LMFDB - Embedded newform 409.2.m.a.4.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [409,2,Mod(4,409)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(409, base_ring=CyclotomicField(102)) chi = DirichletCharacter(H, H._module([41])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("409.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 409 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	409.m (of order $102$, degree $32$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.26588144267$
Analytic rank:	$0$
Dimension:	$1056$
Relative dimension:	$33$ over $\Q(\zeta_{102})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{102}]$

Embedding invariants

Embedding label			4.12
Character	$\chi$	$=$	409.4
Dual form			409.2.m.a.307.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.09959 + 0.136159i) q^{2} +(-0.601511 + 2.74659i) q^{3} +(-0.749037 + 0.188390i) q^{4} +(0.354399 - 0.711729i) q^{5} +(0.287444 - 3.10202i) q^{6} +(3.88313 - 2.24192i) q^{7} +(2.86432 - 1.10964i) q^{8} +(-4.45652 - 2.05032i) q^{9} +(-0.292785 + 0.830864i) q^{10} +(2.30706 - 0.213781i) q^{11} +(-0.0668759 - 2.17061i) q^{12} +(4.88405 + 0.452573i) q^{13} +(-3.96459 + 2.99392i) q^{14} +(1.74165 + 1.40150i) q^{15} +(-1.63756 + 0.879349i) q^{16} +(1.10697 - 7.13123i) q^{17} +(5.17951 + 1.64772i) q^{18} +(-5.48085 - 4.13895i) q^{19} +(-0.131375 + 0.599877i) q^{20} +(3.82189 + 12.0139i) q^{21} +(-2.50771 + 0.549198i) q^{22} +(-0.0160016 + 0.103084i) q^{23} +(1.32481 + 8.53455i) q^{24} +(2.63221 + 3.48561i) q^{25} +(-5.43206 + 0.167360i) q^{26} +(3.22879 - 4.27561i) q^{27} +(-2.48625 + 2.41083i) q^{28} +(3.02334 - 2.59024i) q^{29} +(-2.10592 - 1.30393i) q^{30} +7.50202i q^{31} +(-3.33339 + 2.35966i) q^{32} +(-0.800558 + 6.46514i) q^{33} +(-0.246235 + 7.99215i) q^{34} +(-0.219467 - 3.55827i) q^{35} +(3.72436 + 0.696204i) q^{36} +(0.544789 - 0.0167848i) q^{37} +(6.59024 + 3.80488i) q^{38} +(-4.18084 + 13.1422i) q^{39} +(0.225346 - 2.43187i) q^{40} +(0.406680 + 1.15407i) q^{41} +(-5.83830 - 12.6899i) q^{42} +(0.675456 - 0.510081i) q^{43} +(-1.68780 + 0.594759i) q^{44} +(-3.03866 + 2.44520i) q^{45} +(0.00355940 - 0.115529i) q^{46} +(-1.62226 + 3.02102i) q^{47} +(-1.43020 - 5.02663i) q^{48} +(6.55245 - 11.3492i) q^{49} +(-3.36895 - 3.47434i) q^{50} +(18.9207 + 7.32991i) q^{51} +(-3.74359 + 0.581113i) q^{52} +(-4.70765 - 8.15389i) q^{53} +(-2.96818 + 5.14104i) q^{54} +(0.665467 - 1.71777i) q^{55} +(8.63477 - 10.7305i) q^{56} +(14.6648 - 12.5640i) q^{57} +(-2.97175 + 3.25986i) q^{58} +(-0.0232168 - 0.00660576i) q^{59} +(-1.56859 - 0.721666i) q^{60} +(-2.74854 - 3.01501i) q^{61} +(-1.02146 - 8.24914i) q^{62} +(-21.9019 + 2.02951i) q^{63} +(6.09129 - 5.55295i) q^{64} +(2.05301 - 3.31573i) q^{65} -7.21800i q^{66} +(0.331178 + 0.467841i) q^{67} +(0.514293 + 5.55010i) q^{68} +(-0.273504 - 0.105956i) q^{69} +(0.725812 + 3.88275i) q^{70} +(-13.6498 - 0.841891i) q^{71} +(-15.0400 - 0.927636i) q^{72} +(4.07200 + 3.94847i) q^{73} +(-0.596759 + 0.0926341i) q^{74} +(-11.1568 + 5.13296i) q^{75} +(4.88510 + 2.06769i) q^{76} +(8.47934 - 6.00240i) q^{77} +(2.80778 - 15.0203i) q^{78} +(9.89543 + 4.92734i) q^{79} +(0.0455101 + 1.47714i) q^{80} +(0.226255 + 0.264086i) q^{81} +(-0.604318 - 1.21363i) q^{82} +(9.02263 - 3.49538i) q^{83} +(-5.12604 - 8.27884i) q^{84} +(-4.68319 - 3.31516i) q^{85} +(-0.673272 + 0.652848i) q^{86} +(5.29575 + 9.86194i) q^{87} +(6.37094 - 3.17235i) q^{88} +(2.72343 + 9.57186i) q^{89} +(3.00834 - 3.10246i) q^{90} +(19.9800 - 9.19226i) q^{91} +(-0.00743424 - 0.0802282i) q^{92} +(-20.6049 - 4.51255i) q^{93} +(1.37248 - 3.54277i) q^{94} +(-4.88822 + 2.43404i) q^{95} +(-4.47593 - 10.5748i) q^{96} +(0.793383 + 12.8633i) q^{97} +(-5.65971 + 13.3716i) q^{98} +(-10.7198 - 3.77751i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1056 q - 33 q^{2} - 31 q^{3} + 29 q^{4} - 22 q^{5} - 44 q^{6} - 57 q^{7} - 22 q^{8} + 2 q^{9} - 30 q^{10} + 17 q^{11} + 67 q^{12} - 34 q^{13} - 68 q^{14} - 32 q^{15} + 21 q^{16} - 27 q^{17} + 22 q^{18}+ \cdots - 229 q^{99}+O(q^{100}) $ 1056 * q - 33 * q^2 - 31 * q^3 + 29 * q^4 - 22 * q^5 - 44 * q^6 - 57 * q^7 - 22 * q^8 + 2 * q^9 - 30 * q^10 + 17 * q^11 + 67 * q^12 - 34 * q^13 - 68 * q^14 - 32 * q^15 + 21 * q^16 - 27 * q^17 + 22 * q^18 - 34 * q^19 - 51 * q^20 - 108 * q^21 - 22 * q^22 - 32 * q^23 + 87 * q^24 - 112 * q^25 - 64 * q^26 - 82 * q^27 - 75 * q^28 - 19 * q^29 - 22 * q^30 + 52 * q^32 - 43 * q^33 - 48 * q^34 - 113 * q^35 + 22 * q^36 - 10 * q^37 - 57 * q^38 + 41 * q^39 - 225 * q^40 - 288 * q^41 - 173 * q^42 + 68 * q^43 - 34 * q^44 - 42 * q^45 + 17 * q^46 - 34 * q^47 + 68 * q^48 + 369 * q^49 - 40 * q^50 + 56 * q^51 + 8 * q^52 + 104 * q^53 + 128 * q^54 + 102 * q^55 - 138 * q^56 - 55 * q^57 - 34 * q^58 - 34 * q^59 - 254 * q^60 - 68 * q^61 + 25 * q^62 - 34 * q^63 + 98 * q^64 - 34 * q^65 - 40 * q^67 - 116 * q^68 - 38 * q^69 - 17 * q^70 + 21 * q^71 - 26 * q^72 - 31 * q^73 + 203 * q^74 + 23 * q^75 - 101 * q^76 + 19 * q^77 - 102 * q^78 - 34 * q^79 + 443 * q^80 - 265 * q^81 - 50 * q^82 + 26 * q^83 - 459 * q^84 + 84 * q^85 + 136 * q^86 - 188 * q^87 + 170 * q^88 - 80 * q^89 + 613 * q^90 - 152 * q^91 + 18 * q^92 + 56 * q^93 - 34 * q^94 - 34 * q^95 + 13 * q^96 - 31 * q^97 - 293 * q^98 - 229 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/409\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{41}{102}\right)$

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 $

$2$	−1.09959	+	0.136159i	−0.777527	+	0.0962787i	−0.501830	−	0.864966i	$-0.667340\pi$
$2$	−1.09959	+	0.136159i	−0.777527	+	0.0962787i	−0.275696	+	0.961245i	$0.588908\pi$
$3$	−0.601511	+	2.74659i	−0.347283	+	1.58574i	0.396962	+	0.917835i	$0.370064\pi$
$3$	−0.601511	+	2.74659i	−0.347283	+	1.58574i	−0.744245	+	0.667907i	$0.767190\pi$
$4$	−0.749037	+	0.188390i	−0.374519	+	0.0941952i
$5$	0.354399	−	0.711729i	0.158492	−	0.318295i	−0.801657	−	0.597785i	$-0.796048\pi$
$5$	0.354399	−	0.711729i	0.158492	−	0.318295i	0.960149	+	0.279490i	$0.0901654\pi$
$6$	0.287444	−	3.10202i	0.117349	−	1.26639i
$7$	3.88313	−	2.24192i	1.46768	−	0.847368i	0.468338	−	0.883549i	$-0.344853\pi$
$7$	3.88313	−	2.24192i	1.46768	−	0.847368i	0.999345	+	0.0361816i	$0.0115195\pi$
$8$	2.86432	−	1.10964i	1.01269	−	0.392318i
$9$	−4.45652	−	2.05032i	−1.48551	−	0.683441i
$10$	−0.292785	+	0.830864i	−0.0925868	+	0.262742i
$11$	2.30706	−	0.213781i	0.695606	−	0.0644574i	0.261346	−	0.965245i	$-0.415834\pi$
$11$	2.30706	−	0.213781i	0.695606	−	0.0644574i	0.434260	+	0.900788i	$0.357010\pi$
$12$	−0.0668759	−	2.17061i	−0.0193054	−	0.626602i
$13$	4.88405	+	0.452573i	1.35459	+	0.125521i	0.744931	−	0.667142i	$-0.232483\pi$
$13$	4.88405	+	0.452573i	1.35459	+	0.125521i	0.609660	+	0.792663i	$0.291306\pi$
$14$	−3.96459	+	2.99392i	−1.05958	+	0.800158i
$15$	1.74165	+	1.40150i	0.449692	+	0.361866i
$16$	−1.63756	+	0.879349i	−0.409389	+	0.219837i
$17$	1.10697	−	7.13123i	0.268480	−	1.72958i	−0.343893	−	0.939009i	$-0.611746\pi$
$17$	1.10697	−	7.13123i	0.268480	−	1.72958i	0.612373	−	0.790569i	$-0.290215\pi$
$18$	5.17951	+	1.64772i	1.22082	+	0.388371i
$19$	−5.48085	−	4.13895i	−1.25739	−	0.949540i	−0.257534	−	0.966269i	$-0.582910\pi$
$19$	−5.48085	−	4.13895i	−1.25739	−	0.949540i	−0.999860	+	0.0167295i	$0.994675\pi$
$20$	−0.131375	+	0.599877i	−0.0293764	+	0.134137i
$21$	3.82189	+	12.0139i	0.834005	+	2.62164i
$22$	−2.50771	+	0.549198i	−0.534646	+	0.117089i
$23$	−0.0160016	+	0.103084i	−0.00333656	+	0.0214945i	−0.989775	−	0.142635i	$-0.954442\pi$
$23$	−0.0160016	+	0.103084i	−0.00333656	+	0.0214945i	0.986439	+	0.164130i	$0.0524816\pi$
$24$	1.32481	+	8.53455i	0.270425	+	1.74211i
$25$	2.63221	+	3.48561i	0.526443	+	0.697123i
$26$	−5.43206	+	0.167360i	−1.06532	+	0.0328220i
$27$	3.22879	−	4.27561i	0.621381	−	0.822841i
$28$	−2.48625	+	2.41083i	−0.469857	+	0.455604i
$29$	3.02334	−	2.59024i	0.561421	−	0.480996i	−0.323826	−	0.946117i	$-0.604969\pi$
$29$	3.02334	−	2.59024i	0.561421	−	0.480996i	0.885247	+	0.465120i	$0.153989\pi$
$30$	−2.10592	−	1.30393i	−0.384488	−	0.238065i
$31$			7.50202i			1.34740i	0.739004	+	0.673701i	$0.235297\pi$
$31$			7.50202i			1.34740i	−0.739004	+	0.673701i	$0.764703\pi$
$32$	−3.33339	+	2.35966i	−0.589265	+	0.417132i
$33$	−0.800558	+	6.46514i	−0.139359	+	1.12544i
$34$	−0.246235	+	7.99215i	−0.0422290	+	1.37064i
$35$	−0.219467	−	3.55827i	−0.0370966	−	0.601457i
$36$	3.72436	+	0.696204i	0.620727	+	0.116034i
$37$	0.544789	−	0.0167848i	0.0895628	−	0.00275940i	0.0140173	−	0.999902i	$-0.495538\pi$
$37$	0.544789	−	0.0167848i	0.0895628	−	0.00275940i	0.0755455	+	0.997142i	$0.475930\pi$
$38$	6.59024	+	3.80488i	1.06908	+	0.617232i
$39$	−4.18084	+	13.1422i	−0.669470	+	2.10444i
$40$	0.225346	−	2.43187i	0.0356304	−	0.384513i
$41$	0.406680	+	1.15407i	0.0635128	+	0.180236i	0.970596	−	0.240716i	$-0.0773823\pi$
$41$	0.406680	+	1.15407i	0.0635128	+	0.180236i	−0.907083	+	0.420952i	$0.861696\pi$
$42$	−5.83830	−	12.6899i	−0.900870	−	1.95810i
$43$	0.675456	−	0.510081i	0.103006	−	0.0777866i	−0.549875	−	0.835247i	$-0.685325\pi$
$43$	0.675456	−	0.510081i	0.103006	−	0.0777866i	0.652881	+	0.757460i	$0.273560\pi$
$44$	−1.68780	+	0.594759i	−0.254446	+	0.0896632i
$45$	−3.03866	+	2.44520i	−0.452977	+	0.364509i
$46$	0.00355940	−	0.115529i	0.000524805	−	0.0170338i
$47$	−1.62226	+	3.02102i	−0.236630	+	0.440662i	−0.971331	−	0.237729i	$-0.923597\pi$
$47$	−1.62226	+	3.02102i	−0.236630	+	0.440662i	0.734701	+	0.678391i	$0.237322\pi$
$48$	−1.43020	−	5.02663i	−0.206431	−	0.725531i
$49$	6.55245	−	11.3492i	0.936064	−	1.62131i
$50$	−3.36895	−	3.47434i	−0.476441	−	0.491346i
$51$	18.9207	+	7.32991i	2.64942	+	1.02639i
$52$	−3.74359	+	0.581113i	−0.519143	+	0.0805859i
$53$	−4.70765	−	8.15389i	−0.646645	−	1.12002i	−0.983919	−	0.178616i	$-0.942838\pi$
$53$	−4.70765	−	8.15389i	−0.646645	−	1.12002i	0.337273	−	0.941407i	$-0.390495\pi$
