LMFDB - Embedded newform 100.9.d.c.99.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,9,Mod(99,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.99"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,104] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.5
Character	$\chi$	$=$	100.99
Dual form			100.9.d.c.99.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-14.2118 - 7.35022i) q^{2} -110.171 q^{3} +(147.949 + 208.919i) q^{4} +(1565.72 + 809.778i) q^{6} -3540.70 q^{7} +(-567.011 - 4056.56i) q^{8} +5576.56 q^{9} +15969.8i q^{11} +(-16299.6 - 23016.7i) q^{12} +24176.2i q^{13} +(50319.6 + 26024.9i) q^{14} +(-21758.4 + 61818.6i) q^{16} +43810.0i q^{17} +(-79252.8 - 40988.9i) q^{18} -50919.1i q^{19} +390081. q^{21} +(117382. - 226960. i) q^{22} +270875. q^{23} +(62467.9 + 446914. i) q^{24} +(177701. - 343587. i) q^{26} +108456. q^{27} +(-523841. - 739720. i) q^{28} +1.32588e6 q^{29} +1.18623e6i q^{31} +(763605. - 718623. i) q^{32} -1.75941e6i q^{33} +(322013. - 622618. i) q^{34} +(825045. + 1.16505e6i) q^{36} +2.97108e6i q^{37} +(-374266. + 723650. i) q^{38} -2.66351e6i q^{39} -4.92072e6 q^{41} +(-5.54374e6 - 2.86718e6i) q^{42} -2.86229e6 q^{43} +(-3.33641e6 + 2.36272e6i) q^{44} +(-3.84961e6 - 1.99099e6i) q^{46} +12696.5 q^{47} +(2.39714e6 - 6.81059e6i) q^{48} +6.77174e6 q^{49} -4.82658e6i q^{51} +(-5.05088e6 + 3.57684e6i) q^{52} +5.50364e6i q^{53} +(-1.54135e6 - 797176. i) q^{54} +(2.00761e6 + 1.43631e7i) q^{56} +5.60979e6i q^{57} +(-1.88430e7 - 9.74547e6i) q^{58} +6.68863e6i q^{59} -2.50550e6 q^{61} +(8.71902e6 - 1.68584e7i) q^{62} -1.97449e7 q^{63} +(-1.61342e7 + 4.60023e6i) q^{64} +(-1.29320e7 + 2.50043e7i) q^{66} -3.86718e6 q^{67} +(-9.15275e6 + 6.48163e6i) q^{68} -2.98424e7 q^{69} +3.21701e7i q^{71} +(-3.16197e6 - 2.26217e7i) q^{72} -1.91362e7i q^{73} +(2.18381e7 - 4.22243e7i) q^{74} +(1.06380e7 - 7.53341e6i) q^{76} -5.65444e7i q^{77} +(-1.95774e7 + 3.78532e7i) q^{78} -5.33471e7i q^{79} -4.85365e7 q^{81} +(6.99321e7 + 3.61683e7i) q^{82} +6.22776e6 q^{83} +(5.77119e7 + 8.14954e7i) q^{84} +(4.06782e7 + 2.10385e7i) q^{86} -1.46072e8 q^{87} +(6.47827e7 - 9.05507e6i) q^{88} -3.83322e7 q^{89} -8.56008e7i q^{91} +(4.00755e7 + 5.65909e7i) q^{92} -1.30687e8i q^{93} +(-180440. - 93322.2i) q^{94} +(-8.41269e7 + 7.91711e7i) q^{96} +7.87237e7i q^{97} +(-9.62384e7 - 4.97738e7i) q^{98} +8.90568e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 104 q^{4} + 8736 q^{6} + 77600 q^{9} - 136944 q^{14} - 162848 q^{16} + 828992 q^{21} - 327584 q^{24} + 2074248 q^{26} - 5529792 q^{29} - 7587928 q^{34} - 10937832 q^{36} - 17152896 q^{41} - 33842400 q^{44}+ \cdots - 906779904 q^{96}+O(q^{100}) $ 32 * q + 104 * q^4 + 8736 * q^6 + 77600 * q^9 - 136944 * q^14 - 162848 * q^16 + 828992 * q^21 - 327584 * q^24 + 2074248 * q^26 - 5529792 * q^29 - 7587928 * q^34 - 10937832 * q^36 - 17152896 * q^41 - 33842400 * q^44 - 15948304 * q^46 + 65607200 * q^49 - 17797408 * q^54 + 68269536 * q^56 + 16743424 * q^61 + 95087744 * q^64 + 38716000 * q^66 - 15054528 * q^69 + 276421752 * q^74 + 5140800 * q^76 + 281173344 * q^81 - 139523648 * q^84 - 203449344 * q^86 - 213294912 * q^89 - 110529264 * q^94 - 906779904 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−14.2118	−	7.35022i	−0.888235	−	0.459389i
$2$	−14.2118	−	7.35022i	−0.888235	−	0.459389i
$3$	−110.171			−1.36013			−0.680065	−	0.733151i	$-0.738049\pi$
$3$	−110.171			−1.36013			−0.680065	+	0.733151i	$0.738049\pi$
$4$	147.949	+	208.919i	0.577924	+	0.816090i
$5$		0			0
$5$		0			0
$6$	1565.72	+	809.778i	1.20812	+	0.624829i
$7$	−3540.70			−1.47468			−0.737338	−	0.675524i	$-0.763918\pi$
$7$	−3540.70			−1.47468			−0.737338	+	0.675524i	$0.763918\pi$
$8$	−567.011	−	4056.56i	−0.138430	−	0.990372i
$9$	5576.56			0.849956
$10$		0			0
$11$			15969.8i			1.09076i	0.838188	+	0.545381i	$0.183615\pi$
$11$			15969.8i			1.09076i	−0.838188	+	0.545381i	$0.816385\pi$
$12$	−16299.6	−	23016.7i	−0.786053	−	1.10999i
$13$			24176.2i			0.846477i	0.906018	+	0.423239i	$0.139107\pi$
$13$			24176.2i			0.846477i	−0.906018	+	0.423239i	$0.860893\pi$
$14$	50319.6	+	26024.9i	1.30986	+	0.677449i
$15$		0			0
$16$	−21758.4	+	61818.6i	−0.332007	+	0.943277i
$17$			43810.0i			0.524539i	0.964995	+	0.262269i	$0.0844709\pi$
$17$			43810.0i			0.524539i	−0.964995	+	0.262269i	$0.915529\pi$
$18$	−79252.8	−	40988.9i	−0.754961	−	0.390460i
$19$		−	50919.1i		−	0.390721i	−0.980732	−	0.195360i	$-0.937412\pi$
$19$		−	50919.1i		−	0.390721i	0.980732	−	0.195360i	$-0.0625876\pi$
$20$		0			0
$21$	390081.			2.00575
$22$	117382.	−	226960.i	0.501083	−	0.968853i
$23$	270875.			0.967959			0.483980	−	0.875079i	$-0.339191\pi$
$23$	270875.			0.967959			0.483980	+	0.875079i	$0.339191\pi$
$24$	62467.9	+	446914.i	0.188283	+	1.34704i
$25$		0			0
$26$	177701.	−	343587.i	0.388862	−	0.751871i
$27$	108456.			0.204079
$28$	−523841.	−	739720.i	−0.852251	−	1.20347i
$29$	1.32588e6			1.87461			0.937305	−	0.348511i	$-0.113313\pi$
$29$	1.32588e6			1.87461			0.937305	+	0.348511i	$0.113313\pi$
$30$		0			0
$31$			1.18623e6i			1.28446i	0.766512	+	0.642230i	$0.221991\pi$
$31$			1.18623e6i			1.28446i	−0.766512	+	0.642230i	$0.778009\pi$
$32$	763605.	−	718623.i	0.728231	−	0.685332i
$33$		−	1.75941e6i		−	1.48358i
$34$	322013.	−	622618.i	0.240967	−	0.465914i
$35$		0			0
$36$	825045.	+	1.16505e6i	0.491210	+	0.693641i
$37$			2.97108e6i			1.58529i	0.609686	+	0.792643i	$0.291295\pi$
$37$			2.97108e6i			1.58529i	−0.609686	+	0.792643i	$0.708705\pi$
$38$	−374266.	+	723650.i	−0.179493	+	0.347052i
$39$		−	2.66351e6i		−	1.15132i
$40$		0			0
$41$	−4.92072e6			−1.74138			−0.870689	−	0.491834i	$-0.836327\pi$
$41$	−4.92072e6			−1.74138			−0.870689	+	0.491834i	$0.836327\pi$
$42$	−5.54374e6	−	2.86718e6i	−1.78158	−	0.921420i
$43$	−2.86229e6			−0.837221			−0.418611	−	0.908166i	$-0.637483\pi$
$43$	−2.86229e6			−0.837221			−0.418611	+	0.908166i	$0.637483\pi$
$44$	−3.33641e6	+	2.36272e6i	−0.890160	+	0.630378i
$45$		0			0
$46$	−3.84961e6	−	1.99099e6i	−0.859776	−	0.444669i
$47$	12696.5			0.00260192			0.00130096	−	0.999999i	$-0.499586\pi$
$47$	12696.5			0.00260192			0.00130096	+	0.999999i	$0.499586\pi$
$48$	2.39714e6	−	6.81059e6i	0.451573	−	1.28298i
$49$	6.77174e6			1.17467
$50$		0			0
$51$		−	4.82658e6i		−	0.713442i
$52$	−5.05088e6	+	3.57684e6i	−0.690802	+	0.489200i
$53$			5.50364e6i			0.697504i	0.937215	+	0.348752i	$0.113394\pi$
$53$			5.50364e6i			0.697504i	−0.937215	+	0.348752i	$0.886606\pi$
$54$	−1.54135e6	−	797176.i	−0.181270	−	0.0937517i
$55$		0			0
$56$	2.00761e6	+	1.43631e7i	0.204140	+	1.46048i
$57$			5.60979e6i			0.531431i
$58$	−1.88430e7	−	9.74547e6i	−1.66509	−	0.861174i
$59$			6.68863e6i			0.551987i	0.961159	+	0.275994i	$0.0890068\pi$
$59$			6.68863e6i			0.551987i	−0.961159	+	0.275994i	$0.910993\pi$
$60$		0			0
$61$	−2.50550e6			−0.180957			−0.0904784	−	0.995898i	$-0.528840\pi$
$61$	−2.50550e6			−0.180957			−0.0904784	+	0.995898i	$0.528840\pi$
$62$	8.71902e6	−	1.68584e7i	0.590066	−	1.14090i
$63$	−1.97449e7			−1.25341
$64$	−1.61342e7	+	4.60023e6i	−0.961674	+	0.274195i
$65$		0			0
$66$	−1.29320e7	+	2.50043e7i	−0.681539	+	1.31777i
$67$	−3.86718e6			−0.191909			−0.0959546	−	0.995386i	$-0.530590\pi$
$67$	−3.86718e6			−0.191909			−0.0959546	+	0.995386i	$0.530590\pi$
$68$	−9.15275e6	+	6.48163e6i	−0.428071	+	0.303144i
$69$	−2.98424e7			−1.31655
$70$		0			0
$71$			3.21701e7i			1.26596i	0.774170	+	0.632978i	$0.218168\pi$
$71$			3.21701e7i			1.26596i	−0.774170	+	0.632978i	$0.781832\pi$
$72$	−3.16197e6	−	2.26217e7i	−0.117660	−	0.841773i
$73$		−	1.91362e7i		−	0.673853i	−0.941531	−	0.336927i	$-0.890613\pi$
