LMFDB - Embedded newform 961.2.g.e.448.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(235,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("961.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			448.1
Root			$-0.104528 + 0.994522i$ of defining polynomial
Character	$\chi$	$=$	961.448
Dual form			961.2.g.e.547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 1.53884i) q^{2} +(2.16535 - 2.40487i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.61803 - 4.53457i) q^{6} +(-0.0246758 + 0.234775i) q^{7} +(1.80902 - 1.31433i) q^{8} +(-0.781051 - 7.43120i) q^{9} +O(q^{10})$	\(q+(0.500000 - 1.53884i) q^{2} +(2.16535 - 2.40487i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.61803 - 4.53457i) q^{6} +(-0.0246758 + 0.234775i) q^{7} +(1.80902 - 1.31433i) q^{8} +(-0.781051 - 7.43120i) q^{9} +(1.08268 + 1.20243i) q^{10} +(-1.82709 + 0.813473i) q^{11} +(-1.95630 + 0.415823i) q^{12} +(-3.16535 - 0.672816i) q^{13} +(0.348943 + 0.155360i) q^{14} +(1.00000 + 3.07768i) q^{15} +(-1.50000 - 4.61653i) q^{16} +(-0.697887 - 0.310719i) q^{17} +(-11.8260 - 2.51369i) q^{18} +(2.18720 - 0.464905i) q^{19} +(0.564602 - 0.251377i) q^{20} +(0.511170 + 0.567712i) q^{21} +(0.338261 + 3.21834i) q^{22} +(4.61803 - 3.35520i) q^{23} +(0.756375 - 7.19643i) q^{24} +(2.00000 + 3.46410i) q^{25} +(-2.61803 + 4.53457i) q^{26} +(-11.7082 - 8.50651i) q^{27} +(0.0976248 - 0.108423i) q^{28} +(-0.854102 + 2.62866i) q^{29} +5.23607 q^{30} -3.38197 q^{32} +(-2.00000 + 6.15537i) q^{33} +(-0.827091 + 0.918578i) q^{34} +(-0.190983 - 0.138757i) q^{35} +(-2.30902 + 3.99933i) q^{36} +(-1.00000 - 1.73205i) q^{37} +(0.378188 - 3.59821i) q^{38} +(-8.47214 + 6.15537i) q^{39} +(0.233733 + 2.22382i) q^{40} +(4.68391 + 5.20201i) q^{41} +(1.12920 - 0.502754i) q^{42} +(1.20906 - 0.256993i) q^{43} +(1.20906 + 0.256993i) q^{44} +(6.82614 + 3.03919i) q^{45} +(-2.85410 - 8.78402i) q^{46} +(0.763932 + 2.35114i) q^{47} +(-14.3502 - 6.38910i) q^{48} +(6.79252 + 1.44380i) q^{49} +(6.33070 - 1.34563i) q^{50} +(-2.25841 + 1.00551i) q^{51} +(1.33826 + 1.48629i) q^{52} +(-1.09464 - 10.4148i) q^{53} +(-18.9443 + 13.7638i) q^{54} +(0.209057 - 1.98904i) q^{55} +(0.263932 + 0.457144i) q^{56} +(3.61803 - 6.26662i) q^{57} +(3.61803 + 2.62866i) q^{58} +(1.49622 - 1.66172i) q^{59} +(0.618034 - 1.90211i) q^{60} -8.18034 q^{61} +1.76393 q^{63} +(1.30902 - 4.02874i) q^{64} +(2.16535 - 2.40487i) q^{65} +(8.47214 + 6.15537i) q^{66} +(-4.00000 + 6.92820i) q^{67} +(0.236068 + 0.408882i) q^{68} +(1.93086 - 18.3709i) q^{69} +(-0.309017 + 0.224514i) q^{70} +(0.959607 + 9.13005i) q^{71} +(-11.1800 - 12.4166i) q^{72} +(-7.73968 + 3.44593i) q^{73} +(-3.16535 + 0.672816i) q^{74} +(12.6614 + 2.69127i) q^{75} +(-1.26249 - 0.562096i) q^{76} +(-0.145898 - 0.449028i) q^{77} +(5.23607 + 16.1150i) q^{78} +(10.6960 + 4.76216i) q^{79} +(4.74803 + 1.00922i) q^{80} +(-23.8829 + 5.07646i) q^{81} +(10.3470 - 4.60680i) q^{82} +(9.99967 + 11.1058i) q^{83} +(-0.0493516 - 0.469550i) q^{84} +(0.618034 - 0.449028i) q^{85} +(0.209057 - 1.98904i) q^{86} +(4.47214 + 7.74597i) q^{87} +(-2.23607 + 3.87298i) q^{88} +(9.47214 + 6.88191i) q^{89} +(8.08990 - 8.98475i) q^{90} +(0.236068 - 0.726543i) q^{91} -3.52786 q^{92} +4.00000 q^{94} +(-0.690983 + 2.12663i) q^{95} +(-7.32315 + 8.13318i) q^{96} +(12.8992 + 9.37181i) q^{97} +(5.61803 - 9.73072i) q^{98} +(7.47214 + 12.9421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 12 q^{6} + 3 q^{7} + 10 q^{8} + 13 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 12 * q^6 + 3 * q^7 + 10 * q^8 + 13 * q^9	\( 8 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 12 q^{6} + 3 q^{7} + 10 q^{8} + 13 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} - 4 q^{13} - q^{14} + 8 q^{15} - 12 q^{16} + 2 q^{17} - 6 q^{18} + 5 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} + 28 q^{23} - 10 q^{24} + 16 q^{25} - 12 q^{26} - 40 q^{27} + 11 q^{28} + 20 q^{29} + 24 q^{30} - 36 q^{32} - 16 q^{33} + 6 q^{34} - 6 q^{35} - 14 q^{36} - 8 q^{37} - 5 q^{38} - 32 q^{39} - 5 q^{40} + 7 q^{41} + 4 q^{42} + 6 q^{43} + 6 q^{44} + 13 q^{45} + 4 q^{46} + 24 q^{47} - 24 q^{48} + 22 q^{49} + 8 q^{50} - 8 q^{51} + 2 q^{52} + 16 q^{53} - 80 q^{54} - 2 q^{55} + 20 q^{56} + 20 q^{57} + 20 q^{58} - 5 q^{59} - 4 q^{60} + 24 q^{61} + 32 q^{63} + 6 q^{64} - 4 q^{65} + 32 q^{66} - 32 q^{67} - 16 q^{68} - 24 q^{69} + 2 q^{70} - 23 q^{71} + 5 q^{72} - 14 q^{73} - 4 q^{74} + 16 q^{75} - 28 q^{77} + 24 q^{78} + 20 q^{79} + 6 q^{80} - 19 q^{81} + 21 q^{82} - 14 q^{83} + 6 q^{84} - 4 q^{85} - 2 q^{86} + 40 q^{89} - 6 q^{90} - 16 q^{91} - 64 q^{92} + 32 q^{94} - 10 q^{95} + 18 q^{96} + 54 q^{97} + 36 q^{98} + 24 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 12 * q^6 + 3 * q^7 + 10 * q^8 + 13 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^12 - 4 * q^13 - q^14 + 8 * q^15 - 12 * q^16 + 2 * q^17 - 6 * q^18 + 5 * q^19 + 2 * q^20 + 8 * q^21 - 6 * q^22 + 28 * q^23 - 10 * q^24 + 16 * q^25 - 12 * q^26 - 40 * q^27 + 11 * q^28 + 20 * q^29 + 24 * q^30 - 36 * q^32 - 16 * q^33 + 6 * q^34 - 6 * q^35 - 14 * q^36 - 8 * q^37 - 5 * q^38 - 32 * q^39 - 5 * q^40 + 7 * q^41 + 4 * q^42 + 6 * q^43 + 6 * q^44 + 13 * q^45 + 4 * q^46 + 24 * q^47 - 24 * q^48 + 22 * q^49 + 8 * q^50 - 8 * q^51 + 2 * q^52 + 16 * q^53 - 80 * q^54 - 2 * q^55 + 20 * q^56 + 20 * q^57 + 20 * q^58 - 5 * q^59 - 4 * q^60 + 24 * q^61 + 32 * q^63 + 6 * q^64 - 4 * q^65 + 32 * q^66 - 32 * q^67 - 16 * q^68 - 24 * q^69 + 2 * q^70 - 23 * q^71 + 5 * q^72 - 14 * q^73 - 4 * q^74 + 16 * q^75 - 28 * q^77 + 24 * q^78 + 20 * q^79 + 6 * q^80 - 19 * q^81 + 21 * q^82 - 14 * q^83 + 6 * q^84 - 4 * q^85 - 2 * q^86 + 40 * q^89 - 6 * q^90 - 16 * q^91 - 64 * q^92 + 32 * q^94 - 10 * q^95 + 18 * q^96 + 54 * q^97 + 36 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{15}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	1.53884i	0.353553	−	1.08813i	−0.603290	−	0.797522i	$-0.706144\pi$
$2$	0.500000	−	1.53884i	0.353553	−	1.08813i	0.956844	−	0.290604i	$-0.0938561\pi$
$3$	2.16535	−	2.40487i	1.25017	−	1.38845i	0.359913	−	0.932986i	$-0.382806\pi$
$3$	2.16535	−	2.40487i	1.25017	−	1.38845i	0.890254	−	0.455465i	$-0.150527\pi$
$4$	−0.500000	−	0.363271i	−0.250000	−	0.181636i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$	−2.61803	−	4.53457i	−1.06881	−	1.85123i
$7$	−0.0246758	+	0.234775i	−0.00932658	+	0.0887365i	−0.998195	−	0.0600561i	$-0.980872\pi$
$7$	−0.0246758	+	0.234775i	−0.00932658	+	0.0887365i	0.988868	+	0.148793i	$0.0475387\pi$
$8$	1.80902	−	1.31433i	0.639584	−	0.464685i
$9$	−0.781051	−	7.43120i	−0.260350	−	2.47707i
$10$	1.08268	+	1.20243i	0.342372	+	0.380243i
$11$	−1.82709	+	0.813473i	−0.550889	+	0.245271i	−0.663252	−	0.748396i	$-0.730824\pi$
$11$	−1.82709	+	0.813473i	−0.550889	+	0.245271i	0.112364	+	0.993667i	$0.464158\pi$
$12$	−1.95630	+	0.415823i	−0.564734	+	0.120038i
$13$	−3.16535	−	0.672816i	−0.877911	−	0.186606i	−0.253155	−	0.967426i	$-0.581468\pi$
$13$	−3.16535	−	0.672816i	−0.877911	−	0.186606i	−0.624756	+	0.780820i	$0.714802\pi$
$14$	0.348943	+	0.155360i	0.0932590	+	0.0415216i
$15$	1.00000	+	3.07768i	0.258199	+	0.794654i
$16$	−1.50000	−	4.61653i	−0.375000	−	1.15413i
$17$	−0.697887	−	0.310719i	−0.169262	−	0.0753605i	0.320356	−	0.947297i	$-0.396197\pi$
$17$	−0.697887	−	0.310719i	−0.169262	−	0.0753605i	−0.489619	+	0.871937i	$0.662864\pi$
$18$	−11.8260	−	2.51369i	−2.78741	−	0.592482i
$19$	2.18720	−	0.464905i	0.501779	−	0.106656i	0.0499334	−	0.998753i	$-0.484099\pi$
$19$	2.18720	−	0.464905i	0.501779	−	0.106656i	0.451846	+	0.892096i	$0.350766\pi$
$20$	0.564602	−	0.251377i	0.126249	−	0.0562096i
$21$	0.511170	+	0.567712i	0.111547	+	0.123885i
$22$	0.338261	+	3.21834i	0.0721175	+	0.686152i
$23$	4.61803	−	3.35520i	0.962927	−	0.699607i	0.00909805	−	0.999959i	$-0.497104\pi$
$23$	4.61803	−	3.35520i	0.962927	−	0.699607i	0.953829	+	0.300351i	$0.0971040\pi$
$24$	0.756375	−	7.19643i	0.154394	−	1.46896i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	−2.61803	+	4.53457i	−0.513439	+	0.889302i
$27$	−11.7082	−	8.50651i	−2.25324	−	1.63708i
$28$	0.0976248	−	0.108423i	0.0184494	−	0.0204901i
$29$	−0.854102	+	2.62866i	−0.158603	+	0.488129i	−0.998508	−	0.0546038i	$-0.982610\pi$
$29$	−0.854102	+	2.62866i	−0.158603	+	0.488129i	0.839905	+	0.542733i	$0.182610\pi$
$30$	5.23607			0.955971
$31$		0			0
$31$		0			0
$32$	−3.38197			−0.597853
$33$	−2.00000	+	6.15537i	−0.348155	+	1.07151i
$34$	−0.827091	+	0.918578i	−0.141845	+	0.157535i
$35$	−0.190983	−	0.138757i	−0.0322820	−	0.0234543i
$36$	−2.30902	+	3.99933i	−0.384836	+	0.666556i
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	0.378188	−	3.59821i	0.0613501	−	0.583707i
$39$	−8.47214	+	6.15537i	−1.35663	+	0.985648i
$40$	0.233733	+	2.22382i	0.0369564	+	0.351617i
$41$	4.68391	+	5.20201i	0.731505	+	0.812418i	0.988053	−	0.154113i	$-0.0492521\pi$
$41$	4.68391	+	5.20201i	0.731505	+	0.812418i	−0.256549	+	0.966531i	$0.582585\pi$
$42$	1.12920	−	0.502754i	0.174240	−	0.0775766i
$43$	1.20906	−	0.256993i	0.184379	−	0.0391911i	−0.114796	−	0.993389i	$-0.536622\pi$
$43$	1.20906	−	0.256993i	0.184379	−	0.0391911i	0.299176	+	0.954198i	$0.403288\pi$
$44$	1.20906	+	0.256993i	0.182272	+	0.0387431i
$45$	6.82614	+	3.03919i	1.01758	+	0.453056i
$46$	−2.85410	−	8.78402i	−0.420814	−	1.29513i
$47$	0.763932	+	2.35114i	0.111431	+	0.342949i	0.991186	−	0.132478i	$-0.0422935\pi$
$47$	0.763932	+	2.35114i	0.111431	+	0.342949i	−0.879755	+	0.475427i	$0.842293\pi$
$48$	−14.3502	−	6.38910i	−2.07127	−	0.922187i
$49$	6.79252	+	1.44380i	0.970360	+	0.206256i
$50$	6.33070	−	1.34563i	0.895297	−	0.190301i
$51$	−2.25841	+	1.00551i	−0.316240	+	0.140799i
$52$	1.33826	+	1.48629i	0.185583	+	0.206111i
$53$	−1.09464	−	10.4148i	−0.150360	−	1.43058i	−0.766147	−	0.642666i	$-0.777828\pi$
$53$	−1.09464	−	10.4148i	−0.150360	−	1.43058i	0.615787	−	0.787913i	$-0.288838\pi$
$54$	−18.9443	+	13.7638i	−2.57799	+	1.87302i
$55$	0.209057	−	1.98904i	0.0281892	−	0.268203i
$56$	0.263932	+	0.457144i	0.0352694	+	0.0610884i
