LMFDB - Embedded newform 592.2.bc.d.497.2

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:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 24x^{10} + 264x^{8} - 1687x^{6} + 6600x^{4} - 15000x^{2} + 15625 $ x^12 - 24x^10 + 264x^8 - 1687x^6 + 6600x^4 - 15000*x^2 + 15625
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			497.2
Root			$-2.00752 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	592.497
Dual form			592.2.bc.d.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.04963 - 0.746005i) q^{3} +(-0.326352 + 1.85083i) q^{5} +(0.711830 - 4.03699i) q^{7} +(1.34633 - 1.12971i) q^{9} +O(q^{10})$	\(q+(2.04963 - 0.746005i) q^{3} +(-0.326352 + 1.85083i) q^{5} +(0.711830 - 4.03699i) q^{7} +(1.34633 - 1.12971i) q^{9} +(1.67088 + 2.89404i) q^{11} +(1.48512 + 1.24616i) q^{13} +(0.711830 + 4.03699i) q^{15} +(3.40626 - 2.85819i) q^{17} +(-0.0932770 + 0.0339500i) q^{19} +(-1.55262 - 8.80536i) q^{21} +(4.76146 - 8.24709i) q^{23} +(1.37939 + 0.502055i) q^{25} +(-1.35504 + 2.34700i) q^{27} +(-0.387288 - 0.670802i) q^{29} -10.3914 q^{31} +(5.58365 + 4.68524i) q^{33} +(7.23948 + 2.63496i) q^{35} +(-3.50302 + 4.97281i) q^{37} +(3.97359 + 1.44627i) q^{39} +(4.36218 + 3.66031i) q^{41} +1.11986 q^{43} +(1.65152 + 2.86052i) q^{45} +(-3.55724 + 6.16132i) q^{47} +(-9.21271 - 3.35315i) q^{49} +(4.84936 - 8.39933i) q^{51} +(0.142188 + 0.806388i) q^{53} +(-5.90168 + 2.14804i) q^{55} +(-0.165857 + 0.139170i) q^{57} +(-1.40642 - 7.97622i) q^{59} +(-8.19737 - 6.87841i) q^{61} +(-3.60225 - 6.23929i) q^{63} +(-2.79111 + 2.34202i) q^{65} +(-2.28630 + 12.9663i) q^{67} +(3.60687 - 20.4556i) q^{69} +(-2.79386 + 1.01688i) q^{71} -2.55740 q^{73} +3.20177 q^{75} +(12.8726 - 4.68524i) q^{77} +(0.943888 - 5.35305i) q^{79} +(-1.94203 + 11.0138i) q^{81} +(-0.504249 + 0.423115i) q^{83} +(4.17840 + 7.23720i) q^{85} +(-1.29422 - 1.08598i) q^{87} +(0.612149 + 3.47167i) q^{89} +(6.08790 - 5.10835i) q^{91} +(-21.2986 + 7.75206i) q^{93} +(-0.0323948 - 0.183720i) q^{95} +(-1.81012 + 3.13522i) q^{97} +(5.51897 + 2.00874i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - 6 q^{5} - 6 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - 6 * q^5 - 6 * q^7 - 3 * q^9	$ 12 q + 3 q^{3} - 6 q^{5} - 6 q^{7} - 3 q^{9} - 3 q^{11} - 6 q^{13} - 6 q^{15} - 3 q^{17} + 3 q^{19} - 33 q^{21} + 21 q^{23} - 6 q^{25} - 3 q^{27} + 6 q^{29} - 42 q^{31} + 57 q^{33} + 9 q^{35} - 3 q^{37} + 24 q^{39} - 21 q^{41} - 36 q^{43} - 6 q^{45} - 9 q^{47} - 12 q^{49} - 6 q^{53} - 36 q^{57} + 6 q^{59} - 18 q^{61} - 36 q^{63} + 3 q^{65} + 27 q^{67} - 12 q^{69} + 18 q^{71} + 54 q^{73} + 6 q^{75} + 51 q^{77} + 12 q^{79} - 36 q^{81} + 6 q^{83} + 3 q^{85} - 39 q^{87} - 15 q^{89} + 51 q^{91} + 45 q^{93} + 15 q^{95} - 42 q^{97} + 33 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 - 6 * q^5 - 6 * q^7 - 3 * q^9 - 3 * q^11 - 6 * q^13 - 6 * q^15 - 3 * q^17 + 3 * q^19 - 33 * q^21 + 21 * q^23 - 6 * q^25 - 3 * q^27 + 6 * q^29 - 42 * q^31 + 57 * q^33 + 9 * q^35 - 3 * q^37 + 24 * q^39 - 21 * q^41 - 36 * q^43 - 6 * q^45 - 9 * q^47 - 12 * q^49 - 6 * q^53 - 36 * q^57 + 6 * q^59 - 18 * q^61 - 36 * q^63 + 3 * q^65 + 27 * q^67 - 12 * q^69 + 18 * q^71 + 54 * q^73 + 6 * q^75 + 51 * q^77 + 12 * q^79 - 36 * q^81 + 6 * q^83 + 3 * q^85 - 39 * q^87 - 15 * q^89 + 51 * q^91 + 45 * q^93 + 15 * q^95 - 42 * q^97 + 33 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	2.04963	−	0.746005i	1.18336	−	0.430706i	0.325970	−	0.945380i	$-0.394309\pi$
$3$	2.04963	−	0.746005i	1.18336	−	0.430706i	0.857386	+	0.514674i	$0.172087\pi$
$4$		0			0
$5$	−0.326352	+	1.85083i	−0.145949	+	0.827718i	0.820651	+	0.571429i	$0.193611\pi$
$5$	−0.326352	+	1.85083i	−0.145949	+	0.827718i	−0.966600	+	0.256289i	$0.917500\pi$
$6$		0			0
$7$	0.711830	−	4.03699i	0.269046	−	1.52584i	−0.488214	−	0.872724i	$-0.662351\pi$
$7$	0.711830	−	4.03699i	0.269046	−	1.52584i	0.757260	−	0.653113i	$-0.226537\pi$
$8$		0			0
$9$	1.34633	−	1.12971i	0.448778	−	0.376569i
$10$		0			0
$11$	1.67088	+	2.89404i	0.503788	+	0.872586i	0.999990	+	0.00437929i	$0.00139397\pi$
$11$	1.67088	+	2.89404i	0.503788	+	0.872586i	−0.496203	+	0.868207i	$0.665273\pi$
$12$		0			0
$13$	1.48512	+	1.24616i	0.411898	+	0.345623i	0.825071	−	0.565029i	$-0.191135\pi$
$13$	1.48512	+	1.24616i	0.411898	+	0.345623i	−0.413173	+	0.910653i	$0.635580\pi$
$14$		0			0
$15$	0.711830	+	4.03699i	0.183794	+	1.04235i
$16$		0			0
$17$	3.40626	−	2.85819i	0.826140	−	0.693214i	−0.128261	−	0.991740i	$-0.540940\pi$
$17$	3.40626	−	2.85819i	0.826140	−	0.693214i	0.954401	+	0.298527i	$0.0964952\pi$
$18$		0			0
$19$	−0.0932770	+	0.0339500i	−0.0213992	+	0.00778868i	−0.352698	−	0.935737i	$-0.614736\pi$
$19$	−0.0932770	+	0.0339500i	−0.0213992	+	0.00778868i	0.331298	+	0.943526i	$0.392513\pi$
$20$		0			0
$21$	−1.55262	−	8.80536i	−0.338810	−	1.92149i
$22$		0			0
$23$	4.76146	−	8.24709i	0.992833	−	1.71964i	0.392920	−	0.919573i	$-0.371465\pi$
$23$	4.76146	−	8.24709i	0.992833	−	1.71964i	0.599913	−	0.800065i	$-0.295202\pi$
$24$		0			0
$25$	1.37939	+	0.502055i	0.275877	+	0.100411i
$26$		0			0
$27$	−1.35504	+	2.34700i	−0.260777	+	0.451680i
$28$		0			0
$29$	−0.387288	−	0.670802i	−0.0719175	−	0.124565i	0.827824	−	0.560988i	$-0.189579\pi$
$29$	−0.387288	−	0.670802i	−0.0719175	−	0.124565i	−0.899742	+	0.436423i	$0.856245\pi$
$30$		0			0
$31$	−10.3914			−1.86636			−0.933179	−	0.359413i	$-0.882977\pi$
$31$	−10.3914			−1.86636			−0.933179	+	0.359413i	$0.882977\pi$
$32$		0			0
$33$	5.58365	+	4.68524i	0.971988	+	0.815595i
$34$		0			0
$35$	7.23948	+	2.63496i	1.22370	+	0.445389i
$36$		0			0
$37$	−3.50302	+	4.97281i	−0.575894	+	0.817525i
$37$	−3.50302	+	4.97281i	−0.575894	+	0.817525i
$38$		0			0
$39$	3.97359	+	1.44627i	0.636284	+	0.231588i
$40$		0			0
$41$	4.36218	+	3.66031i	0.681259	+	0.571644i	0.916374	−	0.400324i	$-0.131102\pi$
$41$	4.36218	+	3.66031i	0.681259	+	0.571644i	−0.235115	+	0.971968i	$0.575547\pi$
$42$		0			0
$43$	1.11986			0.170777			0.0853884	−	0.996348i	$-0.472787\pi$
$43$	1.11986			0.170777			0.0853884	+	0.996348i	$0.472787\pi$
$44$		0			0
$45$	1.65152	+	2.86052i	0.246194	+	0.426421i
$46$		0			0
$47$	−3.55724	+	6.16132i	−0.518877	+	0.898721i	0.480883	+	0.876785i	$0.340316\pi$
$47$	−3.55724	+	6.16132i	−0.518877	+	0.898721i	−0.999759	+	0.0219357i	$0.993017\pi$
$48$		0			0
$49$	−9.21271	−	3.35315i	−1.31610	−	0.479022i
$50$		0			0
$51$	4.84936	−	8.39933i	0.679046	−	1.17614i
$52$		0			0
$53$	0.142188	+	0.806388i	0.0195310	+	0.110766i	0.993015	−	0.117990i	$-0.0376452\pi$
$53$	0.142188	+	0.806388i	0.0195310	+	0.110766i	−0.973484	+	0.228756i	$0.926534\pi$
$54$		0			0
$55$	−5.90168	+	2.14804i	−0.795782	+	0.289641i
$56$		0			0
$57$	−0.165857	+	0.139170i	−0.0219682	+	0.0184335i
$58$		0			0
$59$	−1.40642	−	7.97622i	−0.183101	−	1.03842i	−0.928372	−	0.371653i	$-0.878791\pi$
$59$	−1.40642	−	7.97622i	−0.183101	−	1.03842i	0.745271	−	0.666762i	$-0.232320\pi$
$60$		0			0
$61$	−8.19737	−	6.87841i	−1.04957	−	0.880691i	−0.0565183	−	0.998402i	$-0.518000\pi$
$61$	−8.19737	−	6.87841i	−1.04957	−	0.880691i	−0.993048	+	0.117711i	$0.962444\pi$
