LMFDB - Embedded newform 756.2.bs.a.11.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(11,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13, 12]))

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

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

chi := DirichletCharacter("756.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bs (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.7
Character	$\chi$	$=$	756.11
Dual form			756.2.bs.a.275.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40267 - 0.180347i) q^{2} +(0.0171663 + 1.73197i) q^{3} +(1.93495 + 0.505934i) q^{4} +(1.75070 - 0.308695i) q^{5} +(0.288276 - 2.43247i) q^{6} +(2.14695 + 1.54616i) q^{7} +(-2.62285 - 1.05862i) q^{8} +(-2.99941 + 0.0594627i) q^{9} +O(q^{10})$	\(q+(-1.40267 - 0.180347i) q^{2} +(0.0171663 + 1.73197i) q^{3} +(1.93495 + 0.505934i) q^{4} +(1.75070 - 0.308695i) q^{5} +(0.288276 - 2.43247i) q^{6} +(2.14695 + 1.54616i) q^{7} +(-2.62285 - 1.05862i) q^{8} +(-2.99941 + 0.0594627i) q^{9} +(-2.51132 + 0.117263i) q^{10} +(0.331880 - 1.88219i) q^{11} +(-0.843044 + 3.35995i) q^{12} +(-4.77544 + 4.00707i) q^{13} +(-2.73261 - 2.55594i) q^{14} +(0.564702 + 3.02685i) q^{15} +(3.48806 + 1.95791i) q^{16} +4.58880i q^{17} +(4.21790 + 0.457528i) q^{18} +2.82928i q^{19} +(3.54369 + 0.288427i) q^{20} +(-2.64104 + 3.74498i) q^{21} +(-0.804965 + 2.58023i) q^{22} +(5.71414 - 4.79473i) q^{23} +(1.78847 - 4.56085i) q^{24} +(-1.72882 + 0.629239i) q^{25} +(7.42102 - 4.75935i) q^{26} +(-0.154476 - 5.19386i) q^{27} +(3.37198 + 4.07796i) q^{28} +(-3.43681 + 4.09584i) q^{29} +(-0.246206 - 4.34750i) q^{30} +(-2.05819 + 5.65483i) q^{31} +(-4.53949 - 3.37536i) q^{32} +(3.26558 + 0.542495i) q^{33} +(0.827576 - 6.43656i) q^{34} +(4.23595 + 2.04411i) q^{35} +(-5.83379 - 1.40245i) q^{36} +(5.20179 - 9.00977i) q^{37} +(0.510252 - 3.96854i) q^{38} +(-7.02209 - 8.20212i) q^{39} +(-4.91860 - 1.04366i) q^{40} +(-0.268344 - 0.319800i) q^{41} +(4.37990 - 4.77666i) q^{42} +(2.64316 + 7.26202i) q^{43} +(1.59443 - 3.47403i) q^{44} +(-5.23270 + 1.03000i) q^{45} +(-8.87975 + 5.69488i) q^{46} +(6.39232 - 2.32662i) q^{47} +(-3.33116 + 6.07481i) q^{48} +(2.21877 + 6.63905i) q^{49} +(2.53844 - 0.570825i) q^{50} +(-7.94764 + 0.0787725i) q^{51} +(-11.2676 + 5.33743i) q^{52} +(3.28246 + 1.89513i) q^{53} +(-0.720018 + 7.31311i) q^{54} -3.39759i q^{55} +(-3.99432 - 6.32814i) q^{56} +(-4.90022 + 0.0485682i) q^{57} +(5.55938 - 5.12528i) q^{58} +(-7.30142 + 6.12662i) q^{59} +(-0.438714 + 6.14250i) q^{60} +(-8.40397 + 3.05879i) q^{61} +(3.90679 - 7.56065i) q^{62} +(-6.53152 - 4.50991i) q^{63} +(5.75865 + 5.55319i) q^{64} +(-7.12338 + 8.48932i) q^{65} +(-4.48269 - 1.34988i) q^{66} +(8.81080 - 1.55358i) q^{67} +(-2.32163 + 8.87910i) q^{68} +(8.40240 + 9.81438i) q^{69} +(-5.57297 - 3.63114i) q^{70} +(-0.0303390 - 0.0525488i) q^{71} +(7.92994 + 3.01927i) q^{72} +(0.682595 + 1.18229i) q^{73} +(-8.92127 + 11.6996i) q^{74} +(-1.11950 - 2.98345i) q^{75} +(-1.43143 + 5.47452i) q^{76} +(3.62270 - 3.52782i) q^{77} +(8.37042 + 12.7712i) q^{78} +(2.21231 + 0.390090i) q^{79} +(6.71093 + 2.35096i) q^{80} +(8.99293 - 0.356706i) q^{81} +(0.318723 + 0.496969i) q^{82} +(-9.06102 - 7.60310i) q^{83} +(-7.00500 + 5.91016i) q^{84} +(1.41654 + 8.03359i) q^{85} +(-2.39779 - 10.6629i) q^{86} +(-7.15285 - 5.88214i) q^{87} +(-2.86299 + 4.58536i) q^{88} +0.635194i q^{89} +(7.52549 - 0.501051i) q^{90} +(-16.4482 + 1.21937i) q^{91} +(13.4824 - 6.38659i) q^{92} +(-9.82930 - 3.46764i) q^{93} +(-9.38590 + 2.11063i) q^{94} +(0.873385 + 4.95321i) q^{95} +(5.76808 - 7.92018i) q^{96} +(-10.8830 + 3.96110i) q^{97} +(-1.91487 - 9.71253i) q^{98} +(-0.883526 + 5.66519i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} - 6 q^{10} - 3 q^{12} - 24 q^{13} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} - 15 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} + 33 q^{30} + 27 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} + 6 q^{37} - 9 q^{38} + 12 q^{40} - 24 q^{41} - 21 q^{42} - 9 q^{44} - 30 q^{45} + 3 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} + 27 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} + 18 q^{65} - 3 q^{66} + 60 q^{68} - 48 q^{69} + 24 q^{70} - 63 q^{72} + 6 q^{73} - 75 q^{74} + 12 q^{77} + 6 q^{78} + 18 q^{81} - 6 q^{82} + 132 q^{84} + 6 q^{85} - 81 q^{86} + 45 q^{88} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} - 111 q^{96} - 24 q^{97} - 9 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 - 6 * q^10 - 3 * q^12 - 24 * q^13 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 - 15 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 + 33 * q^30 + 27 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 + 6 * q^37 - 9 * q^38 + 12 * q^40 - 24 * q^41 - 21 * q^42 - 9 * q^44 - 30 * q^45 + 3 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 + 27 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 + 18 * q^65 - 3 * q^66 + 60 * q^68 - 48 * q^69 + 24 * q^70 - 63 * q^72 + 6 * q^73 - 75 * q^74 + 12 * q^77 + 6 * q^78 + 18 * q^81 - 6 * q^82 + 132 * q^84 + 6 * q^85 - 81 * q^86 + 45 * q^88 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 - 111 * q^96 - 24 * q^97 - 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.40267	−	0.180347i	−0.991835	−	0.127525i
$2$	−1.40267	−	0.180347i	−0.991835	−	0.127525i
$3$	0.0171663	+	1.73197i	0.00991094	+	0.999951i
$3$	0.0171663	+	1.73197i	0.00991094	+	0.999951i
$4$	1.93495	+	0.505934i	0.967475	+	0.252967i
$5$	1.75070	−	0.308695i	0.782935	−	0.138053i	0.232128	−	0.972685i	$-0.425431\pi$
$5$	1.75070	−	0.308695i	0.782935	−	0.138053i	0.550807	+	0.834633i	$0.314320\pi$
$6$	0.288276	−	2.43247i	0.117688	−	0.993051i
$7$	2.14695	+	1.54616i	0.811470	+	0.584394i
$7$	2.14695	+	1.54616i	0.811470	+	0.584394i
$8$	−2.62285	−	1.05862i	−0.927316	−	0.374278i
$9$	−2.99941	+	0.0594627i	−0.999804	+	0.0198209i
$10$	−2.51132	+	0.117263i	−0.794148	+	0.0370819i
$11$	0.331880	−	1.88219i	0.100066	−	0.567501i	−0.893011	−	0.450035i	$-0.851412\pi$
$11$	0.331880	−	1.88219i	0.100066	−	0.567501i	0.993077	−	0.117466i	$-0.0374772\pi$
$12$	−0.843044	+	3.35995i	−0.243366	+	0.969935i
$13$	−4.77544	+	4.00707i	−1.32447	+	1.11136i	−0.339133	+	0.940738i	$0.610134\pi$
$13$	−4.77544	+	4.00707i	−1.32447	+	1.11136i	−0.985336	+	0.170623i	$0.945422\pi$
$14$	−2.73261	−	2.55594i	−0.730320	−	0.683105i
$15$	0.564702	+	3.02685i	0.145805	+	0.781528i
$16$	3.48806	+	1.95791i	0.872016	+	0.489478i
$17$			4.58880i			1.11295i	0.830865	+	0.556474i	$0.187846\pi$
$17$			4.58880i			1.11295i	−0.830865	+	0.556474i	$0.812154\pi$
$18$	4.21790	+	0.457528i	0.994168	+	0.107840i
$19$			2.82928i			0.649081i	0.945872	+	0.324541i	$0.105210\pi$
$19$			2.82928i			0.649081i	−0.945872	+	0.324541i	$0.894790\pi$
$20$	3.54369	+	0.288427i	0.792393	+	0.0644942i
$21$	−2.64104	+	3.74498i	−0.576323	+	0.817222i
$22$	−0.804965	+	2.58023i	−0.171619	+	0.550107i
$23$	5.71414	−	4.79473i	1.19148	−	0.999770i	0.191647	−	0.981464i	$-0.438617\pi$
$23$	5.71414	−	4.79473i	1.19148	−	0.999770i	0.999832	−	0.0183064i	$-0.00582743\pi$
$24$	1.78847	−	4.56085i	0.365069	−	0.930980i
$25$	−1.72882	+	0.629239i	−0.345764	+	0.125848i
$26$	7.42102	−	4.75935i	1.45538	−	0.933385i
$27$	−0.154476	−	5.19386i	−0.0297289	−	0.999558i
$28$	3.37198	+	4.07796i	0.637245	+	0.770662i
$29$	−3.43681	+	4.09584i	−0.638200	+	0.760578i	−0.984085	−	0.177699i	$-0.943135\pi$
$29$	−3.43681	+	4.09584i	−0.638200	+	0.760578i	0.345884	+	0.938277i	$0.387579\pi$
$30$	−0.246206	−	4.34750i	−0.0449509	−	0.793741i
$31$	−2.05819	+	5.65483i	−0.369662	+	1.01564i	0.605829	+	0.795595i	$0.292842\pi$
$31$	−2.05819	+	5.65483i	−0.369662	+	1.01564i	−0.975490	+	0.220042i	$0.929381\pi$
$32$	−4.53949	−	3.37536i	−0.802475	−	0.596685i
$33$	3.26558	+	0.542495i	0.568465	+	0.0944363i
$34$	0.827576	−	6.43656i	0.141928	−	1.10386i
$35$	4.23595	+	2.04411i	0.716006	+	0.345517i
$36$	−5.83379	−	1.40245i	−0.972299	−	0.233741i
$37$	5.20179	−	9.00977i	0.855170	−	1.48120i	−0.0213176	−	0.999773i	$-0.506786\pi$
$37$	5.20179	−	9.00977i	0.855170	−	1.48120i	0.876487	−	0.481425i	$-0.159881\pi$
$38$	0.510252	−	3.96854i	0.0827739	−	0.643782i
$39$	−7.02209	−	8.20212i	−1.12443	−	1.31339i
$40$	−4.91860	−	1.04366i	−0.777699	−	0.165017i
$41$	−0.268344	−	0.319800i	−0.0419084	−	0.0499444i	0.744683	−	0.667418i	$-0.232601\pi$
$41$	−0.268344	−	0.319800i	−0.0419084	−	0.0499444i	−0.786591	+	0.617474i	$0.788156\pi$
$42$	4.37990	−	4.77666i	0.675833	−	0.737055i
$43$	2.64316	+	7.26202i	0.403078	+	1.10745i	0.960757	+	0.277391i	$0.0894697\pi$
$43$	2.64316	+	7.26202i	0.403078	+	1.10745i	−0.557679	+	0.830056i	$0.688308\pi$
$44$	1.59443	−	3.47403i	0.240370	−	0.523730i
$45$	−5.23270	+	1.03000i	−0.780045	+	0.153544i
$46$	−8.87975	+	5.69488i	−1.30925	+	0.839665i
$47$	6.39232	−	2.32662i	0.932416	−	0.339372i	0.169249	−	0.985573i	$-0.445866\pi$
$47$	6.39232	−	2.32662i	0.932416	−	0.339372i	0.763167	+	0.646201i	$0.223643\pi$
$48$	−3.33116	+	6.07481i	−0.480812	+	0.876824i
$49$	2.21877	+	6.63905i	0.316968	+	0.948436i
$50$	2.53844	−	0.570825i	0.358989	−	0.0807268i
$51$	−7.94764	+	0.0787725i	−1.11289	+	0.0110304i
$52$	−11.2676	+	5.33743i	−1.56253	+	0.740168i
$53$	3.28246	+	1.89513i	0.450881	+	0.260316i	0.708202	−	0.706010i	$-0.249507\pi$
$53$	3.28246	+	1.89513i	0.450881	+	0.260316i	−0.257321	+	0.966326i	$0.582840\pi$
$54$	−0.720018	+	7.31311i	−0.0979820	+	0.995188i
$55$		−	3.39759i		−	0.458131i
$56$	−3.99432	−	6.32814i	−0.533764	−	0.845634i
$57$	−4.90022	+	0.0485682i	−0.649050	+	0.00643301i
$58$	5.55938	−	5.12528i	0.729982	−	0.672982i
$59$	−7.30142	+	6.12662i	−0.950564	+	0.797618i	−0.979392	−	0.201966i	$-0.935267\pi$
$59$	−7.30142	+	6.12662i	−0.950564	+	0.797618i	0.0288284	+	0.999584i	$0.490822\pi$
$60$	−0.438714	+	6.14250i	−0.0566377	+	0.792993i
