LMFDB - Embedded newform 403.2.bl.a.380.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(16,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 6]))

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

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

chi := DirichletCharacter("403.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.bl (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:	$3.21797120146$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 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			380.1
Root			$-0.978148 - 0.207912i$ of defining polynomial
Character	$\chi$	$=$	403.380
Dual form			403.2.bl.a.35.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.373619 - 0.0794152i) q^{2} +(1.49622 - 1.66172i) q^{3} +(-1.69381 + 0.754131i) q^{4} -3.00000 q^{5} +(0.427051 - 0.739674i) q^{6} +(-2.74064 + 1.22021i) q^{7} +(-1.19098 + 0.865300i) q^{8} +(-0.209057 - 1.98904i) q^{9} +O(q^{10})$	\(q+(0.373619 - 0.0794152i) q^{2} +(1.49622 - 1.66172i) q^{3} +(-1.69381 + 0.754131i) q^{4} -3.00000 q^{5} +(0.427051 - 0.739674i) q^{6} +(-2.74064 + 1.22021i) q^{7} +(-1.19098 + 0.865300i) q^{8} +(-0.209057 - 1.98904i) q^{9} +(-1.12086 + 0.238246i) q^{10} +(0.233733 - 2.22382i) q^{11} +(-1.28115 + 3.94298i) q^{12} +(-1.69837 + 3.18049i) q^{13} +(-0.927051 + 0.673542i) q^{14} +(-4.48866 + 4.98517i) q^{15} +(2.10502 - 2.33786i) q^{16} +(0.378188 + 3.59821i) q^{17} +(-0.236068 - 0.726543i) q^{18} +(-4.01478 - 4.45887i) q^{19} +(5.08142 - 2.26239i) q^{20} +(-2.07295 + 6.37988i) q^{21} +(-0.0892780 - 0.849423i) q^{22} +(-7.52402 - 3.34991i) q^{23} +(-0.344086 + 3.27376i) q^{24} +4.00000 q^{25} +(-0.381966 + 1.32317i) q^{26} +(1.80902 + 1.31433i) q^{27} +(3.72191 - 4.13360i) q^{28} +(3.30806 - 0.703150i) q^{29} +(-1.28115 + 2.21902i) q^{30} +(-4.78115 + 2.85317i) q^{31} +(2.07295 - 3.59045i) q^{32} +(-3.34565 - 3.71572i) q^{33} +(0.427051 + 1.31433i) q^{34} +(8.22191 - 3.66063i) q^{35} +(1.85410 + 3.21140i) q^{36} +(-1.54508 - 2.67617i) q^{37} +(-1.85410 - 1.34708i) q^{38} +(2.74395 + 7.58095i) q^{39} +(3.57295 - 2.59590i) q^{40} +(8.14429 - 1.73112i) q^{41} +(-0.267834 + 2.54827i) q^{42} +(1.65418 + 1.83716i) q^{43} +(1.28115 + 3.94298i) q^{44} +(0.627171 + 5.96713i) q^{45} +(-3.07715 - 0.654069i) q^{46} +(-0.145898 - 0.449028i) q^{47} +(-0.735299 - 6.99591i) q^{48} +(1.33826 - 1.48629i) q^{49} +(1.49448 - 0.317661i) q^{50} +(6.54508 + 4.75528i) q^{51} +(0.478211 - 6.66793i) q^{52} +(2.11803 - 1.53884i) q^{53} +(0.780261 + 0.347395i) q^{54} +(-0.701198 + 6.67146i) q^{55} +(2.20820 - 3.82472i) q^{56} -13.4164 q^{57} +(1.18011 - 0.525421i) q^{58} +(-10.9905 - 2.33611i) q^{59} +(3.84346 - 11.8290i) q^{60} +(4.28115 - 7.41517i) q^{61} +(-1.55975 + 1.44569i) q^{62} +(3.00000 + 5.19615i) q^{63} +(-1.45492 + 4.47777i) q^{64} +(5.09512 - 9.54147i) q^{65} +(-1.54508 - 1.12257i) q^{66} +(-3.88197 - 6.72376i) q^{67} +(-3.35410 - 5.80948i) q^{68} +(-16.8242 + 7.49063i) q^{69} +(2.78115 - 2.02063i) q^{70} +(1.40822 + 13.3983i) q^{71} +(1.97010 + 2.18802i) q^{72} +(-8.85410 - 6.43288i) q^{73} +(-0.789802 - 0.877163i) q^{74} +(5.98489 - 6.64689i) q^{75} +(10.1628 + 4.52479i) q^{76} +(2.07295 + 6.37988i) q^{77} +(1.62723 + 2.61448i) q^{78} +(-8.42705 + 6.12261i) q^{79} +(-6.31505 + 7.01357i) q^{80} +(10.7596 - 2.28703i) q^{81} +(2.90539 - 1.29356i) q^{82} +(-1.83688 + 5.65334i) q^{83} +(-1.30009 - 12.3696i) q^{84} +(-1.13456 - 10.7946i) q^{85} +(0.763932 + 0.555029i) q^{86} +(3.78115 - 6.54915i) q^{87} +(1.64590 + 2.85078i) q^{88} +(-0.507392 + 4.82751i) q^{89} +(0.708204 + 2.17963i) q^{90} +(0.773761 - 10.7889i) q^{91} +15.2705 q^{92} +(-2.41249 + 12.2139i) q^{93} +(-0.0901699 - 0.156179i) q^{94} +(12.0444 + 13.3766i) q^{95} +(-2.86475 - 8.81678i) q^{96} +(-1.47815 + 0.658114i) q^{97} +(0.381966 - 0.661585i) q^{98} -4.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 5 q^{3} - 6 q^{4} - 24 q^{5} - 10 q^{6} - 3 q^{7} - 14 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 5 * q^3 - 6 * q^4 - 24 * q^5 - 10 * q^6 - 3 * q^7 - 14 * q^8 + 2 * q^9	\( 8 q - 4 q^{2} - 5 q^{3} - 6 q^{4} - 24 q^{5} - 10 q^{6} - 3 q^{7} - 14 q^{8} + 2 q^{9} + 12 q^{10} - 5 q^{11} + 30 q^{12} - 5 q^{13} + 6 q^{14} + 15 q^{15} + 14 q^{16} - 5 q^{17} + 16 q^{18} - 6 q^{19} + 18 q^{20} - 30 q^{21} + 5 q^{22} - 11 q^{23} - 5 q^{24} + 32 q^{25} - 12 q^{26} + 10 q^{27} - 27 q^{28} - 7 q^{29} + 30 q^{30} + 2 q^{31} + 30 q^{32} - 5 q^{33} - 10 q^{34} + 9 q^{35} - 12 q^{36} + 10 q^{37} + 12 q^{38} - 10 q^{39} + 42 q^{40} + 17 q^{41} + 15 q^{42} - 12 q^{43} - 30 q^{44} - 6 q^{45} + 14 q^{46} - 28 q^{47} + 25 q^{48} + 2 q^{49} - 16 q^{50} + 30 q^{51} + 63 q^{52} + 8 q^{53} + 5 q^{54} + 15 q^{55} - 36 q^{56} - 7 q^{58} + 4 q^{59} - 90 q^{60} - 6 q^{61} - 16 q^{62} + 24 q^{63} - 34 q^{64} + 15 q^{65} + 10 q^{66} - 40 q^{67} - 35 q^{69} - 18 q^{70} - 19 q^{71} - 26 q^{72} - 44 q^{73} + 35 q^{74} - 20 q^{75} + 36 q^{76} + 30 q^{77} + 70 q^{78} - 54 q^{79} - 42 q^{80} - 11 q^{81} + 17 q^{82} - 46 q^{83} + 15 q^{85} + 24 q^{86} - 10 q^{87} + 40 q^{88} + 9 q^{89} - 48 q^{90} - 21 q^{91} - 12 q^{92} - 5 q^{93} + 44 q^{94} + 18 q^{95} - 90 q^{96} - 3 q^{97} + 12 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 5 * q^3 - 6 * q^4 - 24 * q^5 - 10 * q^6 - 3 * q^7 - 14 * q^8 + 2 * q^9 + 12 * q^10 - 5 * q^11 + 30 * q^12 - 5 * q^13 + 6 * q^14 + 15 * q^15 + 14 * q^16 - 5 * q^17 + 16 * q^18 - 6 * q^19 + 18 * q^20 - 30 * q^21 + 5 * q^22 - 11 * q^23 - 5 * q^24 + 32 * q^25 - 12 * q^26 + 10 * q^27 - 27 * q^28 - 7 * q^29 + 30 * q^30 + 2 * q^31 + 30 * q^32 - 5 * q^33 - 10 * q^34 + 9 * q^35 - 12 * q^36 + 10 * q^37 + 12 * q^38 - 10 * q^39 + 42 * q^40 + 17 * q^41 + 15 * q^42 - 12 * q^43 - 30 * q^44 - 6 * q^45 + 14 * q^46 - 28 * q^47 + 25 * q^48 + 2 * q^49 - 16 * q^50 + 30 * q^51 + 63 * q^52 + 8 * q^53 + 5 * q^54 + 15 * q^55 - 36 * q^56 - 7 * q^58 + 4 * q^59 - 90 * q^60 - 6 * q^61 - 16 * q^62 + 24 * q^63 - 34 * q^64 + 15 * q^65 + 10 * q^66 - 40 * q^67 - 35 * q^69 - 18 * q^70 - 19 * q^71 - 26 * q^72 - 44 * q^73 + 35 * q^74 - 20 * q^75 + 36 * q^76 + 30 * q^77 + 70 * q^78 - 54 * q^79 - 42 * q^80 - 11 * q^81 + 17 * q^82 - 46 * q^83 + 15 * q^85 + 24 * q^86 - 10 * q^87 + 40 * q^88 + 9 * q^89 - 48 * q^90 - 21 * q^91 - 12 * q^92 - 5 * q^93 + 44 * q^94 + 18 * q^95 - 90 * q^96 - 3 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.373619	−	0.0794152i	0.264189	−	0.0561550i	−0.0739128	−	0.997265i	$-0.523549\pi$
$2$	0.373619	−	0.0794152i	0.264189	−	0.0561550i	0.338101	+	0.941110i	$0.390215\pi$
$3$	1.49622	−	1.66172i	0.863844	−	0.959396i	−0.135664	−	0.990755i	$-0.543317\pi$
$3$	1.49622	−	1.66172i	0.863844	−	0.959396i	0.999508	+	0.0313590i	$0.00998352\pi$
$4$	−1.69381	+	0.754131i	−0.846903	+	0.377066i
$5$	−3.00000			−1.34164			−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000			−1.34164			−0.670820	+	0.741620i	$0.734058\pi$
$6$	0.427051	−	0.739674i	0.174343	−	0.301971i
$7$	−2.74064	+	1.22021i	−1.03586	+	0.461196i	−0.852983	−	0.521939i	$-0.825209\pi$
$7$	−2.74064	+	1.22021i	−1.03586	+	0.461196i	−0.182880	+	0.983135i	$0.558542\pi$
$8$	−1.19098	+	0.865300i	−0.421076	+	0.305930i
$9$	−0.209057	−	1.98904i	−0.0696856	−	0.663015i
$10$	−1.12086	+	0.238246i	−0.354446	+	0.0753399i
$11$	0.233733	−	2.22382i	0.0704731	−	0.670507i	−0.901075	−	0.433664i	$-0.857221\pi$
$11$	0.233733	−	2.22382i	0.0704731	−	0.670507i	0.971548	−	0.236843i	$-0.0761127\pi$
$12$	−1.28115	+	3.94298i	−0.369837	+	1.13824i
$13$	−1.69837	+	3.18049i	−0.471044	+	0.882109i
$13$	−1.69837	+	3.18049i	−0.471044	+	0.882109i
$14$	−0.927051	+	0.673542i	−0.247765	+	0.180012i
$15$	−4.48866	+	4.98517i	−1.15897	+	1.28716i
$16$	2.10502	−	2.33786i	0.526254	−	0.584464i
$17$	0.378188	+	3.59821i	0.0917239	+	0.872695i	0.939548	+	0.342417i	$0.111246\pi$
$17$	0.378188	+	3.59821i	0.0917239	+	0.872695i	−0.847824	+	0.530278i	$0.822088\pi$
$18$	−0.236068	−	0.726543i	−0.0556418	−	0.171248i
$19$	−4.01478	−	4.45887i	−0.921055	−	1.02293i	−0.999661	−	0.0260290i	$-0.991714\pi$
$19$	−4.01478	−	4.45887i	−0.921055	−	1.02293i	0.0786067	−	0.996906i	$-0.474953\pi$
$20$	5.08142	−	2.26239i	1.13624	−	0.505887i
$21$	−2.07295	+	6.37988i	−0.452355	+	1.39220i
$22$	−0.0892780	−	0.849423i	−0.0190341	−	0.181098i
$23$	−7.52402	−	3.34991i	−1.56887	−	0.698505i	−0.575969	−	0.817472i	$-0.695375\pi$
$23$	−7.52402	−	3.34991i	−1.56887	−	0.698505i	−0.992898	+	0.118967i	$0.962042\pi$
$24$	−0.344086	+	3.27376i	−0.0702363	+	0.668254i
$25$	4.00000			0.800000
$26$	−0.381966	+	1.32317i	−0.0749097	+	0.259495i
$27$	1.80902	+	1.31433i	0.348145	+	0.252942i
$28$	3.72191	−	4.13360i	0.703375	−	0.781177i
$29$	3.30806	−	0.703150i	0.614292	−	0.130572i	0.109750	−	0.993959i	$-0.464995\pi$
$29$	3.30806	−	0.703150i	0.614292	−	0.130572i	0.504541	+	0.863387i	$0.331662\pi$
$30$	−1.28115	+	2.21902i	−0.233905	+	0.405136i
$31$	−4.78115	+	2.85317i	−0.858720	+	0.512444i
$31$	−4.78115	+	2.85317i	−0.858720	+	0.512444i
$32$	2.07295	−	3.59045i	0.366449	−	0.634708i
$33$	−3.34565	−	3.71572i	−0.582403	−	0.646825i
$34$	0.427051	+	1.31433i	0.0732386	+	0.225405i
$35$	8.22191	−	3.66063i	1.38976	−	0.618759i
$36$	1.85410	+	3.21140i	0.309017	+	0.535233i
$37$	−1.54508	−	2.67617i	−0.254010	−	0.439959i	0.710616	−	0.703580i	$-0.248416\pi$
$37$	−1.54508	−	2.67617i	−0.254010	−	0.439959i	−0.964626	+	0.263621i	$0.915083\pi$
$38$	−1.85410	−	1.34708i	−0.300775	−	0.218526i
$39$	2.74395	+	7.58095i	0.439383	+	1.21392i
$40$	3.57295	−	2.59590i	0.564933	−	0.410448i
$41$	8.14429	−	1.73112i	1.27192	−	0.270356i	0.477993	−	0.878364i	$-0.341364\pi$
$41$	8.14429	−	1.73112i	1.27192	−	0.270356i	0.793931	+	0.608008i	$0.208031\pi$
$42$	−0.267834	+	2.54827i	−0.0413277	+	0.393206i
$43$	1.65418	+	1.83716i	0.252260	+	0.280164i	0.855953	−	0.517054i	$-0.172971\pi$
$43$	1.65418	+	1.83716i	0.252260	+	0.280164i	−0.603693	+	0.797217i	$0.706305\pi$
$44$	1.28115	+	3.94298i	0.193141	+	0.594427i
$45$	0.627171	+	5.96713i	0.0934931	+	0.889527i
