LMFDB - Embedded newform 592.2.bc.b.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(33,592)]

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, 10]))

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

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

chi := DirichletCharacter("592.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.bc (of order $9$, 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:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			49.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	592.49
Dual form			592.2.bc.b.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.43969 + 1.20805i) q^{3} +(3.31908 - 1.20805i) q^{5} +(-0.826352 + 0.300767i) q^{7} +(0.0923963 + 0.524005i) q^{9} +O(q^{10})$	\(q+(1.43969 + 1.20805i) q^{3} +(3.31908 - 1.20805i) q^{5} +(-0.826352 + 0.300767i) q^{7} +(0.0923963 + 0.524005i) q^{9} +(1.67365 + 2.89884i) q^{11} +(-1.11334 + 6.31407i) q^{13} +(6.23783 + 2.27038i) q^{15} +(-0.520945 - 2.95442i) q^{17} +(-3.55303 - 2.98135i) q^{19} +(-1.55303 - 0.565258i) q^{21} +(2.91875 - 5.05542i) q^{23} +(5.72668 - 4.80526i) q^{25} +(2.31908 - 4.01676i) q^{27} +(1.63429 + 2.83067i) q^{29} +1.12061 q^{31} +(-1.09240 + 6.19529i) q^{33} +(-2.37939 + 1.99654i) q^{35} +(-3.44356 + 5.01417i) q^{37} +(-9.23055 + 7.74535i) q^{39} +(1.49020 - 8.45134i) q^{41} -5.61587 q^{43} +(0.939693 + 1.62760i) q^{45} +(-2.56418 + 4.44129i) q^{47} +(-4.76991 + 4.00243i) q^{49} +(2.81908 - 4.88279i) q^{51} +(-0.252374 - 0.0918566i) q^{53} +(9.05690 + 7.59964i) q^{55} +(-1.51367 - 8.58445i) q^{57} +(7.15910 + 2.60570i) q^{59} +(0.369585 - 2.09602i) q^{61} +(-0.233956 - 0.405223i) q^{63} +(3.93242 + 22.3019i) q^{65} +(8.01754 - 2.91815i) q^{67} +(10.3093 - 3.75227i) q^{69} +(-10.0719 - 8.45134i) q^{71} -8.57398 q^{73} +14.0496 q^{75} +(-2.25490 - 1.89209i) q^{77} +(-10.8833 + 3.96118i) q^{79} +(9.69119 - 3.52730i) q^{81} +(-0.724155 - 4.10689i) q^{83} +(-5.29813 - 9.17664i) q^{85} +(-1.06670 + 6.04958i) q^{87} +(-7.86959 - 2.86429i) q^{89} +(-0.979055 - 5.55250i) q^{91} +(1.61334 + 1.35375i) q^{93} +(-15.3944 - 5.60310i) q^{95} +(8.53209 - 14.7780i) q^{97} +(-1.36437 + 1.14484i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} + 3 q^{5} - 6 q^{7} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 + 3 * q^5 - 6 * q^7 - 3 * q^9	$ 6 q + 3 q^{3} + 3 q^{5} - 6 q^{7} - 3 q^{9} + 9 q^{11} + 18 q^{15} - 9 q^{19} + 3 q^{21} + 15 q^{23} + 21 q^{25} - 3 q^{27} + 18 q^{31} - 3 q^{33} - 3 q^{35} + 9 q^{37} - 18 q^{39} + 6 q^{41} - 12 q^{43} + 3 q^{47} - 18 q^{53} + 18 q^{55} + 12 q^{57} + 6 q^{59} - 12 q^{61} - 6 q^{63} + 3 q^{67} + 42 q^{69} + 6 q^{71} - 36 q^{73} + 30 q^{75} - 15 q^{77} - 30 q^{79} + 12 q^{81} - 6 q^{83} - 18 q^{85} + 27 q^{87} - 33 q^{89} - 9 q^{91} + 3 q^{93} - 51 q^{95} + 42 q^{97} - 27 q^{99}+O(q^{100}) $ 6 * q + 3 * q^3 + 3 * q^5 - 6 * q^7 - 3 * q^9 + 9 * q^11 + 18 * q^15 - 9 * q^19 + 3 * q^21 + 15 * q^23 + 21 * q^25 - 3 * q^27 + 18 * q^31 - 3 * q^33 - 3 * q^35 + 9 * q^37 - 18 * q^39 + 6 * q^41 - 12 * q^43 + 3 * q^47 - 18 * q^53 + 18 * q^55 + 12 * q^57 + 6 * q^59 - 12 * q^61 - 6 * q^63 + 3 * q^67 + 42 * q^69 + 6 * q^71 - 36 * q^73 + 30 * q^75 - 15 * q^77 - 30 * q^79 + 12 * q^81 - 6 * q^83 - 18 * q^85 + 27 * q^87 - 33 * q^89 - 9 * q^91 + 3 * q^93 - 51 * q^95 + 42 * q^97 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$	$1$

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
$3$	1.43969	+	1.20805i	0.831207	+	0.697465i	0.955568	−	0.294772i	$-0.0952436\pi$
$3$	1.43969	+	1.20805i	0.831207	+	0.697465i	−0.124361	+	0.992237i	$0.539688\pi$
$4$		0			0
$5$	3.31908	−	1.20805i	1.48434	−	0.540254i	0.532385	−	0.846502i	$-0.321296\pi$
$5$	3.31908	−	1.20805i	1.48434	−	0.540254i	0.951952	+	0.306248i	$0.0990737\pi$
$6$		0			0
$7$	−0.826352	+	0.300767i	−0.312332	+	0.113679i	−0.493430	−	0.869786i	$-0.664257\pi$
$7$	−0.826352	+	0.300767i	−0.312332	+	0.113679i	0.181098	+	0.983465i	$0.442035\pi$
$8$		0			0
$9$	0.0923963	+	0.524005i	0.0307988	+	0.174668i
$10$		0			0
$11$	1.67365	+	2.89884i	0.504624	+	0.874034i	0.999986	+	0.00534749i	$0.00170217\pi$
$11$	1.67365	+	2.89884i	0.504624	+	0.874034i	−0.495362	+	0.868687i	$0.664964\pi$
$12$		0			0
$13$	−1.11334	+	6.31407i	−0.308785	+	1.75121i	0.296345	+	0.955081i	$0.404232\pi$
$13$	−1.11334	+	6.31407i	−0.308785	+	1.75121i	−0.605130	+	0.796127i	$0.706879\pi$
$14$		0			0
$15$	6.23783	+	2.27038i	1.61060	+	0.586210i
$16$		0			0
$17$	−0.520945	−	2.95442i	−0.126348	−	0.716553i	−0.980498	−	0.196527i	$-0.937034\pi$
$17$	−0.520945	−	2.95442i	−0.126348	−	0.716553i	0.854151	−	0.520026i	$-0.174078\pi$
$18$		0			0
$19$	−3.55303	−	2.98135i	−0.815122	−	0.683968i	0.136703	−	0.990612i	$-0.456350\pi$
$19$	−3.55303	−	2.98135i	−0.815122	−	0.683968i	−0.951824	+	0.306644i	$0.900794\pi$
$20$		0			0
$21$	−1.55303	−	0.565258i	−0.338900	−	0.123349i
$22$		0			0
$23$	2.91875	−	5.05542i	0.608601	−	1.05413i	−0.382870	−	0.923802i	$-0.625064\pi$
$23$	2.91875	−	5.05542i	0.608601	−	1.05413i	0.991471	−	0.130326i	$-0.0416023\pi$
$24$		0			0
$25$	5.72668	−	4.80526i	1.14534	−	0.961051i
$26$		0			0
$27$	2.31908	−	4.01676i	0.446307	−	0.773026i
$28$		0			0
$29$	1.63429	+	2.83067i	0.303479	+	0.525641i	0.976922	−	0.213598i	$-0.0685184\pi$
$29$	1.63429	+	2.83067i	0.303479	+	0.525641i	−0.673442	+	0.739240i	$0.735185\pi$
$30$		0			0
$31$	1.12061			0.201268			0.100634	−	0.994923i	$-0.467913\pi$
$31$	1.12061			0.201268			0.100634	+	0.994923i	$0.467913\pi$
$32$		0			0
$33$	−1.09240	+	6.19529i	−0.190162	+	1.07846i
$34$		0			0
$35$	−2.37939	+	1.99654i	−0.402190	+	0.337477i
$36$		0			0
$37$	−3.44356	+	5.01417i	−0.566118	+	0.824324i
$37$	−3.44356	+	5.01417i	−0.566118	+	0.824324i
$38$		0			0
$39$	−9.23055	+	7.74535i	−1.47807	+	1.24025i
$40$		0			0
$41$	1.49020	−	8.45134i	0.232730	−	1.31988i	−0.614612	−	0.788830i	$-0.710687\pi$
$41$	1.49020	−	8.45134i	0.232730	−	1.31988i	0.847342	−	0.531048i	$-0.178202\pi$
$42$		0			0
$43$	−5.61587			−0.856412			−0.428206	−	0.903681i	$-0.640854\pi$
$43$	−5.61587			−0.856412			−0.428206	+	0.903681i	$0.640854\pi$
$44$		0			0
$45$	0.939693	+	1.62760i	0.140081	+	0.242628i
$46$		0			0
$47$	−2.56418	+	4.44129i	−0.374024	+	0.647828i	−0.990180	−	0.139795i	$-0.955355\pi$
$47$	−2.56418	+	4.44129i	−0.374024	+	0.647828i	0.616157	+	0.787624i	$0.288689\pi$
$48$		0			0
$49$	−4.76991	+	4.00243i	−0.681416	+	0.571776i
$50$		0			0
$51$	2.81908	−	4.88279i	0.394750	−	0.683727i
$52$		0			0
$53$	−0.252374	−	0.0918566i	−0.0346662	−	0.0126175i	0.324629	−	0.945841i	$-0.394761\pi$
$53$	−0.252374	−	0.0918566i	−0.0346662	−	0.0126175i	−0.359295	+	0.933224i	$0.616983\pi$
$54$		0			0
$55$	9.05690	+	7.59964i	1.22123	+	1.02474i
$56$		0			0
$57$	−1.51367	−	8.58445i	−0.200491	−	1.13704i
$58$		0			0
$59$	7.15910	+	2.60570i	0.932035	+	0.339233i	0.763016	−	0.646380i	$-0.223718\pi$
$59$	7.15910	+	2.60570i	0.932035	+	0.339233i	0.169019	+	0.985613i	$0.445940\pi$
$60$		0			0
$61$	0.369585	−	2.09602i	0.0473205	−	0.268368i	−0.951963	−	0.306213i	$-0.900938\pi$
