LMFDB - Embedded newform 690.2.x.a.77.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(77,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 11, 12]))

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

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

chi := DirichletCharacter("690.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.x (of order $44$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$48$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			77.11
Character	$\chi$	$=$	690.77
Dual form			690.2.x.a.233.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.599278 - 0.800541i) q^{2} +(-0.682476 + 1.59193i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-1.62117 + 1.54007i) q^{5} +(1.68339 - 0.407655i) q^{6} +(-0.461734 - 2.12256i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-2.06845 - 2.17290i) q^{9} +O(q^{10})$	\(q+(-0.599278 - 0.800541i) q^{2} +(-0.682476 + 1.59193i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-1.62117 + 1.54007i) q^{5} +(1.68339 - 0.407655i) q^{6} +(-0.461734 - 2.12256i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-2.06845 - 2.17290i) q^{9} +(2.20442 + 0.374883i) q^{10} +(-1.80400 + 0.259377i) q^{11} +(-1.33517 - 1.10333i) q^{12} +(0.0411206 - 0.189028i) q^{13} +(-1.42249 + 1.64164i) q^{14} +(-1.34527 - 3.63184i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(0.947728 - 1.73563i) q^{17} +(-0.499921 + 2.95805i) q^{18} +(0.434840 - 1.48093i) q^{19} +(-1.02095 - 1.98939i) q^{20} +(3.69408 + 0.713549i) q^{21} +(1.28874 + 1.28874i) q^{22} +(4.53881 + 1.54895i) q^{23} +(-0.0831251 + 1.73005i) q^{24} +(0.256374 - 4.99342i) q^{25} +(-0.175968 + 0.0803617i) q^{26} +(4.87077 - 1.80987i) q^{27} +(2.16666 + 0.154963i) q^{28} +(-7.12702 + 2.09268i) q^{29} +(-2.10125 + 3.25342i) q^{30} +(0.780655 - 1.70940i) q^{31} +(0.0713392 + 0.997452i) q^{32} +(0.818282 - 3.04886i) q^{33} +(-1.95740 + 0.281431i) q^{34} +(4.01743 + 2.72992i) q^{35} +(2.66763 - 1.37249i) q^{36} +(7.43237 - 0.531574i) q^{37} +(-1.44613 + 0.539380i) q^{38} +(0.272855 + 0.194468i) q^{39} +(-0.980754 + 2.00951i) q^{40} +(6.99053 - 6.05733i) q^{41} +(-1.64255 - 3.38487i) q^{42} +(2.64829 + 0.987762i) q^{43} +(0.259377 - 1.80400i) q^{44} +(6.69973 + 0.337081i) q^{45} +(-1.48001 - 4.56175i) q^{46} +(7.90242 - 7.90242i) q^{47} +(1.43480 - 0.970238i) q^{48} +(2.07537 - 0.947790i) q^{49} +(-4.15108 + 2.78721i) q^{50} +(2.11620 + 2.69324i) q^{51} +(0.169786 + 0.0927103i) q^{52} +(-1.88205 - 8.65164i) q^{53} +(-4.36782 - 2.81464i) q^{54} +(2.52514 - 3.19878i) q^{55} +(-1.17438 - 1.82737i) q^{56} +(2.06076 + 1.70293i) q^{57} +(5.94634 + 4.45138i) q^{58} +(-10.9597 + 7.04338i) q^{59} +(3.86373 - 0.267566i) q^{60} +(3.17965 - 6.96245i) q^{61} +(-1.83627 + 0.399456i) q^{62} +(-3.65704 + 5.39371i) q^{63} +(0.755750 - 0.654861i) q^{64} +(0.224453 + 0.369775i) q^{65} +(-2.93111 + 1.17204i) q^{66} +(-2.38206 + 1.78319i) q^{67} +(1.39832 + 1.39832i) q^{68} +(-5.56344 + 6.16832i) q^{69} +(-0.222144 - 4.85210i) q^{70} +(-5.16324 - 0.742361i) q^{71} +(-2.69739 - 1.31305i) q^{72} +(0.609809 - 0.332981i) q^{73} +(-4.87960 - 5.63136i) q^{74} +(7.77419 + 3.81602i) q^{75} +(1.29843 + 0.834451i) q^{76} +(1.38351 + 3.70934i) q^{77} +(-0.00783613 - 0.334972i) q^{78} +(-3.35825 - 5.22554i) q^{79} +(2.19644 - 0.419119i) q^{80} +(-0.443010 + 8.98909i) q^{81} +(-9.03842 - 1.96619i) q^{82} +(-8.47603 + 0.606217i) q^{83} +(-1.72539 + 3.34341i) q^{84} +(1.13657 + 4.27332i) q^{85} +(-0.796319 - 2.71201i) q^{86} +(1.53263 - 12.7739i) q^{87} +(-1.59962 + 0.873458i) q^{88} +(-5.33415 - 11.6802i) q^{89} +(-3.74515 - 5.56542i) q^{90} -0.420210 q^{91} +(-2.76493 + 3.91856i) q^{92} +(2.18845 + 2.40937i) q^{93} +(-11.0620 - 1.59047i) q^{94} +(1.57578 + 3.07052i) q^{95} +(-1.63656 - 0.567171i) q^{96} +(-0.380330 + 5.31770i) q^{97} +(-2.00247 - 1.09343i) q^{98} +(4.29510 + 3.38342i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) $ 960 * q + 8 * q^3 + 8 * q^6	$ 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) $ 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	−0.599278	−	0.800541i	−0.423753	−	0.566068i
$2$	−0.599278	−	0.800541i	−0.423753	−	0.566068i
$3$	−0.682476	+	1.59193i	−0.394028	+	0.919099i
$3$	−0.682476	+	1.59193i	−0.394028	+	0.919099i
$4$	−0.281733	+	0.959493i	−0.140866	+	0.479746i
$5$	−1.62117	+	1.54007i	−0.725009	+	0.688740i
$5$	−1.62117	+	1.54007i	−0.725009	+	0.688740i
$6$	1.68339	−	0.407655i	0.687243	−	0.166424i
$7$	−0.461734	−	2.12256i	−0.174519	−	0.802251i	−0.978278	−	0.207296i	$-0.933534\pi$
$7$	−0.461734	−	2.12256i	−0.174519	−	0.802251i	0.803759	−	0.594955i	$-0.202830\pi$
$8$	0.936950	−	0.349464i	0.331262	−	0.123554i
$9$	−2.06845	−	2.17290i	−0.689484	−	0.724301i
$10$	2.20442	+	0.374883i	0.697098	+	0.118548i
$11$	−1.80400	+	0.259377i	−0.543928	+	0.0782050i	−0.408801	−	0.912623i	$-0.634053\pi$
$11$	−1.80400	+	0.259377i	−0.543928	+	0.0782050i	−0.135126	+	0.990828i	$0.543144\pi$
$12$	−1.33517	−	1.10333i	−0.385429	−	0.318503i
$13$	0.0411206	−	0.189028i	0.0114048	−	0.0524270i	−0.971093	−	0.238702i	$-0.923278\pi$
$13$	0.0411206	−	0.189028i	0.0114048	−	0.0524270i	0.982498	+	0.186275i	$0.0596416\pi$
$14$	−1.42249	+	1.64164i	−0.380176	+	0.438746i
$15$	−1.34527	−	3.63184i	−0.347346	−	0.937737i
$16$	−0.841254	−	0.540641i	−0.210313	−	0.135160i
$17$	0.947728	−	1.73563i	0.229858	−	0.420953i	−0.737139	−	0.675741i	$-0.763824\pi$
$17$	0.947728	−	1.73563i	0.229858	−	0.420953i	0.966997	+	0.254788i	$0.0820056\pi$
$18$	−0.499921	+	2.95805i	−0.117832	+	0.697220i
$19$	0.434840	−	1.48093i	0.0997590	−	0.339748i	−0.894456	−	0.447156i	$-0.852437\pi$
$19$	0.434840	−	1.48093i	0.0997590	−	0.339748i	0.994215	+	0.107408i	$0.0342551\pi$
$20$	−1.02095	−	1.98939i	−0.228291	−	0.444841i
$21$	3.69408	+	0.713549i	0.806113	+	0.155709i
$22$	1.28874	+	1.28874i	0.274761	+	0.274761i
$23$	4.53881	+	1.54895i	0.946406	+	0.322978i
$23$	4.53881	+	1.54895i	0.946406	+	0.322978i
$24$	−0.0831251	+	1.73005i	−0.0169678	+	0.353146i
$25$	0.256374	−	4.99342i	0.0512749	−	0.998685i
$26$	−0.175968	+	0.0803617i	−0.0345101	+	0.0157602i
$27$	4.87077	−	1.80987i	0.937380	−	0.348309i
$28$	2.16666	+	0.154963i	0.409461	+	0.0292852i
$29$	−7.12702	+	2.09268i	−1.32345	+	0.388601i	−0.865738	−	0.500497i	$-0.833151\pi$
$29$	−7.12702	+	2.09268i	−1.32345	+	0.388601i	−0.457716	+	0.889098i	$0.651332\pi$
$30$	−2.10125	+	3.25342i	−0.383634	+	0.593991i
$31$	0.780655	−	1.70940i	0.140210	−	0.307016i	−0.826481	−	0.562965i	$-0.809661\pi$
$31$	0.780655	−	1.70940i	0.140210	−	0.307016i	0.966690	+	0.255949i	$0.0823878\pi$
$32$	0.0713392	+	0.997452i	0.0126111	+	0.176326i
$33$	0.818282	−	3.04886i	0.142445	−	0.530738i
$34$	−1.95740	+	0.281431i	−0.335691	+	0.0482651i
$35$	4.01743	+	2.72992i	0.679070	+	0.461441i
$36$	2.66763	−	1.37249i	0.444606	−	0.228748i
$37$	7.43237	−	0.531574i	1.22187	−	0.0873902i	0.554545	−	0.832153i	$-0.312892\pi$
$37$	7.43237	−	0.531574i	1.22187	−	0.0873902i	0.667329	+	0.744763i	$0.267438\pi$
$38$	−1.44613	+	0.539380i	−0.234594	+	0.0874990i
$39$	0.272855	+	0.194468i	0.0436918	+	0.0311398i
$40$	−0.980754	+	2.00951i	−0.155071	+	0.317731i
$41$	6.99053	−	6.05733i	1.09174	−	0.945996i	0.0929725	−	0.995669i	$-0.470363\pi$
$41$	6.99053	−	6.05733i	1.09174	−	0.945996i	0.998766	+	0.0496722i	$0.0158177\pi$
$42$	−1.64255	−	3.38487i	−0.253451	−	0.522297i
$43$	2.64829	+	0.987762i	0.403861	+	0.150632i	0.543182	−	0.839615i	$-0.317219\pi$
$43$	2.64829	+	0.987762i	0.403861	+	0.150632i	−0.139321	+	0.990247i	$0.544492\pi$
$44$	0.259377	−	1.80400i	0.0391025	−	0.271964i
$45$	6.69973	+	0.337081i	0.998737	+	0.0502491i
$46$	−1.48001	−	4.56175i	−0.218215	−	0.672594i
$47$	7.90242	−	7.90242i	1.15269	−	1.15269i	0.166674	−	0.986012i	$-0.446697\pi$
$47$	7.90242	−	7.90242i	1.15269	−	1.15269i	0.986012	−	0.166674i	$-0.0533027\pi$
$48$	1.43480	−	0.970238i	0.207095	−	0.140042i
$49$	2.07537	−	0.947790i	0.296482	−	0.135399i
$50$	−4.15108	+	2.78721i	−0.587051	+	0.394171i
$51$	2.11620	+	2.69324i	0.296327	+	0.377129i
$52$	0.169786	+	0.0927103i	0.0235451	+	0.0128566i
$53$	−1.88205	−	8.65164i	−0.258519	−	1.18839i	−0.904982	−	0.425449i	$-0.860116\pi$
$53$	−1.88205	−	8.65164i	−0.258519	−	1.18839i	0.646463	−	0.762946i	$-0.276248\pi$
$54$	−4.36782	−	2.81464i	−0.594384	−	0.383024i
$55$	2.52514	−	3.19878i	0.340489	−	0.431324i
$56$	−1.17438	−	1.82737i	−0.156933	−	0.244193i
$57$	2.06076	+	1.70293i	0.272954	+	0.225559i
$58$	5.94634	+	4.45138i	0.780793	+	0.584494i
$59$	−10.9597	+	7.04338i	−1.42683	+	0.916970i	−0.426913	+	0.904293i	$0.640399\pi$
$59$	−10.9597	+	7.04338i	−1.42683	+	0.916970i	−0.999920	+	0.0126769i	$0.995965\pi$
$60$	3.86373	−	0.267566i	0.498805	−	0.0345426i
$61$	3.17965	−	6.96245i	0.407112	−	0.891451i	−0.589387	−	0.807850i	$-0.700631\pi$
$61$	3.17965	−	6.96245i	0.407112	−	0.891451i	0.996499	−	0.0836002i	$-0.0266419\pi$
$62$	−1.83627	+	0.399456i	−0.233207	+	0.0507310i
$63$	−3.65704	+	5.39371i	−0.460743	+	0.679544i
$64$	0.755750	−	0.654861i	0.0944687	−	0.0818576i
$65$	0.224453	+	0.369775i	0.0278400	+	0.0458650i
$66$	−2.93111	+	1.17204i	−0.360795	+	0.144269i
$67$	−2.38206	+	1.78319i	−0.291015	+	0.217851i	−0.734803	−	0.678281i	$-0.762725\pi$
$67$	−2.38206	+	1.78319i	−0.291015	+	0.217851i	0.443788	+	0.896132i	$0.353634\pi$
$68$	1.39832	+	1.39832i	0.169572	+	0.169572i
$69$	−5.56344	+	6.16832i	−0.669759	+	0.742578i
$70$	−0.222144	−	4.85210i	−0.0265513	−	0.579937i
$71$	−5.16324	−	0.742361i	−0.612763	−	0.0881021i	−0.171056	−	0.985261i	$-0.554718\pi$
$71$	−5.16324	−	0.742361i	−0.612763	−	0.0881021i	−0.441707	+	0.897159i	$0.645627\pi$
$72$	−2.69739	−	1.31305i	−0.317890	−	0.154744i
$73$	0.609809	−	0.332981i	0.0713727	−	0.0389724i	−0.443166	−	0.896439i	$-0.646145\pi$
