LMFDB - Embedded newform 99.8.f.b.82.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [99,8,Mod(37,99)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(99, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("99.37"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	99.f (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$30.9261175229$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			82.3
Character	$\chi$	$=$	99.82
Dual form			99.8.f.b.64.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.813458 - 2.50357i) q^{2} +(97.9481 - 71.1634i) q^{4} +(-78.7070 + 242.235i) q^{5} +(-1135.08 + 824.681i) q^{7} +(-530.435 - 385.384i) q^{8} +670.476 q^{10} +(3175.50 + 3066.49i) q^{11} +(-4283.83 - 13184.3i) q^{13} +(2987.98 + 2170.89i) q^{14} +(4255.49 - 13097.1i) q^{16} +(5268.59 - 16215.1i) q^{17} +(-12568.3 - 9131.40i) q^{19} +(9529.09 + 29327.5i) q^{20} +(5094.03 - 10444.5i) q^{22} +58901.9 q^{23} +(10721.4 + 7789.53i) q^{25} +(-29523.0 + 21449.7i) q^{26} +(-52491.4 + 161552. i) q^{28} +(24930.5 - 18113.0i) q^{29} +(-60252.9 - 185439. i) q^{31} -120175. q^{32} -44881.3 q^{34} +(-110428. - 339864. i) q^{35} +(345677. - 251149. i) q^{37} +(-12637.3 + 38893.5i) q^{38} +(135102. - 98157.7i) q^{40} +(-637965. - 463509. i) q^{41} +20485.0 q^{43} +(529256. + 74377.5i) q^{44} +(-47914.2 - 147465. i) q^{46} +(461937. + 335617. i) q^{47} +(353811. - 1.08892e6i) q^{49} +(10780.2 - 33178.1i) q^{50} +(-1.35783e6 - 986521. i) q^{52} +(-478764. - 1.47349e6i) q^{53} +(-992746. + 527863. i) q^{55} +919904. q^{56} +(-65627.0 - 47680.8i) q^{58} +(-1.41091e6 + 1.02508e6i) q^{59} +(565284. - 1.73976e6i) q^{61} +(-415247. + 301694. i) q^{62} +(-446946. - 1.37556e6i) q^{64} +3.53086e6 q^{65} +176715. q^{67} +(-637871. - 1.96317e6i) q^{68} +(-761042. + 552929. i) q^{70} +(-1.10490e6 + 3.40052e6i) q^{71} +(586597. - 426188. i) q^{73} +(-909961. - 661125. i) q^{74} -1.88086e6 q^{76} +(-6.13331e6 - 861928. i) q^{77} +(322974. + 994012. i) q^{79} +(2.83763e6 + 2.06166e6i) q^{80} +(-641467. + 1.97423e6i) q^{82} +(1.96687e6 - 6.05340e6i) q^{83} +(3.51318e6 + 2.55248e6i) q^{85} +(-16663.7 - 51285.6i) q^{86} +(-502621. - 2.85036e6i) q^{88} -1.82683e6 q^{89} +(1.57353e7 + 1.14324e7i) q^{91} +(5.76933e6 - 4.19166e6i) q^{92} +(464473. - 1.42950e6i) q^{94} +(3.20116e6 - 2.32578e6i) q^{95} +(-2.95746e6 - 9.10212e6i) q^{97} -3.01399e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 6 q^{2} + 160 q^{4} - 773 q^{5} + 1289 q^{7} - 2956 q^{8} - 10640 q^{10} - 13209 q^{11} + 13499 q^{13} + 3318 q^{14} - 113196 q^{16} - 30296 q^{17} - 6858 q^{19} - 76725 q^{20} - 48859 q^{22} + 166984 q^{23}+ \cdots - 140532178 q^{98}+O(q^{100}) $ 28 * q + 6 * q^2 + 160 * q^4 - 773 * q^5 + 1289 * q^7 - 2956 * q^8 - 10640 * q^10 - 13209 * q^11 + 13499 * q^13 + 3318 * q^14 - 113196 * q^16 - 30296 * q^17 - 6858 * q^19 - 76725 * q^20 - 48859 * q^22 + 166984 * q^23 + 99832 * q^25 - 340424 * q^26 + 657387 * q^28 - 192014 * q^29 + 396068 * q^31 + 303498 * q^32 - 1229124 * q^34 + 725859 * q^35 + 811053 * q^37 - 1548798 * q^38 - 1427263 * q^40 - 1041497 * q^41 - 5265288 * q^43 + 5341085 * q^44 + 1198651 * q^46 - 1667505 * q^47 + 2968140 * q^49 - 11247432 * q^50 + 2325763 * q^52 + 1625736 * q^53 - 8338690 * q^55 + 18201906 * q^56 + 14965553 * q^58 + 2587454 * q^59 + 5801619 * q^61 - 15631121 * q^62 - 3732846 * q^64 + 15368174 * q^65 - 7141262 * q^67 - 17394545 * q^68 - 4329200 * q^70 - 3569199 * q^71 + 125008 * q^73 + 13691530 * q^74 - 19690428 * q^76 + 6038739 * q^77 + 17075485 * q^79 - 26606436 * q^80 + 19886007 * q^82 + 4645575 * q^83 + 12002715 * q^85 + 12296287 * q^86 - 50905990 * q^88 - 9601664 * q^89 - 14129477 * q^91 + 90776021 * q^92 + 1047679 * q^94 - 58935661 * q^95 - 22170261 * q^97 - 140532178 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	−0.813458	−	2.50357i	−0.0719002	−	0.221286i	0.908649	−	0.417562i	$-0.137115\pi$
$2$	−0.813458	−	2.50357i	−0.0719002	−	0.221286i	−0.980549	+	0.196276i	$0.937115\pi$
$3$		0			0
$3$		0			0
$4$	97.9481	−	71.1634i	0.765219	−	0.555964i
$5$	−78.7070	+	242.235i	−0.281591	+	0.866647i	0.705809	+	0.708402i	$0.250584\pi$
$5$	−78.7070	+	242.235i	−0.281591	+	0.866647i	−0.987400	+	0.158245i	$0.949416\pi$
$6$		0			0
$7$	−1135.08	+	824.681i	−1.25078	+	0.908747i	−0.998267	−	0.0588455i	$-0.981258\pi$
$7$	−1135.08	+	824.681i	−1.25078	+	0.908747i	−0.252516	+	0.967593i	$0.581258\pi$
$8$	−530.435	−	385.384i	−0.366284	−	0.266121i
$9$		0			0
$10$	670.476			0.212023
$11$	3175.50	+	3066.49i	0.719346	+	0.694652i
$11$	3175.50	+	3066.49i	0.719346	+	0.694652i
$12$		0			0
$13$	−4283.83	−	13184.3i	−0.540792	−	1.66439i	−0.730790	−	0.682602i	$-0.760848\pi$
$13$	−4283.83	−	13184.3i	−0.540792	−	1.66439i	0.189998	−	0.981784i	$-0.439152\pi$
$14$	2987.98	+	2170.89i	0.291025	+	0.211442i
$15$		0			0
$16$	4255.49	−	13097.1i	0.259735	−	0.799382i
$17$	5268.59	−	16215.1i	0.260090	−	0.800475i	−0.732694	−	0.680558i	$-0.761737\pi$
$17$	5268.59	−	16215.1i	0.260090	−	0.800475i	0.992784	−	0.119916i	$-0.0382626\pi$
$18$		0			0
$19$	−12568.3	−	9131.40i	−0.420377	−	0.305422i	0.357413	−	0.933947i	$-0.383659\pi$
$19$	−12568.3	−	9131.40i	−0.420377	−	0.305422i	−0.777789	+	0.628525i	$0.783659\pi$
$20$	9529.09	+	29327.5i	0.266346	+	0.819729i
$21$		0			0
$22$	5094.03	−	10444.5i	0.101996	−	0.209127i
$23$	58901.9			1.00944			0.504721	−	0.863282i	$-0.331595\pi$
$23$	58901.9			1.00944			0.504721	+	0.863282i	$0.331595\pi$
$24$		0			0
$25$	10721.4	+	7789.53i	0.137234	+	0.0997060i
$26$	−29523.0	+	21449.7i	−0.329422	+	0.239339i
$27$		0			0
$28$	−52491.4	+	161552.i	−0.451892	+	1.39078i
$29$	24930.5	−	18113.0i	0.189818	−	0.137911i	−0.488818	−	0.872386i	$-0.662572\pi$
$29$	24930.5	−	18113.0i	0.189818	−	0.137911i	0.678635	+	0.734475i	$0.262572\pi$
$30$		0			0
$31$	−60252.9	−	185439.i	−0.363256	−	1.11799i	−0.951066	−	0.308987i	$-0.900010\pi$
$31$	−60252.9	−	185439.i	−0.363256	−	1.11799i	0.587811	−	0.808999i	$-0.299990\pi$
$32$	−120175.			−0.648318
$33$		0			0
$34$	−44881.3			−0.195834
$35$	−110428.	−	339864.i	−0.435354	−	1.33988i
$36$		0			0
$37$	345677.	−	251149.i	1.12193	−	0.815127i	0.137426	−	0.990512i	$-0.456117\pi$
$37$	345677.	−	251149.i	1.12193	−	0.815127i	0.984500	+	0.175385i	$0.0561170\pi$
$38$	−12637.3	+	38893.5i	−0.0373604	+	0.114983i
$39$		0			0
$40$	135102.	−	98157.7i	0.333775	−	0.242501i
$41$	−637965.	−	463509.i	−1.44562	−	1.05030i	−0.986831	−	0.161756i	$-0.948284\pi$
$41$	−637965.	−	463509.i	−1.44562	−	1.05030i	−0.458787	−	0.888547i	$-0.651716\pi$
$42$		0			0
$43$	20485.0			0.0392914			0.0196457	−	0.999807i	$-0.493746\pi$
$43$	20485.0			0.0392914			0.0196457	+	0.999807i	$0.493746\pi$
$44$	529256.	+	74377.5i	0.936659	+	0.131631i
$45$		0			0
$46$	−47914.2	−	147465.i	−0.0725791	−	0.223376i
$47$	461937.	+	335617.i	0.648994	+	0.471522i	0.862928	−	0.505326i	$-0.168628\pi$
$47$	461937.	+	335617.i	0.648994	+	0.471522i	−0.213935	+	0.976848i	$0.568628\pi$
$48$		0			0
$49$	353811.	−	1.08892e6i	0.429620	−	1.32223i
$50$	10780.2	−	33178.1i	0.0121964	−	0.0375367i
$51$		0			0
$52$	−1.35783e6	−	986521.i	−1.33916	−	0.972960i
$53$	−478764.	−	1.47349e6i	−0.441729	−	1.35950i	−0.886031	−	0.463626i	$-0.846548\pi$
$53$	−478764.	−	1.47349e6i	−0.441729	−	1.35950i	0.444302	−	0.895877i	$-0.353452\pi$
$54$		0			0
$55$	−992746.	+	527863.i	−0.804579	+	0.427811i
$56$	919904.			0.699978
$57$		0			0
$58$	−65627.0	−	47680.8i	−0.0441657	−	0.0320882i
$59$	−1.41091e6	+	1.02508e6i	−0.894367	+	0.649796i	−0.937013	−	0.349295i	$-0.886421\pi$
$59$	−1.41091e6	+	1.02508e6i	−0.894367	+	0.649796i	0.0426459	+	0.999090i	$0.486421\pi$
$60$		0			0
$61$	565284.	−	1.73976e6i	0.318869	−	0.981377i	−0.655264	−	0.755400i	$-0.727443\pi$
$61$	565284.	−	1.73976e6i	0.318869	−	0.981377i	0.974133	−	0.225977i	$-0.0725574\pi$
$62$	−415247.	+	301694.i	−0.221276	+	0.160767i
$63$		0			0
$64$	−446946.	−	1.37556e6i	−0.213121	−	0.655918i
$65$	3.53086e6			1.59472
$66$		0			0
$67$	176715.			0.0717812			0.0358906	−	0.999356i	$-0.488573\pi$