$46$	−3.07715	−	0.654069i	−0.453701	−	0.0964372i
$47$	−0.145898	−	0.449028i	−0.0212814	−	0.0654975i	0.939852	−	0.341582i	$-0.110963\pi$
$47$	−0.145898	−	0.449028i	−0.0212814	−	0.0654975i	−0.961133	+	0.276085i	$0.910963\pi$
$48$	−0.735299	−	6.99591i	−0.106131	−	1.00977i
$49$	1.33826	−	1.48629i	0.191180	−	0.212327i
$50$	1.49448	−	0.317661i	0.211351	−	0.0449240i
$51$	6.54508	+	4.75528i	0.916495	+	0.665873i
$52$	0.478211	−	6.66793i	0.0663159	−	0.924676i
$53$	2.11803	−	1.53884i	0.290934	−	0.211376i	−0.432738	−	0.901520i	$-0.642453\pi$
$53$	2.11803	−	1.53884i	0.290934	−	0.211376i	0.723673	+	0.690143i	$0.242453\pi$
$54$	0.780261	+	0.347395i	0.106180	+	0.0472744i
$55$	−0.701198	+	6.67146i	−0.0945496	+	0.899579i
$56$	2.20820	−	3.82472i	0.295084	−	0.511100i
$57$	−13.4164			−1.77705
$58$	1.18011	−	0.525421i	0.154957	−	0.0689911i
$59$	−10.9905	−	2.33611i	−1.43085	−	0.304136i	−0.573639	−	0.819108i	$-0.694469\pi$
$59$	−10.9905	−	2.33611i	−1.43085	−	0.304136i	−0.857207	+	0.514973i	$0.827802\pi$
$60$	3.84346	−	11.8290i	0.496188	−	1.52711i
$61$	4.28115	−	7.41517i	0.548145	−	0.949416i	−0.450256	−	0.892899i	$-0.648667\pi$
$61$	4.28115	−	7.41517i	0.548145	−	0.949416i	0.998402	−	0.0565164i	$-0.0179993\pi$
$62$	−1.55975	+	1.44569i	−0.198088	+	0.183603i
$63$	3.00000	+	5.19615i	0.377964	+	0.654654i
$64$	−1.45492	+	4.47777i	−0.181864	+	0.559721i
$65$	5.09512	−	9.54147i	0.631972	−	1.18347i
$66$	−1.54508	−	1.12257i	−0.190187	−	0.138179i
$67$	−3.88197	−	6.72376i	−0.474258	−	0.821438i	0.525308	−	0.850912i	$-0.323950\pi$
$67$	−3.88197	−	6.72376i	−0.474258	−	0.821438i	−0.999566	+	0.0294739i	$0.990617\pi$
$68$	−3.35410	−	5.80948i	−0.406745	−	0.704502i
$69$	−16.8242	+	7.49063i	−2.02540	+	0.901766i
$70$	2.78115	−	2.02063i	0.332411	−	0.241511i
$71$	1.40822	+	13.3983i	0.167125	+	1.59009i	0.681038	+	0.732248i	$0.261529\pi$
$71$	1.40822	+	13.3983i	0.167125	+	1.59009i	−0.513913	+	0.857842i	$0.671805\pi$
$72$	1.97010	+	2.18802i	0.232179	+	0.257861i
$73$	−8.85410	−	6.43288i	−1.03629	−	0.752912i	−0.0667355	−	0.997771i	$-0.521258\pi$
$73$	−8.85410	−	6.43288i	−1.03629	−	0.752912i	−0.969559	+	0.244859i	$0.921258\pi$
$74$	−0.789802	−	0.877163i	−0.0918126	−	0.101968i
$75$	5.98489	−	6.64689i	0.691075	−	0.767517i
$76$	10.1628	+	4.52479i	1.16576	+	0.519029i
$77$	2.07295	+	6.37988i	0.236234	+	0.727055i
$78$	1.62723	+	2.61448i	0.184248	+	0.296031i
$79$	−8.42705	+	6.12261i	−0.948117	+	0.688848i	−0.950361	−	0.311150i	$-0.899286\pi$
$79$	−8.42705	+	6.12261i	−0.948117	+	0.688848i	0.00224353	+	0.999997i	$0.499286\pi$
$80$	−6.31505	+	7.01357i	−0.706044	+	0.784141i
$81$	10.7596	−	2.28703i	1.19551	−	0.254114i
$82$	2.90539	−	1.29356i	0.320846	−	0.142850i
$83$	−1.83688	+	5.65334i	−0.201624	+	0.620535i	0.798211	+	0.602378i	$0.205780\pi$
$83$	−1.83688	+	5.65334i	−0.201624	+	0.620535i	−0.999835	+	0.0181569i	$0.994220\pi$
$84$	−1.30009	−	12.3696i	−0.141852	−	1.34963i
$85$	−1.13456	−	10.7946i	−0.123061	−	1.17084i
$86$	0.763932	+	0.555029i	0.0823769	+	0.0598503i
$87$	3.78115	−	6.54915i	0.405382	−	0.702142i
$88$	1.64590	+	2.85078i	0.175453	+	0.303894i
$89$	−0.507392	+	4.82751i	−0.0537834	+	0.511715i	0.934155	+	0.356868i	$0.116155\pi$
$89$	−0.507392	+	4.82751i	−0.0537834	+	0.511715i	−0.987938	+	0.154847i	$0.950511\pi$
$90$	0.708204	+	2.17963i	0.0746512	+	0.229753i
$91$	0.773761	−	10.7889i	0.0811122	−	1.13099i
$92$	15.2705			1.59206
$93$	−2.41249	+	12.2139i	−0.250163	+	1.26652i
$94$	−0.0901699	−	0.156179i	−0.00930032	−	0.0161086i
$95$	12.0444	+	13.3766i	1.23572	+	1.37241i
$96$	−2.86475	−	8.81678i	−0.292382	−	0.899859i
$97$	−1.47815	+	0.658114i	−0.150083	+	0.0668213i	−0.480404	−	0.877048i	$-0.659510\pi$
$97$	−1.47815	+	0.658114i	−0.150083	+	0.0668213i	0.330321	+	0.943869i	$0.392843\pi$
$98$	0.381966	−	0.661585i	0.0385844	−	0.0668301i
$99$	−4.47214			−0.449467
$100$	−6.77523	+	3.01652i	−0.677523	+	0.301652i
$101$	8.38666	+	3.73398i	0.834504	+	0.371545i	0.779085	−	0.626918i	$-0.215684\pi$
$101$	8.38666	+	3.73398i	0.834504	+	0.371545i	0.0554186	+	0.998463i	$0.482351\pi$
$102$	2.82301	+	1.25689i	0.279520	+	0.124450i
$103$	−1.21885	+	3.75123i	−0.120097	+	0.369619i	−0.992976	−	0.118317i	$-0.962250\pi$
$103$	−1.21885	+	3.75123i	−0.120097	+	0.369619i	0.872879	+	0.487936i	$0.162250\pi$
$104$	−0.729343	−	5.25751i	−0.0715179	−	0.515542i
$105$	6.21885	−	19.1396i	0.606897	−	1.86784i
$106$	0.669131	−	0.743145i	0.0649917	−	0.0721806i
$107$	−16.5262	−	7.35793i	−1.59765	−	0.711318i	−0.601488	−	0.798882i	$-0.705425\pi$
$107$	−16.5262	−	7.35793i	−1.59765	−	0.711318i	−0.996159	+	0.0875631i	$0.972092\pi$
$108$	−4.05530	−	0.861981i	−0.390221	−	0.0829441i
$109$	−0.954915	−	2.93893i	−0.0914643	−	0.281498i	0.894852	−	0.446363i	$-0.147281\pi$
$109$	−0.954915	−	2.93893i	−0.0914643	−	0.281498i	−0.986316	+	0.164865i	$0.947281\pi$
$110$	0.267834	+	2.54827i	0.0255370	+	0.242968i
$111$	−6.75883	−	1.43663i	−0.641520	−	0.136359i
$112$	−2.91641	+	8.97578i	−0.275575	+	0.848132i
$113$	−9.86481	+	4.39209i	−0.928003	+	0.413173i	−0.814368	−	0.580349i	$-0.802916\pi$
$113$	−9.86481	+	4.39209i	−0.928003	+	0.413173i	−0.113635	+	0.993523i	$0.536249\pi$
$114$	−5.01263	+	1.06547i	−0.469476	+	0.0997901i
$115$	22.5721	+	10.0497i	2.10486	+	0.937142i
$116$	−5.07295	+	3.68571i	−0.471011	+	0.342210i
$117$	6.68119	+	2.71324i	0.617677	+	0.250839i
$118$	−4.29180			−0.395092
$119$	−5.42705	−	9.39993i	−0.497497	−	0.861690i
$120$	1.03226	−	9.82129i	0.0942319	−	0.896557i
$121$	5.86889	+	1.24747i	0.533535	+	0.113406i
$122$	1.01064	−	3.11044i	0.0914993	−	0.281606i
$123$	9.30902	−	16.1237i	0.839366	−	1.45382i
$124$	5.94668	−	8.43833i	0.534028	−	0.757785i
$125$	3.00000			0.268328
$126$	1.53351	+	1.70314i	0.136616	+	0.151727i
$127$	1.55656	−	1.72873i	0.138122	−	0.153400i	−0.670115	−	0.742257i	$-0.733755\pi$
$127$	1.55656	−	1.72873i	0.138122	−	0.153400i	0.808237	+	0.588857i	$0.200422\pi$
$128$	−1.05471	+	10.0349i	−0.0932241	+	0.886968i
$129$	5.52786			0.486701
$130$	1.14590	−	3.96951i	0.100502	−	0.348149i
$131$	5.16312	+	3.75123i	0.451104	+	0.327746i	0.790031	−	0.613066i	$-0.210064\pi$
$131$	5.16312	+	3.75123i	0.451104	+	0.327746i	−0.338928	+	0.940812i	$0.610064\pi$
$132$	8.46903	+	3.77066i	0.737135	+	0.328193i
$133$	16.4438	+	7.32126i	1.42586	+	0.634834i
$134$	−1.98435	−	2.20384i	−0.171421	−	0.190383i
$135$	−5.42705	−	3.94298i	−0.467086	−	0.339358i
$136$	−3.56395	−	3.95817i	−0.305606	−	0.339410i
$137$	21.0029	+	4.46431i	1.79440	+	0.381412i	0.980017	−	0.198915i	$-0.0637418\pi$
$137$	21.0029	+	4.46431i	1.79440	+	0.381412i	0.814384	+	0.580327i	$0.197075\pi$
$138$	−5.69098	+	4.13474i	−0.484449	+	0.351973i
$139$	8.11060	+	1.72396i	0.687932	+	0.146224i	0.538599	−	0.842562i	$-0.318954\pi$
$139$	8.11060	+	1.72396i	0.687932	+	0.146224i	0.149333	+	0.988787i	$0.452287\pi$
$140$	−11.1657	+	12.4008i	−0.943676	+	1.04806i
$141$	−0.964456	−	0.429403i	−0.0812218	−	0.0361623i
$142$	1.59017	+	4.89404i	0.133444	+	0.410699i
$143$	6.67587	+	4.52026i	0.558264	+	0.378003i
$144$	−5.09017	−	3.69822i	−0.424181	−	0.308185i
$145$	−9.92419	+	2.10945i	−0.824159	+	0.175180i
$146$	−3.81893	−	1.70030i	−0.316057	−	0.140718i
$147$	−0.467465	−	4.44764i	−0.0385559	−	0.366835i
$148$	4.63525	+	3.36771i	0.381016	+	0.276824i
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	−0.920904	−	0.389789i	$-0.872548\pi$
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	0.798019	+	0.602632i	$0.205881\pi$
$150$	1.70820	−	2.95870i	0.139474	−	0.241577i
$151$	−14.3262	−	10.4086i	−1.16585	−	0.847042i	−0.175346	−	0.984507i	$-0.556104\pi$
$151$	−14.3262	−	10.4086i	−1.16585	−	0.847042i	−0.990507	+	0.137465i	$0.956104\pi$
$152$	8.63980	+	1.83645i	0.700780	+	0.148955i
$153$	7.07794	−	1.50446i	0.572218	−	0.121629i
$154$	1.28115	+	2.21902i	0.103238	+	0.178814i
$155$	14.3435	−	8.55951i	1.15209	−	0.687516i
$156$	−10.3647	−	10.7714i	−0.829844	−	0.862399i
$157$	−5.83688	+	17.9641i	−0.465834	+	1.43369i	0.392097	+	0.919924i	$0.371750\pi$
$157$	−5.83688	+	17.9641i	−0.465834	+	1.43369i	−0.857931	+	0.513765i	$0.828250\pi$
$158$	−2.66228	+	2.95676i	−0.211800	+	0.235227i
$159$	0.611920	−	5.82203i	0.0485284	−	0.461717i
$160$	−6.21885	+	10.7714i	−0.491643	+	0.851551i
$161$	24.7082			1.94728
$162$	3.83838	−	1.70896i	0.301571	−	0.134268i
$163$	1.35304	+	12.8734i	0.105979	+	1.00832i	0.910251	+	0.414058i	$0.135889\pi$
$163$	1.35304	+	12.8734i	0.105979	+	1.00832i	−0.804272	+	0.594262i	$0.797444\pi$
$164$	−12.4894	+	9.07405i	−0.975255	+	0.708564i
$165$	10.0370	+	11.1472i	0.781376	+	0.867806i
$166$	−0.237333	+	2.25807i	−0.0184206	+	0.175260i
$167$	−13.8705	+	2.94826i	−1.07333	+	0.228143i	−0.710489	−	0.703708i	$-0.751526\pi$
$167$	−13.8705	+	2.94826i	−1.07333	+	0.228143i	−0.362840	+	0.931851i	$0.618193\pi$
$168$	−3.05166	−	9.39205i	−0.235441	−	0.724613i
$169$	−7.23105	−	10.8033i	−0.556234	−	0.831026i
$170$	−1.28115	−	3.94298i	−0.0982599	−	0.302413i
$171$	−8.02957	+	8.91774i	−0.614036	+	0.681956i
$172$	−4.18732	−	1.86431i	−0.319280	−	0.142153i
$173$	8.37520	+	1.78020i	0.636755	+	0.135346i	0.514967	−	0.857210i	$-0.327804\pi$
$173$	8.37520	+	1.78020i	0.636755	+	0.135346i	0.121787	+	0.992556i	$0.461137\pi$
$174$	0.892609	−	2.74717i	0.0676685	−	0.208262i
$175$	−10.9625	+	4.88084i	−0.828691	+	0.368957i
$176$	−4.70696	−	5.22761i	−0.354800	−	0.394046i
$177$	−20.3262	+	14.7679i	−1.52781	+	1.11002i
$178$	0.193806	+	1.84395i	0.0145264	+	0.138210i
$179$	−0.0341011	+	0.324451i	−0.00254884	+	0.0242506i	−0.995722	−	0.0923954i	$-0.970548\pi$
$179$	−0.0341011	+	0.324451i	−0.00254884	+	0.0242506i	0.993174	+	0.116646i	$0.0372143\pi$
$180$	−5.56231	−	9.63420i	−0.414590	−	0.718091i
$181$	−13.5623			−1.00808			−0.504039	−	0.863681i	$-0.668153\pi$
$181$	−13.5623			−1.00808			−0.504039	+	0.863681i	$0.668153\pi$
$182$	−0.567714	−	4.09240i	−0.0420818	−	0.303349i
$183$	−5.91641	−	18.2088i	−0.437353	−	1.34604i
$184$	11.8597	−	2.52085i	0.874306	−	0.185839i
$185$	4.63525	+	8.02850i	0.340791	+	0.590267i
