LMFDB - Embedded newform 207.2.o.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(5,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("207.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.2
Character	$\chi$	$=$	207.11
Dual form			207.2.o.a.113.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.49814 + 0.119001i) q^{2} +(-0.0685285 - 1.73069i) q^{3} +(4.23560 - 0.404451i) q^{4} +(0.378651 + 0.361043i) q^{5} +(0.377149 + 4.31536i) q^{6} +(0.824181 + 4.27626i) q^{7} +(-5.58197 + 0.802566i) q^{8} +(-2.99061 + 0.237204i) q^{9} +O(q^{10})$	\(q+(-2.49814 + 0.119001i) q^{2} +(-0.0685285 - 1.73069i) q^{3} +(4.23560 - 0.404451i) q^{4} +(0.378651 + 0.361043i) q^{5} +(0.377149 + 4.31536i) q^{6} +(0.824181 + 4.27626i) q^{7} +(-5.58197 + 0.802566i) q^{8} +(-2.99061 + 0.237204i) q^{9} +(-0.988888 - 0.856876i) q^{10} +(0.529942 - 0.273204i) q^{11} +(-0.990241 - 7.30282i) q^{12} +(2.87917 + 0.554914i) q^{13} +(-2.56780 - 10.5846i) q^{14} +(0.598907 - 0.680071i) q^{15} +(5.49309 - 1.05871i) q^{16} +(2.39314 + 5.24024i) q^{17} +(7.44273 - 0.948455i) q^{18} +(-0.361856 - 0.165254i) q^{19} +(1.74984 + 1.37609i) q^{20} +(7.34442 - 1.71945i) q^{21} +(-1.29136 + 0.745567i) q^{22} +(4.58390 + 1.40990i) q^{23} +(1.77152 + 9.60569i) q^{24} +(-0.224885 - 4.72092i) q^{25} +(-7.25860 - 1.04363i) q^{26} +(0.615470 + 5.15957i) q^{27} +(5.22044 + 17.7792i) q^{28} +(-0.232137 + 2.43105i) q^{29} +(-1.41522 + 1.77018i) q^{30} +(5.66225 - 4.45284i) q^{31} +(-2.63571 + 0.639416i) q^{32} +(-0.509149 - 0.898446i) q^{33} +(-6.60199 - 12.8061i) q^{34} +(-1.23184 + 1.91677i) q^{35} +(-12.5711 + 2.21426i) q^{36} +(0.882882 - 3.00682i) q^{37} +(0.923634 + 0.369767i) q^{38} +(0.763082 - 5.02099i) q^{39} +(-2.40338 - 1.71144i) q^{40} +(5.98089 - 6.27258i) q^{41} +(-18.1428 + 5.16943i) q^{42} +(-5.40710 + 6.87569i) q^{43} +(2.13413 - 1.37152i) q^{44} +(-1.21804 - 0.989920i) q^{45} +(-11.6190 - 2.97664i) q^{46} +(-8.38011 - 4.83826i) q^{47} +(-2.20873 - 9.43431i) q^{48} +(-11.1085 + 4.44718i) q^{49} +(1.12359 + 11.7668i) q^{50} +(8.90526 - 4.50090i) q^{51} +(12.4195 + 1.18591i) q^{52} +(5.79633 + 6.68932i) q^{53} +(-2.15153 - 12.8161i) q^{54} +(0.299302 + 0.0878829i) q^{55} +(-8.03254 - 23.2085i) q^{56} +(-0.261207 + 0.637588i) q^{57} +(0.290614 - 6.10073i) q^{58} +(-1.04029 + 5.39755i) q^{59} +(2.26168 - 3.12274i) q^{60} +(-0.724578 + 1.80991i) q^{61} +(-13.6152 + 11.7976i) q^{62} +(-3.47915 - 12.5931i) q^{63} +(-4.22688 + 1.24112i) q^{64} +(0.889852 + 1.24962i) q^{65} +(1.37884 + 2.18386i) q^{66} +(-6.35262 + 12.3224i) q^{67} +(12.2558 + 21.2277i) q^{68} +(2.12598 - 8.02996i) q^{69} +(2.84920 - 4.93496i) q^{70} +(-2.85411 - 4.44108i) q^{71} +(16.5031 - 3.72423i) q^{72} +(4.48681 - 9.82474i) q^{73} +(-1.84775 + 7.61652i) q^{74} +(-8.15506 + 0.712725i) q^{75} +(-1.59952 - 0.553598i) q^{76} +(1.60506 + 2.04100i) q^{77} +(-1.30878 + 12.6339i) q^{78} +(-7.16142 + 2.47859i) q^{79} +(2.46220 + 1.58236i) q^{80} +(8.88747 - 1.41877i) q^{81} +(-14.1947 + 16.3815i) q^{82} +(-1.29567 + 1.23542i) q^{83} +(30.4126 - 10.2534i) q^{84} +(-0.985788 + 2.84825i) q^{85} +(12.6895 - 17.8199i) q^{86} +(4.22331 + 0.235162i) q^{87} +(-2.73886 + 1.95033i) q^{88} +(0.859657 - 5.97905i) q^{89} +(3.16063 + 2.32801i) q^{90} +12.7694i q^{91} +(19.9858 + 4.11782i) q^{92} +(-8.09453 - 9.49447i) q^{93} +(21.5105 + 11.0894i) q^{94} +(-0.0773534 - 0.193219i) q^{95} +(1.28725 + 4.51779i) q^{96} +(12.9876 + 3.15075i) q^{97} +(27.2214 - 12.4316i) q^{98} +(-1.52004 + 0.942751i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−2.49814	+	0.119001i	−1.76645	+	0.0841465i	−0.905450	−	0.424454i	$-0.860466\pi$
$2$	−2.49814	+	0.119001i	−1.76645	+	0.0841465i	−0.861003	+	0.508600i	$0.830163\pi$
$3$	−0.0685285	−	1.73069i	−0.0395650	−	0.999217i
$3$	−0.0685285	−	1.73069i	−0.0395650	−	0.999217i
$4$	4.23560	−	0.404451i	2.11780	−	0.202226i
$5$	0.378651	+	0.361043i	0.169338	+	0.161463i	0.770009	−	0.638033i	$-0.220252\pi$
$5$	0.378651	+	0.361043i	0.169338	+	0.161463i	−0.600671	+	0.799496i	$0.705100\pi$
$6$	0.377149	+	4.31536i	0.153970	+	1.76174i
$7$	0.824181	+	4.27626i	0.311511	+	1.61627i	0.713518	+	0.700637i	$0.247101\pi$
$7$	0.824181	+	4.27626i	0.311511	+	1.61627i	−0.402007	+	0.915637i	$0.631687\pi$
$8$	−5.58197	+	0.802566i	−1.97352	+	0.283750i
$9$	−2.99061	+	0.237204i	−0.996869	+	0.0790680i
$10$	−0.988888	−	0.856876i	−0.312714	−	0.270968i
$11$	0.529942	−	0.273204i	0.159784	−	0.0823742i	−0.376480	−	0.926425i	$-0.622866\pi$
$11$	0.529942	−	0.273204i	0.159784	−	0.0823742i	0.536264	+	0.844051i	$0.319835\pi$
$12$	−0.990241	−	7.30282i	−0.285858	−	2.10814i
$13$	2.87917	+	0.554914i	0.798538	+	0.153905i	0.572168	−	0.820136i	$-0.306102\pi$
$13$	2.87917	+	0.554914i	0.798538	+	0.153905i	0.226369	+	0.974042i	$0.427314\pi$
$14$	−2.56780	−	10.5846i	−0.686273	−	2.82886i
$15$	0.598907	−	0.680071i	0.154637	−	0.175594i
$16$	5.49309	−	1.05871i	1.37327	−	0.264676i
$17$	2.39314	+	5.24024i	0.580421	+	1.27094i	0.941060	+	0.338239i	$0.109831\pi$
$17$	2.39314	+	5.24024i	0.580421	+	1.27094i	−0.360639	+	0.932705i	$0.617441\pi$
$18$	7.44273	−	0.948455i	1.75427	−	0.223553i
$19$	−0.361856	−	0.165254i	−0.0830156	−	0.0379119i	0.373475	−	0.927640i	$-0.378166\pi$
$19$	−0.361856	−	0.165254i	−0.0830156	−	0.0379119i	−0.456490	+	0.889729i	$0.650894\pi$
$20$	1.74984	+	1.37609i	0.391276	+	0.307703i
$21$	7.34442	−	1.71945i	1.60268	−	0.375215i
$22$	−1.29136	+	0.745567i	−0.275319	+	0.158955i
$23$	4.58390	+	1.40990i	0.955810	+	0.293985i
$23$	4.58390	+	1.40990i	0.955810	+	0.293985i
$24$	1.77152	+	9.60569i	0.361610	+	1.96075i
$25$	−0.224885	−	4.72092i	−0.0449770	−	0.944184i
$26$	−7.25860	−	1.04363i	−1.42353	−	0.204673i
$27$	0.615470	+	5.15957i	0.118447	+	0.992960i
$28$	5.22044	+	17.7792i	0.986571	+	3.35995i
$29$	−0.232137	+	2.43105i	−0.0431068	+	0.451435i	0.947991	+	0.318298i	$0.103111\pi$
$29$	−0.232137	+	2.43105i	−0.0431068	+	0.451435i	−0.991098	+	0.133137i	$0.957495\pi$
$30$	−1.41522	+	1.77018i	−0.258383	+	0.323190i
$31$	5.66225	−	4.45284i	1.01697	−	0.799753i	0.0370834	−	0.999312i	$-0.488193\pi$
$31$	5.66225	−	4.45284i	1.01697	−	0.799753i	0.979886	+	0.199559i	$0.0639509\pi$
$32$	−2.63571	+	0.639416i	−0.465932	+	0.113034i
$33$	−0.509149	−	0.898446i	−0.0886315	−	0.156399i
$34$	−6.60199	−	12.8061i	−1.13223	−	2.19622i
$35$	−1.23184	+	1.91677i	−0.208218	+	0.323994i
$36$	−12.5711	+	2.21426i	−2.09518	+	0.369043i
$37$	0.882882	−	3.00682i	0.145145	−	0.494318i	−0.854541	−	0.519384i	$-0.826161\pi$
$37$	0.882882	−	3.00682i	0.145145	−	0.494318i	0.999686	+	0.0250661i	$0.00797961\pi$
$38$	0.923634	+	0.369767i	0.149833	+	0.0599842i
$39$	0.763082	−	5.02099i	0.122191	−	0.804002i
$40$	−2.40338	−	1.71144i	−0.380008	−	0.270602i
$41$	5.98089	−	6.27258i	0.934058	−	0.979612i	−0.0657755	−	0.997834i	$-0.520952\pi$
$41$	5.98089	−	6.27258i	0.934058	−	0.979612i	0.999834	+	0.0182221i	$0.00580060\pi$
$42$	−18.1428	+	5.16943i	−2.79949	+	0.797660i
$43$	−5.40710	+	6.87569i	−0.824575	+	1.04853i	0.173395	+	0.984852i	$0.444526\pi$
$43$	−5.40710	+	6.87569i	−0.824575	+	1.04853i	−0.997970	+	0.0636802i	$0.979716\pi$
$44$	2.13413	−	1.37152i	0.321732	−	0.206765i
$45$	−1.21804	−	0.989920i	−0.181574	−	0.147569i
$46$	−11.6190	−	2.97664i	−1.71313	−	0.438882i
$47$	−8.38011	−	4.83826i	−1.22236	−	0.705733i	−0.256943	−	0.966426i	$-0.582715\pi$
$47$	−8.38011	−	4.83826i	−1.22236	−	0.705733i	−0.965422	+	0.260694i	$0.916049\pi$
$48$	−2.20873	−	9.43431i	−0.318803	−	1.36172i
$49$	−11.1085	+	4.44718i	−1.58693	+	0.635312i
$50$	1.12359	+	11.7668i	0.158900	+	1.66407i
$51$	8.90526	−	4.50090i	1.24699	−	0.630252i
$52$	12.4195	+	1.18591i	1.72227	+	0.164457i
$53$	5.79633	+	6.68932i	0.796187	+	0.918848i	0.998166	−	0.0605415i	$-0.0192828\pi$
$53$	5.79633	+	6.68932i	0.796187	+	0.918848i	−0.201979	+	0.979390i	$0.564737\pi$
$54$	−2.15153	−	12.8161i	−0.292785	−	1.74405i
$55$	0.299302	+	0.0878829i	0.0403578	+	0.0118501i
$56$	−8.03254	−	23.2085i	−1.07339	−	3.10136i
$57$	−0.261207	+	0.637588i	−0.0345977	+	0.0844505i
$58$	0.290614	−	6.10073i	0.0381594	−	0.801065i
$59$	−1.04029	+	5.39755i	−0.135435	+	0.702701i	0.849200	+	0.528072i	$0.177085\pi$
$59$	−1.04029	+	5.39755i	−0.135435	+	0.702701i	−0.984634	+	0.174629i	$0.944127\pi$
$60$	2.26168	−	3.12274i	0.291981	−	0.403144i
$61$	−0.724578	+	1.80991i	−0.0927727	+	0.231735i	−0.967495	−	0.252889i	$-0.918619\pi$
$61$	−0.724578	+	1.80991i	−0.0927727	+	0.231735i	0.874723	+	0.484624i	$0.161044\pi$
$62$	−13.6152	+	11.7976i	−1.72913	+	1.49830i
$63$	−3.47915	−	12.5931i	−0.438331	−	1.58658i
$64$	−4.22688	+	1.24112i	−0.528360	+	0.155140i
$65$	0.889852	+	1.24962i	0.110373	+	0.154997i
$66$	1.37884	+	2.18386i	0.169724	+	0.268814i
$67$	−6.35262	+	12.3224i	−0.776096	+	1.50542i	0.0846668	+	0.996409i	$0.473017\pi$
$67$	−6.35262	+	12.3224i	−0.776096	+	1.50542i	−0.860763	+	0.509007i	$0.830013\pi$
$68$	12.2558	+	21.2277i	1.48623	+	2.57423i
$69$	2.12598	−	8.02996i	0.255938	−	0.966693i
$70$	2.84920	−	4.93496i	0.340545	−	0.589840i
$71$	−2.85411	−	4.44108i	−0.338720	−	0.527059i	0.629551	−	0.776959i	$-0.283239\pi$
$71$	−2.85411	−	4.44108i	−0.338720	−	0.527059i	−0.968272	+	0.249900i	$0.919602\pi$
$72$	16.5031	−	3.72423i	1.94491	−	0.438904i
$73$	4.48681	−	9.82474i	0.525141	−	1.14990i	−0.442315	−	0.896860i	$-0.645843\pi$
$73$	4.48681	−	9.82474i	0.525141	−	1.14990i	0.967456	−	0.253039i	$-0.0814301\pi$
$74$	−1.84775	+	7.61652i	−0.214796	+	0.885403i