$61$	0.369585	−	2.09602i	0.0473205	−	0.268368i	0.999284	+	0.0378447i	$0.0120492\pi$
$62$		0			0
$63$	−0.233956	−	0.405223i	−0.0294756	−	0.0510533i
$64$		0			0
$65$	3.93242	+	22.3019i	0.487757	+	2.76620i
$66$		0			0
$67$	8.01754	−	2.91815i	0.979499	−	0.356508i	0.197853	−	0.980232i	$-0.436603\pi$
$67$	8.01754	−	2.91815i	0.979499	−	0.356508i	0.781645	+	0.623723i	$0.214381\pi$
$68$		0			0
$69$	10.3093	−	3.75227i	1.24109	−	0.451720i
$70$		0			0
$71$	−10.0719	−	8.45134i	−1.19532	−	1.00299i	−0.999751	−	0.0222993i	$-0.992901\pi$
$71$	−10.0719	−	8.45134i	−1.19532	−	1.00299i	−0.195565	−	0.980691i	$-0.562654\pi$
$72$		0			0
$73$	−8.57398			−1.00351			−0.501754	−	0.865010i	$-0.667312\pi$
$73$	−8.57398			−1.00351			−0.501754	+	0.865010i	$0.667312\pi$
$74$		0			0
$75$	14.0496			1.62231
$76$		0			0
$77$	−2.25490	−	1.89209i	−0.256970	−	0.215623i
$78$		0			0
$79$	−10.8833	+	3.96118i	−1.22446	+	0.445668i	−0.871697	−	0.490044i	$-0.836981\pi$
$79$	−10.8833	+	3.96118i	−1.22446	+	0.445668i	−0.352764	+	0.935712i	$0.614758\pi$
$80$		0			0
$81$	9.69119	−	3.52730i	1.07680	−	0.391923i
$82$		0			0
$83$	−0.724155	−	4.10689i	−0.0794864	−	0.450790i	−0.998411	−	0.0563559i	$-0.982052\pi$
$83$	−0.724155	−	4.10689i	−0.0794864	−	0.450790i	0.918924	−	0.394434i	$-0.129059\pi$
$84$		0			0
$85$	−5.29813	−	9.17664i	−0.574663	−	0.995346i
$86$		0			0
$87$	−1.06670	+	6.04958i	−0.114363	+	0.648583i
$88$		0			0
$89$	−7.86959	−	2.86429i	−0.834174	−	0.303615i	−0.110603	−	0.993865i	$-0.535278\pi$
$89$	−7.86959	−	2.86429i	−0.834174	−	0.303615i	−0.723571	+	0.690250i	$0.757501\pi$
$90$		0			0
$91$	−0.979055	−	5.55250i	−0.102633	−	0.582060i
$92$		0			0
$93$	1.61334	+	1.35375i	0.167296	+	0.140378i
$94$		0			0
$95$	−15.3944	−	5.60310i	−1.57943	−	0.574866i
$96$		0			0
$97$	8.53209	−	14.7780i	0.866302	−	1.50048i	0.000554205	−	1.00000i	$-0.499824\pi$
$97$	8.53209	−	14.7780i	0.866302	−	1.50048i	0.865748	−	0.500480i	$-0.166843\pi$
$98$		0			0
$99$	−1.36437	+	1.14484i	−0.137124	+	0.115061i
$100$		0			0
$101$	−0.543233	+	0.940908i	−0.0540537	+	0.0936238i	−0.891786	−	0.452457i	$-0.850548\pi$
$101$	−0.543233	+	0.940908i	−0.0540537	+	0.0936238i	0.837732	+	0.546081i	$0.183881\pi$
$102$		0			0
$103$	5.60741	+	9.71232i	0.552515	+	0.956983i	0.998092	+	0.0617401i	$0.0196650\pi$
$103$	5.60741	+	9.71232i	0.552515	+	0.956983i	−0.445578	+	0.895243i	$0.647002\pi$
$104$		0			0
$105$	−5.83750			−0.569681
$106$		0			0
$107$	−1.66637	+	9.45048i	−0.161094	+	0.913612i	0.791906	+	0.610643i	$0.209089\pi$
$107$	−1.66637	+	9.45048i	−0.161094	+	0.913612i	−0.953000	+	0.302969i	$0.902022\pi$
$108$		0			0
$109$	−1.70187	+	1.42804i	−0.163009	+	0.136781i	−0.720644	−	0.693306i	$-0.756154\pi$
$109$	−1.70187	+	1.42804i	−0.163009	+	0.136781i	0.557634	+	0.830087i	$0.311709\pi$
$110$		0			0
$111$	−11.0150	+	3.05888i	−1.04550	+	0.290336i
$112$		0			0
$113$	−3.54710	+	2.97637i	−0.333683	+	0.279994i	−0.794199	−	0.607658i	$-0.792109\pi$
$113$	−3.54710	+	2.97637i	−0.333683	+	0.279994i	0.460515	+	0.887652i	$0.347665\pi$
$114$		0			0
$115$	3.58037	−	20.3053i	0.333872	−	1.89348i
$116$		0			0
$117$	−3.41147			−0.315391
$118$		0			0
$119$	1.31908	+	2.28471i	0.120920	+	0.209439i
$120$		0			0
$121$	−0.102196	+	0.177009i	−0.00929059	+	0.0160918i
$122$		0			0
$123$	12.3550	−	10.3671i	1.11402	−	0.934771i
$124$		0			0
$125$	4.37211	−	7.57272i	0.391054	−	0.677325i
$126$		0			0
$127$	−4.77972	−	1.73967i	−0.424131	−	0.154371i	0.121131	−	0.992636i	$-0.461348\pi$
$127$	−4.77972	−	1.73967i	−0.424131	−	0.154371i	−0.545262	+	0.838265i	$0.683570\pi$
$128$		0			0
$129$	−8.08512	−	6.78422i	−0.711855	−	0.597318i
$130$		0			0
$131$	−0.566237	−	3.21129i	−0.0494724	−	0.280572i	0.950028	−	0.312163i	$-0.101054\pi$
$131$	−0.566237	−	3.21129i	−0.0494724	−	0.280572i	−0.999501	+	0.0315914i	$0.989942\pi$
$132$		0			0
$133$	3.83275	+	1.39501i	0.332341	+	0.120962i
$134$		0			0
$135$	2.84477	−	16.1335i	0.244839	−	1.38855i
$136$		0			0
$137$	0.798133	+	1.38241i	0.0681891	+	0.118107i	0.898104	−	0.439783i	$-0.144945\pi$
$137$	0.798133	+	1.38241i	0.0681891	+	0.118107i	−0.829915	+	0.557890i	$0.811611\pi$
$138$		0			0
$139$	−2.04963	−	11.6240i	−0.173847	−	0.985937i	−0.939466	−	0.342642i	$-0.888678\pi$
$139$	−2.04963	−	11.6240i	−0.173847	−	0.985937i	0.765619	−	0.643295i	$-0.222433\pi$
$140$		0			0
$141$	−9.05690	+	3.29644i	−0.762729	+	0.277611i
$142$		0			0
$143$	−20.1668	+	7.34013i	−1.68644	+	0.613812i
$144$		0			0
$145$	8.84389	+	7.42091i	0.734445	+	0.616273i
$146$		0			0
$147$	−11.7023			−0.965192
$148$		0			0
$149$	−12.6604			−1.03718			−0.518592	−	0.855022i	$-0.673544\pi$
$149$	−12.6604			−1.03718			−0.518592	+	0.855022i	$0.673544\pi$
$150$		0			0
$151$	3.47771	+	2.91815i	0.283012	+	0.237475i	0.773232	−	0.634124i	$-0.218639\pi$
$151$	3.47771	+	2.91815i	0.283012	+	0.237475i	−0.490220	+	0.871599i	$0.663083\pi$
$152$		0			0
$153$	1.50000	−	0.545955i	0.121268	−	0.0441379i
$154$		0			0
$155$	3.71941	−	1.35375i	0.298750	−	0.108736i
$156$		0			0
$157$	−3.10472	−	17.6078i	−0.247784	−	1.40525i	−0.813938	−	0.580952i	$-0.802680\pi$
$157$	−3.10472	−	17.6078i	−0.247784	−	1.40525i	0.566154	−	0.824300i	$-0.308431\pi$
$158$		0			0
$159$	−0.252374	−	0.437124i	−0.0200145	−	0.0346662i
$160$		0			0
$161$	−0.891407	+	5.05542i	−0.0702527	+	0.398423i
$162$		0			0
$163$	−2.13176	−	0.775897i	−0.166972	−	0.0607729i	0.257182	−	0.966363i	$-0.417206\pi$
$163$	−2.13176	−	0.775897i	−0.166972	−	0.0607729i	−0.424154	+	0.905590i	$0.639428\pi$
$164$		0			0
$165$	3.85844	+	21.8823i	0.300379	+	1.70354i
$166$		0			0
$167$	16.4290	+	13.7856i	1.27132	+	1.06676i	0.994380	+	0.105872i	$0.0337633\pi$
$167$	16.4290	+	13.7856i	1.27132	+	1.06676i	0.276936	+	0.960888i	$0.410681\pi$
$168$		0			0
$169$	−26.4119	−	9.61316i	−2.03169	−	0.739474i
$170$		0			0
$171$	1.23396	−	2.13727i	0.0943629	−	0.163441i
$172$		0			0
$173$	−8.63223	+	7.24330i	−0.656296	+	0.550698i	−0.908974	−	0.416853i	$-0.863133\pi$
$173$	−8.63223	+	7.24330i	−0.656296	+	0.550698i	0.252678	+	0.967550i	$0.418689\pi$
$174$		0			0
$175$	−3.28699	+	5.69323i	−0.248473	+	0.430368i
$176$		0			0
$177$	7.15910	+	12.3999i	0.538111	+	0.932035i
$178$		0			0
$179$	6.43107			0.480681			0.240341	−	0.970689i	$-0.422741\pi$
$179$	6.43107			0.480681			0.240341	+	0.970689i	$0.422741\pi$
$180$		0			0
$181$	0.608288	−	3.44977i	0.0452137	−	0.256420i	−0.953820	−	0.300380i	$-0.902886\pi$
$181$	0.608288	−	3.44977i	0.0452137	−	0.256420i	0.999033	+	0.0439605i	$0.0139976\pi$
$182$		0			0
$183$	3.06418	−	2.57115i	0.226511	−	0.190065i
$184$		0			0
$185$	−5.37211	+	20.8024i	−0.394965	+	1.52942i
$186$		0			0
$187$	7.69253	−	6.45480i	0.562534	−	0.472022i
$188$		0			0
$189$	−0.708263	+	4.01676i	−0.0515186	+	0.292176i
$190$		0			0
$191$	13.9240			1.00750			0.503751	−	0.863849i	$-0.331953\pi$
$191$	13.9240			1.00750			0.503751	+	0.863849i	$0.331953\pi$
$192$		0			0
$193$	5.78833	+	10.0257i	0.416653	+	0.721665i	0.995600	−	0.0937004i	$-0.0298696\pi$
$193$	5.78833	+	10.0257i	0.416653	+	0.721665i	−0.578947	+	0.815365i	$0.696536\pi$
