LMFDB - Embedded newform 409.2.m.a.4.8

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			4.8
Character	$\chi$	$=$	409.4
Dual form			409.2.m.a.307.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.62587 + 0.201326i) q^{2} +(0.446735 - 2.03985i) q^{3} +(0.663313 - 0.166830i) q^{4} +(-0.650392 + 1.30616i) q^{5} +(-0.315655 + 3.40647i) q^{6} +(-1.92598 + 1.11196i) q^{7} +(2.01044 - 0.778847i) q^{8} +(-1.23603 - 0.568664i) q^{9} +(0.794486 - 2.25459i) q^{10} +(0.158890 - 0.0147233i) q^{11} +(-0.0439835 - 1.42759i) q^{12} +(2.94417 + 0.272818i) q^{13} +(2.90751 - 2.19565i) q^{14} +(2.37383 + 1.91021i) q^{15} +(-4.31707 + 2.31822i) q^{16} +(-0.983213 + 6.33396i) q^{17} +(2.12411 + 0.675727i) q^{18} +(2.04168 + 1.54180i) q^{19} +(-0.213506 + 0.974900i) q^{20} +(1.40784 + 4.42546i) q^{21} +(-0.255370 + 0.0559268i) q^{22} +(1.15240 - 7.42390i) q^{23} +(-0.690602 - 4.44893i) q^{24} +(1.73012 + 2.29105i) q^{25} +(-4.84176 + 0.149173i) q^{26} +(2.06309 - 2.73198i) q^{27} +(-1.09202 + 1.05889i) q^{28} +(4.89443 - 4.19329i) q^{29} +(-4.24410 - 2.62784i) q^{30} +5.29280i q^{31} +(3.03277 - 2.14685i) q^{32} +(0.0409482 - 0.330690i) q^{33} +(0.323382 - 10.4961i) q^{34} +(-0.199766 - 3.23886i) q^{35} +(-0.914745 - 0.170996i) q^{36} +(11.0836 - 0.341481i) q^{37} +(-3.62990 - 2.09572i) q^{38} +(1.87177 - 5.88380i) q^{39} +(-0.290270 + 3.13252i) q^{40} +(-2.29782 - 6.52075i) q^{41} +(-3.17992 - 6.91178i) q^{42} +(7.28633 - 5.50238i) q^{43} +(0.102938 - 0.0362738i) q^{44} +(1.54667 - 1.24460i) q^{45} +(-0.379029 + 12.3023i) q^{46} +(-5.48758 + 10.2192i) q^{47} +(2.80024 + 9.84181i) q^{48} +(-1.02707 + 1.77894i) q^{49} +(-3.27419 - 3.37662i) q^{50} +(12.4811 + 4.83521i) q^{51} +(1.99842 - 0.310212i) q^{52} +(3.55061 + 6.14983i) q^{53} +(-2.80429 + 4.85718i) q^{54} +(-0.0841098 + 0.217112i) q^{55} +(-3.00601 + 3.73558i) q^{56} +(4.05714 - 3.47595i) q^{57} +(-7.11347 + 7.80310i) q^{58} +(-2.71015 - 0.771103i) q^{59} +(1.89327 + 0.871043i) q^{60} +(4.27031 + 4.68431i) q^{61} +(-1.06558 - 8.60539i) q^{62} +(3.01290 - 0.279187i) q^{63} +(2.74381 - 2.50131i) q^{64} +(-2.27121 + 3.66813i) q^{65} +0.545901i q^{66} +(-0.771220 - 1.08947i) q^{67} +(0.404516 + 4.36543i) q^{68} +(-14.6289 - 5.66725i) q^{69} +(0.976858 + 5.22573i) q^{70} +(-2.92812 - 0.180601i) q^{71} +(-2.92786 - 0.180584i) q^{72} +(3.07978 + 2.98635i) q^{73} +(-17.9517 + 2.78661i) q^{74} +(5.44630 - 2.50570i) q^{75} +(1.61149 + 0.682086i) q^{76} +(-0.289647 + 0.205037i) q^{77} +(-1.85869 + 9.94311i) q^{78} +(5.69647 + 2.83651i) q^{79} +(-0.220183 - 7.14655i) q^{80} +(-7.30681 - 8.52854i) q^{81} +(5.04874 + 10.1392i) q^{82} +(0.263389 - 0.102037i) q^{83} +(1.67214 + 2.70060i) q^{84} +(-7.63372 - 5.40380i) q^{85} +(-10.7388 + 10.4131i) q^{86} +(-6.36718 - 11.8572i) q^{87} +(0.307971 - 0.153351i) q^{88} +(0.447700 + 1.57350i) q^{89} +(-2.26411 + 2.33494i) q^{90} +(-5.97378 + 2.74837i) q^{91} +(-0.474125 - 5.11663i) q^{92} +(10.7965 + 2.36448i) q^{93} +(6.86468 - 17.7198i) q^{94} +(-3.34174 + 1.66399i) q^{95} +(-3.02442 - 7.14548i) q^{96} +(0.400104 + 6.48699i) q^{97} +(1.31173 - 3.09909i) q^{98} +(-0.204766 - 0.0721566i) 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 $

$2$	−1.62587	+	0.201326i	−1.14966	+	0.142359i	−0.675005	−	0.737813i	$-0.735859\pi$
$2$	−1.62587	+	0.201326i	−1.14966	+	0.142359i	−0.474655	+	0.880172i	$0.657427\pi$
$3$	0.446735	−	2.03985i	0.257922	−	1.17771i	−0.650451	−	0.759549i	$-0.725420\pi$
$3$	0.446735	−	2.03985i	0.257922	−	1.17771i	0.908373	−	0.418161i	$-0.137325\pi$
$4$	0.663313	−	0.166830i	0.331656	−	0.0834149i
$5$	−0.650392	+	1.30616i	−0.290864	+	0.584134i	−0.991608	−	0.129278i	$-0.958734\pi$
$5$	−0.650392	+	1.30616i	−0.290864	+	0.584134i	0.700744	+	0.713413i	$0.252852\pi$
$6$	−0.315655	+	3.40647i	−0.128866	+	1.39068i
$7$	−1.92598	+	1.11196i	−0.727951	+	0.420283i	−0.817672	−	0.575684i	$-0.804736\pi$
$7$	−1.92598	+	1.11196i	−0.727951	+	0.420283i	0.0897209	+	0.995967i	$0.471403\pi$
$8$	2.01044	−	0.778847i	0.710797	−	0.275364i
$9$	−1.23603	−	0.568664i	−0.412010	−	0.189555i
$10$	0.794486	−	2.25459i	0.251239	−	0.712963i
$11$	0.158890	−	0.0147233i	0.0479071	−	0.00443925i	−0.0682881	−	0.997666i	$-0.521754\pi$
$11$	0.158890	−	0.0147233i	0.0479071	−	0.00443925i	0.116195	+	0.993226i	$0.462930\pi$
$12$	−0.0439835	−	1.42759i	−0.0126970	−	0.412109i
$13$	2.94417	+	0.272818i	0.816567	+	0.0756661i	0.492439	−	0.870347i	$-0.336106\pi$
$13$	2.94417	+	0.272818i	0.816567	+	0.0756661i	0.324128	+	0.946013i	$0.394929\pi$
$14$	2.90751	−	2.19565i	0.777066	−	0.586813i
$15$	2.37383	+	1.91021i	0.612920	+	0.493215i
$16$	−4.31707	+	2.31822i	−1.07927	+	0.579554i
$17$	−0.983213	+	6.33396i	−0.238464	+	1.53621i	0.502447	+	0.864608i	$0.332433\pi$
$17$	−0.983213	+	6.33396i	−0.238464	+	1.53621i	−0.740911	+	0.671603i	$0.765606\pi$
$18$	2.12411	+	0.675727i	0.500657	+	0.159270i
$19$	2.04168	+	1.54180i	0.468393	+	0.353714i	0.810296	−	0.586021i	$-0.199307\pi$
$19$	2.04168	+	1.54180i	0.468393	+	0.353714i	−0.341902	+	0.939735i	$0.611071\pi$
$20$	−0.213506	+	0.974900i	−0.0477415	+	0.217994i
$21$	1.40784	+	4.42546i	0.307216	+	0.965716i
$22$	−0.255370	+	0.0559268i	−0.0544450	+	0.0119236i
$23$	1.15240	−	7.42390i	0.240293	−	1.54799i	−0.494184	−	0.869357i	$-0.664533\pi$
$23$	1.15240	−	7.42390i	0.240293	−	1.54799i	0.734477	−	0.678634i	$-0.237428\pi$
$24$	−0.690602	−	4.44893i	−0.140969	−	0.908134i
$25$	1.73012	+	2.29105i	0.346024	+	0.458210i
$26$	−4.84176	+	0.149173i	−0.949546	+	0.0292552i
$27$	2.06309	−	2.73198i	0.397042	−	0.525769i
$28$	−1.09202	+	1.05889i	−0.206372	+	0.200112i
$29$	4.89443	−	4.19329i	0.908873	−	0.778674i	−0.0668320	−	0.997764i	$-0.521289\pi$
$29$	4.89443	−	4.19329i	0.908873	−	0.778674i	0.975705	+	0.219090i	$0.0703088\pi$
$30$	−4.24410	−	2.62784i	−0.774864	−	0.479775i
$31$			5.29280i			0.950615i	0.879820	+	0.475308i	$0.157663\pi$
$31$			5.29280i			0.950615i	−0.879820	+	0.475308i	$0.842337\pi$
$32$	3.03277	−	2.14685i	0.536123	−	0.379514i
$33$	0.0409482	−	0.330690i	0.00712818	−	0.0575657i
$34$	0.323382	−	10.4961i	0.0554595	−	1.80007i
$35$	−0.199766	−	3.23886i	−0.0337666	−	0.547467i
$36$	−0.914745	−	0.170996i	−0.152458	−	0.0284993i
$37$	11.0836	−	0.341481i	1.82213	−	0.0561392i	0.898398	−	0.439182i	$-0.144732\pi$
$37$	11.0836	−	0.341481i	1.82213	−	0.0561392i	0.923730	+	0.383043i	$0.125124\pi$
$38$	−3.62990	−	2.09572i	−0.588848	−	0.339971i
$39$	1.87177	−	5.88380i	0.299723	−	0.942162i
$40$	−0.290270	+	3.13252i	−0.0458958	+	0.495294i
$41$	−2.29782	−	6.52075i	−0.358860	−	1.01837i	−0.973326	−	0.229427i	$-0.926315\pi$
$41$	−2.29782	−	6.52075i	−0.358860	−	1.01837i	0.614466	−	0.788943i	$-0.289371\pi$
$42$	−3.17992	−	6.91178i	−0.490673	−	1.06651i
$43$	7.28633	−	5.50238i	1.11115	−	0.839105i	0.122976	−	0.992410i	$-0.460756\pi$
$43$	7.28633	−	5.50238i	1.11115	−	0.839105i	0.988179	+	0.153304i	$0.0489915\pi$
$44$	0.102938	−	0.0362738i	0.0155184	−	0.00546848i
$45$	1.54667	−	1.24460i	0.230565	−	0.185535i
$46$	−0.379029	+	12.3023i	−0.0558848	+	1.81387i
$47$	−5.48758	+	10.2192i	−0.800446	+	1.49062i	0.0695601	+	0.997578i	$0.477840\pi$
$47$	−5.48758	+	10.2192i	−0.800446	+	1.49062i	−0.870006	+	0.493042i	$0.835885\pi$
$48$	2.80024	+	9.84181i	0.404180	+	1.42054i
$49$	−1.02707	+	1.77894i	−0.146725	+	0.254134i
$50$	−3.27419	−	3.37662i	−0.463040	−	0.477526i
$51$	12.4811	+	4.83521i	1.74771	+	0.677065i
$52$	1.99842	−	0.310212i	0.277131	−	0.0430187i
$53$	3.55061	+	6.14983i	0.487713	+	0.844745i	0.999900	−	0.0141296i	$-0.00449775\pi$
$53$	3.55061	+	6.14983i	0.487713	+	0.844745i	−0.512187	+	0.858874i	$0.671164\pi$
$54$	−2.80429	+	4.85718i	−0.381616	+	0.660978i
$55$	−0.0841098	+	0.217112i	−0.0113414	+	0.0292754i
$56$	−3.00601	+	3.73558i	−0.401695	+	0.499187i
$57$	4.05714	−	3.47595i	0.537382	−	0.460400i
$58$	−7.11347	+	7.80310i	−0.934044	+	1.02460i
$59$	−2.71015	−	0.771103i	−0.352831	−	0.100389i	0.0926049	−	0.995703i	$-0.470481\pi$
$59$	−2.71015	−	0.771103i	−0.352831	−	0.100389i	−0.445436	+	0.895314i	$0.646951\pi$
$60$	1.89327	+	0.871043i	0.244420	+	0.112451i
$61$	4.27031	+	4.68431i	0.546758	+	0.599765i	0.948808	−	0.315853i	$-0.102291\pi$
$61$	4.27031	+	4.68431i	0.546758	+	0.599765i	−0.402050	+	0.915618i	$0.631702\pi$
$62$	−1.06558	−	8.60539i	−0.135329	−	1.09289i
$63$	3.01290	−	0.279187i	0.379590	−	0.0351742i
$64$	2.74381	−	2.50131i	0.342976	−	0.312664i
$65$	−2.27121	+	3.66813i	−0.281709	+	0.454976i
$66$			0.545901i			0.0671957i
$67$	−0.771220	−	1.08947i	−0.0942195	−	0.133100i	0.766369	−	0.642400i	$-0.222061\pi$
$67$	−0.771220	−	1.08947i	−0.0942195	−	0.133100i	−0.860589	+	0.509300i	$0.829904\pi$
$68$	0.404516	+	4.36543i	0.0490548	+	0.529386i
$69$	−14.6289	−	5.66725i	−1.76111	−	0.682256i
$70$	0.976858	+	5.22573i	0.116757	+	0.624594i
$71$	−2.92812	−	0.180601i	−0.347504	−	0.0214333i	−0.113131	−	0.993580i	$-0.536088\pi$
$71$	−2.92812	−	0.180601i	−0.347504	−	0.0214333i	−0.234373	+	0.972147i	$0.575304\pi$
$72$	−2.92786	−	0.180584i	−0.345052	−	0.0212821i
$73$	3.07978	+	2.98635i	0.360461	+	0.349526i	0.854070	−	0.520157i	$-0.174127\pi$
$73$	3.07978	+	2.98635i	0.360461	+	0.349526i	−0.493610	+	0.869684i	$0.664323\pi$
$74$	−17.9517	+	2.78661i	−2.08684	+	0.323937i
$75$	5.44630	−	2.50570i	0.628885	−	0.289333i
$76$	1.61149	+	0.682086i	0.184851	+	0.0782406i
$77$	−0.289647	+	0.205037i	−0.0330083	+	0.0233661i
