LMFDB - Embedded newform 207.2.o.a.182.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,2,Mod(5,207)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("207.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([55, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.o (of order $66$, degree $20$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			182.1
Character	$\chi$	$=$	207.182
Dual form			207.2.o.a.149.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.19334 - 2.31476i) q^{2} +(1.07461 - 1.35838i) q^{3} +(-2.77395 + 3.89546i) q^{4} +(-0.904406 - 3.72801i) q^{5} +(-4.42672 - 0.866459i) q^{6} +(2.50349 - 0.866468i) q^{7} +(7.17183 + 1.03115i) q^{8} +(-0.690410 - 2.91948i) q^{9} +(-7.55020 + 6.54229i) q^{10} +(0.0853862 + 1.79248i) q^{11} +(2.31061 + 7.95420i) q^{12} +(-1.08344 + 3.13039i) q^{13} +(-4.99320 - 4.76100i) q^{14} +(-6.03596 - 2.77764i) q^{15} +(-3.04337 - 8.79325i) q^{16} +(-0.919155 + 2.01267i) q^{17} +(-5.93400 + 5.08207i) q^{18} +(5.33902 - 2.43825i) q^{19} +(17.0311 + 6.81823i) q^{20} +(1.51329 - 4.33182i) q^{21} +(4.04726 - 2.33669i) q^{22} +(0.537967 + 4.76556i) q^{23} +(9.10765 - 8.63400i) q^{24} +(-8.63596 + 4.45214i) q^{25} +(8.53903 - 1.22773i) q^{26} +(-4.70769 - 2.19947i) q^{27} +(-3.56927 + 12.1558i) q^{28} +(0.362435 - 0.258089i) q^{29} +(0.773381 + 17.2865i) q^{30} +(3.86186 - 1.54606i) q^{31} +(-6.72245 + 7.05030i) q^{32} +(2.52663 + 1.81023i) q^{33} +(5.75572 - 0.274179i) q^{34} +(-5.49438 - 8.54942i) q^{35} +(13.2879 + 5.40900i) q^{36} +(-2.15828 - 7.35043i) q^{37} +(-12.0153 - 9.44890i) q^{38} +(3.08799 + 4.83569i) q^{39} +(-2.64209 - 27.6693i) q^{40} +(2.19367 - 0.532178i) q^{41} +(-11.8330 + 1.66643i) q^{42} +(0.297622 - 0.743424i) q^{43} +(-7.21938 - 4.63962i) q^{44} +(-10.2594 + 5.21425i) q^{45} +(10.3892 - 6.93222i) q^{46} +(2.64028 + 1.52437i) q^{47} +(-15.2150 - 5.31528i) q^{48} +(0.0143456 - 0.0112815i) q^{49} +(20.6113 + 14.6773i) q^{50} +(1.74624 + 3.41140i) q^{51} +(-9.18893 - 12.9040i) q^{52} +(1.12878 - 1.30268i) q^{53} +(0.526644 + 13.5219i) q^{54} +(6.60515 - 1.93945i) q^{55} +(18.8481 - 3.63267i) q^{56} +(2.42531 - 9.87261i) q^{57} +(-1.02992 - 0.530963i) q^{58} +(-10.9766 - 3.79905i) q^{59} +(27.5636 - 15.8078i) q^{60} +(2.64020 - 3.35729i) q^{61} +(-8.18729 - 7.09433i) q^{62} +(-4.25807 - 6.71067i) q^{63} +(6.48578 + 1.90440i) q^{64} +(12.6500 + 1.20793i) q^{65} +(1.17513 - 8.00877i) q^{66} +(-2.17994 - 0.103843i) q^{67} +(-5.29059 - 9.16356i) q^{68} +(7.05157 + 4.39037i) q^{69} +(-13.2332 + 22.9206i) q^{70} +(8.51253 - 13.2458i) q^{71} +(-1.94107 - 21.6499i) q^{72} +(1.67838 + 3.67515i) q^{73} +(-14.4389 + 13.7675i) q^{74} +(-3.23260 + 16.5153i) q^{75} +(-5.31205 + 27.5615i) q^{76} +(1.76689 + 4.41347i) q^{77} +(7.50844 - 12.9186i) q^{78} +(0.836762 + 4.34153i) q^{79} +(-30.0289 + 19.2984i) q^{80} +(-8.04667 + 4.03127i) q^{81} +(-3.84966 - 4.44275i) q^{82} +(-3.00389 + 12.3822i) q^{83} +(12.6767 + 17.9112i) q^{84} +(8.33454 + 1.60635i) q^{85} +(-2.07601 + 0.198235i) q^{86} +(0.0388942 - 0.769671i) q^{87} +(-1.23594 + 12.9434i) q^{88} +(0.218032 + 1.51645i) q^{89} +(24.3128 + 17.5258i) q^{90} +8.77569i q^{91} +(-20.0564 - 11.1238i) q^{92} +(2.04988 - 6.90731i) q^{93} +(0.377786 - 7.93071i) q^{94} +(-13.9185 - 17.6988i) q^{95} +(2.35297 + 16.7080i) q^{96} +(9.85700 + 10.3377i) q^{97} +(-0.0432332 - 0.0197440i) q^{98} +(5.17414 - 1.48683i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23}+ \cdots + 242 q^{99}+O(q^{100}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.19334	−	2.31476i	−0.843821	−	1.63678i	−0.768699	−	0.639610i	$-0.779096\pi$
$2$	−1.19334	−	2.31476i	−0.843821	−	1.63678i	−0.0751219	−	0.997174i	$-0.523935\pi$
$3$	1.07461	−	1.35838i	0.620429	−	0.784263i
$3$	1.07461	−	1.35838i	0.620429	−	0.784263i
$4$	−2.77395	+	3.89546i	−1.38697	+	1.94773i
$5$	−0.904406	−	3.72801i	−0.404463	−	1.66722i	−0.701745	−	0.712429i	$-0.747595\pi$
$5$	−0.904406	−	3.72801i	−0.404463	−	1.66722i	0.297282	−	0.954790i	$-0.403920\pi$
$6$	−4.42672	−	0.866459i	−1.80720	−	0.353730i
$7$	2.50349	−	0.866468i	0.946232	−	0.327494i	0.189990	−	0.981786i	$-0.439154\pi$
$7$	2.50349	−	0.866468i	0.946232	−	0.327494i	0.756242	+	0.654292i	$0.227033\pi$
$8$	7.17183	+	1.03115i	2.53562	+	0.364568i
$9$	−0.690410	−	2.91948i	−0.230137	−	0.973158i
$10$	−7.55020	+	6.54229i	−2.38758	+	2.06885i
$11$	0.0853862	+	1.79248i	0.0257449	+	0.540452i	0.974493	+	0.224418i	$0.0720482\pi$
$11$	0.0853862	+	1.79248i	0.0257449	+	0.540452i	−0.948748	+	0.316034i	$0.897649\pi$
$12$	2.31061	+	7.95420i	0.667016	+	2.29618i
$13$	−1.08344	+	3.13039i	−0.300492	+	0.868215i	0.689145	+	0.724623i	$0.257986\pi$
$13$	−1.08344	+	3.13039i	−0.300492	+	0.868215i	−0.989637	+	0.143591i	$0.954135\pi$
$14$	−4.99320	−	4.76100i	−1.33449	−	1.27243i
$15$	−6.03596	−	2.77764i	−1.55848	−	0.717185i
$16$	−3.04337	−	8.79325i	−0.760843	−	2.19831i
$17$	−0.919155	+	2.01267i	−0.222928	+	0.488144i	−0.987740	−	0.156110i	$-0.950105\pi$
$17$	−0.919155	+	2.01267i	−0.222928	+	0.488144i	0.764812	+	0.644254i	$0.222832\pi$
$18$	−5.93400	+	5.08207i	−1.39866	+	1.19786i
$19$	5.33902	−	2.43825i	1.22486	−	0.559373i	0.305271	−	0.952266i	$-0.401253\pi$
$19$	5.33902	−	2.43825i	1.22486	−	0.559373i	0.919584	+	0.392893i	$0.128526\pi$
$20$	17.0311	+	6.81823i	3.80827	+	1.52460i
$21$	1.51329	−	4.33182i	0.330228	−	0.945281i
$22$	4.04726	−	2.33669i	0.862880	−	0.498184i
$23$	0.537967	+	4.76556i	0.112174	+	0.993689i
$23$	0.537967	+	4.76556i	0.112174	+	0.993689i
$24$	9.10765	−	8.63400i	1.85909	−	1.76241i
$25$	−8.63596	+	4.45214i	−1.72719	+	0.890429i
$26$	8.53903	−	1.22773i	1.67464	−	0.240777i
$27$	−4.70769	−	2.19947i	−0.905995	−	0.423288i
$28$	−3.56927	+	12.1558i	−0.674528	+	2.29723i
$29$	0.362435	−	0.258089i	0.0673025	−	0.0479259i	−0.545910	−	0.837844i	$-0.683816\pi$
$29$	0.362435	−	0.258089i	0.0673025	−	0.0479259i	0.613213	+	0.789918i	$0.289877\pi$
$30$	0.773381	+	17.2865i	0.141199	+	3.15607i
$31$	3.86186	−	1.54606i	0.693611	−	0.277680i	0.00205010	−	0.999998i	$-0.499347\pi$
$31$	3.86186	−	1.54606i	0.693611	−	0.277680i	0.691561	+	0.722318i	$0.256923\pi$
$32$	−6.72245	+	7.05030i	−1.18837	+	1.24633i
$33$	2.52663	+	1.81023i	0.439829	+	0.315121i
$34$	5.75572	−	0.274179i	0.987097	−	0.0470212i
$35$	−5.49438	−	8.54942i	−0.928720	−	1.44512i
$36$	13.2879	+	5.40900i	2.21464	+	0.901500i
$37$	−2.15828	−	7.35043i	−0.354819	−	1.20840i	−0.922773	−	0.385343i	$-0.874083\pi$
$37$	−2.15828	−	7.35043i	−0.354819	−	1.20840i	0.567954	−	0.823060i	$-0.307735\pi$
$38$	−12.0153	−	9.44890i	−1.94913	−	1.53281i
$39$	3.08799	+	4.83569i	0.494475	+	0.774330i
$40$	−2.64209	−	27.6693i	−0.417752	−	4.37489i
$41$	2.19367	−	0.532178i	0.342593	−	0.0831122i	−0.0607710	−	0.998152i	$-0.519356\pi$
$41$	2.19367	−	0.532178i	0.342593	−	0.0831122i	0.403364	+	0.915040i	$0.367841\pi$
$42$	−11.8330	+	1.66643i	−1.82588	+	0.257136i
$43$	0.297622	−	0.743424i	0.0453869	−	0.113371i	−0.903942	−	0.427654i	$-0.859340\pi$
$43$	0.297622	−	0.743424i	0.0453869	−	0.113371i	0.949329	+	0.314283i	$0.101764\pi$
$44$	−7.21938	−	4.63962i	−1.08836	−	0.699448i
$45$	−10.2594	+	5.21425i	−1.52939	+	0.777294i
$46$	10.3892	−	6.93222i	1.53180	−	1.02210i
$47$	2.64028	+	1.52437i	0.385124	+	0.222352i	0.680045	−	0.733170i	$-0.261960\pi$
$47$	2.64028	+	1.52437i	0.385124	+	0.222352i	−0.294921	+	0.955522i	$0.595293\pi$
$48$	−15.2150	−	5.31528i	−2.19610	−	0.767194i
$49$	0.0143456	−	0.0112815i	0.00204937	−	0.00161164i
$50$	20.6113	+	14.6773i	2.91488	+	2.07568i
$51$	1.74624	+	3.41140i	0.244522	+	0.477692i
$52$	−9.18893	−	12.9040i	−1.27427	−	1.78947i
$53$	1.12878	−	1.30268i	0.155050	−	0.178937i	−0.672910	−	0.739724i	$-0.734956\pi$
$53$	1.12878	−	1.30268i	0.155050	−	0.178937i	0.827960	+	0.560787i	$0.189501\pi$
$54$	0.526644	+	13.5219i	0.0716672	+	1.84010i
$55$	6.60515	−	1.93945i	0.890639	−	0.261515i
$56$	18.8481	−	3.63267i	2.51868	−	0.485436i
$57$	2.42531	−	9.87261i	0.321240	−	1.30766i
$58$	−1.02992	−	0.530963i	−0.135236	−	0.0697188i
$59$	−10.9766	−	3.79905i	−1.42904	−	0.494595i	−0.500469	−	0.865755i	$-0.666839\pi$
$59$	−10.9766	−	3.79905i	−1.42904	−	0.494595i	−0.928569	+	0.371160i	$0.878960\pi$
$60$	27.5636	−	15.8078i	3.55845	−	2.04078i
$61$	2.64020	−	3.35729i	0.338043	−	0.429857i	−0.587077	−	0.809531i	$-0.699721\pi$
$61$	2.64020	−	3.35729i	0.338043	−	0.429857i	0.925120	+	0.379674i	$0.123964\pi$
$62$	−8.18729	−	7.09433i	−1.03979	−	0.900980i
$63$	−4.25807	−	6.71067i	−0.536466	−	0.845465i
$64$	6.48578	+	1.90440i	0.810723	+	0.238050i
$65$	12.6500	+	1.20793i	1.56904	+	0.149825i
$66$	1.17513	−	8.00877i	0.144648	−	0.985812i
$67$	−2.17994	−	0.103843i	−0.266322	−	0.0126865i	−0.0860037	−	0.996295i	$-0.527410\pi$
$67$	−2.17994	−	0.103843i	−0.266322	−	0.0126865i	−0.180318	+	0.983608i	$0.557713\pi$
$68$	−5.29059	−	9.16356i	−0.641578	−	1.11125i
$69$	7.05157	+	4.39037i	0.848909	+	0.528539i
$70$	−13.2332	+	22.9206i	−1.58167	+	2.73953i
$71$	8.51253	−	13.2458i	1.01025	−	1.57198i	0.205250	−	0.978710i	$-0.434199\pi$
$71$	8.51253	−	13.2458i	1.01025	−	1.57198i	0.805002	−	0.593272i	$-0.202164\pi$
$72$	−1.94107	−	21.6499i	−0.228758	−	2.55146i
$73$	1.67838	+	3.67515i	0.196440	+	0.430144i	0.982061	−	0.188565i	$-0.0603835\pi$
$73$	1.67838	+	3.67515i	0.196440	+	0.430144i	−0.785621	+	0.618708i	$0.787656\pi$
$74$	−14.4389	+	13.7675i	−1.67849	+	1.60044i
$75$	−3.23260	+	16.5153i	−0.373269	+	1.90702i
