LMFDB - Embedded newform 700.2.g.l.251.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(251,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("700.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 17x^{12} - 104x^{10} + 713x^{8} + 238x^{6} + 1004x^{4} - 152x^{2} + 64 $ x^16 - 17x^12 - 104x^10 + 713x^8 + 238x^6 + 1004x^4 - 152x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.15
Root			$0.877859 - 2.23141i$ of defining polynomial
Character	$\chi$	$=$	700.251
Dual form			700.2.g.l.251.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37491 + 0.331077i) q^{2} -2.13578 q^{3} +(1.78078 + 0.910404i) q^{4} +(-2.93651 - 0.707107i) q^{6} +(1.19935 + 2.35829i) q^{7} +(2.14700 + 1.84130i) q^{8} +1.56155 q^{9} +O(q^{10})$	\(q+(1.37491 + 0.331077i) q^{2} -2.13578 q^{3} +(1.78078 + 0.910404i) q^{4} +(-2.93651 - 0.707107i) q^{6} +(1.19935 + 2.35829i) q^{7} +(2.14700 + 1.84130i) q^{8} +1.56155 q^{9} -2.33205i q^{11} +(-3.80335 - 1.94442i) q^{12} +1.09190i q^{13} +(0.868230 + 3.63953i) q^{14} +(2.34233 + 3.24245i) q^{16} +4.98074i q^{17} +(2.14700 + 0.516994i) q^{18} -2.57501 q^{19} +(-2.56155 - 5.03680i) q^{21} +(0.772087 - 3.20636i) q^{22} +6.04090i q^{23} +(-4.58552 - 3.93261i) q^{24} +(-0.361501 + 1.50126i) q^{26} +3.07221 q^{27} +(-0.0112214 + 5.29149i) q^{28} -0.561553 q^{29} +6.59603 q^{31} +(2.14700 + 5.23358i) q^{32} +4.98074i q^{33} +(-1.64901 + 6.84809i) q^{34} +(2.78078 + 1.42164i) q^{36} -5.49966 q^{37} +(-3.54042 - 0.852526i) q^{38} -2.33205i q^{39} +8.48528i q^{41} +(-1.85435 - 7.77323i) q^{42} -1.32431i q^{43} +(2.12311 - 4.15286i) q^{44} +(-2.00000 + 8.30571i) q^{46} -9.74247 q^{47} +(-5.00270 - 6.92516i) q^{48} +(-4.12311 + 5.65685i) q^{49} -10.6378i q^{51} +(-0.994066 + 1.94442i) q^{52} +8.58800 q^{53} +(4.22402 + 1.01714i) q^{54} +(-1.76732 + 7.27163i) q^{56} +5.49966 q^{57} +(-0.772087 - 0.185917i) q^{58} +14.3211 q^{59} +0.620058i q^{61} +(9.06897 + 2.18379i) q^{62} +(1.87285 + 3.68260i) q^{63} +(1.21922 + 7.90655i) q^{64} +(-1.64901 + 6.84809i) q^{66} -4.71659i q^{67} +(-4.53448 + 8.86958i) q^{68} -12.9020i q^{69} -11.9473i q^{71} +(3.35265 + 2.87529i) q^{72} -9.96148i q^{73} +(-7.56155 - 1.82081i) q^{74} +(-4.58552 - 2.34430i) q^{76} +(5.49966 - 2.79695i) q^{77} +(0.772087 - 3.20636i) q^{78} -10.6378i q^{79} -11.2462 q^{81} +(-2.80928 + 11.6665i) q^{82} +3.86098 q^{83} +(0.0239665 - 11.3015i) q^{84} +(0.438447 - 1.82081i) q^{86} +1.19935 q^{87} +(4.29400 - 5.00691i) q^{88} +2.82843i q^{89} +(-2.57501 + 1.30957i) q^{91} +(-5.49966 + 10.7575i) q^{92} -14.0877 q^{93} +(-13.3951 - 3.22550i) q^{94} +(-4.58552 - 11.1778i) q^{96} -14.9422i q^{97} +(-7.54177 + 6.41262i) q^{98} -3.64162i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q + 12 * q^4 - 8 * q^9	$ 16 q + 12 q^{4} - 8 q^{9} + 4 q^{14} - 12 q^{16} - 8 q^{21} + 24 q^{29} + 28 q^{36} - 32 q^{44} - 32 q^{46} - 20 q^{56} + 36 q^{64} - 88 q^{74} - 48 q^{81} - 40 q^{84} + 40 q^{86}+O(q^{100}) $ 16 * q + 12 * q^4 - 8 * q^9 + 4 * q^14 - 12 * q^16 - 8 * q^21 + 24 * q^29 + 28 * q^36 - 32 * q^44 - 32 * q^46 - 20 * q^56 + 36 * q^64 - 88 * q^74 - 48 * q^81 - 40 * q^84 + 40 * q^86

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	1.37491	+	0.331077i	0.972211	+	0.234107i
$2$	1.37491	+	0.331077i	0.972211	+	0.234107i
$3$	−2.13578			−1.23309			−0.616546	−	0.787319i	$-0.711469\pi$
$3$	−2.13578			−1.23309			−0.616546	+	0.787319i	$0.711469\pi$
$4$	1.78078	+	0.910404i	0.890388	+	0.455202i
$5$		0			0
$5$		0			0
$6$	−2.93651	−	0.707107i	−1.19883	−	0.288675i
$7$	1.19935	+	2.35829i	0.453313	+	0.891352i
$7$	1.19935	+	2.35829i	0.453313	+	0.891352i
$8$	2.14700	+	1.84130i	0.759079	+	0.650998i
$9$	1.56155			0.520518
$10$		0			0
$11$		−	2.33205i		−	0.703139i	−0.936162	−	0.351569i	$-0.885648\pi$
$11$		−	2.33205i		−	0.703139i	0.936162	−	0.351569i	$-0.114352\pi$
$12$	−3.80335	−	1.94442i	−1.09793	−	0.561306i
$13$			1.09190i			0.302837i	0.988470	+	0.151419i	$0.0483842\pi$
$13$			1.09190i			0.302837i	−0.988470	+	0.151419i	$0.951616\pi$
$14$	0.868230	+	3.63953i	0.232044	+	0.972705i
$15$		0			0
$16$	2.34233	+	3.24245i	0.585582	+	0.810613i
$17$			4.98074i			1.20801i	0.796982	+	0.604003i	$0.206429\pi$
$17$			4.98074i			1.20801i	−0.796982	+	0.604003i	$0.793571\pi$
$18$	2.14700	+	0.516994i	0.506053	+	0.121857i
$19$	−2.57501			−0.590748			−0.295374	−	0.955382i	$-0.595444\pi$
$19$	−2.57501			−0.590748			−0.295374	+	0.955382i	$0.595444\pi$
$20$		0			0
$21$	−2.56155	−	5.03680i	−0.558977	−	1.09912i
$22$	0.772087	−	3.20636i	0.164609	−	0.683599i
$23$			6.04090i			1.25961i	0.776752	+	0.629807i	$0.216866\pi$
$23$			6.04090i			1.25961i	−0.776752	+	0.629807i	$0.783134\pi$
$24$	−4.58552	−	3.93261i	−0.936015	−	0.802741i
$25$		0			0
$26$	−0.361501	+	1.50126i	−0.0708962	+	0.294422i
$27$	3.07221			0.591246
$28$	−0.0112214	+	5.29149i	−0.00212065	+	0.999998i
$29$	−0.561553			−0.104278			−0.0521389	−	0.998640i	$-0.516604\pi$
$29$	−0.561553			−0.104278			−0.0521389	+	0.998640i	$0.516604\pi$
$30$		0			0
$31$	6.59603			1.18468			0.592341	−	0.805688i	$-0.298204\pi$
$31$	6.59603			1.18468			0.592341	+	0.805688i	$0.298204\pi$
$32$	2.14700	+	5.23358i	0.379540	+	0.925175i
$33$			4.98074i			0.867035i
$34$	−1.64901	+	6.84809i	−0.282802	+	1.17444i
$35$		0			0
$36$	2.78078	+	1.42164i	0.463463	+	0.236941i
$37$	−5.49966			−0.904138			−0.452069	−	0.891983i	$-0.649314\pi$
$37$	−5.49966			−0.904138			−0.452069	+	0.891983i	$0.649314\pi$
$38$	−3.54042	−	0.852526i	−0.574332	−	0.138298i
$39$		−	2.33205i		−	0.373427i
$40$		0			0
$41$			8.48528i			1.32518i	0.748983	+	0.662589i	$0.230542\pi$
$41$			8.48528i			1.32518i	−0.748983	+	0.662589i	$0.769458\pi$
$42$	−1.85435	−	7.77323i	−0.286132	−	1.19944i
$43$		−	1.32431i		−	0.201955i	−0.994889	−	0.100977i	$-0.967803\pi$
$43$		−	1.32431i		−	0.201955i	0.994889	−	0.100977i	$-0.0321970\pi$
$44$	2.12311	−	4.15286i	0.320070	−	0.626067i
$45$		0			0
$46$	−2.00000	+	8.30571i	−0.294884	+	1.22461i
$47$	−9.74247			−1.42109			−0.710543	−	0.703654i	$-0.751550\pi$
$47$	−9.74247			−1.42109			−0.710543	+	0.703654i	$0.751550\pi$
$48$	−5.00270	−	6.92516i	−0.722077	−	0.999561i
$49$	−4.12311	+	5.65685i	−0.589015	+	0.808122i
$50$		0			0
$51$		−	10.6378i		−	1.48958i
$52$	−0.994066	+	1.94442i	−0.137852	+	0.269643i
$53$	8.58800			1.17965			0.589826	−	0.807530i	$-0.299196\pi$
$53$	8.58800			1.17965			0.589826	+	0.807530i	$0.299196\pi$
$54$	4.22402	+	1.01714i	0.574816	+	0.138415i
$55$		0			0
$56$	−1.76732	+	7.27163i	−0.236168	+	0.971712i
$57$	5.49966			0.728447
$58$	−0.772087	−	0.185917i	−0.101380	−	0.0244121i
$59$	14.3211			1.86444			0.932222	−	0.361888i	$-0.117868\pi$
$59$	14.3211			1.86444			0.932222	+	0.361888i	$0.117868\pi$
$60$		0			0
$61$			0.620058i			0.0793903i	0.999212	+	0.0396951i	$0.0126387\pi$
$61$			0.620058i			0.0793903i	−0.999212	+	0.0396951i	$0.987361\pi$
$62$	9.06897	+	2.18379i	1.15176	+	0.277342i
$63$	1.87285	+	3.68260i	0.235957	+	0.463964i
$64$	1.21922	+	7.90655i	0.152403	+	0.988318i
$65$		0			0
$66$	−1.64901	+	6.84809i	−0.202979	+	0.842941i
$67$		−	4.71659i		−	0.576223i	−0.957597	−	0.288112i	$-0.906973\pi$
$67$		−	4.71659i		−	0.576223i	0.957597	−	0.288112i	$-0.0930274\pi$
$68$	−4.53448	+	8.86958i	−0.549887	+	1.07559i
$69$		−	12.9020i		−	1.55322i
$70$		0			0
$71$		−	11.9473i		−	1.41789i	−0.705265	−	0.708943i	$-0.749172\pi$
$71$		−	11.9473i		−	1.41789i	0.705265	−	0.708943i	$-0.250828\pi$
$72$	3.35265	+	2.87529i	0.395114	+	0.338856i
$73$		−	9.96148i		−	1.16590i	−0.812507	−	0.582951i	$-0.801898\pi$
