LMFDB - Embedded newform 31.2.g.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [31,2,Mod(7,31)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(31, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([28]))

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

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

chi := DirichletCharacter("31.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	31.g (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.247536246266$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			7.1
Root			$-2.16544i$ of defining polynomial
Character	$\chi$	$=$	31.7
Dual form			31.2.g.a.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.571745 - 1.75965i) q^{2} +(-0.488442 + 0.103822i) q^{3} +(-1.15144 + 0.836573i) q^{4} +(-0.603681 + 1.04561i) q^{5} +(0.461954 + 0.800128i) q^{6} +(3.41030 + 1.51837i) q^{7} +(-0.863288 - 0.627215i) q^{8} +(-2.51284 + 1.11879i) q^{9} +O(q^{10})$	\(q+(-0.571745 - 1.75965i) q^{2} +(-0.488442 + 0.103822i) q^{3} +(-1.15144 + 0.836573i) q^{4} +(-0.603681 + 1.04561i) q^{5} +(0.461954 + 0.800128i) q^{6} +(3.41030 + 1.51837i) q^{7} +(-0.863288 - 0.627215i) q^{8} +(-2.51284 + 1.11879i) q^{9} +(2.18505 + 0.464447i) q^{10} +(0.194058 + 1.84634i) q^{11} +(0.475560 - 0.528162i) q^{12} +(-3.46909 - 3.85281i) q^{13} +(0.721967 - 6.86906i) q^{14} +(0.186307 - 0.573393i) q^{15} +(-1.48972 + 4.58490i) q^{16} +(0.592413 - 5.63643i) q^{17} +(3.40538 + 3.78206i) q^{18} +(-0.962535 + 1.06900i) q^{19} +(-0.179621 - 1.70898i) q^{20} +(-1.82338 - 0.387571i) q^{21} +(3.13796 - 1.39711i) q^{22} +(2.86762 + 2.08345i) q^{23} +(0.486785 + 0.216731i) q^{24} +(1.77114 + 3.06770i) q^{25} +(-4.79617 + 8.30721i) q^{26} +(2.32318 - 1.68789i) q^{27} +(-5.19700 + 1.10466i) q^{28} +(0.424157 + 1.30542i) q^{29} -1.11549 q^{30} +(-1.81847 - 5.26243i) q^{31} +6.78540 q^{32} +(-0.286476 - 0.881683i) q^{33} +(-10.2569 + 2.18016i) q^{34} +(-3.64635 + 2.64923i) q^{35} +(1.95745 - 3.39040i) q^{36} +(-2.25141 - 3.89955i) q^{37} +(2.43140 + 1.08253i) q^{38} +(2.09445 + 1.52171i) q^{39} +(1.17697 - 0.524021i) q^{40} +(4.61599 + 0.981158i) q^{41} +(0.360518 + 3.43010i) q^{42} +(4.38897 - 4.87445i) q^{43} +(-1.76804 - 1.96361i) q^{44} +(0.347141 - 3.30283i) q^{45} +(2.02659 - 6.23721i) q^{46} +(-1.30682 + 4.02199i) q^{47} +(0.251633 - 2.39412i) q^{48} +(4.64083 + 5.15416i) q^{49} +(4.38545 - 4.87053i) q^{50} +(0.295824 + 2.81458i) q^{51} +(7.21762 + 1.53415i) q^{52} +(-11.8426 + 5.27265i) q^{53} +(-4.29836 - 3.12294i) q^{54} +(-2.04769 - 0.911691i) q^{55} +(-1.99173 - 3.44978i) q^{56} +(0.359157 - 0.622078i) q^{57} +(2.05458 - 1.49274i) q^{58} +(2.13389 - 0.453572i) q^{59} +(0.265164 + 0.816089i) q^{60} -2.68087 q^{61} +(-8.22033 + 6.20865i) q^{62} -10.2683 q^{63} +(-0.900071 - 2.77013i) q^{64} +(6.12274 - 1.30143i) q^{65} +(-1.38766 + 1.00820i) q^{66} +(-1.44150 + 2.49675i) q^{67} +(4.03315 + 6.98563i) q^{68} +(-1.61697 - 0.719924i) q^{69} +(6.74649 + 4.90161i) q^{70} +(8.22340 - 3.66129i) q^{71} +(2.87102 + 0.610255i) q^{72} +(0.439443 + 4.18102i) q^{73} +(-5.57462 + 6.19124i) q^{74} +(-1.18359 - 1.31451i) q^{75} +(0.214006 - 2.03613i) q^{76} +(-2.14162 + 6.59123i) q^{77} +(1.48018 - 4.55554i) q^{78} +(-1.17403 + 11.1702i) q^{79} +(-3.89468 - 4.32548i) q^{80} +(4.56212 - 5.06675i) q^{81} +(-0.912672 - 8.68350i) q^{82} +(10.2485 + 2.17838i) q^{83} +(2.42375 - 1.07912i) q^{84} +(5.53585 + 4.02203i) q^{85} +(-11.0867 - 4.93612i) q^{86} +(-0.342708 - 0.593587i) q^{87} +(0.990524 - 1.71564i) q^{88} +(2.18575 - 1.58804i) q^{89} +(-6.01030 + 1.27753i) q^{90} +(-5.98067 - 18.4066i) q^{91} -5.04486 q^{92} +(1.43457 + 2.38160i) q^{93} +7.82446 q^{94} +(-0.536692 - 1.65177i) q^{95} +(-3.31428 + 0.704471i) q^{96} +(6.70942 - 4.87468i) q^{97} +(6.41615 - 11.1131i) q^{98} +(-2.55330 - 4.42244i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9	\( 16 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9} - 2 q^{10} - 7 q^{11} + 5 q^{12} - 7 q^{13} - 6 q^{14} + 14 q^{15} - 2 q^{16} - 6 q^{17} - 3 q^{18} + 16 q^{19} + 37 q^{20} + 9 q^{21} + 9 q^{22} + q^{23} - 20 q^{24} - 13 q^{25} + 9 q^{26} + 9 q^{27} - 30 q^{28} - 14 q^{29} - 22 q^{30} + 15 q^{31} - 42 q^{32} - 13 q^{33} - 32 q^{34} - 9 q^{35} + q^{36} - 8 q^{37} + 8 q^{38} - 3 q^{39} - q^{40} - 8 q^{41} + 69 q^{42} + 23 q^{43} + 39 q^{44} + 65 q^{45} + 34 q^{46} + 14 q^{47} + 34 q^{48} + 2 q^{49} + 3 q^{50} - 42 q^{51} + 29 q^{52} + 6 q^{53} - 46 q^{54} - 7 q^{55} - 30 q^{56} - 17 q^{57} - 15 q^{58} + 4 q^{59} - 75 q^{60} - 60 q^{61} - 25 q^{62} - 46 q^{63} + 23 q^{64} - 12 q^{65} - 30 q^{66} + 13 q^{67} + 30 q^{68} + 38 q^{69} + 12 q^{70} - 14 q^{71} + 37 q^{72} + 2 q^{73} + 13 q^{74} + 13 q^{75} - 12 q^{76} + 18 q^{77} - 15 q^{78} + 18 q^{79} + 36 q^{80} + 23 q^{81} + 14 q^{82} - 16 q^{83} + 8 q^{84} + 37 q^{85} - 26 q^{86} + 15 q^{87} - 17 q^{88} + q^{89} - 23 q^{90} + 8 q^{91} - 64 q^{92} + 17 q^{93} + 44 q^{94} - 22 q^{95} + 8 q^{96} + 3 q^{97} - 10 q^{98} + 6 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9 - 2 * q^10 - 7 * q^11 + 5 * q^12 - 7 * q^13 - 6 * q^14 + 14 * q^15 - 2 * q^16 - 6 * q^17 - 3 * q^18 + 16 * q^19 + 37 * q^20 + 9 * q^21 + 9 * q^22 + q^23 - 20 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 - 30 * q^28 - 14 * q^29 - 22 * q^30 + 15 * q^31 - 42 * q^32 - 13 * q^33 - 32 * q^34 - 9 * q^35 + q^36 - 8 * q^37 + 8 * q^38 - 3 * q^39 - q^40 - 8 * q^41 + 69 * q^42 + 23 * q^43 + 39 * q^44 + 65 * q^45 + 34 * q^46 + 14 * q^47 + 34 * q^48 + 2 * q^49 + 3 * q^50 - 42 * q^51 + 29 * q^52 + 6 * q^53 - 46 * q^54 - 7 * q^55 - 30 * q^56 - 17 * q^57 - 15 * q^58 + 4 * q^59 - 75 * q^60 - 60 * q^61 - 25 * q^62 - 46 * q^63 + 23 * q^64 - 12 * q^65 - 30 * q^66 + 13 * q^67 + 30 * q^68 + 38 * q^69 + 12 * q^70 - 14 * q^71 + 37 * q^72 + 2 * q^73 + 13 * q^74 + 13 * q^75 - 12 * q^76 + 18 * q^77 - 15 * q^78 + 18 * q^79 + 36 * q^80 + 23 * q^81 + 14 * q^82 - 16 * q^83 + 8 * q^84 + 37 * q^85 - 26 * q^86 + 15 * q^87 - 17 * q^88 + q^89 - 23 * q^90 + 8 * q^91 - 64 * q^92 + 17 * q^93 + 44 * q^94 - 22 * q^95 + 8 * q^96 + 3 * q^97 - 10 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{14}{15}\right)$

Coefficient data

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

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

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

$2$	−0.571745	−	1.75965i	−0.404285	−	1.24426i	−0.921491	−	0.388400i	$-0.873028\pi$
$2$	−0.571745	−	1.75965i	−0.404285	−	1.24426i	0.517206	−	0.855861i	$-0.326972\pi$
$3$	−0.488442	+	0.103822i	−0.282002	+	0.0599414i	−0.346741	−	0.937961i	$-0.612712\pi$
$3$	−0.488442	+	0.103822i	−0.282002	+	0.0599414i	0.0647390	+	0.997902i	$0.479379\pi$
$4$	−1.15144	+	0.836573i	−0.575722	+	0.418287i
$5$	−0.603681	+	1.04561i	−0.269974	+	0.467609i	−0.968855	−	0.247629i	$-0.920349\pi$
$5$	−0.603681	+	1.04561i	−0.269974	+	0.467609i	0.698881	+	0.715238i	$0.253682\pi$
$6$	0.461954	+	0.800128i	0.188592	+	0.326651i
$7$	3.41030	+	1.51837i	1.28897	+	0.573888i	0.932754	−	0.360514i	$-0.117399\pi$
$7$	3.41030	+	1.51837i	1.28897	+	0.573888i	0.356220	+	0.934402i	$0.384065\pi$
$8$	−0.863288	−	0.627215i	−0.305218	−	0.221754i
$9$	−2.51284	+	1.11879i	−0.837613	+	0.372929i
$10$	2.18505	+	0.464447i	0.690974	+	0.146871i
$11$	0.194058	+	1.84634i	0.0585107	+	0.556692i	0.984031	+	0.177995i	$0.0569611\pi$
$11$	0.194058	+	1.84634i	0.0585107	+	0.556692i	−0.925521	+	0.378697i	$0.876372\pi$
$12$	0.475560	−	0.528162i	0.137282	−	0.152467i
$13$	−3.46909	−	3.85281i	−0.962152	−	1.06858i	−0.997602	−	0.0692065i	$-0.977953\pi$
$13$	−3.46909	−	3.85281i	−0.962152	−	1.06858i	0.0354505	−	0.999371i	$-0.488713\pi$
$14$	0.721967	−	6.86906i	0.192954	−	1.83583i
$15$	0.186307	−	0.573393i	0.0481042	−	0.148049i
$16$	−1.48972	+	4.58490i	−0.372431	+	1.14622i
$17$	0.592413	−	5.63643i	0.143681	−	1.36703i	−0.650571	−	0.759446i	$-0.725470\pi$
$17$	0.592413	−	5.63643i	0.143681	−	1.36703i	0.794252	−	0.607589i	$-0.207863\pi$
$18$	3.40538	+	3.78206i	0.802656	+	0.891440i
$19$	−0.962535	+	1.06900i	−0.220821	+	0.245246i	−0.843369	−	0.537335i	$-0.819431\pi$
$19$	−0.962535	+	1.06900i	−0.220821	+	0.245246i	0.622548	+	0.782582i	$0.286098\pi$
$20$	−0.179621	−	1.70898i	−0.0401645	−	0.382139i
$21$	−1.82338	−	0.387571i	−0.397893	−	0.0845748i
$22$	3.13796	−	1.39711i	0.669015	−	0.297865i
$23$	2.86762	+	2.08345i	0.597940	+	0.434429i	0.845147	−	0.534534i	$-0.179513\pi$
$23$	2.86762	+	2.08345i	0.597940	+	0.434429i	−0.247207	+	0.968963i	$0.579513\pi$
$24$	0.486785	+	0.216731i	0.0993645	+	0.0442399i
$25$	1.77114	+	3.06770i	0.354228	+	0.613541i
$26$	−4.79617	+	8.30721i	−0.940606	+	1.62918i
$27$	2.32318	−	1.68789i	0.447096	−	0.324835i
$28$	−5.19700	+	1.10466i	−0.982140	+	0.208760i
$29$	0.424157	+	1.30542i	0.0787641	+	0.242411i	0.982684	−	0.185292i	$-0.0593230\pi$
$29$	0.424157	+	1.30542i	0.0787641	+	0.242411i	−0.903919	+	0.427703i	$0.859323\pi$
$30$	−1.11549			−0.203660
$31$	−1.81847	−	5.26243i	−0.326607	−	0.945160i
$31$	−1.81847	−	5.26243i	−0.326607	−	0.945160i
$32$	6.78540			1.19950
$33$	−0.286476	−	0.881683i	−0.0498691	−	0.153481i
$34$	−10.2569	+	2.18016i	−1.75904	+	0.373895i
$35$	−3.64635	+	2.64923i	−0.616345	+	0.447801i
$36$	1.95745	−	3.39040i	0.326241	−	0.565066i
$37$	−2.25141	−	3.89955i	−0.370129	−	0.641082i	0.619456	−	0.785031i	$-0.287353\pi$
$37$	−2.25141	−	3.89955i	−0.370129	−	0.641082i	−0.989585	+	0.143949i	$0.954020\pi$
$38$	2.43140	+	1.08253i	0.394425	+	0.175609i
$39$	2.09445	+	1.52171i	0.335381	+	0.243669i
$40$	1.17697	−	0.524021i	0.186095	−	0.0828550i
$41$	4.61599	+	0.981158i	0.720896	+	0.153231i	0.553728	−	0.832697i	$-0.313205\pi$
$41$	4.61599	+	0.981158i	0.720896	+	0.153231i	0.167168	+	0.985928i	$0.446538\pi$
$42$	0.360518	+	3.43010i	0.0556291	+	0.529275i
$43$	4.38897	−	4.87445i	0.669312	−	0.743347i	−0.308868	−	0.951105i	$-0.599950\pi$
$43$	4.38897	−	4.87445i	0.669312	−	0.743347i	0.978180	+	0.207758i	$0.0666167\pi$
$44$	−1.76804	−	1.96361i	−0.266543	−	0.296026i
$45$	0.347141	−	3.30283i	0.0517488	−	0.492357i
$46$	2.02659	−	6.23721i	0.298805	−	0.919627i
$47$	−1.30682	+	4.02199i	−0.190620	+	0.586667i	−1.00000		0.000618100i	$-0.999803\pi$
$47$	−1.30682	+	4.02199i	−0.190620	+	0.586667i	0.809380	+	0.587285i	$0.199803\pi$
