LMFDB - Embedded newform 85.2.l.a.36.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [85,2,Mod(26,85)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(85, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("85.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.l (of order $8$, degree $4$, 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:	$0.678728417181$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			36.5
Character	$\chi$	$=$	85.36
Dual form			85.2.l.a.26.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.01710 + 1.01710i) q^{2} +(-0.101541 + 0.0420595i) q^{3} +0.0689897i q^{4} +(0.382683 + 0.923880i) q^{5} +(-0.146056 - 0.0604983i) q^{6} +(-0.265997 + 0.642174i) q^{7} +(1.96403 - 1.96403i) q^{8} +(-2.11278 + 2.11278i) q^{9} +(-0.550451 + 1.32891i) q^{10} +(-4.48163 - 1.85635i) q^{11} +(-0.00290167 - 0.00700526i) q^{12} -5.63906i q^{13} +(-0.923703 + 0.382610i) q^{14} +(-0.0777158 - 0.0777158i) q^{15} +4.13322 q^{16} +(1.63113 + 3.78674i) q^{17} -4.29782 q^{18} +(-1.64241 - 1.64241i) q^{19} +(-0.0637382 + 0.0264012i) q^{20} -0.0763945i q^{21} +(-2.67018 - 6.44637i) q^{22} +(4.28390 + 1.77445i) q^{23} +(-0.116823 + 0.282035i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(5.73549 - 5.73549i) q^{26} +(0.251849 - 0.608017i) q^{27} +(-0.0443034 - 0.0183511i) q^{28} +(2.48981 + 6.01093i) q^{29} -0.158090i q^{30} +(-6.12711 + 2.53793i) q^{31} +(0.275837 + 0.275837i) q^{32} +0.533145 q^{33} +(-2.19248 + 5.51052i) q^{34} -0.695085 q^{35} +(-0.145760 - 0.145760i) q^{36} +(0.109595 - 0.0453958i) q^{37} -3.34100i q^{38} +(0.237176 + 0.572593i) q^{39} +(2.56613 + 1.06293i) q^{40} +(-0.412826 + 0.996650i) q^{41} +(0.0777010 - 0.0777010i) q^{42} +(-0.453332 + 0.453332i) q^{43} +(0.128069 - 0.309187i) q^{44} +(-2.76048 - 1.14343i) q^{45} +(2.55237 + 6.16195i) q^{46} -4.93703i q^{47} +(-0.419690 + 0.173841i) q^{48} +(4.60811 + 4.60811i) q^{49} -1.43840 q^{50} +(-0.324894 - 0.315904i) q^{51} +0.389037 q^{52} +(8.47565 + 8.47565i) q^{53} +(0.874571 - 0.362259i) q^{54} -4.85089i q^{55} +(0.738824 + 1.78368i) q^{56} +(0.235850 + 0.0976925i) q^{57} +(-3.58134 + 8.64611i) q^{58} +(7.01329 - 7.01329i) q^{59} +(0.00536159 - 0.00536159i) q^{60} +(0.613413 - 1.48091i) q^{61} +(-8.81322 - 3.65056i) q^{62} +(-0.794779 - 1.91877i) q^{63} -7.70533i q^{64} +(5.20981 - 2.15797i) q^{65} +(0.542263 + 0.542263i) q^{66} +2.99411 q^{67} +(-0.261246 + 0.112531i) q^{68} -0.509622 q^{69} +(-0.706971 - 0.706971i) q^{70} +(-4.33163 + 1.79422i) q^{71} +8.29913i q^{72} +(-2.10442 - 5.08052i) q^{73} +(0.157641 + 0.0652972i) q^{74} +(0.0420595 - 