$73$		−	9.96148i		−	1.16590i	0.812507	−	0.582951i	$-0.198102\pi$
$74$	−7.56155	−	1.82081i	−0.879013	−	0.211665i
$75$		0			0
$76$	−4.58552	−	2.34430i	−0.525995	−	0.268910i
$77$	5.49966	−	2.79695i	0.626744	−	0.318742i
$78$	0.772087	−	3.20636i	0.0874216	−	0.363049i
$79$		−	10.6378i		−	1.19684i	−0.801182	−	0.598421i	$-0.795795\pi$
$79$		−	10.6378i		−	1.19684i	0.801182	−	0.598421i	$-0.204205\pi$
$80$		0			0
$81$	−11.2462			−1.24958
$82$	−2.80928	+	11.6665i	−0.310233	+	1.28835i
$83$	3.86098			0.423798			0.211899	−	0.977292i	$-0.432035\pi$
$83$	3.86098			0.423798			0.211899	+	0.977292i	$0.432035\pi$
$84$	0.0239665	−	11.3015i	0.00261496	−	1.23309i
$85$		0			0
$86$	0.438447	−	1.82081i	0.0472790	−	0.196343i
$87$	1.19935			0.128584
$88$	4.29400	−	5.00691i	0.457742	−	0.533738i
$89$			2.82843i			0.299813i	0.988700	+	0.149906i	$0.0478972\pi$
$89$			2.82843i			0.299813i	−0.988700	+	0.149906i	$0.952103\pi$
$90$		0			0
$91$	−2.57501	+	1.30957i	−0.269935	+	0.137280i
$92$	−5.49966	+	10.7575i	−0.573379	+	1.12155i
$93$	−14.0877			−1.46082
$94$	−13.3951	−	3.22550i	−1.38159	−	0.332685i
$95$		0			0
$96$	−4.58552	−	11.1778i	−0.468008	−	1.14083i
$97$		−	14.9422i		−	1.51715i	−0.651584	−	0.758576i	$-0.725895\pi$
$97$		−	14.9422i		−	1.51715i	0.651584	−	0.758576i	$-0.274105\pi$
$98$	−7.54177	+	6.41262i	−0.761834	+	0.647773i
$99$		−	3.64162i		−	0.365996i
$100$		0			0
$101$		−	15.1104i		−	1.50354i	−0.659425	−	0.751770i	$-0.729200\pi$
$101$		−	15.1104i		−	1.50354i	0.659425	−	0.751770i	$-0.270800\pi$
$102$	3.52191	−	14.6260i	0.348722	−	1.44819i
$103$	−5.47091			−0.539065			−0.269532	−	0.962991i	$-0.586869\pi$
$103$	−5.47091			−0.539065			−0.269532	+	0.962991i	$0.586869\pi$
$104$	−2.01051	+	2.34430i	−0.197147	+	0.229878i
$105$		0			0
$106$	11.8078	+	2.84329i	1.14687	+	0.276165i
$107$			10.0138i			0.968072i	0.875048	+	0.484036i	$0.160830\pi$
$107$			10.0138i			0.968072i	−0.875048	+	0.484036i	$0.839170\pi$
$108$	5.47091	+	2.79695i	0.526439	+	0.269136i
$109$	−4.56155			−0.436918			−0.218459	−	0.975846i	$-0.570103\pi$
$109$	−4.56155			−0.436918			−0.218459	+	0.975846i	$0.570103\pi$
$110$		0			0
$111$	11.7460			1.11489
$112$	−4.83738	+	9.41275i	−0.457089	+	0.889421i
$113$	5.49966			0.517364			0.258682	−	0.965963i	$-0.416712\pi$
$113$	5.49966			0.517364			0.258682	+	0.965963i	$0.416712\pi$
$114$	7.56155	+	1.82081i	0.708204	+	0.170534i
$115$		0			0
$116$	−1.00000	−	0.511240i	−0.0928477	−	0.0474674i
$117$			1.70505i			0.157632i
$118$	19.6902	+	4.74137i	1.81263	+	0.436478i
$119$	−11.7460	+	5.97366i	−1.07676	+	0.547605i
$120$		0			0
$121$	5.56155			0.505596
$122$	−0.205287	+	0.852526i	−0.0185858	+	0.0771841i
$123$		−	18.1227i		−	1.63407i
$124$	11.7460	+	6.00505i	1.05483	+	0.539269i
$125$		0			0
$126$	1.35579	+	5.68332i	0.120783	+	0.506310i
$127$		−	5.29723i		−	0.470053i	−0.971989	−	0.235026i	$-0.924482\pi$
$127$		−	5.29723i		−	0.470053i	0.971989	−	0.235026i	$-0.0755177\pi$
$128$	−0.941346	+	11.2745i	−0.0832041	+	0.996533i
$129$			2.82843i			0.249029i
$130$		0			0
$131$	−2.57501			−0.224980			−0.112490	−	0.993653i	$-0.535883\pi$
$131$	−2.57501			−0.224980			−0.112490	+	0.993653i	$0.535883\pi$
$132$	−4.53448	+	8.86958i	−0.394676	+	0.771998i
$133$	−3.08835	−	6.07263i	−0.267794	−	0.526564i
$134$	1.56155	−	6.48490i	0.134898	−	0.560210i
$135$		0			0
$136$	−9.17104	+	10.6937i	−0.786410	+	0.916973i
$137$	3.08835			0.263855			0.131928	−	0.991259i	$-0.457883\pi$
$137$	3.08835			0.263855			0.131928	+	0.991259i	$0.457883\pi$
$138$	4.27156	−	17.7392i	0.363619	−	1.51006i
$139$	4.02102			0.341058			0.170529	−	0.985353i	$-0.445452\pi$
$139$	4.02102			0.341058			0.170529	+	0.985353i	$0.445452\pi$
$140$		0			0
$141$	20.8078			1.75233
$142$	3.95548	−	16.4265i	0.331937	−	1.37849i
$143$	2.54635			0.212937
$144$	3.65767	+	5.06326i	0.304806	+	0.421938i
$145$		0			0
$146$	3.29801	−	13.6962i	0.272946	−	1.13350i
$147$	8.80604	−	12.0818i	0.726310	−	0.996489i
$148$	−9.79366	−	5.00691i	−0.805034	−	0.411565i
$149$	2.00000			0.163846			0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000			0.163846			0.0819232	+	0.996639i	$0.473894\pi$
$150$		0			0
$151$			4.95118i			0.402922i	0.979497	+	0.201461i	$0.0645689\pi$
$151$			4.95118i			0.402922i	−0.979497	+	0.201461i	$0.935431\pi$
$152$	−5.52855	−	4.74137i	−0.448425	−	0.384576i
$153$			7.77769i			0.628789i
$154$	8.48756	−	2.02475i	0.683947	−	0.163159i
$155$		0			0
$156$	2.12311	−	4.15286i	0.169984	−	0.332495i
$157$		−	3.88884i		−	0.310364i	−0.987886	−	0.155182i	$-0.950404\pi$
$157$		−	3.88884i		−	0.310364i	0.987886	−	0.155182i	$-0.0495963\pi$
$158$	3.52191	−	14.6260i	0.280188	−	1.16358i
$159$	−18.3421			−1.45462
$160$		0			0
$161$	−14.2462	+	7.24517i	−1.12276	+	0.570999i
$162$	−15.4626	−	3.72336i	−1.21485	−	0.292535i
$163$		−	11.5012i		−	0.900840i	−0.892817	−	0.450420i	$-0.851274\pi$
$163$		−	11.5012i		−	0.900840i	0.892817	−	0.450420i	$-0.148726\pi$
$164$	−7.72503	+	15.1104i	−0.603224	+	1.17992i
$165$		0			0
$166$	5.30852	+	1.27828i	0.412021	+	0.0992139i
$167$	0.673500			0.0521170			0.0260585	−	0.999660i	$-0.491704\pi$
$167$	0.673500			0.0521170			0.0260585	+	0.999660i	$0.491704\pi$
$168$	3.77460	−	15.5306i	0.291217	−	1.19821i
$169$	11.8078			0.908290
$170$		0			0
$171$	−4.02102			−0.307495
$172$	1.20565	−	2.35829i	0.0919303	−	0.179818i
$173$		−	11.0534i		−	0.840372i	−0.907438	−	0.420186i	$-0.861965\pi$
$173$		−	11.0534i		−	0.840372i	0.907438	−	0.420186i	$-0.138035\pi$
$174$	1.64901	+	0.397078i	0.125011	+	0.0301024i
$175$		0			0
$176$	7.56155	−	5.46242i	0.569973	−	0.411746i
$177$	−30.5866			−2.29903
$178$	−0.936426	+	3.88884i	−0.0701881	+	0.291481i
$179$			8.30571i			0.620798i	0.950606	+	0.310399i	$0.100463\pi$
$179$			8.30571i			0.620798i	−0.950606	+	0.310399i	$0.899537\pi$
$180$		0			0
$181$		−	3.44849i		−	0.256324i	−0.991753	−	0.128162i	$-0.959092\pi$
$181$		−	3.44849i		−	0.256324i	0.991753	−	0.128162i	$-0.0409077\pi$
$182$	−3.97399	+	0.948017i	−0.294571	+	0.0702717i
$183$		−	1.32431i		−	0.0978956i
$184$	−11.1231	+	12.9698i	−0.820006	+	0.956147i
$185$		0			0
$186$	−19.3693	−	4.66410i	−1.42023	−	0.341988i
$187$	11.6153			0.849396
$188$	−17.3492	−	8.86958i	−1.26532	−	0.646881i
$189$	3.68466	+	7.24517i	0.268019	+	0.527008i
$190$		0			0
$191$			19.9660i			1.44469i	0.691535	+	0.722343i	$0.256935\pi$
$191$			19.9660i			1.44469i	−0.691535	+	0.722343i	$0.743065\pi$
$192$	−2.60399	−	16.8866i	−0.187927	−	1.21869i
$193$	−5.49966			−0.395874			−0.197937	−	0.980215i	$-0.563424\pi$
$193$	−5.49966			−0.395874			−0.197937	+	0.980215i	$0.563424\pi$
$194$	4.94702	−	20.5443i	0.355175	−	1.47499i
$195$		0			0
$196$	−12.4924	+	6.31990i	−0.892311	+	0.451421i
$197$	16.4990			1.17550			0.587751	−	0.809042i	$-0.300013\pi$
$197$	16.4990			1.17550			0.587751	+	0.809042i	$0.300013\pi$
$198$	1.20565	−	5.00691i	0.0856821	−	0.355825i
$199$	18.3421			1.30024			0.650118	−	0.759834i	$-0.274720\pi$
$199$	18.3421			1.30024			0.650118	+	0.759834i	$0.274720\pi$
$200$		0			0
$201$			10.0736i			0.710536i
$202$	5.00270	−	20.7755i	0.351989	−	1.46176i
$203$	−0.673500	−	1.32431i	−0.0472704	−	0.0929481i
$204$	9.68466	−	18.9435i	0.678062	−	1.32631i
$205$		0			0
$206$	−7.52203	−	1.81129i	−0.524085	−	0.126199i
$207$			9.43318i			0.655651i
$208$	−3.54042	+	2.55758i	−0.245484	+	0.177336i
$209$			6.00505i			0.415378i
$210$		0			0
$211$		−	0.287088i		−	0.0197640i	−0.999951	−	0.00988198i	$-0.996854\pi$
$211$		−	0.287088i		−	0.0197640i	0.999951	−	0.00988198i	$-0.00314558\pi$
$212$	15.2933	+	7.81855i	1.05035	+	0.536980i
$213$			25.5169i			1.74839i
