LMFDB - Embedded newform 354.2.e.c.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$3$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			49.3
Character	$\chi$	$=$	354.49
Dual form			354.2.e.c.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.370138 + 0.928977i) q^{2} +(0.994138 + 0.108119i) q^{3} +(-0.725995 - 0.687699i) q^{4} +(1.45282 - 1.71039i) q^{5} +(-0.468408 + 0.883512i) q^{6} +(-1.71569 - 1.03229i) q^{7} +(0.907575 - 0.419889i) q^{8} +(0.976621 + 0.214970i) q^{9} +O(q^{10})$	\(q+(-0.370138 + 0.928977i) q^{2} +(0.994138 + 0.108119i) q^{3} +(-0.725995 - 0.687699i) q^{4} +(1.45282 - 1.71039i) q^{5} +(-0.468408 + 0.883512i) q^{6} +(-1.71569 - 1.03229i) q^{7} +(0.907575 - 0.419889i) q^{8} +(0.976621 + 0.214970i) q^{9} +(1.05117 + 1.98271i) q^{10} +(0.0279740 - 0.515950i) q^{11} +(-0.647386 - 0.762162i) q^{12} +(5.54018 - 1.21948i) q^{13} +(1.59402 - 1.21174i) q^{14} +(1.62923 - 1.54329i) q^{15} +(0.0541389 + 0.998533i) q^{16} +(1.99422 - 1.19988i) q^{17} +(-0.561187 + 0.827689i) q^{18} +(-0.224878 + 0.809936i) q^{19} +(-2.23097 + 0.242633i) q^{20} +(-1.59402 - 1.21174i) q^{21} +(0.468951 + 0.216960i) q^{22} +(-2.30909 - 3.40565i) q^{23} +(0.947653 - 0.319302i) q^{24} +(-0.00584200 - 0.0356346i) q^{25} +(-0.917757 + 5.59807i) q^{26} +(0.947653 + 0.319302i) q^{27} +(0.535672 + 1.92932i) q^{28} +(-1.59058 - 3.99205i) q^{29} +(0.830637 + 2.08474i) q^{30} +(1.01176 + 3.64405i) q^{31} +(-0.947653 - 0.319302i) q^{32} +(0.0835940 - 0.509901i) q^{33} +(0.376526 + 2.29671i) q^{34} +(-4.25820 + 1.43476i) q^{35} +(-0.561187 - 0.827689i) q^{36} +(8.83659 + 4.08824i) q^{37} +(-0.669176 - 0.508694i) q^{38} +(5.63955 - 0.613338i) q^{39} +(0.600368 - 2.16233i) q^{40} +(-5.59929 + 8.25834i) q^{41} +(1.71569 - 1.03229i) q^{42} +(0.440400 + 8.12269i) q^{43} +(-0.375127 + 0.355339i) q^{44} +(1.78653 - 1.35809i) q^{45} +(4.01845 - 0.884527i) q^{46} +(-6.47213 - 7.61958i) q^{47} +(-0.0541389 + 0.998533i) q^{48} +(-1.40091 - 2.64240i) q^{49} +(0.0352661 + 0.00776265i) q^{50} +(2.11226 - 0.977236i) q^{51} +(-4.86078 - 2.92464i) q^{52} +(-4.95106 + 9.33870i) q^{53} +(-0.647386 + 0.762162i) q^{54} +(-0.841834 - 0.797427i) q^{55} +(-1.99056 - 0.216487i) q^{56} +(-0.311129 + 0.780875i) q^{57} +4.29726 q^{58} +(-1.83998 - 7.45751i) q^{59} -2.24413 q^{60} +(0.102756 - 0.257898i) q^{61} +(-3.75973 - 0.408895i) q^{62} +(-1.45366 - 1.37698i) q^{63} +(0.647386 - 0.762162i) q^{64} +(5.96307 - 11.2475i) q^{65} +(0.442745 + 0.266391i) q^{66} +(-2.12829 + 0.984650i) q^{67} +(-2.27296 - 0.500315i) q^{68} +(-1.92733 - 3.63534i) q^{69} +(0.243269 - 4.48683i) q^{70} +(5.07130 + 5.97039i) q^{71} +(0.976621 - 0.214970i) q^{72} +(-6.14456 + 4.67098i) q^{73} +(-7.06864 + 6.69577i) q^{74} +(-0.00195497 - 0.0360574i) q^{75} +(0.720253 - 0.433362i) q^{76} +(-0.580606 + 0.856330i) q^{77} +(-1.51764 + 5.46603i) q^{78} +(-4.42166 + 0.480884i) q^{79} +(1.78653 + 1.35809i) q^{80} +(0.907575 + 0.419889i) q^{81} +(-5.59929 - 8.25834i) q^{82} +(-0.0601995 + 0.0202836i) q^{83} +(0.323936 + 1.97592i) q^{84} +(0.844973 - 5.15411i) q^{85} +(-7.70880 - 2.59740i) q^{86} +(-1.14964 - 4.14062i) q^{87} +(-0.191253 - 0.480009i) q^{88} +(-3.85635 - 9.67870i) q^{89} +(0.600368 + 2.16233i) q^{90} +(-10.7641 - 3.62684i) q^{91} +(-0.665676 + 4.06044i) q^{92} +(0.611843 + 3.73208i) q^{93} +(9.47400 - 3.19216i) q^{94} +(1.05860 + 1.56132i) q^{95} +(-0.907575 - 0.419889i) q^{96} +(-7.52947 - 5.72376i) q^{97} +(2.97326 - 0.323361i) q^{98} +(0.138234 - 0.497874i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{18}{29}\right)$	$1$

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 $

$2$	−0.370138	+	0.928977i	−0.261727	+	0.656886i
$2$	−0.370138	+	0.928977i	−0.261727	+	0.656886i
$3$	0.994138	+	0.108119i	0.573966	+	0.0624225i
$3$	0.994138	+	0.108119i	0.573966	+	0.0624225i
$4$	−0.725995	−	0.687699i	−0.362998	−	0.343850i
$5$	1.45282	−	1.71039i	0.649720	−	0.764909i	−0.334397	−	0.942432i	$-0.608533\pi$
$5$	1.45282	−	1.71039i	0.649720	−	0.764909i	0.984117	+	0.177523i	$0.0568084\pi$
$6$	−0.468408	+	0.883512i	−0.191227	+	0.360692i
$7$	−1.71569	−	1.03229i	−0.648468	−	0.390170i	0.152984	−	0.988229i	$-0.451112\pi$
$7$	−1.71569	−	1.03229i	−0.648468	−	0.390170i	−0.801453	+	0.598058i	$0.795939\pi$
$8$	0.907575	−	0.419889i	0.320876	−	0.148453i
$9$	0.976621	+	0.214970i	0.325540	+	0.0716568i
$10$	1.05117	+	1.98271i	0.332409	+	0.626989i
$11$	0.0279740	−	0.515950i	0.00843447	−	0.155565i	−0.991282	−	0.131757i	$-0.957938\pi$
$11$	0.0279740	−	0.515950i	0.00843447	−	0.155565i	0.999717	−	0.0238079i	$-0.00757902\pi$
$12$	−0.647386	−	0.762162i	−0.186884	−	0.220017i
$13$	5.54018	−	1.21948i	1.53657	−	0.338224i	0.635569	−	0.772044i	$-0.280766\pi$
$13$	5.54018	−	1.21948i	1.53657	−	0.338224i	0.901000	+	0.433820i	$0.142835\pi$
$14$	1.59402	−	1.21174i	0.426019	−	0.323851i
$15$	1.62923	−	1.54329i	0.420665	−	0.398475i
$16$	0.0541389	+	0.998533i	0.0135347	+	0.249633i
$17$	1.99422	−	1.19988i	0.483670	−	0.291014i	−0.252759	−	0.967529i	$-0.581338\pi$
$17$	1.99422	−	1.19988i	0.483670	−	0.291014i	0.736429	+	0.676515i	$0.236510\pi$
$18$	−0.561187	+	0.827689i	−0.132273	+	0.195088i
$19$	−0.224878	+	0.809936i	−0.0515905	+	0.185812i	−0.984856	−	0.173376i	$-0.944532\pi$
$19$	−0.224878	+	0.809936i	−0.0515905	+	0.185812i	0.933265	+	0.359188i	$0.116946\pi$
$20$	−2.23097	+	0.242633i	−0.498861	+	0.0542544i
$21$	−1.59402	−	1.21174i	−0.347843	−	0.264424i
$22$	0.468951	+	0.216960i	0.0999807	+	0.0462560i
$23$	−2.30909	−	3.40565i	−0.481478	−	0.710126i	0.506924	−	0.861991i	$-0.330783\pi$
$23$	−2.30909	−	3.40565i	−0.481478	−	0.710126i	−0.988401	+	0.151865i	$0.951472\pi$
$24$	0.947653	−	0.319302i	0.193439	−	0.0651772i
$25$	−0.00584200	−	0.0356346i	−0.00116840	−	0.00712692i
$26$	−0.917757	+	5.59807i	−0.179987	+	1.09787i
$27$	0.947653	+	0.319302i	0.182376	+	0.0614496i
$28$	0.535672	+	1.92932i	0.101233	+	0.364607i
$29$	−1.59058	−	3.99205i	−0.295363	−	0.741306i	−0.999512	−	0.0312529i	$-0.990050\pi$
$29$	−1.59058	−	3.99205i	−0.295363	−	0.741306i	0.704148	−	0.710053i	$-0.251329\pi$
$30$	0.830637	+	2.08474i	0.151653	+	0.380620i
$31$	1.01176	+	3.64405i	0.181718	+	0.654490i	0.997137	+	0.0756182i	$0.0240930\pi$
$31$	1.01176	+	3.64405i	0.181718	+	0.654490i	−0.815419	+	0.578872i	$0.803493\pi$
$32$	−0.947653	−	0.319302i	−0.167523	−	0.0564451i
$33$	0.0835940	−	0.509901i	0.0145518	−	0.0887623i
$34$	0.376526	+	2.29671i	0.0645737	+	0.393882i
$35$	−4.25820	+	1.43476i	−0.719768	+	0.242518i
$36$	−0.561187	−	0.827689i	−0.0935312	−	0.137948i
$37$	8.83659	+	4.08824i	1.45273	+	0.672102i	0.978110	−	0.208090i	$-0.0667249\pi$
$37$	8.83659	+	4.08824i	1.45273	+	0.672102i	0.474616	+	0.880193i	$0.342587\pi$
$38$	−0.669176	−	0.508694i	−0.108555	−	0.0825211i
$39$	5.63955	−	0.613338i	0.903051	−	0.0982127i
$40$	0.600368	−	2.16233i	0.0949265	−	0.341894i
$41$	−5.59929	+	8.25834i	−0.874463	+	1.28974i	0.0816275	+	0.996663i	$0.473988\pi$
$41$	−5.59929	+	8.25834i	−0.874463	+	1.28974i	−0.956090	+	0.293073i	$0.905322\pi$
$42$	1.71569	−	1.03229i	0.264736	−	0.159286i
$43$	0.440400	+	8.12269i	0.0671603	+	1.23870i	0.816827	+	0.576883i	$0.195731\pi$
$43$	0.440400	+	8.12269i	0.0671603	+	1.23870i	−0.749666	+	0.661816i	$0.769786\pi$
$44$	−0.375127	+	0.355339i	−0.0565526	+	0.0535694i
$45$	1.78653	−	1.35809i	0.266321	−	0.202452i
$46$	4.01845	−	0.884527i	0.592488	−	0.130416i
$47$	−6.47213	−	7.61958i	−0.944058	−	1.11143i	−0.993634	−	0.112660i	$-0.964063\pi$
$47$	−6.47213	−	7.61958i	−0.944058	−	1.11143i	0.0495759	−	0.998770i	$-0.484213\pi$
$48$	−0.0541389	+	0.998533i	−0.00781428	+	0.144126i
$49$	−1.40091	−	2.64240i	−0.200130	−	0.377486i
$50$	0.0352661	+	0.00776265i	0.00498738	+	0.00109780i
$51$	2.11226	−	0.977236i	0.295776	−	0.136840i
$52$	−4.86078	−	2.92464i	−0.674069	−	0.405574i
$53$	−4.95106	+	9.33870i	−0.680081	+	1.28277i	0.267594	+	0.963532i	$0.413771\pi$
$53$	−4.95106	+	9.33870i	−0.680081	+	1.28277i	−0.947675	+	0.319237i	$0.896573\pi$
$54$	−0.647386	+	0.762162i	−0.0880981	+	0.103717i
$55$	−0.841834	−	0.797427i	−0.113513	−	0.107525i
$56$	−1.99056	−	0.216487i	−0.266000	−	0.0289293i
$57$	−0.311129	+	0.780875i	−0.0412100	+	0.103429i
$58$	4.29726			0.564258
$59$	−1.83998	−	7.45751i	−0.239545	−	0.970885i
$59$	−1.83998	−	7.45751i	−0.239545	−	0.970885i
$60$	−2.24413			−0.289716
$61$	0.102756	−	0.257898i	0.0131566	−	0.0330205i	−0.922252	−	0.386590i	$-0.873653\pi$
$61$	0.102756	−	0.257898i	0.0131566	−	0.0330205i	0.935408	+	0.353569i	$0.115032\pi$
$62$	−3.75973	−	0.408895i	−0.477486	−	0.0519297i
$63$	−1.45366	−	1.37698i	−0.183144	−	0.173483i
$64$	0.647386	−	0.762162i	0.0809233	−	0.0952703i
$65$	5.96307	−	11.2475i	0.739628	−	1.39509i
$66$	0.442745	+	0.266391i	0.0544981	+	0.0327904i
$67$	−2.12829	+	0.984650i	−0.260012	+	0.120294i	−0.545565	−	0.838069i	$-0.683685\pi$
$67$	−2.12829	+	0.984650i	−0.260012	+	0.120294i	0.285553	+	0.958363i	$0.407823\pi$
$68$	−2.27296	−	0.500315i	−0.275636	−	0.0606721i
$69$	−1.92733	−	3.63534i	−0.232024	−	0.437643i
$70$	0.243269	−	4.48683i	0.0290762	−	0.536279i
$71$	5.07130	+	5.97039i	0.601852	+	0.708555i	0.975743	−	0.218918i	$-0.0702526\pi$
$71$	5.07130	+	5.97039i	0.601852	+	0.708555i	−0.373891	+	0.927473i	$0.621977\pi$
$72$	0.976621	−	0.214970i	0.115096	−	0.0253345i
$73$	−6.14456	+	4.67098i	−0.719167	+	0.546696i	−0.899506	−	0.436908i	$-0.856073\pi$
$73$	−6.14456	+	4.67098i	−0.719167	+	0.546696i	0.180339	+	0.983604i	$0.442280\pi$
$74$	−7.06864	+	6.69577i	−0.821712	+	0.778367i
