LMFDB - Embedded newform 135.2.q.a.2.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(2,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			2.5
Character	$\chi$	$=$	135.2
Dual form			135.2.q.a.68.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.856769 - 1.22359i) q^{2} +(-0.960742 + 1.44117i) q^{3} +(-0.0790861 + 0.217287i) q^{4} +(-1.10572 + 1.94355i) q^{5} +(2.58654 - 0.0591935i) q^{6} +(-4.36642 - 2.03610i) q^{7} +(-2.55204 + 0.683816i) q^{8} +(-1.15395 - 2.76919i) q^{9} +O(q^{10})$	\(q+(-0.856769 - 1.22359i) q^{2} +(-0.960742 + 1.44117i) q^{3} +(-0.0790861 + 0.217287i) q^{4} +(-1.10572 + 1.94355i) q^{5} +(2.58654 - 0.0591935i) q^{6} +(-4.36642 - 2.03610i) q^{7} +(-2.55204 + 0.683816i) q^{8} +(-1.15395 - 2.76919i) q^{9} +(3.32546 - 0.312216i) q^{10} +(-2.25098 + 2.68262i) q^{11} +(-0.237167 - 0.322733i) q^{12} +(3.11626 + 2.18203i) q^{13} +(1.24966 + 7.08719i) q^{14} +(-1.73867 - 3.46078i) q^{15} +(3.37749 + 2.83405i) q^{16} +(-1.37108 - 0.367380i) q^{17} +(-2.39969 + 3.78452i) q^{18} +(-1.30024 - 0.750693i) q^{19} +(-0.334861 - 0.393967i) q^{20} +(7.12937 - 4.33660i) q^{21} +(5.21100 + 0.455904i) q^{22} +(-0.633988 - 1.35959i) q^{23} +(1.46635 - 4.33489i) q^{24} +(-2.55475 - 4.29805i) q^{25} -5.68253i q^{26} +(5.09952 + 0.997437i) q^{27} +(0.787741 - 0.787741i) q^{28} +(0.168770 - 0.957143i) q^{29} +(-2.74495 + 5.09252i) q^{30} +(-2.44873 - 0.891266i) q^{31} +(0.113453 - 1.29677i) q^{32} +(-1.70350 - 5.82135i) q^{33} +(0.725176 + 1.99240i) q^{34} +(8.78530 - 6.23499i) q^{35} +(0.692970 - 0.0317342i) q^{36} +(-1.79413 + 6.69580i) q^{37} +(0.195461 + 2.23413i) q^{38} +(-6.13860 + 2.39470i) q^{39} +(1.49282 - 5.71612i) q^{40} +(-0.670363 + 0.118203i) q^{41} +(-11.4145 - 5.00798i) q^{42} +(-0.200831 + 0.0175704i) q^{43} +(-0.404877 - 0.701267i) q^{44} +(6.65800 + 0.819200i) q^{45} +(-1.12040 + 1.94060i) q^{46} +(3.68023 - 7.89228i) q^{47} +(-7.32924 + 2.14475i) q^{48} +(10.4204 + 12.4186i) q^{49} +(-3.07023 + 6.80841i) q^{50} +(1.84671 - 1.62300i) q^{51} +(-0.720580 + 0.504555i) q^{52} +(-2.81838 - 2.81838i) q^{53} +(-3.14865 - 7.09431i) q^{54} +(-2.72483 - 7.34112i) q^{55} +(12.5356 + 2.21036i) q^{56} +(2.33107 - 1.15264i) q^{57} +(-1.31575 + 0.613544i) q^{58} +(-5.69079 + 4.77514i) q^{59} +(0.889488 - 0.104091i) q^{60} +(-1.08988 + 0.396683i) q^{61} +(1.00745 + 3.75986i) q^{62} +(-0.599704 + 14.4410i) q^{63} +(5.95268 - 3.43678i) q^{64} +(-7.68660 + 3.64388i) q^{65} +(-5.66346 + 7.07194i) q^{66} +(-8.79548 + 12.5612i) q^{67} +(0.188260 - 0.268864i) q^{68} +(2.56850 + 0.392531i) q^{69} +(-15.1561 - 5.40769i) q^{70} +(-11.1295 + 6.42561i) q^{71} +(4.83854 + 6.27798i) q^{72} +(0.0920100 + 0.343386i) q^{73} +(9.73009 - 3.54146i) q^{74} +(8.64869 + 0.447481i) q^{75} +(0.265947 - 0.223156i) q^{76} +(15.2908 - 7.13022i) q^{77} +(8.18950 + 5.45945i) q^{78} +(-9.66646 - 1.70446i) q^{79} +(-9.24267 + 3.43063i) q^{80} +(-6.33680 + 6.39100i) q^{81} +(0.718978 + 0.718978i) q^{82} +(9.30474 - 6.51525i) q^{83} +(0.378454 + 1.89208i) q^{84} +(2.23006 - 2.25854i) q^{85} +(0.193565 + 0.230681i) q^{86} +(1.21726 + 1.16279i) q^{87} +(3.91017 - 8.38540i) q^{88} +(-2.09630 + 3.63090i) q^{89} +(-4.70200 - 8.84854i) q^{90} +(-9.16409 - 15.8727i) q^{91} +(0.345561 - 0.0302327i) q^{92} +(3.63707 - 2.67277i) q^{93} +(-12.8100 + 2.25876i) q^{94} +(2.89671 - 1.69702i) q^{95} +(1.75987 + 1.40937i) q^{96} +(0.561155 + 6.41403i) q^{97} +(6.26740 - 23.3902i) q^{98} +(10.0262 + 3.13779i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.856769	−	1.22359i	−0.605827	−	0.865211i	0.392689	−	0.919671i	$-0.371545\pi$
$2$	−0.856769	−	1.22359i	−0.605827	−	0.865211i	−0.998516	+	0.0544607i	$0.982656\pi$
$3$	−0.960742	+	1.44117i	−0.554685	+	0.832061i
$3$	−0.960742	+	1.44117i	−0.554685	+	0.832061i
$4$	−0.0790861	+	0.217287i	−0.0395430	+	0.108644i
$5$	−1.10572	+	1.94355i	−0.494494	+	0.869181i
$5$	−1.10572	+	1.94355i	−0.494494	+	0.869181i
$6$	2.58654	−	0.0591935i	1.05595	−	0.0241657i
$7$	−4.36642	−	2.03610i	−1.65035	−	0.769572i	−0.999950	−	0.00998196i	$-0.996823\pi$
$7$	−4.36642	−	2.03610i	−1.65035	−	0.769572i	−0.650402	−	0.759590i	$-0.725400\pi$
$8$	−2.55204	+	0.683816i	−0.902281	+	0.241766i
$9$	−1.15395	−	2.76919i	−0.384650	−	0.923063i
$10$	3.32546	−	0.312216i	1.05160	−	0.0987315i
$11$	−2.25098	+	2.68262i	−0.678697	+	0.808839i	−0.989940	−	0.141491i	$-0.954810\pi$
$11$	−2.25098	+	2.68262i	−0.678697	+	0.808839i	0.311243	+	0.950330i	$0.399255\pi$
$12$	−0.237167	−	0.322733i	−0.0684641	−	0.0931651i
$13$	3.11626	+	2.18203i	0.864295	+	0.605186i	0.919413	−	0.393294i	$-0.128664\pi$
$13$	3.11626	+	2.18203i	0.864295	+	0.605186i	−0.0551175	+	0.998480i	$0.517553\pi$
$14$	1.24966	+	7.08719i	0.333986	+	1.89413i
$15$	−1.73867	−	3.46078i	−0.448923	−	0.893571i
$16$	3.37749	+	2.83405i	0.844372	+	0.708512i
$17$	−1.37108	−	0.367380i	−0.332536	−	0.0891027i	0.0886879	−	0.996059i	$-0.471733\pi$
$17$	−1.37108	−	0.367380i	−0.332536	−	0.0891027i	−0.421224	+	0.906957i	$0.638399\pi$
$18$	−2.39969	+	3.78452i	−0.565612	+	0.892019i
$19$	−1.30024	−	0.750693i	−0.298295	−	0.172221i	0.343382	−	0.939196i	$-0.388428\pi$
$19$	−1.30024	−	0.750693i	−0.298295	−	0.172221i	−0.641677	+	0.766975i	$0.721761\pi$
$20$	−0.334861	−	0.393967i	−0.0748771	−	0.0880937i
$21$	7.12937	−	4.33660i	1.55576	−	0.946323i
$22$	5.21100	+	0.455904i	1.11099	+	0.0971990i
$23$	−0.633988	−	1.35959i	−0.132196	−	0.283494i	0.829057	−	0.559165i	$-0.188878\pi$
$23$	−0.633988	−	1.35959i	−0.132196	−	0.283494i	−0.961252	+	0.275670i	$0.911100\pi$
$24$	1.46635	−	4.33489i	0.299318	−	0.884856i
$25$	−2.55475	−	4.29805i	−0.510951	−	0.859610i
$26$		−	5.68253i		−	1.11444i
$27$	5.09952	+	0.997437i	0.981403	+	0.191957i
$28$	0.787741	−	0.787741i	0.148869	−	0.148869i
$29$	0.168770	−	0.957143i	0.0313398	−	0.177737i	−0.965120	−	0.261808i	$-0.915681\pi$
$29$	0.168770	−	0.957143i	0.0313398	−	0.177737i	0.996460	+	0.0840712i	$0.0267923\pi$
$30$	−2.74495	+	5.09252i	−0.501157	+	0.929762i
$31$	−2.44873	−	0.891266i	−0.439806	−	0.160076i	0.112620	−	0.993638i	$-0.464076\pi$
$31$	−2.44873	−	0.891266i	−0.439806	−	0.160076i	−0.552426	+	0.833562i	$0.686298\pi$
$32$	0.113453	−	1.29677i	0.0200558	−	0.229239i
$33$	−1.70350	−	5.82135i	−0.296541	−	1.01337i
$34$	0.725176	+	1.99240i	0.124367	+	0.341694i
$35$	8.78530	−	6.23499i	1.48499	−	1.05391i
$36$	0.692970	−	0.0317342i	0.115495	−	0.00528903i
$37$	−1.79413	+	6.69580i	−0.294954	+	1.10078i	0.646300	+	0.763083i	$0.276315\pi$
$37$	−1.79413	+	6.69580i	−0.294954	+	1.10078i	−0.941254	+	0.337699i	$0.890351\pi$
$38$	0.195461	+	2.23413i	0.0317080	+	0.362424i
$39$	−6.13860	+	2.39470i	−0.982963	+	0.383459i
$40$	1.49282	−	5.71612i	0.236035	−	0.903797i
$41$	−0.670363	+	0.118203i	−0.104693	+	0.0184602i	−0.225749	−	0.974185i	$-0.572483\pi$
$41$	−0.670363	+	0.118203i	−0.104693	+	0.0184602i	0.121056	+	0.992646i	$0.461372\pi$
$42$	−11.4145	−	5.00798i	−1.76129	−	0.772748i
$43$	−0.200831	+	0.0175704i	−0.0306264	+	0.00267946i	−0.102459	−	0.994737i	$-0.532671\pi$
$43$	−0.200831	+	0.0175704i	−0.0306264	+	0.00267946i	0.0718322	+	0.997417i	$0.477115\pi$
$44$	−0.404877	−	0.701267i	−0.0610375	−	0.105720i
$45$	6.65800	+	0.819200i	0.992515	+	0.122119i
$46$	−1.12040	+	1.94060i	−0.165195	+	0.286126i
$47$	3.68023	−	7.89228i	0.536817	−	1.15121i	−0.431644	−	0.902044i	$-0.642066\pi$
$47$	3.68023	−	7.89228i	0.536817	−	1.15121i	0.968461	−	0.249164i	$-0.0801557\pi$
$48$	−7.32924	+	2.14475i	−1.05789	+	0.309568i
$49$	10.4204	+	12.4186i	1.48863	+	1.77409i
$50$	−3.07023	+	6.80841i	−0.434196	+	0.962855i
$51$	1.84671	−	1.62300i	0.258591	−	0.227266i
$52$	−0.720580	+	0.504555i	−0.0999264	+	0.0699692i
$53$	−2.81838	−	2.81838i	−0.387135	−	0.387135i	0.486529	−	0.873664i	$-0.338263\pi$
$53$	−2.81838	−	2.81838i	−0.387135	−	0.387135i	−0.873664	+	0.486529i	$0.838263\pi$
$54$	−3.14865	−	7.09431i	−0.428478	−	0.965413i
$55$	−2.72483	−	7.34112i	−0.367416	−	0.989877i
$56$	12.5356	+	2.21036i	1.67514	+	0.295372i
$57$	2.33107	−	1.15264i	0.308758	−	0.152671i
$58$	−1.31575	+	0.613544i	−0.172766	+	0.0805623i
$59$	−5.69079	+	4.77514i	−0.740877	+	0.621670i	−0.933073	−	0.359687i	$-0.882884\pi$
$59$	−5.69079	+	4.77514i	−0.740877	+	0.621670i	0.192196	+	0.981357i	$0.438439\pi$
$60$	0.889488	−	0.104091i	0.114832	−	0.0134381i
$61$	−1.08988	+	0.396683i	−0.139544	+	0.0507900i	−0.410848	−	0.911704i	$-0.634767\pi$
$61$	−1.08988	+	0.396683i	−0.139544	+	0.0507900i	0.271304	+	0.962494i	$0.412545\pi$
$62$	1.00745	+	3.75986i	0.127947	+	0.477503i
$63$	−0.599704	+	14.4410i	−0.0755556	+	1.81939i
$64$	5.95268	−	3.43678i	0.744085	−	0.429598i
$65$	−7.68660	+	3.64388i	−0.953405	+	0.451968i
$66$	−5.66346	+	7.07194i	−0.697124	+	0.870496i
$67$	−8.79548	+	12.5612i	−1.07454	+	1.53460i	−0.250457	+	0.968128i	$0.580581\pi$
$67$	−8.79548	+	12.5612i	−1.07454	+	1.53460i	−0.824081	+	0.566472i	$0.808308\pi$
$68$	0.188260	−	0.268864i	0.0228299	−	0.0326045i
$69$	2.56850	+	0.392531i	0.309211	+	0.0472552i
$70$	−15.1561	−	5.40769i	−1.81150	−	0.646342i
$71$	−11.1295	+	6.42561i	−1.32083	+	0.762579i	−0.983860	−	0.178938i	$-0.942734\pi$
$71$	−11.1295	+	6.42561i	−1.32083	+	0.762579i	−0.336966	+	0.941517i	$0.609401\pi$
$72$	4.83854	+	6.27798i	0.570227	+	0.739867i
$73$	0.0920100	+	0.343386i	0.0107690	+	0.0401903i	0.971101	−	0.238668i	$-0.0767107\pi$
$73$	0.0920100	+	0.343386i	0.0107690	+	0.0401903i	−0.960332	+	0.278858i	$0.910044\pi$
$74$	9.73009	−	3.54146i	1.13110	−	0.411687i
$75$	8.64869	+	0.447481i	0.998664	+	0.0516706i
