LMFDB - Embedded newform 135.2.q.a.122.5

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			122.5
Character	$\chi$	$=$	135.122
Dual form			135.2.q.a.83.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22359 - 0.856769i) q^{2} +(-1.44117 + 0.960742i) q^{3} +(0.0790861 + 0.217287i) q^{4} +(2.10603 + 0.751431i) q^{5} +(2.58654 + 0.0591935i) q^{6} +(-2.03610 - 4.36642i) q^{7} +(-0.683816 + 2.55204i) q^{8} +(1.15395 - 2.76919i) q^{9} +O(q^{10})$	\(q+(-1.22359 - 0.856769i) q^{2} +(-1.44117 + 0.960742i) q^{3} +(0.0790861 + 0.217287i) q^{4} +(2.10603 + 0.751431i) q^{5} +(2.58654 + 0.0591935i) q^{6} +(-2.03610 - 4.36642i) q^{7} +(-0.683816 + 2.55204i) q^{8} +(1.15395 - 2.76919i) q^{9} +(-1.93312 - 2.72382i) q^{10} +(-2.25098 - 2.68262i) q^{11} +(-0.322733 - 0.237167i) q^{12} +(-2.18203 - 3.11626i) q^{13} +(-1.24966 + 7.08719i) q^{14} +(-3.75708 + 0.940408i) q^{15} +(3.37749 - 2.83405i) q^{16} +(-0.367380 - 1.37108i) q^{17} +(-3.78452 + 2.39969i) q^{18} +(1.30024 - 0.750693i) q^{19} +(0.00328108 + 0.517040i) q^{20} +(7.12937 + 4.33660i) q^{21} +(0.455904 + 5.21100i) q^{22} +(1.35959 + 0.633988i) q^{23} +(-1.46635 - 4.33489i) q^{24} +(3.87070 + 3.16507i) q^{25} +5.68253i q^{26} +(0.997437 + 5.09952i) q^{27} +(0.787741 - 0.787741i) q^{28} +(-0.168770 - 0.957143i) q^{29} +(5.40285 + 2.06827i) q^{30} +(-2.44873 + 0.891266i) q^{31} +(-1.29677 + 0.113453i) q^{32} +(5.82135 + 1.70350i) q^{33} +(-0.725176 + 1.99240i) q^{34} +(-1.00701 - 10.7258i) q^{35} +(0.692970 + 0.0317342i) q^{36} +(6.69580 - 1.79413i) q^{37} +(-2.23413 - 0.195461i) q^{38} +(6.13860 + 2.39470i) q^{39} +(-3.35782 + 4.86082i) q^{40} +(-0.670363 - 0.118203i) q^{41} +(-5.00798 - 11.4145i) q^{42} +(-0.0175704 + 0.200831i) q^{43} +(0.404877 - 0.701267i) q^{44} +(4.51110 - 4.96487i) q^{45} +(-1.12040 - 1.94060i) q^{46} +(-7.89228 + 3.68023i) q^{47} +(-2.14475 + 7.32924i) q^{48} +(-10.4204 + 12.4186i) q^{49} +(-2.02443 - 7.18905i) q^{50} +(1.84671 + 1.62300i) q^{51} +(0.504555 - 0.720580i) 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} +(-1.15264 + 2.33107i) q^{57} +(-0.613544 + 1.31575i) q^{58} +(5.69079 + 4.77514i) q^{59} +(-0.501471 - 0.741992i) q^{60} +(-1.08988 - 0.396683i) q^{61} +(3.75986 + 1.00745i) q^{62} +(-14.4410 + 0.599704i) q^{63} +(-5.95268 - 3.43678i) q^{64} +(-2.25376 - 8.20258i) q^{65} +(-5.66346 - 7.07194i) q^{66} +(12.5612 - 8.79548i) q^{67} +(0.268864 - 0.188260i) q^{68} +(-2.56850 + 0.392531i) q^{69} +(-7.95735 + 13.9868i) q^{70} +(-11.1295 - 6.42561i) q^{71} +(6.27798 + 4.83854i) q^{72} +(-0.343386 - 0.0920100i) q^{73} +(-9.73009 - 3.54146i) q^{74} +(-8.61916 - 0.842659i) q^{75} +(0.265947 + 0.223156i) q^{76} +(-7.13022 + 15.2908i) q^{77} +(-5.45945 - 8.18950i) 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} +(6.51525 - 9.30474i) q^{83} +(-0.378454 + 1.89208i) q^{84} +(0.256560 - 3.16359i) q^{85} +(0.193565 - 0.230681i) q^{86} +(1.16279 + 1.21726i) q^{87} +(8.38540 - 3.91017i) q^{88} +(2.09630 + 3.63090i) q^{89} +(-9.77350 + 2.21001i) q^{90} +(-9.16409 + 15.8727i) q^{91} +(-0.0302327 + 0.345561i) q^{92} +(2.67277 - 3.63707i) q^{93} +(12.8100 + 2.25876i) q^{94} +(3.30243 - 0.603940i) q^{95} +(1.75987 - 1.40937i) q^{96} +(6.41403 + 0.561155i) q^{97} +(23.3902 - 6.26740i) 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 $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.22359	−	0.856769i	−0.865211	−	0.605827i	0.0544607	−	0.998516i	$-0.482656\pi$
$2$	−1.22359	−	0.856769i	−0.865211	−	0.605827i	−0.919671	+	0.392689i	$0.871545\pi$
$3$	−1.44117	+	0.960742i	−0.832061	+	0.554685i
$3$	−1.44117	+	0.960742i	−0.832061	+	0.554685i
$4$	0.0790861	+	0.217287i	0.0395430	+	0.108644i
$5$	2.10603	+	0.751431i	0.941844	+	0.336050i
$5$	2.10603	+	0.751431i	0.941844	+	0.336050i
$6$	2.58654	+	0.0591935i	1.05595	+	0.0241657i
$7$	−2.03610	−	4.36642i	−0.769572	−	1.65035i	−0.759590	−	0.650402i	$-0.774600\pi$
$7$	−2.03610	−	4.36642i	−0.769572	−	1.65035i	−0.00998196	−	0.999950i	$-0.503177\pi$
$8$	−0.683816	+	2.55204i	−0.241766	+	0.902281i
$9$	1.15395	−	2.76919i	0.384650	−	0.923063i
$10$	−1.93312	−	2.72382i	−0.611305	−	0.861349i
$11$	−2.25098	−	2.68262i	−0.678697	−	0.808839i	0.311243	−	0.950330i	$-0.399255\pi$
$11$	−2.25098	−	2.68262i	−0.678697	−	0.808839i	−0.989940	+	0.141491i	$0.954810\pi$
$12$	−0.322733	−	0.237167i	−0.0931651	−	0.0684641i
$13$	−2.18203	−	3.11626i	−0.605186	−	0.864295i	0.393294	−	0.919413i	$-0.371336\pi$
$13$	−2.18203	−	3.11626i	−0.605186	−	0.864295i	−0.998480	+	0.0551175i	$0.982447\pi$
$14$	−1.24966	+	7.08719i	−0.333986	+	1.89413i
$15$	−3.75708	+	0.940408i	−0.970073	+	0.242812i
$16$	3.37749	−	2.83405i	0.844372	−	0.708512i
$17$	−0.367380	−	1.37108i	−0.0891027	−	0.332536i	0.906957	−	0.421224i	$-0.138399\pi$
$17$	−0.367380	−	1.37108i	−0.0891027	−	0.332536i	−0.996059	+	0.0886879i	$0.971733\pi$
$18$	−3.78452	+	2.39969i	−0.892019	+	0.565612i
$19$	1.30024	−	0.750693i	0.298295	−	0.172221i	−0.343382	−	0.939196i	$-0.611572\pi$
$19$	1.30024	−	0.750693i	0.298295	−	0.172221i	0.641677	+	0.766975i	$0.278239\pi$
$20$	0.00328108	+	0.517040i	0.000733673	+	0.115614i
$21$	7.12937	+	4.33660i	1.55576	+	0.946323i
$22$	0.455904	+	5.21100i	0.0971990	+	1.11099i
$23$	1.35959	+	0.633988i	0.283494	+	0.132196i	0.559165	−	0.829057i	$-0.311122\pi$
$23$	1.35959	+	0.633988i	0.283494	+	0.132196i	−0.275670	+	0.961252i	$0.588900\pi$
$24$	−1.46635	−	4.33489i	−0.299318	−	0.884856i
$25$	3.87070	+	3.16507i	0.774141	+	0.633014i
$26$			5.68253i			1.11444i
$27$	0.997437	+	5.09952i	0.191957	+	0.981403i
$28$	0.787741	−	0.787741i	0.148869	−	0.148869i
$29$	−0.168770	−	0.957143i	−0.0313398	−	0.177737i	0.965120	−	0.261808i	$-0.0843188\pi$
$29$	−0.168770	−	0.957143i	−0.0313398	−	0.177737i	−0.996460	+	0.0840712i	$0.973208\pi$
$30$	5.40285	+	2.06827i	0.986420	+	0.377613i
$31$	−2.44873	+	0.891266i	−0.439806	+	0.160076i	−0.552426	−	0.833562i	$-0.686298\pi$
$31$	−2.44873	+	0.891266i	−0.439806	+	0.160076i	0.112620	+	0.993638i	$0.464076\pi$
$32$	−1.29677	+	0.113453i	−0.229239	+	0.0200558i
$33$	5.82135	+	1.70350i	1.01337	+	0.296541i
$34$	−0.725176	+	1.99240i	−0.124367	+	0.341694i
$35$	−1.00701	−	10.7258i	−0.170216	−	1.81299i
$36$	0.692970	+	0.0317342i	0.115495	+	0.00528903i
$37$	6.69580	−	1.79413i	1.10078	−	0.294954i	0.337699	−	0.941254i	$-0.390351\pi$
$37$	6.69580	−	1.79413i	1.10078	−	0.294954i	0.763083	+	0.646300i	$0.223685\pi$
$38$	−2.23413	−	0.195461i	−0.362424	−	0.0317080i
$39$	6.13860	+	2.39470i	0.982963	+	0.383459i
$40$	−3.35782	+	4.86082i	−0.530917	+	0.768563i
$41$	−0.670363	−	0.118203i	−0.104693	−	0.0184602i	0.121056	−	0.992646i	$-0.461372\pi$
$41$	−0.670363	−	0.118203i	−0.104693	−	0.0184602i	−0.225749	+	0.974185i	$0.572483\pi$
$42$	−5.00798	−	11.4145i	−0.772748	−	1.76129i
$43$	−0.0175704	+	0.200831i	−0.00267946	+	0.0306264i	−0.997417	−	0.0718322i	$-0.977115\pi$
$43$	−0.0175704	+	0.200831i	−0.00267946	+	0.0306264i	0.994737	+	0.102459i	$0.0326709\pi$
$44$	0.404877	−	0.701267i	0.0610375	−	0.105720i
$45$	4.51110	−	4.96487i	0.672475	−	0.740119i
$46$	−1.12040	−	1.94060i	−0.165195	−	0.286126i
$47$	−7.89228	+	3.68023i	−1.15121	+	0.536817i	−0.902044	−	0.431644i	$-0.857934\pi$
$47$	−7.89228	+	3.68023i	−1.15121	+	0.536817i	−0.249164	+	0.968461i	$0.580156\pi$
$48$	−2.14475	+	7.32924i	−0.309568	+	1.05789i
$49$	−10.4204	+	12.4186i	−1.48863	+	1.77409i
$50$	−2.02443	−	7.18905i	−0.286298	−	1.01669i
$51$	1.84671	+	1.62300i	0.258591	+	0.227266i
$52$	0.504555	−	0.720580i	0.0699692	−	0.0999264i
$53$	2.81838	+	2.81838i	0.387135	+	0.387135i	0.873664	−	0.486529i	$-0.161737\pi$
$53$	2.81838	+	2.81838i	0.387135	+	0.387135i	−0.486529	+	0.873664i	$0.661737\pi$
$54$	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
$57$	−1.15264	+	2.33107i	−0.152671	+	0.308758i
$58$	−0.613544	+	1.31575i	−0.0805623	+	0.172766i
$59$	5.69079	+	4.77514i	0.740877	+	0.621670i	0.933073	−	0.359687i	$-0.117116\pi$
$59$	5.69079	+	4.77514i	0.740877	+	0.621670i	−0.192196	+	0.981357i	$0.561561\pi$
$60$	−0.501471	−	0.741992i	−0.0647396	−	0.0957907i
$61$	−1.08988	−	0.396683i	−0.139544	−	0.0507900i	0.271304	−	0.962494i	$-0.412545\pi$
$61$	−1.08988	−	0.396683i	−0.139544	−	0.0507900i	−0.410848	+	0.911704i	$0.634767\pi$
$62$	3.75986	+	1.00745i	0.477503	+	0.127947i
$63$	−14.4410	+	0.599704i	−1.81939	+	0.0755556i
$64$	−5.95268	−	3.43678i	−0.744085	−	0.429598i
$65$	−2.25376	−	8.20258i	−0.279544	−	1.01740i
$66$	−5.66346	−	7.07194i	−0.697124	−	0.870496i
$67$	12.5612	−	8.79548i	1.53460	−	1.07454i	0.566472	−	0.824081i	$-0.308308\pi$
$67$	12.5612	−	8.79548i	1.53460	−	1.07454i	0.968128	−	0.250457i	$-0.0805810\pi$
$68$	0.268864	−	0.188260i	0.0326045	−	0.0228299i
$69$	−2.56850	+	0.392531i	−0.309211	+	0.0472552i
$70$	−7.95735	+	13.9868i	−0.951086	+	1.67174i
$71$	−11.1295	−	6.42561i	−1.32083	−	0.762579i	−0.336966	−	0.941517i	$-0.609401\pi$
$71$	−11.1295	−	6.42561i	−1.32083	−	0.762579i	−0.983860	+	0.178938i	$0.942734\pi$
$72$	6.27798	+	4.83854i	0.739867	+	0.570227i
$73$	−0.343386	−	0.0920100i	−0.0401903	−	0.0107690i	0.238668	−	0.971101i	$-0.423289\pi$
$73$	−0.343386	−	0.0920100i	−0.0401903	−	0.0107690i	−0.278858	+	0.960332i	$0.589956\pi$
$74$	−9.73009	−	3.54146i	−1.13110	−	0.411687i
