LMFDB - Embedded newform 100.9.d.c.99.3

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			99.3
Character	$\chi$	$=$	100.99
Dual form			100.9.d.c.99.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-15.3124 - 4.64016i) q^{2} +75.7492 q^{3} +(212.938 + 142.104i) q^{4} +(-1159.90 - 351.488i) q^{6} -210.345 q^{7} +(-2601.20 - 3164.01i) q^{8} -823.060 q^{9} -141.724i q^{11} +(16129.9 + 10764.2i) q^{12} -17655.5i q^{13} +(3220.88 + 976.035i) q^{14} +(25149.0 + 60518.5i) q^{16} +102231. i q^{17} +(12603.0 + 3819.13i) q^{18} +107088. i q^{19} -15933.5 q^{21} +(-657.620 + 2170.13i) q^{22} +455526. q^{23} +(-197039. - 239671. i) q^{24} +(-81924.3 + 270348. i) q^{26} -559337. q^{27} +(-44790.4 - 29890.8i) q^{28} -865184. q^{29} -429788. i q^{31} +(-104276. - 1.04338e6i) q^{32} -10735.4i q^{33} +(474366. - 1.56539e6i) q^{34} +(-175261. - 116960. i) q^{36} +2.51809e6i q^{37} +(496908. - 1.63978e6i) q^{38} -1.33739e6i q^{39} -2.98042e6 q^{41} +(243979. + 73933.8i) q^{42} +2.22228e6 q^{43} +(20139.5 - 30178.3i) q^{44} +(-6.97518e6 - 2.11371e6i) q^{46} +7.63886e6 q^{47} +(1.90502e6 + 4.58423e6i) q^{48} -5.72056e6 q^{49} +7.74388e6i q^{51} +(2.50891e6 - 3.75952e6i) q^{52} +1.55615e7i q^{53} +(8.56477e6 + 2.59541e6i) q^{54} +(547149. + 665534. i) q^{56} +8.11187e6i q^{57} +(1.32480e7 + 4.01459e6i) q^{58} +6.38433e6i q^{59} +2.03289e6 q^{61} +(-1.99429e6 + 6.58108e6i) q^{62} +173127. q^{63} +(-3.24473e6 + 1.64605e7i) q^{64} +(-49814.2 + 164385. i) q^{66} -2.03503e7 q^{67} +(-1.45274e7 + 2.17688e7i) q^{68} +3.45057e7 q^{69} +4.44463e7i q^{71} +(2.14094e6 + 2.60417e6i) q^{72} +1.79865e7i q^{73} +(1.16843e7 - 3.85579e7i) q^{74} +(-1.52177e7 + 2.28032e7i) q^{76} +29810.9i q^{77} +(-6.20570e6 + 2.04786e7i) q^{78} +2.03988e7i q^{79} -3.69692e7 q^{81} +(4.56374e7 + 1.38296e7i) q^{82} +5.09090e7 q^{83} +(-3.39284e6 - 2.26421e6i) q^{84} +(-3.40284e7 - 1.03117e7i) q^{86} -6.55370e7 q^{87} +(-448415. + 368651. i) q^{88} +2.68313e7 q^{89} +3.71375e6i q^{91} +(9.69986e7 + 6.47319e7i) q^{92} -3.25561e7i q^{93} +(-1.16969e8 - 3.54456e7i) q^{94} +(-7.89880e6 - 7.90351e7i) q^{96} -3.38260e7i q^{97} +(8.75953e7 + 2.65443e7i) q^{98} +116647. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−15.3124	−	4.64016i	−0.957024	−	0.290010i
$2$	−15.3124	−	4.64016i	−0.957024	−	0.290010i
$3$	75.7492			0.935175			0.467588	−	0.883947i	$-0.345123\pi$
$3$	75.7492			0.935175			0.467588	+	0.883947i	$0.345123\pi$
$4$	212.938	+	142.104i	0.831788	+	0.555093i
$5$		0			0
$5$		0			0
$6$	−1159.90	−	351.488i	−0.894985	−	0.271210i
$7$	−210.345			−0.0876072			−0.0438036	−	0.999040i	$-0.513948\pi$
$7$	−210.345			−0.0876072			−0.0438036	+	0.999040i	$0.513948\pi$
$8$	−2601.20	−	3164.01i	−0.635059	−	0.772464i
$9$	−823.060			−0.125447
$10$		0			0
$11$		−	141.724i		−	0.00967991i	−0.999988	−	0.00483996i	$-0.998459\pi$
$11$		−	141.724i		−	0.00967991i	0.999988	−	0.00483996i	$-0.00154061\pi$
$12$	16129.9	+	10764.2i	0.777868	+	0.519109i
$13$		−	17655.5i		−	0.618168i	−0.951035	−	0.309084i	$-0.899978\pi$
$13$		−	17655.5i		−	0.618168i	0.951035	−	0.309084i	$-0.100022\pi$
$14$	3220.88	+	976.035i	0.0838422	+	0.0254070i
$15$		0			0
$16$	25149.0	+	60518.5i	0.383744	+	0.923440i
$17$			102231.i			1.22401i	0.790854	+	0.612005i	$0.209637\pi$
$17$			102231.i			1.22401i	−0.790854	+	0.612005i	$0.790363\pi$
$18$	12603.0	+	3819.13i	0.120056	+	0.0363810i
$19$			107088.i			0.821728i	0.911697	+	0.410864i	$0.134773\pi$
$19$			107088.i			0.821728i	−0.911697	+	0.410864i	$0.865227\pi$
$20$		0			0
$21$	−15933.5			−0.0819281
$22$	−657.620	+	2170.13i	−0.00280727	+	0.00926391i
$23$	455526.			1.62780			0.813901	−	0.581004i	$-0.197340\pi$
$23$	455526.			1.62780			0.813901	+	0.581004i	$0.197340\pi$
$24$	−197039.	−	239671.i	−0.593891	−	0.722389i
$25$		0			0
$26$	−81924.3	+	270348.i	−0.179275	+	0.591601i
$27$	−559337.			−1.05249
$28$	−44790.4	−	29890.8i	−0.0728707	−	0.0486302i
$29$	−865184.			−1.22325			−0.611627	−	0.791146i	$-0.709485\pi$
$29$	−865184.			−1.22325			−0.611627	+	0.791146i	$0.709485\pi$
$30$		0			0
$31$		−	429788.i		−	0.465380i	−0.972551	−	0.232690i	$-0.925247\pi$
$31$		−	429788.i		−	0.465380i	0.972551	−	0.232690i	$-0.0747528\pi$
$32$	−104276.	−	1.04338e6i	−0.0994450	−	0.995043i
$33$		−	10735.4i		−	0.00905241i
$34$	474366.	−	1.56539e6i	0.354975	−	1.17141i
$35$		0			0
$36$	−175261.	−	116960.i	−0.104346	−	0.0696349i
$37$			2.51809e6i			1.34358i	0.740741	+	0.671791i	$0.234475\pi$
$37$			2.51809e6i			1.34358i	−0.740741	+	0.671791i	$0.765525\pi$
$38$	496908.	−	1.63978e6i	0.238310	−	0.786414i
$39$		−	1.33739e6i		−	0.578095i
$40$		0			0
$41$	−2.98042e6			−1.05473			−0.527366	−	0.849638i	$-0.676820\pi$
$41$	−2.98042e6			−1.05473			−0.527366	+	0.849638i	$0.676820\pi$
$42$	243979.	+	73933.8i	0.0784071	+	0.0237600i
$43$	2.22228e6			0.650018			0.325009	−	0.945711i	$-0.394633\pi$
$43$	2.22228e6			0.650018			0.325009	+	0.945711i	$0.394633\pi$
$44$	20139.5	−	30178.3i	0.00537325	−	0.00805164i
$45$		0			0
$46$	−6.97518e6	−	2.11371e6i	−1.55784	−	0.472079i
$47$	7.63886e6			1.56544			0.782722	−	0.622372i	$-0.213831\pi$
$47$	7.63886e6			1.56544			0.782722	+	0.622372i	$0.213831\pi$
$48$	1.90502e6	+	4.58423e6i	0.358868	+	0.863578i
$49$	−5.72056e6			−0.992325
$50$		0			0
$51$			7.74388e6i			1.14466i
$52$	2.50891e6	−	3.75952e6i	0.343141	−	0.514185i
$53$			1.55615e7i			1.97219i	0.166186	+	0.986094i	$0.446855\pi$
$53$			1.55615e7i			1.97219i	−0.166186	+	0.986094i	$0.553145\pi$
$54$	8.56477e6	+	2.59541e6i	1.00726	+	0.305233i
$55$		0			0
$56$	547149.	+	665534.i	0.0556357	+	0.0676734i
$57$			8.11187e6i			0.768460i
$58$	1.32480e7	+	4.01459e6i	1.17068	+	0.354756i
$59$			6.38433e6i			0.526874i	0.964677	+	0.263437i	$0.0848562\pi$
$59$			6.38433e6i			0.526874i	−0.964677	+	0.263437i	$0.915144\pi$
$60$		0			0
$61$	2.03289e6			0.146823			0.0734116	−	0.997302i	$-0.476611\pi$
$61$	2.03289e6			0.146823			0.0734116	+	0.997302i	$0.476611\pi$
$62$	−1.99429e6	+	6.58108e6i	−0.134965	+	0.445380i
$63$	173127.			0.0109901
$64$	−3.24473e6	+	1.64605e7i	−0.193401	+	0.981120i
$65$		0			0
$66$	−49814.2	+	164385.i	−0.00262529	+	0.00866337i
$67$	−2.03503e7			−1.00988			−0.504941	−	0.863154i	$-0.668486\pi$
$67$	−2.03503e7			−1.00988			−0.504941	+	0.863154i	$0.668486\pi$
$68$	−1.45274e7	+	2.17688e7i	−0.679439	+	1.01812i
$69$	3.45057e7			1.52228
$70$		0			0
$71$			4.44463e7i			1.74905i	0.484979	+	0.874526i	$0.338827\pi$
$71$			4.44463e7i			1.74905i	−0.484979	+	0.874526i	$0.661173\pi$
$72$	2.14094e6	+	2.60417e6i	0.0796664	+	0.0969036i
$73$			1.79865e7i			0.633366i	0.948531	+	0.316683i	$0.102569\pi$
$73$			1.79865e7i			0.633366i	−0.948531	+	0.316683i	$0.897431\pi$
$74$	1.16843e7	−	3.85579e7i	0.389652	−	1.28584i
$75$		0			0
$76$	−1.52177e7	+	2.28032e7i	−0.456136	+	0.683504i
$77$			29810.9i			0.000848031i
$78$	−6.20570e6	+	2.04786e7i	−0.167653	+	0.553251i
$79$			2.03988e7i			0.523716i	0.965106	+	0.261858i	$0.0843352\pi$
$79$			2.03988e7i			0.523716i	−0.965106	+	0.261858i	$0.915665\pi$
$80$		0			0
$81$	−3.69692e7			−0.858816
$82$	4.56374e7	+	1.38296e7i	1.00940	+	0.305883i
$83$	5.09090e7			1.07271			0.536355	−	0.843992i	$-0.319801\pi$
$83$	5.09090e7			1.07271			0.536355	+	0.843992i	$0.319801\pi$
$84$	−3.39284e6	−	2.26421e6i	−0.0681469	−	0.0454777i
$85$		0			0
$86$	−3.40284e7	−	1.03117e7i	−0.622082	−	0.188512i
$87$	−6.55370e7			−1.14396
$88$	−448415.	+	368651.i	−0.00747738	+	0.00614731i