$78$	−1.85869	+	9.94311i	−0.210455	+	1.12584i
$79$	5.69647	+	2.83651i	0.640903	+	0.319132i	0.736650	−	0.676274i	$-0.236406\pi$
$79$	5.69647	+	2.83651i	0.640903	+	0.319132i	−0.0957471	+	0.995406i	$0.530524\pi$
$80$	−0.220183	−	7.14655i	−0.0246172	−	0.799009i
$81$	−7.30681	−	8.52854i	−0.811867	−	0.947616i
$82$	5.04874	+	10.1392i	0.557541	+	1.11969i
$83$	0.263389	−	0.102037i	0.0289107	−	0.0112001i	−0.346743	−	0.937960i	$-0.612712\pi$
$83$	0.263389	−	0.102037i	0.0289107	−	0.0112001i	0.375654	+	0.926760i	$0.377418\pi$
$84$	1.67214	+	2.70060i	0.182445	+	0.294659i
$85$	−7.63372	−	5.40380i	−0.827993	−	0.586124i
$86$	−10.7388	+	10.4131i	−1.15800	+	1.12287i
$87$	−6.36718	−	11.8572i	−0.682634	−	1.27123i
$88$	0.307971	−	0.153351i	0.0328298	−	0.0163473i
$89$	0.447700	+	1.57350i	0.0474561	+	0.166791i	0.981931	−	0.189237i	$-0.0606014\pi$
$89$	0.447700	+	1.57350i	0.0474561	+	0.166791i	−0.934475	+	0.356028i	$0.884131\pi$
$90$	−2.26411	+	2.33494i	−0.238658	+	0.246125i
$91$	−5.97378	+	2.74837i	−0.626222	+	0.288108i
$92$	−0.474125	−	5.11663i	−0.0494310	−	0.533445i
$93$	10.7965	+	2.36448i	1.11955	+	0.245185i
$94$	6.86468	−	17.7198i	0.708038	−	1.82766i
$95$	−3.34174	+	1.66399i	−0.342855	+	0.170722i
$96$	−3.02442	−	7.14548i	−0.308679	−	0.729283i
$97$	0.400104	+	6.48699i	0.0406244	+	0.658654i	0.962519	+	0.271214i	$0.0874250\pi$
$97$	0.400104	+	6.48699i	0.0406244	+	0.658654i	−0.921895	+	0.387440i	$0.873359\pi$
$98$	1.31173	−	3.09909i	0.132505	−	0.313056i
$99$	−0.204766	−	0.0721566i	−0.0205797	−	0.00725201i
$100$	1.52983	+	1.23105i	0.152983	+	0.123105i
$101$	−4.67785	+	5.46001i	−0.465463	+	0.543291i	−0.941889	−	0.335923i	$-0.890952\pi$
$101$	−4.67785	+	5.46001i	−0.465463	+	0.543291i	0.476426	+	0.879215i	$0.341932\pi$
$102$	−21.2661	−	5.34863i	−2.10565	−	0.529593i
$103$	−2.77335	+	5.56965i	−0.273267	+	0.548793i	−0.988704	−	0.149884i	$-0.952110\pi$
$103$	−2.77335	+	5.56965i	−0.273267	+	0.548793i	0.715437	+	0.698677i	$0.246228\pi$
$104$	6.13156	−	1.74458i	0.601249	−	0.171070i
$105$	−6.69603	−	1.03942i	−0.653466	−	0.101437i
$106$	−7.01093	−	9.28397i	−0.680962	−	0.901739i
$107$	−9.53976	−	11.8551i	−0.922244	−	1.14608i	−0.988942	−	0.148302i	$-0.952619\pi$
$107$	−9.53976	−	11.8551i	−0.922244	−	1.14608i	0.0666984	−	0.997773i	$-0.478753\pi$
$108$	0.912700	−	2.15634i	0.0878246	−	0.207494i
$109$	−14.3862	+	11.5765i	−1.37794	+	1.10883i	−0.396298	+	0.918122i	$0.629705\pi$
$109$	−14.3862	+	11.5765i	−1.37794	+	1.10883i	−0.981647	+	0.190706i	$0.938922\pi$
$110$	0.0930409	−	0.369929i	0.00887110	−	0.0352713i
$111$	4.25484	−	22.7614i	0.403852	−	2.16042i
$112$	5.73681	−	9.26526i	0.542077	−	0.875485i
$113$	10.1313	−	4.28823i	0.953077	−	0.403403i	0.142997	−	0.989723i	$-0.454326\pi$
$113$	10.1313	−	4.28823i	0.953077	−	0.403403i	0.810079	+	0.586320i	$0.199424\pi$
$114$	−5.89657	+	6.46823i	−0.552264	+	0.605805i
$115$	8.94732	+	6.33368i	0.834342	+	0.590619i
$116$	2.54697	−	3.59800i	0.236480	−	0.334066i
$117$	−3.48395	−	2.01146i	−0.322091	−	0.185959i
$118$	4.56158	+	0.708088i	0.419927	+	0.0651847i
$119$	−5.14949	−	13.2924i	−0.472053	−	1.21851i
$120$	6.26020	+	1.99151i	0.571475	+	0.181799i
$121$	−10.7877	+	2.01657i	−0.980698	+	0.183324i
$122$	−7.88603	−	6.75634i	−0.713968	−	0.611690i
$123$	−14.3279	+	1.77418i	−1.29190	+	0.159972i
$124$	0.882998	+	3.51078i	0.0792955	+	0.315278i
$125$	−11.2892	+	2.11032i	−1.00974	+	0.188752i
$126$	−4.84237	+	1.06049i	−0.431392	+	0.0944764i
$127$	16.1973	+	10.7327i	1.43728	+	0.952373i	0.998554	+	0.0537500i	$0.0171174\pi$
$127$	16.1973	+	10.7327i	1.43728	+	0.952373i	0.438721	+	0.898623i	$0.355432\pi$
$128$	−8.79254	+	10.2627i	−0.777158	+	0.907103i
$129$	−7.96899	−	17.3211i	−0.701630	−	1.52504i
$130$	2.95420	−	6.42115i	0.259100	−	0.563172i
$131$	−9.08130	−	10.5997i	−0.793437	−	0.926103i	0.205178	−	0.978725i	$-0.434223\pi$
$131$	−9.08130	−	10.5997i	−0.793437	−	0.926103i	−0.998615	+	0.0526215i	$0.983242\pi$
$132$	−0.0280074	−	0.226182i	−0.00243773	−	0.0196866i
$133$	−5.64666	−	0.699208i	−0.489627	−	0.0606290i
$134$	1.47324	+	1.61607i	0.127268	+	0.139607i
$135$	2.22659	+	4.47159i	0.191634	+	0.384853i
$136$	2.95650	+	13.4998i	0.253518	+	1.15760i
$137$	3.62970	+	10.3003i	0.310106	+	0.880018i	0.989279	+	0.146039i	$0.0466525\pi$
$137$	3.62970	+	10.3003i	0.310106	+	0.880018i	−0.679173	+	0.733979i	$0.737661\pi$
$138$	24.9255	+	6.26902i	2.12180	+	0.533654i
$139$	−1.65604	−	2.49922i	−0.140464	−	0.211981i	0.756605	−	0.653872i	$-0.226857\pi$
$139$	−1.65604	−	2.49922i	−0.140464	−	0.211981i	−0.897069	+	0.441891i	$0.854308\pi$
$140$	−0.672845	−	2.11505i	−0.0568658	−	0.178754i
$141$	18.3941	+	15.7591i	1.54906	+	1.32716i
$142$	4.79710	−	0.295875i	0.402563	−	0.0248293i
$143$	0.471817			0.0394553
$144$	6.65432	−	0.410424i	0.554527	−	0.0342020i
$145$	2.29383	+	9.12021i	0.190492	+	0.757392i
$146$	−5.60853	−	4.23537i	−0.464166	−	0.350522i
$147$	3.16995	+	2.88979i	0.261453	+	0.238346i
$148$	7.29491	−	2.07558i	0.599638	−	0.170612i
$149$	3.36938	−	10.5914i	0.276030	−	0.867683i	−0.710442	−	0.703755i	$-0.751505\pi$
$149$	3.36938	−	10.5914i	0.276030	−	0.867683i	0.986472	−	0.163928i	$-0.0524165\pi$
$150$	−8.35050	+	5.17041i	−0.681815	+	0.422162i
$151$	−5.27460	−	8.51877i	−0.429241	−	0.693248i	0.561731	−	0.827320i	$-0.310136\pi$
$151$	−5.27460	−	8.51877i	−0.429241	−	0.693248i	−0.990972	+	0.134072i	$0.957195\pi$
$152$	5.30549	+	1.50954i	0.430332	+	0.122440i
$153$	4.81718	−	7.26985i	0.389446	−	0.587733i
$154$	0.429648	−	0.391676i	0.0346220	−	0.0315621i
$155$	−6.91327	−	3.44240i	−0.555287	−	0.276500i
$156$	0.259977	−	4.21507i	0.0208148	−	0.337476i
$157$	16.5845	−	5.84416i	1.32359	−	0.466415i	0.424996	−	0.905195i	$-0.360276\pi$
$157$	16.5845	−	5.84416i	1.32359	−	0.466415i	0.898594	+	0.438780i	$0.144589\pi$
$158$	−9.83276	−	3.46493i	−0.782252	−	0.275655i
$159$	14.1309	−	4.49537i	1.12066	−	0.356506i
$160$	0.831653	+	5.35760i	0.0657479	+	0.423555i
$161$	6.03561	+	15.5797i	0.475673	+	1.22785i
$162$	13.5969	+	12.3952i	1.06827	+	0.973860i
$163$	−5.24586	+	1.31939i	−0.410888	+	0.103342i	−0.443822	−	0.896115i	$-0.646378\pi$
$163$	−5.24586	+	1.31939i	−0.410888	+	0.103342i	0.0329340	+	0.999458i	$0.489515\pi$
$164$	−2.61203	−	3.94195i	−0.203965	−	0.307815i
$165$	0.405302	+	0.268563i	0.0315528	+	0.0209076i
$166$	−0.407692	+	0.218926i	−0.0316430	+	0.0169920i
$167$	−11.5605	+	3.67767i	−0.894581	+	0.284587i	−0.714974	−	0.699151i	$-0.753561\pi$
$167$	−11.5605	+	3.67767i	−0.894581	+	0.284587i	−0.179608	+	0.983738i	$0.557483\pi$
$168$	6.27714	+	7.80062i	0.484292	+	0.601831i
$169$	−4.18492	−	0.782298i	−0.321917	−	0.0601768i
$170$	13.4993	+	7.24899i	1.03535	+	0.555972i
$171$	−1.64681	−	3.06675i	−0.125935	−	0.234520i
$172$	3.91516	−	4.86538i	0.298528	−	0.370982i
$173$	14.9964	+	0.462035i	1.14016	+	0.0351279i	0.595374	−	0.803449i	$-0.297004\pi$
$173$	14.9964	+	0.462035i	1.14016	+	0.0351279i	0.544783	+	0.838577i	$0.316612\pi$
$174$	12.7393	+	17.9963i	0.965767	+	1.36430i
$175$	−5.87973	−	2.48868i	−0.444466	−	0.188126i
$176$	−0.651808	+	0.431903i	−0.0491318	+	0.0325559i
$177$	−2.78365	+	5.18382i	−0.209232	+	0.389640i
$178$	−1.04469	−	2.46817i	−0.0783026	−	0.184997i
$179$	−3.14948	−	1.69123i	−0.235403	−	0.126409i	0.351151	−	0.936319i	$-0.385790\pi$
$179$	−3.14948	−	1.69123i	−0.235403	−	0.126409i	−0.586554	+	0.809910i	$0.699516\pi$
$180$	0.818292	−	1.08359i	0.0609919	−	0.0807663i
$181$	−9.25683	+	13.0767i	−0.688055	+	0.971987i	0.311707	+	0.950178i	$0.399099\pi$
$181$	−9.25683	+	13.0767i	−0.688055	+	0.971987i	−0.999762	+	0.0218084i	$0.993058\pi$
$182$	9.15924	−	5.67116i	0.678928	−	0.420374i
$183$	11.4630	−	6.61817i	0.847370	−	0.489229i
$184$	−3.46525	−	15.8228i	−0.255462	−	1.16647i
$185$	−6.76264	+	14.6991i	−0.497199	+	1.08070i
$186$	−18.0297	−	1.67070i	−1.32201	−	0.122502i
$187$	−0.0629657	+	1.02088i	−0.00460451	+	0.0746541i
$188$	−1.93512	+	7.69400i	−0.141133	+	0.561143i
$189$	−0.935612	+	7.55581i	−0.0680558	+	0.549604i
$190$	5.09822	−	3.37820i	0.369864	−	0.245081i
$191$	18.1868	−	18.7558i	1.31595	−	1.35712i	0.423550	−	0.905873i	$-0.360784\pi$
$191$	18.1868	−	18.7558i	1.31595	−	1.35712i	0.892400	−	0.451246i	$-0.149020\pi$
$192$	−3.87656	−	6.71439i	−0.279766	−	0.484569i
$193$	3.13812	−	11.0293i	0.225887	−	0.793910i	−0.763148	−	0.646224i	$-0.776347\pi$
$193$	3.13812	−	11.0293i	0.225887	−	0.793910i	0.989034	−	0.147686i	$-0.0471823\pi$
$194$	−1.95651	−	10.4664i	−0.140469	−	0.751445i
$195$	6.46782	+	6.27162i	0.463171	+	0.449120i
$196$	−0.384489	+	1.35134i	−0.0274635	+	0.0965243i
$197$	2.01379	+	2.07679i	0.143477	+	0.147965i	0.785828	−	0.618445i	$-0.212237\pi$
$197$	2.01379	+	2.07679i	0.143477	+	0.147965i	−0.642351	+	0.766410i	$0.722041\pi$
$198$	0.347448	+	0.0760923i	0.0246921	+	0.00540765i
$199$	8.19028	+	0.252340i	0.580593	+	0.0178879i	0.319764	−	0.947497i	$-0.396396\pi$
$199$	8.19028	+	0.252340i	0.580593	+	0.0178879i	0.260829	+	0.965385i	$0.416004\pi$
$200$	5.26267	+	3.25851i	0.372127	+	0.230411i
$201$	−2.56689	+	1.08647i	−0.181054	+	0.0766338i
$202$	6.50631	−	9.81901i	0.457783	−	0.690863i
$203$	−4.76378	+	13.5186i	−0.334352	+	0.948821i
$204$	9.08554	+	1.12503i	0.636115	+	0.0787681i
$205$	10.0117	+	1.23971i	0.699244	+	0.0865852i
$206$	3.38779	−	9.61384i	0.236038	−	0.669828i
$207$	−5.64612	+	8.52084i	−0.392432	+	0.592240i
$208$	−13.3427	+	5.64746i	−0.925147	+	0.391581i
$209$	0.347103	+	0.214917i	0.0240096	+	0.0148661i