$73$		−	1.91362e7i		−	0.673853i	0.941531	−	0.336927i	$-0.109387\pi$
$74$	2.18381e7	−	4.22243e7i	0.728262	−	1.40811i
$75$		0			0
$76$	1.06380e7	−	7.53341e6i	0.318863	−	0.225807i
$77$		−	5.65444e7i		−	1.60852i
$78$	−1.95774e7	+	3.78532e7i	−0.528903	+	1.02264i
$79$		−	5.33471e7i		−	1.36963i	−0.728718	−	0.684814i	$-0.759884\pi$
$79$		−	5.33471e7i		−	1.36963i	0.728718	−	0.684814i	$-0.240116\pi$
$80$		0			0
$81$	−4.85365e7			−1.12753
$82$	6.99321e7	+	3.61683e7i	1.54675	+	0.799969i
$83$	6.22776e6			0.131226			0.0656129	−	0.997845i	$-0.479100\pi$
$83$	6.22776e6			0.131226			0.0656129	+	0.997845i	$0.479100\pi$
$84$	5.77119e7	+	8.14954e7i	1.15917	+	1.63688i
$85$		0			0
$86$	4.06782e7	+	2.10385e7i	0.743650	+	0.384610i
$87$	−1.46072e8			−2.54971
$88$	6.47827e7	−	9.05507e6i	1.08026	−	0.150995i
$89$	−3.83322e7			−0.610947			−0.305473	−	0.952201i	$-0.598815\pi$
$89$	−3.83322e7			−0.610947			−0.305473	+	0.952201i	$0.598815\pi$
$90$		0			0
$91$		−	8.56008e7i		−	1.24828i
$92$	4.00755e7	+	5.65909e7i	0.559407	+	0.789942i
$93$		−	1.30687e8i		−	1.74703i
$94$	−180440.	−	93322.2i	−0.00231111	−	0.00119529i
$95$		0			0
$96$	−8.41269e7	+	7.91711e7i	−0.990489	+	0.932141i
$97$			7.87237e7i			0.889239i	0.895720	+	0.444620i	$0.146661\pi$
$97$			7.87237e7i			0.889239i	−0.895720	+	0.444620i	$0.853339\pi$
$98$	−9.62384e7	−	4.97738e7i	−1.04338	−	0.539630i
$99$			8.90568e7i			0.927100i
$100$		0			0
$101$	−1.16450e7			−0.111906			−0.0559530	−	0.998433i	$-0.517820\pi$
$101$	−1.16450e7			−0.111906			−0.0559530	+	0.998433i	$0.517820\pi$
$102$	−3.54764e7	+	6.85942e7i	−0.327747	+	0.633704i
$103$	−6.88569e7			−0.611785			−0.305892	−	0.952066i	$-0.598955\pi$
$103$	−6.88569e7			−0.611785			−0.305892	+	0.952066i	$0.598955\pi$
$104$	9.80725e7	−	1.37082e7i	0.838328	−	0.117178i
$105$		0			0
$106$	4.04529e7	−	7.82164e7i	0.320425	−	0.619547i
$107$	−7.69690e7			−0.587193			−0.293596	−	0.955929i	$-0.594852\pi$
$107$	−7.69690e7			−0.587193			−0.293596	+	0.955929i	$0.594852\pi$
$108$	1.60459e7	+	2.26585e7i	0.117942	+	0.166547i
$109$	4.29484e6			0.0304257			0.0152129	−	0.999884i	$-0.495157\pi$
$109$	4.29484e6			0.0304257			0.0152129	+	0.999884i	$0.495157\pi$
$110$		0			0
$111$		−	3.27326e8i		−	2.15620i
$112$	7.70399e7	−	2.18881e8i	0.489603	−	1.39103i
$113$			2.34309e8i			1.43706i	0.695496	+	0.718530i	$0.255185\pi$
$113$			2.34309e8i			1.43706i	−0.695496	+	0.718530i	$0.744815\pi$
$114$	4.12331e7	−	7.97250e7i	0.244133	−	0.472036i
$115$		0			0
$116$	1.96161e8	+	2.77001e8i	1.08338	+	1.52985i
$117$			1.34820e8i			0.719469i
$118$	4.91629e7	−	9.50572e7i	0.253577	−	0.490294i
$119$		−	1.55118e8i		−	0.773525i
$120$		0			0
$121$	−4.06770e7			−0.189761
$122$	3.56076e7	+	1.84160e7i	0.160732	+	0.0831295i
$123$	5.42118e8			2.36850
$124$	−2.47825e8	+	1.75500e8i	−1.04824	+	0.742321i
$125$		0			0
$126$	2.80610e8	+	1.45129e8i	1.11332	+	0.575802i
$127$	2.94344e8			1.13146			0.565732	−	0.824589i	$-0.308594\pi$
$127$	2.94344e8			1.13146			0.565732	+	0.824589i	$0.308594\pi$
$128$	2.63108e8	+	5.32125e7i	0.980155	+	0.198232i
$129$	3.15341e8			1.13873
$130$		0			0
$131$		−	3.43317e8i		−	1.16576i	−0.812558	−	0.582881i	$-0.801925\pi$
$131$		−	3.43317e8i		−	1.16576i	0.812558	−	0.582881i	$-0.198075\pi$
$132$	3.67574e8	−	2.60302e8i	1.21073	−	0.857396i
$133$			1.80289e8i			0.576186i
$134$	5.49595e7	+	2.84246e7i	0.170461	+	0.0881609i
$135$		0			0
$136$	1.77718e8	−	2.48407e7i	0.519489	−	0.0726121i
$137$			2.03539e8i			0.577784i	0.957362	+	0.288892i	$0.0932869\pi$
$137$			2.03539e8i			0.577784i	−0.957362	+	0.288892i	$0.906713\pi$
$138$	4.24114e8	+	2.19348e8i	1.16941	+	0.604808i
$139$		−	2.51305e8i		−	0.673197i	−0.941648	−	0.336599i	$-0.890723\pi$
$139$		−	2.51305e8i		−	0.673197i	0.941648	−	0.336599i	$-0.109277\pi$
$140$		0			0
$141$	−1.39878e6			−0.00353895
$142$	2.36457e8	−	4.57193e8i	0.581566	−	1.12447i
$143$	−3.86091e8			−0.923305
$144$	−1.21337e8	+	3.44735e8i	−0.282191	+	0.801744i
$145$		0			0
$146$	−1.40656e8	+	2.71960e8i	−0.309560	+	0.598540i
$147$	−7.46047e8			−1.59771
$148$	−6.20716e8	+	4.39567e8i	−1.29374	+	0.916175i
$149$	−7.65026e8			−1.55214			−0.776070	−	0.630647i	$-0.782790\pi$
$149$	−7.65026e8			−1.55214			−0.776070	+	0.630647i	$0.782790\pi$
$150$		0			0
$151$		−	5.12585e8i		−	0.985958i	−0.870041	−	0.492979i	$-0.835908\pi$
$151$		−	5.12585e8i		−	0.985958i	0.870041	−	0.492979i	$-0.164092\pi$
$152$	−2.06557e8	+	2.88717e7i	−0.386959	+	0.0540876i
$153$			2.44309e8i			0.445835i
$154$	−4.15613e8	+	8.03596e8i	−0.738936	+	1.42874i
$155$		0			0
$156$	5.56458e8	−	3.94063e8i	0.939581	−	0.665376i
$157$			1.16971e9i			1.92522i	0.270890	+	0.962610i	$0.412682\pi$
$157$			1.16971e9i			1.92522i	−0.270890	+	0.962610i	$0.587318\pi$
$158$	−3.92113e8	+	7.58157e8i	−0.629191	+	1.21655i
$159$		−	6.06339e8i		−	0.948696i
$160$		0			0
$161$	−9.59085e8			−1.42743
$162$	6.89789e8	+	3.56754e8i	1.00151	+	0.517975i
$163$	8.79268e8			1.24558			0.622789	−	0.782390i	$-0.286000\pi$
$163$	8.79268e8			1.24558			0.622789	+	0.782390i	$0.286000\pi$
$164$	−7.28014e8	−	1.02803e9i	−1.00638	−	1.42112i
$165$		0			0
$166$	−8.85075e7	−	4.57754e7i	−0.116559	−	0.0602837i
$167$	−4.63319e8			−0.595682			−0.297841	−	0.954616i	$-0.596266\pi$
$167$	−4.63319e8			−0.595682			−0.297841	+	0.954616i	$0.596266\pi$
$168$	−2.21180e8	−	1.58239e9i	−0.277657	−	1.98644i
$169$	2.31240e8			0.283476
$170$		0			0
$171$		−	2.83954e8i		−	0.332095i
$172$	−4.23472e8	−	5.97988e8i	−0.483851	−	0.683248i
$173$		−	4.71680e8i		−	0.526579i	−0.964717	−	0.263289i	$-0.915193\pi$
$173$		−	4.71680e8i		−	0.526579i	0.964717	−	0.263289i	$-0.0848074\pi$
$174$	2.07595e9	+	1.07366e9i	2.26475	+	1.17131i
$175$		0			0
$176$	−9.87233e8	−	3.47478e8i	−1.02889	−	0.362140i
$177$		−	7.36890e8i		−	0.750775i
$178$	5.44768e8	+	2.81750e8i	0.542664	+	0.280662i
$179$			8.30768e8i			0.809222i	0.914489	+	0.404611i	$0.132593\pi$
$179$			8.30768e8i			0.809222i	−0.914489	+	0.404611i	$0.867407\pi$
$180$		0			0
$181$	6.19754e8			0.577437			0.288719	−	0.957414i	$-0.406771\pi$
$181$	6.19754e8			0.577437			0.288719	+	0.957414i	$0.406771\pi$
$182$	−6.29184e8	+	1.21654e9i	−0.573446	+	1.10877i
$183$	2.76032e8			0.246125
$184$	−1.53589e8	−	1.09882e9i	−0.133995	−	0.958640i
$185$		0			0
$186$	−9.60579e8	+	1.85730e9i	−0.802567	+	1.55178i
$187$	−6.99639e8			−0.572147
$188$	1.87843e6	+	2.65255e6i	0.00150371	+	0.00212340i
$189$	−3.84010e8			−0.300951
$190$		0			0
$191$		−	4.24020e7i		−	0.0318605i	−0.999873	−	0.0159303i	$-0.994929\pi$
$191$		−	4.24020e7i		−	0.0318605i	0.999873	−	0.0159303i	$-0.00507097\pi$
$192$	1.77752e9	−	5.06810e8i	1.30800	−	0.372941i
$193$		−	4.21151e8i		−	0.303535i	−0.988416	−	0.151767i	$-0.951504\pi$
$193$		−	4.21151e8i		−	0.303535i	0.988416	−	0.151767i	$-0.0484965\pi$
$194$	5.78636e8	−	1.11880e9i	0.408506	−	0.789854i
$195$		0			0
$196$	1.00187e9	+	1.41475e9i	0.678871	+	0.958637i
$197$		−	1.93944e9i		−	1.28769i	−0.765155	−	0.643846i	$-0.777338\pi$
$197$		−	1.93944e9i		−	1.28769i	0.765155	−	0.643846i	$-0.222662\pi$
$198$	6.54587e8	−	1.26565e9i	0.425899	−	0.823483i
$199$		−	2.11255e8i		−	0.134708i	−0.997729	−	0.0673542i	$-0.978544\pi$
$199$		−	2.11255e8i		−	0.134708i	0.997729	−	0.0673542i	$-0.0214557\pi$
$200$		0			0
$201$	4.26050e8			0.261022
$202$	1.65496e8	+	8.55931e7i	0.0993989	+	0.0514083i
$203$	−4.69452e9			−2.76444
$204$	1.00836e9	−	7.14085e8i	0.582233	−	0.412315i
$205$		0			0
$206$	9.78578e8	+	5.06113e8i	0.543409	+	0.281047i
$207$	1.51055e9			0.822723
$208$	−1.49454e9	−	5.26036e8i	−0.798463	−	0.281036i
$209$	8.13170e8			0.426183
$210$		0			0
$211$			2.01406e9i			1.01611i	0.861324	+	0.508056i	$0.169636\pi$
