LMFDB - Embedded newform 261.2.q.a.103.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(7,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([28, 18]))

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

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

chi := DirichletCharacter("261.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.q (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$28$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			103.21
Character	$\chi$	$=$	261.103
Dual form			261.2.q.a.223.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.110732 + 1.47762i) q^{2} +(0.614444 + 1.61940i) q^{3} +(-0.193426 + 0.0291542i) q^{4} +(1.96037 - 1.33656i) q^{5} +(-2.32481 + 1.08723i) q^{6} +(-1.67633 - 0.252667i) q^{7} +(0.594948 + 2.60664i) q^{8} +(-2.24492 + 1.99006i) q^{9} +(2.19200 + 2.74867i) q^{10} +(1.13878 - 0.351267i) q^{11} +(-0.166062 - 0.295320i) q^{12} +(0.355933 + 0.330258i) q^{13} +(0.187721 - 2.50496i) q^{14} +(3.36896 + 2.35338i) q^{15} +(-4.15957 + 1.28306i) q^{16} +1.19292 q^{17} +(-3.18913 - 3.09676i) q^{18} +(-1.43586 - 1.80051i) q^{19} +(-0.340220 + 0.315678i) q^{20} +(-0.620846 - 2.86991i) q^{21} +(0.645137 + 1.64378i) q^{22} +(0.435612 - 5.81284i) q^{23} +(-3.85563 + 2.56509i) q^{24} +(0.229960 - 0.585928i) q^{25} +(-0.448581 + 0.562503i) q^{26} +(-4.60209 - 2.41263i) q^{27} +0.331612 q^{28} +(0.253576 - 5.37919i) q^{29} +(-3.10435 + 5.23863i) q^{30} +(-5.23916 + 3.57200i) q^{31} +(-0.402859 - 1.02647i) q^{32} +(1.26856 + 1.62831i) q^{33} +(0.132094 + 1.76268i) q^{34} +(-3.62394 + 1.74520i) q^{35} +(0.376206 - 0.450378i) q^{36} +(-0.478456 - 2.09625i) q^{37} +(2.50147 - 2.32102i) q^{38} +(-0.316119 + 0.779324i) q^{39} +(4.65024 + 4.31479i) q^{40} +(5.01438 - 8.68515i) q^{41} +(4.17187 - 1.23516i) q^{42} +(2.20994 + 1.50671i) q^{43} +(-0.210028 + 0.101144i) q^{44} +(-1.74103 + 6.90172i) q^{45} +8.63738 q^{46} +(8.91066 - 2.74857i) q^{47} +(-4.63361 - 5.94764i) q^{48} +(-3.94275 - 1.21618i) q^{49} +(0.891241 + 0.274911i) q^{50} +(0.732983 + 1.93181i) q^{51} +(-0.0784751 - 0.0535034i) q^{52} +(7.23932 + 3.48627i) q^{53} +(3.05535 - 7.06727i) q^{54} +(1.76294 - 2.21066i) q^{55} +(-0.338721 - 4.51992i) q^{56} +(2.03349 - 3.43154i) q^{57} +(7.97646 - 0.220961i) q^{58} +(-4.58870 + 7.94786i) q^{59} +(-0.720255 - 0.356986i) q^{60} +(5.47218 + 0.824798i) q^{61} +(-5.85818 - 7.34593i) q^{62} +(4.26605 - 2.76880i) q^{63} +(-6.37164 + 3.06842i) q^{64} +(1.13917 + 0.171702i) q^{65} +(-2.26554 + 2.05475i) q^{66} +(-10.9252 - 3.36998i) q^{67} +(-0.230741 + 0.0347787i) q^{68} +(9.68097 - 2.86624i) q^{69} +(-2.98002 - 5.16154i) q^{70} +(-1.77020 + 7.75573i) q^{71} +(-6.52298 - 4.66770i) q^{72} +(11.7302 - 5.64896i) q^{73} +(3.04447 - 0.939096i) q^{74} +(1.09015 + 0.0123768i) q^{75} +(0.330225 + 0.306404i) q^{76} +(-1.99773 + 0.301109i) q^{77} +(-1.18655 - 0.380806i) q^{78} +(-4.48885 + 4.16505i) q^{79} +(-6.43941 + 8.07477i) q^{80} +(1.07930 - 8.93505i) q^{81} +(13.3886 + 6.44760i) q^{82} +(-4.51785 + 11.5113i) q^{83} +(0.203757 + 0.537013i) q^{84} +(2.33856 - 1.59441i) q^{85} +(-1.98163 + 3.43229i) q^{86} +(8.86687 - 2.89457i) q^{87} +(1.59314 + 2.75940i) q^{88} +(-5.81851 - 2.80205i) q^{89} +(-10.3909 - 1.80834i) q^{90} +(-0.513218 - 0.643555i) q^{91} +(0.0852103 + 1.13705i) q^{92} +(-9.00367 - 6.28950i) q^{93} +(5.04803 + 12.8622i) q^{94} +(-5.22130 - 1.61056i) q^{95} +(1.41473 - 1.28310i) q^{96} +(1.98904 - 5.06799i) q^{97} +(1.36046 - 5.96055i) q^{98} +(-1.85742 + 3.05481i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 5 q^{2} - 10 q^{3} + 21 q^{4} - 9 q^{5} - 40 q^{6} - 5 q^{7} + 2 q^{8} - 6 q^{9} - 28 q^{10} - q^{11} - 22 q^{12} - 5 q^{13} - 9 q^{14} - 26 q^{15} + 21 q^{16} - 60 q^{17} - 90 q^{18} - 20 q^{19}+ \cdots + 196 q^{99}+O(q^{100}) $ 336 * q - 5 * q^2 - 10 * q^3 + 21 * q^4 - 9 * q^5 - 40 * q^6 - 5 * q^7 + 2 * q^8 - 6 * q^9 - 28 * q^10 - q^11 - 22 * q^12 - 5 * q^13 - 9 * q^14 - 26 * q^15 + 21 * q^16 - 60 * q^17 - 90 * q^18 - 20 * q^19 - 15 * q^20 - 2 * q^21 - 13 * q^22 - 32 * q^23 + 44 * q^24 + 15 * q^25 - 4 * q^26 - 43 * q^27 - 72 * q^28 - q^29 - 8 * q^30 - 5 * q^31 + 7 * q^32 - 37 * q^33 - 15 * q^34 + 16 * q^35 - 104 * q^36 - 20 * q^37 + 63 * q^38 + 38 * q^39 + 5 * q^40 - 20 * q^41 + 11 * q^42 - 5 * q^43 - 8 * q^44 + 30 * q^45 - 80 * q^46 + 5 * q^47 + 12 * q^48 - 19 * q^49 - 3 * q^50 - 62 * q^51 + q^52 - 4 * q^53 + 26 * q^54 - 100 * q^55 - 5 * q^56 - 50 * q^57 - 7 * q^58 + 154 * q^59 + 23 * q^60 + 7 * q^61 - 4 * q^62 - 144 * q^63 + 18 * q^64 - 65 * q^65 + 44 * q^66 - 5 * q^67 - 9 * q^68 + 22 * q^69 - 14 * q^70 + 18 * q^71 + 37 * q^72 - 20 * q^73 - 77 * q^74 + 16 * q^75 - 5 * q^76 + 39 * q^77 + 52 * q^78 - 5 * q^79 - 104 * q^80 + 54 * q^81 + 12 * q^82 - 23 * q^83 + 175 * q^84 - 42 * q^85 + 128 * q^86 + 42 * q^87 - 8 * q^88 + 34 * q^89 + 222 * q^90 + 12 * q^91 - 115 * q^92 + 64 * q^93 - 25 * q^94 + 89 * q^95 - 49 * q^96 + 55 * q^97 - 88 * q^98 + 196 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.110732	+	1.47762i	0.0782994	+	1.04483i	0.888559	+	0.458762i	$0.151707\pi$
$2$	0.110732	+	1.47762i	0.0782994	+	1.04483i	−0.810260	+	0.586071i	$0.800674\pi$
$3$	0.614444	+	1.61940i	0.354750	+	0.934961i
$3$	0.614444	+	1.61940i	0.354750	+	0.934961i
$4$	−0.193426	+	0.0291542i	−0.0967129	+	0.0145771i
$5$	1.96037	−	1.33656i	0.876704	−	0.597727i	−0.0391519	−	0.999233i	$-0.512466\pi$
$5$	1.96037	−	1.33656i	0.876704	−	0.597727i	0.915856	+	0.401506i	$0.131513\pi$
$6$	−2.32481	+	1.08723i	−0.949101	+	0.443861i
$7$	−1.67633	−	0.252667i	−0.633595	−	0.0954990i	−0.175611	−	0.984460i	$-0.556190\pi$
$7$	−1.67633	−	0.252667i	−0.633595	−	0.0954990i	−0.457984	+	0.888961i	$0.651428\pi$
$8$	0.594948	+	2.60664i	0.210346	+	0.921585i
$9$	−2.24492	+	1.99006i	−0.748305	+	0.663354i
$10$	2.19200	+	2.74867i	0.693170	+	0.869207i
$11$	1.13878	−	0.351267i	0.343355	−	0.105911i	−0.118282	−	0.992980i	$-0.537739\pi$
$11$	1.13878	−	0.351267i	0.343355	−	0.105911i	0.461637	+	0.887069i	$0.347262\pi$
$12$	−0.166062	−	0.295320i	−0.0479379	−	0.0852516i
$13$	0.355933	+	0.330258i	0.0987182	+	0.0915971i	0.727988	−	0.685590i	$-0.240456\pi$
$13$	0.355933	+	0.330258i	0.0987182	+	0.0915971i	−0.629270	+	0.777187i	$0.716646\pi$
$14$	0.187721	−	2.50496i	0.0501704	−	0.669478i
$15$	3.36896	+	2.35338i	0.869862	+	0.607641i
$16$	−4.15957	+	1.28306i	−1.03989	+	0.320764i
$17$	1.19292			0.289326			0.144663	−	0.989481i	$-0.453790\pi$
$17$	1.19292			0.289326			0.144663	+	0.989481i	$0.453790\pi$
$18$	−3.18913	−	3.09676i	−0.751686	−	0.729913i
$19$	−1.43586	−	1.80051i	−0.329409	−	0.413065i	0.589355	−	0.807875i	$-0.299382\pi$
$19$	−1.43586	−	1.80051i	−0.329409	−	0.413065i	−0.918763	+	0.394809i	$0.870811\pi$
$20$	−0.340220	+	0.315678i	−0.0760754	+	0.0705877i
$21$	−0.620846	−	2.86991i	−0.135480	−	0.626265i
$22$	0.645137	+	1.64378i	0.137544	+	0.350456i
$23$	0.435612	−	5.81284i	0.0908314	−	1.21206i	−0.746508	−	0.665377i	$-0.768271\pi$
$23$	0.435612	−	5.81284i	0.0908314	−	1.21206i	0.837339	−	0.546684i	$-0.184110\pi$
$24$	−3.85563	+	2.56509i	−0.787026	+	0.523597i
$25$	0.229960	−	0.585928i	0.0459920	−	0.117186i
$26$	−0.448581	+	0.562503i	−0.0879740	+	0.110316i
$27$	−4.60209	−	2.41263i	−0.885672	−	0.464312i
$28$	0.331612			0.0626689
$29$	0.253576	−	5.37919i	0.0470878	−	0.998891i
$29$	0.253576	−	5.37919i	0.0470878	−	0.998891i
$30$	−3.10435	+	5.23863i	−0.566773	+	0.956438i
$31$	−5.23916	+	3.57200i	−0.940981	+	0.641550i	−0.933559	−	0.358423i	$-0.883315\pi$
$31$	−5.23916	+	3.57200i	−0.940981	+	0.641550i	−0.00742132	+	0.999972i	$0.502362\pi$
$32$	−0.402859	−	1.02647i	−0.0712161	−	0.181456i
$33$	1.26856	+	1.62831i	0.220828	+	0.283452i
$34$	0.132094	+	1.76268i	0.0226540	+	0.302297i
$35$	−3.62394	+	1.74520i	−0.612558	+	0.294992i
$36$	0.376206	−	0.450378i	0.0627010	−	0.0750630i
$37$	−0.478456	−	2.09625i	−0.0786576	−	0.344622i	0.920251	−	0.391329i	$-0.127984\pi$
$37$	−0.478456	−	2.09625i	−0.0786576	−	0.344622i	−0.998909	+	0.0467071i	$0.985127\pi$
$38$	2.50147	−	2.32102i	0.405791	−	0.376519i
$39$	−0.316119	+	0.779324i	−0.0506195	+	0.124792i
$40$	4.65024	+	4.31479i	0.735267	+	0.682228i
$41$	5.01438	−	8.68515i	0.783114	−	1.35639i	−0.147005	−	0.989136i	$-0.546963\pi$
$41$	5.01438	−	8.68515i	0.783114	−	1.35639i	0.930119	−	0.367257i	$-0.119703\pi$
$42$	4.17187	−	1.23516i	0.643734	−	0.190590i
$43$	2.20994	+	1.50671i	0.337013	+	0.229772i	0.719987	−	0.693987i	$-0.244148\pi$
$43$	2.20994	+	1.50671i	0.337013	+	0.229772i	−0.382974	+	0.923759i	$0.625100\pi$
$44$	−0.210028	+	0.101144i	−0.0316630	+	0.0152481i
$45$	−1.74103	+	6.90172i	−0.259538	+	1.02885i
$46$	8.63738			1.27351
$47$	8.91066	−	2.74857i	1.29975	−	0.400921i	0.433783	−	0.901017i	$-0.357178\pi$
$47$	8.91066	−	2.74857i	1.29975	−	0.400921i	0.865970	+	0.500097i	$0.166702\pi$
$48$	−4.63361	−	5.94764i	−0.668803	−	0.858468i
$49$	−3.94275	−	1.21618i	−0.563251	−	0.173740i
$50$	0.891241	+	0.274911i	0.126040	+	0.0388783i
$51$	0.732983	+	1.93181i	0.102638	+	0.270508i
$52$	−0.0784751	−	0.0535034i	−0.0108825	−	0.00741959i
$53$	7.23932	+	3.48627i	0.994398	+	0.478877i	0.859034	−	0.511919i	$-0.171065\pi$
$53$	7.23932	+	3.48627i	0.994398	+	0.478877i	0.135364	+	0.990796i	$0.456780\pi$
$54$	3.05535	−	7.06727i	0.415780	−	0.961734i
$55$	1.76294	−	2.21066i	0.237715	−	0.298085i
$56$	−0.338721	−	4.51992i	−0.0452635	−	0.603999i
$57$	2.03349	−	3.43154i	0.269342	−	0.454519i
$58$	7.97646	−	0.220961i	1.04736	−	0.0290136i
$59$	−4.58870	+	7.94786i	−0.597398	+	1.03472i	0.395806	+	0.918334i	$0.370465\pi$
$59$	−4.58870	+	7.94786i	−0.597398	+	1.03472i	−0.993204	+	0.116389i	$0.962868\pi$
$60$	−0.720255	−	0.356986i	−0.0929845	−	0.0460866i
$61$	5.47218	+	0.824798i	0.700640	+	0.105605i	0.489696	−	0.871893i	$-0.337108\pi$
