	1.73272e32i	−0.513078	+	0.888677i	0.486807	+	0.873510i	$0.338162\pi$
$383$	−1.00039e32	+	1.73272e32i	−0.513078	+	0.888677i	−0.999885	+	0.0151676i	$0.995172\pi$
$384$		0			0
$385$	2.15494e31	+	3.73246e31i	0.103556	+	0.179364i
$386$	1.65050e31			0.0767844
$387$		0			0
$388$	−2.64555e31			−0.115377
$389$	1.28159e32	+	2.21978e32i	0.541227	+	0.937433i	0.998834	+	0.0482784i	$0.0153735\pi$
$389$	1.28159e32	+	2.21978e32i	0.541227	+	0.937433i	−0.457607	+	0.889155i	$0.651293\pi$
$390$		0			0
$391$	−6.64022e31	+	1.15012e32i	−0.263010	+	0.455547i
$392$	−5.42367e30	+	9.39407e30i	−0.0208074	+	0.0360394i
$393$		0			0
$394$	3.22423e31	+	5.58453e31i	0.116071	+	0.201041i
$395$	−8.42247e31			−0.293749
$396$		0			0
$397$	9.44560e31			0.309277			0.154639	−	0.987971i	$-0.450579\pi$
$397$	9.44560e31			0.309277			0.154639	+	0.987971i	$0.450579\pi$
$398$	−1.74301e31	−	3.01899e31i	−0.0553047	−	0.0957906i
$399$		0			0
$400$	3.20264e31	−	5.54713e31i	0.0954461	−	0.165318i
$401$	2.95530e32	−	5.11873e32i	0.853683	−	1.47862i	−0.0241781	−	0.999708i	$-0.507697\pi$
$401$	2.95530e32	−	5.11873e32i	0.853683	−	1.47862i	0.877861	−	0.478915i	$-0.158970\pi$
$402$		0			0
$403$	5.07905e32	+	8.79718e32i	1.37870	+	2.38798i
$404$	1.42064e32			0.373867
$405$		0			0
$406$	−4.99130e32			−1.23492
$407$	1.03476e32	+	1.79225e32i	0.248261	+	0.430000i
$408$		0			0
$409$	−3.51371e32	+	6.08593e32i	−0.792912	+	1.37336i	0.131244	+	0.991350i	$0.458103\pi$
$409$	−3.51371e32	+	6.08593e32i	−0.792912	+	1.37336i	−0.924156	+	0.382014i	$0.875231\pi$
$410$	−1.12475e31	+	1.94812e31i	−0.0246182	+	0.0426400i
$411$		0			0
$412$	1.02938e32	+	1.78294e32i	0.212012	+	0.367216i
$413$	−1.76554e32			−0.352779
$414$		0			0
$415$	−4.60465e32			−0.866154
$416$	8.82269e31	+	1.52813e32i	0.161040	+	0.278930i
$417$		0			0
$418$	−1.30450e32	+	2.25946e32i	−0.224255	+	0.388420i
$419$	−3.54977e32	+	6.14837e32i	−0.592276	+	1.02585i	0.401649	+	0.915794i	$0.368437\pi$
$419$	−3.54977e32	+	6.14837e32i	−0.592276	+	1.02585i	−0.993925	+	0.110059i	$0.964896\pi$
$420$		0			0
$421$	−4.79284e32	−	8.30145e32i	−0.753472	−	1.30505i	−0.946131	−	0.323785i	$-0.895044\pi$
$421$	−4.79284e32	−	8.30145e32i	−0.753472	−	1.30505i	0.192659	−	0.981266i	$-0.438289\pi$
$422$	8.42607e32			1.28594
$423$		0			0
$424$	3.32921e32			0.478925
$425$	−3.46501e32	−	6.00157e32i	−0.483997	−	0.838308i
$426$		0			0
$427$	2.81466e32	−	4.87513e32i	0.370747	−	0.642152i
$428$	−7.82459e31	+	1.35526e32i	−0.100095	+	0.173370i
$429$		0			0
$430$	5.42027e31	+	9.38818e31i	0.0654131	+	0.113299i
$431$	−1.23517e31			−0.0144798			−0.00723989	−	0.999974i	$-0.502305\pi$
$431$	−1.23517e31			−0.0144798			−0.00723989	+	0.999974i	$0.502305\pi$
$432$		0			0
$433$	−5.28994e32			−0.585264			−0.292632	−	0.956225i	$-0.594531\pi$
$433$	−5.28994e32			−0.585264			−0.292632	+	0.956225i	$0.594531\pi$
$434$	4.67567e32	+	8.09851e32i	0.502600	+	0.870529i
$435$		0			0
$436$	−1.57582e32	+	2.72939e32i	−0.159928	+	0.277003i
$437$	−2.94243e32	+	5.09644e32i	−0.290194	+	0.502631i
$438$		0			0
$439$	−2.47060e32	−	4.27921e32i	−0.230142	−	0.398618i	0.727707	−	0.685888i	$-0.240586\pi$
$439$	−2.47060e32	−	4.27921e32i	−0.230142	−	0.398618i	−0.957850	+	0.287269i	$0.907253\pi$
$440$	−8.61018e31			−0.0779567
$441$		0			0
$442$	1.90909e33			1.63324
$443$	8.61201e32	+	1.49164e33i	0.716239	+	1.24056i	0.962480	+	0.271354i	$0.0874714\pi$
$443$	8.61201e32	+	1.49164e33i	0.716239	+	1.24056i	−0.246240	+	0.969209i	$0.579195\pi$
$444$		0			0
$445$	−1.25688e32	+	2.17698e32i	−0.0988083	+	0.171141i
$446$	7.18678e32	−	1.24479e33i	0.549350	−	0.951502i
$447$		0			0
$448$	8.12199e31	+	1.40677e32i	0.0587066	+	0.101683i
$449$	−1.93531e33			−1.36042			−0.680209	−	0.733019i	$-0.738111\pi$
$449$	−1.93531e33			−1.36042			−0.680209	+	0.733019i	$0.738111\pi$
$450$		0			0
$451$	−9.76567e31			−0.0649374
$452$	−4.02688e32	−	6.97476e32i	−0.260458	−	0.451127i
$453$		0			0
$454$	−3.04643e31	+	5.27657e31i	−0.0186463	+	0.0322964i
$455$	6.98733e32	−	1.21024e33i	0.416072	−	0.720658i
$456$		0			0
$457$	3.28123e32	+	5.68326e32i	0.184963	+	0.320365i	0.943564	−	0.331190i	$-0.107450\pi$
$457$	3.28123e32	+	5.68326e32i	0.184963	+	0.320365i	−0.758601	+	0.651555i	$0.774117\pi$
$458$	−1.58042e33			−0.866868
$459$		0			0
$460$	−1.94211e32			−0.100879
$461$	−3.64612e32	−	6.31526e32i	−0.184319	−	0.319249i	0.759028	−	0.651058i	$-0.225674\pi$
$461$	−3.64612e32	−	6.31526e32i	−0.184319	−	0.319249i	−0.943347	+	0.331809i	$0.892341\pi$
$462$		0			0
$463$	1.64393e33	−	2.84736e33i	0.787263	−	1.36358i	−0.140374	−	0.990099i	$-0.544831\pi$
$463$	1.64393e33	−	2.84736e33i	0.787263	−	1.36358i	0.927638	−	0.373482i	$-0.121836\pi$
$464$	4.98575e32	−	8.63558e32i	0.232411	−	0.402547i