$57$	3.61803	−	6.26662i	0.479220	−	0.830034i
$58$	3.61803	+	2.62866i	0.475071	+	0.345159i
$59$	1.49622	−	1.66172i	0.194791	−	0.216338i	−0.637835	−	0.770173i	$-0.720170\pi$
$59$	1.49622	−	1.66172i	0.194791	−	0.216338i	0.832626	+	0.553836i	$0.186836\pi$
$60$	0.618034	−	1.90211i	0.0797878	−	0.245562i
$61$	−8.18034			−1.04739			−0.523693	−	0.851907i	$-0.675446\pi$
$61$	−8.18034			−1.04739			−0.523693	+	0.851907i	$0.675446\pi$
$62$		0			0
$63$	1.76393			0.222235
$64$	1.30902	−	4.02874i	0.163627	−	0.503593i
$65$	2.16535	−	2.40487i	0.268579	−	0.298287i
$66$	8.47214	+	6.15537i	1.04285	+	0.757673i
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$	0.236068	+	0.408882i	0.0286274	+	0.0495842i
$69$	1.93086	−	18.3709i	0.232449	−	2.21160i
$70$	−0.309017	+	0.224514i	−0.0369346	+	0.0268346i
$71$	0.959607	+	9.13005i	0.113884	+	1.08354i	0.890945	+	0.454112i	$0.150043\pi$
$71$	0.959607	+	9.13005i	0.113884	+	1.08354i	−0.777060	+	0.629426i	$0.783290\pi$
$72$	−11.1800	−	12.4166i	−1.31757	−	1.46331i
$73$	−7.73968	+	3.44593i	−0.905861	+	0.403315i	−0.806157	−	0.591702i	$-0.798456\pi$
$73$	−7.73968	+	3.44593i	−0.905861	+	0.403315i	−0.0997042	+	0.995017i	$0.531790\pi$
$74$	−3.16535	+	0.672816i	−0.367965	+	0.0782133i
$75$	12.6614	+	2.69127i	1.46201	+	0.310761i
$76$	−1.26249	−	0.562096i	−0.144817	−	0.0644769i
$77$	−0.145898	−	0.449028i	−0.0166266	−	0.0511715i
$78$	5.23607	+	16.1150i	0.592868	+	1.82466i
$79$	10.6960	+	4.76216i	1.20339	+	0.535784i	0.907749	−	0.419514i	$-0.137800\pi$
$79$	10.6960	+	4.76216i	1.20339	+	0.535784i	0.295643	+	0.955299i	$0.404466\pi$
$80$	4.74803	+	1.00922i	0.530846	+	0.112835i
$81$	−23.8829	+	5.07646i	−2.65365	+	0.564051i
$82$	10.3470	−	4.60680i	1.14264	−	0.508736i
$83$	9.99967	+	11.1058i	1.09761	+	1.21902i	0.973967	+	0.226688i	$0.0727898\pi$
$83$	9.99967	+	11.1058i	1.09761	+	1.21902i	0.123639	+	0.992327i	$0.460544\pi$
$84$	−0.0493516	−	0.469550i	−0.00538471	−	0.0512321i
$85$	0.618034	−	0.449028i	0.0670352	−	0.0487039i
$86$	0.209057	−	1.98904i	0.0225432	−	0.214484i
$87$	4.47214	+	7.74597i	0.479463	+	0.830455i
$88$	−2.23607	+	3.87298i	−0.238366	+	0.412861i
$89$	9.47214	+	6.88191i	1.00404	+	0.729481i	0.962952	−	0.269674i	$-0.0869161\pi$
$89$	9.47214	+	6.88191i	1.00404	+	0.729481i	0.0410928	+	0.999155i	$0.486916\pi$
$90$	8.08990	−	8.98475i	0.852751	−	0.947076i
$91$	0.236068	−	0.726543i	0.0247466	−	0.0761624i
$92$	−3.52786			−0.367805
$93$		0			0
$94$	4.00000			0.412568
$95$	−0.690983	+	2.12663i	−0.0708934	+	0.218187i
$96$	−7.32315	+	8.13318i	−0.747416	+	0.830089i
$97$	12.8992	+	9.37181i	1.30971	+	0.951563i	1.00000		0.000733244i	$0.000233399\pi$
$97$	12.8992	+	9.37181i	1.30971	+	0.951563i	0.309714	+	0.950830i	$0.399767\pi$
$98$	5.61803	−	9.73072i	0.567507	−	0.982951i
$99$	7.47214	+	12.9421i	0.750978	+	1.30073i
$100$	0.258409	−	2.45859i	0.0258409	−	0.245859i
$101$	2.42705	−	1.76336i	0.241501	−	0.175460i	−0.460451	−	0.887685i	$-0.652312\pi$
$101$	2.42705	−	1.76336i	0.241501	−	0.175460i	0.701952	+	0.712225i	$0.252312\pi$
$102$	0.418114	+	3.97809i	0.0413994	+	0.393889i
$103$	4.17274	+	4.63430i	0.411153	+	0.456631i	0.912779	−	0.408453i	$-0.133932\pi$
$103$	4.17274	+	4.63430i	0.411153	+	0.456631i	−0.501627	+	0.865084i	$0.667265\pi$
$104$	−6.61048	+	2.94317i	−0.648211	+	0.288602i
$105$	−0.747238	+	0.158830i	−0.0729230	+	0.0155003i
$106$	−16.5740	−	3.52291i	−1.60981	−	0.342175i
$107$	5.26561	+	2.34440i	0.509046	+	0.226642i	0.645155	−	0.764052i	$-0.276793\pi$
$107$	5.26561	+	2.34440i	0.509046	+	0.226642i	−0.136109	+	0.990694i	$0.543460\pi$
$108$	2.76393	+	8.50651i	0.265959	+	0.818539i
$109$	−4.30902	−	13.2618i	−0.412729	−	1.27025i	−0.914266	−	0.405113i	$-0.867232\pi$
$109$	−4.30902	−	13.2618i	−0.412729	−	1.27025i	0.501538	−	0.865136i	$-0.332768\pi$
$110$	−2.95630	−	1.31623i	−0.281872	−	0.125497i
$111$	−6.33070	−	1.34563i	−0.600884	−	0.127722i
$112$	1.12086	−	0.238246i	0.105911	−	0.0225121i
$113$	3.17195	−	1.41224i	0.298392	−	0.132853i	−0.252080	−	0.967707i	$-0.581114\pi$
$113$	3.17195	−	1.41224i	0.298392	−	0.132853i	0.550472	+	0.834854i	$0.314448\pi$
$114$	−7.83432	−	8.70089i	−0.733751	−	0.814913i
$115$	0.596670	+	5.67693i	0.0556397	+	0.529377i
$116$	1.38197	−	1.00406i	0.128312	−	0.0932244i
$117$	−2.52753	+	24.0479i	−0.233671	+	2.22323i
$118$	−1.80902	−	3.13331i	−0.166534	−	0.288445i
$119$	0.0901699	−	0.156179i	0.00826587	−	0.0143169i
$120$	5.85410	+	4.25325i	0.534404	+	0.388267i
$121$	−4.68391	+	5.20201i	−0.425810	+	0.472910i
$122$	−4.09017	+	12.5882i	−0.370307	+	1.13969i
$123$	22.6525			2.04250
$124$		0			0
$125$	−9.00000			−0.804984
$126$	0.881966	−	2.71441i	0.0785718	−	0.241819i
$127$	−8.34549	+	9.26860i	−0.740542	+	0.822456i	−0.989267	−	0.146119i	$-0.953322\pi$
$127$	−8.34549	+	9.26860i	−0.740542	+	0.822456i	0.248725	+	0.968574i	$0.419989\pi$
$128$	−11.0172	−	8.00448i	−0.973794	−	0.707503i
$129$	2.00000	−	3.46410i	0.176090	−	0.304997i
$130$	−2.61803	−	4.53457i	−0.229617	−	0.397708i
$131$	−1.25434	+	11.9343i	−0.109592	+	1.04270i	0.792120	+	0.610365i	$0.208977\pi$
$131$	−1.25434	+	11.9343i	−0.109592	+	1.04270i	−0.901712	+	0.432336i	$0.857689\pi$
$132$	3.23607	−	2.35114i	0.281664	−	0.204641i
$133$	0.0551768	+	0.524972i	0.00478444	+	0.0455209i
$134$	8.66141	+	9.61947i	0.748232	+	0.830996i
$135$	13.2210	−	5.88635i	1.13788	−	0.506616i
$136$	−1.67088	+	0.355156i	−0.143276	+	0.0304543i
$137$	6.15431	+	1.30814i	0.525798	+	0.111762i	0.463160	−	0.886275i	$-0.346715\pi$
$137$	6.15431	+	1.30814i	0.525798	+	0.111762i	0.0626376	+	0.998036i	$0.480049\pi$
$138$	−27.3045	−	12.1568i	−2.32432	−	1.03485i
$139$	−4.14590	−	12.7598i	−0.351650	−	1.08227i	−0.957926	−	0.287014i	$-0.907337\pi$
$139$	−4.14590	−	12.7598i	−0.351650	−	1.08227i	0.606276	−	0.795254i	$-0.292663\pi$
$140$	0.0450850	+	0.138757i	0.00381038	+	0.0117271i
$141$	7.30836	+	3.25389i	0.615475	+	0.274027i
$142$	14.5295	+	3.08834i	1.21929	+	0.259168i
$143$	6.33070	−	1.34563i	0.529400	−	0.112527i
$144$	−33.1348	+	14.7525i	−2.76123	+	1.22938i
$145$	−1.84943	−	2.05400i	−0.153587	−	0.170576i
$146$	1.43290	+	13.6331i	0.118587	+	1.12828i
$147$	18.1803	−	13.2088i	1.49949	−	1.08944i
$148$	−0.129204	+	1.22930i	−0.0106205	+	0.101048i
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	0.585231	−	0.810867i	$-0.301004\pi$
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	−0.994847	+	0.101391i	$0.967671\pi$
$150$	10.4721	−	18.1383i	0.855046	−	1.48098i
$151$	−11.4721	−	8.33499i	−0.933589	−	0.678292i	0.0132798	−	0.999912i	$-0.495773\pi$
$151$	−11.4721	−	8.33499i	−0.933589	−	0.678292i	−0.946869	+	0.321620i	$0.895773\pi$
$152$	3.34565	−	3.71572i	0.271368	−	0.301385i
$153$	−1.76393	+	5.42882i	−0.142605	+	0.438894i
$154$	−0.763932			−0.0615594
$155$		0			0
$156$	6.47214			0.518186
$157$	6.45492	−	19.8662i	0.515158	−	1.58549i	−0.267835	−	0.963465i	$-0.586308\pi$
$157$	6.45492	−	19.8662i	0.515158	−	1.58549i	0.782994	−	0.622030i	$-0.213692\pi$
$158$	12.6762	−	14.0783i	1.00846	−	1.12001i
$159$	−27.4164	−	19.9192i	−2.17426	−	1.57969i
$160$	1.69098	−	2.92887i	0.133684	−	0.231547i
$161$	0.673762	+	1.16699i	0.0530999	+	0.0919717i
$162$	−4.12956	+	39.2902i	−0.324449	+	3.08693i
$163$	−8.66312	+	6.29412i	−0.678548	+	0.492994i	−0.872876	−	0.487943i	$-0.837747\pi$
$163$	−8.66312	+	6.29412i	−0.678548	+	0.492994i	0.194328	+	0.980937i	$0.437747\pi$
$164$	−0.452215	−	4.30254i	−0.0353121	−	0.335972i
$165$	−4.33070	−	4.80973i	−0.337145	−	0.374437i
$166$	22.0898	−	9.83503i	1.71450	−	0.763346i
$167$	−6.33070	+	1.34563i	−0.489885	+	0.104128i	−0.446230	−	0.894918i	$-0.647234\pi$
$167$	−6.33070	+	1.34563i	−0.489885	+	0.104128i	−0.0436549	+	0.999047i	$0.513900\pi$
$168$	1.67088	+	0.355156i	0.128911	+	0.0274008i
$169$	−2.30932	−	1.02817i	−0.177640	−	0.0790904i
$170$	−0.381966	−	1.17557i	−0.0292955	−	0.0901621i
$171$	−5.16312	−	15.8904i	−0.394834	−	1.21517i
$172$	−0.697887	−	0.310719i	−0.0532134	−	0.0236921i
$173$	−2.87993	−	0.612149i	−0.218957	−	0.0465408i	0.0971267	−	0.995272i	$-0.469035\pi$
$173$	−2.87993	−	0.612149i	−0.218957	−	0.0465408i	−0.316084	+	0.948731i	$0.602368\pi$
$174$	14.1559	−	3.00893i	1.07315	−	0.228106i
$175$	−0.862635	+	0.384070i	−0.0652091	+	0.0290330i
$176$	6.49606	+	7.21460i	0.489659	+	0.543821i
$177$	−0.756375	−	7.19643i	−0.0568526	−	0.540917i
$178$	15.3262	−	11.1352i	1.14875	−	0.834616i
$179$	0.178556	−	1.69885i	0.0133459	−	0.126978i	−0.985820	−	0.167804i	$-0.946332\pi$
$179$	0.178556	−	1.69885i	0.0133459	−	0.126978i	0.999166	+	0.0408264i	$0.0129991\pi$
$180$	−2.30902	−	3.99933i	−0.172104	−	0.298093i
$181$	−2.09017	+	3.62028i	−0.155361	+	0.269093i	−0.933190	−	0.359382i	$-0.882987\pi$
$181$	−2.09017	+	3.62028i	−0.155361	+	0.269093i	0.777829	+	0.628476i	$0.216321\pi$
$182$	−1.00000	−	0.726543i	−0.0741249	−	0.0538549i
$183$	−17.7133	+	19.6726i	−1.30941	+	1.45424i
$184$	3.94427	−	12.1392i	0.290776	−	0.894915i
$185$	2.00000			0.147043
$186$		0			0
$187$	1.52786			0.111728
$188$	0.472136	−	1.45309i	0.0344341	−	0.105977i
$189$	2.28602	−	2.53889i	0.166284	−	0.184677i
$190$	2.92705	+	2.12663i	0.212351	+	0.154282i
$191$	9.59017	−	16.6107i	0.693920	−	1.20191i	−0.276623	−	0.960979i	$-0.589215\pi$
$191$	9.59017	−	16.6107i	0.693920	−	1.20191i	0.970543	−	0.240927i	$-0.0774514\pi$
$192$	−6.85410	−	11.8717i	−0.494652	−	0.856763i
$193$	−0.362937	+	3.45312i	−0.0261248	+	0.248561i	0.973664	+	0.227989i	$0.0732152\pi$
$193$	−0.362937	+	3.45312i	−0.0261248	+	0.248561i	−0.999788	+	0.0205713i	$0.993452\pi$
$194$	20.8713	−	15.1639i	1.49847	−	1.08870i
$195$	−1.09464	−	10.4148i	−0.0783885	−	0.745817i
$196$	−2.87177	−	3.18943i	−0.205127	−	0.227816i
$197$	−10.4294	+	4.64347i	−0.743065	+	0.330834i	−0.743113	−	0.669166i	$-0.766651\pi$
$197$	−10.4294	+	4.64347i	−0.743065	+	0.330834i	4.81111e−5		1.00000i	$0.499985\pi$
$198$	23.6519	−	5.02738i	1.68087	−	0.357280i
$199$	−18.5303	−	3.93874i	−1.31358	−	0.279210i	−0.502718	−	0.864450i	$-0.667667\pi$
$199$	−18.5303	−	3.93874i	−1.31358	−	0.279210i	−0.810860	+	0.585241i	$0.801000\pi$