$61$	5.47218	+	0.824798i	0.700640	+	0.105605i	0.210945	+	0.977498i	$0.432346\pi$
$62$	−5.85818	−	7.34593i	−0.743990	−	0.932934i
$63$	4.26605	−	2.76880i	0.537472	−	0.348835i
$64$	−6.37164	+	3.06842i	−0.796455	+	0.383553i
$65$	1.13917	+	0.171702i	0.141297	+	0.0212970i
$66$	−2.26554	+	2.05475i	−0.278869	+	0.252922i
$67$	−10.9252	−	3.36998i	−1.33472	−	0.411708i	−0.456401	−	0.889774i	$-0.650862\pi$
$67$	−10.9252	−	3.36998i	−1.33472	−	0.411708i	−0.878324	+	0.478066i	$0.841338\pi$
$68$	−0.230741	+	0.0347787i	−0.0279815	+	0.00421753i
$69$	9.68097	−	2.86624i	1.16545	−	0.345054i
$70$	−2.98002	−	5.16154i	−0.356180	−	0.616922i
$71$	−1.77020	+	7.75573i	−0.210084	+	0.920436i	0.754425	+	0.656386i	$0.227916\pi$
$71$	−1.77020	+	7.75573i	−0.210084	+	0.920436i	−0.964509	+	0.264050i	$0.914942\pi$
$72$	−6.52298	−	4.66770i	−0.768740	−	0.550093i
$73$	11.7302	−	5.64896i	1.37291	−	0.661160i	0.405437	−	0.914123i	$-0.367119\pi$
$73$	11.7302	−	5.64896i	1.37291	−	0.661160i	0.967476	+	0.252963i	$0.0814049\pi$
$74$	3.04447	−	0.939096i	0.353913	−	0.109168i
$75$	1.09015	+	0.0123768i	0.125880	+	0.00142915i
$76$	0.330225	+	0.306404i	0.0378793	+	0.0351469i
$77$	−1.99773	+	0.301109i	−0.227662	+	0.0343146i
$78$	−1.18655	−	0.380806i	−0.134350	−	0.0431178i
$79$	−4.48885	+	4.16505i	−0.505035	+	0.468604i	−0.891061	−	0.453884i	$-0.850038\pi$
$79$	−4.48885	+	4.16505i	−0.505035	+	0.468604i	0.386026	+	0.922488i	$0.373848\pi$
$80$	−6.43941	+	8.07477i	−0.719948	+	0.902787i
$81$	1.07930	−	8.93505i	0.119922	−	0.992783i
$82$	13.3886	+	6.44760i	1.47852	+	0.712018i
$83$	−4.51785	+	11.5113i	−0.495899	+	1.26353i	0.435717	+	0.900084i	$0.356495\pi$
$83$	−4.51785	+	11.5113i	−0.495899	+	1.26353i	−0.931615	+	0.363446i	$0.881600\pi$
$84$	0.203757	+	0.537013i	0.0222318	+	0.0585930i
$85$	2.33856	−	1.59441i	0.253653	−	0.172938i
$86$	−1.98163	+	3.43229i	−0.213685	+	0.370113i
$87$	8.86687	−	2.89457i	0.950629	−	0.310331i
$88$	1.59314	+	2.75940i	0.169829	+	0.294153i
$89$	−5.81851	−	2.80205i	−0.616761	−	0.297016i	0.0992963	−	0.995058i	$-0.468341\pi$
$89$	−5.81851	−	2.80205i	−0.616761	−	0.297016i	−0.716057	+	0.698041i	$0.754055\pi$
$90$	−10.3909	−	1.80834i	−1.09530	−	0.190615i
$91$	−0.513218	−	0.643555i	−0.0537999	−	0.0674629i
$92$	0.0852103	+	1.13705i	0.00888379	+	0.118546i
$93$	−9.00367	−	6.28950i	−0.933637	−	0.652191i
$94$	5.04803	+	12.8622i	0.520665	+	1.32663i
$95$	−5.22130	−	1.61056i	−0.535694	−	0.165240i
$96$	1.41473	−	1.28310i	0.144390	−	0.130956i
$97$	1.98904	−	5.06799i	0.201956	−	0.514577i	−0.793633	−	0.608397i	$-0.791813\pi$
$97$	1.98904	−	5.06799i	0.201956	−	0.514577i	0.995589	+	0.0938205i	$0.0299080\pi$
$98$	1.36046	−	5.96055i	0.137427	−	0.602106i
$99$	−1.85742	+	3.05481i	−0.186678	+	0.307020i
$100$	−0.0273979	+	0.120038i	−0.00273979	+	0.0120038i
$101$	−6.93245	−	4.72646i	−0.689805	−	0.470301i	0.166990	−	0.985959i	$-0.446595\pi$
$101$	−6.93245	−	4.72646i	−0.689805	−	0.470301i	−0.856795	+	0.515658i	$0.827548\pi$
$102$	−2.77332	+	1.29698i	−0.274599	+	0.128420i
$103$	1.68906	+	1.56722i	0.166428	+	0.154423i	0.758990	−	0.651102i	$-0.225693\pi$
$103$	1.68906	+	1.56722i	0.166428	+	0.154423i	−0.592562	+	0.805525i	$0.701884\pi$
$104$	−0.649101	+	1.12428i	−0.0636495	+	0.110244i
$105$	−5.05288	−	4.79628i	−0.493111	−	0.468069i
$106$	−4.34975	+	11.0830i	−0.422485	+	1.07647i
$107$	−1.78529	−	7.82187i	−0.172591	−	0.756169i	−0.984926	−	0.172978i	$-0.944661\pi$
$107$	−1.78529	−	7.82187i	−0.172591	−	0.756169i	0.812335	−	0.583191i	$-0.198196\pi$
$108$	0.960500	+	0.332495i	0.0924242	+	0.0319944i
$109$	3.68797	−	4.62457i	0.353243	−	0.442953i	−0.573184	−	0.819427i	$-0.694292\pi$
$109$	3.68797	−	4.62457i	0.353243	−	0.442953i	0.926427	+	0.376474i	$0.122863\pi$
$110$	3.46172	+	2.36016i	0.330062	+	0.225032i
$111$	3.10069	−	2.06284i	0.294304	−	0.195796i
$112$	7.29701	−	1.09985i	0.689503	−	0.103926i
$113$	2.97136	+	7.57091i	0.279522	+	0.712212i	0.999828	+	0.0185546i	$0.00590644\pi$
$113$	2.97136	+	7.57091i	0.279522	+	0.712212i	−0.720305	+	0.693657i	$0.755998\pi$
$114$	5.29568	+	2.62474i	0.495986	+	0.245829i
$115$	−6.91523	−	11.9775i	−0.644849	−	1.11691i
$116$	0.107778	+	1.04787i	0.0100070	+	0.0972920i
$117$	−1.45627	−	0.0330713i	−0.134633	−	0.00305744i
$118$	−12.2520	−	5.90026i	−1.12789	−	0.543163i
$119$	−1.99973	−	0.301411i	−0.183315	−	0.0276303i
$120$	−4.13006	+	10.1818i	−0.377021	+	0.929467i
$121$	−7.91519	+	5.39649i	−0.719563	+	0.490590i
$122$	−0.612790	+	8.17711i	−0.0554794	+	0.740321i
$123$	17.1458	+	2.78374i	1.54598	+	0.251001i
$124$	0.909249	−	0.843660i	0.0816530	−	0.0757629i
$125$	2.30749	+	10.1098i	0.206389	+	0.904247i
$126$	4.56361	+	5.99699i	0.406558	+	0.534255i
$127$	1.68982	−	7.40358i	0.149947	−	0.656961i	−0.842951	−	0.537991i	$-0.819183\pi$
$127$	1.68982	−	7.40358i	0.149947	−	0.656961i	0.992898	−	0.118970i	$-0.0379594\pi$
$128$	−6.34219	−	10.9850i	−0.560575	−	0.970945i
$129$	−1.08209	+	4.50458i	−0.0952724	+	0.396606i
$130$	−0.127567	+	1.70227i	−0.0111884	+	0.149299i
$131$	−0.268374	+	3.58120i	−0.0234479	+	0.312891i	0.973131	+	0.230250i	$0.0739544\pi$
$131$	−0.268374	+	3.58120i	−0.0234479	+	0.312891i	−0.996579	+	0.0826406i	$0.973665\pi$
$132$	−0.292844	−	0.277973i	−0.0254888	−	0.0241944i
$133$	1.95205	+	3.38105i	0.169264	+	0.293174i
$134$	3.76976	−	16.5164i	0.325658	−	1.42680i
$135$	−12.2464	+	1.42130i	−1.05400	+	0.122326i
$136$	0.709725	+	3.10951i	0.0608584	+	0.266638i
$137$	−11.2772	+	10.4637i	−0.963479	+	0.893978i	−0.994415	−	0.105543i	$-0.966342\pi$
$137$	−11.2772	+	10.4637i	−0.963479	+	0.893978i	0.0309355	+	0.999521i	$0.490151\pi$
$138$	5.30719	+	13.9874i	0.451778	+	1.19068i
$139$	−0.704840	+	9.40544i	−0.0597838	+	0.797759i	0.884061	+	0.467371i	$0.154799\pi$
$139$	−0.704840	+	9.40544i	−0.0597838	+	0.797759i	−0.943845	+	0.330388i	$0.892820\pi$
$140$	0.650083	−	0.443219i	0.0549421	−	0.0374589i
$141$	9.92614	+	12.7411i	0.835932	+	1.07299i
$142$	−11.6560	−	1.75686i	−0.978151	−	0.147432i
$143$	0.521339	+	0.251063i	0.0435965	+	0.0209950i
$144$	6.78452	−	11.1582i	0.565376	−	0.929847i
$145$	−6.69250	−	10.8841i	−0.555782	−	0.903877i
$146$	9.64589	+	16.7072i	0.798300	+	1.38270i
$147$	−0.453123	−	7.13217i	−0.0373730	−	0.588252i
$148$	0.153660	+	0.391520i	0.0126308	+	0.0321827i
$149$	3.43803	−	0.518200i	0.281655	−	0.0424526i	−0.00669566	−	0.999978i	$-0.502131\pi$
$149$	3.43803	−	0.518200i	0.281655	−	0.0424526i	0.288350	+	0.957525i	$0.406893\pi$
$150$	0.102426	+	1.61219i	0.00836308	+	0.131635i
$151$	−17.3172	−	11.8067i	−1.40926	−	0.960816i	−0.998802	−	0.0489351i	$-0.984417\pi$
$151$	−17.3172	−	11.8067i	−1.40926	−	0.960816i	−0.410456	−	0.911881i	$-0.634630\pi$
$152$	3.83901	−	4.81397i	0.311385	−	0.390465i
$153$	−2.67800	+	2.37399i	−0.216504	+	0.191925i
$154$	−0.666137	−	2.91854i	−0.0536788	−	0.235182i
$155$	−5.49651	+	14.0049i	−0.441490	+	1.12490i
$156$	0.0384249	−	0.159957i	0.00307645	−	0.0128068i
$157$	−0.310875	+	0.538451i	−0.0248105	+	0.0429731i	−0.878164	−	0.478360i	$-0.841232\pi$
$157$	−0.310875	+	0.538451i	−0.0248105	+	0.0429731i	0.853354	+	0.521333i	$0.174565\pi$
$158$	−6.65140	−	6.17159i	−0.529157	−	0.490986i
$159$	−1.19751	+	13.8655i	−0.0949689	+	1.09960i
$160$	−2.16169	−	1.47381i	−0.170896	−	0.116515i
$161$	−2.19894	+	9.63419i	−0.173301	+	0.759281i
$162$	13.3221	+	0.605389i	1.04668	+	0.0475638i
$163$	−2.55690	+	11.2025i	−0.200272	+	0.877448i	0.770499	+	0.637441i	$0.220007\pi$
$163$	−2.55690	+	11.2025i	−0.200272	+	0.877448i	−0.970771	+	0.240007i	$0.922850\pi$
$164$	−0.716700	+	1.82612i	−0.0559649	+	0.142596i
$165$	4.66317	+	1.49658i	0.363028	+	0.116509i
$166$	−17.5096	−	5.40098i	−1.35900	−	0.419197i
$167$	−1.46458	−	3.73169i	−0.113333	−	0.288767i	0.862942	−	0.505303i	$-0.168619\pi$
$167$	−1.46458	−	3.73169i	−0.113333	−	0.288767i	−0.976275	+	0.216536i	$0.930524\pi$
$168$	7.11143	−	3.32576i	0.548659	−	0.256588i
$169$	−0.953873	−	12.7285i	−0.0733748	−	0.979119i
$170$	2.61487	+	3.27895i	0.200552	+	0.251484i
$171$	6.80651	+	1.18454i	0.520507	+	0.0905843i
$172$	−0.471387	−	0.227008i	−0.0359429	−	0.0173092i
$173$	−0.558065	−	0.966598i	−0.0424289	−	0.0734891i	0.844031	−	0.536294i	$-0.180176\pi$
$173$	−0.558065	−	0.966598i	−0.0424289	−	0.0734891i	−0.886460	+	0.462805i	$0.846843\pi$
$174$	5.25892	+	12.7813i	0.398677	+	0.968949i
$175$	−0.533534	+	0.924108i	−0.0403314	+	0.0698560i
$176$	−4.28614	+	2.92224i	−0.323080	+	0.220272i
$177$	−15.6903	−	2.54742i	−1.17935	−	0.191476i
$178$	3.49606	−	8.90780i	0.262040	−	0.667668i
$179$	4.03021	+	1.94085i	0.301232	+	0.145066i	0.578394	−	0.815758i	$-0.303680\pi$
$179$	4.03021	+	1.94085i	0.301232	+	0.145066i	−0.277162	+	0.960823i	$0.589394\pi$
$180$	0.135546	−	1.38573i	0.0101030	−	0.103286i
$181$	−15.8253	+	19.8442i	−1.17628	+	1.47501i	−0.328630	+	0.944459i	$0.606587\pi$
$181$	−15.8253	+	19.8442i	−1.17628	+	1.47501i	−0.847652	+	0.530552i	$0.821985\pi$
$182$	0.894098	−	0.829602i	0.0662749	−	0.0614942i
$183$	2.02667	+	9.36844i	0.149816	+	0.692535i
$184$	15.4111	−	2.32285i	1.13612	−	0.171243i
$185$	−3.73971	−	3.46994i	−0.274949	−	0.255115i
$186$	8.29647	−	14.0004i	0.608327	−	1.02656i
$187$	1.35847	−	0.419034i	0.0993414	−	0.0306428i
$188$	−1.64342	+	0.791428i	−0.119859	+	0.0577208i
$189$	7.10504	+	5.20718i	0.516816	+	0.378766i
$190$	1.80162	−	7.89342i	0.130703	−	0.572649i
$191$	−2.52244	−	4.36899i	−0.182517	−	0.316129i	0.760220	−	0.649666i	$-0.225091\pi$
$191$	−2.52244	−	4.36899i	−0.182517	−	0.316129i	−0.942737	+	0.333537i	$0.891758\pi$
$192$	−8.88402	−	8.43287i	−0.641149	−	0.608590i
$193$	6.66412	−	1.00445i	0.479694	−	0.0723022i	0.0952554	−	0.995453i	$-0.469633\pi$
$193$	6.66412	−	1.00445i	0.479694	−	0.0723022i	0.384438	+	0.923151i	$0.374395\pi$
$194$	7.70880	+	2.37785i	0.553459	+	0.170720i
$195$	0.421902	+	1.95027i	0.0302130	+	0.139662i
$196$	0.798087	+	0.120292i	0.0570062	+	0.00859230i