$48$	0.251633	−	2.39412i	0.0363200	−	0.345562i
$49$	4.64083	+	5.15416i	0.662975	+	0.736308i
$50$	4.38545	−	4.87053i	0.620196	−	0.688797i
$51$	0.295824	+	2.81458i	0.0414236	+	0.394119i
$52$	7.21762	+	1.53415i	1.00090	+	0.212749i
$53$	−11.8426	+	5.27265i	−1.62670	+	0.724254i	−0.998550	−	0.0538363i	$-0.982855\pi$
$53$	−11.8426	+	5.27265i	−1.62670	+	0.724254i	−0.628152	+	0.778091i	$0.716188\pi$
$54$	−4.29836	−	3.12294i	−0.584933	−	0.424979i
$55$	−2.04769	−	0.911691i	−0.276111	−	0.122932i
$56$	−1.99173	−	3.44978i	−0.266156	−	0.460996i
$57$	0.359157	−	0.622078i	0.0475715	−	0.0823963i
$58$	2.05458	−	1.49274i	0.269779	−	0.196006i
$59$	2.13389	−	0.453572i	0.277808	−	0.0590500i	−0.0669005	−	0.997760i	$-0.521311\pi$
$59$	2.13389	−	0.453572i	0.277808	−	0.0590500i	0.344709	+	0.938710i	$0.387978\pi$
$60$	0.265164	+	0.816089i	0.0342325	+	0.105357i
$61$	−2.68087			−0.343251			−0.171625	−	0.985162i	$-0.554902\pi$
$61$	−2.68087			−0.343251			−0.171625	+	0.985162i	$0.554902\pi$
$62$	−8.22033	+	6.20865i	−1.04398	+	0.788499i
$63$	−10.2683			−1.29368
$64$	−0.900071	−	2.77013i	−0.112509	−	0.346267i
$65$	6.12274	−	1.30143i	0.759433	−	0.161422i
$66$	−1.38766	+	1.00820i	−0.170809	+	0.124100i
$67$	−1.44150	+	2.49675i	−0.176107	+	0.305027i	−0.940544	−	0.339672i	$-0.889684\pi$
$67$	−1.44150	+	2.49675i	−0.176107	+	0.305027i	0.764437	+	0.644699i	$0.223017\pi$
$68$	4.03315	+	6.98563i	0.489092	+	0.847132i
$69$	−1.61697	−	0.719924i	−0.194661	−	0.0866686i
$70$	6.74649	+	4.90161i	0.806360	+	0.585855i
$71$	8.22340	−	3.66129i	0.975938	−	0.434516i	0.144118	−	0.989561i	$-0.453966\pi$
$71$	8.22340	−	3.66129i	0.975938	−	0.434516i	0.831820	+	0.555045i	$0.187299\pi$
$72$	2.87102	+	0.610255i	0.338353	+	0.0719192i
$73$	0.439443	+	4.18102i	0.0514329	+	0.489352i	0.989671	+	0.143360i	$0.0457907\pi$
$73$	0.439443	+	4.18102i	0.0514329	+	0.489352i	−0.938238	+	0.345991i	$0.887543\pi$
$74$	−5.57462	+	6.19124i	−0.648036	+	0.719717i
$75$	−1.18359	−	1.31451i	−0.136670	−	0.151787i
$76$	0.214006	−	2.03613i	0.0245481	−	0.233560i
$77$	−2.14162	+	6.59123i	−0.244060	+	0.751140i
$78$	1.48018	−	4.55554i	0.167598	−	0.515813i
$79$	−1.17403	+	11.1702i	−0.132089	+	1.25674i	0.704814	+	0.709392i	$0.251030\pi$
$79$	−1.17403	+	11.1702i	−0.132089	+	1.25674i	−0.836903	+	0.547351i	$0.815636\pi$
$80$	−3.89468	−	4.32548i	−0.435438	−	0.483603i
$81$	4.56212	−	5.06675i	0.506902	−	0.562972i
$82$	−0.912672	−	8.68350i	−0.100788	−	0.958932i
$83$	10.2485	+	2.17838i	1.12492	+	0.239108i	0.732558	−	0.680704i	$-0.238326\pi$
$83$	10.2485	+	2.17838i	1.12492	+	0.239108i	0.392358	+	0.919813i	$0.371659\pi$
$84$	2.42375	−	1.07912i	0.264452	−	0.117742i
$85$	5.53585	+	4.02203i	0.600448	+	0.436251i
$86$	−11.0867	−	4.93612i	−1.19551	−	0.532275i
$87$	−0.342708	−	0.593587i	−0.0367421	−	0.0636392i
$88$	0.990524	−	1.71564i	0.105590	−	0.182888i
$89$	2.18575	−	1.58804i	0.231689	−	0.168332i	−0.465884	−	0.884846i	$-0.654263\pi$
$89$	2.18575	−	1.58804i	0.231689	−	0.168332i	0.697573	+	0.716514i	$0.254263\pi$
$90$	−6.01030	+	1.27753i	−0.633542	+	0.134663i
$91$	−5.98067	−	18.4066i	−0.626944	−	1.92954i
$92$	−5.04486			−0.525963
$93$	1.43457	+	2.38160i	0.148758	+	0.246960i
$94$	7.82446			0.807031
$95$	−0.536692	−	1.65177i	−0.0550635	−	0.169468i
$96$	−3.31428	+	0.704471i	−0.338262	+	0.0718998i
$97$	6.70942	−	4.87468i	0.681239	−	0.494949i	−0.192530	−	0.981291i	$-0.561669\pi$
$97$	6.70942	−	4.87468i	0.681239	−	0.494949i	0.873768	+	0.486342i	$0.161669\pi$
$98$	6.41615	−	11.1131i	0.648129	−	1.12259i
$99$	−2.55330	−	4.42244i	−0.256616	−	0.444472i
$100$	−4.60573	−	2.05060i	−0.460573	−	0.205060i
$101$	−1.29317	−	0.939541i	−0.128675	−	0.0934879i	0.521586	−	0.853199i	$-0.325341\pi$
$101$	−1.29317	−	0.939541i	−0.128675	−	0.0934879i	−0.650261	+	0.759711i	$0.725341\pi$
$102$	4.78353	−	2.12977i	0.473640	−	0.210878i
$103$	−17.9078	−	3.80641i	−1.76451	−	0.375057i	−0.792474	−	0.609906i	$-0.791207\pi$
$103$	−17.9078	−	3.80641i	−1.76451	−	0.375057i	−0.972032	+	0.234849i	$0.924540\pi$
$104$	0.578278	+	5.50195i	0.0567048	+	0.539511i
$105$	1.50598	−	1.67256i	0.146969	−	0.163225i
$106$	16.0490	+	17.8242i	1.55881	+	1.73124i
$107$	−1.20995	+	11.5119i	−0.116970	+	1.11289i	0.765797	+	0.643083i	$0.222345\pi$
$107$	−1.20995	+	11.5119i	−0.116970	+	1.11289i	−0.882767	+	0.469812i	$0.844322\pi$
$108$	−1.26297	+	3.88702i	−0.121529	+	0.374029i
$109$	0.430552	−	1.32510i	0.0412394	−	0.126922i	−0.928317	−	0.371789i	$-0.878744\pi$
$109$	0.430552	−	1.32510i	0.0412394	−	0.126922i	0.969557	+	0.244867i	$0.0787444\pi$
$110$	−0.433500	+	4.12448i	−0.0413326	+	0.393254i
$111$	1.50454	+	1.67096i	0.142805	+	0.158601i
$112$	−12.0420	+	13.3740i	−1.13786	+	1.26372i
$113$	0.340299	+	3.23773i	0.0320126	+	0.304580i	0.998799	+	0.0489943i	$0.0156016\pi$
$113$	0.340299	+	3.23773i	0.0320126	+	0.304580i	−0.966786	+	0.255586i	$0.917732\pi$
$114$	−1.29999	−	0.276321i	−0.121755	−	0.0258798i
$115$	−3.90959	+	1.74066i	−0.364571	+	0.162318i
$116$	−1.58047	−	1.14828i	−0.146743	−	0.106615i
$117$	13.0277	+	5.80032i	1.20442	+	0.536240i
$118$	−2.01817	−	3.49557i	−0.185787	−	0.321793i
$119$	10.5785	−	18.3224i	0.969726	−	1.67961i
$120$	−0.520477	+	0.378149i	−0.0475129	+	0.0345201i
$121$	7.38831	−	1.57043i	0.671665	−	0.142767i
$122$	1.53278	+	4.71740i	0.138771	+	0.427093i
$123$	−2.35651			−0.212479
$124$	6.49628	+	4.53811i	0.583383	+	0.407534i
$125$	−10.3136			−0.922478
$126$	5.87084	+	18.0686i	0.523016	+	1.60968i
$127$	−9.38184	+	1.99417i	−0.832504	+	0.176954i	−0.604398	−	0.796682i	$-0.706586\pi$
$127$	−9.38184	+	1.99417i	−0.832504	+	0.176954i	−0.228105	+	0.973636i	$0.573253\pi$
$128$	6.61915	−	4.80909i	0.585056	−	0.425068i
$129$	−1.63769	+	2.83656i	−0.144190	+	0.249745i
$130$	−5.79071	−	10.0298i	−0.507879	−	0.879672i
$131$	−10.4986	−	4.67429i	−0.917269	−	0.408395i	−0.106870	−	0.994273i	$-0.534083\pi$
$131$	−10.4986	−	4.67429i	−0.917269	−	0.408395i	−0.810399	+	0.585878i	$0.800750\pi$
$132$	1.06745	+	0.775550i	0.0929099	+	0.0675030i
$133$	−4.90567	+	2.18415i	−0.425376	+	0.189390i
$134$	5.21758	+	1.10903i	0.450730	+	0.0958057i
$135$	0.362408	+	3.44808i	0.0311911	+	0.296763i
$136$	−4.04668	+	4.49429i	−0.347000	+	0.385382i
$137$	−10.5641	−	11.7326i	−0.902548	−	1.00238i	−0.999975	−	0.00713873i	$-0.997728\pi$
$137$	−10.5641	−	11.7326i	−0.902548	−	1.00238i	0.0974262	−	0.995243i	$-0.468939\pi$
$138$	−0.342316	+	3.25692i	−0.0291399	+	0.277248i
$139$	−3.15460	+	9.70886i	−0.267570	+	0.823494i	0.723521	+	0.690303i	$0.242523\pi$
$139$	−3.15460	+	9.70886i	−0.267570	+	0.823494i	−0.991090	+	0.133192i	$0.957477\pi$
$140$	1.98229	−	6.10087i	0.167534	−	0.515618i
$141$	0.220738	−	2.10018i	0.0185895	−	0.176867i
$142$	−11.1443	−	12.3770i	−0.935208	−	1.03865i
$143$	6.44040	−	7.15278i	0.538573	−	0.598146i
$144$	−1.38609	−	13.1878i	−0.115508	−	1.09898i
$145$	−1.62101	−	0.344557i	−0.134618	−	0.0286139i
$146$	7.10589	−	3.16374i	0.588087	−	0.261833i
$147$	−2.80189	−	2.03569i	−0.231096	−	0.167901i
$148$	5.85463	+	2.60665i	0.481247	+	0.214265i
$149$	−1.91033	−	3.30879i	−0.156501	−	0.271067i	0.777104	−	0.629372i	$-0.216688\pi$
$149$	−1.91033	−	3.30879i	−0.156501	−	0.271067i	−0.933604	+	0.358305i	$0.883355\pi$
$150$	−1.63637	+	2.83428i	−0.133609	+	0.231418i
$151$	7.17402	−	5.21223i	0.583814	−	0.424166i	−0.256283	−	0.966602i	$-0.582498\pi$
$151$	7.17402	−	5.21223i	0.583814	−	0.424166i	0.840097	+	0.542436i	$0.182498\pi$
$152$	1.50144	−	0.319141i	0.121783	−	0.0258857i
$153$	4.81733	+	14.8262i	0.389458	+	1.19863i
$154$	12.8227			1.03328
$155$	6.60020	+	1.27542i	0.530141	+	0.102444i
$156$	−3.68467			−0.295010
$157$	−1.59982	−	4.92372i	−0.127679	−	0.392956i	0.866701	−	0.498829i	$-0.166236\pi$
$157$	−1.59982	−	4.92372i	−0.127679	−	0.392956i	−0.994380	+	0.105873i	$0.966236\pi$
$158$	20.3269	−	4.32061i	1.61712	−	0.343729i
$159$	5.23700	−	3.80490i	0.415321	−	0.301748i
$160$	−4.09621	+	7.09485i	−0.323834	+	0.560897i
$161$	6.61602	+	11.4593i	0.521416	+	0.903119i
$162$	−11.5241	−	5.13085i	−0.905417	−	0.403118i
$163$	−0.448015	−	0.325502i	−0.0350912	−	0.0254953i	0.570101	−	0.821574i	$-0.306904\pi$
$163$	−0.448015	−	0.325502i	−0.0350912	−	0.0254953i	−0.605193	+	0.796079i	$0.706904\pi$
$164$	−6.13586	+	2.73186i	−0.479130	+	0.213323i
$165$	1.09483	+	0.232714i	0.0852326	+	0.0181168i
$166$	−2.02633	−	19.2792i	−0.157274	−	1.49636i
$167$	1.33693	−	1.48481i	0.103454	−	0.114898i	−0.689194	−	0.724577i	$-0.742035\pi$
$167$	1.33693	−	1.48481i	0.103454	−	0.114898i	0.792648	+	0.609679i	$0.208702\pi$
$168$	1.33101	+	1.47823i	0.102689	+	0.114048i
$169$	−1.45072	+	13.8027i	−0.111594	+	1.06175i
$170$	3.91228	−	12.0407i	0.300058	−	0.923483i
$171$	1.22271	−	3.76311i	0.0935028	−	0.287772i
$172$	−0.975825	+	9.28435i	−0.0744060	+	0.707925i
$173$	−2.71506	−	3.01538i	−0.206422	−	0.229255i	0.631040	−	0.775750i	$-0.282628\pi$
$173$	−2.71506	−	3.01538i	−0.206422	−	0.229255i	−0.837462	+	0.546495i	$0.815962\pi$
$174$	−0.848564	+	0.942426i	−0.0643295	+	0.0714451i
$175$	1.38223	+	13.1510i	0.104487	+	0.994125i
$176$	−8.75437	−	1.86080i	−0.659886	−	0.140263i
$177$	−0.995190	+	0.443087i	−0.0748030	+	0.0333045i
$178$	−4.04409	−	2.93820i	−0.303117	−	0.220227i
$179$	−3.62117	−	1.61225i	−0.270659	−	0.120505i	0.266920	−	0.963719i	$-0.413994\pi$
$179$	−3.62117	−	1.61225i	−0.270659	−	0.120505i	−0.537579	+	0.843214i	$0.680661\pi$
$180$	2.36334	+	4.09343i	0.176153	+	0.305106i
$181$	−3.19871	+	5.54033i	−0.237758	+	0.411809i	−0.960071	−	0.279757i	$-0.909746\pi$
$181$	−3.19871	+	5.54033i	−0.237758	+	0.411809i	0.722312	+	0.691567i	$0.243079\pi$
$182$	−28.9698	+	21.0478i	−2.14738	+	1.56016i
$183$	1.30945	−	0.278333i	0.0967975	−	0.0205749i
$184$	−1.16881	−	3.59723i	−0.0861659	−	0.265191i
$185$	5.43652			0.399701
$186$	3.37057	−	3.88601i	0.247142	−	0.284936i
$187$	10.5217			0.769425
$188$	−1.85995	−	5.72434i	−0.135651	−	0.417491i
$189$	10.4856	−	2.22878i	0.762714	−	0.162120i
$190$	−2.59968	+	1.88878i	−0.188601	+	0.137027i
$191$	−5.81282	+	10.0681i	−0.420601	+	0.728502i	−0.995998	−	0.0893720i	$-0.971514\pi$
$191$	−5.81282	+	10.0681i	−0.420601	+	0.728502i	0.575398	+	0.817874i	$0.304847\pi$
$192$	0.727233	+	1.25960i	0.0524835	+	0.0909041i
$193$	12.3726	+	5.50865i	0.890602	+	0.396521i	0.800445	−	0.599406i	$-0.204597\pi$