$75$	−8.15506	+	0.712725i	−0.941665	+	0.0822984i
$76$	−1.59952	−	0.553598i	−0.183477	−	0.0635021i
$77$	1.60506	+	2.04100i	0.182914	+	0.232594i
$78$	−1.30878	+	12.6339i	−0.148190	+	1.43051i
$79$	−7.16142	+	2.47859i	−0.805723	+	0.278864i	−0.698720	−	0.715395i	$-0.746247\pi$
$79$	−7.16142	+	2.47859i	−0.805723	+	0.278864i	−0.107003	+	0.994259i	$0.534125\pi$
$80$	2.46220	+	1.58236i	0.275282	+	0.176913i
$81$	8.88747	−	1.41877i	0.987497	−	0.157641i
$82$	−14.1947	+	16.3815i	−1.56754	+	1.80904i
$83$	−1.29567	+	1.23542i	−0.142218	+	0.135605i	−0.757849	−	0.652430i	$-0.773750\pi$
$83$	−1.29567	+	1.23542i	−0.142218	+	0.135605i	0.615631	+	0.788035i	$0.288901\pi$
$84$	30.4126	−	10.2534i	3.31829	−	1.11873i
$85$	−0.985788	+	2.84825i	−0.106924	+	0.308936i
$86$	12.6895	−	17.8199i	1.36834	−	1.92157i
$87$	4.22331	+	0.235162i	0.452787	+	0.0252120i
$88$	−2.73886	+	1.95033i	−0.291963	+	0.207906i
$89$	0.859657	−	5.97905i	0.0911235	−	0.633778i	−0.892163	−	0.451713i	$-0.850813\pi$
$89$	0.859657	−	5.97905i	0.0911235	−	0.633778i	0.983287	−	0.182064i	$-0.0582779\pi$
$90$	3.16063	+	2.32801i	0.333160	+	0.245394i
$91$			12.7694i			1.33860i
$92$	19.9858	+	4.11782i	2.08367	+	0.429312i
$93$	−8.09453	−	9.49447i	−0.839364	−	0.984531i
$94$	21.5105	+	11.0894i	2.21863	+	1.14379i
$95$	−0.0773534	−	0.193219i	−0.00793629	−	0.0198239i
$96$	1.28725	+	4.51779i	0.131380	+	0.461095i
$97$	12.9876	+	3.15075i	1.31869	+	0.319911i	0.832540	−	0.553965i	$-0.186886\pi$
$97$	12.9876	+	3.15075i	1.31869	+	0.319911i	0.486150	+	0.873876i	$0.338401\pi$
$98$	27.2214	−	12.4316i	2.74978	−	1.25578i
$99$	−1.52004	+	0.942751i	−0.152770	+	0.0947501i
$100$	−2.86190	−	19.9050i	−0.286190	−	1.99050i
$101$	1.45323	+	1.52410i	0.144602	+	0.151654i	0.792052	−	0.610454i	$-0.209013\pi$
$101$	1.45323	+	1.52410i	0.144602	+	0.151654i	−0.647450	+	0.762108i	$0.724165\pi$
$102$	−21.7110	+	12.3036i	−2.14971	+	1.21824i
$103$	−1.33464	−	0.0635767i	−0.131506	−	0.00626440i	−0.0182742	−	0.999833i	$-0.505817\pi$
$103$	−1.33464	−	0.0635767i	−0.131506	−	0.00626440i	−0.113232	+	0.993569i	$0.536120\pi$
$104$	−16.5168	−	0.786792i	−1.61960	−	0.0771513i
$105$	3.40176	+	2.00058i	0.331978	+	0.195236i
$106$	−15.2761	−	16.0211i	−1.48374	−	1.55611i
$107$	1.04794	+	7.28858i	0.101308	+	0.704614i	0.975655	+	0.219312i	$0.0703812\pi$
$107$	1.04794	+	7.28858i	0.101308	+	0.704614i	−0.874347	+	0.485302i	$0.838710\pi$
$108$	4.69368	+	21.6050i	0.451650	+	2.07894i
$109$	14.5354	−	6.63811i	1.39224	−	0.635816i	0.428719	−	0.903438i	$-0.358965\pi$
$109$	14.5354	−	6.63811i	1.39224	−	0.635816i	0.963524	+	0.267622i	$0.0862379\pi$
$110$	−0.758156	−	0.183927i	−0.0722873	−	0.0175367i
$111$	−5.26439	−	1.32195i	−0.499674	−	0.125474i
$112$	9.05460	+	22.6173i	0.855579	+	2.13713i
$113$	−13.1743	−	6.79184i	−1.23934	−	0.638922i	−0.291162	−	0.956674i	$-0.594042\pi$
$113$	−13.1743	−	6.79184i	−1.23934	−	0.638922i	−0.948174	+	0.317752i	$0.897072\pi$
$114$	0.576659	−	1.62387i	0.0540090	−	0.152089i
$115$	1.22666	+	2.18885i	0.114387	+	0.204111i
$116$			10.3909i			0.964767i
$117$	−8.74209	−	0.976580i	−0.808207	−	0.0902849i
$118$	1.95648	−	13.6076i	0.180109	−	1.25268i
$119$	−20.4362	+	14.5526i	−1.87339	+	1.33403i
$120$	−2.79728	+	4.27680i	−0.255355	+	0.390416i
$121$	−6.17443	+	8.67077i	−0.561312	+	0.788252i
$122$	1.59472	−	4.60763i	0.144379	−	0.417155i
$123$	−11.2658	−	9.92125i	−1.01580	−	0.894569i
$124$	22.1821	−	21.1506i	1.99201	−	1.89938i
$125$	3.33239	−	3.84578i	0.298058	−	0.343977i
$126$	10.1900	+	31.0453i	0.907797	+	2.76574i
$127$	−13.5638	−	8.71694i	−1.20359	−	0.773503i	−0.224020	−	0.974585i	$-0.571918\pi$
$127$	−13.5638	−	8.71694i	−1.20359	−	0.773503i	−0.979575	+	0.201082i	$0.935554\pi$
$128$	15.5376	−	5.37763i	1.37335	−	0.475320i
$129$	12.2703	+	8.88686i	1.08034	+	0.782444i
$130$	−2.37168	−	3.01584i	−0.208010	−	0.264507i
$131$	−8.25957	−	2.85866i	−0.721642	−	0.249763i	−0.0585328	−	0.998285i	$-0.518642\pi$
$131$	−8.25957	−	2.85866i	−0.721642	−	0.249763i	−0.663109	+	0.748523i	$0.730763\pi$
$132$	−2.51993	−	3.59954i	−0.219332	−	0.313299i
$133$	0.408435	−	1.68359i	0.0354158	−	0.145986i
$134$	14.4034	−	31.5390i	1.24426	−	2.72455i
$135$	−1.62978	+	2.17589i	−0.140269	+	0.187271i
$136$	−17.5641	−	27.3302i	−1.50611	−	2.34355i
$137$	3.64695	−	6.31670i	0.311580	−	0.539672i	−0.667125	−	0.744946i	$-0.732475\pi$
$137$	3.64695	−	6.31670i	0.311580	−	0.539672i	0.978705	+	0.205274i	$0.0658085\pi$
$138$	−4.35542	+	20.3130i	−0.370758	+	1.72915i
$139$	−0.209712	−	0.363233i	−0.0177876	−	0.0308090i	0.856995	−	0.515325i	$-0.172329\pi$
$139$	−0.209712	−	0.363233i	−0.0177876	−	0.0308090i	−0.874782	+	0.484516i	$0.838996\pi$
$140$	−4.44233	+	8.61691i	−0.375445	+	0.728262i
$141$	−7.79927	+	14.8350i	−0.656817	+	1.24933i
$142$	7.65846	+	10.7548i	0.642684	+	0.902523i
$143$	1.67740	−	0.492528i	0.140271	−	0.0411873i
$144$	−16.1765	+	4.46916i	−1.34805	+	0.372430i
$145$	−0.965612	+	0.836708i	−0.0801897	+	0.0694848i
$146$	−10.0395	+	25.0775i	−0.830877	+	2.07543i
$147$	8.45797	+	18.9207i	0.697601	+	1.56055i
$148$	2.52343	−	13.0928i	0.207424	−	1.07622i
$149$	0.259686	−	5.45147i	0.0212743	−	0.446602i	−0.962950	−	0.269679i	$-0.913082\pi$
$149$	0.259686	−	5.45147i	0.0212743	−	0.446602i	0.984225	−	0.176923i	$-0.0566145\pi$
$150$	20.2877	−	2.75095i	1.65648	−	0.224614i
$151$	−3.54280	−	10.2363i	−0.288309	−	0.833014i	−0.992416	−	0.122921i	$-0.960774\pi$
$151$	−3.54280	−	10.2363i	−0.288309	−	0.833014i	0.704107	−	0.710093i	$-0.251347\pi$
$152$	2.15250	+	0.632031i	0.174591	+	0.0512645i
$153$	−8.39994	−	15.1038i	−0.679095	−	1.22107i
$154$	−4.25255	−	4.90770i	−0.342680	−	0.395474i
$155$	3.75168	+	0.358242i	0.301342	+	0.0287747i
$156$	1.20137	−	21.5755i	0.0961864	−	1.72743i
$157$	−0.871555	−	9.12734i	−0.0695577	−	0.728441i	−0.961228	−	0.275755i	$-0.911072\pi$
$157$	−0.871555	−	9.12734i	−0.0695577	−	0.728441i	0.891670	−	0.452686i	$-0.149534\pi$
$158$	17.5953	−	7.04409i	1.39981	−	0.560398i
$159$	11.1800	−	10.4901i	0.886628	−	0.831917i
$160$	−1.22887	−	0.709488i	−0.0971506	−	0.0560899i
$161$	−2.25113	+	20.7640i	−0.177414	+	1.63643i
$162$	−22.0333	+	4.60190i	−1.73110	+	0.361560i
$163$	8.85607	−	5.69145i	0.693661	−	0.445789i	−0.145725	−	0.989325i	$-0.546551\pi$
$163$	8.85607	−	5.69145i	0.693661	−	0.445789i	0.839386	+	0.543536i	$0.182915\pi$
$164$	22.7957	−	28.9871i	1.78005	−	2.26352i
$165$	0.131588	−	0.524022i	0.0102441	−	0.0407951i
$166$	3.08975	−	3.24043i	0.239811	−	0.251506i
$167$	−9.28018	−	6.60839i	−0.718122	−	0.511372i	0.161603	−	0.986856i	$-0.448334\pi$
$167$	−9.28018	−	6.60839i	−0.718122	−	0.511372i	−0.879725	+	0.475484i	$0.842273\pi$
$168$	−39.6163	+	15.4923i	−3.05647	+	1.19526i
$169$	−4.08710	−	1.63623i	−0.314393	−	0.125864i
$170$	2.12369	−	7.23263i	0.162880	−	0.554718i
$171$	1.12137	+	0.408377i	0.0857533	+	0.0312294i
$172$	−20.1215	+	31.3096i	−1.53425	+	2.38733i
$173$	5.02641	+	9.74987i	0.382151	+	0.741269i	0.998948	−	0.0458528i	$-0.0146005\pi$
$173$	5.02641	+	9.74987i	0.382151	+	0.741269i	−0.616797	+	0.787122i	$0.711570\pi$
$174$	−10.5784	−	0.0848892i	−0.801948	−	0.00643544i
$175$	20.0025	−	4.85256i	1.51205	−	0.366819i
$176$	2.62178	−	2.06179i	0.197624	−	0.155413i
$177$	9.41280	+	1.43054i	0.707509	+	0.107526i
$178$	−1.43603	+	15.0388i	−0.107635	+	1.12721i
$179$	−0.437707	−	1.49069i	−0.0327157	−	0.111420i	0.941516	−	0.336967i	$-0.109401\pi$
$179$	−0.437707	−	1.49069i	−0.0327157	−	0.111420i	−0.974232	+	0.225548i	$0.927583\pi$
$180$	−5.55950	−	3.70027i	−0.414380	−	0.275802i
$181$	−9.49757	−	1.36554i	−0.705949	−	0.101500i	−0.220016	−	0.975496i	$-0.570611\pi$
$181$	−9.49757	−	1.36554i	−0.705949	−	0.101500i	−0.485933	+	0.873996i	$0.661520\pi$
$182$	−1.51957	−	31.8998i	−0.112638	−	2.36457i
$183$	3.18205	+	1.12999i	0.235224	+	0.0835314i
$184$	−26.7188	−	4.19114i	−1.96973	−	0.308975i
$185$	1.41989	−	0.819776i	0.104393	−	0.0602712i
$186$	21.3511	+	22.7553i	1.56554	+	1.66850i
$187$	2.69988	+	2.12321i	0.197435	+	0.155264i
$188$	−37.4517	−	17.1036i	−2.73144	−	1.24741i
$189$	−21.5564	+	6.88433i	−1.56800	+	0.500761i
$190$	0.216233	+	0.473484i	0.0156872	+	0.0343501i
$191$	9.59856	−	1.84997i	0.694527	−	0.133859i	0.170242	−	0.985402i	$-0.445545\pi$
$191$	9.59856	−	1.84997i	0.694527	−	0.133859i	0.524285	+	0.851543i	$0.324333\pi$
$192$	2.43767	+	7.23039i	0.175924	+	0.521808i
$193$	0.467829	+	1.92842i	0.0336751	+	0.138810i	0.986168	−	0.165752i	$-0.0530050\pi$
$193$	0.467829	+	1.92842i	0.0336751	+	0.138810i	−0.952492	+	0.304562i	$0.901490\pi$
$194$	−32.8198	−	6.32549i	−2.35632	−	0.454144i
$195$	2.10173	−	1.62570i	0.150508	−	0.116419i
$196$	−45.2526	+	23.3294i	−3.23233	+	1.66638i
$197$	−10.1485	−	8.79375i	−0.723053	−	0.626529i	0.213546	−	0.976933i	$-0.431499\pi$
$197$	−10.1485	−	8.79375i	−0.723053	−	0.626529i	−0.936599	+	0.350404i	$0.886044\pi$
$198$	3.68510	−	2.53601i	0.261888	−	0.180227i
$199$	−0.161596	+	0.0232340i	−0.0114552	+	0.00164702i	−0.148040	−	0.988981i	$-0.547296\pi$
$199$	−0.161596	+	0.0232340i	−0.0114552	+	0.00164702i	0.136585	+	0.990628i	$0.456387\pi$
$200$	5.04415	+	26.1715i	0.356675	+	1.85061i
$201$	21.7616	+	10.1500i	1.53494	+	0.715926i
$202$	−3.81174	−	3.63449i	−0.268193	−	0.255722i
$203$	−10.5871	+	1.01095i	−0.743070	+	0.0709546i
$204$	35.8988	−	22.6658i	2.51342	−	1.58692i
$205$	4.52934	−	0.215759i	0.316343	−	0.0150693i
$206$	3.34168			0.232826
$207$	−14.0431	−	3.12914i	−0.976062	−	0.217490i
$208$	16.4030			1.13734
$209$	−0.236911	+	0.0112855i	−0.0163875	+	0.000780632i
