LMFDB - Embedded newform 216.2.t.a.133.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(13,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8]))

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

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

chi := DirichletCharacter("216.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			133.7
Character	$\chi$	$=$	216.133
Dual form			216.2.t.a.13.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23486 + 0.689282i) q^{2} +(1.71350 + 0.252809i) q^{3} +(1.04978 - 1.70234i) q^{4} +(2.05804 + 2.45268i) q^{5} +(-2.29020 + 0.868902i) q^{6} +(-4.54005 + 1.65244i) q^{7} +(-0.122943 + 2.82575i) q^{8} +(2.87218 + 0.866376i) q^{9} +O(q^{10})$	\(q+(-1.23486 + 0.689282i) q^{2} +(1.71350 + 0.252809i) q^{3} +(1.04978 - 1.70234i) q^{4} +(2.05804 + 2.45268i) q^{5} +(-2.29020 + 0.868902i) q^{6} +(-4.54005 + 1.65244i) q^{7} +(-0.122943 + 2.82575i) q^{8} +(2.87218 + 0.866376i) q^{9} +(-4.23199 - 1.61015i) q^{10} +(0.638845 - 0.761346i) q^{11} +(2.22917 - 2.65157i) q^{12} +(1.85386 - 0.326885i) q^{13} +(4.46735 - 5.16992i) q^{14} +(2.90640 + 4.72296i) q^{15} +(-1.79592 - 3.57417i) q^{16} +(-0.690426 - 1.19585i) q^{17} +(-4.14392 + 0.909883i) q^{18} +(-1.81438 - 1.04753i) q^{19} +(6.33579 - 0.928715i) q^{20} +(-8.19713 + 1.68370i) q^{21} +(-0.264105 + 1.38050i) q^{22} +(6.79507 + 2.47320i) q^{23} +(-0.925037 + 4.81085i) q^{24} +(-0.911858 + 5.17140i) q^{25} +(-2.06395 + 1.68149i) q^{26} +(4.70245 + 2.21065i) q^{27} +(-1.95303 + 9.46341i) q^{28} +(-1.51798 - 0.267662i) q^{29} +(-6.84447 - 3.82889i) q^{30} +(-7.70194 - 2.80328i) q^{31} +(4.68133 + 3.17571i) q^{32} +(1.28714 - 1.14306i) q^{33} +(1.67686 + 1.00082i) q^{34} +(-13.3965 - 7.73449i) q^{35} +(4.49002 - 3.97992i) q^{36} +(6.22039 - 3.59135i) q^{37} +(2.96255 + 0.0429408i) q^{38} +(3.25923 - 0.0914472i) q^{39} +(-7.18369 + 5.51398i) q^{40} +(-0.0260791 - 0.147902i) q^{41} +(8.96180 - 7.72928i) q^{42} +(7.04138 - 8.39160i) q^{43} +(-0.625423 - 1.88678i) q^{44} +(3.78612 + 8.82757i) q^{45} +(-10.0957 + 1.62965i) q^{46} +(-4.64968 + 1.69234i) q^{47} +(-2.17374 - 6.57836i) q^{48} +(12.5192 - 10.5048i) q^{49} +(-2.43854 - 7.01451i) q^{50} +(-0.880725 - 2.22364i) q^{51} +(1.38967 - 3.49905i) q^{52} +2.04785i q^{53} +(-7.33065 + 0.511467i) q^{54} +3.18211 q^{55} +(-4.11123 - 13.0322i) q^{56} +(-2.84411 - 2.25363i) q^{57} +(2.05900 - 0.715794i) q^{58} +(-0.104687 - 0.124761i) q^{59} +(11.0912 + 0.0103864i) q^{60} +(-2.77834 - 7.63343i) q^{61} +(11.4431 - 1.84714i) q^{62} +(-14.4715 + 0.812718i) q^{63} +(-7.96977 - 0.694812i) q^{64} +(4.61706 + 3.87417i) q^{65} +(-0.801547 + 2.29873i) q^{66} +(-2.85014 + 0.502556i) q^{67} +(-2.76055 - 0.0800424i) q^{68} +(11.0181 + 5.95569i) q^{69} +(21.8741 + 0.317055i) q^{70} +(-6.18008 - 10.7042i) q^{71} +(-2.80128 + 8.00955i) q^{72} +(-2.83664 + 4.91320i) q^{73} +(-5.20589 + 8.72243i) q^{74} +(-2.86984 + 8.63068i) q^{75} +(-3.68795 + 1.98901i) q^{76} +(-1.64231 + 4.51220i) q^{77} +(-3.96167 + 2.35945i) q^{78} +(0.784918 - 4.45149i) q^{79} +(5.07019 - 11.7606i) q^{80} +(7.49879 + 4.97677i) q^{81} +(0.134150 + 0.164663i) q^{82} +(-0.477539 - 0.0842031i) q^{83} +(-5.73896 + 15.7218i) q^{84} +(1.51212 - 4.15451i) q^{85} +(-2.91098 + 15.2160i) q^{86} +(-2.53340 - 0.842398i) q^{87} +(2.07283 + 1.89882i) q^{88} +(1.01658 - 1.76076i) q^{89} +(-10.7600 - 8.29114i) q^{90} +(-7.87644 + 4.54747i) q^{91} +(11.3436 - 8.97120i) q^{92} +(-12.4886 - 6.75053i) q^{93} +(4.57522 - 5.29476i) q^{94} +(-1.16481 - 6.60595i) q^{95} +(7.21862 + 6.62506i) q^{96} +(-6.24806 - 5.24275i) q^{97} +(-8.21869 + 21.6013i) q^{98} +(2.49449 - 1.63324i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−1.23486	+	0.689282i	−0.873181	+	0.487396i
$2$	−1.23486	+	0.689282i	−0.873181	+	0.487396i
$3$	1.71350	+	0.252809i	0.989291	+	0.145959i
$3$	1.71350	+	0.252809i	0.989291	+	0.145959i
$4$	1.04978	−	1.70234i	0.524890	−	0.851170i
$5$	2.05804	+	2.45268i	0.920385	+	1.09687i	0.995021	+	0.0996611i	$0.0317759\pi$
$5$	2.05804	+	2.45268i	0.920385	+	1.09687i	−0.0746367	+	0.997211i	$0.523780\pi$
$6$	−2.29020	+	0.868902i	−0.934970	+	0.354728i
$7$	−4.54005	+	1.65244i	−1.71598	+	0.624565i	−0.997479	−	0.0709635i	$-0.977393\pi$
$7$	−4.54005	+	1.65244i	−1.71598	+	0.624565i	−0.718499	+	0.695528i	$0.755170\pi$
$8$	−0.122943	+	2.82575i	−0.0434668	+	0.999055i
$9$	2.87218	+	0.866376i	0.957392	+	0.288792i
$10$	−4.23199	−	1.61015i	−1.33827	−	0.509176i
$11$	0.638845	−	0.761346i	0.192619	−	0.229554i	−0.661088	−	0.750309i	$-0.729905\pi$
$11$	0.638845	−	0.761346i	0.192619	−	0.229554i	0.853707	+	0.520754i	$0.174349\pi$
$12$	2.22917	−	2.65157i	0.643505	−	0.765442i
$13$	1.85386	−	0.326885i	0.514167	−	0.0906616i	0.0894567	−	0.995991i	$-0.471487\pi$
$13$	1.85386	−	0.326885i	0.514167	−	0.0906616i	0.424711	+	0.905329i	$0.360376\pi$
$14$	4.46735	−	5.16992i	1.19395	−	1.38172i
$15$	2.90640	+	4.72296i	0.750430	+	1.21946i
$16$	−1.79592	−	3.57417i	−0.448981	−	0.893541i
$17$	−0.690426	−	1.19585i	−0.167453	−	0.290037i	0.770071	−	0.637959i	$-0.220221\pi$
$17$	−0.690426	−	1.19585i	−0.167453	−	0.290037i	−0.937524	+	0.347921i	$0.886888\pi$
$18$	−4.14392	+	0.909883i	−0.976732	+	0.214462i
$19$	−1.81438	−	1.04753i	−0.416246	−	0.240320i	0.277224	−	0.960805i	$-0.410586\pi$
$19$	−1.81438	−	1.04753i	−0.416246	−	0.240320i	−0.693470	+	0.720485i	$0.743919\pi$
$20$	6.33579	−	0.928715i	1.41673	−	0.207667i
$21$	−8.19713	+	1.68370i	−1.78876	+	0.367414i
$22$	−0.264105	+	1.38050i	−0.0563073	+	0.294324i
$23$	6.79507	+	2.47320i	1.41687	+	0.515698i	0.933138	−	0.359518i	$-0.117059\pi$
$23$	6.79507	+	2.47320i	1.41687	+	0.515698i	0.483732	+	0.875216i	$0.339281\pi$
$24$	−0.925037	+	4.81085i	−0.188822	+	0.982011i
$25$	−0.911858	+	5.17140i	−0.182372	+	1.03428i
$26$	−2.06395	+	1.68149i	−0.404773	+	0.329767i
$27$	4.70245	+	2.21065i	0.904987	+	0.425439i
$28$	−1.95303	+	9.46341i	−0.369089	+	1.78842i
$29$	−1.51798	−	0.267662i	−0.281883	−	0.0497035i	0.0309193	−	0.999522i	$-0.490156\pi$
$29$	−1.51798	−	0.267662i	−0.281883	−	0.0497035i	−0.312802	+	0.949818i	$0.601268\pi$
$30$	−6.84447	−	3.82889i	−1.24962	−	0.699056i
$31$	−7.70194	−	2.80328i	−1.38331	−	0.503483i	−0.460129	−	0.887852i	$-0.652197\pi$
$31$	−7.70194	−	2.80328i	−1.38331	−	0.503483i	−0.923180	+	0.384369i	$0.874419\pi$
$32$	4.68133	+	3.17571i	0.827550	+	0.561392i
$33$	1.28714	−	1.14306i	0.224062	−	0.198982i
$34$	1.67686	+	1.00082i	0.287580	+	0.171639i
$35$	−13.3965	−	7.73449i	−2.26443	−	1.30737i
$36$	4.49002	−	3.97992i	0.748336	−	0.663319i
$37$	6.22039	−	3.59135i	1.02263	−	0.590414i	0.107763	−	0.994177i	$-0.465631\pi$
$37$	6.22039	−	3.59135i	1.02263	−	0.590414i	0.914864	+	0.403763i	$0.132298\pi$
$38$	2.96255	+	0.0429408i	0.480589	+	0.00696592i
$39$	3.25923	−	0.0914472i	0.521894	−	0.0146433i
$40$	−7.18369	+	5.51398i	−1.13584	+	0.871837i
$41$	−0.0260791	−	0.147902i	−0.00407287	−	0.0230984i	0.982704	−	0.185185i	$-0.0592886\pi$
$41$	−0.0260791	−	0.147902i	−0.00407287	−	0.0230984i	−0.986776	+	0.162087i	$0.948177\pi$
$42$	8.96180	−	7.72928i	1.38284	−	1.19265i
$43$	7.04138	−	8.39160i	1.07380	−	1.27971i	0.115697	−	0.993285i	$-0.463090\pi$
$43$	7.04138	−	8.39160i	1.07380	−	1.27971i	0.958104	−	0.286422i	$-0.0924659\pi$
$44$	−0.625423	−	1.88678i	−0.0942861	−	0.284442i
$45$	3.78612	+	8.82757i	0.564401	+	1.31594i
$46$	−10.0957	+	1.62965i	−1.48853	+	0.240279i
$47$	−4.64968	+	1.69234i	−0.678225	+	0.246854i	−0.658085	−	0.752943i	$-0.728633\pi$
$47$	−4.64968	+	1.69234i	−0.678225	+	0.246854i	−0.0201400	+	0.999797i	$0.506411\pi$
$48$	−2.17374	−	6.57836i	−0.313752	−	0.949505i
$49$	12.5192	−	10.5048i	1.78845	−	1.50069i
$50$	−2.43854	−	7.01451i	−0.344861	−	0.992001i
$51$	−0.880725	−	2.22364i	−0.123326	−	0.311372i
$52$	1.38967	−	3.49905i	0.192713	−	0.485231i
$53$			2.04785i			0.281293i	0.990060	+	0.140647i	$0.0449181\pi$
$53$			2.04785i			0.281293i	−0.990060	+	0.140647i	$0.955082\pi$
$54$	−7.33065	+	0.511467i	−0.997575	+	0.0696019i
$55$	3.18211			0.429075
$56$	−4.11123	−	13.0322i	−0.549386	−	1.74150i
$57$	−2.84411	−	2.25363i	−0.376712	−	0.298501i
$58$	2.05900	−	0.715794i	0.270360	−	0.0939883i
$59$	−0.104687	−	0.124761i	−0.0136291	−	0.0162425i	0.759187	−	0.650873i	$-0.225597\pi$
$59$	−0.104687	−	0.124761i	−0.0136291	−	0.0162425i	−0.772816	+	0.634630i	$0.781152\pi$
$60$	11.0912	+	0.0103864i	1.43186	+	0.00134087i
$61$	−2.77834	−	7.63343i	−0.355730	−	0.977360i	−0.980494	−	0.196547i	$-0.937027\pi$
$61$	−2.77834	−	7.63343i	−0.355730	−	0.977360i	0.624764	−	0.780813i	$-0.285195\pi$
$62$	11.4431	−	1.84714i	1.45327	−	0.234587i
$63$	−14.4715	+	0.812718i	−1.82323	+	0.102393i
$64$	−7.96977	−	0.694812i	−0.996221	−	0.0868515i
$65$	4.61706	+	3.87417i	0.572676	+	0.480532i
$66$	−0.801547	+	2.29873i	−0.0986636	+	0.282954i
$67$	−2.85014	+	0.502556i	−0.348199	+	0.0613970i	−0.345013	−	0.938598i	$-0.612125\pi$
$67$	−2.85014	+	0.502556i	−0.348199	+	0.0613970i	−0.00318663	+	0.999995i	$0.501014\pi$
$68$	−2.76055	−	0.0800424i	−0.334765	−	0.00970657i
$69$	11.0181	+	5.95569i	1.32643	+	0.716981i
$70$	21.8741	+	0.317055i	2.61446	+	0.0378954i
$71$	−6.18008	−	10.7042i	−0.733440	−	1.27036i	−0.955404	−	0.295301i	$-0.904580\pi$
$71$	−6.18008	−	10.7042i	−0.733440	−	1.27036i	0.221964	−	0.975055i	$-0.428753\pi$
$72$	−2.80128	+	8.00955i	−0.330134	+	0.943934i
$73$	−2.83664	+	4.91320i	−0.332003	+	0.575047i	−0.982905	−	0.184116i	$-0.941058\pi$