$54$	−2.96818	+	5.14104i	−0.403918	+	0.699607i
$55$	0.665467	−	1.71777i	0.0897315	−	0.231624i
$56$	8.63477	−	10.7305i	1.15387	−	1.43392i
$57$	14.6648	−	12.5640i	1.94240	−	1.66414i
$58$	−2.97175	+	3.25986i	−0.390210	+	0.428040i
$59$	−0.0232168	−	0.00660576i	−0.00302257	−	0.000859996i	0.272151	−	0.962254i	$-0.412265\pi$
$59$	−0.0232168	−	0.00660576i	−0.00302257	−	0.000859996i	−0.275174	+	0.961394i	$0.588735\pi$
$60$	−1.56859	−	0.721666i	−0.202504	−	0.0931666i
$61$	−2.74854	−	3.01501i	−0.351915	−	0.386032i	0.537400	−	0.843327i	$-0.319406\pi$
$61$	−2.74854	−	3.01501i	−0.351915	−	0.386032i	−0.889315	+	0.457295i	$0.848818\pi$
$62$	−1.02146	−	8.24914i	−0.129726	−	1.04764i
$63$	−21.9019	+	2.02951i	−2.75938	+	0.255694i
$64$	6.09129	−	5.55295i	0.761412	−	0.694118i
$65$	2.05301	−	3.31573i	0.254645	−	0.411265i
$66$		−	7.21800i		−	0.888474i
$67$	0.331178	+	0.467841i	0.0404598	+	0.0571558i	0.835926	−	0.548842i	$-0.184931\pi$
$67$	0.331178	+	0.467841i	0.0404598	+	0.0571558i	−0.795467	+	0.605997i	$0.792774\pi$
$68$	0.514293	+	5.55010i	0.0623671	+	0.673048i
$69$	−0.273504	−	0.105956i	−0.0329260	−	0.0127556i
$70$	0.725812	+	3.88275i	0.0867511	+	0.464077i
$71$	−13.6498	−	0.841891i	−1.61993	−	0.0999141i	−0.773994	−	0.633193i	$-0.781744\pi$
$71$	−13.6498	−	0.841891i	−1.61993	−	0.0999141i	−0.845940	+	0.533278i	$0.820960\pi$
$72$	−15.0400	−	0.927636i	−1.77248	−	0.109323i
$73$	4.07200	+	3.94847i	0.476591	+	0.462134i	0.894962	−	0.446143i	$-0.147203\pi$
$73$	4.07200	+	3.94847i	0.476591	+	0.462134i	−0.418371	+	0.908276i	$0.637399\pi$
$74$	−0.596759	+	0.0926341i	−0.0693718	+	0.0107685i
$75$	−11.1568	+	5.13296i	−1.28828	+	0.592703i
$76$	4.88510	+	2.06769i	0.560360	+	0.237180i
$77$	8.47934	−	6.00240i	0.966310	−	0.684037i
$78$	2.80778	−	15.0203i	0.317918	−	1.70071i
$79$	9.89543	+	4.92734i	1.11332	+	0.554369i	0.905734	−	0.423847i	$-0.139321\pi$
$79$	9.89543	+	4.92734i	1.11332	+	0.554369i	0.207589	+	0.978216i	$0.433438\pi$
$80$	0.0455101	+	1.47714i	0.00508819	+	0.165149i
$81$	0.226255	+	0.264086i	0.0251395	+	0.0293429i
$82$	−0.604318	−	1.21363i	−0.0667358	−	0.134024i
$83$	9.02263	−	3.49538i	0.990362	−	0.383668i	0.189084	−	0.981961i	$-0.439448\pi$
$83$	9.02263	−	3.49538i	0.990362	−	0.383668i	0.801278	+	0.598293i	$0.204154\pi$
$84$	−5.12604	−	8.27884i	−0.559297	−	0.903295i
$85$	−4.68319	−	3.31516i	−0.507964	−	0.359580i
$86$	−0.673272	+	0.652848i	−0.0726008	+	0.0703985i
$87$	5.29575	+	9.86194i	0.567764	+	1.05731i
$88$	6.37094	−	3.17235i	0.679144	−	0.338174i
$89$	2.72343	+	9.57186i	0.288683	+	1.01462i	0.961500	+	0.274806i	$0.0886136\pi$
$89$	2.72343	+	9.57186i	0.288683	+	1.01462i	−0.672817	+	0.739809i	$0.734916\pi$
$90$	3.00834	−	3.10246i	0.317107	−	0.327028i
$91$	19.9800	−	9.19226i	2.09447	−	0.963610i
$92$	−0.00743424	−	0.0802282i	−0.000775073	−	0.00836437i
$93$	−20.6049	−	4.51255i	−2.13663	−	0.467930i
$94$	1.37248	−	3.54277i	0.141560	−	0.365409i
$95$	−4.88822	+	2.43404i	−0.501521	+	0.249728i
$96$	−4.47593	−	10.5748i	−0.456822	−	1.07929i
$97$	0.793383	+	12.8633i	0.0805559	+	1.30607i	0.795098	+	0.606481i	$0.207419\pi$
$97$	0.793383	+	12.8633i	0.0805559	+	1.30607i	−0.714542	+	0.699593i	$0.753365\pi$
$98$	−5.65971	+	13.3716i	−0.571717	+	1.35073i
$99$	−10.7198	−	3.77751i	−1.07738	−	0.379654i
$100$	−2.62828	−	2.11497i	−0.262828	−	0.211497i
$101$	9.58648	−	11.1894i	0.953890	−	1.11339i	−0.0395709	−	0.999217i	$-0.512599\pi$
$101$	9.58648	−	11.1894i	0.953890	−	1.11339i	0.993461	−	0.114169i	$-0.0364205\pi$
$102$	−21.8030	−	5.48367i	−2.15882	−	0.542965i
$103$	−5.25885	+	10.5612i	−0.518170	+	1.04063i	0.469332	+	0.883022i	$0.344495\pi$
$103$	−5.25885	+	10.5612i	−0.518170	+	1.04063i	−0.987502	+	0.157604i	$0.949623\pi$
$104$	14.4916	−	4.12323i	1.42102	−	0.404316i
$105$	9.90510	+	1.53756i	0.966639	+	0.150050i
$106$	6.28670	+	8.32494i	0.610618	+	0.808589i
$107$	3.08749	+	3.83683i	0.298478	+	0.370920i	0.905923	−	0.423441i	$-0.139178\pi$
$107$	3.08749	+	3.83683i	0.298478	+	0.370920i	−0.607445	+	0.794362i	$0.707805\pi$
$108$	−1.61300	+	3.81086i	−0.155211	+	0.366701i
$109$	−13.7394	+	11.0560i	−1.31599	+	1.05898i	−0.322324	+	0.946629i	$0.604464\pi$
$109$	−13.7394	+	11.0560i	−1.31599	+	1.05898i	−0.993669	+	0.112346i	$0.964163\pi$
$110$	−0.497851	+	1.97945i	−0.0474682	+	0.188733i
$111$	−0.281596	+	1.50641i	−0.0267279	+	0.142982i
$112$	−4.38741	+	7.08590i	−0.414571	+	0.669555i
$113$	−9.39804	+	3.97785i	−0.884093	+	0.374205i	−0.783991	−	0.620773i	$-0.786819\pi$
$113$	−9.39804	+	3.97785i	−0.884093	+	0.374205i	−0.100103	+	0.994977i	$0.531917\pi$
$114$	−14.4145	+	15.8120i	−1.35004	+	1.48093i
$115$	0.0676968	+	0.0479216i	0.00631276	+	0.00446871i
$116$	−1.77662	+	2.50976i	−0.164955	+	0.233025i
$117$	−20.8379	−	12.0308i	−1.92647	−	1.11225i
$118$	0.0264284	+	0.00410245i	0.00243293	+	0.000377661i
$119$	−11.6892	−	30.1732i	−1.07154	−	2.76597i
$120$	6.54380	+	2.08173i	0.597364	+	0.190035i
$121$	−5.53586	+	1.03483i	−0.503260	+	0.0940757i
$122$	3.43279	+	2.94103i	0.310790	+	0.266268i
$123$	−3.41439	+	0.422793i	−0.307865	+	0.0381219i
$124$	−1.41331	−	5.61929i	−0.126919	−	0.504627i
$125$	7.32139	−	1.36861i	0.654845	−	0.122412i
$126$	23.8067	−	5.21376i	2.12087	−	0.464479i
$127$	9.81651	+	6.50465i	0.871074	+	0.577195i	0.906513	−	0.422177i	$-0.138734\pi$
$127$	9.81651	+	6.50465i	0.871074	+	0.577195i	−0.0354393	+	0.999372i	$0.511283\pi$
$128$	−0.627523	+	0.732448i	−0.0554658	+	0.0647399i
$129$	0.994686	+	2.16202i	0.0875772	+	0.190355i
$130$	−1.80600	+	3.92547i	−0.158397	+	0.344286i
$131$	−8.83213	−	10.3089i	−0.771667	−	0.900693i	0.225627	−	0.974214i	$-0.427557\pi$
$131$	−8.83213	−	10.3089i	−0.771667	−	0.900693i	−0.997294	+	0.0735206i	$0.976577\pi$
$132$	−0.618323	−	4.99345i	−0.0538181	−	0.434624i
$133$	−30.5620	−	3.78440i	−2.65007	−	0.328149i
$134$	−0.427860	−	0.469340i	−0.0369614	−	0.0405448i
$135$	−1.89880	−	3.81330i	−0.163422	−	0.328196i
$136$	−4.74240	−	21.6544i	−0.406657	−	1.85685i
$137$	−2.80497	−	7.95991i	−0.239644	−	0.680061i	−0.999549	−	0.0300269i	$-0.990441\pi$
$137$	−2.80497	−	7.95991i	−0.239644	−	0.680061i	0.759905	−	0.650034i	$-0.225246\pi$
$138$	0.315168	+	0.0792680i	0.0268289	+	0.00674774i
$139$	2.35362	+	3.55197i	0.199632	+	0.301274i	0.919695	−	0.392634i	$-0.128436\pi$
$139$	2.35362	+	3.55197i	0.199632	+	0.301274i	−0.720063	+	0.693909i	$0.755887\pi$
$140$	0.834732	+	2.62393i	0.0705478	+	0.221763i
$141$	−7.32170	−	6.27285i	−0.616598	−	0.528269i
$142$	15.1238	−	0.932805i	1.26916	−	0.0782792i
$143$	11.3646			0.950352
$144$	9.10076	−	0.561315i	0.758396	−	0.0467763i
$145$	−0.772081	−	3.06978i	−0.0641178	−	0.254931i
$146$	−5.01514	−	3.78726i	−0.415056	−	0.313436i
$147$	27.2301	+	24.8235i	2.24590	+	2.04741i
$148$	−0.404905	+	0.115205i	−0.0332830	+	0.00946983i
$149$	1.90091	−	5.97541i	0.155729	−	0.489525i	−0.843108	−	0.537745i	$-0.819276\pi$
$149$	1.90091	−	5.97541i	0.155729	−	0.489525i	0.998837	+	0.0482200i	$0.0153549\pi$
$150$	11.5690	−	7.16325i	0.944609	−	0.584877i
$151$	11.8380	+	19.1191i	0.963366	+	1.55589i	0.824716	+	0.565548i	$0.191335\pi$
$151$	11.8380	+	19.1191i	0.963366	+	1.55589i	0.138650	+	0.990341i	$0.455724\pi$
$152$	−20.2916	−	5.77347i	−1.64587	−	0.468290i
$153$	−19.5546	+	29.5108i	−1.58089	+	2.38581i
$154$	−8.50651	+	7.75471i	−0.685474	+	0.624892i
$155$	5.33941	+	2.65871i	0.428871	+	0.213553i
$156$	0.655737	−	10.6316i	0.0525010	−	0.851213i
$157$	−6.52591	+	2.29964i	−0.520824	+	0.183531i	−0.579847	−	0.814725i	$-0.696888\pi$
$157$	−6.52591	+	2.29964i	−0.520824	+	0.183531i	0.0590231	+	0.998257i	$0.481201\pi$
$158$	−11.5518	−	4.07070i	−0.919012	−	0.323847i
$159$	25.2271	−	8.02530i	2.00064	−	0.636448i
$160$	0.498087	+	3.20873i	0.0393772	+	0.253672i
$161$	0.168970	+	0.436162i	0.0133167	+	0.0343744i
$162$	−0.284745	−	0.259580i	−0.0223717	−	0.0203945i
$163$	11.2019	−	2.81738i	0.877398	−	0.220674i	0.221168	−	0.975236i	$-0.429013\pi$
$163$	11.2019	−	2.81738i	0.877398	−	0.220674i	0.656230	+	0.754561i	$0.272150\pi$
$164$	−0.522035	−	0.787830i	−0.0407641	−	0.0615192i
$165$	4.31771	+	2.86102i	0.336133	+	0.222730i
$166$	−9.44525	+	5.07199i	−0.733094	+	0.393663i
$167$	−18.0780	+	5.75102i	−1.39892	+	0.445027i	−0.905344	−	0.424679i	$-0.860387\pi$
$167$	−18.0780	+	5.75102i	−1.39892	+	0.445027i	−0.493571	+	0.869706i	$0.664309\pi$
$168$	24.2782	+	30.1706i	1.87310	+	2.32771i
$169$	10.8704	+	2.03203i	0.836186	+	0.156310i
$170$	5.60098	+	3.00766i	0.429575	+	0.230677i
$171$	15.9393	+	29.6828i	1.21891	+	2.26990i
$172$	−0.409848	+	0.509319i	−0.0312506	+	0.0388352i
$173$	−2.31603	−	0.0713560i	−0.176084	−	0.00542510i	−0.0573667	−	0.998353i	$-0.518270\pi$
$173$	−2.31603	−	0.0713560i	−0.176084	−	0.00542510i	−0.118717	+	0.992928i	$0.537878\pi$
$174$	−7.16593	−	10.1230i	−0.543248	−	0.767424i
$175$	18.0357	+	7.63386i	1.36337	+	0.577065i
$176$	−3.58996	+	2.37879i	−0.270603	+	0.179308i
$177$	0.0321085	−	0.0597936i	0.00241342	−	0.00449436i
$178$	−4.29794	−	10.1543i	−0.322144	−	0.761096i
$179$	2.22958	+	1.19726i	0.166647	+	0.0894875i	0.554296	−	0.832319i	$-0.312987\pi$
$179$	2.22958	+	1.19726i	0.166647	+	0.0894875i	−0.387650	+	0.921807i	$0.626713\pi$
$180$	1.81542	−	2.40400i	0.135313	−	0.179184i
$181$	0.814910	−	1.15119i	0.0605718	−	0.0855672i	−0.784789	−	0.619763i	$-0.787229\pi$
$181$	0.814910	−	1.15119i	0.0605718	−	0.0855672i	0.845361	+	0.534196i	$0.179386\pi$
$182$	−20.7182	+	12.8282i	−1.53573	+	0.950886i
$183$	9.93425	−	5.73554i	0.734361	−	0.423984i
$184$	0.0685526	+	0.313021i	0.00505377	+	0.0230762i
$185$	0.181126	−	0.393691i	0.0133167	−	0.0289447i
$186$	23.2714	+	2.15641i	1.70634	+	0.158116i
$187$	1.02933	−	16.6889i	0.0752723	−	1.22041i
$188$	0.645998	−	2.56848i	0.0471143	−	0.187325i
$189$	2.95221	−	23.8414i	0.214742	−	1.73421i
$190$	5.04361	−	3.34202i	0.365902	−	0.242456i
$191$	−2.06669	+	2.13134i	−0.149540	+	0.154219i	−0.788529	−	0.614998i	$-0.789157\pi$