$193$	12.3726	+	5.50865i	0.890602	+	0.396521i	0.0901566	+	0.995928i	$0.471263\pi$
$194$	−12.4138	−	9.01917i	−0.891260	−	0.647538i
$195$	−2.85549	+	1.27135i	−0.204486	+	0.0910430i
$196$	−9.65548	−	2.05234i	−0.689677	−	0.146595i
$197$	−2.44642	−	23.2761i	−0.174300	−	1.65835i	−0.636277	−	0.771461i	$-0.719526\pi$
$197$	−2.44642	−	23.2761i	−0.174300	−	1.65835i	0.461977	−	0.886892i	$-0.347140\pi$
$198$	−6.32212	+	7.02143i	−0.449294	+	0.498991i
$199$	4.41490	+	4.90324i	0.312964	+	0.347582i	0.879020	−	0.476785i	$-0.158198\pi$
$199$	4.41490	+	4.90324i	0.312964	+	0.347582i	−0.566056	+	0.824367i	$0.691531\pi$
$200$	0.395107	−	3.75920i	0.0279383	−	0.265815i
$201$	0.444873	−	1.36918i	0.0313789	−	0.0965744i
$202$	−0.913902	+	2.81270i	−0.0643019	+	0.197901i
$203$	−0.535602	+	5.09591i	−0.0375919	+	0.357663i
$204$	−2.69522	−	2.99335i	−0.188703	−	0.209576i
$205$	−3.81249	+	4.23420i	−0.266276	+	0.295729i
$206$	3.54072	+	33.6877i	0.246694	+	2.34714i
$207$	−9.53681	−	2.02711i	−0.662854	−	0.140894i
$208$	22.8327	−	10.1658i	1.58317	−	0.704871i
$209$	−2.16053	−	1.56972i	−0.149447	−	0.108580i
$210$	−3.80417	−	1.69372i	−0.262512	−	0.116878i
$211$	9.68254	+	16.7707i	0.666574	+	1.15454i	0.978856	+	0.204550i	$0.0655731\pi$
$211$	9.68254	+	16.7707i	0.666574	+	1.15454i	−0.312283	+	0.949989i	$0.601094\pi$
$212$	9.22510	−	15.9783i	0.633582	−	1.09740i
$213$	−3.63654	+	2.64210i	−0.249171	+	0.181034i
$214$	20.9486	−	4.45277i	1.43202	−	0.304385i
$215$	2.44721	+	7.53175i	0.166899	+	0.513661i
$216$	−3.06424			−0.208495
$217$	1.78874	−	20.7076i	0.121428	−	1.40572i
$218$	−2.57788			−0.174596
$219$	−0.648723	−	1.99656i	−0.0438366	−	0.134915i
$220$	3.12050	−	0.663283i	0.210384	−	0.0447185i
$221$	−23.7712	+	17.2708i	−1.59903	+	1.16176i
$222$	2.08009	−	3.60283i	0.139607	−	0.241806i
$223$	−3.52986	−	6.11389i	−0.236377	−	0.409416i	0.723295	−	0.690539i	$-0.242627\pi$
$223$	−3.52986	−	6.11389i	−0.236377	−	0.409416i	−0.959672	+	0.281123i	$0.909293\pi$
$224$	23.1403	+	10.3027i	1.54612	+	0.688379i
$225$	−7.88270	−	5.72712i	−0.525513	−	0.381808i
$226$	5.50271	−	2.44996i	0.366035	−	0.162969i
$227$	8.82270	+	1.87532i	0.585583	+	0.124470i	0.491170	−	0.871064i	$-0.336569\pi$
$227$	8.82270	+	1.87532i	0.585583	+	0.124470i	0.0944130	+	0.995533i	$0.469903\pi$
$228$	0.106865	+	1.01675i	0.00707729	+	0.0673359i
$229$	12.0135	−	13.3423i	0.793872	−	0.881684i	−0.201330	−	0.979523i	$-0.564527\pi$
$229$	12.0135	−	13.3423i	0.793872	−	0.881684i	0.995202	+	0.0978395i	$0.0311932\pi$
$230$	5.29825	+	5.88430i	0.349356	+	0.387999i
$231$	0.361746	−	3.44178i	0.0238011	−	0.226453i
$232$	0.452611	−	1.39299i	0.0297154	−	0.0914545i
$233$	4.21725	−	12.9793i	0.276281	−	0.850305i	−0.712597	−	0.701574i	$-0.752481\pi$
$233$	4.21725	−	12.9793i	0.276281	−	0.850305i	0.988878	−	0.148731i	$-0.0475190\pi$
$234$	2.75800	−	26.2406i	0.180296	−	1.71540i
$235$	−3.41651	−	3.79442i	−0.222868	−	0.247520i
$236$	−2.07760	+	2.30741i	−0.135241	+	0.150200i
$237$	−0.586258	−	5.57788i	−0.0380816	−	0.362322i
$238$	−38.2893	−	8.13864i	−2.48192	−	0.527549i
$239$	−8.99955	+	4.00686i	−0.582132	+	0.259182i	−0.676606	−	0.736345i	$-0.736550\pi$
$239$	−8.99955	+	4.00686i	−0.582132	+	0.259182i	0.0944736	+	0.995527i	$0.469883\pi$
$240$	2.35140	+	1.70840i	0.151783	+	0.110276i
$241$	−6.09318	−	2.71286i	−0.392496	−	0.174751i	0.200993	−	0.979593i	$-0.435583\pi$
$241$	−6.09318	−	2.71286i	−0.392496	−	0.174751i	−0.593489	+	0.804842i	$0.702250\pi$
$242$	−6.98765	−	12.1030i	−0.449183	−	0.778008i
$243$	−6.00971	+	10.4091i	−0.385523	+	0.667746i
$244$	3.08688	−	2.24275i	0.197617	−	0.143577i
$245$	−8.19079	+	1.74101i	−0.523291	+	0.111229i
$246$	1.34732	+	4.14663i	0.0859021	+	0.264380i
$247$	7.45779			0.474528
$248$	−1.73081	+	5.68356i	−0.109907	+	0.360907i
$249$	−5.23195			−0.331562
$250$	5.89676	+	18.1484i	0.372944	+	1.14780i
$251$	28.6773	−	6.09555i	1.81010	−	0.384748i	0.826183	−	0.563402i	$-0.190508\pi$
$251$	28.6773	−	6.09555i	1.81010	−	0.384748i	0.983912	+	0.178654i	$0.0571743\pi$
$252$	11.8233	−	8.59016i	0.744801	−	0.541129i
$253$	−3.29027	+	5.69891i	−0.206857	+	0.358288i
$254$	8.87307	+	15.3686i	0.556746	+	0.964312i
$255$	−3.12152	−	1.38979i	−0.195477	−	0.0870320i
$256$	−16.9596	−	12.3219i	−1.05998	−	0.770118i
$257$	−21.8780	+	9.74073i	−1.36471	+	0.607610i	−0.952796	−	0.303610i	$-0.901808\pi$
$257$	−21.8780	+	9.74073i	−1.36471	+	0.607610i	−0.411919	+	0.911221i	$0.635141\pi$
$258$	5.92769	+	1.25997i	0.369042	+	0.0784423i
$259$	−1.75704	−	16.7171i	−0.109177	−	1.03875i
$260$	−5.96126	+	6.62065i	−0.369701	+	0.410595i
$261$	−2.52633	−	2.80577i	−0.156376	−	0.173673i
$262$	−2.22258	+	21.1464i	−0.137311	+	1.30643i
$263$	1.21883	−	3.75119i	0.0751566	−	0.231308i	−0.906420	−	0.422378i	$-0.861196\pi$
$263$	1.21883	−	3.75119i	0.0751566	−	0.231308i	0.981577	+	0.191070i	$0.0611956\pi$
$264$	−0.305694	+	0.940828i	−0.0188141	+	0.0579040i
$265$	1.63602	−	15.5657i	0.100500	−	0.956191i
$266$	6.64813	+	7.38350i	0.407623	+	0.452711i
$267$	−0.902740	+	1.00259i	−0.0552468	+	0.0613578i
$268$	−0.428908	−	4.08079i	−0.0261997	−	0.249274i
$269$	−12.4736	−	2.65134i	−0.760527	−	0.161655i	−0.188706	−	0.982034i	$-0.560429\pi$
$269$	−12.4736	−	2.65134i	−0.760527	−	0.161655i	−0.571821	+	0.820379i	$0.693763\pi$
$270$	5.86021	−	2.60913i	0.356641	−	0.158787i
$271$	2.68805	+	1.95298i	0.163287	+	0.118635i	0.666428	−	0.745569i	$-0.267822\pi$
$271$	2.68805	+	1.95298i	0.163287	+	0.118635i	−0.503141	+	0.864204i	$0.667822\pi$
$272$	24.9599	+	11.1129i	1.51342	+	0.673817i
$273$	4.83221	+	8.36964i	0.292459	+	0.506554i
$274$	−14.6053	+	25.2971i	−0.882337	+	1.52825i
$275$	−5.32032	+	3.86544i	−0.320827	+	0.233095i
$276$	2.46412	−	0.523766i	0.148323	−	0.0315270i
$277$	6.49451	+	19.9880i	0.390217	+	1.20096i	0.932624	+	0.360849i	$0.117513\pi$
$277$	6.49451	+	19.9880i	0.390217	+	1.20096i	−0.542407	+	0.840116i	$0.682487\pi$
$278$	18.8878			1.13282
$279$	10.4571	+	11.1892i	0.626049	+	0.669877i
$280$	4.80948			0.287421
$281$	−2.89451	−	8.90839i	−0.172672	−	0.531430i	0.826847	−	0.562426i	$-0.190132\pi$
$281$	−2.89451	−	8.90839i	−0.172672	−	0.531430i	−0.999519	+	0.0309964i	$0.990132\pi$
$282$	−3.82180	+	0.812348i	−0.227585	+	0.0483746i
$283$	8.19788	−	5.95611i	0.487313	−	0.354054i	−0.316837	−	0.948480i	$-0.602621\pi$
$283$	8.19788	−	5.95611i	0.487313	−	0.354054i	0.804150	+	0.594426i	$0.202621\pi$
$284$	−6.40585	+	11.0953i	−0.380117	+	0.658382i
$285$	0.433632	+	0.751074i	0.0256862	+	0.0444898i
$286$	−16.2687	−	7.24328i	−0.961986	−	0.428304i
$287$	14.2522	+	10.3548i	0.841278	+	0.611225i
$288$	−17.0506	+	7.59142i	−1.00472	+	0.447329i
$289$	−14.7899	−	3.14368i	−0.869992	−	0.184923i
$290$	0.320506	+	3.04942i	0.0188208	+	0.179068i
$291$	−2.77107	+	3.07758i	−0.162443	+	0.180411i
$292$	−4.00372	−	4.44659i	−0.234300	−	0.260217i
$293$	2.22333	−	21.1536i	0.129888	−	1.23581i	−0.714331	−	0.699808i	$-0.753269\pi$
$293$	2.22333	−	21.1536i	0.129888	−	1.23581i	0.844220	−	0.535997i	$-0.180064\pi$
$294$	−1.98014	+	6.09424i	−0.115484	+	0.355423i
$295$	−0.813929	+	2.50502i	−0.0473888	+	0.145848i
$296$	−0.502246	+	4.77855i	−0.0291925	+	0.277748i
$297$	3.56725	+	3.96183i	0.206993	+	0.229889i
$298$	−4.73010	+	5.25331i	−0.274007	+	0.304316i
$299$	−1.92089	−	18.2761i	−0.111088	−	1.05693i
$300$	2.46253	+	0.523426i	0.142174	+	0.0302200i
$301$	22.3689	−	9.95929i	1.28932	−	0.574044i
$302$	−13.2734	−	9.64371i	−0.763800	−	0.554933i
$303$	0.729183	+	0.324653i	0.0418904	+	0.0186508i
$304$	−3.46736	−	6.00565i	−0.198867	−	0.344447i
$305$	1.61839	−	2.80314i	0.0926688	−	0.160507i
$306$	23.3347	−	16.9536i	1.33396	−	0.969175i
$307$	−15.8863	+	3.37674i	−0.906680	+	0.192721i	−0.637573	−	0.770390i	$-0.720062\pi$
$307$	−15.8863	+	3.37674i	−0.906680	+	0.192721i	−0.269107	+	0.963110i	$0.586728\pi$
$308$	−3.04809	−	9.38105i	−0.173681	−	0.534535i
$309$	9.14210			0.520076
$310$	−1.52934	−	12.3433i	−0.0868606	−	0.701050i
$311$	−10.3858			−0.588924			−0.294462	−	0.955663i	$-0.595141\pi$
$311$	−10.3858			−0.588924			−0.294462	+	0.955663i	$0.595141\pi$
$312$	−0.853677	−	2.62735i	−0.0483299	−	0.148744i
$313$	−31.3434	+	6.66226i	−1.77164	+	0.376573i	−0.973997	−	0.226561i	$-0.927252\pi$
$313$	−31.3434	+	6.66226i	−1.77164	+	0.376573i	−0.797640	+	0.603134i	$0.793918\pi$
$314$	−7.74935	+	5.63023i	−0.437321	+	0.317732i
$315$	6.19876	−	10.7366i	0.349261	−	0.604937i
$316$	−7.99283	−	13.8440i	−0.449632	−	0.778786i
$317$	23.1261	+	10.2964i	1.29889	+	0.578304i	0.935498	−	0.353331i	$-0.114951\pi$
$317$	23.1261	+	10.2964i	1.29889	+	0.578304i	0.363395	+	0.931635i	$0.381618\pi$
$318$	−9.68952	−	7.03985i	−0.543361	−	0.394775i
$319$	−2.32794	+	1.03647i	−0.130340	+	0.0580310i
$320$	3.43982	+	0.731157i	0.192292	+	0.0408729i
$321$	−0.604192	−	5.74850i	−0.0337227	−	0.320850i
$322$	16.3817	−	18.1937i	0.912915	−	1.01389i
$323$	5.45514	+	6.05855i	0.303532	+	0.337107i
$324$	−1.01432	+	9.65063i	−0.0563512	+	0.536146i
$325$	5.67505	−	17.4660i	0.314795	−	0.968839i
$326$	−0.316619	+	0.974453i	−0.0175359	+	0.0539700i
$327$	−0.0727254	+	0.691936i	−0.00402173	+	0.0382642i
$328$	−3.36953	−	3.74224i	−0.186051	−	0.206631i
$329$	−10.5635	+	11.7320i	−0.582385	+	0.646804i
$330$	−0.216470	−	2.05958i	−0.0119163	−	0.113376i
$331$	32.1961	+	6.84349i	1.76966	+	0.376152i	0.973455	−	0.228879i	$-0.0735059\pi$
$331$	32.1961	+	6.84349i	1.76966	+	0.376152i	0.796202	+	0.605031i	$0.206839\pi$
$332$	−13.6229	+	6.06532i	−0.747655	+	0.332877i
$333$	10.0202	+	7.28010i	0.549103	+	0.398947i
$334$	−3.37712	−	1.50359i	−0.184788	−	0.0822729i
$335$	−1.74041	−	3.01448i	−0.0950888	−	0.164699i
$336$	4.49330	−	7.78262i	0.245130	−	0.424577i
$337$	−3.19618	+	2.32216i	−0.174107	+	0.126496i	−0.671426	−	0.741072i	$-0.734318\pi$
$337$	−3.19618	+	2.32216i	−0.174107	+	0.126496i	0.497319	+	0.867568i	$0.334318\pi$
$338$	25.1174	−	5.33887i	1.36621	−	0.290396i
$339$	−0.502363	−	1.54611i	−0.0272846	−	0.0839734i
$340$	−9.73895			−0.528169
$341$	9.36334	−	4.37874i	0.507053	−	0.237122i
$342$	−7.32083			−0.395865
$343$	−0.0742848	−	0.228625i	−0.00401100	−	0.0123446i
$344$	−6.84628	+	1.45522i	−0.369126	+	0.0784603i
$345$	1.72889	−	1.25611i	0.0930804	−	0.0676269i
$346$	−3.75369	+	6.50159i	−0.201800	+	0.349527i