$75$	−0.00195497	−	0.0360574i	−0.000225741	−	0.00416355i
$76$	0.720253	−	0.433362i	0.0826187	−	0.0497100i
$77$	−0.580606	+	0.856330i	−0.0661662	+	0.0975879i
$78$	−1.51764	+	5.46603i	−0.171838	+	0.618906i
$79$	−4.42166	+	0.480884i	−0.497475	+	0.0541037i	−0.353418	−	0.935466i	$-0.614981\pi$
$79$	−4.42166	+	0.480884i	−0.497475	+	0.0541037i	−0.144057	+	0.989569i	$0.546015\pi$
$80$	1.78653	+	1.35809i	0.199741	+	0.151839i
$81$	0.907575	+	0.419889i	0.100842	+	0.0466543i
$82$	−5.59929	−	8.25834i	−0.618338	−	0.911981i
$83$	−0.0601995	+	0.0202836i	−0.00660775	+	0.00222641i	−0.322603	−	0.946534i	$-0.604558\pi$
$83$	−0.0601995	+	0.0202836i	−0.00660775	+	0.00222641i	0.315996	+	0.948761i	$0.397661\pi$
$84$	0.323936	+	1.97592i	0.0353443	+	0.215591i
$85$	0.844973	−	5.15411i	0.0916502	−	0.559041i
$86$	−7.70880	−	2.59740i	−0.831261	−	0.280085i
$87$	−1.14964	−	4.14062i	−0.123254	−	0.443922i
$88$	−0.191253	−	0.480009i	−0.0203877	−	0.0511692i
$89$	−3.85635	−	9.67870i	−0.408772	−	1.02594i	−0.978892	−	0.204379i	$-0.934483\pi$
$89$	−3.85635	−	9.67870i	−0.408772	−	1.02594i	0.570120	−	0.821562i	$-0.306897\pi$
$90$	0.600368	+	2.16233i	0.0632843	+	0.227930i
$91$	−10.7641	−	3.62684i	−1.12838	−	0.380196i
$92$	−0.665676	+	4.06044i	−0.0694015	+	0.423330i
$93$	0.611843	+	3.73208i	0.0634451	+	0.386998i
$94$	9.47400	−	3.19216i	0.977169	−	0.329246i
$95$	1.05860	+	1.56132i	0.108610	+	0.160188i
$96$	−0.907575	−	0.419889i	−0.0926290	−	0.0428548i
$97$	−7.52947	−	5.72376i	−0.764502	−	0.581160i	0.148597	−	0.988898i	$-0.452524\pi$
$97$	−7.52947	−	5.72376i	−0.764502	−	0.581160i	−0.913099	+	0.407738i	$0.866318\pi$
$98$	2.97326	−	0.323361i	0.300344	−	0.0326644i
$99$	0.138234	−	0.497874i	0.0138930	−	0.0500382i
$100$	−0.0202646	+	0.0298881i	−0.00202646	+	0.00298881i
$101$	5.81513	−	3.49885i	0.578627	−	0.348148i	−0.195964	−	0.980611i	$-0.562783\pi$
$101$	5.81513	−	3.49885i	0.578627	−	0.348148i	0.774591	+	0.632463i	$0.217956\pi$
$102$	0.126001	+	2.32395i	0.0124760	+	0.230106i
$103$	−4.42168	+	4.18844i	−0.435681	+	0.412699i	−0.873852	−	0.486193i	$-0.838385\pi$
$103$	−4.42168	+	4.18844i	−0.435681	+	0.412699i	0.438170	+	0.898892i	$0.355627\pi$
$104$	4.51608	−	3.43303i	0.442838	−	0.336637i
$105$	−4.38837	+	0.965952i	−0.428261	+	0.0942673i
$106$	−6.84285	−	8.05603i	−0.664637	−	0.782471i
$107$	−0.191508	+	3.53215i	−0.0185137	+	0.341466i	0.974572	+	0.224075i	$0.0719359\pi$
$107$	−0.191508	+	3.53215i	−0.0185137	+	0.341466i	−0.993086	+	0.117391i	$0.962547\pi$
$108$	−0.468408	−	0.883512i	−0.0450726	−	0.0850160i
$109$	0.473527	+	0.104231i	0.0453557	+	0.00998354i	0.237590	−	0.971365i	$-0.423642\pi$
$109$	0.473527	+	0.104231i	0.0453557	+	0.00998354i	−0.192235	+	0.981349i	$0.561573\pi$
$110$	1.05239	−	0.486886i	0.100341	−	0.0464227i
$111$	8.34277	+	5.01968i	0.791861	+	0.476447i
$112$	0.937895	−	1.76906i	0.0886227	−	0.167160i
$113$	−2.26128	+	2.66218i	−0.212723	+	0.250437i	−0.858167	−	0.513371i	$-0.828397\pi$
$113$	−2.26128	+	2.66218i	−0.212723	+	0.250437i	0.645444	+	0.763808i	$0.276672\pi$
$114$	−0.610254	−	0.578063i	−0.0571555	−	0.0541406i
$115$	−9.17966	−	0.998348i	−0.856008	−	0.0930965i
$116$	−1.59058	+	3.99205i	−0.147682	+	0.370653i
$117$	5.67280			0.524451
$118$	7.60890	+	1.05101i	0.700456	+	0.0967537i
$119$	−4.66009			−0.427190
$120$	0.830637	−	2.08474i	0.0758265	−	0.190310i
$121$	10.6701	+	1.16044i	0.970009	+	0.105495i
$122$	0.201547	+	0.190916i	0.0182472	+	0.0172847i
$123$	−6.45935	+	7.60454i	−0.582420	+	0.685678i
$124$	1.77147	−	3.34135i	0.159083	−	0.300062i
$125$	9.54505	+	5.74307i	0.853735	+	0.513675i
$126$	1.81724	−	0.840744i	0.161893	−	0.0748995i
$127$	−10.8700	−	2.39267i	−0.964556	−	0.212315i	−0.295348	−	0.955390i	$-0.595436\pi$
$127$	−10.8700	−	2.39267i	−0.964556	−	0.212315i	−0.669208	+	0.743075i	$0.733367\pi$
$128$	0.468408	+	0.883512i	0.0414018	+	0.0780922i
$129$	−0.440400	+	8.12269i	−0.0387750	+	0.715163i
$130$	8.24155	+	9.70270i	0.722832	+	0.850983i
$131$	−8.41574	+	1.85245i	−0.735287	+	0.161849i	−0.566800	−	0.823855i	$-0.691819\pi$
$131$	−8.41574	+	1.85245i	−0.735287	+	0.161849i	−0.168486	+	0.985704i	$0.553888\pi$
$132$	−0.411347	+	0.312698i	−0.0358032	+	0.0272169i
$133$	1.22191	−	1.15746i	0.105953	−	0.100364i
$134$	−0.126957	−	2.34158i	−0.0109674	−	0.202282i
$135$	1.92290	−	1.15697i	0.165497	−	0.0995760i
$136$	1.30609	−	1.92634i	0.111996	−	0.165182i
$137$	−0.985920	+	3.55096i	−0.0842329	+	0.303379i	−0.993651	−	0.112503i	$-0.964113\pi$
$137$	−0.985920	+	3.55096i	−0.0842329	+	0.303379i	0.909419	+	0.415882i	$0.136527\pi$
$138$	4.09053	−	0.444871i	0.348209	−	0.0378700i
$139$	17.4344	+	13.2533i	1.47876	+	1.12413i	0.963704	+	0.266975i	$0.0860240\pi$
$139$	17.4344	+	13.2533i	1.47876	+	1.12413i	0.515061	+	0.857153i	$0.327769\pi$
$140$	4.07812	+	1.88674i	0.344664	+	0.159458i
$141$	−5.61037	−	8.27468i	−0.472479	−	0.696854i
$142$	−7.42343	+	2.50125i	−0.622961	+	0.209900i
$143$	−0.474212	−	2.89257i	−0.0396556	−	0.241889i
$144$	−0.161782	+	0.986827i	−0.0134818	+	0.0822355i
$145$	−9.13879	−	3.07922i	−0.758935	−	0.255715i
$146$	−2.06489	−	7.43706i	−0.170892	−	0.615496i
$147$	−1.10701	−	2.77838i	−0.0913043	−	0.229157i
$148$	−3.60384	−	9.04496i	−0.296234	−	0.743491i
$149$	1.09079	+	3.92867i	0.0893611	+	0.321849i	0.994697	−	0.102846i	$-0.0327949\pi$
$149$	1.09079	+	3.92867i	0.0893611	+	0.321849i	−0.905336	+	0.424696i	$0.860381\pi$
$150$	0.0342201	+	0.0115301i	0.00279406	+	0.000941427i
$151$	−0.205443	+	1.25315i	−0.0167187	+	0.101980i	−0.993868	−	0.110576i	$-0.964730\pi$
$151$	−0.205443	+	1.25315i	−0.0167187	+	0.101980i	0.977149	+	0.212556i	$0.0681787\pi$
$152$	0.135990	+	0.829502i	0.0110302	+	0.0672815i
$153$	2.20554	−	0.743132i	0.178307	−	0.0600787i
$154$	−0.580606	−	0.856330i	−0.0467866	−	0.0690051i
$155$	7.70265	+	3.56362i	0.618691	+	0.286237i
$156$	−4.51608	−	3.43303i	−0.361576	−	0.274863i
$157$	8.65295	−	0.941065i	0.690580	−	0.0751051i	0.243902	−	0.969800i	$-0.421572\pi$
$157$	8.65295	−	0.941065i	0.690580	−	0.0751051i	0.446678	+	0.894695i	$0.352607\pi$
$158$	1.18989	−	4.28561i	0.0946628	−	0.340945i
$159$	−5.93173	+	8.74865i	−0.470417	+	0.693813i
$160$	−1.92290	+	1.15697i	−0.152018	+	0.0914664i
$161$	0.446037	+	8.22668i	0.0351527	+	0.648353i
$162$	−0.725995	+	0.687699i	−0.0570396	+	0.0540308i
$163$	−9.31559	+	7.08153i	−0.729653	+	0.554668i	−0.902713	−	0.430243i	$-0.858428\pi$
$163$	−9.31559	+	7.08153i	−0.729653	+	0.554668i	0.173060	+	0.984911i	$0.444635\pi$
$164$	9.74432	−	2.14489i	0.760903	−	0.167487i
$165$	−0.750682	−	0.883771i	−0.0584405	−	0.0688015i
$166$	0.00343916	−	0.0634317i	0.000266931	−	0.00492325i
$167$	4.75730	+	8.97322i	0.368131	+	0.694369i	0.996504	−	0.0835433i	$-0.0266237\pi$
$167$	4.75730	+	8.97322i	0.368131	+	0.694369i	−0.628373	+	0.777912i	$0.716279\pi$
$168$	−1.95549	−	0.430436i	−0.150869	−	0.0332088i
$169$	17.4079	−	8.05376i	1.33907	−	0.619520i
$170$	4.47529	+	2.69269i	0.343239	+	0.206520i
$171$	−0.393732	+	0.742658i	−0.0301095	+	0.0567925i
$172$	5.26624	−	6.19990i	0.401547	−	0.472738i
$173$	7.67716	+	7.27219i	0.583683	+	0.552894i	0.921530	−	0.388307i	$-0.126940\pi$
$173$	7.67716	+	7.27219i	0.583683	+	0.552894i	−0.337847	+	0.941201i	$0.609699\pi$
$174$	4.27207	+	0.464616i	0.323865	+	0.0352224i
$175$	−0.0267624	+	0.0671685i	−0.00202304	+	0.00507746i
$176$	0.516708			0.0389483
$177$	−1.02289	−	7.61273i	−0.0768852	−	0.572208i
$178$	10.4187			0.780912
$179$	−1.93755	+	4.86288i	−0.144819	+	0.363469i	−0.983437	−	0.181252i	$-0.941985\pi$
$179$	−1.93755	+	4.86288i	−0.144819	+	0.363469i	0.838618	+	0.544721i	$0.183364\pi$
$180$	−2.23097	−	0.242633i	−0.166287	−	0.0180848i
$181$	−13.6702	−	12.9491i	−1.01610	−	0.962498i	−0.0167949	−	0.999859i	$-0.505346\pi$
$181$	−13.6702	−	12.9491i	−1.01610	−	0.962498i	−0.999302	+	0.0373610i	$0.988105\pi$
$182$	7.35344	−	8.65714i	0.545073	−	0.641710i
$183$	0.130037	−	0.245276i	0.00961263	−	0.0181313i
$184$	−3.52566	−	2.12132i	−0.259915	−	0.156386i
$185$	19.8304	−	9.17453i	1.45796	−	0.674525i
$186$	−3.69348	−	0.812996i	−0.270819	−	0.0596117i
$187$	−0.563293	−	1.06248i	−0.0411921	−	0.0776965i
$188$	−0.541244	+	9.98267i	−0.0394743	+	0.728061i
$189$	−1.29626	−	1.52608i	−0.0942892	−	0.111006i
$190$	−1.84226	+	0.405511i	−0.133651	+	0.0294189i
$191$	15.0687	−	11.4550i	1.09034	−	0.828851i	0.104161	−	0.994560i	$-0.466784\pi$
$191$	15.0687	−	11.4550i	1.09034	−	0.828851i	0.986175	+	0.165709i	$0.0529912\pi$
$192$	0.725995	−	0.687699i	0.0523942	−	0.0496304i
$193$	0.839600	+	15.4855i	0.0604358	+	1.11467i	0.858738	+	0.512415i	$0.171249\pi$
$193$	0.839600	+	15.4855i	0.0604358	+	1.11467i	−0.798302	+	0.602257i	$0.794268\pi$
$194$	8.10418	−	4.87613i	0.581846	−	0.350085i
$195$	7.14419	−	10.5369i	0.511606	−	0.754562i
$196$	−0.800121	+	2.88178i	−0.0571515	+	0.205841i
$197$	15.1480	−	1.64745i	1.07925	−	0.117376i	0.448821	−	0.893622i	$-0.351844\pi$
$197$	15.1480	−	1.64745i	1.07925	−	0.117376i	0.630430	+	0.776246i	$0.282879\pi$
$198$	0.411347	+	0.312698i	0.0292332	+	0.0222225i
$199$	24.2086	+	11.2001i	1.71611	+	0.793955i	0.994858	+	0.101277i	$0.0322930\pi$
$199$	24.2086	+	11.2001i	1.71611	+	0.793955i	0.721247	+	0.692678i	$0.243569\pi$
$200$	−0.0202646	−	0.0298881i	−0.00143293	−	0.00211341i
$201$	−2.22227	+	0.748770i	−0.156747	+	0.0528141i
$202$	1.09795	+	6.69718i	0.0772513	+	0.471212i
$203$	−1.39204	+	8.49106i	−0.0977019	+	0.595955i
$204$	−2.20554	−	0.743132i	−0.154418	−	0.0520297i
$205$	5.99022	+	21.5748i	0.418375	+	1.50685i
$206$	−2.25433	−	5.65794i	−0.157067	−	0.394207i