$76$	−5.31205	+	27.5615i	−0.609334	+	3.16152i
$77$	1.76689	+	4.41347i	0.201355	+	0.502962i
$78$	7.50844	−	12.9186i	0.850163	−	1.46274i
$79$	0.836762	+	4.34153i	0.0941431	+	0.488461i	0.998142	+	0.0609266i	$0.0194055\pi$
$79$	0.836762	+	4.34153i	0.0941431	+	0.488461i	−0.903999	+	0.427534i	$0.859382\pi$
$80$	−30.0289	+	19.2984i	−3.35733	+	2.15763i
$81$	−8.04667	+	4.03127i	−0.894074	+	0.447919i
$82$	−3.84966	−	4.44275i	−0.425124	−	0.490619i
$83$	−3.00389	+	12.3822i	−0.329720	+	1.35912i	0.529843	+	0.848096i	$0.322251\pi$
$83$	−3.00389	+	12.3822i	−0.329720	+	1.35912i	−0.859563	+	0.511029i	$0.829264\pi$
$84$	12.6767	+	17.9112i	1.38314	+	1.95428i
$85$	8.33454	+	1.60635i	0.904008	+	0.174233i
$86$	−2.07601	+	0.198235i	−0.223862	+	0.0213763i
$87$	0.0388942	−	0.769671i	0.00416990	−	0.0825174i
$88$	−1.23594	+	12.9434i	−0.131752	+	1.37977i
$89$	0.218032	+	1.51645i	0.0231114	+	0.160743i	0.998109	−	0.0614733i	$-0.0195799\pi$
$89$	0.218032	+	1.51645i	0.0231114	+	0.160743i	−0.974997	+	0.222217i	$0.928671\pi$
$90$	24.3128	+	17.5258i	2.56279	+	1.84738i
$91$			8.77569i			0.919942i
$92$	−20.0564	−	11.1238i	−2.09102	−	1.15973i
$93$	2.04988	−	6.90731i	0.212562	−	0.716254i
$94$	0.377786	−	7.93071i	0.0389657	−	0.817990i
$95$	−13.9185	−	17.6988i	−1.42800	−	1.81586i
$96$	2.35297	+	16.7080i	0.240149	+	1.70525i
$97$	9.85700	+	10.3377i	1.00083	+	1.04964i	0.998767	+	0.0496395i	$0.0158072\pi$
$97$	9.85700	+	10.3377i	1.00083	+	1.04964i	0.00206002	+	0.999998i	$0.499344\pi$
$98$	−0.0432332	−	0.0197440i	−0.00436722	−	0.00199444i
$99$	5.17414	−	1.48683i	0.520021	−	0.149432i
$100$	6.61252	−	45.9911i	0.661252	−	4.59911i
$101$	7.42557	+	1.80142i	0.738872	+	0.179248i	0.587495	−	0.809228i	$-0.300114\pi$
$101$	7.42557	+	1.80142i	0.738872	+	0.179248i	0.151377	+	0.988476i	$0.451629\pi$
$102$	5.81273	−	8.11310i	0.575546	−	0.803317i
$103$	−6.77663	+	13.1448i	−0.667722	+	1.29520i	0.274944	+	0.961460i	$0.411341\pi$
$103$	−6.77663	+	13.1448i	−0.667722	+	1.29520i	−0.942666	+	0.333739i	$0.891690\pi$
$104$	−10.9982	+	21.3335i	−1.07846	+	2.09192i
$105$	−17.5177	−	1.72385i	−1.70956	−	0.168231i
$106$	−4.36242	−	1.05831i	−0.423715	−	0.102792i
$107$	−0.219990	+	1.53007i	−0.0212673	+	0.147917i	−0.997688	−	0.0679585i	$-0.978351\pi$
$107$	−0.219990	+	1.53007i	−0.0212673	+	0.147917i	0.976421	+	0.215876i	$0.0692605\pi$
$108$	21.6268	−	12.2374i	2.08104	−	1.17755i
$109$	8.60283	+	3.92878i	0.824001	+	0.376309i	0.782362	−	0.622824i	$-0.214015\pi$
$109$	8.60283	+	3.92878i	0.824001	+	0.376309i	0.0416393	+	0.999133i	$0.486742\pi$
$110$	−12.3716	−	12.9749i	−1.17958	−	1.23711i
$111$	−12.3040	−	4.96710i	−1.16785	−	0.471456i
$112$	−15.2381	−	19.3769i	−1.43987	−	1.83094i
$113$	0.151342	−	3.17705i	0.0142370	−	0.298872i	−0.980507	−	0.196482i	$-0.937048\pi$
$113$	0.151342	−	3.17705i	0.0142370	−	0.298872i	0.994744	−	0.102390i	$-0.0326488\pi$
$114$	−25.7470	+	6.16740i	−2.41143	+	0.577630i
$115$	17.2795	−	6.31555i	1.61133	−	0.588928i
$116$			2.12778i			0.197559i
$117$	9.88712	+	1.00182i	0.914065	+	0.0926184i
$118$	4.30500	+	29.9419i	0.396307	+	2.75638i
$119$	−0.557186	+	5.83512i	−0.0510772	+	0.534905i
$120$	−40.4247	−	26.1448i	−3.69025	−	2.38668i
$121$	7.74451	−	0.739511i	0.704046	−	0.0672283i
$122$	−10.9220	−	2.10504i	−0.988831	−	0.190582i
$123$	1.63444	−	3.55173i	0.147373	−	0.320248i
$124$	−4.69000	+	19.3324i	−0.421174	+	1.73610i
$125$	11.8474	+	13.6726i	1.05966	+	1.22291i
$126$	−10.4523	+	17.8646i	−0.931163	+	1.59150i
$127$	0.209143	−	0.134408i	0.0185585	−	0.0119268i	−0.531329	−	0.847166i	$-0.678307\pi$
$127$	0.209143	−	0.134408i	0.0185585	−	0.0119268i	0.549887	+	0.835239i	$0.314671\pi$
$128$	0.355671	+	1.84540i	0.0314372	+	0.163111i
$129$	−0.690025	−	1.20318i	−0.0607533	−	0.105934i
$130$	−12.2997	−	30.7233i	−1.07876	−	2.69461i
$131$	−0.0338851	+	0.175813i	−0.00296056	+	0.0153608i	−0.983379	−	0.181565i	$-0.941884\pi$
$131$	−0.0338851	+	0.175813i	−0.00296056	+	0.0153608i	0.980418	+	0.196926i	$0.0630958\pi$
$132$	−14.0604	+	4.82089i	−1.22380	+	0.419605i
$133$	11.2535	−	10.7302i	0.975806	−	0.930429i
$134$	2.36104	+	5.16996i	0.203963	+	0.446617i
$135$	−3.94198	+	19.5395i	−0.339272	+	1.68170i
$136$	−8.66739	+	13.4867i	−0.743222	+	1.15648i
$137$	−3.65084	+	6.32345i	−0.311913	+	0.540249i	−0.978776	−	0.204931i	$-0.934303\pi$
$137$	−3.65084	+	6.32345i	−0.311913	+	0.540249i	0.666864	+	0.745180i	$0.267636\pi$
$138$	1.74774	−	21.5619i	0.148777	−	1.83547i
$139$	−10.6526	−	18.4508i	−0.903542	−	1.56498i	−0.822863	−	0.568240i	$-0.807625\pi$
$139$	−10.6526	−	18.4508i	−0.903542	−	1.56498i	−0.0806786	−	0.996740i	$-0.525709\pi$
$140$	48.5451	+	2.31249i	4.10281	+	0.195441i
$141$	4.90795	−	1.94841i	0.413324	−	0.164085i
$142$	−40.8192	−	3.89776i	−3.42547	−	0.327092i
$143$	−5.70367	−	1.67475i	−0.476965	−	0.140049i
$144$	−23.5705	+	14.9560i	−1.96421	+	1.24633i
$145$	−1.28995	−	1.11775i	−0.107124	−	0.0928237i
$146$	6.50421	−	8.27077i	0.538292	−	0.684494i
$147$	9.13756e−5	−	0.0316101i	7.53653e−6	−	0.00260716i
$148$	34.6203	+	11.9822i	2.84577	+	0.984930i
$149$	10.9253	+	5.63237i	0.895034	+	0.461422i	0.843426	−	0.537246i	$-0.180535\pi$
$149$	10.9253	+	5.63237i	0.895034	+	0.461422i	0.0516077	+	0.998667i	$0.483565\pi$
$150$	42.0866	−	12.2257i	3.43635	−	0.998223i
$151$	−2.53066	+	0.487744i	−0.205942	+	0.0396921i	−0.291179	−	0.956669i	$-0.594047\pi$
$151$	−2.53066	+	0.487744i	−0.205942	+	0.0396921i	0.0852368	+	0.996361i	$0.472835\pi$
$152$	40.8047	−	11.9814i	3.30970	−	0.971816i
$153$	6.51053	+	1.29388i	0.526345	+	0.104604i
$154$	8.10764	−	9.35671i	0.653332	−	0.753985i
$155$	−9.25642	−	12.9988i	−0.743493	−	1.04409i
$156$	−27.4032	−	1.38478i	−2.19401	−	0.110871i
$157$	11.9694	+	8.52340i	0.955265	+	0.680241i	0.947509	−	0.319729i	$-0.103592\pi$
$157$	11.9694	+	8.52340i	0.955265	+	0.680241i	0.00775580	+	0.999970i	$0.497531\pi$
$158$	9.05108	−	7.11785i	0.720065	−	0.566266i
$159$	−0.556537	−	2.93319i	−0.0441363	−	0.232617i
$160$	32.3635	+	18.6850i	2.55856	+	1.47718i
$161$	5.47601	+	11.4644i	0.431570	+	0.903524i
$162$	18.9339	+	13.8154i	1.48759	+	1.08544i
$163$	−9.01920	−	5.79629i	−0.706438	−	0.454000i	0.137457	−	0.990508i	$-0.456107\pi$
$163$	−9.01920	−	5.79629i	−0.706438	−	0.454000i	−0.843896	+	0.536507i	$0.819743\pi$
$164$	−4.01204	+	10.0216i	−0.313287	+	0.782554i
$165$	4.46348	−	11.0565i	0.347481	−	0.860746i
$166$	32.2466	−	7.82293i	2.50282	−	0.607178i
$167$	0.493577	+	5.16897i	0.0381941	+	0.399987i	0.994272	+	0.106875i	$0.0340846\pi$
$167$	0.493577	+	5.16897i	0.0381941	+	0.399987i	−0.956078	+	0.293111i	$0.905309\pi$
$168$	15.3199	−	29.5067i	1.18195	−	2.27649i
$169$	1.59317	+	1.25288i	0.122552	+	0.0963757i
$170$	−6.22765	−	21.2094i	−0.477639	−	1.62669i
$171$	−10.8045	−	13.9037i	−0.826242	−	1.06325i
$172$	2.07039	+	3.22159i	0.157866	+	0.245644i
$173$	−9.36625	+	0.446170i	−0.712103	+	0.0339216i	−0.400508	−	0.916293i	$-0.631166\pi$
$173$	−9.36625	+	0.446170i	−0.712103	+	0.0339216i	−0.311595	+	0.950215i	$0.600863\pi$
$174$	−1.82802	+	0.828451i	−0.138582	+	0.0628047i
$175$	−17.7624	+	18.6287i	−1.34271	+	1.40820i
$176$	15.5018	−	6.20600i	1.16849	−	0.467794i
$177$	−16.9562	+	10.8280i	−1.27451	+	0.813881i
$178$	3.25003	−	2.31434i	0.243600	−	0.173467i
$179$	−2.41548	+	8.22638i	−0.180542	+	0.614869i	0.818636	+	0.574313i	$0.194731\pi$
$179$	−2.41548	+	8.22638i	−0.180542	+	0.614869i	−0.999177	+	0.0405554i	$0.987087\pi$
$180$	8.14720	−	54.4293i	0.607257	−	4.05692i
$181$	−21.5546	+	3.09908i	−1.60214	+	0.230353i	−0.884663	−	0.466231i	$-0.845612\pi$
$181$	−21.5546	+	3.09908i	−1.60214	+	0.230353i	−0.717476	+	0.696583i	$0.754703\pi$
$182$	20.3136	−	10.4724i	1.50575	−	0.776266i
$183$	−1.72329	−	7.19419i	−0.127389	−	0.531810i
$184$	−1.05582	+	34.7325i	−0.0778358	+	2.56052i
$185$	−25.4505	+	14.6939i	−1.87116	+	1.08032i
$186$	−18.4350	+	3.49781i	−1.35172	+	0.256472i
$187$	−3.68614	−	1.47571i	−0.269557	−	0.107915i
$188$	−13.2621	+	6.05660i	−0.967238	+	0.441723i
$189$	−13.6914	−	1.42729i	−0.995906	−	0.103820i
$190$	−24.3590	+	53.3387i	−1.76718	+	3.86959i
$191$	−0.871549	−	2.51818i	−0.0630631	−	0.182209i	0.909067	−	0.416649i	$-0.136796\pi$
$191$	−0.871549	−	2.51818i	−0.0630631	−	0.182209i	−0.972131	+	0.234440i	$0.924674\pi$
$192$	9.55661	−	6.76369i	0.689689	−	0.488127i
$193$	−11.5652	−	11.0274i	−0.832481	−	0.793769i	0.148287	−	0.988944i	$-0.452624\pi$
$193$	−11.5652	−	11.0274i	−0.832481	−	0.793769i	−0.980768	+	0.195175i	$0.937472\pi$
$194$	12.1666	−	35.1531i	0.873511	−	2.52384i
$195$	15.2347	−	15.8855i	1.09098	−	1.13759i
$196$	0.00415276	+	0.0871771i	0.000296625	+	0.00622693i
$197$	10.8321	−	9.38607i	0.771755	−	0.668730i	−0.177188	−	0.984177i	$-0.556700\pi$
$197$	10.8321	−	9.38607i	0.771755	−	0.668730i	0.948943	+	0.315447i	$0.102155\pi$
$198$	−9.61618	−	10.2026i	−0.683392	−	0.725068i
$199$	14.1618	+	2.03616i	1.00390	+	0.144339i	0.624610	−	0.780937i	$-0.285258\pi$
$199$	14.1618	+	2.03616i	1.00390	+	0.144339i	0.379293	+	0.925277i	$0.376167\pi$
$200$	−66.5264	+	23.0250i	−4.70413	+	1.62812i
$201$	−2.48365	+	2.84960i	−0.175183	+	0.200995i
$202$	−4.69139	−	19.3382i	−0.330085	−	1.36063i
$203$	0.683728	−	0.960162i	0.0479883	−	0.0673902i
$204$	−18.1330	−	2.66065i	−1.26956	−	0.186283i
$205$	−3.96793	−	7.69671i	−0.277132	−	0.537562i
$206$	38.5140			2.68340
$207$	13.5415	−	4.86077i	0.941201	−	0.337847i
$208$	30.8236			2.13723