$197$	19.2638	−	9.27695i	1.37249	−	0.660955i	0.405104	−	0.914271i	$-0.367235\pi$
$197$	19.2638	−	9.27695i	1.37249	−	0.660955i	0.967384	+	0.253315i	$0.0815210\pi$
$198$	−4.71951	−	2.40629i	−0.335401	−	0.171008i
$199$	1.45204	+	1.82080i	0.102932	+	0.129073i	0.830629	−	0.556826i	$-0.187981\pi$
$199$	1.45204	+	1.82080i	0.102932	+	0.129073i	−0.727697	+	0.685899i	$0.759409\pi$
$200$	1.66412	+	0.250825i	0.117671	+	0.0177360i
$201$	−1.25558	−	19.7629i	−0.0885621	−	1.39397i
$202$	6.21626	−	10.7669i	0.437374	−	0.757554i
$203$	−1.78422	+	8.95325i	−0.125228	+	0.628395i
$204$	−0.198098	−	0.352293i	−0.0138697	−	0.0246655i
$205$	−1.77818	−	23.7281i	−0.124193	−	1.65724i
$206$	−2.12871	+	2.66932i	−0.148314	+	0.185980i
$207$	10.5900	+	13.9162i	0.736056	+	0.967245i
$208$	−1.90427	−	0.917048i	−0.132037	−	0.0635858i
$209$	−2.26759	−	1.54602i	−0.156852	−	0.106940i
$210$	6.52755	−	7.99732i	0.450444	−	0.551868i
$211$	−21.1657	−	6.52875i	−1.45711	−	0.449458i	−0.537824	−	0.843057i	$-0.680753\pi$
$211$	−21.1657	−	6.52875i	−1.45711	−	0.449458i	−0.919282	+	0.393600i	$0.871230\pi$
$212$	−1.50191	−	0.463278i	−0.103152	−	0.0318181i
$213$	−13.6473	+	1.89881i	−0.935099	+	0.130104i
$214$	11.3600	−	3.50411i	0.776556	−	0.239536i
$215$	6.34612			0.432802
$216$	3.55086	−	13.4314i	0.241605	−	0.913888i
$217$	9.68511	−	4.66410i	0.657468	−	0.316620i
$218$	7.24171	+	4.93731i	0.490470	+	0.334397i
$219$	16.3555	+	15.5249i	1.10520	+	1.04907i
$220$	−0.276548	+	0.478996i	−0.0186449	+	0.0322939i
$221$	0.424600	+	0.393971i	0.0285617	+	0.0265014i
$222$	3.39143	+	4.35320i	0.227618	+	0.292168i
$223$	12.9835	−	12.0469i	0.869440	−	0.806723i	−0.112943	−	0.993602i	$-0.536028\pi$
$223$	12.9835	−	12.0469i	0.869440	−	0.806723i	0.982383	+	0.186879i	$0.0598372\pi$
$224$	0.415972	+	1.82249i	0.0277933	+	0.121770i
$225$	0.649794	+	1.77299i	0.0433196	+	0.118200i
$226$	−10.8579	+	5.22888i	−0.722255	+	0.347820i
$227$	−1.33636	−	17.8325i	−0.0886976	−	1.18359i	−0.846967	−	0.531646i	$-0.821574\pi$
$227$	−1.33636	−	17.8325i	−0.0886976	−	1.18359i	0.758269	−	0.651941i	$-0.226045\pi$
$228$	−0.293285	+	0.723034i	−0.0194233	+	0.0478841i
$229$	9.89805	+	25.2198i	0.654082	+	1.66657i	0.741962	+	0.670442i	$0.233896\pi$
$229$	9.89805	+	25.2198i	0.654082	+	1.66657i	−0.0878801	+	0.996131i	$0.528009\pi$
$230$	16.9325	−	11.5444i	1.11649	−	0.761212i
$231$	−1.71511	−	3.05011i	−0.112846	−	0.200682i
$232$	14.1725	−	2.53936i	0.930468	−	0.166717i
$233$	7.98911			0.523384			0.261692	−	0.965151i	$-0.415719\pi$
$233$	7.98911			0.523384			0.261692	+	0.965151i	$0.415719\pi$
$234$	−0.112390	−	2.15548i	−0.00734714	−	0.140908i
$235$	13.7946	−	17.2978i	0.899858	−	1.12839i
$236$	0.655859	−	1.67110i	0.0426928	−	0.108779i
$237$	−9.50303	−	4.71006i	−0.617288	−	0.305951i
$238$	0.223936	−	2.98821i	0.0145156	−	0.193697i
$239$	10.1683	+	25.9084i	0.657734	+	1.67588i	0.734310	+	0.678814i	$0.237506\pi$
$239$	10.1683	+	25.9084i	0.657734	+	1.67588i	−0.0765764	+	0.997064i	$0.524399\pi$
$240$	−17.0329	−	5.46649i	−1.09947	−	0.352861i
$241$	−14.4134	+	13.3737i	−0.928449	+	0.861474i	−0.990628	−	0.136591i	$-0.956386\pi$
$241$	−14.4134	+	13.3737i	−0.928449	+	0.861474i	0.0621790	+	0.998065i	$0.480195\pi$
$242$	−8.85040	−	11.0981i	−0.568925	−	0.713410i
$243$	15.1326	−	3.74228i	0.970756	−	0.240067i
$244$	−1.08251			−0.0693004
$245$	−9.35475	+	2.88556i	−0.597653	+	0.184352i
$246$	−2.21471	+	25.6432i	−0.141205	+	1.63495i
$247$	0.0835626	−	1.11507i	0.00531696	−	0.0709499i
$248$	−12.4279	−	11.5314i	−0.789174	−	0.732247i
$249$	−21.4174	−	0.243158i	−1.35727	−	0.0154095i
$250$	−14.6829	+	4.52907i	−0.928627	+	0.286443i
$251$	−4.18896	−	5.25280i	−0.264405	−	0.331554i	0.631851	−	0.775090i	$-0.282295\pi$
$251$	−4.18896	−	5.25280i	−0.264405	−	0.331554i	−0.896257	+	0.443536i	$0.853724\pi$
$252$	−0.744442	+	0.659930i	−0.0468954	+	0.0415717i
$253$	−1.54579	−	6.77256i	−0.0971832	−	0.425787i
$254$	11.1268	+	1.67709i	0.698155	+	0.105230i
$255$	4.01890	+	2.80740i	0.251673	+	0.175806i
$256$	3.84301	−	2.62012i	0.240188	−	0.163757i
$257$	−29.6252	+	4.46528i	−1.84797	+	0.278536i	−0.977069	−	0.212924i	$-0.931701\pi$
$257$	−29.6252	+	4.46528i	−1.84797	+	0.278536i	−0.870900	+	0.491460i	$0.836463\pi$
$258$	−6.77586	−	1.10011i	−0.421846	−	0.0684897i
$259$	0.272399	+	3.63491i	0.0169260	+	0.225862i
$260$	−0.225351			−0.0139757
$261$	10.1357	+	12.5805i	0.627383	+	0.778711i
$262$	−5.32135			−0.328754
$263$	2.06945	+	27.6149i	0.127608	+	1.70281i	0.582965	+	0.812497i	$0.301892\pi$
$263$	2.06945	+	27.6149i	0.127608	+	1.70281i	−0.455358	+	0.890309i	$0.650489\pi$
$264$	−3.48968	+	4.27543i	−0.214775	+	0.263135i
$265$	18.8514	−	2.84139i	1.15803	−	0.174545i
$266$	−4.77974	+	3.25877i	−0.293065	+	0.199808i
$267$	0.962485	−	11.1442i	0.0589031	−	0.682014i
$268$	2.21146	+	0.333324i	0.135087	+	0.0203610i
$269$	−2.45630	−	10.7618i	−0.149763	−	0.656156i	−0.992950	−	0.118535i	$-0.962180\pi$
$269$	−2.45630	−	10.7618i	−0.149763	−	0.656156i	0.843186	−	0.537621i	$-0.180677\pi$
$270$	−3.45620	−	17.9381i	−0.210338	−	1.09168i
$271$	9.47793	+	11.8849i	0.575743	+	0.721959i	0.981380	−	0.192075i	$-0.0615218\pi$
$271$	9.47793	+	11.8849i	0.575743	+	0.721959i	−0.405637	+	0.914034i	$0.632950\pi$
$272$	−4.96203	+	1.53058i	−0.300867	+	0.0928053i
$273$	0.726830	−	1.22653i	0.0439897	−	0.0742333i
$274$	−16.7101	−	15.5048i	−1.00950	−	0.936676i
$275$	0.0560564	−	0.748021i	0.00338033	−	0.0451073i
$276$	−1.78899	+	0.836645i	−0.107684	+	0.0503601i
$277$	13.2145	−	4.07612i	0.793980	−	0.244910i	0.128876	−	0.991661i	$-0.458863\pi$
$277$	13.2145	−	4.07612i	0.793980	−	0.244910i	0.665105	+	0.746750i	$0.268387\pi$
$278$	−13.9757			−0.838206
$279$	4.65297	−	18.4451i	0.278566	−	1.10428i
$280$	−6.70515	−	8.40799i	−0.400709	−	0.502474i
$281$	22.9015	−	21.2495i	1.36619	−	1.26764i	0.436303	−	0.899800i	$-0.356288\pi$
$281$	22.9015	−	21.2495i	1.36619	−	1.26764i	0.929889	−	0.367840i	$-0.119903\pi$
$282$	−17.7273	+	16.0779i	−1.05564	+	0.957424i
$283$	1.59227	+	4.05703i	0.0946504	+	0.241165i	0.970356	−	0.241680i	$-0.0776985\pi$
$283$	1.59227	+	4.05703i	0.0946504	+	0.241165i	−0.875706	+	0.482846i	$0.839603\pi$
$284$	0.116289	−	1.55177i	0.00690047	−	0.0920804i
$285$	−0.600061	−	9.44498i	−0.0355445	−	0.559472i
$286$	−0.313247	+	0.798139i	−0.0185227	+	0.0471950i
$287$	−10.6002	+	13.2923i	−0.625711	+	0.784617i
$288$	2.94712	+	1.50262i	0.173661	+	0.0885427i
$289$	−15.5769			−0.916291
$290$	15.3415	−	11.0942i	0.900883	−	0.651472i
$291$	9.42927	+	0.107053i	0.552753	+	0.00627557i
$292$	−2.10423	+	1.43464i	−0.123141	+	0.0839558i
$293$	0.320927	+	0.817709i	0.0187488	+	0.0477711i	0.939942	−	0.341335i	$-0.110879\pi$
$293$	0.320927	+	0.817709i	0.0187488	+	0.0477711i	−0.921193	+	0.389106i	$0.872784\pi$
$294$	10.4884	−	1.45930i	0.611698	−	0.0851082i
$295$	1.62723	+	21.7138i	0.0947408	+	1.26423i
$296$	5.17951	−	2.49432i	0.301053	−	0.144979i
$297$	−6.08824	−	1.13090i	−0.353276	−	0.0656214i
$298$	1.14640	+	5.02271i	0.0664092	+	0.290958i
$299$	2.07478	−	1.92512i	0.119988	−	0.111333i
$300$	−0.211224	+	0.0293885i	−0.0121950	+	0.00169675i
$301$	−3.32391	−	3.08414i	−0.191587	−	0.177767i
$302$	15.5282	−	26.8956i	0.893547	−	1.54767i
$303$	3.39443	−	14.1306i	0.195005	−	0.811780i
$304$	8.28271	+	5.64706i	0.475046	+	0.323881i
$305$	11.8299	−	5.69697i	0.677377	−	0.326208i
$306$	−3.80438	−	3.69419i	−0.217482	−	0.211183i
$307$	−15.1308			−0.863559			−0.431779	−	0.901979i	$-0.642114\pi$
$307$	−15.1308			−0.863559			−0.431779	+	0.901979i	$0.642114\pi$
$308$	0.377634	−	0.116485i	0.0215177	−	0.00663732i
$309$	−1.50012	+	3.69823i	−0.0853388	+	0.210385i
$310$	−21.3025	−	6.57094i	−1.20990	−	0.373204i
$311$	26.0429	+	8.03317i	1.47676	+	0.455519i	0.925478	−	0.378801i	$-0.123664\pi$
$311$	26.0429	+	8.03317i	1.47676	+	0.455519i	0.551279	+	0.834321i	$0.314140\pi$
$312$	−2.21949	−	0.360349i	−0.125654	−	0.0204008i
$313$	−9.07926	−	6.19014i	−0.513190	−	0.349887i	0.278871	−	0.960329i	$-0.410040\pi$
$313$	−9.07926	−	6.19014i	−0.513190	−	0.349887i	−0.792062	+	0.610441i	$0.790992\pi$
$314$	−0.830048	−	0.399730i	−0.0468423	−	0.0225581i
$315$	4.66239	−	11.1297i	0.262696	−	0.627087i
$316$	0.746831	−	0.936496i	0.0420125	−	0.0526820i
$317$	−1.64869	−	22.0002i	−0.0925996	−	1.23566i	−0.829054	−	0.559169i	$-0.811120\pi$
$317$	−1.64869	−	22.0002i	−0.0925996	−	1.23566i	0.736454	−	0.676487i	$-0.236499\pi$
$318$	−20.6205	−	0.234110i	−1.15634	−	0.0131283i
$319$	−1.60077	−	6.21479i	−0.0896257	−	0.347961i
$320$	−8.38966	+	14.5313i	−0.468996	+	0.812325i
$321$	11.5698	−	7.69721i	0.645762	−	0.429616i
$322$	−14.4791	−	2.18238i	−0.806891	−	0.121619i
$323$	−1.71286	−	2.14786i	−0.0953063	−	0.119510i
$324$	0.0517310	+	1.75973i	0.00287395	+	0.0977630i
$325$	0.275358	−	0.132605i	0.0152741	−	0.00735562i
$326$	−16.8361	−	2.53764i	−0.932468	−	0.140547i
$327$	9.75508	+	3.13076i	0.539457	+	0.173131i
$328$	25.6223	+	7.90344i	1.41476	+	0.436395i
$329$	−15.6317	+	2.35610i	−0.861804	+	0.129896i
$330$	−1.69501	+	7.05610i	−0.0933073	+	0.388425i
$331$	2.87814	+	4.98509i	0.158197	+	0.274005i	0.934219	−	0.356701i	$-0.116099\pi$
$331$	2.87814	+	4.98509i	0.158197	+	0.274005i	−0.776022	+	0.630706i	$0.782765\pi$
$332$	0.538266	−	2.35830i	0.0295412	−	0.129428i
$333$	5.24576	+	3.75375i	0.287466	+	0.205704i
$334$	5.35183	−	2.57730i	0.292839	−	0.141024i
$335$	−25.9216	+	7.99575i	−1.41625	+	0.436855i
$336$	6.26470	+	11.1410i	0.341768	+	0.607791i
$337$	−5.36741	−	4.98023i	−0.292381	−	0.271290i	0.520319	−	0.853972i	$-0.325813\pi$
$337$	−5.36741	−	4.98023i	−0.292381	−	0.271290i	−0.812701	+	0.582682i	$0.802003\pi$
$338$	18.7023	−	2.81892i	1.01727	−	0.153329i
$339$	−10.4346	+	9.46374i	−0.566730	+	0.514000i
$340$	−0.405855	+	0.376578i	−0.0220106	+	0.0204228i
$341$	−4.71152	+	5.90807i	−0.255143	+	0.319940i
$342$	−0.996602	+	10.1886i	−0.0538901	+	0.550935i