$191$	−2.06669	+	2.13134i	−0.149540	+	0.154219i	0.638989	+	0.769216i	$0.279353\pi$
$192$	11.5877	+	20.0704i	0.836267	+	1.44846i
$193$	−1.27473	+	4.48020i	−0.0917568	+	0.322492i	−0.994092	−	0.108544i	$-0.965381\pi$
$193$	−1.27473	+	4.48020i	−0.0917568	+	0.322492i	0.902335	+	0.431036i	$0.141852\pi$
$194$	−2.62385	−	14.0364i	−0.188381	−	1.00775i
$195$	7.87201	+	7.63321i	0.563727	+	0.546626i
$196$	−2.76995	+	9.73537i	−0.197854	+	0.695383i
$197$	11.5391	+	11.9001i	0.822129	+	0.847849i	0.990448	−	0.137883i	$-0.0440299\pi$
$197$	11.5391	+	11.9001i	0.822129	+	0.847849i	−0.168319	+	0.985733i	$0.553834\pi$
$198$	12.3017	+	2.69412i	0.874244	+	0.191462i
$199$	7.23984	+	0.223057i	0.513219	+	0.0158121i	0.286372	−	0.958118i	$-0.407551\pi$
$199$	7.23984	+	0.223057i	0.513219	+	0.0158121i	0.226846	+	0.973931i	$0.427158\pi$
$200$	11.4073	+	7.06309i	0.806616	+	0.499436i
$201$	−1.48417	+	0.628196i	−0.104685	+	0.0443095i
$202$	−9.01766	+	13.6090i	−0.634480	+	0.957526i
$203$	5.93290	−	16.8363i	0.416408	−	1.18168i
$204$	−15.5532	−	1.92590i	−1.08894	−	0.134840i
$205$	0.965515	+	0.119557i	0.0674345	+	0.00835020i
$206$	4.34458	−	12.3290i	0.302701	−	0.859003i
$207$	0.282667	−	0.426587i	0.0196467	−	0.0296498i
$208$	−8.39587	+	3.55367i	−0.582149	+	0.246403i
$209$	−13.5295	−	8.37711i	−0.935855	−	0.579457i
$210$	−11.1009	−	0.342015i	−0.766034	−	0.0236013i
$211$	−18.4506	−	4.04074i	−1.27019	−	0.278176i	−0.472547	−	0.881305i	$-0.656665\pi$
$211$	−18.4506	−	4.04074i	−1.27019	−	0.278176i	−0.797643	+	0.603129i	$0.793920\pi$
$212$	5.06232	+	5.22069i	0.347682	+	0.358558i
$213$	10.5228	−	36.9840i	0.721013	−	2.53410i
$214$	−3.91738	−	3.79855i	−0.267787	−	0.259663i
$215$	−0.123658	−	0.661514i	−0.00843343	−	0.0451149i
$216$	4.50388	−	15.8295i	0.306450	−	1.07706i
$217$	16.8190	+	29.1313i	1.14175	+	1.97756i
$218$	13.6023	−	14.0278i	0.921263	−	0.950084i
$219$	−13.2942	+	8.80904i	−0.898337	+	0.595260i
$220$	−0.174848	+	1.41204i	−0.0117883	+	0.0951997i
$221$	8.63391	−	34.3283i	0.580779	−	2.30917i
$222$	0.104530	−	1.69477i	0.00701558	−	0.113745i
$223$	−21.7383	−	2.01435i	−1.45570	−	0.134891i	−0.664886	−	0.746945i	$-0.731520\pi$
$223$	−21.7383	−	2.01435i	−1.45570	−	0.134891i	−0.790816	+	0.612054i	$0.790343\pi$
$224$	−7.65380	+	16.6360i	−0.511391	+	1.11154i
$225$	−4.58387	−	20.9306i	−0.305591	−	1.39537i
$226$	9.79236	−	5.65362i	0.651378	−	0.376073i
$227$	−8.41527	+	5.21051i	−0.558541	+	0.345834i	−0.776493	−	0.630125i	$-0.783003\pi$
$227$	−8.41527	+	5.21051i	−0.558541	+	0.345834i	0.217952	+	0.975959i	$0.430062\pi$
$228$	−8.61752	+	12.1736i	−0.570709	+	0.806217i
$229$	14.5730	−	19.2978i	0.963010	−	1.27523i	0.00163231	−	0.999999i	$-0.499480\pi$
$229$	14.5730	−	19.2978i	0.963010	−	1.27523i	0.961378	−	0.275233i	$-0.0887549\pi$
$230$	−0.0809636	−	0.0434766i	−0.00533858	−	0.00286676i
$231$	11.3857	+	26.8997i	0.749123	+	1.76987i
$232$	5.78557	−	10.7741i	0.379841	−	0.707355i
$233$	−13.8732	+	9.19272i	−0.908864	+	0.602235i	−0.917503	−	0.397728i	$-0.869799\pi$
$233$	−13.8732	+	9.19272i	−0.908864	+	0.602235i	0.00863987	+	0.999963i	$0.497250\pi$
$234$	24.5512	+	10.3916i	1.60496	+	0.679323i
$235$	1.57523	+	2.22525i	0.102756	+	0.145160i
$236$	0.0186347		0.000574130i	0.00121302		3.73727e-5i
$237$	−19.4856	+	24.2148i	−1.26572	+	1.57292i
$238$	16.9616	+	31.5865i	1.09946	+	2.04745i
$239$	18.6187	+	9.99803i	1.20434	+	0.646718i	0.947507	−	0.319736i	$-0.103594\pi$
$239$	18.6187	+	9.99803i	1.20434	+	0.646718i	0.256836	+	0.966455i	$0.417320\pi$
$240$	−4.08446	−	0.763518i	−0.263651	−	0.0492848i
$241$	−8.97117	−	11.1485i	−0.577884	−	0.718138i	0.402459	−	0.915438i	$-0.368155\pi$
$241$	−8.97117	−	11.1485i	−0.577884	−	0.718138i	−0.980343	+	0.197299i	$0.936783\pi$
$242$	5.94627	−	1.89165i	0.382241	−	0.121600i
$243$	13.2994	−	7.14163i	0.853157	−	0.458136i
$244$	2.62676	+	1.74055i	0.168161	+	0.111428i
$245$	−5.75535	−	8.68570i	−0.367696	−	0.554909i
$246$	3.69686	−	0.929796i	0.235703	−	0.0592817i
$247$	−24.8956	−	22.6953i	−1.58407	−	1.44407i
$248$	8.32456	+	21.4882i	0.528610	+	1.36450i
$249$	4.17316	+	26.8839i	0.264463	+	1.70370i
$250$	−7.86417	+	2.50177i	−0.497374	+	0.158226i
$251$	−4.11502	−	1.45008i	−0.259738	−	0.0915280i	0.199320	−	0.979934i	$-0.436127\pi$
$251$	−4.11502	−	1.45008i	−0.259738	−	0.0915280i	−0.459058	+	0.888406i	$0.651813\pi$
$252$	16.0230	−	5.64629i	1.00935	−	0.355683i
$253$	−0.0148793	+	0.241242i	−0.000935453	+	0.0151667i
$254$	−11.6798	−	5.81584i	−0.732855	−	0.364918i
$255$	11.9224	−	10.8687i	0.746608	−	0.680623i
$256$	−8.51547	+	12.8511i	−0.532217	+	0.803195i
$257$	−28.3629	−	8.06993i	−1.76923	−	0.503389i	−0.777182	−	0.629275i	$-0.783352\pi$
$257$	−28.3629	−	8.06993i	−1.76923	−	0.503389i	−0.992045	+	0.125887i	$0.959822\pi$
$258$	−1.38812	−	2.24190i	−0.0864208	−	0.139574i
$259$	2.07785	−	1.28655i	0.129112	−	0.0799425i
$260$	−0.913130	+	2.87037i	−0.0566299	+	0.178013i
$261$	−18.7844	+	5.34463i	−1.16273	+	0.330824i
$262$	11.1154	+	10.1330i	0.686709	+	0.626018i
$263$	11.2294	+	8.48003i	0.692433	+	0.522901i	0.889183	−	0.457553i	$-0.151274\pi$
$263$	11.2294	+	8.48003i	0.692433	+	0.522901i	−0.196749	+	0.980454i	$0.563039\pi$
$264$	4.88094	+	19.4065i	0.300401	+	1.19439i
$265$	−7.47174	+	0.460841i	−0.458986	+	0.0283093i
$266$	34.1210			2.09209
$267$	−27.9281	+	1.72255i	−1.70917	+	0.105418i
$268$	−0.336201	−	0.288039i	−0.0205367	−	0.0175948i
$269$	−3.94613	−	12.4044i	−0.240600	−	0.756310i	−0.994998	−	0.0998935i	$-0.968150\pi$
$269$	−3.94613	−	12.4044i	−0.240600	−	0.756310i	0.754399	−	0.656417i	$-0.227929\pi$
$270$	2.60711	+	3.93452i	0.158664	+	0.239447i
$271$	−0.660747	−	0.166185i	−0.0401375	−	0.0100950i	0.223793	−	0.974637i	$-0.428156\pi$
$271$	−0.660747	−	0.166185i	−0.0401375	−	0.0100950i	−0.263930	+	0.964542i	$0.585019\pi$
$272$	4.45811	+	12.6512i	0.270313	+	0.767092i
$273$	13.2291	+	60.4060i	0.800663	+	3.65594i
$274$	4.16812	+	8.37071i	0.251805	+	0.505693i
$275$	6.81784	+	7.47882i	0.411131	+	0.450990i
$276$	0.224825	+	0.0278394i	0.0135329	+	0.00167574i
$277$	−3.32035	−	26.8145i	−0.199500	−	1.61112i	−0.679378	−	0.733789i	$-0.737750\pi$
$277$	−3.32035	−	26.8145i	−0.199500	−	1.61112i	0.479877	−	0.877336i	$-0.340681\pi$
$278$	−3.07165	−	3.58524i	−0.184225	−	0.215029i
$279$	15.3816	−	33.4329i	0.920871	−	2.00158i
$280$	−4.57703	−	9.94848i	−0.273530	−	0.594535i
$281$	18.0974	−	21.1233i	1.07960	−	1.26011i	0.115859	−	0.993266i	$-0.463038\pi$
$281$	18.0974	−	21.1233i	1.07960	−	1.26011i	0.963739	−	0.266847i	$-0.0859817\pi$
$282$	8.90496	+	5.90064i	0.530283	+	0.351378i
$283$	10.3032	−	2.25643i	0.612460	−	0.134131i	0.103081	−	0.994673i	$-0.467130\pi$
$283$	10.3032	−	2.25643i	0.612460	−	0.134131i	0.509379	+	0.860542i	$0.329875\pi$
$284$	10.3828	−	1.94089i	0.616107	−	0.115170i
$285$	−3.74499	−	14.8900i	−0.221834	−	0.882008i
$286$	−12.4963	+	1.54738i	−0.738924	+	0.0914986i
$287$	4.16654	+	3.56967i	0.245943	+	0.210711i
$288$	19.6934	−	3.68133i	1.16044	−	0.216924i
$289$	−33.4290	−	10.6345i	−1.96641	−	0.625561i
$290$	1.26695	+	3.27037i	0.0743978	+	0.192043i
$291$	−35.8075	−	5.55835i	−2.09907	−	0.325836i
$292$	−3.79393	−	2.19043i	−0.222023	−	0.128185i
$293$	−6.16698	+	8.71183i	−0.360279	+	0.508950i	−0.955652	−	0.294499i	$-0.904847\pi$
$293$	−6.16698	+	8.71183i	−0.360279	+	0.508950i	0.595373	+	0.803449i	$0.297004\pi$
$294$	−33.3218	−	23.5880i	−1.94337	−	1.37568i
$295$	−0.0129295	+	0.0141830i	−0.000752786	+	0.000825767i
$296$	1.54182	−	0.652598i	0.0896166	−	0.0379315i
$297$	6.53498	−	10.5544i	0.379198	−	0.612426i
$298$	−1.27662	+	6.82932i	−0.0739527	+	0.395612i
$299$	−0.124805	+	0.496224i	−0.00721769	+	0.0286974i
$300$	7.38989	−	5.94662i	0.426656	−	0.343328i
$301$	1.47932	−	3.49503i	0.0852665	−	0.201450i
$302$	−15.6202	−	19.4113i	−0.898842	−	1.11699i
$303$	24.9662	+	33.0606i	1.43427	+	1.89928i
$304$	12.6148	+	1.95818i	0.723508	+	0.112309i
$305$	−3.11995	+	0.887702i	−0.178648	+	0.0508297i
$306$	17.4838	−	35.1123i	0.999485	−	2.00724i
$307$	2.53158	+	0.636719i	0.144485	+	0.0363395i	0.315479	−	0.948933i	$-0.397835\pi$
$307$	2.53158	+	0.636719i	0.144485	+	0.0363395i	−0.170993	+	0.985272i	$0.554698\pi$
$308$	−5.22055	+	6.09345i	−0.297468	+	0.347206i
$309$	−25.8440	−	20.7966i	−1.47021	−	1.18308i
$310$	−6.23316	−	2.19648i	−0.354020	−	0.124752i
$311$	−5.72875	+	13.5347i	−0.324848	+	0.767483i	0.674720	+	0.738074i	$0.264265\pi$
$311$	−5.72875	+	13.5347i	−0.324848	+	0.767483i	−0.999567	+	0.0294092i	$0.990637\pi$
$312$	2.60791	+	42.2827i	0.147644	+	2.39379i
$313$	0.116897	+	0.276181i	0.00660742	+	0.0156106i	0.924176	−	0.381967i	$-0.124753\pi$
$313$	0.116897	+	0.276181i	0.00660742	+	0.0156106i	−0.917569	+	0.397577i	$0.869851\pi$
$314$	6.86270	−	3.41722i	0.387284	−	0.192845i
$315$	−6.31755	+	16.3075i	−0.355954	+	0.918822i
$316$	−8.34031	−	1.82656i	−0.469179	−	0.102752i
$317$	0.736788	+	7.95121i	0.0413821	+	0.446584i	0.991066	+	0.133374i	$0.0425811\pi$
$317$	0.736788	+	7.95121i	0.0413821	+	0.446584i	−0.949684	+	0.313211i	$0.898595\pi$
$318$	−26.6467	+	12.2594i	−1.49427	+	0.687474i
$319$	6.42130	−	6.62219i	0.359524	−	0.370771i
$320$	−1.79345	−	6.30331i	−0.100257	−	0.352366i
$321$	−12.3953	+	6.17215i	−0.691840	+	0.344496i
$322$	−0.245185	−	0.456592i	−0.0136636	−	0.0254449i
$323$	−35.5829	+	34.5035i	−1.97989	+	1.91983i
$324$	−0.219225	−	0.155186i	−0.0121792	−	0.00862145i
$325$	11.2784	+	18.2152i	0.625611	+	1.01040i
$326$	−11.9338	+	4.62319i	−0.660954	+	0.256055i
$327$	−22.1019	−	44.3867i	−1.22224	−	2.45459i
$328$	2.44547	+	2.85436i	0.135029	+	0.157606i
$329$	0.473483	+	15.3680i	0.0261040	+	0.847265i
$330$	−5.13726	−	2.55805i	−0.282797	−	0.140816i
$331$	0.137553	−	0.735846i	0.00756062	−	0.0404458i	−0.978985	−	0.203934i	$-0.934627\pi$
$331$	0.137553	−	0.735846i	0.00756062	−	0.0404458i	0.986545	+	0.163488i	$0.0522744\pi$
$332$	−6.09979	+	4.31795i	−0.334769	+	0.236978i
$333$	−2.46228	−	1.04219i	−0.134932	−	0.0571118i
