LMFDB - Embedded newform 592.2.bq.b.65.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(65,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 17]))

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

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

chi := DirichletCharacter("592.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.bq (of order $18$, degree $6$, not 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:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			65.2
Root			$-0.984808 - 0.173648i$ of defining polynomial
Character	$\chi$	$=$	592.65
Dual form			592.2.bq.b.337.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.266044 - 1.50881i) q^{3} +(-0.247315 + 0.294739i) q^{5} +(2.50048 + 2.09815i) q^{7} +(0.613341 + 0.223238i) q^{9} +O(q^{10})$	\(q+(0.266044 - 1.50881i) q^{3} +(-0.247315 + 0.294739i) q^{5} +(2.50048 + 2.09815i) q^{7} +(0.613341 + 0.223238i) q^{9} +(1.29236 + 2.23843i) q^{11} +(-0.466831 - 1.28261i) q^{13} +(0.378909 + 0.451566i) q^{15} +(-1.13965 + 3.13118i) q^{17} +(5.89485 + 1.03942i) q^{19} +(3.83095 - 3.21455i) q^{21} +(-6.53507 - 3.77303i) q^{23} +(0.842535 + 4.77825i) q^{25} +(2.79813 - 4.84651i) q^{27} +(2.78251 - 1.60649i) q^{29} +2.53737i q^{31} +(3.72120 - 1.35440i) q^{33} +(-1.23681 + 0.218083i) q^{35} +(0.543196 - 6.05846i) q^{37} +(-2.05941 + 0.363130i) q^{39} +(7.77046 - 2.82822i) q^{41} -4.33920i q^{43} +(-0.217486 + 0.125565i) q^{45} +(2.61455 - 4.52853i) q^{47} +(0.634616 + 3.59909i) q^{49} +(4.42116 + 2.55256i) q^{51} +(-6.64254 + 5.57375i) q^{53} +(-0.979373 - 0.172690i) q^{55} +(3.13658 - 8.61769i) q^{57} +(-8.33530 - 9.93362i) q^{59} +(-2.39847 - 6.58973i) q^{61} +(1.06526 + 1.84508i) q^{63} +(0.493489 + 0.179615i) q^{65} +(8.60881 + 7.22365i) q^{67} +(-7.43141 + 8.85641i) q^{69} +(-2.60464 + 14.7717i) q^{71} -15.0792 q^{73} +7.43364 q^{75} +(-1.46505 + 8.30870i) q^{77} +(-0.940587 + 1.12095i) q^{79} +(-5.06805 - 4.25260i) q^{81} +(-0.0104473 - 0.00380252i) q^{83} +(-0.641025 - 1.11029i) q^{85} +(-1.68361 - 4.62569i) q^{87} +(-0.612745 - 0.730241i) q^{89} +(1.52380 - 4.18661i) q^{91} +(3.82842 + 0.675054i) q^{93} +(-1.76424 + 1.48038i) q^{95} +(12.8332 + 7.40927i) q^{97} +(0.292954 + 1.66142i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 12 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 + 12 * q^7 - 6 * q^9	$ 12 q - 6 q^{3} + 12 q^{7} - 6 q^{9} + 6 q^{11} + 6 q^{13} + 18 q^{19} - 6 q^{21} - 18 q^{25} + 6 q^{27} + 18 q^{29} - 6 q^{33} - 18 q^{35} + 30 q^{37} - 30 q^{39} + 24 q^{41} - 18 q^{45} - 6 q^{47} + 12 q^{49} - 12 q^{53} + 18 q^{55} - 36 q^{57} - 36 q^{61} + 6 q^{63} + 36 q^{65} + 30 q^{67} - 18 q^{69} - 12 q^{71} + 36 q^{75} + 12 q^{77} - 6 q^{79} + 24 q^{81} + 48 q^{83} + 18 q^{85} - 36 q^{87} - 18 q^{89} + 6 q^{91} - 12 q^{93} + 36 q^{97} - 30 q^{99}+O(q^{100}) $ 12 * q - 6 * q^3 + 12 * q^7 - 6 * q^9 + 6 * q^11 + 6 * q^13 + 18 * q^19 - 6 * q^21 - 18 * q^25 + 6 * q^27 + 18 * q^29 - 6 * q^33 - 18 * q^35 + 30 * q^37 - 30 * q^39 + 24 * q^41 - 18 * q^45 - 6 * q^47 + 12 * q^49 - 12 * q^53 + 18 * q^55 - 36 * q^57 - 36 * q^61 + 6 * q^63 + 36 * q^65 + 30 * q^67 - 18 * q^69 - 12 * q^71 + 36 * q^75 + 12 * q^77 - 6 * q^79 + 24 * q^81 + 48 * q^83 + 18 * q^85 - 36 * q^87 - 18 * q^89 + 6 * q^91 - 12 * q^93 + 36 * q^97 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.266044	−	1.50881i	0.153601	−	0.871114i	−0.806453	−	0.591298i	$-0.798616\pi$
$3$	0.266044	−	1.50881i	0.153601	−	0.871114i	0.960054	−	0.279815i	$-0.0902733\pi$
$4$		0			0
$5$	−0.247315	+	0.294739i	−0.110603	+	0.131811i	−0.818506	−	0.574499i	$-0.805197\pi$
$5$	−0.247315	+	0.294739i	−0.110603	+	0.131811i	0.707903	+	0.706310i	$0.249641\pi$
$6$		0			0
$7$	2.50048	+	2.09815i	0.945091	+	0.793026i	0.978464	−	0.206417i	$-0.0661805\pi$
$7$	2.50048	+	2.09815i	0.945091	+	0.793026i	−0.0333729	+	0.999443i	$0.510625\pi$
$8$		0			0
$9$	0.613341	+	0.223238i	0.204447	+	0.0744126i
$10$		0			0
$11$	1.29236	+	2.23843i	0.389661	+	0.674912i	0.992404	−	0.123023i	$-0.0392590\pi$
$11$	1.29236	+	2.23843i	0.389661	+	0.674912i	−0.602743	+	0.797935i	$0.705926\pi$
$12$		0			0
$13$	−0.466831	−	1.28261i	−0.129476	−	0.355731i	0.857968	−	0.513703i	$-0.171727\pi$
$13$	−0.466831	−	1.28261i	−0.129476	−	0.355731i	−0.987444	+	0.157972i	$0.949504\pi$
$14$		0			0
$15$	0.378909	+	0.451566i	0.0978339	+	0.116594i
$16$		0			0
$17$	−1.13965	+	3.13118i	−0.276407	+	0.759422i	0.721356	+	0.692565i	$0.243519\pi$
$17$	−1.13965	+	3.13118i	−0.276407	+	0.759422i	−0.997763	+	0.0668568i	$0.978703\pi$
$18$		0			0
$19$	5.89485	+	1.03942i	1.35237	+	0.238459i	0.802431	−	0.596745i	$-0.203540\pi$
$19$	5.89485	+	1.03942i	1.35237	+	0.238459i	0.549939	+	0.835205i	$0.314651\pi$
$20$		0			0
$21$	3.83095	−	3.21455i	0.835982	−	0.701472i
$22$		0			0
$23$	−6.53507	−	3.77303i	−1.36266	−	0.786730i	−0.372680	−	0.927960i	$-0.621561\pi$
$23$	−6.53507	−	3.77303i	−1.36266	−	0.786730i	−0.989977	+	0.141230i	$0.954894\pi$
$24$		0			0
$25$	0.842535	+	4.77825i	0.168507	+	0.955650i
$26$		0			0
$27$	2.79813	−	4.84651i	0.538501	−	0.932711i
$28$		0			0
$29$	2.78251	−	1.60649i	0.516700	−	0.298317i	−0.218883	−	0.975751i	$-0.570241\pi$
$29$	2.78251	−	1.60649i	0.516700	−	0.298317i	0.735583	+	0.677434i	$0.236908\pi$
$30$		0			0
$31$			2.53737i			0.455726i	0.973693	+	0.227863i	$0.0731738\pi$
$31$			2.53737i			0.455726i	−0.973693	+	0.227863i	$0.926826\pi$
$32$		0			0
$33$	3.72120	−	1.35440i	0.647777	−	0.235772i
$34$		0			0
$35$	−1.23681	+	0.218083i	−0.209059	+	0.0368628i
$36$		0			0
$37$	0.543196	−	6.05846i	0.0893009	−	0.996005i
$37$	0.543196	−	6.05846i	0.0893009	−	0.996005i
$38$		0			0
$39$	−2.05941	+	0.363130i	−0.329770	+	0.0581473i
$40$		0			0
$41$	7.77046	−	2.82822i	1.21354	−	0.441693i	0.345611	−	0.938378i	$-0.387672\pi$
$41$	7.77046	−	2.82822i	1.21354	−	0.441693i	0.867931	+	0.496685i	$0.165449\pi$
$42$		0			0
$43$		−	4.33920i		−	0.661722i	−0.943680	−	0.330861i	$-0.892661\pi$
$43$		−	4.33920i		−	0.661722i	0.943680	−	0.330861i	$-0.107339\pi$
$44$		0			0
$45$	−0.217486	+	0.125565i	−0.0324208	+	0.0187182i
$46$		0			0
$47$	2.61455	−	4.52853i	0.381371	−	0.660554i	−0.609888	−	0.792488i	$-0.708785\pi$
$47$	2.61455	−	4.52853i	0.381371	−	0.660554i	0.991258	+	0.131934i	$0.0421188\pi$
$48$		0			0
$49$	0.634616	+	3.59909i	0.0906594	+	0.514155i
$50$		0			0
$51$	4.42116	+	2.55256i	0.619086	+	0.357430i
$52$		0			0
$53$	−6.64254	+	5.57375i	−0.912423	+	0.765614i	−0.972578	−	0.232575i	$-0.925285\pi$
$53$	−6.64254	+	5.57375i	−0.912423	+	0.765614i	0.0601551	+	0.998189i	$0.480840\pi$
$54$		0			0
$55$	−0.979373	−	0.172690i	−0.132059	−	0.0232855i
$56$		0			0
$57$	3.13658	−	8.61769i	0.415450	−	1.14144i
$58$		0			0
$59$	−8.33530	−	9.93362i	−1.08516	−	1.29325i	−0.953315	−	0.301978i	$-0.902353\pi$
$59$	−8.33530	−	9.93362i	−1.08516	−	1.29325i	−0.131849	−	0.991270i	$-0.542091\pi$
$60$		0			0
$61$	−2.39847	−	6.58973i	−0.307092	−	0.843728i	−0.993220	−	0.116248i	$-0.962913\pi$
$61$	−2.39847	−	6.58973i	−0.307092	−	0.843728i	0.686128	−	0.727481i	$-0.259309\pi$
$62$		0			0
