LMFDB - Embedded newform 65.10.b.a.14.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,10,Mod(14,65)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("65.14");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	65.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:	$33.4773293507$
Analytic rank:	$0$
Dimension:	$54$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			14.6
Character	$\chi$	$=$	65.14
Dual form			65.10.b.a.14.49

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-37.2225i q^{2} +132.249i q^{3} -873.511 q^{4} +(-995.901 - 980.463i) q^{5} +4922.65 q^{6} -6816.48i q^{7} +13456.3i q^{8} +2193.09 q^{9} +(-36495.2 + 37069.9i) q^{10} -40762.4 q^{11} -115521. i q^{12} -28561.0i q^{13} -253726. q^{14} +(129666. - 131707. i) q^{15} +53640.4 q^{16} -491145. i q^{17} -81632.3i q^{18} -713534. q^{19} +(869931. + 856445. i) q^{20} +901476. q^{21} +1.51728e6i q^{22} +1.62288e6i q^{23} -1.77959e6 q^{24} +(30511.2 + 1.95289e6i) q^{25} -1.06311e6 q^{26} +2.89310e6i q^{27} +5.95427e6i q^{28} +2.06761e6 q^{29} +(-4.90247e6 - 4.82647e6i) q^{30} +7.21399e6 q^{31} +4.89302e6i q^{32} -5.39080e6i q^{33} -1.82816e7 q^{34} +(-6.68330e6 + 6.78854e6i) q^{35} -1.91569e6 q^{36} -6.13511e6i q^{37} +2.65595e7i q^{38} +3.77718e6 q^{39} +(1.31934e7 - 1.34012e7i) q^{40} -532270. q^{41} -3.35551e7i q^{42} +2.95343e7i q^{43} +3.56064e7 q^{44} +(-2.18410e6 - 2.15024e6i) q^{45} +6.04077e7 q^{46} -2.98650e7i q^{47} +7.09391e6i q^{48} -6.11080e6 q^{49} +(7.26912e7 - 1.13570e6i) q^{50} +6.49536e7 q^{51} +2.49484e7i q^{52} +1.01037e8i q^{53} +1.07688e8 q^{54} +(4.05953e7 + 3.99660e7i) q^{55} +9.17249e7 q^{56} -9.43645e7i q^{57} -7.69617e7i q^{58} -1.55968e8 q^{59} +(-1.13264e8 + 1.15048e8i) q^{60} -1.25023e7 q^{61} -2.68522e8i q^{62} -1.49492e7i q^{63} +2.09594e8 q^{64} +(-2.80030e7 + 2.84439e7i) q^{65} -2.00659e8 q^{66} +1.62345e8i q^{67} +4.29020e8i q^{68} -2.14625e8 q^{69} +(2.52686e8 + 2.48769e8i) q^{70} -2.03300e8 q^{71} +2.95110e7i q^{72} -1.19966e8i q^{73} -2.28364e8 q^{74} +(-2.58268e8 + 4.03508e6i) q^{75} +6.23280e8 q^{76} +2.77856e8i q^{77} -1.40596e8i q^{78} -1.36039e8 q^{79} +(-5.34205e7 - 5.25924e7i) q^{80} -3.39444e8 q^{81} +1.98124e7i q^{82} -6.00605e8i q^{83} -7.87449e8 q^{84} +(-4.81549e8 + 4.89131e8i) q^{85} +1.09934e9 q^{86} +2.73441e8i q^{87} -5.48513e8i q^{88} +2.21485e7 q^{89} +(-8.00374e7 + 8.12976e7i) q^{90} -1.94685e8 q^{91} -1.41761e9i q^{92} +9.54046e8i q^{93} -1.11165e9 q^{94} +(7.10609e8 + 6.99593e8i) q^{95} -6.47099e8 q^{96} +6.11371e8i q^{97} +2.27459e8i q^{98} -8.93957e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 13140 q^{4} - 2160 q^{5} - 3572 q^{6} - 428346 q^{9} + 74802 q^{10} - 132192 q^{11} + 718916 q^{14} + 339156 q^{15} + 1997244 q^{16} + 1523456 q^{19} + 4945180 q^{20} - 5377256 q^{21} + 7134424 q^{24}+ \cdots - 4284595264 q^{99}+O(q^{100}) $ 54 * q - 13140 * q^4 - 2160 * q^5 - 3572 * q^6 - 428346 * q^9 + 74802 * q^10 - 132192 * q^11 + 718916 * q^14 + 339156 * q^15 + 1997244 * q^16 + 1523456 * q^19 + 4945180 * q^20 - 5377256 * q^21 + 7134424 * q^24 - 948708 * q^25 - 2741856 * q^26 - 8867340 * q^29 + 1587678 * q^30 + 12213796 * q^31 - 37568140 * q^34 - 37980442 * q^35 + 195176200 * q^36 + 18507528 * q^39 - 78122474 * q^40 - 41063084 * q^41 - 86766092 * q^44 - 87904884 * q^45 - 64211420 * q^46 - 293513290 * q^49 + 52576096 * q^50 - 136792788 * q^51 - 3099140 * q^54 + 50401764 * q^55 - 556092908 * q^56 + 991411312 * q^59 + 548166228 * q^60 + 200512988 * q^61 - 1108334388 * q^64 + 33359248 * q^65 + 157425616 * q^66 + 1318334144 * q^69 + 511125000 * q^70 - 470875308 * q^71 - 3711844340 * q^74 - 907655634 * q^75 + 927238960 * q^76 + 823436432 * q^79 - 1831968312 * q^80 + 3976878598 * q^81 + 953649436 * q^84 - 2328860572 * q^85 + 6633016792 * q^86 + 3239933812 * q^89 + 2239917660 * q^90 - 213407792 * q^91 - 8398362628 * q^94 - 3428426984 * q^95 + 4054813436 * q^96 - 4284595264 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	37.2225i		−	1.64502i	−0.568754	−	0.822508i	$-0.692574\pi$
$2$		−	37.2225i		−	1.64502i	0.568754	−	0.822508i	$-0.307426\pi$
$3$			132.249i			0.942645i	0.881961	+	0.471322i	$0.156223\pi$
$3$			132.249i			0.942645i	−0.881961	+	0.471322i	$0.843777\pi$
$4$	−873.511			−1.70608
$5$	−995.901	−	980.463i	−0.712608	−	0.701562i
$5$	−995.901	−	980.463i	−0.712608	−	0.701562i
$6$	4922.65			1.55067
$7$		−	6816.48i		−	1.07305i	−0.843885	−	0.536524i	$-0.819737\pi$
$7$		−	6816.48i		−	1.07305i	0.843885	−	0.536524i	$-0.180263\pi$
$8$			13456.3i			1.16151i
$9$	2193.09			0.111421
$10$	−36495.2	+	37069.9i	−1.15408	+	1.17225i
$11$	−40762.4			−0.839446			−0.419723	−	0.907652i	$-0.637873\pi$
$11$	−40762.4			−0.839446			−0.419723	+	0.907652i	$0.637873\pi$
$12$		−	115521.i		−	1.60822i
$13$		−	28561.0i		−	0.277350i
$13$		−	28561.0i		−	0.277350i
$14$	−253726.			−1.76518
$15$	129666.	−	131707.i	0.661324	−	0.671737i
$16$	53640.4			0.204622
$17$		−	491145.i		−	1.42623i	−0.701048	−	0.713114i	$-0.747284\pi$
$17$		−	491145.i		−	1.42623i	0.701048	−	0.713114i	$-0.252716\pi$
$18$		−	81632.3i		−	0.183289i
$19$	−713534.			−1.25610			−0.628049	−	0.778174i	$-0.716146\pi$
$19$	−713534.			−1.25610			−0.628049	+	0.778174i	$0.716146\pi$
$20$	869931.	+	856445.i	1.21576	+	1.19692i
$21$	901476.			1.01150
$22$			1.51728e6i			1.38090i
$23$			1.62288e6i			1.20924i	0.796514	+	0.604620i	$0.206675\pi$
$23$			1.62288e6i			1.20924i	−0.796514	+	0.604620i	$0.793325\pi$
$24$	−1.77959e6			−1.09489
$25$	30511.2	+	1.95289e6i	0.0156217	+	0.999878i
$26$	−1.06311e6			−0.456245
$27$			2.89310e6i			1.04767i
$28$			5.95427e6i			1.83070i
$29$	2.06761e6			0.542848			0.271424	−	0.962460i	$-0.412505\pi$
$29$	2.06761e6			0.542848			0.271424	+	0.962460i	$0.412505\pi$
$30$	−4.90247e6	−	4.82647e6i	−1.10502	−	1.08789i
$31$	7.21399e6			1.40297			0.701484	−	0.712685i	$-0.252521\pi$
$31$	7.21399e6			1.40297			0.701484	+	0.712685i	$0.252521\pi$
$32$			4.89302e6i			0.824902i
$33$		−	5.39080e6i		−	0.791299i
$34$	−1.82816e7			−2.34617
$35$	−6.68330e6	+	6.78854e6i	−0.752809	+	0.764663i
$36$	−1.91569e6			−0.190092
$37$		−	6.13511e6i		−	0.538164i	−0.963117	−	0.269082i	$-0.913280\pi$
$37$		−	6.13511e6i		−	0.538164i	0.963117	−	0.269082i	$-0.0867203\pi$
$38$			2.65595e7i			2.06630i
$39$	3.77718e6			0.261443
$40$	1.31934e7	−	1.34012e7i	0.814870	−	0.827700i
$41$	−532270.			−0.0294174			−0.0147087	−	0.999892i	$-0.504682\pi$
$41$	−532270.			−0.0294174			−0.0147087	+	0.999892i	$0.504682\pi$
$42$		−	3.35551e7i		−	1.66394i
$43$			2.95343e7i			1.31740i	0.752405	+	0.658701i	$0.228894\pi$
$43$			2.95343e7i			1.31740i	−0.752405	+	0.658701i	$0.771106\pi$
$44$	3.56064e7			1.43216
$45$	−2.18410e6	−	2.15024e6i	−0.0793993	−	0.0781685i
$46$	6.04077e7			1.98922
$47$		−	2.98650e7i		−	0.892735i	−0.894850	−	0.446368i	$-0.852717\pi$
$47$		−	2.98650e7i		−	0.892735i	0.894850	−	0.446368i	$-0.147283\pi$
$48$			7.09391e6i			0.192886i
$49$	−6.11080e6			−0.151431
$50$	7.26912e7	−	1.13570e6i	1.64482	−	0.0256980i
$51$	6.49536e7			1.34443
$52$			2.49484e7i			0.473181i
$53$			1.01037e8i			1.75890i	0.475994	+	0.879449i	$0.342088\pi$
$53$			1.01037e8i			1.75890i	−0.475994	+	0.879449i	$0.657912\pi$
$54$	1.07688e8			1.72344
$55$	4.05953e7	+	3.99660e7i	0.598196	+	0.588923i
$56$	9.17249e7			1.24635
$57$		−	9.43645e7i		−	1.18405i
$58$		−	7.69617e7i		−	0.892994i
$59$	−1.55968e8			−1.67572			−0.837860	−	0.545886i	$-0.816193\pi$
$59$	−1.55968e8			−1.67572			−0.837860	+	0.545886i	$0.816193\pi$
$60$	−1.13264e8	+	1.15048e8i	−1.12827	+	1.14603i
$61$	−1.25023e7			−0.115612			−0.0578062	−	0.998328i	$-0.518411\pi$
