LMFDB - Embedded newform 91.2.f.c.22.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(22,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, 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("91.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.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:	$0.726638658394$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.3
Root			$0.355143 - 0.615126i$ of defining polynomial
Character	$\chi$	$=$	91.22
Dual form			91.2.f.c.29.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.355143 - 0.615126i) q^{2} +(-1.20394 + 2.08529i) q^{3} +(0.747746 + 1.29513i) q^{4} -1.28971 q^{5} +(0.855143 + 1.48115i) q^{6} +(0.500000 + 0.866025i) q^{7} +2.48280 q^{8} +(-1.39895 - 2.42305i) q^{9} +O(q^{10})$	\(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} +(0.500000 + 0.866025i) q^{7} +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} +0.710287 q^{14} +(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} -2.40788 q^{21} +(-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} +(-0.747746 + 1.29513i) q^{28} +(-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} +(-0.644857 - 1.11692i) q^{35} +(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} +(-0.855143 + 1.48115i) q^{42} +(-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} +(-0.500000 + 0.866025i) q^{49} +(-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} +(1.24140 + 2.15017i) q^{56} -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} +(1.39895 - 2.42305i) q^{63} +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} -0.916066 q^{70} +(-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} +2.40788 q^{77} +(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} +(-1.80049 - 3.11853i) q^{84} +(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} +(3.55458 - 0.604136i) q^{91} +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} +(0.355143 + 0.615126i) q^{98} -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} + 4 q^{7} - 12 q^{8} - 7 q^{9}+O(q^{10}) $ 8 * q + q^2 - q^3 - 5 * q^4 - 14 * q^5 + 5 * q^6 + 4 * q^7 - 12 * q^8 - 7 * q^9	\( 8 q + q^{2} - q^{3} - 5 q^{4} - 14 q^{5} + 5 q^{6} + 4 q^{7} - 12 q^{8} - 7 q^{9} + 11 q^{10} + q^{11} + 24 q^{12} + 4 q^{13} + 2 q^{14} - 3 q^{15} - 19 q^{16} + 4 q^{17} - 6 q^{18} - q^{19} + 2 q^{20} - 2 q^{21} - 5 q^{22} + 2 q^{23} + 3 q^{24} + 10 q^{25} + 12 q^{26} - 52 q^{27} + 5 q^{28} - q^{29} + 4 q^{30} - 8 q^{31} + 33 q^{32} + 19 q^{33} + 6 q^{34} - 7 q^{35} + 34 q^{36} + 10 q^{37} - 46 q^{38} + 20 q^{39} - 34 q^{40} + 22 q^{41} - 5 q^{42} - 3 q^{43} - 24 q^{44} + 11 q^{45} - 24 q^{46} + 4 q^{47} - 11 q^{48} - 4 q^{49} - 43 q^{50} + 14 q^{51} + 65 q^{52} + 4 q^{53} - 5 q^{54} + 3 q^{55} - 6 q^{56} - 34 q^{57} + 11 q^{58} + 8 q^{59} - 22 q^{60} - 8 q^{61} + 5 q^{62} + 7 q^{63} + 28 q^{64} + 7 q^{65} + 12 q^{66} + 6 q^{67} + 33 q^{68} + 18 q^{69} + 22 q^{70} + 14 q^{71} - 5 q^{72} - 16 q^{73} - 20 q^{74} + 7 q^{75} - 32 q^{76} + 2 q^{77} - q^{78} - 52 q^{79} - 7 q^{80} - 24 q^{81} + 14 q^{82} + 12 q^{84} - 5 q^{85} + 24 q^{86} - 13 q^{87} - 3 q^{88} + q^{89} + 52 q^{90} - 4 q^{91} + 24 q^{92} + 7 q^{93} - 33 q^{94} - 21 q^{95} - 116 q^{96} - 3 q^{97} + q^{98} + 46 q^{99}+O(q^{100}) \) 8 * q + q^2 - q^3 - 5 * q^4 - 14 * q^5 + 5 * q^6 + 4 * q^7 - 12 * q^8 - 7 * q^9 + 11 * q^10 + q^11 + 24 * q^12 + 4 * q^13 + 2 * q^14 - 3 * q^15 - 19 * q^16 + 4 * q^17 - 6 * q^18 - q^19 + 2 * q^20 - 2 * q^21 - 5 * q^22 + 2 * q^23 + 3 * q^24 + 10 * q^25 + 12 * q^26 - 52 * q^27 + 5 * q^28 - q^29 + 4 * q^30 - 8 * q^31 + 33 * q^32 + 19 * q^33 + 6 * q^34 - 7 * q^35 + 34 * q^36 + 10 * q^37 - 46 * q^38 + 20 * q^39 - 34 * q^40 + 22 * q^41 - 5 * q^42 - 3 * q^43 - 24 * q^44 + 11 * q^45 - 24 * q^46 + 4 * q^47 - 11 * q^48 - 4 * q^49 - 43 * q^50 + 14 * q^51 + 65 * q^52 + 4 * q^53 - 5 * q^54 + 3 * q^55 - 6 * q^56 - 34 * q^57 + 11 * q^58 + 8 * q^59 - 22 * q^60 - 8 * q^61 + 5 * q^62 + 7 * q^63 + 28 * q^64 + 7 * q^65 + 12 * q^66 + 6 * q^67 + 33 * q^68 + 18 * q^69 + 22 * q^70 + 14 * q^71 - 5 * q^72 - 16 * q^73 - 20 * q^74 + 7 * q^75 - 32 * q^76 + 2 * q^77 - q^78 - 52 * q^79 - 7 * q^80 - 24 * q^81 + 14 * q^82 + 12 * q^84 - 5 * q^85 + 24 * q^86 - 13 * q^87 - 3 * q^88 + q^89 + 52 * q^90 - 4 * q^91 + 24 * q^92 + 7 * q^93 - 33 * q^94 - 21 * q^95 - 116 * q^96 - 3 * q^97 + q^98 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	$0.411305\pi$