$61$	−8.40397	+	3.05879i	−1.07602	+	0.391638i	−0.818424	−	0.574615i	$-0.805152\pi$
$61$	−8.40397	+	3.05879i	−1.07602	+	0.391638i	−0.257594	+	0.966253i	$0.582930\pi$
$62$	3.90679	−	7.56065i	0.496162	−	0.960204i
$63$	−6.53152	−	4.50991i	−0.822894	−	0.568195i
$64$	5.75865	+	5.55319i	0.719831	+	0.694149i
$65$	−7.12338	+	8.48932i	−0.883547	+	1.05297i
$66$	−4.48269	−	1.34988i	−0.551781	−	0.166159i
$67$	8.81080	−	1.55358i	1.07641	−	0.189800i	0.392783	−	0.919631i	$-0.371512\pi$
$67$	8.81080	−	1.55358i	1.07641	−	0.189800i	0.683628	+	0.729831i	$0.260401\pi$
$68$	−2.32163	+	8.87910i	−0.281539	+	1.07675i
$69$	8.40240	+	9.81438i	1.01153	+	1.18151i
$70$	−5.57297	−	3.63114i	−0.666098	−	0.434004i
$71$	−0.0303390	−	0.0525488i	−0.00360058	−	0.00623639i	0.864219	−	0.503115i	$-0.167813\pi$
$71$	−0.0303390	−	0.0525488i	−0.00360058	−	0.00623639i	−0.867820	+	0.496879i	$0.834479\pi$
$72$	7.92994	+	3.01927i	0.934553	+	0.355825i
$73$	0.682595	+	1.18229i	0.0798918	+	0.138377i	0.903203	−	0.429213i	$-0.141209\pi$
$73$	0.682595	+	1.18229i	0.0798918	+	0.138377i	−0.823311	+	0.567590i	$0.807876\pi$
$74$	−8.92127	+	11.6996i	−1.03708	+	1.36005i
$75$	−1.11950	−	2.98345i	−0.129268	−	0.344500i
$76$	−1.43143	+	5.47452i	−0.164196	+	0.627970i
$77$	3.62270	−	3.52782i	0.412844	−	0.402032i
$78$	8.37042	+	12.7712i	0.947764	+	1.44606i
$79$	2.21231	+	0.390090i	0.248904	+	0.0438885i	0.296708	−	0.954968i	$-0.404111\pi$
$79$	2.21231	+	0.390090i	0.248904	+	0.0438885i	−0.0478040	+	0.998857i	$0.515222\pi$
$80$	6.71093	+	2.35096i	0.750305	+	0.262846i
$81$	8.99293	−	0.356706i	0.999214	−	0.0396340i
$82$	0.318723	+	0.496969i	0.0351970	+	0.0548810i
$83$	−9.06102	−	7.60310i	−0.994576	−	0.834548i	−0.00835224	−	0.999965i	$-0.502659\pi$
$83$	−9.06102	−	7.60310i	−0.994576	−	0.834548i	−0.986224	+	0.165417i	$0.947103\pi$
$84$	−7.00500	+	5.91016i	−0.764308	+	0.644851i
$85$	1.41654	+	8.03359i	0.153645	+	0.871365i
$86$	−2.39779	−	10.6629i	−0.258560	−	1.14981i
$87$	−7.15285	−	5.88214i	−0.766866	−	0.630631i
$88$	−2.86299	+	4.58536i	−0.305196	+	0.488801i
$89$			0.635194i			0.0673305i	0.999433	+	0.0336652i	$0.0107180\pi$
$89$			0.635194i			0.0673305i	−0.999433	+	0.0336652i	$0.989282\pi$
$90$	7.52549	−	0.501051i	0.793257	−	0.0528154i
$91$	−16.4482	+	1.21937i	−1.72424	+	0.127825i
$92$	13.4824	−	6.38659i	1.40564	−	0.665848i
$93$	−9.82930	−	3.46764i	−1.01925	−	0.359578i
$94$	−9.38590	+	2.11063i	−0.968082	+	0.217695i
$95$	0.873385	+	4.95321i	0.0896074	+	0.508189i
$96$	5.76808	−	7.92018i	0.588703	−	0.808350i
$97$	−10.8830	+	3.96110i	−1.10501	+	0.402189i	−0.829159	−	0.559013i	$-0.811180\pi$
$97$	−10.8830	+	3.96110i	−1.10501	+	0.402189i	−0.275846	+	0.961202i	$0.588958\pi$
$98$	−1.91487	−	9.71253i	−0.193431	−	0.981114i
$99$	−0.883526	+	5.66519i	−0.0887977	+	0.569373i
$100$	−3.66353	+	0.342877i	−0.366353	+	0.0342877i
$101$	−2.22020	+	2.64593i	−0.220918	+	0.263280i	−0.865108	−	0.501586i	$-0.832750\pi$
$101$	−2.22020	+	2.64593i	−0.220918	+	0.263280i	0.644190	+	0.764866i	$0.277195\pi$
$102$	11.1621	+	1.32284i	1.10521	+	0.130981i
$103$	−2.44383	+	0.430913i	−0.240797	+	0.0424591i	−0.292744	−	0.956191i	$-0.594568\pi$
$103$	−2.44383	+	0.430913i	−0.240797	+	0.0424591i	0.0519468	+	0.998650i	$0.483457\pi$
$104$	16.7672	−	5.45456i	1.64416	−	0.534864i
$105$	−3.46761	+	7.37160i	−0.338404	+	0.719395i
$106$	−4.26242	−	3.25022i	−0.414003	−	0.315689i
$107$	−1.49541	−	2.59013i	−0.144567	−	0.250397i	0.784644	−	0.619946i	$-0.212846\pi$
$107$	−1.49541	−	2.59013i	−0.144567	−	0.250397i	−0.929211	+	0.369549i	$0.879512\pi$
$108$	2.32884	−	10.1280i	0.224093	−	0.974568i
$109$	2.52659	−	4.37618i	0.242003	−	0.419162i	−0.719282	−	0.694719i	$-0.755529\pi$
$109$	2.52659	−	4.37618i	0.242003	−	0.419162i	0.961285	+	0.275557i	$0.0888622\pi$
$110$	−0.612745	+	4.76569i	−0.0584229	+	0.454390i
$111$	15.6939	+	8.85467i	1.48960	+	0.840448i
$112$	4.46144	+	9.59664i	0.421566	+	0.906798i
$113$	1.02628	−	2.81969i	0.0965445	−	0.265254i	−0.882014	−	0.471223i	$-0.843813\pi$
$113$	1.02628	−	2.81969i	0.0965445	−	0.265254i	0.978558	+	0.205970i	$0.0660348\pi$
$114$	6.88213	+	0.815615i	0.644571	+	0.0763893i
$115$	8.52361	−	10.1580i	0.794830	−	0.947242i
$116$	−8.72229	+	6.18644i	−0.809844	+	0.574396i
$117$	14.0852	−	12.3028i	1.30218	−	1.13740i
$118$	11.3464	−	7.27682i	1.04452	−	0.669885i
$119$	−7.09502	+	9.85191i	−0.650400	+	0.903123i
$120$	1.72315	−	8.53676i	0.157301	−	0.779296i
$121$	6.90413	+	2.51290i	0.627648	+	0.228445i
$122$	12.3396	−	2.77484i	1.11718	−	0.251222i
$123$	0.549277	−	0.470253i	0.0495266	−	0.0424013i
$124$	−6.84346	+	9.90050i	−0.614561	+	0.889091i
$125$	−10.5301	+	6.07954i	−0.941839	+	0.543771i
$126$	8.34820	+	7.50384i	0.743716	+	0.668495i
$127$	16.9026	+	9.75875i	1.49987	+	0.865949i	1.00000		0.000153077i	$-4.87261e-5\pi$
$127$	16.9026	+	9.75875i	1.49987	+	0.865949i	0.499867	+	0.866102i	$0.333382\pi$
$128$	−7.07597	−	8.82783i	−0.625433	−	0.780278i
$129$	−12.5322	+	4.70252i	−1.10340	+	0.414034i
$130$	11.5228	−	10.6230i	1.01061	−	0.931699i
$131$	10.0853	−	8.46259i	0.881158	−	0.739380i	−0.0852586	−	0.996359i	$-0.527172\pi$
$131$	10.0853	−	8.46259i	0.881158	−	0.739380i	0.966417	+	0.256979i	$0.0827272\pi$
$132$	6.04427	+	2.70187i	0.526086	+	0.235168i
$133$	−4.37452	+	6.07432i	−0.379319	+	0.526710i
$134$	−12.6388	+	0.590156i	−1.09183	+	0.0509817i
$135$	−1.87376	−	9.04518i	−0.161267	−	0.778485i
$136$	4.85779	−	12.0357i	0.416552	−	1.03205i
$137$	−5.22421	−	14.3534i	−0.446335	−	1.22629i	−0.935258	−	0.353967i	$-0.884832\pi$
$137$	−5.22421	−	14.3534i	−0.446335	−	1.22629i	0.488923	−	0.872327i	$-0.337390\pi$
$138$	−10.0158	−	15.2817i	−0.852599	−	1.30086i
$139$	13.1503	−	2.31875i	1.11539	−	0.196674i	0.414575	−	0.910015i	$-0.363930\pi$
$139$	13.1503	−	2.31875i	1.11539	−	0.196674i	0.700817	+	0.713341i	$0.252819\pi$
$140$	7.16216	+	6.09835i	0.605313	+	0.515405i
$141$	4.13935	+	11.0313i	0.348596	+	0.929007i
$142$	0.0330786	+	0.0791800i	0.00277589	+	0.00664463i
$143$	5.95719	+	10.3181i	0.498165	+	0.862847i
$144$	−10.5786	−	5.66517i	−0.881546	−	0.472098i
$145$	−4.75245	+	8.23149i	−0.394670	+	0.683588i
$146$	−0.744232	−	1.78146i	−0.0615930	−	0.147435i
$147$	−11.4605	+	3.95681i	−0.945248	+	0.326352i
$148$	14.6236	−	14.8017i	1.20205	−	1.21669i
$149$	3.06043	−	8.40847i	0.250720	−	0.688848i	−0.748936	−	0.662642i	$-0.769435\pi$
$149$	3.06043	−	8.40847i	0.250720	−	0.688848i	0.999657	−	0.0262063i	$-0.00834268\pi$
$150$	1.03222	+	4.38669i	0.0842808	+	0.358172i
$151$	−19.2152	−	3.38815i	−1.56371	−	0.275724i	−0.676270	−	0.736653i	$-0.736405\pi$
$151$	−19.2152	−	3.38815i	−1.56371	−	0.275724i	−0.887437	+	0.460930i	$0.847516\pi$
$152$	2.99513	−	7.42077i	0.242937	−	0.601904i
$153$	−0.272863	−	13.7637i	−0.0220596	−	1.11273i
$154$	−5.71767	+	4.29501i	−0.460743	+	0.346102i
$155$	−1.85765	+	10.5352i	−0.149210	+	0.846211i
$156$	−9.43766	−	19.4234i	−0.755618	−	1.55512i
$157$	12.3536	−	10.3659i	0.985926	−	0.827290i	0.000953516	−	1.00000i	$-0.499696\pi$
$157$	12.3536	−	10.3659i	0.985926	−	0.827290i	0.984973	+	0.172709i	$0.0552520\pi$
$158$	−3.03278	−	0.946149i	−0.241275	−	0.0752716i
$159$	−3.22595	+	5.71764i	−0.255835	+	0.453439i
$160$	−8.98922	−	4.50792i	−0.710660	−	0.356382i
$161$	19.6814	−	1.45906i	1.55111	−	0.114990i
$162$	−12.6784	−	1.12151i	−0.996110	−	0.0881140i
$163$	6.67955	−	3.85644i	0.523182	−	0.302060i	−0.215053	−	0.976602i	$-0.568993\pi$
$163$	6.67955	−	3.85644i	0.523182	−	0.302060i	0.738236	+	0.674543i	$0.235659\pi$
$164$	−0.357435	−	0.754562i	−0.0279110	−	0.0589214i
$165$	5.88451	−	0.0583239i	0.458108	−	0.00454051i
$166$	11.3384	+	12.2987i	0.880030	+	0.954568i
$167$	22.0877	+	8.03928i	1.70920	+	0.622098i	0.996819	−	0.0796957i	$-0.0253949\pi$
$167$	22.0877	+	8.03928i	1.70920	+	0.622098i	0.712380	+	0.701793i	$0.247617\pi$
$168$	10.8916	−	7.02666i	0.840302	−	0.542118i
$169$	4.49080	−	25.4686i	0.345446	−	1.95912i
$170$	−0.538098	−	11.5239i	−0.0412702	−	0.883845i
$171$	−0.168237	−	8.48617i	−0.0128654	−	0.648954i
$172$	1.44028	+	15.3889i	0.109820	+	1.17339i
$173$	−8.37460	+	9.98046i	−0.636709	+	0.758801i	−0.983847	−	0.179014i	$-0.942709\pi$
$173$	−8.37460	+	9.98046i	−0.636709	+	0.758801i	0.347137	+	0.937814i	$0.387154\pi$
$174$	8.97224	+	9.54067i	0.680183	+	0.723276i
$175$	−4.68459	−	1.32209i	−0.354122	−	0.0999406i
$176$	4.84278	−	5.91539i	0.365038	−	0.445890i
$177$	−10.7364	−	12.5406i	−0.807000	−	0.942612i
$178$	0.114555	−	0.890966i	0.00858629	−	0.0667807i
$179$	−12.0485			−0.900545			−0.450273	−	0.892891i	$-0.648673\pi$
$179$	−12.0485			−0.900545			−0.450273	+	0.892891i	$0.648673\pi$
$180$	−10.6461	−	0.654393i	−0.793515	−	0.0487756i
$181$	−1.26061	+	2.18344i	−0.0937004	+	0.162294i	−0.909065	−	0.416653i	$-0.863203\pi$
$181$	−1.26061	+	2.18344i	−0.0937004	+	0.162294i	0.815365	+	0.578947i	$0.196536\pi$
$182$	23.2913	+	1.25601i	1.72646	+	0.0931017i
$183$	−5.44199	−	14.5029i	−0.402284	−	1.07208i
$184$	−20.0631	+	6.52675i	−1.47907	+	0.481158i
$185$	6.32549	−	17.3791i	0.465059	−	1.27774i
$186$	13.1619	+	6.63663i	0.965074	+	0.486621i
$187$	8.63698	+	1.52293i	0.631599	+	0.111368i
$188$	13.5459	−	1.26779i	0.987939	−	0.0924633i
$189$	7.69888	−	11.3898i	0.560011	−	0.828485i
$190$	−0.331771	−	7.10522i	−0.0240692	−	0.515467i
$191$	1.49228	−	8.46313i	0.107977	−	0.612370i	−0.882012	−	0.471227i	$-0.843811\pi$
$191$	1.49228	−	8.46313i	0.107977	−	0.612370i	0.989989	−	0.141143i	$-0.0450777\pi$
$192$	−9.51908	+	10.0691i	−0.686981	+	0.726676i
$193$	0.737160	+	0.268304i	0.0530619	+	0.0193130i	0.368415	−	0.929662i	$-0.379901\pi$
$193$	0.737160	+	0.268304i	0.0530619	+	0.0193130i	−0.315353	+	0.948974i	$0.602123\pi$
$194$	15.9797	−	3.59338i	1.14727	−	0.257990i
$195$	−14.8255	−	12.1917i	−1.06168	−	0.873068i
$196$	0.934292	+	13.9688i	0.0667352	+	0.997771i
$197$	−8.88369	−	5.12900i	−0.632936	−	0.365426i	0.148952	−	0.988844i	$-0.452410\pi$