$211$			2.01406e9i			1.01611i	−0.861324	+	0.508056i	$0.830364\pi$
$212$	−1.14982e9	+	8.14256e8i	−0.569226	+	0.403104i
$213$		−	3.54420e9i		−	1.72187i
$214$	1.09387e9	+	5.65739e8i	0.521565	+	0.269750i
$215$		0			0
$216$	−6.14958e7	−	4.39959e8i	−0.0282508	−	0.202114i
$217$		−	4.20007e9i		−	1.89416i
$218$	−6.10373e7	−	3.15680e7i	−0.0270252	−	0.0139772i
$219$			2.10825e9i			0.916528i
$220$		0			0
$221$	−1.05916e9			−0.444010
$222$	−2.40592e9	+	4.65188e9i	−0.990532	+	1.91521i
$223$	−9.06863e8			−0.366710			−0.183355	−	0.983047i	$-0.558696\pi$
$223$	−9.06863e8			−0.366710			−0.183355	+	0.983047i	$0.558696\pi$
$224$	−2.70370e9	+	2.54443e9i	−1.07390	+	1.01064i
$225$		0			0
$226$	1.72222e9	−	3.32994e9i	0.660169	−	1.27645i
$227$	−9.31268e7			−0.0350729			−0.0175364	−	0.999846i	$-0.505582\pi$
$227$	−9.31268e7			−0.0350729			−0.0175364	+	0.999846i	$0.505582\pi$
$228$	−1.17199e9	+	8.29960e8i	−0.433696	+	0.307127i
$229$	5.17840e8			0.188301			0.0941507	−	0.995558i	$-0.469986\pi$
$229$	5.17840e8			0.188301			0.0941507	+	0.995558i	$0.469986\pi$
$230$		0			0
$231$			6.22953e9i			2.18780i
$232$	−7.51786e8	−	5.37850e9i	−0.259503	−	1.85656i
$233$			1.20417e9i			0.408569i	0.978912	+	0.204284i	$0.0654867\pi$
$233$			1.20417e9i			0.408569i	−0.978912	+	0.204284i	$0.934513\pi$
$234$	9.90959e8	−	1.91604e9i	0.330516	−	0.639058i
$235$		0			0
$236$	−1.39738e9	+	9.89573e8i	−0.450471	+	0.319007i
$237$			5.87728e9i			1.86287i
$238$	−1.14015e9	+	2.20450e9i	−0.355349	+	0.687072i
$239$			2.12088e9i			0.650018i	0.945711	+	0.325009i	$0.105367\pi$
$239$			2.12088e9i			0.650018i	−0.945711	+	0.325009i	$0.894633\pi$
$240$		0			0
$241$	−6.85448e8			−0.203192			−0.101596	−	0.994826i	$-0.532395\pi$
$241$	−6.85448e8			−0.203192			−0.101596	+	0.994826i	$0.532395\pi$
$242$	5.78092e8	+	2.98984e8i	0.168552	+	0.0871740i
$243$	4.63572e9			1.32951
$244$	−3.70685e8	−	5.23447e8i	−0.104579	−	0.147677i
$245$		0			0
$246$	−7.70446e9	−	3.98469e9i	−2.10379	−	1.08806i
$247$	1.23103e9			0.330736
$248$	4.81200e9	−	6.72603e8i	1.27209	−	0.177808i
$249$	−6.86116e8			−0.178484
$250$		0			0
$251$		−	4.44219e9i		−	1.11919i	−0.828768	−	0.559593i	$-0.810958\pi$
$251$		−	4.44219e9i		−	1.11919i	0.828768	−	0.559593i	$-0.189042\pi$
$252$	−2.92123e9	−	4.12509e9i	−0.724376	−	1.02290i
$253$			4.32582e9i			1.05581i
$254$	−4.18315e9	−	2.16350e9i	−1.00501	−	0.519782i
$255$		0			0
$256$	−3.34811e9	−	2.69015e9i	−0.779543	−	0.626349i
$257$			1.71181e9i			0.392395i	0.980564	+	0.196198i	$0.0628594\pi$
$257$			1.71181e9i			0.392395i	−0.980564	+	0.196198i	$0.937141\pi$
$258$	−4.48155e9	−	2.31782e9i	−1.01146	−	0.523120i
$259$		−	1.05197e10i		−	2.33778i
$260$		0			0
$261$	7.39383e9			1.59334
$262$	−2.52345e9	+	4.87914e9i	−0.535538	+	1.03547i
$263$	2.50597e9			0.523785			0.261892	−	0.965097i	$-0.415653\pi$
$263$	2.50597e9			0.523785			0.261892	+	0.965097i	$0.415653\pi$
$264$	−7.13715e9	+	9.97603e8i	−1.46930	+	0.205372i
$265$		0			0
$266$	1.32516e9	−	2.56223e9i	0.264693	−	0.511789i
$267$	4.22308e9			0.830967
$268$	−5.72145e8	−	8.07929e8i	−0.110909	−	0.156615i
$269$	−3.62847e8			−0.0692970			−0.0346485	−	0.999400i	$-0.511031\pi$
$269$	−3.62847e8			−0.0692970			−0.0346485	+	0.999400i	$0.511031\pi$
$270$		0			0
$271$			1.05662e10i			1.95903i	0.201368	+	0.979516i	$0.435461\pi$
$271$			1.05662e10i			1.95903i	−0.201368	+	0.979516i	$0.564539\pi$
$272$	−2.70827e9	−	9.53236e8i	−0.494785	−	0.174151i
$273$			9.43069e9i			1.69782i
$274$	1.49606e9	−	2.89265e9i	0.265428	−	0.513209i
$275$		0			0
$276$	−4.41515e9	−	6.23465e9i	−0.760867	−	1.07442i
$277$		−	1.36227e9i		−	0.231390i	−0.993285	−	0.115695i	$-0.963091\pi$
$277$		−	1.36227e9i		−	0.231390i	0.993285	−	0.115695i	$-0.0369095\pi$
$278$	−1.84715e9	+	3.57149e9i	−0.309259	+	0.597958i
$279$			6.61506e9i			1.09173i
$280$		0			0
$281$	−3.01499e9			−0.483572			−0.241786	−	0.970330i	$-0.577733\pi$
$281$	−3.01499e9			−0.483572			−0.241786	+	0.970330i	$0.577733\pi$
$282$	1.98792e7	+	1.02814e7i	0.00314342	+	0.00162575i
$283$	−1.38220e9			−0.215490			−0.107745	−	0.994179i	$-0.534363\pi$
$283$	−1.38220e9			−0.215490			−0.107745	+	0.994179i	$0.534363\pi$
$284$	−6.72094e9	+	4.75952e9i	−1.03313	+	0.731627i
$285$		0			0
$286$	5.48703e9	+	2.83785e9i	0.820112	+	0.424156i
$287$	1.74228e10			2.56797
$288$	4.25829e9	−	4.00744e9i	0.618964	−	0.582502i
$289$	5.05644e9			0.724859
$290$		0			0
$291$		−	8.67304e9i		−	1.20948i
$292$	3.99793e9	−	2.83118e9i	0.549925	−	0.389436i
$293$		−	5.86750e9i		−	0.796127i	−0.917358	−	0.398064i	$-0.869682\pi$
$293$		−	5.86750e9i		−	0.796127i	0.917358	−	0.398064i	$-0.130318\pi$
$294$	1.06026e10	+	5.48361e9i	1.41914	+	0.733968i
$295$		0			0
$296$	1.20524e10	−	1.68463e9i	1.57002	−	0.219452i
$297$			1.73203e9i			0.222602i
$298$	1.08724e10	+	5.62310e9i	1.37867	+	0.713035i
$299$			6.54873e9i			0.819355i
$300$		0			0
$301$	1.01345e10			1.23463
$302$	−3.76761e9	+	7.28474e9i	−0.452938	+	0.875762i
$303$	1.28293e9			0.152207
$304$	3.14775e9	+	1.10792e9i	0.368558	+	0.129722i
$305$		0			0
$306$	1.79573e9	−	3.47207e9i	0.204812	−	0.396007i
$307$	−5.79386e9			−0.652250			−0.326125	−	0.945327i	$-0.605743\pi$
$307$	−5.79386e9			−0.652250			−0.326125	+	0.945327i	$0.605743\pi$
$308$	1.18132e10	−	8.36567e9i	1.31270	−	0.929603i
$309$	7.58601e9			0.832107
$310$		0			0
$311$			8.37260e9i			0.894991i	0.894286	+	0.447496i	$0.147684\pi$
$311$			8.37260e9i			0.894991i	−0.894286	+	0.447496i	$0.852316\pi$
$312$	−1.08047e10	+	1.51024e9i	−1.14024	+	0.159378i
$313$		−	1.22771e10i		−	1.27914i	−0.768731	−	0.639572i	$-0.779111\pi$
$313$		−	1.22771e10i		−	1.27914i	0.768731	−	0.639572i	$-0.220889\pi$
$314$	8.59764e9	−	1.66237e10i	0.884424	−	1.71005i
$315$		0			0
$316$	1.11452e10	−	7.89263e9i	1.11774	−	0.791541i
$317$		−	1.38443e10i		−	1.37099i	−0.728077	−	0.685495i	$-0.759586\pi$
$317$		−	1.38443e10i		−	1.37099i	0.728077	−	0.685495i	$-0.240414\pi$
$318$	−4.45672e9	+	8.61715e9i	−0.435820	+	0.842665i
$319$			2.11740e10i			2.04475i
$320$		0			0
$321$	8.47972e9			0.798659
$322$	1.36303e10	+	7.04948e9i	1.26789	+	0.655743i
$323$	2.23077e9			0.204948
$324$	−7.18091e9	−	1.01402e10i	−0.651627	−	0.920167i
$325$		0			0
$326$	−1.24959e10	−	6.46281e9i	−1.10637	−	0.572204i
$327$	−4.73165e8			−0.0413830
$328$	2.79010e9	+	1.99612e10i	0.241060	+	1.72461i
$329$	−4.49546e7			−0.00383699
$330$		0			0
$331$		−	7.71740e9i		−	0.642923i	−0.946923	−	0.321462i	$-0.895826\pi$
$331$		−	7.71740e9i		−	0.642923i	0.946923	−	0.321462i	$-0.104174\pi$
$332$	9.21389e8	+	1.30110e9i	0.0758386	+	0.107092i
$333$			1.65684e10i			1.34742i
$334$	6.58458e9	+	3.40549e9i	0.529105	+	0.273649i
$335$		0			0
$336$	−8.48754e9	+	2.41143e10i	−0.665924	+	1.89198i
$337$		−	1.47787e10i		−	1.14582i	−0.819618	−	0.572910i	$-0.805814\pi$
$337$		−	1.47787e10i		−	1.14582i	0.819618	−	0.572910i	$-0.194186\pi$
$338$	−3.28633e9	−	1.69966e9i	−0.251793	−	0.130226i
$339$		−	2.58139e10i		−	1.95459i
$340$		0			0
$341$	−1.89438e10			−1.40104
$342$	−2.08712e9	+	4.03548e9i	−0.152561	+	0.294979i
$343$	−3.56527e9			−0.257582
$344$	1.62295e9	+	1.16111e10i	0.115897	+	0.829161i
$345$		0			0
$346$	−3.46695e9	+	6.70341e9i	−0.241904	+	0.467726i
$347$	−2.69899e10			−1.86158			−0.930792	−	0.365549i	$-0.880881\pi$
$347$	−2.69899e10			−1.86158			−0.930792	+	0.365549i	$0.880881\pi$
$348$	−2.16112e10	−	3.05173e10i	−1.47354	−	2.08080i
$349$	−2.02677e10			−1.36617			−0.683083	−	0.730340i	$-0.739361\pi$
$349$	−2.02677e10			−1.36617			−0.683083	+	0.730340i	$0.739361\pi$
$350$		0			0
$351$			2.62206e9i			0.172748i
$352$	1.14763e10	+	1.21947e10i	0.747534	+	0.794326i