$61$	−1.25023e7			−0.115612			−0.0578062	+	0.998328i	$0.518411\pi$
$62$		−	2.68522e8i		−	2.30790i
$63$		−	1.49492e7i		−	0.119560i
$64$	2.09594e8			1.56160
$65$	−2.80030e7	+	2.84439e7i	−0.194578	+	0.197642i
$66$	−2.00659e8			−1.30170
$67$			1.62345e8i			0.984240i	0.870527	+	0.492120i	$0.163778\pi$
$67$			1.62345e8i			0.984240i	−0.870527	+	0.492120i	$0.836222\pi$
$68$			4.29020e8i			2.43326i
$69$	−2.14625e8			−1.13988
$70$	2.52686e8	+	2.48769e8i	1.25788	+	1.23838i
$71$	−2.03300e8			−0.949457			−0.474728	−	0.880132i	$-0.657454\pi$
$71$	−2.03300e8			−0.949457			−0.474728	+	0.880132i	$0.657454\pi$
$72$			2.95110e7i			0.129416i
$73$		−	1.19966e8i		−	0.494431i	−0.968961	−	0.247215i	$-0.920484\pi$
$73$		−	1.19966e8i		−	0.494431i	0.968961	−	0.247215i	$-0.0795155\pi$
$74$	−2.28364e8			−0.885289
$75$	−2.58268e8	+	4.03508e6i	−0.942530	+	0.0147257i
$76$	6.23280e8			2.14300
$77$			2.77856e8i			0.900766i
$78$		−	1.40596e8i		−	0.430077i
$79$	−1.36039e8			−0.392953			−0.196477	−	0.980509i	$-0.562950\pi$
$79$	−1.36039e8			−0.392953			−0.196477	+	0.980509i	$0.562950\pi$
$80$	−5.34205e7	−	5.25924e7i	−0.145815	−	0.143555i
$81$	−3.39444e8			−0.876165
$82$			1.98124e7i			0.0483921i
$83$		−	6.00605e8i		−	1.38911i	−0.719438	−	0.694557i	$-0.755601\pi$
$83$		−	6.00605e8i		−	1.38911i	0.719438	−	0.694557i	$-0.244399\pi$
$84$	−7.87449e8			−1.72570
$85$	−4.81549e8	+	4.89131e8i	−1.00059	+	1.01634i
$86$	1.09934e9			2.16715
$87$			2.73441e8i			0.511713i
$88$		−	5.48513e8i		−	0.975023i
$89$	2.21485e7			0.0374188			0.0187094	−	0.999825i	$-0.494044\pi$
$89$	2.21485e7			0.0374188			0.0187094	+	0.999825i	$0.494044\pi$
$90$	−8.00374e7	+	8.12976e7i	−0.128588	+	0.130613i
$91$	−1.94685e8			−0.297610
$92$		−	1.41761e9i		−	2.06306i
$93$			9.54046e8i			1.32250i
$94$	−1.11165e9			−1.46856
$95$	7.10609e8	+	6.99593e8i	0.895106	+	0.881230i
$96$	−6.47099e8			−0.777589
$97$			6.11371e8i			0.701185i	0.936528	+	0.350592i	$0.114020\pi$
$97$			6.11371e8i			0.701185i	−0.936528	+	0.350592i	$0.885980\pi$
$98$			2.27459e8i			0.249107i
$99$	−8.93957e7			−0.0935316
$100$	−2.66519e7	−	1.70587e9i	−0.0266519	−	1.70587i
$101$	1.26038e9			1.20519			0.602595	−	0.798047i	$-0.294133\pi$
$101$	1.26038e9			1.20519			0.602595	+	0.798047i	$0.294133\pi$
$102$		−	2.41773e9i		−	2.21160i
$103$		−	4.51112e8i		−	0.394927i	−0.980310	−	0.197463i	$-0.936730\pi$
$103$		−	4.51112e8i		−	0.394927i	0.980310	−	0.197463i	$-0.0632703\pi$
$104$	3.84327e8			0.322144
$105$	−8.97780e8	−	8.83863e8i	−0.720806	−	0.709632i
$106$	3.76086e9			2.89341
$107$			1.12075e9i			0.826571i	0.910601	+	0.413286i	$0.135619\pi$
$107$			1.12075e9i			0.826571i	−0.910601	+	0.413286i	$0.864381\pi$
$108$		−	2.52716e9i		−	1.78741i
$109$	−1.23127e9			−0.835474			−0.417737	−	0.908568i	$-0.637177\pi$
$109$	−1.23127e9			−0.835474			−0.417737	+	0.908568i	$0.637177\pi$
$110$	1.48763e9	−	1.51106e9i	0.968788	−	0.984042i
$111$	8.11365e8			0.507298
$112$		−	3.65639e8i		−	0.219569i
$113$		−	2.16070e9i		−	1.24664i	−0.781967	−	0.623319i	$-0.785784\pi$
$113$		−	2.16070e9i		−	1.24664i	0.781967	−	0.623319i	$-0.214216\pi$
$114$	−3.51248e9			−1.94779
$115$	1.59118e9	−	1.61623e9i	0.848356	−	0.861714i
$116$	−1.80608e9			−0.926141
$117$		−	6.26369e7i		−	0.0309025i
$118$			5.80551e9i			2.75658i
$119$	−3.34788e9			−1.53041
$120$	1.77230e9	+	1.74483e9i	0.780228	+	0.768133i
$121$	−6.96374e8			−0.295330
$122$			4.65365e8i			0.190184i
$123$		−	7.03924e7i		−	0.0277302i
$124$	−6.30150e9			−2.39357
$125$	1.88435e9	−	1.97480e9i	0.690344	−	0.723481i
$126$	−5.56445e8			−0.196678
$127$			3.64303e9i			1.24264i	0.783556	+	0.621321i	$0.213404\pi$
$127$			3.64303e9i			1.24264i	−0.783556	+	0.621321i	$0.786596\pi$
$128$		−	5.29638e9i		−	1.74395i
$129$	−3.90589e9			−1.24184
$130$	1.05875e9	+	1.04234e9i	0.325124	+	0.320084i
$131$	−4.88121e9			−1.44813			−0.724064	−	0.689733i	$-0.757728\pi$
$131$	−4.88121e9			−1.44813			−0.724064	+	0.689733i	$0.757728\pi$
$132$			4.70893e9i			1.35002i
$133$			4.86379e9i			1.34785i
$134$	6.04286e9			1.61909
$135$	2.83658e9	−	2.88124e9i	0.735009	−	0.746582i
$136$	6.60901e9			1.65658
$137$			1.73487e9i			0.420749i	0.977621	+	0.210375i	$0.0674684\pi$
$137$			1.73487e9i			0.420749i	−0.977621	+	0.210375i	$0.932532\pi$
$138$			7.98889e9i			1.87513i
$139$	−6.60807e8			−0.150144			−0.0750720	−	0.997178i	$-0.523919\pi$
$139$	−6.60807e8			−0.150144			−0.0750720	+	0.997178i	$0.523919\pi$
$140$	5.83794e9	−	5.92986e9i	1.28435	−	1.30457i
$141$	3.94963e9			0.841532
$142$			7.56733e9i			1.56187i
$143$			1.16422e9i			0.232820i
$144$	1.17638e8			0.0227991
$145$	−2.05914e9	−	2.02722e9i	−0.386838	−	0.380842i
$146$	−4.46543e9			−0.813346
$147$		−	8.08150e8i		−	0.142746i
$148$			5.35909e9i			0.918150i
$149$	5.03914e9			0.837565			0.418782	−	0.908087i	$-0.362457\pi$
$149$	5.03914e9			0.837565			0.418782	+	0.908087i	$0.362457\pi$
$150$	1.50196e8	+	9.61337e9i	0.0242241	+	1.55048i
$151$	−3.22365e8			−0.0504606			−0.0252303	−	0.999682i	$-0.508032\pi$
$151$	−3.22365e8			−0.0504606			−0.0252303	+	0.999682i	$0.508032\pi$
$152$		−	9.60156e9i		−	1.45897i
$153$		−	1.07713e9i		−	0.158911i
$154$	1.03425e10			1.48177
$155$	−7.18442e9	−	7.07305e9i	−0.999767	−	0.984269i
$156$	−3.29941e9			−0.446041
$157$			2.20422e9i			0.289539i	0.989465	+	0.144769i	$0.0462440\pi$
$157$			2.20422e9i			0.289539i	−0.989465	+	0.144769i	$0.953756\pi$
$158$			5.06370e9i			0.646414i
$159$	−1.33621e10			−1.65802
$160$	4.79742e9	−	4.87296e9i	0.578720	−	0.587832i
$161$	1.10624e10			1.29757
$162$			1.26349e10i			1.44130i
$163$		−	3.76557e9i		−	0.417818i	−0.977935	−	0.208909i	$-0.933009\pi$
$163$		−	3.76557e9i		−	0.417818i	0.977935	−	0.208909i	$-0.0669912\pi$
$164$	4.64944e8			0.0501884
$165$	−5.28548e9	+	5.36871e9i	−0.555146	+	0.563887i
$166$	−2.23560e10			−2.28511
$167$		−	1.63486e10i		−	1.62651i	−0.581906	−	0.813256i	$-0.697693\pi$
$167$		−	1.63486e10i		−	1.62651i	0.581906	−	0.813256i	$-0.302307\pi$
$168$			1.21306e10i			1.17487i
$169$	−8.15731e8			−0.0769231
$170$	1.82067e10	+	1.79244e10i	1.67190	+	1.64598i
$171$	−1.56485e9			−0.139955
$172$		−	2.57985e10i		−	2.24759i
$173$		−	1.35401e10i		−	1.14925i	−0.818418	−	0.574624i	$-0.805148\pi$
$173$		−	1.35401e10i		−	1.14925i	0.818418	−	0.574624i	$-0.194852\pi$
$174$	1.01781e10			0.841776
$175$	1.33118e10	−	2.07979e8i	1.07292	−	0.0167629i
$176$	−2.18651e9			−0.171769
$177$		−	2.06267e10i		−	1.57961i
$178$		−	8.24422e8i		−	0.0615544i
$179$	−1.49939e10			−1.09163			−0.545817	−	0.837905i	$-0.683781\pi$
$179$	−1.49939e10			−1.09163			−0.545817	+	0.837905i	$0.683781\pi$
$180$	1.90784e9	+	1.87826e9i	0.135461	+	0.133361i
$181$	1.82087e10			1.26103			0.630514	−	0.776178i	$-0.282844\pi$
$181$	1.82087e10			1.26103			0.630514	+	0.776178i	$0.282844\pi$
$182$			7.24667e9i			0.489573i
$183$		−	1.65342e9i		−	0.108981i
$184$	−2.18381e10			−1.40454
$185$	−6.01525e9	+	6.10996e9i	−0.377556	+	0.383500i
$186$	3.55119e10			2.17553
$187$			2.00202e10i			1.19724i
$188$			2.60874e10i			1.52307i
$189$	1.97208e10			1.12421
$190$	2.60406e10	−	2.64506e10i	1.44964	−	1.47246i
$191$	9.54730e9			0.519075			0.259538	−	0.965733i	$-0.416430\pi$
$191$	9.54730e9			0.519075			0.259538	+	0.965733i	$0.416430\pi$
$192$			2.77187e10i			1.47203i
$193$			6.05753e8i			0.0314259i	0.999877	+	0.0157129i	$0.00500179\pi$
$193$			6.05753e8i			0.0314259i	−0.999877	+	0.0157129i	$0.994998\pi$
$194$	2.27567e10			1.15346
$195$	−3.76169e9	−	3.70338e9i	−0.186306	−	0.183418i
$196$	5.33785e9			0.258353
$197$			4.53488e9i			0.214520i	0.994231	+	0.107260i	$0.0342077\pi$
$197$			4.53488e9i			0.214520i	−0.994231	+	0.107260i	$0.965792\pi$
$198$			3.32753e9i			0.153861i
