LMFDB - Embedded newform 116.2.i.a.93.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [116,2,Mod(5,116)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(116, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 11]))

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

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

chi := DirichletCharacter("116.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 116 = 2^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	116.i (of order $14$, degree $6$, 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:	$0.926264663447$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			93.1
Root			$-0.623490 + 0.781831i$ of defining polynomial
Character	$\chi$	$=$	116.93
Dual form			116.2.i.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.90097 - 0.433884i) q^{3} +(1.46950 - 1.84270i) q^{5} +(0.653989 - 2.86531i) q^{7} +(0.722521 + 0.347948i) q^{9} +O(q^{10})$	\(q+(-1.90097 - 0.433884i) q^{3} +(1.46950 - 1.84270i) q^{5} +(0.653989 - 2.86531i) q^{7} +(0.722521 + 0.347948i) q^{9} +(-0.376510 - 0.781831i) q^{11} +(3.87047 - 1.86392i) q^{13} +(-3.59299 + 2.86531i) q^{15} +4.86286i q^{17} +(-5.28501 + 1.20627i) q^{19} +(-2.48643 + 5.16312i) q^{21} +(2.33244 + 2.92478i) q^{23} +(-0.123490 - 0.541044i) q^{25} +(3.35086 + 2.67222i) q^{27} +(-4.38404 - 3.12733i) q^{29} +(4.27144 + 3.40636i) q^{31} +(0.376510 + 1.64960i) q^{33} +(-4.31886 - 5.41568i) q^{35} +(4.51357 - 9.37253i) q^{37} +(-8.16637 + 1.86392i) q^{39} +5.29150i q^{41} +(8.67725 - 6.91988i) q^{43} +(1.70291 - 0.820077i) q^{45} +(1.46466 + 3.04139i) q^{47} +(-1.47554 - 0.710583i) q^{49} +(2.10992 - 9.24415i) q^{51} +(-8.56734 + 10.7431i) q^{53} +(-1.99396 - 0.455108i) q^{55} +10.5700 q^{57} -7.60388 q^{59} +(0.961968 + 0.219563i) q^{61} +(1.46950 - 1.84270i) q^{63} +(2.25302 - 9.87113i) q^{65} +(3.71164 + 1.78743i) q^{67} +(-3.16487 - 6.57193i) q^{69} +(10.3644 - 4.99125i) q^{71} +(1.49127 - 1.18925i) q^{73} +1.08209i q^{75} +(-2.48643 + 0.567511i) q^{77} +(-3.61141 + 7.49917i) q^{79} +(-6.71044 - 8.41462i) q^{81} +(-0.199259 - 0.873009i) q^{83} +(8.96077 + 7.14598i) q^{85} +(6.97703 + 7.84711i) q^{87} +(-1.70679 - 1.36112i) q^{89} +(-2.80947 - 12.3091i) q^{91} +(-6.64191 - 8.32869i) q^{93} +(-5.54354 + 11.5113i) q^{95} +(-9.92274 + 2.26480i) q^{97} -0.695895i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 7 q^{3} - q^{5} + 9 q^{7} + 4 q^{9}+O(q^{10}) $ 6 * q - 7 * q^3 - q^5 + 9 * q^7 + 4 * q^9	$ 6 q - 7 q^{3} - q^{5} + 9 q^{7} + 4 q^{9} - 7 q^{11} + 9 q^{13} - 7 q^{15} - 7 q^{19} - 21 q^{21} + 15 q^{23} + 4 q^{25} - 7 q^{27} - 6 q^{29} + 7 q^{31} + 7 q^{33} - 33 q^{35} + 21 q^{37} - 7 q^{39} + 7 q^{43} - 3 q^{45} + 21 q^{47} - 18 q^{49} + 14 q^{51} - 5 q^{53} + 7 q^{55} + 14 q^{57} - 28 q^{59} + 21 q^{61} - q^{63} + 23 q^{65} + 25 q^{67} - 21 q^{69} + 29 q^{71} - 7 q^{73} - 21 q^{77} + 21 q^{79} - 2 q^{81} - 51 q^{83} + 28 q^{85} + 7 q^{87} - 35 q^{89} + 17 q^{91} - 7 q^{93} - 21 q^{95} - 49 q^{97}+O(q^{100}) $ 6 * q - 7 * q^3 - q^5 + 9 * q^7 + 4 * q^9 - 7 * q^11 + 9 * q^13 - 7 * q^15 - 7 * q^19 - 21 * q^21 + 15 * q^23 + 4 * q^25 - 7 * q^27 - 6 * q^29 + 7 * q^31 + 7 * q^33 - 33 * q^35 + 21 * q^37 - 7 * q^39 + 7 * q^43 - 3 * q^45 + 21 * q^47 - 18 * q^49 + 14 * q^51 - 5 * q^53 + 7 * q^55 + 14 * q^57 - 28 * q^59 + 21 * q^61 - q^63 + 23 * q^65 + 25 * q^67 - 21 * q^69 + 29 * q^71 - 7 * q^73 - 21 * q^77 + 21 * q^79 - 2 * q^81 - 51 * q^83 + 28 * q^85 + 7 * q^87 - 35 * q^89 + 17 * q^91 - 7 * q^93 - 21 * q^95 - 49 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/116\mathbb{Z}\right)^\times$.

$n$	$59$	$89$
$\chi(n)$	$1$	$e\left(\frac{3}{14}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.90097	−	0.433884i	−1.09752	−	0.250503i	−0.364840	−	0.931070i	$-0.618876\pi$
$3$	−1.90097	−	0.433884i	−1.09752	−	0.250503i	−0.732685	+	0.680568i	$0.761733\pi$
$4$		0			0
$5$	1.46950	−	1.84270i	0.657181	−	0.824078i	−0.335852	−	0.941915i	$-0.609024\pi$
$5$	1.46950	−	1.84270i	0.657181	−	0.824078i	0.993033	+	0.117836i	$0.0375958\pi$
$6$		0			0
$7$	0.653989	−	2.86531i	0.247185	−	1.08299i	−0.687129	−	0.726535i	$-0.741129\pi$
$7$	0.653989	−	2.86531i	0.247185	−	1.08299i	0.934314	−	0.356452i	$-0.116014\pi$
$8$		0			0
$9$	0.722521	+	0.347948i	0.240840	+	0.115983i
$10$		0			0
$11$	−0.376510	−	0.781831i	−0.113522	−	0.235731i	0.836465	−	0.548020i	$-0.184618\pi$
$11$	−0.376510	−	0.781831i	−0.113522	−	0.235731i	−0.949987	+	0.312289i	$0.898904\pi$
$12$		0			0
$13$	3.87047	−	1.86392i	1.07348	−	0.516958i	0.188250	−	0.982121i	$-0.439719\pi$
$13$	3.87047	−	1.86392i	1.07348	−	0.516958i	0.885225	+	0.465163i	$0.154004\pi$
$14$		0			0
$15$	−3.59299	+	2.86531i	−0.927706	+	0.739821i
$16$		0			0
$17$			4.86286i			1.17942i	0.807616	+	0.589709i	$0.200757\pi$
$17$			4.86286i			1.17942i	−0.807616	+	0.589709i	$0.799243\pi$
$18$		0			0
$19$	−5.28501	+	1.20627i	−1.21246	+	0.276737i	−0.780501	−	0.625154i	$-0.785036\pi$
$19$	−5.28501	+	1.20627i	−1.21246	+	0.276737i	−0.431963	+	0.901891i	$0.642179\pi$
$20$		0			0
$21$	−2.48643	+	5.16312i	−0.542583	+	1.12668i
$22$		0			0
$23$	2.33244	+	2.92478i	0.486347	+	0.609860i	0.963089	−	0.269184i	$-0.0867539\pi$
$23$	2.33244	+	2.92478i	0.486347	+	0.609860i	−0.476742	+	0.879043i	$0.658182\pi$
$24$		0			0
$25$	−0.123490	−	0.541044i	−0.0246980	−	0.108209i
$26$		0			0
$27$	3.35086	+	2.67222i	0.644872	+	0.514269i
$28$		0			0
$29$	−4.38404	−	3.12733i	−0.814096	−	0.580730i
$29$	−4.38404	−	3.12733i	−0.814096	−	0.580730i
$30$		0			0
$31$	4.27144	+	3.40636i	0.767173	+	0.611800i	0.926877	−	0.375365i	$-0.122483\pi$
$31$	4.27144	+	3.40636i	0.767173	+	0.611800i	−0.159704	+	0.987165i	$0.551054\pi$
$32$		0			0
$33$	0.376510	+	1.64960i	0.0655420	+	0.287158i
$34$		0			0
$35$	−4.31886	−	5.41568i	−0.730021	−	0.915418i
$36$		0			0
$37$	4.51357	−	9.37253i	0.742027	−	1.54083i	−0.0961075	−	0.995371i	$-0.530639\pi$
$37$	4.51357	−	9.37253i	0.742027	−	1.54083i	0.838134	−	0.545464i	$-0.183646\pi$
$38$		0			0
$39$	−8.16637	+	1.86392i	−1.30767	+	0.298466i
$40$		0			0
$41$			5.29150i			0.826394i	0.910642	+	0.413197i	$0.135588\pi$
$41$			5.29150i			0.826394i	−0.910642	+	0.413197i	$0.864412\pi$
$42$		0			0
$43$	8.67725	−	6.91988i	1.32327	−	1.05527i	0.329459	−	0.944170i	$-0.393134\pi$
$43$	8.67725	−	6.91988i	1.32327	−	1.05527i	0.993809	−	0.111102i	$-0.0354379\pi$
$44$		0			0
$45$	1.70291	−	0.820077i	0.253854	−	0.122250i
$46$		0			0
$47$	1.46466	+	3.04139i	0.213642	+	0.443632i	0.980058	−	0.198713i	$-0.0636760\pi$
$47$	1.46466	+	3.04139i	0.213642	+	0.443632i	−0.766416	+	0.642345i	$0.777962\pi$
$48$		0			0
$49$	−1.47554	−	0.710583i	−0.210792	−	0.101512i
$50$		0			0
$51$	2.10992	−	9.24415i	0.295447	−	1.29444i
$52$		0			0
$53$	−8.56734	+	10.7431i	−1.17681	+	1.47568i	−0.329846	+	0.944035i	$0.606997\pi$
$53$	−8.56734	+	10.7431i	−1.17681	+	1.47568i	−0.846968	+	0.531643i	$0.821575\pi$
$54$		0			0
$55$	−1.99396	−	0.455108i	−0.268865	−	0.0613668i
$56$		0			0
$57$	10.5700			1.40003
$58$		0			0
$59$	−7.60388			−0.989940			−0.494970	−	0.868910i	$-0.664821\pi$