$67$	176715.			0.0717812			0.0358906	+	0.999356i	$0.488573\pi$
$68$	−637871.	−	1.96317e6i	−0.246009	−	0.757139i
$69$		0			0
$70$	−761042.	+	552929.i	−0.265195	+	0.192676i
$71$	−1.10490e6	+	3.40052e6i	−0.366368	+	1.12757i	0.582752	+	0.812650i	$0.301976\pi$
$71$	−1.10490e6	+	3.40052e6i	−0.366368	+	1.12757i	−0.949120	+	0.314915i	$0.898024\pi$
$72$		0			0
$73$	586597.	−	426188.i	0.176486	−	0.128224i	−0.496035	−	0.868302i	$-0.665211\pi$
$73$	586597.	−	426188.i	0.176486	−	0.128224i	0.672521	+	0.740078i	$0.265211\pi$
$74$	−909961.	−	661125.i	−0.261043	−	0.189659i
$75$		0			0
$76$	−1.88086e6			−0.491484
$77$	−6.13331e6	−	861928.i	−1.53101	−	0.215156i
$78$		0			0
$79$	322974.	+	994012.i	0.0737009	+	0.226828i	0.981120	−	0.193398i	$-0.0619508\pi$
$79$	322974.	+	994012.i	0.0737009	+	0.226828i	−0.907420	+	0.420226i	$0.861951\pi$
$80$	2.83763e6	+	2.06166e6i	0.619643	+	0.450197i
$81$		0			0
$82$	−641467.	+	1.97423e6i	−0.128477	+	0.395412i
$83$	1.96687e6	−	6.05340e6i	0.377574	−	1.16205i	−0.564152	−	0.825671i	$-0.690797\pi$
$83$	1.96687e6	−	6.05340e6i	0.377574	−	1.16205i	0.941726	−	0.336382i	$-0.109203\pi$
$84$		0			0
$85$	3.51318e6	+	2.55248e6i	0.620490	+	0.450812i
$86$	−16663.7	−	51285.6i	−0.00282506	−	0.00869463i
$87$		0			0
$88$	−502621.	−	2.85036e6i	−0.0786233	−	0.445872i
$89$	−1.82683e6			−0.274683			−0.137342	−	0.990524i	$-0.543856\pi$
$89$	−1.82683e6			−0.274683			−0.137342	+	0.990524i	$0.543856\pi$
$90$		0			0
$91$	1.57353e7	+	1.14324e7i	2.18892	+	1.59034i
$92$	5.76933e6	−	4.19166e6i	0.772445	−	0.561214i
$93$		0			0
$94$	464473.	−	1.42950e6i	0.0576783	−	0.177516i
$95$	3.20116e6	−	2.32578e6i	0.383067	−	0.278314i
$96$		0			0
$97$	−2.95746e6	−	9.10212e6i	−0.329016	−	1.01261i	−0.969595	−	0.244716i	$-0.921305\pi$
$97$	−2.95746e6	−	9.10212e6i	−0.329016	−	1.01261i	0.640579	−	0.767893i	$-0.278695\pi$
$98$	−3.01399e6			−0.323482
$99$		0			0
$100$	1.60447e6			0.160447
$101$	4.73213e6	+	1.45640e7i	0.457016	+	1.40655i	0.868751	+	0.495248i	$0.164923\pi$
$101$	4.73213e6	+	1.45640e7i	0.457016	+	1.40655i	−0.411735	+	0.911304i	$0.635077\pi$
$102$		0			0
$103$	−7.21717e6	+	5.24358e6i	−0.650783	+	0.472822i	−0.863538	−	0.504284i	$-0.831757\pi$
$103$	−7.21717e6	+	5.24358e6i	−0.650783	+	0.472822i	0.212755	+	0.977106i	$0.431757\pi$
$104$	−2.80871e6	+	8.64432e6i	−0.244844	+	0.753553i
$105$		0			0
$106$	−3.29951e6	+	2.39724e6i	−0.269079	+	0.195497i
$107$	−1.30604e7	−	9.48895e6i	−1.03066	−	0.748816i	−0.0622168	−	0.998063i	$-0.519817\pi$
$107$	−1.30604e7	−	9.48895e6i	−1.03066	−	0.748816i	−0.968440	+	0.249247i	$0.919817\pi$
$108$		0			0
$109$	−1.15589e7			−0.854917			−0.427459	−	0.904035i	$-0.640591\pi$
$109$	−1.15589e7			−0.854917			−0.427459	+	0.904035i	$0.640591\pi$
$110$	2.12910e6	+	2.05601e6i	0.152518	+	0.147282i
$111$		0			0
$112$	5.97060e6	+	1.83756e7i	0.401564	+	1.23589i
$113$	1.64688e7	+	1.19653e7i	1.07371	+	0.780097i	0.976576	−	0.215175i	$-0.0690321\pi$
$113$	1.64688e7	+	1.19653e7i	1.07371	+	0.780097i	0.0971352	+	0.995271i	$0.469032\pi$
$114$		0			0
$115$	−4.63599e6	+	1.42681e7i	−0.284250	+	0.874831i
$116$	1.15290e6	−	3.54827e6i	0.0685788	−	0.211064i
$117$		0			0
$118$	3.71407e6	+	2.69843e6i	0.208096	+	0.151190i
$119$	7.39201e6	+	2.27503e7i	0.402113	+	1.23758i
$120$		0			0
$121$	680425.	+	1.94753e7i	0.0349166	+	0.999390i
$122$	−4.81545e6			−0.240092
$123$		0			0
$124$	−1.90982e7	−	1.38756e7i	−0.899530	−	0.653547i
$125$	−1.88290e7	+	1.36801e7i	−0.862267	+	0.626474i
$126$		0			0
$127$	3.70108e6	−	1.13908e7i	0.160330	−	0.493446i	−0.838331	−	0.545161i	$-0.816469\pi$
$127$	3.70108e6	−	1.13908e7i	0.160330	−	0.493446i	0.998662	+	0.0517145i	$0.0164686\pi$
$128$	−1.55248e7	+	1.12794e7i	−0.654323	+	0.475393i
$129$		0			0
$130$	−2.87221e6	−	8.83974e6i	−0.114660	−	0.352889i
$131$	2.91097e7			1.13133			0.565663	−	0.824636i	$-0.308620\pi$
$131$	2.91097e7			1.13133			0.565663	+	0.824636i	$0.308620\pi$
$132$		0			0
$133$	2.17965e7			0.803351
$134$	−143750.	−	442417.i	−0.00516108	−	0.0158842i
$135$		0			0
$136$	−9.04367e6	+	6.57061e6i	−0.308289	+	0.223985i
$137$	8.49976e6	−	2.61596e7i	0.282413	−	0.869178i	−0.704749	−	0.709456i	$-0.748941\pi$
$137$	8.49976e6	−	2.61596e7i	0.282413	−	0.869178i	0.987162	−	0.159721i	$-0.0510595\pi$
$138$		0			0
$139$	6.09754e6	−	4.43012e6i	0.192576	−	0.139915i	−0.487319	−	0.873224i	$-0.662025\pi$
$139$	6.09754e6	−	4.43012e6i	0.192576	−	0.139915i	0.679895	+	0.733309i	$0.262025\pi$
$140$	−3.50021e7	−	2.54305e7i	−1.07807	−	0.783262i
$141$		0			0
$142$	9.41222e6			0.275856
$143$	2.68262e7	−	5.50030e7i	0.767154	−	1.57293i
$144$		0			0
$145$	2.42541e6	+	7.46466e6i	0.0660690	+	0.203340i
$146$	−1.54416e6	−	1.12190e6i	−0.0410636	−	0.0298345i
$147$		0			0
$148$	1.59858e7	−	4.91991e7i	0.405338	−	1.24750i
$149$	11108.9	−	34189.7i	0.000275118	−	0.000846727i	−0.950919	−	0.309440i	$-0.899858\pi$
$149$	11108.9	−	34189.7i	0.000275118	−	0.000846727i	0.951194	+	0.308594i	$0.0998583\pi$
$150$		0			0
$151$	2.81441e7	+	2.04479e7i	0.665224	+	0.483314i	0.868423	−	0.495824i	$-0.165134\pi$
$151$	2.81441e7	+	2.04479e7i	0.665224	+	0.483314i	−0.203199	+	0.979137i	$0.565134\pi$
$152$	3.14757e6	+	9.68723e6i	0.0726981	+	0.223742i
$153$		0			0
$154$	2.83130e6	+	1.60563e7i	0.0624688	+	0.354261i
$155$	4.96623e7			1.07119
$156$		0			0
$157$	7.20681e6	+	5.23606e6i	0.148626	+	0.107983i	0.659613	−	0.751605i	$-0.270720\pi$
$157$	7.20681e6	+	5.23606e6i	0.148626	+	0.107983i	−0.510987	+	0.859588i	$0.670720\pi$
$158$	2.22585e6	−	1.61717e6i	0.0448948	−	0.0326179i
$159$		0			0
$160$	9.45859e6	−	2.91105e7i	0.182560	−	0.561863i
$161$	−6.68582e7	+	4.85753e7i	−1.26259	+	0.917328i
$162$		0			0
$163$	−1.12312e7	−	3.45661e7i	−0.203128	−	0.625163i	−0.999785	−	0.0207319i	$-0.993400\pi$
$163$	−1.12312e7	−	3.45661e7i	−0.203128	−	0.625163i	0.796657	−	0.604431i	$-0.206600\pi$
$164$	−9.54723e7			−1.69014
$165$		0			0
$166$	−1.67550e7			−0.284294
$167$	−606562.	−	1.86681e6i	−0.0100778	−	0.0310164i	0.945891	−	0.324484i	$-0.105191\pi$
$167$	−606562.	−	1.86681e6i	−0.0100778	−	0.0310164i	−0.955969	+	0.293468i	$0.905191\pi$
$168$		0			0
$169$	−1.04709e8	+	7.60756e7i	−1.66871	+	1.21239i
$170$	3.53247e6	−	1.08718e7i	0.0551451	−	0.169719i
$171$		0			0
$172$	2.00647e6	−	1.45779e6i	0.0300665	−	0.0218446i
$173$	−2.96466e7	−	2.15395e7i	−0.435324	−	0.316282i	0.348450	−	0.937327i	$-0.386708\pi$
$173$	−2.96466e7	−	2.15395e7i	−0.435324	−	0.316282i	−0.783774	+	0.621046i	$0.786708\pi$
$174$		0			0
$175$	−1.85935e7			−0.262257
$176$	5.36754e7	−	2.85403e7i	0.742131	−	0.394606i
$177$		0			0
$178$	1.48605e6	+	4.57358e6i	0.0197498	+	0.0607835i
$179$	−7.23809e6	−	5.25878e6i	−0.0943275	−	0.0685330i	0.539622	−	0.841908i	$-0.318567\pi$
$179$	−7.23809e6	−	5.25878e6i	−0.0943275	−	0.0685330i	−0.633949	+	0.773375i	$0.718567\pi$
$180$		0			0
$181$	4.41647e7	−	1.35925e8i	0.553606	−	1.70382i	−0.145991	−	0.989286i	$-0.546637\pi$
$181$	4.41647e7	−	1.35925e8i	0.553606	−	1.70382i	0.699597	−	0.714538i	$-0.253363\pi$
$182$	1.58217e7	−	4.86941e7i	0.194537	−	0.598723i
$183$		0			0
$184$	−3.12436e7	−	2.26998e7i	−0.369742	−	0.268634i
$185$	3.36299e7	+	1.03502e8i	0.390503	+	1.20185i
$186$		0			0
$187$	6.64538e7	−	3.53348e7i	0.743146	−	0.395146i
$188$	6.91295e7			0.758771
$189$		0			0
$190$	−8.42674e6	−	6.12239e6i	−0.0891296	−	0.0647565i
$191$	6.78436e7	−	4.92913e7i	0.704518	−	0.511863i	−0.176882	−	0.984232i	$-0.556601\pi$
$191$	6.78436e7	−	4.92913e7i	0.704518	−	0.511863i	0.881401	+	0.472369i	$0.156601\pi$
$192$		0			0
$193$	4.60395e6	−	1.41695e7i	0.0460978	−	0.141874i	−0.925358	−	0.379093i	$-0.876236\pi$
$193$	4.60395e6	−	1.41695e7i	0.0460978	−	0.141874i	0.971456	+	0.237219i	$0.0762359\pi$
$194$	−2.03820e7	+	1.48084e7i	−0.200420	+	0.145613i
$195$		0			0
$196$	−4.28360e7	−	1.31836e8i	−0.406362	−	1.25065i
$197$	1.20579e8			1.12367			0.561837	−	0.827248i	$-0.310095\pi$
$197$	1.20579e8			1.12367			0.561837	+	0.827248i	$0.310095\pi$
$198$		0			0
$199$	−1.33693e8			−1.20261			−0.601303	−	0.799021i	$-0.705351\pi$