$186$	0.0686193	+	4.75494i	0.00503141	+	0.348649i
$187$	8.09017			0.591612
$188$	0.585749	+	0.650540i	0.0427201	+	0.0474455i
$189$	−6.56161	−	1.39471i	−0.477287	−	0.101451i
$190$	5.56231	+	4.04125i	0.403532	+	0.293183i
$191$	3.57295	−	6.18853i	0.258530	−	0.447786i	−0.707319	−	0.706895i	$-0.750095\pi$
$191$	3.57295	−	6.18853i	0.258530	−	0.447786i	0.965848	+	0.259109i	$0.0834287\pi$
$192$	5.26393	+	9.11740i	0.379892	+	0.657992i
$193$	0.267834	−	2.54827i	0.0192791	−	0.183428i	−0.980644	−	0.195797i	$-0.937271\pi$
$193$	0.267834	−	2.54827i	0.0192791	−	0.183428i	0.999924	+	0.0123688i	$0.00393722\pi$
$194$	−0.500000	+	0.363271i	−0.0358979	+	0.0260814i
$195$	−8.23184	−	22.7428i	−0.589495	−	1.62865i
$196$	−1.14590	+	3.52671i	−0.0818499	+	0.251908i
$197$	−0.830403	+	7.90075i	−0.0591637	+	0.562905i	0.924283	+	0.381708i	$0.124664\pi$
$197$	−0.830403	+	7.90075i	−0.0591637	+	0.562905i	−0.983447	+	0.181197i	$0.942003\pi$
$198$	−1.67088	+	0.355156i	−0.118744	+	0.0252398i
$199$	−17.8376	−	3.79149i	−1.26447	−	0.268772i	−0.473592	−	0.880744i	$-0.657043\pi$
$199$	−17.8376	−	3.79149i	−1.26447	−	0.268772i	−0.790879	+	0.611972i	$0.790376\pi$
$200$	−4.76393	+	3.46120i	−0.336861	+	0.244744i
$201$	−16.9813	−	3.60949i	−1.19777	−	0.254594i
$202$	3.42995	+	0.729059i	0.241330	+	0.0512964i
$203$	−8.20820	+	5.96361i	−0.576103	+	0.418563i
$204$	−14.6722	−	3.11868i	−1.02726	−	0.218351i
$205$	−24.4329	+	5.19337i	−1.70647	+	0.362720i
$206$	−0.157480	+	1.49832i	−0.0109722	+	0.104393i
$207$	−5.09017	+	15.6659i	−0.353791	+	1.08886i
$208$	3.86043	+	10.6655i	0.267673	+	0.739523i
$209$	−10.8541	+	7.88597i	−0.750794	+	0.545484i
$210$	0.803502	−	7.64481i	0.0554469	−	0.527542i
$211$	−13.3541	−	23.1300i	−0.919334	−	1.59233i	−0.800429	−	0.599428i	$-0.795395\pi$
$211$	−13.3541	−	23.1300i	−0.919334	−	1.59233i	−0.118906	−	0.992906i	$-0.537939\pi$
$212$	−2.42705	+	4.20378i	−0.166691	+	0.288716i
$213$	24.3713	+	17.7068i	1.66990	+	1.21325i
$214$	−6.75883	−	1.43663i	−0.462024	−	0.0982063i
$215$	−4.96255	−	5.51147i	−0.338443	−	0.375879i
$216$	−3.29180			−0.223978
$217$	9.62194	−	13.6535i	0.653180	−	0.926861i
$218$	−0.590170	−	1.02220i	−0.0399714	−	0.0692324i
$219$	−23.9374	+	5.08804i	−1.61754	+	0.343818i
$220$	−3.84346	−	11.8290i	−0.259126	−	0.797508i
$221$	−12.0864	−	4.90829i	−0.813019	−	0.330168i
$222$	−2.63932			−0.177140
$223$	−7.59017	−	13.1466i	−0.508275	−	0.880359i	−0.999954	−	0.00958208i	$-0.996950\pi$
$223$	−7.59017	−	13.1466i	−0.508275	−	0.880359i	0.491679	−	0.870777i	$-0.336383\pi$
$224$	−1.30009	+	12.3696i	−0.0868661	+	0.826476i
$225$	−0.836228	−	7.95618i	−0.0557485	−	0.530412i
$226$	−3.33688	+	2.42439i	−0.221966	+	0.161268i
$227$	9.52579	+	10.5795i	0.632249	+	0.702183i	0.971104	−	0.238655i	$-0.0767065\pi$
$227$	9.52579	+	10.5795i	0.632249	+	0.702183i	−0.338856	+	0.940838i	$0.610040\pi$
$228$	22.7248	−	10.1177i	1.50499	−	0.670063i
$229$	7.85410	−	24.1724i	0.519014	−	1.59736i	−0.256845	−	0.966453i	$-0.582683\pi$
$229$	7.85410	−	24.1724i	0.519014	−	1.59736i	0.775858	−	0.630907i	$-0.217317\pi$
$230$	9.23146	+	1.96221i	0.608704	+	0.129384i
$231$	13.7032	+	6.10105i	0.901603	+	0.401420i
$232$	−3.33141	+	3.69991i	−0.218718	+	0.242911i
$233$	−3.82624	−	11.7759i	−0.250665	−	0.771468i	−0.994653	−	0.103275i	$-0.967068\pi$
$233$	−3.82624	−	11.7759i	−0.250665	−	0.771468i	0.743988	−	0.668193i	$-0.232932\pi$
$234$	2.71169	+	0.483129i	0.177269	+	0.0315832i
$235$	0.437694	+	1.34708i	0.0285520	+	0.0878741i
$236$	20.3776	−	4.33139i	1.32647	−	0.281949i
$237$	−2.43466	+	23.1642i	−0.158148	+	1.50468i
$238$	−2.77415	−	3.08100i	−0.179821	−	0.199712i
$239$	−9.78115	+	7.10642i	−0.632690	+	0.459676i	−0.857331	−	0.514765i	$-0.827879\pi$
$239$	−9.78115	+	7.10642i	−0.632690	+	0.459676i	0.224641	+	0.974442i	$0.427879\pi$
$240$	2.20590	+	20.9877i	0.142390	+	1.35475i
$241$	−9.48440	+	4.22273i	−0.610944	+	0.272010i	−0.688796	−	0.724955i	$-0.741860\pi$
$241$	−9.48440	+	4.22273i	−0.610944	+	0.272010i	0.0778522	+	0.996965i	$0.475194\pi$
$242$	2.29180			0.147322
$243$	8.94427	−	15.4919i	0.573775	−	0.993808i
$244$	−1.65943	+	15.7884i	−0.106234	+	1.01075i
$245$	−4.01478	+	4.45887i	−0.256495	+	0.284867i
$246$	2.19756	−	6.76340i	0.140111	−	0.431218i
$247$	21.0000	−	5.19615i	1.33620	−	0.330623i
$248$	3.22542	−	7.53521i	0.204815	−	0.478486i
$249$	6.64590	+	11.5110i	0.421167	+	0.729482i
$250$	1.12086	−	0.238246i	0.0708892	−	0.0150680i
$251$	−3.25355	−	0.691564i	−0.205362	−	0.0436511i	0.104082	−	0.994569i	$-0.466810\pi$
$251$	−3.25355	−	0.691564i	−0.205362	−	0.0436511i	−0.309444	+	0.950918i	$0.600143\pi$
$252$	−9.00000	−	6.53888i	−0.566947	−	0.411911i
$253$	−9.20820	+	15.9491i	−0.578915	+	1.00271i
$254$	0.444272	−	0.769502i	0.0278761	−	0.0482828i
$255$	−19.6353	−	14.2658i	−1.22961	−	0.893362i
$256$	−0.581419	−	5.53184i	−0.0363387	−	0.345740i
$257$	4.26969	+	1.90099i	0.266336	+	0.118581i	0.535560	−	0.844497i	$-0.320101\pi$
$257$	4.26969	+	1.90099i	0.266336	+	0.118581i	−0.269224	+	0.963078i	$0.586767\pi$
$258$	2.06532	−	0.438996i	0.128581	−	0.0273307i
$259$	7.50000	+	5.44907i	0.466027	+	0.338589i
$260$	−1.43463	+	20.0038i	−0.0889721	+	1.24058i
$261$	−2.09017	−	6.43288i	−0.129378	−	0.398185i
$262$	2.22694	+	0.991500i	0.137581	+	0.0612550i
$263$	−11.9840	+	13.3096i	−0.738966	+	0.820705i	−0.989060	−	0.147517i	$-0.952872\pi$
$263$	−11.9840	+	13.3096i	−0.738966	+	0.820705i	0.250094	+	0.968222i	$0.419539\pi$
$264$	7.19983	+	1.53037i	0.443119	+	0.0941878i
$265$	−6.35410	+	4.61653i	−0.390329	+	0.283591i
$266$	6.72514	+	1.42947i	0.412345	+	0.0876466i
$267$	7.26281	+	8.06617i	0.444477	+	0.493642i
$268$	11.6459	+	8.46124i	0.711386	+	0.516853i
$269$	0.157960	+	0.175433i	0.00963101	+	0.0106963i	0.747941	−	0.663765i	$-0.231043\pi$
$269$	0.157960	+	0.175433i	0.00963101	+	0.0106963i	−0.738310	+	0.674461i	$0.764376\pi$
$270$	−2.34078	−	1.04218i	−0.142456	−	0.0634253i
$271$	21.7409	+	9.67967i	1.32067	+	0.587998i	0.941401	−	0.337290i	$-0.109510\pi$
$271$	21.7409	+	9.67967i	1.32067	+	0.587998i	0.379265	+	0.925288i	$0.376177\pi$
$272$	9.20820	+	6.69015i	0.558329	+	0.405650i
$273$	−16.7705	−	17.4284i	−1.01500	−	1.05482i
$274$	8.20163			0.495478
$275$	0.934931	−	8.89527i	0.0563785	−	0.536405i
$276$	22.8481	−	25.3753i	1.37529	−	1.52742i
$277$	−19.8414	−	22.0361i	−1.19215	−	1.32402i	−0.933726	−	0.357989i	$-0.883462\pi$
$277$	−19.8414	−	22.0361i	−1.19215	−	1.32402i	−0.258427	−	0.966031i	$-0.583204\pi$
$278$	3.16718			0.189955
$279$	6.67461	+	8.91345i	0.399599	+	0.533634i
$280$	−6.62461	+	11.4742i	−0.395896	+	0.685712i
$281$	−0.690983	+	2.12663i	−0.0412206	+	0.126864i	−0.969549	−	0.244897i	$-0.921246\pi$
$281$	−0.690983	+	2.12663i	−0.0412206	+	0.126864i	0.928329	+	0.371761i	$0.121246\pi$
$282$	−0.394440	−	0.0838409i	−0.0234886	−	0.00499265i
$283$	−0.0834528	+	0.794000i	−0.00496075	+	0.0471984i	−0.996722	−	0.0808998i	$-0.974221\pi$
$283$	−0.0834528	+	0.794000i	−0.00496075	+	0.0471984i	0.991761	+	0.128098i	$0.0408873\pi$
$284$	−12.4894	−	21.6322i	−0.741107	−	1.28363i
$285$	40.2492			2.38416
$286$	2.85321	+	1.15869i	0.168714	+	0.0685148i
$287$	−20.2082	+	14.6821i	−1.19285	+	0.866658i
$288$	−7.57493	−	3.37258i	−0.446357	−	0.198731i
$289$	3.82439	−	0.812899i	0.224964	−	0.0478176i
$290$	−3.54034	+	1.57626i	−0.207896	+	0.0925613i
$291$	−1.11803	+	3.44095i	−0.0655403	+	0.201712i
$292$	19.8484	+	4.21890i	1.16154	+	0.246893i
$293$	1.71016	+	16.2711i	0.0999084	+	0.950565i	0.923556	+	0.383463i	$0.125269\pi$
$293$	1.71016	+	16.2711i	0.0999084	+	0.950565i	−0.823648	+	0.567102i	$0.808065\pi$
$294$	−0.527864	−	1.62460i	−0.0307857	−	0.0947485i
$295$	32.9716	+	7.00833i	1.91968	+	0.408041i
$296$	4.15586	+	1.85031i	0.241554	+	0.107547i
$297$	3.34565	−	3.71572i	0.194134	−	0.215608i
$298$	−0.354102	+	1.08981i	−0.0205126	+	0.0631312i
$299$	23.4330	−	18.2407i	1.35516	−	1.05489i
$300$	−5.12461	+	15.7719i	−0.295870	+	0.910593i
$301$	−6.77523	−	3.01652i	−0.390518	−	0.173870i
$302$	−6.17916	−	2.75114i	−0.355571	−	0.158310i
$303$	18.7531	−	8.34943i	1.07734	−	0.479662i
$304$	−18.8754			−1.08258
$305$	−12.8435	+	22.2455i	−0.735414	+	1.27377i
$306$	2.52498	−	1.12419i	0.144343	−	0.0642658i
$307$	−2.69098	−	8.28199i	−0.153583	−	0.472678i	0.844432	−	0.535663i	$-0.179938\pi$
$307$	−2.69098	−	8.28199i	−0.153583	−	0.472678i	−0.998015	+	0.0629844i	$0.979938\pi$
$308$	−8.32244	−	9.24301i	−0.474215	−	0.526669i
$309$	4.40983	+	7.63805i	0.250866	+	0.434513i
$310$	4.67924	−	4.33708i	0.265763	−	0.246330i
$311$	33.0689			1.87516			0.937582	−	0.347764i	$-0.113059\pi$
$311$	33.0689			1.87516			0.937582	+	0.347764i	$0.113059\pi$
$312$	−9.82779	−	6.65444i	−0.556389	−	0.376734i
$313$	−0.708204	−	2.17963i	−0.0400301	−	0.123200i	0.929044	−	0.369968i	$-0.120631\pi$
$313$	−0.708204	−	2.17963i	−0.0400301	−	0.123200i	−0.969075	+	0.246768i	$0.920631\pi$
$314$	−0.754150	+	7.17526i	−0.0425591	+	0.404923i
$315$	−9.00000	−	15.5885i	−0.507093	−	0.878310i
$316$	9.65654	−	16.7256i	0.543223	−	0.940890i
$317$	−9.92705	−	7.21242i	−0.557559	−	0.405090i	0.273006	−	0.962012i	$-0.411982\pi$
$317$	−9.92705	−	7.21242i	−0.557559	−	0.405090i	−0.830565	+	0.556922i	$0.811982\pi$
$318$	−0.233733	−	2.22382i	−0.0131071	−	0.124706i
$319$	−0.790476	−	7.52088i	−0.0442582	−	0.421088i
$320$	4.36475	−	13.4333i	0.243997	−	0.750945i
$321$	−36.9537	+	16.4528i	−2.06255	+	0.918308i
$322$	9.23146	−	1.96221i	0.514449	−	0.109350i
$323$	14.5256	−	16.1323i	0.808227	−	0.897627i
$324$	−16.5000	+	11.9880i	−0.916667	+	0.665997i
$325$	−6.79350	+	12.7220i	−0.376836	+	0.705688i
$326$	1.52786	+	4.70228i	0.0846206	+	0.260435i
$327$	−6.31244	−	2.81048i	−0.349079	−	0.155420i
$328$	−8.20177	+	9.10899i	−0.452867	+	0.502960i
$329$	0.947762	+	1.05260i	0.0522518	+	0.0580315i
$330$	4.63525	+	3.36771i	0.255162	+	0.185386i
$331$	−0.706420	−	0.784559i	−0.0388284	−	0.0431233i	0.723418	−	0.690411i	$-0.242570\pi$
$331$	−0.706420	−	0.784559i	−0.0388284	−	0.0431233i	−0.762246	+	0.647287i	$0.775903\pi$
$332$	−1.15204	−	10.9609i	−0.0632263	−	0.601558i