$197$	−8.88369	−	5.12900i	−0.632936	−	0.365426i	−0.781888	+	0.623418i	$0.785743\pi$
$198$	2.26099	−	7.78703i	0.160682	−	0.553400i
$199$		−	6.34304i		−	0.449646i	−0.974400	−	0.224823i	$-0.927820\pi$
$199$		−	6.34304i		−	0.449646i	0.974400	−	0.224823i	$-0.0721805\pi$
$200$	5.20055	+	0.179764i	0.367735	+	0.0127112i
$201$	2.84200	+	15.2333i	0.200459	+	1.07448i
$202$	3.59138	−	3.31095i	0.252689	−	0.232958i
$203$	−13.7115	+	3.47968i	−0.962358	+	0.244226i
$204$	−15.4181	−	3.86856i	−1.07949	−	0.270853i
$205$	−0.568510	−	0.477037i	−0.0397065	−	0.0333177i
$206$	3.50559	−	0.163690i	0.244246	−	0.0114048i
$207$	−16.8539	+	14.7211i	−1.17143	+	1.02319i
$208$	−24.5025	+	4.62702i	−1.69895	+	0.320826i
$209$	5.32524	+	0.938983i	0.368354	+	0.0649508i
$210$	6.19334	−	9.71453i	0.427381	−	0.670366i
$211$	4.65332	−	12.7849i	0.320348	−	0.880149i	−0.670101	−	0.742270i	$-0.733749\pi$
$211$	4.65332	−	12.7849i	0.320348	−	0.880149i	0.990449	−	0.137879i	$-0.0440285\pi$
$212$	5.39259	+	5.32769i	0.370364	+	0.365907i
$213$	0.0904918	−	0.0534482i	0.00620040	−	0.00366221i
$214$	1.63044	+	3.90278i	0.111455	+	0.266788i
$215$	6.86911	+	11.8977i	0.468470	+	0.811413i
$216$	−5.09315	+	13.7862i	−0.346545	+	0.938033i
$217$	−13.1621	+	8.95833i	−0.893502	+	0.608131i
$218$	−4.33319	+	5.68266i	−0.293481	+	0.384878i
$219$	−2.03597	+	1.20253i	−0.137578	+	0.0812593i
$220$	1.71895	−	6.57416i	0.115892	−	0.443230i
$221$	−18.3876	−	21.9135i	−1.23689	−	1.47406i
$222$	−20.4164	−	15.2505i	−1.37026	−	1.02355i
$223$	4.15098	+	0.731930i	0.277970	+	0.0490136i	0.310895	−	0.950444i	$-0.399371\pi$
$223$	4.15098	+	0.731930i	0.277970	+	0.0490136i	−0.0329251	+	0.999458i	$0.510482\pi$
$224$	−4.52719	−	14.2655i	−0.302486	−	0.953154i
$225$	5.14802	−	1.99015i	0.343201	−	0.132676i
$226$	−1.94805	+	3.76999i	−0.129583	+	0.250776i
$227$	2.51647	−	14.2716i	0.167024	−	0.947240i	−0.779929	−	0.625868i	$-0.784745\pi$
$227$	2.51647	−	14.2716i	0.167024	−	0.947240i	0.946953	−	0.321372i	$-0.104144\pi$
$228$	−9.50625	−	2.38521i	−0.629567	−	0.157964i
$229$	1.30472	+	0.474877i	0.0862180	+	0.0313808i	0.384769	−	0.923013i	$-0.374281\pi$
$229$	1.30472	+	0.474877i	0.0862180	+	0.0313808i	−0.298551	+	0.954394i	$0.596503\pi$
$230$	−13.7878	+	12.7111i	−0.909138	+	0.838148i
$231$	6.17225	+	6.21382i	0.406104	+	0.408840i
$232$	13.3502	−	7.10447i	0.876482	−	0.466432i
$233$	9.67228	+	5.58429i	0.633652	+	0.365839i	0.782165	−	0.623071i	$-0.214115\pi$
$233$	9.67228	+	5.58429i	0.633652	+	0.365839i	−0.148513	+	0.988910i	$0.547449\pi$
$234$	−21.9757	+	14.7165i	−1.43660	+	0.962049i
$235$	10.4728	−	6.04647i	0.683170	−	0.394429i
$236$	−17.2275	+	8.16067i	−1.12142	+	0.531214i
$237$	−0.637645	+	3.83834i	−0.0414195	+	0.249327i
$238$	11.7287	−	12.5394i	0.760260	−	0.812808i
$239$	1.40863	+	7.98874i	0.0911168	+	0.516749i	0.995868	+	0.0908091i	$0.0289453\pi$
$239$	1.40863	+	7.98874i	0.0911168	+	0.516749i	−0.904752	+	0.425940i	$0.859944\pi$
$240$	−3.95659	+	11.6635i	−0.255397	+	0.752873i
$241$	19.9257	−	7.25235i	1.28353	−	0.467165i	0.391929	−	0.919996i	$-0.371808\pi$
$241$	19.9257	−	7.25235i	1.28353	−	0.467165i	0.891597	+	0.452831i	$0.149586\pi$
$242$	−9.23101	−	4.76990i	−0.593392	−	0.306621i
$243$	0.772178	+	15.5693i	0.0495353	+	0.998772i
$244$	−17.8088	+	1.66676i	−1.14009	+	0.106704i
$245$	5.93384	+	10.9380i	0.379099	+	0.698806i
$246$	−0.855261	+	0.560548i	−0.0545295	+	0.0357392i
$247$	−11.3371	−	13.5111i	−0.721364	−	0.859688i
$248$	11.3846	−	12.6529i	0.722924	−	0.803461i
$249$	13.0128	−	15.8239i	0.824650	−	1.00280i
$250$	15.8666	−	6.62851i	1.00349	−	0.419223i
$251$	−5.07278	+	8.78631i	−0.320191	+	0.554587i	−0.980527	−	0.196383i	$-0.937080\pi$
$251$	−5.07278	+	8.78631i	−0.320191	+	0.554587i	0.660336	+	0.750970i	$0.270414\pi$
$252$	−10.3564	−	12.0310i	−0.652395	−	0.757879i
$253$	−7.12817	−	12.3464i	−0.448144	−	0.776209i
$254$	−21.9488	−	16.7366i	−1.37719	−	1.05015i
$255$	−13.8896	+	2.59130i	−0.869800	+	0.162274i
$256$	8.33315	+	13.6586i	0.520822	+	0.853665i
$257$	5.30581	−	14.5776i	0.330967	−	0.909325i	−0.656894	−	0.753983i	$-0.728130\pi$
$257$	5.30581	−	14.5776i	0.330967	−	0.909325i	0.987861	−	0.155342i	$-0.0496478\pi$
$258$	18.4266	−	4.33593i	1.14719	−	0.269943i
$259$	25.0985	−	11.3007i	1.55955	−	0.702192i
$260$	−18.0784	+	12.8224i	−1.12118	+	0.795214i
$261$	10.0649	−	12.4895i	0.623000	−	0.773078i
$262$	−15.6725	+	10.0513i	−0.968253	+	0.620974i
$263$	21.0959	+	17.7016i	1.30083	+	1.09153i	0.990001	+	0.141060i	$0.0450512\pi$
$263$	21.0959	+	17.7016i	1.30083	+	1.09153i	0.310829	+	0.950466i	$0.399393\pi$
$264$	−7.99082	−	4.87989i	−0.491801	−	0.300336i
$265$	6.33161	+	2.30452i	0.388948	+	0.141565i
$266$	7.23148	−	7.73131i	0.443391	−	0.474037i
$267$	−1.10013	+	0.0109039i	−0.0673272	+	0.000667309i
$268$	17.8345	+	1.45158i	1.08941	+	0.0886693i
$269$	1.87990	+	1.08536i	0.114620	+	0.0661758i	0.556214	−	0.831039i	$-0.312254\pi$
$269$	1.87990	+	1.08536i	0.114620	+	0.0661758i	−0.441594	+	0.897215i	$0.645587\pi$
$270$	0.996987	+	13.0253i	0.0606747	+	0.792694i
$271$	23.2028	−	13.3961i	1.40947	−	0.813757i	0.414131	−	0.910217i	$-0.364086\pi$
$271$	23.2028	−	13.3961i	1.40947	−	0.813757i	0.995337	+	0.0964607i	$0.0307522\pi$
$272$	−8.98447	+	16.0060i	−0.544763	+	0.970507i
$273$	−2.39427	−	28.4668i	−0.144908	−	1.72289i
$274$	4.73924	+	21.0752i	0.286308	+	1.27320i
$275$	0.610584	+	3.46279i	0.0368196	+	0.208814i
$276$	11.2928	+	23.2414i	0.679746	+	1.39897i
$277$	−0.956280	−	0.802414i	−0.0574573	−	0.0482124i	0.613607	−	0.789612i	$-0.289718\pi$
$277$	−0.956280	−	0.802414i	−0.0574573	−	0.0482124i	−0.671064	+	0.741399i	$0.734162\pi$
$278$	−18.8636	+	0.880819i	−1.13137	+	0.0528280i
$279$	5.83710	−	17.0835i	0.349458	−	1.02276i
$280$	−8.94631	−	9.84563i	−0.534644	−	0.588389i
$281$	8.32064	+	22.8608i	0.496368	+	1.36376i	0.894761	+	0.446545i	$0.147346\pi$
$281$	8.32064	+	22.8608i	0.496368	+	1.36376i	−0.398393	+	0.917215i	$0.630432\pi$
$282$	−3.81666	−	16.2198i	−0.227279	−	0.965877i
$283$	12.6682	−	2.23375i	0.753048	−	0.132783i	0.216069	−	0.976378i	$-0.430677\pi$
$283$	12.6682	−	2.23375i	0.753048	−	0.132783i	0.536979	+	0.843596i	$0.319565\pi$
$284$	−0.0321183	−	0.117029i	−0.00190587	−	0.00694438i
$285$	−8.56380	+	1.59770i	−0.507276	+	0.0946396i
$286$	−6.49510	−	15.5473i	−0.384063	−	0.919330i
$287$	−0.0816586	−	1.10150i	−0.00482016	−	0.0650194i
$288$	13.8165	+	9.85417i	0.814145	+	0.580662i
$289$	−4.05708			−0.238652
$290$	8.15064	−	10.6890i	0.478622	−	0.627677i
$291$	−7.04731	−	18.7811i	−0.413121	−	1.10096i
$292$	0.722628	+	2.63302i	0.0422886	+	0.154086i
$293$	−2.23995	+	0.394963i	−0.130859	+	0.0230740i	−0.238694	−	0.971095i	$-0.576719\pi$
$293$	−2.23995	+	0.394963i	−0.130859	+	0.0230740i	0.107835	+	0.994169i	$0.465608\pi$
$294$	16.7889	−	3.48321i	0.979149	−	0.203145i
$295$	−10.8913	+	12.9798i	−0.634117	+	0.755711i
$296$	−23.1814	+	18.1245i	−1.34739	+	1.05347i
$297$	−9.82708	−	1.43299i	−0.570225	−	0.0831503i
$298$	−5.80921	+	11.2423i	−0.336518	+	0.651251i
$299$	−8.07470	+	45.7939i	−0.466972	+	2.64833i
$300$	−0.656741	−	6.33922i	−0.0379170	−	0.365995i
$301$	−5.55352	+	19.6779i	−0.320100	+	1.13422i
$302$	26.3414	+	8.21784i	1.51578	+	0.472884i
$303$	−4.62077	−	3.79989i	−0.265456	−	0.218298i
$304$	−5.53948	+	9.86871i	−0.317711	+	0.566009i
$305$	−13.7686	+	7.94928i	−0.788385	+	0.455174i
$306$	−2.09951	+	19.3551i	−0.120021	+	1.10646i
$307$	6.62643	−	3.82577i	0.378191	−	0.218348i	−0.298840	−	0.954303i	$-0.596600\pi$
$307$	6.62643	−	3.82577i	0.378191	−	0.218348i	0.677031	+	0.735955i	$0.263266\pi$
$308$	8.79458	−	4.99331i	0.501118	−	0.284520i
$309$	−0.788277	−	4.22523i	−0.0448435	−	0.240365i
$310$	4.50566	−	14.4424i	0.255904	−	0.820274i
$311$	5.17726	+	29.3617i	0.293576	+	1.66495i	0.672936	+	0.739701i	$0.265033\pi$
$311$	5.17726	+	29.3617i	0.293576	+	1.66495i	−0.379361	+	0.925249i	$0.623856\pi$
$312$	9.73494	+	28.9466i	0.551133	+	1.63878i
$313$	−0.152233	−	0.127739i	−0.00860472	−	0.00722022i	0.638475	−	0.769642i	$-0.279566\pi$
$313$	−0.152233	−	0.127739i	−0.00860472	−	0.00722022i	−0.647080	+	0.762422i	$0.724010\pi$
$314$	−19.1975	+	12.3120i	−1.08338	+	0.694806i
$315$	−12.8269	−	5.87923i	−0.722713	−	0.331257i
$316$	4.08335	+	1.87409i	0.229706	+	0.105426i
$317$	6.37833	+	17.5243i	0.358243	+	0.984264i	0.979639	+	0.200768i	$0.0643436\pi$
$317$	6.37833	+	17.5243i	0.358243	+	0.984264i	−0.621396	+	0.783497i	$0.713434\pi$
$318$	5.55610	−	7.43816i	0.311570	−	0.417111i
$319$	6.56852	+	7.82806i	0.367767	+	0.438287i
$320$	11.7959	+	7.94428i	0.659410	+	0.444099i
$321$	4.46034	−	2.63446i	0.248952	−	0.147041i
$322$	−27.8696	−	1.50290i	−1.55311	−	0.0837534i
$323$	−12.9830			−0.722393
$324$	17.5813	+	3.85962i	0.976741	+	0.214423i
$325$	5.73447	−	9.93239i	0.318091	−	0.550950i
$326$	−10.0647	+	4.20466i	−0.557431	+	0.232875i
$327$	7.62276	+	4.30084i	0.421540	+	0.237837i
$328$	0.365279	+	1.12286i	0.0201692	+	0.0619997i
$329$	17.3213	+	4.88844i	0.954955	+	0.269508i
$330$	−8.26452	−	0.979444i	−0.454947	−	0.0539166i
$331$	0.507240	+	1.39363i	0.0278805	+	0.0766009i	0.952852	−	0.303435i	$-0.0981337\pi$
$331$	0.507240	+	1.39363i	0.0278805	+	0.0766009i	−0.924972	+	0.380036i	$0.875911\pi$
$332$	−13.6860	−	19.2959i	−0.751114	−	1.05900i
$333$	−15.0666	+	27.3333i	−0.825643	+	1.49786i
$334$	−29.5319	−	15.2599i	−1.61591	−	0.834984i
$335$	14.9455	−	5.43970i	0.816557	−	0.297203i
$336$	−16.5445	+	7.89180i	−0.902575	+	0.430533i
$337$	27.0441	−	22.6927i	1.47319	−	1.23615i	0.560075	−	0.828442i	$-0.310772\pi$
$337$	27.0441	−	22.6927i	1.47319	−	1.23615i	0.913112	−	0.407709i	$-0.133672\pi$
$338$	−10.8923	+	34.9140i	−0.592462	+	1.89907i
$339$	4.90122	+	1.72908i	0.266198	+	0.0939108i
$340$	−1.32353	+	16.2613i	−0.0717787	+	0.881891i
$341$	9.96038	+	5.75063i	0.539385	+	0.311414i