$209$	4.82638	+	9.36188i	0.333848	+	0.647575i
$210$	16.9143	+	42.6065i	1.16720	+	2.94013i
$211$	5.51685	−	7.74732i	0.379795	−	0.533348i	−0.579790	−	0.814766i	$-0.696865\pi$
$211$	5.51685	−	7.74732i	0.379795	−	0.533348i	0.959585	+	0.281418i	$0.0908048\pi$
$212$	1.94337	+	8.01068i	0.133471	+	0.550176i
$213$	−8.84513	−	25.7974i	−0.606058	−	1.76761i
$214$	3.80426	−	1.31667i	0.260054	−	0.0900056i
$215$	−3.04066	−	0.437181i	−0.207372	−	0.0298155i
$216$	−31.4948	−	20.6286i	−2.14295	−	1.40360i
$217$	8.32855	−	7.21673i	0.565379	−	0.489903i
$218$	−1.17193	−	24.6019i	−0.0793733	−	1.66625i
$219$	6.79587	+	1.66948i	0.459223	+	0.112813i
$220$	−10.7673	+	31.1101i	−0.725931	+	2.09744i
$221$	−5.30459	−	5.05792i	−0.356825	−	0.340232i
$222$	3.18526	+	34.4083i	0.213780	+	2.30934i
$223$	−2.21277	−	6.39338i	−0.148178	−	0.428132i	0.846347	−	0.532632i	$-0.178797\pi$
$223$	−2.21277	−	6.39338i	−0.148178	−	0.428132i	−0.994525	+	0.104500i	$0.966676\pi$
$224$	−10.7208	+	23.4752i	−0.716311	+	1.56850i
$225$	18.9603	+	22.1387i	1.26402	+	1.47591i
$226$	−7.53472	+	3.44099i	−0.501202	+	0.228891i
$227$	1.11066	+	0.444642i	0.0737172	+	0.0295119i	0.408228	−	0.912880i	$-0.366147\pi$
$227$	1.11066	+	0.444642i	0.0737172	+	0.0295119i	−0.334511	+	0.942392i	$0.608571\pi$
$228$	31.7307	+	36.8338i	2.10142	+	2.43938i
$229$	−9.02087	+	5.20820i	−0.596116	+	0.344168i	−0.767512	−	0.641035i	$-0.778506\pi$
$229$	−9.02087	+	5.20820i	−0.596116	+	0.344168i	0.171396	+	0.985202i	$0.445172\pi$
$230$	−35.2394	−	32.4614i	−2.32362	−	2.14044i
$231$	7.89391	+	2.34267i	0.519381	+	0.154136i
$232$	2.86545	−	1.47724i	0.188126	−	0.0969857i
$233$	−26.8065	+	3.85420i	−1.75615	+	0.252497i	−0.943765	−	0.330618i	$-0.892743\pi$
$233$	−26.8065	+	3.85420i	−1.75615	+	0.252497i	−0.812390	+	0.583115i	$0.801834\pi$
$234$	−9.47975	−	24.0819i	−0.619711	−	1.57428i
$235$	3.29497	−	11.2216i	0.214940	−	0.732019i
$236$	45.2477	−	32.2207i	2.94537	−	2.09739i
$237$	6.79666	+	3.52883i	0.441491	+	0.229222i
$238$	14.1718	−	5.67355i	0.918624	−	0.367761i
$239$	−8.87358	+	9.30634i	−0.573984	+	0.601977i	−0.945169	−	0.326582i	$-0.894103\pi$
$239$	−8.87358	+	9.30634i	−0.573984	+	0.601977i	0.371185	+	0.928559i	$0.378952\pi$
$240$	−6.05485	+	61.5291i	−0.390839	+	3.97168i
$241$	−12.7455	+	0.607142i	−0.821009	+	0.0391095i	−0.453882	−	0.891062i	$-0.649961\pi$
$241$	−12.7455	+	0.607142i	−0.821009	+	0.0391095i	−0.367126	+	0.930171i	$0.619658\pi$
$242$	−10.9537	−	17.0442i	−0.704127	−	1.09564i
$243$	−3.17106	+	15.2625i	−0.203423	+	0.979091i
$244$	5.75442	+	19.5977i	0.368389	+	1.25462i
$245$	−0.0550319	−	0.0432775i	−0.00351586	−	0.00276490i
$246$	−10.1719	+	0.455079i	−0.648534	+	0.0290148i
$247$	1.84817	+	19.3549i	0.117596	+	1.23152i
$248$	29.2909	−	7.10588i	1.85997	−	0.451224i
$249$	13.5918	+	17.3865i	0.861343	+	1.10183i
$250$	17.5108	−	43.7399i	1.10748	−	2.76635i
$251$	15.2592	+	9.80651i	0.963154	+	0.618982i	0.924869	−	0.380285i	$-0.124174\pi$
$251$	15.2592	+	9.80651i	0.963154	+	0.618982i	0.0382851	+	0.999267i	$0.487811\pi$
$252$	37.9528	+	2.02790i	2.39080	+	0.127746i
$253$	−8.49623	+	1.37121i	−0.534153	+	0.0862071i
$254$	−0.560703	−	0.323722i	−0.0351816	−	0.0203121i
$255$	11.1385	−	9.59529i	0.697517	−	0.600881i
$256$	14.4740	−	11.3825i	0.904626	−	0.711406i
$257$	19.1620	+	13.6452i	1.19529	+	0.851163i	0.991786	−	0.127910i	$-0.0408270\pi$
$257$	19.1620	+	13.6452i	1.19529	+	0.851163i	0.203506	+	0.979074i	$0.434766\pi$
$258$	−1.96163	+	3.03305i	−0.122126	+	0.188829i
$259$	−11.7722	−	16.5317i	−0.731486	−	1.02723i
$260$	−39.7959	+	45.9269i	−2.46804	+	2.84827i
$261$	−1.00371	−	0.879933i	−0.0621282	−	0.0544665i
$262$	0.447401	−	0.131369i	0.0276405	−	0.00811599i
$263$	3.06444	−	0.590623i	0.188962	−	0.0364194i	−0.0938923	−	0.995582i	$-0.529931\pi$
$263$	3.06444	−	0.590623i	0.188962	−	0.0364194i	0.282854	+	0.959163i	$0.408719\pi$
$264$	16.2539	+	15.5880i	1.00036	+	0.959377i
$265$	−5.87728	−	3.02995i	−0.361039	−	0.186128i
$266$	−38.2673	−	13.2444i	−2.34632	−	0.812068i
$267$	2.29422	+	1.33342i	0.140404	+	0.0816043i
$268$	6.45155	−	8.20381i	0.394091	−	0.501128i
$269$	20.5579	+	17.8135i	1.25344	+	1.08611i	0.992689	+	0.120703i	$0.0385149\pi$
$269$	20.5579	+	17.8135i	1.25344	+	1.08611i	0.260749	+	0.965407i	$0.416031\pi$
$270$	49.9336	−	14.1926i	3.03886	−	0.863736i
$271$	−28.1936	−	8.27839i	−1.71264	−	0.502876i	−0.729229	−	0.684270i	$-0.760121\pi$
$271$	−28.1936	−	8.27839i	−1.71264	−	0.502876i	−0.983410	+	0.181394i	$0.941939\pi$
$272$	20.4952	+	1.95706i	1.24270	+	0.118664i
$273$	11.9207	+	9.43047i	0.721476	+	0.570758i
$274$	18.9940	+	0.904795i	1.14747	+	0.0546607i
$275$	−8.71776	−	15.0996i	−0.525701	−	0.910540i
$276$	−36.6632	+	15.2905i	−2.20687	+	0.920377i
$277$	7.61253	−	13.1853i	0.457393	−	0.792227i	−0.541430	−	0.840746i	$-0.682117\pi$
$277$	7.61253	−	13.1853i	0.457393	−	0.792227i	0.998822	+	0.0485189i	$0.0154501\pi$
$278$	−29.9971	+	46.6764i	−1.79911	+	2.79947i
$279$	−7.17995	−	10.2072i	−0.429852	−	0.611089i
$280$	−30.5890	−	66.9805i	−1.82804	−	4.00285i
$281$	−7.85844	+	7.49301i	−0.468795	+	0.446995i	−0.887282	−	0.461228i	$-0.847409\pi$
$281$	−7.85844	+	7.49301i	−0.468795	+	0.446995i	0.418487	+	0.908223i	$0.362561\pi$
$282$	−10.3670	−	9.03563i	−0.617344	−	0.538064i
$283$	2.88826	−	14.9857i	0.171689	−	0.890808i	−0.789255	−	0.614066i	$-0.789533\pi$
$283$	2.88826	−	14.9857i	0.171689	−	0.890808i	0.960944	−	0.276743i	$-0.0892549\pi$
$284$	27.9850	+	69.9033i	1.66061	+	4.14800i
$285$	−38.9987	−	0.112734i	−2.31008	−	0.00667778i
$286$	2.92979	+	15.2012i	0.173242	+	0.898865i
$287$	5.03072	−	3.23305i	0.296954	−	0.190841i
$288$	25.2244	+	14.7584i	1.48636	+	0.869649i
$289$	7.92665	+	9.14784i	0.466273	+	0.538108i
$290$	−1.04797	+	4.31978i	−0.0615387	+	0.253666i
$291$	24.6351	−	2.28052i	1.44413	−	0.133687i
$292$	−18.9721	−	3.65658i	−1.11026	−	0.213985i
$293$	20.7282	−	1.97930i	1.21095	−	0.115632i	0.530025	−	0.847982i	$-0.322183\pi$
$293$	20.7282	−	1.97930i	1.21095	−	0.115632i	0.680928	+	0.732350i	$0.261576\pi$
$294$	−0.0732789	+	0.0375102i	−0.00427371	+	0.00218764i
$295$	−4.23558	+	44.3570i	−0.246605	+	2.58256i
$296$	−7.89940	−	54.9415i	−0.459143	−	3.19341i
$297$	3.54052	−	8.62623i	0.205442	−	0.500545i
$298$		−	32.0108i		−	1.85433i
$299$	−15.5009	−	3.47915i	−0.896442	−	0.201204i
$300$	−55.3676	−	58.4050i	−3.19665	−	3.37201i
$301$	0.100942	−	2.11904i	0.00581821	−	0.122139i
$302$	4.14896	+	5.27583i	0.238746	+	0.303590i
$303$	10.4267	−	8.15094i	0.598995	−	0.468259i
$304$	−37.6887	−	39.5268i	−2.16160	−	2.26702i
$305$	−14.9038	−	6.80635i	−0.853391	−	0.389731i
$306$	−4.77426	−	16.6144i	−0.272926	−	0.949780i
$307$	−0.243859	+	1.69608i	−0.0139178	+	0.0968002i	−0.995596	−	0.0937445i	$-0.970116\pi$
$307$	−0.243859	+	1.69608i	−0.0139178	+	0.0968002i	0.981679	+	0.190545i	$0.0610254\pi$
$308$	−22.0938	−	5.35989i	−1.25891	−	0.305408i
$309$	10.5735	+	23.3309i	0.601503	+	1.32725i
$310$	−19.0431	+	36.9385i	−1.08158	+	2.09796i
$311$	8.57366	−	16.6306i	0.486168	−	0.943034i	−0.510375	−	0.859952i	$-0.670493\pi$
$311$	8.57366	−	16.6306i	0.486168	−	0.943034i	0.996543	−	0.0830819i	$-0.0264763\pi$
$312$	17.1602	+	37.8649i	0.971507	+	2.14368i
$313$	−3.68935	−	0.895026i	−0.208534	−	0.0505899i	0.130131	−	0.991497i	$-0.458460\pi$
$313$	−3.68935	−	0.895026i	−0.208534	−	0.0505899i	−0.338665	+	0.940907i	$0.609975\pi$
$314$	5.44600	−	37.8777i	0.307335	−	2.13756i
$315$	−21.1664	+	21.9433i	−1.19259	+	1.23637i
$316$	−19.2334	−	8.78361i	−1.08196	−	0.494117i
$317$	−4.08419	−	4.28337i	−0.229391	−	0.240578i	0.598972	−	0.800770i	$-0.295576\pi$
$317$	−4.08419	−	4.28337i	−0.229391	−	0.240578i	−0.828363	+	0.560192i	$0.810727\pi$
$318$	−6.12551	+	4.78856i	−0.343501	+	0.268529i
$319$	0.493565	+	0.627619i	0.0276343	+	0.0351399i
$320$	1.23384	−	25.9014i	0.0689736	−	1.44793i
$321$	1.84201	+	1.94306i	0.102811	+	0.108451i
$322$	20.0027	−	26.3567i	1.11471	−	1.46880i
$323$			12.9868i			0.722605i
$324$	6.61737	−	42.5280i	0.367632	−	2.36267i
$325$	−4.58043	−	31.8576i	−0.254076	−	1.76714i
$326$	−2.65403	+	27.7943i	−0.146993	+	1.53938i
$327$	14.5815	−	7.46401i	0.806359	−	0.412761i
$328$	16.2814	−	1.55468i	0.898988	−	0.0858429i
$329$	7.93074	+	1.52852i	0.437236	+	0.0842703i
$330$	−30.9196	+	2.86230i	−1.70207	+	0.157564i
$331$	0.894900	−	3.68883i	0.0491881	−	0.202756i	−0.941915	−	0.335851i	$-0.890976\pi$
$331$	0.894900	−	3.68883i	0.0491881	−	0.202756i	0.991103	+	0.133094i	$0.0424914\pi$
$332$	−39.9018	−	46.0492i	−2.18990	−	2.52728i
$333$	−19.9693	+	11.3759i	−1.09431	+	0.623393i
$334$	11.3759	−	7.31087i	0.622463	−	0.400033i
$335$	1.58442	+	8.22075i	0.0865661	+	0.449148i
$336$	−42.6963	−	0.123423i	−2.32927	−	0.00673326i
$337$	−4.84211	−	12.0950i	−0.263767	−	0.658857i	0.736070	−	0.676905i	$-0.236679\pi$
$337$	−4.84211	−	12.0950i	−0.263767	−	0.658857i	−0.999837	+	0.0180477i	$0.994255\pi$
$338$	0.998929	−	5.18294i	0.0543346	−	0.281915i
$339$	−4.15302	−	3.61968i	−0.225561	−	0.196594i
$340$	−29.3771	+	28.0110i	−1.59319	+	1.51911i
$341$	3.10102	+	6.79029i	0.167930	+	0.367715i
$342$	−19.2904	+	41.6018i	−1.04310	+	2.24957i
$343$	−9.99971	+	15.5599i	−0.539934	+	0.840153i
$344$	2.90108	−	5.02481i	0.156416	−	0.270920i
$345$	9.98989	−	30.2590i	0.537838	−	1.62909i
$346$	12.2099	+	21.1482i	0.656410	+	1.13694i
$347$	−34.9011	−	1.66255i	−1.87359	−	0.0892501i	−0.920283	−	0.391252i	$-0.872042\pi$
$347$	−34.9011	−	1.66255i	−1.87359	−	0.0892501i	−0.953307	+	0.302002i	$0.902345\pi$
