LMFDB - Embedded newform 592.2.bc.b.81.1

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			81.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	592.81
Dual form			592.2.bc.b.497.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.326352 + 0.118782i) q^{3} +(-0.0209445 - 0.118782i) q^{5} +(-0.233956 - 1.32683i) q^{7} +(-2.20574 - 1.85083i) q^{9} +O(q^{10})$	\(q+(0.326352 + 0.118782i) q^{3} +(-0.0209445 - 0.118782i) q^{5} +(-0.233956 - 1.32683i) q^{7} +(-2.20574 - 1.85083i) q^{9} +(2.26604 - 3.92490i) q^{11} +(-0.592396 + 0.497079i) q^{13} +(0.00727396 - 0.0412527i) q^{15} +(-2.29813 - 1.92836i) q^{17} +(-1.91875 - 0.698367i) q^{19} +(0.0812519 - 0.460802i) q^{21} +(0.0282185 + 0.0488759i) q^{23} +(4.68479 - 1.70513i) q^{25} +(-1.02094 - 1.76833i) q^{27} +(2.89053 - 5.00654i) q^{29} +3.34730 q^{31} +(1.20574 - 1.01173i) q^{33} +(-0.152704 + 0.0555796i) q^{35} +(5.60607 - 2.36051i) q^{37} +(-0.252374 + 0.0918566i) q^{39} +(-5.47565 + 4.59462i) q^{41} -9.31315 q^{43} +(-0.173648 + 0.300767i) q^{45} +(4.25877 + 7.37641i) q^{47} +(4.87211 - 1.77330i) q^{49} +(-0.520945 - 0.902302i) q^{51} +(0.482926 - 2.73881i) q^{53} +(-0.513671 - 0.186961i) q^{55} +(-0.543233 - 0.455827i) q^{57} +(2.25624 - 12.7958i) q^{59} +(-8.82295 + 7.40333i) q^{61} +(-1.93969 + 3.35965i) q^{63} +(0.0714517 + 0.0599551i) q^{65} +(-0.889185 - 5.04282i) q^{67} +(0.00340357 + 0.0193026i) q^{69} +(12.6236 + 4.59462i) q^{71} -8.71688 q^{73} +1.73143 q^{75} +(-5.73783 - 2.08840i) q^{77} +(-0.720285 - 4.08494i) q^{79} +(1.37686 + 7.80856i) q^{81} +(4.53596 + 3.80612i) q^{83} +(-0.180922 + 0.313366i) q^{85} +(1.53802 - 1.29055i) q^{87} +(1.32295 - 7.50281i) q^{89} +(0.798133 + 0.669713i) q^{91} +(1.09240 + 0.397600i) q^{93} +(-0.0427664 + 0.242540i) q^{95} +(5.12061 + 8.86916i) q^{97} +(-12.2626 + 4.46324i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$	$1$

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
$3$	0.326352	+	0.118782i	0.188419	+	0.0685790i	0.434507	−	0.900669i	$-0.356923\pi$
$3$	0.326352	+	0.118782i	0.188419	+	0.0685790i	−0.246087	+	0.969248i	$0.579145\pi$
$4$		0			0
$5$	−0.0209445	−	0.118782i	−0.00936668	−	0.0531211i	0.979766	−	0.200146i	$-0.0641415\pi$
$5$	−0.0209445	−	0.118782i	−0.00936668	−	0.0531211i	−0.989133	+	0.147024i	$0.953030\pi$
$6$		0			0
$7$	−0.233956	−	1.32683i	−0.0884269	−	0.501494i	−0.996564	−	0.0828217i	$-0.973607\pi$
$7$	−0.233956	−	1.32683i	−0.0884269	−	0.501494i	0.908137	−	0.418672i	$-0.137504\pi$
$8$		0			0
$9$	−2.20574	−	1.85083i	−0.735246	−	0.616944i
$10$		0			0
$11$	2.26604	−	3.92490i	0.683238	−	1.18340i	−0.290749	−	0.956799i	$-0.593904\pi$
$11$	2.26604	−	3.92490i	0.683238	−	1.18340i	0.973987	−	0.226604i	$-0.0727622\pi$
$12$		0			0
$13$	−0.592396	+	0.497079i	−0.164301	+	0.137865i	−0.721231	−	0.692694i	$-0.756424\pi$
$13$	−0.592396	+	0.497079i	−0.164301	+	0.137865i	0.556930	+	0.830559i	$0.311979\pi$
$14$		0			0
$15$	0.00727396	−	0.0412527i	0.00187813	−	0.0106514i
$16$		0			0
$17$	−2.29813	−	1.92836i	−0.557379	−	0.467697i	0.320051	−	0.947400i	$-0.396300\pi$
$17$	−2.29813	−	1.92836i	−0.557379	−	0.467697i	−0.877431	+	0.479703i	$0.840744\pi$
$18$		0			0
$19$	−1.91875	−	0.698367i	−0.440191	−	0.160216i	0.112411	−	0.993662i	$-0.464143\pi$
$19$	−1.91875	−	0.698367i	−0.440191	−	0.160216i	−0.552602	+	0.833445i	$0.686365\pi$
$20$		0			0
$21$	0.0812519	−	0.460802i	0.0177306	−	0.100555i
$22$		0			0
$23$	0.0282185	+	0.0488759i	0.00588396	+	0.0101913i	0.868952	−	0.494896i	$-0.164794\pi$
$23$	0.0282185	+	0.0488759i	0.00588396	+	0.0101913i	−0.863068	+	0.505087i	$0.831460\pi$
$24$		0			0
$25$	4.68479	−	1.70513i	0.936959	−	0.341025i
$26$		0			0
$27$	−1.02094	−	1.76833i	−0.196481	−	0.340315i
$28$		0			0
$29$	2.89053	−	5.00654i	0.536758	−	0.929692i	−0.462318	−	0.886714i	$-0.652982\pi$
$29$	2.89053	−	5.00654i	0.536758	−	0.929692i	0.999076	−	0.0429778i	$-0.0136845\pi$
$30$		0			0
$31$	3.34730			0.601192			0.300596	−	0.953752i	$-0.402814\pi$
$31$	3.34730			0.601192			0.300596	+	0.953752i	$0.402814\pi$
$32$		0			0
$33$	1.20574	−	1.01173i	0.209892	−	0.176120i
$34$		0			0
$35$	−0.152704	+	0.0555796i	−0.0258116	+	0.00939466i
$36$		0			0
$37$	5.60607	−	2.36051i	0.921632	−	0.388066i
$37$	5.60607	−	2.36051i	0.921632	−	0.388066i
$38$		0			0
$39$	−0.252374	+	0.0918566i	−0.0404122	+	0.0147088i
$40$		0			0
$41$	−5.47565	+	4.59462i	−0.855153	+	0.717559i	−0.960918	−	0.276832i	$-0.910715\pi$
$41$	−5.47565	+	4.59462i	−0.855153	+	0.717559i	0.105765	+	0.994391i	$0.466271\pi$
$42$		0			0
$43$	−9.31315			−1.42024			−0.710121	−	0.704080i	$-0.751360\pi$
$43$	−9.31315			−1.42024			−0.710121	+	0.704080i	$0.751360\pi$
$44$		0			0
$45$	−0.173648	+	0.300767i	−0.0258859	+	0.0448358i
$46$		0			0
$47$	4.25877	+	7.37641i	0.621206	+	1.07596i	0.989262	+	0.146156i	$0.0466901\pi$
$47$	4.25877	+	7.37641i	0.621206	+	1.07596i	−0.368056	+	0.929804i	$0.619977\pi$
$48$		0			0
$49$	4.87211	−	1.77330i	0.696016	−	0.253329i
$50$		0			0
$51$	−0.520945	−	0.902302i	−0.0729468	−	0.126348i
$52$		0			0
$53$	0.482926	−	2.73881i	0.0663350	−	0.376204i	−0.933509	−	0.358553i	$-0.883270\pi$
$53$	0.482926	−	2.73881i	0.0663350	−	0.376204i	0.999844	−	0.0176510i	$-0.00561877\pi$
$54$		0			0
$55$	−0.513671	−	0.186961i	−0.0692633	−	0.0252098i
$56$		0			0
$57$	−0.543233	−	0.455827i	−0.0719530	−	0.0603757i
$58$		0			0
$59$	2.25624	−	12.7958i	0.293738	−	1.66587i	−0.378550	−	0.925581i	$-0.623577\pi$
$59$	2.25624	−	12.7958i	0.293738	−	1.66587i	0.672288	−	0.740290i	$-0.265312\pi$
$60$		0			0
$61$	−8.82295	+	7.40333i	−1.12966	+	0.947900i	−0.999052	−	0.0435341i	$-0.986138\pi$
$61$	−8.82295	+	7.40333i	−1.12966	+	0.947900i	−0.130611	+	0.991434i	$0.541694\pi$
$62$		0			0
$63$	−1.93969	+	3.35965i	−0.244378	+	0.423276i
$64$		0			0
$65$	0.0714517	+	0.0599551i	0.00886250	+	0.00743652i
$66$		0			0
$67$	−0.889185	−	5.04282i	−0.108631	−	0.616079i	−0.989708	−	0.143104i	$-0.954292\pi$
$67$	−0.889185	−	5.04282i	−0.108631	−	0.616079i	0.881076	−	0.472974i	$-0.156820\pi$
$68$		0			0
$69$	0.00340357	+	0.0193026i	0.000409741	+	0.00232376i
$70$		0			0
$71$	12.6236	+	4.59462i	1.49815	+	0.545281i	0.955580	−	0.294732i	$-0.0952304\pi$
$71$	12.6236	+	4.59462i	1.49815	+	0.545281i	0.542567	+	0.840013i	$0.317453\pi$
$72$		0			0
$73$	−8.71688			−1.02023			−0.510117	−	0.860105i	$-0.670398\pi$
$73$	−8.71688			−1.02023			−0.510117	+	0.860105i	$0.670398\pi$
$74$		0			0
$75$	1.73143			0.199928
$76$		0			0
$77$	−5.73783	−	2.08840i	−0.653886	−	0.237995i
$78$		0			0
$79$	−0.720285	−	4.08494i	−0.0810384	−	0.459592i	−0.998141	−	0.0609412i	$-0.980590\pi$
$79$	−0.720285	−	4.08494i	−0.0810384	−	0.459592i	0.917103	−	0.398650i	$-0.130521\pi$
$80$		0			0
$81$	1.37686	+	7.80856i	0.152984	+	0.867617i
$82$		0			0
$83$	4.53596	+	3.80612i	0.497886	+	0.417776i	0.856843	−	0.515578i	$-0.172423\pi$
