LMFDB - Embedded newform 342.2.x.c.41.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(29,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([3, 17]))

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

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

chi := DirichletCharacter("342.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.x (of order $18$, degree $6$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.3
Character	$\chi$	$=$	342.41
Dual form			342.2.x.c.317.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.984808i) q^{2} +(-1.28007 - 1.16680i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.837833 - 0.998490i) q^{5} +(-1.37136 + 1.05801i) q^{6} +(1.63174 - 2.82626i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.277146 + 2.98717i) q^{9} +O(q^{10})$	\(q+(0.173648 - 0.984808i) q^{2} +(-1.28007 - 1.16680i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.837833 - 0.998490i) q^{5} +(-1.37136 + 1.05801i) q^{6} +(1.63174 - 2.82626i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.277146 + 2.98717i) q^{9} +(-0.837833 - 0.998490i) q^{10} -2.05910i q^{11} +(0.803800 + 1.53424i) q^{12} +(-2.14639 - 2.55796i) q^{13} +(-2.49997 - 2.09773i) q^{14} +(-2.23752 + 0.300550i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-1.31824 + 1.57102i) q^{17} +(2.98992 + 0.245781i) q^{18} +(-4.22785 - 1.06080i) q^{19} +(-1.12881 + 0.651718i) q^{20} +(-5.38643 + 1.71388i) q^{21} +(-2.02782 - 0.357559i) q^{22} +(-2.16911 + 5.95958i) q^{23} +(1.65051 - 0.525170i) q^{24} +(0.573222 + 3.25090i) q^{25} +(-2.89182 + 1.66959i) q^{26} +(3.13067 - 4.14716i) q^{27} +(-2.49997 + 2.09773i) q^{28} +(3.03372 + 1.10418i) q^{29} +(-0.0925577 + 2.25572i) q^{30} -7.77074i q^{31} +(0.766044 - 0.642788i) q^{32} +(-2.40256 + 2.63579i) q^{33} +(1.31824 + 1.57102i) q^{34} +(-1.45487 - 3.99721i) q^{35} +(0.761240 - 2.90181i) q^{36} -8.22998i q^{37} +(-1.77884 + 3.97941i) q^{38} +(-0.237117 + 5.77878i) q^{39} +(0.445801 + 1.22483i) q^{40} +(-0.836193 + 4.74228i) q^{41} +(0.752503 + 5.60221i) q^{42} +(9.85027 - 3.58520i) q^{43} +(-0.704253 + 1.93492i) q^{44} +(3.21486 + 2.22602i) q^{45} +(5.49238 + 3.17102i) q^{46} +(2.53987 - 6.97823i) q^{47} +(-0.230583 - 1.71663i) q^{48} +(-1.82516 - 3.16128i) q^{49} +3.30105 q^{50} +(3.52050 - 0.472883i) q^{51} +(1.14207 + 3.13781i) q^{52} +(0.123794 + 0.702071i) q^{53} +(-3.54052 - 3.80325i) q^{54} +(-2.05599 - 1.72518i) q^{55} +(1.63174 + 2.82626i) q^{56} +(4.17419 + 6.29095i) q^{57} +(1.61421 - 2.79589i) q^{58} +(-2.89399 + 1.05333i) q^{59} +(2.20538 + 0.482853i) q^{60} +(-4.06411 + 3.41020i) q^{61} +(-7.65269 - 1.34938i) q^{62} +(8.89475 + 4.09100i) q^{63} +(-0.500000 - 0.866025i) q^{64} -4.35242 q^{65} +(2.17854 + 2.82376i) q^{66} +(14.2217 - 2.50767i) q^{67} +(1.77606 - 1.02541i) q^{68} +(9.73025 - 5.09774i) q^{69} +(-4.18912 + 0.738655i) q^{70} +(0.465476 - 2.63985i) q^{71} +(-2.72554 - 1.25357i) q^{72} +(6.64344 - 2.41801i) q^{73} +(-8.10495 - 1.42912i) q^{74} +(3.05940 - 4.83021i) q^{75} +(3.61006 + 2.44283i) q^{76} +(-5.81955 - 3.35992i) q^{77} +(5.64981 + 1.23699i) q^{78} +(4.04909 - 4.82552i) q^{79} +(1.28363 - 0.226339i) q^{80} +(-8.84638 + 1.65577i) q^{81} +(4.52503 + 1.64698i) q^{82} +(11.6778 + 6.74220i) q^{83} +(5.64777 + 0.231742i) q^{84} +(0.464180 + 2.63250i) q^{85} +(-1.82026 - 10.3232i) q^{86} +(-2.59500 - 4.95318i) q^{87} +(1.78323 + 1.02955i) q^{88} +(-6.87203 - 2.50121i) q^{89} +(2.75046 - 2.77948i) q^{90} +(-10.7318 + 1.89231i) q^{91} +(4.07659 - 4.85829i) q^{92} +(-9.06692 + 9.94707i) q^{93} +(-6.43117 - 3.71304i) q^{94} +(-4.60143 + 3.33270i) q^{95} +(-1.73059 - 0.0710105i) q^{96} +(8.00928 + 1.41225i) q^{97} +(-3.43019 + 1.24849i) q^{98} +(6.15088 - 0.570672i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9}+O(q^{10}) $ 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9	$ 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9} + 3 q^{13} + 3 q^{14} + 27 q^{15} - 27 q^{17} - 18 q^{18} + 3 q^{19} + 18 q^{23} + 3 q^{24} - 6 q^{27} + 3 q^{28} + 57 q^{33} + 27 q^{34} + 9 q^{38} - 30 q^{39} + 9 q^{41} - 3 q^{43} - 9 q^{44} + 27 q^{45} - 30 q^{49} - 132 q^{50} - 66 q^{51} + 6 q^{52} + 27 q^{54} + 102 q^{57} - 54 q^{59} + 6 q^{60} - 24 q^{61} - 3 q^{62} - 30 q^{64} + 36 q^{65} - 63 q^{66} + 51 q^{67} - 18 q^{68} + 3 q^{69} - 18 q^{71} - 3 q^{72} - 66 q^{73} - 6 q^{74} + 3 q^{78} - 51 q^{79} - 30 q^{81} - 36 q^{83} + 60 q^{84} - 3 q^{86} + 54 q^{87} - 27 q^{89} + 36 q^{90} - 69 q^{91} + 69 q^{93} + 18 q^{94} - 27 q^{95} + 81 q^{97} + 60 q^{98} + 51 q^{99}+O(q^{100}) $ 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9 + 3 * q^13 + 3 * q^14 + 27 * q^15 - 27 * q^17 - 18 * q^18 + 3 * q^19 + 18 * q^23 + 3 * q^24 - 6 * q^27 + 3 * q^28 + 57 * q^33 + 27 * q^34 + 9 * q^38 - 30 * q^39 + 9 * q^41 - 3 * q^43 - 9 * q^44 + 27 * q^45 - 30 * q^49 - 132 * q^50 - 66 * q^51 + 6 * q^52 + 27 * q^54 + 102 * q^57 - 54 * q^59 + 6 * q^60 - 24 * q^61 - 3 * q^62 - 30 * q^64 + 36 * q^65 - 63 * q^66 + 51 * q^67 - 18 * q^68 + 3 * q^69 - 18 * q^71 - 3 * q^72 - 66 * q^73 - 6 * q^74 + 3 * q^78 - 51 * q^79 - 30 * q^81 - 36 * q^83 + 60 * q^84 - 3 * q^86 + 54 * q^87 - 27 * q^89 + 36 * q^90 - 69 * q^91 + 69 * q^93 + 18 * q^94 - 27 * q^95 + 81 * q^97 + 60 * q^98 + 51 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$3$	−1.28007	−	1.16680i	−0.739047	−	0.673653i
$3$	−1.28007	−	1.16680i	−0.739047	−	0.673653i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	0.837833	−	0.998490i	0.374690	−	0.446538i	−0.545441	−	0.838149i	$-0.683638\pi$
$5$	0.837833	−	0.998490i	0.374690	−	0.446538i	0.920131	+	0.391611i	$0.128082\pi$
$6$	−1.37136	+	1.05801i	−0.559854	+	0.431930i
$7$	1.63174	−	2.82626i	0.616740	−	1.06823i	−0.373336	−	0.927696i	$-0.621786\pi$
$7$	1.63174	−	2.82626i	0.616740	−	1.06823i	0.990076	−	0.140530i	$-0.0448805\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	0.277146	+	2.98717i	0.0923821	+	0.995724i
$10$	−0.837833	−	0.998490i	−0.264946	−	0.315750i
$11$		−	2.05910i		−	0.620842i	−0.950599	−	0.310421i	$-0.899530\pi$
$11$		−	2.05910i		−	0.620842i	0.950599	−	0.310421i	$-0.100470\pi$
$12$	0.803800	+	1.53424i	0.232037	+	0.442898i
$13$	−2.14639	−	2.55796i	−0.595301	−	0.709452i	0.381315	−	0.924445i	$-0.375471\pi$
$13$	−2.14639	−	2.55796i	−0.595301	−	0.709452i	−0.976615	+	0.214994i	$0.931027\pi$
$14$	−2.49997	−	2.09773i	−0.668146	−	0.560641i
$15$	−2.23752	+	0.300550i	−0.577726	+	0.0776017i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−1.31824	+	1.57102i	−0.319720	+	0.381027i	−0.901836	−	0.432078i	$-0.857780\pi$
$17$	−1.31824	+	1.57102i	−0.319720	+	0.381027i	0.582116	+	0.813106i	$0.302225\pi$
$18$	2.98992	+	0.245781i	0.704730	+	0.0579311i
$19$	−4.22785	−	1.06080i	−0.969935	−	0.243364i
$19$	−4.22785	−	1.06080i	−0.969935	−	0.243364i
$20$	−1.12881	+	0.651718i	−0.252409	+	0.145729i
$21$	−5.38643	+	1.71388i	−1.17541	+	0.374000i
$22$	−2.02782	−	0.357559i	−0.432332	−	0.0762318i
$23$	−2.16911	+	5.95958i	−0.452290	+	1.24266i	0.478818	+	0.877914i	$0.341065\pi$
$23$	−2.16911	+	5.95958i	−0.452290	+	1.24266i	−0.931108	+	0.364743i	$0.881157\pi$
$24$	1.65051	−	0.525170i	0.336910	−	0.107200i
$25$	0.573222	+	3.25090i	0.114644	+	0.650181i
$26$	−2.89182	+	1.66959i	−0.567132	+	0.327434i
$27$	3.13067	−	4.14716i	0.602498	−	0.798120i
$28$	−2.49997	+	2.09773i	−0.472451	+	0.396433i
$29$	3.03372	+	1.10418i	0.563347	+	0.205042i	0.607967	−	0.793962i	$-0.291985\pi$
$29$	3.03372	+	1.10418i	0.563347	+	0.205042i	−0.0446195	+	0.999004i	$0.514208\pi$
$30$	−0.0925577	+	2.25572i	−0.0168986	+	0.411836i
$31$		−	7.77074i		−	1.39567i	−0.716260	−	0.697833i	$-0.754148\pi$
$31$		−	7.77074i		−	1.39567i	0.716260	−	0.697833i	$-0.245852\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	−2.40256	+	2.63579i	−0.418232	+	0.458831i
$34$	1.31824	+	1.57102i	0.226076	+	0.269427i
$35$	−1.45487	−	3.99721i	−0.245917	−	0.675652i
$36$	0.761240	−	2.90181i	0.126873	−	0.483635i
$37$		−	8.22998i		−	1.35300i	−0.736442	−	0.676500i	$-0.763496\pi$
$37$		−	8.22998i		−	1.35300i	0.736442	−	0.676500i	$-0.236504\pi$
$38$	−1.77884	+	3.97941i	−0.288566	+	0.645546i
$39$	−0.237117	+	5.77878i	−0.0379692	+	0.925345i
$40$	0.445801	+	1.22483i	0.0704874	+	0.193663i
$41$	−0.836193	+	4.74228i	−0.130591	+	0.740620i	0.847237	+	0.531214i	$0.178264\pi$
$41$	−0.836193	+	4.74228i	−0.130591	+	0.740620i	−0.977829	+	0.209406i	$0.932847\pi$
$42$	0.752503	+	5.60221i	0.116114	+	0.864439i
$43$	9.85027	−	3.58520i	1.50215	−	0.546739i	0.545535	−	0.838088i	$-0.316326\pi$
$43$	9.85027	−	3.58520i	1.50215	−	0.546739i	0.956617	+	0.291349i	$0.0941042\pi$
$44$	−0.704253	+	1.93492i	−0.106170	+	0.291700i
$45$	3.21486	+	2.22602i	0.479243	+	0.331836i
$46$	5.49238	+	3.17102i	0.809807	+	0.467542i
$47$	2.53987	−	6.97823i	0.370478	−	1.01788i	−0.604700	−	0.796454i	$-0.706707\pi$
$47$	2.53987	−	6.97823i	0.370478	−	1.01788i	0.975177	−	0.221425i	$-0.0710709\pi$
$48$	−0.230583	−	1.71663i	−0.0332818	−	0.247775i
$49$	−1.82516	−	3.16128i	−0.260738	−	0.451611i
$50$	3.30105			0.466839
$51$	3.52050	−	0.472883i	0.492969	−	0.0662169i
$52$	1.14207	+	3.13781i	0.158376	+	0.435136i
$53$	0.123794	+	0.702071i	0.0170044	+	0.0964368i	0.992129	−	0.125221i	$-0.0399641\pi$
$53$	0.123794	+	0.702071i	0.0170044	+	0.0964368i	−0.975124	+	0.221658i	$0.928853\pi$
$54$	−3.54052	−	3.80325i	−0.481803	−	0.517557i
$55$	−2.05599	−	1.72518i	−0.277230	−	0.232623i
$56$	1.63174	+	2.82626i	0.218051	+	0.377675i
$57$	4.17419	+	6.29095i	0.552885	+	0.833257i
$58$	1.61421	−	2.79589i	0.211956	−	0.367118i
$59$	−2.89399	+	1.05333i	−0.376766	+	0.137131i	−0.523460	−	0.852050i	$-0.675359\pi$