$75$	−8.61916	−	0.842659i	−0.995255	−	0.0973019i
$76$	0.265947	+	0.223156i	0.0305062	+	0.0255977i
$77$	−7.13022	+	15.2908i	−0.812564	+	1.74255i
$78$	−5.45945	−	8.18950i	−0.618161	−	0.927278i
$79$	9.66646	−	1.70446i	1.08756	−	0.191766i	0.399005	−	0.916949i	$-0.369356\pi$
$79$	9.66646	−	1.70446i	1.08756	−	0.191766i	0.688557	+	0.725182i	$0.258245\pi$
$80$	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
$83$	6.51525	−	9.30474i	0.715142	−	1.02133i	−0.282923	−	0.959143i	$-0.591304\pi$
$83$	6.51525	−	9.30474i	0.715142	−	1.02133i	0.998065	−	0.0621857i	$-0.0198071\pi$
$84$	−0.378454	+	1.89208i	−0.0412927	+	0.206443i
$85$	0.256560	−	3.16359i	0.0278279	−	0.343140i
$86$	0.193565	−	0.230681i	0.0208726	−	0.0248750i
$87$	1.16279	+	1.21726i	0.124665	+	0.130504i
$88$	8.38540	−	3.91017i	0.893886	−	0.416826i
$89$	2.09630	+	3.63090i	0.222208	+	0.384875i	0.955478	−	0.295062i	$-0.0953403\pi$
$89$	2.09630	+	3.63090i	0.222208	+	0.384875i	−0.733270	+	0.679937i	$0.762007\pi$
$90$	−9.77350	+	2.21001i	−1.03022	+	0.232955i
$91$	−9.16409	+	15.8727i	−0.960658	+	1.66391i
$92$	−0.0302327	+	0.345561i	−0.00315198	+	0.0360272i
$93$	2.67277	−	3.63707i	0.277153	−	0.377146i
$94$	12.8100	+	2.25876i	1.32126	+	0.232973i
$95$	3.30243	−	0.603940i	0.338822	−	0.0619630i
$96$	1.75987	−	1.40937i	0.179616	−	0.143843i
$97$	6.41403	+	0.561155i	0.651246	+	0.0569767i	0.407991	−	0.912986i	$-0.366229\pi$
$97$	6.41403	+	0.561155i	0.651246	+	0.0569767i	0.243255	+	0.969962i	$0.421785\pi$
$98$	23.3902	−	6.26740i	2.36277	−	0.633103i
$99$	−10.0262	+	3.13779i	−1.00767	+	0.315360i
$100$	−0.381610	+	1.09137i	−0.0381610	+	0.109137i
$101$	−2.09253	+	5.74917i	−0.208214	+	0.572064i	−0.999209	−	0.0397585i	$-0.987341\pi$
$101$	−2.09253	+	5.74917i	−0.208214	+	0.572064i	0.790995	+	0.611823i	$0.209563\pi$
$102$	−0.869084	−	3.56810i	−0.0860521	−	0.353295i
$103$	7.50553	−	0.656648i	0.739541	−	0.0647015i	0.288841	−	0.957377i	$-0.406730\pi$
$103$	7.50553	−	0.656648i	0.739541	−	0.0647015i	0.450700	+	0.892675i	$0.351174\pi$
$104$	9.44492	−	3.43767i	0.926151	−	0.337091i
$105$	11.7560	+	14.4902i	1.14727	+	1.41410i
$106$	−1.03385	−	5.86326i	−0.100416	−	0.569490i
$107$	9.86451	−	9.86451i	0.953639	−	0.953639i	−0.0453334	−	0.998972i	$-0.514435\pi$
$107$	9.86451	−	9.86451i	0.953639	−	0.953639i	0.998972	+	0.0453334i	$0.0144350\pi$
$108$	−1.02918	+	0.620031i	−0.0990326	+	0.0596625i
$109$		−	2.02062i		−	0.193540i	−0.995307	−	0.0967701i	$-0.969149\pi$
$109$		−	2.02062i		−	0.193540i	0.995307	−	0.0967701i	$-0.0308512\pi$
$110$	−2.95556	+	11.3171i	−0.281802	+	1.07904i
$111$	−7.92609	+	9.01859i	−0.752311	+	0.856006i
$112$	−19.2515	−	8.97714i	−1.81910	−	0.848260i
$113$	−0.0677216	−	0.774062i	−0.00637072	−	0.0728176i	0.992344	−	0.123506i	$-0.0394139\pi$
$113$	−0.0677216	−	0.774062i	−0.00637072	−	0.0728176i	−0.998715	+	0.0506887i	$0.983858\pi$
$114$	3.40756	−	1.86473i	0.319147	−	0.174648i
$115$	2.38694	+	2.35683i	0.222583	+	0.219776i
$116$	0.194627	−	0.112368i	0.0180707	−	0.0104331i
$117$	−11.1475	+	2.44644i	−1.03058	+	0.226174i
$118$	−2.87202	−	10.7185i	−0.264391	−	0.986719i
$119$	−5.23869	+	4.39579i	−0.480230	+	0.402961i
$120$	0.169194	−	10.2313i	0.0154452	−	0.933983i
$121$	−0.219379	+	1.24416i	−0.0199435	+	0.113105i
$122$	0.993700	+	1.41915i	0.0899654	+	0.128484i
$123$	1.07967	−	0.473695i	0.0973506	−	0.0427116i
$124$	−0.387321	−	0.461592i	−0.0347825	−	0.0414522i
$125$	5.77347	+	9.57429i	0.516395	+	0.856350i
$126$	18.1837	+	11.6388i	1.61993	+	1.03687i
$127$	−5.08430	+	18.9749i	−0.451159	+	1.68375i	0.247982	+	0.968765i	$0.420232\pi$
$127$	−5.08430	+	18.9749i	−0.451159	+	1.68375i	−0.699141	+	0.714983i	$0.746434\pi$
$128$	5.43940	+	11.6648i	0.480779	+	1.03103i
$129$	−0.167625	−	0.306312i	−0.0147585	−	0.0269693i
$130$	−4.27003	+	11.9676i	−0.374506	+	1.04962i
$131$	−1.67084	−	4.59061i	−0.145982	−	0.401083i	0.845053	−	0.534682i	$-0.179569\pi$
$131$	−1.67084	−	4.59061i	−0.145982	−	0.401083i	−0.991035	+	0.133599i	$0.957347\pi$
$132$	0.0902401	+	1.39963i	0.00785439	+	0.121822i
$133$	−5.92525	−	4.14891i	−0.513784	−	0.359756i
$134$	−22.9055			−1.97874
$135$	−1.73131	+	11.4892i	−0.149007	+	0.988836i
$136$	3.75027			0.321583
$137$	1.49059	+	1.04372i	0.127349	+	0.0891710i	0.635516	−	0.772088i	$-0.280788\pi$
$137$	1.49059	+	1.04372i	0.127349	+	0.0891710i	−0.508166	+	0.861259i	$0.669676\pi$
$138$	3.47911	+	1.72031i	0.296161	+	0.146443i
$139$	0.987166	+	2.71222i	0.0837303	+	0.230047i	0.974491	−	0.224425i	$-0.0720503\pi$
$139$	0.987166	+	2.71222i	0.0837303	+	0.230047i	−0.890761	+	0.454472i	$0.849828\pi$
$140$	2.25094	−	1.06707i	0.190239	−	0.0901839i
$141$	7.83838	−	12.8863i	0.660110	−	1.08522i
$142$	8.11269	+	17.3977i	0.680802	+	1.45998i
$143$	−3.44802	+	12.8682i	−0.288338	+	1.07609i
$144$	−3.95056	−	12.6232i	−0.329214	−	1.05194i
$145$	0.363792	−	2.14259i	0.0302113	−	0.177932i
$146$	0.341333	+	0.406785i	0.0282489	+	0.0336658i
$147$	3.08657	−	27.9087i	0.254576	−	2.30187i
$148$	0.919386	+	1.31302i	0.0755731	+	0.107930i
$149$	2.86013	−	16.2206i	0.234311	−	1.32885i	−0.609748	−	0.792596i	$-0.708729\pi$
$149$	2.86013	−	16.2206i	0.234311	−	1.32885i	0.844059	−	0.536250i	$-0.180160\pi$
$150$	9.82438	+	8.41570i	0.802157	+	0.687139i
$151$	1.98981	−	1.66965i	0.161929	−	0.135874i	−0.558223	−	0.829691i	$-0.688517\pi$
$151$	1.98981	−	1.66965i	0.161929	−	0.135874i	0.720152	+	0.693817i	$0.244072\pi$
$152$	1.02667	+	3.83159i	0.0832741	+	0.310783i
$153$	−4.22072	−	0.564813i	−0.341225	−	0.0456624i
$154$	21.8252	−	12.6008i	1.75872	−	1.01540i
$155$	−5.82683	+	0.0369764i	−0.468022	+	0.00297002i
$156$	−0.0348594	+	1.52323i	−0.00279098	+	0.121956i
$157$	−1.24669	−	14.2497i	−0.0994965	−	1.13725i	−0.867715	−	0.497062i	$-0.834412\pi$
$157$	−1.24669	−	14.2497i	−0.0994965	−	1.13725i	0.768219	−	0.640188i	$-0.221143\pi$
$158$	−13.2881	−	6.19636i	−1.05715	−	0.492956i
$159$	−6.76951	−	1.35403i	−0.536857	−	0.107382i
$160$	−2.81629	−	0.735501i	−0.222648	−	0.0581465i
$161$		−	7.22741i		−	0.569599i
$162$	2.27805	+	13.2492i	0.178981	+	1.04095i
$163$	−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
$165$	10.9799	+	7.96196i	0.854782	+	0.619837i
$166$	−15.9440	+	5.80315i	−1.23750	+	0.450412i
$167$	−13.9146	+	1.21737i	−1.07674	+	0.0942027i	−0.611703	−	0.791088i	$-0.709515\pi$
$167$	−13.9146	+	1.21737i	−1.07674	+	0.0942027i	−0.465039	+	0.885290i	$0.653960\pi$
$168$	−15.9423	+	15.2290i	−1.22998	+	1.17494i
$169$	−0.503569	+	1.38354i	−0.0387361	+	0.106427i
$170$	−3.02439	+	3.65114i	−0.231960	+	0.280029i
$171$	−0.578401	−	4.46687i	−0.0442314	−	0.341590i
$172$	−0.0450275	+	0.0120651i	−0.00343332	+	0.000919955i
$173$	4.02915	+	0.352505i	0.306331	+	0.0268005i	0.239285	−	0.970949i	$-0.423087\pi$
$173$	4.02915	+	0.352505i	0.306331	+	0.0268005i	0.0670460	+	0.997750i	$0.478643\pi$
$174$	−0.379874	−	2.48568i	−0.0287982	−	0.188439i
$175$	5.93890	−	23.3455i	0.448939	−	1.76475i
$176$	−15.2053	−	2.68111i	−1.14614	−	0.202096i
$177$	−12.7891	−	1.41441i	−0.961285	−	0.106314i
$178$	0.545824	−	6.23880i	0.0409112	−	0.467618i
$179$	−3.24205	+	5.61540i	−0.242322	+	0.419714i	−0.961375	−	0.275241i	$-0.911242\pi$
$179$	−3.24205	+	5.61540i	−0.242322	+	0.419714i	0.719053	+	0.694955i	$0.244576\pi$
$180$	1.43557	+	0.587552i	0.107001	+	0.0437936i
$181$	−3.86147	−	6.68826i	−0.287021	−	0.497135i	0.686076	−	0.727530i	$-0.259332\pi$
$181$	−3.86147	−	6.68826i	−0.287021	−	0.497135i	−0.973097	+	0.230395i	$0.925998\pi$
$182$	24.8123	−	11.5702i	1.83921	−	0.857639i
$183$	1.95181	−	0.475403i	0.144282	−	0.0351428i
$184$	−2.54767	+	3.03620i	−0.187817	+	0.223831i
$185$	15.4497	+	1.25294i	1.13588	+	0.0921177i
$186$	−6.38651	+	2.16035i	−0.468281	+	0.158404i
$187$	−2.85112	+	4.07182i	−0.208494	+	0.297761i
$188$	−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	0.167039	−	0.985950i	$-0.446580\pi$
$191$	9.13822	−	1.61131i	0.661218	−	0.116591i	0.494180	+	0.869360i	$0.335468\pi$
$192$	11.8807	−	0.766000i	0.857415	−	0.0552813i
$193$	10.7832	−	23.1246i	0.776191	−	1.66455i	0.0293284	−	0.999570i	$-0.490663\pi$
$193$	10.7832	−	23.1246i	0.776191	−	1.66455i	0.746863	−	0.664978i	$-0.231559\pi$
$194$	−7.36738	−	6.18197i	−0.528947	−	0.443839i
$195$	11.1286	+	9.65604i	0.796937	+	0.691483i
$196$	−3.52251	−	1.28209i	−0.251608	−	0.0915779i
$197$	−12.1103	−	3.24493i	−0.862820	−	0.231192i	−0.199839	−	0.979829i	$-0.564042\pi$
$197$	−12.1103	−	3.24493i	−0.862820	−	0.231192i	−0.662980	+	0.748637i	$0.730709\pi$
$198$	14.9563	+	4.75075i	1.06290	+	0.337621i
$199$	12.0563	+	6.96070i	0.854648	+	0.493431i	0.862216	−	0.506540i	$-0.169076\pi$
$199$	12.0563	+	6.96070i	0.854648	+	0.493431i	−0.00756873	+	0.999971i	$0.502409\pi$
$200$	−10.7242	+	7.71385i	−0.758317	+	0.545452i
$201$	−9.65271	+	24.7439i	−0.680850	+	1.74530i
$202$	7.48611	−	5.24183i	0.526721	−	0.368814i
$203$	−3.83566	+	2.68576i	−0.269210	+	0.188503i
$204$	−0.206609	+	0.529624i	−0.0144655	+	0.0370811i
$205$	−1.32298	−	0.752670i	−0.0924010	−	0.0525688i
$206$	−9.74630	−	5.62703i	−0.679057	−	0.392054i
$207$	3.32453	−	3.03337i	0.231071	−	0.210834i
$208$	−16.2014	−	4.34115i	−1.12337	−	0.301005i
$209$	−4.94063	−	1.79824i	−0.341751	−	0.124387i
$210$	−1.96977	−	27.8023i	−0.135927	−	1.91854i