$194$		0			0
$195$	−21.2802	+	36.8584i	−1.52391	+	2.63948i
$196$		0			0
$197$	11.0740	−	9.29217i	0.788988	−	0.662040i	−0.156507	−	0.987677i	$-0.550023\pi$
$197$	11.0740	−	9.29217i	0.788988	−	0.662040i	0.945495	+	0.325637i	$0.105579\pi$
$198$		0			0
$199$	−2.85844	+	4.95096i	−0.202629	+	0.350965i	−0.949375	−	0.314145i	$-0.898282\pi$
$199$	−2.85844	+	4.95096i	−0.202629	+	0.350965i	0.746745	+	0.665110i	$0.231615\pi$
$200$		0			0
$201$	15.0680	+	5.48432i	1.06282	+	0.386834i
$202$		0			0
$203$	−2.20187	−	1.84759i	−0.154541	−	0.129675i
$204$		0			0
$205$	−5.26352	−	29.8509i	−0.367620	−	2.08488i
$206$		0			0
$207$	2.91875	+	1.06234i	0.202867	+	0.0738376i
$208$		0			0
$209$	2.69594	−	15.2894i	0.186482	−	1.05759i
$210$		0			0
$211$	−3.83275	−	6.63852i	−0.263857	−	0.457014i	0.703406	−	0.710788i	$-0.251661\pi$
$211$	−3.83275	−	6.63852i	−0.263857	−	0.457014i	−0.967264	+	0.253774i	$0.918328\pi$
$212$		0			0
$213$	−4.29086	−	24.3347i	−0.294005	−	1.66738i
$214$		0			0
$215$	−18.6395	+	6.78422i	−1.27120	+	0.462680i
$216$		0			0
$217$	−0.926022	+	0.337044i	−0.0628625	+	0.0228801i
$218$		0			0
$219$	−12.3439	−	10.3578i	−0.834123	−	0.699912i
$220$		0			0
$221$	19.2344			1.29385
$222$		0			0
$223$	1.99226			0.133412			0.0667058	−	0.997773i	$-0.478751\pi$
$223$	1.99226			0.133412			0.0667058	+	0.997773i	$0.478751\pi$
$224$		0			0
$225$	3.04710	+	2.55682i	0.203140	+	0.170455i
$226$		0			0
$227$	−18.3084	+	6.66371i	−1.21517	+	0.442286i	−0.868495	−	0.495699i	$-0.834912\pi$
$227$	−18.3084	+	6.66371i	−1.21517	+	0.442286i	−0.346677	+	0.937985i	$0.612690\pi$
$228$		0			0
$229$	12.0424	−	4.38306i	0.795781	−	0.289641i	0.0880442	−	0.996117i	$-0.471938\pi$
$229$	12.0424	−	4.38306i	0.795781	−	0.289641i	0.707737	+	0.706476i	$0.249716\pi$
$230$		0			0
$231$	−0.960637	−	5.44804i	−0.0632053	−	0.358455i
$232$		0			0
$233$	−1.45811	−	2.52552i	−0.0955240	−	0.165452i	0.814303	−	0.580440i	$-0.197119\pi$
$233$	−1.45811	−	2.52552i	−0.0955240	−	0.165452i	−0.909827	+	0.414987i	$0.863786\pi$
$234$		0			0
$235$	−3.14543	+	17.8386i	−0.205185	+	1.16366i
$236$		0			0
$237$	−20.4538	−	7.44459i	−1.32862	−	0.483578i
$238$		0			0
$239$	−2.78059	−	15.7695i	−0.179862	−	1.02005i	−0.932381	−	0.361476i	$-0.882273\pi$
$239$	−2.78059	−	15.7695i	−0.179862	−	1.02005i	0.752520	−	0.658570i	$-0.228838\pi$
$240$		0			0
$241$	7.49866	+	6.29212i	0.483031	+	0.405311i	0.851521	−	0.524321i	$-0.175681\pi$
$241$	7.49866	+	6.29212i	0.483031	+	0.405311i	−0.368490	+	0.929632i	$0.620125\pi$
$242$		0			0
$243$	5.13816	+	1.87014i	0.329613	+	0.119969i
$244$		0			0
$245$	−10.9966	+	19.0467i	−0.702547	+	1.21685i
$246$		0			0
$247$	22.7802	−	19.1148i	1.44947	−	1.21625i
$248$		0			0
$249$	3.91875	−	6.78747i	0.248341	−	0.430138i
$250$		0			0
$251$	8.37211	+	14.5009i	0.528443	+	0.915290i	0.999450	+	0.0331606i	$0.0105573\pi$
$251$	8.37211	+	14.5009i	0.528443	+	0.915290i	−0.471007	+	0.882129i	$0.656109\pi$
$252$		0			0
$253$	19.5398			1.22846
$254$		0			0
$255$	3.45811	−	19.6119i	0.216555	−	1.22815i
$256$		0			0
$257$	−16.6780	+	13.9945i	−1.04034	+	0.872952i	−0.992045	−	0.125881i	$-0.959824\pi$
$257$	−16.6780	+	13.9945i	−1.04034	+	0.872952i	−0.0482987	+	0.998833i	$0.515380\pi$
$258$		0			0
$259$	1.33750	−	5.17918i	0.0831080	−	0.321818i
$260$		0			0
$261$	−1.33228	+	1.11792i	−0.0824662	+	0.0691973i
$262$		0			0
$263$	−3.67886	+	20.8639i	−0.226848	+	1.28652i	0.632272	+	0.774747i	$0.282123\pi$
$263$	−3.67886	+	20.8639i	−0.226848	+	1.28652i	−0.859120	+	0.511774i	$0.828988\pi$
$264$		0			0
$265$	−0.948615			−0.0582730
$266$		0			0
$267$	−7.86959	−	13.6305i	−0.481611	−	0.834174i
$268$		0			0
$269$	−10.1159	+	17.5212i	−0.616775	+	1.06829i	0.373295	+	0.927713i	$0.378228\pi$
$269$	−10.1159	+	17.5212i	−0.616775	+	1.06829i	−0.990070	+	0.140573i	$0.955105\pi$
$270$		0			0
$271$	10.2194	−	8.57510i	0.620785	−	0.520900i	−0.277265	−	0.960793i	$-0.589428\pi$
$271$	10.2194	−	8.57510i	0.620785	−	0.520900i	0.898050	+	0.439893i	$0.144984\pi$
$272$		0			0
$273$	5.29813	−	9.17664i	0.320658	−	0.555395i
$274$		0			0
$275$	23.5141	+	8.55845i	1.41796	+	0.516094i
$276$		0			0
$277$	24.7147	+	20.7381i	1.48496	+	1.24603i	0.900684	+	0.434474i	$0.143066\pi$
$277$	24.7147	+	20.7381i	1.48496	+	1.24603i	0.584276	+	0.811555i	$0.301379\pi$
$278$		0			0
$279$	0.103541	+	0.587208i	0.00619881	+	0.0351552i
$280$		0			0
$281$	−4.05690	−	1.47659i	−0.242015	−	0.0880861i	0.218165	−	0.975912i	$-0.429993\pi$
$281$	−4.05690	−	1.47659i	−0.242015	−	0.0880861i	−0.460180	+	0.887826i	$0.652215\pi$
$282$		0			0
$283$	−0.233078	+	1.32185i	−0.0138551	+	0.0785760i	−0.990951	−	0.134222i	$-0.957146\pi$
$283$	−0.233078	+	1.32185i	−0.0138551	+	0.0785760i	0.977096	+	0.212798i	$0.0682576\pi$
$284$		0			0
$285$	−15.3944	−	26.6639i	−0.911886	−	1.57943i
$286$		0			0
$287$	1.31046	+	7.43199i	0.0773540	+	0.438696i
$288$		0			0
$289$	7.51754	−	2.73616i	0.442208	−	0.160951i
$290$		0			0
$291$	30.1361	−	10.9686i	1.76661	−	0.642993i
$292$		0			0
$293$	2.11334	+	1.77330i	0.123463	+	0.103597i	0.702428	−	0.711754i	$-0.252099\pi$
$293$	2.11334	+	1.77330i	0.123463	+	0.103597i	−0.578966	+	0.815352i	$0.696544\pi$
$294$		0			0
$295$	26.9094			1.56673
$296$		0			0
$297$	15.5253			0.900868
$298$		0			0
$299$	28.6707	+	24.0576i	1.65807	+	1.39129i
$300$		0			0
$301$	4.64068	−	1.68907i	0.267484	−	0.0973564i
$302$		0			0
$303$	−1.91875	+	0.698367i	−0.110229	+	0.0401201i
$304$		0			0
$305$	−1.30541	−	7.40333i	−0.0747474	−	0.423914i
$306$		0			0
$307$	−3.29426	−	5.70583i	−0.188014	−	0.325649i	0.756574	−	0.653908i	$-0.226872\pi$
$307$	−3.29426	−	5.70583i	−0.188014	−	0.325649i	−0.944588	+	0.328259i	$0.893538\pi$
$308$		0			0
$309$	−3.65998	+	20.7568i	−0.208209	+	1.18081i
$310$		0			0
$311$	−17.8871	−	6.51038i	−1.01429	−	0.369170i	−0.219209	−	0.975678i	$-0.570348\pi$
$311$	−17.8871	−	6.51038i	−1.01429	−	0.369170i	−0.795077	+	0.606508i	$0.792570\pi$
$312$		0			0
$313$	−2.22534	−	12.6205i	−0.125784	−	0.713354i	−0.980839	−	0.194818i	$-0.937588\pi$
$313$	−2.22534	−	12.6205i	−0.125784	−	0.713354i	0.855056	−	0.518536i	$-0.173523\pi$
$314$		0			0
$315$	−1.26604	−	1.06234i	−0.0713335	−	0.0598559i
$316$		0			0
$317$	18.3662	+	6.68474i	1.03155	+	0.375453i	0.801670	−	0.597767i	$-0.203945\pi$
$317$	18.3662	+	6.68474i	1.03155	+	0.375453i	0.229878	+	0.973220i	$0.426167\pi$
$318$		0			0
$319$	−5.47044	+	9.47508i	−0.306286	+	0.530502i
$320$		0			0
$321$	−13.8157	+	11.5927i	−0.771116	+	0.647043i
$322$		0			0
$323$	−6.95723	+	12.0503i	−0.387111	+	0.670496i
$324$		0			0
$325$	23.9650	+	41.5086i	1.32934	+	2.30248i
$326$		0			0
$327$	−4.17530			−0.230894
$328$		0			0
$329$	0.783119	−	4.44129i	0.0431747	−	0.244856i
$330$		0			0
$331$	−10.4927	+	8.80444i	−0.576732	+	0.483936i	−0.883872	−	0.467728i	$-0.845073\pi$
$331$	−10.4927	+	8.80444i	−0.576732	+	0.483936i	0.307140	+	0.951664i	$0.400628\pi$
$332$		0			0
$333$	−2.94562	−	1.34115i	−0.161419	−	0.0734948i
$334$		0			0
$335$	23.0856	−	19.3711i	1.26130	−	1.05836i
$336$		0			0
$337$	−0.888003	+	5.03612i	−0.0483726	+	0.274335i	−0.999395	−	0.0347882i	$-0.988924\pi$