$3$	−1.20394	+	2.08529i	−0.695096	+	1.20394i	−0.970148	+	0.242512i	$0.922029\pi$
$4$	0.747746	+	1.29513i	0.373873	+	0.647567i
$5$	−1.28971			−0.576777			−0.288389	−	0.957513i	$-0.593120\pi$
$5$	−1.28971			−0.576777			−0.288389	+	0.957513i	$0.593120\pi$
$6$	0.855143	+	1.48115i	0.349111	+	0.604678i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	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
$14$	0.710287			0.189832
$15$	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	0.526181	−	0.850373i	$-0.323623\pi$
$17$	−1.95169	−	3.38042i	−0.473354	−	0.819873i	−0.999535	+	0.0304998i	$0.990290\pi$
$18$	−1.98731			−0.468413
$19$	2.94534	+	5.10148i	0.675708	+	1.17036i	0.976261	+	0.216595i	$0.0694952\pi$
$19$	2.94534	+	5.10148i	0.675708	+	1.17036i	−0.300554	+	0.953765i	$0.597171\pi$
$20$	−0.964379	−	1.67035i	−0.215642	−	0.373502i
$21$	−2.40788			−0.525443
$22$	−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
$28$	−0.747746	+	1.29513i	−0.141311	+	0.244757i
$29$	−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	$-0.436528\pi$
$31$	2.20578			0.396170			0.198085	+	0.980185i	$0.436528\pi$
$32$	2.91873	+	5.05540i	0.515964	+	0.893676i
$33$	2.89895	+	5.02113i	0.504642	+	0.874066i
$34$	−2.77252			−0.475482
$35$	−0.644857	−	1.11692i	−0.109001	−	0.188795i
$36$	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	$-0.625336\pi$
$41$	3.89260	−	6.74219i	0.607922	−	1.05295i	0.991582	−	0.129478i	$-0.0413302\pi$
$42$	−0.855143	+	1.48115i	−0.131951	+	0.228547i
$43$	−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	$-0.470311\pi$
$47$	1.27702			0.186273			0.0931364	+	0.995653i	$0.470311\pi$
$48$	−1.47782	−	2.55966i	−0.213305	−	0.369455i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−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
$56$	1.24140	+	2.15017i	0.165889	+	0.287328i
$57$	−14.1841			−1.87873
$58$	1.99365	+	3.45311i	0.261780	+	0.453416i
$59$	2.01528	+	3.49057i	0.262367	+	0.454433i	0.966870	−	0.255268i	$-0.0821636\pi$
$59$	2.01528	+	3.49057i	0.262367	+	0.454433i	−0.704503	+	0.709701i	$0.748830\pi$
$60$	4.64422			0.599566
$61$	2.30049	+	3.98456i	0.294547	+	0.510170i	0.974879	−	0.222733i	$-0.0714979\pi$
$61$	2.30049	+	3.98456i	0.294547	+	0.510170i	−0.680332	+	0.732904i	$0.738165\pi$
$62$	0.783368	−	1.35683i	0.0994878	−	0.172318i
$63$	1.39895	−	2.42305i	0.176251	−	0.305276i
$64$	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
$70$	−0.916066			−0.109491
$71$	−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	$-0.841483\pi$
$73$	−15.0125			−1.75708			−0.878542	+	0.477665i	$0.841483\pi$
$74$	−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
$77$	2.40788			0.274404
$78$	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	$-0.523862\pi$
$83$	−1.36463			−0.149788			−0.0748940	+	0.997192i	$0.523862\pi$
$84$	−1.80049	−	3.11853i	−0.196449	−	0.340260i
$85$	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	−0.841198	−	0.540727i	$-0.818149\pi$
$89$	0.449849	−	0.779162i	0.0476839	−	0.0825910i	0.888882	+	0.458136i	$0.151483\pi$
$90$	2.56306			0.270170
$91$	3.55458	−	0.604136i	0.372621	−	0.0633306i
$92$	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	$-0.873975\pi$
$97$	−7.83288	−	13.5669i	−0.795309	−	1.37752i	0.127334	−	0.991860i	$-0.459358\pi$