0.101541i) q^{75} +(0.113309 - 0.113309i) q^{76} +(2.38421 - 2.38421i) q^{77} +(-0.341153 + 0.823617i) q^{78} +(-13.7140 - 5.68053i) q^{79} +(1.58171 + 3.81860i) q^{80} -8.89143i q^{81} +(-1.43358 + 0.593808i) q^{82} +(-3.56033 - 3.56033i) q^{83} +0.00527044 q^{84} +(-2.87429 + 2.95609i) q^{85} -0.922169 q^{86} +(-0.505633 - 0.505633i) q^{87} +(-12.4480 + 5.15614i) q^{88} -2.35657i q^{89} +(-1.64470 - 3.97067i) q^{90} +(3.62126 + 1.49997i) q^{91} +(-0.122419 + 0.295545i) q^{92} +(0.515406 - 0.515406i) q^{93} +(5.02145 - 5.02145i) q^{94} +(0.888867 - 2.14591i) q^{95} +(-0.0396102 - 0.0164071i) q^{96} +(-1.03355 - 2.49522i) q^{97} +9.37384i q^{98} +(13.3908 - 5.54664i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} + 24 q^{12} - 8 q^{15} - 24 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 32 q^{22} - 16 q^{23} - 8 q^{24} + 16 q^{26} + 24 q^{27} + 48 q^{28} - 8 q^{29} + 16 q^{34} - 32 q^{35}+ \cdots - 8 q^{99}+O(q^{100}) $ 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 + 24 * q^12 - 8 * q^15 - 24 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 32 * q^22 - 16 * q^23 - 8 * q^24 + 16 * q^26 + 24 * q^27 + 48 * q^28 - 8 * q^29 + 16 * q^34 - 32 * q^35 - 24 * q^36 + 24 * q^37 + 8 * q^39 + 16 * q^40 + 16 * q^41 - 24 * q^42 + 8 * q^43 + 16 * q^44 + 16 * q^45 + 8 * q^46 + 80 * q^48 + 8 * q^50 - 56 * q^51 - 48 * q^52 + 24 * q^53 - 32 * q^54 + 64 * q^56 + 32 * q^57 - 64 * q^58 + 32 * q^59 + 24 * q^60 + 32 * q^61 - 32 * q^62 - 56 * q^63 + 8 * q^65 + 96 * q^66 + 16 * q^67 - 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^75 - 8 * q^76 + 24 * q^77 - 112 * q^78 - 32 * q^80 - 80 * q^82 - 96 * q^83 - 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 + 80 * q^92 + 64 * q^93 + 56 * q^94 - 16 * q^95 - 168 * q^96 - 40 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	1.01710	+	1.01710i	0.719199	+	0.719199i	0.968441	−	0.249242i	$-0.0801815\pi$
$2$	1.01710	+	1.01710i	0.719199	+	0.719199i	−0.249242	+	0.968441i	$0.580181\pi$
$3$	−0.101541	+	0.0420595i	−0.0586245	+	0.0242831i	−0.411803	−	0.911273i	$-0.635101\pi$
$3$	−0.101541	+	0.0420595i	−0.0586245	+	0.0242831i	0.353179	+	0.935556i	$0.385101\pi$
$4$			0.0689897i			0.0344949i
$5$	0.382683	+	0.923880i	0.171141	+	0.413171i
$5$	0.382683	+	0.923880i	0.171141	+	0.413171i
$6$	−0.146056	−	0.0604983i	−0.0596271	−	0.0246983i
$7$	−0.265997	+	0.642174i	−0.100538	+	0.242719i	−0.966143	−	0.258008i	$-0.916934\pi$
$7$	−0.265997	+	0.642174i	−0.100538	+	0.242719i	0.865605	+	0.500727i	$0.166934\pi$
$8$	1.96403	−	1.96403i	0.694390	−	0.694390i
$9$	−2.11278	+	2.11278i	−0.704260	+	0.704260i
