LMFDB - Embedded newform 637.2.f.i.295.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(295,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("637.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.f (of order $3$, degree $2$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 7x^{6} + 38x^{4} - 16x^{3} + 15x^{2} + 3x + 1 $ x^8 - x^7 + 7x^6 + 38x^4 - 16x^3 + 15x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			295.3
Root			$0.355143 - 0.615126i$ of defining polynomial
Character	$\chi$	$=$	637.295
Dual form			637.2.f.i.393.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.355143 - 0.615126i) q^{2} +(1.20394 - 2.08529i) q^{3} +(0.747746 + 1.29513i) q^{4} +1.28971 q^{5} +(-0.855143 - 1.48115i) q^{6} +2.48280 q^{8} +(-1.39895 - 2.42305i) q^{9} +O(q^{10})$	\(q+(0.355143 - 0.615126i) q^{2} +(1.20394 - 2.08529i) q^{3} +(0.747746 + 1.29513i) q^{4} +1.28971 q^{5} +(-0.855143 - 1.48115i) q^{6} +2.48280 q^{8} +(-1.39895 - 2.42305i) q^{9} +(0.458033 - 0.793337i) q^{10} +(1.20394 - 2.08529i) q^{11} +3.60097 q^{12} +(-1.25409 + 3.38042i) q^{13} +(1.55274 - 2.68942i) q^{15} +(-0.613742 + 1.06303i) q^{16} +(1.95169 + 3.38042i) q^{17} -1.98731 q^{18} +(-2.94534 - 5.10148i) q^{19} +(0.964379 + 1.67035i) q^{20} +(-0.855143 - 1.48115i) q^{22} +(3.16197 - 5.47670i) q^{23} +(2.98915 - 5.17736i) q^{24} -3.33664 q^{25} +(1.63400 + 1.97196i) q^{26} +0.486640 q^{27} +(-2.80683 + 4.86157i) q^{29} +(-1.10289 - 1.91026i) q^{30} -2.20578 q^{31} +(2.91873 + 5.05540i) q^{32} +(-2.89895 - 5.02113i) q^{33} +2.77252 q^{34} +(2.09212 - 3.62365i) q^{36} +(2.55908 - 4.43246i) q^{37} -4.18407 q^{38} +(5.53930 + 6.68497i) q^{39} +3.20210 q^{40} +(-3.89260 + 6.74219i) q^{41} +(-0.144857 - 0.250899i) q^{43} +3.60097 q^{44} +(-1.80424 - 3.12504i) q^{45} +(-2.24591 - 3.89003i) q^{46} -1.27702 q^{47} +(1.47782 + 2.55966i) q^{48} +(-1.18499 + 2.05245i) q^{50} +9.39887 q^{51} +(-5.31585 + 0.903480i) q^{52} -13.6225 q^{53} +(0.172827 - 0.299345i) q^{54} +(1.55274 - 2.68942i) q^{55} -14.1841 q^{57} +(1.99365 + 3.45311i) q^{58} +(-2.01528 - 3.49057i) q^{59} +4.64422 q^{60} +(-2.30049 - 3.98456i) q^{61} +(-0.783368 + 1.35683i) q^{62} +1.69131 q^{64} +(-1.61742 + 4.35978i) q^{65} -4.11817 q^{66} +(-3.78779 + 6.56065i) q^{67} +(-2.91873 + 5.05540i) q^{68} +(-7.61366 - 13.1872i) q^{69} +(-3.61366 - 6.25905i) q^{71} +(-3.47331 - 6.01595i) q^{72} +15.0125 q^{73} +(-1.81768 - 3.14832i) q^{74} +(-4.01712 + 6.95785i) q^{75} +(4.40474 - 7.62923i) q^{76} +(6.07935 - 1.03324i) q^{78} -9.30758 q^{79} +(-0.791552 + 1.37101i) q^{80} +(4.78273 - 8.28393i) q^{81} +(2.76486 + 4.78888i) q^{82} +1.36463 q^{83} +(2.51712 + 4.35978i) q^{85} -0.205780 q^{86} +(6.75852 + 11.7061i) q^{87} +(2.98915 - 5.17736i) q^{88} +(-0.449849 + 0.779162i) q^{89} -2.56306 q^{90} +9.45742 q^{92} +(-2.65563 + 4.59968i) q^{93} +(-0.453526 + 0.785530i) q^{94} +(-3.79865 - 6.57945i) q^{95} +14.0559 q^{96} +(7.83288 + 13.5669i) q^{97} -6.73701 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + q^{3} - 5 q^{4} + 14 q^{5} - 5 q^{6} - 12 q^{8} - 7 q^{9}+O(q^{10}) $ 8 * q + q^2 + q^3 - 5 * q^4 + 14 * q^5 - 5 * q^6 - 12 * q^8 - 7 * q^9	$ 8 q + q^{2} + q^{3} - 5 q^{4} + 14 q^{5} - 5 q^{6} - 12 q^{8} - 7 q^{9} - 11 q^{10} + q^{11} - 24 q^{12} - 4 q^{13} - 3 q^{15} - 19 q^{16} - 4 q^{17} - 6 q^{18} + q^{19} - 2 q^{20} - 5 q^{22} + 2 q^{23} - 3 q^{24} + 10 q^{25} - 12 q^{26} + 52 q^{27} - q^{29} + 4 q^{30} + 8 q^{31} + 33 q^{32} - 19 q^{33} - 6 q^{34} + 34 q^{36} + 10 q^{37} + 46 q^{38} + 20 q^{39} + 34 q^{40} - 22 q^{41} - 3 q^{43} - 24 q^{44} - 11 q^{45} - 24 q^{46} - 4 q^{47} + 11 q^{48} - 43 q^{50} + 14 q^{51} - 65 q^{52} + 4 q^{53} + 5 q^{54} - 3 q^{55} - 34 q^{57} + 11 q^{58} - 8 q^{59} - 22 q^{60} + 8 q^{61} - 5 q^{62} + 28 q^{64} + 7 q^{65} - 12 q^{66} + 6 q^{67} - 33 q^{68} - 18 q^{69} + 14 q^{71} - 5 q^{72} + 16 q^{73} - 20 q^{74} - 7 q^{75} + 32 q^{76} - q^{78} - 52 q^{79} + 7 q^{80} - 24 q^{81} - 14 q^{82} - 5 q^{85} + 24 q^{86} + 13 q^{87} - 3 q^{88} - q^{89} - 52 q^{90} + 24 q^{92} + 7 q^{93} + 33 q^{94} - 21 q^{95} + 116 q^{96} + 3 q^{97} + 46 q^{99}+O(q^{100}) $ 8 * q + q^2 + q^3 - 5 * q^4 + 14 * q^5 - 5 * q^6 - 12 * q^8 - 7 * q^9 - 11 * q^10 + q^11 - 24 * q^12 - 4 * q^13 - 3 * q^15 - 19 * q^16 - 4 * q^17 - 6 * q^18 + q^19 - 2 * q^20 - 5 * q^22 + 2 * q^23 - 3 * q^24 + 10 * q^25 - 12 * q^26 + 52 * q^27 - q^29 + 4 * q^30 + 8 * q^31 + 33 * q^32 - 19 * q^33 - 6 * q^34 + 34 * q^36 + 10 * q^37 + 46 * q^38 + 20 * q^39 + 34 * q^40 - 22 * q^41 - 3 * q^43 - 24 * q^44 - 11 * q^45 - 24 * q^46 - 4 * q^47 + 11 * q^48 - 43 * q^50 + 14 * q^51 - 65 * q^52 + 4 * q^53 + 5 * q^54 - 3 * q^55 - 34 * q^57 + 11 * q^58 - 8 * q^59 - 22 * q^60 + 8 * q^61 - 5 * q^62 + 28 * q^64 + 7 * q^65 - 12 * q^66 + 6 * q^67 - 33 * q^68 - 18 * q^69 + 14 * q^71 - 5 * q^72 + 16 * q^73 - 20 * q^74 - 7 * q^75 + 32 * q^76 - q^78 - 52 * q^79 + 7 * q^80 - 24 * q^81 - 14 * q^82 - 5 * q^85 + 24 * q^86 + 13 * q^87 - 3 * q^88 - q^89 - 52 * q^90 + 24 * q^92 + 7 * q^93 + 33 * q^94 - 21 * q^95 + 116 * q^96 + 3 * q^97 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.355143	−	0.615126i	0.251124	−	0.434960i	−0.712711	−	0.701457i	$-0.752533\pi$
$2$	0.355143	−	0.615126i	0.251124	−	0.434960i	0.963836	+	0.266497i	$0.0858664\pi$
$3$	1.20394	−	2.08529i	0.695096	−	1.20394i	−0.275053	−	0.961429i	$-0.588695\pi$
$3$	1.20394	−	2.08529i	0.695096	−	1.20394i	0.970148	−	0.242512i	$-0.0779714\pi$
$4$	0.747746	+	1.29513i	0.373873	+	0.647567i
$5$	1.28971			0.576777			0.288389	−	0.957513i	$-0.406880\pi$
$5$	1.28971			0.576777			0.288389	+	0.957513i	$0.406880\pi$
$6$	−0.855143	−	1.48115i	−0.349111	−	0.604678i
$7$		0			0
$7$		0			0
$8$	2.48280			0.877803
$9$	−1.39895	−	2.42305i	−0.466316	−	0.807683i
$10$	0.458033	−	0.793337i	0.144843	−	0.250875i
$11$	1.20394	−	2.08529i	0.363002	−	0.628738i	−0.625451	−	0.780263i	$-0.715085\pi$
$11$	1.20394	−	2.08529i	0.363002	−	0.628738i	0.988453	+	0.151525i	$0.0484185\pi$
$12$	3.60097			1.03951
$13$	−1.25409	+	3.38042i	−0.347823	+	0.937560i
$13$	−1.25409	+	3.38042i	−0.347823	+	0.937560i
$14$		0			0
$15$	1.55274	−	2.68942i	0.400915	−	0.694406i
$16$	−0.613742	+	1.06303i	−0.153436	+	0.265758i
$17$	1.95169	+	3.38042i	0.473354	+	0.819873i	0.999535	−	0.0304998i	$-0.00970990\pi$
$17$	1.95169	+	3.38042i	0.473354	+	0.819873i	−0.526181	+	0.850373i	$0.676377\pi$
$18$	−1.98731			−0.468413
$19$	−2.94534	−	5.10148i	−0.675708	−	1.17036i	−0.976261	−	0.216595i	$-0.930505\pi$
$19$	−2.94534	−	5.10148i	−0.675708	−	1.17036i	0.300554	−	0.953765i	$-0.402829\pi$
$20$	0.964379	+	1.67035i	0.215642	+	0.373502i
$21$		0			0
$22$	−0.855143	−	1.48115i	−0.182317	−	0.315783i
$23$	3.16197	−	5.47670i	0.659317	−	1.14197i	−0.321475	−	0.946918i	$-0.604179\pi$
$23$	3.16197	−	5.47670i	0.659317	−	1.14197i	0.980793	−	0.195053i	$-0.0624879\pi$
$24$	2.98915	−	5.17736i	0.610157	−	1.05682i
$25$	−3.33664			−0.667328
$26$	1.63400	+	1.97196i	0.320455	+	0.386733i
$27$	0.486640			0.0936539
$28$		0			0
$29$	−2.80683	+	4.86157i	−0.521215	+	0.902772i	0.478480	+	0.878098i	$0.341188\pi$
$29$	−2.80683	+	4.86157i	−0.521215	+	0.902772i	−0.999696	+	0.0246732i	$0.992145\pi$
$30$	−1.10289	−	1.91026i	−0.201359	−	0.348764i
$31$	−2.20578			−0.396170			−0.198085	−	0.980185i	$-0.563472\pi$
$31$	−2.20578			−0.396170			−0.198085	+	0.980185i	$0.563472\pi$
$32$	2.91873	+	5.05540i	0.515964	+	0.893676i
$33$	−2.89895	−	5.02113i	−0.504642	−	0.874066i
$34$	2.77252			0.475482
$35$		0			0
$36$	2.09212	−	3.62365i	0.348686	−	0.603942i
$37$	2.55908	−	4.43246i	0.420711	−	0.728693i	−0.575298	−	0.817944i	$-0.695114\pi$
$37$	2.55908	−	4.43246i	0.420711	−	0.728693i	0.996009	+	0.0892511i	$0.0284473\pi$
$38$	−4.18407			−0.678746
$39$	5.53930	+	6.68497i	0.886998	+	1.07045i
$40$	3.20210			0.506297
$41$	−3.89260	+	6.74219i	−0.607922	+	1.05295i	0.383660	+	0.923474i	$0.374664\pi$
$41$	−3.89260	+	6.74219i	−0.607922	+	1.05295i	−0.991582	+	0.129478i	$0.958670\pi$
$42$		0			0
$43$	−0.144857	−	0.250899i	−0.0220904	−	0.0382618i	0.854769	−	0.519009i	$-0.173699\pi$
$43$	−0.144857	−	0.250899i	−0.0220904	−	0.0382618i	−0.876859	+	0.480747i	$0.840366\pi$
$44$	3.60097			0.542867
$45$	−1.80424	−	3.12504i	−0.268961	−	0.465853i
$46$	−2.24591	−	3.89003i	−0.331141	−	0.573553i
$47$	−1.27702			−0.186273			−0.0931364	−	0.995653i	$-0.529689\pi$
$47$	−1.27702			−0.186273			−0.0931364	+	0.995653i	$0.529689\pi$
$48$	1.47782	+	2.55966i	0.213305	+	0.369455i
$49$		0			0
$50$	−1.18499	+	2.05245i	−0.167582	+	0.290261i