$98$	0.355143	+	0.615126i	0.0358749	+	0.0621371i
$99$	−6.73701			−0.677095
$100$	−2.49496	−	4.32140i	−0.249496	−	0.432140i
$101$	−0.342452	+	0.593145i	−0.0340753	+	0.0590201i	−0.882560	−	0.470200i	$-0.844182\pi$
$101$	−0.342452	+	0.593145i	−0.0340753	+	0.0590201i	0.848485	+	0.529220i	$0.177515\pi$
$102$	3.33795	−	5.78149i	0.330506	−	0.572453i
$103$	17.9249			1.76619			0.883097	−	0.469190i	$-0.155454\pi$
$103$	17.9249			1.76619			0.883097	+	0.469190i	$0.155454\pi$
$104$	3.11366	−	8.39292i	0.305320	−	0.822993i
$105$	3.10548			0.303064
$106$	−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
$112$	−1.22748			−0.115986
$113$	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
$119$	1.95169	−	3.38042i	0.178911	−	0.309883i
$120$	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
$126$	−0.993655	−	1.72106i	−0.0885218	−	0.153324i
$127$	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	$-0.822661\pi$
$131$	−19.4294			−1.69756			−0.848778	+	0.528749i	$0.822661\pi$
$132$	−4.33536	+	7.50906i	−0.377344	+	0.653580i
$133$	−2.94534	+	5.10148i	−0.255394	+	0.442355i
$134$	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	0.639929	−	0.768434i	$-0.278964\pi$
$139$	−4.07361	−	7.05571i	−0.345519	−	0.598457i	−0.985448	+	0.169977i	$0.945631\pi$
$140$	0.964379	−	1.67035i	0.0815049	−	0.141171i
$141$	−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
$147$	−1.20394	−	2.08529i	−0.0992994	−	0.171992i
$148$	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
$154$	0.855143	−	1.48115i	0.0689094	−	0.119355i
$155$	−2.84482			−0.228502
$156$	−4.51595	+	12.1728i	−0.361565	+	0.974604i
$157$	20.5844			1.64282			0.821409	−	0.570340i	$-0.193189\pi$
$157$	20.5844			1.64282			0.821409	+	0.570340i	$0.193189\pi$
$158$	−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
$161$	6.32395			0.498397
$162$	−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	−0.983634	−	0.180177i	$-0.942333\pi$
$167$	−4.33923	+	7.51576i	−0.335780	+	0.581587i	0.647855	+	0.761764i	$0.275666\pi$
$168$	−5.97829			−0.461235
$169$	−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	0.847728	−	0.530431i	$-0.177970\pi$
$173$	−0.466967	−	0.808810i	−0.0355028	−	0.0614927i	−0.883231	+	0.468938i	$0.844637\pi$
$174$	−9.60097			−0.727848
$175$	−1.66832	−	2.88961i	−0.126113	−	0.218434i
$176$	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	$-0.606839\pi$
$181$	−8.86269			−0.658759			−0.329379	+	0.944198i	$0.606839\pi$
$182$	0.890765	−	2.40107i	0.0660279	−	0.177979i
$183$	−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
$189$	−0.243320	−	0.421442i	−0.0176989	−	0.0306554i
$190$	−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
$196$	−1.49549			−0.106821
$197$	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	0.939367	−	0.342913i	$-0.111414\pi$
$199$	2.43641	+	4.21998i	0.172712	+	0.299147i	−0.766655	+	0.642059i	$0.778080\pi$
$200$	−8.28421			−0.585782
$201$	−9.12056	−	15.7973i	−0.643315	−	1.11425i
$202$	0.243239	+	0.421303i	0.0171143	+	0.0296428i
$203$	−5.61366			−0.394002
$204$	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
$210$	1.10289	−	1.91026i	0.0761066	−	0.131821i
$211$	−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
$217$	1.10289	+	1.91026i	0.0748690	+	0.129677i
$218$	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	−0.975014	−	0.222145i	$-0.928694\pi$
$223$	−4.40713	+	7.63338i	−0.295123	+	0.511169i	0.679890	+	0.733314i	$0.262027\pi$
$224$	−2.91873	+	5.05540i	−0.195016	+	0.337778i
$225$	4.66779	+	8.08484i	0.311186	+	0.538990i
$226$	10.1235			0.673406
$227$	6.72557	+	11.6490i	0.446391	+	0.773173i	0.998148	−	0.0608325i	$-0.0193756\pi$
$227$	6.72557	+	11.6490i	0.446391	+	0.773173i	−0.551757	+	0.834005i	$0.686042\pi$
$228$	−10.6061	−	18.3703i	−0.702406	−	1.21660i
$229$	6.81576			0.450398			0.225199	−	0.974313i	$-0.427697\pi$
