LMFDB - Embedded newform 961.2.g.e.846.1

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			846.1
Root			$0.913545 - 0.406737i$ of defining polynomial
Character	$\chi$	$=$	961.846
Dual form			961.2.g.e.844.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 1.53884i) q^{2} +(-3.16535 - 0.672816i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.61803 + 4.53457i) q^{6} +(0.215659 - 0.0960175i) q^{7} +(1.80902 - 1.31433i) q^{8} +(6.82614 + 3.03919i) q^{9} +O(q^{10})$	\(q+(0.500000 - 1.53884i) q^{2} +(-3.16535 - 0.672816i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.61803 + 4.53457i) q^{6} +(0.215659 - 0.0960175i) q^{7} +(1.80902 - 1.31433i) q^{8} +(6.82614 + 3.03919i) q^{9} +(-1.58268 + 0.336408i) q^{10} +(0.209057 - 1.98904i) q^{11} +(1.33826 + 1.48629i) q^{12} +(2.16535 - 2.40487i) q^{13} +(-0.0399263 - 0.379874i) q^{14} +(1.00000 + 3.07768i) q^{15} +(-1.50000 - 4.61653i) q^{16} +(0.0798526 + 0.759747i) q^{17} +(8.08990 - 8.98475i) q^{18} +(-1.49622 - 1.66172i) q^{19} +(-0.0646021 + 0.614648i) q^{20} +(-0.747238 + 0.158830i) q^{21} +(-2.95630 - 1.31623i) q^{22} +(4.61803 - 3.35520i) q^{23} +(-6.61048 + 2.94317i) q^{24} +(2.00000 - 3.46410i) q^{25} +(-2.61803 - 4.53457i) q^{26} +(-11.7082 - 8.50651i) q^{27} +(-0.142710 - 0.0303339i) q^{28} +(-0.854102 + 2.62866i) q^{29} +5.23607 q^{30} -3.38197 q^{32} +(-2.00000 + 6.15537i) q^{33} +(1.20906 + 0.256993i) q^{34} +(-0.190983 - 0.138757i) q^{35} +(-2.30902 - 3.99933i) q^{36} +(-1.00000 + 1.73205i) q^{37} +(-3.30524 + 1.47159i) q^{38} +(-8.47214 + 6.15537i) q^{39} +(-2.04275 - 0.909491i) q^{40} +(-6.84703 + 1.45538i) q^{41} +(-0.129204 + 1.22930i) q^{42} +(-0.827091 - 0.918578i) q^{43} +(-0.827091 + 0.918578i) q^{44} +(-0.781051 - 7.43120i) q^{45} +(-2.85410 - 8.78402i) q^{46} +(0.763932 + 2.35114i) q^{47} +(1.64195 + 15.6222i) q^{48} +(-4.64662 + 5.16060i) q^{49} +(-4.33070 - 4.80973i) q^{50} +(0.258409 - 2.45859i) q^{51} +(-1.95630 + 0.415823i) q^{52} +(9.56677 + 4.25940i) q^{53} +(-18.9443 + 13.7638i) q^{54} +(-1.82709 + 0.813473i) q^{55} +(0.263932 - 0.457144i) q^{56} +(3.61803 + 6.26662i) q^{57} +(3.61803 + 2.62866i) q^{58} +(-2.18720 - 0.464905i) q^{59} +(0.618034 - 1.90211i) q^{60} -8.18034 q^{61} +1.76393 q^{63} +(1.30902 - 4.02874i) q^{64} +(-3.16535 - 0.672816i) q^{65} +(8.47214 + 6.15537i) q^{66} +(-4.00000 - 6.92820i) q^{67} +(0.236068 - 0.408882i) q^{68} +(-16.8751 + 7.51329i) q^{69} +(-0.309017 + 0.224514i) q^{70} +(-8.38666 - 3.73398i) q^{71} +(16.3431 - 3.47383i) q^{72} +(0.885579 - 8.42572i) q^{73} +(2.16535 + 2.40487i) q^{74} +(-8.66141 + 9.61947i) q^{75} +(0.144455 + 1.37440i) q^{76} +(-0.145898 - 0.449028i) q^{77} +(5.23607 + 16.1150i) q^{78} +(-1.22384 - 11.6441i) q^{79} +(-3.24803 + 3.60730i) q^{80} +(16.3378 + 18.1449i) q^{81} +(-1.18391 + 11.2642i) q^{82} +(-14.6177 + 3.10709i) q^{83} +(0.431318 + 0.192035i) q^{84} +(0.618034 - 0.449028i) q^{85} +(-1.82709 + 0.813473i) q^{86} +(4.47214 - 7.74597i) q^{87} +(-2.23607 - 3.87298i) q^{88} +(9.47214 + 6.88191i) q^{89} +(-11.8260 - 2.51369i) q^{90} +(0.236068 - 0.726543i) q^{91} -3.52786 q^{92} +4.00000 q^{94} +(-0.690983 + 2.12663i) q^{95} +(10.7051 + 2.27544i) 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 $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{15}\right)$

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	$-0.0938561\pi$
$3$	−3.16535	−	0.672816i	−1.82752	−	0.388451i	−0.839571	−	0.543250i	$-0.817194\pi$
$3$	−3.16535	−	0.672816i	−1.82752	−	0.388451i	−0.987946	+	0.154799i	$0.950527\pi$
$4$	−0.500000	−	0.363271i	−0.250000	−	0.181636i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$	−2.61803	+	4.53457i	−1.06881	+	1.85123i
$7$	0.215659	−	0.0960175i	0.0815114	−	0.0362912i	−0.365576	−	0.930781i	$-0.619128\pi$
$7$	0.215659	−	0.0960175i	0.0815114	−	0.0362912i	0.447087	+	0.894490i	$0.352461\pi$
$8$	1.80902	−	1.31433i	0.639584	−	0.464685i
$9$	6.82614	+	3.03919i	2.27538	+	1.01306i
$10$	−1.58268	+	0.336408i	−0.500486	+	0.106382i
$11$	0.209057	−	1.98904i	0.0630330	−	0.599719i	−0.916723	−	0.399524i	$-0.869176\pi$
$11$	0.209057	−	1.98904i	0.0630330	−	0.599719i	0.979756	−	0.200196i	$-0.0641578\pi$
$12$	1.33826	+	1.48629i	0.386323	+	0.429055i
$13$	2.16535	−	2.40487i	0.600561	−	0.666990i	−0.363832	−	0.931465i	$-0.618532\pi$
$13$	2.16535	−	2.40487i	0.600561	−	0.666990i	0.964393	+	0.264474i	$0.0851985\pi$
$14$	−0.0399263	−	0.379874i	−0.0106708	−	0.101525i
$15$	1.00000	+	3.07768i	0.258199	+	0.794654i
$16$	−1.50000	−	4.61653i	−0.375000	−	1.15413i
$17$	0.0798526	+	0.759747i	0.0193671	+	0.184266i	0.999929	−	0.0119461i	$-0.00380265\pi$
$17$	0.0798526	+	0.759747i	0.0193671	+	0.184266i	−0.980562	+	0.196212i	$0.937136\pi$
$18$	8.08990	−	8.98475i	1.90681	−	2.11773i
$19$	−1.49622	−	1.66172i	−0.343257	−	0.381225i	0.546655	−	0.837358i	$-0.315901\pi$
$19$	−1.49622	−	1.66172i	−0.343257	−	0.381225i	−0.889912	+	0.456133i	$0.849234\pi$
$20$	−0.0646021	+	0.614648i	−0.0144455	+	0.137440i
$21$	−0.747238	+	0.158830i	−0.163061	+	0.0346596i
$22$	−2.95630	−	1.31623i	−0.630284	−	0.280621i
$23$	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	$0.0971040\pi$
$24$	−6.61048	+	2.94317i	−1.34936	+	0.600773i
$25$	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
$28$	−0.142710	−	0.0303339i	−0.0269696	−	0.00573257i
$29$	−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
$34$	1.20906	+	0.256993i	0.207352	+	0.0440739i
$35$	−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	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$	−3.30524	+	1.47159i	−0.536180	+	0.238723i
$39$	−8.47214	+	6.15537i	−1.35663	+	0.985648i
$40$	−2.04275	−	0.909491i	−0.322987	−	0.143803i
$41$	−6.84703	+	1.45538i	−1.06933	+	0.227292i	−0.708766	−	0.705443i	$-0.750748\pi$
$41$	−6.84703	+	1.45538i	−1.06933	+	0.227292i	−0.360561	+	0.932736i	$0.617415\pi$
$42$	−0.129204	+	1.22930i	−0.0199367	+	0.189685i
$43$	−0.827091	−	0.918578i	−0.126130	−	0.140082i	0.676772	−	0.736193i	$-0.263378\pi$
$43$	−0.827091	−	0.918578i	−0.126130	−	0.140082i	−0.802902	+	0.596111i	$0.796712\pi$
$44$	−0.827091	+	0.918578i	−0.124689	+	0.138481i
$45$	−0.781051	−	7.43120i	−0.116432	−	1.10778i
$46$	−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	$0.842293\pi$
$48$	1.64195	+	15.6222i	0.236996	+	2.25486i
$49$	−4.64662	+	5.16060i	−0.663804	+	0.737229i
$50$	−4.33070	−	4.80973i	−0.612454	−	0.680199i
$51$	0.258409	−	2.45859i	0.0361844	−	0.344272i
$52$	−1.95630	+	0.415823i	−0.271289	+	0.0576643i
$53$	9.56677	+	4.25940i	1.31410	+	0.585074i	0.939638	−	0.342170i	$-0.111162\pi$
$53$	9.56677	+	4.25940i	1.31410	+	0.585074i	0.374459	+	0.927243i	$0.377828\pi$
$54$	−18.9443	+	13.7638i	−2.57799	+	1.87302i
$55$	−1.82709	+	0.813473i	−0.246365	+	0.109689i
$56$	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
$59$	−2.18720	−	0.464905i	−0.284750	−	0.0605254i	0.0633226	−	0.997993i	$-0.479830\pi$
$59$	−2.18720	−	0.464905i	−0.284750	−	0.0605254i	−0.348072	+	0.937468i	$0.613164\pi$
$60$	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
$65$	−3.16535	−	0.672816i	−0.392614	−	0.0834526i
$66$	8.47214	+	6.15537i	1.04285	+	0.757673i
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$	0.236068	−	0.408882i	0.0286274	−	0.0495842i
$69$	−16.8751	+	7.51329i	−2.03153	+	0.904494i
$70$	−0.309017	+	0.224514i	−0.0369346	+	0.0268346i
$71$	−8.38666	−	3.73398i	−0.995313	−	0.443142i	−0.156569	−	0.987667i	$-0.550043\pi$
$71$	−8.38666	−	3.73398i	−0.995313	−	0.443142i	−0.838745	+	0.544525i	$0.816710\pi$
$72$	16.3431	−	3.47383i	1.92605	−	0.409395i
$73$	0.885579	−	8.42572i	0.103649	−	0.986156i	−0.811858	−	0.583855i	$-0.801544\pi$
$73$	0.885579	−	8.42572i	0.103649	−	0.986156i	0.915507	−	0.402302i	$-0.131790\pi$