$63$	1.06526	+	1.84508i	0.134210	+	0.232458i
$64$		0			0
$65$	0.493489	+	0.179615i	0.0612098	+	0.0222785i
$66$		0			0
$67$	8.60881	+	7.22365i	1.05173	+	0.882509i	0.993275	−	0.115781i	$-0.0369370\pi$
$67$	8.60881	+	7.22365i	1.05173	+	0.882509i	0.0584586	+	0.998290i	$0.481381\pi$
$68$		0			0
$69$	−7.43141	+	8.85641i	−0.894636	+	1.06619i
$70$		0			0
$71$	−2.60464	+	14.7717i	−0.309114	+	1.75307i	0.294363	+	0.955694i	$0.404893\pi$
$71$	−2.60464	+	14.7717i	−0.309114	+	1.75307i	−0.603477	+	0.797380i	$0.706219\pi$
$72$		0			0
$73$	−15.0792			−1.76489			−0.882445	−	0.470416i	$-0.844104\pi$
$73$	−15.0792			−1.76489			−0.882445	+	0.470416i	$0.844104\pi$
$74$		0			0
$75$	7.43364			0.858363
$76$		0			0
$77$	−1.46505	+	8.30870i	−0.166958	+	0.946864i
$78$		0			0
$79$	−0.940587	+	1.12095i	−0.105824	+	0.126117i	−0.816357	−	0.577548i	$-0.804010\pi$
$79$	−0.940587	+	1.12095i	−0.105824	+	0.126117i	0.710532	+	0.703664i	$0.248454\pi$
$80$		0			0
$81$	−5.06805	−	4.25260i	−0.563116	−	0.472511i
$82$		0			0
$83$	−0.0104473	−	0.00380252i	−0.00114674	−	0.000417381i	0.341447	−	0.939901i	$-0.389083\pi$
$83$	−0.0104473	−	0.00380252i	−0.00114674	−	0.000417381i	−0.342593	+	0.939484i	$0.611305\pi$
$84$		0			0
$85$	−0.641025	−	1.11029i	−0.0695290	−	0.120428i
$86$		0			0
$87$	−1.68361	−	4.62569i	−0.180502	−	0.495926i
$88$		0			0
$89$	−0.612745	−	0.730241i	−0.0649509	−	0.0774054i	0.732591	−	0.680669i	$-0.238311\pi$
$89$	−0.612745	−	0.730241i	−0.0649509	−	0.0774054i	−0.797542	+	0.603264i	$0.793867\pi$
$90$		0			0
$91$	1.52380	−	4.18661i	0.159738	−	0.438876i
$92$		0			0
$93$	3.82842	+	0.675054i	0.396989	+	0.0699998i
$94$		0			0
$95$	−1.76424	+	1.48038i	−0.181008	+	0.151883i
$96$		0			0
$97$	12.8332	+	7.40927i	1.30302	+	0.752297i	0.980920	−	0.194410i	$-0.0622791\pi$
$97$	12.8332	+	7.40927i	1.30302	+	0.752297i	0.322097	+	0.946707i	$0.395612\pi$
$98$		0			0
$99$	0.292954	+	1.66142i	0.0294430	+	0.166979i
$100$		0			0
$101$	−0.636260	+	1.10204i	−0.0633103	+	0.109657i	−0.895943	−	0.444169i	$-0.853499\pi$
$101$	−0.636260	+	1.10204i	−0.0633103	+	0.109657i	0.832633	+	0.553825i	$0.186832\pi$
$102$		0			0
$103$	−9.39301	+	5.42306i	−0.925521	+	0.534350i	−0.885392	−	0.464845i	$-0.846110\pi$
$103$	−9.39301	+	5.42306i	−0.925521	+	0.534350i	−0.0401287	+	0.999195i	$0.512777\pi$
$104$		0			0
$105$			1.92414i			0.187777i
$106$		0			0
$107$	−4.47254	+	1.62787i	−0.432377	+	0.157372i	−0.549034	−	0.835800i	$-0.685004\pi$
$107$	−4.47254	+	1.62787i	−0.432377	+	0.157372i	0.116657	+	0.993172i	$0.462782\pi$
$108$		0			0
$109$	9.49102	−	1.67352i	0.909075	−	0.160294i	0.300492	−	0.953784i	$-0.402849\pi$
$109$	9.49102	−	1.67352i	0.909075	−	0.160294i	0.608583	+	0.793490i	$0.291738\pi$
$110$		0			0
$111$	−8.99657	−	2.43140i	−0.853917	−	0.230778i
$112$		0			0
$113$	−12.7581	+	2.24960i	−1.20018	+	0.211624i	−0.737777	−	0.675044i	$-0.764124\pi$
$113$	−12.7581	+	2.24960i	−1.20018	+	0.211624i	−0.462405	+	0.886669i	$0.653013\pi$
$114$		0			0
$115$	2.72828	−	0.993013i	0.254414	−	0.0925990i
$116$		0			0
$117$		−	0.890890i		−	0.0823628i
$118$		0			0
$119$	−9.41935	+	5.43826i	−0.863470	+	0.498525i
$120$		0			0
$121$	2.15962	−	3.74057i	0.196329	−	0.340052i
$122$		0			0
$123$	−2.19996	−	12.4766i	−0.198364	−	1.12498i
$124$		0			0
$125$	−3.28274	−	1.89529i	−0.293618	−	0.169520i
$126$		0			0
$127$	−8.61094	+	7.22543i	−0.764097	+	0.641154i	−0.939190	−	0.343398i	$-0.888422\pi$
$127$	−8.61094	+	7.22543i	−0.764097	+	0.641154i	0.175093	+	0.984552i	$0.443977\pi$
$128$		0			0
$129$	−6.54704	−	1.15442i	−0.576435	−	0.101641i
$130$		0			0
$131$	−2.86257	+	7.86484i	−0.250104	+	0.687154i	0.749578	+	0.661916i	$0.230257\pi$
$131$	−2.86257	+	7.86484i	−0.250104	+	0.687154i	−0.999681	+	0.0252378i	$0.991966\pi$
$132$		0			0
$133$	12.5591	+	14.9673i	1.08901	+	1.29783i
$134$		0			0
$135$	0.736434	+	2.02334i	0.0633821	+	0.174141i
$136$		0			0
$137$	1.99206	+	3.45036i	0.170194	+	0.294784i	0.938487	−	0.345313i	$-0.112227\pi$
$137$	1.99206	+	3.45036i	0.170194	+	0.294784i	−0.768294	+	0.640097i	$0.778894\pi$
$138$		0			0
$139$	4.80315	+	1.74820i	0.407398	+	0.148281i	0.537586	−	0.843209i	$-0.319336\pi$
$139$	4.80315	+	1.74820i	0.407398	+	0.148281i	−0.130189	+	0.991489i	$0.541558\pi$
$140$		0			0
$141$	−6.13711	−	5.14965i	−0.516838	−	0.433679i
$142$		0			0
$143$	2.26771	−	2.70256i	0.189636	−	0.225999i
$144$		0			0
$145$	−0.214665	+	1.21742i	−0.0178269	+	0.101102i
$146$		0			0
$147$	5.59918			0.461813
$148$		0			0
$149$	−15.8700			−1.30012			−0.650060	−	0.759883i	$-0.725256\pi$
$149$	−15.8700			−1.30012			−0.650060	+	0.759883i	$0.725256\pi$
$150$		0			0
$151$	3.77998	−	21.4373i	0.307611	−	1.74455i	−0.303344	−	0.952881i	$-0.598103\pi$
$151$	3.77998	−	21.4373i	0.307611	−	1.74455i	0.610955	−	0.791665i	$-0.290786\pi$
$152$		0			0
$153$	−1.39799	+	1.66606i	−0.113021	+	0.134693i
$154$		0			0
$155$	−0.747863	−	0.627531i	−0.0600698	−	0.0504045i
$156$		0			0
$157$	9.16333	+	3.33518i	0.731314	+	0.266176i	0.680721	−	0.732543i	$-0.261667\pi$
$157$	9.16333	+	3.33518i	0.731314	+	0.266176i	0.0505928	+	0.998719i	$0.483889\pi$
$158$		0			0
$159$	6.64254	+	11.5052i	0.526788	+	0.912423i
$160$		0			0
$161$	−8.42442	−	23.1459i	−0.663937	−	1.82415i
$162$		0			0
$163$	−8.46213	−	10.0848i	−0.662805	−	0.789901i	0.324980	−	0.945721i	$-0.394642\pi$
$163$	−8.46213	−	10.0848i	−0.662805	−	0.789901i	−0.987785	+	0.155820i	$0.950198\pi$
$164$		0			0
$165$	−0.521113	+	1.43175i	−0.0405686	+	0.111461i
$166$		0			0
$167$	−5.51717	−	0.972826i	−0.426932	−	0.0752796i	−0.0439461	−	0.999034i	$-0.513993\pi$
$167$	−5.51717	−	0.972826i	−0.426932	−	0.0752796i	−0.382986	+	0.923754i	$0.625104\pi$
$168$		0			0
$169$	8.53143	−	7.15872i	0.656264	−	0.550671i
$170$		0			0
$171$	3.38351	+	1.95347i	0.258744	+	0.149386i
$172$		0			0
$173$	−1.88155	−	10.6708i	−0.143051	−	0.811285i	−0.968911	−	0.247409i	$-0.920421\pi$
$173$	−1.88155	−	10.6708i	−0.143051	−	0.811285i	0.825860	−	0.563876i	$-0.190690\pi$
$174$		0			0
$175$	−7.91874	+	13.7157i	−0.598601	+	1.03681i
$176$		0			0
$177$	−17.2055	+	9.93362i	−1.29325	+	0.746657i
$178$		0			0
$179$		−	6.07192i		−	0.453837i	−0.973914	−	0.226918i	$-0.927135\pi$
$179$		−	6.07192i		−	0.453837i	0.973914	−	0.226918i	$-0.0728651\pi$
$180$		0			0
$181$	−20.2540	+	7.37185i	−1.50547	+	0.547945i	−0.957469	−	0.288535i	$-0.906832\pi$
$181$	−20.2540	+	7.37185i	−1.50547	+	0.547945i	−0.547997	+	0.836480i	$0.684610\pi$
$182$		0			0
$183$	−10.5808	+	1.86567i	−0.782153	+	0.137915i
$184$		0			0
$185$	1.65132	+	1.65845i	0.121408	+	0.121932i
$186$		0			0
$187$	−8.48176	+	1.49556i	−0.620248	+	0.109366i
$188$		0			0
$189$	17.1654	−	6.24768i	1.24860	−	0.454452i
$190$		0			0
$191$		−	6.62693i		−	0.479508i	−0.970834	−	0.239754i	$-0.922933\pi$
$191$		−	6.62693i		−	0.479508i	0.970834	−	0.239754i	$-0.0770668\pi$
$192$		0			0
$193$	−19.7925	+	11.4272i	−1.42469	+	0.822548i	−0.996695	−	0.0812309i	$-0.974115\pi$
$193$	−19.7925	+	11.4272i	−1.42469	+	0.822548i	−0.428000	+	0.903779i	$0.640782\pi$
$194$		0			0
$195$	0.402296	−	0.696797i	0.0288090	−	0.0498987i
$196$		0			0