$89$	2.68313e7			0.427644			0.213822	−	0.976873i	$-0.431409\pi$
$89$	2.68313e7			0.427644			0.213822	+	0.976873i	$0.431409\pi$
$90$		0			0
$91$			3.71375e6i			0.0541560i
$92$	9.69986e7	+	6.47319e7i	1.35399	+	0.903581i
$93$		−	3.25561e7i		−	0.435212i
$94$	−1.16969e8	−	3.54456e7i	−1.49817	−	0.453994i
$95$		0			0
$96$	−7.89880e6	−	7.90351e7i	−0.0929985	−	0.930540i
$97$		−	3.38260e7i		−	0.382089i	−0.981581	−	0.191044i	$-0.938813\pi$
$97$		−	3.38260e7i		−	0.382089i	0.981581	−	0.191044i	$-0.0611874\pi$
$98$	8.75953e7	+	2.65443e7i	0.949678	+	0.287784i
$99$			116647.i			0.00121432i
$100$		0			0
$101$	5.46440e7			0.525118			0.262559	−	0.964916i	$-0.415434\pi$
$101$	5.46440e7			0.525118			0.262559	+	0.964916i	$0.415434\pi$
$102$	3.59329e7	−	1.18577e8i	0.331964	−	1.09547i
$103$	5.49350e6			0.0488090			0.0244045	−	0.999702i	$-0.492231\pi$
$103$	5.49350e6			0.0488090			0.0244045	+	0.999702i	$0.492231\pi$
$104$	−5.58622e7	+	4.59255e7i	−0.477513	+	0.392573i
$105$		0			0
$106$	7.22080e7	−	2.38284e8i	0.571955	−	1.88743i
$107$	−4.58185e7			−0.349547			−0.174773	−	0.984609i	$-0.555919\pi$
$107$	−4.58185e7			−0.349547			−0.174773	+	0.984609i	$0.555919\pi$
$108$	−1.19104e8	−	7.94838e7i	−0.875449	−	0.584230i
$109$	−1.34989e8			−0.956295			−0.478147	−	0.878280i	$-0.658692\pi$
$109$	−1.34989e8			−0.956295			−0.478147	+	0.878280i	$0.658692\pi$
$110$		0			0
$111$			1.90743e8i			1.25648i
$112$	−5.28997e6	−	1.27298e7i	−0.0336187	−	0.0809000i
$113$		−	1.52579e8i		−	0.935796i	−0.883783	−	0.467898i	$-0.845011\pi$
$113$		−	1.52579e8i		−	0.935796i	0.883783	−	0.467898i	$-0.154989\pi$
$114$	3.76404e7	−	1.24212e8i	0.222861	−	0.735434i
$115$		0			0
$116$	−1.84230e8	−	1.22946e8i	−1.01749	−	0.679020i
$117$			1.45315e7i			0.0775475i
$118$	2.96243e7	−	9.77592e7i	0.152799	−	0.504231i
$119$		−	2.15037e7i		−	0.107232i
$120$		0			0
$121$	2.14339e8			0.999906
$122$	−3.11284e7	−	9.43293e6i	−0.140513	−	0.0425802i
$123$	−2.25765e8			−0.986360
$124$	6.10746e7	−	9.15182e7i	0.258329	−	0.387098i
$125$		0			0
$126$	−2.65098e6	−	803335.i	−0.0105178	−	0.00318724i
$127$	−3.88910e8			−1.49498			−0.747488	−	0.664275i	$-0.768740\pi$
$127$	−3.88910e8			−1.49498			−0.747488	+	0.664275i	$0.768740\pi$
$128$	1.26064e8	−	2.36993e8i	0.469624	−	0.882866i
$129$	1.68336e8			0.607880
$130$		0			0
$131$			5.32310e8i			1.80750i	0.428056	+	0.903752i	$0.359199\pi$
$131$			5.32310e8i			1.80750i	−0.428056	+	0.903752i	$0.640801\pi$
$132$	1.52555e6	−	2.28598e6i	0.00502493	−	0.00752969i
$133$		−	2.25255e7i		−	0.0719894i
$134$	3.11611e8	+	9.44285e7i	0.966482	+	0.292876i
$135$		0			0
$136$	3.23459e8	−	2.65922e8i	0.945504	−	0.777318i
$137$			5.11356e8i			1.45158i	0.687916	+	0.725790i	$0.258526\pi$
$137$			5.11356e8i			1.45158i	−0.687916	+	0.725790i	$0.741474\pi$
$138$	−5.28364e8	−	1.60112e8i	−1.45686	−	0.441476i
$139$			4.03705e8i			1.08145i	0.841201	+	0.540723i	$0.181849\pi$
$139$			4.03705e8i			1.08145i	−0.841201	+	0.540723i	$0.818151\pi$
$140$		0			0
$141$	5.78638e8			1.46396
$142$	2.06238e8	−	6.80579e8i	0.507243	−	1.67388i
$143$	−2.50220e6			−0.00598381
$144$	−2.06992e7	−	4.98104e7i	−0.0481396	−	0.115843i
$145$		0			0
$146$	8.34602e7	−	2.75416e8i	0.183683	−	0.606146i
$147$	−4.33327e8			−0.927998
$148$	−3.57830e8	+	5.36196e8i	−0.745813	+	1.11758i
$149$	−2.52732e8			−0.512761			−0.256381	−	0.966576i	$-0.582530\pi$
$149$	−2.52732e8			−0.512761			−0.256381	+	0.966576i	$0.582530\pi$
$150$		0			0
$151$		−	1.14787e8i		−	0.220792i	−0.993888	−	0.110396i	$-0.964788\pi$
$151$		−	1.14787e8i		−	0.220792i	0.993888	−	0.110396i	$-0.0352119\pi$
$152$	3.38829e8	−	2.78559e8i	0.634756	−	0.521846i
$153$		−	8.41419e7i		−	0.153549i
$154$	138327.	−	456475.i	0.000245937	−	0.000811585i
$155$		0			0
$156$	1.90048e8	−	2.84781e8i	0.320897	−	0.480853i
$157$		−	3.48763e8i		−	0.574026i	−0.957927	−	0.287013i	$-0.907338\pi$
$157$		−	3.48763e8i		−	0.574026i	0.957927	−	0.287013i	$-0.0926622\pi$
$158$	9.46536e7	−	3.12354e8i	0.151883	−	0.501209i
$159$			1.17877e9i			1.84434i
$160$		0			0
$161$	−9.58175e7			−0.142607
$162$	5.66086e8	+	1.71543e8i	0.821907	+	0.249065i
$163$	2.96216e8			0.419622			0.209811	−	0.977742i	$-0.432715\pi$
$163$	2.96216e8			0.419622			0.209811	+	0.977742i	$0.432715\pi$
$164$	−6.34645e8	−	4.23529e8i	−0.877314	−	0.585475i
$165$		0			0
$166$	−7.79538e8	−	2.36226e8i	−1.02661	−	0.311097i
$167$	−1.56004e8			−0.200572			−0.100286	−	0.994959i	$-0.531976\pi$
$167$	−1.56004e8			−0.200572			−0.100286	+	0.994959i	$0.531976\pi$
$168$	4.14461e7	+	5.04137e7i	0.0520292	+	0.0632865i
$169$	5.04014e8			0.617868
$170$		0			0
$171$		−	8.81402e7i		−	0.103084i
$172$	4.73208e8	+	3.15795e8i	0.540677	+	0.360820i
$173$			4.66034e8i			0.520276i	0.965572	+	0.260138i	$0.0837680\pi$
$173$			4.66034e8i			0.520276i	−0.965572	+	0.260138i	$0.916232\pi$
$174$	1.00353e9	+	3.04102e8i	1.09479	+	0.331759i
$175$		0			0
$176$	8.57691e6	−	3.56421e6i	0.00893882	−	0.00371461i
$177$			4.83608e8i			0.492720i
$178$	−4.10851e8	−	1.24502e8i	−0.409265	−	0.124021i
$179$		−	1.44673e9i		−	1.40921i	−0.709600	−	0.704605i	$-0.751124\pi$
$179$		−	1.44673e9i		−	1.40921i	0.709600	−	0.704605i	$-0.248876\pi$
$180$		0			0
$181$	−5.80491e8			−0.540855			−0.270428	−	0.962740i	$-0.587165\pi$
$181$	−5.80491e8			−0.540855			−0.270428	+	0.962740i	$0.587165\pi$
$182$	1.72324e7	−	5.68663e7i	0.0157058	−	0.0518286i
$183$	1.53990e8			0.137305
$184$	−1.18491e9	−	1.44129e9i	−1.03375	−	1.25742i
$185$		0			0
$186$	−1.51066e8	+	4.98512e8i	−0.126216	+	0.416508i
$187$	1.44885e7			0.0118483
$188$	1.62660e9	+	1.08551e9i	1.30212	+	0.868966i
$189$	1.17654e8			0.0922058
$190$		0			0
$191$			2.29528e9i			1.72465i	0.506351	+	0.862327i	$0.330994\pi$
$191$			2.29528e9i			1.72465i	−0.506351	+	0.862327i	$0.669006\pi$
$192$	−2.45786e8	+	1.24687e9i	−0.180864	+	0.917519i
$193$		−	1.42541e9i		−	1.02733i	−0.857991	−	0.513665i	$-0.828287\pi$
$193$		−	1.42541e9i		−	1.02733i	0.857991	−	0.513665i	$-0.171713\pi$
$194$	−1.56958e8	+	5.17957e8i	−0.110810	+	0.365668i
$195$		0			0
$196$	−1.21812e9	−	8.12913e8i	−0.825404	−	0.550833i
$197$		−	1.42075e9i		−	0.943305i	−0.881785	−	0.471652i	$-0.843658\pi$
$197$		−	1.42075e9i		−	0.943305i	0.881785	−	0.471652i	$-0.156342\pi$
$198$	541261.	−	1.78614e6i	0.000352165	−	0.00116213i
$199$		−	1.90032e9i		−	1.21176i	−0.795557	−	0.605878i	$-0.792822\pi$
$199$		−	1.90032e9i		−	1.21176i	0.795557	−	0.605878i	$-0.207178\pi$
$200$		0			0
$201$	−1.54152e9			−0.944417
$202$	−8.36729e8	−	2.53557e8i	−0.502550	−	0.152289i
$203$	1.81987e8			0.107166
$204$	−1.10044e9	+	1.64897e9i	−0.635395	+	0.952118i
$205$		0			0
$206$	−8.41185e7	−	2.54907e7i	−0.0467114	−	0.0141551i
$207$	−3.74925e8			−0.204203
$208$	1.06848e9	−	4.44019e8i	0.570841	−	0.237218i
$209$	1.51770e7			0.00795426
$210$		0			0
$211$		−	1.67947e9i		−	0.847311i	−0.905823	−	0.423655i	$-0.860747\pi$
$211$		−	1.67947e9i		−	0.847311i	0.905823	−	0.423655i	$-0.139253\pi$
$212$	−2.21135e9	+	3.31364e9i	−1.09475	+	1.64044i
$213$			3.36677e9i			1.63567i
$214$	7.01590e8	+	2.12605e8i	0.334525	+	0.101372i
$215$		0			0
$216$	1.45495e9	+	1.76975e9i	0.668393	+	0.813011i
$217$			9.04039e7i			0.0407707i
$218$	2.06700e9	+	6.26370e8i	0.915197	+	0.277335i
$219$			1.36246e9i			0.592308i
$220$		0			0
$221$	1.80493e9			0.756644
$222$	8.85079e8	−	2.92073e9i	0.364393	−	1.20249i
$223$	1.10738e9			0.447795			0.223897	−	0.974613i	$-0.428122\pi$
$223$	1.10738e9			0.447795			0.223897	+	0.974613i	$0.428122\pi$