$465$		0			0
$466$	8.00537e32	+	1.38657e33i	0.353637	+	0.612517i
$467$	1.54771e33			0.665624			0.332812	−	0.942993i	$-0.392003\pi$
$467$	1.54771e33			0.665624			0.332812	+	0.942993i	$0.392003\pi$
$468$		0			0
$469$	−3.06582e33			−1.24993
$470$	−2.42779e32	−	4.20506e32i	−0.0963802	−	0.166935i
$471$		0			0
$472$	1.76358e32	−	3.05462e32i	0.0663928	−	0.114996i
$473$	−2.35309e32	+	4.07567e32i	−0.0862728	+	0.149429i
$474$		0			0
$475$	−1.53542e33	−	2.65943e33i	−0.534021	−	0.924952i
$476$	1.75747e33			0.595390
$477$		0			0
$478$	2.97502e33			0.956405
$479$	−9.88473e32	−	1.71208e33i	−0.309578	−	0.536206i	0.668692	−	0.743540i	$-0.266855\pi$
$479$	−9.88473e32	−	1.71208e33i	−0.309578	−	0.536206i	−0.978270	+	0.207334i	$0.933521\pi$
$480$		0			0
$481$	3.35517e33	−	5.81133e33i	0.997473	−	1.72767i
$482$	5.68589e32	−	9.84824e32i	0.164706	−	0.285280i
$483$		0			0
$484$	7.21985e32	+	1.25052e33i	0.198592	+	0.343971i
$485$	−4.18574e32			−0.112202
$486$		0			0
$487$	4.90778e33			1.24960			0.624802	−	0.780783i	$-0.285180\pi$
$487$	4.90778e33			1.24960			0.624802	+	0.780783i	$0.285180\pi$
$488$	5.62307e32	+	9.73943e32i	0.139549	+	0.241705i
$489$		0			0
$490$	−8.58125e31	+	1.48632e32i	−0.0202348	+	0.0350478i
$491$	−1.01574e32	+	1.75931e32i	−0.0233488	+	0.0404412i	−0.877464	−	0.479643i	$-0.840766\pi$
$491$	−1.01574e32	+	1.75931e32i	−0.0233488	+	0.0404412i	0.854115	+	0.520084i	$0.174099\pi$
$492$		0			0
$493$	−5.39420e33	−	9.34303e33i	−1.17853	−	2.04127i
$494$	8.45963e33			1.80204
$495$		0			0
$496$	−1.86819e33			−0.378356
$497$	1.72693e33	+	2.99114e33i	0.341052	+	0.590719i
$498$		0			0
$499$	−1.42155e33	+	2.46220e33i	−0.266997	+	0.462452i	−0.968085	−	0.250623i	$-0.919365\pi$
$499$	−1.42155e33	+	2.46220e33i	−0.266997	+	0.462452i	0.701088	+	0.713075i	$0.252698\pi$
$500$	1.17033e33	−	2.02708e33i	0.214380	−	0.371317i
$501$		0			0
$502$	−2.30486e32	−	3.99214e32i	−0.0401651	−	0.0695680i
$503$	−4.97587e33			−0.845802			−0.422901	−	0.906176i	$-0.638988\pi$
$503$	−4.97587e33			−0.845802			−0.422901	+	0.906176i	$0.638988\pi$
$504$		0			0
$505$	2.24772e33			0.363580
$506$	−4.21561e32	−	7.30166e32i	−0.0665242	−	0.115223i
$507$		0			0
$508$	−1.43626e33	+	2.48767e33i	−0.215742	+	0.373677i
$509$	4.63620e33	−	8.03014e33i	0.679501	−	1.17693i	−0.295630	−	0.955303i	$-0.595530\pi$
$509$	4.63620e33	−	8.03014e33i	0.679501	−	1.17693i	0.975131	−	0.221628i	$-0.0711371\pi$
$510$		0			0
$511$	−5.95074e33	−	1.03070e34i	−0.830442	−	1.43837i
$512$	−3.24519e32			−0.0441942
$513$		0			0
$514$	5.70426e33			0.739878
$515$	1.62867e33	+	2.82095e33i	0.206179	+	0.357112i
$516$		0			0
$517$	1.05397e33	−	1.82553e33i	0.127115	−	0.220170i
$518$	3.08870e33	−	5.34979e33i	0.363625	−	0.629817i
$519$		0			0
$520$	1.39591e33	+	2.41779e33i	0.156609	+	0.271255i
$521$	1.64259e34			1.79911			0.899557	−	0.436804i	$-0.143890\pi$
$521$	1.64259e34			1.79911			0.899557	+	0.436804i	$0.143890\pi$
$522$		0			0
$523$	−8.40356e33			−0.877389			−0.438695	−	0.898636i	$-0.644559\pi$
$523$	−8.40356e33			−0.877389			−0.438695	+	0.898636i	$0.644559\pi$
$524$	−1.02920e33	−	1.78263e33i	−0.104920	−	0.181727i
$525$		0			0
$526$	3.06356e33	−	5.30624e33i	0.297786	−	0.515781i
$527$	−1.01062e34	+	1.75045e34i	−0.959302	+	1.66156i
$528$		0			0
$529$	4.57201e33	+	7.91896e33i	0.413915	+	0.716922i
$530$	5.26743e33			0.465747
$531$		0			0
$532$	7.78776e33			0.656927
$533$	1.58325e33	+	2.74226e33i	0.130454	+	0.225953i
$534$		0			0
$535$	−1.23800e33	+	2.14427e33i	−0.0973412	+	0.168600i
$536$	3.06241e33	−	5.30426e33i	0.235236	−	0.407441i
$537$		0			0
$538$	3.76666e33	+	6.52405e33i	0.276171	+	0.478342i
$539$	−7.45072e32			−0.0533751
$540$		0			0
$541$	−2.09754e34			−1.43464			−0.717321	−	0.696742i	$-0.754632\pi$
$541$	−2.09754e34			−1.43464			−0.717321	+	0.696742i	$0.754632\pi$
$542$	9.34986e33	+	1.61944e34i	0.624905	+	1.08237i
$543$		0			0
$544$	−1.75552e33	+	3.04065e33i	−0.112052	+	0.194080i
$545$	−2.49323e33	+	4.31841e33i	−0.155527	+	0.269381i
$546$		0			0
$547$	−2.29840e33	−	3.98095e33i	−0.136957	−	0.237217i	0.789386	−	0.613897i	$-0.210399\pi$
$547$	−2.29840e33	−	3.98095e33i	−0.136957	−	0.237217i	−0.926343	+	0.376680i	$0.877066\pi$
$548$	1.11925e34			0.651883
$549$		0			0
$550$	4.39960e33			0.244838
$551$	−2.39029e34	−	4.14011e34i	−1.30034	−	2.25225i
$552$		0			0
$553$	−5.45714e33	+	9.45204e33i	−0.283727	+	0.491429i
$554$	6.16779e31	−	1.06829e32i	0.00313514	−	0.00543023i
$555$		0			0
$556$	4.75042e33	+	8.22798e33i	0.230833	+	0.399814i
$557$	−3.15350e34			−1.49832			−0.749158	−	0.662391i	$-0.769542\pi$
$557$	−3.15350e34			−1.49832			−0.749158	+	0.662391i	$0.769542\pi$
$558$		0			0
$559$	1.52596e34			0.693261