$214$	−3.31534	+	13.7681i	−0.226632	+	0.941170i
$215$		0			0
$216$	6.59603	+	5.65685i	0.448803	+	0.384900i
$217$	7.91096	+	15.5554i	0.537031	+	1.05597i
$218$	−6.27174	−	1.51022i	−0.424776	−	0.102285i
$219$			21.2755i			1.43767i
$220$		0			0
$221$	−5.43845			−0.365830
$222$	16.1498	+	3.88884i	1.08390	+	0.261002i
$223$	0.147647			0.00988718			0.00494359	−	0.999988i	$-0.498426\pi$
$223$	0.147647			0.00988718			0.00494359	+	0.999988i	$0.498426\pi$
$224$	−9.76732	+	11.3402i	−0.652606	+	0.757697i
$225$		0			0
$226$	7.56155	+	1.82081i	0.502987	+	0.121118i
$227$	−10.1530			−0.673881			−0.336941	−	0.941526i	$-0.609392\pi$
$227$	−10.1530			−0.673881			−0.336941	+	0.941526i	$0.609392\pi$
$228$	9.79366	+	5.00691i	0.648601	+	0.331591i
$229$		−	9.45353i		−	0.624707i	−0.949966	−	0.312354i	$-0.898883\pi$
$229$		−	9.45353i		−	0.624707i	0.949966	−	0.312354i	$-0.101117\pi$
$230$		0			0
$231$	−11.7460	+	5.97366i	−0.772833	+	0.393038i
$232$	−1.20565	−	1.03399i	−0.0791551	−	0.0678846i
$233$	−10.9993			−0.720589			−0.360294	−	0.932839i	$-0.617324\pi$
$233$	−10.9993			−0.720589			−0.360294	+	0.932839i	$0.617324\pi$
$234$	−0.564503	+	2.34430i	−0.0369027	+	0.153252i
$235$		0			0
$236$	25.5026	+	13.0380i	1.66008	+	0.848698i
$237$			22.7199i			1.47582i
$238$	−18.1275	+	4.32443i	−1.17503	+	0.280311i
$239$			2.33205i			0.150848i	0.997152	+	0.0754238i	$0.0240310\pi$
$239$			2.33205i			0.150848i	−0.997152	+	0.0754238i	$0.975969\pi$
$240$		0			0
$241$			16.0786i			1.03572i	0.855466	+	0.517858i	$0.173271\pi$
$241$			16.0786i			1.03572i	−0.855466	+	0.517858i	$0.826729\pi$
$242$	7.64666	+	1.84130i	0.491546	+	0.118363i
$243$	14.8028			0.949601
$244$	−0.564503	+	1.10418i	−0.0361386	+	0.0706882i
$245$		0			0
$246$	6.00000	−	24.9171i	0.382546	−	1.58866i
$247$		−	2.81164i		−	0.178901i
$248$	14.1617	+	12.1453i	0.899267	+	0.771225i
$249$	−8.24621			−0.522582
$250$		0			0
$251$	−9.17104			−0.578871			−0.289435	−	0.957198i	$-0.593468\pi$
$251$	−9.17104			−0.578871			−0.289435	+	0.957198i	$0.593468\pi$
$252$	−0.0175229	+	8.26294i	−0.00110384	+	0.520516i
$253$	14.0877			0.885683
$254$	1.75379	−	7.28323i	0.110042	−	0.456991i
$255$		0			0
$256$	−5.02699	+	15.1898i	−0.314187	+	0.949361i
$257$			6.55137i			0.408663i	0.978902	+	0.204332i	$0.0655021\pi$
$257$			6.55137i			0.408663i	−0.978902	+	0.204332i	$0.934498\pi$
$258$	−0.936426	+	3.88884i	−0.0582994	+	0.242109i
$259$	−6.59603	−	12.9698i	−0.409857	−	0.805905i
$260$		0			0
$261$	−0.876894			−0.0542784
$262$	−3.54042	−	0.852526i	−0.218728	−	0.0526693i
$263$			23.5829i			1.45419i	0.686539	+	0.727093i	$0.259129\pi$
$263$			23.5829i			1.45419i	−0.686539	+	0.727093i	$0.740871\pi$
$264$	−9.17104	+	10.6937i	−0.564438	+	0.658149i
$265$		0			0
$266$	−2.23570	−	9.37183i	−0.137080	−	0.574624i
$267$		−	6.04090i		−	0.369697i
$268$	4.29400	−	8.39919i	0.262298	−	0.513062i
$269$			0.968253i			0.0590354i	0.999564	+	0.0295177i	$0.00939715\pi$
$269$			0.968253i			0.0590354i	−0.999564	+	0.0295177i	$0.990603\pi$
$270$		0			0
$271$	−6.59603			−0.400680			−0.200340	−	0.979726i	$-0.564205\pi$
$271$	−6.59603			−0.400680			−0.200340	+	0.979726i	$0.564205\pi$
$272$	−16.1498	+	11.6665i	−0.979226	+	0.707387i
$273$	5.49966	−	2.79695i	0.332854	−	0.169279i
$274$	4.24621	+	1.02248i	0.256523	+	0.0617703i
$275$		0			0
$276$	11.7460	−	22.9756i	0.707029	−	1.38297i
$277$	−19.5873			−1.17689			−0.588444	−	0.808538i	$-0.700259\pi$
$277$	−19.5873			−1.17689			−0.588444	+	0.808538i	$0.700259\pi$
$278$	5.52855	+	1.33126i	0.331580	+	0.0798440i
$279$	10.3000			0.616648
$280$		0			0
$281$	17.0540			1.01735			0.508677	−	0.860957i	$-0.330135\pi$
$281$	17.0540			1.01735			0.508677	+	0.860957i	$0.330135\pi$
$282$	28.6089	+	6.88897i	1.70363	+	0.410232i
$283$	7.45904			0.443394			0.221697	−	0.975116i	$-0.428840\pi$
$283$	7.45904			0.443394			0.221697	+	0.975116i	$0.428840\pi$
$284$	10.8769	−	21.2755i	0.645425	−	1.26247i
$285$		0			0
$286$	3.50102	+	0.843038i	0.207019	+	0.0498499i
$287$	−20.0108	+	10.1768i	−1.18120	+	0.600720i
$288$	3.35265	+	8.17252i	0.197557	+	0.481570i
$289$	−7.80776			−0.459280
$290$		0			0
$291$			31.9133i			1.87079i
$292$	9.06897	−	17.7392i	0.530721	−	1.03811i
$293$		−	14.4635i		−	0.844965i	−0.906371	−	0.422483i	$-0.861159\pi$
$293$		−	14.4635i		−	0.844965i	0.906371	−	0.422483i	$-0.138841\pi$
$294$	16.1076	−	13.6959i	0.939411	−	0.798764i
$295$		0			0
$296$	−11.8078	−	10.1265i	−0.686312	−	0.588592i
$297$		−	7.16453i		−	0.415728i
$298$	2.74983	+	0.662153i	0.159293	+	0.0383575i
$299$	−6.59603			−0.381458
$300$		0			0
$301$	3.12311	−	1.58831i	0.180013	−	0.0915487i
$302$	−1.63922	+	6.80745i	−0.0943266	+	0.391725i
$303$			32.2725i			1.85400i
$304$	−6.03152	−	8.34935i	−0.345932	−	0.478868i
$305$		0			0
$306$	−2.57501	+	10.6937i	−0.147204	+	0.611315i
$307$	−13.8987			−0.793243			−0.396622	−	0.917982i	$-0.629818\pi$
$307$	−13.8987			−0.793243			−0.396622	+	0.917982i	$0.629818\pi$
$308$	12.3400	+	0.0261689i	0.703137	+	0.00149111i
$309$	11.6847			0.664717
$310$		0			0
$311$	−1.44600			−0.0819954			−0.0409977	−	0.999159i	$-0.513054\pi$
$311$	−1.44600			−0.0819954			−0.0409977	+	0.999159i	$0.513054\pi$
$312$	4.29400	−	5.00691i	0.243100	−	0.283460i
$313$			7.16453i			0.404963i	0.979286	+	0.202482i	$0.0649006\pi$
$313$			7.16453i			0.404963i	−0.979286	+	0.202482i	$0.935099\pi$
$314$	1.28751	−	5.34683i	0.0726581	−	0.301739i
$315$		0			0
$316$	9.68466	−	18.9435i	0.544805	−	1.06565i
$317$	−24.4099			−1.37100			−0.685499	−	0.728073i	$-0.740416\pi$
$317$	−24.4099			−1.37100			−0.685499	+	0.728073i	$0.740416\pi$
$318$	−25.2188	−	6.07263i	−1.41420	−	0.340536i
$319$			1.30957i			0.0733217i
$320$		0			0
$321$		−	21.3873i		−	1.19372i
$322$	−21.9860	+	5.24489i	−1.22523	+	0.292286i
$323$		−	12.8255i		−	0.713628i
$324$	−20.0270	−	10.2386i	−1.11261	−	0.568811i
$325$		0			0
$326$	3.80776	−	15.8131i	0.210893	−	0.875806i
$327$	9.74247			0.538760
$328$	−15.6240	+	18.2179i	−0.862689	+	1.00592i
$329$	−11.6847	−	22.9756i	−0.644196	−	1.26669i
$330$		0			0
$331$		−	8.30571i		−	0.456523i	−0.973600	−	0.228262i	$-0.926696\pi$
$331$		−	8.30571i		−	0.456523i	0.973600	−	0.228262i	$-0.0733041\pi$
$332$	6.87555	+	3.51506i	0.377345	+	0.192914i
$333$	−8.58800			−0.470620
$334$	0.926004	+	0.222980i	0.0506687	+	0.0122009i
$335$		0			0
$336$	10.3316	−	20.1035i	0.563633	−	1.09674i
$337$	30.5866			1.66616			0.833080	−	0.553153i	$-0.186575\pi$
$337$	30.5866			1.66616			0.833080	+	0.553153i	$0.186575\pi$
$338$	16.2347	+	3.90928i	0.883049	+	0.212637i
$339$	−11.7460			−0.637958
$340$		0			0
$341$		−	15.3823i		−	0.832996i
$342$	−5.52855	−	1.33126i	−0.298950	−	0.0719866i
$343$	−18.2856	−	2.93893i	−0.987329	−	0.158687i
$344$	2.43845	−	2.84329i	0.131472	−	0.153300i
$345$		0			0
$346$	3.65951	−	15.1974i	0.196737	−	0.817019i
$347$			1.32431i			0.0710925i	0.999368	+	0.0355463i	$0.0113171\pi$
$347$			1.32431i			0.0710925i	−0.999368	+	0.0355463i	$0.988683\pi$
$348$	2.13578	+	1.09190i	0.114490	+	0.0585317i
$349$			18.8307i			1.00799i	0.863708	+	0.503993i	$0.168136\pi$
$349$			18.8307i			1.00799i	−0.863708	+	0.503993i	$0.831864\pi$
$350$		0			0
$351$			3.35453i			0.179051i
$352$	12.2050	−	5.00691i	0.650527	−	0.266869i
$353$		−	16.1685i		−	0.860564i	−0.902694	−	0.430282i	$-0.858414\pi$
$353$		−	16.1685i		−	0.860564i	0.902694	−	0.430282i	$-0.141586\pi$
$354$	−42.0540	−	10.1265i	−2.23514	−	0.538218i
$355$		0			0
$356$	−2.57501	+	5.03680i	−0.136475	+	0.266950i
$357$	25.0870	−	12.7584i	1.32774	−	0.675248i
$358$	−2.74983	+	11.4196i	−0.145333	+	0.603547i
$359$			10.3507i			0.546288i	0.961973	+	0.273144i	$0.0880635\pi$