$334$	19.0953	−	8.78522i	1.04485	−	0.480706i
$335$	0.450345	−	0.0699064i	0.0246050	−	0.00381940i
$336$	−16.8230	−	16.3126i	−0.917768	−	0.889927i
$337$	−5.27948	−	0.325627i	−0.287591	−	0.0177380i	−0.0828770	−	0.996560i	$-0.526411\pi$
$337$	−5.27948	−	0.325627i	−0.287591	−	0.0177380i	−0.204714	+	0.978822i	$0.565627\pi$
$338$	−12.2297	−	0.754301i	−0.665207	−	0.0410285i
$339$	−5.27247	−	28.2052i	−0.286361	−	1.53190i
$340$	4.13243	+	1.60091i	0.224113	+	0.0868217i
$341$	1.60379	+	17.3076i	0.0868500	+	0.937261i
$342$	−21.5683	−	30.4686i	−1.16628	−	1.64755i
$343$		−	27.3734i		−	1.47802i
$344$	1.36871	−	2.21055i	0.0737961	−	0.119185i
$345$	−0.172341	+	0.157110i	−0.00927854	+	0.00845851i
$346$	2.55639	−	0.236885i	0.137433	−	0.0127350i
$347$	−0.836666	−	6.75674i	−0.0449146	−	0.362721i	−0.998166	−	0.0605416i	$-0.980717\pi$
$347$	−0.836666	−	6.75674i	−0.0449146	−	0.362721i	0.953251	−	0.302179i	$-0.0977142\pi$
$348$	−5.82461	−	6.38929i	−0.312232	−	0.342502i
$349$	−6.03347	−	2.77584i	−0.322964	−	0.148587i	0.249822	−	0.968292i	$-0.419628\pi$
$349$	−6.03347	−	2.77584i	−0.322964	−	0.148587i	−0.572787	+	0.819705i	$0.694138\pi$
$350$	−20.8713	−	5.93839i	−1.11562	−	0.317420i
$351$	17.7046	−	19.4210i	0.945001	−	1.03662i
$352$	−7.18589	+	6.15649i	−0.383009	+	0.328142i
$353$	11.4593	−	14.2405i	0.609915	−	0.757943i	−0.375739	−	0.926726i	$-0.622611\pi$
$353$	11.4593	−	14.2405i	0.609915	−	0.757943i	0.985653	+	0.168782i	$0.0539835\pi$
$354$	−0.0271647	+	0.0701202i	−0.00144379	+	0.00372685i
$355$	−5.43668	+	9.41660i	−0.288549	+	0.499781i
$356$	−3.84320	−	6.65661i	−0.203689	−	0.352800i
$357$	89.9045	−	13.9558i	4.75825	−	0.738617i
$358$	−2.61464	−	1.01292i	−0.138188	−	0.0535344i
$359$	−2.10834	−	2.17429i	−0.111274	−	0.114755i	0.659978	−	0.751284i	$-0.270565\pi$
$359$	−2.10834	−	2.17429i	−0.111274	−	0.114755i	−0.771252	+	0.636530i	$0.780369\pi$
$360$	−5.99039	+	10.3757i	−0.315721	+	0.546845i
$361$	7.70926	+	27.0952i	0.405751	+	1.42607i
$362$	−0.739321	+	1.37679i	−0.0388579	+	0.0723626i
$363$	0.487630	−	15.8272i	0.0255940	−	0.830712i
$364$	−13.2340	+	10.6494i	−0.693652	+	0.558179i
$365$	4.25336	−	1.49882i	0.222631	−	0.0784521i
$366$	−10.1427	+	7.65937i	−0.530165	+	0.400362i
$367$	−11.4467	−	24.8801i	−0.597510	−	1.29873i	−0.934078	−	0.357070i	$-0.883776\pi$
$367$	−11.4467	−	24.8801i	−0.597510	−	1.29873i	0.336567	−	0.941659i	$-0.390734\pi$
$368$	−0.0644433	−	0.182877i	−0.00335934	−	0.00953311i
$369$	0.553849	−	5.97698i	0.0288322	−	0.311149i
$370$	−0.145560	+	0.457560i	−0.00756732	+	0.0237874i
$371$	−36.5608	−	21.1084i	−1.89814	−	1.09589i
$372$	16.2840	−	0.501704i	0.844286	−	0.0260122i
$373$	−6.17830	−	1.15493i	−0.319900	−	0.0597998i	0.0213503	−	0.999772i	$-0.493203\pi$
$373$	−6.17830	−	1.15493i	−0.319900	−	0.0597998i	−0.341251	+	0.939972i	$0.610851\pi$
$374$	1.14049	+	18.4910i	0.0589732	+	0.956148i
$375$	−0.644910	+	20.9321i	−0.0333030	+	1.08093i
$376$	−1.29440	+	10.4533i	−0.0667535	+	0.539087i
$377$	15.9384	−	11.2826i	0.820871	−	0.581082i
$378$			26.6177i			1.36907i
$379$	30.9902	+	19.1883i	1.59186	+	0.985636i	0.981026	+	0.193875i	$0.0621058\pi$
$379$	30.9902	+	19.1883i	1.59186	+	0.985636i	0.610831	+	0.791761i	$0.290835\pi$
$380$	3.20291	−	2.74408i	0.164306	−	0.140768i
$381$	−23.7703	+	23.0492i	−1.21779	+	1.18085i
$382$	1.98231	−	2.62500i	0.101424	−	0.134307i
$383$	−31.5408	+	0.971762i	−1.61166	+	0.0496547i	−0.824049	−	0.566519i	$-0.808290\pi$
$383$	−31.5408	+	0.971762i	−1.61166	+	0.0496547i	−0.787611	+	0.616173i	$0.788682\pi$
$384$	−1.63427	−	2.16412i	−0.0833985	−	0.110437i
$385$	−1.26701	−	8.16223i	−0.0645730	−	0.415986i
$386$	0.791658	−	5.09994i	0.0402943	−	0.259580i
$387$	−4.05602	+	0.888281i	−0.206179	+	0.0451539i
$388$	−3.01760	−	9.48565i	−0.153196	−	0.481561i
$389$	−5.40358	+	24.6735i	−0.273972	+	1.25100i	0.613337	+	0.789821i	$0.289827\pi$
$389$	−5.40358	+	24.6735i	−0.273972	+	1.25100i	−0.887309	+	0.461175i	$0.847428\pi$
$390$	−9.69531	−	7.32156i	−0.490941	−	0.370741i
$391$	0.717402	+	0.228222i	0.0362806	+	0.0115417i
$392$	6.17476	−	39.7785i	0.311873	−	2.00912i
$393$	33.6269	−	18.0573i	1.69625	−	0.910869i
$394$	−14.3086	−	11.5141i	−0.720857	−	0.580072i
$395$	7.01386	−	5.29662i	0.352905	−	0.266502i
$396$	8.74117	+	0.809989i	0.439260	+	0.0407035i
$397$	−0.237815	−	7.71883i	−0.0119356	−	0.387397i	−0.986545	−	0.163487i	$-0.947726\pi$
$397$	−0.237815	−	7.71883i	−0.0119356	−	0.387397i	0.974610	−	0.223910i	$-0.0718821\pi$
$398$	−7.99122	+	0.740496i	−0.400564	+	0.0371177i
$399$	28.7776	−	81.6649i	1.44068	−	4.08836i
$400$	−7.37547	−	3.39326i	−0.368774	−	0.169663i
$401$	20.8620	−	8.08200i	1.04180	−	0.403596i	0.221278	−	0.975211i	$-0.428977\pi$
$401$	20.8620	−	8.08200i	1.04180	−	0.403596i	0.820522	+	0.571615i	$0.193683\pi$
$402$	1.54644	−	0.892840i	0.0771296	−	0.0445308i
$403$	−3.39522	+	36.6402i	−0.169128	+	1.82518i
$404$	−5.07266	+	10.1873i	−0.252374	+	0.506836i
$405$	0.268142	−	0.0674405i	0.0133241	−	0.00335114i
$406$	−4.23134	+	19.3209i	−0.209998	+	0.958879i
$407$	1.25327	−	0.155189i	0.0621225	−	0.00769244i
$408$	62.3284			3.08571
$409$	18.8365	+	7.36118i	0.931404	+	0.363987i
$409$	18.8365	+	7.36118i	0.931404	+	0.363987i
$410$	−1.07795			−0.0532361
$411$	23.5498	−	2.91610i	1.16163	−	0.143840i
$412$	1.94945	−	8.90145i	0.0960424	−	0.438543i
$413$	−0.104963	+	0.0263994i	−0.00516491	+	0.00129903i
$414$	−0.252734	+	0.507558i	−0.0124212	+	0.0249451i
$415$	0.709843	−	7.66042i	0.0348448	−	0.376035i
$416$	−17.3483	+	10.0161i	−0.850572	+	0.491078i
$417$	−11.1715	+	4.32787i	−0.547072	+	0.211937i
$418$	16.0175	+	7.36922i	0.783442	+	0.360440i
$419$	6.55503	−	18.6018i	0.320234	−	0.908758i	−0.666370	−	0.745622i	$-0.732153\pi$
$419$	6.55503	−	18.6018i	0.320234	−	0.908758i	0.986604	−	0.163136i	$-0.0521611\pi$
$420$	−7.70895	+	0.714339i	−0.376158	+	0.0348562i
$421$	0.301869	+	9.79786i	0.0147122	+	0.477519i	0.977946	+	0.208856i	$0.0669739\pi$
$421$	0.301869	+	9.79786i	0.0147122	+	0.477519i	−0.963234	+	0.268663i	$0.913418\pi$
$422$	20.8382	+	1.93095i	1.01439	+	0.0939970i
$423$	13.4237	−	10.1371i	0.652682	−	0.492883i
$424$	−22.5321	−	18.1315i	−1.09426	−	0.880544i
$425$	27.7705	−	14.9124i	1.34707	−	0.723360i
$426$	−6.53512	+	42.0999i	−0.316627	+	2.03975i
$427$	−17.4324	−	5.54563i	−0.843611	−	0.268372i
$428$	−3.03546	−	2.29228i	−0.146725	−	0.110801i
$429$	−6.83591	+	31.2137i	−0.330041	+	1.50701i
$430$	0.226044	+	0.710556i	0.0109008	+	0.0342661i
$431$	28.4566	−	6.23209i	1.37071	−	0.300189i	0.532909	−	0.846172i	$-0.321099\pi$
$431$	28.4566	−	6.23209i	1.37071	−	0.300189i	0.837796	+	0.545983i	$0.183844\pi$
$432$	−1.52757	+	9.84079i	−0.0734954	+	0.473465i
$433$	4.14149	+	26.6799i	0.199027	+	1.28216i	0.851505	+	0.524347i	$0.175691\pi$
$433$	4.14149	+	26.6799i	0.199027	+	1.28216i	−0.652477	+	0.757808i	$0.726270\pi$
$434$	−22.4604	−	29.7424i	−1.07813	−	1.42768i
$435$	8.89583	−	0.274078i	0.426523	−	0.0131410i
$436$	8.20845	−	10.8697i	0.393113	−	0.520566i
$437$	0.514361	−	0.498758i	0.0246052	−	0.0238588i
$438$	13.4187	−	11.4964i	0.641170	−	0.549321i
$439$	−21.2257	−	13.1424i	−1.01305	−	0.627252i	−0.0837117	−	0.996490i	$-0.526677\pi$
$439$	−21.2257	−	13.1424i	−1.01305	−	0.627252i	−0.929335	+	0.369238i	$0.879619\pi$
$440$		−	5.65866i		−	0.269766i
$441$	−52.4706	+	37.1432i	−2.49860	+	1.76872i
$442$	−4.81966	+	38.9226i	−0.229248	+	1.85136i
$443$	−0.796585	+	25.8550i	−0.0378469	+	1.22841i	0.769622	+	0.638500i	$0.220445\pi$
$443$	−0.796585	+	25.8550i	−0.0378469	+	1.22841i	−0.807469	+	0.589910i	$0.799163\pi$
$444$	−0.0728665	−	1.18140i	−0.00345809	−	0.0560670i
$445$	7.77775	+	1.45391i	0.368701	+	0.0689221i
$446$	24.1774	−	0.744898i	1.14483	−	0.0352720i
$447$	15.2686	+	8.81530i	0.722178	+	0.416950i
$448$	11.2040	−	35.2190i	0.529338	−	1.66394i
$449$	−0.380707	+	4.10848i	−0.0179667	+	0.193891i	0.982020	+	0.188776i	$0.0604519\pi$
$449$	−0.380707	+	4.10848i	−0.0179667	+	0.193891i	−0.999987	+	0.00511563i	$0.998372\pi$
$450$	7.89026	+	22.3909i	0.371950	+	1.05552i
$451$	1.18496	+	2.57558i	0.0557974	+	0.121279i
$452$	6.29009	−	4.75006i	0.295861	−	0.223424i
$453$	−59.6329	+	21.0138i	−2.80180	+	0.987316i
$454$	8.54388	−	6.87524i	0.400984	−	0.322671i
$455$	0.538494	−	17.4781i	0.0252450	−	0.819385i
$456$	28.0630	−	52.2599i	1.31417	−	2.44730i
$457$	−9.82284	−	34.5237i	−0.459493	−	1.61495i	−0.752329	−	0.658788i	$-0.771070\pi$
$457$	−9.82284	−	34.5237i	−0.459493	−	1.61495i	0.292836	−	0.956163i	$-0.405401\pi$
$458$	−13.3967	+	23.2038i	−0.625988	+	1.08424i
$459$	−26.9162	−	27.7582i	−1.25634	−	1.29564i
$460$	−0.0597354	−	0.0231416i	−0.00278518	−	0.00107898i
$461$	−5.41439	+	0.840468i	−0.252173	+	0.0391445i	−0.278224	−	0.960516i	$-0.589746\pi$
$461$	−5.41439	+	0.840468i	−0.252173	+	0.0391445i	0.0260513	+	0.999661i	$0.491707\pi$
$462$	−16.1822	−	28.0284i	−0.752864	−	1.30400i
$463$	−8.83015	+	15.2943i	−0.410372	+	0.710785i	−0.994930	−	0.100566i	$-0.967934\pi$
$463$	−8.83015	+	15.2943i	−0.410372	+	0.710785i	0.584558	+	0.811352i	$0.301268\pi$
$464$	−2.67317	+	6.90025i	−0.124099	+	0.320336i
$465$	−10.5141	+	13.0659i	−0.487579	+	0.605916i
$466$	14.0031	−	11.9972i	0.648683	−	0.555758i
$467$	−19.1613	+	21.0189i	−0.886678	+	0.972639i	−0.999781	−	0.0209443i	$-0.993333\pi$
$467$	−19.1613	+	21.0189i	−0.886678	+	0.972639i	0.113103	+	0.993583i	$0.463921\pi$
$468$	17.8749	+	5.08584i	0.826266	+	0.235093i
$469$	2.33487	+	1.07421i	0.107814	+	0.0496024i
$470$	−2.03509	−	2.23238i	−0.0938716	−	0.102972i
$471$	−2.39075	−	19.3072i	−0.110160	−	0.889630i
$472$	−0.0738304	+	0.00684139i	−0.00339832	+	0.000314901i
$473$	1.44927	−	1.32119i	0.0666377	−	0.0607483i
$474$	18.1291	−	29.2794i	0.832695	−	1.34485i
$475$		−	29.9987i		−	1.37644i
$476$	14.4400	+	20.3987i	0.661855	+	0.934974i
$477$	4.26162	+	45.9902i	0.195126	+	2.10575i
$478$	−21.8342	−	8.45862i	−0.998674	−	0.386888i
$479$	5.00356	+	26.7667i	0.228618	+	1.22300i	0.883922	+	0.467635i	$0.154894\pi$