$59$	−2.89399	+	1.05333i	−0.376766	+	0.137131i	0.146694	+	0.989182i	$0.453137\pi$
$60$	2.20538	+	0.482853i	0.284713	+	0.0623361i
$61$	−4.06411	+	3.41020i	−0.520356	+	0.436631i	−0.864756	−	0.502192i	$-0.832527\pi$
$61$	−4.06411	+	3.41020i	−0.520356	+	0.436631i	0.344400	+	0.938823i	$0.388082\pi$
$62$	−7.65269	−	1.34938i	−0.971892	−	0.171371i
$63$	8.89475	+	4.09100i	1.12063	+	0.515418i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−4.35242			−0.539851
$66$	2.17854	+	2.82376i	0.268160	+	0.347581i
$67$	14.2217	−	2.50767i	1.73746	−	0.306361i	0.786941	−	0.617028i	$-0.211664\pi$
$67$	14.2217	−	2.50767i	1.73746	−	0.306361i	0.950519	+	0.310667i	$0.100553\pi$
$68$	1.77606	−	1.02541i	0.215379	−	0.124349i
$69$	9.73025	−	5.09774i	1.17138	−	0.613696i
$70$	−4.18912	+	0.738655i	−0.500696	+	0.0882861i
$71$	0.465476	−	2.63985i	0.0552419	−	0.313292i	−0.944649	−	0.328084i	$-0.893597\pi$
$71$	0.465476	−	2.63985i	0.0552419	−	0.313292i	0.999891	+	0.0147912i	$0.00470836\pi$
$72$	−2.72554	−	1.25357i	−0.321208	−	0.147735i
$73$	6.64344	−	2.41801i	0.777555	−	0.283007i	0.0774025	−	0.997000i	$-0.475337\pi$
$73$	6.64344	−	2.41801i	0.777555	−	0.283007i	0.700153	+	0.713993i	$0.253115\pi$
$74$	−8.10495	−	1.42912i	−0.942181	−	0.166132i
$75$	3.05940	−	4.83021i	0.353269	−	0.557745i
$76$	3.61006	+	2.44283i	0.414103	+	0.280212i
$77$	−5.81955	−	3.35992i	−0.663199	−	0.382898i
$78$	5.64981	+	1.23699i	0.639715	+	0.140061i
$79$	4.04909	−	4.82552i	0.455558	−	0.542913i	−0.488556	−	0.872533i	$-0.662476\pi$
$79$	4.04909	−	4.82552i	0.455558	−	0.542913i	0.944114	+	0.329620i	$0.106920\pi$
$80$	1.28363	−	0.226339i	0.143515	−	0.0253055i
$81$	−8.84638	+	1.65577i	−0.982931	+	0.183974i
$82$	4.52503	+	1.64698i	0.499706	+	0.181878i
$83$	11.6778	+	6.74220i	1.28181	+	0.740053i	0.977179	−	0.212418i	$-0.0681338\pi$
$83$	11.6778	+	6.74220i	1.28181	+	0.740053i	0.304630	+	0.952471i	$0.401467\pi$
$84$	5.64777	+	0.231742i	0.616222	+	0.0252851i
$85$	0.464180	+	2.63250i	0.0503474	+	0.285535i
$86$	−1.82026	−	10.3232i	−0.196283	−	1.11318i
$87$	−2.59500	−	4.95318i	−0.278213	−	0.531036i
$88$	1.78323	+	1.02955i	0.190093	+	0.109750i
$89$	−6.87203	−	2.50121i	−0.728434	−	0.265128i	−0.0489320	−	0.998802i	$-0.515582\pi$
$89$	−6.87203	−	2.50121i	−0.728434	−	0.265128i	−0.679502	+	0.733674i	$0.737804\pi$
$90$	2.75046	−	2.77948i	0.289924	−	0.292983i
$91$	−10.7318	+	1.89231i	−1.12500	+	0.198368i
$92$	4.07659	−	4.85829i	0.425014	−	0.506512i
$93$	−9.06692	+	9.94707i	−0.940195	+	1.03146i
$94$	−6.43117	−	3.71304i	−0.663324	−	0.382970i
$95$	−4.60143	+	3.33270i	−0.472096	+	0.341927i
$96$	−1.73059	−	0.0710105i	−0.176628	−	0.00724748i
$97$	8.00928	+	1.41225i	0.813219	+	0.143393i	0.564766	−	0.825251i	$-0.308967\pi$
$97$	8.00928	+	1.41225i	0.813219	+	0.143393i	0.248454	+	0.968644i	$0.420078\pi$
$98$	−3.43019	+	1.24849i	−0.346501	+	0.126116i
$99$	6.15088	−	0.570672i	0.618187	−	0.0573547i
$100$	0.573222	−	3.25090i	0.0573222	−	0.325090i
$101$	7.87777	−	1.38906i	0.783867	−	0.138217i	0.232630	−	0.972565i	$-0.425267\pi$
$101$	7.87777	−	1.38906i	0.783867	−	0.138217i	0.551237	+	0.834348i	$0.314156\pi$
$102$	0.145630	−	3.54913i	0.0144195	−	0.351416i
$103$	−3.76760	+	2.17523i	−0.371233	+	0.214332i	−0.673997	−	0.738734i	$-0.735424\pi$
$103$	−3.76760	+	2.17523i	−0.371233	+	0.214332i	0.302764	+	0.953066i	$0.402091\pi$
$104$	3.28846	−	0.579844i	0.322460	−	0.0568583i
$105$	−2.80163	+	6.81424i	−0.273411	+	0.665002i
$106$	0.712901			0.0692431
$107$	1.71400	+	2.96874i	0.165699	+	0.286999i	0.936903	−	0.349589i	$-0.113679\pi$
$107$	1.71400	+	2.96874i	0.165699	+	0.286999i	−0.771204	+	0.636588i	$0.780345\pi$
$108$	−4.36028	+	2.82630i	−0.419568	+	0.271961i
$109$	−17.2963	−	3.04980i	−1.65668	−	0.292118i	−0.734425	−	0.678690i	$-0.762548\pi$
$109$	−17.2963	−	3.04980i	−1.65668	−	0.292118i	−0.922259	+	0.386572i	$0.873659\pi$
$110$	−2.05599	+	1.72518i	−0.196031	+	0.164489i
$111$	−9.60276	+	10.5349i	−0.911453	+	0.999931i
$112$	3.06667	−	1.11618i	0.289773	−	0.105469i
$113$	−4.52646	+	7.84006i	−0.425814	+	0.737531i	−0.996496	−	0.0836400i	$-0.973345\pi$
$113$	−4.52646	+	7.84006i	−0.425814	+	0.737531i	0.570682	+	0.821171i	$0.306679\pi$
$114$	6.92022	−	3.01837i	0.648138	−	0.282696i
$115$	4.13323	+	7.15896i	0.385426	+	0.667577i
$116$	−2.47311	−	2.07519i	−0.229623	−	0.192676i
$117$	7.04621	−	7.12056i	0.651423	−	0.658296i
$118$	0.534788	+	3.03293i	0.0492312	+	0.279204i
$119$	2.28907	+	6.28918i	0.209839	+	0.576528i
$120$	0.858477	−	2.08803i	0.0783679	−	0.190610i
$121$	6.76011			0.614556
$122$	2.65266	+	4.59454i	0.240161	+	0.415970i
$123$	6.60369	−	5.09477i	0.595435	−	0.459380i
$124$	−2.65775	+	7.30211i	−0.238673	+	0.655749i
$125$	9.37030	+	5.40995i	0.838105	+	0.483880i
$126$	5.57341	−	8.04923i	0.496519	−	0.717082i
$127$	2.32769	−	6.39527i	0.206549	−	0.567489i	−0.792555	−	0.609800i	$-0.791250\pi$
$127$	2.32769	−	6.39527i	0.206549	−	0.567489i	0.999104	+	0.0423111i	$0.0134721\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	−16.7922	−	6.90401i	−1.47847	−	0.607864i
$130$	−0.755789	+	4.28629i	−0.0662871	+	0.375933i
$131$	−6.96248	−	19.1293i	−0.608315	−	1.67133i	−0.733907	−	0.679250i	$-0.762305\pi$
$131$	−6.96248	−	19.1293i	−0.608315	−	1.67133i	0.125592	−	0.992082i	$-0.459917\pi$
$132$	3.15916	−	1.65510i	0.274970	−	0.144058i
$133$	−9.89685	+	10.2181i	−0.858165	+	0.886018i
$134$		−	14.4411i		−	1.24752i
$135$	−1.51792	−	6.60057i	−0.130641	−	0.568086i
$136$	−0.701421	−	1.92714i	−0.0601463	−	0.165251i
$137$	9.76102	+	11.6327i	0.833940	+	0.993852i	0.999970	+	0.00773082i	$0.00246082\pi$
$137$	9.76102	+	11.6327i	0.833940	+	0.993852i	−0.166030	+	0.986121i	$0.553095\pi$
$138$	−3.33065	−	10.4676i	−0.283524	−	0.891065i
$139$	−7.73291	+	6.48868i	−0.655897	+	0.550363i	−0.908854	−	0.417115i	$-0.863041\pi$
$139$	−7.73291	+	6.48868i	−0.655897	+	0.550363i	0.252957	+	0.967478i	$0.418597\pi$
$140$			4.25374i			0.359507i
$141$	−11.3934	+	5.96908i	−0.959498	+	0.502687i
$142$	−2.51891	−	0.916810i	−0.211383	−	0.0769369i
$143$	−5.26710	+	4.41962i	−0.440457	+	0.369587i
$144$	−1.70781	+	2.46645i	−0.142318	+	0.205538i
$145$	3.64426	−	2.10402i	0.302640	−	0.174729i
$146$	−1.22766	−	6.96239i	−0.101602	−	0.576212i
$147$	−1.35225	+	6.17625i	−0.111532	+	0.509409i
$148$	−2.81482	+	7.73365i	−0.231377	+	0.635702i
$149$	17.1639	+	3.02645i	1.40612	+	0.247937i	0.824655	−	0.565636i	$-0.191369\pi$
$149$	17.1639	+	3.02645i	1.40612	+	0.247937i	0.581463	+	0.813573i	$0.302480\pi$
$150$	−4.22557	−	3.85168i	−0.345017	−	0.314488i
$151$	−0.917053	+	0.529461i	−0.0746287	+	0.0430869i	−0.536850	−	0.843678i	$-0.680386\pi$
$151$	−0.917053	+	0.529461i	−0.0746287	+	0.0430869i	0.462221	+	0.886765i	$0.347053\pi$
$152$	3.03260	−	3.13103i	0.245976	−	0.253960i
$153$	−5.05824	−	3.50240i	−0.408934	−	0.283153i
$154$	−4.31943	+	5.14769i	−0.348069	+	0.414813i
$155$	−7.75901	−	6.51058i	−0.623219	−	0.522942i
$156$	2.19928	−	5.34917i	0.176083	−	0.428277i
$157$	−4.31381	−	3.61972i	−0.344280	−	0.288885i	0.454208	−	0.890895i	$-0.349922\pi$
$157$	−4.31381	−	3.61972i	−0.344280	−	0.288885i	−0.798488	+	0.602010i	$0.794367\pi$
$158$	−4.04909	−	4.82552i	−0.322128	−	0.383898i
$159$	0.660713	−	1.04314i	0.0523979	−	0.0827265i
$160$		−	1.30344i		−	0.103046i
$161$	13.3039	+	15.8550i	1.04849	+	1.24955i
$162$	0.0944545	+	8.99950i	0.00742105	+	0.707068i
$163$	−8.00265	+	13.8610i	−0.626816	+	1.08568i	0.361371	+	0.932422i	$0.382309\pi$
$163$	−8.00265	+	13.8610i	−0.626816	+	1.08568i	−0.988187	+	0.153255i	$0.951024\pi$
$164$	2.40772	−	4.17029i	0.188011	−	0.325645i
$165$	0.618862	+	4.60728i	0.0481784	+	0.358676i
$166$	8.66761	−	10.3297i	0.672737	−	0.801737i
$167$	−0.608877	−	0.221613i	−0.0471163	−	0.0171489i	0.318355	−	0.947972i	$-0.396870\pi$
$167$	−0.608877	−	0.221613i	−0.0471163	−	0.0171489i	−0.365471	+	0.930823i	$0.619092\pi$
$168$	1.20895	−	5.52172i	0.0932722	−	0.426010i
$169$	0.321221	−	1.82174i	0.0247093	−	0.140133i
$170$	2.67311			0.205018
$171$	1.99705	−	12.9233i	0.152718	−	0.988270i
$172$	−10.4824			−0.799278
$173$	1.66107	−	9.42037i	0.126288	−	0.716217i	−0.854246	−	0.519869i	$-0.825981\pi$
$173$	1.66107	−	9.42037i	0.126288	−	0.716217i	0.980534	−	0.196348i	$-0.0629083\pi$
$174$	−5.32855	+	1.69547i	−0.403956	+	0.128533i
$175$	10.1232	+	3.68456i	0.765246	+	0.278527i
$176$	1.32356	−	1.57736i	0.0997673	−	0.118898i
$177$	4.93353	+	2.02839i	0.370827	+	0.152463i
$178$	−3.65653	+	6.33330i	−0.274069	+	0.474701i
$179$	−2.94101	+	5.09398i	−0.219822	+	0.380742i	−0.954753	−	0.297399i	$-0.903881\pi$
$179$	−2.94101	+	5.09398i	−0.219822	+	0.380742i	0.734932	+	0.678141i	$0.237214\pi$
$180$	−2.25964	−	3.19132i	−0.168424	−	0.237867i
$181$	8.38105	+	9.98815i	0.622959	+	0.742413i	0.981576	−	0.191071i	$-0.0611962\pi$
$181$	8.38105	+	9.98815i	0.622959	+	0.742413i	−0.358617	+	0.933485i	$0.616752\pi$
$182$			10.8974i			0.807767i
$183$	9.18136	+	0.376734i	0.678706	+	0.0278490i
$184$	−4.07659	−	4.85829i	−0.300530	−	0.358158i
$185$	−8.21755	−	6.89535i	−0.604167	−	0.506956i
$186$	8.22150	+	10.6565i	0.602830	+	0.781370i
$187$	3.23488	+	2.71438i	0.236558	+	0.198495i
$188$	−4.77339	+	5.68870i	−0.348135	+	0.414891i
$189$	−6.61249	−	15.6152i	−0.480988	−	1.13584i
$190$	2.48304	+	5.11024i	0.180138	+	0.370736i
$191$	−17.1814	+	9.91971i	−1.24320	+	0.717765i	−0.969745	−	0.244119i	$-0.921501\pi$
$191$	−17.1814	+	9.91971i	−1.24320	+	0.717765i	−0.273460	+	0.961883i	$0.588168\pi$
$192$	−0.370446	+	1.69197i	−0.0267347	+	0.122108i
$193$	−1.81485	−	0.320007i	−0.130636	−	0.0230346i	0.107948	−	0.994157i	$-0.465572\pi$
$193$	−1.81485	−	0.320007i	−0.130636	−	0.0230346i	−0.238584	+	0.971122i	$0.576683\pi$
$194$	2.78159	−	7.64237i	0.199707	−	0.548690i
$195$	5.57139	+	5.07841i	0.398975	+	0.363672i