$347$	6.84222	+	11.8511i	0.367310	+	0.636199i	0.989144	−	0.146950i	$-0.0469456\pi$
$347$	6.84222	+	11.8511i	0.367310	+	0.636199i	−0.621834	+	0.783149i	$0.713612\pi$
$348$	0.891187	+	0.396782i	0.0477727	+	0.0212698i
$349$	2.99733	+	2.17769i	0.160443	+	0.116569i	0.665110	−	0.746745i	$-0.268385\pi$
$349$	2.99733	+	2.17769i	0.160443	+	0.116569i	−0.504667	+	0.863314i	$0.668385\pi$
$350$	22.3509	−	9.95128i	1.19471	−	0.531918i
$351$	−14.5624	−	3.09534i	−0.777286	−	0.165217i
$352$	1.31676	+	12.5282i	0.0701836	+	0.667753i
$353$	−10.3658	+	11.5124i	−0.551717	+	0.612744i	−0.952911	−	0.303249i	$-0.901929\pi$
$353$	−10.3658	+	11.5124i	−0.551717	+	0.612744i	0.401194	+	0.915993i	$0.368595\pi$
$354$	1.34867	+	1.49785i	0.0716812	+	0.0796100i
$355$	−1.13604	+	10.8087i	−0.0602947	+	0.573666i
$356$	−1.18826	+	3.65708i	−0.0629775	+	0.193825i
$357$	−3.26470	+	10.0477i	−0.172786	+	0.531782i
$358$	−0.766608	+	7.29379i	−0.0405165	+	0.385489i
$359$	−3.59281	−	3.99022i	−0.189621	−	0.210596i	0.640836	−	0.767677i	$-0.278588\pi$
$359$	−3.59281	−	3.99022i	−0.189621	−	0.210596i	−0.830458	+	0.557082i	$0.811921\pi$
$360$	−2.37127	+	2.63356i	−0.124977	+	0.138801i
$361$	1.76975	+	16.8380i	0.0931445	+	0.886211i
$362$	11.5779	+	2.46096i	0.608520	+	0.129345i
$363$	−3.44572	+	1.53413i	−0.180853	+	0.0805211i
$364$	22.2849	+	16.1909i	1.16804	+	0.848634i
$365$	−4.63698	−	2.06452i	−0.242711	−	0.108062i
$366$	−1.23844	−	2.14504i	−0.0647344	−	0.112123i
$367$	7.36045	−	12.7487i	0.384212	−	0.665475i	−0.607447	−	0.794360i	$-0.707806\pi$
$367$	7.36045	−	12.7487i	0.384212	−	0.665475i	0.991660	+	0.128885i	$0.0411397\pi$
$368$	−13.8244	+	10.0440i	−0.720645	+	0.523579i
$369$	−12.6969	+	2.69882i	−0.660976	+	0.140495i
$370$	−3.10831	−	9.56638i	−0.161593	−	0.497333i
$371$	−48.3926			−2.51242
$372$	−3.64421	−	1.54215i	−0.188943	−	0.0799567i
$373$	23.8449			1.23464			0.617320	−	0.786712i	$-0.288218\pi$
$373$	23.8449			1.23464			0.617320	+	0.786712i	$0.288218\pi$
$374$	−6.01574	−	18.5146i	−0.311067	−	0.957365i
$375$	5.03761	−	1.07078i	0.260141	−	0.0552947i
$376$	3.65081	−	2.65247i	0.188276	−	0.136791i
$377$	3.55811	−	6.16282i	0.183252	−	0.317402i
$378$	−9.91696	−	17.1767i	−0.510073	−	0.883473i
$379$	−20.2141	−	8.99989i	−1.03833	−	0.462294i	−0.184491	−	0.982834i	$-0.559064\pi$
$379$	−20.2141	−	8.99989i	−1.03833	−	0.462294i	−0.853837	+	0.520541i	$0.825730\pi$
$380$	1.99980	+	1.45294i	0.102587	+	0.0745341i
$381$	4.37545	−	1.94808i	0.224161	−	0.0998030i
$382$	21.0398	+	4.47214i	1.07649	+	0.228815i
$383$	2.48763	+	23.6682i	0.127112	+	1.20939i	0.853124	+	0.521708i	$0.174705\pi$
$383$	2.48763	+	23.6682i	0.127112	+	1.20939i	−0.726012	+	0.687682i	$0.758628\pi$
$384$	−2.73378	+	3.03618i	−0.139508	+	0.154939i
$385$	−5.59897	−	6.21829i	−0.285350	−	0.316913i
$386$	2.61931	−	24.9211i	0.133319	−	1.26845i
$387$	−5.57531	+	17.1590i	−0.283409	+	0.872243i
$388$	−3.64750	+	11.2258i	−0.185174	+	0.569906i
$389$	−1.78267	+	16.9610i	−0.0903850	+	0.859956i	0.851575	+	0.524232i	$0.175648\pi$
$389$	−1.78267	+	16.9610i	−0.0903850	+	0.859956i	−0.941960	+	0.335724i	$0.891019\pi$
$390$	3.86974	+	4.29778i	0.195952	+	0.217627i
$391$	13.4420	−	14.9289i	0.679792	−	0.754986i
$392$	−0.773601	−	7.36032i	−0.0390727	−	0.371752i
$393$	5.61327	+	1.19314i	0.283152	+	0.0601858i
$394$	−39.5591	+	17.6128i	−1.99296	+	0.887321i
$395$	−10.9709	−	7.97079i	−0.552004	−	0.401054i
$396$	6.63968	+	2.95618i	0.333656	+	0.148553i
$397$	5.01075	+	8.67887i	0.251482	+	0.435580i	0.963934	−	0.266141i	$-0.0857486\pi$
$397$	5.01075	+	8.67887i	0.251482	+	0.435580i	−0.712452	+	0.701721i	$0.752415\pi$
$398$	6.10380	−	10.5721i	0.305956	−	0.529931i
$399$	2.16938	−	1.57614i	0.108605	−	0.0789059i
$400$	−16.7036	+	3.55046i	−0.835181	+	0.177523i
$401$	−8.82347	−	27.1559i	−0.440623	−	1.35610i	−0.887213	−	0.461360i	$-0.847362\pi$
$401$	−8.82347	−	27.1559i	−0.440623	−	1.35610i	0.446590	−	0.894739i	$-0.352638\pi$
$402$	−2.66363			−0.132850
$403$	−13.9667	+	25.2621i	−0.695731	+	1.25839i
$404$	2.27501			0.113186
$405$	2.54376	+	7.82888i	0.126400	+	0.389020i
$406$	9.27326	−	1.97109i	0.460224	−	0.0978236i
$407$	6.76299	−	4.91360i	0.335229	−	0.243558i
$408$	1.50996	−	2.61533i	0.0747543	−	0.129478i
$409$	11.5051	+	19.9274i	0.568891	+	0.985349i	0.996676	+	0.0814681i	$0.0259609\pi$
$409$	11.5051	+	19.9274i	0.568891	+	0.985349i	−0.427785	+	0.903881i	$0.640706\pi$
$410$	9.63048	+	4.28776i	0.475615	+	0.211758i
$411$	6.37803	+	4.63391i	0.314605	+	0.228574i
$412$	23.8041	−	10.5983i	1.17275	−	0.522140i
$413$	7.96589	+	1.69320i	0.391976	+	0.0833170i
$414$	1.88562	+	17.9404i	0.0926730	+	0.881725i
$415$	−8.46454	+	9.40082i	−0.415508	+	0.461468i
$416$	−23.5391	−	26.1429i	−1.15410	−	1.28176i
$417$	0.532850	−	5.06973i	0.0260938	−	0.248266i
$418$	−1.52688	+	4.69926i	−0.0746822	+	0.229848i
$419$	10.3647	−	31.8994i	0.506351	−	1.55839i	−0.292137	−	0.956377i	$-0.594366\pi$
$419$	10.3647	−	31.8994i	0.506351	−	1.55839i	0.798488	−	0.602011i	$-0.205634\pi$
$420$	−0.334833	+	3.18573i	−0.0163382	+	0.155448i
$421$	6.04042	+	6.70857i	0.294392	+	0.326956i	0.872137	−	0.489262i	$-0.162734\pi$
$421$	6.04042	+	6.70857i	0.294392	+	0.326956i	−0.577745	+	0.816217i	$0.696067\pi$
$422$	23.9745	−	26.6264i	1.16706	−	1.29615i
$423$	−1.21592	−	11.5687i	−0.0591198	−	0.562488i
$424$	13.5306	+	2.87602i	0.657105	+	0.139672i
$425$	18.3401	−	8.16555i	0.889627	−	0.396088i
$426$	6.72834	+	4.88843i	0.325989	+	0.236845i
$427$	−9.14259	−	4.07055i	−0.442441	−	0.196987i
$428$	−8.23733	−	14.2675i	−0.398167	−	0.689645i
$429$	−2.40315	+	4.16237i	−0.116025	+	0.200961i
$430$	11.8541	−	8.61248i	0.571654	−	0.415331i
$431$	−11.0597	+	2.35081i	−0.532726	+	0.113234i	−0.466418	−	0.884565i	$-0.654456\pi$
$431$	−11.0597	+	2.35081i	−0.532726	+	0.113234i	−0.0663088	+	0.997799i	$0.521122\pi$
$432$	4.27791	+	13.1660i	0.205821	+	0.633452i
$433$	9.10433			0.437526			0.218763	−	0.975778i	$-0.429798\pi$
$433$	9.10433			0.437526			0.218763	+	0.975778i	$0.429798\pi$
$434$	−37.4608	+	8.69190i	−1.79818	+	0.417225i
$435$	0.827544			0.0396777
$436$	0.612788	+	1.88597i	0.0293472	+	0.0903215i
$437$	−4.98740	+	1.06010i	−0.238580	+	0.0507117i
$438$	−3.14235	+	2.28305i	−0.150147	+	0.109088i
$439$	19.8026	−	34.2992i	0.945128	−	1.63701i	0.189633	−	0.981855i	$-0.439270\pi$
$439$	19.8026	−	34.2992i	0.945128	−	1.63701i	0.755495	−	0.655155i	$-0.227397\pi$
$440$	1.19592	+	2.07140i	0.0570133	+	0.0987499i
$441$	−17.4281	−	7.75947i	−0.829908	−	0.369499i
$442$	43.9817	+	31.9546i	2.09200	+	1.51992i
$443$	23.0746	−	10.2735i	1.09631	−	0.488108i	0.222774	−	0.974870i	$-0.428489\pi$
$443$	23.0746	−	10.2735i	1.09631	−	0.488108i	0.873534	+	0.486762i	$0.161822\pi$
$444$	−3.13027	−	0.665360i	−0.148556	−	0.0315766i
$445$	0.340969	+	3.24410i	0.0161635	+	0.153785i
$446$	−8.74013	+	9.70690i	−0.413857	+	0.459635i
$447$	1.27661	+	1.41782i	0.0603817	+	0.0670607i
$448$	1.13656	−	10.8136i	0.0536974	−	0.510896i
$449$	0.566090	−	1.74225i	0.0267154	−	0.0822217i	−0.936810	−	0.349839i	$-0.886236\pi$
$449$	0.566090	−	1.74225i	0.0267154	−	0.0822217i	0.963525	+	0.267617i	$0.0862363\pi$
$450$	−5.57083	+	17.1452i	−0.262611	+	0.808235i
$451$	−0.915782	+	8.71308i	−0.0431225	+	0.410283i
$452$	−3.10043	−	3.44338i	−0.145832	−	0.161963i
$453$	−2.96295	+	3.29069i	−0.139212	+	0.154610i
$454$	−1.74442	−	16.5971i	−0.0818699	−	0.778940i
$455$	22.8565	+	4.85829i	1.07153	+	0.227760i
$456$	−0.700233	+	0.311764i	−0.0327914	+	0.0145997i
$457$	−29.0877	−	21.1334i	−1.36066	−	0.988581i	−0.998402	−	0.0565045i	$-0.982004\pi$
$457$	−29.0877	−	21.1334i	−1.36066	−	0.988581i	−0.362262	−	0.932076i	$-0.617996\pi$
$458$	−30.3464	−	13.5111i	−1.41800	−	0.631332i
$459$	−8.13739	−	14.0944i	−0.379821	−	0.657869i
$460$	3.04549	−	5.27494i	0.141997	−	0.245945i
$461$	1.08144	−	0.785711i	0.0503676	−	0.0365942i	−0.562317	−	0.826922i	$-0.690090\pi$
$461$	1.08144	−	0.785711i	0.0503676	−	0.0365942i	0.612684	+	0.790328i	$0.290090\pi$
$462$	−6.26316	+	1.33128i	−0.291389	+	0.0619366i
$463$	−3.63608	−	11.1907i	−0.168983	−	0.520076i	0.830325	−	0.557280i	$-0.188155\pi$
$463$	−3.63608	−	11.1907i	−0.168983	−	0.520076i	−0.999308	+	0.0372039i	$0.988155\pi$
$464$	−6.61711			−0.307192
$465$	−3.35623	+	0.0622743i	−0.155642	+	0.00288790i
$466$	−25.2503			−1.16970
$467$	3.39883	+	10.4605i	0.157279	+	0.484055i	0.998385	−	0.0568157i	$-0.0180947\pi$
$467$	3.39883	+	10.4605i	0.157279	+	0.484055i	−0.841106	+	0.540871i	$0.818095\pi$
$468$	−19.8531	+	4.21991i	−0.917710	+	0.195065i
$469$	−8.70693	+	6.32596i	−0.402049	+	0.292106i
$470$	−4.72348	+	8.18130i	−0.217878	+	0.377375i
$471$	1.29261	+	2.23886i	0.0595602	+	0.103161i
$472$	−2.12664	−	0.946843i	−0.0978867	−	0.0435820i
$473$	9.85161	+	7.15761i	0.452977	+	0.329107i
$474$	−9.47992	+	4.22073i	−0.435427	+	0.193865i
$475$	−4.98417	−	1.05942i	−0.228689	−	0.0486094i
$476$	3.14755	+	29.9469i	0.144268	+	1.37261i
$477$	23.8595	−	26.4986i	1.09245	−	1.21329i
$478$	12.1961	+	13.5452i	0.557837	+	0.619541i
$479$	0.0702175	−	0.668075i	0.00320832	−	0.0305251i	−0.992801	−	0.119779i	$-0.961781\pi$
$479$	0.0702175	−	0.668075i	0.00320832	−	0.0305251i	0.996009	+	0.0892536i	$0.0284482\pi$
$480$	1.26417	−	3.89070i	0.0577010	−	0.177585i
$481$	−7.21391	+	22.2021i	−0.328926	+	1.01233i
$482$	−1.28994	+	12.2729i	−0.0587550	+	0.559017i
$483$	−4.42127	−	4.91032i	−0.201175	−	0.223427i
$484$	−7.19345	+	7.98913i	−0.326975	+	0.363142i
$485$	1.04664	+	9.95816i	0.0475257	+	0.452177i
$486$	21.7524	+	4.62362i	0.986711	+	0.209732i
$487$	−22.4508	+	9.99576i	−1.01734	+	0.452951i	−0.846524	−	0.532351i	$-0.821309\pi$
$487$	−22.4508	+	9.99576i	−1.01734	+	0.452951i	−0.170821	+	0.985302i	$0.554642\pi$
$488$	2.31437	+	1.68148i	0.104766	+	0.0761172i
$489$	0.252623	+	0.112475i	0.0114240	+	0.00508630i
$490$	7.74661	+	13.4175i	0.349956	+	0.606142i
$491$	−4.31714	+	7.47751i	−0.194830	+	0.337455i	−0.946845	−	0.321691i	$-0.895749\pi$
$491$	−4.31714	+	7.47751i	−0.194830	+	0.337455i	0.752015	+	0.659146i	$0.229082\pi$
$492$	2.71339	−	1.97139i	0.122329	−	0.0888772i
$493$	7.60920	−	1.61738i	0.342701	−	0.0728433i
$494$	−4.26395	−	13.1231i	−0.191844	−	0.590436i
$495$	6.16551			0.277119
$496$	26.8367	−	0.497951i	1.20500	−	0.0223586i
$497$	33.6035			1.50732
$498$	2.99134	+	9.20641i	0.134045	+	0.412549i