$73$	0.609809	−	0.332981i	0.0713727	−	0.0389724i	0.514539	+	0.857467i	$0.327963\pi$
$74$	−4.87960	−	5.63136i	−0.567242	−	0.654632i
$75$	7.77419	+	3.81602i	0.897686	+	0.440636i
$76$	1.29843	+	0.834451i	0.148940	+	0.0957181i
$77$	1.38351	+	3.70934i	0.157666	+	0.422719i
$78$	−0.00783613	−	0.334972i	−0.000887267	−	0.0379281i
$79$	−3.35825	−	5.22554i	−0.377832	−	0.587919i	0.599307	−	0.800519i	$-0.295443\pi$
$79$	−3.35825	−	5.22554i	−0.377832	−	0.587919i	−0.977139	+	0.212601i	$0.931807\pi$
$80$	2.19644	−	0.419119i	0.245569	−	0.0468589i
$81$	−0.443010	+	8.98909i	−0.0492233	+	0.998788i
$82$	−9.03842	−	1.96619i	−0.998126	−	0.217129i
$83$	−8.47603	+	0.606217i	−0.930365	+	0.0665410i	−0.528288	−	0.849065i	$-0.677166\pi$
$83$	−8.47603	+	0.606217i	−0.930365	+	0.0665410i	−0.402077	+	0.915606i	$0.631711\pi$
$84$	−1.72539	+	3.34341i	−0.188255	+	0.364796i
$85$	1.13657	+	4.27332i	0.123278	+	0.463507i
$86$	−0.796319	−	2.71201i	−0.0858692	−	0.292444i
$87$	1.53263	−	12.7739i	0.164315	−	1.36950i
$88$	−1.59962	+	0.873458i	−0.170520	+	0.0931109i
$89$	−5.33415	−	11.6802i	−0.565419	−	1.23809i	−0.949201	−	0.314670i	$-0.898106\pi$
$89$	−5.33415	−	11.6802i	−0.565419	−	1.23809i	0.383782	−	0.923424i	$-0.374621\pi$
$90$	−3.74515	−	5.56542i	−0.394774	−	0.586646i
$91$	−0.420210			−0.0440500
$92$	−2.76493	+	3.91856i	−0.288264	+	0.408538i
$93$	2.18845	+	2.40937i	0.226932	+	0.249840i
$94$	−11.0620	−	1.59047i	−1.14095	−	0.164044i
$95$	1.57578	+	3.07052i	0.161672	+	0.315028i
$96$	−1.63656	−	0.567171i	−0.167030	−	0.0578866i
$97$	−0.380330	+	5.31770i	−0.0386166	+	0.539931i	0.940915	+	0.338642i	$0.109968\pi$
$97$	−0.380330	+	5.31770i	−0.0386166	+	0.539931i	−0.979532	+	0.201289i	$0.935487\pi$
$98$	−2.00247	−	1.09343i	−0.202280	−	0.110453i
$99$	4.29510	+	3.38342i	0.431673	+	0.340046i
$100$	4.71893	+	1.65280i	0.471893	+	0.165280i
$101$	−8.75805	−	7.58890i	−0.871459	−	0.755123i	0.0993312	−	0.995054i	$-0.468330\pi$
$101$	−8.75805	−	7.58890i	−0.871459	−	0.755123i	−0.970790	+	0.239931i	$0.922875\pi$
$102$	0.887860	−	3.30810i	0.0879113	−	0.327551i
$103$	2.01275	+	1.50672i	0.198322	+	0.148462i	0.693823	−	0.720145i	$-0.255925\pi$
$103$	2.01275	+	1.50672i	0.198322	+	0.148462i	−0.495502	+	0.868607i	$0.665016\pi$
$104$	−0.0275307	−	0.191480i	−0.00269961	−	0.0187762i
$105$	−7.08763	+	4.53235i	−0.691682	+	0.442312i
$106$	−5.79813	+	6.69140i	−0.563164	+	0.649926i
$107$	−0.0530513	−	0.142236i	−0.00512867	−	0.0137505i	0.934360	−	0.356330i	$-0.115972\pi$
$107$	−0.0530513	−	0.142236i	−0.00512867	−	0.0137505i	−0.939489	+	0.342580i	$0.888699\pi$
$108$	0.364301	+	5.18337i	0.0350549	+	0.498770i
$109$	1.86074	+	6.33709i	0.178226	+	0.606984i	0.999344	+	0.0362240i	$0.0115330\pi$
$109$	1.86074	+	6.33709i	0.178226	+	0.606984i	−0.821117	+	0.570760i	$0.806649\pi$
$110$	−4.07402	−	0.104516i	−0.388442	−	0.00996522i
$111$	−4.22619	+	12.1946i	−0.401132	+	1.15746i
$112$	−0.759106	+	2.03524i	−0.0717288	+	0.192312i
$113$	13.9447	−	10.4388i	1.31180	−	0.982004i	0.312316	−	0.949978i	$-0.398895\pi$
$113$	13.9447	−	10.4388i	1.31180	−	0.982004i	0.999487	−	0.0320254i	$-0.0101957\pi$
$114$	0.128299	−	2.67025i	0.0120163	−	0.250092i
$115$	−9.74366	+	4.47897i	−0.908601	+	0.417666i
$116$		−	7.42790i		−	0.689663i
$117$	−0.495796	+	0.301645i	−0.0458363	+	0.0278871i
$118$	12.2064	+	4.55276i	1.12369	+	0.419116i
$119$	−4.12158	−	1.21021i	−0.377825	−	0.110939i
$120$	−2.52964	−	2.93273i	−0.230924	−	0.267720i
$121$	−7.36727	+	2.16322i	−0.669752	+	0.196657i
$122$	−7.47922	+	1.62700i	−0.677137	+	0.147302i
$123$	4.87195	+	15.2624i	0.439289	+	1.37616i
$124$	1.42022	+	1.23062i	0.127539	+	0.110513i
$125$	7.27459	+	8.49001i	0.650659	+	0.759370i
$126$	6.50947	−	0.304724i	0.579910	−	0.0271469i
$127$	1.21497	−	1.62300i	0.107811	−	0.144018i	−0.743391	−	0.668858i	$-0.766784\pi$
$127$	1.21497	−	1.62300i	0.107811	−	0.144018i	0.851201	+	0.524839i	$0.175875\pi$
$128$	−0.977147	−	0.212565i	−0.0863684	−	0.0187883i
$129$	−3.37984	+	3.54176i	−0.297578	+	0.311835i
$130$	0.161510	−	0.401282i	0.0141654	−	0.0351948i
$131$	4.59660	−	7.15246i	0.401607	−	0.624913i	−0.580272	−	0.814423i	$-0.697054\pi$
$131$	4.59660	−	7.15246i	0.401607	−	0.624913i	0.981879	+	0.189510i	$0.0606899\pi$
$132$	2.69482	+	1.64410i	0.234554	+	0.143100i
$133$	−3.34413	−	0.239177i	−0.289973	−	0.0207393i
$134$	2.85503	+	0.838313i	0.246637	+	0.0724192i
$135$	−5.10901	+	10.4354i	−0.439714	+	0.898138i
$136$	0.281431	−	1.95740i	0.0241325	−	0.167846i
$137$	8.97654	−	8.97654i	0.766918	−	0.766918i	−0.210645	−	0.977563i	$-0.567556\pi$
$137$	8.97654	−	8.97654i	0.766918	−	0.766918i	0.977563	+	0.210645i	$0.0675564\pi$
$138$	8.27204	+	0.757226i	0.704163	+	0.0644593i
$139$			1.96673i			0.166816i	0.996515	+	0.0834078i	$0.0265804\pi$
$139$			1.96673i			0.166816i	−0.996515	+	0.0834078i	$0.973420\pi$
$140$	−3.75118	+	3.08559i	−0.317033	+	0.260780i
$141$	7.18684	+	17.9733i	0.605242	+	1.51362i
$142$	2.49992	+	4.57826i	0.209789	+	0.384199i
$143$	−0.0251522	+	0.351673i	−0.00210333	+	0.0294084i
$144$	0.565333	+	2.94625i	0.0471111	+	0.245521i
$145$	8.33123	−	14.3687i	0.691871	−	1.19326i
$146$	−0.632010	−	0.288629i	−0.0523055	−	0.0238871i
$147$	0.0924197	+	3.95068i	0.00762265	+	0.325847i
$148$	−1.58390	+	7.28107i	−0.130196	+	0.598500i
$149$	−1.63796	−	11.3923i	−0.134187	−	0.933293i	−0.940013	−	0.341140i	$-0.889187\pi$
$149$	−1.63796	−	11.3923i	−0.134187	−	0.933293i	0.805825	−	0.592153i	$-0.201722\pi$
$150$	−1.60401	−	8.51041i	−0.130967	−	0.694872i
$151$	−16.4306	+	10.5593i	−1.33710	+	0.859303i	−0.996716	−	0.0809821i	$-0.974194\pi$
$151$	−16.4306	+	10.5593i	−1.33710	+	0.859303i	−0.340387	+	0.940286i	$0.610558\pi$
$152$	−0.110108	−	1.53952i	−0.00893096	−	0.124871i
$153$	−5.73169	+	1.53076i	−0.463380	+	0.123754i
$154$	2.14037	−	3.33048i	0.172476	−	0.268378i
$155$	1.36701	+	3.97348i	0.109801	+	0.319158i
$156$	−0.263463	+	0.207014i	−0.0210939	+	0.0165744i
$157$	−0.0416421	−	0.0762618i	−0.00332340	−	0.00608635i	0.876012	−	0.482289i	$-0.160195\pi$
$157$	−0.0416421	−	0.0762618i	−0.00332340	−	0.00608635i	−0.879335	+	0.476203i	$0.842013\pi$
$158$	−2.17073	+	5.81996i	−0.172694	+	0.463011i
$159$	15.0572	+	2.90846i	1.19412	+	0.230656i
$160$	−1.65180	−	1.50717i	−0.130586	−	0.119152i
$161$	1.19201	−	10.3491i	0.0939437	−	0.815622i
$162$	7.46162	−	5.03231i	0.586240	−	0.395376i
$163$	−9.21060	−	12.3039i	−0.721430	−	0.963718i	−0.999995	−	0.00330035i	$-0.998949\pi$
$163$	−9.21060	−	12.3039i	−0.721430	−	0.963718i	0.278564	−	0.960418i	$-0.410141\pi$
$164$	3.84251	+	8.41392i	0.300049	+	0.657017i
$165$	3.36888	+	6.20292i	0.262267	+	0.482897i
$166$	5.56480	+	6.42212i	0.431912	+	0.498453i
$167$	−5.38420	+	9.86042i	−0.416642	+	0.763022i	−0.998745	−	0.0500930i	$-0.984048\pi$
$167$	−5.38420	+	9.86042i	−0.416642	+	0.763022i	0.582103	+	0.813115i	$0.302230\pi$
$168$	3.71052	−	0.622388i	0.286273	−	0.0480183i
$169$	11.7912	+	5.38485i	0.907013	+	0.414219i
$170$	2.73985	−	3.47078i	0.210137	−	0.266196i
$171$	−4.11736	+	2.11836i	−0.314862	+	0.161995i
$172$	−1.69386	+	2.26273i	−0.129156	+	0.172532i
$173$	−6.61924	+	8.84227i	−0.503252	+	0.672265i	−0.978180	−	0.207759i	$-0.933383\pi$
$173$	−6.61924	+	8.84227i	−0.503252	+	0.672265i	0.474928	+	0.880024i	$0.342474\pi$
$174$	−11.1445	+	6.42817i	−0.844862	+	0.487319i
$175$	−10.7172	+	1.76146i	−0.810145	+	0.133154i
$176$	1.65785	+	0.757117i	0.124965	+	0.0570698i
$177$	−3.73279	−	22.2540i	−0.280574	−	1.67271i
$178$	−6.15381	+	11.2699i	−0.461248	+	0.844712i
$179$	11.2591	+	12.9937i	0.841544	+	0.971193i	0.999869	−	0.0161940i	$-0.00515492\pi$
$179$	11.2591	+	12.9937i	0.841544	+	0.971193i	−0.158325	+	0.987387i	$0.550609\pi$
$180$	−2.21096	+	6.33338i	−0.164795	+	0.472062i
$181$	−0.557302	−	1.22032i	−0.0414239	−	0.0907057i	0.887789	−	0.460251i	$-0.152241\pi$
$181$	−0.557302	−	1.22032i	−0.0414239	−	0.0907057i	−0.929213	+	0.369545i	$0.879513\pi$
$182$	0.251823	+	0.336395i	0.0186663	+	0.0249353i
$183$	8.91367	+	9.81347i	0.658918	+	0.725432i
$184$	4.79393	−	0.134863i	0.353414	−	0.00994222i
$185$	−11.2305	+	12.3081i	−0.825680	+	0.904912i
$186$	0.617307	−	3.19582i	0.0452631	−	0.234329i
$187$	−1.25952	+	3.37691i	−0.0921054	+	0.246944i
$188$	5.35594	+	9.80868i	0.390622	+	0.715372i
$189$	−6.09055	−	9.50281i	−0.443022	−	0.691228i
$190$	1.51374	−	3.10157i	0.109818	−	0.225012i
$191$	−0.852877	+	1.32710i	−0.0617120	+	0.0960258i	−0.870738	−	0.491747i	$-0.836359\pi$
$191$	−0.852877	+	1.32710i	−0.0617120	+	0.0960258i	0.809026	+	0.587772i	$0.199995\pi$
$192$	0.526708	+	1.65002i	0.0380119	+	0.119080i
$193$	−1.73525	−	24.2619i	−0.124906	−	1.74641i	−0.544556	−	0.838725i	$-0.683302\pi$
$193$	−1.73525	−	24.2619i	−0.124906	−	1.74641i	0.419650	−	0.907686i	$-0.362153\pi$
$194$	4.48497	−	2.88231i	0.322002	−	0.206938i
$195$	−0.741838	+	0.104950i	−0.0531241	+	0.00751562i
$196$	0.324698	+	2.25833i	0.0231927	+	0.161309i
$197$	3.75326	−	17.2535i	0.267409	−	1.22926i	−0.625932	−	0.779878i	$-0.715281\pi$
$197$	3.75326	−	17.2535i	0.267409	−	1.22926i	0.893340	−	0.449380i	$-0.148355\pi$
$198$	0.134609	−	5.46601i	0.00956625	−	0.388452i
$199$	3.13432	+	1.43140i	0.222186	+	0.101469i	0.523398	−	0.852088i	$-0.324664\pi$
$199$	3.13432	+	1.43140i	0.222186	+	0.101469i	−0.301212	+	0.953557i	$0.597391\pi$
$200$	−1.50481	−	4.76818i	−0.106406	−	0.337161i
$201$	−1.21300	−	5.00905i	−0.0855586	−	0.353311i
$202$	−0.826719	+	11.5590i	−0.0581677	+	0.813291i
$203$	7.73263	+	14.1612i	0.542724	+	0.993925i
$204$	−3.18035	+	1.27170i	−0.222669	+	0.0890370i
$205$	−2.00412	+	20.5859i	−0.139974	+	1.43778i
$206$		−	2.51423i		−	0.175175i
$207$	−6.02259	−	13.0663i	−0.418599	−	0.908171i
$208$	−0.136789	+	0.136789i	−0.00948462	+	0.00948462i
$209$	−0.400334	+	2.78439i	−0.0276917	+	0.192600i