$207$	−1.52299	−	3.82241i	−0.105855	−	0.265676i
$208$	1.51764	+	5.46603i	0.105229	+	0.379001i
$209$	0.411596	+	0.138683i	0.0284707	+	0.00959288i
$210$	0.726954	−	4.43423i	0.0501646	−	0.305991i
$211$	0.490787	+	2.99367i	0.0337872	+	0.206093i	0.998325	−	0.0578512i	$-0.0184249\pi$
$211$	0.490787	+	2.99367i	0.0337872	+	0.206093i	−0.964538	+	0.263944i	$0.914977\pi$
$212$	10.0167	−	3.37501i	0.687947	−	0.231796i
$213$	4.39605	+	6.48370i	0.301213	+	0.444255i
$214$	−3.21040	−	1.48529i	−0.219458	−	0.101532i
$215$	14.5328	+	11.0475i	0.991128	+	0.753436i
$216$	0.994138	−	0.108119i	0.0676425	−	0.00735657i
$217$	2.02586	−	7.29648i	0.137524	−	0.495317i
$218$	−0.272099	+	0.401316i	−0.0184289	+	0.0271805i
$219$	−6.61357	+	3.97925i	−0.446903	+	0.268893i
$220$	0.0627772	+	1.15786i	0.00423244	+	0.0780627i
$221$	9.58510	−	9.07949i	0.644764	−	0.610752i
$222$	−7.75114	+	5.89226i	−0.520222	+	0.395463i
$223$	−16.2625	+	3.57966i	−1.08902	+	0.239711i	−0.722967	−	0.690883i	$-0.757222\pi$
$223$	−16.2625	+	3.57966i	−1.08902	+	0.239711i	−0.366053	+	0.930594i	$0.619291\pi$
$224$	1.29626	+	1.52608i	0.0866102	+	0.101965i
$225$	0.00195497	−	0.0360574i	0.000130332	−	0.00240382i
$226$	−1.63612	−	3.08605i	−0.108833	−	0.205281i
$227$	−23.4007	−	5.15087i	−1.55316	−	0.341875i	−0.646222	−	0.763149i	$-0.723652\pi$
$227$	−23.4007	−	5.15087i	−1.55316	−	0.341875i	−0.906933	+	0.421274i	$0.861583\pi$
$228$	0.762885	−	0.352948i	0.0505233	−	0.0233746i
$229$	7.05442	+	4.24450i	0.466169	+	0.280485i	0.729197	−	0.684304i	$-0.239894\pi$
$229$	7.05442	+	4.24450i	0.466169	+	0.280485i	−0.263028	+	0.964788i	$0.584721\pi$
$230$	4.32519	−	8.15817i	0.285194	−	0.537934i
$231$	−0.669788	+	0.788536i	−0.0440688	+	0.0518819i
$232$	−3.11979	−	2.95522i	−0.204824	−	0.194020i
$233$	−8.53137	−	0.927843i	−0.558909	−	0.0607850i	−0.175695	−	0.984445i	$-0.556217\pi$
$233$	−8.53137	−	0.927843i	−0.558909	−	0.0607850i	−0.383214	+	0.923660i	$0.625183\pi$
$234$	−2.09972	+	5.26990i	−0.137263	+	0.344504i
$235$	−22.4353			−1.46352
$236$	−3.79271	+	6.67947i	−0.246885	+	0.434797i
$237$	−4.44773			−0.288911
$238$	1.72488	−	4.32912i	0.111807	−	0.280615i
$239$	−8.28877	−	0.901458i	−0.536156	−	0.0583105i	−0.163964	−	0.986466i	$-0.552428\pi$
$239$	−8.28877	−	0.901458i	−0.536156	−	0.0583105i	−0.372192	+	0.928156i	$0.621394\pi$
$240$	1.62923	+	1.54329i	0.105166	+	0.0996187i
$241$	13.2437	−	15.5916i	0.853099	−	1.00435i	−0.146786	−	0.989168i	$-0.546893\pi$
$241$	13.2437	−	15.5916i	0.853099	−	1.00435i	0.999885	−	0.0151770i	$-0.00483117\pi$
$242$	−5.02743	+	9.48275i	−0.323176	+	0.609574i
$243$	0.856857	+	0.515554i	0.0549674	+	0.0330728i
$244$	−0.251957	+	0.116568i	−0.0161299	+	0.00746247i
$245$	−6.55480	−	1.44282i	−0.418771	−	0.0921784i
$246$	−4.67359	−	8.81532i	−0.297977	−	0.562044i
$247$	−0.258157	+	4.76142i	−0.0164261	+	0.302962i
$248$	2.44835	+	2.88242i	0.155470	+	0.183034i
$249$	−0.0620397	+	0.0136560i	−0.00393160	+	0.000865411i
$250$	−8.86816	+	6.74140i	−0.560872	+	0.426364i
$251$	−1.19026	+	1.12748i	−0.0751288	+	0.0711657i	−0.724343	−	0.689440i	$-0.757857\pi$
$251$	−1.19026	+	1.12748i	−0.0751288	+	0.0711657i	0.649214	+	0.760606i	$0.275098\pi$
$252$	0.108402	+	1.99936i	0.00682871	+	0.125948i
$253$	−1.82174	+	1.09610i	−0.114532	+	0.0689114i
$254$	6.24613	−	9.21235i	0.391917	−	0.578034i
$255$	1.39728	−	5.03254i	0.0875009	−	0.315150i
$256$	−0.994138	+	0.108119i	−0.0621336	+	0.00675744i
$257$	−18.3725	−	13.9664i	−1.14604	−	0.871200i	−0.152917	−	0.988239i	$-0.548867\pi$
$257$	−18.3725	−	13.9664i	−1.14604	−	0.871200i	−0.993127	+	0.117039i	$0.962660\pi$
$258$	−7.38278	−	3.41564i	−0.459632	−	0.212648i
$259$	−10.9405	−	16.1361i	−0.679812	−	1.00265i
$260$	−12.0641	+	4.06487i	−0.748183	+	0.252092i
$261$	−0.695219	−	4.24065i	−0.0430330	−	0.262490i
$262$	1.39411	−	8.50369i	0.0861284	−	0.525360i
$263$	15.8167	+	5.32927i	0.975300	+	0.328617i	0.761431	−	0.648245i	$-0.224497\pi$
$263$	15.8167	+	5.32927i	0.975300	+	0.328617i	0.213869	+	0.976862i	$0.431393\pi$
$264$	−0.138234	−	0.497874i	−0.00850771	−	0.0306420i
$265$	8.77981	+	22.0357i	0.539340	+	1.35364i
$266$	0.622974	+	1.56355i	0.0381970	+	0.0958672i
$267$	−2.78729	−	10.0389i	−0.170579	−	0.614371i
$268$	2.22227	+	0.748770i	0.135747	+	0.0457384i
$269$	4.03849	−	24.6337i	0.246231	−	1.50194i	−0.517095	−	0.855928i	$-0.672986\pi$
$269$	4.03849	−	24.6337i	0.246231	−	1.50194i	0.763326	−	0.646014i	$-0.223565\pi$
$270$	0.363060	+	2.21456i	0.0220951	+	0.134774i
$271$	−4.12390	+	1.38950i	−0.250509	+	0.0844064i	−0.441755	−	0.897136i	$-0.645644\pi$
$271$	−4.12390	+	1.38950i	−0.250509	+	0.0844064i	0.191246	+	0.981542i	$0.438747\pi$
$272$	1.30609	+	1.92634i	0.0791933	+	0.116801i
$273$	−10.3088	−	4.76938i	−0.623919	−	0.288656i
$274$	−2.93384	−	2.23024i	−0.177240	−	0.134734i
$275$	−0.0185491	+	0.00201734i	−0.00111855	+	0.000121650i
$276$	−1.10078	+	3.96467i	−0.0662594	+	0.238645i
$277$	−7.97736	+	11.7657i	−0.479313	+	0.706934i	−0.988075	−	0.153973i	$-0.950793\pi$
$277$	−7.97736	+	11.7657i	−0.479313	+	0.706934i	0.508762	+	0.860907i	$0.330103\pi$
$278$	−18.7651	+	11.2906i	−1.12546	+	0.677165i
$279$	0.204748	+	3.77635i	0.0122579	+	0.226084i
$280$	−3.26220	+	3.09012i	−0.194954	+	0.184670i
$281$	−0.587773	+	0.446813i	−0.0350636	+	0.0266547i	−0.622559	−	0.782573i	$-0.713907\pi$
$281$	−0.587773	+	0.446813i	−0.0350636	+	0.0266547i	0.587496	+	0.809227i	$0.300114\pi$
$282$	9.76360	−	2.14913i	0.581414	−	0.127979i
$283$	−20.7425	−	24.4200i	−1.23301	−	1.45162i	−0.849087	−	0.528253i	$-0.822847\pi$
$283$	−20.7425	−	24.4200i	−1.23301	−	1.45162i	−0.383927	−	0.923363i	$-0.625429\pi$
$284$	0.424097	−	7.82200i	0.0251655	−	0.464151i
$285$	0.883586	+	1.66662i	0.0523391	+	0.0987220i
$286$	2.86265	+	0.630117i	0.169272	+	0.0372596i
$287$	18.1317	−	8.38860i	1.07028	−	0.495163i
$288$	−0.856857	−	0.515554i	−0.0504908	−	0.0303793i
$289$	−5.42574	+	10.2340i	−0.319161	+	0.602002i
$290$	6.24314	−	7.34999i	0.366610	−	0.431606i
$291$	−6.86649	−	6.50428i	−0.402521	−	0.381288i
$292$	7.67315	+	0.834506i	0.449037	+	0.0488358i
$293$	−9.17768	+	23.0342i	−0.536166	+	1.34567i	0.372454	+	0.928051i	$0.378516\pi$
$293$	−9.17768	+	23.0342i	−0.536166	+	1.34567i	−0.908620	+	0.417624i	$0.862863\pi$
$294$	2.99079			0.174426
$295$	−15.4284	−	7.68733i	−0.898276	−	0.447574i
$296$	9.73647			0.565921
$297$	0.191253	−	0.480009i	0.0110976	−	0.0278530i
$298$	−4.05339	−	0.440833i	−0.234807	−	0.0255368i
$299$	−16.9459	−	16.0520i	−0.980005	−	0.928310i
$300$	−0.0233773	+	0.0275219i	−0.00134969	+	0.00158898i
$301$	7.62942	−	14.3906i	0.439752	−	0.829461i
$302$	−1.08810	−	0.654688i	−0.0626131	−	0.0376731i
$303$	6.15934	−	2.84961i	0.353845	−	0.163706i
$304$	−0.820923	−	0.180699i	−0.0470832	−	0.0103638i
$305$	−0.291820	−	0.550431i	−0.0167096	−	0.0315176i
$306$	−0.126001	+	2.32395i	−0.00720301	+	0.132852i
$307$	4.51439	+	5.31475i	0.257650	+	0.303329i	0.875744	−	0.482775i	$-0.160371\pi$
$307$	4.51439	+	5.31475i	0.257650	+	0.303329i	−0.618095	+	0.786104i	$0.712095\pi$
$308$	1.01042	−	0.222409i	0.0575738	−	0.0126729i
$309$	−4.84861	+	3.68582i	−0.275828	+	0.209679i
$310$	−6.16157	+	5.83655i	−0.349953	+	0.331494i
$311$	0.845364	+	15.5918i	0.0479362	+	0.884131i	0.919316	+	0.393521i	$0.128743\pi$
$311$	0.845364	+	15.5918i	0.0479362	+	0.884131i	−0.871379	+	0.490610i	$0.836774\pi$
$312$	4.86078	−	2.92464i	0.275188	−	0.165575i
$313$	15.7099	−	23.1704i	0.887977	−	1.30967i	−0.0622347	−	0.998062i	$-0.519823\pi$
$313$	15.7099	−	23.1704i	0.887977	−	1.30967i	0.950211	−	0.311606i	$-0.100867\pi$
$314$	−2.32856	+	8.38671i	−0.131408	+	0.473289i
$315$	−4.46708	+	0.485824i	−0.251691	+	0.0273731i
$316$	3.54081	+	2.69165i	0.199186	+	0.151417i
$317$	−4.96885	−	2.29883i	−0.279078	−	0.129115i	0.275357	−	0.961342i	$-0.411204\pi$
$317$	−4.96885	−	2.29883i	−0.279078	−	0.129115i	−0.554436	+	0.832227i	$0.687066\pi$
$318$	−5.93173	−	8.74865i	−0.332635	−	0.490600i
$319$	−2.10419	+	0.708986i	−0.117812	+	0.0396956i
$320$	−0.363060	−	2.21456i	−0.0202956	−	0.123798i
$321$	−0.572277	+	3.49074i	−0.0319414	+	0.194834i
$322$	−7.80749	−	2.63065i	−0.435094	−	0.146600i
$323$	0.523373	+	1.88502i	0.0291213	+	0.104885i
$324$	−0.370138	−	0.928977i	−0.0205632	−	0.0516098i
$325$	−0.0758216	−	0.190298i	−0.00420582	−	0.0105558i
$326$	−3.13052	−	11.2751i	−0.173383	−	0.624471i
$327$	0.459482	+	0.154817i	0.0254094	+	0.00856143i
$328$	−1.61419	+	9.84615i	−0.0891289	+	0.543663i
$329$	3.23850	+	19.7540i	0.178544	+	1.08907i
$330$	1.09886	−	0.370249i	0.0604902	−	0.0203815i
$331$	−9.70640	−	14.3159i	−0.533512	−	0.786871i	0.461446	−	0.887169i	$-0.347331\pi$
$331$	−9.70640	−	14.3159i	−0.533512	−	0.786871i	−0.994958	+	0.100297i	$0.968021\pi$
$332$	0.0576536	+	0.0266734i	0.00316415	+	0.00146389i
$333$	7.75114	+	5.89226i	0.424760	+	0.322894i
$334$	−10.0968	+	1.09809i	−0.552471	+	0.0600848i
$335$	−1.40788	+	5.07071i	−0.0769205	+	0.277043i
$336$	1.12367	−	1.65728i	0.0613010	−	0.0904122i
$337$	−1.87726	+	1.12951i	−0.102261	+	0.0615282i	−0.565765	−	0.824566i	$-0.691419\pi$
$337$	−1.87726	+	1.12951i	−0.102261	+	0.0615282i	0.463505	+	0.886094i	$0.346592\pi$
$338$	1.03842	+	19.1526i	0.0564827	+	1.04176i
$339$	−2.53585	+	2.40209i	−0.137729	+	0.130464i
$340$	−4.15792	+	3.16077i	−0.225495	+	0.171417i
$341$	1.90845	−	0.420081i	0.103348	−	0.0227487i
$342$	−0.544177	−	0.640654i	−0.0294257	−	0.0346426i
$343$	−1.08303	+	19.9752i	−0.0584779	+	1.07856i
$344$	3.81033	+	7.18704i	0.205439	+	0.387499i
$345$	−9.01791	−	1.98499i	−0.485508	−	0.106868i
$346$	−9.59730	+	4.44019i	−0.515954	+	0.238706i