$499$	−30.4169	+	6.46530i	−1.36165	+	0.289427i	−0.830105	−	0.557606i	$-0.811720\pi$
$499$	−30.4169	+	6.46530i	−1.36165	+	0.289427i	−0.531540	+	0.847033i	$0.678387\pi$
$500$	11.8756	−	8.62809i	0.531091	−	0.385860i
$501$	−0.498856	+	0.864044i	−0.0222873	+	0.0386027i
$502$	−27.1221	−	46.9769i	−1.21052	−	2.09668i
$503$	−15.1140	−	6.72920i	−0.673901	−	0.300040i	0.0411086	−	0.999155i	$-0.486911\pi$
$503$	−15.1140	−	6.72920i	−0.673901	−	0.300040i	−0.715010	+	0.699115i	$0.753578\pi$
$504$	8.86447	+	6.44042i	0.394855	+	0.286879i
$505$	1.76305	−	0.784960i	0.0784547	−	0.0349303i
$506$	11.9093	+	2.53140i	0.529433	+	0.112534i
$507$	−0.724425	−	6.89244i	−0.0321728	−	0.306104i
$508$	9.13440	−	10.1448i	0.405273	−	0.450102i
$509$	20.6742	+	22.9610i	0.916367	+	1.01773i	0.999775	+	0.0212130i	$0.00675283\pi$
$509$	20.6742	+	22.9610i	0.916367	+	1.01773i	−0.0834081	+	0.996515i	$0.526581\pi$
$510$	−0.660831	+	6.28739i	−0.0292621	+	0.278410i
$511$	−4.84968	+	14.9258i	−0.214537	+	0.660278i
$512$	−6.92906	+	21.3254i	−0.306224	+	0.942460i
$513$	−0.431783	+	4.10814i	−0.0190637	+	0.181379i
$514$	29.6490	+	32.9285i	1.30776	+	1.45241i
$515$	14.7906	−	16.4266i	0.651751	−	0.723843i
$516$	−0.487283	−	4.63618i	−0.0214514	−	0.204097i
$517$	−7.67955	−	1.63234i	−0.337746	−	0.0717902i
$518$	−28.4117	+	12.6497i	−1.24834	+	0.555796i
$519$	1.63921	+	1.19096i	0.0719534	+	0.0522772i
$520$	−6.10197	−	2.71677i	−0.267589	−	0.119138i
$521$	7.36097	+	12.7496i	0.322490	+	0.558569i	0.981001	−	0.194002i	$-0.0621468\pi$
$521$	7.36097	+	12.7496i	0.322490	+	0.558569i	−0.658511	+	0.752571i	$0.728813\pi$
$522$	−3.49277	+	6.04965i	−0.152874	+	0.264786i
$523$	24.5610	−	17.8446i	1.07398	−	0.780290i	0.0973541	−	0.995250i	$-0.468962\pi$
$523$	24.5610	−	17.8446i	1.07398	−	0.780290i	0.976623	+	0.214960i	$0.0689621\pi$
$524$	15.9990	−	3.40069i	0.698918	−	0.148560i
$525$	−2.04050	−	6.28002i	−0.0890548	−	0.274082i
$526$	−7.29764			−0.318192
$527$	−30.7386	+	7.13217i	−1.33899	+	0.310682i
$528$	4.46920			0.194497
$529$	−3.22490	−	9.92522i	−0.140213	−	0.431531i
$530$	−28.3255	+	6.02077i	−1.23038	+	0.261526i
$531$	−4.85466	+	3.52712i	−0.210674	+	0.153064i
$532$	3.82141	−	6.61888i	0.165679	−	0.286965i
$533$	−12.2330	−	21.1883i	−0.529872	−	0.917765i
$534$	2.28035	+	1.01528i	0.0986805	+	0.0439354i
$535$	−11.3065	−	8.21462i	−0.488821	−	0.355149i
$536$	2.81043	−	1.25128i	0.121392	−	0.0540472i
$537$	1.93612	+	0.411535i	0.0835497	+	0.0177590i
$538$	2.46627	+	23.4650i	0.106329	+	1.01165i
$539$	−8.61574	+	9.56875i	−0.371106	+	0.412155i
$540$	−3.30186	−	3.66709i	−0.142090	−	0.157806i
$541$	2.83282	−	26.9525i	0.121793	−	1.15878i	−0.747424	−	0.664347i	$-0.768710\pi$
$541$	2.83282	−	26.9525i	0.121793	−	1.15878i	0.869216	−	0.494432i	$-0.164624\pi$
$542$	1.89969	−	5.84664i	0.0815986	−	0.251135i
$543$	0.987180	−	3.03823i	0.0423639	−	0.130383i
$544$	4.01976	−	38.2454i	0.172346	−	1.63976i
$545$	1.12562	+	1.25013i	0.0482162	+	0.0535495i
$546$	11.9649	−	13.2883i	0.512048	−	0.568687i
$547$	−3.43508	−	32.6826i	−0.146873	−	1.39741i	−0.781171	−	0.624317i	$-0.785377\pi$
$547$	−3.43508	−	32.6826i	−0.146873	−	1.39741i	0.634298	−	0.773089i	$-0.281289\pi$
$548$	21.9791	+	4.67180i	0.938900	+	0.199569i
$549$	6.73661	−	2.99933i	0.287511	−	0.128008i
$550$	9.84368	+	7.15186i	0.419736	+	0.304956i
$551$	−1.80377	−	0.803089i	−0.0768431	−	0.0342127i
$552$	0.944367	+	1.63569i	0.0401949	+	0.0696197i
$553$	−20.9642	+	36.3111i	−0.891489	+	1.54410i
$554$	31.4588	−	22.8561i	1.33655	−	0.971064i
$555$	−2.65543	+	0.564429i	−0.112717	+	0.0239587i
$556$	−4.48982	−	13.8183i	−0.190411	−	0.586025i
$557$	−3.79343			−0.160733			−0.0803663	−	0.996765i	$-0.525609\pi$
$557$	−3.79343			−0.160733			−0.0803663	+	0.996765i	$0.525609\pi$
$558$	13.7102	−	24.7981i	0.580400	−	1.04979i
$559$	−34.0061			−1.43830
$560$	−6.71438	−	20.6647i	−0.283734	−	0.873245i
$561$	−5.13926	+	1.09238i	−0.216980	+	0.0461204i
$562$	−14.0207	+	10.1867i	−0.591429	+	0.429698i
$563$	4.48909	−	7.77534i	0.189193	−	0.327691i	−0.755789	−	0.654816i	$-0.772746\pi$
$563$	4.48909	−	7.77534i	0.189193	−	0.327691i	0.944981	+	0.327124i	$0.106080\pi$
$564$	1.50279	+	2.60291i	0.0632789	+	0.109602i
$565$	−3.59082	−	1.59874i	−0.151067	−	0.0672593i
$566$	−15.1678	−	11.0200i	−0.637549	−	0.463206i
$567$	23.2514	−	10.3522i	0.976467	−	0.434751i
$568$	−9.39558	−	1.99709i	−0.394230	−	0.0837961i
$569$	−0.992559	−	9.44356i	−0.0416102	−	0.395895i	−0.995428	−	0.0955104i	$-0.969552\pi$
$569$	−0.992559	−	9.44356i	−0.0416102	−	0.395895i	0.953818	−	0.300384i	$-0.0971150\pi$
$570$	1.07370	−	1.19246i	0.0449723	−	0.0499468i
$571$	4.28803	+	4.76234i	0.179449	+	0.199298i	0.826158	−	0.563439i	$-0.190522\pi$
$571$	4.28803	+	4.76234i	0.179449	+	0.199298i	−0.646709	+	0.762737i	$0.723855\pi$
$572$	−1.43193	+	13.6239i	−0.0598719	+	0.569644i
$573$	1.79394	−	5.52118i	0.0749429	−	0.230651i
$574$	10.0722	−	30.9991i	0.420407	−	1.29388i
$575$	−1.31245	+	12.4871i	−0.0547328	+	0.520748i
$576$	5.36093	+	5.95391i	0.223372	+	0.248080i
$577$	5.26953	−	5.85240i	0.219373	−	0.243639i	−0.623406	−	0.781899i	$-0.714251\pi$
$577$	5.26953	−	5.85240i	0.219373	−	0.243639i	0.842779	+	0.538260i	$0.180918\pi$
$578$	2.92425	+	27.8224i	0.121633	+	1.15726i
$579$	−6.61523	−	1.40611i	−0.274920	−	0.0584360i
$580$	2.15475	−	0.959358i	0.0894712	−	0.0398352i
$581$	31.6428	+	22.9899i	1.31277	+	0.953781i
$582$	6.99982	+	3.11652i	0.290152	+	0.129184i
$583$	−12.0332	−	20.8422i	−0.498366	−	0.863196i
$584$	2.24303	−	3.88505i	0.0928174	−	0.160764i
$585$	−13.9294	+	10.1203i	−0.575912	+	0.418424i
$586$	−38.4941	+	8.18217i	−1.59018	+	0.338002i
$587$	14.2389	+	43.8227i	0.587701	+	1.80876i	0.588144	+	0.808756i	$0.299859\pi$
$587$	14.2389	+	43.8227i	0.587701	+	1.80876i	−0.000443412		1.00000i	$0.500141\pi$
$588$	4.92922			0.203278
$589$	7.37590	+	3.12132i	0.303919	+	0.128612i
$590$	4.87331			0.200631
$591$	3.61149	+	11.1150i	0.148557	+	0.457211i
$592$	21.2330	−	4.51322i	0.872672	−	0.185492i
$593$	−6.95156	+	5.05060i	−0.285466	+	0.207403i	−0.721298	−	0.692625i	$-0.756454\pi$
$593$	−6.95156	+	5.05060i	−0.285466	+	0.207403i	0.435832	+	0.900028i	$0.356454\pi$
$594$	4.93188	−	8.54227i	0.202358	−	0.350494i
$595$	12.7720	+	22.1218i	0.523602	+	0.906905i
$596$	4.96769	+	2.21176i	0.203485	+	0.0905971i
$597$	−2.66549	−	1.93659i	−0.109091	−	0.0792594i
$598$	−31.0612	+	13.8294i	−1.27019	+	0.565524i
$599$	24.8519	+	5.28244i	1.01542	+	0.215835i	0.685422	−	0.728146i	$-0.259618\pi$
$599$	24.8519	+	5.28244i	1.01542	+	0.215835i	0.330000	+	0.943981i	$0.392951\pi$
$600$	0.197299	+	1.87717i	0.00805468	+	0.0766352i
$601$	−16.8390	+	18.7016i	−0.686878	+	0.762855i	−0.981230	−	0.192842i	$-0.938230\pi$
$601$	−16.8390	+	18.7016i	−0.686878	+	0.762855i	0.294352	+	0.955697i	$0.404896\pi$
$602$	−30.3142	−	33.6673i	−1.23551	−	1.37218i
$603$	0.828922	−	7.88667i	0.0337563	−	0.321170i
$604$	−3.90007	+	12.0032i	−0.158692	+	0.488403i
$605$	−2.81813	+	8.67330i	−0.114573	+	0.352620i
$606$	0.154369	−	1.46873i	0.00627082	−	0.0596629i
$607$	6.28113	+	6.97590i	0.254943	+	0.283143i	0.857007	−	0.515305i	$-0.172321\pi$
$607$	6.28113	+	6.97590i	0.254943	+	0.283143i	−0.602064	+	0.798448i	$0.705655\pi$
$608$	−6.53118	+	7.25361i	−0.264874	+	0.294173i
$609$	−0.267455	−	2.54467i	−0.0108378	−	0.103115i
$610$	−5.85785	−	1.24512i	−0.237177	−	0.0504136i
$611$	20.0294	−	8.91768i	0.810304	−	0.360771i
$612$	−17.9501	−	13.0415i	−0.725590	−	0.527172i
$613$	10.4929	+	4.67176i	0.423806	+	0.188691i	0.607546	−	0.794284i	$-0.292154\pi$
$613$	10.4929	+	4.67176i	0.423806	+	0.188691i	−0.183740	+	0.982975i	$0.558821\pi$
$614$	15.0248	+	26.0237i	0.606352	+	1.05023i
$615$	1.42258	−	2.46398i	0.0573639	−	0.0993572i
$616$	5.98295	−	4.34687i	0.241060	−	0.175140i
$617$	2.20415	−	0.468506i	0.0887357	−	0.0188613i	−0.163330	−	0.986572i	$-0.552223\pi$
$617$	2.20415	−	0.468506i	0.0887357	−	0.0188613i	0.252066	+	0.967710i	$0.418890\pi$
$618$	−5.22695	−	16.0869i	−0.210259	−	0.647110i
$619$	23.6684			0.951314			0.475657	−	0.879631i	$-0.342210\pi$
$619$	23.6684			0.951314			0.475657	+	0.879631i	$0.342210\pi$
$620$	−8.66675	+	4.05298i	−0.348065	+	0.162771i
$621$	10.1786			0.408455
$622$	5.93803	+	18.2754i	0.238093	+	0.732776i
$623$	9.86529	−	2.09693i	0.395245	−	0.0840118i
$624$	−10.0970	+	7.33594i	−0.404205	+	0.293672i
$625$	−2.62956	+	4.55454i	−0.105183	+	0.182182i
$626$	29.6437	+	51.3444i	1.18480	+	2.05214i
$627$	1.21827	+	0.542407i	0.0486528	+	0.0216616i
$628$	5.96115	+	4.33103i	0.237876	+	0.172827i
$629$	−23.3133	+	10.3798i	−0.929562	+	0.413868i
$630$	−22.4367	−	4.76907i	−0.893900	−	0.190004i
$631$	3.62734	+	34.5119i	0.144402	+	1.37390i	0.791351	+	0.611362i	$0.209378\pi$
$631$	3.62734	+	34.5119i	0.144402	+	1.37390i	−0.646949	+	0.762534i	$0.723955\pi$
$632$	8.01963	−	8.90670i	0.319004	−	0.354290i
$633$	−6.47052	−	7.18624i	−0.257180	−	0.285627i
$634$	4.89584	−	46.5808i	0.194439	−	1.84996i
$635$	3.57852	−	11.0136i	0.142009	−	0.437059i
$636$	−2.84703	+	8.76226i	−0.112892	+	0.347446i
$637$	3.75858	−	35.7605i	0.148920	−	1.41688i
$638$	3.15481	+	3.50377i	0.124900	+	0.138716i
$639$	−16.5679	+	18.4005i	−0.655415	+	0.727912i
$640$	1.03256	+	9.82418i	0.0408156	+	0.388335i
$641$	−25.8160	−	5.48736i	−1.01967	−	0.216738i	−0.332400	−	0.943139i	$-0.607858\pi$
$641$	−25.8160	−	5.48736i	−1.01967	−	0.216738i	−0.687271	+	0.726401i	$0.741192\pi$
$642$	−9.76991	+	4.34984i	−0.385588	+	0.171675i
$643$	−9.33144	−	6.77969i	−0.367996	−	0.267365i	0.388383	−	0.921498i	$-0.373034\pi$
$643$	−9.33144	−	6.77969i	−0.367996	−	0.267365i	−0.756379	+	0.654133i	$0.773034\pi$
$644$	−17.2045	−	7.65994i	−0.677953	−	0.301844i
$645$	−1.97728	−	3.42475i	−0.0778554	−	0.134849i
$646$	7.54198	−	13.0631i	0.296735	−	0.513961i
$647$	−34.8256	+	25.3023i	−1.36914	+	0.994736i	−0.371332	+	0.928500i	$0.621099\pi$
$647$	−34.8256	+	25.3023i	−1.36914	+	0.994736i	−0.997804	+	0.0662355i	$0.978901\pi$
$648$	−7.11637	+	1.51263i	−0.279557	+	0.0594217i
$649$	1.25154	+	3.85186i	0.0491274	+	0.151199i
$650$	−33.9787			−1.33276
$651$	1.27620	+	10.3002i	0.0500182	+	0.403696i
$652$	0.788169			0.0308671
$653$	−14.7595	−	45.4249i	−0.577582	−	1.77762i	−0.627213	−	0.778848i	$-0.715805\pi$
$653$	−14.7595	−	45.4249i	−0.577582	−	1.77762i	0.0496311	−	0.998768i	$-0.484195\pi$