$333$	−5.00000	+	3.63271i	−0.273998	+	0.199071i
$334$	−4.94813	+	2.20305i	−0.270750	+	0.120546i
$335$	11.6459	+	20.1713i	0.636283	+	1.10208i
$336$	10.5517	+	18.2760i	0.575640	+	0.997038i
$337$	−21.0623	−	15.3027i	−1.14734	−	0.833589i	−0.159212	−	0.987244i	$-0.550895\pi$
$337$	−21.0623	−	15.3027i	−1.14734	−	0.833589i	−0.988125	+	0.153655i	$0.950895\pi$
$338$	−3.55961	−	3.46208i	−0.193617	−	0.188312i
$339$	−7.46149	+	22.9641i	−0.405253	+	1.24724i
$340$	10.0623	+	17.4284i	0.545705	+	0.945189i
$341$	5.22742	+	11.2993i	0.283081	+	0.611891i
$342$	−2.29180	+	3.96951i	−0.123926	+	0.214646i
$343$	4.63525	−	14.2658i	0.250280	−	0.770283i
$344$	−3.55979	−	0.756657i	−0.191931	−	0.0407962i
$345$	50.4727	−	22.4719i	2.71736	−	1.20985i
$346$	3.27051			0.175824
$347$	−5.32624	+	9.22531i	−0.285927	+	0.495241i	−0.972834	−	0.231505i	$-0.925635\pi$
$347$	−5.32624	+	9.22531i	−0.285927	+	0.495241i	0.686906	+	0.726746i	$0.258968\pi$
$348$	−1.46562	+	13.9445i	−0.0785657	+	0.747502i
$349$	7.25745	+	3.23123i	0.388483	+	0.172964i	0.591678	−	0.806175i	$-0.298466\pi$
$349$	7.25745	+	3.23123i	0.388483	+	0.172964i	−0.203195	+	0.979138i	$0.565133\pi$
$350$	−3.70820	+	2.69417i	−0.198212	+	0.144009i
$351$	−7.25260	+	3.52134i	−0.387115	+	0.187955i
$352$	−7.50000	−	5.44907i	−0.399751	−	0.290436i
$353$	12.6614	−	2.69127i	0.673899	−	0.143242i	0.141763	−	0.989901i	$-0.454723\pi$
$353$	12.6614	−	2.69127i	0.673899	−	0.143242i	0.532136	+	0.846659i	$0.321390\pi$
$354$	−6.42148	+	7.13177i	−0.341298	+	0.379049i
$355$	−4.22467	−	40.1950i	−0.224222	−	2.13333i
$356$	−2.78115	−	8.55951i	−0.147401	−	0.453653i
$357$	−23.7401	−	5.04612i	−1.25646	−	0.267069i
$358$	0.0130255	+	0.123929i	0.000688418	+	0.00654986i
$359$	−10.4271	−	32.0912i	−0.550319	−	1.69371i	−0.707996	−	0.706216i	$-0.750401\pi$
$359$	−10.4271	−	32.0912i	−0.550319	−	1.69371i	0.157678	−	0.987491i	$-0.449599\pi$
$360$	−5.91031	−	6.56406i	−0.311501	−	0.345956i
$361$	−1.77698	+	16.9069i	−0.0935255	+	0.889835i
$362$	−5.06714	+	1.07705i	−0.266323	+	0.0566087i
$363$	10.8541	−	7.88597i	0.569693	−	0.413906i
$364$	6.82568	+	18.8579i	0.357763	+	0.988422i
$365$	26.5623	+	19.2986i	1.39033	+	1.01014i
$366$	−3.65654	−	6.33332i	−0.191130	−	0.331048i
$367$	2.50000	+	4.33013i	0.130499	+	0.226031i	0.923869	−	0.382709i	$-0.125009\pi$
$367$	2.50000	+	4.33013i	0.130499	+	0.226031i	−0.793370	+	0.608740i	$0.791675\pi$
$368$	−23.6698	+	10.5385i	−1.23387	+	0.549356i
$369$	−5.14590	−	15.8374i	−0.267885	−	0.824464i
$370$	2.36940	+	2.63149i	0.123179	+	0.136805i
$371$	−3.92705	+	6.80185i	−0.203882	+	0.353135i
$372$	−5.12461	−	22.5074i	−0.265699	−	1.16695i
$373$	7.70820	−	13.3510i	0.399116	−	0.691289i	−0.594501	−	0.804095i	$-0.702651\pi$
$373$	7.70820	−	13.3510i	0.399116	−	0.691289i	0.993617	+	0.112806i	$0.0359839\pi$
$374$	3.02264	−	0.642482i	0.156297	−	0.0332220i
$375$	4.48866	−	4.98517i	0.231794	−	0.257433i
$376$	0.562306	+	0.408539i	0.0289987	+	0.0210688i
$377$	−3.38197	+	11.7155i	−0.174180	+	0.603378i
$378$	−2.56231			−0.131791
$379$	−0.193806	+	1.84395i	−0.00995517	+	0.0947171i	−0.998371	−	0.0570513i	$-0.981830\pi$
$379$	−0.193806	+	1.84395i	−0.00995517	+	0.0947171i	0.988416	+	0.151768i	$0.0484968\pi$
$380$	−30.4885	−	13.5744i	−1.56403	−	0.696350i
$381$	−0.543718	−	5.17313i	−0.0278555	−	0.265028i
$382$	0.843459	−	2.59590i	0.0431551	−	0.132818i
$383$	2.39169	−	1.06485i	0.122210	−	0.0544113i	−0.344721	−	0.938705i	$-0.612026\pi$
$383$	2.39169	−	1.06485i	0.122210	−	0.0544113i	0.466931	+	0.884294i	$0.345360\pi$
$384$	15.0971	+	16.7671i	0.770422	+	0.855640i
$385$	−6.21885	−	19.1396i	−0.316942	−	0.975447i
$386$	−0.102303	−	0.973352i	−0.00520711	−	0.0495423i
$387$	3.30836	−	3.67431i	0.168174	−	0.186776i
$388$	2.00739	−	2.22943i	0.101910	−	0.113182i
$389$	18.2082	−	13.2290i	0.923193	−	0.670739i	−0.0211240	−	0.999777i	$-0.506724\pi$
$389$	18.2082	−	13.2290i	0.923193	−	0.670739i	0.944317	+	0.329038i	$0.106724\pi$
$390$	−4.88170	−	7.84343i	−0.247195	−	0.397167i
$391$	9.20820	−	28.3399i	0.465679	−	1.43321i
$392$	−0.307760	+	2.92814i	−0.0155442	+	0.147894i
$393$	13.9587	−	2.96701i	0.704122	−	0.149666i
$394$	0.317186	+	3.01782i	0.0159796	+	0.152036i
$395$	25.2812	−	18.3678i	1.27203	−	0.924186i
$396$	7.57493	−	3.37258i	0.380655	−	0.169478i
$397$	−16.6353	+	28.8131i	−0.834900	+	1.44609i	0.0592127	+	0.998245i	$0.481141\pi$
$397$	−16.6353	+	28.8131i	−0.834900	+	1.44609i	−0.894112	+	0.447843i	$0.852192\pi$
$398$	−6.96556			−0.349152
$399$	36.7695	−	16.3708i	1.84078	−	0.819567i
$400$	8.42007	−	9.35143i	0.421003	−	0.467572i
$401$	0.461819	−	0.0981626i	0.0230621	−	0.00490201i	−0.196366	−	0.980531i	$-0.562914\pi$
$401$	0.461819	−	0.0981626i	0.0230621	−	0.00490201i	0.219428	+	0.975629i	$0.429581\pi$
$402$	−6.63119			−0.330734
$403$	−0.954290	−	20.0522i	−0.0475366	−	0.998869i
$404$	−17.0213			−0.846841
$405$	−32.2789	+	6.86109i	−1.60395	+	0.340930i
$406$	−2.59314	+	2.87997i	−0.128695	+	0.142931i
$407$	−6.31244	+	2.81048i	−0.312896	+	0.139310i
$408$	−11.9098			−0.589624
$409$	−10.5172	+	18.2164i	−0.520043	+	0.900741i	0.479685	+	0.877441i	$0.340751\pi$
$409$	−10.5172	+	18.2164i	−0.520043	+	0.900741i	−0.999729	+	0.0233005i	$0.992583\pi$
$410$	−8.71616	+	3.88068i	−0.430460	+	0.191653i
$411$	38.8435	−	28.2214i	1.91601	−	1.39206i
$412$	−0.764425	−	7.27302i	−0.0376605	−	0.358316i
$413$	32.9716	−	7.00833i	1.62243	−	0.344857i
$414$	−0.657672	+	6.25733i	−0.0323228	+	0.307531i
$415$	5.51064	−	16.9600i	0.270507	−	0.832534i
$416$	7.89876	+	12.6909i	0.387269	+	0.622224i
$417$	15.0000	−	10.8981i	0.734553	−	0.533684i
$418$	−3.42903	+	3.80833i	−0.167720	+	0.186271i
$419$	12.2254	−	13.5776i	0.597248	−	0.663311i	−0.366409	−	0.930454i	$-0.619413\pi$
$419$	12.2254	−	13.5776i	0.597248	−	0.663311i	0.963657	+	0.267143i	$0.0860796\pi$
$420$	3.90028	+	37.1087i	0.190314	+	1.81072i
$421$	−1.82624	−	5.62058i	−0.0890054	−	0.273930i	0.896640	−	0.442761i	$-0.146001\pi$
$421$	−1.82624	−	5.62058i	−0.0890054	−	0.273930i	−0.985645	+	0.168830i	$0.946001\pi$
$422$	−6.82622	−	7.58129i	−0.332295	−	0.369051i
$423$	−0.862635	+	0.384070i	−0.0419428	+	0.0186741i
$424$	−1.19098	+	3.66547i	−0.0578392	+	0.178011i
$425$	1.51275	+	14.3929i	0.0733792	+	0.698156i
$426$	10.5118	+	4.68015i	0.509297	+	0.226754i
$427$	−2.68501	+	25.5462i	−0.129937	+	1.23627i
$428$	33.5410			1.62127
$429$	17.5000	−	4.33013i	0.844908	−	0.209061i
$430$	−2.29180	−	1.66509i	−0.110520	−	0.0802976i
$431$	−9.13529	+	10.1458i	−0.440031	+	0.488704i	−0.921839	−	0.387573i	$-0.873314\pi$
$431$	−9.13529	+	10.1458i	−0.440031	+	0.488704i	0.481808	+	0.876277i	$0.339980\pi$
$432$	6.88072	−	1.46254i	0.331049	−	0.0703666i
$433$	−15.3541	+	26.5941i	−0.737871	+	1.27803i	0.215581	+	0.976486i	$0.430835\pi$
$433$	−15.3541	+	26.5941i	−0.737871	+	1.27803i	−0.953452	+	0.301544i	$0.902498\pi$
$434$	2.51064	−	5.86534i	0.120515	−	0.281545i
$435$	−11.3435	+	19.6474i	−0.543877	+	0.942023i
$436$	3.83378	+	4.25784i	0.183605	+	0.203914i
$437$	15.2705	+	46.9978i	0.730488	+	2.24821i
$438$	−8.53939	+	3.80198i	−0.408028	+	0.181666i
$439$	−16.9721	−	29.3966i	−0.810036	−	1.40302i	−0.912838	−	0.408321i	$-0.866114\pi$
$439$	−16.9721	−	29.3966i	−0.810036	−	1.40302i	0.102802	−	0.994702i	$-0.467219\pi$
$440$	−4.93769	−	8.55234i	−0.235395	−	0.407717i
$441$	−3.23607	−	2.35114i	−0.154098	−	0.111959i
$442$	−4.90550	−	0.873989i	−0.233331	−	0.0415714i
$443$	−24.1353	+	17.5353i	−1.14670	+	0.833127i	−0.988039	−	0.154206i	$-0.950718\pi$
$443$	−24.1353	+	17.5353i	−1.14670	+	0.833127i	−0.158662	+	0.987333i	$0.550718\pi$
$444$	12.5316	−	2.66367i	0.594722	−	0.126412i
$445$	1.52218	−	14.4825i	0.0721580	−	0.686538i
$446$	−3.87987	−	4.30903i	−0.183717	−	0.204039i
$447$	2.07295	+	6.37988i	0.0980471	+	0.301758i
$448$	−1.47642	−	14.0472i	−0.0697545	−	0.663670i
$449$	−8.80333	−	1.87121i	−0.415455	−	0.0883076i	−0.00455821	−	0.999990i	$-0.501451\pi$
$449$	−8.80333	−	1.87121i	−0.415455	−	0.0883076i	−0.410897	+	0.911682i	$0.634784\pi$
$450$	−0.944272	−	2.90617i	−0.0445134	−	0.136998i
$451$	−1.94611	−	18.5160i	−0.0916390	−	0.871886i
$452$	13.3969	−	14.8787i	0.630135	−	0.699836i
$453$	−38.7315	+	8.23263i	−1.81976	+	0.386803i
$454$	4.39919	+	3.19620i	0.206464	+	0.150005i
$455$	−2.32128	+	32.3668i	−0.108823	+	1.51738i
$456$	15.9787	−	11.6092i	0.748272	−	0.543651i
$457$	−17.3065	−	7.70533i	−0.809562	−	0.360440i	−0.0401503	−	0.999194i	$-0.512784\pi$
$457$	−17.3065	−	7.70533i	−0.809562	−	0.360440i	−0.769411	+	0.638754i	$0.779450\pi$
$458$	1.01478	−	9.65502i	0.0474177	−	0.451150i
$459$	−4.04508	+	7.00629i	−0.188808	+	0.327026i
$460$	−45.8115			−2.13597
$461$	18.1691	−	8.08940i	0.846219	−	0.376761i	0.0626271	−	0.998037i	$-0.480052\pi$
$461$	18.1691	−	8.08940i	0.846219	−	0.376761i	0.783592	+	0.621276i	$0.213385\pi$
$462$	5.60429	+	1.19123i	0.260735	+	0.0554209i
$463$	−5.78115	+	17.7926i	−0.268673	+	0.826890i	0.722151	+	0.691735i	$0.243153\pi$
$463$	−5.78115	+	17.7926i	−0.268673	+	0.826890i	−0.990824	+	0.135155i	$0.956847\pi$
$464$	5.31966	−	9.21392i	0.246959	−	0.427746i
$465$	7.23747	−	36.6418i	0.335629	−	1.69922i
$466$	−2.36475	−	4.09586i	−0.109545	−	0.189737i
$467$	12.1697	−	37.4545i	0.563146	−	1.73319i	−0.110249	−	0.993904i	$-0.535165\pi$
$467$	12.1697	−	37.4545i	0.563146	−	1.73319i	0.673395	−	0.739282i	$-0.264835\pi$
$468$	−13.3628	+	0.442796i	−0.617695	+	0.0204682i
$469$	18.8435	+	13.6906i	0.870110	+	0.632172i
$470$	0.270510	+	0.468537i	0.0124777	+	0.0216120i
$471$	21.1180	+	36.5775i	0.973068	+	1.68540i
$472$	15.1110	−	6.72784i	0.695539	−	0.309674i
$473$	4.47214	−	3.24920i	0.205629	−	0.149398i
$474$	0.929956	+	8.84794i	0.0427143	+	0.406399i
$475$	−16.0591	−	17.8355i	−0.736844	−	0.818348i
$476$	16.2812	+	11.8290i	0.746245	+	0.542179i
$477$	−3.50361	−	3.89116i	−0.160419	−	0.178164i
$478$	−3.09007	+	3.43187i	−0.141336	+	0.156970i
$479$	−18.4357	−	8.20808i	−0.842347	−	0.375037i	−0.0602419	−	0.998184i	$-0.519187\pi$
$479$	−18.4357	−	8.20808i	−0.842347	−	0.375037i	−0.782105	+	0.623147i	$0.785854\pi$