$83$	4.53596	+	3.80612i	0.497886	+	0.417776i	−0.358956	+	0.933354i	$0.616867\pi$
$84$		0			0
$85$	−0.180922	+	0.313366i	−0.0196238	+	0.0339894i
$86$		0			0
$87$	1.53802	−	1.29055i	0.164893	−	0.138362i
$88$		0			0
$89$	1.32295	−	7.50281i	0.140232	−	0.795297i	−0.830840	−	0.556511i	$-0.812140\pi$
$89$	1.32295	−	7.50281i	0.140232	−	0.795297i	0.971072	−	0.238785i	$-0.0767492\pi$
$90$		0			0
$91$	0.798133	+	0.669713i	0.0836671	+	0.0702050i
$92$		0			0
$93$	1.09240	+	0.397600i	0.113276	+	0.0412292i
$94$		0			0
$95$	−0.0427664	+	0.242540i	−0.00438774	+	0.0248841i
$96$		0			0
$97$	5.12061	+	8.86916i	0.519920	+	0.900527i	0.999732	+	0.0231560i	$0.00737146\pi$
$97$	5.12061	+	8.86916i	0.519920	+	0.900527i	−0.479812	+	0.877371i	$0.659295\pi$
$98$		0			0
$99$	−12.2626	+	4.46324i	−1.23244	+	0.448572i
$100$		0			0
$101$	8.05690	+	13.9550i	0.801692	+	1.38857i	0.918502	+	0.395417i	$0.129400\pi$
$101$	8.05690	+	13.9550i	0.801692	+	1.38857i	−0.116810	+	0.993154i	$0.537267\pi$
$102$		0			0
$103$	−9.81567	+	17.0012i	−0.967167	+	1.67518i	−0.263491	+	0.964662i	$0.584874\pi$
$103$	−9.81567	+	17.0012i	−0.967167	+	1.67518i	−0.703676	+	0.710521i	$0.748459\pi$
$104$		0			0
$105$	−0.0564370			−0.00550769
$106$		0			0
$107$	0.488856	−	0.410199i	0.0472595	−	0.0396554i	−0.618852	−	0.785508i	$-0.712402\pi$
$107$	0.488856	−	0.410199i	0.0472595	−	0.0396554i	0.666111	+	0.745852i	$0.267957\pi$
$108$		0			0
$109$	−6.81908	+	2.48194i	−0.653149	+	0.237727i	−0.647276	−	0.762256i	$-0.724092\pi$
$109$	−6.81908	+	2.48194i	−0.653149	+	0.237727i	−0.00587340	+	0.999983i	$0.501870\pi$
$110$		0			0
$111$	2.10994	−	0.104455i	0.200266	−	0.00991447i
$112$		0			0
$113$	12.9893	−	4.72773i	1.22193	−	0.444747i	0.351105	−	0.936336i	$-0.385806\pi$
$113$	12.9893	−	4.72773i	1.22193	−	0.444747i	0.870827	+	0.491589i	$0.163584\pi$
$114$		0			0
$115$	0.00521457	−	0.00437554i	0.000486261	−	0.000408021i
$116$		0			0
$117$	2.22668			0.205857
$118$		0			0
$119$	−2.02094	+	3.50038i	−0.185260	+	0.320879i
$120$		0			0
$121$	−4.76991	−	8.26173i	−0.433629	−	0.751067i
$122$		0			0
$123$	−2.33275	+	0.849051i	−0.210337	+	0.0765564i
$124$		0			0
$125$	−0.602196	−	1.04303i	−0.0538621	−	0.0932919i
$126$		0			0
$127$	−2.10354	+	11.9298i	−0.186659	+	1.05860i	0.737146	+	0.675733i	$0.236173\pi$
$127$	−2.10354	+	11.9298i	−0.186659	+	1.05860i	−0.923805	+	0.382863i	$0.874938\pi$
$128$		0			0
$129$	−3.03936	−	1.10624i	−0.267601	−	0.0973988i
$130$		0			0
$131$	−16.5817	−	13.9137i	−1.44875	−	1.21565i	−0.933485	−	0.358617i	$-0.883248\pi$
$131$	−16.5817	−	13.9137i	−1.44875	−	1.21565i	−0.515267	−	0.857030i	$-0.672307\pi$
$132$		0			0
$133$	−0.477711	+	2.70924i	−0.0414228	+	0.234921i
$134$		0			0
$135$	−0.188663	+	0.158307i	−0.0162375	+	0.0136249i
$136$		0			0
$137$	−4.31908	+	7.48086i	−0.369004	+	0.639133i	−0.989410	−	0.145147i	$-0.953634\pi$
$137$	−4.31908	+	7.48086i	−0.369004	+	0.639133i	0.620406	+	0.784281i	$0.286968\pi$
$138$		0			0
$139$	10.2686	+	8.61635i	0.870969	+	0.730830i	0.964302	−	0.264805i	$-0.0853077\pi$
$139$	10.2686	+	8.61635i	0.870969	+	0.730830i	−0.0933331	+	0.995635i	$0.529752\pi$
$140$		0			0
$141$	0.513671	+	2.91317i	0.0432589	+	0.245333i
$142$		0			0
$143$	0.608593	+	3.45150i	0.0508931	+	0.288629i
$144$		0			0
$145$	−0.655230	−	0.238484i	−0.0544139	−	0.0198050i
$146$		0			0
$147$	1.80066			0.148516
$148$		0			0
$149$	4.39693			0.360210			0.180105	−	0.983647i	$-0.442356\pi$
$149$	4.39693			0.360210			0.180105	+	0.983647i	$0.442356\pi$
$150$		0			0
$151$	13.8550	+	5.04282i	1.12751	+	0.410379i	0.837387	−	0.546611i	$-0.184082\pi$
$151$	13.8550	+	5.04282i	1.12751	+	0.410379i	0.290120	+	0.956990i	$0.406305\pi$
$152$		0			0
$153$	1.50000	+	8.50692i	0.121268	+	0.687744i
$154$		0			0
$155$	−0.0701076	−	0.397600i	−0.00563117	−	0.0319360i
$156$		0			0
$157$	−11.9907	−	10.0614i	−0.956959	−	0.802984i	0.0234964	−	0.999724i	$-0.492520\pi$
$157$	−11.9907	−	10.0614i	−0.956959	−	0.802984i	−0.980456	+	0.196740i	$0.936965\pi$
$158$		0			0
$159$	0.482926	−	0.836452i	0.0382985	−	0.0663350i
$160$		0			0
$161$	0.0582480	−	0.0488759i	0.00459058	−	0.00385196i
$162$		0			0
$163$	0.830222	−	4.70842i	0.0650280	−	0.368792i	−0.934876	−	0.354973i	$-0.884490\pi$
$163$	0.830222	−	4.70842i	0.0650280	−	0.368792i	0.999905	−	0.0138191i	$-0.00439889\pi$
$164$		0			0
$165$	−0.145430	−	0.122030i	−0.0113217	−	0.00950002i
$166$		0			0
$167$	1.88413	+	0.685768i	0.145799	+	0.0530663i	0.413889	−	0.910327i	$-0.364170\pi$
$167$	1.88413	+	0.685768i	0.145799	+	0.0530663i	−0.268090	+	0.963394i	$0.586392\pi$
$168$		0			0
$169$	−2.15358	+	12.2136i	−0.165660	+	0.939505i
$170$		0			0
$171$	2.93969	+	5.09170i	0.224804	+	0.389372i
$172$		0			0
$173$	12.9500	−	4.71340i	0.984567	−	0.358353i	0.200953	−	0.979601i	$-0.435596\pi$
$173$	12.9500	−	4.71340i	0.984567	−	0.358353i	0.783614	+	0.621248i	$0.213374\pi$
$174$		0			0
$175$	−3.35844	−	5.81699i	−0.253874	−	0.439723i
$176$		0			0
$177$	2.25624	−	3.90793i	0.169590	−	0.293738i
$178$		0			0
$179$	14.7246			1.10057			0.550285	−	0.834977i	$-0.314519\pi$
$179$	14.7246			1.10057			0.550285	+	0.834977i	$0.314519\pi$
$180$		0			0
$181$	−8.34911	+	7.00573i	−0.620584	+	0.520732i	−0.897987	−	0.440022i	$-0.854971\pi$
$181$	−8.34911	+	7.00573i	−0.620584	+	0.520732i	0.277403	+	0.960754i	$0.410526\pi$
$182$		0			0
$183$	−3.75877	+	1.36808i	−0.277856	+	0.101131i
$184$		0			0
$185$	−0.397804	−	0.616462i	−0.0292471	−	0.0453232i
$186$		0			0
$187$	−12.7763	+	4.65020i	−0.934296	+	0.340056i
$188$		0			0
$189$	−2.10741	+	1.76833i	−0.153292	+	0.128627i
$190$		0			0
$191$	−9.05737			−0.655368			−0.327684	−	0.944787i	$-0.606268\pi$
$191$	−9.05737			−0.655368			−0.327684	+	0.944787i	$0.606268\pi$
$192$		0			0
$193$	−6.29473	+	10.9028i	−0.453105	+	0.784800i	−0.998577	−	0.0533286i	$-0.983017\pi$
$193$	−6.29473	+	10.9028i	−0.453105	+	0.784800i	0.545472	+	0.838129i	$0.316350\pi$
$194$		0			0
$195$	0.0161968	+	0.0280537i	0.00115988	+	0.00200896i
$196$		0			0
$197$	11.2169	−	4.08261i	0.799170	−	0.290874i	0.0900273	−	0.995939i	$-0.471305\pi$
$197$	11.2169	−	4.08261i	0.799170	−	0.290874i	0.709142	+	0.705065i	$0.249082\pi$
$198$		0			0
$199$	1.14543	+	1.98394i	0.0811974	+	0.140638i	0.903765	−	0.428030i	$-0.140792\pi$
$199$	1.14543	+	1.98394i	0.0811974	+	0.140638i	−0.822567	+	0.568668i	$0.807459\pi$
$200$		0			0
$201$	0.308811	−	1.75135i	0.0217818	−	0.123531i
$202$		0			0
$203$	−7.31908	−	2.66393i	−0.513699	−	0.186971i
$204$		0			0
$205$	0.660444	+	0.554179i	0.0461274	+	0.0387055i
$206$		0			0
$207$	0.0282185	−	0.160035i	0.00196132	−	0.0111232i
$208$		0			0
$209$	−7.08899	+	5.94837i	−0.490356	+	0.411457i
$210$		0			0
$211$	0.477711	−	0.827420i	0.0328870	−	0.0569620i	−0.849113	−	0.528211i	$-0.822863\pi$
$211$	0.477711	−	0.827420i	0.0328870	−	0.0569620i	0.882000	+	0.471249i	$0.156197\pi$