$197$	−2.56236	−	14.5319i	−0.182561	−	1.03535i	−0.929049	−	0.369956i	$-0.879373\pi$
$197$	−2.56236	−	14.5319i	−0.182561	−	1.03535i	0.746488	−	0.665398i	$-0.231738\pi$
$198$		0			0
$199$	1.27720	+	0.737389i	0.0905380	+	0.0522721i	0.544585	−	0.838705i	$-0.316687\pi$
$199$	1.27720	+	0.737389i	0.0905380	+	0.0522721i	−0.454047	+	0.890978i	$0.650020\pi$
$200$		0			0
$201$	13.1895	−	11.0673i	0.930313	−	0.780625i
$202$		0			0
$203$	10.3283	+	1.82115i	0.724901	+	0.127820i
$204$		0			0
$205$	−1.08817	+	2.98972i	−0.0760010	+	0.208811i
$206$		0			0
$207$	−3.16594	−	3.77303i	−0.220048	−	0.262243i
$208$		0			0
$209$	5.29158	+	14.5385i	0.366026	+	1.00565i
$210$		0			0
$211$	−1.20976	−	2.09537i	−0.0832835	−	0.144251i	0.821375	−	0.570389i	$-0.193207\pi$
$211$	−1.20976	−	2.09537i	−0.0832835	−	0.144251i	−0.904658	+	0.426137i	$0.859874\pi$
$212$		0			0
$213$	21.5947	+	7.85984i	1.47965	+	0.538547i
$214$		0			0
$215$	1.27893	+	1.07315i	0.0872224	+	0.0731883i
$216$		0			0
$217$	−5.32379	+	6.34464i	−0.361402	+	0.430702i
$218$		0			0
$219$	−4.01174	+	22.7517i	−0.271089	+	1.53742i
$220$		0			0
$221$	4.54809			0.305938
$222$		0			0
$223$	6.94726			0.465223			0.232611	−	0.972570i	$-0.425273\pi$
$223$	6.94726			0.465223			0.232611	+	0.972570i	$0.425273\pi$
$224$		0			0
$225$	−0.549925	+	3.11878i	−0.0366617	+	0.207919i
$226$		0			0
$227$	14.0443	−	16.7373i	0.932150	−	1.11089i	−0.0614692	−	0.998109i	$-0.519579\pi$
$227$	14.0443	−	16.7373i	0.932150	−	1.11089i	0.993619	−	0.112785i	$-0.0359770\pi$
$228$		0			0
$229$	−3.25576	−	2.73191i	−0.215147	−	0.180530i	0.528845	−	0.848719i	$-0.322625\pi$
$229$	−3.25576	−	2.73191i	−0.215147	−	0.180530i	−0.743992	+	0.668189i	$0.767070\pi$
$230$		0			0
$231$	12.1465	+	4.42097i	0.799181	+	0.290878i
$232$		0			0
$233$	−8.67215	−	15.0206i	−0.568131	−	0.984032i	−0.996751	−	0.0805473i	$-0.974333\pi$
$233$	−8.67215	−	15.0206i	−0.568131	−	0.984032i	0.428619	−	0.903485i	$-0.359000\pi$
$234$		0			0
$235$	0.688116	+	1.89058i	0.0448877	+	0.123328i
$236$		0			0
$237$	1.44106	+	1.71739i	0.0936071	+	0.111557i
$238$		0			0
$239$	6.27893	−	17.2512i	0.406150	−	1.11589i	−0.553047	−	0.833150i	$-0.686535\pi$
$239$	6.27893	−	17.2512i	0.406150	−	1.11589i	0.959197	−	0.282738i	$-0.0912428\pi$
$240$		0			0
$241$	23.1096	+	4.07485i	1.48862	+	0.262484i	0.858017	−	0.513621i	$-0.171696\pi$
$241$	23.1096	+	4.07485i	1.48862	+	0.262484i	0.630604	+	0.776105i	$0.282807\pi$
$242$		0			0
$243$	5.09627	−	4.27628i	0.326926	−	0.274323i
$244$		0			0
$245$	−1.21774	−	0.703063i	−0.0777986	−	0.0449171i
$246$		0			0
$247$	−1.41873	−	8.04601i	−0.0902715	−	0.511955i
$248$		0			0
$249$	−0.00851674	+	0.0147514i	−0.000539727	+	0.000934834i
$250$		0			0
$251$	−5.28405	+	3.05074i	−0.333526	+	0.192561i	−0.657405	−	0.753537i	$-0.728346\pi$
$251$	−5.28405	+	3.05074i	−0.333526	+	0.192561i	0.323879	+	0.946098i	$0.395013\pi$
$252$		0			0
$253$		−	19.5044i		−	1.22623i
$254$		0			0
$255$	−1.84576	+	0.671801i	−0.115586	+	0.0420698i
$256$		0			0
$257$	4.28106	−	0.754866i	0.267045	−	0.0470873i	−0.0385222	−	0.999258i	$-0.512265\pi$
$257$	4.28106	−	0.754866i	0.267045	−	0.0470873i	0.305567	+	0.952170i	$0.401154\pi$
$258$		0			0
$259$	14.0698	−	14.0093i	0.874255	−	0.870497i
$260$		0			0
$261$	2.06526	−	0.364161i	0.127836	−	0.0225410i
$262$		0			0
$263$	−3.81031	+	1.38684i	−0.234954	+	0.0855163i	−0.456814	−	0.889562i	$-0.651009\pi$
$263$	−3.81031	+	1.38684i	−0.234954	+	0.0855163i	0.221860	+	0.975079i	$0.428787\pi$
$264$		0			0
$265$		−	3.33629i		−	0.204947i
$266$		0			0
$267$	−1.26481	+	0.730241i	−0.0774054	+	0.0446900i
$268$		0			0
$269$	−4.39669	+	7.61528i	−0.268071	+	0.464312i	−0.968364	−	0.249544i	$-0.919719\pi$
$269$	−4.39669	+	7.61528i	−0.268071	+	0.464312i	0.700293	+	0.713856i	$0.253053\pi$
$270$		0			0
$271$	2.24218	+	12.7160i	0.136203	+	0.772444i	0.974015	+	0.226485i	$0.0727235\pi$
$271$	2.24218	+	12.7160i	0.136203	+	0.772444i	−0.837812	+	0.545959i	$0.816165\pi$
$272$		0			0
$273$	−5.91141	−	3.41296i	−0.357775	−	0.206561i
$274$		0			0
$275$	−9.60693	+	8.06117i	−0.579319	+	0.486107i
$276$		0			0
$277$	7.65829	+	1.35036i	0.460142	+	0.0811355i	0.398914	−	0.916988i	$-0.369387\pi$
$277$	7.65829	+	1.35036i	0.460142	+	0.0811355i	0.0612280	+	0.998124i	$0.480498\pi$
$278$		0			0
$279$	−0.566438	+	1.55627i	−0.0339117	+	0.0931717i
$280$		0			0
$281$	0.149454	+	0.178113i	0.00891569	+	0.0106253i	0.770484	−	0.637459i	$-0.220015\pi$
$281$	0.149454	+	0.178113i	0.00891569	+	0.0106253i	−0.761568	+	0.648085i	$0.775570\pi$
$282$		0			0
$283$	4.38915	+	12.0591i	0.260908	+	0.716838i	0.999107	+	0.0422550i	$0.0134542\pi$
$283$	4.38915	+	12.0591i	0.260908	+	0.716838i	−0.738199	+	0.674583i	$0.764324\pi$
$284$		0			0
$285$	1.76424	+	3.05576i	0.104505	+	0.181008i
$286$		0			0
$287$	25.3639	+	9.23169i	1.49718	+	0.544930i
$288$		0			0
$289$	4.51731	+	3.79047i	0.265724	+	0.222969i
$290$		0			0
$291$	14.5934	−	17.3917i	0.855481	−	1.01952i
$292$		0			0
$293$	−4.27944	+	24.2699i	−0.250007	+	1.41786i	0.558563	+	0.829462i	$0.311353\pi$
$293$	−4.27944	+	24.2699i	−0.250007	+	1.41786i	−0.808570	+	0.588400i	$0.799758\pi$
$294$		0			0
$295$	4.98927			0.290487
$296$		0			0
$297$	14.4648			0.839331
$298$		0			0
$299$	−1.78854	+	10.1433i	−0.103434	+	0.586602i
$300$		0			0
$301$	9.10429	−	10.8501i	0.524762	−	0.625387i
$302$		0			0
$303$	1.49349	+	1.25319i	0.0857988	+	0.0719938i
$304$		0			0
$305$	2.53543	+	0.922820i	0.145178	+	0.0528405i
$306$		0			0
$307$	3.45566	+	5.98538i	0.197225	+	0.341604i	0.947628	−	0.319377i	$-0.103474\pi$
$307$	3.45566	+	5.98538i	0.197225	+	0.341604i	−0.750403	+	0.660981i	$0.770140\pi$
$308$		0			0
$309$	5.68342	+	15.6151i	0.323319	+	0.888310i
$310$		0			0
$311$	−1.06612	−	1.27056i	−0.0604542	−	0.0720466i	0.734970	−	0.678100i	$-0.237196\pi$
$311$	−1.06612	−	1.27056i	−0.0604542	−	0.0720466i	−0.795424	+	0.606053i	$0.792752\pi$
$312$		0			0
$313$	8.87573	−	24.3859i	0.501686	−	1.37837i	−0.387942	−	0.921684i	$-0.626814\pi$
$313$	8.87573	−	24.3859i	0.501686	−	1.37837i	0.889628	−	0.456687i	$-0.150964\pi$
$314$		0			0
$315$	−0.807272	−	0.142344i	−0.0454846	−	0.00802017i
$316$		0			0
$317$	−8.69447	+	7.29553i	−0.488330	+	0.409758i	−0.853427	−	0.521212i	$-0.825480\pi$
$317$	−8.69447	+	7.29553i	−0.488330	+	0.409758i	0.365097	+	0.930969i	$0.381036\pi$
$318$		0			0
$319$	7.19201	+	4.15231i	0.402675	+	0.232485i
$320$		0			0
$321$	1.26626	+	7.18132i	0.0706758	+	0.400822i
$322$		0			0
$323$	−9.97269	+	17.2732i	−0.554896	+	0.961107i
$324$		0			0
$325$	5.73530	−	3.31128i	0.318137	−	0.183677i
$326$		0			0
$327$		−	14.7654i		−	0.816529i
$328$		0			0
$329$	16.0391	−	5.83777i	0.884266	−	0.321847i
$330$		0			0
$331$	12.6426	−	2.22924i	0.694903	−	0.122530i	0.184970	−	0.982744i	$-0.440781\pi$
$331$	12.6426	−	2.22924i	0.694903	−	0.122530i	0.509933	+	0.860214i	$0.329670\pi$
$332$		0			0
$333$	1.68564	−	3.59464i	0.0923726	−	0.196985i
$334$		0			0
$335$	−4.25818	+	0.750832i	−0.232649	+	0.0410224i
$336$		0			0
$337$	−5.36736	+	1.95356i	−0.292379	+	0.106417i	−0.484045	−	0.875043i	$-0.660833\pi$