$343$	16.9938	+	8.18377i	0.917578	+	0.441882i
$344$	−2.61266	+	6.65694i	−0.140865	+	0.358918i
$345$	15.1474	−	18.5581i	0.815509	−	0.999133i
$346$	1.36646	−	0.931640i	0.0734616	−	0.0500853i
$347$	−3.89554	+	6.74728i	−0.209124	+	0.362213i	−0.951439	−	0.307838i	$-0.900394\pi$
$347$	−3.89554	+	6.74728i	−0.209124	+	0.362213i	0.742315	+	0.670051i	$0.233728\pi$
$348$	−1.63069	+	0.818392i	−0.0874143	+	0.0438704i
$349$	18.2339	+	31.5820i	0.976037	+	1.69055i	0.676470	+	0.736471i	$0.263509\pi$
$349$	18.2339	+	31.5820i	0.976037	+	1.69055i	0.299568	+	0.954075i	$0.403158\pi$
$350$	−1.42456	−	0.686030i	−0.0761457	−	0.0366699i
$351$	−0.841244	−	2.37861i	−0.0449023	−	0.126961i
$352$	−0.819333	−	1.02741i	−0.0436706	−	0.0547612i
$353$	1.67018	+	22.2870i	0.0888945	+	1.18621i	0.846095	+	0.533032i	$0.178948\pi$
$353$	1.67018	+	22.2870i	0.0888945	+	1.18621i	−0.757200	+	0.653183i	$0.773433\pi$
$354$	2.02670	−	23.4663i	0.107718	−	1.24722i
$355$	6.89575	+	17.5701i	0.365988	+	0.932523i
$356$	1.20714	+	0.372354i	0.0639784	+	0.0197347i
$357$	−0.740619	−	3.42357i	−0.0391977	−	0.181194i
$358$	−2.42155	+	6.17001i	−0.127983	+	0.326095i
$359$	−0.288932	+	1.26589i	−0.0152492	+	0.0668113i	−0.981980	−	0.188985i	$-0.939480\pi$
$359$	−0.288932	+	1.26589i	−0.0152492	+	0.0668113i	0.966731	+	0.255796i	$0.0823375\pi$
$360$	−19.0261	−	0.432074i	−1.00276	−	0.0227723i
$361$	3.04775	−	13.3531i	0.160408	−	0.702793i
$362$	−31.0745	−	21.1863i	−1.63324	−	1.11353i
$363$	−13.6025	−	9.50203i	−0.713947	−	0.498727i
$364$	0.118032	+	0.109518i	0.00618656	+	0.00574028i
$365$	15.4453	−	26.7521i	0.808446	−	1.40027i
$366$	−13.6185	+	4.03203i	−0.711852	+	0.210757i
$367$	−10.6835	+	27.2212i	−0.557677	+	1.42094i	0.322627	+	0.946526i	$0.395434\pi$
$367$	−10.6835	+	27.2212i	−0.557677	+	1.42094i	−0.880304	+	0.474410i	$0.842661\pi$
$368$	5.64624	+	24.7378i	0.294331	+	1.28955i
$369$	6.02715	+	29.4764i	0.313761	+	1.53448i
$370$	4.71314	−	5.91009i	0.245024	−	0.307251i
$371$	−11.2547	−	7.67330i	−0.584313	−	0.398378i
$372$	1.92491	+	0.954056i	0.0998018	+	0.0494655i
$373$	−3.70840	+	0.558952i	−0.192014	+	0.0289414i	−0.244345	−	0.969688i	$-0.578573\pi$
$373$	−3.70840	+	0.558952i	−0.192014	+	0.0289414i	0.0523312	+	0.998630i	$0.483335\pi$
$374$	0.769597	+	1.96090i	0.0397949	+	0.101396i
$375$	−14.9540	+	9.94866i	−0.772220	+	0.513747i
$376$	12.4659	+	21.5916i	0.642880	+	1.11350i
$377$	1.86678	−	1.83089i	0.0961439	−	0.0942956i
$378$	−6.90745	+	11.0751i	−0.355281	+	0.569643i
$379$	20.5471	+	9.89498i	1.05544	+	0.508271i	0.879386	−	0.476110i	$-0.157954\pi$
$379$	20.5471	+	9.89498i	1.05544	+	0.508271i	0.176050	+	0.984381i	$0.443668\pi$
$380$	1.05689	+	0.159300i	0.0542172	+	0.00817193i
$381$	13.0277	−	1.81259i	0.667427	−	0.0928620i
$382$	6.17637	−	4.21098i	0.316011	−	0.215452i
$383$	−1.11689	+	14.9038i	−0.0570702	+	0.761549i	0.893108	+	0.449842i	$0.148520\pi$
$383$	−1.11689	+	14.9038i	−0.0570702	+	0.761549i	−0.950178	+	0.311707i	$0.899099\pi$
$384$	13.8922	−	17.0202i	0.708932	−	0.868559i
$385$	−3.51384	+	3.26037i	−0.179082	+	0.166164i
$386$	2.22213	+	9.73578i	0.113103	+	0.495538i
$387$	−7.95960	+	1.01548i	−0.404609	+	0.0516198i
$388$	−0.236978	+	1.03827i	−0.0120307	+	0.0527101i
$389$	−14.6790	−	25.4248i	−0.744255	−	1.28909i	−0.950542	−	0.310596i	$-0.899471\pi$
$389$	−14.6790	−	25.4248i	−0.744255	−	1.28909i	0.206287	−	0.978492i	$-0.433862\pi$
$390$	−2.83504	+	0.839367i	−0.143558	+	0.0425030i
$391$	0.519650	−	6.93425i	0.0262798	−	0.350680i
$392$	0.824403	−	11.0009i	0.0416386	−	0.555629i
$393$	−5.96429	+	1.76584i	−0.300859	+	0.0890750i
$394$	15.8409	+	27.4372i	0.798052	+	1.38227i
$395$	−3.23299	+	14.1646i	−0.162669	+	0.712700i
$396$	0.270213	−	0.645031i	0.0135787	−	0.0324140i
$397$	4.65684	+	20.4029i	0.233720	+	1.02399i	0.946525	+	0.322632i	$0.104567\pi$
$397$	4.65684	+	20.4029i	0.233720	+	1.02399i	−0.712805	+	0.701363i	$0.752575\pi$
$398$	−2.52965	+	2.34718i	−0.126800	+	0.117653i
$399$	−4.27585	+	5.23862i	−0.214060	+	0.262259i
$400$	−0.204755	+	2.73226i	−0.0102377	+	0.136613i
$401$	−23.2359	+	15.8420i	−1.16035	+	0.791110i	−0.981253	−	0.192722i	$-0.938268\pi$
$401$	−23.2359	+	15.8420i	−1.16035	+	0.791110i	−0.179092	+	0.983832i	$0.557316\pi$
$402$	29.0630	−	4.04366i	1.44953	−	0.201679i
$403$	−3.04447	−	0.458880i	−0.151656	−	0.0228585i
$404$	1.47871	+	0.712109i	0.0735686	+	0.0354288i
$405$	−9.82639	−	18.9585i	−0.488277	−	0.942058i
$406$	−13.4270	−	1.64498i	−0.666373	−	0.0816390i
$407$	−1.28120	−	2.21910i	−0.0635067	−	0.109997i
$408$	−4.59945	+	3.05995i	−0.227707	+	0.151490i
$409$	0.0789584	+	0.201183i	0.00390424	+	0.00994785i	0.932813	−	0.360362i	$-0.117347\pi$
$409$	0.0789584	+	0.201183i	0.00390424	+	0.00994785i	−0.928908	+	0.370310i	$0.879252\pi$
$410$	34.8642	−	5.25493i	1.72182	−	0.259522i
$411$	−23.8742	−	11.8330i	−1.17763	−	0.583677i
$412$	−0.372398	−	0.253897i	−0.0183468	−	0.0125086i
$413$	9.70036	−	12.1639i	0.477323	−	0.598545i
$414$	−19.3902	+	17.1889i	−0.952976	+	0.844790i
$415$	6.52886	+	28.6048i	0.320489	+	1.40415i
$416$	0.195608	−	0.498402i	0.00959049	−	0.0244362i
$417$	−15.6643	+	4.63770i	−0.767082	+	0.227109i
$418$	2.03332	−	3.52182i	0.0994530	−	0.172258i
$419$	5.40755	+	5.01748i	0.264176	+	0.245120i	0.801128	−	0.598493i	$-0.204234\pi$
$419$	5.40755	+	5.01748i	0.264176	+	0.245120i	−0.536951	+	0.843613i	$0.680424\pi$
$420$	1.11719	+	0.780411i	0.0545133	+	0.0380802i
$421$	7.81819	+	5.33035i	0.381035	+	0.259785i	0.738657	−	0.674081i	$-0.235460\pi$
$421$	7.81819	+	5.33035i	0.381035	+	0.259785i	−0.357622	+	0.933866i	$0.616413\pi$
$422$	7.30327	−	31.9977i	0.355517	−	1.55762i
$423$	−14.5338	+	23.9031i	−0.706659	+	1.16221i
$424$	−4.78043	+	20.9444i	−0.232158	+	1.01715i
$425$	0.274324	−	0.698965i	0.0133067	−	0.0339048i
$426$	−4.31691	−	19.9552i	−0.209155	−	0.966835i
$427$	−8.96480	−	2.76527i	−0.433837	−	0.133821i
$428$	0.573362	+	1.46090i	0.0277145	+	0.0706154i
$429$	−0.0862387	+	0.998521i	−0.00416364	+	0.0482090i
$430$	0.702719	+	9.37713i	0.0338881	+	0.452205i
$431$	−9.29129	−	11.6509i	−0.447546	−	0.561205i	0.505969	−	0.862552i	$-0.331135\pi$
$431$	−9.29129	−	11.6509i	−0.447546	−	0.561205i	−0.953514	+	0.301347i	$0.902564\pi$
$432$	22.2382	+	4.13078i	1.06994	+	0.198742i
$433$	31.8592	+	15.3426i	1.53105	+	0.737317i	0.994320	−	0.106435i	$-0.0339435\pi$
$433$	31.8592	+	15.3426i	1.53105	+	0.737317i	0.536734	+	0.843751i	$0.319658\pi$
$434$	7.96420	+	13.7944i	0.382294	+	0.662153i
$435$	13.5136	−	17.5255i	0.647927	−	0.840285i
$436$	−0.578522	+	1.00203i	−0.0277062	+	0.0479885i
$437$	−11.0916	+	7.56209i	−0.530581	+	0.361744i
$438$	−21.1287	+	25.8862i	−1.00957	+	1.23689i
$439$	11.3866	−	29.0125i	0.543451	−	1.38469i	−0.350516	−	0.936557i	$-0.613994\pi$
$439$	11.3866	−	29.0125i	0.543451	−	1.38469i	0.893967	−	0.448134i	$-0.147911\pi$
$440$	6.81124	+	3.28012i	0.324713	+	0.156374i
$441$	11.2714	−	5.11611i	0.536734	−	0.243624i
$442$	−0.535121	+	0.671021i	−0.0254531	+	0.0319172i
$443$	6.74435	−	6.25784i	0.320434	−	0.297319i	−0.503512	−	0.863988i	$-0.667959\pi$
$443$	6.74435	−	6.25784i	0.320434	−	0.297319i	0.823945	+	0.566670i	$0.191768\pi$
$444$	−0.539612	+	0.489405i	−0.0256088	+	0.0232261i
$445$	−15.1515	+	2.28373i	−0.718252	+	0.108259i
$446$	19.2384	+	17.8507i	0.910967	+	0.845253i
$447$	2.95165	+	5.24915i	0.139608	+	0.248276i
$448$	11.4563	−	3.53380i	0.541259	−	0.166956i
$449$	20.3897	−	9.81916i	0.962249	−	0.463395i	0.114285	−	0.993448i	$-0.463542\pi$
$449$	20.3897	−	9.81916i	0.962249	−	0.463395i	0.847964	+	0.530053i	$0.177828\pi$
$450$	−2.54785	+	1.15647i	−0.120107	+	0.0545166i
$451$	2.65946	−	11.6519i	0.125229	−	0.548665i
$452$	−0.795463	−	1.37778i	−0.0374154	−	0.0648054i
$453$	8.47929	−	35.2981i	0.398392	−	1.65845i
$454$	26.2017	−	3.94927i	1.22970	−	0.185348i
$455$	−1.86625	−	0.575661i	−0.0874910	−	0.0269874i
$456$	10.1546	+	3.25898i	0.475533	+	0.152616i
$457$	5.50164	+	0.829239i	0.257356	+	0.0387902i	0.276453	−	0.961027i	$-0.410841\pi$
$457$	5.50164	+	0.829239i	0.257356	+	0.0387902i	−0.0190970	+	0.999818i	$0.506079\pi$
$458$	−36.1692	+	17.4182i	−1.69008	+	0.813897i
$459$	−5.48992	−	2.87808i	−0.256247	−	0.134337i
$460$	1.68678	+	2.11516i	0.0786465	+	0.0986196i
$461$	22.8053	+	3.43735i	1.06215	+	0.160093i	0.656798	−	0.754067i	$-0.271911\pi$
$461$	22.8053	+	3.43735i	1.06215	+	0.160093i	0.405353	+	0.914160i	$0.367149\pi$
$462$	4.31697	−	2.87202i	0.200844	−	0.133618i
$463$	5.18095	−	8.97367i	0.240779	−	0.417042i	−0.720157	−	0.693811i	$-0.755930\pi$
$463$	5.18095	−	8.97367i	0.240779	−	0.417042i	0.960936	+	0.276769i	$0.0892637\pi$
$464$	5.84704	+	22.7005i	0.271442	+	1.05384i
$465$	−26.0568	−	0.295831i	−1.20836	−	0.0137188i
$466$	0.884651	+	11.8048i	0.0409807	+	0.546849i
$467$	−1.99525	+	2.50196i	−0.0923291	+	0.115777i	−0.825850	−	0.563890i	$-0.809304\pi$
$467$	−1.99525	+	2.50196i	−0.0923291	+	0.115777i	0.733521	+	0.679667i	$0.237876\pi$
$468$	0.282645	−	0.0360597i	0.0130653	−	0.00166686i
$469$	17.4628	+	8.40964i	0.806357	+	0.388321i
$470$	27.0870	+	18.4676i	1.24943	+	0.851849i
$471$	−1.06298	−	0.172583i	−0.0489797	−	0.00795219i
$472$	−23.4472	−	7.23251i	−1.07925	−	0.332903i
$473$	3.04590	+	0.939536i	0.140051	+	0.0431999i
$474$	5.90737	−	14.5634i	0.271334	−	0.668918i
$475$	−1.38516	+	0.427265i	−0.0635555	+	0.0196043i
$476$	0.395587			0.0181317
$477$	−23.1896	+	6.58032i	−1.06178	+	0.301292i
$478$	−37.1568	+	17.8938i	−1.69951	+	0.818441i
$479$	−18.7634	−	12.7927i	−0.857322	−	0.584512i	0.0529153	−	0.998599i	$-0.483149\pi$
$479$	−18.7634	−	12.7927i	−0.857322	−	0.584512i	−0.910237	+	0.414087i	$0.864101\pi$
$480$	1.05846	−	4.40621i	0.0483118	−	0.201115i
$481$	0.522005	−	0.904139i	0.0238014	−	0.0412252i
$482$	−21.3572	−	19.8166i	−0.972793	−	0.902620i
$483$	−16.9527	+	2.35871i	−0.771377	+	0.107325i