$348$	2.89034	+	2.28654i	0.154938	+	0.122571i
$349$	16.3206	+	1.55843i	0.873623	+	0.0834209i	0.522228	−	0.852806i	$-0.325101\pi$
$349$	16.3206	+	1.55843i	0.873623	+	0.0834209i	0.351396	+	0.936227i	$0.385707\pi$
$350$	64.3177	+	18.8854i	3.43793	+	1.00947i
$351$	11.9857	−	12.3539i	0.639749	−	0.659404i
$352$	−13.2115	−	11.4478i	−0.704176	−	0.610172i
$353$	−19.4996	+	24.7958i	−1.03786	+	1.31975i	−0.0917905	+	0.995778i	$0.529259\pi$
$353$	−19.4996	+	24.7958i	−1.03786	+	1.31975i	−0.946068	+	0.323967i	$0.894983\pi$
$354$	45.2988	+	26.3282i	2.40760	+	1.39933i
$355$	−57.0791	−	19.7553i	−3.02945	−	1.04850i
$356$	−6.51208	−	3.35721i	−0.345139	−	0.177932i
$357$	7.32757	+	7.02737i	0.387816	+	0.371928i
$358$	21.9246	−	4.22563i	1.15875	−	0.223331i
$359$	24.3292	−	7.14369i	1.28404	−	0.377030i	0.432653	−	0.901560i	$-0.357577\pi$
$359$	24.3292	−	7.14369i	1.28404	−	0.377030i	0.851391	+	0.524531i	$0.175759\pi$
$360$	−78.9556	+	26.8167i	−4.16132	+	1.41336i
$361$	10.1177	−	11.6765i	0.532512	−	0.614551i
$362$	32.8956	+	46.1955i	1.72896	+	2.42798i
$363$	7.31782	−	11.3147i	0.384086	−	0.593868i
$364$	−34.1854	−	24.3433i	−1.79180	−	1.27593i
$365$	12.1831	−	9.58086i	0.637691	−	0.501485i
$366$	−14.5964	+	12.5741i	−0.762965	+	0.657261i
$367$	22.8849	+	13.2126i	1.19458	+	0.689694i	0.959343	−	0.282243i	$-0.0910785\pi$
$367$	22.8849	+	13.2126i	1.19458	+	0.689694i	0.235242	+	0.971937i	$0.424412\pi$
$368$	40.2675	−	19.2339i	2.09909	−	1.00263i
$369$	−3.06821	−	6.03693i	−0.159725	−	0.314270i
$370$	64.3841	+	41.3771i	3.34717	+	2.15109i
$371$	1.69716	−	4.23930i	0.0881122	−	0.220094i
$372$	21.2209	+	27.1457i	1.10025	+	1.40744i
$373$	27.5314	−	6.67904i	1.42552	−	0.345828i	0.552501	−	0.833512i	$-0.313673\pi$
$373$	27.5314	−	6.67904i	1.42552	−	0.345828i	0.873020	+	0.487684i	$0.162158\pi$
$374$	0.982917	+	10.2936i	0.0508254	+	0.532268i
$375$	31.3039	−	1.40051i	1.61653	−	0.0723218i
$376$	17.3638	+	13.6550i	0.895468	+	0.704204i
$377$	0.415243	+	1.41419i	0.0213861	+	0.0728344i
$378$	13.0347	+	33.3957i	0.670435	+	1.71769i
$379$	10.7760	+	16.7677i	0.553524	+	0.861300i	0.999429	−	0.0337799i	$-0.0107545\pi$
$379$	10.7760	+	16.7677i	0.553524	+	0.861300i	−0.445905	+	0.895080i	$0.647118\pi$
$380$	107.554	−	5.12343i	5.51740	−	0.262826i
$381$	0.0421704	−	0.428534i	0.00216046	−	0.0219545i
$382$	−4.78892	+	5.02248i	−0.245023	+	0.256972i
$383$	−16.0786	+	6.43689i	−0.821577	+	0.328910i	−0.744086	−	0.668083i	$-0.767115\pi$
$383$	−16.0786	+	6.43689i	−0.821577	+	0.328910i	−0.0774905	+	0.996993i	$0.524691\pi$
$384$	2.88896	+	1.49995i	0.147427	+	0.0765440i
$385$	14.8555	−	10.5785i	0.757106	−	0.539133i
$386$	−11.7246	+	39.9302i	−0.596764	+	2.03239i
$387$	−2.37589	−	0.355633i	−0.120773	−	0.0180778i
$388$	−67.6130	+	9.72129i	−3.43253	+	0.493524i
$389$	−5.04145	+	2.59905i	−0.255611	+	0.131777i	−0.581270	−	0.813710i	$-0.697444\pi$
$389$	−5.04145	+	2.59905i	−0.255611	+	0.131777i	0.325659	+	0.945487i	$0.394414\pi$
$390$	−54.9514	−	16.3079i	−2.78257	−	0.825782i
$391$	−10.0860	−	3.29754i	−0.510069	−	0.166764i
$392$	0.114517	−	0.0661165i	0.00578399	−	0.00333939i
$393$	0.202408	+	0.234960i	0.0102101	+	0.0118521i
$394$	−34.6529	−	13.8729i	−1.74579	−	0.698909i
$395$	15.4285	−	7.04597i	0.776293	−	0.354521i
$396$	−8.56091	+	24.2800i	−0.430202	+	1.22012i
$397$	6.66528	−	14.5949i	0.334521	−	0.732499i	−0.665381	−	0.746504i	$-0.731731\pi$
$397$	6.66528	−	14.5949i	0.334521	−	0.732499i	0.999902	+	0.0140053i	$0.00445816\pi$
$398$	−12.1867	−	35.2110i	−0.610862	−	1.76497i
$399$	−2.48255	−	26.8175i	−0.124283	−	1.34255i
$400$	65.4312	+	62.3886i	3.27156	+	3.11943i
$401$	−2.00823	+	5.80239i	−0.100286	+	0.289757i	−0.983972	−	0.178323i	$-0.942933\pi$
$401$	−2.00823	+	5.80239i	−0.100286	+	0.289757i	0.883686	+	0.468080i	$0.155054\pi$
$402$	9.56000	+	2.34851i	0.476809	+	0.117133i
$403$	0.655670	+	13.7642i	0.0326613	+	0.685644i
$404$	−27.6155	+	23.9290i	−1.37392	+	1.19051i
$405$	22.3061	+	26.3522i	1.10840	+	1.30945i
$406$	−3.03847	−	0.436866i	−0.150797	−	0.0216813i
$407$	12.9912	−	4.49629i	0.643949	−	0.222873i
$408$	9.00604	+	26.2667i	0.445865	+	1.30039i
$409$	5.04888	+	20.8118i	0.249651	+	1.02908i	0.949246	+	0.314535i	$0.101849\pi$
$409$	5.04888	+	20.8118i	0.249651	+	1.02908i	−0.699595	+	0.714540i	$0.746636\pi$
$410$	−13.0810	+	18.3696i	−0.646023	+	0.907212i
$411$	4.66642	+	11.7545i	0.230177	+	0.579807i
$412$	−32.4072	−	62.8612i	−1.59659	−	3.09695i
$413$	−30.7717			−1.51418
$414$	−27.4112	−	25.5449i	−1.34719	−	1.25546i
$415$	48.8778			2.39932
$416$	−14.7869	−	28.6825i	−0.724985	−	1.40627i
$417$	−36.5107	−	5.35722i	−1.78794	−	0.262344i
$418$	15.9110	−	22.3439i	0.778232	−	1.09287i
$419$	−3.26276	−	13.4493i	−0.159396	−	0.657041i	−0.994298	−	0.106641i	$-0.965990\pi$
$419$	−3.26276	−	13.4493i	−0.159396	−	0.657041i	0.834901	−	0.550400i	$-0.185525\pi$
$420$	55.3084	−	63.4578i	2.69878	−	3.09642i
$421$	19.1830	−	6.63930i	0.934922	−	0.323580i	0.183212	−	0.983073i	$-0.441351\pi$
$421$	19.1830	−	6.63930i	0.934922	−	0.323580i	0.751710	+	0.659494i	$0.229229\pi$
$422$	−24.5167	−	3.52497i	−1.19345	−	0.171593i
$423$	2.62747	−	8.76066i	0.127752	−	0.425958i
$424$	9.43867	−	8.17866i	0.458382	−	0.397191i
$425$	−1.02291	−	21.4735i	−0.0496184	−	1.04162i
$426$	−49.1595	+	51.2595i	−2.38178	+	2.48353i
$427$	3.70075	−	10.6926i	0.179092	−	0.517451i
$428$	−5.35007	−	5.10128i	−0.258606	−	0.246580i
$429$	−8.40419	+	5.94806i	−0.405758	+	0.287175i
$430$	2.61658	+	7.56012i	0.126183	+	0.364582i
$431$	7.12729	−	15.6066i	0.343309	−	0.751743i	−0.656688	−	0.754163i	$-0.728043\pi$
$431$	7.12729	−	15.6066i	0.343309	−	0.751743i	0.999997	+	0.00241981i	$0.000770251\pi$
$432$	−5.01321	+	48.0897i	−0.241198	+	2.31372i
$433$	−21.2797	+	9.71810i	−1.02264	+	0.467022i	−0.854891	−	0.518808i	$-0.826376\pi$
$433$	−21.2797	+	9.71810i	−1.02264	+	0.467022i	−0.167745	+	0.985830i	$0.553649\pi$
$434$	−26.6438	−	10.6666i	−1.27894	−	0.512012i
$435$	−2.90452	+	0.551097i	−0.139261	+	0.0264231i
$436$	−39.1682	+	22.6138i	−1.87582	+	1.08300i
$437$	14.4918	+	24.1317i	0.693239	+	1.15438i
$438$	−4.24537	−	17.7231i	−0.202852	−	0.846842i
$439$	1.01209	−	0.521771i	0.0483046	−	0.0249028i	−0.433905	−	0.900959i	$-0.642865\pi$
$439$	1.01209	−	0.521771i	0.0483046	−	0.0249028i	0.482210	+	0.876056i	$0.339834\pi$
$440$	49.3709	−	7.09846i	2.35367	−	0.338406i
$441$	−0.0428404	−	0.0340928i	−0.00204002	−	0.00162347i
$442$	−5.37768	+	18.3147i	−0.255790	+	0.871142i
$443$	23.0851	−	16.4388i	1.09681	−	0.781033i	0.119495	−	0.992835i	$-0.461873\pi$
$443$	23.0851	−	16.4388i	1.09681	−	0.781033i	0.977313	+	0.211802i	$0.0679331\pi$
$444$	53.4798	−	34.1514i	2.53804	−	1.62075i
$445$	5.45615	−	2.18431i	0.258646	−	0.103546i
$446$	−12.1586	+	12.7515i	−0.575725	+	0.603803i
$447$	19.3914	−	8.78809i	0.917181	−	0.415662i
$448$	17.8872	−	0.852073i	0.845092	−	0.0402567i
$449$	−17.8738	−	27.8121i	−0.843516	−	1.31254i	−0.948085	−	0.318018i	$-0.896983\pi$
$449$	−17.8738	−	27.8121i	−0.843516	−	1.31254i	0.104569	−	0.994518i	$-0.466654\pi$
$450$	28.6196	−	70.3076i	1.34914	−	3.31433i
$451$	1.14123	+	3.88666i	0.0537382	+	0.183015i
$452$	11.9563	+	9.40252i	0.562376	+	0.442257i
$453$	−2.05694	+	3.96174i	−0.0966433	+	0.186139i
$454$	−0.296160	−	3.10153i	−0.0138995	−	0.145562i
$455$	32.7159	−	7.93679i	1.53374	−	0.372082i
$456$	27.5741	−	68.3038i	1.29127	−	3.19862i
$457$	−8.73113	+	21.8093i	−0.408425	+	1.02020i	0.571460	+	0.820630i	$0.306377\pi$
$457$	−8.73113	+	21.8093i	−0.408425	+	1.02020i	−0.979884	+	0.199566i	$0.936047\pi$
$458$	22.8208	+	14.6660i	1.06634	+	0.685297i
$459$	8.75389	−	7.45336i	0.408597	−	0.347893i
$460$	−23.3305	+	84.8308i	−1.08779	+	3.95526i
$461$	−2.99383	−	1.72849i	−0.139437	−	0.0805038i	0.428659	−	0.903466i	$-0.358986\pi$
$461$	−2.99383	−	1.72849i	−0.139437	−	0.0805038i	−0.568095	+	0.822963i	$0.692320\pi$
$462$	−3.99742	−	21.0681i	−0.185977	−	0.980178i
$463$	−30.0270	+	23.6135i	−1.39547	+	1.09741i	−0.413057	+	0.910705i	$0.635539\pi$
$463$	−30.0270	+	23.6135i	−1.39547	+	1.09741i	−0.982416	+	0.186707i	$0.940218\pi$
$464$	−3.37246	−	2.40152i	−0.156563	−	0.111488i
$465$	−27.6045	−	1.39495i	−1.28013	−	0.0646893i
$466$	40.9109	+	57.4514i	1.89516	+	2.66138i
$467$	−22.8932	+	26.4201i	−1.05937	+	1.22258i	−0.0852940	+	0.996356i	$0.527183\pi$
$467$	−22.8932	+	26.4201i	−1.05937	+	1.22258i	−0.974076	+	0.226222i	$0.927362\pi$
$468$	−31.3289	+	35.7359i	−1.44818	+	1.65189i
$469$	−5.54744	+	1.62887i	−0.256157	+	0.0752145i
$470$	−29.9075	+	5.76419i	−1.37953	+	0.265882i
$471$	24.4406	−	7.09972i	1.12616	−	0.327138i
$472$	−74.8052	−	38.5648i	−3.44319	−	1.77509i
$473$	1.35798	+	0.470002i	0.0624401	+	0.0216107i
$474$	0.0576517	−	19.9438i	0.00264803	−	0.916048i
$475$	−35.2521	+	44.8267i	−1.61748	+	2.05679i
$476$	−21.1849	−	18.3568i	−0.971008	−	0.841383i
$477$	−4.58246	−	2.39606i	−0.209817	−	0.109708i
$478$	32.1312	+	9.43457i	1.46965	+	0.431527i
$479$	−20.3430	−	1.94252i	−0.929497	−	0.0887562i	−0.380688	−	0.924704i	$-0.624313\pi$
$479$	−20.3430	−	1.94252i	−0.929497	−	0.0887562i	−0.548809	+	0.835948i	$0.684919\pi$
$480$	60.1597	−	23.8828i	2.74590	−	1.09009i
$481$	25.3481	+	1.20748i	1.15577	+	0.0550563i
$482$	16.6151	+	28.7782i	0.756798	+	1.31081i
$483$	21.4577	+	4.88132i	0.976358	+	0.222108i
$484$	−18.6021	+	32.2198i	−0.845551	+	1.46454i
$485$	29.6245	−	46.0966i	1.34518	−	2.09314i