$654$	1.25915	−	0.267640i	0.0492365	−	0.0104655i
$655$	11.2253	−	8.15565i	0.438608	−	0.318668i
$656$	−11.3751	+	19.7022i	−0.444121	+	0.769241i
$657$	−5.78193	−	10.0146i	−0.225574	−	0.390706i
$658$	26.6838	+	11.8804i	1.04024	+	0.463146i
$659$	18.4987	+	13.4401i	0.720607	+	0.523552i	0.886578	−	0.462579i	$-0.153076\pi$
$659$	18.4987	+	13.4401i	0.720607	+	0.523552i	−0.165971	+	0.986131i	$0.553076\pi$
$660$	−1.45532	+	0.647951i	−0.0566483	+	0.0252214i
$661$	19.4694	+	4.13835i	0.757273	+	0.160963i	0.570339	−	0.821409i	$-0.306812\pi$
$661$	19.4694	+	4.13835i	0.757273	+	0.160963i	0.186933	+	0.982373i	$0.440145\pi$
$662$	−6.36581	−	60.5666i	−0.247414	−	2.35399i
$663$	9.81779	−	10.9038i	0.381291	−	0.423467i
$664$	−7.48107	−	8.30857i	−0.290322	−	0.322435i
$665$	0.677705	−	6.44793i	0.0262803	−	0.250040i
$666$	7.08143	−	21.7944i	0.274400	−	0.844516i
$667$	−1.50346	+	4.62717i	−0.0582141	+	0.179165i
$668$	−0.297246	+	2.82811i	−0.0115008	+	0.109423i
$669$	2.35889	+	2.61981i	0.0911998	+	0.101288i
$670$	−4.30936	+	4.78603i	−0.166485	+	0.184901i
$671$	−0.520245	−	4.94980i	−0.0200838	−	0.191085i
$672$	−12.3723	−	2.62982i	−0.477273	−	0.101448i
$673$	15.9204	−	7.08821i	0.613686	−	0.273230i	−0.0762642	−	0.997088i	$-0.524299\pi$
$673$	15.9204	−	7.08821i	0.613686	−	0.273230i	0.689950	+	0.723857i	$0.257633\pi$
$674$	5.91359	+	4.29648i	0.227783	+	0.165494i
$675$	9.29262	+	4.13734i	0.357673	+	0.159246i
$676$	−9.87655	−	17.1067i	−0.379867	−	0.657949i
$677$	−15.9129	+	27.5619i	−0.611581	+	1.05929i	0.379393	+	0.925236i	$0.376133\pi$
$677$	−15.9129	+	27.5619i	−0.611581	+	1.05929i	−0.990974	+	0.134054i	$0.957200\pi$
$678$	−2.43340	+	1.76797i	−0.0934540	+	0.0678983i
$679$	30.2827	−	6.43679i	1.16214	−	0.247021i
$680$	−2.25635	−	6.94434i	−0.0865272	−	0.266303i
$681$	−4.50408			−0.172597
$682$	−13.0585	−	13.9727i	−0.500035	−	0.535042i
$683$	19.9935			0.765031			0.382515	−	0.923949i	$-0.375058\pi$
$683$	19.9935			0.765031			0.382515	+	0.923949i	$0.375058\pi$
$684$	1.74023	+	5.35589i	0.0665395	+	0.204788i
$685$	18.6450	−	3.96311i	0.712387	−	0.151423i
$686$	−0.359828	+	0.261431i	−0.0137383	+	0.00998147i
$687$	−4.48266	+	7.76420i	−0.171024	+	0.296223i
$688$	15.8105	+	27.3846i	0.602770	+	1.04403i
$689$	61.3974	+	27.3359i	2.33906	+	1.04141i
$690$	−3.19881	−	2.32407i	−0.121777	−	0.0884758i
$691$	−13.0267	+	5.79988i	−0.495561	+	0.220638i	−0.639270	−	0.768982i	$-0.720764\pi$
$691$	−13.0267	+	5.79988i	−0.495561	+	0.220638i	0.143710	+	0.989620i	$0.454097\pi$
$692$	5.64883	+	1.20070i	0.214736	+	0.0456436i
$693$	−1.99264	−	18.9587i	−0.0756942	−	0.720182i
$694$	16.9417	−	18.8157i	0.643100	−	0.714235i
$695$	−8.24726	−	9.15952i	−0.312837	−	0.347440i
$696$	−0.0764515	+	0.727388i	−0.00289789	+	0.0275716i
$697$	8.26480	−	25.4364i	0.313052	−	0.963473i
$698$	2.11826	−	6.51934i	0.0801773	−	0.246760i
$699$	−0.712344	+	6.77750i	−0.0269433	+	0.256349i
$700$	−12.5934	−	13.9863i	−0.475984	−	0.528634i
$701$	−31.1448	+	34.5898i	−1.17632	+	1.30644i	−0.233802	+	0.972284i	$0.575117\pi$
$701$	−31.1448	+	34.5898i	−1.17632	+	1.30644i	−0.942519	+	0.334153i	$0.891550\pi$
$702$	2.87928	+	27.3946i	0.108672	+	1.03394i
$703$	6.33569	+	1.34669i	0.238955	+	0.0507915i
$704$	4.93994	−	2.19940i	0.186181	−	0.0828932i
$705$	2.06271	+	1.49865i	0.0776861	+	0.0564423i
$706$	26.1844	+	11.6581i	0.985464	+	0.438757i
$707$	−2.98353	−	5.16762i	−0.112207	−	0.194348i
$708$	0.775231	−	1.34274i	0.0291350	−	0.0504632i
$709$	−17.9815	+	13.0643i	−0.675309	+	0.490640i	−0.871798	−	0.489866i	$-0.837046\pi$
$709$	−17.9815	+	13.0643i	−0.675309	+	0.490640i	0.196489	+	0.980506i	$0.437046\pi$
$710$	19.6690	−	4.18078i	0.738166	−	0.156902i
$711$	−9.54690	−	29.3823i	−0.358037	−	1.10192i
$712$	−2.88297			−0.108044
$713$	5.74931	−	18.8793i	0.215313	−	0.707037i
$714$	19.5471			0.731531
$715$	3.59105	+	11.0521i	0.134298	+	0.413326i
$716$	5.51834	−	1.17296i	0.206230	−	0.0438355i
$717$	3.97976	−	2.89147i	0.148627	−	0.107984i
$718$	−4.96722	+	8.60348i	−0.185375	+	0.321079i
$719$	−22.0457	−	38.1842i	−0.822165	−	1.42403i	−0.904067	−	0.427391i	$-0.859433\pi$
$719$	−22.0457	−	38.1842i	−0.822165	−	1.42403i	0.0819018	−	0.996640i	$-0.473901\pi$
$720$	14.6260	+	6.51191i	0.545079	+	0.242685i
$721$	−55.2914	−	40.1716i	−2.05916	−	1.49607i
$722$	28.6172	−	12.7412i	1.06502	−	0.474178i
$723$	3.25782	+	0.692471i	0.121160	+	0.0257533i
$724$	−0.951754	−	9.05533i	−0.0353717	−	0.336539i
$725$	−3.25341	+	3.61327i	−0.120828	+	0.134194i
$726$	4.66961	+	5.18613i	0.173306	+	0.192475i
$727$	−4.07768	+	38.7965i	−0.151233	+	1.43888i	0.611025	+	0.791611i	$0.290757\pi$
$727$	−4.07768	+	38.7965i	−0.151233	+	1.43888i	−0.762258	+	0.647273i	$0.775909\pi$
$728$	−6.38186	+	19.6414i	−0.236528	+	0.727957i
$729$	−4.46591	+	13.7447i	−0.165404	+	0.509062i
$730$	−0.981658	+	9.33985i	−0.0363328	+	0.345683i
$731$	−24.8744	−	27.6258i	−0.920013	−	1.02178i
$732$	−1.27492	+	1.41594i	−0.0471222	+	0.0523345i
$733$	−0.711951	−	6.77377i	−0.0262965	−	0.250195i	−0.999771	−	0.0213991i	$-0.993188\pi$
$733$	−0.711951	−	6.77377i	−0.0262965	−	0.250195i	0.973474	−	0.228796i	$-0.0734787\pi$
$734$	−26.6415	−	5.66283i	−0.983356	−	0.209019i
$735$	3.81998	−	1.70076i	0.140902	−	0.0627336i
$736$	19.4580	+	14.1370i	0.717230	+	0.521098i
$737$	−4.88958	−	2.17698i	−0.180110	−	0.0801902i
$738$	12.0084	+	20.7991i	0.442035	+	0.765627i
$739$	16.6002	−	28.7524i	0.610649	−	1.05767i	−0.380482	−	0.924788i	$-0.624242\pi$
$739$	16.6002	−	28.7524i	0.610649	−	1.05767i	0.991131	−	0.132887i	$-0.0424246\pi$
$740$	−6.25985	+	4.54805i	−0.230117	+	0.167190i
$741$	−3.64270	+	0.774280i	−0.133818	+	0.0284439i
$742$	27.6682	+	85.1540i	1.01573	+	3.12610i
$743$	22.5011			0.825484			0.412742	−	0.910848i	$-0.364571\pi$
$743$	22.5011			0.825484			0.412742	+	0.910848i	$0.364571\pi$
$744$	0.255324	−	2.95579i	0.00936063	−	0.108364i
$745$	4.61293			0.169005
$746$	−13.6332	−	41.9586i	−0.499146	−	1.53621i
$747$	−28.1899	+	5.99195i	−1.03142	+	0.219234i
$748$	−12.1152	+	8.80219i	−0.442975	+	0.321840i
$749$	−21.6055	+	37.4218i	−0.789448	+	1.36736i
$750$	−4.76442	−	8.25222i	−0.173972	−	0.301328i
$751$	5.85996	+	2.60902i	0.213833	+	0.0952046i	0.510858	−	0.859665i	$-0.329328\pi$
$751$	5.85996	+	2.60902i	0.213833	+	0.0952046i	−0.297025	+	0.954870i	$0.595994\pi$
$752$	−16.4936	−	11.9833i	−0.601460	−	0.436986i
$753$	−13.3744	+	5.95465i	−0.487389	+	0.216999i
$754$	−12.8787	−	2.73746i	−0.469016	−	0.0996925i
$755$	1.11912	+	10.6477i	0.0407290	+	0.387510i
$756$	−10.2090	+	11.3383i	−0.371299	+	0.412369i
$757$	−17.3130	−	19.2280i	−0.629252	−	0.698855i	0.341244	−	0.939975i	$-0.389152\pi$
$757$	−17.3130	−	19.2280i	−0.629252	−	0.698855i	−0.970495	+	0.241120i	$0.922485\pi$
$758$	−4.27936	+	40.7154i	−0.155433	+	1.47885i
$759$	1.01544	−	3.12519i	0.0368580	−	0.113437i
$760$	−0.572695	+	1.76257i	−0.0207738	+	0.0639352i
$761$	4.67583	−	44.4875i	0.169499	−	1.61267i	−0.497398	−	0.867522i	$-0.665711\pi$
$761$	4.67583	−	44.4875i	0.169499	−	1.61267i	0.666897	−	0.745150i	$-0.267622\pi$
$762$	−5.92958	−	6.58546i	−0.214806	−	0.238566i
$763$	3.48030	−	3.86526i	0.125995	−	0.139932i
$764$	−1.72956	−	16.4557i	−0.0625734	−	0.595346i
$765$	−18.4105	−	3.91328i	−0.665634	−	0.141485i
$766$	40.2255	−	17.9096i	1.45341	−	0.647098i
$767$	−9.15016	−	6.64798i	−0.330393	−	0.240045i
$768$	9.56308	+	4.25776i	0.345078	+	0.153639i
$769$	−6.34376	−	10.9877i	−0.228762	−	0.396227i	0.728680	−	0.684855i	$-0.240134\pi$
$769$	−6.34376	−	10.9877i	−0.228762	−	0.396227i	−0.957441	+	0.288628i	$0.906801\pi$
$770$	−7.74083	+	13.4075i	−0.278960	+	0.483173i
$771$	9.67486	−	7.02920i	0.348432	−	0.253150i
$772$	−18.8548	+	4.00771i	−0.678598	+	0.144241i
$773$	2.84535	+	8.75710i	0.102340	+	0.314971i	0.989097	−	0.147265i	$-0.0470471\pi$
$773$	2.84535	+	8.75710i	0.102340	+	0.314971i	−0.886757	+	0.462236i	$0.847047\pi$
$774$	33.3816			1.19988
$775$	12.9228	−	14.8990i	0.464201	−	0.535189i
$776$	−8.84964			−0.317683
$777$	2.59381	+	7.98293i	0.0930524	+	0.286386i
$778$	30.8646	−	6.56048i	1.10655	−	0.235205i
$779$	−5.49191	+	3.99011i	−0.196768	+	0.142960i
$780$	2.22436	−	3.85271i	0.0796450	−	0.137949i
$781$	8.35581	+	14.4727i	0.298994	+	0.517873i
$782$	−33.9550	−	15.1178i	−1.21423	−	0.540610i
$783$	3.18880	+	2.31680i	0.113959	+	0.0827958i
$784$	−30.5448	+	13.5994i	−1.09089	+	0.485694i
$785$	6.11405	+	1.29958i	0.218220	+	0.0463841i
$786$	−1.10985	−	10.5596i	−0.0395872	−	0.376647i
$787$	−31.2854	+	34.7460i	−1.11521	+	1.23856i	−0.146803	+	0.989166i	$0.546898\pi$
$787$	−31.2854	+	34.7460i	−1.11521	+	1.23856i	−0.968402	+	0.249395i	$0.919768\pi$
$788$	22.2891	+	24.7545i	0.794015	+	0.881843i
$789$	−0.205876	+	1.95878i	−0.00732938	+	0.0697344i
$790$	−7.75328	+	23.8621i	−0.275849	+	0.848977i
$791$	−3.75553	+	11.5583i	−0.133531	+	0.410967i
$792$	−0.569592	+	5.41931i	−0.0202396	+	0.192567i
$793$	9.30019	+	10.3289i	0.330259	+	0.366790i
$794$	12.4069	−	13.7793i	0.440305	−	0.489008i
$795$	0.816952	+	7.77278i	0.0289743	+	0.275672i
$796$	−9.18543	−	1.95242i	−0.325569	−	0.0692018i
$797$	−0.328857	+	0.146417i	−0.0116487	+	0.00518634i	−0.412553	−	0.910934i	$-0.635363\pi$
$797$	−0.328857	+	0.146417i	−0.0116487	+	0.00518634i	0.400904	+	0.916120i	$0.368696\pi$
$798$	−4.01380	−	2.91619i	−0.142087	−	0.103232i
$799$	21.8955	+	9.74849i	0.774606	+	0.344877i
$800$	12.0179	+	20.8156i	0.424896	+	0.735942i
$801$	−3.71576	+	6.43588i	−0.131290	+	0.227401i
$802$	−42.7400	+	31.0525i	−1.50920	+	1.09650i
$803$	−7.63431	+	1.62272i	−0.269409	+	0.0572646i
$804$	0.633171	+	1.94870i	0.0223302	+	0.0687254i
$805$	−15.9759			−0.563075
$806$	52.4378	+	10.1331i	1.84704	+	0.356922i
$807$	6.36789			0.224160
$808$	0.527081	+	1.62219i	0.0185426	+	0.0570684i
$809$	28.0935	−	5.97145i	0.987713	−	0.209945i	0.314391	−	0.949294i	$-0.398200\pi$
$809$	28.0935	−	5.97145i	0.987713	−	0.209945i	0.673323	+	0.739349i	$0.264867\pi$
$810$	12.3217	−	8.95225i	0.432941	−	0.314550i
$811$	9.95675	−	17.2456i	0.349629	−	0.605575i	−0.636555	−	0.771232i	$-0.719641\pi$
$811$	9.95675	−	17.2456i	0.349629	−	0.605575i	0.986183	+	0.165657i	$0.0529744\pi$
$812$	−3.64639	−	6.31573i	−0.127963	−	0.221639i
$813$	−1.51572	−	0.674842i	−0.0531586	−	0.0236677i
$814$	−12.5129	−	9.09117i	−0.438578	−	0.318646i