$74$	2.16535	+	2.40487i	0.251717	+	0.279560i
$75$	−8.66141	+	9.61947i	−1.00013	+	1.11076i
$76$	0.144455	+	1.37440i	0.0165701	+	0.157654i
$77$	−0.145898	−	0.449028i	−0.0166266	−	0.0511715i
$78$	5.23607	+	16.1150i	0.592868	+	1.82466i
$79$	−1.22384	−	11.6441i	−0.137693	−	1.31006i	−0.817184	−	0.576376i	$-0.804466\pi$
$79$	−1.22384	−	11.6441i	−0.137693	−	1.31006i	0.679492	−	0.733683i	$-0.262200\pi$
$80$	−3.24803	+	3.60730i	−0.363141	+	0.403308i
$81$	16.3378	+	18.1449i	1.81531	+	2.01610i
$82$	−1.18391	+	11.2642i	−0.130741	+	1.24392i
$83$	−14.6177	+	3.10709i	−1.60450	+	0.341047i	−0.921200	−	0.389089i	$-0.872790\pi$
$83$	−14.6177	+	3.10709i	−1.60450	+	0.341047i	−0.683301	+	0.730136i	$0.739456\pi$
$84$	0.431318	+	0.192035i	0.0470606	+	0.0209527i
$85$	0.618034	−	0.449028i	0.0670352	−	0.0487039i
$86$	−1.82709	+	0.813473i	−0.197020	+	0.0877191i
$87$	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	$0.486916\pi$
$90$	−11.8260	−	2.51369i	−1.24657	−	0.264966i
$91$	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
$96$	10.7051	+	2.27544i	1.09259	+	0.232236i
$97$	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
$100$	−2.25841	+	1.00551i	−0.225841	+	0.100551i
$101$	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	$0.252312\pi$
$102$	−3.65418	−	1.62695i	−0.361818	−	0.161092i
$103$	−6.09979	+	1.29655i	−0.601031	+	0.127753i	−0.498371	−	0.866964i	$-0.666068\pi$
$103$	−6.09979	+	1.29655i	−0.601031	+	0.127753i	−0.102659	+	0.994717i	$0.532735\pi$
$104$	0.756375	−	7.19643i	0.0741687	−	0.705668i
$105$	0.511170	+	0.567712i	0.0498851	+	0.0554030i
$106$	11.3379	−	12.5920i	1.10124	−	1.22305i
$107$	−0.602495	−	5.73236i	−0.0582454	−	0.554168i	−0.984266	−	0.176694i	$-0.943460\pi$
$107$	−0.602495	−	5.73236i	−0.0582454	−	0.554168i	0.926020	−	0.377473i	$-0.123207\pi$
$108$	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	$-0.332768\pi$
$110$	0.338261	+	3.21834i	0.0322519	+	0.306857i
$111$	4.33070	−	4.80973i	0.411052	−	0.456520i
$112$	−0.766755	−	0.851568i	−0.0724516	−	0.0804656i
$113$	−0.362937	+	3.45312i	−0.0341422	+	0.324842i	0.964098	+	0.265546i	$0.0855522\pi$
$113$	−0.362937	+	3.45312i	−0.0341422	+	0.324842i	−0.998240	+	0.0592958i	$0.981114\pi$
$114$	11.4524	−	2.43427i	1.07261	−	0.227991i
$115$	−5.21470	−	2.32174i	−0.486274	−	0.216503i
$116$	1.38197	−	1.00406i	0.128312	−	0.0932244i
$117$	22.0898	−	9.83503i	2.04221	−	0.909249i
$118$	−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
$121$	6.84703	+	1.45538i	0.622458	+	0.132307i
$122$	−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
$127$	12.1996	+	2.59310i	1.08254	+	0.230101i	0.714447	−	0.699689i	$-0.246678\pi$
$127$	12.1996	+	2.59310i	1.08254	+	0.230101i	0.368091	+	0.929790i	$0.380011\pi$
$128$	−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
$131$	10.9625	−	4.88084i	0.957802	−	0.426441i	0.132532	−	0.991179i	$-0.457689\pi$
$131$	10.9625	−	4.88084i	0.957802	−	0.426441i	0.825270	+	0.564738i	$0.191023\pi$
$132$	3.23607	−	2.35114i	0.281664	−	0.204641i
$133$	−0.482228	−	0.214702i	−0.0418145	−	0.0186170i
$134$	−12.6614	+	2.69127i	−1.09378	+	0.232490i
$135$	−1.51275	+	14.3929i	−0.130197	+	1.23874i
$136$	1.14301	+	1.26944i	0.0980124	+	0.108854i
$137$	−4.21003	+	4.67572i	−0.359687	+	0.399473i	−0.895644	−	0.444772i	$-0.853285\pi$
$137$	−4.21003	+	4.67572i	−0.359687	+	0.399473i	0.535956	+	0.844246i	$0.319951\pi$
$138$	3.12420	+	29.7248i	0.265950	+	2.53034i
$139$	−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
$141$	−0.836228	−	7.95618i	−0.0704231	−	0.670031i
$142$	−9.93933	+	11.0387i	−0.834090	+	0.926351i
$143$	−4.33070	−	4.80973i	−0.362152	−	0.402210i
$144$	3.79130	−	36.0718i	0.315942	−	3.00598i
$145$	2.70353	−	0.574654i	0.224516	−	0.0477224i
$146$	−12.5231	−	5.57563i	−1.03642	−	0.461442i
$147$	18.1803	−	13.2088i	1.49949	−	1.08944i
$148$	1.12920	−	0.502754i	0.0928200	−	0.0413261i
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	−0.994847	−	0.101391i	$-0.967671\pi$
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	0.585231	+	0.810867i	$0.301004\pi$
$150$	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	$0.895773\pi$
$152$	−4.89074	−	1.03956i	−0.396691	−	0.0843193i
$153$	−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	$-0.213692\pi$
$158$	−18.5303	−	3.93874i	−1.47419	−	0.313349i
$159$	−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
$162$	36.0911	−	16.0688i	2.83558	−	1.26248i
$163$	−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	$0.437747\pi$
$164$	3.95222	+	1.75964i	0.308616	+	0.137405i
$165$	6.33070	−	1.34563i	0.492845	−	0.104757i
$166$	−2.52753	+	24.0479i	−0.196175	+	1.86648i
$167$	4.33070	+	4.80973i	0.335120	+	0.372188i	0.887027	−	0.461717i	$-0.152766\pi$
$167$	4.33070	+	4.80973i	0.335120	+	0.372188i	−0.551907	+	0.833905i	$0.686100\pi$
$168$	−1.14301	+	1.26944i	−0.0881853	+	0.0979396i
$169$	0.264234	+	2.51402i	0.0203257	+	0.193386i
$170$	−0.381966	−	1.17557i	−0.0292955	−	0.0901621i
$171$	−5.16312	−	15.8904i	−0.394834	−	1.21517i
$172$	0.0798526	+	0.759747i	0.00608871	+	0.0579302i
$173$	1.97010	−	2.18802i	0.149784	−	0.166352i	−0.663583	−	0.748102i	$-0.730965\pi$
$173$	1.97010	−	2.18802i	0.149784	−	0.166352i	0.813367	+	0.581750i	$0.197632\pi$
$174$	−9.68375	−	10.7549i	−0.734123	−	0.815326i
$175$	0.0987033	−	0.939099i	0.00746127	−	0.0709892i
$176$	−9.49606	+	2.01845i	−0.715792	+	0.152146i
$177$	6.61048	+	2.94317i	0.496874	+	0.221223i
$178$	15.3262	−	11.1352i	1.14875	−	0.834616i
$179$	−1.56052	+	0.694789i	−0.116639	+	0.0519310i	−0.464226	−	0.885717i	$-0.653668\pi$
$179$	−1.56052	+	0.694789i	−0.116639	+	0.0519310i	0.347588	+	0.937648i	$0.387001\pi$
$180$	−2.30902	+	3.99933i	−0.172104	+	0.298093i
$181$	−2.09017	−	3.62028i	−0.155361	−	0.269093i	0.777829	−	0.628476i	$-0.216321\pi$
$181$	−2.09017	−	3.62028i	−0.155361	−	0.269093i	−0.933190	+	0.359382i	$0.882987\pi$
$182$	−1.00000	−	0.726543i	−0.0741249	−	0.0538549i
$183$	25.8937	+	5.50387i	1.91411	+	0.406858i
$184$	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
$189$	−3.34175	−	0.710311i	−0.243077	−	0.0516675i
$190$	2.92705	+	2.12663i	0.212351	+	0.154282i
$191$	9.59017	+	16.6107i	0.693920	+	1.20191i	0.970543	+	0.240927i	$0.0774514\pi$
$191$	9.59017	+	16.6107i	0.693920	+	1.20191i	−0.276623	+	0.960979i	$0.589215\pi$
$192$	−6.85410	+	11.8717i	−0.494652	+	0.856763i
$193$	3.17195	−	1.41224i	0.228322	−	0.101656i	−0.289387	−	0.957212i	$-0.593452\pi$
$193$	3.17195	−	1.41224i	0.228322	−	0.101656i	0.517709	+	0.855557i	$0.326785\pi$
$194$	20.8713	−	15.1639i	1.49847	−	1.08870i
$195$	9.56677	+	4.25940i	0.685091	+	0.305022i
$196$	4.19801	−	0.892315i	0.299858	−	0.0637368i
$197$	1.19334	−	11.3539i	0.0850219	−	0.808930i	−0.866049	−	0.499958i	$-0.833349\pi$
$197$	1.19334	−	11.3539i	0.0850219	−	0.808930i	0.951071	−	0.308971i	$-0.0999847\pi$
$198$	−16.1798	−	17.9695i	−1.14985	−	1.27704i
$199$	12.6762	−	14.0783i	0.898591	−	0.997987i	−0.101404	−	0.994845i	$-0.532333\pi$
$199$	12.6762	−	14.0783i	0.898591	−	0.997987i	0.999995	−	0.00314153i	$-0.000999981\pi$
$200$	−0.934931	−	8.89527i	−0.0661096	−	0.628991i
$201$	8.00000	+	24.6215i	0.564276	+	1.73666i
$202$	−1.50000	−	4.61653i	−0.105540	−	0.324818i
$203$	0.0682023	+	0.648902i	0.00478686	+	0.0455440i
$204$	−1.02234	+	1.13542i	−0.0715782	+	0.0794956i
$205$	4.68391	+	5.20201i	0.327139	+	0.363324i
$206$	−1.05471	+	10.0349i	−0.0734851	+	0.699164i
$207$	41.7204	−	8.86795i	2.89977	−	0.616365i
$208$	−14.3502	−	6.38910i	−0.995004	−	0.443005i
$209$	−3.61803	+	2.62866i	−0.250265	+	0.181828i
$210$	1.12920	−	0.502754i	0.0779225	−	0.0346933i
$211$	−11.5902	+	20.0748i	−0.797900	+	1.38200i	0.123081	+	0.992397i	$0.460723\pi$
$211$	−11.5902	+	20.0748i	−0.797900	+	1.38200i	−0.920981	+	0.389607i	$0.872611\pi$