$212$		0			0
$213$	3.57398	+	2.99892i	0.244885	+	0.205483i
$214$		0			0
$215$	0.195060	+	1.10624i	0.0133030	+	0.0754448i
$216$		0			0
$217$	−0.783119	−	4.44129i	−0.0531616	−	0.301494i
$218$		0			0
$219$	−2.84477	−	1.03541i	−0.192232	−	0.0699666i
$220$		0			0
$221$	2.31996			0.156057
$222$		0			0
$223$	17.8648			1.19632			0.598159	−	0.801377i	$-0.295899\pi$
$223$	17.8648			1.19632			0.598159	+	0.801377i	$0.295899\pi$
$224$		0			0
$225$	−13.4893	−	4.90971i	−0.899288	−	0.327314i
$226$		0			0
$227$	−1.53684	−	8.71583i	−0.102003	−	0.578490i	−0.992375	−	0.123256i	$-0.960667\pi$
$227$	−1.53684	−	8.71583i	−0.102003	−	0.578490i	0.890372	−	0.455235i	$-0.150445\pi$
$228$		0			0
$229$	−3.02347	−	17.1470i	−0.199797	−	1.13310i	−0.905420	−	0.424516i	$-0.860444\pi$
$229$	−3.02347	−	17.1470i	−0.199797	−	1.13310i	0.705624	−	0.708587i	$-0.250667\pi$
$230$		0			0
$231$	−1.62449	−	1.36310i	−0.106883	−	0.0896857i
$232$		0			0
$233$	2.09627	−	3.63084i	0.137331	−	0.237864i	−0.789155	−	0.614195i	$-0.789481\pi$
$233$	2.09627	−	3.63084i	0.137331	−	0.237864i	0.926485	+	0.376330i	$0.122814\pi$
$234$		0			0
$235$	0.786989	−	0.660362i	0.0513375	−	0.0430773i
$236$		0			0
$237$	0.250152	−	1.41868i	0.0162491	−	0.0921535i
$238$		0			0
$239$	−6.57011	−	5.51297i	−0.424985	−	0.356605i	0.405071	−	0.914285i	$-0.367247\pi$
$239$	−6.57011	−	5.51297i	−0.424985	−	0.356605i	−0.830056	+	0.557681i	$0.811691\pi$
$240$		0			0
$241$	19.6532	+	7.15317i	1.26597	+	0.460776i	0.885769	−	0.464127i	$-0.153632\pi$
$241$	19.6532	+	7.15317i	1.26597	+	0.460776i	0.380203	+	0.924903i	$0.375854\pi$
$242$		0			0
$243$	−1.54189	+	8.74449i	−0.0989122	+	0.560959i
$244$		0			0
$245$	−0.312681	−	0.541580i	−0.0199765	−	0.0346003i
$246$		0			0
$247$	1.48380	−	0.540060i	0.0944121	−	0.0343632i
$248$		0			0
$249$	1.02822	+	1.78093i	0.0651607	+	0.112862i
$250$		0			0
$251$	3.39780	−	5.88517i	0.214467	−	0.371469i	−0.738640	−	0.674100i	$-0.764532\pi$
$251$	3.39780	−	5.88517i	0.214467	−	0.371469i	0.953108	+	0.302631i	$0.0978651\pi$
$252$		0			0
$253$	0.255777			0.0160806
$254$		0			0
$255$	−0.0962667	+	0.0807773i	−0.00602845	+	0.00505847i
$256$		0			0
$257$	9.28611	−	3.37987i	0.579252	−	0.210830i	−0.0357438	−	0.999361i	$-0.511380\pi$
$257$	9.28611	−	3.37987i	0.579252	−	0.210830i	0.614996	+	0.788531i	$0.289158\pi$
$258$		0			0
$259$	−4.44356	−	6.88603i	−0.276110	−	0.427877i
$260$		0			0
$261$	−15.6420	+	5.69323i	−0.968217	+	0.352402i
$262$		0			0
$263$	15.8195	−	13.2742i	0.975475	−	0.818521i	−0.00792564	−	0.999969i	$-0.502523\pi$
$263$	15.8195	−	13.2742i	0.975475	−	0.818521i	0.983401	+	0.181448i	$0.0580784\pi$
$264$		0			0
$265$	−0.335437			−0.0206057
$266$		0			0
$267$	1.32295	−	2.29141i	0.0809631	−	0.140232i
$268$		0			0
$269$	−13.8131	−	23.9251i	−0.842203	−	1.45874i	−0.888029	−	0.459788i	$-0.847925\pi$
$269$	−13.8131	−	23.9251i	−0.842203	−	1.45874i	0.0458262	−	0.998949i	$-0.485408\pi$
$270$		0			0
$271$	6.42989	−	2.34029i	0.390588	−	0.142162i	−0.139258	−	0.990256i	$-0.544472\pi$
$271$	6.42989	−	2.34029i	0.390588	−	0.142162i	0.529846	+	0.848094i	$0.322250\pi$
$272$		0			0
$273$	0.180922	+	0.313366i	0.0109499	+	0.0189658i
$274$		0			0
$275$	3.92350	−	22.2513i	0.236596	−	1.34180i
$276$		0			0
$277$	22.3957	+	8.15138i	1.34563	+	0.489769i	0.911581	−	0.411120i	$-0.134862\pi$
$277$	22.3957	+	8.15138i	1.34563	+	0.489769i	0.434049	+	0.900889i	$0.357085\pi$
$278$		0			0
$279$	−7.38326	−	6.19529i	−0.442024	−	0.370902i
$280$		0			0
$281$	5.51367	−	31.2696i	0.328918	−	1.86539i	−0.151657	−	0.988433i	$-0.548461\pi$
$281$	5.51367	−	31.2696i	0.328918	−	1.86539i	0.480575	−	0.876954i	$-0.340428\pi$
$282$		0			0
$283$	4.52687	−	3.79850i	0.269095	−	0.225797i	−0.498248	−	0.867035i	$-0.666023\pi$
$283$	4.52687	−	3.79850i	0.269095	−	0.225797i	0.767343	+	0.641237i	$0.221579\pi$
$284$		0			0
$285$	−0.0427664	+	0.0740736i	−0.00253326	+	0.00438774i
$286$		0			0
$287$	7.37733	+	6.19031i	0.435470	+	0.365403i
$288$		0			0
$289$	−1.38919	−	7.87846i	−0.0817168	−	0.463439i
$290$		0			0
$291$	0.617622	+	3.50271i	0.0362056	+	0.205332i
$292$		0			0
$293$	1.59240	+	0.579585i	0.0930288	+	0.0338597i	0.388115	−	0.921611i	$-0.373126\pi$
$293$	1.59240	+	0.579585i	0.0930288	+	0.0338597i	−0.295086	+	0.955471i	$0.595348\pi$
$294$		0			0
$295$	−1.56717			−0.0912442
$296$		0			0
$297$	−9.25402			−0.536973
$298$		0			0
$299$	−0.0410117	−	0.0149270i	−0.00237177	−	0.000863253i
$300$		0			0
$301$	2.17886	+	12.3569i	0.125588	+	0.712242i
$302$		0			0
$303$	0.971782	+	5.51125i	0.0558274	+	0.316613i
$304$		0			0
$305$	1.06418	+	0.892951i	0.0609346	+	0.0511302i
$306$		0			0
$307$	−6.11334	+	10.5886i	−0.348907	+	0.604324i	−0.986056	−	0.166417i	$-0.946780\pi$
$307$	−6.11334	+	10.5886i	−0.348907	+	0.604324i	0.637149	+	0.770741i	$0.280114\pi$
$308$		0			0
$309$	−5.22281	+	4.38246i	−0.297115	+	0.249309i
$310$		0			0
$311$	0.212134	−	1.20307i	0.0120290	−	0.0682198i	−0.978202	−	0.207654i	$-0.933417\pi$
$311$	0.212134	−	1.20307i	0.0120290	−	0.0682198i	0.990231	+	0.139434i	$0.0445283\pi$
$312$		0			0
$313$	−13.3380	−	11.1919i	−0.753906	−	0.632602i	0.182627	−	0.983182i	$-0.441540\pi$
$313$	−13.3380	−	11.1919i	−0.753906	−	0.632602i	−0.936533	+	0.350580i	$0.885985\pi$
$314$		0			0
$315$	0.439693	+	0.160035i	0.0247739	+	0.00901695i
$316$		0			0
$317$	−1.51027	+	8.56515i	−0.0848250	+	0.481067i	0.912569	+	0.408922i	$0.134095\pi$
$317$	−1.51027	+	8.56515i	−0.0848250	+	0.481067i	−0.997394	+	0.0721443i	$0.977016\pi$
$318$		0			0
$319$	−13.1001	−	22.6901i	−0.733467	−	1.27040i
$320$		0			0
$321$	0.208263	−	0.0758016i	0.0116241	−	0.00423083i
$322$		0			0
$323$	3.06283	+	5.30498i	0.170421	+	0.295177i
$324$		0			0
$325$	−1.92767	+	3.33882i	−0.106928	+	0.185205i
$326$		0			0
$327$	−2.52023			−0.139369
$328$		0			0
$329$	8.79086	−	7.37641i	0.484656	−	0.406674i
$330$		0			0
$331$	−7.74510	+	2.81899i	−0.425709	+	0.154945i	−0.545985	−	0.837795i	$-0.683844\pi$
$331$	−7.74510	+	2.81899i	−0.425709	+	0.154945i	0.120276	+	0.992741i	$0.461622\pi$
$332$		0			0
$333$	−16.7344	−	5.16923i	−0.917041	−	0.283272i
$334$		0			0
$335$	−0.580375	+	0.211239i	−0.0317092	+	0.0115412i
$336$		0			0
$337$	10.7456	−	9.01660i	0.585348	−	0.491166i	−0.301350	−	0.953514i	$-0.597437\pi$
$337$	10.7456	−	9.01660i	0.585348	−	0.491166i	0.886699	+	0.462348i	$0.152993\pi$
$338$		0			0
$339$	4.80066			0.260736
$340$		0			0
$341$	7.58512	−	13.1378i	0.410757	−	0.711453i
$342$		0			0
$343$	−8.20826	−	14.2171i	−0.443205	−	0.767653i
$344$		0			0
$345$	0.00222152		0.000808567i	0.000119603		4.35318e-5i
$346$		0			0
$347$	9.92262	+	17.1865i	0.532674	+	0.922619i	0.999272	+	0.0381490i	$0.0121462\pi$
$347$	9.92262	+	17.1865i	0.532674	+	0.922619i	−0.466598	+	0.884470i	$0.654521\pi$
$348$		0			0
$349$	2.98633	−	16.9363i	0.159855	−	0.906580i	−0.794358	−	0.607450i	$-0.792192\pi$