$51$	9.39887			1.31610
$52$	−5.31585	+	0.903480i	−0.737175	+	0.125290i
$53$	−13.6225			−1.87120			−0.935598	−	0.353067i	$-0.885139\pi$
$53$	−13.6225			−1.87120			−0.935598	+	0.353067i	$0.885139\pi$
$54$	0.172827	−	0.299345i	0.0235188	−	0.0407357i
$55$	1.55274	−	2.68942i	0.209371	−	0.362642i
$56$		0			0
$57$	−14.1841			−1.87873
$58$	1.99365	+	3.45311i	0.261780	+	0.453416i
$59$	−2.01528	−	3.49057i	−0.262367	−	0.454433i	0.704503	−	0.709701i	$-0.251170\pi$
$59$	−2.01528	−	3.49057i	−0.262367	−	0.454433i	−0.966870	+	0.255268i	$0.917836\pi$
$60$	4.64422			0.599566
$61$	−2.30049	−	3.98456i	−0.294547	−	0.510170i	0.680332	−	0.732904i	$-0.261835\pi$
$61$	−2.30049	−	3.98456i	−0.294547	−	0.510170i	−0.974879	+	0.222733i	$0.928502\pi$
$62$	−0.783368	+	1.35683i	−0.0994878	+	0.172318i
$63$		0			0
$64$	1.69131			0.211413
$65$	−1.61742	+	4.35978i	−0.200616	+	0.540764i
$66$	−4.11817			−0.506912
$67$	−3.78779	+	6.56065i	−0.462753	+	0.801511i	−0.999097	−	0.0424881i	$-0.986472\pi$
$67$	−3.78779	+	6.56065i	−0.462753	+	0.801511i	0.536344	+	0.843999i	$0.319805\pi$
$68$	−2.91873	+	5.05540i	−0.353949	+	0.613057i
$69$	−7.61366	−	13.1872i	−0.916577	−	1.58756i
$70$		0			0
$71$	−3.61366	−	6.25905i	−0.428863	−	0.742812i	0.567910	−	0.823091i	$-0.307752\pi$
$71$	−3.61366	−	6.25905i	−0.428863	−	0.742812i	−0.996772	+	0.0802788i	$0.974419\pi$
$72$	−3.47331	−	6.01595i	−0.409334	−	0.708987i
$73$	15.0125			1.75708			0.878542	−	0.477665i	$-0.158517\pi$
$73$	15.0125			1.75708			0.878542	+	0.477665i	$0.158517\pi$
$74$	−1.81768	−	3.14832i	−0.211301	−	0.365985i
$75$	−4.01712	+	6.95785i	−0.463857	+	0.803424i
$76$	4.40474	−	7.62923i	0.505258	−	0.875133i
$77$		0			0
$78$	6.07935	−	1.03324i	0.688350	−	0.116992i
$79$	−9.30758			−1.04718			−0.523592	−	0.851969i	$-0.675408\pi$
$79$	−9.30758			−1.04718			−0.523592	+	0.851969i	$0.675408\pi$
$80$	−0.791552	+	1.37101i	−0.0884982	+	0.153283i
$81$	4.78273	−	8.28393i	0.531415	−	0.920437i
$82$	2.76486	+	4.78888i	0.305328	+	0.528844i
$83$	1.36463			0.149788			0.0748940	−	0.997192i	$-0.476138\pi$
$83$	1.36463			0.149788			0.0748940	+	0.997192i	$0.476138\pi$
$84$		0			0
$85$	2.51712	+	4.35978i	0.273020	+	0.472884i
$86$	−0.205780			−0.0221898
$87$	6.75852	+	11.7061i	0.724589	+	1.25503i
$88$	2.98915	−	5.17736i	0.318644	−	0.551908i
$89$	−0.449849	+	0.779162i	−0.0476839	+	0.0825910i	−0.888882	−	0.458136i	$-0.848517\pi$
$89$	−0.449849	+	0.779162i	−0.0476839	+	0.0825910i	0.841198	+	0.540727i	$0.181851\pi$
$90$	−2.56306			−0.270170
$91$		0			0
$92$	9.45742			0.986004
$93$	−2.65563	+	4.59968i	−0.275376	+	0.476965i
$94$	−0.453526	+	0.785530i	−0.0467776	+	0.0810212i
$95$	−3.79865	−	6.57945i	−0.389733	−	0.675037i
$96$	14.0559			1.43458
$97$	7.83288	+	13.5669i	0.795309	+	1.37752i	0.922643	+	0.385655i	$0.126025\pi$
$97$	7.83288	+	13.5669i	0.795309	+	1.37752i	−0.127334	+	0.991860i	$0.540642\pi$
$98$		0			0
$99$	−6.73701			−0.677095
$100$	−2.49496	−	4.32140i	−0.249496	−	0.432140i
$101$	0.342452	−	0.593145i	0.0340753	−	0.0590201i	−0.848485	−	0.529220i	$-0.822485\pi$
$101$	0.342452	−	0.593145i	0.0340753	−	0.0590201i	0.882560	+	0.470200i	$0.155818\pi$
$102$	3.33795	−	5.78149i	0.330506	−	0.572453i
$103$	−17.9249			−1.76619			−0.883097	−	0.469190i	$-0.844546\pi$
$103$	−17.9249			−1.76619			−0.883097	+	0.469190i	$0.844546\pi$
$104$	−3.11366	+	8.39292i	−0.305320	+	0.822993i
$105$		0			0
$106$	−4.83795	+	8.37957i	−0.469903	+	0.813895i
$107$	−4.24775	+	7.35731i	−0.410645	+	0.711258i	−0.994960	−	0.100268i	$-0.968030\pi$
$107$	−4.24775	+	7.35731i	−0.410645	+	0.711258i	0.584315	+	0.811527i	$0.301363\pi$
$108$	0.363883	+	0.630264i	0.0350147	+	0.0606472i
$109$	12.0928			1.15828			0.579139	−	0.815228i	$-0.303389\pi$
$109$	12.0928			1.15828			0.579139	+	0.815228i	$0.303389\pi$
$110$	−1.10289	−	1.91026i	−0.105156	−	0.182136i
$111$	−6.16197	−	10.6729i	−0.584869	−	1.01302i
$112$		0			0
$113$	7.12635	+	12.3432i	0.670391	+	1.16115i	0.977793	+	0.209571i	$0.0672069\pi$
$113$	7.12635	+	12.3432i	0.670391	+	1.16115i	−0.307402	+	0.951580i	$0.599460\pi$
$114$	−5.03738	+	8.72500i	−0.471794	+	0.817171i
$115$	4.07804	−	7.06337i	0.380279	−	0.658663i
$116$	−8.39519			−0.779474
$117$	9.94534	−	1.69031i	0.919447	−	0.156269i
$118$	−2.86285			−0.263547
$119$		0			0
$120$	3.85514	−	6.67730i	0.351925	−	0.609552i
$121$	2.60105	+	4.50515i	0.236459	+	0.409559i
$122$	−3.26801			−0.295872
$123$	9.37293	+	16.2344i	0.845129	+	1.46381i
$124$	−1.64936	−	2.85678i	−0.148117	−	0.256547i
$125$	−10.7519			−0.961677
$126$		0			0
$127$	4.41231	−	7.64234i	0.391529	−	0.678148i	−0.601122	−	0.799157i	$-0.705280\pi$
$127$	4.41231	−	7.64234i	0.391529	−	0.678148i	0.992651	+	0.121009i	$0.0386129\pi$
$128$	−5.23681	+	9.07043i	−0.462873	+	0.801720i
$129$	−0.697596			−0.0614199
$130$	2.10740	+	2.54326i	0.184831	+	0.223059i
$131$	19.4294			1.69756			0.848778	−	0.528749i	$-0.177339\pi$
$131$	19.4294			1.69756			0.848778	+	0.528749i	$0.177339\pi$
$132$	4.33536	−	7.50906i	0.377344	−	0.653580i
$133$		0			0
$134$	2.69042	+	4.65994i	0.232417	+	0.402558i
$135$	0.627626			0.0540174
$136$	4.84565	+	8.39292i	0.415511	+	0.719687i
$137$	−5.11809	−	8.86479i	−0.437268	−	0.757370i	0.560210	−	0.828351i	$-0.310720\pi$
$137$	−5.11809	−	8.86479i	−0.437268	−	0.757370i	−0.997478	+	0.0709806i	$0.977387\pi$
$138$	−10.8158			−0.920699
$139$	4.07361	+	7.05571i	0.345519	+	0.598457i	0.985448	−	0.169977i	$-0.0543694\pi$
$139$	4.07361	+	7.05571i	0.345519	+	0.598457i	−0.639929	+	0.768434i	$0.721036\pi$
$140$		0			0
$141$	−1.53746	+	2.66296i	−0.129477	+	0.224262i
$142$	−5.13347			−0.430791
$143$	5.53930	+	6.68497i	0.463219	+	0.559025i
$144$	3.43438			0.286198
$145$	−3.62001	+	6.27004i	−0.300625	+	0.520698i
$146$	5.33160	−	9.23460i	0.441246	−	0.764261i
$147$		0			0
$148$	7.65419			0.629170
$149$	4.89444	+	8.47742i	0.400968	+	0.694497i	0.993843	−	0.110797i	$-0.0353404\pi$
$149$	4.89444	+	8.47742i	0.400968	+	0.694497i	−0.592875	+	0.805295i	$0.702007\pi$
$150$	2.85330	+	4.94207i	0.232971	+	0.403518i
$151$	14.7407			1.19958			0.599790	−	0.800158i	$-0.295251\pi$
$151$	14.7407			1.19958			0.599790	+	0.800158i	$0.295251\pi$
$152$	−7.31270	−	12.6660i	−0.593138	−	1.02735i
$153$	5.46062	−	9.45807i	0.441465	−	0.764640i
$154$		0			0
$155$	−2.84482			−0.228502
$156$	−4.51595	+	12.1728i	−0.361565	+	0.974604i
$157$	−20.5844			−1.64282			−0.821409	−	0.570340i	$-0.806811\pi$
$157$	−20.5844			−1.64282			−0.821409	+	0.570340i	$0.806811\pi$
$158$	−3.30553	+	5.72534i	−0.262973	+	0.455483i
$159$	−16.4007	+	28.4069i	−1.30066	+	2.25281i
$160$	3.76433	+	6.52001i	0.297597	+	0.515452i
$161$		0			0
$162$	−3.39711	−	5.88397i	−0.266902	−	0.462288i
$163$	1.99043	+	3.44753i	0.155902	+	0.270031i	0.933387	−	0.358871i	$-0.116838\pi$
$163$	1.99043	+	3.44753i	0.155902	+	0.270031i	−0.777485	+	0.628902i	$0.783505\pi$
$164$	−11.6427			−0.909144
$165$	−3.73881	−	6.47581i	−0.291066	−	0.504141i
$166$	0.484640	−	0.839422i	0.0376154	−	0.0651518i
$167$	4.33923	−	7.51576i	0.335780	−	0.581587i	−0.647855	−	0.761764i	$-0.724334\pi$
$167$	4.33923	−	7.51576i	0.335780	−	0.581587i	0.983634	+	0.180177i	$0.0576670\pi$
$168$		0			0
$169$	−9.85451	−	8.47872i	−0.758039	−	0.652209i
$170$	3.57575			0.274248
$171$	−8.24076	+	14.2734i	−0.630187	+	1.09152i
$172$	0.216632	−	0.375218i	0.0165180	−	0.0286101i
$173$	0.466967	+	0.808810i	0.0355028	+	0.0614927i	0.883231	−	0.468938i	$-0.155363\pi$
$173$	0.466967	+	0.808810i	0.0355028	+	0.0614927i	−0.847728	+	0.530431i	$0.822030\pi$
$174$	9.60097			0.727848
$175$		0			0
$176$	1.47782	+	2.55966i	0.111395	+	0.192942i
$177$	−9.70511			−0.729481
$178$	0.319522	+	0.553428i	0.0239492	+	0.0414812i
$179$	−6.77305	+	11.7313i	−0.506241	+	0.876836i	0.493733	+	0.869614i	$0.335632\pi$
$179$	−6.77305	+	11.7313i	−0.506241	+	0.876836i	−0.999974	+	0.00722197i	$0.997701\pi$
$180$	2.69823	−	4.67348i	0.201114	−	0.348340i
$181$	8.86269			0.658759			0.329379	−	0.944198i	$-0.393161\pi$
$181$	8.86269			0.658759			0.329379	+	0.944198i	$0.393161\pi$
$182$		0			0
$183$	−11.0786			−0.818953
$184$	7.85056	−	13.5976i	0.578751	−	1.00243i
$185$	3.30049	−	5.71661i	0.242657	−	0.420293i
$186$	1.88626	+	3.26709i	0.138307	+	0.239555i
$187$	9.39887			0.687313
$188$	−0.954889	−	1.65392i	−0.0696424	−	0.120624i
$189$		0			0
$190$	−5.39626			−0.391486
$191$	7.68674	+	13.3138i	0.556193	+	0.963355i	0.997810	+	0.0661509i	$0.0210719\pi$
$191$	7.68674	+	13.3138i	0.556193	+	0.963355i	−0.441616	+	0.897204i	$0.645595\pi$
$192$	2.03623	−	3.52686i	0.146953	−	0.254529i