$229$	6.81576			0.450398			0.225199	+	0.974313i	$0.427697\pi$
$230$	2.89658	+	5.01702i	0.190995	+	0.330812i
$231$	−2.89895	+	5.02113i	−0.190737	+	0.330366i
$232$	−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
$238$	−1.38626	−	2.40107i	−0.0898577	−	0.155638i
$239$	−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	0.731490	−	0.681852i	$-0.238825\pi$
$241$	−3.48915	−	6.04338i	−0.224756	−	0.389288i	−0.956246	+	0.292563i	$0.905492\pi$
$242$	3.69498			0.237523
$243$	10.7863	+	18.6824i	0.691941	+	1.19848i
$244$	−3.44036	+	5.95888i	−0.220246	+	0.381478i
$245$	0.644857	−	1.11692i	0.0411984	−	0.0713577i
$246$	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	0.878117	−	0.478446i	$-0.158800\pi$
$251$	0.391515	+	0.678123i	0.0247122	+	0.0428028i	−0.853405	+	0.521249i	$0.825466\pi$
$252$	4.18424			0.263582
$253$	−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	−0.912350	−	0.409410i	$-0.865734\pi$
$257$	−1.62902	+	2.82155i	−0.101616	+	0.176003i	0.810735	+	0.585414i	$0.199068\pi$
$258$	0.247746	−	0.429109i	0.0154240	−	0.0267152i
$259$	5.11817			0.318028
$260$	−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
$266$	2.09204	+	3.62351i	0.128271	+	0.222172i
$267$	1.08318	+	1.87613i	0.0662898	+	0.114817i
$268$	−11.3292			−0.692043
$269$	−0.618249	−	1.07084i	−0.0376953	−	0.0652902i	0.846562	−	0.532290i	$-0.178668\pi$
$269$	−0.618249	−	1.07084i	−0.0376953	−	0.0652902i	−0.884258	+	0.467000i	$0.845335\pi$
$270$	0.222897	−	0.386069i	0.0135651	−	0.0234954i
$271$	−12.6036	+	21.8300i	−0.765612	+	1.32608i	0.174311	+	0.984691i	$0.444230\pi$
$271$	−12.6036	+	21.8300i	−0.765612	+	1.32608i	−0.939923	+	0.341388i	$0.889103\pi$
$272$	4.79133			0.290517
$273$	−3.01971	+	8.13966i	−0.182761	+	0.492635i
$274$	−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
$280$	−1.60105	−	2.77310i	−0.0956811	−	0.165725i
$281$	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	−0.984392	−	0.175992i	$-0.943687\pi$
$283$	−5.71602	+	9.90044i	−0.339782	+	0.588520i	0.644609	+	0.764512i	$0.277020\pi$
$284$	5.40421	−	9.36036i	0.320681	−	0.555435i
$285$	18.2934			1.08361
$286$	−6.07935	+	1.03324i	−0.359479	+	0.0610971i
$287$	7.78521			0.459546
$288$	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	0.969700	−	0.244299i	$-0.0785579\pi$
$293$	4.67781	+	8.10220i	0.273281	+	0.473336i	−0.696419	+	0.717635i	$0.745225\pi$
$294$	−1.71029			−0.0997459
$295$	−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
$301$	0.144857	−	0.250899i	0.00834940	−	0.0144616i
$302$	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	$-0.425617\pi$
$307$	8.11449			0.463119			0.231559	+	0.972821i	$0.425617\pi$
$308$	1.80049	+	3.11853i	0.102592	+	0.177695i
$309$	−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	$-0.578778\pi$
$311$	−8.64016			−0.489938			−0.244969	+	0.969531i	$0.578778\pi$
$312$	13.7530	+	16.5975i	0.778609	+	0.939646i
$313$	−5.22732			−0.295466			−0.147733	−	0.989027i	$-0.547198\pi$
$313$	−5.22732			−0.295466			−0.147733	+	0.989027i	$0.547198\pi$
$314$	7.31043	−	12.6620i	0.412551	−	0.714560i
$315$	−1.80424	+	3.12504i	−0.101658	+	0.176076i
$316$	−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
$322$	2.24591	−	3.89003i	0.125160	−	0.216783i
$323$	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
$329$	0.638511	+	1.10593i	0.0352023	+	0.0609721i
$330$	−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
$336$	1.47782	−	2.55966i	0.0806217	−	0.139641i
$337$	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
$343$	−1.00000			−0.0539949
$344$	−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	−0.959319	−	0.282323i	$-0.908895\pi$
$349$	−4.39316	+	7.60917i	−0.235160	+	0.407310i	0.724159	+	0.689633i	$0.242228\pi$
$350$	−2.36997			−0.126680
$351$	−0.610291	+	1.64505i	−0.0325749	+	0.0878061i
$352$	14.0559			0.749184
