LMFDB - Embedded newform 512.2.o.a.157.52

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(5,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(128))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("512.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.o (of order $128$, degree $64$, 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$4032$
Relative dimension:	$63$ over $\Q(\zeta_{128})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{128}]$

Embedding invariants

Embedding label			157.52
Character	$\chi$	$=$	512.157
Dual form			512.2.o.a.437.52

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22173 - 0.712308i) q^{2} +(3.03797 - 1.17187i) q^{3} +(0.985234 - 1.74049i) q^{4} +(-1.20847 + 1.54851i) q^{5} +(2.87684 - 3.59568i) q^{6} +(-0.246458 + 0.688804i) q^{7} +(-0.0360811 - 2.82820i) q^{8} +(5.63312 - 5.10557i) q^{9} +O(q^{10})$	\(q+(1.22173 - 0.712308i) q^{2} +(3.03797 - 1.17187i) q^{3} +(0.985234 - 1.74049i) q^{4} +(-1.20847 + 1.54851i) q^{5} +(2.87684 - 3.59568i) q^{6} +(-0.246458 + 0.688804i) q^{7} +(-0.0360811 - 2.82820i) q^{8} +(5.63312 - 5.10557i) q^{9} +(-0.373403 + 2.75266i) q^{10} +(1.32570 + 5.90362i) q^{11} +(0.953472 - 6.44214i) q^{12} +(-2.44917 + 0.677778i) q^{13} +(0.189536 + 1.01708i) q^{14} +(-1.85664 + 6.12051i) q^{15} +(-2.05863 - 3.42958i) q^{16} +(-3.53867 + 1.07344i) q^{17} +(3.24540 - 10.2501i) q^{18} +(-2.36543 - 4.69930i) q^{19} +(1.50455 + 3.62898i) q^{20} +(0.0584597 + 2.38138i) q^{21} +(5.82485 + 6.26831i) q^{22} +(-7.19511 + 1.06729i) q^{23} +(-3.42391 - 8.54970i) q^{24} +(0.277414 + 1.10750i) q^{25} +(-2.50943 + 2.57263i) q^{26} +(6.73817 - 13.3864i) q^{27} +(0.956039 + 1.10759i) q^{28} +(-0.978479 - 5.63912i) q^{29} +(2.09139 + 8.80009i) q^{30} +(-0.729208 + 1.09134i) q^{31} +(-4.95800 - 2.72364i) q^{32} +(10.9458 + 16.3815i) q^{33} +(-3.55866 + 3.83208i) q^{34} +(-0.768783 - 1.21404i) q^{35} +(-3.33626 - 14.8346i) q^{36} +(3.55190 - 3.06389i) q^{37} +(-6.23726 - 4.05635i) q^{38} +(-6.64625 + 4.92919i) q^{39} +(4.42310 + 3.36192i) q^{40} +(0.612628 - 2.44575i) q^{41} +(1.76770 + 2.86776i) q^{42} +(-0.598926 - 1.35116i) q^{43} +(11.5813 + 3.50907i) q^{44} +(1.09856 + 14.8929i) q^{45} +(-8.03022 + 6.42908i) q^{46} +(1.64432 + 2.00361i) q^{47} +(-10.2731 - 8.00652i) q^{48} +(4.99736 + 4.10123i) q^{49} +(1.12780 + 1.15546i) q^{50} +(-9.49242 + 7.40796i) q^{51} +(-1.23334 + 4.93054i) q^{52} +(-1.96963 + 11.3512i) q^{53} +(-1.30307 - 21.1542i) q^{54} +(-10.7439 - 5.08149i) q^{55} +(1.95696 + 0.672179i) q^{56} +(-12.6931 - 11.5044i) q^{57} +(-5.21222 - 6.19248i) q^{58} +(0.183176 - 0.661913i) q^{59} +(8.82348 + 9.26159i) q^{60} +(4.36902 + 0.107253i) q^{61} +(-0.113525 + 1.85274i) q^{62} +(2.12840 + 5.13842i) q^{63} +(-7.99740 + 0.204089i) q^{64} +(1.91021 - 4.61165i) q^{65} +(25.0414 + 12.2169i) q^{66} +(4.62905 - 4.40722i) q^{67} +(-1.61809 + 7.21661i) q^{68} +(-20.6078 + 11.6742i) q^{69} +(-1.80401 - 0.935616i) q^{70} +(9.73301 - 0.478152i) q^{71} +(-14.6428 - 15.7474i) q^{72} +(-1.79053 - 5.00419i) q^{73} +(2.15702 - 6.27329i) q^{74} +(2.14062 + 3.03945i) q^{75} +(-10.5096 - 0.512897i) q^{76} +(-4.39317 - 0.541846i) q^{77} +(-4.60879 + 10.7563i) q^{78} +(13.7293 - 1.35222i) q^{79} +(7.79854 + 0.956738i) q^{80} +(2.54759 - 25.8661i) q^{81} +(-0.993662 - 3.42441i) q^{82} +(3.82989 + 3.30368i) q^{83} +(4.20238 + 2.24447i) q^{84} +(2.61413 - 6.77689i) q^{85} +(-1.69416 - 1.22412i) q^{86} +(-9.58093 - 15.9848i) q^{87} +(16.6488 - 3.96236i) q^{88} +(17.6636 + 2.62015i) q^{89} +(11.9505 + 17.4125i) q^{90} +(0.136762 - 1.85404i) q^{91} +(-5.23125 + 13.5746i) q^{92} +(-0.936402 + 4.16999i) q^{93} +(3.43610 + 1.27660i) q^{94} +(10.1355 + 2.01607i) q^{95} +(-18.2540 - 2.46417i) q^{96} +(-14.8934 + 2.96247i) q^{97} +(9.02676 + 1.45092i) q^{98} +(37.6092 + 26.4874i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) $ 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{91}{128}\right)$	$1$

Coefficient data

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

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

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

$2$	1.22173	−	0.712308i	0.863891	−	0.503678i
$2$	1.22173	−	0.712308i	0.863891	−	0.503678i
$3$	3.03797	−	1.17187i	1.75397	−	0.676582i	0.754172	−	0.656677i	$-0.228039\pi$
$3$	3.03797	−	1.17187i	1.75397	−	0.676582i	0.999802	−	0.0199047i	$-0.00633629\pi$
$4$	0.985234	−	1.74049i	0.492617	−	0.870246i
$5$	−1.20847	+	1.54851i	−0.540444	+	0.692515i	−0.978456	−	0.206454i	$-0.933808\pi$
$5$	−1.20847	+	1.54851i	−0.540444	+	0.692515i	0.438012	+	0.898969i	$0.355683\pi$
$6$	2.87684	−	3.59568i	1.17446	−	1.46793i
$7$	−0.246458	+	0.688804i	−0.0931523	+	0.260343i	−0.979078	−	0.203483i	$-0.934774\pi$
$7$	−0.246458	+	0.688804i	−0.0931523	+	0.260343i	0.885926	+	0.463826i	$0.153524\pi$
$8$	−0.0360811	−	2.82820i	−0.0127566	−	0.999919i
$9$	5.63312	−	5.10557i	1.87771	−	1.70186i
$10$	−0.373403	+	2.75266i	−0.118080	+	0.870468i
$11$	1.32570	+	5.90362i	0.399714	+	1.78001i	0.599715	+	0.800214i	$0.295281\pi$
$11$	1.32570	+	5.90362i	0.399714	+	1.78001i	−0.200001	+	0.979796i	$0.564094\pi$
$12$	0.953472	−	6.44214i	0.275244	−	1.85968i
$13$	−2.44917	+	0.677778i	−0.679279	+	0.187982i	−0.589242	−	0.807957i	$-0.700573\pi$
$13$	−2.44917	+	0.677778i	−0.679279	+	0.187982i	−0.0900368	+	0.995938i	$0.528698\pi$
$14$	0.189536	+	1.01708i	0.0506557	+	0.271827i
$15$	−1.85664	+	6.12051i	−0.479381	+	1.58031i
$16$	−2.05863	−	3.42958i	−0.514657	−	0.857396i
$17$	−3.53867	+	1.07344i	−0.858253	+	0.260348i	−0.688587	−	0.725154i	$-0.741769\pi$
$17$	−3.53867	+	1.07344i	−0.858253	+	0.260348i	−0.169665	+	0.985502i	$0.554269\pi$
$18$	3.24540	−	10.2501i	0.764949	−	2.41598i
$19$	−2.36543	−	4.69930i	−0.542667	−	1.07809i	−0.983568	−	0.180538i	$-0.942216\pi$
$19$	−2.36543	−	4.69930i	−0.542667	−	1.07809i	0.440901	−	0.897556i	$-0.354659\pi$
$20$	1.50455	+	3.62898i	0.336427	+	0.811464i
$21$	0.0584597	+	2.38138i	0.0127569	+	0.519660i
$22$	5.82485	+	6.26831i	1.24186	+	1.33641i
$23$	−7.19511	+	1.06729i	−1.50028	+	0.222546i	−0.845788	−	0.533519i	$-0.820869\pi$
$23$	−7.19511	+	1.06729i	−1.50028	+	0.222546i	−0.654496	+	0.756065i	$0.727119\pi$
$24$	−3.42391	−	8.54970i	−0.698902	−	1.74520i
$25$	0.277414	+	1.10750i	0.0554828	+	0.221500i
$26$	−2.50943	+	2.57263i	−0.492141	+	0.504533i
$27$	6.73817	−	13.3864i	1.29676	−	2.57622i
$28$	0.956039	+	1.10759i	0.180674	+	0.209315i
$29$	−0.978479	−	5.63912i	−0.181699	−	1.04716i	−0.925498	−	0.378754i	$-0.876353\pi$
$29$	−0.978479	−	5.63912i	−0.181699	−	1.04716i	0.743798	−	0.668404i	$-0.233022\pi$
$30$	2.09139	+	8.80009i	0.381833	+	1.60667i
$31$	−0.729208	+	1.09134i	−0.130970	+	0.196010i	−0.891158	−	0.453693i	$-0.850106\pi$
$31$	−0.729208	+	1.09134i	−0.130970	+	0.196010i	0.760189	+	0.649702i	$0.225106\pi$
$32$	−4.95800	−	2.72364i	−0.876460	−	0.481475i
$33$	10.9458	+	16.3815i	1.90541	+	2.85165i
$34$	−3.55866	+	3.83208i	−0.610305	+	0.657195i
$35$	−0.768783	−	1.21404i	−0.129948	−	0.205210i
$36$	−3.33626	−	14.8346i	−0.556043	−	2.47243i
$37$	3.55190	−	3.06389i	0.583929	−	0.503701i	−0.310701	−	0.950508i	$-0.600564\pi$
$37$	3.55190	−	3.06389i	0.583929	−	0.503701i	0.894630	+	0.446807i	$0.147439\pi$
$38$	−6.23726	−	4.05635i	−1.01182	−	0.658027i
$39$	−6.64625	+	4.92919i	−1.06425	+	0.789303i
$40$	4.42310	+	3.36192i	0.699353	+	0.531566i
$41$	0.612628	−	2.44575i	0.0956764	−	0.381961i	−0.903207	−	0.429205i	$-0.858794\pi$
$41$	0.612628	−	2.44575i	0.0956764	−	0.381961i	0.998883	+	0.0472437i	$0.0150437\pi$
$42$	1.76770	+	2.86776i	0.272762	+	0.442505i
$43$	−0.598926	−	1.35116i	−0.0913354	−	0.206049i	0.862718	−	0.505685i	$-0.168760\pi$
$43$	−0.598926	−	1.35116i	−0.0913354	−	0.206049i	−0.954054	+	0.299635i	$0.903135\pi$
$44$	11.5813	+	3.50907i	1.74595	+	0.529012i
$45$	1.09856	+	14.8929i	0.163764	+	2.22010i
$46$	−8.03022	+	6.42908i	−1.18399	+	0.947916i
$47$	1.64432	+	2.00361i	0.239849	+	0.292257i	0.878997	−	0.476827i	$-0.158213\pi$
$47$	1.64432	+	2.00361i	0.239849	+	0.292257i	−0.639148	+	0.769083i	$0.720713\pi$
$48$	−10.2731	−	8.00652i	−1.48279	−	1.15564i
$49$	4.99736	+	4.10123i	0.713909	+	0.585890i
$50$	1.12780	+	1.15546i	0.159496	+	0.163406i
$51$	−9.49242	+	7.40796i	−1.32921	+	1.03732i
$52$	−1.23334	+	4.93054i	−0.171034	+	0.683743i
$53$	−1.96963	+	11.3512i	−0.270549	+	1.55921i	0.467209	+	0.884147i	$0.345260\pi$
$53$	−1.96963	+	11.3512i	−0.270549	+	1.55921i	−0.737758	+	0.675065i	$0.764115\pi$
$54$	−1.30307	−	21.1542i	−0.177326	−	2.87873i
$55$	−10.7439	−	5.08149i	−1.44871	−	0.685187i
$56$	1.95696	+	0.672179i	0.261510	+	0.0898237i
$57$	−12.6931	−	11.5044i	−1.68124	−	1.52379i
$58$	−5.21222	−	6.19248i	−0.684399	−	0.813113i
$59$	0.183176	−	0.661913i	0.0238475	−	0.0861738i	−0.950889	−	0.309533i	$-0.899827\pi$
$59$	0.183176	−	0.661913i	0.0238475	−	0.0861738i	0.974736	+	0.223359i	$0.0717023\pi$
$60$	8.82348	+	9.26159i	1.13911	+	1.19567i
$61$	4.36902	+	0.107253i	0.559396	+	0.0137324i	0.303259	−	0.952908i	$-0.401925\pi$
$61$	4.36902	+	0.107253i	0.559396	+	0.0137324i	0.256137	+	0.966641i	$0.417550\pi$
$62$	−0.113525	+	1.85274i	−0.0144176	+	0.235298i
$63$	2.12840	+	5.13842i	0.268154	+	0.647381i
$64$	−7.99740	+	0.204089i	−0.999675	+	0.0255111i
$65$	1.91021	−	4.61165i	0.236932	−	0.572004i
$66$	25.0414	+	12.2169i	3.08238	+	1.50380i
$67$	4.62905	−	4.40722i	0.565528	−	0.538427i	−0.352051	−	0.935981i	$-0.614516\pi$
$67$	4.62905	−	4.40722i	0.565528	−	0.538427i	0.917579	+	0.397553i	$0.130141\pi$