$337$	−5.36736	+	1.95356i	−0.292379	+	0.106417i	0.191666	+	0.981460i	$0.438611\pi$
$338$		0			0
$339$			19.8481i			1.07800i
$340$		0			0
$341$	−5.67973	+	3.27919i	−0.307575	+	0.177578i
$342$		0			0
$343$	5.45991	−	9.45685i	0.294808	−	0.510622i
$344$		0			0
$345$	−0.772427	−	4.38065i	−0.0415861	−	0.235846i
$346$		0			0
$347$	−28.0087	−	16.1708i	−1.50358	−	0.868095i	−0.999991	−	0.00415382i	$-0.998678\pi$
$347$	−28.0087	−	16.1708i	−1.50358	−	0.868095i	−0.503593	−	0.863941i	$-0.667989\pi$
$348$		0			0
$349$	−19.0990	+	16.0260i	−1.02235	+	0.857852i	−0.989921	−	0.141622i	$-0.954768\pi$
$349$	−19.0990	+	16.0260i	−1.02235	+	0.857852i	−0.0324270	+	0.999474i	$0.510324\pi$
$350$		0			0
$351$	−7.52242	−	1.32641i	−0.401517	−	0.0707983i
$352$		0			0
$353$	2.95544	−	8.12001i	0.157302	−	0.432185i	−0.835858	−	0.548946i	$-0.815029\pi$
$353$	2.95544	−	8.12001i	0.157302	−	0.432185i	0.993160	+	0.116762i	$0.0372513\pi$
$354$		0			0
$355$	−3.70962	−	4.42095i	−0.196886	−	0.234640i
$356$		0			0
$357$	5.69936	+	15.6589i	0.301642	+	0.828755i
$358$		0			0
$359$	1.92924	+	3.34154i	0.101821	+	0.176360i	0.912435	−	0.409221i	$-0.134200\pi$
$359$	1.92924	+	3.34154i	0.101821	+	0.176360i	−0.810614	+	0.585581i	$0.800866\pi$
$360$		0			0
$361$	15.8146	+	5.75606i	0.832350	+	0.302951i
$362$		0			0
$363$	−5.06927	−	4.25362i	−0.266068	−	0.223257i
$364$		0			0
$365$	3.72932	−	4.44444i	0.195202	−	0.232632i
$366$		0			0
$367$	−1.81571	+	10.2974i	−0.0947794	+	0.537521i	0.900035	+	0.435817i	$0.143540\pi$
$367$	−1.81571	+	10.2974i	−0.0947794	+	0.537521i	−0.994815	+	0.101704i	$0.967571\pi$
$368$		0			0
$369$	5.39731			0.280973
$370$		0			0
$371$	−28.3041			−1.46947
$372$		0			0
$373$	1.71315	−	9.71578i	0.0887038	−	0.503064i	−0.907792	−	0.419421i	$-0.862233\pi$
$373$	1.71315	−	9.71578i	0.0887038	−	0.503064i	0.996496	−	0.0836434i	$-0.0266557\pi$
$374$		0			0
$375$	−3.73300	+	4.44882i	−0.192771	+	0.229736i
$376$		0			0
$377$	−3.35945	−	2.81892i	−0.173021	−	0.145182i
$378$		0			0
$379$	2.33157	+	0.848623i	0.119765	+	0.0435908i	0.401207	−	0.915987i	$-0.368591\pi$
$379$	2.33157	+	0.848623i	0.119765	+	0.0435908i	−0.281443	+	0.959578i	$0.590813\pi$
$380$		0			0
$381$	8.61094	+	14.9146i	0.441152	+	0.764097i
$382$		0			0
$383$	−8.74336	−	24.0222i	−0.446765	−	1.22748i	−0.934963	−	0.354744i	$-0.884568\pi$
$383$	−8.74336	−	24.0222i	−0.446765	−	1.22748i	0.488199	−	0.872733i	$-0.337654\pi$
$384$		0			0
$385$	−2.08657	−	2.48668i	−0.106341	−	0.126733i
$386$		0			0
$387$	0.968674	−	2.66141i	0.0492404	−	0.135287i
$388$		0			0
$389$	−6.27824	−	1.10702i	−0.318319	−	0.0561283i	0.0122057	−	0.999926i	$-0.496115\pi$
$389$	−6.27824	−	1.10702i	−0.318319	−	0.0561283i	−0.330525	+	0.943797i	$0.607226\pi$
$390$		0			0
$391$	19.2617	−	16.1625i	0.974107	−	0.817373i
$392$		0			0
$393$	11.1050	+	6.41147i	0.560173	+	0.323416i
$394$		0			0
$395$	−0.0977655	−	0.554456i	−0.00491911	−	0.0278977i
$396$		0			0
$397$	18.7489	−	32.4740i	0.940979	−	1.62982i	0.177370	−	0.984144i	$-0.443241\pi$
$397$	18.7489	−	32.4740i	0.940979	−	1.62982i	0.763609	−	0.645679i	$-0.223426\pi$
$398$		0			0
$399$	25.9241	−	14.9673i	1.29783	−	0.749303i
$400$		0			0
$401$			35.1464i			1.75513i	0.479462	+	0.877563i	$0.340832\pi$
$401$			35.1464i			1.75513i	−0.479462	+	0.877563i	$0.659168\pi$
$402$		0			0
$403$	3.25445	−	1.18452i	0.162116	−	0.0590054i
$404$		0			0
$405$	2.50681	−	0.442019i	0.124565	−	0.0219641i
$406$		0			0
$407$	14.2634	−	6.61379i	0.707013	−	0.327834i
$408$		0			0
$409$	0.443894	−	0.0782704i	0.0219491	−	0.00387022i	−0.162663	−	0.986682i	$-0.552008\pi$
$409$	0.443894	−	0.0782704i	0.0219491	−	0.00387022i	0.184612	+	0.982811i	$0.440897\pi$
$410$		0			0
$411$	5.73592	−	2.08770i	0.282932	−	0.102979i
$412$		0			0
$413$		−	42.3275i		−	2.08280i
$414$		0			0
$415$	0.00370454	−	0.00213882i	0.000181849	−	0.000104990i
$416$		0			0
$417$	3.91556	−	6.78195i	0.191746	−	0.332114i
$418$		0			0
$419$	2.65878	+	15.0787i	0.129890	+	0.736642i	0.978283	+	0.207275i	$0.0664594\pi$
$419$	2.65878	+	15.0787i	0.129890	+	0.736642i	−0.848393	+	0.529367i	$0.822429\pi$
$420$		0			0
$421$	−19.3959	−	11.1982i	−0.945299	−	0.545769i	−0.0536815	−	0.998558i	$-0.517096\pi$
$421$	−19.3959	−	11.1982i	−0.945299	−	0.545769i	−0.891617	+	0.452789i	$0.850429\pi$
$422$		0			0
$423$	2.61455	−	2.19386i	0.127124	−	0.106669i
$424$		0			0
$425$	−15.9217	−	2.80743i	−0.772318	−	0.136180i
$426$		0			0
$427$	7.82893	−	21.5098i	0.378868	−	1.04093i
$428$		0			0
$429$	−3.47434	−	4.14056i	−0.167743	−	0.199908i
$430$		0			0
$431$	0.0349134	+	0.0959236i	0.00168172	+	0.00462048i	0.940531	−	0.339709i	$-0.110329\pi$
$431$	0.0349134	+	0.0959236i	0.00168172	+	0.00462048i	−0.938849	+	0.344329i	$0.888106\pi$
$432$		0			0
$433$	−3.96357	−	6.86510i	−0.190477	−	0.329916i	0.754931	−	0.655804i	$-0.227670\pi$
$433$	−3.96357	−	6.86510i	−0.190477	−	0.329916i	−0.945408	+	0.325888i	$0.894337\pi$
$434$		0			0
$435$	1.77976	+	0.647778i	0.0853327	+	0.0310586i
$436$		0			0
$437$	−34.6015	−	29.0341i	−1.65521	−	1.38889i
$438$		0			0
$439$	−4.86630	+	5.79944i	−0.232256	+	0.276792i	−0.869567	−	0.493815i	$-0.835602\pi$
$439$	−4.86630	+	5.79944i	−0.232256	+	0.276792i	0.637311	+	0.770607i	$0.280047\pi$
$440$		0			0
$441$	−0.414216	+	2.34914i	−0.0197246	+	0.111864i
$442$		0			0
$443$	−15.9856			−0.759499			−0.379749	−	0.925089i	$-0.623990\pi$
$443$	−15.9856			−0.759499			−0.379749	+	0.925089i	$0.623990\pi$
$444$		0			0
$445$	0.366772			0.0173867
$446$		0			0
$447$	−4.22212	+	23.9448i	−0.199700	+	1.13255i
$448$		0			0
$449$	−18.4321	+	21.9666i	−0.869866	+	1.03667i	0.129119	+	0.991629i	$0.458785\pi$
$449$	−18.4321	+	21.9666i	−0.869866	+	1.03667i	−0.998985	+	0.0450373i	$0.985659\pi$
$450$		0			0
$451$	16.3730	+	13.7386i	0.770974	+	0.646924i
$452$		0			0
$453$	−31.3393	−	11.4066i	−1.47245	−	0.535928i
$454$		0			0
$455$	0.857098	+	1.48454i	0.0401814	+	0.0695962i
$456$		0			0
$457$	0.0359519	+	0.0987770i	0.00168176	+	0.00462059i	0.940531	−	0.339709i	$-0.110329\pi$
$457$	0.0359519	+	0.0987770i	0.00168176	+	0.00462059i	−0.938849	+	0.344329i	$0.888106\pi$
$458$		0			0
$459$	11.9864	+	14.2848i	0.559476	+	0.666757i
$460$		0			0
$461$	8.19825	−	22.5245i	0.381831	−	1.04907i	−0.588754	−	0.808312i	$-0.700381\pi$
$461$	8.19825	−	22.5245i	0.381831	−	1.04907i	0.970585	−	0.240759i	$-0.0773964\pi$
$462$		0			0
$463$	20.4361	+	3.60344i	0.949747	+	0.167466i	0.627000	−	0.779019i	$-0.284283\pi$
$463$	20.4361	+	3.60344i	0.949747	+	0.167466i	0.322747	+	0.946485i	$0.395394\pi$
$464$		0			0
$465$	−1.14579	+	0.961434i	−0.0531348	+	0.0445854i
$466$		0			0
$467$	−15.1492	−	8.74642i	−0.701023	−	0.404736i	0.106705	−	0.994291i	$-0.465970\pi$
$467$	−15.1492	−	8.74642i	−0.701023	−	0.404736i	−0.807728	+	0.589555i	$0.799303\pi$
$468$		0			0
$469$	6.36983	+	36.1251i	0.294132	+	1.66810i
$470$		0			0
$471$	7.47002	−	12.9385i	0.344200	−	0.596172i
$472$		0			0
$473$	9.71300	−	5.60780i	0.446604	−	0.257847i
$474$		0			0
$475$			29.0428i			1.33258i
$476$		0			0
$477$	−5.31841	+	1.93574i	−0.243513	+	0.0886317i
$478$		0			0
$479$	6.77593	−	1.19478i	0.309600	−	0.0545909i	−0.0166894	−	0.999861i	$-0.505313\pi$