$62$		0			0
$63$	−3.60225	−	6.23929i	−0.453841	−	0.786076i
$64$		0			0
$65$	−2.79111	+	2.34202i	−0.346195	+	0.290492i
$66$		0			0
$67$	−2.28630	+	12.9663i	−0.279317	+	1.58408i	0.445591	+	0.895237i	$0.352994\pi$
$67$	−2.28630	+	12.9663i	−0.279317	+	1.58408i	−0.724907	+	0.688846i	$0.758117\pi$
$68$		0			0
$69$	3.60687	−	20.4556i	0.434216	−	2.46256i
$70$		0			0
$71$	−2.79386	+	1.01688i	−0.331570	+	0.120682i	−0.502440	−	0.864612i	$-0.667564\pi$
$71$	−2.79386	+	1.01688i	−0.331570	+	0.120682i	0.170870	+	0.985294i	$0.445342\pi$
$72$		0			0
$73$	−2.55740			−0.299321			−0.149660	−	0.988737i	$-0.547818\pi$
$73$	−2.55740			−0.299321			−0.149660	+	0.988737i	$0.547818\pi$
$74$		0			0
$75$	3.20177			0.369708
$76$		0			0
$77$	12.8726	−	4.68524i	1.46697	−	0.533932i
$78$		0			0
$79$	0.943888	−	5.35305i	0.106196	−	0.602265i	−0.884540	−	0.466464i	$-0.845528\pi$
$79$	0.943888	−	5.35305i	0.106196	−	0.602265i	0.990736	−	0.135802i	$-0.0433610\pi$
$80$		0			0
$81$	−1.94203	+	11.0138i	−0.215781	+	1.22375i
$82$		0			0
$83$	−0.504249	+	0.423115i	−0.0553485	+	0.0464429i	−0.670042	−	0.742323i	$-0.733724\pi$
$83$	−0.504249	+	0.423115i	−0.0553485	+	0.0464429i	0.614694	+	0.788766i	$0.289280\pi$
$84$		0			0
$85$	4.17840	+	7.23720i	0.453211	+	0.784985i
$86$		0			0
$87$	−1.29422	−	1.08598i	−0.138755	−	0.116429i
$88$		0			0
$89$	0.612149	+	3.47167i	0.0648877	+	0.367996i	0.999910	+	0.0134078i	$0.00426798\pi$
$89$	0.612149	+	3.47167i	0.0648877	+	0.367996i	−0.935022	+	0.354589i	$0.884621\pi$
$90$		0			0
$91$	6.08790	−	5.10835i	0.638185	−	0.535501i
$92$		0			0
$93$	−21.2986	+	7.75206i	−2.20856	+	0.803852i
$94$		0			0
$95$	−0.0323948	−	0.183720i	−0.00332363	−	0.0188493i
$96$		0			0
$97$	−1.81012	+	3.13522i	−0.183790	+	0.318334i	−0.943168	−	0.332316i	$-0.892170\pi$
$97$	−1.81012	+	3.13522i	−0.183790	+	0.318334i	0.759378	+	0.650650i	$0.225503\pi$
$98$		0			0
$99$	5.51897	+	2.00874i	0.554678	+	0.201886i
$100$		0			0
$101$	−1.97406	+	3.41917i	−0.196426	+	0.340220i	−0.947367	−	0.320149i	$-0.896267\pi$
$101$	−1.97406	+	3.41917i	−0.196426	+	0.340220i	0.750941	+	0.660369i	$0.229600\pi$
$102$		0			0
$103$	−0.989402	−	1.71369i	−0.0974887	−	0.168855i	0.813156	−	0.582046i	$-0.197748\pi$
$103$	−0.989402	−	1.71369i	−0.0974887	−	0.168855i	−0.910645	+	0.413191i	$0.864414\pi$
$104$		0			0
$105$	16.8040			1.63990
$106$		0			0
$107$	−6.31896	−	5.30224i	−0.610877	−	0.512587i	0.284044	−	0.958811i	$-0.408324\pi$
$107$	−6.31896	−	5.30224i	−0.610877	−	0.512587i	−0.894921	+	0.446225i	$0.852768\pi$
$108$		0			0
$109$	8.25476	+	3.00449i	0.790663	+	0.287778i	0.705612	−	0.708599i	$-0.250672\pi$
$109$	8.25476	+	3.00449i	0.790663	+	0.287778i	0.0850513	+	0.996377i	$0.472895\pi$
$110$		0			0
$111$	−3.47017	+	12.8057i	−0.329374	+	1.21546i
$112$		0			0
$113$	−9.37522	−	3.41230i	−0.881946	−	0.321002i	−0.138951	−	0.990299i	$-0.544373\pi$
$113$	−9.37522	−	3.41230i	−0.881946	−	0.321002i	−0.742995	+	0.669297i	$0.766595\pi$
$114$		0			0
$115$	13.7101	+	11.5041i	1.27847	+	1.07277i
$116$		0			0
$117$	3.40727			0.315002
$118$		0			0
$119$	−9.11381	−	15.7856i	−0.835462	−	1.44706i
$120$		0			0
$121$	−0.0836467	+	0.144880i	−0.00760425	+	0.0131709i
$122$		0			0
$123$	11.6715	+	4.24807i	1.05238	+	0.383036i
$124$		0			0
$125$	−6.07785	+	10.5271i	−0.543619	+	0.941576i
$126$		0			0
$127$	2.91336	+	16.5225i	0.258519	+	1.46613i	0.786876	+	0.617112i	$0.211697\pi$
$127$	2.91336	+	16.5225i	0.258519	+	1.46613i	−0.528356	+	0.849023i	$0.677192\pi$
$128$		0			0
$129$	2.29530	−	0.835420i	0.202090	−	0.0735546i
$130$		0			0
$131$	−1.07527	+	0.902259i	−0.0939468	+	0.0788307i	−0.688551	−	0.725188i	$-0.741753\pi$
$131$	−1.07527	+	0.902259i	−0.0939468	+	0.0788307i	0.594605	+	0.804018i	$0.297309\pi$
$132$		0			0
$133$	0.0706586	+	0.400725i	0.00612687	+	0.0347472i
$134$		0			0
$135$	−3.90168	−	3.27390i	−0.335803	−	0.281772i
$136$		0			0
$137$	−6.20963	−	10.7554i	−0.530525	−	0.918896i	−0.999366	−	0.0356133i	$-0.988662\pi$
$137$	−6.20963	−	10.7554i	−0.530525	−	0.918896i	0.468841	−	0.883283i	$-0.344672\pi$
$138$		0			0
$139$	−14.0949	+	11.8270i	−1.19551	+	1.00315i	−0.195766	+	0.980651i	$0.562719\pi$
$139$	−14.0949	+	11.8270i	−1.19551	+	1.00315i	−0.999747	+	0.0225036i	$0.992836\pi$
$140$		0			0
$141$	−2.69466	+	15.2821i	−0.226931	+	1.28699i
$142$		0			0
$143$	−1.12500	+	6.38018i	−0.0940770	+	0.533537i
$144$		0			0
$145$	1.36794	−	0.497888i	0.113601	−	0.0413473i
$146$		0			0
$147$	−21.3841			−1.76373
$148$		0			0
$149$	12.4068			1.01640			0.508201	−	0.861238i	$-0.330311\pi$
$149$	12.4068			1.01640			0.508201	+	0.861238i	$0.330311\pi$
$150$		0			0
$151$	−11.7921	+	4.29198i	−0.959628	+	0.349276i	−0.773888	−	0.633323i	$-0.781691\pi$
$151$	−11.7921	+	4.29198i	−0.959628	+	0.349276i	−0.185740	+	0.982599i	$0.559468\pi$
$152$		0			0
$153$	1.35704	−	7.69616i	0.109710	−	0.622198i
$154$		0			0
$155$	3.39126	−	19.2328i	0.272393	−	1.54482i
$156$		0			0
$157$	2.69131	−	2.25828i	0.214790	−	0.180230i	−0.529045	−	0.848594i	$-0.677450\pi$
$157$	2.69131	−	2.25828i	0.214790	−	0.180230i	0.743834	+	0.668364i	$0.233005\pi$
$158$		0			0
$159$	0.893002	+	1.54672i	0.0708197	+	0.122663i
$160$		0			0
$161$	−29.9041	−	25.0925i	−2.35677	−	1.97756i
$162$		0			0
$163$	0.415269	+	2.35511i	0.0325264	+	0.184466i	0.996742	−	0.0806519i	$-0.0257002\pi$
$163$	0.415269	+	2.35511i	0.0325264	+	0.184466i	−0.964216	+	0.265118i	$0.914589\pi$
$164$		0			0
$165$	−10.4938	+	8.80536i	−0.816943	+	0.685497i
$166$		0			0
$167$	−14.6442	+	5.33004i	−1.13320	+	0.412451i	−0.839453	−	0.543433i	$-0.817124\pi$
$167$	−14.6442	+	5.33004i	−1.13320	+	0.412451i	−0.293746	+	0.955884i	$0.594902\pi$
$168$		0			0
$169$	−1.60477	−	9.10110i	−0.123444	−	0.700085i
$170$		0			0
$171$	−0.0872283	+	0.151084i	−0.00667051	+	0.0115537i
$172$		0			0
$173$	16.7991	+	6.11436i	1.27721	+	0.464866i	0.889508	−	0.456919i	$-0.151047\pi$
$173$	16.7991	+	6.11436i	1.27721	+	0.464866i	0.387701	+	0.921785i	$0.373269\pi$
$174$		0			0
$175$	3.00868	−	5.21118i	0.227435	−	0.393928i
$176$		0			0
$177$	−8.83294	−	15.2991i	−0.663925	−	1.14995i
$178$		0			0
$179$	20.4063			1.52524			0.762619	−	0.646848i	$-0.223913\pi$
$179$	20.4063			1.52524			0.762619	+	0.646848i	$0.223913\pi$
$180$		0			0
$181$	−14.0006	−	11.7479i	−1.04065	−	0.873212i	−0.0485737	−	0.998820i	$-0.515468\pi$
$181$	−14.0006	−	11.7479i	−1.04065	−	0.873212i	−0.992080	+	0.125607i	$0.959912\pi$
$182$		0			0
$183$	−21.9329	−	7.98293i	−1.62133	−	0.590115i
$184$		0			0
$185$	−8.06062	−	8.10640i	−0.592629	−	0.595994i
$186$		0			0
$187$	13.9632	+	5.08218i	1.02109	+	0.371646i
$188$		0			0
$189$	8.51024	+	7.14094i	0.619029	+	0.519427i
$190$		0			0
$191$	−5.76567			−0.417189			−0.208595	−	0.978002i	$-0.566889\pi$
$191$	−5.76567			−0.417189			−0.208595	+	0.978002i	$0.566889\pi$
$192$		0			0
$193$	0.179712	+	0.311271i	0.0129360	+	0.0224057i	0.872421	−	0.488755i	$-0.162549\pi$
$193$	0.179712	+	0.311271i	0.0129360	+	0.0224057i	−0.859485	+	0.511161i	$0.829216\pi$
$194$		0			0
$195$	−3.97359	+	6.88246i	−0.284555	+	0.492863i
$196$		0			0