$68$	−1.61809	+	7.21661i	−0.196223	+	0.875143i
$69$	−20.6078	+	11.6742i	−2.48089	+	1.40541i
$70$	−1.80401	−	0.935616i	−0.215621	−	0.111828i
$71$	9.73301	−	0.478152i	1.15510	−	0.0567462i	0.537515	−	0.843254i	$-0.319363\pi$
$71$	9.73301	−	0.478152i	1.15510	−	0.0567462i	0.617581	+	0.786508i	$0.288113\pi$
$72$	−14.6428	−	15.7474i	−1.72567	−	1.85585i
$73$	−1.79053	−	5.00419i	−0.209565	−	0.585696i	0.790061	−	0.613028i	$-0.210049\pi$
$73$	−1.79053	−	5.00419i	−0.209565	−	0.585696i	−0.999626	+	0.0273324i	$0.991299\pi$
$74$	2.15702	−	6.27329i	0.250748	−	0.729255i
$75$	2.14062	+	3.03945i	0.247178	+	0.350966i
$76$	−10.5096	−	0.512897i	−1.20553	−	0.0588333i
$77$	−4.39317	−	0.541846i	−0.500648	−	0.0617490i
$78$	−4.60879	+	10.7563i	−0.521843	+	1.21791i
$79$	13.7293	−	1.35222i	1.54466	−	0.152136i	0.710518	−	0.703679i	$-0.248461\pi$
$79$	13.7293	−	1.35222i	1.54466	−	0.152136i	0.834147	+	0.551543i	$0.185961\pi$
$80$	7.79854	+	0.956738i	0.871903	+	0.106967i
$81$	2.54759	−	25.8661i	0.283065	−	2.87401i
$82$	−0.993662	−	3.42441i	−0.109732	−	0.378163i
$83$	3.82989	+	3.30368i	0.420385	+	0.362626i	0.837696	−	0.546138i	$-0.183902\pi$
$83$	3.82989	+	3.30368i	0.420385	+	0.362626i	−0.417311	+	0.908764i	$0.637027\pi$
$84$	4.20238	+	2.24447i	0.458517	+	0.244892i
$85$	2.61413	−	6.77689i	0.283543	−	0.735057i
$86$	−1.69416	−	1.22412i	−0.182686	−	0.132001i
$87$	−9.58093	−	15.9848i	−1.02718	−	1.71375i
$88$	16.6488	−	3.96236i	1.77477	−	0.422389i
$89$	17.6636	+	2.62015i	1.87234	+	0.277735i	0.983558	−	0.180594i	$-0.0578019\pi$
$89$	17.6636	+	2.62015i	1.87234	+	0.277735i	0.888783	+	0.458329i	$0.151552\pi$
$90$	11.9505	+	17.4125i	1.25969	+	1.83544i
$91$	0.136762	−	1.85404i	0.0143366	−	0.194357i
$92$	−5.23125	+	13.5746i	−0.545395	+	1.41525i
$93$	−0.936402	+	4.16999i	−0.0971004	+	0.432408i
$94$	3.43610	+	1.27660i	0.354407	+	0.131672i
$95$	10.1355	+	2.01607i	1.03988	+	0.206845i
$96$	−18.2540	−	2.46417i	−1.86304	−	0.251498i
$97$	−14.8934	+	2.96247i	−1.51219	+	0.300794i	−0.880358	−	0.474310i	$-0.842697\pi$
$97$	−14.8934	+	2.96247i	−1.51219	+	0.300794i	−0.631834	+	0.775104i	$0.717697\pi$
$98$	9.02676	+	1.45092i	0.911840	+	0.146565i
$99$	37.6092	+	26.4874i	3.77987	+	2.66208i
$100$	2.20091	+	0.608308i	0.220091	+	0.0608308i
$101$	−4.03819	+	1.33404i	−0.401815	+	0.132742i	−0.507487	−	0.861659i	$-0.669426\pi$
$101$	−4.03819	+	1.33404i	−0.401815	+	0.132742i	0.105672	+	0.994401i	$0.466301\pi$
$102$	−6.32040	+	15.8120i	−0.625813	+	1.56563i
$103$	0.707576	+	0.424105i	0.0697195	+	0.0417883i	0.548538	−	0.836126i	$-0.315185\pi$
$103$	0.707576	+	0.424105i	0.0697195	+	0.0417883i	−0.478818	+	0.877914i	$0.658935\pi$
$104$	2.00526	+	6.90229i	0.196632	+	0.676825i
$105$	−3.75825	−	2.78730i	−0.366767	−	0.272013i
$106$	5.67923	+	15.2711i	0.551616	+	1.48326i
$107$	−4.18528	−	3.98472i	−0.404606	−	0.385217i	0.459790	−	0.888027i	$-0.347925\pi$
$107$	−4.18528	−	3.98472i	−0.404606	−	0.385217i	−0.864397	+	0.502810i	$0.832300\pi$
$108$	−16.6603	−	24.9165i	−1.60314	−	2.39759i
$109$	5.65869	−	17.1291i	0.542004	−	1.64067i	−0.207177	−	0.978304i	$-0.566428\pi$
$109$	5.65869	−	17.1291i	0.542004	−	1.64067i	0.749181	−	0.662366i	$-0.230447\pi$
$110$	−16.7457	+	1.44478i	−1.59664	+	0.137754i
$111$	7.20008	−	13.4704i	0.683401	−	1.27855i
$112$	2.86968	−	0.572744i	0.271159	−	0.0541192i
$113$	−2.76596	+	1.47844i	−0.260199	+	0.139079i	−0.596339	−	0.802733i	$-0.703379\pi$
$113$	−2.76596	+	1.47844i	−0.260199	+	0.139079i	0.336140	+	0.941812i	$0.390879\pi$
$114$	−23.7022	−	5.01378i	−2.21991	−	0.469584i
$115$	7.04236	−	12.4315i	0.656703	−	1.15924i
$116$	−10.7789	−	3.85281i	−1.00079	−	0.357724i
$117$	−10.3361	+	16.3224i	−0.955569	+	1.50901i
$118$	−0.247695	−	0.939155i	−0.0228022	−	0.0864563i
$119$	0.132741	−	2.70200i	0.0121683	−	0.247692i
$120$	17.3770	+	5.03010i	1.58629	+	0.459183i
$121$	−23.1514	+	10.9498i	−2.10467	+	0.995436i
$122$	5.41415	−	2.98106i	0.490174	−	0.269892i
$123$	−1.00496	−	8.14803i	−0.0906145	−	0.734683i
$124$	1.18102	+	2.34440i	0.106059	+	0.210533i
$125$	−11.0289	−	4.88878i	−0.986456	−	0.437266i
$126$	6.26047	+	4.76167i	0.557727	+	0.424203i
$127$	3.26501	−	3.26501i	0.289723	−	0.289723i	−0.547248	−	0.836971i	$-0.684324\pi$
$127$	3.26501	−	3.26501i	0.289723	−	0.289723i	0.836971	+	0.547248i	$0.184324\pi$
$128$	−9.62526	+	5.94595i	−0.850761	+	0.525553i
$129$	−3.40291	−	3.40291i	−0.299609	−	0.299609i
$130$	−0.951163	−	6.99483i	−0.0834226	−	0.613487i
$131$	−0.183006	+	0.412855i	−0.0159893	+	0.0360713i	−0.922026	−	0.387127i	$-0.873468\pi$
$131$	−0.183006	+	0.412855i	−0.0159893	+	0.0360713i	0.906037	+	0.423198i	$0.139093\pi$
$132$	39.2960	−	2.91142i	3.42028	−	0.253407i
$133$	3.81988	−	0.471137i	0.331225	−	0.0408527i
$134$	2.51613	−	8.68173i	0.217361	−	0.749987i
$135$	12.5862	+	26.6112i	1.08325	+	2.29033i
$136$	3.16359	+	9.96931i	0.271275	+	0.854862i
$137$	3.27282	+	0.160783i	0.279616	+	0.0137366i	0.188392	−	0.982094i	$-0.439672\pi$
$137$	3.27282	+	0.160783i	0.279616	+	0.0137366i	0.0912233	+	0.995830i	$0.470922\pi$
$138$	−16.8615	+	28.9418i	−1.43535	+	2.46369i
$139$	−6.64568	−	4.20833i	−0.563679	−	0.356946i	0.222511	−	0.974930i	$-0.428575\pi$
$139$	−6.64568	−	4.20833i	−0.563679	−	0.356946i	−0.786191	+	0.617984i	$0.787950\pi$
$140$	−2.87046	+	0.141947i	−0.242598	+	0.0119967i
$141$	7.34339	+	4.15998i	0.618425	+	0.350333i
$142$	11.5505	−	7.51708i	0.969296	−	0.630819i
$143$	−7.24822	−	13.5605i	−0.606127	−	1.13398i
$144$	−29.1065	−	8.80880i	−2.42554	−	0.734067i
$145$	9.91470	+	5.29952i	0.823371	+	0.440101i
$146$	−5.75206	−	4.83834i	−0.476044	−	0.400424i
$147$	19.9880	+	6.60314i	1.64858	+	0.544617i
$148$	−1.83323	−	9.20071i	−0.150690	−	0.756293i
$149$	1.28077	−	1.34524i	0.104925	−	0.110206i	−0.669685	−	0.742645i	$-0.733571\pi$
$149$	1.28077	−	1.34524i	0.104925	−	0.110206i	0.774610	+	0.632439i	$0.217946\pi$
$150$	4.78029	+	2.18860i	0.390309	+	0.178698i
$151$	7.07825	−	9.54392i	0.576020	−	0.776673i	−0.415081	−	0.909784i	$-0.636247\pi$
$151$	7.07825	−	9.54392i	0.576020	−	0.776673i	0.991101	+	0.133111i	$0.0424968\pi$
$152$	−13.2052	+	6.85946i	−1.07108	+	0.556376i
$153$	−14.4532	+	24.1137i	−1.16847	+	1.94948i
$154$	−5.75321	+	2.46730i	−0.463607	+	0.198821i
$155$	−0.808721	−	2.44803i	−0.0649580	−	0.196631i
$156$	2.03112	+	16.4242i	0.162620	+	1.31498i
$157$	−10.5133	+	14.9277i	−0.839052	+	1.19136i	0.140481	+	0.990083i	$0.455135\pi$
$157$	−10.5133	+	14.9277i	−0.839052	+	1.19136i	−0.979534	+	0.201280i	$0.935490\pi$
$158$	15.8102	−	11.4315i	1.25779	−	0.909443i
$159$	7.31856	+	36.7929i	0.580400	+	2.91787i
$160$	10.2092	−	4.38609i	0.807106	−	0.346751i
$161$	1.03814	−	5.21906i	0.0818166	−	0.411320i
$162$	−15.3122	−	33.4159i	−1.20304	−	2.62540i
$163$	−15.8253	−	3.55368i	−1.23953	−	0.278346i	−0.450542	−	0.892755i	$-0.648769\pi$
$163$	−15.8253	−	3.55368i	−1.23953	−	0.278346i	−0.788987	+	0.614409i	$0.789394\pi$
$164$	−3.65322	−	3.47591i	−0.285269	−	0.271423i
$165$	−38.5945	−	2.84690i	−3.00458	−	0.221631i
$166$	7.03231	+	1.30814i	0.545813	+	0.101531i
$167$	0.712505	−	4.80332i	0.0551353	−	0.371692i	−0.943994	−	0.329964i	$-0.892964\pi$
$167$	0.712505	−	4.80332i	0.0551353	−	0.371692i	0.999129	−	0.0417286i	$-0.0132865\pi$
$168$	6.73291	−	0.251258i	0.519455	−	0.0193850i
$169$	−5.61140	+	3.36335i	−0.431646	+	0.258719i
$170$	−1.63348	−	10.1416i	−0.125282	−	0.777823i
$171$	−37.3174	−	14.3949i	−2.85373	−	1.10081i
$172$	−2.94176	−	0.288778i	−0.224307	−	0.0220191i
$173$	−3.19080	+	3.69903i	−0.242592	+	0.281232i	−0.865334	−	0.501196i	$-0.832894\pi$
$173$	−3.19080	+	3.69903i	−0.242592	+	0.281232i	0.622742	+	0.782427i	$0.286019\pi$
$174$	−23.0914	−	12.7045i	−1.75055	−	0.963126i
$175$	−0.831220	−	0.0818680i	−0.0628343	−	0.00618864i
$176$	17.5178	−	16.7000i	1.32046	−	1.25881i
$177$	−0.219196	−	2.22553i	−0.0164758	−	0.167281i
$178$	23.4465	−	9.38084i	1.75739	−	0.703124i
$179$	−1.97756	+	16.0337i	−0.147810	+	1.19841i	0.717276	+	0.696789i	$0.245388\pi$
$179$	−1.97756	+	16.0337i	−0.147810	+	1.19841i	−0.865086	+	0.501623i	$0.832737\pi$
$180$	27.0033	+	12.7609i	2.01271	+	0.951143i
$181$	−19.6388	+	13.8312i	−1.45974	+	1.02806i	−0.470398	+	0.882455i	$0.655890\pi$
$181$	−19.6388	+	13.8312i	−1.45974	+	1.02806i	−0.989342	+	0.145610i	$0.953485\pi$
$182$	−1.15356	−	2.36255i	−0.0855079	−	0.175124i
$183$	13.3986	−	4.79411i	0.990457	−	0.354391i
$184$	3.27813	+	20.3107i	0.241667	+	1.49732i
$185$	0.452103	+	9.20278i	0.0332393	+	0.676602i
$186$	1.82629	+	5.76159i	0.133910	+	0.422461i
$187$	−11.0284	−	19.4679i	−0.806478	−	1.42363i
$188$	5.10731	−	0.887905i	0.372489	−	0.0647571i
$189$	7.55996	+	7.94047i	0.549906	+	0.577584i
$190$	13.8188	−	4.75650i	1.00252	−	0.345072i
$191$	2.34270	+	0.970379i	0.169512	+	0.0702142i	0.465826	−	0.884877i	$-0.345757\pi$
$191$	2.34270	+	0.970379i	0.169512	+	0.0702142i	−0.296314	+	0.955091i	$0.595757\pi$
$192$	−24.0567	+	9.99196i	−1.73614	+	0.721108i
$193$	−8.49161	+	3.51734i	−0.611239	+	0.253184i	−0.666758	−	0.745274i	$-0.732319\pi$
$193$	−8.49161	+	3.51734i	−0.611239	+	0.253184i	0.0555190	+	0.998458i	$0.482319\pi$
$194$	−16.0854	+	14.2280i	−1.15487	+	1.02151i
$195$	0.398880	−	16.2486i	0.0285644	−	1.16358i
$196$	12.0617	−	4.65721i	0.861552	−	0.332658i
$197$	24.6677	+	6.82648i	1.75750	+	0.486367i	0.988285	−	0.152620i	$-0.0487711\pi$
$197$	24.6677	+	6.82648i	1.75750	+	0.486367i	0.769218	+	0.638987i	$0.220646\pi$
$198$	64.8153	+	5.57101i	4.60623	+	0.395914i
$199$	3.49675	−	3.85806i	0.247878	−	0.273491i	−0.604284	−	0.796769i	$-0.706541\pi$