$199$	−1.33693e8			−1.20261			−0.601303	+	0.799021i	$0.705351\pi$
$200$	−2.68503e6	−	8.26368e6i	−0.0237326	−	0.0730413i
$201$		0			0
$202$	3.26125e7	−	2.36944e7i	0.278391	−	0.202263i
$203$	−1.33605e7	+	4.11194e7i	−0.112095	+	0.344993i
$204$		0			0
$205$	1.62490e8	−	1.18056e8i	1.31731	−	0.957084i
$206$	1.89985e7	+	1.38032e7i	0.151420	+	0.110013i
$207$		0			0
$208$	−1.90905e8			−1.47094
$209$	−1.19092e7	−	6.75373e7i	−0.0902344	−	0.511719i
$210$		0			0
$211$	−1.45065e7	−	4.46463e7i	−0.106310	−	0.327188i	0.883726	−	0.468005i	$-0.155027\pi$
$211$	−1.45065e7	−	4.46463e7i	−0.106310	−	0.327188i	−0.990036	+	0.140817i	$0.955027\pi$
$212$	−1.51752e8	−	1.10254e8i	−1.09385	−	0.794732i
$213$		0			0
$214$	−1.31321e7	+	4.04165e7i	−0.0915981	+	0.281910i
$215$	−1.61232e6	+	4.96220e6i	−0.0110641	+	0.0340517i
$216$		0			0
$217$	2.21320e8	+	1.60799e8i	1.47032	+	1.06825i
$218$	9.40268e6	+	2.89385e7i	0.0614687	+	0.189181i
$219$		0			0
$220$	−5.96730e7	+	1.22350e8i	−0.377832	+	0.774687i
$221$	−2.36354e8			−1.47295
$222$		0			0
$223$	1.01382e8	+	7.36582e7i	0.612200	+	0.444789i	0.850188	−	0.526479i	$-0.176488\pi$
$223$	1.01382e8	+	7.36582e7i	0.612200	+	0.444789i	−0.237988	+	0.971268i	$0.576488\pi$
$224$	1.36408e8	−	9.91059e7i	0.810906	−	0.589157i
$225$		0			0
$226$	1.65592e7	−	5.09640e7i	0.0954244	−	0.293686i
$227$	−1.68600e8	+	1.22495e8i	−0.956682	+	0.695070i	−0.952378	−	0.304921i	$-0.901370\pi$
$227$	−1.68600e8	+	1.22495e8i	−0.956682	+	0.695070i	−0.00430400	+	0.999991i	$0.501370\pi$
$228$		0			0
$229$	8.33162e7	+	2.56421e8i	0.458464	+	1.41101i	0.867020	+	0.498274i	$0.166033\pi$
$229$	8.33162e7	+	2.56421e8i	0.458464	+	1.41101i	−0.408555	+	0.912733i	$0.633967\pi$
$230$	3.94923e7			0.214025
$231$		0			0
$232$	−2.02045e7			−0.106228
$233$	−2.08449e7	−	6.41540e7i	−0.107958	−	0.332260i	0.882455	−	0.470396i	$-0.155889\pi$
$233$	−2.08449e7	−	6.41540e7i	−0.107958	−	0.332260i	−0.990413	+	0.138136i	$0.955889\pi$
$234$		0			0
$235$	−1.17656e8	+	8.54820e7i	−0.591393	+	0.429672i
$236$	−6.52470e7	+	2.00810e8i	−0.323124	+	0.994472i
$237$		0			0
$238$	5.09437e7	−	3.70127e7i	0.244946	−	0.177964i
$239$	−1.35612e8	−	9.85280e7i	−0.642549	−	0.466839i	0.218176	−	0.975909i	$-0.429989\pi$
$239$	−1.35612e8	−	9.85280e7i	−0.642549	−	0.466839i	−0.860725	+	0.509070i	$0.829989\pi$
$240$		0			0
$241$	1.09790e7			0.0505246			0.0252623	−	0.999681i	$-0.491958\pi$
$241$	1.09790e7			0.0505246			0.0252623	+	0.999681i	$0.491958\pi$
$242$	4.82042e7	−	1.75458e7i	0.218641	−	0.0795829i
$243$		0			0
$244$	−6.84391e7	−	2.10634e8i	−0.301606	−	0.928248i
$245$	2.35927e8	+	1.71411e8i	1.02493	+	0.744658i
$246$		0			0
$247$	−6.65504e7	+	2.04821e8i	−0.281003	+	0.864839i
$248$	−3.95051e7	+	1.21584e8i	−0.164464	+	0.506170i
$249$		0			0
$250$	4.95655e7	+	3.60115e7i	0.200627	+	0.145764i
$251$	−1.78934e7	−	5.50701e7i	−0.0714224	−	0.219815i	0.908973	−	0.416854i	$-0.136867\pi$
$251$	−1.78934e7	−	5.50701e7i	−0.0714224	−	0.219815i	−0.980396	+	0.197039i	$0.936867\pi$
$252$		0			0
$253$	1.87043e8	+	1.80622e8i	0.726138	+	0.701212i
$254$	−3.15282e7			−0.120721
$255$		0			0
$256$	−1.08908e8	−	7.91262e7i	−0.405713	−	0.294768i
$257$	−8.56638e7	+	6.22384e7i	−0.314798	+	0.228714i	−0.733952	−	0.679201i	$-0.762326\pi$
$257$	−8.56638e7	+	6.22384e7i	−0.314798	+	0.228714i	0.419155	+	0.907915i	$0.362326\pi$
$258$		0			0
$259$	−1.85252e8	+	5.70147e8i	−0.662542	+	2.03909i
$260$	3.45841e8	−	2.51268e8i	1.22031	−	0.886606i
$261$		0			0
$262$	−2.36795e7	−	7.28780e7i	−0.0813426	−	0.250347i
$263$	1.98561e8			0.673052			0.336526	−	0.941674i	$-0.390748\pi$
$263$	1.98561e8			0.673052			0.336526	+	0.941674i	$0.390748\pi$
$264$		0			0
$265$	3.94612e8			1.30260
$266$	−1.77305e7	−	5.45689e7i	−0.0577611	−	0.177770i
$267$		0			0
$268$	1.73089e7	−	1.25756e7i	0.0549284	−	0.0399078i
$269$	−1.08402e8	+	3.33628e8i	−0.339551	+	1.04503i	0.624885	+	0.780717i	$0.285146\pi$
$269$	−1.08402e8	+	3.33628e8i	−0.339551	+	1.04503i	−0.964436	+	0.264315i	$0.914854\pi$
$270$		0			0
$271$	7.18501e7	−	5.22022e7i	0.219298	−	0.159329i	−0.472712	−	0.881217i	$-0.656725\pi$
$271$	7.18501e7	−	5.22022e7i	0.219298	−	0.159329i	0.692011	+	0.721887i	$0.256725\pi$
$272$	−1.89949e8	−	1.38006e8i	−0.572330	−	0.415822i
$273$		0			0
$274$	−7.24064e7			−0.212642
$275$	1.01592e7	+	5.76126e7i	0.0294574	+	0.167053i
$276$		0			0
$277$	−6.36863e7	−	1.96006e8i	−0.180039	−	0.554104i	0.819788	−	0.572666i	$-0.194091\pi$
$277$	−6.36863e7	−	1.96006e8i	−0.180039	−	0.554104i	−0.999828	+	0.0185627i	$0.994091\pi$
$278$	−1.60512e7	−	1.16619e7i	−0.0448075	−	0.0325545i
$279$		0			0
$280$	−7.24028e7	+	2.22833e8i	−0.197107	+	0.606633i
$281$	−1.28571e8	+	3.95702e8i	−0.345679	+	1.06389i	0.615541	+	0.788105i	$0.288938\pi$
$281$	−1.28571e8	+	3.95702e8i	−0.345679	+	1.06389i	−0.961220	+	0.275784i	$0.911062\pi$
$282$		0			0
$283$	−1.78935e8	−	1.30004e8i	−0.469292	−	0.340960i	0.327874	−	0.944722i	$-0.393668\pi$
$283$	−1.78935e8	−	1.30004e8i	−0.469292	−	0.340960i	−0.797165	+	0.603761i	$0.793668\pi$
$284$	1.33770e8	+	4.11703e8i	0.346534	+	1.06652i
$285$		0			0
$286$	−1.59525e8	−	2.24184e7i	−0.403226	−	0.0566662i
$287$	1.10639e9			2.76261
$288$		0			0
$289$	9.68006e7	+	7.03298e7i	0.235904	+	0.171394i
$290$	1.67153e7	−	1.21444e7i	0.0402458	−	0.0292403i
$291$		0			0
$292$	2.71271e7	−	8.34885e7i	0.0637621	−	0.196240i
$293$	−1.02733e8	+	7.46400e7i	−0.238602	+	0.173355i	−0.700660	−	0.713495i	$-0.747111\pi$
$293$	−1.02733e8	+	7.46400e7i	−0.238602	+	0.173355i	0.462058	+	0.886850i	$0.347111\pi$
$294$		0			0
$295$	−1.37263e8	−	4.22452e8i	−0.311298	−	0.958077i
$296$	−2.80148e8			−0.627865
$297$		0			0
$298$	−94632.8			−0.000207150
$299$	−2.52326e8	−	7.76578e8i	−0.545899	−	1.68010i
$300$		0			0
$301$	−2.32521e7	+	1.68936e7i	−0.0491450	+	0.0357059i
$302$	2.82986e7	−	8.70941e7i	0.0591208	−	0.181955i
$303$		0			0
$304$	−1.73079e8	+	1.25749e8i	−0.353335	+	0.256713i
$305$	3.76940e8	+	2.73863e8i	0.760717	+	0.552693i
$306$		0			0
$307$	4.24137e8			0.836608			0.418304	−	0.908307i	$-0.362625\pi$
$307$	4.24137e8			0.836608			0.418304	+	0.908307i	$0.362625\pi$
$308$	−6.62084e8	+	3.52044e8i	−1.29118	+	0.686545i
$309$		0			0
$310$	−4.03982e7	−	1.24333e8i	−0.0770186	−	0.237039i
$311$	9.19886e7	+	6.68336e7i	0.173409	+	0.125989i	0.671105	−	0.741363i	$-0.265820\pi$
$311$	9.19886e7	+	6.68336e7i	0.173409	+	0.125989i	−0.497695	+	0.867352i	$0.665820\pi$
$312$		0			0
$313$	1.40449e8	−	4.32257e8i	0.258889	−	0.796777i	−0.734150	−	0.678987i	$-0.762419\pi$
$313$	1.40449e8	−	4.32257e8i	0.258889	−	0.796777i	0.993039	−	0.117790i	$-0.0375809\pi$
$314$	7.24637e6	−	2.23020e7i	0.0132089	−	0.0406528i
$315$		0			0
$316$	1.02372e8	+	7.43776e7i	0.182506	+	0.132598i
$317$	−3.28362e8	−	1.01060e9i	−0.578957	−	1.78185i	−0.622293	−	0.782785i	$-0.713799\pi$
$317$	−3.28362e8	−	1.01060e9i	−0.578957	−	1.78185i	0.0433361	−	0.999061i	$-0.486201\pi$
$318$		0			0
$319$	1.34710e8	+	1.89311e7i	0.232345	+	0.0326519i
$320$	3.68387e8			0.628462
$321$		0			0
$322$	1.75998e8	+	1.27870e8i	0.293773	+	0.213438i
$323$	−2.14284e8	+	1.55686e8i	−0.353818	+	0.257064i
$324$		0			0
$325$	5.67707e7	−	1.74722e8i	0.0917345	−	0.282330i
$326$	−7.74023e7	+	5.62361e7i	−0.123735	+	0.0898987i
$327$		0			0
$328$	1.59770e8	+	4.91723e8i	0.249999	+	0.769417i
$329$	−8.01111e8			−1.24024
$330$		0			0
$331$	−5.54435e8			−0.840336			−0.420168	−	0.907446i	$-0.638029\pi$
$331$	−5.54435e8			−0.840336			−0.420168	+	0.907446i	$0.638029\pi$
$332$	−2.38130e8	−	7.32888e8i	−0.357133	−	1.09914i
$333$		0			0
$334$	−4.18026e6	+	3.03714e6i	−0.00613890	+	0.00446017i
$335$	−1.39087e7	+	4.28065e7i	−0.0202129	+	0.0622090i
$336$		0			0
$337$	−2.88719e8	+	2.09767e8i	−0.410933	+	0.298561i	−0.773980	−	0.633211i	$-0.781737\pi$
$337$	−2.88719e8	+	2.09767e8i	−0.410933	+	0.298561i	0.363046	+	0.931771i	$0.381737\pi$
$338$	2.75637e8	+	2.00262e8i	0.388265	+	0.282091i
$339$		0			0
$340$	5.25753e8			0.725446
$341$	3.77315e8	−	7.73628e8i	0.515305	−	1.05655i
$342$		0			0
$343$	1.39352e8	+	4.28881e8i	0.186459	+	0.573862i