$200$	8.17100	+	3.63796i	0.577777	+	0.257243i
$201$	8.00000	+	24.6215i	0.564276	+	1.73666i
$202$	−1.50000	−	4.61653i	−0.105540	−	0.324818i
$203$	−0.596066	−	0.265386i	−0.0418357	−	0.0186264i
$204$	1.49448	+	0.317661i	0.104634	+	0.0222407i
$205$	−6.84703	+	1.45538i	−0.478218	+	0.101648i
$206$	9.21783	−	4.10404i	0.642237	−	0.285942i
$207$	−28.5401	−	31.6970i	−1.98367	−	2.20309i
$208$	1.64195	+	15.6222i	0.113849	+	1.08320i
$209$	−3.61803	+	2.62866i	−0.250265	+	0.181828i
$210$	−0.129204	+	1.22930i	−0.00891594	+	0.0848295i
$211$	−11.5902	−	20.0748i	−0.797900	−	1.38200i	−0.920981	−	0.389607i	$-0.872611\pi$
$211$	−11.5902	−	20.0748i	−0.797900	−	1.38200i	0.123081	−	0.992397i	$-0.460723\pi$
$212$	−3.23607	+	5.60503i	−0.222254	+	0.384955i
$213$	24.0344	+	17.4620i	1.64681	+	1.19648i
$214$	6.24047	−	6.93075i	0.426590	−	0.473776i
$215$	−0.381966	+	1.17557i	−0.0260499	+	0.0801732i
$216$	−32.3607			−2.20187
$217$		0			0
$218$	−22.5623			−1.52811
$219$	−8.47214	+	26.0746i	−0.572494	+	1.76196i
$220$	−0.827091	+	0.918578i	−0.0557625	+	0.0619305i
$221$	2.00000	+	1.45309i	0.134535	+	0.0977451i
$222$	−5.23607	+	9.06914i	−0.351422	+	0.608681i
$223$	2.00000	+	3.46410i	0.133930	+	0.231973i	0.925188	−	0.379509i	$-0.123907\pi$
$223$	2.00000	+	3.46410i	0.133930	+	0.231973i	−0.791258	+	0.611482i	$0.790574\pi$
$224$	0.0834528	−	0.794000i	0.00557592	−	0.0530514i
$225$	24.1803	−	17.5680i	1.61202	−	1.17120i
$226$	−0.587244	−	5.58726i	−0.0390629	−	0.371659i
$227$	−4.33070	−	4.80973i	−0.287439	−	0.319233i	0.582081	−	0.813131i	$-0.302239\pi$
$227$	−4.33070	−	4.80973i	−0.287439	−	0.319233i	−0.869520	+	0.493897i	$0.835572\pi$
$228$	−4.08550	+	1.81898i	−0.270569	+	0.120465i
$229$	−13.1232	+	2.78943i	−0.867207	+	0.184331i	−0.619971	−	0.784625i	$-0.712856\pi$
$229$	−13.1232	+	2.78943i	−0.867207	+	0.184331i	−0.247236	+	0.968955i	$0.579522\pi$
$230$	9.03424	+	1.92029i	0.595700	+	0.126620i
$231$	−1.39577	−	0.621438i	−0.0918351	−	0.0408876i
$232$	1.90983	+	5.87785i	0.125386	+	0.385900i
$233$	5.54508	+	17.0660i	0.363271	+	1.11803i	0.951057	+	0.309016i	$0.0999996\pi$
$233$	5.54508	+	17.0660i	0.363271	+	1.11803i	−0.587786	+	0.809016i	$0.700000\pi$
$234$	35.7421	+	15.9134i	2.33653	+	1.04029i
$235$	−2.41811	−	0.513986i	−0.157740	−	0.0335287i
$236$	−1.35177	+	0.287327i	−0.0879925	+	0.0187034i
$237$	34.6129	−	15.4107i	2.24835	−	1.00103i
$238$	−0.195250	−	0.216847i	−0.0126562	−	0.0140561i
$239$	−1.22384	−	11.6441i	−0.0791637	−	0.753192i	−0.960043	−	0.279852i	$-0.909715\pi$
$239$	−1.22384	−	11.6441i	−0.0791637	−	0.753192i	0.880880	−	0.473340i	$-0.156952\pi$
$240$	12.7082	−	9.23305i	0.820311	−	0.595991i
$241$	1.50110	−	14.2820i	0.0966943	−	0.919985i	−0.833401	−	0.552668i	$-0.813610\pi$
$241$	1.50110	−	14.2820i	0.0966943	−	0.919985i	0.930096	−	0.367317i	$-0.119724\pi$
$242$	5.66312	+	9.80881i	0.364039	+	0.630534i
$243$	−17.7984	+	30.8277i	−1.14177	+	1.97760i
$244$	4.09017	+	2.97168i	0.261846	+	0.190242i
$245$	−4.64662	+	5.16060i	−0.296862	+	0.329699i
$246$	11.3262	−	34.8586i	0.722135	−	2.22250i
$247$	−7.23607			−0.460420
$248$		0			0
$249$	48.3607			3.06473
$250$	−4.50000	+	13.8496i	−0.284605	+	0.875924i
$251$	1.21759	−	1.35227i	0.0768536	−	0.0853546i	−0.703492	−	0.710704i	$-0.748377\pi$
$251$	1.21759	−	1.35227i	0.0768536	−	0.0853546i	0.780345	+	0.625349i	$0.215043\pi$
$252$	−0.881966	−	0.640786i	−0.0555586	−	0.0403657i
$253$	−5.70820	+	9.88690i	−0.358872	+	0.621584i
$254$	10.0902	+	17.4767i	0.633114	+	1.09658i
$255$	0.258409	−	2.45859i	0.0161822	−	0.153963i
$256$	−10.9721	+	7.97172i	−0.685758	+	0.498233i
$257$	−0.203232	−	1.93362i	−0.0126772	−	0.120616i	0.986353	−	0.164644i	$-0.0526475\pi$
$257$	−0.203232	−	1.93362i	−0.0126772	−	0.120616i	−0.999030	+	0.0440281i	$0.985981\pi$
$258$	−4.33070	−	4.80973i	−0.269618	−	0.299441i
$259$	0.431318	−	0.192035i	0.0268008	−	0.0119325i
$260$	−1.95630	+	0.415823i	−0.121324	+	0.0257883i
$261$	20.2012	+	4.29389i	1.25042	+	0.265785i
$262$	17.7378	+	7.89736i	1.09584	+	0.487901i
$263$	7.18034	+	22.0988i	0.442759	+	1.36267i	0.884923	+	0.465737i	$0.154211\pi$
$263$	7.18034	+	22.0988i	0.442759	+	1.36267i	−0.442164	+	0.896934i	$0.645789\pi$
$264$	4.47214	+	13.7638i	0.275241	+	0.847105i
$265$	9.56677	+	4.25940i	0.587682	+	0.261653i
$266$	0.835438	+	0.177578i	0.0512240	+	0.0108880i
$267$	37.0606	−	7.87747i	2.26807	−	0.482093i
$268$	4.51682	−	2.01102i	0.275909	−	0.122842i
$269$	7.39773	+	8.21601i	0.451047	+	0.500939i	0.925187	−	0.379511i	$-0.123908\pi$
$269$	7.39773	+	8.21601i	0.451047	+	0.500939i	−0.474140	+	0.880449i	$0.657241\pi$
$270$	−2.44768	−	23.2881i	−0.148961	−	1.41727i
$271$	−11.4721	+	8.33499i	−0.696883	+	0.506315i	−0.878915	−	0.476978i	$-0.841732\pi$
$271$	−11.4721	+	8.33499i	−0.696883	+	0.506315i	0.182033	+	0.983292i	$0.441732\pi$
$272$	−0.387613	+	3.68789i	−0.0235025	+	0.223611i
$273$	−1.23607	−	2.14093i	−0.0748102	−	0.129575i
$274$	5.09017	−	8.81643i	0.307508	−	0.532620i
$275$	−6.47214	−	4.70228i	−0.390284	−	0.283558i
$276$	−7.63907	+	8.48404i	−0.459818	+	0.510679i
$277$	3.90983	−	12.0332i	0.234919	−	0.723006i	−0.762213	−	0.647326i	$-0.775887\pi$
$277$	3.90983	−	12.0332i	0.234919	−	0.723006i	0.997132	−	0.0756801i	$-0.0241128\pi$
$278$	−21.7082			−1.30197
$279$		0			0
$280$	−0.527864			−0.0315459
$281$	5.25329	−	16.1680i	0.313385	−	0.964500i	−0.663029	−	0.748594i	$-0.730729\pi$
$281$	5.25329	−	16.1680i	0.313385	−	0.964500i	0.976414	−	0.215906i	$-0.0692705\pi$
$282$	8.66141	−	9.61947i	0.515779	−	0.572831i
$283$	11.2361	+	8.16348i	0.667915	+	0.485269i	0.869327	−	0.494238i	$-0.164553\pi$
$283$	11.2361	+	8.16348i	0.667915	+	0.485269i	−0.201412	+	0.979507i	$0.564553\pi$
$284$	2.83688	−	4.91362i	0.168338	−	0.291570i
$285$	3.61803	+	6.26662i	0.214314	+	0.371202i
$286$	1.09464	−	10.4148i	0.0647272	−	0.615838i
$287$	−1.33688	+	0.971301i	−0.0789136	+	0.0573341i
$288$	2.64149	+	25.1321i	0.155651	+	1.48092i
$289$	−10.9847	−	12.1998i	−0.646160	−	0.717633i
$290$	−4.08550	+	1.81898i	−0.239909	+	0.106814i
$291$	50.4692	−	10.7276i	2.95856	−	0.628861i
$292$	5.12165	+	1.08864i	0.299722	+	0.0637078i
$293$	−0.431318	−	0.192035i	−0.0251978	−	0.0112188i	0.394099	−	0.919068i	$-0.371057\pi$
$293$	−0.431318	−	0.192035i	−0.0251978	−	0.0112188i	−0.419297	+	0.907849i	$0.637723\pi$
$294$	−11.2361	−	34.5811i	−0.655301	−	2.01681i
$295$	0.690983	+	2.12663i	0.0402306	+	0.123817i
$296$	−4.08550	−	1.81898i	−0.237465	−	0.105726i
$297$	28.3118	+	6.01785i	1.64282	+	0.349191i
$298$	−15.8268	+	3.36408i	−0.916820	+	0.194876i
$299$	−16.8751	+	7.51329i	−0.975914	+	0.434505i
$300$	−5.35304	−	5.94516i	−0.309058	−	0.343244i
$301$	0.0305010	+	0.290198i	0.00175805	+	0.0167267i
$302$	−18.5623	+	13.4863i	−1.06814	+	0.776050i
$303$	1.01478	−	9.65502i	0.0582978	−	0.554666i
$304$	−5.42705	−	9.39993i	−0.311263	−	0.539123i
$305$	4.09017	−	7.08438i	0.234202	−	0.405651i
$306$	7.47214	+	5.42882i	0.427154	+	0.310345i
$307$	−19.2095	+	21.3344i	−1.09635	+	1.21762i	−0.122007	+	0.992529i	$0.538933\pi$
$307$	−19.2095	+	21.3344i	−1.09635	+	1.21762i	−0.974339	+	0.225087i	$0.927733\pi$
$308$	−0.0901699	+	0.277515i	−0.00513791	+	0.0158129i
$309$	20.1803			1.14802
$310$		0			0
$311$	−29.1803			−1.65467			−0.827333	−	0.561712i	$-0.810143\pi$
$311$	−29.1803			−1.65467			−0.827333	+	0.561712i	$0.810143\pi$
$312$	−7.23607	+	22.2703i	−0.409662	+	1.26081i
$313$	−11.2173	+	12.4580i	−0.634037	+	0.704169i	−0.971465	−	0.237182i	$-0.923776\pi$
$313$	−11.2173	+	12.4580i	−0.634037	+	0.704169i	0.337428	+	0.941351i	$0.390443\pi$
$314$	−27.3435	−	19.8662i	−1.54308	−	1.12111i
$315$	−0.881966	+	1.52761i	−0.0496932	+	0.0860711i
$316$	−3.61803	−	6.26662i	−0.203530	−	0.352525i
$317$	−0.423939	+	4.03351i	−0.0238108	+	0.226545i	0.976145	+	0.217121i	$0.0696665\pi$
$317$	−0.423939	+	4.03351i	−0.0238108	+	0.226545i	−0.999956	+	0.00942400i	$0.997000\pi$
$318$	−44.3607	+	32.2299i	−2.48762	+	1.80736i
$319$	−0.577819	−	5.49758i	−0.0323517	−	0.307805i
$320$	2.83448	+	3.14801i	0.158452	+	0.175979i
$321$	17.0399	−	7.58665i	0.951074	−	0.423445i
$322$	2.13269	−	0.453318i	0.118850	−	0.0252624i
$323$	−1.67088	−	0.355156i	−0.0929700	−	0.0197614i
$324$	13.7856	+	6.13773i	0.765864	+	0.340985i
$325$	−4.00000	−	12.3107i	−0.221880	−	0.682877i
$326$	5.35410	+	16.4782i	0.296536	+	0.912645i
$327$	−41.2234	−	18.3538i	−2.27966	−	1.01497i
$328$	15.3104	+	3.25433i	0.845377	+	0.179690i
$329$	−0.570839	+	0.121336i	−0.0314714	+	0.00668945i
$330$	−9.56677	+	4.25940i	−0.526633	+	0.234472i
$331$	−1.33826	−	1.48629i	−0.0735575	−	0.0816939i	0.705243	−	0.708966i	$-0.250838\pi$
$331$	−1.33826	−	1.48629i	−0.0735575	−	0.0816939i	−0.778800	+	0.627272i	$0.784171\pi$
$332$	−0.965432	−	9.18547i	−0.0529850	−	0.504118i
$333$	−12.0902	+	8.78402i	−0.662537	+	0.481361i
$334$	−1.09464	+	10.4148i	−0.0598958	+	0.569871i
$335$	−4.00000	−	6.92820i	−0.218543	−	0.378528i
$336$	1.85410	−	3.21140i	0.101150	−	0.175196i
$337$	−11.9443	−	8.67802i	−0.650646	−	0.472722i	0.212845	−	0.977086i	$-0.431727\pi$
$337$	−11.9443	−	8.67802i	−0.650646	−	0.472722i	−0.863491	+	0.504364i	$0.831727\pi$
$338$	−2.73686	+	3.03959i	−0.148865	+	0.165332i
$339$	3.47214	−	10.6861i	0.188581	−	0.580391i
$340$	−0.472136			−0.0256052
$341$		0			0
$342$	−27.0344			−1.46186
$343$	−1.01722	+	3.13068i	−0.0549248	+	0.169041i
$344$	1.84943	−	2.05400i	0.0997147	−	0.110744i
$345$	14.9443	+	10.8576i	0.804573	+	0.584556i
$346$	−2.38197	+	4.12569i	−0.128055	+	0.221798i
$347$	12.0902	+	20.9408i	0.649034	+	1.12416i	0.983354	+	0.181701i	$0.0581602\pi$
$347$	12.0902	+	20.9408i	0.649034	+	1.12416i	−0.334320	+	0.942460i	$0.608506\pi$
$348$	0.577819	−	5.49758i	0.0309744	−	0.294701i
$349$	6.38197	−	4.63677i	0.341619	−	0.248201i	−0.403726	−	0.914880i	$-0.632285\pi$
$349$	6.38197	−	4.63677i	0.341619	−	0.248201i	0.745345	+	0.666679i	$0.232285\pi$
$350$	0.159705	+	1.51949i	0.00853661	+	0.0812204i
$351$	31.3373	+	34.8036i	1.67266	+	1.85768i
$352$	6.17916	−	2.75114i	0.329350	−	0.146636i
$353$	7.25434	−	1.54196i	0.386110	−	0.0820701i	−0.0107671	−	0.999942i	$-0.503427\pi$