$199$	3.49675	−	3.85806i	0.247878	−	0.273491i	0.852162	+	0.523278i	$0.175291\pi$
$200$	3.12221	−	0.824541i	0.220774	−	0.0583038i
$201$	8.89820	−	18.8137i	0.627631	−	1.32701i
$202$	−3.98332	+	4.50627i	−0.280266	+	0.317060i
$203$	4.12540	+	0.715824i	0.289546	+	0.0502410i
$204$	3.54125	+	23.8201i	0.247937	+	1.66774i
$205$	3.04692	+	3.90427i	0.212806	+	0.272686i
$206$	1.16656	+	0.0141279i	0.0812779	+	0.000984336i
$207$	−35.0818	+	42.7473i	−2.43836	+	2.97114i
$208$	7.36644	+	7.00435i	0.510770	+	0.485664i
$209$	24.6071	−	20.1945i	1.70211	−	1.39688i
$210$	−6.57697	−	0.728296i	−0.453854	−	0.0502572i
$211$	3.22256	−	0.237710i	0.221850	−	0.0163646i	0.0378169	−	0.999285i	$-0.487960\pi$
$211$	3.22256	−	0.237710i	0.221850	−	0.0163646i	0.184033	+	0.982920i	$0.441085\pi$
$212$	17.8162	+	14.6117i	1.22362	+	1.00354i
$213$	29.0083	−	12.8585i	1.98761	−	0.881049i
$214$	−7.95162	−	1.88703i	−0.543562	−	0.128995i
$215$	2.81606	+	0.705388i	0.192054	+	0.0481070i
$216$	−38.1026	−	18.5739i	−2.59255	−	1.26379i
$217$	−0.571997	−	0.771249i	−0.0388297	−	0.0523558i
$218$	−5.28782	−	24.9578i	−0.358137	−	1.69036i
$219$	−11.3038	−	13.1043i	−0.763843	−	0.885507i
$220$	−19.4295	+	13.6932i	−1.30994	+	0.923197i
$221$	7.93925	−	5.02748i	0.534052	−	0.338185i
$222$	−0.798548	−	21.5858i	−0.0535950	−	1.44875i
$223$	16.9272	−	11.3104i	1.13353	−	0.757398i	0.160260	−	0.987075i	$-0.448767\pi$
$223$	16.9272	−	11.3104i	1.13353	−	0.757398i	0.973267	+	0.229676i	$0.0737668\pi$
$224$	3.09799	−	2.74383i	0.206993	−	0.183330i
$225$	7.21711	+	4.82232i	0.481141	+	0.321488i
$226$	−2.32614	+	3.77646i	−0.154733	+	0.251206i
$227$	1.82351	−	0.316409i	0.121031	−	0.0210008i	−0.110124	−	0.993918i	$-0.535125\pi$
$227$	1.82351	−	0.316409i	0.121031	−	0.0210008i	0.231154	+	0.972917i	$0.425750\pi$
$228$	−32.5289	+	10.7578i	−2.15428	+	0.712451i
$229$	−20.2569	−	10.1965i	−1.33862	−	0.673803i	−0.371570	−	0.928405i	$-0.621181\pi$
$229$	−20.2569	−	10.1965i	−1.33862	−	0.673803i	−0.967046	+	0.254602i	$0.918056\pi$
$230$	−0.251223	−	20.2042i	−0.0165652	−	1.33223i
$231$	−13.9813	+	3.50213i	−0.919901	+	0.230423i
$232$	−15.9132	+	2.97080i	−1.04475	+	0.195042i
$233$	1.60781	+	10.8390i	0.105331	+	0.710087i	0.975929	+	0.218090i	$0.0699828\pi$
$233$	1.60781	+	10.8390i	0.105331	+	0.710087i	−0.870597	+	0.491997i	$0.836267\pi$
$234$	−1.00125	+	27.3040i	−0.0654535	+	1.78492i
$235$	−5.08973	+	0.124946i	−0.332017	+	0.00815057i
$236$	−0.971584	−	0.970956i	−0.0632448	−	0.0632039i
$237$	40.1245	−	20.1970i	2.60637	−	1.31194i
$238$	−1.76249	−	3.39566i	−0.114245	−	0.220108i
$239$	1.96448	+	6.47602i	0.127072	+	0.418899i	0.997273	−	0.0737966i	$-0.0235116\pi$
$239$	1.96448	+	6.47602i	0.127072	+	0.418899i	−0.870202	+	0.492696i	$0.836012\pi$
$240$	24.8129	−	6.23237i	1.60167	−	0.402298i
$241$	23.4749	+	7.12105i	1.51215	+	0.458707i	0.934016	−	0.357232i	$-0.116279\pi$
$241$	23.4749	+	7.12105i	1.51215	+	0.458707i	0.578138	+	0.815939i	$0.303779\pi$
$242$	−20.4851	+	29.8686i	−1.31683	+	1.92003i
$243$	−10.5809	−	38.2345i	−0.678765	−	2.45274i
$244$	4.49118	−	7.49858i	0.287518	−	0.480047i
$245$	−12.3900	+	2.78226i	−0.791566	+	0.177752i
$246$	−7.03170	−	9.23882i	−0.448325	−	0.589046i
$247$	8.97843	+	9.90617i	0.571284	+	0.630315i
$248$	3.11282	+	2.02297i	0.197665	+	0.128458i
$249$	15.5066	+	5.54834i	0.982690	+	0.351612i
$250$	−16.9566	+	1.88323i	−1.07243	+	0.119106i
$251$	−18.8492	−	14.7101i	−1.18975	−	0.928492i	−0.191162	−	0.981559i	$-0.561226\pi$
$251$	−18.8492	−	14.7101i	−1.18975	−	0.928492i	−0.998591	+	0.0530663i	$0.983101\pi$
$252$	11.0404	+	1.35807i	0.695478	+	0.0855507i
$253$	−15.8395	−	41.0623i	−0.995820	−	2.58157i
$254$	1.66326	−	6.31465i	0.104362	−	0.396217i
$255$		−	23.6514i		−	1.48111i
$256$	−7.52409	+	14.1205i	−0.470256	+	0.882530i
$257$		−	5.57513i		−	0.347767i	−0.984766	−	0.173884i	$-0.944368\pi$
$257$		−	5.57513i		−	0.347767i	0.984766	−	0.173884i	$-0.0556316\pi$
$258$	−6.58134	−	1.73350i	−0.409736	−	0.107923i
$259$	1.23503	+	3.20168i	0.0767407	+	0.198943i
$260$	−6.14454	−	7.86825i	−0.381068	−	0.487968i
$261$	−34.3028	−	26.7702i	−2.12329	−	1.65703i
$262$	0.0704967	+	0.634753i	0.00435530	+	0.0392152i
$263$	16.3223	+	5.84022i	1.00648	+	0.360123i	0.787971	−	0.615712i	$-0.211132\pi$
$263$	16.3223	+	5.84022i	1.00648	+	0.360123i	0.218506	+	0.975836i	$0.429882\pi$
$264$	45.9351	−	31.5478i	2.82711	−	1.94163i
$265$	−15.1973	−	16.7676i	−0.933562	−	1.03003i
$266$	4.33125	−	3.29653i	0.265566	−	0.202123i
$267$	56.7321	−	12.7396i	3.47195	−	0.779652i
$268$	−3.11004	−	12.3990i	−0.189976	−	0.757387i
$269$	−6.55536	−	23.6880i	−0.399687	−	1.44428i	−0.838103	−	0.545512i	$-0.816335\pi$
$269$	−6.55536	−	23.6880i	−0.399687	−	1.44428i	0.438415	−	0.898773i	$-0.355540\pi$
$270$	34.3323	+	23.5464i	2.08940	+	1.43299i
$271$	−19.8978	−	6.03592i	−1.20870	−	0.366656i	−0.379282	−	0.925281i	$-0.623829\pi$
$271$	−19.8978	−	6.03592i	−1.20870	−	0.366656i	−0.829420	+	0.558625i	$0.811329\pi$
$272$	10.9663	+	9.92633i	0.664927	+	0.601872i
$273$	−1.75723	−	5.79280i	−0.106352	−	0.350596i
$274$	4.11302	−	2.13482i	0.248476	−	0.128969i
$275$	−6.17049	+	3.10596i	−0.372094	+	0.187297i
$276$	0.0153187	+	47.3695i	0.000922076	+	2.85131i
$277$	−4.02662	+	0.0988479i	−0.241936	+	0.00593920i	−0.145329	−	0.989383i	$-0.546424\pi$
$277$	−4.02662	+	0.0988479i	−0.241936	+	0.00593920i	−0.0966071	+	0.995323i	$0.530799\pi$
$278$	−11.1168	−	0.407657i	−0.666744	−	0.0244497i
$279$	1.46417	+	9.87065i	0.0876577	+	0.590940i
$280$	−3.40581	+	2.21807i	−0.203536	+	0.132555i
$281$	−9.51701	+	2.38389i	−0.567737	+	0.142211i	−0.516212	−	0.856461i	$-0.672658\pi$
$281$	−9.51701	+	2.38389i	−0.567737	+	0.142211i	−0.0515252	+	0.998672i	$0.516408\pi$
$282$	11.9348	−	0.148399i	0.710707	−	0.00883706i
$283$	12.8682	+	6.47732i	0.764937	+	0.385037i	0.788777	−	0.614679i	$-0.210714\pi$
$283$	12.8682	+	6.47732i	0.764937	+	0.385037i	−0.0238407	+	0.999716i	$0.507589\pi$
$284$	8.75707	−	17.4113i	0.519636	−	1.03317i
$285$	33.1539	−	5.75274i	1.96387	−	0.340763i
$286$	−18.5146	−	11.4042i	−1.09479	−	0.674346i
$287$	1.53365	+	1.02475i	0.0905286	+	0.0604893i
$288$	−41.8348	+	9.97084i	−2.46514	+	0.587537i
$289$	−2.76511	+	1.84758i	−0.162653	+	0.108681i
$290$	15.8879	−	0.587760i	0.932972	−	0.0345145i
$291$	−41.7739	+	26.4531i	−2.44883	+	1.55071i
$292$	−10.4738	−	1.81389i	−0.612935	−	0.106150i
$293$	11.2528	+	13.0451i	0.657396	+	0.762104i	0.983041	−	0.183388i	$-0.0587064\pi$
$293$	11.2528	+	13.0451i	0.657396	+	0.762104i	−0.325645	+	0.945492i	$0.605581\pi$
$294$	29.1233	−	6.17037i	1.69851	−	0.359864i
$295$	0.803617	+	1.08355i	0.0467884	+	0.0630869i
$296$	−8.79344	−	9.93493i	−0.511109	−	0.577456i
$297$	87.9613	+	22.0332i	5.10403	+	1.27849i
$298$	0.606531	−	2.55582i	0.0351354	−	0.148055i
$299$	16.8987	−	7.49067i	0.977277	−	0.433197i
$300$	7.39916	−	0.731170i	0.427191	−	0.0422141i
$301$	1.07829	−	0.0795396i	0.0621517	−	0.00458458i
$302$	1.84948	−	16.7020i	0.106426	−	0.961090i
$303$	−10.7046	+	8.78503i	−0.614963	+	0.504687i
$304$	−11.2471	+	17.7866i	−0.645066	+	1.02013i
$305$	−5.44591	+	6.63587i	−0.311832	+	0.379969i
$306$	−0.481469	+	39.7555i	−0.0275238	+	2.27267i
$307$	−15.2049	−	19.4832i	−0.867788	−	1.11197i	−0.992797	−	0.119812i	$-0.961771\pi$
$307$	−15.2049	−	19.4832i	−0.867788	−	1.11197i	0.125009	−	0.992156i	$-0.460104\pi$
$308$	−5.27137	+	7.11243i	−0.300364	+	0.405268i
$309$	2.64659	+	0.459227i	0.150559	+	0.0261245i
$310$	−2.73179	−	2.41477i	−0.155155	−	0.137150i
$311$	4.78813	−	10.1237i	0.271510	−	0.574060i	−0.721456	−	0.692460i	$-0.756527\pi$
$311$	4.78813	−	10.1237i	0.271510	−	0.574060i	0.992966	+	0.118401i	$0.0377767\pi$
$312$	14.1805	+	18.6190i	0.802815	+	1.05410i
$313$	−19.1935	+	21.1768i	−1.08488	+	1.19698i	−0.105613	+	0.994407i	$0.533681\pi$
$313$	−19.1935	+	21.1768i	−1.08488	+	1.19698i	−0.979267	+	0.202574i	$0.935069\pi$
$314$	−2.21123	+	25.7263i	−0.124787	+	1.45182i
$315$	−10.5290	−	2.91377i	−0.593243	−	0.164172i
$316$	11.1730	−	25.2280i	0.628532	−	1.41918i
$317$	−0.610579	+	24.8722i	−0.0342935	+	1.39696i	0.698060	+	0.716039i	$0.254047\pi$
$317$	−0.610579	+	24.8722i	−0.0342935	+	1.39696i	−0.732353	+	0.680925i	$0.761578\pi$
$318$	35.1492	+	39.7378i	1.97107	+	2.22838i
$319$	31.9940	−	13.2524i	1.79132	−	0.741990i
$320$	9.34858	−	12.6307i	0.522601	−	0.706077i
$321$	−17.3844	−	7.20084i	−0.970300	−	0.401911i
$322$	−2.44926	−	7.11574i	−0.136492	−	0.396545i
$323$	13.4149	+	14.0901i	0.746425	+	0.783995i
$324$	−42.5097	−	29.9182i	−2.36165	−	1.66212i
$325$	−1.43007	−	2.52443i	−0.0793261	−	0.140030i
$326$	−21.8655	+	6.93084i	−1.21102	+	0.383863i
$327$	−2.88222	−	58.6689i	−0.159387	−	3.24440i
$328$	−6.93916	−	1.64439i	−0.383151	−	0.0907961i
$329$	−1.78535	+	0.638809i	−0.0984296	+	0.0352187i
$330$	−49.1798	+	24.0131i	−2.70726	+	1.32188i
$331$	13.6735	−	9.62997i	0.751564	−	0.529311i	−0.135601	−	0.990764i	$-0.543297\pi$
$331$	13.6735	−	9.62997i	0.751564	−	0.529311i	0.887165	+	0.461453i	$0.152672\pi$
$332$	9.52337	−	3.41099i	0.522663	−	0.187202i
$333$	4.36540	−	35.3937i	0.239223	−	1.93957i
$334$	−2.55096	−	6.37587i	−0.139582	−	0.348872i
$335$	1.23056	+	12.4941i	0.0672329	+	0.682627i
$336$	8.04681	−	5.10288i	0.438989	−	0.278385i
$337$	5.57545	+	0.549134i	0.303714	+	0.0299132i	0.248726	−	0.968574i	$-0.419988\pi$
$337$	5.57545	+	0.549134i	0.303714	+	0.0299132i	0.0549878	+	0.998487i	$0.482488\pi$
$338$	−4.45986	+	8.10614i	−0.242585	+	0.440916i
$339$	−6.67036	+	7.73280i	−0.362284	+	0.419988i
$340$	−9.21959	−	11.2267i	−0.500002	−	0.608853i