$337$	−0.888003	+	5.03612i	−0.0483726	+	0.274335i	0.951022	+	0.309123i	$0.100035\pi$
$338$		0			0
$339$	−8.70233			−0.472646
$340$		0			0
$341$	1.87551	+	3.24849i	0.101565	+	0.175915i
$342$		0			0
$343$	5.81567	−	10.0730i	0.314017	−	0.543893i
$344$		0			0
$345$	29.6844	−	24.9082i	1.59815	−	1.34101i
$346$		0			0
$347$	7.48158	−	12.9585i	0.401632	−	0.695648i	−0.592291	−	0.805724i	$-0.701776\pi$
$347$	7.48158	−	12.9585i	0.401632	−	0.695648i	0.993923	+	0.110077i	$0.0351096\pi$
$348$		0			0
$349$	12.5569	+	4.57034i	0.672156	+	0.244645i	0.655476	−	0.755216i	$-0.272468\pi$
$349$	12.5569	+	4.57034i	0.672156	+	0.244645i	0.0166799	+	0.999861i	$0.494690\pi$
$350$		0			0
$351$	22.7802	+	19.1148i	1.21592	+	1.02027i
$352$		0			0
$353$	1.41576	+	8.02915i	0.0753530	+	0.427348i	0.999024	+	0.0441626i	$0.0140620\pi$
$353$	1.41576	+	8.02915i	0.0753530	+	0.427348i	−0.923671	+	0.383186i	$0.874827\pi$
$354$		0			0
$355$	−43.6391	−	15.8833i	−2.31612	−	0.843000i
$356$		0			0
$357$	−0.860967	+	4.88279i	−0.0455672	+	0.258424i
$358$		0			0
$359$	0.543233	+	0.940908i	0.0286708	+	0.0496592i	0.880005	−	0.474965i	$-0.157539\pi$
$359$	0.543233	+	0.940908i	0.0286708	+	0.0496592i	−0.851334	+	0.524624i	$0.824206\pi$
$360$		0			0
$361$	0.436289	+	2.47432i	0.0229626	+	0.130227i
$362$		0			0
$363$	−0.360967	+	0.131381i	−0.0189459	+	0.00689573i
$364$		0			0
$365$	−28.4577	+	10.3578i	−1.48954	+	0.542150i
$366$		0			0
$367$	24.2931	+	20.3844i	1.26809	+	1.06406i	0.994771	+	0.102132i	$0.0325664\pi$
$367$	24.2931	+	20.3844i	1.26809	+	1.06406i	0.273321	+	0.961923i	$0.411878\pi$
$368$		0			0
$369$	4.56624			0.237709
$370$		0			0
$371$	0.236177			0.0122617
$372$		0			0
$373$	2.69665	+	2.26276i	0.139627	+	0.117161i	0.709926	−	0.704276i	$-0.248728\pi$
$373$	2.69665	+	2.26276i	0.139627	+	0.117161i	−0.570299	+	0.821437i	$0.693173\pi$
$374$		0			0
$375$	15.4427	−	5.62068i	0.797457	−	0.290251i
$376$		0			0
$377$	−19.6925	+	7.16750i	−1.01422	+	0.369145i
$378$		0			0
$379$	2.14068	+	12.1404i	0.109959	+	0.623611i	0.989123	+	0.147091i	$0.0469910\pi$
$379$	2.14068	+	12.1404i	0.109959	+	0.623611i	−0.879164	+	0.476520i	$0.841898\pi$
$380$		0			0
$381$	−4.77972	−	8.27871i	−0.244872	−	0.424131i
$382$		0			0
$383$	−4.24732	+	24.0878i	−0.217028	+	1.23083i	0.660324	+	0.750980i	$0.270419\pi$
$383$	−4.24732	+	24.0878i	−0.217028	+	1.23083i	−0.877352	+	0.479846i	$0.840692\pi$
$384$		0			0
$385$	−9.76991	−	3.55596i	−0.497921	−	0.181228i
$386$		0			0
$387$	−0.518885	−	2.94274i	−0.0263764	−	0.149588i
$388$		0			0
$389$	10.7909	+	9.05461i	0.547118	+	0.459087i	0.873964	−	0.485991i	$-0.161541\pi$
$389$	10.7909	+	9.05461i	0.547118	+	0.459087i	−0.326846	+	0.945078i	$0.605986\pi$
$390$		0			0
$391$	−16.4564	−	5.98962i	−0.832234	−	0.302908i
$392$		0			0
$393$	3.06418	−	5.30731i	0.154567	−	0.267718i
$394$		0			0
$395$	−31.3371	+	26.2949i	−1.57674	+	1.32304i
$396$		0			0
$397$	8.17412	−	14.1580i	0.410247	−	0.710569i	−0.584669	−	0.811272i	$-0.698776\pi$
$397$	8.17412	−	14.1580i	0.410247	−	0.710569i	0.994917	+	0.100703i	$0.0321091\pi$
$398$		0			0
$399$	3.83275	+	6.63852i	0.191877	+	0.332341i
$400$		0			0
$401$	32.2763			1.61180			0.805901	−	0.592050i	$-0.201681\pi$
$401$	32.2763			1.61180			0.805901	+	0.592050i	$0.201681\pi$
$402$		0			0
$403$	−1.24763	+	7.07564i	−0.0621487	+	0.352463i
$404$		0			0
$405$	27.9047	−	23.4148i	1.38659	−	1.16349i
$406$		0			0
$407$	−20.2986	−	1.59040i	−1.00616	−	0.0788331i
$408$		0			0
$409$	−11.4855	+	9.63744i	−0.567919	+	0.476541i	−0.880955	−	0.473201i	$-0.843099\pi$
$409$	−11.4855	+	9.63744i	−0.567919	+	0.476541i	0.313036	+	0.949741i	$0.398654\pi$
$410$		0			0
$411$	−0.520945	+	2.95442i	−0.0256963	+	0.145731i
$412$		0			0
$413$	−6.69965			−0.329668
$414$		0			0
$415$	−7.36484	−	12.7563i	−0.361526	−	0.626181i
$416$		0			0
$417$	11.0915	−	19.2111i	0.543154	−	0.940770i
$418$		0			0
$419$	26.6125	−	22.3305i	1.30010	−	1.09092i	0.309977	−	0.950744i	$-0.399679\pi$
$419$	26.6125	−	22.3305i	1.30010	−	1.09092i	0.990127	−	0.140173i	$-0.0447657\pi$
$420$		0			0
$421$	−7.92262	+	13.7224i	−0.386125	+	0.668788i	−0.991925	−	0.126829i	$-0.959520\pi$
$421$	−7.92262	+	13.7224i	−0.386125	+	0.668788i	0.605800	+	0.795617i	$0.292853\pi$
$422$		0			0
$423$	−2.56418	−	0.933284i	−0.124675	−	0.0453778i
$424$		0			0
$425$	−17.1800	−	14.4158i	−0.833355	−	0.699268i
$426$		0			0
$427$	0.325008	+	1.84321i	0.0157282	+	0.0891992i
$428$		0			0
$429$	−37.9013	−	13.7949i	−1.82989	−	0.666026i
$430$		0			0
$431$	3.90167	−	22.1275i	0.187937	−	1.06584i	−0.734186	−	0.678948i	$-0.762436\pi$
$431$	3.90167	−	22.1275i	0.187937	−	1.06584i	0.922123	−	0.386896i	$-0.126453\pi$
$432$		0			0
$433$	2.43124	+	4.21103i	0.116838	+	0.202369i	0.918513	−	0.395391i	$-0.129391\pi$
$433$	2.43124	+	4.21103i	0.116838	+	0.202369i	−0.801675	+	0.597760i	$0.796058\pi$
$434$		0			0
$435$	3.76769	+	21.3677i	0.180647	+	1.02450i
$436$		0			0
$437$	−25.4424	+	9.26027i	−1.21707	+	0.442979i
$438$		0			0
$439$	−30.4136	+	11.0696i	−1.45156	+	0.528325i	−0.943027	−	0.332716i	$-0.892035\pi$
$439$	−30.4136	+	11.0696i	−1.45156	+	0.528325i	−0.508535	+	0.861042i	$0.669813\pi$
$440$		0			0
$441$	−2.53802	−	2.12965i	−0.120858	−	0.101412i
$442$		0			0
$443$	19.8844			0.944738			0.472369	−	0.881401i	$-0.343399\pi$
$443$	19.8844			0.944738			0.472369	+	0.881401i	$0.343399\pi$
$444$		0			0
$445$	−29.5800			−1.40222
$446$		0			0
$447$	−18.2271	−	15.2944i	−0.862115	−	0.723400i
$448$		0			0
$449$	−14.3503	+	5.22308i	−0.677232	+	0.246492i	−0.657659	−	0.753316i	$-0.728453\pi$
$449$	−14.3503	+	5.22308i	−0.677232	+	0.246492i	−0.0195734	+	0.999808i	$0.506231\pi$
$450$		0			0
$451$	26.9932	−	9.82472i	1.27106	−	0.462628i
$452$		0			0
$453$	1.48158	+	8.40247i	0.0696108	+	0.394782i
$454$		0			0
$455$	−9.95723	−	17.2464i	−0.466802	−	0.808525i
$456$		0			0
$457$	−2.33733	+	13.2557i	−0.109336	+	0.620075i	0.880064	+	0.474856i	$0.157500\pi$
$457$	−2.33733	+	13.2557i	−0.109336	+	0.620075i	−0.989400	+	0.145219i	$0.953611\pi$
$458$		0			0
$459$	−13.0753	−	4.75903i	−0.610304	−	0.222132i
$460$		0			0
$461$	−2.29948	−	13.0410i	−0.107097	−	0.607379i	−0.990362	−	0.138504i	$-0.955771\pi$
$461$	−2.29948	−	13.0410i	−0.107097	−	0.607379i	0.883265	−	0.468875i	$-0.155341\pi$
$462$		0			0
$463$	−8.20162	−	6.88197i	−0.381162	−	0.319832i	0.431997	−	0.901875i	$-0.357809\pi$
$463$	−8.20162	−	6.88197i	−0.381162	−	0.319832i	−0.813158	+	0.582043i	$0.802254\pi$
$464$		0			0
$465$	6.99020	+	2.54422i	0.324163	+	0.117986i
$466$		0			0
$467$	−7.86143	+	13.6164i	−0.363784	+	0.630092i	−0.988580	−	0.150696i	$-0.951849\pi$
$467$	−7.86143	+	13.6164i	−0.363784	+	0.630092i	0.624796	+	0.780788i	$0.285182\pi$
$468$		0			0
$469$	−5.74763	+	4.82283i	−0.265401	+	0.222698i
$470$		0			0
$471$	16.8011	−	29.1004i	0.774155	−	1.34088i
$472$		0			0
$473$	−9.39899	−	16.2795i	−0.432166	−	0.748533i
$474$		0			0
$475$	−34.6732			−1.59092
$476$		0			0
$477$	0.0248149	−	0.140732i	0.00113620	−	0.00644370i
$478$		0			0