$73$	−2.83664	+	4.91320i	−0.332003	+	0.575047i	0.650901	+	0.759162i	$0.274391\pi$
$74$	−5.20589	+	8.72243i	−0.605173	+	1.01396i
$75$	−2.86984	+	8.63068i	−0.331381	+	0.996585i
$76$	−3.68795	+	1.98901i	−0.423037	+	0.228155i
$77$	−1.64231	+	4.51220i	−0.187158	+	0.514213i
$78$	−3.96167	+	2.35945i	−0.448571	+	0.267155i
$79$	0.784918	−	4.45149i	0.0883102	−	0.500832i	−0.908283	−	0.418357i	$-0.862606\pi$
$79$	0.784918	−	4.45149i	0.0883102	−	0.500832i	0.996593	−	0.0824755i	$-0.0262826\pi$
$80$	5.07019	−	11.7606i	0.566865	−	1.31488i
$81$	7.49879	+	4.97677i	0.833199	+	0.552974i
$82$	0.134150	+	0.164663i	0.0148144	+	0.0181840i
$83$	−0.477539	−	0.0842031i	−0.0524167	−	0.00924249i	0.147378	−	0.989080i	$-0.452917\pi$
$83$	−0.477539	−	0.0842031i	−0.0524167	−	0.00924249i	−0.199795	+	0.979838i	$0.564028\pi$
$84$	−5.73896	+	15.7218i	−0.626171	+	1.71539i
$85$	1.51212	−	4.15451i	0.164012	−	0.450620i
$86$	−2.91098	+	15.2160i	−0.313899	+	1.64078i
$87$	−2.53340	−	0.842398i	−0.271609	−	0.0903145i
$88$	2.07283	+	1.89882i	0.220965	+	0.202415i
$89$	1.01658	−	1.76076i	0.107757	−	0.186640i	−0.807104	−	0.590409i	$-0.798967\pi$
$89$	1.01658	−	1.76076i	0.107757	−	0.186640i	0.914861	+	0.403769i	$0.132300\pi$
$90$	−10.7600	−	8.29114i	−1.13421	−	0.873963i
$91$	−7.87644	+	4.54747i	−0.825676	+	0.476704i
$92$	11.3436	−	8.97120i	1.18265	−	0.935312i
$93$	−12.4886	−	6.75053i	−1.29501	−	0.699998i
$94$	4.57522	−	5.29476i	0.471898	−	0.546113i
$95$	−1.16481	−	6.60595i	−0.119507	−	0.677756i
$96$	7.21862	+	6.62506i	0.736748	+	0.676168i
$97$	−6.24806	−	5.24275i	−0.634395	−	0.532320i	0.267897	−	0.963448i	$-0.413671\pi$
$97$	−6.24806	−	5.24275i	−0.634395	−	0.532320i	−0.902291	+	0.431127i	$0.858116\pi$
$98$	−8.21869	+	21.6013i	−0.830213	+	2.18206i
$99$	2.49449	−	1.63324i	0.250705	−	0.164147i
$100$	7.84624	+	6.98113i	0.784624	+	0.698113i
$101$	−0.681498	−	1.87240i	−0.0678116	−	0.186311i	0.901158	−	0.433491i	$-0.142718\pi$
$101$	−0.681498	−	1.87240i	−0.0678116	−	0.186311i	−0.968970	+	0.247180i	$0.920496\pi$
$102$	2.62029	+	2.13883i	0.259448	+	0.211776i
$103$	3.13576	−	2.63121i	0.308975	−	0.259261i	−0.475093	−	0.879936i	$-0.657586\pi$
$103$	3.13576	−	2.63121i	0.308975	−	0.259261i	0.784068	+	0.620675i	$0.213141\pi$
$104$	0.695778	+	5.27873i	0.0682267	+	0.517622i
$105$	−20.9996	−	16.6398i	−2.04935	−	1.62388i
$106$	−1.41154	−	2.52881i	−0.137101	−	0.245620i
$107$			16.0097i			1.54772i	0.633357	+	0.773860i	$0.281677\pi$
$107$			16.0097i			1.54772i	−0.633357	+	0.773860i	$0.718323\pi$
$108$	8.69981	−	5.68448i	0.837140	−	0.546989i
$109$			1.87880i			0.179957i	0.995944	+	0.0899783i	$0.0286798\pi$
$109$			1.87880i			0.179957i	−0.995944	+	0.0899783i	$0.971320\pi$
$110$	−3.92947	+	2.19337i	−0.374660	+	0.209130i
$111$	11.5666	−	4.58121i	1.09785	−	0.434829i
$112$	14.0597	+	13.2592i	1.32852	+	1.25288i
$113$	−9.62723	+	8.07821i	−0.905654	+	0.759934i	−0.971287	−	0.237910i	$-0.923538\pi$
$113$	−9.62723	+	8.07821i	−0.905654	+	0.759934i	0.0656335	+	0.997844i	$0.479093\pi$
$114$	5.06548	+	0.822538i	0.474426	+	0.0770377i
$115$	7.91857	+	21.7561i	0.738410	+	2.02877i
$116$	−2.04920	+	2.30314i	−0.190263	+	0.213841i
$117$	5.60781	+	0.667265i	0.518442	+	0.0616887i
$118$	0.215270	+	0.0819041i	0.0198172	+	0.00753989i
$119$	5.11065	+	4.28834i	0.468493	+	0.393112i
$120$	−13.7032	+	7.63212i	−1.25093	+	0.696714i
$121$	1.73861	+	9.86012i	0.158055	+	0.896375i
$122$	8.69246	+	7.51119i	0.786978	+	0.680031i
$123$	−0.00729571	−	0.260023i	−0.000657832	−	0.0234455i
$124$	−12.8575	+	10.1685i	−1.15463	+	0.913158i
$125$	−0.696470	+	0.402107i	−0.0622942	+	0.0359656i
$126$	17.3101	−	10.9785i	1.54211	−	0.978044i
$127$	−5.12850	+	8.88281i	−0.455080	+	0.788222i	−0.998693	−	0.0511140i	$-0.983723\pi$
$127$	−5.12850	+	8.88281i	−0.455080	+	0.788222i	0.543612	+	0.839336i	$0.317056\pi$
$128$	10.3205	−	4.63542i	0.912213	−	0.409717i
$129$	14.1869	−	12.5989i	1.24909	−	1.10927i
$130$	−8.37184	−	1.60162i	−0.734259	−	0.140471i
$131$	5.52701	−	15.1853i	0.482897	−	1.32675i	−0.424101	−	0.905615i	$-0.639410\pi$
$131$	5.52701	−	15.1853i	0.482897	−	1.32675i	0.906998	−	0.421134i	$-0.138368\pi$
$132$	−0.594670	−	3.39111i	−0.0517594	−	0.295158i
$133$	9.96834	+	1.75769i	0.864365	+	0.152411i
$134$	3.17313	−	2.58514i	0.274117	−	0.223322i
$135$	4.25584	+	16.0832i	0.366284	+	1.38422i
$136$	3.46407	−	1.80395i	0.297042	−	0.154688i
$137$	−1.20634	+	6.84148i	−0.103064	+	0.584507i	0.888911	+	0.458079i	$0.151462\pi$
$137$	−1.20634	+	6.84148i	−0.103064	+	0.584507i	−0.991976	+	0.126428i	$0.959649\pi$
$138$	−17.7110	+	0.240124i	−1.50766	+	0.0204407i
$139$	0.774820	−	2.12880i	0.0657194	−	0.180563i	−0.902486	−	0.430719i	$-0.858260\pi$
$139$	0.774820	−	2.12880i	0.0657194	−	0.180563i	0.968205	+	0.250157i	$0.0804821\pi$
$140$	−27.2301	+	14.6859i	−2.30137	+	1.24119i
$141$	−8.39507	+	1.72436i	−0.706993	+	0.145217i
$142$	15.0098	+	8.95843i	1.25959	+	0.751775i
$143$	0.935455	−	1.62026i	0.0782267	−	0.135493i
$144$	−2.06164	−	11.8216i	−0.171803	−	0.985131i
$145$	−2.46759	−	4.27399i	−0.204922	−	0.354935i
$146$	0.116281	−	8.02238i	0.00962345	−	0.663937i
$147$	24.1073	−	14.8351i	1.98834	−	1.22358i
$148$	0.416352	−	14.3594i	0.0342239	−	1.18033i
$149$	−4.50367	+	0.794119i	−0.368955	+	0.0650568i	−0.355052	−	0.934847i	$-0.615537\pi$
$149$	−4.50367	+	0.794119i	−0.368955	+	0.0650568i	−0.0139034	+	0.999903i	$0.504426\pi$
$150$	−2.40511	−	12.6359i	−0.196376	−	1.03171i
$151$	8.18905	+	6.87143i	0.666416	+	0.559189i	0.912002	−	0.410186i	$-0.134536\pi$
$151$	8.18905	+	6.87143i	0.666416	+	0.559189i	−0.245587	+	0.969375i	$0.578981\pi$
$152$	3.18313	−	4.99819i	0.258186	−	0.405407i
$153$	−0.946968	−	4.03287i	−0.0765578	−	0.326038i
$154$	−1.08215	−	6.70397i	−0.0872025	−	0.540222i
$155$	−8.97538	−	24.6596i	−0.720920	−	1.98071i
$156$	3.26580	−	5.64431i	0.261473	−	0.451907i
$157$	−15.1579	−	18.0645i	−1.20973	−	1.44170i	−0.864090	−	0.503337i	$-0.832106\pi$
$157$	−15.1579	−	18.0645i	−1.20973	−	1.44170i	−0.345642	−	0.938366i	$-0.612339\pi$
$158$	2.09907	+	6.03802i	0.166993	+	0.480359i
$159$	−0.517713	+	3.50899i	−0.0410573	+	0.278281i
$160$	1.84538	+	18.0176i	0.145890	+	1.42441i
$161$	−34.9368			−2.75340
$162$	−12.6904	−	0.976850i	−0.997050	−	0.0767486i
$163$			14.1348i			1.10712i	0.832809	+	0.553560i	$0.186731\pi$
$163$			14.1348i			1.10712i	−0.832809	+	0.553560i	$0.813269\pi$
$164$	−0.279157	−	0.110869i	−0.0217985	−	0.00865741i
$165$	5.45255	+	0.804464i	0.424480	+	0.0626274i
$166$	0.647736	−	0.225180i	0.0502741	−	0.0174774i
$167$	10.7822	−	9.04730i	0.834348	−	0.700101i	−0.121937	−	0.992538i	$-0.538911\pi$
$167$	10.7822	−	9.04730i	0.834348	−	0.700101i	0.956285	+	0.292437i	$0.0944661\pi$
$168$	−3.74994	−	23.3701i	−0.289315	−	1.80304i
$169$	−8.88607	+	3.23427i	−0.683544	+	0.248790i
$170$	0.996370	+	6.17254i	0.0764181	+	0.473412i
$171$	−4.30365	−	4.58062i	−0.329108	−	0.350289i
$172$	−6.89345	−	20.7962i	−0.525620	−	1.58569i
$173$	−5.51213	+	6.56911i	−0.419080	+	0.499440i	−0.933739	−	0.357955i	$-0.883474\pi$
$173$	−5.51213	+	6.56911i	−0.419080	+	0.499440i	0.514659	+	0.857395i	$0.327919\pi$
$174$	3.70906	−	0.705982i	0.281183	−	0.0535203i
$175$	−4.40557	−	24.9852i	−0.333030	−	1.88871i
$176$	−3.86849	−	0.916018i	−0.291599	−	0.0690475i
$177$	−0.147841	−	0.240244i	−0.0111124	−	0.0180579i
$178$	−0.0416719	+	2.87501i	−0.00312344	+	0.215491i
$179$	−4.64521	+	2.68191i	−0.347199	+	0.200455i	−0.663451	−	0.748220i	$-0.730909\pi$
$179$	−4.64521	+	2.68191i	−0.347199	+	0.200455i	0.316252	+	0.948675i	$0.397576\pi$
$180$	19.0021	+	2.82174i	1.41633	+	0.210320i
$181$	7.45952	+	4.30676i	0.554462	+	0.320119i	0.750920	−	0.660394i	$-0.229611\pi$
$181$	7.45952	+	4.30676i	0.554462	+	0.320119i	−0.196458	+	0.980512i	$0.562944\pi$
$182$	6.59185	−	11.0446i	0.488621	−	0.818680i
$183$	−2.83090	−	13.7823i	−0.209266	−	1.01882i
$184$	−7.82407	+	18.8971i	−0.576798	+	1.39312i
$185$	21.6103	+	7.86549i	1.58882	+	0.578283i
$186$	20.0747	−	0.272171i	1.47195	−	0.0199566i
$187$	−1.35153	−	0.238312i	−0.0988339	−	0.0174271i
$188$	−2.00019	+	9.69193i	−0.145879	+	0.706856i
$189$	−25.0023	−	2.26591i	−1.81865	−	0.164821i
$190$	5.99174	+	7.35457i	0.434687	+	0.533556i
$191$	−3.29778	+	18.7027i	−0.238619	+	1.35328i	0.596237	+	0.802809i	$0.296662\pi$
$191$	−3.29778	+	18.7027i	−0.238619	+	1.35328i	−0.834856	+	0.550469i	$0.814449\pi$
$192$	−13.4806	−	3.20539i	−0.972876	−	0.231329i
$193$	3.49795	+	1.27315i	0.251788	+	0.0916434i	0.464831	−	0.885399i	$-0.346115\pi$
$193$	3.49795	+	1.27315i	0.251788	+	0.0916434i	−0.213043	+	0.977043i	$0.568337\pi$
$194$	11.3292	+	2.16740i	0.813392	+	0.155610i
$195$	6.93192	+	7.80564i	0.496405	+	0.558973i
$196$	−4.74043	−	32.3397i	−0.338602	−	2.30998i
$197$	9.72565	+	5.61511i	0.692924	+	0.400060i	0.804706	−	0.593673i	$-0.202323\pi$
$197$	9.72565	+	5.61511i	0.692924	+	0.400060i	−0.111783	+	0.993733i	$0.535656\pi$
$198$	−1.95459	+	3.73623i	−0.138907	+	0.265523i
$199$	2.89877	+	5.02081i	0.205488	+	0.355916i	0.950288	−	0.311372i	$-0.100789\pi$
$199$	2.89877	+	5.02081i	0.205488	+	0.355916i	−0.744800	+	0.667288i	$0.767455\pi$
$200$	−14.5010	−	3.21247i	−1.02538	−	0.227156i
$201$	−5.01076	+	0.140592i	−0.353432	+	0.00991657i
$202$	2.13217	+	1.84242i	0.150019	+	0.129632i
$203$	7.33402	−	1.29319i	0.514747	−	0.0907638i
$204$	−4.70996	−	0.835042i	−0.329763	−	0.0584646i
$205$	0.309084	−	0.368352i	0.0215874	−	0.0257268i
$206$	−2.05859	+	5.41061i	−0.143428	+	0.376975i
$207$	17.3739	+	12.9906i	1.20757	+	0.902906i