$349$	2.98633	−	16.9363i	0.159855	−	0.906580i	0.954212	−	0.299130i	$-0.0966964\pi$
$350$		0			0
$351$	1.48380	+	0.540060i	0.0791996	+	0.0288263i
$352$		0			0
$353$	12.9272	+	10.8472i	0.688046	+	0.577339i	0.918345	−	0.395781i	$-0.129526\pi$
$353$	12.9272	+	10.8472i	0.688046	+	0.577339i	−0.230299	+	0.973120i	$0.573971\pi$
$354$		0			0
$355$	0.281364	−	1.59569i	0.0149332	−	0.0846906i
$356$		0			0
$357$	−1.07532	+	0.902302i	−0.0569121	+	0.0477549i
$358$		0			0
$359$	−8.05690	+	13.9550i	−0.425227	+	0.736515i	−0.996442	−	0.0842859i	$-0.973139\pi$
$359$	−8.05690	+	13.9550i	−0.425227	+	0.736515i	0.571214	+	0.820801i	$0.306472\pi$
$360$		0			0
$361$	−11.3610	−	9.53298i	−0.597946	−	0.501736i
$362$		0			0
$363$	−0.575322	−	3.26281i	−0.0301966	−	0.171253i
$364$		0			0
$365$	0.182571	+	1.03541i	0.00955620	+	0.0541959i
$366$		0			0
$367$	−32.9666	−	11.9989i	−1.72084	−	0.626336i	−0.722931	−	0.690920i	$-0.757206\pi$
$367$	−32.9666	−	11.9989i	−1.72084	−	0.626336i	−0.997912	+	0.0645839i	$0.979428\pi$
$368$		0			0
$369$	20.5817			1.07144
$370$		0			0
$371$	−3.74691			−0.194530
$372$		0			0
$373$	27.9047	+	10.1565i	1.44485	+	0.525882i	0.941148	−	0.337996i	$-0.109749\pi$
$373$	27.9047	+	10.1565i	1.44485	+	0.525882i	0.503701	+	0.863878i	$0.331971\pi$
$374$		0			0
$375$	−0.0726338	−	0.411927i	−0.00375079	−	0.0212718i
$376$		0			0
$377$	0.776311	+	4.40268i	0.0399821	+	0.226750i
$378$		0			0
$379$	−0.321137	−	0.269466i	−0.0164957	−	0.0138415i	0.634502	−	0.772921i	$-0.281205\pi$
$379$	−0.321137	−	0.269466i	−0.0164957	−	0.0138415i	−0.650998	+	0.759079i	$0.725649\pi$
$380$		0			0
$381$	−2.10354	+	3.64344i	−0.107768	+	0.186659i
$382$		0			0
$383$	4.92443	−	4.13209i	0.251627	−	0.211140i	−0.508246	−	0.861212i	$-0.669706\pi$
$383$	4.92443	−	4.13209i	0.251627	−	0.211140i	0.759872	+	0.650072i	$0.225261\pi$
$384$		0			0
$385$	−0.127889	+	0.725293i	−0.00651781	+	0.0369644i
$386$		0			0
$387$	20.5424	+	17.2371i	1.04423	+	0.876210i
$388$		0			0
$389$	2.92602	+	1.06498i	0.148355	+	0.0539969i	0.415130	−	0.909762i	$-0.363736\pi$
$389$	2.92602	+	1.06498i	0.148355	+	0.0539969i	−0.266775	+	0.963759i	$0.585958\pi$
$390$		0			0
$391$	0.0294005	−	0.166739i	0.00148685	−	0.00843234i
$392$		0			0
$393$	−3.75877	−	6.51038i	−0.189605	−	0.328405i
$394$		0			0
$395$	−0.470133	+	0.171114i	−0.0236549	+	0.00860969i
$396$		0			0
$397$	−9.85369	−	17.0671i	−0.494543	−	0.856573i	0.505438	−	0.862863i	$-0.331331\pi$
$397$	−9.85369	−	17.0671i	−0.494543	−	0.856573i	−0.999980	+	0.00629016i	$0.997998\pi$
$398$		0			0
$399$	−0.477711	+	0.827420i	−0.0239155	+	0.0414228i
$400$		0			0
$401$	18.9162			0.944631			0.472316	−	0.881430i	$-0.343418\pi$
$401$	18.9162			0.944631			0.472316	+	0.881430i	$0.343418\pi$
$402$		0			0
$403$	−1.98293	+	1.66387i	−0.0987766	+	0.0828834i
$404$		0			0
$405$	0.898681	−	0.327093i	0.0446558	−	0.0162534i
$406$		0			0
$407$	3.43882	−	27.3523i	0.170456	−	1.35580i
$408$		0			0
$409$	−5.99020	+	2.18025i	−0.296196	+	0.107807i	−0.485844	−	0.874046i	$-0.661488\pi$
$409$	−5.99020	+	2.18025i	−0.296196	+	0.107807i	0.189648	+	0.981852i	$0.439265\pi$
$410$		0			0
$411$	−2.29813	+	1.92836i	−0.113359	+	0.0951191i
$412$		0			0
$413$	−17.5057			−0.861398
$414$		0			0
$415$	0.357097	−	0.618509i	0.0175292	−	0.0303614i
$416$		0			0
$417$	2.32770	+	4.03169i	0.113988	+	0.197433i
$418$		0			0
$419$	19.6258	−	7.14322i	0.958785	−	0.348969i	0.185227	−	0.982696i	$-0.440698\pi$
$419$	19.6258	−	7.14322i	0.958785	−	0.348969i	0.773557	+	0.633727i	$0.218476\pi$
$420$		0			0
$421$	2.90420	+	5.03022i	0.141542	+	0.245158i	0.928077	−	0.372387i	$-0.121461\pi$
$421$	2.90420	+	5.03022i	0.141542	+	0.245158i	−0.786535	+	0.617545i	$0.788127\pi$
$422$		0			0
$423$	4.25877	−	24.1527i	0.207069	−	1.17434i
$424$		0			0
$425$	−14.0544	−	5.11538i	−0.681737	−	0.248132i
$426$		0			0
$427$	11.8871	+	9.97448i	0.575258	+	0.482699i
$428$		0			0
$429$	−0.211362	+	1.19869i	−0.0102047	+	0.0578735i
$430$		0			0
$431$	−8.70233	+	7.30212i	−0.419177	+	0.351731i	−0.827850	−	0.560950i	$-0.810436\pi$
$431$	−8.70233	+	7.30212i	−0.419177	+	0.351731i	0.408673	+	0.912681i	$0.365992\pi$
$432$		0			0
$433$	−17.8025	+	30.8348i	−0.855532	+	1.48183i	0.0206183	+	0.999787i	$0.493437\pi$
$433$	−17.8025	+	30.8348i	−0.855532	+	1.48183i	−0.876150	+	0.482038i	$0.839897\pi$
$434$		0			0
$435$	−0.185508	−	0.155659i	−0.00889442	−	0.00746330i
$436$		0			0
$437$	−0.0200109	−	0.113487i	−0.000957250	−	0.00542884i
$438$		0			0
$439$	−3.90777	−	22.1620i	−0.186507	−	1.05774i	−0.924003	−	0.382385i	$-0.875103\pi$
$439$	−3.90777	−	22.1620i	−0.186507	−	1.05774i	0.737496	−	0.675352i	$-0.236008\pi$
$440$		0			0
$441$	−14.0287	−	5.10602i	−0.668033	−	0.243144i
$442$		0			0
$443$	26.0942			1.23977			0.619887	−	0.784691i	$-0.287179\pi$
$443$	26.0942			1.23977			0.619887	+	0.784691i	$0.287179\pi$
$444$		0			0
$445$	−0.918910			−0.0435605
$446$		0			0
$447$	1.43494	+	0.522277i	0.0678706	+	0.0247029i
$448$		0			0
$449$	−1.13310	−	6.42615i	−0.0534745	−	0.303269i	0.946327	−	0.323212i	$-0.104763\pi$
$449$	−1.13310	−	6.42615i	−0.0534745	−	0.303269i	−0.999801	+	0.0199431i	$0.993651\pi$
$450$		0			0
$451$	5.62536	+	31.9030i	0.264888	+	1.50225i
$452$		0			0
$453$	3.92262	+	3.29147i	0.184301	+	0.154647i
$454$		0			0
$455$	0.0628336	−	0.108831i	0.00294568	−	0.00510208i
$456$		0			0
$457$	−25.0835	+	21.0476i	−1.17336	+	0.984564i	−1.00000		0.000294571i	$-0.999906\pi$
$457$	−25.0835	+	21.0476i	−1.17336	+	0.984564i	−0.173358	+	0.984859i	$0.555462\pi$
$458$		0			0
$459$	−1.06371	+	6.03260i	−0.0496498	+	0.281578i
$460$		0			0
$461$	14.9722	+	12.5632i	0.697327	+	0.585127i	0.921012	−	0.389535i	$-0.127364\pi$
$461$	14.9722	+	12.5632i	0.697327	+	0.585127i	−0.223685	+	0.974662i	$0.571809\pi$
$462$		0			0
$463$	40.2943	+	14.6659i	1.87264	+	0.681584i	0.965278	+	0.261224i	$0.0841262\pi$
$463$	40.2943	+	14.6659i	1.87264	+	0.681584i	0.907358	+	0.420359i	$0.138096\pi$
$464$		0			0
$465$	0.0243481	−	0.138085i	0.00112912	−	0.00640354i
$466$		0			0
$467$	10.5444	+	18.2635i	0.487937	+	0.845132i	0.999904	−	0.0138732i	$-0.00441611\pi$
$467$	10.5444	+	18.2635i	0.487937	+	0.845132i	−0.511966	+	0.859005i	$0.671083\pi$
$468$		0			0
$469$	−6.48293	+	2.35959i	−0.299354	+	0.108956i
$470$		0			0
$471$	−2.71806	−	4.70782i	−0.125242	−	0.216925i
$472$		0			0
$473$	−21.1040	+	36.5532i	−0.970363	+	1.68072i
$474$		0			0
$475$	−10.1797			−0.467079
$476$		0			0
$477$	−6.13429	+	5.14728i	−0.280870	+	0.235678i
$478$		0			0
$479$	−22.7430	+	8.27779i	−1.03916	+	0.378222i	−0.804560	−	0.593871i	$-0.797599\pi$
$479$	−22.7430	+	8.27779i	−1.03916	+	0.378222i	−0.234596	+	0.972093i	$0.575377\pi$
$480$		0			0
$481$	−2.14765	+	4.18502i	−0.0979245	+	0.190820i
$482$		0			0
$483$	0.0248149	−	0.00903189i	0.00112912	−	0.000410965i