$484$	1.37367	−	1.27458i	0.0624396	−	0.0579355i
$485$	−2.87441	−	12.5936i	−0.130520	−	0.571846i
$486$	7.20532	+	21.9458i	0.326840	+	0.995480i
$487$	−6.54678	+	3.15276i	−0.296663	+	0.142865i	−0.576295	−	0.817242i	$-0.695502\pi$
$487$	−6.54678	+	3.15276i	−0.296663	+	0.142865i	0.279632	+	0.960107i	$0.409788\pi$
$488$	1.10571	+	14.7547i	0.0500532	+	0.667913i
$489$	−19.7124	+	2.74268i	−0.891427	+	0.124028i
$490$	−5.29962	−	13.5032i	−0.239412	−	0.610013i
$491$	34.8781	−	23.7795i	1.57403	−	1.07315i	0.615507	−	0.788131i	$-0.288951\pi$
$491$	34.8781	−	23.7795i	1.57403	−	1.07315i	0.958521	−	0.285023i	$-0.0920011\pi$
$492$	−3.39760	−	0.0385739i	−0.153175	−	0.00173905i
$493$	0.302495	−	6.41694i	0.0136237	−	0.289005i
$494$	1.65689			0.0745471
$495$	0.441695	+	8.47111i	0.0198527	+	0.380748i
$496$	17.2096	−	21.5801i	0.772732	−	0.968975i
$497$	4.92705	−	12.5539i	0.221009	−	0.563121i
$498$	−2.01230	−	31.6736i	−0.0901731	−	1.41933i
$499$	2.56688	−	34.2527i	0.114909	−	1.53336i	−0.580210	−	0.814467i	$-0.697030\pi$
$499$	2.56688	−	34.2527i	0.114909	−	1.53336i	0.695120	−	0.718894i	$-0.255351\pi$
$500$	−0.741072	−	1.88822i	−0.0331417	−	0.0844438i
$501$	5.14320	−	4.66466i	0.229781	−	0.208402i
$502$	7.29776	−	6.77133i	0.325715	−	0.302219i
$503$	1.68384	+	2.11147i	0.0750786	+	0.0941456i	0.817952	−	0.575286i	$-0.195109\pi$
$503$	1.68384	+	2.11147i	0.0750786	+	0.0941456i	−0.742874	+	0.669431i	$0.766538\pi$
$504$	9.75532	+	9.47276i	0.434537	+	0.421950i
$505$	−19.9074			−0.885866
$506$	9.83608	−	3.03403i	0.437267	−	0.134879i
$507$	20.0265	−	9.36569i	0.889409	−	0.415945i
$508$	−0.111009	+	1.48131i	−0.00492521	+	0.0657224i
$509$	−28.1110	−	26.0832i	−1.24600	−	1.15612i	−0.981444	−	0.191748i	$-0.938584\pi$
$509$	−28.1110	−	26.0832i	−1.24600	−	1.15612i	−0.264555	−	0.964371i	$-0.585225\pi$
$510$	−3.70324	+	6.24926i	−0.163982	+	0.276722i
$511$	−21.0910	+	6.50571i	−0.933011	+	0.287796i
$512$	−11.5201	−	14.4457i	−0.509120	−	0.638417i
$513$	2.26397	+	11.7503i	0.0999568	+	0.518789i
$514$	−9.87842	−	43.2802i	−0.435719	−	1.90901i
$515$	5.40586	+	0.814802i	0.238211	+	0.0359045i
$516$	0.0779758	−	0.902848i	0.00343269	−	0.0397457i
$517$	9.18180	−	6.26004i	0.403815	−	0.275316i
$518$	−5.34083	+	0.805001i	−0.234663	+	0.0353697i
$519$	1.22241	−	1.49765i	0.0536578	−	0.0657396i
$520$	0.230181	+	3.07156i	0.0100941	+	0.134697i
$521$	−3.67935			−0.161195			−0.0805977	−	0.996747i	$-0.525683\pi$
$521$	−3.67935			−0.161195			−0.0805977	+	0.996747i	$0.525683\pi$
$522$	−17.4668	+	16.3697i	−0.764499	+	0.716482i
$523$	−24.6642			−1.07849			−0.539244	−	0.842149i	$-0.681290\pi$
$523$	−24.6642			−1.07849			−0.539244	+	0.842149i	$0.681290\pi$
$524$	−0.0524967	−	0.700520i	−0.00229333	−	0.0306024i
$525$	−1.82433	−	0.296192i	−0.0796202	−	0.0129269i
$526$	−40.5750	+	6.11570i	−1.76915	+	0.266657i
$527$	−6.24990	+	4.26111i	−0.272250	+	0.185617i
$528$	−7.36587	−	5.14542i	−0.320558	−	0.223926i
$529$	−10.8562	−	1.63631i	−0.472010	−	0.0711440i
$530$	6.28593	+	27.5404i	0.273043	+	1.19628i
$531$	−5.51550	−	26.9741i	−0.239352	−	1.17058i
$532$	−0.476149	−	0.597072i	−0.0206437	−	0.0258863i
$533$	4.65313	−	1.43530i	0.201549	−	0.0621697i
$534$	16.5734	+	0.188163i	0.717203	+	0.00814261i
$535$	−13.9542	−	12.9476i	−0.603293	−	0.559774i
$536$	2.28438	−	30.4830i	0.0986703	−	1.31666i
$537$	−0.666668	+	7.71906i	−0.0287688	+	0.333102i
$538$	15.6298	−	4.82114i	0.673847	−	0.207854i
$539$	−4.91713			−0.211796
$540$	2.32734	−	0.631950i	0.100153	−	0.0271948i
$541$	−2.13649	−	2.67908i	−0.0918549	−	0.115182i	0.733780	−	0.679387i	$-0.237754\pi$
$541$	−2.13649	−	2.67908i	−0.0918549	−	0.115182i	−0.825635	+	0.564205i	$0.809183\pi$
$542$	−16.5119	+	15.3208i	−0.709246	+	0.658084i
$543$	−41.8595	−	13.4342i	−1.79636	−	0.576519i
$544$	−0.480579	−	1.22449i	−0.0206046	−	0.0524998i
$545$	1.04878	−	13.9950i	0.0449250	−	0.599482i
$546$	1.89283	+	0.938158i	0.0810057	+	0.0401495i
$547$	15.7297	−	40.0787i	0.672555	−	1.71364i	−0.0275680	−	0.999620i	$-0.508776\pi$
$547$	15.7297	−	40.0787i	0.672555	−	1.71364i	0.700123	−	0.714022i	$-0.253128\pi$
$548$	1.87624	−	2.35274i	0.0801492	−	0.100504i
$549$	−13.9260	+	9.03838i	−0.594346	+	0.385749i
$550$	1.11149			0.0473943
$551$	−10.0494	+	7.26719i	−0.428118	+	0.309593i
$552$	13.2309	+	23.5295i	0.563145	+	1.00148i
$553$	8.57718	−	5.84783i	0.364739	−	0.248675i
$554$	7.48621	+	19.0745i	0.318058	+	0.810400i
$555$	3.32139	−	8.18818i	0.140985	−	0.347569i
$556$	−0.137874	−	1.83980i	−0.00584717	−	0.0780250i
$557$	5.53572	−	2.66586i	0.234556	−	0.112956i	−0.312914	−	0.949781i	$-0.601305\pi$
$557$	5.53572	−	2.66586i	0.234556	−	0.112956i	0.547470	+	0.836825i	$0.315591\pi$
$558$	27.7700	+	4.83284i	1.17560	+	0.204590i
$559$	0.288989	+	1.26614i	0.0122229	+	0.0535521i
$560$	12.8348	−	11.9090i	0.542371	−	0.503247i
$561$	1.51329	+	1.94244i	0.0638911	+	0.0820099i
$562$	33.9346	+	31.4867i	1.43144	+	1.32819i
$563$	8.03249	−	13.9127i	0.338529	−	0.586350i	−0.645627	−	0.763653i	$-0.723404\pi$
$563$	8.03249	−	13.9127i	0.338529	−	0.586350i	0.984156	+	0.177303i	$0.0567373\pi$
$564$	−2.29143	−	2.17506i	−0.0964865	−	0.0915867i
$565$	15.9439	+	10.8704i	0.670767	+	0.457321i
$566$	−5.81842	+	2.80200i	−0.244566	+	0.117777i
$567$	−4.06685	+	14.7054i	−0.170792	+	0.617570i
$568$	−21.2695			−0.892450
$569$	8.95112	−	2.76105i	0.375250	−	0.115749i	−0.101392	−	0.994847i	$-0.532330\pi$
$569$	8.95112	−	2.76105i	0.375250	−	0.115749i	0.476643	+	0.879097i	$0.341854\pi$
$570$	13.8896	−	1.93252i	0.581771	−	0.0809444i
$571$	−35.1012	−	10.8273i	−1.46894	−	0.453108i	−0.545913	−	0.837842i	$-0.683817\pi$
$571$	−35.1012	−	10.8273i	−1.46894	−	0.453108i	−0.923028	+	0.384734i	$0.874293\pi$
$572$	−0.108160	−	0.0333629i	−0.00452239	−	0.00139497i
$573$	5.52525	−	6.76934i	0.230820	−	0.282793i
$574$	−20.8146	−	14.1912i	−0.868786	−	0.592328i
$575$	−3.30573	−	1.59196i	−0.137859	−	0.0663892i
$576$	8.19745	−	19.5683i	0.341560	−	0.815347i
$577$	−16.5313	+	20.7296i	−0.688208	+	0.862985i	−0.996081	−	0.0884420i	$-0.971811\pi$
$577$	−16.5313	+	20.7296i	−0.688208	+	0.862985i	0.307874	+	0.951427i	$0.400383\pi$
$578$	−1.72487	−	23.0167i	−0.0717450	−	0.957370i
$579$	5.72135	+	10.1747i	0.237771	+	0.422846i
$580$	1.61182	+	1.91016i	0.0669272	+	0.0793149i
$581$	10.4820	−	18.1553i	0.434865	−	0.753208i
$582$	0.885938	+	13.9447i	0.0367233	+	0.578026i
$583$	9.46861	+	1.42716i	0.392150	+	0.0591071i
$584$	21.7036	+	27.2155i	0.898102	+	1.12618i
$585$	−2.89904	+	1.88156i	−0.119861	+	0.0777931i
$586$	−1.17272	+	0.564754i	−0.0484448	+	0.0233298i
$587$	25.1115	+	3.78495i	1.03646	+	0.156222i	0.645166	−	0.764043i	$-0.276788\pi$
$587$	25.1115	+	3.78495i	1.03646	+	0.156222i	0.391297	+	0.920264i	$0.372026\pi$
$588$	0.295579	+	1.36633i	0.0121895	+	0.0563467i
$589$	13.9541	+	4.30427i	0.574969	+	0.177354i
$590$	−31.9045	+	4.80883i	−1.31349	+	0.197976i
$591$	26.8596	+	25.4956i	1.10486	+	1.04875i
$592$	4.67978	+	8.10561i	0.192338	+	0.333139i
$593$	1.83226	−	8.02767i	0.0752421	−	0.329657i	−0.923272	−	0.384146i	$-0.874496\pi$
$593$	1.83226	−	8.02767i	0.0752421	−	0.329657i	0.998514	+	0.0544891i	$0.0173530\pi$
$594$	0.996871	−	9.12131i	0.0409021	−	0.374252i
$595$	−4.32307	+	2.08188i	−0.177229	+	0.0853488i
$596$	−0.649896	+	0.200467i	−0.0266208	+	0.00821143i
$597$	−2.05641	+	3.47021i	−0.0841631	+	0.142026i
$598$	3.07433	+	2.85256i	0.125719	+	0.116650i
$599$	−26.4568	+	3.98772i	−1.08099	+	0.162934i	−0.665304	−	0.746572i	$-0.731698\pi$
$599$	−26.4568	+	3.98772i	−1.08099	+	0.162934i	−0.415691	+	0.909506i	$0.636460\pi$
$600$	0.616320	+	2.84899i	0.0251612	+	0.116309i
$601$	9.14414	−	8.48452i	0.372997	−	0.346091i	−0.471293	−	0.881977i	$-0.656213\pi$
$601$	9.14414	−	8.48452i	0.372997	−	0.346091i	0.844291	+	0.535886i	$0.180022\pi$
$602$	4.18911	−	5.25297i	0.170735	−	0.214095i
$603$	31.2326	−	14.1765i	1.27189	−	0.577312i
$604$	3.69382	+	1.77885i	0.150299	+	0.0723803i
$605$	−8.30399	+	21.1582i	−0.337605	+	0.860204i
$606$	21.2554	+	3.45096i	0.863442	+	0.140186i
$607$	−5.57311	+	3.79968i	−0.226206	+	0.154224i	−0.671120	−	0.741349i	$-0.734186\pi$
$607$	−5.57311	+	3.79968i	−0.226206	+	0.154224i	0.444914	+	0.895573i	$0.353234\pi$
$608$	−1.26972	+	2.19922i	−0.0514939	+	0.0891900i
$609$	−15.5952	+	2.61191i	−0.631950	+	0.105840i
$610$	9.72788	+	16.8492i	0.393870	+	0.682204i
$611$	4.07934	+	1.96451i	0.165032	+	0.0794754i
$612$	0.448783	−	0.537265i	0.0181410	−	0.0217177i
$613$	−17.1169	−	21.4639i	−0.691346	−	0.866921i	0.304998	−	0.952353i	$-0.401344\pi$
$613$	−17.1169	−	21.4639i	−0.691346	−	0.866921i	−0.996344	+	0.0854323i	$0.972773\pi$
$614$	−1.67546	−	22.3575i	−0.0676161	−	0.902274i
$615$	37.3327	−	17.4592i	1.50540	−	0.704023i
$616$	−1.97343	−	5.02821i	−0.0795117	−	0.202592i
$617$	20.8069	+	6.41808i	0.837654	+	0.258382i	0.683762	−	0.729705i	$-0.260343\pi$
$617$	20.8069	+	6.41808i	0.837654	+	0.258382i	0.153893	+	0.988088i	$0.450819\pi$
$618$	−5.63068	−	1.80709i	−0.226499	−	0.0726918i
$619$	15.2485	−	38.8526i	0.612890	−	1.56162i	−0.200371	−	0.979720i	$-0.564215\pi$
$619$	15.2485	−	38.8526i	0.612890	−	1.56162i	0.813261	−	0.581898i	$-0.197690\pi$
$620$	0.654865	−	2.86915i	0.0263000	−	0.115228i
$621$	−16.0290	+	25.7002i	−0.643221	+	1.03131i
$622$	−8.98616	+	39.3709i	−0.360312	+	1.57863i
$623$	9.04579	+	6.16731i	0.362412	+	0.247088i
$624$	0.315000	−	3.64725i	0.0126101	−	0.146007i
$625$	20.3429	+	18.8755i	0.813717	+	0.755019i
$626$	8.14128	−	14.1011i	0.325391	−	0.563594i
$627$	1.11031	−	4.62207i	0.0443415	−	0.184588i
$628$	0.0444331	−	0.113214i	0.00177307	−	0.00451772i
$629$	−0.570759	−	2.50066i	−0.0227577	−	0.0997078i
$630$	16.9617	+	5.65680i	0.675770	+	0.225372i
$631$	16.2775	−	20.4114i	0.647999	−	0.812564i	−0.343979	−	0.938977i	$-0.611775\pi$
$631$	16.2775	−	20.4114i	0.647999	−	0.812564i	0.991978	+	0.126413i	$0.0403464\pi$