$208$	−4.49773	−	6.03893i	−0.311861	−	0.418724i
$209$	−1.95664	+	0.712158i	−0.135343	+	0.0492610i
$210$	37.4012	+	6.07325i	2.58093	+	0.419094i
$211$	0.157189	+	0.187331i	0.0108213	+	0.0128964i	0.771428	−	0.636317i	$-0.219543\pi$
$211$	0.157189	+	0.187331i	0.0108213	+	0.0128964i	−0.760607	+	0.649213i	$0.775098\pi$
$212$	3.48613	+	2.14979i	0.239428	+	0.147648i
$213$	−7.88346	−	19.9041i	−0.540166	−	1.36380i
$214$	−11.0352	−	19.7699i	−0.754353	−	1.35144i
$215$	35.0734			2.39198
$216$	−6.82488	+	13.0162i	−0.464374	+	0.885639i
$217$	39.5994			2.68818
$218$	−1.29502	−	2.32006i	−0.0877101	−	0.157135i
$219$	−6.10268	+	7.70165i	−0.412381	+	0.520429i
$220$	3.34051	−	5.41703i	0.225217	−	0.365216i
$221$	−1.67086	−	1.99125i	−0.112394	−	0.133946i
$222$	−11.1254	+	13.6298i	−0.746689	+	0.914773i
$223$	−4.29149	+	1.56197i	−0.287379	+	0.104598i	−0.481688	−	0.876343i	$-0.659976\pi$
$223$	−4.29149	+	1.56197i	−0.287379	+	0.104598i	0.194308	+	0.980941i	$0.437754\pi$
$224$	−26.5012	−	6.68225i	−1.77068	−	0.446477i
$225$	−7.09939	+	14.0632i	−0.473293	+	0.937544i
$226$	6.32016	−	16.6114i	0.420411	−	1.10497i
$227$	−12.0018	+	14.3032i	−0.796589	+	0.949338i	−0.999554	−	0.0298479i	$-0.990498\pi$
$227$	−12.0018	+	14.3032i	−0.796589	+	0.949338i	0.202965	+	0.979186i	$0.434942\pi$
$228$	−6.82214	+	2.47583i	−0.451808	+	0.163966i
$229$	−4.88193	+	0.860816i	−0.322607	+	0.0568844i	−0.332607	−	0.943066i	$-0.607928\pi$
$229$	−4.88193	+	0.860816i	−0.322607	+	0.0568844i	0.00999944	+	0.999950i	$0.496817\pi$
$230$	−24.7744	−	21.4077i	−1.63358	−	1.41158i
$231$	−3.95482	+	7.31648i	−0.260208	+	0.481389i
$232$	0.942971	−	4.25654i	0.0619091	−	0.279456i
$233$	−3.10686	−	5.38123i	−0.203537	−	0.352536i	0.746129	−	0.665802i	$-0.231910\pi$
$233$	−3.10686	−	5.38123i	−0.203537	−	0.352536i	−0.949666	+	0.313265i	$0.898577\pi$
$234$	−7.38482	+	3.04138i	−0.482761	+	0.198821i
$235$	−13.7200	−	7.92126i	−0.894995	−	0.516726i
$236$	−0.322284	+	0.0472412i	−0.0209789	+	0.00307514i
$237$	2.47033	−	7.42921i	0.160465	−	0.482579i
$238$	−9.26684	−	1.77284i	−0.600680	−	0.114916i
$239$	0.473540	+	0.172355i	0.0306308	+	0.0111487i	0.357290	−	0.933993i	$-0.383701\pi$
$239$	0.473540	+	0.172355i	0.0306308	+	0.0111487i	−0.326659	+	0.945142i	$0.605923\pi$
$240$	11.6610	−	18.8700i	0.752712	−	1.21806i
$241$	−4.22505	+	23.9614i	−0.272159	+	1.54349i	0.475684	+	0.879616i	$0.342201\pi$
$241$	−4.22505	+	23.9614i	−0.272159	+	1.54349i	−0.747843	+	0.663875i	$0.768910\pi$
$242$	−8.94335	−	10.9775i	−0.574900	−	0.705662i
$243$	11.5910	+	10.4235i	0.743564	+	0.668665i
$244$	−15.9113	−	3.28374i	−1.01862	−	0.210220i
$245$	51.5300	+	9.08613i	3.29213	+	0.580491i
$246$	0.188238	+	0.316064i	0.0120016	+	0.0201515i
$247$	−3.70602	−	1.34888i	−0.235808	−	0.0858271i
$248$	8.86826	−	21.4191i	0.563135	−	1.36012i
$249$	−0.796977	−	0.265008i	−0.0505064	−	0.0167942i
$250$	0.582881	−	0.976612i	0.0368646	−	0.0617664i
$251$	22.7502	+	13.1348i	1.43598	+	0.829062i	0.997567	−	0.0697132i	$-0.0222084\pi$
$251$	22.7502	+	13.1348i	1.43598	+	0.829062i	0.438410	+	0.898775i	$0.355542\pi$
$252$	−13.8083	+	25.4885i	−0.869843	+	1.60563i
$253$	6.22396	−	3.59340i	0.391297	−	0.225915i
$254$	0.210229	−	14.5041i	0.0131910	−	0.910065i
$255$	3.64131	−	6.73649i	0.228028	−	0.421855i
$256$	−9.54931	+	12.8379i	−0.596832	+	0.802366i
$257$	4.10470	+	23.2789i	0.256044	+	1.45210i	0.793379	+	0.608729i	$0.208320\pi$
$257$	4.10470	+	23.2789i	0.256044	+	1.45210i	−0.537334	+	0.843369i	$0.680569\pi$
$258$	−8.83469	+	25.3367i	−0.550024	+	1.57739i
$259$	−22.3064	+	26.5837i	−1.38605	+	1.65183i
$260$	11.4421	−	3.79278i	0.709607	−	0.235218i
$261$	−4.12802	−	2.08392i	−0.255518	−	0.128991i
$262$	3.64188	+	22.5615i	0.224996	+	1.39385i
$263$	−17.8317	+	6.49021i	−1.09955	+	0.400204i	−0.827151	−	0.561980i	$-0.810040\pi$
$263$	−17.8317	+	6.49021i	−1.09955	+	0.400204i	−0.272400	+	0.962184i	$0.587817\pi$
$264$	3.07177	+	3.77766i	0.189054	+	0.232499i
$265$	−5.02271	+	4.21455i	−0.308543	+	0.258898i
$266$	−13.5211	+	4.70050i	−0.829031	+	0.288206i
$267$	2.18704	−	2.76007i	0.133845	−	0.168913i
$268$	−2.13649	+	5.37947i	−0.130507	+	0.328604i
$269$		−	27.2792i		−	1.66324i	−0.555344	−	0.831621i	$-0.687413\pi$
$269$		−	27.2792i		−	1.66324i	0.555344	−	0.831621i	$-0.312587\pi$
$270$	−16.3413	−	16.9271i	−0.994497	−	1.03015i
$271$	13.0428			0.792292			0.396146	−	0.918187i	$-0.370347\pi$
$271$	13.0428			0.792292			0.396146	+	0.918187i	$0.370347\pi$
$272$	−3.03422	+	4.61536i	−0.183977	+	0.279847i
$273$	−14.6459	+	5.80086i	−0.886413	+	0.351084i
$274$	−3.22605	−	9.27980i	−0.194893	−	0.560613i
$275$	3.35469	+	3.99796i	0.202295	+	0.241086i
$276$	21.7052	−	12.5044i	1.30650	−	0.752678i
$277$	−6.21064	−	17.0636i	−0.373161	−	1.02525i	−0.974132	−	0.225981i	$-0.927441\pi$
$277$	−6.21064	−	17.0636i	−0.373161	−	1.02525i	0.600970	−	0.799271i	$-0.294781\pi$
$278$	0.510547	+	3.16285i	0.0306206	+	0.189695i
$279$	−19.6926	−	14.7243i	−1.17897	−	0.881519i
$280$	23.5028	−	36.9044i	1.40456	−	2.20546i
$281$	−14.0423	−	11.7829i	−0.837696	−	0.702910i	0.119348	−	0.992852i	$-0.461919\pi$
$281$	−14.0423	−	11.7829i	−0.837696	−	0.702910i	−0.957044	+	0.289942i	$0.906364\pi$
$282$	9.17821	−	7.91592i	0.546554	−	0.471386i
$283$	−2.81328	+	0.496058i	−0.167232	+	0.0294876i	−0.256637	−	0.966508i	$-0.582615\pi$
$283$	−2.81328	+	0.496058i	−0.167232	+	0.0294876i	0.0894049	+	0.995995i	$0.471503\pi$
$284$	−24.7099	−	0.716468i	−1.46626	−	0.0425146i
$285$	−0.325858	−	11.6138i	−0.0193022	−	0.687941i
$286$	−0.0383466	+	2.64559i	−0.00226748	+	0.156437i
$287$	0.362800	+	0.628387i	0.0214154	+	0.0370925i
$288$	10.6942	+	13.1770i	0.630165	+	0.776462i
$289$	7.54662	−	13.0711i	0.443919	−	0.768890i
$290$	5.99312	+	3.57693i	0.351928	+	0.210045i
$291$	−9.38065	−	10.5630i	−0.549904	−	0.619215i
$292$	5.38609	+	9.98670i	0.315197	+	0.584428i
$293$	3.33183	−	9.15412i	0.194648	−	0.534790i	−0.803522	−	0.595276i	$-0.797043\pi$
$293$	3.33183	−	9.15412i	0.194648	−	0.534790i	0.998169	+	0.0604860i	$0.0192651\pi$
$294$	−19.5437	+	34.9361i	−1.13981	+	2.03751i
$295$	0.0905487	−	0.513527i	0.00527195	−	0.0298987i
$296$	9.38351	+	18.0188i	0.545405	+	1.04732i
$297$	4.68720	−	2.16793i	0.271979	−	0.125796i
$298$	5.01406	−	4.08493i	0.290456	−	0.236634i
$299$	13.4055	+	2.36376i	0.775262	+	0.136700i
$300$	11.6797	+	13.9458i	0.674325	+	0.805159i
$301$	−18.1016	+	49.7337i	−1.04336	+	2.86661i
$302$	−14.8487	−	2.84072i	−0.854448	−	0.163465i
$303$	−0.694389	−	3.38065i	−0.0398916	−	0.194213i
$304$	−0.485565	+	8.36617i	−0.0278490	+	0.479832i
$305$	13.0044	−	22.5243i	0.744630	−	1.28974i
$306$	3.94916	+	4.32732i	0.225759	+	0.247376i
$307$	19.9588	−	11.5232i	1.13911	−	0.657664i	0.192898	−	0.981219i	$-0.438211\pi$
$307$	19.9588	−	11.5232i	1.13911	−	0.657664i	0.946210	+	0.323554i	$0.104878\pi$
$308$	5.95724	+	7.53259i	0.339445	+	0.429209i
$309$	6.03831	−	3.71584i	0.343508	−	0.211387i
$310$	28.0808	+	24.2647i	1.59488	+	1.37815i
$311$	−4.32744	−	24.5421i	−0.245387	−	1.39166i	−0.819593	−	0.572946i	$-0.805800\pi$
$311$	−4.32744	−	24.5421i	−0.245387	−	1.39166i	0.574207	−	0.818710i	$-0.305311\pi$
$312$	−0.142291	+	9.22101i	−0.00805566	+	0.522037i
$313$	−14.6304	−	12.2764i	−0.826960	−	0.693902i	0.127631	−	0.991822i	$-0.459263\pi$
$313$	−14.6304	−	12.2764i	−0.826960	−	0.693902i	−0.954591	+	0.297920i	$0.903707\pi$
$314$	31.1695	+	11.8591i	1.75900	+	0.669249i
$315$	−31.7762	−	33.8212i	−1.79039	−	1.90561i
$316$	−6.75396	−	6.00929i	−0.379940	−	0.338049i
$317$	1.56322	+	4.29492i	0.0877994	+	0.241227i	0.975820	−	0.218578i	$-0.0701417\pi$
$317$	1.56322	+	4.29492i	0.0877994	+	0.241227i	−0.888020	+	0.459804i	$0.847919\pi$
$318$	−1.77938	−	4.68997i	−0.0997825	−	0.263001i
$319$	−1.17354	+	0.984717i	−0.0657056	+	0.0551336i
$320$	−14.6980	−	20.9772i	−0.821642	−	1.17266i
$321$	−4.04740	+	27.4327i	−0.225904	+	1.53114i
$322$	43.1422	−	24.0813i	2.40422	−	1.34200i
$323$			2.89297i			0.160969i
$324$	16.3442	−	7.54098i	0.908012	−	0.418943i
$325$			9.88511i			0.548327i
$326$	−9.74285	−	17.4545i	−0.539606	−	0.966717i
$327$	−0.474977	+	3.21933i	−0.0262663	+	0.178029i
$328$	0.421140	−	0.0555096i	0.0232536	−	0.00306500i
$329$	18.3133	−	15.3667i	1.00964	−	0.847191i
$330$	−7.28766	+	2.76494i	−0.401172	+	0.152205i
$331$	0.192521	+	0.528948i	0.0105819	+	0.0290736i	0.944871	−	0.327442i	$-0.106187\pi$
$331$	0.192521	+	0.528948i	0.0105819	+	0.0290736i	−0.934289	+	0.356516i	$0.883965\pi$
$332$	−0.644653	+	0.724540i	−0.0353800	+	0.0397643i
$333$	20.9775	−	4.92578i	1.14956	−	0.269931i
$334$	−7.07835	+	18.6041i	−0.387310	+	1.01797i
$335$	−7.09831	−	5.95619i	−0.387822	−	0.325421i
$336$	20.7393	+	26.2741i	1.13142	+	1.43337i
$337$	0.591009	+	3.35178i	0.0321943	+	0.182583i	0.996664	−	0.0816090i	$-0.0260059\pi$
$337$	0.591009	+	3.35178i	0.0321943	+	0.182583i	−0.964470	+	0.264192i	$0.914895\pi$
$338$	8.74377	−	10.1189i	0.475598	−	0.550395i
$339$	−18.5385	+	11.4082i	−1.00687	+	0.619607i
$340$	−5.48500	−	6.93547i	−0.297466	−	0.376128i
$341$	−7.05461	+	4.07298i	−0.382028	+	0.220564i
$342$	8.47177	+	2.69002i	0.458101	+	0.145459i
$343$	−22.5691	+	39.0908i	−1.21862	+	2.11070i
$344$	22.8469	+	20.9289i	1.23182	+	1.12841i
$345$	8.06836	+	39.2810i	0.434386	+	2.11482i
$346$	2.27877	−	11.9114i	0.122507	−	0.640359i
$347$	−7.26027	+	19.9474i	−0.389752	+	1.07083i	0.577362	+	0.816488i	$0.304082\pi$
$347$	−7.26027	+	19.9474i	−0.389752	+	1.07083i	−0.967113	+	0.254345i	$0.918140\pi$
$348$	−4.09356	+	3.42838i	−0.219438	+	0.183780i