$210$	−8.73616	−	4.59291i	−0.602852	−	0.316941i
$211$	22.8905	−	2.18578i	1.57585	−	0.150475i	0.729829	−	0.683630i	$-0.239600\pi$
$211$	22.8905	−	2.18578i	1.57585	−	0.150475i	0.846018	+	0.533154i	$0.178994\pi$
$212$	27.2564	+	25.9890i	1.87198	+	1.78493i
$213$	−7.49057	+	5.24393i	−0.513245	+	0.359308i
$214$	−3.48525	−	18.0832i	−0.238247	−	1.23614i
$215$	−4.52982	+	0.651290i	−0.308931	+	0.0444176i
$216$	−7.57643	−	28.3066i	−0.515511	−	1.92602i
$217$	23.7082	+	20.5433i	1.60942	+	1.39457i
$218$	−35.5216	+	18.3127i	−2.40583	+	1.24029i
$219$	−17.3111	−	7.09202i	−1.16978	−	0.479234i
$220$	1.30327	+	0.251184i	0.0878663	+	0.0169348i
$221$	3.98236	+	16.4155i	0.267883	+	1.10423i
$222$	13.3085	+	2.67594i	0.893208	+	0.179597i
$223$	11.2274	−	2.16390i	0.751840	−	0.144905i	0.201087	−	0.979573i	$-0.435553\pi$
$223$	11.2274	−	2.16390i	0.751840	−	0.144905i	0.550753	+	0.834668i	$0.314341\pi$
$224$	−4.90660	−	10.7440i	−0.327836	−	0.717861i
$225$	1.79236	+	14.0651i	0.119491	+	0.937671i
$226$	33.7196	+	15.3992i	2.24299	+	1.02434i
$227$	−19.6143	−	15.4249i	−1.30185	−	1.02379i	−0.997459	−	0.0712376i	$-0.977305\pi$
$227$	−19.6143	−	15.4249i	−1.30185	−	1.02379i	−0.304389	−	0.952548i	$-0.598452\pi$
$228$	−0.848497	+	2.80621i	−0.0561931	+	0.185846i
$229$	−12.6798	+	7.32068i	−0.837905	+	0.483764i	−0.856551	−	0.516062i	$-0.827398\pi$
$229$	−12.6798	+	7.32068i	−0.837905	+	0.483764i	0.0186469	+	0.999826i	$0.494064\pi$
$230$	−3.32486	−	5.32207i	−0.219235	−	0.350927i
$231$	3.42236	−	2.91774i	0.225174	−	0.191973i
$232$	−0.655296	−	13.7564i	−0.0430223	−	0.903149i
$233$	8.82010	+	1.26814i	0.577824	+	0.0830786i	0.425030	−	0.905179i	$-0.360264\pi$
$233$	8.82010	+	1.26814i	0.577824	+	0.0830786i	0.152794	+	0.988258i	$0.451173\pi$
$234$	21.9552	+	1.39932i	1.43526	+	0.0914762i
$235$	−1.42632	−	4.85759i	−0.0930427	−	0.316874i
$236$	−2.22322	+	23.2826i	−0.144719	+	1.51557i
$237$	4.78045	+	12.2244i	0.310524	+	0.794059i
$238$	49.3208	−	38.7863i	3.19699	−	2.51414i
$239$	17.6418	−	4.27985i	1.14115	−	0.276841i	0.379730	−	0.925097i	$-0.376017\pi$
$239$	17.6418	−	4.27985i	1.14115	−	0.276841i	0.761422	+	0.648257i	$0.224502\pi$
$240$	2.56985	−	4.36975i	0.165883	−	0.282066i
$241$	3.77753	+	7.32739i	0.243332	+	0.471999i	0.978598	−	0.205780i	$-0.0659731\pi$
$241$	3.77753	+	7.32739i	0.243332	+	0.471999i	−0.735266	+	0.677779i	$0.762943\pi$
$242$	14.3928	−	22.3956i	0.925202	−	1.43964i
$243$	−3.06450	−	15.2843i	−0.196588	−	0.980486i
$244$	−2.33701	+	7.95911i	−0.149611	+	0.509530i
$245$	−5.81188	−	2.32672i	−0.371307	−	0.148649i
$246$	29.3242	+	23.4440i	1.86964	+	1.49474i
$247$	−0.950143	−	0.676594i	−0.0604562	−	0.0430507i
$248$	−28.0328	+	29.3999i	−1.78008	+	1.86690i
$249$	2.22692	+	2.15775i	0.141125	+	0.136742i
$250$	−7.86712	+	10.0039i	−0.497560	+	0.632699i
$251$	−16.7739	+	10.7799i	−1.05876	+	0.680422i	−0.949556	−	0.313597i	$-0.898466\pi$
$251$	−16.7739	+	10.7799i	−1.05876	+	0.680422i	−0.109202	+	0.994020i	$0.534829\pi$
$252$	−19.8296	−	51.9323i	−1.24915	−	3.27143i
$253$	2.81440	−	0.505176i	0.176940	−	0.0317601i
$254$	34.9217	+	20.1620i	2.19118	+	1.26508i
$255$	4.99700	+	1.51091i	0.312924	+	0.0946169i
$256$	−29.9957	+	12.0085i	−1.87473	+	0.750530i
$257$	−1.10037	−	11.5236i	−0.0686393	−	0.718823i	−0.962645	−	0.270767i	$-0.912723\pi$
$257$	−1.10037	−	11.5236i	−0.0686393	−	0.718823i	0.894005	−	0.448056i	$-0.147883\pi$
$258$	−31.7104	−	20.7405i	−1.97420	−	1.29124i
$259$	13.5856	+	1.29727i	0.844167	+	0.0806082i
$260$	4.27447	+	4.93300i	0.265091	+	0.305932i
$261$	0.117576	−	7.32538i	0.00727780	−	0.453430i
$262$	20.9738	+	6.15845i	1.29576	+	0.380470i
$263$	−6.71341	−	19.3971i	−0.413967	−	1.19608i	−0.938677	−	0.344798i	$-0.887948\pi$
$263$	−6.71341	−	19.3971i	−0.413967	−	1.19608i	0.524710	−	0.851281i	$-0.324174\pi$
$264$	3.56312	+	4.60647i	0.219295	+	0.283509i
$265$	−0.220346	+	4.62564i	−0.0135358	+	0.284151i
$266$	−0.819978	+	4.25445i	−0.0502761	+	0.260857i
$267$	−10.4068	−	1.07807i	−0.636887	−	0.0659767i
$268$	−21.9234	+	54.7620i	−1.33918	+	3.34512i
$269$	20.5489	−	17.8057i	1.25289	−	1.08563i	0.260122	−	0.965576i	$-0.416237\pi$
$269$	20.5489	−	17.8057i	1.25289	−	1.08563i	0.992767	−	0.120059i	$-0.0383084\pi$
$270$	3.81248	−	5.62962i	0.232020	−	0.342608i
$271$	−0.827991	+	0.243120i	−0.0502969	+	0.0147685i	−0.306784	−	0.951779i	$-0.599253\pi$
$271$	−0.827991	+	0.243120i	−0.0502969	+	0.0147685i	0.256487	+	0.966548i	$0.417435\pi$
$272$	18.6936	+	26.2515i	1.13347	+	1.59173i
$273$	22.1000	−	0.875069i	1.33755	−	0.0529616i
$274$	−8.35890	+	16.2140i	−0.504980	+	0.979524i
$275$	−1.40895	−	2.44037i	−0.0849629	−	0.147160i
$276$	5.75708	−	34.8716i	0.346536	−	2.09902i
$277$	4.71153	−	8.16060i	0.283088	−	0.490323i	−0.689056	−	0.724709i	$-0.741974\pi$
$277$	4.71153	−	8.16060i	0.283088	−	0.490323i	0.972144	+	0.234385i	$0.0753078\pi$
$278$	0.567116	+	0.882450i	0.0340134	+	0.0529258i
$279$	−15.8773	+	14.6598i	−0.950550	+	0.877659i
$280$	5.33773	−	11.6880i	0.318990	−	0.698492i
$281$	3.32250	−	13.6955i	0.198204	−	0.817007i	−0.782682	−	0.622422i	$-0.786149\pi$
$281$	3.32250	−	13.6955i	0.198204	−	0.817007i	0.980886	−	0.194585i	$-0.0623361\pi$
$282$	17.7183	−	37.9880i	1.05511	−	2.26215i
$283$	−11.8987	−	4.11819i	−0.707307	−	0.244801i	−0.0503523	−	0.998732i	$-0.516034\pi$
$283$	−11.8987	−	4.11819i	−0.707307	−	0.244801i	−0.656954	+	0.753930i	$0.728156\pi$
$284$	−13.8851	−	17.6563i	−0.823928	−	1.04771i
$285$	−0.329103	+	0.147116i	−0.0194944	+	0.00871440i
$286$	−4.13177	+	1.43002i	−0.244316	+	0.0845587i
$287$	31.7525	+	20.4061i	1.87429	+	1.20453i
$288$	7.73069	−	2.53744i	0.455535	−	0.149520i
$289$	−10.6004	+	12.2335i	−0.623552	+	0.719617i
$290$	2.31267	−	2.20512i	0.135804	−	0.129489i
$291$	4.56297	−	22.6935i	0.267486	−	1.33031i
$292$	15.0307	−	43.4284i	0.879606	−	2.54145i
$293$	−11.2996	+	15.8681i	−0.660130	+	0.927023i	−0.999909	−	0.0134822i	$-0.995708\pi$
$293$	−11.2996	+	15.8681i	−0.660130	+	0.927023i	0.339779	+	0.940505i	$0.389648\pi$
$294$	−23.3808	−	46.2601i	−1.36359	−	2.69794i
$295$	−2.34265	+	1.66820i	−0.136395	+	0.0971262i
$296$	−2.51505	+	17.4925i	−0.146184	+	1.01673i
$297$	1.73578	+	2.56613i	0.100720	+	0.148902i
$298$			13.6495i			0.790692i
$299$	12.4155	+	6.60302i	0.718004	+	0.381862i
$300$	−34.2533	+	6.31714i	−1.97762	+	0.364720i
$301$	−33.8586	−	17.4553i	−1.95158	−	1.00611i
$302$	10.0685	+	25.1500i	0.579380	+	1.44722i
$303$	2.53817	−	2.61954i	0.145814	−	0.150489i
$304$	−2.16266	−	0.524657i	−0.124037	−	0.0300911i
$305$	−0.927816	+	0.423719i	−0.0531266	+	0.0242621i
$306$	22.7816	+	36.7319i	1.30234	+	2.09982i
$307$	3.01615	+	20.9778i	0.172141	+	1.19726i	0.874351	+	0.485295i	$0.161288\pi$
$307$	3.01615	+	20.9778i	0.172141	+	1.19726i	−0.702210	+	0.711970i	$0.747803\pi$
$308$	7.62388	+	7.99570i	0.434411	+	0.455597i
$309$	−0.0185710	+	2.31421i	−0.00105647	+	0.131651i
$310$	−9.41486	−	0.448485i	−0.534728	−	0.0254722i
$311$	−22.4903	−	1.07134i	−1.27531	−	0.0607503i	−0.601028	−	0.799228i	$-0.705242\pi$
$311$	−22.4903	−	1.07134i	−1.27531	−	0.0607503i	−0.674278	+	0.738478i	$0.735545\pi$
$312$	−0.229825	+	28.6394i	−0.0130113	+	1.62139i
$313$	−13.3805	−	14.0331i	−0.756311	−	0.793196i	0.227237	−	0.973839i	$-0.427031\pi$
$313$	−13.3805	−	14.0331i	−0.756311	−	0.793196i	−0.983549	+	0.180643i	$0.942182\pi$
$314$	3.26343	+	22.6977i	0.184166	+	1.28090i
$315$	3.22927	−	6.02451i	0.181949	−	0.339443i
$316$	−29.3305	+	13.3948i	−1.64997	+	0.753516i
$317$	−12.6945	−	3.07965i	−0.712993	−	0.172970i	−0.137173	−	0.990547i	$-0.543802\pi$
$317$	−12.6945	−	3.07965i	−0.712993	−	0.172970i	−0.575819	+	0.817577i	$0.695317\pi$
$318$	−26.6808	+	27.5361i	−1.49618	+	1.54415i
$319$	0.541154	+	1.35174i	0.0302988	+	0.0756828i
$320$	−2.04861	−	1.05613i	−0.114521	−	0.0590396i
$321$	12.5425	−	2.31314i	0.700054	−	0.129107i
$322$	3.15271	−	52.1392i	0.175694	−	2.90560i
$323$		−	2.29169i		−	0.127513i
$324$	37.0700	−	9.60389i	2.05944	−	0.533549i
$325$	1.97222	−	13.7171i	0.109399	−	0.760888i
$326$	−21.4464	+	15.2719i	−1.18781	+	0.845834i
$327$	−12.4846	−	24.7015i	−0.690402	−	1.36600i
$328$	−28.3510	+	39.8134i	−1.56542	+	2.19833i
$329$	13.7829	−	39.8231i	0.759877	−	2.19552i
$330$	−0.266365	+	1.32474i	−0.0146629	+	0.0729245i
$331$	1.72162	−	1.64156i	0.0946287	−	0.0902282i	−0.641288	−	0.767300i	$-0.721600\pi$
$331$	1.72162	−	1.64156i	0.0946287	−	0.0902282i	0.735917	+	0.677072i	$0.236751\pi$
$332$	−4.98827	+	5.75677i	−0.273767	+	0.315944i
$333$	−1.92712	+	9.20164i	−0.105606	+	0.504247i
$334$	23.9696	+	15.4043i	1.31156	+	0.842888i
$335$	−6.85432	+	2.37230i	−0.374492	+	0.129613i
$336$	38.5231	−	17.2207i	2.10161	−	0.939465i
$337$	−2.04960	−	2.60628i	−0.111649	−	0.141973i	0.727017	−	0.686620i	$-0.240906\pi$
$337$	−2.04960	−	2.60628i	−0.111649	−	0.141973i	−0.838666	+	0.544647i	$0.816664\pi$
$338$	10.4049	+	3.60116i	0.565951	+	0.195877i
$339$	−10.8518	+	23.2662i	−0.589388	+	1.26364i
$340$	−3.02343	+	12.4627i	−0.163969	+	0.675887i
$341$	1.78413	−	3.90670i	0.0966160	−	0.211560i
$342$	−2.84994	−	0.886739i	−0.154107	−	0.0479494i
$343$	−11.6915	−	18.1923i	−0.631280	−	0.982290i
$344$	24.6641	−	42.7194i	1.32980	−	2.30328i
$345$	3.70416	−	2.27298i	0.199425	−	0.122373i
$346$	−13.7169	−	23.7584i	−0.737426	−	1.27726i
$347$	4.55623	−	8.83786i	0.244591	−	0.474441i	−0.734299	−	0.678826i	$-0.762489\pi$
$347$	4.55623	−	8.83786i	0.244591	−	0.474441i	0.978891	+	0.204385i	$0.0655194\pi$
$348$	17.9834	−	0.712070i	0.964011	−	0.0381710i