$76$	0.265947	−	0.223156i	0.0305062	−	0.0255977i
$77$	15.2908	−	7.13022i	1.74255	−	0.812564i
$78$	8.18950	+	5.45945i	0.927278	+	0.618161i
$79$	−9.66646	−	1.70446i	−1.08756	−	0.191766i	−0.399005	−	0.916949i	$-0.630644\pi$
$79$	−9.66646	−	1.70446i	−1.08756	−	0.191766i	−0.688557	+	0.725182i	$0.741755\pi$
$80$	−9.24267	+	3.43063i	−1.03336	+	0.383557i
$81$	−6.33680	+	6.39100i	−0.704089	+	0.710112i
$82$	0.718978	+	0.718978i	0.0793979	+	0.0793979i
$83$	9.30474	−	6.51525i	1.02133	−	0.715142i	0.0621857	−	0.998065i	$-0.480193\pi$
$83$	9.30474	−	6.51525i	1.02133	−	0.715142i	0.959143	+	0.282923i	$0.0913040\pi$
$84$	0.378454	+	1.89208i	0.0412927	+	0.206443i
$85$	2.23006	−	2.25854i	0.241883	−	0.244973i
$86$	0.193565	+	0.230681i	0.0208726	+	0.0248750i
$87$	1.21726	+	1.16279i	0.130504	+	0.124665i
$88$	3.91017	−	8.38540i	0.416826	−	0.893886i
$89$	−2.09630	+	3.63090i	−0.222208	+	0.384875i	−0.955478	−	0.295062i	$-0.904660\pi$
$89$	−2.09630	+	3.63090i	−0.222208	+	0.384875i	0.733270	+	0.679937i	$0.237993\pi$
$90$	−4.70200	−	8.84854i	−0.495634	−	0.932718i
$91$	−9.16409	−	15.8727i	−0.960658	−	1.66391i
$92$	0.345561	−	0.0302327i	0.0360272	−	0.00315198i
$93$	3.63707	−	2.67277i	0.377146	−	0.277153i
$94$	−12.8100	+	2.25876i	−1.32126	+	0.232973i
$95$	2.89671	−	1.69702i	0.297196	−	0.174110i
$96$	1.75987	+	1.40937i	0.179616	+	0.143843i
$97$	0.561155	+	6.41403i	0.0569767	+	0.651246i	0.969962	+	0.243255i	$0.0782151\pi$
$97$	0.561155	+	6.41403i	0.0569767	+	0.651246i	−0.912986	+	0.407991i	$0.866229\pi$
$98$	6.26740	−	23.3902i	0.633103	−	2.36277i
$99$	10.0262	+	3.13779i	1.00767	+	0.315360i
$100$	1.13596	−	0.215199i	0.113596	−	0.0215199i
$101$	−2.09253	−	5.74917i	−0.208214	−	0.572064i	0.790995	−	0.611823i	$-0.209563\pi$
$101$	−2.09253	−	5.74917i	−0.208214	−	0.572064i	−0.999209	+	0.0397585i	$0.987341\pi$
$102$	−3.56810	−	0.869084i	−0.353295	−	0.0860521i
$103$	0.656648	−	7.50553i	0.0647015	−	0.739541i	−0.892675	−	0.450700i	$-0.851174\pi$
$103$	0.656648	−	7.50553i	0.0647015	−	0.739541i	0.957377	−	0.288841i	$-0.0932700\pi$
$104$	−9.44492	−	3.43767i	−0.926151	−	0.337091i
$105$	0.545279	+	18.6513i	0.0532137	+	1.82018i
$106$	−1.03385	+	5.86326i	−0.100416	+	0.569490i
$107$	−9.86451	+	9.86451i	−0.953639	+	0.953639i	−0.998972	−	0.0453334i	$-0.985565\pi$
$107$	−9.86451	+	9.86451i	−0.953639	+	0.953639i	0.0453334	+	0.998972i	$0.485565\pi$
$108$	−0.620031	+	1.02918i	−0.0596625	+	0.0990326i
$109$		−	2.02062i		−	0.193540i	−0.995307	−	0.0967701i	$-0.969149\pi$
$109$		−	2.02062i		−	0.193540i	0.995307	−	0.0967701i	$-0.0308512\pi$
$110$	−6.64799	+	9.62373i	−0.633861	+	0.917586i
$111$	−7.92609	−	9.01859i	−0.752311	−	0.856006i
$112$	−8.97714	−	19.2515i	−0.848260	−	1.81910i
$113$	0.774062	+	0.0677216i	0.0728176	+	0.00637072i	0.123506	−	0.992344i	$-0.460586\pi$
$113$	0.774062	+	0.0677216i	0.0728176	+	0.00637072i	−0.0506887	+	0.998715i	$0.516142\pi$
$114$	−3.40756	−	1.86473i	−0.319147	−	0.174648i
$115$	3.34344	+	0.271146i	0.311778	+	0.0252845i
$116$	0.194627	+	0.112368i	0.0180707	+	0.0104331i
$117$	2.44644	−	11.1475i	0.226174	−	1.03058i
$118$	10.7185	+	2.87202i	0.986719	+	0.264391i
$119$	5.23869	+	4.39579i	0.480230	+	0.402961i
$120$	6.80369	+	7.64312i	0.621089	+	0.697718i
$121$	−0.219379	−	1.24416i	−0.0199435	−	0.113105i
$122$	1.41915	+	0.993700i	0.128484	+	0.0899654i
$123$	0.473695	−	1.07967i	0.0427116	−	0.0973506i
$124$	0.387321	−	0.461592i	0.0347825	−	0.0414522i
$125$	11.1783	−	0.212832i	0.999819	−	0.0190363i
$126$	18.1837	−	11.6388i	1.61993	−	1.03687i
$127$	18.9749	−	5.08430i	1.68375	−	0.451159i	0.714983	−	0.699141i	$-0.246434\pi$
$127$	18.9749	−	5.08430i	1.68375	−	0.451159i	0.968765	+	0.247982i	$0.0797675\pi$
$128$	−11.6648	−	5.43940i	−1.03103	−	0.480779i
$129$	0.167625	−	0.306312i	0.0147585	−	0.0269693i
$130$	11.0443	+	6.28330i	0.968646	+	0.551082i
$131$	−1.67084	+	4.59061i	−0.145982	+	0.401083i	−0.991035	−	0.133599i	$-0.957347\pi$
$131$	−1.67084	+	4.59061i	−0.145982	+	0.401083i	0.845053	+	0.534682i	$0.179569\pi$
$132$	1.39963	+	0.0902401i	0.121822	+	0.00785439i
$133$	4.14891	+	5.92525i	0.359756	+	0.513784i
$134$	22.9055			1.97874
$135$	−7.57722	+	8.80827i	−0.652144	+	0.758095i
$136$	3.75027			0.321583
$137$	1.04372	+	1.49059i	0.0891710	+	0.127349i	0.861259	−	0.508166i	$-0.169676\pi$
$137$	1.04372	+	1.49059i	0.0891710	+	0.127349i	−0.772088	+	0.635516i	$0.780788\pi$
$138$	−1.72031	−	3.47911i	−0.146443	−	0.296161i
$139$	−0.987166	+	2.71222i	−0.0837303	+	0.230047i	−0.974491	−	0.224425i	$-0.927950\pi$
$139$	−0.987166	+	2.71222i	−0.0837303	+	0.230047i	0.890761	+	0.454472i	$0.150172\pi$
$140$	0.659988	+	2.40203i	0.0557792	+	0.203009i
$141$	7.83838	+	12.8863i	0.660110	+	1.08522i
$142$	17.3977	+	8.11269i	1.45998	+	0.680802i
$143$	−12.8682	+	3.44802i	−1.07609	+	0.288338i
$144$	3.95056	−	12.6232i	0.329214	−	1.05194i
$145$	1.67364	+	1.38635i	0.138988	+	0.115130i
$146$	0.341333	−	0.406785i	0.0282489	−	0.0336658i
$147$	−27.9087	+	3.08657i	−2.30187	+	0.254576i
$148$	−1.31302	−	0.919386i	−0.107930	−	0.0755731i
$149$	−2.86013	−	16.2206i	−0.234311	−	1.32885i	−0.844059	−	0.536250i	$-0.819840\pi$
$149$	−2.86013	−	16.2206i	−0.234311	−	1.32885i	0.609748	−	0.792596i	$-0.291271\pi$
$150$	−6.86239	−	10.9659i	−0.560312	−	0.895358i
$151$	1.98981	+	1.66965i	0.161929	+	0.135874i	0.720152	−	0.693817i	$-0.244072\pi$
$151$	1.98981	+	1.66965i	0.161929	+	0.135874i	−0.558223	+	0.829691i	$0.688517\pi$
$152$	3.83159	+	1.02667i	0.310783	+	0.0832741i
$153$	0.564813	+	4.22072i	0.0456624	+	0.341225i
$154$	−21.8252	−	12.6008i	−1.75872	−	1.01540i
$155$	4.43984	−	3.77374i	0.356616	−	0.303114i
$156$	−0.0348594	−	1.52323i	−0.00279098	−	0.121956i
$157$	−14.2497	−	1.24669i	−1.13725	−	0.0994965i	−0.497062	−	0.867715i	$-0.665588\pi$
$157$	−14.2497	−	1.24669i	−1.13725	−	0.0994965i	−0.640188	+	0.768219i	$0.721143\pi$
$158$	6.19636	+	13.2881i	0.492956	+	1.05715i
$159$	6.76951	−	1.35403i	0.536857	−	0.107382i
$160$	2.39489	+	1.65437i	0.189333	+	0.130790i
$161$			7.22741i			0.569599i
$162$	13.2492	+	2.27805i	1.04095	+	0.178981i
$163$	−8.00886	+	8.00886i	−0.627302	+	0.627302i	−0.947388	−	0.320086i	$-0.896288\pi$
$163$	−8.00886	+	8.00886i	−0.627302	+	0.627302i	0.320086	+	0.947388i	$0.396288\pi$
$164$	0.0273323	−	0.155009i	0.00213430	−	0.0121042i
$165$	13.1977	+	3.12598i	1.02744	+	0.243357i
$166$	−15.9440	−	5.80315i	−1.23750	−	0.450412i
$167$	1.21737	−	13.9146i	0.0942027	−	1.07674i	−0.791088	−	0.611703i	$-0.790485\pi$
$167$	1.21737	−	13.9146i	0.0942027	−	1.07674i	0.885290	−	0.465039i	$-0.153960\pi$
$168$	−15.2290	+	15.9423i	−1.17494	+	1.22998i
$169$	0.503569	+	1.38354i	0.0387361	+	0.106427i
$170$	−4.67417	−	0.793633i	−0.358493	−	0.0608689i
$171$	−0.578401	+	4.46687i	−0.0442314	+	0.341590i
$172$	0.0120651	−	0.0450275i	0.000919955	−	0.00343332i
$173$	−0.352505	−	4.02915i	−0.0268005	−	0.306331i	−0.997750	−	0.0670460i	$-0.978643\pi$
$173$	−0.352505	−	4.02915i	−0.0268005	−	0.306331i	0.970949	−	0.239285i	$-0.0769130\pi$
$174$	0.379874	−	2.48568i	0.0287982	−	0.188439i
$175$	2.40389	+	23.9688i	0.181717	+	1.81187i
$176$	−15.2053	+	2.68111i	−1.14614	+	0.202096i
$177$	−1.41441	−	12.7891i	−0.106314	−	0.961285i
$178$	6.23880	−	0.545824i	0.467618	−	0.0409112i
$179$	3.24205	+	5.61540i	0.242322	+	0.419714i	0.961375	−	0.275241i	$-0.0887576\pi$
$179$	3.24205	+	5.61540i	0.242322	+	0.419714i	−0.719053	+	0.694955i	$0.755424\pi$
$180$	−0.704556	+	1.38191i	−0.0525145	+	0.103001i
$181$	−3.86147	+	6.68826i	−0.287021	+	0.497135i	−0.973097	−	0.230395i	$-0.925998\pi$
$181$	−3.86147	+	6.68826i	−0.287021	+	0.497135i	0.686076	+	0.727530i	$0.259332\pi$
$182$	−11.5702	+	24.8123i	−0.857639	+	1.83921i
$183$	0.475403	−	1.95181i	0.0351428	−	0.144282i
$184$	2.54767	+	3.03620i	0.187817	+	0.223831i
$185$	−11.0298	−	10.8907i	−0.810926	−	0.800699i
$186$	−6.38651	−	2.16035i	−0.468281	−	0.158404i
$187$	4.07182	−	2.85112i	0.297761	−	0.208494i
$188$	1.42384	+	1.42384i	0.103844	+	0.103844i
$189$	−20.2358	−	14.7383i	−1.47194	−	1.07206i
$190$	−4.55827	−	2.09044i	−0.330692	−	0.151657i
$191$	9.13822	+	1.61131i	0.661218	+	0.116591i	0.494180	−	0.869360i	$-0.335468\pi$
$191$	9.13822	+	1.61131i	0.661218	+	0.116591i	0.167039	+	0.985950i	$0.446580\pi$
$192$	−0.766000	+	11.8807i	−0.0552813	+	0.857415i
$193$	23.1246	−	10.7832i	1.66455	−	0.776191i	0.664978	−	0.746863i	$-0.268441\pi$
$193$	23.1246	−	10.7832i	1.66455	−	0.776191i	0.999570	−	0.0293284i	$-0.00933685\pi$
$194$	7.36738	−	6.18197i	0.528947	−	0.443839i
$195$	2.13338	−	14.5785i	0.152775	−	1.04399i
$196$	−3.52251	+	1.28209i	−0.251608	+	0.0915779i
$197$	−3.24493	−	12.1103i	−0.231192	−	0.862820i	−0.979829	−	0.199839i	$-0.935958\pi$
$197$	−3.24493	−	12.1103i	−0.231192	−	0.862820i	0.748637	−	0.662980i	$-0.230709\pi$
$198$	−4.75075	−	14.9563i	−0.337621	−	1.06290i
$199$	−12.0563	+	6.96070i	−0.854648	+	0.493431i	−0.862216	−	0.506540i	$-0.830924\pi$
$199$	−12.0563	+	6.96070i	−0.854648	+	0.493431i	0.00756873	+	0.999971i	$0.497591\pi$
$200$	9.45890	+	9.22180i	0.668845	+	0.652080i
$201$	−9.65271	−	24.7439i	−0.680850	−	1.74530i
$202$	−5.24183	+	7.48611i	−0.368814	+	0.526721i
$203$	−2.68576	+	3.83566i	−0.188503	+	0.269210i
$204$	0.206609	+	0.529624i	0.0144655	+	0.0370811i
$205$	0.511502	−	1.43358i	0.0357249	−	0.100126i
$206$	−9.74630	+	5.62703i	−0.679057	+	0.392054i
$207$	−3.03337	+	3.32453i	−0.210834	+	0.231071i
$208$	4.34115	+	16.2014i	0.301005	+	1.12337i
$209$	4.94063	−	1.79824i	0.341751	−	0.124387i
$210$	22.3545	−	16.6471i	1.54261	−	1.14876i