$59$	−7.60388			−0.989940			−0.494970	+	0.868910i	$0.664821\pi$
$60$		0			0
$61$	0.961968	+	0.219563i	0.123167	+	0.0281121i	0.283660	−	0.958925i	$-0.408451\pi$
$61$	0.961968	+	0.219563i	0.123167	+	0.0281121i	−0.160493	+	0.987037i	$0.551308\pi$
$62$		0			0
$63$	1.46950	−	1.84270i	0.185140	−	0.232158i
$64$		0			0
$65$	2.25302	−	9.87113i	0.279453	−	1.22436i
$66$		0			0
$67$	3.71164	+	1.78743i	0.453448	+	0.218369i	0.646645	−	0.762791i	$-0.276171\pi$
$67$	3.71164	+	1.78743i	0.453448	+	0.218369i	−0.193197	+	0.981160i	$0.561886\pi$
$68$		0			0
$69$	−3.16487	−	6.57193i	−0.381006	−	0.791167i
$70$		0			0
$71$	10.3644	−	4.99125i	1.23003	−	0.592352i	0.297943	−	0.954584i	$-0.403699\pi$
$71$	10.3644	−	4.99125i	1.23003	−	0.592352i	0.932088	+	0.362232i	$0.117985\pi$
$72$		0			0
$73$	1.49127	−	1.18925i	0.174540	−	0.139191i	−0.532323	−	0.846541i	$-0.678681\pi$
$73$	1.49127	−	1.18925i	0.174540	−	0.139191i	0.706863	+	0.707350i	$0.250110\pi$
$74$		0			0
$75$			1.08209i			0.124949i
$76$		0			0
$77$	−2.48643	+	0.567511i	−0.283355	+	0.0646738i
$78$		0			0
$79$	−3.61141	+	7.49917i	−0.406315	+	0.843722i	0.592944	+	0.805244i	$0.297965\pi$
$79$	−3.61141	+	7.49917i	−0.406315	+	0.843722i	−0.999259	+	0.0384786i	$0.987749\pi$
$80$		0			0
$81$	−6.71044	−	8.41462i	−0.745604	−	0.934958i
$82$		0			0
$83$	−0.199259	−	0.873009i	−0.0218715	−	0.0958252i	0.962814	−	0.270165i	$-0.0870781\pi$
$83$	−0.199259	−	0.873009i	−0.0218715	−	0.0958252i	−0.984686	+	0.174339i	$0.944221\pi$
$84$		0			0
$85$	8.96077	+	7.14598i	0.971932	+	0.775090i
$86$		0			0
$87$	6.97703	+	7.84711i	0.748016	+	0.841299i
$88$		0			0
$89$	−1.70679	−	1.36112i	−0.180920	−	0.144279i	0.528843	−	0.848720i	$-0.322626\pi$
$89$	−1.70679	−	1.36112i	−0.180920	−	0.144279i	−0.709762	+	0.704441i	$0.751198\pi$
$90$		0			0
$91$	−2.80947	−	12.3091i	−0.294513	−	1.29034i
$92$		0			0
$93$	−6.64191	−	8.32869i	−0.688734	−	0.863645i
$94$		0			0
$95$	−5.54354	+	11.5113i	−0.568755	+	1.18103i
$96$		0			0
$97$	−9.92274	+	2.26480i	−1.00750	+	0.229956i	−0.694265	−	0.719719i	$-0.744270\pi$
$97$	−9.92274	+	2.26480i	−1.00750	+	0.229956i	−0.313237	+	0.949675i	$0.601413\pi$
$98$		0			0
$99$		−	0.695895i		−	0.0699401i
$100$		0			0
$101$	−4.00269	+	3.19204i	−0.398282	+	0.317620i	−0.802067	−	0.597235i	$-0.796266\pi$
$101$	−4.00269	+	3.19204i	−0.398282	+	0.317620i	0.403784	+	0.914854i	$0.367695\pi$
$102$		0			0
$103$	−5.78232	+	2.78462i	−0.569749	+	0.274377i	−0.696499	−	0.717558i	$-0.745260\pi$
$103$	−5.78232	+	2.78462i	−0.569749	+	0.274377i	0.126750	+	0.991935i	$0.459546\pi$
$104$		0			0
$105$	5.86025	+	12.1689i	0.571902	+	1.18757i
$106$		0			0
$107$	16.9291	+	8.15261i	1.63660	+	0.788143i	0.999854	+	0.0170652i	$0.00543228\pi$
$107$	16.9291	+	8.15261i	1.63660	+	0.788143i	0.636741	+	0.771078i	$0.280282\pi$
$108$		0			0
$109$	−2.41239	+	10.5694i	−0.231065	+	1.01236i	0.717694	+	0.696359i	$0.245198\pi$
$109$	−2.41239	+	10.5694i	−0.231065	+	1.01236i	−0.948759	+	0.316002i	$0.897659\pi$
$110$		0			0
$111$	−12.6468	+	15.8585i	−1.20038	+	1.50522i
$112$		0			0
$113$	−15.0356	−	3.43179i	−1.41443	−	0.322835i	−0.554051	−	0.832483i	$-0.686919\pi$
$113$	−15.0356	−	3.43179i	−1.41443	−	0.322835i	−0.860383	+	0.509648i	$0.829776\pi$
$114$		0			0
$115$	8.81700			0.822190
$116$		0			0
$117$	3.44504			0.318494
$118$		0			0
$119$	13.9336	+	3.18026i	1.27729	+	0.291534i
$120$		0			0
$121$	6.38889	−	8.01141i	0.580808	−	0.728310i
$122$		0			0
$123$	2.29590	−	10.0590i	0.207014	−	0.906988i
$124$		0			0
$125$	9.43900	+	4.54558i	0.844250	+	0.406569i
$126$		0			0
$127$	−1.58426	−	3.28975i	−0.140580	−	0.291918i	0.818777	−	0.574111i	$-0.194652\pi$
$127$	−1.58426	−	3.28975i	−0.140580	−	0.291918i	−0.959358	+	0.282193i	$0.908938\pi$
$128$		0			0
$129$	−19.4976	+	9.38955i	−1.71667	+	0.826704i
$130$		0			0
$131$	−7.46950	+	5.95673i	−0.652613	+	0.520442i	−0.892897	−	0.450261i	$-0.851331\pi$
$131$	−7.46950	+	5.95673i	−0.652613	+	0.520442i	0.240284	+	0.970703i	$0.422760\pi$
$132$		0			0
$133$			15.9321i			1.38149i
$134$		0			0
$135$	9.84817	−	2.24778i	0.847595	−	0.193458i
$136$		0			0
$137$	4.21528	−	8.75313i	0.360136	−	0.747830i	−0.639647	−	0.768669i	$-0.720919\pi$
$137$	4.21528	−	8.75313i	0.360136	−	0.747830i	0.999783	+	0.0208388i	$0.00663368\pi$
$138$		0			0
$139$	−11.7654	−	14.7533i	−0.997928	−	1.25136i	−0.967775	−	0.251817i	$-0.918972\pi$
$139$	−11.7654	−	14.7533i	−0.997928	−	1.25136i	−0.0301531	−	0.999545i	$-0.509599\pi$
$140$		0			0
$141$	−1.46466	−	6.41708i	−0.123346	−	0.540415i
$142$		0			0
$143$	−2.91454	−	2.32427i	−0.243726	−	0.194365i
$144$		0			0
$145$	−12.2051	+	3.48285i	−1.01358	+	0.289235i
$146$		0			0
$147$	2.49665	+	1.99101i	0.205920	+	0.164216i
$148$		0			0
$149$	−4.08157	−	17.8825i	−0.334375	−	1.46499i	−0.810563	−	0.585651i	$-0.800839\pi$
$149$	−4.08157	−	17.8825i	−0.334375	−	1.46499i	0.476188	−	0.879344i	$-0.342018\pi$
$150$		0			0
$151$	−2.83848	−	3.55934i	−0.230992	−	0.289655i	0.652804	−	0.757527i	$-0.273592\pi$
$151$	−2.83848	−	3.55934i	−0.230992	−	0.289655i	−0.883796	+	0.467872i	$0.845021\pi$
$152$		0			0
$153$	−1.69202	+	3.51352i	−0.136792	+	0.284051i
$154$		0			0
$155$	12.5538	−	2.86531i	1.00834	−	0.230148i
$156$		0			0
$157$		−	1.11613i		−	0.0890768i	−0.999008	−	0.0445384i	$-0.985818\pi$
$157$		−	1.11613i		−	0.0890768i	0.999008	−	0.0445384i	$-0.0141817\pi$
$158$		0			0
$159$	20.9475	−	16.7051i	1.66124	−	1.32480i
$160$		0			0
$161$	9.90581	−	4.77039i	0.780687	−	0.375959i
$162$		0			0
$163$	−5.72132	−	11.8805i	−0.448129	−	0.930549i	−0.995598	−	0.0937233i	$-0.970123\pi$
$163$	−5.72132	−	11.8805i	−0.448129	−	0.930549i	0.547470	−	0.836826i	$-0.315591\pi$
$164$		0			0
$165$	3.59299	+	1.73029i	0.279714	+	0.134703i
$166$		0			0
$167$	0.0893425	−	0.391435i	0.00691353	−	0.0302901i	−0.971354	−	0.237639i	$-0.923626\pi$
$167$	0.0893425	−	0.391435i	0.00691353	−	0.0302901i	0.978267	+	0.207349i	$0.0664836\pi$
$168$		0			0
$169$	3.40097	−	4.26468i	0.261613	−	0.328052i
$170$		0			0
$171$	−4.23825	−	0.967353i	−0.324107	−	0.0739753i
$172$		0			0
$173$	13.6039			1.03428			0.517142	−	0.855900i	$-0.326996\pi$
$173$	13.6039			1.03428			0.517142	+	0.855900i	$0.326996\pi$
$174$		0			0
$175$	−1.63102			−0.123294
$176$		0			0
$177$	14.4547	+	3.29920i	1.08648	+	0.247983i
$178$		0			0
$179$	−7.51842	+	9.42780i	−0.561953	+	0.704667i	−0.978917	−	0.204256i	$-0.934522\pi$
$179$	−7.51842	+	9.42780i	−0.561953	+	0.704667i	0.416965	+	0.908923i	$0.363094\pi$
$180$		0			0
$181$	−4.27963	+	18.7503i	−0.318103	+	1.39370i	0.522773	+	0.852472i	$0.324897\pi$
$181$	−4.27963	+	18.7503i	−0.318103	+	1.39370i	−0.840876	+	0.541228i	$0.817960\pi$
$182$		0			0
$183$	−1.73341	−	0.834764i	−0.128137	−	0.0617076i
$184$		0			0
$185$	−10.6380	−	22.0901i	−0.782123	−	1.62410i
$186$		0			0
$187$	3.80194	−	1.83092i	0.278025	−	0.133890i
$188$		0			0
$189$	9.84817	−	7.85365i	0.716349	−	0.571269i
$190$		0			0
$191$		−	3.12733i		−	0.226285i	−0.993579	−	0.113143i	$-0.963908\pi$
$191$		−	3.12733i		−	0.226285i	0.993579	−	0.113143i	$-0.0360917\pi$
$192$		0			0