$10$	−0.550451	+	1.32891i	−0.174068	+	0.420237i
$11$	−4.48163	−	1.85635i	−1.35126	−	0.559712i	−0.414620	−	0.909995i	$-0.636085\pi$
$11$	−4.48163	−	1.85635i	−1.35126	−	0.559712i	−0.936644	+	0.350283i	$0.886085\pi$
$12$	−0.00290167	−	0.00700526i	−0.000837641	−	0.00202224i
$13$		−	5.63906i		−	1.56399i	−0.623283	−	0.781996i	$-0.714202\pi$
$13$		−	5.63906i		−	1.56399i	0.623283	−	0.781996i	$-0.285798\pi$
$14$	−0.923703	+	0.382610i	−0.246870	+	0.102257i
$15$	−0.0777158	−	0.0777158i	−0.0200661	−	0.0200661i
$16$	4.13322			1.03330
$17$	1.63113	+	3.78674i	0.395606	+	0.918420i
$17$	1.63113	+	3.78674i	0.395606	+	0.918420i
$18$	−4.29782			−1.01301
$19$	−1.64241	−	1.64241i	−0.376795	−	0.376795i	0.493150	−	0.869945i	$-0.335846\pi$
$19$	−1.64241	−	1.64241i	−0.376795	−	0.376795i	−0.869945	+	0.493150i	$0.835846\pi$
$20$	−0.0637382	+	0.0264012i	−0.0142523	+	0.00590349i
$21$		−	0.0763945i		−	0.0166706i
$22$	−2.67018	−	6.44637i	−0.569283	−	1.37437i
$23$	4.28390	+	1.77445i	0.893255	+	0.369998i	0.781623	−	0.623751i	$-0.214392\pi$
$23$	4.28390	+	1.77445i	0.893255	+	0.369998i	0.111632	+	0.993750i	$0.464392\pi$
$24$	−0.116823	+	0.282035i	−0.0238464	+	0.0575702i
$25$	−0.707107	+	0.707107i	−0.141421	+	0.141421i
$26$	5.73549	−	5.73549i	1.12482	−	1.12482i
$27$	0.251849	−	0.608017i	0.0484684	−	0.117013i
$28$	−0.0443034	−	0.0183511i	−0.00837256	−	0.00346803i
$29$	2.48981	+	6.01093i	0.462346	+	1.11620i	0.967432	+	0.253132i	$0.0814608\pi$
$29$	2.48981	+	6.01093i	0.462346	+	1.11620i	−0.505086	+	0.863069i	$0.668539\pi$
$30$		−	0.158090i		−	0.0288631i
$31$	−6.12711	+	2.53793i	−1.10046	+	0.455826i	−0.857643	−	0.514246i	$-0.828072\pi$
$31$	−6.12711	+	2.53793i	−1.10046	+	0.455826i	−0.242819	+	0.970072i	$0.578072\pi$
$32$	0.275837	+	0.275837i	0.0487616	+	0.0487616i
$33$	0.533145			0.0928087
$34$	−2.19248	+	5.51052i	−0.376008	+	0.945047i
$35$	−0.695085			−0.117491
$36$	−0.145760	−	0.145760i	−0.0242933	−	0.0242933i
$37$	0.109595	−	0.0453958i	0.0180173	−	0.00746302i	−0.373657	−	0.927567i	$-0.621896\pi$
$37$	0.109595	−	0.0453958i	0.0180173	−	0.00746302i	0.391674	+	0.920104i	$0.371896\pi$
$38$		−	3.34100i		−	0.541981i
$39$	0.237176	+	0.572593i	0.0379785	+	0.0916883i
$40$	2.56613	+	1.06293i	0.405741	+	0.168064i
$41$	−0.412826	+	0.996650i	−0.0644726	+	0.155651i	−0.952832	−	0.303498i	$-0.901845\pi$
$41$	−0.412826	+	0.996650i	−0.0644726	+	0.155651i	0.888359	+	0.459149i	$0.151845\pi$
$42$	0.0777010	−	0.0777010i	0.0119895	−	0.0119895i
$43$	−0.453332	+	0.453332i	−0.0691325	+	0.0691325i	−0.740828	−	0.671695i	$-0.765566\pi$
$43$	−0.453332	+	0.453332i	−0.0691325	+	0.0691325i	0.671695	+	0.740828i	$0.265566\pi$