$211$	15.4091	+	12.9298i	1.06081	+	0.890124i	0.994188	−	0.107654i	$-0.0343339\pi$
$211$	15.4091	+	12.9298i	1.06081	+	0.890124i	0.0666204	+	0.997778i	$0.478778\pi$
$212$	−0.389504	+	0.835293i	−0.0267512	+	0.0573682i
$213$	22.2128	−	1.43216i	1.52200	−	0.0981299i
$214$	−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
$218$	−1.73120	+	2.47242i	−0.117252	+	0.167453i
$219$	0.583276	−	0.197303i	0.0394141	−	0.0133325i
$220$	1.37964	−	1.17265i	0.0930150	−	0.0790601i
$221$	−3.47101	+	4.13659i	−0.233485	+	0.278257i
$222$	17.4252	−	4.24425i	1.16950	−	0.284855i
$223$	−19.8549	+	9.25851i	−1.32959	+	0.619996i	−0.952034	−	0.305993i	$-0.901012\pi$
$223$	−19.8549	+	9.25851i	−1.32959	+	0.619996i	−0.377552	+	0.925989i	$0.623234\pi$
$224$	3.13574	+	5.43126i	0.209515	+	0.362891i
$225$	13.2313	−	7.06637i	0.882084	−	0.471092i
$226$	−0.580328	+	1.00516i	−0.0386029	+	0.0668621i
$227$	−0.431671	+	4.93402i	−0.0286510	+	0.327482i	0.968320	+	0.249712i	$0.0803358\pi$
$227$	−0.431671	+	4.93402i	−0.0286510	+	0.327482i	−0.996971	+	0.0777708i	$0.975220\pi$
$228$	−0.597670	−	0.0660995i	−0.0395816	−	0.00437754i
$229$	−1.07319	−	0.189232i	−0.0709183	−	0.0125048i	0.138076	−	0.990422i	$-0.455908\pi$
$229$	−1.07319	−	0.189232i	−0.0709183	−	0.0125048i	−0.208995	+	0.977917i	$0.567019\pi$
$230$	−0.901377	−	4.92886i	−0.0594351	−	0.324999i
$231$	−4.41465	−	28.8870i	−0.290463	−	1.90062i
$232$	2.55807	+	0.223802i	0.167946	+	0.0146933i
$233$	−25.6297	+	6.86746i	−1.67906	+	0.449903i	−0.967530	−	0.252755i	$-0.918663\pi$
$233$	−25.6297	+	6.86746i	−1.67906	+	0.449903i	−0.711529	+	0.702657i	$0.751997\pi$
$234$	15.7360	+	6.55735i	1.02869	+	0.428667i
$235$	−19.3868	+	1.82016i	−1.26466	+	0.118734i
$236$	−0.587514	+	1.61418i	−0.0382439	+	0.105074i
$237$	−12.2935	+	11.7434i	−0.798547	+	0.762815i
$238$	10.1762	−	0.890302i	0.659625	−	0.0577097i
$239$	1.41158	−	0.513773i	0.0913075	−	0.0332332i	−0.295962	−	0.955200i	$-0.595640\pi$
$239$	1.41158	−	0.513773i	0.0913075	−	0.0332332i	0.387270	+	0.921966i	$0.373418\pi$
$240$	−10.0243	+	13.8240i	−0.647067	+	0.892332i
$241$	0.572431	+	3.24642i	0.0368735	+	0.209120i	0.997678	−	0.0681065i	$-0.0216958\pi$
$241$	0.572431	+	3.24642i	0.0368735	+	0.209120i	−0.960805	+	0.277227i	$0.910585\pi$
$242$	1.33439	−	1.33439i	0.0857777	−	0.0857777i
$243$	15.2725	+	3.12250i	0.979733	+	0.200308i
$244$		−	0.268188i		−	0.0171690i
$245$	−31.2775	+	18.3237i	−1.99824	+	1.17066i
$246$	−1.72692	−	0.345418i	−0.110105	−	0.0220231i
$247$	−5.17651	−	2.41385i	−0.329374	−	0.153589i
$248$	−0.600060	−	6.85872i	−0.0381039	−	0.435529i
$249$	−0.450134	+	19.6692i	−0.0285261	+	1.24649i
$250$	1.13857	−	16.6616i	0.0720095	−	1.05377i
$251$	16.2363	−	9.37404i	1.02483	−	0.591684i	0.109328	−	0.994006i	$-0.465130\pi$
$251$	16.2363	−	9.37404i	1.02483	−	0.591684i	0.915498	+	0.402322i	$0.131797\pi$
$252$	−1.27239	−	3.09041i	−0.0801530	−	0.194678i
$253$	−1.35967	−	5.07436i	−0.0854817	−	0.319022i
$254$	22.4782	−	18.8614i	1.41041	−	1.18347i
$255$	2.66965	+	4.80577i	0.167180	+	0.300949i
$256$	0.951288	−	5.39502i	0.0594555	−	0.337189i
$257$	11.8010	+	16.8536i	0.736129	+	1.05130i	0.996317	+	0.0857431i	$0.0273264\pi$
$257$	11.8010	+	16.8536i	0.736129	+	1.05130i	−0.260188	+	0.965558i	$0.583785\pi$
$258$	−0.0573345	+	0.518417i	−0.00356949	+	0.0322752i
$259$	−21.4672	−	25.5836i	−1.33391	−	1.58969i
$260$	1.60407	−	1.13842i	0.0994804	−	0.0706019i
$261$	−2.84526	−	0.637138i	−0.176117	−	0.0394378i
$262$	−1.88866	+	7.04856i	−0.116682	+	0.435461i
$263$	7.24374	+	15.5342i	0.446668	+	0.957882i	0.992755	+	0.120154i	$0.0383389\pi$
$263$	7.24374	+	15.5342i	0.446668	+	0.957882i	−0.546087	+	0.837728i	$0.683883\pi$
$264$	−8.32812	+	13.6914i	−0.512560	+	0.842649i
$265$	3.81777	+	8.05341i	0.234524	+	0.494717i
$266$	3.69544	+	10.1531i	0.226582	+	0.622529i
$267$	−6.50950	−	3.21875i	−0.398375	−	0.196984i
$268$	2.90456	+	2.03380i	0.177424	+	0.124234i
$269$	−5.61280			−0.342218			−0.171109	−	0.985252i	$-0.554735\pi$
$269$	−5.61280			−0.342218			−0.171109	+	0.985252i	$0.554735\pi$
$270$	11.9620	−	12.5748i	0.727986	−	0.765279i
$271$	15.6827			0.952656			0.476328	−	0.879268i	$-0.341968\pi$
$271$	15.6827			0.952656			0.476328	+	0.879268i	$0.341968\pi$
$272$	−5.12653	−	3.58963i	−0.310841	−	0.217654i
$273$	−2.04252	−	31.6796i	−0.123619	−	1.91733i
$274$	−0.929644	−	2.55418i	−0.0561619	−	0.154303i
$275$	−0.222218	−	17.5081i	−0.0134003	−	1.05578i
$276$	−0.288425	−	0.527059i	−0.0173611	−	0.0317252i
$277$	−10.3807	−	22.2616i	−0.623718	−	1.33757i	−0.923514	−	0.383564i	$-0.874696\pi$
$277$	−10.3807	−	22.2616i	−0.623718	−	1.33757i	0.299796	−	0.954003i	$-0.403081\pi$
$278$	1.11585	−	4.16442i	0.0669244	−	0.249765i
$279$	−0.357631	+	7.80948i	−0.0214108	+	0.467541i
$280$	28.0612	+	4.76455i	1.67698	+	0.284736i
$281$	0.467705	+	0.557389i	0.0279010	+	0.0332511i	0.779814	−	0.626011i	$-0.215313\pi$
$281$	0.467705	+	0.557389i	0.0279010	+	0.0332511i	−0.751914	+	0.659262i	$0.770869\pi$
$282$	−20.6316	+	9.05190i	−1.22859	+	0.539033i
$283$	12.3891	+	17.6935i	0.736457	+	1.05177i	0.996285	+	0.0861152i	$0.0274453\pi$
$283$	12.3891	+	17.6935i	0.736457	+	1.05177i	−0.259828	+	0.965655i	$0.583666\pi$
$284$	0.516015	−	2.92647i	0.0306199	−	0.173654i
$285$	−4.17914	+	4.04317i	−0.247551	+	0.239497i
$286$	15.2440	−	12.7913i	0.901399	−	0.756364i
$287$	0.848799	+	3.16776i	0.0501030	+	0.186987i
$288$	−1.18224	+	3.72193i	−0.0696641	+	0.219317i
$289$	12.9775	−	7.49259i	0.763385	−	0.440740i
$290$	−2.28084	+	2.30997i	−0.133935	+	0.135646i
$291$	−9.78284	+	5.35351i	−0.573480	+	0.313828i
$292$	−0.00716445	−	0.0818900i	−0.000419268	−	0.00479225i
$293$	8.30888	+	3.87450i	0.485410	+	0.226350i	0.649888	−	0.760030i	$-0.274816\pi$
$293$	8.30888	+	3.87450i	0.485410	+	0.226350i	−0.164477	+	0.986381i	$0.552594\pi$
$294$	−27.6880	+	31.5044i	−1.61480	+	1.83737i
$295$	8.39676	+	14.3328i	0.488879	+	0.834488i
$296$			18.3148i			1.06452i
$297$	11.4348	−	14.1547i	0.663517	−	0.821338i
$298$	−17.3970	+	17.3970i	−1.00778	+	1.00778i
$299$	−0.990996	−	5.62022i	−0.0573108	−	0.325026i
$300$	−0.498556	−	1.93948i	−0.0287842	−	0.111976i
$301$	0.912687	−	0.332191i	0.0526064	−	0.0191472i
$302$	−3.86523	+	0.338164i	−0.222419	+	0.0194591i
$303$	−2.50778	−	10.2959i	−0.144068	−	0.591485i
$304$	2.26404	−	6.22039i	0.129851	−	0.356764i
$305$	−1.99723	−	1.65439i	−0.114361	−	0.0947303i
$306$	4.68052	+	4.30728i	0.267568	+	0.246231i
$307$	−7.01141	+	1.87870i	−0.400162	+	0.107223i	−0.453287	−	0.891365i	$-0.649749\pi$
$307$	−7.01141	+	1.87870i	−0.400162	+	0.107223i	0.0531246	+	0.998588i	$0.483082\pi$
$308$	−3.88640	−	0.340016i	−0.221448	−	0.0193742i
$309$	−10.1859	+	8.15722i	−0.579454	+	0.464048i
$310$	7.16134	+	4.94700i	0.406737	+	0.280971i
$311$	22.2915	+	3.93059i	1.26404	+	0.222884i	0.765188	−	0.643807i	$-0.222646\pi$
$311$	22.2915	+	3.93059i	1.26404	+	0.222884i	0.498847	+	0.866690i	$0.333757\pi$
$312$	−10.3090	+	14.0284i	−0.583634	+	0.794202i
$313$	−0.360352	+	4.11885i	−0.0203683	+	0.232811i	0.979186	+	0.202964i	$0.0650575\pi$
$313$	−0.360352	+	4.11885i	−0.0203683	+	0.232811i	−0.999554	+	0.0298468i	$0.990498\pi$
$314$	−10.6833	+	18.5039i	−0.602891	+	1.04424i
$315$	−30.8638	−	9.58842i	−1.73898	−	0.540246i
$316$	1.13484	+	1.96560i	0.0638397	+	0.110574i
$317$	29.1740	−	13.6040i	1.63857	−	0.764080i	0.638589	−	0.769548i	$-0.279518\pi$
$317$	29.1740	−	13.6040i	1.63857	−	0.764080i	0.999985	+	0.00546854i	$0.00174070\pi$
$318$	7.12303	+	7.45669i	0.399440	+	0.418151i
$319$	−2.18775	+	2.60726i	−0.122490	+	0.145978i
$320$	−9.95400	−	11.7110i	−0.556446	−	0.654664i
$321$	−4.73920	+	23.6937i	−0.264516	+	1.32245i
$322$	−6.19222	+	8.84340i	−0.345079	+	0.492824i
$323$	−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
$327$	1.94129	+	2.91206i	0.107354	+	0.161037i
$328$	0.760064	−	1.62996i	0.0419675	−	0.0899996i
$329$	32.1389	+	26.9677i	1.77187	+	1.48678i
$330$	−6.61333	−	19.1494i	−0.364052	−	1.05414i
$331$	1.84234	+	0.670556i	0.101264	+	0.0368571i	0.392155	−	0.919899i	$-0.371730\pi$
$331$	1.84234	+	0.670556i	0.101264	+	0.0368571i	−0.290891	+	0.956756i	$0.593952\pi$
$332$	2.53707	+	0.679805i	0.139240	+	0.0373091i
$333$	2.75832	−	20.6123i	0.151155	−	1.12954i
$334$	18.0688	+	10.4320i	0.988679	+	0.570814i
$335$	33.0635	−	9.08461i	1.80645	−	0.496345i
$336$	36.3695	−	5.55817i	1.98412	−	0.303223i
$337$	−13.7556	+	9.63175i	−0.749313	+	0.524675i	−0.884724	−	0.466115i	$-0.845653\pi$
$337$	−13.7556	+	9.63175i	−0.749313	+	0.524675i	0.135411	+	0.990789i	$0.456764\pi$
$338$	1.80154	−	1.26145i	0.0979909	−	0.0686140i
$339$	0.841272	+	1.05049i	0.0456916	+	0.0570549i
$340$	0.707699	−	0.194449i	0.0383803	−	0.0105455i
$341$	7.90298	+	4.56279i	0.427970	+	0.247089i
$342$	−3.11934	+	5.96118i	−0.168675	+	0.322344i
$343$	42.8663	+	11.4860i	2.31456	+	0.620185i
$344$	−0.500513	−	0.182172i	−0.0269858	−	0.00982205i
$345$	−5.70430	−	1.10337i	−0.307109	−	0.0594034i
$346$	−4.62803	−	3.88338i	−0.248804	−	0.208772i
$347$	1.32763	−	2.84711i	0.0712708	−	0.152841i	−0.867445	−	0.497534i	$-0.834239\pi$
$347$	1.32763	−	2.84711i	0.0712708	−	0.152841i	0.938716	+	0.344693i	$0.112017\pi$
$348$	−0.172535	+	0.348929i	−0.00924883	+	0.0187045i