$212$	−3.23607	−	5.60503i	−0.222254	−	0.384955i
$213$	24.0344	+	17.4620i	1.64681	+	1.19648i
$214$	−9.12244	−	1.93903i	−0.623597	−	0.132550i
$215$	−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
$220$	1.20906	+	0.256993i	0.0815146	+	0.0173265i
$221$	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	−0.791258	−	0.611482i	$-0.790574\pi$
$223$	2.00000	−	3.46410i	0.133930	−	0.231973i	0.925188	+	0.379509i	$0.123907\pi$
$224$	−0.729351	+	0.324728i	−0.0487318	+	0.0216968i
$225$	24.1803	−	17.5680i	1.61202	−	1.17120i
$226$	5.13233	+	2.28506i	0.341397	+	0.152000i
$227$	6.33070	−	1.34563i	0.420184	−	0.0893128i	0.00703250	−	0.999975i	$-0.497761\pi$
$227$	6.33070	−	1.34563i	0.420184	−	0.0893128i	0.413151	+	0.910662i	$0.364428\pi$
$228$	0.467465	−	4.44764i	0.0309587	−	0.294552i
$229$	8.97733	+	9.97033i	0.593239	+	0.658858i	0.962758	−	0.270365i	$-0.0871443\pi$
$229$	8.97733	+	9.97033i	0.593239	+	0.658858i	−0.369519	+	0.929223i	$0.620478\pi$
$230$	−6.18014	+	6.86374i	−0.407506	+	0.452581i
$231$	0.159705	+	1.51949i	0.0105078	+	0.0999754i
$232$	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	$0.700000\pi$
$234$	−4.08964	−	38.9103i	−0.267348	−	2.54364i
$235$	1.65418	−	1.83716i	0.107907	−	0.119843i
$236$	0.924716	+	1.02700i	0.0601939	+	0.0668521i
$237$	−3.96043	+	37.6810i	−0.257258	+	2.44764i
$238$	0.285420	−	0.0606678i	0.0185010	−	0.00393251i
$239$	10.6960	+	4.76216i	0.691865	+	0.308038i	0.722380	−	0.691496i	$-0.243048\pi$
$239$	10.6960	+	4.76216i	0.691865	+	0.308038i	−0.0305150	+	0.999534i	$0.509715\pi$
$240$	12.7082	−	9.23305i	0.820311	−	0.595991i
$241$	−13.1191	+	5.84101i	−0.845078	+	0.376253i	−0.783154	−	0.621828i	$-0.786390\pi$
$241$	−13.1191	+	5.84101i	−0.845078	+	0.376253i	−0.0619239	+	0.998081i	$0.519724\pi$
$242$	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
$245$	6.79252	+	1.44380i	0.433958	+	0.0922407i
$246$	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
$251$	−1.77990	−	0.378329i	−0.112346	−	0.0238799i	0.151396	−	0.988473i	$-0.451623\pi$
$251$	−1.77990	−	0.378329i	−0.112346	−	0.0238799i	−0.263742	+	0.964593i	$0.584957\pi$
$252$	−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
$255$	−2.25841	+	1.00551i	−0.141427	+	0.0629674i
$256$	−10.9721	+	7.97172i	−0.685758	+	0.498233i
$257$	1.77618	+	0.790807i	0.110795	+	0.0493292i	0.461386	−	0.887200i	$-0.347352\pi$
$257$	1.77618	+	0.790807i	0.110795	+	0.0493292i	−0.350591	+	0.936529i	$0.614019\pi$
$258$	6.33070	−	1.34563i	0.394132	−	0.0837754i
$259$	−0.0493516	+	0.469550i	−0.00306656	+	0.0291764i
$260$	1.33826	+	1.48629i	0.0829954	+	0.0921758i
$261$	−13.8192	+	15.3478i	−0.855387	+	0.950004i
$262$	−2.02957	−	19.3100i	−0.125387	−	1.19298i
$263$	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
$265$	−1.09464	−	10.4148i	−0.0672430	−	0.639774i
$266$	−0.571506	+	0.634721i	−0.0350413	+	0.0389173i
$267$	−25.3524	−	28.1567i	−1.55154	−	1.72316i
$268$	−0.516817	+	4.91719i	−0.0315696	+	0.300365i
$269$	−10.8141	+	2.29862i	−0.659349	+	0.140149i	−0.525422	−	0.850842i	$-0.676092\pi$
$269$	−10.8141	+	2.29862i	−0.659349	+	0.140149i	−0.133928	+	0.990991i	$0.542759\pi$
$270$	21.3920	+	9.52431i	1.30187	+	0.579631i
$271$	−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	$0.441732\pi$
$272$	3.38761	−	1.50826i	0.205404	−	0.0914518i
$273$	−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
$276$	11.1669	+	2.37360i	0.672170	+	0.142874i
$277$	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	$-0.0692705\pi$
$282$	−12.6614	−	2.69127i	−0.753976	−	0.160263i
$283$	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
$286$	−9.56677	+	4.25940i	−0.565695	+	0.251864i
$287$	−1.33688	+	0.971301i	−0.0789136	+	0.0573341i
$288$	−23.0858	−	10.2784i	−1.36034	−	0.605663i
$289$	16.0577	−	3.41316i	0.944569	−	0.200774i
$290$	0.467465	−	4.44764i	0.0274505	−	0.261174i
$291$	−34.5250	−	38.3439i	−2.02389	−	2.24776i
$292$	−3.50361	+	3.89116i	−0.205033	+	0.227713i
$293$	0.0493516	+	0.469550i	0.00288315	+	0.0274314i	0.995869	−	0.0908028i	$-0.0289433\pi$
$293$	0.0493516	+	0.469550i	0.00288315	+	0.0274314i	−0.992986	+	0.118234i	$0.962277\pi$
$294$	−11.2361	−	34.5811i	−0.655301	−	2.01681i
$295$	0.690983	+	2.12663i	0.0402306	+	0.123817i
$296$	0.467465	+	4.44764i	0.0271709	+	0.258514i
$297$	−19.3675	+	21.5098i	−1.12382	+	1.24812i
$298$	10.8268	+	12.0243i	0.627177	+	0.696551i
$299$	1.93086	−	18.3709i	0.111665	−	1.06242i
$300$	7.82518	−	1.66329i	0.451787	−	0.0960303i
$301$	−0.266569	−	0.118684i	−0.0153648	−	0.00684084i
$302$	−18.5623	+	13.4863i	−1.06814	+	0.776050i
$303$	−8.86889	+	3.94868i	−0.509504	+	0.226846i
$304$	−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
$307$	28.0809	+	5.96877i	1.60266	+	0.340656i	0.920559	−	0.390603i	$-0.127733\pi$
$307$	28.0809	+	5.96877i	1.60266	+	0.340656i	0.682100	+	0.731259i	$0.261067\pi$
$308$	−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
$313$	16.3976	+	3.48542i	0.926847	+	0.197007i	0.646520	−	0.762897i	$-0.276224\pi$
$313$	16.3976	+	3.48542i	0.926847	+	0.197007i	0.280327	+	0.959905i	$0.409557\pi$
$314$	−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
$317$	3.70509	−	1.64961i	0.208099	−	0.0926515i	−0.300041	−	0.953926i	$-0.597000\pi$
$317$	3.70509	−	1.64961i	0.208099	−	0.0926515i	0.508139	+	0.861275i	$0.330334\pi$
$318$	−44.3607	+	32.2299i	−2.48762	+	1.80736i
$319$	5.04996	+	2.24838i	0.282743	+	0.125885i
$320$	−4.14350	+	0.880728i	−0.231629	+	0.0492342i
$321$	−1.94971	+	18.5503i	−0.108822	+	1.03538i
$322$	−1.45893	−	1.62031i	−0.0813031	−	0.0902963i
$323$	1.14301	−	1.26944i	0.0635989	−	0.0706337i
$324$	−1.57735	−	15.0075i	−0.0876307	−	0.833750i
$325$	−4.00000	−	12.3107i	−0.221880	−	0.682877i
$326$	5.35410	+	16.4782i	0.296536	+	0.912645i
$327$	4.71681	+	44.8774i	0.260840	+	2.48173i
$328$	−10.4736	+	11.6321i	−0.578305	+	0.642273i
$329$	0.390499	+	0.433693i	0.0215289	+	0.0239103i
$330$	1.09464	−	10.4148i	0.0602577	−	0.573314i
$331$	1.95630	−	0.415823i	0.107528	−	0.0228557i	−0.153834	−	0.988097i	$-0.549162\pi$
$331$	1.95630	−	0.415823i	0.107528	−	0.0228557i	0.261361	+	0.965241i	$0.415829\pi$
$332$	8.43757	+	3.75665i	0.463072	+	0.206173i
$333$	−12.0902	+	8.78402i	−0.662537	+	0.481361i
$334$	9.56677	−	4.25940i	0.523470	−	0.233064i
$335$	−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	$0.831727\pi$
$338$	4.00079	+	0.850394i	0.217614	+	0.0462553i
$339$	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
$344$	−2.70353	−	0.574654i	−0.145765	−	0.0309833i
$345$	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	−0.334320	−	0.942460i	$-0.608506\pi$
$347$	12.0902	−	20.9408i	0.649034	−	1.12416i	0.983354	−	0.181701i	$-0.0581602\pi$
$348$	−5.04996	+	2.24838i	−0.270706	+	0.120526i
$349$	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	$0.232285\pi$
$350$	−1.39577	−	0.621438i	−0.0746072	−	0.0332173i
$351$	−45.8094	+	9.73709i	−2.44513	+	0.519727i
$352$	−0.707023	+	6.72688i	−0.0376845	+	0.358544i
$353$	−4.96255	−	5.51147i	−0.264130	−	0.293346i	0.596462	−	0.802641i	$-0.296573\pi$
$353$	−4.96255	−	5.51147i	−0.264130	−	0.293346i	−0.860592	+	0.509296i	$0.829906\pi$
$354$	7.83432	−	8.70089i	0.416389	−	0.462447i
$355$	0.959607	+	9.13005i	0.0509306	+	0.484573i
$356$	−2.23607	−	6.88191i	−0.118511	−	0.364740i
$357$	−0.180340	−	0.555029i	−0.00954460	−	0.0293753i
$358$	0.288910	+	2.74879i	0.0152693	+	0.145278i
$359$	14.8788	−	16.5246i	0.785275	−	0.872136i	−0.209117	−	0.977891i	$-0.567059\pi$
$359$	14.8788	−	16.5246i	0.785275	−	0.872136i	0.994392	+	0.105755i	$0.0337258\pi$
$360$	−11.1800	−	12.4166i	−0.589236	−	0.654413i
$361$	1.46340	−	13.9233i	0.0770210	−	0.732806i
$362$	−6.61612	+	1.40630i	−0.347736	+	0.0739135i
$363$	−20.6941	−	9.21359i	−1.08616	−	0.483588i