$349$	−3.08812	−	0.544519i	−0.165303	−	0.0291474i	0.0903839	−	0.995907i	$-0.471191\pi$
$349$	−3.08812	−	0.544519i	−0.165303	−	0.0291474i	−0.255687	+	0.966760i	$0.582302\pi$
$350$	22.6621	+	27.8167i	1.21134	+	1.48686i
$351$	9.44030	+	2.56106i	0.503886	+	0.136699i
$352$	5.40846	−	1.53533i	0.288272	−	0.0818331i
$353$	5.50456	−	31.2179i	0.292978	−	1.66156i	−0.382329	−	0.924026i	$-0.624878\pi$
$353$	5.50456	−	31.2179i	0.292978	−	1.66156i	0.675307	−	0.737537i	$-0.264011\pi$
$354$	0.348159	+	0.194765i	0.0185044	+	0.0103516i
$355$	13.5351	−	37.1875i	0.718370	−	1.97371i
$356$	−1.93023	−	3.57897i	−0.102302	−	0.189685i
$357$	7.67298	+	8.64010i	0.406097	+	0.457283i
$358$	3.88761	−	6.51365i	0.205466	−	0.344257i
$359$	−1.84427	+	3.19437i	−0.0973369	+	0.168592i	−0.910582	−	0.413330i	$-0.864366\pi$
$359$	−1.84427	+	3.19437i	−0.0973369	+	0.168592i	0.813245	+	0.581922i	$0.197699\pi$
$360$	−25.4100	+	9.61335i	−1.33922	+	0.506668i
$361$	−7.30536	−	12.6533i	−0.384493	−	0.665961i
$362$	−12.1801	−	0.176544i	−0.640170	−	0.00927897i
$363$	0.486381	+	17.3349i	0.0255284	+	0.909845i
$364$	−0.527196	+	18.1822i	−0.0276326	+	0.953008i
$365$	−17.8884	+	3.15421i	−0.936323	+	0.165099i
$366$	12.9957	+	15.0680i	0.679294	+	0.787615i
$367$	−7.83970	−	6.57829i	−0.409229	−	0.343384i	0.414819	−	0.909904i	$-0.363845\pi$
$367$	−7.83970	−	6.57829i	−0.409229	−	0.343384i	−0.824048	+	0.566520i	$0.808289\pi$
$368$	−3.36380	−	28.7284i	−0.175350	−	1.49757i
$369$	0.0532348	−	0.447394i	0.00277129	−	0.0232904i
$370$	−32.1073	+	5.18276i	−1.66918	+	0.269439i
$371$	−3.38395	−	9.29732i	−0.175686	−	0.482693i
$372$	−24.6020	+	14.1733i	−1.27555	+	0.734849i
$373$	17.0363	+	20.3031i	0.882107	+	1.05125i	0.998315	+	0.0580293i	$0.0184817\pi$
$373$	17.0363	+	20.3031i	0.882107	+	1.05125i	−0.116208	+	0.993225i	$0.537074\pi$
$374$	1.83322	−	0.637305i	0.0947938	−	0.0329543i
$375$	−1.29506	+	0.512938i	−0.0668766	+	0.0264880i
$376$	−4.21051	−	13.3469i	−0.217140	−	0.688314i
$377$	−2.90162			−0.149441
$378$	32.4363	−	14.4356i	1.66835	−	0.742485i
$379$		−	27.2164i		−	1.39801i	−0.715114	−	0.699007i	$-0.753625\pi$
$379$		−	27.2164i		−	1.39801i	0.715114	−	0.699007i	$-0.246375\pi$
$380$	−12.4684	−	4.95189i	−0.639613	−	0.254027i
$381$	−11.0333	+	13.9242i	−0.565255	+	0.713358i
$382$	−8.81910	−	25.3684i	−0.451224	−	1.29796i
$383$	−9.05624	+	7.59909i	−0.462752	+	0.388295i	−0.844143	−	0.536119i	$-0.819890\pi$
$383$	−9.05624	+	7.59909i	−0.462752	+	0.388295i	0.381390	+	0.924414i	$0.375445\pi$
$384$	18.8561	−	5.33369i	0.962245	−	0.272184i
$385$	−14.4469	+	5.25825i	−0.736284	+	0.267985i
$386$	−5.19706	+	0.838909i	−0.264523	+	0.0426993i
$387$	27.4944	−	18.0017i	1.39762	−	0.915075i
$388$	−15.4840	+	5.13260i	−0.786082	+	0.260568i
$389$	−15.2882	+	18.2198i	−0.775143	+	0.923780i	−0.998703	−	0.0509105i	$-0.983788\pi$
$389$	−15.2882	+	18.2198i	−0.775143	+	0.923780i	0.223560	+	0.974690i	$0.428232\pi$
$390$	−13.9403	−	4.86085i	−0.705893	−	0.246139i
$391$	−1.73391	−	9.83347i	−0.0876874	−	0.497300i
$392$	28.1449	+	36.6676i	1.42153	+	1.85199i
$393$	13.3095	−	24.6228i	0.671377	−	1.24206i
$394$	−15.8803	−	0.230177i	−0.800036	−	0.0115961i
$395$	12.5335	−	7.23621i	0.630628	−	0.364093i
$396$	−0.161667	−	5.96101i	−0.00812408	−	0.299552i
$397$	−18.5130	−	10.6885i	−0.929143	−	0.536441i	−0.0426022	−	0.999092i	$-0.513565\pi$
$397$	−18.5130	−	10.6885i	−0.929143	−	0.536441i	−0.886540	+	0.462651i	$0.846898\pi$
$398$	−7.04034	−	4.20195i	−0.352900	−	0.210625i
$399$	16.6364	+	5.53188i	0.832862	+	0.276941i
$400$	20.1211	−	6.02832i	1.00605	−	0.301416i
$401$	8.00805	+	2.91469i	0.399903	+	0.145553i	0.534139	−	0.845397i	$-0.320636\pi$
$401$	8.00805	+	2.91469i	0.399903	+	0.145553i	−0.134236	+	0.990949i	$0.542858\pi$
$402$	6.09070	−	3.62744i	0.303777	−	0.180920i
$403$	−15.1946	−	2.67922i	−0.756899	−	0.133462i
$404$	−3.90289	−	0.805467i	−0.194176	−	0.0400735i
$405$	3.22641	+	28.6345i	0.160322	+	1.42286i
$406$	−8.16515	+	6.65212i	−0.405230	+	0.330139i
$407$	1.23961	−	7.03019i	0.0614453	−	0.348473i
$408$	6.39175	−	2.21533i	0.316439	−	0.109675i
$409$	−13.0223	−	4.73975i	−0.643913	−	0.234365i	−0.000637580	−	1.00000i	$-0.500203\pi$
$409$	−13.0223	−	4.73975i	−0.643913	−	0.234365i	−0.643276	+	0.765634i	$0.722425\pi$
$410$	−0.127778	+	0.667911i	−0.00631052	+	0.0329858i
$411$	−3.79664	+	11.4179i	−0.187275	+	0.563204i
$412$	−1.18736	−	8.10031i	−0.0584972	−	0.399074i
$413$	0.681445	+	0.393432i	0.0335317	+	0.0193595i
$414$	−30.4086	−	4.06605i	−1.49450	−	0.199835i
$415$	−0.776273	−	1.34454i	−0.0381058	−	0.0660011i
$416$	9.71661	+	4.35706i	0.476396	+	0.213622i
$417$	1.86583	−	3.45182i	0.0913703	−	0.169036i
$418$	1.92530	−	2.22809i	0.0941697	−	0.108980i
$419$	18.4397	−	3.25141i	0.900836	−	0.158842i	0.295997	−	0.955189i	$-0.404348\pi$
$419$	18.4397	−	3.25141i	0.900836	−	0.158842i	0.604840	+	0.796347i	$0.293237\pi$
$420$	−50.3716	+	18.2804i	−2.45788	+	0.891991i
$421$	−9.52650	+	11.3532i	−0.464293	+	0.553323i	−0.946487	−	0.322741i	$-0.895396\pi$
$421$	−9.52650	+	11.3532i	−0.464293	+	0.553323i	0.482194	+	0.876065i	$0.339840\pi$
$422$	−0.323231	−	0.122980i	−0.0157346	−	0.00598659i
$423$	−14.8209	+	0.832343i	−0.720617	+	0.0404699i
$424$	−5.78671	−	0.251768i	−0.281027	−	0.0122269i
$425$	6.81381	−	2.48002i	0.330518	−	0.120299i
$426$	23.4545	+	19.1449i	1.13638	+	0.927573i
$427$	25.2276	+	30.0651i	1.22085	+	1.45495i
$428$	27.2540	+	16.8067i	1.31737	+	0.812383i
$429$	2.01252	−	2.53982i	0.0971653	−	0.122624i
$430$	−43.3109	+	24.1755i	−2.08863	+	1.16584i
$431$	−13.2343			−0.637472			−0.318736	−	0.947844i	$-0.603258\pi$
$431$	−13.2343			−0.637472			−0.318736	+	0.947844i	$0.603258\pi$
$432$	−0.544030	−	20.7775i	−0.0261747	−	0.999657i
$433$	−33.7081			−1.61991			−0.809954	−	0.586494i	$-0.800508\pi$
$433$	−33.7081			−1.61991			−0.809954	+	0.586494i	$0.800508\pi$
$434$	−48.8999	+	27.2952i	−2.34727	+	1.31021i
$435$	−3.14772	−	7.94731i	−0.150921	−	0.381045i
$436$	3.19836	+	1.97233i	0.153174	+	0.0944574i
$437$	−9.73806	−	11.6054i	−0.465834	−	0.555160i
$438$	2.22737	−	13.7170i	0.106428	−	0.655422i
$439$	20.0359	−	7.29248i	0.956263	−	0.348051i	0.183695	−	0.982983i	$-0.441194\pi$
$439$	20.0359	−	7.29248i	0.956263	−	0.348051i	0.772568	+	0.634932i	$0.218972\pi$
$440$	−0.391217	+	8.99186i	−0.0186506	+	0.428670i
$441$	45.0584	−	19.3254i	2.14564	−	0.920258i
$442$	3.43582	+	1.30723i	0.163425	+	0.0621787i
$443$	−1.83638	+	2.18851i	−0.0872491	+	0.103979i	−0.807903	−	0.589316i	$-0.799397\pi$
$443$	−1.83638	+	2.18851i	−0.0872491	+	0.103979i	0.720654	+	0.693295i	$0.243842\pi$
$444$	4.34359	−	24.4995i	0.206137	−	1.16270i
$445$	6.41074	−	1.13039i	0.303898	−	0.0535854i
$446$	4.22277	−	4.88688i	0.199954	−	0.231400i
$447$	−7.91781	+	0.222158i	−0.374500	+	0.0105077i
$448$	37.3313	−	10.0151i	1.76374	−	0.473169i
$449$	−6.08759	−	10.5440i	−0.287291	−	0.497602i	0.685871	−	0.727723i	$-0.259421\pi$
$449$	−6.08759	−	10.5440i	−0.287291	−	0.497602i	−0.973162	+	0.230120i	$0.926088\pi$
$450$	−0.926704	−	22.2596i	−0.0436852	−	1.04933i
$451$	−0.129265	−	0.0746311i	−0.00608685	−	0.00351424i
$452$	3.64538	+	24.8692i	0.171464	+	1.16975i
$453$	12.2948	+	13.8445i	0.577660	+	0.650470i
$454$	4.96167	−	25.9352i	0.232863	−	1.21720i
$455$	−27.3635	−	9.95952i	−1.28282	−	0.466909i
$456$	6.71788	−	7.75969i	0.314594	−	0.363381i
$457$	4.03205	−	22.8669i	0.188611	−	1.06967i	−0.732616	−	0.680642i	$-0.761701\pi$
$457$	4.03205	−	22.8669i	0.188611	−	1.06967i	0.921227	−	0.389025i	$-0.127188\pi$
$458$	5.43518	−	4.42802i	0.253969	−	0.206908i
$459$	−0.603086	−	7.14973i	−0.0281497	−	0.333721i
$460$	45.3490	+	9.35901i	2.11441	+	0.436366i
$461$	−0.632433	−	0.111515i	−0.0294553	−	0.00519377i	0.158901	−	0.987295i	$-0.449205\pi$
$461$	−0.632433	−	0.111515i	−0.0294553	−	0.00519377i	−0.188356	+	0.982101i	$0.560316\pi$
$462$	−0.159452	−	11.7608i	−0.00741839	−	0.547164i
$463$	21.3542	+	7.77228i	0.992413	+	0.361209i	0.786654	−	0.617394i	$-0.211812\pi$
$463$	21.3542	+	7.77228i	0.992413	+	0.361209i	0.205759	+	0.978603i	$0.434034\pi$
$464$	1.76952	+	5.90623i	0.0821478	+	0.274190i
$465$	−9.14516	−	44.5234i	−0.424096	−	2.06472i
$466$	7.54574	+	4.50359i	0.349549	+	0.208625i
$467$	−9.58039	−	5.53124i	−0.443328	−	0.255955i	0.261681	−	0.965155i	$-0.415723\pi$
$467$	−9.58039	−	5.53124i	−0.443328	−	0.255955i	−0.705008	+	0.709199i	$0.749057\pi$
$468$	7.02288	−	8.84592i	0.324633	−	0.408903i
$469$	12.1093	−	6.99132i	0.559156	−	0.322829i
$470$	22.4023	+	0.324711i	1.03334	+	0.0149778i
$471$	−21.4062	−	34.7856i	−0.986347	−	1.60283i
$472$	0.365415	−	0.280481i	0.0168196	−	0.0129102i
$473$	−1.89055	−	10.7219i	−0.0869277	−	0.492992i
$474$	2.07029	+	10.8768i	0.0950917	+	0.499589i
$475$	7.07166	−	8.42767i	0.324470	−	0.386688i
$476$	12.6653	−	4.19825i	0.580512	−	0.192426i
$477$	−1.77420	+	5.88177i	−0.0812352	+	0.269308i
$478$	−0.703559	+	0.113568i	−0.0321800	+	0.00519450i
$479$	−8.82538	+	3.21217i	−0.403242	+	0.146768i	−0.535676	−	0.844424i	$-0.679943\pi$
$479$	−8.82538	+	3.21217i	−0.403242	+	0.146768i	0.132434	+	0.991192i	$0.457721\pi$
$480$	−1.39293	+	31.3396i	−0.0635782	+	1.43045i
$481$	10.3578	−	8.69120i	0.472273	−	0.396284i
$482$	−11.2988	−	32.5014i	−0.514648	−	1.48040i
$483$	−59.8642	−	8.83232i	−2.72392	−	0.401884i
$484$	18.6104	+	7.39126i	0.845929	+	0.335966i
$485$		−	26.1143i		−	1.18579i
$486$	−21.4980	−	4.88207i	−0.975171	−	0.221455i
$487$	13.0881			0.593080			0.296540	−	0.955020i	$-0.404167\pi$