$353$	−3.85949	+	6.68483i	−0.205420	+	0.355798i	−0.950266	−	0.311438i	$-0.899189\pi$
$353$	−3.85949	+	6.68483i	−0.205420	+	0.355798i	0.744847	+	0.667236i	$0.232523\pi$
$354$	−3.44671	+	5.96987i	−0.183190	+	0.317295i
$355$	4.66059	+	8.07238i	0.247358	+	0.428437i
$356$	1.34549			0.0713110
$357$	4.69943	+	8.13966i	0.248720	+	0.430796i
$358$	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
$364$	3.44036	+	4.15192i	0.180324	+	0.217620i
$365$	19.3619			1.01345
$366$	−3.93449	+	6.81474i	−0.205659	+	0.356212i
$367$	−2.91033	+	5.04085i	−0.151918	+	0.263130i	−0.931933	−	0.362632i	$-0.881878\pi$
$367$	−2.91033	+	5.04085i	−0.151918	+	0.263130i	0.780014	+	0.625762i	$0.215212\pi$
$368$	3.88128	+	6.72257i	0.202325	+	0.350438i
$369$	−21.7822			−1.13394
$370$	2.34429	+	4.06043i	0.121874	+	0.211092i
$371$	−6.81126	−	11.7974i	−0.353623	−	0.612493i
$372$	−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
$378$	−0.345654			−0.0177785
$379$	−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	0.980666	−	0.195688i	$-0.0626941\pi$
$383$	6.27939	+	10.8762i	0.320862	+	0.555749i	−0.659804	+	0.751438i	$0.729361\pi$
$384$	−12.6096	−	21.8405i	−0.643482	−	1.11454i
$385$	−3.10548			−0.158270
$386$	−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
$392$	−1.24140	+	2.15017i	−0.0627002	+	0.108600i
$393$	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	0.894009	−	0.448049i	$-0.147881\pi$
$397$	1.17522	+	2.03554i	0.0589827	+	0.102161i	−0.835026	+	0.550210i	$0.814548\pi$
$398$	3.46110			0.173489
$399$	−7.09204	−	12.2838i	−0.355046	−	0.614958i
$400$	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
$406$	−1.99365	+	3.45311i	−0.0989434	+	0.171375i
$407$	−6.16197	−	10.6729i	−0.305438	−	0.529034i
$408$	23.3355			1.15528
$409$	4.01205	+	6.94908i	0.198383	+	0.343610i	0.948004	−	0.318257i	$-0.103098\pi$
$409$	4.01205	+	6.94908i	0.198383	+	0.343610i	−0.749621	+	0.661867i	$0.769764\pi$
$410$	3.56588	+	6.17629i	0.176106	+	0.305025i
$411$	24.6475			1.21577
$412$	13.4033	+	23.2152i	0.660333	+	1.14373i
$413$	−2.01528	+	3.49057i	−0.0991654	+	0.171760i
$414$	−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	−0.687575	−	0.726113i	$-0.741325\pi$
$419$	5.83472	−	10.1060i	0.285045	−	0.493712i	0.972620	+	0.232401i	$0.0746582\pi$
$420$	2.32211	+	4.02201i	0.113307	+	0.196254i
$421$	−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
$427$	−2.30049	+	3.98456i	−0.111328	+	0.192826i
$428$	−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	$0.0957291\pi$
$433$	15.2756	+	26.4582i	0.734100	+	1.27150i	−0.221017	+	0.975270i	$0.570938\pi$
$434$	1.56674			0.0752057
$435$	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	−0.683903	−	0.729573i	$-0.739719\pi$
$439$	6.07361	−	10.5198i	0.289878	−	0.502083i	0.973780	+	0.227490i	$0.0730520\pi$
$440$	−3.85514	+	6.67730i	−0.183787	+	0.318328i
$441$	2.79790			0.133233
$442$	−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
$448$	0.845654	+	1.46472i	0.0399534	+	0.0692013i
$449$	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
$455$	−4.58439	+	0.779162i	−0.214919	+	0.0365277i
$456$	−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	0.953629	−	0.300985i	$-0.0973154\pi$
$461$	4.64102	+	8.03848i	0.216154	+	0.374389i	−0.737475	+	0.675374i	$0.763982\pi$
$462$	2.05908	+	3.56644i	0.0957973	+	0.165926i
$463$	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	$-0.521182\pi$
$467$	−2.87393			−0.132990			−0.0664948	+	0.997787i	$0.521182\pi$
$468$	−9.62577	−	11.6166i	−0.444951	−	0.536979i
$469$	−7.57559			−0.349808
$470$	−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
$476$	5.83747			0.267560
$477$	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	$-0.660569\pi$
$479$	11.3041	−	19.5792i	0.516497	−	0.894598i	0.999817	−	0.0191546i	$-0.00609749\pi$
$480$	18.1281			0.827432
$481$	−11.7743	−	14.2095i	−0.536861	−	0.647898i