$364$	−0.381966	+	0.277515i	−0.0200205	+	0.0145457i
$365$	−7.73968	+	3.44593i	−0.405113	+	0.180368i
$366$	21.4164	−	37.0943i	1.11945	−	1.93895i
$367$	9.00000	+	15.5885i	0.469796	+	0.813711i	0.999404	−	0.0345320i	$-0.0109941\pi$
$367$	9.00000	+	15.5885i	0.469796	+	0.813711i	−0.529607	+	0.848243i	$0.677661\pi$
$368$	−22.4164	−	16.2865i	−1.16854	−	0.848991i
$369$	−51.1620	−	10.8748i	−2.66339	−	0.566120i
$370$	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
$375$	28.4882	+	6.05535i	1.47112	+	0.312697i
$376$	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
$379$	−1.92891	+	0.858807i	−0.0990815	+	0.0441139i	−0.455679	−	0.890144i	$-0.650603\pi$
$379$	−1.92891	+	0.858807i	−0.0990815	+	0.0441139i	0.356597	+	0.934258i	$0.383937\pi$
$380$	1.11803	−	0.812299i	0.0573539	−	0.0416701i
$381$	−36.8713	−	16.4162i	−1.88897	−	0.841026i
$382$	30.3563	−	6.45242i	1.55316	−	0.330135i
$383$	−2.49703	+	23.7577i	−0.127592	+	1.21396i	0.724016	+	0.689783i	$0.242294\pi$
$383$	−2.49703	+	23.7577i	−0.127592	+	1.21396i	−0.851609	+	0.524178i	$0.824373\pi$
$384$	29.4878	+	32.7496i	1.50479	+	1.67124i
$385$	−0.315921	+	0.350865i	−0.0161008	+	0.0178818i
$386$	−0.587244	−	5.58726i	−0.0298900	−	0.284384i
$387$	−2.85410	−	8.78402i	−0.145082	−	0.446517i
$388$	−3.04508	−	9.37181i	−0.154591	−	0.475781i
$389$	−1.86986	−	17.7905i	−0.0948058	−	0.902017i	−0.933781	−	0.357846i	$-0.883511\pi$
$389$	−1.86986	−	17.7905i	−0.0948058	−	0.902017i	0.838975	−	0.544170i	$-0.183155\pi$
$390$	11.3379	−	12.5920i	0.574118	−	0.637623i
$391$	2.91786	+	3.24062i	0.147563	+	0.163885i
$392$	−1.62310	+	15.4428i	−0.0819791	+	0.779979i
$393$	−37.9842	+	8.07380i	−1.91605	+	0.407269i
$394$	−16.8751	−	7.51329i	−0.850157	−	0.378514i
$395$	−9.47214	+	6.88191i	−0.476595	+	0.346266i
$396$	−8.43757	+	3.75665i	−0.424004	+	0.188779i
$397$	3.50000	−	6.06218i	0.175660	−	0.304252i	−0.764730	−	0.644351i	$-0.777127\pi$
$397$	3.50000	−	6.06218i	0.175660	−	0.304252i	0.940389	+	0.340099i	$0.110461\pi$
$398$	−15.3262	−	26.5458i	−0.768235	−	1.33062i
$399$	1.38197	+	1.00406i	0.0691848	+	0.0502657i
$400$	−18.9921	−	4.03690i	−0.949606	−	0.201845i
$401$	−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
$406$	1.03266	+	0.219498i	0.0512500	+	0.0108935i
$407$	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	−0.909373	−	0.415982i	$-0.863438\pi$
$409$	−1.90983	+	3.30792i	−0.0944350	+	0.163566i	0.814938	+	0.579549i	$0.196771\pi$
$410$	10.3470	−	4.60680i	0.511004	−	0.227513i
$411$	16.4721	−	11.9677i	0.812511	−	0.590323i
$412$	3.52090	+	1.56760i	0.173462	+	0.0772303i
$413$	−0.516329	+	0.109749i	−0.0254069	+	0.00540040i
$414$	7.21384	−	68.6351i	0.354541	−	3.37323i
$415$	9.99967	+	11.1058i	0.490864	+	0.545160i
$416$	−7.32315	+	8.13318i	−0.359047	+	0.398762i
$417$	4.53825	+	43.1786i	0.222239	+	2.11446i
$418$	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	$0.979547\pi$
$420$	−0.0493516	−	0.469550i	−0.00240811	−	0.0229117i
$421$	19.6461	−	21.8192i	0.957494	−	1.06340i	−0.0404418	−	0.999182i	$-0.512877\pi$
$421$	19.6461	−	21.8192i	0.957494	−	1.06340i	0.997936	−	0.0642227i	$-0.0204568\pi$
$422$	25.0968	+	27.8728i	1.22169	+	1.35683i
$423$	−1.93086	+	18.3709i	−0.0938818	+	0.893226i
$424$	22.9047	−	4.86854i	1.11235	−	0.236437i
$425$	2.79155	+	1.24288i	0.135410	+	0.0602884i
$426$	38.8885	−	28.2542i	1.88416	−	1.36892i
$427$	−1.76416	+	0.785456i	−0.0853738	+	0.0380109i
$428$	−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
$431$	−11.7378	−	2.49494i	−0.565389	−	0.120177i	−0.0836550	−	0.996495i	$-0.526659\pi$
$431$	−11.7378	−	2.49494i	−0.565389	−	0.120177i	−0.481734	+	0.876318i	$0.659993\pi$
$432$	−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
$437$	−12.4850	−	2.65377i	−0.597239	−	0.126947i
$438$	35.8885	+	26.0746i	1.71482	+	1.24589i
$439$	0.590170	+	1.02220i	0.0281673	+	0.0487872i	0.879765	−	0.475408i	$-0.157700\pi$
$439$	0.590170	+	1.02220i	0.0281673	+	0.0487872i	−0.851598	+	0.524195i	$0.824366\pi$
$440$	−2.23607	+	3.87298i	−0.106600	+	0.184637i
$441$	−47.4025	+	21.1050i	−2.25726	+	1.00500i
$442$	3.23607	−	2.35114i	0.153924	−	0.111832i
$443$	28.0533	+	12.4902i	1.33285	+	0.593425i	0.944629	−	0.328140i	$-0.106422\pi$
$443$	28.0533	+	12.4902i	1.33285	+	0.593425i	0.388225	+	0.921565i	$0.373088\pi$
$444$	−3.91259	+	0.831647i	−0.185683	+	0.0394682i
$445$	1.22384	−	11.6441i	0.0580156	−	0.551982i
$446$	−4.33070	−	4.80973i	−0.205065	−	0.227748i
$447$	21.6535	−	24.0487i	1.02418	−	1.13746i
$448$	−0.104528	−	0.994522i	−0.00493851	−	0.0469867i
$449$	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
$451$	1.46340	+	13.9233i	0.0689087	+	0.655623i
$452$	1.43589	−	1.59471i	0.0675384	−	0.0750090i
$453$	30.7054	+	34.1018i	1.44267	+	1.60224i
$454$	1.09464	−	10.4148i	0.0513738	−	0.488789i
$455$	−0.747238	+	0.158830i	−0.0350311	+	0.00744608i
$456$	14.7815	+	6.58114i	0.692206	+	0.308190i
$457$	−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	$0.322769\pi$
$458$	19.8314	−	8.82952i	0.926662	−	0.412576i
$459$	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	$0.404744\pi$
$462$	2.41811	+	0.513986i	0.112501	+	0.0239128i
$463$	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	$0.0652560\pi$
$468$	−14.6177	−	3.10709i	−0.675704	−	0.143625i
$469$	−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
$472$	−4.56773	+	2.03368i	−0.210247	+	0.0936079i
$473$	−2.00000	+	1.45309i	−0.0919601	+	0.0668129i
$474$	56.0049	+	24.9350i	2.57239	+	1.14530i
$475$	−8.74882	+	1.85962i	−0.401423	+	0.0853252i
$476$	0.0116503	−	0.110846i	0.000533993	−	0.00508060i
$477$	52.3590	+	58.1505i	2.39735	+	2.66253i
$478$	12.6762	−	14.0783i	0.579796	−	0.643928i
$479$	−2.43466	−	23.1642i	−0.111242	−	1.05840i	−0.897655	−	0.440698i	$-0.854731\pi$
$479$	−2.43466	−	23.1642i	−0.111242	−	1.05840i	0.786413	−	0.617701i	$-0.211936\pi$
$480$	−3.38197	−	10.4086i	−0.154365	−	0.475086i
$481$	2.00000	+	6.15537i	0.0911922	+	0.280661i
$482$	2.42883	+	23.1088i	0.110630	+	1.05258i
$483$	−2.91786	+	3.24062i	−0.132767	+	0.147453i
$484$	−2.89482	−	3.21502i	−0.131583	−	0.146137i
$485$	1.66663	−	15.8569i	0.0756778	−	0.720026i
$486$	−56.3381	+	11.9750i	−2.55555	+	0.543199i
$487$	17.5730	+	7.82401i	0.796310	+	0.354540i	0.764229	−	0.644945i	$-0.223120\pi$
$487$	17.5730	+	7.82401i	0.796310	+	0.354540i	0.0320810	+	0.999485i	$0.489787\pi$
$488$	−14.7984	+	10.7516i	−0.669891	+	0.486704i
$489$	31.6566	−	14.0944i	1.43156	−	0.637372i
$490$	5.61803	−	9.73072i	0.253797	−	0.439589i
$491$	2.18034	+	3.77646i	0.0983974	+	0.170429i	0.911021	−	0.412359i	$-0.135295\pi$
$491$	2.18034	+	3.77646i	0.0983974	+	0.170429i	−0.812624	+	0.582788i	$0.801962\pi$
$492$	−11.3262	−	8.22899i	−0.510626	−	0.370992i
$493$	−2.06532	−	0.438996i	−0.0930171	−	0.0197714i
$494$	−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
$499$	−6.43972	−	1.36881i	−0.288282	−	0.0612762i	0.0615010	−	0.998107i	$-0.480411\pi$
$499$	−6.43972	−	1.36881i	−0.288282	−	0.0612762i	−0.349783	+	0.936831i	$0.613745\pi$
$500$	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
$503$	27.0889	−	12.0607i	1.20783	−	0.537762i	0.298732	−	0.954337i	$-0.403436\pi$
$503$	27.0889	−	12.0607i	1.20783	−	0.537762i	0.909101	+	0.416575i	$0.136770\pi$
$504$	3.19098	−	2.31838i	0.142138	−	0.103269i
$505$	−2.74064	−	1.22021i	−0.121957	−	0.0542986i
$506$	−18.0685	+	3.84057i	−0.803242	+	0.170734i
$507$	0.855078	−	8.13553i	0.0379754	−	0.361311i
$508$	−5.15780	−	5.72831i	−0.228840	−	0.254153i
$509$	−19.8041	+	21.9947i	−0.877801	+	0.974897i	−0.999845	−	0.0176281i	$-0.994389\pi$
$509$	−19.8041	+	21.9947i	−0.877801	+	0.974897i	0.122044	+	0.992525i	$0.461055\pi$
$510$	0.418114	+	3.97809i	0.0185144	+	0.176153i
$511$	−0.618034	−	1.90211i	−0.0273402	−	0.0841445i