$479$	−22.8353	+	19.1611i	−1.04337	+	0.875492i	−0.992381	−	0.123208i	$-0.960682\pi$
$479$	−22.8353	+	19.1611i	−1.04337	+	0.875492i	−0.0509894	+	0.998699i	$0.516237\pi$
$480$		0			0
$481$	−27.8259	−	27.3254i	−1.26875	−	1.24593i
$482$		0			0
$483$	−7.39053	+	6.20139i	−0.336281	+	0.282173i
$484$		0			0
$485$	10.4662	−	59.3565i	0.475244	−	2.69524i
$486$		0			0
$487$	11.2550			0.510011			0.255005	−	0.966940i	$-0.417923\pi$
$487$	11.2550			0.510011			0.255005	+	0.966940i	$0.417923\pi$
$488$		0			0
$489$	−2.13176	−	3.69232i	−0.0964015	−	0.166972i
$490$		0			0
$491$	0.519762	−	0.900255i	0.0234566	−	0.0406279i	−0.854059	−	0.520176i	$-0.825866\pi$
$491$	0.519762	−	0.900255i	0.0234566	−	0.0406279i	0.877515	+	0.479548i	$0.159200\pi$
$492$		0			0
$493$	7.51161	−	6.30299i	0.338306	−	0.283872i
$494$		0			0
$495$	−3.14543	+	5.44804i	−0.141377	+	0.244871i
$496$		0			0
$497$	10.8648	+	3.95448i	0.487355	+	0.177383i
$498$		0			0
$499$	−27.3332	−	22.9353i	−1.22360	−	1.02672i	−0.998628	−	0.0523600i	$-0.983326\pi$
$499$	−27.3332	−	22.9353i	−1.22360	−	1.02672i	−0.224974	−	0.974365i	$-0.572230\pi$
$500$		0			0
$501$	6.99912	+	39.6940i	0.312698	+	1.77340i
$502$		0			0
$503$	23.8926	+	8.69621i	1.06532	+	0.387745i	0.814425	−	0.580269i	$-0.197053\pi$
$503$	23.8926	+	8.69621i	1.06532	+	0.387745i	0.250896	+	0.968014i	$0.419275\pi$
$504$		0			0
$505$	−0.666374	+	3.77920i	−0.0296533	+	0.168172i
$506$		0			0
$507$	−26.4119	−	45.7468i	−1.17300	−	2.03169i
$508$		0			0
$509$	0.00118205	+	0.00670372i	5.23933e−5	+	0.000297137i	0.984834	−	0.173500i	$-0.0555075\pi$
$509$	0.00118205	+	0.00670372i	5.23933e−5	+	0.000297137i	−0.984782	+	0.173797i	$0.944396\pi$
$510$		0			0
$511$	7.08512	−	2.57877i	0.313427	−	0.114078i
$512$		0			0
$513$	−20.2151	+	7.35770i	−0.892520	+	0.324851i
$514$		0			0
$515$	30.3444	+	25.4619i	1.33713	+	1.12199i
$516$		0			0
$517$	−17.1661			−0.754965
$518$		0			0
$519$	−21.1780			−0.929610
$520$		0			0
$521$	5.34595	+	4.48579i	0.234210	+	0.196526i	0.752338	−	0.658778i	$-0.228926\pi$
$521$	5.34595	+	4.48579i	0.234210	+	0.196526i	−0.518127	+	0.855304i	$0.673371\pi$
$522$		0			0
$523$	37.1562	−	13.5237i	1.62473	−	0.591352i	0.640451	−	0.767999i	$-0.278747\pi$
$523$	37.1562	−	13.5237i	1.62473	−	0.591352i	0.984274	+	0.176647i	$0.0565251\pi$
$524$		0			0
$525$	−11.6099	+	4.22567i	−0.506699	+	0.184423i
$526$		0			0
$527$	−0.583778	−	3.31077i	−0.0254298	−	0.144219i
$528$		0			0
$529$	−5.53818	−	9.59241i	−0.240790	−	0.417061i
$530$		0			0
$531$	−0.703926	+	3.99216i	−0.0305478	+	0.173245i
$532$		0			0
$533$	51.7033	+	18.8185i	2.23952	+	0.815118i
$534$		0			0
$535$	5.88578	+	33.3799i	0.254465	+	1.44314i
$536$		0			0
$537$	9.25877	+	7.76903i	0.399545	+	0.335258i
$538$		0			0
$539$	−19.5856	−	7.12857i	−0.843611	−	0.307049i
$540$		0			0
$541$	5.90554	−	10.2287i	0.253899	−	0.439766i	−0.710697	−	0.703498i	$-0.751620\pi$
$541$	5.90554	−	10.2287i	0.253899	−	0.439766i	0.964596	+	0.263732i	$0.0849535\pi$
$542$		0			0
$543$	5.04323	−	4.23178i	0.216426	−	0.181603i
$544$		0			0
$545$	−3.92350	+	6.79569i	−0.168064	+	0.291096i
$546$		0			0
$547$	21.0582	+	36.4740i	0.900386	+	1.55951i	0.826994	+	0.562211i	$0.190049\pi$
$547$	21.0582	+	36.4740i	0.900386	+	1.55951i	0.0733915	+	0.997303i	$0.476618\pi$
$548$		0			0
$549$	1.13247			0.0483328
$550$		0			0
$551$	2.63253	−	14.9298i	0.112150	−	0.636032i
$552$		0			0
$553$	7.80200	−	6.54666i	0.331775	−	0.278392i
$554$		0			0
$555$	−32.8644	+	23.4593i	−1.39502	+	0.995792i
$556$		0			0
$557$	9.44537	−	7.92561i	0.400213	−	0.335819i	−0.420363	−	0.907356i	$-0.638097\pi$
$557$	9.44537	−	7.92561i	0.400213	−	0.335819i	0.820576	+	0.571537i	$0.193653\pi$
$558$		0			0
$559$	6.25237	−	35.4590i	0.264447	−	1.49975i
$560$		0			0
$561$	18.8726			0.796801
$562$		0			0
$563$	4.18866	+	7.25498i	0.176531	+	0.305761i	0.940690	−	0.339267i	$-0.110179\pi$
$563$	4.18866	+	7.25498i	0.176531	+	0.305761i	−0.764159	+	0.645028i	$0.776846\pi$
$564$		0			0
$565$	−8.17752	+	14.1639i	−0.344031	+	0.595879i
$566$		0			0
$567$	−6.94743	+	5.82959i	−0.291765	+	0.244820i
$568$		0			0
$569$	4.14543	−	7.18009i	0.173785	−	0.301005i	−0.765955	−	0.642894i	$-0.777733\pi$
$569$	4.14543	−	7.18009i	0.173785	−	0.301005i	0.939740	+	0.341889i	$0.111067\pi$
$570$		0			0
$571$	0.0184183	+	0.00670372i	0.000770782	+	0.000280542i	0.342406	−	0.939552i	$-0.388758\pi$
$571$	0.0184183	+	0.00670372i	0.000770782	+	0.000280542i	−0.341635	+	0.939833i	$0.610981\pi$
$572$		0			0
$573$	20.0462	+	16.8208i	0.837443	+	0.702698i
$574$		0			0
$575$	−7.57785	−	42.9761i	−0.316018	−	1.79223i
$576$		0			0
$577$	−5.45811	−	1.98659i	−0.227224	−	0.0827028i	0.225899	−	0.974151i	$-0.427468\pi$
$577$	−5.45811	−	1.98659i	−0.227224	−	0.0827028i	−0.453123	+	0.891448i	$0.649690\pi$
$578$		0			0
$579$	−3.77807	+	21.4265i	−0.157011	+	0.890454i
$580$		0			0
$581$	1.83363	+	3.17593i	0.0760716	+	0.131760i
$582$		0			0
$583$	−0.156107	−	0.885328i	−0.00646530	−	0.0366665i
$584$		0			0
$585$	−11.3229	+	4.12122i	−0.468146	+	0.170391i
$586$		0			0
$587$	−1.50640	+	0.548284i	−0.0621756	+	0.0226301i	−0.372921	−	0.927863i	$-0.621644\pi$
$587$	−1.50640	+	0.548284i	−0.0621756	+	0.0226301i	0.310745	+	0.950493i	$0.399421\pi$
$588$		0			0
$589$	−3.98158	−	3.34094i	−0.164058	−	0.137661i
$590$		0			0
$591$	27.1685			1.11756
$592$		0			0
$593$	26.7543			1.09867			0.549334	−	0.835603i	$-0.314881\pi$
$593$	26.7543			1.09867			0.549334	+	0.835603i	$0.314881\pi$
$594$		0			0
$595$	7.13816	+	5.98962i	0.292636	+	0.245551i
$596$		0			0
$597$	−10.0963	+	3.67474i	−0.413213	+	0.150397i
$598$		0			0
$599$	−13.5077	+	4.91642i	−0.551911	+	0.200879i	−0.602895	−	0.797820i	$-0.705986\pi$
$599$	−13.5077	+	4.91642i	−0.551911	+	0.200879i	0.0509842	+	0.998699i	$0.483764\pi$
$600$		0			0
$601$	0.333930	+	1.89381i	0.0136213	+	0.0772503i	0.990861	−	0.134889i	$-0.0430679\pi$
$601$	0.333930	+	1.89381i	0.0136213	+	0.0772503i	−0.977239	+	0.212140i	$0.931957\pi$
$602$		0			0
$603$	2.26991	+	3.93161i	0.0924381	+	0.160107i
$604$		0			0
$605$	−0.125362	+	0.710966i	−0.00509671	+	0.0289049i
$606$		0			0
$607$	25.4354	+	9.25773i	1.03239	+	0.375760i	0.801991	−	0.597336i	$-0.203774\pi$
$607$	25.4354	+	9.25773i	1.03239	+	0.375760i	0.230401	+	0.973096i	$0.425996\pi$
$608$		0			0
$609$	−0.938044	−	5.31991i	−0.0380115	−	0.215574i
$610$		0			0
$611$	−25.1878	−	21.1351i	−1.01899	−	0.855033i
$612$		0			0
$613$	−28.3332	−	10.3124i	−1.14437	−	0.416516i	−0.300879	−	0.953662i	$-0.597280\pi$
$613$	−28.3332	−	10.3124i	−1.14437	−	0.416516i	−0.843489	+	0.537147i	$0.819502\pi$
$614$		0			0
$615$	28.4834	−	49.3347i	1.14856	−	1.98937i
$616$		0			0
$617$	−14.3289	+	12.0234i	−0.576859	+	0.484042i	−0.883914	−	0.467650i	$-0.845101\pi$
$617$	−14.3289	+	12.0234i	−0.576859	+	0.484042i	0.307055	+	0.951692i	$0.400656\pi$
$618$		0			0
$619$	−11.6891	+	20.2462i	−0.469826	+	0.813762i	−0.999405	−	0.0344985i	$-0.989017\pi$
$619$	−11.6891	+	20.2462i	−0.469826	+	0.813762i	0.529579	+	0.848261i	$0.322350\pi$
$620$		0			0
$621$	−13.5376	−	23.4478i	−0.543246	−	0.940929i
$622$		0			0