$349$	4.18237	+	5.87332i	0.223877	+	0.314392i	0.911203	−	0.411958i	$-0.135155\pi$
$349$	4.18237	+	5.87332i	0.223877	+	0.314392i	−0.687326	+	0.726349i	$0.741215\pi$
$350$	−49.3916	+	14.5027i	−2.64009	+	0.775202i
$351$	−1.09108	+	15.1968i	−0.0582375	+	0.811146i
$352$	−1.22208	+	1.05894i	−0.0651372	+	0.0564417i
$353$	0.691792	−	1.72801i	0.0368204	−	0.0919729i	−0.908818	−	0.417193i	$-0.863014\pi$
$353$	0.691792	−	1.72801i	0.0368204	−	0.0919729i	0.945638	+	0.325220i	$0.105438\pi$
$354$	−23.6847	−	2.45356i	−1.25883	−	0.130405i
$355$	0.522710	−	2.71207i	0.0277425	−	0.143942i
$356$	1.22293	−	25.6726i	0.0648154	−	1.36064i
$357$	26.5865	+	34.3716i	1.40711	+	1.81914i
$358$	1.27085	+	3.67187i	0.0671663	+	0.194064i
$359$	7.49860	+	2.20179i	0.395761	+	0.116206i	0.473557	−	0.880763i	$-0.342970\pi$
$359$	7.49860	+	2.20179i	0.395761	+	0.116206i	−0.0777956	+	0.996969i	$0.524788\pi$
$360$	7.59352	+	4.54815i	0.400214	+	0.239709i
$361$	−12.3387	−	14.2396i	−0.649406	−	0.749455i
$362$	23.8888	+	2.28110i	1.25557	+	0.119892i
$363$	15.4296	+	10.0919i	0.809843	+	0.529685i
$364$	5.16460	+	54.0862i	0.270699	+	2.83489i
$365$	5.24609	−	2.10022i	0.274593	−	0.109930i
$366$	−8.08368	−	2.44421i	−0.422541	−	0.127761i
$367$	7.59002	+	4.38210i	0.396196	+	0.228744i	0.684841	−	0.728692i	$-0.259872\pi$
$367$	7.59002	+	4.38210i	0.396196	+	0.228744i	−0.288645	+	0.957436i	$0.593205\pi$
$368$	26.6725	+	2.89170i	1.39040	+	0.150741i
$369$	−16.3986	+	20.1775i	−0.853678	+	1.05040i
$370$	−3.44954	+	2.21689i	−0.179333	+	0.115250i
$371$	−23.8280	+	30.2998i	−1.23709	+	1.57309i
$372$	−38.1253	−	36.9410i	−1.97670	−	1.91530i
$373$	9.31564	−	9.76996i	0.482346	−	0.505869i	−0.436924	−	0.899499i	$-0.643932\pi$
$373$	9.31564	−	9.76996i	0.482346	−	0.505869i	0.919269	+	0.393629i	$0.128781\pi$
$374$	−6.99735	−	4.98279i	−0.361824	−	0.257654i
$375$	−6.88423	−	5.50380i	−0.355500	−	0.284215i
$376$	50.6606	+	20.2814i	2.61262	+	1.04594i
$377$	−2.01739	+	6.87059i	−0.103901	+	0.353853i
$378$	53.0317	−	19.7633i	2.72766	−	1.01651i
$379$	15.4725	−	24.0756i	0.794767	−	1.23668i	−0.173021	−	0.984918i	$-0.555353\pi$
$379$	15.4725	−	24.0756i	0.794767	−	1.23668i	0.967789	−	0.251764i	$-0.0810107\pi$
$380$	−0.405786	−	0.787115i	−0.0208164	−	0.0403781i
$381$	−14.1568	+	24.0722i	−0.725277	+	1.23326i
$382$	−23.7584	+	5.76372i	−1.21559	+	0.294898i
$383$	−13.8057	+	10.8569i	−0.705439	+	0.554763i	−0.905150	−	0.425091i	$-0.860242\pi$
$383$	−13.8057	+	10.8569i	−0.705439	+	0.554763i	0.199711	+	0.979855i	$0.436000\pi$
$384$	−10.3718	−	26.5224i	−0.529284	−	1.35346i
$385$	−0.129131	+	1.35232i	−0.00658113	+	0.0689207i
$386$	−1.39819	−	4.76178i	−0.0711658	−	0.242368i
$387$	14.5396	−	21.8451i	0.739088	−	1.11045i
$388$	56.2846	+	8.09251i	2.85742	+	0.410835i
$389$	−0.174393	−	3.66096i	−0.00884208	−	0.185618i	−0.998967	−	0.0454330i	$-0.985533\pi$
$389$	−0.174393	−	3.66096i	−0.00884208	−	0.185618i	0.990125	−	0.140185i	$-0.0447698\pi$
$390$	−5.05697	+	4.31133i	−0.256069	+	0.218313i
$391$	3.58169	+	27.3948i	0.181134	+	1.38542i
$392$	58.4383	−	33.7394i	2.95158	−	1.70410i
$393$	−4.38146	+	14.4907i	−0.221015	+	0.730959i
$394$	26.3989	+	20.7603i	1.32996	+	1.04589i
$395$	−3.60656	−	1.64706i	−0.181466	−	0.0828726i
$396$	−6.05701	+	4.60790i	−0.304376	+	0.231556i
$397$	9.49735	+	20.7963i	0.476658	+	1.04374i	0.983369	+	0.181620i	$0.0581341\pi$
$397$	9.49735	+	20.7963i	0.476658	+	1.04374i	−0.506710	+	0.862116i	$0.669139\pi$
$398$	0.400925	−	0.0772720i	0.0200966	−	0.00387329i
$399$	−2.94177	−	0.591502i	−0.147273	−	0.0296121i
$400$	−6.23338	−	25.6943i	−0.311669	−	1.28472i
$401$	19.3623	+	3.73178i	0.966907	+	0.186356i	0.648177	−	0.761489i	$-0.275532\pi$
$401$	19.3623	+	3.73178i	0.966907	+	0.186356i	0.318730	+	0.947846i	$0.396744\pi$
$402$	−55.5714	−	22.7665i	−2.77165	−	1.13549i
$403$	18.7735	−	9.67841i	0.935175	−	0.482116i
$404$	6.77173	+	5.86774i	0.336906	+	0.291931i
$405$	3.87748	+	2.67154i	0.192674	+	0.132750i
$406$	26.3278	−	3.78537i	1.30663	−	0.187865i
$407$	−0.353599	−	1.83465i	−0.0175273	−	0.0909401i
$408$	−46.0966	+	32.2709i	−2.28212	+	1.59765i
$409$	8.02684	+	7.65357i	0.396902	+	0.378445i	0.862080	−	0.506772i	$-0.169161\pi$
$409$	8.02684	+	7.65357i	0.396902	+	0.378445i	−0.465179	+	0.885217i	$0.654010\pi$
$410$	−11.2893	+	1.07799i	−0.557537	+	0.0532383i
$411$	−11.1822	−	5.87888i	−0.551577	−	0.289984i
$412$	−5.67871	+	0.270511i	−0.279770	+	0.0133271i
$413$	−23.9387			−1.17795
$414$	35.4540	+	6.14589i	1.74247	+	0.302054i
$415$	−0.936645			−0.0459781
$416$	−7.94346	+	0.378394i	−0.389460	+	0.0185523i
$417$	−0.614273	+	0.387840i	−0.0300811	+	0.0189926i
$418$	0.590495	−	0.0563854i	0.0288820	−	0.00275790i
$419$	9.29579	+	8.86352i	0.454129	+	0.433011i	0.882301	−	0.470686i	$-0.155994\pi$
$419$	9.29579	+	8.86352i	0.454129	+	0.433011i	−0.428172	+	0.903697i	$0.640842\pi$
$420$	15.2177	+	7.09780i	0.742546	+	0.346337i
$421$	−1.66182	−	8.62236i	−0.0809924	−	0.420228i	−0.999681	−	0.0252464i	$-0.991963\pi$
$421$	−1.66182	−	8.62236i	−0.0809924	−	0.420228i	0.918689	−	0.394982i	$-0.129249\pi$
$422$	−56.9236	+	8.18438i	−2.77100	+	0.398409i
$423$	26.2093	+	12.4815i	1.27434	+	0.606873i
$424$	−37.7235	−	32.6876i	−1.83202	−	1.58745i
$425$	24.2006	−	12.4763i	1.17390	−	0.605187i
$426$	18.0885	−	13.9915i	0.876389	−	0.677889i
$427$	−8.33681	−	1.60679i	−0.403447	−	0.0777580i
$428$	7.38654	+	30.4477i	0.357042	+	1.47175i
$429$	−0.967366	−	2.86931i	−0.0467049	−	0.138532i
$430$	11.2386	−	2.16607i	0.541975	−	0.104457i
$431$	−10.6441	−	23.3073i	−0.512708	−	1.12267i	−0.972127	−	0.234455i	$-0.924670\pi$
$431$	−10.6441	−	23.3073i	−0.512708	−	1.12267i	0.459419	−	0.888220i	$-0.348058\pi$
$432$	8.84330	+	27.6904i	0.425473	+	1.33225i
$433$	−13.1044	−	5.98458i	−0.629758	−	0.287601i	0.0748533	−	0.997195i	$-0.476151\pi$
$433$	−13.1044	−	5.98458i	−0.629758	−	0.287601i	−0.704611	+	0.709594i	$0.748878\pi$
$434$	−61.6711	−	48.4987i	−2.96031	−	2.32801i
$435$	1.51426	+	1.61384i	0.0726031	+	0.0773778i
$436$	58.8816	−	33.9953i	2.81992	−	1.62808i
$437$	−1.42572	−	1.26769i	−0.0682016	−	0.0606419i
$438$	44.0895	+	15.6568i	2.10668	+	0.748112i
$439$	1.43826	+	30.1928i	0.0686444	+	1.44102i	0.726131	+	0.687557i	$0.241317\pi$
$439$	1.43826	+	30.1928i	0.0686444	+	1.44102i	−0.657486	+	0.753467i	$0.728380\pi$
$440$	−1.74122	−	0.250350i	−0.0830096	−	0.0119350i
$441$	32.1664	−	15.9348i	1.53173	−	0.758798i
$442$	−11.9020	−	40.5344i	−0.566119	−	1.92802i
$443$	−1.91475	+	20.0522i	−0.0909726	+	0.952708i	0.828614	+	0.559820i	$0.189130\pi$
$443$	−1.91475	+	20.0522i	−0.0909726	+	0.952708i	−0.919587	+	0.392888i	$0.871476\pi$
$444$	−22.8325	−	3.47005i	−1.08358	−	0.164681i
$445$	2.48420	−	1.95360i	0.117762	−	0.0926094i
$446$	−27.7900	+	6.74179i	−1.31590	+	0.319233i
$447$	−9.45263	−	0.0758551i	−0.447094	−	0.00358782i
$448$	−8.79108	−	17.0523i	−0.415339	−	0.805646i
$449$	7.68955	−	11.9652i	0.362892	−	0.564672i	−0.611015	−	0.791619i	$-0.709238\pi$
$449$	7.68955	−	11.9652i	0.362892	−	0.564672i	0.973907	+	0.226948i	$0.0728747\pi$
$450$	−6.15134	−	34.9232i	−0.289977	−	1.64630i
$451$	1.45583	−	4.95811i	0.0685525	−	0.233468i
$452$	−58.5482	−	23.4392i	−2.75387	−	1.10249i
$453$	−17.4730	+	6.83298i	−0.820955	+	0.321042i
$454$	50.8349	+	36.1994i	2.38580	+	1.69892i
$455$	−4.61031	+	4.83515i	−0.216134	+	0.226675i
$456$	0.946345	−	3.76863i	0.0443167	−	0.176482i
$457$	−8.20759	+	10.4368i	−0.383935	+	0.488213i	−0.939156	−	0.343490i	$-0.888391\pi$
$457$	−8.20759	+	10.4368i	−0.383935	+	0.488213i	0.555222	+	0.831702i	$0.312633\pi$
$458$	30.8048	−	19.7970i	1.43941	−	0.925054i
$459$	−25.5645	+	15.5728i	−1.19325	+	0.726875i
$460$	6.08095	+	8.77496i	0.283526	+	0.409135i
$461$	6.52808	+	3.76899i	0.304043	+	0.175539i	0.644258	−	0.764809i	$-0.277166\pi$
$461$	6.52808	+	3.76899i	0.304043	+	0.175539i	−0.340215	+	0.940348i	$0.610500\pi$
$462$	−8.20231	+	7.69618i	−0.381606	+	0.358059i
$463$	−17.3028	+	6.92701i	−0.804131	+	0.321925i	−0.737064	−	0.675823i	$-0.763788\pi$
$463$	−17.3028	+	6.92701i	−0.804131	+	0.321925i	−0.0670670	+	0.997748i	$0.521364\pi$
$464$	1.29862	+	13.5997i	0.0602868	+	0.631352i
$465$	0.362910	−	6.51756i	0.0168296	−	0.302245i
$466$	−22.1848	−	2.11839i	−1.02769	−	0.0981325i
$467$	−5.38765	−	6.21768i	−0.249311	−	0.287720i	0.617276	−	0.786747i	$-0.288236\pi$
$467$	−5.38765	−	6.21768i	−0.249311	−	0.287720i	−0.866586	+	0.499027i	$0.833691\pi$
$468$	−37.4230	−	0.600660i	−1.72988	−	0.0277655i
$469$	−57.9293	−	17.0096i	−2.67493	−	0.785429i
$470$	4.14120	+	11.9652i	0.191019	+	0.551914i
$471$	−15.7369	+	2.13388i	−0.725119	+	0.0983240i
$472$	1.47499	−	30.9639i	0.0678920	−	1.42523i
$473$	−0.986984	+	5.12096i	−0.0453816	+	0.235462i
$474$	−13.3970	−	29.9694i	−0.615342	−	1.37654i
$475$	−0.698776	+	1.74546i	−0.0320620	+	0.0800871i
$476$	−80.6740	+	69.9044i	−3.69769	+	3.20406i
$477$	−18.9213	−	18.6302i	−0.866345	−	0.853019i
$478$	−43.5624	+	12.7911i	−1.99250	+	0.585050i
$479$	4.87072	+	6.83997i	0.222549	+	0.312526i	0.910722	−	0.413021i	$-0.135526\pi$
$479$	4.87072	+	6.83997i	0.222549	+	0.312526i	−0.688173	+	0.725547i	$0.741587\pi$
$480$	−1.14369	+	2.17542i	−0.0522023	+	0.0992938i
$481$	4.21049	−	8.16721i	0.191982	−	0.372393i
$482$	−10.3088	−	17.8553i	−0.469552	−	0.813288i
$483$	36.0904	+	2.47310i	1.64217	+	0.112530i
$484$	−22.6455	+	39.2232i	−1.02934	+	1.78287i
$485$	3.78020	+	5.88211i	0.171650	+	0.267093i
$486$	9.47440	+	37.8176i	0.429767	+	1.71544i
$487$	0.765532	−	1.67628i	0.0346896	−	0.0759595i	−0.891494	−	0.453033i	$-0.850342\pi$