$512$	−1.63525	−	5.03280i	−0.0722687	−	0.222420i
$513$	3.38261	+	32.1834i	0.149346	+	1.42093i
$514$	2.10502	−	2.33786i	0.0928483	−	0.103118i
$515$	4.17274	+	4.63430i	0.183873	+	0.204212i
$516$	0.258409	−	2.45859i	0.0113758	−	0.108234i
$517$	4.83623	−	1.02797i	0.212697	−	0.0452102i
$518$	0.697887	+	0.310719i	0.0306634	+	0.0136522i
$519$	−7.70820	+	5.60034i	−0.338353	+	0.245828i
$520$	−6.61048	+	2.94317i	−0.289889	+	0.129067i
$521$	−1.00000	+	1.73205i	−0.0438108	+	0.0758825i	−0.887099	−	0.461579i	$-0.847283\pi$
$521$	−1.00000	+	1.73205i	−0.0438108	+	0.0758825i	0.843288	+	0.537461i	$0.180617\pi$
$522$	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	$0.826545\pi$
$524$	−7.25434	−	1.54196i	−0.316907	−	0.0673607i
$525$	−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
$530$	−16.5740	−	3.52291i	−0.719929	−	0.153026i
$531$	−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
$534$	−56.0049	+	24.9350i	−2.42357	+	1.07904i
$535$	−4.66312	+	3.38795i	−0.201604	+	0.146474i
$536$	−16.3420	−	7.27593i	−0.705867	−	0.314272i
$537$	5.40707	−	1.14931i	0.233332	−	0.0495963i
$538$	−1.86986	+	17.7905i	−0.0806155	+	0.767005i
$539$	9.29325	+	10.3212i	0.400289	+	0.444566i
$540$	5.98489	−	6.64689i	0.257548	−	0.286037i
$541$	2.65091	+	25.2218i	0.113972	+	1.08437i	0.890719	+	0.454555i	$0.150202\pi$
$541$	2.65091	+	25.2218i	0.113972	+	1.08437i	−0.776747	+	0.629813i	$0.783132\pi$
$542$	7.09017	+	21.8213i	0.304549	+	0.937305i
$543$	4.18034	+	12.8658i	0.179396	+	0.552123i
$544$	−0.270059	−	2.56944i	−0.0115787	−	0.110164i
$545$	−9.33054	+	10.3626i	−0.399676	+	0.443886i
$546$	2.67652	+	2.97258i	0.114545	+	0.127215i
$547$	1.26737	−	12.0582i	0.0541887	−	0.515571i	−0.933437	−	0.358741i	$-0.883206\pi$
$547$	1.26737	−	12.0582i	0.0541887	−	0.515571i	0.987626	−	0.156830i	$-0.0501274\pi$
$548$	3.80357	−	0.808474i	0.162480	−	0.0345363i
$549$	−55.8401	−	24.8616i	−2.38320	−	1.06107i
$550$	−10.4721	+	7.60845i	−0.446533	+	0.324425i
$551$	5.64602	−	2.51377i	0.240529	−	0.107090i
$552$	−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
$555$	−6.33070	−	1.34563i	−0.268723	−	0.0571189i
$556$	−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
$561$	−4.83623	−	1.02797i	−0.204186	−	0.0434010i
$562$	−22.2533	−	16.1680i	−0.938698	−	0.682004i
$563$	−13.7705	−	23.8512i	−0.580358	−	1.00521i	−0.995437	−	0.0954238i	$-0.969579\pi$
$563$	−13.7705	−	23.8512i	−0.580358	−	1.00521i	0.415079	−	0.909785i	$-0.363754\pi$
$564$	−2.47214	+	4.28187i	−0.104096	+	0.180299i
$565$	3.17195	−	1.41224i	0.133445	−	0.0594136i
$566$	18.1803	−	13.2088i	0.764177	−	0.555207i
$567$	5.26561	+	2.34440i	0.221135	+	0.0984556i
$568$	−20.0793	+	4.26798i	−0.842508	+	0.179081i
$569$	0.577819	−	5.49758i	0.0242234	−	0.230471i	−0.975711	−	0.219060i	$-0.929701\pi$
$569$	0.577819	−	5.49758i	0.0242234	−	0.230471i	0.999935	−	0.0114109i	$-0.00363228\pi$
$570$	−7.83432	−	8.70089i	−0.328143	−	0.364440i
$571$	−18.8563	+	20.9421i	−0.789113	+	0.876399i	−0.994761	−	0.102227i	$-0.967403\pi$
$571$	−18.8563	+	20.9421i	−0.789113	+	0.876399i	0.205648	+	0.978626i	$0.434070\pi$
$572$	0.418114	+	3.97809i	0.0174822	+	0.166332i
$573$	−19.1803	−	59.0310i	−0.801270	−	2.46606i
$574$	0.826238	+	2.54290i	0.0344865	+	0.106139i
$575$	−2.38668	−	22.7077i	−0.0995314	−	0.946978i
$576$	21.1796	−	23.5224i	0.882485	−	0.980099i
$577$	−19.2929	−	21.4270i	−0.803175	−	0.892016i	0.192838	−	0.981231i	$-0.438231\pi$
$577$	−19.2929	−	21.4270i	−0.803175	−	0.892016i	−0.996012	+	0.0892147i	$0.971564\pi$
$578$	2.77652	−	26.4168i	0.115488	−	1.09879i
$579$	−10.9905	+	2.33611i	−0.456751	+	0.0970854i
$580$	−1.56052	−	0.694789i	−0.0647971	−	0.0288495i
$581$	−2.85410	+	2.07363i	−0.118408	+	0.0860285i
$582$	−76.2676	+	33.9565i	−3.16139	+	1.40754i
$583$	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
$586$	0.747238	+	0.158830i	0.0308681	+	0.00656122i
$587$	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
$592$	9.49606	+	2.01845i	0.390286	+	0.0829577i
$593$	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
$596$	5.64602	−	2.51377i	0.231270	−	0.102968i
$597$	−49.5967	+	36.0341i	−2.02986	+	1.47478i
$598$	−27.3045	−	12.1568i	−1.11657	−	0.497127i
$599$	14.2778	−	3.03483i	0.583374	−	0.124000i	0.0932348	−	0.995644i	$-0.470279\pi$
$599$	14.2778	−	3.03483i	0.583374	−	0.124000i	0.490139	+	0.871644i	$0.336946\pi$
$600$	−3.02550	+	28.7857i	−0.123516	+	1.17517i
$601$	−20.4359	−	22.6964i	−0.833599	−	0.925805i	0.164566	−	0.986366i	$-0.447378\pi$
$601$	−20.4359	−	22.6964i	−0.833599	−	0.925805i	−0.998165	+	0.0605607i	$0.980711\pi$
$602$	−0.315921	+	0.350865i	−0.0128760	+	0.0143002i
$603$	−6.24841	−	59.4496i	−0.254455	−	2.42098i
$604$	2.70820	+	8.33499i	0.110195	+	0.339146i
$605$	−2.16312	−	6.65740i	−0.0879433	−	0.270662i
$606$	1.64195	+	15.6222i	0.0666998	+	0.634607i
$607$	15.0368	−	16.7001i	0.610325	−	0.677834i	−0.356199	−	0.934410i	$-0.615928\pi$
$607$	15.0368	−	16.7001i	0.610325	−	0.677834i	0.966524	+	0.256576i	$0.0825943\pi$
$608$	5.06017	+	5.61989i	0.205217	+	0.227917i
$609$	0.220707	−	2.09989i	0.00894351	−	0.0850918i
$610$	12.9468	−	2.75193i	0.524202	−	0.111423i
$611$	7.30836	+	3.25389i	0.295665	+	0.131638i
$612$	2.85410	−	2.07363i	0.115370	−	0.0838214i
$613$	40.0942	−	17.8511i	1.61939	−	0.720998i	0.621346	−	0.783536i	$-0.286586\pi$
$613$	40.0942	−	17.8511i	1.61939	−	0.720998i	0.998043	+	0.0625380i	$0.0199194\pi$
$614$	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
$617$	−31.7625	−	6.75134i	−1.27871	−	0.271799i	−0.482007	−	0.876167i	$-0.660092\pi$
$617$	−31.7625	−	6.75134i	−1.27871	−	0.271799i	−0.796705	+	0.604369i	$0.793425\pi$
$618$	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
$623$	2.70353	+	0.574654i	0.108315	+	0.0230230i
$624$	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
$627$	13.2210	−	5.88635i	0.527994	−	0.235078i
$628$	−10.4443	+	7.58821i	−0.416772	+	0.302802i
$629$	−1.39577	−	0.621438i	−0.0556531	−	0.0247784i
$630$	−2.79173	+	0.593401i	−0.111225	+	0.0236417i
$631$	3.59167	−	34.1724i	0.142982	−	1.36038i	−0.654052	−	0.756450i	$-0.726932\pi$
$631$	3.59167	−	34.1724i	0.142982	−	1.36038i	0.797034	−	0.603934i	$-0.206401\pi$
$632$	−17.5181	−	19.4558i	−0.696831	−	0.773910i
$633$	50.1936	−	55.7456i	1.99502	−	2.21569i
$634$	−0.685948	−	6.52636i	−0.0272425	−	0.259195i
$635$	−3.85410	−	11.8617i	−0.152945	−	0.470717i
$636$	6.47214	+	19.9192i	0.256637	+	0.789847i
$637$	2.34898	+	22.3490i	0.0930699	+	0.885501i
$638$	5.98489	−	6.64689i	0.236944	−	0.263153i
$639$	−45.9002	−	50.9773i	−1.81578	−	2.01663i
$640$	−1.42347	+	13.5434i	−0.0562677	+	0.535351i
$641$	11.7378	−	2.49494i	0.463614	−	0.0985442i	0.0298181	−	0.999555i	$-0.490507\pi$
$641$	11.7378	−	2.49494i	0.463614	−	0.0985442i	0.433796	+	0.901011i	$0.357174\pi$
$642$	27.5711	+	12.2755i	1.08815	+	0.484473i
$643$	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	$0.174184\pi$
$644$	−0.760815	+	0.338737i	−0.0299803	+	0.0133481i
$645$	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	$0.705909\pi$
$648$	53.4037	+	11.3513i	2.09789	+	0.445921i
$649$	−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	$0.723567\pi$
$654$	71.4176	+	15.1803i	2.79265	+	0.593596i
$655$	−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
$658$	0.862635	−	0.384070i	0.0336290	−	0.0149726i
$659$	−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	$0.466534\pi$
$660$	−3.65418	−	1.62695i	−0.142239	−	0.0633288i
$661$	0.625350	−	0.132922i	0.0243233	−	0.00517007i	−0.195734	−	0.980657i	$-0.562709\pi$
$661$	0.625350	−	0.132922i	0.0243233	−	0.00517007i	0.220057	+	0.975487i	$0.429376\pi$
$662$	0.338261	−	3.21834i	0.0131469	−	0.125084i
$663$	−5.35304	−	5.94516i	−0.207895	−	0.230891i
$664$	−22.3599	+	24.8332i	−0.867734	+	0.963716i