$210$	11.0961	+	0.341868i	0.765704	+	0.0235911i
$211$	5.26379	+	1.15279i	0.362374	+	0.0793612i	0.391408	−	0.920217i	$-0.371988\pi$
$211$	5.26379	+	1.15279i	0.362374	+	0.0793612i	−0.0290338	+	0.999578i	$0.509243\pi$
$212$	3.38114	+	3.48692i	0.232218	+	0.239482i
$213$	−1.67649	+	5.89226i	−0.114871	+	0.403731i
$214$	17.8971	+	17.3542i	1.22342	+	1.18631i
$215$	2.44804	+	13.0959i	0.166955	+	0.893130i
$216$	2.01992	−	7.09930i	0.137438	−	0.483046i
$217$	−5.88541	−	10.1938i	−0.399527	−	0.692002i
$218$	21.0593	−	21.7181i	1.42632	−	1.47094i
$219$	7.46756	−	4.94819i	0.504611	−	0.334367i
$220$	−0.0195703	+	0.158045i	−0.00131943	+	0.0106554i
$221$	−4.62277	+	18.3800i	−0.310961	+	1.23638i
$222$	−2.33535	+	37.8636i	−0.156738	+	2.54124i
$223$	17.2204	+	1.59571i	1.15317	+	0.106857i	0.651808	−	0.758384i	$-0.274011\pi$
$223$	17.2204	+	1.59571i	1.15317	+	0.106857i	0.501357	+	0.865240i	$0.332834\pi$
$224$	−3.45383	+	7.50713i	−0.230769	+	0.501591i
$225$	−0.835643	−	3.81566i	−0.0557095	−	0.254377i
$226$	−15.6089	+	9.01179i	−1.03829	+	0.599455i
$227$	6.31576	−	3.91055i	0.419192	−	0.259553i	−0.300589	−	0.953754i	$-0.597183\pi$
$227$	6.31576	−	3.91055i	0.419192	−	0.259553i	0.719781	+	0.694201i	$0.244242\pi$
$228$	2.11126	−	2.98249i	0.139822	−	0.197520i
$229$	10.8970	−	14.4300i	0.720094	−	0.953559i	−0.279885	−	0.960034i	$-0.590296\pi$
$229$	10.8970	−	14.4300i	0.720094	−	0.953559i	0.999979	+	0.00647453i	$0.00206092\pi$
$230$	−15.8223	−	8.49638i	−1.04329	−	0.560235i
$231$	0.288850	+	0.682434i	0.0190049	+	0.0449009i
$232$	6.57401	−	12.2424i	0.431605	−	0.803750i
$233$	−8.78608	+	5.82187i	−0.575595	+	0.381403i	−0.806199	−	0.591645i	$-0.798479\pi$
$233$	−8.78608	+	5.82187i	−0.575595	+	0.381403i	0.230604	+	0.973048i	$0.425930\pi$
$234$	6.06939	+	2.56895i	0.396768	+	0.167938i
$235$	−9.77883	−	13.8142i	−0.637901	−	0.901136i
$236$	−1.92632	−	0.0593492i	−0.125393	−	0.00386330i
$237$	8.33087	−	10.3528i	0.541148	−	0.672486i
$238$	11.0485	+	20.5749i	0.716167	+	1.33367i
$239$	4.72010	+	2.53464i	0.305318	+	0.163952i	0.618596	−	0.785709i	$-0.287702\pi$
$239$	4.72010	+	2.53464i	0.305318	+	0.163952i	−0.313278	+	0.949661i	$0.601427\pi$
$240$	−14.6763	−	2.74347i	−0.947350	−	0.177090i
$241$	−17.3592	−	21.5724i	−1.11821	−	1.38960i	−0.911551	−	0.411187i	$-0.865114\pi$
$241$	−17.3592	−	21.5724i	−1.11821	−	1.38960i	−0.206656	−	0.978414i	$-0.566258\pi$
$242$	17.1333	−	5.45050i	1.10137	−	0.350372i
$243$	−11.6129	+	6.23597i	−0.744965	+	0.400038i
$244$	3.61404	+	2.39475i	0.231365	+	0.153308i
$245$	−1.65559	−	2.49853i	−0.105772	−	0.159625i
$246$	22.9380	−	5.76914i	1.46247	−	0.367827i
$247$	5.59042	+	5.09634i	0.355710	+	0.324273i
$248$	4.12228	+	10.6408i	0.261765	+	0.675694i
$249$	−0.0904763	−	0.582858i	−0.00573370	−	0.0369371i
$250$	17.9298	−	5.70390i	1.13398	−	0.360746i
$251$	0.321613	+	0.113332i	0.0203001	+	0.00715346i	0.342486	−	0.939523i	$-0.388731\pi$
$251$	0.321613	+	0.113332i	0.0203001	+	0.00715346i	−0.322186	+	0.946677i	$0.604417\pi$
$252$	1.95192	−	0.687830i	0.122959	−	0.0433292i
$253$	0.0738008	−	1.19655i	0.00463981	−	0.0752266i
$254$	−28.4954	−	14.1890i	−1.78796	−	0.890297i
$255$	−14.4332	+	13.1576i	−0.903842	+	0.823961i
$256$	8.12767	−	12.2659i	0.507980	−	0.766618i
$257$	−16.7983	−	4.77953i	−1.04785	−	0.298139i	−0.294427	−	0.955674i	$-0.595129\pi$
$257$	−16.7983	−	4.77953i	−1.04785	−	0.298139i	−0.753424	+	0.657535i	$0.771599\pi$
$258$	16.4437	+	26.5575i	1.02374	+	1.65340i
$259$	−20.9670	+	12.9822i	−1.30283	+	0.806676i
$260$	−0.894570	+	2.81203i	−0.0554789	+	0.174395i
$261$	−8.43424	+	2.39975i	−0.522066	+	0.148541i
$262$	16.8990	+	15.4054i	1.04402	+	0.951752i
$263$	1.06318	+	0.802876i	0.0655585	+	0.0495075i	0.634905	−	0.772590i	$-0.281039\pi$
$263$	1.06318	+	0.802876i	0.0655585	+	0.0495075i	−0.569347	+	0.822097i	$0.692804\pi$
$264$	−0.175233	−	0.696723i	−0.0107848	−	0.0428803i
$265$	−10.3420	+	0.637871i	−0.635303	+	0.0391841i
$266$	9.32148			0.571536
$267$	3.40972	−	0.210304i	0.208671	−	0.0128704i
$268$	−0.693317	−	0.593997i	−0.0423510	−	0.0362842i
$269$	0.852172	+	2.67875i	0.0519578	+	0.163326i	0.975415	−	0.220374i	$-0.0707279\pi$
$269$	0.852172	+	2.67875i	0.0519578	+	0.163326i	−0.923458	+	0.383701i	$0.874649\pi$
$270$	−4.52038	−	6.82194i	−0.275102	−	0.415170i
$271$	−11.2230	−	2.82271i	−0.681751	−	0.171467i	−0.112526	−	0.993649i	$-0.535894\pi$
$271$	−11.2230	−	2.82271i	−0.681751	−	0.171467i	−0.569225	+	0.822182i	$0.692757\pi$
$272$	−10.4389	−	29.6235i	−0.632952	−	1.79619i
$273$	2.93758	+	13.4134i	0.177791	+	0.811817i
$274$	−7.97513	−	16.0162i	−0.481795	−	0.967575i
$275$	0.308630	+	0.338551i	0.0186111	+	0.0204154i
$276$	−10.6490	−	1.31863i	−0.640993	−	0.0793721i
$277$	−2.90790	−	23.4836i	−0.174718	−	1.41099i	−0.785338	−	0.619067i	$-0.787511\pi$
$277$	−2.90790	−	23.4836i	−0.174718	−	1.41099i	0.610620	−	0.791924i	$-0.290920\pi$
$278$	3.19566	+	3.72999i	0.191663	+	0.223710i
$279$	3.00983	−	6.54207i	0.180194	−	0.391663i
$280$	−2.92419	−	6.35593i	−0.174754	−	0.379839i
$281$	−1.42493	+	1.66318i	−0.0850041	+	0.0992172i	−0.800285	−	0.599620i	$-0.795318\pi$
$281$	−1.42493	+	1.66318i	−0.0850041	+	0.0992172i	0.715281	+	0.698837i	$0.246299\pi$
$282$	−33.0791	−	21.9190i	−1.96983	−	1.30526i
$283$	−4.31865	+	0.945799i	−0.256717	+	0.0562219i	−0.340437	−	0.940267i	$-0.610575\pi$
$283$	−4.31865	+	0.945799i	−0.256717	+	0.0562219i	0.0837195	+	0.996489i	$0.473320\pi$
$284$	−1.97239	+	0.368704i	−0.117040	+	0.0218786i
$285$	1.90142	+	7.56002i	0.112631	+	0.447817i
$286$	−0.767110	+	0.0949888i	−0.0453602	+	0.00561681i
$287$	11.6764	+	10.0037i	0.689236	+	0.590501i
$288$	−4.96944	+	0.928949i	−0.292827	+	0.0547389i
$289$	−22.9524	−	7.30167i	−1.35014	−	0.429510i
$290$	−5.56559	−	14.3664i	−0.326822	−	0.843626i
$291$	13.4112	+	2.08181i	0.786181	+	0.122038i
$292$	2.54107	+	1.46709i	0.148705	+	0.0858548i
$293$	5.43039	−	7.67129i	0.317247	−	0.448161i	−0.626211	−	0.779654i	$-0.715395\pi$
$293$	5.43039	−	7.67129i	0.317247	−	0.448161i	0.943458	+	0.331492i	$0.107552\pi$
$294$	−5.73570	−	4.06022i	−0.334513	−	0.236797i
$295$	2.76985	−	3.03838i	0.161267	−	0.176901i
$296$	22.0169	−	9.31894i	1.27970	−	0.541652i
$297$	0.287581	−	0.464459i	0.0166871	−	0.0269507i
$298$	−3.34582	+	17.8986i	−0.193818	+	1.03684i
$299$	5.41825	−	21.5429i	0.313345	−	1.24586i
$300$	3.19458	−	2.57067i	0.184439	−	0.148418i
$301$	−7.91486	+	18.6996i	−0.456205	+	1.07783i
$302$	10.2908	+	12.7885i	0.592171	+	0.735893i
$303$	9.04786	+	11.9813i	0.519786	+	0.688308i
$304$	−12.3883	−	1.92302i	−0.710518	−	0.110293i
$305$	−8.89586	+	2.53109i	−0.509376	+	0.144930i
$306$	−6.36848	+	12.7896i	−0.364062	+	0.731134i
$307$	21.5711	+	5.42536i	1.23113	+	0.309641i	0.804044	−	0.594570i	$-0.202678\pi$
$307$	21.5711	+	5.42536i	1.23113	+	0.309641i	0.427085	+	0.904211i	$0.359540\pi$
$308$	−0.157920	+	0.184325i	−0.00899834	+	0.0105029i
$309$	10.1223	+	8.14539i	0.575838	+	0.463375i
$310$	11.9331	+	4.20506i	0.677754	+	0.238831i
$311$	9.39613	−	22.1992i	0.532806	−	1.25880i	−0.405847	−	0.913941i	$-0.633024\pi$
$311$	9.39613	−	22.1992i	0.532806	−	1.25880i	0.938653	−	0.344863i	$-0.112075\pi$
$312$	−0.819504	−	13.2868i	−0.0463953	−	0.752219i
$313$	−7.72258	−	18.2453i	−0.436506	−	1.03129i	−0.981260	−	0.192690i	$-0.938279\pi$
$313$	−7.72258	−	18.2453i	−0.436506	−	1.03129i	0.544753	−	0.838596i	$-0.316623\pi$
$314$	−25.7876	+	12.8407i	−1.45528	+	0.724644i
$315$	−1.59491	+	4.11693i	−0.0898628	+	0.231963i
$316$	4.25176	+	0.931149i	0.239180	+	0.0523812i
$317$	2.08162	+	22.4642i	0.116915	+	1.26172i	0.828850	+	0.559470i	$0.188995\pi$
$317$	2.08162	+	22.4642i	0.116915	+	1.26172i	−0.711935	+	0.702245i	$0.752181\pi$
$318$	−22.0700	+	10.1538i	−1.23762	+	0.569396i
$319$	0.715937	−	0.738334i	0.0400848	−	0.0413388i
$320$	1.48257	+	5.21070i	0.0828783	+	0.291287i
$321$	−28.4444	+	14.1636i	−1.58761	+	0.790536i
$322$	−12.9497	−	24.1154i	−0.721658	−	1.34390i
$323$	−11.7731	+	11.4160i	−0.655075	+	0.635203i
$324$	−6.26951	−	4.43810i	−0.348306	−	0.246561i
$325$	4.46873	+	7.21725i	0.247881	+	0.400341i
$326$	8.26344	−	3.20127i	0.457670	−	0.177302i
$327$	17.1876	+	34.5173i	0.950475	+	1.90881i
$328$	−9.69829	−	11.3199i	−0.535499	−	0.625037i
$329$	−0.794393	−	25.7839i	−0.0437963	−	1.42151i
$330$	−0.713036	−	0.355050i	−0.0392513	−	0.0195448i
$331$	−1.81966	+	9.73434i	−0.100018	+	0.535048i	0.895860	+	0.444337i	$0.146561\pi$
$331$	−1.81966	+	9.73434i	−0.100018	+	0.535048i	−0.995877	+	0.0907104i	$0.971086\pi$
$332$	0.157686	−	0.111624i	0.00865416	−	0.00612615i
$333$	−13.8938	−	5.88075i	−0.761377	−	0.322263i
$334$	18.0555	−	8.30684i	0.987952	−	0.454530i
$335$	1.92462	−	0.298757i	0.105153	−	0.0163228i
$336$	−16.3369	−	15.8414i	−0.891253	−	0.864217i
$337$	−33.5194	−	2.06740i	−1.82592	−	0.112619i	−0.888079	−	0.459691i	$-0.847960\pi$
$337$	−33.5194	−	2.06740i	−1.82592	−	0.112619i	−0.937838	+	0.347073i	$0.887176\pi$
$338$	6.96162	+	0.429378i	0.378662	+	0.0233551i
$339$	−4.22133	−	22.5821i	−0.229271	−	1.22649i
$340$	−5.96506	−	2.31088i	−0.323501	−	0.125325i
$341$	0.0779277	+	0.840974i	0.00422002	+	0.0455413i
$342$	3.29490	+	4.65457i	0.178168	+	0.251691i
$343$		−	20.1358i		−	1.08723i
$344$	10.3632	−	16.7371i	0.558746	−	0.902405i
$345$	16.9169	−	15.4217i	0.910773	−	0.830279i
$346$	−24.4752	+	2.26796i	−1.31579	+	0.121926i
$347$	−1.65495	−	13.3650i	−0.0888422	−	0.717471i	−0.969736	−	0.244157i	$-0.921489\pi$