$224$	2.19339e7	+	2.19469e8i	0.00871210	+	0.0871730i
$225$		0			0
$226$	−7.07991e8	+	2.33635e9i	−0.271390	+	0.895579i
$227$	4.15603e9			1.56522			0.782610	−	0.622512i	$-0.213888\pi$
$227$	4.15603e9			1.56522			0.782610	+	0.622512i	$0.213888\pi$
$228$	−1.15273e9	+	1.72732e9i	−0.426567	+	0.639196i
$229$	−1.34641e9			−0.489594			−0.244797	−	0.969574i	$-0.578721\pi$
$229$	−1.34641e9			−0.489594			−0.244797	+	0.969574i	$0.578721\pi$
$230$		0			0
$231$			2.25815e6i			0.000793057i
$232$	2.25052e9	+	2.73745e9i	0.776838	+	0.944920i
$233$			2.57794e8i			0.0874681i	0.999043	+	0.0437341i	$0.0139254\pi$
$233$			2.57794e8i			0.0874681i	−0.999043	+	0.0437341i	$0.986075\pi$
$234$	6.74286e7	−	2.22512e8i	0.0224896	−	0.0742148i
$235$		0			0
$236$	−9.07237e8	+	1.35946e9i	−0.292464	+	0.438248i
$237$			1.54519e9i			0.489766i
$238$	−9.97806e7	+	3.29273e8i	−0.0310984	+	0.102624i
$239$			3.82549e8i			0.117245i	0.998280	+	0.0586227i	$0.0186709\pi$
$239$			3.82549e8i			0.117245i	−0.998280	+	0.0586227i	$0.981329\pi$
$240$		0			0
$241$	−5.49743e9			−1.62964			−0.814820	−	0.579714i	$-0.803164\pi$
$241$	−5.49743e9			−1.62964			−0.814820	+	0.579714i	$0.803164\pi$
$242$	−3.28204e9	−	9.94566e8i	−0.956934	−	0.289983i
$243$	8.69420e8			0.249347
$244$	4.32879e8	+	2.88881e8i	0.122126	+	0.0815005i
$245$		0			0
$246$	3.45699e9	+	1.04758e9i	0.943970	+	0.286054i
$247$	1.89070e9			0.507966
$248$	−1.35986e9	+	1.11797e9i	−0.359490	+	0.295544i
$249$	3.85632e9			1.00317
$250$		0			0
$251$		−	7.22250e9i		−	1.81967i	−0.414971	−	0.909835i	$-0.636208\pi$
$251$		−	7.22250e9i		−	1.81967i	0.414971	−	0.909835i	$-0.363792\pi$
$252$	3.68652e7	+	2.46019e7i	0.00914143	+	0.00610052i
$253$		−	6.45587e7i		−	0.0157570i
$254$	5.95514e9	+	1.80460e9i	1.43073	+	0.433558i
$255$		0			0
$256$	−3.03002e9	+	3.04396e9i	−0.705482	+	0.708728i
$257$			1.49317e9i			0.342277i	0.985247	+	0.171138i	$0.0547445\pi$
$257$			1.49317e9i			0.342277i	−0.985247	+	0.171138i	$0.945256\pi$
$258$	−2.57762e9	−	7.81106e8i	−0.581756	−	0.176291i
$259$		−	5.29667e8i		−	0.117707i
$260$		0			0
$261$	7.12099e8			0.153454
$262$	2.47000e9	−	8.15093e9i	0.524195	−	1.72982i
$263$	−4.58536e9			−0.958409			−0.479205	−	0.877703i	$-0.659075\pi$
$263$	−4.58536e9			−0.958409			−0.479205	+	0.877703i	$0.659075\pi$
$264$	−3.39671e7	+	2.79250e7i	−0.00699266	+	0.00574881i
$265$		0			0
$266$	−1.04522e8	+	3.44919e8i	−0.0208776	+	0.0688955i
$267$	2.03245e9			0.399922
$268$	−4.33334e9	−	2.89185e9i	−0.840009	−	0.560579i
$269$	−5.70969e9			−1.09044			−0.545222	−	0.838292i	$-0.683555\pi$
$269$	−5.70969e9			−1.09044			−0.545222	+	0.838292i	$0.683555\pi$
$270$		0			0
$271$		−	8.61657e9i		−	1.59756i	−0.601623	−	0.798780i	$-0.705479\pi$
$271$		−	8.61657e9i		−	1.59756i	0.601623	−	0.798780i	$-0.294521\pi$
$272$	−6.18684e9	+	2.57100e9i	−1.13030	+	0.469706i
$273$			2.81313e8i			0.0506453i
$274$	2.37277e9	−	7.83008e9i	0.420973	−	1.38920i
$275$		0			0
$276$	7.34757e9	+	4.90339e9i	1.26621	+	0.845007i
$277$		−	5.74438e9i		−	0.975717i	−0.872923	−	0.487858i	$-0.837778\pi$
$277$		−	5.74438e9i		−	0.975717i	0.872923	−	0.487858i	$-0.162222\pi$
$278$	1.87326e9	−	6.18168e9i	0.313630	−	1.03497i
$279$			3.53742e8i			0.0583807i
$280$		0			0
$281$	7.75176e9			1.24330			0.621648	−	0.783296i	$-0.286463\pi$
$281$	7.75176e9			1.24330			0.621648	+	0.783296i	$0.286463\pi$
$282$	−8.86032e9	−	2.68497e9i	−1.40105	−	0.424564i
$283$	−3.56052e9			−0.555096			−0.277548	−	0.960712i	$-0.589522\pi$
$283$	−3.56052e9			−0.555096			−0.277548	+	0.960712i	$0.589522\pi$
$284$	−6.31599e9	+	9.46431e9i	−0.970886	+	1.45484i
$285$		0			0
$286$	3.83146e7	+	1.16106e7i	0.00572665	+	0.00173537i
$287$	6.26917e8			0.0924022
$288$	8.58251e7	+	8.58763e8i	0.0124751	+	0.124826i
$289$	−3.47533e9			−0.498201
$290$		0			0
$291$		−	2.56229e9i		−	0.357320i
$292$	−2.55595e9	+	3.83000e9i	−0.351577	+	0.526826i
$293$		−	5.61859e9i		−	0.762355i	−0.924502	−	0.381177i	$-0.875519\pi$
$293$		−	5.61859e9i		−	0.762355i	0.924502	−	0.381177i	$-0.124481\pi$
$294$	6.63527e9	+	2.01071e9i	0.888116	+	0.269129i
$295$		0			0
$296$	7.96726e9	−	6.55005e9i	1.03787	−	0.853253i
$297$			7.92712e7i			0.0101880i
$298$	3.86993e9	+	1.17272e9i	0.490725	+	0.148706i
$299$		−	8.04253e9i		−	1.00625i
$300$		0			0
$301$	−4.67446e8			−0.0569463
$302$	−5.32628e8	+	1.75766e9i	−0.0640319	+	0.211303i
$303$	4.13924e9			0.491077
$304$	−6.48084e9	+	2.69317e9i	−0.758817	+	0.315333i
$305$		0			0
$306$	−3.90432e8	+	1.28841e9i	−0.0445307	+	0.146950i
$307$	1.17341e10			1.32099			0.660493	−	0.750832i	$-0.270347\pi$
$307$	1.17341e10			1.32099			0.660493	+	0.750832i	$0.270347\pi$
$308$	−4.23623e6	+	6.34786e6i	−0.000470736	+	0.000705382i
$309$	4.16128e8			0.0456450
$310$		0			0
$311$			8.30766e9i			0.888050i	0.896014	+	0.444025i	$0.146450\pi$
$311$			8.30766e9i			0.888050i	−0.896014	+	0.444025i	$0.853550\pi$
$312$	−4.23152e9	+	3.47882e9i	−0.446558	+	0.367124i
$313$		−	8.58561e9i		−	0.894528i	−0.894402	−	0.447264i	$-0.852399\pi$
$313$		−	8.58561e9i		−	0.894528i	0.894402	−	0.447264i	$-0.147601\pi$
$314$	−1.61831e9	+	5.34038e9i	−0.166473	+	0.549356i
$315$		0			0
$316$	−2.89874e9	+	4.34367e9i	−0.290711	+	0.435621i
$317$			2.51112e9i			0.248674i	0.992240	+	0.124337i	$0.0396803\pi$
$317$			2.51112e9i			0.248674i	−0.992240	+	0.124337i	$0.960320\pi$
$318$	5.46969e9	−	1.80498e10i	0.534878	−	1.76508i
$319$			1.22617e8i			0.0118410i
$320$		0			0
$321$	−3.47071e9			−0.326888
$322$	1.46719e9	+	4.44609e8i	0.136478	+	0.0413575i
$323$	−1.09477e10			−1.00580
$324$	−7.87214e9	−	5.25346e9i	−0.714353	−	0.476722i
$325$		0			0
$326$	−4.53577e9	−	1.37449e9i	−0.401588	−	0.121694i
$327$	−1.02253e10			−0.894303
$328$	7.75267e9	+	9.43009e9i	0.669817	+	0.814743i
$329$	−1.60680e9			−0.137144
$330$		0			0
$331$		−	1.38910e10i		−	1.15724i	−0.815599	−	0.578618i	$-0.803592\pi$
$331$		−	1.38910e10i		−	1.15724i	0.815599	−	0.578618i	$-0.196408\pi$
$332$	1.08405e10	+	7.23437e9i	0.892268	+	0.595454i
$333$		−	2.07254e9i		−	0.168549i
$334$	2.38879e9	+	7.23883e8i	0.191952	+	0.0581678i
$335$		0			0
$336$	−4.00711e8	−	9.64270e8i	−0.0314394	−	0.0756557i
$337$		−	1.74804e10i		−	1.35529i	−0.735391	−	0.677643i	$-0.763001\pi$
$337$		−	1.74804e10i		−	1.35529i	0.735391	−	0.677643i	$-0.236999\pi$
$338$	−7.71766e9	−	2.33871e9i	−0.591315	−	0.179188i
$339$		−	1.15577e10i		−	0.875133i
$340$		0			0
$341$	−6.09112e7			−0.00450484
$342$	−4.08985e8	+	1.34964e9i	−0.0298953	+	0.0986535i
$343$	2.41589e9			0.174542
$344$	−5.78060e9	−	7.03133e9i	−0.412799	−	0.502115i
$345$		0			0
$346$	2.16247e9	−	7.13609e9i	0.150885	−	0.497916i
$347$	−4.08751e8			−0.0281930			−0.0140965	−	0.999901i	$-0.504487\pi$
$347$	−4.08751e8			−0.0281930			−0.0140965	+	0.999901i	$0.504487\pi$
$348$	−1.39553e10	−	9.31306e9i	−0.951530	−	0.635002i
$349$	1.52539e10			1.02820			0.514102	−	0.857729i	$-0.328125\pi$
$349$	1.52539e10			1.02820			0.514102	+	0.857729i	$0.328125\pi$
$350$		0			0
$351$			9.87536e9i			0.650616i
$352$	−1.47871e8	+	1.47783e7i	−0.00963193	+	0.000962619i
$353$		−	2.36311e9i		−	0.152190i	−0.997101	−	0.0760950i	$-0.975755\pi$
$353$		−	2.36311e9i		−	0.152190i	0.997101	−	0.0760950i	$-0.0242452\pi$
$354$	2.24402e9	−	7.40518e9i	0.142894	−	0.471544i
$355$		0			0
$356$	5.71340e9	+	3.81283e9i	0.355709	+	0.237382i
$357$		−	1.62889e9i		−	0.100281i
$358$	−6.71306e9	+	2.21529e10i	−0.408685	+	1.34865i
$359$			1.95665e10i			1.17797i	0.808143	+	0.588987i	$0.200473\pi$