$210$	7.87579	+	2.95781i	0.543481	+	0.204108i
$211$	11.6983	+	3.43493i	0.805344	+	0.236470i	0.658394	−	0.752674i	$-0.271236\pi$
$211$	11.6983	+	3.43493i	0.805344	+	0.236470i	0.146950	+	0.989144i	$0.453054\pi$
$212$	8.83143	+	0.631636i	0.606545	+	0.0433809i
$213$	4.70557	−	7.71284i	0.322420	−	0.528475i
$214$	−0.0820734	+	0.127709i	−0.00561042	+	0.00872999i
$215$	−5.81455	+	2.47723i	−0.396549	+	0.168945i
$216$	3.93118	−	3.39791i	0.267483	−	0.231199i
$217$	−3.98875	−	0.867698i	−0.270774	−	0.0589032i
$218$	3.95801	−	5.28728i	0.268070	−	0.358100i
$219$	0.113901	+	1.19802i	0.00769668	+	0.0809548i
$220$	2.35780	+	3.32405i	0.158963	+	0.224108i
$221$	−0.289113	−	0.250518i	−0.0194478	−	0.0168516i
$222$	12.2949	−	3.92469i	0.825181	−	0.263408i
$223$	−15.3524	+	3.33972i	−1.02808	+	0.223644i	−0.694814	−	0.719190i	$-0.744513\pi$
$223$	−15.3524	+	3.33972i	−1.02808	+	0.223644i	−0.333262	+	0.942834i	$0.608149\pi$
$224$	2.08421	−	0.611979i	0.139257	−	0.0408896i
$225$	−11.3805	+	9.77158i	−0.758701	+	0.651439i
$226$	−16.7134	−	4.90751i	−1.11176	−	0.326443i
$227$	6.03361	+	2.25042i	0.400465	+	0.149366i	0.541623	−	0.840621i	$-0.317810\pi$
$227$	6.03361	+	2.25042i	0.400465	+	0.149366i	−0.141158	+	0.989987i	$0.545083\pi$
$228$	−2.21453	+	1.49751i	−0.146661	+	0.0991752i
$229$			4.23573i			0.279905i	0.990158	+	0.139953i	$0.0446950\pi$
$229$			4.23573i			0.279905i	−0.990158	+	0.139953i	$0.955305\pi$
$230$	9.42475	+	5.11605i	0.621450	+	0.337343i
$231$	−6.84921	−	0.329088i	−0.450645	−	0.0216524i
$232$	−5.94634	+	4.45138i	−0.390396	+	0.292247i
$233$	2.92337	−	7.83786i	0.191516	−	0.513475i	−0.805330	−	0.592826i	$-0.798012\pi$
$233$	2.92337	−	7.83786i	0.191516	−	0.513475i	0.996847	+	0.0793510i	$0.0252848\pi$
$234$	0.538598	+	0.216136i	0.0352093	+	0.0141292i
$235$	−0.640881	+	24.9814i	−0.0418065	+	1.62961i
$236$	−3.67036	−	12.5001i	−0.238920	−	0.813688i
$237$	10.6106	−	1.77978i	0.689232	−	0.115609i
$238$	1.50115	+	4.02474i	0.0973052	+	0.260885i
$239$	−15.8342	+	18.2736i	−1.02423	+	1.18202i	−0.0410892	+	0.999155i	$0.513083\pi$
$239$	−15.8342	+	18.2736i	−1.02423	+	1.18202i	−0.983138	+	0.182866i	$0.941463\pi$
$240$	−0.831811	+	3.78260i	−0.0536932	+	0.244166i
$241$	−2.03588	−	14.1599i	−0.131143	−	0.912117i	−0.944068	−	0.329750i	$-0.893036\pi$
$241$	−2.03588	−	14.1599i	−0.131143	−	0.912117i	0.812926	−	0.582367i	$-0.197873\pi$
$242$	6.14679	+	4.60143i	0.395131	+	0.295791i
$243$	−14.0076	−	6.84008i	−0.898589	−	0.438791i
$244$	5.78461	+	5.01240i	0.370322	+	0.320886i
$245$	−1.90486	+	4.73274i	−0.121697	+	0.302364i
$246$	9.29853	−	13.0466i	0.592852	−	0.831821i
$247$	−0.262056	−	0.143094i	−0.0166742	−	0.00910482i
$248$	0.134062	−	1.87443i	0.00851293	−	0.119026i
$249$	4.81963	−	13.9069i	0.305432	−	0.881316i
$250$	2.43711	−	10.9115i	0.154136	−	0.690103i
$251$	−6.51430	−	0.936615i	−0.411179	−	0.0591186i	−0.0663782	−	0.997795i	$-0.521144\pi$
$251$	−6.51430	−	0.936615i	−0.411179	−	0.0591186i	−0.344801	+	0.938676i	$0.612053\pi$
$252$	−4.14492	−	5.02848i	−0.261106	−	0.316765i
$253$	−8.58979	−	1.61705i	−0.540035	−	0.101663i
$254$	−2.02738			−0.127209
$255$	−7.57849	−	1.10711i	−0.474583	−	0.0693297i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−6.28250	+	3.43051i	−0.391892	+	0.213989i	−0.663099	−	0.748532i	$-0.730759\pi$
$257$	−6.28250	+	3.43051i	−0.391892	+	0.213989i	0.271207	+	0.962521i	$0.412577\pi$
$258$	4.86079	+	0.583204i	0.302620	+	0.0363087i
$259$	−4.56008	−	15.5302i	−0.283349	−	0.964999i
$260$	−0.418032	+	0.111184i	−0.0259253	+	0.00689531i
$261$	19.2891	+	11.1577i	1.19396	+	0.690645i
$262$	−8.48048	+	0.606536i	−0.523926	+	0.0374719i
$263$	23.0153	+	5.00667i	1.41918	+	0.308725i	0.855730	−	0.517422i	$-0.173108\pi$
$263$	23.0153	+	5.00667i	1.41918	+	0.308725i	0.563455	+	0.826147i	$0.309472\pi$
$264$	−0.298778	−	3.14259i	−0.0183885	−	0.193413i
$265$	16.3753	+	11.1273i	1.00592	+	0.683544i
$266$	1.81259	+	2.82045i	0.111137	+	0.172933i
$267$	22.2344	−	0.520137i	1.36072	−	0.0318319i
$268$	−1.03985	−	2.78795i	−0.0635191	−	0.170301i
$269$	−23.7950	−	15.2921i	−1.45081	−	0.932376i	−0.999193	−	0.0401625i	$-0.987212\pi$
$269$	−23.7950	−	15.2921i	−1.45081	−	0.932376i	−0.451613	−	0.892214i	$-0.649151\pi$
$270$	11.4157	−	2.16374i	0.694737	−	0.131681i
$271$	−5.19858	−	5.99948i	−0.315791	−	0.364442i	0.575557	−	0.817762i	$-0.304785\pi$
$271$	−5.19858	−	5.99948i	−0.315791	−	0.364442i	−0.891348	+	0.453319i	$0.850240\pi$
$272$	−1.73563	+	0.947728i	−0.105238	+	0.0574644i
$273$	0.286783	−	0.668943i	0.0173569	−	0.0404863i
$274$	−12.5655	−	1.80665i	−0.759112	−	0.109144i
$275$	0.832677	+	9.07465i	0.0502123	+	0.547222i
$276$	−4.35106	−	7.07590i	−0.261903	−	0.425919i
$277$	7.95483	+	7.95483i	0.477960	+	0.477960i	0.904479	−	0.426519i	$-0.140260\pi$
$277$	7.95483	+	7.95483i	0.477960	+	0.477960i	−0.426519	+	0.904479i	$0.640260\pi$
$278$	1.57445	−	1.17862i	0.0944290	−	0.0706887i
$279$	−5.32910	+	1.83952i	−0.319045	+	0.110129i
$280$	4.71814	+	1.15385i	0.281963	+	0.0689557i
$281$	12.8167	−	11.1057i	0.764580	−	0.662512i	−0.182610	−	0.983185i	$-0.558455\pi$
$281$	12.8167	−	11.1057i	0.764580	−	0.662512i	0.947190	+	0.320673i	$0.103909\pi$
$282$	10.0814	−	16.5243i	0.600340	−	0.984010i
$283$	−6.61436	+	1.43887i	−0.393183	+	0.0855317i	−0.404810	−	0.914401i	$-0.632662\pi$
$283$	−6.61436	+	1.43887i	−0.393183	+	0.0855317i	0.0116274	+	0.999932i	$0.496299\pi$
$284$	2.16694	−	4.74494i	0.128584	−	0.281560i
$285$	−5.96347	+	0.412974i	−0.353245	+	0.0244625i
$286$	0.296602	−	0.190615i	0.0175385	−	0.0112713i
$287$	−16.0848	−	12.0409i	−0.949456	−	0.710754i
$288$	2.01980	−	2.21820i	0.119018	−	0.130708i
$289$	7.07666	+	11.0115i	0.416274	+	0.647735i
$290$	−16.4954	+	1.94135i	−0.968646	+	0.114000i
$291$	−8.20582	−	4.23466i	−0.481034	−	0.248240i
$292$	0.147690	+	0.678919i	0.00864289	+	0.0397307i
$293$	7.48614	+	4.08774i	0.437345	+	0.238808i	0.682808	−	0.730597i	$-0.260758\pi$
$293$	7.48614	+	4.08774i	0.437345	+	0.238808i	−0.245464	+	0.969406i	$0.578940\pi$
$294$	3.10730	−	2.44154i	0.181221	−	0.142393i
$295$	6.92025	−	28.2972i	0.402912	−	1.64753i
$296$	6.77799	−	3.09540i	0.393963	−	0.179917i
$297$	−8.31745	+	4.52837i	−0.482627	+	0.262763i
$298$	−8.13840	+	8.13840i	−0.471445	+	0.471445i
$299$	0.479433	−	0.794269i	0.0277263	−	0.0459337i
$300$	−5.85169	+	6.38418i	−0.337847	+	0.368591i
$301$	0.873775	−	6.07724i	0.0503636	−	0.350286i
$302$	18.2996	+	6.82541i	1.05303	+	0.392758i
$303$	18.0581	−	8.76292i	1.03741	−	0.503417i
$304$	−1.16646	+	1.01074i	−0.0669011	+	0.0579701i
$305$	5.56792	+	16.1842i	0.318818	+	0.926704i
$306$	4.66031	+	3.67111i	0.266412	+	0.209863i
$307$	7.86487	−	2.93345i	0.448872	−	0.167421i	−0.114854	−	0.993382i	$-0.536640\pi$
$307$	7.86487	−	2.93345i	0.448872	−	0.167421i	0.563726	+	0.825962i	$0.309367\pi$
$308$	−3.94887	+	0.282428i	−0.225008	+	0.0160929i
$309$	−3.77225	+	2.17584i	−0.214596	+	0.123779i
$310$	2.36171	−	3.47557i	0.134136	−	0.197399i
$311$	−22.1150	+	3.17966i	−1.25403	+	0.180302i	−0.737133	−	0.675748i	$-0.763821\pi$
$311$	−22.1150	+	3.17966i	−1.25403	+	0.180302i	−0.516893	+	0.856050i	$0.672912\pi$
$312$	0.323611	+	0.0868538i	0.0183209	+	0.00491713i
$313$	−2.23990	−	31.3179i	−0.126607	−	1.77019i	−0.523212	−	0.852203i	$-0.675266\pi$
$313$	−2.23990	−	31.3179i	−0.126607	−	1.77019i	0.396605	−	0.917989i	$-0.370188\pi$
$314$	−0.0360955	+	0.0790382i	−0.00203699	+	0.00446038i
$315$	−2.37802	−	14.3762i	−0.133986	−	0.810007i
$316$	5.95999	−	1.75001i	0.335276	−	0.0984458i
$317$	−9.32742	−	0.667111i	−0.523880	−	0.0374687i	−0.193105	−	0.981178i	$-0.561856\pi$
$317$	−9.32742	−	0.667111i	−0.523880	−	0.0374687i	−0.330775	+	0.943709i	$0.607310\pi$
$318$	−6.69512	−	13.7969i	−0.375444	−	0.773692i
$319$	12.3144	−	5.62379i	0.689473	−	0.314872i
$320$	−0.216667	+	2.22555i	−0.0121120	+	0.124412i
$321$	0.262636	+	0.0126190i	0.0146589	+	0.000704325i
$322$	−8.99921	+	5.24772i	−0.501506	+	0.292444i
$323$	−2.15824	−	2.15824i	−0.120088	−	0.120088i
$324$	−8.50016	−	2.95758i	−0.472231	−	0.164310i
$325$	−0.933356	−	0.253794i	−0.0517732	−	0.0140780i
$326$	−4.33009	+	14.7469i	−0.239822	+	0.816757i
$327$	−11.3581	−	1.36276i	−0.628104	−	0.0753608i
$328$	4.43296	−	8.11836i	0.244769	−	0.448261i
$329$	−20.4222	−	13.1245i	−1.12591	−	0.723578i
$330$	2.94680	−	6.41420i	0.162216	−	0.353090i
$331$	17.9771	−	20.7467i	0.988109	−	1.14034i	−0.00199373	−	0.999998i	$-0.500635\pi$
$331$	17.9771	−	20.7467i	0.988109	−	1.14034i	0.990103	−	0.140341i	$-0.0448199\pi$
$332$	1.80631	−	8.30348i	0.0991342	−	0.455713i
$333$	−16.5286	−	15.0503i	−0.905760	−	0.824750i
$334$	11.1203	−	1.59886i	0.608476	−	0.0874856i
$335$	1.11549	−	6.55939i	0.0609456	−	0.358378i
$336$	−2.72188	−	2.59744i	−0.148491	−	0.141702i
$337$	−0.849429	+	0.316821i	−0.0462713	+	0.0172583i	−0.372493	−	0.928035i	$-0.621497\pi$
$337$	−0.849429	+	0.316821i	−0.0462713	+	0.0172583i	0.326222	+	0.945293i	$0.394224\pi$
$338$	−2.75539	−	12.6663i	−0.149874	−	0.688958i
$339$	7.10096	+	29.3231i	0.385671	+	1.59261i
$340$	−4.42043	−	0.113403i	−0.239731	−	0.00615014i
$341$	−0.964927	+	3.28624i	−0.0522537	+	0.177960i
$342$	4.16328	+	2.02663i	0.225124	+	0.109587i
$343$	−12.0823	−	16.1400i	−0.652381	−	0.871479i
$344$	2.82651			0.152395
$345$	−0.480367	−	18.5680i	−0.0258621	−	0.999666i
$346$	11.0454			0.593803
$347$	8.13882	+	10.8722i	0.436915	+	0.583650i	0.963913	−	0.266217i	$-0.0857736\pi$
$347$	8.13882	+	10.8722i	0.436915	+	0.583650i	−0.526999	+	0.849866i	$0.676683\pi$
$348$	11.8247	+	5.06937i	0.633869	+	0.271747i
$349$	−1.43360	+	4.88239i	−0.0767387	+	0.261348i	−0.988922	−	0.148433i	$-0.952577\pi$
$349$	−1.43360	+	4.88239i	−0.0767387	+	0.261348i	0.912184	+	0.409782i	$0.134395\pi$
$350$	7.83271	+	7.52396i	0.418676	+	0.402172i