$479$	5.00356	+	26.7667i	0.228618	+	1.22300i	−0.655303	+	0.755366i	$0.727459\pi$
$480$	−9.11265	−	0.562049i	−0.415934	−	0.0256539i
$481$	2.66837	+	0.164579i	0.121667	+	0.00750418i
$482$	11.3826	+	11.0373i	0.518462	+	0.502734i
$483$	−1.29959	+	0.201734i	−0.0591336	+	0.00917923i
$484$	3.95162	−	1.81803i	0.179619	−	0.0826378i
$485$	9.43638	+	3.99408i	0.428484	+	0.181362i
$486$	−13.6515	+	9.66369i	−0.619244	+	0.438354i
$487$	7.07675	−	37.8573i	0.320678	−	1.71548i	−0.319787	−	0.947489i	$-0.603611\pi$
$487$	7.07675	−	37.8573i	0.320678	−	1.71548i	0.640465	−	0.767987i	$-0.278742\pi$
$488$	−11.2183	−	5.58604i	−0.507827	−	0.252868i
$489$	1.00013	+	32.4616i	0.0452275	+	1.46796i
$490$	7.51115	+	8.76706i	0.339319	+	0.396055i
$491$	4.49165	+	9.02044i	0.202705	+	0.407087i	0.973068	−	0.230519i	$-0.0740425\pi$
$491$	4.49165	+	9.02044i	0.202705	+	0.407087i	−0.770363	+	0.637606i	$0.779925\pi$
$492$	2.47785	−	0.959925i	0.111710	−	0.0432768i
$493$	−15.1249	−	24.4275i	−0.681190	−	1.10016i
$494$	30.4650	+	21.5658i	1.37069	+	0.970289i
$495$	−6.48765	+	6.29084i	−0.291598	+	0.282752i
$496$	−6.59690	−	12.2850i	−0.296209	−	0.551612i
$497$	−54.8914	+	27.3327i	−2.46221	+	1.22604i
$498$	−8.24924	−	28.9931i	−0.369657	−	1.29921i
$499$	−28.3419	+	29.2286i	−1.26876	+	1.30845i	−0.338766	+	0.940871i	$0.610009\pi$
$499$	−28.3419	+	29.2286i	−1.26876	+	1.30845i	−0.929992	+	0.367579i	$0.880187\pi$
$500$	−5.22616	+	2.40442i	−0.233721	+	0.107529i
$501$	−4.92155	−	53.1120i	−0.219879	−	2.37287i
$502$	4.72227	+	1.03419i	0.210765	+	0.0461583i
$503$	−11.2188	+	28.9591i	−0.500223	+	1.29122i	0.422711	+	0.906265i	$0.361079\pi$
$503$	−11.2188	+	28.9591i	−0.500223	+	1.29122i	−0.922934	+	0.384959i	$0.874215\pi$
$504$	−60.4819	+	30.1164i	−2.69408	+	1.34149i
$505$	−4.56637	−	10.7885i	−0.203201	−	0.480081i
$506$	−0.0164861	−	0.267293i	−0.000732895	−	0.0118826i
$507$	−12.1198	+	28.6343i	−0.538261	+	1.27169i
$508$	−8.57834	−	3.02289i	−0.380602	−	0.134119i
$509$	6.02865	+	4.85124i	0.267215	+	0.215027i	0.751244	−	0.660025i	$-0.229454\pi$
$509$	6.02865	+	4.85124i	0.267215	+	0.215027i	−0.484028	+	0.875052i	$0.660827\pi$
$510$	−11.6298	+	13.5744i	−0.514978	+	0.601085i
$511$	24.6643	+	6.20331i	1.09108	+	0.274418i
$512$	8.47355	−	17.0172i	0.374482	−	0.752061i
$513$	−35.3930	+	10.0702i	−1.56264	+	0.444610i
$514$	32.2863	+	5.01176i	1.42409	+	0.221059i
$515$	5.65298	+	7.48576i	0.249100	+	0.329862i
$516$	−1.15236	−	1.43204i	−0.0507298	−	0.0630422i
$517$	−3.09681	+	7.31650i	−0.136198	+	0.321779i
$518$	−2.10961	+	1.69760i	−0.0926910	+	0.0745881i
$519$	1.58910	−	6.31824i	0.0697538	−	0.277340i
$520$	2.20120	−	11.7754i	0.0965291	−	0.516385i
$521$	8.52115	−	13.7621i	0.373318	−	0.602930i	−0.608318	−	0.793694i	$-0.708155\pi$
$521$	8.52115	−	13.7621i	0.373318	−	0.602930i	0.981636	+	0.190764i	$0.0610965\pi$
$522$	19.9274	−	8.43456i	0.872200	−	0.369171i
$523$	14.7533	−	16.1836i	0.645118	−	0.707661i	−0.326239	−	0.945287i	$-0.605781\pi$
$523$	14.7533	−	16.1836i	0.645118	−	0.707661i	0.971357	+	0.237627i	$0.0763695\pi$
$524$	8.55769	+	6.05787i	0.373845	+	0.264639i
$525$	−31.8157	+	44.9447i	−1.38855	+	1.96155i
$526$	−13.5023	−	7.79557i	−0.588730	−	0.339903i
$527$	53.4986	+	8.30453i	2.33044	+	0.361751i
$528$	−4.37416	−	11.2910i	−0.190361	−	0.491378i
$529$	21.9073	+	6.96921i	0.952491	+	0.303009i
$530$	8.15310	−	1.52408i	0.354148	−	0.0662017i
$531$	0.0899223	+	0.0770407i	0.00390230	+	0.00334328i
$532$	23.6051	−	2.92294i	1.02341	−	0.126726i
$533$	1.46394	+	5.82061i	0.0634103	+	0.252118i
$534$	30.4749	−	5.69674i	1.31878	−	0.246522i
$535$	3.82498	−	0.837685i	0.165369	−	0.0362163i
$536$	1.46773	+	0.972555i	0.0633964	+	0.0420080i
$537$	−4.62950	+	5.40357i	−0.199778	+	0.233181i
$538$	6.02808	+	13.1025i	0.259889	+	0.564887i
$539$	12.6907	−	27.5840i	0.546626	−	1.18813i
$540$	2.14066	+	2.49859i	0.0921192	+	0.107522i
$541$	−1.17094	−	9.45628i	−0.0503427	−	0.406557i	−0.996550	−	0.0829960i	$-0.973551\pi$
$541$	−1.17094	−	9.45628i	−0.0503427	−	0.406557i	0.946207	−	0.323561i	$-0.104880\pi$
$542$	0.749178	+	0.0927683i	0.0321799	+	0.00398474i
$543$	2.67166	+	2.93067i	0.114652	+	0.125767i
$544$	13.1373	+	26.3832i	0.563257	+	1.13117i
$545$	2.99968	+	13.6970i	0.128492	+	0.586713i
$546$	−22.7714	−	64.6205i	−0.974526	−	2.76550i
$547$	11.8623	+	2.98348i	0.507194	+	0.127564i	0.489024	−	0.872270i	$-0.337353\pi$
$547$	11.8623	+	2.98348i	0.507194	+	0.127564i	0.0181703	+	0.999835i	$0.494216\pi$
$548$	3.60060	+	5.43384i	0.153810	+	0.232122i
$549$	6.06719	+	19.0718i	0.258941	+	0.813966i
$550$	−8.51513	−	7.29532i	−0.363086	−	0.311073i
$551$	−27.2914	+	1.68328i	−1.16265	+	0.0717099i
$552$	−0.900974			−0.0383480
$553$	49.4719	−	3.05132i	2.10376	−	0.129755i
$554$	7.30204	+	29.0328i	0.310234	+	1.23348i
$555$	0.972355	+	0.734289i	0.0412742	+	0.0311688i
$556$	−2.43211	−	2.21716i	−0.103144	−	0.0940285i
$557$	−13.5122	+	3.84455i	−0.572530	+	0.162899i	−0.547526	−	0.836789i	$-0.684430\pi$
$557$	−13.5122	+	3.84455i	−0.572530	+	0.162899i	−0.0250036	+	0.999687i	$0.507960\pi$
$558$	−12.3612	+	38.8568i	−0.523293	+	1.64494i
$559$	3.52981	−	2.18556i	0.149295	−	0.0924395i
$560$	3.48835	+	5.63388i	0.147410	+	0.238075i
$561$	45.2182	+	12.8657i	1.90911	+	0.543190i
$562$	−17.0235	+	25.6911i	−0.718094	+	1.08371i
$563$	14.9622	−	13.6399i	0.630582	−	0.574852i	−0.294013	−	0.955801i	$-0.594991\pi$
$563$	14.9622	−	13.6399i	0.630582	−	0.574852i	0.924596	+	0.380949i	$0.124403\pi$
$564$	6.66597	+	3.31926i	0.280688	+	0.139766i
$565$	−0.499505	+	8.09860i	−0.0210143	+	0.340711i
$566$	−11.0220	+	3.88401i	−0.463290	+	0.163257i
$567$	1.47064	+	0.518233i	0.0617610	+	0.0217637i
$568$	−40.0316	+	12.7350i	−1.67969	+	0.534347i
$569$	−1.18914	−	7.66055i	−0.0498512	−	0.321147i	−0.999957	−	0.00922059i	$-0.997065\pi$
$569$	−1.18914	−	7.66055i	−0.0498512	−	0.321147i	0.950106	−	0.311926i	$-0.100974\pi$
$570$	6.14535	+	15.8630i	0.257400	+	0.664427i
$571$	−9.30210	−	8.47999i	−0.389281	−	0.354876i	0.455268	−	0.890354i	$-0.349543\pi$
$571$	−9.30210	−	8.47999i	−0.389281	−	0.354876i	−0.844549	+	0.535478i	$0.820132\pi$
$572$	−8.51247	+	2.14097i	−0.355924	+	0.0895186i
$573$	−4.61078	−	6.95836i	−0.192618	−	0.290690i
$574$	−5.06752	−	3.35786i	−0.211514	−	0.140154i
$575$	−0.401430	+	0.215563i	−0.0167408	+	0.00898962i
$576$	−38.5313	+	12.2577i	−1.60547	+	0.510737i
$577$	−14.9784	−	18.6137i	−0.623558	−	0.774898i	0.364128	−	0.931349i	$-0.381367\pi$
$577$	−14.9784	−	18.6137i	−0.623558	−	0.774898i	−0.987686	+	0.156451i	$0.949995\pi$
$578$	38.2062	+	7.14198i	1.58917	+	0.297067i
$579$	−11.5385	−	6.19604i	−0.479523	−	0.257499i
$580$	1.15663	+	2.15393i	0.0480267	+	0.0894370i
$581$	27.1996	−	33.8011i	1.12843	−	1.40230i
$582$	40.1303	+	1.23640i	1.66346	+	0.0512505i
$583$	−12.6040	−	17.8051i	−0.522004	−	0.737413i
$584$	16.0449	+	6.79122i	0.663942	+	0.281023i
$585$	−15.9476	+	10.5673i	−0.659352	+	0.436902i
$586$	5.59495	−	10.4191i	0.231125	−	0.430410i
$587$	6.75596	+	15.9616i	0.278848	+	0.658805i	0.999401	−	0.0345945i	$-0.0110140\pi$
$587$	6.75596	+	15.9616i	0.278848	+	0.658805i	−0.720553	+	0.693400i	$0.756112\pi$
$588$	−25.0729	−	13.4638i	−1.03399	−	0.555240i
$589$	31.0505	−	41.1175i	1.27941	−	1.69422i
$590$	0.0122860	−	0.0173560i	0.000505808	−	0.000714533i
$591$	−39.6256	+	24.5352i	−1.62998	+	1.00924i
$592$	−0.877363	+	0.506546i	−0.0360594	+	0.0208189i
$593$	4.32684	+	19.7569i	0.177682	+	0.811320i	0.977476	+	0.211046i	$0.0676870\pi$
$593$	4.32684	+	19.7569i	0.177682	+	0.811320i	−0.799794	+	0.600274i	$0.795058\pi$
$594$	−5.74873	+	12.4952i	−0.235873	+	0.512686i
$595$	−25.6178	−	2.37384i	−1.05023	−	0.0973178i
$596$	−0.298146	+	4.83392i	−0.0122125	+	0.198005i
$597$	−4.96749	+	19.7507i	−0.203306	+	0.808341i
$598$	0.0696695	−	0.562636i	0.00284900	−	0.0230079i
$599$	−14.5063	+	9.61225i	−0.592713	+	0.392746i	−0.812636	−	0.582771i	$-0.801968\pi$
$599$	−14.5063	+	9.61225i	−0.592713	+	0.392746i	0.219923	+	0.975517i	$0.429419\pi$
$600$	−26.2610	+	27.0825i	−1.07210	+	1.10564i
$601$	−7.74673	−	13.4177i	−0.315996	−	0.547320i	0.663653	−	0.748041i	$-0.269005\pi$
$601$	−7.74673	−	13.4177i	−0.315996	−	0.547320i	−0.979649	+	0.200720i	$0.935672\pi$
$602$	−1.15076	+	4.04452i	−0.0469017	+	0.164842i
$603$	−0.516674	−	2.76396i	−0.0210406	−	0.112557i
$604$	−12.4690	−	12.0907i	−0.507356	−	0.491965i
$605$	−1.22538	+	4.30678i	−0.0498190	+	0.175095i
$606$	−31.9541	−	32.9537i	−1.29805	−	1.33865i
$607$	4.21573	+	0.923258i	0.171111	+	0.0374739i	0.298667	−	0.954358i	$-0.403458\pi$
$607$	4.21573	+	0.923258i	0.171111	+	0.0374739i	−0.127555	+	0.991831i	$0.540713\pi$
$608$	28.0363	+	0.863789i	1.13702	+	0.0350313i
$609$	42.6738	+	26.4225i	1.72923	+	1.07069i
$610$	3.30979	−	1.40091i	0.134010	−	0.0567214i
$611$	−9.29041	+	14.0206i	−0.375850	+	0.567214i
$612$	9.08755	−	25.7886i	0.367342	−	1.04244i
$613$	−1.19498	−	0.147970i	−0.0482647	−	0.00597646i	0.0987196	−	0.995115i	$-0.468525\pi$
$613$	−1.19498	−	0.147970i	−0.0482647	−	0.00597646i	−0.146984	+	0.989139i	$0.546957\pi$
$614$	−2.87040	−	0.355432i	−0.115840	−	0.0143441i
$615$	−0.909141	+	2.57996i	−0.0366601	+	0.104034i
$616$	17.6270	−	26.6018i	0.710212	−	1.07182i
$617$	−29.9501	+	12.6768i	−1.20575	+	0.510348i	−0.897524	−	0.440966i	$-0.854636\pi$
$617$	−29.9501	+	12.6768i	−1.20575	+	0.510348i	−0.308222	+	0.951314i	$0.599734\pi$
$618$	31.2494	+	19.3488i	1.25703	+	0.778323i
$619$	−5.88644	−	0.181359i	−0.236596	−	0.00728944i	−0.0877193	−	0.996145i	$-0.527958\pi$
$619$	−5.88644	−	0.181359i	−0.236596	−	0.00728944i	−0.148877	+	0.988856i	$0.547566\pi$
$620$	−4.50029	−	0.985579i	−0.180736	−	0.0395818i
$621$	0.389081	+	0.401253i	0.0156133	+	0.0161017i
$622$	4.45641	−	15.6626i	0.178686	−	0.628015i
$623$	32.0348	+	31.0630i	1.28345	+	1.24451i
$624$	−4.71024	−	25.1976i	−0.188560	−	1.00871i
$625$	−4.35597	+	15.3096i	−0.174239	+	0.612386i