$347$	−1.65495	−	13.3650i	−0.0888422	−	0.717471i	0.880894	−	0.473314i	$-0.156943\pi$
$348$	−6.20157	−	6.80280i	−0.332439	−	0.364668i
$349$	−20.4337	−	9.40100i	−1.09379	−	0.503224i	−0.213156	−	0.977018i	$-0.568374\pi$
$349$	−20.4337	−	9.40100i	−1.09379	−	0.503224i	−0.880635	+	0.473794i	$0.842884\pi$
$350$	10.0607	+	2.86251i	0.537767	+	0.153008i
$351$	6.81943	−	7.48056i	0.363994	−	0.399283i
$352$	0.450268	−	0.385766i	0.0239994	−	0.0205614i
$353$	−10.2233	+	12.7045i	−0.544131	+	0.676193i	−0.973961	−	0.226716i	$-0.927201\pi$
$353$	−10.2233	+	12.7045i	−0.544131	+	0.676193i	0.429830	+	0.902910i	$0.358573\pi$
$354$	3.48221	−	8.98861i	0.185077	−	0.477739i
$355$	2.14032	−	3.70715i	0.113597	−	0.196755i
$356$	0.559473	+	0.969035i	0.0296520	+	0.0513588i
$357$	−29.4149	+	4.56604i	−1.55680	+	0.241661i
$358$	5.46112	+	2.11565i	0.288629	+	0.111816i
$359$	14.8051	+	15.2682i	0.781382	+	0.805827i	0.984878	−	0.173249i	$-0.0554266\pi$
$359$	14.8051	+	15.2682i	0.781382	+	0.805827i	−0.203496	+	0.979076i	$0.565231\pi$
$360$	2.14013	−	3.70682i	0.112795	−	0.195367i
$361$	−3.40831	−	11.9789i	−0.179384	−	0.630471i
$362$	12.4177	−	23.1247i	0.652659	−	1.21541i
$363$	−0.705730	+	22.9061i	−0.0370412	+	1.20226i
$364$	−3.50397	+	2.81964i	−0.183658	+	0.147789i
$365$	−5.90373	+	2.08039i	−0.309015	+	0.108893i
$366$	−17.3049	+	13.0681i	−0.904541	+	0.683078i
$367$	−0.380501	−	0.827046i	−0.0198620	−	0.0431714i	0.898278	−	0.439428i	$-0.144819\pi$
$367$	−0.380501	−	0.827046i	−0.0198620	−	0.0431714i	−0.918140	+	0.396257i	$0.870309\pi$
$368$	12.2352	+	34.7210i	0.637805	+	1.80996i
$369$	−0.867937	+	9.36653i	−0.0451830	+	0.487602i
$370$	8.03585	−	25.2602i	0.417764	−	1.31322i
$371$	−13.6768	−	7.89630i	−0.710063	−	0.409955i
$372$	7.55595	−	0.232796i	0.391758	−	0.0120699i
$373$	−1.50032	−	0.280458i	−0.0776835	−	0.0145216i	0.144764	−	0.989466i	$-0.453758\pi$
$373$	−1.50032	−	0.280458i	−0.0776835	−	0.0145216i	−0.222448	+	0.974945i	$0.571405\pi$
$374$	−0.103156	−	1.67249i	−0.00533405	−	0.0864824i
$375$	−0.738540	+	23.9710i	−0.0381380	+	1.23786i
$376$	−3.07326	+	24.8190i	−0.158491	+	1.27994i
$377$	15.5541	−	11.0105i	0.801074	−	0.567069i
$378$		−	12.4731i		−	0.641547i
$379$	−1.39552	−	0.864071i	−0.0716832	−	0.0443843i	0.490123	−	0.871654i	$-0.336952\pi$
$379$	−1.39552	−	0.864071i	−0.0716832	−	0.0443843i	−0.561806	+	0.827269i	$0.689893\pi$
$380$	−1.93902	+	1.66125i	−0.0994695	+	0.0852202i
$381$	29.1290	−	28.2454i	1.49232	−	1.44705i
$382$	−25.7933	+	34.1558i	−1.31970	+	1.74756i
$383$	−12.0787	+	0.372140i	−0.617192	+	0.0190155i	−0.337886	−	0.941187i	$-0.609712\pi$
$383$	−12.0787	+	0.372140i	−0.617192	+	0.0190155i	−0.279305	+	0.960202i	$0.590104\pi$
$384$	17.0065	+	22.5202i	0.867857	+	1.14923i
$385$	−0.0794276	−	0.511681i	−0.00404800	−	0.0260777i
$386$	−2.88167	+	18.5640i	−0.146673	+	0.944884i
$387$	−12.1351	+	2.65764i	−0.616864	+	0.135095i
$388$	1.34762	+	4.23615i	0.0684149	+	0.215058i
$389$	−3.18422	+	14.5396i	−0.161446	+	0.737187i	0.823916	+	0.566713i	$0.191785\pi$
$389$	−3.18422	+	14.5396i	−0.161446	+	0.737187i	−0.985362	+	0.170475i	$0.945470\pi$
$390$	−11.7785	−	8.89467i	−0.596425	−	0.450399i
$391$	45.8897	+	14.5986i	2.32074	+	0.738281i
$392$	−0.679340	+	4.37638i	−0.0343118	+	0.221040i
$393$	−25.6788	+	13.7892i	−1.29533	+	0.695575i
$394$	−3.69226	−	2.97115i	−0.186013	−	0.149684i
$395$	−7.40989	+	5.59569i	−0.372832	+	0.281549i
$396$	−0.147862	−	0.0137014i	−0.00743032	−	0.000688521i
$397$	0.532263	+	17.2758i	0.0267135	+	0.867050i	0.913972	+	0.405777i	$0.132999\pi$
$397$	0.532263	+	17.2758i	0.0267135	+	0.867050i	−0.887258	+	0.461273i	$0.847393\pi$
$398$	−13.3671	+	1.23864i	−0.670032	+	0.0620876i
$399$	−3.94884	+	11.2060i	−0.197689	+	0.561001i
$400$	−12.7802	−	5.87982i	−0.639010	−	0.293991i
$401$	21.7232	−	8.41563i	1.08481	−	0.420256i	0.248564	−	0.968615i	$-0.420041\pi$
$401$	21.7232	−	8.41563i	1.08481	−	0.420256i	0.836243	+	0.548359i	$0.184747\pi$
$402$	3.95468	−	2.28324i	0.197242	−	0.113878i
$403$	−1.44397	+	15.5829i	−0.0719293	+	0.776241i
$404$	−2.19199	+	4.40210i	−0.109055	+	0.219013i
$405$	15.8920	−	3.99699i	0.789678	−	0.198612i
$406$	5.02361	−	22.9385i	0.249318	−	1.13842i
$407$	1.75604	−	0.217445i	0.0870438	−	0.0107784i
$408$	28.8584			1.42870
$409$	9.70950	+	17.7405i	0.480104	+	0.877212i
$409$	9.70950	+	17.7405i	0.480104	+	0.877212i
$410$	−16.5272			−0.816220
$411$	22.6327	−	2.80253i	1.11639	−	0.138239i
$412$	−0.910418	+	4.15710i	−0.0448531	+	0.204805i
$413$	6.07712	−	1.52846i	0.299036	−	0.0752105i
$414$	7.46436	−	14.9905i	0.366853	−	0.736741i
$415$	−0.0380285	+	0.410393i	−0.00186675	+	0.0201454i
$416$	9.51471	−	5.49332i	0.466497	−	0.269332i
$417$	−5.83785	+	2.26159i	−0.285881	+	0.110751i
$418$	−0.607611	−	0.279545i	−0.0297192	−	0.0136730i
$419$	−10.0684	+	28.5721i	−0.491874	+	1.39584i	0.388452	+	0.921469i	$0.373010\pi$
$419$	−10.0684	+	28.5721i	−0.491874	+	1.39584i	−0.880326	+	0.474369i	$0.842676\pi$
$420$	−4.61497	+	0.427640i	−0.225187	+	0.0208667i
$421$	−0.491399	−	15.9495i	−0.0239493	−	0.777331i	−0.932839	−	0.360294i	$-0.882676\pi$
$421$	−0.491399	−	15.9495i	−0.0239493	−	0.777331i	0.908889	−	0.417037i	$-0.136931\pi$
$422$	−8.79030	−	0.814541i	−0.427905	−	0.0396512i
$423$	12.5941	−	9.51062i	0.612346	−	0.462422i
$424$	11.9281	+	9.59847i	0.579277	+	0.466143i
$425$	−16.2125	+	8.70592i	−0.786421	+	0.422299i
$426$	1.53949	−	9.91755i	0.0745884	−	0.480507i
$427$	−13.4333	−	4.27345i	−0.650084	−	0.206807i
$428$	−8.30563	−	6.27212i	−0.401468	−	0.303174i
$429$	0.210777	−	0.962436i	0.0101764	−	0.0464669i
$430$	−6.61671	−	20.7992i	−0.319086	−	1.00303i
$431$	−19.3273	+	4.23275i	−0.930966	+	0.203885i	−0.653566	−	0.756870i	$-0.726728\pi$
$431$	−19.3273	+	4.23275i	−0.930966	+	0.203885i	−0.277400	+	0.960754i	$0.589473\pi$
$432$	−2.57320	+	16.5768i	−0.123803	+	0.797553i
$433$	3.65263	+	23.5306i	0.175534	+	1.13081i	0.898192	+	0.439604i	$0.144881\pi$
$433$	3.65263	+	23.5306i	0.175534	+	1.13081i	−0.722657	+	0.691207i	$0.757079\pi$
$434$	11.6212	+	15.3889i	0.557834	+	0.738691i
$435$	19.6286	−	0.604751i	0.941120	−	0.0289956i
$436$	−7.61122	+	10.0789i	−0.364511	+	0.482691i
$437$	13.7990	−	13.3804i	0.660098	−	0.640074i
$438$	−11.1451	+	9.54850i	−0.532531	+	0.456245i
$439$	−0.791788	−	0.490255i	−0.0377900	−	0.0233986i	0.507407	−	0.861706i	$-0.330604\pi$
$439$	−0.791788	−	0.490255i	−0.0377900	−	0.0233986i	−0.545197	+	0.838308i	$0.683545\pi$
$440$			0.501999i			0.0239319i
$441$	2.28111	−	1.61477i	0.108624	−	0.0768936i
$442$	3.81562	−	30.8142i	0.181491	−	1.46568i
$443$	0.680158	−	22.0761i	0.0323153	−	1.04887i	−0.834736	−	0.550650i	$-0.814380\pi$
$443$	0.680158	−	22.0761i	0.0323153	−	1.04887i	0.867052	−	0.498218i	$-0.166012\pi$
$444$	−0.974990	−	15.8078i	−0.0462710	−	0.750204i
$445$	−2.34643	−	0.438625i	−0.111232	−	0.0207928i
$446$	−28.3194	+	0.872510i	−1.34096	+	0.0413146i
$447$	−20.0997	−	11.6046i	−0.950685	−	0.548878i
$448$	−2.50315	+	7.86849i	−0.118263	+	0.371751i
$449$	2.34352	−	25.2906i	0.110598	−	1.19354i	−0.741792	−	0.670630i	$-0.766024\pi$
$449$	2.34352	−	25.2906i	0.110598	−	1.19354i	0.852390	−	0.522907i	$-0.175153\pi$
$450$	2.12683	+	6.03552i	0.100260	+	0.284517i
$451$	−0.461108	−	1.00225i	−0.0217127	−	0.0471941i
$452$	6.00485	−	4.53465i	0.282444	−	0.213292i
$453$	−19.7334	+	6.95378i	−0.927155	+	0.326717i
$454$	−9.48128	+	7.62956i	−0.444979	+	0.358073i
$455$	0.295473	−	9.59026i	0.0138520	−	0.449598i
$456$	5.44939	−	10.1481i	0.255191	−	0.475227i
$457$	−4.08850	−	14.3696i	−0.191252	−	0.672181i	−0.996821	−	0.0796784i	$-0.974611\pi$
$457$	−4.08850	−	14.3696i	−0.191252	−	0.672181i	0.805569	−	0.592502i	$-0.201860\pi$
$458$	−14.8119	+	25.6550i	−0.692117	+	1.19878i
$459$	15.2758	+	15.7537i	0.713012	+	0.735318i
$460$	6.99152	+	2.70853i	0.325981	+	0.126286i
$461$	5.73643	−	0.890459i	0.267172	−	0.0414728i	−0.0183974	−	0.999831i	$-0.505856\pi$
$461$	5.73643	−	0.890459i	0.267172	−	0.0414728i	0.285570	+	0.958358i	$0.407817\pi$
$462$	−0.607022	−	1.05139i	−0.0282412	−	0.0489152i
$463$	5.39295	−	9.34086i	0.250632	−	0.434107i	−0.713068	−	0.701095i	$-0.752695\pi$
$463$	5.39295	−	9.34086i	0.250632	−	0.434107i	0.963700	+	0.266988i	$0.0860284\pi$
$464$	−11.4086	+	29.4491i	−0.529633	+	1.36714i
$465$	−10.1104	+	12.5642i	−0.468858	+	0.582651i
$466$	13.1129	−	11.2344i	0.607443	−	0.520425i
$467$	−9.66926	+	10.6067i	−0.447440	+	0.490818i	−0.920791	−	0.390055i	$-0.872456\pi$
$467$	−9.66926	+	10.6067i	−0.447440	+	0.490818i	0.473351	+	0.880874i	$0.343044\pi$
$468$	−2.64652	−	0.752999i	−0.122335	−	0.0348074i
$469$	2.69681	+	1.24073i	0.124527	+	0.0572915i
$470$	18.6802	+	20.4912i	0.861654	+	0.945189i
$471$	−4.51235	−	36.4408i	−0.207918	−	1.67910i
$472$	−6.04915	+	0.560536i	−0.278435	+	0.0258008i
$473$	1.07671	−	0.981553i	0.0495073	−	0.0451318i
$474$	−11.4606	+	18.5095i	−0.526402	+	0.850168i
$475$			7.34509i			0.337016i
$476$	−5.63329	−	7.95791i	−0.258201	−	0.364750i
$477$	−0.891469	−	9.62049i	−0.0408176	−	0.440492i
$478$	−8.18454	−	3.17071i	−0.374352	−	0.145025i
$479$	−3.69223	−	19.7517i	−0.168702	−	0.902477i	−0.957632	−	0.287994i	$-0.907012\pi$
$479$	−3.69223	−	19.7517i	−0.168702	−	0.902477i	0.788930	−	0.614483i	$-0.210635\pi$
$480$	11.3002	+	0.696975i	0.515783	+	0.0318124i
$481$	32.7251	+	2.01842i	1.49214	+	0.0920319i
$482$	32.5669	+	31.5790i	1.48338	+	1.43838i
$483$	34.4766	−	5.35176i	1.56874	−	0.243514i