$353$	7.25434	−	1.54196i	0.386110	−	0.0820701i	0.396877	+	0.917872i	$0.370094\pi$
$354$	−11.4524	−	2.43427i	−0.608686	−	0.129380i
$355$	−8.38666	−	3.73398i	−0.445118	−	0.198179i
$356$	−2.23607	−	6.88191i	−0.118511	−	0.364740i
$357$	−0.180340	−	0.555029i	−0.00954460	−	0.0293753i
$358$	−2.52498	−	1.12419i	−0.133449	−	0.0594154i
$359$	−21.7502	−	4.62314i	−1.14793	−	0.244000i	−0.405610	−	0.914046i	$-0.632941\pi$
$359$	−21.7502	−	4.62314i	−1.14793	−	0.244000i	−0.742319	+	0.670046i	$0.766274\pi$
$360$	16.3431	−	3.47383i	0.861356	−	0.183087i
$361$	−12.7896	+	5.69431i	−0.673139	+	0.299701i
$362$	4.52595	+	5.02658i	0.237879	+	0.264191i
$363$	2.36783	+	22.5284i	0.124279	+	1.18243i
$364$	−0.381966	+	0.277515i	−0.0200205	+	0.0145457i
$365$	0.885579	−	8.42572i	0.0463533	−	0.441023i
$366$	21.4164	+	37.0943i	1.11945	+	1.93895i
$367$	9.00000	−	15.5885i	0.469796	−	0.813711i	−0.529607	−	0.848243i	$-0.677661\pi$
$367$	9.00000	−	15.5885i	0.469796	−	0.813711i	0.999404	+	0.0345320i	$0.0109941\pi$
$368$	−22.4164	−	16.2865i	−1.16854	−	0.848991i
$369$	34.9988	−	38.8702i	1.82197	−	2.02350i
$370$	1.00000	−	3.07768i	0.0519875	−	0.160001i
$371$	2.47214			0.128347
$372$		0			0
$373$	19.0000			0.983783			0.491891	−	0.870657i	$-0.336306\pi$
$373$	19.0000			0.983783			0.491891	+	0.870657i	$0.336306\pi$
$374$	0.763932	−	2.35114i	0.0395020	−	0.121575i
$375$	−19.4882	+	21.6438i	−1.00636	+	1.11768i
$376$	4.47214	+	3.24920i	0.230633	+	0.167565i
$377$	4.47214	−	7.74597i	0.230327	−	0.398938i
$378$	−2.76393	−	4.78727i	−0.142161	−	0.246231i
$379$	0.220707	−	2.09989i	0.0113370	−	0.107864i	−0.987390	−	0.158307i	$-0.949397\pi$
$379$	0.220707	−	2.09989i	0.0113370	−	0.107864i	0.998727	+	0.0504426i	$0.0160632\pi$
$380$	1.11803	−	0.812299i	0.0573539	−	0.0416701i
$381$	4.21884	+	40.1396i	0.216138	+	2.05641i
$382$	−20.7661	−	23.0631i	−1.06249	−	1.18001i
$383$	21.8233	−	9.71635i	1.11512	−	0.496482i	0.235361	−	0.971908i	$-0.424373\pi$
$383$	21.8233	−	9.71635i	1.11512	−	0.496482i	0.879756	+	0.475426i	$0.157706\pi$
$384$	−43.1059	+	9.16244i	−2.19974	+	0.467569i
$385$	0.461819	+	0.0981626i	0.0235365	+	0.00500283i
$386$	5.13233	+	2.28506i	0.261229	+	0.116307i
$387$	−2.85410	−	8.78402i	−0.145082	−	0.446517i
$388$	−3.04508	−	9.37181i	−0.154591	−	0.475781i
$389$	16.3420	+	7.27593i	0.828572	+	0.368904i	0.776794	−	0.629755i	$-0.216845\pi$
$389$	16.3420	+	7.27593i	0.828572	+	0.368904i	0.0517780	+	0.998659i	$0.483511\pi$
$390$	−16.5740	−	3.52291i	−0.839257	−	0.178390i
$391$	−4.26539	+	0.906636i	−0.215710	+	0.0458506i
$392$	14.1854	−	6.31575i	0.716471	−	0.318994i
$393$	25.9842	+	28.8584i	1.31073	+	1.45571i
$394$	1.93086	+	18.3709i	0.0972755	+	0.925515i
$395$	−9.47214	+	6.88191i	−0.476595	+	0.346266i
$396$	0.965432	−	9.18547i	0.0485148	−	0.461587i
$397$	3.50000	+	6.06218i	0.175660	+	0.304252i	0.940389	−	0.340099i	$-0.110461\pi$
$397$	3.50000	+	6.06218i	0.175660	+	0.304252i	−0.764730	+	0.644351i	$0.777127\pi$
$398$	−15.3262	+	26.5458i	−0.768235	+	1.33062i
$399$	1.38197	+	1.00406i	0.0691848	+	0.0502657i
$400$	12.9921	−	14.4292i	0.649606	−	0.721460i
$401$	−11.7984	+	36.3117i	−0.589183	+	1.81332i	−0.00740130	+	0.999973i	$0.502356\pi$
$401$	−11.7984	+	36.3117i	−0.589183	+	1.81332i	−0.581781	+	0.813345i	$0.697644\pi$
$402$	41.8885			2.08921
$403$		0			0
$404$	−1.85410			−0.0922450
$405$	7.54508	−	23.2214i	0.374918	−	1.15388i
$406$	−0.706420	+	0.784559i	−0.0350590	+	0.0389370i
$407$	3.23607	+	2.35114i	0.160406	+	0.116542i
$408$	−2.76393	+	4.78727i	−0.136835	+	0.237005i
$409$	−1.90983	−	3.30792i	−0.0944350	−	0.163566i	0.814938	−	0.579549i	$-0.196771\pi$
$409$	−1.90983	−	3.30792i	−0.0944350	−	0.163566i	−0.909373	+	0.415982i	$0.863438\pi$
$410$	−1.18391	+	11.2642i	−0.0584694	+	0.556299i
$411$	16.4721	−	11.9677i	0.812511	−	0.590323i
$412$	−0.402863	−	3.83299i	−0.0198477	−	0.188838i
$413$	0.353210	+	0.392279i	0.0173803	+	0.0193028i
$414$	−63.0467	+	28.0702i	−3.09857	+	1.37957i
$415$	−14.6177	+	3.10709i	−0.717555	+	0.152521i
$416$	10.7051	+	2.27544i	0.524861	+	0.111563i
$417$	−39.6629	−	17.6590i	−1.94230	−	0.864767i
$418$	2.23607	+	6.88191i	0.109370	+	0.336605i
$419$	−3.12868	−	9.62908i	−0.152846	−	0.470411i	0.845090	−	0.534623i	$-0.179547\pi$
$419$	−3.12868	−	9.62908i	−0.152846	−	0.470411i	−0.997936	+	0.0642122i	$0.979547\pi$
$420$	0.431318	+	0.192035i	0.0210461	+	0.00937035i
$421$	−28.7191	−	6.10443i	−1.39968	−	0.297512i	−0.554586	−	0.832126i	$-0.687123\pi$
$421$	−28.7191	−	6.10443i	−1.39968	−	0.297512i	−0.845096	+	0.534615i	$0.820457\pi$
$422$	−36.6870	+	7.79806i	−1.78589	+	0.379603i
$423$	16.8751	−	7.51329i	0.820497	−	0.365309i
$424$	−15.6686	−	17.4018i	−0.760936	−	0.845105i
$425$	−0.319411	−	3.03899i	−0.0154937	−	0.147413i
$426$	38.8885	−	28.2542i	1.88416	−	1.36892i
$427$	0.201857	−	1.92054i	0.00976853	−	0.0929413i
$428$	−1.78115	−	3.08505i	−0.0860953	−	0.149121i
$429$	10.4721	−	18.1383i	0.505599	−	0.875724i
$430$	1.61803	+	1.17557i	0.0780285	+	0.0566910i
$431$	8.02957	−	8.91774i	0.386771	−	0.429552i	−0.518047	−	0.855352i	$-0.673341\pi$
$431$	8.02957	−	8.91774i	0.386771	−	0.429552i	0.904817	+	0.425800i	$0.140007\pi$
$432$	−21.7082	+	66.8110i	−1.04444	+	3.21444i
$433$	−10.1803			−0.489236			−0.244618	−	0.969620i	$-0.578663\pi$
$433$	−10.1803			−0.489236			−0.244618	+	0.969620i	$0.578663\pi$
$434$		0			0
$435$	−8.94427			−0.428845
$436$	−2.66312	+	8.19624i	−0.127540	+	0.392529i
$437$	8.54074	−	9.48545i	0.408559	−	0.453751i
$438$	35.8885	+	26.0746i	1.71482	+	1.24589i
$439$	0.590170	−	1.02220i	0.0281673	−	0.0487872i	−0.851598	−	0.524195i	$-0.824366\pi$
$439$	0.590170	−	1.02220i	0.0281673	−	0.0487872i	0.879765	+	0.475408i	$0.157700\pi$
$440$	−2.23607	−	3.87298i	−0.106600	−	0.184637i
$441$	5.42383	−	51.6043i	0.258278	−	2.45735i
$442$	3.23607	−	2.35114i	0.153924	−	0.111832i
$443$	−3.20988	−	30.5400i	−0.152506	−	1.45100i	−0.756492	−	0.654003i	$-0.773088\pi$
$443$	−3.20988	−	30.5400i	−0.152506	−	1.45100i	0.603986	−	0.796995i	$-0.293578\pi$
$444$	2.67652	+	2.97258i	0.127022	+	0.141072i
$445$	−10.6960	+	4.76216i	−0.507038	+	0.225748i
$446$	6.33070	−	1.34563i	0.299768	−	0.0637176i
$447$	−31.6535	−	6.72816i	−1.49716	−	0.318231i
$448$	0.913545	+	0.406737i	0.0431610	+	0.0192165i
$449$	9.67376	+	29.7728i	0.456533	+	1.40506i	0.869326	+	0.494239i	$0.164553\pi$
$449$	9.67376	+	29.7728i	0.456533	+	1.40506i	−0.412793	+	0.910825i	$0.635447\pi$
$450$	−14.9443	−	45.9937i	−0.704480	−	2.16817i
$451$	−12.7896	−	5.69431i	−0.602240	−	0.268135i
$452$	−2.09901	−	0.446157i	−0.0987289	−	0.0209855i
$453$	−44.8858	+	9.54076i	−2.10892	+	0.448264i
$454$	−9.56677	+	4.25940i	−0.448991	+	0.199904i
$455$	0.511170	+	0.567712i	0.0239640	+	0.0266148i
$456$	−1.69131	−	16.0917i	−0.0792027	−	0.753563i
$457$	−2.47214	+	1.79611i	−0.115642	+	0.0840186i	−0.644103	−	0.764939i	$-0.722769\pi$
$457$	−2.47214	+	1.79611i	−0.115642	+	0.0840186i	0.528461	+	0.848957i	$0.322769\pi$
$458$	−2.26913	+	21.5893i	−0.106029	+	1.00880i
$459$	5.52786	+	9.57454i	0.258019	+	0.446901i
$460$	1.76393	−	3.05522i	0.0822438	−	0.142450i
$461$	27.7984	+	20.1967i	1.29470	+	0.940654i	0.999889	−	0.0149016i	$-0.00474351\pi$
$461$	27.7984	+	20.1967i	1.29470	+	0.940654i	0.294810	+	0.955556i	$0.404744\pi$
$462$	−1.65418	+	1.83716i	−0.0769595	+	0.0854722i
$463$	0.798374	−	2.45714i	0.0371036	−	0.114193i	−0.930789	−	0.365556i	$-0.880879\pi$
$463$	0.798374	−	2.45714i	0.0371036	−	0.114193i	0.967893	+	0.251363i	$0.0808788\pi$
$464$	13.4164			0.622841
$465$		0			0
$466$	29.0344			1.34499
$467$	1.45492	−	4.47777i	0.0673254	−	0.207206i	−0.911734	−	0.410781i	$-0.865256\pi$
$467$	1.45492	−	4.47777i	0.0673254	−	0.207206i	0.979059	+	0.203575i	$0.0652560\pi$
$468$	9.99967	−	11.1058i	0.462235	−	0.513364i
$469$	−1.52786	−	1.11006i	−0.0705502	−	0.0512577i
$470$	−2.00000	+	3.46410i	−0.0922531	+	0.159787i
$471$	−33.7984	−	58.5405i	−1.55735	−	2.69740i
$472$	0.522642	−	4.97261i	0.0240566	−	0.228883i
$473$	−2.00000	+	1.45309i	−0.0919601	+	0.0668129i
$474$	−6.40811	−	60.9691i	−0.294334	−	2.80040i
$475$	5.98489	+	6.64689i	0.274605	+	0.304980i
$476$	−0.101820	+	0.0453333i	−0.00466693	+	0.00207785i
$477$	−76.5393	+	16.2689i	−3.50449	+	0.744903i
$478$	−18.5303	−	3.93874i	−0.847556	−	0.180154i
$479$	21.2781	+	9.47363i	0.972222	+	0.432861i	0.830484	−	0.557043i	$-0.188064\pi$
$479$	21.2781	+	9.47363i	0.972222	+	0.432861i	0.141738	+	0.989904i	$0.454731\pi$
$480$	−3.38197	−	10.4086i	−0.154365	−	0.475086i
$481$	2.00000	+	6.15537i	0.0911922	+	0.280661i
$482$	−21.2272	−	9.45096i	−0.966873	−	0.430479i
$483$	4.26539	+	0.906636i	0.194082	+	0.0412534i
$484$	4.23170	−	0.899475i	0.192350	−	0.0408852i
$485$	−14.5658	+	6.48512i	−0.661400	+	0.294474i
$486$	38.5397	+	42.8027i	1.74820	+	1.94157i
$487$	−2.01072	−	19.1307i	−0.0911143	−	0.866894i	−0.940653	−	0.339369i	$-0.889787\pi$
$487$	−2.01072	−	19.1307i	−0.0911143	−	0.866894i	0.849539	−	0.527526i	$-0.176880\pi$
$488$	−14.7984	+	10.7516i	−0.669891	+	0.486704i
$489$	−3.62217	+	34.4626i	−0.163800	+	1.55845i
$490$	5.61803	+	9.73072i	0.253797	+	0.439589i
$491$	2.18034	−	3.77646i	0.0983974	−	0.170429i	−0.812624	−	0.582788i	$-0.801962\pi$
$491$	2.18034	−	3.77646i	0.0983974	−	0.170429i	0.911021	+	0.412359i	$0.135295\pi$
$492$	−11.3262	−	8.22899i	−0.510626	−	0.370992i
$493$	1.41284	−	1.56912i	0.0636311	−	0.0706695i
$494$	−3.61803	+	11.1352i	−0.162783	+	0.500995i
$495$	−14.9443			−0.671695
$496$		0			0
$497$	−2.16718			−0.0972115
$498$	24.1803	−	74.4194i	1.08355	−	3.33481i
$499$	4.40528	−	4.89256i	0.197208	−	0.219021i	−0.636428	−	0.771336i	$-0.719589\pi$
$499$	4.40528	−	4.89256i	0.197208	−	0.219021i	0.833636	+	0.552315i	$0.186255\pi$
$500$	4.50000	+	3.26944i	0.201246	+	0.146214i
$501$	−10.4721	+	18.1383i	−0.467861	+	0.810358i
$502$	−1.47214	−	2.54981i	−0.0657046	−	0.113804i
$503$	−3.09953	+	29.4900i	−0.138201	+	1.31490i	0.677114	+	0.735878i	$0.263230\pi$
$503$	−3.09953	+	29.4900i	−0.138201	+	1.31490i	−0.815315	+	0.579018i	$0.803436\pi$
$504$	3.19098	−	2.31838i	0.142138	−	0.103269i