$487$	0.765532	−	1.67628i	0.0346896	−	0.0759595i	0.926184	+	0.377073i	$0.123069\pi$
$488$	2.59200	−	10.6844i	0.117334	−	0.483659i
$489$	−10.4571	−	14.9371i	−0.472884	−	0.675480i
$490$	14.7958	+	5.12087i	0.668405	+	0.231337i
$491$	14.1768	+	18.0273i	0.639791	+	0.813560i	0.992509	−	0.122169i	$-0.0389851\pi$
$491$	14.1768	+	18.0273i	0.639791	+	0.813560i	−0.352718	+	0.935730i	$0.614743\pi$
$492$	−51.7301	−	37.4660i	−2.33217	−	1.68910i
$493$	−13.2948	+	4.60138i	−0.598769	+	0.207236i
$494$	2.45411	+	1.57716i	0.110416	+	0.0709598i
$495$	−0.915940	−	0.191828i	−0.0411684	−	0.00862201i
$496$	26.3890	−	30.4545i	1.18490	−	1.36745i
$497$	16.6389	−	15.8652i	0.746357	−	0.711650i
$498$	−5.81994	−	5.12535i	−0.260798	−	0.229672i
$499$	2.85343	−	8.24444i	0.127737	−	0.369072i	−0.862939	−	0.505307i	$-0.831379\pi$
$499$	2.85343	−	8.24444i	0.127737	−	0.369072i	0.990676	+	0.136235i	$0.0435004\pi$
$500$	12.5592	−	17.6370i	0.561666	−	0.788750i
$501$	−10.8011	+	16.5140i	−0.482560	+	0.737792i
$502$	40.6207	−	28.9259i	1.81299	−	1.29102i
$503$	0.731035	−	5.08446i	0.0325952	−	0.226705i	−0.967012	−	0.254731i	$-0.918013\pi$
$503$	0.731035	−	5.08446i	0.0325952	−	0.226705i	0.999607	+	0.0280261i	$0.00892216\pi$
$504$	29.5273	+	67.5021i	1.31525	+	3.00678i
$505$			1.10178i			0.0490286i
$506$	−6.97064	+	1.59692i	−0.309883	+	0.0709916i
$507$	−2.55173	+	7.18566i	−0.113326	+	0.319126i
$508$	−60.9765	−	31.4356i	−2.70540	−	1.39473i
$509$	−2.51014	−	6.27003i	−0.111260	−	0.277914i	0.862279	−	0.506433i	$-0.169036\pi$
$509$	−2.51014	−	6.27003i	−0.111260	−	0.277914i	−0.973540	+	0.228518i	$0.926612\pi$
$510$	−12.6630	−	3.17982i	−0.560728	−	0.140805i
$511$	45.7111	+	11.0894i	2.02214	+	0.490565i
$512$	43.5923	−	19.9080i	1.92653	−	0.879815i
$513$	0.629930	−	1.96873i	0.0278121	−	0.0869217i
$514$	4.12021	+	28.6567i	0.181735	+	1.26399i
$515$	−0.482408	−	0.505935i	−0.0212574	−	0.0222942i
$516$	55.5662	+	32.6785i	2.44617	+	1.43859i
$517$	−5.76281	−	0.274516i	−0.253448	−	0.0120732i
$518$	−34.0931	−	1.62405i	−1.49796	−	0.0713568i
$519$	16.5296	−	9.36732i	0.725569	−	0.411180i
$520$	−5.97003	−	6.26119i	−0.261803	−	0.274571i
$521$	−1.17681	−	8.18491i	−0.0515571	−	0.358587i	−0.999226	−	0.0393330i	$-0.987477\pi$
$521$	−1.17681	−	8.18491i	−0.0515571	−	0.358587i	0.947669	−	0.319254i	$-0.103432\pi$
$522$	0.578006	+	18.3138i	0.0252986	+	0.801574i
$523$	28.5892	−	13.0563i	1.25012	−	0.570911i	0.323257	−	0.946311i	$-0.395222\pi$
$523$	28.5892	−	13.0563i	1.25012	−	0.570911i	0.926863	+	0.375401i	$0.122495\pi$
$524$	−36.1405	−	8.76758i	−1.57880	−	0.383013i
$525$	−9.76904	−	34.2857i	−0.426356	−	1.49635i
$526$	19.0793	+	47.6579i	0.831899	+	2.07798i
$527$	36.8845	+	19.0153i	1.60671	+	0.828318i
$528$	−3.74799	−	4.39620i	−0.163110	−	0.191320i
$529$	19.0244	+	12.9257i	0.827146	+	0.561987i
$530$		−	11.5817i		−	0.503078i
$531$	1.83079	−	16.3887i	0.0794494	−	0.711210i
$532$	1.04904	−	7.29621i	0.0454815	−	0.316331i
$533$	20.7007	−	14.7409i	0.896649	−	0.638501i
$534$	26.1260	+	1.45474i	1.13058	+	0.0629530i
$535$	−2.23469	+	3.13818i	−0.0966140	+	0.135675i
$536$	25.5706	−	73.8815i	1.10448	−	3.19119i
$537$	−2.54994	+	0.859691i	−0.110038	+	0.0370984i
$538$	−49.2152	+	46.9266i	−2.12182	+	2.02315i
$539$	−4.67189	+	5.39165i	−0.201232	+	0.232235i
$540$	−6.02306	+	9.87536i	−0.259191	+	0.424968i
$541$	22.4958	+	14.4571i	0.967168	+	0.621561i	0.925973	−	0.377590i	$-0.123247\pi$
$541$	22.4958	+	14.4571i	0.967168	+	0.621561i	0.0411950	+	0.999151i	$0.486884\pi$
$542$	2.03951	−	0.705880i	0.0876044	−	0.0303202i
$543$	−1.71249	+	16.5310i	−0.0734898	+	0.709412i
$544$	−9.65830	−	12.2815i	−0.414096	−	0.526566i
$545$	7.90050	+	2.73439i	0.338420	+	0.117128i
$546$	−55.1047	+	4.81597i	−2.35826	+	0.206104i
$547$	−2.74974	+	11.3346i	−0.117570	+	0.484632i	0.882331	+	0.470629i	$0.155973\pi$
$547$	−2.74974	+	11.3346i	−0.117570	+	0.484632i	−0.999902	+	0.0140036i	$0.995542\pi$
$548$	12.8922	−	28.2301i	0.550729	−	1.20593i
$549$	1.73761	−	5.58460i	0.0741594	−	0.238345i
$550$	3.81017	+	5.92873i	0.162466	+	0.252802i
$551$	0.485742	−	0.841329i	0.0206933	−	0.0358418i
$552$	−5.42259	+	46.5292i	−0.230801	+	1.98042i
$553$	−16.5014	−	28.5813i	−0.701711	−	1.21540i
$554$	−10.7989	+	20.9470i	−0.458803	+	0.889953i
$555$	−1.51609	−	2.40123i	−0.0643543	−	0.101926i
$556$	−1.03517	−	1.45369i	−0.0439009	−	0.0616502i
$557$	−17.0039	+	4.99280i	−0.720479	+	0.211552i	−0.621362	−	0.783524i	$-0.713420\pi$
$557$	−17.0039	+	4.99280i	−0.720479	+	0.211552i	−0.0991177	+	0.995076i	$0.531602\pi$
$558$	37.9193	−	38.5117i	1.60525	−	1.63033i
$559$	−19.3834	+	16.7958i	−0.819829	+	0.710386i
$560$	−4.73728	+	11.8332i	−0.200187	+	0.500042i
$561$	3.48961	−	4.81817i	0.147331	−	0.203423i
$562$	−6.67029	+	34.6088i	−0.281369	+	1.45988i
$563$	−0.0575159	+	1.20741i	−0.00242401	+	0.0508862i	−0.999755	−	0.0221234i	$-0.992957\pi$
$563$	−0.0575159	+	1.20741i	−0.00242401	+	0.0508862i	0.997331	+	0.0730096i	$0.0232604\pi$
$564$	−27.0346	+	65.9895i	−1.13836	+	2.77866i
$565$	−2.53632	−	7.32823i	−0.106704	−	0.308301i
$566$	30.2148	+	8.87187i	1.27002	+	0.372912i
$567$	13.3919	+	36.8358i	0.562407	+	1.54696i
$568$	19.4958	+	22.4994i	0.818026	+	0.944053i
$569$	6.69076	+	0.638891i	0.280491	+	0.0267837i	0.234354	−	0.972151i	$-0.424703\pi$
$569$	6.69076	+	0.638891i	0.280491	+	0.0267837i	0.0461378	+	0.998935i	$0.485309\pi$
$570$	0.804638	−	0.406680i	0.0337026	−	0.0170340i
$571$	−3.06601	−	32.1087i	−0.128309	−	1.34371i	−0.798713	−	0.601712i	$-0.794486\pi$
$571$	−3.06601	−	32.1087i	−0.128309	−	1.34371i	0.670405	−	0.741996i	$-0.266120\pi$
$572$	6.90559	−	2.76458i	0.288737	−	0.115593i
$573$	−3.85951	−	16.4854i	−0.161233	−	0.688687i
$574$	−81.7506	−	47.1987i	−3.41220	−	1.97004i
$575$	5.62518	−	21.9573i	0.234586	−	0.915683i
$576$	12.3465	−	4.71435i	0.514439	−	0.196431i
$577$	26.8568	−	17.2598i	1.11806	−	0.718535i	0.155027	−	0.987910i	$-0.450453\pi$
$577$	26.8568	−	17.2598i	1.11806	−	0.718535i	0.963035	+	0.269375i	$0.0868171\pi$
$578$	25.0254	−	31.8224i	1.04092	−	1.32364i
$579$	3.30544	−	0.941820i	0.137369	−	0.0391407i
$580$	−3.75154	+	3.93451i	−0.155774	+	0.163371i
$581$	−6.35083	−	4.52240i	−0.263477	−	0.187621i
$582$	−8.69841	+	57.2345i	−0.360560	+	2.37245i
$583$	4.89927	+	1.96137i	0.202907	+	0.0812317i
$584$	−17.1602	+	58.4424i	−0.710095	+	2.41836i
$585$	−2.95761	−	3.52605i	−0.122282	−	0.145784i
$586$	26.3397	−	40.9854i	1.08808	−	1.69309i
$587$	16.0754	+	31.1818i	0.663501	+	1.28701i	0.944880	+	0.327416i	$0.106178\pi$
$587$	16.0754	+	31.1818i	0.663501	+	1.28701i	−0.281380	+	0.959597i	$0.590792\pi$
$588$	43.4771	+	76.7198i	1.79297	+	3.16387i
$589$	−2.78477	+	0.675578i	−0.114744	+	0.0278367i
$590$	5.65376	−	4.44617i	0.232762	−	0.183046i
$591$	−14.5238	+	18.1666i	−0.597431	+	0.747275i
$592$	1.66641	−	17.4514i	0.0684890	−	0.717249i
$593$	9.21620	+	31.3875i	0.378464	+	1.28893i	0.900071	+	0.435744i	$0.143515\pi$
$593$	9.21620	+	31.3875i	0.378464	+	1.28893i	−0.521606	+	0.853186i	$0.674667\pi$
$594$	−4.64160	−	6.20399i	−0.190447	−	0.254553i
$595$	−12.9923	−	1.86801i	−0.532632	−	0.0765810i
$596$	−1.10493	−	23.1953i	−0.0452597	−	0.950117i
$597$	0.0512849	+	0.278081i	0.00209895	+	0.0113811i
$598$	−31.8013	−	15.0178i	−1.30045	−	0.614124i
$599$	38.4469	−	22.1973i	1.57090	−	0.906958i	0.574839	−	0.818267i	$-0.305065\pi$
$599$	38.4469	−	22.1973i	1.57090	−	0.906958i	0.996059	−	0.0886914i	$-0.0282685\pi$
$600$	44.9493	−	10.5234i	1.83505	−	0.429615i
$601$	−22.2700	−	17.5134i	−0.908414	−	0.714384i	0.0503070	−	0.998734i	$-0.483980\pi$
$601$	−22.2700	−	17.5134i	−0.908414	−	0.714384i	−0.958721	+	0.284349i	$0.908222\pi$
$602$	86.6609	+	39.5767i	3.53203	+	1.61303i
$603$	16.0753	−	38.3582i	0.654636	−	1.56207i
$604$	−19.1460	−	41.9238i	−0.779038	−	1.70586i
$605$	−5.46847	+	1.05396i	−0.222325	+	0.0428496i
$606$	−6.02898	+	6.84603i	−0.244910	+	0.278101i
$607$	1.62415	+	6.69484i	0.0659222	+	0.271735i	0.995228	−	0.0975760i	$-0.0311089\pi$
$607$	1.62415	+	6.69484i	0.0659222	+	0.271735i	−0.929306	+	0.369311i	$0.879594\pi$
$608$	1.05941	+	0.204185i	0.0429649	+	0.00828080i
$609$	2.47516	+	18.2538i	0.100299	+	0.739681i
$610$	2.26739	−	1.16892i	0.0918040	−	0.0473283i
$611$	−21.4429	−	18.5804i	−0.867488	−	0.751683i
$612$	−41.6876	−	60.5765i	−1.68512	−	2.44866i
$613$	24.5204	−	3.52551i	0.990371	−	0.142394i	0.371960	−	0.928249i	$-0.378686\pi$
$613$	24.5204	−	3.52551i	0.990371	−	0.142394i	0.618411	+	0.785855i	$0.287777\pi$
$614$	−10.0311	−	52.0465i	−0.404824	−	2.10043i
$615$	−0.683802	−	7.82412i	−0.0275736	−	0.315499i
$616$	−10.5974	−	10.1046i	−0.426983	−	0.407127i
$617$	−0.111496	+	0.0106466i	−0.00448866	+	0.000428615i	−0.0973001	−	0.995255i	$-0.531021\pi$
$617$	−0.111496	+	0.0106466i	−0.00448866	+	0.000428615i	0.0928115	+	0.995684i	$0.470415\pi$
$618$	−0.229001	−	5.78343i	−0.00921175	−	0.232644i
$619$	12.5768	−	0.599106i	0.505503	−	0.0240801i	0.206718	−	0.978401i	$-0.433722\pi$
$619$	12.5768	−	0.599106i	0.505503	−	0.0240801i	0.298785	+	0.954320i	$0.403419\pi$
$620$	16.0355			0.644002
$621$	−4.45323	+	24.5187i	−0.178702	+	0.983903i
$622$	56.3114			2.25788
$623$	26.2765	−	1.25170i	1.05274	−	0.0501484i
$624$	−1.12407	−	28.3886i	−0.0449990	−	1.13645i
$625$	−20.8741	+	1.99323i	−0.834962	+	0.0797292i
$626$	35.0964	+	33.4643i	1.40273	+	1.33750i
$627$	0.0357669	+	0.409248i	0.00142839	+	0.0163438i
$628$	−7.38313	−	38.3073i	−0.294619	−	1.52863i
$629$	17.8693	−	2.56922i	0.712496	−	0.102441i