$344$	−1.08660e7	−	7.89460e6i	−0.0143918	−	0.0104562i
$345$		0			0
$346$	−2.98093e7	+	9.17436e7i	−0.0386888	+	0.119072i
$347$	−1.64537e8	+	5.06391e8i	−0.211402	+	0.650629i	0.787987	+	0.615691i	$0.211123\pi$
$347$	−1.64537e8	+	5.06391e8i	−0.211402	+	0.650629i	−0.999390	+	0.0349373i	$0.988877\pi$
$348$		0			0
$349$	−9.26512e8	−	6.73150e8i	−1.16671	−	0.847663i	−0.176096	−	0.984373i	$-0.556347\pi$
$349$	−9.26512e8	−	6.73150e8i	−1.16671	−	0.847663i	−0.990611	+	0.136710i	$0.956347\pi$
$350$	1.51250e7	+	4.65499e7i	0.0188563	+	0.0580338i
$351$		0			0
$352$	−3.81615e8	−	3.68515e8i	−0.466365	−	0.450356i
$353$	−4.20718e8			−0.509072			−0.254536	−	0.967063i	$-0.581923\pi$
$353$	−4.20718e8			−0.509072			−0.254536	+	0.967063i	$0.581923\pi$
$354$		0			0
$355$	−7.36763e8	−	5.35290e8i	−0.874035	−	0.635024i
$356$	−1.78934e8	+	1.30003e8i	−0.210193	+	0.152714i
$357$		0			0
$358$	−7.27782e6	+	2.23988e7i	−0.00838322	+	0.0258009i
$359$	4.86535e8	−	3.53488e8i	0.554988	−	0.403222i	−0.274633	−	0.961549i	$-0.588557\pi$
$359$	4.86535e8	−	3.53488e8i	0.554988	−	0.403222i	0.829621	+	0.558327i	$0.188557\pi$
$360$		0			0
$361$	−2.01642e8	−	6.20590e8i	−0.225583	−	0.694272i
$362$	−3.76224e8			−0.416837
$363$		0			0
$364$	2.35481e9			2.55918
$365$	5.70684e7	+	1.75638e8i	0.0614286	+	0.189058i
$366$		0			0
$367$	8.36144e8	−	6.07494e8i	0.882978	−	0.641521i	−0.0510595	−	0.998696i	$-0.516260\pi$
$367$	8.36144e8	−	6.07494e8i	0.882978	−	0.641521i	0.934038	+	0.357174i	$0.116260\pi$
$368$	2.50657e8	−	7.71442e8i	0.262187	−	0.806930i
$369$		0			0
$370$	2.31768e8	−	1.68389e8i	0.237874	−	0.172826i
$371$	1.75859e9	+	1.27769e9i	1.78795	+	1.29902i
$372$		0			0
$373$	−1.78117e9			−1.77715			−0.888575	−	0.458731i	$-0.848304\pi$
$373$	−1.78117e9			−1.77715			−0.888575	+	0.458731i	$0.848304\pi$
$374$	−1.42520e8	−	1.37628e8i	−0.140873	−	0.136037i
$375$		0			0
$376$	−1.15686e8	−	3.56046e8i	−0.112234	−	0.345421i
$377$	−3.45605e8	−	2.51097e8i	−0.332189	−	0.241349i
$378$		0			0
$379$	−1.83004e8	+	5.63228e8i	−0.172672	+	0.531431i	−0.999520	−	0.0309956i	$-0.990132\pi$
$379$	−1.83004e8	+	5.63228e8i	−0.172672	+	0.531431i	0.826847	+	0.562427i	$0.190132\pi$
$380$	1.48037e8	−	4.55611e8i	0.138397	−	0.425943i
$381$		0			0
$382$	−1.78592e8	−	1.29755e8i	−0.163923	−	0.119097i
$383$	−5.11794e8	−	1.57514e9i	−0.465479	−	1.43260i	−0.858379	−	0.513015i	$-0.828528\pi$
$383$	−5.11794e8	−	1.57514e9i	−0.465479	−	1.43260i	0.392901	−	0.919581i	$-0.371472\pi$
$384$		0			0
$385$	6.91524e8	−	1.41786e9i	0.617582	−	1.26626i
$386$	−3.92194e7			−0.0347093
$387$		0			0
$388$	−9.37415e8	−	6.81072e8i	−0.814744	−	0.591946i
$389$	−5.75264e8	+	4.17954e8i	−0.495500	+	0.360002i	−0.807295	−	0.590147i	$-0.799070\pi$
$389$	−5.75264e8	+	4.17954e8i	−0.495500	+	0.360002i	0.311796	+	0.950149i	$0.399070\pi$
$390$		0			0
$391$	3.10330e8	−	9.55098e8i	0.262546	−	0.808033i
$392$	−6.07325e8	+	4.41247e8i	−0.509237	+	0.369982i
$393$		0			0
$394$	−9.80860e7	−	3.01878e8i	−0.0807923	−	0.248653i
$395$	−2.66205e8			−0.217333
$396$		0			0
$397$	1.35778e7			0.0108909			0.00544544	−	0.999985i	$-0.498267\pi$
$397$	1.35778e7			0.0108909			0.00544544	+	0.999985i	$0.498267\pi$
$398$	1.08754e8	+	3.34709e8i	0.0864676	+	0.266120i
$399$		0			0
$400$	1.47645e8	−	1.07270e8i	0.115347	−	0.0838048i
$401$	−6.02875e8	+	1.85546e9i	−0.466898	+	1.43696i	0.389682	+	0.920949i	$0.372585\pi$
$401$	−6.02875e8	+	1.85546e9i	−0.466898	+	1.43696i	−0.856580	+	0.516014i	$0.827415\pi$
$402$		0			0
$403$	−2.18677e9	+	1.58878e9i	−1.66431	+	1.20920i
$404$	1.49993e9	+	1.08976e9i	1.13171	+	0.822236i
$405$		0			0
$406$	1.13813e8			0.0844018
$407$	1.86784e9	+	2.62492e8i	1.37328	+	0.192990i
$408$		0			0
$409$	−3.31520e8	−	1.02031e9i	−0.239595	−	0.737399i	−0.996479	−	0.0838485i	$-0.973279\pi$
$409$	−3.31520e8	−	1.02031e9i	−0.239595	−	0.737399i	0.756883	−	0.653550i	$-0.226721\pi$
$410$	−4.27740e8	−	3.10772e8i	−0.306504	−	0.222689i
$411$		0			0
$412$	−3.33756e8	+	1.02720e9i	−0.235120	+	0.723625i
$413$	7.56119e8	−	2.32709e9i	0.528159	−	1.62551i
$414$		0			0
$415$	1.31154e9	+	9.52889e8i	0.900768	+	0.654446i
$416$	5.14808e8	+	1.58442e9i	0.350605	+	1.07905i
$417$		0			0
$418$	−1.59396e8	+	8.47543e7i	−0.106748	+	0.0567603i
$419$	−6.32009e8			−0.419734			−0.209867	−	0.977730i	$-0.567303\pi$
$419$	−6.32009e8			−0.419734			−0.209867	+	0.977730i	$0.567303\pi$
$420$		0			0
$421$	2.34865e9	+	1.70639e9i	1.53402	+	1.11453i	0.953951	+	0.299962i	$0.0969739\pi$
$421$	2.34865e9	+	1.70639e9i	1.53402	+	1.11453i	0.580068	+	0.814568i	$0.303026\pi$
$422$	−9.99746e7	+	7.26358e7i	−0.0647584	+	0.0470497i
$423$		0			0
$424$	−3.13904e8	+	9.66097e8i	−0.199994	+	0.615517i
$425$	1.82794e8	−	1.32808e8i	0.115505	−	0.0839194i
$426$		0			0
$427$	7.93111e8	+	2.44094e9i	0.492988	+	1.51726i
$428$	−1.95451e9			−1.20499
$429$		0			0
$430$	1.37347e7			0.00833068
$431$	9.35203e7	+	2.87826e8i	0.0562647	+	0.173165i	0.975239	−	0.221151i	$-0.0709815\pi$
$431$	9.35203e7	+	2.87826e8i	0.0562647	+	0.173165i	−0.918975	+	0.394316i	$0.870981\pi$
$432$		0			0
$433$	−5.08287e8	+	3.69292e8i	−0.300886	+	0.218606i	−0.727976	−	0.685603i	$-0.759539\pi$
$433$	−5.08287e8	+	3.69292e8i	−0.300886	+	0.218606i	0.427090	+	0.904209i	$0.359539\pi$
$434$	2.22535e8	−	6.84892e8i	0.130673	−	0.402169i
$435$		0			0
$436$	−1.13217e9	+	8.22572e8i	−0.654199	+	0.475303i
$437$	−7.40296e8	−	5.37857e8i	−0.424346	−	0.308306i
$438$		0			0
$439$	5.93586e8			0.334856			0.167428	−	0.985884i	$-0.446454\pi$
$439$	5.93586e8			0.334856			0.167428	+	0.985884i	$0.446454\pi$
$440$	7.30018e8	+	1.02591e8i	0.408554	+	0.0574149i
$441$		0			0
$442$	1.92264e8	+	5.91726e8i	0.105906	+	0.325944i
$443$	5.98625e8	+	4.34927e8i	0.327146	+	0.237686i	0.739219	−	0.673465i	$-0.235195\pi$
$443$	5.98625e8	+	4.34927e8i	0.327146	+	0.237686i	−0.412073	+	0.911151i	$0.635195\pi$
$444$		0			0
$445$	1.43784e8	−	4.42521e8i	0.0773482	−	0.238053i
$446$	1.01938e8	−	3.13734e8i	0.0544083	−	0.167452i
$447$		0			0
$448$	1.64172e9	+	1.19278e9i	0.862631	+	0.626738i
$449$	−2.42574e8	−	7.46566e8i	−0.126468	−	0.389230i	0.867697	−	0.497093i	$-0.165599\pi$
$449$	−2.42574e8	−	7.46566e8i	−0.126468	−	0.389230i	−0.994166	+	0.107863i	$0.965599\pi$
$450$		0			0
$451$	−6.04512e8	−	3.42819e9i	−0.310304	−	1.75973i
$452$	2.46458e9			1.25533
$453$		0			0
$454$	4.43824e8	+	3.22457e8i	0.222595	+	0.161725i
$455$	−4.00780e9	+	2.91183e9i	−1.99465	+	1.44920i
$456$		0			0
$457$	−6.19943e8	+	1.90799e9i	−0.303840	+	0.935123i	0.676268	+	0.736656i	$0.263596\pi$
$457$	−6.19943e8	+	1.90799e9i	−0.303840	+	0.935123i	−0.980108	+	0.198467i	$0.936404\pi$
$458$	5.74192e8	−	4.17175e8i	0.279273	−	0.202903i
$459$		0			0
$460$	5.61281e8	+	1.72745e9i	0.268861	+	0.827470i
$461$	−2.66565e9			−1.26721			−0.633607	−	0.773655i	$-0.718426\pi$
$461$	−2.66565e9			−1.26721			−0.633607	+	0.773655i	$0.718426\pi$
$462$		0			0
$463$	2.88189e9			1.34941			0.674705	−	0.738087i	$-0.264271\pi$
$463$	2.88189e9			1.34941			0.674705	+	0.738087i	$0.264271\pi$
$464$	−1.31136e8	−	4.03596e8i	−0.0609410	−	0.187557i
$465$		0			0
$466$	−1.43657e8	+	1.04373e8i	−0.0657623	+	0.0477791i
$467$	6.35733e8	−	1.95658e9i	0.288846	−	0.888975i	−0.696374	−	0.717679i	$-0.745205\pi$
$467$	6.35733e8	−	1.95658e9i	0.288846	−	0.888975i	0.985220	−	0.171296i	$-0.0547955\pi$
$468$		0			0
$469$	−2.00585e8	+	1.45733e8i	−0.0897828	+	0.0652310i
$470$	3.09718e8	+	2.25023e8i	0.137602	+	0.0999735i
$471$		0			0
$472$	1.14344e9			0.500516
$473$	6.50502e7	+	6.28172e7i	0.0282641	+	0.0272938i
$474$		0			0
$475$	−6.36200e7	−	1.95802e8i	−0.0272374	−	0.0838282i
$476$	2.34302e9	+	1.70230e9i	0.995753	+	0.723457i
$477$		0			0
$478$	−1.36357e8	+	4.19662e8i	−0.0571056	+	0.175753i
$479$	6.62997e7	−	2.04049e8i	0.0275637	−	0.0848322i	−0.936328	−	0.351126i	$-0.885799\pi$
$479$	6.62997e7	−	2.04049e8i	0.0275637	−	0.0848322i	0.963892	+	0.266293i	$0.0857990\pi$
$480$		0			0
$481$	−4.79203e9	−	3.48162e9i	−1.96342	−	1.42650i
$482$	−8.93095e6	−	2.74866e7i	−0.00363273	−	0.0111804i
$483$		0			0
$484$	1.45257e9	+	1.85915e9i	0.582344	+	0.745340i