$342$	−1.29448	+	11.9336i	−0.0699973	+	0.645296i
$343$	−5.50146	+	17.6843i	−0.297051	+	0.954862i
$344$	0.755111	−	21.8453i	0.0407129	−	1.17782i
$345$	17.7397	+	14.5882i	0.955073	+	0.785403i
$346$	13.5467	−	12.4889i	0.728277	−	0.671409i
$347$	−27.8335	−	10.1306i	−1.49418	−	0.543838i	−0.539635	−	0.841899i	$-0.681438\pi$
$347$	−27.8335	−	10.1306i	−1.49418	−	0.543838i	−0.954547	+	0.298061i	$0.903660\pi$
$348$	−10.8644	−	15.0005i	−0.582394	−	0.804111i
$349$	−21.9425	−	18.4119i	−1.17455	−	0.985567i	−1.00000		0.000918789i	$-0.999708\pi$
$349$	−21.9425	−	18.4119i	−1.17455	−	0.985567i	−0.174553	−	0.984648i	$-0.555848\pi$
$350$	6.33248	+	2.69930i	0.338486	+	0.144284i
$351$	21.5498	+	24.1840i	1.15025	+	1.29084i
$352$	−7.85963	+	7.42395i	−0.418920	+	0.395698i
$353$	0.842388	+	2.31444i	0.0448358	+	0.123185i	0.960090	−	0.279692i	$-0.0902323\pi$
$353$	0.842388	+	2.31444i	0.0448358	+	0.123185i	−0.915254	+	0.402877i	$0.868010\pi$
$354$	12.7980	+	19.5266i	0.680205	+	1.03783i
$355$	−0.0693360	−	0.0826314i	−0.00367997	−	0.00438562i
$356$	−0.321366	+	1.22907i	−0.0170324	+	0.0651405i
$357$	−17.1850	−	12.1192i	−0.909525	−	0.641417i
$358$	16.9000	+	2.17291i	0.893193	+	0.114842i
$359$	1.69668			0.0895472			0.0447736	−	0.998997i	$-0.485743\pi$
$359$	1.69668			0.0895472			0.0447736	+	0.998997i	$0.485743\pi$
$360$	14.8150	+	2.83789i	0.780817	+	0.149570i
$361$	10.9952			0.578693
$362$	2.16199	−	2.83529i	0.113632	−	0.149020i
$363$	−4.23374	+	12.0009i	−0.222214	+	0.629882i
$364$	−32.4434	−	5.96228i	−1.70049	−	0.312508i
$365$	1.55998	+	1.85912i	0.0816533	+	0.0973106i
$366$	5.01775	+	21.3242i	0.262282	+	1.11463i
$367$	11.1079	+	1.95862i	0.579828	+	0.102239i	0.455867	−	0.890048i	$-0.349329\pi$
$367$	11.1079	+	1.95862i	0.579828	+	0.102239i	0.123961	+	0.992287i	$0.460440\pi$
$368$	29.3189	−	5.53653i	1.52835	−	0.288612i
$369$	0.823891	+	0.943256i	0.0428901	+	0.0491040i
$370$	−12.0068	+	23.2364i	−0.624206	+	1.20800i
$371$	4.11710	+	9.14396i	0.213749	+	0.474731i
$372$	−17.2648	−	11.6827i	−0.895139	−	0.605719i
$373$	4.33892	+	24.6072i	0.224661	+	1.27411i	0.863333	+	0.504635i	$0.168373\pi$
$373$	4.33892	+	24.6072i	0.224661	+	1.27411i	−0.638672	+	0.769479i	$0.720516\pi$
$374$	−11.8402	−	3.69382i	−0.612240	−	0.191003i
$375$	−10.7103	−	18.1334i	−0.553079	−	0.936403i
$376$	−19.2291	−	0.664680i	−0.991664	−	0.0342782i
$377$		−	33.3310i		−	1.71663i
$378$	−12.8531	+	14.5876i	−0.661091	+	0.750305i
$379$		−	4.03801i		−	0.207419i	−0.994608	−	0.103709i	$-0.966929\pi$
$379$		−	4.03801i		−	0.207419i	0.994608	−	0.103709i	$-0.0330712\pi$
$380$	−0.816041	+	10.0261i	−0.0418620	+	0.514327i
$381$	−16.6117	+	29.4423i	−0.851041	+	1.50838i
$382$	−3.61947	+	11.6018i	−0.185188	+	0.593601i
$383$	−5.03279	−	28.5424i	−0.257164	−	1.45845i	−0.790457	−	0.612517i	$-0.790157\pi$
$383$	−5.03279	−	28.5424i	−0.257164	−	1.45845i	0.533294	−	0.845930i	$-0.320954\pi$
$384$	15.1680	−	12.4069i	0.774041	−	0.633136i
$385$	5.25322	−	7.29445i	0.267729	−	0.371759i
$386$	−0.985602	−	0.509286i	−0.0501658	−	0.0259220i
$387$	−8.35974	−	21.6246i	−0.424949	−	1.09924i
$388$	−23.0622	+	2.15844i	−1.17081	+	0.109578i
$389$	−17.7577	−	3.13116i	−0.900351	−	0.158756i	−0.295732	−	0.955271i	$-0.595563\pi$
$389$	−17.7577	−	3.13116i	−0.900351	−	0.158756i	−0.604619	+	0.796515i	$0.706675\pi$
$390$	18.5965	+	19.7747i	0.941670	+	1.00133i
$391$	22.0021	+	26.2210i	1.11269	+	1.32605i
$392$	1.20873	−	19.7621i	0.0610500	−	0.998135i
$393$	14.8300	+	17.3222i	0.748076	+	0.873787i
$394$	11.5359	+	8.79642i	0.581168	+	0.443157i
$395$	3.99350			0.200935
$396$	−4.57579	+	10.5149i	−0.229942	+	0.528391i
$397$	24.1443			1.21177			0.605884	−	0.795553i	$-0.292819\pi$
$397$	24.1443			1.21177			0.605884	+	0.795553i	$0.292819\pi$
$398$	−1.14395	+	8.89718i	−0.0573410	+	0.445975i
$399$	−10.5956	−	7.47225i	−0.530444	−	0.374080i
$400$	−7.26222	−	1.19005i	−0.363111	−	0.0595027i
$401$	−2.44243	−	2.91078i	−0.121969	−	0.145357i	0.701604	−	0.712567i	$-0.252467\pi$
$401$	−2.44243	−	2.91078i	−0.121969	−	0.145357i	−0.823574	+	0.567210i	$0.808023\pi$
$402$	−1.23909	−	21.8798i	−0.0618003	−	1.09127i
$403$	−12.8305	−	35.2516i	−0.639135	−	1.75601i
$404$	−5.63464	+	3.99647i	−0.280334	+	0.198832i
$405$	15.6338	−	3.40056i	0.776848	−	0.168975i
$406$	19.8602	−	2.40801i	0.985645	−	0.119507i
$407$	−15.2317	−	12.7809i	−0.755008	−	0.633527i
$408$	20.9288	+	8.20692i	1.03613	+	0.406303i
$409$	−10.6987	−	3.89400i	−0.529015	−	0.192546i	0.0636833	−	0.997970i	$-0.479715\pi$
$409$	−10.6987	−	3.89400i	−0.529015	−	0.192546i	−0.592699	+	0.805424i	$0.701937\pi$
$410$	0.711399	+	0.771653i	0.0351335	+	0.0381092i
$411$	24.7699	−	9.29455i	1.22181	−	0.458466i
$412$	−4.94670	−	0.402620i	−0.243706	−	0.0198357i
$413$	−25.1485	+	1.86436i	−1.23748	+	0.0917393i
$414$	26.2954	−	17.6093i	1.29235	−	0.865450i
$415$	−18.2101	−	10.5136i	−0.893900	−	0.516093i
$416$	35.2034	−	2.07120i	1.72599	−	0.101549i
$417$	4.24174	+	22.7360i	0.207719	+	1.11339i
$418$	−7.30019	−	2.27747i	−0.357064	−	0.111395i
$419$	4.74969	−	3.98546i	0.232038	−	0.194703i	−0.519354	−	0.854559i	$-0.673827\pi$
$419$	4.74969	−	3.98546i	0.232038	−	0.194703i	0.751392	+	0.659856i	$0.229383\pi$
$420$	−10.4392	+	12.5093i	−0.509380	+	0.610391i
$421$	−36.3137	+	13.2171i	−1.76982	+	0.644162i	−0.769839	+	0.638238i	$0.779663\pi$
$421$	−36.3137	+	13.2171i	−1.76982	+	0.644162i	−0.999982	+	0.00592405i	$0.998114\pi$
$422$	−8.83278	+	17.0937i	−0.429973	+	0.832111i
$423$	−19.0349	+	7.35858i	−0.925506	+	0.357786i
$424$	−6.60317	−	8.44551i	−0.320678	−	0.410150i
$425$	−2.88745	−	7.93320i	−0.140062	−	0.384817i
$426$	−0.136569	+	0.0586501i	−0.00661680	+	0.00284161i
$427$	−22.7723	−	6.42681i	−1.10203	−	0.311015i
$428$	−1.58311	−	5.76834i	−0.0765226	−	0.278823i
$429$	−17.7684	+	10.4948i	−0.857867	+	0.506692i
$430$	−7.48937	−	17.9273i	−0.361170	−	0.864530i
$431$	10.6425	−	18.4333i	0.512629	−	0.887899i	−0.487264	−	0.873255i	$-0.662005\pi$
$431$	10.6425	−	18.4333i	0.512629	−	0.887899i	0.999893	−	0.0146446i	$-0.00466170\pi$
$432$	9.63029	−	18.4189i	0.463338	−	0.886182i
$433$	−13.5643			−0.651857			−0.325929	−	0.945394i	$-0.605677\pi$
$433$	−13.5643			−0.651857			−0.325929	+	0.945394i	$0.605677\pi$
$434$	20.0777	−	10.1918i	0.963758	−	0.489223i
$435$	−14.3382	−	8.08978i	−0.687466	−	0.387875i
$436$	7.10288	−	7.18940i	0.340166	−	0.344310i
$437$	13.5656	+	16.1669i	0.648932	+	0.773367i
$438$	3.07266	−	1.31956i	0.146817	−	0.0630512i
$439$	1.17763	+	3.23552i	0.0562054	+	0.154423i	0.964618	−	0.263652i	$-0.0849271\pi$
$439$	1.17763	+	3.23552i	0.0562054	+	0.154423i	−0.908412	+	0.418075i	$0.862705\pi$
$440$	−3.59675	+	8.91135i	−0.171468	+	0.424832i
$441$	−7.04979	−	19.7813i	−0.335704	−	0.941967i
$442$	21.8397	+	34.0536i	1.03881	+	1.61976i
$443$	0.767417	+	0.643940i	0.0364611	+	0.0305945i	0.660836	−	0.750530i	$-0.270202\pi$
$443$	0.767417	+	0.643940i	0.0364611	+	0.0305945i	−0.624375	+	0.781125i	$0.714646\pi$
$444$	25.8871	+	25.0734i	1.22855	+	1.18993i
$445$	0.196081	+	1.11203i	0.00929515	+	0.0527154i
$446$	−5.69044	−	1.77527i	−0.269450	−	0.0840615i
$447$	14.6157	+	5.15622i	0.691299	+	0.243881i
$448$	3.77740	+	20.8262i	0.178465	+	0.983946i
$449$	29.9811	−	17.3096i	1.41490	−	0.816890i	0.419051	−	0.907963i	$-0.362363\pi$
$449$	29.9811	−	17.3096i	1.41490	−	0.816890i	0.995844	+	0.0910723i	$0.0290294\pi$
$450$	−7.57988	+	1.86308i	−0.357319	+	0.0878265i
$451$	−0.690983	+	0.398939i	−0.0325371	+	0.0187853i
$452$	3.41238	−	4.93672i	0.160505	−	0.232204i
$453$	5.53831	−	33.3382i	0.260212	−	1.56636i
$454$	−6.10361	+	19.5645i	−0.286457	+	0.918207i
$455$	−28.4194	+	7.21223i	−1.33232	+	0.338115i
$456$	12.9039	+	5.06008i	0.604282	+	0.236960i
$457$	5.48151	−	31.0872i	0.256414	−	1.45420i	−0.536002	−	0.844217i	$-0.680066\pi$
$457$	5.48151	−	31.0872i	0.256414	−	1.45420i	0.792416	−	0.609981i	$-0.208823\pi$
$458$	−1.74444	−	0.901397i	−0.0815122	−	0.0421195i
$459$	23.8336	−	0.708860i	1.11246	−	0.0330867i
$460$	21.6320	−	15.3429i	1.00860	−	0.715367i
$461$	−15.5176	+	18.4931i	−0.722726	+	0.861311i	−0.994893	−	0.100939i	$-0.967815\pi$
$461$	−15.5176	+	18.4931i	−0.722726	+	0.861311i	0.272167	+	0.962250i	$0.412260\pi$
$462$	−7.53697	−	9.82907i	−0.350651	−	0.457290i
$463$	−33.7574	+	5.95233i	−1.56884	+	0.276628i	−0.889409	−	0.457113i	$-0.848883\pi$
$463$	−33.7574	+	5.95233i	−1.56884	+	0.276628i	−0.679429	+	0.733741i	$0.737772\pi$
$464$	−20.0071	+	7.55755i	−0.928807	+	0.350850i
$465$	−18.2786	−	3.03653i	−0.847648	−	0.140816i
$466$	−12.5599	−	9.57727i	−0.581825	−	0.443658i
$467$	17.9747			0.831772			0.415886	−	0.909417i	$-0.363472\pi$
$467$	17.9747			0.831772			0.415886	+	0.909417i	$0.363472\pi$
$468$	33.4786	−	16.6791i	1.54755	−	0.770993i
$469$	21.3184	+	10.2875i	0.984393	+	0.475031i
$470$	−15.7803	+	6.59245i	−0.727892	+	0.304087i
$471$	18.1655	+	21.2181i	0.837021	+	0.977679i
$472$	25.6363	−	8.33976i	1.18000	−	0.383869i
$473$	14.5457	−	2.56480i	0.668812	−	0.117930i
$474$	1.58664	−	5.26891i	0.0728766	−	0.242009i
$475$	−1.78029	−	4.89131i	−0.0816854	−	0.224429i
$476$	−18.7129	+	15.4733i	−0.857706	+	0.709220i
$477$	−9.95814	−	5.48909i	−0.455952	−	0.251328i
$478$	−0.535094	−	11.4596i	−0.0244746	−	0.524149i
$479$	−14.1111	−	11.8406i	−0.644754	−	0.541013i	0.260720	−	0.965414i	$-0.416040\pi$
$479$	−14.1111	−	11.8406i	−0.644754	−	0.541013i	−0.905474	+	0.424402i	$0.860485\pi$
$480$	7.65324	−	15.6464i	0.349321	−	0.714157i
$481$	11.2619	+	63.8696i	0.513500	+	2.91220i
$482$	−29.2570	+	6.57910i	−1.33262	+	0.299670i
$483$	2.86490	+	34.0624i	0.130357	+	1.54989i
$484$	12.0878	+	8.35537i	0.549445	+	0.379789i
$485$	−17.8301	+	10.2942i	−0.809624	+	0.467437i
$486$	1.72477	−	21.9778i	0.0782372	−	0.996935i
$487$	2.67745	+	1.54582i	0.121327	+	0.0700480i	0.559435	−	0.828874i	$-0.311018\pi$
$487$	2.67745	+	1.54582i	0.121327	+	0.0700480i	−0.438108	+	0.898922i	$0.644351\pi$