$486$	39.1133	−	10.8732i	1.77421	−	0.493217i
$487$	−0.0167778	−	0.0367382i	−0.000760273	−	0.00166477i	0.909251	−	0.416247i	$-0.136655\pi$
$487$	−0.0167778	−	0.0367382i	−0.000760273	−	0.00166477i	−0.910012	+	0.414582i	$0.863928\pi$
$488$	22.3969	−	21.3554i	1.01386	−	0.966716i
$489$	−17.5657	+	6.02276i	−0.794350	+	0.272358i
$490$	−0.0345053	+	0.179031i	−0.00155879	+	0.00808778i
$491$	−11.4600	−	28.6257i	−0.517183	−	1.29186i	−0.925406	−	0.378977i	$-0.876276\pi$
$491$	−11.4600	−	28.6257i	−0.517183	−	1.29186i	0.408223	−	0.912882i	$-0.366148\pi$
$492$	9.30176	+	16.2192i	0.419356	+	0.731218i
$493$	0.186313	+	0.966685i	0.00839112	+	0.0435373i
$494$	42.5966	−	27.3752i	1.91651	−	1.23167i
$495$	−10.2224	−	17.9446i	−0.459464	−	0.806548i
$496$	−25.3480	−	29.2531i	−1.13816	−	1.31350i
$497$	9.83405	−	40.5365i	0.441117	−	1.81831i
$498$	24.0261	−	52.2098i	1.07663	−	2.33958i
$499$	−6.18830	−	1.19270i	−0.277026	−	0.0533925i	0.0488456	−	0.998806i	$-0.484446\pi$
$499$	−6.18830	−	1.19270i	−0.277026	−	0.0533925i	−0.325872	+	0.945414i	$0.605658\pi$
$500$	−86.1249	+	8.22393i	−3.85162	+	0.367786i
$501$	7.55184	+	4.88418i	0.337392	+	0.218209i
$502$	4.49025	−	47.0241i	0.200410	−	2.09879i
$503$	1.47746	+	10.2760i	0.0658768	+	0.458183i	0.995884	+	0.0906409i	$0.0288915\pi$
$503$	1.47746	+	10.2760i	0.0658768	+	0.458183i	−0.930007	+	0.367542i	$0.880199\pi$
$504$	−23.6184	−	52.5185i	−1.05205	−	2.33936i
$505$		−	29.3119i		−	1.30436i
$506$	13.3129	+	18.0304i	0.591832	+	0.801550i
$507$	3.41394	−	0.817771i	0.151618	−	0.0363185i
$508$	−0.0565701	+	1.18755i	−0.00250989	+	0.0526891i
$509$	6.83816	+	8.69542i	0.303096	+	0.385418i	0.913613	−	0.406585i	$-0.133281\pi$
$509$	6.83816	+	8.69542i	0.303096	+	0.385418i	−0.610517	+	0.792003i	$0.709038\pi$
$510$	−35.5028	−	14.3324i	−1.57209	−	0.634650i
$511$	7.38622	+	7.74645i	0.326747	+	0.342683i
$512$	−40.2012	−	18.3593i	−1.77666	−	0.811373i
$513$	−30.4973	−	0.264482i	−1.34649	−	0.0116772i
$514$	8.71855	−	60.6388i	0.384559	−	2.67466i
$515$	55.1330	+	13.3751i	2.42945	+	0.589378i
$516$	6.60103	+	0.649583i	0.290594	+	0.0285963i
$517$	−2.50695	+	4.86280i	−0.110255	+	0.213866i
$518$	−24.2187	+	46.9777i	−1.06411	+	2.06408i
$519$	−9.45904	+	13.2024i	−0.415206	+	0.579522i
$520$	89.4782	+	21.7072i	3.92388	+	0.951923i
$521$	0.289337	−	2.01239i	0.0126761	−	0.0881642i	−0.982501	−	0.186256i	$-0.940365\pi$
$521$	0.289337	−	2.01239i	0.0126761	−	0.0881642i	0.995177	+	0.0980915i	$0.0312738\pi$
$522$	−0.839063	+	3.37342i	−0.0367248	+	0.147651i
$523$	−11.5481	−	5.27386i	−0.504965	−	0.230610i	0.146610	−	0.989194i	$-0.453164\pi$
$523$	−11.5481	−	5.27386i	−0.504965	−	0.230610i	−0.651574	+	0.758585i	$0.725891\pi$
$524$	−0.590876	−	0.619693i	−0.0258125	−	0.0270714i
$525$	6.21716	+	44.1468i	0.271339	+	1.92673i
$526$	−5.02409	−	6.38864i	−0.219061	−	0.278558i
$527$	−0.437951	+	9.19372i	−0.0190774	+	0.400485i
$528$	8.22836	−	27.7265i	0.358093	−	1.20664i
$529$	−22.4212	+	5.12743i	−0.974834	+	0.222932i
$530$			17.2203i			0.748002i
$531$	−3.51286	+	34.6690i	−0.152445	+	1.50450i
$532$	10.5825	+	73.6028i	0.458809	+	3.19109i
$533$	−0.710780	+	7.44362i	−0.0307873	+	0.322419i
$534$	0.348773	−	6.90181i	0.0150929	−	0.298670i
$535$	5.90307	−	0.563674i	0.255212	−	0.0243698i
$536$	−15.5271	−	2.99260i	−0.670667	−	0.129260i
$537$	8.57887	+	12.1213i	0.370205	+	0.523074i
$538$	16.7015	−	68.8443i	0.720051	−	2.96809i
$539$	0.0214468	+	0.0247509i	0.000923777	+	0.00106610i
$540$	−65.1807	−	69.5575i	−2.80493	−	2.99328i
$541$	4.54887	−	2.92338i	0.195571	−	0.125686i	−0.439190	−	0.898394i	$-0.644735\pi$
$541$	4.54887	−	2.92338i	0.195571	−	0.125686i	0.634762	+	0.772708i	$0.281098\pi$
$542$	14.4821	+	75.1405i	0.622061	+	3.22756i
$543$	−18.9531	+	32.6097i	−0.813356	+	1.39942i
$544$	−8.01095	−	20.0104i	−0.343466	−	0.857938i
$545$	6.86609	−	35.6247i	0.294111	−	1.52599i
$546$	7.60377	−	38.8475i	0.325411	−	1.66252i
$547$	10.6017	−	10.1087i	0.453294	−	0.432215i	−0.428720	−	0.903437i	$-0.641035\pi$
$547$	10.6017	−	10.1087i	0.453294	−	0.432215i	0.882015	+	0.471222i	$0.156187\pi$
$548$	−14.5055	−	31.7626i	−0.619645	−	1.35683i
$549$	−11.6243	−	5.39010i	−0.496115	−	0.230044i
$550$	−24.5487	+	38.1985i	−1.04676	+	1.62879i
$551$	1.30576	−	2.26165i	0.0556274	−	0.0963494i
$552$	46.0455	+	38.7583i	1.95983	+	1.64966i
$553$	5.85663	+	10.1440i	0.249049	+	0.431366i
$554$	−39.6052	−	1.88663i	−1.68266	−	0.0801551i
$555$	−7.38959	+	50.3618i	−0.313671	+	2.13774i
$556$	101.424	+	9.68485i	4.30135	+	0.410729i
$557$	29.7304	+	8.72965i	1.25972	+	0.369887i	0.842390	−	0.538868i	$-0.181148\pi$
$557$	29.7304	+	8.72965i	1.25972	+	0.369887i	0.417329	+	0.908755i	$0.362966\pi$
$558$	−15.0591	+	28.8006i	−0.637503	+	1.21923i
$559$	2.00475	+	1.73713i	0.0847920	+	0.0734727i
$560$	−58.4557	+	74.3325i	−2.47021	+	3.14112i
$561$	−5.96576	+	3.42138i	−0.251875	+	0.144451i
$562$	26.7223	+	9.24869i	1.12721	+	0.390133i
$563$	−9.44881	−	4.87120i	−0.398220	−	0.205297i	0.247471	−	0.968895i	$-0.420400\pi$
$563$	−9.44881	−	4.87120i	−0.398220	−	0.205297i	−0.645691	+	0.763599i	$0.723431\pi$
$564$	−6.02446	+	24.5235i	−0.253675	+	1.03263i
$565$	−11.9810	+	2.30914i	−0.504043	+	0.0971463i
$566$	−38.1351	+	11.1975i	−1.60294	+	0.470665i
$567$	−16.6518	+	17.0644i	−0.699311	+	0.716639i
$568$	74.7088	−	86.2186i	3.13471	−	3.61765i
$569$	−13.7824	−	19.3547i	−0.577790	−	0.811392i	0.417465	−	0.908693i	$-0.362919\pi$
$569$	−13.7824	−	19.3547i	−0.577790	−	0.811392i	−0.995255	+	0.0973007i	$0.968979\pi$
$570$	46.2779	+	90.4073i	1.93837	+	3.78674i
$571$	−7.19014	−	5.12008i	−0.300898	−	0.214269i	0.419628	−	0.907696i	$-0.362160\pi$
$571$	−7.19014	−	5.12008i	−0.300898	−	0.214269i	−0.720526	+	0.693427i	$0.756100\pi$
$572$	22.3456	−	17.5728i	0.934316	−	0.734754i
$573$	−4.35723	−	1.52217i	−0.182026	−	0.0635895i
$574$	−13.4871	−	7.78679i	−0.562941	−	0.325014i
$575$	−25.8628	−	38.7601i	−1.07855	−	1.61641i
$576$	1.08199	−	20.2499i	0.0450831	−	0.843746i
$577$	−30.3039	−	19.4751i	−1.26157	−	0.810760i	−0.273069	−	0.961994i	$-0.588039\pi$
$577$	−30.3039	−	19.4751i	−1.26157	−	0.810760i	−0.988498	+	0.151235i	$0.951675\pi$
$578$	11.7159	−	29.2648i	0.487316	−	1.21726i
$579$	−27.4075	+	3.85978i	−1.13902	+	0.160407i
$580$	7.93238	−	1.92437i	0.329374	−	0.0799053i
$581$	3.20856	+	33.6016i	0.133114	+	1.39403i
$582$	−34.6770	−	54.3029i	−1.43741	−	2.25093i
$583$	2.43141	+	1.91208i	0.100699	+	0.0791902i
$584$	8.24744	+	28.0882i	0.341282	+	1.16230i
$585$	−5.20717	−	37.7654i	−0.215290	−	1.56141i
$586$	−29.3175	−	45.6189i	−1.21109	−	1.88450i
$587$	6.46343	−	0.307891i	0.266774	−	0.0127080i	0.0862313	−	0.996275i	$-0.472518\pi$
$587$	6.46343	−	0.307891i	0.266774	−	0.0127080i	0.180543	+	0.983567i	$0.442215\pi$
$588$	0.122882	+	0.0880406i	0.00506759	+	0.00363074i
$589$	16.8489	−	17.6706i	0.694247	−	0.728105i
$590$	107.730	−	43.1287i	4.43519	−	1.77558i
$591$	−1.10955	−	24.8005i	−0.0456409	−	1.02016i
$592$	−58.0657	+	41.3484i	−2.38648	+	1.69941i
$593$	3.77109	−	12.8432i	0.154860	−	0.527405i	−0.845114	−	0.534586i	$-0.820468\pi$
$593$	3.77109	−	12.8432i	0.154860	−	0.527405i	0.999974	+	0.00718076i	$0.00228573\pi$
$594$	−24.1927	+	2.09858i	−0.992640	+	0.0861058i
$595$	22.2573	−	3.20012i	0.912461	−	0.131192i
$596$	−52.2468	+	26.9351i	−2.14011	+	1.10331i
$597$	17.9843	−	17.0491i	0.736050	−	0.697771i
$598$	10.4445	+	40.0328i	0.427109	+	1.63706i
$599$	1.02406	−	0.591240i	0.0418419	−	0.0241574i	−0.478933	−	0.877851i	$-0.658976\pi$
$599$	1.02406	−	0.591240i	0.0418419	−	0.0241574i	0.520775	+	0.853694i	$0.325643\pi$
$600$	−40.2134	+	115.111i	−1.64171	+	4.69940i
$601$	−30.2389	−	12.1058i	−1.23347	−	0.493807i	−0.338937	−	0.940809i	$-0.610067\pi$
$601$	−30.2389	−	12.1058i	−1.23347	−	0.493807i	−0.894533	+	0.447003i	$0.852491\pi$
$602$	−5.02553	+	2.29508i	−0.204825	+	0.0935405i
$603$	1.20188	+	6.43597i	0.0489444	+	0.262093i
$604$	5.11992	−	11.2111i	0.208327	−	0.456172i
$605$	−9.76109	−	28.2028i	−0.396845	−	1.14661i
$606$	−31.3101	−	14.4084i	−1.27188	−	0.585300i
$607$	17.9570	+	17.1219i	0.728851	+	0.694958i	0.960636	−	0.277809i	$-0.0896083\pi$
$607$	17.9570	+	17.1219i	0.728851	+	0.694958i	−0.231786	+	0.972767i	$0.574457\pi$
$608$	−18.7009	+	54.0327i	−0.758422	+	2.19132i
$609$	−0.569524	−	1.96057i	−0.0230783	−	0.0794463i
$610$	2.03030	+	42.6212i	0.0822043	+	1.72568i
$611$	−7.63244	+	6.61355i	−0.308776	+	0.267556i
$612$	−23.1001	+	21.7723i	−0.933767	+	0.880095i
$613$	−26.4982	−	3.80986i	−1.07025	−	0.153879i	−0.415401	−	0.909638i	$-0.636359\pi$
$613$	−26.4982	−	3.80986i	−1.07025	−	0.153879i	−0.654849	+	0.755760i	$0.727268\pi$
$614$	4.21702	−	1.45953i	0.170185	−	0.0589017i
$615$	−14.7191	−	2.88102i	−0.593531	−	0.116174i
$616$	8.12085	+	33.4746i	0.327198	+	1.34873i
$617$	−7.73635	+	10.8642i	−0.311454	+	0.437376i	−0.940399	−	0.340074i	$-0.889548\pi$
$617$	−7.73635	+	10.8642i	−0.311454	+	0.437376i	0.628945	+	0.777450i	$0.283487\pi$
$618$	41.3877	−	52.3168i	1.66486	−	2.10449i
$619$	0.404571	+	0.784759i	0.0162611	+	0.0315421i	0.896826	−	0.442383i	$-0.145867\pi$
$619$	0.404571	+	0.784759i	0.0162611	+	0.0315421i	−0.880565	+	0.473925i	$0.842837\pi$
$620$	76.3132			3.06481
$621$	7.94912	−	23.6180i	0.318987	−	0.947759i
$622$	−48.7272			−1.95378
$623$	1.85980	+	3.60750i	0.0745112	+	0.144531i
$624$	33.1235	−	41.8703i	1.32600	−	1.67615i
$625$	12.0775	−	16.9604i	0.483098	−	0.678417i
$626$	2.33089	+	9.60804i	0.0931609	+	0.384015i