$484$		0			0
$485$	0.946251	−	0.793999i	0.0429671	−	0.0360536i
$486$		0			0
$487$	−28.9682			−1.31268			−0.656338	−	0.754467i	$-0.727895\pi$
$487$	−28.9682			−1.31268			−0.656338	+	0.754467i	$0.727895\pi$
$488$		0			0
$489$	0.830222	−	1.43799i	0.0375439	−	0.0650280i
$490$		0			0
$491$	−14.0758	−	24.3800i	−0.635231	−	1.10025i	−0.986466	−	0.163966i	$-0.947571\pi$
$491$	−14.0758	−	24.3800i	−0.635231	−	1.10025i	0.351235	−	0.936287i	$-0.385762\pi$
$492$		0			0
$493$	−16.2973	+	5.93172i	−0.733991	+	0.267151i
$494$		0			0
$495$	0.786989	+	1.36310i	0.0353725	+	0.0612670i
$496$		0			0
$497$	3.14290	−	17.8243i	0.140978	−	0.799529i
$498$		0			0
$499$	−4.40255	−	1.60240i	−0.197085	−	0.0717332i	0.241592	−	0.970378i	$-0.422331\pi$
$499$	−4.40255	−	1.60240i	−0.197085	−	0.0717332i	−0.438677	+	0.898645i	$0.644553\pi$
$500$		0			0
$501$	0.533433	+	0.447603i	0.0238320	+	0.0199974i
$502$		0			0
$503$	−4.39037	+	24.8990i	−0.195757	+	1.11019i	0.715580	+	0.698531i	$0.246162\pi$
$503$	−4.39037	+	24.8990i	−0.195757	+	1.11019i	−0.911337	+	0.411661i	$0.864949\pi$
$504$		0			0
$505$	1.48886	−	1.24930i	0.0662532	−	0.0555930i
$506$		0			0
$507$	−2.15358	+	3.73011i	−0.0956439	+	0.165660i
$508$		0			0
$509$	16.3739	+	13.7394i	0.725761	+	0.608986i	0.928972	−	0.370149i	$-0.120693\pi$
$509$	16.3739	+	13.7394i	0.725761	+	0.608986i	−0.203211	+	0.979135i	$0.565138\pi$
$510$		0			0
$511$	2.03936	+	11.5658i	0.0902161	+	0.511641i
$512$		0			0
$513$	0.723993	+	4.10597i	0.0319651	+	0.181283i
$514$		0			0
$515$	2.22503	+	0.809846i	0.0980467	+	0.0356861i
$516$		0			0
$517$	38.6023			1.69773
$518$		0			0
$519$	4.78611			0.210087
$520$		0			0
$521$	18.6853	+	6.80088i	0.818616	+	0.297952i	0.717178	−	0.696890i	$-0.245433\pi$
$521$	18.6853	+	6.80088i	0.818616	+	0.297952i	0.101438	+	0.994842i	$0.467656\pi$
$522$		0			0
$523$	2.94919	+	16.7257i	0.128959	+	0.731363i	0.978877	+	0.204448i	$0.0655401\pi$
$523$	2.94919	+	16.7257i	0.128959	+	0.731363i	−0.849918	+	0.526914i	$0.823349\pi$
$524$		0			0
$525$	−0.405078	−	2.29731i	−0.0176790	−	0.100263i
$526$		0			0
$527$	−7.69253	−	6.45480i	−0.335092	−	0.281176i
$528$		0			0
$529$	11.4984	−	19.9158i	0.499931	−	0.865905i
$530$		0			0
$531$	−28.6596	+	24.0482i	−1.24372	+	1.04360i
$532$		0			0
$533$	0.959866	−	5.44367i	0.0415764	−	0.235791i
$534$		0			0
$535$	−0.0589632	−	0.0494760i	−0.00254920	−	0.00213903i
$536$		0			0
$537$	4.80541	+	1.74903i	0.207369	+	0.0754760i
$538$		0			0
$539$	4.08037	−	23.1410i	0.175754	−	0.996751i
$540$		0			0
$541$	−14.6348	−	25.3481i	−0.629197	−	1.08980i	−0.987713	−	0.156278i	$-0.950050\pi$
$541$	−14.6348	−	25.3481i	−0.629197	−	1.08980i	0.358516	−	0.933524i	$-0.383283\pi$
$542$		0			0
$543$	−3.55690	+	1.29461i	−0.152641	+	0.0555569i
$544$		0			0
$545$	0.437633	+	0.758003i	0.0187461	+	0.0324693i
$546$		0			0
$547$	−0.666841	+	1.15500i	−0.0285121	+	0.0493843i	−0.879929	−	0.475105i	$-0.842410\pi$
$547$	−0.666841	+	1.15500i	−0.0285121	+	0.0493843i	0.851417	+	0.524489i	$0.175744\pi$
$548$		0			0
$549$	33.1634			1.41538
$550$		0			0
$551$	−9.04260	+	7.58765i	−0.385228	+	0.323245i
$552$		0			0
$553$	−5.25150	+	1.91139i	−0.223316	+	0.0812805i
$554$		0			0
$555$	−0.0565991	−	0.248436i	−0.00240250	−	0.0105455i
$556$		0			0
$557$	−30.3790	+	11.0570i	−1.28720	+	0.468502i	−0.892807	−	0.450440i	$-0.851267\pi$
$557$	−30.3790	+	11.0570i	−1.28720	+	0.468502i	−0.394392	+	0.918942i	$0.629045\pi$
$558$		0			0
$559$	5.51707	−	4.62937i	0.233347	−	0.195802i
$560$		0			0
$561$	−4.72193			−0.199360
$562$		0			0
$563$	−8.34389	+	14.4520i	−0.351653	+	0.609081i	−0.986539	−	0.163525i	$-0.947714\pi$
$563$	−8.34389	+	14.4520i	−0.351653	+	0.609081i	0.634886	+	0.772606i	$0.281047\pi$
$564$		0			0
$565$	−0.833626	−	1.44388i	−0.0350709	−	0.0607446i
$566$		0			0
$567$	10.0385	−	3.65371i	0.421577	−	0.153441i
$568$		0			0
$569$	0.213011	+	0.368946i	0.00892989	+	0.0154670i	0.870456	−	0.492247i	$-0.163824\pi$
$569$	0.213011	+	0.368946i	0.00892989	+	0.0154670i	−0.861526	+	0.507714i	$0.830491\pi$
$570$		0			0
$571$	−2.42262	+	13.7394i	−0.101383	+	0.574974i	0.891220	+	0.453571i	$0.149850\pi$
$571$	−2.42262	+	13.7394i	−0.101383	+	0.574974i	−0.992603	+	0.121403i	$0.961261\pi$
$572$		0			0
$573$	−2.95589	−	1.07586i	−0.123484	−	0.0449445i
$574$		0			0
$575$	0.215537	+	0.180857i	0.00898852	+	0.00754227i
$576$		0			0
$577$	−1.90373	+	10.7966i	−0.0792535	+	0.449469i	0.919196	+	0.393801i	$0.128840\pi$
$577$	−1.90373	+	10.7966i	−0.0792535	+	0.449469i	−0.998449	+	0.0556680i	$0.982271\pi$
$578$		0			0
$579$	−3.34936	+	2.81044i	−0.139194	+	0.116798i
$580$		0			0
$581$	3.98886	−	6.90890i	0.165486	−	0.286629i
$582$		0			0
$583$	−9.65523	−	8.10170i	−0.399879	−	0.335538i
$584$		0			0
$585$	−0.0466368	−	0.264490i	−0.00192819	−	0.0109353i
$586$		0			0
$587$	2.21167	+	12.5430i	0.0912853	+	0.517704i	0.995823	+	0.0913099i	$0.0291054\pi$
$587$	2.21167	+	12.5430i	0.0912853	+	0.517704i	−0.904537	+	0.426395i	$0.859784\pi$
$588$		0			0
$589$	−6.42262	−	2.33764i	−0.264639	−	0.0963209i
$590$		0			0
$591$	4.14559			0.170527
$592$		0			0
$593$	33.6786			1.38301			0.691507	−	0.722369i	$-0.256947\pi$
$593$	33.6786			1.38301			0.691507	+	0.722369i	$0.256947\pi$
$594$		0			0
$595$	0.458111	+	0.166739i	0.0187807	+	0.00683562i
$596$		0			0
$597$	0.138156	+	0.783520i	0.00565434	+	0.0320673i
$598$		0			0
$599$	2.36484	+	13.4117i	0.0966246	+	0.547986i	0.994237	+	0.107201i	$0.0341887\pi$
$599$	2.36484	+	13.4117i	0.0966246	+	0.547986i	−0.897613	+	0.440785i	$0.854700\pi$
$600$		0			0
$601$	12.3962	+	10.4017i	0.505652	+	0.424292i	0.859596	−	0.510974i	$-0.170715\pi$
$601$	12.3962	+	10.4017i	0.505652	+	0.424292i	−0.353944	+	0.935267i	$0.615160\pi$
$602$		0			0
$603$	−7.37211	+	12.7689i	−0.300216	+	0.519989i
$604$		0			0
$605$	−0.881445	+	0.739620i	−0.0358358	+	0.0300698i
$606$		0			0
$607$	7.17247	−	40.6771i	0.291121	−	1.65103i	−0.391440	−	0.920204i	$-0.628023\pi$
$607$	7.17247	−	40.6771i	0.291121	−	1.65103i	0.682562	−	0.730828i	$-0.260866\pi$
$608$		0			0
$609$	−2.07217	−	1.73875i	−0.0839684	−	0.0704579i
$610$		0			0
$611$	−6.18954	−	2.25281i	−0.250402	−	0.0911389i
$612$		0			0
$613$	−5.40255	+	30.6394i	−0.218207	+	1.23751i	0.657047	+	0.753850i	$0.271805\pi$
$613$	−5.40255	+	30.6394i	−0.218207	+	1.23751i	−0.875254	+	0.483664i	$0.839306\pi$
$614$		0			0
$615$	0.149711	+	0.259306i	0.00603691	+	0.0104562i
$616$		0			0
$617$	−17.9547	+	6.53498i	−0.722829	+	0.263088i	−0.677126	−	0.735867i	$-0.736775\pi$
$617$	−17.9547	+	6.53498i	−0.722829	+	0.263088i	−0.0457029	+	0.998955i	$0.514553\pi$
$618$		0			0
$619$	19.4636	+	33.7120i	0.782309	+	1.35500i	0.930593	+	0.366055i	$0.119292\pi$
$619$	19.4636	+	33.7120i	0.782309	+	1.35500i	−0.148284	+	0.988945i	$0.547375\pi$
$620$		0			0
$621$	0.0576190	−	0.0997991i	0.00231217	−	0.00400480i
$622$		0			0