$193$	5.47099	−	1.24872i	0.393811	−	0.0898847i	−0.0210299	−	0.999779i	$-0.506695\pi$
$193$	5.47099	−	1.24872i	0.393811	−	0.0898847i	0.414841	+	0.909894i	$0.363837\pi$
$194$		0			0
$195$	−8.56584	+	17.7872i	−0.613413	+	1.27376i
$196$		0			0
$197$	−12.7533	−	15.9922i	−0.908636	−	1.13939i	−0.989767	−	0.142690i	$-0.954425\pi$
$197$	−12.7533	−	15.9922i	−0.908636	−	1.13939i	0.0811313	−	0.996703i	$-0.474147\pi$
$198$		0			0
$199$	3.51453	+	15.3982i	0.249139	+	1.09155i	0.932415	+	0.361388i	$0.117697\pi$
$199$	3.51453	+	15.3982i	0.249139	+	1.09155i	−0.683277	+	0.730159i	$0.739446\pi$
$200$		0			0
$201$	−6.28017	−	5.00827i	−0.442969	−	0.353256i
$202$		0			0
$203$	−11.8279	+	10.5164i	−0.830155	+	0.738108i
$204$		0			0
$205$	9.75063	+	7.77587i	0.681013	+	0.543090i
$206$		0			0
$207$	0.667563	+	2.92478i	0.0463988	+	0.203287i
$208$		0			0
$209$	2.93296	+	3.67782i	0.202877	+	0.254400i
$210$		0			0
$211$	−7.49612	+	15.5658i	−0.516054	+	1.07160i	0.466311	+	0.884621i	$0.345583\pi$
$211$	−7.49612	+	15.5658i	−0.516054	+	1.07160i	−0.982365	+	0.186976i	$0.940131\pi$
$212$		0			0
$213$	−21.8681	+	4.99125i	−1.49838	+	0.341995i
$214$		0			0
$215$		−	26.1583i		−	1.78398i
$216$		0			0
$217$	12.5538	−	10.0113i	0.852205	−	0.679611i
$218$		0			0
$219$	−3.35086	+	1.61369i	−0.226430	+	0.109043i
$220$		0			0
$221$	9.06398	+	18.8216i	0.609709	+	1.26607i
$222$		0			0
$223$	−20.3523	−	9.80117i	−1.36289	−	0.656335i	−0.397614	−	0.917553i	$-0.630162\pi$
$223$	−20.3523	−	9.80117i	−1.36289	−	0.656335i	−0.965280	+	0.261218i	$0.915876\pi$
$224$		0			0
$225$	0.0990311	−	0.433884i	0.00660208	−	0.0289256i
$226$		0			0
$227$	3.61327	−	4.53090i	0.239821	−	0.300726i	−0.647326	−	0.762214i	$-0.724113\pi$
$227$	3.61327	−	4.53090i	0.239821	−	0.300726i	0.887147	+	0.461487i	$0.152684\pi$
$228$		0			0
$229$	9.08695	+	2.07404i	0.600483	+	0.137056i	0.511947	−	0.859017i	$-0.328924\pi$
$229$	9.08695	+	2.07404i	0.600483	+	0.137056i	0.0885352	+	0.996073i	$0.471781\pi$
$230$		0			0
$231$	4.97285			0.327190
$232$		0			0
$233$	12.7138			0.832908			0.416454	−	0.909157i	$-0.363273\pi$
$233$	12.7138			0.832908			0.416454	+	0.909157i	$0.363273\pi$
$234$		0			0
$235$	7.75667	+	1.77041i	0.505989	+	0.115489i
$236$		0			0
$237$	10.1189	−	12.6888i	0.657296	−	0.824223i
$238$		0			0
$239$	−0.104408	+	0.457441i	−0.00675359	+	0.0295894i	−0.978192	−	0.207701i	$-0.933402\pi$
$239$	−0.104408	+	0.457441i	−0.00675359	+	0.0295894i	0.971439	+	0.237290i	$0.0762592\pi$
$240$		0			0
$241$	16.3034	+	7.85132i	1.05020	+	0.505748i	0.877674	−	0.479258i	$-0.159094\pi$
$241$	16.3034	+	7.85132i	1.05020	+	0.505748i	0.172522	+	0.985006i	$0.444808\pi$
$242$		0			0
$243$	3.52661	+	7.32309i	0.226232	+	0.469776i
$244$		0			0
$245$	−3.47770	+	1.67477i	−0.222182	+	0.106997i
$246$		0			0
$247$	−18.2071	+	14.5197i	−1.15849	+	0.923864i
$248$		0			0
$249$			1.74602i			0.110649i
$250$		0			0
$251$	−9.50484	+	2.16942i	−0.599940	+	0.136932i	−0.511696	−	0.859166i	$-0.670983\pi$
$251$	−9.50484	+	2.16942i	−0.599940	+	0.136932i	−0.0882441	+	0.996099i	$0.528126\pi$
$252$		0			0
$253$	1.40850	−	2.92478i	0.0885517	−	0.183880i
$254$		0			0
$255$	−13.9336	−	17.4722i	−0.872557	−	1.09415i
$256$		0			0
$257$	4.65937	+	20.4140i	0.290643	+	1.27339i	0.883633	+	0.468181i	$0.155090\pi$
$257$	4.65937	+	20.4140i	0.290643	+	1.27339i	−0.592989	+	0.805210i	$0.702052\pi$
$258$		0			0
$259$	−23.9034	−	19.0623i	−1.48529	−	1.18448i
$260$		0			0
$261$	−2.07942	−	3.78498i	−0.128713	−	0.234284i
$262$		0			0
$263$	−4.30098	−	3.42992i	−0.265210	−	0.211498i	0.481852	−	0.876253i	$-0.339964\pi$
$263$	−4.30098	−	3.42992i	−0.265210	−	0.211498i	−0.747061	+	0.664755i	$0.768536\pi$
$264$		0			0
$265$	7.20655	+	31.5740i	0.442695	+	1.93957i
$266$		0			0
$267$	2.65399	+	3.32800i	0.162422	+	0.203670i
$268$		0			0
$269$	−2.50687	+	5.20557i	−0.152846	+	0.317389i	−0.963306	−	0.268406i	$-0.913503\pi$
$269$	−2.50687	+	5.20557i	−0.152846	+	0.317389i	0.810459	+	0.585795i	$0.199218\pi$
$270$		0			0
$271$	−16.1238	+	3.68015i	−0.979450	+	0.223553i	−0.682135	−	0.731226i	$-0.738948\pi$
$271$	−16.1238	+	3.68015i	−0.979450	+	0.223553i	−0.297315	+	0.954779i	$0.596091\pi$
$272$		0			0
$273$			24.6182i			1.48996i
$274$		0			0
$275$	−0.376510	+	0.300257i	−0.0227044	+	0.0181062i
$276$		0			0
$277$	−17.2371	+	8.30093i	−1.03567	+	0.498754i	−0.872895	−	0.487908i	$-0.837760\pi$
$277$	−17.2371	+	8.30093i	−1.03567	+	0.498754i	−0.162779	+	0.986663i	$0.552046\pi$
$278$		0			0
$279$	1.90097	+	3.94740i	0.113808	+	0.236325i
$280$		0			0
$281$	6.05107	+	2.91404i	0.360977	+	0.173837i	0.605577	−	0.795787i	$-0.292942\pi$
$281$	6.05107	+	2.91404i	0.360977	+	0.173837i	−0.244600	+	0.969624i	$0.578657\pi$
$282$		0			0
$283$	−1.70291	+	7.46092i	−0.101227	+	0.443506i	0.898760	+	0.438441i	$0.144469\pi$
$283$	−1.70291	+	7.46092i	−0.101227	+	0.443506i	−0.999987	+	0.00506456i	$0.998388\pi$
$284$		0			0
$285$	15.5327	−	19.4773i	0.920075	−	1.15374i
$286$		0			0
$287$	15.1618	+	3.46059i	0.894974	+	0.204272i
$288$		0			0
$289$	−6.64742			−0.391024
$290$		0			0
$291$	19.8455			1.16336
$292$		0			0
$293$	−16.7736	−	3.82846i	−0.979924	−	0.223661i	−0.297583	−	0.954696i	$-0.596181\pi$
$293$	−16.7736	−	3.82846i	−0.979924	−	0.223661i	−0.682340	+	0.731035i	$0.739038\pi$
$294$		0			0
$295$	−11.1739	+	14.0116i	−0.650570	+	0.815788i
$296$		0			0
$297$	0.827593	−	3.62592i	0.0480218	−	0.210397i
$298$		0			0
$299$	14.4792	+	6.97281i	0.837353	+	0.403248i
$300$		0			0
$301$	−14.1528	−	29.3886i	−0.815753	−	1.69393i
$302$		0			0
$303$	8.99396	−	4.33126i	0.516689	−	0.248825i
$304$		0			0
$305$	1.81820	−	1.44997i	0.104110	−	0.0830248i
$306$		0			0
$307$			15.7215i			0.897275i	0.893714	+	0.448637i	$0.148091\pi$
$307$			15.7215i			0.897275i	−0.893714	+	0.448637i	$0.851909\pi$
$308$		0			0
$309$	12.2002	−	2.78462i	0.694046	−	0.158412i
$310$		0			0
$311$	2.99114	−	6.21116i	0.169612	−	0.352203i	−0.798785	−	0.601616i	$-0.794524\pi$
$311$	2.99114	−	6.21116i	0.169612	−	0.352203i	0.968397	+	0.249414i	$0.0802379\pi$
$312$		0			0
$313$	4.75033	+	5.95673i	0.268505	+	0.336694i	0.897744	−	0.440517i	$-0.145205\pi$
$313$	4.75033	+	5.95673i	0.268505	+	0.336694i	−0.629239	+	0.777211i	$0.716634\pi$
$314$		0			0
$315$	−1.23609	−	5.41568i	−0.0696460	−	0.305139i
$316$		0			0
$317$	18.0928	+	14.4285i	1.01619	+	0.810385i	0.981971	−	0.189030i	$-0.0605342\pi$
$317$	18.0928	+	14.4285i	1.01619	+	0.810385i	0.0342189	+	0.999414i	$0.489106\pi$
$318$		0			0
$319$	−0.794405	+	4.60505i	−0.0444781	+	0.257833i
$320$		0			0
$321$	−28.6444	−	22.8431i	−1.59877	−	1.27498i
$322$		0			0
$323$	−5.86592	−	25.7003i	−0.326389	−	1.43000i
$324$		0			0
$325$	−1.48643	−	1.86392i	−0.0824521	−	0.103392i
$326$		0			0
$327$	9.17174	−	19.0453i	0.507199	−	1.05321i
$328$		0			0
$329$	9.67241	−	2.20766i	0.533257	−	0.121712i
$330$		0			0
$331$		−	14.7416i		−	0.810270i	−0.914257	−	0.405135i	$-0.867225\pi$
$331$		−	14.7416i		−	0.810270i	0.914257	−	0.405135i	$-0.132775\pi$
$332$		0			0
$333$	6.52230	−	5.20136i	0.357420	−	0.285033i
$334$		0			0
$335$	8.74794	−	4.21279i	0.477951	−	0.230169i
$336$		0			0