$482$	−4.95659			−0.225766
$483$	−7.61366	+	13.1872i	−0.346434	+	0.600041i
$484$	−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
$490$	−0.458033	−	0.793337i	−0.0206918	−	0.0358393i
$491$	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
$497$	3.61366	−	6.25905i	0.162095	−	0.280757i
$498$	−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	$0.0776841\pi$
$503$	15.5748	+	26.9764i	0.694447	+	1.20282i	−0.275920	+	0.961181i	$0.588983\pi$
$504$	3.47331	−	6.01595i	0.154714	−	0.267972i
$505$	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	$-0.493902\pi$
$509$	19.7509	−	34.2096i	0.875444	−	1.51631i	0.856289	−	0.516497i	$-0.172764\pi$
$510$	−4.30499	+	7.45647i	−0.190628	+	0.330178i
$511$	−7.50626	−	13.0012i	−0.332058	−	0.575141i
$512$	−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
$518$	1.81768	−	3.14832i	0.0798644	−	0.138329i
$519$	2.24880			0.0987115
$520$	−4.01573	+	10.8245i	−0.176101	+	0.474684i
$521$	−17.7672			−0.778394			−0.389197	−	0.921155i	$-0.627247\pi$
$521$	−17.7672			−0.778394			−0.389197	+	0.921155i	$0.627247\pi$
$522$	5.57804	−	9.66145i	0.244144	−	0.422870i
$523$	0.894522	−	1.54936i	0.0391147	−	0.0677487i	−0.845805	−	0.533492i	$-0.820880\pi$
$523$	0.894522	−	1.54936i	0.0391147	−	0.0677487i	0.884920	+	0.465743i	$0.154213\pi$
$524$	−14.5283	−	25.1637i	−0.634671	−	1.09928i
$525$	8.03424			0.350643
$526$	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
$532$	−8.80948			−0.381939
$533$	−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
$539$	1.20394	+	2.08529i	0.0518574	+	0.0898197i
$540$	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
$546$	3.93449	+	4.74825i	0.168381	+	0.203206i
$547$	−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
$553$	−4.65379	−	8.06060i	−0.197899	−	0.342772i
$554$	−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
$560$	1.58310			0.0668983
$561$	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	$-0.889378\pi$
$563$	−18.1530	−	31.4418i	−0.765056	−	1.32512i	0.175161	−	0.984540i	$-0.443955\pi$
$564$	−4.59852			−0.193633
$565$	−9.19095	−	15.9192i	−0.386666	−	0.669726i
$566$	4.06001	+	7.03215i	0.170655	+	0.295583i
$567$	9.56546			0.401712
$568$	−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
$574$	2.76486	−	4.78888i	0.115403	−	0.199884i
$575$	−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	$-0.849740\pi$
$577$	−42.7876			−1.78127			−0.890636	+	0.454717i	$0.849740\pi$
$578$	−0.626353	−	1.08487i	−0.0260528	−	0.0451248i
$579$	29.4909	+	51.0798i	1.22560	+	2.12280i
$580$	10.8274			0.449583
$581$	−0.682316	−	1.18181i	−0.0283073	−	0.0490296i
$582$	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	$-0.537907\pi$
$587$	19.3943	−	33.5919i	0.800488	−	1.38649i	0.919296	−	0.393568i	$-0.128759\pi$
$588$	1.80049	−	3.11853i	0.0742508	−	0.128606i
$589$	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	$-0.710877\pi$
$593$	−29.9564			−1.23016			−0.615081	+	0.788464i	$0.710877\pi$
$594$	0.416147	+	0.720787i	0.0170747	+	0.0295743i
$595$	−2.51712	+	4.35978i	−0.103192	+	0.178733i
$596$	−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	−0.925533	−	0.378666i	$-0.876383\pi$
$601$	−3.30544	+	5.72520i	−0.134832	+	0.233536i	0.790701	+	0.612202i	$0.209716\pi$
$602$	−0.102890	−	0.178210i	−0.00419347	−	0.00726331i
$603$	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	0.996309	−	0.0858444i	$-0.0273588\pi$
$607$	10.4416	+	18.0854i	0.423811	+	0.734062i	−0.572498	+	0.819906i	$0.694025\pi$
$608$	−17.1933	+	29.7797i	−0.697282	+	1.20773i
$609$	6.75852	−	11.7061i	0.273869	−	0.474355i
$610$	−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
$616$	5.97829			0.240872
$617$	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	$-0.636159\pi$
$619$	−20.6417			−0.829658			−0.414829	+	0.909899i	$0.636159\pi$
$620$	−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