$351$	−0.141827	−	0.995135i	−0.00757018	−	0.0531164i
$352$	−0.387412	−	1.78090i	−0.0206491	−	0.0949225i
$353$	−2.88642	+	1.07658i	−0.153629	+	0.0573006i	−0.425102	−	0.905145i	$-0.639762\pi$
$353$	−2.88642	+	1.07658i	−0.153629	+	0.0573006i	0.271473	+	0.962446i	$0.412489\pi$
$354$	−15.5782	+	16.3246i	−0.827975	+	0.867641i
$355$	9.51376	−	6.74825i	0.504938	−	0.358160i
$356$	12.7098	−	1.82740i	0.673620	−	0.0968519i
$357$	4.73944	−	5.73531i	0.250838	−	0.303545i
$358$	3.65466	−	16.8002i	0.193155	−	0.887917i
$359$	17.9636	−	20.7311i	0.948085	−	1.09415i	−0.0473668	−	0.998878i	$-0.515083\pi$
$359$	17.9636	−	20.7311i	0.948085	−	1.09415i	0.995451	−	0.0952704i	$-0.0303716\pi$
$360$	6.39511	−	2.02549i	0.337052	−	0.106753i
$361$	13.9798	+	8.98424i	0.735777	+	0.472855i
$362$	−0.642939	+	1.17745i	−0.0337921	+	0.0618856i
$363$	1.58429	−	13.2045i	0.0831538	−	0.693056i
$364$	0.118387	−	0.403189i	0.00620516	−	0.0211328i
$365$	−0.475789	+	1.47897i	−0.0249039	+	0.0774126i
$366$	2.51432	−	13.0168i	0.131426	−	0.680397i
$367$	15.3587	+	15.3587i	0.801718	+	0.801718i	0.983364	−	0.181646i	$-0.0581426\pi$
$367$	15.3587	+	15.3587i	0.801718	+	0.801718i	−0.181646	+	0.983364i	$0.558143\pi$
$368$	−2.98086	−	3.75692i	−0.155388	−	0.195843i
$369$	−27.6216	−	2.66045i	−1.43792	−	0.138497i
$370$	16.5833	+	1.61446i	0.862127	+	0.0839318i
$371$	−17.4946	+	7.98952i	−0.908275	+	0.414795i
$372$	−2.92833	+	1.42101i	−0.151827	+	0.0736758i
$373$	−17.1877	−	1.22929i	−0.889947	−	0.0636503i	−0.381127	−	0.924523i	$-0.624464\pi$
$373$	−17.1877	−	1.22929i	−0.889947	−	0.0636503i	−0.508821	+	0.860873i	$0.669918\pi$
$374$	3.45816	−	1.01541i	0.178817	−	0.0525054i
$375$	−18.4802	+	5.78637i	−0.954314	+	0.298807i
$376$	4.64256	−	10.1658i	0.239422	−	0.524260i
$377$	0.102509	+	1.43326i	0.00527947	+	0.0738166i
$378$	−3.95746	+	10.5706i	−0.203550	+	0.543691i
$379$	−4.71122	+	0.677372i	−0.241999	+	0.0347943i	−0.262247	−	0.965001i	$-0.584464\pi$
$379$	−4.71122	+	0.677372i	−0.241999	+	0.0347943i	0.0202478	+	0.999795i	$0.493554\pi$
$380$	−3.39009	+	0.646888i	−0.173908	+	0.0331847i
$381$	1.75452	+	3.04180i	0.0898866	+	0.155836i
$382$	1.57351	−	0.112540i	0.0805078	−	0.00575803i
$383$	−31.9377	+	11.9121i	−1.63194	+	0.608681i	−0.987730	−	0.156169i	$-0.950085\pi$
$383$	−31.9377	+	11.9121i	−1.63194	+	0.608681i	−0.644208	+	0.764851i	$0.722813\pi$
$384$	1.00527	−	1.41047i	0.0512998	−	0.0719780i
$385$	−7.95555	−	3.88276i	−0.405452	−	0.197884i
$386$	−18.3828	+	15.9288i	−0.935658	+	0.810752i
$387$	−3.33156	−	7.79762i	−0.169353	−	0.396375i
$388$	−4.99515	−	1.86309i	−0.253590	−	0.0945843i
$389$	3.22437	−	22.4260i	0.163482	−	1.13704i	−0.728524	−	0.685020i	$-0.759793\pi$
$389$	3.22437	−	22.4260i	0.163482	−	1.13704i	0.892006	−	0.452023i	$-0.149298\pi$
$390$	0.528584	+	0.530978i	0.0267659	+	0.0268871i
$391$	6.98996	−	6.40972i	0.353497	−	0.324154i
$392$	1.61330	−	1.61330i	0.0814839	−	0.0814839i
$393$	8.24910	+	12.1988i	0.416112	+	0.615350i
$394$	−16.0614	+	7.33497i	−0.809159	+	0.369531i
$395$	13.4920	+	3.29954i	0.678855	+	0.166018i
$396$	−4.45643	+	3.16790i	−0.223944	+	0.159193i
$397$	5.71989	+	3.12330i	0.287073	+	0.156754i	0.616333	−	0.787485i	$-0.288617\pi$
$397$	5.71989	+	3.12330i	0.287073	+	0.156754i	−0.329260	+	0.944239i	$0.606799\pi$
$398$	−0.732436	−	3.36696i	−0.0367137	−	0.168770i
$399$	2.66304	−	5.16038i	0.133319	−	0.258342i
$400$	−2.91532	+	4.06213i	−0.145766	+	0.203106i
$401$	6.13325	+	9.54352i	0.306280	+	0.476581i	0.959939	−	0.280208i	$-0.0904035\pi$
$401$	6.13325	+	9.54352i	0.306280	+	0.476581i	−0.653659	+	0.756789i	$0.726767\pi$
$402$	−3.28302	+	3.97287i	−0.163742	+	0.198149i
$403$	−0.291023	−	0.217857i	−0.0144969	−	0.0108522i
$404$	9.74892	−	6.26525i	0.485027	−	0.311708i
$405$	−13.1256	−	15.2551i	−0.652218	−	0.758032i
$406$	6.70267	−	14.6768i	0.332648	−	0.728398i
$407$	−13.2701	+	2.88674i	−0.657777	+	0.143091i
$408$	2.92396	+	1.78390i	0.144758	+	0.0883160i
$409$	22.3570	−	19.3724i	1.10548	−	0.957905i	0.106146	−	0.994351i	$-0.466149\pi$
$409$	22.3570	−	19.3724i	1.10548	−	0.957905i	0.999336	+	0.0364450i	$0.0116034\pi$
$410$	17.6809	−	10.7323i	0.873195	−	0.530029i
$411$	8.16371	+	20.4163i	0.402686	+	1.00706i
$412$	−2.01275	+	1.50672i	−0.0991610	+	0.0742310i
$413$	20.0104	+	20.0104i	0.984650	+	0.984650i
$414$	−6.85092	+	12.6517i	−0.336704	+	0.621796i
$415$	12.8075	−	14.0364i	0.628693	−	0.689022i
$416$	0.191480	+	0.0275307i	0.00938808	+	0.00134980i
$417$	−3.13088	−	1.34224i	−0.153320	−	0.0657300i
$418$	2.46893	−	1.34814i	0.120759	−	0.0659395i
$419$	17.5250	+	20.2249i	0.856150	+	0.988050i	0.999999	−	0.00154996i	$-0.000493367\pi$
$419$	17.5250	+	20.2249i	0.856150	+	0.988050i	−0.143849	+	0.989600i	$0.545948\pi$
$420$	−2.35194	−	8.07745i	−0.114763	−	0.394139i
$421$	−27.4756	−	17.6575i	−1.33908	−	0.860574i	−0.342208	−	0.939624i	$-0.611175\pi$
$421$	−27.4756	−	17.6575i	−1.33908	−	0.860574i	−0.996871	+	0.0790503i	$0.974811\pi$
$422$	−4.26073	−	11.4234i	−0.207409	−	0.556085i
$423$	−33.5169	−	0.825408i	−1.62965	−	0.0401327i
$424$	−4.78683	−	7.44845i	−0.232469	−	0.361729i
$425$	−8.42378	−	5.17738i	−0.408613	−	0.251140i
$426$	−8.99439	+	0.855131i	−0.435780	+	0.0414313i
$427$	−16.2464	−	3.53418i	−0.786216	−	0.171031i
$428$	0.151421	−	0.0108298i	0.00731920	−	0.000523480i
$429$	−0.542672	−	0.280049i	−0.0262005	−	0.0135209i
$430$	5.46765	+	3.17024i	0.263674	+	0.152883i
$431$	−2.07494	−	7.06660i	−0.0999464	−	0.340386i	0.894305	−	0.447458i	$-0.147671\pi$
$431$	−2.07494	−	7.06660i	−0.0999464	−	0.340386i	−0.994251	+	0.107072i	$0.965852\pi$
$432$	−5.07604	−	1.11078i	−0.244221	−	0.0534424i
$433$	−26.4130	+	14.4226i	−1.26933	+	0.693107i	−0.965694	−	0.259682i	$-0.916382\pi$
$433$	−26.4130	+	14.4226i	−1.26933	+	0.693107i	−0.303636	+	0.952788i	$0.598201\pi$
$434$	1.69574	+	3.71315i	0.0813980	+	0.178237i
$435$	17.1880	+	23.0690i	0.824103	+	1.10607i
$436$	−6.60463			−0.316304
$437$	4.26753	−	6.04810i	0.204144	−	0.289320i
$438$	0.890807	−	0.809129i	0.0425644	−	0.0386617i
$439$	−6.32861	−	0.909916i	−0.302048	−	0.0434279i	−0.0103754	−	0.999946i	$-0.503303\pi$
$439$	−6.32861	−	0.909916i	−0.302048	−	0.0434279i	−0.291673	+	0.956518i	$0.594212\pi$
$440$	1.24807	−	3.87955i	0.0594992	−	0.184950i
$441$	−6.35226	−	2.54912i	−0.302489	−	0.121387i
$442$	−0.0272909	+	0.381576i	−0.00129809	+	0.0181497i
$443$	20.1645	+	11.0106i	0.958043	+	0.523131i	0.880597	−	0.473865i	$-0.157142\pi$
$443$	20.1645	+	11.0106i	0.958043	+	0.523131i	0.0774459	+	0.996997i	$0.475323\pi$
$444$	−10.5099	−	7.49061i	−0.498780	−	0.355488i
$445$	26.6358	+	10.7205i	1.26266	+	0.508202i
$446$	11.8740	+	10.2888i	0.562248	+	0.487191i
$447$	19.2535	+	5.16745i	0.910662	+	0.244412i
$448$	−1.73894	−	1.30175i	−0.0821570	−	0.0615019i
$449$	4.82113	+	33.5317i	0.227523	+	1.58246i	0.708490	+	0.705720i	$0.249377\pi$
$449$	4.82113	+	33.5317i	0.227523	+	1.58246i	−0.480967	+	0.876739i	$0.659714\pi$
$450$	14.6426	+	3.25468i	0.690261	+	0.153427i
$451$	−11.0398	+	12.7406i	−0.519845	+	0.599933i
$452$	6.08733	+	16.3208i	0.286324	+	0.767664i
$453$	−5.59613	−	33.3627i	−0.262929	−	1.56752i
$454$	−1.81425	−	6.17878i	−0.0851472	−	0.289985i
$455$	0.681231	−	0.647153i	0.0319366	−	0.0303390i
$456$	2.52594	+	0.875399i	0.118288	+	0.0409943i
$457$	−0.0541674	+	0.145228i	−0.00253385	+	0.00679350i	−0.938210	−	0.346065i	$-0.887518\pi$
$457$	−0.0541674	+	0.145228i	−0.00253385	+	0.00679350i	0.935677	+	0.352859i	$0.114790\pi$
$458$	3.39088	−	2.53838i	0.158445	−	0.118611i
$459$	1.47489	−	10.1691i	0.0688422	−	0.474654i
$460$	−1.55243	−	10.6108i	−0.0723825	−	0.494733i
$461$		−	13.2872i		−	0.618846i	−0.950925	−	0.309423i	$-0.899864\pi$
$461$		−	13.2872i		−	0.618846i	0.950925	−	0.309423i	$-0.100136\pi$
$462$	3.84113	+	5.68029i	0.178705	+	0.264271i
$463$	3.87974	+	1.44707i	0.180307	+	0.0672509i	0.437996	−	0.898977i	$-0.355688\pi$
$463$	3.87974	+	1.44707i	0.180307	+	0.0672509i	−0.257689	+	0.966228i	$0.582961\pi$
$464$	7.12702	+	2.09268i	0.330864	+	0.0971503i
$465$	−7.25844	−	0.535621i	−0.336602	−	0.0248388i
$466$	−8.02644	+	2.35678i	−0.371818	+	0.109176i
$467$	19.8118	−	4.30980i	0.916781	−	0.199434i	0.270666	−	0.962673i	$-0.412756\pi$
$467$	19.8118	−	4.30980i	0.916781	−	0.199434i	0.646115	+	0.763240i	$0.276392\pi$
$468$	−0.149744	−	0.560696i	−0.00692193	−	0.0259182i
$469$	4.88480	+	4.23270i	0.225559	+	0.195448i
$470$	20.3827	−	14.4578i	0.940185	−	0.666886i
$471$	0.149823	−	0.0142442i	0.00690347	−	0.000656339i
$472$	−7.80729	+	10.4293i	−0.359360	+	0.480048i
$473$	−5.03374	−	1.09502i	−0.231451	−	0.0503492i
$474$	−7.78347	−	7.42763i	−0.357507	−	0.341162i
$475$	−7.28342	−	2.55101i	−0.334186	−	0.117048i
$476$	2.32237	−	3.61367i	0.106446	−	0.165632i
$477$	−14.9062	+	21.9850i	−0.682510	+	1.00663i
$478$	24.1178	+	1.72494i	1.10312	+	0.0788970i
$479$	36.6140	+	10.7508i	1.67294	+	0.491218i	0.974487	−	0.224443i	$-0.0720562\pi$
$479$	36.6140	+	10.7508i	1.67294	+	0.491218i	0.698448	+	0.715661i	$0.253874\pi$
$480$	3.52662	−	1.60093i	0.160967	−	0.0730722i
$481$	0.205141	−	1.42679i	0.00935362	−	0.0650559i
$482$	−10.1155	+	10.1155i	−0.460748	+	0.460748i
$483$	15.6614	+	8.96060i	0.712620	+	0.407721i
$484$		−	7.67829i		−	0.349013i
$485$	−7.57305	−	9.20663i	−0.343875	−	0.418052i
$486$	2.91869	+	15.3128i	0.132394	+	0.694602i
$487$	13.9714	+	25.5867i	0.633105	+	1.15945i	0.975523	+	0.219898i	$0.0705724\pi$
$487$	13.9714	+	25.5867i	0.633105	+	1.15945i	−0.342418	+	0.939548i	$0.611246\pi$
$488$	0.546040	−	7.63464i	0.0247181	−	0.345604i
$489$	25.8730	−	6.26546i	1.17002	−	0.283334i
$490$	4.93030	−	1.31130i	0.222728	−	0.0592387i
$491$	22.8123	+	10.4180i	1.02950	+	0.470159i	0.857254	−	0.514895i	$-0.172169\pi$
$491$	22.8123	+	10.4180i	1.02950	+	0.470159i	0.172250	+	0.985053i	$0.444896\pi$