$560$	1.28505e33	+	2.22577e33i	0.0570912	+	0.0988849i
$561$		0			0
$562$	−1.14566e34	+	1.98433e34i	−0.486800	+	0.843162i
$563$	−4.91693e33	+	8.51638e33i	−0.204333	+	0.353916i	−0.949920	−	0.312493i	$-0.898836\pi$
$563$	−4.91693e33	+	8.51638e33i	−0.204333	+	0.353916i	0.745587	+	0.666409i	$0.232169\pi$
$564$		0			0
$565$	−6.37128e33	−	1.10354e34i	−0.253292	−	0.438714i
$566$	3.03122e33			0.117873
$567$		0			0
$568$	−6.90006e33			−0.256743
$569$	7.27436e33	+	1.25996e34i	0.264784	+	0.458619i	0.967507	−	0.252844i	$-0.0813660\pi$
$569$	7.27436e33	+	1.25996e34i	0.264784	+	0.458619i	−0.702723	+	0.711464i	$0.748033\pi$
$570$		0			0
$571$	5.50961e33	−	9.54292e33i	0.191942	−	0.332453i	−0.753952	−	0.656930i	$-0.771855\pi$
$571$	5.50961e33	−	9.54292e33i	0.191942	−	0.332453i	0.945894	+	0.324477i	$0.105188\pi$
$572$	−6.06005e33	+	1.04963e34i	−0.206550	+	0.357755i
$573$		0			0
$574$	1.45750e33	+	2.52447e33i	0.0475566	+	0.0823705i
$575$	9.92372e33			0.316830
$576$		0			0
$577$	4.28784e34			1.31081			0.655406	−	0.755277i	$-0.272497\pi$
$577$	4.28784e34			1.31081			0.655406	+	0.755277i	$0.272497\pi$
$578$	7.17514e33	+	1.24277e34i	0.214651	+	0.371786i
$579$		0			0
$580$	7.88839e33	−	1.36631e34i	0.226016	−	0.391470i
$581$	−2.98347e34	+	5.16752e34i	−0.836604	+	1.44904i
$582$		0			0
$583$	1.14337e34	+	1.98037e34i	0.307135	+	0.531973i
$584$	2.37765e34			0.625154
$585$		0			0
$586$	4.83447e33			0.121795
$587$	−3.25757e34	−	5.64228e34i	−0.803374	−	1.39148i	−0.917383	−	0.398005i	$-0.869703\pi$
$587$	−3.25757e34	−	5.64228e34i	−0.803374	−	1.39148i	0.114009	−	0.993480i	$-0.463631\pi$
$588$		0			0
$589$	−4.47829e34	+	7.75662e34i	−1.05845	+	1.83329i
$590$	2.79032e33	−	4.83297e33i	0.0645659	−	0.111831i
$591$		0			0
$592$	6.17054e33	+	1.06877e34i	0.136868	+	0.237062i
$593$	−6.49827e34			−1.41128			−0.705641	−	0.708569i	$-0.749341\pi$
$593$	−6.49827e34			−1.41128			−0.705641	+	0.708569i	$0.749341\pi$
$594$		0			0
$595$	2.78065e34			0.579007
$596$	−9.32391e33	−	1.61495e34i	−0.190117	−	0.329292i
$597$		0			0
$598$	−1.36690e34	+	2.36754e34i	−0.267284	+	0.462949i
$599$	−3.34332e34	+	5.79079e34i	−0.640239	+	1.10893i	0.345140	+	0.938551i	$0.387831\pi$
$599$	−3.34332e34	+	5.79079e34i	−0.640239	+	1.10893i	−0.985379	+	0.170375i	$0.945502\pi$
$600$		0			0
$601$	−4.00918e34	−	6.94411e34i	−0.736419	−	1.27552i	−0.954098	−	0.299495i	$-0.903182\pi$
$601$	−4.00918e34	−	6.94411e34i	−0.736419	−	1.27552i	0.217679	−	0.976020i	$-0.430152\pi$
$602$	1.40477e34			0.252726
$603$		0			0
$604$	1.27054e34			0.219294
$605$	1.14231e34	+	1.97855e34i	0.193127	+	0.334506i
$606$		0			0
$607$	−2.20568e34	+	3.82036e34i	−0.357837	+	0.619791i	−0.987599	−	0.156997i	$-0.949819\pi$
$607$	−2.20568e34	+	3.82036e34i	−0.357837	+	0.619791i	0.629763	+	0.776788i	$0.283152\pi$
$608$	−7.77911e33	+	1.34738e34i	−0.123633	+	0.214139i
$609$		0			0
$610$	8.89673e33	+	1.54096e34i	0.135709	+	0.235054i
$611$	−6.83494e34			−1.02146
$612$		0			0
$613$	−8.57385e34			−1.23004			−0.615021	−	0.788511i	$-0.710853\pi$
$613$	−8.57385e34			−1.23004			−0.615021	+	0.788511i	$0.710853\pi$
$614$	−2.96420e34	−	5.13415e34i	−0.416681	−	0.721712i
$615$		0			0
$616$	−5.57875e33	+	9.66269e33i	−0.0752971	+	0.130418i
$617$	4.85117e34	−	8.40247e34i	0.641626	−	1.11133i	−0.343444	−	0.939173i	$-0.611594\pi$
$617$	4.85117e34	−	8.40247e34i	0.641626	−	1.11133i	0.985070	−	0.172155i	$-0.0550731\pi$
$618$		0			0
$619$	−2.10368e34	−	3.64367e34i	−0.267206	−	0.462814i	0.700933	−	0.713227i	$-0.252767\pi$
$619$	−2.10368e34	−	3.64367e34i	−0.267206	−	0.462814i	−0.968139	+	0.250413i	$0.919434\pi$
$620$	−2.95583e34			−0.367945
$621$		0			0
$622$	4.79799e34			0.573692
$623$	1.62873e34	+	2.82104e34i	0.190875	+	0.330604i
$624$		0			0
$625$	−1.53924e34	+	2.66604e34i	−0.173303	+	0.300170i
$626$	1.31033e34	−	2.26955e34i	0.144611	−	0.250473i
$627$		0			0
$628$	−6.80243e33	−	1.17822e34i	−0.0721388	−	0.124948i
$629$	1.33521e35			1.38809
$630$		0			0
$631$	−7.03375e34			−0.702781			−0.351390	−	0.936229i	$-0.614291\pi$
$631$	−7.03375e34			−0.702781			−0.351390	+	0.936229i	$0.614291\pi$
$632$	−1.09021e34	−	1.88831e34i	−0.106794	−	0.184973i
$633$		0			0
$634$	−3.36715e33	+	5.83207e33i	−0.0317064	+	0.0549170i
$635$	−2.27242e34	+	3.93596e34i	−0.209806	+	0.363395i
$636$		0			0
$637$	1.20794e34	+	2.09221e34i	0.107226	+	0.185721i
$638$	6.84913e34			0.596180
$639$		0			0
$640$	−5.13449e33			−0.0429781
$641$	−4.16184e34	−	7.20852e34i	−0.341633	−	0.591726i	0.643103	−	0.765780i	$-0.277647\pi$
$641$	−4.16184e34	−	7.20852e34i	−0.341633	−	0.591726i	−0.984736	+	0.174053i	$0.944313\pi$
$642$		0			0
$643$	4.34702e34	−	7.52926e34i	0.343206	−	0.594450i	−0.641820	−	0.766855i	$-0.721821\pi$