$349$	−12.2555	+	2.16098i	−0.656022	+	0.115674i	−0.491744	−	0.870740i	$-0.663640\pi$
$349$	−12.2555	+	2.16098i	−0.656022	+	0.115674i	−0.164278	+	0.986414i	$0.552529\pi$
$350$	−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
$353$	−10.4080	+	14.8642i	−0.553964	+	0.791143i	−0.994292	−	0.106694i	$-0.965973\pi$
$353$	−10.4080	+	14.8642i	−0.553964	+	0.791143i	0.440327	+	0.897837i	$0.354862\pi$
$354$	14.4368	+	12.6879i	0.767307	+	0.674356i
$355$	−18.6106	−	21.8955i	−0.987747	−	1.16209i
$356$	−0.623160	+	0.742654i	−0.0330274	+	0.0393606i
$357$	3.32664	−	11.3681i	0.176064	−	0.601665i
$358$	8.77805	−	4.09327i	0.463934	−	0.216336i
$359$	−5.27373	−	9.13437i	−0.278337	−	0.482094i	0.692635	−	0.721289i	$-0.256450\pi$
$359$	−5.27373	−	9.13437i	−0.278337	−	0.482094i	−0.970972	+	0.239195i	$0.923117\pi$
$360$	9.58577	+	14.9076i	0.505215	+	0.785697i
$361$	−8.37292	+	14.5023i	−0.440680	+	0.763280i
$362$	−1.00543	+	11.4921i	−0.0528441	+	0.604011i
$363$	−0.879154	−	2.00381i	−0.0461436	−	0.105173i
$364$	−4.17368	−	0.735932i	−0.218760	−	0.0385733i
$365$	−0.654041	−	0.451806i	−0.0342341	−	0.0236486i
$366$	−2.79553	−	1.09055i	−0.146125	−	0.0570040i
$367$	−3.55196	−	0.310757i	−0.185411	−	0.0162214i	−0.00592799	−	0.999982i	$-0.501887\pi$
$367$	−3.55196	−	0.310757i	−0.185411	−	0.0162214i	−0.179483	+	0.983761i	$0.557443\pi$
$368$	6.38875	−	1.71186i	0.333037	−	0.0892369i
$369$	−1.10089	+	1.71996i	−0.0573101	+	0.0895376i
$370$	−17.8307	−	14.7699i	−0.926972	−	0.767851i
$371$	6.56775	−	18.0448i	0.340981	−	0.936837i
$372$	1.00167	+	0.293117i	0.0519340	+	0.0151974i
$373$	−25.1438	+	2.19980i	−1.30190	+	0.113901i	−0.716925	−	0.697151i	$-0.754451\pi$
$373$	−25.1438	+	2.19980i	−1.30190	+	0.113901i	−0.584974	+	0.811052i	$0.698895\pi$
$374$	6.97721	−	2.53950i	0.360783	−	0.131314i
$375$	−17.5190	−	8.25137i	−0.904677	−	0.426099i
$376$	−3.99522	−	22.6580i	−0.206038	−	1.16850i
$377$	−2.61445	+	2.61445i	−0.134651	+	0.134651i
$378$	−37.3877	+	0.696344i	−1.92302	+	0.0358161i
$379$			27.8698i			1.43158i	0.698317	+	0.715788i	$0.253932\pi$
$379$			27.8698i			1.43158i	−0.698317	+	0.715788i	$0.746068\pi$
$380$	0.392405	+	0.669813i	0.0201299	+	0.0343607i
$381$	−10.9026	−	32.2307i	−0.558558	−	1.65123i
$382$	−12.5620	−	5.85775i	−0.642727	−	0.299709i
$383$	−3.29980	−	37.7169i	−0.168612	−	1.92724i	−0.336965	−	0.941517i	$-0.609401\pi$
$383$	−3.29980	−	37.7169i	−0.168612	−	1.92724i	0.168353	−	0.985727i	$-0.446155\pi$
$384$	−19.0460	−	11.5851i	−0.971936	−	0.591202i
$385$	−26.5064	+	26.8450i	−1.35089	+	1.36815i
$386$	−33.0067	+	19.0564i	−1.68000	+	0.969947i
$387$	0.535863	+	0.280404i	0.0272395	+	0.0142538i
$388$	0.385329	+	1.43807i	0.0195621	+	0.0730067i
$389$	2.93798	−	2.46526i	0.148962	−	0.124994i	−0.565261	−	0.824912i	$-0.691225\pi$
$389$	2.93798	−	2.46526i	0.148962	−	0.124994i	0.714223	+	0.699918i	$0.246780\pi$
$390$	−5.34390	−	21.3497i	−0.270599	−	1.08108i
$391$	0.369762	−	2.09702i	0.0186997	−	0.106051i
$392$	−24.5671	−	35.0854i	−1.24082	−	1.77208i
$393$	6.81836	+	5.01060i	0.343941	+	0.252751i
$394$	12.0379	+	14.3462i	0.606459	+	0.722749i
$395$	21.6386	+	3.67404i	1.08876	+	0.184861i
$396$	−1.47473	−	1.93041i	−0.0741081	−	0.0970066i
$397$	1.16267	−	4.33915i	0.0583528	−	0.217776i	−0.930592	−	0.366057i	$-0.880707\pi$
$397$	1.16267	−	4.33915i	0.0583528	−	0.217776i	0.988945	+	0.148281i	$0.0473742\pi$
$398$	−8.78827	−	18.8465i	−0.440516	−	0.944690i
$399$	12.5253	+	0.286645i	0.627051	+	0.0143502i
$400$	22.0432	−	0.279779i	1.10216	−	0.0139889i
$401$	−3.48616	−	9.57816i	−0.174091	−	0.478310i	0.821705	−	0.569913i	$-0.193023\pi$
$401$	−3.48616	−	9.57816i	−0.174091	−	0.478310i	−0.995796	+	0.0916029i	$0.970801\pi$
$402$	33.0108	−	22.0063i	1.64643	−	1.09757i
$403$	8.12063	+	5.68612i	0.404517	+	0.283246i
$404$	−1.41471			−0.0703845
$405$	−8.54308	−	18.2213i	−0.424509	−	0.905424i
$406$	6.99435			0.347124
$407$	−19.8851	−	13.9237i	−0.985667	−	0.690172i
$408$	−5.40478	+	3.60304i	−0.267576	+	0.178377i
$409$	8.00244	+	21.9865i	0.395695	+	1.08716i	0.964360	+	0.264594i	$0.0852380\pi$
$409$	8.00244	+	21.9865i	0.395695	+	1.08716i	−0.568665	+	0.822569i	$0.692540\pi$
$410$	0.973926	+	2.05445i	0.0480988	+	0.101462i
$411$	−3.15094	−	0.0721099i	−0.155424	−	0.00355692i
$412$	0.736264	+	1.57892i	0.0362731	+	0.0777879i
$413$	9.26327	−	34.5710i	0.455816	−	1.70113i
$414$	−6.66677	+	0.863260i	−0.327654	+	0.0424269i
$415$	20.7132	−	14.7003i	1.01677	−	0.721609i
$416$	3.18315	+	3.79353i	0.156067	+	0.185993i
$417$	−4.02842	−	2.96036i	−0.197272	−	0.144969i
$418$	4.50465	+	6.43330i	0.220329	+	0.314663i
$419$	0.258905	−	1.46832i	0.0126483	−	0.0717323i	−0.977830	−	0.209399i	$-0.932849\pi$
$419$	0.258905	−	1.46832i	0.0126483	−	0.0717323i	0.990479	+	0.137667i	$0.0439603\pi$
$420$	−2.21880	+	3.70040i	−0.108267	+	0.180561i
$421$	−14.1741	+	11.8935i	−0.690802	+	0.579652i	−0.919140	−	0.393930i	$-0.871115\pi$
$421$	−14.1741	+	11.8935i	−0.690802	+	0.579652i	0.228338	+	0.973582i	$0.426671\pi$
$422$	−7.77666	−	29.0229i	−0.378562	−	1.41281i
$423$	1.08396	+	26.1020i	0.0527040	+	1.26912i
$424$	−9.11988	+	5.26536i	−0.442900	+	0.255709i
$425$	2.91755	−	6.46983i	0.141522	−	0.313833i
$426$	−28.4065	−	17.2789i	−1.37630	−	0.837165i
$427$	0.487010	+	5.56655i	0.0235681	+	0.269384i
$428$	2.92358	+	1.36329i	0.141316	+	0.0658969i
$429$	−7.39383	−	21.8579i	−0.356977	−	1.05531i
$430$	0.580994	−	0.340371i	0.0280180	−	0.0164141i
$431$		−	19.2978i		−	0.929541i	−0.885431	−	0.464771i	$-0.846137\pi$
$431$		−	19.2978i		−	0.929541i	0.885431	−	0.464771i	$-0.153863\pi$
$432$	17.8211	+	14.3968i	0.857419	+	0.692665i
$433$	−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
$435$	1.53419	+	3.43735i	0.0735587	+	0.164808i
$436$	0.439055	−	0.159803i	0.0210269	−	0.00765317i
$437$	2.24372	−	0.196300i	0.107332	−	0.00939031i
$438$	−0.882735	−	0.258314i	−0.0421787	−	0.0123427i
$439$	3.41885	−	9.39321i	0.163173	−	0.448314i	−0.830979	−	0.556303i	$-0.812219\pi$
$439$	3.41885	−	9.39321i	0.163173	−	0.448314i	0.994152	+	0.107990i	$0.0344414\pi$
$440$	20.5981	−	1.93389i	0.981976	−	0.0921944i
$441$	22.3648	+	43.1866i	1.06499	+	2.05650i
$442$	7.79120	−	2.08765i	0.370590	−	0.0992992i
$443$	−30.7678	−	2.69183i	−1.46182	−	0.127893i	−0.671690	−	0.740832i	$-0.734431\pi$
$443$	−30.7678	−	2.69183i	−1.46182	−	0.127893i	−0.790130	+	0.612939i	$0.789987\pi$
$444$	−2.58647	−	1.00899i	−0.122748	−	0.0478847i
$445$	1.68650	+	9.22201i	0.0799477	+	0.437165i
$446$	32.2268	+	5.68245i	1.52598	+	0.269072i
$447$	11.4619	+	26.1246i	0.542129	+	1.23565i
$448$	−2.88621	+	32.9895i	−0.136361	+	1.55861i
$449$	−0.854949	+	1.48081i	−0.0403475	+	0.0698840i	−0.885494	−	0.464651i	$-0.846180\pi$
$449$	−0.854949	+	1.48081i	−0.0403475	+	0.0698840i	0.845146	+	0.534535i	$0.179513\pi$
$450$	−22.2439	−	2.68977i	−1.04859	−	0.126797i
$451$	1.19188	+	2.06440i	0.0561235	+	0.0972088i
$452$	0.162838	−	0.0759325i	0.00765925	−	0.00357157i
$453$	−1.26356	+	4.31795i	−0.0593671	+	0.202875i
$454$	4.75550	−	5.66739i	0.223187	−	0.265984i
$455$	−31.2270	+	26.5421i	−1.46395	+	1.24431i
$456$	−5.16078	−	4.53561i	−0.241676	−	0.212400i
$457$	20.8928	−	29.8380i	0.977323	−	1.39576i	0.0597413	−	0.998214i	$-0.480972\pi$
$457$	20.8928	−	29.8380i	0.977323	−	1.39576i	0.917582	−	0.397548i	$-0.130139\pi$
$458$	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	−0.555327	−	0.831632i	$-0.687407\pi$
$461$	−17.0206	+	3.00119i	−0.792728	+	0.139779i	−0.237401	+	0.971412i	$0.576296\pi$
$462$	−19.3477	+	39.1282i	−0.900137	+	1.82041i
$463$	−12.1257	+	26.0036i	−0.563527	+	1.20849i	0.393724	+	0.919229i	$0.371187\pi$
$463$	−12.1257	+	26.0036i	−0.563527	+	1.20849i	−0.957251	+	0.289259i	$0.906591\pi$
$464$	−3.28261	−	2.75443i	−0.152391	−	0.127871i
$465$	8.36193	−	5.65137i	0.387775	−	0.262076i
$466$	37.2442	+	13.5558i	1.72530	+	0.627959i
$467$	23.0066	+	6.16460i	1.06462	+	0.285264i	0.748280	−	0.663382i	$-0.230880\pi$
$467$	23.0066	+	6.16460i	1.06462	+	0.285264i	0.316339	+	0.948646i	$0.397546\pi$
$468$	−1.41319	−	2.22872i	−0.0653247	−	0.103023i
$469$	−63.9806	−	36.9392i	−2.95435	−	1.70570i
$470$	25.2810	+	14.3829i	1.16613	+	0.663432i
$471$	15.4870	+	19.3385i	0.713602	+	0.891071i
$472$	−16.0778	+	11.2578i	−0.740040	+	0.518181i
$473$	0.578303	−	0.404932i	0.0265904	−	0.0186188i
$474$	25.1036	−	3.83646i	1.15305	−	0.176214i
$475$	7.40883	+	1.20963i	0.339940	+	0.0555018i
$476$	−1.36946	−	0.790656i	−0.0627689	−	0.0362396i
$477$	11.0569	−	4.55236i	0.506261	−	0.208438i
$478$	−2.16738	−	0.580749i	−0.0991338	−	0.0265628i
$479$	−3.81746	−	1.38944i	−0.174424	−	0.0634853i	0.253332	−	0.967379i	$-0.418474\pi$
$479$	−3.81746	−	1.38944i	−0.174424	−	0.0634853i	−0.427756	+	0.903894i	$0.640696\pi$
$480$	4.76539	−	1.64575i	0.217509	−	0.0751178i
$481$	−20.2014	−	16.9510i	−0.921105	−	0.772899i
$482$	2.08101	−	4.46274i	0.0947873	−	0.203272i
$483$	6.94367	+	10.4159i	0.315948	+	0.473941i
$484$	−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	$0.951511\pi$
$488$	1.75763	−	2.51015i	0.0795640	−	0.113629i
$489$	3.84769	−	19.2366i	0.173998	−	0.869908i
$490$	53.9700	+	4.37685i	2.43812	+	0.197726i
$491$	−16.4502	+	19.6046i	−0.742387	+	0.884743i	−0.996599	−	0.0824057i	$-0.973740\pi$