$815$	0.610804	−	0.271947i	0.0213955	−	0.00952590i
$816$	−13.3452	−	2.83662i	−0.467177	−	0.0993015i
$817$	0.986262	+	9.38366i	0.0345049	+	0.328293i
$818$	28.4873	−	31.6384i	0.996037	−	1.10621i
$819$	35.6215	+	39.5617i	1.24472	+	1.38240i
$820$	0.847651	−	8.06486i	0.0296013	−	0.281637i
$821$	14.2250	−	43.7800i	0.496456	−	1.52793i	−0.318220	−	0.948017i	$-0.603085\pi$
$821$	14.2250	−	43.7800i	0.496456	−	1.52793i	0.814676	−	0.579917i	$-0.196915\pi$
$822$	4.50745	−	13.8725i	0.157216	−	0.483860i
$823$	1.38296	−	13.1580i	0.0482069	−	0.458658i	−0.943616	−	0.331041i	$-0.892600\pi$
$823$	1.38296	−	13.1580i	0.0482069	−	0.458658i	0.991823	−	0.127618i	$-0.0407331\pi$
$824$	13.0721	+	14.5181i	0.455389	+	0.505761i
$825$	2.19735	−	2.44041i	0.0765020	−	0.0849641i
$826$	−1.57501	−	14.9853i	−0.0548018	−	0.521404i
$827$	−11.1584	−	2.37179i	−0.388015	−	0.0824751i	0.00977360	−	0.999952i	$-0.496889\pi$
$827$	−11.1584	−	2.37179i	−0.388015	−	0.0824751i	−0.397789	+	0.917477i	$0.630222\pi$
$828$	12.6769	−	5.64413i	0.440554	−	0.196147i
$829$	−34.8386	−	25.3118i	−1.21000	−	0.879114i	−0.214766	−	0.976666i	$-0.568899\pi$
$829$	−34.8386	−	25.3118i	−1.21000	−	0.879114i	−0.995230	+	0.0975520i	$0.968899\pi$
$830$	21.3817	+	9.51975i	0.742170	+	0.330435i
$831$	−5.24738	−	9.08873i	−0.182030	−	0.315285i
$832$	−7.55038	+	13.0776i	−0.261762	+	0.453386i
$833$	31.8003	−	23.1043i	1.10182	−	0.800516i
$834$	−9.22561	+	1.96096i	−0.319457	+	0.0679026i
$835$	0.745446	+	2.29425i	0.0257972	+	0.0793957i
$836$	3.80091			0.131457
$837$	−13.1070	−	9.15619i	−0.453046	−	0.316484i
$838$	−62.0578			−2.14375
$839$	13.4023	+	41.2479i	0.462697	+	1.42404i	0.861856	+	0.507153i	$0.169302\pi$
$839$	13.4023	+	41.2479i	0.462697	+	1.42404i	−0.399159	+	0.916882i	$0.630698\pi$
$840$	−2.34915	+	0.499328i	−0.0810535	+	0.0172285i
$841$	21.9373	−	15.9384i	0.756458	−	0.549599i
$842$	8.35115	−	14.4646i	0.287800	−	0.498484i
$843$	2.33868	+	4.05072i	0.0805486	+	0.139514i
$844$	−25.1788	−	11.2103i	−0.866689	−	0.385875i
$845$	−13.5564	−	9.84931i	−0.466355	−	0.338827i
$846$	−19.6616	+	8.75391i	−0.675980	+	0.300966i
$847$	27.5809	+	5.86250i	0.947690	+	0.201438i
$848$	−6.53241	−	62.1518i	−0.224324	−	2.13430i
$849$	−3.38582	+	3.76033i	−0.116201	+	0.129054i
$850$	−24.8544	−	27.6036i	−0.852499	−	0.946796i
$851$	1.66833	−	15.8731i	0.0571897	−	0.544124i
$852$	1.97696	−	6.08446i	0.0677295	−	0.208450i
$853$	2.08658	−	6.42185i	0.0714433	−	0.219880i	−0.908959	−	0.416885i	$-0.863122\pi$
$853$	2.08658	−	6.42185i	0.0714433	−	0.219880i	0.980402	+	0.197005i	$0.0631217\pi$
$854$	−1.93550	+	18.4151i	−0.0662316	+	0.630151i
$855$	3.19660	+	3.55018i	0.109321	+	0.121414i
$856$	8.26495	−	9.17916i	0.282490	−	0.313737i
$857$	2.59713	+	24.7100i	0.0887162	+	0.844078i	0.944889	+	0.327389i	$0.106169\pi$
$857$	2.59713	+	24.7100i	0.0887162	+	0.844078i	−0.856173	+	0.516689i	$0.827164\pi$
$858$	8.69831	+	1.84888i	0.296956	+	0.0631198i
$859$	1.45973	−	0.649912i	0.0498052	−	0.0221747i	−0.381683	−	0.924293i	$-0.624655\pi$
$859$	1.45973	−	0.649912i	0.0498052	−	0.0221747i	0.431488	+	0.902119i	$0.357989\pi$
$860$	−9.11869	−	6.62511i	−0.310945	−	0.225915i
$861$	−8.03641	−	3.57804i	−0.273880	−	0.121939i
$862$	10.4599	+	18.1171i	0.356266	+	0.617072i
$863$	15.3856	−	26.6487i	0.523734	−	0.907133i	−0.475885	−	0.879508i	$-0.657872\pi$
$863$	15.3856	−	26.6487i	0.523734	−	0.907133i	0.999618	−	0.0276255i	$-0.00879457\pi$
$864$	15.7637	−	11.4530i	0.536292	−	0.389639i
$865$	4.79193	−	1.01856i	0.162930	−	0.0346319i
$866$	−5.20536	−	16.0204i	−0.176885	−	0.544397i
$867$	7.55038			0.256424
$868$	15.2638	+	25.3400i	0.518086	+	0.860097i
$869$	−20.8518			−0.707348
$870$	−0.473144	−	1.45619i	−0.0160411	−	0.0493694i
$871$	14.6202	−	3.10762i	0.495387	−	0.105298i
$872$	−1.20281	+	0.873895i	−0.0407324	+	0.0295938i
$873$	−11.4060	+	19.7557i	−0.386033	+	0.668630i
$874$	4.71693	+	8.16997i	0.159553	+	0.276353i
$875$	−35.1726	−	15.6598i	−1.18905	−	0.529399i
$876$	2.41724	+	1.75623i	0.0816710	+	0.0593374i
$877$	7.61062	−	3.38847i	0.256992	−	0.114420i	−0.274197	−	0.961674i	$-0.588412\pi$
$877$	7.61062	−	3.38847i	0.256992	−	0.114420i	0.531189	+	0.847253i	$0.321745\pi$
$878$	−71.6766	−	15.2353i	−2.41897	−	0.514168i
$879$	1.11023	+	10.5631i	0.0374471	+	0.356286i
$880$	7.23051	−	8.03029i	0.243740	−	0.270701i
$881$	14.6295	+	16.2477i	0.492879	+	0.547398i	0.937347	−	0.348397i	$-0.113274\pi$
$881$	14.6295	+	16.2477i	0.492879	+	0.547398i	−0.444468	+	0.895795i	$0.646607\pi$
$882$	−3.68955	+	35.1037i	−0.124234	+	1.18200i
$883$	−3.85357	+	11.8601i	−0.129683	+	0.399123i	−0.994725	−	0.102576i	$-0.967292\pi$
$883$	−3.85357	+	11.8601i	−0.129683	+	0.399123i	0.865042	+	0.501699i	$0.167292\pi$
$884$	12.9229	−	39.7727i	0.434646	−	1.33770i
$885$	0.137483	−	1.30806i	0.00462143	−	0.0439699i
$886$	−31.2705	−	34.7295i	−1.05055	−	1.16676i
$887$	−16.5556	+	18.3868i	−0.555882	+	0.617369i	−0.953942	−	0.299990i	$-0.903017\pi$
$887$	−16.5556	+	18.3868i	−0.555882	+	0.617369i	0.398060	+	0.917359i	$0.369683\pi$
$888$	−0.250799	−	2.38619i	−0.00841625	−	0.0800753i
$889$	−35.0228	−	7.44433i	−1.17463	−	0.249675i
$890$	5.51354	−	2.45478i	0.184814	−	0.0822846i
$891$	10.2403	+	7.43998i	0.343062	+	0.249249i
$892$	9.17915	+	4.08682i	0.307341	+	0.136837i
$893$	−3.04165	−	5.26830i	−0.101785	−	0.176297i
$894$	1.76497	−	3.05702i	0.0590295	−	0.102242i
$895$	3.87181	−	2.81303i	0.129420	−	0.0940293i
$896$	29.8753	−	6.35018i	0.998063	−	0.212145i
$897$	2.83570	+	8.72738i	0.0946812	+	0.291399i
$898$	−3.38940			−0.113106
$899$	6.09837	−	4.60597i	0.203392	−	0.153618i
$900$	13.8676			0.462255
$901$	22.7032	+	69.8734i	0.756354	+	2.32782i
$902$	15.8556	−	3.37021i	0.527933	−	0.112216i
$903$	−9.89194	+	7.18692i	−0.329183	+	0.239166i
$904$	1.73698	−	3.00853i	0.0577710	−	0.100062i
$905$	−3.86200	−	6.68918i	−0.128377	−	0.222356i
$906$	7.48453	+	3.33233i	0.248657	+	0.110709i
$907$	25.4366	+	18.4808i	0.844609	+	0.613644i	0.923654	−	0.383227i	$-0.125187\pi$
$907$	25.4366	+	18.4808i	0.844609	+	0.613644i	−0.0790457	+	0.996871i	$0.525187\pi$
$908$	−11.7277	+	5.22151i	−0.389197	+	0.173282i
$909$	4.30067	+	0.914136i	0.142644	+	0.0303200i
$910$	−4.51918	−	42.9971i	−0.149809	−	1.42534i
$911$	5.60989	−	6.23041i	0.185864	−	0.206423i	−0.643011	−	0.765857i	$-0.722315\pi$
$911$	5.60989	−	6.23041i	0.185864	−	0.206423i	0.828875	+	0.559434i	$0.188982\pi$
$912$	2.31712	+	2.57342i	0.0767276	+	0.0852146i
$913$	−2.03323	+	19.3449i	−0.0672901	+	0.640223i
$914$	−20.5567	+	63.2671i	−0.679956	+	2.09269i
$915$	−0.499465	+	1.53719i	−0.0165118	+	0.0508181i
$916$	−2.67102	+	25.4130i	−0.0882529	+	0.839671i
$917$	−28.7062	−	31.8815i	−0.947963	−	1.05282i
$918$	−20.1487	+	22.3774i	−0.665005	+	0.738563i
$919$	4.19556	+	39.9181i	0.138399	+	1.31678i	0.814584	+	0.580045i	$0.196965\pi$
$919$	4.19556	+	39.9181i	0.138399	+	1.31678i	−0.676186	+	0.736731i	$0.736368\pi$
$920$	4.46687	+	0.949463i	0.147268	+	0.0313029i
$921$	7.40897	−	3.29869i	0.244134	−	0.108695i
$922$	−2.00088	−	1.45373i	−0.0658956	−	0.0478759i
$923$	−42.6340	−	18.9819i	−1.40331	−	0.624796i
$924$	2.46277	+	4.26565i	0.0810193	+	0.140329i
$925$	7.97511	−	13.8133i	0.262220	−	0.454178i
$926$	−17.6128	+	12.7965i	−0.578793	+	0.420518i
$927$	49.2579	−	10.4701i	1.61784	−	0.343883i
$928$	2.87808	+	8.85781i	0.0944775	+	0.290772i
$929$	54.6187			1.79198			0.895991	−	0.444072i	$-0.146467\pi$
$929$	54.6187			1.79198			0.895991	+	0.444072i	$0.146467\pi$
$930$	2.02849	+	5.87020i	0.0665169	+	0.192491i
$931$	−9.97677			−0.326975
$932$	6.00225	+	18.4730i	0.196610	+	0.605104i
$933$	5.07286	−	1.07827i	0.166078	−	0.0353010i
$934$	16.4636	−	11.9615i	0.538705	−	0.391392i
$935$	−6.35176	+	11.0016i	−0.207725	+	0.359790i
$936$	−7.60864	−	13.1785i	−0.248696	−	0.430754i
$937$	−12.2323	−	5.44615i	−0.399611	−	0.177918i	0.197084	−	0.980387i	$-0.436853\pi$
$937$	−12.2323	−	5.44615i	−0.399611	−	0.177918i	−0.596694	+	0.802469i	$0.703520\pi$
$938$	16.1096	+	11.7043i	0.525998	+	0.382160i
$939$	14.6178	−	6.50826i	0.477033	−	0.212389i
$940$	7.10822	+	1.51090i	0.231845	+	0.0492801i
$941$	4.00884	+	38.1416i	0.130685	+	1.24338i	0.841599	+	0.540102i	$0.181614\pi$
$941$	4.00884	+	38.1416i	0.130685	+	1.24338i	−0.710915	+	0.703278i	$0.751719\pi$
$942$	3.20057	−	3.55459i	0.104280	−	0.115815i
$943$	11.1927	+	12.4308i	0.364485	+	0.404801i
$944$	−1.09932	+	10.4593i	−0.0357799	+	0.340423i
$945$	−3.99952	+	12.3093i	−0.130104	+	0.400420i
$946$	6.96229	−	21.4277i	0.226363	−	0.696675i
$947$	−4.54568	+	43.2493i	−0.147715	+	1.40541i	0.629902	+	0.776674i	$0.283095\pi$
$947$	−4.54568	+	43.2493i	−0.147715	+	1.40541i	−0.777617	+	0.628738i	$0.783572\pi$
$948$	5.34134	+	5.93216i	0.173479	+	0.192668i
$949$	14.5842	−	16.1974i	0.473424	−	0.525791i
$950$	0.985469	+	9.37611i	0.0319728	+	0.304201i
$951$	−12.3648	−	2.62821i	−0.400955	−	0.0852257i
$952$	−20.6244	+	9.18256i	−0.668440	+	0.297608i
$953$	32.5345	+	23.6377i	1.05390	+	0.765700i	0.972949	−	0.231018i	$-0.0742057\pi$
$953$	32.5345	+	23.6377i	1.05390	+	0.765700i	0.0809464	+	0.996718i	$0.474206\pi$
$954$	−60.2699	−	26.8339i	−1.95131	−	0.868779i
$955$	−7.01817	−	12.1558i	−0.227103	−	0.393353i
$956$	7.01045	−	12.1424i	0.226734	−	0.392715i
$957$	1.02946	−	0.747945i	0.0332776	−	0.0241776i
$958$	−1.21573	+	0.258410i	−0.0392783	+	0.00834886i
$959$	−18.2123	−	56.0517i	−0.588106	−	1.81001i
$960$	−1.75607			−0.0566768
$961$	−24.3863	+	19.1392i	−0.786655	+	0.617393i
$962$	43.1925			1.39258
$963$	−9.83894	−	30.2811i	−0.317055	−	0.975796i
$964$	9.28546	−	1.97369i	0.299064	−	0.0635681i
$965$	−13.2290	+	9.61143i	−0.425856	+	0.309403i
$966$	−6.11260	+	10.5873i	−0.196670	+	0.340642i
$967$	−21.9360	−	37.9943i	−0.705414	−	1.22181i	−0.966542	−	0.256509i	$-0.917428\pi$
$967$	−21.9360	−	37.9943i	−0.705414	−	1.22181i	0.261128	−	0.965304i	$-0.415906\pi$
$968$	−7.36324	−	3.27833i	−0.236663	−	0.105369i
$969$	−3.29353	−	2.39289i	−0.105803	−	0.0768707i
$970$	16.9245	−	7.53526i	0.543412	−	0.241943i
$971$	−50.3926	−	10.7113i	−1.61718	−	0.343741i	−0.691594	−	0.722287i	$-0.743091\pi$
$971$	−50.3926	−	10.7113i	−1.61718	−	0.343741i	−0.925583	+	0.378545i	$0.876424\pi$
$972$	−1.78815	−	17.0131i	−0.0573549	−	0.545695i
$973$	−25.4997	+	28.3203i	−0.817484	+	0.907908i
$974$	30.4252	+	33.7906i	0.974886	+	1.08272i