$353$		−	9.41747e9i		−	0.606506i	−0.952910	−	0.303253i	$-0.901927\pi$
$353$		−	9.41747e9i		−	0.606506i	0.952910	−	0.303253i	$-0.0980728\pi$
$354$	−5.41630e9	+	1.04725e10i	−0.344897	+	0.666865i
$355$		0			0
$356$	−5.67119e9	−	8.00832e9i	−0.353081	−	0.498588i
$357$			1.70894e10i			1.05210i
$358$	6.10633e9	−	1.18067e10i	0.371747	−	0.718780i
$359$		−	3.30369e9i		−	0.198894i	−0.995043	−	0.0994469i	$-0.968293\pi$
$359$		−	3.30369e9i		−	0.198894i	0.995043	−	0.0994469i	$-0.0317073\pi$
$360$		0			0
$361$	1.43908e10			0.847337
$362$	−8.80780e9	−	4.55533e9i	−0.512900	−	0.265268i
$363$	4.48141e9			0.258100
$364$	1.78836e10	−	1.26645e10i	1.01871	−	0.721412i
$365$		0			0
$366$	−3.92291e9	−	2.02890e9i	−0.218617	−	0.113067i
$367$	1.14531e10			0.631335			0.315667	−	0.948870i	$-0.397772\pi$
$367$	1.14531e10			0.631335			0.315667	+	0.948870i	$0.397772\pi$
$368$	−5.89380e9	+	1.67451e10i	−0.321369	+	0.913053i
$369$	−2.74407e10			−1.48009
$370$		0			0
$371$		−	1.94867e10i		−	1.02859i
$372$	2.73031e10	−	1.93350e10i	1.42574	−	1.00965i
$373$		−	2.26449e10i		−	1.16986i	−0.811083	−	0.584932i	$-0.801121\pi$
$373$		−	2.26449e10i		−	1.16986i	0.811083	−	0.584932i	$-0.198879\pi$
$374$	9.94311e9	+	5.14250e9i	0.508201	+	0.262838i
$375$		0			0
$376$	−7.19907e6	−	5.15043e7i	−0.000360184	−	0.00257687i
$377$			3.20547e10i			1.58681i
$378$	5.45746e9	+	2.82256e9i	0.267315	+	0.138253i
$379$		−	5.61760e9i		−	0.272266i	−0.990691	−	0.136133i	$-0.956533\pi$
$379$		−	5.61760e9i		−	0.272266i	0.990691	−	0.136133i	$-0.0434675\pi$
$380$		0			0
$381$	−3.24281e10			−1.53894
$382$	−3.11664e8	+	6.02607e8i	−0.0146364	+	0.0282996i
$383$	−4.10535e9			−0.190790			−0.0953950	−	0.995440i	$-0.530411\pi$
$383$	−4.10535e9			−0.190790			−0.0953950	+	0.995440i	$0.530411\pi$
$384$	−2.89868e10	−	5.86246e9i	−1.33314	−	0.269622i
$385$		0			0
$386$	−3.09555e9	+	5.98530e9i	−0.139440	+	0.269610i
$387$	−1.59618e10			−0.711602
$388$	−1.64469e10	+	1.16471e10i	−0.725699	+	0.513913i
$389$	1.37663e9			0.0601199			0.0300599	−	0.999548i	$-0.490430\pi$
$389$	1.37663e9			0.0601199			0.0300599	+	0.999548i	$0.490430\pi$
$390$		0			0
$391$			1.18670e10i			0.507732i
$392$	−3.83965e9	−	2.74700e10i	−0.162610	−	1.16336i
$393$			3.78234e10i			1.58559i
$394$	−1.42553e10	+	2.75629e10i	−0.591551	+	1.14377i
$395$		0			0
$396$	−1.86057e10	+	1.31758e10i	−0.756597	+	0.535793i
$397$		−	3.04208e10i		−	1.22464i	−0.790610	−	0.612321i	$-0.790236\pi$
$397$		−	3.04208e10i		−	1.22464i	0.790610	−	0.612321i	$-0.209764\pi$
$398$	−1.55277e9	+	3.00231e9i	−0.0618835	+	0.119653i
$399$		−	1.98626e10i		−	0.783689i
$400$		0			0
$401$	−1.95473e10			−0.755977			−0.377989	−	0.925810i	$-0.623384\pi$
$401$	−1.95473e10			−0.755977			−0.377989	+	0.925810i	$0.623384\pi$
$402$	−6.05492e9	−	3.13156e9i	−0.231849	−	0.119910i
$403$	−2.86785e10			−1.08727
$404$	−1.72286e9	−	2.43286e9i	−0.0646732	−	0.0913254i
$405$		0			0
$406$	6.67175e10	+	3.45058e10i	2.45548	+	1.26995i
$407$	−4.74477e10			−1.72917
$408$	−1.95793e10	+	2.73672e9i	−0.706573	+	0.0987620i
$409$	4.37475e10			1.56336			0.781681	−	0.623678i	$-0.214362\pi$
$409$	4.37475e10			1.56336			0.781681	+	0.623678i	$0.214362\pi$
$410$		0			0
$411$		−	2.24240e10i		−	0.785862i
$412$	−1.01873e10	−	1.43855e10i	−0.353565	−	0.499271i
$413$		−	2.36824e10i		−	0.814002i
$414$	−2.14676e10	−	1.11029e10i	−0.730772	−	0.377949i
$415$		0			0
$416$	1.73736e10	+	1.84611e10i	0.580118	+	0.616431i
$417$			2.76865e10i			0.915637i
$418$	−1.15566e10	−	5.97697e9i	−0.378551	−	0.195784i
$419$			1.93115e10i			0.626555i	0.949662	+	0.313277i	$0.101427\pi$
$419$			1.93115e10i			0.626555i	−0.949662	+	0.313277i	$0.898573\pi$
$420$		0			0
$421$	−3.65545e10			−1.16362			−0.581812	−	0.813323i	$-0.697656\pi$
$421$	−3.65545e10			−1.16362			−0.581812	+	0.813323i	$0.697656\pi$
$422$	1.48038e10	−	2.86233e10i	0.466791	−	0.902547i
$423$	7.08030e7			0.00221152
$424$	2.23259e10	−	3.12062e9i	0.690788	−	0.0965557i
$425$		0			0
$426$	−2.60506e10	+	5.03693e10i	−0.791005	+	1.52942i
$427$	8.87121e9			0.266853
$428$	−1.13875e10	−	1.60803e10i	−0.339353	−	0.479202i
$429$	4.25359e10			1.25582
$430$		0			0
$431$			3.98669e10i			1.15532i	0.816276	+	0.577662i	$0.196035\pi$
$431$			3.98669e10i			1.15532i	−0.816276	+	0.577662i	$0.803965\pi$
$432$	−2.35983e9	+	6.70460e9i	−0.0677557	+	0.192503i
$433$		−	3.21564e10i		−	0.914779i	−0.889266	−	0.457389i	$-0.848785\pi$
$433$		−	3.21564e10i		−	0.914779i	0.889266	−	0.457389i	$-0.151215\pi$
$434$	−3.08714e10	+	5.96904e10i	−0.870157	+	1.68246i
$435$		0			0
$436$	6.35416e8	+	8.97275e8i	0.0175838	+	0.0248302i
$437$		−	1.37927e10i		−	0.378201i
$438$	1.54961e10	−	2.99620e10i	0.421043	−	0.814093i
$439$		−	2.72016e10i		−	0.732379i	−0.930540	−	0.366189i	$-0.880662\pi$
$439$		−	2.72016e10i		−	0.732379i	0.930540	−	0.366189i	$-0.119338\pi$
$440$		0			0
$441$	3.77630e10			0.998418
$442$	1.50526e10	+	7.78507e9i	0.394386	+	0.203973i
$443$	−1.32228e10			−0.343327			−0.171663	−	0.985156i	$-0.554914\pi$
$443$	−1.32228e10			−0.343327			−0.171663	+	0.985156i	$0.554914\pi$
$444$	6.83846e10	−	4.84274e10i	1.75965	−	1.24612i
$445$		0			0
$446$	1.28881e10	+	6.66564e9i	0.325724	+	0.168462i
$447$	8.42834e10			2.11111
$448$	5.71264e10	−	1.62880e10i	1.41816	−	0.404349i
$449$	−2.82958e10			−0.696203			−0.348102	−	0.937457i	$-0.613174\pi$
$449$	−2.82958e10			−0.696203			−0.348102	+	0.937457i	$0.613174\pi$
$450$		0			0
$451$		−	7.85831e10i		−	1.89943i
$452$	−4.89516e10	+	3.46657e10i	−1.17277	+	0.830512i
$453$			5.64718e10i			1.34103i
$454$	1.32350e9	+	6.84502e8i	0.0311530	+	0.0161121i
$455$		0			0
$456$	2.27565e10	−	3.18081e9i	0.526315	−	0.0735662i
$457$			7.89688e10i			1.81047i	0.424914	+	0.905234i	$0.360304\pi$
$457$			7.89688e10i			1.81047i	−0.424914	+	0.905234i	$0.639696\pi$
$458$	−7.35942e9	−	3.80623e9i	−0.167256	−	0.0865035i
$459$			4.75146e9i			0.107047i
$460$		0			0
$461$	2.63713e10			0.583885			0.291943	−	0.956436i	$-0.405698\pi$
$461$	2.63713e10			0.583885			0.291943	+	0.956436i	$0.405698\pi$
$462$	4.57884e10	−	8.85326e10i	1.00505	−	1.94328i
$463$	2.74281e10			0.596858			0.298429	−	0.954432i	$-0.403537\pi$
$463$	2.74281e10			0.596858			0.298429	+	0.954432i	$0.403537\pi$
$464$	−2.88489e10	+	8.19638e10i	−0.622383	+	1.76828i
$465$		0			0
$466$	8.85093e9	−	1.71134e10i	0.187692	−	0.362905i
$467$	−8.24023e10			−1.73249			−0.866247	−	0.499616i	$-0.833475\pi$
$467$	−8.24023e10			−1.73249			−0.866247	+	0.499616i	$0.833475\pi$
$468$	−2.81665e10	+	1.99465e10i	−0.587151	+	0.415799i
$469$	1.36925e10			0.283004
$470$		0			0
$471$		−	1.28868e11i		−	2.61855i
$472$	2.71328e10	−	3.79252e9i	0.546673	−	0.0764118i
$473$		−	4.57104e10i		−	0.913209i
$474$	4.31993e10	−	8.35266e10i	0.855782	−	1.65467i
$475$		0			0
$476$	3.24071e10	−	2.29495e10i	0.631266	−	0.447039i
$477$			3.06914e10i			0.592847i
$478$	1.55890e10	−	3.01415e10i	0.298611	−	0.577369i
$479$		−	1.28142e10i		−	0.243415i	−0.992566	−	0.121708i	$-0.961163\pi$
$479$		−	1.28142e10i		−	0.243415i	0.992566	−	0.121708i	$-0.0388370\pi$
$480$		0			0
$481$	−7.18296e10			−1.34191
$482$	9.74143e9	+	5.03819e9i	0.180482	+	0.0933441i
$483$	1.05663e11			1.94149
$484$	−6.01810e9	−	8.49820e9i	−0.109668	−	0.154862i
$485$		0			0
$486$	−6.58817e10	−	3.40735e10i	−1.18092	−	0.610762i
$487$	−2.27188e10			−0.403895			−0.201948	−	0.979396i	$-0.564727\pi$
$487$	−2.27188e10			−0.403895			−0.201948	+	0.979396i	$0.564727\pi$
$488$	1.42064e9	+	1.01637e10i	0.0250499	+	0.179215i
$489$	−9.68695e10			−1.69415
$490$		0			0
$491$			8.70411e10i			1.49761i	0.662791	+	0.748805i	$0.269372\pi$
$491$			8.70411e10i			1.49761i	−0.662791	+	0.748805i	$0.730628\pi$