$347$	8.21638	+	4.94363i	0.441078	+	0.265388i	0.718724	−	0.695296i	$-0.244727\pi$
$347$	8.21638	+	4.94363i	0.441078	+	0.265388i	−0.277646	+	0.960684i	$0.589554\pi$
$348$	−2.01287	+	3.79668i	−0.107901	+	0.203523i
$349$	9.57156	−	11.2685i	0.512354	−	0.603190i	−0.443774	−	0.896139i	$-0.646361\pi$
$349$	9.57156	−	11.2685i	0.512354	−	0.603190i	0.956128	+	0.292949i	$0.0946366\pi$
$350$	−0.0524922	−	0.0497232i	−0.00280583	−	0.00265782i
$351$	5.63955	+	0.613338i	0.301017	+	0.0327376i
$352$	−0.191253	+	0.480009i	−0.0101938	+	0.0255846i
$353$	−14.7918			−0.787290			−0.393645	−	0.919263i	$-0.628786\pi$
$353$	−14.7918			−0.787290			−0.393645	+	0.919263i	$0.628786\pi$
$354$	7.45066	+	1.86752i	0.395998	+	0.0992576i
$355$	17.5794			0.933016
$356$	−3.85635	+	9.67870i	−0.204386	+	0.512970i
$357$	−4.63277	−	0.503844i	−0.245192	−	0.0266663i
$358$	−3.80034	−	3.59987i	−0.200854	−	0.190259i
$359$	13.4654	−	15.8527i	0.710677	−	0.836673i	−0.281753	−	0.959487i	$-0.590916\pi$
$359$	13.4654	−	15.8527i	0.710677	−	0.836673i	0.992430	+	0.122814i	$0.0391917\pi$
$360$	1.05117	−	1.98271i	0.0554014	−	0.104498i
$361$	15.6749	+	9.43125i	0.824993	+	0.496382i
$362$	17.0893	−	7.90633i	0.898191	−	0.415548i
$363$	10.4821	+	2.30728i	0.550167	+	0.121101i
$364$	5.32049	+	10.0355i	0.278870	+	0.526004i
$365$	−0.937744	+	17.2957i	−0.0490838	+	0.905297i
$366$	0.179724	+	0.211588i	0.00939434	+	0.0110599i
$367$	−11.4283	+	2.51557i	−0.596554	+	0.131311i	−0.502976	−	0.864301i	$-0.667762\pi$
$367$	−11.4283	+	2.51557i	−0.596554	+	0.131311i	−0.0935781	+	0.995612i	$0.529830\pi$
$368$	3.27564	−	2.49008i	0.170755	−	0.129804i
$369$	−7.24368	+	6.86158i	−0.377091	+	0.357200i
$370$	1.18293	+	21.8179i	0.0614976	+	1.13426i
$371$	18.1347	−	10.9113i	0.941509	−	0.566487i
$372$	2.12235	−	3.13023i	0.110039	−	0.162295i
$373$	7.69539	−	27.7163i	0.398452	−	1.43509i	−0.443856	−	0.896098i	$-0.646390\pi$
$373$	7.69539	−	27.7163i	0.398452	−	1.43509i	0.842308	−	0.538996i	$-0.181196\pi$
$374$	1.19552	−	0.130021i	0.0618188	−	0.00672320i
$375$	8.86816	+	6.74140i	0.457950	+	0.348124i
$376$	−9.07333	−	4.19777i	−0.467921	−	0.216483i
$377$	−13.6803	−	20.1770i	−0.704573	−	1.03917i
$378$	1.89749	−	0.639338i	0.0975962	−	0.0328840i
$379$	−3.70862	−	22.6216i	−0.190499	−	1.16199i	−0.892914	−	0.450226i	$-0.851343\pi$
$379$	−3.70862	−	22.6216i	−0.190499	−	1.16199i	0.702415	−	0.711767i	$-0.252105\pi$
$380$	0.305179	−	1.86151i	0.0156553	−	0.0954934i
$381$	−10.5476	−	3.55389i	−0.540369	−	0.182071i
$382$	5.06387	+	18.2384i	0.259090	+	0.933159i
$383$	2.18624	+	5.48704i	0.111712	+	0.280375i	0.974194	−	0.225712i	$-0.0724708\pi$
$383$	2.18624	+	5.48704i	0.111712	+	0.280375i	−0.862483	+	0.506087i	$0.831092\pi$
$384$	0.370138	+	0.928977i	0.0188885	+	0.0474066i
$385$	0.621143	+	2.23715i	0.0316564	+	0.114016i
$386$	−14.6965	−	4.95181i	−0.748030	−	0.252041i
$387$	−1.31604	+	8.02746i	−0.0668978	+	0.408059i
$388$	1.53014	+	9.33344i	0.0776811	+	0.473834i
$389$	−7.35523	+	2.47826i	−0.372925	+	0.125653i	−0.499522	−	0.866301i	$-0.666491\pi$
$389$	−7.35523	+	2.47826i	−0.372925	+	0.125653i	0.126597	+	0.991954i	$0.459594\pi$
$390$	7.14419	+	10.5369i	0.361760	+	0.533556i
$391$	−8.69121	−	4.02098i	−0.439533	−	0.203350i
$392$	−2.38095	−	1.80995i	−0.120256	−	0.0914163i
$393$	−8.56669	+	0.931684i	−0.432133	+	0.0469972i
$394$	−4.07642	+	14.6819i	−0.205367	+	0.739665i
$395$	−5.60136	+	8.26139i	−0.281835	+	0.415676i
$396$	−0.442745	+	0.266391i	−0.0222488	+	0.0133866i
$397$	−2.03434	−	37.5211i	−0.102100	−	1.88313i	−0.383500	−	0.923541i	$-0.625282\pi$
$397$	−2.03434	−	37.5211i	−0.102100	−	1.88313i	0.281400	−	0.959591i	$-0.409201\pi$
$398$	−19.3652	+	18.3437i	−0.970689	+	0.919486i
$399$	1.33989	−	1.01856i	0.0670785	−	0.0509917i
$400$	0.0352661	−	0.00776265i	0.00176330	−	0.000388133i
$401$	−9.39688	−	11.0629i	−0.469258	−	0.552453i	0.475716	−	0.879599i	$-0.342189\pi$
$401$	−9.39688	−	11.0629i	−0.469258	−	0.552453i	−0.944974	+	0.327146i	$0.893913\pi$
$402$	0.126957	−	2.34158i	0.00633204	−	0.116788i
$403$	10.0492	+	18.9548i	0.500587	+	0.944207i
$404$	−6.62792	−	1.45891i	−0.329751	−	0.0725837i
$405$	2.03672	−	0.942285i	0.101205	−	0.0468225i
$406$	−7.37275	−	4.43604i	−0.365903	−	0.220157i
$407$	2.35652	−	4.44487i	0.116808	−	0.220324i
$408$	1.50671	−	1.77383i	0.0745931	−	0.0878177i
$409$	23.0439	+	21.8283i	1.13945	+	1.07934i	0.995970	+	0.0896872i	$0.0285867\pi$
$409$	23.0439	+	21.8283i	1.13945	+	1.07934i	0.143476	+	0.989654i	$0.454172\pi$
$410$	−22.2597	−	2.42089i	−1.09933	−	0.119559i
$411$	−1.36407	+	3.42355i	−0.0672845	+	0.168871i
$412$	6.09051			0.300058
$413$	−4.54152	+	14.6941i	−0.223474	+	0.723052i
$414$	4.11465			0.202224
$415$	−0.0527661	+	0.132433i	−0.00259019	+	0.00650088i
$416$	−5.63955	−	0.613338i	−0.276502	−	0.0300714i
$417$	15.8992	+	15.0606i	0.778590	+	0.737519i
$418$	−0.281180	+	0.331031i	−0.0137530	+	0.0161913i
$419$	12.8569	−	24.2506i	0.628099	−	1.18472i	−0.341467	−	0.939894i	$-0.610924\pi$
$419$	12.8569	−	24.2506i	0.628099	−	1.18472i	0.969567	−	0.244828i	$-0.0787314\pi$
$420$	3.85022	+	2.31660i	0.187871	+	0.113038i
$421$	−22.1406	+	10.2433i	−1.07907	+	0.499230i	−0.877172	−	0.480177i	$-0.840572\pi$
$421$	−22.1406	+	10.2433i	−1.07907	+	0.499230i	−0.201896	+	0.979407i	$0.564710\pi$
$422$	−2.96271	−	0.652141i	−0.144222	−	0.0317457i
$423$	−4.68283	−	8.83276i	−0.227687	−	0.429464i
$424$	−0.572247	+	10.5545i	−0.0277908	+	0.512570i
$425$	−0.0544076	−	0.0640536i	−0.00263916	−	0.00310706i
$426$	−7.65035	+	1.68397i	−0.370661	+	0.0815886i
$427$	−0.442523	+	0.336398i	−0.0214152	+	0.0162794i
$428$	2.56809	−	2.43262i	0.124133	−	0.117585i
$429$	−0.158691	−	2.92688i	−0.00766167	−	0.141311i
$430$	−15.6420	+	9.41150i	−0.754326	+	0.453863i
$431$	18.5080	−	27.2972i	0.891498	−	1.31486i	−0.0570976	−	0.998369i	$-0.518185\pi$
$431$	18.5080	−	27.2972i	0.891498	−	1.31486i	0.948595	−	0.316492i	$-0.102505\pi$
$432$	−0.267528	+	0.963550i	−0.0128715	+	0.0463588i
$433$	3.91924	−	0.426243i	0.188346	−	0.0204839i	−0.0134596	−	0.999909i	$-0.504284\pi$
$433$	3.91924	−	0.426243i	0.188346	−	0.0204839i	0.201806	+	0.979426i	$0.435319\pi$
$434$	6.02841	+	4.58268i	0.289373	+	0.219976i
$435$	−8.75230	−	4.04924i	−0.419640	−	0.194146i
$436$	−0.272099	−	0.401316i	−0.0130312	−	0.0192195i
$437$	3.27762	−	1.10436i	0.156790	−	0.0528286i
$438$	−1.24870	−	7.61672i	−0.0596651	−	0.363941i
$439$	5.22285	−	31.8580i	0.249273	−	1.52050i	−0.504528	−	0.863396i	$-0.668333\pi$
$439$	5.22285	−	31.8580i	0.249273	−	1.52050i	0.753801	−	0.657103i	$-0.228218\pi$
$440$	−1.09886	−	0.370249i	−0.0523860	−	0.0176509i
$441$	−0.800121	−	2.88178i	−0.0381010	−	0.137227i
$442$	4.88682	+	12.2650i	0.232442	+	0.583386i
$443$	0.688647	+	1.72837i	0.0327186	+	0.0821176i	0.944428	−	0.328718i	$-0.106616\pi$
$443$	0.688647	+	1.72837i	0.0327186	+	0.0821176i	−0.911710	+	0.410835i	$0.865237\pi$
$444$	−2.60478	−	9.38158i	−0.123618	−	0.445230i
$445$	−22.1569	−	7.46553i	−1.05034	−	0.353900i
$446$	2.69397	−	16.4325i	0.127563	−	0.778101i
$447$	0.659632	+	4.02358i	0.0311995	+	0.190309i
$448$	−1.89749	+	0.639338i	−0.0896478	+	0.0302059i
$449$	−6.76942	−	9.98414i	−0.319469	−	0.471181i	0.633718	−	0.773564i	$-0.281528\pi$
$449$	−6.76942	−	9.98414i	−0.319469	−	0.471181i	−0.953186	+	0.302383i	$0.902218\pi$
$450$	0.0327728	+	0.0151623i	0.00154493	+	0.000714759i
$451$	4.10425	+	3.11997i	0.193262	+	0.146914i
$452$	3.47246	−	0.377653i	0.163331	−	0.0177633i
$453$	−0.339727	+	1.22359i	−0.0159618	+	0.0574891i
$454$	13.4465	−	19.8321i	0.631076	−	0.930768i
$455$	−21.8415	+	13.1416i	−1.02395	+	0.616088i
$456$	0.0455078	+	0.839342i	0.00213110	+	0.0393058i
$457$	−30.4375	+	28.8319i	−1.42381	+	1.34870i	−0.577062	+	0.816700i	$0.695801\pi$
$457$	−30.4375	+	28.8319i	−1.42381	+	1.34870i	−0.846744	+	0.532000i	$0.821441\pi$
$458$	−6.55415	+	4.98234i	−0.306255	+	0.232809i
$459$	2.27296	−	0.500315i	0.106092	−	0.0233527i
$460$	5.97783	+	7.03765i	0.278718	+	0.328132i
$461$	−1.60017	+	29.5135i	−0.0745275	+	1.37458i	0.687100	+	0.726563i	$0.258884\pi$
$461$	−1.60017	+	29.5135i	−0.0745275	+	1.37458i	−0.761627	+	0.648016i	$0.775599\pi$
$462$	−0.484617	−	0.914085i	−0.0225464	−	0.0425271i
$463$	22.7638	+	5.01070i	1.05793	+	0.232867i	0.709671	−	0.704533i	$-0.248844\pi$
$463$	22.7638	+	5.01070i	1.05793	+	0.232867i	0.348254	+	0.937400i	$0.386775\pi$
$464$	3.90009	−	1.80437i	0.181057	−	0.0837659i
$465$	7.27220	+	4.37554i	0.337240	+	0.202911i
$466$	4.01973	−	7.58202i	0.186210	−	0.351230i
$467$	15.3639	−	18.0878i	0.710958	−	0.837004i	−0.281504	−	0.959560i	$-0.590833\pi$
$467$	15.3639	−	18.0878i	0.710958	−	0.837004i	0.992462	+	0.122556i	$0.0391091\pi$
$468$	−4.11843	−	3.90118i	−0.190374	−	0.180332i
$469$	4.66792	+	0.507667i	0.215544	+	0.0234419i
$470$	8.30415	−	20.8419i	0.383042	−	0.961363i
$471$	8.70397			0.401058
$472$	−4.80125	−	5.99567i	−0.220995	−	0.275973i
$473$	4.20322			0.193264
$474$	1.64627	−	4.13184i	0.0756159	−	0.189782i
$475$	0.0301755	+	0.00328178i	0.00138455	+	0.000150579i
$476$	3.38320	+	3.20474i	0.155069	+	0.146889i
$477$	−6.84285	+	8.05603i	−0.313313	+	0.368860i
$478$	3.90543	−	7.36641i	0.178630	−	0.336932i
$479$	18.0353	+	10.8515i	0.824052	+	0.495816i	0.864063	−	0.503383i	$-0.167912\pi$
$479$	18.0353	+	10.8515i	0.824052	+	0.495816i	−0.0400108	+	0.999199i	$0.512739\pi$
$480$	−2.03672	+	0.942285i	−0.0929629	+	0.0430092i
$481$	53.9418	+	11.8735i	2.45953	+	0.541384i
$482$	9.58228	+	18.0741i	0.436461	+	0.823253i
$483$	−0.446037	+	8.22668i	−0.0202954	+	0.374327i