$484$	−6.81918	+	3.13732i	−0.309963	+	0.142605i
$485$	−8.73330	−	3.69649i	−0.396559	−	0.167849i
$486$	17.6255	−	12.4768i	0.799508	−	0.565960i
$487$	−2.13828	+	11.4388i	−0.0968946	+	0.518340i	0.899744	+	0.436418i	$0.143753\pi$
$487$	−2.13828	+	11.4388i	−0.0968946	+	0.518340i	−0.996639	+	0.0819225i	$0.973894\pi$
$488$	12.2336	+	6.09159i	0.553787	+	0.275753i
$489$	0.347847	+	11.2902i	0.0157302	+	0.510561i
$490$	3.19478	+	3.72897i	0.144326	+	0.168458i
$491$	2.21333	+	4.44496i	0.0998861	+	0.200598i	0.939470	−	0.342632i	$-0.111319\pi$
$491$	2.21333	+	4.44496i	0.0998861	+	0.200598i	−0.839583	+	0.543231i	$0.817201\pi$
$492$	−9.20788	+	3.56715i	−0.415123	+	0.160820i
$493$	21.7479	+	35.1240i	0.979475	+	1.58191i
$494$	−10.1153	−	7.16048i	−0.455109	−	0.322165i
$495$	0.227426	−	0.220527i	0.0102221	−	0.00991197i
$496$	−12.2699	−	22.8494i	−0.550933	−	1.02597i
$497$	5.84033	−	2.90814i	0.261974	−	0.130448i
$498$	0.264447	+	0.929433i	0.0118501	+	0.0416489i
$499$	−3.93397	+	4.05704i	−0.176109	+	0.181618i	−0.800200	−	0.599733i	$-0.795273\pi$
$499$	−3.93397	+	4.05704i	−0.176109	+	0.181618i	0.624091	+	0.781351i	$0.285469\pi$
$500$	−7.13620	+	3.28317i	−0.319141	+	0.146828i
$501$	2.33742	+	25.2247i	0.104428	+	1.12696i
$502$	−0.545717	−	0.119514i	−0.0243565	−	0.00533416i
$503$	13.1211	−	33.8696i	0.585043	−	1.51017i	−0.254609	−	0.967044i	$-0.581947\pi$
$503$	13.1211	−	33.8696i	0.585043	−	1.51017i	0.839652	−	0.543125i	$-0.182759\pi$
$504$	5.83980	−	2.90788i	0.260126	−	0.129527i
$505$	−4.08923	−	9.66119i	−0.181968	−	0.429917i
$506$	0.120907	+	1.96029i	0.00537495	+	0.0871455i
$507$	−3.46532	+	8.18715i	−0.153900	+	0.363604i
$508$	12.5344	+	4.41695i	0.556124	+	0.195970i
$509$	−25.3280	−	20.3814i	−1.12264	−	0.903389i	−0.126575	−	0.991957i	$-0.540398\pi$
$509$	−25.3280	−	20.3814i	−1.12264	−	0.903389i	−0.996070	+	0.0885682i	$0.971771\pi$
$510$	20.8175	−	24.2983i	0.921813	−	1.07595i
$511$	−9.25230	−	2.32705i	−0.409298	−	0.102943i
$512$	1.30247	−	2.61571i	0.0575614	−	0.115599i
$513$	8.42434	−	2.39693i	0.371944	−	0.105827i
$514$	28.2741	+	4.38895i	1.24712	+	0.193588i
$515$	−5.47110	−	7.24491i	−0.241086	−	0.319249i
$516$	−8.17562	−	10.1599i	−0.359912	−	0.447263i
$517$	−0.721461	+	1.70452i	−0.0317298	+	0.0749647i
$518$	31.4759	−	25.3285i	1.38297	−	1.11287i
$519$	7.64191	−	30.3841i	0.335442	−	1.33371i
$520$	−1.70921	+	9.14348i	−0.0749539	+	0.400968i
$521$	18.6332	−	30.0936i	0.816333	−	1.31842i	−0.128778	−	0.991674i	$-0.541105\pi$
$521$	18.6332	−	30.0936i	0.816333	−	1.31842i	0.945111	−	0.326750i	$-0.105953\pi$
$522$	13.2298	−	5.59970i	0.579053	−	0.245092i
$523$	6.05860	−	6.64597i	0.264924	−	0.290608i	−0.592121	−	0.805849i	$-0.701709\pi$
$523$	6.05860	−	6.64597i	0.264924	−	0.290608i	0.857045	+	0.515241i	$0.172298\pi$
$524$	−7.79209	−	5.51591i	−0.340399	−	0.240964i
$525$	−7.70322	+	10.8820i	−0.336196	+	0.474930i
$526$	−1.89023	−	1.09132i	−0.0824179	−	0.0475840i
$527$	−33.5244	−	5.20395i	−1.46035	−	0.226688i
$528$	0.589834	+	1.52254i	0.0256692	+	0.0662599i
$529$	−31.8687	−	10.1382i	−1.38559	−	0.440789i
$530$	16.6862	−	3.11920i	0.724804	−	0.135489i
$531$	2.91132	+	2.49427i	0.126341	+	0.108242i
$532$	−3.86215	+	0.478238i	−0.167445	+	0.0207342i
$533$	−4.98621	−	19.8251i	−0.215977	−	0.858720i
$534$	−5.50140	+	1.02839i	−0.238069	+	0.0445028i
$535$	21.6893	−	4.75003i	0.937710	−	0.205362i
$536$	−2.39902	−	1.58965i	−0.103622	−	0.0686624i
$537$	−4.85685	+	5.66894i	−0.209589	+	0.244633i
$538$	−1.92482	−	4.18372i	−0.0829848	−	0.180373i
$539$	−0.137000	+	0.297778i	−0.00590099	+	0.0128262i
$540$	2.22292	+	2.59460i	0.0956593	+	0.111654i
$541$	3.18768	+	25.7431i	0.137049	+	1.10678i	0.892331	+	0.451381i	$0.149068\pi$
$541$	3.18768	+	25.7431i	0.137049	+	1.10678i	−0.755282	+	0.655400i	$0.772500\pi$
$542$	18.8154	+	2.32986i	0.808192	+	0.100076i
$543$	22.5393	+	24.7244i	0.967253	+	1.06103i
$544$	10.6162	+	21.3203i	0.455167	+	0.914100i
$545$	−5.76416	−	26.3200i	−0.246910	−	1.12742i
$546$	−7.47658	−	21.2170i	−0.319968	−	0.908004i
$547$	−13.3820	−	3.36571i	−0.572174	−	0.143908i	−0.0530279	−	0.998593i	$-0.516887\pi$
$547$	−13.3820	−	3.36571i	−0.572174	−	0.143908i	−0.519146	+	0.854685i	$0.673750\pi$
$548$	4.12603	+	6.22681i	0.176255	+	0.265996i
$549$	−2.61444	−	8.21833i	−0.111582	−	0.350750i
$550$	−0.569951	−	0.488304i	−0.0243028	−	0.0208213i
$551$	16.4581	−	1.01510i	0.701138	−	0.0432447i
$552$	−33.8243			−1.43966
$553$	−14.1254	+	0.871223i	−0.600672	+	0.0370482i
$554$	9.45569	+	37.5957i	0.401734	+	1.59729i
$555$	26.9628	+	20.3614i	1.14451	+	0.864292i
$556$	−1.51542	−	1.38149i	−0.0642680	−	0.0585880i
$557$	3.42957	−	0.975796i	0.145315	−	0.0413458i	−0.200223	−	0.979750i	$-0.564167\pi$
$557$	3.42957	−	0.975796i	0.145315	−	0.0413458i	0.345539	+	0.938404i	$0.387696\pi$
$558$	−3.57649	+	11.2425i	−0.151405	+	0.475932i
$559$	22.9534	−	14.2121i	0.970824	−	0.601109i
$560$	8.37078	+	13.5193i	0.353730	+	0.571294i
$561$	2.05431	+	0.584503i	0.0867332	+	0.0246777i
$562$	1.98190	−	2.99099i	0.0836014	−	0.126167i
$563$	−23.7349	+	21.6372i	−1.00031	+	0.911899i	−0.996112	−	0.0880923i	$-0.971923\pi$
$563$	−23.7349	+	21.6372i	−1.00031	+	0.911899i	−0.00419316	+	0.999991i	$0.501335\pi$
$564$	14.8301	+	7.38453i	0.624462	+	0.310945i
$565$	−0.988217	+	16.0222i	−0.0415746	+	0.674060i
$566$	6.83113	−	2.40720i	0.287134	−	0.101182i
$567$	23.5562	+	8.30088i	0.989267	+	0.348604i
$568$	−6.02747	+	1.91748i	−0.252907	+	0.0804555i
$569$	1.32340	+	8.52548i	0.0554798	+	0.357407i	0.999612	+	0.0278407i	$0.00886313\pi$
$569$	1.32340	+	8.52548i	0.0554798	+	0.357407i	−0.944133	+	0.329566i	$0.893098\pi$
$570$	−4.61348	−	11.9088i	−0.193238	−	0.498804i
$571$	−27.9526	−	25.4821i	−1.16978	−	1.06639i	−0.996674	−	0.0814912i	$-0.974032\pi$
$571$	−27.9526	−	25.4821i	−1.16978	−	1.06639i	−0.173105	−	0.984903i	$-0.555380\pi$
$572$	0.312962	−	0.0787131i	0.0130856	−	0.00329116i
$573$	−30.1343	−	45.4772i	−1.25888	−	1.89984i
$574$	−20.9983	−	13.9139i	−0.876450	−	0.580757i
$575$	19.0023	−	10.2040i	0.792451	−	0.425537i
$576$	−4.81384	+	1.53139i	−0.200577	+	0.0638081i
$577$	−11.3025	−	14.0456i	−0.470528	−	0.584727i	0.486879	−	0.873469i	$-0.338135\pi$
$577$	−11.3025	−	14.0456i	−0.470528	−	0.584727i	−0.957407	+	0.288743i	$0.906763\pi$
$578$	38.7875	+	7.25063i	1.61335	+	0.301587i
$579$	−21.0963	−	11.3285i	−0.876734	−	0.470796i
$580$	3.04305	+	5.66688i	0.126356	+	0.235304i
$581$	−0.393819	+	0.489401i	−0.0163384	+	0.0203038i
$582$	−22.2240	−	0.684714i	−0.921215	−	0.0283823i
$583$	0.654702	+	0.924870i	0.0271150	+	0.0383042i
$584$	8.51761	+	3.60519i	0.352461	+	0.149184i
$585$	4.89323	−	3.24237i	0.202310	−	0.134055i
$586$	−7.28466	+	13.5658i	−0.300926	+	0.560396i
$587$	5.47198	+	12.9281i	0.225853	+	0.533599i	0.994337	−	0.106270i	$-0.0338908\pi$
$587$	5.47198	+	12.9281i	0.225853	+	0.533599i	−0.768484	+	0.639869i	$0.778989\pi$
$588$	2.58477	+	1.38799i	0.106594	+	0.0572398i
$589$	−8.16047	+	10.8062i	−0.336246	+	0.445262i
$590$	−3.89169	+	5.49763i	−0.160218	+	0.226334i
$591$	5.13597	−	3.18006i	0.211266	−	0.130810i
$592$	−47.0569	+	27.1683i	−1.93403	+	1.11661i
$593$	4.39168	+	20.0530i	0.180345	+	0.823479i	0.976007	+	0.217739i	$0.0698681\pi$
$593$	4.39168	+	20.0530i	0.180345	+	0.823479i	−0.795662	+	0.605741i	$0.792877\pi$
$594$	−0.374060	+	0.813046i	−0.0153479	+	0.0333597i
$595$	20.7112	+	1.91918i	0.849077	+	0.0786786i
$596$	0.467984	−	7.58754i	0.0191694	−	0.310798i
$597$	4.17361	−	16.5942i	0.170815	−	0.679156i
$598$	−4.47221	+	36.1166i	−0.182882	+	1.47692i
$599$	−6.99264	+	4.63349i	−0.285712	+	0.189319i	−0.687049	−	0.726611i	$-0.741094\pi$
$599$	−6.99264	+	4.63349i	−0.285712	+	0.189319i	0.401338	+	0.915930i	$0.368545\pi$
$600$	8.99789	−	9.27938i	0.367337	−	0.378829i
$601$	−13.4155	−	23.2363i	−0.547230	−	0.947830i	−0.998463	−	0.0554235i	$-0.982349\pi$
$601$	−13.4155	−	23.2363i	−0.547230	−	0.947830i	0.451233	−	0.892406i	$-0.350984\pi$
$602$	9.10379	−	31.9965i	0.371043	−	1.30408i
$603$	0.333709	+	1.78518i	0.0135897	+	0.0726983i
$604$	−4.91990	−	4.77065i	−0.200188	−	0.194115i
$605$	4.38226	−	15.4020i	0.178164	−	0.626182i
$606$	−17.1227	−	17.6584i	−0.695564	−	0.717324i
$607$	−43.5652	−	9.54094i	−1.76826	−	0.387255i	−0.793158	−	0.609016i	$-0.791565\pi$
$607$	−43.5652	−	9.54094i	−1.76826	−	0.387255i	−0.975101	+	0.221761i	$0.928819\pi$
$608$	9.50198	+	0.292753i	0.385356	+	0.0118727i
$609$	25.4478	+	15.7566i	1.03120	+	0.638491i
$610$	13.9539	−	5.90618i	0.564977	−	0.239134i
$611$	−18.9444	+	28.5899i	−0.766407	+	1.15662i
$612$	1.98247	−	5.62584i	0.0801365	−	0.227411i
$613$	2.59713	+	0.321595i	0.104897	+	0.0129891i	0.175165	−	0.984539i	$-0.443954\pi$
$613$	2.59713	+	0.321595i	0.104897	+	0.0129891i	−0.0702680	+	0.997528i	$0.522385\pi$
$614$	−36.1640	−	4.47808i	−1.45946	−	0.180720i
$615$	7.00138	−	19.8685i	0.282323	−	0.801174i
$616$	−0.422624	+	0.637804i	−0.0170280	+	0.0256979i
$617$	27.7457	−	11.7437i	1.11700	−	0.472785i	0.248578	−	0.968612i	$-0.420037\pi$
$617$	27.7457	−	11.7437i	1.11700	−	0.472785i	0.868422	+	0.495827i	$0.165135\pi$
$618$	−18.0974	−	11.2054i	−0.727983	−	0.450748i
$619$	−1.20398	−	0.0370944i	−0.0483922	−	0.00149095i	0.00658991	−	0.999978i	$-0.497902\pi$
$619$	−1.20398	−	0.0370944i	−0.0483922	−	0.00149095i	−0.0549822	+	0.998487i	$0.517510\pi$
$620$	−5.15996	−	1.13005i	−0.207229	−	0.0453838i
$621$	−17.9044	−	18.4645i	−0.718479	−	0.740956i