$487$	13.0881			0.593080			0.296540	+	0.955020i	$0.404167\pi$
$488$	21.9118	−	6.91243i	0.991899	−	0.312911i
$489$	−3.57339	+	24.2200i	−0.161594	+	1.09526i
$490$	−69.8955	+	24.2986i	−3.15756	+	1.09770i
$491$	2.41149	+	2.87390i	0.108829	+	0.129697i	0.817709	−	0.575632i	$-0.195244\pi$
$491$	2.41149	+	2.87390i	0.108829	+	0.129697i	−0.708880	+	0.705329i	$0.750799\pi$
$492$	−0.450307	−	0.260547i	−0.0203014	−	0.0117464i
$493$	0.727972	+	2.00009i	0.0327862	+	0.0900794i
$494$	5.50619	−	0.888808i	0.247735	−	0.0399894i
$495$	9.13957	+	2.75690i	0.410793	+	0.123913i
$496$	3.81273	+	32.5625i	0.171196	+	1.46210i
$497$	45.7460	+	38.3854i	2.05199	+	1.72182i
$498$	1.16682	−	0.222093i	0.0522866	−	0.00995223i
$499$	−9.17294	+	1.61744i	−0.410637	+	0.0724064i	−0.375151	−	0.926964i	$-0.622409\pi$
$499$	−9.17294	+	1.61744i	−0.410637	+	0.0724064i	−0.0354863	+	0.999370i	$0.511298\pi$
$500$	−0.0466170	+	1.60775i	−0.00208478	+	0.0719009i
$501$	20.7625	−	12.7767i	0.927599	−	0.570823i
$502$	−37.1469	−	0.538428i	−1.65795	−	0.0240312i
$503$	15.5610	+	26.9524i	0.693830	+	1.20175i	0.970573	+	0.240805i	$0.0774115\pi$
$503$	15.5610	+	26.9524i	0.693830	+	1.20175i	−0.276743	+	0.960944i	$0.589255\pi$
$504$	−0.517380	−	40.9927i	−0.0230459	−	1.82596i
$505$	3.18985	−	5.52498i	0.141946	−	0.245858i
$506$	−5.20888	+	8.72743i	−0.231563	+	0.387982i
$507$	−16.0439	+	3.29544i	−0.712537	+	0.146356i
$508$	9.73778	+	18.0554i	0.432044	+	0.801081i
$509$	−5.33369	+	14.6542i	−0.236411	+	0.649535i	0.763581	+	0.645712i	$0.223439\pi$
$509$	−5.33369	+	14.6542i	−0.236411	+	0.649535i	−0.999993	+	0.00382339i	$0.998783\pi$
$510$	0.146812	+	10.8285i	0.00650095	+	0.479496i
$511$	4.75969	−	26.9936i	0.210556	−	1.19412i
$512$	2.94319	−	22.4352i	0.130072	−	0.991505i
$513$	−6.21629	−	8.93690i	−0.274456	−	0.394574i
$514$	−21.1145	−	25.9170i	−0.931320	−	1.14315i
$515$	12.9070	+	2.27586i	0.568752	+	0.100286i
$516$	−6.55449	−	37.3770i	−0.288545	−	1.64543i
$517$	−1.68196	+	4.62116i	−0.0739727	+	0.203238i
$518$	9.22169	−	48.2027i	0.405178	−	2.11791i
$519$	−11.1058	+	9.86266i	−0.487490	+	0.432923i
$520$	−11.5151	+	12.5704i	−0.504970	+	0.551248i
$521$	−13.7160	+	23.7568i	−0.600909	+	1.04080i	0.391775	+	0.920061i	$0.371861\pi$
$521$	−13.7160	+	23.7568i	−0.600909	+	1.04080i	−0.992684	+	0.120744i	$0.961472\pi$
$522$	6.53395	−	0.272019i	0.285983	−	0.0119060i
$523$	−24.8748	+	14.3615i	−1.08770	+	0.627984i	−0.932963	−	0.359972i	$-0.882786\pi$
$523$	−24.8748	+	14.3615i	−1.08770	+	0.627984i	−0.154737	+	0.987956i	$0.549453\pi$
$524$	−20.0485	−	25.3501i	−0.875821	−	1.10742i
$525$	−1.23247	−	43.9260i	−0.0537895	−	1.91709i
$526$	17.5462	−	20.3056i	0.765049	−	0.885367i
$527$	1.96531	+	11.1458i	0.0856104	+	0.485521i
$528$	−6.39709	−	2.54759i	−0.278398	−	0.110869i
$529$	22.4372	+	18.8271i	0.975531	+	0.818568i
$530$	3.29735	−	8.66647i	0.143228	−	0.376447i
$531$	−0.192589	−	0.449034i	−0.00835767	−	0.0194864i
$532$	13.4567	−	15.1243i	0.583424	−	0.655723i
$533$	−0.0966938	−	0.265664i	−0.00418827	−	0.0115072i
$534$	−0.798231	+	4.91580i	−0.0345428	+	0.212727i
$535$	−39.2668	+	32.9487i	−1.69765	+	1.42450i
$536$	−1.06970	−	8.11557i	−0.0462038	−	0.350539i
$537$	−8.63758	+	3.42111i	−0.372739	+	0.147632i
$538$	18.8031	+	33.6861i	0.810658	+	1.45231i
$539$		−	16.2424i		−	0.699609i
$540$	31.8468	+	9.63895i	1.37047	+	0.414794i
$541$		−	21.9494i		−	0.943679i	−0.881685	−	0.471839i	$-0.843590\pi$
$541$		−	21.9494i		−	0.943679i	0.881685	−	0.471839i	$-0.156410\pi$
$542$	−16.1061	+	8.99016i	−0.691815	+	0.386160i
$543$	11.6931	+	9.26547i	0.501800	+	0.397619i
$544$	0.565569	−	7.79078i	0.0242486	−	0.334027i
$545$	−4.60810	+	3.86665i	−0.197389	+	0.165629i
$546$	14.0873	−	17.2585i	0.602882	−	0.738594i
$547$	−9.09630	−	24.9919i	−0.388930	−	1.06858i	−0.967484	−	0.252932i	$-0.918605\pi$
$547$	−9.09630	−	24.9919i	−0.388930	−	1.06858i	0.578554	−	0.815644i	$-0.303617\pi$
$548$	10.3801	+	9.23564i	0.443417	+	0.394527i
$549$	−1.36647	−	24.3316i	−0.0583194	−	1.03845i
$550$	−6.89831	−	2.62461i	−0.294145	−	0.111914i
$551$	2.47381	+	2.07577i	0.105388	+	0.0884309i
$552$	−18.1839	+	30.4023i	−0.773959	+	1.29401i
$553$	3.79227	+	21.5070i	0.161264	+	0.914572i
$554$	19.4309	+	16.7903i	0.825541	+	0.713353i
$555$	35.0408	+	18.9408i	1.48740	+	0.803992i
$556$	−2.81055	−	3.55378i	−0.119194	−	0.150714i
$557$	3.97092	−	2.29261i	0.168253	−	0.0971411i	−0.413509	−	0.910500i	$-0.635697\pi$
$557$	3.97092	−	2.29261i	0.168253	−	0.0971411i	0.581762	+	0.813359i	$0.302364\pi$
$558$	34.4669	+	4.60870i	1.45910	+	0.195102i
$559$	10.3106	−	17.8585i	0.436093	−	0.755336i
$560$	−3.58519	+	61.7720i	−0.151502	+	2.61034i
$561$	−2.25561	−	0.750027i	−0.0952318	−	0.0316662i
$562$	25.4621	+	4.87117i	1.07406	+	0.205478i
$563$	4.02884	−	11.0691i	0.169795	−	0.466508i	−0.825385	−	0.564570i	$-0.809042\pi$
$563$	4.02884	−	11.0691i	0.169795	−	0.466508i	0.995180	+	0.0980616i	$0.0312642\pi$
$564$	−5.87754	+	16.1015i	−0.247489	+	0.677994i
$565$	−39.6265	−	6.98722i	−1.66710	−	0.293955i
$566$	3.13210	−	2.55171i	0.131652	−	0.107256i
$567$	−42.2687	−	10.2034i	−1.77512	−	0.428505i
$568$	31.0073	−	16.1474i	1.30104	−	0.677529i
$569$	−4.06015	+	23.0263i	−0.170210	+	0.965311i	0.773318	+	0.634019i	$0.218596\pi$
$569$	−4.06015	+	23.0263i	−0.170210	+	0.965311i	−0.943528	+	0.331293i	$0.892515\pi$
$570$	8.40756	+	14.1168i	0.352154	+	0.591289i
$571$	6.26320	−	17.2080i	0.262107	−	0.720133i	−0.736918	−	0.675982i	$-0.763720\pi$
$571$	6.26320	−	17.2080i	0.262107	−	0.720133i	0.999025	−	0.0441505i	$-0.0140581\pi$
$572$	−1.77620	−	3.29337i	−0.0742668	−	0.137703i
$573$	−10.3790	+	31.2133i	−0.433587	+	1.30396i
$574$	−0.881145	−	0.525902i	−0.0367783	−	0.0219507i
$575$	−18.9861	+	32.8848i	−0.791774	+	1.37139i
$576$	−22.2886	−	8.90044i	−0.928692	−	0.370852i
$577$	−8.36154	−	14.4826i	−0.348095	−	0.602919i	0.637816	−	0.770189i	$-0.279838\pi$
$577$	−8.36154	−	14.4826i	−0.348095	−	0.602919i	−0.985911	+	0.167270i	$0.946505\pi$
$578$	−0.309354	+	21.3428i	−0.0128674	+	0.887745i
$579$	5.67189	+	3.06586i	0.235716	+	0.127413i
$580$	−9.86621	−	0.286072i	−0.409672	−	0.0118785i
$581$	2.30719	−	0.406820i	0.0957185	−	0.0168778i
$582$	18.8647	+	6.57798i	0.781968	+	0.272666i
$583$	1.55912	+	1.30826i	0.0645721	+	0.0541824i
$584$	−13.5348	−	8.61968i	−0.560072	−	0.356685i
$585$	9.90452	+	15.1274i	0.409502	+	0.625442i
$586$	2.19542	+	13.6007i	0.0906919	+	0.561839i
$587$	−0.548520	−	1.50705i	−0.0226398	−	0.0622024i	0.927858	−	0.372934i	$-0.121648\pi$
$587$	−0.548520	−	1.50705i	−0.0226398	−	0.0622024i	−0.950498	+	0.310732i	$0.899426\pi$
$588$	0.0530149	−	56.6125i	0.00218630	−	2.33466i
$589$	11.0377	+	13.1542i	0.454800	+	0.542010i
$590$	0.242150	+	0.696550i	0.00996915	+	0.0286765i
$591$	15.2454	+	12.0802i	0.627111	+	0.496914i
$592$	−24.0074	−	15.7829i	−0.986699	−	0.648674i
$593$	28.2534			1.16023			0.580114	−	0.814536i	$-0.303008\pi$
$593$	28.2534			1.16023			0.580114	+	0.814536i	$0.303008\pi$
$594$	−4.29374	+	5.90791i	−0.176174	+	0.242404i
$595$			21.3604i			0.875691i
$596$	−3.37601	+	8.50044i	−0.138287	+	0.348191i
$597$	3.69774	+	9.33600i	0.151338	+	0.382097i
$598$	−18.1833	+	6.32128i	−0.743571	+	0.258496i
$599$	25.1983	−	21.1439i	1.02958	−	0.863916i	0.0387752	−	0.999248i	$-0.487654\pi$
$599$	25.1983	−	21.1439i	1.02958	−	0.863916i	0.990800	+	0.135331i	$0.0432099\pi$
$600$	−24.0354	−	9.17055i	−0.981239	−	0.374386i
$601$	−1.45003	+	0.527767i	−0.0591479	+	0.0215281i	−0.371425	−	0.928463i	$-0.621131\pi$
$601$	−1.45003	+	0.527767i	−0.0591479	+	0.0215281i	0.312277	+	0.949991i	$0.398908\pi$
$602$	−11.9276	−	73.8915i	−0.486131	−	3.01159i
$603$	−8.62149	−	1.02586i	−0.351094	−	0.0417762i
$604$	20.2942	−	6.72706i	0.825760	−	0.273720i
$605$	−20.6056	+	24.5568i	−0.837737	+	0.998376i
$606$	3.18770	+	3.69601i	0.129491	+	0.150140i
$607$	−3.48342	−	19.7555i	−0.141388	−	0.801850i	−0.970197	−	0.242318i	$-0.922092\pi$
$607$	−3.48342	−	19.7555i	−0.141388	−	0.801850i	0.828809	−	0.559532i	$-0.189019\pi$
$608$	−5.16704	−	10.6658i	−0.209551	−	0.432554i
$609$	12.8938	−	0.361773i	0.522482	−	0.0146598i
$610$	−0.533082	+	36.7782i	−0.0215839	+	1.48910i
$611$	−8.06664	+	4.65728i	−0.326341	+	0.188413i
$612$	−7.85942	−	2.62157i	−0.317698	−	0.105970i
$613$	33.0061	+	19.0561i	1.33311	+	0.769669i	0.985774	−	0.168074i	$-0.0537547\pi$
$613$	33.0061	+	19.0561i	1.33311	+	0.769669i	0.347331	+	0.937743i	$0.387088\pi$
$614$	−16.7036	+	27.9868i	−0.674104	+	1.12946i
$615$	0.622738	−	0.553033i	0.0251112	−	0.0223004i
$616$	−12.5485	−	5.19550i	−0.505592	−	0.209333i
$617$	−37.6906	−	13.7182i	−1.51737	−	0.552276i	−0.556877	−	0.830595i	$-0.688000\pi$
$617$	−37.6906	−	13.7182i	−1.51737	−	0.552276i	−0.960489	+	0.278319i	$0.910223\pi$
$618$	−4.89524	+	8.75066i	−0.196915	+	0.352003i
$619$	43.5901	+	7.68610i	1.75203	+	0.308931i	0.955352	−	0.295470i	$-0.0954763\pi$
$619$	43.5901	+	7.68610i	1.75203	+	0.308931i	0.796680	+	0.604401i	$0.206587\pi$
$620$	−51.4013	−	10.6081i	−2.06433	−	0.426030i
$621$	26.4861	+	26.6516i	1.06285	+	1.06949i
$622$	22.2603	+	27.3234i	0.892555	+	1.09557i
$623$	−1.70575	+	9.67377i	−0.0683393	+	0.387572i
$624$	−6.18017	−	11.4848i	−0.247405	−	0.459759i
$625$	22.2529	+	8.09938i	0.890115	+	0.323975i
$626$	26.5285	+	5.07517i	1.06029	+	0.202845i
$627$	−3.53274	+	0.725629i	−0.141084	+	0.0289788i
$628$	−46.6644	+	6.84018i	−1.86211	+	0.272953i
$629$	−8.58945	−	4.95912i	−0.342484	−	0.197733i
$630$	62.5517	+	19.8619i	2.49212	+	0.791316i