$627$	17.9035	+	3.50433i	0.714997	+	0.139949i
$628$	−66.4051	+	22.9830i	−2.64985	+	0.917123i
$629$	16.7778	+	2.41228i	0.668973	+	0.0961838i
$630$	76.0524	+	22.8094i	3.03000	+	0.908749i
$631$	−5.95890	+	5.16342i	−0.237220	+	0.205552i	−0.765356	−	0.643608i	$-0.777437\pi$
$631$	−5.95890	+	5.16342i	−0.237220	+	0.205552i	0.528135	+	0.849160i	$0.322891\pi$
$632$	1.52433	+	31.9996i	0.0606345	+	1.27287i
$633$	−4.59536	−	15.8194i	−0.182649	−	0.628764i
$634$	−5.04115	+	14.5655i	−0.200210	+	0.578468i
$635$	−0.690226	−	0.658130i	−0.0273908	−	0.0261171i
$636$	12.9699	+	5.96855i	0.514292	+	0.236668i
$637$	0.0197730	+	0.0571302i	0.000783433	+	0.00226358i
$638$	0.863797	−	1.89145i	0.0341980	−	0.0748833i
$639$	−44.5478	−	15.7071i	−1.76228	−	0.621364i
$640$	6.55799	−	2.99493i	0.259227	−	0.118385i
$641$	37.5848	+	15.0467i	1.48451	+	0.594309i	0.965487	−	0.260451i	$-0.0838713\pi$
$641$	37.5848	+	15.0467i	1.48451	+	0.594309i	0.519024	+	0.854760i	$0.326296\pi$
$642$	2.29957	−	6.58256i	0.0907570	−	0.259793i
$643$	−6.46771	+	3.73413i	−0.255061	+	0.147260i	−0.622080	−	0.782954i	$-0.713712\pi$
$643$	−6.46771	+	3.73413i	−0.255061	+	0.147260i	0.367018	+	0.930214i	$0.380379\pi$
$644$	−59.8494	−	10.4701i	−2.35840	−	0.412581i
$645$	−3.86140	+	3.66059i	−0.152042	+	0.144135i
$646$	30.0614	−	15.4977i	1.18275	−	0.609749i
$647$	−32.7053	+	4.70232i	−1.28578	+	0.184867i	−0.751100	−	0.660188i	$-0.770476\pi$
$647$	−32.7053	+	4.70232i	−1.28578	+	0.184867i	−0.534679	+	0.845055i	$0.679567\pi$
$648$	−61.8662	+	20.6142i	−2.43033	+	0.809803i
$649$	5.87246	−	19.9998i	0.230514	−	0.785060i
$650$	−68.2767	+	48.6196i	−2.67803	+	1.90702i
$651$	−0.853108	−	19.0686i	−0.0334359	−	0.747356i
$652$	47.5980	−	19.0554i	1.86408	−	0.746266i
$653$	22.0717	−	23.1482i	0.863734	−	0.905858i	−0.132621	−	0.991167i	$-0.542339\pi$
$653$	22.0717	−	23.1482i	0.863734	−	0.905858i	0.996355	+	0.0853088i	$0.0271877\pi$
$654$	−34.6782	−	24.8456i	−1.35602	−	0.971540i
$655$	0.686078	−	0.0326819i	0.0268073	−	0.00127699i
$656$	−11.3557	−	17.6698i	−0.443366	−	0.689891i
$657$	9.57073	−	7.43736i	0.373390	−	0.290159i
$658$	−5.92592	−	20.1818i	−0.231016	−	0.786770i
$659$	−8.78200	−	6.90624i	−0.342098	−	0.269029i	0.432297	−	0.901731i	$-0.357703\pi$
$659$	−8.78200	−	6.90624i	−0.342098	−	0.269029i	−0.774395	+	0.632702i	$0.781946\pi$
$660$	30.6887	+	48.0574i	1.19456	+	1.87063i
$661$	2.83114	+	29.6490i	0.110119	+	1.15321i	0.866532	+	0.499121i	$0.166344\pi$
$661$	2.83114	+	29.6490i	0.110119	+	1.15321i	−0.756414	+	0.654093i	$0.773050\pi$
$662$	−9.60668	+	2.33056i	−0.373374	+	0.0905797i
$663$	−12.5710	+	1.77036i	−0.488216	+	0.0687551i
$664$	−34.3114	+	85.7057i	−1.33154	+	3.32603i
$665$	−50.1802	−	32.2489i	−1.94591	−	1.25056i
$666$	50.1626	+	32.6489i	1.94376	+	1.26512i
$667$	1.42492	+	1.58836i	0.0551730	+	0.0615017i
$668$	−21.5047	−	12.4157i	−0.832041	−	0.480379i
$669$	−11.0625	−	3.86463i	−0.427702	−	0.149415i
$670$	17.1383	−	13.4777i	0.662112	−	0.520691i
$671$	6.24330	+	4.44583i	0.241020	+	0.171629i
$672$	20.3676	+	39.7897i	0.785698	+	1.53492i
$673$	−14.0259	−	19.6966i	−0.540659	−	0.759250i	0.450378	−	0.892838i	$-0.351289\pi$
$673$	−14.0259	−	19.6966i	−0.540659	−	0.759250i	−0.991037	+	0.133588i	$0.957350\pi$
$674$	−22.2188	+	25.6418i	−0.855836	+	0.987687i
$675$	50.4478	−	1.96481i	1.94173	−	0.0756256i
$676$	−9.29994	+	2.73071i	−0.357690	+	0.105027i
$677$	−45.2015	+	8.71187i	−1.73723	+	0.334824i	−0.956874	−	0.290505i	$-0.906177\pi$
$677$	−45.2015	+	8.71187i	−1.73723	+	0.334824i	−0.780361	+	0.625329i	$0.784965\pi$
$678$	−3.42273	+	13.9328i	−0.131449	+	0.535085i
$679$	33.6343	+	17.3397i	1.29076	+	0.665435i
$680$	58.1175	+	20.1147i	2.22870	+	0.771362i
$681$	1.79753	−	1.03089i	0.0688813	−	0.0395036i
$682$	12.0173	−	15.2813i	0.460167	−	0.585150i
$683$	−0.675703	−	0.585500i	−0.0258551	−	0.0224035i	0.641837	−	0.766841i	$-0.278172\pi$
$683$	−0.675703	−	0.585500i	−0.0258551	−	0.0224035i	−0.667692	+	0.744437i	$0.732718\pi$
$684$	84.1327	−	3.52035i	3.21689	−	0.134604i
$685$	26.8757	+	7.89143i	1.02687	+	0.301516i
$686$	47.9505	+	4.57872i	1.83076	+	0.174816i
$687$	−2.61922	+	17.8506i	−0.0999294	+	0.681043i
$688$	−7.44288	−	0.354548i	−0.283757	−	0.0135170i
$689$	2.85494	+	4.94490i	0.108764	+	0.188386i
$690$	−81.9638	+	12.9852i	−3.12031	+	0.494337i
$691$	−5.62405	+	9.74115i	−0.213949	+	0.370571i	−0.952947	−	0.303137i	$-0.901966\pi$
$691$	−5.62405	+	9.74115i	−0.213949	+	0.370571i	0.738998	+	0.673708i	$0.235299\pi$
$692$	24.2434	−	37.7235i	0.921597	−	1.43403i
$693$	11.6651	−	8.20549i	0.443122	−	0.311701i
$694$	37.8006	+	82.7718i	1.43489	+	3.14198i
$695$	−59.1507	+	56.4001i	−2.24371	+	2.13938i
$696$	1.07259	−	5.47985i	0.0406565	−	0.207713i
$697$	−0.945222	+	4.90428i	−0.0358028	+	0.185763i
$698$	−15.8687	−	39.6381i	−0.600640	−	1.50033i
$699$	−23.5712	+	40.5553i	−0.891544	+	1.53394i
$700$	−23.2954	−	120.868i	−0.880482	−	4.56838i
$701$	−19.2081	+	12.3443i	−0.725479	+	0.466237i	−0.850539	−	0.525912i	$-0.823724\pi$
$701$	−19.2081	+	12.3443i	−0.725479	+	0.466237i	0.125060	+	0.992149i	$0.460088\pi$
$702$	−42.8995	−	13.0016i	−1.61914	−	0.490712i
$703$	−29.4453	−	33.9817i	−1.11055	−	1.28164i
$704$	−2.85979	+	11.7882i	−0.107782	+	0.444285i
$705$	−11.7025	−	16.5348i	−0.440740	−	0.622735i
$706$	80.6660	+	15.5471i	3.03591	+	0.585123i
$707$	20.1508	−	1.92416i	0.757847	−	0.0723656i
$708$	4.85570	−	96.0886i	0.182488	−	3.61123i
$709$	0.301620	−	3.15871i	0.0113276	−	0.118628i	−0.988039	−	0.154201i	$-0.950720\pi$
$709$	0.301620	−	3.15871i	0.0113276	−	0.118628i	0.999367	+	0.0355733i	$0.0113257\pi$
$710$	22.3862	+	155.700i	0.840140	+	5.84330i
$711$	12.0973	−	5.44034i	0.453684	−	0.204029i
$712$			11.1005i			0.416010i
$713$	9.44539	+	17.5722i	0.353733	+	0.658085i
$714$	7.52240	−	25.3477i	0.281519	−	0.948612i
$715$	−1.08505	+	22.7780i	−0.0405786	+	0.851849i
$716$	−25.3451	−	32.2290i	−0.947193	−	1.20445i
$717$	3.10591	+	22.0544i	0.115992	+	0.823638i
$718$	−45.5690	−	47.7914i	−1.70062	−	1.78356i
$719$	−7.99664	−	3.65194i	−0.298224	−	0.136194i	0.260683	−	0.965424i	$-0.416052\pi$
$719$	−7.99664	−	3.65194i	−0.298224	−	0.136194i	−0.558908	+	0.829230i	$0.688779\pi$
$720$	77.0734	+	74.3448i	2.87236	+	2.77067i
$721$	−5.57569	+	38.7798i	−0.207649	+	1.44423i
$722$	−39.1022	−	9.48609i	−1.45523	−	0.353036i
$723$	−12.8717	+	17.9657i	−0.478705	+	0.668151i
$724$	47.7189	−	92.5617i	1.77346	−	3.44003i
$725$	−1.98092	+	3.84246i	−0.0735697	+	0.142705i
$726$	−34.9235	−	3.43669i	−1.29613	−	0.127548i
$727$	−42.6376	−	10.3438i	−1.58134	−	0.383629i	−0.653596	−	0.756844i	$-0.726740\pi$
$727$	−42.6376	−	10.3438i	−1.58134	−	0.383629i	−0.927745	+	0.373215i	$0.878256\pi$
$728$	−9.04908	+	62.9377i	−0.335381	+	2.33263i
$729$	17.3247	+	20.7088i	0.641655	+	0.766993i
$730$	−36.7160	−	16.7676i	−1.35892	−	0.620598i
$731$	1.22270	+	1.28234i	0.0452233	+	0.0474289i
$732$	32.8050	+	13.2433i	1.21251	+	0.489487i
$733$	−21.4708	−	27.3024i	−0.793043	−	1.00844i	−0.999550	−	0.0299915i	$-0.990452\pi$
$733$	−21.4708	−	27.3024i	−0.793043	−	1.00844i	0.206507	−	0.978445i	$-0.433790\pi$
$734$	3.27451	−	68.7404i	0.120864	−	2.53726i
$735$	−0.117925	+	0.0282477i	−0.00434975	+	0.00104193i
$736$	−37.2151	−	28.2434i	−1.37177	−	1.04107i
$737$		−	3.91635i		−	0.144261i
$738$	−10.3126	+	14.3063i	−0.379614	+	0.526623i
$739$	5.64224	+	39.2426i	0.207553	+	1.44356i	0.781108	+	0.624396i	$0.214655\pi$
$739$	5.64224	+	39.2426i	0.207553	+	1.44356i	−0.573555	+	0.819167i	$0.694436\pi$
$740$	13.3590	−	139.902i	0.491086	−	5.14289i
$741$	28.2775	+	18.2885i	1.03880	+	0.671847i
$742$	−11.8383	+	1.13042i	−0.434597	+	0.0414990i
$743$	37.4594	+	7.21971i	1.37425	+	0.264865i	0.822321	−	0.569024i	$-0.192679\pi$
$743$	37.4594	+	7.21971i	1.37425	+	0.264865i	0.551931	+	0.833890i	$0.313891\pi$
$744$	21.8238	−	47.4243i	0.800101	−	1.73866i
$745$	11.1167	−	45.8235i	0.407283	−	1.67884i
$746$	−48.3148	−	55.7583i	−1.76893	−	2.04146i
$747$	38.2235	+	0.220988i	1.39852	+	0.00808552i
$748$	15.9737	−	10.2657i	0.584057	−	0.375351i
$749$	0.775008	+	4.02113i	0.0283182	+	0.146929i
$750$	−40.5982	−	70.7899i	−1.48244	−	2.58488i
$751$	2.97584	+	7.43329i	0.108590	+	0.271244i	0.972703	−	0.232053i	$-0.0745443\pi$
$751$	2.97584	+	7.43329i	0.108590	+	0.271244i	−0.864113	+	0.503297i	$0.832120\pi$
$752$	5.36877	−	27.8558i	0.195779	−	1.01580i
$753$	29.7188	−	10.1897i	1.08301	−	0.371332i
$754$	2.77798	−	2.64880i	0.101168	−	0.0964636i
$755$	4.10706	+	8.99321i	0.149471	+	0.327296i
$756$	43.5393	−	49.3753i	1.58351	−	1.79576i
$757$	−23.3456	+	36.3264i	−0.848509	+	1.32031i	0.0971909	+	0.995266i	$0.469014\pi$
$757$	−23.3456	+	36.3264i	−0.848509	+	1.32031i	−0.945700	+	0.325040i	$0.894622\pi$
$758$	25.9539	−	44.9535i	0.942688	−	1.63278i
$759$	−7.26754	+	13.0146i	−0.263795	+	0.472402i
$760$	−81.5707	−	141.285i	−2.95888	−	5.12493i
$761$	−5.38610	−	0.256572i	−0.195246	−	0.00930071i	−0.0502689	−	0.998736i	$-0.516008\pi$
$761$	−5.38610	−	0.256572i	−0.195246	−	0.00930071i	−0.144977	+	0.989435i	$0.546311\pi$
$762$	−1.04228	+	0.413773i	−0.0377578	+	0.0149894i
$763$	24.9413	+	2.38160i	0.902935	+	0.0862199i
$764$	12.2271	+	3.59020i	0.442361	+	0.129889i
$765$	−1.06455	−	25.4415i	−0.0384888	−	0.919840i
$766$	34.0871	+	29.5367i	1.23162	+	1.06720i
$767$	23.7851	−	30.2452i	0.858829	−	1.09209i
$768$	0.0921935	−	31.8930i	0.00332675	−	1.15084i
$769$	28.6413	+	9.91287i	1.03283	+	0.357467i	0.790329	−	0.612683i	$-0.209910\pi$