$44$	0.128069	−	0.309187i	0.0193072	−	0.0466116i
$45$	−2.76048	−	1.14343i	−0.411508	−	0.170452i
$46$	2.55237	+	6.16195i	0.376326	+	0.908531i
$47$		−	4.93703i		−	0.720139i	−0.932925	−	0.360070i	$-0.882753\pi$
$47$		−	4.93703i		−	0.720139i	0.932925	−	0.360070i	$-0.117247\pi$
$48$	−0.419690	+	0.173841i	−0.0605770	+	0.0250918i
$49$	4.60811	+	4.60811i	0.658302	+	0.658302i
$50$	−1.43840			−0.203420
$51$	−0.324894	−	0.315904i	−0.0454943	−	0.0442354i
$52$	0.389037			0.0539497
$53$	8.47565	+	8.47565i	1.16422	+	1.16422i	0.983542	+	0.180678i	$0.0578292\pi$
$53$	8.47565	+	8.47565i	1.16422	+	1.16422i	0.180678	+	0.983542i	$0.442171\pi$
$54$	0.874571	−	0.362259i	0.119014	−	0.0492972i
$55$		−	4.85089i		−	0.654093i
$56$	0.738824	+	1.78368i	0.0987295	+	0.238354i
$57$	0.235850	+	0.0976925i	0.0312392	+	0.0129397i
$58$	−3.58134	+	8.64611i	−0.470252	+	1.13529i
$59$	7.01329	−	7.01329i	0.913053	−	0.913053i	−0.0834587	−	0.996511i	$-0.526597\pi$
$59$	7.01329	−	7.01329i	0.913053	−	0.913053i	0.996511	+	0.0834587i	$0.0265967\pi$
$60$	0.00536159	−	0.00536159i	0.000692179	−	0.000692179i
$61$	0.613413	−	1.48091i	0.0785394	−	0.189611i	−0.879733	−	0.475469i	$-0.842278\pi$
$61$	0.613413	−	1.48091i	0.0785394	−	0.189611i	0.958272	+	0.285858i	$0.0922785\pi$
$62$	−8.81322	−	3.65056i	−1.11928	−	0.463621i
$63$	−0.794779	−	1.91877i	−0.100133	−	0.241742i
$64$		−	7.70533i		−	0.963166i
$65$	5.20981	−	2.15797i	0.646197	−	0.267664i
$66$	0.542263	+	0.542263i	0.0667479	+	0.0667479i
$67$	2.99411			0.365789			0.182894	−	0.983133i	$-0.441453\pi$
$67$	2.99411			0.365789			0.182894	+	0.983133i	$0.441453\pi$
$68$	−0.261246	+	0.112531i	−0.0316808	+	0.0136464i
$69$	−0.509622			−0.0613513
$70$	−0.706971	−	0.706971i	−0.0844992	−	0.0844992i
$71$	−4.33163	+	1.79422i	−0.514070	+	0.212935i	−0.624610	−	0.780937i	$-0.714742\pi$
$71$	−4.33163	+	1.79422i	−0.514070	+	0.212935i	0.110540	+	0.993872i	$0.464742\pi$
$72$			8.29913i			0.978062i
$73$	−2.10442	−	5.08052i	−0.246304	−	0.594629i	0.751581	−	0.659641i	$-0.229292\pi$
$73$	−2.10442	−	5.08052i	−0.246304	−	0.594629i	−0.997885	+	0.0650115i	$0.979292\pi$
$74$	0.157641	+	0.0652972i	0.0183254	+	0.00759065i
$75$	0.0420595	−	0.101541i	0.00485661	−	0.0117249i
$76$	0.113309	−	0.113309i	0.0129975	−	0.0129975i
$77$	2.38421	−	2.38421i	0.271705	−	0.271705i
$78$	−0.341153	+	0.823617i	−0.0386280	+	0.0932563i
$79$	−13.7140	−	5.68053i	−1.54295	−	0.639110i	−0.560924	−	0.827867i	$-0.689554\pi$
$79$	−13.7140	−	5.68053i	−1.54295	−	0.639110i	−0.982024	+	0.188757i	$0.939554\pi$
$80$	1.58171	+	3.81860i	0.176841	+	0.426932i
$81$		−	8.89143i		−	0.987937i
$82$	−1.43358	+	0.593808i	−0.158312	+	0.0655752i