$484$	−6.94841	−	8.18030i	−0.315837	−	0.371832i
$485$	−20.7288	+	4.56276i	−0.941247	+	0.207184i
$486$	−0.796093	+	0.605174i	−0.0361115	+	0.0274513i
$487$	22.5483	−	21.3589i	1.02176	−	0.967864i	0.0222701	−	0.999752i	$-0.492911\pi$
$487$	22.5483	−	21.3589i	1.02176	−	0.967864i	0.999491	+	0.0318881i	$0.0101520\pi$
$488$	−0.0150298	−	0.277208i	−0.000680366	−	0.0125486i
$489$	−10.0266	+	6.03282i	−0.453420	+	0.272814i
$490$	3.76653	−	5.55521i	0.170154	−	0.250959i
$491$	−0.205728	+	0.740965i	−0.00928437	+	0.0334393i	−0.968047	−	0.250768i	$-0.919317\pi$
$491$	−0.205728	+	0.740965i	−0.00928437	+	0.0334393i	0.958763	+	0.284208i	$0.0917305\pi$
$492$	9.91910	−	1.07877i	0.447187	−	0.0486346i
$493$	−7.96197	−	6.05253i	−0.358589	−	0.272592i
$494$	−4.32770	−	2.00221i	−0.194712	−	0.0900835i
$495$	−0.650729	−	0.959753i	−0.0292481	−	0.0431377i
$496$	−3.58393	+	1.20757i	−0.160923	+	0.0542213i
$497$	−2.53755	−	15.4784i	−0.113825	−	0.694300i
$498$	0.0102772	−	0.0626880i	0.000460531	−	0.00280912i
$499$	−29.2020	−	9.83931i	−1.30726	−	0.440468i	−0.422437	−	0.906392i	$-0.638825\pi$
$499$	−29.2020	−	9.83931i	−1.30726	−	0.440468i	−0.884825	+	0.465924i	$0.845722\pi$
$500$	−2.98016	−	10.7336i	−0.133277	−	0.480020i
$501$	3.75924	+	9.43497i	0.167950	+	0.421524i
$502$	−0.606838	−	1.52305i	−0.0270845	−	0.0679770i
$503$	11.5052	+	41.4381i	0.512993	+	1.84763i	0.530343	+	0.847783i	$0.322063\pi$
$503$	11.5052	+	41.4381i	0.512993	+	1.84763i	−0.0173507	+	0.999849i	$0.505523\pi$
$504$	−1.89749	−	0.639338i	−0.0845208	−	0.0284784i
$505$	2.46393	−	15.0293i	0.109644	−	0.668796i
$506$	−0.343960	−	2.09806i	−0.0152909	−	0.0932702i
$507$	18.1766	−	6.12442i	0.807253	−	0.271995i
$508$	6.24613	+	9.21235i	0.277127	+	0.408732i
$509$	−38.0656	−	17.6110i	−1.68723	−	0.780595i	−0.998452	−	0.0556205i	$-0.982286\pi$
$509$	−38.0656	−	17.6110i	−1.68723	−	0.780595i	−0.688776	−	0.724974i	$-0.741852\pi$
$510$	4.15792	+	3.16077i	0.184116	+	0.139961i
$511$	15.3640	−	1.67093i	0.679662	−	0.0739177i
$512$	0.267528	−	0.963550i	0.0118232	−	0.0425833i
$513$	−0.471720	+	0.695735i	−0.0208269	+	0.0307174i
$514$	19.7748	−	11.8981i	0.872230	−	0.524803i
$515$	0.739964	+	13.6478i	0.0326067	+	0.601395i
$516$	5.90570	−	5.59418i	0.259984	−	0.246270i
$517$	−4.11237	+	3.12615i	−0.180862	+	0.137488i
$518$	19.0396	−	4.19092i	0.836550	−	0.184139i
$519$	6.84589	+	8.05961i	0.300501	+	0.353777i
$520$	0.689215	−	12.7118i	0.0302241	−	0.557450i
$521$	−12.2474	−	23.1011i	−0.536569	−	1.01208i	−0.992521	−	0.122072i	$-0.961046\pi$
$521$	−12.2474	−	23.1011i	−0.536569	−	1.01208i	0.455953	−	0.890004i	$-0.349299\pi$
$522$	4.19679	+	0.923784i	0.183689	+	0.0404329i
$523$	33.8825	−	15.6757i	1.48158	−	0.685452i	0.498209	−	0.867057i	$-0.333991\pi$
$523$	33.8825	−	15.6757i	1.48158	−	0.685452i	0.983372	+	0.181605i	$0.0581293\pi$
$524$	7.38372	+	4.44264i	0.322559	+	0.194077i
$525$	−0.0338677	+	0.0638812i	−0.00147811	+	0.00278800i
$526$	−10.8051	+	12.7208i	−0.471126	+	0.554653i
$527$	6.39011	+	6.05304i	0.278358	+	0.263674i
$528$	0.513679	+	0.0558659i	0.0223550	+	0.00243125i
$529$	2.24662	−	5.63860i	0.0976793	−	0.245157i
$530$	−23.7204			−1.03035
$531$	−0.193814	−	7.67870i	−0.00841082	−	0.333227i
$532$	−1.68308			−0.0729710
$533$	−20.9501	+	52.5809i	−0.907452	+	2.27753i
$534$	10.3576	+	1.12646i	0.448217	+	0.0487465i
$535$	5.76312	+	5.45912i	0.249162	+	0.236018i
$536$	−1.51814	+	1.78729i	−0.0655735	+	0.0771991i
$537$	−2.45196	+	4.62489i	−0.105810	+	0.199579i
$538$	21.3893	+	12.8695i	0.922159	+	0.554845i
$539$	−1.40253	+	0.648882i	−0.0604114	+	0.0279493i
$540$	−2.19166	−	0.482421i	−0.0943141	−	0.0207601i
$541$	−11.4694	−	21.6336i	−0.493108	−	0.930100i	−0.997768	−	0.0667820i	$-0.978727\pi$
$541$	−11.4694	−	21.6336i	−0.493108	−	0.930100i	0.504660	−	0.863318i	$-0.331618\pi$
$542$	0.235596	−	4.34532i	0.0101197	−	0.186647i
$543$	−12.1900	−	14.3512i	−0.523123	−	0.615868i
$544$	−2.27296	+	0.500315i	−0.0974521	+	0.0214508i
$545$	0.866224	−	0.658487i	0.0371050	−	0.0282065i
$546$	8.24633	−	7.81134i	0.352911	−	0.334295i
$547$	0.726476	+	13.3991i	0.0310619	+	0.572902i	0.972095	+	0.234588i	$0.0753740\pi$
$547$	0.726476	+	13.3991i	0.0310619	+	0.572902i	−0.941033	+	0.338315i	$0.890143\pi$
$548$	3.15777	−	1.89997i	0.134893	−	0.0811626i
$549$	0.155794	−	0.229779i	0.00664913	−	0.00980673i
$550$	0.00499167	−	0.0179784i	0.000212846	−	0.000766600i
$551$	3.59099	−	0.390544i	0.152982	−	0.0166377i
$552$	−3.27564	−	2.49008i	−0.139421	−	0.105985i
$553$	8.08259	+	3.73940i	0.343707	+	0.159016i
$554$	−7.97736	−	11.7657i	−0.338926	−	0.499878i
$555$	20.7061	−	6.97670i	0.878926	−	0.296145i
$556$	−3.54301	−	21.6114i	−0.150257	−	0.916529i
$557$	−1.86987	+	11.4057i	−0.0792290	+	0.483276i	0.917171	+	0.398495i	$0.130467\pi$
$557$	−1.86987	+	11.4057i	−0.0792290	+	0.483276i	−0.996400	+	0.0847808i	$0.972981\pi$
$558$	−3.58393	−	1.20757i	−0.151720	−	0.0511203i
$559$	12.3454	+	44.4641i	0.522154	+	1.88063i
$560$	−1.66319	−	4.17428i	−0.0702824	−	0.176396i
$561$	−0.445116	−	1.11716i	−0.0187928	−	0.0471665i
$562$	−0.197522	−	0.711410i	−0.00833197	−	0.0300090i
$563$	30.0754	+	10.1336i	1.26753	+	0.427079i	0.871153	−	0.491011i	$-0.163373\pi$
$563$	30.0754	+	10.1336i	1.26753	+	0.427079i	0.396372	+	0.918090i	$0.370269\pi$
$564$	−1.61739	+	9.86563i	−0.0681043	+	0.415418i
$565$	1.26814	+	7.73533i	0.0533512	+	0.325428i
$566$	30.3632	−	10.2305i	1.27626	−	0.430022i
$567$	−1.12367	−	1.65728i	−0.0471895	−	0.0695993i
$568$	7.10949	+	3.28920i	0.298307	+	0.138012i
$569$	−26.2932	−	19.9876i	−1.10227	−	0.837923i	−0.114435	−	0.993431i	$-0.536506\pi$
$569$	−26.2932	−	19.9876i	−1.10227	−	0.837923i	−0.987835	+	0.155507i	$0.950299\pi$
$570$	−1.87530	+	0.203951i	−0.0785477	+	0.00854257i
$571$	3.33191	−	12.0004i	0.139436	−	0.502203i	−0.860538	−	0.509386i	$-0.829873\pi$
$571$	3.33191	−	12.0004i	0.139436	−	0.502203i	0.999974	+	0.00718278i	$0.00228637\pi$
$572$	−1.64494	+	2.42611i	−0.0687784	+	0.101441i
$573$	16.2189	−	9.75859i	0.677554	−	0.407671i
$574$	1.08159	+	19.9488i	0.0451449	+	0.832648i
$575$	−0.107869	+	0.102179i	−0.00449846	+	0.00426117i
$576$	0.796093	−	0.605174i	0.0331705	−	0.0252156i
$577$	10.5720	−	2.32707i	0.440118	−	0.0968773i	0.0106168	−	0.999944i	$-0.496620\pi$
$577$	10.5720	−	2.32707i	0.440118	−	0.0968773i	0.429501	+	0.903066i	$0.358689\pi$
$578$	−7.49891	−	8.82840i	−0.311913	−	0.367213i
$579$	−0.839600	+	15.4855i	−0.0348926	+	0.643556i
$580$	4.51714	+	8.52024i	0.187564	+	0.353784i
$581$	0.124222	+	0.0273433i	0.00515360	+	0.00113439i
$582$	8.58388	−	3.97132i	0.355813	−	0.164617i
$583$	4.67980	+	2.81574i	0.193817	+	0.116616i
$584$	−3.61536	+	6.81930i	−0.149605	+	0.282185i
$585$	8.24155	−	9.70270i	0.340746	−	0.401157i
$586$	−18.0013	−	17.0517i	−0.743625	−	0.704399i
$587$	−23.2485	−	2.52843i	−0.959570	−	0.104359i	−0.385091	−	0.922879i	$-0.625830\pi$
$587$	−23.2485	−	2.52843i	−0.959570	−	0.104359i	−0.574479	+	0.818519i	$0.694795\pi$
$588$	−1.10701	+	2.77838i	−0.0456521	+	0.114578i
$589$	−3.17897			−0.130987
$590$	12.8520	−	11.4872i	0.529108	−	0.472923i
$591$	15.2373			0.626780
$592$	−3.60384	+	9.04496i	−0.148117	+	0.371745i
$593$	−9.31101	−	1.01263i	−0.382357	−	0.0415839i	−0.0850777	−	0.996374i	$-0.527114\pi$
$593$	−9.31101	−	1.01263i	−0.382357	−	0.0415839i	−0.297280	+	0.954790i	$0.596079\pi$
$594$	0.375127	+	0.355339i	0.0153917	+	0.0145798i
$595$	−6.77026	+	7.97057i	−0.277554	+	0.326761i
$596$	1.90984	−	3.60234i	0.0782300	−	0.147557i
$597$	22.8558	+	13.7519i	0.935425	+	0.562827i
$598$	21.1842	−	9.80087i	0.866288	−	0.400787i
$599$	−16.9059	−	3.72127i	−0.690756	−	0.152047i	−0.144299	−	0.989534i	$-0.546093\pi$
$599$	−16.9059	−	3.72127i	−0.690756	−	0.152047i	−0.546457	+	0.837487i	$0.684024\pi$
$600$	−0.0169144	−	0.0319039i	−0.000690527	−	0.00130247i
$601$	1.23416	−	22.7628i	0.0503426	−	0.928515i	−0.858873	−	0.512189i	$-0.828835\pi$
$601$	1.23416	−	22.7628i	0.0503426	−	0.928515i	0.909215	−	0.416326i	$-0.136683\pi$
$602$	10.5446	+	12.4141i	0.429766	+	0.505960i
$603$	−2.29020	+	0.504111i	−0.0932641	+	0.0205290i
$604$	1.01094	−	0.768495i	0.0411345	−	0.0312696i
$605$	17.4865	−	16.5641i	0.710928	−	0.673427i
$606$	0.367418	+	6.77663i	0.0149253	+	0.275282i
$607$	38.0100	−	22.8699i	1.54278	−	0.928259i	0.546935	−	0.837175i	$-0.315794\pi$
$607$	38.0100	−	22.8699i	1.54278	−	0.928259i	0.995843	−	0.0910843i	$-0.0290333\pi$
$608$	0.471720	−	0.695735i	0.0191308	−	0.0282158i
$609$	−2.30192	+	8.29078i	−0.0932786	+	0.335959i
$610$	0.619352	−	0.0673586i	0.0250768	−	0.00272727i
$611$	−45.1487	−	34.3212i	−1.82652	−	1.38849i
$612$	−2.11226	−	0.977236i	−0.0853831	−	0.0395024i
$613$	−6.95346	−	10.2556i	−0.280848	−	0.414219i	0.660934	−	0.750444i	$-0.270160\pi$
$613$	−6.95346	−	10.2556i	−0.280848	−	0.414219i	−0.941782	+	0.336225i	$0.890850\pi$
$614$	−6.60822	+	2.22657i	−0.266686	+	0.0898570i
$615$	3.62246	+	22.0960i	0.146072	+	0.890997i
$616$	−0.167380	+	1.02097i	−0.00674394	+	0.0411362i
$617$	14.9148	+	5.02537i	0.600446	+	0.202314i	0.603077	−	0.797683i	$-0.293941\pi$
$617$	14.9148	+	5.02537i	0.600446	+	0.202314i	−0.00263116	+	0.999997i	$0.500838\pi$
$618$	−1.62938	−	5.86851i	−0.0655434	−	0.236066i
$619$	−14.7838	−	37.1045i	−0.594210	−	1.49135i	−0.851147	−	0.524927i	$-0.824093\pi$
$619$	−14.7838	−	37.1045i	−0.594210	−	1.49135i	0.256937	−	0.966428i	$-0.417287\pi$
$620$	−3.14138	−	7.88428i	−0.126161	−	0.316640i
$621$	−1.10078	−	3.96467i	−0.0441730	−	0.159097i
$622$	−14.7973	−	4.98580i	−0.593319	−	0.199913i
$623$	−3.37498	+	20.5865i	−0.135216	+	0.824781i