$337$	−8.73341	−	18.1351i	−0.475739	−	0.987882i	−0.991373	−	0.131073i	$-0.958158\pi$
$337$	−8.73341	−	18.1351i	−0.475739	−	0.987882i	0.515634	−	0.856809i	$-0.327557\pi$
$338$		0			0
$339$	27.0933	+	13.0474i	1.47151	+	0.708640i
$340$		0			0
$341$	1.05496	−	4.62207i	0.0571292	−	0.250299i
$342$		0			0
$343$	9.82603	−	12.3214i	0.530556	−	0.665296i
$344$		0			0
$345$	−16.7608	−	3.82555i	−0.902374	−	0.205961i
$346$		0			0
$347$	−21.5013			−1.15425			−0.577124	−	0.816657i	$-0.695825\pi$
$347$	−21.5013			−1.15425			−0.577124	+	0.816657i	$0.695825\pi$
$348$		0			0
$349$	−5.23191			−0.280058			−0.140029	−	0.990147i	$-0.544720\pi$
$349$	−5.23191			−0.280058			−0.140029	+	0.990147i	$0.544720\pi$
$350$		0			0
$351$	17.9502	+	4.09701i	0.958110	+	0.218682i
$352$		0			0
$353$	8.44235	−	10.5864i	0.449341	−	0.563456i	−0.504637	−	0.863332i	$-0.668374\pi$
$353$	8.44235	−	10.5864i	0.449341	−	0.563456i	0.953978	+	0.299876i	$0.0969452\pi$
$354$		0			0
$355$	6.03319	−	26.4331i	0.320208	−	1.40292i
$356$		0			0
$357$	−25.1075	−	12.0911i	−1.32883	−	0.639931i
$358$		0			0
$359$	0.897616	+	1.86392i	0.0473744	+	0.0983739i	0.923312	−	0.384050i	$-0.125471\pi$
$359$	0.897616	+	1.86392i	0.0473744	+	0.0983739i	−0.875938	+	0.482424i	$0.839757\pi$
$360$		0			0
$361$	9.35786	−	4.50651i	0.492519	−	0.237185i
$362$		0			0
$363$	−15.6211	+	12.4574i	−0.819895	+	0.653844i
$364$		0			0
$365$		−	4.49556i		−	0.235308i
$366$		0			0
$367$	3.67576	−	0.838968i	0.191873	−	0.0437938i	−0.125504	−	0.992093i	$-0.540055\pi$
$367$	3.67576	−	0.838968i	0.191873	−	0.0437938i	0.317377	+	0.948299i	$0.397198\pi$
$368$		0			0
$369$	−1.84117	+	3.82322i	−0.0958473	+	0.199029i
$370$		0			0
$371$	25.1794	+	31.5740i	1.30725	+	1.63924i
$372$		0			0
$373$	2.13826	+	9.36833i	0.110715	+	0.485074i	0.999635	+	0.0270116i	$0.00859911\pi$
$373$	2.13826	+	9.36833i	0.110715	+	0.485074i	−0.888920	+	0.458062i	$0.848544\pi$
$374$		0			0
$375$	−15.9710	−	12.7364i	−0.824739	−	0.657707i
$376$		0			0
$377$	−22.7974	−	3.93271i	−1.17413	−	0.202545i
$378$		0			0
$379$	15.6240	+	12.4597i	0.802552	+	0.640014i	0.936379	−	0.350991i	$-0.114155\pi$
$379$	15.6240	+	12.4597i	0.802552	+	0.640014i	−0.133827	+	0.991005i	$0.542727\pi$
$380$		0			0
$381$	1.58426	+	6.94110i	0.0811642	+	0.355603i
$382$		0			0
$383$	0.640416	+	0.803056i	0.0327237	+	0.0410342i	0.797924	−	0.602758i	$-0.205932\pi$
$383$	0.640416	+	0.803056i	0.0327237	+	0.0410342i	−0.765200	+	0.643792i	$0.777360\pi$
$384$		0			0
$385$	−2.60806	+	5.41568i	−0.132919	+	0.276009i
$386$		0			0
$387$	8.67725	−	1.98053i	0.441089	−	0.100676i
$388$		0			0
$389$		−	14.0541i		−	0.712570i	−0.934377	−	0.356285i	$-0.884043\pi$
$389$		−	14.0541i		−	0.712570i	0.934377	−	0.356285i	$-0.115957\pi$
$390$		0			0
$391$	−14.2228	+	11.3423i	−0.719279	+	0.573606i
$392$		0			0
$393$	16.7838	−	8.08266i	0.846631	−	0.407716i
$394$		0			0
$395$	8.51171	+	17.6748i	0.428271	+	0.889313i
$396$		0			0
$397$	10.8802	+	5.23961i	0.546059	+	0.262968i	0.686511	−	0.727119i	$-0.259141\pi$
$397$	10.8802	+	5.23961i	0.546059	+	0.262968i	−0.140452	+	0.990088i	$0.544856\pi$
$398$		0			0
$399$	6.91268	−	30.2864i	0.346067	−	1.51622i
$400$		0			0
$401$	−17.1712	+	21.5320i	−0.857489	+	1.07526i	0.138896	+	0.990307i	$0.455645\pi$
$401$	−17.1712	+	21.5320i	−0.857489	+	1.07526i	−0.996385	+	0.0849506i	$0.972927\pi$
$402$		0			0
$403$	22.8817	+	5.22259i	1.13982	+	0.260156i
$404$		0			0
$405$	−25.3666			−1.26048
$406$		0			0
$407$	−9.02715			−0.447459
$408$		0			0
$409$	−18.6057	−	4.24662i	−0.919991	−	0.209982i	−0.263800	−	0.964577i	$-0.584976\pi$
$409$	−18.6057	−	4.24662i	−0.919991	−	0.209982i	−0.656190	+	0.754595i	$0.727833\pi$
$410$		0			0
$411$	−11.8110	+	14.8105i	−0.582592	+	0.730547i
$412$		0			0
$413$	−4.97285	+	21.7875i	−0.244698	+	1.07209i
$414$		0			0
$415$	−1.90150	−	0.915715i	−0.0933410	−	0.0449507i
$416$		0			0
$417$	15.9644	+	33.1505i	0.781781	+	1.62338i
$418$		0			0
$419$	−26.3838	+	12.7058i	−1.28893	+	0.620718i	−0.947670	−	0.319250i	$-0.896569\pi$
$419$	−26.3838	+	12.7058i	−1.28893	+	0.620718i	−0.341263	+	0.939968i	$0.610855\pi$
$420$		0			0
$421$	14.6555	−	11.6874i	0.714264	−	0.569607i	−0.197509	−	0.980301i	$-0.563285\pi$
$421$	14.6555	−	11.6874i	0.714264	−	0.569607i	0.911773	+	0.410694i	$0.134714\pi$
$422$		0			0
$423$			2.70709i			0.131623i
$424$		0			0
$425$	2.63102	−	0.600514i	0.127623	−	0.0291292i
$426$		0			0
$427$	1.25823	−	2.61275i	0.0608902	−	0.126440i
$428$		0			0
$429$	4.53199	+	5.68294i	0.218807	+	0.274375i
$430$		0			0
$431$	−8.00849	−	35.0875i	−0.385755	−	1.69011i	−0.679057	−	0.734085i	$-0.737611\pi$
$431$	−8.00849	−	35.0875i	−0.385755	−	1.69011i	0.293302	−	0.956020i	$-0.405246\pi$
$432$		0			0
$433$	23.6163	+	18.8333i	1.13492	+	0.905072i	0.996357	−	0.0852807i	$-0.0271787\pi$
$433$	23.6163	+	18.8333i	1.13492	+	0.905072i	0.138568	+	0.990353i	$0.455750\pi$
$434$		0			0
$435$	24.7126	−	1.32521i	1.18488	−	0.0635389i
$436$		0			0
$437$	−15.8550	−	12.6440i	−0.758449	−	0.604843i
$438$		0			0
$439$	1.08695	+	4.76224i	0.0518773	+	0.227289i	0.994220	−	0.107359i	$-0.0342395\pi$
$439$	1.08695	+	4.76224i	0.0518773	+	0.227289i	−0.942343	+	0.334649i	$0.891382\pi$
$440$		0			0
$441$	−0.818864	−	1.02682i	−0.0389935	−	0.0488963i
$442$		0			0
$443$	4.73639	−	9.83522i	0.225033	−	0.467285i	−0.757631	−	0.652683i	$-0.773643\pi$
$443$	4.73639	−	9.83522i	0.225033	−	0.467285i	0.982663	+	0.185398i	$0.0593575\pi$
$444$		0			0
$445$	−5.01626	+	1.14493i	−0.237794	+	0.0542748i
$446$		0			0
$447$			35.7651i			1.69163i
$448$		0			0
$449$	−20.5673	+	16.4019i	−0.970633	+	0.774054i	−0.974141	−	0.225940i	$-0.927455\pi$
$449$	−20.5673	+	16.4019i	−0.970633	+	0.774054i	0.00350861	+	0.999994i	$0.498883\pi$
$450$		0			0
$451$	4.13706	−	1.99230i	0.194807	−	0.0938140i
$452$		0			0
$453$	3.85152	+	7.99776i	0.180960	+	0.375768i
$454$		0			0
$455$	−26.8104	−	12.9112i	−1.25689	−	0.605287i
$456$		0			0
$457$	1.06949	−	4.68575i	0.0500287	−	0.219190i	−0.943734	−	0.330705i	$-0.892713\pi$
$457$	1.06949	−	4.68575i	0.0500287	−	0.219190i	0.993763	+	0.111515i	$0.0355705\pi$
$458$		0			0
$459$	−12.9946	+	16.2947i	−0.606537	+	0.760573i
$460$		0			0
$461$	26.9421	+	6.14936i	1.25482	+	0.286404i	0.797729	−	0.603016i	$-0.206034\pi$
$461$	26.9421	+	6.14936i	1.25482	+	0.286404i	0.457090	+	0.889420i	$0.348892\pi$
$462$		0			0
$463$	17.5991			0.817899			0.408950	−	0.912557i	$-0.365895\pi$
$463$	17.5991			0.817899			0.408950	+	0.912557i	$0.365895\pi$
$464$		0			0
$465$	−25.1075			−1.16433
$466$		0			0
$467$	−20.1576	−	4.60085i	−0.932784	−	0.212902i	−0.270985	−	0.962583i	$-0.587350\pi$
$467$	−20.1576	−	4.60085i	−0.932784	−	0.212902i	−0.661799	+	0.749682i	$0.730207\pi$
$468$		0			0
$469$	7.54892	−	9.46604i	0.348577	−	0.437101i
$470$		0			0
$471$	−0.484271	+	2.12173i	−0.0223140	+	0.0977641i
$472$		0			0
$473$	−8.67725	−	4.17874i	−0.398980	−	0.192139i
$474$		0			0
$475$	1.30529	+	2.71046i	0.0598908	+	0.124365i
$476$		0			0
$477$	−9.92812	+	4.78113i	−0.454577	+	0.218913i
$478$		0			0
$479$	9.01238	−	7.18713i	0.411786	−	0.328388i	−0.395588	−	0.918428i	$-0.629459\pi$