$480$	8.59424	+	26.4503i	0.392271	+	1.20729i
$481$	11.1357	−	0.368996i	0.507742	−	0.0168248i
$482$	−3.20820	+	2.33090i	−0.146130	+	0.106169i
$483$	36.9689	−	41.0582i	1.68215	−	1.86821i
$484$	−10.8815	+	2.31294i	−0.494614	+	0.105133i
$485$	4.43444	−	1.97434i	0.201358	−	0.0896502i
$486$	2.11146	−	6.49839i	0.0957776	−	0.294773i
$487$	−3.09953	−	29.4900i	−0.140453	−	1.33632i	−0.806864	−	0.590737i	$-0.798837\pi$
$487$	−3.09953	−	29.4900i	−0.140453	−	1.33632i	0.666411	−	0.745584i	$-0.267830\pi$
$488$	1.31757	+	12.5358i	0.0596435	+	0.567470i
$489$	23.4164	+	17.0130i	1.05893	+	0.769355i
$490$	−1.14590	+	1.98475i	−0.0517664	+	0.0896620i
$491$	−13.6074	−	23.5687i	−0.614093	−	1.06364i	−0.990543	−	0.137203i	$-0.956189\pi$
$491$	−13.6074	−	23.5687i	−0.614093	−	1.06364i	0.376450	−	0.926437i	$-0.377145\pi$
$492$	−3.60829	+	34.3306i	−0.162674	+	1.54774i
$493$	3.78115	+	11.6372i	0.170295	+	0.524113i
$494$	7.43335	−	3.60910i	0.334442	−	0.162381i
$495$	13.4164			0.603023
$496$	−3.39410	+	17.1836i	−0.152400	+	0.771568i
$497$	−20.2082	−	35.0016i	−0.906462	−	1.57004i
$498$	3.39719	+	3.77296i	0.152232	+	0.169070i
$499$	12.6180	+	38.8343i	0.564861	+	1.73846i	0.668365	+	0.743834i	$0.266995\pi$
$499$	12.6180	+	38.8343i	0.564861	+	1.73846i	−0.103504	+	0.994629i	$0.533005\pi$
$500$	−5.08142	+	2.26239i	−0.227248	+	0.101177i
$501$	−15.8541	+	27.4601i	−0.708309	+	1.22683i
$502$	−1.27051			−0.0567056
$503$	16.9260	−	7.53596i	0.754695	−	0.336012i	0.00693062	−	0.999976i	$-0.497794\pi$
$503$	16.9260	−	7.53596i	0.754695	−	0.336012i	0.747764	+	0.663964i	$0.231127\pi$
$504$	−8.06918	−	3.59263i	−0.359430	−	0.160028i
$505$	−25.1600	−	11.2019i	−1.11960	−	0.498480i
$506$	−2.17376	+	6.69015i	−0.0966355	+	0.297414i
$507$	−28.7714	−	4.14819i	−1.27778	−	0.184227i
$508$	−1.33282	+	4.10199i	−0.0591341	+	0.181996i
$509$	9.76713	−	10.8475i	0.432920	−	0.480807i	−0.486726	−	0.873555i	$-0.661809\pi$
$509$	9.76713	−	10.8475i	0.432920	−	0.480807i	0.919646	+	0.392748i	$0.128476\pi$
$510$	−8.46903	−	3.77066i	−0.375015	−	0.166967i
$511$	32.1153	+	6.82633i	1.42070	+	0.301979i
$512$	−6.89261	−	21.2133i	−0.304613	−	0.937503i
$513$	−1.40240	−	13.3429i	−0.0619173	−	0.589104i
$514$	1.74621	+	0.371168i	0.0770219	+	0.0163715i
$515$	3.65654	−	11.2537i	0.161126	−	0.495896i
$516$	−9.36313	+	4.16873i	−0.412189	+	0.183518i
$517$	−1.03266	+	0.219498i	−0.0454162	+	0.00965352i
$518$	3.23488	+	1.44026i	0.142133	+	0.0632815i
$519$	15.4894	−	11.2537i	0.679907	−	0.493982i
$520$	2.18803	+	15.7725i	0.0959514	+	0.691672i
$521$	−32.8885			−1.44087			−0.720437	−	0.693521i	$-0.756059\pi$
$521$	−32.8885			−1.44087			−0.720437	+	0.693521i	$0.756059\pi$
$522$	−1.29180	−	2.23746i	−0.0565404	−	0.0979308i
$523$	−3.65267	+	34.7528i	−0.159720	+	1.51964i	0.561818	+	0.827261i	$0.310102\pi$
$523$	−3.65267	+	34.7528i	−0.159720	+	1.51964i	−0.721538	+	0.692375i	$0.756564\pi$
$524$	−11.5742	−	2.46018i	−0.505623	−	0.107473i
$525$	−8.29180	+	25.5195i	−0.361884	+	1.11376i
$526$	−3.42047	+	5.92443i	−0.149140	+	0.258318i
$527$	−12.0745	−	16.1246i	−0.525973	−	0.702398i
$528$	−15.7295			−0.684538
$529$	29.9990	+	33.3173i	1.30430	+	1.44858i
$530$	−2.00739	+	2.22943i	−0.0871955	+	0.0968404i
$531$	−2.34898	+	22.3490i	−0.101937	+	0.969865i
$532$	−33.3738			−1.44694
$533$	−8.32624	+	28.8429i	−0.360649	+	1.24933i
$534$	3.35410	+	2.43690i	0.145146	+	0.105455i
$535$	49.5786	+	22.0738i	2.14347	+	0.954334i
$536$	10.4414	+	4.64882i	0.451001	+	0.200799i
$537$	0.488124	+	0.542117i	0.0210641	+	0.0233941i
$538$	0.0729490	+	0.0530006i	0.00314506	+	0.00228502i
$539$	−2.99244	−	3.32344i	−0.128894	−	0.143151i
$540$	12.1659	+	2.58594i	0.523537	+	0.111281i
$541$	−16.0902	+	11.6902i	−0.691770	+	0.502601i	−0.877242	−	0.480049i	$-0.840619\pi$
$541$	−16.0902	+	11.6902i	−0.691770	+	0.502601i	0.185471	+	0.982650i	$0.440619\pi$
$542$	8.89153	+	1.88995i	0.381924	+	0.0811804i
$543$	−20.2922	+	22.5368i	−0.870822	+	0.967146i
$544$	13.7032	+	6.10105i	0.587519	+	0.261580i
$545$	2.86475	+	8.81678i	0.122712	+	0.377669i
$546$	−7.64987	−	5.17976i	−0.327384	−	0.221673i
$547$	25.8262	+	18.7639i	1.10425	+	0.802285i	0.981749	−	0.190184i	$-0.0609083\pi$
$547$	25.8262	+	18.7639i	1.10425	+	0.802285i	0.122502	+	0.992468i	$0.460908\pi$
$548$	−38.9416	+	8.27728i	−1.66350	+	0.353588i
$549$	−15.6441	−	6.96521i	−0.667674	−	0.297268i
$550$	−0.357112	−	3.39769i	−0.0152273	−	0.144878i
$551$	−16.4164	−	11.9272i	−0.699362	−	0.508117i
$552$	13.5557	−	23.4792i	0.576970	−	0.999342i
$553$	15.6246	−	27.0626i	0.664426	−	1.15082i
$554$	−9.16312	−	6.65740i	−0.389304	−	0.282846i
$555$	20.2765	+	4.30990i	0.860690	+	0.182945i
$556$	−15.0379	+	3.19640i	−0.637748	+	0.135558i
$557$	3.92705	+	6.80185i	0.166394	+	0.288204i	0.937150	−	0.348928i	$-0.113454\pi$
$557$	3.92705	+	6.80185i	0.166394	+	0.288204i	−0.770755	+	0.637131i	$0.780121\pi$
$558$	3.20163	+	2.80017i	0.135536	+	0.118541i
$559$	−8.65248	+	2.14093i	−0.365961	+	0.0905518i
$560$	8.74922	−	26.9273i	0.369722	−	1.13789i
$561$	12.1047	−	13.4436i	0.511060	−	0.567590i
$562$	−0.0892780	+	0.849423i	−0.00376596	+	0.0358308i
$563$	1.25329	−	2.17076i	0.0528198	−	0.0914866i	−0.838407	−	0.545045i	$-0.816512\pi$
$563$	1.25329	−	2.17076i	0.0528198	−	0.0914866i	0.891226	+	0.453559i	$0.149846\pi$
$564$	1.95743			0.0824226
$565$	29.5944	−	13.1763i	1.24505	−	0.554330i
$566$	0.0318761	+	0.303281i	0.00133985	+	0.0127479i
$567$	−26.6976	+	19.3969i	−1.12119	+	0.814594i
$568$	−13.2707	−	14.7387i	−0.556828	−	0.618420i
$569$	2.11525	−	20.1252i	0.0886757	−	0.843693i	−0.856284	−	0.516506i	$-0.827233\pi$
$569$	2.11525	−	20.1252i	0.0886757	−	0.843693i	0.944960	−	0.327187i	$-0.106101\pi$
$570$	15.0379	−	3.19640i	0.629867	−	0.133882i
$571$	−11.4271	−	35.1688i	−0.478207	−	1.47177i	−0.841583	−	0.540128i	$-0.818376\pi$
$571$	−11.4271	−	35.1688i	−0.478207	−	1.47177i	0.363376	−	0.931643i	$-0.381624\pi$
$572$	−14.7165	−	2.62197i	−0.615328	−	0.109630i
$573$	−4.93769	−	15.1967i	−0.206275	−	0.634850i
$574$	−6.38419	+	7.09036i	−0.266471	+	0.295946i
$575$	−30.0961	−	13.3996i	−1.25509	−	0.558804i
$576$	9.21064	+	1.95778i	0.383777	+	0.0815742i
$577$	−7.77051	+	23.9152i	−0.323491	+	0.995602i	0.648627	+	0.761107i	$0.275344\pi$
$577$	−7.77051	+	23.9152i	−0.323491	+	0.995602i	−0.972117	+	0.234495i	$0.924656\pi$
$578$	1.36431	−	0.607430i	0.0567478	−	0.0252657i
$579$	−3.83378	−	4.25784i	−0.159326	−	0.176950i
$580$	15.2188	−	11.0571i	0.631928	−	0.459123i
$581$	−1.86404	−	17.7351i	−0.0773333	−	0.735777i
$582$	−0.144455	+	1.37440i	−0.00598784	+	0.0569705i
$583$	−2.92705	−	5.06980i	−0.121226	−	0.209970i
$584$	16.1115			0.666697
$585$	−20.0436	−	8.13971i	−0.828700	−	0.336536i
$586$	1.93112	+	5.94336i	0.0797737	+	0.245518i
$587$	22.0356	−	4.68381i	0.909506	−	0.193321i	0.270677	−	0.962670i	$-0.412753\pi$
$587$	22.0356	−	4.68381i	0.909506	−	0.193321i	0.638829	+	0.769349i	$0.279419\pi$
$588$	4.14590	+	7.18091i	0.170974	+	0.296136i
$589$	31.9172	+	9.86368i	1.31513	+	0.406426i
$590$	12.8754			0.530071
$591$	11.8864	+	13.2012i	0.488941	+	0.543024i
$592$	−9.50892	−	2.02118i	−0.390814	−	0.0830702i
$593$	28.9443	+	21.0292i	1.18860	+	0.863568i	0.993115	−	0.117139i	$-0.0373725\pi$
$593$	28.9443	+	21.0292i	1.18860	+	0.863568i	0.195483	+	0.980707i	$0.437372\pi$
$594$	0.954915	−	1.65396i	0.0391806	−	0.0678629i
$595$	16.2812	+	28.1998i	0.667462	+	1.15608i
$596$	0.581419	−	5.53184i	0.0238159	−	0.226593i
$597$	−32.9894	+	23.9682i	−1.35016	+	0.980952i
$598$	7.30642	−	8.67600i	0.298782	−	0.354788i
$599$	4.71885	−	14.5231i	0.192807	−	0.593399i	−0.807188	−	0.590294i	$-0.799012\pi$
$599$	4.71885	−	14.5231i	0.192807	−	0.593399i	0.999995	−	0.00310450i	$-0.000988194\pi$
$600$	−1.37635	+	13.0951i	−0.0561891	+	0.534603i
$601$	−1.08717	+	0.231085i	−0.0443465	+	0.00942614i	−0.230032	−	0.973183i	$-0.573883\pi$
$601$	−1.08717	+	0.231085i	−0.0443465	+	0.00942614i	0.185685	+	0.982609i	$0.440550\pi$
$602$	−2.77091	−	0.588976i	−0.112934	−	0.0240048i
$603$	−12.5623	+	9.12705i	−0.511577	+	0.371682i
$604$	32.1153	+	6.82633i	1.30675	+	0.277759i
$605$	−17.6067	−	3.74241i	−0.715812	−	0.152151i
$606$	6.34346	−	4.60879i	0.257685	−	0.187219i
$607$	17.2667	+	3.67016i	0.700835	+	0.148967i	0.544529	−	0.838742i	$-0.316708\pi$
$607$	17.2667	+	3.67016i	0.700835	+	0.148967i	0.156305	+	0.987709i	$0.450042\pi$
$608$	−24.3318	+	5.17188i	−0.986785	+	0.209748i
$609$	−2.37143	+	22.5626i	−0.0960951	+	0.914284i
$610$	−3.03193	+	9.33132i	−0.122759	+	0.377814i
$611$	1.67592	+	0.298590i	0.0678004	+	0.0120797i
$612$	−10.8541	+	7.88597i	−0.438751	+	0.318771i
$613$	2.73437	−	26.0158i	0.110440	−	1.05077i	−0.789201	−	0.614135i	$-0.789505\pi$
$613$	2.73437	−	26.0158i	0.110440	−	1.05077i	0.899641	−	0.436631i	$-0.143828\pi$
$614$	−1.66312	−	2.88061i	−0.0671180	−	0.116252i
$615$	−27.9271	+	48.3711i	−1.12613	+	1.95051i
$616$	−7.98936	−	5.80461i	−0.321900	−	0.233874i
$617$	−15.4195	−	3.27751i	−0.620764	−	0.131947i	−0.113215	−	0.993571i	$-0.536115\pi$
$617$	−15.4195	−	3.27751i	−0.620764	−	0.131947i	−0.507549	+	0.861623i	$0.669448\pi$
$618$	2.25417	+	2.50351i	0.0906762	+	0.100706i
$619$	−4.27051			−0.171646			−0.0858231	−	0.996310i	$-0.527352\pi$
$619$	−4.27051			−0.171646			−0.0858231	+	0.996310i	$0.527352\pi$
$620$	−17.8401	+	25.3150i	−0.716474	+	1.01667i
$621$	−9.20820	−	15.9491i	−0.369512	−	0.640014i
$622$	12.3552	−	2.62617i	0.495397	−	0.105300i
$623$	−4.50000	−	13.8496i	−0.180289	−	0.554872i
$624$	23.4992	+	9.54306i	0.940722	+	0.382028i
$625$	−29.0000			−1.16000
$626$	−0.437694	−	0.758108i	−0.0174938	−	0.0303001i
$627$	−3.13585	+	29.8357i	−0.125234	+	1.19152i
$628$	−3.66072	−	34.8294i	−0.146079	−	1.38985i
$629$	9.04508	−	6.57164i	0.360651	−	0.262028i
$630$	−4.60053	−	5.10941i	−0.183290	−	0.203564i
$631$	20.0786	−	8.93955i	0.799315	−	0.355878i	0.0339082	−	0.999425i	$-0.489205\pi$
$631$	20.0786	−	8.93955i	0.799315	−	0.355878i	0.765406	+	0.643547i	$0.222538\pi$
$632$	4.73858	−	14.5839i	0.188491	−	0.580114i