$623$	7.36453			0.295054
$624$		0			0
$625$	−1.12748	+	6.39425i	−0.0450991	+	0.255770i
$626$		0			0
$627$	22.3516	−	18.7552i	0.892638	−	0.749012i
$628$		0			0
$629$	16.6079	+	7.56164i	0.662199	+	0.301502i
$630$		0			0
$631$	−16.5077	+	13.8516i	−0.657163	+	0.551425i	−0.909235	−	0.416283i	$-0.863332\pi$
$631$	−16.5077	+	13.8516i	−0.657163	+	0.551425i	0.252072	+	0.967708i	$0.418888\pi$
$632$		0			0
$633$	2.50165	−	14.1876i	0.0994316	−	0.563905i
$634$		0			0
$635$	−17.9659			−0.712953
$636$		0			0
$637$	−19.9611	−	34.5736i	−0.790888	−	1.36986i
$638$		0			0
$639$	3.49794	−	6.05861i	0.138376	−	0.239675i
$640$		0			0
$641$	−4.34595	+	3.64669i	−0.171655	+	0.144035i	−0.724568	−	0.689203i	$-0.757961\pi$
$641$	−4.34595	+	3.64669i	−0.171655	+	0.144035i	0.552913	+	0.833239i	$0.313516\pi$
$642$		0			0
$643$	−12.9479	+	22.4264i	−0.510615	+	0.884412i	0.489309	+	0.872110i	$0.337249\pi$
$643$	−12.9479	+	22.4264i	−0.510615	+	0.884412i	−0.999924	+	0.0123012i	$0.996084\pi$
$644$		0			0
$645$	−35.0308	−	12.7502i	−1.37934	−	0.502037i
$646$		0			0
$647$	−7.85638	−	6.59229i	−0.308866	−	0.259170i	0.475157	−	0.879901i	$-0.342391\pi$
$647$	−7.85638	−	6.59229i	−0.308866	−	0.259170i	−0.784023	+	0.620732i	$0.786836\pi$
$648$		0			0
$649$	4.42830	+	25.1141i	0.173826	+	0.985816i
$650$		0			0
$651$	−1.74035	−	0.633436i	−0.0682098	−	0.0248263i
$652$		0			0
$653$	−5.75743	+	32.6520i	−0.225306	+	1.27777i	0.636795	+	0.771033i	$0.280260\pi$
$653$	−5.75743	+	32.6520i	−0.225306	+	1.27777i	−0.862100	+	0.506738i	$0.830851\pi$
$654$		0			0
$655$	−5.75877	−	9.97448i	−0.225014	−	0.389735i
$656$		0			0
$657$	−0.792204	−	4.49281i	−0.0309068	−	0.175281i
$658$		0			0
$659$	11.4957	−	4.18410i	0.447810	−	0.162989i	−0.108264	−	0.994122i	$-0.534529\pi$
$659$	11.4957	−	4.18410i	0.447810	−	0.162989i	0.556074	+	0.831133i	$0.312307\pi$
$660$		0			0
$661$	−15.5141	+	5.64668i	−0.603430	+	0.219631i	−0.625626	−	0.780123i	$-0.715156\pi$
$661$	−15.5141	+	5.64668i	−0.603430	+	0.219631i	0.0221961	+	0.999754i	$0.492934\pi$
$662$		0			0
$663$	27.6917	+	23.2361i	1.07545	+	0.902414i
$664$		0			0
$665$	14.4064			0.558657
$666$		0			0
$667$	19.0803			0.738791
$668$		0			0
$669$	2.86824	+	2.40674i	0.110893	+	0.0930499i
$670$		0			0
$671$	6.69459	−	2.43663i	0.258442	−	0.0940652i
$672$		0			0
$673$	44.5861	−	16.2280i	1.71867	−	0.625543i	0.720944	−	0.692994i	$-0.243709\pi$
$673$	44.5861	−	16.2280i	1.71867	−	0.625543i	0.997723	+	0.0674505i	$0.0214865\pi$
$674$		0			0
$675$	−6.02094	−	34.1465i	−0.231746	−	1.31430i
$676$		0			0
$677$	4.41622	+	7.64912i	0.169729	+	0.293980i	0.938325	−	0.345756i	$-0.112377\pi$
$677$	4.41622	+	7.64912i	0.169729	+	0.293980i	−0.768595	+	0.639735i	$0.779044\pi$
$678$		0			0
$679$	−2.60576	+	14.7780i	−0.100000	+	0.567128i
$680$		0			0
$681$	−34.4085	−	12.5237i	−1.31854	−	0.479909i
$682$		0			0
$683$	−7.12092	−	40.3847i	−0.272474	−	1.54528i	−0.746872	−	0.664968i	$-0.768445\pi$
$683$	−7.12092	−	40.3847i	−0.272474	−	1.54528i	0.474397	−	0.880311i	$-0.342666\pi$
$684$		0			0
$685$	4.31908	+	3.62414i	0.165023	+	0.138471i
$686$		0			0
$687$	22.6322	+	8.23746i	0.863473	+	0.314279i
$688$		0			0
$689$	0.860967	−	1.49124i	0.0328002	−	0.0568117i
$690$		0			0
$691$	−35.5276	+	29.8112i	−1.35153	+	1.13407i	−0.373033	+	0.927818i	$0.621682\pi$
$691$	−35.5276	+	29.8112i	−1.35153	+	1.13407i	−0.978499	+	0.206252i	$0.933873\pi$
$692$		0			0
$693$	0.783119	−	1.35640i	0.0297482	−	0.0515254i
$694$		0			0
$695$	−20.8452	−	36.1050i	−0.790705	−	1.36954i
$696$		0			0
$697$	−25.7452			−0.975167
$698$		0			0
$699$	0.951714	−	5.39744i	0.0359971	−	0.204150i
$700$		0			0
$701$	5.03390	−	4.22394i	0.190128	−	0.159536i	−0.542755	−	0.839891i	$-0.682619\pi$
$701$	5.03390	−	4.22394i	0.190128	−	0.159536i	0.732883	+	0.680355i	$0.238174\pi$
$702$		0			0
$703$	27.1841	−	7.54904i	1.02527	−	0.284717i
$704$		0			0
$705$	−26.0783	+	21.8823i	−0.982166	+	0.824135i
$706$		0			0
$707$	0.165907	−	0.940908i	0.00623959	−	0.0353865i
$708$		0			0
$709$	−13.3105			−0.499885			−0.249942	−	0.968261i	$-0.580412\pi$
$709$	−13.3105			−0.499885			−0.249942	+	0.968261i	$0.580412\pi$
$710$		0			0
$711$	−3.08125	−	5.33688i	−0.115556	−	0.200149i
$712$		0			0
$713$	3.27079	−	5.66518i	0.122492	−	0.212163i
$714$		0			0
$715$	−58.0681	+	48.7249i	−2.17162	+	1.82221i
$716$		0			0
$717$	15.0471	−	26.0623i	0.561944	−	0.973316i
$718$		0			0
$719$	17.4106	+	6.33694i	0.649306	+	0.236328i	0.645612	−	0.763665i	$-0.276602\pi$
$719$	17.4106	+	6.33694i	0.649306	+	0.236328i	0.00369326	+	0.999993i	$0.498824\pi$
$720$		0			0
$721$	−7.55484	−	6.33927i	−0.281357	−	0.236087i
$722$		0			0
$723$	3.19459	+	18.1174i	0.118808	+	0.673795i
$724$		0			0
$725$	22.9611	+	8.35716i	0.852754	+	0.310377i
$726$		0			0
$727$	3.89456	−	22.0872i	0.144441	−	0.819167i	−0.823373	−	0.567501i	$-0.807910\pi$
$727$	3.89456	−	22.0872i	0.144441	−	0.819167i	0.967814	−	0.251666i	$-0.0809786\pi$
$728$		0			0
$729$	−10.3316	−	17.8948i	−0.382651	−	0.662770i
$730$		0			0
$731$	2.92556	+	16.5916i	0.108206	+	0.613664i
$732$		0			0
$733$	23.5205	−	8.56077i	0.868751	−	0.316199i	0.131090	−	0.991371i	$-0.458152\pi$
$733$	23.5205	−	8.56077i	0.868751	−	0.316199i	0.737661	+	0.675171i	$0.235930\pi$
$734$		0			0
$735$	−38.8410	+	14.1370i	−1.43267	+	0.521449i
$736$		0			0
$737$	21.8778	+	18.3576i	0.805879	+	0.676213i
$738$		0			0
$739$	−27.2327			−1.00177			−0.500885	−	0.865514i	$-0.666992\pi$
$739$	−27.2327			−1.00177			−0.500885	+	0.865514i	$0.666992\pi$
$740$		0			0
$741$	55.8881			2.05310
$742$		0			0
$743$	1.71095	+	1.43566i	0.0627687	+	0.0526692i	0.673632	−	0.739067i	$-0.264733\pi$
$743$	1.71095	+	1.43566i	0.0627687	+	0.0526692i	−0.610864	+	0.791736i	$0.709178\pi$
$744$		0			0
$745$	−42.0210	+	15.2944i	−1.53953	+	0.560343i
$746$		0			0
$747$	2.08512	−	0.758922i	0.0762906	−	0.0277675i
$748$		0			0
$749$	−1.46538	−	8.31061i	−0.0535440	−	0.303663i
$750$		0			0
$751$	−0.0839403	−	0.145389i	−0.00306302	−	0.00530531i	0.864490	−	0.502650i	$-0.167642\pi$
$751$	−0.0839403	−	0.145389i	−0.00306302	−	0.00530531i	−0.867553	+	0.497345i	$0.834308\pi$
$752$		0			0
$753$	−5.46451	+	30.9908i	−0.199138	+	1.12937i
$754$		0			0
$755$	15.0680	+	5.48432i	0.548382	+	0.199595i
$756$		0			0
$757$	−6.06371	−	34.3890i	−0.220389	−	1.24989i	−0.871306	−	0.490741i	$-0.836726\pi$
$757$	−6.06371	−	34.3890i	−0.220389	−	1.24989i	0.650916	−	0.759149i	$-0.274385\pi$
$758$		0			0
$759$	28.1313	+	23.6050i	1.02110	+	0.856807i
$760$		0			0
$761$	2.08347	+	0.758322i	0.0755259	+	0.0274892i	0.379507	−	0.925189i	$-0.376094\pi$
$761$	2.08347	+	0.758322i	0.0755259	+	0.0274892i	−0.303981	+	0.952678i	$0.598316\pi$
$762$		0			0
$763$	0.976834	−	1.69193i	0.0353638	−	0.0612518i
$764$		0			0
$765$	4.31908	−	3.62414i	0.156157	−	0.131031i
$766$		0			0
$767$	−24.4231	+	42.3020i	−0.881866	+	1.52744i
$768$		0			0
$769$	26.0710	+	45.1564i	0.940146	+	1.62838i	0.765191	+	0.643804i	$0.222645\pi$
$769$	26.0710	+	45.1564i	0.940146	+	1.62838i	0.174955	+	0.984576i	$0.444022\pi$
$770$		0			0
$771$	−40.9172			−1.47360