$491$	−16.4502	+	19.6046i	−0.742387	+	0.884743i	0.254211	+	0.967149i	$0.418184\pi$
$492$	0.188315	+	0.197136i	0.00848988	+	0.00888757i
$493$	−1.25032	+	0.583032i	−0.0563114	+	0.0262585i
$494$	4.26583	+	7.38864i	0.191929	+	0.332431i
$495$	−23.4733	−	0.925716i	−1.05504	−	0.0416079i
$496$	−5.74468	+	9.95007i	−0.257944	+	0.446771i
$497$	−5.39623	+	61.6791i	−0.242054	+	2.76669i
$498$	17.4027	−	23.6814i	0.779836	−	1.06119i
$499$	5.75147	+	1.01414i	0.257471	+	0.0453991i	0.300894	−	0.953658i	$-0.402715\pi$
$499$	5.75147	+	1.01414i	0.257471	+	0.0453991i	−0.0434226	+	0.999057i	$0.513826\pi$
$500$	−1.62377	+	2.01169i	−0.0726171	+	0.0899657i
$501$	18.8837	−	15.1228i	0.843662	−	0.675635i
$502$	−27.8980	−	2.44076i	−1.24515	−	0.108936i
$503$	−20.0094	+	5.36150i	−0.892174	+	0.239057i	−0.675652	−	0.737221i	$-0.736138\pi$
$503$	−20.0094	+	5.36150i	−0.892174	+	0.239057i	−0.216522	+	0.976278i	$0.569471\pi$
$504$	8.34452	−	37.2640i	0.371695	−	1.65987i
$505$	−8.72703	+	10.5355i	−0.388348	+	0.468825i
$506$	−2.68387	+	7.37387i	−0.119312	+	0.327808i
$507$	−0.603500	−	2.47772i	−0.0268024	−	0.110040i
$508$	−4.52509	+	0.395894i	−0.200769	+	0.0175650i
$509$	7.40545	−	2.69536i	0.328241	−	0.119470i	−0.172643	−	0.984984i	$-0.555231\pi$
$509$	7.40545	−	2.69536i	0.328241	−	0.119470i	0.500884	+	0.865515i	$0.333008\pi$
$510$	0.850868	−	8.16758i	0.0376771	−	0.361666i
$511$	0.297412	+	1.68671i	0.0131567	+	0.0746156i
$512$	12.4157	−	12.4157i	0.548699	−	0.548699i
$513$	5.12508	+	5.88182i	0.226278	+	0.259689i
$514$		−	30.7328i		−	1.35556i
$515$	16.3003	+	4.25697i	0.718276	+	0.187584i
$516$	0.0533010	−	0.0606477i	0.00234644	−	0.00266987i
$517$	27.6380	+	12.8878i	1.21552	+	0.566806i
$518$	4.34787	+	49.6964i	0.191035	+	2.18354i
$519$	−6.14537	+	3.36296i	−0.269752	+	0.147617i
$520$	22.4744	−	0.142620i	0.985569	−	0.00625432i
$521$	−7.49714	+	4.32848i	−0.328456	+	0.189634i	−0.655155	−	0.755494i	$-0.727397\pi$
$521$	−7.49714	+	4.32848i	−0.328456	+	0.189634i	0.326700	+	0.945128i	$0.394063\pi$
$522$	2.93556	+	3.21733i	0.128486	+	0.140819i
$523$	3.40449	+	12.7057i	0.148868	+	0.555583i	0.999553	+	0.0299067i	$0.00952102\pi$
$523$	3.40449	+	12.7057i	0.148868	+	0.555583i	−0.850685	+	0.525676i	$0.823812\pi$
$524$	0.865339	−	0.726106i	0.0378025	−	0.0317201i
$525$	13.8700	+	39.3506i	0.605338	+	1.71740i
$526$	4.44587	−	25.2138i	0.193849	−	1.09937i
$527$	2.12161	+	3.02998i	0.0924189	+	0.131988i
$528$	24.4893	−	10.7445i	1.06576	−	0.467593i
$529$	−13.3376	−	15.8951i	−0.579894	−	0.691091i
$530$	2.22852	−	13.1250i	0.0968006	−	0.570116i
$531$	19.7901	−	10.2486i	0.858818	−	0.444751i
$532$	0.432899	−	1.61560i	0.0187686	−	0.0700452i
$533$	1.09440	+	2.34695i	0.0474037	+	0.101658i
$534$	5.20725	+	9.51557i	0.225340	+	0.411779i
$535$	28.1874	−	13.3624i	1.21865	−	0.577708i
$536$	13.8568	+	38.0712i	0.598523	+	1.64443i
$537$	−0.722598	−	11.2075i	−0.0311824	−	0.483640i
$538$	6.86778	+	4.80887i	0.296091	+	0.207325i
$539$	56.7706			2.44528
$540$	−2.63339	+	0.532447i	−0.113323	+	0.0229129i
$541$	27.5170			1.18305			0.591523	−	0.806288i	$-0.298527\pi$
$541$	27.5170			1.18305			0.591523	+	0.806288i	$0.298527\pi$
$542$	−19.1892	−	13.4364i	−0.824248	−	0.577145i
$543$	11.9907	+	5.92906i	0.514572	+	0.254440i
$544$	0.631962	+	1.73630i	0.0270951	+	0.0744433i
$545$	1.51836	−	4.25548i	0.0650392	−	0.182285i
$546$	−24.6429	+	40.5128i	−1.05462	+	1.73379i
$547$	13.8936	+	29.7950i	0.594049	+	1.27394i	0.941743	+	0.336334i	$0.109187\pi$
$547$	13.8936	+	29.7950i	0.594049	+	1.27394i	−0.347694	+	0.937608i	$0.613035\pi$
$548$	−0.108902	+	0.406429i	−0.00465208	+	0.0173618i
$549$	−2.35615	+	2.56032i	−0.100558	+	0.109272i
$550$	−14.7285	+	21.6132i	−0.628026	+	0.921590i
$551$	−0.937961	−	1.11782i	−0.0399585	−	0.0476207i
$552$	0.754628	−	6.82333i	0.0321191	−	0.290420i
$553$	−27.1242	−	38.7374i	−1.15344	−	1.64728i
$554$	−6.37122	+	36.1330i	−0.270687	+	1.53514i
$555$	−23.4694	+	13.0375i	−0.996221	+	0.553410i
$556$	−0.511259	+	0.428997i	−0.0216822	+	0.0181935i
$557$	−6.74775	−	25.1830i	−0.285911	−	1.06704i	−0.948171	−	0.317761i	$-0.897069\pi$
$557$	−6.74775	−	25.1830i	−0.285911	−	1.06704i	0.662259	−	0.749275i	$-0.269598\pi$
$558$	7.12851	−	9.24922i	0.301774	−	0.391551i
$559$	0.664181	−	0.383465i	0.0280919	−	0.0162188i
$560$	−33.7986	−	33.3723i	−1.42825	−	1.41024i
$561$	0.196982	−	8.60737i	0.00831657	−	0.363404i
$562$	−0.0947268	−	1.08273i	−0.00399581	−	0.0456723i
$563$	−27.4015	−	12.7775i	−1.15484	−	0.538510i	−0.251676	−	0.967811i	$-0.580982\pi$
$563$	−27.4015	−	12.7775i	−1.15484	−	0.538510i	−0.903161	+	0.429302i	$0.858760\pi$
$564$	3.41993	+	0.684052i	0.144005	+	0.0288038i
$565$	0.439031	−	1.68108i	0.0184702	−	0.0707237i
$566$		−	32.2643i		−	1.35617i
$567$	−15.0035	+	40.6819i	−0.630087	+	1.70848i
$568$	24.0089	−	24.0089i	1.00739	−	1.00739i
$569$	3.82709	+	21.7045i	0.160440	+	0.909901i	0.953642	+	0.300943i	$0.0973013\pi$
$569$	3.82709	+	21.7045i	0.160440	+	0.909901i	−0.793202	+	0.608959i	$0.791588\pi$
$570$	8.57762	−	1.36663i	0.359277	−	0.0572420i
$571$	−5.69726	+	2.07363i	−0.238423	+	0.0867789i	−0.458468	−	0.888711i	$-0.651602\pi$
$571$	−5.69726	+	2.07363i	−0.238423	+	0.0867789i	0.220045	+	0.975490i	$0.429380\pi$
$572$	−3.06878	+	0.268484i	−0.128312	+	0.0112259i
$573$	−11.6217	+	11.1017i	−0.485503	+	0.463778i
$574$	1.67545	−	4.60327i	0.0699321	−	0.192137i
$575$	3.25596	+	6.75718i	0.135783	+	0.281794i
$576$	−16.3862	+	12.5182i	−0.682758	+	0.521592i
$577$	−15.9120	+	4.26360i	−0.662424	+	0.177496i	−0.574340	−	0.818617i	$-0.694741\pi$
$577$	−15.9120	+	4.26360i	−0.662424	+	0.177496i	−0.0880841	+	0.996113i	$0.528074\pi$
$578$	−22.2986	−	1.95088i	−0.927501	−	0.0811458i
$579$	6.67638	+	43.6864i	0.277461	+	1.81555i
$580$	0.494328	−	0.0904014i	0.0205258	−	0.00375371i
$581$	−53.8941	−	9.50299i	−2.23590	−	0.394250i
$582$	16.5569	+	1.83112i	0.686307	+	0.0759023i
$583$	1.21651	−	13.9048i	0.0503827	−	0.575877i
$584$	0.469626	−	0.813416i	0.0194332	−	0.0336594i
$585$	−25.3152	−	3.22427i	−1.04665	−	0.133307i
$586$	−6.84714	−	11.8596i	−0.282853	−	0.489916i
$587$	2.17389	−	1.01370i	0.0897262	−	0.0418400i	−0.377237	−	0.926117i	$-0.623126\pi$
$587$	2.17389	−	1.01370i	0.0897262	−	0.0418400i	0.466963	+	0.884277i	$0.345348\pi$
$588$	6.30830	−	1.53652i	0.260150	−	0.0633648i
$589$	−2.51487	+	2.99711i	−0.103623	+	0.123494i
$590$	2.00568	−	24.7316i	0.0825724	−	1.01818i
$591$	20.5705	−	6.95833i	0.846157	−	0.286227i
$592$	17.5303	−	25.0359i	0.720491	−	1.02897i
$593$	19.8531	+	19.8531i	0.815268	+	0.815268i	0.985418	−	0.170150i	$-0.0544254\pi$
$593$	19.8531	+	19.8531i	0.815268	+	0.815268i	−0.170150	+	0.985418i	$0.554425\pi$
$594$	−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
$597$	−24.0626	+	1.55142i	−0.984817	+	0.0634955i
$598$	−3.60265	+	7.72592i	−0.147323	+	0.315936i
$599$	−12.9672	−	10.8807i	−0.529824	−	0.444575i	0.338217	−	0.941068i	$-0.390176\pi$
$599$	−12.9672	−	10.8807i	−0.529824	−	0.444575i	−0.868041	+	0.496493i	$0.834621\pi$
$600$	8.04442	−	21.4202i	0.328412	−	0.874476i
$601$	−24.9557	−	9.08314i	−1.01796	−	0.370509i	−0.221478	−	0.975165i	$-0.571088\pi$
$601$	−24.9557	−	9.08314i	−1.01796	−	0.370509i	−0.796486	+	0.604656i	$0.793310\pi$
$602$	−1.40137	−	0.375496i	−0.0571155	−	0.0153041i
$603$	−9.86129	−	44.9340i	−0.401583	−	1.82985i
$604$	0.520160	+	0.300315i	0.0211650	+	0.0122196i
$605$	−1.39692	+	2.45539i	−0.0567928	+	0.0998256i
$606$	−5.75272	+	14.7466i	−0.233688	+	0.599040i
$607$	5.34086	−	3.73971i	0.216779	−	0.151790i	−0.460144	−	0.887844i	$-0.652202\pi$
$607$	5.34086	−	3.73971i	0.216779	−	0.151790i	0.676922	+	0.736054i	$0.263313\pi$
$608$	−1.60095	+	1.12099i	−0.0649270	+	0.0454623i
$609$	2.94752	−	7.55571i	0.119440	−	0.306173i
$610$	1.02637	+	3.73547i	0.0415563	+	0.151245i
$611$	28.6898	+	16.5640i	1.16066	+	0.670109i
$612$	−0.211073	−	0.961776i	−0.00853213	−	0.0388775i
$613$	10.5860	+	2.83651i	0.427565	+	0.114566i	0.466183	−	0.884688i	$-0.345629\pi$
$613$	10.5860	+	2.83651i	0.427565	+	0.114566i	−0.0386179	+	0.999254i	$0.512296\pi$
$614$	10.1887	+	3.70839i	0.411183	+	0.149658i
$615$	2.62976	−	0.186317i	0.106042	−	0.00751302i
$616$	−34.1469	−	28.6527i	−1.37582	−	1.15445i
$617$	14.6963	−	31.5164i	0.591652	−	1.26880i	−0.351421	−	0.936217i	$-0.614302\pi$
$617$	14.6963	−	31.5164i	0.591652	−	1.26880i	0.943073	−	0.332585i	$-0.107921\pi$
$618$	19.4522	−	1.25417i	0.782483	−	0.0504501i
$619$	−31.5714	+	5.56690i	−1.26896	+	0.223753i	−0.767288	−	0.641303i	$-0.778394\pi$
$619$	−31.5714	+	5.56690i	−1.26896	+	0.223753i	−0.501676	+	0.865056i	$0.667283\pi$
$620$	−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
$623$	11.5858	−	16.5462i	0.464175	−	0.662910i
$624$	27.5197	−	9.30903i	1.10167	−	0.372659i
$625$	4.96468	+	24.5021i	0.198587	+	0.980083i
$626$	3.96982	−	4.73105i	0.158666	−	0.189091i
$627$	8.84795	−	2.15510i	0.353353	−	0.0860663i
$628$	2.99768	−	1.39784i	0.119620	−	0.0557799i
$629$	−4.91980	−	8.52135i	−0.196165	−	0.339768i
$630$	29.5496	+	38.1754i	1.17729	+	1.52095i
$631$	22.4076	−	38.8111i	0.892033	−	1.54505i	0.0545987	−	0.998508i	$-0.482612\pi$
$631$	22.4076	−	38.8111i	0.892033	−	1.54505i	0.837434	−	0.546538i	$-0.184055\pi$
$632$	−2.26024	+	25.8347i	−0.0899076	+	1.02765i