$211$	15.4091	−	12.9298i	1.06081	−	0.890124i	0.0666204	−	0.997778i	$-0.478778\pi$
$211$	15.4091	−	12.9298i	1.06081	−	0.890124i	0.994188	+	0.107654i	$0.0343339\pi$
$212$	0.835293	−	0.389504i	0.0573682	−	0.0267512i
$213$	1.43216	−	22.2128i	0.0981299	−	1.52200i
$214$	20.5218	+	3.61854i	1.40284	+	0.247358i
$215$	0.187914	−	0.409752i	0.0128157	−	0.0279449i
$216$	−13.6962	+	0.941639i	−0.931911	+	0.0640704i
$217$	8.87750	+	8.87750i	0.602644	+	0.602644i
$218$	−2.47242	+	1.73120i	−0.167453	+	0.117252i
$219$	−0.583276	−	0.197303i	−0.0394141	−	0.0133325i
$220$	1.81063	−	0.0114900i	0.122072	−	0.000774659i
$221$	−3.47101	−	4.13659i	−0.233485	−	0.278257i
$222$	−4.24425	+	17.4252i	−0.284855	+	1.16950i
$223$	−9.25851	+	19.8549i	−0.619996	+	1.32959i	0.305993	+	0.952034i	$0.401012\pi$
$223$	−9.25851	+	19.8549i	−0.619996	+	1.32959i	−0.925989	+	0.377552i	$0.876766\pi$
$224$	−3.13574	+	5.43126i	−0.209515	+	0.362891i
$225$	−8.95405	+	12.0343i	−0.596937	+	0.802288i
$226$	−0.580328	−	1.00516i	−0.0386029	−	0.0668621i
$227$	4.93402	−	0.431671i	0.327482	−	0.0286510i	0.0777708	−	0.996971i	$-0.475220\pi$
$227$	4.93402	−	0.431671i	0.327482	−	0.0286510i	0.249712	+	0.968320i	$0.419664\pi$
$228$	0.0660995	+	0.597670i	0.00437754	+	0.0395816i
$229$	1.07319	−	0.189232i	0.0709183	−	0.0125048i	−0.138076	−	0.990422i	$-0.544092\pi$
$229$	1.07319	−	0.189232i	0.0709183	−	0.0125048i	0.208995	+	0.977917i	$0.432981\pi$
$230$	−2.53279	−	4.32332i	−0.167007	−	0.285071i
$231$	−4.41465	+	28.8870i	−0.290463	+	1.90062i
$232$	0.223802	+	2.55807i	0.0146933	+	0.167946i
$233$	−6.86746	+	25.6297i	−0.449903	+	1.67906i	0.252755	+	0.967530i	$0.418663\pi$
$233$	−6.86746	+	25.6297i	−0.449903	+	1.67906i	−0.702657	+	0.711529i	$0.748003\pi$
$234$	−15.7360	+	6.55735i	−1.02869	+	0.428667i
$235$	11.2697	+	15.8794i	0.735155	+	1.03586i
$236$	−0.587514	−	1.61418i	−0.0382439	−	0.105074i
$237$	11.7434	−	12.2935i	0.762815	−	0.798547i
$238$	0.890302	−	10.1762i	0.0577097	−	0.659625i
$239$	−1.41158	−	0.513773i	−0.0913075	−	0.0332332i	0.295962	−	0.955200i	$-0.404360\pi$
$239$	−1.41158	−	0.513773i	−0.0913075	−	0.0332332i	−0.387270	+	0.921966i	$0.626582\pi$
$240$	3.93569	−	16.6162i	0.254048	−	1.07257i
$241$	0.572431	−	3.24642i	0.0368735	−	0.209120i	−0.960805	−	0.277227i	$-0.910585\pi$
$241$	0.572431	−	3.24642i	0.0368735	−	0.209120i	0.997678	+	0.0681065i	$0.0216958\pi$
$242$	−1.33439	+	1.33439i	−0.0857777	+	0.0857777i
$243$	−3.12250	−	15.2725i	−0.200308	−	0.979733i
$244$		−	0.268188i		−	0.0171690i
$245$	−35.6583	+	6.52109i	−2.27812	+	0.416617i
$246$	−1.72692	+	0.345418i	−0.110105	+	0.0220231i
$247$	−2.41385	−	5.17651i	−0.153589	−	0.329374i
$248$	6.85872	+	0.600060i	0.435529	+	0.0381039i
$249$	0.450134	+	19.6692i	0.0285261	+	1.24649i
$250$	−9.83765	−	13.4954i	−0.622188	−	0.853521i
$251$	16.2363	+	9.37404i	1.02483	+	0.591684i	0.915498	−	0.402322i	$-0.131797\pi$
$251$	16.2363	+	9.37404i	1.02483	+	0.591684i	0.109328	+	0.994006i	$0.465130\pi$
$252$	−3.09041	−	1.27239i	−0.194678	−	0.0801530i
$253$	5.07436	+	1.35967i	0.319022	+	0.0854817i
$254$	−22.4782	−	18.8614i	−1.41041	−	1.18347i
$255$	1.11243	+	5.38377i	0.0696633	+	0.337144i
$256$	0.951288	+	5.39502i	0.0594555	+	0.337189i
$257$	16.8536	+	11.8010i	1.05130	+	0.736129i	0.965558	−	0.260188i	$-0.0837847\pi$
$257$	16.8536	+	11.8010i	1.05130	+	0.736129i	0.0857431	+	0.996317i	$0.472674\pi$
$258$	−0.518417	+	0.0573345i	−0.0322752	+	0.00356949i
$259$	21.4672	−	25.5836i	1.33391	−	1.58969i
$260$	−0.183866	−	1.95838i	−0.0114029	−	0.121454i
$261$	−2.84526	+	0.637138i	−0.176117	+	0.0394378i
$262$	7.04856	−	1.88866i	0.435461	−	0.116682i
$263$	−15.5342	−	7.24374i	−0.957882	−	0.446668i	−0.120154	−	0.992755i	$-0.538339\pi$
$263$	−15.5342	−	7.24374i	−0.957882	−	0.446668i	−0.837728	+	0.546087i	$0.816117\pi$
$264$	8.32812	+	13.6914i	0.512560	+	0.842649i
$265$	8.59401	−	2.36131i	0.527926	−	0.145054i
$266$	3.69544	−	10.1531i	0.226582	−	0.622529i
$267$	−3.21875	−	6.50950i	−0.196984	−	0.398375i
$268$	−2.03380	−	2.90456i	−0.124234	−	0.177424i
$269$	5.61280			0.342218			0.171109	−	0.985252i	$-0.445265\pi$
$269$	5.61280			0.342218			0.171109	+	0.985252i	$0.445265\pi$
$270$	17.2697	+	1.72478i	1.05100	+	0.104967i
$271$	15.6827			0.952656			0.476328	−	0.879268i	$-0.341968\pi$
$271$	15.6827			0.952656			0.476328	+	0.879268i	$0.341968\pi$
$272$	−3.58963	−	5.12653i	−0.217654	−	0.310841i
$273$	31.6796	+	2.04252i	1.91733	+	0.123619i
$274$	0.929644	−	2.55418i	0.0561619	−	0.154303i
$275$	17.2807	+	2.82141i	1.04207	+	0.170138i
$276$	−0.288425	+	0.527059i	−0.0173611	+	0.0317252i
$277$	−22.2616	−	10.3807i	−1.33757	−	0.623718i	−0.383564	−	0.923514i	$-0.625304\pi$
$277$	−22.2616	−	10.3807i	−1.33757	−	0.623718i	−0.954003	+	0.299796i	$0.903081\pi$
$278$	4.16442	−	1.11585i	0.249765	−	0.0669244i
$279$	0.357631	+	7.80948i	0.0214108	+	0.467541i
$280$	−18.1568	+	21.9195i	−1.08508	+	1.30994i
$281$	0.467705	−	0.557389i	0.0279010	−	0.0332511i	−0.751914	−	0.659262i	$-0.770869\pi$
$281$	0.467705	−	0.557389i	0.0279010	−	0.0332511i	0.779814	+	0.626011i	$0.215313\pi$
$282$	9.05190	−	20.6316i	0.539033	−	1.22859i
$283$	−17.6935	−	12.3891i	−1.05177	−	0.736457i	−0.0861152	−	0.996285i	$-0.527445\pi$
$283$	−17.6935	−	12.3891i	−1.05177	−	0.736457i	−0.965655	+	0.259828i	$0.916334\pi$
$284$	−0.516015	−	2.92647i	−0.0306199	−	0.173654i
$285$	−0.337301	+	5.80505i	−0.0199800	+	0.343862i
$286$	15.2440	+	12.7913i	0.901399	+	0.756364i
$287$	3.16776	+	0.848799i	0.186987	+	0.0501030i
$288$	−3.72193	+	1.18224i	−0.219317	+	0.0696641i
$289$	−12.9775	−	7.49259i	−0.763385	−	0.440740i
$290$	0.262402	−	3.23563i	0.0154088	−	0.190003i
$291$	−9.78284	−	5.35351i	−0.573480	−	0.313828i
$292$	−0.0818900	−	0.00716445i	−0.00479225	−	0.000419268i
$293$	−3.87450	−	8.30888i	−0.226350	−	0.485410i	0.760030	−	0.649888i	$-0.225184\pi$
$293$	−3.87450	−	8.30888i	−0.226350	−	0.485410i	−0.986381	+	0.164477i	$0.947406\pi$
$294$	27.6880	+	31.5044i	1.61480	+	1.83737i
$295$	−2.98827	−	16.3403i	−0.173984	−	0.951368i
$296$		−	18.3148i		−	1.06452i
$297$	−14.1547	+	11.4348i	−0.821338	+	0.663517i
$298$	−17.3970	+	17.3970i	−1.00778	+	1.00778i
$299$	0.990996	−	5.62022i	0.0573108	−	0.325026i
$300$	−0.781222	+	1.84386i	−0.0451039	+	0.106455i
$301$	0.912687	+	0.332191i	0.0526064	+	0.0191472i
$302$	0.338164	−	3.86523i	0.0194591	−	0.222419i
$303$	10.2959	+	2.50778i	0.591485	+	0.144068i
$304$	−2.26404	−	6.22039i	−0.129851	−	0.356764i
$305$	0.434130	−	2.55685i	0.0248582	−	0.146405i
$306$	4.68052	−	4.30728i	0.267568	−	0.246231i
$307$	1.87870	−	7.01141i	0.107223	−	0.400162i	−0.891365	−	0.453287i	$-0.850251\pi$
$307$	1.87870	−	7.01141i	0.107223	−	0.400162i	0.998588	+	0.0531246i	$0.0169181\pi$
$308$	0.340016	+	3.88640i	0.0193742	+	0.221448i
$309$	10.1859	+	8.15722i	0.579454	+	0.464048i
$310$	−8.42143	−	2.19934i	−0.478305	−	0.124914i
$311$	22.2915	−	3.93059i	1.26404	−	0.222884i	0.498847	−	0.866690i	$-0.333757\pi$
$311$	22.2915	−	3.93059i	1.26404	−	0.222884i	0.765188	+	0.643807i	$0.222646\pi$
$312$	14.0284	−	10.3090i	0.794202	−	0.583634i
$313$	−4.11885	+	0.360352i	−0.232811	+	0.0203683i	−0.202964	−	0.979186i	$-0.565057\pi$
$313$	−4.11885	+	0.360352i	−0.232811	+	0.0203683i	−0.0298468	+	0.999554i	$0.509502\pi$
$314$	10.6833	+	18.5039i	0.602891	+	1.04424i
$315$	−27.4037	−	17.1333i	−1.54402	−	0.965352i
$316$	1.13484	−	1.96560i	0.0638397	−	0.110574i
$317$	−13.6040	+	29.1740i	−0.764080	+	1.63857i	0.00546854	+	0.999985i	$0.498259\pi$
$317$	−13.6040	+	29.1740i	−0.764080	+	1.63857i	−0.769548	+	0.638589i	$0.779518\pi$
$318$	−7.45669	−	7.12303i	−0.418151	−	0.399440i
$319$	2.18775	+	2.60726i	0.122490	+	0.145978i
$320$	0.0975328	+	15.3694i	0.00545225	+	0.859178i
$321$	−4.73920	−	23.6937i	−0.264516	−	1.32245i
$322$	8.84340	−	6.19222i	0.492824	−	0.345079i
$323$	1.50694	+	1.50694i	0.0838485	+	0.0838485i
$324$	−0.887530	−	1.88235i	−0.0493072	−	0.104575i
$325$	1.41719	−	18.9684i	0.0786117	−	1.05218i
$326$	16.6613	+	2.93784i	0.922785	+	0.162712i
$327$	2.91206	+	1.94129i	0.161037	+	0.107354i
$328$	1.62996	−	0.760064i	0.0899996	−	0.0419675i
$329$	−32.1389	+	26.9677i	−1.77187	+	1.48678i
$330$	−7.48243	−	18.8268i	−0.411894	−	1.03638i
$331$	1.84234	−	0.670556i	0.101264	−	0.0368571i	−0.290891	−	0.956756i	$-0.593952\pi$
$331$	1.84234	−	0.670556i	0.101264	−	0.0368571i	0.392155	+	0.919899i	$0.371730\pi$
$332$	0.679805	+	2.53707i	0.0373091	+	0.139240i
$333$	20.6123	−	2.75832i	1.12954	−	0.151155i
$334$	−18.0688	+	10.4320i	−0.988679	+	0.570814i
$335$	−14.6880	−	30.9837i	−0.802492	−	1.69282i
$336$	36.3695	+	5.55817i	1.98412	+	0.303223i
$337$	9.63175	−	13.7556i	0.524675	−	0.749313i	−0.466115	−	0.884724i	$-0.654347\pi$
$337$	9.63175	−	13.7556i	0.524675	−	0.749313i	0.990789	+	0.135411i	$0.0432355\pi$
$338$	1.26145	−	1.80154i	0.0686140	−	0.0979909i
$339$	−0.841272	+	1.05049i	−0.0456916	+	0.0570549i
$340$	0.314385	+	0.663181i	0.0170499	+	0.0359661i
$341$	7.90298	−	4.56279i	0.427970	−	0.247089i
$342$	5.96118	−	3.11934i	0.322344	−	0.168675i
$343$	−11.4860	−	42.8663i	−0.620185	−	2.31456i
$344$	0.500513	−	0.182172i	0.0269858	−	0.00982205i
$345$	−3.60296	+	4.55797i	−0.193977	+	0.245393i
$346$	−4.62803	+	3.88338i	−0.248804	+	0.208772i
$347$	−2.84711	+	1.32763i	−0.152841	+	0.0712708i	−0.497534	−	0.867445i	$-0.665761\pi$
$347$	−2.84711	+	1.32763i	−0.152841	+	0.0712708i	0.344693	+	0.938716i	$0.387983\pi$
$348$	−0.348929	+	0.172535i	−0.0187045	+	0.00924883i
$349$	12.2555	+	2.16098i	0.656022	+	0.115674i	0.491744	−	0.870740i	$-0.336360\pi$