$193$	12.2477	−	21.2136i	0.881606	−	1.52699i	0.0320517	−	0.999486i	$-0.489796\pi$
$193$	12.2477	−	21.2136i	0.881606	−	1.52699i	0.849555	−	0.527501i	$-0.176871\pi$
$194$	11.1272			0.798885
$195$	7.14411	+	8.62170i	0.511600	+	0.617413i
$196$		0			0
$197$	3.35706	−	5.81460i	0.239181	−	0.414273i	−0.721299	−	0.692624i	$-0.756454\pi$
$197$	3.35706	−	5.81460i	0.239181	−	0.414273i	0.960479	+	0.278351i	$0.0897878\pi$
$198$	−2.39260	+	4.14411i	−0.170035	+	0.294509i
$199$	−2.43641	−	4.21998i	−0.172712	−	0.299147i	0.766655	−	0.642059i	$-0.221920\pi$
$199$	−2.43641	−	4.21998i	−0.172712	−	0.299147i	−0.939367	+	0.342913i	$0.888586\pi$
$200$	−8.28421			−0.585782
$201$	9.12056	+	15.7973i	0.643315	+	1.11425i
$202$	−0.243239	−	0.421303i	−0.0171143	−	0.0296428i
$203$		0			0
$204$	7.02797	+	12.1728i	0.492056	+	0.852267i
$205$	−5.02034	+	8.69549i	−0.350636	+	0.607319i
$206$	−6.36592	+	11.0261i	−0.443534	+	0.768224i
$207$	−17.6938			−1.22980
$208$	−2.82381	−	3.40785i	−0.195796	−	0.236292i
$209$	−14.1841			−0.981133
$210$		0			0
$211$	−1.84373	+	3.19344i	−0.126928	+	0.219846i	−0.922485	−	0.386033i	$-0.873845\pi$
$211$	−1.84373	+	3.19344i	−0.126928	+	0.219846i	0.795557	+	0.605879i	$0.207178\pi$
$212$	−10.1862	−	17.6430i	−0.699590	−	1.21173i
$213$	−17.4025			−1.19240
$214$	3.01712	+	5.22580i	0.206246	+	0.357228i
$215$	−0.186824	−	0.323588i	−0.0127413	−	0.0220685i
$216$	1.20823			0.0822096
$217$		0			0
$218$	4.29467	−	7.43859i	0.290872	−	0.503805i
$219$	18.0742	−	31.3054i	1.22134	−	2.11543i
$220$	4.64422			0.313113
$221$	−13.8748	+	2.35817i	−0.933323	+	0.158628i
$222$	−8.75354			−0.587499
$223$	4.40713	−	7.63338i	0.295123	−	0.511169i	−0.679890	−	0.733314i	$-0.737973\pi$
$223$	4.40713	−	7.63338i	0.295123	−	0.511169i	0.975014	+	0.222145i	$0.0713059\pi$
$224$		0			0
$225$	4.66779	+	8.08484i	0.311186	+	0.538990i
$226$	10.1235			0.673406
$227$	−6.72557	−	11.6490i	−0.446391	−	0.773173i	0.551757	−	0.834005i	$-0.313958\pi$
$227$	−6.72557	−	11.6490i	−0.446391	−	0.773173i	−0.998148	+	0.0608325i	$0.980624\pi$
$228$	−10.6061	−	18.3703i	−0.702406	−	1.21660i
$229$	−6.81576			−0.450398			−0.225199	−	0.974313i	$-0.572303\pi$
$229$	−6.81576			−0.450398			−0.225199	+	0.974313i	$0.572303\pi$
$230$	−2.89658	−	5.01702i	−0.190995	−	0.330812i
$231$		0			0
$232$	−6.96881	+	12.0703i	−0.457524	+	0.792456i
$233$	−25.0672			−1.64221			−0.821105	−	0.570777i	$-0.806642\pi$
$233$	−25.0672			−1.64221			−0.821105	+	0.570777i	$0.806642\pi$
$234$	2.49227	−	6.71794i	0.162925	−	0.439166i
$235$	−1.64699			−0.107438
$236$	3.01384	−	5.22012i	0.196184	−	0.339801i
$237$	−11.2058	+	19.4090i	−0.727894	+	1.26075i
$238$		0			0
$239$	−2.78521			−0.180160			−0.0900800	−	0.995935i	$-0.528712\pi$
$239$	−2.78521			−0.180160			−0.0900800	+	0.995935i	$0.528712\pi$
$240$	1.90596	+	3.30123i	0.123029	+	0.213093i
$241$	3.48915	+	6.04338i	0.224756	+	0.389288i	0.956246	−	0.292563i	$-0.0945082\pi$
$241$	3.48915	+	6.04338i	0.224756	+	0.389288i	−0.731490	+	0.681852i	$0.761175\pi$
$242$	3.69498			0.237523
$243$	−10.7863	−	18.6824i	−0.691941	−	1.19848i
$244$	3.44036	−	5.95888i	0.220246	−	0.381478i
$245$		0			0
$246$	13.3149			0.848929
$247$	20.9389	−	3.55877i	1.33231	−	0.226439i
$248$	−5.47651			−0.347759
$249$	1.64294	−	2.84565i	0.104117	−	0.180336i
$250$	−3.81846	+	6.61376i	−0.241500	+	0.418291i
$251$	−0.391515	−	0.678123i	−0.0247122	−	0.0428028i	0.853405	−	0.521249i	$-0.174534\pi$
$251$	−0.391515	−	0.678123i	−0.0247122	−	0.0428028i	−0.878117	+	0.478446i	$0.841200\pi$
$252$		0			0
$253$	−7.61366	−	13.1872i	−0.478667	−	0.829075i
$254$	−3.13400	−	5.42825i	−0.196645	−	0.340599i
$255$	12.1218			0.759099
$256$	5.41095	+	9.37203i	0.338184	+	0.585752i
$257$	1.62902	−	2.82155i	0.101616	−	0.176003i	−0.810735	−	0.585414i	$-0.800932\pi$
$257$	1.62902	−	2.82155i	0.101616	−	0.176003i	0.912350	+	0.409410i	$0.134266\pi$
$258$	−0.247746	+	0.429109i	−0.0154240	+	0.0267152i
$259$		0			0
$260$	−6.85592	+	1.16523i	−0.425186	+	0.0722645i
$261$	15.7064			0.972205
$262$	6.90023	−	11.9516i	0.426298	−	0.738369i
$263$	−14.7915	+	25.6196i	−0.912081	+	1.57977i	−0.100962	+	0.994890i	$0.532192\pi$
$263$	−14.7915	+	25.6196i	−0.912081	+	1.57977i	−0.811119	+	0.584881i	$0.801141\pi$
$264$	−7.19752	−	12.4665i	−0.442976	−	0.767258i
$265$	−17.5691			−1.07926
$266$		0			0
$267$	1.08318	+	1.87613i	0.0662898	+	0.114817i
$268$	−11.3292			−0.692043
$269$	0.618249	+	1.07084i	0.0376953	+	0.0652902i	0.884258	−	0.467000i	$-0.154665\pi$
$269$	0.618249	+	1.07084i	0.0376953	+	0.0652902i	−0.846562	+	0.532290i	$0.821332\pi$
$270$	0.222897	−	0.386069i	0.0135651	−	0.0234954i
$271$	12.6036	−	21.8300i	0.765612	−	1.32608i	−0.174311	−	0.984691i	$-0.555770\pi$
$271$	12.6036	−	21.8300i	0.765612	−	1.32608i	0.939923	−	0.341388i	$-0.110897\pi$
$272$	−4.79133			−0.290517
$273$		0			0
$274$	−7.27062			−0.439234
$275$	−4.01712	+	6.95785i	−0.242241	+	0.419574i
$276$	11.3862	−	19.7214i	0.685367	−	1.18709i
$277$	−4.76801	−	8.25843i	−0.286482	−	0.496201i	0.686486	−	0.727143i	$-0.259152\pi$
$277$	−4.76801	−	8.25843i	−0.286482	−	0.496201i	−0.972967	+	0.230942i	$0.925819\pi$
$278$	5.78687			0.347073
$279$	3.08577	+	5.34471i	0.184740	+	0.319980i
$280$		0			0
$281$	9.56546			0.570628			0.285314	−	0.958434i	$-0.407902\pi$
$281$	9.56546			0.570628			0.285314	+	0.958434i	$0.407902\pi$
$282$	1.09204	+	1.89146i	0.0650299	+	0.112635i
$283$	5.71602	−	9.90044i	0.339782	−	0.588520i	−0.644609	−	0.764512i	$-0.722980\pi$
$283$	5.71602	−	9.90044i	0.339782	−	0.588520i	0.984392	+	0.175992i	$0.0563134\pi$
$284$	5.40421	−	9.36036i	0.320681	−	0.555435i
$285$	−18.2934			−1.08361
$286$	6.07935	−	1.03324i	0.359479	−	0.0610971i
$287$		0			0
$288$	8.16632	−	14.1445i	0.481205	−	0.833472i
$289$	0.881831	−	1.52738i	0.0518724	−	0.0898457i
$290$	2.57124	+	4.45352i	0.150989	+	0.261520i
$291$	37.7213			2.21126
$292$	11.2256	+	19.4433i	0.656927	+	1.13783i
$293$	−4.67781	−	8.10220i	−0.273281	−	0.473336i	0.696419	−	0.717635i	$-0.254775\pi$
$293$	−4.67781	−	8.10220i	−0.273281	−	0.473336i	−0.969700	+	0.244299i	$0.921442\pi$
$294$		0			0
$295$	−2.59913	−	4.50183i	−0.151327	−	0.262107i
$296$	6.35370	−	11.0049i	0.369301	−	0.639649i
$297$	0.585886	−	1.01478i	0.0339965	−	0.0588837i
$298$	6.95291			0.402771
$299$	14.5482	+	17.5571i	0.841341	+	1.01535i
$300$	−12.0151			−0.693695
$301$		0			0
$302$	5.23506	−	9.06738i	0.301244	−	0.521769i
$303$	−0.824585	−	1.42822i	−0.0473712	−	0.0820493i
$304$	7.23072			0.414711
$305$	−2.96697	−	5.13894i	−0.169888	−	0.294255i
$306$	−3.87861	−	6.71794i	−0.221725	−	0.384039i
$307$	−8.11449			−0.463119			−0.231559	−	0.972821i	$-0.574383\pi$
$307$	−8.11449			−0.463119			−0.231559	+	0.972821i	$0.574383\pi$
$308$		0			0
$309$	−21.5805	+	37.3786i	−1.22767	+	2.12639i
$310$	−1.01032	+	1.74993i	−0.0573823	+	0.0993891i
$311$	8.64016			0.489938			0.244969	−	0.969531i	$-0.421222\pi$
$311$	8.64016			0.489938			0.244969	+	0.969531i	$0.421222\pi$
$312$	13.7530	+	16.5975i	0.778609	+	0.939646i
$313$	5.22732			0.295466			0.147733	−	0.989027i	$-0.452802\pi$
$313$	5.22732			0.295466			0.147733	+	0.989027i	$0.452802\pi$
$314$	−7.31043	+	12.6620i	−0.412551	+	0.714560i
$315$		0			0
$316$	−6.95971	−	12.0546i	−0.391514	−	0.678123i
$317$	11.1929			0.628657			0.314329	−	0.949314i	$-0.398221\pi$
$317$	11.1929			0.628657			0.314329	+	0.949314i	$0.398221\pi$
$318$	11.6492	+	20.1770i	0.653255	+	1.13147i
$319$	6.75852	+	11.7061i	0.378404	+	0.655416i
$320$	2.18130			0.121938
$321$	10.2281	+	17.7155i	0.570875	+	0.988785i
$322$		0			0
$323$	11.4968	−	19.9130i	0.639698	−	1.10799i
$324$	14.3051			0.794727
$325$	4.18445	−	11.2792i	0.232112	−	0.625660i
$326$	2.82755			0.156604
$327$	14.5590	−	25.2169i	0.805115	−	1.39450i
$328$	−9.66456	+	16.7395i	−0.533636	+	0.924285i
$329$		0			0
$330$	−5.31126			−0.292375
$331$	−10.0234	−	17.3610i	−0.550935	−	0.954247i	−0.998207	−	0.0598495i	$-0.980938\pi$
$331$	−10.0234	−	17.3610i	−0.550935	−	0.954247i	0.447272	−	0.894398i	$-0.352395\pi$
$332$	1.02040	+	1.76738i	0.0560017	+	0.0969978i
$333$	−14.3201			−0.784737
$334$	−3.08210	−	5.33835i	−0.168645	−	0.292101i
$335$	−4.88517	+	8.46136i	−0.266905	+	0.462294i
$336$		0			0
$337$	18.5866			1.01248			0.506239	−	0.862393i	$-0.331035\pi$
$337$	18.5866			1.01248			0.506239	+	0.862393i	$0.331035\pi$
$338$	−8.71525	+	3.05061i	−0.474047	+	0.165931i
$339$	34.3188			1.86394
$340$	−3.76433	+	6.52001i	−0.204150	+	0.353597i
$341$	−2.65563	+	4.59968i	−0.143810	+	0.249087i
$342$	5.85330	+	10.1382i	0.316510	+	0.548212i