$197$	−6.54591	−	2.38251i	−0.466376	−	0.169747i	0.0981338	−	0.995173i	$-0.468713\pi$
$197$	−6.54591	−	2.38251i	−0.466376	−	0.169747i	−0.564510	+	0.825426i	$0.690935\pi$
$198$		0			0
$199$	5.58897	−	9.68037i	0.396191	−	0.686223i	−0.597061	−	0.802196i	$-0.703665\pi$
$199$	5.58897	−	9.68037i	0.396191	−	0.686223i	0.993252	+	0.115972i	$0.0369984\pi$
$200$		0			0
$201$	4.98683	+	28.2817i	0.351744	+	1.99484i
$202$		0			0
$203$	−2.98370	+	1.08598i	−0.209415	+	0.0762208i
$204$		0			0
$205$	−8.19823	+	6.87913i	−0.572589	+	0.480459i
$206$		0			0
$207$	−2.90629	−	16.4824i	−0.202001	−	1.14561i
$208$		0			0
$209$	−0.254107	−	0.213221i	−0.0175770	−	0.0147488i
$210$		0			0
$211$	−6.10513	−	10.5744i	−0.420295	−	0.727972i	0.575673	−	0.817680i	$-0.304740\pi$
$211$	−6.10513	−	10.5744i	−0.420295	−	0.727972i	−0.995968	+	0.0897080i	$0.971407\pi$
$212$		0			0
$213$	−4.96778	+	4.16846i	−0.340387	+	0.285618i
$214$		0			0
$215$	−0.365468	+	2.07267i	−0.0249247	+	0.141355i
$216$		0			0
$217$	−7.39693	+	41.9501i	−0.502137	+	2.84776i
$218$		0			0
$219$	−5.24172	+	1.90783i	−0.354203	+	0.128919i
$220$		0			0
$221$	8.62048			0.579876
$222$		0			0
$223$	10.7545			0.720177			0.360088	−	0.932918i	$-0.382747\pi$
$223$	10.7545			0.720177			0.360088	+	0.932918i	$0.382747\pi$
$224$		0			0
$225$	2.42429	−	0.882369i	0.161619	−	0.0588246i
$226$		0			0
$227$	0.514913	−	2.92021i	0.0341759	−	0.193821i	−0.962940	−	0.269716i	$-0.913070\pi$
$227$	0.514913	−	2.92021i	0.0341759	−	0.193821i	0.997116	+	0.0758946i	$0.0241813\pi$
$228$		0			0
$229$	−0.526610	+	2.98655i	−0.0347994	+	0.197357i	−0.997251	−	0.0740958i	$-0.976393\pi$
$229$	−0.526610	+	2.98655i	−0.0347994	+	0.197357i	0.962452	+	0.271453i	$0.0875041\pi$
$230$		0			0
$231$	22.8888	−	19.2060i	1.50597	−	1.26366i
$232$		0			0
$233$	0.144403	+	0.250113i	0.00946016	+	0.0163855i	0.870717	−	0.491785i	$-0.163655\pi$
$233$	0.144403	+	0.250113i	0.00946016	+	0.0163855i	−0.861257	+	0.508170i	$0.830322\pi$
$234$		0			0
$235$	−10.2427	−	8.59461i	−0.668157	−	0.560651i
$236$		0			0
$237$	−2.05878	−	11.6759i	−0.133732	−	0.758433i
$238$		0			0
$239$	3.85711	−	3.23650i	0.249496	−	0.209352i	−0.509460	−	0.860495i	$-0.670155\pi$
$239$	3.85711	−	3.23650i	0.249496	−	0.209352i	0.758955	+	0.651143i	$0.225710\pi$
$240$		0			0
$241$	16.3281	−	5.94293i	1.05178	−	0.382818i	0.242448	−	0.970164i	$-0.422050\pi$
$241$	16.3281	−	5.94293i	1.05178	−	0.382818i	0.809336	+	0.587347i	$0.199827\pi$
$242$		0			0
$243$	2.82410	+	16.0162i	0.181166	+	1.02744i
$244$		0			0
$245$	9.21271	−	15.9569i	0.588578	−	1.01945i
$246$		0			0
$247$	−0.180835	−	0.0658185i	−0.0115062	−	0.00418793i
$248$		0			0
$249$	−0.717878	+	1.24340i	−0.0454937	+	0.0787974i
$250$		0			0
$251$	−0.877844	−	1.52047i	−0.0554090	−	0.0959713i	0.836990	−	0.547218i	$-0.184313\pi$
$251$	−0.877844	−	1.52047i	−0.0554090	−	0.0959713i	−0.892399	+	0.451246i	$0.850980\pi$
$252$		0			0
$253$	31.8232			2.00071
$254$		0			0
$255$	13.9632	+	11.7165i	0.874407	+	0.733715i
$256$		0			0
$257$	11.9849	+	4.36215i	0.747598	+	0.272103i	0.687595	−	0.726095i	$-0.258667\pi$
$257$	11.9849	+	4.36215i	0.747598	+	0.272103i	0.0600034	+	0.998198i	$0.480889\pi$
$258$		0			0
$259$	17.5816	+	17.6815i	1.09247	+	1.09867i
$260$		0			0
$261$	−1.27923	−	0.465601i	−0.0791823	−	0.0288200i
$262$		0			0
$263$	20.1968	+	16.9472i	1.24539	+	1.04501i	0.997083	+	0.0763250i	$0.0243187\pi$
$263$	20.1968	+	16.9472i	1.24539	+	1.04501i	0.248307	+	0.968681i	$0.420126\pi$
$264$		0			0
$265$	−1.53889			−0.0945334
$266$		0			0
$267$	3.84457	+	6.65898i	0.235284	+	0.407523i
$268$		0			0
$269$	−6.80289	+	11.7829i	−0.414779	+	0.718419i	−0.995405	−	0.0957514i	$-0.969475\pi$
$269$	−6.80289	+	11.7829i	−0.414779	+	0.718419i	0.580626	+	0.814171i	$0.302808\pi$
$270$		0			0
$271$	−4.05562	−	1.47612i	−0.246361	−	0.0896682i	0.215888	−	0.976418i	$-0.430735\pi$
$271$	−4.05562	−	1.47612i	−0.246361	−	0.0896682i	−0.462249	+	0.886750i	$0.652958\pi$
$272$		0			0
$273$	8.66709	−	15.0118i	0.524556	−	0.908558i
$274$		0			0
$275$	0.851812	+	4.83087i	0.0513662	+	0.291312i
$276$		0			0
$277$	3.28276	−	1.19483i	0.197242	−	0.0717902i	−0.241510	−	0.970398i	$-0.577643\pi$
$277$	3.28276	−	1.19483i	0.197242	−	0.0717902i	0.438752	+	0.898608i	$0.355421\pi$
$278$		0			0
$279$	−13.9903	+	11.7393i	−0.837580	+	0.702813i
$280$		0			0
$281$	−1.27419	−	7.22628i	−0.0760116	−	0.431083i	−0.998937	−	0.0461037i	$-0.985320\pi$
$281$	−1.27419	−	7.22628i	−0.0760116	−	0.431083i	0.922925	−	0.384980i	$-0.125792\pi$
$282$		0			0
$283$	−10.7268	−	9.00087i	−0.637643	−	0.535046i	0.265650	−	0.964070i	$-0.414413\pi$
$283$	−10.7268	−	9.00087i	−0.637643	−	0.535046i	−0.903294	+	0.429023i	$0.858858\pi$
$284$		0			0
$285$	−0.203453	−	0.352391i	−0.0120515	−	0.0208739i
$286$		0			0
$287$	17.8817	−	15.0046i	1.05553	−	0.885691i
$288$		0			0
$289$	0.481334	−	2.72978i	0.0283138	−	0.160575i
$290$		0			0
$291$	−1.37119	+	7.77641i	−0.0803807	+	0.455861i
$292$		0			0
$293$	23.7505	−	8.64447i	1.38752	−	0.505015i	0.463070	−	0.886322i	$-0.346748\pi$
$293$	23.7505	−	8.64447i	1.38752	−	0.505015i	0.924449	+	0.381306i	$0.124526\pi$
$294$		0			0
$295$	15.2216			0.886238
$296$		0			0
$297$	−9.05640			−0.525506
$298$		0			0
$299$	17.3486	−	6.31436i	1.00329	−	0.365169i
$300$		0			0
$301$	0.797148	−	4.52085i	0.0459469	−	0.260578i
$302$		0			0
$303$	−1.49537	+	8.48069i	−0.0859070	+	0.487203i
$304$		0			0
$305$	15.4060	−	12.9272i	0.882146	−	0.740209i
$306$		0			0
$307$	−12.2995	−	21.3034i	−0.701972	−	1.21585i	−0.967773	−	0.251823i	$-0.918970\pi$
$307$	−12.2995	−	21.3034i	−0.701972	−	1.21585i	0.265801	−	0.964028i	$-0.414363\pi$
$308$		0			0
$309$	−3.30633	−	2.77434i	−0.188091	−	0.157827i
$310$		0			0
$311$	−0.904212	−	5.12804i	−0.0512732	−	0.290785i	0.948380	−	0.317138i	$-0.102722\pi$
$311$	−0.904212	−	5.12804i	−0.0512732	−	0.290785i	−0.999653	+	0.0263531i	$0.991611\pi$
$312$		0			0
$313$	5.54340	−	4.65147i	0.313332	−	0.262916i	−0.472536	−	0.881311i	$-0.656661\pi$
$313$	5.54340	−	4.65147i	0.313332	−	0.262916i	0.785867	+	0.618395i	$0.212217\pi$
$314$		0			0
$315$	12.7235	−	4.63097i	0.716887	−	0.260926i
$316$		0			0
$317$	−2.31803	−	13.1462i	−0.130194	−	0.738365i	−0.978087	−	0.208198i	$-0.933240\pi$
$317$	−2.31803	−	13.1462i	−0.130194	−	0.738365i	0.847893	−	0.530167i	$-0.177871\pi$
$318$		0			0
$319$	1.29422	−	2.24165i	0.0724624	−	0.125508i
$320$		0			0
$321$	−16.9070	−	6.15366i	−0.943659	−	0.343464i
$322$		0			0
$323$	−0.220690	+	0.382246i	−0.0122795	+	0.0212688i
$324$		0			0
$325$	1.42291	+	2.46455i	0.0789288	+	0.136709i
$326$		0			0
$327$	19.1606			1.05958
$328$		0			0
$329$	22.3410	+	18.7463i	1.23170	+	1.03352i
$330$		0			0
$331$	−4.29733	−	1.56410i	−0.236203	−	0.0859708i	0.221207	−	0.975227i	$-0.429000\pi$
$331$	−4.29733	−	1.56410i	−0.236203	−	0.0859708i	−0.457410	+	0.889256i	$0.651223\pi$
$332$		0			0
$333$	0.901584	+	10.6525i	0.0494065	+	0.583751i
$334$		0			0
$335$	−23.2523	−	8.46314i	−1.27041	−	0.462391i
$336$		0			0
$337$	2.49218	+	2.09118i	0.135757	+	0.113914i	0.708138	−	0.706074i	$-0.249536\pi$
$337$	2.49218	+	2.09118i	0.135757	+	0.113914i	−0.572380	+	0.819988i	$0.693980\pi$