$485$	2.43763e9			0.970222
$486$		0			0
$487$	2.18325e9	+	1.58622e9i	0.856548	+	0.622319i	0.926944	−	0.375201i	$-0.122426\pi$
$487$	2.18325e9	+	1.58622e9i	0.856548	+	0.622319i	−0.0703957	+	0.997519i	$0.522426\pi$
$488$	−9.70323e8	+	7.04981e8i	−0.377961	+	0.274605i
$489$		0			0
$490$	2.37222e8	−	7.30093e8i	0.0910895	−	0.280345i
$491$	−3.13389e9	+	2.27690e9i	−1.19481	+	0.868079i	−0.993764	−	0.111503i	$-0.964434\pi$
$491$	−3.13389e9	+	2.27690e9i	−1.19481	+	0.868079i	−0.201044	+	0.979582i	$0.564434\pi$
$492$		0			0
$493$	−1.62356e8	−	4.99679e8i	−0.0610243	−	0.187814i
$494$	5.66919e8			0.211581
$495$		0			0
$496$	−2.68512e9			−0.988047
$497$	−1.55021e9	−	4.77104e9i	−0.566425	−	1.74328i
$498$		0			0
$499$	−1.32646e9	+	9.63731e8i	−0.477906	+	0.347219i	−0.800515	−	0.599313i	$-0.795440\pi$
$499$	−1.32646e9	+	9.63731e8i	−0.477906	+	0.347219i	0.322608	+	0.946533i	$0.395440\pi$
$500$	−8.70743e8	+	2.67987e9i	−0.311526	+	0.958780i
$501$		0			0
$502$	−1.23316e8	+	8.95945e7i	−0.0435068	+	0.0316095i
$503$	1.16889e9	+	8.49249e8i	0.409530	+	0.297541i	0.773412	−	0.633904i	$-0.218549\pi$
$503$	1.16889e9	+	8.49249e8i	0.409530	+	0.297541i	−0.363881	+	0.931445i	$0.618549\pi$
$504$		0			0
$505$	−3.90036e9			−1.34768
$506$	3.00048e8	−	6.15203e8i	0.102959	−	0.211102i
$507$		0			0
$508$	−4.48092e8	−	1.37909e9i	−0.151651	−	0.466733i
$509$	2.84767e9	+	2.06895e9i	0.957144	+	0.695406i	0.952486	−	0.304583i	$-0.0985172\pi$
$509$	2.84767e9	+	2.06895e9i	0.957144	+	0.695406i	0.00465836	+	0.999989i	$0.498517\pi$
$510$		0			0
$511$	−3.14364e8	+	9.67512e8i	−0.104222	+	0.320762i
$512$	−8.68540e8	+	2.67309e9i	−0.285986	+	0.880175i
$513$		0			0
$514$	2.25502e8	+	1.63837e8i	0.0732452	+	0.0532157i
$515$	−7.02138e8	−	2.16096e9i	−0.226515	−	0.697142i
$516$		0			0
$517$	4.37715e8	+	2.48228e9i	0.139307	+	0.790012i
$518$	1.57809e9			0.498860
$519$		0			0
$520$	−1.87289e9	−	1.36074e9i	−0.584119	−	0.424387i
$521$	2.62867e9	−	1.90984e9i	0.814336	−	0.591650i	−0.100749	−	0.994912i	$-0.532124\pi$
$521$	2.62867e9	−	1.90984e9i	0.814336	−	0.591650i	0.915084	+	0.403262i	$0.132124\pi$
$522$		0			0
$523$	1.92151e9	−	5.91379e9i	0.587335	−	1.80763i	−0.00234717	−	0.999997i	$-0.500747\pi$
$523$	1.92151e9	−	5.91379e9i	0.587335	−	1.80763i	0.589683	−	0.807635i	$-0.299253\pi$
$524$	2.85124e9	−	2.07155e9i	0.865713	−	0.628977i
$525$		0			0
$526$	−1.61521e8	−	4.97110e8i	−0.0483925	−	0.148937i
$527$	−3.32436e9			−0.989398
$528$		0			0
$529$	6.46069e7			0.0189751
$530$	−3.21000e8	−	9.87937e8i	−0.0936569	−	0.288246i
$531$		0			0
$532$	2.13492e9	−	1.55111e9i	0.614740	−	0.446635i
$533$	−3.37809e9	+	1.03967e10i	−0.966331	+	2.97406i
$534$		0			0
$535$	3.32651e9	−	2.41685e9i	0.939182	−	0.682356i
$536$	−9.37357e7	−	6.81030e7i	−0.0262923	−	0.0191025i
$537$		0			0
$538$	9.23440e8			0.255665
$539$	4.46268e9	−	2.37290e9i	1.22754	−	0.652707i
$540$		0			0
$541$	−6.12651e8	−	1.88555e9i	−0.166350	−	0.511973i	0.832783	−	0.553599i	$-0.186746\pi$
$541$	−6.12651e8	−	1.88555e9i	−0.166350	−	0.511973i	−0.999133	+	0.0416266i	$0.986746\pi$
$542$	−1.89139e8	−	1.37417e8i	−0.0510250	−	0.0370718i
$543$		0			0
$544$	−6.33152e8	+	1.94864e9i	−0.168621	+	0.518962i
$545$	9.09767e8	−	2.79997e9i	0.240737	−	0.740911i
$546$		0			0
$547$	1.33445e9	+	9.69532e8i	0.348615	+	0.253283i	0.748288	−	0.663374i	$-0.230876\pi$
$547$	1.33445e9	+	9.69532e8i	0.348615	+	0.253283i	−0.399673	+	0.916658i	$0.630876\pi$
$548$	−1.02907e9	−	3.16715e9i	−0.267124	−	0.822123i
$549$		0			0
$550$	1.35973e8	−	7.22996e7i	0.0348484	−	0.0185296i
$551$	−4.78731e8			−0.121916
$552$		0			0
$553$	−1.18634e9	−	8.61929e8i	−0.298313	−	0.216737i
$554$	−4.38909e8	+	3.18886e8i	−0.109671	+	0.0796803i
$555$		0			0
$556$	2.81980e8	−	8.67844e8i	0.0695754	−	0.214131i
$557$	3.93895e9	−	2.86181e9i	0.965799	−	0.701694i	0.0113089	−	0.999936i	$-0.496400\pi$
$557$	3.93895e9	−	2.86181e9i	0.965799	−	0.701694i	0.954490	+	0.298242i	$0.0964002\pi$
$558$		0			0
$559$	−8.77544e7	−	2.70080e8i	−0.0212485	−	0.0653960i
$560$	−4.92114e9			−1.18415
$561$		0			0
$562$	1.09525e9			0.260278
$563$	−1.98867e9	−	6.12050e9i	−0.469660	−	1.44546i	−0.853026	−	0.521868i	$-0.825235\pi$
$563$	−1.98867e9	−	6.12050e9i	−0.469660	−	1.44546i	0.383366	−	0.923596i	$-0.374765\pi$
$564$		0			0
$565$	−4.19462e9	+	3.04757e9i	−0.978415	+	0.710860i
$566$	−1.79917e8	+	5.53728e8i	−0.0417076	+	0.128363i
$567$		0			0
$568$	1.89658e9	−	1.37795e9i	0.434263	−	0.315511i
$569$	−3.04969e9	−	2.21573e9i	−0.694005	−	0.504224i	0.183969	−	0.982932i	$-0.441105\pi$
$569$	−3.04969e9	−	2.21573e9i	−0.694005	−	0.504224i	−0.877974	+	0.478708i	$0.841105\pi$
$570$		0			0
$571$	−1.24590e9			−0.280063			−0.140032	−	0.990147i	$-0.544720\pi$
$571$	−1.24590e9			−0.280063			−0.140032	+	0.990147i	$0.544720\pi$
$572$	−1.28663e9	−	7.29647e9i	−0.287453	−	1.63015i
$573$		0			0
$574$	−8.99998e8	−	2.76991e9i	−0.198632	−	0.611328i
$575$	6.31509e8	+	4.58818e8i	0.138529	+	0.100648i
$576$		0			0
$577$	−2.30342e9	+	7.08920e9i	−0.499181	+	1.53632i	0.311157	+	0.950359i	$0.399284\pi$
$577$	−2.30342e9	+	7.08920e9i	−0.499181	+	1.53632i	−0.810338	+	0.585963i	$0.800716\pi$
$578$	9.73320e7	−	2.99557e8i	0.0209656	−	0.0645256i
$579$		0			0
$580$	7.68775e8	+	5.58548e8i	0.163607	+	0.118867i
$581$	2.75958e9	+	8.49311e9i	0.583749	+	1.79660i
$582$		0			0
$583$	2.99811e9	−	6.14718e9i	0.626626	−	1.28480i
$584$	−4.75398e8			−0.0987671
$585$		0			0
$586$	2.70435e8	+	1.96483e8i	0.0555165	+	0.0403351i
$587$	−5.53296e9	+	4.01993e9i	−1.12908	+	0.820324i	−0.985561	−	0.169323i	$-0.945842\pi$
$587$	−5.53296e9	+	4.01993e9i	−1.12908	+	0.820324i	−0.143519	+	0.989648i	$0.545842\pi$
$588$		0			0
$589$	−9.36045e8	+	2.88085e9i	−0.188753	+	0.580921i
$590$	−9.45978e8	+	6.87294e8i	−0.189627	+	0.137772i
$591$		0			0
$592$	−1.81829e9	−	5.59612e9i	−0.360194	−	1.10856i
$593$	3.59261e9			0.707487			0.353743	−	0.935342i	$-0.384909\pi$
$593$	3.59261e9			0.707487			0.353743	+	0.935342i	$0.384909\pi$
$594$		0			0
$595$	−6.09271e9			−1.18577
$596$	−1.34496e6	−	4.13936e6i	−0.000260224	−	0.000800888i
$597$		0			0
$598$	−1.73896e9	+	1.26343e9i	−0.332533	+	0.241599i
$599$	−1.25482e9	+	3.86194e9i	−0.238555	+	0.734196i	0.758075	+	0.652167i	$0.226140\pi$
$599$	−1.25482e9	+	3.86194e9i	−0.238555	+	0.734196i	−0.996630	+	0.0820289i	$0.973860\pi$
$600$		0			0
$601$	6.45943e9	−	4.69305e9i	1.21376	−	0.881850i	0.218195	−	0.975905i	$-0.429983\pi$
$601$	6.45943e9	−	4.69305e9i	1.21376	−	0.881850i	0.995567	+	0.0940554i	$0.0299831\pi$
$602$	6.12089e7	+	4.44709e7i	0.0114348	+	0.00830784i
$603$		0			0
$604$	4.21180e9			0.777747
$605$	−4.77115e9	−	1.36802e9i	−0.875951	−	0.251159i
$606$		0			0
$607$	−1.12194e9	−	3.45299e9i	−0.203615	−	0.626664i	−0.999767	−	0.0215671i	$-0.993134\pi$
$607$	−1.12194e9	−	3.45299e9i	−0.203615	−	0.626664i	0.796152	−	0.605097i	$-0.206866\pi$
$608$	1.51039e9	+	1.09736e9i	0.272538	+	0.198010i
$609$		0			0
$610$	3.79009e8	−	1.16647e9i	0.0676076	−	0.208075i
$611$	2.44600e9	−	7.52803e9i	0.433824	−	1.33517i
$612$		0			0
$613$	8.99143e9	+	6.53266e9i	1.57658	+	1.14546i	0.920482	+	0.390784i	$0.127796\pi$
$613$	8.99143e9	+	6.53266e9i	1.57658	+	1.14546i	0.656102	+	0.754672i	$0.272204\pi$
$614$	−3.45018e8	−	1.06186e9i	−0.0601523	−	0.185130i
$615$		0			0
$616$	2.92115e9	+	2.82088e9i	0.503526	+	0.486241i
$617$	4.55088e9			0.780004			0.390002	−	0.920814i	$-0.372474\pi$
$617$	4.55088e9			0.780004			0.390002	+	0.920814i	$0.372474\pi$
$618$		0			0
$619$	4.34497e8	+	3.15680e8i	0.0736325	+	0.0534971i	0.623993	−	0.781430i	$-0.285510\pi$
$619$	4.34497e8	+	3.15680e8i	0.0736325	+	0.0534971i	−0.550360	+	0.834927i	$0.685510\pi$
$620$	4.86432e9	−	3.53414e9i	0.819694	−	0.595542i
$621$		0			0
$622$	9.24935e7	−	2.84666e8i	0.0154115	−	0.0474317i
$623$	2.07359e9	−	1.50655e9i	0.343569	−	0.249618i
$624$		0			0
$625$	−1.51188e9	−	4.65309e9i	−0.247707	−	0.762363i
$626$	−1.19643e9			−0.194930
$627$		0			0
$628$	1.07851e9			0.173766
$629$	−2.25117e9	−	6.92837e9i	−0.360687	−	1.11008i
$630$		0			0