$633$	−58.4163	−	12.4168i	−2.32184	−	0.493522i
$634$	−4.28171	−	1.90634i	−0.170049	−	0.0757105i
$635$	−4.66967	+	5.18620i	−0.185310	+	0.205808i
$636$	3.35410	+	10.3229i	0.132999	+	0.409328i
$637$	2.45426	+	6.78060i	0.0972414	+	0.268657i
$638$	−0.892609	−	2.74717i	−0.0353387	−	0.108761i
$639$	26.3555	−	5.60203i	1.04261	−	0.221613i
$640$	3.16413	−	30.1047i	0.125073	−	1.18999i
$641$	−24.5253	−	27.2381i	−0.968691	−	1.07584i	−0.997089	−	0.0762435i	$-0.975707\pi$
$641$	−24.5253	−	27.2381i	−0.968691	−	1.07584i	0.0283984	−	0.999597i	$-0.490959\pi$
$642$	−12.5000	+	9.08178i	−0.493336	+	0.358429i
$643$	2.60739	+	24.8076i	0.102825	+	0.978317i	0.917321	+	0.398148i	$0.130347\pi$
$643$	2.60739	+	24.8076i	0.102825	+	0.978317i	−0.814496	+	0.580169i	$0.802986\pi$
$644$	−41.8509	+	18.6332i	−1.64916	+	0.734252i
$645$	−16.5836			−0.652978
$646$	4.14590	−	7.18091i	0.163118	−	0.282529i
$647$	−2.00129	+	19.0410i	−0.0786789	+	0.748580i	0.882062	+	0.471133i	$0.156155\pi$
$647$	−2.00129	+	19.0410i	−0.0786789	+	0.748580i	−0.960741	+	0.277447i	$0.910512\pi$
$648$	−10.8356	+	12.0341i	−0.425661	+	0.472745i
$649$	−7.76393	+	23.8949i	−0.304761	+	0.937958i
$650$	−1.52786	+	5.29268i	−0.0599278	+	0.207596i
$651$	−8.29180	−	36.4177i	−0.324981	−	1.42732i
$652$	−12.0000	−	20.7846i	−0.469956	−	0.813988i
$653$	5.49527	−	1.16805i	0.215046	−	0.0457095i	−0.0991285	−	0.995075i	$-0.531605\pi$
$653$	5.49527	−	1.16805i	0.215046	−	0.0457095i	0.314175	+	0.949365i	$0.398272\pi$
$654$	−2.58164	−	0.548746i	−0.100950	−	0.0214576i
$655$	−15.4894	−	11.2537i	−0.605219	−	0.439718i
$656$	13.0967	−	22.6842i	0.511342	−	0.885670i
$657$	−10.9443	+	18.9560i	−0.426977	+	0.739545i
$658$	0.437694	+	0.318003i	0.0170631	+	0.0123971i
$659$	0.944356	+	8.98495i	0.0367869	+	0.350004i	0.997397	+	0.0721046i	$0.0229715\pi$
$659$	0.944356	+	8.98495i	0.0367869	+	0.350004i	−0.960610	+	0.277899i	$0.910362\pi$
$660$	−25.4071	−	11.3120i	−0.988970	−	0.440318i
$661$	2.66984	−	0.567493i	0.103845	−	0.0220729i	−0.155696	−	0.987805i	$-0.549762\pi$
$661$	2.66984	−	0.567493i	0.103845	−	0.0220729i	0.259541	+	0.965732i	$0.416429\pi$
$662$	−0.326238	−	0.237026i	−0.0126796	−	0.00921227i
$663$	−26.2401	+	12.7403i	−1.01908	+	0.494793i
$664$	−2.70414	−	8.32248i	−0.104941	−	0.322975i
$665$	−49.3315	−	21.9638i	−1.91299	−	0.851719i
$666$	−1.57960	+	1.75433i	−0.0612084	+	0.0679788i
$667$	−27.2454	−	5.79119i	−1.05495	−	0.224236i
$668$	21.2705	−	15.4539i	0.822981	−	0.597931i
$669$	−33.2025	−	7.05741i	−1.28368	−	0.272855i
$670$	5.95304	+	6.61152i	0.229986	+	0.255425i
$671$	−15.4894	−	11.2537i	−0.597960	−	0.434443i
$672$	18.6095	+	20.6680i	0.717879	+	0.797285i
$673$	9.08454	+	4.04470i	0.350183	+	0.155912i	0.574288	−	0.818653i	$-0.305279\pi$
$673$	9.08454	+	4.04470i	0.350183	+	0.155912i	−0.224104	+	0.974565i	$0.571946\pi$
$674$	−9.08454	−	4.04470i	−0.349924	−	0.155796i
$675$	7.23607	+	5.25731i	0.278516	+	0.202354i
$676$	20.3951	+	12.8456i	0.784428	+	0.494061i
$677$	−1.49342			−0.0573969			−0.0286984	−	0.999588i	$-0.509136\pi$
$677$	−1.49342			−0.0573969			−0.0286984	+	0.999588i	$0.509136\pi$
$678$	−0.964057	+	9.17239i	−0.0370244	+	0.352263i
$679$	3.24803	−	3.60730i	0.124648	−	0.138435i
$680$	10.6918	+	11.8745i	0.410014	+	0.455366i
$681$	31.8328			1.21984
$682$	2.85040	+	3.80650i	0.109147	+	0.145758i
$683$	−17.9443	+	31.0804i	−0.686618	+	1.18926i	0.286307	+	0.958138i	$0.407572\pi$
$683$	−17.9443	+	31.0804i	−0.686618	+	1.18926i	−0.972925	+	0.231120i	$0.925761\pi$
$684$	6.87539	−	21.1603i	0.262887	−	0.809083i
$685$	−63.0088	−	13.3929i	−2.40744	−	0.511717i
$686$	0.598895	−	5.69810i	0.0228659	−	0.217555i
$687$	−28.4164	−	49.2187i	−1.08415	−	1.87781i
$688$	7.77709			0.296499
$689$	1.29706	+	9.34992i	0.0494139	+	0.356204i
$690$	17.0729	−	12.4042i	0.649956	−	0.472221i
$691$	7.68877	+	3.42326i	0.292495	+	0.130227i	0.547738	−	0.836650i	$-0.315489\pi$
$691$	7.68877	+	3.42326i	0.292495	+	0.130227i	−0.255244	+	0.966877i	$0.582156\pi$
$692$	−15.5285	+	3.30068i	−0.590304	+	0.125473i
$693$	12.2565	−	5.45694i	0.465586	−	0.207292i
$694$	−1.25735	+	3.86974i	−0.0477285	+	0.146893i
$695$	−24.3318	−	5.17188i	−0.922958	−	0.196181i
$696$	1.16369	+	11.0718i	0.0441095	+	0.419674i
$697$	9.30902	+	28.6502i	0.352604	+	1.08520i
$698$	2.96813	+	0.630896i	0.112345	+	0.0238798i
$699$	−25.2933	−	11.2613i	−0.956679	−	0.425941i
$700$	14.8876	−	16.5344i	0.562700	−	0.624941i
$701$	−15.0000	+	46.1653i	−0.566542	+	1.74364i	0.0967822	+	0.995306i	$0.469145\pi$
$701$	−15.0000	+	46.1653i	−0.566542	+	1.74364i	−0.663324	+	0.748332i	$0.730855\pi$
$702$	−2.43006	+	1.89161i	−0.0917167	+	0.0713941i
$703$	−5.72949	+	17.6336i	−0.216092	+	0.665062i
$704$	9.61768	+	4.28207i	0.362480	+	0.161387i
$705$	2.89337	+	1.28821i	0.108970	+	0.0485168i
$706$	4.51682	−	2.01102i	0.169993	−	0.0756856i
$707$	−27.5410			−1.03579
$708$	23.2918	−	40.3426i	0.875359	−	1.51617i
$709$	42.4859	−	18.9159i	1.59559	−	0.710403i	0.599637	−	0.800272i	$-0.295312\pi$
$709$	42.4859	−	18.9159i	1.59559	−	0.710403i	0.995954	+	0.0898696i	$0.0286450\pi$
$710$	−4.77051	−	14.6821i	−0.179034	−	0.551010i
$711$	13.9399	+	15.4818i	0.522786	+	0.580613i
$712$	−3.57295	−	6.18853i	−0.133902	−	0.231925i
$713$	45.5314	−	5.45088i	1.70516	−	0.204137i
$714$	−9.27051			−0.346940
$715$	−20.0276	−	13.5608i	−0.748990	−	0.507145i
$716$	−0.186918	−	0.575274i	−0.00698544	−	0.0214990i
$717$	−2.82587	+	26.8863i	−0.105534	+	1.00409i
$718$	−6.44427	−	11.1618i	−0.240498	−	0.416555i
$719$	4.47214	−	7.74597i	0.166783	−	0.288876i	−0.770504	−	0.637435i	$-0.779996\pi$
$719$	4.47214	−	7.74597i	0.166783	−	0.288876i	0.937287	+	0.348559i	$0.113329\pi$
$720$	15.2705	+	11.0947i	0.569098	+	0.413474i
$721$	−1.23687	−	11.7680i	−0.0460633	−	0.438263i
$722$	0.678747	+	6.45785i	0.0252604	+	0.240336i
$723$	−7.17376	+	22.0786i	−0.266795	+	0.821111i
$724$	22.9719	−	10.2278i	0.853745	−	0.380112i
$725$	13.2322	−	2.81260i	0.491433	−	0.104457i
$726$	3.42903	−	3.80833i	0.127263	−	0.141340i
$727$	−0.809017	+	0.587785i	−0.0300048	+	0.0217997i	−0.602687	−	0.797978i	$-0.705903\pi$
$727$	−0.809017	+	0.587785i	−0.0300048	+	0.0217997i	0.572682	+	0.819778i	$0.305903\pi$
$728$	8.41413	+	13.5190i	0.311849	+	0.501047i
$729$	−2.16312	−	6.65740i	−0.0801155	−	0.246570i
$730$	11.4568	+	5.10089i	0.424035	+	0.188792i
$731$	−5.98489	+	6.64689i	−0.221359	+	0.245844i
$732$	23.7531	+	26.3805i	0.877940	+	0.975051i
$733$	9.68034	+	7.03318i	0.357552	+	0.259776i	0.752030	−	0.659129i	$-0.229075\pi$
$733$	9.68034	+	7.03318i	0.357552	+	0.259776i	−0.394479	+	0.918905i	$0.629075\pi$
$734$	1.27793	+	1.41928i	0.0471691	+	0.0523866i
$735$	1.40240	+	13.3429i	0.0517282	+	0.492161i
$736$	−27.6246	+	20.0705i	−1.01826	+	0.739807i
$737$	−15.8598	+	7.06122i	−0.584202	+	0.260104i
$738$	−3.18034	−	5.50851i	−0.117070	−	0.202771i
$739$	23.5172	+	40.7330i	0.865095	+	1.49839i	0.866953	+	0.498390i	$0.166075\pi$
$739$	23.5172	+	40.7330i	0.865095	+	1.49839i	−0.00185791	+	0.999998i	$0.500591\pi$
$740$	−13.9058	−	10.1031i	−0.511186	−	0.371398i
$741$	22.7861	−	42.6708i	0.837068	−	1.56755i
$742$	−0.927051	+	2.85317i	−0.0340331	+	0.104743i
$743$	6.23607	+	10.8012i	0.228779	+	0.396257i	0.957447	−	0.288611i	$-0.0931933\pi$
$743$	6.23607	+	10.8012i	0.228779	+	0.396257i	−0.728667	+	0.684868i	$0.759860\pi$
$744$	−7.69547	−	16.6341i	−0.282130	−	0.609836i
$745$	4.50000	−	7.79423i	0.164867	−	0.285558i
$746$	1.81966	−	5.60034i	0.0666225	−	0.205043i
$747$	11.6288	+	2.47177i	0.425474	+	0.0904372i
$748$	−13.7032	+	6.10105i	−0.501038	+	0.223076i
$749$	54.2705			1.98300
$750$	1.28115	−	2.21902i	0.0467811	−	0.0810272i
$751$	−0.611920	+	5.82203i	−0.0223293	+	0.212449i	0.977668	+	0.210155i	$0.0673969\pi$
$751$	−0.611920	+	5.82203i	−0.0223293	+	0.212449i	−0.999997	+	0.00229399i	$0.999270\pi$
$752$	−1.35688	−	0.604123i	−0.0494804	−	0.0220301i
$753$	−6.01722	+	4.37177i	−0.219280	+	0.159316i
$754$	−0.333181	+	4.64570i	−0.0121337	+	0.169187i
$755$	42.9787	+	31.2259i	1.56416	+	1.13643i
$756$	12.1659	−	2.58594i	0.442470	−	0.0940498i
$757$	1.26368	−	1.40346i	0.0459293	−	0.0510097i	−0.719742	−	0.694241i	$-0.755740\pi$
$757$	1.26368	−	1.40346i	0.0459293	−	0.0510097i	0.765672	+	0.643232i	$0.222407\pi$
$758$	0.0740275	+	0.704324i	0.00268880	+	0.0255822i
$759$	12.7254	+	39.1648i	0.461904	+	1.42159i
$760$	−25.9194	−	5.50934i	−0.940195	−	0.199845i
$761$	1.56793	+	14.9178i	0.0568373	+	0.540771i	0.985480	+	0.169794i	$0.0543103\pi$
$761$	1.56793	+	14.9178i	0.0568373	+	0.540771i	−0.928642	+	0.370977i	$0.879023\pi$
$762$	−0.613969	−	1.88960i	−0.0222417	−	0.0684530i
$763$	6.20318	+	6.88933i	0.224570	+	0.249411i
$764$	−1.38492	+	13.1766i	−0.0501047	+	0.476714i
$765$	−21.2338	+	4.51339i	−0.767711	+	0.163182i
$766$	0.809017	−	0.587785i	0.0292310	−	0.0212375i
$767$	26.0960	−	30.9877i	0.942273	−	1.11890i
$768$	−10.0623	−	7.31069i	−0.363092	−	0.263802i
$769$	−0.791796	−	1.37143i	−0.0285529	−	0.0494551i	0.851396	−	0.524524i	$-0.175757\pi$
$769$	−0.791796	−	1.37143i	−0.0285529	−	0.0494551i	−0.879949	+	0.475069i	$0.842423\pi$
$770$	−3.84346	−	6.65707i	−0.138509	−	0.239904i
$771$	9.54733	−	4.25074i	0.343839	−	0.153087i
$772$	1.46807	+	4.51826i	0.0528370	+	0.162616i
$773$	−4.90221	−	5.44446i	−0.176320	−	0.195823i	0.648506	−	0.761209i	$-0.275394\pi$
$773$	−4.90221	−	5.44446i	−0.176320	−	0.195823i	−0.824827	+	0.565386i	$0.808727\pi$
$774$	0.944272	−	1.63553i	0.0339412	−	0.0587878i
$775$	−19.1246	+	11.4127i	−0.686976	+	0.409956i
$776$	1.19098	−	2.06284i	0.0427538	−	0.0740518i
$777$	20.2765	−	4.30990i	0.727415	−	0.154617i
$778$	5.75235	−	6.38863i	0.206232	−	0.229043i
$779$	−40.4164	−	29.3642i	−1.44807	−	1.05208i
$780$	31.0942	+	32.3141i	1.11335	+	1.15703i
$781$	30.1246			1.07794
$782$	1.18974	−	11.3196i	0.0425450	−	0.404789i
$783$	6.90851	+	3.07587i	0.246890	+	0.109923i
$784$	−0.657672	−	6.25733i	−0.0234883	−	0.223476i
$785$	17.5106	−	53.8922i	0.624982	−	1.92350i
$786$	4.97960	−	2.21706i	0.177616	−	0.0790799i