$338$		0			0
$339$	−21.7613			−1.18191
$340$		0			0
$341$	−17.3628	−	30.0732i	−0.940248	−	1.62856i
$342$		0			0
$343$	−5.74708	+	9.95424i	−0.310313	+	0.537479i
$344$		0			0
$345$	36.6827	+	13.3514i	1.97493	+	0.718817i
$346$		0			0
$347$	12.2387	−	21.1981i	0.657008	−	1.13797i	−0.324379	−	0.945927i	$-0.605155\pi$
$347$	12.2387	−	21.1981i	0.657008	−	1.13797i	0.981386	−	0.192044i	$-0.0615115\pi$
$348$		0			0
$349$	0.990209	+	5.61576i	0.0530047	+	0.300604i	0.999773	−	0.0213116i	$-0.00678421\pi$
$349$	0.990209	+	5.61576i	0.0530047	+	0.300604i	−0.946768	+	0.321916i	$0.895673\pi$
$350$		0			0
$351$	−4.93713	+	1.79697i	−0.263525	+	0.0959152i
$352$		0			0
$353$	18.7175	−	15.7059i	0.996233	−	0.835939i	0.00977486	−	0.999952i	$-0.496889\pi$
$353$	18.7175	−	15.7059i	0.996233	−	0.835939i	0.986458	+	0.164014i	$0.0524441\pi$
$354$		0			0
$355$	−0.970296	−	5.50282i	−0.0514980	−	0.292059i
$356$		0			0
$357$	−30.4561	−	25.5557i	−1.61191	−	1.35255i
$358$		0			0
$359$	9.35461	+	16.2027i	0.493717	+	0.855144i	0.999974	−	0.00723934i	$-0.00230437\pi$
$359$	9.35461	+	16.2027i	0.493717	+	0.855144i	−0.506256	+	0.862383i	$0.668971\pi$
$360$		0			0
$361$	−14.5473	+	12.2066i	−0.765647	+	0.642454i
$362$		0			0
$363$	−0.0633635	+	0.359352i	−0.00332572	+	0.0188611i
$364$		0			0
$365$	0.834611	−	4.73331i	0.0436855	−	0.247753i
$366$		0			0
$367$	31.6892	−	11.5339i	1.65416	−	0.602067i	0.664735	−	0.747080i	$-0.268545\pi$
$367$	31.6892	−	11.5339i	1.65416	−	0.602067i	0.989430	+	0.145013i	$0.0463224\pi$
$368$		0			0
$369$	10.0080			0.520997
$370$		0			0
$371$	3.35659			0.174265
$372$		0			0
$373$	−29.5389	+	10.7513i	−1.52947	+	0.556681i	−0.963491	−	0.267740i	$-0.913723\pi$
$373$	−29.5389	+	10.7513i	−1.52947	+	0.556681i	−0.565977	+	0.824421i	$0.691501\pi$
$374$		0			0
$375$	−4.60405	+	26.1109i	−0.237752	+	1.34836i
$376$		0			0
$377$	0.260760	−	1.47885i	0.0134298	−	0.0761644i
$378$		0			0
$379$	−5.33697	+	4.47825i	−0.274142	+	0.230032i	−0.769485	−	0.638665i	$-0.779487\pi$
$379$	−5.33697	+	4.47825i	−0.274142	+	0.230032i	0.495343	+	0.868697i	$0.335042\pi$
$380$		0			0
$381$	18.2972	+	31.6916i	0.937393	+	1.62361i
$382$		0			0
$383$	2.20412	+	1.84948i	0.112625	+	0.0945038i	0.697361	−	0.716720i	$-0.254357\pi$
$383$	2.20412	+	1.84948i	0.112625	+	0.0945038i	−0.584736	+	0.811224i	$0.698802\pi$
$384$		0			0
$385$	4.47060	+	25.3540i	0.227843	+	1.29216i
$386$		0			0
$387$	1.50770	−	1.26511i	0.0766408	−	0.0643093i
$388$		0			0
$389$	11.0993	−	4.03981i	0.562756	−	0.204827i	−0.0449488	−	0.998989i	$-0.514312\pi$
$389$	11.0993	−	4.03981i	0.562756	−	0.204827i	0.607705	+	0.794163i	$0.292090\pi$
$390$		0			0
$391$	−7.35300	−	41.7009i	−0.371857	−	2.10891i
$392$		0			0
$393$	−1.53082	+	2.65146i	−0.0772196	+	0.133748i
$394$		0			0
$395$	9.59957	+	3.49396i	0.483007	+	0.175800i
$396$		0			0
$397$	15.6563	−	27.1174i	0.785765	−	1.36098i	−0.142776	−	0.989755i	$-0.545603\pi$
$397$	15.6563	−	27.1174i	0.785765	−	1.36098i	0.928541	−	0.371230i	$-0.121064\pi$
$398$		0			0
$399$	0.443767	+	0.768626i	0.0222161	+	0.0384794i
$400$		0			0
$401$	−14.0281			−0.700531			−0.350266	−	0.936650i	$-0.613909\pi$
$401$	−14.0281			−0.700531			−0.350266	+	0.936650i	$0.613909\pi$
$402$		0			0
$403$	−15.4325	−	12.9494i	−0.768749	−	0.645057i
$404$		0			0
$405$	−19.7509	−	7.18874i	−0.981430	−	0.357211i
$406$		0			0
$407$	−20.2446	−	1.82895i	−1.00349	−	0.0906577i
$408$		0			0
$409$	0.0761808	+	0.0277275i	0.00376690	+	0.00137104i	0.343903	−	0.939005i	$-0.388251\pi$
$409$	0.0761808	+	0.0277275i	0.00376690	+	0.00137104i	−0.340136	+	0.940376i	$0.610473\pi$
$410$		0			0
$411$	−20.7510	−	17.4122i	−1.02357	−	0.858880i
$412$		0			0
$413$	−33.2010			−1.63372
$414$		0			0
$415$	−0.618553	−	1.07136i	−0.0303636	−	0.0525912i
$416$		0			0
$417$	−20.0663	+	34.7559i	−0.982652	+	1.70200i
$418$		0			0
$419$	4.35652	+	1.58564i	0.212830	+	0.0774637i	0.446235	−	0.894916i	$-0.352765\pi$
$419$	4.35652	+	1.58564i	0.212830	+	0.0774637i	−0.233405	+	0.972380i	$0.574987\pi$
$420$		0			0
$421$	9.66110	−	16.7335i	0.470853	−	0.815542i	−0.528591	−	0.848877i	$-0.677279\pi$
$421$	9.66110	−	16.7335i	0.470853	−	0.815542i	0.999444	+	0.0333350i	$0.0106128\pi$
$422$		0			0
$423$	2.17126	+	12.3138i	0.105570	+	0.598719i
$424$		0			0
$425$	6.13352	−	2.23242i	0.297519	−	0.108288i
$426$		0			0
$427$	−33.6032	+	28.1964i	−1.62617	+	1.36452i
$428$		0			0
$429$	2.45381	+	13.9163i	0.118471	+	0.671884i
$430$		0			0
$431$	−5.77729	−	4.84772i	−0.278282	−	0.233507i	0.492954	−	0.870055i	$-0.335917\pi$
$431$	−5.77729	−	4.84772i	−0.278282	−	0.233507i	−0.771237	+	0.636549i	$0.780361\pi$
$432$		0			0
$433$	−14.9169	−	25.8369i	−0.716863	−	1.24164i	−0.962237	−	0.272214i	$-0.912244\pi$
$433$	−14.9169	−	25.8369i	−0.716863	−	1.24164i	0.245374	−	0.969428i	$-0.421089\pi$
$434$		0			0
$435$	2.43234	−	2.04097i	0.116622	−	0.0978571i
$436$		0			0
$437$	−0.164146	+	0.930916i	−0.00785215	+	0.0445317i
$438$		0			0
$439$	−3.81229	+	21.6206i	−0.181951	+	1.03189i	0.747860	+	0.663856i	$0.231081\pi$
$439$	−3.81229	+	21.6206i	−0.181951	+	1.03189i	−0.929811	+	0.368038i	$0.880030\pi$
$440$		0			0
$441$	−16.1915	+	5.89321i	−0.771022	+	0.280629i
$442$		0			0
$443$	34.6241			1.64504			0.822520	−	0.568736i	$-0.192567\pi$
$443$	34.6241			1.64504			0.822520	+	0.568736i	$0.192567\pi$
$444$		0			0
$445$	−6.62526			−0.314068
$446$		0			0
$447$	25.4293	−	9.25552i	1.20277	−	0.437771i
$448$		0			0
$449$	−3.46279	+	19.6385i	−0.163419	+	0.926796i	0.787260	+	0.616621i	$0.211499\pi$
$449$	−3.46279	+	19.6385i	−0.163419	+	0.926796i	−0.950679	+	0.310175i	$0.899612\pi$
$450$		0			0
$451$	−3.30441	+	18.7403i	−0.155599	+	0.882444i
$452$		0			0
$453$	−20.9676	+	17.5939i	−0.985146	+	0.826635i
$454$		0			0
$455$	7.46791	+	12.9348i	0.350101	+	0.606393i
$456$		0			0
$457$	24.6964	+	20.7227i	1.15525	+	0.969368i	0.999829	−	0.0184812i	$-0.00588309\pi$
$457$	24.6964	+	20.7227i	1.15525	+	0.969368i	0.155418	+	0.987849i	$0.450328\pi$
$458$		0			0
$459$	2.09255	+	11.8674i	0.0976719	+	0.553925i
$460$		0			0
$461$	5.61373	−	4.71048i	0.261458	−	0.219389i	−0.502630	−	0.864502i	$-0.667634\pi$
$461$	5.61373	−	4.71048i	0.261458	−	0.219389i	0.764087	+	0.645113i	$0.223190\pi$
$462$		0			0
$463$	6.09514	−	2.21845i	0.283265	−	0.103100i	−0.196480	−	0.980508i	$-0.562951\pi$
$463$	6.09514	−	2.21845i	0.283265	−	0.103100i	0.479745	+	0.877408i	$0.340729\pi$
$464$		0			0
$465$	−7.39693	−	41.9501i	−0.343025	−	1.94539i
$466$		0			0
$467$	−5.99288	+	10.3800i	−0.277317	+	0.480328i	−0.970717	−	0.240225i	$-0.922779\pi$
$467$	−5.99288	+	10.3800i	−0.277317	+	0.480328i	0.693400	+	0.720553i	$0.256112\pi$
$468$		0			0
$469$	50.7172	+	18.4596i	2.34190	+	0.852383i
$470$		0			0
$471$	3.83151	−	6.63637i	0.176547	−	0.305788i
$472$		0			0
$473$	1.87114	+	3.24091i	0.0860352	+	0.149017i
$474$		0			0
$475$	−0.145710			−0.00668562
$476$		0			0
$477$	1.10241	+	0.925036i	0.0504761	+	0.0423545i
$478$		0			0
$479$	21.3237	+	7.76119i	0.974305	+	0.354618i	0.779623	−	0.626249i	$-0.215410\pi$
$479$	21.3237	+	7.76119i	0.974305	+	0.354618i	0.194681	+	0.980867i	$0.437633\pi$