$772$		0			0
$773$	7.81046	−	44.2953i	0.280923	−	1.59319i	−0.438573	−	0.898695i	$-0.644516\pi$
$773$	7.81046	−	44.2953i	0.280923	−	1.59319i	0.719496	−	0.694496i	$-0.244373\pi$
$774$		0			0
$775$	6.41740	−	5.38484i	0.230520	−	0.193429i
$776$		0			0
$777$	8.18227	−	5.84067i	0.293537	−	0.209533i
$778$		0			0
$779$	−30.4911	+	25.5851i	−1.09246	+	0.916681i
$780$		0			0
$781$	7.64227	−	43.3415i	0.273462	−	1.55088i
$782$		0			0
$783$	15.1601			0.541779
$784$		0			0
$785$	−31.5758	−	54.6909i	−1.12699	−	1.95200i
$786$		0			0
$787$	27.4984	−	47.6286i	0.980212	−	1.69778i	0.318678	−	0.947863i	$-0.396761\pi$
$787$	27.4984	−	47.6286i	0.980212	−	1.69778i	0.661535	−	0.749914i	$-0.269905\pi$
$788$		0			0
$789$	−30.5009	+	25.5933i	−1.08586	+	0.911146i
$790$		0			0
$791$	2.03596	−	3.52638i	0.0723904	−	0.125384i
$792$		0			0
$793$	12.8229	+	4.66717i	0.455356	+	0.165736i
$794$		0			0
$795$	−1.36571	−	1.14597i	−0.0484369	−	0.0406434i
$796$		0			0
$797$	−3.66637	−	20.7930i	−0.129870	−	0.736527i	−0.978296	−	0.207213i	$-0.933561\pi$
$797$	−3.66637	−	20.7930i	−0.129870	−	0.736527i	0.848426	−	0.529314i	$-0.177551\pi$
$798$		0			0
$799$	14.4572	+	5.26200i	0.511460	+	0.186156i
$800$		0			0
$801$	0.773785	−	4.38835i	0.0273404	−	0.155055i
$802$		0			0
$803$	−14.3498	−	24.8546i	−0.506394	−	0.877101i
$804$		0			0
$805$	3.14853	+	17.8562i	0.110971	+	0.629348i
$806$		0			0
$807$	−35.7301	+	13.0047i	−1.25776	+	0.457787i
$808$		0			0
$809$	−44.3191	+	16.1308i	−1.55818	+	0.567130i	−0.970318	−	0.241833i	$-0.922252\pi$
$809$	−44.3191	+	16.1308i	−1.55818	+	0.567130i	−0.587860	+	0.808963i	$0.700029\pi$
$810$		0			0
$811$	13.5947	+	11.4073i	0.477374	+	0.400564i	0.849476	−	0.527628i	$-0.176918\pi$
$811$	13.5947	+	11.4073i	0.477374	+	0.400564i	−0.372102	+	0.928192i	$0.621363\pi$
$812$		0			0
$813$	25.0719			0.879311
$814$		0			0
$815$	−8.01279			−0.280676
$816$		0			0
$817$	19.9534	+	16.7429i	0.698080	+	0.585759i
$818$		0			0
$819$	2.81908	−	1.02606i	0.0985066	−	0.0358535i
$820$		0			0
$821$	0.331100	−	0.120510i	0.0115555	−	0.00420584i	−0.336236	−	0.941778i	$-0.609154\pi$
$821$	0.331100	−	0.120510i	0.0115555	−	0.00420584i	0.347791	+	0.937572i	$0.386932\pi$
$822$		0			0
$823$	−7.84302	−	44.4800i	−0.273390	−	1.55047i	−0.744029	−	0.668147i	$-0.767088\pi$
$823$	−7.84302	−	44.4800i	−0.273390	−	1.55047i	0.470639	−	0.882326i	$-0.344024\pi$
$824$		0			0
$825$	23.5141	+	40.7277i	0.818657	+	1.41796i
$826$		0			0
$827$	0.178863	−	1.01438i	0.00621967	−	0.0352735i	−0.981540	−	0.191257i	$-0.938744\pi$
$827$	0.178863	−	1.01438i	0.00621967	−	0.0352735i	0.987760	+	0.155984i	$0.0498547\pi$
$828$		0			0
$829$	42.8080	+	15.5808i	1.48678	+	0.541145i	0.952600	−	0.304224i	$-0.0983973\pi$
$829$	42.8080	+	15.5808i	1.48678	+	0.541145i	0.534183	+	0.845369i	$0.320619\pi$
$830$		0			0
$831$	10.5290	+	59.7129i	0.365247	+	2.07142i
$832$		0			0
$833$	14.3097	+	12.0073i	0.495803	+	0.416028i
$834$		0			0
$835$	71.1828	+	25.9084i	2.46338	+	0.896598i
$836$		0			0
$837$	2.59879	−	4.50124i	0.0898274	−	0.155586i
$838$		0			0
$839$	29.7827	−	24.9907i	1.02821	−	0.862773i	0.0375760	−	0.999294i	$-0.488036\pi$
$839$	29.7827	−	24.9907i	1.02821	−	0.862773i	0.990637	+	0.136520i	$0.0435919\pi$
$840$		0			0
$841$	9.15822	−	15.8625i	0.315801	−	0.546983i
$842$		0			0
$843$	−4.05690	−	7.02676i	−0.139727	−	0.242015i
$844$		0			0
$845$	−99.2764			−3.41521
$846$		0			0
$847$	0.0312115	−	0.177009i	0.00107244	−	0.00608212i
$848$		0			0
$849$	−1.93242	+	1.62149i	−0.0663204	+	0.0556495i
$850$		0			0
$851$	15.2978	+	32.0437i	0.524403	+	1.09845i
$852$		0			0
$853$	−29.6293	+	24.8619i	−1.01449	+	0.851256i	−0.988925	−	0.148417i	$-0.952582\pi$
$853$	−29.6293	+	24.8619i	−1.01449	+	0.851256i	−0.0255627	+	0.999673i	$0.508138\pi$
$854$		0			0
$855$	1.51367	−	8.58445i	0.0517664	−	0.293582i
$856$		0			0
$857$	43.6965			1.49264			0.746321	−	0.665586i	$-0.231818\pi$
$857$	43.6965			1.49264			0.746321	+	0.665586i	$0.231818\pi$
$858$		0			0
$859$	−21.6682	−	37.5304i	−0.739309	−	1.28052i	−0.952807	−	0.303577i	$-0.901819\pi$
$859$	−21.6682	−	37.5304i	−0.739309	−	1.28052i	0.213498	−	0.976944i	$-0.431514\pi$
$860$		0			0
$861$	−7.09152	+	12.2829i	−0.241678	+	0.418599i
$862$		0			0
$863$	30.7067	−	25.7660i	1.04527	−	0.877083i	0.0526792	−	0.998611i	$-0.483224\pi$
$863$	30.7067	−	25.7660i	1.04527	−	0.877083i	0.992588	+	0.121528i	$0.0387795\pi$
$864$		0			0
$865$	−19.9008	+	34.4692i	−0.676647	+	1.17199i
$866$		0			0
$867$	14.1284	+	5.14230i	0.479824	+	0.174642i
$868$		0			0
$869$	−29.6976	−	24.9192i	−1.00742	−	0.845327i
$870$		0			0
$871$	9.49912	+	53.8722i	0.321865	+	1.82539i
$872$		0			0
$873$	8.53209	+	3.10543i	0.288767	+	0.105103i
$874$		0			0
$875$	−1.33527	+	7.57272i	−0.0451405	+	0.256005i
$876$		0			0
$877$	26.1366	+	45.2699i	0.882569	+	1.52865i	0.848475	+	0.529236i	$0.177521\pi$
$877$	26.1366	+	45.2699i	0.882569	+	1.52865i	0.0340942	+	0.999419i	$0.489145\pi$
$878$		0			0
$879$	0.900330	+	5.10602i	0.0303674	+	0.172222i
$880$		0			0
$881$	22.4770	−	8.18096i	0.757269	−	0.275623i	0.0656079	−	0.997845i	$-0.479101\pi$
$881$	22.4770	−	8.18096i	0.757269	−	0.275623i	0.691661	+	0.722222i	$0.256879\pi$
$882$		0			0
$883$	12.6211	−	4.59370i	0.424733	−	0.154590i	−0.120805	−	0.992676i	$-0.538548\pi$
$883$	12.6211	−	4.59370i	0.424733	−	0.154590i	0.545538	+	0.838086i	$0.316325\pi$
$884$		0			0
$885$	38.7413	+	32.5078i	1.30227	+	1.09274i
$886$		0			0
$887$	−49.3242			−1.65614			−0.828072	−	0.560622i	$-0.810562\pi$
$887$	−49.3242			−1.65614			−0.828072	+	0.560622i	$0.810562\pi$
$888$		0			0
$889$	4.47296			0.150018
$890$		0			0
$891$	26.4447	+	22.1898i	0.885932	+	0.743385i
$892$		0			0
$893$	22.3516	−	8.13533i	0.747969	−	0.272238i
$894$		0			0
$895$	21.3452	−	7.76903i	0.713493	−	0.259690i
$896$		0			0
$897$	12.2144	+	69.2711i	0.407825	+	2.31289i
$898$		0			0
$899$	1.83140	+	3.17209i	0.0610808	+	0.105795i
$900$		0			0
$901$	−0.139910	+	0.793471i	−0.00466109	+	0.0264344i
$902$		0			0
$903$	8.72163	+	3.17441i	0.290238	+	0.105638i
$904$		0			0
$905$	−2.14853	−	12.1849i	−0.0714195	−	0.405040i
$906$		0			0
$907$	33.6694	+	28.2520i	1.11797	+	0.938091i	0.998500	−	0.0547468i	$-0.0174352\pi$
$907$	33.6694	+	28.2520i	1.11797	+	0.938091i	0.119473	+	0.992837i	$0.461880\pi$
$908$		0			0
$909$	−0.543233	−	0.197721i	−0.0180179	−	0.00655798i
$910$		0			0
$911$	8.02987	−	13.9081i	0.266041	−	0.460797i	−0.701795	−	0.712379i	$-0.747618\pi$
$911$	8.02987	−	13.9081i	0.266041	−	0.460797i	0.967836	+	0.251582i	$0.0809509\pi$
$912$		0			0
$913$	10.6932	−	8.97270i	0.353895	−	0.296953i
$914$		0			0
$915$	7.06418	−	12.2355i	0.233535	−	0.404494i
$916$		0			0
$917$	1.43376	+	2.48335i	0.0473470	+	0.0820074i
$918$		0			0
$919$	−34.6468			−1.14289			−0.571447	−	0.820639i	$-0.693618\pi$
$919$	−34.6468			−1.14289			−0.571447	+	0.820639i	$0.693618\pi$
$920$		0			0
$921$	2.15018	−	12.1943i	0.0708508	−	0.401815i
$922$		0			0
$923$	64.5758	−	54.1856i	2.12554	−	1.78354i
$924$		0			0
$925$	4.37417	+	45.2617i	0.143822	+	1.48820i
$926$		0			0