$643$	4.34702e34	−	7.52926e34i	0.343206	−	0.594450i	0.985026	+	0.172405i	$0.0551539\pi$
$644$	−1.25834e34	+	2.17951e34i	−0.0974373	+	0.168766i
$645$		0			0
$646$	8.41640e34	+	1.45776e35i	0.626931	+	1.08588i
$647$	−2.39516e35			−1.74997			−0.874987	−	0.484147i	$-0.839130\pi$
$647$	−2.39516e35			−1.74997			−0.874987	+	0.484147i	$0.839130\pi$
$648$		0			0
$649$	2.42271e34			0.170311
$650$	−7.13279e34	−	1.23544e35i	−0.491861	−	0.851928i
$651$		0			0
$652$	−3.84714e34	+	6.66344e34i	−0.255295	+	0.442184i
$653$	−6.00416e34	+	1.03995e35i	−0.390875	+	0.677015i	−0.992565	−	0.121715i	$-0.961161\pi$
$653$	−6.00416e34	+	1.03995e35i	−0.390875	+	0.677015i	0.601690	+	0.798729i	$0.294494\pi$
$654$		0			0
$655$	−1.62839e34	−	2.82045e34i	−0.102033	−	0.176727i
$656$	−5.82354e33			−0.0358005
$657$		0			0
$658$	−6.29211e34			−0.372368
$659$	4.13089e34	+	7.15492e34i	0.239870	+	0.415467i	0.960677	−	0.277669i	$-0.0895618\pi$
$659$	4.13089e34	+	7.15492e34i	0.239870	+	0.415467i	−0.720807	+	0.693136i	$0.756228\pi$
$660$		0			0
$661$	−3.31071e34	+	5.73431e34i	−0.185098	+	0.320600i	−0.943610	−	0.331060i	$-0.892594\pi$
$661$	−3.31071e34	+	5.73431e34i	−0.185098	+	0.320600i	0.758511	+	0.651660i	$0.225927\pi$
$662$	6.07179e33	−	1.05167e34i	0.0333113	−	0.0576969i
$663$		0			0
$664$	−5.96031e34	−	1.03236e35i	−0.314897	−	0.545417i
$665$	1.23217e35			0.638851
$666$		0			0
$667$	1.54489e35			0.771479
$668$	6.68347e34	+	1.15761e35i	0.327564	+	0.567358i
$669$		0			0
$670$	4.84531e34	−	8.39232e34i	0.228763	−	0.396230i
$671$	−3.86232e34	+	6.68973e34i	−0.178985	+	0.310011i
$672$		0			0
$673$	−3.53069e34	−	6.11533e34i	−0.157642	−	0.273043i	0.776376	−	0.630270i	$-0.217056\pi$
$673$	−3.53069e34	−	6.11533e34i	−0.157642	−	0.273043i	−0.934018	+	0.357227i	$0.883722\pi$
$674$	−1.34813e35			−0.590858
$675$		0			0
$676$	2.74604e35			1.15977
$677$	1.17229e35	+	2.03047e35i	0.486046	+	0.841856i	0.999871	−	0.0160384i	$-0.00510541\pi$
$677$	1.17229e35	+	2.03047e35i	0.486046	+	0.841856i	−0.513825	+	0.857895i	$0.671772\pi$
$678$		0			0
$679$	−2.71205e34	+	4.69741e34i	−0.108374	+	0.187710i
$680$	−2.77756e34	+	4.81088e34i	−0.108969	+	0.188739i
$681$		0			0
$682$	−6.41603e34	−	1.11129e35i	−0.242640	−	0.420264i
$683$	−1.42849e35			−0.530420			−0.265210	−	0.964191i	$-0.585441\pi$
$683$	−1.42849e35			−0.530420			−0.265210	+	0.964191i	$0.585441\pi$
$684$		0			0
$685$	1.77086e35			0.633946
$686$	1.05594e35	+	1.82895e35i	0.371184	+	0.642909i
$687$		0			0
$688$	−1.40321e34	+	2.43043e34i	−0.0475628	+	0.0823812i
$689$	3.70734e35	−	6.42130e35i	1.23402	−	2.13738i
$690$		0			0
$691$	2.88162e34	+	4.99111e34i	0.0925041	+	0.160222i	0.908564	−	0.417745i	$-0.137180\pi$
$691$	2.88162e34	+	4.99111e34i	0.0925041	+	0.160222i	−0.816060	+	0.577967i	$0.803846\pi$
$692$	−1.52616e35			−0.481141
$693$		0			0
$694$	−2.03584e35			−0.619084
$695$	7.51605e34	+	1.30182e35i	0.224481	+	0.388813i
$696$		0			0
$697$	−3.15031e34	+	5.45650e34i	−0.0907703	+	0.157219i
$698$	6.08904e34	−	1.05465e35i	0.172328	−	0.298481i
$699$		0			0
$700$	−6.56630e34	−	1.13732e35i	−0.179306	−	0.310567i
$701$	6.28311e35			1.68539			0.842693	−	0.538395i	$-0.180969\pi$
$701$	6.28311e35			1.68539			0.842693	+	0.538395i	$0.180969\pi$
$702$		0			0
$703$	5.91662e35			1.53155
$704$	−1.11451e34	−	1.93039e34i	−0.0283417	−	0.0490893i
$705$		0			0
$706$	−1.63461e35	+	2.83123e35i	−0.401195	+	0.694891i
$707$	1.45635e35	−	2.52248e35i	0.351176	−	0.608254i
$708$		0			0
$709$	−3.60866e35	−	6.25039e35i	−0.839979	−	1.45489i	−0.889911	−	0.456134i	$-0.849234\pi$
$709$	−3.60866e35	−	6.25039e35i	−0.839979	−	1.45489i	0.0499322	−	0.998753i	$-0.484099\pi$
$710$	−1.09172e35			−0.249678
$711$		0			0
$712$	−6.50768e34			−0.143690
$713$	−1.44720e35	−	2.50662e35i	−0.313985	−	0.543838i
$714$		0			0
$715$	−9.58812e34	+	1.66071e35i	−0.200867	+	0.347911i
$716$	−8.79764e34	+	1.52380e35i	−0.181115	+	0.313700i
$717$		0			0
$718$	−3.03497e35	−	5.25673e35i	−0.603391	−	1.04510i
$719$	7.06277e35			1.37995			0.689975	−	0.723833i	$-0.257621\pi$
$719$	7.06277e35			1.37995			0.689975	+	0.723833i	$0.257621\pi$
$720$		0			0
$721$	4.22104e35			0.796578
$722$	1.82329e35	+	3.15803e35i	0.338175	+	0.585736i
$723$		0			0
$724$	8.89986e34	−	1.54150e35i	0.159460	−	0.276193i
$725$	−4.03078e35	+	6.98152e35i	−0.709846	+	1.22949i
$726$		0			0
$727$	−1.02681e35	−	1.77849e35i	−0.174707	−	0.302601i	0.765353	−	0.643611i	$-0.222564\pi$
$727$	−1.02681e35	−	1.77849e35i	−0.174707	−	0.302601i	−0.940060	+	0.341010i	$0.889231\pi$
$728$	3.61779e35			0.605064
$729$		0			0
$730$	3.76188e35			0.607953
$731$	1.51817e35	+	2.62954e35i	0.241186	+	0.417747i
$732$		0			0
$733$	−3.49051e35	+	6.04573e35i	−0.535906	+	0.928216i	0.463213	+	0.886247i	$0.346697\pi$