$624$	0.917757	+	5.59807i	0.0367397	+	0.224102i
$625$	23.8612	−	8.03977i	0.954448	−	0.321591i
$626$	15.7099	+	23.1704i	0.627894	+	0.926075i
$627$	0.394189	+	0.182371i	0.0157424	+	0.00728320i
$628$	−6.92917	−	5.26742i	−0.276504	−	0.210193i
$629$	22.5275	−	2.45002i	0.898231	−	0.0976885i
$630$	1.20212	−	4.32963i	0.0478935	−	0.172497i
$631$	13.6956	−	20.1994i	0.545211	−	0.804126i	−0.450868	−	0.892591i	$-0.648886\pi$
$631$	13.6956	−	20.1994i	0.545211	−	0.804126i	0.996079	+	0.0884641i	$0.0281959\pi$
$632$	−3.81107	+	2.29304i	−0.151596	+	0.0912124i
$633$	0.164238	+	3.02918i	0.00652786	+	0.120399i
$634$	3.97473	−	3.76506i	0.157856	−	0.149530i
$635$	−19.8845	+	15.1158i	−0.789093	+	0.599853i
$636$	10.3228	−	2.27223i	0.409328	−	0.0900998i
$637$	−10.9837	−	12.9310i	−0.435189	−	0.512344i
$638$	0.120211	−	2.21717i	0.00475922	−	0.0877786i
$639$	3.66927	+	6.92098i	0.145154	+	0.273790i
$640$	2.19166	+	0.482421i	0.0866330	+	0.0190694i
$641$	−42.4464	+	19.6378i	−1.67653	+	0.775647i	−0.677332	+	0.735678i	$0.736864\pi$
$641$	−42.4464	+	19.6378i	−1.67653	+	0.775647i	−0.999201	+	0.0399690i	$0.987274\pi$
$642$	−3.03099	−	1.82369i	−0.119624	−	0.0719752i
$643$	−12.1110	+	22.8438i	−0.477612	+	0.900872i	0.521260	+	0.853398i	$0.325462\pi$
$643$	−12.1110	+	22.8438i	−0.477612	+	0.900872i	−0.998872	+	0.0474742i	$0.984883\pi$
$644$	5.33366	−	6.27927i	0.210176	−	0.247438i
$645$	13.2531	+	12.5540i	0.521842	+	0.494315i
$646$	−1.94486	−	0.211516i	−0.0765195	−	0.00832199i
$647$	−11.5582	+	29.0090i	−0.454401	+	1.14046i	0.506171	+	0.862433i	$0.331060\pi$
$647$	−11.5582	+	29.0090i	−0.454401	+	1.14046i	−0.960573	+	0.278029i	$0.910319\pi$
$648$	1.00000			0.0392837
$649$	−3.89917	+	0.740719i	−0.153056	+	0.0290758i
$650$	0.204847			0.00803475
$651$	2.80287	−	7.03467i	0.109853	−	0.275710i
$652$	11.6330	+	1.26517i	0.455585	+	0.0495478i
$653$	−20.7757	−	19.6798i	−0.813017	−	0.770131i	0.163277	−	0.986580i	$-0.447794\pi$
$653$	−20.7757	−	19.6798i	−0.813017	−	0.770131i	−0.976294	+	0.216450i	$0.930552\pi$
$654$	−0.313894	+	0.369544i	−0.0122742	+	0.0144503i
$655$	−9.05814	+	17.0855i	−0.353931	+	0.667584i
$656$	−8.54937	−	5.14398i	−0.333797	−	0.200839i
$657$	−7.00503	+	3.24087i	−0.273292	+	0.126438i
$658$	−19.5497	−	4.30321i	−0.762125	−	0.167756i
$659$	−5.40011	−	10.1857i	−0.210358	−	0.396778i	0.755771	−	0.654836i	$-0.227262\pi$
$659$	−5.40011	−	10.1857i	−0.210358	−	0.396778i	−0.966129	+	0.258058i	$0.916917\pi$
$660$	−0.0627772	+	1.15786i	−0.00244360	+	0.0450695i
$661$	17.1612	+	20.2037i	0.667494	+	0.785834i	0.986822	−	0.161810i	$-0.0517332\pi$
$661$	17.1612	+	20.2037i	0.667494	+	0.785834i	−0.319328	+	0.947644i	$0.603457\pi$
$662$	16.8918	−	3.71817i	0.656519	−	0.144511i
$663$	10.5106	−	7.98993i	0.408197	−	0.310303i
$664$	−0.0461187	+	0.0436860i	−0.00178975	+	0.00169535i
$665$	−0.204486	−	3.77152i	−0.00792962	−	0.146253i
$666$	−8.34277	+	5.01968i	−0.323276	+	0.194509i
$667$	−9.92274	+	14.6349i	−0.384210	+	0.566668i
$668$	2.71710	−	9.78611i	0.105128	−	0.378636i
$669$	−16.5542	+	1.80038i	−0.640024	+	0.0696068i
$670$	−4.18947	−	3.18475i	−0.161853	−	0.123038i
$671$	−0.130188	−	0.0602313i	−0.00502585	−	0.00232521i
$672$	1.12367	+	1.65728i	0.0433463	+	0.0639311i
$673$	−36.9044	+	12.4345i	−1.42256	+	0.479316i	−0.922272	−	0.386542i	$-0.873669\pi$
$673$	−36.9044	+	12.4345i	−1.42256	+	0.479316i	−0.500289	+	0.865859i	$0.666773\pi$
$674$	−0.354442	−	2.16200i	−0.0136526	−	0.0832772i
$675$	0.00584200	−	0.0356346i	0.000224859	−	0.00137158i
$676$	−18.1766	−	6.12442i	−0.699102	−	0.235555i
$677$	10.7585	+	38.7487i	0.413483	+	1.48923i	0.818277	+	0.574824i	$0.194930\pi$
$677$	10.7585	+	38.7487i	0.413483	+	1.48923i	−0.404794	+	0.914408i	$0.632657\pi$
$678$	−1.29287	−	3.24485i	−0.0496523	−	0.124618i
$679$	7.00961	+	17.5928i	0.269004	+	0.675150i
$680$	−1.39728	−	5.03254i	−0.0535831	−	0.192989i
$681$	−22.7066	−	7.65073i	−0.870118	−	0.293177i
$682$	−0.316144	+	1.92839i	−0.0121058	+	0.0738419i
$683$	−3.89511	−	23.7591i	−0.149042	−	0.909117i	−0.950422	−	0.310962i	$-0.899349\pi$
$683$	−3.89511	−	23.7591i	−0.149042	−	0.909117i	0.801380	−	0.598155i	$-0.204099\pi$
$684$	0.796574	−	0.268397i	0.0304578	−	0.0102624i
$685$	4.64117	+	6.84521i	0.177330	+	0.261542i
$686$	−18.1557	−	8.39970i	−0.693186	−	0.320702i
$687$	6.55415	+	4.98234i	0.250056	+	0.190088i
$688$	−8.08694	+	0.879507i	−0.308312	+	0.0335309i
$689$	−16.0414	+	57.7758i	−0.611127	+	2.20108i
$690$	5.18188	−	7.64271i	0.197271	−	0.290953i
$691$	−11.2362	+	6.76059i	−0.427445	+	0.257185i	−0.712982	−	0.701183i	$-0.752656\pi$
$691$	−11.2362	+	6.76059i	−0.427445	+	0.257185i	0.285537	+	0.958368i	$0.407828\pi$
$692$	−0.572501	−	10.5592i	−0.0217632	−	0.401399i
$693$	−0.751118	+	0.711497i	−0.0285326	+	0.0270275i
$694$	−7.63371	+	5.80300i	−0.289772	+	0.220279i
$695$	47.9972	−	10.5650i	1.82064	−	0.400753i
$696$	−2.78199	−	3.27521i	−0.105451	−	0.124146i
$697$	−1.25719	+	23.1875i	−0.0476194	+	0.878288i
$698$	6.92539	+	13.0627i	0.262130	+	0.494429i
$699$	−8.38105	−	1.84481i	−0.317000	−	0.0697770i
$700$	0.0656211	−	0.0303595i	0.00248024	−	0.00114748i
$701$	14.2517	+	8.57495i	0.538279	+	0.323871i	0.758601	−	0.651556i	$-0.225883\pi$
$701$	14.2517	+	8.57495i	0.538279	+	0.323871i	−0.220322	+	0.975427i	$0.570711\pi$
$702$	−2.65719	+	5.01199i	−0.100289	+	0.189165i
$703$	−5.29836	+	6.23772i	−0.199832	+	0.235260i
$704$	−0.375127	−	0.355339i	−0.0141381	−	0.0133924i
$705$	−22.3038	−	2.42568i	−0.840009	−	0.0913564i
$706$	5.47502	−	13.7413i	0.206055	−	0.517160i
$707$	−13.5888			−0.511059
$708$	−4.49266	+	6.23025i	−0.168844	+	0.234147i
$709$	−25.7101			−0.965563			−0.482781	−	0.875741i	$-0.660373\pi$
$709$	−25.7101			−0.965563			−0.482781	+	0.875741i	$0.660373\pi$
$710$	−6.50679	+	16.3308i	−0.244196	+	0.612885i
$711$	−4.42166	−	0.480884i	−0.165825	−	0.0180346i
$712$	−7.56391	−	7.16491i	−0.283469	−	0.268516i
$713$	10.0741	−	11.8601i	0.377277	−	0.444165i
$714$	2.18283	−	4.11725i	0.0816902	−	0.154084i
$715$	−5.63636	−	3.39128i	−0.210788	−	0.126827i
$716$	4.75085	−	2.19798i	0.177548	−	0.0821423i
$717$	−8.14272	−	1.79235i	−0.304095	−	0.0669365i
$718$	9.74273	+	18.3767i	0.363595	+	0.685814i
$719$	2.07418	−	38.2560i	0.0773538	−	1.42671i	−0.660033	−	0.751237i	$-0.729458\pi$
$719$	2.07418	−	38.2560i	0.0773538	−	1.42671i	0.737387	−	0.675471i	$-0.236060\pi$
$720$	1.45282	+	1.71039i	0.0541433	+	0.0637424i
$721$	11.9099	−	2.62157i	0.443548	−	0.0976324i
$722$	−14.5633	+	11.0707i	−0.541989	+	0.412009i
$723$	14.8518	−	14.0683i	0.552343	−	0.523207i
$724$	1.01941	+	18.8020i	0.0378862	+	0.698769i
$725$	−0.132963	+	0.0800013i	−0.00493813	+	0.00297117i
$726$	−6.02323	+	8.88360i	−0.223543	+	0.329701i
$727$	−7.00736	+	25.2382i	−0.259889	+	0.936034i	0.712308	+	0.701867i	$0.247650\pi$
$727$	−7.00736	+	25.2382i	−0.259889	+	0.936034i	−0.972196	+	0.234167i	$0.924764\pi$
$728$	−11.2921	+	1.22809i	−0.418512	+	0.0455159i
$729$	0.796093	+	0.605174i	0.0294849	+	0.0224139i
$730$	−15.7202	−	7.27293i	−0.581830	−	0.269183i
$731$	10.6245	+	15.6700i	0.392963	+	0.579577i
$732$	−0.263083	+	0.0886429i	−0.00972382	+	0.00327634i
$733$	−2.29929	−	14.0250i	−0.0849262	−	0.518027i	−0.994691	−	0.102904i	$-0.967187\pi$
$733$	−2.29929	−	14.0250i	−0.0849262	−	0.518027i	0.909765	−	0.415123i	$-0.136262\pi$
$734$	1.89316	−	11.5478i	0.0698778	−	0.426236i
$735$	−6.36038	−	2.14306i	−0.234606	−	0.0790480i
$736$	1.10078	+	3.96467i	0.0405754	+	0.146140i
$737$	0.448493	+	1.12563i	0.0165205	+	0.0414632i
$738$	−3.69309	−	9.26895i	−0.135944	−	0.341195i
$739$	6.60795	+	23.7997i	0.243077	+	0.875485i	0.979915	+	0.199416i	$0.0639044\pi$
$739$	6.60795	+	23.7997i	0.243077	+	0.875485i	−0.736838	+	0.676070i	$0.763682\pi$
$740$	−20.7061	−	6.97670i	−0.761172	−	0.256469i
$741$	−0.771444	+	4.70560i	−0.0283397	+	0.172865i
$742$	3.42400	+	20.8855i	0.125699	+	0.766729i
$743$	23.3098	−	7.85399i	0.855155	−	0.288135i	0.142625	−	0.989777i	$-0.454446\pi$
$743$	23.3098	−	7.85399i	0.855155	−	0.288135i	0.712530	+	0.701642i	$0.247549\pi$
$744$	2.12235	+	3.13023i	0.0778092	+	0.114760i
$745$	8.30428	+	3.84197i	0.304245	+	0.140759i
$746$	22.8994	+	17.4077i	0.838407	+	0.637341i
$747$	−0.0631524	+	0.00686824i	−0.00231063	+	0.000251296i
$748$	−0.321721	+	1.15873i	−0.0117633	+	0.0423675i
$749$	3.97478	−	5.86237i	0.145235	−	0.214206i
$750$	−9.54505	+	5.74307i	−0.348536	+	0.209707i
$751$	−0.174376	−	3.21617i	−0.00636306	−	0.117360i	−0.999989	−	0.00463455i	$-0.998525\pi$
$751$	−0.174376	−	3.21617i	−0.00636306	−	0.117360i	0.993626	−	0.112725i	$-0.0359580\pi$
$752$	7.25802	−	6.87516i	0.264673	−	0.250711i
$753$	−1.30519	+	0.992178i	−0.0475637	+	0.0361570i
$754$	23.8076	−	5.24044i	0.867021	−	0.190846i
$755$	1.84490	+	2.17198i	0.0671426	+	0.0790464i
$756$	−0.108402	+	1.99936i	−0.00394256	+	0.0727162i
$757$	1.65110	+	3.11430i	0.0600101	+	0.113191i	0.911703	−	0.410851i	$-0.134768\pi$
$757$	1.65110	+	3.11430i	0.0600101	+	0.113191i	−0.851692	+	0.524042i	$0.824423\pi$
$758$	22.3876	+	4.92789i	0.813156	+	0.178989i
$759$	−1.92957	+	0.892713i	−0.0700389	+	0.0324034i
$760$	1.61634	+	0.972519i	0.0586308	+	0.0352770i
$761$	−8.52338	+	16.0768i	−0.308972	+	0.582784i	−0.988563	−	0.150808i	$-0.951813\pi$
$761$	−8.52338	+	16.0768i	−0.308972	+	0.582784i	0.679591	+	0.733591i	$0.262157\pi$
$762$	7.20555	−	8.48302i	0.261029	−	0.307308i
$763$	−0.704827	−	0.667647i	−0.0255164	−	0.0241705i
$764$	−18.8174	−	2.04652i	−0.680790	−	0.0740403i
$765$	1.93320	−	4.85196i	0.0698949	−	0.175423i
$766$	−5.90655			−0.213412