$479$	9.01238	−	7.18713i	0.411786	−	0.328388i	0.807374	+	0.590040i	$0.200888\pi$
$480$		0			0
$481$		−	44.6890i		−	2.03764i
$482$		0			0
$483$	−20.9004	+	4.77039i	−0.951003	+	0.217060i
$484$		0			0
$485$	−10.4081	+	21.6127i	−0.472609	+	0.981383i
$486$		0			0
$487$	4.29859	+	5.39026i	0.194787	+	0.244256i	0.869628	−	0.493708i	$-0.164359\pi$
$487$	4.29859	+	5.39026i	0.194787	+	0.244256i	−0.674840	+	0.737964i	$0.735787\pi$
$488$		0			0
$489$	5.72132	+	25.0668i	0.258727	+	1.13356i
$490$		0			0
$491$	14.7882	+	11.7932i	0.667384	+	0.532221i	0.897540	−	0.440933i	$-0.145352\pi$
$491$	14.7882	+	11.7932i	0.667384	+	0.532221i	−0.230156	+	0.973154i	$0.573924\pi$
$492$		0			0
$493$	15.2078	−	21.3190i	0.684923	−	0.960159i
$494$		0			0
$495$	−1.28232	−	1.02262i	−0.0576362	−	0.0459633i
$496$		0			0
$497$	−7.52326	−	32.9616i	−0.337464	−	1.47853i
$498$		0			0
$499$	11.4152	+	14.3142i	0.511015	+	0.640792i	0.968674	−	0.248335i	$-0.0798835\pi$
$499$	11.4152	+	14.3142i	0.511015	+	0.640792i	−0.457659	+	0.889128i	$0.651312\pi$
$500$		0			0
$501$	−0.339674	+	0.705341i	−0.0151755	+	0.0315123i
$502$		0			0
$503$	29.4740	−	6.72724i	1.31418	−	0.299953i	0.492704	−	0.870197i	$-0.336008\pi$
$503$	29.4740	−	6.72724i	1.31418	−	0.299953i	0.821475	+	0.570244i	$0.193151\pi$
$504$		0			0
$505$			12.0664i			0.536949i
$506$		0			0
$507$	−8.31551	+	6.63140i	−0.369305	+	0.294511i
$508$		0			0
$509$	−8.18814	+	3.94320i	−0.362933	+	0.174779i	−0.606458	−	0.795115i	$-0.707410\pi$
$509$	−8.18814	+	3.94320i	−0.362933	+	0.174779i	0.243526	+	0.969894i	$0.421696\pi$
$510$		0			0
$511$	−2.43230	−	5.05072i	−0.107598	−	0.223430i
$512$		0			0
$513$	−20.9327	−	10.0807i	−0.924202	−	0.445072i
$514$		0			0
$515$	−3.36592	+	14.7471i	−0.148320	+	0.649833i
$516$		0			0
$517$	1.82640	−	2.29023i	0.0803248	−	0.100724i
$518$		0			0
$519$	−25.8605	−	5.90250i	−1.13515	−	0.259091i
$520$		0			0
$521$	21.5448			0.943895			0.471947	−	0.881627i	$-0.343551\pi$
$521$	21.5448			0.943895			0.471947	+	0.881627i	$0.343551\pi$
$522$		0			0
$523$	−3.25129			−0.142169			−0.0710845	−	0.997470i	$-0.522646\pi$
$523$	−3.25129			−0.142169			−0.0710845	+	0.997470i	$0.522646\pi$
$524$		0			0
$525$	3.10052	+	0.707674i	0.135318	+	0.0308854i
$526$		0			0
$527$	−16.5646	+	20.7714i	−0.721567	+	0.904817i
$528$		0			0
$529$	2.00388	−	8.77959i	0.0871254	−	0.381721i
$530$		0			0
$531$	−5.49396	−	2.64575i	−0.238418	−	0.114816i
$532$		0			0
$533$	9.86294	+	20.4806i	0.427211	+	0.887113i
$534$		0			0
$535$	39.9001	−	19.2149i	1.72503	−	0.830731i
$536$		0			0
$537$	18.3828	−	14.6598i	0.793278	−	0.632618i
$538$		0			0
$539$			1.42117i			0.0612140i
$540$		0			0
$541$	−3.62983	+	0.828484i	−0.156058	+	0.0356193i	−0.299836	−	0.953991i	$-0.596932\pi$
$541$	−3.62983	+	0.828484i	−0.156058	+	0.0356193i	0.143778	+	0.989610i	$0.454075\pi$
$542$		0			0
$543$	16.2709	−	33.7869i	0.698251	−	1.44993i
$544$		0			0
$545$	15.9311	+	19.9770i	0.682413	+	0.855719i
$546$		0			0
$547$	−4.92812	−	21.5915i	−0.210711	−	0.923185i	−0.964085	−	0.265593i	$-0.914432\pi$
$547$	−4.92812	−	21.5915i	−0.210711	−	0.923185i	0.753374	−	0.657592i	$-0.228425\pi$
$548$		0			0
$549$	0.618645	+	0.493353i	0.0264031	+	0.0210558i
$550$		0			0
$551$	26.9421	+	11.2396i	1.14777	+	0.478824i
$552$		0			0
$553$	19.1256	+	15.2522i	0.813305	+	0.648589i
$554$		0			0
$555$	10.6380	+	46.6082i	0.451559	+	1.97841i
$556$		0			0
$557$	−1.88069	−	2.35831i	−0.0796874	−	0.0999249i	0.740390	−	0.672178i	$-0.234641\pi$
$557$	−1.88069	−	2.35831i	−0.0796874	−	0.0999249i	−0.820077	+	0.572253i	$0.806070\pi$
$558$		0			0
$559$	20.6869	−	42.9569i	0.874964	−	1.81688i
$560$		0			0
$561$	−8.02177	+	1.83092i	−0.338679	+	0.0773014i
$562$		0			0
$563$		−	21.0130i		−	0.885594i	−0.896622	−	0.442797i	$-0.853986\pi$
$563$		−	21.0130i		−	0.885594i	0.896622	−	0.442797i	$-0.146014\pi$
$564$		0			0
$565$	−28.4186	+	22.6631i	−1.19558	+	0.953443i
$566$		0			0
$567$	−28.4991	+	13.7244i	−1.19685	+	0.576372i
$568$		0			0
$569$	−19.7377	−	40.9858i	−0.827448	−	1.71821i	−0.685165	−	0.728388i	$-0.740270\pi$
$569$	−19.7377	−	40.9858i	−0.827448	−	1.71821i	−0.142283	−	0.989826i	$-0.545444\pi$
$570$		0			0
$571$	−34.4424	−	16.5866i	−1.44137	−	0.694127i	−0.460297	−	0.887765i	$-0.652257\pi$
$571$	−34.4424	−	16.5866i	−1.44137	−	0.694127i	−0.981073	+	0.193638i	$0.937971\pi$
$572$		0			0
$573$	−1.35690	+	5.94495i	−0.0566851	+	0.248354i
$574$		0			0
$575$	1.29440	−	1.62313i	0.0539804	−	0.0676893i
$576$		0			0
$577$	−36.9746	−	8.43922i	−1.53927	−	0.351329i	−0.633045	−	0.774115i	$-0.718195\pi$
$577$	−36.9746	−	8.43922i	−1.53927	−	0.351329i	−0.906230	+	0.422786i	$0.861052\pi$
$578$		0			0
$579$	−10.9420			−0.454733
$580$		0			0
$581$	−2.63176			−0.109184
$582$		0			0
$583$	11.6250	+	2.65333i	0.481458	+	0.109890i
$584$		0			0
$585$	5.06249	−	6.34816i	0.209308	−	0.262464i
$586$		0			0
$587$	3.72228	−	16.3084i	0.153635	−	0.673119i	−0.838175	−	0.545401i	$-0.816377\pi$
$587$	3.72228	−	16.3084i	0.153635	−	0.673119i	0.991810	−	0.127719i	$-0.0407654\pi$
$588$		0			0
$589$	−26.6836	−	12.8501i	−1.09948	−	0.529481i
$590$		0			0
$591$	17.3049	+	35.9340i	0.711829	+	1.47813i
$592$		0			0
$593$	17.7528	−	8.54929i	0.729019	−	0.351077i	−0.0322790	−	0.999479i	$-0.510277\pi$
$593$	17.7528	−	8.54929i	0.729019	−	0.351077i	0.761298	+	0.648402i	$0.224562\pi$
$594$		0			0
$595$	26.3357	−	21.0020i	1.07966	−	0.860999i
$596$		0			0
$597$		−	30.7964i		−	1.26041i
$598$		0			0
$599$	−8.63951	+	1.97191i	−0.353001	+	0.0805702i	−0.395344	−	0.918533i	$-0.629375\pi$
$599$	−8.63951	+	1.97191i	−0.353001	+	0.0805702i	0.0423435	+	0.999103i	$0.486518\pi$
$600$		0			0
$601$	11.3185	−	23.5031i	0.461691	−	0.958711i	−0.532019	−	0.846732i	$-0.678567\pi$
$601$	11.3185	−	23.5031i	0.461691	−	0.958711i	0.993711	−	0.111979i	$-0.0357190\pi$
$602$		0			0
$603$	2.05980	+	2.58291i	0.0838816	+	0.105184i
$604$		0			0
$605$	−5.37412	−	23.5455i	−0.218489	−	0.957263i
$606$		0			0
$607$	−18.6966	−	14.9101i	−0.758873	−	0.605181i	0.165704	−	0.986175i	$-0.447010\pi$
$607$	−18.6966	−	14.9101i	−0.758873	−	0.605181i	−0.924577	+	0.380995i	$0.875582\pi$
$608$		0			0
$609$	27.0474	−	14.8595i	1.09601	−	0.602136i
$610$		0			0
$611$	11.3378	+	9.04160i	0.458679	+	0.365784i
$612$		0			0
$613$	4.06757	+	17.8212i	0.164288	+	0.719791i	0.988212	+	0.153092i	$0.0489229\pi$
$613$	4.06757	+	17.8212i	0.164288	+	0.719791i	−0.823924	+	0.566700i	$0.808220\pi$
$614$		0			0
$615$	−15.1618	−	19.0123i	−0.611383	−	0.766651i
$616$		0			0
$617$	−2.90837	+	6.03929i	−0.117087	+	0.243133i	−0.951273	−	0.308350i	$-0.900223\pi$
$617$	−2.90837	+	6.03929i	−0.117087	+	0.243133i	0.834187	+	0.551482i	$0.185938\pi$
$618$		0			0
$619$	38.6371	−	8.81867i	1.55296	−	0.354452i	0.641918	−	0.766773i	$-0.278139\pi$
$619$	38.6371	−	8.81867i	1.55296	−	0.354452i	0.911039	+	0.412321i	$0.135282\pi$
$620$		0			0
$621$			16.0333i			0.643394i
$622$		0			0
$623$	−5.01626	+	4.00034i	−0.200972	+	0.160270i
$624$		0			0
$625$	24.7467	−	11.9174i	0.989870	−	0.476696i
$626$		0			0
$627$	−3.97972	−	8.26398i	−0.158935	−	0.330031i