$505$	0.313585	+	2.98357i	0.0139544	+	0.132767i
$506$	12.3603	+	13.7275i	0.549481	+	0.610261i
$507$	−7.47311	+	3.32724i	−0.331893	+	0.147768i
$508$	7.53976	−	1.60263i	0.334523	−	0.0711050i
$509$	28.9500	+	6.15351i	1.28319	+	0.272750i	0.798530	−	0.601955i	$-0.205611\pi$
$509$	28.9500	+	6.15351i	1.28319	+	0.272750i	0.484656	+	0.874705i	$0.338945\pi$
$510$	−3.65418	−	1.62695i	−0.161810	−	0.0720424i
$511$	−0.618034	−	1.90211i	−0.0273402	−	0.0841445i
$512$	−1.63525	−	5.03280i	−0.0722687	−	0.222420i
$513$	−29.5630	−	13.1623i	−1.30524	−	0.581129i
$514$	−3.07715	−	0.654069i	−0.135727	−	0.0288497i
$515$	−6.09979	+	1.29655i	−0.268789	+	0.0571329i
$516$	−2.25841	+	1.00551i	−0.0994209	+	0.0442650i
$517$	−3.30836	−	3.67431i	−0.145502	−	0.161596i
$518$	−0.0798526	−	0.759747i	−0.00350852	−	0.0333814i
$519$	−7.70820	+	5.60034i	−0.338353	+	0.245828i
$520$	0.756375	−	7.19643i	0.0331692	−	0.315584i
$521$	−1.00000	−	1.73205i	−0.0438108	−	0.0758825i	0.843288	−	0.537461i	$-0.180617\pi$
$521$	−1.00000	−	1.73205i	−0.0438108	−	0.0758825i	−0.887099	+	0.461579i	$0.847283\pi$
$522$	16.7082	−	28.9395i	0.731298	−	1.26665i
$523$	−14.3262	−	10.4086i	−0.626443	−	0.455137i	0.228723	−	0.973491i	$-0.426545\pi$
$523$	−14.3262	−	10.4086i	−0.626443	−	0.455137i	−0.855166	+	0.518354i	$0.826545\pi$
$524$	4.96255	−	5.51147i	0.216790	−	0.240769i
$525$	−0.944272	+	2.90617i	−0.0412114	+	0.126836i
$526$	37.5967			1.63930
$527$		0			0
$528$	31.4164			1.36722
$529$	2.96149	−	9.11454i	0.128761	−	0.396284i
$530$	11.3379	−	12.5920i	0.492488	−	0.546964i
$531$	−13.5172	−	9.82084i	−0.586597	−	0.426188i
$532$	0.163119	−	0.282530i	0.00707210	−	0.0122492i
$533$	−11.3262	−	19.6176i	−0.490594	−	0.849733i
$534$	6.40811	−	60.9691i	0.277306	−	2.63839i
$535$	−4.66312	+	3.38795i	−0.201604	+	0.146474i
$536$	1.86986	+	17.7905i	0.0807657	+	0.768435i
$537$	−3.69886	−	4.10800i	−0.159618	−	0.177273i
$538$	16.3420	−	7.27593i	0.704554	−	0.313687i
$539$	−13.5850	+	2.88759i	−0.585149	+	0.124377i
$540$	−8.74882	−	1.85962i	−0.376489	−	0.0800252i
$541$	−23.1681	−	10.3151i	−0.996076	−	0.443482i	−0.157060	−	0.987589i	$-0.550202\pi$
$541$	−23.1681	−	10.3151i	−0.996076	−	0.443482i	−0.839016	+	0.544107i	$0.816868\pi$
$542$	7.09017	+	21.8213i	0.304549	+	0.937305i
$543$	4.18034	+	12.8658i	0.179396	+	0.552123i
$544$	2.36023	+	1.05084i	0.101194	+	0.0450545i
$545$	13.6396	+	2.89918i	0.584254	+	0.124187i
$546$	−3.91259	+	0.831647i	−0.167443	+	0.0355912i
$547$	−11.0764	+	4.93152i	−0.473592	+	0.210857i	−0.629631	−	0.776894i	$-0.716794\pi$
$547$	−11.0764	+	4.93152i	−0.473592	+	0.210857i	0.156039	+	0.987751i	$0.450127\pi$
$548$	−2.60194	−	2.88975i	−0.111150	−	0.123444i
$549$	6.38926	+	60.7898i	0.272687	+	2.59444i
$550$	−10.4721	+	7.60845i	−0.446533	+	0.324425i
$551$	−0.646021	+	6.14648i	−0.0275214	+	0.261849i
$552$	−20.6525	−	35.7711i	−0.879028	−	1.52252i
$553$	−1.38197	+	2.39364i	−0.0587672	+	0.101788i
$554$	−16.5623	−	12.0332i	−0.703665	−	0.511243i
$555$	4.33070	−	4.80973i	0.183828	−	0.204162i
$556$	−2.56231	+	7.88597i	−0.108666	+	0.334439i
$557$	12.0000			0.508456			0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000			0.508456			0.254228	+	0.967144i	$0.418179\pi$
$558$		0			0
$559$	−4.00000			−0.169182
$560$	−0.354102	+	1.08981i	−0.0149635	+	0.0460530i
$561$	3.30836	−	3.67431i	0.139679	−	0.155129i
$562$	−22.2533	−	16.1680i	−0.938698	−	0.682004i
$563$	−13.7705	+	23.8512i	−0.580358	+	1.00521i	0.415079	+	0.909785i	$0.363754\pi$
$563$	−13.7705	+	23.8512i	−0.580358	+	1.00521i	−0.995437	+	0.0954238i	$0.969579\pi$
$564$	−2.47214	−	4.28187i	−0.104096	−	0.180299i
$565$	−0.362937	+	3.45312i	−0.0152689	+	0.145274i
$566$	18.1803	−	13.2088i	0.764177	−	0.555207i
$567$	−0.602495	−	5.73236i	−0.0253024	−	0.240736i
$568$	13.7358	+	15.2552i	0.576342	+	0.640093i
$569$	−5.04996	+	2.24838i	−0.211705	+	0.0942572i	−0.509850	−	0.860264i	$-0.670299\pi$
$569$	−5.04996	+	2.24838i	−0.211705	+	0.0942572i	0.298144	+	0.954521i	$0.403632\pi$
$570$	11.4524	−	2.43427i	0.479686	−	0.101960i
$571$	27.5645	+	5.85902i	1.15354	+	0.245192i	0.744691	−	0.667410i	$-0.232597\pi$
$571$	27.5645	+	5.85902i	1.15354	+	0.245192i	0.408849	+	0.912602i	$0.365930\pi$
$572$	−3.65418	−	1.62695i	−0.152789	−	0.0680261i
$573$	−19.1803	−	59.0310i	−0.801270	−	2.46606i
$574$	0.826238	+	2.54290i	0.0344865	+	0.106139i
$575$	20.8588	+	9.28694i	0.869873	+	0.387292i
$576$	−30.9608	−	6.58092i	−1.29003	−	0.274205i
$577$	28.2027	−	5.99468i	1.17410	−	0.249562i	0.420744	−	0.907179i	$-0.361769\pi$
$577$	28.2027	−	5.99468i	1.17410	−	0.249562i	0.753352	+	0.657618i	$0.228436\pi$
$578$	−24.2659	+	10.8039i	−1.00933	+	0.449381i
$579$	7.51840	+	8.35003i	0.312454	+	0.347015i
$580$	0.178556	+	1.69885i	0.00741413	+	0.0705407i
$581$	−2.85410	+	2.07363i	−0.118408	+	0.0860285i
$582$	8.72659	−	83.0280i	0.361729	−	3.44162i
$583$	10.4721	+	18.1383i	0.433712	+	0.751210i
$584$	−9.47214	+	16.4062i	−0.391960	+	0.678894i
$585$	−19.5623	−	14.2128i	−0.808802	−	0.587629i
$586$	−0.511170	+	0.567712i	−0.0211163	+	0.0234520i
$587$	2.00000	−	6.15537i	0.0825488	−	0.254059i	−0.901260	−	0.433278i	$-0.857357\pi$
$587$	2.00000	−	6.15537i	0.0825488	−	0.254059i	0.983809	+	0.179219i	$0.0573569\pi$
$588$	−13.8885			−0.572754
$589$		0			0
$590$	3.61803			0.148952
$591$	−11.4164	+	35.1361i	−0.469608	+	1.44531i
$592$	−6.49606	+	7.21460i	−0.266986	+	0.296518i
$593$	5.28115	+	3.83698i	0.216871	+	0.157566i	0.690917	−	0.722934i	$-0.257207\pi$
$593$	5.28115	+	3.83698i	0.216871	+	0.157566i	−0.474046	+	0.880500i	$0.657207\pi$
$594$	23.4164	−	40.5584i	0.960787	−	1.66413i
$595$	0.0901699	+	0.156179i	0.00369661	+	0.00640271i
$596$	−0.646021	+	6.14648i	−0.0264621	+	0.251770i
$597$	−49.5967	+	36.0341i	−2.02986	+	1.47478i
$598$	3.12420	+	29.7248i	0.127758	+	1.21554i
$599$	−9.76713	−	10.8475i	−0.399074	−	0.443217i	0.509796	−	0.860295i	$-0.329721\pi$
$599$	−9.76713	−	10.8475i	−0.399074	−	0.443217i	−0.908871	+	0.417078i	$0.863054\pi$
$600$	26.4419	−	11.7727i	1.07949	−	0.480618i
$601$	29.8736	−	6.34984i	1.21857	−	0.259015i	0.446635	−	0.894716i	$-0.352622\pi$
$601$	29.8736	−	6.34984i	1.21857	−	0.259015i	0.771935	+	0.635701i	$0.219289\pi$
$602$	0.461819	+	0.0981626i	0.0188223	+	0.00400081i
$603$	54.6091	+	24.3135i	2.22385	+	0.990124i
$604$	2.70820	+	8.33499i	0.110195	+	0.339146i
$605$	−2.16312	−	6.65740i	−0.0879433	−	0.270662i
$606$	−14.3502	−	6.38910i	−0.582935	−	0.259540i
$607$	−21.9811	−	4.67222i	−0.892184	−	0.189640i	−0.261061	−	0.965322i	$-0.584072\pi$
$607$	−21.9811	−	4.67222i	−0.892184	−	0.189640i	−0.631123	+	0.775683i	$0.717406\pi$
$608$	−7.39705	+	1.57229i	−0.299990	+	0.0637649i
$609$	−1.92891	+	0.858807i	−0.0781634	+	0.0348006i
$610$	−8.85666	−	9.83632i	−0.358596	−	0.398261i
$611$	−0.836228	−	7.95618i	−0.0338302	−	0.321872i
$612$	2.85410	−	2.07363i	0.115370	−	0.0838214i
$613$	−4.58760	+	43.6481i	−0.185292	+	1.76293i	0.367889	+	0.929870i	$0.380081\pi$
$613$	−4.58760	+	43.6481i	−0.185292	+	1.76293i	−0.553181	+	0.833061i	$0.686586\pi$
$614$	23.2254	+	40.2276i	0.937302	+	1.62345i
$615$	−11.3262	+	19.6176i	−0.456718	+	0.791059i
$616$	−0.854102	−	0.620541i	−0.0344127	−	0.0250023i
$617$	21.7281	−	24.1315i	0.874740	−	0.971498i	−0.125046	−	0.992151i	$-0.539908\pi$
$617$	21.7281	−	24.1315i	0.874740	−	0.971498i	0.999787	+	0.0206533i	$0.00657462\pi$
$618$	10.0902	−	31.0543i	0.405886	−	1.24919i
$619$	−6.18034			−0.248409			−0.124204	−	0.992257i	$-0.539638\pi$
$619$	−6.18034			−0.248409			−0.124204	+	0.992257i	$0.539638\pi$
$620$		0			0
$621$	−82.6099			−3.31502
$622$	−14.5902	+	44.9039i	−0.585013	+	1.80048i
$623$	−1.84943	+	2.05400i	−0.0740959	+	0.0822918i
$624$	41.1246	+	29.8788i	1.64630	+	1.19611i
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	13.5623	+	23.4906i	0.542059	+	0.938873i
$627$	−1.51275	+	14.3929i	−0.0604134	+	0.574795i
$628$	−10.4443	+	7.58821i	−0.416772	+	0.302802i
$629$	0.159705	+	1.51949i	0.00636787	+	0.0605862i
$630$	1.90977	+	2.12101i	0.0760869	+	0.0845031i
$631$	−31.3900	+	13.9757i	−1.24962	+	0.556366i	−0.921539	−	0.388285i	$-0.873068\pi$
$631$	−31.3900	+	13.9757i	−1.24962	+	0.556366i	−0.328078	+	0.944650i	$0.606401\pi$
$632$	25.6082	−	5.44320i	1.01864	−	0.216519i
$633$	−73.3739	−	15.5961i	−2.91635	−	0.619890i
$634$	5.99496	+	2.66913i	0.238090	+	0.106005i
$635$	−3.85410	−	11.8617i	−0.152945	−	0.470717i
$636$	6.47214	+	19.9192i	0.256637	+	0.789847i
$637$	−20.5293	−	9.14024i	−0.813401	−	0.362150i
$638$	−8.74882	−	1.85962i	−0.346369	−	0.0736230i
$639$	67.0977	−	14.2621i	2.65435	−	0.564199i
$640$	12.4407	−	5.53895i	0.491762	−	0.218946i
$641$	−8.02957	−	8.91774i	−0.317149	−	0.352229i	0.563401	−	0.826184i	$-0.309493\pi$
$641$	−8.02957	−	8.91774i	−0.317149	−	0.352229i	−0.880549	+	0.473954i	$0.842826\pi$
$642$	−3.15470	−	30.0150i	−0.124506	−	1.18460i
$643$	15.7984	−	11.4782i	0.623027	−	0.452656i	−0.230951	−	0.972966i	$-0.574184\pi$
$643$	15.7984	−	11.4782i	0.623027	−	0.452656i	0.853978	+	0.520310i	$0.174184\pi$
$644$	0.0870529	−	0.828253i	0.00343037	−	0.0326378i
$645$	2.00000	+	3.46410i	0.0787499	+	0.136399i
$646$	−1.38197	+	2.39364i	−0.0543727	+	0.0941763i
$647$	−0.763932	−	0.555029i	−0.0300333	−	0.0218204i	0.572667	−	0.819788i	$-0.305909\pi$
$647$	−0.763932	−	0.555029i	−0.0300333	−	0.0218204i	−0.602701	+	0.797967i	$0.705909\pi$
$648$	−36.5324	+	40.5733i	−1.43513	+	1.59387i
$649$	−1.38197	+	4.25325i	−0.0542469	+	0.166955i
$650$	−20.9443			−0.821502
$651$		0			0
$652$	6.61803			0.259182
$653$	−14.6180	+	44.9897i	−0.572048	+	1.76058i	0.0739705	+	0.997260i	$0.476433\pi$
$653$	−14.6180	+	44.9897i	−0.572048	+	1.76058i	−0.646018	+	0.763322i	$0.723567\pi$
$654$	−48.8553	+	54.2593i	−1.91039	+	2.12171i
$655$	−9.70820	−	7.05342i	−0.379331	−	0.275600i
$656$	16.9894	−	29.4264i	0.663323	−	1.14891i
$657$	31.6525	+	54.8237i	1.23488	+	2.13888i
$658$	−0.0987033	+	0.939099i	−0.00384785	+	0.0366099i
$659$	−20.7533	+	15.0781i	−0.808433	+	0.587361i	−0.913376	−	0.407117i	$-0.866534\pi$
$659$	−20.7533	+	15.0781i	−0.808433	+	0.587361i	0.104943	+	0.994478i	$0.466534\pi$