$479$	6.77593	−	1.19478i	0.309600	−	0.0545909i	0.326290	+	0.945270i	$0.394202\pi$
$480$		0			0
$481$	−8.02421	+	2.13157i	−0.365872	+	0.0971912i
$482$		0			0
$483$	−37.1641	+	6.55304i	−1.69103	+	0.298174i
$484$		0			0
$485$	−5.35766	+	1.95003i	−0.243279	+	0.0885462i
$486$		0			0
$487$		−	1.70810i		−	0.0774014i	−0.999251	−	0.0387007i	$-0.987678\pi$
$487$		−	1.70810i		−	0.0774014i	0.999251	−	0.0387007i	$-0.0123219\pi$
$488$		0			0
$489$	−17.4673	+	10.0848i	−0.789901	+	0.456049i
$490$		0			0
$491$	5.31153	−	9.19983i	0.239706	−	0.415183i	−0.720924	−	0.693014i	$-0.756282\pi$
$491$	5.31153	−	9.19983i	0.239706	−	0.415183i	0.960630	+	0.277831i	$0.0896157\pi$
$492$		0			0
$493$	1.85908	+	10.5434i	0.0837288	+	0.474850i
$494$		0			0
$495$	−0.562138	−	0.324551i	−0.0252662	−	0.0145875i
$496$		0			0
$497$	−37.5060	+	31.4713i	−1.68237	+	1.41168i
$498$		0			0
$499$	−34.9319	−	6.15943i	−1.56376	−	0.275734i	−0.676306	−	0.736621i	$-0.736420\pi$
$499$	−34.9319	−	6.15943i	−1.56376	−	0.275734i	−0.887459	+	0.460887i	$0.847531\pi$
$500$		0			0
$501$	−2.93563	+	8.06557i	−0.131154	+	0.360343i
$502$		0			0
$503$	19.3402	+	23.0487i	0.862336	+	1.02769i	0.999311	+	0.0371171i	$0.0118174\pi$
$503$	19.3402	+	23.0487i	0.862336	+	1.02769i	−0.136975	+	0.990574i	$0.543738\pi$
$504$		0			0
$505$	−0.167456	−	0.460081i	−0.00745168	−	0.0204733i
$506$		0			0
$507$	−8.53143	−	14.7769i	−0.378894	−	0.656264i
$508$		0			0
$509$	22.6380	+	8.23957i	1.00341	+	0.365213i	0.790900	−	0.611946i	$-0.209613\pi$
$509$	22.6380	+	8.23957i	1.00341	+	0.365213i	0.212513	+	0.977158i	$0.431835\pi$
$510$		0			0
$511$	−37.7052	−	31.6385i	−1.66798	−	1.39960i
$512$		0			0
$513$	21.5321	−	25.6610i	0.950666	−	1.13296i
$514$		0			0
$515$	0.724650	−	4.10969i	0.0319319	−	0.181095i
$516$		0			0
$517$	13.5157			0.594421
$518$		0			0
$519$	−16.6008			−0.728694
$520$		0			0
$521$	−0.130158	+	0.738160i	−0.00570231	+	0.0323394i	−0.987526	−	0.157455i	$-0.949671\pi$
$521$	−0.130158	+	0.738160i	−0.00570231	+	0.0323394i	0.981824	+	0.189794i	$0.0607822\pi$
$522$		0			0
$523$	−1.31038	+	1.56165i	−0.0572989	+	0.0682862i	−0.793933	−	0.608006i	$-0.791970\pi$
$523$	−1.31038	+	1.56165i	−0.0572989	+	0.0682862i	0.736634	+	0.676292i	$0.236414\pi$
$524$		0			0
$525$	18.5876	+	15.5969i	0.811231	+	0.680704i
$526$		0			0
$527$	−7.94496	−	2.89173i	−0.346088	−	0.125966i
$528$		0			0
$529$	16.9714	+	29.3954i	0.737889	+	1.27806i
$530$		0			0
$531$	−2.89482	−	7.95345i	−0.125624	−	0.345150i
$532$		0			0
$533$	−7.25498	−	8.64615i	−0.314248	−	0.374506i
$534$		0			0
$535$	0.626331	−	1.72083i	0.0270787	−	0.0743980i
$536$		0			0
$537$	−9.16140	−	1.61540i	−0.395343	−	0.0697097i
$538$		0			0
$539$	−7.23615	+	6.07185i	−0.311683	+	0.261533i
$540$		0			0
$541$	−27.1442	−	15.6717i	−1.16702	−	0.673778i	−0.214042	−	0.976824i	$-0.568663\pi$
$541$	−27.1442	−	15.6717i	−1.16702	−	0.673778i	−0.952976	+	0.303046i	$0.901996\pi$
$542$		0			0
$543$	5.73428	+	32.5207i	0.246081	+	1.39560i
$544$		0			0
$545$	−1.85402	+	3.21126i	−0.0794176	+	0.137555i
$546$		0			0
$547$	−15.7325	+	9.08317i	−0.672674	+	0.388368i	−0.797089	−	0.603862i	$-0.793628\pi$
$547$	−15.7325	+	9.08317i	−0.672674	+	0.388368i	0.124415	+	0.992230i	$0.460294\pi$
$548$		0			0
$549$		−	4.57718i		−	0.195349i
$550$		0			0
$551$	18.0723	−	6.57778i	0.769906	−	0.280223i
$552$		0			0
$553$	−4.70383	+	0.829413i	−0.200027	+	0.0352702i
$554$		0			0
$555$	2.94162	−	2.05032i	0.124865	−	0.0870311i
$556$		0			0
$557$	32.4061	−	5.71408i	1.37309	−	0.242113i	0.562051	−	0.827102i	$-0.310012\pi$
$557$	32.4061	−	5.71408i	1.37309	−	0.242113i	0.811041	+	0.584989i	$0.198901\pi$
$558$		0			0
$559$	−5.56549	+	2.02567i	−0.235395	+	0.0856768i
$560$		0			0
$561$			13.1953i			0.557105i
$562$		0			0
$563$	−29.7054	+	17.1504i	−1.25193	+	0.722804i	−0.971493	−	0.237068i	$-0.923814\pi$
$563$	−29.7054	+	17.1504i	−1.25193	+	0.722804i	−0.280440	+	0.959872i	$0.590480\pi$
$564$		0			0
$565$	2.49223	−	4.31667i	0.104849	−	0.181604i
$566$		0			0
$567$	−3.74995	−	21.2670i	−0.157483	−	0.893132i
$568$		0			0
$569$	18.3769	+	10.6099i	0.770398	+	0.444789i	0.833017	−	0.553248i	$-0.186612\pi$
$569$	18.3769	+	10.6099i	0.770398	+	0.444789i	−0.0626186	+	0.998038i	$0.519945\pi$
$570$		0			0
$571$	−12.5989	+	10.5717i	−0.527247	+	0.442413i	−0.867150	−	0.498048i	$-0.834050\pi$
$571$	−12.5989	+	10.5717i	−0.527247	+	0.442413i	0.339902	+	0.940461i	$0.389606\pi$
$572$		0			0
$573$	−9.99880	−	1.76306i	−0.417706	−	0.0736528i
$574$		0			0
$575$	12.5224	−	34.4051i	0.522222	−	1.43479i
$576$		0			0
$577$	−23.3471	−	27.8240i	−0.971952	−	1.15833i	−0.987368	−	0.158446i	$-0.949352\pi$
$577$	−23.3471	−	27.8240i	−0.971952	−	1.15833i	0.0154162	−	0.999881i	$-0.495093\pi$
$578$		0			0
$579$	11.9758	+	32.9033i	0.497698	+	1.36742i
$580$		0			0
$581$	−0.0181451	−	0.0314282i	−0.000752784	−	0.00130386i
$582$		0			0
$583$	−21.0610	−	7.66558i	−0.872258	−	0.317476i
$584$		0			0
$585$	0.262580	+	0.220331i	0.0108563	+	0.00910956i
$586$		0			0
$587$	−24.1202	+	28.7453i	−0.995547	+	1.18645i	−0.0130981	+	0.999914i	$0.504169\pi$
$587$	−24.1202	+	28.7453i	−0.995547	+	1.18645i	−0.982449	+	0.186532i	$0.940275\pi$
$588$		0			0
$589$	−2.63740	+	14.9574i	−0.108672	+	0.616310i
$590$		0			0
$591$	−22.6076			−0.929953
$592$		0			0
$593$	−10.0159			−0.411302			−0.205651	−	0.978625i	$-0.565931\pi$
$593$	−10.0159			−0.411302			−0.205651	+	0.978625i	$0.565931\pi$
$594$		0			0
$595$	0.726682	−	4.12122i	0.0297910	−	0.168953i
$596$		0			0
$597$	1.45237	−	1.73087i	0.0594417	−	0.0708398i
$598$		0			0
$599$	25.7808	+	21.6326i	1.05337	+	0.883886i	0.993444	−	0.114317i	$-0.0364678\pi$
$599$	25.7808	+	21.6326i	1.05337	+	0.883886i	0.0599300	+	0.998203i	$0.480912\pi$
$600$		0			0
$601$	40.2252	+	14.6408i	1.64082	+	0.597209i	0.987182	−	0.159599i	$-0.0510202\pi$
$601$	40.2252	+	14.6408i	1.64082	+	0.597209i	0.653637	+	0.756808i	$0.273242\pi$
$602$		0			0
$603$	3.66754	+	6.35237i	0.149354	+	0.258688i
$604$		0			0
$605$	0.568385	+	1.56163i	0.0231081	+	0.0634891i
$606$		0			0
$607$	−3.45545	−	4.11804i	−0.140252	−	0.167146i	0.691346	−	0.722524i	$-0.257018\pi$
$607$	−3.45545	−	4.11804i	−0.140252	−	0.167146i	−0.831598	+	0.555378i	$0.812574\pi$
$608$		0			0
$609$	5.49555	−	15.0989i	0.222691	−	0.611838i
$610$		0			0
$611$	−7.02887	−	1.23938i	−0.284358	−	0.0501400i
$612$		0			0
$613$	−25.6002	+	21.4811i	−1.03398	+	0.867614i	−0.991319	−	0.131476i	$-0.958028\pi$
$613$	−25.6002	+	21.4811i	−1.03398	+	0.867614i	−0.0426623	+	0.999090i	$0.513584\pi$
$614$		0			0
$615$	4.22143	+	2.43724i	0.170224	+	0.0982791i
$616$		0			0
$617$	−0.878588	−	4.98272i	−0.0353706	−	0.200597i	0.962002	−	0.273044i	$-0.0880303\pi$
$617$	−0.878588	−	4.98272i	−0.0353706	−	0.200597i	−0.997372	+	0.0724469i	$0.976919\pi$
$618$		0			0
$619$	17.8909	−	30.9879i	0.719096	−	1.24551i	−0.242263	−	0.970211i	$-0.577890\pi$
$619$	17.8909	−	30.9879i	0.719096	−	1.24551i	0.961358	−	0.275300i	$-0.0887771\pi$
$620$		0			0
$621$	−36.5720	+	21.1149i	−1.46758	+	0.847310i
$622$		0			0
$623$		−	3.11158i		−	0.124663i