$631$	15.4788	+	26.8101i	0.616202	+	1.06729i	0.990172	+	0.139852i	$0.0446627\pi$
$631$	15.4788	+	26.8101i	0.616202	+	1.06729i	−0.373971	+	0.927441i	$0.622004\pi$
$632$	12.4823	+	2.76527i	0.496520	+	0.109996i
$633$	0.221985	+	0.360730i	0.00882311	+	0.0143377i
$634$	−4.89078	−	4.22614i	−0.194238	−	0.167842i
$635$	−32.3414	+	5.70266i	−1.28343	+	0.226303i
$636$	5.43001	+	4.56499i	0.215314	+	0.181014i
$637$	19.7749	−	23.5668i	0.783510	−	0.933750i
$638$	0.770415	−	2.02489i	0.0305010	−	0.0801662i
$639$	−8.47641	−	36.0986i	−0.335321	−	1.42804i
$640$	32.6093	+	15.7730i	1.28899	+	0.623483i
$641$	11.5323	−	4.19742i	0.455499	−	0.165788i	−0.104073	−	0.994570i	$-0.533188\pi$
$641$	11.5323	−	4.19742i	0.455499	−	0.165788i	0.559572	+	0.828782i	$0.310965\pi$
$642$	−13.9109	−	36.6655i	−0.549019	−	1.44707i
$643$	−14.1055	−	16.8103i	−0.556268	−	0.662935i	0.412484	−	0.910965i	$-0.364661\pi$
$643$	−14.1055	−	16.8103i	−0.556268	−	0.662935i	−0.968752	+	0.248030i	$0.920217\pi$
$644$	−36.6759	+	59.4743i	−1.44523	+	2.34362i
$645$	60.0983	+	8.86685i	2.36637	+	0.349132i
$646$	−1.99407	−	3.57243i	−0.0784558	−	0.140555i
$647$	−31.2893			−1.23011			−0.615055	−	0.788484i	$-0.710866\pi$
$647$	−31.2893			−1.23011			−0.615055	+	0.788484i	$0.710866\pi$
$648$	−14.9850	+	20.5779i	−0.588668	+	0.808375i
$649$	−0.161865			−0.00635376
$650$	−6.81363	−	12.2068i	−0.267253	−	0.478789i
$651$	67.8537	+	10.0111i	2.65940	+	0.392365i
$652$	24.0622	+	14.8384i	0.942348	+	0.581117i
$653$	−18.6398	−	22.2141i	−0.729434	−	0.869305i	0.266077	−	0.963952i	$-0.414272\pi$
$653$	−18.6398	−	22.2141i	−0.729434	−	0.869305i	−0.995511	+	0.0946466i	$0.969828\pi$
$654$	−1.63249	−	4.30283i	−0.0638356	−	0.168254i
$655$	48.6196	−	17.6961i	1.89972	−	0.691443i
$656$	−0.481789	+	0.358831i	−0.0188107	+	0.0140100i
$657$	−12.4040	+	11.6540i	−0.483926	+	0.454665i
$658$	−12.0224	+	31.5988i	−0.468684	+	1.23185i
$659$	−20.4268	+	24.3438i	−0.795716	+	0.948298i	−0.999528	−	0.0307122i	$-0.990222\pi$
$659$	−20.4268	+	24.3438i	−0.795716	+	0.948298i	0.203812	+	0.979010i	$0.434667\pi$
$660$	7.09345	−	8.43758i	0.276112	−	0.328432i
$661$	41.1487	−	7.25563i	1.60050	−	0.282211i	0.699043	−	0.715079i	$-0.253610\pi$
$661$	41.1487	−	7.25563i	1.60050	−	0.282211i	0.901457	+	0.432868i	$0.142498\pi$
$662$	−0.602332	−	0.520477i	−0.0234103	−	0.0202289i
$663$	−2.35961	−	3.83442i	−0.0916398	−	0.148917i
$664$	0.296647	−	1.33906i	0.0115121	−	0.0519655i
$665$	16.2042	+	28.0666i	0.628373	+	1.08837i
$666$	−22.5091	+	20.5421i	−0.872211	+	0.795990i
$667$	−9.65283	−	5.57306i	−0.373759	−	0.215790i
$668$	−4.08270	−	27.8526i	−0.157964	−	1.07765i
$669$	−7.74836	+	1.59152i	−0.299569	+	0.0615318i
$670$	12.8709	+	2.46235i	0.497248	+	0.0951287i
$671$	−7.58661	−	2.76130i	−0.292878	−	0.106599i
$672$	−43.7205	−	18.1498i	−1.68655	−	0.700142i
$673$	0.0416438	−	0.236174i	0.00160525	−	0.00910382i	−0.983995	−	0.178198i	$-0.942973\pi$
$673$	0.0416438	−	0.236174i	0.00160525	−	0.00910382i	0.985600	+	0.169094i	$0.0540843\pi$
$674$	−3.04014	−	3.73162i	−0.117102	−	0.143737i
$675$	−15.7201	+	22.3025i	−0.605067	+	0.858422i
$676$	−3.82260	+	18.5224i	−0.147023	+	0.712399i
$677$	−35.9433	−	6.33778i	−1.38141	−	0.243581i	−0.566930	−	0.823766i	$-0.691869\pi$
$677$	−35.9433	−	6.33778i	−1.38141	−	0.243581i	−0.814484	+	0.580185i	$0.802980\pi$
$678$	15.0291	−	26.8658i	0.577189	−	1.03178i
$679$	37.0299	+	13.4778i	1.42108	+	0.517229i
$680$	11.5537	+	4.78364i	0.443065	+	0.183444i
$681$	−24.1811	+	21.4744i	−0.926623	+	0.822902i
$682$	5.90405	−	9.89219i	0.226078	−	0.378792i
$683$	2.39199	+	1.38102i	0.0915271	+	0.0528432i	0.545065	−	0.838394i	$-0.316505\pi$
$683$	2.39199	+	1.38102i	0.0915271	+	0.0528432i	−0.453538	+	0.891237i	$0.649838\pi$
$684$	−12.3157	+	2.51763i	−0.470901	+	0.0962641i
$685$	−19.2626	+	11.1213i	−0.735988	+	0.424923i
$686$	0.925161	−	63.8283i	0.0353228	−	2.43697i
$687$	−8.58282	+	0.240816i	−0.327455	+	0.00918771i
$688$	−42.6387	−	10.0964i	−1.62559	−	0.384922i
$689$	0.669410	+	3.79641i	0.0255025	+	0.144632i
$690$	−37.0390	−	42.9453i	−1.41005	−	1.63490i
$691$	22.4044	−	26.7005i	0.852303	−	1.01573i	−0.147342	−	0.989086i	$-0.547072\pi$
$691$	22.4044	−	26.7005i	0.852303	−	1.01573i	0.999645	−	0.0266492i	$-0.00848370\pi$
$692$	5.39633	+	16.2796i	0.205138	+	0.618859i
$693$	−8.62626	+	11.5370i	−0.327685	+	0.438254i
$694$	−4.78396	−	29.6367i	−0.181597	−	1.12499i
$695$	6.81588	−	2.48078i	0.258541	−	0.0941013i
$696$	2.69187	−	7.05520i	0.102035	−	0.267427i
$697$	−0.158863	+	0.133302i	−0.00601737	+	0.00504918i
$698$	4.18874	−	1.45618i	0.158546	−	0.0551172i
$699$	−3.96318	−	10.0062i	−0.149901	−	0.378469i
$700$	−47.1582	−	18.7292i	−1.78241	−	0.707897i
$701$			14.7036i			0.555346i	0.960676	+	0.277673i	$0.0895631\pi$
$701$			14.7036i			0.555346i	−0.960676	+	0.277673i	$0.910437\pi$
$702$	−13.4228	+	3.34447i	−0.506610	+	0.126229i
$703$	−15.0482			−0.567553
$704$	−5.62044	+	5.62387i	−0.211828	+	0.211958i
$705$	−21.5067	−	17.0416i	−0.809990	−	0.641825i
$706$	14.7206	+	42.3441i	0.554016	+	1.59364i
$707$	6.18807	+	7.37466i	0.232726	+	0.277353i
$708$	−0.564177		0.000528326i	−0.0212031		1.98557e-5i
$709$	13.3434	+	36.6606i	0.501121	+	1.37682i	0.890182	+	0.455606i	$0.150577\pi$
$709$	13.3434	+	36.6606i	0.501121	+	1.37682i	−0.389061	+	0.921212i	$0.627200\pi$
$710$	8.91861	+	55.2510i	0.334710	+	2.07353i
$711$	6.11109	−	12.1054i	0.229184	−	0.453989i
$712$	4.85050	+	3.08907i	0.181780	+	0.115768i
$713$	−45.4021	−	38.0969i	−1.70032	−	1.42674i
$714$	−15.4306	−	5.38051i	−0.577474	−	0.201360i
$715$	5.89917	−	1.04018i	0.220617	−	0.0389007i
$716$	−0.310919	+	10.7231i	−0.0116196	+	0.400742i
$717$	0.767839	+	0.415045i	0.0286755	+	0.0155001i
$718$	0.0756011	−	5.21584i	0.00282141	−	0.194653i
$719$	10.5503	+	18.2736i	0.393458	+	0.681490i	0.992903	−	0.118926i	$-0.0379452\pi$
$719$	10.5503	+	18.2736i	0.393458	+	0.681490i	−0.599445	+	0.800416i	$0.704612\pi$
$720$	24.7516	−	29.3859i	0.922437	−	1.09515i
$721$	−9.88856	+	17.1275i	−0.368269	+	0.637861i
$722$	17.7428	+	10.5896i	0.660318	+	0.394104i
$723$	−13.2973	+	39.9898i	−0.494531	+	1.48724i
$724$	15.1624	−	8.17750i	0.563507	−	0.303914i
$725$	2.76837	−	7.60604i	0.102815	−	0.282481i
$726$	−12.5492	−	21.0710i	−0.465746	−	0.782017i
$727$	−7.23521	+	41.0329i	−0.268339	+	1.52183i	0.491016	+	0.871151i	$0.336626\pi$
$727$	−7.23521	+	41.0329i	−0.268339	+	1.52183i	−0.759355	+	0.650676i	$0.774485\pi$
$728$	−11.8817	−	22.8160i	−0.440364	−	0.845616i
$729$	17.2261	+	20.7909i	0.638003	+	0.770034i
$730$	19.9156	−	16.2252i	0.737111	−	0.600522i
$731$	−14.8967	−	2.62669i	−0.550973	−	0.0971515i
$732$	−26.4339	−	9.64921i	−0.977027	−	0.356645i
$733$	−1.78906	+	4.91541i	−0.0660806	+	0.181555i	−0.968338	−	0.249643i	$-0.919687\pi$
$733$	−1.78906	+	4.91541i	−0.0660806	+	0.181555i	0.902257	+	0.431198i	$0.141909\pi$
$734$	14.2153	+	2.71953i	0.524695	+	0.100380i
$735$	85.9997	+	28.5963i	3.17215	+	1.05479i
$736$	23.9558	+	33.1571i	0.883022	+	1.22219i
$737$	−1.43818	+	2.49099i	−0.0529759	+	0.0917570i
$738$	0.242643	+	0.589165i	0.00893182	+	0.0216875i
$739$	33.2814	−	19.2150i	1.22428	−	0.706837i	0.258450	−	0.966025i	$-0.416788\pi$
$739$	33.2814	−	19.2150i	1.22428	−	0.706837i	0.965827	+	0.259188i	$0.0834549\pi$
$740$	36.0758	−	28.5310i	1.32617	−	1.04882i
$741$	−6.00926	−	3.24822i	−0.220756	−	0.119326i
$742$	10.5872	+	9.14844i	0.388668	+	0.335850i
$743$	7.80101	+	44.2417i	0.286191	+	1.62307i	0.700999	+	0.713162i	$0.252738\pi$
$743$	7.80101	+	44.2417i	0.286191	+	1.62307i	−0.414808	+	0.909909i	$0.636151\pi$
$744$	20.6107	−	34.4597i	0.755626	−	1.26336i
$745$	−11.2165	−	9.41174i	−0.410940	−	0.344820i
$746$	−35.0321	−	13.3287i	−1.28262	−	0.488000i
$747$	−1.29863	−	0.655574i	−0.0475142	−	0.0239862i
$748$	−1.82450	+	2.05060i	−0.0667104	+	0.0749772i
$749$	−26.4552	−	72.6850i	−0.966651	−	2.65585i
$750$	1.24566	−	1.52607i	0.0454852	−	0.0557242i
$751$	−33.4712	+	28.0857i	−1.22138	+	1.02486i	−0.222632	+	0.974903i	$0.571465\pi$
$751$	−33.4712	+	28.0857i	−1.22138	+	1.02486i	−0.998751	+	0.0499593i	$0.984091\pi$
$752$	14.3992	+	13.5794i	0.525085	+	0.495190i
$753$	35.6618	+	28.2580i	1.29959	+	1.02978i
$754$	3.58311	−	2.00004i	0.130489	−	0.0728370i
$755$			34.2268i			1.24564i
$756$	−30.1043	+	40.1838i	−1.09488	+	1.46147i
$757$			29.4804i			1.07148i	0.844382	+	0.535742i	$0.179968\pi$
$757$			29.4804i			1.07148i	−0.844382	+	0.535742i	$0.820032\pi$
$758$	18.7598	+	33.6086i	0.681387	+	1.22072i
$759$	11.5732	−	4.58384i	0.420081	−	0.166383i
$760$	18.8100	−	2.47930i	0.682310	−	0.0899338i
$761$	−15.0210	+	12.6041i	−0.544510	+	0.456898i	−0.873077	−	0.487582i	$-0.837879\pi$
$761$	−15.0210	+	12.6041i	−0.544510	+	0.456898i	0.328567	+	0.944481i	$0.393434\pi$
$762$	4.02698	−	24.7996i	0.145882	−	0.898394i
$763$	−3.10461	−	8.52985i	−0.112395	−	0.308801i
$764$	28.3764	+	25.2476i	1.02662	+	0.913427i
$765$	7.94244	−	10.6224i	0.287160	−	0.384055i
$766$	5.94531	−	15.6262i	0.214813	−	0.564596i
$767$	−0.234857	−	0.197069i	−0.00848020	−	0.00711574i
$768$	−19.6083	+	19.5835i	−0.707553	+	0.706660i
$769$	1.06391	+	6.03372i	0.0383655	+	0.217582i	0.997963	−	0.0637946i	$-0.0203203\pi$
$769$	1.06391	+	6.03372i	0.0383655	+	0.217582i	−0.959598	+	0.281376i	$0.909209\pi$
$770$	14.2156	−	16.4512i	0.512294	−	0.592862i
$771$	1.14830	+	40.9261i	0.0413551	+	1.47392i
$772$	5.83942	−	4.61818i	0.210165	−	0.166212i
$773$	21.6541	−	12.5020i	0.778842	−	0.449665i	−0.0571775	−	0.998364i	$-0.518210\pi$