$480$		0			0
$481$	−11.3993	+	3.01988i	−0.519765	+	0.137694i
$482$		0			0
$483$	−80.0114	−	29.1218i	−3.64064	−	1.32509i
$484$		0			0
$485$	−5.21204	−	4.37342i	−0.236666	−	0.198587i
$486$		0			0
$487$	−12.3108			−0.557856			−0.278928	−	0.960312i	$-0.589979\pi$
$487$	−12.3108			−0.557856			−0.278928	+	0.960312i	$0.589979\pi$
$488$		0			0
$489$	2.60807	+	4.51731i	0.117941	+	0.204280i
$490$		0			0
$491$	0.575398	−	0.996619i	0.0259674	−	0.0449768i	−0.852750	−	0.522320i	$-0.825067\pi$
$491$	0.575398	−	0.996619i	0.0259674	−	0.0449768i	0.878717	+	0.477343i	$0.158400\pi$
$492$		0			0
$493$	−3.23649	−	1.17798i	−0.145764	−	0.0530538i
$494$		0			0
$495$	−5.51897	+	9.55914i	−0.248059	+	0.429652i
$496$		0			0
$497$	2.11638	+	12.0026i	0.0949327	+	0.538390i
$498$		0			0
$499$	26.2321	−	9.54769i	1.17431	−	0.427413i	0.320120	−	0.947377i	$-0.396277\pi$
$499$	26.2321	−	9.54769i	1.17431	−	0.427413i	0.854189	+	0.519963i	$0.174054\pi$
$500$		0			0
$501$	−26.0389	+	21.8492i	−1.16333	+	0.976151i
$502$		0			0
$503$	2.84222	+	16.1191i	0.126728	+	0.718713i	0.980266	+	0.197682i	$0.0633413\pi$
$503$	2.84222	+	16.1191i	0.126728	+	0.718713i	−0.853538	+	0.521031i	$0.825548\pi$
$504$		0			0
$505$	−5.68407	−	4.76950i	−0.252938	−	0.212240i
$506$		0			0
$507$	−10.0787	−	17.4567i	−0.447609	−	0.775281i
$508$		0			0
$509$	3.32007	−	2.78587i	0.147159	−	0.123481i	−0.566236	−	0.824243i	$-0.691601\pi$
$509$	3.32007	−	2.78587i	0.147159	−	0.123481i	0.713395	+	0.700762i	$0.247156\pi$
$510$		0			0
$511$	−1.82043	+	10.3242i	−0.0805311	+	0.456715i
$512$		0			0
$513$	0.0467133	−	0.264924i	0.00206244	−	0.0116967i
$514$		0			0
$515$	3.49466	−	1.27195i	0.153993	−	0.0560488i
$516$		0			0
$517$	−23.7748			−1.04561
$518$		0			0
$519$	38.9932			1.71161
$520$		0			0
$521$	−1.75997	+	0.640577i	−0.0771057	+	0.0280642i	−0.380285	−	0.924869i	$-0.624174\pi$
$521$	−1.75997	+	0.640577i	−0.0771057	+	0.0280642i	0.303179	+	0.952934i	$0.401952\pi$
$522$		0			0
$523$	−6.43474	+	36.4932i	−0.281371	+	1.59574i	0.436595	+	0.899658i	$0.356184\pi$
$523$	−6.43474	+	36.4932i	−0.281371	+	1.59574i	−0.717966	+	0.696078i	$0.754927\pi$
$524$		0			0
$525$	2.27911	−	12.9255i	0.0994686	−	0.564115i
$526$		0			0
$527$	−35.3960	+	29.7007i	−1.54187	+	1.29378i
$528$		0			0
$529$	−33.8430	−	58.6178i	−1.47144	−	2.54860i
$530$		0			0
$531$	−10.9043	−	9.14980i	−0.473207	−	0.397068i
$532$		0			0
$533$	1.91702	+	10.8720i	0.0830356	+	0.470918i
$534$		0			0
$535$	11.8758	−	9.96494i	0.513434	−	0.430822i
$536$		0			0
$537$	41.8254	−	15.2232i	1.80490	−	0.656929i
$538$		0			0
$539$	−5.68913	−	32.2646i	−0.245048	−	1.38974i
$540$		0			0
$541$	−7.75312	+	13.4288i	−0.333332	+	0.577349i	−0.983163	−	0.182730i	$-0.941506\pi$
$541$	−7.75312	+	13.4288i	−0.333332	+	0.577349i	0.649831	+	0.760079i	$0.274840\pi$
$542$		0			0
$543$	−37.4600	−	13.6343i	−1.60756	−	0.585104i
$544$		0			0
$545$	−8.25476	+	14.2977i	−0.353595	+	0.612445i
$546$		0			0
$547$	−20.5925	−	35.6673i	−0.880472	−	1.52502i	−0.850817	−	0.525462i	$-0.823893\pi$
$547$	−20.5925	−	35.6673i	−0.880472	−	1.52502i	−0.0296544	−	0.999560i	$-0.509441\pi$
$548$		0			0
$549$	−18.8070			−0.802663
$550$		0			0
$551$	0.0588988	+	0.0494220i	0.00250917	+	0.00210545i
$552$		0			0
$553$	−20.9383	−	7.62092i	−0.890388	−	0.324075i
$554$		0			0
$555$	−22.5687	−	10.6019i	−0.957989	−	0.450024i
$556$		0			0
$557$	11.4686	+	4.17423i	0.485940	+	0.176868i	0.573359	−	0.819304i	$-0.305640\pi$
$557$	11.4686	+	4.17423i	0.485940	+	0.176868i	−0.0874196	+	0.996172i	$0.527862\pi$
$558$		0			0
$559$	1.66312	+	1.39553i	0.0703426	+	0.0590245i
$560$		0			0
$561$	32.4107			1.36838
$562$		0			0
$563$	−5.70965	−	9.88940i	−0.240633	−	0.416788i	0.720262	−	0.693702i	$-0.244022\pi$
$563$	−5.70965	−	9.88940i	−0.240633	−	0.416788i	−0.960895	+	0.276914i	$0.910688\pi$
$564$		0			0
$565$	9.37522	−	16.2384i	0.394418	−	0.683153i
$566$		0			0
$567$	43.0801	+	15.6799i	1.80919	+	0.658493i
$568$		0			0
$569$	11.1732	−	19.3526i	0.468406	−	0.811303i	−0.530942	−	0.847408i	$-0.678162\pi$
$569$	11.1732	−	19.3526i	0.468406	−	0.811303i	0.999348	+	0.0361049i	$0.0114951\pi$
$570$		0			0
$571$	2.29253	+	13.0016i	0.0959395	+	0.544100i	0.994455	+	0.105159i	$0.0335352\pi$
$571$	2.29253	+	13.0016i	0.0959395	+	0.544100i	−0.898516	+	0.438941i	$0.855354\pi$
$572$		0			0
$573$	−11.8175	+	4.30122i	−0.493683	+	0.179686i
$574$		0			0
$575$	10.7084	−	8.98540i	0.446571	−	0.374717i
$576$		0			0
$577$	5.09708	+	28.9070i	0.212194	+	1.20341i	0.885709	+	0.464241i	$0.153673\pi$
$577$	5.09708	+	28.9070i	0.212194	+	1.20341i	−0.673515	+	0.739174i	$0.735216\pi$
$578$		0			0
$579$	0.600553	+	0.503924i	0.0249581	+	0.0209424i
$580$		0			0
$581$	1.34917	+	2.33683i	0.0559730	+	0.0969481i
$582$		0			0
$583$	−2.09614	+	1.75887i	−0.0868133	+	0.0728450i
$584$		0			0
$585$	−1.11197	+	6.30628i	−0.0459742	+	0.260733i
$586$		0			0
$587$	3.68838	−	20.9178i	0.152236	−	0.863371i	−0.809034	−	0.587762i	$-0.800009\pi$
$587$	3.68838	−	20.9178i	0.152236	−	0.863371i	0.961270	−	0.275609i	$-0.0888797\pi$
$588$		0			0
$589$	0.969282	−	0.352790i	0.0399386	−	0.0145365i
$590$		0			0
$591$	−15.1941			−0.625000
$592$		0			0
$593$	31.4119			1.28993			0.644965	−	0.764212i	$-0.276872\pi$
$593$	31.4119			1.28993			0.644965	+	0.764212i	$0.276872\pi$
$594$		0			0
$595$	32.1908	−	11.7165i	1.31969	−	0.480329i
$596$		0			0
$597$	4.23372	−	24.0106i	0.173274	−	0.982688i
$598$		0			0
$599$	3.52563	−	19.9949i	0.144053	−	0.816967i	−0.824069	−	0.566490i	$-0.808301\pi$
$599$	3.52563	−	19.9949i	0.144053	−	0.816967i	0.968122	−	0.250478i	$-0.0805877\pi$
$600$		0			0
$601$	−34.1524	+	28.6573i	−1.39311	+	1.16896i	−0.429044	+	0.903284i	$0.641149\pi$
$601$	−34.1524	+	28.6573i	−1.39311	+	1.16896i	−0.964063	+	0.265672i	$0.914406\pi$
$602$		0			0
$603$	11.5700	+	20.0398i	0.471166	+	0.816083i
$604$		0			0
$605$	−0.240851	−	0.202098i	−0.00979199	−	0.00821646i
$606$		0			0
$607$	3.49184	+	19.8032i	0.141730	+	0.803788i	0.969935	+	0.243364i	$0.0782509\pi$
$607$	3.49184	+	19.8032i	0.141730	+	0.803788i	−0.828205	+	0.560425i	$0.810638\pi$
$608$		0			0
$609$	−5.30534	+	4.45171i	−0.214983	+	0.180393i
$610$		0			0
$611$	−12.9609	+	4.71739i	−0.524343	+	0.190845i
$612$		0			0
$613$	5.59486	+	31.7300i	0.225974	+	1.28156i	0.860814	+	0.508920i	$0.169955\pi$
$613$	5.59486	+	31.7300i	0.225974	+	1.28156i	−0.634839	+	0.772644i	$0.718934\pi$
$614$		0			0
$615$	−11.6715	+	20.2156i	−0.470639	+	0.815172i
$616$		0			0
$617$	−36.5834	−	13.3153i	−1.47279	−	0.536052i	−0.523934	−	0.851759i	$-0.675536\pi$
$617$	−36.5834	−	13.3153i	−1.47279	−	0.536052i	−0.948857	+	0.315707i	$0.897758\pi$
$618$		0			0
$619$	−13.1812	+	22.8305i	−0.529796	+	0.917634i	0.469600	+	0.882879i	$0.344398\pi$
$619$	−13.1812	+	22.8305i	−0.529796	+	0.917634i	−0.999396	+	0.0347545i	$0.988935\pi$
$620$		0			0
$621$	12.9039	+	22.3503i	0.517817	+	0.896885i
$622$		0			0
$623$	14.4508			0.578961
$624$		0			0
$625$	−11.8780	−	9.96686i	−0.475122	−	0.398674i
$626$		0			0
$627$	−0.679890	−	0.247460i	−0.0271522	−	0.00988259i
$628$		0			0