$628$		0			0
$629$	45.5773	+	21.9489i	1.81729	+	0.875159i
$630$		0			0
$631$	−2.96197	+	12.9772i	−0.117914	+	0.516615i	0.881129	+	0.472876i	$0.156784\pi$
$631$	−2.96197	+	12.9772i	−0.117914	+	0.516615i	−0.999043	+	0.0437392i	$0.986073\pi$
$632$		0			0
$633$	21.0036	−	26.3377i	0.834820	−	1.04683i
$634$		0			0
$635$	−8.39008	−	1.91498i	−0.332950	−	0.0759937i
$636$		0			0
$637$	−7.03551			−0.278757
$638$		0			0
$639$	9.22521			0.364944
$640$		0			0
$641$	−46.7417	−	10.6685i	−1.84618	−	0.421380i	−0.851501	−	0.524354i	$-0.824307\pi$
$641$	−46.7417	−	10.6685i	−1.84618	−	0.421380i	−0.994684	+	0.102974i	$0.967164\pi$
$642$		0			0
$643$	4.97853	−	6.24287i	0.196334	−	0.246195i	−0.673913	−	0.738811i	$-0.735388\pi$
$643$	4.97853	−	6.24287i	0.196334	−	0.246195i	0.870247	+	0.492616i	$0.163959\pi$
$644$		0			0
$645$	−11.3497	+	49.7261i	−0.446892	+	1.95796i
$646$		0			0
$647$	−7.97607	−	3.84107i	−0.313572	−	0.151008i	0.270478	−	0.962726i	$-0.412818\pi$
$647$	−7.97607	−	3.84107i	−0.313572	−	0.151008i	−0.584050	+	0.811718i	$0.698533\pi$
$648$		0			0
$649$	2.86294	+	5.94495i	0.112380	+	0.233360i
$650$		0			0
$651$	−28.2080	+	13.5843i	−1.10556	+	0.532410i
$652$		0			0
$653$	−23.5203	+	18.7568i	−0.920422	+	0.734012i	−0.964241	−	0.265028i	$-0.914619\pi$
$653$	−23.5203	+	18.7568i	−0.920422	+	0.734012i	0.0438189	+	0.999039i	$0.486048\pi$
$654$		0			0
$655$			22.5174i			0.879829i
$656$		0			0
$657$	1.49127	−	0.340373i	0.0581800	−	0.0132792i
$658$		0			0
$659$	2.75518	−	5.72118i	0.107326	−	0.222866i	−0.840388	−	0.541985i	$-0.817673\pi$
$659$	2.75518	−	5.72118i	0.107326	−	0.222866i	0.947714	+	0.319120i	$0.103387\pi$
$660$		0			0
$661$	5.49127	+	6.88584i	0.213586	+	0.267828i	0.877070	−	0.480362i	$-0.159495\pi$
$661$	5.49127	+	6.88584i	0.213586	+	0.267828i	−0.663485	+	0.748190i	$0.730923\pi$
$662$		0			0
$663$	−9.06398	−	39.7119i	−0.352016	−	1.54228i
$664$		0			0
$665$	29.3580	+	23.4122i	1.13846	+	0.907888i
$666$		0			0
$667$	−1.07875	−	20.1167i	−0.0417695	−	0.778921i
$668$		0			0
$669$	34.4366	+	27.4623i	1.33140	+	1.06175i
$670$		0			0
$671$	−0.190530	−	0.834764i	−0.00735531	−	0.0322257i
$672$		0			0
$673$	8.43565	+	10.5780i	0.325170	+	0.407751i	0.917367	−	0.398043i	$-0.130310\pi$
$673$	8.43565	+	10.5780i	0.325170	+	0.407751i	−0.592196	+	0.805794i	$0.701739\pi$
$674$		0			0
$675$	1.03199	−	2.14295i	0.0397214	−	0.0824823i
$676$		0			0
$677$	17.2947	−	3.94740i	0.664689	−	0.151711i	0.123152	−	0.992388i	$-0.460700\pi$
$677$	17.2947	−	3.94740i	0.664689	−	0.151711i	0.541537	+	0.840677i	$0.317843\pi$
$678$		0			0
$679$			29.9129i			1.14795i
$680$		0			0
$681$	−8.83459	+	7.04535i	−0.338542	+	0.269979i
$682$		0			0
$683$	−20.5015	+	9.87300i	−0.784468	+	0.377780i	−0.782843	−	0.622219i	$-0.786231\pi$
$683$	−20.5015	+	9.87300i	−0.784468	+	0.377780i	−0.00162449	+	0.999999i	$0.500517\pi$
$684$		0			0
$685$	−9.93498	−	20.6302i	−0.379596	−	0.788240i
$686$		0			0
$687$	−16.3741	−	7.88536i	−0.624712	−	0.300845i
$688$		0			0
$689$	−13.1353	+	57.5497i	−0.500416	+	2.19247i
$690$		0			0
$691$	−25.6652	+	32.1831i	−0.976349	+	1.22430i	−0.00183001	+	0.999998i	$0.500583\pi$
$691$	−25.6652	+	32.1831i	−0.976349	+	1.22430i	−0.974519	+	0.224305i	$0.927989\pi$
$692$		0			0
$693$	−1.99396	−	0.455108i	−0.0757442	−	0.0172881i
$694$		0			0
$695$	−44.4752			−1.68704
$696$		0			0
$697$	−25.7318			−0.974663
$698$		0			0
$699$	−24.1685	−	5.51631i	−0.914137	−	0.208646i
$700$		0			0
$701$	24.5311	−	30.7610i	0.926526	−	1.16183i	−0.0599955	−	0.998199i	$-0.519109\pi$
$701$	24.5311	−	30.7610i	0.926526	−	1.16183i	0.986522	−	0.163629i	$-0.0523199\pi$
$702$		0			0
$703$	−12.5485	+	54.9785i	−0.473275	+	2.07355i
$704$		0			0
$705$	−13.9770	−	6.73098i	−0.526406	−	0.253504i
$706$		0			0
$707$	6.52848	+	13.5565i	0.245529	+	0.509845i
$708$		0			0
$709$	17.8995	−	8.61996i	0.672231	−	0.323729i	−0.0664449	−	0.997790i	$-0.521166\pi$
$709$	17.8995	−	8.61996i	0.672231	−	0.323729i	0.738676	+	0.674061i	$0.235451\pi$
$710$		0			0
$711$	−5.21864	+	4.16172i	−0.195714	+	0.156077i
$712$		0			0
$713$			20.4382i			0.765415i
$714$		0			0
$715$	−8.56584	+	1.95510i	−0.320344	+	0.0731165i
$716$		0			0
$717$	0.396952	−	0.824280i	0.0148245	−	0.0307833i
$718$		0			0
$719$	20.7955	+	26.0768i	0.775542	+	0.972499i	0.999998	−	0.00198496i	$-0.000631831\pi$
$719$	20.7955	+	26.0768i	0.775542	+	0.972499i	−0.224456	+	0.974484i	$0.572060\pi$
$720$		0			0
$721$	4.19723	+	18.3893i	0.156313	+	0.684853i
$722$		0			0
$723$	−27.5858	−	21.9989i	−1.02593	−	0.818148i
$724$		0			0
$725$	−1.15064	+	2.75815i	−0.0427336	+	0.102435i
$726$		0			0
$727$	−5.03175	−	4.01269i	−0.186617	−	0.148822i	0.525725	−	0.850655i	$-0.323794\pi$
$727$	−5.03175	−	4.01269i	−0.186617	−	0.148822i	−0.712342	+	0.701832i	$0.752366\pi$
$728$		0			0
$729$	3.65817	+	16.0275i	0.135488	+	0.593611i
$730$		0			0
$731$	33.6504	+	42.1963i	1.24460	+	1.56069i
$732$		0			0
$733$	−11.8946	+	24.6995i	−0.439338	+	0.912295i	0.557296	+	0.830314i	$0.311839\pi$
$733$	−11.8946	+	24.6995i	−0.439338	+	0.912295i	−0.996634	+	0.0819812i	$0.973875\pi$
$734$		0			0
$735$	7.33765	−	1.67477i	0.270653	−	0.0617748i
$736$		0			0
$737$		−	3.57486i		−	0.131682i
$738$		0			0
$739$	0.767790	−	0.612292i	0.0282436	−	0.0225235i	−0.609266	−	0.792966i	$-0.708536\pi$
$739$	0.767790	−	0.612292i	0.0282436	−	0.0225235i	0.637510	+	0.770442i	$0.279965\pi$
$740$		0			0
$741$	40.9110	−	19.7017i	1.50290	−	0.723759i
$742$		0			0
$743$	−20.6767	−	42.9356i	−0.758555	−	1.57516i	−0.816845	−	0.576857i	$-0.804279\pi$
$743$	−20.6767	−	42.9356i	−0.758555	−	1.57516i	0.0582902	−	0.998300i	$-0.481435\pi$
$744$		0			0
$745$	−38.9499	−	18.7573i	−1.42702	−	0.687214i
$746$		0			0
$747$	0.159793	−	0.700099i	0.00584652	−	0.0256153i
$748$		0			0
$749$	34.4312	−	43.1754i	1.25809	−	1.57759i
$750$		0			0
$751$	41.5664	+	9.48727i	1.51678	+	0.346195i	0.898222	−	0.439543i	$-0.144860\pi$
$751$	41.5664	+	9.48727i	1.51678	+	0.346195i	0.618559	+	0.785738i	$0.287717\pi$
$752$		0			0
$753$	19.0097			0.692752
$754$		0			0
$755$	−10.7299			−0.390502
$756$		0			0
$757$	10.0260	+	2.28836i	0.364399	+	0.0831718i	0.400800	−	0.916165i	$-0.368732\pi$
$757$	10.0260	+	2.28836i	0.364399	+	0.0831718i	−0.0364008	+	0.999337i	$0.511589\pi$
$758$		0			0
$759$	−3.94653	+	4.94880i	−0.143250	+	0.179630i
$760$		0			0
$761$	9.82358	−	43.0399i	0.356104	−	1.56020i	−0.406697	−	0.913563i	$-0.633320\pi$
$761$	9.82358	−	43.0399i	0.356104	−	1.56020i	0.762802	−	0.646632i	$-0.223823\pi$
$762$		0			0
$763$	28.7068	+	13.8245i	1.03926	+	0.500480i
$764$		0			0
$765$	3.98792	+	8.28100i	0.144183	+	0.299400i
$766$		0			0
$767$	−29.4306	+	14.1730i	−1.06268	+	0.511758i
$768$		0			0
$769$	19.0908	−	15.2244i	0.688433	−	0.549007i	−0.215594	−	0.976483i	$-0.569169\pi$
$769$	19.0908	−	15.2244i	0.688433	−	0.549007i	0.904027	+	0.427476i	$0.140597\pi$
$770$		0			0
$771$		−	40.8280i		−	1.47039i
$772$		0			0
$773$	−28.9029	+	6.59690i	−1.03956	+	0.237274i	−0.708040	−	0.706173i	$-0.750420\pi$
$773$	−28.9029	+	6.59690i	−1.03956	+	0.237274i	−0.331525	+	0.943446i	$0.607563\pi$
$774$		0			0