$199$	−2.63037e10			−1.18899			−0.594494	−	0.804100i	$-0.702648\pi$
$199$	−2.63037e10			−1.18899			−0.594494	+	0.804100i	$0.702648\pi$
$200$	−2.62787e10	+	4.10569e8i	−1.16137	+	0.0181448i
$201$	−2.14700e10			−0.927789
$202$		−	4.69145e10i		−	1.98256i
$203$		−	1.40938e10i		−	0.582502i
$204$	−5.67377e10			−2.29370
$205$	5.30088e8	+	5.21871e8i	0.0209631	+	0.0206382i
$206$	−1.67915e10			−0.649661
$207$			3.55913e9i			0.134734i
$208$		−	1.53202e9i		−	0.0567519i
$209$	2.90854e10			1.05443
$210$	−3.28996e10	+	3.34176e10i	−1.16736	+	1.18574i
$211$	−4.77575e10			−1.65871			−0.829355	−	0.558721i	$-0.811292\pi$
$211$	−4.77575e10			−1.65871			−0.829355	+	0.558721i	$0.811292\pi$
$212$		−	8.82573e10i		−	3.00081i
$213$		−	2.68863e10i		−	0.895001i
$214$	4.17169e10			1.35972
$215$	2.89572e10	−	2.94132e10i	0.924239	−	0.938792i
$216$	−3.89306e10			−1.21688
$217$		−	4.91740e10i		−	1.50545i
$218$			4.58308e10i			1.37437i
$219$	1.58654e10			0.466073
$220$	−3.54605e10	−	3.49108e10i	−1.02057	−	1.00475i
$221$	−1.40276e10			−0.395565
$222$		−	3.02010e10i		−	0.834513i
$223$			6.38736e10i			1.72961i	0.502104	+	0.864807i	$0.332559\pi$
$223$			6.38736e10i			1.72961i	−0.502104	+	0.864807i	$0.667441\pi$
$224$	3.33532e10			0.885159
$225$	6.69138e7	+	4.28286e9i	0.00174058	+	0.111407i
$226$	−8.04264e10			−2.05074
$227$			4.22941e10i			1.05722i	0.848866	+	0.528608i	$0.177286\pi$
$227$			4.22941e10i			1.05722i	−0.848866	+	0.528608i	$0.822714\pi$
$228$			8.24284e10i			2.02009i
$229$	−2.40369e10			−0.577588			−0.288794	−	0.957391i	$-0.593254\pi$
$229$	−2.40369e10			−0.577588			−0.288794	+	0.957391i	$0.593254\pi$
$230$	−6.01601e10	−	5.92275e10i	−1.41753	−	1.39556i
$231$	−3.67463e10			−0.849102
$232$			2.78225e10i			0.630522i
$233$		−	6.02252e10i		−	1.33868i	−0.742957	−	0.669339i	$-0.766577\pi$
$233$		−	6.02252e10i		−	1.33868i	0.742957	−	0.669339i	$-0.233423\pi$
$234$	−2.33150e9			−0.0508351
$235$	−2.92815e10	+	2.97426e10i	−0.626309	+	0.636171i
$236$	1.36240e11			2.85891
$237$		−	1.79911e10i		−	0.370415i
$238$			1.24616e11i			2.51755i
$239$	1.55942e9			0.0309153			0.0154577	−	0.999881i	$-0.495079\pi$
$239$	1.55942e9			0.0309153			0.0154577	+	0.999881i	$0.495079\pi$
$240$	6.95531e9	−	7.06483e9i	0.135321	−	0.137452i
$241$	−3.22896e10			−0.616575			−0.308288	−	0.951293i	$-0.599756\pi$
$241$	−3.22896e10			−0.616575			−0.308288	+	0.951293i	$0.599756\pi$
$242$			2.59207e10i			0.485823i
$243$			1.20536e10i			0.221763i
$244$	1.09209e10			0.197244
$245$	6.08575e9	+	5.99141e9i	0.107911	+	0.106238i
$246$	−2.62018e9			−0.0456166
$247$			2.03792e10i			0.348379i
$248$			9.70739e10i			1.62956i
$249$	7.94297e10			1.30944
$250$	−7.35068e10	−	7.01400e10i	−1.19014	−	1.13563i
$251$	1.05445e11			1.67685			0.838424	−	0.545019i	$-0.183478\pi$
$251$	1.05445e11			1.67685			0.838424	+	0.545019i	$0.183478\pi$
$252$			1.30583e10i			0.203978i
$253$		−	6.61527e10i		−	1.01509i
$254$	1.35602e11			2.04416
$255$	−6.46873e10	−	6.36846e10i	−0.958050	−	0.943199i
$256$	−8.98322e10			−1.30723
$257$		−	8.39088e10i		−	1.19980i	−0.800075	−	0.599900i	$-0.795207\pi$
$257$		−	8.39088e10i		−	1.19980i	0.800075	−	0.599900i	$-0.204793\pi$
$258$			1.45387e11i			2.04285i
$259$	−4.18199e10			−0.577476
$260$	2.44609e10	−	2.48461e10i	0.331966	−	0.337193i
$261$	4.53447e9			0.0604845
$262$			1.81691e11i			2.38219i
$263$		−	7.08565e10i		−	0.913227i	−0.889665	−	0.456613i	$-0.849062\pi$
$263$		−	7.08565e10i		−	0.913227i	0.889665	−	0.456613i	$-0.150938\pi$
$264$	7.25405e10			0.919101
$265$	9.90633e10	−	1.00623e11i	1.23398	−	1.25341i
$266$	1.81042e11			2.21724
$267$			2.92913e9i			0.0352726i
$268$		−	1.41810e11i		−	1.67919i
$269$	−9.05787e9			−0.105473			−0.0527364	−	0.998608i	$-0.516794\pi$
$269$	−9.05787e9			−0.105473			−0.0527364	+	0.998608i	$0.516794\pi$
$270$	−1.07247e11	−	1.05584e11i	−1.22814	−	1.20910i
$271$	−9.36362e10			−1.05459			−0.527293	−	0.849683i	$-0.676793\pi$
$271$	−9.36362e10			−1.05459			−0.527293	+	0.849683i	$0.676793\pi$
$272$		−	2.63452e10i		−	0.291837i
$273$		−	2.57470e10i		−	0.280540i
$274$	6.45760e10			0.692139
$275$	−1.24371e9	−	7.96044e10i	−0.0131136	−	0.839344i
$276$	1.87478e11			1.94473
$277$			1.77801e11i			1.81458i	0.420511	+	0.907288i	$0.361851\pi$
$277$			1.77801e11i			1.81458i	−0.420511	+	0.907288i	$0.638149\pi$
$278$			2.45969e10i			0.246989i
$279$	1.58209e10			0.156320
$280$	−9.13489e10	−	8.99328e10i	−0.888162	−	0.874394i
$281$	−5.62732e10			−0.538422			−0.269211	−	0.963081i	$-0.586763\pi$
$281$	−5.62732e10			−0.538422			−0.269211	+	0.963081i	$0.586763\pi$
$282$		−	1.47015e11i		−	1.38433i
$283$			8.99873e10i			0.833955i	0.908917	+	0.416977i	$0.136911\pi$
$283$			8.99873e10i			0.833955i	−0.908917	+	0.416977i	$0.863089\pi$
$284$	1.77585e11			1.61985
$285$	−9.25208e10	+	9.39776e10i	−0.830687	+	0.843767i
$286$	4.33350e10			0.382993
$287$			3.62821e9i			0.0315663i
$288$			1.07308e10i			0.0919111i
$289$	−1.22635e11			−1.03413
$290$	−7.54580e10	+	7.66462e10i	−0.626490	+	0.636355i
$291$	−8.08535e10			−0.660968
$292$			1.04792e11i			0.843537i
$293$			9.29810e10i			0.737038i	0.929620	+	0.368519i	$0.120135\pi$
$293$			9.29810e10i			0.737038i	−0.929620	+	0.368519i	$0.879865\pi$
$294$	−3.00813e10			−0.234819
$295$	1.55329e11	+	1.52921e11i	1.19413	+	1.17562i
$296$	8.25562e10			0.625082
$297$		−	1.17930e11i		−	0.879467i
$298$		−	1.87569e11i		−	1.37781i
$299$	4.63512e10			0.335383
$300$	2.25600e11	−	3.52469e9i	1.60803	−	0.0251232i
$301$	2.01320e11			1.41363
$302$			1.19992e10i			0.0830084i
$303$			1.66685e11i			1.13607i
$304$	−3.82742e10			−0.257025
$305$	1.24510e10	+	1.22580e10i	0.0823864	+	0.0811092i
$306$	−4.00933e10			−0.261412
$307$		−	2.69852e10i		−	0.173381i	−0.996235	−	0.0866907i	$-0.972371\pi$
$307$		−	2.69852e10i		−	0.173381i	0.996235	−	0.0866907i	$-0.0276292\pi$
$308$		−	2.42711e11i		−	1.53678i
$309$	5.96592e10			0.372276
$310$	−2.63276e11	+	2.67422e11i	−1.61914	+	1.64463i
$311$	−2.25101e11			−1.36445			−0.682223	−	0.731144i	$-0.738987\pi$
$311$	−2.25101e11			−1.36445			−0.682223	+	0.731144i	$0.738987\pi$
$312$			5.08270e10i			0.303668i
$313$			4.35700e10i			0.256589i	0.991736	+	0.128295i	$0.0409503\pi$
$313$			4.35700e10i			0.256589i	−0.991736	+	0.128295i	$0.959050\pi$
$314$	8.20466e10			0.476296
$315$	−1.46571e10	+	1.48879e10i	−0.0838785	+	0.0851992i
$316$	1.18831e11			0.670408
$317$			2.47102e11i			1.37439i	0.726475	+	0.687193i	$0.241157\pi$
$317$			2.47102e11i			1.37439i	−0.726475	+	0.687193i	$0.758843\pi$
$318$			4.97371e11i			2.72746i
$319$	−8.42809e10			−0.455692
$320$	−2.08735e11	−	2.05499e11i	−1.11281	−	1.09556i
$321$	−1.48218e11			−0.779163
$322$		−	4.11768e11i		−	2.13453i
$323$			3.50448e11i			1.79148i
$324$	2.96508e11			1.49480
$325$	5.57764e10	−	8.71430e8i	0.277316	−	0.00433269i
$326$	−1.40164e11			−0.687316
$327$		−	1.62834e11i		−	0.787555i
$328$		−	7.16241e9i		−	0.0341686i
$329$	−2.03574e11			−0.957947
$330$	1.99836e11	+	1.96739e11i	0.927603	+	0.913223i
$331$	−2.07256e11			−0.949032			−0.474516	−	0.880247i	$-0.657377\pi$
$331$	−2.07256e11			−0.949032			−0.474516	+	0.880247i	$0.657377\pi$
$332$			5.24635e11i			2.36993i
$333$		−	1.34549e10i		−	0.0599626i
$334$	−6.08536e11			−2.67564
$335$	1.59173e11	−	1.61679e11i	0.690505	−	0.701378i
$336$	4.83555e10			0.206976
$337$		−	7.53957e10i		−	0.318429i	−0.987244	−	0.159214i	$-0.949104\pi$
$337$		−	7.53957e10i		−	0.318429i	0.987244	−	0.159214i	$-0.0508961\pi$
$338$			3.03635e10i			0.126540i
$339$	2.85751e11			1.17514
$340$	4.20638e11	−	4.27262e11i	1.70708	−	1.73396i
$341$	−2.94060e11			−1.17772
$342$			5.82474e10i			0.230229i
$343$		−	2.33415e11i		−	0.910555i