$626$	−0.166143	−	0.287769i	−0.00664042	−	0.0115015i
$627$	31.1466	−	32.1210i	1.24388	−	1.28279i
$628$	4.45492	−	2.95193i	0.177771	−	0.117795i
$629$	0.483370	−	3.90360i	0.0192732	−	0.155647i
$630$	4.72630	−	18.7917i	0.188300	−	0.748679i
$631$	−1.40113	+	22.7169i	−0.0557781	+	0.904346i	0.861914	+	0.507054i	$0.169266\pi$
$631$	−1.40113	+	22.7169i	−0.0557781	+	0.904346i	−0.917692	+	0.397292i	$0.869950\pi$
$632$	33.8112	+	3.13307i	1.34494	+	0.124627i
$633$	22.1965	−	48.2456i	0.882231	−	1.91759i
$634$	−1.89279	−	8.64274i	−0.0751723	−	0.343247i
$635$	8.10851	−	4.68145i	0.321776	−	0.185778i
$636$	−17.3841	+	10.7638i	−0.689325	+	0.426812i
$637$	37.1388	−	52.4644i	1.47149	−	2.07871i
$638$	−6.15913	+	8.15600i	−0.243842	+	0.322899i
$639$	59.1045	+	31.7384i	2.33814	+	1.25555i
$640$	0.298911	+	0.706206i	0.0118155	+	0.0279152i
$641$	−13.6258	+	25.3745i	−0.538188	+	1.00223i	0.455519	+	0.890226i	$0.349454\pi$
$641$	−13.6258	+	25.3745i	−0.538188	+	1.00223i	−0.993707	+	0.112008i	$0.964272\pi$
$642$	12.7894	−	8.47455i	0.504757	−	0.334464i
$643$	−25.7065	−	10.8806i	−1.01377	−	0.429091i	−0.181455	−	0.983399i	$-0.558081\pi$
$643$	−25.7065	−	10.8806i	−1.01377	−	0.429091i	−0.832311	+	0.554309i	$0.812983\pi$
$644$	−0.208734	−	0.294869i	−0.00822526	−	0.0116195i
$645$	1.89129	+	0.0582699i	0.0744693	+	0.00229438i
$646$	34.4287	−	42.7846i	1.35458	−	1.68334i
$647$	−8.79216	−	16.3731i	−0.345656	−	0.643692i	0.647293	−	0.762242i	$-0.275901\pi$
$647$	−8.79216	−	16.3731i	−0.345656	−	0.643692i	−0.992948	+	0.118549i	$0.962176\pi$
$648$	0.941107	+	0.505364i	0.0369702	+	0.0198526i
$649$	−0.0549749	−	0.0102766i	−0.00215795	−	0.000403391i
$650$	−14.8817	−	18.4936i	−0.583708	−	0.725377i
$651$	−90.1284	+	28.6719i	−3.53241	+	1.12374i
$652$	−7.85985	+	4.22065i	−0.307815	+	0.165293i
$653$	−15.5861	−	10.3277i	−0.609932	−	0.404156i	0.209107	−	0.977893i	$-0.432944\pi$
$653$	−15.5861	−	10.3277i	−0.609932	−	0.404156i	−0.819040	+	0.573737i	$0.805493\pi$
$654$	30.3467	+	45.7977i	1.18665	+	1.79083i
$655$	−10.4672	+	2.63262i	−0.408989	+	0.102865i
$656$	−1.68080	−	1.53225i	−0.0656241	−	0.0598243i
$657$	−10.0513	−	25.9454i	−0.392138	−	1.01223i
$658$	−2.61312	−	16.8340i	−0.101870	−	0.656258i
$659$	−37.3699	+	11.8882i	−1.45572	+	0.463099i	−0.923531	−	0.383524i	$-0.874710\pi$
$659$	−37.3699	+	11.8882i	−1.45572	+	0.463099i	−0.532193	+	0.846623i	$0.678632\pi$
$660$	−3.77311	−	1.32959i	−0.146868	−	0.0517544i
$661$	−33.6828	+	11.8694i	−1.31011	+	0.461665i	−0.894170	−	0.447727i	$-0.852234\pi$
$661$	−33.6828	+	11.8694i	−1.31011	+	0.461665i	−0.415940	+	0.909392i	$0.636547\pi$
$662$	−0.0510605	+	0.827857i	−0.00198452	+	0.0321756i
$663$	89.0921	+	44.3626i	3.46005	+	1.72290i
$664$	21.9650	−	20.0238i	0.852408	−	0.777073i
$665$	−13.5246	+	20.4107i	−0.524462	+	0.791493i
$666$	2.84940	+	0.810723i	0.110412	+	0.0314149i
$667$	0.218634	+	0.353106i	0.00846554	+	0.0136723i
$668$	12.4576	−	7.71344i	0.482000	−	0.298442i
$669$	18.6084	−	58.4943i	0.719442	−	2.26152i
$670$	−0.485676	+	0.138187i	−0.0187633	+	0.00533862i
$671$	−6.98561	−	6.36823i	−0.269677	−	0.245843i
$672$	−41.0885	−	31.0286i	−1.58502	−	1.19695i
$673$	1.95530	+	7.77424i	0.0753712	+	0.299675i	0.995837	−	0.0911475i	$-0.0290535\pi$
$673$	1.95530	+	7.77424i	0.0753712	+	0.299675i	−0.920466	+	0.390822i	$0.872191\pi$
$674$	5.84959	−	0.360790i	0.225318	−	0.0138971i
$675$	23.4020			0.900743
$676$	−8.52517	+	0.525814i	−0.327891	+	0.0202236i
$677$	21.6237	+	18.5260i	0.831065	+	0.712013i	0.960109	−	0.279626i	$-0.0902104\pi$
$677$	21.6237	+	18.5260i	0.831065	+	0.712013i	−0.129044	+	0.991639i	$0.541191\pi$
$678$	9.63794	+	30.2963i	0.370143	+	1.16352i
$679$	31.9194	+	48.1712i	1.22495	+	1.84864i
$680$	−17.0928	−	4.29901i	−0.655479	−	0.164860i
$681$	−9.24924	−	26.2474i	−0.354432	−	1.00580i
$682$	−4.12009	−	18.8129i	−0.157767	−	0.720384i
$683$	−2.78854	−	5.60014i	−0.106700	−	0.214283i	0.835378	−	0.549676i	$-0.185249\pi$
$683$	−2.78854	−	5.60014i	−0.106700	−	0.214283i	−0.942078	+	0.335392i	$0.891131\pi$
$684$	−17.5311	−	19.2307i	−0.670319	−	0.735305i
$685$	−6.65938	−	0.824610i	−0.254442	−	0.0315067i
$686$	3.72712	+	30.0995i	0.142302	+	1.14920i
$687$	44.2371	+	51.6338i	1.68775	+	1.96995i
$688$	−0.657559	+	1.42925i	−0.0250692	+	0.0544896i
$689$	−19.3021	−	41.9545i	−0.735353	−	1.59834i
$690$	0.168113	−	0.196222i	0.00639994	−	0.00747004i
$691$	18.9218	+	12.5380i	0.719819	+	0.476969i	0.858138	−	0.513418i	$-0.171621\pi$
$691$	18.9218	+	12.5380i	0.719819	+	0.476969i	−0.138320	+	0.990388i	$0.544170\pi$
$692$	1.74823	−	0.382869i	0.0664578	−	0.0145545i
$693$	−50.0952	+	9.36442i	−1.90296	+	0.355725i
$694$	1.83998	+	7.31572i	0.0698446	+	0.277701i
$695$	3.36216	−	0.416326i	0.127534	−	0.0157921i
$696$	26.1119	+	22.3713i	0.989769	+	0.847983i
$697$	8.68016	−	1.62260i	0.328784	−	0.0614604i
$698$	7.01229	+	2.23077i	0.265419	+	0.0844359i
$699$	−16.9037	−	43.6335i	−0.639356	−	1.65037i
$700$	−14.9476	−	2.32029i	−0.564965	−	0.0876987i
$701$	12.9380	+	7.46973i	0.488660	+	0.282128i	0.724018	−	0.689781i	$-0.242293\pi$
$701$	12.9380	+	7.46973i	0.488660	+	0.282128i	−0.235359	+	0.971909i	$0.575626\pi$
$702$	−16.8234	+	23.7658i	−0.634959	+	0.896981i
$703$	−3.05538	−	2.16286i	−0.115236	−	0.0815738i
$704$	12.8659	−	14.1132i	0.484901	−	0.531911i
$705$	−7.05937	+	2.98797i	−0.265871	+	0.112534i
$706$	−10.6615	+	17.2189i	−0.401251	+	0.648043i
$707$	12.1398	−	64.9420i	0.456563	−	2.44239i
$708$	−0.0127859	+	0.0508365i	−0.000480524	+	0.00191055i
$709$	36.9341	−	29.7207i	1.38709	−	1.11619i	0.407947	−	0.913005i	$-0.366245\pi$
$709$	36.9341	−	29.7207i	1.38709	−	1.11619i	0.979141	−	0.203181i	$-0.0651279\pi$
$710$	4.69596	−	11.0946i	0.176236	−	0.416374i
$711$	−33.9965	−	42.2476i	−1.27497	−	1.58441i
$712$	18.4221	+	24.3948i	0.690397	+	0.914234i
$713$	−0.773337	−	0.120044i	−0.0289617	−	0.00449569i
$714$	−96.9578	+	27.5869i	−3.62855	+	1.03241i
$715$	4.02759	−	8.08848i	0.150623	−	0.302492i
$716$	−1.89559	−	0.476761i	−0.0708416	−	0.0178174i
$717$	−38.6598	+	45.1239i	−1.44378	+	1.68518i
$718$	2.61435	+	2.10376i	0.0975668	+	0.0785117i
$719$	9.66682	+	3.40645i	0.360511	+	0.127039i	0.506484	−	0.862249i	$-0.330945\pi$
$719$	9.66682	+	3.40645i	0.360511	+	0.127039i	−0.145973	+	0.989289i	$0.546631\pi$
$720$	2.82579	−	6.67620i	0.105311	−	0.248807i
$721$	3.25662	+	52.8004i	0.121283	+	1.96639i
$722$	−12.1663	−	28.7439i	−0.452782	−	1.06974i
$723$	36.0166	−	17.9341i	1.33947	−	0.666977i
$724$	−0.393525	+	1.01580i	−0.0146252	+	0.0377521i
$725$	16.9867	+	3.72014i	0.630869	+	0.138163i
$726$	1.61882	+	17.4698i	0.0600799	+	0.648365i
$727$	14.0282	−	6.45398i	0.520276	−	0.239365i	−0.140321	−	0.990106i	$-0.544813\pi$
$727$	14.0282	−	6.45398i	0.520276	−	0.239365i	0.660596	+	0.750741i	$0.270304\pi$
$728$	47.0289	−	48.5002i	1.74301	−	1.79754i
$729$	11.9009	+	41.8272i	0.440772	+	1.54915i
$730$	−4.47286	+	2.22722i	−0.165548	+	0.0824332i
$731$	−2.88979	−	5.38148i	−0.106883	−	0.199041i
$732$	−6.36060	+	6.16765i	−0.235095	+	0.227963i
$733$	−34.1852	−	24.1992i	−1.26266	−	0.893817i	−0.265138	−	0.964210i	$-0.585418\pi$
$733$	−34.1852	−	24.1992i	−1.26266	−	0.893817i	−0.997519	+	0.0703938i	$0.977574\pi$
$734$	15.9742	+	25.7993i	0.589620	+	0.952269i
$735$	27.3179	−	10.5830i	1.00764	−	0.390361i
$736$	−0.189903	−	0.381377i	−0.00699992	−	0.0140577i
$737$	0.864063	+	1.00854i	0.0318282	+	0.0371500i
$738$	0.204811	+	6.64763i	0.00753921	+	0.244703i
$739$	11.4619	+	5.70732i	0.421631	+	0.209947i	0.644017	−	0.765011i	$-0.277267\pi$
$739$	11.4619	+	5.70732i	0.421631	+	0.209947i	−0.222386	+	0.974959i	$0.571384\pi$
$740$	−0.0615029	+	0.329011i	−0.00226089	+	0.0120947i
$741$	77.3095	−	54.7263i	2.84004	−	2.01042i
$742$	43.0759	+	18.2325i	1.58137	+	0.669335i
$743$	24.2837	−	11.1723i	0.890882	−	0.409871i	0.0811715	−	0.996700i	$-0.474134\pi$
$743$	24.2837	−	11.1723i	0.890882	−	0.409871i	0.809711	+	0.586829i	$0.199624\pi$
$744$	−64.0264	+	9.93873i	−2.34732	+	0.364372i
$745$	−3.57919	−	3.47062i	−0.131131	−	0.127154i
$746$	6.95085	+	0.428714i	0.254489	+	0.0156963i
$747$	−47.3762	−	2.92206i	−1.73340	−	0.106913i
$748$	2.37301	+	12.6945i	0.0867659	+	0.464156i
$749$	20.5910	+	7.97699i	0.752378	+	0.291473i
$750$	−2.14094	−	23.1045i	−0.0781762	−	0.843656i
$751$	4.92783	+	6.96134i	0.179819	+	0.254023i	0.896164	−	0.443724i	$-0.146343\pi$
$751$	4.92783	+	6.96134i	0.179819	+	0.254023i	−0.716344	+	0.697747i	$0.754186\pi$
$752$		−	6.37363i		−	0.232422i
$753$	6.45799	−	10.4300i	0.235342	−	0.380091i
$754$	−15.9895	+	14.5764i	−0.582303	+	0.530839i
$755$	17.8030	−	1.64969i	0.647917	−	0.0600384i
$756$	2.28018	+	18.4143i	0.0829295	+	0.669721i
$757$	28.8986	+	31.7002i	1.05034	+	1.15216i	0.988054	+	0.154106i	$0.0492497\pi$
$757$	28.8986	+	31.7002i	1.05034	+	1.15216i	0.0622825	+	0.998059i	$0.480162\pi$
$758$	−36.6891	−	16.8797i	−1.33261	−	0.613097i
$759$	−0.653641	−	0.185977i	−0.0237257	−	0.00675054i
$760$	−11.3005	+	12.3960i	−0.409912	+	0.449652i
$761$	−6.46494	+	5.53882i	−0.234354	+	0.200782i	−0.760003	−	0.649919i	$-0.774803\pi$
$761$	−6.46494	+	5.53882i	−0.234354	+	0.200782i	0.525649	+	0.850701i	$0.323822\pi$
$762$	22.9992	−	28.5812i	0.833174	−	1.03539i
$763$	−28.5649	+	73.7346i	−1.03412	+	2.66937i
$764$	1.14650	−	1.98580i	0.0414790	−	0.0718437i
$765$	14.0736	+	24.3762i	0.508831	+	0.881322i
$766$	34.5496	−	5.36309i	1.24833	−	0.193776i
$767$	−0.110402	−	0.0427701i	−0.00398640	−	0.00154434i
$768$	−30.1746	−	31.1186i	−1.08883	−	1.12289i
$769$	5.77038	−	9.99459i	0.208085	−	0.360414i	−0.743026	−	0.669262i	$-0.766610\pi$
$769$	5.77038	−	9.99459i	0.208085	−	0.360414i	0.951111	+	0.308848i	$0.0999435\pi$
$770$	2.50455	+	8.80259i	0.0902578	+	0.317223i
$771$	39.2253	−	73.0469i	1.41267	−	2.63072i
$772$	0.110791	−	3.59598i	0.00398746	−	0.129422i
$773$	9.01791	−	7.25668i	0.324351	−	0.261005i	−0.451015	−	0.892516i	$-0.648938\pi$