$767$	−19.2881	−	39.0721i	−0.696454	−	1.41081i
$768$	−1.00000			−0.0360844
$769$	−16.9860	+	42.6317i	−0.612532	+	1.53734i	0.215409	+	0.976524i	$0.430892\pi$
$769$	−16.9860	+	42.6317i	−0.612532	+	1.53734i	−0.827941	+	0.560815i	$0.810488\pi$
$770$	−2.30817	−	0.251029i	−0.0831808	−	0.00904646i
$771$	−16.7548	−	15.8709i	−0.603408	−	0.571578i
$772$	10.0398	−	11.8198i	0.361342	−	0.425404i
$773$	−3.64975	+	6.88416i	−0.131272	+	0.247606i	−0.940431	−	0.339984i	$-0.889578\pi$
$773$	−3.64975	+	6.88416i	−0.131272	+	0.247606i	0.809159	+	0.587590i	$0.199923\pi$
$774$	−6.97021	−	4.19384i	−0.250539	−	0.150744i
$775$	0.123943	−	0.0573424i	0.00445218	−	0.00205980i
$776$	−9.23691	−	2.03320i	−0.331586	−	0.0729875i
$777$	−9.13179	−	17.2244i	−0.327601	−	0.617921i
$778$	0.420200	−	7.75014i	0.0150649	−	0.277856i
$779$	−5.42957	−	6.39218i	−0.194535	−	0.229024i
$780$	−12.4329	+	2.73668i	−0.445168	+	0.0979889i
$781$	3.22229	−	2.44952i	0.115302	−	0.0876506i
$782$	6.95235	−	6.58561i	0.248615	−	0.235501i
$783$	−0.232649	−	4.29096i	−0.00831420	−	0.153346i
$784$	2.56268	−	1.54191i	0.0915243	−	0.0550683i
$785$	10.9616	−	16.1671i	0.391235	−	0.577029i
$786$	2.30535	−	8.30311i	0.0822290	−	0.296162i
$787$	−41.5335	+	4.51704i	−1.48051	+	0.161015i	−0.812422	−	0.583070i	$-0.801851\pi$
$787$	−41.5335	+	4.51704i	−1.48051	+	0.161015i	−0.668086	+	0.744084i	$0.732886\pi$
$788$	−12.1303	−	9.22124i	−0.432125	−	0.328493i
$789$	15.1478	+	7.00812i	0.539276	+	0.249496i
$790$	−5.60136	−	8.26139i	−0.199287	−	0.293927i
$791$	6.62780	−	2.23316i	0.235657	−	0.0794022i
$792$	−0.0835940	−	0.509901i	−0.00297038	−	0.0181185i
$793$	0.254783	−	1.55411i	0.00904762	−	0.0551880i
$794$	35.6092	+	11.9981i	1.26372	+	0.425798i
$795$	6.34587	+	22.8558i	0.225065	+	0.810610i
$796$	−9.87306	−	24.7795i	−0.349941	−	0.878286i
$797$	−3.45998	−	8.68389i	−0.122559	−	0.307599i	0.854877	−	0.518830i	$-0.173632\pi$
$797$	−3.45998	−	8.68389i	−0.122559	−	0.307599i	−0.977436	+	0.211231i	$0.932253\pi$
$798$	0.450273	+	1.62174i	0.0159395	+	0.0574088i
$799$	−22.0495	−	7.42934i	−0.780055	−	0.262831i
$800$	−0.00584200	+	0.0356346i	−0.000206546	+	0.00125987i
$801$	−1.68555	−	10.2814i	−0.0595561	−	0.363276i
$802$	13.7553	−	4.63470i	0.485716	−	0.163657i
$803$	2.23810	+	3.30095i	0.0789809	+	0.116488i
$804$	2.12829	+	0.984650i	0.0750589	+	0.0347259i
$805$	14.7188	+	11.1890i	0.518771	+	0.394359i
$806$	−21.3282	+	2.31958i	−0.751253	+	0.0817037i
$807$	6.67818	−	24.0526i	0.235083	−	0.846693i
$808$	3.80854	−	5.61718i	0.133984	−	0.197612i
$809$	−1.78885	+	1.07632i	−0.0628927	+	0.0378413i	−0.546653	−	0.837359i	$-0.684098\pi$
$809$	−1.78885	+	1.07632i	−0.0628927	+	0.0378413i	0.483760	+	0.875201i	$0.339271\pi$
$810$	0.121495	+	2.24084i	0.00426889	+	0.0787350i
$811$	−1.05321	+	0.997658i	−0.0369834	+	0.0350325i	−0.705968	−	0.708244i	$-0.749488\pi$
$811$	−1.05321	+	0.997658i	−0.0369834	+	0.0350325i	0.668985	+	0.743276i	$0.266729\pi$
$812$	6.84991	−	5.20717i	0.240385	−	0.182736i
$813$	−4.24996	+	0.935487i	−0.149053	+	0.0328090i
$814$	3.25694	+	3.83437i	0.114156	+	0.134395i
$815$	−1.42169	+	26.2215i	−0.0497995	+	0.918497i
$816$	1.09016	+	2.05626i	0.0381632	+	0.0719834i
$817$	−6.67790	−	1.46992i	−0.233630	−	0.0514259i
$818$	−28.8074	+	13.3277i	−1.00723	+	0.465993i
$819$	−9.73275	−	5.85600i	−0.340090	−	0.204625i
$820$	10.4881	−	19.7827i	0.366261	−	0.690842i
$821$	32.5422	−	38.3116i	1.13573	−	1.33709i	0.201885	−	0.979409i	$-0.435293\pi$
$821$	32.5422	−	38.3116i	1.13573	−	1.33709i	0.933846	−	0.357676i	$-0.116431\pi$
$822$	−2.67551	−	2.53437i	−0.0933190	−	0.0883964i
$823$	40.0815	+	4.35912i	1.39715	+	0.151949i	0.775502	−	0.631346i	$-0.217497\pi$
$823$	40.0815	+	4.35912i	1.39715	+	0.151949i	0.621650	+	0.783295i	$0.286463\pi$
$824$	−2.25433	+	5.65794i	−0.0785333	+	0.197104i
$825$	−0.0186585			−0.000649605
$826$	−11.9695	−	9.65783i	−0.416473	−	0.336039i
$827$	−28.5382			−0.992371			−0.496185	−	0.868217i	$-0.665266\pi$
$827$	−28.5382			−0.992371			−0.496185	+	0.868217i	$0.665266\pi$
$828$	−1.52299	+	3.82241i	−0.0529275	+	0.132838i
$829$	−36.9742	−	4.02118i	−1.28417	−	0.139662i	−0.559540	−	0.828803i	$-0.689022\pi$
$829$	−36.9742	−	4.02118i	−1.28417	−	0.139662i	−0.724626	+	0.689142i	$0.757988\pi$
$830$	−0.103496	−	0.0980370i	−0.00359241	−	0.00340291i
$831$	−9.20270	+	10.8343i	−0.319238	+	0.375836i
$832$	2.65719	−	5.01199i	0.0921214	−	0.173759i
$833$	−5.96430	−	3.58860i	−0.206651	−	0.124338i
$834$	−19.8758	+	9.19554i	−0.688244	+	0.318416i
$835$	22.2592	+	4.89962i	0.770311	+	0.169558i
$836$	−0.203445	−	0.383737i	−0.00703628	−	0.0132718i
$837$	−0.204748	+	3.77635i	−0.00707712	+	0.130530i
$838$	17.7695	+	20.9198i	0.613836	+	0.722663i
$839$	−41.8087	+	9.20279i	−1.44340	+	0.317715i	−0.866531	−	0.499124i	$-0.833655\pi$
$839$	−41.8087	+	9.20279i	−1.44340	+	0.317715i	−0.576865	+	0.816839i	$0.695724\pi$
$840$	−3.57718	+	2.71930i	−0.123424	+	0.0938248i
$841$	7.64732	−	7.24392i	0.263701	−	0.249790i
$842$	−1.32074	−	24.3596i	−0.0455156	−	0.839486i
$843$	−0.632637	+	0.380645i	−0.0217892	+	0.0131101i
$844$	1.70244	−	2.51090i	0.0586002	−	0.0864289i
$845$	11.5155	−	41.4750i	0.396144	−	1.42678i
$846$	9.93872	−	1.08090i	0.341700	−	0.0371622i
$847$	−17.1086	−	13.0056i	−0.587859	−	0.446879i
$848$	−9.59304	−	4.43822i	−0.329427	−	0.152409i
$849$	−17.9807	−	26.5195i	−0.617094	−	0.910146i
$850$	0.0796427	−	0.0268347i	0.00273172	−	0.000920424i
$851$	−6.48133	−	39.5344i	−0.222177	−	1.35522i
$852$	1.26732	−	7.73030i	0.0434176	−	0.264836i
$853$	−53.5062	−	18.0283i	−1.83202	−	0.617279i	−0.997833	−	0.0657937i	$-0.979042\pi$
$853$	−53.5062	−	18.0283i	−1.83202	−	0.617279i	−0.834185	−	0.551485i	$-0.814061\pi$
$854$	−0.148711	−	0.535608i	−0.00508878	−	0.0183281i
$855$	0.698213	+	1.75238i	0.0238784	+	0.0599302i
$856$	1.30930	+	3.28610i	0.0447511	+	0.112317i
$857$	8.73824	+	31.4723i	0.298493	+	1.07507i	0.948923	+	0.315508i	$0.102175\pi$
$857$	8.73824	+	31.4723i	0.298493	+	1.07507i	−0.650430	+	0.759566i	$0.725411\pi$
$858$	2.77774	+	0.935930i	0.0948305	+	0.0319521i
$859$	2.27788	−	13.8945i	0.0777204	−	0.474073i	−0.919075	−	0.394082i	$-0.871063\pi$
$859$	2.27788	−	13.8945i	0.0777204	−	0.474073i	0.996796	−	0.0799911i	$-0.0254892\pi$
$860$	−2.95335	−	18.0146i	−0.100708	−	0.614294i
$861$	18.9323	−	6.37905i	0.645212	−	0.217397i
$862$	18.5080	+	27.2972i	0.630384	+	0.929747i
$863$	12.3017	+	5.69138i	0.418755	+	0.193737i	0.617940	−	0.786225i	$-0.287967\pi$
$863$	12.3017	+	5.69138i	0.418755	+	0.193737i	−0.199185	+	0.979962i	$0.563829\pi$
$864$	−0.796093	−	0.605174i	−0.0270836	−	0.0205884i
$865$	23.5918	−	2.56576i	0.802145	−	0.0872385i
$866$	−1.05469	+	3.79865i	−0.0358398	+	0.129083i
$867$	−6.50043	+	9.58742i	−0.220766	+	0.325606i
$868$	−6.48855	+	3.90403i	−0.220236	+	0.132511i
$869$	0.124421	+	2.29480i	0.00422068	+	0.0778459i
$870$	7.00121	−	6.63190i	0.237363	−	0.224842i
$871$	−10.5903	+	8.05055i	−0.358839	+	0.272782i
$872$	0.473527	−	0.104231i	0.0160357	−	0.00352971i
$873$	−6.12300	−	7.20855i	−0.207232	−	0.243973i
$874$	−0.187249	+	3.45360i	−0.00633378	+	0.116820i
$875$	−10.4478	−	19.7066i	−0.353199	−	0.666204i
$876$	7.53795	+	1.65923i	0.254684	+	0.0560601i
$877$	−18.3306	+	8.48066i	−0.618982	+	0.286371i	−0.704212	−	0.709990i	$-0.748699\pi$
$877$	−18.3306	+	8.48066i	−0.618982	+	0.286371i	0.0852303	+	0.996361i	$0.472837\pi$
$878$	27.6621	+	16.6438i	0.933552	+	0.561700i
$879$	−11.6143	+	21.9069i	−0.391741	+	0.738902i
$880$	0.750682	−	0.883771i	0.0253055	−	0.0297919i
$881$	33.8402	+	32.0552i	1.14011	+	1.07997i	0.995904	+	0.0904172i	$0.0288201\pi$
$881$	33.8402	+	32.0552i	1.14011	+	1.07997i	0.144202	+	0.989548i	$0.453939\pi$
$882$	2.97326	+	0.323361i	0.100115	+	0.0108881i
$883$	−11.3982	+	28.6072i	−0.383578	+	0.962709i	0.602752	+	0.797929i	$0.294071\pi$
$883$	−11.3982	+	28.6072i	−0.383578	+	0.962709i	−0.986330	+	0.164781i	$0.947308\pi$
$884$	−13.2027			−0.444055
$885$	−14.5068	−	9.31037i	−0.487641	−	0.312965i
$886$	−1.86051			−0.0625052
$887$	20.3088	−	50.9712i	0.681902	−	1.71145i	−0.0206231	−	0.999787i	$-0.506565\pi$
$887$	20.3088	−	50.9712i	0.681902	−	1.71145i	0.702525	−	0.711659i	$-0.252056\pi$
$888$	9.67940	+	1.05270i	0.324819	+	0.0353262i
$889$	16.1796	+	15.3261i	0.542645	+	0.514021i
$890$	15.1364	−	17.8200i	0.507374	−	0.597327i
$891$	0.242030	−	0.456517i	0.00810832	−	0.0152939i
$892$	14.2683	+	8.58492i	0.477737	+	0.287445i
$893$	7.62681	−	3.52854i	0.255222	−	0.118078i
$894$	−3.98197	−	0.876497i	−0.133177	−	0.0293144i
$895$	5.50251	+	10.3788i	0.183929	+	0.346926i
$896$	0.108402	−	1.99936i	0.00362147	−	0.0667941i
$897$	−15.1110	−	17.7901i	−0.504542	−	0.593993i
$898$	11.7807	−	2.59312i	0.393126	−	0.0865335i
$899$	12.9379	−	9.83516i	0.431504	−	0.328021i
$900$	−0.0262159	+	0.0248330i	−0.000873864	+	0.000827768i
$901$	1.33183	+	24.5641i	0.0443696	+	0.818350i
$902$	−4.41752	+	2.65793i	−0.147087	+	0.0884996i
$903$	9.14059	−	13.4814i	0.304180	−	0.448632i
$904$	−0.934459	+	3.36562i	−0.0310796	+	0.111939i
$905$	−42.0083	+	4.56867i	−1.39640	+	0.151868i
$906$	−1.01094	−	0.768495i	−0.0335862	−	0.0255315i
$907$	−40.3019	−	18.6456i	−1.33820	−	0.619118i	−0.385411	−	0.922745i	$-0.625940\pi$
$907$	−40.3019	−	18.6456i	−1.33820	−	0.619118i	−0.952791	+	0.303627i	$0.901802\pi$
$908$	13.4465	+	19.8321i	0.446238	+	0.658152i
$909$	6.43133	−	2.16697i	0.213314	−	0.0718737i
$910$	−4.12387	−	25.1545i	−0.136705	−	0.833863i
$911$	−5.03247	+	30.6967i	−0.166733	+	1.01703i	0.762353	+	0.647162i	$0.224044\pi$