$775$	1.31551	−	2.73169i	0.0472546	−	0.0981251i
$776$		0			0
$777$	37.1688	+	46.6082i	1.33342	+	1.67206i
$778$		0			0
$779$	−6.38298	−	27.9657i	−0.228694	−	1.00197i
$780$		0			0
$781$	−7.80463	−	6.22398i	−0.279271	−	0.222712i
$782$		0			0
$783$	−6.33340	−	22.1943i	−0.226337	−	0.793161i
$784$		0			0
$785$	−2.05669	−	1.64015i	−0.0734063	−	0.0585396i
$786$		0			0
$787$	−3.10142	−	13.5882i	−0.110554	−	0.484368i	−0.999645	−	0.0266381i	$-0.991520\pi$
$787$	−3.10142	−	13.5882i	−0.110554	−	0.484368i	0.889091	−	0.457730i	$-0.151337\pi$
$788$		0			0
$789$	6.68784	+	8.38629i	0.238093	+	0.298560i
$790$		0			0
$791$	−19.6663	+	40.8375i	−0.699253	+	1.45201i
$792$		0			0
$793$	4.13251	−	0.943219i	0.146750	−	0.0334947i
$794$		0			0
$795$		−	63.1480i		−	2.23963i
$796$		0			0
$797$	−10.2661	+	8.18691i	−0.363643	+	0.289995i	−0.788217	−	0.615398i	$-0.788995\pi$
$797$	−10.2661	+	8.18691i	−0.363643	+	0.289995i	0.424574	+	0.905393i	$0.360424\pi$
$798$		0			0
$799$	−14.7899	+	7.12242i	−0.523227	+	0.251973i
$800$		0			0
$801$	−0.759594	−	1.57731i	−0.0268389	−	0.0557316i
$802$		0			0
$803$	−1.49127	−	0.718158i	−0.0526258	−	0.0253433i
$804$		0			0
$805$	5.76623	−	25.2635i	0.203233	−	0.890421i
$806$		0			0
$807$	7.02409	−	8.80793i	0.247260	−	0.310054i
$808$		0			0
$809$	1.28800	+	0.293977i	0.0452835	+	0.0103357i	0.245103	−	0.969497i	$-0.421178\pi$
$809$	1.28800	+	0.293977i	0.0452835	+	0.0103357i	−0.199819	+	0.979833i	$0.564035\pi$
$810$		0			0
$811$	−27.4336			−0.963322			−0.481661	−	0.876358i	$-0.659966\pi$
$811$	−27.4336			−0.963322			−0.481661	+	0.876358i	$0.659966\pi$
$812$		0			0
$813$	32.2476			1.13097
$814$		0			0
$815$	−30.2995	−	6.91567i	−1.06135	−	0.242245i
$816$		0			0
$817$	−37.5121	+	47.0387i	−1.31238	+	1.64568i
$818$		0			0
$819$	2.25302	−	9.87113i	0.0787269	−	0.344925i
$820$		0			0
$821$	−39.9049	−	19.2172i	−1.39269	−	0.670685i	−0.421026	−	0.907048i	$-0.638330\pi$
$821$	−39.9049	−	19.2172i	−1.39269	−	0.670685i	−0.971665	+	0.236364i	$0.924044\pi$
$822$		0			0
$823$	18.5577	+	38.5355i	0.646881	+	1.34326i	0.923987	+	0.382423i	$0.124910\pi$
$823$	18.5577	+	38.5355i	0.646881	+	1.34326i	−0.277106	+	0.960839i	$0.589375\pi$
$824$		0			0
$825$	0.846011	−	0.407417i	0.0294543	−	0.0141844i
$826$		0			0
$827$	−1.74363	+	1.39050i	−0.0606319	+	0.0483523i	−0.653337	−	0.757067i	$-0.726631\pi$
$827$	−1.74363	+	1.39050i	−0.0606319	+	0.0483523i	0.592705	+	0.805420i	$0.298060\pi$
$828$		0			0
$829$		−	37.0918i		−	1.28825i	−0.764920	−	0.644125i	$-0.777221\pi$
$829$		−	37.0918i		−	1.28825i	0.764920	−	0.644125i	$-0.222779\pi$
$830$		0			0
$831$	36.3687	−	8.30093i	1.26162	−	0.287956i
$832$		0			0
$833$	3.45547	−	7.17535i	0.119725	−	0.248611i
$834$		0			0
$835$	−0.590006	−	0.739845i	−0.0204180	−	0.0256034i
$836$		0			0
$837$	5.21044	+	22.8284i	0.180099	+	0.789066i
$838$		0			0
$839$	21.5359	+	17.1743i	0.743501	+	0.592922i	0.920249	−	0.391334i	$-0.127986\pi$
$839$	21.5359	+	17.1743i	0.743501	+	0.592922i	−0.176748	+	0.984256i	$0.556558\pi$
$840$		0			0
$841$	9.43967	+	27.4207i	0.325506	+	0.945540i
$842$		0			0
$843$	−10.2385	−	8.16497i	−0.352634	−	0.281216i
$844$		0			0
$845$	−2.86078	−	12.5339i	−0.0984138	−	0.431179i
$846$		0			0
$847$	−18.7769	−	23.5455i	−0.645184	−	0.809035i
$848$		0			0
$849$	6.47434	−	13.4441i	0.222199	−	0.461401i
$850$		0			0
$851$	37.9403	−	8.65962i	1.30058	−	0.296848i
$852$		0			0
$853$		−	14.5415i		−	0.497890i	−0.968518	−	0.248945i	$-0.919916\pi$
$853$		−	14.5415i		−	0.497890i	0.968518	−	0.248945i	$-0.0800839\pi$
$854$		0			0
$855$	−8.01065	+	6.38828i	−0.273958	+	0.218475i
$856$		0			0
$857$	−1.09999	+	0.529728i	−0.0375750	+	0.0180951i	−0.452577	−	0.891725i	$-0.649495\pi$
$857$	−1.09999	+	0.529728i	−0.0375750	+	0.0180951i	0.415002	+	0.909821i	$0.363781\pi$
$858$		0			0
$859$	14.8885	+	30.9163i	0.507990	+	1.05485i	0.984452	+	0.175656i	$0.0562048\pi$
$859$	14.8885	+	30.9163i	0.507990	+	1.05485i	−0.476462	+	0.879195i	$0.658081\pi$
$860$		0			0
$861$	−27.3207	−	13.1569i	−0.931085	−	0.448387i
$862$		0			0
$863$	5.22880	−	22.9089i	0.177990	−	0.779827i	−0.804566	−	0.593863i	$-0.797602\pi$
$863$	5.22880	−	22.9089i	0.177990	−	0.779827i	0.982557	−	0.185964i	$-0.0595407\pi$
$864$		0			0
$865$	19.9909	−	25.0678i	0.679711	−	0.852331i
$866$		0			0
$867$	12.6365	+	2.88421i	0.429159	+	0.0979528i
$868$		0			0
$869$	7.22282			0.245017
$870$		0			0
$871$	17.6974			0.599653
$872$		0			0
$873$	−7.95742	−	1.81623i	−0.269318	−	0.0614700i
$874$		0			0
$875$	19.1975	−	24.0729i	0.648995	−	0.813814i
$876$		0			0
$877$	−10.0846	+	44.1833i	−0.340531	+	1.49197i	0.457424	+	0.889249i	$0.348772\pi$
$877$	−10.0846	+	44.1833i	−0.340531	+	1.49197i	−0.797955	+	0.602716i	$0.794085\pi$
$878$		0			0
$879$	30.2250	+	14.5556i	1.01946	+	0.490948i
$880$		0			0
$881$	−12.5926	−	26.1488i	−0.424256	−	0.880977i	−0.998076	−	0.0619958i	$-0.980253\pi$
$881$	−12.5926	−	26.1488i	−0.424256	−	0.880977i	0.573820	−	0.818981i	$-0.305461\pi$
$882$		0			0
$883$	−8.32520	+	4.00920i	−0.280165	+	0.134920i	−0.568690	−	0.822552i	$-0.692550\pi$
$883$	−8.32520	+	4.00920i	−0.280165	+	0.134920i	0.288525	+	0.957472i	$0.406835\pi$
$884$		0			0
$885$	27.3207	−	21.7875i	0.918374	−	0.732379i
$886$		0			0
$887$			41.8394i			1.40483i	0.711767	+	0.702416i	$0.247895\pi$
$887$			41.8394i			1.40483i	−0.711767	+	0.702416i	$0.752105\pi$
$888$		0			0
$889$	−10.4623	+	2.38794i	−0.350893	+	0.0800890i
$890$		0			0
$891$	−4.05227	+	8.41462i	−0.135756	+	0.281901i
$892$		0			0
$893$	−11.4095	−	14.3070i	−0.381803	−	0.478766i
$894$		0			0
$895$	6.32424	+	27.7083i	0.211396	+	0.926187i
$896$		0			0
$897$	−24.4991	−	19.5374i	−0.818001	−	0.652334i
$898$		0			0
$899$	−8.07338	−	28.2918i	−0.269262	−	0.943584i
$900$		0			0
$901$	−52.2422	−	41.6618i	−1.74044	−	1.38795i
$902$		0			0
$903$	14.1528	+	62.0074i	0.470975	+	2.06348i
$904$		0			0
$905$	28.2622	+	35.4396i	0.939467	+	1.17805i
$906$		0			0
$907$	25.2594	−	52.4517i	0.838725	−	1.74163i	0.188223	−	0.982126i	$-0.439727\pi$
$907$	25.2594	−	52.4517i	0.838725	−	1.74163i	0.650502	−	0.759504i	$-0.274558\pi$
$908$		0			0
$909$	−4.00269	+	0.913588i	−0.132761	+	0.0303018i
$910$		0			0
$911$		−	5.80920i		−	0.192467i	−0.995359	−	0.0962336i	$-0.969320\pi$
$911$		−	5.80920i		−	0.192467i	0.995359	−	0.0962336i	$-0.0306796\pi$
$912$		0			0
$913$	−0.607523	+	0.484484i	−0.0201061	+	0.0160341i
$914$		0			0
$915$	−4.08546	+	1.96745i	−0.135061	+	0.0650420i
$916$		0			0
$917$	12.1829	+	25.2981i	0.402316	+	0.835417i
$918$		0			0
$919$	14.2981	+	6.88558i	0.471649	+	0.227134i	0.654582	−	0.755991i	$-0.272845\pi$
$919$	14.2981	+	6.88558i	0.471649	+	0.227134i	−0.182933	+	0.983125i	$0.558559\pi$
$920$		0			0
$921$	6.82132	−	29.8861i	0.224770	−	0.984782i
$922$		0			0
$923$	30.8119	−	38.6369i	1.01419	−	1.27175i
$924$		0			0
$925$	−5.62833	−	1.28463i	−0.185058	−	0.0422384i
$926$		0			0
$927$	−5.14675			−0.169042
$928$		0			0
$929$	7.30559			0.239688			0.119844	−	0.992793i	$-0.461760\pi$
$929$	7.30559			0.239688			0.119844	+	0.992793i	$0.461760\pi$
$930$		0			0
$931$	8.65541	+	1.97554i	0.283670	+	0.0647457i