$665$	0.0551768	+	0.524972i	0.00213967	+	0.0203576i
$666$	7.47214	+	22.9969i	0.289539	+	0.891111i
$667$	4.87539	+	15.0049i	0.188776	+	0.580992i
$668$	−0.418114	−	3.97809i	−0.0161773	−	0.153917i
$669$	−8.66141	+	9.61947i	−0.334869	+	0.371910i
$670$	8.66141	+	9.61947i	0.334619	+	0.371632i
$671$	−1.71016	+	16.2711i	−0.0660199	+	0.628137i
$672$	2.52713	−	0.537159i	0.0974863	−	0.0207214i
$673$	26.5048	+	11.8007i	1.02169	+	0.454884i	0.848045	−	0.529925i	$-0.177780\pi$
$673$	26.5048	+	11.8007i	1.02169	+	0.454884i	0.173642	+	0.984809i	$0.444447\pi$
$674$	−19.3262	+	14.0413i	−0.744419	+	0.540852i
$675$	−52.8838	+	23.5454i	−2.03550	+	0.906263i
$676$	0.781153	−	1.35300i	0.0300443	−	0.0520383i
$677$	−23.3607	−	40.4619i	−0.897824	−	1.55508i	−0.830270	−	0.557361i	$-0.811814\pi$
$677$	−23.3607	−	40.4619i	−0.897824	−	1.55508i	−0.0675535	−	0.997716i	$-0.521519\pi$
$678$	−14.7082	−	10.6861i	−0.564865	−	0.410399i
$679$	3.68168	+	0.782565i	0.141290	+	0.0300321i
$680$	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
$685$	6.15431	+	1.30814i	0.235144	+	0.0499814i
$686$	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
$689$	30.9587	−	13.7837i	1.17943	−	0.525118i
$690$	24.1803	−	17.5680i	0.920530	−	0.668804i
$691$	2.90539	+	1.29356i	0.110526	+	0.0492094i	0.461255	−	0.887268i	$-0.347399\pi$
$691$	2.90539	+	1.29356i	0.110526	+	0.0492094i	−0.350729	+	0.936477i	$0.614066\pi$
$692$	−1.77990	+	0.378329i	−0.0676615	+	0.0143819i
$693$	0.368762	−	3.50854i	0.0140081	−	0.133278i
$694$	−26.1795	−	29.0753i	−0.993759	−	1.10368i
$695$	−8.97733	+	9.97033i	−0.340530	+	0.378196i
$696$	−2.09057	−	19.8904i	−0.0792428	−	0.753945i
$697$	−1.65248	−	5.08580i	−0.0625920	−	0.192638i
$698$	−3.94427	−	12.1392i	−0.149293	−	0.459476i
$699$	−6.06985	−	57.7508i	−0.229583	−	2.18433i
$700$	−0.390499	+	0.433693i	−0.0147595	+	0.0163921i
$701$	4.68391	+	5.20201i	0.176909	+	0.196477i	0.825077	−	0.565020i	$-0.191131\pi$
$701$	4.68391	+	5.20201i	0.176909	+	0.196477i	−0.648168	+	0.761497i	$0.724465\pi$
$702$	−7.92086	+	75.3620i	−0.298954	+	2.84435i
$703$	4.37441	−	0.929809i	0.164984	−	0.0350684i
$704$	−7.73968	−	3.44593i	−0.291700	−	0.129873i
$705$	−6.47214	+	4.70228i	−0.243755	+	0.177098i
$706$	−10.9625	+	4.88084i	−0.412581	+	0.183693i
$707$	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	$0.540869\pi$
$710$	14.5295	+	3.08834i	0.545283	+	0.115903i
$711$	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
$716$	1.03266	+	0.219498i	0.0385922	+	0.00820303i
$717$	−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	−0.965624	−	0.259945i	$-0.916296\pi$
$719$	−6.90983	+	11.9682i	−0.257693	+	0.446338i	0.707930	+	0.706282i	$0.249629\pi$
$720$	−33.1348	+	14.7525i	−1.23486	+	0.549795i
$721$	−1.19098	+	0.865300i	−0.0443545	+	0.0322254i
$722$	−20.6941	−	9.21359i	−0.770153	−	0.342894i
$723$	45.4566	−	9.66210i	1.69055	−	0.359337i
$724$	−0.270059	+	2.56944i	−0.0100367	+	0.0954924i
$725$	7.39773	+	8.21601i	0.274745	+	0.305135i
$726$	−24.5253	+	27.2381i	−0.910219	+	1.01090i
$727$	4.62393	+	43.9937i	0.171492	+	1.63164i	0.654529	+	0.756037i	$0.272867\pi$
$727$	4.62393	+	43.9937i	0.171492	+	1.63164i	−0.483037	+	0.875600i	$0.660466\pi$
$728$	−0.527864	−	1.62460i	−0.0195639	−	0.0602116i
$729$	12.9615	+	39.8914i	0.480055	+	1.47746i
$730$	1.43290	+	13.6331i	0.0530339	+	0.504584i
$731$	0.631841	−	0.701731i	0.0233695	−	0.0259545i
$732$	−10.9474	−	12.1584i	−0.404629	−	0.449386i
$733$	−0.362937	+	3.45312i	−0.0134054	+	0.127544i	−0.999178	−	0.0405415i	$-0.987092\pi$
$733$	−0.362937	+	3.45312i	−0.0134054	+	0.127544i	0.985772	+	0.168085i	$0.0537584\pi$
$734$	28.4882	−	6.05535i	1.05152	−	0.223507i
$735$	−20.5293	−	9.14024i	−0.757235	−	0.337143i
$736$	−15.6180	+	11.3472i	−0.575688	+	0.418262i
$737$	−14.6167	+	6.50779i	−0.538414	+	0.239717i
$738$	−42.3156	+	73.2928i	−1.55766	+	2.69794i
$739$	3.09017	+	5.35233i	0.113674	+	0.196889i	0.917249	−	0.398315i	$-0.130405\pi$
$739$	3.09017	+	5.35233i	0.113674	+	0.196889i	−0.803575	+	0.595203i	$0.797071\pi$
$740$	−1.00000	−	0.726543i	−0.0367607	−	0.0267082i
$741$	22.9047	+	4.86854i	0.841425	+	0.178850i
$742$	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
$747$	−109.225	−	23.2166i	−3.99635	−	0.849451i
$748$	−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
$751$	−19.6787	+	8.76152i	−0.718086	+	0.319712i	−0.733049	−	0.680176i	$-0.761904\pi$
$751$	−19.6787	+	8.76152i	−0.718086	+	0.319712i	0.0149633	+	0.999888i	$0.495237\pi$
$752$	9.70820	−	7.05342i	0.354022	−	0.257212i
$753$	5.37945	+	2.39509i	0.196038	+	0.0872818i
$754$	14.1559	−	3.00893i	0.515527	−	0.109579i
$755$	−1.48225	+	14.1027i	−0.0539446	+	0.513248i
$756$	1.41284	+	1.56912i	0.0513845	+	0.0570683i
$757$	−5.78964	+	6.43004i	−0.210428	+	0.233704i	−0.839114	−	0.543955i	$-0.816926\pi$
$757$	−5.78964	+	6.43004i	−0.210428	+	0.233704i	0.628686	+	0.777659i	$0.283593\pi$
$758$	0.357112	+	3.39769i	0.0129709	+	0.123410i
$759$	11.4164	+	35.1361i	0.414389	+	1.27536i
$760$	1.54508	+	4.75528i	0.0560461	+	0.172492i
$761$	0.209057	+	1.98904i	0.00757831	+	0.0721028i	0.997657	−	0.0684084i	$-0.0217921\pi$
$761$	0.209057	+	1.98904i	0.00757831	+	0.0721028i	−0.990079	+	0.140511i	$0.955125\pi$
$762$	−43.6975	+	48.5310i	−1.58299	+	1.75809i
$763$	−2.20264	−	2.44628i	−0.0797410	−	0.0885613i
$764$	1.23909	−	11.7892i	0.0448287	−	0.426517i
$765$	5.58347	−	1.18680i	0.201871	−	0.0429089i
$766$	35.3108	+	15.7214i	1.27583	+	0.568036i
$767$	−5.85410	+	4.25325i	−0.211379	+	0.153576i
$768$	40.0942	−	17.8511i	1.44677	−	0.644145i
$769$	23.6803	−	41.0156i	0.853935	−	1.47906i	−0.0236947	−	0.999719i	$-0.507543\pi$
$769$	23.6803	−	41.0156i	0.853935	−	1.47906i	0.877630	−	0.479339i	$-0.159124\pi$
$770$	0.381966	+	0.661585i	0.0137651	+	0.0238419i
$771$	−5.09017	−	3.69822i	−0.183318	−	0.133188i
$772$	−2.09901	−	0.446157i	−0.0755448	−	0.0160576i
$773$	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
$778$	−28.3118	−	6.01785i	−1.01503	−	0.215750i
$779$	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
$782$	6.44573	−	2.86982i	0.230499	−	0.102625i
$783$	32.3607	−	23.5114i	1.15648	−	0.840229i
$784$	30.7940	+	13.7104i	1.09978	+	0.489656i
$785$	−20.4321	+	4.34297i	−0.729252	+	0.155007i
$786$	−6.56782	+	62.4886i	−0.234266	+	2.22889i
$787$	−4.91645	−	5.46027i	−0.175253	−	0.194638i	0.649119	−	0.760687i	$-0.275138\pi$
$787$	−4.91645	−	5.46027i	−0.175253	−	0.194638i	−0.824371	+	0.566049i	$0.808471\pi$
$788$	−4.72120	+	5.24343i	−0.168186	+	0.186789i
$789$	−7.85986	−	74.7816i	−0.279818	−	2.66229i
$790$	5.85410	+	18.0171i	0.208280	+	0.641019i
$791$	0.253289	+	0.779543i	0.00900592	+	0.0277174i
$792$	−3.49297	−	33.2333i	−0.124117	−	1.18090i
$793$	−17.7133	+	19.6726i	−0.629018	+	0.698596i
$794$	−7.57873	−	8.41704i	−0.268959	−	0.298709i
$795$	−3.54232	+	33.7029i	−0.125633	+	1.19532i
$796$	−11.4524	+	2.43427i	−0.405918	+	0.0862805i
$797$	50.6254	+	22.5399i	1.79324	+	0.798404i	0.974549	+	0.224175i	$0.0719688\pi$
$797$	50.6254	+	22.5399i	1.79324	+	0.798404i	0.818695	+	0.574229i	$0.194698\pi$
$798$	2.23607	−	1.62460i	0.0791559	−	0.0575102i
$799$	−1.72527	+	0.768140i	−0.0610357	+	0.0271748i
$800$	−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
$803$	−16.5740	−	3.52291i	−0.584884	−	0.124321i
$804$	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
$809$	22.9047	+	4.86854i	0.805286	+	0.171169i	0.592123	−	0.805848i	$-0.298290\pi$
$809$	22.9047	+	4.86854i	0.805286	+	0.171169i	0.213164	+	0.977017i	$0.431623\pi$
$810$	−31.9615	−	23.2214i	−1.12301	−	0.815916i
$811$	14.0000	+	24.2487i	0.491606	+	0.851487i	0.999953	−	0.00966502i	$-0.00307652\pi$
$811$	14.0000	+	24.2487i	0.491606	+	0.851487i	−0.508347	+	0.861152i	$0.669743\pi$