$633$	−34.6294	−	3.82985i	−1.37640	−	0.152223i
$634$	−47.3526	−	8.34954i	−1.88061	−	0.331603i
$635$	−24.9660	+	36.1411i	−0.990745	+	1.43422i
$636$	−0.241160	−	1.57801i	−0.00956262	−	0.0625723i
$637$	61.4373	+	5.37507i	2.43423	+	0.212968i
$638$	4.91073	−	1.31583i	0.194418	−	0.0520940i
$639$	−30.6366	+	23.4048i	−1.21196	+	0.925879i
$640$	2.69021	+	28.6538i	0.106340	+	1.13264i
$641$	−15.6160	+	42.9045i	−0.616794	+	1.69463i	0.0979055	+	0.995196i	$0.468786\pi$
$641$	−15.6160	+	42.9045i	−0.616794	+	1.69463i	−0.714699	+	0.699432i	$0.753437\pi$
$642$	26.0989	−	24.9311i	1.03004	−	0.983950i
$643$	36.2904	−	3.17500i	1.43115	−	0.125210i	0.654940	−	0.755681i	$-0.272694\pi$
$643$	36.2904	−	3.17500i	1.43115	−	0.125210i	0.776212	+	0.630472i	$0.217138\pi$
$644$	1.57042	−	0.571587i	0.0618833	−	0.0225237i
$645$	−0.122850	−	0.771061i	−0.00483720	−	0.0303605i
$646$	0.552782	+	3.13498i	0.0217489	+	0.123344i
$647$	−32.3432	+	32.3432i	−1.27154	+	1.27154i	−0.326266	+	0.945278i	$0.605791\pi$
$647$	−32.3432	+	32.3432i	−1.27154	+	1.27154i	−0.945278	+	0.326266i	$0.894209\pi$
$648$	20.6433	−	11.8015i	0.810945	−	0.463606i
$649$		−	26.0149i		−	1.02118i
$650$	−17.9856	+	21.9954i	−0.705453	+	0.862730i
$651$	−21.3230	−	4.26501i	−0.835714	−	0.167159i
$652$	−2.37361	−	1.10683i	−0.0929578	−	0.0433469i
$653$	−1.03997	−	11.8869i	−0.0406971	−	0.465170i	−0.989012	−	0.147838i	$-0.952769\pi$
$653$	−1.03997	−	11.8869i	−0.0406971	−	0.465170i	0.948314	−	0.317332i	$-0.102787\pi$
$654$	0.119608	−	5.22642i	0.00467703	−	0.204369i
$655$	−0.0693192	−	10.9235i	−0.00270852	−	0.426815i
$656$	−2.59913	+	1.50061i	−0.101479	+	0.0585890i
$657$	−0.651043	+	0.844725i	−0.0253996	+	0.0329559i
$658$	−16.2198	−	60.5331i	−0.632314	−	2.35983i
$659$	17.0150	−	14.2773i	0.662811	−	0.556165i	−0.248117	−	0.968730i	$-0.579812\pi$
$659$	17.0150	−	14.2773i	0.662811	−	0.556165i	0.910928	+	0.412565i	$0.135367\pi$
$660$	−0.861676	+	3.01546i	−0.0335407	+	0.117377i
$661$	−7.45553	+	42.2824i	−0.289986	+	1.64460i	0.396923	+	0.917852i	$0.370078\pi$
$661$	−7.45553	+	42.2824i	−0.289986	+	1.64460i	−0.686909	+	0.726743i	$0.741033\pi$
$662$	−1.67976	−	2.39894i	−0.0652857	−	0.0932376i
$663$	1.02813	−	9.29628i	0.0399291	−	0.361038i
$664$	19.2908	+	22.9899i	0.748629	+	0.892181i
$665$	−9.36113	−	13.1901i	−0.363009	−	0.511491i
$666$	−21.0350	+	22.8578i	−0.815090	+	0.885721i
$667$	0.377358	−	1.40832i	0.0146114	−	0.0545304i
$668$	−1.36497	−	2.92718i	−0.0528122	−	0.113256i
$669$	19.7193	−	32.4186i	0.762393	−	1.25337i
$670$	−48.2397	−	17.2119i	−1.86366	−	0.664955i
$671$	1.38915	+	3.81665i	0.0536274	+	0.147340i
$672$	−9.73718	−	4.81474i	−0.375620	−	0.185733i
$673$	35.1820	+	24.6347i	1.35617	+	0.949599i	0.999884	+	0.0152212i	$0.00484525\pi$
$673$	35.1820	+	24.6347i	1.35617	+	0.949599i	0.356284	+	0.934378i	$0.384044\pi$
$674$	25.0834			0.966176
$675$	−12.2796	+	22.8957i	−0.472640	+	0.881255i
$676$	−0.340452			−0.0130943
$677$	22.0638	+	15.4492i	0.847979	+	0.593761i	0.914756	−	0.404007i	$-0.132383\pi$
$677$	22.0638	+	15.4492i	0.847979	+	0.593761i	−0.0667769	+	0.997768i	$0.521272\pi$
$678$	−0.129345	−	2.00615i	−0.00496748	−	0.0770458i
$679$	−10.6093	−	29.1489i	−0.407149	−	1.11863i
$680$	7.89817	+	2.81807i	0.302881	+	0.108068i
$681$	−4.11821	−	7.52549i	−0.157810	−	0.288377i
$682$	−5.76078	−	12.3540i	−0.220592	−	0.473060i
$683$	−4.90923	+	18.3215i	−0.187846	+	0.701053i	0.806157	+	0.591702i	$0.201544\pi$
$683$	−4.90923	+	18.3215i	−0.187846	+	0.701053i	−0.994003	+	0.109351i	$0.965123\pi$
$684$	0.924849	−	0.478946i	0.0353625	−	0.0183130i
$685$	2.35493	+	3.31818i	0.0899774	+	0.126781i
$686$	−42.6101	−	50.7807i	−1.62686	−	1.93882i
$687$	1.72845	−	0.758341i	0.0659445	−	0.0289325i
$688$	0.509820	+	0.728099i	0.0194367	+	0.0277585i
$689$	2.63302	−	14.9326i	0.100310	−	0.568887i
$690$	6.03440	+	6.23734i	0.229726	+	0.237451i
$691$	17.4026	−	14.6025i	0.662025	−	0.555505i	−0.248668	−	0.968589i	$-0.579993\pi$
$691$	17.4026	−	14.6025i	0.662025	−	0.555505i	0.910693	+	0.413084i	$0.135548\pi$
$692$	0.242055	+	0.903362i	0.00920155	+	0.0343407i
$693$	34.1152	+	37.3897i	1.29593	+	1.42032i
$694$	−4.06379	+	2.34623i	−0.154259	+	0.0890616i
$695$	0.0409551	+	6.45379i	0.00155351	+	0.244806i
$696$	−3.90164	+	2.13511i	−0.147891	+	0.0809311i
$697$	0.0842119	+	0.962547i	0.00318975	+	0.0364591i
$698$	16.8472	+	7.85598i	0.637676	+	0.297353i
$699$	30.3390	−	34.5207i	1.14752	−	1.30569i
$700$	5.54236	−	0.555856i	0.209482	−	0.0210094i
$701$		−	28.7752i		−	1.08682i	−0.839466	−	0.543412i	$-0.817132\pi$
$701$		−	28.7752i		−	1.08682i	0.839466	−	0.543412i	$-0.182868\pi$
$702$	−28.9782	+	5.66797i	−1.09371	+	0.213924i
$703$	7.35929	−	7.35929i	0.277561	−	0.277561i
$704$	4.17981	+	23.7049i	0.157533	+	0.893412i
$705$	26.1910	−	21.2489i	0.986410	−	0.800279i
$706$	25.4704	−	9.27048i	0.958592	−	0.348899i
$707$	29.3639	−	2.56901i	1.10434	−	0.0966175i
$708$	−0.704104	−	2.89076i	−0.0264618	−	0.108641i
$709$	−0.183502	+	0.504167i	−0.00689155	+	0.0189344i	−0.943091	−	0.332536i	$-0.892096\pi$
$709$	−0.183502	+	0.504167i	−0.00689155	+	0.0189344i	0.936199	+	0.351470i	$0.114318\pi$
$710$	4.01236	+	42.7362i	0.150581	+	1.60386i
$711$	6.43464	−	28.7351i	0.241318	−	1.07765i
$712$	−10.6997	+	2.86697i	−0.400988	+	0.107444i
$713$	−3.89433	−	0.340710i	−0.145844	−	0.0127597i
$714$	−13.8103	+	11.0598i	−0.516837	+	0.413902i
$715$	−16.9312	+	24.5098i	−0.633191	+	0.916615i
$716$	−1.47655	−	0.260356i	−0.0551814	−	0.00972997i
$717$	−1.54073	+	2.09660i	−0.0575394	+	0.0782989i
$718$	−1.37315	+	15.6951i	−0.0512453	+	0.585737i
$719$	2.44660	−	4.23763i	0.0912427	−	0.158037i	−0.816792	−	0.576933i	$-0.804249\pi$
$719$	2.44660	−	4.23763i	0.0912427	−	0.158037i	0.908034	+	0.418896i	$0.137583\pi$
$720$	1.16550	−	29.5535i	0.0434357	−	1.10139i
$721$	−18.1492	−	31.4353i	−0.675911	−	1.17071i
$722$	22.6702	−	10.5713i	0.843697	−	0.393422i
$723$	−3.94394	−	4.12869i	−0.146677	−	0.153548i
$724$	1.14789	−	1.36800i	0.0426608	−	0.0508412i
$725$	2.37616	−	4.23898i	0.0882485	−	0.157432i
$726$	−0.641079	+	3.20508i	−0.0237927	+	0.118952i
$727$	−2.82025	+	4.02773i	−0.104597	+	0.149380i	−0.868038	−	0.496497i	$-0.834619\pi$
$727$	−2.82025	+	4.02773i	−0.104597	+	0.149380i	0.763441	+	0.645877i	$0.223508\pi$
$728$	−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
$732$	0.257660	+	0.386505i	0.00952339	+	0.0142857i
$733$	−6.00742	+	12.8830i	−0.221889	+	0.475843i	−0.985466	−	0.169874i	$-0.945664\pi$
$733$	−6.00742	+	12.8830i	−0.221889	+	0.475843i	0.763576	+	0.645717i	$0.223442\pi$
$734$	4.07991	+	3.42345i	0.150592	+	0.126362i
$735$	27.4719	−	56.4571i	1.01331	−	2.08245i
$736$	−1.83501	−	0.667889i	−0.0676394	−	0.0246187i
$737$	−51.8700	−	13.8985i	−1.91066	−	0.511959i
$738$	2.82065	−	1.16132i	0.103830	−	0.0427488i
$739$	28.3320	+	16.3575i	1.04221	+	0.601721i	0.920459	−	0.390840i	$-0.127815\pi$
$739$	28.3320	+	16.3575i	1.04221	+	0.601721i	0.121752	+	0.992561i	$0.461149\pi$
$740$	0.949609	+	3.45611i	0.0349083	+	0.127049i
$741$	9.77933	−	1.49453i	0.359253	−	0.0549028i
$742$	−23.4964	+	16.4524i	−0.862581	+	0.603986i
$743$	0.889212	−	0.622633i	0.0326220	−	0.0228422i	−0.557152	−	0.830411i	$-0.688106\pi$
$743$	0.889212	−	0.622633i	0.0326220	−	0.0228422i	0.589774	+	0.807569i	$0.299217\pi$
$744$	7.45425	+	9.30809i	0.273286	+	0.341251i
$745$	18.2122	−	32.0119i	0.667244	−	1.17283i
$746$	32.6505	+	18.8508i	1.19542	+	0.690177i
$747$	−18.2483	−	28.7792i	−0.667671	−	1.05297i
$748$	−1.11024	−	0.297487i	−0.0405943	−	0.0108772i
$749$	−63.1577	−	22.9875i	−2.30773	−	0.839946i
$750$	14.3666	+	25.1060i	0.524594	+	0.916743i
$751$	−9.61953	−	8.07175i	−0.351022	−	0.294542i	0.450178	−	0.892939i	$-0.351360\pi$
$751$	−9.61953	−	8.07175i	−0.351022	−	0.294542i	−0.801200	+	0.598396i	$0.795805\pi$
$752$	−16.2261	+	34.7970i	−0.591706	+	1.26892i
$753$	−14.3933	+	29.1085i	−0.524520	+	1.06077i
$754$	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	$0.774925\pi$
$758$	23.8780	−	34.1013i	0.867288	−	1.23862i
$759$	6.83466	+	6.00672i	0.248083	+	0.218030i
$760$	−0.716978	+	8.84091i	−0.0260075	+	0.320694i
$761$	−11.3467	+	13.5225i	−0.411319	+	0.490191i	−0.931437	−	0.363904i	$-0.881444\pi$
$761$	−11.3467	+	13.5225i	−0.411319	+	0.490191i	0.520117	+	0.854095i	$0.325888\pi$
$762$	−14.2739	+	48.7783i	−0.517090	+	1.76705i
$763$	−8.82288	+	4.11418i	−0.319410	+	0.148943i
$764$	1.07282	+	1.85819i	0.0388134	+	0.0672268i
$765$	−8.46453	−	4.36109i	−0.306036	−	0.157676i
$766$	−28.2771	+	48.9773i	−1.02169	+	1.76962i
$767$	2.46311	−	28.1535i	0.0889377	−	1.01656i
$768$	3.81226	+	8.68909i	0.137563	+	0.313541i
$769$	29.6816	+	5.23367i	1.07035	+	0.188731i	0.680943	−	0.732336i	$-0.261570\pi$
$769$	29.6816	+	5.23367i	1.07035	+	0.188731i	0.389404	+	0.921067i	$0.372681\pi$
$770$	55.4330	−	10.1375i	1.99767	−	0.365328i
$771$	−33.1993	−	12.9512i	−1.19564	−	0.466427i
$772$	5.87749	+	0.514213i	0.211535	+	0.0185069i
$773$	43.5713	−	11.6749i	1.56715	−	0.419917i	0.632232	−	0.774779i	$-0.282139\pi$
$773$	43.5713	−	11.6749i	1.56715	−	0.419917i	0.934919	+	0.354862i	$0.115472\pi$
$774$	−0.415436	−	0.802212i	−0.0149326	−	0.0288349i
$775$	−12.2992	−	4.30058i	−0.441802	−	0.154482i
$776$	−5.81811	+	15.9851i	−0.208858	+	0.573832i