$341$	−7.40955	−	2.85818i	−0.401250	−	0.154779i
$342$	−55.8452	+	8.99484i	−3.01977	+	0.486385i
$343$	−8.44899	+	5.06413i	−0.456203	+	0.273437i
$344$	−3.79973	+	1.74263i	−0.204868	+	0.0939565i
$345$	6.82632	−	46.0193i	0.367517	−	2.47760i
$346$	−1.26344	+	6.79204i	−0.0679231	+	0.365142i
$347$	−26.6330	−	1.96457i	−1.42974	−	0.105464i	−0.663574	−	0.748111i	$-0.730961\pi$
$347$	−26.6330	−	1.96457i	−1.42974	−	0.105464i	−0.766162	+	0.642647i	$0.777836\pi$
$348$	−37.2609	+	0.926761i	−1.99739	+	0.0496796i
$349$	−14.8823	−	3.34194i	−0.796632	−	0.178890i	−0.198304	−	0.980141i	$-0.563543\pi$
$349$	−14.8823	−	3.34194i	−0.796632	−	0.178890i	−0.598329	+	0.801251i	$0.704168\pi$
$350$	−1.07384	+	0.492064i	−0.0573991	+	0.0263020i
$351$	−7.42991	+	37.3527i	−0.396580	+	1.99374i
$352$	9.50648	−	32.8809i	0.506697	−	1.75256i
$353$	−1.07360	−	5.39734i	−0.0571418	−	0.287271i	0.941640	−	0.336623i	$-0.109285\pi$
$353$	−1.07360	−	5.39734i	−0.0571418	−	0.287271i	−0.998781	+	0.0493512i	$0.984285\pi$
$354$	−1.85306	−	2.56286i	−0.0984892	−	0.136214i
$355$	−11.0216	+	15.6495i	−0.584967	+	0.830590i
$356$	21.9631	−	28.1619i	1.16404	−	1.49258i
$357$	−2.76315	−	8.36417i	−0.146241	−	0.442679i
$358$	9.00486	+	20.9974i	0.475922	+	1.10975i
$359$	5.32145	−	8.87830i	0.280855	−	0.468579i	−0.684683	−	0.728841i	$-0.740059\pi$
$359$	5.32145	−	8.87830i	0.280855	−	0.468579i	0.965538	+	0.260263i	$0.0838092\pi$
$360$	42.0804	−	3.64431i	2.21783	−	0.192072i
$361$	−5.16991	+	6.97081i	−0.272100	+	0.366885i
$362$	−14.1412	+	30.8868i	−0.743243	+	1.62338i
$363$	−57.5015	+	60.3957i	−3.01805	+	3.16995i
$364$	−3.09221	−	2.06470i	−0.162076	−	0.108220i
$365$	9.91284	+	3.27476i	0.518862	+	0.171409i
$366$	12.9546	−	15.4011i	0.677148	−	0.805027i
$367$	−2.46934	−	1.31989i	−0.128898	−	0.0688976i	0.405687	−	0.914012i	$-0.367032\pi$
$367$	−2.46934	−	1.31989i	−0.128898	−	0.0688976i	−0.534586	+	0.845114i	$0.679532\pi$
$368$	18.4724	+	22.4791i	0.962943	+	1.17180i
$369$	−9.03591	−	16.9050i	−0.470391	−	0.880039i
$370$	7.10756	+	10.9212i	0.369505	+	0.567768i
$371$	−7.33334	−	4.15429i	−0.380728	−	0.215680i
$372$	6.33526	+	5.73821i	0.328468	+	0.297513i
$373$	−5.96804	−	3.77922i	−0.309013	−	0.195680i	0.371468	−	0.928446i	$-0.378854\pi$
$373$	−5.96804	−	3.77922i	−0.309013	−	0.195680i	−0.680482	+	0.732765i	$0.738229\pi$
$374$	−27.3409	−	15.9288i	−1.41376	−	0.823659i
$375$	−39.2346	−	1.92747i	−2.02606	−	0.0995341i
$376$	5.60728	−	4.72276i	0.289173	−	0.243558i
$377$	6.21853	+	13.1480i	0.320271	+	0.677156i
$378$	14.8923	+	4.31607i	0.765976	+	0.221995i
$379$	5.92853	−	0.731214i	0.304528	−	0.0375599i	0.0313024	−	0.999510i	$-0.490034\pi$
$379$	5.92853	−	0.731214i	0.304528	−	0.0375599i	0.273225	+	0.961950i	$0.411909\pi$
$380$	13.4948	−	15.6544i	0.692267	−	0.803055i
$381$	6.09283	−	13.7452i	0.312145	−	0.704188i
$382$	3.55335	−	0.483188i	0.181805	−	0.0247221i
$383$	11.4719	+	11.4719i	0.586185	+	0.586185i	0.936596	−	0.350411i	$-0.113958\pi$
$383$	11.4719	+	11.4719i	0.586185	+	0.586185i	−0.350411	+	0.936596i	$0.613958\pi$
$384$	−22.2734	+	29.3432i	−1.13663	+	1.49742i
$385$	6.14806	−	6.14806i	0.313334	−	0.313334i
$386$	−7.86900	+	10.3459i	−0.400521	+	0.526591i
$387$	−10.2722	−	4.55337i	−0.522168	−	0.231461i
$388$	−9.51727	+	28.8405i	−0.483166	+	1.46416i
$389$	0.324156	+	2.62819i	0.0164353	+	0.133254i	0.998458	−	0.0555074i	$-0.0176776\pi$
$389$	0.324156	+	2.62819i	0.0164353	+	0.133254i	−0.982023	+	0.188762i	$0.939553\pi$
$390$	−11.0867	−	20.1354i	−0.561395	−	1.01960i
$391$	24.3154	−	11.5003i	1.22968	−	0.581597i
$392$	11.4188	−	14.2815i	0.576735	−	0.721325i
$393$	−0.0721527	+	1.46870i	−0.00363962	+	0.0740862i
$394$	34.9998	−	9.23093i	1.76326	−	0.465048i
$395$	−14.4975	+	22.8941i	−0.729448	+	1.15192i
$396$	83.1549	−	39.3623i	4.17869	−	1.97803i
$397$	0.206291	−	0.364154i	0.0103534	−	0.0182764i	−0.864862	−	0.502009i	$-0.832594\pi$
$397$	0.206291	−	0.364154i	0.0103534	−	0.0182764i	0.875216	+	0.483733i	$0.160719\pi$
$398$	1.52394	−	7.20426i	0.0763881	−	0.361117i
$399$	11.0526	−	5.90772i	0.553320	−	0.295756i
$400$	3.22717	−	3.23134i	0.161358	−	0.161567i
$401$	−10.5457	+	19.7296i	−0.526627	+	0.985251i	0.468195	+	0.883625i	$0.344904\pi$
$401$	−10.5457	+	19.7296i	−0.526627	+	0.985251i	−0.994823	+	0.101626i	$0.967596\pi$
$402$	−2.52996	−	29.3234i	−0.126183	−	1.46252i
$403$	1.04627	−	3.16711i	0.0521186	−	0.157765i
$404$	−1.65668	+	8.34279i	−0.0824229	+	0.415069i
$405$	36.9752	+	35.2033i	1.83731	+	1.74927i
$406$	5.55000	−	2.06401i	0.275442	−	0.102435i
$407$	22.7968	+	16.9073i	1.13000	+	0.838063i
$408$	21.2937	+	26.5792i	1.05419	+	1.31586i
$409$	26.4115	+	15.8304i	1.30596	+	0.782765i	0.986331	−	0.164776i	$-0.0526902\pi$
$409$	26.4115	+	15.8304i	1.30596	+	0.782765i	0.319634	+	0.947541i	$0.396440\pi$
$410$	6.50355	+	2.59960i	0.321188	+	0.128385i
$411$	10.1311	−	3.34688i	0.499733	−	0.165089i
$412$	1.43528	−	0.813688i	0.0707111	−	0.0400876i
$413$	0.410783	+	0.289306i	0.0202133	+	0.0142358i
$414$	−12.4111	+	77.2146i	−0.609974	+	3.79489i
$415$	−9.74409	+	1.93822i	−0.478319	+	0.0951435i
$416$	13.9890	+	3.31023i	0.685869	+	0.162298i
$417$	−25.1210	−	4.99688i	−1.23018	−	0.244698i
$418$	15.6784	−	42.2000i	0.766856	−	2.06407i
$419$	3.36931	−	15.0042i	0.164602	−	0.733005i	−0.821951	−	0.569559i	$-0.807114\pi$
$419$	3.36931	−	15.0042i	0.164602	−	0.733005i	0.986552	−	0.163446i	$-0.0522609\pi$
$420$	−8.55403	+	3.79505i	−0.417394	+	0.185180i
$421$	−0.580892	+	7.87496i	−0.0283110	+	0.383802i	0.964498	+	0.264091i	$0.0850719\pi$
$421$	−0.580892	+	7.87496i	−0.0283110	+	0.383802i	−0.992809	+	0.119711i	$0.961803\pi$
$422$	3.76776	−	2.58587i	0.183412	−	0.125878i
$423$	19.4922	+	2.89140i	0.947745	+	0.140585i
$424$	32.1746	+	5.16093i	1.56254	+	0.250637i
$425$	−2.17051	−	3.62128i	−0.105285	−	0.175658i
$426$	26.2810	−	36.3724i	1.27332	−	1.76225i
$427$	−1.15066	+	2.98296i	−0.0556842	+	0.144356i
$428$	−11.0589	+	3.35857i	−0.534550	+	0.162343i
$429$	−37.9111	−	32.7023i	−1.83036	−	1.57888i
$430$	3.94292	−	1.14412i	0.190144	−	0.0551742i
$431$	0.123099	−	1.24984i	0.00592946	−	0.0602028i	−0.991765	−	0.128074i	$-0.959121\pi$
$431$	0.123099	−	1.24984i	0.00592946	−	0.0602028i	0.997694	+	0.0678709i	$0.0216206\pi$
$432$	−59.7813	+	4.44861i	−2.87623	+	0.214034i
$433$	31.4811	−	3.10062i	1.51289	−	0.149006i	0.692752	−	0.721176i	$-0.256398\pi$
$433$	31.4811	−	3.10062i	1.51289	−	0.149006i	0.820135	+	0.572170i	$0.193898\pi$
$434$	−1.24819	−	0.534818i	−0.0599151	−	0.0256721i
$435$	36.3309	+	4.48099i	1.74193	+	0.214847i
$436$	−24.2379	−	26.7251i	−1.16079	−	1.27990i
$437$	22.0351	+	31.2874i	1.05408	+	1.49668i
$438$	−23.1445	−	7.95805i	−1.10589	−	0.380250i
$439$	−3.57433	−	9.98959i	−0.170594	−	0.476777i	0.825569	−	0.564302i	$-0.190854\pi$
$439$	−3.57433	−	9.98959i	−0.170594	−	0.476777i	−0.996162	+	0.0875243i	$0.972104\pi$
$440$	−13.9838	+	30.5692i	−0.666651	+	1.45733i
$441$	49.0899	−	2.41163i	2.33761	−	0.114840i
$442$	6.11849	−	11.7974i	0.291027	−	0.561145i
$443$	5.03461	−	2.85207i	0.239202	−	0.135506i	−0.368619	−	0.929581i	$-0.620169\pi$
$443$	5.03461	−	2.85207i	0.239202	−	0.135506i	0.607820	+	0.794075i	$0.292044\pi$
$444$	−16.3514	−	25.8032i	−0.776002	−	1.22456i
$445$	−25.4033	+	24.1859i	−1.20423	+	1.14652i
$446$	12.6239	−	25.8755i	0.597759	−	1.22524i
$447$	2.31450	−	5.58771i	0.109472	−	0.264289i
$448$	1.83044	−	5.55894i	0.0864804	−	0.262635i
$449$	−5.03227	−	12.1490i	−0.237488	−	0.573346i	0.759534	−	0.650468i	$-0.225427\pi$
$449$	−5.03227	−	12.1490i	−0.237488	−	0.573346i	−0.997022	+	0.0771216i	$0.975427\pi$
$450$	12.2523	+	0.750749i	0.577580	+	0.0353907i
$451$	15.2509	+	0.374389i	0.718138	+	0.0176293i
$452$	−0.151909	+	6.27073i	−0.00714519	+	0.294950i
$453$	10.3192	−	37.2890i	0.484841	−	1.75199i
$454$	2.00245	−	1.68547i	0.0939797	−	0.0791029i
$455$	2.70573	+	2.45233i	0.126847	+	0.114967i
$456$	−32.0786	+	36.3137i	−1.50222	+	1.70054i
$457$	32.4048	+	15.3263i	1.51583	+	0.716936i	0.990949	−	0.134238i	$-0.0428588\pi$
$457$	32.4048	+	15.3263i	1.51583	+	0.716936i	0.524884	+	0.851174i	$0.324109\pi$
$458$	−32.0115	+	1.97187i	−1.49580	+	0.0921392i
$459$	−9.47455	+	54.6032i	−0.442234	+	2.54866i
$460$	−14.6986	−	24.5051i	−0.685324	−	1.14256i
$461$	−1.08139	+	0.843926i	−0.0503654	+	0.0393056i	−0.640100	−	0.768291i	$-0.721107\pi$
$461$	−1.08139	+	0.843926i	−0.0503654	+	0.0393056i	0.589735	+	0.807597i	$0.299232\pi$
$462$	−14.5867	+	14.2376i	−0.678636	+	0.662395i
$463$	−14.9497	−	12.2689i	−0.694772	−	0.570184i	0.219339	−	0.975649i	$-0.429610\pi$
$463$	−14.9497	−	12.2689i	−0.694772	−	0.570184i	−0.914111	+	0.405464i	$0.867110\pi$
$464$	−17.3255	+	14.9646i	−0.804316	+	0.694715i
$465$	−5.32566	−	6.48933i	−0.246972	−	0.300936i
$466$	9.68503	+	12.0970i	0.448650	+	0.560385i
$467$	0.505285	+	6.84999i	0.0233818	+	0.316980i	0.996307	+	0.0858601i	$0.0273638\pi$
$467$	0.505285	+	6.84999i	0.0233818	+	0.316980i	−0.972925	+	0.231119i	$0.925761\pi$
$468$	18.2256	+	34.0712i	0.842480	+	1.57494i
$469$	1.89484	+	4.27470i	0.0874957	+	0.197387i
$470$	−6.12926	+	3.77811i	−0.282722	+	0.174271i
$471$	−14.4457	+	57.6703i	−0.665621	+	2.65731i
$472$	−1.87863	−	0.494176i	−0.0864710	−	0.0227463i
$473$	7.18272	−	5.32707i	0.330262	−	0.244939i
$474$	34.6347	−	53.2562i	1.59083	−	2.44614i
$475$	4.54827	−	3.92336i	0.208689	−	0.180016i
$476$	−4.57204	−	2.89314i	−0.209559	−	0.132607i
$477$	46.8593	+	73.9990i	2.14554	+	3.38818i
$478$	7.01298	+	6.51262i	0.320766	+	0.297880i
$479$	−22.1482	−	33.1472i	−1.01198	−	1.51453i	−0.849339	−	0.527847i	$-0.822999\pi$