$622$	−10.8076	+	37.9847i	−0.433344	+	1.52305i
$623$	−2.61194	−	2.53271i	−0.104645	−	0.101471i
$624$	5.55936	+	29.7400i	0.222553	+	1.19055i
$625$	0.657657	−	2.31143i	0.0263063	−	0.0924570i
$626$	16.2291	+	28.1097i	0.648647	+	1.12349i
$627$	0.593462	−	0.612028i	0.0237006	−	0.0244420i
$628$	10.0258	−	6.64331i	0.400071	−	0.265097i
$629$	−8.73458	+	70.5387i	−0.348271	+	2.81256i
$630$	1.76426	−	7.01466i	0.0702898	−	0.279471i
$631$	−1.68950	+	27.3924i	−0.0672581	+	1.09047i	0.802390	+	0.596800i	$0.203562\pi$
$631$	−1.68950	+	27.3924i	−0.0672581	+	1.09047i	−0.869648	+	0.493673i	$0.835654\pi$
$632$	13.6616	+	1.26593i	0.543429	+	0.0503561i
$633$	4.70303	−	10.2224i	0.186929	−	0.406302i
$634$	−7.90705	−	36.1047i	−0.314029	−	1.43390i
$635$	−24.5533	+	14.1758i	−0.974366	+	0.562551i
$636$	8.62327	−	5.33930i	0.341935	−	0.211717i
$637$	−3.50920	+	4.95731i	−0.139040	+	0.196416i
$638$	−1.01537	+	1.34457i	−0.0401989	+	0.0532320i
$639$	3.51655	+	1.88835i	0.139113	+	0.0747019i
$640$	−7.68616	−	18.1593i	−0.303822	−	0.717809i
$641$	−17.9863	+	33.4947i	−0.710415	+	1.32296i	0.226709	+	0.973963i	$0.427204\pi$
$641$	−17.9863	+	33.4947i	−0.710415	+	1.32296i	−0.937123	+	0.348998i	$0.886522\pi$
$642$	43.3953	−	28.7547i	1.71267	−	1.13486i
$643$	9.84804	+	4.16832i	0.388369	+	0.164382i	0.575206	−	0.818008i	$-0.304922\pi$
$643$	9.84804	+	4.16832i	0.388369	+	0.164382i	−0.186837	+	0.982391i	$0.559824\pi$
$644$	6.60266	+	9.32730i	0.260181	+	0.367547i
$645$	27.8072	+	0.856732i	1.09491	+	0.0337338i
$646$	16.8432	−	20.9311i	0.662687	−	0.823523i
$647$	8.98788	+	16.7376i	0.353350	+	0.658021i	0.993948	−	0.109856i	$-0.0350388\pi$
$647$	8.98788	+	16.7376i	0.353350	+	0.658021i	−0.640598	+	0.767877i	$0.721313\pi$
$648$	−21.3323	−	11.4552i	−0.838012	−	0.450003i
$649$	−0.441968	−	0.0826182i	−0.0173488	−	0.00324305i
$650$	−8.71857	−	10.8346i	−0.341971	−	0.424968i
$651$	−23.4231	+	7.45143i	−0.918024	+	0.292044i
$652$	−3.25953	+	1.75033i	−0.127653	+	0.0685483i
$653$	−28.9810	−	19.2035i	−1.13411	−	0.751491i	−0.162183	−	0.986761i	$-0.551854\pi$
$653$	−28.9810	−	19.2035i	−1.13411	−	0.751491i	−0.971930	+	0.235270i	$0.924403\pi$
$654$	−34.8939	−	52.6602i	−1.36446	−	2.05918i
$655$	19.7514	−	4.96768i	0.771751	−	0.194103i
$656$	25.0364	+	22.8237i	0.977506	+	0.891115i
$657$	−2.10847	−	5.44258i	−0.0822592	−	0.212335i
$658$	6.48254	+	41.7612i	0.252716	+	1.62802i
$659$	−20.7958	+	6.61563i	−0.810090	+	0.257708i	−0.679450	−	0.733722i	$-0.737782\pi$
$659$	−20.7958	+	6.61563i	−0.810090	+	0.257708i	−0.130640	+	0.991430i	$0.541703\pi$
$660$	0.313647	+	0.110525i	0.0122087	+	0.00430217i
$661$	18.6155	−	6.55985i	0.724059	−	0.255149i	0.0551347	−	0.998479i	$-0.482441\pi$
$661$	18.6155	−	6.55985i	0.724059	−	0.255149i	0.668925	+	0.743330i	$0.266755\pi$
$662$	0.998754	−	16.1931i	0.0388177	−	0.629362i
$663$	35.4274	+	17.6408i	1.37589	+	0.685111i
$664$	0.450055	−	0.410279i	0.0174655	−	0.0159219i
$665$	4.58583	−	6.92070i	0.177831	−	0.268373i
$666$	23.7734	+	6.76413i	0.921202	+	0.262105i
$667$	−25.4902	−	41.1681i	−0.986986	−	1.59404i
$668$	−7.05471	+	4.36809i	−0.272955	+	0.169007i
$669$	10.9480	−	34.4143i	0.423273	−	1.33053i
$670$	−3.06903	+	0.873215i	−0.118567	+	0.0337352i
$671$	0.747479	+	0.681417i	0.0288561	+	0.0263058i
$672$	13.7705	+	10.3990i	0.531208	+	0.401150i
$673$	0.273292	+	1.08661i	0.0105346	+	0.0418856i	0.974838	−	0.222914i	$-0.0715569\pi$
$673$	0.273292	+	1.08661i	0.0105346	+	0.0418856i	−0.964303	+	0.264800i	$0.914694\pi$
$674$	54.9142	−	3.38699i	2.11522	−	0.130462i
$675$	9.82848			0.378298
$676$	−2.90642	+	0.179262i	−0.111786	+	0.00689470i
$677$	−14.8615	−	12.7325i	−0.571172	−	0.489350i	0.317272	−	0.948335i	$-0.397233\pi$
$677$	−14.8615	−	12.7325i	−0.571172	−	0.489350i	−0.888445	+	0.458984i	$0.848214\pi$
$678$	11.4097	+	35.8657i	0.438187	+	1.37741i
$679$	−7.98389	−	12.0489i	−0.306394	−	0.462394i
$680$	−19.5558	−	4.91849i	−0.749932	−	0.188616i
$681$	−5.15548	−	14.6302i	−0.197559	−	0.560630i
$682$	−0.296010	−	1.35162i	−0.0113348	−	0.0517562i
$683$	13.6555	+	27.4240i	0.522514	+	1.04935i	0.986539	+	0.163528i	$0.0522873\pi$
$683$	13.6555	+	27.4240i	0.522514	+	1.04935i	−0.464024	+	0.885822i	$0.653595\pi$
$684$	−1.60397	−	1.75948i	−0.0613295	−	0.0672752i
$685$	−15.8147	−	1.95828i	−0.604247	−	0.0748220i
$686$	4.05385	+	32.7380i	0.154777	+	1.24994i
$687$	−24.5669	−	28.6747i	−0.937287	−	1.09401i
$688$	−18.6999	+	40.6455i	−0.712926	+	1.54959i
$689$	8.77582	+	19.0748i	0.334332	+	0.726694i
$690$	−24.3997	+	28.4795i	−0.928882	+	1.08420i
$691$	16.6163	+	11.0103i	0.632112	+	0.418853i	0.827180	−	0.561937i	$-0.189944\pi$
$691$	16.6163	+	11.0103i	0.632112	+	0.418853i	−0.195068	+	0.980790i	$0.562493\pi$
$692$	10.0244	−	2.19538i	0.381071	−	0.0834558i
$693$	0.474610	−	0.0887199i	0.0180289	−	0.00337019i
$694$	5.38144	+	21.3965i	0.204277	+	0.812201i
$695$	4.34147	−	0.537590i	0.164681	−	0.0203919i
$696$	−22.0358	−	18.8791i	−0.835263	−	0.715610i
$697$	43.5614	−	8.14304i	1.65001	−	0.308440i
$698$	35.1151	+	11.1709i	1.32913	+	0.422826i
$699$	7.95070	+	20.5231i	0.300723	+	0.776256i
$700$	−4.31529	−	0.669857i	−0.163103	−	0.0253182i
$701$	−28.7525	−	16.6003i	−1.08597	−	0.626984i	−0.153467	−	0.988154i	$-0.549044\pi$
$701$	−28.7525	−	16.6003i	−1.08597	−	0.626984i	−0.932500	+	0.361170i	$0.882377\pi$
$702$	−9.58145	+	13.5353i	−0.361629	+	0.510857i
$703$	23.1556	+	16.3915i	0.873330	+	0.618217i
$704$	0.399136	−	0.437832i	0.0150430	−	0.0165014i
$705$	−32.5474	+	13.7761i	−1.22580	+	0.518839i
$706$	14.0639	−	22.7141i	0.529304	−	0.854855i
$707$	2.93810	−	15.7175i	0.110499	−	0.591116i
$708$	−0.981616	+	3.90289i	−0.0368914	+	0.146680i
$709$	−17.9669	+	14.4579i	−0.674763	+	0.542980i	−0.902471	−	0.430750i	$-0.858249\pi$
$709$	−17.9669	+	14.4579i	−0.674763	+	0.542980i	0.227709	+	0.973729i	$0.426877\pi$
$710$	−2.73353	+	6.45823i	−0.102588	+	0.242373i
$711$	−5.42799	−	6.74539i	−0.203566	−	0.252972i
$712$	2.12559	+	2.81474i	0.0796599	+	0.105487i
$713$	39.2933	+	6.09944i	1.47154	+	0.228426i
$714$	46.9055	−	13.3458i	1.75539	−	0.499452i
$715$	−0.306866	+	0.616270i	−0.0114761	+	0.0230472i
$716$	−2.37124	−	0.596390i	−0.0886174	−	0.0222882i
$717$	7.27893	−	8.49600i	0.271837	−	0.317289i
$718$	−27.1449	−	21.8435i	−1.01304	−	0.815190i
$719$	4.81751	+	1.69762i	0.179663	+	0.0633107i	0.420675	−	0.907211i	$-0.361793\pi$
$719$	4.81751	+	1.69762i	0.179663	+	0.0633107i	−0.241012	+	0.970522i	$0.577479\pi$
$720$	−3.79184	+	8.95857i	−0.141313	+	0.333866i
$721$	−0.851826	−	13.8109i	−0.0317237	−	0.514344i
$722$	7.95312	+	18.7900i	0.295984	+	0.699291i
$723$	−51.7595	+	25.7732i	−1.92496	+	0.958514i
$724$	−3.95859	+	10.2183i	−0.147120	+	0.379760i
$725$	18.0750	+	3.95848i	0.671288	+	0.147014i
$726$	−3.46417	−	37.3844i	−0.128568	−	1.38746i
$727$	27.2418	−	12.5332i	1.01034	−	0.464832i	0.157790	−	0.987473i	$-0.449563\pi$
$727$	27.2418	−	12.5332i	1.01034	−	0.464832i	0.852553	+	0.522641i	$0.175053\pi$
$728$	−9.86934	+	10.1781i	−0.365782	+	0.377225i
$729$	−1.68757	−	5.93118i	−0.0625024	−	0.219673i
$730$	9.17984	−	4.57101i	0.339761	−	0.169181i
$731$	27.6879	+	51.5614i	1.02407	+	1.90707i
$732$	6.49945	−	6.30229i	0.240227	−	0.232939i
$733$	27.8835	+	19.7383i	1.02990	+	0.729052i	0.963218	−	0.268722i	$-0.0866012\pi$
$733$	27.8835	+	19.7383i	1.02990	+	0.729052i	0.0666838	+	0.997774i	$0.478758\pi$
$734$	0.785150	+	1.26806i	0.0289804	+	0.0468050i
$735$	−5.83625	+	2.26097i	−0.215273	+	0.0833973i
$736$	−12.4431	−	24.9891i	−0.458658	−	0.921109i
$737$	−0.138580	−	0.161751i	−0.00510465	−	0.00595818i
$738$	−0.474576	−	15.4035i	−0.0174694	−	0.567009i
$739$	−1.36706	−	0.680713i	−0.0502880	−	0.0250404i	0.420418	−	0.907330i	$-0.361883\pi$
$739$	−1.36706	−	0.680713i	−0.0502880	−	0.0250404i	−0.470706	+	0.882290i	$0.656001\pi$
$740$	−2.03350	+	10.8783i	−0.0747531	+	0.399894i
$741$	12.8932	−	9.12693i	0.473645	−	0.335286i
$742$	23.8263	+	10.0848i	0.874693	+	0.370226i
$743$	34.9989	−	16.1021i	1.28399	−	0.590727i	0.346271	−	0.938134i	$-0.387448\pi$
$743$	34.9989	−	16.1021i	1.28399	−	0.590727i	0.937714	+	0.347407i	$0.112938\pi$
$744$	23.5473	−	3.65522i	0.863287	−	0.134007i
$745$	11.6427	+	11.2895i	0.426556	+	0.413617i
$746$	2.49578	+	0.153934i	0.0913769	+	0.00563593i
$747$	−0.383582	−	0.0236585i	−0.0140345	−	0.000865620i
$748$	0.128547	+	0.687667i	0.00470015	+	0.0251436i
$749$	31.5558	+	12.2248i	1.15302	+	0.446684i
$750$	−3.62522	−	39.1224i	−0.132374	−	1.42855i
$751$	16.5954	+	23.4436i	0.605573	+	0.855468i	0.997928	−	0.0643461i	$-0.0204962\pi$
$751$	16.5954	+	23.4436i	0.605573	+	0.855468i	−0.392354	+	0.919814i	$0.628339\pi$
$752$		−	56.8383i		−	2.07268i
$753$	0.374857	−	0.605414i	0.0136605	−	0.0220625i
$754$	−23.0721	+	21.0330i	−0.840236	+	0.765977i
$755$	14.5575	−	1.34895i	0.529801	−	0.0490933i
$756$	0.639931	+	5.16795i	0.0232741	+	0.187957i
$757$	−24.2720	−	26.6251i	−0.882180	−	0.967706i	0.117498	−	0.993073i	$-0.462513\pi$
$757$	−24.2720	−	26.6251i	−0.882180	−	0.967706i	−0.999678	+	0.0253675i	$0.991924\pi$
$758$	2.44289	+	1.12391i	0.0887298	+	0.0408222i
$759$	−2.40782	−	0.685084i	−0.0873983	−	0.0248670i
$760$	−5.42237	+	5.94805i	−0.196690	+	0.215758i
$761$	−18.7443	+	16.0592i	−0.679481	+	0.582144i	−0.921618	−	0.388098i	$-0.873132\pi$
$761$	−18.7443	+	16.0592i	−0.679481	+	0.582144i	0.242137	+	0.970242i	$0.422152\pi$
$762$	−41.6733	+	51.7876i	−1.50967	+	1.87607i