$773$	21.6541	−	12.5020i	0.778842	−	0.449665i	0.836020	+	0.548699i	$0.184877\pi$
$774$	−21.5436	+	41.1810i	−0.774368	+	1.48022i
$775$	21.5199	−	37.2736i	0.773019	−	1.33891i
$776$	15.5829	−	17.0109i	0.559392	−	0.610657i
$777$	−44.9427	+	39.9120i	−1.61231	+	1.43184i
$778$	6.32030	−	33.0369i	0.226594	−	1.18443i
$779$	−0.107614	+	0.295668i	−0.00385569	+	0.0105934i
$780$	20.5648	−	3.60628i	0.736339	−	0.129126i
$781$	−12.0977	−	2.13315i	−0.432890	−	0.0763303i
$782$	8.91918	+	10.9479i	0.318949	+	0.391494i
$783$	−6.54654	−	4.61439i	−0.233954	−	0.164905i
$784$	−60.0295	−	25.8797i	−2.14391	−	0.924275i
$785$	13.1108	−	74.3550i	0.467944	−	2.65384i
$786$	0.536620	+	39.5799i	0.0191406	+	1.41177i
$787$	7.34606	−	20.1831i	0.261859	−	0.719451i	−0.737183	−	0.675693i	$-0.763845\pi$
$787$	7.34606	−	20.1831i	0.261859	−	0.719451i	0.999042	−	0.0437584i	$-0.0139332\pi$
$788$	19.7686	−	10.6617i	0.704228	−	0.379809i
$789$	−32.1955	+	6.61298i	−1.14619	+	0.235428i
$790$	−10.4894	+	17.5748i	−0.373195	+	0.625285i
$791$	30.3593	−	52.5839i	1.07945	−	1.86967i
$792$	4.30845	+	7.24960i	0.153094	+	0.257603i
$793$	−7.64590	−	13.2431i	−0.271514	−	0.470276i
$794$	30.2285	+	0.438148i	1.07277	+	0.0155493i
$795$	−9.67190	+	5.95186i	−0.343027	+	0.211091i
$796$	11.5902	+	0.336059i	0.410803	+	0.0119113i
$797$	13.5545	−	2.39003i	0.480126	−	0.0846592i	0.0716532	−	0.997430i	$-0.477173\pi$
$797$	13.5545	−	2.39003i	0.480126	−	0.0846592i	0.408473	+	0.912770i	$0.366061\pi$
$798$	−24.3567	+	4.63606i	−0.862219	+	0.164115i
$799$	5.23406	+	4.39190i	0.185168	+	0.155374i
$800$	−20.6916	+	21.3133i	−0.731558	+	0.753537i
$801$	4.44526	−	4.17648i	0.157066	−	0.147569i
$802$	−11.8979	+	1.92056i	−0.420130	+	0.0678173i
$803$	1.92847	+	5.29844i	0.0680543	+	0.186978i
$804$	−5.02086	+	8.67761i	−0.177072	+	0.306036i
$805$	−71.9014	−	85.6888i	−2.53419	−	3.02013i
$806$	20.6101	−	7.16492i	0.725958	−	0.252373i
$807$	6.89641	−	46.7429i	0.242765	−	1.64543i
$808$	5.37473	−	1.69555i	0.189082	−	0.0596492i
$809$	23.7409			0.834685			0.417342	−	0.908749i	$-0.362962\pi$
$809$	23.7409			0.834685			0.417342	+	0.908749i	$0.362962\pi$
$810$	−23.7214	−	33.1358i	−0.833487	−	1.16427i
$811$		−	19.2432i		−	0.675720i	−0.941196	−	0.337860i	$-0.890297\pi$
$811$		−	19.2432i		−	0.675720i	0.941196	−	0.337860i	$-0.109703\pi$
$812$	5.49766	−	13.8426i	0.192930	−	0.485779i
$813$	22.3488	+	3.29733i	0.783807	+	0.115642i
$814$	3.31503	+	9.53577i	0.116192	+	0.334229i
$815$	−34.6681	+	29.0900i	−1.21437	+	1.01898i
$816$	−6.36595	+	7.14135i	−0.222853	+	0.249997i
$817$	−21.5662	+	7.84944i	−0.754505	+	0.274617i
$818$	19.3479	−	3.12313i	0.676482	−	0.109198i
$819$	−26.5623	+	6.23717i	−0.928164	+	0.217944i
$820$	−0.302590	−	0.912854i	−0.0105669	−	0.0318783i
$821$	20.9082	−	24.9174i	0.729702	−	0.869624i	−0.265833	−	0.964019i	$-0.585647\pi$
$821$	20.9082	−	24.9174i	0.729702	−	0.869624i	0.995535	+	0.0943946i	$0.0300915\pi$
$822$	−3.18182	−	16.7165i	−0.110979	−	0.583056i
$823$	1.89564	+	10.7507i	0.0660777	+	0.374746i	0.999857	+	0.0168966i	$0.00537861\pi$
$823$	1.89564	+	10.7507i	0.0660777	+	0.374746i	−0.933779	+	0.357849i	$0.883510\pi$
$824$	7.04964	+	9.18436i	0.245586	+	0.319952i
$825$	4.73755	+	7.69861i	0.164940	+	0.268031i
$826$	−1.11268	−	0.0161277i	−0.0387150	−	0.000561156i
$827$	−36.9569	+	21.3371i	−1.28512	+	0.741962i	−0.977779	−	0.209639i	$-0.932771\pi$
$827$	−36.9569	+	21.3371i	−1.28512	+	0.741962i	−0.307337	+	0.951601i	$0.599438\pi$
$828$	40.3531	−	15.9391i	1.40237	−	0.553921i
$829$	1.40814	+	0.812989i	0.0489067	+	0.0282363i	0.524254	−	0.851562i	$-0.324344\pi$
$829$	1.40814	+	0.812989i	0.0489067	+	0.0282363i	−0.475347	+	0.879798i	$0.657678\pi$
$830$	1.88536	+	1.12526i	0.0654419	+	0.0390583i
$831$	−6.32812	−	30.8086i	−0.219520	−	1.06874i
$832$	−15.0019	+	1.31712i	−0.520099	+	0.0456628i
$833$	−21.2058	−	7.71828i	−0.734738	−	0.267423i
$834$	0.0752276	+	5.54862i	0.00260492	+	0.192133i
$835$	44.3803	+	7.82544i	1.53584	+	0.270811i
$836$	−0.841704	+	4.07847i	−0.0291109	+	0.141057i
$837$	−30.0209	−	30.2085i	−1.03767	−	1.04416i
$838$	−20.5293	+	16.7252i	−0.709174	+	0.577762i
$839$	6.84833	−	38.8388i	0.236431	−	1.34086i	−0.603149	−	0.797628i	$-0.706088\pi$
$839$	6.84833	−	38.8388i	0.236431	−	1.34086i	0.839580	−	0.543236i	$-0.182801\pi$
$840$	49.6018	−	57.2941i	1.71142	−	1.97683i
$841$	−25.0185	−	9.10597i	−0.862705	−	0.313999i
$842$	3.93835	−	20.5862i	0.135724	−	0.709446i
$843$	−21.0827	−	23.7401i	−0.726128	−	0.817652i
$844$	0.483915	−	0.0709334i	0.0166570	−	0.00244163i
$845$	−26.2205	−	15.1384i	−0.902014	−	0.520778i
$846$	17.7281	−	11.2436i	0.609504	−	0.386563i
$847$	−24.1866	−	41.8925i	−0.831063	−	1.43944i
$848$	7.31934	−	3.67778i	0.251347	−	0.126295i
$849$	−4.94598	+	0.138774i	−0.169745	+	0.00476271i
$850$	−6.70470	+	7.75913i	−0.229969	+	0.266136i
$851$	51.1501	−	9.01915i	1.75340	−	0.309173i
$852$	−42.1594	−	7.47455i	−1.44436	−	0.256074i
$853$	11.9585	−	14.2516i	0.409453	−	0.487967i	−0.521425	−	0.853297i	$-0.674600\pi$
$853$	11.9585	−	14.2516i	0.409453	−	0.487967i	0.930878	+	0.365330i	$0.119044\pi$
$854$	−51.8760	−	19.7374i	−1.77516	−	0.675399i
$855$	2.37770	−	19.9826i	0.0813157	−	0.683390i
$856$	−45.2396	−	1.96828i	−1.54626	−	0.0672745i
$857$	17.0821	−	6.21736i	0.583512	−	0.212381i	−0.0333613	−	0.999443i	$-0.510621\pi$
$857$	17.0821	−	6.21736i	0.583512	−	0.212381i	0.616874	+	0.787062i	$0.288399\pi$
$858$	−0.734534	+	4.52352i	−0.0250766	+	0.154431i
$859$	15.5298	+	18.5076i	0.529869	+	0.631473i	0.962885	−	0.269913i	$-0.0869951\pi$
$859$	15.5298	+	18.5076i	0.529869	+	0.631473i	−0.433016	+	0.901386i	$0.642551\pi$
$860$	36.8193	−	59.7068i	1.25553	−	2.03599i
$861$	0.462796	+	1.16846i	0.0157720	+	0.0398211i
$862$	16.3425	−	9.12215i	0.556629	−	0.310701i
$863$	49.5439			1.68649			0.843247	−	0.537526i	$-0.180641\pi$
$863$	49.5439			1.68649			0.843247	+	0.537526i	$0.180641\pi$
$864$	14.9934	+	25.2824i	0.510084	+	0.860124i
$865$	−27.4561			−0.933536
$866$	41.6249	−	23.2344i	1.41447	−	0.789537i
$867$	16.2356	−	20.4896i	0.551391	−	0.695862i
$868$	41.5707	−	67.4117i	1.41100	−	2.28810i
$869$	−2.88768	−	3.44141i	−0.0979580	−	0.116742i
$870$	9.36494	+	7.64419i	0.317501	+	0.259162i
$871$	−5.11947	+	1.86333i	−0.173466	+	0.0631366i
$872$	−5.30903	−	0.230985i	−0.179786	−	0.00782214i
$873$	−13.4033	−	20.4713i	−0.453634	−	0.692847i
$874$	20.0245	+	7.61878i	0.677340	+	0.257709i
$875$	2.49755	−	2.97646i	0.0844326	−	0.100623i
$876$	6.70436	+	18.4739i	0.226519	+	0.624175i
$877$	−15.7471	+	2.77664i	−0.531741	+	0.0937603i	−0.433071	−	0.901360i	$-0.642570\pi$
$877$	−15.7471	+	2.77664i	−0.531741	+	0.0937603i	−0.0986704	+	0.995120i	$0.531459\pi$
$878$	−19.7151	+	22.8156i	−0.665351	+	0.769990i
$879$	8.02333	−	14.8433i	0.270620	−	0.500652i
$880$	−5.71483	−	11.3734i	−0.192647	−	0.383397i
$881$	−17.0789	−	29.5815i	−0.575402	−	0.996626i	−0.995998	−	0.0893777i	$-0.971512\pi$
$881$	−17.0789	−	29.5815i	−0.575402	−	0.996626i	0.420596	−	0.907248i	$-0.361821\pi$
$882$	−42.3203	+	54.9222i	−1.42500	+	1.84933i
$883$	−23.3181	−	13.4627i	−0.784718	−	0.453057i	0.0533817	−	0.998574i	$-0.483000\pi$
$883$	−23.3181	−	13.4627i	−0.784718	−	0.453057i	−0.838100	+	0.545517i	$0.816333\pi$
$884$	−5.14382	+	0.753994i	−0.173005	+	0.0253596i
$885$	0.284979	−	0.857038i	0.00957948	−	0.0288090i
$886$	0.759178	−	3.96830i	0.0255051	−	0.133318i
$887$	5.55395	+	2.02147i	0.186483	+	0.0678744i	0.433574	−	0.901118i	$-0.357252\pi$
$887$	5.55395	+	2.02147i	0.186483	+	0.0678744i	−0.247091	+	0.968992i	$0.579475\pi$
$888$	11.5233	+	33.2475i	0.386698	+	1.11571i
$889$	8.60528	−	48.8030i	0.288612	−	1.63680i
$890$	−7.13724	+	5.81468i	−0.239241	+	0.194909i
$891$	8.57960	−	2.52979i	0.287428	−	0.0847511i
$892$	−1.84611	+	8.94531i	−0.0618123	+	0.299511i
$893$	10.2090	+	1.80013i	0.341633	+	0.0602391i
$894$	9.62430	−	5.73194i	0.321885	−	0.191705i
$895$	−16.1379	−	5.87372i	−0.539431	−	0.196337i
$896$	−39.1958	+	38.0991i	−1.30944	+	1.27280i
$897$	22.3728	+	7.43934i	0.747007	+	0.248392i
$898$	14.7851	+	8.82435i	0.493386	+	0.294472i
$899$	10.9411	+	6.31684i	0.364906	+	0.210678i
$900$	16.4875	+	26.8488i	0.549583	+	0.894960i
$901$	2.44892	−	1.41389i	0.0815855	−	0.0471034i
$902$	0.211067	+	0.00305931i	0.00702775	+	0.000101864i
$903$	−43.5902	+	80.6426i	−1.45059	+	2.68362i
$904$	−21.6434	−	28.1973i	−0.719849	−	0.937830i
$905$	4.78892	+	27.1593i	0.159189	+	0.902806i
$906$	−24.7252	−	8.62145i	−0.821438	−	0.286429i
$907$	−19.8160	+	23.6157i	−0.657978	+	0.784148i	−0.987094	−	0.160142i	$-0.948805\pi$
$907$	−19.8160	+	23.6157i	−0.657978	+	0.784148i	0.329116	+	0.944290i	$0.393249\pi$
$908$	11.7497	+	35.4464i	0.389926	+	1.17633i
$909$	−0.335180	−	5.96830i	−0.0111172	−	0.197956i
$910$	40.6552	−	6.56256i	1.34771	−	0.217547i
$911$	−36.1026	+	13.1403i	−1.19613	+	0.435356i	−0.861872	−	0.507125i	$-0.830708\pi$
$911$	−36.1026	+	13.1403i	−1.19613	+	0.435356i	−0.334259	+	0.942481i	$0.608486\pi$
$912$	−2.94705	+	14.2127i	−0.0975867	+	0.470629i
$913$	−0.369181	+	0.309780i	−0.0122181	+	0.0102522i
$914$	10.7827	+	31.0167i	0.356660	+	1.02594i
$915$	27.9774	−	35.3078i	0.924905	−	1.16724i
$916$	−3.65955	+	9.21438i	−0.120915	+	0.304452i
$917$			78.0753i			2.57827i
$918$	5.67291	+	8.41325i	0.187234	+	0.277679i
$919$	−27.3708			−0.902879			−0.451440	−	0.892302i	$-0.649089\pi$
$919$	−27.3708			−0.902879			−0.451440	+	0.892302i	$0.649089\pi$
$920$	−62.4509	+	19.7012i	−2.05894	+	0.649528i