$343$		0			0
$344$	−0.359650	−	0.622933i	−0.0193911	−	0.0335863i
$345$	−9.81944	−	17.0078i	−0.528661	−	0.915668i
$346$	0.663361			0.0356625
$347$	−11.1708	−	19.3484i	−0.599681	−	1.03868i	−0.992868	−	0.119220i	$-0.961961\pi$
$347$	−11.1708	−	19.3484i	−0.599681	−	1.03868i	0.393186	−	0.919459i	$-0.371373\pi$
$348$	−10.1073	+	17.5064i	−0.541809	+	0.938441i
$349$	4.39316	−	7.60917i	0.235160	−	0.407310i	−0.724159	−	0.689633i	$-0.757772\pi$
$349$	4.39316	−	7.60917i	0.235160	−	0.407310i	0.959319	+	0.282323i	$0.0911051\pi$
$350$		0			0
$351$	−0.610291	+	1.64505i	−0.0325749	+	0.0878061i
$352$	14.0559			0.749184
$353$	3.85949	−	6.68483i	0.205420	−	0.355798i	−0.744847	−	0.667236i	$-0.767477\pi$
$353$	3.85949	−	6.68483i	0.205420	−	0.355798i	0.950266	+	0.311438i	$0.100811\pi$
$354$	−3.44671	+	5.96987i	−0.183190	+	0.317295i
$355$	−4.66059	−	8.07238i	−0.247358	−	0.428437i
$356$	−1.34549			−0.0713110
$357$		0			0
$358$	4.81081	+	8.33256i	0.254259	+	0.440389i
$359$	−10.5956			−0.559216			−0.279608	−	0.960114i	$-0.590205\pi$
$359$	−10.5956			−0.559216			−0.279608	+	0.960114i	$0.590205\pi$
$360$	−4.47958	−	7.75886i	−0.236094	−	0.408928i
$361$	−7.85008	+	13.5967i	−0.413162	+	0.715618i
$362$	3.14753	−	5.45167i	0.165430	−	0.286534i
$363$	12.5261			0.657447
$364$		0			0
$365$	19.3619			1.01345
$366$	−3.93449	+	6.81474i	−0.205659	+	0.356212i
$367$	2.91033	−	5.04085i	0.151918	−	0.263130i	−0.780014	−	0.625762i	$-0.784788\pi$
$367$	2.91033	−	5.04085i	0.151918	−	0.263130i	0.931933	+	0.362632i	$0.118122\pi$
$368$	3.88128	+	6.72257i	0.202325	+	0.350438i
$369$	21.7822			1.13394
$370$	−2.34429	−	4.06043i	−0.121874	−	0.211092i
$371$		0			0
$372$	−7.94295			−0.411823
$373$	−13.0284	−	22.5659i	−0.674587	−	1.16842i	−0.976589	−	0.215112i	$-0.930988\pi$
$373$	−13.0284	−	22.5659i	−0.674587	−	1.16842i	0.302002	−	0.953307i	$-0.402345\pi$
$374$	3.33795	−	5.78149i	0.172601	−	0.298954i
$375$	−12.9446	+	22.4207i	−0.668458	+	1.15780i
$376$	−3.17059			−0.163511
$377$	−12.9141	−	15.5851i	−0.665112	−	0.802675i
$378$		0			0
$379$	−7.82662	+	13.5561i	−0.402026	+	0.696330i	−0.993970	−	0.109649i	$-0.965027\pi$
$379$	−7.82662	+	13.5561i	−0.402026	+	0.696330i	0.591944	+	0.805979i	$0.298361\pi$
$380$	5.68085	−	9.83952i	0.291421	−	0.504757i
$381$	−10.6243	−	18.4019i	−0.544300	−	0.942756i
$382$	10.9196			0.558694
$383$	−6.27939	−	10.8762i	−0.320862	−	0.555749i	0.659804	−	0.751438i	$-0.270639\pi$
$383$	−6.27939	−	10.8762i	−0.320862	−	0.555749i	−0.980666	+	0.195688i	$0.937306\pi$
$384$	12.6096	+	21.8405i	0.643482	+	1.11454i
$385$		0			0
$386$	−8.69935	−	15.0677i	−0.442785	−	0.766927i
$387$	−0.405294	+	0.701990i	−0.0206023	+	0.0356842i
$388$	−11.7140	+	20.2893i	−0.594689	+	1.03003i
$389$	−0.503007			−0.0255035			−0.0127517	−	0.999919i	$-0.504059\pi$
$389$	−0.503007			−0.0255035			−0.0127517	+	0.999919i	$0.504059\pi$
$390$	7.84061	−	1.33259i	0.397025	−	0.0674783i
$391$	24.6847			1.24836
$392$		0			0
$393$	23.3919	−	40.5159i	1.17996	−	2.04376i
$394$	−2.38448	−	4.13003i	−0.120128	−	0.208068i
$395$	−12.0041			−0.603992
$396$	−5.03757	−	8.72533i	−0.253148	−	0.438464i
$397$	−1.17522	−	2.03554i	−0.0589827	−	0.102161i	0.835026	−	0.550210i	$-0.185452\pi$
$397$	−1.17522	−	2.03554i	−0.0589827	−	0.102161i	−0.894009	+	0.448049i	$0.852119\pi$
$398$	−3.46110			−0.173489
$399$		0			0
$400$	2.04784	−	3.54696i	0.102392	−	0.177348i
$401$	17.3023	−	29.9685i	0.864037	−	1.49656i	−0.00396357	−	0.999992i	$-0.501262\pi$
$401$	17.3023	−	29.9685i	0.864037	−	1.49656i	0.868000	−	0.496564i	$-0.165405\pi$
$402$	12.9564			0.646208
$403$	2.76625	−	7.45647i	0.137797	−	0.371433i
$404$	1.02427			0.0509593
$405$	6.16835	−	10.6839i	0.306508	−	0.530887i
$406$		0			0
$407$	−6.16197	−	10.6729i	−0.305438	−	0.529034i
$408$	23.3355			1.15528
$409$	−4.01205	−	6.94908i	−0.198383	−	0.343610i	0.749621	−	0.661867i	$-0.230236\pi$
$409$	−4.01205	−	6.94908i	−0.198383	−	0.343610i	−0.948004	+	0.318257i	$0.896902\pi$
$410$	3.56588	+	6.17629i	0.176106	+	0.305025i
$411$	−24.6475			−1.21577
$412$	−13.4033	−	23.2152i	−0.660333	−	1.14373i
$413$		0			0
$414$	−6.28382	+	10.8839i	−0.308833	+	0.534914i
$415$	1.75999			0.0863943
$416$	−20.7497	+	3.52662i	−1.01734	+	0.172907i
$417$	19.6176			0.960676
$418$	−5.03738	+	8.72500i	−0.246386	+	0.426754i
$419$	−5.83472	+	10.1060i	−0.285045	+	0.493712i	−0.972620	−	0.232401i	$-0.925342\pi$
$419$	−5.83472	+	10.1060i	−0.285045	+	0.493712i	0.687575	+	0.726113i	$0.258675\pi$
$420$		0			0
$421$	−18.3381			−0.893746			−0.446873	−	0.894597i	$-0.647462\pi$
$421$	−18.3381			−0.893746			−0.446873	+	0.894597i	$0.647462\pi$
$422$	1.30958	+	2.26826i	0.0637494	+	0.110417i
$423$	1.78649	+	3.09429i	0.0868621	+	0.150449i
$424$	−33.8220			−1.64254
$425$	−6.51208	−	11.2792i	−0.315882	−	0.547124i
$426$	−6.18040	+	10.7048i	−0.299441	+	0.518647i
$427$		0			0
$428$	−12.7049			−0.614117
$429$	20.6091	−	3.50272i	0.995015	−	0.169113i
$430$	−0.265397			−0.0127986
$431$	15.6218	−	27.0577i	0.752474	−	1.30332i	−0.194146	−	0.980973i	$-0.562194\pi$
$431$	15.6218	−	27.0577i	0.752474	−	1.30332i	0.946620	−	0.322351i	$-0.104473\pi$
$432$	−0.298671	+	0.517314i	−0.0143698	+	0.0248893i
$433$	−15.2756	−	26.4582i	−0.734100	−	1.27150i	−0.955117	−	0.296229i	$-0.904271\pi$
$433$	−15.2756	−	26.4582i	−0.734100	−	1.27150i	0.221017	−	0.975270i	$-0.429062\pi$
$434$		0			0
$435$	8.71655	+	15.0975i	0.417927	+	0.723870i
$436$	9.04234	+	15.6618i	0.433049	+	0.750064i
$437$	−37.2524			−1.78202
$438$	−12.8379	−	22.2358i	−0.613417	−	1.06247i
$439$	−6.07361	+	10.5198i	−0.289878	+	0.502083i	−0.973780	−	0.227490i	$-0.926948\pi$
$439$	−6.07361	+	10.5198i	−0.289878	+	0.502083i	0.683903	+	0.729573i	$0.260281\pi$
$440$	3.85514	−	6.67730i	0.183787	−	0.318328i
$441$		0			0
$442$	−3.47699	+	9.37227i	−0.165384	+	0.445794i
$443$	−8.46532			−0.402200			−0.201100	−	0.979571i	$-0.564452\pi$
$443$	−8.46532			−0.402200			−0.201100	+	0.979571i	$0.564452\pi$
$444$	9.21519	−	15.9612i	0.437333	−	0.757484i
$445$	−0.580177	+	1.00490i	−0.0275030	+	0.0476366i
$446$	−3.13033	−	5.42189i	−0.148225	−	0.256734i
$447$	23.5705			1.11485
$448$		0			0
$449$	11.6632	+	20.2013i	0.550420	+	0.953356i	0.998244	+	0.0592342i	$0.0188659\pi$
$449$	11.6632	+	20.2013i	0.550420	+	0.953356i	−0.447824	+	0.894122i	$0.647801\pi$
$450$	6.63093			0.312585
$451$	9.37293	+	16.2344i	0.441354	+	0.764448i
$452$	−10.6574	+	18.4592i	−0.501282	+	0.868247i
$453$	17.7469	−	30.7386i	0.833823	−	1.44422i
$454$	−9.55416			−0.448399
$455$		0			0
$456$	−35.2162			−1.64915
$457$	−7.74332	+	13.4118i	−0.362217	+	0.627379i	−0.988325	−	0.152358i	$-0.951313\pi$
$457$	−7.74332	+	13.4118i	−0.362217	+	0.627379i	0.626108	+	0.779736i	$0.284647\pi$
$458$	−2.42057	+	4.19256i	−0.113106	+	0.195905i
$459$	0.949769	+	1.64505i	0.0443314	+	0.0767842i
$460$	12.1974			0.568705
$461$	−4.64102	−	8.03848i	−0.216154	−	0.374389i	0.737475	−	0.675374i	$-0.236018\pi$
$461$	−4.64102	−	8.03848i	−0.216154	−	0.374389i	−0.953629	+	0.300985i	$0.902685\pi$
$462$		0			0
$463$	28.8283			1.33976			0.669882	−	0.742467i	$-0.266345\pi$
$463$	28.8283			1.33976			0.669882	+	0.742467i	$0.266345\pi$
$464$	−3.44534	−	5.96751i	−0.159946	−	0.277035i
$465$	−3.42500	+	5.93227i	−0.158831	+	0.275103i
$466$	−8.90246	+	15.4195i	−0.412399	+	0.714295i
$467$	2.87393			0.132990			0.0664948	−	0.997787i	$-0.478818\pi$
$467$	2.87393			0.132990			0.0664948	+	0.997787i	$0.478818\pi$
$468$	9.62577	+	11.6166i	0.444951	+	0.536979i
$469$		0			0
$470$	−0.584919	+	1.01311i	−0.0269803	+	0.0467312i
$471$	−24.7825	+	42.9245i	−1.14192	+	1.97786i
$472$	−5.00354	−	8.66638i	−0.230307	−	0.398903i
$473$	−0.697596			−0.0320755
$474$	7.95932	+	13.7859i	0.365583	+	0.633209i
$475$	9.82754	+	17.0218i	0.450919	+	0.781014i
$476$		0			0
$477$	19.0572	+	33.0080i	0.872569	+	1.51133i
$478$	−0.989147	+	1.71325i	−0.0452425	+	0.0783624i
$479$	−11.3041	+	19.5792i	−0.516497	+	0.894598i	0.483320	+	0.875444i	$0.339431\pi$
$479$	−11.3041	+	19.5792i	−0.516497	+	0.894598i	−0.999817	+	0.0191546i	$0.993903\pi$
$480$	18.1281			0.827432
$481$	11.7743	+	14.2095i	0.536861	+	0.647898i
$482$	4.95659			0.225766
$483$		0			0
$484$	−3.88985	+	6.73742i	−0.176812	+	0.306247i
$485$	10.1022	+	17.4975i	0.458716	+	0.794519i
$486$	−15.3227			−0.695053
$487$	−1.43401	−	2.48379i	−0.0649814	−	0.112551i	0.831704	−	0.555219i	$-0.187365\pi$
$487$	−1.43401	−	2.48379i	−0.0649814	−	0.112551i	−0.896686	+	0.442668i	$0.854032\pi$
$488$	−5.71165	−	9.89287i	−0.258554	−	0.447829i
$489$	9.58544			0.433469