$660$	0.418114	+	3.97809i	0.0162751	+	0.154847i
$661$	−0.427789	−	0.475108i	−0.0166391	−	0.0184795i	0.734768	−	0.678319i	$-0.237291\pi$
$661$	−0.427789	−	0.475108i	−0.0166391	−	0.0184795i	−0.751407	+	0.659839i	$0.770624\pi$
$662$	−2.95630	+	1.31623i	−0.114900	+	0.0511566i
$663$	7.82518	−	1.66329i	0.303905	−	0.0645970i
$664$	32.6862	+	6.94766i	1.26847	+	0.269622i
$665$	−0.482228	−	0.214702i	−0.0187000	−	0.00832577i
$666$	7.47214	+	22.9969i	0.289539	+	0.891111i
$667$	4.87539	+	15.0049i	0.188776	+	0.580992i
$668$	3.65418	+	1.62695i	0.141385	+	0.0629485i
$669$	12.6614	+	2.69127i	0.489518	+	0.104050i
$670$	−12.6614	+	2.69127i	−0.489153	+	0.103973i
$671$	14.9462	−	6.65449i	0.576993	−	0.256894i
$672$	−1.72876	−	1.91998i	−0.0666884	−	0.0740650i
$673$	−3.03270	−	28.8542i	−0.116902	−	1.11225i	−0.882951	−	0.469466i	$-0.844447\pi$
$673$	−3.03270	−	28.8542i	−0.116902	−	1.11225i	0.766049	−	0.642783i	$-0.222220\pi$
$674$	−19.3262	+	14.0413i	−0.744419	+	0.540852i
$675$	6.05100	−	57.5714i	0.232903	−	2.21593i
$676$	0.781153	+	1.35300i	0.0300443	+	0.0520383i
$677$	−23.3607	+	40.4619i	−0.897824	+	1.55508i	−0.0675535	+	0.997716i	$0.521519\pi$
$677$	−23.3607	+	40.4619i	−0.897824	+	1.55508i	−0.830270	+	0.557361i	$0.811814\pi$
$678$	−14.7082	−	10.6861i	−0.564865	−	0.410399i
$679$	−2.51856	+	2.79715i	−0.0966535	+	0.107345i
$680$	0.527864	−	1.62460i	0.0202427	−	0.0623005i
$681$	−20.9443			−0.802586
$682$		0			0
$683$	5.18034			0.198220			0.0991101	−	0.995076i	$-0.468400\pi$
$683$	5.18034			0.198220			0.0991101	+	0.995076i	$0.468400\pi$
$684$	−3.19098	+	9.82084i	−0.122010	+	0.375509i
$685$	−4.21003	+	4.67572i	−0.160857	+	0.178650i
$686$	4.30902	+	3.13068i	0.164519	+	0.119530i
$687$	−21.7082	+	37.5997i	−0.828220	+	1.43452i
$688$	−3.00000	−	5.19615i	−0.114374	−	0.198101i
$689$	−3.54232	+	33.7029i	−0.134952	+	1.28398i
$690$	24.1803	−	17.5680i	0.920530	−	0.668804i
$691$	−0.332436	−	3.16292i	−0.0126465	−	0.120323i	0.986377	−	0.164499i	$-0.0526006\pi$
$691$	−0.332436	−	3.16292i	−0.0126465	−	0.120323i	−0.999024	+	0.0441755i	$0.985934\pi$
$692$	1.21759	+	1.35227i	0.0462858	+	0.0514056i
$693$	−3.22286	+	1.43491i	−0.122426	+	0.0545078i
$694$	38.2696	−	8.13446i	1.45270	−	0.308780i
$695$	13.1232	+	2.78943i	0.497792	+	0.105809i
$696$	18.2709	+	8.13473i	0.692557	+	0.308346i
$697$	−1.65248	−	5.08580i	−0.0625920	−	0.192638i
$698$	−3.94427	−	12.1392i	−0.149293	−	0.459476i
$699$	53.0486	+	23.6187i	2.00648	+	0.893343i
$700$	0.570839	+	0.121336i	0.0215757	+	0.00458606i
$701$	−6.84703	+	1.45538i	−0.258609	+	0.0549690i	−0.335391	−	0.942079i	$-0.608869\pi$
$701$	−6.84703	+	1.45538i	−0.258609	+	0.0549690i	0.0767826	+	0.997048i	$0.475535\pi$
$702$	69.2258	−	30.8213i	2.61276	−	1.16328i
$703$	−2.99244	−	3.32344i	−0.112862	−	0.125346i
$704$	0.885579	+	8.42572i	0.0333765	+	0.317556i
$705$	−6.47214	+	4.70228i	−0.243755	+	0.177098i
$706$	1.25434	−	11.9343i	0.0472078	−	0.449152i
$707$	0.354102	+	0.613323i	0.0133174	+	0.0230664i
$708$	−2.23607	+	3.87298i	−0.0840366	+	0.145556i
$709$	20.6525	+	15.0049i	0.775620	+	0.563521i	0.903661	−	0.428248i	$-0.140869\pi$
$709$	20.6525	+	15.0049i	0.775620	+	0.563521i	−0.128041	+	0.991769i	$0.540869\pi$
$710$	−9.93933	+	11.0387i	−0.373017	+	0.414277i
$711$	27.0344	−	83.2035i	1.01387	−	3.12037i
$712$	26.1803			0.981150
$713$		0			0
$714$	−0.944272			−0.0353385
$715$	−2.00000	+	6.15537i	−0.0747958	+	0.230198i
$716$	−0.706420	+	0.784559i	−0.0264002	+	0.0293203i
$717$	−30.6525	−	22.2703i	−1.14474	−	0.831701i
$718$	−17.9894	+	31.1585i	−0.671357	+	1.16282i
$719$	−6.90983	−	11.9682i	−0.257693	−	0.446338i	0.707930	−	0.706282i	$-0.249629\pi$
$719$	−6.90983	−	11.9682i	−0.257693	−	0.446338i	−0.965624	+	0.259945i	$0.916296\pi$
$720$	3.79130	−	36.0718i	0.141293	−	1.34432i
$721$	−1.19098	+	0.865300i	−0.0443545	+	0.0322254i
$722$	2.36783	+	22.5284i	0.0881215	+	0.838420i
$723$	−31.0959	−	34.5355i	−1.15647	−	1.28439i
$724$	2.36023	−	1.05084i	0.0877172	−	0.0390542i
$725$	−10.8141	+	2.29862i	−0.401627	+	0.0853684i
$726$	35.8515	+	7.62048i	1.33058	+	0.282822i
$727$	−40.4117	−	17.9924i	−1.49879	−	0.667302i	−0.516774	−	0.856122i	$-0.672867\pi$
$727$	−40.4117	−	17.9924i	−1.49879	−	0.667302i	−0.982012	+	0.188820i	$0.939534\pi$
$728$	−0.527864	−	1.62460i	−0.0195639	−	0.0602116i
$729$	12.9615	+	39.8914i	0.480055	+	1.47746i
$730$	−12.5231	−	5.57563i	−0.463500	−	0.206363i
$731$	−0.923637	−	0.196325i	−0.0341620	−	0.00726135i
$732$	16.0032	−	3.40158i	0.591494	−	0.125726i
$733$	3.17195	−	1.41224i	0.117159	−	0.0521625i	−0.347320	−	0.937747i	$-0.612908\pi$
$733$	3.17195	−	1.41224i	0.117159	−	0.0521625i	0.464479	+	0.885584i	$0.346242\pi$
$734$	−19.4882	−	21.6438i	−0.719321	−	0.798887i
$735$	2.34898	+	22.3490i	0.0866434	+	0.824356i
$736$	−15.6180	+	11.3472i	−0.575688	+	0.418262i
$737$	1.67246	−	15.9124i	0.0616057	−	0.586139i
$738$	−42.3156	−	73.2928i	−1.55766	−	2.69794i
$739$	3.09017	−	5.35233i	0.113674	−	0.196889i	−0.803575	−	0.595203i	$-0.797071\pi$
$739$	3.09017	−	5.35233i	0.113674	−	0.196889i	0.917249	+	0.398315i	$0.130405\pi$
$740$	−1.00000	−	0.726543i	−0.0367607	−	0.0267082i
$741$	−15.6686	+	17.4018i	−0.575602	+	0.639270i
$742$	1.23607	−	3.80423i	0.0453775	−	0.139658i
$743$	−50.1803			−1.84094			−0.920469	−	0.390815i	$-0.872193\pi$
$743$	−50.1803			−1.84094			−0.920469	+	0.390815i	$0.872193\pi$
$744$		0			0
$745$	10.0000			0.366372
$746$	9.50000	−	29.2380i	0.347820	−	1.07048i
$747$	74.7189	−	82.9837i	2.73382	−	3.03622i
$748$	−0.763932	−	0.555029i	−0.0279321	−	0.0202939i
$749$	−0.680340	+	1.17838i	−0.0248591	+	0.0430572i
$750$	23.5623	+	40.8111i	0.860374	+	1.49021i
$751$	2.25165	−	21.4230i	0.0821639	−	0.781737i	−0.873410	−	0.486985i	$-0.838096\pi$
$751$	2.25165	−	21.4230i	0.0821639	−	0.781737i	0.955574	−	0.294751i	$-0.0952369\pi$
$752$	9.70820	−	7.05342i	0.354022	−	0.257212i
$753$	−0.615520	−	5.85629i	−0.0224308	−	0.213415i
$754$	−9.68375	−	10.7549i	−0.352661	−	0.391670i
$755$	12.9544	−	5.76766i	0.471458	−	0.209907i
$756$	−2.06532	+	0.438996i	−0.0751148	+	0.0159661i
$757$	8.46340	+	1.79895i	0.307607	+	0.0653840i	0.359129	−	0.933288i	$-0.383074\pi$
$757$	8.46340	+	1.79895i	0.307607	+	0.0653840i	−0.0515216	+	0.998672i	$0.516407\pi$
$758$	−3.12104	−	1.38958i	−0.113361	−	0.0504718i
$759$	11.4164	+	35.1361i	0.414389	+	1.27536i
$760$	1.54508	+	4.75528i	0.0560461	+	0.172492i
$761$	−1.82709	−	0.813473i	−0.0662320	−	0.0294884i	0.373353	−	0.927689i	$-0.378208\pi$
$761$	−1.82709	−	0.813473i	−0.0662320	−	0.0294884i	−0.439585	+	0.898201i	$0.644875\pi$
$762$	63.8779	+	13.5777i	2.31405	+	0.491867i
$763$	3.21986	−	0.684403i	0.116567	−	0.0247770i
$764$	−10.8293	+	4.82150i	−0.391789	+	0.174436i
$765$	−3.81953	−	4.24202i	−0.138096	−	0.153371i
$766$	−4.04028	−	38.4407i	−0.145981	−	1.38892i
$767$	−5.85410	+	4.25325i	−0.211379	+	0.153576i
$768$	−4.58760	+	43.6481i	−0.165541	+	1.57502i
$769$	23.6803	+	41.0156i	0.853935	+	1.47906i	0.877630	+	0.479339i	$0.159124\pi$
$769$	23.6803	+	41.0156i	0.853935	+	1.47906i	−0.0236947	+	0.999719i	$0.507543\pi$
$770$	0.381966	−	0.661585i	0.0137651	−	0.0238419i
$771$	−5.09017	−	3.69822i	−0.183318	−	0.133188i
$772$	1.43589	−	1.59471i	0.0516787	−	0.0573950i
$773$	3.43769	−	10.5801i	0.123645	−	0.380541i	−0.870007	−	0.493040i	$-0.835886\pi$
$773$	3.43769	−	10.5801i	0.123645	−	0.380541i	0.993652	+	0.112499i	$0.0358856\pi$
$774$	−14.9443			−0.537161
$775$		0			0
$776$	35.6525			1.27985
$777$	0.472136	−	1.45309i	0.0169378	−	0.0521291i
$778$	19.3675	−	21.5098i	0.694358	−	0.771163i
$779$	12.6631	+	9.20029i	0.453703	+	0.329635i
$780$	−3.23607	+	5.60503i	−0.115870	+	0.200692i
$781$	−9.18034	−	15.9008i	−0.328498	−	0.568976i
$782$	−0.737524	+	7.01708i	−0.0263738	+	0.250930i
$783$	32.3607	−	23.5114i	1.15648	−	0.840229i
$784$	−3.52347	−	33.5235i	−0.125838	−	1.19727i
$785$	13.9772	+	15.5232i	0.498866	+	0.554047i
$786$	57.4006	−	25.5564i	2.04741	−	0.911567i
$787$	7.18696	−	1.52764i	0.256188	−	0.0544543i	−0.0780274	−	0.996951i	$-0.524862\pi$
$787$	7.18696	−	1.52764i	0.256188	−	0.0544543i	0.334215	+	0.942497i	$0.391529\pi$
$788$	6.90154	+	1.46697i	0.245857	+	0.0522586i
$789$	68.6927	+	30.5839i	2.44552	+	1.08882i
$790$	5.85410	+	18.0171i	0.208280	+	0.641019i
$791$	0.253289	+	0.779543i	0.00900592	+	0.0277174i
$792$	30.5274	+	13.5917i	1.08474	+	0.482959i
$793$	25.8937	+	5.50387i	0.919511	+	0.195448i
$794$	11.0787	−	2.35486i	0.393170	−	0.0835708i
$795$	30.9587	−	13.7837i	1.09799	−	0.488858i
$796$	7.83432	+	8.70089i	0.277680	+	0.308395i
$797$	−5.79259	−	55.1128i	−0.205184	−	1.95220i	−0.293133	−	0.956072i	$-0.594698\pi$
$797$	−5.79259	−	55.1128i	−0.205184	−	1.95220i	0.0879489	−	0.996125i	$-0.471969\pi$
$798$	2.23607	−	1.62460i	0.0791559	−	0.0575102i
$799$	0.197407	−	1.87820i	0.00698374	−	0.0664459i
$800$	−6.76393	−	11.7155i	−0.239141	−	0.414205i
$801$	43.7426	−	75.7645i	1.54557	−	2.67701i
$802$	49.9787	+	36.3117i	1.76481	+	1.28221i
$803$	11.3379	−	12.5920i	0.400107	−	0.444364i
$804$	4.94427	−	15.2169i	0.174371	−	0.536659i
$805$	−1.34752			−0.0474940
$806$		0			0
$807$	35.7771			1.25941
$808$	2.07295	−	6.37988i	0.0729261	−	0.224443i
$809$	−15.6686	+	17.4018i	−0.550880	+	0.611814i	−0.952703	−	0.303903i	$-0.901710\pi$
$809$	−15.6686	+	17.4018i	−0.550880	+	0.611814i	0.401823	+	0.915717i	$0.368377\pi$
$810$	−31.9615	−	23.2214i	−1.12301	−	0.815916i
$811$	14.0000	−	24.2487i	0.491606	−	0.851487i	−0.508347	−	0.861152i	$-0.669743\pi$
$811$	14.0000	−	24.2487i	0.491606	−	0.851487i	0.999953	+	0.00966502i	$0.00307652\pi$
$812$	0.201626	+	0.349227i	0.00707569	+	0.0122555i
$813$	−4.79666	+	45.6372i	−0.168226	+	1.60057i
$814$	5.23607	−	3.80423i	0.183524	−	0.133338i
$815$	−1.11931	−	10.6495i	−0.0392078	−	0.373037i
$816$	8.02957	+	8.91774i	0.281091	+	0.312183i
$817$	2.52498	−	1.12419i	0.0883378	−	0.0393305i
$818$	−6.04528	+	1.28496i	−0.211368	+	0.0449277i
$819$	−5.58347	−	1.18680i	−0.195102	−	0.0414702i
$820$	3.95222	+	1.75964i	0.138017	+	0.0614493i