$479$	−22.1482	−	33.1472i	−1.01198	−	1.51453i	−0.162639	−	0.986686i	$-0.552001\pi$
$480$	25.8752	−	25.2887i	1.18104	−	1.15427i
$481$	−6.62259	+	9.91140i	−0.301964	+	0.451921i
$482$	33.7524	−	8.02142i	1.53738	−	0.365366i
$483$	−2.96226	−	17.0719i	−0.134788	−	0.776800i
$484$	−3.75150	+	51.0829i	−0.170523	+	2.32195i
$485$	13.4108	−	26.6426i	0.608951	−	1.20978i
$486$	−40.1617	−	39.1752i	−1.82177	−	1.77702i
$487$	−3.59739	−	14.3616i	−0.163013	−	0.650785i	−0.995334	−	0.0964906i	$-0.969238\pi$
$487$	−3.59739	−	14.3616i	−0.163013	−	0.650785i	0.832321	−	0.554294i	$-0.187012\pi$
$488$	0.145695	−	12.3603i	0.00659530	−	0.559526i
$489$	−52.2411	+	7.74924i	−2.36243	+	0.350433i
$490$	−13.1553	+	12.2246i	−0.594297	+	0.552253i
$491$	−0.116675	−	4.75283i	−0.00526549	−	0.214492i	−0.996562	−	0.0828465i	$-0.973599\pi$
$491$	−0.116675	−	4.75283i	−0.00526549	−	0.214492i	0.991297	−	0.131646i	$-0.0420261\pi$
$492$	−15.1717	−	6.27858i	−0.683994	−	0.283060i
$493$	9.51578	+	18.9046i	0.428569	+	0.851421i
$494$	18.0254	+	5.70723i	0.811003	+	0.256780i
$495$	−86.4656	+	26.2290i	−3.88634	+	1.17891i
$496$	5.24400	+	0.254221i	0.235462	+	0.0114149i
$497$	−2.06942	+	6.82198i	−0.0928264	+	0.306008i
$498$	22.8969	−	4.26691i	1.02604	−	0.191205i
$499$	−8.35540	+	2.31225i	−0.374039	+	0.103511i	−0.448663	−	0.893701i	$-0.648099\pi$
$499$	−8.35540	+	2.31225i	−0.374039	+	0.103511i	0.0746235	+	0.997212i	$0.476224\pi$
$500$	−19.3749	+	14.3791i	−0.866474	+	0.643055i
$501$	−3.46432	−	15.4273i	−0.154774	−	0.689242i
$502$	−33.5067	−	4.54524i	−1.49548	−	0.202864i
$503$	−15.2343	+	13.8076i	−0.679265	+	0.615650i	−0.936487	−	0.350703i	$-0.885943\pi$
$503$	−15.2343	+	13.8076i	−0.679265	+	0.615650i	0.257222	+	0.966352i	$0.417193\pi$
$504$	14.4557	−	6.20495i	0.643907	−	0.276390i
$505$	2.81426	−	7.86534i	0.125233	−	0.350003i
$506$	−48.6006	−	38.8843i	−2.16056	−	1.72862i
$507$	−13.1059	+	16.7936i	−0.582052	+	0.745830i
$508$	−2.46593	−	8.89953i	−0.109408	−	0.394853i
$509$	−5.95433	+	2.29684i	−0.263921	+	0.101806i	−0.488238	−	0.872711i	$-0.662360\pi$
$509$	−5.95433	+	2.29684i	−0.263921	+	0.101806i	0.224317	+	0.974516i	$0.427985\pi$
$510$	−16.8471	−	28.8956i	−0.746002	−	1.27952i
$511$	3.88819			0.172003
$512$	0.865758	+	22.6108i	0.0382614	+	0.999268i
$513$	−78.8456			−3.48112
$514$	−3.97121	−	6.81129i	−0.175163	−	0.300433i
$515$	−1.51181	+	0.583171i	−0.0666185	+	0.0256976i
$516$	−9.27539	+	2.57008i	−0.408326	+	0.113141i
$517$	−9.64869	+	12.3637i	−0.424349	+	0.543753i
$518$	3.78945	+	3.03186i	0.166499	+	0.133212i
$519$	−5.35877	+	14.9768i	−0.235224	+	0.657407i
$520$	−13.1116	−	5.23605i	−0.574980	−	0.229616i
$521$	−10.0931	+	9.14785i	−0.442186	+	0.400774i	−0.862058	−	0.506809i	$-0.830825\pi$
$521$	−10.0931	+	9.14785i	−0.442186	+	0.400774i	0.419872	+	0.907583i	$0.362075\pi$
$522$	−60.9772	−	8.27166i	−2.66890	−	0.362041i
$523$	−4.11756	−	18.3363i	−0.180048	−	0.801791i	−0.979562	−	0.201143i	$-0.935534\pi$
$523$	−4.11756	−	18.3363i	−0.180048	−	0.801791i	0.799514	−	0.600648i	$-0.205091\pi$
$524$	0.538267	+	0.725279i	0.0235143	+	0.0316840i
$525$	−2.62116	+	0.725373i	−0.114397	+	0.0316579i
$526$	24.1015	−	4.49137i	1.05087	−	0.195833i
$527$	1.40894	−	4.64464i	0.0613742	−	0.202324i
$528$	33.6484	−	71.2628i	1.46436	−	3.10131i
$529$	28.6209	−	8.68205i	1.24439	−	0.377481i
$530$	−30.5106	−	9.66030i	−1.32530	−	0.419617i
$531$	−2.34759	−	4.66386i	−0.101877	−	0.202394i
$532$	2.94346	−	7.11265i	0.127615	−	0.308372i
$533$	0.157241	+	6.40528i	0.00681086	+	0.277444i
$534$	60.2366	−	55.9751i	2.60669	−	2.42228i
$535$	11.2282	−	1.66554i	0.485436	−	0.0720076i
$536$	−12.6315	−	12.9328i	−0.545598	−	0.558613i
$537$	12.7817	+	51.0272i	0.551569	+	2.20199i
$538$	−24.8820	−	24.2709i	−1.07274	−	1.04639i
$539$	−17.5871	+	34.9396i	−0.757530	+	1.50495i
$540$	58.7170	+	4.31214i	2.52678	+	0.185565i
$541$	1.41290	+	8.14272i	0.0607451	+	0.350083i	0.999977	+	0.00679908i	$0.00216423\pi$
$541$	1.41290	+	8.14272i	0.0607451	+	0.350083i	−0.939232	+	0.343284i	$0.888461\pi$
$542$	−28.6091	+	6.79910i	−1.22886	+	0.292046i
$543$	−43.4536	+	65.0330i	−1.86477	+	2.79083i
$544$	20.4684	+	4.31590i	0.877575	+	0.185043i
$545$	19.6862	+	29.4625i	0.843265	+	1.26204i
$546$	−6.27311	−	5.82553i	−0.268464	−	0.249310i
$547$	0.600024	+	0.947541i	0.0256552	+	0.0405139i	0.857438	−	0.514587i	$-0.172055\pi$
$547$	0.600024	+	0.947541i	0.0256552	+	0.0405139i	−0.831783	+	0.555101i	$0.812680\pi$
$548$	3.50433	−	5.53791i	0.149698	−	0.236568i
$549$	25.1588	−	21.7022i	1.07375	−	0.926225i
$550$	−5.32625	+	8.18992i	−0.227112	+	0.349220i
$551$	−24.1854	+	17.9371i	−1.03033	+	0.764147i
$552$	33.7604	+	57.8617i	1.43694	+	2.46276i
$553$	−2.45228	+	9.79004i	−0.104281	+	0.416315i
$554$	−4.84902	+	2.98896i	−0.206015	+	0.126989i
$555$	12.1580	+	27.4280i	0.516078	+	1.16425i
$556$	−13.8721	+	7.42057i	−0.588309	+	0.314702i
$557$	2.11670	+	28.6954i	0.0896873	+	1.21586i	0.835418	+	0.549615i	$0.185225\pi$
$557$	2.11670	+	28.6954i	0.0896873	+	1.21586i	−0.745731	+	0.666247i	$0.767900\pi$
$558$	8.81977	+	11.0163i	0.373371	+	0.466357i
$559$	2.38266	+	2.90328i	0.100776	+	0.122796i
$560$	−2.58102	+	5.13587i	−0.109068	+	0.217030i
$561$	−56.3179	−	46.2189i	−2.37775	−	1.95137i
$562$	−9.92912	+	9.69150i	−0.418835	+	0.408811i
$563$	−2.02198	+	1.57797i	−0.0852162	+	0.0665034i	−0.656940	−	0.753942i	$-0.728150\pi$
$563$	−2.02198	+	1.57797i	−0.0852162	+	0.0665034i	0.571724	+	0.820446i	$0.306275\pi$
$564$	14.4754	−	8.68256i	0.609523	−	0.365602i
$565$	1.05320	−	6.06976i	0.0443086	−	0.255357i
$566$	20.3353	−	1.25263i	0.854757	−	0.0526519i
$567$	17.1888	+	8.12968i	0.721860	+	0.341415i
$568$	−1.70349	−	27.5096i	−0.0714767	−	1.15428i
$569$	−5.85396	−	5.30572i	−0.245411	−	0.222427i	0.539581	−	0.841934i	$-0.318583\pi$
$569$	−5.85396	−	5.30572i	−0.245411	−	0.222427i	−0.784991	+	0.619507i	$0.787333\pi$
$570$	36.4072	−	30.6441i	1.52493	−	1.28354i
$571$	10.6803	−	38.5937i	0.446958	−	1.61510i	−0.302571	−	0.953127i	$-0.597845\pi$
$571$	10.6803	−	38.5937i	0.446958	−	1.61510i	0.749529	−	0.661971i	$-0.230280\pi$
$572$	−30.7431	−	0.744752i	−1.28543	−	0.0311397i
$573$	8.25423	+	0.202630i	0.344825	+	0.00846498i
$574$	2.60365	+	0.159536i	0.108674	+	0.00665890i
$575$	−3.17805	−	7.67249i	−0.132534	−	0.319965i
$576$	−44.0083	+	41.9809i	−1.83368	+	1.74920i
$577$	−5.21988	+	12.6019i	−0.217306	+	0.524624i	−0.994512	−	0.104623i	$-0.966636\pi$
$577$	−5.21988	+	12.6019i	−0.217306	+	0.524624i	0.777206	+	0.629247i	$0.216636\pi$
$578$	−2.06215	+	4.22685i	−0.0857743	+	0.175814i
$579$	−21.6754	+	20.6367i	−0.900798	+	0.857631i
$580$	18.9921	−	12.0352i	0.788602	−	0.499734i
$581$	−3.21949	+	1.82382i	−0.133567	+	0.0756648i
$582$	−32.1936	+	62.0743i	−1.33447	+	2.57306i
$583$	−69.6246	+	3.42044i	−2.88355	+	0.141660i
$584$	−14.0882	+	5.24452i	−0.582975	+	0.217020i
$585$	−12.7846	−	35.7307i	−0.528580	−	1.47728i
$586$	23.0400	+	7.92212i	0.951774	+	0.327260i
$587$	6.47749	+	9.19734i	0.267355	+	0.379615i	0.928925	−	0.370269i	$-0.120734\pi$
$587$	6.47749	+	9.19734i	0.267355	+	0.379615i	−0.661570	+	0.749884i	$0.730109\pi$
$588$	31.1855	−	28.2833i	1.28607	−	1.16638i
$589$	6.85341	+	0.845288i	0.282390	+	0.0348295i
$590$	1.75362	+	0.751382i	0.0721956	+	0.0309339i
$591$	82.9396	−	8.16884i	3.41168	−	0.336021i
$592$	−17.8199	−	5.87413i	−0.732394	−	0.241425i
$593$	−1.62226	+	16.4711i	−0.0666183	+	0.676387i	0.902649	+	0.430377i	$0.141619\pi$
$593$	−1.62226	+	16.4711i	−0.0666183	+	0.676387i	−0.969267	+	0.246010i	$0.920881\pi$
$594$	123.159	−	35.7371i	5.05328	−	1.46631i
$595$	4.02367	+	3.47084i	0.164954	+	0.142291i
$596$	−1.07952	−	3.55455i	−0.0442188	−	0.145600i
$597$	6.10184	−	15.8184i	0.249732	−	0.647406i
$598$	15.3099	−	21.1886i	0.626069	−	0.866468i
$599$	22.2471	+	37.1170i	0.908991	+	1.51656i	0.855382	+	0.517998i	$0.173323\pi$
$599$	22.2471	+	37.1170i	0.908991	+	1.51656i	0.0536092	+	0.998562i	$0.482927\pi$
$600$	8.51894	−	6.16378i	0.347784	−	0.251635i
$601$	−29.5285	−	4.38014i	−1.20449	−	0.178670i	−0.485845	−	0.874045i	$-0.661488\pi$
$601$	−29.5285	−	4.38014i	−1.20449	−	0.178670i	−0.718647	+	0.695375i	$0.755238\pi$
$602$	1.26072	−	0.865252i	0.0513832	−	0.0352650i
$603$	3.57465	−	48.4603i	0.145571	−	1.97346i
$604$	−9.63739	−	21.7226i	−0.392140	−	0.883882i
$605$	11.0219	−	49.0827i	0.448103	−	1.99550i
$606$	−6.82044	+	18.3579i	−0.277061	+	0.745738i
$607$	32.8615	+	6.53657i	1.33381	+	0.265311i	0.809953	−	0.586495i	$-0.199493\pi$
$607$	32.8615	+	6.53657i	1.33381	+	0.265311i	0.523857	+	0.851806i	$0.324493\pi$
$608$	−1.07138	+	29.7417i	−0.0434500	+	1.20619i
$609$	13.3717	−	2.65980i	0.541848	−	0.107780i
$610$	−1.92664	+	11.9864i	−0.0780073	+	0.485315i
$611$	−5.38523	−	3.79271i	−0.217863	−	0.153437i
$612$	27.7300	+	48.9134i	1.12092	+	1.97721i
$613$	13.3312	−	4.40405i	0.538444	−	0.177878i	−0.0315871	−	0.999501i	$-0.510056\pi$
$613$	13.3312	−	4.40405i	0.538444	−	0.177878i	0.570031	+	0.821623i	$0.306931\pi$
$614$	−32.4543	−	12.9726i	−1.30975	−	0.523533i
$615$	13.8318	+	8.29045i	0.557751	+	0.334303i
$616$	−1.37394	+	12.4443i	−0.0553574	+	0.501395i
$617$	23.0868	+	17.1224i	0.929441	+	0.689321i	0.950588	−	0.310456i	$-0.100482\pi$
$617$	23.0868	+	17.1224i	0.929441	+	0.689321i	−0.0211464	+	0.999776i	$0.506732\pi$
$618$	3.56052	−	1.32414i	0.143225	−	0.0532647i
$619$	−11.8482	−	11.2805i	−0.476221	−	0.453400i	0.413099	−	0.910686i	$-0.364446\pi$
$619$	−11.8482	−	11.2805i	−0.476221	−	0.453400i	−0.889320	+	0.457286i	$0.848821\pi$