$349$	12.2555	+	2.16098i	0.656022	+	0.115674i	0.164278	+	0.986414i	$0.447471\pi$
$350$	27.2685	−	23.4771i	1.45756	−	1.25491i
$351$	13.7150	+	14.2356i	0.732053	+	0.759839i
$352$	3.22337	+	3.22337i	0.171806	+	0.171806i
$353$	−14.8642	+	10.4080i	−0.791143	+	0.553964i	−0.897837	−	0.440327i	$-0.854862\pi$
$353$	−14.8642	+	10.4080i	−0.791143	+	0.553964i	0.106694	+	0.994292i	$0.465973\pi$
$354$	−14.4368	+	12.6879i	−0.767307	+	0.674356i
$355$	−0.182353	−	28.7356i	−0.00967830	−	1.52513i
$356$	−0.623160	−	0.742654i	−0.0330274	−	0.0393606i
$357$	−11.3681	+	3.32664i	−0.601665	+	0.176064i
$358$	4.09327	−	8.77805i	0.216336	−	0.463934i
$359$	5.27373	−	9.13437i	0.278337	−	0.482094i	−0.692635	−	0.721289i	$-0.743550\pi$
$359$	5.27373	−	9.13437i	0.278337	−	0.482094i	0.970972	+	0.239195i	$0.0768835\pi$
$360$	−17.5516	+	2.46222i	−0.925052	+	0.129770i
$361$	−8.37292	−	14.5023i	−0.440680	−	0.763280i
$362$	11.4921	−	1.00543i	0.604011	−	0.0528441i
$363$	2.00381	+	0.879154i	0.105173	+	0.0461436i
$364$	4.17368	−	0.735932i	0.218760	−	0.0385733i
$365$	−0.769124	−	0.200864i	−0.0402578	−	0.0105137i
$366$	−2.79553	+	1.09055i	−0.146125	+	0.0570040i
$367$	−0.310757	−	3.55196i	−0.0162214	−	0.185411i	−0.999982	−	0.00592799i	$-0.998113\pi$
$367$	−0.310757	−	3.55196i	−0.0162214	−	0.185411i	0.983761	−	0.179483i	$-0.0574425\pi$
$368$	1.71186	−	6.38875i	0.0892369	−	0.333037i
$369$	1.10089	+	1.71996i	0.0573101	+	0.0895376i
$370$	−3.87578	+	22.8268i	−0.201492	+	1.18671i
$371$	6.56775	+	18.0448i	0.340981	+	0.936837i
$372$	0.293117	+	1.00167i	0.0151974	+	0.0519340i
$373$	−2.19980	+	25.1438i	−0.113901	+	1.30190i	0.697151	+	0.716925i	$0.254451\pi$
$373$	−2.19980	+	25.1438i	−0.113901	+	1.30190i	−0.811052	+	0.584974i	$0.801105\pi$
$374$	−6.97721	−	2.53950i	−0.360783	−	0.131314i
$375$	−10.4327	+	16.3143i	−0.538745	+	0.842469i
$376$	−3.99522	+	22.6580i	−0.206038	+	1.16850i
$377$	2.61445	−	2.61445i	0.134651	−	0.134651i
$378$	−0.696344	+	37.3877i	−0.0358161	+	1.92302i
$379$			27.8698i			1.43158i	0.698317	+	0.715788i	$0.253932\pi$
$379$			27.8698i			1.43158i	−0.698317	+	0.715788i	$0.746068\pi$
$380$	0.139650	+	0.763628i	0.00716392	+	0.0391733i
$381$	−10.9026	+	32.2307i	−0.558558	+	1.65123i
$382$	−5.85775	−	12.5620i	−0.299709	−	0.642727i
$383$	37.7169	+	3.29980i	1.92724	+	0.168612i	0.985727	−	0.168353i	$-0.0538450\pi$
$383$	37.7169	+	3.29980i	1.92724	+	0.168612i	0.941517	+	0.336965i	$0.109401\pi$
$384$	19.0460	−	11.5851i	0.971936	−	0.591202i
$385$	−3.04947	+	37.6024i	−0.155416	+	1.91640i
$386$	−33.0067	−	19.0564i	−1.68000	−	0.969947i
$387$	0.280404	+	0.535863i	0.0142538	+	0.0272395i
$388$	−1.43807	−	0.385329i	−0.0730067	−	0.0195621i
$389$	−2.93798	−	2.46526i	−0.148962	−	0.124994i	0.565261	−	0.824912i	$-0.308775\pi$
$389$	−2.93798	−	2.46526i	−0.148962	−	0.124994i	−0.714223	+	0.699918i	$0.753220\pi$
$390$	−19.6660	+	9.88004i	−0.995827	+	0.500296i
$391$	0.369762	+	2.09702i	0.0186997	+	0.106051i
$392$	−35.0854	−	24.5671i	−1.77208	−	1.24082i
$393$	−5.01060	−	6.81836i	−0.252751	−	0.343941i
$394$	−12.0379	+	14.3462i	−0.606459	+	0.722749i
$395$	14.0011	−	16.9026i	0.704473	−	0.850460i
$396$	−1.47473	+	1.93041i	−0.0741081	+	0.0970066i
$397$	−4.33915	+	1.16267i	−0.217776	+	0.0583528i	−0.366057	−	0.930592i	$-0.619293\pi$
$397$	−4.33915	+	1.16267i	−0.217776	+	0.0583528i	0.148281	+	0.988945i	$0.452626\pi$
$398$	18.8465	+	8.78827i	0.944690	+	0.440516i
$399$	−12.5253	+	0.286645i	−0.627051	+	0.0143502i
$400$	3.55223	−	21.7569i	0.177612	−	1.08785i
$401$	−3.48616	+	9.57816i	−0.174091	+	0.478310i	−0.995796	−	0.0916029i	$-0.970801\pi$
$401$	−3.48616	+	9.57816i	−0.174091	+	0.478310i	0.821705	+	0.569913i	$0.193023\pi$
$402$	−22.0063	+	33.0108i	−1.09757	+	1.64643i
$403$	−5.68612	−	8.12063i	−0.283246	−	0.404517i
$404$	1.41471			0.0703845
$405$	−5.41447	−	19.3826i	−0.269047	−	0.963127i
$406$	6.99435			0.347124
$407$	−13.9237	−	19.8851i	−0.690172	−	0.985667i
$408$	−3.60304	+	5.40478i	−0.178377	+	0.267576i
$409$	−8.00244	+	21.9865i	−0.395695	+	1.08716i	0.568665	+	0.822569i	$0.307460\pi$
$409$	−8.00244	+	21.9865i	−0.395695	+	1.08716i	−0.964360	+	0.264594i	$0.914762\pi$
$410$	−2.19236	+	0.602378i	−0.108273	+	0.0297493i
$411$	−3.15094	+	0.0721099i	−0.155424	+	0.00355692i
$412$	1.57892	+	0.736264i	0.0777879	+	0.0362731i
$413$	34.5710	−	9.26327i	1.70113	−	0.455816i
$414$	6.66677	+	0.863260i	0.327654	+	0.0424269i
$415$	2.37423	+	25.2883i	0.116546	+	1.24135i
$416$	3.18315	−	3.79353i	0.156067	−	0.185993i
$417$	−2.96036	−	4.02842i	−0.144969	−	0.197272i
$418$	−6.43330	−	4.50465i	−0.314663	−	0.220329i
$419$	−0.258905	−	1.46832i	−0.0126483	−	0.0717323i	0.977830	−	0.209399i	$-0.0671508\pi$
$419$	−0.258905	−	1.46832i	−0.0126483	−	0.0717323i	−0.990479	+	0.137667i	$0.956040\pi$
$420$	−4.09582	−	1.35658i	−0.199856	−	0.0661943i
$421$	−14.1741	−	11.8935i	−0.690802	−	0.579652i	0.228338	−	0.973582i	$-0.426671\pi$
$421$	−14.1741	−	11.8935i	−0.690802	−	0.579652i	−0.919140	+	0.393930i	$0.871115\pi$
$422$	−29.0229	−	7.77666i	−1.41281	−	0.378562i
$423$	−26.1020	−	1.08396i	−1.26912	−	0.0527040i
$424$	9.11988	+	5.26536i	0.442900	+	0.255709i
$425$	1.92376	+	6.83154i	0.0933158	+	0.331378i
$426$	−28.4065	+	17.2789i	−1.37630	+	0.837165i
$427$	5.56655	+	0.487010i	0.269384	+	0.0235681i
$428$	−1.36329	−	2.92358i	−0.0658969	−	0.141316i
$429$	7.39383	−	21.8579i	0.356977	−	1.05531i
$430$	−0.662369	+	0.121132i	−0.0319423	+	0.00584152i
$431$			19.2978i			0.929541i	0.885431	+	0.464771i	$0.153863\pi$
$431$			19.2978i			0.929541i	−0.885431	+	0.464771i	$0.846137\pi$
$432$	14.3968	+	17.8211i	0.692665	+	0.857419i
$433$	−15.0405	+	15.0405i	−0.722800	+	0.722800i	−0.969175	−	0.246375i	$-0.920761\pi$
$433$	−15.0405	+	15.0405i	−0.722800	+	0.722800i	0.246375	+	0.969175i	$0.420761\pi$
$434$	3.25648	−	18.4684i	0.156316	−	0.886512i
$435$	−3.60590	+	1.08008i	−0.172890	+	0.0517858i
$436$	0.439055	+	0.159803i	0.0210269	+	0.00765317i
$437$	−0.196300	+	2.24372i	−0.00939031	+	0.107332i
$438$	0.258314	+	0.882735i	0.0123427	+	0.0421787i
$439$	−3.41885	−	9.39321i	−0.163173	−	0.448314i	0.830979	−	0.556303i	$-0.187781\pi$
$439$	−3.41885	−	9.39321i	−0.163173	−	0.448314i	−0.994152	+	0.107990i	$0.965559\pi$
$440$	11.9738	+	16.8715i	0.570831	+	0.804319i
$441$	22.3648	−	43.1866i	1.06499	−	2.05650i
$442$	−2.08765	+	7.79120i	−0.0992992	+	0.370590i
$443$	2.69183	+	30.7678i	0.127893	+	1.46182i	0.740832	+	0.671690i	$0.234431\pi$
$443$	2.69183	+	30.7678i	0.127893	+	1.46182i	−0.612939	+	0.790130i	$0.710013\pi$
$444$	2.58647	−	1.00899i	0.122748	−	0.0478847i
$445$	−4.73890	−	8.08904i	−0.224646	−	0.383457i
$446$	32.2268	−	5.68245i	1.52598	−	0.269072i
$447$	26.1246	+	11.4619i	1.23565	+	0.542129i
$448$	−32.9895	+	2.88621i	−1.55861	+	0.136361i
$449$	0.854949	+	1.48081i	0.0403475	+	0.0698840i	0.885494	−	0.464651i	$-0.153820\pi$
$449$	0.854949	+	1.48081i	0.0403475	+	0.0698840i	−0.845146	+	0.534535i	$0.820487\pi$
$450$	22.3967	+	0.645480i	1.05579	+	0.0304282i
$451$	1.19188	−	2.06440i	0.0561235	−	0.0972088i
$452$	−0.0759325	+	0.162838i	−0.00357157	+	0.00765925i
$453$	−4.31795	+	1.26356i	−0.202875	+	0.0593671i
$454$	−4.75550	−	5.66739i	−0.223187	−	0.265984i
$455$	40.9822	−	0.260069i	1.92128	−	0.0121922i
$456$	−5.16078	+	4.53561i	−0.241676	+	0.212400i
$457$	−29.8380	+	20.8928i	−1.39576	+	0.977323i	−0.397548	+	0.917582i	$0.630139\pi$
$457$	−29.8380	+	20.8928i	−1.39576	+	0.977323i	−0.998214	+	0.0597413i	$0.980972\pi$
$458$	−1.15102	−	1.15102i	−0.0537835	−	0.0537835i
$459$	−6.62542	−	3.24103i	−0.309248	−	0.151278i
$460$	−0.323336	+	0.705044i	−0.0150756	+	0.0328728i
$461$	−17.0206	−	3.00119i	−0.792728	−	0.139779i	−0.237401	−	0.971412i	$-0.576296\pi$
$461$	−17.0206	−	3.00119i	−0.792728	−	0.139779i	−0.555327	+	0.831632i	$0.687407\pi$
$462$	39.1282	−	19.3477i	1.82041	−	0.900137i
$463$	−26.0036	+	12.1257i	−1.20849	+	0.563527i	−0.919229	−	0.393724i	$-0.871187\pi$
$463$	−26.0036	+	12.1257i	−1.20849	+	0.563527i	−0.289259	+	0.957251i	$0.593409\pi$
$464$	3.28261	−	2.75443i	0.152391	−	0.127871i
$465$	1.17306	+	10.0242i	0.0543994	+	0.464859i
$466$	37.2442	−	13.5558i	1.72530	−	0.627959i
$467$	6.16460	+	23.0066i	0.285264	+	1.06462i	0.948646	+	0.316339i	$0.102454\pi$
$467$	6.16460	+	23.0066i	0.285264	+	1.06462i	−0.663382	+	0.748280i	$0.730880\pi$
$468$	2.22872	+	1.41319i	0.103023	+	0.0653247i
$469$	63.9806	−	36.9392i	2.95435	−	1.70570i
$470$	9.77436	−	27.3945i	0.450858	−	1.26361i
$471$	15.4870	−	19.3385i	0.713602	−	0.891071i
$472$	11.2578	−	16.0778i	0.518181	−	0.740040i
$473$	0.404932	−	0.578303i	0.0186188	−	0.0265904i
$474$	−25.1036	−	3.83646i	−1.15305	−	0.176214i
$475$	0.0952725	+	7.50632i	0.00437140	+	0.344414i
$476$	−1.36946	+	0.790656i	−0.0627689	+	0.0362396i
$477$	−4.55236	+	11.0569i	−0.208438	+	0.506261i
$478$	0.580749	+	2.16738i	0.0265628	+	0.0991338i
$479$	3.81746	−	1.38944i	0.174424	−	0.0634853i	−0.253332	−	0.967379i	$-0.581526\pi$
$479$	3.81746	−	1.38944i	0.174424	−	0.0634853i	0.427756	+	0.903894i	$0.359304\pi$
$480$	−4.68511	+	1.86203i	−0.213845	+	0.0849894i
$481$	−20.2014	+	16.9510i	−0.921105	+	0.772899i
$482$	−4.46274	+	2.08101i	−0.203272	+	0.0947873i
$483$	−10.4159	−	6.94367i	−0.473941	−	0.315948i
$484$	0.287690	+	0.0507274i	0.0130768	+	0.00230579i
$485$	−13.0865	−	6.00151i	−0.594225	−	0.272515i
$486$	−16.0121	+	16.9057i	−0.726323	+	0.766858i
$487$	−18.4638	−	18.4638i	−0.836676	−	0.836676i	0.151744	−	0.988420i	$-0.451511\pi$
$487$	−18.4638	−	18.4638i	−0.836676	−	0.836676i	−0.988420	+	0.151744i	$0.951511\pi$