$787$	−4.03783	−	4.48446i	−0.143933	−	0.159854i	0.666868	−	0.745176i	$-0.267635\pi$
$787$	−4.03783	−	4.48446i	−0.143933	−	0.159854i	−0.810801	+	0.585322i	$0.800968\pi$
$788$	−4.55166	−	14.0086i	−0.162146	−	0.499035i
$789$	4.18611	+	39.8282i	0.149030	+	1.41792i
$790$	7.98684	−	8.87028i	0.284159	−	0.315590i
$791$	21.6766	−	24.0743i	0.770730	−	0.855982i
$792$	5.32624	−	3.86974i	0.189260	−	0.137505i
$793$	16.3129	+	26.2099i	0.579288	+	0.930741i
$794$	−3.92705	+	12.0862i	−0.139366	+	0.428924i
$795$	−1.83576	+	17.4661i	−0.0651077	+	0.619459i
$796$	33.0727	−	7.02981i	1.17223	−	0.249165i
$797$	0.746950	+	7.10675i	0.0264583	+	0.251734i	0.999754	+	0.0221791i	$0.00706040\pi$
$797$	0.746950	+	7.10675i	0.0264583	+	0.251734i	−0.973296	+	0.229555i	$0.926273\pi$
$798$	12.4377	−	9.03651i	0.440290	−	0.319889i
$799$	1.56052	−	0.694789i	0.0552073	−	0.0245799i
$800$	8.29180	−	14.3618i	0.293159	−	0.507767i
$801$	9.70820			0.343023
$802$	0.164749	−	0.0733508i	0.00581748	−	0.00259011i
$803$	−16.3751	+	18.1863i	−0.577863	+	0.641782i
$804$	31.4851	−	6.69236i	1.11039	−	0.236021i
$805$	−74.1246			−2.61255
$806$	−1.94899	−	7.41609i	−0.0686502	−	0.261221i
$807$	0.527864			0.0185817
$808$	−13.2194	+	2.80987i	−0.465056	+	0.0988507i
$809$	27.5550	−	30.6030i	0.968783	−	1.07594i	−0.0282985	−	0.999600i	$-0.509009\pi$
$809$	27.5550	−	30.6030i	0.968783	−	1.07594i	0.997082	−	0.0763431i	$-0.0243244\pi$
$810$	−11.5151	+	5.12687i	−0.404600	+	0.180140i
$811$	33.2705			1.16829			0.584143	−	0.811651i	$-0.301431\pi$
$811$	33.2705			1.16829			0.584143	+	0.811651i	$0.301431\pi$
$812$	9.40576	−	16.2913i	0.330078	−	0.571711i
$813$	48.6141	−	21.6444i	1.70497	−	0.759102i
$814$	−2.13525	+	1.55135i	−0.0748406	+	0.0543749i
$815$	−4.05913	−	38.6201i	−0.142185	−	1.35280i
$816$	24.8947	−	5.29153i	0.871488	−	0.185241i
$817$	1.55045	−	14.7516i	0.0542434	−	0.516092i
$818$	−2.48278	+	7.64121i	−0.0868083	+	0.267169i
$819$	−21.6214	+	0.716459i	−0.755514	+	0.0250351i
$820$	37.4681	−	27.2221i	1.30844	−	0.950639i
$821$	14.3073	−	15.8899i	0.499329	−	0.554561i	−0.439813	−	0.898089i	$-0.644955\pi$
$821$	14.3073	−	15.8899i	0.499329	−	0.554561i	0.939142	+	0.343528i	$0.111622\pi$
$822$	12.2714	−	13.6288i	0.428016	−	0.475360i
$823$	2.18567	+	20.7953i	0.0761878	+	0.724878i	0.964221	+	0.265099i	$0.0854047\pi$
$823$	2.18567	+	20.7953i	0.0761878	+	0.724878i	−0.888033	+	0.459779i	$0.847929\pi$
$824$	−1.79431	−	5.52231i	−0.0625077	−	0.192379i
$825$	−13.3826	−	14.8629i	−0.465923	−	0.517460i
$826$	11.7623	−	5.23689i	0.409261	−	0.182215i
$827$	9.12461	−	28.0827i	0.317294	−	0.976530i	−0.657506	−	0.753449i	$-0.728389\pi$
$827$	9.12461	−	28.0827i	0.317294	−	0.976530i	0.974800	−	0.223081i	$-0.0716114\pi$
$828$	−3.19241	−	30.3737i	−0.110944	−	1.05556i
$829$	−28.3199	−	12.6088i	−0.983591	−	0.437923i	−0.149027	−	0.988833i	$-0.547614\pi$
$829$	−28.3199	−	12.6088i	−0.983591	−	0.437923i	−0.834565	+	0.550910i	$0.814281\pi$
$830$	0.711999	−	6.77422i	0.0247138	−	0.235136i
$831$	−66.3050			−2.30009
$832$	−11.7705	−	12.2323i	−0.408069	−	0.424078i
$833$	5.85410	+	4.25325i	0.202833	+	0.147367i
$834$	4.73881	−	5.26298i	0.164092	−	0.182242i
$835$	41.6114	−	8.84478i	1.44002	−	0.306086i
$836$	12.4377	−	21.5427i	0.430167	−	0.745070i
$837$	−12.3992	−	1.12257i	−0.428579	−	0.0388017i
$838$	3.48936	−	6.04374i	0.120538	−	0.208778i
$839$	−7.96923	−	8.85073i	−0.275128	−	0.305561i	0.589706	−	0.807618i	$-0.299244\pi$
$839$	−7.96923	−	8.85073i	−0.275128	−	0.305561i	−0.864835	+	0.502057i	$0.832577\pi$
$840$	9.15499	+	28.1762i	0.315877	+	0.972170i
$841$	−16.0440	+	7.14323i	−0.553240	+	0.246318i
$842$	−1.12868	−	1.95493i	−0.0388968	−	0.0673712i
$843$	2.50000	+	4.33013i	0.0861046	+	0.149137i
$844$	40.0623	+	29.1070i	1.37900	+	1.00190i
$845$	21.6931	+	32.4100i	0.746267	+	1.11494i
$846$	−0.291796	+	0.212002i	−0.0100322	+	0.00728879i
$847$	−17.6067	+	3.74241i	−0.604972	+	0.128591i
$848$	0.860904	−	8.19095i	0.0295635	−	0.281278i
$849$	1.19454	+	1.32668i	0.0409966	+	0.0455314i
$850$	1.70820	+	5.25731i	0.0585909	+	0.180324i
$851$	2.66034	+	25.3114i	0.0911952	+	0.867665i
$852$	−54.6336	−	11.6127i	−1.87171	−	0.397845i
$853$	4.05573	+	12.4822i	0.138865	+	0.427384i	0.996171	−	0.0874236i	$-0.0278634\pi$
$853$	4.05573	+	12.4822i	0.138865	+	0.427384i	−0.857306	+	0.514808i	$0.827863\pi$
$854$	1.02558	+	9.75778i	0.0350948	+	0.333904i
$855$	24.0887	−	26.7532i	0.823816	−	0.914941i
$856$	26.0492	−	5.53694i	0.890344	−	0.189249i
$857$	2.71885	+	1.97536i	0.0928740	+	0.0674769i	0.633253	−	0.773945i	$-0.281719\pi$
$857$	2.71885	+	1.97536i	0.0928740	+	0.0674769i	−0.540379	+	0.841422i	$0.681719\pi$
$858$	6.19446	−	3.00758i	0.211475	−	0.102677i
$859$	−44.2705	+	32.1644i	−1.51049	+	1.09744i	−0.544531	+	0.838741i	$0.683292\pi$
$859$	−44.2705	+	32.1644i	−1.51049	+	1.09744i	−0.965959	+	0.258695i	$0.916708\pi$
$860$	12.5620	+	5.59294i	0.428359	+	0.190718i
$861$	−5.83834	+	55.5481i	−0.198970	+	1.89308i
$862$	−2.60739	+	4.51613i	−0.0888081	+	0.153820i
$863$	8.32624			0.283428			0.141714	−	0.989908i	$-0.454739\pi$
$863$	8.32624			0.283428			0.141714	+	0.989908i	$0.454739\pi$
$864$	8.46903	−	3.77066i	0.288122	−	0.128280i
$865$	−25.1256	−	5.34061i	−0.854296	−	0.181586i
$866$	−3.62461	+	11.1554i	−0.123169	+	0.379076i
$867$	4.37132	−	7.57135i	0.148458	−	0.257137i
$868$	−6.00116	+	30.3826i	−0.203693	+	1.03125i
$869$	11.6459	+	20.1713i	0.395060	+	0.684264i
$870$	−2.67783	+	8.24151i	−0.0907869	+	0.279413i
$871$	27.9779	−	0.927089i	0.947995	−	0.0314132i
$872$	3.68034	+	2.67392i	0.124632	+	0.0905505i
$873$	1.61803	+	2.80252i	0.0547622	+	0.0948508i
$874$	9.43769	+	16.3466i	0.319235	+	0.552931i
$875$	−8.22191	+	3.66063i	−0.277951	+	0.123752i
$876$	36.7082	−	26.6701i	1.24026	−	0.901098i
$877$	−1.75231	−	16.6721i	−0.0591712	−	0.562977i	−0.983440	−	0.181234i	$-0.941991\pi$
$877$	−1.75231	−	16.6721i	−0.0591712	−	0.562977i	0.924269	−	0.381742i	$-0.124676\pi$
$878$	−8.67565	−	9.63529i	−0.292789	−	0.325175i
$879$	29.5967	+	21.5033i	0.998274	+	0.725288i
$880$	14.1209	+	15.6828i	0.476015	+	0.528668i
$881$	6.27776	−	6.97216i	0.211503	−	0.234898i	−0.628054	−	0.778170i	$-0.716148\pi$
$881$	6.27776	−	6.97216i	0.211503	−	0.234898i	0.839557	+	0.543272i	$0.182815\pi$
$882$	−1.39577	−	0.621438i	−0.0469981	−	0.0209249i
$883$	9.57295	+	29.4625i	0.322155	+	0.991492i	0.972708	+	0.232031i	$0.0745372\pi$
$883$	9.57295	+	29.4625i	0.322155	+	0.991492i	−0.650553	+	0.759461i	$0.725463\pi$
$884$	24.1735	−	0.801025i	0.813043	−	0.0269414i
$885$	60.9787	−	44.3036i	2.04978	−	1.48925i
$886$	−7.62482	+	8.46823i	−0.256161	+	0.284496i
$887$	−9.70614	+	2.06310i	−0.325900	+	0.0692723i	−0.367957	−	0.929843i	$-0.619942\pi$
$887$	−9.70614	+	2.06310i	−0.325900	+	0.0692723i	0.0420561	+	0.999115i	$0.486609\pi$
$888$	9.29278	−	4.13741i	0.311845	−	0.138842i
$889$	−2.15654	+	6.63715i	−0.0723281	+	0.222603i
$890$	−0.581419	−	5.53184i	−0.0194892	−	0.185428i
$891$	−2.57106	−	24.4620i	−0.0861338	−	0.819508i
$892$	22.7705	+	16.5437i	0.762413	+	0.553926i
$893$	−1.41641	+	2.45329i	−0.0473983	+	0.0820962i
$894$	1.28115	+	2.21902i	0.0428482	+	0.0742152i
$895$	0.102303	−	0.973352i	0.00341963	−	0.0325356i
$896$	−9.35410	−	28.7890i	−0.312499	−	0.961772i
$897$	4.74997	−	66.2312i	0.158597	−	2.21140i
$898$	−3.43769			−0.114717
$899$	−13.8101	+	12.8003i	−0.460594	+	0.426915i
$900$	7.41641	+	12.8456i	0.247214	+	0.428187i
$901$	6.33810	+	7.03917i	0.211153	+	0.234509i
$902$	−2.19756	−	6.76340i	−0.0731708	−	0.225196i
$903$	−15.1499	+	6.74515i	−0.504156	+	0.224465i
$904$	7.94834	−	13.7669i	0.264358	−	0.457881i
$905$	40.6869			1.35248
$906$	−13.8170	+	6.15173i	−0.459040	+	0.204378i
$907$	28.4532	+	12.6682i	0.944773	+	0.420640i	0.820525	−	0.571611i	$-0.193681\pi$
$907$	28.4532	+	12.6682i	0.944773	+	0.420640i	0.124248	+	0.992251i	$0.460348\pi$
$908$	−24.1131	−	10.7359i	−0.800223	−	0.356282i
$909$	5.67376	−	17.4620i	0.188187	−	0.579179i
$910$	1.70314	+	12.2772i	0.0564586	+	0.406986i
$911$	−3.06637	+	9.43732i	−0.101593	+	0.312672i	−0.988916	−	0.148477i	$-0.952563\pi$
$911$	−3.06637	+	9.43732i	−0.101593	+	0.312672i	0.887322	+	0.461150i	$0.152563\pi$
$912$	−28.2418	+	31.3657i	−0.935178	+	1.03862i
$913$	12.1427	+	5.40626i	0.401863	+	0.178921i
$914$	−7.07794	−	1.50446i	−0.234118	−	0.0497632i
$915$	17.7492	+	54.6265i	0.586771	+	1.80590i
$916$	4.92586	+	46.8665i	0.162755	+	1.54851i
$917$	−18.7275	−	3.98066i	−0.618437	−	0.131453i
$918$	−0.954915	+	2.93893i	−0.0315169	+	0.0969990i
$919$	−52.8524	+	23.5314i	−1.74344	+	0.776229i	−0.750056	+	0.661374i	$0.769973\pi$
$919$	−52.8524	+	23.5314i	−1.74344	+	0.776229i	−0.993382	+	0.114854i	$0.963360\pi$
$920$	−35.5790	+	7.56255i	−1.17300	+	0.249330i
$921$	−17.7887	−	7.92003i	−0.586157	−	0.260974i
$922$	6.14590	−	4.46526i	0.202404	−	0.147055i
$923$	−45.0050	−	18.2766i	−1.48136	−	0.601580i
$924$	−27.8115			−0.914932
$925$	−6.18034	−	10.7047i	−0.203208	−	0.351967i
$926$	−0.746950	+	7.10675i	−0.0245463	+	0.233542i
$927$	7.71616	+	1.64012i	0.253432	+	0.0538686i
$928$	4.33282	−	13.3350i	0.142232	−	0.437744i
$929$	9.53444	−	16.5141i	0.312815	−	0.541811i	−0.666156	−	0.745813i	$-0.732061\pi$
$929$	9.53444	−	16.5141i	0.312815	−	0.541811i	0.978971	+	0.204001i	$0.0653947\pi$
$930$	−0.205858	−	14.2648i	−0.00675034	−	0.467762i
$931$	−12.0000			−0.393284
$932$	15.3615	+	17.0607i	0.503183	+	0.558842i
$933$	49.4784	−	54.9513i	1.61985	−	1.79902i
$934$	1.57238	−	14.9602i	0.0514497	−	0.489512i
$935$	−24.2705			−0.793731
$936$	−10.3050	+	2.54981i	−0.336828	+	0.0833433i
$937$	−0.218847	−	0.159002i	−0.00714942	−	0.00519436i	0.584205	−	0.811606i	$-0.301406\pi$
$937$	−0.218847	−	0.159002i	−0.00714942	−	0.00519436i	−0.591354	+	0.806412i	$0.701406\pi$
$938$	8.12752	+	3.61860i	0.265373	+	0.118152i
$939$	−4.68157	−	2.08437i	−0.152777	−	0.0680208i
$940$	−1.75725	−	1.95162i	−0.0573151	−	0.0636548i
$941$	−8.59017	−	6.24112i	−0.280032	−	0.203455i	0.438900	−	0.898536i	$-0.355368\pi$
$941$	−8.59017	−	6.24112i	−0.280032	−	0.203455i	−0.718931	+	0.695081i	$0.755368\pi$