$359$			10.3507i			0.546288i	−0.961973	+	0.273144i	$0.911937\pi$
$360$		0			0
$361$	−12.3693			−0.651017
$362$	1.14171	−	4.74137i	0.0600071	−	0.249201i
$363$	−11.8782			−0.623446
$364$	−5.77776	−	0.0122526i	−0.302837	−	0.000642213i
$365$		0			0
$366$	0.438447	−	1.82081i	0.0229180	−	0.0951752i
$367$	23.3783			1.22034			0.610168	−	0.792272i	$-0.291102\pi$
$367$	23.3783			1.22034			0.610168	+	0.792272i	$0.291102\pi$
$368$	−19.5873	+	14.1498i	−1.02106	+	0.737608i
$369$			13.2502i			0.689779i
$370$		0			0
$371$	10.3000	+	20.2530i	0.534752	+	1.05149i
$372$	−25.0870	−	12.8255i	−1.30070	−	0.664969i
$373$	11.6763			0.604578			0.302289	−	0.953216i	$-0.402249\pi$
$373$	11.6763			0.604578			0.302289	+	0.953216i	$0.402249\pi$
$374$	15.9701	+	3.84556i	0.825793	+	0.198849i
$375$		0			0
$376$	−20.9171	−	17.9388i	−1.07872	−	0.925124i
$377$		−	0.613157i		−	0.0315792i
$378$	2.66738	+	11.1814i	0.137195	+	0.575108i
$379$		−	24.9171i		−	1.27991i	−0.768414	−	0.639954i	$-0.778954\pi$
$379$		−	24.9171i		−	1.27991i	0.768414	−	0.639954i	$-0.221046\pi$
$380$		0			0
$381$			11.3137i			0.579619i
$382$	−6.61026	+	27.4515i	−0.338210	+	1.40454i
$383$	−18.6638			−0.953675			−0.476838	−	0.878991i	$-0.658217\pi$
$383$	−18.6638			−0.953675			−0.476838	+	0.878991i	$0.658217\pi$
$384$	2.01051	−	24.0798i	0.102598	−	1.22882i
$385$		0			0
$386$	−7.56155	−	1.82081i	−0.384873	−	0.0926767i
$387$		−	2.06798i		−	0.105121i
$388$	13.6035	−	26.6087i	0.690611	−	1.35085i
$389$	11.9309			0.604919			0.302460	−	0.953162i	$-0.402192\pi$
$389$	11.9309			0.604919			0.302460	+	0.953162i	$0.402192\pi$
$390$		0			0
$391$	−30.0881			−1.52162
$392$	−19.2683	+	4.55339i	−0.973195	+	0.229981i
$393$	5.49966			0.277421
$394$	22.6847	+	5.46242i	1.14284	+	0.275193i
$395$		0			0
$396$	3.31534	−	6.48490i	0.166602	−	0.325879i
$397$		−	21.0149i		−	1.05471i	−0.849647	−	0.527353i	$-0.823185\pi$
$397$		−	21.0149i		−	1.05471i	0.849647	−	0.527353i	$-0.176815\pi$
$398$	25.2188	+	6.07263i	1.26410	+	0.304394i
$399$	6.59603	+	12.9698i	0.330214	+	0.649303i
$400$		0			0
$401$	13.4384			0.671084			0.335542	−	0.942025i	$-0.391081\pi$
$401$	13.4384			0.671084			0.335542	+	0.942025i	$0.391081\pi$
$402$	−3.33513	+	13.8503i	−0.166341	+	0.690791i
$403$			7.20217i			0.358766i
$404$	13.7566	−	26.9082i	0.684414	−	1.33873i
$405$		0			0
$406$	−0.487557	−	2.04379i	−0.0241971	−	0.101432i
$407$			12.8255i			0.635734i
$408$	19.5873	−	22.8393i	0.969717	−	1.13071i
$409$		−	30.2208i		−	1.49432i	−0.664643	−	0.747161i	$-0.731417\pi$
$409$		−	30.2208i		−	1.49432i	0.664643	−	0.747161i	$-0.268583\pi$
$410$		0			0
$411$	−6.59603			−0.325358
$412$	−9.74247	−	4.98074i	−0.479977	−	0.245383i
$413$	17.1760	+	33.7733i	0.845176	+	1.66187i
$414$	−3.12311	+	12.9698i	−0.153492	+	0.637431i
$415$		0			0
$416$	−5.71453	+	2.34430i	−0.280178	+	0.114939i
$417$	−8.58800			−0.420556
$418$	−1.98813	+	8.25643i	−0.0972427	+	0.403835i
$419$	−22.3631			−1.09251			−0.546254	−	0.837619i	$-0.683947\pi$
$419$	−22.3631			−1.09251			−0.546254	+	0.837619i	$0.683947\pi$
$420$		0			0
$421$	12.5616			0.612213			0.306106	−	0.951997i	$-0.400974\pi$
$421$	12.5616			0.612213			0.306106	+	0.951997i	$0.400974\pi$
$422$	0.0950482	−	0.394722i	0.00462688	−	0.0192147i
$423$	−15.2134			−0.739700
$424$	18.4384	+	15.8131i	0.895450	+	0.767952i
$425$		0			0
$426$	−8.44804	+	35.0835i	−0.409309	+	1.69980i
$427$	−1.46228	+	0.743668i	−0.0707647	+	0.0359886i
$428$	−9.11662	+	17.8324i	−0.440668	+	0.861960i
$429$	−5.43845			−0.262571
$430$		0			0
$431$		−	11.6602i		−	0.561654i	−0.959758	−	0.280827i	$-0.909391\pi$
$431$		−	11.6602i		−	0.561654i	0.959758	−	0.280827i	$-0.0906087\pi$
$432$	7.19612	+	9.96148i	0.346223	+	0.479272i
$433$			9.00400i			0.432705i	0.976315	+	0.216352i	$0.0694160\pi$
$433$			9.00400i			0.432705i	−0.976315	+	0.216352i	$0.930584\pi$
$434$	5.72687	+	24.0064i	0.274899	+	1.15235i
$435$		0			0
$436$	−8.12311	−	4.15286i	−0.389026	−	0.198886i
$437$		−	15.5554i		−	0.744114i
$438$	−7.04383	+	29.2520i	−0.336567	+	1.39771i
$439$	31.5341			1.50504			0.752521	−	0.658568i	$-0.228838\pi$
$439$	31.5341			1.50504			0.752521	+	0.658568i	$0.228838\pi$
$440$		0			0
$441$	−6.43845	+	8.83348i	−0.306593	+	0.420642i
$442$	−7.47740	−	1.80054i	−0.355663	−	0.0856431i
$443$		−	17.5420i		−	0.833448i	−0.909033	−	0.416724i	$-0.863178\pi$
$443$		−	17.5420i		−	0.833448i	0.909033	−	0.416724i	$-0.136822\pi$
$444$	20.9171	+	10.6937i	0.992681	+	0.507498i
$445$		0			0
$446$	0.203002	+	0.0488825i	0.00961242	+	0.00231465i
$447$	−4.27156			−0.202038
$448$	−17.1837	+	12.3580i	−0.811853	+	0.583862i
$449$	−6.31534			−0.298039			−0.149020	−	0.988834i	$-0.547612\pi$
$449$	−6.31534			−0.298039			−0.149020	+	0.988834i	$0.547612\pi$
$450$		0			0
$451$	19.7881			0.931784
$452$	9.79366	+	5.00691i	0.460655	+	0.235505i
$453$		−	10.5746i		−	0.496840i
$454$	−13.9596	−	3.36144i	−0.655155	−	0.157760i
$455$		0			0
$456$	11.8078	+	10.1265i	0.552949	+	0.474218i
$457$	−10.3223			−0.482856			−0.241428	−	0.970419i	$-0.577616\pi$
$457$	−10.3223			−0.482856			−0.241428	+	0.970419i	$0.577616\pi$
$458$	3.12985	−	12.9978i	0.146248	−	0.607347i
$459$			15.3019i			0.714229i
$460$		0			0
$461$			21.1154i			0.983444i	0.870752	+	0.491722i	$0.163632\pi$
$461$			21.1154i			0.983444i	−0.870752	+	0.491722i	$0.836368\pi$
$462$	−18.1275	+	4.32443i	−0.843370	+	0.201191i
$463$			24.3266i			1.13055i	0.824901	+	0.565277i	$0.191231\pi$
$463$			24.3266i			1.13055i	−0.824901	+	0.565277i	$0.808769\pi$
$464$	−1.31534	−	1.82081i	−0.0610632	−	0.0845289i
$465$		0			0
$466$	−15.1231	−	3.64162i	−0.700564	−	0.168695i
$467$	23.1983			1.07349			0.536744	−	0.843745i	$-0.319654\pi$
$467$	23.1983			1.07349			0.536744	+	0.843745i	$0.319654\pi$
$468$	−1.55229	+	3.03632i	−0.0717545	+	0.140354i
$469$	11.1231	−	5.65685i	0.513617	−	0.261209i
$470$		0			0
$471$			8.30571i			0.382707i
$472$	30.7473	+	26.3694i	1.41526	+	1.21375i
$473$	−3.08835			−0.142002
$474$	−7.52203	+	31.2379i	−0.345498	+	1.43480i
$475$		0			0
$476$	−26.3555	−	0.0558911i	−1.20800	−	0.00256176i
$477$	13.4106			0.614030
$478$	−0.772087	+	3.20636i	−0.0353144	+	0.146656i
$479$	−30.0881			−1.37476			−0.687381	−	0.726297i	$-0.741240\pi$
$479$	−30.0881			−1.37476			−0.687381	+	0.726297i	$0.741240\pi$
$480$		0			0
$481$		−	6.00505i		−	0.273807i
$482$	−5.32326	+	22.1067i	−0.242468	+	1.00693i
$483$	30.4268	−	15.4741i	1.38447	−	0.704095i
$484$	9.90388	+	5.06326i	0.450176	+	0.230148i
$485$		0			0
$486$	20.3526	+	4.90086i	0.923212	+	0.222308i
$487$			1.16128i			0.0526225i	0.999654	+	0.0263112i	$0.00837610\pi$
$487$			1.16128i			0.0526225i	−0.999654	+	0.0263112i	$0.991624\pi$
$488$	−1.14171	+	1.33126i	−0.0516829	+	0.0602635i
$489$			24.5639i			1.11082i
$490$		0			0
$491$			14.2794i			0.644419i	0.946668	+	0.322210i	$0.104426\pi$
$491$			14.2794i			0.644419i	−0.946668	+	0.322210i	$0.895574\pi$
$492$	16.4990	−	32.2725i	0.743831	−	1.45495i
$493$		−	2.79695i		−	0.125968i
$494$	0.930870	−	3.86577i	0.0418818	−	0.173929i
$495$		0			0
$496$	15.4501	+	21.3873i	0.693729	+	0.960318i
$497$	28.1753	−	14.3291i	1.26384	−	0.642746i
$498$	−11.3378	−	2.73013i	−0.508060	−	0.122340i
$499$		−	25.6525i		−	1.14836i	−0.818727	−	0.574182i	$-0.805320\pi$
$499$		−	25.6525i		−	1.14836i	0.818727	−	0.574182i	$-0.194680\pi$
$500$		0			0
$501$	−1.43845			−0.0642651
$502$	−12.6094	−	3.03632i	−0.562785	−	0.135517i
$503$	−18.8114			−0.838761			−0.419380	−	0.907811i	$-0.637753\pi$
$503$	−18.8114			−0.838761			−0.419380	+	0.907811i	$0.637753\pi$