$490$		0			0
$491$	11.3600	−	19.6762i	0.512672	−	0.887973i	−0.487220	−	0.873279i	$-0.661989\pi$
$491$	11.3600	−	19.6762i	0.512672	−	0.887973i	0.999892	−	0.0146943i	$-0.00467751\pi$
$492$	−14.0172	+	24.2784i	−0.631942	+	1.09456i
$493$	−21.9122			−0.986877
$494$	5.24721	−	14.1439i	0.236083	−	0.636366i
$495$	−8.68881			−0.390533
$496$	1.35378	−	2.34482i	0.0607865	−	0.105285i
$497$		0			0
$498$	−1.16696	−	2.02123i	−0.0522926	−	0.0905734i
$499$	−18.0151			−0.806466			−0.403233	−	0.915097i	$-0.632114\pi$
$499$	−18.0151			−0.806466			−0.403233	+	0.915097i	$0.632114\pi$
$500$	−8.03968	−	13.9251i	−0.359545	−	0.622751i
$501$	−10.4483	−	18.0971i	−0.466798	−	0.808518i
$502$	−0.556175			−0.0248233
$503$	−15.5748	−	26.9764i	−0.694447	−	1.20282i	−0.970367	−	0.241636i	$-0.922316\pi$
$503$	−15.5748	−	26.9764i	−0.694447	−	1.20282i	0.275920	−	0.961181i	$-0.411017\pi$
$504$		0			0
$505$	0.441665	−	0.764987i	0.0196539	−	0.0340415i
$506$	−10.8158			−0.480819
$507$	−29.5448	+	10.3416i	−1.31213	+	0.459286i
$508$	13.1972			0.585529
$509$	−19.7509	+	34.2096i	−0.875444	+	1.51631i	−0.0191556	+	0.999817i	$0.506098\pi$
$509$	−19.7509	+	34.2096i	−0.875444	+	1.51631i	−0.856289	+	0.516497i	$0.827236\pi$
$510$	4.30499	−	7.45647i	0.190628	−	0.330178i
$511$		0			0
$512$	−13.2606			−0.586042
$513$	−1.43332	−	2.48258i	−0.0632826	−	0.109609i
$514$	−1.15707	−	2.00411i	−0.0510363	−	0.0883974i
$515$	−23.1180			−1.01870
$516$	−0.521625	−	0.903480i	−0.0229632	−	0.0397735i
$517$	−1.53746	+	2.66296i	−0.0676174	+	0.117117i
$518$		0			0
$519$	2.24880			0.0987115
$520$	−4.01573	+	10.8245i	−0.176101	+	0.474684i
$521$	17.7672			0.778394			0.389197	−	0.921155i	$-0.372753\pi$
$521$	17.7672			0.778394			0.389197	+	0.921155i	$0.372753\pi$
$522$	5.57804	−	9.66145i	0.244144	−	0.422870i
$523$	−0.894522	+	1.54936i	−0.0391147	+	0.0677487i	−0.884920	−	0.465743i	$-0.845787\pi$
$523$	−0.894522	+	1.54936i	−0.0391147	+	0.0677487i	0.845805	+	0.533492i	$0.179120\pi$
$524$	14.5283	+	25.1637i	0.634671	+	1.09928i
$525$		0			0
$526$	10.5062	+	18.1972i	0.458091	+	0.793438i
$527$	−4.30499	−	7.45647i	−0.187528	−	0.324809i
$528$	7.11683			0.309720
$529$	−8.49616	−	14.7158i	−0.369398	−	0.639817i
$530$	−6.23956	+	10.8072i	−0.271029	+	0.469436i
$531$	−5.63854	+	9.76624i	−0.244692	+	0.423819i
$532$		0			0
$533$	−17.9098	−	21.6140i	−0.775758	−	0.936205i
$534$	1.53874			0.0665879
$535$	−5.47838	+	9.48882i	−0.236851	+	0.410238i
$536$	−9.40434	+	16.2888i	−0.406206	+	0.703569i
$537$	16.3087	+	28.2475i	0.703772	+	1.21897i
$538$	0.878269			0.0378649
$539$		0			0
$540$	0.469305	+	0.812860i	0.0201957	+	0.0349799i
$541$	15.4027			0.662214			0.331107	−	0.943593i	$-0.392578\pi$
$541$	15.4027			0.662214			0.331107	+	0.943593i	$0.392578\pi$
$542$	−8.95214	−	15.5056i	−0.384527	−	0.666021i
$543$	10.6702	−	18.4813i	0.457900	−	0.793107i
$544$	−11.3929	+	19.7331i	−0.488467	+	0.846050i
$545$	15.5962			0.668069
$546$		0			0
$547$	−3.96944			−0.169721			−0.0848605	−	0.996393i	$-0.527044\pi$
$547$	−3.96944			−0.169721			−0.0848605	+	0.996393i	$0.527044\pi$
$548$	7.65406	−	13.2572i	0.326965	−	0.566321i
$549$	−6.43652	+	11.1484i	−0.274704	+	0.475801i
$550$	2.85330	+	4.94207i	0.121665	+	0.210731i
$551$	33.0683			1.40876
$552$	−18.9032	−	32.7413i	−0.804574	−	1.39356i
$553$		0			0
$554$	−6.77331			−0.287770
$555$	−7.94718	−	13.7649i	−0.337339	−	0.584288i
$556$	−6.09206	+	10.5518i	−0.258361	+	0.447494i
$557$	−9.34504	+	16.1861i	−0.395962	+	0.685826i	−0.993223	−	0.116220i	$-0.962922\pi$
$557$	−9.34504	+	16.1861i	−0.395962	+	0.685826i	0.597261	+	0.802047i	$0.296255\pi$
$558$	4.38357			0.185571
$559$	1.02981	−	0.175026i	0.0435563	−	0.00740282i
$560$		0			0
$561$	11.3157	−	19.5993i	0.477749	−	0.827485i
$562$	3.39711	−	5.88397i	0.143298	−	0.248200i
$563$	18.1530	+	31.4418i	0.765056	+	1.32512i	0.940217	+	0.340576i	$0.110622\pi$
$563$	18.1530	+	31.4418i	0.765056	+	1.32512i	−0.175161	+	0.984540i	$0.556045\pi$
$564$	−4.59852			−0.193633
$565$	9.19095	+	15.9192i	0.386666	+	0.669726i
$566$	−4.06001	−	7.03215i	−0.170655	−	0.295583i
$567$		0			0
$568$	−8.97201	−	15.5400i	−0.376457	−	0.652043i
$569$	−5.48798	+	9.50546i	−0.230068	+	0.398489i	−0.957828	−	0.287343i	$-0.907228\pi$
$569$	−5.48798	+	9.50546i	−0.230068	+	0.398489i	0.727760	+	0.685832i	$0.240562\pi$
$570$	−6.49678	+	11.2527i	−0.272120	+	0.471326i
$571$	31.3363			1.31138			0.655692	−	0.755028i	$-0.272377\pi$
$571$	31.3363			1.31138			0.655692	+	0.755028i	$0.272377\pi$
$572$	−4.51595	+	12.1728i	−0.188821	+	0.508970i
$573$	37.0175			1.54643
$574$		0			0
$575$	−10.5504	+	18.2738i	−0.439981	+	0.762069i
$576$	−2.36605	−	4.09812i	−0.0985855	−	0.170755i
$577$	42.7876			1.78127			0.890636	−	0.454717i	$-0.150260\pi$
$577$	42.7876			1.78127			0.890636	+	0.454717i	$0.150260\pi$
$578$	−0.626353	−	1.08487i	−0.0260528	−	0.0451248i
$579$	−29.4909	−	51.0798i	−1.22560	−	2.12280i
$580$	−10.8274			−0.449583
$581$		0			0
$582$	13.3965	−	23.2034i	0.555302	−	0.961811i
$583$	−16.4007	+	28.4069i	−0.679248	+	1.17649i
$584$	37.2731			1.54237
$585$	12.8266	−	2.18001i	0.530316	−	0.0901325i
$586$	−6.64517			−0.274509
$587$	−19.3943	+	33.5919i	−0.800488	+	1.38649i	0.118808	+	0.992917i	$0.462093\pi$
$587$	−19.3943	+	33.5919i	−0.800488	+	1.38649i	−0.919296	+	0.393568i	$0.871241\pi$
$588$		0			0
$589$	6.49678	+	11.2527i	0.267695	+	0.463661i
$590$	−3.69226			−0.152008
$591$	−8.08341	−	14.0009i	−0.332507	−	0.575919i
$592$	3.14124	+	5.44078i	0.129104	+	0.223615i
$593$	29.9564			1.23016			0.615081	−	0.788464i	$-0.289123\pi$
$593$	29.9564			1.23016			0.615081	+	0.788464i	$0.289123\pi$
$594$	−0.416147	−	0.720787i	−0.0170747	−	0.0295743i
$595$		0			0
$596$	−7.31960	+	12.6779i	−0.299823	+	0.519308i
$597$	−11.7332			−0.480207
$598$	15.9665	−	2.71367i	0.652919	−	0.110970i
$599$	41.2539			1.68559			0.842794	−	0.538236i	$-0.180909\pi$
$599$	41.2539			1.68559			0.842794	+	0.538236i	$0.180909\pi$
$600$	−9.97371	+	17.2750i	−0.407175	+	0.705248i
$601$	3.30544	−	5.72520i	0.134832	−	0.233536i	−0.790701	−	0.612202i	$-0.790284\pi$
$601$	3.30544	−	5.72520i	0.134832	−	0.233536i	0.925533	+	0.378666i	$0.123617\pi$
$602$		0			0
$603$	21.1957			0.863156
$604$	11.0223	+	19.0912i	0.448491	+	0.776809i
$605$	3.35461	+	5.81036i	0.136384	+	0.236225i
$606$	−1.17138			−0.0475842
$607$	−10.4416	−	18.0854i	−0.423811	−	0.734062i	0.572498	−	0.819906i	$-0.305975\pi$
$607$	−10.4416	−	18.0854i	−0.423811	−	0.734062i	−0.996309	+	0.0858444i	$0.972641\pi$
$608$	17.1933	−	29.7797i	0.697282	−	1.20773i
$609$		0			0
$610$	−4.21479			−0.170652
$611$	1.60150	−	4.31687i	0.0647899	−	0.174642i
$612$	16.3326			0.660208
$613$	2.14828	−	3.72092i	0.0867680	−	0.150287i	−0.819375	−	0.573258i	$-0.805679\pi$
$613$	2.14828	−	3.72092i	0.0867680	−	0.150287i	0.906143	+	0.422971i	$0.139013\pi$
$614$	−2.88181	+	4.99144i	−0.116300	+	0.201438i
$615$	12.0884	+	20.9377i	0.487451	+	0.844290i
$616$		0			0
$617$	15.3690	+	26.6199i	0.618732	+	1.07167i	0.989717	+	0.143036i	$0.0456866\pi$
$617$	15.3690	+	26.6199i	0.618732	+	1.07167i	−0.370986	+	0.928639i	$0.620980\pi$
$618$	15.3284	+	26.5495i	0.616598	+	1.06798i
$619$	20.6417			0.829658			0.414829	−	0.909899i	$-0.363841\pi$
$619$	20.6417			0.829658			0.414829	+	0.909899i	$0.363841\pi$
$620$	−2.12721	−	3.68443i	−0.0854307	−	0.147970i
$621$	1.53874	−	2.66518i	0.0617476	−	0.106950i
$622$	3.06849	−	5.31479i	0.123035	−	0.213104i
$623$		0			0
$624$	−10.5060	+	1.78561i	−0.420578	+	0.0714815i
$625$	2.81636			0.112654
$626$	1.85645	−	3.21546i	0.0741986	−	0.128516i
$627$	−17.0768	+	29.5779i	−0.681981	+	1.18123i
$628$	−15.3919	−	26.6596i	−0.614205	−	1.06383i
$629$	19.9781			0.796580
$630$		0			0
$631$	−14.6683	−	25.4063i	−0.583937	−	1.01141i	−0.995007	−	0.0998043i	$-0.968178\pi$
$631$	−14.6683	−	25.4063i	−0.583937	−	1.01141i	0.411070	−	0.911604i	$-0.365155\pi$
$632$	−23.1089			−0.919222
$633$	4.43950	+	7.68943i	0.176454	+	0.305628i
$634$	3.97509	−	6.88506i	0.157871	−	0.273441i
$635$	5.69061	−	9.85643i	0.225825	−	0.391141i
$636$	−49.0543			−1.94513
$637$		0			0
$638$	9.60097			0.380106
$639$	−10.1107	+	17.5122i	−0.399971	+	0.692771i
$640$	−6.75399	+	11.6983i	−0.266975	+	0.462414i
$641$	2.00840	+	3.47865i	0.0793271	+	0.137399i	0.902960	−	0.429725i	$-0.141390\pi$
$641$	2.00840	+	3.47865i	0.0793271	+	0.137399i	−0.823633	+	0.567124i	$0.808056\pi$
$642$	14.5297			0.573443
$643$	−3.43641	−	5.95203i	−0.135519	−	0.234725i	0.790277	−	0.612750i	$-0.209937\pi$
$643$	−3.43641	−	5.95203i	−0.135519	−	0.234725i	−0.925795	+	0.378025i	$0.876603\pi$