$942$	10.7949	+	11.9890i	0.351717	+	0.390622i
$943$	−67.0769	−	14.2576i	−2.18433	−	0.464293i
$944$	−28.5967	+	20.7768i	−0.930745	+	0.676226i
$945$	19.6848	+	4.18414i	0.640348	+	0.136110i
$946$	1.41284	−	1.56912i	0.0459354	−	0.0510164i
$947$	−14.9971	−	6.67715i	−0.487341	−	0.216978i	0.148330	−	0.988938i	$-0.452610\pi$
$947$	−14.9971	−	6.67715i	−0.487341	−	0.216978i	−0.635672	+	0.771960i	$0.719277\pi$
$948$	−13.3450	−	41.0717i	−0.433426	−	1.33395i
$949$	35.4973	−	17.2349i	1.15229	−	0.559470i
$950$	−7.41641	−	5.38834i	−0.240620	−	0.174821i
$951$	−26.8381	+	5.70462i	−0.870285	+	0.184985i
$952$	14.5973	+	6.49913i	0.473101	+	0.210638i
$953$	−1.59260	−	15.1526i	−0.0515895	−	0.490841i	−0.989560	−	0.144125i	$-0.953963\pi$
$953$	−1.59260	−	15.1526i	−0.0515895	−	0.490841i	0.937970	−	0.346716i	$-0.112703\pi$
$954$	−1.61803	−	1.17557i	−0.0523858	−	0.0380605i
$955$	−10.7188	+	18.5656i	−0.346854	+	0.600768i
$956$	11.2082	−	19.4132i	0.362499	−	0.627867i
$957$	−13.6803	−	9.93935i	−0.442223	−	0.321294i
$958$	−7.53976	−	1.60263i	−0.243599	−	0.0517785i
$959$	−63.0088	+	13.3929i	−2.03466	+	0.432480i
$960$	−15.7918	−	27.3522i	−0.509678	−	0.882788i
$961$	14.7188	−	27.2829i	0.474802	−	0.880093i
$962$	4.13119	−	1.02220i	0.133195	−	0.0329572i
$963$	−11.1803	+	34.4095i	−0.360281	+	1.10883i
$964$	12.8802	−	14.3050i	0.414845	−	0.460732i
$965$	−0.803502	+	7.64481i	−0.0258656	+	0.246095i
$966$	10.5517	−	18.2760i	0.339494	−	0.588021i
$967$	−54.1033			−1.73985			−0.869923	−	0.493188i	$-0.835832\pi$
$967$	−54.1033			−1.73985			−0.869923	+	0.493188i	$0.835832\pi$
$968$	−8.06918	+	3.59263i	−0.259353	+	0.115471i
$969$	−5.07392	−	48.2751i	−0.162998	−	1.55082i
$970$	1.50000	−	1.08981i	0.0481621	−	0.0349918i
$971$	−29.0743	−	32.2903i	−0.933038	−	1.03624i	−0.999261	−	0.0384393i	$-0.987761\pi$
$971$	−29.0743	−	32.2903i	−0.933038	−	1.03624i	0.0662225	−	0.997805i	$-0.478905\pi$
$972$	−3.46691	+	32.9855i	−0.111201	+	1.05801i
$973$	−24.3318	+	5.17188i	−0.780042	+	0.165803i
$974$	−3.50000	−	10.7719i	−0.112147	−	0.345154i
$975$	10.9758	+	30.3238i	0.351507	+	0.971138i
$976$	−8.32373	−	25.6178i	−0.266436	−	0.820006i
$977$	−12.5182	+	13.9029i	−0.400494	+	0.444793i	−0.909334	−	0.416068i	$-0.863408\pi$
$977$	−12.5182	+	13.9029i	−0.400494	+	0.444793i	0.508840	+	0.860861i	$0.330075\pi$
$978$	10.0999	+	4.49677i	0.322960	+	0.143791i
$979$	10.6169	+	2.25669i	0.339318	+	0.0721243i
$980$	3.43769	−	10.5801i	0.109813	−	0.337970i
$981$	−5.64602	+	2.51377i	−0.180264	+	0.0802585i
$982$	−6.95569	−	7.72508i	−0.221965	−	0.246517i
$983$	−26.9164	+	19.5559i	−0.858500	+	0.623737i	−0.927476	−	0.373881i	$-0.878027\pi$
$983$	−26.9164	+	19.5559i	−0.858500	+	0.623737i	0.0689764	+	0.997618i	$0.478027\pi$
$984$	2.86495	+	27.2581i	0.0913311	+	0.868958i
$985$	2.49121	−	23.7023i	0.0793765	−	0.755217i
$986$	2.33688	+	4.04760i	0.0744215	+	0.128902i
$987$	3.16718			0.100813
$988$	−31.6514	+	24.6380i	−1.00696	+	0.783840i
$989$	−6.29180	−	19.3642i	−0.200067	−	0.615744i
$990$	5.01263	−	1.06547i	0.159312	−	0.0338628i
$991$	18.3156	+	31.7235i	0.581814	+	1.00773i	0.995264	+	0.0972048i	$0.0309902\pi$
$991$	18.3156	+	31.7235i	0.581814	+	1.00773i	−0.413450	+	0.910527i	$0.635676\pi$
$992$	0.333085	+	23.0810i	0.0105755	+	0.732822i
$993$	−2.36068			−0.0749139
$994$	−10.3298	−	11.4724i	−0.327642	−	0.363884i
$995$	53.5127	+	11.3745i	1.69647	+	0.360595i
$996$	−19.9377	−	14.4856i	−0.631750	−	0.458993i
$997$	−14.3435	+	24.8436i	−0.454262	+	0.786805i	−0.998645	−	0.0520317i	$-0.983430\pi$
$997$	−14.3435	+	24.8436i	−0.454262	+	0.786805i	0.544384	+	0.838836i	$0.316764\pi$
$998$	7.79837	+	13.5072i	0.246853	+	0.427562i
$999$	0.722274	−	6.87198i	0.0228517	−	0.217420i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bl.a.380.1	yes	8
13.9	even	3	inner	403.2.bl.a.256.1	yes	8
31.4	even	5	inner	403.2.bl.a.159.1	yes	8
403.35	even	15	inner	403.2.bl.a.35.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bl.a.35.1	✓	8	403.35	even	15	inner
403.2.bl.a.159.1	yes	8	31.4	even	5	inner
403.2.bl.a.256.1	yes	8	13.9	even	3	inner
403.2.bl.a.380.1	yes	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bl (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.373619 - 0.0794152i) q^{2} +(1.49622 - 1.66172i) q^{3} +(-1.69381 + 0.754131i) q^{4} -3.00000 q^{5} +(0.427051 - 0.739674i) q^{6} +(-2.74064 + 1.22021i) q^{7} +(-1.19098 + 0.865300i) q^{8} +(-0.209057 - 1.98904i) q^{9} +O(q^{10})\)	\(q+(0.373619 - 0.0794152i) q^{2} +(1.49622 - 1.66172i) q^{3} +(-1.69381 + 0.754131i) q^{4} -3.00000 q^{5} +(0.427051 - 0.739674i) q^{6} +(-2.74064 + 1.22021i) q^{7} +(-1.19098 + 0.865300i) q^{8} +(-0.209057 - 1.98904i) q^{9} +(-1.12086 + 0.238246i) q^{10} +(0.233733 - 2.22382i) q^{11} +(-1.28115 + 3.94298i) q^{12} +(-1.69837 + 3.18049i) q^{13} +(-0.927051 + 0.673542i) q^{14} +(-4.48866 + 4.98517i) q^{15} +(2.10502 - 2.33786i) q^{16} +(0.378188 + 3.59821i) q^{17} +(-0.236068 - 0.726543i) q^{18} +(-4.01478 - 4.45887i) q^{19} +(5.08142 - 2.26239i) q^{20} +(-2.07295 + 6.37988i) q^{21} +(-0.0892780 - 0.849423i) q^{22} +(-7.52402 - 3.34991i) q^{23} +(-0.344086 + 3.27376i) q^{24} +4.00000 q^{25} +(-0.381966 + 1.32317i) q^{26} +(1.80902 + 1.31433i) q^{27} +(3.72191 - 4.13360i) q^{28} +(3.30806 - 0.703150i) q^{29} +(-1.28115 + 2.21902i) q^{30} +(-4.78115 + 2.85317i) q^{31} +(2.07295 - 3.59045i) q^{32} +(-3.34565 - 3.71572i) q^{33} +(0.427051 + 1.31433i) q^{34} +(8.22191 - 3.66063i) q^{35} +(1.85410 + 3.21140i) q^{36} +(-1.54508 - 2.67617i) q^{37} +(-1.85410 - 1.34708i) q^{38} +(2.74395 + 7.58095i) q^{39} +(3.57295 - 2.59590i) q^{40} +(8.14429 - 1.73112i) q^{41} +(-0.267834 + 2.54827i) q^{42} +(1.65418 + 1.83716i) q^{43} +(1.28115 + 3.94298i) q^{44} +(0.627171 + 5.96713i) q^{45} +(-3.07715 - 0.654069i) q^{46} +(-0.145898 - 0.449028i) q^{47} +(-0.735299 - 6.99591i) q^{48} +(1.33826 - 1.48629i) q^{49} +(1.49448 - 0.317661i) q^{50} +(6.54508 + 4.75528i) q^{51} +(0.478211 - 6.66793i) q^{52} +(2.11803 - 1.53884i) q^{53} +(0.780261 + 0.347395i) q^{54} +(-0.701198 + 6.67146i) q^{55} +(2.20820 - 3.82472i) q^{56} -13.4164 q^{57} +(1.18011 - 0.525421i) q^{58} +(-10.9905 - 2.33611i) q^{59} +(3.84346 - 11.8290i) q^{60} +(4.28115 - 7.41517i) q^{61} +(-1.55975 + 1.44569i) q^{62} +(3.00000 + 5.19615i) q^{63} +(-1.45492 + 4.47777i) q^{64} +(5.09512 - 9.54147i) q^{65} +(-1.54508 - 1.12257i) q^{66} +(-3.88197 - 6.72376i) q^{67} +(-3.35410 - 5.80948i) q^{68} +(-16.8242 + 7.49063i) q^{69} +(2.78115 - 2.02063i) q^{70} +(1.40822 + 13.3983i) q^{71} +(1.97010 + 2.18802i) q^{72} +(-8.85410 - 6.43288i) q^{73} +(-0.789802 - 0.877163i) q^{74} +(5.98489 - 6.64689i) q^{75} +(10.1628 + 4.52479i) q^{76} +(2.07295 + 6.37988i) q^{77} +(1.62723 + 2.61448i) q^{78} +(-8.42705 + 6.12261i) q^{79} +(-6.31505 + 7.01357i) q^{80} +(10.7596 - 2.28703i) q^{81} +(2.90539 - 1.29356i) q^{82} +(-1.83688 + 5.65334i) q^{83} +(-1.30009 - 12.3696i) q^{84} +(-1.13456 - 10.7946i) q^{85} +(0.763932 + 0.555029i) q^{86} +(3.78115 - 6.54915i) q^{87} +(1.64590 + 2.85078i) q^{88} +(-0.507392 + 4.82751i) q^{89} +(0.708204 + 2.17963i) q^{90} +(0.773761 - 10.7889i) q^{91} +15.2705 q^{92} +(-2.41249 + 12.2139i) q^{93} +(-0.0901699 - 0.156179i) q^{94} +(12.0444 + 13.3766i) q^{95} +(-2.86475 - 8.81678i) q^{96} +(-1.47815 + 0.658114i) q^{97} +(0.381966 - 0.661585i) q^{98} -4.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 5 q^{3} - 6 q^{4} - 24 q^{5} - 10 q^{6} - 3 q^{7} - 14 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 5 * q^3 - 6 * q^4 - 24 * q^5 - 10 * q^6 - 3 * q^7 - 14 * q^8 + 2 * q^9	\( 8 q - 4 q^{2} - 5 q^{3} - 6 q^{4} - 24 q^{5} - 10 q^{6} - 3 q^{7} - 14 q^{8} + 2 q^{9} + 12 q^{10} - 5 q^{11} + 30 q^{12} - 5 q^{13} + 6 q^{14} + 15 q^{15} + 14 q^{16} - 5 q^{17} + 16 q^{18} - 6 q^{19} + 18 q^{20} - 30 q^{21} + 5 q^{22} - 11 q^{23} - 5 q^{24} + 32 q^{25} - 12 q^{26} + 10 q^{27} - 27 q^{28} - 7 q^{29} + 30 q^{30} + 2 q^{31} + 30 q^{32} - 5 q^{33} - 10 q^{34} + 9 q^{35} - 12 q^{36} + 10 q^{37} + 12 q^{38} - 10 q^{39} + 42 q^{40} + 17 q^{41} + 15 q^{42} - 12 q^{43} - 30 q^{44} - 6 q^{45} + 14 q^{46} - 28 q^{47} + 25 q^{48} + 2 q^{49} - 16 q^{50} + 30 q^{51} + 63 q^{52} + 8 q^{53} + 5 q^{54} + 15 q^{55} - 36 q^{56} - 7 q^{58} + 4 q^{59} - 90 q^{60} - 6 q^{61} - 16 q^{62} + 24 q^{63} - 34 q^{64} + 15 q^{65} + 10 q^{66} - 40 q^{67} - 35 q^{69} - 18 q^{70} - 19 q^{71} - 26 q^{72} - 44 q^{73} + 35 q^{74} - 20 q^{75} + 36 q^{76} + 30 q^{77} + 70 q^{78} - 54 q^{79} - 42 q^{80} - 11 q^{81} + 17 q^{82} - 46 q^{83} + 15 q^{85} + 24 q^{86} - 10 q^{87} + 40 q^{88} + 9 q^{89} - 48 q^{90} - 21 q^{91} - 12 q^{92} - 5 q^{93} + 44 q^{94} + 18 q^{95} - 90 q^{96} - 3 q^{97} + 12 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 5 * q^3 - 6 * q^4 - 24 * q^5 - 10 * q^6 - 3 * q^7 - 14 * q^8 + 2 * q^9 + 12 * q^10 - 5 * q^11 + 30 * q^12 - 5 * q^13 + 6 * q^14 + 15 * q^15 + 14 * q^16 - 5 * q^17 + 16 * q^18 - 6 * q^19 + 18 * q^20 - 30 * q^21 + 5 * q^22 - 11 * q^23 - 5 * q^24 + 32 * q^25 - 12 * q^26 + 10 * q^27 - 27 * q^28 - 7 * q^29 + 30 * q^30 + 2 * q^31 + 30 * q^32 - 5 * q^33 - 10 * q^34 + 9 * q^35 - 12 * q^36 + 10 * q^37 + 12 * q^38 - 10 * q^39 + 42 * q^40 + 17 * q^41 + 15 * q^42 - 12 * q^43 - 30 * q^44 - 6 * q^45 + 14 * q^46 - 28 * q^47 + 25 * q^48 + 2 * q^49 - 16 * q^50 + 30 * q^51 + 63 * q^52 + 8 * q^53 + 5 * q^54 + 15 * q^55 - 36 * q^56 - 7 * q^58 + 4 * q^59 - 90 * q^60 - 6 * q^61 - 16 * q^62 + 24 * q^63 - 34 * q^64 + 15 * q^65 + 10 * q^66 - 40 * q^67 - 35 * q^69 - 18 * q^70 - 19 * q^71 - 26 * q^72 - 44 * q^73 + 35 * q^74 - 20 * q^75 + 36 * q^76 + 30 * q^77 + 70 * q^78 - 54 * q^79 - 42 * q^80 - 11 * q^81 + 17 * q^82 - 46 * q^83 + 15 * q^85 + 24 * q^86 - 10 * q^87 + 40 * q^88 + 9 * q^89 - 48 * q^90 - 21 * q^91 - 12 * q^92 - 5 * q^93 + 44 * q^94 + 18 * q^95 - 90 * q^96 - 3 * q^97 + 12 * q^98

Introduction

L-functions

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