$623$	−10.2645			−0.411237
$624$		0			0
$625$	18.9841	−	15.9296i	0.759364	−	0.637182i
$626$		0			0
$627$	−3.02007	+	1.09921i	−0.120610	+	0.0438984i
$628$		0			0
$629$	−17.4354	−	5.38576i	−0.695195	−	0.214744i
$630$		0			0
$631$	−0.635163	+	0.231180i	−0.0252854	+	0.00920314i	−0.354632	−	0.935006i	$-0.615394\pi$
$631$	−0.635163	+	0.231180i	−0.0252854	+	0.00920314i	0.329346	+	0.944209i	$0.393172\pi$
$632$		0			0
$633$	0.254185	−	0.213286i	0.0101029	−	0.00847737i
$634$		0			0
$635$	1.46110			0.0579821
$636$		0			0
$637$	−2.00475	+	3.47232i	−0.0794310	+	0.137579i
$638$		0			0
$639$	−19.3405	−	33.4987i	−0.765098	−	1.32519i
$640$		0			0
$641$	−17.6853	+	6.43691i	−0.698526	+	0.254243i	−0.666781	−	0.745253i	$-0.732328\pi$
$641$	−17.6853	+	6.43691i	−0.698526	+	0.254243i	−0.0317444	+	0.999496i	$0.510106\pi$
$642$		0			0
$643$	22.6582	+	39.2452i	0.893553	+	1.54768i	0.835585	+	0.549361i	$0.185129\pi$
$643$	22.6582	+	39.2452i	0.893553	+	1.54768i	0.0579679	+	0.998318i	$0.481538\pi$
$644$		0			0
$645$	−0.0677435	+	0.384192i	−0.00266740	+	0.0151276i
$646$		0			0
$647$	18.9859	+	6.91031i	0.746413	+	0.271672i	0.687096	−	0.726567i	$-0.258885\pi$
$647$	18.9859	+	6.91031i	0.746413	+	0.271672i	0.0593177	+	0.998239i	$0.481107\pi$
$648$		0			0
$649$	−45.1095	−	37.8514i	−1.77070	−	1.48580i
$650$		0			0
$651$	0.271974	−	1.54244i	0.0106595	−	0.0604531i
$652$		0			0
$653$	−13.4586	+	11.2931i	−0.526675	+	0.441933i	−0.866951	−	0.498393i	$-0.833924\pi$
$653$	−13.4586	+	11.2931i	−0.526675	+	0.441933i	0.340277	+	0.940325i	$0.389479\pi$
$654$		0			0
$655$	−1.30541	+	2.26103i	−0.0510065	+	0.0883458i
$656$		0			0
$657$	19.2271	+	16.1335i	0.750123	+	0.629428i
$658$		0			0
$659$	−5.65389	−	32.0648i	−0.220244	−	1.24907i	−0.871571	−	0.490269i	$-0.836898\pi$
$659$	−5.65389	−	32.0648i	−0.220244	−	1.24907i	0.651327	−	0.758797i	$-0.274213\pi$
$660$		0			0
$661$	4.07650	+	23.1190i	0.158558	+	0.899225i	0.955461	+	0.295118i	$0.0953590\pi$
$661$	4.07650	+	23.1190i	0.158558	+	0.899225i	−0.796903	+	0.604107i	$0.793530\pi$
$662$		0			0
$663$	0.757122	+	0.275570i	0.0294042	+	0.0107022i
$664$		0			0
$665$	0.331815			0.0128672
$666$		0			0
$667$	0.326266			0.0126331
$668$		0			0
$669$	5.83022	+	2.12203i	0.225409	+	0.0820423i
$670$		0			0
$671$	9.06418	+	51.4055i	0.349919	+	1.98449i
$672$		0			0
$673$	2.29989	+	13.0433i	0.0886542	+	0.502783i	0.996508	+	0.0834962i	$0.0266086\pi$
$673$	2.29989	+	13.0433i	0.0886542	+	0.502783i	−0.907854	+	0.419287i	$0.862280\pi$
$674$		0			0
$675$	−7.79813	−	6.54341i	−0.300150	−	0.251856i
$676$		0			0
$677$	−2.69253	+	4.66360i	−0.103482	+	0.179237i	−0.913117	−	0.407697i	$-0.866332\pi$
$677$	−2.69253	+	4.66360i	−0.103482	+	0.179237i	0.809635	+	0.586934i	$0.199665\pi$
$678$		0			0
$679$	10.5699	−	8.86916i	0.405634	−	0.340367i
$680$		0			0
$681$	0.533738	−	3.02698i	0.0204529	−	0.115994i
$682$		0			0
$683$	−19.2547	−	16.1566i	−0.736759	−	0.618214i	0.195206	−	0.980762i	$-0.437462\pi$
$683$	−19.2547	−	16.1566i	−0.736759	−	0.618214i	−0.931965	+	0.362548i	$0.881907\pi$
$684$		0			0
$685$	0.979055	+	0.356347i	0.0374078	+	0.0136153i
$686$		0			0
$687$	1.05004	−	5.95507i	0.0400615	−	0.227200i
$688$		0			0
$689$	1.07532	+	1.86251i	0.0409665	+	0.0709561i
$690$		0			0
$691$	38.6467	−	14.0662i	1.47019	−	0.535105i	0.522037	−	0.852923i	$-0.325172\pi$
$691$	38.6467	−	14.0662i	1.47019	−	0.535105i	0.948152	+	0.317818i	$0.102950\pi$
$692$		0			0
$693$	8.79086	+	15.2262i	0.333937	+	0.578396i
$694$		0			0
$695$	0.808400	−	1.40019i	0.0306644	−	0.0531123i
$696$		0			0
$697$	21.4439			0.812244
$698$		0			0
$699$	1.11540	−	0.935932i	0.0421883	−	0.0354002i
$700$		0			0
$701$	−29.1523	+	10.6106i	−1.10107	+	0.400756i	−0.827709	−	0.561157i	$-0.810356\pi$
$701$	−29.1523	+	10.6106i	−1.10107	+	0.400756i	−0.273357	+	0.961913i	$0.588134\pi$
$702$		0			0
$703$	−12.4051	+	0.614134i	−0.467868	+	0.0231625i
$704$		0			0
$705$	0.335275	−	0.122030i	0.0126272	−	0.00459592i
$706$		0			0
$707$	16.6309	−	13.9550i	0.625469	−	0.524831i
$708$		0			0
$709$	−19.3773			−0.727731			−0.363865	−	0.931452i	$-0.618543\pi$
$709$	−19.3773			−0.727731			−0.363865	+	0.931452i	$0.618543\pi$
$710$		0			0
$711$	−5.97178	+	10.3434i	−0.223959	+	0.387909i
$712$		0			0
$713$	0.0944557	+	0.163602i	0.00353739	+	0.00612694i
$714$		0			0
$715$	0.397231	−	0.144580i	0.0148556	−	0.00540699i
$716$		0			0
$717$	−1.48932	−	2.57958i	−0.0556198	−	0.0963363i
$718$		0			0
$719$	5.30675	−	30.0961i	0.197908	−	1.12239i	−0.710307	−	0.703892i	$-0.751444\pi$
$719$	5.30675	−	30.0961i	0.197908	−	1.12239i	0.908216	−	0.418503i	$-0.137445\pi$
$720$		0			0
$721$	24.8542	+	9.04617i	0.925617	+	0.336897i
$722$		0			0
$723$	5.56418	+	4.66890i	0.206934	+	0.173638i
$724$		0			0
$725$	5.00475	−	28.3833i	0.185872	−	1.05413i
$726$		0			0
$727$	−39.9843	+	33.5508i	−1.48294	+	1.24433i	−0.579958	+	0.814647i	$0.696931\pi$
$727$	−39.9843	+	33.5508i	−1.48294	+	1.24433i	−0.902979	+	0.429685i	$0.858625\pi$
$728$		0			0
$729$	10.3516	−	17.9296i	0.383394	−	0.664058i
$730$		0			0
$731$	21.4029	+	17.9591i	0.791613	+	0.664242i
$732$		0			0
$733$	0.211829	+	1.20134i	0.00782408	+	0.0443726i	0.988470	−	0.151418i	$-0.0483839\pi$
$733$	0.211829	+	1.20134i	0.00782408	+	0.0443726i	−0.980646	+	0.195790i	$0.937273\pi$
$734$		0			0
$735$	−0.0377140	−	0.213887i	−0.00139110	−	0.00788933i
$736$		0			0
$737$	−21.8075	−	7.93729i	−0.803290	−	0.292374i
$738$		0			0
$739$	2.61318			0.0961273			0.0480637	−	0.998844i	$-0.484695\pi$
$739$	2.61318			0.0961273			0.0480637	+	0.998844i	$0.484695\pi$
$740$		0			0
$741$	0.548392			0.0201457
$742$		0			0
$743$	−21.1989	−	7.71578i	−0.777713	−	0.283064i	−0.0774945	−	0.996993i	$-0.524692\pi$
$743$	−21.1989	−	7.71578i	−0.777713	−	0.283064i	−0.700219	+	0.713928i	$0.746914\pi$
$744$		0			0
$745$	−0.0920916	−	0.522277i	−0.00337397	−	0.0191348i
$746$		0			0
$747$	−2.96064	−	16.7906i	−0.108324	−	0.614336i
$748$		0			0
$749$	−0.658633	−	0.552659i	−0.0240659	−	0.0201937i
$750$		0			0
$751$	21.3346	−	36.9525i	0.778509	−	1.34842i	−0.154292	−	0.988025i	$-0.549310\pi$
$751$	21.3346	−	36.9525i	0.778509	−	1.34842i	0.932801	−	0.360392i	$-0.117357\pi$
$752$		0			0
$753$	1.80793	−	1.51704i	0.0658848	−	0.0552839i
$754$		0			0
$755$	0.308811	−	1.75135i	0.0112388	−	0.0637383i
$756$		0			0
$757$	−17.8610	−	14.9871i	−0.649168	−	0.544717i	0.257650	−	0.966238i	$-0.417052\pi$
$757$	−17.8610	−	14.9871i	−0.649168	−	0.544717i	−0.906818	+	0.421522i	$0.861496\pi$
$758$		0			0
$759$	0.0834734	+	0.0303818i	0.00302989	+	0.00110279i
$760$		0			0
$761$	−0.714822	+	4.05396i	−0.0259123	+	0.146956i	−0.995019	−	0.0996862i	$-0.968216\pi$
$761$	−0.714822	+	4.05396i	−0.0259123	+	0.146956i	0.969107	+	0.246642i	$0.0793272\pi$
$762$		0			0
$763$	4.88847	+	8.46708i	0.176975	+	0.306529i
$764$		0			0
$765$	0.979055	−	0.356347i	0.0353978	−	0.0128838i