$359$			1.95665e10i			1.17797i	−0.808143	+	0.588987i	$0.799527\pi$
$360$		0			0
$361$	5.51562e9			0.324762
$362$	8.88870e9	+	2.69357e9i	0.517611	+	0.156854i
$363$	1.62360e10			0.935088
$364$	−5.27737e8	+	7.90797e8i	−0.0300616	+	0.0450463i
$365$		0			0
$366$	−2.35795e9	−	7.14537e8i	−0.131404	−	0.0398199i
$367$	−2.40655e10			−1.32657			−0.663285	−	0.748367i	$-0.730838\pi$
$367$	−2.40655e10			−1.32657			−0.663285	+	0.748367i	$0.730838\pi$
$368$	1.14560e10	+	2.75677e10i	0.624659	+	1.50318i
$369$	2.45307e9			0.132313
$370$		0			0
$371$		−	3.27329e9i		−	0.172778i
$372$	4.62635e9	−	6.93243e9i	0.241583	−	0.362004i
$373$			1.70488e10i			0.880760i	0.897811	+	0.440380i	$0.145156\pi$
$373$			1.70488e10i			0.880760i	−0.897811	+	0.440380i	$0.854844\pi$
$374$	−2.21853e8	−	6.72289e7i	−0.0113391	−	0.00343613i
$375$		0			0
$376$	−1.98702e10	−	2.41695e10i	−0.994148	−	1.20925i
$377$			1.52753e10i			0.756176i
$378$	−1.80156e9	−	5.45932e8i	−0.0882431	−	0.0267406i
$379$			1.60429e10i			0.777545i	0.921334	+	0.388772i	$0.127101\pi$
$379$			1.60429e10i			0.777545i	−0.921334	+	0.388772i	$0.872899\pi$
$380$		0			0
$381$	−2.94596e10			−1.39806
$382$	1.06505e10	−	3.51462e10i	0.500167	−	1.65054i
$383$	1.23891e10			0.575765			0.287883	−	0.957666i	$-0.407049\pi$
$383$	1.23891e10			0.575765			0.287883	+	0.957666i	$0.407049\pi$
$384$	9.54923e9	−	1.79520e10i	0.439181	−	0.825635i
$385$		0			0
$386$	−6.61413e9	+	2.18264e10i	−0.297936	+	0.983180i
$387$	−1.82907e9			−0.0815430
$388$	4.80681e9	−	7.20284e9i	0.212095	−	0.317817i
$389$	1.27527e10			0.556935			0.278467	−	0.960446i	$-0.410174\pi$
$389$	1.27527e10			0.556935			0.278467	+	0.960446i	$0.410174\pi$
$390$		0			0
$391$			4.65686e10i			1.99245i
$392$	1.48803e10	+	1.80999e10i	0.630184	+	0.766535i
$393$			4.03221e10i			1.69033i
$394$	−6.59250e9	+	2.17550e10i	−0.273568	+	0.902765i
$395$		0			0
$396$	−1.65760e7	+	2.48386e7i	−0.000674060	+	0.00101006i
$397$			1.95226e10i			0.785914i	0.919557	+	0.392957i	$0.128548\pi$
$397$			1.95226e10i			0.785914i	−0.919557	+	0.392957i	$0.871452\pi$
$398$	−8.81781e9	+	2.90985e10i	−0.351422	+	1.15968i
$399$		−	1.70629e9i		−	0.0673227i
$400$		0			0
$401$	2.44896e10			0.947119			0.473559	−	0.880762i	$-0.342969\pi$
$401$	2.44896e10			0.947119			0.473559	+	0.880762i	$0.342969\pi$
$402$	2.36043e10	+	7.15288e9i	0.903830	+	0.273891i
$403$	−7.58813e9			−0.287683
$404$	1.16358e10	+	7.76512e9i	0.436787	+	0.291489i
$405$		0			0
$406$	−2.78666e9	−	8.44450e8i	−0.102560	−	0.0310792i
$407$	3.56873e8			0.0130058
$408$	2.45017e10	−	2.01434e10i	0.884212	−	0.726929i
$409$	−1.79748e10			−0.642350			−0.321175	−	0.947020i	$-0.604078\pi$
$409$	−1.79748e10			−0.642350			−0.321175	+	0.947020i	$0.604078\pi$
$410$		0			0
$411$			3.87348e10i			1.35748i
$412$	1.16977e9	+	7.80647e8i	0.0405988	+	0.0270935i
$413$		−	1.34291e9i		−	0.0461580i
$414$	5.74099e9	+	1.73971e9i	0.195427	+	0.0592210i
$415$		0			0
$416$	−1.84214e10	+	1.84104e9i	−0.615104	+	0.0614737i
$417$			3.05803e10i			1.01134i
$418$	−2.32395e8	−	7.04236e7i	−0.00761241	−	0.00230682i
$419$			3.49871e10i			1.13515i	0.823323	+	0.567573i	$0.192117\pi$
$419$			3.49871e10i			1.13515i	−0.823323	+	0.567573i	$0.807883\pi$
$420$		0			0
$421$	1.17473e10			0.373947			0.186973	−	0.982365i	$-0.440132\pi$
$421$	1.17473e10			0.373947			0.186973	+	0.982365i	$0.440132\pi$
$422$	−7.79302e9	+	2.57167e10i	−0.245729	+	0.810896i
$423$	−6.28724e9			−0.196381
$424$	4.92368e10	−	4.04786e10i	1.52344	−	1.25246i
$425$		0			0
$426$	1.56224e10	−	5.15533e10i	0.474361	−	1.56537i
$427$	−4.27608e8			−0.0128628
$428$	−9.75649e9	−	6.51098e9i	−0.290749	−	0.194031i
$429$	−1.89540e8			−0.00559591
$430$		0			0
$431$			4.11908e10i			1.19369i	0.802357	+	0.596845i	$0.203579\pi$
$431$			4.11908e10i			1.19369i	−0.802357	+	0.596845i	$0.796421\pi$
$432$	−1.40668e10	−	3.38502e10i	−0.403887	−	0.971911i
$433$		−	1.38879e10i		−	0.395079i	−0.980295	−	0.197540i	$-0.936705\pi$
$433$		−	1.38879e10i		−	0.395079i	0.980295	−	0.197540i	$-0.0632951\pi$
$434$	4.19488e8	−	1.38430e9i	0.0118239	−	0.0390185i
$435$		0			0
$436$	−2.87442e10	−	1.91824e10i	−0.795435	−	0.530833i
$437$			4.87815e10i			1.33761i
$438$	6.32204e9	−	2.08625e10i	0.171775	−	0.566853i
$439$		−	2.26777e10i		−	0.610577i	−0.952260	−	0.305289i	$-0.901247\pi$
$439$		−	2.26777e10i		−	0.610577i	0.952260	−	0.305289i	$-0.0987530\pi$
$440$		0			0
$441$	4.70836e9			0.124485
$442$	−2.76378e10	−	8.37517e9i	−0.724126	−	0.219434i
$443$	4.08182e10			1.05984			0.529919	−	0.848049i	$-0.322222\pi$
$443$	4.08182e10			1.05984			0.529919	+	0.848049i	$0.322222\pi$
$444$	−2.71053e10	+	4.06164e10i	−0.697466	+	1.04513i
$445$		0			0
$446$	−1.69567e10	−	5.13844e9i	−0.428550	−	0.129865i
$447$	−1.91442e10			−0.479521
$448$	6.82514e8	−	3.46237e9i	0.0169434	−	0.0859532i
$449$	−4.15880e10			−1.02325			−0.511626	−	0.859208i	$-0.670957\pi$
$449$	−4.15880e10			−1.02325			−0.511626	+	0.859208i	$0.670957\pi$
$450$		0			0
$451$			4.22396e8i			0.0102097i
$452$	2.16821e10	−	3.24898e10i	0.519454	−	0.778384i
$453$		−	8.69500e9i		−	0.206479i
$454$	−6.36387e10	−	1.92847e10i	−1.49795	−	0.453929i
$455$		0			0
$456$	2.56660e10	−	2.11006e10i	0.593608	−	0.488017i
$457$		−	7.96321e10i		−	1.82567i	−0.408324	−	0.912837i	$-0.633887\pi$
$457$		−	7.96321e10i		−	1.82567i	0.408324	−	0.912837i	$-0.366113\pi$
$458$	2.06168e10	+	6.24756e9i	0.468553	+	0.141987i
$459$		−	5.71813e10i		−	1.28826i
$460$		0			0
$461$	−2.32904e10			−0.515671			−0.257836	−	0.966189i	$-0.583009\pi$
$461$	−2.32904e10			−0.515671			−0.257836	+	0.966189i	$0.583009\pi$
$462$	1.04782e7	−	3.45776e7i	0.000229995	−	0.000758974i
$463$	−3.77433e10			−0.821327			−0.410664	−	0.911787i	$-0.634703\pi$
$463$	−3.77433e10			−0.821327			−0.410664	+	0.911787i	$0.634703\pi$
$464$	−2.17585e10	−	5.23597e10i	−0.469416	−	1.12960i
$465$		0			0
$466$	1.19621e9	−	3.94745e9i	0.0253666	−	0.0837091i
$467$	−3.59265e10			−0.755349			−0.377674	−	0.925938i	$-0.623276\pi$
$467$	−3.59265e10			−0.755349			−0.377674	+	0.925938i	$0.623276\pi$
$468$	−2.06499e9	+	3.09431e9i	−0.0430461	+	0.0645031i
$469$	4.28058e9			0.0884731
$470$		0			0
$471$		−	2.64185e10i		−	0.536814i
$472$	2.02001e10	−	1.66069e10i	0.406991	−	0.334596i
$473$		−	3.14950e8i		−	0.00629212i
$474$	7.16994e9	−	2.36605e10i	0.142037	−	0.468718i
$475$		0			0
$476$	3.05576e9	−	4.57895e9i	0.0595238	−	0.0891945i
$477$		−	1.28081e10i		−	0.247406i
$478$	1.77509e9	−	5.85774e9i	0.0340024	−	0.112207i
$479$			4.40663e10i			0.837076i	0.908199	+	0.418538i	$0.137457\pi$
$479$			4.40663e10i			0.837076i	−0.908199	+	0.418538i	$0.862543\pi$
$480$		0			0
$481$	4.44581e10			0.830559
$482$	8.41787e10	+	2.55090e10i	1.55960	+	0.472612i
$483$	−7.25810e9			−0.133363
$484$	4.56408e10	+	3.04584e10i	0.831710	+	0.555041i
$485$		0			0
$486$	−1.33129e10	−	4.03425e9i	−0.238631	−	0.0723132i
$487$	−3.99322e10			−0.709916			−0.354958	−	0.934882i	$-0.615505\pi$
$487$	−3.99322e10			−0.709916			−0.354958	+	0.934882i	$0.615505\pi$
$488$	−5.28795e9	−	6.43209e9i	−0.0932413	−	0.113416i
$489$	2.24381e10			0.392420
$490$		0			0
$491$		−	7.96737e10i		−	1.37085i	−0.728145	−	0.685423i	$-0.759617\pi$
$491$		−	7.96737e10i		−	1.37085i	0.728145	−	0.685423i	$-0.240383\pi$
$492$	−4.80738e10	−	3.20820e10i	−0.820443	−	0.547521i
$493$		−	8.84483e10i		−	1.49728i
$494$	−2.89511e10	−	8.77315e9i	−0.486136	−	0.147315i
$495$		0			0
$496$	2.60102e10	−	1.08088e10i	0.429751	−	0.178587i
$497$		−	9.34907e9i		−	0.153230i