$196$	0.633873	+	3.59487i	0.0452766	+	0.256776i
$197$	−7.38730	+	4.26506i	−0.526323	+	0.303873i	−0.739518	−	0.673137i	$-0.764946\pi$
$197$	−7.38730	+	4.26506i	−0.526323	+	0.303873i	0.213195	+	0.977010i	$0.431613\pi$
$198$	0.506087	−	6.15653i	0.0359660	−	0.437526i
$199$	−11.1938	+	9.39272i	−0.793508	+	0.665832i	−0.946611	−	0.322378i	$-0.895518\pi$
$199$	−11.1938	+	9.39272i	−0.793508	+	0.665832i	0.153103	+	0.988210i	$0.451073\pi$
$200$	−3.10198	−	1.12903i	−0.219343	−	0.0798343i
$201$	−21.1307	−	13.3839i	−1.49045	−	0.944030i
$202$		−	7.99929i		−	0.562828i
$203$	8.07095	−	6.77234i	0.566470	−	0.475325i
$204$	−3.46992	−	0.759717i	−0.242943	−	0.0531909i
$205$	4.03453	+	4.80817i	0.281784	+	0.335817i
$206$	1.48794	+	4.08809i	0.103670	+	0.284831i
$207$	−18.4034	−	4.82782i	−1.27913	−	0.335557i
$208$		−	3.33919i		−	0.231531i
$209$	−2.18429	+	8.70556i	−0.151090	+	0.602176i
$210$	6.22422	+	3.94234i	0.429512	+	0.272048i
$211$	0.00200613	+	0.00551179i	0.000138107	+	0.000379447i	0.939762	−	0.341830i	$-0.111047\pi$
$211$	0.00200613	+	0.00551179i	0.000138107	+	0.000379447i	−0.939624	+	0.342210i	$0.888825\pi$
$212$	0.123794	−	0.702071i	0.00850221	−	0.0482184i
$213$	−3.67602	+	2.83607i	−0.251877	+	0.194324i
$214$	3.22127	−	1.17245i	0.220202	−	0.0801469i
$215$	4.67309	−	12.8392i	0.318702	−	0.875626i
$216$	2.02621	+	4.78482i	0.137866	+	0.325566i
$217$	−21.9621	−	12.6798i	−1.49089	−	0.860764i
$218$	−6.00694	+	16.5039i	−0.406841	+	1.11779i
$219$	−11.3254	−	4.65635i	−0.765299	−	0.314647i
$220$	1.34195	+	2.32433i	0.0904744	+	0.156706i
$221$	6.84806			0.460650
$222$	8.70738	+	11.2862i	0.584401	+	0.757483i
$223$	0.0644913	+	0.177188i	0.00431866	+	0.0118654i	0.941833	−	0.336081i	$-0.109101\pi$
$223$	0.0644913	+	0.177188i	0.00431866	+	0.0118654i	−0.937515	+	0.347946i	$0.886879\pi$
$224$	−0.566698	−	3.21390i	−0.0378641	−	0.214738i
$225$	−9.55214	+	2.61329i	−0.636809	+	0.174219i
$226$	6.93494	+	5.81911i	0.461305	+	0.387081i
$227$	−13.7189	−	23.7619i	−0.910557	−	1.57713i	−0.813279	−	0.581874i	$-0.802320\pi$
$227$	−13.7189	−	23.7619i	−0.910557	−	1.57713i	−0.0972776	−	0.995257i	$-0.531013\pi$
$228$	−1.77083	−	7.33922i	−0.117276	−	0.486052i
$229$	11.9232	−	20.6515i	0.787905	−	1.36469i	−0.139343	−	0.990244i	$-0.544499\pi$
$229$	11.9232	−	20.6515i	0.787905	−	1.36469i	0.927248	−	0.374447i	$-0.122168\pi$
$230$	7.76793	−	2.82730i	0.512202	−	0.186426i
$231$	3.52906	+	11.0912i	0.232195	+	0.729746i
$232$	−2.47311	+	2.07519i	−0.162368	+	0.136243i
$233$	8.80860	+	1.55319i	0.577071	+	0.101753i	0.454563	−	0.890714i	$-0.349795\pi$
$233$	8.80860	+	1.55319i	0.577071	+	0.101753i	0.122507	+	0.992468i	$0.460906\pi$
$234$	−5.78882	−	8.17564i	−0.378427	−	0.534458i
$235$	−4.83971	−	8.38262i	−0.315708	−	0.546822i
$236$	3.07972			0.200473
$237$	−10.8135	+	1.45250i	−0.702415	+	0.0943502i
$238$	6.59113	−	1.16219i	0.427239	−	0.0753338i
$239$	0.406447	−	0.234662i	0.0262909	−	0.0151790i	−0.486797	−	0.873515i	$-0.661835\pi$
$239$	0.406447	−	0.234662i	0.0262909	−	0.0151790i	0.513088	+	0.858336i	$0.328502\pi$
$240$	−1.90723	−	1.20802i	−0.123111	−	0.0779772i
$241$	−3.83319	+	0.675894i	−0.246917	+	0.0435382i	−0.295737	−	0.955269i	$-0.595565\pi$
$241$	−3.83319	+	0.675894i	−0.246917	+	0.0435382i	0.0488196	+	0.998808i	$0.484454\pi$
$242$	1.17388	−	6.65741i	0.0754600	−	0.427955i
$243$	13.2559	+	8.20248i	0.850367	+	0.526189i
$244$	4.98537	−	1.81453i	0.319156	−	0.116163i
$245$	−4.68569	−	0.826213i	−0.299357	−	0.0527848i
$246$	−3.87065	−	7.38806i	−0.246784	−	0.471046i
$247$	6.36112	+	13.0916i	0.404748	+	0.832997i
$248$	6.72966	+	3.88537i	0.427334	+	0.246721i
$249$	−7.08161	−	22.2562i	−0.448779	−	1.41043i
$250$	6.95489	−	8.28852i	0.439866	−	0.524212i
$251$	27.0739	−	4.77386i	1.70889	−	0.301323i	0.768103	−	0.640326i	$-0.221201\pi$
$251$	27.0739	−	4.77386i	1.70889	−	0.301323i	0.940785	+	0.339003i	$0.110090\pi$
$252$	−6.95913	−	6.88647i	−0.438384	−	0.433807i
$253$	12.2714	+	4.46641i	0.771494	+	0.280801i
$254$	−5.89392	−	3.40285i	−0.369817	−	0.213514i
$255$	2.47742	−	3.91138i	0.155142	−	0.244940i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−0.906906	−	5.14332i	−0.0565713	−	0.320832i	0.943369	−	0.331745i	$-0.107637\pi$
$257$	−0.906906	−	5.14332i	−0.0565713	−	0.320832i	−0.999940	+	0.0109132i	$0.996526\pi$
$258$	−9.71506	+	15.3383i	−0.604833	+	0.954918i
$259$	−23.2601	−	13.4292i	−1.44531	−	0.834450i
$260$	4.08993	+	1.48861i	0.253647	+	0.0923199i
$261$	−2.45760	+	9.36826i	−0.152122	+	0.579881i
$262$	−20.0477	+	3.53495i	−1.23855	+	0.218390i
$263$	17.1955	−	20.4928i	1.06032	−	1.26364i	0.0970036	−	0.995284i	$-0.469074\pi$
$263$	17.1955	−	20.4928i	1.06032	−	1.26364i	0.963319	−	0.268359i	$-0.0864814\pi$
$264$	−1.08138	−	3.39857i	−0.0665542	−	0.209168i
$265$	0.804729	+	0.464611i	0.0494341	+	0.0285408i
$266$	8.34425	+	11.5208i	0.511619	+	0.706388i
$267$	5.87824	+	11.2200i	0.359743	+	0.686654i
$268$	−14.2217	−	2.50767i	−0.868730	−	0.153181i
$269$	8.99743	−	3.27480i	0.548583	−	0.199668i	−0.0528339	−	0.998603i	$-0.516825\pi$
$269$	8.99743	−	3.27480i	0.548583	−	0.199668i	0.601417	+	0.798935i	$0.294603\pi$
$270$	−6.76387	+	0.348679i	−0.411636	+	0.0212199i
$271$	−4.41057	+	25.0136i	−0.267923	+	1.51947i	0.492658	+	0.870223i	$0.336025\pi$
$271$	−4.41057	+	25.0136i	−0.267923	+	1.51947i	−0.760581	+	0.649243i	$0.775086\pi$
$272$	−2.01966	+	0.356121i	−0.122460	+	0.0215930i
$273$	15.9454	+	10.0996i	0.965060	+	0.611257i
$274$	13.1510	−	7.59273i	0.794480	−	0.458693i
$275$	6.69393	−	1.18032i	0.403659	−	0.0711760i
$276$	−10.8870	+	1.46237i	−0.655319	+	0.0880242i
$277$	11.5060			0.691331			0.345666	−	0.938358i	$-0.387653\pi$
$277$	11.5060			0.691331			0.345666	+	0.938358i	$0.387653\pi$
$278$	5.04730	+	8.74218i	0.302717	+	0.524321i
$279$	23.2125	−	2.15363i	1.38970	−	0.128935i
$280$	4.18912	+	0.738655i	0.250348	+	0.0441431i
$281$	−12.7946	+	10.7359i	−0.763262	+	0.640453i	−0.938974	−	0.343989i	$-0.888222\pi$
$281$	−12.7946	+	10.7359i	−0.763262	+	0.640453i	0.175712	+	0.984442i	$0.443777\pi$
$282$	3.89995	+	12.2568i	0.232239	+	0.729884i
$283$	−19.1024	+	6.95272i	−1.13552	+	0.413296i	−0.840294	−	0.542130i	$-0.817618\pi$
$283$	−19.1024	+	6.95272i	−1.13552	+	0.413296i	−0.295228	+	0.955427i	$0.595396\pi$
$284$	−1.34029	+	2.32144i	−0.0795313	+	0.137752i
$285$	9.77873	+	1.10288i	0.579242	+	0.0653288i
$286$	3.43786	+	5.95454i	0.203285	+	0.352099i
$287$	12.0385	+	10.1015i	0.710609	+	0.596272i
$288$	2.13242	+	2.11016i	0.125654	+	0.124342i
$289$	2.22168	+	12.5998i	0.130687	+	0.741164i
$290$	−1.43923	−	3.95426i	−0.0845146	−	0.232202i
$291$	−8.60460	−	11.1530i	−0.504411	−	0.653802i
$292$	−7.06980			−0.413729
$293$	16.3791	+	28.3694i	0.956876	+	1.65736i	0.730016	+	0.683430i	$0.239513\pi$
$293$	16.3791	+	28.3694i	0.956876	+	1.65736i	0.226860	+	0.973927i	$0.427154\pi$
$294$	5.84761	+	2.40420i	0.341039	+	0.140216i
$295$	−1.37294	+	3.77213i	−0.0799359	+	0.219622i
$296$	7.12737	+	4.11499i	0.414270	+	0.239179i
$297$	−8.53940	−	6.44636i	−0.495506	−	0.374056i
$298$	5.96095	−	16.3776i	0.345308	−	0.948727i
$299$	19.9001	−	7.24306i	1.15085	−	0.418877i
$300$	−4.52692	+	3.49254i	−0.261362	+	0.201642i
$301$	5.94038	−	33.6895i	0.342398	−	1.94183i
$302$	0.362172	+	0.995061i	0.0208407	+	0.0572593i
$303$	−11.7048	−	7.41370i	−0.672425	−	0.425906i
$304$	−2.55685	−	3.53023i	−0.146646	−	0.202472i
$305$			6.91515i			0.395960i
$306$	−4.32755	+	4.37321i	−0.247390	+	0.250000i
$307$	5.79322	+	15.9167i	0.330636	+	0.908416i	0.987946	+	0.154796i	$0.0494720\pi$
$307$	5.79322	+	15.9167i	0.330636	+	0.908416i	−0.657310	+	0.753620i	$0.728306\pi$
$308$	4.31943	+	5.14769i	0.246122	+	0.293317i
$309$	7.36085	+	1.61161i	0.418744	+	0.0916813i
$310$	−7.75901	+	6.51058i	−0.440682	+	0.369776i
$311$			22.0770i			1.25187i	0.779874	+	0.625937i	$0.215283\pi$
$311$			22.0770i			1.25187i	−0.779874	+	0.625937i	$0.784717\pi$
$312$	−4.88601	−	3.09474i	−0.276616	−	0.175205i
$313$	−15.6367	−	5.69128i	−0.883837	−	0.321690i	−0.140080	−	0.990140i	$-0.544736\pi$
$313$	−15.6367	−	5.69128i	−0.883837	−	0.321690i	−0.743757	+	0.668450i	$0.766958\pi$
$314$	−4.31381	+	3.61972i	−0.243443	+	0.204273i
$315$	11.5371	−	5.45375i	0.650044	−	0.307284i
$316$	−5.45533	+	3.14963i	−0.306886	+	0.177181i
$317$	−2.23492	−	12.6748i	−0.125525	−	0.711890i	−0.980994	−	0.194036i	$-0.937842\pi$
$317$	−2.23492	−	12.6748i	−0.125525	−	0.711890i	0.855469	−	0.517854i	$-0.173269\pi$
$318$	−0.912562	−	0.831815i	−0.0511739	−	0.0466459i
$319$	2.27362	−	6.24673i	0.127298	−	0.349749i
$320$	−1.28363	−	0.226339i	−0.0717573	−	0.0126528i
$321$	1.26989	−	5.80009i	0.0708785	−	0.323730i
$322$	17.9243	−	10.3486i	0.998881	−	0.576704i
$323$	7.23985	−	5.24364i	0.402836	−	0.291764i
$324$	8.87918	+	1.46973i	0.493288	+	0.0816516i
$325$	7.08534	−	8.44398i	0.393024	−	0.468388i
$326$	12.2608	+	10.2880i	0.679061	+	0.569800i
$327$	18.5819	+	24.0853i	1.02758	+	1.33192i
$328$	−3.68884	−	3.09531i	−0.203682	−	0.170910i
$329$	−15.5779	−	18.5650i	−0.858836	−	1.02352i
$330$	4.64475	+	0.190585i	0.255685	+	0.0104914i
$331$			15.0705i			0.828349i	0.910198	+	0.414174i	$0.135930\pi$
$331$			15.0705i			0.828349i	−0.910198	+	0.414174i	$0.864070\pi$
$332$	−8.66761	−	10.3297i	−0.475697	−	0.566913i
$333$	24.5844	−	2.28091i	1.34721	−	0.124993i
$334$	−0.323976	+	0.561144i	−0.0177272	+	0.0307044i
$335$	9.41154	−	16.3013i	0.514207	−	0.890633i
$336$	−5.22791	−	2.14942i	−0.285206	−	0.117260i
$337$	−7.95511	+	9.48053i	−0.433342	+	0.516437i	−0.937883	−	0.346950i	$-0.887217\pi$
$337$	−7.95511	+	9.48053i	−0.433342	+	0.516437i	0.504541	+	0.863388i	$0.331662\pi$
$338$	−1.73828	−	0.632682i	−0.0945499	−	0.0344134i
$339$	14.9420	−	4.75432i	0.811537	−	0.258219i