$630$	−7.35025	+	15.4344i	−0.292841	+	0.614920i
$631$	−36.0765	−	31.2605i	−1.43618	−	1.24446i	−0.922229	−	0.386644i	$-0.873634\pi$
$631$	−36.0765	−	31.2605i	−1.43618	−	1.24446i	−0.513955	−	0.857817i	$-0.671820\pi$
$632$	37.9856	−	19.5830i	1.51099	−	0.778968i
$633$	−5.35157	−	39.4667i	−0.212706	−	1.56866i
$634$	32.0791	+	6.18273i	1.27402	+	0.245548i
$635$	−1.98876	−	8.19780i	−0.0789217	−	0.325320i
$636$	43.1111	−	48.9536i	1.70947	−	1.94114i
$637$	−34.4511	+	6.63991i	−1.36500	+	0.263083i
$638$	−1.51274	−	3.31243i	−0.0598898	−	0.131140i
$639$	9.58896	+	12.6045i	0.379333	+	0.498627i
$640$	7.82489	+	3.57351i	0.309306	+	0.141255i
$641$	11.3548	+	8.92952i	0.448488	+	0.352695i	0.816715	−	0.577041i	$-0.195793\pi$
$641$	11.3548	+	8.92952i	0.448488	+	0.352695i	−0.368227	+	0.929736i	$0.620035\pi$
$642$	−31.0577	+	7.27112i	−1.22575	+	0.286968i
$643$	13.2461	−	7.64763i	0.522375	−	0.301593i	−0.215531	−	0.976497i	$-0.569148\pi$
$643$	13.2461	−	7.64763i	0.522375	−	0.301593i	0.737906	+	0.674904i	$0.235815\pi$
$644$	−1.13690	+	88.8584i	−0.0448001	+	3.50151i
$645$	1.43761	+	7.79510i	0.0566057	+	0.306932i
$646$	0.272714	+	5.72497i	0.0107298	+	0.225246i
$647$	−0.717557	−	0.103169i	−0.0282101	−	0.00405600i	0.128195	−	0.991749i	$-0.459082\pi$
$647$	−0.717557	−	0.103169i	−0.0282101	−	0.00405600i	−0.156405	+	0.987693i	$0.549991\pi$
$648$	−48.4709	+	15.0523i	−1.90412	+	0.591310i
$649$	0.923338	+	3.14460i	0.0362442	+	0.123436i
$650$	−3.29454	+	34.5020i	−0.129222	+	1.35328i
$651$	33.9294	−	42.4395i	1.32980	−	1.66333i
$652$	35.2089	−	27.6886i	1.37889	−	1.08437i
$653$	−7.45164	+	1.80775i	−0.291605	+	0.0707427i	−0.378893	−	0.925440i	$-0.623695\pi$
$653$	−7.45164	+	1.80775i	−0.291605	+	0.0707427i	0.0872878	+	0.996183i	$0.472180\pi$
$654$	34.1279	+	60.2222i	1.33451	+	2.35487i
$655$	−2.09539	−	4.06449i	−0.0818738	−	0.158813i
$656$	26.2127	−	40.7878i	1.02344	−	1.59250i
$657$	−11.0878	+	30.4462i	−0.432577	+	1.18782i
$658$	−29.6927	+	101.124i	−1.15754	+	3.94222i
$659$	3.55657	+	1.42384i	0.138544	+	0.0554647i	0.439898	−	0.898048i	$-0.355014\pi$
$659$	3.55657	+	1.42384i	0.138544	+	0.0554647i	−0.301354	+	0.953512i	$0.597439\pi$
$660$	0.345412	−	2.27277i	0.0134451	−	0.0884675i
$661$	−31.4065	−	22.3644i	−1.22157	−	0.869876i	−0.226995	−	0.973896i	$-0.572890\pi$
$661$	−31.4065	−	22.3644i	−1.22157	−	0.869876i	−0.994575	+	0.104020i	$0.966829\pi$
$662$	−4.10550	+	4.30572i	−0.159565	+	0.167347i
$663$	28.1373	−	8.01718i	1.09276	−	0.311362i
$664$	6.24088	−	7.93593i	0.242193	−	0.307974i
$665$	0.762502	−	0.490031i	0.0295686	−	0.0190026i
$666$	3.71922	−	23.2163i	0.144117	−	0.899614i
$667$	−4.49163	+	10.8164i	−0.173917	+	0.418813i
$668$	−41.9799	−	24.2371i	−1.62425	−	0.937763i
$669$	−4.51444	−	19.2828i	−0.174538	−	0.745518i
$670$	16.8408	−	6.74202i	0.650615	−	0.260467i
$671$	0.110490	+	1.15710i	0.00426542	+	0.0446695i
$672$	−18.2583	+	9.22810i	−0.704328	+	0.355982i
$673$	−49.6563	−	4.74160i	−1.91411	−	0.182775i	−0.930902	−	0.365270i	$-0.880977\pi$
$673$	−49.6563	−	4.74160i	−1.91411	−	0.182775i	−0.983207	+	0.182495i	$0.941583\pi$
$674$	5.43035	+	6.26696i	0.209169	+	0.241394i
$675$	24.2195	−	4.06589i	0.932210	−	0.156496i
$676$	−17.9731	−	5.27739i	−0.691274	−	0.202976i
$677$	11.9841	+	34.6257i	0.460585	+	1.33077i	0.901327	+	0.433139i	$0.142594\pi$
$677$	11.9841	+	34.6257i	0.460585	+	1.33077i	−0.440742	+	0.897634i	$0.645285\pi$
$678$	24.3406	−	59.4135i	0.934794	−	2.28176i
$679$	−2.76931	+	58.1351i	−0.106277	+	2.23102i
$680$	3.21673	−	16.6900i	0.123356	−	0.640032i
$681$	−25.3516	+	35.0035i	−0.971476	+	1.34134i
$682$	−3.99210	+	9.97179i	−0.152866	+	0.381840i
$683$	1.35289	−	1.17229i	0.0517669	−	0.0448563i	−0.628593	−	0.777734i	$-0.716369\pi$
$683$	1.35289	−	1.17229i	0.0517669	−	0.0448563i	0.680360	+	0.732878i	$0.261823\pi$
$684$	4.91485	+	1.27618i	0.187924	+	0.0487961i
$685$	3.66152	−	1.07512i	0.139899	−	0.0410782i
$686$	31.3718	+	44.0556i	1.19778	+	1.68205i
$687$	13.5388	+	21.4432i	0.516537	+	0.818108i
$688$	−22.4223	+	43.4933i	−0.854844	+	1.65817i
$689$	12.9766	+	22.4761i	0.494369	+	0.856272i
$690$	−8.98303	+	6.11902i	−0.341978	+	0.232947i
$691$	−18.2990	+	31.6948i	−0.696127	+	1.20573i	0.273672	+	0.961823i	$0.411762\pi$
$691$	−18.2990	+	31.6948i	−0.696127	+	1.20573i	−0.969799	+	0.243905i	$0.921572\pi$
$692$	25.2332	+	39.2637i	0.959223	+	1.49258i
$693$	−5.28424	−	5.72310i	−0.200732	−	0.217403i
$694$	−10.3304	+	22.6204i	−0.392137	+	0.858659i
$695$	0.0517347	−	0.213253i	0.00196241	−	0.00808917i
$696$	−23.7631	+	2.07682i	−0.900740	+	0.0787217i
$697$	47.1829	+	16.3302i	1.78718	+	0.618549i
$698$	−11.1471	−	14.1747i	−0.421924	−	0.536519i
$699$	1.59033	−	15.3518i	0.0601519	−	0.580659i
$700$	82.7601	−	28.6436i	3.12804	−	1.08262i
$701$	10.6538	+	6.84679i	0.402389	+	0.258600i	0.726146	−	0.687541i	$-0.241310\pi$
$701$	10.6538	+	6.84679i	0.402389	+	0.258600i	−0.323757	+	0.946140i	$0.604946\pi$
$702$	0.917234	−	38.0936i	0.0346188	−	1.43775i
$703$	−0.816366	+	0.942137i	−0.0307898	+	0.0355334i
$704$	−1.90092	+	1.81253i	−0.0716437	+	0.0683121i
$705$	−8.30926	+	2.80140i	−0.312945	+	0.105507i
$706$	−1.52256	+	4.39914i	−0.0573023	+	0.165564i
$707$	−5.31973	+	7.47052i	−0.200069	+	0.280958i
$708$	40.4475	+	2.25219i	1.52011	+	0.0846426i
$709$	−38.8800	+	27.6863i	−1.46017	+	1.03978i	−0.472831	+	0.881153i	$0.656768\pi$
$709$	−38.8800	+	27.6863i	−1.46017	+	1.03978i	−0.987338	+	0.158629i	$0.949293\pi$
$710$	−0.983062	+	6.83735i	−0.0368937	+	0.256601i
$711$	20.8291	−	9.11122i	0.781152	−	0.341697i
$712$			34.0648i			1.27663i
$713$	32.2333	−	12.4282i	1.20714	−	0.465439i
$714$	−70.5072	−	82.7013i	−2.63866	−	3.09502i
$715$	0.812972	+	0.419116i	0.0304034	+	0.0156741i
$716$	−2.45686	−	6.13695i	−0.0918173	−	0.229349i
$717$	−8.61608	−	30.2393i	−0.321773	−	1.12931i
$718$	−18.9946	−	4.60803i	−0.708871	−	0.171970i
$719$	−14.7801	+	6.74982i	−0.551203	+	0.251726i	−0.671491	−	0.741013i	$-0.734346\pi$
$719$	−14.7801	+	6.74982i	−0.551203	+	0.251726i	0.120288	+	0.992739i	$0.461618\pi$
$720$	−7.73882	−	4.14817i	−0.288409	−	0.154593i
$721$	−0.828114	−	5.75966i	−0.0308406	−	0.214501i
$722$	32.5184	+	34.1043i	1.21021	+	1.26923i
$723$	12.4226	−	7.03989i	0.462002	−	0.261816i
$724$	−40.7803	−	1.94260i	−1.51559	−	0.0721963i
$725$	11.5290	+	0.549194i	0.428176	+	0.0203965i
$726$	−39.7462	−	23.3747i	−1.47512	−	0.867518i
$727$	−33.4783	−	35.1110i	−1.24164	−	1.30219i	−0.936831	−	0.349781i	$-0.886256\pi$
$727$	−33.4783	−	35.1110i	−1.24164	−	1.30219i	−0.304809	−	0.952414i	$-0.598593\pi$
$728$	−10.2483	−	71.2785i	−0.379827	−	2.64176i
$729$	−26.2424	+	6.35112i	−0.971941	+	0.235227i
$730$	−12.8555	+	5.87093i	−0.475805	+	0.217293i
$731$	−48.9702	−	11.8800i	−1.81123	−	0.439399i
$732$	13.9349	+	3.49922i	0.515050	+	0.129335i
$733$	−8.46951	−	21.1558i	−0.312828	−	0.781407i	−0.998565	−	0.0535575i	$-0.982944\pi$
$733$	−8.46951	−	21.1558i	−0.312828	−	0.781407i	0.685736	−	0.727850i	$-0.259480\pi$
$734$	−19.4824	−	10.0439i	−0.719109	−	0.370726i
$735$	−3.62857	+	10.2180i	−0.133842	+	0.376898i
$736$	−12.9833	−	0.785066i	−0.478572	−	0.0289379i
$737$			8.26570i			0.304471i
$738$	38.5649	−	52.3577i	1.41959	−	1.92731i
$739$	−4.62534	+	32.1699i	−0.170146	+	1.18339i	0.708428	+	0.705783i	$0.249405\pi$
$739$	−4.62534	+	32.1699i	−0.170146	+	1.18339i	−0.878574	+	0.477607i	$0.841504\pi$
$740$	5.68255	−	4.04653i	0.208895	−	0.148753i
$741$	−1.10587	+	1.69077i	−0.0406250	+	0.0621121i
$742$	55.9200	−	78.5287i	2.05289	−	2.88288i
$743$	−6.73344	+	19.4550i	−0.247026	+	0.713734i	0.751514	+	0.659717i	$0.229324\pi$
$743$	−6.73344	+	19.4550i	−0.247026	+	0.713734i	−0.998540	+	0.0540174i	$0.982797\pi$
$744$	52.8034	+	46.5015i	1.93587	+	1.70483i
$745$	2.06655	−	1.97045i	0.0757124	−	0.0721916i
$746$	−22.1091	+	25.5153i	−0.809473	+	0.934182i
$747$	3.58179	−	4.00199i	0.131051	−	0.146425i
$748$	12.2944	+	7.90111i	0.449526	+	0.288893i
$749$	−30.3042	+	10.4884i	−1.10729	+	0.383237i
$750$	17.8527	+	12.9300i	0.651890	+	0.472138i
$751$	1.34091	+	1.70510i	0.0489304	+	0.0622200i	0.809902	−	0.586565i	$-0.199520\pi$
$751$	1.34091	+	1.70510i	0.0489304	+	0.0622200i	−0.760972	+	0.648785i	$0.775278\pi$
$752$	−51.1550	−	17.7049i	−1.86543	−	0.645632i
$753$	19.8062	+	28.2917i	0.721779	+	1.03101i
$754$	4.22211	−	17.4038i	0.153760	−	0.633808i
$755$	2.35424	−	5.15507i	0.0856796	−	0.187612i
$756$	−88.5200	+	37.8778i	−3.21944	+	1.37760i
$757$	6.88308	+	10.7103i	0.250170	+	0.389272i	0.943513	−	0.331336i	$-0.107499\pi$
$757$	6.88308	+	10.7103i	0.250170	+	0.389272i	−0.693343	+	0.720608i	$0.743863\pi$
$758$	−35.7874	+	61.9856i	−1.29986	+	2.25142i
$759$	−1.06717	−	4.83624i	−0.0387359	−	0.175544i
$760$	0.586856	+	1.01646i	0.0212875	+	0.0368710i
$761$	−23.9743	+	46.5036i	−0.869067	+	1.68576i	−0.152425	+	0.988315i	$0.548708\pi$
$761$	−23.9743	+	46.5036i	−0.869067	+	1.68576i	−0.716643	+	0.697440i	$0.754322\pi$
$762$	32.5012	−	61.8204i	1.17739	−	2.23952i
$763$	40.3661	+	56.6863i	1.46135	+	2.05218i
$764$	39.9075	−	11.7179i	1.44380	−	0.423938i
$765$	2.27249	−	8.75182i	0.0821620	−	0.316423i
$766$	33.1966	−	28.7650i	1.19944	−	1.03932i
$767$	−5.99035	+	14.9632i	−0.216299	+	0.540289i
$768$	22.8386	+	51.0905i	0.824116	+	1.84357i
$769$	0.650327	−	3.37422i	0.0234514	−	0.121677i	−0.968316	−	0.249726i	$-0.919659\pi$
$769$	0.650327	−	3.37422i	0.0234514	−	0.121677i	0.991768	+	0.128049i	$0.0408714\pi$
$770$	0.161660	−	3.39366i	0.00582582	−	0.122299i