$504$	−2.75976	+	11.3550i	−0.122929	+	0.505793i
$505$		0			0
$506$	19.3693	+	4.66410i	0.861071	+	0.207344i
$507$	−25.2188			−1.12001
$508$	4.82262	−	9.43318i	0.213969	−	0.418530i
$509$			28.0124i			1.24163i	0.783958	+	0.620814i	$0.213198\pi$
$509$			28.0124i			1.24163i	−0.783958	+	0.620814i	$0.786802\pi$
$510$		0			0
$511$	23.4921	−	11.9473i	1.03923	−	0.528519i
$512$	−11.9407	+	19.2203i	−0.527707	+	0.849426i
$513$	−7.91096			−0.349278
$514$	−2.16901	+	9.00757i	−0.0956708	+	0.397307i
$515$		0			0
$516$	−2.57501	+	5.03680i	−0.113359	+	0.221733i
$517$			22.7199i			0.999220i
$518$	−4.77497	−	20.0162i	−0.209800	−	0.879460i
$519$			23.6076i			1.03626i
$520$		0			0
$521$			2.82843i			0.123916i	0.998079	+	0.0619578i	$0.0197344\pi$
$521$			2.82843i			0.123916i	−0.998079	+	0.0619578i	$0.980266\pi$
$522$	−1.20565	−	0.290319i	−0.0527701	−	0.0127069i
$523$	20.9472			0.915958			0.457979	−	0.888963i	$-0.348574\pi$
$523$	20.9472			0.915958			0.457979	+	0.888963i	$0.348574\pi$
$524$	−4.58552	−	2.34430i	−0.200319	−	0.102411i
$525$		0			0
$526$	−7.80776	+	32.4245i	−0.340435	+	1.41378i
$527$			32.8531i			1.43110i
$528$	−16.1498	+	11.6665i	−0.702830	+	0.507721i
$529$	−13.4924			−0.586627
$530$		0			0
$531$	22.3631			0.970476
$532$	0.0288954	−	13.6256i	0.00125277	−	0.590747i
$533$	−9.26504			−0.401313
$534$	2.00000	−	8.30571i	0.0865485	−	0.359423i
$535$		0			0
$536$	8.68466	−	10.1265i	0.375120	−	0.437399i
$537$		−	17.7392i		−	0.765502i
$538$	−0.320566	+	1.33126i	−0.0138206	+	0.0573949i
$539$	13.1921	+	9.61528i	0.568222	+	0.414159i
$540$		0			0
$541$	−19.4384			−0.835724			−0.417862	−	0.908510i	$-0.637220\pi$
$541$	−19.4384			−0.835724			−0.417862	+	0.908510i	$0.637220\pi$
$542$	−9.06897	−	2.18379i	−0.389546	−	0.0938019i
$543$			7.36520i			0.316071i
$544$	−26.0671	+	10.6937i	−1.11762	+	0.458486i
$545$		0			0
$546$	8.48756	−	2.02475i	0.363234	−	0.0866515i
$547$		−	33.4337i		−	1.42952i	−0.699368	−	0.714762i	$-0.746535\pi$
$547$		−	33.4337i		−	1.42952i	0.699368	−	0.714762i	$-0.253465\pi$
$548$	5.49966	+	2.81164i	0.234934	+	0.120107i
$549$			0.968253i			0.0413240i
$550$		0			0
$551$	1.44600			0.0616019
$552$	23.7565	−	27.7006i	1.01114	−	1.17902i
$553$	25.0870	−	12.7584i	1.06681	−	0.542543i
$554$	−26.9309	−	6.48490i	−1.14418	−	0.275517i
$555$		0			0
$556$	7.16053	+	3.66075i	0.303674	+	0.155250i
$557$	8.58800			0.363885			0.181943	−	0.983309i	$-0.441761\pi$
$557$	8.58800			0.363885			0.181943	+	0.983309i	$0.441761\pi$
$558$	14.1617	+	3.41011i	0.599512	+	0.144361i
$559$	1.44600			0.0611595
$560$		0			0
$561$	−24.8078			−1.04738
$562$	23.4477	+	5.64617i	0.989084	+	0.238169i
$563$	6.78554			0.285977			0.142988	−	0.989724i	$-0.454329\pi$
$563$	6.78554			0.285977			0.142988	+	0.989724i	$0.454329\pi$
$564$	37.0540	+	18.9435i	1.56025	+	0.797664i
$565$		0			0
$566$	10.2555	+	2.46952i	0.431073	+	0.103801i
$567$	−13.4882	−	26.5219i	−0.566450	−	1.11381i
$568$	21.9986	−	25.6509i	0.923042	−	1.07629i
$569$	43.8617			1.83878			0.919390	−	0.393347i	$-0.128683\pi$
$569$	43.8617			1.83878			0.919390	+	0.393347i	$0.128683\pi$
$570$		0			0
$571$		−	15.5889i		−	0.652377i	−0.945305	−	0.326188i	$-0.894236\pi$
$571$		−	15.5889i		−	0.652377i	0.945305	−	0.326188i	$-0.105764\pi$
$572$	4.53448	+	2.31821i	0.189596	+	0.0969292i
$573$		−	42.6429i		−	1.78143i
$574$	−30.8824	+	7.36718i	−1.28901	+	0.307500i
$575$		0			0
$576$	1.90388	+	12.3465i	0.0793284	+	0.514437i
$577$			36.0915i			1.50251i	0.660013	+	0.751254i	$0.270551\pi$
$577$			36.0915i			1.50251i	−0.660013	+	0.751254i	$0.729449\pi$
$578$	−10.7350	−	2.58497i	−0.446517	−	0.107521i
$579$	11.7460			0.488149
$580$		0			0
$581$	4.63068	+	9.10534i	0.192113	+	0.377753i
$582$	−10.5657	+	43.8780i	−0.437964	+	1.81880i
$583$		−	20.0276i		−	0.829460i
$584$	18.3421	−	21.3873i	0.759001	−	0.885013i
$585$		0			0
$586$	4.78852	−	19.8860i	0.197812	−	0.821485i
$587$	2.80928			0.115951			0.0579757	−	0.998318i	$-0.481535\pi$
$587$	2.80928			0.115951			0.0579757	+	0.998318i	$0.481535\pi$
$588$	26.6809	−	13.4979i	1.10030	−	0.556645i
$589$	−16.9848			−0.699848
$590$		0			0
$591$	−35.2381			−1.44950
$592$	−12.8820	−	17.8324i	−0.529447	−	0.732906i
$593$			6.20705i			0.254893i	0.991845	+	0.127447i	$0.0406781\pi$
$593$			6.20705i			0.254893i	−0.991845	+	0.127447i	$0.959322\pi$
$594$	2.37201	−	9.85061i	0.0973247	−	0.404176i
$595$		0			0
$596$	3.56155	+	1.82081i	0.145887	+	0.0745832i
$597$	−39.1746			−1.60331
$598$	−9.06897	−	2.18379i	−0.370858	−	0.0893019i
$599$		−	17.9210i		−	0.732232i	−0.930569	−	0.366116i	$-0.880687\pi$
$599$		−	17.9210i		−	0.732232i	0.930569	−	0.366116i	$-0.119313\pi$
$600$		0			0
$601$		−	42.2309i		−	1.72263i	−0.508068	−	0.861317i	$-0.669640\pi$
$601$		−	42.2309i		−	1.72263i	0.508068	−	0.861317i	$-0.330360\pi$
$602$	4.81985	−	1.14980i	0.196443	−	0.0468625i
$603$		−	7.36520i		−	0.299934i
$604$	−4.50758	+	8.81695i	−0.183411	+	0.358757i
$605$		0			0
$606$	−10.6847	+	44.3718i	−0.434035	+	1.80248i
$607$	−44.9666			−1.82514			−0.912570	−	0.408921i	$-0.865905\pi$
$607$	−44.9666			−1.82514			−0.912570	+	0.408921i	$0.865905\pi$
$608$	−5.52855	−	13.4765i	−0.224212	−	0.546546i
$609$	1.43845	+	2.82843i	0.0582888	+	0.114614i
$610$		0			0
$611$		−	10.6378i		−	0.430358i
$612$	−7.08084	+	13.8503i	−0.286226	+	0.559866i
$613$	−47.7626			−1.92911			−0.964557	−	0.263874i	$-0.915000\pi$
$613$	−47.7626			−1.92911			−0.964557	+	0.263874i	$0.915000\pi$
$614$	−19.1096	−	4.60155i	−0.771200	−	0.185704i
$615$		0			0
$616$	16.9578	+	4.12147i	0.683249	+	0.166059i
$617$	−14.7647			−0.594404			−0.297202	−	0.954815i	$-0.596054\pi$
$617$	−14.7647			−0.594404			−0.297202	+	0.954815i	$0.596054\pi$
$618$	16.0654	+	3.86852i	0.646245	+	0.155615i
$619$	−26.0671			−1.04773			−0.523863	−	0.851803i	$-0.675510\pi$
$619$	−26.0671			−1.04773			−0.523863	+	0.851803i	$0.675510\pi$
$620$		0			0
$621$			18.5589i			0.744742i
$622$	−1.98813	−	0.478739i	−0.0797168	−	0.0191957i
$623$	−6.67026	+	3.39228i	−0.267238	+	0.135909i
$624$	7.56155	−	5.46242i	0.302704	−	0.218672i
$625$		0			0
$626$	−2.37201	+	9.85061i	−0.0948046	+	0.393710i
$627$		−	12.8255i		−	0.512200i
$628$	3.54042	−	6.92516i	0.141278	−	0.276344i
$629$		−	27.3924i		−	1.09220i
$630$		0			0
$631$		−	33.9582i		−	1.35186i	−0.736968	−	0.675928i	$-0.763743\pi$
$631$		−	33.9582i		−	1.35186i	0.736968	−	0.675928i	$-0.236257\pi$
$632$	19.5873	−	22.8393i	0.779142	−	0.908498i
$633$			0.613157i			0.0243708i
$634$	−33.5616	−	8.08156i	−1.33290	−	0.320960i
$635$		0			0
$636$	−32.6631	−	16.6987i	−1.29518	−	0.662147i
$637$	−6.17669	−	4.50200i	−0.244730	−	0.178376i
$638$	−0.433567	+	1.80054i	−0.0171651	+	0.0712842i
$639$		−	18.6564i		−	0.738035i
$640$		0			0
$641$	39.8617			1.57444			0.787222	−	0.616670i	$-0.211519\pi$
$641$	39.8617			1.57444			0.787222	+	0.616670i	$0.211519\pi$
$642$	7.08084	−	29.4057i	0.279458	−	1.16055i
$643$	36.8341			1.45260			0.726298	−	0.687380i	$-0.241239\pi$
$643$	36.8341			1.45260			0.726298	+	0.687380i	$0.241239\pi$
$644$	−31.9653	−	0.0677876i	−1.25961	−	0.00267121i
$645$		0			0
$646$	4.24621	−	17.6339i	0.167065	−	0.693797i
$647$	36.5712			1.43776			0.718881	−	0.695134i	$-0.244655\pi$
$647$	36.5712			1.43776			0.718881	+	0.695134i	$0.244655\pi$
$648$	−24.1456	−	20.7077i	−0.948530	−	0.813474i
$649$		−	33.3974i		−	1.31096i
$650$		0			0
$651$	−16.8961	−	33.2228i	−0.662209	−	1.30211i
$652$	10.4707	−	20.4810i	0.410064	−	0.802097i
$653$	−16.4990			−0.645654			−0.322827	−	0.946458i	$-0.604633\pi$
$653$	−16.4990			−0.645654			−0.322827	+	0.946458i	$0.604633\pi$
$654$	13.3951	+	3.22550i	0.523788	+	0.126127i