$766$		0			0
$767$	5.02394	+	8.70172i	0.181404	+	0.314201i
$768$		0			0
$769$	−3.09017	+	5.35234i	−0.111435	+	0.193010i	−0.916349	−	0.400381i	$-0.868878\pi$
$769$	−3.09017	+	5.35234i	−0.111435	+	0.193010i	0.804914	+	0.593391i	$0.202211\pi$
$770$		0			0
$771$	3.43201			0.123601
$772$		0			0
$773$	13.8773	−	11.6445i	0.499133	−	0.418822i	−0.358153	−	0.933663i	$-0.616593\pi$
$773$	13.8773	−	11.6445i	0.499133	−	0.418822i	0.857286	+	0.514841i	$0.172149\pi$
$774$		0			0
$775$	15.6814	−	5.70756i	0.563292	−	0.205022i
$776$		0			0
$777$	−0.632226	−	2.77509i	−0.0226810	−	0.0995556i
$778$		0			0
$779$	13.7151	−	4.99190i	0.491395	−	0.178853i
$780$		0			0
$781$	46.6391	−	39.1348i	1.66888	−	1.40035i
$782$		0			0
$783$	−11.8043			−0.421851
$784$		0			0
$785$	−0.943974	+	1.63501i	−0.0336919	+	0.0583560i
$786$		0			0
$787$	−13.9602	−	24.1798i	−0.497628	−	0.861918i	0.502368	−	0.864654i	$-0.332462\pi$
$787$	−13.9602	−	24.1798i	−0.497628	−	0.861918i	−0.999996	+	0.00273640i	$0.999129\pi$
$788$		0			0
$789$	6.73947	−	2.45297i	0.239932	−	0.0873280i
$790$		0			0
$791$	−9.31180	−	16.1285i	−0.331090	−	0.573464i
$792$		0			0
$793$	1.54664	−	8.77141i	0.0549227	−	0.311482i
$794$		0			0
$795$	−0.109470	−	0.0398440i	−0.00388252	−	0.00141312i
$796$		0			0
$797$	−1.51114	−	1.26800i	−0.0535275	−	0.0449149i	0.615631	−	0.788034i	$-0.288901\pi$
$797$	−1.51114	−	1.26800i	−0.0535275	−	0.0449149i	−0.669159	+	0.743119i	$0.733345\pi$
$798$		0			0
$799$	4.43717	−	25.1644i	0.156976	−	0.890253i
$800$		0			0
$801$	−16.8045	+	14.1007i	−0.593759	+	0.498223i
$802$		0			0
$803$	−19.7528	+	34.2129i	−0.697063	+	1.20735i
$804$		0			0
$805$	−0.00702557	−	0.00589515i	−0.000247619	−	0.000207777i
$806$		0			0
$807$	−1.66607	−	9.44875i	−0.0586484	−	0.332612i
$808$		0			0
$809$	2.72699	+	15.4655i	0.0958757	+	0.543738i	0.994475	+	0.104969i	$0.0334743\pi$
$809$	2.72699	+	15.4655i	0.0958757	+	0.543738i	−0.898600	+	0.438769i	$0.855415\pi$
$810$		0			0
$811$	−38.0984	−	13.8667i	−1.33782	−	0.486925i	−0.428691	−	0.903451i	$-0.641025\pi$
$811$	−38.0984	−	13.8667i	−1.33782	−	0.486925i	−0.909124	+	0.416526i	$0.863247\pi$
$812$		0			0
$813$	2.37639			0.0833437
$814$		0			0
$815$	−0.576666			−0.0201997
$816$		0			0
$817$	17.8696	+	6.50400i	0.625178	+	0.227546i
$818$		0			0
$819$	−0.520945	−	2.95442i	−0.0182033	−	0.103236i
$820$		0			0
$821$	−1.73190	−	9.82207i	−0.0604436	−	0.342793i	−1.00000		0.000398276i	$-0.999873\pi$
$821$	−1.73190	−	9.82207i	−0.0604436	−	0.342793i	0.939556	−	0.342394i	$-0.111238\pi$
$822$		0			0
$823$	8.12180	+	6.81500i	0.283108	+	0.237556i	0.773272	−	0.634074i	$-0.218619\pi$
$823$	8.12180	+	6.81500i	0.283108	+	0.237556i	−0.490164	+	0.871630i	$0.663063\pi$
$824$		0			0
$825$	3.92350	−	6.79569i	0.136599	−	0.236596i
$826$		0			0
$827$	−19.3195	+	16.2110i	−0.671806	+	0.563712i	−0.913599	−	0.406615i	$-0.866709\pi$
$827$	−19.3195	+	16.2110i	−0.671806	+	0.563712i	0.241793	+	0.970328i	$0.422264\pi$
$828$		0			0
$829$	0.950532	−	5.39074i	0.0330134	−	0.187228i	−0.963842	−	0.266476i	$-0.914141\pi$
$829$	0.950532	−	5.39074i	0.0330134	−	0.187228i	0.996855	+	0.0792478i	$0.0252519\pi$
$830$		0			0
$831$	6.34065	+	5.32044i	0.219955	+	0.184564i
$832$		0			0
$833$	−14.6163	−	5.31991i	−0.506426	−	0.184324i
$834$		0			0
$835$	0.0419949	−	0.238165i	0.00145329	−	0.00824203i
$836$		0			0
$837$	−3.41740	−	5.91912i	−0.118123	−	0.204595i
$838$		0			0
$839$	12.7046	−	4.62408i	0.438610	−	0.159641i	−0.113271	−	0.993564i	$-0.536133\pi$
$839$	12.7046	−	4.62408i	0.438610	−	0.159641i	0.551880	+	0.833923i	$0.313910\pi$
$840$		0			0
$841$	−2.21032	−	3.82839i	−0.0762180	−	0.132013i
$842$		0			0
$843$	5.51367	−	9.54996i	0.189901	−	0.328918i
$844$		0			0
$845$	1.49586			0.0514592
$846$		0			0
$847$	−9.84595	+	8.26173i	−0.338311	+	0.283877i
$848$		0			0
$849$	1.92855	−	0.701934i	0.0661876	−	0.0240903i
$850$		0			0
$851$	0.273567	+	0.207391i	0.00937775	+	0.00710928i
$852$		0			0
$853$	21.2570	−	7.73692i	0.727826	−	0.264907i	0.0485819	−	0.998819i	$-0.484530\pi$
$853$	21.2570	−	7.73692i	0.727826	−	0.264907i	0.679244	+	0.733912i	$0.262308\pi$
$854$		0			0
$855$	0.543233	−	0.455827i	0.0185782	−	0.0155889i
$856$		0			0
$857$	−28.4148			−0.970630			−0.485315	−	0.874339i	$-0.661295\pi$
$857$	−28.4148			−0.970630			−0.485315	+	0.874339i	$0.661295\pi$
$858$		0			0
$859$	11.2618	−	19.5059i	0.384246	−	0.665534i	−0.607418	−	0.794382i	$-0.707795\pi$
$859$	11.2618	−	19.5059i	0.384246	−	0.665534i	0.991664	+	0.128848i	$0.0411280\pi$
$860$		0			0
$861$	1.67230	+	2.89652i	0.0569920	+	0.0987130i
$862$		0			0
$863$	−9.35282	+	3.40415i	−0.318374	+	0.115878i	−0.496264	−	0.868172i	$-0.665295\pi$
$863$	−9.35282	+	3.40415i	−0.318374	+	0.115878i	0.177890	+	0.984050i	$0.443073\pi$
$864$		0			0
$865$	−0.831100	−	1.43951i	−0.0282582	−	0.0489447i
$866$		0			0
$867$	0.482459	−	2.73616i	0.0163852	−	0.0929249i
$868$		0			0
$869$	−17.6652	−	6.42960i	−0.599251	−	0.218109i
$870$		0			0
$871$	3.03343	+	2.54535i	0.102784	+	0.0862460i
$872$		0			0
$873$	5.12061	−	29.0404i	0.173307	−	0.982870i
$874$		0			0
$875$	−1.24304	+	1.04303i	−0.0420224	+	0.0352610i
$876$		0			0
$877$	−22.0021	+	38.1088i	−0.742959	+	1.28684i	0.208184	+	0.978090i	$0.433245\pi$
$877$	−22.0021	+	38.1088i	−0.742959	+	1.28684i	−0.951142	+	0.308752i	$0.900089\pi$
$878$		0			0
$879$	0.450837	+	0.378297i	0.0152064	+	0.0127596i
$880$		0			0
$881$	−2.13862	−	12.1287i	−0.0720520	−	0.408627i	−0.999407	−	0.0344437i	$-0.989034\pi$
$881$	−2.13862	−	12.1287i	−0.0720520	−	0.408627i	0.927355	−	0.374184i	$-0.122077\pi$
$882$		0			0
$883$	−3.77244	−	21.3946i	−0.126953	−	0.719985i	−0.980129	−	0.198362i	$-0.936438\pi$
$883$	−3.77244	−	21.3946i	−0.126953	−	0.719985i	0.853176	−	0.521623i	$-0.174673\pi$
$884$		0			0
$885$	−0.511449	−	0.186152i	−0.0171922	−	0.00625744i
$886$		0			0
$887$	−10.7145			−0.359758			−0.179879	−	0.983689i	$-0.557571\pi$
$887$	−10.7145			−0.359758			−0.179879	+	0.983689i	$0.557571\pi$
$888$		0			0
$889$	16.3209			0.547385
$890$		0			0
$891$	33.7679	+	12.2905i	1.13127	+	0.411747i
$892$		0			0
$893$	−3.02007	−	17.1277i	−0.101063	−	0.573155i
$894$		0			0
$895$	−0.308400	−	1.74903i	−0.0103087	−	0.0584635i
$896$		0			0
$897$	−0.0116112	−	0.00974294i	−0.000387686	−	0.000325307i
$898$		0			0
$899$	9.67546	−	16.7584i	0.322695	−	0.558923i
$900$		0			0
$901$	−6.39124	+	5.36289i	−0.212923	+	0.178664i
$902$		0			0
$903$	−0.756711	+	4.29152i	−0.0251818	+	0.142813i
$904$		0			0
$905$	1.00703	+	0.844995i	0.0334747	+	0.0280886i
$906$		0			0
$907$	17.1122	+	6.22832i	0.568200	+	0.206808i	0.610114	−	0.792313i	$-0.291123\pi$
$907$	17.1122	+	6.22832i	0.568200	+	0.206808i	−0.0419145	+	0.999121i	$0.513346\pi$
$908$		0			0
$909$	8.05690	−	45.6930i	0.267231	−	1.51554i
$910$		0			0