$488$	25.2804	+	0.873852i	1.14439	+	0.0395574i
$489$	6.79388	+	11.5025i	0.307230	+	0.520163i
$490$	−6.35056	−	16.4126i	−0.286889	−	0.741445i
$491$	5.43380	+	1.97774i	0.245224	+	0.0892543i	0.461708	−	0.887032i	$-0.347237\pi$
$491$	5.43380	+	1.97774i	0.245224	+	0.0892543i	−0.216484	+	0.976286i	$0.569459\pi$
$492$	1.30074	−	0.632019i	0.0586419	−	0.0284936i
$493$	−18.7950	−	15.7709i	−0.846483	−	0.710283i
$494$	13.4655	+	20.9961i	0.605843	+	0.944661i
$495$	0.202030	+	10.1908i	0.00908057	+	0.458041i
$496$	−18.2508	+	15.6946i	−0.819483	+	0.704710i
$497$	0.0161125	−	0.159728i	0.000722744	−	0.00716480i
$498$	−21.1064	+	19.8488i	−0.945799	+	0.889448i
$499$	2.55622	−	7.02315i	0.114432	−	0.314400i	−0.869234	−	0.494400i	$-0.835388\pi$
$499$	2.55622	−	7.02315i	0.114432	−	0.314400i	0.983666	+	0.180001i	$0.0576100\pi$
$500$	−23.4510	+	6.43609i	−1.04876	+	0.287831i
$501$	−13.5446	+	38.3932i	−0.605127	+	1.71528i
$502$	8.70001	−	11.4094i	0.388300	−	0.509227i
$503$	−13.4980	−	23.3792i	−0.601847	−	1.04243i	−0.992541	−	0.121908i	$-0.961099\pi$
$503$	−13.4980	−	23.3792i	−0.601847	−	1.04243i	0.390695	−	0.920520i	$-0.372235\pi$
$504$	12.3569	+	18.7432i	0.550420	+	0.834888i
$505$	−3.07011	+	5.31758i	−0.136618	+	0.236629i
$506$	7.77182	+	18.6034i	0.345500	+	0.827021i
$507$	44.1878	+	7.34071i	1.96245	+	0.326012i
$508$	27.7685	+	27.4343i	1.23203	+	1.21720i
$509$	−14.8349	−	17.6796i	−0.657546	−	0.783633i	0.329485	−	0.944161i	$-0.393125\pi$
$509$	−14.8349	−	17.6796i	−0.657546	−	0.783633i	−0.987031	+	0.160527i	$0.948680\pi$
$510$	19.9498	−	1.12979i	0.883392	−	0.0500279i
$511$	−0.362514	+	3.59372i	−0.0160367	+	0.158977i
$512$	−9.22535	−	20.6614i	−0.407707	−	0.913113i
$513$	14.6949	−	0.437056i	0.648795	−	0.0192965i
$514$	−10.0713	+	19.4906i	−0.444226	+	0.859694i
$515$	−4.14538	+	1.50879i	−0.182667	+	0.0664854i
$516$	−26.6283	+	2.75868i	−1.17225	+	0.121444i
$517$	−2.25764	−	12.8037i	−0.0992909	−	0.563107i
$518$	−37.2429	+	11.3247i	−1.63636	+	0.497578i
$519$	−17.4296	−	14.3332i	−0.765074	−	0.629158i
$520$	27.6705	−	14.7252i	1.21343	−	0.645744i
$521$	1.50064	−	0.866395i	0.0657442	−	0.0379574i	−0.466768	−	0.884380i	$-0.654582\pi$
$521$	1.50064	−	0.866395i	0.0657442	−	0.0379574i	0.532512	+	0.846423i	$0.321248\pi$
$522$	−16.3701	+	15.7034i	−0.716500	+	0.687318i
$523$	−9.09857	−	5.25306i	−0.397853	−	0.229700i	0.287704	−	0.957719i	$-0.407108\pi$
$523$	−9.09857	−	5.25306i	−0.397853	−	0.229700i	−0.685557	+	0.728019i	$0.740441\pi$
$524$	23.7961	−	11.2722i	1.03954	−	0.492427i
$525$	2.20940	−	8.13624i	0.0964260	−	0.355095i
$526$	−26.3981	−	28.6340i	−1.15101	−	1.24850i
$527$	−25.9489	−	9.44462i	−1.13035	−	0.411414i
$528$	10.3284	+	8.28598i	0.449486	+	0.360601i
$529$	5.66801	−	32.1449i	0.246435	−	1.39760i
$530$	−8.46553	−	4.37436i	−0.367719	−	0.190010i
$531$	21.5357	−	18.8104i	0.934568	−	0.816302i
$532$	−11.5377	+	9.54028i	−0.500222	+	0.413624i
$533$	2.56293	+	0.451913i	0.111013	+	0.0195745i
$534$	1.54509	+	0.183112i	0.0668626	+	0.00792401i
$535$	−3.41757	−	4.07290i	−0.147754	−	0.176087i
$536$	−24.7540	−	5.25248i	−1.06921	−	0.226872i
$537$	−0.206827	−	20.8675i	−0.00892526	−	0.900501i
$538$	−2.44114	−	1.86144i	−0.105245	−	0.0802523i
$539$	13.2323	−	1.97277i	0.569956	−	0.0849734i
$540$	0.950633	−	18.4500i	0.0409087	−	0.793960i
$541$	6.25975	+	10.8422i	0.269128	+	0.466143i	0.968637	−	0.248481i	$-0.0799313\pi$
$541$	6.25975	+	10.8422i	0.269128	+	0.466143i	−0.699509	+	0.714624i	$0.746598\pi$
$542$	−34.9617	+	14.6058i	−1.50173	+	0.627371i
$543$	−3.80328	−	2.14585i	−0.163215	−	0.0920873i
$544$	15.4889	−	20.8308i	0.664079	−	0.893113i
$545$	3.07238	−	8.44130i	0.131606	−	0.361586i
$546$	−1.77554	+	40.3612i	−0.0759862	+	1.72730i
$547$	−42.8594	−	7.55727i	−1.83254	−	0.323125i	−0.852619	−	0.522534i	$-0.824987\pi$
$547$	−42.8594	−	7.55727i	−1.83254	−	0.323125i	−0.979917	+	0.199408i	$0.936098\pi$
$548$	−2.84672	−	30.4162i	−0.121606	−	1.29932i
$549$	25.0251	−	9.67430i	1.06804	−	0.412889i
$550$	−0.231941	−	4.96726i	−0.00989002	−	0.211805i
$551$	−11.5883	−	9.72371i	−0.493677	−	0.414244i
$552$	−11.6485	−	34.6366i	−0.495794	−	1.47423i
$553$	4.14657	+	4.25809i	0.176330	+	0.181072i
$554$	1.19663	+	1.29798i	0.0508399	+	0.0551460i
$555$	30.2087	+	10.6572i	1.28229	+	0.452373i
$556$	26.6183	+	2.16651i	1.12887	+	0.0918804i
$557$		−	0.228924i		−	0.00969980i	−0.999988	−	0.00484990i	$-0.998456\pi$
$557$		−	0.228924i		−	0.00969980i	0.999988	−	0.00484990i	$-0.00154378\pi$
$558$	−11.2685	+	22.9098i	−0.477033	+	0.969850i
$559$	−41.7217	−	24.0880i	−1.76464	−	1.01881i
$560$	10.7731	+	15.4236i	0.455245	+	0.651765i
$561$	−2.48940	+	14.9851i	−0.105103	+	0.632671i
$562$	−7.54822	−	33.5667i	−0.318402	−	1.41592i
$563$	28.8678	+	10.5070i	1.21663	+	0.442817i	0.868999	−	0.494814i	$-0.164764\pi$
$563$	28.8678	+	10.5070i	1.21663	+	0.442817i	0.347632	+	0.937631i	$0.386986\pi$
$564$	2.42831	+	23.4393i	0.102250	+	0.986974i
$565$	0.926285	−	5.25322i	0.0389691	−	0.221005i
$566$	−18.1721	+	0.848530i	−0.763832	+	0.0356664i
$567$	19.8589	+	13.1387i	0.833994	+	0.551773i
$568$	0.0239455	+	0.169945i	0.00100473	+	0.00713073i
$569$	−33.0907	−	5.83478i	−1.38723	−	0.244607i	−0.570347	−	0.821404i	$-0.693191\pi$
$569$	−33.0907	−	5.83478i	−1.38723	−	0.244607i	−0.816887	+	0.576797i	$0.804302\pi$
$570$	12.3003	−	0.696586i	0.515203	−	0.0291768i
$571$	−4.26092	+	11.7068i	−0.178314	+	0.489914i	−0.996361	−	0.0852383i	$-0.972835\pi$
$571$	−4.26092	+	11.7068i	−0.178314	+	0.489914i	0.818047	+	0.575152i	$0.195057\pi$
$572$	6.30656	+	22.9790i	0.263690	+	0.960802i
$573$	14.6835	+	2.43929i	0.613410	+	0.101903i
$574$	−0.0841122	+	1.55976i	−0.00351077	+	0.0651032i
$575$	−6.86168	+	11.8848i	−0.286152	+	0.495629i
$576$	−17.6028	−	16.3139i	−0.733449	−	0.679745i
$577$	22.1240			0.921034			0.460517	−	0.887651i	$-0.347664\pi$
$577$	22.1240			0.921034			0.460517	+	0.887651i	$0.347664\pi$
$578$	5.69073	+	0.731682i	0.236703	+	0.0304340i
$579$	−0.452039	+	1.28134i	−0.0187861	+	0.0532507i
$580$	−13.3603	+	13.5231i	−0.554758	+	0.561516i
$581$	−7.69792	−	30.3332i	−0.319364	−	1.25844i
$582$	6.49793	+	27.6145i	0.269348	+	1.14466i
$583$	4.65638	−	5.54925i	0.192847	−	0.229827i
$584$	−0.538749	−	3.82357i	−0.0222936	−	0.158221i
$585$	20.8612	−	25.8865i	0.862503	−	1.07028i
$586$	3.21313	−	0.150034i	0.132733	−	0.00619784i
$587$	1.13488	−	6.43621i	0.0468414	−	0.265651i	−0.952389	−	0.304887i	$-0.901381\pi$
$587$	1.13488	−	6.43621i	0.0468414	−	0.265651i	0.999230	+	0.0392361i	$0.0124924\pi$
$588$	−24.1774	+	1.85795i	−0.997060	+	0.0766207i
$589$	−15.9991	−	5.82320i	−0.659231	−	0.239941i
$590$	17.6177	−	16.2421i	0.725311	−	0.668675i
$591$	8.73075	−	15.4743i	0.359135	−	0.636527i
$592$	35.7845	−	21.2420i	1.47074	−	0.873040i
$593$	14.7519	−	8.51700i	0.605787	−	0.349751i	−0.165528	−	0.986205i	$-0.552933\pi$
$593$	14.7519	−	8.51700i	0.605787	−	0.349751i	0.771315	+	0.636454i	$0.219599\pi$
$594$	13.5257	+	3.78229i	0.554966	+	0.155189i
$595$	−9.37999	+	19.4379i	−0.384542	+	0.796876i
$596$	10.1759	−	14.7216i	0.416821	−	0.603020i
$597$	10.9859	−	0.108886i	0.449624	−	0.00445642i
$598$	19.5849	−	62.7774i	0.800887	−	2.56716i
$599$	−18.6003	+	15.6075i	−0.759987	+	0.637705i	−0.938124	−	0.346301i	$-0.887438\pi$
$599$	−18.6003	+	15.6075i	−0.759987	+	0.637705i	0.178136	+	0.984006i	$0.442993\pi$
$600$	−0.222071	+	9.01026i	−0.00906603	+	0.367842i
$601$	−2.58652	+	14.6689i	−0.105506	+	0.598356i	0.885511	+	0.464619i	$0.153809\pi$
$601$	−2.58652	+	14.6689i	−0.105506	+	0.598356i	−0.991017	+	0.133737i	$0.957302\pi$
$602$	11.3386	−	26.6000i	0.462127	−	1.08414i
$603$	−26.3348	+	5.18375i	−1.07244	+	0.211098i
$604$	−35.4662	−	16.2775i	−1.44310	−	0.662322i
$605$	12.8628	+	2.26805i	0.522945	+	0.0922094i
$606$	5.79610	+	6.16332i	0.235451	+	0.250368i
$607$	−7.34963	+	20.1929i	−0.298312	+	0.819606i	0.696470	+	0.717586i	$0.254753\pi$
$607$	−7.34963	+	20.1929i	−0.298312	+	0.819606i	−0.994782	+	0.102020i	$0.967469\pi$
$608$	9.54984	−	12.8435i	0.387297	−	0.520872i
$609$	−6.26206	−	23.6881i	−0.253752	−	0.959890i
$610$	20.7463	−	8.66708i	0.839994	−	0.350920i
$611$	−21.2033	+	36.7251i	−0.857792	+	1.48574i
$612$	6.43554	−	26.7701i	0.260141	−	1.08212i
$613$	18.7681	+	32.5073i	0.758037	+	1.31296i	0.943850	+	0.330374i	$0.107175\pi$
$613$	18.7681	+	32.5073i	0.758037	+	1.31296i	−0.185813	+	0.982585i	$0.559492\pi$
$614$	−9.98465	+	4.17123i	−0.402948	+	0.168337i
$615$	0.816452	−	0.992829i	0.0329225	−	0.0400347i
$616$	−13.2364	+	5.41787i	−0.533309	+	0.218292i
$617$	19.7855	−	3.48871i	0.796533	−	0.140450i	0.239452	−	0.970908i	$-0.423032\pi$
$617$	19.7855	−	3.48871i	0.796533	−	0.140450i	0.557081	+	0.830458i	$0.311921\pi$
$618$	0.343683	+	6.06875i	0.0138250	+	0.244121i
$619$	2.27278	+	6.24441i	0.0913507	+	0.250984i	0.976951	−	0.213465i	$-0.0684748\pi$
$619$	2.27278	+	6.24441i	0.0913507	+	0.250984i	−0.885600	+	0.464449i	$0.846253\pi$
$620$	−8.92459	+	19.4453i	−0.358420	+	0.780943i
$621$	−25.7858	−	28.9377i	−1.03475	−	1.16123i
$622$	−1.96668	−	42.1184i	−0.0788565	−	1.68879i
$623$	−0.982113	+	1.36373i	−0.0393475	+	0.0546367i
$624$	−8.43445	−	42.3581i	−0.337648	−	1.69568i
$625$	−9.51151	+	7.98110i	−0.380460	+	0.319244i
$626$	0.190495	+	0.206630i	0.00761371	+	0.00825858i
$627$	−1.53487	+	9.23925i	−0.0612969	+	0.368980i
$628$	29.1481	−	13.8074i	1.16314	−	0.550976i
$629$	41.3440	+	23.8700i	1.64849	+	0.951759i
$630$	16.9316	+	10.5599i	0.674569	+	0.420716i
$631$	20.9026	−	12.0681i	0.832119	−	0.480424i	−0.0224588	−	0.999748i	$-0.507149\pi$
$631$	20.9026	−	12.0681i	0.832119	−	0.480424i	0.854578	+	0.519324i	$0.173816\pi$
$632$	−5.38959	−	3.36514i	−0.214386	−	0.133858i
$633$	22.2229	+	7.83993i	0.883281	+	0.311609i
$634$	−5.78622	−	25.7311i	−0.229800	−	1.02191i
$635$	32.6039	+	11.8668i	1.29385	+	0.470921i