$488$	2.51015	−	1.75763i	0.113629	−	0.0795640i
$489$	−3.84769	−	19.2366i	−0.173998	−	0.869908i
$490$	38.5300	+	38.0441i	1.74061	+	1.71866i
$491$	−16.4502	−	19.6046i	−0.742387	−	0.884743i	0.254211	−	0.967149i	$-0.418184\pi$
$491$	−16.4502	−	19.6046i	−0.742387	−	0.884743i	−0.996599	+	0.0824057i	$0.973740\pi$
$492$	0.197136	+	0.188315i	0.00888757	+	0.00848988i
$493$	−0.583032	+	1.25032i	−0.0262585	+	0.0563114i
$494$	−4.26583	+	7.38864i	−0.191929	+	0.332431i
$495$	−17.1846	+	16.0168i	−0.772392	+	0.719904i
$496$	−5.74468	−	9.95007i	−0.257944	−	0.446771i
$497$	61.6791	−	5.39623i	2.76669	−	0.242054i
$498$	23.6814	−	17.4027i	1.06119	−	0.779836i
$499$	−5.75147	+	1.01414i	−0.257471	+	0.0453991i	−0.300894	−	0.953658i	$-0.597285\pi$
$499$	−5.75147	+	1.01414i	−0.257471	+	0.0453991i	0.0434226	+	0.999057i	$0.486174\pi$
$500$	−0.837803	+	2.44574i	−0.0374677	+	0.109377i
$501$	18.8837	+	15.1228i	0.843662	+	0.675635i
$502$	−2.44076	−	27.8980i	−0.108936	−	1.24515i
$503$	−5.36150	+	20.0094i	−0.239057	+	0.892174i	0.737221	+	0.675652i	$0.236138\pi$
$503$	−5.36150	+	20.0094i	−0.239057	+	0.892174i	−0.976278	+	0.216522i	$0.930529\pi$
$504$	−8.34452	−	37.2640i	−0.371695	−	1.65987i
$505$	13.4875	+	2.29007i	0.600188	+	0.101907i
$506$	−2.68387	−	7.37387i	−0.119312	−	0.327808i
$507$	−2.47772	−	0.603500i	−0.110040	−	0.0268024i
$508$	−0.395894	+	4.52509i	−0.0175650	+	0.200769i
$509$	−7.40545	−	2.69536i	−0.328241	−	0.119470i	0.172643	−	0.984984i	$-0.444769\pi$
$509$	−7.40545	−	2.69536i	−0.328241	−	0.119470i	−0.500884	+	0.865515i	$0.666992\pi$
$510$	5.63444	−	5.97381i	0.249497	−	0.264525i
$511$	0.297412	−	1.68671i	0.0131567	−	0.0746156i
$512$	−12.4157	+	12.4157i	−0.548699	+	0.548699i
$513$	−5.88182	−	5.12508i	−0.259689	−	0.226278i
$514$		−	30.7328i		−	1.35556i
$515$	13.8613	+	9.57526i	0.610801	+	0.421936i
$516$	0.0533010	+	0.0606477i	0.00234644	+	0.00266987i
$517$	12.8878	+	27.6380i	0.566806	+	1.21552i
$518$	−49.6964	−	4.34787i	−2.18354	−	0.191035i
$519$	6.14537	+	3.36296i	0.269752	+	0.147617i
$520$	17.1247	−	14.5555i	0.750970	−	0.638303i
$521$	−7.49714	−	4.32848i	−0.328456	−	0.189634i	0.326700	−	0.945128i	$-0.394063\pi$
$521$	−7.49714	−	4.32848i	−0.328456	−	0.189634i	−0.655155	+	0.755494i	$0.727397\pi$
$522$	3.21733	+	2.93556i	0.140819	+	0.128486i
$523$	−12.7057	−	3.40449i	−0.555583	−	0.148868i	−0.0299067	−	0.999553i	$-0.509521\pi$
$523$	−12.7057	−	3.40449i	−0.555583	−	0.148868i	−0.525676	+	0.850685i	$0.676188\pi$
$524$	−0.865339	−	0.726106i	−0.0378025	−	0.0317201i
$525$	−36.8527	−	19.5634i	−1.60838	−	0.853819i
$526$	4.44587	+	25.2138i	0.193849	+	1.09937i
$527$	3.02998	+	2.12161i	0.131988	+	0.0924189i
$528$	10.7445	−	24.4893i	0.467593	−	1.06576i
$529$	13.3376	−	15.8951i	0.579894	−	0.691091i
$530$	−10.2524	−	8.49248i	−0.445334	−	0.368890i
$531$	19.7901	+	10.2486i	0.858818	+	0.444751i
$532$	−1.61560	+	0.432899i	−0.0700452	+	0.0187686i
$533$	−2.34695	−	1.09440i	−0.101658	−	0.0474037i
$534$	−5.20725	+	9.51557i	−0.225340	+	0.411779i
$535$	−8.26473	−	30.0796i	−0.357315	−	1.30045i
$536$	13.8568	−	38.0712i	0.598523	−	1.64443i
$537$	−11.2075	−	0.722598i	−0.483640	−	0.0311824i
$538$	−4.80887	−	6.86778i	−0.207325	−	0.296091i
$539$	−56.7706			−2.44528
$540$	−1.31467	−	2.34305i	−0.0565745	−	0.100829i
$541$	27.5170			1.18305			0.591523	−	0.806288i	$-0.298527\pi$
$541$	27.5170			1.18305			0.591523	+	0.806288i	$0.298527\pi$
$542$	−13.4364	−	19.1892i	−0.577145	−	0.824248i
$543$	−5.92906	−	11.9907i	−0.254440	−	0.514572i
$544$	−0.631962	+	1.73630i	−0.0270951	+	0.0744433i
$545$	3.92717	+	2.23425i	0.168222	+	0.0957046i
$546$	−24.6429	−	40.5128i	−1.05462	−	1.73379i
$547$	29.7950	+	13.8936i	1.27394	+	0.594049i	0.937608	−	0.347694i	$-0.113035\pi$
$547$	29.7950	+	13.8936i	1.27394	+	0.594049i	0.336334	+	0.941743i	$0.390813\pi$
$548$	−0.406429	+	0.108902i	−0.0173618	+	0.00465208i
$549$	2.35615	+	2.56032i	0.100558	+	0.109272i
$550$	−11.3533	−	23.5619i	−0.484108	−	1.00468i
$551$	−0.937961	+	1.11782i	−0.0399585	+	0.0476207i
$552$	−6.82333	+	0.754628i	−0.290420	+	0.0321191i
$553$	38.7374	+	27.1242i	1.64728	+	1.15344i
$554$	6.37122	+	36.1330i	0.270687	+	1.53514i
$555$	26.2921	−	5.43267i	1.11604	−	0.230604i
$556$	−0.511259	−	0.428997i	−0.0216822	−	0.0181935i
$557$	−25.1830	−	6.74775i	−1.06704	−	0.285911i	−0.317761	−	0.948171i	$-0.602931\pi$
$557$	−25.1830	−	6.74775i	−1.06704	−	0.285911i	−0.749275	+	0.662259i	$0.769598\pi$
$558$	9.24922	−	7.12851i	0.391551	−	0.301774i
$559$	−0.664181	−	0.383465i	−0.0280919	−	0.0162188i
$560$	47.3425	+	3.83937i	2.00059	+	0.162243i
$561$	0.196982	+	8.60737i	0.00831657	+	0.363404i
$562$	−1.08273	−	0.0947268i	−0.0456723	−	0.00399581i
$563$	12.7775	+	27.4015i	0.538510	+	1.15484i	0.967811	+	0.251676i	$0.0809818\pi$
$563$	12.7775	+	27.4015i	0.538510	+	1.15484i	−0.429302	+	0.903161i	$0.641240\pi$
$564$	−3.41993	+	0.684052i	−0.144005	+	0.0288038i
$565$	−0.987518	+	1.42954i	−0.0415452	+	0.0601414i
$566$			32.2643i			1.35617i
$567$	40.6819	−	15.0035i	1.70848	−	0.630087i
$568$	24.0089	−	24.0089i	1.00739	−	1.00739i
$569$	−3.82709	+	21.7045i	−0.160440	+	0.909901i	0.793202	+	0.608959i	$0.208412\pi$
$569$	−3.82709	+	21.7045i	−0.160440	+	0.909901i	−0.953642	+	0.300943i	$0.902699\pi$
$570$	7.39201	−	4.56087i	0.309617	−	0.191034i
$571$	−5.69726	−	2.07363i	−0.238423	−	0.0867789i	0.220045	−	0.975490i	$-0.429380\pi$
$571$	−5.69726	−	2.07363i	−0.238423	−	0.0867789i	−0.458468	+	0.888711i	$0.651602\pi$
$572$	0.268484	−	3.06878i	0.0112259	−	0.128312i
$573$	−11.1017	+	11.6217i	−0.463778	+	0.485503i
$574$	−1.67545	−	4.60327i	−0.0699321	−	0.192137i
$575$	−4.22391	+	6.19833i	−0.176149	+	0.258488i
$576$	−16.3862	−	12.5182i	−0.682758	−	0.521592i
$577$	4.26360	−	15.9120i	0.177496	−	0.662424i	−0.818617	−	0.574340i	$-0.805259\pi$
$577$	4.26360	−	15.9120i	0.177496	−	0.662424i	0.996113	−	0.0880841i	$-0.0280744\pi$
$578$	1.95088	+	22.2986i	0.0811458	+	0.927501i
$579$	−6.67638	+	43.6864i	−0.277461	+	1.81555i
$580$	−0.433597	+	0.254020i	−0.0180041	+	0.0105476i
$581$	−53.8941	+	9.50299i	−2.23590	+	0.394250i
$582$	1.83112	+	16.5569i	0.0759023	+	0.686307i
$583$	13.9048	−	1.21651i	0.575877	−	0.0503827i
$584$	−0.469626	−	0.813416i	−0.0194332	−	0.0336594i
$585$	18.9605	+	17.0808i	0.783922	+	0.706204i
$586$	−6.84714	+	11.8596i	−0.282853	+	0.489916i
$587$	−1.01370	+	2.17389i	−0.0418400	+	0.0897262i	−0.926117	−	0.377237i	$-0.876874\pi$
$587$	−1.01370	+	2.17389i	−0.0418400	+	0.0897262i	0.884277	+	0.466963i	$0.154652\pi$
$588$	1.53652	−	6.30830i	0.0633648	−	0.260150i
$589$	2.51487	+	2.99711i	0.103623	+	0.123494i
$590$	−17.4336	+	17.6563i	−0.717730	+	0.726897i
$591$	20.5705	+	6.95833i	0.846157	+	0.286227i
$592$	−25.0359	+	17.5303i	−1.02897	+	0.720491i
$593$	−19.8531	−	19.8531i	−0.815268	−	0.815268i	0.170150	−	0.985418i	$-0.445575\pi$
$593$	−19.8531	−	19.8531i	−0.815268	−	0.815268i	−0.985418	+	0.170150i	$0.945575\pi$
$594$	26.1189	+	7.52254i	1.07167	+	0.308653i
$595$	−14.3360	+	5.32113i	−0.587717	+	0.218145i
$596$	3.75073	+	0.661355i	0.153636	+	0.0270902i
$597$	1.55142	−	24.0626i	0.0634955	−	0.984817i
$598$	−7.72592	+	3.60265i	−0.315936	+	0.147323i
$599$	12.9672	−	10.8807i	0.529824	−	0.444575i	−0.338217	−	0.941068i	$-0.609824\pi$
$599$	12.9672	−	10.8807i	0.529824	−	0.444575i	0.868041	+	0.496493i	$0.165379\pi$
$600$	−22.3778	+	4.77213i	−0.913568	+	0.194821i
$601$	−24.9557	+	9.08314i	−1.01796	+	0.370509i	−0.796486	−	0.604656i	$-0.793310\pi$
$601$	−24.9557	+	9.08314i	−1.01796	+	0.370509i	−0.221478	+	0.975165i	$0.571088\pi$
$602$	−0.375496	−	1.40137i	−0.0153041	−	0.0571155i
$603$	44.9340	+	9.86129i	1.82985	+	0.401583i
$604$	−0.520160	+	0.300315i	−0.0211650	+	0.0122196i
$605$	2.66066	+	0.949322i	0.108171	+	0.0385954i
$606$	−5.75272	−	14.7466i	−0.233688	−	0.599040i
$607$	−3.73971	+	5.34086i	−0.151790	+	0.216779i	−0.887844	−	0.460144i	$-0.847798\pi$
$607$	−3.73971	+	5.34086i	−0.151790	+	0.216779i	0.736054	+	0.676922i	$0.236687\pi$
$608$	−1.12099	+	1.60095i	−0.0454623	+	0.0649270i
$609$	−2.94752	−	7.55571i	−0.119440	−	0.306173i
$610$	−3.50049	+	1.65943i	−0.141731	+	0.0671884i
$611$	28.6898	−	16.5640i	1.16066	−	0.670109i
$612$	−0.961776	−	0.211073i	−0.0388775	−	0.00853213i
$613$	−2.83651	−	10.5860i	−0.114566	−	0.427565i	0.884688	−	0.466183i	$-0.154371\pi$
$613$	−2.83651	−	10.5860i	−0.114566	−	0.427565i	−0.999254	+	0.0386179i	$0.987704\pi$
$614$	−10.1887	+	3.70839i	−0.411183	+	0.149658i
$615$	1.57462	+	2.11447i	0.0634946	+	0.0852635i
$616$	−34.1469	+	28.6527i	−1.37582	+	1.15445i
$617$	−31.5164	+	14.6963i	−1.26880	+	0.591652i	−0.936217	−	0.351421i	$-0.885698\pi$
$617$	−31.5164	+	14.6963i	−1.26880	+	0.591652i	−0.332585	+	0.943073i	$0.607921\pi$
$618$	1.25417	−	19.4522i	0.0504501	−	0.782483i
$619$	31.5714	+	5.56690i	1.26896	+	0.223753i	0.767288	−	0.641303i	$-0.221606\pi$
$619$	31.5714	+	5.56690i	1.26896	+	0.223753i	0.501676	+	0.865056i	$0.332717\pi$
$620$	0.468855	+	1.26317i	0.0188297	+	0.0507301i
$621$	−1.87693	−	7.56563i	−0.0753185	−	0.303598i
$622$	−23.9081	−	23.9081i	−0.958628	−	0.958628i
$623$	16.5462	−	11.5858i	0.662910	−	0.464175i
$624$	−27.5197	−	9.30903i	−1.10167	−	0.372659i
$625$	−11.9465	+	21.9609i	−0.477859	+	0.878437i
$626$	3.96982	+	4.73105i	0.158666	+	0.189091i
$627$	−2.15510	+	8.84795i	−0.0860663	+	0.353353i
$628$	1.39784	−	2.99768i	0.0557799	−	0.119620i
$629$	4.91980	−	8.52135i	0.196165	−	0.339768i
$630$	2.51442	+	48.2102i	0.100177	+	1.92074i
$631$	22.4076	+	38.8111i	0.892033	+	1.54505i	0.837434	+	0.546538i	$0.184055\pi$