$921$	37.1126	−	14.6993i	1.22290	−	0.484358i
$922$	0.857834	−	0.298219i	0.0282513	−	0.00982131i
$923$	−14.9560	−	17.8239i	−0.492284	−	0.586681i
$924$	8.30345	+	14.4131i	0.273163	+	0.474158i
$925$	12.9002	+	35.4430i	0.424155	+	1.16536i
$926$	−31.7268	+	5.12134i	−1.04261	+	0.168298i
$927$	11.2861	−	4.84056i	0.370683	−	0.158985i
$928$	−6.25617	−	6.07369i	−0.205369	−	0.199379i
$929$	22.8280	+	19.1549i	0.748961	+	0.628453i	0.935228	−	0.354046i	$-0.115195\pi$
$929$	22.8280	+	19.1549i	0.748961	+	0.628453i	−0.186267	+	0.982499i	$0.559639\pi$
$930$	41.9822	+	48.6768i	1.37665	+	1.59617i
$931$	−33.7186	+	5.94550i	−1.10508	+	0.194856i
$932$	−12.4222	−	0.360184i	−0.406903	−	0.0117982i
$933$	−1.21062	−	43.1470i	−0.0396338	−	1.41257i
$934$	15.6431	+	0.226739i	0.511857	+	0.00741912i
$935$	−2.19701	−	3.80534i	−0.0718500	−	0.124448i
$936$	−2.57497	+	15.7643i	−0.0841654	+	0.515271i
$937$	4.12479	−	7.14434i	0.134751	−	0.233395i	−0.790751	−	0.612137i	$-0.790310\pi$
$937$	4.12479	−	7.14434i	0.134751	−	0.233395i	0.925502	+	0.378742i	$0.123643\pi$
$938$	−10.1344	+	16.9801i	−0.330899	+	0.554419i
$939$	−21.9657	−	24.7343i	−0.716822	−	0.807173i
$940$	−27.8877	+	15.0406i	−0.909596	+	0.490569i
$941$	−10.7018	+	29.4028i	−0.348867	+	0.958505i	0.633860	+	0.773447i	$0.281469\pi$
$941$	−10.7018	+	29.4028i	−0.348867	+	0.958505i	−0.982728	+	0.185057i	$0.940753\pi$
$942$	50.4109	+	28.2005i	1.64248	+	0.918823i
$943$	0.188582	−	1.06950i	0.00614108	−	0.0348278i
$944$	−0.257907	+	0.598230i	−0.00839415	+	0.0194707i
$945$	−45.8983	−	65.9861i	−1.49307	−	2.14653i
$946$	9.72496	+	11.9369i	0.316186	+	0.388103i
$947$	47.7893	+	8.42654i	1.55294	+	0.273826i	0.883283	−	0.468841i	$-0.155328\pi$
$947$	47.7893	+	8.42654i	1.55294	+	0.273826i	0.669661	+	0.742667i	$0.266439\pi$
$948$	−10.0537	−	12.0044i	−0.326530	−	0.389884i
$949$	−3.65267	+	10.0356i	−0.118571	+	0.325770i
$950$	−2.92349	+	15.2814i	−0.0948506	+	0.495794i
$951$	1.59279	+	7.75455i	0.0516499	+	0.251458i
$952$	−12.7461	+	13.9142i	−0.413104	+	0.450962i
$953$	−11.7810	+	20.4053i	−0.381625	+	0.660993i	−0.991295	−	0.131662i	$-0.957969\pi$
$953$	−11.7810	+	20.4053i	−0.381625	+	0.660993i	0.609670	+	0.792655i	$0.291302\pi$
$954$	−1.86330	−	8.48612i	−0.0603266	−	0.274748i
$955$	−52.6586	+	30.4025i	−1.70399	+	0.983801i
$956$	0.790519	−	0.625192i	0.0255672	−	0.0202202i
$957$	−2.25981	+	1.39063i	−0.0730492	+	0.0449528i
$958$	8.68405	−	10.0498i	0.280569	−	0.324693i
$959$	−5.82832	−	33.0541i	−0.188206	−	1.06737i
$960$	−19.8818	−	39.6603i	−0.641682	−	1.28003i
$961$	27.7141	+	23.2549i	0.894003	+	0.750158i
$962$	−6.79975	+	17.8719i	−0.219233	+	0.576212i
$963$	−13.8704	+	45.9828i	−0.446969	+	1.48177i
$964$	36.3551	+	32.3467i	1.17092	+	1.04182i
$965$	4.07631	+	11.1996i	0.131221	+	0.360527i
$966$	80.0122	−	30.3566i	2.57435	−	0.976709i
$967$	16.8327	−	14.1243i	0.541302	−	0.454206i	−0.330681	−	0.943743i	$-0.607278\pi$
$967$	16.8327	−	14.1243i	0.541302	−	0.454206i	0.871983	+	0.489536i	$0.162834\pi$
$968$	−28.0760	+	3.70064i	−0.902398	+	0.118943i
$969$	−0.731368	+	4.95711i	−0.0234949	+	0.159245i
$970$	18.0001	+	32.2476i	0.577949	+	1.03541i
$971$			7.25307i			0.232762i	0.993205	+	0.116381i	$0.0371294\pi$
$971$			7.25307i			0.232762i	−0.993205	+	0.116381i	$0.962871\pi$
$972$	29.9123	−	8.78952i	0.959437	−	0.281924i
$973$			10.9452i			0.350887i
$974$	−16.1621	+	9.02142i	−0.517866	+	0.289065i
$975$	−2.49904	+	16.9382i	−0.0800334	+	0.542455i
$976$	−22.2934	+	23.6393i	−0.713596	+	0.756676i
$977$	−3.79069	+	3.18077i	−0.121275	+	0.101762i	−0.701408	−	0.712760i	$-0.747445\pi$
$977$	−3.79069	+	3.18077i	−0.121275	+	0.101762i	0.580133	+	0.814522i	$0.303000\pi$
$978$	−12.2817	−	32.3714i	−0.392727	−	1.03512i
$979$	−0.691114	−	1.89882i	−0.0220881	−	0.0606865i
$980$	69.5628	−	78.1832i	2.22210	−	2.49747i
$981$	−1.62775	+	5.39625i	−0.0519700	+	0.172289i
$982$	−4.95879	−	1.88668i	−0.158241	−	0.0602064i
$983$	7.44708	+	6.24884i	0.237525	+	0.199307i	0.753778	−	0.657129i	$-0.228229\pi$
$983$	7.44708	+	6.24884i	0.237525	+	0.199307i	−0.516253	+	0.856436i	$0.672674\pi$
$984$	0.735658	+	0.0113521i	0.0234519	+	0.000361891i
$985$	6.24375	+	35.4100i	0.198942	+	1.12826i
$986$	−2.27757	−	1.96806i	−0.0725327	−	0.0626757i
$987$	35.2646	−	21.7010i	1.12249	−	0.690752i
$988$	−6.18675	+	4.89287i	−0.196827	+	0.155663i
$989$	68.6008	−	39.6067i	2.18138	−	1.25942i
$990$	−13.1864	+	2.89535i	−0.419092	+	0.0920202i
$991$	−0.907067	+	1.57109i	−0.0288139	+	0.0499072i	−0.880073	−	0.474839i	$-0.842506\pi$
$991$	−0.907067	+	1.57109i	−0.0288139	+	0.0499072i	0.851259	+	0.524746i	$0.175840\pi$
$992$	−27.1529	−	37.5822i	−0.862106	−	1.19324i
$993$	0.196163	+	0.955024i	0.00622504	+	0.0303068i
$994$	−82.9485	−	15.8689i	−2.63097	−	0.503331i
$995$	−6.34865	+	17.4428i	−0.201266	+	0.552973i
$996$	−1.28778	+	1.07853i	−0.0408050	+	0.0341744i
$997$	−7.40689	−	1.30604i	−0.234579	−	0.0413625i	0.0551229	−	0.998480i	$-0.482445\pi$
$997$	−7.40689	−	1.30604i	−0.234579	−	0.0413625i	−0.289702	+	0.957117i	$0.593556\pi$
$998$	10.2125	−	8.32006i	0.323270	−	0.263367i
$999$	37.1903	−	3.13704i	1.17665	−	0.0992514i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.133.7	yes	204
3.2	odd	2		648.2.t.a.397.28		204
4.3	odd	2		864.2.bf.a.241.2		204
8.3	odd	2		864.2.bf.a.241.33		204
8.5	even	2	inner	216.2.t.a.133.24	yes	204
24.5	odd	2		648.2.t.a.397.11		204
27.13	even	9	inner	216.2.t.a.13.24	yes	204
27.14	odd	18		648.2.t.a.253.11		204
108.67	odd	18		864.2.bf.a.337.33		204
216.13	even	18	inner	216.2.t.a.13.7	✓	204
216.67	odd	18		864.2.bf.a.337.2		204
216.149	odd	18		648.2.t.a.253.28		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.7	✓	204	216.13	even	18	inner
216.2.t.a.13.24	yes	204	27.13	even	9	inner
216.2.t.a.133.7	yes	204	1.1	even	1	trivial
216.2.t.a.133.24	yes	204	8.5	even	2	inner
648.2.t.a.253.11		204	27.14	odd	18
648.2.t.a.253.28		204	216.149	odd	18
648.2.t.a.397.11		204	24.5	odd	2
648.2.t.a.397.28		204	3.2	odd	2
864.2.bf.a.241.2		204	4.3	odd	2
864.2.bf.a.241.33		204	8.3	odd	2
864.2.bf.a.337.2		204	216.67	odd	18
864.2.bf.a.337.33		204	108.67	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23486 + 0.689282i) q^{2} +(1.71350 + 0.252809i) q^{3} +(1.04978 - 1.70234i) q^{4} +(2.05804 + 2.45268i) q^{5} +(-2.29020 + 0.868902i) q^{6} +(-4.54005 + 1.65244i) q^{7} +(-0.122943 + 2.82575i) q^{8} +(2.87218 + 0.866376i) q^{9} +O(q^{10})\)	\(q+(-1.23486 + 0.689282i) q^{2} +(1.71350 + 0.252809i) q^{3} +(1.04978 - 1.70234i) q^{4} +(2.05804 + 2.45268i) q^{5} +(-2.29020 + 0.868902i) q^{6} +(-4.54005 + 1.65244i) q^{7} +(-0.122943 + 2.82575i) q^{8} +(2.87218 + 0.866376i) q^{9} +(-4.23199 - 1.61015i) q^{10} +(0.638845 - 0.761346i) q^{11} +(2.22917 - 2.65157i) q^{12} +(1.85386 - 0.326885i) q^{13} +(4.46735 - 5.16992i) q^{14} +(2.90640 + 4.72296i) q^{15} +(-1.79592 - 3.57417i) q^{16} +(-0.690426 - 1.19585i) q^{17} +(-4.14392 + 0.909883i) q^{18} +(-1.81438 - 1.04753i) q^{19} +(6.33579 - 0.928715i) q^{20} +(-8.19713 + 1.68370i) q^{21} +(-0.264105 + 1.38050i) q^{22} +(6.79507 + 2.47320i) q^{23} +(-0.925037 + 4.81085i) q^{24} +(-0.911858 + 5.17140i) q^{25} +(-2.06395 + 1.68149i) q^{26} +(4.70245 + 2.21065i) q^{27} +(-1.95303 + 9.46341i) q^{28} +(-1.51798 - 0.267662i) q^{29} +(-6.84447 - 3.82889i) q^{30} +(-7.70194 - 2.80328i) q^{31} +(4.68133 + 3.17571i) q^{32} +(1.28714 - 1.14306i) q^{33} +(1.67686 + 1.00082i) q^{34} +(-13.3965 - 7.73449i) q^{35} +(4.49002 - 3.97992i) q^{36} +(6.22039 - 3.59135i) q^{37} +(2.96255 + 0.0429408i) q^{38} +(3.25923 - 0.0914472i) q^{39} +(-7.18369 + 5.51398i) q^{40} +(-0.0260791 - 0.147902i) q^{41} +(8.96180 - 7.72928i) q^{42} +(7.04138 - 8.39160i) q^{43} +(-0.625423 - 1.88678i) q^{44} +(3.78612 + 8.82757i) q^{45} +(-10.0957 + 1.62965i) q^{46} +(-4.64968 + 1.69234i) q^{47} +(-2.17374 - 6.57836i) q^{48} +(12.5192 - 10.5048i) q^{49} +(-2.43854 - 7.01451i) q^{50} +(-0.880725 - 2.22364i) q^{51} +(1.38967 - 3.49905i) q^{52} +2.04785i q^{53} +(-7.33065 + 0.511467i) q^{54} +3.18211 q^{55} +(-4.11123 - 13.0322i) q^{56} +(-2.84411 - 2.25363i) q^{57} +(2.05900 - 0.715794i) q^{58} +(-0.104687 - 0.124761i) q^{59} +(11.0912 + 0.0103864i) q^{60} +(-2.77834 - 7.63343i) q^{61} +(11.4431 - 1.84714i) q^{62} +(-14.4715 + 0.812718i) q^{63} +(-7.96977 - 0.694812i) q^{64} +(4.61706 + 3.87417i) q^{65} +(-0.801547 + 2.29873i) q^{66} +(-2.85014 + 0.502556i) q^{67} +(-2.76055 - 0.0800424i) q^{68} +(11.0181 + 5.95569i) q^{69} +(21.8741 + 0.317055i) q^{70} +(-6.18008 - 10.7042i) q^{71} +(-2.80128 + 8.00955i) q^{72} +(-2.83664 + 4.91320i) q^{73} +(-5.20589 + 8.72243i) q^{74} +(-2.86984 + 8.63068i) q^{75} +(-3.68795 + 1.98901i) q^{76} +(-1.64231 + 4.51220i) q^{77} +(-3.96167 + 2.35945i) q^{78} +(0.784918 - 4.45149i) q^{79} +(5.07019 - 11.7606i) q^{80} +(7.49879 + 4.97677i) q^{81} +(0.134150 + 0.164663i) q^{82} +(-0.477539 - 0.0842031i) q^{83} +(-5.73896 + 15.7218i) q^{84} +(1.51212 - 4.15451i) q^{85} +(-2.91098 + 15.2160i) q^{86} +(-2.53340 - 0.842398i) q^{87} +(2.07283 + 1.89882i) q^{88} +(1.01658 - 1.76076i) q^{89} +(-10.7600 - 8.29114i) q^{90} +(-7.87644 + 4.54747i) q^{91} +(11.3436 - 8.97120i) q^{92} +(-12.4886 - 6.75053i) q^{93} +(4.57522 - 5.29476i) q^{94} +(-1.16481 - 6.60595i) q^{95} +(7.21862 + 6.62506i) q^{96} +(-6.24806 - 5.24275i) q^{97} +(-8.21869 + 21.6013i) q^{98} +(2.49449 - 1.63324i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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