$636$	−9.13481	+	9.43123i	−0.362219	+	0.373973i
$637$	−37.1988	−	22.8136i	−1.47387	−	0.903909i
$638$	−7.80168	−	12.1648i	−0.308872	−	0.481608i
$639$	0.0941239	+	0.155811i	0.00372348	+	0.00616380i
$640$	−15.1130	−	13.2705i	−0.597393	−	0.524564i
$641$	−2.25891	+	2.69206i	−0.0892215	+	0.106330i	−0.808808	−	0.588073i	$-0.799887\pi$
$641$	−2.25891	+	2.69206i	−0.0892215	+	0.106330i	0.719587	+	0.694403i	$0.244331\pi$
$642$	−6.73149	+	2.89086i	−0.265671	+	0.114093i
$643$	8.84481	−	24.3009i	0.348805	−	0.958335i	−0.633942	−	0.773381i	$-0.718564\pi$
$643$	8.84481	−	24.3009i	0.348805	−	0.958335i	0.982747	−	0.184954i	$-0.0592136\pi$
$644$	38.8207	+	7.13426i	1.52975	+	0.281129i
$645$	−20.4884	+	12.1013i	−0.806731	+	0.476489i
$646$	18.2108	+	2.34145i	0.716495	+	0.0921230i
$647$	14.4073	−	24.9542i	0.566410	−	0.981051i	−0.430507	−	0.902587i	$-0.641665\pi$
$647$	14.4073	−	24.9542i	0.566410	−	0.981051i	0.996917	−	0.0784634i	$-0.0250014\pi$
$648$	−23.9647	−	8.58450i	−0.941422	−	0.337231i
$649$	9.10825	+	15.7760i	0.357530	+	0.619260i
$650$	−9.83483	+	12.8976i	−0.385754	+	0.505887i
$651$	−15.7415	−	22.6425i	−0.616957	−	0.887431i
$652$	14.8757	−	4.08261i	0.582577	−	0.159887i
$653$	0.189876	−	0.0334803i	0.00743043	−	0.00131018i	−0.169932	−	0.985456i	$-0.554355\pi$
$653$	0.189876	−	0.0334803i	0.00743043	−	0.00131018i	0.177362	+	0.984146i	$0.443244\pi$
$654$	−9.91655	−	7.40739i	−0.387768	−	0.289652i
$655$	15.0440	−	17.9287i	0.587816	−	0.700532i
$656$	−0.309861	−	1.64088i	−0.0120980	−	0.0640656i
$657$	−2.11769	−	3.50558i	−0.0826188	−	0.136766i
$658$	−23.4144	−	9.98070i	−0.912789	−	0.389088i
$659$	0.101420	−	0.0369138i	0.00395075	−	0.00143796i	−0.340044	−	0.940410i	$-0.610442\pi$
$659$	0.101420	−	0.0369138i	0.00395075	−	0.00143796i	0.343995	+	0.938972i	$0.388220\pi$
$660$	11.4157	+	2.86432i	0.444357	+	0.111493i
$661$	−1.05921	−	6.00710i	−0.0411986	−	0.233649i	0.957255	−	0.289247i	$-0.0934048\pi$
$661$	−1.05921	−	6.00710i	−0.0411986	−	0.233649i	−0.998453	+	0.0555975i	$0.982294\pi$
$662$	−0.460152	−	2.04628i	−0.0178843	−	0.0795310i
$663$	37.6379	−	32.2229i	1.46173	−	1.25144i
$664$	15.7169	+	29.5339i	0.609933	+	1.14614i
$665$	−5.78335	+	11.9847i	−0.224269	+	0.464746i
$666$	26.0629	−	35.6223i	1.00992	−	1.38034i
$667$			39.8828i			1.54427i
$668$	38.6713	+	26.7305i	1.49624	+	1.03423i
$669$	−1.19642	+	7.20192i	−0.0462563	+	0.278442i
$670$	−21.9445	+	4.93472i	−0.847791	+	0.190645i
$671$	2.96811	+	16.8330i	0.114583	+	0.649831i
$672$	24.6296	−	8.08582i	0.950109	−	0.311917i
$673$	1.07391	+	0.901115i	0.0413961	+	0.0347354i	0.663251	−	0.748397i	$-0.269176\pi$
$673$	1.07391	+	0.901115i	0.0413961	+	0.0347354i	−0.621855	+	0.783132i	$0.713621\pi$
$674$	−42.0265	+	26.9530i	−1.61880	+	1.03819i
$675$	3.53524	+	8.88203i	0.136071	+	0.341870i
$676$	21.5749	−	47.0084i	0.829803	−	1.80801i
$677$	−41.9836	−	7.40284i	−1.61356	−	0.284514i	−0.707198	−	0.707016i	$-0.750041\pi$
$677$	−41.9836	−	7.40284i	−1.61356	−	0.284514i	−0.906362	+	0.422502i	$0.861152\pi$
$678$	−6.56294	−	3.30925i	−0.252048	−	0.127091i
$679$	−29.4898	−	8.32265i	−1.13172	−	0.319394i
$680$	4.78915	−	22.5705i	0.183655	−	0.865538i
$681$	24.7611	+	4.11345i	0.948849	+	0.157628i
$682$	−12.9340	−	9.86254i	−0.495268	−	0.377656i
$683$	−8.06552	−	13.9699i	−0.308619	−	0.534543i	0.669442	−	0.742865i	$-0.266533\pi$
$683$	−8.06552	−	13.9699i	−0.308619	−	0.534543i	−0.978060	+	0.208321i	$0.933200\pi$
$684$	3.96791	−	16.5054i	0.151717	−	0.631101i
$685$	−13.5768	−	23.5158i	−0.518744	−	0.898491i
$686$	10.9060	−	23.8130i	0.416394	−	0.909184i
$687$	−0.800074	+	2.26787i	−0.0305247	+	0.0865248i
$688$	−4.99890	+	30.5054i	−0.190581	+	1.16301i
$689$	−23.2691	+	4.10297i	−0.886483	+	0.156311i
$690$	−22.2519	−	23.6617i	−0.847117	−	0.900786i
$691$	−3.38862	+	4.03840i	−0.128909	+	0.153628i	−0.826638	−	0.562734i	$-0.809750\pi$
$691$	−3.38862	+	4.03840i	−0.128909	+	0.153628i	0.697729	+	0.716362i	$0.254194\pi$
$692$	−21.2539	+	15.0747i	−0.807952	+	0.573054i
$693$	−10.6562	+	10.7968i	−0.404795	+	0.410136i
$694$	37.2142	+	19.2295i	1.41263	+	0.729943i
$695$	22.3064	−	8.11885i	0.846128	−	0.307966i
$696$	12.5339	+	23.0001i	0.475095	+	0.871816i
$697$	1.46750	−	1.23138i	0.0555855	−	0.0466418i
$698$	27.4574	+	29.7830i	1.03928	+	1.12730i
$699$	−9.50576	+	16.8479i	−0.359541	+	0.637247i
$700$	−8.39556	−	4.92827i	−0.317322	−	0.186271i
$701$		−	4.12598i		−	0.155836i	−0.996960	−	0.0779181i	$-0.975173\pi$
$701$		−	4.12598i		−	0.155836i	0.996960	−	0.0779181i	$-0.0248273\pi$
$702$	−25.8657	−	37.8085i	−0.976240	−	1.42699i
$703$	25.4912	+	14.7173i	0.961418	+	0.555075i
$704$	12.3633	−	8.99587i	0.465961	−	0.339044i
$705$	10.6521	+	18.0347i	0.401180	+	0.679228i
$706$	−0.764187	−	3.39831i	−0.0287606	−	0.127897i
$707$	−8.85768	+	2.24789i	−0.333127	+	0.0845406i
$708$	−14.4297	−	29.6974i	−0.542302	−	1.11610i
$709$	−18.9137	+	6.88403i	−0.710319	+	0.258535i	−0.671810	−	0.740723i	$-0.734483\pi$
$709$	−18.9137	+	6.88403i	−0.710319	+	0.258535i	−0.0385089	+	0.999258i	$0.512261\pi$
$710$	0.0823529	+	0.128409i	0.00309065	+	0.00481910i
$711$	−6.65882	−	1.03849i	−0.249725	−	0.0389464i
$712$	0.672429	−	1.66602i	0.0252003	−	0.0624366i
$713$	15.3526	+	42.1809i	0.574959	+	1.57969i
$714$	21.9191	+	20.0985i	0.820303	+	0.752167i
$715$	13.6144	+	16.2250i	0.509149	+	0.606780i
$716$	−23.3132	−	6.09573i	−0.871255	−	0.227808i
$717$	−13.8120	+	2.57684i	−0.515820	+	0.0962338i
$718$	−2.37987	−	0.305991i	−0.0888161	−	0.0114195i
$719$	0.636712	−	1.10282i	0.0237454	−	0.0411282i	−0.853909	−	0.520423i	$-0.825774\pi$
$719$	0.636712	−	1.10282i	0.0237454	−	0.0411282i	0.877654	+	0.479295i	$0.159108\pi$
$720$	−20.2686	−	6.65245i	−0.755368	−	0.247922i
$721$	−5.91303	−	2.85340i	−0.220213	−	0.106266i
$722$	−15.4226	−	1.98295i	−0.573968	−	0.0737976i
$723$	12.9029	+	34.3861i	0.479863	+	1.27883i
$724$	−3.54389	+	3.58706i	−0.131708	+	0.133312i
$725$	3.36437	−	9.24354i	0.124950	−	0.343296i
$726$	8.10284	−	16.0697i	0.300725	−	0.596401i
$727$	2.48214	−	2.95810i	0.0920573	−	0.109710i	−0.718049	−	0.695992i	$-0.754965\pi$
$727$	2.48214	−	2.95810i	0.0920573	−	0.109710i	0.810107	+	0.586283i	$0.199409\pi$
$728$	44.4320	+	14.2142i	1.64676	+	0.526812i
$729$	−26.9523	+	1.60465i	−0.998232	+	0.0594316i
$730$	−1.85285	−	2.88906i	−0.0685771	−	0.106929i
$731$	−33.3239	+	12.1289i	−1.23253	+	0.448604i
$732$	−3.19249	−	30.8156i	−0.117998	−	1.13898i
$733$	−19.1276	+	16.0500i	−0.706494	+	0.592819i	−0.923613	−	0.383326i	$-0.874778\pi$
$733$	−19.1276	+	16.0500i	−0.706494	+	0.592819i	0.217119	+	0.976145i	$0.430334\pi$
$734$	−15.2275	−	4.75058i	−0.562056	−	0.175347i
$735$	−18.8425	+	10.4650i	−0.695014	+	0.386006i
$736$	−42.1232	+	2.47833i	−1.55268	+	0.0913525i
$737$		−	17.0992i		−	0.629857i
$738$	−0.985532	−	1.47166i	−0.0362779	−	0.0541726i
$739$			0.946193i			0.0348063i	0.999849	+	0.0174031i	$0.00553987\pi$
$739$			0.946193i			0.0348063i	−0.999849	+	0.0174031i	$0.994460\pi$
$740$	21.0322	−	30.4275i	0.773159	−	1.11854i
$741$	23.2061	−	19.8675i	0.852497	−	0.729849i
$742$	−4.12583	−	13.5684i	−0.151464	−	0.498113i
$743$	11.0399	−	9.26359i	0.405015	−	0.339848i	−0.417413	−	0.908717i	$-0.637063\pi$
$743$	11.0399	−	9.26359i	0.405015	−	0.339848i	0.822428	+	0.568869i	$0.192619\pi$
$744$	22.1098	+	19.5006i	0.810586	+	0.714926i
$745$	2.76223	−	15.6654i	0.101200	−	0.573936i
$746$	−1.64822	−	35.2983i	−0.0603455	−	1.29236i
$747$	27.6298	+	22.2660i	1.01092	+	0.814671i
$748$	15.9416	+	7.31654i	0.582883	+	0.267519i
$749$	0.794184	−	7.87301i	0.0290189	−	0.287674i
$750$	11.7527	+	27.3667i	0.429148	+	0.999289i
$751$	22.3940	−	3.94867i	0.817169	−	0.144089i	0.250587	−	0.968094i	$-0.419376\pi$
$751$	22.3940	−	3.94867i	0.817169	−	0.144089i	0.566582	+	0.824005i	$0.308265\pi$
$752$	26.8521	+	4.40023i	0.979197	+	0.160460i
$753$	−15.3047	−	8.63505i	−0.557733	−	0.314679i
$754$	−6.01115	+	46.7523i	−0.218913	+	1.70262i
$755$	−34.6858			−1.26235
$756$	20.6594	−	18.1435i	0.751376	−	0.659874i
$757$	−21.0945			−0.766692			−0.383346	−	0.923605i	$-0.625228\pi$
$757$	−21.0945			−0.766692			−0.383346	+	0.923605i	$0.625228\pi$
$758$	−0.728243	+	5.66398i	−0.0264510	+	0.205725i
$759$	21.2611	−	12.5577i	0.771729	−	0.455815i
$760$	2.95281	−	13.9161i	0.107110	−	0.504790i
$761$	−24.3479	+	4.29319i	−0.882611	+	0.155628i	−0.596543	−	0.802581i	$-0.703459\pi$
$761$	−24.3479	+	4.29319i	−0.882611	+	0.155628i	−0.286068	+	0.958209i	$0.592348\pi$
$762$	28.6105	−	38.3019i	1.03645	−	1.38753i
$763$	12.1907	−	5.48892i	0.441334	−	0.198712i
$764$	7.16926	−	15.6207i	0.259375	−	0.565138i
$765$	−4.72648	−	24.0118i	−0.170886	−	0.868149i
$766$	1.91180	+	40.9431i	0.0690760	+	1.47933i
$767$	10.3177	−	58.5146i	0.372551	−	2.11284i
$768$	−23.5133	+	14.6672i	−0.848461	+	0.529257i
$769$	−4.67024	+	3.91880i	−0.168413	+	0.141315i	−0.723099	−	0.690744i	$-0.757283\pi$
$769$	−4.67024	+	3.91880i	−0.168413	+	0.141315i	0.554686	+	0.832060i	$0.312838\pi$
$770$	−8.68405	+	9.28428i	−0.312951	+	0.334582i
$771$	25.3390	+	8.93923i	0.912560	+	0.321939i
$772$	1.29062	+	0.892109i	0.0464505	+	0.0321077i
$773$			30.7940i			1.10758i	0.832656	+	0.553791i	$0.186819\pi$
$773$			30.7940i			1.10758i	−0.832656	+	0.553791i	$0.813181\pi$
$774$	7.82599	+	31.8398i	0.281300	+	1.14446i
$775$		−	11.0713i		−	0.397692i
$776$	32.7378	+	1.13163i	1.17522	+	0.0406231i
$777$	20.0033	+	43.2758i	0.717614	+	1.55251i
$778$	24.3434	+	7.59452i	0.872754	+	0.272277i
$779$	0.904805	−	0.759222i	0.0324180	−	0.0272019i
$780$	−22.5184	−	31.0911i	−0.806287	−	1.11324i
$781$	−0.108976	+	0.0396639i	−0.00389945	+	0.00141928i
$782$	−26.1327	−	40.7474i	−0.934502	−	1.45712i
$783$	21.8041	+	17.2176i	0.779215	+	0.615307i
$784$	−5.25947	+	27.5016i	−0.187838	+	0.982200i
$785$	18.4275	−	21.9611i	0.657707	−	0.783824i
$786$	−17.6776	−	26.9718i	−0.630539	−	0.962051i