$733$	−3.49051e35	+	6.04573e35i	−0.535906	+	0.928216i	−0.999119	+	0.0419694i	$0.986637\pi$
$734$	1.68846e35	−	2.92451e35i	0.254854	−	0.441420i
$735$		0			0
$736$	−2.51389e34	−	4.35418e34i	−0.0366753	−	0.0635234i
$737$	4.20697e35			0.603428
$738$		0			0
$739$	1.04387e36			1.44741			0.723704	−	0.690110i	$-0.242438\pi$
$739$	1.04387e36			1.44741			0.723704	+	0.690110i	$0.242438\pi$
$740$	9.76294e34	+	1.69099e35i	0.133102	+	0.230539i
$741$		0			0
$742$	3.41290e35	−	5.91132e35i	0.449857	−	0.779176i
$743$	4.89050e35	−	8.47060e35i	0.633860	−	1.09788i	−0.352896	−	0.935663i	$-0.614803\pi$
$743$	4.89050e35	−	8.47060e35i	0.633860	−	1.09788i	0.986755	−	0.162215i	$-0.0518637\pi$
$744$		0			0
$745$	−1.47522e35	−	2.55515e35i	−0.184885	−	0.320231i
$746$	−4.36519e35			−0.537983
$747$		0			0
$748$	−2.41163e35			−0.287436
$749$	1.60426e35	+	2.77866e35i	0.188041	+	0.325696i
$750$		0			0
$751$	−1.26972e35	+	2.19922e35i	−0.143949	+	0.249327i	−0.928980	−	0.370129i	$-0.879313\pi$
$751$	−1.26972e35	+	2.19922e35i	−0.143949	+	0.249327i	0.785031	+	0.619456i	$0.212647\pi$
$752$	6.28512e34	−	1.08861e35i	0.0700794	−	0.121381i
$753$		0			0
$754$	−1.11041e36	−	1.92328e36i	−1.19768	−	2.07444i
$755$	2.01023e35			0.213260
$756$		0			0
$757$	−7.81917e35			−0.802532			−0.401266	−	0.915962i	$-0.631430\pi$
$757$	−7.81917e35			−0.802532			−0.401266	+	0.915962i	$0.631430\pi$
$758$	−3.06093e35	−	5.30169e35i	−0.309021	−	0.535241i
$759$		0			0
$760$	−1.23080e35	+	2.13181e35i	−0.120231	+	0.208247i
$761$	8.13655e35	−	1.40929e36i	0.781865	−	1.35423i	−0.148988	−	0.988839i	$-0.547602\pi$
$761$	8.13655e35	−	1.40929e36i	0.781865	−	1.35423i	0.930854	−	0.365392i	$-0.119065\pi$
$762$		0			0
$763$	3.23086e35	+	5.59601e35i	0.300442	+	0.520382i
$764$	−6.66738e35			−0.609941
$765$		0			0
$766$	−8.19517e35			−0.725602
$767$	−3.92778e35	−	6.80312e35i	−0.342141	−	0.592606i
$768$		0			0
$769$	−1.40603e35	+	2.43531e35i	−0.118553	+	0.205340i	−0.919195	−	0.393804i	$-0.871159\pi$
$769$	−1.40603e35	+	2.43531e35i	−0.118553	+	0.205340i	0.800641	+	0.599144i	$0.204492\pi$
$770$	−8.82663e34	+	1.52882e35i	−0.0732252	+	0.126830i
$771$		0			0
$772$	3.38022e34	+	5.85471e34i	0.0271474	+	0.0470207i
$773$	−6.80034e35			−0.537387			−0.268693	−	0.963226i	$-0.586592\pi$
$773$	−6.80034e35			−0.537387			−0.268693	+	0.963226i	$0.586592\pi$
$774$		0			0
$775$	1.51036e36			1.15560
$776$	−5.41808e34	−	9.38438e34i	−0.0407919	−	0.0706536i
$777$		0			0
$778$	−5.24940e35	+	9.09223e35i	−0.382705	+	0.662865i
$779$	−1.39597e35	+	2.41790e35i	−0.100152	+	0.173468i
$780$		0			0
$781$	−2.36972e35	−	4.10448e35i	−0.164649	−	0.285181i
$782$	−5.43967e35			−0.371953
$783$		0			0
$784$	−4.44307e34			−0.0294261
$785$	−1.07627e35	−	1.86416e35i	−0.0701538	−	0.121510i
$786$		0			0
$787$	5.70824e35	−	9.88697e35i	0.360428	−	0.624279i	−0.627603	−	0.778533i	$-0.715964\pi$
$787$	5.70824e35	−	9.88697e35i	0.360428	−	0.624279i	0.988031	+	0.154254i	$0.0492974\pi$
$788$	−1.32064e35	+	2.28742e35i	−0.0820745	+	0.142157i
$789$		0			0
$790$	−1.72492e35	−	2.98765e35i	−0.103856	−	0.179884i
$791$	−1.65125e36			−0.978601
$792$		0			0
$793$	2.50469e36			1.43827
$794$	1.93446e35	+	3.35058e35i	0.109346	+	0.189393i
$795$		0			0
$796$	7.13938e34	−	1.23658e35i	0.0391064	−	0.0677342i
$797$	4.10949e35	−	7.11785e35i	0.221595	−	0.383813i	−0.733698	−	0.679476i	$-0.762207\pi$
$797$	4.10949e35	−	7.11785e35i	0.221595	−	0.383813i	0.955292	+	0.295663i	$0.0955405\pi$
$798$		0			0
$799$	−6.80002e35	−	1.17780e36i	−0.355365	−	0.615511i
$800$	2.62360e35			0.134981
$801$		0			0
$802$	2.42098e36			1.20729
$803$	8.16569e35	+	1.41434e36i	0.400912	+	0.694399i
$804$		0			0
$805$	−1.99093e35	+	3.44839e35i	−0.0947562	+	0.164123i
$806$	−2.08038e36	+	3.60332e36i	−0.974888	+	1.68856i
$807$		0			0
$808$	2.90947e35	+	5.03936e35i	0.132182	+	0.228946i
$809$	5.29083e35			0.236683			0.118341	−	0.992973i	$-0.462242\pi$
$809$	5.29083e35			0.236683			0.118341	+	0.992973i	$0.462242\pi$
$810$		0			0
$811$	1.68688e36			0.731682			0.365841	−	0.930677i	$-0.380781\pi$
$811$	1.68688e36			0.731682			0.365841	+	0.930677i	$0.380781\pi$
$812$	−1.02222e36	−	1.77053e36i	−0.436609	−	0.756230i
$813$		0			0
$814$	−4.23836e35	+	7.34106e35i	−0.175547	+	0.304056i
$815$	−6.08689e35	+	1.05428e36i	−0.248270	+	0.430017i
$816$		0			0
$817$	6.72734e35	+	1.16521e36i	0.266114	+	0.460923i
$818$	−2.87843e36			−1.12135
$819$		0			0
$820$	−9.21392e34			−0.0348154
$821$	1.60023e36	+	2.77169e36i	0.595517	+	1.03147i	0.993474	+	0.114061i	$0.0363859\pi$
$821$	1.60023e36	+	2.77169e36i	0.595517	+	1.03147i	−0.397957	+	0.917404i	$0.630281\pi$
$822$		0			0
$823$	−2.28957e36	+	3.96566e36i	−0.826527	+	1.43159i	0.0742202	+	0.997242i	$0.476353\pi$