$623$	0.899698			0.0360457
$624$	−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
$630$	1.28153	+	2.21967i	0.0510574	+	0.0884339i
$631$	−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
$637$	2.30049	+	2.77629i	0.0911486	+	0.110000i
$638$	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	0.925795	−	0.378025i	$-0.123397\pi$
$643$	3.43641	+	5.95203i	0.135519	+	0.234725i	−0.790277	+	0.612750i	$0.790063\pi$
$644$	4.72871	+	8.19037i	0.186337	+	0.322746i
$645$	−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	$-0.602493\pi$
$647$	16.8715	−	29.2224i	0.663289	−	1.14885i	0.979746	−	0.200243i	$-0.0641732\pi$
$648$	11.8746	−	20.5674i	0.466477	−	0.807962i
$649$	9.70511			0.380959
$650$	5.45208	+	6.57972i	0.213848	+	0.258078i
$651$	−5.31126			−0.208165
$652$	−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
$658$	0.907052			0.0353606
$659$	−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	−0.847807	−	0.530306i	$-0.822077\pi$
$661$	0.908971	−	1.57438i	0.0353549	−	0.0612364i	0.883161	+	0.469069i	$0.155411\pi$
$662$	−14.2389			−0.553412
$663$	11.7870	−	31.7721i	0.457771	−	1.23393i
$664$	−3.38811			−0.131484
$665$	3.79865	−	6.57945i	0.147305	−	0.255140i
$666$	−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
$672$	−7.02797	−	12.1728i	−0.271110	−	0.469576i
$673$	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	$-0.239166\pi$
$677$	38.0276			1.46152			0.730760	+	0.682634i	$0.239166\pi$
$678$	−12.1881	+	21.1104i	−0.468081	+	0.810741i
$679$	7.83288	−	13.5669i	0.300598	−	0.520652i
$680$	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
$686$	−0.355143	+	0.615126i	−0.0135594	+	0.0234856i
$687$	−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	−0.834735	−	0.550651i	$-0.814379\pi$
$691$	1.56434	−	2.70952i	0.0595104	−	0.103075i	0.894246	+	0.447576i	$0.147713\pi$
$692$	0.698346	−	1.20957i	0.0265471	−	0.0459809i
$693$	−3.36850	−	5.83442i	−0.127959	−	0.221631i
$694$	−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
$700$	2.49496	−	4.32140i	0.0943006	−	0.163333i
$701$	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
$707$	−0.684905			−0.0257585
$708$	−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
$714$	6.67589			0.249839
$715$	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	0.534784	−	0.844989i	$-0.320393\pi$
$719$	−12.4522	−	21.5679i	−0.464389	−	0.804346i	−0.999174	+	0.0406425i	$0.987060\pi$
$720$	−4.42936			−0.165073
$721$	8.96246	+	15.5234i	0.333779	+	0.578123i
$722$	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	$-0.648215\pi$
$727$	−24.2120			−0.897974			−0.448987	+	0.893538i	$0.648215\pi$
$728$	8.82531	−	1.49995i	0.327088	−	0.0555918i
$729$	−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	$-0.573539\pi$
$733$	−12.3989			−0.457963			−0.228981	+	0.973431i	$0.573539\pi$
$734$	2.06717	+	3.58045i	0.0763007	+	0.132157i
$735$	1.55274	+	2.68942i	0.0572736	+	0.0992009i
$736$	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
$742$	−9.67589			−0.355213
$743$	−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
$749$	−8.49549			−0.310419
$750$	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
$756$	0.363883	−	0.630264i	0.0132343	−	0.0229225i
$757$	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	0.670651	−	0.741773i	$-0.266015\pi$
$761$	−8.47086	−	14.6720i	−0.307068	−	0.531858i	−0.977720	+	0.209915i	$0.932681\pi$
$762$	15.0926			0.546748
$763$	6.04639	+	10.4727i	0.218894	+	0.379136i
$764$	−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	−0.924758	−	0.380556i	$-0.875733\pi$
$769$	−3.68287	+	6.37892i	−0.132808	+	0.230030i	0.791950	+	0.610586i	$0.209066\pi$
$770$	−1.10289	+	1.91026i	−0.0397454