$340$	0.464180	−	2.63250i	0.0251737	−	0.142767i
$341$	−16.0007			−0.866488
$342$	−12.3802	−	4.21082i	−0.669444	−	0.227695i
$343$	10.9316			0.590251
$344$	−1.82026	+	10.3232i	−0.0981416	+	0.556589i
$345$	3.06228	−	13.9866i	0.164868	−	0.753014i
$346$	−8.98881	−	3.27166i	−0.483242	−	0.175886i
$347$	−6.98358	+	8.32271i	−0.374898	+	0.446786i	−0.920197	−	0.391455i	$-0.871972\pi$
$347$	−6.98358	+	8.32271i	−0.374898	+	0.446786i	0.545299	+	0.838242i	$0.316416\pi$
$348$	0.744417	+	5.54201i	0.0399050	+	0.297083i
$349$	10.3027	−	17.8448i	0.551492	−	0.955212i	−0.446675	−	0.894696i	$-0.647392\pi$
$349$	10.3027	−	17.8448i	0.551492	−	0.955212i	0.998167	−	0.0605162i	$-0.0192747\pi$
$350$	5.38647	−	9.32964i	0.287919	−	0.498690i
$351$	−17.3279	+	0.893257i	−0.924895	+	0.0476785i
$352$	−1.32356	−	1.57736i	−0.0705461	−	0.0840736i
$353$		−	3.87396i		−	0.206190i	−0.994672	−	0.103095i	$-0.967125\pi$
$353$		−	3.87396i		−	0.206190i	0.994672	−	0.103095i	$-0.0328746\pi$
$354$	2.85427	−	4.50635i	0.151703	−	0.239510i
$355$	−2.24587	−	2.67652i	−0.119198	−	0.142055i
$356$	5.60213	+	4.70075i	0.296912	+	0.249139i
$357$	4.40806	−	10.7215i	0.233299	−	0.567441i
$358$	4.50589	+	3.78089i	0.238144	+	0.199826i
$359$	16.2229	−	19.3337i	0.856212	−	1.02039i	−0.143316	−	0.989677i	$-0.545777\pi$
$359$	16.2229	−	19.3337i	0.856212	−	1.02039i	0.999528	−	0.0307166i	$-0.00977895\pi$
$360$	−3.53522	+	1.67114i	−0.186323	+	0.0880769i
$361$	16.7494	+	8.96978i	0.881548	+	0.472094i
$362$	11.2918	−	6.51930i	0.593482	−	0.342647i
$363$	−8.65340	−	7.88771i	−0.454186	−	0.413998i
$364$	10.7318	+	1.89231i	0.562500	+	0.0991840i
$365$	3.15173	−	8.65930i	0.164969	−	0.453248i
$366$	1.96534	−	8.97646i	0.102730	−	0.469207i
$367$	1.31839	+	7.47696i	0.0688194	+	0.390294i	0.999689	+	0.0249424i	$0.00794024\pi$
$367$	1.31839	+	7.47696i	0.0688194	+	0.390294i	−0.930869	+	0.365352i	$0.880949\pi$
$368$	−5.49238	+	3.17102i	−0.286310	+	0.165301i
$369$	−14.3978	−	1.18354i	−0.749517	−	0.0616128i
$370$	−8.21755	+	6.89535i	−0.427210	+	0.358472i
$371$	2.18623	+	0.795724i	0.113504	+	0.0413119i
$372$	11.9222	−	6.24612i	0.618138	−	0.323846i
$373$			17.6787i			0.915368i	0.889115	+	0.457684i	$0.151321\pi$
$373$			17.6787i			0.915368i	−0.889115	+	0.457684i	$0.848679\pi$
$374$	3.23488	−	2.71438i	0.167272	−	0.140357i
$375$	−5.68229	−	17.8584i	−0.293432	−	0.922203i
$376$	4.77339	+	5.68870i	0.246169	+	0.293372i
$377$	−3.68707	−	10.1301i	−0.189894	−	0.521729i
$378$	−16.5262	+	3.80049i	−0.850016	+	0.195476i
$379$		−	13.2983i		−	0.683086i	−0.939866	−	0.341543i	$-0.889051\pi$
$379$		−	13.2983i		−	0.683086i	0.939866	−	0.341543i	$-0.110949\pi$
$380$	5.46377	−	1.55793i	0.280286	−	0.0799201i
$381$	−10.4416	+	5.47043i	−0.534940	+	0.280259i
$382$	6.78548	+	18.6429i	0.347175	+	0.953856i
$383$	−6.04666	+	34.2923i	−0.308970	+	1.75225i	0.295234	+	0.955425i	$0.404602\pi$
$383$	−6.04666	+	34.2923i	−0.308970	+	1.75225i	−0.604204	+	0.796830i	$0.706509\pi$
$384$	1.60194	+	0.658626i	0.0817487	+	0.0336104i
$385$	−8.23065	+	2.99571i	−0.419473	+	0.152676i
$386$	−0.630290	+	1.73171i	−0.0320809	+	0.0881416i
$387$	13.4396	+	28.4308i	0.683172	+	1.44522i
$388$	−7.04324	−	4.06642i	−0.357567	−	0.206441i
$389$	−6.52938	+	17.9393i	−0.331053	+	0.909560i	0.656786	+	0.754077i	$0.271916\pi$
$389$	−6.52938	+	17.9393i	−0.331053	+	0.909560i	−0.987839	+	0.155483i	$0.950307\pi$
$390$	5.96872	−	4.60489i	0.302238	−	0.233178i
$391$	−6.50319	−	11.2639i	−0.328880	−	0.569638i
$392$	3.65033			0.184369
$393$	−13.4076	+	32.6106i	−0.676325	+	1.64499i
$394$	2.91747	+	8.01569i	0.146980	+	0.403824i
$395$	−1.42577	−	8.08596i	−0.0717384	−	0.406849i
$396$	−5.97512	−	1.56747i	−0.300261	−	0.0787683i
$397$	10.1733	+	8.53639i	0.510582	+	0.428429i	0.861334	−	0.508039i	$-0.169630\pi$
$397$	10.1733	+	8.53639i	0.510582	+	0.428429i	−0.350752	+	0.936468i	$0.614074\pi$
$398$	7.30624	+	12.6548i	0.366229	+	0.634326i
$399$	24.5911	−	1.53214i	1.23109	−	0.0767030i
$400$	−1.65053	+	2.85880i	−0.0825263	+	0.142940i
$401$	−10.1925	+	3.70978i	−0.508991	+	0.185258i	−0.583734	−	0.811945i	$-0.698409\pi$
$401$	−10.1925	+	3.70978i	−0.508991	+	0.185258i	0.0747424	+	0.997203i	$0.476187\pi$
$402$	−16.8499	+	18.4856i	−0.840398	+	0.921978i
$403$	−19.8773	+	16.6790i	−0.990158	+	0.830841i
$404$	−7.87777	−	1.38906i	−0.391934	−	0.0691085i
$405$	−5.75852	+	10.2203i	−0.286143	+	0.507850i
$406$	−5.26794	−	9.12434i	−0.261444	−	0.452834i
$407$	−16.9463			−0.839999
$408$	−1.35072	+	3.28528i	−0.0668707	+	0.162646i
$409$	17.7258	−	3.12554i	0.876485	−	0.154548i	0.282736	−	0.959198i	$-0.408758\pi$
$409$	17.7258	−	3.12554i	0.876485	−	0.154548i	0.593750	+	0.804650i	$0.297647\pi$
$410$	5.43571	−	3.13831i	0.268451	−	0.154990i
$411$	1.07833	−	26.2799i	0.0531900	−	1.29629i
$412$	4.28436	−	0.755449i	0.211075	−	0.0372183i
$413$	−1.74527	+	9.89793i	−0.0858792	+	0.487045i
$414$	−7.95020	+	17.2855i	−0.390731	+	0.849536i
$415$	16.5161	−	6.01137i	0.810743	−	0.295086i
$416$	−3.28846	−	0.579844i	−0.161230	−	0.0284292i
$417$	17.4697	+	0.716823i	0.855493	+	0.0351030i
$418$	8.19400	+	3.66281i	0.400782	+	0.179154i
$419$	−16.9080	−	9.76182i	−0.826008	−	0.476896i	0.0264758	−	0.999649i	$-0.491572\pi$
$419$	−16.9080	−	9.76182i	−0.826008	−	0.476896i	−0.852484	+	0.522753i	$0.824905\pi$
$420$	4.96328	−	5.44508i	0.242183	−	0.265693i
$421$	13.9378	−	16.6104i	0.679288	−	0.809544i	−0.310728	−	0.950499i	$-0.600573\pi$
$421$	13.9378	−	16.6104i	0.679288	−	0.809544i	0.990016	+	0.140955i	$0.0450173\pi$
$422$	0.00577641	−	0.00101854i	0.000281191	−	4.95816e-5i
$423$	21.5491	+	5.65303i	1.04775	+	0.274859i
$424$	−0.669908	−	0.243827i	−0.0325336	−	0.0118413i
$425$	−5.86287	−	3.38493i	−0.284391	−	0.164193i
$426$	2.15464	+	4.11265i	0.104393	+	0.199259i
$427$	3.00652	+	17.0508i	0.145495	+	0.825146i
$428$	−0.595267	−	3.37593i	−0.0287733	−	0.163182i
$429$	11.8991	+	0.488248i	0.574493	+	0.0235728i
$430$	−11.8327	−	6.83159i	−0.570622	−	0.329449i
$431$	−35.8614	−	13.0525i	−1.72738	−	0.628716i	−0.728944	−	0.684574i	$-0.759988\pi$
$431$	−35.8614	−	13.0525i	−1.72738	−	0.628716i	−0.998439	+	0.0558578i	$0.982211\pi$
$432$	5.06397	−	1.16455i	0.243641	−	0.0560294i
$433$	4.82012	−	0.849918i	0.231640	−	0.0408444i	−0.0566230	−	0.998396i	$-0.518033\pi$
$433$	4.82012	−	0.849918i	0.231640	−	0.0408444i	0.288263	+	0.957551i	$0.406922\pi$
$434$	−16.3009	+	19.4266i	−0.782468	+	0.932509i
$435$	−7.11988	−	1.55885i	−0.341372	−	0.0747412i
$436$	15.2101	+	8.78155i	0.728432	+	0.420560i
$437$	15.4926	−	22.8952i	0.741110	−	1.09523i
$438$	−6.55225	+	10.3448i	−0.313078	+	0.494292i
$439$	6.74531	+	1.18938i	0.321936	+	0.0567661i	0.332281	−	0.943180i	$-0.392182\pi$
$439$	6.74531	+	1.18938i	0.321936	+	0.0567661i	−0.0103447	+	0.999946i	$0.503293\pi$
$440$	2.52204	−	0.917949i	0.120234	−	0.0437615i
$441$	8.93743	−	6.32821i	0.425592	−	0.301343i
$442$	1.18915	−	6.74402i	0.0565622	−	0.320780i
$443$	−34.6880	+	6.11642i	−1.64807	+	0.290600i	−0.919125	−	0.393967i	$-0.871102\pi$
$443$	−34.6880	+	6.11642i	−1.64807	+	0.290600i	−0.728950	+	0.684567i	$0.759991\pi$
$444$	12.6268	−	6.61526i	0.599241	−	0.313946i
$445$	−8.25505	+	4.76605i	−0.391327	+	0.225933i
$446$	0.185695	−	0.0327431i	0.00879292	−	0.00155043i
$447$	−18.4396	−	23.9009i	−0.872165	−	1.13047i
$448$	−3.26348			−0.154185
$449$	19.6875	+	34.0997i	0.929108	+	1.60926i	0.784817	+	0.619727i	$0.212757\pi$
$449$	19.6875	+	34.0997i	0.929108	+	1.60926i	0.144291	+	0.989535i	$0.453910\pi$
$450$	0.914875	+	9.86081i	0.0431276	+	0.464843i
$451$	9.76483	+	1.72180i	0.459808	+	0.0810765i
$452$	6.93494	−	5.81911i	0.326192	−	0.273708i
$453$	1.79167	+	0.392274i	0.0841798	+	0.0184306i
$454$	−25.7831	+	9.38430i	−1.21006	+	0.440427i
$455$	−7.10202	+	12.3011i	−0.332948	+	0.576683i
$456$	−7.53522	+	0.469480i	−0.352869	+	0.0219854i
$457$	10.5125	+	18.2081i	0.491752	+	0.851740i	0.999955	−	0.00949775i	$-0.00302327\pi$
$457$	10.5125	+	18.2081i	0.491752	+	0.851740i	−0.508203	+	0.861237i	$0.669690\pi$
$458$	−18.2674	−	15.3281i	−0.853577	−	0.716236i
$459$	2.38828	+	10.3853i	0.111475	+	0.484743i
$460$	−1.43546	−	8.14087i	−0.0669285	−	0.379570i
$461$	3.64989	+	10.0280i	0.169992	+	0.467050i	0.995209	−	0.0977655i	$-0.0311695\pi$
$461$	3.64989	+	10.0280i	0.169992	+	0.467050i	−0.825217	+	0.564816i	$0.808947\pi$
$462$	11.5355	−	1.54948i	0.536680	−	0.0720883i
$463$	−1.68591			−0.0783509			−0.0391754	−	0.999232i	$-0.512473\pi$
$463$	−1.68591			−0.0783509			−0.0391754	+	0.999232i	$0.512473\pi$
$464$	1.61421	+	2.79589i	0.0749377	+	0.129796i
$465$	2.33550	+	17.3872i	0.108306	+	0.806313i
$466$	3.05920	−	8.40507i	0.141715	−	0.389357i
$467$	−36.2276	−	20.9160i	−1.67641	−	0.967878i	−0.963917	−	0.266202i	$-0.914231\pi$
$467$	−36.2276	−	20.9160i	−1.67641	−	0.967878i	−0.712496	−	0.701676i	$-0.752435\pi$
$468$	−9.05665	+	4.28119i	−0.418644	+	0.197898i
$469$	16.1188	−	44.2862i	0.744299	−	2.04494i
$470$	−9.09567	+	3.31055i	−0.419552	+	0.152704i
$471$	1.29848	+	9.66685i	0.0598307	+	0.445425i
$472$	0.534788	−	3.03293i	0.0246156	−	0.139602i
$473$	−7.38229	−	20.2827i	−0.339438	−	0.932598i
$474$	−0.447314	+	10.9015i	−0.0205458	+	0.500721i
$475$	1.02505	−	14.3524i	0.0470326	−	0.658533i
$476$		−	6.69281i		−	0.306764i
$477$	−2.06290	+	0.564370i	−0.0944535	+	0.0258407i
$478$	−0.160518	−	0.441021i	−0.00734194	−	0.0201718i
$479$	−25.1200	−	29.9369i	−1.14776	−	1.36785i	−0.918947	−	0.394381i	$-0.870959\pi$
$479$	−25.1200	−	29.9369i	−1.14776	−	1.36785i	−0.228816	−	0.973470i	$-0.573485\pi$
$480$	−1.52085	+	1.66849i	−0.0694171	+	0.0761557i
$481$	−21.0520	+	17.6647i	−0.959889	+	0.805442i
$482$			3.89232i			0.177290i
$483$	1.46972	−	35.8184i	0.0668745	−	1.62979i
$484$	−6.35243	−	2.31209i	−0.288747	−	0.105095i