$631$	22.4076	+	38.8111i	0.892033	+	1.54505i	0.0545987	+	0.998508i	$0.482612\pi$
$632$	25.8347	−	2.26024i	1.02765	−	0.0899076i
$633$	3.82985	+	34.6294i	0.152223	+	1.37640i
$634$	47.3526	−	8.34954i	1.88061	−	0.331603i
$635$	−11.0994	+	42.5004i	−0.440465	+	1.68658i
$636$	−0.241160	+	1.57801i	−0.00956262	+	0.0625723i
$637$	5.37507	+	61.4373i	0.212968	+	2.43423i
$638$	1.31583	−	4.91073i	0.0520940	−	0.194418i
$639$	30.6366	+	23.4048i	1.21196	+	0.925879i
$640$	23.4698	−	16.6567i	0.927725	−	0.658413i
$641$	−15.6160	−	42.9045i	−0.616794	−	1.69463i	−0.714699	−	0.699432i	$-0.753437\pi$
$641$	−15.6160	−	42.9045i	−0.616794	−	1.69463i	0.0979055	−	0.995196i	$-0.468786\pi$
$642$	−24.9311	+	26.0989i	−0.983950	+	1.03004i
$643$	3.17500	−	36.2904i	0.125210	−	1.43115i	−0.630472	−	0.776212i	$-0.717138\pi$
$643$	3.17500	−	36.2904i	0.125210	−	1.43115i	0.755681	−	0.654940i	$-0.227306\pi$
$644$	−1.57042	−	0.571587i	−0.0618833	−	0.0225237i
$645$	0.409986	+	0.664483i	0.0161432	+	0.0261640i
$646$	0.552782	−	3.13498i	0.0217489	−	0.123344i
$647$	32.3432	−	32.3432i	1.27154	−	1.27154i	0.326266	−	0.945278i	$-0.394209\pi$
$647$	32.3432	−	32.3432i	1.27154	−	1.27154i	0.945278	−	0.326266i	$-0.105791\pi$
$648$	11.8015	−	20.6433i	0.463606	−	0.810945i
$649$		−	26.0149i		−	1.02118i
$650$	−24.4238	+	14.5175i	−0.957980	+	0.569422i
$651$	−21.3230	+	4.26501i	−0.835714	+	0.167159i
$652$	−1.10683	−	2.37361i	−0.0433469	−	0.0929578i
$653$	11.8869	+	1.03997i	0.465170	+	0.0406971i	0.317332	−	0.948314i	$-0.397213\pi$
$653$	11.8869	+	1.03997i	0.465170	+	0.0406971i	0.147838	+	0.989012i	$0.452769\pi$
$654$	−0.119608	−	5.22642i	−0.00467703	−	0.204369i
$655$	−7.07457	−	8.32330i	−0.276426	−	0.325218i
$656$	−2.59913	−	1.50061i	−0.101479	−	0.0585890i
$657$	0.844725	−	0.651043i	0.0329559	−	0.0253996i
$658$	60.5331	+	16.2198i	2.35983	+	0.632314i
$659$	−17.0150	−	14.2773i	−0.662811	−	0.556165i	0.248117	−	0.968730i	$-0.420188\pi$
$659$	−17.0150	−	14.2773i	−0.662811	−	0.556165i	−0.910928	+	0.412565i	$0.864633\pi$
$660$	−1.72299	+	2.62046i	−0.0670672	+	0.102001i
$661$	−7.45553	−	42.2824i	−0.289986	−	1.64460i	−0.686909	−	0.726743i	$-0.741033\pi$
$661$	−7.45553	−	42.2824i	−0.289986	−	1.64460i	0.396923	−	0.917852i	$-0.370078\pi$
$662$	−2.39894	−	1.67976i	−0.0932376	−	0.0652857i
$663$	9.29628	−	1.02813i	0.361038	−	0.0399291i
$664$	−19.2908	+	22.9899i	−0.748629	+	0.892181i
$665$	−16.1035	+	1.51191i	−0.624469	+	0.0586293i
$666$	−21.0350	−	22.8578i	−0.815090	−	0.885721i
$667$	−1.40832	+	0.377358i	−0.0545304	+	0.0146114i
$668$	2.92718	+	1.36497i	0.113256	+	0.0528122i
$669$	−19.7193	−	32.4186i	−0.762393	−	1.25337i
$670$	−25.3272	+	44.5180i	−0.978474	+	1.71988i
$671$	1.38915	−	3.81665i	0.0536274	−	0.147340i
$672$	−4.81474	−	9.73718i	−0.185733	−	0.375620i
$673$	−24.6347	−	35.1820i	−0.949599	−	1.35617i	−0.934378	−	0.356284i	$-0.884044\pi$
$673$	−24.6347	−	35.1820i	−0.949599	−	1.35617i	−0.0152212	−	0.999884i	$-0.504845\pi$
$674$	−25.0834			−0.966176
$675$	−8.74099	−	24.4662i	−0.336441	−	0.941705i
$676$	−0.340452			−0.0130943
$677$	15.4492	+	22.0638i	0.593761	+	0.847979i	0.997768	−	0.0667769i	$-0.0212716\pi$
$677$	15.4492	+	22.0638i	0.593761	+	0.847979i	−0.404007	+	0.914756i	$0.632383\pi$
$678$	2.00615	+	0.129345i	0.0770458	+	0.00496748i
$679$	10.6093	−	29.1489i	0.407149	−	1.11863i
$680$	−4.14676	+	7.28882i	−0.159021	+	0.279514i
$681$	−4.11821	+	7.52549i	−0.157810	+	0.288377i
$682$	−12.3540	−	5.76078i	−0.473060	−	0.220592i
$683$	−18.3215	+	4.90923i	−0.701053	+	0.187846i	−0.591702	−	0.806157i	$-0.701544\pi$
$683$	−18.3215	+	4.90923i	−0.701053	+	0.187846i	−0.109351	+	0.994003i	$0.534877\pi$
$684$	−0.924849	−	0.478946i	−0.0353625	−	0.0183130i
$685$	−4.05109	+	0.380344i	−0.154784	+	0.0145322i
$686$	−42.6101	+	50.7807i	−1.62686	+	1.93882i
$687$	−0.758341	+	1.72845i	−0.0289325	+	0.0659445i
$688$	−0.728099	−	0.509820i	−0.0277585	−	0.0194367i
$689$	−2.63302	−	14.9326i	−0.100310	−	0.568887i
$690$	8.66400	+	0.503419i	0.329833	+	0.0191648i
$691$	17.4026	+	14.6025i	0.662025	+	0.555505i	0.910693	−	0.413084i	$-0.135548\pi$
$691$	17.4026	+	14.6025i	0.662025	+	0.555505i	−0.248668	+	0.968589i	$0.579993\pi$
$692$	0.903362	+	0.242055i	0.0343407	+	0.00920155i
$693$	−37.3897	−	34.1152i	−1.42032	−	1.29593i
$694$	4.06379	+	2.34623i	0.154259	+	0.0890616i
$695$	−4.17979	−	4.91756i	−0.158548	−	0.186534i
$696$	−3.90164	−	2.13511i	−0.147891	−	0.0809311i
$697$	0.962547	+	0.0842119i	0.0364591	+	0.00318975i
$698$	−7.85598	−	16.8472i	−0.297353	−	0.637676i
$699$	−30.3390	−	34.5207i	−1.14752	−	1.30569i
$700$	−5.39823	−	1.37327i	−0.204034	−	0.0519046i
$701$			28.7752i			1.08682i	0.839466	+	0.543412i	$0.182868\pi$
$701$			28.7752i			1.08682i	−0.839466	+	0.543412i	$0.817132\pi$
$702$	5.66797	−	28.9782i	0.213924	−	1.09371i
$703$	7.35929	−	7.35929i	0.277561	−	0.277561i
$704$	−4.17981	+	23.7049i	−0.157533	+	0.893412i
$705$	−33.7122	+	0.985588i	−1.26967	+	0.0371194i
$706$	25.4704	+	9.27048i	0.958592	+	0.348899i
$707$	−2.56901	+	29.3639i	−0.0966175	+	1.10434i
$708$	2.89076	+	0.704104i	0.108641	+	0.0264618i
$709$	0.183502	+	0.504167i	0.00689155	+	0.0189344i	0.943091	−	0.332536i	$-0.107904\pi$
$709$	0.183502	+	0.504167i	0.00689155	+	0.0189344i	−0.936199	+	0.351470i	$0.885682\pi$
$710$	−35.0044	+	24.8429i	−1.31369	+	0.932337i
$711$	6.43464	+	28.7351i	0.241318	+	1.07765i
$712$	2.86697	−	10.6997i	0.107444	−	0.400988i
$713$	0.340710	+	3.89433i	0.0127597	+	0.145844i
$714$	13.8103	+	11.0598i	0.516837	+	0.413902i
$715$	7.52726	−	28.8225i	0.281504	−	1.07790i
$716$	−1.47655	+	0.260356i	−0.0551814	+	0.00972997i
$717$	2.09660	−	1.54073i	0.0782989	−	0.0575394i
$718$	−15.6951	+	1.37315i	−0.585737	+	0.0512453i
$719$	−2.44660	−	4.23763i	−0.0912427	−	0.158037i	0.816792	−	0.576933i	$-0.195751\pi$
$719$	−2.44660	−	4.23763i	−0.0912427	−	0.158037i	−0.908034	+	0.418896i	$0.862417\pi$
$720$	20.1656	+	21.6359i	0.751529	+	0.806323i
$721$	−18.1492	+	31.4353i	−0.675911	+	1.17071i
$722$	−10.5713	+	22.6702i	−0.393422	+	0.843697i
$723$	4.12869	+	3.94394i	0.153548	+	0.146677i
$724$	−1.14789	−	1.36800i	−0.0426608	−	0.0508412i
$725$	−4.54501	+	1.71988i	−0.168798	+	0.0638748i
$726$	−0.641079	−	3.20508i	−0.0237927	−	0.118952i
$727$	4.02773	−	2.82025i	0.149380	−	0.104597i	−0.496497	−	0.868038i	$-0.665381\pi$
$727$	4.02773	−	2.82025i	0.149380	−	0.104597i	0.645877	+	0.763441i	$0.276492\pi$
$728$	34.2411	+	34.2411i	1.26906	+	1.26906i
$729$	25.0102	+	10.1729i	0.926305	+	0.376774i
$730$	0.413186	+	1.11319i	0.0152927	+	0.0412010i
$731$	0.281810	+	0.0496908i	0.0104231	+	0.00183788i
$732$	0.386505	+	0.257660i	0.0142857	+	0.00952339i
$733$	−12.8830	+	6.00742i	−0.475843	+	0.221889i	−0.645717	−	0.763576i	$-0.723442\pi$
$733$	−12.8830	+	6.00742i	−0.475843	+	0.221889i	0.169874	+	0.985466i	$0.445664\pi$
$734$	−4.07991	+	3.42345i	−0.150592	+	0.126362i
$735$	24.8604	−	57.6547i	0.916989	−	2.12663i
$736$	−1.83501	+	0.667889i	−0.0676394	+	0.0246187i
$737$	−13.8985	−	51.8700i	−0.511959	−	1.91066i
$738$	1.16132	−	2.82065i	0.0427488	−	0.103830i
$739$	−28.3320	+	16.3575i	−1.04221	+	0.601721i	−0.920459	−	0.390840i	$-0.872185\pi$
$739$	−28.3320	+	16.3575i	−1.04221	+	0.601721i	−0.121752	+	0.992561i	$0.538851\pi$
$740$	3.23871	−	1.53533i	0.119057	−	0.0564398i
$741$	9.77933	+	1.49453i	0.359253	+	0.0549028i
$742$	16.4524	−	23.4964i	0.603986	−	0.862581i
$743$	0.622633	−	0.889212i	0.0228422	−	0.0326220i	−0.807569	−	0.589774i	$-0.799217\pi$
$743$	0.622633	−	0.889212i	0.0228422	−	0.0326220i	0.830411	+	0.557152i	$0.188106\pi$
$744$	−7.45425	+	9.30809i	−0.273286	+	0.341251i
$745$	34.6881	+	12.3767i	1.27087	+	0.453448i
$746$	32.6505	−	18.8508i	1.19542	−	0.690177i
$747$	−28.7792	−	18.2483i	−1.05297	−	0.667671i
$748$	0.297487	+	1.11024i	0.0108772	+	0.0405943i
$749$	63.1577	−	22.9875i	2.30773	−	0.839946i
$750$	28.9006	−	1.21218i	1.05530	−	0.0442627i
$751$	−9.61953	+	8.07175i	−0.351022	+	0.294542i	−0.801200	−	0.598396i	$-0.795805\pi$
$751$	−9.61953	+	8.07175i	−0.351022	+	0.294542i	0.450178	+	0.892939i	$0.351360\pi$
$752$	34.7970	−	16.2261i	1.26892	−	0.591706i
$753$	−29.1085	+	14.3933i	−1.06077	+	0.524520i
$754$	−5.43899	−	0.959041i	−0.198076	−	0.0349262i
$755$	−5.44523	+	2.02112i	−0.198172	+	0.0735563i
$756$	4.80282	−	3.23138i	0.174677	−	0.117524i
$757$	−3.04376	−	3.04376i	−0.110627	−	0.110627i	0.649626	−	0.760254i	$-0.274925\pi$
$757$	−3.04376	−	3.04376i	−0.110627	−	0.110627i	−0.760254	+	0.649626i	$0.774925\pi$
$758$	34.1013	−	23.8780i	1.23862	−	0.867288i
$759$	−6.83466	+	6.00672i	−0.248083	+	0.218030i
$760$	−6.23207	+	6.31167i	−0.226061	+	0.228948i
$761$	−11.3467	−	13.5225i	−0.411319	−	0.490191i	0.520117	−	0.854095i	$-0.325888\pi$
$761$	−11.3467	−	13.5225i	−0.411319	−	0.490191i	−0.931437	+	0.363904i	$0.881444\pi$
$762$	48.7783	−	14.2739i	1.76705	−	0.517090i
$763$	−4.11418	+	8.82288i	−0.148943	+	0.319410i
$764$	−1.07282	+	1.85819i	−0.0388134	+	0.0672268i
$765$	−8.82769	−	3.56920i	−0.319166	−	0.129045i
$766$	−28.2771	−	48.9773i	−1.02169	−	1.76962i
$767$	−28.1535	+	2.46311i	−1.01656	+	0.0889377i
$768$	−8.68909	−	3.81226i	−0.313541	−	0.137563i
$769$	−29.6816	+	5.23367i	−1.07035	+	0.188731i	−0.680943	−	0.732336i	$-0.738430\pi$
$769$	−29.6816	+	5.23367i	−1.07035	+	0.188731i	−0.389404	+	0.921067i	$0.627319\pi$
$770$	48.6228	−	28.4853i	1.75224	−	1.02654i
$771$	−33.1993	+	12.9512i	−1.19564	+	0.466427i
$772$	0.514213	+	5.87749i	0.0185069	+	0.211535i
$773$	11.6749	−	43.5713i	0.419917	−	1.56715i	−0.354862	−	0.934919i	$-0.615472\pi$