$492$	8.02057e10	+	1.13259e11i	1.36882	+	1.93291i
$493$			5.80866e10i			0.983305i
$494$	−1.74951e10	−	9.04835e9i	−0.293772	−	0.151936i
$495$		0			0
$496$	−7.33308e10	−	2.58104e10i	−1.21160	−	0.426449i
$497$		−	1.13904e11i		−	1.86688i
$498$	9.75092e9	+	5.04310e9i	0.158536	+	0.0819937i
$499$		−	1.34972e10i		−	0.217691i	−0.994059	−	0.108846i	$-0.965285\pi$
$499$		−	1.34972e10i		−	0.217691i	0.994059	−	0.108846i	$-0.0347154\pi$
$500$		0			0
$501$	5.10441e10			0.810205
$502$	−3.26510e10	+	6.31313e10i	−0.514141	+	0.994100i
$503$	−4.13249e10			−0.645565			−0.322782	−	0.946473i	$-0.604618\pi$
$503$	−4.13249e10			−0.645565			−0.322782	+	0.946473i	$0.604618\pi$
$504$	1.11956e10	+	8.00966e10i	0.173510	+	1.24134i
$505$		0			0
$506$	3.17957e10	−	6.14776e10i	0.485028	−	0.937810i
$507$	−2.54759e10			−0.385564
$508$	4.35479e10	+	6.14942e10i	0.653901	+	0.923377i
$509$	3.37390e9			0.0502645			0.0251322	−	0.999684i	$-0.491999\pi$
$509$	3.37390e9			0.0502645			0.0251322	+	0.999684i	$0.491999\pi$
$510$		0			0
$511$			6.77557e10i			0.993715i
$512$	2.78094e10	+	6.28411e10i	0.404680	+	0.914458i
$513$		−	5.52248e9i		−	0.0797379i
$514$	1.25822e10	−	2.43279e10i	0.180262	−	0.348539i
$515$		0			0
$516$	4.66542e10	+	6.58807e10i	0.658100	+	0.929307i
$517$			2.02761e8i			0.00283807i
$518$	−7.73221e10	+	1.49504e11i	−1.07395	+	2.07650i
$519$			5.19653e10i			0.716216i
$520$		0			0
$521$	1.24497e11			1.68969			0.844847	−	0.535007i	$-0.179691\pi$
$521$	1.24497e11			1.68969			0.844847	+	0.535007i	$0.179691\pi$
$522$	−1.05079e11	−	5.43462e10i	−1.41526	−	0.731960i
$523$	4.47960e10			0.598733			0.299366	−	0.954138i	$-0.403225\pi$
$523$	4.47960e10			0.598733			0.299366	+	0.954138i	$0.403225\pi$
$524$	7.17254e10	−	5.07932e10i	0.951367	−	0.673722i
$525$		0			0
$526$	−3.56142e10	−	1.84194e10i	−0.465244	−	0.240621i
$527$	−5.19686e10			−0.673749
$528$	1.08764e11	+	3.82819e10i	1.39943	+	0.492558i
$529$	−4.93792e9			−0.0630553
$530$		0			0
$531$			3.72995e10i			0.469165i
$532$	−3.76658e10	+	2.66735e10i	−0.470220	+	0.332992i
$533$		−	1.18964e11i		−	1.47404i
$534$	−6.00174e10	−	3.10405e10i	−0.738095	−	0.381737i
$535$		0			0
$536$	2.19274e9	+	1.56875e10i	0.0265661	+	0.190061i
$537$		−	9.15263e10i		−	1.10065i
$538$	5.15670e9	+	2.66700e9i	0.0615520	+	0.0318342i
$539$			1.08144e11i			1.28129i
$540$		0			0
$541$	−8.68526e10			−1.01390			−0.506948	−	0.861977i	$-0.669226\pi$
$541$	−8.68526e10			−1.01390			−0.506948	+	0.861977i	$0.669226\pi$
$542$	7.76638e10	−	1.50164e11i	0.899957	−	1.74008i
$543$	−6.82787e10			−0.785391
$544$	3.14829e10	+	3.34536e10i	0.359483	+	0.381985i
$545$		0			0
$546$	6.93176e10	−	1.34027e11i	0.779961	−	1.50807i
$547$	1.65768e11			1.85162			0.925808	−	0.377993i	$-0.123386\pi$
$547$	1.65768e11			1.85162			0.925808	+	0.377993i	$0.123386\pi$
$548$	−4.25232e10	+	3.01133e10i	−0.471524	+	0.333916i
$549$	−1.39721e10			−0.153805
$550$		0			0
$551$		−	6.75124e10i		−	0.732448i
$552$	1.69210e10	+	1.21058e11i	0.182251	+	1.30388i
$553$			1.88886e11i			2.01976i
$554$	−1.00130e10	+	1.93603e10i	−0.106298	+	0.205529i
$555$		0			0
$556$	5.25025e10	−	3.71803e10i	0.549390	−	0.389057i
$557$		−	9.73769e10i		−	1.01166i	−0.862633	−	0.505831i	$-0.831186\pi$
$557$		−	9.73769e10i		−	1.01166i	0.862633	−	0.505831i	$-0.168814\pi$
$558$	4.86221e10	−	9.40117e10i	0.501530	−	0.969717i
$559$		−	6.91995e10i		−	0.708689i
$560$		0			0
$561$	7.70796e10			0.778195
$562$	4.28484e10	+	2.21608e10i	0.429525	+	0.222147i
$563$	−1.96004e9			−0.0195088			−0.00975440	−	0.999952i	$-0.503105\pi$
$563$	−1.96004e9			−0.0195088			−0.00975440	+	0.999952i	$0.503105\pi$
$564$	−2.06948e8	−	2.92233e8i	−0.00204524	−	0.00288810i
$565$		0			0
$566$	1.96435e10	+	1.01595e10i	0.191405	+	0.0989934i
$567$	1.71853e11			1.66274
$568$	1.30500e11	−	1.82408e10i	1.25377	−	0.175247i
$569$	−7.88598e10			−0.752327			−0.376164	−	0.926553i	$-0.622757\pi$
$569$	−7.88598e10			−0.752327			−0.376164	+	0.926553i	$0.622757\pi$
$570$		0			0
$571$			5.71331e10i			0.537457i	0.963216	+	0.268728i	$0.0866034\pi$
$571$			5.71331e10i			0.537457i	−0.963216	+	0.268728i	$0.913397\pi$
$572$	−5.71216e10	−	8.06617e10i	−0.533601	−	0.753500i
$573$			4.67145e9i			0.0433345i
$574$	−2.47608e11	−	1.28061e11i	−2.28096	−	1.17970i
$575$		0			0
$576$	−8.99735e10	+	2.56535e10i	−0.817381	+	0.233054i
$577$			1.51459e11i			1.36644i	0.730212	+	0.683221i	$0.239421\pi$
$577$			1.51459e11i			1.36644i	−0.730212	+	0.683221i	$0.760579\pi$
$578$	−7.18610e10	−	3.71659e10i	−0.643845	−	0.332992i
$579$			4.63984e10i			0.412847i
$580$		0			0
$581$	−2.20506e10			−0.193516
$582$	−6.37487e10	+	1.23259e11i	−0.555622	+	1.07430i
$583$	−8.78922e10			−0.760810
$584$	−7.76274e10	+	1.08505e10i	−0.667365	+	0.0932817i
$585$		0			0
$586$	−4.31274e10	+	8.33875e10i	−0.365732	+	0.707148i
$587$	1.33645e11			1.12564			0.562819	−	0.826580i	$-0.309717\pi$
$587$	1.33645e11			1.12564			0.562819	+	0.826580i	$0.309717\pi$
$588$	−1.10377e11	−	1.55863e11i	−0.923353	−	1.30387i
$589$	6.04015e10			0.501865
$590$		0			0
$591$			2.13670e11i			1.75143i
$592$	−1.83668e11	−	6.46460e10i	−1.49536	−	0.526326i
$593$			1.58419e11i			1.28112i	0.767910	+	0.640558i	$0.221297\pi$
$593$			1.58419e11i			1.28112i	−0.767910	+	0.640558i	$0.778703\pi$
$594$	1.27308e10	−	2.46152e10i	0.102261	−	0.197723i
$595$		0			0
$596$	−1.13185e11	−	1.59829e11i	−0.897020	−	1.26669i
$597$			2.32741e10i			0.183221i
$598$	4.81346e10	−	9.30690e10i	0.376403	−	0.727781i
$599$			4.31245e10i			0.334978i	0.985874	+	0.167489i	$0.0535659\pi$
$599$			4.31245e10i			0.334978i	−0.985874	+	0.167489i	$0.946434\pi$
$600$		0			0
$601$	4.15092e10			0.318160			0.159080	−	0.987266i	$-0.449147\pi$
$601$	4.15092e10			0.318160			0.159080	+	0.987266i	$0.449147\pi$
$602$	−1.44029e11	−	7.44909e10i	−1.09664	−	0.567175i
$603$	−2.15656e10			−0.163114
$604$	1.07089e11	−	7.58363e10i	0.804630	−	0.569809i
$605$		0			0
$606$	−1.82328e10	−	9.42985e9i	−0.135195	−	0.0699221i
$607$	−2.83174e10			−0.208592			−0.104296	−	0.994546i	$-0.533259\pi$
$607$	−2.83174e10			−0.208592			−0.104296	+	0.994546i	$0.533259\pi$
$608$	−3.65916e10	−	3.88821e10i	−0.267773	−	0.284535i
$609$	5.17199e11			3.76000
$610$		0			0
$611$			3.06954e8i			0.00220246i
$612$	−5.10409e10	+	3.61452e10i	−0.363842	+	0.257659i
$613$		−	2.40024e11i		−	1.69986i	−0.526899	−	0.849928i	$-0.676645\pi$
$613$		−	2.40024e11i		−	1.69986i	0.526899	−	0.849928i	$-0.323355\pi$
$614$	8.23410e10	+	4.25861e10i	0.579352	+	0.299636i
$615$		0			0
$616$	−2.29376e11	+	3.20613e10i	−1.59303	+	0.222668i
$617$		−	1.16795e10i		−	0.0805904i	−0.999188	−	0.0402952i	$-0.987170\pi$
$617$		−	1.16795e10i		−	0.0805904i	0.999188	−	0.0402952i	$-0.0128298\pi$
$618$	−1.07811e11	−	5.57588e10i	−0.739107	−	0.382260i
$619$		−	2.19401e11i		−	1.49443i	−0.664583	−	0.747215i	$-0.731391\pi$
$619$		−	2.19401e11i		−	1.49443i	0.664583	−	0.747215i	$-0.268609\pi$
$620$		0			0
$621$	2.93780e10			0.197540
$622$	6.15404e10	−	1.18989e11i	0.411149	−	0.794963i
$623$	1.35723e11			0.900948
$624$	1.64655e11	+	5.79537e10i	1.08601	+	0.382246i
$625$		0			0
$626$	−9.02396e10	+	1.74480e11i	−0.587624	+	1.13618i
$627$	−8.95874e10			−0.579665
$628$	−2.44375e11	+	1.73057e11i	−1.57115	+	1.11263i
$629$	−1.30163e11			−0.831544
$630$		0			0
$631$			2.35335e10i			0.148446i	0.997242	+	0.0742230i	$0.0236477\pi$
$631$			2.35335e10i			0.148446i	−0.997242	+	0.0742230i	$0.976352\pi$
$632$	−2.16406e11	+	3.02484e10i	−1.35644	+	0.189598i
$633$		−	2.21890e11i		−	1.38205i
$634$	−1.01759e11	+	1.96752e11i	−0.629817	+	1.21776i
$635$		0			0
$636$	1.26676e11	−	8.97071e10i	0.774222	−	0.548275i
$637$			1.63715e11i			0.994332i