$629$	2.28103	+	26.9510i	0.0909507	+	1.07461i
$630$		0			0
$631$	38.8218	+	14.1300i	1.54547	+	0.562506i	0.967350	−	0.253445i	$-0.0815636\pi$
$631$	38.8218	+	14.1300i	1.54547	+	0.562506i	0.578122	+	0.815950i	$0.303786\pi$
$632$		0			0
$633$	−20.4018	−	17.1192i	−0.810900	−	0.680426i
$634$		0			0
$635$	−31.5312			−1.25128
$636$		0			0
$637$	−9.50340	−	16.4604i	−0.376538	−	0.652184i
$638$		0			0
$639$	−2.61268	+	4.52530i	−0.103356	+	0.179018i
$640$		0			0
$641$	41.1013	+	14.9596i	1.62340	+	0.590871i	0.984026	−	0.178023i	$-0.0569701\pi$
$641$	41.1013	+	14.9596i	1.62340	+	0.590871i	0.639377	+	0.768893i	$0.279192\pi$
$642$		0			0
$643$	−1.65777	+	2.87133i	−0.0653759	+	0.113234i	−0.896861	−	0.442313i	$-0.854158\pi$
$643$	−1.65777	+	2.87133i	−0.0653759	+	0.113234i	0.831485	+	0.555548i	$0.187491\pi$
$644$		0			0
$645$	0.797148	+	4.52085i	0.0313877	+	0.178008i
$646$		0			0
$647$	−21.4630	+	7.81189i	−0.843797	+	0.307117i	−0.727509	−	0.686099i	$-0.759322\pi$
$647$	−21.4630	+	7.81189i	−0.843797	+	0.307117i	−0.116288	+	0.993216i	$0.537100\pi$
$648$		0			0
$649$	20.7335	−	17.3975i	0.813863	−	0.682912i
$650$		0			0
$651$	16.1340	+	91.5004i	0.632341	+	3.58618i
$652$		0			0
$653$	1.62966	+	1.36745i	0.0637735	+	0.0535124i	0.674117	−	0.738624i	$-0.264524\pi$
$653$	1.62966	+	1.36745i	0.0637735	+	0.0535124i	−0.610344	+	0.792137i	$0.708969\pi$
$654$		0			0
$655$	−1.31901	−	2.28460i	−0.0515382	−	0.0892667i
$656$		0			0
$657$	−3.44311	+	2.88911i	−0.134328	+	0.112715i
$658$		0			0
$659$	1.48751	−	8.43610i	0.0579452	−	0.328624i	−0.942031	−	0.335526i	$-0.891086\pi$
$659$	1.48751	−	8.43610i	0.0579452	−	0.328624i	0.999976	+	0.00690225i	$0.00219707\pi$
$660$		0			0
$661$	0.139199	−	0.789436i	0.00541421	−	0.0307055i	−0.981981	−	0.188980i	$-0.939482\pi$
$661$	0.139199	−	0.789436i	0.00541421	−	0.0307055i	0.987395	+	0.158274i	$0.0505930\pi$
$662$		0			0
$663$	17.6688	−	6.43092i	0.686200	−	0.249756i
$664$		0			0
$665$	−0.764734			−0.0296551
$666$		0			0
$667$	−7.37622			−0.285609
$668$		0			0
$669$	22.0428	−	8.02294i	0.852225	−	0.310185i
$670$		0			0
$671$	6.20962	−	35.2165i	0.239720	−	1.35952i
$672$		0			0
$673$	7.47353	−	42.3845i	0.288083	−	1.63380i	−0.405976	−	0.913884i	$-0.633068\pi$
$673$	7.47353	−	42.3845i	0.288083	−	1.63380i	0.694059	−	0.719918i	$-0.255821\pi$
$674$		0			0
$675$	−3.04744	+	2.55711i	−0.117296	+	0.0984231i
$676$		0			0
$677$	−9.99716	−	17.3156i	−0.384222	−	0.665492i	0.607439	−	0.794367i	$-0.292197\pi$
$677$	−9.99716	−	17.3156i	−0.384222	−	0.665492i	−0.991661	+	0.128874i	$0.958864\pi$
$678$		0			0
$679$	11.3684	+	9.53918i	0.436277	+	0.366080i
$680$		0			0
$681$	−1.12311	−	6.36949i	−0.0430378	−	0.244079i
$682$		0			0
$683$	−28.2126	+	23.6732i	−1.07953	+	0.905830i	−0.995881	−	0.0906653i	$-0.971101\pi$
$683$	−28.2126	+	23.6732i	−1.07953	+	0.905830i	−0.0836451	+	0.996496i	$0.526656\pi$
$684$		0			0
$685$	21.9330	−	7.98295i	0.838016	−	0.305013i
$686$		0			0
$687$	1.14863	+	6.51419i	0.0438228	+	0.248532i
$688$		0			0
$689$	−0.793725	+	1.37477i	−0.0302385	+	0.0523746i
$690$		0			0
$691$	0.825837	+	0.300580i	0.0314163	+	0.0114346i	0.357681	−	0.933844i	$-0.383568\pi$
$691$	0.825837	+	0.300580i	0.0314163	+	0.0114346i	−0.326264	+	0.945279i	$0.605790\pi$
$692$		0			0
$693$	12.0378	−	20.8501i	0.457280	−	0.792031i
$694$		0			0
$695$	−17.2899	−	29.9471i	−0.655845	−	1.13596i
$696$		0			0
$697$	25.3206			0.959087
$698$		0			0
$699$	0.482559	+	0.404915i	0.0182521	+	0.0153153i
$700$		0			0
$701$	19.5851	+	7.12840i	0.739719	+	0.269236i	0.684273	−	0.729226i	$-0.260120\pi$
$701$	19.5851	+	7.12840i	0.739719	+	0.269236i	0.0554462	+	0.998462i	$0.482342\pi$
$702$		0			0
$703$	0.157924	−	0.582776i	0.00595623	−	0.0219798i
$704$		0			0
$705$	−27.4053	−	9.97471i	−1.03214	−	0.375669i
$706$		0			0
$707$	12.3979	+	10.4031i	0.466273	+	0.391249i
$708$		0			0
$709$	−21.6348			−0.812512			−0.406256	−	0.913759i	$-0.633166\pi$
$709$	−21.6348			−0.812512			−0.406256	+	0.913759i	$0.633166\pi$
$710$		0			0
$711$	−4.77660	−	8.27331i	−0.179136	−	0.310273i
$712$		0			0
$713$	−49.4784	+	85.6991i	−1.85298	+	3.20946i
$714$		0			0
$715$	−11.4415	−	4.16437i	−0.427888	−	0.155738i
$716$		0			0
$717$	5.49121	−	9.51105i	0.205073	−	0.355197i
$718$		0			0
$719$	−4.46063	−	25.2975i	−0.166353	−	0.943437i	−0.947658	−	0.319287i	$-0.896557\pi$
$719$	−4.46063	−	25.2975i	−0.166353	−	0.943437i	0.781305	−	0.624150i	$-0.214555\pi$
$720$		0			0
$721$	−7.62245	+	2.77434i	−0.283875	+	0.103322i
$722$		0			0
$723$	29.0331	−	24.3616i	1.07975	−	0.906019i
$724$		0			0
$725$	−0.197439	−	1.11973i	−0.00733272	−	0.0415859i
$726$		0			0
$727$	−20.4343	−	17.1464i	−0.757868	−	0.635927i	0.179703	−	0.983721i	$-0.442486\pi$
$727$	−20.4343	−	17.1464i	−0.757868	−	0.635927i	−0.937571	+	0.347794i	$0.886931\pi$
$728$		0			0
$729$	0.961018	+	1.66453i	0.0355933	+	0.0616493i
$730$		0			0
$731$	3.81453	−	3.20077i	0.141086	−	0.118385i
$732$		0			0
$733$	−1.97614	+	11.2073i	−0.0729906	+	0.413950i	0.926317	+	0.376745i	$0.122957\pi$
$733$	−1.97614	+	11.2073i	−0.0729906	+	0.413950i	−0.999308	+	0.0372052i	$0.988154\pi$
$734$		0			0
$735$	6.97875	−	39.5785i	0.257415	−	1.45987i
$736$		0			0
$737$	−41.3451	+	15.0484i	−1.52297	+	0.554314i
$738$		0			0
$739$	−3.18059			−0.117000			−0.0584999	−	0.998287i	$-0.518632\pi$
$739$	−3.18059			−0.117000			−0.0584999	+	0.998287i	$0.518632\pi$
$740$		0			0
$741$	−0.419746			−0.0154197
$742$		0			0
$743$	−49.7669	+	18.1137i	−1.82577	+	0.664527i	−0.831776	+	0.555112i	$0.812675\pi$
$743$	−49.7669	+	18.1137i	−1.82577	+	0.664527i	−0.993996	+	0.109415i	$0.965102\pi$
$744$		0			0
$745$	−4.04897	+	22.9629i	−0.148343	+	0.841295i
$746$		0			0
$747$	−0.200891	+	1.13931i	−0.00735020	+	0.0416851i
$748$		0			0
$749$	−25.9031	+	21.7353i	−0.946478	+	0.794189i
$750$		0			0
$751$	−3.21483	−	5.56825i	−0.117311	−	0.203188i	0.801390	−	0.598142i	$-0.204094\pi$
$751$	−3.21483	−	5.56825i	−0.117311	−	0.203188i	−0.918701	+	0.394954i	$0.870761\pi$
$752$		0			0
$753$	−2.93354	−	2.46153i	−0.106904	−	0.0897031i
$754$		0			0
$755$	−4.09536	−	23.2259i	−0.149045	−	0.845278i
$756$		0			0
$757$	−24.3176	+	20.4049i	−0.883837	+	0.741627i	−0.966964	−	0.254912i	$-0.917954\pi$
$757$	−24.3176	+	20.4049i	−0.883837	+	0.741627i	0.0831276	+	0.996539i	$0.473509\pi$
$758$		0			0
$759$	65.2259	−	23.7403i	2.36755	−	0.861718i
$760$		0			0
$761$	−4.00842	−	22.7329i	−0.145305	−	0.824065i	−0.967122	−	0.254314i	$-0.918150\pi$
$761$	−4.00842	−	22.7329i	−0.145305	−	0.824065i	0.821817	−	0.569752i	$-0.192961\pi$
$762$		0			0
$763$	18.0051	−	31.1857i	0.651827	−	1.12900i
$764$		0			0
$765$	13.8014	+	5.02331i	0.498992	+	0.181618i
$766$		0			0
$767$	7.85096	−	13.5983i	0.283482	−	0.491005i
$768$		0			0
$769$	−23.5799	−	40.8416i	−0.850312	−	1.47278i	−0.880926	−	0.473253i	$-0.843080\pi$
$769$	−23.5799	−	40.8416i	−0.850312	−	1.47278i	0.0306140	−	0.999531i	$-0.490254\pi$
$770$		0			0
$771$	27.8188			1.00187
$772$		0			0
$773$	−3.06540	−	2.57218i	−0.110255	−	0.0925148i	0.585994	−	0.810316i	$-0.300704\pi$
$773$	−3.06540	−	2.57218i	−0.110255	−	0.0925148i	−0.696248	+	0.717801i	$0.745149\pi$