$498$	−5.90494e10	−	1.78939e10i	−0.960060	−	0.290930i
$499$			1.56191e10i			0.251915i	0.992036	+	0.125957i	$0.0402002\pi$
$499$			1.56191e10i			0.251915i	−0.992036	+	0.125957i	$0.959800\pi$
$500$		0			0
$501$	−1.18172e10			−0.187570
$502$	−3.35136e10	+	1.10594e11i	−0.527722	+	1.74147i
$503$	6.13884e10			0.958990			0.479495	−	0.877544i	$-0.340820\pi$
$503$	6.13884e10			0.958990			0.479495	+	0.877544i	$0.340820\pi$
$504$	−4.50337e8	−	5.47775e8i	−0.00697935	−	0.00848945i
$505$		0			0
$506$	−2.99563e8	+	9.88548e8i	−0.00456968	+	0.0150798i
$507$	3.81787e10			0.577815
$508$	−8.28136e10	−	5.52656e10i	−1.24350	−	0.829850i
$509$	1.27845e10			0.190464			0.0952322	−	0.995455i	$-0.469641\pi$
$509$	1.27845e10			0.190464			0.0952322	+	0.995455i	$0.469641\pi$
$510$		0			0
$511$		−	3.78337e9i		−	0.0554875i
$512$	6.05213e10	−	3.25506e10i	0.880701	−	0.473673i
$513$		−	5.98985e10i		−	0.864861i
$514$	6.92856e9	−	2.28640e10i	0.0992637	−	0.327567i
$515$		0			0
$516$	3.58451e10	+	2.39212e10i	0.505628	+	0.337430i
$517$		−	1.08261e9i		−	0.0151534i
$518$	−2.45774e9	+	8.11047e9i	−0.0341364	+	0.112649i
$519$			3.53017e10i			0.486549i
$520$		0			0
$521$	2.70385e10			0.366971			0.183486	−	0.983022i	$-0.441262\pi$
$521$	2.70385e10			0.366971			0.183486	+	0.983022i	$0.441262\pi$
$522$	−1.09039e10	−	3.30425e9i	−0.146859	−	0.0445032i
$523$	−1.26822e11			−1.69508			−0.847538	−	0.530734i	$-0.821916\pi$
$523$	−1.26822e11			−1.69508			−0.847538	+	0.530734i	$0.821916\pi$
$524$	−7.56433e10	+	1.13349e11i	−1.00333	+	1.50346i
$525$		0			0
$526$	7.02128e10	+	2.12768e10i	0.917220	+	0.277948i
$527$	4.39375e10			0.569630
$528$	6.49694e8	−	2.69986e8i	0.00835936	−	0.00347381i
$529$	1.29193e11			1.64974
$530$		0			0
$531$		−	5.25468e9i		−	0.0660950i
$532$	3.20096e9	−	4.79654e9i	0.0399608	−	0.0598799i
$533$			5.26208e10i			0.652002i
$534$	−3.11217e10	−	9.43090e9i	−0.382735	−	0.115981i
$535$		0			0
$536$	5.29351e10	+	6.43885e10i	0.641335	+	0.780098i
$537$		−	1.09589e11i		−	1.31786i
$538$	8.74289e10	+	2.64939e10i	1.04358	+	0.316240i
$539$			8.10738e8i			0.00960562i
$540$		0			0
$541$	1.86619e10			0.217854			0.108927	−	0.994050i	$-0.465259\pi$
$541$	1.86619e10			0.217854			0.108927	+	0.994050i	$0.465259\pi$
$542$	−3.99823e10	+	1.31940e11i	−0.463308	+	1.52890i
$543$	−4.39717e10			−0.505795
$544$	1.06665e11	−	1.06602e10i	1.21794	−	0.121722i
$545$		0			0
$546$	1.30534e9	−	4.30757e9i	0.0146877	−	0.0484688i
$547$	−2.19453e9			−0.0245128			−0.0122564	−	0.999925i	$-0.503901\pi$
$547$	−2.19453e9			−0.0245128			−0.0122564	+	0.999925i	$0.503901\pi$
$548$	−7.26656e10	+	1.08887e11i	−0.805762	+	1.20741i
$549$	−1.67319e9			−0.0184186
$550$		0			0
$551$		−	9.26513e10i		−	1.00518i
$552$	−8.97562e10	−	1.09176e11i	−0.966737	−	1.17591i
$553$		−	4.29078e9i		−	0.0458813i
$554$	−2.66548e10	+	8.79601e10i	−0.282968	+	0.933784i
$555$		0			0
$556$	−5.73680e10	+	8.59640e10i	−0.600303	+	0.899534i
$557$			1.97889e10i			0.205590i	0.994703	+	0.102795i	$0.0327786\pi$
$557$			1.97889e10i			0.205590i	−0.994703	+	0.102795i	$0.967221\pi$
$558$	1.64142e9	−	5.41663e9i	0.0169310	−	0.0558717i
$559$		−	3.92355e10i		−	0.401820i
$560$		0			0
$561$	1.09749e9			0.0110803
$562$	−1.18698e11	−	3.59694e10i	−1.18986	−	0.360569i
$563$	3.05862e10			0.304433			0.152216	−	0.988347i	$-0.451359\pi$
$563$	3.05862e10			0.304433			0.152216	+	0.988347i	$0.451359\pi$
$564$	1.23214e11	+	8.22266e10i	1.21771	+	0.812636i
$565$		0			0
$566$	5.45200e10	+	1.65214e10i	0.531240	+	0.160983i
$567$	7.77629e9			0.0752385
$568$	1.40629e11	−	1.15614e11i	1.35108	−	1.11075i
$569$	−1.99299e11			−1.90132			−0.950661	−	0.310230i	$-0.899594\pi$
$569$	−1.99299e11			−1.90132			−0.950661	+	0.310230i	$0.899594\pi$
$570$		0			0
$571$			8.63094e10i			0.811921i	0.913891	+	0.405960i	$0.133063\pi$
$571$			8.63094e10i			0.811921i	−0.913891	+	0.405960i	$0.866937\pi$
$572$	−5.32813e8	−	3.55572e8i	−0.00497727	−	0.00332157i
$573$			1.73866e11i			1.61285i
$574$	−9.59959e9	−	2.90900e9i	−0.0884311	−	0.0267976i
$575$		0			0
$576$	2.67061e9	−	1.35479e10i	0.0242617	−	0.123079i
$577$			8.87088e10i			0.800320i	0.916445	+	0.400160i	$0.131045\pi$
$577$			8.87088e10i			0.800320i	−0.916445	+	0.400160i	$0.868955\pi$
$578$	5.32156e10	+	1.61261e10i	0.476791	+	0.144483i
$579$		−	1.07974e11i		−	0.960734i
$580$		0			0
$581$	−1.07085e10			−0.0939772
$582$	−1.18895e10	+	3.92348e10i	−0.103626	+	0.341963i
$583$	2.20543e9			0.0190906
$584$	5.69095e10	−	4.67864e10i	0.489252	−	0.402225i
$585$		0			0
$586$	−2.60712e10	+	8.60340e10i	−0.221091	+	0.729591i
$587$	1.67947e11			1.41456			0.707278	−	0.706936i	$-0.249923\pi$
$587$	1.67947e11			1.41456			0.707278	+	0.706936i	$0.249923\pi$
$588$	−9.22718e10	−	6.15775e10i	−0.771898	−	0.515125i
$589$	4.60254e10			0.382416
$590$		0			0
$591$		−	1.07620e11i		−	0.882155i
$592$	−1.52391e11	+	6.33275e10i	−1.24072	+	0.515591i
$593$		−	1.04027e11i		−	0.841252i	−0.907234	−	0.420626i	$-0.861810\pi$
$593$		−	1.04027e11i		−	0.841252i	0.907234	−	0.420626i	$-0.138190\pi$
$594$	3.67831e8	−	1.21383e9i	0.00295463	−	0.00975017i
$595$		0			0
$596$	−5.38162e10	−	3.59142e10i	−0.426509	−	0.284630i
$597$		−	1.43948e11i		−	1.13320i
$598$	−3.73186e10	+	1.23150e11i	−0.291824	+	0.963009i
$599$		−	1.28089e11i		−	0.994960i	−0.867475	−	0.497480i	$-0.834259\pi$
$599$		−	1.28089e11i		−	0.994960i	0.867475	−	0.497480i	$-0.165741\pi$
$600$		0			0
$601$	−6.55306e10			−0.502281			−0.251140	−	0.967951i	$-0.580806\pi$
$601$	−6.55306e10			−0.502281			−0.251140	+	0.967951i	$0.580806\pi$
$602$	7.15771e9	+	2.16902e9i	0.0544989	+	0.0165150i
$603$	1.67495e10			0.126687
$604$	1.63116e10	−	2.44424e10i	0.122560	−	0.183652i
$605$		0			0
$606$	−6.33816e10	−	1.92067e10i	−0.469973	−	0.142417i
$607$	2.09475e11			1.54304			0.771521	−	0.636204i	$-0.219496\pi$
$607$	2.09475e11			1.54304			0.771521	+	0.636204i	$0.219496\pi$
$608$	1.11734e11	−	1.11667e10i	0.817655	−	0.0817168i
$609$	1.37854e10			0.100219
$610$		0			0
$611$		−	1.34868e11i		−	0.967707i
$612$	1.19569e10	−	1.79170e10i	0.0852339	−	0.127720i
$613$			1.26502e11i			0.895894i	0.894060	+	0.447947i	$0.147845\pi$
$613$			1.26502e11i			0.895894i	−0.894060	+	0.447947i	$0.852155\pi$
$614$	−1.79678e11	−	5.44483e10i	−1.26421	−	0.383099i
$615$		0			0
$616$	9.43219e7	−	7.75440e7i	0.000655073	−	0.000538549i
$617$			2.25072e11i			1.55303i	0.630096	+	0.776517i	$0.283016\pi$
$617$			2.25072e11i			1.55303i	−0.630096	+	0.776517i	$0.716984\pi$
$618$	−6.37191e9	−	1.93090e9i	−0.0436833	−	0.0132375i
$619$			6.03060e10i			0.410769i	0.978681	+	0.205385i	$0.0658445\pi$
$619$			6.03060e10i			0.410769i	−0.978681	+	0.205385i	$0.934155\pi$
$620$		0			0
$621$	−2.54792e11			−1.71325
$622$	3.85489e10	−	1.27210e11i	0.257543	−	0.849884i
$623$	−5.64383e9			−0.0374647
$624$	8.09369e10	−	3.36340e10i	0.533836	−	0.221840i
$625$		0			0
$626$	−3.98386e10	+	1.31466e11i	−0.259422	+	0.856084i
$627$	1.14964e9			0.00743863
$628$	4.95605e10	−	7.42647e10i	0.318638	−	0.477468i
$629$	−2.57426e11			−1.64456
$630$		0			0
$631$		−	1.40158e11i		−	0.884097i	−0.896991	−	0.442049i	$-0.854252\pi$
$631$		−	1.40158e11i		−	0.884097i	0.896991	−	0.442049i	$-0.145748\pi$
$632$	6.45420e10	−	5.30613e10i	0.404552	−	0.332590i
$633$		−	1.27219e11i		−	0.792384i
$634$	1.16520e10	−	3.84512e10i	0.0721179	−	0.237987i
$635$		0			0
$636$	−1.67508e11	+	2.51005e11i	−1.02378	+	1.53410i
$637$			1.00999e11i			0.613424i
$638$	5.68963e8	−	1.87756e9i	0.00343401	−	0.0113321i