$631$	4.25854e9	−	3.09401e9i	0.674773	−	0.490251i	−0.196847	−	0.980434i	$-0.563070\pi$
$631$	4.25854e9	−	3.09401e9i	0.674773	−	0.490251i	0.871619	+	0.490183i	$0.163070\pi$
$632$	2.11759e8	−	6.51728e8i	0.0333682	−	0.102697i
$633$		0			0
$634$	−2.26298e9	+	1.64415e9i	−0.352670	+	0.256230i
$635$	2.46794e9	+	1.79307e9i	0.382496	+	0.277900i
$636$		0			0
$637$	−1.58722e10			−2.43305
$638$	−6.21857e7	−	3.52655e8i	−0.00948022	−	0.0537623i
$639$		0			0
$640$	−1.51037e9	−	4.64843e9i	−0.227747	−	0.700933i
$641$	−1.23774e9	−	8.99269e8i	−0.185620	−	0.134861i	0.491094	−	0.871106i	$-0.336597\pi$
$641$	−1.23774e9	−	8.99269e8i	−0.185620	−	0.134861i	−0.676715	+	0.736245i	$0.736597\pi$
$642$		0			0
$643$	2.82338e9	−	8.68948e9i	0.418824	−	1.28901i	−0.489962	−	0.871744i	$-0.662989\pi$
$643$	2.82338e9	−	8.68948e9i	0.418824	−	1.28901i	0.908786	−	0.417263i	$-0.137011\pi$
$644$	−3.09184e9	+	9.51571e9i	−0.456160	+	1.40391i
$645$		0			0
$646$	5.64081e8	+	4.09829e8i	0.0823242	+	0.0598120i
$647$	3.37047e9	+	1.03732e10i	0.489244	+	1.50574i	0.825738	+	0.564053i	$0.190759\pi$
$647$	3.37047e9	+	1.03732e10i	0.489244	+	1.50574i	−0.336494	+	0.941686i	$0.609241\pi$
$648$		0			0
$649$	−7.62374e9	−	1.07138e9i	−1.09474	−	0.153846i
$650$	−4.83609e8			−0.0690714
$651$		0			0
$652$	−3.55991e9	−	2.58643e9i	−0.503006	−	0.365455i
$653$	5.73199e9	−	4.16453e9i	0.805581	−	0.585289i	−0.106965	−	0.994263i	$-0.534113\pi$
$653$	5.73199e9	−	4.16453e9i	0.805581	−	0.585289i	0.912546	+	0.408974i	$0.134113\pi$
$654$		0			0
$655$	−2.29114e9	+	7.05139e9i	−0.318571	+	0.980461i
$656$	−8.78546e9	+	6.38301e9i	−1.21507	+	0.882800i
$657$		0			0
$658$	6.51670e8	+	2.00563e9i	0.0891738	+	0.274449i
$659$	3.97176e9			0.540611			0.270305	−	0.962775i	$-0.412875\pi$
$659$	3.97176e9			0.540611			0.270305	+	0.962775i	$0.412875\pi$
$660$		0			0
$661$	4.61874e9			0.622040			0.311020	−	0.950403i	$-0.399329\pi$
$661$	4.61874e9			0.622040			0.311020	+	0.950403i	$0.399329\pi$
$662$	4.51010e8	+	1.38806e9i	0.0604203	+	0.185955i
$663$		0			0
$664$	−3.37618e9	+	2.45294e9i	−0.447545	+	0.325161i
$665$	−1.71553e9	+	5.27987e9i	−0.226216	+	0.696222i
$666$		0			0
$667$	1.46845e9	−	1.06689e9i	0.191610	−	0.139213i
$668$	−1.92260e8	−	1.39685e8i	−0.0249558	−	0.0181314i
$669$		0			0
$670$	1.18483e8			0.0152193
$671$	7.13003e9	−	3.79118e9i	0.911093	−	0.484447i
$672$		0			0
$673$	1.42742e9	+	4.39314e9i	0.180509	+	0.555549i	0.999842	−	0.0177683i	$-0.00565613\pi$
$673$	1.42742e9	+	4.39314e9i	0.180509	+	0.555549i	−0.819333	+	0.573318i	$0.805656\pi$
$674$	7.60026e8	+	5.52191e8i	0.0956135	+	0.0694672i
$675$		0			0
$676$	−4.84225e9	+	1.49029e10i	−0.602884	+	1.85549i
$677$	−1.36263e9	+	4.19374e9i	−0.168779	+	0.519447i	−0.999295	−	0.0375472i	$-0.988046\pi$
$677$	−1.36263e9	+	4.19374e9i	−0.168779	+	0.519447i	0.830516	+	0.556994i	$0.188046\pi$
$678$		0			0
$679$	1.08633e10	+	7.89264e9i	1.33173	+	0.967561i
$680$	−8.79833e8	−	2.70785e9i	−0.107305	−	0.330250i
$681$		0			0
$682$	−2.24376e9	−	3.15320e8i	−0.270851	−	0.0380633i
$683$	1.34123e10			1.61076			0.805378	−	0.592761i	$-0.201962\pi$
$683$	1.34123e10			1.61076			0.805378	+	0.592761i	$0.201962\pi$
$684$		0			0
$685$	5.66778e9	+	4.11788e9i	0.673745	+	0.489505i
$686$	9.60374e8	−	6.97753e8i	0.113581	−	0.0825215i
$687$		0			0
$688$	8.71740e7	−	2.68294e8i	0.0102053	−	0.0314088i
$689$	−1.73759e10	+	1.26243e10i	−2.02386	+	1.47042i
$690$		0			0
$691$	3.78591e9	+	1.16518e10i	0.436513	+	1.34345i	0.891529	+	0.452964i	$0.149634\pi$
$691$	3.78591e9	+	1.16518e10i	0.436513	+	1.34345i	−0.455016	+	0.890483i	$0.650366\pi$
$692$	−4.43665e9			−0.508960
$693$		0			0
$694$	1.40163e9			0.159175
$695$	5.93213e8	+	1.82572e9i	0.0670291	+	0.206294i
$696$		0			0
$697$	−1.08770e10	+	7.90261e9i	−1.21673	+	0.884007i
$698$	−9.31597e8	+	2.86716e9i	−0.103689	+	0.319123i
$699$		0			0
$700$	−1.82119e9	+	1.32317e9i	−0.200684	+	0.145805i
$701$	8.27646e9	+	6.01320e9i	0.907468	+	0.659314i	0.940373	−	0.340144i	$-0.110476\pi$
$701$	8.27646e9	+	6.01320e9i	0.907468	+	0.659314i	−0.0329050	+	0.999458i	$0.510476\pi$
$702$		0			0
$703$	−6.63791e9			−0.720589
$704$	2.79886e9	−	5.73864e9i	0.302327	−	0.619876i
$705$		0			0
$706$	3.42236e8	+	1.05329e9i	0.0366024	+	0.112651i
$707$	−1.73820e10	−	1.26288e10i	−1.84983	−	1.34398i
$708$		0			0
$709$	2.20176e9	−	6.77631e9i	0.232011	−	0.714055i	−0.765493	−	0.643444i	$-0.777505\pi$
$709$	2.20176e9	−	6.77631e9i	0.232011	−	0.714055i	0.997504	−	0.0706112i	$-0.0224950\pi$
$710$	−7.40808e8	+	2.27997e9i	−0.0776786	+	0.239070i
$711$		0			0
$712$	9.69013e8	+	7.04029e8i	0.100612	+	0.0730988i
$713$	−3.54901e9	−	1.09227e10i	−0.366686	−	1.12854i
$714$		0			0
$715$	1.12122e10	+	1.08274e10i	1.14715	+	1.10777i
$716$	−1.08319e9			−0.110283
$717$		0			0
$718$	−1.28076e9	−	9.30524e8i	−0.129131	−	0.0938192i
$719$	−5.94949e9	+	4.32256e9i	−0.596938	+	0.433701i	−0.844791	−	0.535097i	$-0.820275\pi$
$719$	−5.94949e9	+	4.32256e9i	−0.596938	+	0.433701i	0.247853	+	0.968798i	$0.420275\pi$
$720$		0			0
$721$	3.86776e9	−	1.19037e10i	0.384313	−	1.18280i
$722$	−1.38966e9	+	1.00965e9i	−0.137413	+	0.0998366i
$723$		0			0
$724$	−5.34705e9	−	1.64565e10i	−0.523635	−	1.61158i
$725$	4.08381e8			0.0397999
$726$		0			0
$727$	1.90225e10			1.83610			0.918052	−	0.396459i	$-0.129761\pi$
$727$	1.90225e10			1.83610			0.918052	+	0.396459i	$0.129761\pi$
$728$	−3.94071e9	−	1.21283e10i	−0.378542	−	1.16503i
$729$		0			0
$730$	3.93299e8	−	2.85749e8i	0.0374191	−	0.0271866i
$731$	1.07927e8	−	3.32166e8i	0.0102193	−	0.0314517i
$732$		0			0
$733$	−6.22682e9	+	4.52405e9i	−0.583986	+	0.424291i	−0.840159	−	0.542340i	$-0.817538\pi$
$733$	−6.22682e9	+	4.52405e9i	−0.583986	+	0.424291i	0.256173	+	0.966631i	$0.417538\pi$
$734$	−2.20107e9	−	1.59917e9i	−0.205446	−	0.149265i
$735$		0			0
$736$	−7.07852e9			−0.654440
$737$	5.61157e8	+	5.41894e8i	0.0516355	+	0.0498630i
$738$		0			0
$739$	4.51689e9	+	1.39016e10i	0.411703	+	1.26709i	0.915167	+	0.403076i	$0.132059\pi$
$739$	4.51689e9	+	1.39016e10i	0.411703	+	1.26709i	−0.503464	+	0.864016i	$0.667941\pi$
$740$	1.06596e10	+	7.74462e9i	0.967004	+	0.702570i
$741$		0			0
$742$	1.76824e9	−	5.44209e9i	0.158902	−	0.489049i
$743$	−5.13843e8	+	1.58145e9i	−0.0459589	+	0.141447i	−0.971403	−	0.237438i	$-0.923692\pi$
$743$	−5.13843e8	+	1.58145e9i	−0.0459589	+	0.141447i	0.925444	+	0.378885i	$0.123692\pi$
$744$		0			0
$745$	7.40760e6	+	5.38194e6i	0.000656343	+	0.000476861i
$746$	1.44891e9	+	4.45927e9i	0.127777	+	0.393258i
$747$		0			0
$748$	3.99447e9	−	8.19006e9i	0.348983	−	0.715536i
$749$	2.26499e10			1.96961
$750$		0			0
$751$	1.16796e10	+	8.48570e9i	1.00621	+	0.731052i	0.963410	−	0.268032i	$-0.0863734\pi$
$751$	1.16796e10	+	8.48570e9i	1.00621	+	0.731052i	0.0427962	+	0.999084i	$0.486373\pi$
$752$	6.36137e9	−	4.62181e9i	0.545492	−	0.396323i
$753$		0			0
$754$	−3.47502e8	+	1.06950e9i	−0.0295228	+	0.0908618i
$755$	−7.16833e9	+	5.20810e9i	−0.606183	+	0.440418i
$756$		0			0
$757$	2.68924e8	+	8.27663e8i	0.0225317	+	0.0693454i	0.961690	−	0.274139i	$-0.0883928\pi$
$757$	2.68924e8	+	8.27663e8i	0.0225317	+	0.0693454i	−0.939158	+	0.343484i	$0.888393\pi$
$758$	1.55894e9			0.130013
$759$		0			0
$760$	−2.59432e9			−0.214376
$761$	−5.76503e9	−	1.77429e10i	−0.474193	−	1.45942i	−0.847043	−	0.531525i	$-0.821619\pi$
$761$	−5.76503e9	−	1.77429e10i	−0.474193	−	1.45942i	0.372850	−	0.927892i	$-0.378381\pi$
$762$		0			0
$763$	1.31202e10	−	9.53242e9i	1.06932	−	0.776904i
$764$	3.13742e9	−	9.65597e9i	0.254534	−	0.783374i
$765$		0			0
$766$	−3.52715e9	+	2.56262e9i	−0.283545	+	0.206008i
$767$	1.95590e10	+	1.42105e10i	1.56518	+	1.13717i
$768$		0			0
$769$	5.65386e9			0.448335			0.224167	−	0.974551i	$-0.428034\pi$
$769$	5.65386e9			0.448335			0.224167	+	0.974551i	$0.428034\pi$
$770$	−4.11224e9	−	5.77902e8i	−0.324609	−	0.0456181i
$771$		0			0
$772$	−5.57403e8	−	1.71551e9i	−0.0436022	−	0.134194i
$773$	−8.11450e9	−	5.89553e9i	−0.631878	−	0.459087i	0.225172	−	0.974319i	$-0.427706\pi$
$773$	−8.11450e9	−	5.89553e9i	−0.631878	−	0.459087i	−0.857050	+	0.515233i	$0.827706\pi$