$485$	8.12056	−	6.81396i	0.368736	−	0.309406i
$486$	10.3797	−	11.6302i	0.470834	−	0.527556i
$487$	−8.93455	+	5.15837i	−0.404863	+	0.233748i	−0.688580	−	0.725160i	$-0.741766\pi$
$487$	−8.93455	+	5.15837i	−0.404863	+	0.233748i	0.283717	+	0.958908i	$0.408432\pi$
$488$	−0.921260	−	5.22472i	−0.0417035	−	0.236512i
$489$	26.4170	−	8.40550i	1.19462	−	0.380110i
$490$	−1.62732	+	4.47103i	−0.0735149	+	0.201980i
$491$	−19.8293	−	3.49645i	−0.894886	−	0.157792i	−0.292753	−	0.956188i	$-0.594571\pi$
$491$	−19.8293	−	3.49645i	−0.894886	−	0.157792i	−0.602133	+	0.798396i	$0.705682\pi$
$492$	−7.94795	+	2.52893i	−0.358321	+	0.114013i
$493$	−5.73386	+	3.31044i	−0.258240	+	0.149095i
$494$	13.9973	−	3.99115i	0.629767	−	0.179570i
$495$	4.58360	−	6.61972i	0.206017	−	0.297534i
$496$	4.99494	−	5.95273i	0.224279	−	0.267286i
$497$	−6.70136	−	5.62311i	−0.300597	−	0.252231i
$498$	−23.1478	+	3.10927i	−1.03728	+	0.139330i
$499$	−2.89465	−	2.42890i	−0.129583	−	0.108733i	0.575693	−	0.817666i	$-0.304732\pi$
$499$	−2.89465	−	2.42890i	−0.129583	−	0.108733i	−0.705276	+	0.708933i	$0.749177\pi$
$500$	−6.95489	−	8.28852i	−0.311032	−	0.370674i
$501$	0.520825	+	0.994118i	0.0232687	+	0.0444139i
$502$		−	27.4915i		−	1.22701i
$503$	4.01366	+	4.78329i	0.178960	+	0.213277i	0.848066	−	0.529891i	$-0.177767\pi$
$503$	4.01366	+	4.78329i	0.178960	+	0.213277i	−0.669106	+	0.743167i	$0.733323\pi$
$504$	−7.99029	+	5.65758i	−0.355916	+	0.252009i
$505$	5.21329	−	9.02967i	0.231988	−	0.401815i
$506$	6.52945	−	11.3093i	0.290270	−	0.502762i
$507$	−2.53679	+	1.95714i	−0.112663	+	0.0869198i
$508$	−4.37462	+	5.21347i	−0.194093	+	0.231311i
$509$	−34.7466	−	12.6467i	−1.54012	−	0.560557i	−0.574044	−	0.818824i	$-0.694626\pi$
$509$	−34.7466	−	12.6467i	−1.54012	−	0.560557i	−0.966073	+	0.258267i	$0.916848\pi$
$510$	−3.42176	−	3.11899i	−0.151518	−	0.138111i
$511$	4.00644	−	22.7217i	0.177234	−	1.00515i
$512$	1.00000			0.0441942
$513$	−17.6353	+	14.2125i	−0.778617	+	0.627499i
$514$	−5.22267			−0.230362
$515$	−0.984679	+	5.58439i	−0.0433901	+	0.246078i
$516$	13.4182	+	12.2309i	0.590705	+	0.538437i
$517$	−14.3689	−	5.22984i	−0.631941	−	0.230008i
$518$	−17.2643	+	20.5747i	−0.758548	+	0.904002i
$519$	−13.1180	+	10.1206i	−0.575815	+	0.444244i
$520$	2.17621	−	3.76930i	0.0954330	−	0.165295i
$521$	−18.8850	+	32.7097i	−0.827365	+	1.43304i	0.0727336	+	0.997351i	$0.476828\pi$
$521$	−18.8850	+	32.7097i	−0.827365	+	1.43304i	−0.900098	+	0.435687i	$0.856506\pi$
$522$	8.79917	+	4.04704i	0.385129	+	0.177134i
$523$	−6.21220	−	7.40341i	−0.271640	−	0.323728i	0.612928	−	0.790139i	$-0.289992\pi$
$523$	−6.21220	−	7.40341i	−0.271640	−	0.323728i	−0.884569	+	0.466410i	$0.845547\pi$
$524$			20.3569i			0.889297i
$525$	−8.65929	−	16.5283i	−0.377922	−	0.721355i
$526$	−17.1955	−	20.4928i	−0.749761	−	0.893531i
$527$	12.2080	+	10.2437i	0.531787	+	0.446222i
$528$	−3.53472	+	0.474793i	−0.153829	+	0.0206627i
$529$	−13.1925	−	11.0698i	−0.573587	−	0.481297i
$530$	0.597292	−	0.711825i	0.0259447	−	0.0309197i
$531$	−3.94853	−	8.35292i	−0.171351	−	0.362486i
$532$	12.7948	−	6.21691i	0.554724	−	0.269537i
$533$	13.9254	−	8.03983i	0.603175	−	0.348244i
$534$	12.0703	−	3.84060i	0.522333	−	0.166199i
$535$	4.40031	+	0.775893i	0.190242	+	0.0335448i
$536$	−4.93915	+	13.5702i	−0.213339	+	0.586144i
$537$	9.70836	−	3.08906i	0.418947	−	0.133303i
$538$	−1.66266	−	9.42940i	−0.0716823	−	0.406530i
$539$	−6.50938	+	3.75819i	−0.280379	+	0.161877i
$540$	−0.831153	+	6.72166i	−0.0357671	+	0.289254i
$541$	1.66447	−	1.39665i	0.0715610	−	0.0600468i	−0.606306	−	0.795232i	$-0.707349\pi$
$541$	1.66447	−	1.39665i	0.0715610	−	0.0600468i	0.677867	+	0.735185i	$0.262905\pi$
$542$	23.8677	+	8.68712i	1.02520	+	0.373144i
$543$	0.925878	−	22.5645i	0.0397332	−	0.968337i
$544$			2.05082i			0.0879280i
$545$	−17.5366	+	14.7149i	−0.751185	+	0.630319i
$546$	12.7151	−	13.9494i	0.544155	−	0.596978i
$547$	26.8775	+	32.0314i	1.14920	+	1.36956i	0.917963	+	0.396665i	$0.129833\pi$
$547$	26.8775	+	32.0314i	1.14920	+	1.36956i	0.231236	+	0.972898i	$0.425723\pi$
$548$	−5.19373	−	14.2697i	−0.221865	−	0.609570i
$549$	−11.3132	−	11.1951i	−0.482835	−	0.477794i
$550$		−	6.79719i		−	0.289833i
$551$	−11.6548	−	7.88648i	−0.496511	−	0.335975i
$552$	−0.450352	+	10.9755i	−0.0191683	+	0.467149i
$553$	−7.03110	−	19.3178i	−0.298993	−	0.821476i
$554$	1.99800	−	11.3312i	0.0848871	−	0.481419i
$555$	2.47352	+	18.4148i	0.104995	+	0.781663i
$556$	9.48582	−	3.45256i	0.402288	−	0.146421i
$557$	4.23483	−	11.6351i	0.179435	−	0.492995i	−0.817069	−	0.576541i	$-0.804402\pi$
$557$	4.23483	−	11.6351i	0.179435	−	0.492995i	0.996504	+	0.0835459i	$0.0266245\pi$
$558$	1.90990	−	23.2339i	0.0808525	−	0.983568i
$559$	−30.3133	−	17.5014i	−1.28212	−	0.740230i
$560$	1.45487	−	3.99721i	0.0614793	−	0.168913i
$561$	−0.973713	−	7.24906i	−0.0411102	−	0.306055i
$562$	8.35108	+	14.4645i	0.352269	+	0.610148i
$563$	0.0602887			0.00254086			0.00127043	−	0.999999i	$-0.499596\pi$
$563$	0.0602887			0.00254086			0.00127043	+	0.999999i	$0.499596\pi$
$564$	12.7478	−	1.71233i	0.536781	−	0.0721019i
$565$	4.03581	+	11.0883i	0.169788	+	0.466488i
$566$	3.52999	+	20.0196i	0.148377	+	0.841485i
$567$	−9.75538	+	27.7040i	−0.409687	+	1.16346i
$568$	2.05344	+	1.72304i	0.0861603	+	0.0722971i
$569$	−8.28506	−	14.3501i	−0.347328	−	0.601589i	0.638446	−	0.769667i	$-0.279578\pi$
$569$	−8.28506	−	14.3501i	−0.347328	−	0.601589i	−0.985774	+	0.168077i	$0.946244\pi$
$570$	2.78418	−	9.43866i	0.116616	−	0.395342i
$571$	−21.3078	+	36.9061i	−0.891702	+	1.54447i	−0.0538677	+	0.998548i	$0.517155\pi$
$571$	−21.3078	+	36.9061i	−0.891702	+	1.54447i	−0.837834	+	0.545925i	$0.816178\pi$
$572$	6.46106	−	2.35163i	0.270150	−	0.0983267i
$573$	33.5677	+	7.34944i	1.40231	+	0.307027i
$574$	12.0385	−	10.1015i	0.502476	−	0.421628i
$575$	−20.6174	−	3.63540i	−0.859805	−	0.151607i
$576$	2.44839	−	1.73360i	0.102016	−	0.0722334i
$577$	−10.8760	−	18.8377i	−0.452772	−	0.784224i	0.545785	−	0.837925i	$-0.316232\pi$
$577$	−10.8760	−	18.8377i	−0.452772	−	0.784224i	−0.998557	+	0.0537009i	$0.982898\pi$
$578$	12.7942			0.532167
$579$	1.94974	+	2.52720i	0.0810286	+	0.105027i
$580$	−4.14411	+	0.730718i	−0.172075	+	0.0303414i
$581$	38.1104	−	22.0031i	1.58109	−	0.912841i
$582$	−12.4778	+	6.53718i	−0.517220	+	0.270975i
$583$	1.44563	−	0.254904i	0.0598720	−	0.0105570i
$584$	−1.22766	+	6.96239i	−0.0508008	+	0.288106i
$585$	−1.20626	−	13.0014i	−0.0498726	−	0.537542i
$586$	30.7826	−	11.2039i	1.27162	−	0.462831i
$587$	19.6857	+	3.47112i	0.812515	+	0.143268i	0.564442	−	0.825473i	$-0.309092\pi$
$587$	19.6857	+	3.47112i	0.812515	+	0.143268i	0.248073	+	0.968741i	$0.420203\pi$
$588$	3.38310	−	5.34128i	0.139517	−	0.220271i
$589$	−8.24318	+	32.8535i	−0.339654	+	1.35371i
$590$	3.47642	+	2.00711i	0.143122	+	0.0826314i
$591$	14.4327	+	3.15995i	0.593683	+	0.129983i
$592$	5.29013	−	6.30453i	0.217423	−	0.259115i
$593$	21.4741	−	3.78646i	0.881835	−	0.155491i	0.285646	−	0.958335i	$-0.407792\pi$
$593$	21.4741	−	3.78646i	0.881835	−	0.155491i	0.596189	+	0.802844i	$0.296681\pi$
$594$	−7.83128	+	7.29027i	−0.321321	+	0.299123i
$595$	8.19755	+	2.98366i	0.336067	+	0.122318i
$596$	−15.0936	−	8.71432i	−0.618260	−	0.356952i
$597$	25.2883	+	1.03764i	1.03498	+	0.0424678i
$598$	−3.67740	−	20.8556i	−0.150380	−	0.852847i
$599$	5.97084	+	33.8623i	0.243962	+	1.38358i	0.822891	+	0.568200i	$0.192360\pi$
$599$	5.97084	+	33.8623i	0.243962	+	1.38358i	−0.578929	+	0.815378i	$0.696529\pi$
$600$	2.65339	+	5.06462i	0.108324	+	0.206762i
$601$	12.9174	+	7.45785i	0.526911	+	0.304212i	0.739758	−	0.672874i	$-0.234940\pi$
$601$	12.9174	+	7.45785i	0.526911	+	0.304212i	−0.212847	+	0.977086i	$0.568274\pi$
$602$	−32.1462	−	11.7003i	−1.31018	−	0.476867i
$603$	11.4323	+	41.7877i	0.465561	+	1.70173i
$604$	1.04283	−	0.183880i	0.0424323	−	0.00748196i
$605$	5.66384	−	6.74991i	0.230268	−	0.274423i
$606$	−9.33359	+	10.2396i	−0.379151	+	0.415957i
$607$	26.1965	+	15.1246i	1.06328	+	0.613888i	0.926339	−	0.376691i	$-0.122938\pi$
$607$	26.1965	+	15.1246i	1.06328	+	0.613888i	0.136946	+	0.990579i	$0.456271\pi$
$608$	−3.92059	+	1.90499i	−0.159001	+	0.0772576i
$609$	−18.2333	−	0.748159i	−0.738852	−	0.0303169i
$610$	6.81009	+	1.20080i	0.275733	+	0.0486191i
$611$	−23.3016	+	8.48109i	−0.942681	+	0.343108i
$612$	3.55530	+	5.02120i	0.143714	+	0.202970i
$613$	1.85619	−	10.5270i	0.0749710	−	0.425181i	−0.924103	−	0.382145i	$-0.875186\pi$
$613$	1.85619	−	10.5270i	0.0749710	−	0.425181i	0.999073	−	0.0430368i	$-0.0137033\pi$
$614$	16.6809	−	2.94129i	0.673187	−	0.118701i
$615$	0.445706	−	10.8623i	0.0179726	−	0.438010i
$616$	5.81955	−	3.35992i	0.234476	−	0.135375i
$617$	−16.6774	+	2.94068i	−0.671407	+	0.118387i	−0.498951	−	0.866630i	$-0.666281\pi$
$617$	−16.6774	+	2.94068i	−0.671407	+	0.118387i	−0.172456	+	0.985017i	$0.555170\pi$
$618$	2.86532	−	6.96917i	0.115260	−	0.280341i
$619$	−35.7970			−1.43880			−0.719401	−	0.694595i	$-0.755584\pi$
$619$	−35.7970			−1.43880			−0.719401	+	0.694595i	$0.755584\pi$
$620$	5.06433	+	8.77168i	0.203389	+	0.352279i
$621$	17.9245	+	27.6531i	0.719287	+	1.10968i
$622$	21.7416	+	3.83364i	0.871760	+	0.153715i
$623$	−18.2825	+	15.3408i	−0.732471	+	0.614616i
$624$	−3.89617	+	4.27438i	−0.155972	+	0.171112i
$625$	−2.25735	+	0.821609i	−0.0902941	+	0.0328644i
$626$	−8.32010	+	14.4108i	−0.332538	+	0.575973i
$627$	12.9537	−	8.59508i	0.517321	−	0.343254i
$628$	2.81564	+	4.87684i	0.112356	+	0.194607i
$629$	12.9294	+	10.8491i	0.515530	+	0.432581i
$630$	−3.36749	−	12.3089i	−0.134164	−	0.490398i
$631$	2.75282	+	15.6120i	0.109588	+	0.621505i	0.989288	+	0.145976i	$0.0466323\pi$
$631$	2.75282	+	15.6120i	0.109588	+	0.621505i	−0.879700	+	0.475529i	$0.842257\pi$