$638$	1.55634e11	−	3.00920e11i	0.939336	−	1.81622i
$639$			1.79398e11i			1.07601i
$640$		0			0
$641$	−8.47231e10			−0.501845			−0.250923	−	0.968007i	$-0.580734\pi$
$641$	−8.47231e10			−0.501845			−0.250923	+	0.968007i	$0.580734\pi$
$642$	−1.20512e11	−	6.23278e10i	−0.709397	−	0.366895i
$643$	−2.37102e11			−1.38705			−0.693523	−	0.720435i	$-0.743942\pi$
$643$	−2.37102e11			−1.38705			−0.693523	+	0.720435i	$0.743942\pi$
$644$	−1.41895e11	−	2.00371e11i	−0.824944	−	1.16491i
$645$		0			0
$646$	−3.17031e10	−	1.63966e10i	−0.182042	−	0.0941508i
$647$	−2.88712e11			−1.64758			−0.823792	−	0.566892i	$-0.808146\pi$
$647$	−2.88712e11			−1.64758			−0.823792	+	0.566892i	$0.808146\pi$
$648$	2.75207e10	+	1.96891e11i	0.156084	+	1.11667i
$649$	−1.06816e11			−0.602086
$650$		0			0
$651$			4.62724e11i			2.57631i
$652$	1.30086e11	+	1.83696e11i	0.719850	+	1.01650i
$653$		−	7.01205e10i		−	0.385649i	−0.981233	−	0.192824i	$-0.938235\pi$
$653$		−	7.01205e10i		−	0.385649i	0.981233	−	0.192824i	$-0.0617648\pi$
$654$	6.72451e9	+	3.47787e9i	0.0367578	+	0.0190109i
$655$		0			0
$656$	1.07067e11	−	3.04192e11i	0.578149	−	1.64260i
$657$		−	1.06714e11i		−	0.572746i
$658$	6.38884e8	+	3.30426e8i	0.00340815	+	0.00176267i
$659$			1.30280e11i			0.690774i	0.938460	+	0.345387i	$0.112252\pi$
$659$			1.30280e11i			0.690774i	−0.938460	+	0.345387i	$0.887748\pi$
$660$		0			0
$661$	−9.13098e10			−0.478312			−0.239156	−	0.970981i	$-0.576871\pi$
$661$	−9.13098e10			−0.478312			−0.239156	+	0.970981i	$0.576871\pi$
$662$	−5.67246e10	+	1.09678e11i	−0.295352	+	0.571067i
$663$	1.16688e11			0.603912
$664$	−3.53121e9	−	2.52633e10i	−0.0181656	−	0.129962i
$665$		0			0
$666$	1.21781e11	−	2.35466e11i	0.618991	−	1.19683i
$667$	3.59146e11			1.81454
$668$	−6.85474e10	−	9.67962e10i	−0.344259	−	0.486130i
$669$	9.99097e10			0.498773
$670$		0			0
$671$		−	4.00124e10i		−	0.197381i
$672$	2.97868e11	−	2.80321e11i	1.46065	−	1.37461i
$673$			2.19105e11i			1.06805i	0.845468	+	0.534026i	$0.179321\pi$
$673$			2.19105e11i			1.06805i	−0.845468	+	0.534026i	$0.820679\pi$
$674$	−1.08627e11	+	2.10031e11i	−0.526377	+	1.01776i
$675$		0			0
$676$	3.42117e10	+	4.83105e10i	0.163828	+	0.231342i
$677$		−	8.12354e10i		−	0.386715i	−0.981128	−	0.193357i	$-0.938062\pi$
$677$		−	8.12354e10i		−	0.386715i	0.981128	−	0.193357i	$-0.0619377\pi$
$678$	−1.89738e11	+	3.66862e11i	−0.897916	+	1.73614i
$679$		−	2.78737e11i		−	1.31134i
$680$		0			0
$681$	1.02598e10			0.0477037
$682$	2.69225e11	+	1.39241e11i	1.24445	+	0.643622i
$683$	−2.91761e11			−1.34074			−0.670369	−	0.742028i	$-0.733864\pi$
$683$	−2.91761e11			−1.34074			−0.670369	+	0.742028i	$0.733864\pi$
$684$	5.93233e10	−	4.20105e10i	0.271020	−	0.191926i
$685$		0			0
$686$	5.06688e10	+	2.62055e10i	0.228794	+	0.118330i
$687$	−5.70507e10			−0.256115
$688$	6.22789e10	−	1.76943e11i	0.277963	−	0.789732i
$689$	−1.33057e11			−0.590421
$690$		0			0
$691$		−	1.35594e11i		−	0.594743i	−0.954762	−	0.297371i	$-0.903890\pi$
$691$		−	1.35594e11i		−	0.594743i	0.954762	−	0.297371i	$-0.0961100\pi$
$692$	9.85430e10	−	6.97845e10i	0.429736	−	0.304323i
$693$		−	3.15323e11i		−	1.36717i
$694$	3.83574e11	+	1.98381e11i	1.65353	+	0.855191i
$695$		0			0
$696$	8.28247e10	+	5.92552e11i	0.352958	+	2.52517i
$697$		−	2.15577e11i		−	0.913420i
$698$	2.88040e11	+	1.48972e11i	1.21348	+	0.627601i
$699$		−	1.32664e11i		−	0.555707i
$700$		0			0
$701$	1.48441e11			0.614725			0.307363	−	0.951592i	$-0.400554\pi$
$701$	1.48441e11			0.614725			0.307363	+	0.951592i	$0.400554\pi$
$702$	1.92727e10	−	3.72641e10i	0.0793587	−	0.153441i
$703$	1.51285e11			0.619404
$704$	−7.34650e10	−	2.57661e11i	−0.299082	−	1.04896i
$705$		0			0
$706$	−6.92204e10	+	1.33839e11i	−0.278622	+	0.538720i
$707$	4.12314e10			0.165025
$708$	1.53950e11	−	1.09022e11i	0.612700	−	0.433891i
$709$	−4.79726e11			−1.89849			−0.949245	−	0.314536i	$-0.898151\pi$
$709$	−4.79726e11			−1.89849			−0.949245	+	0.314536i	$0.898151\pi$
$710$		0			0
$711$		−	2.97493e11i		−	1.16412i
$712$	2.17347e10	+	1.55497e11i	0.0845735	+	0.605064i
$713$			3.21318e11i			1.24330i
$714$	1.25611e11	−	2.42871e11i	0.483321	−	0.934508i
$715$		0			0
$716$	−1.73563e11	+	1.22911e11i	−0.660399	+	0.467669i
$717$		−	2.33659e11i		−	0.884110i
$718$	−2.42828e10	+	4.69512e10i	−0.0913695	+	0.176664i
$719$			4.02314e11i			1.50539i	0.658368	+	0.752696i	$0.271247\pi$
$719$			4.02314e11i			1.50539i	−0.658368	+	0.752696i	$0.728753\pi$
$720$		0			0
$721$	2.43801e11			0.902184
$722$	−2.04519e11	−	1.05776e11i	−0.752635	−	0.389257i
$723$	7.55163e10			0.276368
$724$	9.16917e10	+	1.29478e11i	0.333715	+	0.471241i
$725$		0			0
$726$	−6.36887e10	−	3.29393e10i	−0.229253	−	0.118568i
$727$	−3.49293e11			−1.25041			−0.625204	−	0.780461i	$-0.714984\pi$
$727$	−3.49293e11			−1.25041			−0.625204	+	0.780461i	$0.714984\pi$
$728$	−3.47245e11	+	4.85366e10i	−1.23626	+	0.172800i
$729$	−1.92272e11			−0.680777
$730$		0			0
$731$		−	1.25397e11i		−	0.439155i
$732$	4.08386e10	+	5.76684e10i	0.142242	+	0.200860i
$733$			1.75651e11i			0.608464i	0.952598	+	0.304232i	$0.0983998\pi$
$733$			1.75651e11i			0.608464i	−0.952598	+	0.304232i	$0.901600\pi$
$734$	−1.62769e11	−	8.41829e10i	−0.560774	−	0.290028i
$735$		0			0
$736$	2.06841e11	−	1.94657e11i	0.704898	−	0.663373i
$737$		−	6.17583e10i		−	0.209327i
$738$	3.89981e11	+	2.01695e11i	1.31467	+	0.679939i
$739$			1.85701e11i			0.622640i	0.950305	+	0.311320i	$0.100771\pi$
$739$			1.85701e11i			0.622640i	−0.950305	+	0.311320i	$0.899229\pi$
$740$		0			0
$741$	−1.35624e11			−0.449844
$742$	−1.43232e11	+	2.76941e11i	−0.472523	+	0.913632i
$743$	2.85901e11			0.938126			0.469063	−	0.883165i	$-0.344592\pi$
$743$	2.85901e11			0.938126			0.469063	+	0.883165i	$0.344592\pi$
$744$	−5.30141e11	+	7.41010e10i	−1.73021	+	0.241842i
$745$		0			0
$746$	−1.66445e11	+	3.21824e11i	−0.537422	+	1.03911i
$747$	3.47295e10			0.111536
$748$	−1.03511e11	−	1.46168e11i	−0.330658	−	0.466924i
$749$	2.72524e11			0.865919
$750$		0			0
$751$		−	6.18679e11i		−	1.94494i	−0.233031	−	0.972469i	$-0.574864\pi$
$751$		−	6.18679e11i		−	1.94494i	0.233031	−	0.972469i	$-0.425136\pi$
$752$	−2.76256e8	+	7.84881e8i	−0.000863854	+	0.00245433i
$753$			4.89399e11i			1.52224i
$754$	2.35609e11	−	4.55554e11i	0.728964	−	1.40946i
$755$		0			0
$756$	−5.68138e10	−	8.02271e10i	−0.173927	−	0.245603i
$757$			9.34034e10i			0.284433i	0.989836	+	0.142216i	$0.0454229\pi$
$757$			9.34034e10i			0.284433i	−0.989836	+	0.142216i	$0.954577\pi$
$758$	−4.12905e10	+	7.98360e10i	−0.125076	+	0.241836i
$759$		−	4.76579e11i		−	1.43604i
$760$		0			0
$761$	−3.21388e11			−0.958276			−0.479138	−	0.877740i	$-0.659051\pi$
$761$	−3.21388e11			−0.958276			−0.479138	+	0.877740i	$0.659051\pi$
$762$	4.60861e11	+	2.38354e11i	1.36694	+	0.706971i
$763$	−1.52067e10			−0.0448681
$764$	8.85859e9	−	6.27332e9i	0.0260011	−	0.0184130i
$765$		0			0
$766$	5.83443e10	+	3.01752e10i	0.169466	+	0.0876467i
$767$	−1.61706e11			−0.467245
$768$	3.68863e11	+	2.96375e11i	1.06028	+	0.851916i
$769$	−2.44957e10			−0.0700461			−0.0350231	−	0.999387i	$-0.511150\pi$
$769$	−2.44957e10			−0.0700461			−0.0350231	+	0.999387i	$0.511150\pi$
$770$		0			0
$771$		−	1.88591e11i		−	0.533709i
$772$	8.79865e10	−	6.23087e10i	0.247712	−	0.175420i
$773$		−	1.61194e11i		−	0.451472i	−0.974189	−	0.225736i	$-0.927521\pi$
$773$		−	1.61194e11i		−	0.451472i	0.974189	−	0.225736i	$-0.0724787\pi$
$774$	2.26845e11	+	1.17322e11i	0.632070	+	0.326902i
$775$		0			0
$776$	3.19348e11	−	4.46372e10i	0.880678	−	0.123098i
$777$			1.15896e12i			3.17969i
$778$	−1.95643e10	−	1.01185e10i	−0.0534006	−	0.0276184i
$779$			2.50558e11i			0.680392i