$773$	11.6749	−	43.5713i	0.419917	−	1.56715i	0.774779	−	0.632232i	$-0.217861\pi$
$774$	0.415436	−	0.802212i	0.0149326	−	0.0288349i
$775$	2.42520	+	12.8017i	0.0871159	+	0.459852i
$776$	−5.81811	−	15.9851i	−0.208858	−	0.573832i
$777$	16.2459	+	55.5172i	0.582820	+	1.99167i
$778$	−0.499302	+	5.70705i	−0.0179008	+	0.204608i
$779$	0.960366	+	0.349545i	0.0344087	+	0.0125237i
$780$	2.99901	+	1.61652i	0.107382	+	0.0578805i
$781$	7.81482	−	44.3200i	0.279636	−	1.58590i
$782$	2.24910	−	2.24910i	0.0804277	−	0.0804277i
$783$	1.81534	−	4.71263i	0.0648748	−	0.168416i
$784$			71.4757i			2.55270i
$785$	18.1792	−	26.3165i	0.648844	−	0.939275i
$786$	−4.04997	+	11.9727i	−0.144458	+	0.427052i
$787$	14.8817	+	31.9138i	0.530474	+	1.13761i	0.970827	+	0.239780i	$0.0770755\pi$
$787$	14.8817	+	31.9138i	0.530474	+	1.13761i	−0.440353	+	0.897825i	$0.645147\pi$
$788$	2.88803	+	0.252670i	0.102882	+	0.00900100i
$789$	25.3639	−	15.4281i	0.902978	−	0.549256i
$790$	−32.6776	−	2.65008i	−1.16262	−	0.0942855i
$791$	−3.24199	−	1.87177i	−0.115272	−	0.0665523i
$792$	−27.7329	−	1.15169i	−0.985445	−	0.0409234i
$793$	−4.26192	−	1.14198i	−0.151345	−	0.0405528i
$794$	5.14028	+	4.31321i	0.182422	+	0.153070i
$795$	−4.85358	+	14.6541i	−0.172139	+	0.519726i
$796$	−0.558987	−	3.17017i	−0.0198128	−	0.112364i
$797$	28.1820	+	19.7333i	0.998259	+	0.698989i	0.953930	−	0.300028i	$-0.0969961\pi$
$797$	28.1820	+	19.7333i	0.998259	+	0.698989i	0.0443290	+	0.999017i	$0.485885\pi$
$798$	11.0821	+	15.0803i	0.392300	+	0.533837i
$799$	−7.94536	+	9.46891i	−0.281087	+	0.334986i
$800$	−5.86344	+	2.82531i	−0.207304	+	0.0998898i
$801$	12.4737	+	1.61518i	0.440736	+	0.0570696i
$802$	14.7066	−	3.94062i	0.519308	−	0.139148i
$803$	−1.12829	−	0.526128i	−0.0398163	−	0.0185667i
$804$	6.13993	−	0.140514i	0.216539	−	0.00495553i
$805$	−14.0468	−	7.99151i	−0.495085	−	0.281664i
$806$	−5.06465	+	13.9150i	−0.178395	+	0.490135i
$807$	−5.39245	+	8.08901i	−0.189823	+	0.284746i
$808$	9.27159	+	13.2412i	0.326173	+	0.465824i
$809$	54.0630			1.90075			0.950377	−	0.311100i	$-0.100698\pi$
$809$	54.0630			1.90075			0.950377	+	0.311100i	$0.100698\pi$
$810$	−19.0774	+	23.2315i	−0.670312	+	0.816271i
$811$	24.1241			0.847112			0.423556	−	0.905870i	$-0.360782\pi$
$811$	24.1241			0.847112			0.423556	+	0.905870i	$0.360782\pi$
$812$	−0.621033	−	0.886927i	−0.0217940	−	0.0311250i
$813$	−15.0670	+	22.6014i	−0.528424	+	0.792667i
$814$	−12.4019	+	34.0739i	−0.434685	+	1.19429i
$815$	−6.71002	−	24.4212i	−0.235042	−	0.855436i
$816$	10.8369	−	0.248005i	0.379368	−	0.00868192i
$817$	0.274318	+	0.127917i	0.00959717	+	0.00447523i
$818$	33.7588	−	9.04564i	1.18035	−	0.316273i
$819$	−33.3795	+	43.6933i	−1.16637	+	1.52677i
$820$	0.271046	+	0.224519i	0.00946534	+	0.00784055i
$821$	−5.28957	+	6.30386i	−0.184607	+	0.220006i	−0.850409	−	0.526123i	$-0.823645\pi$
$821$	−5.28957	+	6.30386i	−0.184607	+	0.220006i	0.665802	+	0.746129i	$0.268090\pi$
$822$	2.78786	+	3.79368i	0.0972377	+	0.132320i
$823$	2.18373	+	1.52906i	0.0761200	+	0.0532998i	0.611017	−	0.791617i	$-0.290761\pi$
$823$	2.18373	+	1.52906i	0.0761200	+	0.0532998i	−0.534897	+	0.844917i	$0.679650\pi$
$824$	3.45661	+	19.6034i	0.120417	+	0.682917i
$825$	−20.6685	+	22.1938i	−0.719583	+	0.772690i
$826$	−40.9538	−	34.3643i	−1.42497	−	1.19569i
$827$	7.49264	+	2.00765i	0.260545	+	0.0698128i	0.386727	−	0.922194i	$-0.373606\pi$
$827$	7.49264	+	2.00765i	0.260545	+	0.0698128i	−0.126182	+	0.992007i	$0.540272\pi$
$828$	−0.482480	−	0.922037i	−0.0167673	−	0.0320430i
$829$	−36.4123	−	21.0226i	−1.26465	−	0.730147i	−0.290680	−	0.956820i	$-0.593882\pi$
$829$	−36.4123	−	21.0226i	−1.26465	−	0.730147i	−0.973971	+	0.226674i	$0.927215\pi$
$830$	28.9084	−	24.5713i	1.00342	−	0.852882i
$831$	36.3480	−	22.1095i	1.26090	−	0.766971i
$832$	26.0493	+	2.27902i	0.903096	+	0.0790106i
$833$	−9.72492	−	20.8552i	−0.336948	−	0.722588i
$834$	−2.39280	+	7.07369i	−0.0828559	+	0.244942i
$835$	25.6976	+	17.7517i	0.889301	+	0.614322i
$836$			1.21575i			0.0420477i
$837$	−11.5984	−	6.98749i	−0.400899	−	0.241523i
$838$	−1.57481	+	1.57481i	−0.0544008	+	0.0544008i
$839$	7.44120	−	42.2011i	0.256899	−	1.45694i	−0.534253	−	0.845325i	$-0.679407\pi$
$839$	7.44120	−	42.2011i	0.256899	−	1.45694i	0.791152	−	0.611620i	$-0.209482\pi$
$840$	−14.1457	−	47.2260i	−0.488072	−	1.62945i
$841$	26.3634	+	9.59551i	0.909084	+	0.330880i
$842$	−2.40885	+	27.5332i	−0.0830143	+	0.948858i
$843$	0.353949	+	1.20955i	0.0121907	+	0.0416591i
$844$	1.59083	+	4.37077i	0.0547587	+	0.150448i
$845$	−3.24579	−	0.551107i	−0.111659	−	0.0189586i
$846$	21.0371	+	32.8669i	0.723269	+	1.12999i
$847$	−1.57533	+	5.87920i	−0.0541289	+	0.202012i
$848$	−1.53162	−	17.5065i	−0.0525960	−	0.601175i
$849$	34.8538	−	13.5966i	1.19618	−	0.466635i
$850$	6.71081	−	8.20694i	0.230179	−	0.281496i
$851$	10.2410	−	1.80577i	0.351057	−	0.0619008i
$852$	4.71330	+	2.06791i	0.161475	+	0.0708456i
$853$	17.1159	−	1.49745i	0.586038	−	0.0512717i	0.209719	−	0.977762i	$-0.432745\pi$
$853$	17.1159	−	1.49745i	0.586038	−	0.0512717i	0.376319	+	0.926490i	$0.377190\pi$
$854$	−4.17334	−	7.22844i	−0.142809	−	0.247352i
$855$	−8.04201	−	6.06327i	−0.275031	−	0.207359i
$856$	18.4291	−	31.9201i	0.629893	−	1.09101i
$857$	−8.99607	+	19.2921i	−0.307300	+	0.659007i	−0.997937	−	0.0641943i	$-0.979552\pi$
$857$	−8.99607	+	19.2921i	−0.307300	+	0.659007i	0.690637	+	0.723201i	$0.257330\pi$
$858$	−33.0800	+	9.68017i	−1.12933	+	0.330475i
$859$	5.67148	+	6.75901i	0.193509	+	0.230615i	0.854071	−	0.520157i	$-0.174126\pi$
$859$	5.67148	+	6.75901i	0.193509	+	0.230615i	−0.660562	+	0.750771i	$0.729682\pi$
$860$	0.0741725	+	0.0732371i	0.00252926	+	0.00249736i
$861$	−4.26666	+	3.74981i	−0.145408	+	0.127793i
$862$	23.6126	−	16.5337i	0.804249	−	0.563141i
$863$	−31.7542	−	31.7542i	−1.08093	−	1.08093i	−0.996423	−	0.0845039i	$-0.973069\pi$
$863$	−31.7542	−	31.7542i	−1.08093	−	1.08093i	−0.0845039	−	0.996423i	$-0.526931\pi$
$864$	1.87201	−	6.49976i	0.0636870	−	0.221126i
$865$	8.22063	+	3.77002i	0.279510	+	0.128184i
$866$	31.2896	+	5.51721i	1.06327	+	0.187482i
$867$	23.2662	−	11.5044i	0.790160	−	0.390710i
$868$	−2.63105	+	1.22688i	−0.0893038	+	0.0416430i
$869$	26.3314	−	22.0947i	0.893233	−	0.749511i
$870$	4.41100	+	3.48677i	0.149547	+	0.118213i
$871$	−54.8180	+	19.9521i	−1.85744	+	0.676052i
$872$	1.38173	+	5.15670i	0.0467914	+	0.174628i
$873$	17.1141	−	8.95541i	0.579225	−	0.303095i
$874$	2.91359	−	1.68216i	0.0985535	−	0.0568999i
$875$	−49.2426	−	21.8308i	−1.66470	−	0.738016i
$876$	0.0890004	−	0.111134i	0.00300705	−	0.00375488i
$877$	11.1328	−	15.8993i	0.375928	−	0.536880i	−0.585955	−	0.810344i	$-0.699280\pi$
$877$	11.1328	−	15.8993i	0.375928	−	0.536880i	0.961882	+	0.273464i	$0.0881693\pi$
$878$	−8.56430	+	12.2311i	−0.289031	+	0.412779i
$879$	15.6969	+	2.39888i	0.529444	+	0.0809123i
$880$	11.6020	−	32.5168i	0.391104	−	1.09614i
$881$	−11.7101	+	6.76081i	−0.394522	+	0.227778i	−0.684118	−	0.729372i	$-0.739813\pi$
$881$	−11.7101	+	6.76081i	−0.394522	+	0.227778i	0.289595	+	0.957149i	$0.406479\pi$
$882$	−72.0042	+	9.63555i	−2.42451	+	0.324446i
$883$	8.04527	+	30.0253i	0.270745	+	1.01043i	0.958640	+	0.284623i	$0.0918684\pi$
$883$	8.04527	+	30.0253i	0.270745	+	1.01043i	−0.687895	+	0.725810i	$0.741465\pi$
$884$	1.17334	−	0.427060i	0.0394636	−	0.0143636i
$885$	26.4201	+	11.3922i	0.888102	+	0.382944i
$886$	35.3409	−	29.6546i	1.18730	−	0.996264i
$887$	−21.6538	+	10.0974i	−0.727065	+	0.339036i	−0.750663	−	0.660686i	$-0.770266\pi$
$887$	−21.6538	+	10.0974i	−0.727065	+	0.339036i	0.0235979	+	0.999722i	$0.492488\pi$
$888$	26.3947	+	17.5958i	0.885749	+	0.590476i
$889$	−93.2044	−	16.4345i	−3.12598	−	0.551194i
$890$	−5.83755	+	12.7289i	−0.195675	+	0.426675i
$891$	−2.88058	−	31.3852i	−0.0965030	−	1.05145i
$892$	−3.58201	−	3.58201i	−0.119934	−	0.119934i
$893$	−10.7099	+	7.49912i	−0.358392	+	0.250949i
$894$	−8.35801	−	41.7860i	−0.279534	−	1.39753i
$895$	−14.4986	+	0.0920065i	−0.484635	+	0.00307544i
$896$	39.8584	+	47.5014i	1.33158	+	1.58691i
$897$	7.14761	+	6.82778i	0.238652	+	0.227973i
$898$	1.07942	−	2.31483i	0.0360207	−	0.0772467i
$899$	−1.26634	+	2.19337i	−0.0422349	+	0.0731529i
$900$	−1.90676	−	2.89735i	−0.0635588	−	0.0965783i
$901$	2.82881	+	4.89965i	0.0942414	+	0.163231i
$902$	−3.54715	+	0.310336i	−0.118107	+	0.0103330i
$903$	−1.35560	+	0.996189i	−0.0451116	+	0.0331511i
$904$	−2.02174	+	0.356488i	−0.0672422	+	0.0118566i
$905$	−8.72924	−	14.9003i	−0.290170	−	0.495303i
$906$	5.24557	+	4.20084i	0.174272	+	0.139563i
$907$	−1.82905	−	20.9061i	−0.0607325	−	0.694175i	−0.964140	−	0.265393i	$-0.914498\pi$
$907$	−1.82905	−	20.9061i	−0.0607325	−	0.694175i	0.903408	−	0.428782i	$-0.141057\pi$
$908$	−0.296416	+	1.10624i	−0.00983690	+	0.0367118i
$909$	−13.5059	+	12.4289i	−0.447961	+	0.412239i
$910$	−35.4305	−	49.9227i	−1.17451	−	1.65492i
$911$	−9.46462	−	26.0038i	−0.313577	−	0.861545i	−0.991927	−	0.126807i	$-0.959527\pi$
$911$	−9.46462	−	26.0038i	−0.313577	−	0.861545i	0.678351	−	0.734738i	$-0.262695\pi$
$912$	11.1398	+	2.71333i	0.368876	+	0.0898472i
$913$	−3.46689	+	39.6268i	−0.114737	+	1.31145i
$914$	51.1285	+	18.6093i	1.69118	+	0.615539i
$915$	3.26777	+	3.08213i	0.108029	+	0.101892i
$916$	−0.0437565	+	0.248156i	−0.00144576	+	0.00819929i
$917$	16.6425	−	16.6425i	0.549585	−	0.549585i
$918$	1.71075	+	10.8836i	0.0564632	+	0.359213i
$919$			21.5936i			0.712307i	0.934427	+	0.356154i	$0.115912\pi$
$919$			21.5936i			0.712307i	−0.934427	+	0.356154i	$0.884088\pi$
$920$	−8.71801	+	1.59433i	−0.287424	+	0.0525634i