$932$		0			0
$933$	−8.38099	+	10.5094i	−0.274381	+	0.344063i
$934$		0			0
$935$	2.21313	−	9.69635i	0.0723770	−	0.317104i
$936$		0			0
$937$	−37.1422	−	17.8867i	−1.21338	−	0.584334i	−0.285921	−	0.958253i	$-0.592300\pi$
$937$	−37.1422	−	17.8867i	−1.21338	−	0.584334i	−0.927461	+	0.373919i	$0.878014\pi$
$938$		0			0
$939$	−6.44571	−	13.3846i	−0.210348	−	0.436791i
$940$		0			0
$941$	−24.6308	+	11.8616i	−0.802941	+	0.386676i	−0.789897	−	0.613239i	$-0.789866\pi$
$941$	−24.6308	+	11.8616i	−0.802941	+	0.386676i	−0.0130433	+	0.999915i	$0.504152\pi$
$942$		0			0
$943$	−15.4765	+	12.3421i	−0.503984	+	0.401914i
$944$		0			0
$945$		−	29.6881i		−	0.965754i
$946$		0			0
$947$	42.1908	−	9.62976i	1.37102	−	0.312925i	0.527283	−	0.849690i	$-0.323211\pi$
$947$	42.1908	−	9.62976i	1.37102	−	0.312925i	0.843732	+	0.536764i	$0.180354\pi$
$948$		0			0
$949$	3.55525	−	7.38256i	0.115408	−	0.239648i
$950$		0			0
$951$	−28.1335	−	35.2783i	−0.912290	−	1.14398i
$952$		0			0
$953$	4.62253	+	20.2526i	0.149738	+	0.656047i	0.992957	+	0.118476i	$0.0378009\pi$
$953$	4.62253	+	20.2526i	0.149738	+	0.656047i	−0.843218	+	0.537571i	$0.819342\pi$
$954$		0			0
$955$	−5.76271	−	4.59561i	−0.186477	−	0.148710i
$956$		0			0
$957$	3.50820	−	8.40938i	0.113404	−	0.271837i
$958$		0			0
$959$	−22.3237	−	17.8026i	−0.720870	−	0.574875i
$960$		0			0
$961$	−0.256241	−	1.12267i	−0.00826585	−	0.0362150i
$962$		0			0
$963$	9.39493	+	11.7809i	0.302747	+	0.379633i
$964$		0			0
$965$	5.73862	−	11.9164i	0.184733	−	0.383601i
$966$		0			0
$967$	−24.7863	+	5.65730i	−0.797073	+	0.181927i	−0.601616	−	0.798786i	$-0.705476\pi$
$967$	−24.7863	+	5.65730i	−0.797073	+	0.181927i	−0.195457	+	0.980712i	$0.562619\pi$
$968$		0			0
$969$			51.4006i			1.65122i
$970$		0			0
$971$	−24.9863	+	19.9259i	−0.801848	+	0.639453i	−0.936195	−	0.351482i	$-0.885678\pi$
$971$	−24.9863	+	19.9259i	−0.801848	+	0.639453i	0.134346	+	0.990934i	$0.457107\pi$
$972$		0			0
$973$	−49.9674	+	24.0630i	−1.60188	+	0.771425i
$974$		0			0
$975$	2.01693	+	4.18819i	0.0645933	+	0.134129i
$976$		0			0
$977$	42.2812	+	20.3615i	1.35269	+	0.651424i	0.962995	−	0.269518i	$-0.0868645\pi$
$977$	42.2812	+	20.3615i	1.35269	+	0.651424i	0.389700	+	0.920942i	$0.372579\pi$
$978$		0			0
$979$	−0.421543	+	1.84690i	−0.0134726	+	0.0590272i
$980$		0			0
$981$	−5.42058	+	6.79720i	−0.173066	+	0.217018i
$982$		0			0
$983$	43.0061	+	9.81586i	1.37168	+	0.313077i	0.843990	−	0.536359i	$-0.180201\pi$
$983$	43.0061	+	9.81586i	1.37168	+	0.313077i	0.527691	+	0.849436i	$0.323058\pi$
$984$		0			0
$985$	−48.2097			−1.53609
$986$		0			0
$987$	−19.3448			−0.615752
$988$		0			0
$989$	40.4783	+	9.23891i	1.28713	+	0.293780i
$990$		0			0
$991$	−37.6711	+	47.2381i	−1.19666	+	1.50057i	−0.378481	+	0.925609i	$0.623553\pi$
$991$	−37.6711	+	47.2381i	−1.19666	+	1.50057i	−0.818182	+	0.574959i	$0.805018\pi$
$992$		0			0
$993$	−6.39612	+	28.0233i	−0.202975	+	0.889291i
$994$		0			0
$995$	33.5388	+	16.1514i	1.06325	+	0.512034i
$996$		0			0
$997$	−1.14997	−	2.38794i	−0.0364200	−	0.0756269i	0.881965	−	0.471315i	$-0.156220\pi$
$997$	−1.14997	−	2.38794i	−0.0364200	−	0.0756269i	−0.918385	+	0.395688i	$0.870506\pi$
$998$		0			0
$999$	40.1698	−	19.3447i	1.27092	−	0.612041i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	116.2.i.a.93.1	yes	6
3.2	odd	2		1044.2.z.b.325.1		6
4.3	odd	2		464.2.y.b.209.1		6
29.5	even	14	inner	116.2.i.a.5.1	✓	6
29.11	odd	28		3364.2.a.n.1.6		6
29.13	even	14		3364.2.c.f.1681.1		6
29.16	even	7		3364.2.c.f.1681.6		6
29.18	odd	28		3364.2.a.n.1.1		6
87.5	odd	14		1044.2.z.b.469.1		6
116.63	odd	14		464.2.y.b.353.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
116.2.i.a.5.1	✓	6	29.5	even	14	inner
116.2.i.a.93.1	yes	6	1.1	even	1	trivial
464.2.y.b.209.1		6	4.3	odd	2
464.2.y.b.353.1		6	116.63	odd	14
1044.2.z.b.325.1		6	3.2	odd	2
1044.2.z.b.469.1		6	87.5	odd	14
3364.2.a.n.1.1		6	29.18	odd	28
3364.2.a.n.1.6		6	29.11	odd	28
3364.2.c.f.1681.1		6	29.13	even	14
3364.2.c.f.1681.6		6	29.16	even	7

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:	\( N \)	\(=\)	\( 116 = 2^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	116.i (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.90097 - 0.433884i) q^{3} +(1.46950 - 1.84270i) q^{5} +(0.653989 - 2.86531i) q^{7} +(0.722521 + 0.347948i) q^{9} +O(q^{10})\)	\(q+(-1.90097 - 0.433884i) q^{3} +(1.46950 - 1.84270i) q^{5} +(0.653989 - 2.86531i) q^{7} +(0.722521 + 0.347948i) q^{9} +(-0.376510 - 0.781831i) q^{11} +(3.87047 - 1.86392i) q^{13} +(-3.59299 + 2.86531i) q^{15} +4.86286i q^{17} +(-5.28501 + 1.20627i) q^{19} +(-2.48643 + 5.16312i) q^{21} +(2.33244 + 2.92478i) q^{23} +(-0.123490 - 0.541044i) q^{25} +(3.35086 + 2.67222i) q^{27} +(-4.38404 - 3.12733i) q^{29} +(4.27144 + 3.40636i) q^{31} +(0.376510 + 1.64960i) q^{33} +(-4.31886 - 5.41568i) q^{35} +(4.51357 - 9.37253i) q^{37} +(-8.16637 + 1.86392i) q^{39} +5.29150i q^{41} +(8.67725 - 6.91988i) q^{43} +(1.70291 - 0.820077i) q^{45} +(1.46466 + 3.04139i) q^{47} +(-1.47554 - 0.710583i) q^{49} +(2.10992 - 9.24415i) q^{51} +(-8.56734 + 10.7431i) q^{53} +(-1.99396 - 0.455108i) q^{55} +10.5700 q^{57} -7.60388 q^{59} +(0.961968 + 0.219563i) q^{61} +(1.46950 - 1.84270i) q^{63} +(2.25302 - 9.87113i) q^{65} +(3.71164 + 1.78743i) q^{67} +(-3.16487 - 6.57193i) q^{69} +(10.3644 - 4.99125i) q^{71} +(1.49127 - 1.18925i) q^{73} +1.08209i q^{75} +(-2.48643 + 0.567511i) q^{77} +(-3.61141 + 7.49917i) q^{79} +(-6.71044 - 8.41462i) q^{81} +(-0.199259 - 0.873009i) q^{83} +(8.96077 + 7.14598i) q^{85} +(6.97703 + 7.84711i) q^{87} +(-1.70679 - 1.36112i) q^{89} +(-2.80947 - 12.3091i) q^{91} +(-6.64191 - 8.32869i) q^{93} +(-5.54354 + 11.5113i) q^{95} +(-9.92274 + 2.26480i) q^{97} -0.695895i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 7 q^{3} - q^{5} + 9 q^{7} + 4 q^{9}+O(q^{10}) \) 6 * q - 7 * q^3 - q^5 + 9 * q^7 + 4 * q^9	\( 6 q - 7 q^{3} - q^{5} + 9 q^{7} + 4 q^{9} - 7 q^{11} + 9 q^{13} - 7 q^{15} - 7 q^{19} - 21 q^{21} + 15 q^{23} + 4 q^{25} - 7 q^{27} - 6 q^{29} + 7 q^{31} + 7 q^{33} - 33 q^{35} + 21 q^{37} - 7 q^{39} + 7 q^{43} - 3 q^{45} + 21 q^{47} - 18 q^{49} + 14 q^{51} - 5 q^{53} + 7 q^{55} + 14 q^{57} - 28 q^{59} + 21 q^{61} - q^{63} + 23 q^{65} + 25 q^{67} - 21 q^{69} + 29 q^{71} - 7 q^{73} - 21 q^{77} + 21 q^{79} - 2 q^{81} - 51 q^{83} + 28 q^{85} + 7 q^{87} - 35 q^{89} + 17 q^{91} - 7 q^{93} - 21 q^{95} - 49 q^{97}+O(q^{100}) \) 6 * q - 7 * q^3 - q^5 + 9 * q^7 + 4 * q^9 - 7 * q^11 + 9 * q^13 - 7 * q^15 - 7 * q^19 - 21 * q^21 + 15 * q^23 + 4 * q^25 - 7 * q^27 - 6 * q^29 + 7 * q^31 + 7 * q^33 - 33 * q^35 + 21 * q^37 - 7 * q^39 + 7 * q^43 - 3 * q^45 + 21 * q^47 - 18 * q^49 + 14 * q^51 - 5 * q^53 + 7 * q^55 + 14 * q^57 - 28 * q^59 + 21 * q^61 - q^63 + 23 * q^65 + 25 * q^67 - 21 * q^69 + 29 * q^71 - 7 * q^73 - 21 * q^77 + 21 * q^79 - 2 * q^81 - 51 * q^83 + 28 * q^85 + 7 * q^87 - 35 * q^89 + 17 * q^91 - 7 * q^93 - 21 * q^95 - 49 * q^97

Introduction

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Database

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