$780$		0			0
$781$	−5.13751e11			−1.38086
$782$	8.72252e10	−	1.68651e11i	0.233246	−	0.450986i
$783$	1.43799e11			0.382569
$784$	−1.47342e11	+	4.18620e11i	−0.389999	+	1.10804i
$785$		0			0
$786$	2.78010e11	−	5.37538e11i	0.728401	−	1.40838i
$787$	−4.76190e11			−1.24131			−0.620657	−	0.784083i	$-0.713134\pi$
$787$	−4.76190e11			−1.24131			−0.620657	+	0.784083i	$0.713134\pi$
$788$	4.05187e11	−	2.86938e11i	1.05087	−	0.744189i
$789$	−2.76084e11			−0.712416
$790$		0			0
$791$		−	8.29617e11i		−	2.11920i
$792$	3.61265e11	−	5.04962e10i	0.918174	−	0.128339i
$793$		−	6.05735e10i		−	0.153176i
$794$	−2.23600e11	+	4.32334e11i	−0.562586	+	1.08777i
$795$		0			0
$796$	4.41352e10	−	3.12549e10i	0.109934	−	0.0778512i
$797$		−	1.59422e11i		−	0.395107i	−0.980292	−	0.197553i	$-0.936700\pi$
$797$		−	1.59422e11i		−	0.395107i	0.980292	−	0.197553i	$-0.0632996\pi$
$798$	−1.45994e11	+	2.82282e11i	−0.360018	+	0.696100i
$799$			5.56235e8i			0.00136481i
$800$		0			0
$801$	−2.13762e11			−0.519278
$802$	2.77801e11	+	1.43677e11i	0.671486	+	0.347287i
$803$	3.05603e11			0.735013
$804$	6.30335e10	+	8.90100e10i	0.150851	+	0.213017i
$805$		0			0
$806$	4.07572e11	+	2.10793e11i	0.965748	+	0.499478i
$807$	3.99751e10			0.0942530
$808$	6.60283e9	+	4.72386e10i	0.0154912	+	0.110829i
$809$	4.86253e11			1.13519			0.567594	−	0.823308i	$-0.307874\pi$
$809$	4.86253e11			1.13519			0.567594	+	0.823308i	$0.307874\pi$
$810$		0			0
$811$			3.39760e11i			0.785396i	0.919667	+	0.392698i	$0.128458\pi$
$811$			3.39760e11i			0.785396i	−0.919667	+	0.392698i	$0.871542\pi$
$812$	−6.94548e11	−	9.80776e11i	−1.59764	−	2.25603i
$813$		−	1.16408e12i		−	2.66454i
$814$	6.74315e11	+	3.48751e11i	1.53591	+	0.794360i
$815$		0			0
$816$	2.98372e11	+	1.05019e11i	0.672973	+	0.236867i
$817$			1.45745e11i			0.327120i
$818$	−6.21729e11	−	3.21553e11i	−1.38863	−	0.718191i
$819$		−	4.77358e11i		−	1.06098i
$820$		0			0
$821$	6.74268e11			1.48409			0.742044	−	0.670351i	$-0.233856\pi$
$821$	6.74268e11			1.48409			0.742044	+	0.670351i	$0.233856\pi$
$822$	−1.64822e11	+	3.18685e11i	−0.361016	+	0.698031i
$823$	−3.11660e11			−0.679332			−0.339666	−	0.940546i	$-0.610314\pi$
$823$	−3.11660e11			−0.679332			−0.339666	+	0.940546i	$0.610314\pi$
$824$	3.90426e10	+	2.79322e11i	0.0846896	+	0.605894i
$825$		0			0
$826$	−1.74071e11	+	3.36569e11i	−0.373943	+	0.723026i
$827$	3.10210e11			0.663183			0.331592	−	0.943423i	$-0.392414\pi$
$827$	3.10210e11			0.663183			0.331592	+	0.943423i	$0.392414\pi$
$828$	2.23484e11	+	3.15583e11i	0.475472	+	0.671416i
$829$	3.09076e11			0.654406			0.327203	−	0.944954i	$-0.393894\pi$
$829$	3.09076e11			0.654406			0.327203	+	0.944954i	$0.393894\pi$
$830$		0			0
$831$			1.50082e11i			0.314720i
$832$	−1.11216e11	−	3.90065e11i	−0.232100	−	0.814035i
$833$			2.96670e11i			0.616160i
$834$	2.03501e11	−	3.93473e11i	0.420633	−	0.813301i
$835$		0			0
$836$	1.20307e11	+	1.69887e11i	0.246302	+	0.347804i
$837$			1.28653e11i			0.262132i
$838$	1.41943e11	−	2.74450e11i	0.287832	−	0.556528i
$839$		−	5.22492e11i		−	1.05446i	−0.849722	−	0.527232i	$-0.823230\pi$
$839$		−	5.22492e11i		−	1.05446i	0.849722	−	0.527232i	$-0.176770\pi$
$840$		0			0
$841$	1.25770e12			2.51416
$842$	5.19504e11	+	2.68684e11i	1.03357	+	0.534556i
$843$	3.32163e11			0.657721
$844$	−4.20775e11	+	2.97977e11i	−0.829240	+	0.587236i
$845$		0			0
$846$	−1.00624e9	−	5.20417e8i	−0.00196435	−	0.00101594i
$847$	1.44025e11			0.279836
$848$	−3.40227e11	−	1.19750e11i	−0.657939	−	0.231576i
$849$	1.52278e11			0.293094
$850$		0			0
$851$			8.04790e11i			1.53449i
$852$	7.40450e11	−	5.24359e11i	1.40520	−	0.995108i
$853$			5.25270e11i			0.992171i	0.868274	+	0.496086i	$0.165230\pi$
$853$			5.25270e11i			0.992171i	−0.868274	+	0.496086i	$0.834770\pi$
$854$	−1.26076e11	−	6.52053e10i	−0.237028	−	0.122589i
$855$		0			0
$856$	4.36422e10	+	3.12230e11i	0.0812853	+	0.581539i
$857$			3.18270e11i			0.590028i	0.955493	+	0.295014i	$0.0953243\pi$
$857$			3.18270e11i			0.590028i	−0.955493	+	0.295014i	$0.904676\pi$
$858$	−6.04510e11	−	3.12648e11i	−1.11546	−	0.576907i
$859$		−	8.61467e11i		−	1.58222i	−0.611676	−	0.791108i	$-0.709504\pi$
$859$		−	8.61467e11i		−	1.58222i	0.611676	−	0.791108i	$-0.290496\pi$
$860$		0			0
$861$	−1.91948e12			−3.49277
$862$	2.93031e11	−	5.66579e11i	0.530742	−	1.02620i
$863$	−1.40931e11			−0.254075			−0.127038	−	0.991898i	$-0.540547\pi$
$863$	−1.40931e11			−0.254075			−0.127038	+	0.991898i	$0.540547\pi$
$864$	8.28176e10	−	7.79390e10i	0.148617	−	0.139862i
$865$		0			0
$866$	−2.36357e11	+	4.57000e11i	−0.420239	+	0.812539i
$867$	−5.57071e11			−0.985903
$868$	8.77474e11	−	6.21394e11i	1.54581	−	1.09468i
$869$	8.51945e11			1.49394
$870$		0			0
$871$		−	9.34940e10i		−	0.162447i
$872$	−2.43522e9	−	1.74223e10i	−0.00421185	−	0.0301328i
$873$			4.39008e11i			0.755814i
$874$	−1.01379e11	+	1.96018e11i	−0.173741	+	0.335932i
$875$		0			0
$876$	−4.40454e11	+	3.11913e11i	−0.747970	+	0.529684i
$877$		−	4.00362e11i		−	0.676790i	−0.941004	−	0.338395i	$-0.890116\pi$
$877$		−	4.00362e11i		−	0.676790i	0.941004	−	0.338395i	$-0.109884\pi$
$878$	−1.99937e11	+	3.86582e11i	−0.336447	+	0.650525i
$879$			6.46426e11i			1.08284i
$880$		0			0
$881$	4.94890e11			0.821496			0.410748	−	0.911749i	$-0.365268\pi$
$881$	4.94890e11			0.821496			0.410748	+	0.911749i	$0.365268\pi$
$882$	−5.36680e11	−	2.77567e11i	−0.886831	−	0.458662i
$883$	7.88039e11			1.29630			0.648149	−	0.761513i	$-0.275543\pi$
$883$	7.88039e11			1.29630			0.648149	+	0.761513i	$0.275543\pi$
$884$	−1.56701e11	−	2.21279e11i	−0.256604	−	0.362353i
$885$		0			0
$886$	1.87919e11	+	9.71903e10i	0.304955	+	0.157720i
$887$	2.78785e10			0.0450375			0.0225188	−	0.999746i	$-0.492831\pi$
$887$	2.78785e10			0.0450375			0.0225188	+	0.999746i	$0.492831\pi$
$888$	−1.32782e12	+	1.85597e11i	−2.13544	+	0.298483i
$889$	−1.04218e12			−1.66854
$890$		0			0
$891$		−	7.75120e11i		−	1.22987i
$892$	−1.34169e11	−	1.89461e11i	−0.211930	−	0.299268i
$893$		−	6.46496e8i		−	0.00101662i
$894$	−1.19782e12	−	6.19501e11i	−1.87517	−	0.969822i
$895$		0			0
$896$	−9.31587e11	−	1.88410e11i	−1.44541	−	0.292328i
$897$		−	7.21478e11i		−	1.11443i
$898$	4.02133e11	+	2.07980e11i	0.618392	+	0.319828i
$899$			1.57279e12i			2.40786i
$900$		0			0
$901$	−2.41114e11			−0.365868
$902$	−5.77603e11	+	1.11680e12i	−0.872576	+	1.68714i
$903$	−1.11653e12			−1.67926
$904$	9.50489e11	−	1.32856e11i	1.42322	−	0.198933i
$905$		0			0
$906$	4.15080e11	−	8.02564e11i	0.616054	−	1.19115i
$907$	5.94476e11			0.878426			0.439213	−	0.898383i	$-0.355257\pi$
$907$	5.94476e11			0.878426			0.439213	+	0.898383i	$0.355257\pi$
$908$	−1.37780e10	−	1.94560e10i	−0.0202695	−	0.0286226i
$909$	−6.49390e10			−0.0951152
$910$		0			0
$911$			5.11180e11i			0.742165i	0.928600	+	0.371082i	$0.121013\pi$
$911$			5.11180e11i			0.742165i	−0.928600	+	0.371082i	$0.878987\pi$
$912$	−3.46789e11	−	1.22060e11i	−0.501287	−	0.176439i
$913$			9.94564e10i			0.143136i
$914$	5.80438e11	−	1.12229e12i	0.831708	−	1.60812i
$915$		0			0
$916$	7.66137e10	+	1.08187e11i	0.108824	+	0.153671i
$917$			1.21558e12i			1.71912i
$918$	3.49243e10	−	6.75267e10i	0.0491764	−	0.0950834i
$919$		−	7.89745e11i		−	1.10720i	−0.832784	−	0.553598i	$-0.813254\pi$
$919$		−	7.89745e11i		−	1.10720i	0.832784	−	0.553598i	$-0.186746\pi$
$920$		0			0
$921$	6.38313e11			0.887146
$922$	−3.74783e11	−	1.93835e11i	−0.518628	−	0.268230i
$923$	−7.77751e11			−1.07160
$924$	−1.30147e12	+	9.21650e11i	−1.78544	+	1.26438i
$925$		0			0
$926$	−3.89801e11	−	2.01602e11i	−0.530151	−	0.274190i
$927$	−3.83985e11			−0.519990
$928$	1.01245e12	−	9.52804e11i	1.36515	−	1.28473i