$644$		0			0
$645$	−0.899698			−0.0354256
$646$	−8.16601	−	14.1439i	−0.321287	−	0.556486i
$647$	−16.8715	+	29.2224i	−0.663289	+	1.14885i	0.316457	+	0.948607i	$0.397507\pi$
$647$	−16.8715	+	29.2224i	−0.663289	+	1.14885i	−0.979746	+	0.200243i	$0.935827\pi$
$648$	11.8746	−	20.5674i	0.466477	−	0.807962i
$649$	−9.70511			−0.380959
$650$	−5.45208	−	6.57972i	−0.213848	−	0.258078i
$651$		0			0
$652$	−2.97667	+	5.15575i	−0.116576	+	0.201915i
$653$	−16.2001	+	28.0594i	−0.633958	+	1.09805i	0.352777	+	0.935708i	$0.385238\pi$
$653$	−16.2001	+	28.0594i	−0.633958	+	1.09805i	−0.986735	+	0.162340i	$0.948096\pi$
$654$	−10.3411	−	17.9113i	−0.404368	−	0.700385i
$655$	25.0584			0.979112
$656$	−4.77811	−	8.27593i	−0.186554	−	0.323121i
$657$	−21.0018	−	36.3761i	−0.819357	−	1.41917i
$658$		0			0
$659$	−2.00518	−	3.47307i	−0.0781106	−	0.135291i	0.824324	−	0.566118i	$-0.191555\pi$
$659$	−2.00518	−	3.47307i	−0.0781106	−	0.135291i	−0.902435	+	0.430827i	$0.858222\pi$
$660$	5.59137	−	9.68453i	0.217644	−	0.376970i
$661$	−0.908971	+	1.57438i	−0.0353549	+	0.0612364i	−0.883161	−	0.469069i	$-0.844589\pi$
$661$	−0.908971	+	1.57438i	−0.0353549	+	0.0612364i	0.847807	+	0.530306i	$0.177923\pi$
$662$	−14.2389			−0.553412
$663$	−11.7870	+	31.7721i	−0.457771	+	1.23393i
$664$	3.38811			0.131484
$665$		0			0
$666$	−5.08569	+	8.80868i	−0.197067	+	0.341329i
$667$	17.7503	+	30.7443i	0.687293	+	1.19043i
$668$	12.9786			0.502156
$669$	−10.6119	−	18.3803i	−0.410278	−	0.710622i
$670$	3.46987	+	6.00999i	0.134053	+	0.232186i
$671$	−11.0786			−0.427684
$672$		0			0
$673$	11.4871	−	19.8963i	0.442797	−	0.766947i	−0.555099	−	0.831784i	$-0.687320\pi$
$673$	11.4871	−	19.8963i	0.442797	−	0.766947i	0.997896	+	0.0648375i	$0.0206529\pi$
$674$	6.60091	−	11.4331i	0.254258	−	0.440387i
$675$	−1.62374			−0.0624978
$676$	3.61241	−	19.1028i	0.138939	−	0.734725i
$677$	−38.0276			−1.46152			−0.730760	−	0.682634i	$-0.760834\pi$
$677$	−38.0276			−1.46152			−0.730760	+	0.682634i	$0.760834\pi$
$678$	12.1881	−	21.1104i	0.468081	−	0.810741i
$679$		0			0
$680$	6.24950	+	10.8245i	0.239658	+	0.415099i
$681$	−32.3887			−1.24114
$682$	1.88626	+	3.26709i	0.0722285	+	0.125103i
$683$	20.3893	+	35.3153i	0.780176	+	1.35130i	0.931839	+	0.362872i	$0.118204\pi$
$683$	20.3893	+	35.3153i	0.780176	+	1.35130i	−0.151663	+	0.988432i	$0.548463\pi$
$684$	−24.6480			−0.942440
$685$	−6.60087	−	11.4330i	−0.252206	−	0.436834i
$686$		0			0
$687$	−8.20578	+	14.2128i	−0.313070	+	0.542253i
$688$	0.355619			0.0135578
$689$	17.0839	−	46.0499i	0.650844	−	1.75436i
$690$	−13.9492			−0.531038
$691$	−1.56434	+	2.70952i	−0.0595104	+	0.103075i	−0.894246	−	0.447576i	$-0.852287\pi$
$691$	−1.56434	+	2.70952i	−0.0595104	+	0.103075i	0.834735	+	0.550651i	$0.185621\pi$
$692$	−0.698346	+	1.20957i	−0.0265471	+	0.0459809i
$693$		0			0
$694$	−15.8690			−0.602378
$695$	5.25379	+	9.09984i	0.199288	+	0.345177i
$696$	16.7801	+	29.0639i	0.636047	+	1.10167i
$697$	−30.3886			−1.15105
$698$	−3.12040	−	5.40470i	−0.118109	−	0.204571i
$699$	−30.1795	+	52.2724i	−1.14149	+	1.97712i
$700$		0			0
$701$	9.61382			0.363109			0.181555	−	0.983381i	$-0.441887\pi$
$701$	9.61382			0.363109			0.181555	+	0.983381i	$0.441887\pi$
$702$	0.795171	+	0.959634i	0.0300118	+	0.0362190i
$703$	−30.1495			−1.13711
$704$	2.03623	−	3.52686i	0.0767435	−	0.132924i
$705$	−1.98288	+	3.43445i	−0.0746797	+	0.129349i
$706$	−2.74134	−	4.74815i	−0.103172	−	0.178699i
$707$		0			0
$708$	−7.25696	−	12.5694i	−0.272733	−	0.472388i
$709$	−14.0647	−	24.3608i	−0.528211	−	0.914889i	−0.999459	−	0.0328880i	$-0.989530\pi$
$709$	−14.0647	−	24.3608i	−0.528211	−	0.914889i	0.471248	−	0.882001i	$-0.343804\pi$
$710$	−6.62071			−0.248471
$711$	13.0208	+	22.5527i	0.488319	+	0.845794i
$712$	−1.11689	+	1.93450i	−0.0418571	+	0.0724986i
$713$	−6.97462	+	12.0804i	−0.261201	+	0.452414i
$714$		0			0
$715$	7.14411	+	8.62170i	0.267174	+	0.322433i
$716$	−20.2581			−0.757080
$717$	−3.35322	+	5.80796i	−0.125228	+	0.216902i
$718$	−3.76297	+	6.51765i	−0.140433	+	0.243237i
$719$	12.4522	+	21.5679i	0.464389	+	0.804346i	0.999174	−	0.0406425i	$-0.0129405\pi$
$719$	12.4522	+	21.5679i	0.464389	+	0.804346i	−0.534784	+	0.844989i	$0.679607\pi$
$720$	4.42936			0.165073
$721$		0			0
$722$	5.57581	+	9.65758i	0.207510	+	0.359418i
$723$	16.8029			0.624907
$724$	6.62705	+	11.4784i	0.246292	+	0.426591i
$725$	9.36538	−	16.2213i	0.347822	−	0.602445i
$726$	4.44854	−	7.70510i	0.165101	−	0.285963i
$727$	24.2120			0.897974			0.448987	−	0.893538i	$-0.351785\pi$
$727$	24.2120			0.897974			0.448987	+	0.893538i	$0.351785\pi$
$728$		0			0
$729$	−23.2479			−0.861032
$730$	6.87624	−	11.9100i	0.254501	−	0.440808i
$731$	0.565430	−	0.979353i	0.0209132	−	0.0362227i
$732$	−8.28398	−	14.3483i	−0.306185	−	0.530328i
$733$	12.3989			0.457963			0.228981	−	0.973431i	$-0.426461\pi$
$733$	12.3989			0.457963			0.228981	+	0.973431i	$0.426461\pi$
$734$	−2.06717	−	3.58045i	−0.0763007	−	0.132157i
$735$		0			0
$736$	36.9159			1.36074
$737$	9.12056	+	15.7973i	0.335960	+	0.581900i
$738$	7.73581	−	13.3988i	0.284759	−	0.493217i
$739$	5.48019	−	9.49197i	0.201592	−	0.349168i	−0.747450	−	0.664319i	$-0.768722\pi$
$739$	5.48019	−	9.49197i	0.201592	−	0.349168i	0.949042	+	0.315151i	$0.102055\pi$
$740$	9.87170			0.362891
$741$	17.7881	−	47.9482i	0.653463	−	1.76142i
$742$		0			0
$743$	−20.3462	+	35.2407i	−0.746431	+	1.29286i	0.203092	+	0.979160i	$0.434901\pi$
$743$	−20.3462	+	35.2407i	−0.746431	+	1.29286i	−0.949523	+	0.313697i	$0.898432\pi$
$744$	−6.59340	+	11.4201i	−0.241726	+	0.418681i
$745$	6.31243	+	10.9334i	0.231269	+	0.400570i
$746$	−18.5079			−0.677621
$747$	−1.90905	−	3.30657i	−0.0698485	−	0.120981i
$748$	7.02797	+	12.1728i	0.256968	+	0.445082i
$749$		0			0
$750$	9.19439	+	15.9252i	0.335732	+	0.581505i
$751$	−4.70236	+	8.14473i	−0.171592	+	0.297205i	−0.938976	−	0.343981i	$-0.888224\pi$
$751$	−4.70236	+	8.14473i	−0.171592	+	0.297205i	0.767385	+	0.641187i	$0.221558\pi$
$752$	0.783763	−	1.35752i	0.0285809	−	0.0495035i
$753$	−1.88544			−0.0687093
$754$	−14.1732	+	2.40888i	−0.516157	+	0.0877261i
$755$	19.0113			0.691890
$756$		0			0
$757$	14.7904	−	25.6177i	0.537566	−	0.931091i	−0.461469	−	0.887156i	$-0.652677\pi$
$757$	14.7904	−	25.6177i	0.537566	−	0.931091i	0.999034	−	0.0439345i	$-0.0139893\pi$
$758$	5.55914	+	9.62872i	0.201917	+	0.349731i
$759$	−36.6656			−1.33088
$760$	−9.43129	−	16.3355i	−0.342109	−	0.592550i
$761$	8.47086	+	14.6720i	0.307068	+	0.531858i	0.977720	−	0.209915i	$-0.0673186\pi$
$761$	8.47086	+	14.6720i	0.307068	+	0.531858i	−0.670651	+	0.741773i	$0.733985\pi$
$762$	−15.0926			−0.546748
$763$		0			0
$764$	−11.4955	+	19.9107i	−0.415891	+	0.720345i
$765$	7.04264	−	12.1982i	0.254627	−	0.441027i
$766$	−8.92034			−0.322305
$767$	14.3269	−	2.43500i	0.517316	−	0.0879229i
$768$	26.0578			0.940281
$769$	3.68287	−	6.37892i	0.132808	−	0.230030i	−0.791950	−	0.610586i	$-0.790934\pi$
$769$	3.68287	−	6.37892i	0.132808	−	0.230030i	0.924758	+	0.380556i	$0.124267\pi$
$770$		0			0
$771$	−3.92249	−	6.79396i	−0.141265	−	0.244678i
$772$	36.6326			1.31844
$773$	−22.3867	−	38.7749i	−0.805194	−	1.39464i	−0.916160	−	0.400813i	$-0.868728\pi$
$773$	−22.3867	−	38.7749i	−0.805194	−	1.39464i	0.110966	−	0.993824i	$-0.464606\pi$
$774$	0.287875	+	0.498614i	0.0103475	+	0.0179223i
$775$	7.35989			0.264375
$776$	19.4475	+	33.6840i	0.698124	+	1.20919i
$777$		0			0
$778$	−0.178640	+	0.309413i	−0.00640454	+	0.0110930i
$779$	45.8602			1.64311
$780$	−5.82428	+	15.6994i	−0.208543	+	0.562130i
$781$	−17.4025			−0.622712
$782$	8.76662	−	15.1842i	0.313494	−	0.542987i
$783$	−1.36592	+	2.36583i	−0.0488138	+	0.0845480i
$784$		0			0
$785$	−26.5480			−0.947540
$786$	−16.6149	−	28.7779i	−0.592635	−	1.02647i
$787$	−9.38412	−	16.2538i	−0.334508	−	0.579385i	0.648882	−	0.760889i	$-0.275237\pi$
$787$	−9.38412	−	16.2538i	−0.334508	−	0.579385i	−0.983390	+	0.181504i	$0.941903\pi$
$788$	10.0409			0.357693
$789$	35.6161	+	61.6889i	1.26797	+	2.19618i
$790$	−4.26318	+	7.38404i	−0.151677	+	0.262713i
$791$		0			0
$792$	−16.7267			−0.594356
$793$	16.3545	−	2.77961i	0.580766	−	0.0987069i
$794$	−1.66949			−0.0592479
$795$	−21.1522	+	36.6367i	−0.750192	+	1.29937i
$796$	3.64363	−	6.31095i	0.129145	−	0.223686i
$797$	3.60849	+	6.25008i	0.127819	+	0.221389i	0.922831	−	0.385204i	$-0.125869\pi$
$797$	3.60849	+	6.25008i	0.127819	+	0.221389i	−0.795012	+	0.606593i	$0.792536\pi$
$798$		0			0
$799$	−2.49235	−	4.31687i	−0.0881730	−	0.152720i
$800$	−9.73877	−	16.8680i	−0.344317	−	0.596375i