$777$	55.5172	+	16.2459i	1.99167	+	0.582820i
$778$	−5.70705	+	0.499302i	−0.204608	+	0.0179008i
$779$	−0.960366	+	0.349545i	−0.0344087	+	0.0125237i
$780$	−1.21801	+	3.18176i	−0.0436119	+	0.113925i
$781$	7.81482	+	44.3200i	0.279636	+	1.58590i
$782$	−2.24910	+	2.24910i	−0.0804277	+	0.0804277i
$783$	4.71263	−	1.81534i	0.168416	−	0.0648748i
$784$			71.4757i			2.55270i
$785$	8.08211	−	30.9471i	0.288463	−	1.10455i
$786$	−4.04997	−	11.9727i	−0.144458	−	0.427052i
$787$	31.9138	+	14.8817i	1.13761	+	0.530474i	0.897825	−	0.440353i	$-0.145147\pi$
$787$	31.9138	+	14.8817i	1.13761	+	0.530474i	0.239780	+	0.970827i	$0.422925\pi$
$788$	−0.252670	−	2.88803i	−0.00900100	−	0.102882i
$789$	−25.3639	−	15.4281i	−0.902978	−	0.549256i
$790$	−23.3290	−	23.0348i	−0.830010	−	0.819542i
$791$	−3.24199	+	1.87177i	−0.115272	+	0.0665523i
$792$	−1.15169	−	27.7329i	−0.0409234	−	0.985445i
$793$	1.14198	+	4.26192i	0.0405528	+	0.151345i
$794$	−5.14028	+	4.31321i	−0.182422	+	0.153070i
$795$	−13.2393	−	7.93845i	−0.469550	−	0.281548i
$796$	−0.558987	+	3.17017i	−0.0198128	+	0.112364i
$797$	19.7333	+	28.1820i	0.698989	+	0.998259i	0.999017	+	0.0443290i	$0.0141150\pi$
$797$	19.7333	+	28.1820i	0.698989	+	0.998259i	−0.300028	+	0.953930i	$0.596996\pi$
$798$	−15.0803	−	11.0821i	−0.533837	−	0.392300i
$799$	7.94536	+	9.46891i	0.281087	+	0.334986i
$800$	−5.37851	−	3.66524i	−0.190159	−	0.129586i
$801$	12.4737	−	1.61518i	0.440736	−	0.0570696i
$802$	−3.94062	+	14.7066i	−0.139148	+	0.519308i
$803$	0.526128	+	1.12829i	0.0185667	+	0.0398163i
$804$	−6.13993	−	0.140514i	−0.216539	−	0.00495553i
$805$	5.43090	−	15.2211i	0.191414	−	0.536474i
$806$	−5.06465	−	13.9150i	−0.178395	−	0.490135i
$807$	8.08901	−	5.39245i	0.284746	−	0.189823i
$808$	−13.2412	−	9.27159i	−0.465824	−	0.326173i
$809$	−54.0630			−1.90075			−0.950377	−	0.311100i	$-0.899302\pi$
$809$	−54.0630			−1.90075			−0.950377	+	0.311100i	$0.899302\pi$
$810$	−5.15819	+	29.6149i	−0.181240	+	1.04056i
$811$	24.1241			0.847112			0.423556	−	0.905870i	$-0.360782\pi$
$811$	24.1241			0.847112			0.423556	+	0.905870i	$0.360782\pi$
$812$	−0.886927	−	0.621033i	−0.0311250	−	0.0217940i
$813$	−22.6014	+	15.0670i	−0.792667	+	0.528424i
$814$	12.4019	+	34.0739i	0.434685	+	1.19429i
$815$	−22.8850	+	10.8488i	−0.801626	+	0.380016i
$816$	10.8369	+	0.248005i	0.379368	+	0.00868192i
$817$	0.127917	+	0.274318i	0.00447523	+	0.00959717i
$818$	9.04564	−	33.7588i	0.316273	−	1.18035i
$819$	33.3795	+	43.6933i	1.16637	+	1.52677i
$820$	0.0589162	−	0.346993i	0.00205744	−	0.0121175i
$821$	−5.28957	−	6.30386i	−0.184607	−	0.220006i	0.665802	−	0.746129i	$-0.268090\pi$
$821$	−5.28957	−	6.30386i	−0.184607	−	0.220006i	−0.850409	+	0.526123i	$0.823645\pi$
$822$	3.79368	+	2.78786i	0.132320	+	0.0972377i
$823$	−1.52906	−	2.18373i	−0.0532998	−	0.0761200i	0.791617	−	0.611017i	$-0.209239\pi$
$823$	−1.52906	−	2.18373i	−0.0532998	−	0.0761200i	−0.844917	+	0.534897i	$0.820350\pi$
$824$	−3.45661	+	19.6034i	−0.120417	+	0.682917i
$825$	17.1410	+	25.0187i	0.596775	+	0.871040i
$826$	−40.9538	+	34.3643i	−1.42497	+	1.19569i
$827$	2.00765	+	7.49264i	0.0698128	+	0.260545i	0.992007	−	0.126182i	$-0.0402723\pi$
$827$	2.00765	+	7.49264i	0.0698128	+	0.260545i	−0.922194	+	0.386727i	$0.873606\pi$
$828$	0.922037	+	0.482480i	0.0320430	+	0.0167673i
$829$	36.4123	−	21.0226i	1.26465	−	0.730147i	0.290680	−	0.956820i	$-0.406118\pi$
$829$	36.4123	−	21.0226i	1.26465	−	0.730147i	0.973971	+	0.226674i	$0.0727851\pi$
$830$	−37.9392	+	0.240758i	−1.31689	+	0.00835684i
$831$	36.3480	+	22.1095i	1.26090	+	0.766971i
$832$	2.27902	+	26.0493i	0.0790106	+	0.903096i
$833$	20.8552	+	9.72492i	0.722588	+	0.336948i
$834$	2.39280	+	7.07369i	0.0828559	+	0.244942i
$835$	−30.2192	−	7.89203i	−1.04578	−	0.273115i
$836$		−	1.21575i		−	0.0420477i
$837$	−6.98749	−	11.5984i	−0.241523	−	0.400899i
$838$	−1.57481	+	1.57481i	−0.0544008	+	0.0544008i
$839$	−7.44120	−	42.2011i	−0.256899	−	1.45694i	−0.791152	−	0.611620i	$-0.790518\pi$
$839$	−7.44120	−	42.2011i	−0.256899	−	1.45694i	0.534253	−	0.845325i	$-0.320593\pi$
$840$	−45.0185	+	20.0931i	−1.55329	+	0.693277i
$841$	26.3634	−	9.59551i	0.909084	−	0.330880i
$842$	27.5332	−	2.40885i	0.948858	−	0.0830143i
$843$	−1.20955	−	0.353949i	−0.0416591	−	0.0121907i
$844$	−1.59083	+	4.37077i	−0.0547587	+	0.150448i
$845$	−2.10017	+	2.53539i	−0.0722480	+	0.0872199i
$846$	21.0371	−	32.8669i	0.723269	−	1.12999i
$847$	5.87920	−	1.57533i	0.202012	−	0.0541289i
$848$	17.5065	+	1.53162i	0.601175	+	0.0525960i
$849$	−34.8538	−	13.5966i	−1.19618	−	0.466635i
$850$	−9.11303	+	5.41677i	−0.312574	+	0.185794i
$851$	10.2410	+	1.80577i	0.351057	+	0.0619008i
$852$	2.06791	+	4.71330i	0.0708456	+	0.161475i
$853$	1.49745	−	17.1159i	0.0512717	−	0.586038i	−0.926490	−	0.376319i	$-0.877190\pi$
$853$	1.49745	−	17.1159i	0.0512717	−	0.586038i	0.977762	−	0.209719i	$-0.0672549\pi$
$854$	4.17334	−	7.22844i	0.142809	−	0.247352i
$855$	2.13841	−	9.84197i	0.0731322	−	0.336588i
$856$	18.4291	+	31.9201i	0.629893	+	1.09101i
$857$	19.2921	−	8.99607i	0.659007	−	0.307300i	−0.0641943	−	0.997937i	$-0.520448\pi$
$857$	19.2921	−	8.99607i	0.659007	−	0.307300i	0.723201	+	0.690637i	$0.242670\pi$
$858$	−9.68017	+	33.0800i	−0.330475	+	1.12933i
$859$	−5.67148	+	6.75901i	−0.193509	+	0.230615i	−0.854071	−	0.520157i	$-0.825874\pi$
$859$	−5.67148	+	6.75901i	−0.193509	+	0.230615i	0.660562	+	0.750771i	$0.270318\pi$
$860$	−0.103895	−	0.00842568i	−0.00354280	−	0.000287313i
$861$	−4.26666	−	3.74981i	−0.145408	−	0.127793i
$862$	−16.5337	+	23.6126i	−0.563141	+	0.804249i
$863$	31.7542	+	31.7542i	1.08093	+	1.08093i	0.996423	+	0.0845039i	$0.0269306\pi$
$863$	31.7542	+	31.7542i	1.08093	+	1.08093i	0.0845039	+	0.996423i	$0.473069\pi$
$864$	−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
$867$	−11.5044	+	23.2662i	−0.390710	+	0.790160i
$868$	−1.22688	+	2.63105i	−0.0416430	+	0.0893038i
$869$	−26.3314	−	22.0947i	−0.893233	−	0.749511i
$870$	1.06779	−	5.52036i	0.0362015	−	0.187158i
$871$	−54.8180	−	19.9521i	−1.85744	−	0.676052i
$872$	5.15670	+	1.38173i	0.174628	+	0.0467914i
$873$	8.95541	−	17.1141i	0.303095	−	0.579225i
$874$	−2.91359	−	1.68216i	−0.0985535	−	0.0568999i
$875$	30.0500	−	44.7036i	1.01588	−	1.51126i
$876$	0.0890004	+	0.111134i	0.00300705	+	0.00375488i
$877$	−15.8993	+	11.1328i	−0.536880	+	0.375928i	−0.810344	−	0.585955i	$-0.800720\pi$
$877$	−15.8993	+	11.1328i	−0.536880	+	0.375928i	0.273464	+	0.961882i	$0.411831\pi$
$878$	−12.2311	+	8.56430i	−0.412779	+	0.289031i
$879$	−15.6969	+	2.39888i	−0.529444	+	0.0809123i
$880$	−30.0082	−	17.0722i	−1.01158	−	0.575505i
$881$	−11.7101	−	6.76081i	−0.394522	−	0.227778i	0.289595	−	0.957149i	$-0.406479\pi$
$881$	−11.7101	−	6.76081i	−0.394522	−	0.227778i	−0.684118	+	0.729372i	$0.739813\pi$
$882$	9.63555	−	72.0042i	0.324446	−	2.42451i
$883$	−30.0253	−	8.04527i	−1.01043	−	0.270745i	−0.284623	−	0.958640i	$-0.591868\pi$
$883$	−30.0253	−	8.04527i	−1.01043	−	0.270745i	−0.725810	+	0.687895i	$0.758535\pi$
$884$	−1.17334	−	0.427060i	−0.0394636	−	0.0143636i
$885$	−25.8713	−	12.5889i	−0.869654	−	0.423171i
$886$	35.3409	+	29.6546i	1.18730	+	0.996264i
$887$	10.0974	−	21.6538i	0.339036	−	0.727065i	−0.660686	−	0.750663i	$-0.729734\pi$
$887$	10.0974	−	21.6538i	0.339036	−	0.727065i	0.999722	+	0.0235979i	$0.00751215\pi$
$888$	−17.5958	−	26.3947i	−0.590476	−	0.885749i
$889$	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
$893$	−7.49912	+	10.7099i	−0.250949	+	0.358392i
$894$	8.35801	−	41.7860i	0.279534	−	1.39753i
$895$	−11.0474	+	9.39000i	−0.369275	+	0.313873i
$896$	39.8584	−	47.5014i	1.33158	−	1.58691i
$897$	6.82778	+	7.14761i	0.227973	+	0.238652i
$898$	2.31483	−	1.07942i	0.0772467	−	0.0360207i
$899$	1.26634	+	2.19337i	0.0422349	+	0.0731529i
$900$	2.58184	+	2.31613i	0.0860614	+	0.0772044i
$901$	2.82881	−	4.89965i	0.0942414	−	0.163231i
$902$	0.310336	−	3.54715i	0.0103330	−	0.118107i
$903$	−0.996189	+	1.35560i	−0.0331511	+	0.0451116i
$904$	2.02174	+	0.356488i	0.0672422	+	0.0118566i
$905$	−3.10659	−	16.9873i	−0.103267	−	0.564677i
$906$	5.24557	−	4.20084i	0.174272	−	0.139563i
$907$	−20.9061	−	1.82905i	−0.694175	−	0.0607325i	−0.265393	−	0.964140i	$-0.585502\pi$
$907$	−20.9061	−	1.82905i	−0.694175	−	0.0607325i	−0.428782	+	0.903408i	$0.641057\pi$
$908$	−1.10624	+	0.296416i	−0.0367118	+	0.00983690i
$909$	13.5059	+	12.4289i	0.447961	+	0.412239i
$910$	60.9496	−	5.72236i	2.02046	−	0.189694i
$911$	−9.46462	+	26.0038i	−0.313577	+	0.861545i	0.678351	+	0.734738i	$0.262695\pi$
$911$	−9.46462	+	26.0038i	−0.313577	+	0.861545i	−0.991927	+	0.126807i	$0.959527\pi$
$912$	2.71333	+	11.1398i	0.0898472	+	0.368876i
$913$	−39.6268	+	3.46689i	−1.31145	+	0.114737i
$914$	−51.1285	+	18.6093i	−1.69118	+	0.615539i
$915$	4.46780	+	0.465439i	0.147701	+	0.0153869i
$916$	−0.0437565	−	0.248156i	−0.00144576	−	0.00819929i
$917$	−16.6425	+	16.6425i	−0.549585	+	0.549585i
$918$	−10.8836	−	1.71075i	−0.359213	−	0.0564632i
$919$			21.5936i			0.712307i	0.934427	+	0.356154i	$0.115912\pi$
$919$			21.5936i			0.712307i	−0.934427	+	0.356154i	$0.884088\pi$
$920$	−7.64695	+	4.47991i	−0.252113	+	0.147698i
$921$	8.29969	−	9.44368i	0.273484	−	0.311180i
$922$	23.3976	+	10.9105i	0.770559	+	0.359318i
$923$	4.26098	+	48.7032i	0.140252	+	1.60309i