$823$	−2.28957e36	+	3.96566e36i	−0.826527	+	1.43159i	−0.900747	+	0.434344i	$0.856980\pi$
$824$	−4.21635e35	+	7.30293e35i	−0.149915	+	0.259661i
$825$		0			0
$826$	−3.61584e35	−	6.26281e35i	−0.124726	−	0.216032i
$827$	−1.41774e36			−0.481701			−0.240851	−	0.970562i	$-0.577426\pi$
$827$	−1.41774e36			−0.481701			−0.240851	+	0.970562i	$0.577426\pi$
$828$		0			0
$829$	−2.97714e36			−0.981450			−0.490725	−	0.871315i	$-0.663268\pi$
$829$	−2.97714e36			−0.981450			−0.490725	+	0.871315i	$0.663268\pi$
$830$	−9.43032e35	−	1.63338e36i	−0.306232	−	0.530409i
$831$		0			0
$832$	−3.61377e35	+	6.25924e35i	−0.113873	+	0.197233i
$833$	−2.40353e35	+	4.16304e35i	−0.0746083	+	0.129225i
$834$		0			0
$835$	1.05745e36	+	1.83156e36i	0.318551	+	0.551746i
$836$	−1.06865e36			−0.317144
$837$		0			0
$838$	−2.90797e36			−0.837605
$839$	−1.35797e36	−	2.35208e36i	−0.385360	−	0.667463i	0.606459	−	0.795115i	$-0.292589\pi$
$839$	−1.35797e36	−	2.35208e36i	−0.385360	−	0.667463i	−0.991819	+	0.127652i	$0.959256\pi$
$840$		0			0
$841$	−4.45979e36	+	7.72458e36i	−1.22847	+	2.12777i
$842$	1.96315e36	−	3.40027e36i	0.532785	−	0.922810i
$843$		0			0
$844$	1.72566e36	+	2.98893e36i	0.454647	+	0.787472i
$845$	4.34474e36			1.12786
$846$		0			0
$847$	2.96054e36			0.746154
$848$	6.81822e35	+	1.18095e36i	0.169326	+	0.293281i
$849$		0			0
$850$	1.41927e36	−	2.45824e36i	0.342238	−	0.592773i
$851$	−9.56004e35	+	1.65585e36i	−0.227164	+	0.393460i
$852$		0			0
$853$	−2.52908e34	−	4.38049e34i	−0.00583578	−	0.0101079i	0.863093	−	0.505045i	$-0.168524\pi$
$853$	−2.52908e34	−	4.38049e34i	−0.00583578	−	0.0101079i	−0.868929	+	0.494938i	$0.835191\pi$
$854$	2.30577e36			0.524315
$855$		0			0
$856$	−6.40990e35			−0.141556
$857$	2.07326e36	+	3.59100e36i	0.451226	+	0.781546i	0.998462	−	0.0554317i	$-0.0176535\pi$
$857$	2.07326e36	+	3.59100e36i	0.451226	+	0.781546i	−0.547237	+	0.836978i	$0.684320\pi$
$858$		0			0
$859$	−1.38778e36	+	2.40370e36i	−0.293362	+	0.508119i	−0.974603	−	0.223941i	$-0.928108\pi$
$859$	−1.38778e36	+	2.40370e36i	−0.293362	+	0.508119i	0.681240	+	0.732060i	$0.261441\pi$
$860$	−2.22014e35	+	3.84540e35i	−0.0462541	+	0.0801144i
$861$		0			0
$862$	−2.52963e34	−	4.38145e34i	−0.00511937	−	0.00886702i
$863$	−1.35077e36			−0.269431			−0.134715	−	0.990884i	$-0.543012\pi$
$863$	−1.35077e36			−0.269431			−0.134715	+	0.990884i	$0.543012\pi$
$864$		0			0
$865$	−2.41466e36			−0.467902
$866$	−1.08338e36	−	1.87647e36i	−0.206922	−	0.358399i
$867$		0			0
$868$	−1.91516e36	+	3.31715e36i	−0.355392	+	0.615557i
$869$	7.48836e35	−	1.29702e36i	0.136975	−	0.237247i
$870$		0			0
$871$	−6.82049e36	−	1.18134e37i	−1.21224	−	2.09966i
$872$	−1.29091e36			−0.226172
$873$		0			0
$874$	−2.41044e36			−0.410396
$875$	−2.39951e36	−	4.15607e36i	−0.402737	−	0.697561i
$876$		0			0
$877$	−3.29641e36	+	5.70955e36i	−0.537707	+	0.931337i	0.461320	+	0.887234i	$0.347376\pi$
$877$	−3.29641e36	+	5.70955e36i	−0.537707	+	0.931337i	−0.999027	+	0.0441026i	$0.985957\pi$
$878$	1.01196e36	−	1.75277e36i	0.162735	−	0.281866i
$879$		0			0
$880$	−1.76336e35	−	3.05424e35i	−0.0275619	−	0.0477386i
$881$	−1.19143e37			−1.83599			−0.917995	−	0.396593i	$-0.870192\pi$
$881$	−1.19143e37			−1.83599			−0.917995	+	0.396593i	$0.870192\pi$
$882$		0			0
$883$	1.83480e36			0.274841			0.137420	−	0.990513i	$-0.456119\pi$
$883$	1.83480e36			0.274841			0.137420	+	0.990513i	$0.456119\pi$
$884$	3.90982e36	+	6.77201e36i	0.577436	+	1.00015i
$885$		0			0
$886$	−3.52748e36	+	6.10978e36i	−0.506458	+	0.877210i
$887$	−6.33369e36	+	1.09703e37i	−0.896626	+	1.55300i	−0.0648476	+	0.997895i	$0.520656\pi$
$887$	−6.33369e36	+	1.09703e37i	−0.896626	+	1.55300i	−0.831779	+	0.555107i	$0.812677\pi$
$888$		0			0
$889$	2.94472e36	+	5.10041e36i	0.405296	+	0.701994i
$890$	−1.02964e36			−0.139736
$891$		0			0
$892$	5.88741e36			0.776898
$893$	−3.01324e36	−	5.21909e36i	−0.392094	−	0.679127i
$894$		0			0
$895$	−1.39195e36	+	2.41093e36i	−0.176131	+	0.305068i
$896$	−3.32677e35	+	5.76213e35i	−0.0415119	+	0.0719006i
$897$		0			0
$898$	−3.96352e36	−	6.86502e36i	−0.480980	−	0.833082i
$899$	2.35127e37			2.81389
$900$		0			0
$901$	1.47536e37			1.71727
$902$	−2.00001e35	−	3.46412e35i	−0.0229589	−	0.0397659i
$903$		0			0
$904$	1.64941e36	−	2.85686e36i	0.184172	−	0.318995i
$905$	1.40812e36	−	2.43894e36i	0.155072	−	0.268593i
$906$		0			0
$907$	−3.20559e35	−	5.55225e35i	−0.0343413	−	0.0594809i	0.848344	−	0.529446i	$-0.177600\pi$
$907$	−3.20559e35	−	5.55225e35i	−0.0343413	−	0.0594809i	−0.882685	+	0.469965i	$0.844267\pi$
$908$	−2.49564e35			−0.0263699
$909$		0			0
$910$	5.72402e36			0.588415
$911$	−4.43527e36	−	7.68211e36i	−0.449718	−	0.778934i	0.548650	−	0.836052i	$-0.315142\pi$