$620$	−5.05756	−	1.00431i	−0.203117	−	0.0403341i
$621$	−34.1946	+	103.509i	−1.37218	+	4.15366i
$622$	−1.36137	−	15.7790i	−0.0545861	−	0.632679i
$623$	−6.15811	+	11.5210i	−0.246719	+	0.461580i
$624$	30.5872	+	12.6465i	1.22447	+	0.506264i
$625$	15.8639	−	8.47945i	0.634557	−	0.339178i
$626$	−8.36483	+	39.5439i	−0.334326	+	1.58049i
$627$	51.0901	−	90.1867i	2.04034	−	3.60171i
$628$	15.6236	+	33.0056i	0.623448	+	1.31707i
$629$	−9.28008	+	14.6548i	−0.370021	+	0.584327i
$630$	−14.9391	+	3.94007i	−0.595188	+	0.156976i
$631$	0.923075	−	18.7896i	0.0367471	−	0.748003i	−0.907756	−	0.419500i	$-0.862206\pi$
$631$	0.923075	−	18.7896i	0.0367471	−	0.748003i	0.944503	−	0.328504i	$-0.106544\pi$
$632$	−4.31970	−	38.7803i	−0.171828	−	1.54260i
$633$	9.51147	−	4.49859i	0.378047	−	0.178803i
$634$	16.9707	+	30.8220i	0.673994	+	1.22410i
$635$	1.11024	+	9.00158i	0.0440585	+	0.357217i
$636$	71.2482	+	23.5117i	2.82518	+	0.932299i
$637$	−15.0191	−	6.65752i	−0.595080	−	0.263781i
$638$	29.6482	−	38.9804i	1.17378	−	1.54325i
$639$	52.3860	−	52.3860i	2.07236	−	2.07236i
$640$	2.42446	−	22.0903i	0.0958353	−	0.873197i
$641$	13.9464	+	13.9464i	0.550849	+	0.550849i	0.926686	−	0.375837i	$-0.122645\pi$
$641$	13.9464	+	13.9464i	0.550849	+	0.550849i	−0.375837	+	0.926686i	$0.622645\pi$
$642$	−26.3682	+	3.58557i	−1.04067	+	0.141511i
$643$	−3.79211	+	8.55486i	−0.149546	+	0.337371i	−0.973286	−	0.229598i	$-0.926259\pi$
$643$	−3.79211	+	8.55486i	−0.149546	+	0.337371i	0.823739	+	0.566969i	$0.191884\pi$
$644$	−8.06093	−	6.94886i	−0.317645	−	0.273824i
$645$	9.38175	−	1.15713i	0.369406	−	0.0455619i
$646$	26.4259	+	7.65872i	1.03971	+	0.301328i
$647$	−1.18597	−	2.50753i	−0.0466255	−	0.0985812i	0.879332	−	0.476210i	$-0.157990\pi$
$647$	−1.18597	−	2.50753i	−0.0466255	−	0.0985812i	−0.925957	+	0.377628i	$0.876740\pi$
$648$	−73.2463	−	6.27180i	−2.87738	−	0.246379i
$649$	4.15052	+	0.203902i	0.162922	+	0.00800386i
$650$	−3.54533	−	2.06551i	−0.139059	−	0.0810161i
$651$	−2.64152	−	1.67272i	−0.103529	−	0.0655592i
$652$	−21.7767	+	24.0425i	−0.852842	+	0.941578i
$653$	−32.1071	−	18.1884i	−1.25645	−	0.711769i	−0.287203	−	0.957870i	$-0.592725\pi$
$653$	−32.1071	−	18.1884i	−1.25645	−	0.711769i	−0.969244	+	0.246101i	$0.920850\pi$
$654$	−45.3117	−	69.6244i	−1.77183	−	2.72253i
$655$	−0.418153	−	0.782310i	−0.0163386	−	0.0305674i
$656$	−9.64907	+	2.93383i	−0.376733	+	0.114547i
$657$	−35.6355	−	19.0476i	−1.39027	−	0.743116i
$658$	−1.72618	+	2.05217i	−0.0672936	+	0.0800020i
$659$	23.1934	+	7.66208i	0.903488	+	0.298472i	0.727651	−	0.685947i	$-0.240612\pi$
$659$	23.1934	+	7.66208i	0.903488	+	0.298472i	0.175837	+	0.984419i	$0.443737\pi$
$660$	−42.9796	+	64.3686i	−1.67298	+	2.50554i
$661$	0.928215	−	0.974935i	0.0361034	−	0.0379206i	−0.705947	−	0.708264i	$-0.749478\pi$
$661$	0.928215	−	0.974935i	0.0361034	−	0.0379206i	0.742051	+	0.670344i	$0.233853\pi$
$662$	9.84578	−	21.5049i	0.382667	−	0.835813i
$663$	18.2276	−	24.5771i	0.707903	−	0.954497i
$664$	9.20528	−	10.9509i	0.357234	−	0.424976i
$665$	−3.88665	+	6.48448i	−0.150718	+	0.251457i
$666$	−19.8779	−	46.3510i	−0.770254	−	1.79606i
$667$	13.0589	+	39.5297i	0.505641	+	1.53060i
$668$	−7.65816	−	5.97250i	−0.296303	−	0.231083i
$669$	38.1699	−	54.1971i	1.47573	−	2.09538i
$670$	10.4031	+	14.3879i	0.401906	+	0.555852i
$671$	5.15884	+	25.9352i	0.199155	+	1.00122i
$672$	6.19618	−	11.9661i	0.239023	−	0.461604i
$673$	0.504576	−	2.53668i	0.0194500	−	0.0977817i	−0.969841	−	0.243739i	$-0.921626\pi$
$673$	0.504576	−	2.53668i	0.0194500	−	0.0977817i	0.989291	+	0.145957i	$0.0466261\pi$
$674$	7.20283	−	3.30055i	0.277443	−	0.127132i
$675$	16.6947	+	3.74893i	0.642580	+	0.144296i
$676$	0.325336	+	13.0803i	0.0125129	+	0.503088i
$677$	−47.1655	−	3.47914i	−1.81272	−	0.133714i	−0.875669	−	0.482911i	$-0.839579\pi$
$677$	−47.1655	−	3.47914i	−1.81272	−	0.133714i	−0.937049	+	0.349197i	$0.886454\pi$
$678$	−2.64122	+	14.1987i	−0.101435	+	0.545299i
$679$	1.63002	−	10.9887i	0.0625546	−	0.421709i
$680$	−19.2607	−	7.14877i	−0.738614	−	0.274143i
$681$	5.16898	−	3.09817i	0.198076	−	0.118722i
$682$	−11.0884	+	1.78597i	−0.424595	+	0.0683883i
$683$	23.2904	+	8.98409i	0.891182	+	0.343767i	0.761788	−	0.647827i	$-0.224322\pi$
$683$	23.2904	+	8.98409i	0.891182	+	0.343767i	0.129394	+	0.991593i	$0.458697\pi$
$684$	−61.8205	+	50.7683i	−2.36377	+	1.94117i
$685$	−4.20408	+	4.87369i	−0.160630	+	0.186214i
$686$	−6.71514	+	12.2053i	−0.256385	+	0.465999i
$687$	−73.4890	−	7.23804i	−2.80378	−	0.276148i
$688$	−3.40094	+	4.83560i	−0.129659	+	0.184355i
$689$	−2.86966	−	29.1361i	−0.109325	−	1.11000i
$690$	−24.4400	−	61.0855i	−0.930416	−	2.32548i
$691$	−5.52907	+	44.8285i	−0.210336	+	1.70536i	0.402724	+	0.915322i	$0.368064\pi$
$691$	−5.52907	+	44.8285i	−0.210336	+	1.70536i	−0.613059	+	0.790037i	$0.710061\pi$
$692$	3.29444	+	9.19798i	0.125236	+	0.349655i
$693$	−27.5137	+	19.3773i	−1.04516	+	0.736084i
$694$	−33.9377	+	16.5708i	−1.28826	+	0.629017i
$695$	14.5478	−	5.20527i	0.551828	−	0.197447i
$696$	−44.8625	+	27.6735i	−1.70051	+	1.04896i
$697$	0.457484	+	9.31230i	0.0173284	+	0.352729i
$698$	−20.5626	+	6.51787i	−0.778307	+	0.246705i
$699$	17.5865	+	31.0444i	0.665181	+	1.17421i
$700$	−0.961436	+	1.36607i	−0.0363389	+	0.0516327i
$701$	−3.78393	−	3.97439i	−0.142917	−	0.150111i	0.648889	−	0.760883i	$-0.275234\pi$
$701$	−3.78393	−	3.97439i	−0.142917	−	0.150111i	−0.791806	+	0.610773i	$0.790859\pi$
$702$	17.5293	+	50.9272i	0.661601	+	1.92212i
$703$	−22.7999	−	9.44404i	−0.859916	−	0.356189i
$704$	−11.8070	−	46.9431i	−0.444994	−	1.76923i
$705$	−15.3160	+	6.34411i	−0.576835	+	0.238933i
$706$	−5.15621	−	5.82934i	−0.194057	−	0.219390i
$707$	0.0763538	−	3.11031i	0.00287158	−	0.116975i
$708$	−4.08948	−	1.81116i	−0.153692	−	0.0680676i
$709$	−15.2160	−	4.21085i	−0.571450	−	0.158142i	−0.0310028	−	0.999519i	$-0.509870\pi$
$709$	−15.2160	−	4.21085i	−0.571450	−	0.158142i	−0.540448	+	0.841378i	$0.681745\pi$
$710$	−2.31814	+	26.9702i	−0.0869984	+	1.01217i
$711$	70.4349	−	77.7129i	2.64152	−	2.91446i
$712$	6.77298	−	50.0507i	0.253828	−	1.87573i
$713$	4.08195	−	8.63057i	0.152870	−	0.323217i
$714$	−9.33368	−	8.25052i	−0.349304	−	0.308768i
$715$	29.7578	+	5.16347i	1.11288	+	0.193103i
$716$	25.9581	+	19.2388i	0.970100	+	0.718989i
$717$	13.5571	+	17.3718i	0.506300	+	0.648763i
$718$	0.177269	−	14.6374i	0.00661564	−	0.546262i
$719$	2.67338	−	3.25753i	0.0997004	−	0.121485i	−0.720770	−	0.693174i	$-0.756212\pi$
$719$	2.67338	−	3.25753i	0.0997004	−	0.121485i	0.820470	+	0.571689i	$0.193712\pi$
$720$	48.8148	−	34.4265i	1.81922	−	1.28300i
$721$	−0.466512	+	0.382857i	−0.0173738	+	0.0142583i
$722$	−1.35085	+	12.1990i	−0.0502733	+	0.454000i
$723$	79.6612	−	5.87616i	2.96263	−	0.218537i
$724$	4.72430	+	47.8081i	0.175577	+	1.77678i
$725$	5.97387	−	2.64803i	0.221864	−	0.0983455i
$726$	−27.2308	+	114.746i	−1.01063	+	4.25862i
$727$	16.5010	+	4.13328i	0.611987	+	0.153295i	0.536568	−	0.843857i	$-0.319720\pi$
$727$	16.5010	+	4.13328i	0.611987	+	0.153295i	0.0754192	+	0.997152i	$0.475970\pi$
$728$	−5.24853	−	0.319895i	−0.194524	−	0.0118561i
$729$	−30.5017	−	41.1267i	−1.12969	−	1.52321i
$730$	14.4434	−	3.06013i	0.534575	−	0.113261i
$731$	3.56979	+	4.13838i	0.132033	+	0.153063i
$732$	4.85668	−	28.0436i	0.179508	−	1.03652i
$733$	4.71343	−	2.98475i	0.174095	−	0.110244i	−0.445103	−	0.895479i	$-0.646833\pi$
$733$	4.71343	−	2.98475i	0.174095	−	0.110244i	0.619198	+	0.785235i	$0.287458\pi$
$734$	−3.95703	+	0.146387i	−0.146056	+	0.00540323i
$735$	−34.3799	+	22.9719i	−1.26812	+	0.847332i
$736$	38.5803	+	14.3052i	1.42209	+	0.527297i
$737$	32.1553	+	21.4855i	1.18446	+	0.791428i
$738$	−23.0810	−	14.2169i	−0.849623	−	0.523333i
$739$	32.9436	−	5.71625i	1.21185	−	0.210276i	0.471114	−	0.882073i	$-0.343852\pi$
$739$	32.9436	−	5.71625i	1.21185	−	0.210276i	0.740736	+	0.671797i	$0.234477\pi$
$740$	16.4628	+	8.28000i	0.605184	+	0.304379i
$741$	38.8850	+	19.5731i	1.42848	+	0.719035i
$742$	−11.9185	+	0.148196i	−0.437541	+	0.00544046i
$743$	41.9689	−	10.5127i	1.53969	−	0.385672i	0.622015	−	0.783005i	$-0.286314\pi$
$743$	41.9689	−	10.5127i	1.53969	−	0.385672i	0.917674	+	0.397333i	$0.130064\pi$
$744$	11.8273	+	2.49787i	0.433611	+	0.0915764i
$745$	0.535341	+	3.60897i	0.0196134	+	0.132223i
$746$	−9.98328	−	0.366089i	−0.365514	−	0.0134035i
$747$	38.4414	−	0.943683i	1.40650	−	0.0345276i
$748$	−44.7493	+	0.0144713i	−1.63620	+	0.000529124i
$749$	3.77619	−	1.90077i	0.137979	−	0.0694527i
$750$	−49.3069	+	25.5923i	−1.80043	+	0.934497i
$751$	−3.12159	−	10.2905i	−0.113908	−	0.375506i	0.881387	−	0.472396i	$-0.156611\pi$
$751$	−3.12159	−	10.2905i	−0.113908	−	0.375506i	−0.995295	+	0.0968896i	$0.969111\pi$
$752$	3.48651	−	9.76404i	0.127140	−	0.356058i
$753$	−74.5018	−	22.5999i	−2.71500	−	0.823585i
$754$	16.9628	+	11.6337i	0.617748	+	0.423676i
$755$	6.22501	+	22.4943i	0.226551	+	0.818651i
$756$	21.2687	−	5.33483i	0.773533	−	0.194026i
$757$	10.5722	−	2.37407i	0.384253	−	0.0862869i	−0.0226850	−	0.999743i	$-0.507221\pi$
$757$	10.5722	−	2.37407i	0.384253	−	0.0862869i	0.406938	+	0.913456i	$0.366596\pi$
$758$	6.72219	−	5.11628i	0.244161	−	0.185832i
$759$	−96.2398	−	106.184i	−3.49328	−	3.85424i
$760$	5.33615	−	28.7379i	0.193562	−	1.04243i
$761$	−10.9134	−	3.90486i	−0.395609	−	0.141551i	0.131567	−	0.991307i	$-0.457999\pi$
$761$	−10.9134	−	3.90486i	−0.395609	−	0.141551i	−0.527176	+	0.849756i	$0.676749\pi$
$762$	−2.34705	−	21.1329i	−0.0850246	−	0.765563i
$763$	10.4040	+	8.11932i	0.376648	+	0.293939i
$764$	3.99705	−	3.12141i	0.144608	−	0.112929i