$929$	−1.28241e12			−1.72172			−0.860862	−	0.508839i	$-0.830075\pi$
$929$	−1.28241e12			−1.72172			−0.860862	+	0.508839i	$0.830075\pi$
$930$		0			0
$931$		−	3.44811e11i		−	0.458968i
$932$	−2.51575e11	+	1.78156e11i	−0.333429	+	0.236122i
$933$		−	9.22414e11i		−	1.21730i
$934$	1.17108e12	+	6.05675e11i	1.53886	+	0.795888i
$935$		0			0
$936$	5.46907e11	−	7.64446e10i	0.712542	−	0.0995963i
$937$		−	4.16365e11i		−	0.540152i	−0.962839	−	0.270076i	$-0.912951\pi$
$937$		−	4.16365e11i		−	0.540152i	0.962839	−	0.270076i	$-0.0870488\pi$
$938$	−1.94595e11	−	1.00643e11i	−0.251374	−	0.130009i
$939$			1.35258e12i			1.73980i
$940$		0			0
$941$	−1.33006e12			−1.69634			−0.848171	−	0.529723i	$-0.822296\pi$
$941$	−1.33006e12			−1.69634			−0.848171	+	0.529723i	$0.822296\pi$
$942$	−9.47207e11	+	1.83144e12i	−1.20293	+	2.32589i
$943$	−1.33290e12			−1.68558
$944$	−4.13482e11	−	1.45534e11i	−0.520677	−	0.183264i
$945$		0			0
$946$	−3.35981e11	+	6.49625e11i	−0.419518	+	0.811145i
$947$	−1.36285e11			−0.169453			−0.0847265	−	0.996404i	$-0.527002\pi$
$947$	−1.36285e11			−0.169453			−0.0847265	+	0.996404i	$0.527002\pi$
$948$	−1.22788e12	+	8.69536e11i	−1.52027	+	1.07660i
$949$	4.62642e11			0.570401
$950$		0			0
$951$			1.52524e12i			1.86473i
$952$	−6.29246e11	+	8.79536e10i	−0.766078	+	0.107079i
$953$		−	1.22326e12i		−	1.48302i	−0.670943	−	0.741509i	$-0.734111\pi$
$953$		−	1.22326e12i		−	1.48302i	0.670943	−	0.741509i	$-0.265889\pi$
$954$	2.25588e11	−	4.36179e11i	0.272347	−	0.526588i
$955$		0			0
$956$	−4.43093e11	+	3.13782e11i	−0.530473	+	0.375661i
$957$		−	2.33275e12i		−	2.78113i
$958$	−9.41868e10	+	1.82112e11i	−0.111822	+	0.216210i
$959$		−	7.20671e11i		−	0.852045i
$960$		0			0
$961$	−5.54240e11			−0.649837
$962$	1.02083e12	+	5.27963e11i	1.19193	+	0.616457i
$963$	−4.29222e11			−0.499088
$964$	−1.01411e11	−	1.43203e11i	−0.117430	−	0.165823i
$965$		0			0
$966$	−1.50166e12	−	7.76646e11i	−1.72450	−	0.891897i
$967$	7.99217e10			0.0914027			0.0457014	−	0.998955i	$-0.485448\pi$
$967$	7.99217e10			0.0914027			0.0457014	+	0.998955i	$0.485448\pi$
$968$	2.30643e10	+	1.65009e11i	0.0262687	+	0.187934i
$969$	−2.45765e11			−0.278756
$970$		0			0
$971$		−	3.43166e11i		−	0.386036i	−0.981195	−	0.193018i	$-0.938172\pi$
$971$		−	3.43166e11i		−	0.386036i	0.981195	−	0.193018i	$-0.0618276\pi$
$972$	6.85848e11	+	9.68490e11i	0.768356	+	1.08500i
$973$			8.89796e11i			0.992748i
$974$	3.22874e11	+	1.66988e11i	0.358754	+	0.185545i
$975$		0			0
$976$	5.45156e10	−	1.54886e11i	0.0600789	−	0.170692i
$977$		−	2.96831e11i		−	0.325785i	−0.986644	−	0.162893i	$-0.947918\pi$
$977$		−	2.96831e11i		−	0.325785i	0.986644	−	0.162893i	$-0.0520824\pi$
$978$	1.37669e12	+	7.12011e11i	1.50480	+	0.778272i
$979$		−	6.12158e11i		−	0.666397i
$980$		0			0
$981$	2.39505e10			0.0258605
$982$	6.39771e11	−	1.23701e12i	0.687984	−	1.33023i
$983$	9.12247e11			0.977009			0.488504	−	0.872561i	$-0.337543\pi$
$983$	9.12247e11			0.977009			0.488504	+	0.872561i	$0.337543\pi$
$984$	−3.07387e11	−	2.19914e12i	−0.327873	−	2.34570i
$985$		0			0
$986$	4.26949e11	−	8.25513e11i	0.451719	−	0.873407i
$987$	4.95267e9			0.00521880
$988$	1.82130e11	+	2.57186e11i	0.191140	+	0.269911i
$989$	−7.75323e11			−0.810396
$990$		0			0
$991$			9.63646e11i			0.999132i	0.866276	+	0.499566i	$0.166507\pi$
$991$			9.63646e11i			0.999132i	−0.866276	+	0.499566i	$0.833493\pi$
$992$	8.52449e11	+	9.05808e11i	0.880281	+	0.935383i
$993$			8.50231e11i			0.874460i
$994$	−8.37223e11	+	1.61878e12i	−0.857621	+	1.65822i
$995$		0			0
$996$	−1.01510e11	−	1.43343e11i	−0.103150	−	0.145659i
$997$		−	1.13678e12i		−	1.15052i	−0.817970	−	0.575261i	$-0.804900\pi$
$997$		−	1.13678e12i		−	1.15052i	0.817970	−	0.575261i	$-0.195100\pi$
$998$	−9.92073e10	+	1.91819e11i	−0.100005	+	0.193361i
$999$			3.22232e11i			0.323524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.d.c.99.5		32
4.3	odd	2	inner	100.9.d.c.99.27		32
5.2	odd	4		100.9.b.d.51.11		16
5.3	odd	4		20.9.b.a.11.6	yes	16
5.4	even	2	inner	100.9.d.c.99.28		32
15.8	even	4		180.9.c.a.91.11		16
20.3	even	4		20.9.b.a.11.5	✓	16
20.7	even	4		100.9.b.d.51.12		16
20.19	odd	2	inner	100.9.d.c.99.6		32
40.3	even	4		320.9.b.d.191.3		16
40.13	odd	4		320.9.b.d.191.14		16
60.23	odd	4		180.9.c.a.91.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.b.a.11.5	✓	16	20.3	even	4
20.9.b.a.11.6	yes	16	5.3	odd	4
100.9.b.d.51.11		16	5.2	odd	4
100.9.b.d.51.12		16	20.7	even	4
100.9.d.c.99.5		32	1.1	even	1	trivial
100.9.d.c.99.6		32	20.19	odd	2	inner
100.9.d.c.99.27		32	4.3	odd	2	inner
100.9.d.c.99.28		32	5.4	even	2	inner
180.9.c.a.91.11		16	15.8	even	4
180.9.c.a.91.12		16	60.23	odd	4
320.9.b.d.191.3		16	40.3	even	4
320.9.b.d.191.14		16	40.13	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-14.2118 - 7.35022i) q^{2} -110.171 q^{3} +(147.949 + 208.919i) q^{4} +(1565.72 + 809.778i) q^{6} -3540.70 q^{7} +(-567.011 - 4056.56i) q^{8} +5576.56 q^{9} +15969.8i q^{11} +(-16299.6 - 23016.7i) q^{12} +24176.2i q^{13} +(50319.6 + 26024.9i) q^{14} +(-21758.4 + 61818.6i) q^{16} +43810.0i q^{17} +(-79252.8 - 40988.9i) q^{18} -50919.1i q^{19} +390081. q^{21} +(117382. - 226960. i) q^{22} +270875. q^{23} +(62467.9 + 446914. i) q^{24} +(177701. - 343587. i) q^{26} +108456. q^{27} +(-523841. - 739720. i) q^{28} +1.32588e6 q^{29} +1.18623e6i q^{31} +(763605. - 718623. i) q^{32} -1.75941e6i q^{33} +(322013. - 622618. i) q^{34} +(825045. + 1.16505e6i) q^{36} +2.97108e6i q^{37} +(-374266. + 723650. i) q^{38} -2.66351e6i q^{39} -4.92072e6 q^{41} +(-5.54374e6 - 2.86718e6i) q^{42} -2.86229e6 q^{43} +(-3.33641e6 + 2.36272e6i) q^{44} +(-3.84961e6 - 1.99099e6i) q^{46} +12696.5 q^{47} +(2.39714e6 - 6.81059e6i) q^{48} +6.77174e6 q^{49} -4.82658e6i q^{51} +(-5.05088e6 + 3.57684e6i) q^{52} +5.50364e6i q^{53} +(-1.54135e6 - 797176. i) q^{54} +(2.00761e6 + 1.43631e7i) q^{56} +5.60979e6i q^{57} +(-1.88430e7 - 9.74547e6i) q^{58} +6.68863e6i q^{59} -2.50550e6 q^{61} +(8.71902e6 - 1.68584e7i) q^{62} -1.97449e7 q^{63} +(-1.61342e7 + 4.60023e6i) q^{64} +(-1.29320e7 + 2.50043e7i) q^{66} -3.86718e6 q^{67} +(-9.15275e6 + 6.48163e6i) q^{68} -2.98424e7 q^{69} +3.21701e7i q^{71} +(-3.16197e6 - 2.26217e7i) q^{72} -1.91362e7i q^{73} +(2.18381e7 - 4.22243e7i) q^{74} +(1.06380e7 - 7.53341e6i) q^{76} -5.65444e7i q^{77} +(-1.95774e7 + 3.78532e7i) q^{78} -5.33471e7i q^{79} -4.85365e7 q^{81} +(6.99321e7 + 3.61683e7i) q^{82} +6.22776e6 q^{83} +(5.77119e7 + 8.14954e7i) q^{84} +(4.06782e7 + 2.10385e7i) q^{86} -1.46072e8 q^{87} +(6.47827e7 - 9.05507e6i) q^{88} -3.83322e7 q^{89} -8.56008e7i q^{91} +(4.00755e7 + 5.65909e7i) q^{92} -1.30687e8i q^{93} +(-180440. - 93322.2i) q^{94} +(-8.41269e7 + 7.91711e7i) q^{96} +7.87237e7i q^{97} +(-9.62384e7 - 4.97738e7i) q^{98} +8.90568e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 104 q^{4} + 8736 q^{6} + 77600 q^{9} - 136944 q^{14} - 162848 q^{16} + 828992 q^{21} - 327584 q^{24} + 2074248 q^{26} - 5529792 q^{29} - 7587928 q^{34} - 10937832 q^{36} - 17152896 q^{41} - 33842400 q^{44}+ \cdots - 906779904 q^{96}+O(q^{100}) \) 32 * q + 104 * q^4 + 8736 * q^6 + 77600 * q^9 - 136944 * q^14 - 162848 * q^16 + 828992 * q^21 - 327584 * q^24 + 2074248 * q^26 - 5529792 * q^29 - 7587928 * q^34 - 10937832 * q^36 - 17152896 * q^41 - 33842400 * q^44 - 15948304 * q^46 + 65607200 * q^49 - 17797408 * q^54 + 68269536 * q^56 + 16743424 * q^61 + 95087744 * q^64 + 38716000 * q^66 - 15054528 * q^69 + 276421752 * q^74 + 5140800 * q^76 + 281173344 * q^81 - 139523648 * q^84 - 203449344 * q^86 - 213294912 * q^89 - 110529264 * q^94 - 906779904 * q^96

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