$492$	−16.0167	+	0.374686i	−0.722091	+	0.0168921i
$493$	−3.12235	+	14.3532i	−0.140623	+	0.646435i
$494$	0.0424922	+	0.295540i	0.00191181	+	0.0132970i
$495$	−12.1738	+	1.12966i	−0.547170	+	0.0507743i
$496$	−1.58090	+	1.01598i	−0.0709844	+	0.0456189i
$497$	0.808338	+	11.3020i	0.0362589	+	0.506966i
$498$	−14.0214	+	4.47580i	−0.628313	+	0.200565i
$499$	10.7371	−	16.7072i	0.480657	−	0.747917i	−0.513238	−	0.858246i	$-0.671554\pi$
$499$	10.7371	−	16.7072i	0.480657	−	0.747917i	0.993895	+	0.110329i	$0.0351905\pi$
$500$	−10.1956	+	4.58800i	−0.455961	+	0.205182i
$501$	−12.0225	−	15.3007i	−0.537124	−	0.683587i
$502$	3.15408	+	5.77626i	0.140773	+	0.257807i
$503$	−1.09898	+	2.94647i	−0.0490010	+	0.131377i	−0.959145	−	0.282916i	$-0.908698\pi$
$503$	−1.09898	+	2.94647i	−0.0490010	+	0.131377i	0.910144	+	0.414293i	$0.135971\pi$
$504$	−1.54155	+	6.33164i	−0.0686661	+	0.282034i
$505$	25.8857	−	1.18513i	1.15190	−	0.0527375i
$506$	3.85315	+	7.84554i	0.171293	+	0.348777i
$507$	−16.6195	+	15.0956i	−0.738097	+	0.670421i
$508$	1.21497	+	1.62300i	0.0539054	+	0.0720092i
$509$	10.9578	+	23.9943i	0.485697	+	1.06353i	0.980858	+	0.194726i	$0.0623819\pi$
$509$	10.9578	+	23.9943i	0.485697	+	1.06353i	−0.495161	+	0.868801i	$0.664891\pi$
$510$	3.65534	+	6.73036i	0.161861	+	0.298025i
$511$	−0.988340	−	1.14061i	−0.0437216	−	0.0504574i
$512$	0.479249	−	0.877679i	0.0211800	−	0.0387883i
$513$	−0.562280	−	8.00026i	−0.0248253	−	0.353220i
$514$	6.51122	+	2.97358i	0.287198	+	0.131159i
$515$	−5.58346	+	0.657117i	−0.246037	+	0.0289560i
$516$	−2.44608	−	4.24076i	−0.107683	−	0.186689i
$517$	−12.2063	+	16.3057i	−0.536832	+	0.717124i
$518$	−9.69981	+	12.9574i	−0.426185	+	0.569317i
$519$	−9.55876	−	16.5720i	−0.419583	−	0.727429i
$520$	0.339524	+	0.268022i	0.0148891	+	0.0117536i
$521$	−18.1753	−	8.30040i	−0.796276	−	0.363647i	−0.0246280	−	0.999697i	$-0.507840\pi$
$521$	−18.1753	−	8.30040i	−0.796276	−	0.363647i	−0.771648	+	0.636050i	$0.780567\pi$
$522$	−2.62732	−	22.1283i	−0.114995	−	0.968529i
$523$	10.5577	−	19.3350i	0.461657	−	0.845462i	−0.538339	−	0.842728i	$-0.680948\pi$
$523$	10.5577	−	19.3350i	0.461657	−	0.845462i	0.999996	−	0.00273378i	$-0.000870191\pi$
$524$	5.56772	+	6.42549i	0.243227	+	0.280699i
$525$	4.51012	−	18.2631i	0.196838	−	0.797069i
$526$	−9.78451	−	21.4251i	−0.426625	−	0.934178i
$527$	−2.22704	−	2.97497i	−0.0970112	−	0.129592i
$528$	−2.33672	+	2.12247i	−0.101693	+	0.0923685i
$529$	18.2015	+	14.0608i	0.791370	+	0.611337i
$530$	−0.905471	−	19.7774i	−0.0393311	−	0.859075i
$531$	37.9742	+	9.24549i	1.64794	+	0.401220i
$532$	1.17164	−	3.14129i	0.0507971	−	0.136192i
$533$	−0.857552	−	1.57049i	−0.0371447	−	0.0680254i
$534$	−13.7409	−	17.4878i	−0.594629	−	0.756772i
$535$	0.305059	+	0.148886i	0.0131888	+	0.00643690i
$536$	−1.60871	+	2.50320i	−0.0694857	+	0.108122i
$537$	−28.3690	+	9.05575i	−1.22421	+	0.390784i
$538$	2.01784	+	28.2131i	0.0869953	+	1.21635i
$539$	−3.49814	+	2.24812i	−0.150676	+	0.0968334i
$540$	−8.57334	−	7.84206i	−0.368938	−	0.337469i
$541$	0.680720	+	4.73451i	0.0292665	+	0.203553i	0.999208	−	0.0397842i	$-0.0126670\pi$
$541$	0.680720	+	4.73451i	0.0292665	+	0.203553i	−0.969942	+	0.243337i	$0.921758\pi$
$542$	−1.68744	+	7.75703i	−0.0724817	+	0.333193i
$543$	2.32300	−	0.0543429i	0.0996897	−	0.00233208i
$544$	1.79882	+	0.821494i	0.0771238	+	0.0352213i
$545$	−12.7761	−	7.40783i	−0.547269	−	0.317317i
$546$	−0.707379	+	0.171301i	−0.0302730	+	0.00733099i
$547$	1.91380	−	26.7584i	0.0818281	−	1.14411i	−0.776194	−	0.630494i	$-0.782852\pi$
$547$	1.91380	−	26.7584i	0.0818281	−	1.14411i	0.858022	−	0.513612i	$-0.171693\pi$
$548$	6.08395	+	11.1419i	0.259893	+	0.475959i
$549$	−21.7057	+	7.49244i	−0.926376	+	0.319770i
$550$	6.76563	−	6.10483i	0.288487	−	0.260311i
$551$			11.4646i			0.488408i
$552$	−3.05706	+	7.72363i	−0.130117	+	0.328739i
$553$	−9.54088	+	9.54088i	−0.405720	+	0.405720i
$554$	1.60102	−	11.1353i	0.0680208	−	0.473095i
$555$	−11.9291	−	26.2781i	−0.506362	−	1.11544i
$556$	−1.88706	−	0.554091i	−0.0800292	−	0.0234987i
$557$	35.3169	+	2.52591i	1.49642	+	0.107026i	0.795388	−	0.606101i	$-0.207267\pi$
$557$	35.3169	+	2.52591i	1.49642	+	0.107026i	0.701035	+	0.713127i	$0.252722\pi$
$558$	4.66622	+	3.16378i	0.197537	+	0.133933i
$559$	0.295614	−	0.459985i	0.0125032	−	0.0194553i
$560$	−1.90377	−	4.46854i	−0.0804491	−	0.188830i
$561$	−4.51619	−	4.30972i	−0.190674	−	0.181957i
$562$	−16.5714	−	3.60488i	−0.699020	−	0.152063i
$563$	26.5079	−	35.4104i	1.11717	−	1.49237i	0.268631	−	0.963243i	$-0.413429\pi$
$563$	26.5079	−	35.4104i	1.11717	−	1.49237i	0.848543	−	0.529126i	$-0.177480\pi$
$564$	−19.2700	+	1.83207i	−0.811413	+	0.0771442i
$565$	−6.53011	+	38.3989i	−0.274724	+	1.61545i
$566$	5.11571	+	4.43279i	0.215029	+	0.186324i
$567$	19.2844	−	3.21026i	0.809869	−	0.134818i
$568$	−5.09712	+	1.10881i	−0.213870	+	0.0465247i
$569$	44.3007	−	13.0079i	1.85718	−	0.545318i	0.857667	−	0.514206i	$-0.171913\pi$
$569$	44.3007	−	13.0079i	1.85718	−	0.545318i	0.999516	−	0.0311120i	$-0.00990485\pi$
$570$	3.90438	+	4.52651i	0.163536	+	0.189595i
$571$	24.3328	+	7.14476i	1.01830	+	0.298999i	0.747944	−	0.663762i	$-0.231041\pi$
$571$	24.3328	+	7.14476i	1.01830	+	0.298999i	0.270353	+	0.962761i	$0.412859\pi$
$572$	−0.330342	−	0.123211i	−0.0138123	−	0.00515172i
$573$	−1.53058	−	2.26343i	−0.0639409	−	0.0945563i
$574$			20.0924i			0.838641i
$575$	8.89819	−	22.2671i	0.371080	−	0.928601i
$576$	−2.98618	−	0.287622i	−0.124424	−	0.0119842i
$577$	−34.7170	+	25.9888i	−1.44529	+	1.08193i	−0.464785	+	0.885423i	$0.653868\pi$
$577$	−34.7170	+	25.9888i	−1.44529	+	1.08193i	−0.980503	+	0.196505i	$0.937041\pi$
$578$	4.57427	−	12.2641i	0.190265	−	0.510119i
$579$	39.8074	+	13.7958i	1.65434	+	0.573334i
$580$	11.4395	+	12.0419i	0.474999	+	0.500012i
$581$	5.20040	+	17.7109i	0.215749	+	0.734774i
$582$	1.52754	+	9.10684i	0.0633187	+	0.377491i
$583$	5.63926	+	15.1194i	0.233554	+	0.626183i
$584$	0.454995	−	0.525092i	0.0188278	−	0.0217285i
$585$	0.339215	−	1.25258i	0.0140248	−	0.0517877i
$586$	−1.21387	−	8.44266i	−0.0501445	−	0.348763i
$587$	−0.603988	−	0.452140i	−0.0249292	−	0.0186618i	0.586740	−	0.809775i	$-0.300411\pi$
$587$	−0.603988	−	0.452140i	−0.0249292	−	0.0186618i	−0.611670	+	0.791113i	$0.709502\pi$
$588$	−3.81669	−	1.02436i	−0.157398	−	0.0422439i
$589$	−2.19203	−	1.89941i	−0.0903211	−	0.0782637i
$590$	−26.8002	+	11.4179i	−1.10335	+	0.470069i
$591$	24.9047	+	17.7500i	1.02444	+	0.730137i
$592$	−6.53990	−	3.57105i	−0.268788	−	0.146769i
$593$	−3.33207	+	46.5885i	−0.136832	+	1.91316i	0.214189	+	0.976792i	$0.431289\pi$
$593$	−3.33207	+	46.5885i	−0.136832	+	1.91316i	−0.351021	+	0.936368i	$0.614165\pi$
$594$	8.60961	+	3.94471i	0.353257	+	0.161853i
$595$	8.54558	−	4.38557i	0.350335	−	0.179791i
$596$	11.3923	+	1.63796i	0.466646	+	0.0670936i
$597$	−4.41777	+	4.01271i	−0.180807	+	0.164229i
$598$	−0.923158	+	0.0921813i	−0.0377508	+	0.00376957i
$599$	−9.38497			−0.383460			−0.191730	−	0.981448i	$-0.561410\pi$
$599$	−9.38497			−0.383460			−0.191730	+	0.981448i	$0.561410\pi$
$600$	8.61758	+	0.858620i	0.351811	+	0.0350530i
$601$	−9.37870	−	20.5365i	−0.382565	−	0.837701i	−0.998744	−	0.0500948i	$-0.984048\pi$
$601$	−9.37870	−	20.5365i	−0.382565	−	0.837701i	0.616179	−	0.787606i	$-0.288680\pi$
$602$	−5.38871	+	2.94246i	−0.219628	+	0.119926i
$603$	8.80187	+	1.48755i	0.358440	+	0.0605775i
$604$	−5.50254	−	18.7399i	−0.223895	−	0.762517i
$605$	8.61207	−	14.8531i	0.350130	−	0.603862i
$606$	−17.8369	−	9.20484i	−0.724575	−	0.373921i
$607$	−3.65362	+	0.261312i	−0.148296	+	0.0106063i	−0.145290	−	0.989389i	$-0.546411\pi$
$607$	−3.65362	+	0.261312i	−0.148296	+	0.0106063i	−0.00300618	+	0.999995i	$0.500957\pi$
$608$	1.50818	+	0.328084i	0.0611646	+	0.0133055i
$609$	−27.8210	+	2.64505i	−1.12736	+	0.107183i
$610$	9.61938	−	14.1562i	0.389477	−	0.573166i
$611$	−1.16883	−	1.81873i	−0.0472857	−	0.0735780i
$612$	0.146055	−	5.93078i	0.00590392	−	0.239738i
$613$	14.4099	+	38.6344i	0.582009	+	1.56043i	0.809793	+	0.586715i	$0.199579\pi$
$613$	14.4099	+	38.6344i	0.582009	+	1.56043i	−0.227784	+	0.973712i	$0.573148\pi$
$614$	−7.06159	−	4.53821i	−0.284983	−	0.183147i
$615$	−31.4034	−	17.2398i	−1.26631	−	0.695175i
$616$	2.59256	+	2.99198i	0.104457	+	0.120550i
$617$	−24.2930	+	13.2650i	−0.977999	+	0.534028i	−0.886973	−	0.461821i	$-0.847196\pi$
$617$	−24.2930	+	13.2650i	−0.977999	+	0.534028i	−0.0910257	+	0.995849i	$0.529015\pi$
$618$	4.00247	+	1.71591i	0.161003	+	0.0690238i
$619$	0.868284	+	0.124840i	0.0348993	+	0.00501776i	0.159742	−	0.987159i	$-0.448934\pi$
$619$	0.868284	+	0.124840i	0.0348993	+	0.00501776i	−0.124843	+	0.992176i	$0.539843\pi$
$620$	−4.19766	+	0.192182i	−0.168582	+	0.00771821i
$621$	24.9109	−	0.670066i	0.999638	−	0.0268888i
$622$	15.7985	+	15.7985i	0.633461	+	0.633461i
$623$	−22.3288	+	16.7152i	−0.894586	+	0.669679i
$624$	−0.124403	−	0.311114i	−0.00498010	−	0.0124545i
$625$	−24.8685	−	2.56037i	−0.994742	−	0.102415i
$626$	−23.7289	+	20.5612i	−0.948399	+	0.821793i
$627$	−4.15932	−	2.53758i	−0.166107	−	0.101341i
$628$	0.0849046	−	0.0184699i	0.00338806	−	0.000737028i
$629$	6.12125	−	13.4037i	0.244070	−	0.534439i
$630$	−10.0837	+	10.5190i	−0.401742	+	0.419089i
$631$	−32.5351	+	20.9090i	−1.29520	+	0.832374i	−0.992681	−	0.120769i	$-0.961464\pi$
$631$	−32.5351	+	20.9090i	−1.29520	+	0.832374i	−0.302519	+	0.953143i	$0.597828\pi$
$632$	−4.97265	−	3.72248i	−0.197801	−	0.148072i
$633$	−13.4520	+	16.2786i	−0.534668	+	0.647015i
$634$	5.05567	+	7.86677i	0.200786	+	0.312429i
$635$	0.529875	+	4.50230i	0.0210274	+	0.178668i
$636$	−7.03276	+	13.6279i	−0.278867	+	0.540381i
$637$	−0.0938186	−	0.431277i	−0.00371723	−	0.0170878i
$638$	−11.8818	−	6.48796i	−0.470405	−	0.256861i