$655$		0			0
$656$	−27.5131	+	19.8753i	−1.07421	+	0.776001i
$657$		−	15.5554i		−	0.606873i
$658$	−8.45871	−	35.4580i	−0.329755	−	1.38230i
$659$			42.8381i			1.66874i	0.551207	+	0.834368i	$0.314167\pi$
$659$			42.8381i			1.66874i	−0.551207	+	0.834368i	$0.685833\pi$
$660$		0			0
$661$			1.51198i			0.0588092i	0.999568	+	0.0294046i	$0.00936112\pi$
$661$			1.51198i			0.0588092i	−0.999568	+	0.0294046i	$0.990639\pi$
$662$	2.74983	−	11.4196i	0.106875	−	0.443837i
$663$	11.6153			0.451102
$664$	8.28954	+	7.10923i	0.321696	+	0.275892i
$665$		0			0
$666$	−11.8078	−	2.84329i	−0.457542	−	0.110175i
$667$		−	3.39228i		−	0.131350i
$668$	1.19935	+	0.613157i	0.0464044	+	0.0237238i
$669$	−0.315342			−0.0121918
$670$		0			0
$671$	1.44600			0.0558224
$672$	20.8608	−	24.2201i	0.804724	−	0.934311i
$673$	−14.0877			−0.543039			−0.271520	−	0.962433i	$-0.587526\pi$
$673$	−14.0877			−0.543039			−0.271520	+	0.962433i	$0.587526\pi$
$674$	42.0540	+	10.1265i	1.61986	+	0.390059i
$675$		0			0
$676$	21.0270	+	10.7498i	0.808730	+	0.413455i
$677$			46.5317i			1.78836i	0.447709	+	0.894179i	$0.352240\pi$
$677$			46.5317i			1.78836i	−0.447709	+	0.894179i	$0.647760\pi$
$678$	−16.1498	−	3.88884i	−0.620230	−	0.149350i
$679$	35.2381	−	17.9210i	1.35232	−	0.687745i
$680$		0			0
$681$	21.6847			0.830958
$682$	5.09271	−	21.1493i	0.195010	−	0.809847i
$683$		−	20.1907i		−	0.772574i	−0.922379	−	0.386287i	$-0.873757\pi$
$683$		−	20.1907i		−	0.772574i	0.922379	−	0.386287i	$-0.126243\pi$
$684$	−7.16053	−	3.66075i	−0.273790	−	0.139972i
$685$		0			0
$686$	−24.1681	−	10.0947i	−0.922742	−	0.385418i
$687$			20.1907i			0.770322i
$688$	4.29400	−	3.10196i	0.163707	−	0.118261i
$689$			9.37720i			0.357243i
$690$		0			0
$691$	37.8132			1.43848			0.719240	−	0.694761i	$-0.244490\pi$
$691$	37.8132			1.43848			0.719240	+	0.694761i	$0.244490\pi$
$692$	10.0630	−	19.6836i	0.382539	−	0.748258i
$693$	8.58800	−	4.36758i	0.326231	−	0.165911i
$694$	−0.438447	+	1.82081i	−0.0166432	+	0.0691169i
$695$		0			0
$696$	2.57501	+	2.20837i	0.0976056	+	0.0837080i
$697$	−42.2630			−1.60082
$698$	−6.23442	+	25.8906i	−0.235976	+	0.979975i
$699$	23.4921			0.888553
$700$		0			0
$701$	−30.6695			−1.15837			−0.579186	−	0.815196i	$-0.696629\pi$
$701$	−30.6695			−1.15837			−0.579186	+	0.815196i	$0.696629\pi$
$702$	−1.11061	+	4.61219i	−0.0419171	+	0.174076i
$703$	14.1617			0.534118
$704$	18.4384	−	2.84329i	0.694925	−	0.107160i
$705$		0			0
$706$	5.35302	−	22.2303i	0.201464	−	0.836650i
$707$	35.6347	−	18.1227i	1.34018	−	0.681574i
$708$	−54.4679	−	27.8462i	−2.04703	−	1.04652i
$709$	−30.8078			−1.15701			−0.578505	−	0.815679i	$-0.696364\pi$
$709$	−30.8078			−1.15701			−0.578505	+	0.815679i	$0.696364\pi$
$710$		0			0
$711$		−	16.6114i		−	0.622977i
$712$	−5.20798	+	6.07263i	−0.195177	+	0.227582i
$713$			39.8459i			1.49224i
$714$	38.7164	−	9.23603i	1.44893	−	0.345650i
$715$		0			0
$716$	−7.56155	+	14.7906i	−0.282588	+	0.552751i
$717$		−	4.98074i		−	0.186009i
$718$	−3.42687	+	14.2313i	−0.127890	+	0.531107i
$719$	27.1961			1.01424			0.507122	−	0.861874i	$-0.330709\pi$
$719$	27.1961			1.01424			0.507122	+	0.861874i	$0.330709\pi$
$720$		0			0
$721$	−6.56155	−	12.9020i	−0.244365	−	0.480496i
$722$	−17.0067	−	4.09519i	−0.632926	−	0.152407i
$723$		−	34.3404i		−	1.27713i
$724$	3.13951	−	6.14098i	0.116679	−	0.228228i
$725$		0			0
$726$	−16.3316	−	3.93261i	−0.606121	−	0.145953i
$727$	32.8255			1.21743			0.608715	−	0.793389i	$-0.291685\pi$
$727$	32.8255			1.21743			0.608715	+	0.793389i	$0.291685\pi$
$728$	−7.93986	−	1.92973i	−0.294271	−	0.0715204i
$729$	2.12311			0.0786335
$730$		0			0
$731$	6.59603			0.243963
$732$	1.20565	−	2.35829i	0.0445623	−	0.0871651i
$733$			24.4250i			0.902156i	0.892484	+	0.451078i	$0.148960\pi$
$733$			24.4250i			0.902156i	−0.892484	+	0.451078i	$0.851040\pi$
$734$	32.1431	+	7.74001i	1.18642	+	0.285689i
$735$		0			0
$736$	−31.6155	+	12.9698i	−1.16536	+	0.478073i
$737$	−10.9993			−0.405165
$738$	−4.38684	+	18.2179i	−0.161482	+	0.670610i
$739$		−	49.5472i		−	1.82262i	−0.411718	−	0.911311i	$-0.635071\pi$
$739$		−	49.5472i		−	1.82262i	0.411718	−	0.911311i	$-0.364929\pi$
$740$		0			0
$741$			6.00505i			0.220601i
$742$	7.45637	+	31.2563i	0.273732	+	1.14745i
$743$			9.43318i			0.346070i	0.984916	+	0.173035i	$0.0553573\pi$
$743$			9.43318i			0.346070i	−0.984916	+	0.173035i	$0.944643\pi$
$744$	−30.2462	−	25.9396i	−1.10888	−	0.950992i
$745$		0			0
$746$	16.0540	+	3.86577i	0.587778	+	0.141536i
$747$	6.02913			0.220594
$748$	20.6843	+	10.5746i	0.756293	+	0.386647i
$749$	−23.6155	+	12.0101i	−0.862893	+	0.438839i
$750$		0			0
$751$		−	37.5999i		−	1.37204i	−0.727584	−	0.686019i	$-0.759357\pi$
$751$		−	37.5999i		−	1.37204i	0.727584	−	0.686019i	$-0.240643\pi$
$752$	−22.8201	−	31.5895i	−0.832162	−	1.15195i
$753$	19.5873			0.713801
$754$	0.203002	−	0.843038i	0.00739290	−	0.0307016i
$755$		0			0
$756$	−0.0344746	+	16.2565i	−0.00125383	+	0.591245i
$757$	25.7640			0.936409			0.468204	−	0.883620i	$-0.344901\pi$
$757$	25.7640			0.936409			0.468204	+	0.883620i	$0.344901\pi$
$758$	8.24948	−	34.2589i	0.299635	−	1.24434i
$759$	−30.0881			−1.09213
$760$		0			0
$761$		−	43.1228i		−	1.56320i	−0.623780	−	0.781600i	$-0.714404\pi$
$761$		−	43.1228i		−	1.56320i	0.623780	−	0.781600i	$-0.285596\pi$
$762$	−3.74571	+	15.5554i	−0.135693	+	0.563512i
$763$	−5.47091	−	10.7575i	−0.198060	−	0.389447i
$764$	−18.1771	+	35.5549i	−0.657624	+	1.28633i
$765$		0			0
$766$	−25.6611	−	6.17915i	−0.927173	−	0.223262i
$767$			15.6371i			0.564623i
$768$	10.7365	−	32.4420i	0.387421	−	1.17065i
$769$			14.4903i			0.522535i	0.965266	+	0.261267i	$0.0841404\pi$
$769$			14.4903i			0.522535i	−0.965266	+	0.261267i	$0.915860\pi$
$770$		0			0
$771$		−	13.9923i		−	0.503920i
$772$	−9.79366	−	5.00691i	−0.352481	−	0.180203i
$773$			15.6898i			0.564323i	0.959367	+	0.282161i	$0.0910513\pi$
$773$			15.6898i			0.564323i	−0.959367	+	0.282161i	$0.908949\pi$
$774$	0.684658	−	2.84329i	0.0246095	−	0.102200i
$775$		0			0
$776$	27.5131	−	32.0810i	0.987663	−	1.15164i
$777$	14.0877	+	27.7006i	0.505392	+	0.993755i
$778$	16.4039	+	3.95003i	0.588109	+	0.141616i
$779$		−	21.8497i		−	0.782847i
$780$		0			0
$781$	−27.8617			−0.996971
$782$	−41.3686	−	9.96148i	−1.47934	−	0.356222i
$783$	−1.72521			−0.0616538
$784$	−27.9997	−	0.118756i	−0.999991	−	0.00424130i
$785$		0			0
$786$	7.56155	+	1.82081i	0.269712	+	0.0649461i
$787$	−32.8578			−1.17126			−0.585628	−	0.810580i	$-0.699152\pi$
$787$	−32.8578			−1.17126			−0.585628	+	0.810580i	$0.699152\pi$
$788$	29.3810	+	15.0207i	1.04665	+	0.535091i
$789$		−	50.3680i		−	1.79315i
$790$		0			0
$791$	6.59603	+	12.9698i	0.234528	+	0.461153i
$792$	6.70531	−	7.81855i	0.238263	−	0.277820i
$793$	−0.677039			−0.0240423
$794$	6.95753	−	28.8936i	0.246913	−	1.02540i
$795$		0			0
$796$	32.6631	+	16.6987i	1.15771	+	0.591870i
$797$		−	2.04937i		−	0.0725925i	−0.999341	−	0.0362963i	$-0.988444\pi$
$797$		−	2.04937i		−	0.0725925i	0.999341	−	0.0362963i	$-0.0115560\pi$
$798$	4.77497	+	20.0162i	0.169032	+	0.708564i
$799$		−	48.5247i		−	1.71668i
$800$		0			0
$801$			4.41674i			0.156058i
$802$	18.4767	+	4.44916i	0.652435	+	0.157105i
$803$	−23.2306			−0.819792
$804$	−9.17104	+	17.9388i	−0.323438	+	0.632653i
$805$		0			0
$806$	−2.38447	+	9.90237i	−0.0839894	+	0.348796i
$807$		−	2.06798i		−	0.0727962i
$808$	27.8228	−	32.4420i	0.978802	−	1.14131i
$809$	27.0540			0.951167			0.475584	−	0.879671i	$-0.342237\pi$
$809$	27.0540			0.951167			0.475584	+	0.879671i	$0.342237\pi$
$810$		0			0