$639$		−	3.65820e10i		−	0.219414i
$640$		0			0
$641$	−1.84845e11			−1.09490			−0.547452	−	0.836837i	$-0.684402\pi$
$641$	−1.84845e11			−1.09490			−0.547452	+	0.836837i	$0.684402\pi$
$642$	5.31449e10	+	1.61047e10i	0.312839	+	0.0948007i
$643$	2.62671e11			1.53662			0.768312	−	0.640076i	$-0.221097\pi$
$643$	2.62671e11			1.53662			0.768312	+	0.640076i	$0.221097\pi$
$644$	−2.04032e10	−	1.36160e10i	−0.118619	−	0.0791602i
$645$		0			0
$646$	1.67636e11	+	5.07992e10i	0.962578	+	0.291693i
$647$	2.14765e11			1.22560			0.612798	−	0.790240i	$-0.290044\pi$
$647$	2.14765e11			1.22560			0.612798	+	0.790240i	$0.290044\pi$
$648$	9.61643e10	+	1.16971e11i	0.545398	+	0.663404i
$649$	9.04810e8			0.00510010
$650$		0			0
$651$			6.84802e9i			0.0381277i
$652$	6.30755e10	+	4.20934e10i	0.349036	+	0.232929i
$653$			2.41679e11i			1.32919i	0.747206	+	0.664593i	$0.231395\pi$
$653$			2.41679e11i			1.32919i	−0.747206	+	0.664593i	$0.768605\pi$
$654$	1.56574e11	+	4.74470e10i	0.855869	+	0.259357i
$655$		0			0
$656$	−7.49547e10	−	1.80371e11i	−0.404747	−	0.973982i
$657$		−	1.48040e10i		−	0.0794541i
$658$	2.46039e10	+	7.45579e9i	0.131250	+	0.0397732i
$659$			1.45001e11i			0.768828i	0.923161	+	0.384414i	$0.125597\pi$
$659$			1.45001e11i			0.768828i	−0.923161	+	0.384414i	$0.874403\pi$
$660$		0			0
$661$	9.94275e10			0.520836			0.260418	−	0.965496i	$-0.416140\pi$
$661$	9.94275e10			0.520836			0.260418	+	0.965496i	$0.416140\pi$
$662$	−6.44566e10	+	2.12705e11i	−0.335610	+	1.10750i
$663$	1.36722e11			0.707595
$664$	−1.32425e11	−	1.61077e11i	−0.681234	−	0.828630i
$665$		0			0
$666$	−9.61691e9	+	3.17355e10i	−0.0488808	+	0.161305i
$667$	−3.94114e11			−1.99121
$668$	−3.32191e10	−	2.21687e10i	−0.166833	−	0.111336i
$669$	8.38835e10			0.418767
$670$		0			0
$671$		−	2.88108e8i		−	0.00142123i
$672$	1.66147e9	+	1.66246e10i	0.00814734	+	0.0815220i
$673$			2.01911e10i			0.0984239i	0.998788	+	0.0492120i	$0.0156710\pi$
$673$			2.01911e10i			0.0984239i	−0.998788	+	0.0492120i	$0.984329\pi$
$674$	−8.11117e10	+	2.67666e11i	−0.393047	+	1.29704i
$675$		0			0
$676$	1.07324e11	+	7.16223e10i	0.513936	+	0.342974i
$677$		−	3.25587e10i		−	0.154993i	−0.996993	−	0.0774966i	$-0.975307\pi$
$677$		−	3.25587e10i		−	0.154993i	0.996993	−	0.0774966i	$-0.0246927\pi$
$678$	−5.36298e10	+	1.76976e11i	−0.253797	+	0.837523i
$679$			7.11514e9i			0.0334737i
$680$		0			0
$681$	3.14816e11			1.46375
$682$	9.32695e8	+	2.82638e8i	0.00431124	+	0.00130645i
$683$	2.46509e10			0.113279			0.0566396	−	0.998395i	$-0.481961\pi$
$683$	2.46509e10			0.113279			0.0566396	+	0.998395i	$0.481961\pi$
$684$	1.25251e10	−	1.87684e10i	0.0572210	−	0.0857438i
$685$		0			0
$686$	−3.69930e10	−	1.12101e10i	−0.167041	−	0.0506190i
$687$	−1.01990e11			−0.457856
$688$	5.58882e10	+	1.34489e11i	0.249440	+	0.600252i
$689$	2.74746e11			1.21914
$690$		0			0
$691$			3.02518e11i			1.32690i	0.748220	+	0.663451i	$0.230909\pi$
$691$			3.02518e11i			1.32690i	−0.748220	+	0.663451i	$0.769091\pi$
$692$	−6.62252e10	+	9.92363e10i	−0.288801	+	0.432759i
$693$		−	2.45361e7i		−	0.000106383i
$694$	6.25894e9	+	1.89667e9i	0.0269813	+	0.00817624i
$695$		0			0
$696$	1.70475e11	+	2.07360e11i	0.726480	+	0.883665i
$697$		−	3.04690e11i		−	1.29100i
$698$	−2.33573e11	−	7.07805e10i	−0.984015	−	0.298189i
$699$			1.95277e10i			0.0817980i
$700$		0			0
$701$	−1.07716e11			−0.446076			−0.223038	−	0.974810i	$-0.571597\pi$
$701$	−1.07716e11			−0.446076			−0.223038	+	0.974810i	$0.571597\pi$
$702$	4.58233e10	−	1.51215e11i	0.188685	−	0.622655i
$703$	−2.69658e11			−1.10406
$704$	2.33284e9	+	4.59856e8i	0.00949715	+	0.00187211i
$705$		0			0
$706$	−1.09652e10	+	3.61849e10i	−0.0441366	+	0.145649i
$707$	−1.14941e10			−0.0460041
$708$	−6.87225e10	+	1.02978e11i	−0.273505	+	0.409839i
$709$	2.10543e10			0.0833213			0.0416606	−	0.999132i	$-0.486735\pi$
$709$	2.10543e10			0.0833213			0.0416606	+	0.999132i	$0.486735\pi$
$710$		0			0
$711$		−	1.67894e10i		−	0.0656988i
$712$	−6.97936e10	−	8.48946e10i	−0.271579	−	0.330339i
$713$		−	1.95780e11i		−	0.757547i
$714$	−7.55830e9	+	2.49421e10i	−0.0290825	+	0.0959712i
$715$		0			0
$716$	2.05586e11	−	3.08064e11i	0.782242	−	1.17216i
$717$			2.89778e10i			0.109645i
$718$	9.07918e10	−	2.99610e11i	0.341624	−	1.12735i
$719$		−	1.84186e11i		−	0.689193i	−0.938751	−	0.344597i	$-0.888016\pi$
$719$		−	1.84186e11i		−	0.689193i	0.938751	−	0.344597i	$-0.111984\pi$
$720$		0			0
$721$	−1.15553e9			−0.00427602
$722$	−8.44573e10	−	2.55934e10i	−0.310805	−	0.0941843i
$723$	−4.16426e11			−1.52400
$724$	−1.23608e11	−	8.24900e10i	−0.449877	−	0.300225i
$725$		0			0
$726$	−2.48612e11	−	7.53376e10i	−0.894901	−	0.271185i
$727$	−1.34820e11			−0.482632			−0.241316	−	0.970447i	$-0.577579\pi$
$727$	−1.34820e11			−0.482632			−0.241316	+	0.970447i	$0.577579\pi$
$728$	1.17503e10	−	9.66019e9i	0.0418336	−	0.0343922i
$729$	3.08413e11			1.09200
$730$		0			0
$731$			2.27185e11i			0.795628i
$732$	3.27902e10	+	2.18825e10i	0.114209	+	0.0762172i
$733$		−	5.46288e10i		−	0.189237i	−0.995514	−	0.0946184i	$-0.969837\pi$
$733$		−	5.46288e10i		−	0.189237i	0.995514	−	0.0946184i	$-0.0301631\pi$
$734$	3.68500e11	+	1.11668e11i	1.26956	+	0.384719i
$735$		0			0
$736$	−4.75002e10	−	4.75285e11i	−0.161877	−	1.61973i
$737$			2.88411e9i			0.00977558i
$738$	−3.75623e10	−	1.13826e10i	−0.126627	−	0.0383722i
$739$			2.87010e11i			0.962320i	0.876633	+	0.481160i	$0.159784\pi$
$739$			2.87010e11i			0.962320i	−0.876633	+	0.481160i	$0.840216\pi$
$740$		0			0
$741$	1.43219e11			0.475037
$742$	−1.51886e10	+	5.01218e10i	−0.0501074	+	0.165353i
$743$	−1.72722e11			−0.566750			−0.283375	−	0.959009i	$-0.591454\pi$
$743$	−1.72722e11			−0.566750			−0.283375	+	0.959009i	$0.591454\pi$
$744$	−1.03008e11	+	8.46850e10i	−0.336186	+	0.276385i
$745$		0			0
$746$	7.91090e10	−	2.61057e11i	0.255429	−	0.842908i
$747$	−4.19012e10			−0.134569
$748$	3.08515e9	+	2.05887e9i	0.00985529	+	0.00657692i
$749$	9.63769e9			0.0306228
$750$		0			0
$751$			1.75776e11i			0.552586i	0.961073	+	0.276293i	$0.0891060\pi$
$751$			1.75776e11i			0.552586i	−0.961073	+	0.276293i	$0.910894\pi$
$752$	1.92110e11	+	4.62293e11i	0.600729	+	1.44559i
$753$		−	5.47098e11i		−	1.70171i
$754$	7.08796e10	−	2.33901e11i	0.219299	−	0.723679i
$755$		0			0
$756$	2.50529e10	+	1.67190e10i	0.0766957	+	0.0511828i
$757$		−	2.40268e11i		−	0.731665i	−0.930681	−	0.365833i	$-0.880784\pi$
$757$		−	2.40268e11i		−	0.731665i	0.930681	−	0.365833i	$-0.119216\pi$
$758$	7.44415e10	−	2.45655e11i	0.225496	−	0.744129i
$759$		−	4.89027e9i		−	0.0147355i
$760$		0			0
$761$	5.00466e11			1.49223			0.746115	−	0.665817i	$-0.231917\pi$
$761$	5.00466e11			1.49223			0.746115	+	0.665817i	$0.231917\pi$
$762$	4.51097e11	+	1.36697e11i	1.33798	+	0.405453i
$763$	2.83942e10			0.0837784
$764$	−3.26168e11	+	4.88752e11i	−0.957344	+	1.43455i
$765$		0			0
$766$	−1.89707e11	−	5.74875e10i	−0.551021	−	0.166978i
$767$	1.12718e11			0.325697
$768$	−2.29522e11	+	2.30578e11i	−0.659749	+	0.662785i
$769$	−1.02605e11			−0.293402			−0.146701	−	0.989181i	$-0.546865\pi$
$769$	−1.02605e11			−0.293402			−0.146701	+	0.989181i	$0.546865\pi$
$770$		0			0
$771$			1.13107e11i			0.320089i
$772$	2.02556e11	−	3.03523e11i	0.570264	−	0.854522i
$773$			5.93175e11i			1.66136i	0.556747	+	0.830682i	$0.312049\pi$
$773$			5.93175e11i			1.66136i	−0.556747	+	0.830682i	$0.687951\pi$
$774$	2.80074e10	+	8.48718e9i	0.0780386	+	0.0236483i
$775$		0			0
$776$	−1.07026e11	+	8.79883e10i	−0.295150	+	0.242649i