$639$	9.06683	+	12.7547i	0.358678	+	0.504570i
$640$	1.91148	−	1.16027i	0.0755581	−	0.0458637i
$641$	30.5888	−	13.9694i	1.20818	−	0.551759i	0.293511	−	0.955956i	$-0.405176\pi$
$641$	30.5888	−	13.9694i	1.20818	−	0.551759i	0.914672	+	0.404197i	$0.132449\pi$
$642$	−0.147290	−	0.217813i	−0.00581306	−	0.00859639i
$643$	−14.0717	+	14.0717i	−0.554933	+	0.554933i	−0.927860	−	0.372928i	$-0.878354\pi$
$643$	−14.0717	+	14.0717i	−0.554933	+	0.554933i	0.372928	+	0.927860i	$0.378354\pi$
$644$	9.59404	+	4.05940i	0.378058	+	0.159963i
$645$	0.0247355	−	10.9470i	0.000973959	−	0.431037i
$646$	−0.434375	+	3.02114i	−0.0170902	+	0.118865i
$647$	−41.2120	−	15.3713i	−1.62021	−	0.604308i	−0.634526	−	0.772902i	$-0.718805\pi$
$647$	−41.2120	−	15.3713i	−1.62021	−	0.604308i	−0.985686	+	0.168594i	$0.946077\pi$
$648$	2.72629	+	8.57714i	0.107099	+	0.336942i
$649$	17.9445	−	15.5490i	0.704382	−	0.610351i
$650$	0.356166	+	0.899283i	0.0139700	+	0.0352728i
$651$	4.10353	−	5.75760i	0.160830	−	0.225658i
$652$	14.4005	−	5.37109i	0.563965	−	0.210348i
$653$	−12.2655	+	0.877242i	−0.479984	+	0.0343292i	−0.309236	−	0.950985i	$-0.600073\pi$
$653$	−12.2655	+	0.877242i	−0.479984	+	0.0343292i	−0.170749	+	0.985315i	$0.554619\pi$
$654$	5.71570	+	9.90929i	0.223502	+	0.387484i
$655$	3.56341	+	18.6744i	0.139234	+	0.729670i
$656$	−9.15565	+	1.31638i	−0.357468	+	0.0513962i
$657$	−1.98489	−	0.636300i	−0.0774381	−	0.0248244i
$658$	1.73182	+	24.2140i	0.0675134	+	0.943960i
$659$	−9.01838	+	19.7475i	−0.351306	+	0.769253i	0.648661	+	0.761078i	$0.275329\pi$
$659$	−9.01838	+	19.7475i	−0.351306	+	0.769253i	−0.999967	+	0.00817505i	$0.997398\pi$
$660$	−6.90078	+	1.48485i	−0.268613	+	0.0577978i
$661$	21.1579	−	6.21252i	0.822947	−	0.241639i	0.156962	−	0.987605i	$-0.449830\pi$
$661$	21.1579	−	6.21252i	0.822947	−	0.241639i	0.665984	+	0.745966i	$0.268012\pi$
$662$	−27.3818	−	1.95839i	−1.06422	−	0.0761148i
$663$	0.596118	−	0.289273i	0.0231513	−	0.0112344i
$664$	−7.72976	+	3.53006i	−0.299973	+	0.136993i
$665$	5.78976	−	4.76245i	0.224517	−	0.184680i
$666$	−2.14317	+	22.2511i	−0.0830463	+	0.862212i
$667$	−35.5896	−	1.54111i	−1.37804	−	0.0596721i
$668$	−7.94410	−	7.94410i	−0.307366	−	0.307366i
$669$	5.16110	−	26.7192i	0.199539	−	1.03303i
$670$	−5.91955	+	3.03790i	−0.228692	+	0.117364i
$671$	−3.93020	+	13.3850i	−0.151724	+	0.516723i
$672$	−0.448199	+	3.73557i	−0.0172896	+	0.144103i
$673$	−0.628033	+	1.15016i	−0.0242089	+	0.0443353i	−0.889503	−	0.456928i	$-0.848950\pi$
$673$	−0.628033	+	1.15016i	−0.0242089	+	0.0443353i	0.865295	+	0.501264i	$0.167131\pi$
$674$	0.762672	+	0.490139i	0.0293770	+	0.0188795i
$675$	−7.78869	−	24.7858i	−0.299787	−	0.954006i
$676$	−8.48868	+	9.79646i	−0.326488	+	0.376787i
$677$	1.05304	−	4.84073i	0.0404715	−	0.186044i	−0.952473	−	0.304622i	$-0.901470\pi$
$677$	1.05304	−	4.84073i	0.0404715	−	0.186044i	0.992945	+	0.118578i	$0.0378335\pi$
$678$	19.2189	−	23.2573i	0.738098	−	0.893191i
$679$	11.4627	−	1.64809i	0.439900	−	0.0632481i
$680$	2.55828	+	3.60670i	0.0981056	+	0.138310i
$681$	−7.70030	+	8.06920i	−0.295076	+	0.309212i
$682$	3.20903	−	1.19691i	0.122880	−	0.0458319i
$683$	−7.22260	−	33.2018i	−0.276365	−	1.27043i	−0.880690	−	0.473692i	$-0.842921\pi$
$683$	−7.22260	−	33.2018i	−0.276365	−	1.27043i	0.604325	−	0.796738i	$-0.293443\pi$
$684$	−0.872562	−	4.54739i	−0.0333633	−	0.173874i
$685$	−0.727992	+	28.3770i	−0.0278151	+	1.08423i
$686$	−5.68012	+	19.3447i	−0.216868	+	0.738584i
$687$	−6.74297	−	2.89079i	−0.257260	−	0.110290i
$688$	−1.69386	−	2.26273i	−0.0645779	−	0.0862659i
$689$	−1.71280			−0.0652523
$690$	−14.5765	+	11.5119i	−0.554920	+	0.438251i
$691$	−38.4084			−1.46112			−0.730562	−	0.682846i	$-0.760742\pi$
$691$	−38.4084			−1.46112			−0.730562	+	0.682846i	$0.760742\pi$
$692$	−6.61924	−	8.84227i	−0.251626	−	0.336133i
$693$	5.19830	−	10.6788i	0.197467	−	0.405655i
$694$	3.82622	−	13.0309i	0.145241	−	0.494647i
$695$	−3.02890	−	3.18840i	−0.114893	−	0.120943i
$696$	−3.02802	−	12.5041i	−0.114777	−	0.473966i
$697$	−3.88819	−	17.8737i	−0.147276	−	0.677015i
$698$	4.76767	−	1.77825i	0.180459	−	0.0673078i
$699$	10.4822	+	10.0029i	0.396472	+	0.378346i
$700$	1.32927	−	10.7793i	0.0502418	−	0.407421i
$701$	−25.3503	+	3.64482i	−0.957466	+	0.137663i	−0.603295	−	0.797518i	$-0.706146\pi$
$701$	−25.3503	+	3.64482i	−0.957466	+	0.137663i	−0.354171	+	0.935181i	$0.615237\pi$
$702$	−0.711653	+	0.709901i	−0.0268596	+	0.0267935i
$703$	2.44467	−	11.2380i	0.0922024	−	0.423847i
$704$	−1.19352	+	1.37740i	−0.0449825	+	0.0519125i
$705$	−39.3312	−	18.0695i	−1.48130	−	0.680535i
$706$	2.59162	+	1.66553i	0.0975368	+	0.0626831i
$707$	−12.0640	+	22.0935i	−0.453713	+	0.830912i
$708$	22.4042	+	2.68808i	0.842001	+	0.101024i
$709$	5.20210	−	17.7167i	0.195369	−	0.665365i	−0.802287	−	0.596938i	$-0.796384\pi$
$709$	5.20210	−	17.7167i	0.195369	−	0.665365i	0.997656	−	0.0684270i	$-0.0217980\pi$
$710$	−11.1036	−	3.57209i	−0.416712	−	0.134058i
$711$	−4.40820	+	18.1059i	−0.165321	+	0.679025i
$712$	−9.07963	−	9.07963i	−0.340273	−	0.340273i
$713$	6.19101	−	6.54942i	0.231855	−	0.245278i
$714$	−7.43159	−	0.357071i	−0.278120	−	0.0133630i
$715$	−0.500825	−	0.608858i	−0.0187298	−	0.0227700i
$716$	−15.6394	+	7.14227i	−0.584472	+	0.266919i
$717$	−18.2838	−	37.6781i	−0.682820	−	1.40711i
$718$	−27.3613	−	1.95692i	−1.02112	−	0.0730317i
$719$	−20.2360	+	5.94183i	−0.754676	+	0.221593i	−0.636370	−	0.771384i	$-0.719565\pi$
$719$	−20.2360	+	5.94183i	−0.754676	+	0.221593i	−0.118306	+	0.992977i	$0.537746\pi$
$720$	−5.45393	−	3.90572i	−0.203256	−	0.145558i
$721$	2.26876	−	4.96788i	0.0844929	−	0.185014i
$722$	−1.18550	−	16.5754i	−0.0441197	−	0.616874i
$723$	23.9309	+	6.42280i	0.889999	+	0.238867i
$724$	1.32790	−	0.190923i	0.0493510	−	0.00709560i
$725$	8.62246	+	36.1247i	0.320230	+	1.34164i
$726$	−11.5202	+	6.64486i	−0.427554	+	0.246614i
$727$	33.7424	−	2.41331i	1.25144	−	0.0895046i	0.570163	−	0.821532i	$-0.306880\pi$
$727$	33.7424	−	2.41331i	1.25144	−	0.0895046i	0.681275	+	0.732027i	$0.261426\pi$
$728$	−0.393716	+	0.146848i	−0.0145921	+	0.00544256i
$729$	20.4488	−	17.6309i	0.757362	−	0.652996i
$730$	1.46910	−	0.505422i	0.0543739	−	0.0187065i
$731$	4.22425	−	3.66034i	0.156240	−	0.135382i
$732$	−11.9272	+	5.78783i	−0.440843	+	0.213924i
$733$	35.7458	+	13.3325i	1.32030	+	0.492447i	0.908141	−	0.418664i	$-0.137502\pi$
$733$	35.7458	+	13.3325i	1.32030	+	0.492447i	0.412160	+	0.911111i	$0.364774\pi$
$734$	3.09115	−	21.4994i	0.114096	−	0.793557i
$735$	−6.23415	−	6.26238i	−0.229950	−	0.230992i
$736$	−1.22121	+	4.63774i	−0.0450143	+	0.170949i
$737$	3.83473	−	3.83473i	0.141254	−	0.141254i
$738$	14.4232	+	23.7066i	0.530925	+	0.872651i
$739$	−48.1240	+	21.9775i	−1.77027	+	0.808454i	−0.789374	+	0.613913i	$0.789595\pi$
$739$	−48.1240	+	21.9775i	−1.77027	+	0.808454i	−0.980894	+	0.194542i	$0.937678\pi$
$740$	−8.64558	−	14.2432i	−0.317818	−	0.523589i
$741$	0.406641	−	0.319516i	0.0149383	−	0.0117377i
$742$	16.8801	+	9.21721i	0.619687	+	0.338375i
$743$	−5.41546	−	24.8945i	−0.198674	−	0.913289i	−0.963219	−	0.268719i	$-0.913400\pi$
$743$	−5.41546	−	24.8945i	−0.198674	−	0.913289i	0.764545	−	0.644571i	$-0.222964\pi$
$744$	2.89246	+	1.49267i	0.106043	+	0.0547239i
$745$	20.2003	+	15.9462i	0.740083	+	0.584225i
$746$	9.31613	+	14.4962i	0.341088	+	0.530743i
$747$	18.8495	+	17.1636i	0.689667	+	0.627985i
$748$	−2.88527	−	2.15989i	−0.105496	−	0.0789733i
$749$	−0.277409	+	0.178280i	−0.0101363	+	0.00651420i
$750$	15.7070	+	11.3265i	0.573539	+	0.413586i
$751$	−18.5547	+	40.6291i	−0.677071	+	1.48258i	0.188647	+	0.982045i	$0.439590\pi$
$751$	−18.5547	+	40.6291i	−0.677071	+	1.48258i	−0.865718	+	0.500533i	$0.833137\pi$
$752$	−10.9203	+	2.37557i	−0.398223	+	0.0866280i
$753$	5.93688	−	9.73106i	0.216352	−	0.354620i
$754$	1.08595	−	0.940983i	0.0395481	−	0.0342686i
$755$	10.3747	−	42.4226i	0.377574	−	1.54392i
$756$	10.8338	−	3.16659i	0.394021	−	0.115168i
$757$	−31.7233	+	23.7478i	−1.15300	+	0.863128i	−0.992298	−	0.123874i	$-0.960468\pi$
$757$	−31.7233	+	23.7478i	−1.15300	+	0.863128i	−0.160707	+	0.987002i	$0.551377\pi$
$758$	3.36560	+	3.36560i	0.122244	+	0.122244i
$759$	8.43655	−	12.5707i	0.306227	−	0.456287i
$760$	2.54946	+	2.32624i	0.0924788	+	0.0843816i
$761$	32.0031	+	4.60135i	1.16011	+	0.166799i	0.695372	−	0.718649i	$-0.255239\pi$
$761$	32.0031	+	4.60135i	1.16011	+	0.166799i	0.464738	+	0.885448i	$0.346148\pi$
$762$	1.38364	−	3.22744i	0.0501240	−	0.116918i
$763$	12.5917	−	6.87558i	0.455849	−	0.248913i
$764$	−1.03306	−	1.19222i	−0.0373749	−	0.0431329i
$765$	6.93457	−	11.3088i	0.250720	−	0.408871i
$766$	28.6757	+	18.4287i	1.03609	+	0.665857i
$767$	0.880728	+	2.36132i	0.0318012	+	0.0852624i
$768$	−1.73158	+	0.0405074i	−0.0624829	+	0.00146169i
$769$	7.77776	+	12.1024i	0.280473	+	0.436425i	0.952696	−	0.303924i	$-0.0982969\pi$
$769$	7.77776	+	12.1024i	0.280473	+	0.436425i	−0.672223	+	0.740348i	$0.734661\pi$
$770$	1.65927	+	8.69559i	0.0597960	+	0.313367i
$771$	−1.17345	−	12.3425i	−0.0422608	−	0.444505i
$772$	23.7680	+	5.17041i	0.855429	+	0.186087i
$773$	−22.1373	+	1.58329i	−0.796223	+	0.0569470i	−0.463522	−	0.886085i	$-0.653415\pi$
$773$	−22.1373	+	1.58329i	−0.796223	+	0.0569470i	−0.332701	+	0.943032i	$0.607960\pi$
$774$	−4.24579	+	7.33999i	−0.152612	+	0.263831i
$775$	−8.33559	−	4.33638i	−0.299423	−	0.155768i
$776$	1.50200	+	5.11533i	0.0539186	+	0.183630i
$777$	27.8350	+	3.33969i	0.998577	+	0.119811i
$778$	−19.8852	+	10.8582i	−0.712920	+	0.389284i
$779$	−5.93071	−	12.9864i	−0.212490	−	0.465288i
$780$	0.108301	−	0.741356i	0.00387781	−	0.0265448i
$781$	9.50705			0.340189
$782$	−9.32017	−	1.75455i	−0.333289	−	0.0627425i
$783$	−30.9266	+	23.0919i	−1.10523	+	0.825238i
$784$	−2.25833	−	0.324698i	−0.0806545	−	0.0115964i