$787$	−7.19335	+	19.7636i	−0.256415	+	0.704495i	0.742966	+	0.669329i	$0.233418\pi$
$787$	−7.19335	+	19.7636i	−0.256415	+	0.704495i	−0.999381	+	0.0351664i	$0.988804\pi$
$788$	−14.5946	−	14.4189i	−0.519909	−	0.513652i
$789$	−30.2964	+	36.8413i	−1.07858	+	1.31158i
$790$	−5.60155	−	0.720216i	−0.199294	−	0.0256241i
$791$	6.56306	−	4.46692i	0.233356	−	0.158826i
$792$	8.31463	−	13.9236i	0.295447	−	0.494754i
$793$	27.8759	−	48.2824i	0.989901	−	1.71456i
$794$	−33.8664	−	4.35436i	−1.20187	−	0.154530i
$795$	−3.88266	+	11.0057i	−0.137704	+	0.390332i
$796$	3.20916	−	12.2735i	0.113746	−	0.435022i
$797$	30.6278	+	36.5008i	1.08489	+	1.29292i	0.953434	+	0.301602i	$0.0975215\pi$
$797$	30.6278	+	36.5008i	1.08489	+	1.29292i	0.131458	+	0.991322i	$0.458034\pi$
$798$	13.5145	+	12.3920i	0.478408	+	0.438671i
$799$	10.6764	+	29.3331i	0.377703	+	1.03773i
$800$	9.97186	+	2.97897i	0.352558	+	0.105322i
$801$	−0.0377704	−	1.90521i	−0.00133455	−	0.0673172i
$802$	2.90097	+	4.52333i	0.102437	+	0.159724i
$803$	2.45183	−	0.892394i	0.0865233	−	0.0314919i
$804$	−2.20793	+	30.9136i	−0.0778678	+	1.09024i
$805$	34.0057	−	8.62992i	1.19854	−	0.304165i
$806$	11.6395	+	51.7602i	0.409982	+	1.82318i
$807$	−1.84754	+	3.27456i	−0.0650365	+	0.115270i
$808$	8.62427	−	4.58952i	0.303401	−	0.161459i
$809$	−25.5024	−	14.7238i	−0.896616	−	0.517662i	−0.0205154	−	0.999790i	$-0.506531\pi$
$809$	−25.5024	−	14.7238i	−0.896616	−	0.517662i	−0.876101	+	0.482128i	$0.839864\pi$
$810$	−22.5423	+	1.95034i	−0.792054	+	0.0685281i
$811$		−	15.8744i		−	0.557425i	−0.960375	−	0.278712i	$-0.910092\pi$
$811$		−	15.8744i		−	0.557425i	0.960375	−	0.278712i	$-0.0899076\pi$
$812$	−28.2915	−	0.204098i	−0.992838	−	0.00716242i
$813$	23.5999	+	39.9564i	0.827686	+	1.40133i
$814$	19.0600	+	20.6744i	0.668053	+	0.724636i
$815$	10.5034	−	8.81339i	0.367918	−	0.308720i
$816$	−27.8761	−	15.2860i	−0.975859	−	0.535118i
$817$	−20.5463	+	7.47824i	−0.718823	+	0.261630i
$818$	14.3044	+	7.39146i	0.500142	+	0.258436i
$819$	49.2624	−	4.63546i	1.72137	−	0.161976i
$820$	−0.858690	−	1.21067i	−0.0299868	−	0.0422785i
$821$	1.65951	−	1.97773i	0.0579174	−	0.0690233i	−0.736308	−	0.676647i	$-0.763433\pi$
$821$	1.65951	−	1.97773i	0.0579174	−	0.0690233i	0.794225	+	0.607623i	$0.207877\pi$
$822$	−36.4202	+	8.56998i	−1.27030	+	0.298912i
$823$	2.24226	−	0.395370i	0.0781601	−	0.0137817i	−0.134431	−	0.990923i	$-0.542921\pi$
$823$	2.24226	−	0.395370i	0.0781601	−	0.0137817i	0.212591	+	0.977141i	$0.431810\pi$
$824$	6.86596	+	1.45686i	0.239187	+	0.0507523i
$825$	−5.98696	+	1.11695i	−0.208439	+	0.0388873i
$826$	35.6112	+	1.92038i	1.23907	+	0.0668186i
$827$	5.87011	+	10.1673i	0.204124	+	0.353553i	0.949853	−	0.312696i	$-0.101232\pi$
$827$	5.87011	+	10.1673i	0.204124	+	0.353553i	−0.745729	+	0.666249i	$0.767899\pi$
$828$	−40.0594	+	19.9577i	−1.39216	+	0.693578i
$829$	14.8461	+	25.7141i	0.515625	+	0.893089i	0.999836	+	0.0181374i	$0.00577364\pi$
$829$	14.8461	+	25.7141i	0.515625	+	0.893089i	−0.484210	+	0.874952i	$0.660893\pi$
$830$	23.6466	+	18.0313i	0.820787	+	0.625874i
$831$	1.37334	−	1.67002i	0.0476406	−	0.0579323i
$832$	−49.7521	−	3.44362i	−1.72485	−	0.119386i
$833$	−30.4653	+	10.1815i	−1.05556	+	0.352768i
$834$	−1.84937	−	32.6561i	−0.0640383	−	1.13079i
$835$	41.1506	+	7.25596i	1.42407	+	0.251103i
$836$	9.82900	+	4.51110i	0.339943	+	0.156020i
$837$	29.6883	+	9.81640i	1.02618	+	0.339305i
$838$	−7.38100	+	4.73369i	−0.254973	+	0.163523i
$839$	5.30933	+	4.45506i	0.183298	+	0.153806i	0.729820	−	0.683639i	$-0.239604\pi$
$839$	5.30933	+	4.45506i	0.183298	+	0.153806i	−0.546522	+	0.837445i	$0.684048\pi$
$840$	16.8987	−	15.6637i	0.583061	−	0.540449i
$841$	0.0716174	+	0.406163i	0.00246957	+	0.0140056i
$842$	53.3197	−	11.9901i	1.83752	−	0.413207i
$843$	−39.4512	+	14.8035i	−1.35877	+	0.509860i
$844$	15.4723	−	22.3839i	0.532577	−	0.770485i
$845$		−	45.9740i		−	1.58155i
$846$	28.0267	−	6.88876i	0.963577	−	0.236840i
$847$	10.9375	+	16.0700i	0.375816	+	0.552170i
$848$	7.73893	+	13.0371i	0.265756	+	0.447696i
$849$	4.08624	+	21.9026i	0.140239	+	0.751695i
$850$	2.61940	+	11.6484i	0.0898447	+	0.399536i
$851$	−13.4757	−	76.4243i	−0.461940	−	2.61979i
$852$	0.202138	−	0.0576368i	0.00692515	−	0.00197460i
$853$	22.9098	−	8.33849i	0.784417	−	0.285504i	0.0814036	−	0.996681i	$-0.474060\pi$
$853$	22.9098	−	8.33849i	0.784417	−	0.285504i	0.703013	+	0.711177i	$0.251837\pi$
$854$	30.7829	+	13.1216i	1.05337	+	0.449012i
$855$	−2.91417	−	14.8048i	−0.0996625	−	0.506313i
$856$	1.18027	+	8.37657i	0.0403410	+	0.286305i
$857$	−17.2921	+	20.6080i	−0.590688	+	0.703955i	−0.975738	−	0.218941i	$-0.929740\pi$
$857$	−17.2921	+	20.6080i	−0.590688	+	0.703955i	0.385050	+	0.922896i	$0.374184\pi$
$858$	26.8159	−	11.5162i	0.915479	−	0.393156i
$859$	29.9078	−	5.27355i	1.02044	−	0.179931i	0.361694	−	0.932297i	$-0.382198\pi$
$859$	29.9078	−	5.27355i	1.02044	−	0.179931i	0.658746	+	0.752366i	$0.271087\pi$
$860$	7.27197	+	26.4967i	0.247972	+	0.903529i
$861$	1.90636	−	0.160339i	0.0649684	−	0.00546432i
$862$	−18.2522	+	23.9364i	−0.621673	+	0.815277i
$863$	17.0277	+	29.4928i	0.579629	+	1.00395i	0.995522	+	0.0945334i	$0.0301359\pi$
$863$	17.0277	+	29.4928i	0.579629	+	1.00395i	−0.415892	+	0.909414i	$0.636531\pi$
$864$	−16.8299	+	24.0988i	−0.572565	+	0.819859i
$865$	−11.5805	+	20.0580i	−0.393748	+	0.681991i
$866$	19.0262	+	2.44628i	0.646535	+	0.0831278i
$867$	−0.0696448	−	7.02672i	−0.00236526	−	0.238640i
$868$	−30.0003	+	10.6748i	−1.01828	+	0.362325i
$869$	1.46844	−	4.03452i	0.0498135	−	0.136862i
$870$	18.6528	+	13.9331i	0.632390	+	0.472377i
$871$	−35.8502	+	42.7246i	−1.21474	+	1.44767i
$872$	−11.2596	+	8.80335i	−0.381297	+	0.298119i
$873$	32.4072	−	12.5281i	1.09682	−	0.424012i
$874$	−16.1124	−	25.1233i	−0.545011	−	0.849808i
$875$	−32.0075	−	3.22873i	−1.08205	−	0.109151i
$876$	−4.54790	+	1.29677i	−0.153659	+	0.0438136i
$877$	−6.73358	−	2.45082i	−0.227377	−	0.0827584i	0.225819	−	0.974169i	$-0.427494\pi$
$877$	−6.73358	−	2.45082i	−0.227377	−	0.0827584i	−0.453196	+	0.891411i	$0.649716\pi$
$878$	−1.06831	−	4.75074i	−0.0360537	−	0.160330i
$879$	−0.722514	−	3.87273i	−0.0243698	−	0.130624i
$880$	6.65218	−	11.8510i	0.224245	−	0.399497i
$881$	2.89340	−	1.67051i	0.0974812	−	0.0562808i	−0.450467	−	0.892793i	$-0.648742\pi$
$881$	2.89340	−	1.67051i	0.0974812	−	0.0562808i	0.547948	+	0.836512i	$0.315409\pi$
$882$	6.32100	+	29.0180i	0.212839	+	0.977087i
$883$	−20.3703	−	11.7608i	−0.685515	−	0.395782i	0.116415	−	0.993201i	$-0.462860\pi$
$883$	−20.3703	−	11.7608i	−0.685515	−	0.395782i	−0.801930	+	0.597418i	$0.796193\pi$
$884$	−24.4924	−	51.7045i	−0.823768	−	1.73901i
$885$	−22.6675	−	18.6406i	−0.761958	−	0.626596i
$886$	−0.960298	−	1.04163i	−0.0322619	−	0.0349944i
$887$	8.72265	−	7.31917i	0.292878	−	0.245754i	−0.484495	−	0.874794i	$-0.660996\pi$
$887$	8.72265	−	7.31917i	0.292878	−	0.245754i	0.777373	+	0.629040i	$0.216552\pi$
$888$	−31.7890	−	39.8383i	−1.06677	−	1.33689i
$889$	21.2005	+	47.0857i	0.711042	+	1.57921i
$890$	−0.0744850	−	1.59517i	−0.00249674	−	0.0534703i
$891$	2.31319	−	17.0448i	0.0774947	−	0.571021i
$892$	7.66163	+	3.51637i	0.256530	+	0.117737i
$893$	6.58265	+	18.0857i	0.220280	+	0.605214i
$894$	−19.5711	−	9.86836i	−0.654554	−	0.330047i
$895$	−21.0932	+	3.71930i	−0.705069	+	0.124323i
$896$	−1.54248	−	29.8935i	−0.0515308	−	0.998671i
$897$	−79.4521	−	13.1990i	−2.65283	−	0.440702i
$898$	−45.1752	+	18.8726i	−1.50752	+	0.629787i
$899$	−16.0876	−	27.8646i	−0.536553	−	0.929337i
$900$	10.9680	−	1.24627i	0.365602	−	0.0415425i
$901$	−8.69637	+	15.0626i	−0.289718	+	0.501807i
$902$	1.04117	−	0.434962i	0.0346670	−	0.0144827i
$903$	−34.1768	−	9.28072i	−1.13733	−	0.308843i
$904$	−5.67675	+	6.30916i	−0.188806	+	0.209840i
$905$	−1.53293	+	4.21168i	−0.0509562	+	0.140001i
$906$	−13.7808	+	45.7635i	−0.457838	+	1.52039i
$907$	−17.2720	−	3.04553i	−0.573509	−	0.101125i	−0.120631	−	0.992697i	$-0.538492\pi$
$907$	−17.2720	−	3.04553i	−0.573509	−	0.101125i	−0.452878	+	0.891572i	$0.649603\pi$
$908$	12.0897	−	26.3417i	0.401212	−	0.874180i
$909$	6.50195	−	8.06825i	0.215656	−	0.267607i
$910$	41.1636	−	4.99100i	1.36456	−	0.165450i
$911$	−7.85465	+	44.5459i	−0.260236	+	1.47587i	0.522030	+	0.852927i	$0.325175\pi$
$911$	−7.85465	+	44.5459i	−0.260236	+	1.47587i	−0.782266	+	0.622945i	$0.785936\pi$
$912$	−17.1874	−	9.42479i	−0.569130	−	0.312086i
$913$	−17.3176	+	14.5312i	−0.573130	+	0.480913i
$914$	−13.2952	+	42.6164i	−0.439767	+	1.40963i
$915$	−14.0042	−	23.7102i	−0.462966	−	0.783835i
$916$	2.28430	+	1.57896i	0.0754755	+	0.0521704i
$917$	34.7372	−	2.57521i	1.14712	−	0.0850409i
$918$	−33.5584	−	3.30402i	−1.10759	−	0.109049i
$919$	−24.8558	+	14.3505i	−0.819918	+	0.473380i	−0.850388	−	0.526156i	$-0.823633\pi$
$919$	−24.8558	+	14.3505i	−0.819918	+	0.473380i	0.0304702	+	0.999536i	$0.490300\pi$
$920$	−33.1096	+	17.6197i	−1.09159	+	0.580905i
$921$	6.73986	+	11.4111i	0.222086	+	0.376008i
$922$	25.1012	−	23.1412i	0.826664	−	0.762114i
$923$	0.355449	+	0.129373i	0.0116997	+	0.00425836i
$924$	8.79921	+	15.1462i	0.289473	+	0.498273i
$925$	−3.32366	+	18.8494i	−0.109281	+	0.619766i
$926$	48.4238	−	2.26110i	1.59131	−	0.0743044i
$927$	7.30442	−	1.43780i	0.239909	−	0.0472236i
$928$	29.4263	−	6.99250i	0.965966	−	0.229540i
$929$	−8.28649	+	9.87545i	−0.271871	+	0.324003i	−0.884654	−	0.466248i	$-0.845605\pi$
$929$	−8.28649	+	9.87545i	−0.271871	+	0.324003i	0.612783	+	0.790251i	$0.290050\pi$
$930$	25.0911	+	7.55573i	0.822770	+	0.247762i
$931$	−18.7837	+	6.27753i	−0.615612	+	0.205738i
$932$	15.8901	+	15.6989i	0.520497	+	0.514233i
$933$	−50.7646	+	9.47087i	−1.66196	+	0.310062i
$934$	−25.2126	−	3.24169i	−0.824981	−	0.106071i
$935$	15.5909			0.509875
$936$	−49.9674	+	17.3575i	−1.63324	+	0.567347i
$937$	6.63039	−	11.4842i	0.216605	−	0.375172i	−0.737163	−	0.675715i	$-0.763835\pi$