$811$	9.17104			0.322039			0.161019	−	0.986951i	$-0.448522\pi$
$811$	9.17104			0.322039			0.161019	+	0.986951i	$0.448522\pi$
$812$	0.00630143	−	2.97145i	0.000221137	−	0.104278i
$813$	14.0877			0.494076
$814$	−4.24621	+	17.6339i	−0.148830	+	0.618068i
$815$		0			0
$816$	34.4924	−	24.9171i	1.20748	−	0.872274i
$817$			3.41011i			0.119304i
$818$	10.0054	−	41.5510i	0.349830	−	1.45280i
$819$	−4.02102	+	2.04496i	−0.140506	+	0.0714567i
$820$		0			0
$821$	−35.9309			−1.25400			−0.626998	−	0.779021i	$-0.715717\pi$
$821$	−35.9309			−1.25400			−0.626998	+	0.779021i	$0.715717\pi$
$822$	−9.06897	−	2.18379i	−0.316317	−	0.0761685i
$823$			22.8393i			0.796127i	0.917358	+	0.398064i	$0.130318\pi$
$823$			22.8393i			0.796127i	−0.917358	+	0.398064i	$0.869682\pi$
$824$	−11.7460	−	10.0736i	−0.409193	−	0.350930i
$825$		0			0
$826$	12.4340	+	52.1219i	0.432634	+	1.81355i
$827$		−	4.71659i		−	0.164012i	−0.996632	−	0.0820059i	$-0.973867\pi$
$827$		−	4.71659i		−	0.164012i	0.996632	−	0.0820059i	$-0.0261326\pi$
$828$	−8.58800	+	16.7984i	−0.298454	+	0.583784i
$829$			43.3947i			1.50716i	0.657357	+	0.753579i	$0.271674\pi$
$829$			43.3947i			1.50716i	−0.657357	+	0.753579i	$0.728326\pi$
$830$		0			0
$831$	41.8342			1.45121
$832$	−8.63312	+	1.33126i	−0.299300	+	0.0461533i
$833$	−28.1753	−	20.5361i	−0.976217	−	0.711534i
$834$	−11.8078	−	2.84329i	−0.408869	−	0.0984550i
$835$		0			0
$836$	−5.46702	+	10.6937i	−0.189081	+	0.369848i
$837$	20.2644			0.700438
$838$	−30.7473	−	7.40390i	−1.06215	−	0.255763i
$839$	−32.3461			−1.11671			−0.558356	−	0.829601i	$-0.688568\pi$
$839$	−32.3461			−1.11671			−0.558356	+	0.829601i	$0.688568\pi$
$840$		0			0
$841$	−28.6847			−0.989126
$842$	17.2711	+	4.15884i	0.595200	+	0.143323i
$843$	−36.4235			−1.25449
$844$	0.261366	−	0.511240i	0.00899660	−	0.0175976i
$845$		0			0
$846$	−20.9171	−	5.03680i	−0.719144	−	0.173169i
$847$	6.67026	+	13.1158i	0.229193	+	0.450664i
$848$	20.1159	+	27.8462i	0.690784	+	0.956242i
$849$	−15.9309			−0.546746
$850$		0			0
$851$		−	33.2228i		−	1.13886i
$852$	−23.2306	+	45.4398i	−0.795869	+	1.55674i
$853$		−	2.93137i		−	0.100368i	−0.998740	−	0.0501840i	$-0.984019\pi$
$853$		−	2.93137i		−	0.100368i	0.998740	−	0.0501840i	$-0.0159808\pi$
$854$	−2.25672	+	0.538353i	−0.0772233	+	0.0184221i
$855$		0			0
$856$	−18.4384	+	21.4997i	−0.630213	+	0.734844i
$857$		−	5.59390i		−	0.191084i	−0.995425	−	0.0955419i	$-0.969542\pi$
$857$		−	5.59390i		−	0.191084i	0.995425	−	0.0955419i	$-0.0304584\pi$
$858$	−7.47740	−	1.80054i	−0.255274	−	0.0614695i
$859$	9.17104			0.312912			0.156456	−	0.987685i	$-0.449993\pi$
$859$	9.17104			0.312912			0.156456	+	0.987685i	$0.449993\pi$
$860$		0			0
$861$	42.7386	−	21.7355i	1.45653	−	0.740744i
$862$	3.86043	−	16.0318i	0.131487	−	0.546046i
$863$			30.7851i			1.04794i	0.851737	+	0.523969i	$0.175549\pi$
$863$			30.7851i			1.04794i	−0.851737	+	0.523969i	$0.824451\pi$
$864$	6.59603	+	16.0786i	0.224401	+	0.547007i
$865$		0			0
$866$	−2.98102	+	12.3797i	−0.101299	+	0.420680i
$867$	16.6757			0.566335
$868$	−0.0740170	+	34.9028i	−0.00251230	+	1.18468i
$869$	−24.8078			−0.841546
$870$		0			0
$871$	5.15002			0.174502
$872$	−9.79366	−	8.39919i	−0.331655	−	0.284432i
$873$		−	23.3331i		−	0.789705i
$874$	5.15002	−	21.3873i	0.174202	−	0.723436i
$875$		0			0
$876$	−19.3693	+	37.8869i	−0.654429	+	1.28008i
$877$	5.49966			0.185710			0.0928551	−	0.995680i	$-0.470401\pi$
$877$	5.49966			0.185710			0.0928551	+	0.995680i	$0.470401\pi$
$878$	43.3567	+	10.4402i	1.46322	+	0.352340i
$879$			30.8908i			1.04192i
$880$		0			0
$881$			30.7645i			1.03648i	0.855234	+	0.518241i	$0.173413\pi$
$881$			30.7645i			1.03648i	−0.855234	+	0.518241i	$0.826587\pi$
$882$	−11.7769	+	10.0136i	−0.396548	+	0.337177i
$883$		−	48.4902i		−	1.63183i	−0.578175	−	0.815913i	$-0.696235\pi$
$883$		−	48.4902i		−	1.63183i	0.578175	−	0.815913i	$-0.303765\pi$
$884$	−9.68466	−	4.95118i	−0.325730	−	0.166526i
$885$		0			0
$886$	5.80776	−	24.1188i	0.195116	−	0.810287i
$887$	−31.7738			−1.06686			−0.533429	−	0.845845i	$-0.679097\pi$
$887$	−31.7738			−1.06686			−0.533429	+	0.845845i	$0.679097\pi$
$888$	25.2188	+	21.6280i	0.846287	+	0.725788i
$889$	12.4924	−	6.35324i	0.418982	−	0.213081i
$890$		0			0
$891$			26.2267i			0.878628i
$892$	0.262926	+	0.134418i	0.00880343	+	0.00450066i
$893$	25.0870			0.839503
$894$	−5.87302	−	1.41421i	−0.196423	−	0.0472984i
$895$		0			0
$896$	−27.7175	+	11.3021i	−0.925978	+	0.377577i
$897$	14.0877			0.470373
$898$	−8.68305	−	2.09086i	−0.289757	−	0.0697730i
$899$	−3.70402			−0.123536
$900$		0			0
$901$			42.7746i			1.42503i
$902$	27.2069	+	6.55137i	0.905891	+	0.218137i
$903$	−6.67026	+	3.39228i	−0.221972	+	0.112888i
$904$	11.8078	+	10.1265i	0.392720	+	0.336803i
$905$		0			0
$906$	3.50102	−	14.5392i	0.116313	−	0.483033i
$907$			53.7874i			1.78598i	0.450074	+	0.892991i	$0.351397\pi$
$907$			53.7874i			1.78598i	−0.450074	+	0.892991i	$0.648603\pi$
$908$	−18.0803	−	9.24337i	−0.600016	−	0.306752i
$909$		−	23.5957i		−	0.782619i
$910$		0			0
$911$			56.0950i			1.85851i	0.369438	+	0.929255i	$0.379550\pi$
$911$			56.0950i			1.85851i	−0.369438	+	0.929255i	$0.620450\pi$
$912$	12.8820	+	17.8324i	0.426566	+	0.590489i
$913$		−	9.00400i		−	0.297989i
$914$	−14.1922	−	3.41746i	−0.469437	−	0.113040i
$915$		0			0
$916$	8.60654	−	16.8346i	0.284368	−	0.556232i
$917$	−3.08835	−	6.07263i	−0.101986	−	0.200536i
$918$	−5.06609	+	21.0387i	−0.167206	+	0.694382i
$919$			39.1965i			1.29297i	0.762925	+	0.646487i	$0.223762\pi$
$919$			39.1965i			1.29297i	−0.762925	+	0.646487i	$0.776238\pi$
$920$		0			0
$921$	29.6847			0.978143
$922$	−6.99083	+	29.0319i	−0.230231	+	0.956115i
$923$	13.0452			0.429389
$924$	−26.3555	−	0.0558911i	−0.867033	−	0.00183868i
$925$		0			0
$926$	−8.05398	+	33.4470i	−0.264670	+	1.09914i
$927$	−8.54312			−0.280593
$928$	−1.20565	−	2.93893i	−0.0395775	−	0.0964752i
$929$			28.9807i			0.950825i	0.879763	+	0.475412i	$0.157701\pi$
$929$			28.9807i			0.950825i	−0.879763	+	0.475412i	$0.842299\pi$
$930$		0			0
$931$	10.6170	−	14.5665i	0.347960	−	0.477397i
$932$	−19.5873	−	10.0138i	−0.641604	−	0.328013i
$933$	3.08835			0.101108
$934$	31.8956	+	7.68041i	1.04366	+	0.251311i
$935$		0			0
$936$	−3.13951	+	3.66075i	−0.102618	+	0.119655i
$937$		−	49.4631i		−	1.61589i	−0.589259	−	0.807944i	$-0.700580\pi$
$937$		−	49.4631i		−	1.61589i	0.589259	−	0.807944i	$-0.299420\pi$
$938$	17.1662	−	4.09509i	0.560495	−	0.133709i
$939$		−	15.3019i		−	0.499357i
$940$		0			0
$941$		−	8.75714i		−	0.285475i	−0.989761	−	0.142737i	$-0.954410\pi$
$941$		−	8.75714i		−	0.285475i	0.989761	−	0.142737i	$-0.0455904\pi$
$942$	−2.74983	+	11.4196i	−0.0895942	+	0.372072i
$943$	−51.2587			−1.66921
$944$	33.5446	+	46.4354i	1.09179	+	1.51134i
$945$		0			0
$946$	−4.24621	−	1.02248i	−0.138056	−	0.0332437i
$947$		−	52.6261i		−	1.71012i	−0.518529	−	0.855060i	$-0.673520\pi$
$947$		−	52.6261i		−	1.71012i	0.518529	−	0.855060i	$-0.326480\pi$
$948$	−20.6843	+	40.4591i	−0.671795	+	1.31405i
$949$	10.8769			0.353079
$950$		0			0
$951$	52.1342			1.69057
$952$	−36.2181	−	8.80255i	−1.17383	−	0.285292i
$953$	31.2637			1.01273			0.506365	−	0.862319i	$-0.330989\pi$
$953$	31.2637			1.01273			0.506365	+	0.862319i	$0.330989\pi$
$954$	18.4384	+	4.43994i	0.596967	+	0.143748i
$955$		0			0
$956$	−2.12311	+	4.15286i	−0.0686661	+	0.134313i
$957$		−	2.79695i		−	0.0904125i
$958$	−41.3686	−	9.96148i	−1.33656	−	0.321841i
$959$	3.70402	+	7.28323i	0.119609	+	0.235188i
$960$		0			0
$961$	12.5076			0.403470
$962$	1.98813	−	8.25643i	0.0641000	−	0.266198i
$963$			15.6371i			0.503899i
$964$	−14.6381	+	28.6325i	−0.471460	+	0.922190i