$785$	0.184957	+	0.0595015i	0.00660141	+	0.00212370i
$786$	4.82217	−	13.9142i	0.172001	−	0.496304i
$787$	0.715081	−	9.99814i	0.0254899	−	0.356395i	−0.968660	−	0.248389i	$-0.920099\pi$
$787$	0.715081	−	9.99814i	0.0254899	−	0.356395i	0.994150	−	0.108006i	$-0.0344466\pi$
$788$	15.4972	+	8.46209i	0.552063	+	0.301449i
$789$	−23.6777	+	33.2217i	−0.842947	+	1.18272i
$790$	−5.44402	−	12.7782i	−0.193690	−	0.454629i
$791$	−28.5958	−	24.7784i	−1.01675	−	0.881018i
$792$	5.20667	+	1.66911i	0.185011	+	0.0593092i
$793$	−1.18535	−	0.887343i	−0.0420931	−	0.0315105i
$794$	−0.927476	−	6.45074i	−0.0329149	−	0.228928i
$795$	−28.8895	+	18.4741i	−1.02461	+	0.655208i
$796$	−2.25645	+	2.60409i	−0.0799779	+	0.0922994i
$797$	15.5781	+	41.7664i	0.551803	+	1.47944i	0.850957	+	0.525236i	$0.176023\pi$
$797$	15.5781	+	41.7664i	0.551803	+	1.47944i	−0.299154	+	0.954205i	$0.596704\pi$
$798$	−5.72700	+	0.960623i	−0.202734	+	0.0340057i
$799$	−6.22636	−	21.2050i	−0.220273	−	0.750180i
$800$	4.99899	−	0.100506i	0.176741	−	0.00355341i
$801$	−14.3464	+	35.7504i	−0.506905	+	1.26318i
$802$	3.96446	−	10.6291i	0.139990	−	0.375328i
$803$	−1.01373	+	0.758869i	−0.0357738	+	0.0267799i
$804$	5.14789	+	0.247344i	0.181552	+	0.00872314i
$805$	14.0058	+	18.6134i	0.493641	+	0.656036i
$806$			0.363533i			0.0128049i
$807$	40.5834	−	27.4433i	1.42860	−	0.966051i
$808$	−10.8579	−	4.04979i	−0.381980	−	0.142471i
$809$	32.0629	+	9.41452i	1.12727	+	0.330997i	0.791635	−	0.610995i	$-0.209230\pi$
$809$	32.0629	+	9.41452i	1.12727	+	0.330997i	0.335637	+	0.941991i	$0.391049\pi$
$810$	−4.34644	+	19.6496i	−0.152718	+	0.690418i
$811$	−14.2683	+	4.18955i	−0.501028	+	0.147115i	−0.522474	−	0.852655i	$-0.674991\pi$
$811$	−14.2683	+	4.18955i	−0.501028	+	0.147115i	0.0214466	+	0.999770i	$0.493173\pi$
$812$	−15.7662	+	3.42972i	−0.553283	+	0.120359i
$813$	13.0986	−	4.18125i	0.459389	−	0.146643i
$814$	10.2635	+	8.89334i	0.359734	+	0.311711i
$815$	33.8808	+	5.76177i	1.18679	+	0.201826i
$816$	−0.324183	−	3.40980i	−0.0113487	−	0.119367i
$817$	2.61439	−	3.49241i	0.0914658	−	0.122184i
$818$	−28.9065	−	6.28822i	−1.01069	−	0.219862i
$819$	0.869184	+	0.913075i	0.0303718	+	0.0319054i
$820$	−19.1874	−	7.72265i	−0.670052	−	0.269687i
$821$	22.7108	−	35.3387i	0.792613	−	1.23333i	−0.175911	−	0.984406i	$-0.556287\pi$
$821$	22.7108	−	35.3387i	0.792613	−	1.23333i	0.968523	−	0.248923i	$-0.0800767\pi$
$822$	11.4517	−	18.7704i	0.399425	−	0.654693i
$823$	−7.49500	−	0.536053i	−0.261259	−	0.0186856i	−0.0599050	−	0.998204i	$-0.519080\pi$
$823$	−7.49500	−	0.536053i	−0.261259	−	0.0186856i	−0.201354	+	0.979518i	$0.564534\pi$
$824$	2.41239	+	0.708342i	0.0840396	+	0.0246763i
$825$	−15.0145	−	4.86768i	−0.522736	−	0.169471i
$826$	4.02737	−	28.0110i	0.140130	−	0.974627i
$827$	35.2683	−	35.2683i	1.22640	−	1.22640i	0.261085	−	0.965316i	$-0.415920\pi$
$827$	35.2683	−	35.2683i	1.22640	−	1.22640i	0.965316	−	0.261085i	$-0.0840802\pi$
$828$	14.2338	−	2.09743i	0.494658	−	0.0728906i
$829$		−	6.50347i		−	0.225875i	−0.993602	−	0.112937i	$-0.963974\pi$
$829$		−	6.50347i		−	0.225875i	0.993602	−	0.112937i	$-0.0360259\pi$
$830$	−18.9120	−	1.84116i	−0.656444	−	0.0639077i
$831$	−18.0925	+	7.23452i	−0.627621	+	0.250963i
$832$	−0.0927103	−	0.169786i	−0.00321415	−	0.00588628i
$833$	0.321870	−	4.50033i	0.0111521	−	0.155927i
$834$	0.801746	+	3.31078i	0.0277622	+	0.114643i
$835$	−6.45704	−	24.2774i	−0.223455	−	0.840155i
$836$	−2.55881	−	1.16857i	−0.0884984	−	0.0404159i
$837$	0.708609	−	9.73895i	0.0244931	−	0.336627i
$838$	5.68853	−	26.1498i	0.196507	−	0.903329i
$839$	−5.12147	−	35.6206i	−0.176813	−	1.22976i	−0.864080	−	0.503355i	$-0.832099\pi$
$839$	−5.12147	−	35.6206i	−0.176813	−	1.22976i	0.687267	−	0.726405i	$-0.258810\pi$
$840$	−5.05686	+	6.72346i	−0.174478	+	0.231981i
$841$	22.0187	−	14.1506i	0.759267	−	0.487951i
$842$	2.32996	+	32.5771i	0.0802957	+	1.12268i
$843$	8.93240	+	27.9826i	0.307648	+	0.963773i
$844$	−6.59158	+	10.2567i	−0.226892	+	0.353050i
$845$	−27.4085	+	9.42948i	−0.942882	+	0.324384i
$846$	19.4252	+	27.3263i	0.667852	+	0.939499i
$847$	7.99329	+	14.6386i	0.274653	+	0.502989i
$848$	−3.09415	+	8.29574i	−0.106254	+	0.284877i
$849$	2.22358	−	11.5116i	0.0763129	−	0.395076i
$850$	0.903479	+	9.84627i	0.0309891	+	0.337724i
$851$	34.5575	+	9.09965i	1.18461	+	0.311932i
$852$	6.07471	+	6.68792i	0.208116	+	0.229124i
$853$	−26.3687	−	35.2245i	−0.902848	−	1.20606i	−0.977940	−	0.208887i	$-0.933016\pi$
$853$	−26.3687	−	35.2245i	−0.902848	−	1.20606i	0.0750917	−	0.997177i	$-0.476075\pi$
$854$	6.90682	+	15.1238i	0.236347	+	0.517527i
$855$	3.41250	−	9.77524i	0.116705	−	0.334306i
$856$	−0.0994129	−	0.114729i	−0.00339786	−	0.00392134i
$857$	11.8248	−	21.6555i	0.403927	−	0.739736i	−0.593975	−	0.804483i	$-0.702442\pi$
$857$	11.8248	−	21.6555i	0.403927	−	0.739736i	0.997902	+	0.0647472i	$0.0206241\pi$
$858$	0.101020	+	0.602259i	0.00344878	+	0.0205608i
$859$	−37.5902	−	17.1669i	−1.28256	−	0.585726i	−0.346661	−	0.937991i	$-0.612685\pi$
$859$	−37.5902	−	17.1669i	−1.28256	−	0.585726i	−0.935901	+	0.352264i	$0.885412\pi$
$860$	−0.738732	−	6.27694i	−0.0251906	−	0.214042i
$861$	30.1458	−	17.3882i	1.02737	−	0.592587i
$862$	−4.41364	+	5.89593i	−0.150329	+	0.200816i
$863$	26.5624	−	35.4832i	0.904193	−	1.20786i	−0.0733885	−	0.997303i	$-0.523381\pi$
$863$	26.5624	−	35.4832i	0.904193	−	1.20786i	0.977582	−	0.210557i	$-0.0675278\pi$
$864$	2.15273	+	4.72924i	0.0732374	+	0.160892i
$865$	−2.88680	−	24.5289i	−0.0981543	−	0.834008i
$866$	27.3746	+	12.5016i	0.930228	+	0.424821i
$867$	−22.3591	+	3.75043i	−0.759356	+	0.127371i
$868$	1.95631	−	3.58271i	0.0664015	−	0.121605i
$869$	7.41368	+	8.55584i	0.251492	+	0.290237i
$870$	8.16727	−	27.5844i	0.276896	−	0.935200i
$871$	0.239121	+	0.523602i	0.00810231	+	0.0177416i
$872$	3.95801	+	5.28728i	0.134035	+	0.179050i
$873$	12.3415	−	10.1730i	0.417698	−	0.344304i
$874$	−7.39919	+	0.208154i	−0.250281	+	0.00704091i
$875$	14.6616	−	19.3609i	0.495653	−	0.654517i
$876$	−1.18158	−	0.228235i	−0.0399220	−	0.00771134i
$877$	5.92733	−	15.8918i	0.200152	−	0.536627i	−0.797634	−	0.603142i	$-0.793915\pi$
$877$	5.92733	−	15.8918i	0.200152	−	0.536627i	0.997785	+	0.0665148i	$0.0211880\pi$
$878$	3.06417	+	5.61160i	0.103411	+	0.189382i
$879$	−11.6165	+	9.12759i	−0.391815	+	0.307866i
$880$	−3.85367	+	1.32580i	−0.129907	+	0.0446926i
$881$	−1.57546	+	2.45147i	−0.0530786	+	0.0825920i	−0.866779	−	0.498693i	$-0.833813\pi$
$881$	−1.57546	+	2.45147i	−0.0530786	+	0.0825920i	0.813700	+	0.581285i	$0.197450\pi$
$882$	1.76609	+	6.61288i	0.0594674	+	0.222667i
$883$	0.739397	+	10.3381i	0.0248827	+	0.347905i	0.994608	+	0.103707i	$0.0330704\pi$
$883$	0.739397	+	10.3381i	0.0248827	+	0.347905i	−0.969725	+	0.244199i	$0.921475\pi$
$884$	0.321822	−	0.206823i	0.0108241	−	0.00695620i
$885$	40.3241	+	30.3287i	1.35548	+	1.01949i
$886$	−3.26965	−	22.7409i	−0.109846	−	0.763996i
$887$	−4.21201	+	19.3623i	−0.141425	+	0.650122i	0.850781	+	0.525520i	$0.176129\pi$
$887$	−4.21201	+	19.3623i	−0.141425	+	0.650122i	−0.992207	+	0.124602i	$0.960235\pi$
$888$	0.301835	+	12.9026i	0.0101289	+	0.432983i
$889$	−4.00591	−	1.82944i	−0.134354	−	0.0613574i
$890$	−7.38000	−	27.7476i	−0.247378	−	0.930103i
$891$	−1.53237	−	16.3313i	−0.0513363	−	0.547118i
$892$	1.12085	−	15.6715i	0.0375287	−	0.524720i
$893$	−8.26662	−	15.1392i	−0.276632	−	0.506614i
$894$	−7.40146	−	18.5100i	−0.247542	−	0.619067i
$895$	−38.2640	−	3.72517i	−1.27903	−	0.124519i
$896$			2.17220i			0.0725681i
$897$	0.937215	+	1.30529i	0.0312927	+	0.0435824i
$898$	23.9543	−	23.9543i	0.799366	−	0.799366i
$899$	−1.98652	+	13.8166i	−0.0662542	+	0.460808i
$900$	−6.16950	−	13.6725i	−0.205650	−	0.455750i
$901$	−16.7998	−	4.93285i	−0.559681	−	0.164337i
$902$	16.8153	+	1.20266i	0.559889	+	0.0400441i
$903$	9.07818	+	5.53856i	0.302103	+	0.184312i
$904$	9.41744	−	14.6538i	0.313220	−	0.487379i
$905$	2.78286	+	1.12006i	0.0925053	+	0.0372321i
$906$	−23.3546	+	24.4735i	−0.775905	+	0.813077i
$907$	24.3231	+	5.29117i	0.807636	+	0.175691i	0.597383	−	0.801956i	$-0.296207\pi$
$907$	24.3231	+	5.29117i	0.807636	+	0.175691i	0.210254	+	0.977647i	$0.432571\pi$
$908$	−3.85913	+	5.15519i	−0.128070	+	0.171081i
$909$	1.62568	+	34.7277i	0.0539205	+	1.15184i
$910$	−0.926319	−	0.157530i	−0.0307072	−	0.00522206i
$911$	2.43969	+	2.11401i	0.0808306	+	0.0700401i	0.694339	−	0.719648i	$-0.255697\pi$
$911$	2.43969	+	2.11401i	0.0808306	+	0.0700401i	−0.613508	+	0.789688i	$0.710242\pi$
$912$	−0.812947	−	2.54673i	−0.0269194	−	0.0843305i
$913$	15.1335	−	3.29210i	0.500847	−	0.108953i
$914$	0.148723	−	0.0436689i	0.00491931	−	0.00144444i
$915$	−29.5640	−	2.18161i	−0.977355	−	0.0721219i
$916$	−4.06415	−	1.19334i	−0.134283	−	0.0394292i
$917$	−17.3039	−	6.45403i	−0.571426	−	0.213131i
$918$	−9.02468	+	4.91342i	−0.297859	+	0.162167i
$919$			3.51731i			0.116025i	0.998316	+	0.0580126i	$0.0184764\pi$
$919$			3.51731i			0.116025i	−0.998316	+	0.0580126i	$0.981524\pi$
$920$	−7.56408	+	7.60163i	−0.249380	+	0.250618i
$921$	−0.697762	+	14.5223i	−0.0229920	+	0.478526i
$922$	−10.6369	+	7.96271i	−0.350309	+	0.262238i
$923$	−0.352642	+	0.945471i	−0.0116074	+	0.0311206i
$924$	2.24540	−	6.47905i	0.0738683	−	0.213145i
$925$	−0.748903	−	37.2493i	−0.0246238	−	1.22475i
$926$	−1.16660	−	3.97309i	−0.0383370	−	0.130564i
$927$	−0.889309	−	7.49009i	−0.0292087	−	0.246007i
$928$	−2.59579	−	6.95957i	−0.0852108	−	0.228459i
$929$	−19.5361	+	22.5458i	−0.640958	+	0.739705i	−0.979544	−	0.201231i	$-0.935506\pi$
$929$	−19.5361	+	22.5458i	−0.640958	+	0.739705i	0.338586	+	0.940935i	$0.390051\pi$
$930$	3.92103	+	6.13166i	0.128576	+	0.201065i
$931$	−0.501155	−	3.48561i	−0.0164247	−	0.114236i
$932$	6.69676	+	5.01313i	0.219360	+	0.164211i
$933$	10.0312	−	37.3755i	0.328406	−	1.22362i