$765$	−19.8741	−	51.5217i	−0.718550	−	1.86277i
$766$	22.1870	+	5.84398i	0.801648	+	0.211152i
$767$			1.74529i			0.0630189i
$768$	−6.31052	+	51.7149i	−0.227711	+	1.86610i
$769$		−	17.9027i		−	0.645589i	−0.946469	−	0.322795i	$-0.895378\pi$
$769$		−	17.9027i		−	0.645589i	0.946469	−	0.322795i	$-0.104622\pi$
$770$	3.13194	−	11.8906i	0.112867	−	0.428507i
$771$	−6.53335	−	16.9371i	−0.235293	−	0.609974i
$772$	−2.24431	+	18.2450i	−0.0807746	+	0.656651i
$773$	−30.2319	−	23.5932i	−1.08736	−	0.848587i	−0.0981658	−	0.995170i	$-0.531298\pi$
$773$	−30.2319	−	23.5932i	−1.08736	−	0.848587i	−0.989198	+	0.146583i	$0.953173\pi$
$774$	−15.7933	+	1.75403i	−0.567678	+	0.0630472i
$775$	−1.41095	−	0.504844i	−0.0506827	−	0.0181345i
$776$	8.91583	+	42.0145i	0.320059	+	1.50823i
$777$	7.50394	+	8.27932i	0.269202	+	0.297019i
$778$	2.26811	+	2.98003i	0.0813156	+	0.106839i
$779$	−12.9424	+	2.90632i	−0.463711	+	0.104130i
$780$	−27.8875	−	16.7029i	−0.998534	−	0.598059i
$781$	15.7259	+	56.8261i	0.562717	+	2.03340i
$782$	21.5150	−	31.3704i	0.769376	−	1.12180i
$783$	−82.0809	−	24.8990i	−2.93333	−	0.889816i
$784$	3.77779	−	25.5818i	0.134921	−	0.913635i
$785$	−10.4108	−	34.3197i	−0.371576	−	1.22492i
$786$	0.958018	+	1.84575i	0.0341714	+	0.0658356i
$787$	5.93054	−	2.98518i	0.211401	−	0.106410i	−0.340752	−	0.940153i	$-0.610682\pi$
$787$	5.93054	−	2.98518i	0.211401	−	0.106410i	0.552153	+	0.833743i	$0.313807\pi$
$788$	36.1849	−	36.2083i	1.28903	−	1.28987i
$789$	56.4307	−	1.38530i	2.00899	−	0.0493179i
$790$	−1.40436	+	38.2970i	−0.0499649	+	1.36255i
$791$	−0.336659	−	2.26957i	−0.0119702	−	0.0806968i
$792$	73.5545	−	107.322i	2.61365	−	3.81352i
$793$	−10.7732	+	2.69854i	−0.382567	+	0.0958281i
$794$	−0.00735904	−	0.591840i	−0.000261163	−	0.0210036i
$795$	−65.8184	−	33.1302i	−2.33434	−	1.17501i
$796$	−3.26982	−	9.88716i	−0.115896	−	0.350441i
$797$	3.81629	−	0.662189i	0.135180	−	0.0234559i	−0.102969	−	0.994685i	$-0.532834\pi$
$797$	3.81629	−	0.662189i	0.135180	−	0.0234559i	0.238149	+	0.971229i	$0.423459\pi$
$798$	9.29510	−	15.0904i	0.329043	−	0.534196i
$799$	−7.96947	−	5.32503i	−0.281940	−	0.188386i
$800$	1.64100	−	6.24656i	0.0580182	−	0.220849i
$801$	112.879	−	75.4232i	3.98837	−	2.66495i
$802$	1.16961	+	31.6160i	0.0413002	+	1.11640i
$803$	27.1691	−	17.2047i	0.958778	−	0.607139i
$804$	−23.9782	−	34.0231i	−0.845647	−	1.19990i
$805$	6.82722	+	7.91465i	0.240628	+	0.278955i
$806$	−0.977701	−	4.61462i	−0.0344381	−	0.162543i
$807$	−47.6744	−	64.2815i	−1.67822	−	2.26282i
$808$	3.91863	+	11.3727i	0.137857	+	0.400089i
$809$	49.7598	+	12.4642i	1.74946	+	0.438217i	0.979758	−	0.200185i	$-0.0641542\pi$
$809$	49.7598	+	12.4642i	1.74946	+	0.438217i	0.769703	+	0.638402i	$0.220404\pi$
$810$	70.2492	+	16.6711i	2.46831	+	0.585763i
$811$	−28.6104	+	12.6821i	−1.00465	+	0.445329i	−0.840910	−	0.541175i	$-0.817980\pi$
$811$	−28.6104	+	12.6821i	−1.00465	+	0.445329i	−0.163737	+	0.986504i	$0.552355\pi$
$812$	5.31037	−	6.47497i	0.186357	−	0.227227i
$813$	−67.5222	+	4.98073i	−2.36811	+	0.174682i
$814$	39.8947	+	4.41771i	1.39831	+	0.154841i
$815$	24.6273	−	20.2111i	0.862655	−	0.707963i
$816$	44.9476	+	17.3048i	1.57348	+	0.605790i
$817$	−4.93278	+	6.01060i	−0.172576	+	0.210284i
$818$	43.5438	+	0.527348i	1.52247	+	0.0184383i
$819$	−8.69554	−	11.1423i	−0.303847	−	0.389344i
$820$	9.79729	−	1.45653i	0.342136	−	0.0508642i
$821$	3.00402	+	0.521247i	0.104841	+	0.0181917i	0.223140	−	0.974786i	$-0.428369\pi$
$821$	3.00402	+	0.521247i	0.104841	+	0.0181917i	−0.118299	+	0.992978i	$0.537744\pi$
$822$	9.99348	−	11.3055i	0.348563	−	0.394324i
$823$	−11.6941	+	24.7251i	−0.407631	+	0.861863i	0.590851	+	0.806781i	$0.298792\pi$
$823$	−11.6941	+	24.7251i	−0.407631	+	0.861863i	−0.998482	+	0.0550824i	$0.982458\pi$
$824$	1.17392	−	2.01647i	0.0408955	−	0.0702469i
$825$	−15.1060	+	16.6669i	−0.525922	+	0.580265i
$826$	0.707940	+	0.0608488i	0.0246324	+	0.00211720i
$827$	−33.3392	−	9.22619i	−1.15932	−	0.320826i	−0.366577	−	0.930388i	$-0.619471\pi$
$827$	−33.3392	−	9.22619i	−1.15932	−	0.320826i	−0.792739	+	0.609561i	$0.791346\pi$
$828$	39.8376	+	103.176i	1.38445	+	3.58561i
$829$	−0.470245	+	19.1557i	−0.0163323	+	0.665304i	0.934564	+	0.355795i	$0.115790\pi$
$829$	−0.470245	+	19.1557i	−0.0163323	+	0.665304i	−0.950896	+	0.309509i	$0.899835\pi$
$830$	−10.5240	+	9.30877i	−0.365294	+	0.323112i
$831$	−12.1169	+	5.01899i	−0.420331	+	0.174107i
$832$	19.4487	−	5.92030i	0.674262	−	0.205250i
$833$	−22.0864	−	9.14850i	−0.765250	−	0.316977i
$834$	−34.2504	+	11.7891i	−1.18599	+	0.408223i
$835$	6.57695	+	6.90799i	0.227605	+	0.239061i
$836$	−10.9047	−	62.7247i	−0.377146	−	2.16938i
$837$	9.69559	+	17.1151i	0.335129	+	0.591585i
$838$	−6.57126	−	20.7311i	−0.227000	−	0.716143i
$839$	2.08294	+	42.3991i	0.0719109	+	1.46378i	0.715609	+	0.698501i	$0.246149\pi$
$839$	2.08294	+	42.3991i	0.0719109	+	1.46378i	−0.643698	+	0.765280i	$0.722601\pi$
$840$	−7.74745	+	10.7296i	−0.267312	+	0.370207i
$841$	−3.53743	+	1.26571i	−0.121980	+	0.0436453i
$842$	4.89971	+	10.0348i	0.168855	+	0.345823i
$843$	−26.1188	+	18.3949i	−0.899578	+	0.633555i
$844$	2.76124	−	5.84304i	0.0950458	−	0.201126i
$845$	1.57303	−	12.7538i	0.0541140	−	0.438745i
$846$	25.8738	−	10.3520i	0.889559	−	0.355909i
$847$	−1.83641	−	18.6454i	−0.0631000	−	0.640665i
$848$	42.9847	−	16.6130i	1.47610	−	0.570493i
$849$	46.6839	+	4.59796i	1.60219	+	0.157802i
$850$	−5.23124	−	2.87814i	−0.179430	−	0.0987194i
$851$	−22.2863	+	25.8360i	−0.763963	+	0.885645i
$852$	6.19983	−	63.1573i	0.212403	−	2.16373i
$853$	7.84958	+	3.02792i	0.268764	+	0.103674i	0.490525	−	0.871427i	$-0.336805\pi$
$853$	7.84958	+	3.02792i	0.268764	+	0.103674i	−0.221760	+	0.975101i	$0.571180\pi$
$854$	0.719003	+	4.46399i	0.0246038	+	0.152755i
$855$	67.3876	−	40.3906i	2.30461	−	1.38133i
$856$	−11.1186	+	11.9806i	−0.380025	+	0.409488i
$857$	0.577174	−	3.89099i	0.0197159	−	0.132914i	−0.977084	−	0.212856i	$-0.931724\pi$
$857$	0.577174	−	3.89099i	0.0197159	−	0.132914i	0.996800	+	0.0799421i	$0.0254735\pi$
$858$	−69.6111	−	12.9489i	−2.37648	−	0.442069i
$859$	−6.66558	−	0.491683i	−0.227427	−	0.0167760i	−0.0406286	−	0.999174i	$-0.512936\pi$
$859$	−6.66558	−	0.491683i	−0.227427	−	0.0167760i	−0.186798	+	0.982398i	$0.559811\pi$
$860$	4.00220	−	4.20637i	0.136474	−	0.143436i
$861$	5.86007	+	1.31592i	0.199711	+	0.0448466i
$862$	−0.739881	−	1.61465i	−0.0252004	−	0.0549952i
$863$	6.54707	−	32.9144i	0.222865	−	1.12042i	−0.693618	−	0.720343i	$-0.743984\pi$
$863$	6.54707	−	32.9144i	0.222865	−	1.12042i	0.916483	−	0.400074i	$-0.131016\pi$
$864$	−69.8677	+	48.0177i	−2.37695	+	1.63360i
$865$	−1.87200	−	9.41116i	−0.0636498	−	0.319989i
$866$	36.2528	−	26.2124i	1.23192	−	0.890733i
$867$	−6.23517	+	8.85326i	−0.211758	+	0.300673i
$868$	−1.90590	+	0.235697i	−0.0646906	+	0.00800007i
$869$	26.1839	+	79.2599i	0.888229	+	2.68871i
$870$	47.5783	−	20.4043i	1.61306	−	0.691770i
$871$	−8.35022	+	13.9315i	−0.282937	+	0.472051i
$872$	−48.6486	−	15.3858i	−1.64745	−	0.521030i
$873$	−68.7710	+	92.7270i	−2.32755	+	3.13833i
$874$	49.2071	+	22.5289i	1.66446	+	0.762051i
$875$	6.08557	−	6.39188i	0.205730	−	0.216085i
$876$	−33.9449	+	6.76347i	−1.14689	+	0.228516i
$877$	10.0788	+	3.32958i	0.340336	+	0.112432i	0.478771	−	0.877940i	$-0.341082\pi$
$877$	10.0788	+	3.32958i	0.340336	+	0.112432i	−0.138435	+	0.990371i	$0.544207\pi$
$878$	−11.4825	−	9.65853i	−0.387517	−	0.325959i
$879$	49.4729	+	26.4438i	1.66868	+	0.891929i
$880$	4.69033	+	47.3080i	0.158111	+	1.59475i
$881$	−12.0881	−	22.6152i	−0.407258	−	0.761926i	0.591766	−	0.806110i	$-0.298431\pi$
$881$	−12.0881	−	22.6152i	−0.407258	−	0.761926i	−0.999023	+	0.0441844i	$0.985931\pi$
$882$	58.2566	−	37.9135i	1.96160	−	1.27661i
$883$	−30.1287	−	17.0677i	−1.01391	−	0.574375i	−0.106367	−	0.994327i	$-0.533922\pi$
$883$	−30.1287	−	17.0677i	−1.01391	−	0.574375i	−0.907546	+	0.419952i	$0.862047\pi$
$884$	−0.928267	−	18.7714i	−0.0312210	−	0.631352i
$885$	3.71115	+	2.35006i	0.124749	+	0.0789965i
$886$	4.11936	−	7.07065i	0.138393	−	0.237543i
$887$	21.8694	+	1.07437i	0.734302	+	0.0360739i	0.412783	−	0.910829i	$-0.364557\pi$
$887$	21.8694	+	1.07437i	0.734302	+	0.0360739i	0.321519	+	0.946903i	$0.395807\pi$
$888$	−38.3567	−	19.8772i	−1.28717	−	0.667035i
$889$	1.44427	+	3.05364i	0.0484391	+	0.102416i
$890$	−13.8080	+	47.6436i	−0.462846	+	1.59702i
$891$	156.081	−	19.2507i	5.22891	−	0.644924i
$892$	−3.00840	−	40.6050i	−0.100729	−	1.35955i
$893$	5.52605	−	12.4666i	0.184922	−	0.417178i
$894$	−1.15248	−	8.47529i	−0.0385446	−	0.283456i
$895$	−22.4385	−	22.4385i	−0.750035	−	0.750035i
$896$	−1.72337	−	8.09534i	−0.0575738	−	0.270446i
$897$	42.5596	−	42.5596i	1.42102	−	1.42102i
$898$	−14.8019	−	11.2582i	−0.493945	−	0.375691i
$899$	6.86769	+	3.04424i	0.229050	+	0.101531i
$900$	15.5038	−	7.81022i	0.516792	−	0.260341i
$901$	−5.21505	−	42.2825i	−0.173739	−	1.40863i
$902$	18.8992	−	10.4060i	0.629273	−	0.346481i
$903$	3.18261	−	1.50526i	0.105911	−	0.0500920i
$904$	4.28110	+	7.76933i	0.142387	+	0.258404i
$905$	2.31513	−	47.1255i	0.0769574	−	1.56650i
$906$	−13.9539	−	52.9074i	−0.463589	−	1.75773i
$907$	1.40462	−	2.21814i	0.0466398	−	0.0736522i	−0.820731	−	0.571315i	$-0.806433\pi$
$907$	1.40462	−	2.21814i	0.0466398	−	0.0736522i	0.867370	+	0.497663i	$0.165808\pi$
$908$	1.24588	−	3.48555i	0.0413459	−	0.115672i
$909$	−15.9366	+	28.1321i	−0.528585	+	0.933082i
$910$	5.05249	+	1.06877i	0.167488	+	0.0354292i
$911$	−32.7838	+	17.5233i	−1.08618	+	0.580574i	−0.914503	−	0.404580i	$-0.867418\pi$