$632$	−13.5274	−	9.22282i	−0.538091	−	0.366864i
$633$	−2.43248	−	38.2873i	−0.0966823	−	1.52178i
$634$	32.3253	−	4.87226i	1.28380	−	0.193502i
$635$	−6.58264	−	16.7723i	−0.261224	−	0.665588i
$636$	−0.172608	−	2.71685i	−0.00684435	−	0.107730i
$637$	−1.00171	−	1.73500i	−0.0396890	−	0.0687434i
$638$	9.00582	−	3.05349i	0.356544	−	0.120889i
$639$	−11.4605	−	20.9338i	−0.453369	−	0.828127i
$640$	−27.1151	−	13.0579i	−1.07182	−	0.516161i
$641$	28.3698	+	4.27606i	1.12054	+	0.168894i	0.683080	−	0.730343i	$-0.260640\pi$
$641$	28.3698	+	4.27606i	1.12054	+	0.168894i	0.437461	+	0.899238i	$0.355878\pi$
$642$	12.6547	+	16.2434i	0.499440	+	0.641074i
$643$	38.8484	−	26.4864i	1.53203	−	1.04452i	0.554892	−	0.831923i	$-0.312760\pi$
$643$	38.8484	−	26.4864i	1.53203	−	1.04452i	0.977140	−	0.212599i	$-0.0681927\pi$
$644$	0.144454	−	1.92761i	0.00569230	−	0.0759585i
$645$	3.89934	+	10.2769i	0.153536	+	0.404653i
$646$	2.98405	−	2.76879i	0.117406	−	0.108937i
$647$	1.36263	+	5.97008i	0.0535706	+	0.234708i	0.994624	−	0.103549i	$-0.0330198\pi$
$647$	1.36263	+	5.97008i	0.0535706	+	0.234708i	−0.941054	+	0.338257i	$0.890163\pi$
$648$	23.9326	−	2.50256i	0.940159	−	0.0983097i
$649$	−2.43370	+	10.6627i	−0.0955310	+	0.418549i
$650$	0.226431	+	0.392189i	0.00888134	+	0.0153829i
$651$	13.5040	+	12.8182i	0.529264	+	0.502386i
$652$	0.167970	−	2.24140i	0.00657820	−	0.0877799i
$653$	1.49435	−	19.9406i	0.0584782	−	0.780338i	−0.888466	−	0.458941i	$-0.848229\pi$
$653$	1.49435	−	19.9406i	0.0584782	−	0.780338i	0.946945	−	0.321396i	$-0.104152\pi$
$654$	−3.54586	+	14.7609i	−0.138654	+	0.577198i
$655$	4.26037	+	7.37917i	0.166466	+	0.288328i
$656$	−9.71409	+	42.5602i	−0.379272	+	1.66170i
$657$	−15.0915	+	36.0252i	−0.588775	+	1.40548i
$658$	−5.21234	−	22.8368i	−0.203198	−	0.890270i
$659$	32.6701	−	30.3134i	1.27265	−	1.18084i	0.298629	−	0.954369i	$-0.403471\pi$
$659$	32.6701	−	30.3134i	1.27265	−	1.18084i	0.974017	−	0.226473i	$-0.0727196\pi$
$660$	−0.945609	−	0.153526i	−0.0368078	−	0.00597600i
$661$	−2.11516	+	28.2249i	−0.0822703	+	1.09782i	0.791399	+	0.611300i	$0.209353\pi$
$661$	−2.11516	+	28.2249i	−0.0822703	+	1.09782i	−0.873669	+	0.486520i	$0.838266\pi$
$662$	−7.04735	+	4.80480i	−0.273903	+	0.186744i
$663$	−0.377104	+	0.929671i	−0.0146455	+	0.0361054i
$664$	−32.6937	−	4.92778i	−1.26876	−	0.191235i
$665$	8.34571	+	4.01908i	0.323633	+	0.155853i
$666$	−4.96573	+	8.16689i	−0.192418	+	0.316460i
$667$	−31.1579	−	3.81723i	−1.20644	−	0.147804i
$668$	0.392082	+	0.679106i	0.0151701	+	0.0262754i
$669$	27.4865	+	13.6233i	1.06269	+	0.526708i
$670$	−14.6850	−	37.4168i	−0.567331	−	1.44554i
$671$	6.52133	−	0.982933i	0.251753	−	0.0379457i
$672$	−2.69575	+	1.79345i	−0.103991	+	0.0691837i
$673$	0.0744191	+	0.0507381i	0.00286865	+	0.00195581i	0.564754	−	0.825260i	$-0.308971\pi$
$673$	0.0744191	+	0.0507381i	0.00286865	+	0.00195581i	−0.561885	+	0.827215i	$0.689924\pi$
$674$	6.76452	−	8.48244i	0.260560	−	0.326731i
$675$	−2.47193	+	2.14168i	−0.0951445	+	0.0824334i
$676$	0.555595	+	2.43422i	0.0213690	+	0.0936238i
$677$	−4.17246	+	10.6313i	−0.160361	+	0.408593i	−0.988359	−	0.152138i	$-0.951384\pi$
$677$	−4.17246	+	10.6313i	−0.160361	+	0.408593i	0.827999	+	0.560730i	$0.189480\pi$
$678$	−15.1392	−	14.3704i	−0.581418	−	0.551892i
$679$	−4.61481	+	7.99309i	−0.177100	+	0.306746i
$680$	5.54736	+	5.14720i	0.212732	+	0.197386i
$681$	28.0569	−	13.1212i	1.07514	−	0.502806i
$682$	−9.25157	−	6.30761i	−0.354261	−	0.241531i
$683$	−6.89006	+	30.1873i	−0.263641	+	1.15509i	0.653627	+	0.756817i	$0.273246\pi$
$683$	−6.89006	+	30.1873i	−0.263641	+	1.15509i	−0.917268	+	0.398270i	$0.869611\pi$
$684$	−1.35109	−	0.0306826i	−0.0516602	−	0.00117318i
$685$	−8.12216	+	35.5855i	−0.310332	+	1.35965i
$686$	−10.2107	+	26.0165i	−0.389847	+	0.993314i
$687$	−34.7592	+	31.5251i	−1.32615	+	1.20276i
$688$	−11.1256	−	3.43180i	−0.424160	−	0.130836i
$689$	1.42535	+	3.63173i	0.0543014	+	0.138358i
$690$	29.0990	+	20.3271i	1.10778	+	0.773838i
$691$	−1.61314	−	21.5259i	−0.0613669	−	0.818884i	−0.939954	−	0.341302i	$-0.889132\pi$
$691$	−1.61314	−	21.5259i	−0.0613669	−	0.818884i	0.878587	−	0.477582i	$-0.158487\pi$
$692$	0.136125	+	0.170695i	0.00517468	+	0.00648885i
$693$	3.88551	−	4.65157i	0.147598	−	0.176699i
$694$	−10.4012	−	5.00897i	−0.394826	−	0.190138i
$695$	11.1892	+	19.3802i	0.424429	+	0.735133i
$696$	12.8204	+	21.3906i	0.485957	+	0.810808i
$697$	5.98175	−	10.3607i	0.226575	−	0.392439i
$698$	−44.6470	+	30.4398i	−1.68991	+	1.15216i
$699$	4.90887	+	12.9376i	0.185670	+	0.489344i
$700$	0.0762576	−	0.194301i	0.00288226	−	0.00734389i
$701$	−17.6626	−	8.50585i	−0.667106	−	0.321261i	0.0695013	−	0.997582i	$-0.477859\pi$
$701$	−17.6626	−	8.50585i	−0.667106	−	0.321261i	−0.736608	+	0.676320i	$0.763573\pi$
$702$	3.42152	−	1.50642i	0.129137	−	0.0568563i
$703$	−3.08733	+	3.87138i	−0.116441	+	0.146012i
$704$	−6.17806	+	5.73241i	−0.232845	+	0.216048i
$705$	36.4881	+	11.7104i	1.37422	+	0.441038i
$706$	−32.7466	+	4.93576i	−1.23244	+	0.185760i
$707$	10.4269	+	9.67473i	0.392143	+	0.363856i
$708$	3.10917	+	0.0352993i	0.116850	+	0.00132663i
$709$	−31.7711	+	9.80007i	−1.19319	+	0.368049i	−0.826844	−	0.562431i	$-0.809866\pi$
$709$	−31.7711	+	9.80007i	−1.19319	+	0.368049i	−0.366342	+	0.930480i	$0.619390\pi$
$710$	−25.1982	+	12.1348i	−0.945673	+	0.455412i
$711$	1.78839	−	18.2833i	0.0670699	−	0.685676i
$712$	3.84221	−	16.8338i	0.143993	−	0.630874i
$713$	18.4812	+	32.0104i	0.692127	+	1.19880i
$714$	4.97671	−	1.47345i	0.186249	−	0.0551424i
$715$	1.35758	−	0.204622i	0.0507705	−	0.00765243i
$716$	−0.836130	−	0.257912i	−0.0312476	−	0.00963862i
$717$	−35.7083	+	32.3859i	−1.33355	+	1.20947i
$718$	−1.90250	−	0.286755i	−0.0710006	−	0.0107016i
$719$	20.1130	−	9.68591i	0.750088	−	0.361223i	−0.0194614	−	0.999811i	$-0.506195\pi$
$719$	20.1130	−	9.68591i	0.750088	−	0.361223i	0.769549	+	0.638587i	$0.220481\pi$
$720$	−1.61336	−	30.9420i	−0.0601264	−	1.15314i
$721$	−2.43544	−	3.05395i	−0.0907007	−	0.113735i
$722$	20.0682	+	3.02479i	0.746861	+	0.112571i
$723$	−30.5136	−	15.1237i	−1.13481	−	0.562456i
$724$	2.48247	−	4.29976i	0.0922602	−	0.159799i
$725$	−3.09351	−	1.38558i	−0.114890	−	0.0514590i
$726$	12.5341	−	21.1515i	0.465185	−	0.785005i
$727$	1.78256	+	23.7866i	0.0661116	+	0.882197i	0.927398	+	0.374077i	$0.122040\pi$
$727$	1.78256	+	23.7866i	0.0661116	+	0.882197i	−0.861286	+	0.508120i	$0.830340\pi$
$728$	1.37218	−	1.72065i	0.0508562	−	0.0637717i
$729$	15.3584	+	22.2063i	0.568829	+	0.822456i
$730$	41.2396	+	19.8600i	1.52635	+	0.735050i
$731$	2.63629	+	1.79739i	0.0975066	+	0.0664788i
$732$	−0.665140	−	1.75301i	−0.0245843	−	0.0647931i
$733$	−3.76516	−	1.16140i	−0.139069	−	0.0428973i	0.224439	−	0.974488i	$-0.427945\pi$
$733$	−3.76516	−	1.16140i	−0.139069	−	0.0428973i	−0.363508	+	0.931591i	$0.618421\pi$
$734$	−41.4055	−	12.7719i	−1.52831	−	0.471420i
$735$	−10.4208	−	13.3761i	−0.384379	−	0.493384i
$736$	−6.14219	+	1.89461i	−0.226404	+	0.0698364i
$737$	−13.6252			−0.501889
$738$	−42.8874	+	12.1698i	−1.57871	+	0.447976i
$739$	6.74041	−	3.24601i	0.247950	−	0.119406i	−0.305781	−	0.952102i	$-0.598918\pi$
$739$	6.74041	−	3.24601i	0.247950	−	0.119406i	0.553732	+	0.832695i	$0.313203\pi$
$740$	0.824520	+	0.562148i	0.0303100	+	0.0206650i
$741$	1.85708	−	0.549824i	0.0682216	−	0.0201983i
$742$	10.0919	−	17.4797i	0.370487	−	0.641702i
$743$	8.90875	+	8.26611i	0.326830	+	0.303254i	0.826472	−	0.562978i	$-0.190344\pi$
$743$	8.90875	+	8.26611i	0.326830	+	0.303254i	−0.499641	+	0.866232i	$0.666535\pi$
$744$	11.0377	−	27.2112i	0.404663	−	0.997611i
$745$	6.04722	−	5.61100i	0.221553	−	0.205571i
$746$	−1.23655	−	5.41770i	−0.0452735	−	0.198356i
$747$	−12.7660	−	34.8327i	−0.467084	−	1.27446i
$748$	−0.250547	+	0.120657i	−0.00916091	+	0.00441166i
$749$	1.01642	+	13.5632i	0.0371391	+	0.495587i
$750$	−16.3562	−	20.9946i	−0.597244	−	0.766614i
$751$	1.45323	+	3.70278i	0.0530292	+	0.135116i	0.954934	−	0.296820i	$-0.0959260\pi$
$751$	1.45323	+	3.70278i	0.0530292	+	0.135116i	−0.901904	+	0.431936i	$0.857831\pi$
$752$	−33.5379	+	22.8658i	−1.22300	+	0.833828i
$753$	5.93249	−	10.0112i	0.216192	−	0.364827i
$754$	2.91206	+	2.55564i	0.106051	+	0.0930710i
$755$	−49.7286			−1.80981
$756$	−1.52611	−	0.800060i	−0.0555040	−	0.0290979i
$757$	20.2010	−	25.3313i	0.734219	−	0.920681i	−0.264829	−	0.964295i	$-0.585316\pi$
$757$	20.2010	−	25.3313i	0.734219	−	0.920681i	0.999048	+	0.0436138i	$0.0138871\pi$
$758$	−12.3458	+	31.4565i	−0.448418	+	1.14255i
$759$	10.0177	−	6.66462i	0.363619	−	0.241910i
$760$	1.09174	−	14.5682i	0.0396015	−	0.528445i
$761$	−0.382102	−	0.973581i	−0.0138512	−	0.0352923i	0.923781	−	0.382922i	$-0.125082\pi$
$761$	−0.382102	−	0.973581i	−0.0138512	−	0.0352923i	−0.937632	+	0.347629i	$0.886987\pi$
$762$	4.12090	+	19.0492i	0.149284	+	0.690078i
$763$	−7.35074	+	6.82049i	−0.266115	+	0.246918i
$764$	0.615279	+	0.771535i	0.0222600	+	0.0279132i
$765$	−2.07691	+	8.23320i	−0.0750909	+	0.297672i
$766$	−22.1458			−0.800159
$767$	−4.25812	+	1.31346i	−0.153752	+	0.0474261i
$768$	6.60434	+	4.61345i	0.238313	+	0.166474i
$769$	−3.70329	+	49.4170i	−0.133544	+	1.78202i	0.381015	+	0.924569i	$0.375575\pi$
$769$	−3.70329	+	49.4170i	−0.133544	+	1.78202i	−0.514559	+	0.857455i	$0.672045\pi$
$770$	−5.20667	−	4.83108i	−0.187635	−	0.174100i
$771$	−25.4341	−	45.2314i	−0.915987	−	1.62897i
$772$	−1.25973	+	0.388575i	−0.0453386	+	0.0139851i
$773$	7.84108	+	9.83240i	0.282024	+	0.353647i	0.902585	−	0.430511i	$-0.141667\pi$
$773$	7.84108	+	9.83240i	0.282024	+	0.353647i	−0.620561	+	0.784158i	$0.713095\pi$
$774$	−2.38187	−	11.6488i	−0.0856147	−	0.418707i
$775$	0.888138	+	3.89119i	0.0319029	+	0.139776i
$776$	14.3938	+	2.16951i	0.516707	+	0.0778810i
$777$	−5.71900	+	2.67457i	−0.205168	+	0.0959497i
$778$	35.9426	−	24.5053i	1.28861	−	0.878557i
$779$	−22.8376	+	3.44222i	−0.818243	+	0.123330i