$934$	−15.3229	−	13.2774i	−0.501382	−	0.434450i
$935$	−3.15878	−	7.41429i	−0.103303	−	0.242473i
$936$	−0.359122	+	0.455889i	−0.0117383	+	0.0149012i
$937$	14.5422	+	7.94062i	0.475072	+	0.259409i	0.698899	−	0.715220i	$-0.253673\pi$
$937$	14.5422	+	7.94062i	0.475072	+	0.259409i	−0.223828	+	0.974629i	$0.571855\pi$
$938$	0.461102	−	6.44705i	0.0150555	−	0.210504i
$939$	51.3844	+	17.8080i	1.67687	+	0.581141i
$940$	−23.7889	−	7.65300i	−0.775909	−	0.249613i
$941$	−42.0226	−	6.04194i	−1.36990	−	0.196962i	−0.582212	−	0.813037i	$-0.697813\pi$
$941$	−42.0226	−	6.04194i	−1.36990	−	0.196962i	−0.787687	+	0.616075i	$0.788722\pi$
$942$	−0.101189	−	0.111403i	−0.00329690	−	0.00362971i
$943$	41.1112	−	16.6651i	1.33876	−	0.542690i
$944$	13.0278			0.424020
$945$	24.5088	+	6.02579i	0.797271	+	0.196019i
$946$	2.13999	+	4.68593i	0.0695772	+	0.152353i
$947$	−1.01975	+	0.556823i	−0.0331373	+	0.0180943i	−0.495732	−	0.868475i	$-0.665100\pi$
$947$	−1.01975	+	0.556823i	−0.0331373	+	0.0180943i	0.462595	+	0.886570i	$0.346918\pi$
$948$	−1.28167	+	10.6822i	−0.0416266	+	0.346942i
$949$	−0.0378671	−	0.128963i	−0.00122922	−	0.00418633i
$950$	2.32260	+	7.35944i	0.0753551	+	0.238772i
$951$	7.42774	−	14.3933i	0.240861	−	0.466734i
$952$	−4.28464	+	0.306443i	−0.138866	+	0.00993189i
$953$	−2.52510	−	0.549303i	−0.0817961	−	0.0177937i	0.171481	−	0.985187i	$-0.445145\pi$
$953$	−2.52510	−	0.549303i	−0.0817961	−	0.0177937i	−0.253277	+	0.967394i	$0.581508\pi$
$954$	26.5329	−	1.24207i	0.859034	−	0.0402134i
$955$	−0.661172	−	3.46495i	−0.0213950	−	0.112123i
$956$	−13.0724	−	20.3410i	−0.422791	−	0.657876i
$957$	0.548380	+	23.4417i	0.0177266	+	0.757762i
$958$	−13.3355	−	35.7537i	−0.430849	−	1.15515i
$959$	−23.1980	−	14.9085i	−0.749103	−	0.481419i
$960$	−3.39503	−	1.86380i	−0.109574	−	0.0601539i
$961$	17.9881	+	20.7593i	0.580260	+	0.669656i
$962$	−1.26514	+	0.690817i	−0.0407897	+	0.0222728i
$963$	−0.199331	+	0.409484i	−0.00642335	+	0.0131954i
$964$	14.1599	+	2.03588i	0.456059	+	0.0655713i
$965$	40.1781	+	36.6602i	1.29338	+	1.18014i
$966$	−2.21223	−	17.9075i	−0.0711772	−	0.576165i
$967$	−17.4807	−	17.4807i	−0.562142	−	0.562142i	0.367773	−	0.929916i	$-0.380120\pi$
$967$	−17.4807	−	17.4807i	−0.562142	−	0.562142i	−0.929916	+	0.367773i	$0.880120\pi$
$968$	−6.14679	+	4.60143i	−0.197565	+	0.147896i
$969$	4.90870	−	1.96281i	0.157690	−	0.0630545i
$970$	−2.83192	+	11.5799i	−0.0909276	+	0.371807i
$971$	14.9572	−	12.9605i	0.479999	−	0.415921i	−0.380963	−	0.924590i	$-0.624408\pi$
$971$	14.9572	−	12.9605i	0.479999	−	0.415921i	0.860962	+	0.508669i	$0.169862\pi$
$972$	10.5094	−	11.5131i	0.337089	−	0.369284i
$973$	4.17449	−	0.908105i	0.133828	−	0.0291125i
$974$	12.1105	−	26.5183i	0.388045	−	0.849700i
$975$	1.04101	−	1.31262i	0.0333392	−	0.0420376i
$976$	−6.43907	+	4.13814i	−0.206110	+	0.132459i
$977$	26.1913	+	19.6066i	0.837934	+	0.627269i	0.929620	−	0.368519i	$-0.120135\pi$
$977$	26.1913	+	19.6066i	0.837934	+	0.627269i	−0.0916868	+	0.995788i	$0.529226\pi$
$978$	−20.5208	−	16.9576i	−0.656184	−	0.542245i
$979$	12.6524	+	19.6875i	0.404372	+	0.629215i
$980$	−4.00437	−	3.16107i	−0.127915	−	0.100977i
$981$	9.92104	−	17.1512i	0.316754	−	0.547595i
$982$	−5.33084	−	24.5055i	−0.170114	−	0.782001i
$983$	6.40377	+	3.49672i	0.204248	+	0.111528i	0.578118	−	0.815953i	$-0.303787\pi$
$983$	6.40377	+	3.49672i	0.204248	+	0.111528i	−0.373869	+	0.927481i	$0.621969\pi$
$984$	9.89843	+	12.5975i	0.315550	+	0.401594i
$985$	20.4869	+	33.7511i	0.652766	+	1.07540i
$986$	13.3615	−	6.10198i	0.425516	−	0.194327i
$987$	34.8309	−	23.5534i	1.10868	−	0.749712i
$988$	0.211127	−	0.211127i	0.00671685	−	0.00671685i
$989$	10.4901	+	8.58533i	0.333566	+	0.272998i
$990$	8.19981	+	9.06863i	0.260607	+	0.288220i
$991$	−2.77044	+	19.2688i	−0.0880058	+	0.612094i	0.897316	+	0.441388i	$0.145514\pi$
$991$	−2.77044	+	19.2688i	−0.0880058	+	0.612094i	−0.985322	+	0.170706i	$0.945395\pi$
$992$	1.76073	+	0.656719i	0.0559033	+	0.0208508i
$993$	20.7582	+	42.7773i	0.658741	+	1.35750i
$994$	8.56333	−	7.42017i	0.271612	−	0.235353i
$995$	−7.28571	+	2.50654i	−0.230973	+	0.0794625i
$996$	11.9858	+	8.54244i	0.379783	+	0.270678i
$997$	−14.2709	+	5.32278i	−0.451965	+	0.168574i	−0.565130	−	0.825002i	$-0.691174\pi$
$997$	−14.2709	+	5.32278i	−0.451965	+	0.168574i	0.113165	+	0.993576i	$0.463901\pi$
$998$	−19.8093	+	1.41679i	−0.627052	+	0.0448476i
$999$	35.2393	−	16.0408i	1.11492	−	0.507508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.x.a.77.11	✓	960
3.2	odd	2	inner	690.2.x.a.77.40	yes	960
5.3	odd	4	inner	690.2.x.a.353.3	yes	960
15.8	even	4	inner	690.2.x.a.353.46	yes	960
23.3	even	11	inner	690.2.x.a.647.46	yes	960
69.26	odd	22	inner	690.2.x.a.647.3	yes	960
115.3	odd	44	inner	690.2.x.a.233.40	yes	960
345.233	even	44	inner	690.2.x.a.233.11	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.x.a.77.11	✓	960	1.1	even	1	trivial
690.2.x.a.77.40	yes	960	3.2	odd	2	inner
690.2.x.a.233.11	yes	960	345.233	even	44	inner
690.2.x.a.233.40	yes	960	115.3	odd	44	inner
690.2.x.a.353.3	yes	960	5.3	odd	4	inner
690.2.x.a.353.46	yes	960	15.8	even	4	inner
690.2.x.a.647.3	yes	960	69.26	odd	22	inner
690.2.x.a.647.46	yes	960	23.3	even	11	inner

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.599278 - 0.800541i) q^{2} +(-0.682476 + 1.59193i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-1.62117 + 1.54007i) q^{5} +(1.68339 - 0.407655i) q^{6} +(-0.461734 - 2.12256i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-2.06845 - 2.17290i) q^{9} +O(q^{10})\)	\(q+(-0.599278 - 0.800541i) q^{2} +(-0.682476 + 1.59193i) q^{3} +(-0.281733 + 0.959493i) q^{4} +(-1.62117 + 1.54007i) q^{5} +(1.68339 - 0.407655i) q^{6} +(-0.461734 - 2.12256i) q^{7} +(0.936950 - 0.349464i) q^{8} +(-2.06845 - 2.17290i) q^{9} +(2.20442 + 0.374883i) q^{10} +(-1.80400 + 0.259377i) q^{11} +(-1.33517 - 1.10333i) q^{12} +(0.0411206 - 0.189028i) q^{13} +(-1.42249 + 1.64164i) q^{14} +(-1.34527 - 3.63184i) q^{15} +(-0.841254 - 0.540641i) q^{16} +(0.947728 - 1.73563i) q^{17} +(-0.499921 + 2.95805i) q^{18} +(0.434840 - 1.48093i) q^{19} +(-1.02095 - 1.98939i) q^{20} +(3.69408 + 0.713549i) q^{21} +(1.28874 + 1.28874i) q^{22} +(4.53881 + 1.54895i) q^{23} +(-0.0831251 + 1.73005i) q^{24} +(0.256374 - 4.99342i) q^{25} +(-0.175968 + 0.0803617i) q^{26} +(4.87077 - 1.80987i) q^{27} +(2.16666 + 0.154963i) q^{28} +(-7.12702 + 2.09268i) q^{29} +(-2.10125 + 3.25342i) q^{30} +(0.780655 - 1.70940i) q^{31} +(0.0713392 + 0.997452i) q^{32} +(0.818282 - 3.04886i) q^{33} +(-1.95740 + 0.281431i) q^{34} +(4.01743 + 2.72992i) q^{35} +(2.66763 - 1.37249i) q^{36} +(7.43237 - 0.531574i) q^{37} +(-1.44613 + 0.539380i) q^{38} +(0.272855 + 0.194468i) q^{39} +(-0.980754 + 2.00951i) q^{40} +(6.99053 - 6.05733i) q^{41} +(-1.64255 - 3.38487i) q^{42} +(2.64829 + 0.987762i) q^{43} +(0.259377 - 1.80400i) q^{44} +(6.69973 + 0.337081i) q^{45} +(-1.48001 - 4.56175i) q^{46} +(7.90242 - 7.90242i) q^{47} +(1.43480 - 0.970238i) q^{48} +(2.07537 - 0.947790i) q^{49} +(-4.15108 + 2.78721i) q^{50} +(2.11620 + 2.69324i) q^{51} +(0.169786 + 0.0927103i) q^{52} +(-1.88205 - 8.65164i) q^{53} +(-4.36782 - 2.81464i) q^{54} +(2.52514 - 3.19878i) q^{55} +(-1.17438 - 1.82737i) q^{56} +(2.06076 + 1.70293i) q^{57} +(5.94634 + 4.45138i) q^{58} +(-10.9597 + 7.04338i) q^{59} +(3.86373 - 0.267566i) q^{60} +(3.17965 - 6.96245i) q^{61} +(-1.83627 + 0.399456i) q^{62} +(-3.65704 + 5.39371i) q^{63} +(0.755750 - 0.654861i) q^{64} +(0.224453 + 0.369775i) q^{65} +(-2.93111 + 1.17204i) q^{66} +(-2.38206 + 1.78319i) q^{67} +(1.39832 + 1.39832i) q^{68} +(-5.56344 + 6.16832i) q^{69} +(-0.222144 - 4.85210i) q^{70} +(-5.16324 - 0.742361i) q^{71} +(-2.69739 - 1.31305i) q^{72} +(0.609809 - 0.332981i) q^{73} +(-4.87960 - 5.63136i) q^{74} +(7.77419 + 3.81602i) q^{75} +(1.29843 + 0.834451i) q^{76} +(1.38351 + 3.70934i) q^{77} +(-0.00783613 - 0.334972i) q^{78} +(-3.35825 - 5.22554i) q^{79} +(2.19644 - 0.419119i) q^{80} +(-0.443010 + 8.98909i) q^{81} +(-9.03842 - 1.96619i) q^{82} +(-8.47603 + 0.606217i) q^{83} +(-1.72539 + 3.34341i) q^{84} +(1.13657 + 4.27332i) q^{85} +(-0.796319 - 2.71201i) q^{86} +(1.53263 - 12.7739i) q^{87} +(-1.59962 + 0.873458i) q^{88} +(-5.33415 - 11.6802i) q^{89} +(-3.74515 - 5.56542i) q^{90} -0.420210 q^{91} +(-2.76493 + 3.91856i) q^{92} +(2.18845 + 2.40937i) q^{93} +(-11.0620 - 1.59047i) q^{94} +(1.57578 + 3.07052i) q^{95} +(-1.63656 - 0.567171i) q^{96} +(-0.380330 + 5.31770i) q^{97} +(-2.00247 - 1.09343i) q^{98} +(4.29510 + 3.38342i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q + 8 q^{3} + 8 q^{6}+O(q^{10}) \) 960 * q + 8 * q^3 + 8 * q^6	\( 960 q + 8 q^{3} + 8 q^{6} - 8 q^{12} - 16 q^{13} + 8 q^{15} + 96 q^{16} + 72 q^{18} + 16 q^{22} + 32 q^{25} + 8 q^{27} - 16 q^{31} + 36 q^{33} - 8 q^{36} + 24 q^{37} - 48 q^{43} - 16 q^{46} - 8 q^{48} - 32 q^{51} + 16 q^{52} - 64 q^{55} - 16 q^{57} + 8 q^{60} - 96 q^{61} + 72 q^{63} - 144 q^{66} + 64 q^{67} - 16 q^{70} + 16 q^{72} + 48 q^{73} + 4 q^{75} - 24 q^{78} - 248 q^{81} - 32 q^{82} + 64 q^{85} - 8 q^{87} + 16 q^{88} + 40 q^{90} - 96 q^{91} - 104 q^{93} - 8 q^{96} - 264 q^{97}+O(q^{100}) \) 960 * q + 8 * q^3 + 8 * q^6 - 8 * q^12 - 16 * q^13 + 8 * q^15 + 96 * q^16 + 72 * q^18 + 16 * q^22 + 32 * q^25 + 8 * q^27 - 16 * q^31 + 36 * q^33 - 8 * q^36 + 24 * q^37 - 48 * q^43 - 16 * q^46 - 8 * q^48 - 32 * q^51 + 16 * q^52 - 64 * q^55 - 16 * q^57 + 8 * q^60 - 96 * q^61 + 72 * q^63 - 144 * q^66 + 64 * q^67 - 16 * q^70 + 16 * q^72 + 48 * q^73 + 4 * q^75 - 24 * q^78 - 248 * q^81 - 32 * q^82 + 64 * q^85 - 8 * q^87 + 16 * q^88 + 40 * q^90 - 96 * q^91 - 104 * q^93 - 8 * q^96 - 264 * q^97

Introduction

L-functions

Modular forms

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