$624$		0			0
$625$	−21.4263	+	7.79853i	−0.857051	+	0.311941i
$626$		0			0
$627$	23.3437	−	4.11612i	0.932257	−	0.164382i
$628$		0			0
$629$	18.3510	+	8.60539i	0.731704	+	0.343119i
$630$		0			0
$631$	−6.52046	+	1.14973i	−0.259576	+	0.0457702i	−0.301921	−	0.953333i	$-0.597628\pi$
$631$	−6.52046	+	1.14973i	−0.259576	+	0.0457702i	0.0423458	+	0.999103i	$0.486517\pi$
$632$		0			0
$633$	−3.48337	+	1.26784i	−0.138452	+	0.0503923i
$634$		0			0
$635$		−	4.32494i		−	0.171630i
$636$		0			0
$637$	4.31996	−	2.49413i	0.171163	−	0.0988210i
$638$		0			0
$639$	−4.89513	+	8.47861i	−0.193648	+	0.335409i
$640$		0			0
$641$	−6.18098	−	35.0541i	−0.244134	−	1.38455i	−0.822495	−	0.568772i	$-0.807418\pi$
$641$	−6.18098	−	35.0541i	−0.244134	−	1.38455i	0.578361	−	0.815781i	$-0.303693\pi$
$642$		0			0
$643$	−4.34087	−	2.50620i	−0.171187	−	0.0988350i	0.411958	−	0.911203i	$-0.364845\pi$
$643$	−4.34087	−	2.50620i	−0.171187	−	0.0988350i	−0.583146	+	0.812368i	$0.698178\pi$
$644$		0			0
$645$	1.95944	−	1.64416i	0.0771528	−	0.0647388i
$646$		0			0
$647$	34.7348	+	6.12469i	1.36557	+	0.240786i	0.807920	−	0.589292i	$-0.200593\pi$
$647$	34.7348	+	6.12469i	1.36557	+	0.240786i	0.557647	+	0.830078i	$0.311704\pi$
$648$		0			0
$649$	11.4635	−	31.4958i	0.449983	−	1.23632i
$650$		0			0
$651$	8.15651	+	9.72055i	0.319679	+	0.380979i
$652$		0			0
$653$	0.925218	+	2.54201i	0.0362066	+	0.0994767i	0.956479	−	0.291802i	$-0.0942549\pi$
$653$	0.925218	+	2.54201i	0.0362066	+	0.0994767i	−0.920272	+	0.391279i	$0.872033\pi$
$654$		0			0
$655$	−1.61012	−	2.78881i	−0.0629125	−	0.108968i
$656$		0			0
$657$	−9.24871	−	3.36625i	−0.360826	−	0.131330i
$658$		0			0
$659$	−21.3419	−	17.9080i	−0.831363	−	0.697597i	0.124240	−	0.992252i	$-0.460351\pi$
$659$	−21.3419	−	17.9080i	−0.831363	−	0.697597i	−0.955604	+	0.294655i	$0.904795\pi$
$660$		0			0
$661$	−6.82156	+	8.12962i	−0.265328	+	0.316205i	−0.882216	−	0.470846i	$-0.843949\pi$
$661$	−6.82156	+	8.12962i	−0.265328	+	0.316205i	0.616888	+	0.787051i	$0.288393\pi$
$662$		0			0
$663$	1.21000	−	6.86222i	0.0469923	−	0.266507i
$664$		0			0
$665$	−7.51750			−0.291516
$666$		0			0
$667$	−24.2452			−0.938779
$668$		0			0
$669$	1.84828	−	10.4821i	0.0714586	−	0.405262i
$670$		0			0
$671$	11.6510	−	13.8851i	0.449781	−	0.536028i
$672$		0			0
$673$	−0.503594	−	0.422565i	−0.0194121	−	0.0162887i	0.633030	−	0.774127i	$-0.281811\pi$
$673$	−0.503594	−	0.422565i	−0.0194121	−	0.0162887i	−0.652442	+	0.757839i	$0.726255\pi$
$674$		0			0
$675$	25.5154	+	9.28683i	0.982087	+	0.357450i
$676$		0			0
$677$	16.0036	+	27.7190i	0.615067	+	1.06533i	0.990373	+	0.138426i	$0.0442043\pi$
$677$	16.0036	+	27.7190i	0.615067	+	1.06533i	−0.375306	+	0.926901i	$0.622462\pi$
$678$		0			0
$679$	16.5434	+	45.4527i	0.634879	+	1.74432i
$680$		0			0
$681$	−21.5171	−	25.6430i	−0.824535	−	0.982643i
$682$		0			0
$683$	1.36647	−	3.75435i	0.0522866	−	0.143656i	−0.910800	−	0.412848i	$-0.864534\pi$
$683$	1.36647	−	3.75435i	0.0522866	−	0.143656i	0.963087	+	0.269191i	$0.0867564\pi$
$684$		0			0
$685$	−1.50962	−	0.266187i	−0.0576797	−	0.0101705i
$686$		0			0
$687$	−4.98812	+	4.18553i	−0.190309	+	0.159688i
$688$		0			0
$689$	10.2499	+	5.91777i	0.390489	+	0.225449i
$690$		0			0
$691$	0.763380	+	4.32934i	0.0290404	+	0.164696i	0.995879	−	0.0906920i	$-0.0289079\pi$
$691$	0.763380	+	4.32934i	0.0290404	+	0.164696i	−0.966839	+	0.255388i	$0.917797\pi$
$692$		0			0
$693$	−2.75339	+	4.76901i	−0.104593	+	0.181160i
$694$		0			0
$695$	−1.70316	+	0.983317i	−0.0646044	+	0.0372993i
$696$		0			0
$697$			27.5539i			1.04368i
$698$		0			0
$699$	−24.9705	+	9.08850i	−0.944469	+	0.343759i
$700$		0			0
$701$	14.1350	−	2.49237i	0.533870	−	0.0941356i	0.0997873	−	0.995009i	$-0.468184\pi$
$701$	14.1350	−	2.49237i	0.533870	−	0.0941356i	0.434082	+	0.900873i	$0.357073\pi$
$702$		0			0
$703$	9.49934	−	35.1491i	0.358274	−	1.32567i
$704$		0			0
$705$	3.03561	−	0.535259i	0.114328	−	0.0201590i
$706$		0			0
$707$	−3.90319	+	1.42064i	−0.146794	+	0.0534288i
$708$		0			0
$709$			6.87475i			0.258187i	0.991632	+	0.129093i	$0.0412067\pi$
$709$			6.87475i			0.258187i	−0.991632	+	0.129093i	$0.958793\pi$
$710$		0			0
$711$	−0.827139	+	0.477549i	−0.0310201	+	0.0179095i
$712$		0			0
$713$	9.57357	−	16.5819i	0.358533	−	0.620998i
$714$		0			0
$715$	0.235708	+	1.33677i	0.00881499	+	0.0499923i
$716$		0			0
$717$	−24.3584	−	14.0633i	−0.909681	−	0.525204i
$718$		0			0
$719$	13.0967	−	10.9894i	0.488424	−	0.409836i	−0.365037	−	0.930993i	$-0.618944\pi$
$719$	13.0967	−	10.9894i	0.488424	−	0.409836i	0.853461	+	0.521157i	$0.174499\pi$
$720$		0			0
$721$	−34.8654	−	6.14771i	−1.29845	−	0.228953i
$722$		0			0
$723$	12.2964	−	33.7840i	0.457307	−	1.25644i
$724$		0			0
$725$	10.0206	+	11.9420i	0.372154	+	0.443516i
$726$		0			0
$727$	14.5792	+	40.0561i	0.540713	+	1.48560i	0.845919	+	0.533311i	$0.179052\pi$
$727$	14.5792	+	40.0561i	0.540713	+	1.48560i	−0.305206	+	0.952286i	$0.598725\pi$
$728$		0			0
$729$	−15.0201	−	26.0155i	−0.556299	−	0.963538i
$730$		0			0
$731$	13.5868	+	4.94519i	0.502526	+	0.182904i
$732$		0			0
$733$	32.6482	+	27.3951i	1.20589	+	1.01186i	0.999442	+	0.0334033i	$0.0106346\pi$
$733$	32.6482	+	27.3951i	1.20589	+	1.01186i	0.206447	+	0.978458i	$0.433810\pi$
$734$		0			0
$735$	−1.38476	+	1.65030i	−0.0510778	+	0.0608722i
$736$		0			0
$737$	−5.04397	+	28.6058i	−0.185797	+	1.05371i
$738$		0			0
$739$	−1.69175			−0.0622321			−0.0311161	−	0.999516i	$-0.509906\pi$
$739$	−1.69175			−0.0622321			−0.0311161	+	0.999516i	$0.509906\pi$
$740$		0			0
$741$	−12.5174			−0.459837
$742$		0			0
$743$	2.22382	−	12.6119i	0.0815839	−	0.462685i	−0.916458	−	0.400132i	$-0.868964\pi$
$743$	2.22382	−	12.6119i	0.0815839	−	0.462685i	0.998042	−	0.0625538i	$-0.0199245\pi$
$744$		0			0
$745$	3.92489	−	4.67751i	0.143797	−	0.171371i
$746$		0			0
$747$	−0.00555891	−	0.00466448i	−0.000203390	−	0.000170664i
$748$		0			0
$749$	−14.5990	−	5.31360i	−0.533436	−	0.194155i
$750$		0			0
$751$	−24.2360	−	41.9780i	−0.884384	−	1.53180i	−0.846418	−	0.532520i	$-0.821245\pi$
$751$	−24.2360	−	41.9780i	−0.884384	−	1.53180i	−0.0379668	−	0.999279i	$-0.512088\pi$
$752$		0			0
$753$	3.19721	+	8.78427i	0.116513	+	0.320117i
$754$		0			0
$755$	5.38357	+	6.41589i	0.195928	+	0.233498i
$756$		0			0
$757$	10.9913	−	30.1984i	0.399486	−	1.09758i	−0.563049	−	0.826424i	$-0.690372\pi$
$757$	10.9913	−	30.1984i	0.399486	−	1.09758i	0.962535	−	0.271156i	$-0.0874060\pi$
$758$		0			0
$759$	−29.4285	−	5.18904i	−1.06819	−	0.188350i
$760$		0			0
$761$	7.94619	−	6.66765i	0.288049	−	0.241702i	−0.487300	−	0.873235i	$-0.662018\pi$
$761$	7.94619	−	6.66765i	0.288049	−	0.241702i	0.775349	+	0.631533i	$0.217574\pi$
$762$		0			0
$763$	27.2434	+	15.7290i	0.986277	+	0.569427i
$764$		0			0
$765$	−0.145309	−	0.824086i	−0.00525365	−	0.0297949i
$766$		0			0
$767$	−8.84976	+	15.3282i	−0.319546	+	0.553471i
$768$		0			0
$769$	29.3819	−	16.9637i	1.05954	−	0.611725i	0.134234	−	0.990950i	$-0.457143\pi$
$769$	29.3819	−	16.9637i	1.05954	−	0.611725i	0.925305	+	0.379225i	$0.123809\pi$
$770$		0			0
$771$		−	6.66015i		−	0.239859i
$772$		0			0