$344$	−3.97423e11			−1.53017
$345$	2.13746e11	+	2.10432e11i	0.812290	+	0.799699i
$346$	−5.03995e11			−1.89053
$347$		−	3.72852e11i		−	1.38056i	−0.723545	−	0.690278i	$-0.757488\pi$
$347$		−	3.72852e11i		−	1.38056i	0.723545	−	0.690278i	$-0.242512\pi$
$348$		−	2.38854e11i		−	0.873022i
$349$	−1.75594e11			−0.633570			−0.316785	−	0.948497i	$-0.602603\pi$
$349$	−1.75594e11			−0.633570			−0.316785	+	0.948497i	$0.602603\pi$
$350$	−7.74148e9	−	4.95498e11i	−0.0275752	−	1.76496i
$351$	8.26298e10			0.290573
$352$		−	1.99451e11i		−	0.692460i
$353$			4.04373e11i			1.38610i	0.720887	+	0.693052i	$0.243735\pi$
$353$			4.04373e11i			1.38610i	−0.720887	+	0.693052i	$0.756265\pi$
$354$	−7.67775e11			−2.59848
$355$	2.02467e11	+	1.99328e11i	0.676591	+	0.666103i
$356$	−1.93470e10			−0.0638393
$357$		−	4.42755e11i		−	1.44263i
$358$			5.58111e11i			1.79575i
$359$	−1.84093e11			−0.584941			−0.292471	−	0.956275i	$-0.594477\pi$
$359$	−1.84093e11			−0.584941			−0.292471	+	0.956275i	$0.594477\pi$
$360$	2.89344e10	−	2.93900e10i	0.0907933	−	0.0922229i
$361$	1.86443e11			0.577782
$362$		−	6.77771e11i		−	2.07441i
$363$		−	9.20950e10i		−	0.278392i
$364$	1.70060e11			0.507745
$365$	−1.17622e11	+	1.19474e11i	−0.346874	+	0.352335i
$366$	−6.15442e10			−0.179276
$367$			2.79309e11i			0.803689i	0.915708	+	0.401845i	$0.131631\pi$
$367$			2.79309e11i			0.803689i	−0.915708	+	0.401845i	$0.868369\pi$
$368$			8.70521e10i			0.247437i
$369$	−1.16732e9			−0.00327771
$370$	2.27428e11	+	2.23902e11i	0.630864	+	0.621085i
$371$	6.88719e11			1.88738
$372$		−	8.33370e11i		−	2.25629i
$373$		−	5.69504e11i		−	1.52338i	−0.647944	−	0.761688i	$-0.724371\pi$
$373$		−	5.69504e11i		−	1.52338i	0.647944	−	0.761688i	$-0.275629\pi$
$374$	7.45202e11			1.96948
$375$	2.61166e11	+	2.49204e11i	0.681986	+	0.650749i
$376$	4.01874e11			1.03692
$377$		−	5.90531e10i		−	0.150559i
$378$		−	7.34055e11i		−	1.84934i
$379$	−5.46281e10			−0.136000			−0.0680001	−	0.997685i	$-0.521662\pi$
$379$	−5.46281e10			−0.136000			−0.0680001	+	0.997685i	$0.521662\pi$
$380$	−6.20725e11	−	6.11103e11i	−1.52712	−	1.50345i
$381$	−4.81788e11			−1.17137
$382$		−	3.55374e11i		−	0.853887i
$383$			5.83372e11i			1.38532i	0.721263	+	0.692661i	$0.243562\pi$
$383$			5.83372e11i			1.38532i	−0.721263	+	0.692661i	$0.756438\pi$
$384$	7.00444e11			1.64393
$385$	2.72428e11	−	2.76717e11i	0.631943	−	0.641893i
$386$	2.25476e10			0.0516961
$387$			6.47714e10i			0.146786i
$388$		−	5.34040e11i		−	1.19627i
$389$	−4.24751e11			−0.940506			−0.470253	−	0.882532i	$-0.655837\pi$
$389$	−4.24751e11			−0.940506			−0.470253	+	0.882532i	$0.655837\pi$
$390$	−1.37849e11	+	1.40019e11i	−0.301726	+	0.306477i
$391$	7.97071e11			1.72465
$392$		−	8.22290e10i		−	0.175889i
$393$		−	6.45538e11i		−	1.36507i
$394$	1.68799e11			0.352889
$395$	1.35481e11	+	1.33381e11i	0.280022	+	0.275681i
$396$	7.80882e10			0.159572
$397$			1.61966e11i			0.327241i	0.986523	+	0.163620i	$0.0523172\pi$
$397$			1.61966e11i			0.327241i	−0.986523	+	0.163620i	$0.947683\pi$
$398$			9.79088e11i			1.95590i
$399$	−6.43233e11			−1.27055
$400$	1.63663e9	+	1.04754e11i	0.00319654	+	0.204597i
$401$	1.70193e11			0.328695			0.164347	−	0.986403i	$-0.447448\pi$
$401$	1.70193e11			0.328695			0.164347	+	0.986403i	$0.447448\pi$
$402$			7.99165e11i			1.52623i
$403$		−	2.06039e11i		−	0.389113i
$404$	−1.10096e12			−2.05615
$405$	3.38053e11	+	3.32812e11i	0.624362	+	0.614684i
$406$	−5.24608e11			−0.958225
$407$			2.50082e11i			0.451760i
$408$			8.74038e11i			1.56156i
$409$	4.66309e11			0.823985			0.411992	−	0.911187i	$-0.364833\pi$
$409$	4.66309e11			0.823985			0.411992	+	0.911187i	$0.364833\pi$
$410$	1.94253e10	−	1.97312e10i	0.0339501	−	0.0344847i
$411$	−2.29435e11			−0.396617
$412$			3.94051e11i			0.673775i
$413$			1.06315e12i			1.79813i
$414$	1.32480e11			0.221640
$415$	−5.88871e11	+	5.98143e11i	−0.974549	+	0.989894i
$416$	1.39750e11			0.228787
$417$		−	8.73913e10i		−	0.141532i
$418$		−	1.08263e12i		−	1.73455i
$419$	1.12343e12			1.78066			0.890331	−	0.455313i	$-0.150473\pi$
$419$	1.12343e12			1.78066			0.890331	+	0.455313i	$0.150473\pi$
$420$	7.84221e11	+	7.72064e11i	1.22975	+	1.21069i
$421$	1.85868e11			0.288361			0.144180	−	0.989551i	$-0.453945\pi$
$421$	1.85868e11			0.288361			0.144180	+	0.989551i	$0.453945\pi$
$422$			1.77765e12i			2.72861i
$423$		−	6.54968e10i		−	0.0994691i
$424$	−1.35959e12			−2.04297
$425$	9.59150e11	−	1.49854e10i	1.42605	−	0.0222801i
$426$	−1.00078e12			−1.47229
$427$			8.52214e10i			0.124058i
$428$		−	9.78984e11i		−	1.41019i
$429$	−1.53967e11			−0.219467
$430$	−1.09483e12	−	1.07786e12i	−1.54433	−	1.52039i
$431$	−9.96119e11			−1.39048			−0.695238	−	0.718780i	$-0.744701\pi$
$431$	−9.96119e11			−1.39048			−0.695238	+	0.718780i	$0.744701\pi$
$432$			1.55187e11i			0.214377i
$433$			7.07735e11i			0.967554i	0.875191	+	0.483777i	$0.160735\pi$
$433$			7.07735e11i			0.967554i	−0.875191	+	0.483777i	$0.839265\pi$
$434$	−1.83038e12			−2.47649
$435$	2.68098e11	−	2.72320e11i	0.358998	−	0.364651i
$436$	1.07553e12			1.42538
$437$		−	1.15798e12i		−	1.51892i
$438$		−	5.90551e11i		−	0.766697i
$439$	−5.59583e11			−0.719075			−0.359537	−	0.933131i	$-0.617066\pi$
$439$	−5.59583e11			−0.719075			−0.359537	+	0.933131i	$0.617066\pi$
$440$	−5.37797e11	+	5.46264e11i	−0.684039	+	0.694810i
$441$	−1.34015e10			−0.0168726
$442$			5.22141e11i			0.650710i
$443$		−	9.38157e11i		−	1.15733i	−0.815564	−	0.578667i	$-0.803573\pi$
$443$		−	9.38157e11i		−	1.15733i	0.815564	−	0.578667i	$-0.196427\pi$
$444$	−7.08737e11			−0.865489
$445$	−2.20577e10	−	2.17158e10i	−0.0266649	−	0.0262516i
$446$	2.37753e12			2.84524
$447$			6.66424e11i			0.789526i
$448$		−	1.42869e12i		−	1.67567i
$449$	−9.59461e11			−1.11409			−0.557043	−	0.830484i	$-0.688064\pi$
$449$	−9.59461e11			−1.11409			−0.557043	+	0.830484i	$0.688064\pi$
$450$	1.59419e11	−	2.49070e9i	0.183266	−	0.00286328i
$451$	2.16966e10			0.0246943
$452$			1.88739e12i			2.12686i
$453$		−	4.26326e10i		−	0.0475664i
$454$	1.57429e12			1.73914
$455$	1.93887e11	+	1.90882e11i	0.212079	+	0.208792i
$456$	1.26980e12			1.37529
$457$			1.57983e12i			1.69429i	0.531364	+	0.847144i	$0.321680\pi$
$457$			1.57983e12i			1.69429i	−0.531364	+	0.847144i	$0.678320\pi$
$458$			8.94711e11i			0.950141i
$459$	1.42093e12			1.49422
$460$	−1.38991e12	+	1.41180e12i	−1.44736	+	1.47015i
$461$	−8.03099e10			−0.0828161			−0.0414080	−	0.999142i	$-0.513184\pi$
$461$	−8.03099e10			−0.0828161			−0.0414080	+	0.999142i	$0.513184\pi$
$462$			1.36779e12i			1.39679i
$463$		−	1.49606e12i		−	1.51299i	−0.654001	−	0.756494i	$-0.726911\pi$
$463$		−	1.49606e12i		−	1.51299i	0.654001	−	0.756494i	$-0.273089\pi$
$464$	1.10908e11			0.111079
$465$	9.35406e11	−	9.50135e11i	0.927816	−	0.942425i
$466$	−2.24173e12			−2.20215
$467$			5.13408e11i			0.499501i	0.968310	+	0.249750i	$0.0803486\pi$
$467$			5.13408e11i			0.499501i	−0.968310	+	0.249750i	$0.919651\pi$
$468$			5.47141e10i			0.0527221i
$469$	1.10662e12			1.05614
$470$	1.10709e12	+	1.08993e12i	1.04651	+	1.03029i
$471$	−2.91507e11			−0.272932
$472$		−	2.09876e12i		−	1.94636i
$473$		−	1.20389e12i		−	1.10589i
$474$	−6.69671e11			−0.609339
$475$	−2.17708e10	−	1.39345e12i	−0.0196224	−	1.25594i
$476$	2.92441e12			2.61100
$477$			2.21584e11i			0.195977i
$478$		−	5.80456e10i		−	0.0508562i
$479$	2.14608e12			1.86267			0.931335	−	0.364163i	$-0.118645\pi$
$479$	2.14608e12			1.86267			0.931335	+	0.364163i	$0.118645\pi$
$480$	6.44447e11	+	6.34457e11i	0.554117	+	0.545527i
$481$	−1.75225e11			−0.149260
$482$			1.20190e12i			1.01428i
$483$			1.46299e12i			1.22315i
$484$	6.08290e11			0.503857
$485$	5.99427e11	−	6.08865e11i	0.491924	−	0.499670i