$911$	−5.03247	+	30.6967i	−0.166733	+	1.01703i	−0.929086	+	0.369865i	$0.879404\pi$
$912$	−0.796574	−	0.268397i	−0.0263772	−	0.00888751i
$913$	0.00878129	+	0.0316273i	0.000290618	+	0.00104671i
$914$	−15.5181	−	38.9475i	−0.513294	−	1.28827i
$915$	−0.230597	−	0.578756i	−0.00762332	−	0.0191331i
$916$	−2.20253	−	7.93281i	−0.0727737	−	0.262107i
$917$	16.3510	+	5.50931i	0.539959	+	0.181933i
$918$	−0.376526	+	2.29671i	−0.0124272	+	0.0758027i
$919$	0.0851643	+	0.519479i	0.00280931	+	0.0171360i	0.988194	−	0.153208i	$-0.0489604\pi$
$919$	0.0851643	+	0.519479i	0.00280931	+	0.0171360i	−0.985385	+	0.170344i	$0.945512\pi$
$920$	−8.75043	+	2.94836i	−0.288493	+	0.0972047i
$921$	3.91330	+	5.77168i	0.128948	+	0.190183i
$922$	−26.8250	−	12.4106i	−0.883435	−	0.408721i
$923$	35.3767	+	26.8926i	1.16444	+	0.885182i
$924$	1.02854	−	0.111860i	0.0338365	−	0.00367994i
$925$	0.0940595	−	0.338772i	0.00309266	−	0.0111387i
$926$	−13.0806	+	19.2924i	−0.429855	+	0.633988i
$927$	−5.21869	+	3.13998i	−0.171404	+	0.103131i
$928$	0.232649	+	4.29096i	0.00763708	+	0.140858i
$929$	9.79424	−	9.27760i	0.321339	−	0.304388i	−0.509978	−	0.860188i	$-0.670346\pi$
$929$	9.79424	−	9.27760i	0.321339	−	0.304388i	0.831316	+	0.555799i	$0.187588\pi$
$930$	−6.75649	+	5.13615i	−0.221554	+	0.168421i
$931$	2.45521	−	0.540432i	0.0804662	−	0.0177120i
$932$	5.55566	+	6.54063i	0.181982	+	0.214246i
$933$	−0.845364	+	15.5918i	−0.0276760	+	0.510453i
$934$	11.1164	+	20.9677i	0.363739	+	0.686085i
$935$	−2.63562	−	0.580144i	−0.0861941	−	0.0189728i
$936$	5.14850	−	2.38195i	0.168284	−	0.0778564i
$937$	20.3125	+	12.2216i	0.663579	+	0.399262i	0.807124	−	0.590382i	$-0.201023\pi$
$937$	20.3125	+	12.2216i	0.663579	+	0.399262i	−0.143545	+	0.989644i	$0.545850\pi$
$938$	−2.19939	+	4.14848i	−0.0718125	+	0.135453i
$939$	18.1230	−	21.3360i	0.591421	−	0.696275i
$940$	16.2879	+	15.4287i	0.531253	+	0.503230i
$941$	−43.1269	−	4.69034i	−1.40590	−	0.152901i	−0.626496	−	0.779425i	$-0.715511\pi$
$941$	−43.1269	−	4.69034i	−1.40590	−	0.152901i	−0.779402	+	0.626524i	$0.784477\pi$
$942$	−3.22167	+	8.08579i	−0.104968	+	0.263449i
$943$	41.0542			1.33691
$944$	7.34696	−	2.24102i	0.239123	−	0.0729390i
$945$	−4.49342			−0.146171
$946$	−1.55577	+	3.90469i	−0.0505825	+	0.126953i
$947$	−1.52441	−	0.165790i	−0.0495368	−	0.00538745i	0.0833171	−	0.996523i	$-0.473449\pi$
$947$	−1.52441	−	0.165790i	−0.0495368	−	0.00538745i	−0.132854	+	0.991136i	$0.542414\pi$
$948$	3.22903	+	3.05870i	0.104874	+	0.0993420i
$949$	−28.3458	+	33.3712i	−0.920143	+	1.08328i
$950$	−0.0142178	+	0.0268176i	−0.000461286	+	0.000870079i
$951$	−4.69117	−	2.82259i	−0.152122	−	0.0915286i
$952$	−4.22938	+	1.95672i	−0.137075	+	0.0634177i
$953$	57.8114	+	12.7252i	1.87269	+	0.412211i	0.997444	−	0.0714576i	$-0.0227651\pi$
$953$	57.8114	+	12.7252i	1.87269	+	0.412211i	0.875251	+	0.483669i	$0.160696\pi$
$954$	−4.95106	−	9.33870i	−0.160297	−	0.302351i
$955$	2.29969	−	42.4154i	0.0744164	−	1.37253i
$956$	5.39768	+	6.35464i	0.174573	+	0.205524i
$957$	−2.16851	+	0.477326i	−0.0700981	+	0.0154298i
$958$	−16.7563	+	12.7378i	−0.541371	+	0.411540i
$959$	5.35717	−	5.07458i	0.172992	−	0.163867i
$960$	−0.121495	−	2.24084i	−0.00392122	−	0.0723227i
$961$	14.3072	−	8.60834i	0.461522	−	0.277688i
$962$	−30.9961	+	45.7158i	−0.999354	+	1.47394i
$963$	−0.946338	+	3.40840i	−0.0304953	+	0.109834i
$964$	−20.3372	+	2.21180i	−0.655017	+	0.0712374i
$965$	27.7061	+	21.0616i	0.891889	+	0.677997i
$966$	−7.47729	−	3.45936i	−0.240578	−	0.111303i
$967$	−14.5835	−	21.5090i	−0.468973	−	0.691684i	0.517486	−	0.855692i	$-0.326868\pi$
$967$	−14.5835	−	21.5090i	−0.468973	−	0.691684i	−0.986459	+	0.164008i	$0.947558\pi$
$968$	10.1712	−	3.42707i	0.326914	−	0.110150i
$969$	0.316499	+	1.93056i	0.0101674	+	0.0620184i
$970$	3.43383	−	20.9454i	0.110254	−	0.672517i
$971$	39.0310	+	13.1511i	1.25256	+	0.422038i	0.865916	−	0.500189i	$-0.166736\pi$
$971$	39.0310	+	13.1511i	1.25256	+	0.422038i	0.386648	+	0.922227i	$0.373633\pi$
$972$	−0.267528	−	0.963550i	−0.00858098	−	0.0309059i
$973$	−16.2307	−	40.7359i	−0.520331	−	1.30593i
$974$	11.4959	+	28.8526i	0.368353	+	0.924497i
$975$	−0.0548023	−	0.197380i	−0.00175508	−	0.00632122i
$976$	0.263083	+	0.0886429i	0.00842108	+	0.00283739i
$977$	0.656147	−	4.00232i	0.0209920	−	0.128046i	−0.974252	−	0.225464i	$-0.927610\pi$
$977$	0.656147	−	4.00232i	0.0209920	−	0.128046i	0.995244	+	0.0974184i	$0.0310585\pi$
$978$	−1.89311	−	11.5475i	−0.0605351	−	0.369248i
$979$	−5.10160	+	1.71893i	−0.163048	+	0.0549372i
$980$	3.76653	+	5.55521i	0.120317	+	0.177455i
$981$	0.440050	+	0.203589i	0.0140497	+	0.00650009i
$982$	−0.612191	−	0.465376i	−0.0195358	−	0.0148507i
$983$	−13.9998	+	1.52258i	−0.446526	+	0.0485626i	−0.328620	−	0.944462i	$-0.606584\pi$
$983$	−13.9998	+	1.52258i	−0.446526	+	0.0485626i	−0.117906	+	0.993025i	$0.537618\pi$
$984$	−2.66929	+	9.61390i	−0.0850938	+	0.306480i
$985$	19.1895	−	28.3024i	0.611429	−	0.901791i
$986$	8.56969	−	5.15621i	0.272914	−	0.164207i
$987$	1.08373	+	19.9883i	0.0344956	+	0.636235i
$988$	3.46185	−	3.27924i	0.110136	−	0.104326i
$989$	26.6461	−	20.2558i	0.847297	−	0.644098i
$990$	1.13245	−	0.249271i	0.0359916	−	0.00792234i
$991$	21.8410	+	25.7132i	0.693803	+	0.816808i	0.990405	−	0.138193i	$-0.0441295\pi$
$991$	21.8410	+	25.7132i	0.693803	+	0.816808i	−0.296602	+	0.955001i	$0.595854\pi$
$992$	0.204748	−	3.77635i	0.00650075	−	0.119899i
$993$	−8.10168	−	15.2814i	−0.257099	−	0.484940i
$994$	15.3183	+	3.37181i	0.485867	+	0.106947i
$995$	54.3273	−	25.1345i	1.72229	−	0.796817i
$996$	0.0544317	+	0.0327505i	0.00172473	+	0.00103774i
$997$	3.35919	−	6.33610i	0.106387	−	0.200666i	−0.824603	−	0.565711i	$-0.808602\pi$
$997$	3.35919	−	6.33610i	0.106387	−	0.200666i	0.930990	+	0.365045i	$0.118946\pi$
$998$	19.9493	−	23.4861i	0.631483	−	0.743439i
$999$	7.06864	+	6.69577i	0.223642	+	0.211845i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.c.49.3	✓	84
59.53	even	29	inner	354.2.e.c.289.3	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.c.49.3	✓	84	1.1	even	1	trivial
354.2.e.c.289.3	yes	84	59.53	even	29	inner

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.370138 + 0.928977i) q^{2} +(0.994138 + 0.108119i) q^{3} +(-0.725995 - 0.687699i) q^{4} +(1.45282 - 1.71039i) q^{5} +(-0.468408 + 0.883512i) q^{6} +(-1.71569 - 1.03229i) q^{7} +(0.907575 - 0.419889i) q^{8} +(0.976621 + 0.214970i) q^{9} +O(q^{10})\)	\(q+(-0.370138 + 0.928977i) q^{2} +(0.994138 + 0.108119i) q^{3} +(-0.725995 - 0.687699i) q^{4} +(1.45282 - 1.71039i) q^{5} +(-0.468408 + 0.883512i) q^{6} +(-1.71569 - 1.03229i) q^{7} +(0.907575 - 0.419889i) q^{8} +(0.976621 + 0.214970i) q^{9} +(1.05117 + 1.98271i) q^{10} +(0.0279740 - 0.515950i) q^{11} +(-0.647386 - 0.762162i) q^{12} +(5.54018 - 1.21948i) q^{13} +(1.59402 - 1.21174i) q^{14} +(1.62923 - 1.54329i) q^{15} +(0.0541389 + 0.998533i) q^{16} +(1.99422 - 1.19988i) q^{17} +(-0.561187 + 0.827689i) q^{18} +(-0.224878 + 0.809936i) q^{19} +(-2.23097 + 0.242633i) q^{20} +(-1.59402 - 1.21174i) q^{21} +(0.468951 + 0.216960i) q^{22} +(-2.30909 - 3.40565i) q^{23} +(0.947653 - 0.319302i) q^{24} +(-0.00584200 - 0.0356346i) q^{25} +(-0.917757 + 5.59807i) q^{26} +(0.947653 + 0.319302i) q^{27} +(0.535672 + 1.92932i) q^{28} +(-1.59058 - 3.99205i) q^{29} +(0.830637 + 2.08474i) q^{30} +(1.01176 + 3.64405i) q^{31} +(-0.947653 - 0.319302i) q^{32} +(0.0835940 - 0.509901i) q^{33} +(0.376526 + 2.29671i) q^{34} +(-4.25820 + 1.43476i) q^{35} +(-0.561187 - 0.827689i) q^{36} +(8.83659 + 4.08824i) q^{37} +(-0.669176 - 0.508694i) q^{38} +(5.63955 - 0.613338i) q^{39} +(0.600368 - 2.16233i) q^{40} +(-5.59929 + 8.25834i) q^{41} +(1.71569 - 1.03229i) q^{42} +(0.440400 + 8.12269i) q^{43} +(-0.375127 + 0.355339i) q^{44} +(1.78653 - 1.35809i) q^{45} +(4.01845 - 0.884527i) q^{46} +(-6.47213 - 7.61958i) q^{47} +(-0.0541389 + 0.998533i) q^{48} +(-1.40091 - 2.64240i) q^{49} +(0.0352661 + 0.00776265i) q^{50} +(2.11226 - 0.977236i) q^{51} +(-4.86078 - 2.92464i) q^{52} +(-4.95106 + 9.33870i) q^{53} +(-0.647386 + 0.762162i) q^{54} +(-0.841834 - 0.797427i) q^{55} +(-1.99056 - 0.216487i) q^{56} +(-0.311129 + 0.780875i) q^{57} +4.29726 q^{58} +(-1.83998 - 7.45751i) q^{59} -2.24413 q^{60} +(0.102756 - 0.257898i) q^{61} +(-3.75973 - 0.408895i) q^{62} +(-1.45366 - 1.37698i) q^{63} +(0.647386 - 0.762162i) q^{64} +(5.96307 - 11.2475i) q^{65} +(0.442745 + 0.266391i) q^{66} +(-2.12829 + 0.984650i) q^{67} +(-2.27296 - 0.500315i) q^{68} +(-1.92733 - 3.63534i) q^{69} +(0.243269 - 4.48683i) q^{70} +(5.07130 + 5.97039i) q^{71} +(0.976621 - 0.214970i) q^{72} +(-6.14456 + 4.67098i) q^{73} +(-7.06864 + 6.69577i) q^{74} +(-0.00195497 - 0.0360574i) q^{75} +(0.720253 - 0.433362i) q^{76} +(-0.580606 + 0.856330i) q^{77} +(-1.51764 + 5.46603i) q^{78} +(-4.42166 + 0.480884i) q^{79} +(1.78653 + 1.35809i) q^{80} +(0.907575 + 0.419889i) q^{81} +(-5.59929 - 8.25834i) q^{82} +(-0.0601995 + 0.0202836i) q^{83} +(0.323936 + 1.97592i) q^{84} +(0.844973 - 5.15411i) q^{85} +(-7.70880 - 2.59740i) q^{86} +(-1.14964 - 4.14062i) q^{87} +(-0.191253 - 0.480009i) q^{88} +(-3.85635 - 9.67870i) q^{89} +(0.600368 + 2.16233i) q^{90} +(-10.7641 - 3.62684i) q^{91} +(-0.665676 + 4.06044i) q^{92} +(0.611843 + 3.73208i) q^{93} +(9.47400 - 3.19216i) q^{94} +(1.05860 + 1.56132i) q^{95} +(-0.907575 - 0.419889i) q^{96} +(-7.52947 - 5.72376i) q^{97} +(2.97326 - 0.323361i) q^{98} +(0.138234 - 0.497874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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