$771$	−19.8685	+	2.69410i	−0.715545	+	0.0970258i
$772$	2.76149	+	7.97880i	0.0993881	+	0.287163i
$773$	10.7609	+	3.15969i	0.387043	+	0.113646i	0.469464	−	0.882951i	$-0.344447\pi$
$773$	10.7609	+	3.15969i	0.387043	+	0.113646i	−0.0824211	+	0.996598i	$0.526265\pi$
$774$	−33.7223	+	56.3023i	−1.21212	+	2.02374i
$775$	−22.2948	−	25.7296i	−0.800854	−	0.924235i
$776$	−75.0250	−	7.16402i	−2.69324	−	0.257173i
$777$	1.31417	−	23.6014i	0.0471456	−	0.846695i
$778$	0.871317	+	9.12485i	0.0312382	+	0.327142i
$779$	−3.20079	+	1.28140i	−0.114680	+	0.0459111i
$780$	8.24460	−	7.73585i	0.295204	−	0.276988i
$781$	−2.72584	−	1.57376i	−0.0975381	−	0.0563136i
$782$	−12.2076	−	68.0100i	−0.436543	−	2.43203i
$783$	−12.6861	+	0.298509i	−0.453363	+	0.0106678i
$784$	−56.3118	+	36.1894i	−2.01114	+	1.29248i
$785$	2.96535	−	3.77074i	0.105838	−	0.134584i
$786$	9.22109	−	36.7212i	0.328906	−	1.30980i
$787$	−12.8684	+	13.4960i	−0.458710	+	0.481081i	−0.911947	−	0.410309i	$-0.865421\pi$
$787$	−12.8684	+	13.4960i	−0.458710	+	0.481081i	0.453236	+	0.891390i	$0.350269\pi$
$788$	−46.5418	−	33.1423i	−1.65798	−	1.18064i
$789$	−33.1105	+	12.9481i	−1.17876	+	0.460966i
$790$	9.20569	+	3.68540i	0.327524	+	0.131121i
$791$	18.1856	−	61.9345i	0.646606	−	2.20214i
$792$	7.72822	−	6.48235i	0.274610	−	0.230340i
$793$	−3.09052	+	4.80895i	−0.109748	+	0.170771i
$794$	−26.2005	−	50.8219i	−0.929821	−	1.80360i
$795$	8.02067	+	0.0643639i	0.284464	+	0.00228275i
$796$	−0.675060	+	0.163768i	−0.0239269	+	0.00580460i
$797$	26.9448	−	21.1896i	0.954434	−	0.750575i	−0.0139852	−	0.999902i	$-0.504452\pi$
$797$	26.9448	−	21.1896i	0.954434	−	0.750575i	0.968419	+	0.249327i	$0.0802094\pi$
$798$	7.41935	+	1.12758i	0.262642	+	0.0399159i
$799$	5.29888	−	55.4924i	0.187461	−	1.96318i
$800$	3.61136	+	12.2992i	0.127681	+	0.434841i
$801$	−1.15264	+	18.0849i	−0.0407267	+	0.638998i
$802$	−48.8139	−	7.01837i	−1.72368	−	0.247827i
$803$	−0.306411	−	6.43236i	−0.0108130	−	0.226993i
$804$	96.2786	+	34.1899i	3.39548	+	1.20579i
$805$	−8.34908	+	7.04954i	−0.294266	+	0.248464i
$806$	−45.7471	+	26.4121i	−1.61137	+	0.930327i
$807$	−32.2245	−	34.3437i	−1.13436	−	1.20896i
$808$	−9.33508	−	7.34119i	−0.328407	−	0.258262i
$809$	−50.1100	−	22.8845i	−1.76177	−	0.804576i	−0.984493	−	0.175423i	$-0.943871\pi$
$809$	−50.1100	−	22.8845i	−1.76177	−	0.804576i	−0.777282	−	0.629153i	$-0.783402\pi$
$810$	−10.0044	−	6.21246i	−0.351519	−	0.218284i
$811$	1.43024	+	3.13178i	0.0502224	+	0.109972i	0.933080	−	0.359669i	$-0.117111\pi$
$811$	1.43024	+	3.13178i	0.0502224	+	0.109972i	−0.882857	+	0.469641i	$0.844383\pi$
$812$	−44.4340	+	8.56394i	−1.55933	+	0.300536i
$813$	0.477508	+	1.41634i	0.0167469	+	0.0496732i
$814$	1.10167	+	4.54113i	0.0386134	+	0.159167i
$815$	5.40821	+	1.04235i	0.189441	+	0.0365119i
$816$	44.1522	−	34.1519i	1.54564	−	1.19555i
$817$	3.09283	−	1.59447i	0.108204	−	0.0557833i
$818$	−20.9630	−	18.1645i	−0.732953	−	0.635107i
$819$	−3.02896	−	38.1883i	−0.105840	−	1.33441i
$820$	19.0972	−	2.74577i	0.666904	−	0.0958863i
$821$	−6.47408	−	33.5907i	−0.225947	−	1.17232i	−0.900754	−	0.434330i	$-0.856985\pi$
$821$	−6.47408	−	33.5907i	−0.225947	−	1.17232i	0.674807	−	0.737994i	$-0.264227\pi$
$822$	28.6343	+	13.3556i	0.998736	+	0.465829i
$823$	7.19169	+	6.85727i	0.250687	+	0.239029i	0.804994	−	0.593283i	$-0.202168\pi$
$823$	7.19169	+	6.85727i	0.250687	+	0.239029i	−0.554308	+	0.832312i	$0.687017\pi$
$824$	7.50094	−	0.716253i	0.261308	−	0.0249519i
$825$	−4.12699	+	2.60570i	−0.143683	+	0.0907188i
$826$	59.8022	−	2.84873i	2.08079	−	0.0991201i
$827$	−46.4867			−1.61650			−0.808251	−	0.588838i	$-0.799585\pi$
$827$	−46.4867			−1.61650			−0.808251	+	0.588838i	$0.799585\pi$
$828$	−60.7466	−	7.57406i	−2.11109	−	0.263217i
$829$	31.3410			1.08852			0.544259	−	0.838918i	$-0.316811\pi$
$829$	31.3410			1.08852			0.544259	+	0.838918i	$0.316811\pi$
$830$	2.33987	−	0.111462i	0.0812181	−	0.00386889i
$831$	−14.4464	−	7.59498i	−0.501140	−	0.263467i
$832$	−12.8586	+	1.22785i	−0.445792	+	0.0425680i
$833$	−49.8885	−	47.5686i	−1.72854	−	1.64816i
$834$	1.48839	−	1.04198i	0.0515387	−	0.0360808i
$835$	−1.12804	−	5.85282i	−0.0390374	−	0.202545i
$836$	−0.998898	+	0.143620i	−0.0345476	+	0.00496719i
$837$	26.4597	+	26.4742i	0.914581	+	0.915082i
$838$	−24.2770	−	21.0361i	−0.838634	−	0.726680i
$839$	39.2566	−	20.2382i	1.35529	−	0.698699i	0.381120	−	0.924526i	$-0.375539\pi$
$839$	39.2566	−	20.2382i	1.35529	−	0.698699i	0.974167	+	0.225827i	$0.0725083\pi$
$840$	−20.5941	−	8.43702i	−0.710566	−	0.291105i
$841$	22.6198	+	4.35961i	0.779994	+	0.150331i
$842$	5.17754	+	21.3421i	0.178430	+	0.735498i
$843$	−23.9305	−	4.81170i	−0.824209	−	0.165724i
$844$	96.0711	−	18.5162i	3.30690	−	0.637353i
$845$	−0.956836	−	2.09518i	−0.0329162	−	0.0720764i
$846$	−66.9598	−	28.0617i	−2.30213	−	0.964782i
$847$	−42.1673	−	19.2572i	−1.44889	−	0.661684i
$848$	38.9217	+	30.6084i	1.33658	+	1.05110i
$849$	−6.31193	+	20.8753i	−0.216625	+	0.716438i
$850$	−58.9717	+	34.0474i	−2.02271	+	1.16781i
$851$	8.28636	−	12.5382i	0.284053	−	0.429804i
$852$	−29.6062	+	25.2408i	−1.01429	+	0.864735i
$853$	0.304560	+	6.39349i	0.0104279	+	0.218909i	0.998066	+	0.0621592i	$0.0197986\pi$
$853$	0.304560	+	6.39349i	0.0104279	+	0.218909i	−0.987638	+	0.156750i	$0.949898\pi$
$854$	21.0177	+	3.02190i	0.719212	+	0.103407i
$855$	0.277166	+	0.559495i	0.00947887	+	0.0191343i
$856$	−11.6991	−	39.8436i	−0.399868	−	1.36183i
$857$	−2.03901	+	21.3535i	−0.0696512	+	0.729420i	0.891431	+	0.453157i	$0.149702\pi$
$857$	−2.03901	+	21.3535i	−0.0696512	+	0.729420i	−0.961082	+	0.276263i	$0.910904\pi$
$858$	2.75807	+	7.05283i	0.0941589	+	0.240780i
$859$	−6.28930	+	4.94596i	−0.214588	+	0.168754i	−0.719667	−	0.694319i	$-0.755706\pi$
$859$	−6.28930	+	4.94596i	−0.214588	+	0.168754i	0.505079	+	0.863073i	$0.331463\pi$
$860$	−18.9231	+	4.59070i	−0.645273	+	0.156541i
$861$	33.1408	−	56.3523i	1.12943	−	1.92048i
$862$	29.3641	+	56.9583i	1.00014	+	1.94001i
$863$	0.961258	−	1.49575i	0.0327216	−	0.0509158i	−0.824507	−	0.565851i	$-0.808548\pi$
$863$	0.961258	−	1.49575i	0.0327216	−	0.0509158i	0.857229	+	0.514935i	$0.172184\pi$
$864$	−4.92131	−	13.2056i	−0.167426	−	0.449263i
$865$	−1.61687	+	5.50655i	−0.0549752	+	0.187228i
$866$	33.4488	+	13.3909i	1.13664	+	0.455041i
$867$	21.8989	+	17.5077i	0.743724	+	0.594592i
$868$	108.727	+	77.4244i	3.69044	+	2.62795i
$869$	−3.11798	+	3.27004i	−0.105770	+	0.110929i
$870$	−3.97488	−	3.85141i	−0.134761	−	0.130575i
$871$	−25.1281	+	31.9530i	−0.851433	+	1.08269i
$872$	−75.8089	+	48.7194i	−2.56721	+	1.64985i
$873$	−39.5882	−	6.34196i	−1.33986	−	0.214643i
$874$	3.71251	+	2.99721i	0.125578	+	0.101382i
$875$	19.1920	+	11.0805i	0.648809	+	0.374590i
$876$	−76.1913	−	23.0375i	−2.57427	−	0.778365i
$877$	−18.0502	+	7.22621i	−0.609512	+	0.244012i	−0.655822	−	0.754915i	$-0.727678\pi$
$877$	−18.0502	+	7.22621i	−0.609512	+	0.244012i	0.0463105	+	0.998927i	$0.485254\pi$
$878$	−7.18595	−	75.2547i	−0.242514	−	2.53972i
$879$	28.2371	+	18.4688i	0.952415	+	0.622936i
$880$	1.73713	+	0.165876i	0.0585587	+	0.00559168i
$881$	34.5173	+	39.8351i	1.16292	+	1.34208i	0.929114	+	0.369793i	$0.120571\pi$
$881$	34.5173	+	39.8351i	1.16292	+	1.34208i	0.233803	+	0.972284i	$0.424883\pi$
$882$	−78.4598	+	43.6351i	−2.64188	+	1.46927i
$883$	22.9400	+	6.73580i	0.771994	+	0.226678i	0.643926	−	0.765088i	$-0.277304\pi$
$883$	22.9400	+	6.73580i	0.771994	+	0.226678i	0.128068	+	0.991765i	$0.459123\pi$
$884$	23.5070	+	67.9190i	0.790625	+	2.28436i
$885$	3.04768	+	3.94010i	0.102447	+	0.132445i
$886$	2.39709	−	50.3210i	0.0805317	−	1.69057i
$887$	−2.27832	+	11.8211i	−0.0764985	+	0.396912i	0.923416	+	0.383802i	$0.125385\pi$
$887$	−2.27832	+	11.8211i	−0.0764985	+	0.396912i	−0.999914	+	0.0131104i	$0.995827\pi$
$888$	30.4466	+	3.15404i	1.02172	+	0.105843i
$889$	26.0968	−	65.1867i	0.875259	−	2.18629i
$890$	−5.97341	+	5.17599i	−0.200229	+	0.173499i
$891$	4.32223	−	3.17996i	0.144800	−	0.106533i
$892$	46.6795	−	13.7063i	1.56294	−	0.458922i
$893$	2.23285	+	3.13560i	0.0747196	+	0.104929i
$894$	23.6230	−	0.935377i	0.790073	−	0.0312837i
$895$	0.372466	−	0.722482i	0.0124502	−	0.0241499i
$896$	35.8019	+	62.0108i	1.19606	+	2.07163i
$897$	10.5770	−	21.9399i	0.353155	−	0.732551i
$898$	−17.7857	+	30.8058i	−0.593517	+	1.02800i
$899$	9.51066	+	14.7989i	0.317198	+	0.493570i
$900$	13.2804	+	58.8491i	0.442679	+	1.96164i
$901$	−21.1822	+	46.3826i	−0.705682	+	1.54523i
$902$	−3.04685	+	12.5593i	−0.101449	+	0.418179i
$903$	−27.8896	+	59.7952i	−0.928107	+	1.98986i
$904$	78.9896	+	27.3386i	2.62715	+	0.909267i
$905$	−3.10324	−	3.94610i	−0.103155	−	0.131173i
$906$	42.8370	−	19.1491i	1.42316	−	0.636185i
$907$	28.1871	−	9.75567i	0.935939	−	0.323932i	0.183821	−	0.982960i	$-0.441153\pi$
$907$	28.1871	−	9.75567i	0.935939	−	0.323932i	0.752118	+	0.659028i	$0.229032\pi$
$908$	−89.3171	−	57.4006i	−2.96409	−	1.90491i
$909$	−4.70756	−	4.21328i	−0.156140	−	0.139746i
$910$	10.9418	−	12.6275i	0.362717	−	0.418598i
$911$	−11.2492	+	10.7261i	−0.372702	+	0.355371i	−0.853162	−	0.521646i	$-0.825318\pi$
$911$	−11.2492	+	10.7261i	−0.372702	+	0.355371i	0.480460	+	0.877017i	$0.340470\pi$
$912$	−0.759816	+	3.77887i	−0.0251600	+	0.125131i
$913$	−0.349108	+	1.00868i	−0.0115538	+	0.0333825i
$914$	19.2617	−	27.0493i	0.637121	−	0.894711i
$915$	0.796911	+	1.57673i	0.0263451	+	0.0521251i
$916$	−50.7457	+	36.1359i	−1.67669	+	1.19396i
$917$	5.41700	−	37.6761i	0.178885	−	1.24417i
$918$	62.0106	−	41.9452i	2.04665	−	1.38440i