$774$		0			0
$775$	−14.3338	−	5.21707i	−0.514885	−	0.187403i
$776$		0			0
$777$	49.2263	+	23.1245i	1.76598	+	0.829587i
$778$		0			0
$779$	−0.531159	−	0.193326i	−0.0190308	−	0.00692663i
$780$		0			0
$781$	−7.61108	−	6.38645i	−0.272346	−	0.228525i
$782$		0			0
$783$	2.09916			0.0750179
$784$		0			0
$785$	3.30138	+	5.71816i	0.117831	+	0.204090i
$786$		0			0
$787$	5.78344	−	10.0172i	0.206157	−	0.357075i	−0.744344	−	0.667797i	$-0.767237\pi$
$787$	5.78344	−	10.0172i	0.206157	−	0.357075i	0.950501	+	0.310722i	$0.100571\pi$
$788$		0			0
$789$	54.0387	+	19.6685i	1.92383	+	0.700217i
$790$		0			0
$791$	−20.4490	+	35.4186i	−0.727081	+	1.25934i
$792$		0			0
$793$	−3.60245	−	20.4305i	−0.127927	−	0.725509i
$794$		0			0
$795$	−3.15416	+	1.14802i	−0.111867	+	0.0407161i
$796$		0			0
$797$	−28.0792	+	23.5612i	−0.994615	+	0.834581i	−0.986229	−	0.165384i	$-0.947114\pi$
$797$	−28.0792	+	23.5612i	−0.994615	+	0.834581i	−0.00838538	+	0.999965i	$0.502669\pi$
$798$		0			0
$799$	5.49335	+	31.1543i	0.194341	+	1.10216i
$800$		0			0
$801$	4.74613	+	3.98248i	0.167696	+	0.140714i
$802$		0			0
$803$	−4.27309	−	7.40121i	−0.150794	−	0.261183i
$804$		0			0
$805$	56.2012	−	47.1584i	1.98083	−	1.66212i
$806$		0			0
$807$	−5.15328	+	29.2257i	−0.181404	+	1.02879i
$808$		0			0
$809$	−1.35385	+	7.67809i	−0.0475990	+	0.269947i	−0.999314	−	0.0370359i	$-0.988208\pi$
$809$	−1.35385	+	7.67809i	−0.0475990	+	0.269947i	0.951715	+	0.306983i	$0.0993195\pi$
$810$		0			0
$811$	−27.9730	+	10.1813i	−0.982265	+	0.357515i	−0.782720	−	0.622374i	$-0.786168\pi$
$811$	−27.9730	+	10.1813i	−0.982265	+	0.357515i	−0.199545	+	0.979889i	$0.563946\pi$
$812$		0			0
$813$	−9.41372			−0.330154
$814$		0			0
$815$	−4.49443			−0.157433
$816$		0			0
$817$	−0.104457	+	0.0380192i	−0.00365449	+	0.00133012i
$818$		0			0
$819$	2.42539	−	13.7551i	0.0847501	−	0.480642i
$820$		0			0
$821$	6.80968	−	38.6196i	0.237659	−	1.34783i	−0.599281	−	0.800539i	$-0.704547\pi$
$821$	6.80968	−	38.6196i	0.237659	−	1.34783i	0.836940	−	0.547294i	$-0.184342\pi$
$822$		0			0
$823$	9.28031	−	7.78710i	0.323491	−	0.271441i	−0.466550	−	0.884495i	$-0.654503\pi$
$823$	9.28031	−	7.78710i	0.323491	−	0.271441i	0.790042	+	0.613053i	$0.210059\pi$
$824$		0			0
$825$	5.34975	+	9.26604i	0.186254	+	0.322602i
$826$		0			0
$827$	10.7589	+	9.02779i	0.374124	+	0.313927i	0.810390	−	0.585890i	$-0.199255\pi$
$827$	10.7589	+	9.02779i	0.374124	+	0.313927i	−0.436267	+	0.899817i	$0.643700\pi$
$828$		0			0
$829$	5.56767	+	31.5758i	0.193373	+	1.09667i	0.914716	+	0.404096i	$0.132414\pi$
$829$	5.56767	+	31.5758i	0.193373	+	1.09667i	−0.721343	+	0.692578i	$0.756475\pi$
$830$		0			0
$831$	5.83710	−	4.89791i	0.202487	−	0.169907i
$832$		0			0
$833$	−40.9649	+	14.9100i	−1.41935	+	0.516601i
$834$		0			0
$835$	−5.08586	−	28.8433i	−0.176003	−	0.998165i
$836$		0			0
$837$	14.0808	−	24.3887i	0.486704	−	0.842996i
$838$		0			0
$839$	−10.3875	−	3.78073i	−0.358616	−	0.130525i	0.156428	−	0.987689i	$-0.450002\pi$
$839$	−10.3875	−	3.78073i	−0.358616	−	0.130525i	−0.515044	+	0.857164i	$0.672224\pi$
$840$		0			0
$841$	14.2000	−	24.5951i	0.489656	−	0.848109i
$842$		0			0
$843$	−8.00245	−	13.8607i	−0.275619	−	0.477386i
$844$		0			0
$845$	17.3683			0.597489
$846$		0			0
$847$	0.525338	+	0.440811i	0.0180508	+	0.0151464i
$848$		0			0
$849$	−28.7007	−	10.4462i	−0.985007	−	0.358513i
$850$		0			0
$851$	24.3317	+	52.5676i	0.834080	+	1.80199i
$852$		0			0
$853$	−48.0604	−	17.4925i	−1.64556	−	0.598933i	−0.657558	−	0.753404i	$-0.728411\pi$
$853$	−48.0604	−	17.4925i	−1.64556	−	0.598933i	−0.987997	+	0.154471i	$0.950633\pi$
$854$		0			0
$855$	−0.251164	−	0.210751i	−0.00858962	−	0.00720755i
$856$		0			0
$857$	−11.4315			−0.390493			−0.195246	−	0.980754i	$-0.562551\pi$
$857$	−11.4315			−0.390493			−0.195246	+	0.980754i	$0.562551\pi$
$858$		0			0
$859$	−5.49634	−	9.51995i	−0.187533	−	0.324816i	0.756894	−	0.653537i	$-0.226716\pi$
$859$	−5.49634	−	9.51995i	−0.187533	−	0.324816i	−0.944427	+	0.328721i	$0.893382\pi$
$860$		0			0
$861$	25.4575	−	44.0937i	0.867590	−	1.50271i
$862$		0			0
$863$	−14.1266	−	5.14167i	−0.480876	−	0.175024i	0.0901969	−	0.995924i	$-0.471250\pi$
$863$	−14.1266	−	5.14167i	−0.480876	−	0.175024i	−0.571073	+	0.820899i	$0.693473\pi$
$864$		0			0
$865$	−16.7991	+	29.0968i	−0.571185	+	0.989322i
$866$		0			0
$867$	−1.04987	−	5.95412i	−0.0356555	−	0.202213i
$868$		0			0
$869$	17.0691	−	6.21263i	0.579028	−	0.210749i
$870$		0			0
$871$	−19.5535	+	16.4074i	−0.662546	+	0.555942i
$872$		0			0
$873$	1.10486	+	6.26596i	0.0373938	+	0.212071i
$874$		0			0
$875$	38.1715	+	32.0297i	1.29043	+	1.08280i
$876$		0			0
$877$	14.7236	+	25.5020i	0.497180	+	0.861141i	0.999995	−	0.00325344i	$-0.00103560\pi$
$877$	14.7236	+	25.5020i	0.497180	+	0.861141i	−0.502815	+	0.864394i	$0.667702\pi$
$878$		0			0
$879$	42.2309	−	35.4360i	1.42441	−	1.19523i
$880$		0			0
$881$	3.19146	−	18.0997i	0.107523	−	0.609793i	−0.882660	−	0.470013i	$-0.844249\pi$
$881$	3.19146	−	18.0997i	0.107523	−	0.609793i	0.990183	−	0.139780i	$-0.0446396\pi$
$882$		0			0
$883$	−5.06999	+	28.7534i	−0.170619	+	0.967628i	0.772461	+	0.635062i	$0.219025\pi$
$883$	−5.06999	+	28.7534i	−0.170619	+	0.967628i	−0.943080	+	0.332566i	$0.892086\pi$
$884$		0			0
$885$	31.1987	−	11.3554i	1.04873	−	0.381708i
$886$		0			0
$887$	36.5446			1.22705			0.613524	−	0.789676i	$-0.289751\pi$
$887$	36.5446			1.22705			0.613524	+	0.789676i	$0.289751\pi$
$888$		0			0
$889$	68.7749			2.30664
$890$		0			0
$891$	−35.1192	+	12.7823i	−1.17654	+	0.428225i
$892$		0			0
$893$	0.122631	−	0.695478i	0.00410371	−	0.0232733i
$894$		0			0
$895$	−6.65963	+	37.7686i	−0.222607	+	1.26247i
$896$		0			0
$897$	30.8476	−	25.8842i	1.02997	−	0.864249i
$898$		0			0
$899$	4.02448	+	6.97060i	0.134224	+	0.232482i
$900$		0			0
$901$	2.78914	+	2.34037i	0.0929198	+	0.0779689i
$902$		0			0
$903$	−1.73872	−	9.86076i	−0.0578609	−	0.328145i
$904$		0			0
$905$	26.3125	−	22.0788i	0.874656	−	0.733923i
$906$		0			0
$907$	17.1239	−	6.23258i	0.568589	−	0.206949i	−0.0416975	−	0.999130i	$-0.513277\pi$
$907$	17.1239	−	6.23258i	0.568589	−	0.206949i	0.610286	+	0.792181i	$0.291054\pi$
$908$		0			0
$909$	1.20492	+	6.83345i	0.0399647	+	0.226651i
$910$		0			0
$911$	−26.2373	+	45.4443i	−0.869280	+	1.50564i	−0.00654696	+	0.999979i	$0.502084\pi$
$911$	−26.2373	+	45.4443i	−0.869280	+	1.50564i	−0.862733	+	0.505659i	$0.831249\pi$
$912$		0			0
$913$	−2.06705	−	0.752344i	−0.0684093	−	0.0248990i
$914$		0			0
$915$	21.9329	−	37.9889i	0.725080	−	1.25588i
$916$		0			0
$917$	2.87700	+	4.98311i	0.0950068	+	0.164557i
$918$		0			0
$919$	44.3955			1.46447			0.732236	−	0.681051i	$-0.238477\pi$
$919$	44.3955			1.46447			0.732236	+	0.681051i	$0.238477\pi$
$920$		0			0
$921$	−41.1020	−	34.4887i	−1.35436	−	1.13644i
$922$		0			0
$923$	−5.41641	−	1.97141i	−0.178283	−	0.0648898i
$924$		0			0
$925$	−7.32864	+	5.10071i	−0.240964	+	0.167710i
$926$		0			0
$927$	−3.26804	−	1.18947i	−0.107336	−	0.0390673i
$928$		0			0
$929$	22.9234	+	19.2350i	0.752092	+	0.631080i	0.936055	−	0.351853i	$-0.114448\pi$