$773$	9.01791	−	7.25668i	0.324351	−	0.261005i	0.775366	+	0.631512i	$0.217565\pi$
$774$	4.33900	−	1.52901i	0.155962	−	0.0549590i
$775$	−26.1492	+	19.7469i	−0.939305	+	0.709330i
$776$	16.5462	+	35.9643i	0.593974	+	1.29104i
$777$	2.28377	+	6.48088i	0.0819300	+	0.232500i
$778$	2.58221	−	27.8664i	0.0925766	−	0.999060i
$779$	2.54770	−	8.00854i	0.0912808	−	0.286936i
$780$	−7.33446	−	4.23455i	−0.262616	−	0.151621i
$781$	−31.6710	+	0.975772i	−1.13328	+	0.0349159i
$782$	−0.819921	−	0.153270i	−0.0293203	−	0.00548092i
$783$	−1.31312	−	21.2900i	−0.0469271	−	0.760842i
$784$	−0.750117	+	24.3468i	−0.0267899	+	0.869528i
$785$	−0.676053	+	5.45967i	−0.0241294	+	0.194864i
$786$	−34.5171	+	24.4342i	−1.23119	+	0.871538i
$787$		−	38.3466i		−	1.36691i	−0.729994	−	0.683454i	$-0.760477\pi$
$787$		−	38.3466i		−	1.36691i	0.729994	−	0.683454i	$-0.239523\pi$
$788$	−10.8851	−	6.73978i	−0.387766	−	0.240095i
$789$	−30.0457	+	25.7416i	−1.06966	+	0.916426i
$790$	−6.99118	+	6.77910i	−0.248735	+	0.241190i
$791$	−27.5757	+	36.5162i	−0.980480	+	1.29837i
$792$	−34.8966	+	1.07515i	−1.24000	+	0.0382038i
$793$	−12.0595	−	15.9693i	−0.428245	−	0.567088i
$794$	1.31248	+	8.45516i	0.0465783	+	0.300063i
$795$	3.22860	−	20.7990i	0.114507	−	0.737664i
$796$	−5.46493	+	1.19684i	−0.193699	+	0.0424208i
$797$	−3.49960	−	11.0008i	−0.123962	−	0.389667i	0.870831	−	0.491582i	$-0.163581\pi$
$797$	−3.49960	−	11.0008i	−0.123962	−	0.389667i	−0.994793	+	0.101915i	$0.967503\pi$
$798$	−20.5242	+	93.7162i	−0.726547	+	3.31752i
$799$	19.7478	+	14.9129i	0.698628	+	0.527579i
$800$	−16.9990	−	5.40778i	−0.601007	−	0.191194i
$801$	7.48840	−	48.2411i	0.264590	−	1.70452i
$802$	−21.8392	+	11.7274i	−0.771170	+	0.414110i
$803$	10.2385	+	8.23886i	0.361308	+	0.290743i
$804$	0.993353	−	0.750146i	0.0350329	−	0.0264556i
$805$	0.370312	+	0.0343145i	0.0130518	+	0.00120943i
$806$	−1.25554	−	40.7515i	−0.0442245	−	1.43541i
$807$	36.4434	−	3.37698i	1.28287	−	0.118875i
$808$	15.0425	−	42.6875i	0.529193	−	1.50174i
$809$	−12.6640	−	5.82636i	−0.445242	−	0.204844i	0.182596	−	0.983188i	$-0.441550\pi$
$809$	−12.6640	−	5.82636i	−0.445242	−	0.204844i	−0.627838	+	0.778344i	$0.716060\pi$
$810$	−0.285664	+	0.110667i	−0.0100372	+	0.00388843i
$811$	−32.9361	+	19.0156i	−1.15654	+	0.667729i	−0.950473	−	0.310808i	$-0.899400\pi$
$811$	−32.9361	+	19.0156i	−1.15654	+	0.667729i	−0.206069	+	0.978538i	$0.566067\pi$
$812$	−1.27216	+	13.7288i	−0.0446439	+	0.481785i
$813$	0.853887	−	1.71484i	0.0299471	−	0.0601419i
$814$	−1.35696	+	0.341288i	−0.0475613	+	0.0119621i
$815$	1.96472	−	8.97117i	0.0688210	−	0.314246i
$816$	−37.4292	+	4.63474i	−1.31029	+	0.162248i
$817$	−5.81327			−0.203381
$818$	−21.7147	−	5.52952i	−0.759236	−	0.193335i
$819$	−107.888			−3.76992
$820$	−0.745730	+	0.0923414i	−0.0260420	+	0.00322470i
$821$	11.3608	−	51.8749i	0.396494	−	1.81045i	−0.168909	−	0.985632i	$-0.554024\pi$
$821$	11.3608	−	51.8749i	0.396494	−	1.81045i	0.565403	−	0.824815i	$-0.308721\pi$
$822$	−25.4981	+	6.41302i	−0.889347	+	0.223680i
$823$	−16.3337	+	32.8026i	−0.569358	+	1.14343i	0.404133	+	0.914700i	$0.367573\pi$
$823$	−16.3337	+	32.8026i	−0.569358	+	1.14343i	−0.973491	+	0.228725i	$0.926544\pi$
$824$	−3.34387	+	36.0861i	−0.116489	+	1.25712i
$825$	−24.6422	+	14.2272i	−0.857932	+	0.495327i
$826$	0.111822	−	0.0433201i	0.00389079	−	0.00150730i
$827$	−3.26506	−	1.50217i	−0.113537	−	0.0522355i	0.360375	−	0.932808i	$-0.382649\pi$
$827$	−3.26506	−	1.50217i	−0.113537	−	0.0522355i	−0.473912	+	0.880572i	$0.657159\pi$
$828$	−0.131363	+	0.372781i	−0.00456518	+	0.0129550i
$829$	−3.41242	+	0.316207i	−0.118518	+	0.0109823i	−0.151364	−	0.988478i	$-0.548367\pi$
$829$	−3.41242	+	0.316207i	−0.118518	+	0.0109823i	0.0328457	+	0.999460i	$0.489543\pi$
$830$	0.262497	+	8.51997i	0.00911142	+	0.295732i
$831$	75.6454	+	7.00958i	2.62411	+	0.243160i
$832$	32.2633	−	24.3641i	1.11853	−	0.844673i
$833$	−73.6802	−	59.2902i	−2.55287	−	2.05428i
$834$	11.6948	−	6.27998i	0.404958	−	0.217458i
$835$	−2.31365	+	14.9048i	−0.0800671	+	0.515801i
$836$	11.7123	+	3.72594i	0.405077	+	0.128864i
$837$	32.0757	+	24.2225i	1.10870	+	0.837250i
$838$	−4.67504	+	21.3469i	−0.161496	+	0.737415i
$839$	−12.9763	−	40.7901i	−0.447991	−	1.40823i	−0.866117	−	0.499842i	$-0.833391\pi$
$839$	−12.9763	−	40.7901i	−0.447991	−	1.40823i	0.418126	−	0.908389i	$-0.362687\pi$
$840$	30.0775	−	6.58707i	1.03777	−	0.227275i
$841$	−2.01710	+	12.9944i	−0.0695553	+	0.448083i
$842$	−1.66600	−	10.7325i	−0.0574140	−	0.369867i
$843$	47.1313	+	62.4119i	1.62329	+	2.14958i
$844$	14.5814	−	0.449248i	0.501913	−	0.0154638i
$845$	5.29872	−	7.01665i	0.182282	−	0.241380i
$846$	−13.3803	+	12.9744i	−0.460024	+	0.446069i
$847$	−19.1764	+	16.4294i	−0.658910	+	0.564520i
$848$	14.8792	+	9.21279i	0.510953	+	0.316368i
$849$			29.6558i			1.01778i
$850$	−28.5057	+	20.1788i	−0.977737	+	0.692126i
$851$	−0.00698725	+	0.0564276i	−0.000239520	+	0.00193431i
$852$	−0.914578	+	29.6848i	−0.0313329	+	1.01698i
$853$	1.08329	+	17.5636i	0.0370911	+	0.601367i	0.970281	+	0.241983i	$0.0777977\pi$
$853$	1.08329	+	17.5636i	0.0370911	+	0.601367i	−0.933190	+	0.359385i	$0.882987\pi$
$854$	19.9235	+	3.72435i	0.681768	+	0.127445i
$855$	26.7750	−	0.824929i	0.915686	−	0.0282120i
$856$	13.1010	+	7.56389i	0.447784	+	0.258528i
$857$	2.63637	−	8.28726i	0.0900565	−	0.283087i	−0.897343	−	0.441334i	$-0.854506\pi$
$857$	2.63637	−	8.28726i	0.0900565	−	0.283087i	0.987400	+	0.158246i	$0.0505840\pi$
$858$	3.26667	−	35.2530i	0.111522	−	1.20352i
$859$	6.65852	+	18.8955i	0.227186	+	0.644706i	0.999950	+	0.0100131i	$0.00318732\pi$
$859$	6.65852	+	18.8955i	0.227186	+	0.644706i	−0.772764	+	0.634693i	$0.781126\pi$
$860$	0.217248	+	0.472203i	0.00740808	+	0.0161020i
$861$	−12.3106	+	9.29655i	−0.419545	+	0.316826i
$862$	−30.4420	+	10.7273i	−1.03686	+	0.365375i
$863$	−35.9755	+	28.9494i	−1.22462	+	0.985449i	−0.224682	+	0.974432i	$0.572134\pi$
$863$	−35.9755	+	28.9494i	−1.22462	+	0.985449i	−0.999939	+	0.0110174i	$0.996493\pi$
$864$	−0.673841	+	21.8711i	−0.0229245	+	0.744070i
$865$	−0.871583	+	1.62309i	−0.0296347	+	0.0551869i
$866$	−8.18664	−	28.7731i	−0.278193	−	0.977748i
$867$	49.3166	−	85.4189i	1.67488	−	2.90098i
$868$	−18.0861	−	18.6519i	−0.613882	−	0.633087i
$869$	23.8827	+	9.25223i	0.810167	+	0.313860i
$870$	−9.74444	+	1.51262i	−0.330367	+	0.0512825i
$871$	1.40575	+	2.43484i	0.0476321	+	0.0825013i
$872$	−27.0857	+	46.9138i	−0.917236	+	1.58870i
$873$	22.8383	−	58.9524i	0.772959	−	1.99524i
$874$	−0.497676	+	0.618463i	−0.0168341	+	0.0209198i
$875$	25.3616	−	21.7285i	0.857378	−	0.734556i
$876$	8.29829	−	9.10279i	0.280373	−	0.307555i
$877$	−3.79654	−	1.08021i	−0.128200	−	0.0364761i	0.208955	−	0.977925i	$-0.432994\pi$
$877$	−3.79654	−	1.08021i	−0.128200	−	0.0364761i	−0.337155	+	0.941449i	$0.609465\pi$
$878$	25.1290	+	11.5612i	0.848062	+	0.390170i
$879$	−20.2183	−	22.1784i	−0.681946	−	0.748059i
$880$	0.420778	+	3.39812i	0.0141844	+	0.114551i
$881$	22.2839	−	2.06491i	0.750763	−	0.0695685i	0.289921	−	0.957051i	$-0.406371\pi$
$881$	22.2839	−	2.06491i	0.750763	−	0.0695685i	0.460842	+	0.887482i	$0.347547\pi$
$882$	52.6387	−	47.9865i	1.77244	−	1.61579i
$883$	12.0454	−	19.4540i	0.405361	−	0.654680i	−0.581996	−	0.813191i	$-0.697728\pi$
$883$	12.0454	−	19.4540i	0.405361	−	0.654680i	0.987357	+	0.158511i	$0.0506693\pi$
$884$			27.3397i			0.919533i
$885$	−0.0311776	−	0.0440433i	−0.00104802	−	0.00148050i
$886$	−2.64447	−	28.5384i	−0.0888427	−	0.958766i
$887$	9.58362	+	3.71271i	0.321787	+	0.124661i	0.516717	−	0.856156i	$-0.327154\pi$
$887$	9.58362	+	3.71271i	0.321787	+	0.124661i	−0.194930	+	0.980817i	$0.562448\pi$
$888$	0.864991	+	4.62729i	0.0290272	+	0.155282i
$889$	52.7017	+	3.25053i	1.76756	+	0.109019i
$890$	−8.75029	−	0.539699i	−0.293310	−	0.0180908i
$891$	0.578441	+	0.560894i	0.0193785	+	0.0187907i
$892$	16.6622	−	2.58646i	0.557893	−	0.0866011i
$893$	21.3952	−	9.84336i	0.715963	−	0.329395i
$894$	−17.9894	−	7.61426i	−0.601656	−	0.254659i
$895$	1.64229	−	1.16255i	0.0548956	−	0.0388598i
$896$	−0.794659	+	4.25105i	−0.0265477	+	0.142018i
$897$	−1.28785	−	0.641274i	−0.0430001	−	0.0214115i
$898$	−0.140784	−	4.56948i	−0.00469803	−	0.152485i
$899$	19.4321	+	22.6812i	0.648095	+	0.756460i
$900$	7.37662	+	14.8142i	0.245887	+	0.493808i
$901$	−63.3585	+	24.5452i	−2.11078	+	0.817720i
$902$	−1.65365	−	2.67074i	−0.0550606	−	0.0889259i
$903$	8.70957	+	6.16538i	0.289836	+	0.205171i
$904$	−22.5050	+	21.8223i	−0.748504	+	0.725798i
$905$	−0.530531	−	0.987975i	−0.0176355	−	0.0328414i
$906$	62.7105	−	31.2261i	2.08342	−	1.03742i
$907$	−2.46142	−	8.65098i	−0.0817300	−	0.287251i	0.910177	−	0.414220i	$-0.135946\pi$
$907$	−2.46142	−	8.65098i	−0.0817300	−	0.287251i	−0.991907	+	0.126969i	$0.959475\pi$
$908$	5.32174	−	5.48823i	0.176608	−	0.182133i
$909$	−65.6642	+	30.2103i	−2.17794	+	1.00201i
$910$	1.78767	+	19.2920i	0.0592606	+	0.639524i
$911$	19.9330	+	4.36539i	0.660409	+	0.144632i	0.531544	−	0.847030i	$-0.321612\pi$
$911$	19.9330	+	4.36539i	0.660409	+	0.144632i	0.128864	+	0.991662i	$0.458867\pi$
$912$	−12.9662	+	33.4697i	−0.429355	+	1.10829i
$913$	20.0685	−	9.99294i	0.664171	−	0.330718i
$914$	15.5018	+	36.6244i	0.512753	+	1.21143i
$915$	−0.561464	−	9.10317i	−0.0185614	−	0.300941i
$916$	−7.28020	+	17.2001i	−0.240544	+	0.568309i
$917$	−57.4080	−	20.2298i	−1.89578	−	0.668047i
$918$	33.3763	+	26.8578i	1.10158	+	0.886438i
$919$	−5.08709	+	5.93768i	−0.167808	+	0.195866i	−0.836968	−	0.547252i	$-0.815674\pi$
$919$	−5.08709	+	5.93768i	−0.167808	+	0.195866i	0.669160	+	0.743119i	$0.266654\pi$
$920$	0.247081	+	0.0621434i	0.00814602	+	0.00204881i
$921$	−3.27158	+	6.57022i	−0.107802	+	0.216496i
$922$	5.83916	−	1.66139i	0.192303	−	0.0547148i
$923$	−66.2853	−	10.2894i	−2.18181	−	0.338679i
$924$	−13.5960	−	18.0040i	−0.447274	−	0.592287i
$925$	1.49251	+	1.85474i	0.0490733	+	0.0609836i
$926$	7.62709	−	18.0197i	0.250642	−	0.592165i
$927$	45.0901	−	36.2838i	1.48095	−	1.19172i