$777$		−	4.01219e10i		−	0.110077i
$778$	−1.95274e11	−	5.91747e10i	−0.533000	−	0.161517i
$779$		−	3.19169e11i		−	0.866704i
$780$		0			0
$781$	6.29910e9			0.0169307
$782$	2.16086e11	−	7.13077e11i	0.577829	−	1.90682i
$783$	4.83929e11			1.28746
$784$	−1.43866e11	−	3.46200e11i	−0.380798	−	0.916352i
$785$		0			0
$786$	1.87101e11	−	6.17427e11i	0.490214	−	1.61769i
$787$	−1.93252e11			−0.503761			−0.251880	−	0.967758i	$-0.581049\pi$
$787$	−1.93252e11			−0.503761			−0.251880	+	0.967758i	$0.581049\pi$
$788$	2.01894e11	−	3.02531e11i	0.523622	−	0.784630i
$789$	−3.47338e11			−0.896280
$790$		0			0
$791$			3.20942e10i			0.0819825i
$792$	3.69073e8	−	3.03422e8i	0.000938018	−	0.000771164i
$793$		−	3.58917e10i		−	0.0907613i
$794$	9.05879e10	−	2.98937e11i	0.227923	−	0.752139i
$795$		0			0
$796$	2.70043e11	−	4.04651e11i	0.672638	−	1.00793i
$797$			4.34328e11i			1.07643i	0.842809	+	0.538213i	$0.180901\pi$
$797$			4.34328e11i			1.07643i	−0.842809	+	0.538213i	$0.819099\pi$
$798$	−7.91746e9	+	2.61274e10i	−0.0195243	+	0.0644294i
$799$			7.80925e11i			1.91612i
$800$		0			0
$801$	−2.20838e10			−0.0536468
$802$	−3.74994e11	−	1.13636e11i	−0.906415	−	0.274674i
$803$	2.54911e9			0.00613093
$804$	−3.28247e11	−	2.19055e11i	−0.785555	−	0.524239i
$805$		0			0
$806$	1.16192e11	+	3.52101e10i	0.275320	+	0.0834310i
$807$	−4.32504e11			−1.01976
$808$	−1.42140e11	−	1.72894e11i	−0.333481	−	0.405635i
$809$	−7.57515e11			−1.76847			−0.884234	−	0.467044i	$-0.845319\pi$
$809$	−7.57515e11			−1.76847			−0.884234	+	0.467044i	$0.845319\pi$
$810$		0			0
$811$		−	1.15001e11i		−	0.265838i	−0.991127	−	0.132919i	$-0.957565\pi$
$811$		−	1.15001e11i		−	0.265838i	0.991127	−	0.132919i	$-0.0424350\pi$
$812$	3.87520e10	+	2.58611e10i	0.0891394	+	0.0594870i
$813$		−	6.52698e11i		−	1.49400i
$814$	−5.46457e9	−	1.65595e9i	−0.0124468	−	0.00377180i
$815$		0			0
$816$	−4.68649e11	+	1.94751e11i	−1.05703	+	0.439258i
$817$			2.37981e11i			0.534138i
$818$	2.75238e11	+	8.34061e10i	0.614744	+	0.186288i
$819$		−	3.05663e9i		−	0.00679373i
$820$		0			0
$821$	−2.18337e11			−0.480568			−0.240284	−	0.970703i	$-0.577240\pi$
$821$	−2.18337e11			−0.480568			−0.240284	+	0.970703i	$0.577240\pi$
$822$	1.79736e11	−	5.93122e11i	0.393683	−	1.29914i
$823$	−2.44330e11			−0.532572			−0.266286	−	0.963894i	$-0.585797\pi$
$823$	−2.44330e11			−0.532572			−0.266286	+	0.963894i	$0.585797\pi$
$824$	−1.42897e10	−	1.73815e10i	−0.0309966	−	0.0377032i
$825$		0			0
$826$	−6.23132e9	+	2.05632e10i	−0.0133863	+	0.0441743i
$827$	−6.25569e11			−1.33738			−0.668688	−	0.743543i	$-0.733144\pi$
$827$	−6.25569e11			−1.33738			−0.668688	+	0.743543i	$0.733144\pi$
$828$	−7.98357e10	−	5.32782e10i	−0.169854	−	0.113352i
$829$	7.91341e11			1.67550			0.837752	−	0.546051i	$-0.183869\pi$
$829$	7.91341e11			1.67550			0.837752	+	0.546051i	$0.183869\pi$
$830$		0			0
$831$		−	4.35132e11i		−	0.912466i
$832$	2.90618e11	+	5.72874e10i	0.606497	+	0.119554i
$833$		−	5.84816e11i		−	1.21462i
$834$	1.41898e11	−	4.68257e11i	0.293299	−	0.967878i
$835$		0			0
$836$	3.23175e9	+	2.15670e9i	0.00661626	+	0.00441535i
$837$			2.40396e11i			0.489808i
$838$	1.62346e11	−	5.35735e11i	0.329204	−	1.08636i
$839$		−	1.97673e11i		−	0.398933i	−0.979905	−	0.199466i	$-0.936079\pi$
$839$		−	1.97673e11i		−	0.398933i	0.979905	−	0.199466i	$-0.0639209\pi$
$840$		0			0
$841$	2.48297e11			0.496350
$842$	−1.79879e11	−	5.45094e10i	−0.357876	−	0.108448i
$843$	5.87189e11			1.16270
$844$	2.38659e11	−	3.57623e11i	0.470336	−	0.704783i
$845$		0			0
$846$	9.62726e10	+	2.91738e10i	0.187941	+	0.0569524i
$847$	−4.50851e10			−0.0875990
$848$	−9.41760e11	+	3.91357e11i	−1.82120	+	0.756815i
$849$	−2.69707e11			−0.519112
$850$		0			0
$851$			1.14705e12i			2.18708i
$852$	−4.78431e11	+	7.16914e11i	−0.907949	+	1.36053i
$853$			9.60505e11i			1.81428i	0.420833	+	0.907138i	$0.361738\pi$
$853$			9.60505e11i			1.81428i	−0.420833	+	0.907138i	$0.638262\pi$
$854$	6.54770e9	+	1.98417e9i	0.0123100	+	0.00373033i
$855$		0			0
$856$	1.19183e11	+	1.44970e11i	0.221983	+	0.270012i
$857$		−	1.83889e10i		−	0.0340904i	−0.999855	−	0.0170452i	$-0.994574\pi$
$857$		−	1.83889e10i		−	0.0340904i	0.999855	−	0.0170452i	$-0.00542592\pi$
$858$	2.90230e9	+	8.79495e8i	0.00535542	+	0.00162287i
$859$			2.58648e11i			0.475048i	0.971382	+	0.237524i	$0.0763358\pi$
$859$			2.58648e11i			0.475048i	−0.971382	+	0.237524i	$0.923664\pi$
$860$		0			0
$861$	4.74884e10			0.0864123
$862$	1.91132e11	−	6.30729e11i	0.346182	−	1.14239i
$863$	4.58083e11			0.825849			0.412925	−	0.910765i	$-0.364507\pi$
$863$	4.58083e11			0.825849			0.412925	+	0.910765i	$0.364507\pi$
$864$	5.83252e10	+	5.83600e11i	0.104665	+	1.04727i
$865$		0			0
$866$	−6.44420e10	+	2.12656e11i	−0.114577	+	0.378100i
$867$	−2.63254e11			−0.465906
$868$	−1.28467e10	+	1.92504e10i	−0.0226315	+	0.0339126i
$869$	2.89099e9			0.00506953
$870$		0			0
$871$			3.59294e11i			0.624277i
$872$	3.51133e11	+	4.27106e11i	0.607303	+	0.738703i
$873$			2.78409e10i			0.0479320i
$874$	2.26354e11	−	7.46961e11i	0.387921	−	1.28012i
$875$		0			0
$876$	−1.93611e11	+	2.90120e11i	−0.328786	+	0.492675i
$877$			9.94220e11i			1.68068i	0.542062	+	0.840338i	$0.317644\pi$
$877$			9.94220e11i			1.68068i	−0.542062	+	0.840338i	$0.682356\pi$
$878$	−1.05228e11	+	3.47249e11i	−0.177074	+	0.584337i
$879$		−	4.25604e11i		−	0.712935i
$880$		0			0
$881$	4.02463e11			0.668071			0.334036	−	0.942560i	$-0.391589\pi$
$881$	4.02463e11			0.668071			0.334036	+	0.942560i	$0.391589\pi$
$882$	−7.20962e10	−	2.18476e10i	−0.119135	−	0.0361018i
$883$	−7.19682e11			−1.18385			−0.591926	−	0.805992i	$-0.701632\pi$
$883$	−7.19682e11			−1.18385			−0.591926	+	0.805992i	$0.701632\pi$
$884$	3.84338e11	+	2.56488e11i	0.629368	+	0.420008i
$885$		0			0
$886$	−6.25024e11	−	1.89403e11i	−1.01429	−	0.307363i
$887$	4.82885e11			0.780097			0.390049	−	0.920794i	$-0.372458\pi$
$887$	4.82885e11			0.780097			0.390049	+	0.920794i	$0.372458\pi$
$888$	6.03514e11	−	4.96161e11i	0.970589	−	0.797941i
$889$	8.18053e10			0.130971
$890$		0			0
$891$			5.23941e9i			0.00831326i
$892$	2.35804e11	+	1.57364e11i	0.372470	+	0.248568i
$893$			8.18034e11i			1.28637i
$894$	2.93144e11	+	8.88324e10i	0.458913	+	0.139066i
$895$		0			0
$896$	−2.65169e10	+	4.98502e10i	−0.0411425	+	0.0773455i
$897$		−	6.09215e11i		−	0.941024i
$898$	6.36811e11	+	1.92975e11i	0.979277	+	0.296753i
$899$			3.71846e11i			0.569278i
$900$		0			0
$901$	−1.59086e12			−2.41398
$902$	1.95999e9	−	6.46789e9i	0.00296092	−	0.00977094i
$903$	−3.54086e10			−0.0532547
$904$	−4.82762e11	+	3.96889e11i	−0.722869	+	0.594285i
$905$		0			0
$906$	−4.03462e10	+	1.33141e11i	−0.0598811	+	0.197606i
$907$	1.11961e12			1.65439			0.827194	−	0.561917i	$-0.189936\pi$
$907$	1.11961e12			1.65439			0.827194	+	0.561917i	$0.189936\pi$
$908$	8.84976e11	+	5.90588e11i	1.30193	+	0.868842i
$909$	−4.49753e10			−0.0658746
$910$		0			0
$911$		−	1.90411e10i		−	0.0276451i	−0.999904	−	0.0138225i	$-0.995600\pi$
$911$		−	1.90411e10i		−	0.0276451i	0.999904	−	0.0138225i	$-0.00439999\pi$
$912$	−4.90918e11	+	2.04006e11i	−0.709626	+	0.294892i
$913$		−	7.21501e9i		−	0.0103837i
$914$	−3.69506e11	+	1.21936e12i	−0.529464	+	1.74721i
$915$		0			0
$916$	−2.86702e11	−	1.91330e11i	−0.407238	−	0.271770i
$917$		−	1.11969e11i		−	0.158351i
$918$	−2.65330e11	+	8.75582e11i	−0.373608	+	1.23289i
$919$			1.16760e11i			0.163694i	0.996645	+	0.0818470i	$0.0260819\pi$
$919$			1.16760e11i			0.163694i	−0.996645	+	0.0818470i	$0.973918\pi$