$763$	14.8348	−	38.2930i	0.537055	−	1.38630i
$764$	8.93451	−	15.4750i	0.323239	−	0.559867i
$765$	6.36256	+	11.0203i	0.230039	+	0.398439i
$766$	19.5634	−	3.03680i	0.706854	−	0.109724i
$767$	−7.76877	−	3.00964i	−0.280514	−	0.108672i
$768$	−21.3897	−	22.0589i	−0.771834	−	0.795980i
$769$	−10.7559	+	18.6298i	−0.387868	+	0.671807i	−0.992163	−	0.124954i	$-0.960122\pi$
$769$	−10.7559	+	18.6298i	−0.387868	+	0.671807i	0.604295	+	0.796761i	$0.293455\pi$
$770$	0.232153	+	0.815933i	0.00836622	+	0.0294042i
$771$	−17.2539	+	32.1309i	−0.621385	+	1.15717i
$772$	0.241531	−	7.83944i	0.00869288	−	0.282148i
$773$	16.4122	−	13.2069i	0.590306	−	0.475018i	−0.285039	−	0.958516i	$-0.592007\pi$
$773$	16.4122	−	13.2069i	0.590306	−	0.475018i	0.875345	+	0.483498i	$0.160634\pi$
$774$	19.1950	−	6.76407i	0.689952	−	0.243130i
$775$	−12.1261	+	9.15718i	−0.435581	+	0.328936i
$776$	5.85676	+	12.7301i	0.210245	+	0.456983i
$777$	17.1151	+	48.5692i	0.614002	+	1.74241i
$778$	2.24992	−	24.2805i	0.0806636	−	0.870498i
$779$	5.36230	−	16.8561i	0.192124	−	0.603931i
$780$	5.33649	+	3.08102i	0.191077	+	0.110318i
$781$	−0.467909	+	0.0144161i	−0.0167431	+	0.000515849i
$782$	−77.5495	−	14.4965i	−2.77316	−	0.518394i
$783$	−1.35831	−	22.0226i	−0.0485420	−	0.787024i
$784$	0.309970	−	10.0608i	0.0110703	−	0.359314i
$785$	−3.15302	+	25.4631i	−0.112536	+	0.908818i
$786$	38.9742	−	27.5893i	1.39016	−	0.984076i
$787$		−	24.4814i		−	0.872669i	−0.899784	−	0.436335i	$-0.856276\pi$
$787$		−	24.4814i		−	0.872669i	0.899784	−	0.436335i	$-0.143724\pi$
$788$	1.68224	+	1.04160i	0.0599274	+	0.0371055i
$789$	2.11271	−	1.81006i	0.0752144	−	0.0644398i
$790$	10.9209	−	10.5896i	0.388549	−	0.376762i
$791$	−14.7444	+	19.5247i	−0.524250	+	0.694219i
$792$	−0.467867	+	0.0144148i	−0.0166249	+	0.000512209i
$793$	11.2946	+	14.9564i	0.401082	+	0.531119i
$794$	−4.34346	−	27.9810i	−0.154144	−	0.993010i
$795$	−3.31896	+	21.3811i	−0.117711	+	0.758308i
$796$	5.47481	−	1.19900i	0.194050	−	0.0424975i
$797$	14.6579	+	46.0761i	0.519208	+	1.63210i	0.751703	+	0.659502i	$0.229233\pi$
$797$	14.6579	+	46.0761i	0.519208	+	1.63210i	−0.232495	+	0.972598i	$0.574689\pi$
$798$	4.16423	−	19.0144i	0.147412	−	0.673104i
$799$	−59.3324	−	44.8057i	−2.09903	−	1.58511i
$800$	10.1656	+	3.23391i	0.359408	+	0.114336i
$801$	0.341424	−	2.19949i	0.0120636	−	0.0777151i
$802$	−33.6248	+	18.0561i	−1.18733	+	0.637584i
$803$	0.533315	+	0.429157i	0.0188203	+	0.0151446i
$804$	−1.52140	+	1.14890i	−0.0536555	+	0.0405187i
$805$	−24.2752	−	2.24943i	−0.855587	−	0.0792819i
$806$	−0.789543	−	25.6265i	−0.0278105	−	0.902653i
$807$	5.84495	−	0.541614i	0.205752	−	0.0190657i
$808$	−5.15201	+	14.6203i	−0.181247	+	0.514341i
$809$	−6.66999	−	3.06868i	−0.234504	−	0.107889i	0.297212	−	0.954811i	$-0.403943\pi$
$809$	−6.66999	−	3.06868i	−0.234504	−	0.107889i	−0.531717	+	0.846922i	$0.678453\pi$
$810$	−25.0335	+	9.69803i	−0.879588	+	0.340754i
$811$	−7.14905	+	4.12751i	−0.251037	+	0.144936i	−0.620239	−	0.784413i	$-0.712964\pi$
$811$	−7.14905	+	4.12751i	−0.251037	+	0.144936i	0.369202	+	0.929349i	$0.379631\pi$
$812$	−0.904565	+	9.76181i	−0.0317440	+	0.342572i
$813$	−10.7716	+	21.6323i	−0.377777	+	0.758679i
$814$	−2.81131	+	0.707073i	−0.0985364	+	0.0247829i
$815$	1.68853	−	7.71008i	0.0591467	−	0.270072i
$816$	−65.0909	+	8.06000i	−2.27864	+	0.282157i
$817$	23.3599			0.817261
$818$	−19.3580	−	26.8889i	−0.676835	−	0.940149i
$819$	8.94667			0.312622
$820$	6.84768	−	0.847926i	0.239131	−	0.0296109i
$821$	−8.76090	+	40.0035i	−0.305757	+	1.39613i	0.530449	+	0.847717i	$0.322023\pi$
$821$	−8.76090	+	40.0035i	−0.305757	+	1.39613i	−0.836207	+	0.548414i	$0.815232\pi$
$822$	−36.2335	+	9.11309i	−1.26379	+	0.317855i
$823$	11.1826	−	22.4576i	0.389800	−	0.782824i	−0.610155	−	0.792282i	$-0.708893\pi$
$823$	11.1826	−	22.4576i	0.389800	−	0.782824i	0.999955	+	0.00945799i	$0.00301062\pi$
$824$	−1.23775	+	13.3574i	−0.0431190	+	0.465328i
$825$	0.828471	−	0.478318i	0.0288437	−	0.0166529i
$826$	−9.57286	+	3.70855i	−0.333083	+	0.129037i
$827$	1.36695	+	0.628898i	0.0475336	+	0.0218689i	0.441584	−	0.897220i	$-0.354417\pi$
$827$	1.36695	+	0.628898i	0.0475336	+	0.0218689i	−0.394050	+	0.919089i	$0.628926\pi$
$828$	−2.32361	+	6.59393i	−0.0807510	+	0.229155i
$829$	47.7308	−	4.42291i	1.65776	−	0.153614i	0.777751	−	0.628573i	$-0.216361\pi$
$829$	47.7308	−	4.42291i	1.65776	−	0.153614i	0.880008	+	0.474959i	$0.157537\pi$
$830$	−0.0207935	−	0.674901i	−0.000721752	−	0.0234261i
$831$	−49.2021	−	4.55924i	−1.70680	−	0.158158i
$832$	8.76066	−	6.61574i	0.303721	−	0.229360i
$833$	−10.2579	−	8.25451i	−0.355416	−	0.286002i
$834$	9.03624	−	4.85236i	0.312899	−	0.168023i
$835$	2.71524	−	17.4919i	0.0939649	−	0.605332i
$836$	0.266092	+	0.0846501i	0.00920300	+	0.00292768i
$837$	14.4598	+	10.9195i	0.499804	+	0.377434i
$838$	10.6176	−	48.4814i	0.366779	−	1.67476i
$839$	14.1394	+	44.4463i	0.488146	+	1.53446i	0.809280	+	0.587423i	$0.199858\pi$
$839$	14.1394	+	44.4463i	0.488146	+	1.53446i	−0.321134	+	0.947034i	$0.604064\pi$
$840$	−14.2715	+	3.12551i	−0.492413	+	0.107840i
$841$	1.92340	−	12.3907i	0.0663240	−	0.427266i
$842$	4.00999	+	25.8328i	0.138194	+	0.890258i
$843$	2.75608	+	3.64965i	0.0949246	+	0.125700i
$844$	3.68386	−	0.113498i	0.126804	−	0.00390678i
$845$	3.74365	−	4.95740i	0.128786	−	0.170540i
$846$	−18.5616	+	17.9985i	−0.638160	+	0.618801i
$847$	18.5345	−	15.8794i	0.636852	−	0.545622i
$848$	−29.5849	−	18.3182i	−1.01595	−	0.629049i
$849$			9.23194i			0.316839i
$850$	24.6066	−	17.4186i	0.843999	−	0.597455i
$851$	10.2376	−	82.6769i	0.350941	−	2.83413i
$852$	−0.129034	+	4.18810i	−0.00442063	+	0.143482i
$853$	−1.04673	−	16.9709i	−0.0358392	−	0.581071i	−0.972802	−	0.231640i	$-0.925591\pi$
$853$	−1.04673	−	16.9709i	−0.0358392	−	0.581071i	0.936962	−	0.349431i	$-0.113625\pi$
$854$	22.7011	+	4.24358i	0.776817	+	0.145212i
$855$	5.07675	−	0.156413i	0.173621	−	0.00534921i
$856$	−28.4124	−	16.4039i	−0.971116	−	0.560674i
$857$	4.42287	−	13.9030i	0.151082	−	0.474919i	−0.847341	−	0.531049i	$-0.821798\pi$
$857$	4.42287	−	13.9030i	0.151082	−	0.474919i	0.998423	+	0.0561307i	$0.0178763\pi$
$858$	−0.148931	+	1.60723i	−0.00508444	+	0.0548698i
$859$	−11.0078	−	31.2378i	−0.375580	−	1.06582i	−0.965960	−	0.258693i	$-0.916708\pi$
$859$	−11.0078	−	31.2378i	−0.375580	−	1.06582i	0.590380	−	0.807126i	$-0.298978\pi$
$860$	3.80859	+	8.27824i	0.129872	+	0.282286i
$861$	25.6224	−	19.3491i	0.873208	−	0.659416i
$862$	30.5715	−	10.7730i	1.04127	−	0.366929i
$863$	−8.14791	+	6.55660i	−0.277358	+	0.223189i	−0.755591	−	0.655044i	$-0.772650\pi$
$863$	−8.14791	+	6.55660i	−0.277358	+	0.223189i	0.478233	+	0.878233i	$0.341278\pi$
$864$	0.391733	−	12.7146i	0.0133270	−	0.432560i
$865$	−10.3571	+	19.2873i	−0.352150	+	0.655787i
$866$	−10.6760	−	37.5223i	−0.362786	−	1.27506i
$867$	−25.1479	+	43.5575i	−0.854069	+	1.47929i
$868$	−5.60450	−	5.77983i	−0.190229	−	0.196180i
$869$	0.946875	+	0.366821i	0.0321205	+	0.0124436i
$870$	−31.7917	+	4.93499i	−1.07784	+	0.167312i
$871$	−1.97338	−	3.41799i	−0.0668654	−	0.115814i
$872$	−19.9061	+	34.4785i	−0.674107	+	1.16759i
$873$	3.19438	−	8.24564i	0.108113	−	0.279073i
$874$	−19.7416	+	24.5329i	−0.667768	+	0.829838i
$875$	19.3961	−	16.6176i	0.655709	−	0.561777i
$876$	4.12782	−	4.52801i	0.139466	−	0.152987i
$877$	28.2584	+	8.04020i	0.954217	+	0.271498i	0.714729	−	0.699401i	$-0.246550\pi$
$877$	28.2584	+	8.04020i	0.954217	+	0.271498i	0.239488	+	0.970899i	$0.423020\pi$
$878$	1.38604	+	0.637681i	0.0467767	+	0.0215207i
$879$	−13.2223	−	14.5042i	−0.445979	−	0.489215i
$880$	−0.140206	−	1.13227i	−0.00472634	−	0.0381690i
$881$	52.9788	−	4.90921i	1.78490	−	0.165395i	0.851529	−	0.524307i	$-0.175676\pi$
$881$	52.9788	−	4.90921i	1.78490	−	0.165395i	0.933372	+	0.358911i	$0.116852\pi$
$882$	−3.38369	+	3.08464i	−0.113935	+	0.103865i
$883$	11.7723	−	19.0129i	0.396170	−	0.639836i	−0.589647	−	0.807661i	$-0.700733\pi$
$883$	11.7723	−	19.0129i	0.396170	−	0.639836i	0.985817	+	0.167825i	$0.0536744\pi$
$884$			12.9629i			0.435991i
$885$	−4.96045	−	7.00742i	−0.166744	−	0.235552i
$886$	3.33865	+	36.0297i	0.112164	+	1.21044i
$887$	−25.2292	−	9.77383i	−0.847112	−	0.328173i	−0.101731	−	0.994812i	$-0.532438\pi$
$887$	−25.2292	−	9.77383i	−0.847112	−	0.328173i	−0.745381	+	0.666639i	$0.767732\pi$
$888$	−9.17356	−	49.0742i	−0.307845	−	1.64682i
$889$	−43.1300	−	2.66017i	−1.44653	−	0.0892191i
$890$	3.90329	+	0.240747i	0.130839	+	0.00806985i
$891$	−1.28655	−	1.24752i	−0.0431010	−	0.0417935i
$892$	11.6887	−	1.81443i	0.391368	−	0.0607516i
$893$	−26.9598	+	12.4035i	−0.902176	+	0.415067i
$894$	35.0158	+	14.8209i	1.17110	+	0.495685i
$895$	4.25743	−	3.01377i	0.142310	−	0.100739i
$896$	5.52249	−	29.5427i	0.184493	−	0.986953i
$897$	−41.5237	−	20.6764i	−1.38644	−	0.690364i
$898$	1.28140	+	41.5909i	0.0427610	+	1.38791i
$899$	22.1943	+	25.9052i	0.740220	+	0.863988i
$900$	−1.19086	−	2.39157i	−0.0396953	−	0.0797189i
$901$	−42.4438	+	16.4428i	−1.41401	+	0.547790i
$902$	0.951479	+	1.53669i	0.0316808	+	0.0511662i
$903$	34.6086	+	24.4989i	1.15170	+	0.815273i
$904$	17.0285	−	16.5120i	0.566361	−	0.549180i
$905$	−11.0598	−	20.5960i	−0.367640	−	0.684633i
$906$	30.6839	−	15.2787i	1.01940	−	0.507602i
$907$	4.22086	+	14.8348i	0.140151	+	0.492581i	0.999833	−	0.0182482i	$-0.00580891\pi$
$907$	4.22086	+	14.8348i	0.140151	+	0.492581i	−0.859682	+	0.510830i	$0.829338\pi$
$908$	3.53693	−	3.64758i	0.117377	−	0.121049i