$927$	−4.57120	+	3.83570i	−0.150138	+	0.125981i
$928$		0			0
$929$	−8.43195	+	47.8200i	−0.276643	+	1.56892i	0.457050	+	0.889441i	$0.348906\pi$
$929$	−8.43195	+	47.8200i	−0.276643	+	1.56892i	−0.733693	+	0.679481i	$0.762205\pi$
$930$		0			0
$931$	28.8803			0.946514
$932$		0			0
$933$	−17.8871	−	30.9814i	−0.585598	−	1.01429i
$934$		0			0
$935$	17.7344	−	30.7169i	0.579978	−	1.00455i
$936$		0			0
$937$	37.5069	−	31.4720i	1.22530	−	1.02815i	0.226765	−	0.973949i	$-0.427185\pi$
$937$	37.5069	−	31.4720i	1.22530	−	1.02815i	0.998530	−	0.0541959i	$-0.0172595\pi$
$938$		0			0
$939$	12.0424	−	20.8580i	0.392987	−	0.680674i
$940$		0			0
$941$	16.4458	+	5.98578i	0.536117	+	0.195131i	0.595868	−	0.803083i	$-0.296808\pi$
$941$	16.4458	+	5.98578i	0.536117	+	0.195131i	−0.0597504	+	0.998213i	$0.519030\pi$
$942$		0			0
$943$	−38.3756	−	32.2009i	−1.24968	−	1.04861i
$944$		0			0
$945$	2.50165	+	14.1876i	0.0813786	+	0.461521i
$946$		0			0
$947$	−16.2777	−	5.92458i	−0.528953	−	0.192523i	0.0637179	−	0.997968i	$-0.479704\pi$
$947$	−16.2777	−	5.92458i	−0.528953	−	0.192523i	−0.592671	+	0.805445i	$0.701926\pi$
$948$		0			0
$949$	9.54576	−	54.1367i	0.309868	−	1.75735i
$950$		0			0
$951$	18.3662	+	31.8112i	0.595564	+	1.03155i
$952$		0			0
$953$	−6.74661	−	38.2619i	−0.218544	−	1.23942i	−0.874650	−	0.484756i	$-0.838909\pi$
$953$	−6.74661	−	38.2619i	−0.218544	−	1.23942i	0.656106	−	0.754669i	$-0.272203\pi$
$954$		0			0
$955$	46.2147	−	16.8208i	1.49547	−	0.544308i
$956$		0			0
$957$	−19.3221	+	7.03266i	−0.624594	+	0.227334i
$958$		0			0
$959$	−1.07532	−	0.902302i	−0.0347240	−	0.0291369i
$960$		0			0
$961$	−29.7442			−0.959491
$962$		0			0
$963$	−5.10607			−0.164541
$964$		0			0
$965$	31.3234	+	26.2835i	1.00834	+	0.846095i
$966$		0			0
$967$	−41.8940	+	15.2482i	−1.34722	+	0.490348i	−0.912079	−	0.410014i	$-0.865524\pi$
$967$	−41.8940	+	15.2482i	−1.34722	+	0.490348i	−0.435141	+	0.900362i	$0.643301\pi$
$968$		0			0
$969$	−24.5736	+	8.94405i	−0.789417	+	0.287324i
$970$		0			0
$971$	9.92443	+	56.2842i	0.318490	+	1.80625i	0.551946	+	0.833880i	$0.313885\pi$
$971$	9.92443	+	56.2842i	0.318490	+	1.80625i	−0.233456	+	0.972367i	$0.575004\pi$
$972$		0			0
$973$	5.18984	+	8.98908i	0.166379	+	0.288177i
$974$		0			0
$975$	−15.6420	+	88.7103i	−0.500946	+	2.84100i
$976$		0			0
$977$	32.7472	+	11.9190i	1.04768	+	0.381323i	0.807785	−	0.589477i	$-0.200666\pi$
$977$	32.7472	+	11.9190i	1.04768	+	0.381323i	0.239891	+	0.970800i	$0.422888\pi$
$978$		0			0
$979$	−4.86777	−	27.6065i	−0.155575	−	0.882308i
$980$		0			0
$981$	−0.905544	−	0.759842i	−0.0289118	−	0.0242599i
$982$		0			0
$983$	−1.00505	−	0.365809i	−0.0320562	−	0.0116675i	0.325942	−	0.945390i	$-0.394318\pi$
$983$	−1.00505	−	0.365809i	−0.0320562	−	0.0116675i	−0.357998	+	0.933722i	$0.616541\pi$
$984$		0			0
$985$	25.5300	−	44.2193i	0.813454	−	1.40894i
$986$		0			0
$987$	6.49273	−	5.44804i	0.206666	−	0.173413i
$988$		0			0
$989$	−16.3913	+	28.3906i	−0.521213	+	0.902767i
$990$		0			0
$991$	−10.1625	−	17.6020i	−0.322823	−	0.559145i	0.658247	−	0.752802i	$-0.271298\pi$
$991$	−10.1625	−	17.6020i	−0.322823	−	0.559145i	−0.981069	+	0.193657i	$0.937965\pi$
$992$		0			0
$993$	−25.7425			−0.816913
$994$		0			0
$995$	−3.50640	+	19.8858i	−0.111160	+	0.630421i
$996$		0			0
$997$	−35.4222	+	29.7228i	−1.12183	+	0.941329i	−0.998696	−	0.0510604i	$-0.983740\pi$
$997$	−35.4222	+	29.7228i	−1.12183	+	0.941329i	−0.123137	+	0.992390i	$0.539295\pi$
$998$		0			0
$999$	12.1548	+	25.4602i	0.384561	+	0.805525i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.bc.b.49.1		6
4.3	odd	2		74.2.f.a.49.1	✓	6
12.11	even	2		666.2.x.c.271.1		6
37.34	even	9	inner	592.2.bc.b.145.1		6
148.71	odd	18		74.2.f.a.71.1	yes	6
148.95	odd	18		2738.2.a.p.1.1		3
148.127	odd	18		2738.2.a.m.1.1		3
444.71	even	18		666.2.x.c.145.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.a.49.1	✓	6	4.3	odd	2
74.2.f.a.71.1	yes	6	148.71	odd	18
592.2.bc.b.49.1		6	1.1	even	1	trivial
592.2.bc.b.145.1		6	37.34	even	9	inner
666.2.x.c.145.1		6	444.71	even	18
666.2.x.c.271.1		6	12.11	even	2
2738.2.a.m.1.1		3	148.127	odd	18
2738.2.a.p.1.1		3	148.95	odd	18

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.bc (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.43969 + 1.20805i) q^{3} +(3.31908 - 1.20805i) q^{5} +(-0.826352 + 0.300767i) q^{7} +(0.0923963 + 0.524005i) q^{9} +O(q^{10})\)	\(q+(1.43969 + 1.20805i) q^{3} +(3.31908 - 1.20805i) q^{5} +(-0.826352 + 0.300767i) q^{7} +(0.0923963 + 0.524005i) q^{9} +(1.67365 + 2.89884i) q^{11} +(-1.11334 + 6.31407i) q^{13} +(6.23783 + 2.27038i) q^{15} +(-0.520945 - 2.95442i) q^{17} +(-3.55303 - 2.98135i) q^{19} +(-1.55303 - 0.565258i) q^{21} +(2.91875 - 5.05542i) q^{23} +(5.72668 - 4.80526i) q^{25} +(2.31908 - 4.01676i) q^{27} +(1.63429 + 2.83067i) q^{29} +1.12061 q^{31} +(-1.09240 + 6.19529i) q^{33} +(-2.37939 + 1.99654i) q^{35} +(-3.44356 + 5.01417i) q^{37} +(-9.23055 + 7.74535i) q^{39} +(1.49020 - 8.45134i) q^{41} -5.61587 q^{43} +(0.939693 + 1.62760i) q^{45} +(-2.56418 + 4.44129i) q^{47} +(-4.76991 + 4.00243i) q^{49} +(2.81908 - 4.88279i) q^{51} +(-0.252374 - 0.0918566i) q^{53} +(9.05690 + 7.59964i) q^{55} +(-1.51367 - 8.58445i) q^{57} +(7.15910 + 2.60570i) q^{59} +(0.369585 - 2.09602i) q^{61} +(-0.233956 - 0.405223i) q^{63} +(3.93242 + 22.3019i) q^{65} +(8.01754 - 2.91815i) q^{67} +(10.3093 - 3.75227i) q^{69} +(-10.0719 - 8.45134i) q^{71} -8.57398 q^{73} +14.0496 q^{75} +(-2.25490 - 1.89209i) q^{77} +(-10.8833 + 3.96118i) q^{79} +(9.69119 - 3.52730i) q^{81} +(-0.724155 - 4.10689i) q^{83} +(-5.29813 - 9.17664i) q^{85} +(-1.06670 + 6.04958i) q^{87} +(-7.86959 - 2.86429i) q^{89} +(-0.979055 - 5.55250i) q^{91} +(1.61334 + 1.35375i) q^{93} +(-15.3944 - 5.60310i) q^{95} +(8.53209 - 14.7780i) q^{97} +(-1.36437 + 1.14484i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} + 3 q^{5} - 6 q^{7} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 + 3 * q^5 - 6 * q^7 - 3 * q^9	\( 6 q + 3 q^{3} + 3 q^{5} - 6 q^{7} - 3 q^{9} + 9 q^{11} + 18 q^{15} - 9 q^{19} + 3 q^{21} + 15 q^{23} + 21 q^{25} - 3 q^{27} + 18 q^{31} - 3 q^{33} - 3 q^{35} + 9 q^{37} - 18 q^{39} + 6 q^{41} - 12 q^{43} + 3 q^{47} - 18 q^{53} + 18 q^{55} + 12 q^{57} + 6 q^{59} - 12 q^{61} - 6 q^{63} + 3 q^{67} + 42 q^{69} + 6 q^{71} - 36 q^{73} + 30 q^{75} - 15 q^{77} - 30 q^{79} + 12 q^{81} - 6 q^{83} - 18 q^{85} + 27 q^{87} - 33 q^{89} - 9 q^{91} + 3 q^{93} - 51 q^{95} + 42 q^{97} - 27 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 + 3 * q^5 - 6 * q^7 - 3 * q^9 + 9 * q^11 + 18 * q^15 - 9 * q^19 + 3 * q^21 + 15 * q^23 + 21 * q^25 - 3 * q^27 + 18 * q^31 - 3 * q^33 - 3 * q^35 + 9 * q^37 - 18 * q^39 + 6 * q^41 - 12 * q^43 + 3 * q^47 - 18 * q^53 + 18 * q^55 + 12 * q^57 + 6 * q^59 - 12 * q^61 - 6 * q^63 + 3 * q^67 + 42 * q^69 + 6 * q^71 - 36 * q^73 + 30 * q^75 - 15 * q^77 - 30 * q^79 + 12 * q^81 - 6 * q^83 - 18 * q^85 + 27 * q^87 - 33 * q^89 - 9 * q^91 + 3 * q^93 - 51 * q^95 + 42 * q^97 - 27 * q^99

Introduction

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