$821$	−9.43769	−	29.0462i	−0.329378	−	1.01372i	−0.969426	−	0.245386i	$-0.921085\pi$
$821$	−9.43769	−	29.0462i	−0.329378	−	1.01372i	0.640048	−	0.768335i	$-0.278915\pi$
$822$	−10.1803	−	31.3319i	−0.355080	−	1.09282i
$823$	13.0562	+	5.81300i	0.455111	+	0.202628i	0.621472	−	0.783437i	$-0.286535\pi$
$823$	13.0562	+	5.81300i	0.455111	+	0.202628i	−0.166361	+	0.986065i	$0.553202\pi$
$824$	13.6396	+	2.89918i	0.475156	+	0.100998i
$825$	−25.3228	+	5.38253i	−0.881627	+	0.187396i
$826$	0.780261	−	0.347395i	0.0271488	−	0.0120874i
$827$	−11.6078	−	12.8917i	−0.403641	−	0.448289i	0.506715	−	0.862113i	$-0.330859\pi$
$827$	−11.6078	−	12.8917i	−0.403641	−	0.448289i	−0.910357	+	0.413824i	$0.864193\pi$
$828$	2.75544	+	26.2163i	0.0957582	+	0.911078i
$829$	13.6180	−	9.89408i	0.472974	−	0.343636i	−0.325625	−	0.945499i	$-0.605575\pi$
$829$	13.6180	−	9.89408i	0.472974	−	0.343636i	0.798599	+	0.601863i	$0.205575\pi$
$830$	−2.52753	+	24.0479i	−0.0877320	+	0.834714i
$831$	−20.4721	−	35.4588i	−0.710171	−	1.23005i
$832$	−6.85410	+	11.8717i	−0.237623	+	0.411576i
$833$	−4.29180	−	3.11817i	−0.148702	−	0.108038i
$834$	−47.0059	+	52.2053i	−1.62768	+	1.80772i
$835$	2.00000	−	6.15537i	0.0692129	−	0.213015i
$836$	2.76393			0.0955926
$837$		0			0
$838$	−16.3820			−0.565906
$839$	8.94427	−	27.5276i	0.308791	−	0.950360i	−0.669445	−	0.742862i	$-0.733468\pi$
$839$	8.94427	−	27.5276i	0.308791	−	0.950360i	0.978235	−	0.207498i	$-0.0665320\pi$
$840$	−1.14301	+	1.26944i	−0.0394376	+	0.0437999i
$841$	17.2812	+	12.5555i	0.595902	+	0.432948i
$842$	−23.7533	+	41.1419i	−0.818592	+	1.41784i
$843$	−27.5066	−	47.6428i	−0.947377	−	1.64090i
$844$	−1.49750	+	14.2478i	−0.0515461	+	0.490428i
$845$	2.04508	−	1.48584i	0.0703531	−	0.0511145i
$846$	−3.12420	−	29.7248i	−0.107412	−	1.02196i
$847$	−1.10572	−	1.22803i	−0.0379931	−	0.0421956i
$848$	−46.4381	+	20.6756i	−1.59469	+	0.710002i
$849$	43.9621	−	9.34444i	1.50878	−	0.320700i
$850$	−4.83623	−	1.02797i	−0.165881	−	0.0352591i
$851$	−10.4294	−	4.64347i	−0.357515	−	0.159176i
$852$	−5.67376	−	17.4620i	−0.194380	−	0.598240i
$853$	3.27051	+	10.0656i	0.111980	+	0.344639i	0.991305	−	0.131583i	$-0.0420059\pi$
$853$	3.27051	+	10.0656i	0.111980	+	0.344639i	−0.879325	+	0.476222i	$0.842006\pi$
$854$	−2.85447	−	1.27089i	−0.0976781	−	0.0434891i
$855$	16.3431	+	3.47383i	0.558922	+	0.118803i
$856$	12.6069	−	2.67968i	0.430895	−	0.0915895i
$857$	−50.8531	+	22.6413i	−1.73711	+	0.773410i	−0.742484	+	0.669864i	$0.766352\pi$
$857$	−50.8531	+	22.6413i	−1.73711	+	0.773410i	−0.994625	+	0.103546i	$0.966981\pi$
$858$	−22.6759	−	25.1841i	−0.774141	−	0.859771i
$859$	0.220707	+	2.09989i	0.00753043	+	0.0716473i	0.997642	−	0.0686370i	$-0.0218650\pi$
$859$	0.220707	+	2.09989i	0.00753043	+	0.0716473i	−0.990111	+	0.140284i	$0.955198\pi$
$860$	0.618034	−	0.449028i	0.0210748	−	0.0153117i
$861$	−0.558968	+	5.31823i	−0.0190496	+	0.181245i
$862$	−9.70820	−	16.8151i	−0.330663	−	0.572725i
$863$	−4.90983	+	8.50408i	−0.167133	+	0.289482i	−0.937411	−	0.348226i	$-0.886784\pi$
$863$	−4.90983	+	8.50408i	−0.167133	+	0.289482i	0.770278	+	0.637708i	$0.220117\pi$
$864$	39.5967	+	28.7687i	1.34711	+	0.978732i
$865$	1.97010	−	2.18802i	0.0669855	−	0.0743949i
$866$	−5.09017	+	15.6659i	−0.172971	+	0.532350i
$867$	−53.1246			−1.80421
$868$		0			0
$869$	−23.4164			−0.794347
$870$	−4.47214	+	13.7638i	−0.151620	+	0.466637i
$871$	17.3228	−	19.2389i	0.586961	−	0.651887i
$872$	−25.2254	−	18.3273i	−0.854241	−	0.620642i
$873$	59.5689	−	103.176i	2.01610	−	3.49199i
$874$	−10.3262	−	17.8856i	−0.349290	−	0.604988i
$875$	0.222082	−	2.11297i	0.00750776	−	0.0714315i
$876$	13.7082	−	9.95959i	0.463157	−	0.336503i
$877$	1.88734	+	17.9568i	0.0637309	+	0.606359i	0.979049	+	0.203626i	$0.0652728\pi$
$877$	1.88734	+	17.9568i	0.0637309	+	0.606359i	−0.915318	+	0.402732i	$0.868061\pi$
$878$	−1.27793	−	1.41928i	−0.0431279	−	0.0478984i
$879$	−1.39577	+	0.621438i	−0.0470783	+	0.0209606i
$880$	−9.49606	+	2.01845i	−0.320112	+	0.0680419i
$881$	−19.9158	−	4.23322i	−0.670979	−	0.142621i	−0.140189	−	0.990125i	$-0.544771\pi$
$881$	−19.9158	−	4.23322i	−0.670979	−	0.142621i	−0.530789	+	0.847504i	$0.678104\pi$
$882$	−76.6989	−	34.1486i	−2.58259	−	1.14984i
$883$	9.81966	+	30.2218i	0.330458	+	1.01704i	0.968916	+	0.247389i	$0.0795724\pi$
$883$	9.81966	+	30.2218i	0.330458	+	1.01704i	−0.638458	+	0.769656i	$0.720428\pi$
$884$	−0.472136	−	1.45309i	−0.0158797	−	0.0488725i
$885$	6.61048	+	2.94317i	0.222209	+	0.0989337i
$886$	−48.6011	−	10.3305i	−1.63279	−	0.347060i
$887$	−26.4774	+	5.62794i	−0.889023	+	0.188968i	−0.629714	−	0.776827i	$-0.716828\pi$
$887$	−26.4774	+	5.62794i	−0.889023	+	0.188968i	−0.259309	+	0.965795i	$0.583495\pi$
$888$	−13.2210	+	5.88635i	−0.443666	+	0.197533i
$889$	−1.97010	−	2.18802i	−0.0660751	−	0.0733839i
$890$	1.98022	+	18.8405i	0.0663770	+	0.631535i
$891$	39.5066	−	28.7032i	1.32352	−	0.961594i
$892$	0.258409	−	2.45859i	0.00865216	−	0.0823198i
$893$	2.76393	+	4.78727i	0.0924915	+	0.160200i
$894$	−26.1803	+	45.3457i	−0.875602	+	1.51659i
$895$	1.38197	+	1.00406i	0.0461940	+	0.0335619i
$896$	2.15111	−	2.38905i	0.0718635	−	0.0798125i
$897$	−18.4721	+	56.8514i	−0.616767	+	1.89821i
$898$	50.6525			1.69030
$899$		0			0
$900$	−18.4721			−0.615738
$901$	−2.47214	+	7.60845i	−0.0823588	+	0.253474i
$902$	−15.1575	+	16.8341i	−0.504688	+	0.560513i
$903$	0.763932	+	0.555029i	0.0254221	+	0.0184702i
$904$	3.88197	−	6.72376i	0.129112	−	0.223629i
$905$	−2.09017	−	3.62028i	−0.0694796	−	0.120342i
$906$	−7.76116	+	73.8425i	−0.257847	+	2.45325i
$907$	19.6074	−	14.2456i	0.651053	−	0.473017i	−0.212577	−	0.977144i	$-0.568186\pi$
$907$	19.6074	−	14.2456i	0.651053	−	0.473017i	0.863630	+	0.504127i	$0.168186\pi$
$908$	0.418114	+	3.97809i	0.0138756	+	0.132017i
$909$	−14.9995	−	16.6586i	−0.497502	−	0.552532i
$910$	1.12920	−	0.502754i	0.0374328	−	0.0166661i
$911$	17.7831	−	3.77991i	0.589179	−	0.125234i	0.0963311	−	0.995349i	$-0.469289\pi$
$911$	17.7831	−	3.77991i	0.589179	−	0.125234i	0.492848	+	0.870116i	$0.335956\pi$
$912$	−34.3571	−	7.30282i	−1.13768	−	0.241820i
$913$	−27.3045	−	12.1568i	−0.903648	−	0.402330i
$914$	1.52786	+	4.70228i	0.0505373	+	0.155538i
$915$	−8.18034	−	25.1765i	−0.270434	−	0.832309i
$916$	7.57493	+	3.37258i	0.250283	+	0.111433i
$917$	−2.77091	−	0.588976i	−0.0915036	−	0.0194497i
$918$	17.4976	−	3.71924i	0.577508	−	0.122753i
$919$	−13.2210	+	5.88635i	−0.436119	+	0.194173i	−0.613039	−	0.790053i	$-0.710053\pi$
$919$	−13.2210	+	5.88635i	−0.436119	+	0.194173i	0.176920	+	0.984225i	$0.443387\pi$
$920$	8.54074	+	9.48545i	0.281580	+	0.312726i
$921$	9.71087	+	92.3928i	0.319984	+	3.04445i
$922$	44.9787	−	32.6789i	1.48130	−	1.07622i
$923$	3.10535	−	29.5455i	0.102214	−	0.972501i
$924$	0.472136	+	0.817763i	0.0155321	+	0.0269024i
$925$	4.00000	−	6.92820i	0.131519	−	0.227798i
$926$	−3.38197	−	2.45714i	−0.111138	−	0.0807467i
$927$	31.1793	−	34.6281i	1.02406	−	1.13734i
$928$	2.88854	−	8.89002i	0.0948211	−	0.291829i
$929$	20.0000			0.656179			0.328089	−	0.944647i	$-0.393595\pi$
$929$	20.0000			0.656179			0.328089	+	0.944647i	$0.393595\pi$
$930$		0			0
$931$	15.5279			0.508905
$932$	3.42705	−	10.5474i	0.112257	−	0.345491i
$933$	−63.1857	+	70.1748i	−2.06861	+	2.29742i
$934$	−6.16312	−	4.47777i	−0.201663	−	0.146517i
$935$	−0.763932	+	1.32317i	−0.0249832	+	0.0432723i
$936$	27.0344	+	46.8250i	0.883648	+	1.53052i
$937$	−0.946581	+	9.00612i	−0.0309235	+	0.294217i	0.968120	+	0.250487i	$0.0805908\pi$
$937$	−0.946581	+	9.00612i	−0.0309235	+	0.294217i	−0.999043	+	0.0437300i	$0.986076\pi$
$938$	−2.47214	+	1.79611i	−0.0807181	+	0.0586451i
$939$	5.67059	+	53.9520i	0.185053	+	1.76066i
$940$	1.02234	+	1.13542i	0.0333451	+	0.0370335i
$941$	34.7147	−	15.4560i	1.13167	−	0.503851i	0.246509	−	0.969140i	$-0.420716\pi$
$941$	34.7147	−	15.4560i	1.13167	−	0.503851i	0.885159	+	0.465289i	$0.154050\pi$
$942$	−106.984	+	22.7401i	−3.48572	+	0.740912i
$943$	39.0843	+	8.30762i	1.27276	+	0.270533i
$944$	−9.91572	−	4.41476i	−0.322729	−	0.143688i
$945$	1.05573	+	3.24920i	0.0343428	+	0.105696i
$946$	1.23607	+	3.80423i	0.0401880	+	0.123686i
$947$	11.9270	+	5.31024i	0.387575	+	0.172560i	0.591268	−	0.806475i	$-0.298628\pi$
$947$	11.9270	+	5.31024i	0.387575	+	0.172560i	−0.203692	+	0.979035i	$0.565294\pi$
$948$	−22.9047	−	4.86854i	−0.743910	−	0.158123i
$949$	26.8173	−	5.70019i	0.870526	−	0.185036i
$950$	13.2210	−	5.88635i	0.428944	−	0.190978i
$951$	8.78208	+	9.75349i	0.284778	+	0.316278i
$952$	−0.0421513	−	0.401043i	−0.00136613	−	0.0129979i
$953$	36.9787	−	26.8666i	1.19786	−	0.870295i	0.203786	−	0.979016i	$-0.434675\pi$
$953$	36.9787	−	26.8666i	1.19786	−	0.870295i	0.994072	+	0.108721i	$0.0346754\pi$
$954$	−13.2343	+	125.916i	−0.428478	+	4.07669i
$955$	9.59017	+	16.6107i	0.310331	+	0.537508i
$956$	−3.61803	+	6.26662i	−0.117016	+	0.202677i
$957$	−14.4721	−	10.5146i	−0.467818	−	0.339889i
$958$	25.2175	−	28.0068i	0.814739	−	0.904860i
$959$	−0.458980	+	1.41260i	−0.0148212	+	0.0456151i
$960$	13.7082			0.442430
$961$		0			0
$962$	10.4721			0.337635
$963$	13.3090	−	40.9609i	0.428877	−	1.31995i
$964$	−5.93879	+	6.59570i	−0.191276	+	0.212433i
$965$	−2.80902	−	2.04087i	−0.0904255	−	0.0656979i
$966$	3.52786	−	6.11044i	0.113507	−	0.196600i
$967$	30.1803	+	52.2739i	0.970534	+	1.68101i	0.693947	+	0.720026i	$0.255870\pi$
$967$	30.1803	+	52.2739i	0.970534	+	1.68101i	0.276587	+	0.960989i	$0.410797\pi$
$968$	−1.63613	+	15.5667i	−0.0525872	+	0.500334i
$969$	−4.47214	+	3.24920i	−0.143666	+	0.104379i
$970$	2.69666	+	25.6570i	0.0865847	+	0.823798i
$971$	−18.7357	−	20.8081i	−0.601256	−	0.667762i	0.363290	−	0.931676i	$-0.381653\pi$
$971$	−18.7357	−	20.8081i	−0.601256	−	0.667762i	−0.964546	+	0.263914i	$0.914987\pi$
$972$	20.0980	−	8.94821i	0.644644	−	0.287014i
$973$	3.09797	−	0.658495i	0.0993165	−	0.0211104i
$974$	−30.4445	−	6.47117i	−0.975504	−	0.207350i
$975$	−38.2671	−	17.0376i	−1.22553	−	0.545640i
$976$	12.2705	+	37.7647i	0.392769	+	1.20882i
$977$	−14.6008	−	44.9367i	−0.467121	−	1.43765i	−0.856295	−	0.516487i	$-0.827239\pi$