$774$		0			0
$775$	7.98492e8	−	2.45751e9i	0.0616190	−	0.189644i
$776$	−1.93907e9	+	5.96784e9i	−0.148963	+	0.458460i
$777$		0			0
$778$	1.51433e9	+	1.10022e9i	0.115290	+	0.0837630i
$779$	3.78565e9	+	1.16510e10i	0.286919	+	0.883046i
$780$		0			0
$781$	−1.39363e10	+	7.41021e9i	−1.04681	+	0.556611i
$782$	−2.64359e9			−0.197684
$783$		0			0
$784$	−1.27560e10	−	9.26776e9i	−0.945383	−	0.686861i
$785$	−1.83558e9	+	1.33363e9i	−0.135435	+	0.0983991i
$786$		0			0
$787$	−6.95170e9	+	2.13951e10i	−0.508369	+	1.56460i	0.286663	+	0.958032i	$0.407454\pi$
$787$	−6.95170e9	+	2.13951e10i	−0.508369	+	1.56460i	−0.795032	+	0.606568i	$0.792546\pi$
$788$	1.18105e10	−	8.58082e9i	0.859857	−	0.624722i
$789$		0			0
$790$	2.16546e8	+	6.66461e8i	0.0156263	+	0.0480928i
$791$	−2.85609e10			−2.05189
$792$		0			0
$793$	−2.53591e10			−1.80583
$794$	−1.10450e7	−	3.39930e7i	−0.000783057	−	0.00241000i
$795$		0			0
$796$	−1.30950e10	+	9.51406e9i	−0.920257	+	0.668606i
$797$	−6.49597e9	+	1.99925e10i	−0.454506	+	1.39883i	0.417208	+	0.908811i	$0.363009\pi$
$797$	−6.49597e9	+	1.99925e10i	−0.454506	+	1.39883i	−0.871714	+	0.490015i	$0.836991\pi$
$798$		0			0
$799$	7.87581e9	−	5.72211e9i	0.546238	−	0.396865i
$800$	−1.28844e9	−	9.36105e8i	−0.0889710	−	0.0646412i
$801$		0			0
$802$	5.13567e9			0.351550
$803$	3.16964e9	+	4.45436e8i	0.216026	+	0.0303586i
$804$		0			0
$805$	−6.50444e9	−	2.00186e10i	−0.439465	−	1.35253i
$806$	5.75646e9	+	4.18232e9i	0.387243	+	0.281348i
$807$		0			0
$808$	3.10264e9	−	9.54895e9i	0.206915	−	0.636818i
$809$	3.33730e9	−	1.02712e10i	0.221603	−	0.682024i	−0.777016	−	0.629481i	$-0.783267\pi$
$809$	3.33730e9	−	1.02712e10i	0.221603	−	0.682024i	0.998619	−	0.0525426i	$-0.0167325\pi$
$810$		0			0
$811$	5.40531e9	+	3.92719e9i	0.355834	+	0.258529i	0.751313	−	0.659947i	$-0.229421\pi$
$811$	5.40531e9	+	3.92719e9i	0.355834	+	0.258529i	−0.395478	+	0.918475i	$0.629421\pi$
$812$	1.61756e9	+	4.97834e9i	0.106027	+	0.326316i
$813$		0			0
$814$	−8.62245e8	−	4.88979e9i	−0.0560332	−	0.317764i
$815$	9.25709e9			0.598995
$816$		0			0
$817$	−2.57462e8	−	1.87057e8i	−0.0165172	−	0.0120004i
$818$	−2.28475e9	+	1.65997e9i	−0.145949	+	0.106038i
$819$		0			0
$820$	7.51434e9	−	2.31267e10i	0.475929	−	1.46476i
$821$	5.60406e9	−	4.07159e9i	0.353429	−	0.256781i	−0.396877	−	0.917872i	$-0.629906\pi$
$821$	5.60406e9	−	4.07159e9i	0.353429	−	0.256781i	0.750306	+	0.661091i	$0.229906\pi$
$822$		0			0
$823$	−6.53196e9	−	2.01033e10i	−0.408455	−	1.25709i	−0.917976	−	0.396636i	$-0.870177\pi$
$823$	−6.53196e9	−	2.01033e10i	−0.408455	−	1.25709i	0.509521	−	0.860458i	$-0.329823\pi$
$824$	5.84903e9			0.364199
$825$		0			0
$826$	−6.44110e9			−0.397677
$827$	8.35592e9	+	2.57169e10i	0.513718	+	1.58106i	0.785602	+	0.618732i	$0.212353\pi$
$827$	8.35592e9	+	2.57169e10i	0.513718	+	1.58106i	−0.271884	+	0.962330i	$0.587647\pi$
$828$		0			0
$829$	1.60321e10	−	1.16480e10i	0.977351	−	0.710087i	0.0202363	−	0.999795i	$-0.493558\pi$
$829$	1.60321e10	−	1.16480e10i	0.977351	−	0.710087i	0.957115	+	0.289708i	$0.0935581\pi$
$830$	1.31874e9	−	4.05866e9i	0.0800544	−	0.246382i
$831$		0			0
$832$	−1.62211e10	+	1.17853e10i	−0.976447	+	0.709430i
$833$	−1.57928e10	−	1.14741e10i	−0.946676	−	0.687800i
$834$		0			0
$835$	4.99947e8			0.0297181
$836$	−5.97268e9	−	5.76765e9i	−0.353547	−	0.341410i
$837$		0			0
$838$	5.14113e8	+	1.58228e9i	0.0301790	+	0.0928813i
$839$	5.18702e9	+	3.76859e9i	0.303215	+	0.220299i	0.728980	−	0.684535i	$-0.239995\pi$
$839$	5.18702e9	+	3.76859e9i	0.303215	+	0.220299i	−0.425765	+	0.904834i	$0.639995\pi$
$840$		0			0
$841$	−5.03706e9	+	1.55025e10i	−0.292006	+	0.898701i
$842$	2.36154e9	−	7.26807e9i	0.136334	−	0.419592i
$843$		0			0
$844$	−4.59807e9	−	3.34069e9i	−0.263255	−	0.191266i
$845$	−1.01869e10	−	3.13519e10i	−0.580820	−	1.78758i
$846$		0			0
$847$	−1.68332e10	−	2.15448e10i	−0.951866	−	1.21829i
$848$	−2.13357e10			−1.20149
$849$		0			0
$850$	−4.81188e8	−	3.49604e8i	−0.0268750	−	0.0195259i
$851$	2.03610e10	−	1.47931e10i	1.13252	−	0.822824i
$852$		0			0
$853$	5.23023e9	−	1.60970e10i	0.288535	−	0.888020i	−0.696781	−	0.717284i	$-0.745385\pi$
$853$	5.23023e9	−	1.60970e10i	0.288535	−	0.888020i	0.985317	−	0.170737i	$-0.0546148\pi$
$854$	5.46590e9	−	3.97121e9i	0.300303	−	0.218183i
$855$		0			0
$856$	3.27082e9	+	1.00666e10i	0.178237	+	0.548558i
$857$	−1.19710e10			−0.649678			−0.324839	−	0.945769i	$-0.605310\pi$
$857$	−1.19710e10			−0.649678			−0.324839	+	0.945769i	$0.605310\pi$
$858$		0			0
$859$	3.00358e10			1.61682			0.808412	−	0.588617i	$-0.200327\pi$
$859$	3.00358e10			1.61682			0.808412	+	0.588617i	$0.200327\pi$
$860$	1.95204e8	+	6.00775e8i	0.0104651	+	0.0322083i
$861$		0			0
$862$	6.44516e8	−	4.68269e8i	0.0342735	−	0.0249012i
$863$	−6.06852e9	+	1.86770e10i	−0.321399	+	0.989165i	0.651641	+	0.758528i	$0.274081\pi$
$863$	−6.06852e9	+	1.86770e10i	−0.321399	+	0.989165i	−0.973040	+	0.230637i	$0.925919\pi$
$864$		0			0
$865$	7.55101e9	−	5.48613e9i	0.396688	−	0.288211i
$866$	1.33802e9	+	9.72126e8i	0.0700082	+	0.0508640i
$867$		0			0
$868$	3.31209e10			1.71903
$869$	−2.02253e9	+	4.14688e9i	−0.104550	+	0.214364i
$870$		0			0
$871$	−7.57015e8	−	2.32985e9i	−0.0388187	−	0.119472i
$872$	6.13125e9	+	4.45462e9i	0.313142	+	0.227511i
$873$		0			0
$874$	−7.44360e8	+	2.29090e9i	−0.0377132	+	0.116069i
$875$	1.00907e10	−	3.10558e10i	0.509203	−	1.56717i
$876$		0			0
$877$	−2.83339e10	−	2.05858e10i	−1.41843	−	1.03055i	−0.992028	−	0.126018i	$-0.959780\pi$
$877$	−2.83339e10	−	2.05858e10i	−1.41843	−	1.03055i	−0.426404	−	0.904533i	$-0.640220\pi$
$878$	−4.82857e8	−	1.48608e9i	−0.0240762	−	0.0740989i
$879$		0			0
$880$	2.68884e9	+	1.52484e10i	0.133007	+	0.754283i
$881$	−3.55317e10			−1.75065			−0.875326	−	0.483532i	$-0.839354\pi$
$881$	−3.55317e10			−1.75065			−0.875326	+	0.483532i	$0.839354\pi$
$882$		0			0
$883$	−9.41080e9	−	6.83735e9i	−0.460007	−	0.334214i	0.333527	−	0.942740i	$-0.391761\pi$
$883$	−9.41080e9	−	6.83735e9i	−0.460007	−	0.334214i	−0.793534	+	0.608526i	$0.791761\pi$
$884$	−2.31504e10	+	1.68197e10i	−1.12713	+	0.818910i
$885$		0			0
$886$	6.01911e8	−	1.85249e9i	0.0290746	−	0.0894825i
$887$	2.33369e10	−	1.69552e10i	1.12282	−	0.815777i	0.138187	−	0.990406i	$-0.455873\pi$
$887$	2.33369e10	−	1.69552e10i	1.12282	−	0.815777i	0.984634	+	0.174629i	$0.0558726\pi$
$888$		0			0
$889$	5.19274e9	+	1.59816e10i	0.247879	+	0.762894i
$890$	−1.22484e9			−0.0582392
$891$		0			0
$892$	1.51719e10			0.715754
$893$	−2.74111e9	−	8.43627e9i	−0.128809	−	0.396433i
$894$		0			0
$895$	1.84355e9	−	1.33942e9i	0.0859556	−	0.0624504i
$896$	8.31992e9	−	2.56061e10i	0.386403	−	1.18923i
$897$		0			0
$898$	−1.67175e9	+	1.21460e9i	−0.0770380	+	0.0559714i
$899$	−4.86101e9	−	3.53173e9i	−0.223135	−	0.162117i
$900$		0			0
$901$	−2.64151e10			−1.20314
$902$	−8.09094e9	+	4.30212e9i	−0.367093	+	0.195191i
$903$		0			0
$904$	−4.12441e9	−	1.26936e10i	−0.185683	−	0.571473i
$905$	2.94498e10	+	2.13965e10i	1.32072	+	0.959562i
$906$		0			0
$907$	−2.96422e9	+	9.12294e9i	−0.131912	+	0.405984i	−0.995097	−	0.0989040i	$-0.968466\pi$
$907$	−2.96422e9	+	9.12294e9i	−0.131912	+	0.405984i	0.863185	+	0.504888i	$0.168466\pi$
$908$	−7.79688e9	+	2.39963e10i	−0.345637	+	1.06376i
$909$		0			0
$910$	1.05501e10	+	7.66513e9i	0.464102	+	0.337190i
$911$	−1.08217e10	−	3.33058e10i	−0.474223	−	1.45951i	−0.847003	−	0.531588i	$-0.821596\pi$
$911$	−1.08217e10	−	3.33058e10i	−0.474223	−	1.45951i	0.372781	−	0.927919i	$-0.378404\pi$
$912$		0			0
$913$	2.48085e10	−	1.31912e10i	1.07883	−	0.573635i
$914$	5.28107e9			0.228776
$915$		0			0
$916$	2.64085e10	+	1.91869e10i	1.13530	+	0.824840i
$917$	−3.30417e10	+	2.40062e10i	−1.41504	+	1.02809i
$918$		0			0
$919$	−9.80963e9	+	3.01909e10i	−0.416916	+	1.28313i	0.493610	+	0.869683i	$0.335677\pi$
$919$	−9.80963e9	+	3.01909e10i	−0.416916	+	1.28313i	−0.910526	+	0.413452i	$0.864323\pi$
$920$	7.95779e9	−	5.78167e9i	0.336926	−	0.244791i
$921$		0			0
$922$	2.16839e9	+	6.67363e9i	0.0911129	+	0.280417i
$923$	4.95666e10			2.07483
$924$		0			0