$975$	−0.958585	+	9.12033i	−0.0306993	+	0.292084i
$976$	3.99376	−	12.2915i	0.127837	−	0.393442i
$977$	4.44223	−	13.6718i	0.142119	−	0.437399i	−0.854510	−	0.519435i	$-0.826142\pi$
$977$	4.44223	−	13.6718i	0.142119	−	0.437399i	0.996629	+	0.0820365i	$0.0261424\pi$
$978$	0.0534808	−	0.508836i	0.00171013	−	0.0162708i
$979$	3.35622	+	3.72746i	0.107265	+	0.119130i
$980$	7.97476	−	8.85687i	0.254744	−	0.282922i
$981$	0.400601	+	3.81146i	0.0127902	+	0.121691i
$982$	15.6261	+	3.32143i	0.498649	+	0.105991i
$983$	−49.0338	+	21.8312i	−1.56393	+	0.696308i	−0.992261	−	0.124173i	$-0.960372\pi$
$983$	−49.0338	+	21.8312i	−1.56393	+	0.696308i	−0.571674	+	0.820481i	$0.693706\pi$
$984$	2.03434	+	1.47804i	0.0648525	+	0.0471181i
$985$	25.8145	+	11.4933i	0.822517	+	0.366208i
$986$	−7.19655	−	12.4648i	−0.229185	−	0.396960i
$987$	3.94163	−	6.82711i	0.125464	−	0.217309i
$988$	−8.58723	+	6.23898i	−0.273196	+	0.198489i
$989$	22.7416	−	4.83387i	0.723140	−	0.153708i
$990$	−3.52510	−	10.8491i	−0.112035	−	0.344808i
$991$	−35.5382			−1.12891			−0.564453	−	0.825465i	$-0.690913\pi$
$991$	−35.5382			−1.12891			−0.564453	+	0.825465i	$0.690913\pi$
$992$	−12.3391	−	35.7077i	−0.391766	−	1.13372i
$993$	−16.4364			−0.521594
$994$	−19.2126	−	59.1304i	−0.609388	−	1.87550i
$995$	−7.79205	+	1.65625i	−0.247025	+	0.0525067i
$996$	6.02430	−	4.37691i	0.190887	−	0.138688i
$997$	15.2613	−	26.4333i	0.483329	−	0.837151i	−0.516488	−	0.856295i	$-0.672761\pi$
$997$	15.2613	−	26.4333i	0.483329	−	0.837151i	0.999817	+	0.0191440i	$0.00609410\pi$
$998$	28.7674	+	49.8265i	0.910615	+	1.57723i
$999$	−11.8124	−	5.25924i	−0.373729	−	0.166395i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.2.g.a.7.1	✓	16
3.2	odd	2		279.2.y.c.100.2		16
4.3	odd	2		496.2.bg.c.193.1		16
5.2	odd	4		775.2.ck.a.224.4		32
5.3	odd	4		775.2.ck.a.224.1		32
5.4	even	2		775.2.bl.a.751.2		16
31.2	even	5		961.2.g.s.338.2		16
31.3	odd	30		961.2.a.j.1.2		8
31.4	even	5		961.2.g.t.732.2		16
31.5	even	3		961.2.g.k.547.1		16
31.6	odd	6		961.2.d.n.531.2		16
31.7	even	15		961.2.d.p.374.3		16
31.8	even	5		961.2.g.k.448.1		16
31.9	even	15	inner	31.2.g.a.9.1	yes	16
31.10	even	15		961.2.g.t.235.2		16
31.11	odd	30		961.2.g.m.816.2		16
31.12	odd	30		961.2.d.q.388.3		16
31.13	odd	30		961.2.c.i.439.2		16
31.14	even	15		961.2.d.o.628.2		16
31.15	odd	10		961.2.c.i.521.2		16
31.16	even	5		961.2.c.j.521.2		16
31.17	odd	30		961.2.d.n.628.2		16
31.18	even	15		961.2.c.j.439.2		16
31.19	even	15		961.2.d.p.388.3		16
31.20	even	15		961.2.g.s.816.2		16
31.21	odd	30		961.2.g.n.235.2		16
31.22	odd	30		961.2.g.l.846.1		16
31.23	odd	10		961.2.g.j.448.1		16
31.24	odd	30		961.2.d.q.374.3		16
31.25	even	3		961.2.d.o.531.2		16
31.26	odd	6		961.2.g.j.547.1		16
31.27	odd	10		961.2.g.n.732.2		16
31.28	even	15		961.2.a.i.1.2		8
31.29	odd	10		961.2.g.m.338.2		16
31.30	odd	2		961.2.g.l.844.1		16
93.59	odd	30		8649.2.a.bf.1.7		8
93.65	even	30		8649.2.a.be.1.7		8
93.71	odd	30		279.2.y.c.226.2		16
124.71	odd	30		496.2.bg.c.257.1		16
155.9	even	30		775.2.bl.a.226.2		16
155.102	odd	60		775.2.ck.a.474.1		32
155.133	odd	60		775.2.ck.a.474.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.7.1	✓	16	1.1	even	1	trivial
31.2.g.a.9.1	yes	16	31.9	even	15	inner
279.2.y.c.100.2		16	3.2	odd	2
279.2.y.c.226.2		16	93.71	odd	30
496.2.bg.c.193.1		16	4.3	odd	2
496.2.bg.c.257.1		16	124.71	odd	30
775.2.bl.a.226.2		16	155.9	even	30
775.2.bl.a.751.2		16	5.4	even	2
775.2.ck.a.224.1		32	5.3	odd	4
775.2.ck.a.224.4		32	5.2	odd	4
775.2.ck.a.474.1		32	155.102	odd	60
775.2.ck.a.474.4		32	155.133	odd	60
961.2.a.i.1.2		8	31.28	even	15
961.2.a.j.1.2		8	31.3	odd	30
961.2.c.i.439.2		16	31.13	odd	30
961.2.c.i.521.2		16	31.15	odd	10
961.2.c.j.439.2		16	31.18	even	15
961.2.c.j.521.2		16	31.16	even	5
961.2.d.n.531.2		16	31.6	odd	6
961.2.d.n.628.2		16	31.17	odd	30
961.2.d.o.531.2		16	31.25	even	3
961.2.d.o.628.2		16	31.14	even	15
961.2.d.p.374.3		16	31.7	even	15
961.2.d.p.388.3		16	31.19	even	15
961.2.d.q.374.3		16	31.24	odd	30
961.2.d.q.388.3		16	31.12	odd	30
961.2.g.j.448.1		16	31.23	odd	10
961.2.g.j.547.1		16	31.26	odd	6
961.2.g.k.448.1		16	31.8	even	5
961.2.g.k.547.1		16	31.5	even	3
961.2.g.l.844.1		16	31.30	odd	2
961.2.g.l.846.1		16	31.22	odd	30
961.2.g.m.338.2		16	31.29	odd	10
961.2.g.m.816.2		16	31.11	odd	30
961.2.g.n.235.2		16	31.21	odd	30
961.2.g.n.732.2		16	31.27	odd	10
961.2.g.s.338.2		16	31.2	even	5
961.2.g.s.816.2		16	31.20	even	15
961.2.g.t.235.2		16	31.10	even	15
961.2.g.t.732.2		16	31.4	even	5
8649.2.a.be.1.7		8	93.65	even	30
8649.2.a.bf.1.7		8	93.59	odd	30

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	31.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.571745 - 1.75965i) q^{2} +(-0.488442 + 0.103822i) q^{3} +(-1.15144 + 0.836573i) q^{4} +(-0.603681 + 1.04561i) q^{5} +(0.461954 + 0.800128i) q^{6} +(3.41030 + 1.51837i) q^{7} +(-0.863288 - 0.627215i) q^{8} +(-2.51284 + 1.11879i) q^{9} +O(q^{10})\)	\(q+(-0.571745 - 1.75965i) q^{2} +(-0.488442 + 0.103822i) q^{3} +(-1.15144 + 0.836573i) q^{4} +(-0.603681 + 1.04561i) q^{5} +(0.461954 + 0.800128i) q^{6} +(3.41030 + 1.51837i) q^{7} +(-0.863288 - 0.627215i) q^{8} +(-2.51284 + 1.11879i) q^{9} +(2.18505 + 0.464447i) q^{10} +(0.194058 + 1.84634i) q^{11} +(0.475560 - 0.528162i) q^{12} +(-3.46909 - 3.85281i) q^{13} +(0.721967 - 6.86906i) q^{14} +(0.186307 - 0.573393i) q^{15} +(-1.48972 + 4.58490i) q^{16} +(0.592413 - 5.63643i) q^{17} +(3.40538 + 3.78206i) q^{18} +(-0.962535 + 1.06900i) q^{19} +(-0.179621 - 1.70898i) q^{20} +(-1.82338 - 0.387571i) q^{21} +(3.13796 - 1.39711i) q^{22} +(2.86762 + 2.08345i) q^{23} +(0.486785 + 0.216731i) q^{24} +(1.77114 + 3.06770i) q^{25} +(-4.79617 + 8.30721i) q^{26} +(2.32318 - 1.68789i) q^{27} +(-5.19700 + 1.10466i) q^{28} +(0.424157 + 1.30542i) q^{29} -1.11549 q^{30} +(-1.81847 - 5.26243i) q^{31} +6.78540 q^{32} +(-0.286476 - 0.881683i) q^{33} +(-10.2569 + 2.18016i) q^{34} +(-3.64635 + 2.64923i) q^{35} +(1.95745 - 3.39040i) q^{36} +(-2.25141 - 3.89955i) q^{37} +(2.43140 + 1.08253i) q^{38} +(2.09445 + 1.52171i) q^{39} +(1.17697 - 0.524021i) q^{40} +(4.61599 + 0.981158i) q^{41} +(0.360518 + 3.43010i) q^{42} +(4.38897 - 4.87445i) q^{43} +(-1.76804 - 1.96361i) q^{44} +(0.347141 - 3.30283i) q^{45} +(2.02659 - 6.23721i) q^{46} +(-1.30682 + 4.02199i) q^{47} +(0.251633 - 2.39412i) q^{48} +(4.64083 + 5.15416i) q^{49} +(4.38545 - 4.87053i) q^{50} +(0.295824 + 2.81458i) q^{51} +(7.21762 + 1.53415i) q^{52} +(-11.8426 + 5.27265i) q^{53} +(-4.29836 - 3.12294i) q^{54} +(-2.04769 - 0.911691i) q^{55} +(-1.99173 - 3.44978i) q^{56} +(0.359157 - 0.622078i) q^{57} +(2.05458 - 1.49274i) q^{58} +(2.13389 - 0.453572i) q^{59} +(0.265164 + 0.816089i) q^{60} -2.68087 q^{61} +(-8.22033 + 6.20865i) q^{62} -10.2683 q^{63} +(-0.900071 - 2.77013i) q^{64} +(6.12274 - 1.30143i) q^{65} +(-1.38766 + 1.00820i) q^{66} +(-1.44150 + 2.49675i) q^{67} +(4.03315 + 6.98563i) q^{68} +(-1.61697 - 0.719924i) q^{69} +(6.74649 + 4.90161i) q^{70} +(8.22340 - 3.66129i) q^{71} +(2.87102 + 0.610255i) q^{72} +(0.439443 + 4.18102i) q^{73} +(-5.57462 + 6.19124i) q^{74} +(-1.18359 - 1.31451i) q^{75} +(0.214006 - 2.03613i) q^{76} +(-2.14162 + 6.59123i) q^{77} +(1.48018 - 4.55554i) q^{78} +(-1.17403 + 11.1702i) q^{79} +(-3.89468 - 4.32548i) q^{80} +(4.56212 - 5.06675i) q^{81} +(-0.912672 - 8.68350i) q^{82} +(10.2485 + 2.17838i) q^{83} +(2.42375 - 1.07912i) q^{84} +(5.53585 + 4.02203i) q^{85} +(-11.0867 - 4.93612i) q^{86} +(-0.342708 - 0.593587i) q^{87} +(0.990524 - 1.71564i) q^{88} +(2.18575 - 1.58804i) q^{89} +(-6.01030 + 1.27753i) q^{90} +(-5.98067 - 18.4066i) q^{91} -5.04486 q^{92} +(1.43457 + 2.38160i) q^{93} +7.82446 q^{94} +(-0.536692 - 1.65177i) q^{95} +(-3.31428 + 0.704471i) q^{96} +(6.70942 - 4.87468i) q^{97} +(6.41615 - 11.1131i) q^{98} +(-2.55330 - 4.42244i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9	\( 16 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9} - 2 q^{10} - 7 q^{11} + 5 q^{12} - 7 q^{13} - 6 q^{14} + 14 q^{15} - 2 q^{16} - 6 q^{17} - 3 q^{18} + 16 q^{19} + 37 q^{20} + 9 q^{21} + 9 q^{22} + q^{23} - 20 q^{24} - 13 q^{25} + 9 q^{26} + 9 q^{27} - 30 q^{28} - 14 q^{29} - 22 q^{30} + 15 q^{31} - 42 q^{32} - 13 q^{33} - 32 q^{34} - 9 q^{35} + q^{36} - 8 q^{37} + 8 q^{38} - 3 q^{39} - q^{40} - 8 q^{41} + 69 q^{42} + 23 q^{43} + 39 q^{44} + 65 q^{45} + 34 q^{46} + 14 q^{47} + 34 q^{48} + 2 q^{49} + 3 q^{50} - 42 q^{51} + 29 q^{52} + 6 q^{53} - 46 q^{54} - 7 q^{55} - 30 q^{56} - 17 q^{57} - 15 q^{58} + 4 q^{59} - 75 q^{60} - 60 q^{61} - 25 q^{62} - 46 q^{63} + 23 q^{64} - 12 q^{65} - 30 q^{66} + 13 q^{67} + 30 q^{68} + 38 q^{69} + 12 q^{70} - 14 q^{71} + 37 q^{72} + 2 q^{73} + 13 q^{74} + 13 q^{75} - 12 q^{76} + 18 q^{77} - 15 q^{78} + 18 q^{79} + 36 q^{80} + 23 q^{81} + 14 q^{82} - 16 q^{83} + 8 q^{84} + 37 q^{85} - 26 q^{86} + 15 q^{87} - 17 q^{88} + q^{89} - 23 q^{90} + 8 q^{91} - 64 q^{92} + 17 q^{93} + 44 q^{94} - 22 q^{95} + 8 q^{96} + 3 q^{97} - 10 q^{98} + 6 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9 - 2 * q^10 - 7 * q^11 + 5 * q^12 - 7 * q^13 - 6 * q^14 + 14 * q^15 - 2 * q^16 - 6 * q^17 - 3 * q^18 + 16 * q^19 + 37 * q^20 + 9 * q^21 + 9 * q^22 + q^23 - 20 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 - 30 * q^28 - 14 * q^29 - 22 * q^30 + 15 * q^31 - 42 * q^32 - 13 * q^33 - 32 * q^34 - 9 * q^35 + q^36 - 8 * q^37 + 8 * q^38 - 3 * q^39 - q^40 - 8 * q^41 + 69 * q^42 + 23 * q^43 + 39 * q^44 + 65 * q^45 + 34 * q^46 + 14 * q^47 + 34 * q^48 + 2 * q^49 + 3 * q^50 - 42 * q^51 + 29 * q^52 + 6 * q^53 - 46 * q^54 - 7 * q^55 - 30 * q^56 - 17 * q^57 - 15 * q^58 + 4 * q^59 - 75 * q^60 - 60 * q^61 - 25 * q^62 - 46 * q^63 + 23 * q^64 - 12 * q^65 - 30 * q^66 + 13 * q^67 + 30 * q^68 + 38 * q^69 + 12 * q^70 - 14 * q^71 + 37 * q^72 + 2 * q^73 + 13 * q^74 + 13 * q^75 - 12 * q^76 + 18 * q^77 - 15 * q^78 + 18 * q^79 + 36 * q^80 + 23 * q^81 + 14 * q^82 - 16 * q^83 + 8 * q^84 + 37 * q^85 - 26 * q^86 + 15 * q^87 - 17 * q^88 + q^89 - 23 * q^90 + 8 * q^91 - 64 * q^92 + 17 * q^93 + 44 * q^94 - 22 * q^95 + 8 * q^96 + 3 * q^97 - 10 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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