$911$	−32.7838	+	17.5233i	−1.08618	+	0.580574i	−0.171674	+	0.985154i	$0.554918\pi$
$912$	−13.3248	+	67.2153i	−0.441227	+	2.22572i
$913$	−14.4264	+	26.9899i	−0.477444	+	0.893235i
$914$	50.5069	−	4.35762i	1.67062	−	0.144137i
$915$	−8.76813	+	26.5415i	−0.289865	+	0.877435i
$916$	−37.7047	+	25.2111i	−1.24580	+	0.832999i
$917$	−0.239273	−	0.227807i	−0.00790148	−	0.00752284i
$918$	27.3190	+	73.4590i	0.901661	+	2.42451i
$919$	−7.41664	−	5.50055i	−0.244652	−	0.181446i	0.466424	−	0.884561i	$-0.345542\pi$
$919$	−7.41664	−	5.50055i	−0.244652	−	0.181446i	−0.711076	+	0.703115i	$0.751792\pi$
$920$	−35.4128	−	19.4686i	−1.16753	−	0.641862i
$921$	−69.0239	−	41.3713i	−2.27441	−	1.36323i
$922$	−0.720029	+	1.80133i	−0.0237129	+	0.0593237i
$923$	−23.5138	+	7.76790i	−0.773965	+	0.255683i
$924$	−7.67940	+	27.7848i	−0.252634	+	0.914051i
$925$	4.37860	+	3.08376i	0.143968	+	0.101393i
$926$	−27.0037	−	4.34045i	−0.887396	−	0.142636i
$927$	6.15116	−	1.22354i	0.202031	−	0.0401864i
$928$	−10.5076	+	30.6238i	−0.344929	+	1.00527i
$929$	−13.5662	−	2.69848i	−0.445091	−	0.0885341i	−0.0325438	−	0.999470i	$-0.510361\pi$
$929$	−13.5662	−	2.69848i	−0.445091	−	0.0885341i	−0.412547	+	0.910936i	$0.635361\pi$
$930$	−11.1289	−	4.13468i	−0.364931	−	0.135582i
$931$	7.45201	−	33.1853i	0.244230	−	1.08760i
$932$	20.4493	+	7.88056i	0.669839	+	0.258136i
$933$	2.68255	−	36.3665i	0.0878228	−	1.19058i
$934$	5.49662	+	8.00889i	0.179855	+	0.262059i
$935$	43.4737	+	6.44872i	1.42174	+	0.210896i
$936$	46.5360	+	28.6435i	1.52108	+	0.936242i
$937$	−22.6517	−	37.7920i	−0.739997	−	1.23461i	−0.965509	−	0.260370i	$-0.916155\pi$
$937$	−22.6517	−	37.7920i	−0.739997	−	1.23461i	0.225512	−	0.974240i	$-0.427595\pi$
$938$	5.35988	+	3.87280i	0.175006	+	0.126451i
$939$	−33.4928	+	86.8267i	−1.09300	+	2.83348i
$940$	−4.79711	+	8.98174i	−0.156464	+	0.292952i
$941$	21.8435	+	18.8424i	0.712079	+	0.614244i	0.932504	−	0.361160i	$-0.117619\pi$
$941$	21.8435	+	18.8424i	0.712079	+	0.614244i	−0.220425	+	0.975404i	$0.570744\pi$
$942$	23.4304	+	80.7471i	0.763403	+	2.63088i
$943$	−1.79759	+	18.2513i	−0.0585377	+	0.594343i
$944$	−2.64718	+	0.734417i	−0.0861584	+	0.0239032i
$945$	−21.4319	+	2.11086i	−0.697179	+	0.0686662i
$946$	4.98081	−	11.6245i	0.161940	−	0.377946i
$947$	18.2258	+	2.24794i	0.592260	+	0.0730484i	0.412965	−	0.910747i	$-0.364493\pi$
$947$	18.2258	+	2.24794i	0.592260	+	0.0730484i	0.179295	+	0.983795i	$0.442618\pi$
$948$	4.37932	−	89.7352i	0.142234	−	2.91446i
$949$	7.77704	+	11.0425i	0.252453	+	0.358456i
$950$	2.76210	−	8.03305i	0.0896143	−	0.260626i
$951$	27.2922	+	76.2767i	0.885011	+	2.47344i
$952$	−7.64659	−	0.277926i	−0.247827	−	0.00900765i
$953$	−25.4046	+	1.24805i	−0.822937	+	0.0404283i	−0.456179	−	0.889888i	$-0.650782\pi$
$953$	−25.4046	+	1.24805i	−0.822937	+	0.0404283i	−0.366758	+	0.930316i	$0.619532\pi$
$954$	109.959	+	57.0283i	3.56007	+	1.84636i
$955$	−4.33373	+	2.45503i	−0.140236	+	0.0794428i
$956$	13.2069	+	2.96123i	0.427143	+	0.0957731i
$957$	81.6669	−	77.7533i	2.63991	−	2.51341i
$958$	−50.6701	−	24.7204i	−1.63708	−	0.798681i
$959$	−0.917360	+	2.21470i	−0.0296231	+	0.0715165i
$960$	13.5991	−	49.3270i	0.438910	−	1.59202i
$961$	11.2039	+	27.0486i	0.361417	+	0.872537i
$962$	−1.03102	+	16.8263i	−0.0332414	+	0.542503i
$963$	−43.9205	−	1.07819i	−1.41532	−	0.0347441i
$964$	35.5224	−	33.8421i	1.14410	−	1.08998i
$965$	4.81521	−	17.3999i	0.155007	−	0.560124i
$966$	−15.7796	−	18.7472i	−0.507699	−	0.603181i
$967$	32.6665	+	29.6072i	1.05048	+	0.952104i	0.998915	−	0.0465653i	$-0.0148276\pi$
$967$	32.6665	+	29.6072i	1.05048	+	0.952104i	0.0515697	+	0.998669i	$0.483578\pi$
$968$	31.8035	+	65.0816i	1.02220	+	2.09180i
$969$	57.2659	+	27.0848i	1.83965	+	0.870088i
$970$	−2.59346	−	42.1026i	−0.0832710	−	1.35183i
$971$	4.62807	−	26.6722i	0.148522	−	0.855953i	−0.813212	−	0.581968i	$-0.802283\pi$
$971$	4.62807	−	26.6722i	0.148522	−	0.855953i	0.961734	−	0.273985i	$-0.0883420\pi$
$972$	−76.9715	−	19.2539i	−2.46886	−	0.617569i
$973$	4.53660	−	3.54039i	0.145437	−	0.113500i
$974$	−14.6249	−	14.9835i	−0.468612	−	0.480101i
$975$	−7.30284	−	5.99328i	−0.233878	−	0.191939i
$976$	−8.62636	−	15.2047i	−0.276123	−	0.486691i
$977$	7.33713	+	8.94032i	0.234736	+	0.286026i	0.877034	−	0.480429i	$-0.159519\pi$
$977$	7.33713	+	8.94032i	0.234736	+	0.286026i	−0.642298	+	0.766455i	$0.722019\pi$
$978$	−58.3046	+	46.6793i	−1.86437	+	1.49264i
$979$	7.94833	+	107.753i	0.254030	+	3.44380i
$980$	−7.36451	+	24.3058i	−0.235251	+	0.776421i
$981$	−55.5776	−	125.381i	−1.77446	−	4.00311i
$982$	−3.52803	−	5.72355i	−0.112584	−	0.182646i
$983$	1.46945	−	5.86638i	0.0468682	−	0.187109i	−0.942075	−	0.335402i	$-0.891128\pi$
$983$	1.46945	−	5.86638i	0.0468682	−	0.187109i	0.988943	+	0.148293i	$0.0473779\pi$
$984$	−23.0080	+	3.13622i	−0.733467	+	0.0999792i
$985$	−40.3811	+	29.9487i	−1.28665	+	0.954243i
$986$	25.0916	+	16.3181i	0.799079	+	0.519674i
$987$	−4.67524	+	4.03289i	−0.148815	+	0.128368i
$988$	26.0875	−	5.86700i	0.829953	−	0.186654i
$989$	5.75142	+	9.08249i	0.182885	+	0.288806i
$990$	−86.9542	+	93.6349i	−2.76358	+	2.97591i
$991$	−23.0240	−	34.4578i	−0.731381	−	1.09459i	−0.991638	−	0.129049i	$-0.958807\pi$
$991$	−23.0240	−	34.4578i	−0.731381	−	1.09459i	0.260257	−	0.965539i	$-0.416193\pi$
$992$	6.58782	−	3.42475i	0.209163	−	0.108736i
$993$	30.2546	−	45.2792i	0.960100	−	1.43689i
$994$	2.33108	+	9.80866i	0.0739374	+	0.311112i
$995$	1.74854	+	10.0771i	0.0554326	+	0.319466i
$996$	24.9345	−	21.5227i	0.790079	−	0.681972i
$997$	−20.6526	+	41.0296i	−0.654073	+	1.29942i	0.285929	+	0.958251i	$0.407698\pi$
$997$	−20.6526	+	41.0296i	−0.654073	+	1.29942i	−0.940002	+	0.341169i	$0.889177\pi$
$998$	−8.56098	+	8.77656i	−0.270993	+	0.277817i
$999$	−17.0813	−	68.1923i	−0.540428	−	2.15751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.o.a.157.52	✓	4032
512.437	even	128	inner	512.2.o.a.437.52	yes	4032

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
512.2.o.a.157.52	✓	4032	1.1	even	1	trivial
512.2.o.a.437.52	yes	4032	512.437	even	128	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.o (of order \(128\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22173 - 0.712308i) q^{2} +(3.03797 - 1.17187i) q^{3} +(0.985234 - 1.74049i) q^{4} +(-1.20847 + 1.54851i) q^{5} +(2.87684 - 3.59568i) q^{6} +(-0.246458 + 0.688804i) q^{7} +(-0.0360811 - 2.82820i) q^{8} +(5.63312 - 5.10557i) q^{9} +O(q^{10})\)	\(q+(1.22173 - 0.712308i) q^{2} +(3.03797 - 1.17187i) q^{3} +(0.985234 - 1.74049i) q^{4} +(-1.20847 + 1.54851i) q^{5} +(2.87684 - 3.59568i) q^{6} +(-0.246458 + 0.688804i) q^{7} +(-0.0360811 - 2.82820i) q^{8} +(5.63312 - 5.10557i) q^{9} +(-0.373403 + 2.75266i) q^{10} +(1.32570 + 5.90362i) q^{11} +(0.953472 - 6.44214i) q^{12} +(-2.44917 + 0.677778i) q^{13} +(0.189536 + 1.01708i) q^{14} +(-1.85664 + 6.12051i) q^{15} +(-2.05863 - 3.42958i) q^{16} +(-3.53867 + 1.07344i) q^{17} +(3.24540 - 10.2501i) q^{18} +(-2.36543 - 4.69930i) q^{19} +(1.50455 + 3.62898i) q^{20} +(0.0584597 + 2.38138i) q^{21} +(5.82485 + 6.26831i) q^{22} +(-7.19511 + 1.06729i) q^{23} +(-3.42391 - 8.54970i) q^{24} +(0.277414 + 1.10750i) q^{25} +(-2.50943 + 2.57263i) q^{26} +(6.73817 - 13.3864i) q^{27} +(0.956039 + 1.10759i) q^{28} +(-0.978479 - 5.63912i) q^{29} +(2.09139 + 8.80009i) q^{30} +(-0.729208 + 1.09134i) q^{31} +(-4.95800 - 2.72364i) q^{32} +(10.9458 + 16.3815i) q^{33} +(-3.55866 + 3.83208i) q^{34} +(-0.768783 - 1.21404i) q^{35} +(-3.33626 - 14.8346i) q^{36} +(3.55190 - 3.06389i) q^{37} +(-6.23726 - 4.05635i) q^{38} +(-6.64625 + 4.92919i) q^{39} +(4.42310 + 3.36192i) q^{40} +(0.612628 - 2.44575i) q^{41} +(1.76770 + 2.86776i) q^{42} +(-0.598926 - 1.35116i) q^{43} +(11.5813 + 3.50907i) q^{44} +(1.09856 + 14.8929i) q^{45} +(-8.03022 + 6.42908i) q^{46} +(1.64432 + 2.00361i) q^{47} +(-10.2731 - 8.00652i) q^{48} +(4.99736 + 4.10123i) q^{49} +(1.12780 + 1.15546i) q^{50} +(-9.49242 + 7.40796i) q^{51} +(-1.23334 + 4.93054i) q^{52} +(-1.96963 + 11.3512i) q^{53} +(-1.30307 - 21.1542i) q^{54} +(-10.7439 - 5.08149i) q^{55} +(1.95696 + 0.672179i) q^{56} +(-12.6931 - 11.5044i) q^{57} +(-5.21222 - 6.19248i) q^{58} +(0.183176 - 0.661913i) q^{59} +(8.82348 + 9.26159i) q^{60} +(4.36902 + 0.107253i) q^{61} +(-0.113525 + 1.85274i) q^{62} +(2.12840 + 5.13842i) q^{63} +(-7.99740 + 0.204089i) q^{64} +(1.91021 - 4.61165i) q^{65} +(25.0414 + 12.2169i) q^{66} +(4.62905 - 4.40722i) q^{67} +(-1.61809 + 7.21661i) q^{68} +(-20.6078 + 11.6742i) q^{69} +(-1.80401 - 0.935616i) q^{70} +(9.73301 - 0.478152i) q^{71} +(-14.6428 - 15.7474i) q^{72} +(-1.79053 - 5.00419i) q^{73} +(2.15702 - 6.27329i) q^{74} +(2.14062 + 3.03945i) q^{75} +(-10.5096 - 0.512897i) q^{76} +(-4.39317 - 0.541846i) q^{77} +(-4.60879 + 10.7563i) q^{78} +(13.7293 - 1.35222i) q^{79} +(7.79854 + 0.956738i) q^{80} +(2.54759 - 25.8661i) q^{81} +(-0.993662 - 3.42441i) q^{82} +(3.82989 + 3.30368i) q^{83} +(4.20238 + 2.24447i) q^{84} +(2.61413 - 6.77689i) q^{85} +(-1.69416 - 1.22412i) q^{86} +(-9.58093 - 15.9848i) q^{87} +(16.6488 - 3.96236i) q^{88} +(17.6636 + 2.62015i) q^{89} +(11.9505 + 17.4125i) q^{90} +(0.136762 - 1.85404i) q^{91} +(-5.23125 + 13.5746i) q^{92} +(-0.936402 + 4.16999i) q^{93} +(3.43610 + 1.27660i) q^{94} +(10.1355 + 2.01607i) q^{95} +(-18.2540 - 2.46417i) q^{96} +(-14.8934 + 2.96247i) q^{97} +(9.02676 + 1.45092i) q^{98} +(37.6092 + 26.4874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Introduction

L-functions

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