$632$	2.15448	+	5.91938i	0.0857005	+	0.235460i
$633$	0.00386319	−	0.00939621i	0.000153548	−	0.000373466i
$634$	−12.8704			−0.511148
$635$	−4.43540	−	7.68234i	−0.176014	−	0.304865i
$636$	−0.977642	+	0.754255i	−0.0387660	+	0.0299082i
$637$	−4.16892	+	11.4540i	−0.165179	+	0.453825i
$638$	−5.75701	−	3.32381i	−0.227922	−	0.131591i
$639$	8.01468	+	0.658833i	0.317056	+	0.0260630i
$640$	−0.445801	+	1.22483i	−0.0176219	+	0.0484156i
$641$	17.4262	−	6.34262i	0.688294	−	0.250519i	0.0258895	−	0.999665i	$-0.491758\pi$
$641$	17.4262	−	6.34262i	0.688294	−	0.250519i	0.662405	+	0.749146i	$0.269536\pi$
$642$	−5.49146	−	2.25778i	−0.216731	−	0.0891073i
$643$	1.21339	−	6.88148i	0.0478514	−	0.271379i	−0.951489	−	0.307682i	$-0.900447\pi$
$643$	1.21339	−	6.88148i	0.0478514	−	0.271379i	0.999341	+	0.0363025i	$0.0115580\pi$
$644$	−7.07885	−	19.4490i	−0.278946	−	0.766397i
$645$	−20.9627	+	10.9825i	−0.825404	+	0.432435i
$646$	−3.90679	−	8.04041i	−0.153711	−	0.316346i
$647$		−	33.8004i		−	1.32883i	−0.747364	−	0.664415i	$-0.768681\pi$
$647$		−	33.8004i		−	1.32883i	0.747364	−	0.664415i	$-0.231319\pi$
$648$	2.98925	−	8.48907i	0.117429	−	0.333482i
$649$	2.16890	+	5.95901i	0.0851369	+	0.233912i
$650$	−7.08534	−	8.44398i	−0.277910	−	0.331200i
$651$	13.3182	+	41.8565i	0.521979	+	1.64049i
$652$	12.2608	−	10.2880i	0.480169	−	0.402909i
$653$			9.43824i			0.369347i	0.982800	+	0.184673i	$0.0591227\pi$
$653$			9.43824i			0.369347i	−0.982800	+	0.184673i	$0.940877\pi$
$654$	26.9461	−	14.1172i	1.05368	−	0.552027i
$655$	−24.9338	−	9.07515i	−0.974243	−	0.354596i
$656$	−3.68884	+	3.09531i	−0.144025	+	0.120851i
$657$	9.06422	+	19.1749i	0.353629	+	0.748086i
$658$	−20.9880	+	12.1174i	−0.818198	+	0.472387i
$659$	5.15509	+	29.2360i	0.200814	+	1.13887i	0.903892	+	0.427760i	$0.140697\pi$
$659$	5.15509	+	29.2360i	0.200814	+	1.13887i	−0.703079	+	0.711112i	$0.748192\pi$
$660$	0.994242	−	4.54109i	0.0387008	−	0.176762i
$661$	9.11421	−	25.0411i	0.354502	−	0.973985i	−0.626404	−	0.779499i	$-0.715474\pi$
$661$	9.11421	−	25.0411i	0.354502	−	0.973985i	0.980905	−	0.194486i	$-0.0623040\pi$
$662$	14.8415	+	2.61696i	0.576833	+	0.101711i
$663$	−8.76598	−	7.99033i	−0.340442	−	0.310319i
$664$	−11.6778	+	6.74220i	−0.453188	+	0.261648i
$665$	1.91072	+	18.4429i	0.0740947	+	0.715186i
$666$	2.02277	−	24.6069i	0.0783808	−	0.953500i
$667$	−13.1609	+	15.6846i	−0.509593	+	0.607310i
$668$	0.496361	+	0.416496i	0.0192048	+	0.0161147i
$669$	0.124191	−	0.302062i	0.00480148	−	0.0116784i
$670$	−14.4193	−	12.0992i	−0.557067	−	0.467434i
$671$	7.02193	+	8.36841i	0.271079	+	0.323059i
$672$	−3.02458	+	4.77524i	−0.116676	+	0.184209i
$673$		−	38.2565i		−	1.47468i	−0.675521	−	0.737341i	$-0.736081\pi$
$673$		−	38.2565i		−	1.47468i	0.675521	−	0.737341i	$-0.263919\pi$
$674$	7.95511	+	9.48053i	0.306419	+	0.365176i
$675$	15.2766	+	7.80027i	0.587995	+	0.300232i
$676$	−0.924919	+	1.60201i	−0.0355738	+	0.0616157i
$677$	6.58446	−	11.4046i	0.253061	−	0.438315i	−0.711306	−	0.702883i	$-0.751896\pi$
$677$	6.58446	−	11.4046i	0.253061	−	0.438315i	0.964367	+	0.264568i	$0.0852292\pi$
$678$	−2.08745	−	15.5406i	−0.0801680	−	0.596831i
$679$	17.0605	−	20.3319i	0.654721	−	0.780266i
$680$	−2.51190	−	0.914257i	−0.0963270	−	0.0350602i
$681$	−10.1642	+	46.4241i	−0.389495	+	1.77897i
$682$	−2.77850	+	15.7576i	−0.106394	+	0.603391i
$683$	−12.6975			−0.485856			−0.242928	−	0.970044i	$-0.578108\pi$
$683$	−12.6975			−0.485856			−0.242928	+	0.970044i	$0.578108\pi$
$684$	−6.29664	+	11.4609i	−0.240758	+	0.438219i
$685$	19.7933			0.756262
$686$	1.89825	−	10.7655i	0.0724756	−	0.411030i
$687$	−39.3587	+	12.5234i	−1.50163	+	0.477797i
$688$	9.85027	+	3.58520i	0.375538	+	0.136685i
$689$	1.53016	−	1.82358i	0.0582945	−	0.0694727i
$690$	−13.2424	−	5.44451i	−0.504128	−	0.207269i
$691$	16.4826	−	28.5486i	0.627026	−	1.08604i	−0.361119	−	0.932520i	$-0.617605\pi$
$691$	16.4826	−	28.5486i	0.627026	−	1.08604i	0.988145	−	0.153522i	$-0.0490614\pi$
$692$	−4.78285	+	8.28413i	−0.181817	+	0.314916i
$693$	8.42378	−	18.3152i	0.319993	−	0.695736i
$694$	6.98358	+	8.32271i	0.265093	+	0.315926i
$695$			13.1577i			0.499099i
$696$	5.58708	+	0.229252i	0.211778	+	0.00868976i
$697$	−6.34790	−	7.56514i	−0.240444	−	0.286550i
$698$	−15.7847	−	13.2449i	−0.597459	−	0.501328i
$699$	−9.46334	−	12.2661i	−0.357936	−	0.463946i
$700$	−8.25255	−	6.92471i	−0.311917	−	0.261729i
$701$	−14.9596	+	17.8281i	−0.565015	+	0.673359i	−0.970600	−	0.240698i	$-0.922624\pi$
$701$	−14.9596	+	17.8281i	−0.565015	+	0.673359i	0.405585	+	0.914058i	$0.367068\pi$
$702$	−2.12927	+	17.2198i	−0.0803643	+	0.649918i
$703$	−8.73034	+	34.7951i	−0.329271	+	1.31232i
$704$	−1.78323	+	1.02955i	−0.0672081	+	0.0388026i
$705$	−3.58570	+	16.3773i	−0.135045	+	0.616805i
$706$	−3.81511	−	0.672707i	−0.143583	−	0.0253176i
$707$	8.92863	−	24.5312i	0.335796	−	0.922591i
$708$	−3.94225	−	3.59342i	−0.148159	−	0.135049i
$709$	−1.84026	−	10.4366i	−0.0691123	−	0.391955i	−0.999667	−	0.0258025i	$-0.991786\pi$
$709$	−1.84026	−	10.4366i	−0.0691123	−	0.391955i	0.930555	−	0.366153i	$-0.119325\pi$
$710$	−3.02585	+	1.74698i	−0.113558	+	0.0655629i
$711$	15.5368	+	10.7580i	0.582677	+	0.403455i
$712$	5.60213	−	4.70075i	0.209949	−	0.176168i
$713$	46.3103	+	16.8556i	1.73434	+	0.631247i
$714$	−9.79314	−	6.20285i	−0.366499	−	0.232136i
$715$			8.96205i			0.335162i
$716$	4.50589	−	3.78089i	0.168393	−	0.141299i
$717$	−0.794084	−	0.173860i	−0.0296556	−	0.00649291i
$718$	−16.2229	−	19.3337i	−0.605433	−	0.721527i
$719$	−1.32071	−	3.62861i	−0.0492541	−	0.135324i	0.912626	−	0.408795i	$-0.134051\pi$
$719$	−1.32071	−	3.62861i	−0.0492541	−	0.135324i	−0.961880	+	0.273470i	$0.911829\pi$
$720$	1.03187	+	3.77171i	0.0384555	+	0.140563i
$721$			14.1976i			0.528748i
$722$	11.7420	−	14.9374i	0.436993	−	0.555911i
$723$	5.69537	+	3.60738i	0.211813	+	0.134160i
$724$	−4.45946	−	12.2523i	−0.165735	−	0.455352i
$725$	−1.85060	+	10.4953i	−0.0687295	+	0.389784i
$726$	−9.27053	+	7.15225i	−0.344062	+	0.265445i
$727$	46.6599	−	16.9828i	1.73052	−	0.629858i	0.731852	−	0.681463i	$-0.238656\pi$
$727$	46.6599	−	16.9828i	1.73052	−	0.629858i	0.998668	+	0.0516058i	$0.0164339\pi$
$728$	3.72712	−	10.2402i	0.138136	−	0.379527i
$729$	−7.39780	−	25.9668i	−0.273993	−	0.961732i
$730$	−7.98045	−	4.60752i	−0.295370	−	0.170532i
$731$	−7.35260	+	20.2011i	−0.271946	+	0.747164i
$732$	−8.49881	−	3.49422i	−0.314125	−	0.129150i
$733$	−5.17277	−	8.95949i	−0.191060	−	0.330926i	0.754541	−	0.656252i	$-0.227859\pi$
$733$	−5.17277	−	8.95949i	−0.191060	−	0.330926i	−0.945602	+	0.325326i	$0.894526\pi$
$734$	7.59231			0.280237
$735$	5.03397	+	6.52487i	0.185681	+	0.240674i
$736$	2.16911	+	5.95958i	0.0799544	+	0.219673i
$737$	−5.16355	−	29.2839i	−0.190202	−	1.07869i
$738$	−3.66571	+	13.9735i	−0.134937	+	0.514372i
$739$	41.1169	+	34.5012i	1.51251	+	1.26915i	0.858691	+	0.512493i	$0.171278\pi$
$739$	41.1169	+	34.5012i	1.51251	+	1.26915i	0.653818	+	0.756652i	$0.273166\pi$
$740$	5.36363	+	9.29008i	0.197171	+	0.341510i
$741$	7.13260	−	24.1803i	0.262023	−	0.888284i
$742$	1.16327	−	2.01484i	0.0427050	−	0.0739673i
$743$	24.1156	−	8.77737i	0.884717	−	0.322011i	0.140605	−	0.990066i	$-0.455095\pi$
$743$	24.1156	−	8.77737i	0.884717	−	0.322011i	0.744112	+	0.668055i	$0.232873\pi$
$744$	−4.08096	−	12.8257i	−0.149615	−	0.470214i
$745$	17.4023	−	14.6023i	0.637572	−	0.534986i
$746$	17.4101	+	3.06987i	0.637429	+	0.112396i
$747$	−16.9036	+	36.7523i	−0.618472	+	1.34470i
$748$	−2.11142	−	3.65708i	−0.0772010	−	0.133716i
$749$	11.1872			0.408773
$750$	−18.5738	+	2.49488i	−0.678219	+	0.0911002i
$751$	−16.1624	+	2.84987i	−0.589774	+	0.103993i	−0.460568	−	0.887625i	$-0.652354\pi$
$751$	−16.1624	+	2.84987i	−0.589774	+	0.103993i	−0.129207	+	0.991618i	$0.541243\pi$
$752$	6.43117	−	3.71304i	0.234521	−	0.135400i
$753$	−40.2266	−	25.4790i	−1.46594	−	0.928507i
$754$	−10.6165	+	1.87198i	−0.386630	+	0.0681733i
$755$	−0.239676	+	1.35927i	−0.00872269	+	0.0494688i
$756$	0.873006	+	16.9351i	0.0317509	+	0.615923i
$757$	0.0178338	−	0.00649098i	0.000648181	−	0.000235919i	−0.341696	−	0.939811i	$-0.611001\pi$
$757$	0.0178338	−	0.00649098i	0.000648181	−	0.000235919i	0.342344	+	0.939575i	$0.388779\pi$
$758$	−13.0962	−	2.30922i	−0.475676	−	0.0838746i
$759$	−10.4968	−	20.0355i	−0.381008	−	0.727244i
$760$	−0.585486	−	5.65130i	−0.0212378	−	0.204994i
$761$	−31.1010	−	17.9562i	−1.12741	−	0.650911i	−0.184129	−	0.982902i	$-0.558946\pi$
$761$	−31.1010	−	17.9562i	−1.12741	−	0.650911i	−0.943283	+	0.331991i	$0.892280\pi$
$762$	3.57415	+	11.2329i	0.129478	+	0.406926i
$763$	−36.8426	+	43.9073i	−1.33379	+	1.58955i
$764$	19.5380	−	3.44508i	0.706860	−	0.124639i
$765$	−7.73508	+	2.11617i	−0.279662	+	0.0765104i
$766$	32.7213	+	11.9096i	1.18227	+	0.430311i
$767$	8.90600	+	5.14188i	0.321577	+	0.185663i
$768$	0.926794	−	1.46323i	0.0334428	−	0.0527999i
$769$	8.37623	+	47.5040i	0.302055	+	1.71304i	0.637055	+	0.770819i	$0.280153\pi$
$769$	8.37623	+	47.5040i	0.302055	+	1.71304i	−0.335000	+	0.942218i	$0.608736\pi$
$770$	1.52096	+	8.62581i	0.0548117	+	0.310853i
$771$	−4.84034	+	7.64198i	−0.174320	+	0.275219i
$772$	1.59595	+	0.921423i	0.0574395	+	0.0331627i
$773$	33.5218	+	12.2009i	1.20570	+	0.438837i	0.865209	−	0.501412i	$-0.167186\pi$
$773$	33.5218	+	12.2009i	1.20570	+	0.438837i	0.340487	+	0.940249i	$0.389408\pi$
$774$	30.3326	−	8.29845i	1.09028	−	0.298282i
$775$	25.2619	−	4.45436i	0.907435	−	0.160005i
$776$	−5.22769	+	6.23012i	−0.187663	+	0.223648i
$777$	14.1052	+	44.3302i	0.506022	+	1.59034i
$778$	16.5330	+	9.54532i	0.592736	+	0.342216i
$779$	8.56590	−	19.1626i	0.306905	−	0.686572i
$780$	−3.49847	−	6.67767i	−0.125265	−	0.239099i
$781$	−5.43571	−	0.958462i	−0.194505	−	0.0342965i