$924$	5.92763	−	3.24380i	0.195005	−	0.106713i
$925$	31.5960	+	14.2481i	1.03887	+	0.468475i
$926$	37.1159	−	21.4289i	1.21970	−	0.704197i
$927$	6.84261	−	21.5419i	0.224741	−	0.707530i
$928$	0.327447	+	1.22205i	0.0107490	+	0.0401158i
$929$	−12.2976	+	10.3189i	−0.403472	+	0.338553i	−0.821834	−	0.569727i	$-0.807049\pi$
$929$	−12.2976	+	10.3189i	−0.403472	+	0.338553i	0.418362	+	0.908280i	$0.362604\pi$
$930$	−15.0735	−	0.249269i	−0.494280	−	0.00817387i
$931$	−4.22650	+	23.9697i	−0.138518	+	0.785575i
$932$	−3.51917	−	5.02589i	−0.115274	−	0.164628i
$933$	−35.9022	+	15.7517i	−1.17538	+	0.515688i
$934$	−22.8691	−	27.2543i	−0.748299	−	0.891788i
$935$	−9.06422	+	6.43294i	−0.296432	+	0.210380i
$936$	1.37940	−	30.1217i	0.0450872	−	0.984557i
$937$	−5.65242	+	21.0951i	−0.184657	+	0.689148i	0.810047	+	0.586365i	$0.199441\pi$
$937$	−5.65242	+	21.0951i	−0.184657	+	0.689148i	−0.994704	+	0.102783i	$0.967225\pi$
$938$	46.6379	+	100.015i	1.52278	+	3.26561i
$939$	−3.43782	−	6.28217i	−0.112189	−	0.205011i
$940$	−1.92872	−	4.06855i	−0.0629080	−	0.132702i
$941$	−4.53610	−	12.4628i	−0.147872	−	0.406276i	0.843537	−	0.537071i	$-0.180469\pi$
$941$	−4.53610	−	12.4628i	−0.147872	−	0.406276i	−0.991409	+	0.130795i	$0.958247\pi$
$942$	−2.38112	−	36.9312i	−0.0775810	−	1.20328i
$943$	−0.836480	−	0.585710i	−0.0272395	−	0.0190733i
$944$	32.7535			1.06604
$945$	53.6920	−	15.8336i	1.74660	−	0.515066i
$946$	−1.05454			−0.0342861
$947$	−13.5354	−	9.47761i	−0.439843	−	0.307981i	0.332597	−	0.943069i	$-0.392075\pi$
$947$	−13.5354	−	9.47761i	−0.439843	−	0.307981i	−0.772440	+	0.635088i	$0.780964\pi$
$948$	−3.52393	−	1.74248i	−0.114452	−	0.0565930i
$949$	0.462551	+	1.27085i	0.0150150	+	0.0412535i
$950$	−8.02901	−	7.82776i	−0.260496	−	0.253966i
$951$	−28.9747	+	47.6344i	−0.939570	+	1.54465i
$952$	−7.63591	−	16.3753i	−0.247481	−	0.530725i
$953$	1.40298	−	5.23599i	0.0454469	−	0.169610i	−0.939472	−	0.342625i	$-0.888684\pi$
$953$	1.40298	−	5.23599i	0.0454469	−	0.169610i	0.984919	+	0.173014i	$0.0553507\pi$
$954$	−17.4295	−	3.90297i	−0.564300	−	0.126363i
$955$	20.4561	+	3.47327i	0.661945	+	0.112392i
$956$	0.223273	+	0.266086i	0.00722115	+	0.00860583i
$957$	0.648018	−	5.85937i	0.0209475	−	0.189406i
$958$	3.48059	+	4.97080i	0.112453	+	0.160599i
$959$	1.52234	−	8.63365i	0.0491591	−	0.278795i
$960$	25.5967	+	7.31430i	0.826128	+	0.236068i
$961$	−18.5454	+	15.5615i	−0.598240	+	0.501983i
$962$	10.1952	+	38.0491i	0.328707	+	1.22675i
$963$	−15.9335	−	38.6998i	−0.513451	−	1.24708i
$964$	−0.660134	+	0.381128i	−0.0212615	+	0.0122753i
$965$	40.0863	−	40.5983i	1.29042	−	1.30691i
$966$	0.427816	−	18.6940i	0.0137647	−	0.601469i
$967$	−5.15797	−	58.9559i	−0.165869	−	1.89589i	−0.389204	−	0.921152i	$-0.627250\pi$
$967$	−5.15797	−	58.9559i	−0.165869	−	1.89589i	0.223335	−	0.974742i	$-0.428306\pi$
$968$	−3.02513	−	1.41064i	−0.0972312	−	0.0453397i
$969$	3.61954	+	0.723979i	0.116276	+	0.0232575i
$970$	−10.8706	−	18.5555i	−0.349033	−	0.595780i
$971$			27.0614i			0.868442i	0.900806	+	0.434221i	$0.142976\pi$
$971$			27.0614i			0.868442i	−0.900806	+	0.434221i	$0.857024\pi$
$972$	0.529365	+	3.56547i	0.0169794	+	0.114362i
$973$	9.83272	−	9.83272i	0.315222	−	0.315222i
$974$	6.77297	+	38.4114i	0.217020	+	1.23078i
$975$	16.1813	+	28.6983i	0.518217	+	0.919080i
$976$	−4.80526	+	1.74897i	−0.153813	+	0.0559833i
$977$	−16.0579	+	1.40489i	−0.513738	+	0.0449463i	−0.341078	−	0.940035i	$-0.610792\pi$
$977$	−16.0579	+	1.40489i	−0.513738	+	0.0449463i	−0.172661	+	0.984981i	$0.555236\pi$
$978$	−21.1893	+	20.2412i	−0.677559	+	0.647241i
$979$	5.02158	−	13.7967i	0.160490	−	0.440944i
$980$	−6.45511	−	5.34704i	−0.206201	−	0.170805i
$981$	−5.59548	−	2.33169i	−0.178650	−	0.0744452i
$982$	36.9250	−	9.89401i	1.17832	−	0.315731i
$983$	−43.1392	−	3.77419i	−1.37593	−	0.120378i	−0.624929	−	0.780682i	$-0.714872\pi$
$983$	−43.1392	−	3.77419i	−1.37593	−	0.120378i	−0.750999	+	0.660304i	$0.770427\pi$
$984$	0.470591	+	3.07928i	0.0150019	+	0.0981638i
$985$	−23.0662	−	15.9339i	−0.734950	−	0.507697i
$986$	2.02940	+	0.357838i	0.0646293	+	0.0113959i
$987$	−72.2267	−	7.98793i	−2.29900	−	0.254259i
$988$	0.115108	−	1.31569i	0.00366208	−	0.0418577i
$989$	−0.151213	+	0.261908i	−0.00480829	+	0.00832820i
$990$	27.9286	+	21.2439i	0.887629	+	0.675174i
$991$	−23.2675	−	40.3005i	−0.739117	−	1.28019i	−0.952893	−	0.303306i	$-0.901910\pi$
$991$	−23.2675	−	40.3005i	−0.739117	−	1.28019i	0.213776	−	0.976883i	$-0.431424\pi$
$992$	3.07434	−	1.43359i	0.0976103	−	0.0455164i
$993$	−3.29935	+	0.803625i	−0.104702	+	0.0255023i
$994$	59.4476	−	70.8468i	1.88556	−	2.24713i
$995$	20.1604	+	23.7189i	0.639127	+	0.751939i
$996$	−4.30947	+	1.45775i	−0.136551	+	0.0461906i
$997$	−5.81058	+	8.29837i	−0.184023	+	0.262812i	−0.900555	−	0.434742i	$-0.856839\pi$
$997$	−5.81058	+	8.29837i	−0.184023	+	0.262812i	0.716532	+	0.697554i	$0.245728\pi$
$998$	−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.122.5	yes	192
3.2	odd	2		405.2.r.a.152.12		192
5.2	odd	4		675.2.ba.b.68.12		192
5.3	odd	4	inner	135.2.q.a.68.5	yes	192
5.4	even	2		675.2.ba.b.257.12		192
15.8	even	4		405.2.r.a.233.12		192
27.2	odd	18	inner	135.2.q.a.2.5	✓	192
27.25	even	9		405.2.r.a.332.12		192
135.2	even	36		675.2.ba.b.218.12		192
135.29	odd	18		675.2.ba.b.407.12		192
135.83	even	36	inner	135.2.q.a.83.5	yes	192
135.133	odd	36		405.2.r.a.8.12		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.5	✓	192	27.2	odd	18	inner
135.2.q.a.68.5	yes	192	5.3	odd	4	inner
135.2.q.a.83.5	yes	192	135.83	even	36	inner
135.2.q.a.122.5	yes	192	1.1	even	1	trivial
405.2.r.a.8.12		192	135.133	odd	36
405.2.r.a.152.12		192	3.2	odd	2
405.2.r.a.233.12		192	15.8	even	4
405.2.r.a.332.12		192	27.25	even	9
675.2.ba.b.68.12		192	5.2	odd	4
675.2.ba.b.218.12		192	135.2	even	36
675.2.ba.b.257.12		192	5.4	even	2
675.2.ba.b.407.12		192	135.29	odd	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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22359 - 0.856769i) q^{2} +(-1.44117 + 0.960742i) q^{3} +(0.0790861 + 0.217287i) q^{4} +(2.10603 + 0.751431i) q^{5} +(2.58654 + 0.0591935i) q^{6} +(-2.03610 - 4.36642i) q^{7} +(-0.683816 + 2.55204i) q^{8} +(1.15395 - 2.76919i) q^{9} +O(q^{10})\)	\(q+(-1.22359 - 0.856769i) q^{2} +(-1.44117 + 0.960742i) q^{3} +(0.0790861 + 0.217287i) q^{4} +(2.10603 + 0.751431i) q^{5} +(2.58654 + 0.0591935i) q^{6} +(-2.03610 - 4.36642i) q^{7} +(-0.683816 + 2.55204i) q^{8} +(1.15395 - 2.76919i) q^{9} +(-1.93312 - 2.72382i) q^{10} +(-2.25098 - 2.68262i) q^{11} +(-0.322733 - 0.237167i) q^{12} +(-2.18203 - 3.11626i) q^{13} +(-1.24966 + 7.08719i) q^{14} +(-3.75708 + 0.940408i) q^{15} +(3.37749 - 2.83405i) q^{16} +(-0.367380 - 1.37108i) q^{17} +(-3.78452 + 2.39969i) q^{18} +(1.30024 - 0.750693i) q^{19} +(0.00328108 + 0.517040i) q^{20} +(7.12937 + 4.33660i) q^{21} +(0.455904 + 5.21100i) q^{22} +(1.35959 + 0.633988i) q^{23} +(-1.46635 - 4.33489i) q^{24} +(3.87070 + 3.16507i) q^{25} +5.68253i q^{26} +(0.997437 + 5.09952i) q^{27} +(0.787741 - 0.787741i) q^{28} +(-0.168770 - 0.957143i) q^{29} +(5.40285 + 2.06827i) q^{30} +(-2.44873 + 0.891266i) q^{31} +(-1.29677 + 0.113453i) q^{32} +(5.82135 + 1.70350i) q^{33} +(-0.725176 + 1.99240i) q^{34} +(-1.00701 - 10.7258i) q^{35} +(0.692970 + 0.0317342i) q^{36} +(6.69580 - 1.79413i) q^{37} +(-2.23413 - 0.195461i) q^{38} +(6.13860 + 2.39470i) q^{39} +(-3.35782 + 4.86082i) q^{40} +(-0.670363 - 0.118203i) q^{41} +(-5.00798 - 11.4145i) q^{42} +(-0.0175704 + 0.200831i) q^{43} +(0.404877 - 0.701267i) q^{44} +(4.51110 - 4.96487i) q^{45} +(-1.12040 - 1.94060i) q^{46} +(-7.89228 + 3.68023i) q^{47} +(-2.14475 + 7.32924i) q^{48} +(-10.4204 + 12.4186i) q^{49} +(-2.02443 - 7.18905i) q^{50} +(1.84671 + 1.62300i) q^{51} +(0.504555 - 0.720580i) 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} +(-1.15264 + 2.33107i) q^{57} +(-0.613544 + 1.31575i) q^{58} +(5.69079 + 4.77514i) q^{59} +(-0.501471 - 0.741992i) q^{60} +(-1.08988 - 0.396683i) q^{61} +(3.75986 + 1.00745i) q^{62} +(-14.4410 + 0.599704i) q^{63} +(-5.95268 - 3.43678i) q^{64} +(-2.25376 - 8.20258i) q^{65} +(-5.66346 - 7.07194i) q^{66} +(12.5612 - 8.79548i) q^{67} +(0.268864 - 0.188260i) q^{68} +(-2.56850 + 0.392531i) q^{69} +(-7.95735 + 13.9868i) q^{70} +(-11.1295 - 6.42561i) q^{71} +(6.27798 + 4.83854i) q^{72} +(-0.343386 - 0.0920100i) q^{73} +(-9.73009 - 3.54146i) q^{74} +(-8.61916 - 0.842659i) q^{75} +(0.265947 + 0.223156i) q^{76} +(-7.13022 + 15.2908i) q^{77} +(-5.45945 - 8.18950i) 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} +(6.51525 - 9.30474i) q^{83} +(-0.378454 + 1.89208i) q^{84} +(0.256560 - 3.16359i) q^{85} +(0.193565 - 0.230681i) q^{86} +(1.16279 + 1.21726i) q^{87} +(8.38540 - 3.91017i) q^{88} +(2.09630 + 3.63090i) q^{89} +(-9.77350 + 2.21001i) q^{90} +(-9.16409 + 15.8727i) q^{91} +(-0.0302327 + 0.345561i) q^{92} +(2.67277 - 3.63707i) q^{93} +(12.8100 + 2.25876i) q^{94} +(3.30243 - 0.603940i) q^{95} +(1.75987 - 1.40937i) q^{96} +(6.41403 + 0.561155i) q^{97} +(23.3902 - 6.26740i) 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

Fields

Representations

Groups

Database

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