$812$	0.201626	−	0.349227i	0.00707569	−	0.0122555i
$813$	41.9213	−	18.6646i	1.47024	−	0.654594i
$814$	5.23607	−	3.80423i	0.183524	−	0.133338i
$815$	9.78243	+	4.35542i	0.342664	+	0.152564i
$816$	−11.7378	+	2.49494i	−0.410904	+	0.0873404i
$817$	−0.288910	+	2.74879i	−0.0101077	+	0.0961680i
$818$	4.13545	+	4.59289i	0.144593	+	0.160587i
$819$	3.81953	−	4.24202i	0.133465	−	0.148228i
$820$	−0.452215	−	4.30254i	−0.0157920	−	0.150251i
$821$	−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
$823$	−1.49390	−	14.2135i	−0.0520741	−	0.495452i	−0.989212	−	0.146492i	$-0.953202\pi$
$823$	−1.49390	−	14.2135i	−0.0520741	−	0.495452i	0.937138	−	0.348960i	$-0.113465\pi$
$824$	−9.33054	+	10.3626i	−0.325045	+	0.360999i
$825$	17.3228	+	19.2389i	0.603103	+	0.669814i
$826$	−0.0892780	+	0.849423i	−0.00310638	+	0.0295552i
$827$	16.9684	−	3.60675i	0.590050	−	0.125419i	0.0967961	−	0.995304i	$-0.469141\pi$
$827$	16.9684	−	3.60675i	0.590050	−	0.125419i	0.493254	+	0.869885i	$0.335807\pi$
$828$	−24.0817	−	10.7219i	−0.836896	−	0.372610i
$829$	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	$0.205575\pi$
$830$	22.0898	−	9.83503i	0.766750	−	0.341379i
$831$	−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
$834$	68.7141	+	14.6056i	2.37938	+	0.505752i
$835$	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	$-0.0665320\pi$
$840$	1.67088	+	0.355156i	0.0576507	+	0.0122540i
$841$	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
$844$	13.0877	−	5.82701i	0.450496	−	0.200574i
$845$	2.04508	−	1.48584i	0.0703531	−	0.0511145i
$846$	27.3045	+	12.1568i	0.938750	+	0.417958i
$847$	1.61637	−	0.343569i	0.0555390	−	0.0118052i
$848$	5.31348	−	50.5543i	0.182466	−	1.73604i
$849$	−30.0736	−	33.4001i	−1.03212	−	1.14629i
$850$	3.30836	−	3.67431i	0.113476	−	0.126028i
$851$	1.19334	+	11.3539i	0.0409072	+	0.389206i
$852$	−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	$0.842006\pi$
$854$	0.326611	+	3.10749i	0.0111764	+	0.106336i
$855$	−11.1800	+	12.4166i	−0.382347	+	0.424639i
$856$	−8.62412	−	9.57805i	−0.294766	−	0.327371i
$857$	5.81864	−	55.3607i	0.198761	−	1.89109i	−0.208878	−	0.977942i	$-0.566981\pi$
$857$	5.81864	−	55.3607i	0.198761	−	1.89109i	0.407639	−	0.913143i	$-0.366352\pi$
$858$	33.1480	−	7.04582i	1.13165	−	0.240540i
$859$	−1.92891	−	0.858807i	−0.0658136	−	0.0293021i	0.373566	−	0.927604i	$-0.378135\pi$
$859$	−1.92891	−	0.858807i	−0.0658136	−	0.0293021i	−0.439379	+	0.898302i	$0.644802\pi$
$860$	0.618034	−	0.449028i	0.0210748	−	0.0153117i
$861$	4.88521	−	2.17503i	0.166487	−	0.0741250i
$862$	−9.70820	+	16.8151i	−0.330663	+	0.572725i
$863$	−4.90983	−	8.50408i	−0.167133	−	0.289482i	0.770278	−	0.637708i	$-0.220117\pi$
$863$	−4.90983	−	8.50408i	−0.167133	−	0.289482i	−0.937411	+	0.348226i	$0.886784\pi$
$864$	39.5967	+	28.7687i	1.34711	+	0.978732i
$865$	−2.87993	−	0.612149i	−0.0979206	−	0.0208137i
$866$	−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
$871$	−25.3228	−	5.38253i	−0.858031	−	0.182380i
$872$	−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
$875$	−1.94093	+	0.864157i	−0.0656154	+	0.0292139i
$876$	13.7082	−	9.95959i	0.463157	−	0.336503i
$877$	−16.4947	−	7.34393i	−0.556987	−	0.247987i	0.108883	−	0.994055i	$-0.465273\pi$
$877$	−16.4947	−	7.34393i	−0.556987	−	0.247987i	−0.665870	+	0.746068i	$0.731939\pi$
$878$	1.86810	−	0.397076i	0.0630452	−	0.0134007i
$879$	0.159705	−	1.51949i	0.00538673	−	0.0512513i
$880$	6.49606	+	7.21460i	0.218982	+	0.243204i
$881$	13.6240	−	15.1309i	0.459003	−	0.509774i	−0.468565	−	0.883429i	$-0.655229\pi$
$881$	13.6240	−	15.1309i	0.459003	−	0.509774i	0.927568	+	0.373655i	$0.121896\pi$
$882$	8.77594	+	83.4975i	0.295501	+	2.81151i
$883$	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
$885$	−0.756375	−	7.19643i	−0.0254253	−	0.241905i
$886$	33.2470	−	36.9246i	1.11696	−	1.24051i
$887$	18.1126	+	20.1161i	0.608162	+	0.675433i	0.966057	−	0.258329i	$-0.0831720\pi$
$887$	18.1126	+	20.1161i	0.608162	+	0.675433i	−0.357895	+	0.933762i	$0.616505\pi$
$888$	1.51275	−	14.3929i	0.0507646	−	0.482993i
$889$	2.87993	−	0.612149i	0.0965898	−	0.0205308i
$890$	−17.3065	−	7.70533i	−0.580114	−	0.258283i
$891$	39.5066	−	28.7032i	1.32352	−	0.961594i
$892$	−2.25841	+	1.00551i	−0.0756171	+	0.0336669i
$893$	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
$896$	−3.14453	−	0.668391i	−0.105051	−	0.0223294i
$897$	−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
$902$	22.1575	+	4.70971i	0.737763	+	0.156816i
$903$	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
$906$	67.8300	−	30.1999i	2.25350	−	1.00332i
$907$	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	$0.168186\pi$
$908$	−3.65418	−	1.62695i	−0.121268	−	0.0539921i
$909$	21.9266	−	4.66063i	0.727258	−	0.154583i
$910$	−0.129204	+	1.22930i	−0.00428308	+	0.0407508i
$911$	−12.1650	−	13.5106i	−0.403045	−	0.447627i	0.507118	−	0.861877i	$-0.330711\pi$
$911$	−12.1650	−	13.5106i	−0.403045	−	0.447627i	−0.910163	+	0.414250i	$0.864044\pi$
$912$	23.5030	−	26.1027i	0.778261	−	0.864346i
$913$	3.12420	+	29.7248i	0.103396	+	0.983748i
$914$	1.52786	+	4.70228i	0.0505373	+	0.155538i
$915$	−8.18034	−	25.1765i	−0.270434	−	0.832309i
$916$	−0.866729	−	8.24637i	−0.0286375	−	0.272468i
$917$	1.89552	−	2.10519i	0.0625957	−	0.0695196i
$918$	−11.9698	−	13.2938i	−0.395061	−	0.438760i
$919$	1.51275	−	14.3929i	0.0499010	−	0.474777i	−0.940824	−	0.338895i	$-0.889947\pi$
$919$	1.51275	−	14.3929i	0.0499010	−	0.474777i	0.990725	−	0.135881i	$-0.0433866\pi$
$920$	−12.4850	+	2.65377i	−0.411619	+	0.0874922i
$921$	−84.8699	−	37.7865i	−2.79656	−	1.24511i
$922$	44.9787	−	32.6789i	1.48130	−	1.07622i
$923$	−27.1398	+	12.0834i	−0.893317	+	0.397730i
$924$	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
$927$	−45.5785	−	9.68801i	−1.49699	−	0.318196i
$928$	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
$933$	92.3661	+	19.6330i	3.02393	+	0.642756i
$934$	−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
$937$	8.27282	−	3.68330i	0.270261	−	0.120328i	−0.267132	−	0.963660i	$-0.586076\pi$
$937$	8.27282	−	3.68330i	0.270261	−	0.120328i	0.537393	+	0.843332i	$0.319409\pi$
$938$	−2.47214	+	1.79611i	−0.0807181	+	0.0586451i
$939$	−49.5591	−	22.0651i	−1.61730	−	0.720069i
$940$	−1.49448	+	0.317661i	−0.0487445	+	0.0103610i
$941$	−3.97208	+	37.7918i	−0.129486	+	1.23198i	0.716046	+	0.698053i	$0.245950\pi$
$941$	−3.97208	+	37.7918i	−0.129486	+	1.23198i	−0.845532	+	0.533925i	$0.820716\pi$
$942$	73.1854	+	81.2806i	2.38451	+	2.64827i
$943$	−26.7367	+	29.6942i	−0.870668	+	0.966975i
$944$	1.13456	+	10.7946i	0.0369269	+	0.351336i
$945$	1.05573	+	3.24920i	0.0343428	+	0.105696i
$946$	1.23607	+	3.80423i	0.0401880	+	0.123686i
$947$	−1.36470	−	12.9842i	−0.0443466	−	0.421930i	−0.994062	−	0.108815i	$-0.965294\pi$
$947$	−1.36470	−	12.9842i	−0.0443466	−	0.421930i	0.949715	−	0.313115i	$-0.101372\pi$
$948$	15.6686	−	17.4018i	0.508894	−	0.565184i
$949$	−18.3452	−	20.3744i	−0.595509	−	0.661380i
$950$	−1.51275	+	14.3929i	−0.0490801	+	0.466966i
$951$	−12.8378	+	2.72876i	−0.416294	+	0.0884861i
$952$	0.368389	+	0.164017i	0.0119396	+	0.00531584i
$953$	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	$0.0346754\pi$
$954$	115.664	−	51.4969i	3.74476	−	1.66727i
$955$	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
$958$	−36.8634	−	7.83555i	−1.19100	−	0.253155i
$959$	−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
$964$	8.68144	+	1.84530i	0.279610	+	0.0594330i
$965$	−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	0.276587	−	0.960989i	$-0.410797\pi$
$967$	30.1803	−	52.2739i	0.970534	−	1.68101i	0.693947	−	0.720026i	$-0.255870\pi$
$968$	14.2992	−	6.36644i	0.459595	−	0.204625i
$969$	−4.47214	+	3.24920i	−0.143666	+	0.104379i
$970$	−23.5680	−	10.4931i	−0.756722	−	0.336915i