$965$		0			0
$966$	46.9573	−	11.2019i	1.51083	−	0.360416i
$967$		−	16.2177i		−	0.521527i	−0.965403	−	0.260764i	$-0.916026\pi$
$967$		−	16.2177i		−	0.521527i	0.965403	−	0.260764i	$-0.0839743\pi$
$968$	11.9407	+	10.2405i	0.383787	+	0.329142i
$969$			27.3924i			0.879969i
$970$		0			0
$971$	−36.3672			−1.16708			−0.583539	−	0.812085i	$-0.698332\pi$
$971$	−36.3672			−1.16708			−0.583539	+	0.812085i	$0.698332\pi$
$972$	26.3605	+	13.4765i	0.845513	+	0.432260i
$973$	4.82262	+	9.48274i	0.154606	+	0.304003i
$974$	−0.384472	+	1.59666i	−0.0123193	+	0.0511602i
$975$		0			0
$976$	−2.01051	+	1.45238i	−0.0643548	+	0.0464895i
$977$	14.0877			0.450704			0.225352	−	0.974277i	$-0.427647\pi$
$977$	14.0877			0.450704			0.225352	+	0.974277i	$0.427647\pi$
$978$	−8.13254	+	33.7733i	−0.260050	+	1.07995i
$979$	6.59603			0.210810
$980$		0			0
$981$	−7.12311			−0.227423
$982$	−4.72757	+	19.6329i	−0.150863	+	0.626511i
$983$	44.7361			1.42686			0.713430	−	0.700727i	$-0.247141\pi$
$983$	44.7361			1.42686			0.713430	+	0.700727i	$0.247141\pi$
$984$	33.3693	−	38.9094i	1.06377	−	1.24039i
$985$		0			0
$986$	0.926004	−	3.84556i	0.0294900	−	0.122468i
$987$	24.9559	+	49.0708i	0.794353	+	1.56194i
$988$	2.55973	−	5.00691i	0.0814359	−	0.159291i
$989$	8.00000			0.254385
$990$		0			0
$991$		−	0.574176i		−	0.0182393i	−0.999958	−	0.00911966i	$-0.997097\pi$
$991$		−	0.574176i		−	0.0182393i	0.999958	−	0.00911966i	$-0.00290292\pi$
$992$	14.1617	+	34.5209i	0.449634	+	1.09604i
$993$			17.7392i			0.562935i
$994$	43.4827	−	10.3730i	1.37919	−	0.329013i
$995$		0			0
$996$	−14.6847	−	7.50738i	−0.465301	−	0.237881i
$997$		−	47.7580i		−	1.51251i	−0.654276	−	0.756256i	$-0.727027\pi$
$997$		−	47.7580i		−	1.51251i	0.654276	−	0.756256i	$-0.272973\pi$
$998$	8.49295	−	35.2700i	0.268840	−	1.11645i
$999$	−16.8961			−0.534568

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.g.l.251.15		16
4.3	odd	2	inner	700.2.g.l.251.14		16
5.2	odd	4		140.2.c.b.139.8	yes	16
5.3	odd	4		140.2.c.b.139.9	yes	16
5.4	even	2	inner	700.2.g.l.251.2		16
7.6	odd	2	inner	700.2.g.l.251.16		16
20.3	even	4		140.2.c.b.139.6	yes	16
20.7	even	4		140.2.c.b.139.11	yes	16
20.19	odd	2	inner	700.2.g.l.251.3		16
28.27	even	2	inner	700.2.g.l.251.13		16
35.2	odd	12		980.2.s.f.619.15		32
35.3	even	12		980.2.s.f.19.12		32
35.12	even	12		980.2.s.f.619.16		32
35.13	even	4		140.2.c.b.139.10	yes	16
35.17	even	12		980.2.s.f.19.5		32
35.18	odd	12		980.2.s.f.19.11		32
35.23	odd	12		980.2.s.f.619.2		32
35.27	even	4		140.2.c.b.139.7	yes	16
35.32	odd	12		980.2.s.f.19.6		32
35.33	even	12		980.2.s.f.619.1		32
35.34	odd	2	inner	700.2.g.l.251.1		16
40.3	even	4		2240.2.e.f.2239.3		16
40.13	odd	4		2240.2.e.f.2239.15		16
40.27	even	4		2240.2.e.f.2239.13		16
40.37	odd	4		2240.2.e.f.2239.1		16
140.3	odd	12		980.2.s.f.19.15		32
140.23	even	12		980.2.s.f.619.5		32
140.27	odd	4		140.2.c.b.139.12	yes	16
140.47	odd	12		980.2.s.f.619.11		32
140.67	even	12		980.2.s.f.19.1		32
140.83	odd	4		140.2.c.b.139.5	✓	16
140.87	odd	12		980.2.s.f.19.2		32
140.103	odd	12		980.2.s.f.619.6		32
140.107	even	12		980.2.s.f.619.12		32
140.123	even	12		980.2.s.f.19.16		32
140.139	even	2	inner	700.2.g.l.251.4		16
280.13	even	4		2240.2.e.f.2239.2		16
280.27	odd	4		2240.2.e.f.2239.4		16
280.83	odd	4		2240.2.e.f.2239.14		16
280.237	even	4		2240.2.e.f.2239.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.c.b.139.5	✓	16	140.83	odd	4
140.2.c.b.139.6	yes	16	20.3	even	4
140.2.c.b.139.7	yes	16	35.27	even	4
140.2.c.b.139.8	yes	16	5.2	odd	4
140.2.c.b.139.9	yes	16	5.3	odd	4
140.2.c.b.139.10	yes	16	35.13	even	4
140.2.c.b.139.11	yes	16	20.7	even	4
140.2.c.b.139.12	yes	16	140.27	odd	4
700.2.g.l.251.1		16	35.34	odd	2	inner
700.2.g.l.251.2		16	5.4	even	2	inner
700.2.g.l.251.3		16	20.19	odd	2	inner
700.2.g.l.251.4		16	140.139	even	2	inner
700.2.g.l.251.13		16	28.27	even	2	inner
700.2.g.l.251.14		16	4.3	odd	2	inner
700.2.g.l.251.15		16	1.1	even	1	trivial
700.2.g.l.251.16		16	7.6	odd	2	inner
980.2.s.f.19.1		32	140.67	even	12
980.2.s.f.19.2		32	140.87	odd	12
980.2.s.f.19.5		32	35.17	even	12
980.2.s.f.19.6		32	35.32	odd	12
980.2.s.f.19.11		32	35.18	odd	12
980.2.s.f.19.12		32	35.3	even	12
980.2.s.f.19.15		32	140.3	odd	12
980.2.s.f.19.16		32	140.123	even	12
980.2.s.f.619.1		32	35.33	even	12
980.2.s.f.619.2		32	35.23	odd	12
980.2.s.f.619.5		32	140.23	even	12
980.2.s.f.619.6		32	140.103	odd	12
980.2.s.f.619.11		32	140.47	odd	12
980.2.s.f.619.12		32	140.107	even	12
980.2.s.f.619.15		32	35.2	odd	12
980.2.s.f.619.16		32	35.12	even	12
2240.2.e.f.2239.1		16	40.37	odd	4
2240.2.e.f.2239.2		16	280.13	even	4
2240.2.e.f.2239.3		16	40.3	even	4
2240.2.e.f.2239.4		16	280.27	odd	4
2240.2.e.f.2239.13		16	40.27	even	4
2240.2.e.f.2239.14		16	280.83	odd	4
2240.2.e.f.2239.15		16	40.13	odd	4
2240.2.e.f.2239.16		16	280.237	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37491 + 0.331077i) q^{2} -2.13578 q^{3} +(1.78078 + 0.910404i) q^{4} +(-2.93651 - 0.707107i) q^{6} +(1.19935 + 2.35829i) q^{7} +(2.14700 + 1.84130i) q^{8} +1.56155 q^{9} +O(q^{10})\)	\(q+(1.37491 + 0.331077i) q^{2} -2.13578 q^{3} +(1.78078 + 0.910404i) q^{4} +(-2.93651 - 0.707107i) q^{6} +(1.19935 + 2.35829i) q^{7} +(2.14700 + 1.84130i) q^{8} +1.56155 q^{9} -2.33205i q^{11} +(-3.80335 - 1.94442i) q^{12} +1.09190i q^{13} +(0.868230 + 3.63953i) q^{14} +(2.34233 + 3.24245i) q^{16} +4.98074i q^{17} +(2.14700 + 0.516994i) q^{18} -2.57501 q^{19} +(-2.56155 - 5.03680i) q^{21} +(0.772087 - 3.20636i) q^{22} +6.04090i q^{23} +(-4.58552 - 3.93261i) q^{24} +(-0.361501 + 1.50126i) q^{26} +3.07221 q^{27} +(-0.0112214 + 5.29149i) q^{28} -0.561553 q^{29} +6.59603 q^{31} +(2.14700 + 5.23358i) q^{32} +4.98074i q^{33} +(-1.64901 + 6.84809i) q^{34} +(2.78078 + 1.42164i) q^{36} -5.49966 q^{37} +(-3.54042 - 0.852526i) q^{38} -2.33205i q^{39} +8.48528i q^{41} +(-1.85435 - 7.77323i) q^{42} -1.32431i q^{43} +(2.12311 - 4.15286i) q^{44} +(-2.00000 + 8.30571i) q^{46} -9.74247 q^{47} +(-5.00270 - 6.92516i) q^{48} +(-4.12311 + 5.65685i) q^{49} -10.6378i q^{51} +(-0.994066 + 1.94442i) q^{52} +8.58800 q^{53} +(4.22402 + 1.01714i) q^{54} +(-1.76732 + 7.27163i) q^{56} +5.49966 q^{57} +(-0.772087 - 0.185917i) q^{58} +14.3211 q^{59} +0.620058i q^{61} +(9.06897 + 2.18379i) q^{62} +(1.87285 + 3.68260i) q^{63} +(1.21922 + 7.90655i) q^{64} +(-1.64901 + 6.84809i) q^{66} -4.71659i q^{67} +(-4.53448 + 8.86958i) q^{68} -12.9020i q^{69} -11.9473i q^{71} +(3.35265 + 2.87529i) q^{72} -9.96148i q^{73} +(-7.56155 - 1.82081i) q^{74} +(-4.58552 - 2.34430i) q^{76} +(5.49966 - 2.79695i) q^{77} +(0.772087 - 3.20636i) q^{78} -10.6378i q^{79} -11.2462 q^{81} +(-2.80928 + 11.6665i) q^{82} +3.86098 q^{83} +(0.0239665 - 11.3015i) q^{84} +(0.438447 - 1.82081i) q^{86} +1.19935 q^{87} +(4.29400 - 5.00691i) q^{88} +2.82843i q^{89} +(-2.57501 + 1.30957i) q^{91} +(-5.49966 + 10.7575i) q^{92} -14.0877 q^{93} +(-13.3951 - 3.22550i) q^{94} +(-4.58552 - 11.1778i) q^{96} -14.9422i q^{97} +(-7.54177 + 6.41262i) q^{98} -3.64162i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q + 12 * q^4 - 8 * q^9	\( 16 q + 12 q^{4} - 8 q^{9} + 4 q^{14} - 12 q^{16} - 8 q^{21} + 24 q^{29} + 28 q^{36} - 32 q^{44} - 32 q^{46} - 20 q^{56} + 36 q^{64} - 88 q^{74} - 48 q^{81} - 40 q^{84} + 40 q^{86}+O(q^{100}) \) 16 * q + 12 * q^4 - 8 * q^9 + 4 * q^14 - 12 * q^16 - 8 * q^21 + 24 * q^29 + 28 * q^36 - 32 * q^44 - 32 * q^46 - 20 * q^56 + 36 * q^64 - 88 * q^74 - 48 * q^81 - 40 * q^84 + 40 * q^86

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more