$925$	5.66246e9			0.235239
$926$	−2.34430e9	−	7.21500e9i	−0.0970229	−	0.298606i
$927$		0			0
$928$	−2.99601e9	+	2.17673e9i	−0.123062	+	0.0894101i
$929$	6.55945e9	−	2.01879e10i	0.268418	−	0.826107i	−0.722468	−	0.691405i	$-0.756992\pi$
$929$	6.55945e9	−	2.01879e10i	0.268418	−	0.826107i	0.990886	−	0.134702i	$-0.0430078\pi$
$930$		0			0
$931$	−1.43901e10	+	1.04550e10i	−0.584441	+	0.424622i
$932$	−6.60713e9	−	4.80036e9i	−0.267336	−	0.194231i
$933$		0			0
$934$	−5.41558e9			−0.217486
$935$	3.32896e9	+	1.88785e10i	0.133189	+	0.755315i
$936$		0			0
$937$	−2.98336e8	−	9.18183e8i	−0.0118472	−	0.0364620i	0.944958	−	0.327191i	$-0.106102\pi$
$937$	−2.98336e8	−	9.18183e8i	−0.0118472	−	0.0364620i	−0.956805	+	0.290729i	$0.906102\pi$
$938$	5.28020e8	+	3.83629e8i	0.0208901	+	0.0151775i
$939$		0			0
$940$	−5.44097e9	+	1.67456e10i	−0.213663	+	0.657587i
$941$	−5.82146e9	+	1.79166e10i	−0.227755	+	0.700959i	0.770245	+	0.637748i	$0.220134\pi$
$941$	−5.82146e9	+	1.79166e10i	−0.227755	+	0.700959i	−0.998000	+	0.0632106i	$0.979866\pi$
$942$		0			0
$943$	−3.75773e10	−	2.73015e10i	−1.45927	−	1.06022i
$944$	7.42148e9	+	2.28410e10i	0.287136	+	0.883715i
$945$		0			0
$946$	1.04351e8	−	2.13957e8i	0.00400755	−	0.00821688i
$947$	−9.77060e9			−0.373849			−0.186925	−	0.982374i	$-0.559852\pi$
$947$	−9.77060e9			−0.373849			−0.186925	+	0.982374i	$0.559852\pi$
$948$		0			0
$949$	−8.13185e9	−	5.90814e9i	−0.308857	−	0.224398i
$950$	−4.38451e8	+	3.18554e8i	−0.0165916	+	0.0120545i
$951$		0			0
$952$	4.84660e9	−	1.49163e10i	0.182057	−	0.560314i
$953$	−8.10446e9	+	5.88824e9i	−0.303319	+	0.220374i	−0.729024	−	0.684488i	$-0.760026\pi$
$953$	−8.10446e9	+	5.88824e9i	−0.303319	+	0.220374i	0.425706	+	0.904862i	$0.360026\pi$
$954$		0			0
$955$	6.60032e9	+	2.03137e10i	0.245218	+	0.754704i
$956$	−2.02945e10			−0.751236
$957$		0			0
$958$	−5.64783e8			−0.0207540
$959$	1.19254e10	+	3.67027e10i	0.436625	+	1.34379i
$960$		0			0
$961$	−8.49921e9	+	6.17504e9i	−0.308920	+	0.224444i
$962$	−4.81834e9	+	1.48293e10i	−0.174496	+	0.537042i
$963$		0			0
$964$	1.07537e9	−	7.81303e8i	0.0386624	−	0.0280899i
$965$	3.06999e9	+	2.23048e9i	0.109974	+	0.0799010i
$966$		0			0
$967$	3.79569e10			1.34989			0.674944	−	0.737869i	$-0.264168\pi$
$967$	3.79569e10			1.34989			0.674944	+	0.737869i	$0.264168\pi$
$968$	7.14454e9	−	1.05926e10i	0.253169	−	0.375352i
$969$		0			0
$970$	−1.98291e9	−	6.10276e9i	−0.0697591	−	0.214696i
$971$	−9.04105e9	−	6.56871e9i	−0.316921	−	0.230257i	0.417939	−	0.908475i	$-0.362752\pi$
$971$	−9.04105e9	−	6.56871e9i	−0.316921	−	0.230257i	−0.734861	+	0.678218i	$0.762752\pi$
$972$		0			0
$973$	−3.26774e9	+	1.00571e10i	−0.113724	+	0.350006i
$974$	2.19523e9	−	6.75623e9i	0.0761244	−	0.234287i
$975$		0			0
$976$	−2.03802e10	−	1.48071e10i	−0.701673	−	0.509796i
$977$	−2.99951e9	−	9.23154e9i	−0.102901	−	0.316696i	0.886331	−	0.463052i	$-0.153246\pi$
$977$	−2.99951e9	−	9.23154e9i	−0.102901	−	0.316696i	−0.989232	+	0.146356i	$0.953246\pi$
$978$		0			0
$979$	−5.80108e9	−	5.60195e9i	−0.197592	−	0.190809i
$980$	3.53067e10			1.19830
$981$		0			0
$982$	8.24966e9	+	5.99373e9i	0.278001	+	0.201979i
$983$	−2.27603e9	+	1.65363e9i	−0.0764259	+	0.0555266i	−0.625342	−	0.780351i	$-0.715041\pi$
$983$	−2.27603e9	+	1.65363e9i	−0.0764259	+	0.0555266i	0.548916	+	0.835877i	$0.315041\pi$
$984$		0			0
$985$	−9.49042e9	+	2.92085e10i	−0.316416	+	0.973828i
$986$	−1.11891e9	+	8.12936e8i	−0.0371729	+	0.0270077i
$987$		0			0
$988$	8.05729e9	+	2.47978e10i	0.265791	+	0.818019i
$989$	1.20661e9			0.0396624
$990$		0			0
$991$	−2.01304e10			−0.657043			−0.328522	−	0.944496i	$-0.606550\pi$
$991$	−2.01304e10			−0.657043			−0.328522	+	0.944496i	$0.606550\pi$
$992$	7.24088e9	+	2.22851e10i	0.235505	+	0.724811i
$993$		0			0
$994$	−1.06836e10	+	7.76209e9i	−0.345036	+	0.250684i
$995$	1.05226e10	−	3.23852e10i	0.338642	−	1.04223i
$996$		0			0
$997$	1.29314e10	−	9.39518e9i	0.413248	−	0.300243i	−0.361667	−	0.932307i	$-0.617792\pi$
$997$	1.29314e10	−	9.39518e9i	0.413248	−	0.300243i	0.774916	+	0.632065i	$0.217792\pi$
$998$	3.49178e9	+	2.53693e9i	0.111196	+	0.0807889i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.8.f.b.82.3		28
3.2	odd	2		33.8.e.b.16.5	✓	28
11.9	even	5	inner	99.8.f.b.64.3		28
33.8	even	10		363.8.a.r.1.7		14
33.14	odd	10		363.8.a.o.1.8		14
33.20	odd	10		33.8.e.b.31.5	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.e.b.16.5	✓	28	3.2	odd	2
33.8.e.b.31.5	yes	28	33.20	odd	10
99.8.f.b.64.3		28	11.9	even	5	inner
99.8.f.b.82.3		28	1.1	even	1	trivial
363.8.a.o.1.8		14	33.14	odd	10
363.8.a.r.1.7		14	33.8	even	10

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.813458 - 2.50357i) q^{2} +(97.9481 - 71.1634i) q^{4} +(-78.7070 + 242.235i) q^{5} +(-1135.08 + 824.681i) q^{7} +(-530.435 - 385.384i) q^{8} +670.476 q^{10} +(3175.50 + 3066.49i) q^{11} +(-4283.83 - 13184.3i) q^{13} +(2987.98 + 2170.89i) q^{14} +(4255.49 - 13097.1i) q^{16} +(5268.59 - 16215.1i) q^{17} +(-12568.3 - 9131.40i) q^{19} +(9529.09 + 29327.5i) q^{20} +(5094.03 - 10444.5i) q^{22} +58901.9 q^{23} +(10721.4 + 7789.53i) q^{25} +(-29523.0 + 21449.7i) q^{26} +(-52491.4 + 161552. i) q^{28} +(24930.5 - 18113.0i) q^{29} +(-60252.9 - 185439. i) q^{31} -120175. q^{32} -44881.3 q^{34} +(-110428. - 339864. i) q^{35} +(345677. - 251149. i) q^{37} +(-12637.3 + 38893.5i) q^{38} +(135102. - 98157.7i) q^{40} +(-637965. - 463509. i) q^{41} +20485.0 q^{43} +(529256. + 74377.5i) q^{44} +(-47914.2 - 147465. i) q^{46} +(461937. + 335617. i) q^{47} +(353811. - 1.08892e6i) q^{49} +(10780.2 - 33178.1i) q^{50} +(-1.35783e6 - 986521. i) q^{52} +(-478764. - 1.47349e6i) q^{53} +(-992746. + 527863. i) q^{55} +919904. q^{56} +(-65627.0 - 47680.8i) q^{58} +(-1.41091e6 + 1.02508e6i) q^{59} +(565284. - 1.73976e6i) q^{61} +(-415247. + 301694. i) q^{62} +(-446946. - 1.37556e6i) q^{64} +3.53086e6 q^{65} +176715. q^{67} +(-637871. - 1.96317e6i) q^{68} +(-761042. + 552929. i) q^{70} +(-1.10490e6 + 3.40052e6i) q^{71} +(586597. - 426188. i) q^{73} +(-909961. - 661125. i) q^{74} -1.88086e6 q^{76} +(-6.13331e6 - 861928. i) q^{77} +(322974. + 994012. i) q^{79} +(2.83763e6 + 2.06166e6i) q^{80} +(-641467. + 1.97423e6i) q^{82} +(1.96687e6 - 6.05340e6i) q^{83} +(3.51318e6 + 2.55248e6i) q^{85} +(-16663.7 - 51285.6i) q^{86} +(-502621. - 2.85036e6i) q^{88} -1.82683e6 q^{89} +(1.57353e7 + 1.14324e7i) q^{91} +(5.76933e6 - 4.19166e6i) q^{92} +(464473. - 1.42950e6i) q^{94} +(3.20116e6 - 2.32578e6i) q^{95} +(-2.95746e6 - 9.10212e6i) q^{97} -3.01399e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 6 q^{2} + 160 q^{4} - 773 q^{5} + 1289 q^{7} - 2956 q^{8} - 10640 q^{10} - 13209 q^{11} + 13499 q^{13} + 3318 q^{14} - 113196 q^{16} - 30296 q^{17} - 6858 q^{19} - 76725 q^{20} - 48859 q^{22} + 166984 q^{23}+ \cdots - 140532178 q^{98}+O(q^{100}) \) 28 * q + 6 * q^2 + 160 * q^4 - 773 * q^5 + 1289 * q^7 - 2956 * q^8 - 10640 * q^10 - 13209 * q^11 + 13499 * q^13 + 3318 * q^14 - 113196 * q^16 - 30296 * q^17 - 6858 * q^19 - 76725 * q^20 - 48859 * q^22 + 166984 * q^23 + 99832 * q^25 - 340424 * q^26 + 657387 * q^28 - 192014 * q^29 + 396068 * q^31 + 303498 * q^32 - 1229124 * q^34 + 725859 * q^35 + 811053 * q^37 - 1548798 * q^38 - 1427263 * q^40 - 1041497 * q^41 - 5265288 * q^43 + 5341085 * q^44 + 1198651 * q^46 - 1667505 * q^47 + 2968140 * q^49 - 11247432 * q^50 + 2325763 * q^52 + 1625736 * q^53 - 8338690 * q^55 + 18201906 * q^56 + 14965553 * q^58 + 2587454 * q^59 + 5801619 * q^61 - 15631121 * q^62 - 3732846 * q^64 + 15368174 * q^65 - 7141262 * q^67 - 17394545 * q^68 - 4329200 * q^70 - 3569199 * q^71 + 125008 * q^73 + 13691530 * q^74 - 19690428 * q^76 + 6038739 * q^77 + 17075485 * q^79 - 26606436 * q^80 + 19886007 * q^82 + 4645575 * q^83 + 12002715 * q^85 + 12296287 * q^86 - 50905990 * q^88 - 9601664 * q^89 - 14129477 * q^91 + 90776021 * q^92 + 1047679 * q^94 - 58935661 * q^95 - 22170261 * q^97 - 140532178 * q^98

Introduction

L-functions

Modular forms

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