$971$	27.3881	−	5.82153i	0.878927	−	0.186822i	0.253717	−	0.967278i	$-0.418347\pi$
$971$	27.3881	−	5.82153i	0.878927	−	0.186822i	0.625210	+	0.780457i	$0.285013\pi$
$972$	−2.29963	+	21.8795i	−0.0737605	+	0.701785i
$973$	−2.11926	−	2.35368i	−0.0679404	−	0.0754554i
$974$	20.8264	−	23.1301i	0.667322	−	0.741136i
$975$	4.37855	+	41.6591i	0.140226	+	1.33416i
$976$	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	$-0.372761\pi$
$978$	−5.86079	−	55.7617i	−0.187408	−	1.78306i
$979$	15.6686	−	17.4018i	0.500772	−	0.556163i
$980$	−2.87177	−	3.18943i	−0.0917354	−	0.101882i
$981$	10.8912	−	103.623i	0.347729	−	3.30842i
$982$	6.90154	−	1.46697i	0.220237	−	0.0468128i
$983$	−36.1105	−	16.0774i	−1.15175	−	0.512790i	−0.260126	−	0.965575i	$-0.583764\pi$
$983$	−36.1105	−	16.0774i	−1.15175	−	0.512790i	−0.891620	+	0.452784i	$0.850431\pi$
$984$	40.9787	−	29.7728i	1.30635	−	0.949122i
$985$	−10.4294	+	4.64347i	−0.332309	+	0.147953i
$986$	−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
$989$	−6.90154	−	1.46697i	−0.219456	−	0.0466469i
$990$	−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
$995$	−18.5303	−	3.93874i	−0.587450	−	0.124866i
$996$	−24.1803	−	17.5680i	−0.766183	−	0.556665i
$997$	14.6803	+	25.4271i	0.464931	+	0.805284i	0.999198	−	0.0400314i	$-0.0127458\pi$
$997$	14.6803	+	25.4271i	0.464931	+	0.805284i	−0.534267	+	0.845316i	$0.679412\pi$
$998$	−5.32624	+	9.22531i	−0.168599	+	0.292022i
$999$	26.4419	−	11.7727i	0.836585	−	0.372472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.e.846.1		8
31.2	even	5		961.2.c.c.439.2		4
31.3	odd	30		961.2.g.a.732.1		8
31.4	even	5	inner	961.2.g.e.547.1		8
31.5	even	3		961.2.d.g.628.1		4
31.6	odd	6		961.2.g.h.448.1		8
31.7	even	15	inner	961.2.g.e.844.1		8
31.8	even	5		961.2.g.d.235.1		8
31.9	even	15		961.2.d.a.388.1		4
31.10	even	15		961.2.a.f.1.2		2
31.11	odd	30		961.2.d.d.531.1		4
31.12	odd	30		961.2.c.e.521.2		4
31.13	odd	30		961.2.d.c.374.1		4
31.14	even	15		961.2.g.d.338.1		8
31.15	odd	10		961.2.g.a.816.1		8
31.16	even	5		961.2.g.d.816.1		8
31.17	odd	30		961.2.g.a.338.1		8
31.18	even	15		961.2.d.a.374.1		4
31.19	even	15		961.2.c.c.521.2		4
31.20	even	15		961.2.d.g.531.1		4
31.21	odd	30		31.2.a.a.1.2	✓	2
31.22	odd	30		961.2.d.c.388.1		4
31.23	odd	10		961.2.g.a.235.1		8
31.24	odd	30		961.2.g.h.844.1		8
31.25	even	3	inner	961.2.g.e.448.1		8
31.26	odd	6		961.2.d.d.628.1		4
31.27	odd	10		961.2.g.h.547.1		8
31.28	even	15		961.2.g.d.732.1		8
31.29	odd	10		961.2.c.e.439.2		4
31.30	odd	2		961.2.g.h.846.1		8
93.41	odd	30		8649.2.a.c.1.1		2
93.83	even	30		279.2.a.a.1.1		2
124.83	even	30		496.2.a.i.1.2		2
155.52	even	60		775.2.b.d.249.4		4
155.83	even	60		775.2.b.d.249.1		4
155.114	odd	30		775.2.a.d.1.1		2
217.83	even	30		1519.2.a.a.1.2		2
248.21	odd	30		1984.2.a.r.1.2		2
248.83	even	30		1984.2.a.n.1.1		2
341.21	even	30		3751.2.a.b.1.1		2
372.83	odd	30		4464.2.a.bf.1.1		2
403.207	odd	30		5239.2.a.f.1.1		2
465.269	even	30		6975.2.a.y.1.2		2
527.424	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	31.21	odd	30
279.2.a.a.1.1		2	93.83	even	30
496.2.a.i.1.2		2	124.83	even	30
775.2.a.d.1.1		2	155.114	odd	30
775.2.b.d.249.1		4	155.83	even	60
775.2.b.d.249.4		4	155.52	even	60
961.2.a.f.1.2		2	31.10	even	15
961.2.c.c.439.2		4	31.2	even	5
961.2.c.c.521.2		4	31.19	even	15
961.2.c.e.439.2		4	31.29	odd	10
961.2.c.e.521.2		4	31.12	odd	30
961.2.d.a.374.1		4	31.18	even	15
961.2.d.a.388.1		4	31.9	even	15
961.2.d.c.374.1		4	31.13	odd	30
961.2.d.c.388.1		4	31.22	odd	30
961.2.d.d.531.1		4	31.11	odd	30
961.2.d.d.628.1		4	31.26	odd	6
961.2.d.g.531.1		4	31.20	even	15
961.2.d.g.628.1		4	31.5	even	3
961.2.g.a.235.1		8	31.23	odd	10
961.2.g.a.338.1		8	31.17	odd	30
961.2.g.a.732.1		8	31.3	odd	30
961.2.g.a.816.1		8	31.15	odd	10
961.2.g.d.235.1		8	31.8	even	5
961.2.g.d.338.1		8	31.14	even	15
961.2.g.d.732.1		8	31.28	even	15
961.2.g.d.816.1		8	31.16	even	5
961.2.g.e.448.1		8	31.25	even	3	inner
961.2.g.e.547.1		8	31.4	even	5	inner
961.2.g.e.844.1		8	31.7	even	15	inner
961.2.g.e.846.1		8	1.1	even	1	trivial
961.2.g.h.448.1		8	31.6	odd	6
961.2.g.h.547.1		8	31.27	odd	10
961.2.g.h.844.1		8	31.24	odd	30
961.2.g.h.846.1		8	31.30	odd	2
1519.2.a.a.1.2		2	217.83	even	30
1984.2.a.n.1.1		2	248.83	even	30
1984.2.a.r.1.2		2	248.21	odd	30
3751.2.a.b.1.1		2	341.21	even	30
4464.2.a.bf.1.1		2	372.83	odd	30
5239.2.a.f.1.1		2	403.207	odd	30
6975.2.a.y.1.2		2	465.269	even	30
8649.2.a.c.1.1		2	93.41	odd	30
8959.2.a.b.1.2		2	527.424	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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 1.53884i) q^{2} +(-3.16535 - 0.672816i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.61803 + 4.53457i) q^{6} +(0.215659 - 0.0960175i) q^{7} +(1.80902 - 1.31433i) q^{8} +(6.82614 + 3.03919i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 1.53884i) q^{2} +(-3.16535 - 0.672816i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.61803 + 4.53457i) q^{6} +(0.215659 - 0.0960175i) q^{7} +(1.80902 - 1.31433i) q^{8} +(6.82614 + 3.03919i) q^{9} +(-1.58268 + 0.336408i) q^{10} +(0.209057 - 1.98904i) q^{11} +(1.33826 + 1.48629i) q^{12} +(2.16535 - 2.40487i) q^{13} +(-0.0399263 - 0.379874i) q^{14} +(1.00000 + 3.07768i) q^{15} +(-1.50000 - 4.61653i) q^{16} +(0.0798526 + 0.759747i) q^{17} +(8.08990 - 8.98475i) q^{18} +(-1.49622 - 1.66172i) q^{19} +(-0.0646021 + 0.614648i) q^{20} +(-0.747238 + 0.158830i) q^{21} +(-2.95630 - 1.31623i) q^{22} +(4.61803 - 3.35520i) q^{23} +(-6.61048 + 2.94317i) q^{24} +(2.00000 - 3.46410i) q^{25} +(-2.61803 - 4.53457i) q^{26} +(-11.7082 - 8.50651i) q^{27} +(-0.142710 - 0.0303339i) q^{28} +(-0.854102 + 2.62866i) q^{29} +5.23607 q^{30} -3.38197 q^{32} +(-2.00000 + 6.15537i) q^{33} +(1.20906 + 0.256993i) q^{34} +(-0.190983 - 0.138757i) q^{35} +(-2.30902 - 3.99933i) q^{36} +(-1.00000 + 1.73205i) q^{37} +(-3.30524 + 1.47159i) q^{38} +(-8.47214 + 6.15537i) q^{39} +(-2.04275 - 0.909491i) q^{40} +(-6.84703 + 1.45538i) q^{41} +(-0.129204 + 1.22930i) q^{42} +(-0.827091 - 0.918578i) q^{43} +(-0.827091 + 0.918578i) q^{44} +(-0.781051 - 7.43120i) q^{45} +(-2.85410 - 8.78402i) q^{46} +(0.763932 + 2.35114i) q^{47} +(1.64195 + 15.6222i) q^{48} +(-4.64662 + 5.16060i) q^{49} +(-4.33070 - 4.80973i) q^{50} +(0.258409 - 2.45859i) q^{51} +(-1.95630 + 0.415823i) q^{52} +(9.56677 + 4.25940i) q^{53} +(-18.9443 + 13.7638i) q^{54} +(-1.82709 + 0.813473i) q^{55} +(0.263932 - 0.457144i) q^{56} +(3.61803 + 6.26662i) q^{57} +(3.61803 + 2.62866i) q^{58} +(-2.18720 - 0.464905i) q^{59} +(0.618034 - 1.90211i) q^{60} -8.18034 q^{61} +1.76393 q^{63} +(1.30902 - 4.02874i) q^{64} +(-3.16535 - 0.672816i) q^{65} +(8.47214 + 6.15537i) q^{66} +(-4.00000 - 6.92820i) q^{67} +(0.236068 - 0.408882i) q^{68} +(-16.8751 + 7.51329i) q^{69} +(-0.309017 + 0.224514i) q^{70} +(-8.38666 - 3.73398i) q^{71} +(16.3431 - 3.47383i) q^{72} +(0.885579 - 8.42572i) q^{73} +(2.16535 + 2.40487i) q^{74} +(-8.66141 + 9.61947i) q^{75} +(0.144455 + 1.37440i) q^{76} +(-0.145898 - 0.449028i) q^{77} +(5.23607 + 16.1150i) q^{78} +(-1.22384 - 11.6441i) q^{79} +(-3.24803 + 3.60730i) q^{80} +(16.3378 + 18.1449i) q^{81} +(-1.18391 + 11.2642i) q^{82} +(-14.6177 + 3.10709i) q^{83} +(0.431318 + 0.192035i) q^{84} +(0.618034 - 0.449028i) q^{85} +(-1.82709 + 0.813473i) q^{86} +(4.47214 - 7.74597i) q^{87} +(-2.23607 - 3.87298i) q^{88} +(9.47214 + 6.88191i) q^{89} +(-11.8260 - 2.51369i) q^{90} +(0.236068 - 0.726543i) q^{91} -3.52786 q^{92} +4.00000 q^{94} +(-0.690983 + 2.12663i) q^{95} +(10.7051 + 2.27544i) 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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Database

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