$782$	−12.2220	+	4.44844i	−0.437058	+	0.159076i
$783$	14.0768	−	9.12447i	0.503064	−	0.326082i
$784$	0.633873	−	3.59487i	0.0226383	−	0.128388i
$785$	−7.22851	+	1.27458i	−0.257997	+	0.0454918i
$786$	29.7870	+	18.8667i	1.06247	+	0.672953i
$787$	−18.8925	+	10.9076i	−0.673444	+	0.388813i	−0.797380	−	0.603477i	$-0.793781\pi$
$787$	−18.8925	+	10.9076i	−0.673444	+	0.388813i	0.123937	+	0.992290i	$0.460448\pi$
$788$	8.40052	−	1.48124i	0.299256	−	0.0527670i
$789$	−45.9226	+	6.16844i	−1.63489	+	0.219602i
$790$	−8.21069			−0.292123
$791$	14.7720	+	25.5859i	0.525233	+	0.909730i
$792$	−2.58122	+	5.61215i	−0.0917198	+	0.199419i
$793$	17.4463	+	3.07626i	0.619537	+	0.109241i
$794$	10.1733	−	8.53639i	0.361036	−	0.302945i
$795$	−0.487999	−	1.53369i	−0.0173076	−	0.0543945i
$796$	13.7312	−	4.99776i	0.486691	−	0.177141i
$797$	15.9377	−	27.6049i	0.564542	−	0.977815i	−0.432550	−	0.901610i	$-0.642386\pi$
$797$	15.9377	−	27.6049i	0.564542	−	0.977815i	0.997092	−	0.0762056i	$-0.0242805\pi$
$798$	2.76133	−	24.4835i	0.0977501	−	0.866708i
$799$	7.61476	+	13.1891i	0.269391	+	0.466598i
$800$	2.52875	+	2.12188i	0.0894049	+	0.0750197i
$801$	5.56700	−	21.2211i	0.196700	−	0.749812i
$802$	1.88351	+	10.6819i	0.0665089	+	0.377191i
$803$	−4.97893	−	13.6795i	−0.175703	−	0.482739i
$804$	15.2788	+	19.8039i	0.538842	+	0.698430i
$805$	26.9775			0.950830
$806$	12.9740	+	22.4716i	0.456989	+	0.791528i
$807$	−15.3384	−	6.30626i	−0.539936	−	0.221991i
$808$	−2.73592	+	7.51688i	−0.0962493	+	0.264443i
$809$	11.1159	+	6.41776i	0.390814	+	0.225637i	0.682513	−	0.730874i	$-0.260887\pi$
$809$	11.1159	+	6.41776i	0.390814	+	0.225637i	−0.291699	+	0.956510i	$0.594220\pi$
$810$	9.06505	+	7.44577i	0.318514	+	0.261618i
$811$	18.8697	−	51.8440i	0.662603	−	1.82049i	0.0978953	−	0.995197i	$-0.468789\pi$
$811$	18.8697	−	51.8440i	0.662603	−	1.82049i	0.564708	−	0.825291i	$-0.308989\pi$
$812$	−9.90049	+	3.60348i	−0.347439	+	0.126458i
$813$	34.8317	−	26.8728i	1.22160	−	0.942470i
$814$	−2.94270	+	16.6889i	−0.103142	+	0.584945i
$815$	7.13519	+	19.6038i	0.249935	+	0.686690i
$816$	3.00082	+	1.90068i	0.105050	+	0.0665373i
$817$	−45.4486	+	4.70857i	−1.59005	+	0.164732i
$818$		−	17.9993i		−	0.629329i
$819$	−8.62694	−	31.5333i	−0.301450	−	1.10186i
$820$	−2.14673	−	5.89809i	−0.0749671	−	0.205970i
$821$	12.2406	+	14.5877i	0.427199	+	0.509116i	0.936112	−	0.351702i	$-0.114397\pi$
$821$	12.2406	+	14.5877i	0.427199	+	0.509116i	−0.508913	+	0.860818i	$0.669953\pi$
$822$	−25.6934	−	5.62540i	−0.896159	−	0.196208i
$823$	0.593422	−	0.497940i	0.0206854	−	0.0173571i	−0.632386	−	0.774653i	$-0.717924\pi$
$823$	0.593422	−	0.497940i	0.0206854	−	0.0173571i	0.653072	+	0.757296i	$0.273480\pi$
$824$		−	4.35045i		−	0.151555i
$825$	−9.94588	−	6.29960i	−0.346271	−	0.219324i
$826$	9.44449	+	3.43751i	0.328616	+	0.119606i
$827$	12.5187	−	10.5045i	0.435320	−	0.365276i	−0.398635	−	0.917110i	$-0.630516\pi$
$827$	12.5187	−	10.5045i	0.435320	−	0.365276i	0.833955	+	0.551833i	$0.186071\pi$
$828$	15.6424	+	10.8310i	0.543610	+	0.376404i
$829$	−10.7675	+	6.21661i	−0.373970	+	0.215912i	−0.675192	−	0.737642i	$-0.735939\pi$
$829$	−10.7675	+	6.21661i	−0.373970	+	0.215912i	0.301221	+	0.953554i	$0.402606\pi$
$830$	−3.05205	−	17.3090i	−0.105938	−	0.600806i
$831$	−14.7285	−	13.4253i	−0.510927	−	0.465718i
$832$	−1.14207	+	3.13781i	−0.0395941	+	0.108784i
$833$	7.37242	+	1.29996i	0.255439	+	0.0450408i
$834$	3.73951	−	17.0798i	0.129489	−	0.591424i
$835$	−0.731415	+	0.422283i	−0.0253117	+	0.0146137i
$836$	5.03003	−	7.43348i	0.173967	−	0.257092i
$837$	−32.2265	−	24.3276i	−1.11391	−	0.840886i
$838$	−12.5496	+	14.9560i	−0.433517	+	0.516646i
$839$	−4.49386	−	3.77080i	−0.155145	−	0.130182i	0.561911	−	0.827198i	$-0.310066\pi$
$839$	−4.49386	−	3.77080i	−0.155145	−	0.130182i	−0.717056	+	0.697016i	$0.754511\pi$
$840$	−4.50049	−	5.83340i	−0.155282	−	0.201271i
$841$	−14.2311	−	11.9413i	−0.490726	−	0.411768i
$842$	−13.9378	−	16.6104i	−0.480329	−	0.572434i
$843$	28.9047	+	1.18603i	0.995530	+	0.0408490i
$844$		−	0.00586552i		−	0.000201900i
$845$	−1.54986	−	1.84705i	−0.0533166	−	0.0635403i
$846$	9.30910	−	20.2401i	0.320053	−	0.695867i
$847$	11.0308	−	19.1058i	0.379021	−	0.656484i
$848$	−0.356451	+	0.617391i	−0.0122406	+	0.0212013i
$849$	32.5649	+	13.3888i	1.11762	+	0.459503i
$850$	−4.35158	+	5.18601i	−0.149258	+	0.177879i
$851$	49.0472	+	17.8517i	1.68132	+	0.611949i
$852$	4.42432	−	1.40776i	0.151575	−	0.0482289i
$853$	−1.56258	+	8.86184i	−0.0535017	+	0.303424i	−0.999803	−	0.0198635i	$-0.993677\pi$
$853$	−1.56258	+	8.86184i	−0.0535017	+	0.303424i	0.946301	+	0.323287i	$0.104788\pi$
$854$	17.3138			0.592467
$855$	−11.2306	−	12.8216i	−0.384078	−	0.438490i
$856$	−3.42801			−0.117167
$857$	5.51278	−	31.2645i	0.188313	−	1.06798i	−0.733311	−	0.679893i	$-0.762026\pi$
$857$	5.51278	−	31.2645i	0.188313	−	1.06798i	0.921624	−	0.388083i	$-0.126863\pi$
$858$	2.54708	−	11.6335i	0.0869560	−	0.397162i
$859$	−15.7874	−	5.74614i	−0.538658	−	0.196056i	0.0583418	−	0.998297i	$-0.481419\pi$
$859$	−15.7874	−	5.74614i	−0.538658	−	0.196056i	−0.597000	+	0.802241i	$0.703641\pi$
$860$	−8.78253	+	10.4666i	−0.299482	+	0.356908i
$861$	−3.62364	−	26.9771i	−0.123493	−	0.919377i
$862$	−19.0814	+	33.0500i	−0.649917	+	1.12569i
$863$	−20.1485	+	34.8982i	−0.685862	+	1.18795i	0.287303	+	0.957840i	$0.407241\pi$
$863$	−20.1485	+	34.8982i	−0.685862	+	1.18795i	−0.973165	+	0.230108i	$0.926092\pi$
$864$	−0.267507	−	5.18926i	−0.00910079	−	0.176542i
$865$	−8.01445	−	9.55125i	−0.272500	−	0.324752i
$866$		−	4.89448i		−	0.166321i
$867$	11.8575	−	18.7208i	0.402703	−	0.635793i
$868$	16.3009	+	19.4266i	0.553288	+	0.659383i
$869$	−9.93622	−	8.33748i	−0.337063	−	0.282830i
$870$	−2.77152	+	6.74102i	−0.0939634	+	0.228542i
$871$	−36.9399	−	30.9962i	−1.25166	−	1.05027i
$872$	11.2893	−	13.4541i	0.382306	−	0.455614i
$873$	−1.99890	+	24.3165i	−0.0676524	+	0.822989i
$874$	−19.8571	−	19.2329i	−0.671677	−	0.650563i
$875$	30.5798	−	17.6553i	1.03379	−	0.596857i
$876$	9.04982	+	8.24905i	0.305765	+	0.278710i
$877$	15.9597	+	2.81413i	0.538922	+	0.0950265i	0.436483	−	0.899713i	$-0.356224\pi$
$877$	15.9597	+	2.81413i	0.538922	+	0.0950265i	0.102440	+	0.994739i	$0.467335\pi$
$878$	2.34262	−	6.43630i	0.0790597	−	0.217215i
$879$	12.1351	−	55.4259i	0.409308	−	1.86947i
$880$	−0.466055	−	2.64313i	−0.0157107	−	0.0890999i
$881$	−12.0959	+	6.98359i	−0.407522	+	0.235283i	−0.689725	−	0.724072i	$-0.742268\pi$
$881$	−12.0959	+	6.98359i	−0.407522	+	0.235283i	0.282202	+	0.959355i	$0.408935\pi$
$882$	−4.68010	−	9.90054i	−0.157587	−	0.333368i
$883$	11.2108	−	9.40701i	0.377275	−	0.316571i	−0.434357	−	0.900741i	$-0.643024\pi$
$883$	11.2108	−	9.40701i	0.377275	−	0.316571i	0.811631	+	0.584170i	$0.198580\pi$
$884$	−6.43507	−	2.34217i	−0.216435	−	0.0787758i
$885$	6.15879	−	3.22663i	0.207026	−	0.108462i
$886$			35.2231i			1.18334i
$887$	−13.1067	+	10.9978i	−0.440078	+	0.369270i	−0.835739	−	0.549127i	$-0.814960\pi$
$887$	−13.1067	+	10.9978i	−0.440078	+	0.369270i	0.395660	+	0.918397i	$0.370516\pi$
$888$	−4.32214	−	13.5837i	−0.145042	−	0.455839i
$889$	−14.2765	−	17.0141i	−0.478819	−	0.570634i
$890$	3.26017	+	8.95725i	0.109281	+	0.300248i
$891$	3.40939	+	18.2156i	0.114219	+	0.610244i
$892$		−	0.188560i		−	0.00631345i
$893$	−18.1407	+	26.8086i	−0.607054	+	0.897116i
$894$	−26.7398	+	14.0091i	−0.894312	+	0.468536i
$895$	2.62221	+	7.20448i	0.0876510	+	0.240819i
$896$	−0.566698	+	3.21390i	−0.0189321	+	0.107369i
$897$	−33.9247	−	13.9479i	−1.13271	−	0.465707i
$898$	37.0003	−	13.4670i	1.23472	−	0.449400i
$899$	8.58032	−	23.5742i	0.286170	−	0.786245i
$900$	9.86987	+	0.811336i	0.328996	+	0.0270445i
$901$	−1.26616	−	0.731015i	−0.0421817	−	0.0243536i
$902$	3.39129	−	9.31749i	0.112918	−	0.310239i
$903$	−46.9131	+	36.1937i	−1.56117	+	1.20445i
$904$	−4.52646	−	7.84006i	−0.150548	−	0.260757i
$905$	16.9950			0.564933
$906$	0.697433	−	1.69633i	0.0231707	−	0.0563567i
$907$	−4.32837	−	11.8921i	−0.143721	−	0.394871i	0.846857	−	0.531821i	$-0.178492\pi$
$907$	−4.32837	−	11.8921i	−0.143721	−	0.394871i	−0.990578	+	0.136950i	$0.956270\pi$
$908$	4.76453	+	27.0210i	0.158117	+	0.896723i
$909$	6.33266	+	23.1473i	0.210041	+	0.767746i
$910$	10.8809	+	9.13018i	0.360699	+	0.302663i
$911$	6.97830	+	12.0868i	0.231201	+	0.400452i	0.958162	−	0.286227i	$-0.0924011\pi$
$911$	6.97830	+	12.0868i	0.231201	+	0.400452i	−0.726961	+	0.686679i	$0.759068\pi$
$912$	−0.846130	+	7.50227i	−0.0280182	+	0.248425i
$913$	13.8829	−	24.0458i	0.459456	−	0.795800i
$914$	19.7570	−	7.19095i	0.653502	−	0.237855i
$915$	8.06861	−	8.85186i	0.266740	−	0.292633i
$916$	−18.2674	+	15.3281i	−0.603570	+	0.506456i
$917$	−65.4252	−	11.5362i	−2.16053	−	0.380960i
$918$	10.6422	−	0.548609i	0.351246	−	0.0181068i
$919$	−12.4599	−	21.5812i	−0.411015	−	0.711898i	0.583986	−	0.811763i	$-0.301492\pi$
$919$	−12.4599	−	21.5812i	−0.411015	−	0.711898i	−0.995001	+	0.0998653i	$0.968159\pi$
$920$	−8.26646			−0.272537
$921$	11.1560	−	27.1340i	0.367602	−	0.894097i
$922$	10.5094	−	1.85310i	0.346110	−	0.0610285i
$923$	−7.75173	+	4.47546i	−0.255151	+	0.147312i
$924$	0.477179	−	11.6293i	0.0156980	−	0.382576i
$925$	26.7549	−	4.71761i	0.879695	−	0.155114i
$926$	−0.292755	+	1.66030i	−0.00962053	+	0.0545607i
$927$	−7.54195	−	10.6516i	−0.247710	−	0.349845i
$928$	3.03372	−	1.10418i	0.0995867	−	0.0362466i
$929$	42.5954	+	7.51072i	1.39751	+	0.246419i	0.821120	−	0.570756i	$-0.193350\pi$
$929$	42.5954	+	7.51072i	1.39751	+	0.246419i	0.576390	+	0.817175i	$0.304461\pi$
$930$	17.5286	+	0.719242i	0.574786	+	0.0235849i
$931$	4.36304	+	15.3015i	0.142993	+	0.501487i
$932$	−7.74616	−	4.47224i	−0.253734	−	0.146493i
$933$	25.7595	−	28.2601i	0.843329	−	0.925194i