$911$	−4.43527e36	−	7.68211e36i	−0.449718	−	0.778934i	−0.998367	+	0.0571183i	$0.981809\pi$
$912$		0			0
$913$	4.09396e36	−	7.09095e36i	0.403886	−	0.699552i
$914$	−1.34399e36	+	2.32786e36i	−0.130789	+	0.226532i
$915$		0			0
$916$	−3.23669e36	−	5.60612e36i	−0.306484	−	0.530846i
$917$	−4.22030e36			−0.394209
$918$		0			0
$919$	1.08231e37			0.983800			0.491900	−	0.870652i	$-0.336303\pi$
$919$	1.08231e37			0.983800			0.491900	+	0.870652i	$0.336303\pi$
$920$	−3.97744e35	−	6.88912e35i	−0.0356661	−	0.0617755i
$921$		0			0
$922$	1.49345e36	−	2.58673e36i	0.130333	−	0.225743i
$923$	−7.68376e36	+	1.33087e37i	−0.661535	+	1.14581i
$924$		0			0
$925$	−4.98864e36	−	8.64057e36i	−0.418033	−	0.724054i
$926$	1.34670e37			1.11336
$927$		0			0
$928$	4.08433e36			0.328678
$929$	−2.23607e35	−	3.87298e35i	−0.0177537	−	0.0307503i	0.857012	−	0.515296i	$-0.172318\pi$
$929$	−2.23607e35	−	3.87298e35i	−0.0177537	−	0.0307503i	−0.874766	+	0.484546i	$0.838985\pi$
$930$		0			0
$931$	−1.06506e36	+	1.84474e36i	−0.0823195	+	0.142581i
$932$	−3.27900e36	+	5.67939e36i	−0.250059	+	0.433115i
$933$		0			0
$934$	3.16971e36	+	5.49010e36i	0.235334	+	0.407610i
$935$	−3.81565e36			−0.279527
$936$		0			0
$937$	−1.11792e37			−0.797383			−0.398692	−	0.917085i	$-0.630536\pi$
$937$	−1.11792e37			−0.797383			−0.398692	+	0.917085i	$0.630536\pi$
$938$	−6.27880e36	−	1.08752e37i	−0.441918	−	0.765424i
$939$		0			0
$940$	9.94423e35	−	1.72239e36i	0.0681511	−	0.118041i
$941$	9.90013e36	−	1.71475e37i	0.669531	−	1.15966i	−0.308505	−	0.951223i	$-0.599829\pi$
$941$	9.90013e36	−	1.71475e37i	0.669531	−	1.15966i	0.978036	−	0.208438i	$-0.0668381\pi$
$942$		0			0
$943$	−4.51121e35	−	7.81365e35i	−0.0297096	−	0.0514586i
$944$	1.44473e36			0.0938936
$945$		0			0
$946$	−1.92765e36			−0.122008
$947$	−1.08685e37	−	1.88247e37i	−0.678881	−	1.17586i	−0.975318	−	0.220804i	$-0.929132\pi$
$947$	−1.08685e37	−	1.88247e37i	−0.678881	−	1.17586i	0.296437	−	0.955052i	$-0.404201\pi$
$948$		0			0
$949$	2.64770e37	−	4.58596e37i	1.61080	−	2.78999i
$950$	6.28910e36	−	1.08930e37i	0.377610	−	0.654040i
$951$		0			0
$952$	3.59931e36	+	6.23418e36i	0.210502	+	0.364601i
$953$	−2.05005e37			−1.18332			−0.591661	−	0.806187i	$-0.701528\pi$
$953$	−2.05005e37			−1.18332			−0.591661	+	0.806187i	$0.701528\pi$
$954$		0			0
$955$	−1.05490e37			−0.593158
$956$	6.09285e36	+	1.05531e37i	0.338140	+	0.585676i
$957$		0			0
$958$	4.04878e36	−	7.01270e36i	0.218905	−	0.379155i
$959$	1.14739e37	−	1.98733e37i	0.612318	−	1.06057i
$960$		0			0
$961$	−1.24095e37	−	2.14939e37i	−0.645226	−	1.11756i
$962$	2.74856e37			1.41064
$963$		0			0
$964$	4.65788e36			0.232930
$965$	5.34813e35	+	9.26323e35i	0.0264004	+	0.0457268i
$966$		0			0
$967$	−1.26084e37	+	2.18383e37i	−0.606495	+	1.05048i	0.385318	+	0.922784i	$0.374092\pi$
$967$	−1.26084e37	+	2.18383e37i	−0.606495	+	1.05048i	−0.991813	+	0.127697i	$0.959242\pi$
$968$	−2.95725e36	+	5.12211e36i	−0.140426	+	0.243224i
$969$		0			0
$970$	−8.57241e35	−	1.48478e36i	−0.0396694	−	0.0687095i
$971$	1.87523e37			0.856669			0.428335	−	0.903620i	$-0.359100\pi$
$971$	1.87523e37			0.856669			0.428335	+	0.903620i	$0.359100\pi$
$972$		0			0
$973$	1.94794e37			0.867290
$974$	1.00511e37	+	1.74091e37i	0.441802	+	0.765224i
$975$		0			0
$976$	−2.30321e36	+	3.98927e36i	−0.0986757	+	0.170911i
$977$	−1.83554e37	+	3.17925e37i	−0.776393	+	1.34475i	0.157616	+	0.987501i	$0.449619\pi$
$977$	−1.83554e37	+	3.17925e37i	−0.776393	+	1.34475i	−0.934008	+	0.357251i	$0.883714\pi$
$978$		0			0
$979$	−2.23497e36	−	3.87107e36i	−0.0921483	−	0.159605i
$980$	−7.02976e35			−0.0286164
$981$		0			0
$982$	−8.32094e35			−0.0330201
$983$	1.22359e37	+	2.11933e37i	0.479422	+	0.830383i	0.999721	−	0.0236005i	$-0.00751297\pi$
$983$	1.22359e37	+	2.11933e37i	0.479422	+	0.830383i	−0.520299	+	0.853984i	$0.674180\pi$
$984$		0			0
$985$	−2.08951e36	+	3.61913e36i	−0.0798161	+	0.138246i
$986$	2.20946e37	−	3.82691e37i	0.833347	−	1.44340i
$987$		0			0
$988$	1.73253e37	+	3.00083e37i	0.637117	+	1.10352i
$989$	−4.34800e36			−0.157883
$990$		0			0
$991$	−5.14810e37			−1.82274			−0.911372	−	0.411583i	$-0.864976\pi$
$991$	−5.14810e37			−1.82274			−0.911372	+	0.411583i	$0.864976\pi$
$992$	−3.82606e36	−	6.62693e36i	−0.133769	−	0.231695i
$993$		0			0
$994$	−7.07352e36	+	1.22517e37i	−0.241160	+	0.417702i
$995$	1.12958e36	−	1.95650e36i	0.0380303	−	0.0658704i
$996$		0			0
$997$	−2.18392e37	−	3.78266e37i	−0.717047	−	1.24196i	−0.962165	−	0.272468i	$-0.912160\pi$
$997$	−2.18392e37	−	3.78266e37i	−0.717047	−	1.24196i	0.245118	−	0.969493i	$-0.421173\pi$
$998$	−1.16454e37			−0.377591
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.26.c.b.37.5		26
3.2	odd	2		18.26.c.b.13.4	yes	26
9.2	odd	6		18.26.c.b.7.4	✓	26