$769$	28.6413	+	9.91287i	1.03283	+	0.357467i	0.242505	+	0.970150i	$0.422031\pi$
$770$	−42.2145	−	21.7631i	−1.52131	−	0.784288i
$771$	39.1271	−	11.3660i	1.40913	−	0.409337i
$772$	75.0380	−	14.4624i	2.70068	−	0.520513i
$773$	5.06971	−	1.48860i	0.182345	−	0.0535413i	−0.189285	−	0.981922i	$-0.560617\pi$
$773$	5.06971	−	1.48860i	0.182345	−	0.0535413i	0.371630	+	0.928381i	$0.378799\pi$
$774$	2.01204	+	5.92401i	0.0723214	+	0.212934i
$775$	−26.4676	+	30.5453i	−0.950745	+	1.09722i
$776$	60.0330	+	84.3045i	2.15506	+	3.02636i
$777$	−35.1069	−	1.77407i	−1.25945	−	0.0636446i
$778$	12.0324	+	8.56820i	0.431381	+	0.307185i
$779$	10.4144	−	8.19001i	0.373136	−	0.293438i
$780$	19.6211	+	103.412i	0.702549	+	3.70274i
$781$	24.4696	+	14.1275i	0.875590	+	0.505522i
$782$	4.40300	+	27.2817i	0.157451	+	0.975593i
$783$	−2.27389	+	0.417838i	−0.0812622	+	0.0149323i
$784$	−0.142860	−	0.0918106i	−0.00510215	−	0.00327895i
$785$	20.9501	−	52.3308i	0.747741	−	1.86777i
$786$	0.302334	−	0.748913i	0.0107839	−	0.0267128i
$787$	−3.83849	+	0.931209i	−0.136828	+	0.0331940i	−0.303588	−	0.952803i	$-0.598185\pi$
$787$	−3.83849	+	0.931209i	−0.136828	+	0.0331940i	0.166760	+	0.985997i	$0.446669\pi$
$788$	6.51541	+	68.2325i	0.232102	+	2.43068i
$789$	2.49080	−	4.79738i	0.0886749	−	0.170791i
$790$	−34.7213	−	27.3051i	−1.23533	−	0.971473i
$791$	−2.37393	−	8.08486i	−0.0844072	−	0.287465i
$792$	38.6412	−	5.32793i	1.37305	−	0.189320i
$793$	7.64913	+	11.9023i	0.271629	+	0.422662i
$794$	−41.7378	+	1.98822i	−1.48122	+	0.0705591i
$795$	−10.4316	+	4.72758i	−0.369972	+	0.167670i
$796$	−47.2158	+	49.5185i	−1.67352	+	1.75514i
$797$	−8.60197	+	3.44371i	−0.304697	+	0.121982i	−0.518973	−	0.854791i	$-0.673685\pi$
$797$	−8.60197	+	3.44371i	−0.304697	+	0.121982i	0.214275	+	0.976773i	$0.431261\pi$
$798$	−59.1136	+	37.7490i	−2.09260	+	1.33630i
$799$	−5.49486	+	3.91288i	−0.194394	+	0.138428i
$800$	26.6658	−	90.8154i	0.942779	−	3.21081i
$801$	4.27670	−	1.68351i	0.151110	−	0.0594839i
$802$	15.8277	−	2.27567i	0.558894	−	0.0803568i
$803$	−6.44431	+	3.32227i	−0.227415	+	0.117240i
$804$	−4.21100	−	17.5796i	−0.148510	−	0.619985i
$805$	37.7870	−	30.7831i	1.33182	−	1.08496i
$806$	31.0785	−	17.9432i	1.09469	−	0.632021i
$807$	46.2894	−	8.78285i	1.62946	−	0.309171i
$808$	51.3974	+	20.5764i	1.80815	+	0.723876i
$809$	−26.5830	+	12.1401i	−0.934610	+	0.426822i	−0.823711	−	0.567010i	$-0.808100\pi$
$809$	−26.5830	+	12.1401i	−0.934610	+	0.426822i	−0.110899	+	0.993832i	$0.535373\pi$
$810$	34.3803	−	83.0805i	1.20800	−	2.91915i
$811$	8.15328	−	17.8532i	0.286300	−	0.626910i	−0.710768	−	0.703426i	$-0.751652\pi$
$811$	8.15328	−	17.8532i	0.286300	−	0.626910i	0.997068	+	0.0765163i	$0.0243797\pi$
$812$	1.84365	+	5.32688i	0.0646994	+	0.186937i
$813$	−41.5425	+	29.4016i	−1.45696	+	1.03116i
$814$	−25.9108	−	24.7059i	−0.908173	−	0.865941i
$815$	−13.4516	+	38.8659i	−0.471190	+	1.36141i
$816$	24.6829	−	25.7373i	0.864073	−	0.900985i
$817$	−0.223642	−	4.69483i	−0.00782425	−	0.164251i
$818$	42.1492	−	36.5225i	1.47371	−	1.27698i
$819$	25.6204	−	6.05882i	0.895249	−	0.211712i
$820$	40.9891	+	5.89334i	1.43140	+	0.205804i
$821$	−11.0066	+	3.80944i	−0.384135	+	0.132950i	−0.512309	−	0.858801i	$-0.671210\pi$
$821$	−11.0066	+	3.80944i	−0.384135	+	0.132950i	0.128174	+	0.991752i	$0.459088\pi$
$822$	21.6403	−	24.8288i	0.754791	−	0.866004i
$823$	1.08444	+	4.47010i	0.0378010	+	0.155818i	0.987584	−	0.157091i	$-0.0502116\pi$
$823$	1.08444	+	4.47010i	0.0378010	+	0.155818i	−0.949783	+	0.312909i	$0.898696\pi$
$824$	−62.1552	+	87.2848i	−2.16528	+	3.04071i
$825$	−29.8793	−	4.38418i	−1.04026	−	0.152638i
$826$	36.7212	+	71.2293i	1.27770	+	2.47838i
$827$	−15.7706			−0.548398			−0.274199	−	0.961673i	$-0.588413\pi$
$827$	−15.7706			−0.548398			−0.274199	+	0.961673i	$0.588413\pi$
$828$	−18.6285	+	66.2340i	−0.647385	+	2.30179i
$829$	−22.6475			−0.786580			−0.393290	−	0.919414i	$-0.628663\pi$
$829$	−22.6475			−0.786580			−0.393290	+	0.919414i	$0.628663\pi$
$830$	−58.3280	−	113.141i	−2.02459	−	3.92717i
$831$	−9.73014	−	24.5098i	−0.337535	−	0.850236i
$832$	−12.9885	+	18.2397i	−0.450294	+	0.632349i
$833$	0.00952010	+	0.0392424i	0.000329852	+	0.00135967i
$834$	31.1692	+	90.9067i	1.07930	+	3.14784i
$835$	18.8236	−	6.51491i	0.651417	−	0.225458i
$836$	−49.8570	−	7.16835i	−1.72434	−	0.247923i
$837$	−21.5810	−	1.21569i	−0.745947	−	0.0420203i
$838$	−27.2383	+	23.6021i	−0.940933	+	0.815323i
$839$	−1.64814	−	34.5987i	−0.0569000	−	1.19448i	−0.829100	−	0.559100i	$-0.811147\pi$
$839$	−1.64814	−	34.5987i	−0.0569000	−	1.19448i	0.772200	−	0.635379i	$-0.219156\pi$
$840$	−123.857	−	30.4267i	−4.27346	−	1.04982i
$841$	−9.42022	+	27.2179i	−0.324835	+	0.938550i
$842$	−38.2603	−	36.4811i	−1.31854	−	1.25722i
$843$	1.73359	+	18.7269i	0.0597079	+	0.644987i
$844$	14.8760	+	42.9813i	0.512052	+	1.47948i
$845$	3.22989	−	7.07248i	0.111112	−	0.243301i
$846$	−23.4143	+	4.37250i	−0.805002	+	0.150330i
$847$	18.7476	−	8.56173i	0.644174	−	0.294185i
$848$	−14.8901	−	5.96109i	−0.511328	−	0.204705i
$849$	−17.2526	−	20.0272i	−0.592107	−	0.687332i
$850$	−48.4854	+	27.9931i	−1.66304	+	0.960155i
$851$	33.8679	−	14.2397i	1.16098	−	0.488131i
$852$	125.029	+	37.1046i	4.28341	+	1.27118i
$853$	−5.17638	+	2.66861i	−0.177236	+	0.0913715i	−0.544561	−	0.838721i	$-0.683304\pi$
$853$	−5.17638	+	2.66861i	−0.177236	+	0.0913715i	0.367325	+	0.930093i	$0.380274\pi$
$854$	−29.1671	+	4.19360i	−0.998078	+	0.143502i
$855$	−42.0617	+	52.8540i	−1.43848	+	1.80757i
$856$	−3.15546	+	10.7465i	−0.107852	+	0.367309i
$857$	−12.3086	+	8.76492i	−0.420454	+	0.299404i	−0.770634	−	0.637279i	$-0.780060\pi$
$857$	−12.3086	+	8.76492i	−0.420454	+	0.299404i	0.350179	+	0.936683i	$0.386121\pi$
$858$	23.7974	+	12.3556i	0.812431	+	0.421814i
$859$	−24.4581	+	9.79156i	−0.834500	+	0.334084i	−0.749259	−	0.662277i	$-0.769590\pi$
$859$	−24.4581	+	9.79156i	−0.834500	+	0.334084i	−0.0852412	+	0.996360i	$0.527166\pi$
$860$	10.1377	−	10.6321i	0.345691	−	0.362551i
$861$	1.01436	−	10.3079i	0.0345694	−	0.351293i
$862$	−44.6309	+	2.12603i	−1.52013	+	0.0724129i
$863$	26.3014	+	40.9258i	0.895312	+	1.39313i	0.919358	+	0.393421i	$0.128709\pi$
$863$	26.3014	+	40.9258i	0.895312	+	1.39313i	−0.0240467	+	0.999711i	$0.507655\pi$
$864$	47.1541	−	18.4048i	1.60422	−	0.626145i
$865$	10.1342	+	34.5140i	0.344574	+	1.17351i
$866$	47.8890	+	37.6604i	1.62734	+	1.27975i
$867$	20.9444	−	0.937029i	0.711308	−	0.0318232i
$868$	5.00955	+	52.4624i	0.170035	+	1.78069i
$869$	−7.71065	+	1.87058i	−0.261566	+	0.0634552i
$870$	4.74175	+	6.06563i	0.160760	+	0.205644i
$871$	2.68690	−	6.71155i	0.0910422	−	0.227412i
$872$	57.6468	+	37.0474i	1.95217	+	1.25458i
$873$	23.3754	−	35.9145i	0.791136	−	1.21552i
$874$	38.5655	−	62.3426i	1.30450	−	2.10877i
$875$	41.5066	+	23.9639i	1.40318	+	0.810126i
$876$	−25.3548	+	21.8420i	−0.856658	+	0.737974i
$877$	−15.5380	+	12.2192i	−0.524681	+	0.412614i	−0.845057	−	0.534677i	$-0.820433\pi$
$877$	−15.5380	+	12.2192i	−0.524681	+	0.412614i	0.320376	+	0.947291i	$0.396191\pi$
$878$	−2.41555	−	1.72011i	−0.0815209	−	0.0580508i
$879$	19.5861	−	30.2838i	0.660624	−	1.02145i
$880$	−37.1560	−	52.1783i	−1.25253	−	1.75893i
$881$	19.6113	−	22.6326i	0.660721	−	0.762512i	−0.322174	−	0.946680i	$-0.604414\pi$
$881$	19.6113	−	22.6326i	0.660721	−	0.762512i	0.982895	+	0.184168i	$0.0589591\pi$
$882$	−0.0277933	+	0.139850i	−0.000935851	+	0.00470899i
$883$	48.1840	−	14.1481i	1.62152	−	0.476121i	0.660093	−	0.751184i	$-0.270517\pi$
$883$	48.1840	−	14.1481i	1.62152	−	0.476121i	0.961426	+	0.275062i	$0.0886985\pi$
$884$	34.4176	−	6.63345i	1.15759	−	0.223107i
$885$	55.7022	+	53.4202i	1.87241	+	1.79570i
$886$	−65.6005	−	33.8194i	−2.20389	−	1.13619i
$887$	5.11936	+	1.77183i	0.171891	+	0.0594921i	0.411658	−	0.911338i	$-0.364950\pi$
$887$	5.11936	+	1.77183i	0.171891	+	0.0594921i	−0.239767	+	0.970830i	$0.577071\pi$
$888$	−83.1205	−	48.3105i	−2.78934	−	1.62120i
$889$	0.407129	−	0.517706i	0.0136547	−	0.0173633i
$890$	−11.5672	−	10.0231i	−0.387734	−	0.335974i
$891$	−7.91303	−	14.0793i	−0.265096	−	0.471673i
$892$	31.0433	+	9.11513i	1.03941	+	0.305197i
$893$	17.8133	+	1.70096i	0.596099	+	0.0569205i
$894$	−43.4829	−	34.3992i	−1.45429	−	1.15048i
$895$	32.8526	+	1.56496i	1.09814	+	0.0523110i
$896$	2.48940	+	4.31176i	0.0831649	+	0.144046i
$897$	−21.3835	+	17.3175i	−0.713976	+	0.578214i
$898$	−43.0490	+	74.5630i	−1.43656	+	2.48820i
$899$	1.00065	−	1.55705i	0.0333737	−	0.0519305i
$900$	−138.835	+	12.4476i	−4.62784	+	0.414920i
$901$	1.58434	+	3.46922i	0.0527820	+	0.115577i
$902$	7.63481	−	7.27978i	0.254212	−	0.242390i
$903$	−2.76999	−	2.41426i	−0.0921795	−	0.0803417i
$904$	4.36142	−	22.6292i	0.145059	−	0.752636i
$905$	31.0475	+	77.5529i	1.03205	+	2.57795i
$906$	11.6251	+	0.0336049i	0.386219	+	0.00111645i
$907$	3.12973	+	16.2386i	0.103921	+	0.539193i	0.996154	+	0.0876181i	$0.0279255\pi$
$907$	3.12973	+	16.2386i	0.103921	+	0.539193i	−0.892233	+	0.451575i	$0.850862\pi$
$908$	−4.81300	+	3.09313i	−0.159725	+	0.102649i
$909$	0.132526	−	22.9225i	0.00439560	−	0.760291i
$910$	−57.4131	−	66.2582i	−1.90322	−	2.19644i
$911$	6.86130	−	28.2827i	0.227325	−	0.937047i	−0.737750	−	0.675074i	$-0.764112\pi$
$911$	6.86130	−	28.2827i	0.227325	−	0.937047i	0.965075	−	0.261973i	$-0.0843731\pi$
$912$	−94.1934	+	8.71969i	−3.11906	+	0.288738i
$913$	−22.4513	−	4.32714i	−0.743030	−	0.143207i