$773$	27.2363	−	9.91322i	0.979623	−	0.356554i	0.197930	−	0.980216i	$-0.436578\pi$
$773$	27.2363	−	9.91322i	0.979623	−	0.356554i	0.781694	+	0.623662i	$0.214356\pi$
$774$		0			0
$775$	−12.1242	+	2.13782i	−0.435514	+	0.0767929i
$776$		0			0
$777$	−17.3943	−	24.9558i	−0.624016	−	0.895284i
$778$		0			0
$779$	48.7454	−	8.59512i	1.74648	−	0.307952i
$780$		0			0
$781$	−36.4315	+	13.2600i	−1.30362	+	0.474479i
$782$		0			0
$783$		−	17.9806i		−	0.642576i
$784$		0			0
$785$	−3.24924	+	1.87595i	−0.115970	+	0.0669555i
$786$		0			0
$787$	−8.35500	+	14.4713i	−0.297823	+	0.515845i	−0.975638	−	0.219388i	$-0.929594\pi$
$787$	−8.35500	+	14.4713i	−0.297823	+	0.515845i	0.677814	+	0.735233i	$0.262927\pi$
$788$		0			0
$789$	1.07877	+	6.11801i	0.0384052	+	0.217807i
$790$		0			0
$791$	−36.6213	−	21.1433i	−1.30210	−	0.751771i
$792$		0			0
$793$	−7.33236	+	6.15258i	−0.260380	+	0.218484i
$794$		0			0
$795$	−5.03384	−	0.887602i	−0.178532	−	0.0314800i
$796$		0			0
$797$	1.78348	−	4.90007i	0.0631741	−	0.173569i	−0.904090	−	0.427343i	$-0.859450\pi$
$797$	1.78348	−	4.90007i	0.0631741	−	0.173569i	0.967264	+	0.253774i	$0.0816719\pi$
$798$		0			0
$799$	11.1999	+	13.3476i	0.396225	+	0.472203i
$800$		0			0
$801$	−0.212804	−	0.584675i	−0.00751907	−	0.0206585i
$802$		0			0
$803$	−19.4878	−	33.7538i	−0.687708	−	1.19115i
$804$		0			0
$805$	8.90549	+	3.24133i	0.313877	+	0.114242i
$806$		0			0
$807$	10.3203	+	8.65978i	0.363293	+	0.304839i
$808$		0			0
$809$	32.5001	−	38.7321i	1.14264	−	1.36175i	0.220274	−	0.975438i	$-0.429305\pi$
$809$	32.5001	−	38.7321i	1.14264	−	1.36175i	0.922369	−	0.386310i	$-0.126251\pi$
$810$		0			0
$811$	−6.26321	+	35.5205i	−0.219931	+	1.24729i	0.652210	+	0.758038i	$0.273842\pi$
$811$	−6.26321	+	35.5205i	−0.219931	+	1.24729i	−0.872141	+	0.489254i	$0.837269\pi$
$812$		0			0
$813$	19.7826			0.693808
$814$		0			0
$815$	5.06519			0.177426
$816$		0			0
$817$	4.51025	−	25.5789i	0.157794	−	0.894893i
$818$		0			0
$819$	1.86922	−	2.22765i	0.0653158	−	0.0778403i
$820$		0			0
$821$	39.1705	+	32.8679i	1.36706	+	1.14710i	0.973731	+	0.227701i	$0.0731208\pi$
$821$	39.1705	+	32.8679i	1.36706	+	1.14710i	0.393328	+	0.919398i	$0.371324\pi$
$822$		0			0
$823$	7.59472	+	2.76425i	0.264735	+	0.0963558i	0.470978	−	0.882145i	$-0.343901\pi$
$823$	7.59472	+	2.76425i	0.264735	+	0.0963558i	−0.206242	+	0.978501i	$0.566123\pi$
$824$		0			0
$825$	9.60693	+	16.6397i	0.334470	+	0.579319i
$826$		0			0
$827$	−8.84209	−	24.2934i	−0.307469	−	0.844765i	−0.993148	−	0.116861i	$-0.962717\pi$
$827$	−8.84209	−	24.2934i	−0.307469	−	0.844765i	0.685679	−	0.727904i	$-0.259505\pi$
$828$		0			0
$829$	5.26941	+	6.27984i	0.183014	+	0.218108i	0.849749	−	0.527187i	$-0.176753\pi$
$829$	5.26941	+	6.27984i	0.183014	+	0.218108i	−0.666735	+	0.745295i	$0.732309\pi$
$830$		0			0
$831$	4.07489	−	11.1957i	0.141356	−	0.388373i
$832$		0			0
$833$	−11.9926	−	2.11462i	−0.415519	−	0.0732673i
$834$		0			0
$835$	1.65121	−	1.38553i	0.0571425	−	0.0479483i
$836$		0			0
$837$	12.2974	+	7.09991i	0.425060	+	0.245409i
$838$		0			0
$839$	9.17699	+	52.0453i	0.316825	+	1.79680i	0.561800	+	0.827273i	$0.310109\pi$
$839$	9.17699	+	52.0453i	0.316825	+	1.79680i	−0.244975	+	0.969529i	$0.578780\pi$
$840$		0			0
$841$	−9.33841	+	16.1746i	−0.322014	+	0.557745i
$842$		0			0
$843$	0.308500	−	0.178113i	0.0106253	−	0.00613453i
$844$		0			0
$845$			4.28501i			0.147409i
$846$		0			0
$847$	13.2484	−	4.82201i	0.455219	−	0.165686i
$848$		0			0
$849$	19.3626	−	3.41415i	0.664523	−	0.117173i
$850$		0			0
$851$	−26.4085	+	37.5430i	−0.905273	+	1.28696i
$852$		0			0
$853$	−32.4894	+	5.72875i	−1.11241	+	0.196149i	−0.699508	−	0.714625i	$-0.746598\pi$
$853$	−32.4894	+	5.72875i	−1.11241	+	0.196149i	−0.412907	+	0.910773i	$0.635486\pi$
$854$		0			0
$855$	−1.41256	+	0.514129i	−0.0483085	+	0.0175828i
$856$		0			0
$857$			38.4078i			1.31199i	0.754767	+	0.655993i	$0.227750\pi$
$857$			38.4078i			1.31199i	−0.754767	+	0.655993i	$0.772250\pi$
$858$		0			0
$859$	17.9404	−	10.3579i	0.612119	−	0.353407i	−0.161676	−	0.986844i	$-0.551690\pi$
$859$	17.9404	−	10.3579i	0.612119	−	0.353407i	0.773794	+	0.633437i	$0.218356\pi$
$860$		0			0
$861$	20.6768	−	35.8133i	0.704664	−	1.22051i
$862$		0			0
$863$	−6.14125	−	34.8288i	−0.209051	−	1.18559i	−0.890937	−	0.454127i	$-0.849951\pi$
$863$	−6.14125	−	34.8288i	−0.209051	−	1.18559i	0.681886	−	0.731458i	$-0.261160\pi$
$864$		0			0
$865$	3.61043	+	2.08448i	0.122758	+	0.0708746i
$866$		0			0
$867$	6.92092	−	5.80734i	0.235047	−	0.197228i
$868$		0			0
$869$	−3.72474	−	0.656772i	−0.126353	−	0.0222795i
$870$		0			0
$871$	5.24625	−	14.4139i	0.177762	−	0.488398i
$872$		0			0
$873$	6.21711	+	7.40927i	0.210417	+	0.250766i
$874$		0			0
$875$	−4.23182	−	11.6268i	−0.143062	−	0.393058i
$876$		0			0
$877$	−13.1851	−	22.8373i	−0.445230	−	0.771160i	0.552839	−	0.833288i	$-0.313545\pi$
$877$	−13.1851	−	22.8373i	−0.445230	−	0.771160i	−0.998068	+	0.0621282i	$0.980211\pi$
$878$		0			0
$879$	35.4802	+	12.9137i	1.19672	+	0.435570i
$880$		0			0
$881$	25.8314	+	21.6752i	0.870283	+	0.730254i	0.964158	−	0.265330i	$-0.0854808\pi$
$881$	25.8314	+	21.6752i	0.870283	+	0.730254i	−0.0938745	+	0.995584i	$0.529925\pi$
$882$		0			0
$883$	37.1901	−	44.3215i	1.25155	−	1.49154i	0.450690	−	0.892680i	$-0.351178\pi$
$883$	37.1901	−	44.3215i	1.25155	−	1.49154i	0.800857	−	0.598856i	$-0.204378\pi$
$884$		0			0
$885$	1.32737	−	7.52788i	0.0446190	−	0.253047i
$886$		0			0
$887$	44.4679			1.49309			0.746544	−	0.665336i	$-0.231712\pi$
$887$	44.4679			1.49309			0.746544	+	0.665336i	$0.231712\pi$
$888$		0			0
$889$	−36.6915			−1.23059
$890$		0			0
$891$	2.96941	−	16.8404i	0.0994789	−	0.564173i
$892$		0			0
$893$	20.1194	−	23.9774i	0.673270	−	0.802372i
$894$		0			0
$895$	1.78963	+	1.50168i	0.0598208	+	0.0501956i
$896$		0			0
$897$	14.8285	+	5.39714i	0.495109	+	0.180205i
$898$		0			0
$899$	4.07625	+	7.06028i	0.135951	+	0.235473i
$900$		0			0
$901$	−9.88220	−	27.1511i	−0.329224	−	0.904535i
$902$		0			0
$903$	−13.9486	−	16.6233i	−0.464180	−	0.553188i
$904$		0			0
$905$	2.83635	−	7.79281i	0.0942835	−	0.259042i
$906$		0			0
$907$	12.8961	+	2.27393i	0.428209	+	0.0755048i	0.383599	−	0.923500i	$-0.374684\pi$
$907$	12.8961	+	2.27393i	0.428209	+	0.0755048i	0.0446097	+	0.999004i	$0.485796\pi$
$908$		0			0
$909$	−0.636260	+	0.533886i	−0.0211034	+	0.0177079i
$910$		0			0
$911$	33.2957	+	19.2233i	1.10314	+	0.636896i	0.937043	−	0.349215i	$-0.113552\pi$
$911$	33.2957	+	19.2233i	1.10314	+	0.636896i	0.166093	+	0.986110i	$0.446885\pi$
$912$		0			0
$913$	−0.00499003	−	0.0282998i	−0.000165146	−	0.000936588i
$914$		0			0
$915$	2.06690	−	3.57997i	0.0683296	−	0.118350i
$916$		0			0
$917$	−23.6594	+	13.6597i	−0.781301	+	0.451085i
$918$		0			0
$919$			14.8613i			0.490229i	0.969494	+	0.245115i	$0.0788256\pi$
$919$			14.8613i			0.490229i	−0.969494	+	0.245115i	$0.921174\pi$
$920$		0			0
$921$	9.95018	−	3.62157i	0.327869	−	0.119335i
$922$		0			0
$923$	20.1622	−	3.55514i	0.663646	−	0.117019i
$924$		0			0
$925$	29.4065	−	2.50894i	0.966880	−	0.0824933i
$926$		0			0
$927$	−6.97175	+	1.22931i	−0.228982	+	0.0403757i