9.7	even	3	inner	54.26.c.b.19.5		26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.26.c.b.7.4	✓	26	9.2	odd	6
18.26.c.b.13.4	yes	26	3.2	odd	2
54.26.c.b.19.5		26	9.7	even	3	inner
54.26.c.b.37.5		26	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	54.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2048.00 + 3547.24i) q^{2} +(-8.38861e6 + 1.45295e7i) q^{4} +(-1.32723e8 + 2.29884e8i) q^{5} +(1.71990e10 + 2.97895e10i) q^{7} -6.87195e10 q^{8} -1.08727e12 q^{10} +(-2.36007e12 - 4.08776e12i) q^{11} +(-7.65246e13 + 1.32545e14i) q^{13} +(-7.04470e13 + 1.22018e14i) q^{14} +(-1.40737e14 - 2.43764e14i) q^{16} -3.04534e15 q^{17} -1.34946e16 q^{19} +(-2.22673e15 - 3.85681e15i) q^{20} +(9.66685e15 - 1.67435e16i) q^{22} +(2.18045e16 - 3.77665e16i) q^{23} +(1.13781e17 + 1.97074e17i) q^{25} -6.26890e17 q^{26} -5.77102e17 q^{28} +(1.77130e18 + 3.06797e18i) q^{29} +(3.31858e18 - 5.74794e18i) q^{31} +(5.76461e17 - 9.98459e17i) q^{32} +(-6.23686e18 - 1.08026e19i) q^{34} -9.13082e18 q^{35} -4.38443e19 q^{37} +(-2.76370e19 - 4.78686e19i) q^{38} +(9.12068e18 - 1.57975e19i) q^{40} +(1.03447e19 - 1.79175e19i) q^{41} +(-4.98521e19 - 8.63463e19i) q^{43} +7.91908e19 q^{44} +1.78622e20 q^{46} +(2.23292e20 + 3.86754e20i) q^{47} +(7.89248e19 - 1.36702e20i) q^{49} +(-4.66045e20 + 8.07214e20i) q^{50} +(-1.28387e21 - 2.22373e21i) q^{52} -4.84464e21 q^{53} +1.25295e21 q^{55} +(-1.18190e21 - 2.04712e21i) q^{56} +(-7.25522e21 + 1.25664e22i) q^{58} +(-2.56635e21 + 4.44505e21i) q^{59} +(-8.18264e21 - 1.41727e22i) q^{61} +2.71858e22 q^{62} +4.72237e21 q^{64} +(-2.03132e22 - 3.51835e22i) q^{65} +(-4.45640e22 + 7.71871e22i) q^{67} +(2.55462e22 - 4.42473e22i) q^{68} +(-1.86999e22 - 3.23892e22i) q^{70} +1.00409e23 q^{71} -3.45994e23 q^{73} +(-8.97932e22 - 1.55526e23i) q^{74} +(1.13201e23 - 1.96070e23i) q^{76} +(8.11816e22 - 1.40611e23i) q^{77} +(1.58647e23 + 2.74785e23i) q^{79} +7.47166e22 q^{80} +8.47436e22 q^{82} +(8.67339e23 + 1.50228e24i) q^{83} +(4.04188e23 - 7.00075e23i) q^{85} +(2.04194e23 - 3.53675e23i) q^{86} +(1.62183e23 + 2.80909e23i) q^{88} +9.46991e23 q^{89} -5.26458e24 q^{91} +(3.65819e23 + 6.33617e23i) q^{92} +(-9.14605e23 + 1.58414e24i) q^{94} +(1.79105e24 - 3.10219e24i) q^{95} +(7.88434e23 + 1.36561e24i) q^{97} +6.46552e23 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 53248 q^{2} - 218103808 q^{4} - 49854096 q^{5} - 35213963498 q^{7} - 1786706395136 q^{8} - 408404754432 q^{10} + 1998346177329 q^{11} - 158355783504242 q^{13} + 144236394487808 q^{14} - 36\!\cdots\!28 q^{16}+ \cdots - 14\!\cdots\!64 q^{98}+O(q^{100}) \) 26 * q + 53248 * q^2 - 218103808 * q^4 - 49854096 * q^5 - 35213963498 * q^7 - 1786706395136 * q^8 - 408404754432 * q^10 + 1998346177329 * q^11 - 158355783504242 * q^13 + 144236394487808 * q^14 - 3659174697238528 * q^16 - 3616705586624034 * q^17 - 5058456299228762 * q^19 - 836412937076736 * q^20 - 8185225942339584 * q^22 + 155570710082203362 * q^23 - 888197302847183911 * q^25 - 1297250578466750464 * q^26 + 1181584543644123136 * q^28 + 3925320594794185038 * q^29 - 6592704741949460996 * q^31 + 14987979559889010688 * q^32 - 7407013041406021632 * q^34 + 49533545961137501568 * q^35 + 78961008772462984600 * q^37 - 10359718500820504576 * q^38 + 3425947390266310656 * q^40 + 13758002834178626109 * q^41 - 191473700412044564123 * q^43 - 67053370919645872128 * q^44 + 1274435256993409941504 * q^46 - 154470707996501871078 * q^47 - 1713680737743395735817 * q^49 + 3638056152462065299456 * q^50 - 2656769184699904950272 * q^52 + 1171350014833338971736 * q^53 + 23890981280754645933408 * q^55 + 2419885145383164182528 * q^56 - 16078113156276981915648 * q^58 - 545848631253825283329 * q^59 - 10067352509024211048296 * q^61 - 54007437246049984479232 * q^62 + 122781528554610775556096 * q^64 - 12640794081283966054032 * q^65 + 79389140801664567200479 * q^67 + 30339125417599064604672 * q^68 + 101444702128409603211264 * q^70 - 415430508733527088013160 * q^71 - 539343970915021400375282 * q^73 + 161712145966004192460800 * q^74 + 42433406979360786743296 * q^76 + 327594537754607633577834 * q^77 + 611076271613290617275908 * q^79 + 28065361021061616893952 * q^80 + 112705559217591305084928 * q^82 + 400615093454630506593780 * q^83 - 1703025287061576739254000 * q^85 + 784276276887734534647808 * q^86 - 137325303643434746118144 * q^88 - 18509149037385930189952524 * q^89 + 10266453492659369810870360 * q^91 + 2610043406322503560200192 * q^92 + 632712019953671663935488 * q^94 + 16882199861176698021554184 * q^95 + 3205637813401802510221951 * q^97 - 14038472603593897867812864 * q^98

Introduction

L-functions

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