$914$	60.9026	−	5.81549i	2.01448	−	0.192359i
$915$	−25.2615	+	12.9309i	−0.835119	+	0.427483i
$916$	4.73506	−	49.5877i	0.156451	−	1.63843i
$917$	0.0675048	+	0.469506i	0.00222921	+	0.0155045i
$918$	−27.6992	−	11.3688i	−0.914209	−	0.375225i
$919$		−	30.9735i		−	1.02172i	−0.859663	−	0.510861i	$-0.829327\pi$
$919$		−	30.9735i		−	1.02172i	0.859663	−	0.510861i	$-0.170673\pi$
$920$	130.438	−	27.4762i	4.30042	−	0.905864i
$921$	2.04187	+	2.15388i	0.0672818	+	0.0709728i
$922$	−0.428375	+	8.99269i	−0.0141078	+	0.296159i
$923$	32.2416	+	40.9985i	1.06125	+	1.34948i
$924$	−31.0230	+	24.2520i	−1.02058	+	0.797832i
$925$	51.3640	+	53.8690i	1.68884	+	1.77120i
$926$	90.4922	+	41.3264i	2.97376	+	1.35807i
$927$	43.0547	+	10.7089i	1.41410	+	0.351726i
$928$	−0.616847	+	4.29027i	−0.0202490	+	0.140835i
$929$	10.0362	+	2.43476i	0.329277	+	0.0798818i	0.396990	−	0.917823i	$-0.370055\pi$
$929$	10.0362	+	2.43476i	0.329277	+	0.0798818i	−0.0677124	+	0.997705i	$0.521570\pi$
$930$	29.7126	+	65.5624i	0.974315	+	2.14988i
$931$	0.0490843	−	0.0952103i	0.00160867	−	0.00312039i
$932$	59.3460	−	115.115i	1.94394	−	3.77072i
$933$	−13.3773	−	29.5178i	−0.437954	−	0.966369i
$934$	88.4758	+	21.4640i	2.89502	+	0.702323i
$935$	−2.16769	+	15.0766i	−0.0708911	+	0.493059i
$936$	69.8757	+	17.3800i	2.28396	+	0.568084i
$937$	−49.8660	−	22.7730i	−1.62905	−	0.743962i	−0.629594	−	0.776924i	$-0.716779\pi$
$937$	−49.8660	−	22.7730i	−1.62905	−	0.743962i	−0.999457	+	0.0329618i	$0.989506\pi$
$938$	10.3905	+	10.8972i	0.339261	+	0.355806i
$939$	−5.18041	+	4.04974i	−0.169056	+	0.132158i
$940$	34.5734	+	43.9637i	1.12766	+	1.43394i
$941$	2.29060	−	48.0856i	0.0746715	−	1.56755i	−0.581886	−	0.813271i	$-0.697685\pi$
$941$	2.29060	−	48.0856i	0.0746715	−	1.56755i	0.656557	−	0.754276i	$-0.272012\pi$
$942$	−45.6001	−	48.1017i	−1.48573	−	1.56724i
$943$	3.71625	+	10.1678i	0.121018	+	0.331108i
$944$			108.082i			3.51778i
$945$	7.06166	+	52.3327i	0.229716	+	1.70238i
$946$	−0.532595	−	3.70428i	−0.0173162	−	0.120437i
$947$	3.19103	−	33.4180i	0.103694	−	1.08594i	−0.782508	−	0.622640i	$-0.786060\pi$
$947$	3.19103	−	33.4180i	0.103694	−	1.08594i	0.886203	−	0.463298i	$-0.153334\pi$
$948$	−32.6000	+	16.6874i	−1.05880	+	0.541980i
$949$	−13.3231	+	1.27220i	−0.432486	+	0.0412974i
$950$	145.831	+	28.1066i	4.73138	+	0.911900i
$951$	−10.2074	+	0.944920i	−0.330997	+	0.0306411i
$952$	−10.0129	+	41.2739i	−0.324522	+	1.33770i
$953$	39.2866	+	45.3391i	1.27262	+	1.46868i	0.814924	+	0.579568i	$0.196779\pi$
$953$	39.2866	+	45.3391i	1.27262	+	1.46868i	0.457693	+	0.889110i	$0.348676\pi$
$954$	−0.0778569	+	13.4666i	−0.00252071	+	0.435998i
$955$	−8.59956	+	5.52660i	−0.278275	+	0.178837i
$956$	−11.6377	−	60.3820i	−0.376389	−	1.95289i
$957$	1.38294	+	0.00399768i	0.0447041	+	0.000129227i
$958$	19.7797	+	49.4074i	0.639054	+	1.59628i
$959$	−3.66080	+	18.9941i	−0.118214	+	0.613350i
$960$	−33.8582	−	29.5101i	−1.09277	−	0.952433i
$961$	−9.91205	+	9.45112i	−0.319744	+	0.304875i
$962$	−27.4540	−	60.1158i	−0.885151	−	1.93821i
$963$	4.61887	−	0.414116i	0.148841	−	0.0133447i
$964$	32.9902	−	51.3337i	1.06254	−	1.65335i
$965$	−30.6506	+	53.0884i	−0.986679	+	1.70898i
$966$	−14.3073	−	55.4945i	−0.460329	−	1.78551i
$967$	−8.46492	−	14.6617i	−0.272213	−	0.471487i	0.697215	−	0.716862i	$-0.254422\pi$
$967$	−8.46492	−	14.6617i	−0.272213	−	0.471487i	−0.969428	+	0.245375i	$0.921089\pi$
$968$	56.3048	+	2.68213i	1.80971	+	0.0862069i
$969$	17.6411	+	13.9558i	0.566712	+	0.448325i
$970$	−142.055	−	13.5646i	−4.56110	−	0.435533i
$971$	−15.3885	−	4.51848i	−0.493842	−	0.145005i	0.0253229	−	0.999679i	$-0.491939\pi$
$971$	−15.3885	−	4.51848i	−0.493842	−	0.145005i	−0.519164	+	0.854674i	$0.673757\pi$
$972$	−50.6582	−	54.6901i	−1.62486	−	1.75419i
$973$	−42.6558	−	36.9614i	−1.36748	−	1.18493i
$974$	−0.0650186	+	0.0826778i	−0.00208333	+	0.00264917i
$975$	−48.1970	−	28.0126i	−1.54354	−	0.897121i
$976$	−37.5566	−	12.9985i	−1.20216	−	0.416070i
$977$	4.06958	+	2.09802i	0.130197	+	0.0671215i	0.522095	−	0.852888i	$-0.325151\pi$
$977$	4.06958	+	2.09802i	0.130197	+	0.0671215i	−0.391897	+	0.920009i	$0.628181\pi$
$978$	34.9032	+	33.4733i	1.11608	+	1.07036i
$979$	−2.69958	+	0.520302i	−0.0862790	+	0.0166289i
$980$	0.321241	−	0.0943250i	0.0102617	−	0.00301310i
$981$	5.53050	−	27.8282i	0.176575	−	0.888486i
$982$	−52.5860	+	60.6875i	−1.67809	+	1.93661i
$983$	−15.1105	−	21.2197i	−0.481949	−	0.676803i	0.499983	−	0.866035i	$-0.333340\pi$
$983$	−15.1105	−	21.2197i	−0.481949	−	0.676803i	−0.981932	+	0.189232i	$0.939400\pi$
$984$	15.3843	−	23.7870i	0.490434	−	0.758302i
$985$	−44.7880	−	31.8934i	−1.42706	−	1.01621i
$986$	2.01531	−	1.58486i	0.0641806	−	0.0504722i
$987$	10.5988	−	9.13040i	0.337364	−	0.290624i
$988$	−80.5231	−	46.4900i	−2.56178	−	1.47905i
$989$	3.70294	+	1.01840i	0.117747	+	0.0323832i
$990$	−29.3385	+	45.0765i	−0.932440	+	1.43263i
$991$	31.6171	+	20.3191i	1.00435	+	0.645456i	0.935925	−	0.352200i	$-0.114566\pi$
$991$	31.6171	+	20.3191i	1.00435	+	0.645456i	0.0684244	+	0.997656i	$0.478203\pi$
$992$	−15.0610	+	37.6206i	−0.478188	+	1.19446i
$993$	−4.04917	−	5.17968i	−0.128497	−	0.164372i
$994$	−105.568	+	25.6105i	−3.34841	+	0.812315i
$995$	−5.21719	−	54.6369i	−0.165396	−	1.73211i
$996$	−105.431	+	4.71690i	−3.34072	+	0.149461i
$997$	2.90201	+	2.28216i	0.0919075	+	0.0722768i	0.663055	−	0.748570i	$-0.269259\pi$
$997$	2.90201	+	2.28216i	0.0919075	+	0.0722768i	−0.571148	+	0.820847i	$0.693502\pi$
$998$	4.62396	+	15.7478i	0.146369	+	0.498486i
$999$	−6.00651	+	39.3506i	−0.190038	+	1.24500i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.o.a.182.1	yes	440
3.2	odd	2		621.2.s.a.251.22		440
9.4	even	3		621.2.s.a.44.22		440
9.5	odd	6	inner	207.2.o.a.113.1	yes	440
23.11	odd	22	inner	207.2.o.a.11.1	✓	440
69.11	even	22		621.2.s.a.494.22		440
207.103	odd	66		621.2.s.a.287.22		440
207.149	even	66	inner	207.2.o.a.149.1	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.1	✓	440	23.11	odd	22	inner
207.2.o.a.113.1	yes	440	9.5	odd	6	inner
207.2.o.a.149.1	yes	440	207.149	even	66	inner
207.2.o.a.182.1	yes	440	1.1	even	1	trivial
621.2.s.a.44.22		440	9.4	even	3
621.2.s.a.251.22		440	3.2	odd	2
621.2.s.a.287.22		440	207.103	odd	66
621.2.s.a.494.22		440	69.11	even	22

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19334 - 2.31476i) q^{2} +(1.07461 - 1.35838i) q^{3} +(-2.77395 + 3.89546i) q^{4} +(-0.904406 - 3.72801i) q^{5} +(-4.42672 - 0.866459i) q^{6} +(2.50349 - 0.866468i) q^{7} +(7.17183 + 1.03115i) q^{8} +(-0.690410 - 2.91948i) q^{9} +(-7.55020 + 6.54229i) q^{10} +(0.0853862 + 1.79248i) q^{11} +(2.31061 + 7.95420i) q^{12} +(-1.08344 + 3.13039i) q^{13} +(-4.99320 - 4.76100i) q^{14} +(-6.03596 - 2.77764i) q^{15} +(-3.04337 - 8.79325i) q^{16} +(-0.919155 + 2.01267i) q^{17} +(-5.93400 + 5.08207i) q^{18} +(5.33902 - 2.43825i) q^{19} +(17.0311 + 6.81823i) q^{20} +(1.51329 - 4.33182i) q^{21} +(4.04726 - 2.33669i) q^{22} +(0.537967 + 4.76556i) q^{23} +(9.10765 - 8.63400i) q^{24} +(-8.63596 + 4.45214i) q^{25} +(8.53903 - 1.22773i) q^{26} +(-4.70769 - 2.19947i) q^{27} +(-3.56927 + 12.1558i) q^{28} +(0.362435 - 0.258089i) q^{29} +(0.773381 + 17.2865i) q^{30} +(3.86186 - 1.54606i) q^{31} +(-6.72245 + 7.05030i) q^{32} +(2.52663 + 1.81023i) q^{33} +(5.75572 - 0.274179i) q^{34} +(-5.49438 - 8.54942i) q^{35} +(13.2879 + 5.40900i) q^{36} +(-2.15828 - 7.35043i) q^{37} +(-12.0153 - 9.44890i) q^{38} +(3.08799 + 4.83569i) q^{39} +(-2.64209 - 27.6693i) q^{40} +(2.19367 - 0.532178i) q^{41} +(-11.8330 + 1.66643i) q^{42} +(0.297622 - 0.743424i) q^{43} +(-7.21938 - 4.63962i) q^{44} +(-10.2594 + 5.21425i) q^{45} +(10.3892 - 6.93222i) q^{46} +(2.64028 + 1.52437i) q^{47} +(-15.2150 - 5.31528i) q^{48} +(0.0143456 - 0.0112815i) q^{49} +(20.6113 + 14.6773i) q^{50} +(1.74624 + 3.41140i) q^{51} +(-9.18893 - 12.9040i) q^{52} +(1.12878 - 1.30268i) q^{53} +(0.526644 + 13.5219i) q^{54} +(6.60515 - 1.93945i) q^{55} +(18.8481 - 3.63267i) q^{56} +(2.42531 - 9.87261i) q^{57} +(-1.02992 - 0.530963i) q^{58} +(-10.9766 - 3.79905i) q^{59} +(27.5636 - 15.8078i) q^{60} +(2.64020 - 3.35729i) q^{61} +(-8.18729 - 7.09433i) q^{62} +(-4.25807 - 6.71067i) q^{63} +(6.48578 + 1.90440i) q^{64} +(12.6500 + 1.20793i) q^{65} +(1.17513 - 8.00877i) q^{66} +(-2.17994 - 0.103843i) q^{67} +(-5.29059 - 9.16356i) q^{68} +(7.05157 + 4.39037i) q^{69} +(-13.2332 + 22.9206i) q^{70} +(8.51253 - 13.2458i) q^{71} +(-1.94107 - 21.6499i) q^{72} +(1.67838 + 3.67515i) q^{73} +(-14.4389 + 13.7675i) q^{74} +(-3.23260 + 16.5153i) q^{75} +(-5.31205 + 27.5615i) q^{76} +(1.76689 + 4.41347i) q^{77} +(7.50844 - 12.9186i) q^{78} +(0.836762 + 4.34153i) q^{79} +(-30.0289 + 19.2984i) q^{80} +(-8.04667 + 4.03127i) q^{81} +(-3.84966 - 4.44275i) q^{82} +(-3.00389 + 12.3822i) q^{83} +(12.6767 + 17.9112i) q^{84} +(8.33454 + 1.60635i) q^{85} +(-2.07601 + 0.198235i) q^{86} +(0.0388942 - 0.769671i) q^{87} +(-1.23594 + 12.9434i) q^{88} +(0.218032 + 1.51645i) q^{89} +(24.3128 + 17.5258i) q^{90} +8.77569i q^{91} +(-20.0564 - 11.1238i) q^{92} +(2.04988 - 6.90731i) q^{93} +(0.377786 - 7.93071i) q^{94} +(-13.9185 - 17.6988i) q^{95} +(2.35297 + 16.7080i) q^{96} +(9.85700 + 10.3377i) q^{97} +(-0.0432332 - 0.0197440i) q^{98} +(5.17414 - 1.48683i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23}+ \cdots + 242 q^{99}+O(q^{100}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more