$486$	4.48665e11			0.364803
$487$		−	1.20344e12i		−	0.969489i	−0.874656	−	0.484745i	$-0.838913\pi$
$487$		−	1.20344e12i		−	0.969489i	0.874656	−	0.484745i	$-0.161087\pi$
$488$		−	1.68235e11i		−	0.134285i
$489$	4.97995e11			0.393854
$490$	2.23015e11	−	2.26527e11i	0.174764	−	0.177516i
$491$	−1.67385e12			−1.29972			−0.649858	−	0.760055i	$-0.725172\pi$
$491$	−1.67385e12			−1.29972			−0.649858	+	0.760055i	$0.725172\pi$
$492$			6.14886e10i			0.0473098i
$493$		−	1.01550e12i		−	0.774226i
$494$	7.58566e11			0.573089
$495$	8.90293e10	+	8.76492e10i	0.0666514	+	0.0656182i
$496$	3.86961e11			0.287078
$497$			1.38579e12i			1.01881i
$498$		−	2.95657e12i		−	2.15405i
$499$	5.48884e11			0.396304			0.198152	−	0.980171i	$-0.436506\pi$
$499$	5.48884e11			0.396304			0.198152	+	0.980171i	$0.436506\pi$
$500$	−1.64600e12	+	1.72501e12i	−1.17778	+	1.23431i
$501$	2.16210e12			1.53322
$502$		−	3.92492e12i		−	2.75844i
$503$			1.49726e12i			1.04289i	0.853283	+	0.521447i	$0.174608\pi$
$503$			1.49726e12i			1.04289i	−0.853283	+	0.521447i	$0.825392\pi$
$504$	2.01161e11			0.138869
$505$	−1.25521e12	−	1.23576e12i	−0.858829	−	0.845516i
$506$	−2.46236e12			−1.66984
$507$		−	1.07880e11i		−	0.0725111i
$508$		−	3.18223e12i		−	2.12004i
$509$	−3.00504e12			−1.98436			−0.992179	−	0.124822i	$-0.960164\pi$
$509$	−3.00504e12			−1.98436			−0.992179	+	0.124822i	$0.960164\pi$
$510$	−2.37050e12	+	2.40782e12i	−1.55158	+	1.57601i
$511$	−8.17746e11			−0.530548
$512$			6.32027e11i			0.406463i
$513$		−	2.06433e12i		−	1.31598i
$514$	−3.12329e12			−1.97369
$515$	−4.42298e11	+	4.49262e11i	−0.277066	+	0.281428i
$516$	3.41184e12			2.11868
$517$			1.21737e12i			0.749403i
$518$			1.55664e12i			0.949957i
$519$	1.79067e12			1.08333
$520$	−3.82751e11	−	3.76818e11i	−0.229563	−	0.226004i
$521$	−1.15582e12			−0.687258			−0.343629	−	0.939105i	$-0.611656\pi$
$521$	−1.15582e12			−0.687258			−0.343629	+	0.939105i	$0.611656\pi$
$522$		−	1.68784e11i		−	0.0994979i
$523$			1.64038e12i			0.958710i	0.877621	+	0.479355i	$0.159129\pi$
$523$			1.64038e12i			0.958710i	−0.877621	+	0.479355i	$0.840871\pi$
$524$	4.26380e12			2.47062
$525$	2.75051e10	+	1.76048e12i	0.0158014	+	1.01138i
$526$	−2.63745e12			−1.50227
$527$		−	3.54311e12i		−	2.00095i
$528$		−	2.89165e11i		−	0.161917i
$529$	−8.32600e11			−0.462260
$530$	−3.74544e12	−	3.68738e12i	−2.06187	−	2.02991i
$531$	−3.42052e11			−0.186710
$532$		−	4.24858e12i		−	2.29954i
$533$			1.52022e10i			0.00815893i
$534$	1.09029e11			0.0580240
$535$	1.09885e12	−	1.11615e12i	0.579891	−	0.589022i
$536$	−2.18456e12			−1.14320
$537$		−	1.98294e12i		−	1.02902i
$538$			3.37156e11i			0.173504i
$539$	2.49091e11			0.127118
$540$	−2.47778e12	+	2.51680e12i	−1.25398	+	1.27373i
$541$	−6.56694e11			−0.329591			−0.164796	−	0.986328i	$-0.552696\pi$
$541$	−6.56694e11			−0.329591			−0.164796	+	0.986328i	$0.552696\pi$
$542$			3.48537e12i			1.73481i
$543$			2.40809e12i			1.18870i
$544$	2.40318e12			1.17650
$545$	1.22622e12	+	1.20721e12i	0.595366	+	0.586137i
$546$	−9.58368e11			−0.461493
$547$			1.75594e12i			0.838621i	0.907843	+	0.419311i	$0.137728\pi$
$547$			1.75594e12i			0.838621i	−0.907843	+	0.419311i	$0.862272\pi$
$548$		−	1.51543e12i		−	0.717831i
$549$	−2.74186e10			−0.0128816
$550$	−2.96307e12	+	4.62939e10i	−1.38073	+	0.0215721i
$551$	−1.47531e12			−0.681870
$552$		−	2.88807e12i		−	1.32398i
$553$			9.27306e11i			0.421658i
$554$	6.61819e12			2.98500
$555$	−8.08039e11	−	7.95513e11i	−0.361505	−	0.355901i
$556$	5.77222e11			0.256157
$557$			7.12754e11i			0.313755i	0.987618	+	0.156878i	$0.0501428\pi$
$557$			7.12754e11i			0.313755i	−0.987618	+	0.156878i	$0.949857\pi$
$558$		−	5.88894e11i		−	0.257148i
$559$	8.43528e11			0.365381
$560$	−3.58495e11	+	3.64140e11i	−0.154041	+	0.156467i
$561$	−2.64766e12			−1.12857
$562$			2.09463e12i			0.885713i
$563$			1.27950e12i			0.536725i	0.963318	+	0.268362i	$0.0864825\pi$
$563$			1.27950e12i			0.536725i	−0.963318	+	0.268362i	$0.913518\pi$
$564$	−3.45005e12			−1.43572
$565$	−2.11848e12	+	2.15184e12i	−0.874594	+	0.888365i
$566$	3.34955e12			1.37187
$567$			2.31381e12i			0.940167i
$568$		−	2.73568e12i		−	1.10280i
$569$	1.72251e12			0.688901			0.344450	−	0.938804i	$-0.388065\pi$
$569$	1.72251e12			0.688901			0.344450	+	0.938804i	$0.388065\pi$
$570$	3.49808e12	+	3.44385e12i	1.38801	+	1.36649i
$571$	−3.40060e12			−1.33873			−0.669366	−	0.742933i	$-0.733434\pi$
$571$	−3.40060e12			−1.33873			−0.669366	+	0.742933i	$0.733434\pi$
$572$		−	1.01696e12i		−	0.397210i
$573$			1.26262e12i			0.489304i
$574$	1.35051e11			0.0519271
$575$	−3.16931e12	+	4.95161e10i	−1.20909	+	0.0188904i
$576$	4.59659e11			0.173994
$577$			1.32866e11i			0.0499027i	0.999689	+	0.0249513i	$0.00794308\pi$
$577$			1.32866e11i			0.0499027i	−0.999689	+	0.0249513i	$0.992057\pi$
$578$			4.56478e12i			1.70116i
$579$	−8.01104e10			−0.0296234
$580$	1.79868e12	+	1.77080e12i	0.659976	+	0.649745i
$581$	−4.09401e12			−1.49058
$582$			3.00957e12i			1.08730i
$583$		−	4.11853e12i		−	1.47650i
$584$	1.61430e12			0.574285
$585$	−6.14131e10	+	6.23801e10i	−0.0216800	+	0.0220214i
$586$	3.46098e12			1.21244
$587$		−	1.22335e12i		−	0.425284i	−0.977130	−	0.212642i	$-0.931793\pi$
$587$		−	1.22335e12i		−	0.425284i	0.977130	−	0.212642i	$-0.0682069\pi$
$588$			7.05928e11i			0.243536i
$589$	−5.14743e12			−1.76227
$590$	5.69209e12	−	5.78171e12i	1.93392	−	1.96437i
$591$	−5.99736e11			−0.202216
$592$		−	3.29090e11i		−	0.110120i
$593$			3.47329e11i			0.115344i	0.998336	+	0.0576720i	$0.0183677\pi$
$593$			3.47329e11i			0.115344i	−0.998336	+	0.0576720i	$0.981632\pi$
$594$	−4.38963e12			−1.44674
$595$	3.33415e12	+	3.28247e12i	1.09058	+	1.07368i
$596$	−4.40175e12			−1.42895
$597$		−	3.47865e12i		−	1.12079i
$598$		−	1.72531e12i		−	0.551710i
$599$	1.75228e12			0.556137			0.278069	−	0.960561i	$-0.410306\pi$
$599$	1.75228e12			0.556137			0.278069	+	0.960561i	$0.410306\pi$
$600$	−5.42975e10	−	3.47534e12i	−0.0171041	−	1.09476i
$601$	2.93977e12			0.919133			0.459567	−	0.888143i	$-0.348005\pi$
$601$	2.93977e12			0.919133			0.459567	+	0.888143i	$0.348005\pi$
$602$		−	7.49362e12i		−	2.32545i
$603$			3.56036e11i			0.109665i
$604$	2.81590e11			0.0860896
$605$	6.93519e11	+	6.82768e11i	0.210455	+	0.207193i
$606$	6.20441e12			1.86885
$607$			2.63365e12i			0.787425i	0.919234	+	0.393712i	$0.128809\pi$
$607$			2.63365e12i			0.787425i	−0.919234	+	0.393712i	$0.871191\pi$
$608$		−	3.49134e12i		−	1.03616i
$609$	1.86390e12			0.549092
$610$	4.56273e11	−	4.63457e11i	0.133426	−	0.135527i
$611$	−8.52975e11			−0.247600
$612$			9.40881e11i			0.271115i
$613$		−	1.15480e11i		−	0.0330321i	−0.999864	−	0.0165160i	$-0.994743\pi$
$613$		−	1.15480e11i		−	0.0330321i	0.999864	−	0.0165160i	$-0.00525745\pi$
$614$	−1.00445e12			−0.285215
$615$	−6.90171e10	+	7.01039e10i	−0.0194544	+	0.0197608i
$616$	−3.73893e12			−1.04625
$617$		−	3.75780e12i		−	1.04388i	−0.852983	−	0.521939i	$-0.825209\pi$
$617$		−	3.75780e12i		−	1.04388i	0.852983	−	0.521939i	$-0.174791\pi$
$618$		−	2.22066e12i		−	0.612399i
$619$	2.17044e12			0.594210			0.297105	−	0.954845i	$-0.403979\pi$
$619$	2.17044e12			0.594210			0.297105	+	0.954845i	$0.403979\pi$
$620$	6.27567e12	+	6.17839e12i	1.70568	+	1.67924i
$621$	−4.69517e12			−1.26689
$622$			8.37883e12i			2.24454i
$623$		−	1.50975e11i		−	0.0401521i
$624$	2.02609e11			0.0534969
$625$	−3.81284e12	+	1.19170e11i	−0.999512	+	0.0312396i
$626$	1.62178e12			0.422093
$627$			3.84652e12i			0.993950i
$628$		−	1.92541e12i		−	0.493976i
$629$	−3.01323e12			−0.767545
$630$	5.54164e11	+	5.45573e11i	0.140154	+	0.137981i
$631$	−5.99337e12			−1.50501			−0.752505	−	0.658587i	$-0.771154\pi$