$921$	8.29969	+	9.44368i	0.273484	+	0.311180i
$922$	10.9105	+	23.3976i	0.359318	+	0.770559i
$923$	−48.7032	−	4.26098i	−1.60309	−	0.140252i
$924$	−5.92763	−	3.24380i	−0.195005	−	0.106713i
$925$	33.3624	−	9.39484i	1.09695	−	0.308900i
$926$	37.1159	+	21.4289i	1.21970	+	0.704197i
$927$	−21.5419	+	6.84261i	−0.707530	+	0.224741i
$928$	−1.22205	−	0.327447i	−0.0401158	−	0.0107490i
$929$	12.2976	+	10.3189i	0.403472	+	0.338553i	0.821834	−	0.569727i	$-0.192951\pi$
$929$	12.2976	+	10.3189i	0.403472	+	0.338553i	−0.418362	+	0.908280i	$0.637396\pi$
$930$	11.2604	−	10.0237i	0.369245	−	0.328691i
$931$	−4.22650	−	23.9697i	−0.138518	−	0.785575i
$932$	−5.02589	−	3.51917i	−0.164628	−	0.115274i
$933$	−15.7517	+	35.9022i	−0.515688	+	1.17538i
$934$	22.8691	−	27.2543i	0.748299	−	0.891788i
$935$	1.03898	+	11.0663i	0.0339783	+	0.361907i
$936$	1.37940	+	30.1217i	0.0450872	+	0.984557i
$937$	21.0951	−	5.65242i	0.689148	−	0.184657i	0.102783	−	0.994704i	$-0.467225\pi$
$937$	21.0951	−	5.65242i	0.689148	−	0.184657i	0.586365	+	0.810047i	$0.300559\pi$
$938$	−100.015	−	46.6379i	−3.26561	−	1.52278i
$939$	3.43782	−	6.28217i	0.112189	−	0.205011i
$940$	−4.34166	+	1.19293i	−0.141609	+	0.0389089i
$941$	−4.53610	+	12.4628i	−0.147872	+	0.406276i	−0.991409	−	0.130795i	$-0.958247\pi$
$941$	−4.53610	+	12.4628i	−0.147872	+	0.406276i	0.843537	+	0.537071i	$0.180469\pi$
$942$	−36.9312	−	2.38112i	−1.20328	−	0.0775810i
$943$	0.585710	+	0.836480i	0.0190733	+	0.0272395i
$944$	−32.7535			−1.06604
$945$	51.0198	−	23.0327i	1.65968	−	0.749253i
$946$	−1.05454			−0.0342861
$947$	−9.47761	−	13.5354i	−0.307981	−	0.439843i	0.635088	−	0.772440i	$-0.280964\pi$
$947$	−9.47761	−	13.5354i	−0.307981	−	0.439843i	−0.943069	+	0.332597i	$0.892075\pi$
$948$	1.74248	+	3.52393i	0.0565930	+	0.114452i
$949$	−0.462551	+	1.27085i	−0.0150150	+	0.0412535i
$950$	9.10306	−	6.54776i	0.295342	−	0.212437i
$951$	−28.9747	−	47.6344i	−0.939570	−	1.54465i
$952$	−16.3753	−	7.63591i	−0.530725	−	0.247481i
$953$	5.23599	−	1.40298i	0.169610	−	0.0454469i	−0.173014	−	0.984919i	$-0.555351\pi$
$953$	5.23599	−	1.40298i	0.169610	−	0.0454469i	0.342625	+	0.939472i	$0.388684\pi$
$954$	17.4295	−	3.90297i	0.564300	−	0.126363i
$955$	−13.2360	+	15.9789i	−0.428307	+	0.517065i
$956$	0.223273	−	0.266086i	0.00722115	−	0.00860583i
$957$	−5.85937	+	0.648018i	−0.189406	+	0.0209475i
$958$	−4.97080	−	3.48059i	−0.160599	−	0.112453i
$959$	−1.52234	−	8.63365i	−0.0491591	−	0.278795i
$960$	−22.2437	−	14.6255i	−0.717912	−	0.472036i
$961$	−18.5454	−	15.5615i	−0.598240	−	0.501983i
$962$	38.0491	+	10.1952i	1.22675	+	0.328707i
$963$	38.6998	+	15.9335i	1.24708	+	0.513451i
$964$	0.660134	+	0.381128i	0.0212615	+	0.0122753i
$965$	−4.61179	+	56.8671i	−0.148459	+	1.83062i
$966$	0.427816	+	18.6940i	0.0137647	+	0.601469i
$967$	−58.9559	−	5.15797i	−1.89589	−	0.165869i	−0.921152	−	0.389204i	$-0.872750\pi$
$967$	−58.9559	−	5.15797i	−1.89589	−	0.165869i	−0.974742	+	0.223335i	$0.928306\pi$
$968$	1.41064	+	3.02513i	0.0453397	+	0.0972312i
$969$	−3.61954	+	0.723979i	−0.116276	+	0.0232575i
$970$	3.86866	+	21.1544i	0.124215	+	0.679227i
$971$		−	27.0614i		−	0.868442i	−0.900806	−	0.434221i	$-0.857024\pi$
$971$		−	27.0614i		−	0.868442i	0.900806	−	0.434221i	$-0.142976\pi$
$972$	3.56547	+	0.529365i	0.114362	+	0.0169794i
$973$	9.83272	−	9.83272i	0.315222	−	0.315222i
$974$	−6.77297	+	38.4114i	−0.217020	+	1.23078i
$975$	25.9751	+	20.2662i	0.831870	+	0.649036i
$976$	−4.80526	−	1.74897i	−0.153813	−	0.0559833i
$977$	1.40489	−	16.0579i	0.0449463	−	0.513738i	−0.940035	−	0.341078i	$-0.889208\pi$
$977$	1.40489	−	16.0579i	0.0449463	−	0.513738i	0.984981	−	0.172661i	$-0.0552364\pi$
$978$	−20.2412	+	21.1893i	−0.647241	+	0.677559i
$979$	−5.02158	−	13.7967i	−0.160490	−	0.440944i
$980$	1.40312	−	8.26381i	0.0448211	−	0.263978i
$981$	−5.59548	+	2.33169i	−0.178650	+	0.0744452i
$982$	−9.89401	+	36.9250i	−0.315731	+	1.17832i
$983$	3.77419	+	43.1392i	0.120378	+	1.37593i	0.780682	+	0.624929i	$0.214872\pi$
$983$	3.77419	+	43.1392i	0.120378	+	1.37593i	−0.660304	+	0.750999i	$0.729573\pi$
$984$	−0.470591	+	3.07928i	−0.0150019	+	0.0981638i
$985$	27.1248	+	7.08390i	0.864270	+	0.225712i
$986$	2.02940	−	0.357838i	0.0646293	−	0.0113959i
$987$	−7.98793	−	72.2267i	−0.254259	−	2.29900i
$988$	1.31569	−	0.115108i	0.0418577	−	0.00366208i
$989$	0.151213	+	0.261908i	0.00480829	+	0.00832820i
$990$	34.3214	+	7.30426i	1.09080	+	0.232144i
$991$	−23.2675	+	40.3005i	−0.739117	+	1.28019i	0.213776	+	0.976883i	$0.431424\pi$
$991$	−23.2675	+	40.3005i	−0.739117	+	1.28019i	−0.952893	+	0.303306i	$0.901910\pi$
$992$	−1.43359	+	3.07434i	−0.0455164	+	0.0976103i
$993$	−0.803625	+	3.29935i	−0.0255023	+	0.104702i
$994$	−59.4476	−	70.8468i	−1.88556	−	2.24713i
$995$	−0.197539	−	31.1286i	−0.00626239	−	0.986842i
$996$	−4.30947	−	1.45775i	−0.136551	−	0.0461906i
$997$	8.29837	−	5.81058i	0.262812	−	0.184023i	−0.434742	−	0.900555i	$-0.643161\pi$
$997$	8.29837	−	5.81058i	0.262812	−	0.184023i	0.697554	+	0.716532i	$0.254272\pi$
$998$	6.16857	+	6.16857i	0.195263	+	0.195263i
$999$	−15.8279	+	32.3558i	−0.500771	+	1.02369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.2.5	✓	192
3.2	odd	2		405.2.r.a.332.12		192
5.2	odd	4		675.2.ba.b.218.12		192
5.3	odd	4	inner	135.2.q.a.83.5	yes	192
5.4	even	2		675.2.ba.b.407.12		192
15.8	even	4		405.2.r.a.8.12		192
27.13	even	9		405.2.r.a.152.12		192
27.14	odd	18	inner	135.2.q.a.122.5	yes	192
135.13	odd	36		405.2.r.a.233.12		192
135.14	odd	18		675.2.ba.b.257.12		192
135.68	even	36	inner	135.2.q.a.68.5	yes	192
135.122	even	36		675.2.ba.b.68.12		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.5	✓	192	1.1	even	1	trivial
135.2.q.a.68.5	yes	192	135.68	even	36	inner
135.2.q.a.83.5	yes	192	5.3	odd	4	inner
135.2.q.a.122.5	yes	192	27.14	odd	18	inner
405.2.r.a.8.12		192	15.8	even	4
405.2.r.a.152.12		192	27.13	even	9
405.2.r.a.233.12		192	135.13	odd	36
405.2.r.a.332.12		192	3.2	odd	2
675.2.ba.b.68.12		192	135.122	even	36
675.2.ba.b.218.12		192	5.2	odd	4
675.2.ba.b.257.12		192	135.14	odd	18
675.2.ba.b.407.12		192	5.4	even	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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.856769 - 1.22359i) q^{2} +(-0.960742 + 1.44117i) q^{3} +(-0.0790861 + 0.217287i) q^{4} +(-1.10572 + 1.94355i) q^{5} +(2.58654 - 0.0591935i) q^{6} +(-4.36642 - 2.03610i) q^{7} +(-2.55204 + 0.683816i) q^{8} +(-1.15395 - 2.76919i) q^{9} +O(q^{10})\)	\(q+(-0.856769 - 1.22359i) q^{2} +(-0.960742 + 1.44117i) q^{3} +(-0.0790861 + 0.217287i) q^{4} +(-1.10572 + 1.94355i) q^{5} +(2.58654 - 0.0591935i) q^{6} +(-4.36642 - 2.03610i) q^{7} +(-2.55204 + 0.683816i) q^{8} +(-1.15395 - 2.76919i) q^{9} +(3.32546 - 0.312216i) q^{10} +(-2.25098 + 2.68262i) q^{11} +(-0.237167 - 0.322733i) q^{12} +(3.11626 + 2.18203i) q^{13} +(1.24966 + 7.08719i) q^{14} +(-1.73867 - 3.46078i) q^{15} +(3.37749 + 2.83405i) q^{16} +(-1.37108 - 0.367380i) q^{17} +(-2.39969 + 3.78452i) q^{18} +(-1.30024 - 0.750693i) q^{19} +(-0.334861 - 0.393967i) q^{20} +(7.12937 - 4.33660i) q^{21} +(5.21100 + 0.455904i) q^{22} +(-0.633988 - 1.35959i) q^{23} +(1.46635 - 4.33489i) q^{24} +(-2.55475 - 4.29805i) q^{25} -5.68253i q^{26} +(5.09952 + 0.997437i) q^{27} +(0.787741 - 0.787741i) q^{28} +(0.168770 - 0.957143i) q^{29} +(-2.74495 + 5.09252i) q^{30} +(-2.44873 - 0.891266i) q^{31} +(0.113453 - 1.29677i) q^{32} +(-1.70350 - 5.82135i) q^{33} +(0.725176 + 1.99240i) q^{34} +(8.78530 - 6.23499i) q^{35} +(0.692970 - 0.0317342i) q^{36} +(-1.79413 + 6.69580i) q^{37} +(0.195461 + 2.23413i) q^{38} +(-6.13860 + 2.39470i) q^{39} +(1.49282 - 5.71612i) q^{40} +(-0.670363 + 0.118203i) q^{41} +(-11.4145 - 5.00798i) q^{42} +(-0.200831 + 0.0175704i) q^{43} +(-0.404877 - 0.701267i) q^{44} +(6.65800 + 0.819200i) q^{45} +(-1.12040 + 1.94060i) q^{46} +(3.68023 - 7.89228i) q^{47} +(-7.32924 + 2.14475i) q^{48} +(10.4204 + 12.4186i) q^{49} +(-3.07023 + 6.80841i) q^{50} +(1.84671 - 1.62300i) q^{51} +(-0.720580 + 0.504555i) q^{52} +(-2.81838 - 2.81838i) q^{53} +(-3.14865 - 7.09431i) q^{54} +(-2.72483 - 7.34112i) q^{55} +(12.5356 + 2.21036i) q^{56} +(2.33107 - 1.15264i) q^{57} +(-1.31575 + 0.613544i) q^{58} +(-5.69079 + 4.77514i) q^{59} +(0.889488 - 0.104091i) q^{60} +(-1.08988 + 0.396683i) q^{61} +(1.00745 + 3.75986i) q^{62} +(-0.599704 + 14.4410i) q^{63} +(5.95268 - 3.43678i) q^{64} +(-7.68660 + 3.64388i) q^{65} +(-5.66346 + 7.07194i) q^{66} +(-8.79548 + 12.5612i) q^{67} +(0.188260 - 0.268864i) q^{68} +(2.56850 + 0.392531i) q^{69} +(-15.1561 - 5.40769i) q^{70} +(-11.1295 + 6.42561i) q^{71} +(4.83854 + 6.27798i) q^{72} +(0.0920100 + 0.343386i) q^{73} +(9.73009 - 3.54146i) q^{74} +(8.64869 + 0.447481i) q^{75} +(0.265947 - 0.223156i) q^{76} +(15.2908 - 7.13022i) q^{77} +(8.18950 + 5.45945i) q^{78} +(-9.66646 - 1.70446i) q^{79} +(-9.24267 + 3.43063i) q^{80} +(-6.33680 + 6.39100i) q^{81} +(0.718978 + 0.718978i) q^{82} +(9.30474 - 6.51525i) q^{83} +(0.378454 + 1.89208i) q^{84} +(2.23006 - 2.25854i) q^{85} +(0.193565 + 0.230681i) q^{86} +(1.21726 + 1.16279i) q^{87} +(3.91017 - 8.38540i) q^{88} +(-2.09630 + 3.63090i) q^{89} +(-4.70200 - 8.84854i) q^{90} +(-9.16409 - 15.8727i) q^{91} +(0.345561 - 0.0302327i) q^{92} +(3.63707 - 2.67277i) q^{93} +(-12.8100 + 2.25876i) q^{94} +(2.89671 - 1.69702i) q^{95} +(1.75987 + 1.40937i) q^{96} +(0.561155 + 6.41403i) q^{97} +(6.26740 - 23.3902i) q^{98} +(10.0262 + 3.13779i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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