$934$	−26.8891	+	32.0452i	−0.879839	+	1.04855i
$935$	5.42057	−	0.955793i	0.177272	−	0.0312578i
$936$	2.64348	+	9.66248i	0.0864047	+	0.315828i
$937$	−28.2272	−	10.2739i	−0.922142	−	0.335632i	−0.163052	−	0.986618i	$-0.552134\pi$
$937$	−28.2272	−	10.2739i	−0.922142	−	0.335632i	−0.759090	+	0.650985i	$0.774356\pi$
$938$	−40.8143	−	23.5642i	−1.33264	−	0.769397i
$939$	13.3754	+	25.5301i	0.436489	+	0.833144i
$940$	1.68081	+	9.53236i	0.0548221	+	0.310911i
$941$	−10.1033	−	57.2988i	−0.329359	−	1.86789i	−0.477084	−	0.878858i	$-0.658306\pi$
$941$	−10.1033	−	57.2988i	−0.329359	−	1.86789i	0.147725	−	0.989028i	$-0.452805\pi$
$942$	9.74547	+	0.399881i	0.317525	+	0.0130288i
$943$	−26.4482	−	15.2699i	−0.861272	−	0.497256i
$944$	−2.89399	−	1.05333i	−0.0941914	−	0.0342829i
$945$	−21.1318	−	6.48040i	−0.687416	−	0.210807i
$946$	−21.2565	+	3.74809i	−0.691107	+	0.121861i
$947$	−24.5463	+	29.2531i	−0.797648	+	0.950599i	−0.999585	−	0.0287990i	$-0.990832\pi$
$947$	−24.5463	+	29.2531i	−0.797648	+	0.950599i	0.201938	+	0.979398i	$0.435276\pi$
$948$	10.6582	+	2.33354i	0.346162	+	0.0757899i
$949$	−20.4446	−	11.8037i	−0.663659	−	0.383164i
$950$	−13.9564	−	3.50175i	−0.452804	−	0.113612i
$951$	−11.9282	+	18.8324i	−0.386798	+	0.610681i
$952$	−6.59113	−	1.16219i	−0.213620	−	0.0376669i
$953$	50.5030	−	18.3816i	1.63595	−	0.595438i	0.649627	−	0.760253i	$-0.274925\pi$
$953$	50.5030	−	18.3816i	1.63595	−	0.595438i	0.986324	+	0.164815i	$0.0527028\pi$
$954$	0.197578	+	2.12956i	0.00639682	+	0.0689470i
$955$	−4.49044	+	25.4665i	−0.145307	+	0.824078i
$956$	−0.462195	+	0.0814974i	−0.0149484	+	0.00263581i
$957$	−10.1991	+	5.34336i	−0.329689	+	0.172726i
$958$	−33.8441	+	19.5399i	−1.09345	+	0.631306i
$959$	48.8046	−	8.60557i	1.57598	−	0.277888i
$960$	1.37905	+	1.78748i	0.0445085	+	0.0576906i
$961$	−29.3844			−0.947884
$962$	13.7407	+	23.7996i	0.443018	+	0.767331i
$963$	−8.39311	+	5.94280i	−0.270464	+	0.191504i
$964$	3.83319	+	0.675894i	0.123459	+	0.0217691i
$965$	−1.84006	+	1.54400i	−0.0592337	+	0.0497030i
$966$	−35.0190	−	7.66719i	−1.12672	−	0.246688i
$967$	40.0031	−	14.5599i	1.28641	−	0.468216i	0.393865	−	0.919168i	$-0.371138\pi$
$967$	40.0031	−	14.5599i	1.28641	−	0.468216i	0.892548	+	0.450953i	$0.148916\pi$
$968$	−3.38006	+	5.85443i	−0.108639	+	0.188168i
$969$	−15.3858	−	1.73526i	−0.494262	−	0.0557445i
$970$	−5.30032	−	9.18042i	−0.170183	−	0.294766i
$971$	26.4248	+	22.1730i	0.848011	+	0.711566i	0.959351	−	0.282217i	$-0.0910697\pi$
$971$	26.4248	+	22.1730i	0.848011	+	0.711566i	−0.111340	+	0.993782i	$0.535514\pi$
$972$	−9.65107	−	12.2416i	−0.309558	−	0.392650i
$973$	5.72059	+	32.4431i	0.183394	+	1.04008i
$974$	3.52853	+	9.69456i	0.113061	+	0.310634i
$975$	−18.9222	+	2.54168i	−0.605994	+	0.0813988i
$976$	−5.30532			−0.169819
$977$	0.650130	+	1.12606i	0.0207995	+	0.0360258i	0.876238	−	0.481879i	$-0.160046\pi$
$977$	0.650130	+	1.12606i	0.0207995	+	0.0360258i	−0.855438	+	0.517905i	$0.826712\pi$
$978$	−3.69055	−	27.4752i	−0.118011	−	0.878561i
$979$	−5.15025	+	14.1502i	−0.164603	+	0.452242i
$980$	4.12052	+	2.37898i	0.131625	+	0.0759939i
$981$	4.31668	−	52.5122i	0.137821	−	1.67659i
$982$	−6.88666	+	18.9209i	−0.219762	+	0.603791i
$983$	−14.0394	+	5.10993i	−0.447788	+	0.162982i	−0.556064	−	0.831139i	$-0.687689\pi$
$983$	−14.0394	+	5.10993i	−0.447788	+	0.162982i	0.108276	+	0.994121i	$0.465467\pi$
$984$	1.11036	+	8.26635i	0.0353969	+	0.263522i
$985$	−1.93070	+	10.9495i	−0.0615172	+	0.348882i
$986$	2.26448	+	6.22160i	0.0721156	+	0.198136i
$987$	−1.72093	+	41.9407i	−0.0547778	+	1.33499i
$988$	−1.49992	−	14.4777i	−0.0477187	−	0.460596i
$989$			66.4801i			2.11395i
$990$	−5.72322	−	5.66347i	−0.181896	−	0.179997i
$991$	−16.0640	−	44.1356i	−0.510291	−	1.40201i	−0.880934	−	0.473238i	$-0.843085\pi$
$991$	−16.0640	−	44.1356i	−0.510291	−	1.40201i	0.370643	−	0.928775i	$-0.379137\pi$
$992$	−4.99494	−	5.95273i	−0.158589	−	0.188999i
$993$	17.5843	−	19.2912i	0.558020	−	0.612189i
$994$	−6.70136	+	5.62311i	−0.212554	+	0.178354i
$995$			19.0464i			0.603812i
$996$	−0.957535	+	23.3360i	−0.0303407	+	0.739431i
$997$	10.6799	+	3.88717i	0.338236	+	0.123108i	0.505554	−	0.862795i	$-0.331288\pi$
$997$	10.6799	+	3.88717i	0.338236	+	0.123108i	−0.167317	+	0.985903i	$0.553510\pi$
$998$	−2.89465	+	2.42890i	−0.0916287	+	0.0768856i
$999$	−34.1310	−	25.7654i	−1.07986	−	0.815180i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.x.c.41.3	✓	60
9.2	odd	6		342.2.bf.c.155.6	yes	60
19.13	odd	18		342.2.bf.c.203.6	yes	60
171.146	even	18	inner	342.2.x.c.317.3	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.x.c.41.3	✓	60	1.1	even	1	trivial
342.2.x.c.317.3	yes	60	171.146	even	18	inner
342.2.bf.c.155.6	yes	60	9.2	odd	6
342.2.bf.c.203.6	yes	60	19.13	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(-1.28007 - 1.16680i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.837833 - 0.998490i) q^{5} +(-1.37136 + 1.05801i) q^{6} +(1.63174 - 2.82626i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.277146 + 2.98717i) q^{9} +O(q^{10})\)	\(q+(0.173648 - 0.984808i) q^{2} +(-1.28007 - 1.16680i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.837833 - 0.998490i) q^{5} +(-1.37136 + 1.05801i) q^{6} +(1.63174 - 2.82626i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.277146 + 2.98717i) q^{9} +(-0.837833 - 0.998490i) q^{10} -2.05910i q^{11} +(0.803800 + 1.53424i) q^{12} +(-2.14639 - 2.55796i) q^{13} +(-2.49997 - 2.09773i) q^{14} +(-2.23752 + 0.300550i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-1.31824 + 1.57102i) q^{17} +(2.98992 + 0.245781i) q^{18} +(-4.22785 - 1.06080i) q^{19} +(-1.12881 + 0.651718i) q^{20} +(-5.38643 + 1.71388i) q^{21} +(-2.02782 - 0.357559i) q^{22} +(-2.16911 + 5.95958i) q^{23} +(1.65051 - 0.525170i) q^{24} +(0.573222 + 3.25090i) q^{25} +(-2.89182 + 1.66959i) q^{26} +(3.13067 - 4.14716i) q^{27} +(-2.49997 + 2.09773i) q^{28} +(3.03372 + 1.10418i) q^{29} +(-0.0925577 + 2.25572i) q^{30} -7.77074i q^{31} +(0.766044 - 0.642788i) q^{32} +(-2.40256 + 2.63579i) q^{33} +(1.31824 + 1.57102i) q^{34} +(-1.45487 - 3.99721i) q^{35} +(0.761240 - 2.90181i) q^{36} -8.22998i q^{37} +(-1.77884 + 3.97941i) q^{38} +(-0.237117 + 5.77878i) q^{39} +(0.445801 + 1.22483i) q^{40} +(-0.836193 + 4.74228i) q^{41} +(0.752503 + 5.60221i) q^{42} +(9.85027 - 3.58520i) q^{43} +(-0.704253 + 1.93492i) q^{44} +(3.21486 + 2.22602i) q^{45} +(5.49238 + 3.17102i) q^{46} +(2.53987 - 6.97823i) q^{47} +(-0.230583 - 1.71663i) q^{48} +(-1.82516 - 3.16128i) q^{49} +3.30105 q^{50} +(3.52050 - 0.472883i) q^{51} +(1.14207 + 3.13781i) q^{52} +(0.123794 + 0.702071i) q^{53} +(-3.54052 - 3.80325i) q^{54} +(-2.05599 - 1.72518i) q^{55} +(1.63174 + 2.82626i) q^{56} +(4.17419 + 6.29095i) q^{57} +(1.61421 - 2.79589i) q^{58} +(-2.89399 + 1.05333i) q^{59} +(2.20538 + 0.482853i) q^{60} +(-4.06411 + 3.41020i) q^{61} +(-7.65269 - 1.34938i) q^{62} +(8.89475 + 4.09100i) q^{63} +(-0.500000 - 0.866025i) q^{64} -4.35242 q^{65} +(2.17854 + 2.82376i) q^{66} +(14.2217 - 2.50767i) q^{67} +(1.77606 - 1.02541i) q^{68} +(9.73025 - 5.09774i) q^{69} +(-4.18912 + 0.738655i) q^{70} +(0.465476 - 2.63985i) q^{71} +(-2.72554 - 1.25357i) q^{72} +(6.64344 - 2.41801i) q^{73} +(-8.10495 - 1.42912i) q^{74} +(3.05940 - 4.83021i) q^{75} +(3.61006 + 2.44283i) q^{76} +(-5.81955 - 3.35992i) q^{77} +(5.64981 + 1.23699i) q^{78} +(4.04909 - 4.82552i) q^{79} +(1.28363 - 0.226339i) q^{80} +(-8.84638 + 1.65577i) q^{81} +(4.52503 + 1.64698i) q^{82} +(11.6778 + 6.74220i) q^{83} +(5.64777 + 0.231742i) q^{84} +(0.464180 + 2.63250i) q^{85} +(-1.82026 - 10.3232i) q^{86} +(-2.59500 - 4.95318i) q^{87} +(1.78323 + 1.02955i) q^{88} +(-6.87203 - 2.50121i) q^{89} +(2.75046 - 2.77948i) q^{90} +(-10.7318 + 1.89231i) q^{91} +(4.07659 - 4.85829i) q^{92} +(-9.06692 + 9.94707i) q^{93} +(-6.43117 - 3.71304i) q^{94} +(-4.60143 + 3.33270i) q^{95} +(-1.73059 - 0.0710105i) q^{96} +(8.00928 + 1.41225i) q^{97} +(-3.43019 + 1.24849i) q^{98} +(6.15088 - 0.570672i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9}+O(q^{10}) \) 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9	\( 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9} + 3 q^{13} + 3 q^{14} + 27 q^{15} - 27 q^{17} - 18 q^{18} + 3 q^{19} + 18 q^{23} + 3 q^{24} - 6 q^{27} + 3 q^{28} + 57 q^{33} + 27 q^{34} + 9 q^{38} - 30 q^{39} + 9 q^{41} - 3 q^{43} - 9 q^{44} + 27 q^{45} - 30 q^{49} - 132 q^{50} - 66 q^{51} + 6 q^{52} + 27 q^{54} + 102 q^{57} - 54 q^{59} + 6 q^{60} - 24 q^{61} - 3 q^{62} - 30 q^{64} + 36 q^{65} - 63 q^{66} + 51 q^{67} - 18 q^{68} + 3 q^{69} - 18 q^{71} - 3 q^{72} - 66 q^{73} - 6 q^{74} + 3 q^{78} - 51 q^{79} - 30 q^{81} - 36 q^{83} + 60 q^{84} - 3 q^{86} + 54 q^{87} - 27 q^{89} + 36 q^{90} - 69 q^{91} + 69 q^{93} + 18 q^{94} - 27 q^{95} + 81 q^{97} + 60 q^{98} + 51 q^{99}+O(q^{100}) \) 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9 + 3 * q^13 + 3 * q^14 + 27 * q^15 - 27 * q^17 - 18 * q^18 + 3 * q^19 + 18 * q^23 + 3 * q^24 - 6 * q^27 + 3 * q^28 + 57 * q^33 + 27 * q^34 + 9 * q^38 - 30 * q^39 + 9 * q^41 - 3 * q^43 - 9 * q^44 + 27 * q^45 - 30 * q^49 - 132 * q^50 - 66 * q^51 + 6 * q^52 + 27 * q^54 + 102 * q^57 - 54 * q^59 + 6 * q^60 - 24 * q^61 - 3 * q^62 - 30 * q^64 + 36 * q^65 - 63 * q^66 + 51 * q^67 - 18 * q^68 + 3 * q^69 - 18 * q^71 - 3 * q^72 - 66 * q^73 - 6 * q^74 + 3 * q^78 - 51 * q^79 - 30 * q^81 - 36 * q^83 + 60 * q^84 - 3 * q^86 + 54 * q^87 - 27 * q^89 + 36 * q^90 - 69 * q^91 + 69 * q^93 + 18 * q^94 - 27 * q^95 + 81 * q^97 + 60 * q^98 + 51 * q^99

Introduction

L-functions

Modular forms

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Database

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