$631$	−5.99337e12			−1.50501			−0.752505	+	0.658587i	$0.771154\pi$
$632$		−	1.83058e12i		−	0.456418i
$633$		−	6.31590e12i		−	1.56358i
$634$	9.19773e12			2.26089
$635$	3.57185e12	−	3.62809e12i	0.871790	−	0.885517i
$636$	1.16720e13			2.82870
$637$			1.74531e11i			0.0419995i
$638$			3.13714e12i			0.749620i
$639$	−4.45856e11			−0.105789
$640$	−5.19291e12	+	5.27467e12i	−1.22349	+	1.24276i
$641$	−6.26847e12			−1.46656			−0.733281	−	0.679926i	$-0.762012\pi$
$641$	−6.26847e12			−1.46656			−0.733281	+	0.679926i	$0.762012\pi$
$642$			5.51704e12i			1.28174i
$643$		−	9.05874e11i		−	0.208987i	−0.994526	−	0.104493i	$-0.966678\pi$
$643$		−	9.05874e11i		−	0.208987i	0.994526	−	0.104493i	$-0.0333221\pi$
$644$	−9.66310e12			−2.21376
$645$	3.88988e12	+	3.82958e12i	0.884947	+	0.871229i
$646$	1.30445e13			2.94702
$647$		−	5.25490e12i		−	1.17895i	−0.807787	−	0.589474i	$-0.799335\pi$
$647$		−	5.25490e12i		−	1.17895i	0.807787	−	0.589474i	$-0.200665\pi$
$648$		−	4.56768e12i		−	1.01767i
$649$	6.35763e12			1.40668
$650$	−3.24368e10	−	2.07613e12i	−0.00712734	−	0.456190i
$651$	6.50323e12			1.41911
$652$			3.28927e12i			0.712829i
$653$			4.71722e12i			1.01526i	0.861575	+	0.507630i	$0.169478\pi$
$653$			4.71722e12i			1.01526i	−0.861575	+	0.507630i	$0.830522\pi$
$654$	−6.06109e12			−1.29554
$655$	4.86120e12	+	4.78585e12i	1.03195	+	1.01595i
$656$	−2.85512e10			−0.00601945
$657$		−	2.63097e11i		−	0.0550898i
$658$			7.57754e12i			1.57584i
$659$	8.11959e12			1.67707			0.838533	−	0.544852i	$-0.183414\pi$
$659$	8.11959e12			1.67707			0.838533	+	0.544852i	$0.183414\pi$
$660$	4.61693e12	−	4.68963e12i	0.947121	−	0.962034i
$661$	−9.75841e12			−1.98826			−0.994128	−	0.108211i	$-0.965488\pi$
$661$	−9.75841e12			−1.98826			−0.994128	+	0.108211i	$0.965488\pi$
$662$			7.71457e12i			1.56117i
$663$		−	1.85514e12i		−	0.372877i
$664$	8.08195e12			1.61347
$665$	4.76876e12	−	4.84385e12i	0.945602	−	0.960491i
$666$	−5.00823e11			−0.0986394
$667$			3.35550e12i			0.656433i
$668$			1.42807e13i			2.77495i
$669$	−8.44724e12			−1.63041
$670$	−6.01809e12	−	5.92480e12i	−1.15378	−	1.13589i
$671$	5.09622e11			0.0970503
$672$			4.41094e12i			0.834391i
$673$		−	6.37456e12i		−	1.19779i	−0.800826	−	0.598897i	$-0.795606\pi$
$673$		−	6.37456e12i		−	1.19779i	0.800826	−	0.598897i	$-0.204394\pi$
$674$	−2.80641e12			−0.523820
$675$	−5.64990e12	+	8.82719e10i	−1.04755	+	0.0163665i
$676$	7.12550e11			0.131237
$677$		−	9.25132e12i		−	1.69260i	−0.532706	−	0.846301i	$-0.678825\pi$
$677$		−	9.25132e12i		−	1.69260i	0.532706	−	0.846301i	$-0.321175\pi$
$678$		−	1.06363e13i		−	1.93312i
$679$	4.16740e12			0.752404
$680$	−6.58192e12	−	6.47989e12i	−1.18049	−	1.16219i
$681$	−5.59337e12			−0.996579
$682$			1.09456e13i			1.93736i
$683$		−	4.14563e12i		−	0.728949i	−0.931213	−	0.364474i	$-0.881249\pi$
$683$		−	4.14563e12i		−	0.728949i	0.931213	−	0.364474i	$-0.118751\pi$
$684$	1.36691e12			0.238774
$685$	1.70097e12	−	1.72775e12i	0.295182	−	0.299830i
$686$	−8.68830e12			−1.49788
$687$		−	3.17886e12i		−	0.544460i
$688$			1.58423e12i			0.269569i
$689$	2.88573e12			0.487830
$690$	7.83281e12	−	7.95614e12i	1.31552	−	1.33623i
$691$	7.23801e12			1.20772			0.603862	−	0.797089i	$-0.293628\pi$
$691$	7.23801e12			1.20772			0.603862	+	0.797089i	$0.293628\pi$
$692$			1.18274e13i			1.96071i
$693$			6.09364e11i			0.100364i
$694$	−1.38785e13			−2.27104
$695$	6.58098e11	+	6.47896e11i	0.106994	+	0.105335i
$696$	−3.67951e12			−0.594359
$697$			2.61422e11i			0.0419560i
$698$			6.53603e12i			1.04223i
$699$	7.96474e12			1.26190
$700$	−1.16280e13	+	1.81672e11i	−1.83048	+	0.0285987i
$701$	1.11053e13			1.73700			0.868502	−	0.495685i	$-0.165083\pi$
$701$	1.11053e13			1.73700			0.868502	+	0.495685i	$0.165083\pi$
$702$		−	3.07569e12i		−	0.477997i
$703$			4.37761e12i			0.675987i
$704$	−8.54356e12			−1.31088
$705$	−3.93344e12	−	3.87247e12i	−0.599683	−	0.590387i
$706$	1.50518e13			2.28016
$707$		−	8.59137e12i		−	1.29323i
$708$			1.80176e13i			2.69493i
$709$	−1.24916e13			−1.85656			−0.928280	−	0.371882i	$-0.878712\pi$
$709$	−1.24916e13			−1.85656			−0.928280	+	0.371882i	$0.878712\pi$
$710$	7.41949e12	−	7.53631e12i	1.09575	−	1.11300i
$711$	−2.98346e11			−0.0437831
$712$			2.98038e11i			0.0434622i
$713$			1.17075e13i			1.69652i
$714$	−1.64804e13			−2.37316
$715$	1.14147e12	−	1.15944e12i	0.163338	−	0.165910i
$716$	1.30974e13			1.86241
$717$			2.06233e11i			0.0291422i
$718$			6.85239e12i			0.962238i
$719$	−1.65992e12			−0.231636			−0.115818	−	0.993270i	$-0.536949\pi$
$719$	−1.65992e12			−0.231636			−0.115818	+	0.993270i	$0.536949\pi$
$720$	−1.17156e11	−	1.15340e11i	−0.0162468	−	0.0159950i
$721$	−3.07499e12			−0.423775
$722$		−	6.93987e12i		−	0.950460i
$723$		−	4.27028e12i		−	0.581211i
$724$	−1.59055e13			−2.15141
$725$	6.30853e10	+	4.03781e12i	0.00848022	+	0.542782i
$726$	−3.42800e12			−0.457959
$727$		−	5.15944e11i		−	0.0685011i	−0.999413	−	0.0342506i	$-0.989096\pi$
$727$		−	5.15944e11i		−	0.0685011i	0.999413	−	0.0342506i	$-0.0109044\pi$
$728$		−	2.61976e12i		−	0.345676i
$729$	−8.27536e12			−1.08521
$730$	4.44713e12	+	4.37819e12i	0.579597	+	0.570613i
$731$	1.45056e13			1.87892
$732$			1.44428e12i			0.185931i
$733$			1.45685e12i			0.186400i	0.995647	+	0.0932000i	$0.0297096\pi$
$733$			1.45685e12i			0.186400i	−0.995647	+	0.0932000i	$0.970290\pi$
$734$	1.03966e13			1.32208
$735$	−7.92360e11	+	8.04837e11i	−0.100145	+	0.101722i
$736$	−7.94081e12			−0.997504
$737$		−	6.61755e12i		−	0.826216i
$738$			4.34504e10i			0.00539188i
$739$	−8.71221e12			−1.07455			−0.537277	−	0.843406i	$-0.680547\pi$
$739$	−8.71221e12			−1.07455			−0.537277	+	0.843406i	$0.680547\pi$
$740$	5.25439e12	−	5.33712e12i	0.644139	−	0.654281i
$741$	−2.69514e12			−0.328398
$742$		−	2.56358e13i		−	3.10477i
$743$			3.64808e12i			0.439152i	0.975595	+	0.219576i	$0.0704673\pi$
$743$			3.64808e12i			0.439152i	−0.975595	+	0.219576i	$0.929533\pi$
$744$	−1.28380e13			−1.53610
$745$	−5.01849e12	−	4.94069e12i	−0.596856	−	0.587604i
$746$	−2.11983e13			−2.50598
$747$		−	1.31718e12i		−	0.154776i
$748$		−	1.74879e13i		−	2.04259i
$749$	7.63954e12			0.886950
$750$	9.27597e12	−	9.72123e12i	1.07049	−	1.12188i
$751$	−1.41139e12			−0.161908			−0.0809538	−	0.996718i	$-0.525797\pi$
$751$	−1.41139e12			−0.161908			−0.0809538	+	0.996718i	$0.525797\pi$
$752$		−	1.60197e12i		−	0.182673i
$753$			1.39450e13i			1.58067i
$754$	−2.19810e12			−0.247672
$755$	3.21044e11	+	3.16067e11i	0.0359586	+	0.0354012i
$756$	−1.72263e13			−1.91798
$757$		−	1.11659e13i		−	1.23584i	−0.786243	−	0.617918i	$-0.787976\pi$
$757$		−	1.11659e13i		−	1.23584i	0.786243	−	0.617918i	$-0.212024\pi$
$758$			2.03339e12i			0.223722i
$759$	8.74865e12			0.956870
$760$	−9.41397e12	+	9.56220e12i	−1.02356	+	1.03967i
$761$	1.74660e13			1.88783			0.943916	−	0.330185i	$-0.107111\pi$
$761$	1.74660e13			1.88783			0.943916	+	0.330185i	$0.107111\pi$
$762$			1.79333e13i			1.92692i
$763$			8.39291e12i			0.896503i
$764$	−8.33968e12			−0.885583
$765$	−1.05608e12	+	1.07271e12i	−0.111486	+	0.113242i
$766$	2.17145e13			2.27888
$767$			4.45460e12i			0.464761i
$768$		−	1.18803e13i		−	1.23225i
$769$	6.53695e12			0.674073			0.337036	−	0.941492i	$-0.390575\pi$
$769$	6.53695e12			0.674073			0.337036	+	0.941492i	$0.390575\pi$
$770$	−1.03001e13	−	1.01404e13i	−1.05592	−	1.03956i
$771$	1.10969e13			1.13098
$772$		−	5.29132e11i		−	0.0536150i
$773$		−	1.43446e13i		−	1.44504i	−0.691348	−	0.722522i	$-0.742983\pi$
$773$		−	1.43446e13i		−	1.44504i	0.691348	−	0.722522i	$-0.257017\pi$
$774$	2.41095e12			0.241465
$775$	2.20107e11	+	1.40881e13i	0.0219168	+	1.40280i
$776$	−8.22682e12			−0.814431