$919$		−	14.2557i		−	0.470251i	−0.971965	−	0.235125i	$-0.924450\pi$
$919$		−	14.2557i		−	0.470251i	0.971965	−	0.235125i	$-0.0755501\pi$
$920$	−8.60390	−	11.2336i	−0.283662	−	0.370361i
$921$	36.0994	−	6.65761i	1.18952	−	0.219376i
$922$	−16.7566	−	8.63861i	−0.551848	−	0.284498i
$923$	−5.75304	−	14.3704i	−0.189364	−	0.473008i
$924$	13.3157	−	13.7425i	0.438053	−	0.452097i
$925$	−14.3935	−	3.49182i	−0.473255	−	0.114810i
$926$	42.4006	−	19.3637i	1.39337	−	0.636331i
$927$	4.00646	−	0.126449i	0.131589	−	0.00415312i
$928$	−0.942606	−	6.55597i	−0.0309425	−	0.215210i
$929$	−22.2959	−	23.3832i	−0.731504	−	0.767179i	0.247966	−	0.968769i	$-0.420238\pi$
$929$	−22.2959	−	23.3832i	−0.731504	−	0.767179i	−0.979470	+	0.201590i	$0.935389\pi$
$930$	−0.131004	+	16.3250i	−0.00429579	+	0.535317i
$931$	4.75461	+	0.226490i	0.155826	+	0.00742291i
$932$	37.8714	+	1.80404i	1.24052	+	0.0590931i
$933$	−0.312943	+	38.9972i	−0.0102453	+	1.27671i
$934$	14.1990	+	14.8915i	0.464606	+	0.487265i
$935$	0.255742	+	1.77873i	0.00836367	+	0.0581706i
$936$	49.5819	−	1.56486i	1.62063	−	0.0511491i
$937$	−33.2017	+	15.1627i	−1.08465	+	0.495343i	−0.875835	−	0.482612i	$-0.839688\pi$
$937$	−33.2017	+	15.1627i	−1.08465	+	0.495343i	−0.208816	+	0.977955i	$0.566961\pi$
$938$	146.740	+	35.5987i	4.79122	+	1.16234i
$939$	−23.3700	+	24.1192i	−0.762652	+	0.787102i
$940$	−8.00597	−	19.9980i	−0.261126	−	0.652261i
$941$	−37.8252	−	19.5003i	−1.23307	−	0.635690i	−0.286464	−	0.958091i	$-0.592480\pi$
$941$	−37.8252	−	19.5003i	−1.23307	−	0.635690i	−0.946603	+	0.322401i	$0.895510\pi$
$942$	39.0591	−	7.20344i	1.27261	−	0.234701i
$943$	36.2596	−	20.3204i	1.18077	−	0.661724i
$944$			30.7506i			1.00085i
$945$	−10.6479	−	5.17603i	−0.346376	−	0.168376i
$946$	1.85623	−	12.9103i	0.0603511	−	0.419751i
$947$	42.8896	−	30.5415i	1.39372	−	0.992467i	0.396499	−	0.918035i	$-0.370225\pi$
$947$	42.8896	−	30.5415i	1.39372	−	0.992467i	0.997226	−	0.0744316i	$-0.0237142\pi$
$948$	25.1923	+	49.8442i	0.818207	+	1.61886i
$949$	18.3702	−	25.7973i	0.596321	−	0.837415i
$950$	1.53793	−	4.44355i	0.0498970	−	0.144168i
$951$	−4.45999	+	22.1813i	−0.144625	+	0.719278i
$952$	102.395	−	97.6335i	3.31864	−	3.16432i
$953$	−9.64413	+	11.1299i	−0.312404	+	0.360533i	−0.890137	−	0.455692i	$-0.849392\pi$
$953$	−9.64413	+	11.1299i	−0.312404	+	0.360533i	0.577734	+	0.816225i	$0.303937\pi$
$954$	49.4850	+	44.2892i	1.60214	+	1.43392i
$955$	4.30242	+	2.76500i	0.139223	+	0.0894732i
$956$	72.9926	−	25.2630i	2.36075	−	0.817064i
$957$	2.30236	−	1.02920i	0.0744247	−	0.0332695i
$958$	−12.9817	−	16.5076i	−0.419420	−	0.533336i
$959$	30.0176	+	10.3892i	0.969318	+	0.335484i
$960$	−1.68745	+	3.61789i	−0.0544623	+	0.116767i
$961$	4.92472	−	20.3000i	0.158862	−	0.654838i
$962$	−9.54649	+	20.9039i	−0.307791	+	0.673969i
$963$	−4.86286	−	21.5487i	−0.156703	−	0.694398i
$964$	18.9637	+	29.5081i	0.610780	+	0.950392i
$965$	−0.519097	+	0.899103i	−0.0167103	+	0.0289431i
$966$	−90.4531	−	1.88336i	−2.91028	−	0.0605961i
$967$	18.1163	+	31.3784i	0.582581	+	1.00906i	0.995172	+	0.0981438i	$0.0312905\pi$
$967$	18.1163	+	31.3784i	0.582581	+	1.00906i	−0.412591	+	0.910916i	$0.635376\pi$
$968$	27.5066	−	53.3554i	0.884096	−	1.71491i
$969$	−3.96622	+	0.157046i	−0.127413	+	0.00504505i
$970$	−10.1435	−	14.2445i	−0.325687	−	0.457363i
$971$	−50.2911	+	14.7668i	−1.61392	+	0.473890i	−0.959375	−	0.282134i	$-0.908958\pi$
$971$	−50.2911	+	14.7668i	−1.61392	+	0.473890i	−0.654545	+	0.756023i	$0.727140\pi$
$972$	−19.1617	−	63.4987i	−0.614613	−	2.03672i
$973$	1.38043	−	1.19615i	0.0442547	−	0.0383469i
$974$	−1.71293	+	4.27868i	−0.0548857	+	0.137098i
$975$	−23.8753	−	2.47330i	−0.764621	−	0.0792090i
$976$	−2.06401	+	10.7091i	−0.0660673	+	0.342790i
$977$	−1.58305	+	33.2323i	−0.0506462	+	1.06319i	0.820337	+	0.571881i	$0.193786\pi$
$977$	−1.58305	+	33.2323i	−0.0506462	+	1.06319i	−0.870983	+	0.491313i	$0.836517\pi$
$978$	27.9007	+	36.0706i	0.892167	+	1.15341i
$979$	−1.17793	−	3.40341i	−0.0376469	−	0.108774i
$980$	−25.5579	−	7.50446i	−0.816416	−	0.239721i
$981$	−41.8952	+	23.2999i	−1.33761	+	0.743907i
$982$	−37.5610	−	43.3477i	−1.19862	−	1.38328i
$983$	3.93667	+	0.375906i	0.125560	+	0.0119895i	0.157647	−	0.987496i	$-0.449609\pi$
$983$	3.93667	+	0.375906i	0.125560	+	0.0119895i	−0.0320867	+	0.999485i	$0.510215\pi$
$984$	70.8477	+	46.3386i	2.25854	+	1.47722i
$985$	−0.667828	−	6.99381i	−0.0212788	−	0.222841i
$986$	32.6648	−	13.0770i	1.04026	−	0.416457i
$987$	−69.8662	−	21.1250i	−2.22386	−	0.672416i
$988$	−4.29808	−	2.48150i	−0.136740	−	0.0789470i
$989$	−34.4797	+	23.8940i	−1.09639	+	0.759786i
$990$	2.31097	+	0.370215i	0.0734476	+	0.0117662i
$991$	28.0445	−	18.0231i	0.890863	−	0.572523i	−0.0132042	−	0.999913i	$-0.504203\pi$
$991$	28.0445	−	18.0231i	0.890863	−	0.572523i	0.904067	+	0.427390i	$0.140567\pi$
$992$	−12.0768	+	15.3569i	−0.383439	+	0.487582i
$993$	−2.95902	−	2.86710i	−0.0939016	−	0.0909847i
$994$	−39.6783	+	41.6135i	−1.25852	+	1.31990i
$995$	−0.0695770	−	0.0495456i	−0.00220574	−	0.00157070i
$996$	10.3051	+	8.23867i	0.326528	+	0.261052i
$997$	−20.9678	−	8.39423i	−0.664056	−	0.265848i	0.0150513	−	0.999887i	$-0.495209\pi$
$997$	−20.9678	−	8.39423i	−0.664056	−	0.265848i	−0.679108	+	0.734039i	$0.737633\pi$
$998$	−6.14717	+	20.9353i	−0.194585	+	0.662697i
$999$	16.0573	+	2.70469i	0.508030	+	0.0855725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.o.a.11.2	✓	440
3.2	odd	2		621.2.s.a.494.21		440
9.4	even	3		621.2.s.a.287.21		440
9.5	odd	6	inner	207.2.o.a.149.2	yes	440
23.21	odd	22	inner	207.2.o.a.182.2	yes	440
69.44	even	22		621.2.s.a.251.21		440
207.67	odd	66		621.2.s.a.44.21		440
207.113	even	66	inner	207.2.o.a.113.2	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.2	✓	440	1.1	even	1	trivial
207.2.o.a.113.2	yes	440	207.113	even	66	inner
207.2.o.a.149.2	yes	440	9.5	odd	6	inner
207.2.o.a.182.2	yes	440	23.21	odd	22	inner
621.2.s.a.44.21		440	207.67	odd	66
621.2.s.a.251.21		440	69.44	even	22
621.2.s.a.287.21		440	9.4	even	3
621.2.s.a.494.21		440	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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.49814 + 0.119001i) q^{2} +(-0.0685285 - 1.73069i) q^{3} +(4.23560 - 0.404451i) q^{4} +(0.378651 + 0.361043i) q^{5} +(0.377149 + 4.31536i) q^{6} +(0.824181 + 4.27626i) q^{7} +(-5.58197 + 0.802566i) q^{8} +(-2.99061 + 0.237204i) q^{9} +O(q^{10})\)	\(q+(-2.49814 + 0.119001i) q^{2} +(-0.0685285 - 1.73069i) q^{3} +(4.23560 - 0.404451i) q^{4} +(0.378651 + 0.361043i) q^{5} +(0.377149 + 4.31536i) q^{6} +(0.824181 + 4.27626i) q^{7} +(-5.58197 + 0.802566i) q^{8} +(-2.99061 + 0.237204i) q^{9} +(-0.988888 - 0.856876i) q^{10} +(0.529942 - 0.273204i) q^{11} +(-0.990241 - 7.30282i) q^{12} +(2.87917 + 0.554914i) q^{13} +(-2.56780 - 10.5846i) q^{14} +(0.598907 - 0.680071i) q^{15} +(5.49309 - 1.05871i) q^{16} +(2.39314 + 5.24024i) q^{17} +(7.44273 - 0.948455i) q^{18} +(-0.361856 - 0.165254i) q^{19} +(1.74984 + 1.37609i) q^{20} +(7.34442 - 1.71945i) q^{21} +(-1.29136 + 0.745567i) q^{22} +(4.58390 + 1.40990i) q^{23} +(1.77152 + 9.60569i) q^{24} +(-0.224885 - 4.72092i) q^{25} +(-7.25860 - 1.04363i) q^{26} +(0.615470 + 5.15957i) q^{27} +(5.22044 + 17.7792i) q^{28} +(-0.232137 + 2.43105i) q^{29} +(-1.41522 + 1.77018i) q^{30} +(5.66225 - 4.45284i) q^{31} +(-2.63571 + 0.639416i) q^{32} +(-0.509149 - 0.898446i) q^{33} +(-6.60199 - 12.8061i) q^{34} +(-1.23184 + 1.91677i) q^{35} +(-12.5711 + 2.21426i) q^{36} +(0.882882 - 3.00682i) q^{37} +(0.923634 + 0.369767i) q^{38} +(0.763082 - 5.02099i) q^{39} +(-2.40338 - 1.71144i) q^{40} +(5.98089 - 6.27258i) q^{41} +(-18.1428 + 5.16943i) q^{42} +(-5.40710 + 6.87569i) q^{43} +(2.13413 - 1.37152i) q^{44} +(-1.21804 - 0.989920i) q^{45} +(-11.6190 - 2.97664i) q^{46} +(-8.38011 - 4.83826i) q^{47} +(-2.20873 - 9.43431i) q^{48} +(-11.1085 + 4.44718i) q^{49} +(1.12359 + 11.7668i) q^{50} +(8.90526 - 4.50090i) q^{51} +(12.4195 + 1.18591i) q^{52} +(5.79633 + 6.68932i) q^{53} +(-2.15153 - 12.8161i) q^{54} +(0.299302 + 0.0878829i) q^{55} +(-8.03254 - 23.2085i) q^{56} +(-0.261207 + 0.637588i) q^{57} +(0.290614 - 6.10073i) q^{58} +(-1.04029 + 5.39755i) q^{59} +(2.26168 - 3.12274i) q^{60} +(-0.724578 + 1.80991i) q^{61} +(-13.6152 + 11.7976i) q^{62} +(-3.47915 - 12.5931i) q^{63} +(-4.22688 + 1.24112i) q^{64} +(0.889852 + 1.24962i) q^{65} +(1.37884 + 2.18386i) q^{66} +(-6.35262 + 12.3224i) q^{67} +(12.2558 + 21.2277i) q^{68} +(2.12598 - 8.02996i) q^{69} +(2.84920 - 4.93496i) q^{70} +(-2.85411 - 4.44108i) q^{71} +(16.5031 - 3.72423i) q^{72} +(4.48681 - 9.82474i) q^{73} +(-1.84775 + 7.61652i) q^{74} +(-8.15506 + 0.712725i) q^{75} +(-1.59952 - 0.553598i) q^{76} +(1.60506 + 2.04100i) q^{77} +(-1.30878 + 12.6339i) q^{78} +(-7.16142 + 2.47859i) q^{79} +(2.46220 + 1.58236i) q^{80} +(8.88747 - 1.41877i) q^{81} +(-14.1947 + 16.3815i) q^{82} +(-1.29567 + 1.23542i) q^{83} +(30.4126 - 10.2534i) q^{84} +(-0.985788 + 2.84825i) q^{85} +(12.6895 - 17.8199i) q^{86} +(4.22331 + 0.235162i) q^{87} +(-2.73886 + 1.95033i) q^{88} +(0.859657 - 5.97905i) q^{89} +(3.16063 + 2.32801i) q^{90} +12.7694i q^{91} +(19.9858 + 4.11782i) q^{92} +(-8.09453 - 9.49447i) q^{93} +(21.5105 + 11.0894i) q^{94} +(-0.0773534 - 0.193219i) q^{95} +(1.28725 + 4.51779i) q^{96} +(12.9876 + 3.15075i) q^{97} +(27.2214 - 12.4316i) q^{98} +(-1.52004 + 0.942751i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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