$929$	22.9234	+	19.2350i	0.752092	+	0.631080i	−0.183963	+	0.982933i	$0.558893\pi$
$930$		0			0
$931$	0.973173			0.0318945
$932$		0			0
$933$	−5.67884	−	9.83605i	−0.185917	−	0.322018i
$934$		0			0
$935$	−13.9632	+	24.1849i	−0.456644	+	0.790931i
$936$		0			0
$937$	−9.34478	−	3.40122i	−0.305281	−	0.111113i	0.184837	−	0.982769i	$-0.440824\pi$
$937$	−9.34478	−	3.40122i	−0.305281	−	0.111113i	−0.490118	+	0.871656i	$0.663046\pi$
$938$		0			0
$939$	7.89191	−	13.6692i	0.257543	−	0.446077i
$940$		0			0
$941$	2.14576	+	12.1692i	0.0699497	+	0.396704i	0.999601	+	0.0282626i	$0.00899747\pi$
$941$	2.14576	+	12.1692i	0.0699497	+	0.396704i	−0.929651	+	0.368442i	$0.879891\pi$
$942$		0			0
$943$	50.9573	−	18.5469i	1.65940	−	0.603971i
$944$		0			0
$945$	−15.9940	+	13.4206i	−0.520285	+	0.436571i
$946$		0			0
$947$	4.86165	+	27.5718i	0.157982	+	0.895962i	0.956008	+	0.293339i	$0.0947666\pi$
$947$	4.86165	+	27.5718i	0.157982	+	0.895962i	−0.798026	+	0.602623i	$0.794122\pi$
$948$		0			0
$949$	−3.79804	−	3.18693i	−0.123290	−	0.103452i
$950$		0			0
$951$	−14.5583	−	25.2156i	−0.472084	−	0.817673i
$952$		0			0
$953$	33.5552	−	28.1562i	1.08696	−	0.912068i	0.0904798	−	0.995898i	$-0.471160\pi$
$953$	33.5552	−	28.1562i	1.08696	−	0.912068i	0.996480	+	0.0838307i	$0.0267155\pi$
$954$		0			0
$955$	1.88164	−	10.6713i	0.0608884	−	0.345315i
$956$		0			0
$957$	0.980388	−	5.56006i	0.0316914	−	0.179731i
$958$		0			0
$959$	−47.8396	+	17.4122i	−1.54482	+	0.562269i
$960$		0			0
$961$	76.9820			2.48329
$962$		0			0
$963$	−14.4974			−0.467172
$964$		0			0
$965$	−0.634759	+	0.231033i	−0.0204336	+	0.00743723i
$966$		0			0
$967$	9.60416	−	54.4679i	0.308849	−	1.75157i	−0.295961	−	0.955200i	$-0.595640\pi$
$967$	9.60416	−	54.4679i	0.308849	−	1.75157i	0.604810	−	0.796370i	$-0.293249\pi$
$968$		0			0
$969$	−0.167176	+	0.948100i	−0.00537046	+	0.0304574i
$970$		0			0
$971$	42.2703	−	35.4690i	1.35652	−	1.13825i	0.379477	−	0.925201i	$-0.376104\pi$
$971$	42.2703	−	35.4690i	1.35652	−	1.13825i	0.977041	−	0.213053i	$-0.0683406\pi$
$972$		0			0
$973$	37.7123	+	65.3197i	1.20900	+	2.09405i
$974$		0			0
$975$	4.75501	+	3.98992i	0.152282	+	0.127780i
$976$		0			0
$977$	−4.43401	−	25.1465i	−0.141857	−	0.804509i	−0.969837	−	0.243753i	$-0.921621\pi$
$977$	−4.43401	−	25.1465i	−0.141857	−	0.804509i	0.827981	−	0.560757i	$-0.189490\pi$
$978$		0			0
$979$	−9.02433	+	7.57232i	−0.288419	+	0.242012i
$980$		0			0
$981$	14.5079	−	5.28043i	0.463200	−	0.168591i
$982$		0			0
$983$	5.43056	+	30.7982i	0.173208	+	0.982311i	0.940192	+	0.340645i	$0.110645\pi$
$983$	5.43056	+	30.7982i	0.173208	+	0.982311i	−0.766984	+	0.641666i	$0.778243\pi$
$984$		0			0
$985$	6.54591	−	11.3378i	0.208570	−	0.361254i
$986$		0			0
$987$	59.7757	+	21.7566i	1.90268	+	0.692519i
$988$		0			0
$989$	5.33216	−	9.23557i	0.169553	−	0.293674i
$990$		0			0
$991$	−3.80674	−	6.59347i	−0.120925	−	0.209448i	0.799208	−	0.601055i	$-0.205253\pi$
$991$	−3.80674	−	6.59347i	−0.120925	−	0.209448i	−0.920133	+	0.391607i	$0.871919\pi$
$992$		0			0
$993$	−9.97478			−0.316540
$994$		0			0
$995$	16.0928	+	13.5035i	0.510176	+	0.428088i
$996$		0			0
$997$	−14.6618	−	5.33644i	−0.464342	−	0.169007i	0.0992454	−	0.995063i	$-0.468357\pi$
$997$	−14.6618	−	5.33644i	−0.464342	−	0.169007i	−0.563588	+	0.826056i	$0.690579\pi$
$998$		0			0
$999$	−6.92443	−	14.9599i	−0.219079	−	0.473311i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.bc.d.497.2		12
4.3	odd	2		74.2.f.b.53.1	yes	12
12.11	even	2		666.2.x.g.127.1		12
37.7	even	9	inner	592.2.bc.d.81.2		12
148.7	odd	18		74.2.f.b.7.1	✓	12
148.83	odd	18		2738.2.a.t.1.5		6
148.139	odd	18		2738.2.a.q.1.5		6
444.155	even	18		666.2.x.g.451.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.b.7.1	✓	12	148.7	odd	18
74.2.f.b.53.1	yes	12	4.3	odd	2
592.2.bc.d.81.2		12	37.7	even	9	inner
592.2.bc.d.497.2		12	1.1	even	1	trivial
666.2.x.g.127.1		12	12.11	even	2
666.2.x.g.451.1		12	444.155	even	18
2738.2.a.q.1.5		6	148.139	odd	18
2738.2.a.t.1.5		6	148.83	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)

\(f(q)\)	\(=\)	\(q+(2.04963 - 0.746005i) q^{3} +(-0.326352 + 1.85083i) q^{5} +(0.711830 - 4.03699i) q^{7} +(1.34633 - 1.12971i) q^{9} +O(q^{10})\)	\(q+(2.04963 - 0.746005i) q^{3} +(-0.326352 + 1.85083i) q^{5} +(0.711830 - 4.03699i) q^{7} +(1.34633 - 1.12971i) q^{9} +(1.67088 + 2.89404i) q^{11} +(1.48512 + 1.24616i) q^{13} +(0.711830 + 4.03699i) q^{15} +(3.40626 - 2.85819i) q^{17} +(-0.0932770 + 0.0339500i) q^{19} +(-1.55262 - 8.80536i) q^{21} +(4.76146 - 8.24709i) q^{23} +(1.37939 + 0.502055i) q^{25} +(-1.35504 + 2.34700i) q^{27} +(-0.387288 - 0.670802i) q^{29} -10.3914 q^{31} +(5.58365 + 4.68524i) q^{33} +(7.23948 + 2.63496i) q^{35} +(-3.50302 + 4.97281i) q^{37} +(3.97359 + 1.44627i) q^{39} +(4.36218 + 3.66031i) q^{41} +1.11986 q^{43} +(1.65152 + 2.86052i) q^{45} +(-3.55724 + 6.16132i) q^{47} +(-9.21271 - 3.35315i) q^{49} +(4.84936 - 8.39933i) q^{51} +(0.142188 + 0.806388i) q^{53} +(-5.90168 + 2.14804i) q^{55} +(-0.165857 + 0.139170i) q^{57} +(-1.40642 - 7.97622i) q^{59} +(-8.19737 - 6.87841i) q^{61} +(-3.60225 - 6.23929i) q^{63} +(-2.79111 + 2.34202i) q^{65} +(-2.28630 + 12.9663i) q^{67} +(3.60687 - 20.4556i) q^{69} +(-2.79386 + 1.01688i) q^{71} -2.55740 q^{73} +3.20177 q^{75} +(12.8726 - 4.68524i) q^{77} +(0.943888 - 5.35305i) q^{79} +(-1.94203 + 11.0138i) q^{81} +(-0.504249 + 0.423115i) q^{83} +(4.17840 + 7.23720i) q^{85} +(-1.29422 - 1.08598i) q^{87} +(0.612149 + 3.47167i) q^{89} +(6.08790 - 5.10835i) q^{91} +(-21.2986 + 7.75206i) q^{93} +(-0.0323948 - 0.183720i) q^{95} +(-1.81012 + 3.13522i) q^{97} +(5.51897 + 2.00874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 6 q^{5} - 6 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - 6 * q^5 - 6 * q^7 - 3 * q^9	\( 12 q + 3 q^{3} - 6 q^{5} - 6 q^{7} - 3 q^{9} - 3 q^{11} - 6 q^{13} - 6 q^{15} - 3 q^{17} + 3 q^{19} - 33 q^{21} + 21 q^{23} - 6 q^{25} - 3 q^{27} + 6 q^{29} - 42 q^{31} + 57 q^{33} + 9 q^{35} - 3 q^{37} + 24 q^{39} - 21 q^{41} - 36 q^{43} - 6 q^{45} - 9 q^{47} - 12 q^{49} - 6 q^{53} - 36 q^{57} + 6 q^{59} - 18 q^{61} - 36 q^{63} + 3 q^{65} + 27 q^{67} - 12 q^{69} + 18 q^{71} + 54 q^{73} + 6 q^{75} + 51 q^{77} + 12 q^{79} - 36 q^{81} + 6 q^{83} + 3 q^{85} - 39 q^{87} - 15 q^{89} + 51 q^{91} + 45 q^{93} + 15 q^{95} - 42 q^{97} + 33 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 6 * q^5 - 6 * q^7 - 3 * q^9 - 3 * q^11 - 6 * q^13 - 6 * q^15 - 3 * q^17 + 3 * q^19 - 33 * q^21 + 21 * q^23 - 6 * q^25 - 3 * q^27 + 6 * q^29 - 42 * q^31 + 57 * q^33 + 9 * q^35 - 3 * q^37 + 24 * q^39 - 21 * q^41 - 36 * q^43 - 6 * q^45 - 9 * q^47 - 12 * q^49 - 6 * q^53 - 36 * q^57 + 6 * q^59 - 18 * q^61 - 36 * q^63 + 3 * q^65 + 27 * q^67 - 12 * q^69 + 18 * q^71 + 54 * q^73 + 6 * q^75 + 51 * q^77 + 12 * q^79 - 36 * q^81 + 6 * q^83 + 3 * q^85 - 39 * q^87 - 15 * q^89 + 51 * q^91 + 45 * q^93 + 15 * q^95 - 42 * q^97 + 33 * q^99

Introduction

L-functions

Modular forms

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Database

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