$937$	6.63039	−	11.4842i	0.216605	−	0.375172i	0.953768	+	0.300544i	$0.0971681\pi$
$938$	−28.0473	−	18.2746i	−0.915778	−	0.596687i
$939$	0.218626	−	0.265855i	0.00713458	−	0.00867585i
$940$	23.3235	−	6.40108i	0.760727	−	0.208780i
$941$	−11.7201	+	32.2006i	−0.382063	+	1.04971i	0.588423	+	0.808553i	$0.299749\pi$
$941$	−11.7201	+	32.2006i	−0.382063	+	1.04971i	−0.970486	+	0.241157i	$0.922473\pi$
$942$	−21.6535	−	33.0380i	−0.705509	−	1.07644i
$943$	−3.06671	−	0.540744i	−0.0998659	−	0.0176091i
$944$	−37.4632	+	7.07448i	−1.21932	+	0.230255i
$945$	9.96244	−	22.3167i	0.324078	−	0.725961i
$946$	−20.8653	+	0.974285i	−0.678390	+	0.0316767i
$947$	−1.32713	+	7.52650i	−0.0431258	+	0.244579i	−0.998748	−	0.0500149i	$-0.984073\pi$
$947$	−1.32713	+	7.52650i	−0.0431258	+	0.244579i	0.955623	+	0.294593i	$0.0951842\pi$
$948$	−3.17576	+	7.10439i	−0.103144	+	0.230740i
$949$	−7.99722	−	2.91075i	−0.259601	−	0.0944869i
$950$	1.61502	+	7.18196i	0.0523983	+	0.233013i
$951$	−30.2420	+	11.3479i	−0.980665	+	0.367980i
$952$	29.0386	−	18.3291i	0.941146	−	0.594051i
$953$	3.30419	+	1.90768i	0.107033	+	0.0617957i	0.552561	−	0.833472i	$-0.313651\pi$
$953$	3.30419	+	1.90768i	0.107033	+	0.0617957i	−0.445528	+	0.895268i	$0.646984\pi$
$954$	12.9780	+	9.49529i	0.420179	+	0.307421i
$955$		−	15.2770i		−	0.494353i
$956$	−1.31614	+	16.1705i	−0.0425671	+	0.522991i
$957$	−13.4452	+	11.5108i	−0.434621	+	0.372092i
$958$	17.6578	+	19.1534i	0.570497	+	0.618818i
$959$	10.9766	−	38.8935i	0.354452	−	1.25594i
$960$	−13.5567	+	20.5665i	−0.437542	+	0.663779i
$961$	−3.99357	−	3.35100i	−0.128825	−	0.108097i
$962$	−4.27805	−	91.6189i	−0.137930	−	2.95391i
$963$	4.63937	+	7.67993i	0.149501	+	0.247482i
$964$	42.2244	−	3.95187i	1.35996	−	0.127281i
$965$	1.37337	+	0.242162i	0.0442102	+	0.00779546i
$966$	2.12456	−	48.2949i	0.0683565	−	1.55386i
$967$	18.2276	−	50.0798i	0.586159	−	1.61046i	−0.191305	−	0.981531i	$-0.561272\pi$
$967$	18.2276	−	50.0798i	0.586159	−	1.61046i	0.777464	−	0.628928i	$-0.216506\pi$
$968$	−15.4483	−	13.8998i	−0.496527	−	0.446756i
$969$	−0.222870	−	22.4861i	−0.00715960	−	0.722358i
$970$	26.8663	−	11.2238i	0.862624	−	0.360373i
$971$	−27.4635	−	47.5682i	−0.881347	−	1.52654i	−0.849845	−	0.527033i	$-0.823304\pi$
$971$	−27.4635	−	47.5682i	−0.881347	−	1.52654i	−0.0315020	−	0.999504i	$-0.510029\pi$
$972$	−6.38292	+	30.5165i	−0.204732	+	0.978818i
$973$	31.8181	+	15.3542i	1.02004	+	0.492234i
$974$	−3.47678	−	2.65115i	−0.111403	−	0.0849482i
$975$	17.3010	+	9.76140i	0.554076	+	0.312615i
$976$	−35.3024	−	5.78497i	−1.13000	−	0.185172i
$977$	0.673146	+	0.802224i	0.0215358	+	0.0256654i	0.776705	−	0.629865i	$-0.216890\pi$
$977$	0.673146	+	0.802224i	0.0215358	+	0.0256654i	−0.755169	+	0.655530i	$0.772445\pi$
$978$	−7.45510	−	17.3595i	−0.238388	−	0.555096i
$979$	1.19556	+	0.210809i	0.0382101	+	0.00673747i
$980$	5.94776	+	24.1667i	0.189994	+	0.771977i
$981$	−7.31805	+	13.2762i	−0.233647	+	0.423876i
$982$	−7.26514	−	3.75408i	−0.231840	−	0.119798i
$983$	4.70641	−	26.6914i	0.150111	−	0.851322i	−0.813009	−	0.582251i	$-0.802172\pi$
$983$	4.70641	−	26.6914i	0.150111	−	0.851322i	0.963120	−	0.269071i	$-0.0867168\pi$
$984$	−1.93849	+	0.651927i	−0.0617967	+	0.0207827i
$985$	−17.1359	−	6.23697i	−0.545996	−	0.198726i
$986$	23.5189	+	25.5109i	0.748993	+	0.812432i
$987$	−8.16927	+	30.0838i	−0.260031	+	0.957579i
$988$	−15.1011	−	31.8791i	−0.480429	−	1.01421i
$989$	49.9228	+	28.8229i	1.58745	+	0.916516i
$990$	1.55449	−	14.3307i	0.0494050	−	0.455459i
$991$	−47.2700	+	27.2914i	−1.50158	+	0.866939i	−0.501584	+	0.865109i	$0.667249\pi$
$991$	−47.2700	+	27.2914i	−1.50158	+	0.866939i	−0.999998	+	0.00182961i	$0.999418\pi$
$992$	28.4302	−	18.7229i	0.902660	−	0.594452i
$993$	−2.40501	+	0.902447i	−0.0763208	+	0.0286383i
$994$	−0.0514070	+	0.221140i	−0.00163053	+	0.00701414i
$995$	−1.95807	−	11.1047i	−0.0620749	−	0.352044i
$996$	33.1849	−	24.0348i	1.05150	−	0.761573i
$997$	19.1801	−	6.98098i	0.607439	−	0.221090i	−0.0199432	−	0.999801i	$-0.506349\pi$
$997$	19.1801	−	6.98098i	0.607439	−	0.221090i	0.627382	+	0.778711i	$0.284126\pi$
$998$	−4.85213	+	9.39014i	−0.153591	+	0.297240i
$999$	−47.5990	−	25.6256i	−1.50597	−	0.810757i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bs.a.11.7	✓	840
4.3	odd	2	inner	756.2.bs.a.11.11	yes	840
7.2	even	3		756.2.ci.a.443.88	yes	840
27.5	odd	18		756.2.ci.a.599.83	yes	840
28.23	odd	6		756.2.ci.a.443.83	yes	840
108.59	even	18		756.2.ci.a.599.88	yes	840
189.86	odd	18	inner	756.2.bs.a.275.11	yes	840
756.275	even	18	inner	756.2.bs.a.275.7	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bs.a.11.7	✓	840	1.1	even	1	trivial
756.2.bs.a.11.11	yes	840	4.3	odd	2	inner
756.2.bs.a.275.7	yes	840	756.275	even	18	inner
756.2.bs.a.275.11	yes	840	189.86	odd	18	inner
756.2.ci.a.443.83	yes	840	28.23	odd	6
756.2.ci.a.443.88	yes	840	7.2	even	3
756.2.ci.a.599.83	yes	840	27.5	odd	18
756.2.ci.a.599.88	yes	840	108.59	even	18

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bs (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40267 - 0.180347i) q^{2} +(0.0171663 + 1.73197i) q^{3} +(1.93495 + 0.505934i) q^{4} +(1.75070 - 0.308695i) q^{5} +(0.288276 - 2.43247i) q^{6} +(2.14695 + 1.54616i) q^{7} +(-2.62285 - 1.05862i) q^{8} +(-2.99941 + 0.0594627i) q^{9} +O(q^{10})\)	\(q+(-1.40267 - 0.180347i) q^{2} +(0.0171663 + 1.73197i) q^{3} +(1.93495 + 0.505934i) q^{4} +(1.75070 - 0.308695i) q^{5} +(0.288276 - 2.43247i) q^{6} +(2.14695 + 1.54616i) q^{7} +(-2.62285 - 1.05862i) q^{8} +(-2.99941 + 0.0594627i) q^{9} +(-2.51132 + 0.117263i) q^{10} +(0.331880 - 1.88219i) q^{11} +(-0.843044 + 3.35995i) q^{12} +(-4.77544 + 4.00707i) q^{13} +(-2.73261 - 2.55594i) q^{14} +(0.564702 + 3.02685i) q^{15} +(3.48806 + 1.95791i) q^{16} +4.58880i q^{17} +(4.21790 + 0.457528i) q^{18} +2.82928i q^{19} +(3.54369 + 0.288427i) q^{20} +(-2.64104 + 3.74498i) q^{21} +(-0.804965 + 2.58023i) q^{22} +(5.71414 - 4.79473i) q^{23} +(1.78847 - 4.56085i) q^{24} +(-1.72882 + 0.629239i) q^{25} +(7.42102 - 4.75935i) q^{26} +(-0.154476 - 5.19386i) q^{27} +(3.37198 + 4.07796i) q^{28} +(-3.43681 + 4.09584i) q^{29} +(-0.246206 - 4.34750i) q^{30} +(-2.05819 + 5.65483i) q^{31} +(-4.53949 - 3.37536i) q^{32} +(3.26558 + 0.542495i) q^{33} +(0.827576 - 6.43656i) q^{34} +(4.23595 + 2.04411i) q^{35} +(-5.83379 - 1.40245i) q^{36} +(5.20179 - 9.00977i) q^{37} +(0.510252 - 3.96854i) q^{38} +(-7.02209 - 8.20212i) q^{39} +(-4.91860 - 1.04366i) q^{40} +(-0.268344 - 0.319800i) q^{41} +(4.37990 - 4.77666i) q^{42} +(2.64316 + 7.26202i) q^{43} +(1.59443 - 3.47403i) q^{44} +(-5.23270 + 1.03000i) q^{45} +(-8.87975 + 5.69488i) q^{46} +(6.39232 - 2.32662i) q^{47} +(-3.33116 + 6.07481i) q^{48} +(2.21877 + 6.63905i) q^{49} +(2.53844 - 0.570825i) q^{50} +(-7.94764 + 0.0787725i) q^{51} +(-11.2676 + 5.33743i) q^{52} +(3.28246 + 1.89513i) q^{53} +(-0.720018 + 7.31311i) q^{54} -3.39759i q^{55} +(-3.99432 - 6.32814i) q^{56} +(-4.90022 + 0.0485682i) q^{57} +(5.55938 - 5.12528i) q^{58} +(-7.30142 + 6.12662i) q^{59} +(-0.438714 + 6.14250i) q^{60} +(-8.40397 + 3.05879i) q^{61} +(3.90679 - 7.56065i) q^{62} +(-6.53152 - 4.50991i) q^{63} +(5.75865 + 5.55319i) q^{64} +(-7.12338 + 8.48932i) q^{65} +(-4.48269 - 1.34988i) q^{66} +(8.81080 - 1.55358i) q^{67} +(-2.32163 + 8.87910i) q^{68} +(8.40240 + 9.81438i) q^{69} +(-5.57297 - 3.63114i) q^{70} +(-0.0303390 - 0.0525488i) q^{71} +(7.92994 + 3.01927i) q^{72} +(0.682595 + 1.18229i) q^{73} +(-8.92127 + 11.6996i) q^{74} +(-1.11950 - 2.98345i) q^{75} +(-1.43143 + 5.47452i) q^{76} +(3.62270 - 3.52782i) q^{77} +(8.37042 + 12.7712i) q^{78} +(2.21231 + 0.390090i) q^{79} +(6.71093 + 2.35096i) q^{80} +(8.99293 - 0.356706i) q^{81} +(0.318723 + 0.496969i) q^{82} +(-9.06102 - 7.60310i) q^{83} +(-7.00500 + 5.91016i) q^{84} +(1.41654 + 8.03359i) q^{85} +(-2.39779 - 10.6629i) q^{86} +(-7.15285 - 5.88214i) q^{87} +(-2.86299 + 4.58536i) q^{88} +0.635194i q^{89} +(7.52549 - 0.501051i) q^{90} +(-16.4482 + 1.21937i) q^{91} +(13.4824 - 6.38659i) q^{92} +(-9.82930 - 3.46764i) q^{93} +(-9.38590 + 2.11063i) q^{94} +(0.873385 + 4.95321i) q^{95} +(5.76808 - 7.92018i) q^{96} +(-10.8830 + 3.96110i) q^{97} +(-1.91487 - 9.71253i) q^{98} +(-0.883526 + 5.66519i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} - 6 q^{10} - 3 q^{12} - 24 q^{13} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} - 15 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} + 33 q^{30} + 27 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} + 6 q^{37} - 9 q^{38} + 12 q^{40} - 24 q^{41} - 21 q^{42} - 9 q^{44} - 30 q^{45} + 3 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} + 27 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} + 18 q^{65} - 3 q^{66} + 60 q^{68} - 48 q^{69} + 24 q^{70} - 63 q^{72} + 6 q^{73} - 75 q^{74} + 12 q^{77} + 6 q^{78} + 18 q^{81} - 6 q^{82} + 132 q^{84} + 6 q^{85} - 81 q^{86} + 45 q^{88} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} - 111 q^{96} - 24 q^{97} - 9 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 - 6 * q^10 - 3 * q^12 - 24 * q^13 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 - 15 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 + 33 * q^30 + 27 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 + 6 * q^37 - 9 * q^38 + 12 * q^40 - 24 * q^41 - 21 * q^42 - 9 * q^44 - 30 * q^45 + 3 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 + 27 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 + 18 * q^65 - 3 * q^66 + 60 * q^68 - 48 * q^69 + 24 * q^70 - 63 * q^72 + 6 * q^73 - 75 * q^74 + 12 * q^77 + 6 * q^78 + 18 * q^81 - 6 * q^82 + 132 * q^84 + 6 * q^85 - 81 * q^86 + 45 * q^88 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 - 111 * q^96 - 24 * q^97 - 9 * q^98

Introduction

L-functions

Modular forms

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