$977$	−14.6008	−	44.9367i	−0.467121	−	1.43765i	0.389173	−	0.921164i	$-0.372761\pi$
$978$	51.2215	+	22.8053i	1.63788	+	0.729232i
$979$	−22.9047	−	4.86854i	−0.732037	−	0.155599i
$980$	4.19801	−	0.892315i	0.134101	−	0.0285039i
$981$	−95.1855	+	42.3793i	−3.03904	+	1.35307i
$982$	−4.72120	−	5.24343i	−0.150660	−	0.167325i
$983$	4.13179	+	39.3113i	0.131784	+	1.25384i	0.837933	+	0.545774i	$0.183764\pi$
$983$	4.13179	+	39.3113i	0.131784	+	1.25384i	−0.706149	+	0.708063i	$0.749569\pi$
$984$	40.9787	−	29.7728i	1.30635	−	0.949122i
$985$	1.19334	−	11.3539i	0.0380230	−	0.361764i
$986$	−1.70820	−	2.95870i	−0.0544003	−	0.0942241i
$987$	−0.944272	+	1.63553i	−0.0300565	+	0.0520594i
$988$	3.61803	+	2.62866i	0.115105	+	0.0836287i
$989$	4.72120	−	5.24343i	0.150126	−	0.166731i
$990$	−7.47214	+	22.9969i	−0.237480	+	0.730889i
$991$	16.5410			0.525443			0.262721	−	0.964872i	$-0.415380\pi$
$991$	16.5410			0.525443			0.262721	+	0.964872i	$0.415380\pi$
$992$		0			0
$993$	−6.47214			−0.205387
$994$	−1.08359	+	3.33495i	−0.0343695	+	0.105778i
$995$	12.6762	−	14.0783i	0.401862	−	0.446313i
$996$	−24.1803	−	17.5680i	−0.766183	−	0.556665i
$997$	14.6803	−	25.4271i	0.464931	−	0.805284i	−0.534267	−	0.845316i	$-0.679412\pi$
$997$	14.6803	−	25.4271i	0.464931	−	0.805284i	0.999198	+	0.0400314i	$0.0127458\pi$
$998$	−5.32624	−	9.22531i	−0.168599	−	0.292022i
$999$	−3.02550	+	28.7857i	−0.0957226	+	0.910740i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.e.448.1		8
31.2	even	5		961.2.c.c.521.2		4
31.3	odd	30		961.2.d.c.374.1		4
31.4	even	5	inner	961.2.g.e.844.1		8
31.5	even	3	inner	961.2.g.e.846.1		8
31.6	odd	6		961.2.d.d.628.1		4
31.7	even	15		961.2.d.g.531.1		4
31.8	even	5		961.2.g.d.338.1		8
31.9	even	15		961.2.g.d.235.1		8
31.10	even	15		961.2.c.c.439.2		4
31.11	odd	30		961.2.g.h.547.1		8
31.12	odd	30		31.2.a.a.1.2	✓	2
31.13	odd	30		961.2.g.a.816.1		8
31.14	even	15		961.2.d.a.388.1		4
31.15	odd	10		961.2.g.a.732.1		8
31.16	even	5		961.2.g.d.732.1		8
31.17	odd	30		961.2.d.c.388.1		4
31.18	even	15		961.2.g.d.816.1		8
31.19	even	15		961.2.a.f.1.2		2
31.20	even	15	inner	961.2.g.e.547.1		8
31.21	odd	30		961.2.c.e.439.2		4
31.22	odd	30		961.2.g.a.235.1		8
31.23	odd	10		961.2.g.a.338.1		8
31.24	odd	30		961.2.d.d.531.1		4
31.25	even	3		961.2.d.g.628.1		4
31.26	odd	6		961.2.g.h.846.1		8
31.27	odd	10		961.2.g.h.844.1		8
31.28	even	15		961.2.d.a.374.1		4
31.29	odd	10		961.2.c.e.521.2		4
31.30	odd	2		961.2.g.h.448.1		8
93.50	odd	30		8649.2.a.c.1.1		2
93.74	even	30		279.2.a.a.1.1		2
124.43	even	30		496.2.a.i.1.2		2
155.12	even	60		775.2.b.d.249.4		4
155.43	even	60		775.2.b.d.249.1		4
155.74	odd	30		775.2.a.d.1.1		2
217.167	even	30		1519.2.a.a.1.2		2
248.43	even	30		1984.2.a.n.1.1		2
248.229	odd	30		1984.2.a.r.1.2		2
341.43	even	30		3751.2.a.b.1.1		2
372.167	odd	30		4464.2.a.bf.1.1		2
403.12	odd	30		5239.2.a.f.1.1		2
465.74	even	30		6975.2.a.y.1.2		2
527.322	odd	30		8959.2.a.b.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.a.a.1.2	✓	2	31.12	odd	30
279.2.a.a.1.1		2	93.74	even	30
496.2.a.i.1.2		2	124.43	even	30
775.2.a.d.1.1		2	155.74	odd	30
775.2.b.d.249.1		4	155.43	even	60
775.2.b.d.249.4		4	155.12	even	60
961.2.a.f.1.2		2	31.19	even	15
961.2.c.c.439.2		4	31.10	even	15
961.2.c.c.521.2		4	31.2	even	5
961.2.c.e.439.2		4	31.21	odd	30
961.2.c.e.521.2		4	31.29	odd	10
961.2.d.a.374.1		4	31.28	even	15
961.2.d.a.388.1		4	31.14	even	15
961.2.d.c.374.1		4	31.3	odd	30
961.2.d.c.388.1		4	31.17	odd	30
961.2.d.d.531.1		4	31.24	odd	30
961.2.d.d.628.1		4	31.6	odd	6
961.2.d.g.531.1		4	31.7	even	15
961.2.d.g.628.1		4	31.25	even	3
961.2.g.a.235.1		8	31.22	odd	30
961.2.g.a.338.1		8	31.23	odd	10
961.2.g.a.732.1		8	31.15	odd	10
961.2.g.a.816.1		8	31.13	odd	30
961.2.g.d.235.1		8	31.9	even	15
961.2.g.d.338.1		8	31.8	even	5
961.2.g.d.732.1		8	31.16	even	5
961.2.g.d.816.1		8	31.18	even	15
961.2.g.e.448.1		8	1.1	even	1	trivial
961.2.g.e.547.1		8	31.20	even	15	inner
961.2.g.e.844.1		8	31.4	even	5	inner
961.2.g.e.846.1		8	31.5	even	3	inner
961.2.g.h.448.1		8	31.30	odd	2
961.2.g.h.547.1		8	31.11	odd	30
961.2.g.h.844.1		8	31.27	odd	10
961.2.g.h.846.1		8	31.26	odd	6
1519.2.a.a.1.2		2	217.167	even	30
1984.2.a.n.1.1		2	248.43	even	30
1984.2.a.r.1.2		2	248.229	odd	30
3751.2.a.b.1.1		2	341.43	even	30
4464.2.a.bf.1.1		2	372.167	odd	30
5239.2.a.f.1.1		2	403.12	odd	30
6975.2.a.y.1.2		2	465.74	even	30
8649.2.a.c.1.1		2	93.50	odd	30
8959.2.a.b.1.2		2	527.322	odd	30

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 1.53884i) q^{2} +(2.16535 - 2.40487i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.61803 - 4.53457i) q^{6} +(-0.0246758 + 0.234775i) q^{7} +(1.80902 - 1.31433i) q^{8} +(-0.781051 - 7.43120i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 1.53884i) q^{2} +(2.16535 - 2.40487i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.61803 - 4.53457i) q^{6} +(-0.0246758 + 0.234775i) q^{7} +(1.80902 - 1.31433i) q^{8} +(-0.781051 - 7.43120i) q^{9} +(1.08268 + 1.20243i) q^{10} +(-1.82709 + 0.813473i) q^{11} +(-1.95630 + 0.415823i) q^{12} +(-3.16535 - 0.672816i) q^{13} +(0.348943 + 0.155360i) q^{14} +(1.00000 + 3.07768i) q^{15} +(-1.50000 - 4.61653i) q^{16} +(-0.697887 - 0.310719i) q^{17} +(-11.8260 - 2.51369i) q^{18} +(2.18720 - 0.464905i) q^{19} +(0.564602 - 0.251377i) q^{20} +(0.511170 + 0.567712i) q^{21} +(0.338261 + 3.21834i) q^{22} +(4.61803 - 3.35520i) q^{23} +(0.756375 - 7.19643i) q^{24} +(2.00000 + 3.46410i) q^{25} +(-2.61803 + 4.53457i) q^{26} +(-11.7082 - 8.50651i) q^{27} +(0.0976248 - 0.108423i) q^{28} +(-0.854102 + 2.62866i) q^{29} +5.23607 q^{30} -3.38197 q^{32} +(-2.00000 + 6.15537i) q^{33} +(-0.827091 + 0.918578i) q^{34} +(-0.190983 - 0.138757i) q^{35} +(-2.30902 + 3.99933i) q^{36} +(-1.00000 - 1.73205i) q^{37} +(0.378188 - 3.59821i) q^{38} +(-8.47214 + 6.15537i) q^{39} +(0.233733 + 2.22382i) q^{40} +(4.68391 + 5.20201i) q^{41} +(1.12920 - 0.502754i) q^{42} +(1.20906 - 0.256993i) q^{43} +(1.20906 + 0.256993i) q^{44} +(6.82614 + 3.03919i) q^{45} +(-2.85410 - 8.78402i) q^{46} +(0.763932 + 2.35114i) q^{47} +(-14.3502 - 6.38910i) q^{48} +(6.79252 + 1.44380i) q^{49} +(6.33070 - 1.34563i) q^{50} +(-2.25841 + 1.00551i) q^{51} +(1.33826 + 1.48629i) q^{52} +(-1.09464 - 10.4148i) q^{53} +(-18.9443 + 13.7638i) q^{54} +(0.209057 - 1.98904i) q^{55} +(0.263932 + 0.457144i) q^{56} +(3.61803 - 6.26662i) q^{57} +(3.61803 + 2.62866i) q^{58} +(1.49622 - 1.66172i) q^{59} +(0.618034 - 1.90211i) q^{60} -8.18034 q^{61} +1.76393 q^{63} +(1.30902 - 4.02874i) q^{64} +(2.16535 - 2.40487i) q^{65} +(8.47214 + 6.15537i) q^{66} +(-4.00000 + 6.92820i) q^{67} +(0.236068 + 0.408882i) q^{68} +(1.93086 - 18.3709i) q^{69} +(-0.309017 + 0.224514i) q^{70} +(0.959607 + 9.13005i) q^{71} +(-11.1800 - 12.4166i) q^{72} +(-7.73968 + 3.44593i) q^{73} +(-3.16535 + 0.672816i) q^{74} +(12.6614 + 2.69127i) q^{75} +(-1.26249 - 0.562096i) q^{76} +(-0.145898 - 0.449028i) q^{77} +(5.23607 + 16.1150i) q^{78} +(10.6960 + 4.76216i) q^{79} +(4.74803 + 1.00922i) q^{80} +(-23.8829 + 5.07646i) q^{81} +(10.3470 - 4.60680i) q^{82} +(9.99967 + 11.1058i) q^{83} +(-0.0493516 - 0.469550i) q^{84} +(0.618034 - 0.449028i) q^{85} +(0.209057 - 1.98904i) q^{86} +(4.47214 + 7.74597i) q^{87} +(-2.23607 + 3.87298i) q^{88} +(9.47214 + 6.88191i) q^{89} +(8.08990 - 8.98475i) q^{90} +(0.236068 - 0.726543i) q^{91} -3.52786 q^{92} +4.00000 q^{94} +(-0.690983 + 2.12663i) q^{95} +(-7.32315 + 8.13318i) q^{96} +(12.8992 + 9.37181i) q^{97} +(5.61803 - 9.73072i) q^{98} +(7.47214 + 12.9421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 12 q^{6} + 3 q^{7} + 10 q^{8} + 13 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 12 * q^6 + 3 * q^7 + 10 * q^8 + 13 * q^9	\( 8 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 12 q^{6} + 3 q^{7} + 10 q^{8} + 13 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} - 4 q^{13} - q^{14} + 8 q^{15} - 12 q^{16} + 2 q^{17} - 6 q^{18} + 5 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} + 28 q^{23} - 10 q^{24} + 16 q^{25} - 12 q^{26} - 40 q^{27} + 11 q^{28} + 20 q^{29} + 24 q^{30} - 36 q^{32} - 16 q^{33} + 6 q^{34} - 6 q^{35} - 14 q^{36} - 8 q^{37} - 5 q^{38} - 32 q^{39} - 5 q^{40} + 7 q^{41} + 4 q^{42} + 6 q^{43} + 6 q^{44} + 13 q^{45} + 4 q^{46} + 24 q^{47} - 24 q^{48} + 22 q^{49} + 8 q^{50} - 8 q^{51} + 2 q^{52} + 16 q^{53} - 80 q^{54} - 2 q^{55} + 20 q^{56} + 20 q^{57} + 20 q^{58} - 5 q^{59} - 4 q^{60} + 24 q^{61} + 32 q^{63} + 6 q^{64} - 4 q^{65} + 32 q^{66} - 32 q^{67} - 16 q^{68} - 24 q^{69} + 2 q^{70} - 23 q^{71} + 5 q^{72} - 14 q^{73} - 4 q^{74} + 16 q^{75} - 28 q^{77} + 24 q^{78} + 20 q^{79} + 6 q^{80} - 19 q^{81} + 21 q^{82} - 14 q^{83} + 6 q^{84} - 4 q^{85} - 2 q^{86} + 40 q^{89} - 6 q^{90} - 16 q^{91} - 64 q^{92} + 32 q^{94} - 10 q^{95} + 18 q^{96} + 54 q^{97} + 36 q^{98} + 24 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 12 * q^6 + 3 * q^7 + 10 * q^8 + 13 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^12 - 4 * q^13 - q^14 + 8 * q^15 - 12 * q^16 + 2 * q^17 - 6 * q^18 + 5 * q^19 + 2 * q^20 + 8 * q^21 - 6 * q^22 + 28 * q^23 - 10 * q^24 + 16 * q^25 - 12 * q^26 - 40 * q^27 + 11 * q^28 + 20 * q^29 + 24 * q^30 - 36 * q^32 - 16 * q^33 + 6 * q^34 - 6 * q^35 - 14 * q^36 - 8 * q^37 - 5 * q^38 - 32 * q^39 - 5 * q^40 + 7 * q^41 + 4 * q^42 + 6 * q^43 + 6 * q^44 + 13 * q^45 + 4 * q^46 + 24 * q^47 - 24 * q^48 + 22 * q^49 + 8 * q^50 - 8 * q^51 + 2 * q^52 + 16 * q^53 - 80 * q^54 - 2 * q^55 + 20 * q^56 + 20 * q^57 + 20 * q^58 - 5 * q^59 - 4 * q^60 + 24 * q^61 + 32 * q^63 + 6 * q^64 - 4 * q^65 + 32 * q^66 - 32 * q^67 - 16 * q^68 - 24 * q^69 + 2 * q^70 - 23 * q^71 + 5 * q^72 - 14 * q^73 - 4 * q^74 + 16 * q^75 - 28 * q^77 + 24 * q^78 + 20 * q^79 + 6 * q^80 - 19 * q^81 + 21 * q^82 - 14 * q^83 + 6 * q^84 - 4 * q^85 - 2 * q^86 + 40 * q^89 - 6 * q^90 - 16 * q^91 - 64 * q^92 + 32 * q^94 - 10 * q^95 + 18 * q^96 + 54 * q^97 + 36 * q^98 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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