$777$		−	5.53066e12i		−	0.544355i
$778$			1.58103e13i			1.54715i
$779$	3.79793e11			0.0369512
$780$	3.28588e12	+	3.23494e12i	0.317853	+	0.312926i
$781$	8.28700e12			0.797018
$782$		−	2.96689e13i		−	2.83708i
$783$			5.98181e12i			0.568728i
$784$	−3.27786e11			−0.0309861
$785$	2.16116e12	−	2.19519e12i	0.203129	−	0.206328i
$786$	−2.40285e13			−2.24556
$787$			1.15418e13i			1.07248i	0.844066	+	0.536239i	$0.180155\pi$
$787$			1.15418e13i			1.07248i	−0.844066	+	0.536239i	$0.819845\pi$
$788$		−	3.96127e12i		−	0.365988i
$789$	9.37073e12			0.860849
$790$	4.96477e12	−	5.04294e12i	0.453500	−	0.460640i
$791$	−1.47283e13			−1.33770
$792$		−	1.20294e12i		−	0.108638i
$793$			3.57077e11i			0.0320651i
$794$	6.02878e12			0.538316
$795$	1.33074e13	+	1.31011e13i	1.18152	+	1.16320i
$796$	2.29766e13			2.02851
$797$		−	2.04626e13i		−	1.79638i	−0.439609	−	0.898189i	$-0.644883\pi$
$797$		−	2.04626e13i		−	1.79638i	0.439609	−	0.898189i	$-0.355117\pi$
$798$			2.39427e13i			2.09007i
$799$	−1.46680e13			−1.27324
$800$	−9.55552e12	+	1.49292e11i	−0.824801	+	0.0128864i
$801$	4.85737e10			0.00416922
$802$		−	6.33502e12i		−	0.540708i
$803$			4.89010e12i			0.415048i
$804$	1.87543e13			1.58288
$805$	−1.10170e13	−	1.08462e13i	−0.924660	−	0.910327i
$806$	−7.66927e12			−0.640098
$807$		−	1.19790e12i		−	0.0994234i
$808$			1.69601e13i			1.39984i
$809$	9.11347e12			0.748024			0.374012	−	0.927424i	$-0.377982\pi$
$809$	9.11347e12			0.748024			0.374012	+	0.927424i	$0.377982\pi$
$810$	1.23881e13	−	1.25832e13i	1.01116	−	1.02709i
$811$	−6.43474e12			−0.522321			−0.261160	−	0.965295i	$-0.584105\pi$
$811$	−6.43474e12			−0.522321			−0.261160	+	0.965295i	$0.584105\pi$
$812$			1.23111e13i			0.993793i
$813$		−	1.23833e13i		−	0.994100i
$814$	9.30867e12			0.743152
$815$	−3.69200e12	+	3.75014e12i	−0.293125	+	0.297740i
$816$	3.48413e12			0.275099
$817$		−	2.10737e13i		−	1.65479i
$818$		−	1.73572e13i		−	1.35547i
$819$	−4.26963e11			−0.0331599
$820$	−4.63038e11	−	4.55860e11i	−0.0357647	−	0.0352103i
$821$	1.49394e13			1.14759			0.573796	−	0.818998i	$-0.305470\pi$
$821$	1.49394e13			1.14759			0.573796	+	0.818998i	$0.305470\pi$
$822$			8.54014e12i			0.652442i
$823$			6.42394e11i			0.0488093i	0.999702	+	0.0244046i	$0.00776901\pi$
$823$			6.42394e11i			0.0488093i	−0.999702	+	0.0244046i	$0.992231\pi$
$824$	6.07031e12			0.458710
$825$	1.05276e13	−	1.64480e11i	0.791203	−	0.0123615i
$826$	3.95731e13			2.95795
$827$			1.16049e13i			0.862715i	0.902181	+	0.431358i	$0.141965\pi$
$827$			1.16049e13i			0.862715i	−0.902181	+	0.431358i	$0.858035\pi$
$828$		−	3.10894e12i		−	0.229867i
$829$	−1.57628e13			−1.15914			−0.579572	−	0.814921i	$-0.696780\pi$
$829$	−1.57628e13			−1.15914			−0.579572	+	0.814921i	$0.696780\pi$
$830$	2.22644e13	+	2.19192e13i	1.62839	+	1.60315i
$831$	−2.35141e13			−1.71050
$832$		−	5.98622e12i		−	0.433109i
$833$			3.00129e12i			0.215976i
$834$	−3.25292e12			−0.232823
$835$	−1.60292e13	+	1.62816e13i	−1.14110	+	1.15907i
$836$	−2.54064e13			−1.79893
$837$			2.08708e13i			1.46985i
$838$		−	4.18167e13i		−	2.92922i
$839$	6.01495e12			0.419086			0.209543	−	0.977799i	$-0.432802\pi$
$839$	6.01495e12			0.419086			0.209543	+	0.977799i	$0.432802\pi$
$840$	1.18936e13	−	1.20808e13i	0.824243	−	0.837221i
$841$	−1.02321e13			−0.705316
$842$		−	6.91848e12i		−	0.474358i
$843$		−	7.44209e12i		−	0.507541i
$844$	4.17167e13			2.82989
$845$	8.12387e11	+	7.99793e11i	0.0548160	+	0.0539663i
$846$	−2.43795e12			−0.163628
$847$			4.74682e12i			0.316904i
$848$			5.41968e12i			0.359909i
$849$	−1.19008e13			−0.786123
$850$	−5.57793e11	−	3.57019e13i	−0.0366512	−	2.34588i
$851$	9.95658e12			0.650769
$852$			2.34855e13i			1.52694i
$853$		−	7.80932e12i		−	0.505059i	−0.967589	−	0.252530i	$-0.918737\pi$
$853$		−	7.80932e12i		−	0.505059i	0.967589	−	0.252530i	$-0.0812625\pi$
$854$	3.17215e12			0.204077
$855$	1.55843e12	+	1.53427e12i	0.0997333	+	0.0981873i
$856$	−1.50811e13			−0.960069
$857$		−	7.77957e12i		−	0.492654i	−0.969187	−	0.246327i	$-0.920776\pi$
$857$		−	7.77957e12i		−	0.492654i	0.969187	−	0.246327i	$-0.0792237\pi$
$858$			5.73102e12i			0.361027i
$859$	−7.85737e12			−0.492389			−0.246194	−	0.969220i	$-0.579180\pi$
$859$	−7.85737e12			−0.492389			−0.246194	+	0.969220i	$0.579180\pi$
$860$	−2.52945e13	+	2.56928e13i	−1.57682	+	1.60165i
$861$	−4.79829e11			−0.0297558
$862$			3.70780e13i			2.28736i
$863$			2.65186e13i			1.62743i	0.581266	+	0.813713i	$0.302557\pi$
$863$			2.65186e13i			1.62743i	−0.581266	+	0.813713i	$0.697443\pi$
$864$	−1.41560e13			−0.864229
$865$	−1.32755e13	+	1.34846e13i	−0.806269	+	0.818964i
$866$	2.63436e13			1.59164
$867$		−	1.62184e13i		−	0.974816i
$868$			4.29541e13i			2.56842i
$869$	5.54527e12			0.329863
$870$	−1.01364e13	−	9.97928e12i	−0.599857	−	0.590558i
$871$	4.63672e12			0.272979
$872$		−	1.65684e13i		−	0.970410i
$873$			1.34079e12i			0.0781264i
$874$	−4.31030e13			−2.49865
$875$	−1.34612e13	−	1.28446e13i	−0.776330	−	0.740772i
$876$	−1.38586e13			−0.795156
$877$			6.14488e12i			0.350764i	0.984500	+	0.175382i	$0.0561160\pi$
$877$			6.14488e12i			0.350764i	−0.984500	+	0.175382i	$0.943884\pi$
$878$			2.08291e13i			1.18289i
$879$	−1.22967e13			−0.694765
$880$	2.17755e12	+	2.14379e12i	0.122404	+	0.120507i
$881$	−2.66681e13			−1.49142			−0.745711	−	0.666269i	$-0.767890\pi$
$881$	−2.66681e13			−1.49142			−0.745711	+	0.666269i	$0.767890\pi$
$882$			4.98838e11i			0.0277556i
$883$			4.25527e12i			0.235561i	0.993040	+	0.117781i	$0.0375780\pi$
$883$			4.25527e12i			0.235561i	−0.993040	+	0.117781i	$0.962422\pi$
$884$	1.22533e13			0.674864
$885$	−2.02237e13	+	2.05421e13i	−1.10819	+	1.12564i
$886$	−3.49205e13			−1.90383
$887$			1.61561e13i			0.876355i	0.898889	+	0.438177i	$0.144376\pi$
$887$			1.61561e13i			0.876355i	−0.898889	+	0.438177i	$0.855624\pi$
$888$			1.09180e13i			0.589230i
$889$	2.48326e13			1.33341
$890$	−8.08315e11	+	8.21042e11i	−0.0431842	+	0.0438642i
$891$	1.38366e13			0.735493
$892$		−	5.57943e13i		−	2.95086i
$893$			2.13097e13i			1.12136i
$894$	2.48059e13			1.29878
$895$	1.49325e13	+	1.47010e13i	0.777907	+	0.765848i
$896$	−3.61027e13			−1.87134
$897$			6.12992e12i			0.316147i
$898$			3.57135e13i			1.83269i
$899$	1.49157e13			0.761599
$900$	−5.84500e10	−	3.74113e12i	−0.00296957	−	0.190069i
$901$	4.96239e13			2.50859
$902$		−	8.07601e11i		−	0.0406226i
$903$			2.66244e13i			1.33256i
$904$	2.90751e13			1.44798
$905$	−1.81340e13	−	1.78529e13i	−0.898619	−	0.884689i
$906$	−1.58689e12			−0.0782475
$907$			1.61349e13i			0.791651i	0.918326	+	0.395826i	$0.129542\pi$
$907$			1.61349e13i			0.791651i	−0.918326	+	0.395826i	$0.870458\pi$
$908$		−	3.69444e13i		−	1.80369i
$909$	2.76413e12			0.134283
$910$	7.10509e12	−	7.21697e12i	0.343466	−	0.348874i
$911$	1.70662e13			0.820924			0.410462	−	0.911878i	$-0.365367\pi$
$911$	1.70662e13			0.820924			0.410462	+	0.911878i	$0.365367\pi$
$912$		−	5.06175e12i		−	0.242283i
$913$			2.44821e13i			1.16609i
$914$	5.88051e13			2.78713
$915$	−1.62111e12	+	1.64664e12i	−0.0764572	+	0.0776611i
$916$	2.09965e13			0.985410
$917$			3.32727e13i			1.55391i
$918$		−	5.28905e13i		−	2.45802i
$919$	2.39159e13			1.10603			0.553015	−	0.833171i	$-0.313477\pi$
$919$	2.39159e13			1.10603			0.553015	+	0.833171i	$0.313477\pi$
$920$	2.17486e13	+	2.14114e13i	1.00089	+	0.985372i
$921$	3.56877e12			0.163437
$922$			2.98933e12i			0.136234i
$923$			5.80646e12i			0.263332i
$924$	3.20983e13			1.44863
$925$	1.19812e13	−	1.87190e11i	0.538099	−	0.00840705i
$926$	−5.56871e13			−2.48889
$927$		−	9.89329e11i		−	0.0440030i
$928$			1.01169e13i			0.447796i
$929$	−3.53859e12			−0.155869			−0.0779345	−	0.996958i	$-0.524832\pi$