$928$	−3.96590	+	15.7683i	−0.130187	+	0.517621i
$929$	−3.05709	+	16.3540i	−0.100300	+	0.536556i	0.895505	+	0.445052i	$0.146815\pi$
$929$	−3.05709	+	16.3540i	−0.100300	+	0.536556i	−0.995805	+	0.0915047i	$0.970832\pi$
$930$	9.78214	−	15.7987i	0.320769	−	0.518060i
$931$	−82.8866	+	35.0829i	−2.71650	+	1.14980i
$932$	8.65972	−	9.49926i	0.283659	−	0.311159i
$933$	−33.7283	−	23.8758i	−1.10422	−	0.781659i
$934$	18.2076	−	25.7211i	0.595771	−	0.841621i
$935$	−11.5131	−	6.64712i	−0.376520	−	0.217384i
$936$	−73.0362	−	11.3373i	−2.38726	−	0.370572i
$937$	−6.89522	−	17.7986i	−0.225257	−	0.581456i	0.773363	−	0.633963i	$-0.218573\pi$
$937$	−6.89522	−	17.7986i	−0.225257	−	0.581456i	−0.998621	+	0.0525074i	$0.983279\pi$
$938$	−2.71366	−	0.863276i	−0.0886040	−	0.0281870i
$939$	−0.828869	+	0.154942i	−0.0270491	+	0.00505635i
$940$	−1.59912	−	1.37004i	−0.0521575	−	0.0446858i
$941$	−17.1715	+	2.12629i	−0.559774	+	0.0693151i	−0.397787	−	0.917478i	$-0.630222\pi$
$941$	−17.1715	+	2.12629i	−0.559774	+	0.0693151i	−0.161987	+	0.986793i	$0.551790\pi$
$942$	5.25769	+	20.9045i	0.171305	+	0.681105i
$943$	−0.125474	+	0.0234552i	−0.00408600	+	0.000763805i
$944$	0.0438276	−	0.00959840i	0.00142647	−	0.000312401i
$945$	−15.9224	−	10.5506i	−0.517955	−	0.343209i
$946$	−1.41372	+	1.65010i	−0.0459639	+	0.0536492i
$947$	13.5347	+	29.4185i	0.439818	+	0.955974i	0.992462	+	0.122556i	$0.0391093\pi$
$947$	13.5347	+	29.4185i	0.439818	+	0.955974i	−0.552644	+	0.833418i	$0.686381\pi$
$948$	10.0336	−	21.8087i	0.325876	−	0.708313i
$949$	18.1009	+	21.1274i	0.587578	+	0.685825i
$950$	4.08459	+	32.9863i	0.132521	+	1.07022i
$951$	−22.2819	−	2.75909i	−0.722539	−	0.0894697i
$952$	−66.9629	−	73.4548i	−2.17028	−	2.38068i
$953$	6.37385	+	12.8004i	0.206469	+	0.414646i	0.974059	−	0.226296i	$-0.0726616\pi$
$953$	6.37385	+	12.8004i	0.206469	+	0.414646i	−0.767589	+	0.640942i	$0.778544\pi$
$954$	−10.9480	−	49.9900i	−0.354454	−	1.61849i
$955$	0.784506	+	2.22627i	0.0253860	+	0.0720403i
$956$	−15.8296	−	3.98131i	−0.511967	−	0.128765i
$957$	14.3259	+	21.6200i	0.463091	+	0.698875i
$958$	−9.14637	−	28.7511i	−0.295506	−	0.928905i
$959$	−28.7376	−	24.6208i	−0.927984	−	0.795048i
$960$	18.3914	−	1.13434i	0.593578	−	0.0366107i
$961$	−25.2803			−0.815494
$962$	−2.95652	+	0.182352i	−0.0953220	+	0.00587926i
$963$	−5.89269	−	23.4293i	−0.189889	−	0.754997i
$964$	8.82001	+	6.66056i	0.284073	+	0.214522i
$965$	2.73693	+	2.49504i	0.0881048	+	0.0803181i
$966$	1.40155	−	0.398776i	0.0450942	−	0.0128304i
$967$	17.9976	−	56.5745i	0.578765	−	1.81931i	0.00544031	−	0.999985i	$-0.498268\pi$
$967$	17.9976	−	56.5745i	0.578765	−	1.81931i	0.573325	−	0.819328i	$-0.305653\pi$
$968$	−14.7082	+	9.10691i	−0.472739	+	0.292707i
$969$	−73.3633	−	118.486i	−2.35677	−	3.80631i
$970$	−10.9200	−	3.10700i	−0.350619	−	0.0997597i
$971$	−6.09842	+	9.20344i	−0.195708	+	0.295352i	−0.918271	−	0.395952i	$-0.870415\pi$
$971$	−6.09842	+	9.20344i	−0.195708	+	0.295352i	0.722564	+	0.691304i	$0.242964\pi$
$972$	−8.61634	+	7.85483i	−0.276369	+	0.251944i
$973$	17.1027	+	8.51611i	0.548286	+	0.273014i
$974$	−2.62692	+	42.5910i	−0.0841720	+	1.36470i
$975$	−56.8136	+	20.0203i	−1.81949	+	0.641164i
$976$	7.15214	+	2.52032i	0.228934	+	0.0806734i
$977$	1.93091	−	0.614268i	0.0617754	−	0.0196522i	−0.272106	−	0.962267i	$-0.587720\pi$
$977$	1.93091	−	0.614268i	0.0617754	−	0.0196522i	0.333881	+	0.942615i	$0.391642\pi$
$978$	−5.51965	−	35.5582i	−0.176499	−	1.13703i
$979$	8.32940	+	21.5007i	0.266209	+	0.687164i
$980$	5.94728	+	5.42166i	0.189979	+	0.173189i
$981$	83.8982	−	21.1013i	2.67866	−	0.673711i
$982$	−6.16717	−	9.30720i	−0.196802	−	0.297005i
$983$	−19.6024	−	12.9890i	−0.625220	−	0.414285i	0.199444	−	0.979909i	$-0.436086\pi$
$983$	−19.6024	−	12.9890i	−0.625220	−	0.414285i	−0.824663	+	0.565624i	$0.808635\pi$
$984$	−9.31074	+	4.99976i	−0.296815	+	0.159387i
$985$	12.5591	−	3.99535i	0.400167	−	0.127302i
$986$	19.9571	+	24.8008i	0.635565	+	0.789819i
$987$	−42.4943	−	7.94356i	−1.35261	−	0.252846i
$988$	22.9233	+	12.3095i	0.729287	+	0.391619i
$989$	0.0417727	+	0.0777907i	0.00132830	+	0.00247360i
$990$	6.27719	−	7.80069i	0.199502	−	0.247922i
$991$	−49.7659	−	1.53327i	−1.58087	−	0.0487060i	−0.771585	−	0.636126i	$-0.780536\pi$
$991$	−49.7659	−	1.53327i	−1.58087	−	0.0487060i	−0.809282	+	0.587420i	$0.800144\pi$
$992$	−17.7022	−	25.0071i	−0.562045	−	0.793978i
$993$	1.93832	+	0.820422i	0.0615109	+	0.0260353i
$994$	56.6364	−	37.5286i	1.79640	−	1.19034i
$995$	2.72455	−	5.07375i	0.0863740	−	0.160849i
$996$	−8.19052	−	19.3509i	−0.259527	−	0.613156i
$997$	−6.48706	−	3.48348i	−0.205447	−	0.110323i	0.367143	−	0.930164i	$-0.380336\pi$
$997$	−6.48706	−	3.48348i	−0.205447	−	0.110323i	−0.572590	+	0.819842i	$0.694061\pi$
$998$	27.1847	−	35.9984i	0.860517	−	1.13951i
$999$	1.68724	−	2.38350i	0.0533821	−	0.0754106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	409.2.m.a.4.12	✓	1056
409.307	even	102	inner	409.2.m.a.307.12	yes	1056

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
409.2.m.a.4.12	✓	1056	1.1	even	1	trivial
409.2.m.a.307.12	yes	1056	409.307	even	102	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 409 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	409.m (of order \(102\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09959 + 0.136159i) q^{2} +(-0.601511 + 2.74659i) q^{3} +(-0.749037 + 0.188390i) q^{4} +(0.354399 - 0.711729i) q^{5} +(0.287444 - 3.10202i) q^{6} +(3.88313 - 2.24192i) q^{7} +(2.86432 - 1.10964i) q^{8} +(-4.45652 - 2.05032i) q^{9} +(-0.292785 + 0.830864i) q^{10} +(2.30706 - 0.213781i) q^{11} +(-0.0668759 - 2.17061i) q^{12} +(4.88405 + 0.452573i) q^{13} +(-3.96459 + 2.99392i) q^{14} +(1.74165 + 1.40150i) q^{15} +(-1.63756 + 0.879349i) q^{16} +(1.10697 - 7.13123i) q^{17} +(5.17951 + 1.64772i) q^{18} +(-5.48085 - 4.13895i) q^{19} +(-0.131375 + 0.599877i) q^{20} +(3.82189 + 12.0139i) q^{21} +(-2.50771 + 0.549198i) q^{22} +(-0.0160016 + 0.103084i) q^{23} +(1.32481 + 8.53455i) q^{24} +(2.63221 + 3.48561i) q^{25} +(-5.43206 + 0.167360i) q^{26} +(3.22879 - 4.27561i) q^{27} +(-2.48625 + 2.41083i) q^{28} +(3.02334 - 2.59024i) q^{29} +(-2.10592 - 1.30393i) q^{30} +7.50202i q^{31} +(-3.33339 + 2.35966i) q^{32} +(-0.800558 + 6.46514i) q^{33} +(-0.246235 + 7.99215i) q^{34} +(-0.219467 - 3.55827i) q^{35} +(3.72436 + 0.696204i) q^{36} +(0.544789 - 0.0167848i) q^{37} +(6.59024 + 3.80488i) q^{38} +(-4.18084 + 13.1422i) q^{39} +(0.225346 - 2.43187i) q^{40} +(0.406680 + 1.15407i) q^{41} +(-5.83830 - 12.6899i) q^{42} +(0.675456 - 0.510081i) q^{43} +(-1.68780 + 0.594759i) q^{44} +(-3.03866 + 2.44520i) q^{45} +(0.00355940 - 0.115529i) q^{46} +(-1.62226 + 3.02102i) q^{47} +(-1.43020 - 5.02663i) q^{48} +(6.55245 - 11.3492i) q^{49} +(-3.36895 - 3.47434i) q^{50} +(18.9207 + 7.32991i) q^{51} +(-3.74359 + 0.581113i) q^{52} +(-4.70765 - 8.15389i) q^{53} +(-2.96818 + 5.14104i) q^{54} +(0.665467 - 1.71777i) q^{55} +(8.63477 - 10.7305i) q^{56} +(14.6648 - 12.5640i) q^{57} +(-2.97175 + 3.25986i) q^{58} +(-0.0232168 - 0.00660576i) q^{59} +(-1.56859 - 0.721666i) q^{60} +(-2.74854 - 3.01501i) q^{61} +(-1.02146 - 8.24914i) q^{62} +(-21.9019 + 2.02951i) q^{63} +(6.09129 - 5.55295i) q^{64} +(2.05301 - 3.31573i) q^{65} -7.21800i q^{66} +(0.331178 + 0.467841i) q^{67} +(0.514293 + 5.55010i) q^{68} +(-0.273504 - 0.105956i) q^{69} +(0.725812 + 3.88275i) q^{70} +(-13.6498 - 0.841891i) q^{71} +(-15.0400 - 0.927636i) q^{72} +(4.07200 + 3.94847i) q^{73} +(-0.596759 + 0.0926341i) q^{74} +(-11.1568 + 5.13296i) q^{75} +(4.88510 + 2.06769i) q^{76} +(8.47934 - 6.00240i) q^{77} +(2.80778 - 15.0203i) q^{78} +(9.89543 + 4.92734i) q^{79} +(0.0455101 + 1.47714i) q^{80} +(0.226255 + 0.264086i) q^{81} +(-0.604318 - 1.21363i) q^{82} +(9.02263 - 3.49538i) q^{83} +(-5.12604 - 8.27884i) q^{84} +(-4.68319 - 3.31516i) q^{85} +(-0.673272 + 0.652848i) q^{86} +(5.29575 + 9.86194i) q^{87} +(6.37094 - 3.17235i) q^{88} +(2.72343 + 9.57186i) q^{89} +(3.00834 - 3.10246i) q^{90} +(19.9800 - 9.19226i) q^{91} +(-0.00743424 - 0.0802282i) q^{92} +(-20.6049 - 4.51255i) q^{93} +(1.37248 - 3.54277i) q^{94} +(-4.88822 + 2.43404i) q^{95} +(-4.47593 - 10.5748i) q^{96} +(0.793383 + 12.8633i) q^{97} +(-5.65971 + 13.3716i) q^{98} +(-10.7198 - 3.77751i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1056 q - 33 q^{2} - 31 q^{3} + 29 q^{4} - 22 q^{5} - 44 q^{6} - 57 q^{7} - 22 q^{8} + 2 q^{9} - 30 q^{10} + 17 q^{11} + 67 q^{12} - 34 q^{13} - 68 q^{14} - 32 q^{15} + 21 q^{16} - 27 q^{17} + 22 q^{18}+ \cdots - 229 q^{99}+O(q^{100}) \) 1056 * q - 33 * q^2 - 31 * q^3 + 29 * q^4 - 22 * q^5 - 44 * q^6 - 57 * q^7 - 22 * q^8 + 2 * q^9 - 30 * q^10 + 17 * q^11 + 67 * q^12 - 34 * q^13 - 68 * q^14 - 32 * q^15 + 21 * q^16 - 27 * q^17 + 22 * q^18 - 34 * q^19 - 51 * q^20 - 108 * q^21 - 22 * q^22 - 32 * q^23 + 87 * q^24 - 112 * q^25 - 64 * q^26 - 82 * q^27 - 75 * q^28 - 19 * q^29 - 22 * q^30 + 52 * q^32 - 43 * q^33 - 48 * q^34 - 113 * q^35 + 22 * q^36 - 10 * q^37 - 57 * q^38 + 41 * q^39 - 225 * q^40 - 288 * q^41 - 173 * q^42 + 68 * q^43 - 34 * q^44 - 42 * q^45 + 17 * q^46 - 34 * q^47 + 68 * q^48 + 369 * q^49 - 40 * q^50 + 56 * q^51 + 8 * q^52 + 104 * q^53 + 128 * q^54 + 102 * q^55 - 138 * q^56 - 55 * q^57 - 34 * q^58 - 34 * q^59 - 254 * q^60 - 68 * q^61 + 25 * q^62 - 34 * q^63 + 98 * q^64 - 34 * q^65 - 40 * q^67 - 116 * q^68 - 38 * q^69 - 17 * q^70 + 21 * q^71 - 26 * q^72 - 31 * q^73 + 203 * q^74 + 23 * q^75 - 101 * q^76 + 19 * q^77 - 102 * q^78 - 34 * q^79 + 443 * q^80 - 265 * q^81 - 50 * q^82 + 26 * q^83 - 459 * q^84 + 84 * q^85 + 136 * q^86 - 188 * q^87 + 170 * q^88 - 80 * q^89 + 613 * q^90 - 152 * q^91 + 18 * q^92 + 56 * q^93 - 34 * q^94 - 34 * q^95 + 13 * q^96 - 31 * q^97 - 293 * q^98 - 229 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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