$780$	−0.138465	−	0.364933i	−0.00495786	−	0.0130667i
$781$	0.708471	+	9.45389i	0.0253511	+	0.338287i
$782$	10.3037			0.368460
$783$	−14.1450	+	24.1437i	−0.505501	+	0.862826i
$784$	17.9606			0.641449
$785$	0.110241	+	1.47107i	0.00393468	+	0.0525046i
$786$	−3.26968	−	8.61740i	−0.116625	−	0.307373i
$787$	−2.05042	+	0.309051i	−0.0730897	+	0.0110165i	−0.185485	−	0.982647i	$-0.559386\pi$
$787$	−2.05042	+	0.309051i	−0.0730897	+	0.0110165i	0.112396	+	0.993664i	$0.464148\pi$
$788$	−3.45565	+	2.35602i	−0.123102	+	0.0839298i
$789$	−43.4480	+	20.3191i	−1.54679	+	0.723378i
$790$	−21.2879	−	3.20863i	−0.757389	−	0.114158i
$791$	−3.06808	−	13.4421i	−0.109088	−	0.477948i
$792$	−9.06785	−	3.02417i	−0.322212	−	0.107459i
$793$	1.67533	+	2.10080i	0.0594929	+	0.0746017i
$794$	−29.6320	+	9.14028i	−1.05160	+	0.324376i
$795$	16.1845	+	28.7820i	0.574004	+	1.02079i
$796$	−0.333946	−	0.309856i	−0.0118364	−	0.0109826i
$797$	2.47153	−	32.9802i	0.0875460	−	1.16822i	−0.764454	−	0.644678i	$-0.776991\pi$
$797$	2.47153	−	32.9802i	0.0875460	−	1.16822i	0.852000	−	0.523542i	$-0.175390\pi$
$798$	−8.21414	−	5.73798i	−0.290777	−	0.203122i
$799$	10.6297	−	3.27883i	0.376052	−	0.115997i
$800$	−0.694078			−0.0245394
$801$	18.6383	−	5.28885i	0.658553	−	0.186872i
$802$	−25.9813	−	32.5795i	−0.917432	−	1.15042i
$803$	11.3738	−	10.5533i	0.401373	−	0.372419i
$804$	0.819035	+	3.78605i	0.0288851	+	0.133524i
$805$	8.56592	+	21.8256i	0.301909	+	0.769251i
$806$	0.340928	−	4.54937i	0.0120087	−	0.160245i
$807$	15.9183	−	10.5902i	0.560352	−	0.372794i
$808$	8.19573	−	20.8824i	0.288325	−	0.734639i
$809$	−7.95699	+	9.97774i	−0.279753	+	0.350799i	−0.901779	−	0.432198i	$-0.857738\pi$
$809$	−7.95699	+	9.97774i	−0.279753	+	0.350799i	0.622026	+	0.782996i	$0.286310\pi$
$810$	26.9254	−	16.6190i	0.946061	−	0.583930i
$811$	30.1273			1.05791			0.528957	−	0.848649i	$-0.322583\pi$
$811$	30.1273			1.05791			0.528957	+	0.848649i	$0.322583\pi$
$812$	0.0840888	−	1.78381i	0.00295094	−	0.0625993i
$813$	−13.4228	+	22.6512i	−0.470759	+	0.794412i
$814$	3.13711	−	2.13885i	0.109956	−	0.0749666i
$815$	9.96033	+	25.3785i	0.348895	+	0.888971i
$816$	−5.52752	−	7.09506i	−0.193502	−	0.248377i
$817$	−0.460313	−	6.14246i	−0.0161043	−	0.214897i
$818$	−0.288528	+	0.138948i	−0.0100881	+	0.00485819i
$819$	2.43285	+	0.423391i	0.0850106	+	0.0147945i
$820$	1.03572	+	4.53779i	0.0361689	+	0.158466i
$821$	27.8261	−	25.8188i	0.971137	−	0.901084i	−0.0239871	−	0.999712i	$-0.507636\pi$
$821$	27.8261	−	25.8188i	0.971137	−	0.901084i	0.995124	+	0.0986286i	$0.0314456\pi$
$822$	14.8409	−	36.5872i	0.517637	−	1.27613i
$823$	−20.8518	−	19.3477i	−0.726850	−	0.674418i	0.227274	−	0.973831i	$-0.427019\pi$
$823$	−20.8518	−	19.3477i	−0.726850	−	0.674418i	−0.954124	+	0.299413i	$0.903209\pi$
$824$	−3.08026	+	5.33517i	−0.107306	+	0.185860i
$825$	1.24579	−	0.368839i	0.0433728	−	0.0128413i
$826$	19.0477	+	12.9865i	0.662753	+	0.451857i
$827$	−36.3103	+	17.4861i	−1.26263	+	0.608052i	−0.940870	−	0.338768i	$-0.889990\pi$
$827$	−36.3103	+	17.4861i	−1.26263	+	0.608052i	−0.321764	+	0.946820i	$0.604276\pi$
$828$	−2.45410	−	2.38301i	−0.0852857	−	0.0828154i
$829$	−4.92548			−0.171069			−0.0855345	−	0.996335i	$-0.527260\pi$
$829$	−4.92548			−0.171069			−0.0855345	+	0.996335i	$0.527260\pi$
$830$	−41.5439	+	12.8146i	−1.44201	+	0.444801i
$831$	14.7204	+	18.8950i	0.510646	+	0.655459i
$832$	−3.28125	−	1.01213i	−0.113757	−	0.0350894i
$833$	−4.70339	−	1.45080i	−0.162963	−	0.0502674i
$834$	−8.58728	−	22.6322i	−0.297353	−	0.783690i
$835$	−7.85874	−	5.35800i	−0.271963	−	0.185421i
$836$	0.483683	+	0.232929i	0.0167285	+	0.00805603i
$837$	32.7290	−	3.79847i	1.13128	−	0.131294i
$838$	−6.81511	+	8.54588i	−0.235424	+	0.295213i
$839$	1.36443	+	18.2070i	0.0471053	+	0.628577i	0.969934	+	0.243367i	$0.0782519\pi$
$839$	1.36443	+	18.2070i	0.0471053	+	0.628577i	−0.922829	+	0.385210i	$0.874129\pi$
$840$	9.49596	−	16.0246i	0.327642	−	0.552900i
$841$	−28.8714	−	2.72806i	−0.995565	−	0.0940711i
$842$	−7.01048	+	12.1425i	−0.241597	+	0.418459i
$843$	48.4832	+	24.0301i	1.66985	+	0.827641i
$844$	4.28433	+	0.645759i	0.147473	+	0.0222279i
$845$	−18.8824	−	23.6778i	−0.649574	−	0.814540i
$846$	−36.9289	−	18.8286i	−1.26964	−	0.647340i
$847$	14.6320	−	7.04641i	0.502762	−	0.242118i
$848$	−34.5855	−	5.21293i	−1.18767	−	0.179013i
$849$	−5.59159	+	5.07134i	−0.191903	+	0.174048i
$850$	1.06318	+	0.327947i	0.0364667	+	0.0112485i
$851$	−12.3936	+	1.86803i	−0.424847	+	0.0640353i
$852$	2.58438	−	0.765156i	0.0885396	−	0.0262138i
$853$	18.2432	+	31.5981i	0.624634	+	1.08190i	0.988612	+	0.150490i	$0.0480851\pi$
$853$	18.2432	+	31.5981i	0.624634	+	1.08190i	−0.363978	+	0.931408i	$0.618582\pi$
$854$	3.09332	−	13.5527i	0.105851	−	0.463765i
$855$	14.9265	−	6.77515i	0.510475	−	0.231705i
$856$	19.3266	−	9.30721i	0.660570	−	0.318114i
$857$	−11.6319	+	3.58796i	−0.397337	+	0.122562i	−0.486983	−	0.873411i	$-0.661903\pi$
$857$	−11.6319	+	3.58796i	−0.397337	+	0.122562i	0.0896459	+	0.995974i	$0.471426\pi$
$858$	−1.48498	−	0.0168594i	−0.0506964	−	0.000575571i
$859$	−27.1627	−	25.2033i	−0.926778	−	0.859925i	0.0636472	−	0.997972i	$-0.479727\pi$
$859$	−27.1627	−	25.2033i	−0.926778	−	0.859925i	−0.990426	+	0.138048i	$0.955917\pi$
$860$	−1.22750	+	0.185016i	−0.0418575	+	0.00630900i
$861$	−28.0387	−	8.99865i	−0.955557	−	0.306673i
$862$	16.1867	−	15.0191i	0.551322	−	0.511552i
$863$	4.52326	−	5.67199i	0.153974	−	0.193077i	−0.698862	−	0.715257i	$-0.746310\pi$
$863$	4.52326	−	5.67199i	0.153974	−	0.193077i	0.852835	+	0.522180i	$0.174881\pi$
$864$	−0.622501	+	5.69585i	−0.0211779	+	0.193777i
$865$	−2.38593	−	1.14900i	−0.0811240	−	0.0390673i
$866$	−19.1426	+	48.7745i	−0.650492	+	1.65743i
$867$	−9.57117	−	25.2253i	−0.325054	−	0.856696i
$868$	−1.73737	+	1.18452i	−0.0589702	+	0.0402052i
$869$	−3.64877	+	6.31986i	−0.123776	+	0.214386i
$870$	27.3924	+	18.0273i	0.928689	+	0.611181i
$871$	−2.77568	−	4.80762i	−0.0940503	−	0.162900i
$872$	14.2487	+	6.86182i	0.482522	+	0.232370i
$873$	5.62040	+	15.3355i	0.190222	+	0.519029i
$874$	−12.4021	−	15.5517i	−0.419506	−	0.526044i
$875$	−1.31372	−	17.5304i	−0.0444120	−	0.592636i
$876$	−3.61618	−	2.52608i	−0.122180	−	0.0853484i
$877$	16.2748	+	41.4674i	0.549560	+	1.40026i	0.888251	+	0.459359i	$0.151921\pi$
$877$	16.2748	+	41.4674i	0.549560	+	1.40026i	−0.338691	+	0.940898i	$0.609984\pi$
$878$	44.1302	+	13.6124i	1.48932	+	0.459395i
$879$	−1.12701	+	1.02215i	−0.0380130	+	0.0344762i
$880$	−4.49668	+	11.4573i	−0.151583	+	0.386227i
$881$	−2.77395	+	12.1535i	−0.0934569	+	0.409461i	−0.999918	−	0.0128285i	$-0.995916\pi$
$881$	−2.77395	+	12.1535i	−0.0934569	+	0.409461i	0.906461	+	0.422290i	$0.138774\pi$
$882$	8.80775	+	16.0883i	0.296573	+	0.541722i
$883$	−6.36852	+	27.9023i	−0.214318	+	0.938987i	0.747277	+	0.664513i	$0.231361\pi$
$883$	−6.36852	+	27.9023i	−0.214318	+	0.938987i	−0.961594	+	0.274474i	$0.911496\pi$
$884$	−0.0936145	−	0.0638253i	−0.00314860	−	0.00214668i
$885$	−34.1635	+	15.9771i	−1.14839	+	0.537063i
$886$	9.99350	+	9.27261i	0.335738	+	0.311519i
$887$	9.19224	−	15.9214i	0.308645	−	0.534589i	−0.669421	−	0.742883i	$-0.733458\pi$
$887$	9.19224	−	15.9214i	0.308645	−	0.534589i	0.978066	+	0.208294i	$0.0667911\pi$
$888$	7.22182	+	6.85508i	0.242348	+	0.230041i
$889$	−4.70334	+	11.9839i	−0.157745	+	0.401927i
$890$	−5.05223	−	22.1353i	−0.169351	−	0.741976i
$891$	−1.90951	−	10.5542i	−0.0639710	−	0.353578i
$892$	−2.16013	+	2.70871i	−0.0723264	+	0.0906944i
$893$	−17.7433	−	12.0972i	−0.593756	−	0.404816i
$894$	−7.42938	+	4.94266i	−0.248476	+	0.165307i
$895$	10.4948	−	1.58183i	0.350801	−	0.0528747i
$896$	7.85608	+	20.0170i	0.262453	+	0.668720i
$897$	4.39238	+	2.17703i	0.146657	+	0.0726889i
$898$	16.7667	+	29.0408i	0.559513	+	0.969105i
$899$	17.8859	+	29.0882i	0.596529	+	0.970146i
$900$	−0.177377	−	0.323998i	−0.00591257	−	0.0107999i
$901$	8.63593	+	4.15885i	0.287705	+	0.138551i
$902$	17.5115	+	2.63943i	0.583068	+	0.0878834i
$903$	2.95209	−	7.27777i	0.0982396	−	0.242189i
$904$	−17.9668	+	12.2496i	−0.597567	+	0.407414i
$905$	−4.50038	+	60.0534i	−0.149598	+	1.99624i
$906$	53.0960	+	8.62050i	1.76400	+	0.286397i
$907$	21.4042	−	19.8602i	0.710714	−	0.659446i	−0.239553	−	0.970883i	$-0.577001\pi$
$907$	21.4042	−	19.8602i	0.710714	−	0.659446i	0.950267	+	0.311437i	$0.100810\pi$
$908$	0.778381	+	3.41031i	0.0258315	+	0.113175i
$909$	24.9687	−	3.18550i	0.828161	−	0.105656i
$910$	0.643952	−	2.82134i	0.0213468	−	0.0935265i
$911$	−27.1866	−	47.0886i	−0.900732	−	1.56011i	−0.826546	−	0.562869i	$-0.809697\pi$
$911$	−27.1866	−	47.0886i	−0.900732	−	1.56011i	−0.0741863	−	0.997244i	$-0.523636\pi$
$912$	−4.05558	+	16.8828i	−0.134294	+	0.559046i
$913$	−1.10130	+	14.6958i	−0.0364477	+	0.486360i
$914$	−0.616089	+	8.22113i	−0.0203784	+	0.271931i
$915$	16.4945	+	15.6568i	0.545291	+	0.517599i
$916$	−2.64980	−	4.58959i	−0.0875519	−	0.151644i
$917$	1.35473	−	5.93548i	0.0447372	−	0.196007i
$918$	3.64479	−	8.43069i	0.120296	−	0.278254i
$919$	7.51745	+	32.9361i	0.247978	+	1.08646i	0.933547	+	0.358455i	$0.116696\pi$
$919$	7.51745	+	32.9361i	0.247978	+	1.08646i	−0.685569	+	0.728007i	$0.740447\pi$
$920$	27.1069	−	25.1515i	0.893687	−	0.829221i
$921$	−9.29702	−	24.5028i	−0.306347	−	0.807394i
$922$	−2.55380	+	34.0782i	−0.0841051	+	1.12230i
$923$	−3.19146	+	2.17590i	−0.105048	+	0.0716207i
$924$	0.420670	+	0.539967i	0.0138390	+	0.0177636i
$925$	−1.33828	−	0.201713i	−0.0440023	−	0.00663228i
$926$	13.8333	+	6.66179i	0.454592	+	0.218920i
$927$	−6.91066	−	0.156938i	−0.226976	−	0.00515451i
$928$	−5.62373	+	1.90677i	−0.184608	+	0.0625928i
$929$	−1.93749	−	3.35583i	−0.0635670	−	0.110101i	0.832490	−	0.554039i	$-0.186914\pi$
$929$	−1.93749	−	3.35583i	−0.0635670	−	0.110101i	−0.896057	+	0.443938i	$0.853581\pi$
$930$	−2.44820	−	38.5347i	−0.0802796	−	1.26360i