$909$	8.88688	−	4.08861i	0.294759	−	0.135611i
$910$	1.45037	+	15.6520i	0.0480792	+	0.518857i
$911$	−57.9828	−	12.6984i	−1.92106	−	0.420718i	−0.999470	−	0.0325433i	$-0.989639\pi$
$911$	−57.9828	−	12.6984i	−1.92106	−	0.420718i	−0.921586	−	0.388175i	$-0.873106\pi$
$912$	−9.45697	+	24.4112i	−0.313151	+	0.808337i
$913$	0.0403475	−	0.0200907i	0.00133531	−	0.000664904i
$914$	9.54032	+	22.5399i	0.315566	+	0.745553i
$915$	1.18896	+	19.2770i	0.0393059	+	0.637277i
$916$	4.82077	−	11.3895i	0.159283	−	0.376321i
$917$	29.2769	+	10.3168i	0.966809	+	0.340690i
$918$	−28.0080	−	22.5379i	−0.924401	−	0.743862i
$919$	−32.0346	+	37.3909i	−1.05672	+	1.23341i	−0.0852250	+	0.996362i	$0.527161\pi$
$919$	−32.0346	+	37.3909i	−1.05672	+	1.23341i	−0.971497	+	0.237050i	$0.923819\pi$
$920$	22.9210	+	5.76486i	0.755683	+	0.190062i
$921$	20.7035	−	41.5782i	0.682203	−	1.37005i
$922$	−9.14740	+	2.60266i	−0.301253	+	0.0857140i
$923$	−8.57164	−	1.33056i	−0.282139	−	0.0437960i
$924$	0.305448	+	0.404479i	0.0100485	+	0.0133064i
$925$	19.9583	+	24.8022i	0.656223	+	0.815491i
$926$	−6.88766	+	16.2727i	−0.226342	+	0.534755i
$927$	6.59521	−	5.30714i	0.216615	−	0.174310i
$928$	5.84130	−	23.2249i	0.191750	−	0.762395i
$929$	−10.9544	+	58.6008i	−0.359402	+	1.92263i	0.0255019	+	0.999675i	$0.491882\pi$
$929$	−10.9544	+	58.6008i	−0.359402	+	1.92263i	−0.384904	+	0.922957i	$0.625765\pi$
$930$	13.9086	−	22.4632i	0.456082	−	0.736597i
$931$	−4.83973	+	2.04848i	−0.158616	+	0.0671363i
$932$	−4.85666	+	5.32750i	−0.159085	+	0.174508i
$933$	−41.0856	−	29.0839i	−1.34508	−	0.952164i
$934$	13.5855	−	19.1917i	0.444532	−	0.627971i
$935$	−1.29248	−	0.746216i	−0.0422687	−	0.0244039i
$936$	−8.57087	−	1.33045i	−0.280148	−	0.0434870i
$937$	1.59570	+	4.11899i	0.0521294	+	0.134561i	0.956106	−	0.293019i	$-0.0946601\pi$
$937$	1.59570	+	4.11899i	0.0521294	+	0.134561i	−0.903977	+	0.427581i	$0.859366\pi$
$938$	−4.63443	−	1.47432i	−0.151320	−	0.0481382i
$939$	−40.6677	+	7.60211i	−1.32714	+	0.248086i
$940$	−8.79104	−	7.53170i	−0.286732	−	0.245657i
$941$	15.0597	−	1.86480i	0.490933	−	0.0607907i	0.126397	−	0.991980i	$-0.459659\pi$
$941$	15.0597	−	1.86480i	0.490933	−	0.0607907i	0.364537	+	0.931189i	$0.381227\pi$
$942$	14.6729	+	58.3394i	0.478070	+	1.90080i
$943$	−51.0574	+	9.54429i	−1.66266	+	0.310805i
$944$	13.4875	−	2.95380i	0.438980	−	0.0961381i
$945$	−9.26061	−	6.13630i	−0.301248	−	0.199614i
$946$	−1.55298	+	1.81264i	−0.0504916	+	0.0589341i
$947$	−23.4683	−	51.0098i	−0.762616	−	1.65760i	−0.753332	−	0.657640i	$-0.771555\pi$
$947$	−23.4683	−	51.0098i	−0.762616	−	1.65760i	−0.00928375	−	0.999957i	$-0.502955\pi$
$948$	3.79881	−	8.25698i	0.123380	−	0.268174i
$949$	8.25267	+	9.63256i	0.267893	+	0.312686i
$950$	−1.47876	−	11.9421i	−0.0479772	−	0.387454i
$951$	46.7536	+	5.78935i	1.51609	+	0.187733i
$952$	−20.7055	−	22.7128i	−0.671068	−	0.736126i
$953$	1.18833	+	2.38650i	0.0384939	+	0.0773063i	0.913575	−	0.406669i	$-0.133310\pi$
$953$	1.18833	+	2.38650i	0.0384939	+	0.0773063i	−0.875081	+	0.483976i	$0.839192\pi$
$954$	3.38626	+	15.4621i	0.109634	+	0.500605i
$955$	12.6695	+	35.9535i	0.409977	+	1.16343i
$956$	3.55376	+	0.893806i	0.114937	+	0.0289078i
$957$	−1.18626	−	1.79024i	−0.0383463	−	0.0578704i
$958$	9.97958	+	31.3702i	0.322426	+	1.01353i
$959$	−18.4443	−	15.8021i	−0.595599	−	0.510278i
$960$	11.2914	−	0.696429i	0.364428	−	0.0224771i
$961$	2.98624			0.0963303
$962$	−53.6130	+	3.30674i	−1.72855	+	0.106613i
$963$	5.04987	+	20.0782i	0.162730	+	0.647011i
$964$	−15.1135	−	11.4132i	−0.486774	−	0.367595i
$965$	12.3651	+	11.2723i	0.398048	+	0.362868i
$966$	−54.9769	+	15.6423i	−1.76885	+	0.503282i
$967$	−0.663475	+	2.08559i	−0.0213359	+	0.0670682i	−0.963020	−	0.269431i	$-0.913164\pi$
$967$	−0.663475	+	2.08559i	−0.0213359	+	0.0670682i	0.941684	+	0.336499i	$0.109243\pi$
$968$	−20.1173	+	12.4561i	−0.646596	+	0.400355i
$969$	18.0275	+	29.1154i	0.579126	+	0.935321i
$970$	14.9434	+	4.25175i	0.479803	+	0.136516i
$971$	18.6469	−	28.1410i	0.598408	−	0.903088i	−0.401510	−	0.915854i	$-0.631515\pi$
$971$	18.6469	−	28.1410i	0.598408	−	0.903088i	0.999919	+	0.0127660i	$0.00406366\pi$
$972$	−6.66261	+	6.07377i	−0.213703	+	0.194816i
$973$	5.96854	+	2.97198i	0.191343	+	0.0952773i
$974$	1.17363	−	19.0284i	0.0376056	−	0.609709i
$975$	16.7185	−	5.89136i	0.535419	−	0.188674i
$976$	−29.2945	−	10.3230i	−0.937694	−	0.330431i
$977$	51.1872	−	16.2838i	1.63762	−	0.520966i	0.663730	−	0.747972i	$-0.268972\pi$
$977$	51.1872	−	16.2838i	1.63762	−	0.520966i	0.973893	+	0.227007i	$0.0728939\pi$
$978$	−2.83856	−	18.2863i	−0.0907672	−	0.584732i
$979$	0.0943023	+	0.243422i	0.00301391	+	0.00777981i
$980$	−1.51500	−	1.38111i	−0.0483950	−	0.0441179i
$981$	24.3649	−	6.12802i	0.777911	−	0.195652i
$982$	−4.49346	−	6.78131i	−0.143392	−	0.216400i
$983$	−32.5432	−	21.5639i	−1.03797	−	0.687782i	−0.0867263	−	0.996232i	$-0.527641\pi$
$983$	−32.5432	−	21.5639i	−1.03797	−	0.687782i	−0.951240	+	0.308451i	$0.900190\pi$
$984$	−27.4235	+	14.7261i	−0.874228	+	0.469451i
$985$	−4.02238	+	1.27961i	−0.128164	+	0.0407718i
$986$	−42.4305	−	52.7285i	−1.35126	−	1.67922i
$987$	−52.9502	−	9.89811i	−1.68542	−	0.315060i
$988$	4.55842	+	2.44782i	0.145023	+	0.0778756i
$989$	−32.4524	−	60.4340i	−1.03193	−	1.92169i
$990$	−0.325367	+	0.404335i	−0.0103408	+	0.0128506i
$991$	47.9735	+	1.47805i	1.52393	+	0.0469517i	0.781894	−	0.623411i	$-0.214254\pi$
$991$	47.9735	+	1.47805i	1.52393	+	0.0469517i	0.742033	+	0.670363i	$0.233862\pi$
$992$	11.3629	+	16.0519i	0.360772	+	0.509647i
$993$	19.0437	+	8.06051i	0.604334	+	0.255793i
$994$	−8.91010	+	5.90405i	−0.282611	+	0.187265i
$995$	−5.65649	+	10.5337i	−0.179323	+	0.333941i
$996$	−0.157252	−	0.371523i	−0.00498273	−	0.0117722i
$997$	21.6736	+	11.6385i	0.686410	+	0.368595i	0.778925	−	0.627117i	$-0.215765\pi$
$997$	21.6736	+	11.6385i	0.686410	+	0.368595i	−0.0925149	+	0.995711i	$0.529491\pi$
$998$	5.57932	−	7.38821i	0.176610	−	0.233870i
$999$	21.9335	−	30.9846i	0.693946	−	0.980308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	409.2.m.a.4.8	✓	1056
409.307	even	102	inner	409.2.m.a.307.8	yes	1056

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
409.2.m.a.4.8	✓	1056	1.1	even	1	trivial
409.2.m.a.307.8	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+(-1.62587 + 0.201326i) q^{2} +(0.446735 - 2.03985i) q^{3} +(0.663313 - 0.166830i) q^{4} +(-0.650392 + 1.30616i) q^{5} +(-0.315655 + 3.40647i) q^{6} +(-1.92598 + 1.11196i) q^{7} +(2.01044 - 0.778847i) q^{8} +(-1.23603 - 0.568664i) q^{9} +(0.794486 - 2.25459i) q^{10} +(0.158890 - 0.0147233i) q^{11} +(-0.0439835 - 1.42759i) q^{12} +(2.94417 + 0.272818i) q^{13} +(2.90751 - 2.19565i) q^{14} +(2.37383 + 1.91021i) q^{15} +(-4.31707 + 2.31822i) q^{16} +(-0.983213 + 6.33396i) q^{17} +(2.12411 + 0.675727i) q^{18} +(2.04168 + 1.54180i) q^{19} +(-0.213506 + 0.974900i) q^{20} +(1.40784 + 4.42546i) q^{21} +(-0.255370 + 0.0559268i) q^{22} +(1.15240 - 7.42390i) q^{23} +(-0.690602 - 4.44893i) q^{24} +(1.73012 + 2.29105i) q^{25} +(-4.84176 + 0.149173i) q^{26} +(2.06309 - 2.73198i) q^{27} +(-1.09202 + 1.05889i) q^{28} +(4.89443 - 4.19329i) q^{29} +(-4.24410 - 2.62784i) q^{30} +5.29280i q^{31} +(3.03277 - 2.14685i) q^{32} +(0.0409482 - 0.330690i) q^{33} +(0.323382 - 10.4961i) q^{34} +(-0.199766 - 3.23886i) q^{35} +(-0.914745 - 0.170996i) q^{36} +(11.0836 - 0.341481i) q^{37} +(-3.62990 - 2.09572i) q^{38} +(1.87177 - 5.88380i) q^{39} +(-0.290270 + 3.13252i) q^{40} +(-2.29782 - 6.52075i) q^{41} +(-3.17992 - 6.91178i) q^{42} +(7.28633 - 5.50238i) q^{43} +(0.102938 - 0.0362738i) q^{44} +(1.54667 - 1.24460i) q^{45} +(-0.379029 + 12.3023i) q^{46} +(-5.48758 + 10.2192i) q^{47} +(2.80024 + 9.84181i) q^{48} +(-1.02707 + 1.77894i) q^{49} +(-3.27419 - 3.37662i) q^{50} +(12.4811 + 4.83521i) q^{51} +(1.99842 - 0.310212i) q^{52} +(3.55061 + 6.14983i) q^{53} +(-2.80429 + 4.85718i) q^{54} +(-0.0841098 + 0.217112i) q^{55} +(-3.00601 + 3.73558i) q^{56} +(4.05714 - 3.47595i) q^{57} +(-7.11347 + 7.80310i) q^{58} +(-2.71015 - 0.771103i) q^{59} +(1.89327 + 0.871043i) q^{60} +(4.27031 + 4.68431i) q^{61} +(-1.06558 - 8.60539i) q^{62} +(3.01290 - 0.279187i) q^{63} +(2.74381 - 2.50131i) q^{64} +(-2.27121 + 3.66813i) q^{65} +0.545901i q^{66} +(-0.771220 - 1.08947i) q^{67} +(0.404516 + 4.36543i) q^{68} +(-14.6289 - 5.66725i) q^{69} +(0.976858 + 5.22573i) q^{70} +(-2.92812 - 0.180601i) q^{71} +(-2.92786 - 0.180584i) q^{72} +(3.07978 + 2.98635i) q^{73} +(-17.9517 + 2.78661i) q^{74} +(5.44630 - 2.50570i) q^{75} +(1.61149 + 0.682086i) q^{76} +(-0.289647 + 0.205037i) q^{77} +(-1.85869 + 9.94311i) q^{78} +(5.69647 + 2.83651i) q^{79} +(-0.220183 - 7.14655i) q^{80} +(-7.30681 - 8.52854i) q^{81} +(5.04874 + 10.1392i) q^{82} +(0.263389 - 0.102037i) q^{83} +(1.67214 + 2.70060i) q^{84} +(-7.63372 - 5.40380i) q^{85} +(-10.7388 + 10.4131i) q^{86} +(-6.36718 - 11.8572i) q^{87} +(0.307971 - 0.153351i) q^{88} +(0.447700 + 1.57350i) q^{89} +(-2.26411 + 2.33494i) q^{90} +(-5.97378 + 2.74837i) q^{91} +(-0.474125 - 5.11663i) q^{92} +(10.7965 + 2.36448i) q^{93} +(6.86468 - 17.7198i) q^{94} +(-3.34174 + 1.66399i) q^{95} +(-3.02442 - 7.14548i) q^{96} +(0.400104 + 6.48699i) q^{97} +(1.31173 - 3.09909i) q^{98} +(-0.204766 - 0.0721566i) 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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