$911$	10.3072	+	17.8526i	0.341493	+	0.591484i	0.984710	−	0.174200i	$-0.0557340\pi$
$911$	10.3072	+	17.8526i	0.341493	+	0.591484i	−0.643217	+	0.765684i	$0.722401\pi$
$912$		0			0
$913$	25.2173	−	9.17836i	0.834572	−	0.303760i
$914$		0			0
$915$	0.241230	+	0.417822i	0.00797480	+	0.0138128i
$916$		0			0
$917$	−14.5817	+	25.2563i	−0.481531	+	0.834036i
$918$		0			0
$919$	25.1462			0.829497			0.414748	−	0.909936i	$-0.363870\pi$
$919$	25.1462			0.829497			0.414748	+	0.909936i	$0.363870\pi$
$920$		0			0
$921$	−3.25284	+	2.72946i	−0.107185	+	0.0899387i
$922$		0			0
$923$	−9.76207	+	3.55310i	−0.321322	+	0.116952i
$924$		0			0
$925$	22.2383	−	20.6176i	0.731191	−	0.677901i
$926$		0			0
$927$	53.1173	−	19.3331i	1.74460	−	0.634982i
$928$		0			0
$929$	−23.1912	+	19.4597i	−0.760878	+	0.638453i	−0.938355	−	0.345672i	$-0.887651\pi$
$929$	−23.1912	+	19.4597i	−0.760878	+	0.638453i	0.177477	+	0.984125i	$0.443206\pi$
$930$		0			0
$931$	−10.5868			−0.346967
$932$		0			0
$933$	0.212134	−	0.367426i	0.00694494	−	0.0120290i
$934$		0			0
$935$	0.819955	+	1.42020i	0.0268154	+	0.0464456i
$936$		0			0
$937$	15.1686	−	5.52092i	0.495536	−	0.180361i	−0.0821489	−	0.996620i	$-0.526178\pi$
$937$	15.1686	−	5.52092i	0.495536	−	0.180361i	0.577685	+	0.816260i	$0.303956\pi$
$938$		0			0
$939$	−3.02347	−	5.23680i	−0.0986672	−	0.170897i
$940$		0			0
$941$	1.70733	−	9.68275i	0.0556574	−	0.315649i	−0.944250	−	0.329228i	$-0.893212\pi$
$941$	1.70733	−	9.68275i	0.0556574	−	0.315649i	0.999908	+	0.0135795i	$0.00432262\pi$
$942$		0			0
$943$	−0.379081	−	0.137974i	−0.0123446	−	0.00449305i
$944$		0			0
$945$	0.254185	+	0.213286i	0.00826863	+	0.00693821i
$946$		0			0
$947$	9.23695	−	52.3853i	0.300160	−	1.70229i	−0.345293	−	0.938495i	$-0.612220\pi$
$947$	9.23695	−	52.3853i	0.300160	−	1.70229i	0.645453	−	0.763800i	$-0.276669\pi$
$948$		0			0
$949$	5.16385	−	4.33298i	0.167626	−	0.140655i
$950$		0			0
$951$	−1.51027	+	2.61586i	−0.0489738	+	0.0848250i
$952$		0			0
$953$	37.4181	+	31.3975i	1.21209	+	1.01706i	0.999200	+	0.0399889i	$0.0127323\pi$
$953$	37.4181	+	31.3975i	1.21209	+	1.01706i	0.212891	+	0.977076i	$0.431712\pi$
$954$		0			0
$955$	0.189702	+	1.07586i	0.00613863	+	0.0348139i
$956$		0			0
$957$	−1.58007	−	8.96102i	−0.0510764	−	0.289669i
$958$		0			0
$959$	10.9363	+	3.98048i	0.353151	+	0.128537i
$960$		0			0
$961$	−19.7956			−0.638568
$962$		0			0
$963$	−1.83750			−0.0592125
$964$		0			0
$965$	1.42690	+	0.519349i	0.0459335	+	0.0167184i
$966$		0			0
$967$	−1.45646	−	8.26001i	−0.0468367	−	0.265624i	0.952393	−	0.304874i	$-0.0986143\pi$
$967$	−1.45646	−	8.26001i	−0.0468367	−	0.265624i	−0.999229	+	0.0392499i	$0.987503\pi$
$968$		0			0
$969$	0.369423	+	2.09510i	0.0118676	+	0.0673044i
$970$		0			0
$971$	−31.6771	−	26.5802i	−1.01657	−	0.853001i	−0.0273745	−	0.999625i	$-0.508715\pi$
$971$	−31.6771	−	26.5802i	−1.01657	−	0.853001i	−0.989192	+	0.146624i	$0.953159\pi$
$972$		0			0
$973$	9.03003	−	15.6405i	0.289489	−	0.501410i
$974$		0			0
$975$	−1.02569	+	0.860658i	−0.0328484	+	0.0275631i
$976$		0			0
$977$	8.39662	−	47.6196i	0.268632	−	1.52349i	−0.489859	−	0.871802i	$-0.662952\pi$
$977$	8.39662	−	47.6196i	0.268632	−	1.52349i	0.758490	−	0.651684i	$-0.225937\pi$
$978$		0			0
$979$	−26.4500	−	22.1942i	−0.845344	−	0.709328i
$980$		0			0
$981$	19.6348	+	7.14647i	0.626889	+	0.228169i
$982$		0			0
$983$	−9.44150	+	53.5454i	−0.301137	+	1.70783i	0.340015	+	0.940420i	$0.389568\pi$
$983$	−9.44150	+	53.5454i	−0.301137	+	1.70783i	−0.641152	+	0.767414i	$0.721543\pi$
$984$		0			0
$985$	−0.719874	−	1.24686i	−0.0229371	−	0.0397282i
$986$		0			0
$987$	3.74510	−	1.36310i	0.119208	−	0.0433881i
$988$		0			0
$989$	−0.262803	−	0.455188i	−0.00835665	−	0.0144741i
$990$		0			0
$991$	−15.9436	+	27.6151i	−0.506464	+	0.877221i	0.493508	+	0.869741i	$0.335714\pi$
$991$	−15.9436	+	27.6151i	−0.506464	+	0.877221i	−0.999972	+	0.00748010i	$0.997619\pi$
$992$		0			0
$993$	−2.86247			−0.0908378
$994$		0			0
$995$	0.211667	−	0.177610i	0.00671029	−	0.00563060i
$996$		0			0
$997$	0.490505	−	0.178529i	0.0155344	−	0.00565407i	−0.334241	−	0.942488i	$-0.608480\pi$
$997$	0.490505	−	0.178529i	0.0155344	−	0.00565407i	0.349776	+	0.936833i	$0.386258\pi$
$998$		0			0
$999$	−9.89764	−	7.50341i	−0.313148	−	0.237397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.bc.b.81.1		6
4.3	odd	2		74.2.f.a.7.1	✓	6
12.11	even	2		666.2.x.c.451.1		6
37.16	even	9	inner	592.2.bc.b.497.1		6
148.107	odd	18		2738.2.a.m.1.2		3
148.115	odd	18		2738.2.a.p.1.2		3
148.127	odd	18		74.2.f.a.53.1	yes	6
444.275	even	18		666.2.x.c.127.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.a.7.1	✓	6	4.3	odd	2
74.2.f.a.53.1	yes	6	148.127	odd	18
592.2.bc.b.81.1		6	1.1	even	1	trivial
592.2.bc.b.497.1		6	37.16	even	9	inner
666.2.x.c.127.1		6	444.275	even	18
666.2.x.c.451.1		6	12.11	even	2
2738.2.a.m.1.2		3	148.107	odd	18
2738.2.a.p.1.2		3	148.115	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)

\(f(q)\)	\(=\)	\(q+(0.326352 + 0.118782i) q^{3} +(-0.0209445 - 0.118782i) q^{5} +(-0.233956 - 1.32683i) q^{7} +(-2.20574 - 1.85083i) q^{9} +O(q^{10})\)	\(q+(0.326352 + 0.118782i) q^{3} +(-0.0209445 - 0.118782i) q^{5} +(-0.233956 - 1.32683i) q^{7} +(-2.20574 - 1.85083i) q^{9} +(2.26604 - 3.92490i) q^{11} +(-0.592396 + 0.497079i) q^{13} +(0.00727396 - 0.0412527i) q^{15} +(-2.29813 - 1.92836i) q^{17} +(-1.91875 - 0.698367i) q^{19} +(0.0812519 - 0.460802i) q^{21} +(0.0282185 + 0.0488759i) q^{23} +(4.68479 - 1.70513i) q^{25} +(-1.02094 - 1.76833i) q^{27} +(2.89053 - 5.00654i) q^{29} +3.34730 q^{31} +(1.20574 - 1.01173i) q^{33} +(-0.152704 + 0.0555796i) q^{35} +(5.60607 - 2.36051i) q^{37} +(-0.252374 + 0.0918566i) q^{39} +(-5.47565 + 4.59462i) q^{41} -9.31315 q^{43} +(-0.173648 + 0.300767i) q^{45} +(4.25877 + 7.37641i) q^{47} +(4.87211 - 1.77330i) q^{49} +(-0.520945 - 0.902302i) q^{51} +(0.482926 - 2.73881i) q^{53} +(-0.513671 - 0.186961i) q^{55} +(-0.543233 - 0.455827i) q^{57} +(2.25624 - 12.7958i) q^{59} +(-8.82295 + 7.40333i) q^{61} +(-1.93969 + 3.35965i) q^{63} +(0.0714517 + 0.0599551i) q^{65} +(-0.889185 - 5.04282i) q^{67} +(0.00340357 + 0.0193026i) q^{69} +(12.6236 + 4.59462i) q^{71} -8.71688 q^{73} +1.73143 q^{75} +(-5.73783 - 2.08840i) q^{77} +(-0.720285 - 4.08494i) q^{79} +(1.37686 + 7.80856i) q^{81} +(4.53596 + 3.80612i) q^{83} +(-0.180922 + 0.313366i) q^{85} +(1.53802 - 1.29055i) q^{87} +(1.32295 - 7.50281i) q^{89} +(0.798133 + 0.669713i) q^{91} +(1.09240 + 0.397600i) q^{93} +(-0.0427664 + 0.242540i) q^{95} +(5.12061 + 8.86916i) q^{97} +(-12.2626 + 4.46324i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} + 3 q^{5} - 6 q^{7} - 3 q^{9}+O(q^{10}) \) 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

L-functions

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Groups

Database

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