$929$	−3.53859e12			−0.155869			−0.0779345	+	0.996958i	$0.524832\pi$
$930$	−3.53664e13	−	3.48181e13i	−1.55030	−	1.52627i
$931$	4.36026e12			0.190213
$932$			5.26074e13i			2.28389i
$933$		−	2.97695e13i		−	1.28619i
$934$	1.91103e13			0.821687
$935$	1.96291e13	−	1.99382e13i	0.839939	−	0.853165i
$936$	8.42864e11			0.0358935
$937$			6.50586e12i			0.275725i	0.990451	+	0.137863i	$0.0440232\pi$
$937$			6.50586e12i			0.275725i	−0.990451	+	0.137863i	$0.955977\pi$
$938$		−	4.11910e13i		−	1.73736i
$939$	−5.76211e12			−0.241873
$940$	2.55778e13	−	2.59805e13i	1.06853	−	1.08536i
$941$	−2.57328e13			−1.06988			−0.534939	−	0.844891i	$-0.679665\pi$
$941$	−2.57328e13			−1.06988			−0.534939	+	0.844891i	$0.679665\pi$
$942$			1.08506e13i			0.448978i
$943$		−	8.63813e11i		−	0.0355727i
$944$	−8.36618e12			−0.342889
$945$	−1.96399e13	−	1.93355e13i	−0.801118	−	0.788700i
$946$	−4.48117e13			−1.81920
$947$			1.90853e13i			0.771123i	0.922682	+	0.385562i	$0.125992\pi$
$947$			1.90853e13i			0.771123i	−0.922682	+	0.385562i	$0.874008\pi$
$948$			1.57154e13i			0.631957i
$949$	−3.42635e12			−0.137130
$950$	−5.18677e13	+	8.10361e11i	−2.06605	+	0.0322792i
$951$	−3.26790e13			−1.29556
$952$		−	4.50502e13i		−	1.77758i
$953$		−	3.48712e13i		−	1.36946i	−0.728798	−	0.684729i	$-0.759921\pi$
$953$		−	3.48712e13i		−	1.36946i	0.728798	−	0.684729i	$-0.240079\pi$
$954$	8.24791e12			0.322386
$955$	−9.50816e12	−	9.36077e12i	−0.369898	−	0.364164i
$956$	−1.36217e12			−0.0527439
$957$		−	1.11461e13i		−	0.429555i
$958$		−	7.98823e13i		−	3.06412i
$959$	1.18257e13			0.451484
$960$	2.71772e13	−	2.76051e13i	1.03272	−	1.04898i
$961$	2.56020e13			0.968320
$962$			6.52231e12i			0.245535i
$963$			2.45790e12i			0.0920971i
$964$	2.82053e13			1.05192
$965$	5.93918e11	−	6.03269e11i	0.0220472	−	0.0223943i
$966$	5.44561e13			2.01210
$967$		−	9.08047e12i		−	0.333956i	−0.985961	−	0.166978i	$-0.946599\pi$
$967$		−	9.08047e12i		−	0.333956i	0.985961	−	0.166978i	$-0.0534009\pi$
$968$		−	9.37065e12i		−	0.343029i
$969$	−4.63466e13			−1.68873
$970$	−2.26635e13	−	2.23121e13i	−0.821965	−	0.809223i
$971$	−4.96409e12			−0.179206			−0.0896032	−	0.995978i	$-0.528560\pi$
$971$	−4.96409e12			−0.179206			−0.0896032	+	0.995978i	$0.528560\pi$
$972$		−	1.05290e13i		−	0.378344i
$973$			4.50438e12i			0.161112i
$974$	−4.47949e13			−1.59483
$975$	1.15246e11	+	7.37640e12i	0.00408418	+	0.261411i
$976$	−6.70626e11			−0.0236568
$977$		−	3.59885e13i		−	1.26368i	−0.775098	−	0.631842i	$-0.782299\pi$
$977$		−	3.59885e13i		−	1.26368i	0.775098	−	0.631842i	$-0.217701\pi$
$978$		−	1.85366e13i		−	0.647895i
$979$	−9.02826e11			−0.0314110
$980$	−5.31597e12	−	5.23357e12i	−0.184105	−	0.181251i
$981$	−2.70028e12			−0.0930890
$982$			6.23046e13i			2.13805i
$983$		−	3.04093e13i		−	1.03876i	−0.854543	−	0.519381i	$-0.826163\pi$
$983$		−	3.04093e13i		−	1.03876i	0.854543	−	0.519381i	$-0.173837\pi$
$984$	9.47225e11			0.0322088
$985$	4.44628e12	−	4.51629e12i	0.150499	−	0.152869i
$986$	−3.77993e13			−1.27361
$987$		−	2.69226e13i		−	0.903004i
$988$		−	1.78015e13i		−	0.594361i
$989$	−4.79307e13			−1.59305
$990$	3.26252e12	−	3.31389e12i	0.107943	−	0.109643i
$991$	5.24412e13			1.72719			0.863597	−	0.504182i	$-0.168206\pi$
$991$	5.24412e13			1.72719			0.863597	+	0.504182i	$0.168206\pi$
$992$			3.52982e13i			1.15731i
$993$		−	2.74095e13i		−	0.894600i
$994$	5.15826e13			1.67596
$995$	2.61958e13	+	2.57898e13i	0.847283	+	0.834149i
$996$	−6.93827e13			−2.23401
$997$			2.53718e13i			0.813248i	0.913596	+	0.406624i	$0.133294\pi$
$997$			2.53718e13i			0.813248i	−0.913596	+	0.406624i	$0.866706\pi$
$998$		−	2.04308e13i		−	0.651926i
$999$	1.77495e13			0.563821

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.10.b.a.14.6	✓	54
5.2	odd	4		325.10.a.l.1.24		27
5.3	odd	4		325.10.a.k.1.4		27
5.4	even	2	inner	65.10.b.a.14.49	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.10.b.a.14.6	✓	54	1.1	even	1	trivial
65.10.b.a.14.49	yes	54	5.4	even	2	inner
325.10.a.k.1.4		27	5.3	odd	4
325.10.a.l.1.24		27	5.2	odd	4

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	65.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-37.2225i q^{2} +132.249i q^{3} -873.511 q^{4} +(-995.901 - 980.463i) q^{5} +4922.65 q^{6} -6816.48i q^{7} +13456.3i q^{8} +2193.09 q^{9} +(-36495.2 + 37069.9i) q^{10} -40762.4 q^{11} -115521. i q^{12} -28561.0i q^{13} -253726. q^{14} +(129666. - 131707. i) q^{15} +53640.4 q^{16} -491145. i q^{17} -81632.3i q^{18} -713534. q^{19} +(869931. + 856445. i) q^{20} +901476. q^{21} +1.51728e6i q^{22} +1.62288e6i q^{23} -1.77959e6 q^{24} +(30511.2 + 1.95289e6i) q^{25} -1.06311e6 q^{26} +2.89310e6i q^{27} +5.95427e6i q^{28} +2.06761e6 q^{29} +(-4.90247e6 - 4.82647e6i) q^{30} +7.21399e6 q^{31} +4.89302e6i q^{32} -5.39080e6i q^{33} -1.82816e7 q^{34} +(-6.68330e6 + 6.78854e6i) q^{35} -1.91569e6 q^{36} -6.13511e6i q^{37} +2.65595e7i q^{38} +3.77718e6 q^{39} +(1.31934e7 - 1.34012e7i) q^{40} -532270. q^{41} -3.35551e7i q^{42} +2.95343e7i q^{43} +3.56064e7 q^{44} +(-2.18410e6 - 2.15024e6i) q^{45} +6.04077e7 q^{46} -2.98650e7i q^{47} +7.09391e6i q^{48} -6.11080e6 q^{49} +(7.26912e7 - 1.13570e6i) q^{50} +6.49536e7 q^{51} +2.49484e7i q^{52} +1.01037e8i q^{53} +1.07688e8 q^{54} +(4.05953e7 + 3.99660e7i) q^{55} +9.17249e7 q^{56} -9.43645e7i q^{57} -7.69617e7i q^{58} -1.55968e8 q^{59} +(-1.13264e8 + 1.15048e8i) q^{60} -1.25023e7 q^{61} -2.68522e8i q^{62} -1.49492e7i q^{63} +2.09594e8 q^{64} +(-2.80030e7 + 2.84439e7i) q^{65} -2.00659e8 q^{66} +1.62345e8i q^{67} +4.29020e8i q^{68} -2.14625e8 q^{69} +(2.52686e8 + 2.48769e8i) q^{70} -2.03300e8 q^{71} +2.95110e7i q^{72} -1.19966e8i q^{73} -2.28364e8 q^{74} +(-2.58268e8 + 4.03508e6i) q^{75} +6.23280e8 q^{76} +2.77856e8i q^{77} -1.40596e8i q^{78} -1.36039e8 q^{79} +(-5.34205e7 - 5.25924e7i) q^{80} -3.39444e8 q^{81} +1.98124e7i q^{82} -6.00605e8i q^{83} -7.87449e8 q^{84} +(-4.81549e8 + 4.89131e8i) q^{85} +1.09934e9 q^{86} +2.73441e8i q^{87} -5.48513e8i q^{88} +2.21485e7 q^{89} +(-8.00374e7 + 8.12976e7i) q^{90} -1.94685e8 q^{91} -1.41761e9i q^{92} +9.54046e8i q^{93} -1.11165e9 q^{94} +(7.10609e8 + 6.99593e8i) q^{95} -6.47099e8 q^{96} +6.11371e8i q^{97} +2.27459e8i q^{98} -8.93957e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 13140 q^{4} - 2160 q^{5} - 3572 q^{6} - 428346 q^{9} + 74802 q^{10} - 132192 q^{11} + 718916 q^{14} + 339156 q^{15} + 1997244 q^{16} + 1523456 q^{19} + 4945180 q^{20} - 5377256 q^{21} + 7134424 q^{24}+ \cdots - 4284595264 q^{99}+O(q^{100}) \) 54 * q - 13140 * q^4 - 2160 * q^5 - 3572 * q^6 - 428346 * q^9 + 74802 * q^10 - 132192 * q^11 + 718916 * q^14 + 339156 * q^15 + 1997244 * q^16 + 1523456 * q^19 + 4945180 * q^20 - 5377256 * q^21 + 7134424 * q^24 - 948708 * q^25 - 2741856 * q^26 - 8867340 * q^29 + 1587678 * q^30 + 12213796 * q^31 - 37568140 * q^34 - 37980442 * q^35 + 195176200 * q^36 + 18507528 * q^39 - 78122474 * q^40 - 41063084 * q^41 - 86766092 * q^44 - 87904884 * q^45 - 64211420 * q^46 - 293513290 * q^49 + 52576096 * q^50 - 136792788 * q^51 - 3099140 * q^54 + 50401764 * q^55 - 556092908 * q^56 + 991411312 * q^59 + 548166228 * q^60 + 200512988 * q^61 - 1108334388 * q^64 + 33359248 * q^65 + 157425616 * q^66 + 1318334144 * q^69 + 511125000 * q^70 - 470875308 * q^71 - 3711844340 * q^74 - 907655634 * q^75 + 927238960 * q^76 + 823436432 * q^79 - 1831968312 * q^80 + 3976878598 * q^81 + 953649436 * q^84 - 2328860572 * q^85 + 6633016792 * q^86 + 3239933812 * q^89 + 2239917660 * q^90 - 213407792 * q^91 - 8398362628 * q^94 - 3428426984 * q^95 + 4054813436 * q^96 - 4284595264 * q^99

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