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.355143 - 0.615126i) q^{2} +(-1.20394 + 2.08529i) q^{3} +(0.747746 + 1.29513i) q^{4} -1.28971 q^{5} +(0.855143 + 1.48115i) q^{6} +(0.500000 + 0.866025i) q^{7} +2.48280 q^{8} +(-1.39895 - 2.42305i) q^{9} +O(q^{10})\)	\(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} +(0.500000 + 0.866025i) q^{7} +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} +0.710287 q^{14} +(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} -2.40788 q^{21} +(-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} +(-0.747746 + 1.29513i) q^{28} +(-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} +(-0.644857 - 1.11692i) q^{35} +(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} +(-0.855143 + 1.48115i) q^{42} +(-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} +(-0.500000 + 0.866025i) q^{49} +(-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} +(1.24140 + 2.15017i) q^{56} -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} +(1.39895 - 2.42305i) q^{63} +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} -0.916066 q^{70} +(-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} +2.40788 q^{77} +(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} +(-1.80049 - 3.11853i) q^{84} +(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} +(3.55458 - 0.604136i) q^{91} +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} +(0.355143 + 0.615126i) q^{98} -6.73701 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - q^{3} - 5 q^{4} - 14 q^{5} + 5 q^{6} + 4 q^{7} - 12 q^{8} - 7 q^{9}+O(q^{10}) \) 8 * q + q^2 - q^3 - 5 * q^4 - 14 * q^5 + 5 * q^6 + 4 * q^7 - 12 * q^8 - 7 * q^9	\( 8 q + q^{2} - q^{3} - 5 q^{4} - 14 q^{5} + 5 q^{6} + 4 q^{7} - 12 q^{8} - 7 q^{9} + 11 q^{10} + q^{11} + 24 q^{12} + 4 q^{13} + 2 q^{14} - 3 q^{15} - 19 q^{16} + 4 q^{17} - 6 q^{18} - q^{19} + 2 q^{20} - 2 q^{21} - 5 q^{22} + 2 q^{23} + 3 q^{24} + 10 q^{25} + 12 q^{26} - 52 q^{27} + 5 q^{28} - q^{29} + 4 q^{30} - 8 q^{31} + 33 q^{32} + 19 q^{33} + 6 q^{34} - 7 q^{35} + 34 q^{36} + 10 q^{37} - 46 q^{38} + 20 q^{39} - 34 q^{40} + 22 q^{41} - 5 q^{42} - 3 q^{43} - 24 q^{44} + 11 q^{45} - 24 q^{46} + 4 q^{47} - 11 q^{48} - 4 q^{49} - 43 q^{50} + 14 q^{51} + 65 q^{52} + 4 q^{53} - 5 q^{54} + 3 q^{55} - 6 q^{56} - 34 q^{57} + 11 q^{58} + 8 q^{59} - 22 q^{60} - 8 q^{61} + 5 q^{62} + 7 q^{63} + 28 q^{64} + 7 q^{65} + 12 q^{66} + 6 q^{67} + 33 q^{68} + 18 q^{69} + 22 q^{70} + 14 q^{71} - 5 q^{72} - 16 q^{73} - 20 q^{74} + 7 q^{75} - 32 q^{76} + 2 q^{77} - q^{78} - 52 q^{79} - 7 q^{80} - 24 q^{81} + 14 q^{82} + 12 q^{84} - 5 q^{85} + 24 q^{86} - 13 q^{87} - 3 q^{88} + q^{89} + 52 q^{90} - 4 q^{91} + 24 q^{92} + 7 q^{93} - 33 q^{94} - 21 q^{95} - 116 q^{96} - 3 q^{97} + q^{98} + 46 q^{99}+O(q^{100}) \) 8 * q + q^2 - q^3 - 5 * q^4 - 14 * q^5 + 5 * q^6 + 4 * q^7 - 12 * q^8 - 7 * q^9 + 11 * q^10 + q^11 + 24 * q^12 + 4 * q^13 + 2 * q^14 - 3 * q^15 - 19 * q^16 + 4 * q^17 - 6 * q^18 - q^19 + 2 * q^20 - 2 * q^21 - 5 * q^22 + 2 * q^23 + 3 * q^24 + 10 * q^25 + 12 * q^26 - 52 * q^27 + 5 * q^28 - q^29 + 4 * q^30 - 8 * q^31 + 33 * q^32 + 19 * q^33 + 6 * q^34 - 7 * q^35 + 34 * q^36 + 10 * q^37 - 46 * q^38 + 20 * q^39 - 34 * q^40 + 22 * q^41 - 5 * q^42 - 3 * q^43 - 24 * q^44 + 11 * q^45 - 24 * q^46 + 4 * q^47 - 11 * q^48 - 4 * q^49 - 43 * q^50 + 14 * q^51 + 65 * q^52 + 4 * q^53 - 5 * q^54 + 3 * q^55 - 6 * q^56 - 34 * q^57 + 11 * q^58 + 8 * q^59 - 22 * q^60 - 8 * q^61 + 5 * q^62 + 7 * q^63 + 28 * q^64 + 7 * q^65 + 12 * q^66 + 6 * q^67 + 33 * q^68 + 18 * q^69 + 22 * q^70 + 14 * q^71 - 5 * q^72 - 16 * q^73 - 20 * q^74 + 7 * q^75 - 32 * q^76 + 2 * q^77 - q^78 - 52 * q^79 - 7 * q^80 - 24 * q^81 + 14 * q^82 + 12 * q^84 - 5 * q^85 + 24 * q^86 - 13 * q^87 - 3 * q^88 + q^89 + 52 * q^90 - 4 * q^91 + 24 * q^92 + 7 * q^93 - 33 * q^94 - 21 * q^95 - 116 * q^96 - 3 * q^97 + q^98 + 46 * q^99

Introduction

L-functions

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