$928$		0			0
$929$	−6.82712	+	2.48487i	−0.223990	+	0.0815258i	−0.451578	−	0.892232i	$-0.649139\pi$
$929$	−6.82712	+	2.48487i	−0.223990	+	0.0815258i	0.227587	+	0.973758i	$0.426916\pi$
$930$		0			0
$931$			21.8757i			0.716947i
$932$		0			0
$933$	−2.20067	+	1.27056i	−0.0720466	+	0.0415961i
$934$		0			0
$935$	1.65687	−	2.86978i	0.0541854	−	0.0938519i
$936$		0			0
$937$	−4.58137	−	25.9822i	−0.149667	−	0.848802i	−0.963501	−	0.267705i	$-0.913735\pi$
$937$	−4.58137	−	25.9822i	−0.149667	−	0.848802i	0.813834	−	0.581097i	$-0.197376\pi$
$938$		0			0
$939$	−34.4324	−	19.8795i	−1.12366	−	0.648744i
$940$		0			0
$941$	27.6990	−	23.2422i	0.902961	−	0.757674i	−0.0678062	−	0.997699i	$-0.521600\pi$
$941$	27.6990	−	23.2422i	0.902961	−	0.757674i	0.970767	+	0.240025i	$0.0771555\pi$
$942$		0			0
$943$	−61.4514	−	10.8355i	−2.00113	−	0.352854i
$944$		0			0
$945$	−2.40382	+	6.60445i	−0.0781964	+	0.214843i
$946$		0			0
$947$	30.2846	+	36.0917i	0.984116	+	1.17282i	0.984953	+	0.172824i	$0.0552892\pi$
$947$	30.2846	+	36.0917i	0.984116	+	1.17282i	−0.000836789		1.00000i	$0.500266\pi$
$948$		0			0
$949$	7.03945	+	19.3407i	0.228510	+	0.627827i
$950$		0			0
$951$	8.69447	+	15.0593i	0.281937	+	0.488330i
$952$		0			0
$953$	−8.78776	−	3.19848i	−0.284663	−	0.103609i	0.195742	−	0.980655i	$-0.437288\pi$
$953$	−8.78776	−	3.19848i	−0.284663	−	0.103609i	−0.480406	+	0.877046i	$0.659511\pi$
$954$		0			0
$955$	1.95322	+	1.63894i	0.0632046	+	0.0530349i
$956$		0			0
$957$	8.17845	−	9.74670i	0.264372	−	0.315066i
$958$		0			0
$959$	−2.25825	+	12.8072i	−0.0729228	+	0.413565i
$960$		0			0
$961$	24.5617			0.792314
$962$		0			0
$963$	−3.10660			−0.100109
$964$		0			0
$965$	1.52695	−	8.65974i	0.0491541	−	0.278767i
$966$		0			0
$967$	−32.1046	+	38.2608i	−1.03242	+	1.23039i	−0.0597409	+	0.998214i	$0.519027\pi$
$967$	−32.1046	+	38.2608i	−1.03242	+	1.23039i	−0.972675	+	0.232171i	$0.925417\pi$
$968$		0			0
$969$	23.4089	+	19.6424i	0.752001	+	0.631004i
$970$		0			0
$971$	35.3500	+	12.8664i	1.13444	+	0.412901i	0.839901	−	0.542739i	$-0.182613\pi$
$971$	35.3500	+	12.8664i	1.13444	+	0.412901i	0.294536	+	0.955641i	$0.404835\pi$
$972$		0			0
$973$	8.34216	+	14.4491i	0.267437	+	0.463215i
$974$		0			0
$975$	−3.47025	−	9.53444i	−0.111137	−	0.305347i
$976$		0			0
$977$	18.0852	+	21.5531i	0.578597	+	0.689545i	0.973372	−	0.229233i	$-0.0736219\pi$
$977$	18.0852	+	21.5531i	0.578597	+	0.689545i	−0.394775	+	0.918778i	$0.629177\pi$
$978$		0			0
$979$	0.842708	−	2.31532i	0.0269331	−	0.0739980i
$980$		0			0
$981$	6.19483	+	1.09231i	0.197786	+	0.0348749i
$982$		0			0
$983$	25.2349	−	21.1746i	0.804867	−	0.675364i	−0.144510	−	0.989503i	$-0.546160\pi$
$983$	25.2349	−	21.1746i	0.804867	−	0.675364i	0.949377	+	0.314140i	$0.101716\pi$
$984$		0			0
$985$	4.91683	+	2.83873i	0.156663	+	0.0904495i
$986$		0			0
$987$	−4.54098	−	25.7532i	−0.144541	−	0.819732i
$988$		0			0
$989$	−16.3719	+	28.3570i	−0.520597	+	0.901700i
$990$		0			0
$991$	−33.7743	+	19.4996i	−1.07288	+	0.619426i	−0.928966	−	0.370164i	$-0.879301\pi$
$991$	−33.7743	+	19.4996i	−1.07288	+	0.619426i	−0.143911	+	0.989591i	$0.545968\pi$
$992$		0			0
$993$		−	19.6685i		−	0.624160i
$994$		0			0
$995$	−0.533207	+	0.194072i	−0.0169038	+	0.00615248i
$996$		0			0
$997$	−7.85922	+	1.38579i	−0.248904	+	0.0438885i	−0.296708	−	0.954968i	$-0.595889\pi$
$997$	−7.85922	+	1.38579i	−0.248904	+	0.0438885i	0.0478041	+	0.998857i	$0.484778\pi$
$998$		0			0
$999$	−27.8424	−	19.5850i	−0.880896	−	0.619641i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.bq.b.65.2		12
4.3	odd	2		74.2.h.a.65.2	yes	12
12.11	even	2		666.2.bj.c.361.1		12
37.4	even	18	inner	592.2.bq.b.337.2		12
148.35	even	36		2738.2.a.r.1.5		6
148.39	even	36		2738.2.a.s.1.6		6
148.115	odd	18		74.2.h.a.41.2	✓	12
444.263	even	18		666.2.bj.c.559.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.h.a.41.2	✓	12	148.115	odd	18
74.2.h.a.65.2	yes	12	4.3	odd	2
592.2.bq.b.65.2		12	1.1	even	1	trivial
592.2.bq.b.337.2		12	37.4	even	18	inner
666.2.bj.c.361.1		12	12.11	even	2
666.2.bj.c.559.1		12	444.263	even	18
2738.2.a.r.1.5		6	148.35	even	36
2738.2.a.s.1.6		6	148.39	even	36

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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.bq (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.266044 - 1.50881i) q^{3} +(-0.247315 + 0.294739i) q^{5} +(2.50048 + 2.09815i) q^{7} +(0.613341 + 0.223238i) q^{9} +O(q^{10})\)	\(q+(0.266044 - 1.50881i) q^{3} +(-0.247315 + 0.294739i) q^{5} +(2.50048 + 2.09815i) q^{7} +(0.613341 + 0.223238i) q^{9} +(1.29236 + 2.23843i) q^{11} +(-0.466831 - 1.28261i) q^{13} +(0.378909 + 0.451566i) q^{15} +(-1.13965 + 3.13118i) q^{17} +(5.89485 + 1.03942i) q^{19} +(3.83095 - 3.21455i) q^{21} +(-6.53507 - 3.77303i) q^{23} +(0.842535 + 4.77825i) q^{25} +(2.79813 - 4.84651i) q^{27} +(2.78251 - 1.60649i) q^{29} +2.53737i q^{31} +(3.72120 - 1.35440i) q^{33} +(-1.23681 + 0.218083i) q^{35} +(0.543196 - 6.05846i) q^{37} +(-2.05941 + 0.363130i) q^{39} +(7.77046 - 2.82822i) q^{41} -4.33920i q^{43} +(-0.217486 + 0.125565i) q^{45} +(2.61455 - 4.52853i) q^{47} +(0.634616 + 3.59909i) q^{49} +(4.42116 + 2.55256i) q^{51} +(-6.64254 + 5.57375i) q^{53} +(-0.979373 - 0.172690i) q^{55} +(3.13658 - 8.61769i) q^{57} +(-8.33530 - 9.93362i) q^{59} +(-2.39847 - 6.58973i) q^{61} +(1.06526 + 1.84508i) q^{63} +(0.493489 + 0.179615i) q^{65} +(8.60881 + 7.22365i) q^{67} +(-7.43141 + 8.85641i) q^{69} +(-2.60464 + 14.7717i) q^{71} -15.0792 q^{73} +7.43364 q^{75} +(-1.46505 + 8.30870i) q^{77} +(-0.940587 + 1.12095i) q^{79} +(-5.06805 - 4.25260i) q^{81} +(-0.0104473 - 0.00380252i) q^{83} +(-0.641025 - 1.11029i) q^{85} +(-1.68361 - 4.62569i) q^{87} +(-0.612745 - 0.730241i) q^{89} +(1.52380 - 4.18661i) q^{91} +(3.82842 + 0.675054i) q^{93} +(-1.76424 + 1.48038i) q^{95} +(12.8332 + 7.40927i) q^{97} +(0.292954 + 1.66142i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 12 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 + 12 * q^7 - 6 * q^9	\( 12 q - 6 q^{3} + 12 q^{7} - 6 q^{9} + 6 q^{11} + 6 q^{13} + 18 q^{19} - 6 q^{21} - 18 q^{25} + 6 q^{27} + 18 q^{29} - 6 q^{33} - 18 q^{35} + 30 q^{37} - 30 q^{39} + 24 q^{41} - 18 q^{45} - 6 q^{47} + 12 q^{49} - 12 q^{53} + 18 q^{55} - 36 q^{57} - 36 q^{61} + 6 q^{63} + 36 q^{65} + 30 q^{67} - 18 q^{69} - 12 q^{71} + 36 q^{75} + 12 q^{77} - 6 q^{79} + 24 q^{81} + 48 q^{83} + 18 q^{85} - 36 q^{87} - 18 q^{89} + 6 q^{91} - 12 q^{93} + 36 q^{97} - 30 q^{99}+O(q^{100}) \) 12 * q - 6 * q^3 + 12 * q^7 - 6 * q^9 + 6 * q^11 + 6 * q^13 + 18 * q^19 - 6 * q^21 - 18 * q^25 + 6 * q^27 + 18 * q^29 - 6 * q^33 - 18 * q^35 + 30 * q^37 - 30 * q^39 + 24 * q^41 - 18 * q^45 - 6 * q^47 + 12 * q^49 - 12 * q^53 + 18 * q^55 - 36 * q^57 - 36 * q^61 + 6 * q^63 + 36 * q^65 + 30 * q^67 - 18 * q^69 - 12 * q^71 + 36 * q^75 + 12 * q^77 - 6 * q^79 + 24 * q^81 + 48 * q^83 + 18 * q^85 - 36 * q^87 - 18 * q^89 + 6 * q^91 - 12 * q^93 + 36 * q^97 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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