$920$		0			0
$921$	8.88852e11			1.23535
$922$	3.56631e11	+	1.08071e11i	0.493509	+	0.149550i
$923$	7.84722e11			1.08121
$924$	−3.20891e8	+	4.80845e8i	−0.000440220	+	0.000659656i
$925$		0			0
$926$	5.77940e11	+	1.75135e11i	0.786030	+	0.238193i
$927$	−4.52148e9			−0.00612296
$928$	9.02177e10	+	9.02714e11i	0.121647	+	1.21719i
$929$	8.06361e11			1.08260			0.541298	−	0.840831i	$-0.317933\pi$
$929$	8.06361e11			1.08260			0.541298	+	0.840831i	$0.317933\pi$
$930$		0			0
$931$		−	6.12606e11i		−	0.815422i
$932$	−3.66336e10	+	5.48942e10i	−0.0485529	+	0.0727550i
$933$			6.29299e11i			0.830482i
$934$	5.50120e11	+	1.66705e11i	0.722887	+	0.219059i
$935$		0			0
$936$	4.59779e10	−	3.77994e10i	0.0599027	−	0.0492472i
$937$		−	1.43350e12i		−	1.85968i	−0.367959	−	0.929842i	$-0.619943\pi$
$937$		−	1.43350e12i		−	1.85968i	0.367959	−	0.929842i	$-0.380057\pi$
$938$	−6.55458e10	−	1.98626e10i	−0.0846708	−	0.0256581i
$939$		−	6.50353e11i		−	0.836540i
$940$		0			0
$941$	−1.41766e12			−1.80806			−0.904029	−	0.427472i	$-0.859404\pi$
$941$	−1.41766e12			−1.80806			−0.904029	+	0.427472i	$0.859404\pi$
$942$	−1.22586e11	+	4.04530e11i	−0.155682	+	0.513744i
$943$	−1.35766e12			−1.71690
$944$	−3.86370e11	+	1.60560e11i	−0.486537	+	0.202185i
$945$		0			0
$946$	−1.46142e9	+	4.82263e9i	−0.00182478	+	0.00602170i
$947$	7.59493e11			0.944331			0.472165	−	0.881510i	$-0.343473\pi$
$947$	7.59493e11			0.944331			0.472165	+	0.881510i	$0.343473\pi$
$948$	−2.19578e11	+	3.29030e11i	−0.271866	+	0.407382i
$949$	3.17560e11			0.391527
$950$		0			0
$951$			1.90215e11i			0.232553i
$952$	−6.80379e10	+	5.59354e10i	−0.0828330	+	0.0680987i
$953$			3.72618e11i			0.451743i	0.974157	+	0.225872i	$0.0725230\pi$
$953$			3.72618e11i			0.451743i	−0.974157	+	0.225872i	$0.927477\pi$
$954$	−5.94315e10	+	1.96122e11i	−0.0717502	+	0.236773i
$955$		0			0
$956$	−5.43617e10	+	8.14592e10i	−0.0650821	+	0.0975234i
$957$			9.28814e9i			0.0110734i
$958$	2.04475e11	−	6.74760e11i	0.242760	−	0.801101i
$959$		−	1.07561e11i		−	0.127169i
$960$		0			0
$961$	6.68173e11			0.783421
$962$	−6.80759e11	−	2.06293e11i	−0.794865	−	0.240870i
$963$	3.77114e10			0.0438497
$964$	−1.17061e12	−	7.81206e11i	−1.35552	−	0.904601i
$965$		0			0
$966$	1.11139e11	+	3.36787e10i	0.127631	+	0.0386765i
$967$	7.07203e11			0.808794			0.404397	−	0.914584i	$-0.367481\pi$
$967$	7.07203e11			0.808794			0.404397	+	0.914584i	$0.367481\pi$
$968$	−5.57538e11	−	6.78171e11i	−0.634999	−	0.772392i
$969$	−8.29281e11			−0.940603
$970$		0			0
$971$		−	1.48456e12i		−	1.67001i	−0.550240	−	0.835007i	$-0.685464\pi$
$971$		−	1.48456e12i		−	1.67001i	0.550240	−	0.835007i	$-0.314536\pi$
$972$	1.85133e11	+	1.23548e11i	0.207404	+	0.138411i
$973$		−	8.49173e10i		−	0.0947425i
$974$	6.11457e11	+	1.85292e11i	0.679407	+	0.205883i
$975$		0			0
$976$	5.11252e10	+	1.23027e11i	0.0563424	+	0.135582i
$977$			4.31329e10i			0.0473402i	0.999720	+	0.0236701i	$0.00753513\pi$
$977$			4.31329e10i			0.0473402i	−0.999720	+	0.0236701i	$0.992465\pi$
$978$	−3.43581e11	−	1.04116e11i	−0.375555	−	0.113806i
$979$		−	3.80263e9i		−	0.00413955i
$980$		0			0
$981$	1.11104e11			0.119965
$982$	−3.69699e11	+	1.21999e12i	−0.397559	+	1.31193i
$983$	1.13842e12			1.21923			0.609617	−	0.792696i	$-0.291323\pi$
$983$	1.13842e12			1.21923			0.609617	+	0.792696i	$0.291323\pi$
$984$	5.87259e11	+	7.14322e11i	0.626396	+	0.761927i
$985$		0			0
$986$	−4.10414e11	+	1.35435e12i	−0.434225	+	1.43293i
$987$	−1.21714e11			−0.128254
$988$	4.02602e11	+	2.68676e11i	0.422520	+	0.281968i
$989$	1.01231e12			1.05810
$990$		0			0
$991$			6.27241e11i			0.650339i	0.945656	+	0.325170i	$0.105421\pi$
$991$			6.27241e11i			0.650339i	−0.945656	+	0.325170i	$0.894579\pi$
$992$	−4.48432e11	+	4.48165e10i	−0.463073	+	0.0462797i
$993$		−	1.05223e12i		−	1.08222i
$994$	−4.33812e10	+	1.43156e11i	−0.0444381	+	0.146644i
$995$		0			0
$996$	8.21156e11	+	5.47997e11i	0.834427	+	0.556854i
$997$		−	2.64260e11i		−	0.267455i	−0.991018	−	0.133728i	$-0.957305\pi$
$997$		−	2.64260e11i		−	0.267455i	0.991018	−	0.133728i	$-0.0426947\pi$
$998$	7.24750e10	−	2.39165e11i	0.0730578	−	0.241088i
$999$		−	1.40846e12i		−	1.41411i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.d.c.99.3		32
4.3	odd	2	inner	100.9.d.c.99.29		32
5.2	odd	4		20.9.b.a.11.9	✓	16
5.3	odd	4		100.9.b.d.51.8		16
5.4	even	2	inner	100.9.d.c.99.30		32
15.2	even	4		180.9.c.a.91.8		16
20.3	even	4		100.9.b.d.51.7		16
20.7	even	4		20.9.b.a.11.10	yes	16
20.19	odd	2	inner	100.9.d.c.99.4		32
40.27	even	4		320.9.b.d.191.5		16
40.37	odd	4		320.9.b.d.191.12		16
60.47	odd	4		180.9.c.a.91.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.b.a.11.9	✓	16	5.2	odd	4
20.9.b.a.11.10	yes	16	20.7	even	4
100.9.b.d.51.7		16	20.3	even	4
100.9.b.d.51.8		16	5.3	odd	4
100.9.d.c.99.3		32	1.1	even	1	trivial
100.9.d.c.99.4		32	20.19	odd	2	inner
100.9.d.c.99.29		32	4.3	odd	2	inner
100.9.d.c.99.30		32	5.4	even	2	inner
180.9.c.a.91.7		16	60.47	odd	4
180.9.c.a.91.8		16	15.2	even	4
320.9.b.d.191.5		16	40.27	even	4
320.9.b.d.191.12		16	40.37	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)

\(f(q)\)	\(=\)	\(q+(-15.3124 - 4.64016i) q^{2} +75.7492 q^{3} +(212.938 + 142.104i) q^{4} +(-1159.90 - 351.488i) q^{6} -210.345 q^{7} +(-2601.20 - 3164.01i) q^{8} -823.060 q^{9} -141.724i q^{11} +(16129.9 + 10764.2i) q^{12} -17655.5i q^{13} +(3220.88 + 976.035i) q^{14} +(25149.0 + 60518.5i) q^{16} +102231. i q^{17} +(12603.0 + 3819.13i) q^{18} +107088. i q^{19} -15933.5 q^{21} +(-657.620 + 2170.13i) q^{22} +455526. q^{23} +(-197039. - 239671. i) q^{24} +(-81924.3 + 270348. i) q^{26} -559337. q^{27} +(-44790.4 - 29890.8i) q^{28} -865184. q^{29} -429788. i q^{31} +(-104276. - 1.04338e6i) q^{32} -10735.4i q^{33} +(474366. - 1.56539e6i) q^{34} +(-175261. - 116960. i) q^{36} +2.51809e6i q^{37} +(496908. - 1.63978e6i) q^{38} -1.33739e6i q^{39} -2.98042e6 q^{41} +(243979. + 73933.8i) q^{42} +2.22228e6 q^{43} +(20139.5 - 30178.3i) q^{44} +(-6.97518e6 - 2.11371e6i) q^{46} +7.63886e6 q^{47} +(1.90502e6 + 4.58423e6i) q^{48} -5.72056e6 q^{49} +7.74388e6i q^{51} +(2.50891e6 - 3.75952e6i) q^{52} +1.55615e7i q^{53} +(8.56477e6 + 2.59541e6i) q^{54} +(547149. + 665534. i) q^{56} +8.11187e6i q^{57} +(1.32480e7 + 4.01459e6i) q^{58} +6.38433e6i q^{59} +2.03289e6 q^{61} +(-1.99429e6 + 6.58108e6i) q^{62} +173127. q^{63} +(-3.24473e6 + 1.64605e7i) q^{64} +(-49814.2 + 164385. i) q^{66} -2.03503e7 q^{67} +(-1.45274e7 + 2.17688e7i) q^{68} +3.45057e7 q^{69} +4.44463e7i q^{71} +(2.14094e6 + 2.60417e6i) q^{72} +1.79865e7i q^{73} +(1.16843e7 - 3.85579e7i) q^{74} +(-1.52177e7 + 2.28032e7i) q^{76} +29810.9i q^{77} +(-6.20570e6 + 2.04786e7i) q^{78} +2.03988e7i q^{79} -3.69692e7 q^{81} +(4.56374e7 + 1.38296e7i) q^{82} +5.09090e7 q^{83} +(-3.39284e6 - 2.26421e6i) q^{84} +(-3.40284e7 - 1.03117e7i) q^{86} -6.55370e7 q^{87} +(-448415. + 368651. i) q^{88} +2.68313e7 q^{89} +3.71375e6i q^{91} +(9.69986e7 + 6.47319e7i) q^{92} -3.25561e7i q^{93} +(-1.16969e8 - 3.54456e7i) q^{94} +(-7.89880e6 - 7.90351e7i) q^{96} -3.38260e7i q^{97} +(8.75953e7 + 2.65443e7i) q^{98} +116647. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 104 q^{4} + 8736 q^{6} + 77600 q^{9} - 136944 q^{14} - 162848 q^{16} + 828992 q^{21} - 327584 q^{24} + 2074248 q^{26} - 5529792 q^{29} - 7587928 q^{34} - 10937832 q^{36} - 17152896 q^{41} - 33842400 q^{44}+ \cdots - 906779904 q^{96}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more