$931$	3.47150	+	8.84523i	0.113774	+	0.289891i
$932$	−1.54530	+	0.232917i	−0.0506180	+	0.00762943i
$933$	2.99299	+	47.1098i	0.0979862	+	1.54231i
$934$	−3.91788	−	2.67116i	−0.128197	−	0.0874032i
$935$	2.10305	−	2.63714i	0.0687770	−	0.0862437i
$936$	−0.780203	−	3.81565i	−0.0255017	−	0.124719i
$937$	−5.28133	−	23.1390i	−0.172533	−	0.755919i	−0.984950	−	0.172841i	$-0.944705\pi$
$937$	−5.28133	−	23.1390i	−0.172533	−	0.755919i	0.812416	−	0.583078i	$-0.198152\pi$
$938$	−10.4925	+	26.7345i	−0.342593	+	0.872913i
$939$	4.44561	−	18.5065i	0.145077	−	0.603935i
$940$	−2.16392	+	3.74801i	−0.0705792	+	0.122247i
$941$	22.9557	+	21.2998i	0.748335	+	0.694354i	0.959064	−	0.283191i	$-0.0913931\pi$
$941$	22.9557	+	21.2998i	0.748335	+	0.694354i	−0.210728	+	0.977545i	$0.567584\pi$
$942$	0.137305	−	1.58979i	0.00447363	−	0.0517982i
$943$	−48.3011	−	32.9311i	−1.57290	−	1.07238i
$944$	8.88945	−	38.9472i	0.289327	−	1.26762i
$945$	20.8882	+	0.711695i	0.679493	+	0.0231514i
$946$	−1.05099	+	4.60471i	−0.0341708	+	0.149712i
$947$	−4.93282	+	12.5686i	−0.160295	+	0.408425i	−0.988345	−	0.152229i	$-0.951355\pi$
$947$	−4.93282	+	12.5686i	−0.160295	+	0.408425i	0.828050	+	0.560654i	$0.189450\pi$
$948$	1.97545	+	0.633993i	0.0641596	+	0.0205911i
$949$	6.04077	+	1.86333i	0.196092	+	0.0604863i
$950$	−0.784715	−	1.99942i	−0.0254595	−	0.0648698i
$951$	34.6142	−	16.1878i	1.12244	−	0.524926i
$952$	−0.404067	−	5.39190i	−0.0130959	−	0.174752i
$953$	−35.1253	−	44.0458i	−1.13782	−	1.42678i	−0.888806	−	0.458283i	$-0.848465\pi$
$953$	−35.1253	−	44.0458i	−1.13782	−	1.42678i	−0.249015	−	0.968500i	$-0.580107\pi$
$954$	−12.2910	−	33.5366i	−0.397936	−	1.08579i
$955$	−10.7843	−	5.19345i	−0.348972	−	0.168056i
$956$	−2.72215	−	4.71491i	−0.0880408	−	0.152491i
$957$	9.08065	−	6.41093i	0.293536	−	0.207236i
$958$	16.8250	−	29.1417i	0.543590	−	0.941525i
$959$	21.5483	−	14.6914i	0.695829	−	0.474409i
$960$	−28.6870	−	4.65753i	−0.925869	−	0.150321i
$961$	3.36405	−	8.57145i	0.108518	−	0.276498i
$962$	1.39377	+	0.671206i	0.0449371	+	0.0216406i
$963$	19.5738	+	14.0066i	0.630758	+	0.451356i
$964$	2.39802	−	3.00703i	0.0772351	−	0.0968498i
$965$	11.7216	−	10.8761i	0.377333	−	0.350114i
$966$	−5.36248	−	24.7885i	−0.172535	−	0.797556i
$967$	3.55025	−	0.535114i	0.114168	−	0.0172081i	−0.0917096	−	0.995786i	$-0.529233\pi$
$967$	3.55025	−	0.535114i	0.114168	−	0.0172081i	0.205878	+	0.978578i	$0.433995\pi$
$968$	−18.7758	−	17.4214i	−0.603477	−	0.559945i
$969$	2.42579	−	4.09356i	0.0779277	−	0.131504i
$970$	18.2902	−	5.64179i	0.587264	−	0.181147i
$971$	2.49414	−	1.20111i	0.0800408	−	0.0385456i	−0.393435	−	0.919352i	$-0.628713\pi$
$971$	2.49414	−	1.20111i	0.0800408	−	0.0385456i	0.473476	+	0.880807i	$0.342999\pi$
$972$	−2.81793	+	1.16503i	−0.0903851	+	0.0373684i
$973$	3.55799	−	15.5886i	0.114064	−	0.499747i
$974$	−5.38351	−	9.32451i	−0.172499	−	0.298777i
$975$	0.383933	+	0.364436i	0.0122957	+	0.0116713i
$976$	−23.8202	+	3.59031i	−0.762465	+	0.114923i
$977$	30.7808	+	9.49460i	0.984764	+	0.303759i	0.744994	−	0.667071i	$-0.232452\pi$
$977$	30.7808	+	9.49460i	0.984764	+	0.303759i	0.239769	+	0.970830i	$0.422928\pi$
$978$	−6.23542	−	28.8237i	−0.199387	−	0.921680i
$979$	−7.61027	−	1.14706i	−0.243225	−	0.0366603i
$980$	1.72532	−	0.830872i	0.0551134	−	0.0265412i
$981$	0.924000	+	17.7211i	0.0295011	+	0.565790i
$982$	38.9991	+	48.9033i	1.24451	+	1.56057i
$983$	14.2991	+	2.15525i	0.456071	+	0.0687417i	0.373061	−	0.927807i	$-0.378308\pi$
$983$	14.2991	+	2.15525i	0.456071	+	0.0687417i	0.0830106	+	0.996549i	$0.473546\pi$
$984$	2.94466	+	46.3490i	0.0938724	+	1.47755i
$985$	25.3650	−	43.9334i	0.808195	−	1.39984i
$986$	9.51527	−	0.263589i	0.303028	−	0.00839439i
$987$	−13.4203	−	23.8663i	−0.427173	−	0.759673i
$988$	0.0163457	+	0.218119i	0.000520027	+	0.00693927i
$989$	9.72096	−	12.1897i	0.309109	−	0.387610i
$990$	−12.4681	+	1.59068i	−0.396263	+	0.0505551i
$991$	5.73753	+	2.76305i	0.182259	+	0.0877712i	0.522788	−	0.852463i	$-0.324892\pi$
$991$	5.73753	+	2.76305i	0.182259	+	0.0877712i	−0.340529	+	0.940234i	$0.610606\pi$
$992$	5.77719	+	3.93882i	0.183426	+	0.125058i
$993$	−6.30440	+	7.72393i	−0.200064	+	0.245111i
$994$	19.0955	+	5.89017i	0.605672	+	0.186825i
$995$	5.28014	+	1.62871i	0.167392	+	0.0516335i
$996$	4.14976	−	0.577374i	0.131490	−	0.0182948i
$997$	−20.7028	+	6.38595i	−0.655663	+	0.202245i	−0.604698	−	0.796455i	$-0.706706\pi$
$997$	−20.7028	+	6.38595i	−0.655663	+	0.202245i	−0.0509653	+	0.998700i	$0.516230\pi$
$998$	50.8965			1.61110
$999$	−2.85559	+	10.8015i	−0.0903470	+	0.341743i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.q.a.103.21	yes	336
3.2	odd	2		783.2.u.a.712.8		336
9.2	odd	6		783.2.u.a.451.8		336
9.7	even	3	inner	261.2.q.a.16.21	✓	336
29.20	even	7	inner	261.2.q.a.49.21	yes	336
87.20	odd	14		783.2.u.a.658.8		336
261.20	odd	42		783.2.u.a.397.8		336
261.223	even	21	inner	261.2.q.a.223.21	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.q.a.16.21	✓	336	9.7	even	3	inner
261.2.q.a.49.21	yes	336	29.20	even	7	inner
261.2.q.a.103.21	yes	336	1.1	even	1	trivial
261.2.q.a.223.21	yes	336	261.223	even	21	inner
783.2.u.a.397.8		336	261.20	odd	42
783.2.u.a.451.8		336	9.2	odd	6
783.2.u.a.658.8		336	87.20	odd	14
783.2.u.a.712.8		336	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.110732 + 1.47762i) q^{2} +(0.614444 + 1.61940i) q^{3} +(-0.193426 + 0.0291542i) q^{4} +(1.96037 - 1.33656i) q^{5} +(-2.32481 + 1.08723i) q^{6} +(-1.67633 - 0.252667i) q^{7} +(0.594948 + 2.60664i) q^{8} +(-2.24492 + 1.99006i) q^{9} +(2.19200 + 2.74867i) q^{10} +(1.13878 - 0.351267i) q^{11} +(-0.166062 - 0.295320i) q^{12} +(0.355933 + 0.330258i) q^{13} +(0.187721 - 2.50496i) q^{14} +(3.36896 + 2.35338i) q^{15} +(-4.15957 + 1.28306i) q^{16} +1.19292 q^{17} +(-3.18913 - 3.09676i) q^{18} +(-1.43586 - 1.80051i) q^{19} +(-0.340220 + 0.315678i) q^{20} +(-0.620846 - 2.86991i) q^{21} +(0.645137 + 1.64378i) q^{22} +(0.435612 - 5.81284i) q^{23} +(-3.85563 + 2.56509i) q^{24} +(0.229960 - 0.585928i) q^{25} +(-0.448581 + 0.562503i) q^{26} +(-4.60209 - 2.41263i) q^{27} +0.331612 q^{28} +(0.253576 - 5.37919i) q^{29} +(-3.10435 + 5.23863i) q^{30} +(-5.23916 + 3.57200i) q^{31} +(-0.402859 - 1.02647i) q^{32} +(1.26856 + 1.62831i) q^{33} +(0.132094 + 1.76268i) q^{34} +(-3.62394 + 1.74520i) q^{35} +(0.376206 - 0.450378i) q^{36} +(-0.478456 - 2.09625i) q^{37} +(2.50147 - 2.32102i) q^{38} +(-0.316119 + 0.779324i) q^{39} +(4.65024 + 4.31479i) q^{40} +(5.01438 - 8.68515i) q^{41} +(4.17187 - 1.23516i) q^{42} +(2.20994 + 1.50671i) q^{43} +(-0.210028 + 0.101144i) q^{44} +(-1.74103 + 6.90172i) q^{45} +8.63738 q^{46} +(8.91066 - 2.74857i) q^{47} +(-4.63361 - 5.94764i) q^{48} +(-3.94275 - 1.21618i) q^{49} +(0.891241 + 0.274911i) q^{50} +(0.732983 + 1.93181i) q^{51} +(-0.0784751 - 0.0535034i) q^{52} +(7.23932 + 3.48627i) q^{53} +(3.05535 - 7.06727i) q^{54} +(1.76294 - 2.21066i) q^{55} +(-0.338721 - 4.51992i) q^{56} +(2.03349 - 3.43154i) q^{57} +(7.97646 - 0.220961i) q^{58} +(-4.58870 + 7.94786i) q^{59} +(-0.720255 - 0.356986i) q^{60} +(5.47218 + 0.824798i) q^{61} +(-5.85818 - 7.34593i) q^{62} +(4.26605 - 2.76880i) q^{63} +(-6.37164 + 3.06842i) q^{64} +(1.13917 + 0.171702i) q^{65} +(-2.26554 + 2.05475i) q^{66} +(-10.9252 - 3.36998i) q^{67} +(-0.230741 + 0.0347787i) q^{68} +(9.68097 - 2.86624i) q^{69} +(-2.98002 - 5.16154i) q^{70} +(-1.77020 + 7.75573i) q^{71} +(-6.52298 - 4.66770i) q^{72} +(11.7302 - 5.64896i) q^{73} +(3.04447 - 0.939096i) q^{74} +(1.09015 + 0.0123768i) q^{75} +(0.330225 + 0.306404i) q^{76} +(-1.99773 + 0.301109i) q^{77} +(-1.18655 - 0.380806i) q^{78} +(-4.48885 + 4.16505i) q^{79} +(-6.43941 + 8.07477i) q^{80} +(1.07930 - 8.93505i) q^{81} +(13.3886 + 6.44760i) q^{82} +(-4.51785 + 11.5113i) q^{83} +(0.203757 + 0.537013i) q^{84} +(2.33856 - 1.59441i) q^{85} +(-1.98163 + 3.43229i) q^{86} +(8.86687 - 2.89457i) q^{87} +(1.59314 + 2.75940i) q^{88} +(-5.81851 - 2.80205i) q^{89} +(-10.3909 - 1.80834i) q^{90} +(-0.513218 - 0.643555i) q^{91} +(0.0852103 + 1.13705i) q^{92} +(-9.00367 - 6.28950i) q^{93} +(5.04803 + 12.8622i) q^{94} +(-5.22130 - 1.61056i) q^{95} +(1.41473 - 1.28310i) q^{96} +(1.98904 - 5.06799i) q^{97} +(1.36046 - 5.96055i) q^{98} +(-1.85742 + 3.05481i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 5 q^{2} - 10 q^{3} + 21 q^{4} - 9 q^{5} - 40 q^{6} - 5 q^{7} + 2 q^{8} - 6 q^{9} - 28 q^{10} - q^{11} - 22 q^{12} - 5 q^{13} - 9 q^{14} - 26 q^{15} + 21 q^{16} - 60 q^{17} - 90 q^{18} - 20 q^{19}+ \cdots + 196 q^{99}+O(q^{100}) \) 336 * q - 5 * q^2 - 10 * q^3 + 21 * q^4 - 9 * q^5 - 40 * q^6 - 5 * q^7 + 2 * q^8 - 6 * q^9 - 28 * q^10 - q^11 - 22 * q^12 - 5 * q^13 - 9 * q^14 - 26 * q^15 + 21 * q^16 - 60 * q^17 - 90 * q^18 - 20 * q^19 - 15 * q^20 - 2 * q^21 - 13 * q^22 - 32 * q^23 + 44 * q^24 + 15 * q^25 - 4 * q^26 - 43 * q^27 - 72 * q^28 - q^29 - 8 * q^30 - 5 * q^31 + 7 * q^32 - 37 * q^33 - 15 * q^34 + 16 * q^35 - 104 * q^36 - 20 * q^37 + 63 * q^38 + 38 * q^39 + 5 * q^40 - 20 * q^41 + 11 * q^42 - 5 * q^43 - 8 * q^44 + 30 * q^45 - 80 * q^46 + 5 * q^47 + 12 * q^48 - 19 * q^49 - 3 * q^50 - 62 * q^51 + q^52 - 4 * q^53 + 26 * q^54 - 100 * q^55 - 5 * q^56 - 50 * q^57 - 7 * q^58 + 154 * q^59 + 23 * q^60 + 7 * q^61 - 4 * q^62 - 144 * q^63 + 18 * q^64 - 65 * q^65 + 44 * q^66 - 5 * q^67 - 9 * q^68 + 22 * q^69 - 14 * q^70 + 18 * q^71 + 37 * q^72 - 20 * q^73 - 77 * q^74 + 16 * q^75 - 5 * q^76 + 39 * q^77 + 52 * q^78 - 5 * q^79 - 104 * q^80 + 54 * q^81 + 12 * q^82 - 23 * q^83 + 175 * q^84 - 42 * q^85 + 128 * q^86 + 42 * q^87 - 8 * q^88 + 34 * q^89 + 222 * q^90 + 12 * q^91 - 115 * q^92 + 64 * q^93 - 25 * q^94 + 89 * q^95 - 49 * q^96 + 55 * q^97 - 88 * q^98 + 196 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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