$801$	2.51726			0.0889431
$802$	−12.2896	−	21.2862i	−0.433961	−	0.751643i
$803$	18.0742	−	31.3054i	0.637825	−	1.10474i
$804$	−13.6397	+	23.6247i	−0.481036	+	0.833180i
$805$		0			0
$806$	−3.60425	−	4.34971i	−0.126954	−	0.153212i
$807$	2.97734			0.104807
$808$	0.850241	−	1.47266i	0.0299114	−	0.0518080i
$809$	−7.41591	+	12.8447i	−0.260729	+	0.451596i	−0.966436	−	0.256908i	$-0.917296\pi$
$809$	−7.41591	+	12.8447i	−0.260729	+	0.451596i	0.705707	+	0.708504i	$0.250630\pi$
$810$	−4.38130	−	7.58863i	−0.153943	−	0.266637i
$811$	−18.5831			−0.652541			−0.326271	−	0.945276i	$-0.605792\pi$
$811$	−18.5831			−0.652541			−0.326271	+	0.945276i	$0.605792\pi$
$812$		0			0
$813$	−30.3479	−	52.5641i	−1.06435	−	1.84350i
$814$	−8.75354			−0.306811
$815$	2.56708	+	4.44632i	0.0899210	+	0.155748i
$816$	−5.76848	+	9.99131i	−0.201937	+	0.349766i
$817$	−0.853305	+	1.47797i	−0.0298534	+	0.0517075i
$818$	−5.69942			−0.199275
$819$		0			0
$820$	−15.0158			−0.524374
$821$	13.3118	−	23.0567i	0.464585	−	0.804684i	−0.534598	−	0.845106i	$-0.679537\pi$
$821$	13.3118	−	23.0567i	0.464585	−	0.804684i	0.999183	+	0.0404222i	$0.0128703\pi$
$822$	−8.75340	+	15.1613i	−0.305310	+	0.528812i
$823$	−3.37568	−	5.84685i	−0.117669	−	0.203808i	0.801175	−	0.598431i	$-0.204209\pi$
$823$	−3.37568	−	5.84685i	−0.117669	−	0.203808i	−0.918843	+	0.394622i	$0.870875\pi$
$824$	−44.5040			−1.55037
$825$	9.67275	+	16.7537i	0.336762	+	0.583289i
$826$		0			0
$827$	−21.7430			−0.756079			−0.378039	−	0.925789i	$-0.623402\pi$
$827$	−21.7430			−0.756079			−0.378039	+	0.925789i	$0.623402\pi$
$828$	−13.2304	−	22.9158i	−0.459790	−	0.796379i
$829$	−7.31078	+	12.6626i	−0.253914	+	0.439792i	−0.964600	−	0.263717i	$-0.915051\pi$
$829$	−7.31078	+	12.6626i	−0.253914	+	0.439792i	0.710686	+	0.703509i	$0.248385\pi$
$830$	0.625047	−	1.08261i	0.0216957	−	0.0375781i
$831$	−22.9616			−0.796529
$832$	−2.12105	+	5.71733i	−0.0735343	+	0.198213i
$833$		0			0
$834$	6.96705	−	12.0673i	0.241249	−	0.417856i
$835$	5.59636	−	9.69318i	0.193670	−	0.335446i
$836$	−10.6061	−	18.3703i	−0.366819	−	0.635350i
$837$	−1.07342			−0.0371028
$838$	4.14432	+	7.17818i	0.143163	+	0.247966i
$839$	−5.37343	−	9.30705i	−0.185511	−	0.321315i	0.758237	−	0.651979i	$-0.226061\pi$
$839$	−5.37343	−	9.30705i	−0.185511	−	0.321315i	−0.943749	+	0.330663i	$0.892727\pi$
$840$		0			0
$841$	−1.25660	−	2.17649i	−0.0433310	−	0.0750515i
$842$	−6.51267	+	11.2803i	−0.224441	+	0.388744i
$843$	11.5163	−	19.9467i	0.396641	−	0.687002i
$844$	−5.51458			−0.189820
$845$	−12.7095	−	10.9351i	−0.437220	−	0.376180i
$846$	2.53784			0.0872527
$847$		0			0
$848$	8.36071	−	14.4812i	0.287108	−	0.497286i
$849$	−13.7635	−	23.8391i	−0.472362	−	0.818155i
$850$	−9.25088			−0.317303
$851$	−16.1835	−	28.0307i	−0.554764	−	0.960879i
$852$	−13.0127	−	22.5386i	−0.445807	−	0.772161i
$853$	31.7709			1.08782			0.543908	−	0.839145i	$-0.316944\pi$
$853$	31.7709			1.08782			0.543908	+	0.839145i	$0.316944\pi$
$854$		0			0
$855$	−10.6282	+	18.4086i	−0.363478	+	0.629562i
$856$	−10.5463	+	18.2667i	−0.360466	+	0.624345i
$857$	0.648105			0.0221388			0.0110694	−	0.999939i	$-0.496476\pi$
$857$	0.648105			0.0221388			0.0110694	+	0.999939i	$0.496476\pi$
$858$	5.16456	−	13.9211i	0.176315	−	0.475260i
$859$	43.1902			1.47363			0.736815	−	0.676095i	$-0.236329\pi$
$859$	43.1902			1.47363			0.736815	+	0.676095i	$0.236329\pi$
$860$	0.279393	−	0.483923i	0.00952723	−	0.0165017i
$861$		0			0
$862$	−11.0959	−	19.2187i	−0.377929	−	0.654592i
$863$	21.6094			0.735592			0.367796	−	0.929906i	$-0.380112\pi$
$863$	21.6094			0.735592			0.367796	+	0.929906i	$0.380112\pi$
$864$	1.42037	+	2.46016i	0.0483220	+	0.0836962i
$865$	0.602253	+	1.04313i	0.0204772	+	0.0354676i
$866$	−21.7002			−0.737401
$867$	−2.12335	−	3.67774i	−0.0721126	−	0.124903i
$868$		0			0
$869$	−11.2058	+	19.4090i	−0.380130	+	0.658405i
$870$	12.3825			0.419806
$871$	−17.4275	−	21.0320i	−0.590509	−	0.712642i
$872$	30.0240			1.01674
$873$	21.9156	−	37.9589i	0.741731	−	1.28472i
$874$	−13.2299	+	22.9149i	−0.447509	+	0.775109i
$875$		0			0
$876$	54.0597			1.82651
$877$	0.440383	+	0.762766i	0.0148707	+	0.0257568i	0.873365	−	0.487066i	$-0.161933\pi$
$877$	0.440383	+	0.762766i	0.0148707	+	0.0257568i	−0.858494	+	0.512823i	$0.828600\pi$
$878$	4.31401	+	7.47208i	0.145591	+	0.252170i
$879$	−22.5272			−0.759825
$880$	1.90596	+	3.30123i	0.0642500	+	0.111284i
$881$	−0.0700176	+	0.121274i	−0.00235895	+	0.00408583i	−0.867202	−	0.497956i	$-0.834084\pi$
$881$	−0.0700176	+	0.121274i	−0.00235895	+	0.00408583i	0.864844	+	0.502042i	$0.167418\pi$
$882$		0			0
$883$	−18.8253			−0.633522			−0.316761	−	0.948505i	$-0.602595\pi$
$883$	−18.8253			−0.633522			−0.316761	+	0.948505i	$0.602595\pi$
$884$	−13.4290	−	16.2065i	−0.451667	−	0.545083i
$885$	−12.5168			−0.420748
$886$	−3.00640	+	5.20724i	−0.101002	+	0.174941i
$887$	−16.6505	+	28.8395i	−0.559069	+	0.968337i	0.438505	+	0.898729i	$0.355508\pi$
$887$	−16.6505	+	28.8395i	−0.559069	+	0.968337i	−0.997574	+	0.0696078i	$0.977825\pi$
$888$	−15.2990	−	26.4986i	−0.513400	−	0.889234i
$889$		0			0
$890$	0.412092	+	0.713764i	0.0138133	+	0.0239254i
$891$	−11.5163	−	19.9467i	−0.385809	−	0.668241i
$892$	13.1817			0.441355
$893$	3.76127	+	6.51471i	0.125866	+	0.218006i
$894$	8.37090	−	14.4988i	0.279965	−	0.484913i
$895$	−8.73529	+	15.1300i	−0.291989	+	0.505739i
$896$		0			0
$897$	54.1267	−	9.19937i	1.80724	−	0.307158i
$898$	16.5684			0.552896
$899$	6.19125	−	10.7236i	0.206490	−	0.357651i
$900$	−6.98064	+	12.0908i	−0.232688	+	0.403028i
$901$	−26.5869	−	46.0499i	−0.885738	−	1.53414i
$902$	13.3149			0.443339
$903$		0			0
$904$	17.6933	+	30.6457i	0.588471	+	1.01926i
$905$	11.4303			0.379957
$906$	−12.6054	−	21.8332i	−0.418786	−	0.725359i
$907$	−5.79350	+	10.0346i	−0.192370	+	0.333195i	−0.946035	−	0.324064i	$-0.894951\pi$
$907$	−5.79350	+	10.0346i	−0.192370	+	0.333195i	0.753665	+	0.657259i	$0.228284\pi$
$908$	10.0580	−	17.4210i	0.333788	−	0.578137i
$909$	−1.91629			−0.0635594
$910$		0			0
$911$	52.5489			1.74102			0.870512	−	0.492147i	$-0.163788\pi$
$911$	52.5489			1.74102			0.870512	+	0.492147i	$0.163788\pi$
$912$	8.70537	−	15.0781i	0.288264	−	0.499287i
$913$	1.64294	−	2.84565i	0.0543733	−	0.0941773i
$914$	5.49998	+	9.52624i	0.181923	+	0.315100i
$915$	−14.2882			−0.472354
$916$	−5.09646	−	8.82733i	−0.168392	−	0.291663i
$917$		0			0
$918$	1.34922			0.0445308
$919$	10.0267	+	17.3668i	0.330751	+	0.572878i	0.982659	−	0.185420i	$-0.0593646\pi$
$919$	10.0267	+	17.3668i	0.330751	+	0.572878i	−0.651908	+	0.758298i	$0.726031\pi$
$920$	10.1250	−	17.5370i	0.333810	−	0.578176i
$921$	−9.76937	+	16.9210i	−0.321912	+	0.557567i
$922$	−6.59291			−0.217126
$923$	25.6901	−	4.36628i	0.845599	−	0.143718i
$924$		0			0
$925$	−8.53874	+	14.7895i	−0.280752	+	0.486277i
$926$	10.2382	−	17.7330i	0.336447	−	0.582744i
$927$	25.0760	+	43.4330i	0.823605	+	1.42653i
$928$	−32.7696			−1.07571
$929$	−7.95425	−	13.7772i	−0.260971	−	0.452014i	0.705530	−	0.708681i	$-0.250709\pi$
$929$	−7.95425	−	13.7772i	−0.260971	−	0.452014i	−0.966500	+	0.256666i	$0.917376\pi$
$930$	2.43273	+	4.21361i	0.0797724	+	0.138170i
$931$		0			0
$932$	−18.7439	−	32.4655i	−0.613978	−	1.06344i
$933$	10.4022	−	18.0172i	0.340554	−	0.589857i
$934$	1.02066	−	1.76783i	0.0333969	−	0.0578451i
$935$	12.1218			0.396427
$936$	24.6923	−	4.19670i	0.807094	−	0.137174i
$937$	−26.1978			−0.855846			−0.427923	−	0.903815i	$-0.640755\pi$
$937$	−26.1978			−0.855846			−0.427923	+	0.903815i	$0.640755\pi$
$938$		0			0
$939$	6.29339	−	10.9005i	0.205377	−	0.355723i
$940$	−1.23153	−	2.13308i	−0.0401682	−	0.0695733i
$941$	36.3059			1.18354			0.591769	−	0.806108i	$-0.298430\pi$
$941$	36.3059			1.18354			0.591769	+	0.806108i	$0.298430\pi$
$942$	17.6026	+	30.4887i	0.573525	+	0.993375i
$943$	24.6166	+	42.6372i	0.801627	+	1.38846i
$944$	4.94745			0.161026
$945$		0			0
$946$	−0.247746	+	0.429109i	−0.00805493	+	0.0139516i
$947$	0.459419	−	0.795738i	0.0149291	−	0.0258580i	−0.858464	−	0.512873i	$-0.828581\pi$
$947$	0.459419	−	0.795738i	0.0149291	−	0.0258580i	0.873393	+	0.487015i	$0.161914\pi$
$948$	−33.5163			−1.08856
$949$	−18.8271	+	50.7487i	−0.611153	+	1.64737i
$950$	13.9607			0.452946
$951$	13.4756	−	23.3405i	0.436977	−	0.756867i
$952$		0			0
$953$	9.17943	+	15.8992i	0.297351	+	0.515027i	0.975529	−	0.219871i	$-0.0705635\pi$
$953$	9.17943	+	15.8992i	0.297351	+	0.515027i	−0.678178	+	0.734898i	$0.737230\pi$
$954$	27.0721			0.876493
$955$	9.91370	+	17.1710i	0.320800	+	0.555641i
$956$	−2.08263	−	3.60722i	−0.0673570	−	0.116666i
$957$	32.5474			1.05211
$958$	8.02914	+	13.9069i	0.259410	+	0.449311i
$959$		0			0
$960$	2.62616	−	4.54864i	0.0847589	−	0.146807i
$961$	−26.1345			−0.843050
$962$	12.9222	−	2.19625i	0.416628	−	0.0708101i
$963$	23.7695			0.765962
$964$	−5.21800	+	9.03783i	−0.168060	+	0.291089i
$965$	15.7960	−	27.3594i	0.508491	−	0.880731i
$966$		0			0
$967$	12.5923			0.404940			0.202470	−	0.979288i	$-0.435103\pi$
$967$	12.5923			0.404940			0.202470	+	0.979288i	$0.435103\pi$
$968$	6.45790	+	11.1854i	0.207565	+	0.359512i
$969$	−27.6829	−	47.9482i	−0.889302	−	1.54032i
$970$	14.3509			0.460779
$971$	−10.6654	−	18.4730i	−0.342269	−	0.592827i	0.642585	−	0.766214i	$-0.277862\pi$
$971$	−10.6654	−	18.4730i	−0.342269	−	0.592827i	−0.984854	+	0.173388i	$0.944529\pi$
$972$	16.1308	−	27.9394i	0.517397	−	0.896157i
$973$		0			0
$974$	−2.03712			−0.0652736
$975$	−18.4826	−	22.3053i	−0.591918	−	0.714343i
$976$	5.64762			0.180776
$977$	21.2140	−	36.7437i	0.678695	−	1.17553i	−0.296679	−	0.954977i	$-0.595879\pi$
$977$	21.2140	−	36.7437i	0.678695	−	1.17553i	0.975374	−	0.220557i	$-0.0707874\pi$
$978$	3.40421	−	5.89626i	0.108854	−	0.188542i
$979$	1.08318	+	1.87613i	0.0346187	+	0.0599614i
$980$		0			0
$981$	−16.9172	−	29.3014i	−0.540124	−	0.935523i
$982$	−8.06889	−	13.9757i	−0.257489	−	0.445983i
$983$	−2.09758			−0.0669023			−0.0334511	−	0.999440i	$-0.510650\pi$
$983$	−2.09758			−0.0669023			−0.0334511	+	0.999440i	$0.510650\pi$
$984$	23.2711	+	40.3068i	0.741856	+	1.28493i
$985$	4.32965	−	7.49917i	0.137954	−	0.238943i
$986$	−7.78198	+	13.4788i	−0.247829	+	0.429252i
$987$		0			0
$988$	20.2661	+	24.4576i	0.644750	+	0.778101i
$989$	−1.83213			−0.0582584
$990$	−3.08577	+	5.34471i	−0.0980723	+	0.169866i
$991$	13.8174	−	23.9325i	0.438926	−	0.760241i	−0.558681	−	0.829382i	$-0.688693\pi$
$991$	13.8174	−	23.9325i	0.438926	−	0.760241i	0.997607	+	0.0691411i	$0.0220259\pi$
$992$	−6.43809	−	11.1511i	−0.204409	−	0.354048i
$993$	−48.2703			−1.53181
$994$		0			0
$995$	−3.14227	−	5.44257i	−0.0996166	−	0.172541i
$996$	4.91400			0.155706
$997$	−1.01392	−	1.75615i	−0.0321110	−	0.0556180i	0.849523	−	0.527551i	$-0.176890\pi$
$997$	−1.01392	−	1.75615i	−0.0321110	−	0.0556180i	−0.881634	+	0.471933i	$0.843556\pi$
$998$	−6.39794	+	11.0816i	−0.202523	+	0.350781i
$999$	1.24535	−	2.15701i	0.0394012	−	0.0682449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.f.i.295.3		8
7.2	even	3		637.2.h.i.165.2		8
7.3	odd	6		637.2.g.k.373.3		8
7.4	even	3		637.2.g.j.373.3		8
7.5	odd	6		637.2.h.h.165.2		8
7.6	odd	2		91.2.f.c.22.3	✓	8
13.3	even	3	inner	637.2.f.i.393.3		8
13.4	even	6		8281.2.a.bt.1.3		4
13.9	even	3		8281.2.a.bp.1.2		4
21.20	even	2		819.2.o.h.568.2		8
28.27	even	2		1456.2.s.q.113.4		8
91.3	odd	6		637.2.h.h.471.2		8
91.6	even	12		1183.2.c.g.337.6		8
91.16	even	3		637.2.g.j.263.3		8
91.20	even	12		1183.2.c.g.337.3		8
91.48	odd	6		1183.2.a.k.1.2		4
91.55	odd	6		91.2.f.c.29.3	yes	8
91.68	odd	6		637.2.g.k.263.3		8
91.69	odd	6		1183.2.a.l.1.3		4
91.81	even	3		637.2.h.i.471.2		8
273.146	even	6		819.2.o.h.757.2		8
364.55	even	6		1456.2.s.q.1121.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.3	✓	8	7.6	odd	2
91.2.f.c.29.3	yes	8	91.55	odd	6
637.2.f.i.295.3		8	1.1	even	1	trivial
637.2.f.i.393.3		8	13.3	even	3	inner
637.2.g.j.263.3		8	91.16	even	3
637.2.g.j.373.3		8	7.4	even	3
637.2.g.k.263.3		8	91.68	odd	6
637.2.g.k.373.3		8	7.3	odd	6
637.2.h.h.165.2		8	7.5	odd	6
637.2.h.h.471.2		8	91.3	odd	6
637.2.h.i.165.2		8	7.2	even	3
637.2.h.i.471.2		8	91.81	even	3
819.2.o.h.568.2		8	21.20	even	2
819.2.o.h.757.2		8	273.146	even	6
1183.2.a.k.1.2		4	91.48	odd	6
1183.2.a.l.1.3		4	91.69	odd	6
1183.2.c.g.337.3		8	91.20	even	12
1183.2.c.g.337.6		8	91.6	even	12
1456.2.s.q.113.4		8	28.27	even	2
1456.2.s.q.1121.4		8	364.55	even	6
8281.2.a.bp.1.2		4	13.9	even	3
8281.2.a.bt.1.3		4	13.4	even	6

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.355143 - 0.615126i) q^{2} +(1.20394 - 2.08529i) q^{3} +(0.747746 + 1.29513i) q^{4} +1.28971 q^{5} +(-0.855143 - 1.48115i) q^{6} +2.48280 q^{8} +(-1.39895 - 2.42305i) q^{9} +O(q^{10})\)	\(q+(0.355143 - 0.615126i) q^{2} +(1.20394 - 2.08529i) q^{3} +(0.747746 + 1.29513i) q^{4} +1.28971 q^{5} +(-0.855143 - 1.48115i) q^{6} +2.48280 q^{8} +(-1.39895 - 2.42305i) q^{9} +(0.458033 - 0.793337i) q^{10} +(1.20394 - 2.08529i) q^{11} +3.60097 q^{12} +(-1.25409 + 3.38042i) q^{13} +(1.55274 - 2.68942i) q^{15} +(-0.613742 + 1.06303i) q^{16} +(1.95169 + 3.38042i) q^{17} -1.98731 q^{18} +(-2.94534 - 5.10148i) q^{19} +(0.964379 + 1.67035i) q^{20} +(-0.855143 - 1.48115i) q^{22} +(3.16197 - 5.47670i) q^{23} +(2.98915 - 5.17736i) q^{24} -3.33664 q^{25} +(1.63400 + 1.97196i) q^{26} +0.486640 q^{27} +(-2.80683 + 4.86157i) q^{29} +(-1.10289 - 1.91026i) q^{30} -2.20578 q^{31} +(2.91873 + 5.05540i) q^{32} +(-2.89895 - 5.02113i) q^{33} +2.77252 q^{34} +(2.09212 - 3.62365i) q^{36} +(2.55908 - 4.43246i) q^{37} -4.18407 q^{38} +(5.53930 + 6.68497i) q^{39} +3.20210 q^{40} +(-3.89260 + 6.74219i) q^{41} +(-0.144857 - 0.250899i) q^{43} +3.60097 q^{44} +(-1.80424 - 3.12504i) q^{45} +(-2.24591 - 3.89003i) q^{46} -1.27702 q^{47} +(1.47782 + 2.55966i) q^{48} +(-1.18499 + 2.05245i) q^{50} +9.39887 q^{51} +(-5.31585 + 0.903480i) q^{52} -13.6225 q^{53} +(0.172827 - 0.299345i) q^{54} +(1.55274 - 2.68942i) q^{55} -14.1841 q^{57} +(1.99365 + 3.45311i) q^{58} +(-2.01528 - 3.49057i) q^{59} +4.64422 q^{60} +(-2.30049 - 3.98456i) q^{61} +(-0.783368 + 1.35683i) q^{62} +1.69131 q^{64} +(-1.61742 + 4.35978i) q^{65} -4.11817 q^{66} +(-3.78779 + 6.56065i) q^{67} +(-2.91873 + 5.05540i) q^{68} +(-7.61366 - 13.1872i) q^{69} +(-3.61366 - 6.25905i) q^{71} +(-3.47331 - 6.01595i) q^{72} +15.0125 q^{73} +(-1.81768 - 3.14832i) q^{74} +(-4.01712 + 6.95785i) q^{75} +(4.40474 - 7.62923i) q^{76} +(6.07935 - 1.03324i) q^{78} -9.30758 q^{79} +(-0.791552 + 1.37101i) q^{80} +(4.78273 - 8.28393i) q^{81} +(2.76486 + 4.78888i) q^{82} +1.36463 q^{83} +(2.51712 + 4.35978i) q^{85} -0.205780 q^{86} +(6.75852 + 11.7061i) q^{87} +(2.98915 - 5.17736i) q^{88} +(-0.449849 + 0.779162i) q^{89} -2.56306 q^{90} +9.45742 q^{92} +(-2.65563 + 4.59968i) q^{93} +(-0.453526 + 0.785530i) q^{94} +(-3.79865 - 6.57945i) q^{95} +14.0559 q^{96} +(7.83288 + 13.5669i) q^{97} -6.73701 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + q^{3} - 5 q^{4} + 14 q^{5} - 5 q^{6} - 12 q^{8} - 7 q^{9}+O(q^{10}) \) 8 * q + q^2 + q^3 - 5 * q^4 + 14 * q^5 - 5 * q^6 - 12 * q^8 - 7 * q^9	\( 8 q + q^{2} + q^{3} - 5 q^{4} + 14 q^{5} - 5 q^{6} - 12 q^{8} - 7 q^{9} - 11 q^{10} + q^{11} - 24 q^{12} - 4 q^{13} - 3 q^{15} - 19 q^{16} - 4 q^{17} - 6 q^{18} + q^{19} - 2 q^{20} - 5 q^{22} + 2 q^{23} - 3 q^{24} + 10 q^{25} - 12 q^{26} + 52 q^{27} - q^{29} + 4 q^{30} + 8 q^{31} + 33 q^{32} - 19 q^{33} - 6 q^{34} + 34 q^{36} + 10 q^{37} + 46 q^{38} + 20 q^{39} + 34 q^{40} - 22 q^{41} - 3 q^{43} - 24 q^{44} - 11 q^{45} - 24 q^{46} - 4 q^{47} + 11 q^{48} - 43 q^{50} + 14 q^{51} - 65 q^{52} + 4 q^{53} + 5 q^{54} - 3 q^{55} - 34 q^{57} + 11 q^{58} - 8 q^{59} - 22 q^{60} + 8 q^{61} - 5 q^{62} + 28 q^{64} + 7 q^{65} - 12 q^{66} + 6 q^{67} - 33 q^{68} - 18 q^{69} + 14 q^{71} - 5 q^{72} + 16 q^{73} - 20 q^{74} - 7 q^{75} + 32 q^{76} - q^{78} - 52 q^{79} + 7 q^{80} - 24 q^{81} - 14 q^{82} - 5 q^{85} + 24 q^{86} + 13 q^{87} - 3 q^{88} - q^{89} - 52 q^{90} + 24 q^{92} + 7 q^{93} + 33 q^{94} - 21 q^{95} + 116 q^{96} + 3 q^{97} + 46 q^{99}+O(q^{100}) \) 8 * q + q^2 + q^3 - 5 * q^4 + 14 * q^5 - 5 * q^6 - 12 * q^8 - 7 * q^9 - 11 * q^10 + q^11 - 24 * q^12 - 4 * q^13 - 3 * q^15 - 19 * q^16 - 4 * q^17 - 6 * q^18 + q^19 - 2 * q^20 - 5 * q^22 + 2 * q^23 - 3 * q^24 + 10 * q^25 - 12 * q^26 + 52 * q^27 - q^29 + 4 * q^30 + 8 * q^31 + 33 * q^32 - 19 * q^33 - 6 * q^34 + 34 * q^36 + 10 * q^37 + 46 * q^38 + 20 * q^39 + 34 * q^40 - 22 * q^41 - 3 * q^43 - 24 * q^44 - 11 * q^45 - 24 * q^46 - 4 * q^47 + 11 * q^48 - 43 * q^50 + 14 * q^51 - 65 * q^52 + 4 * q^53 + 5 * q^54 - 3 * q^55 - 34 * q^57 + 11 * q^58 - 8 * q^59 - 22 * q^60 + 8 * q^61 - 5 * q^62 + 28 * q^64 + 7 * q^65 - 12 * q^66 + 6 * q^67 - 33 * q^68 - 18 * q^69 + 14 * q^71 - 5 * q^72 + 16 * q^73 - 20 * q^74 - 7 * q^75 + 32 * q^76 - q^78 - 52 * q^79 + 7 * q^80 - 24 * q^81 - 14 * q^82 - 5 * q^85 + 24 * q^86 + 13 * q^87 - 3 * q^88 - q^89 - 52 * q^90 + 24 * q^92 + 7 * q^93 + 33 * q^94 - 21 * q^95 + 116 * q^96 + 3 * q^97 + 46 * q^99

Introduction

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