$83$	−3.56033	−	3.56033i	−0.390797	−	0.390797i	0.484175	−	0.874971i	$-0.339120\pi$
$83$	−3.56033	−	3.56033i	−0.390797	−	0.390797i	−0.874971	+	0.484175i	$0.839120\pi$
$84$	0.00527044			0.000575052
$85$	−2.87429	+	2.95609i	−0.311761	+	0.320633i
$86$	−0.922169			−0.0994400
$87$	−0.505633	−	0.505633i	−0.0542096	−	0.0542096i
$88$	−12.4480	+	5.15614i	−1.32696	+	0.549646i
$89$		−	2.35657i		−	0.249796i	−0.992170	−	0.124898i	$-0.960140\pi$
$89$		−	2.35657i		−	0.249796i	0.992170	−	0.124898i	$-0.0398604\pi$
$90$	−1.64470	−	3.97067i	−0.173367	−	0.418545i
$91$	3.62126	+	1.49997i	0.379611	+	0.157240i
$92$	−0.122419	+	0.295545i	−0.0127630	+	0.0308127i
$93$	0.515406	−	0.515406i	0.0534452	−	0.0534452i
$94$	5.02145	−	5.02145i	0.517924	−	0.517924i
$95$	0.888867	−	2.14591i	0.0911958	−	0.220166i
$96$	−0.0396102	−	0.0164071i	−0.00404270	−	0.00167454i
$97$	−1.03355	−	2.49522i	−0.104941	−	0.253351i	0.862683	−	0.505745i	$-0.168782\pi$
$97$	−1.03355	−	2.49522i	−0.104941	−	0.253351i	−0.967625	+	0.252394i	$0.918782\pi$
$98$			9.37384i			0.946900i
$99$	13.3908	−	5.54664i	1.34582	−	0.557458i
$100$	−0.0487831	−	0.0487831i	−0.00487831	−	0.00487831i
$101$	−14.3025			−1.42315			−0.711575	−	0.702610i	$-0.752018\pi$
$101$	−14.3025			−1.42315			−0.711575	+	0.702610i	$0.752018\pi$
$102$	−0.00914379	−	0.651756i	−0.000905370	−	0.0645335i
$103$	−10.8963			−1.07365			−0.536824	−	0.843694i	$-0.680376\pi$
$103$	−10.8963			−1.07365			−0.536824	+	0.843694i	$0.680376\pi$
$104$	−11.0753	−	11.0753i	−1.08602	−	1.08602i
$105$	0.0705793	−	0.0292349i	0.00688784	−	0.00285304i
$106$			17.2412i			1.67461i
$107$	6.36300	+	15.3616i	0.615134	+	1.48507i	0.857293	+	0.514829i	$0.172145\pi$
$107$	6.36300	+	15.3616i	0.615134	+	1.48507i	−0.242158	+	0.970237i	$0.577855\pi$
$108$	0.0419469	+	0.0173750i	0.00403635	+	0.00167191i
$109$	4.05640	−	9.79302i	0.388533	−	0.938002i	−0.601718	−	0.798708i	$-0.705517\pi$
$109$	4.05640	−	9.79302i	0.388533	−	0.938002i	0.990251	−	0.139293i	$-0.0444830\pi$
$110$	4.93384	−	4.93384i	0.470423	−	0.470423i
$111$	−0.00921903	+	0.00921903i	−0.000875032	+	0.000875032i
$112$	−1.09943	+	2.65425i	−0.103886	+	0.250803i
$113$	10.6613	+	4.41604i	1.00293	+	0.415426i	0.822869	−	0.568230i	$-0.192372\pi$
$113$	10.6613	+	4.41604i	1.00293	+	0.415426i	0.180057	+	0.983656i	$0.442372\pi$
$114$	0.140521	+	0.339247i	0.0131610	+	0.0317734i
$115$			4.63686i			0.432389i
$116$	−0.414692	+	0.171771i	−0.0385032	+	0.0159485i
$117$	11.9141	+	11.9141i	1.10146	+	1.10146i
$118$	14.2665			1.31333
$119$	−2.86563	+	0.0402032i	−0.262691	+	0.00368542i
$120$	−0.305273			−0.0278675
$121$	8.86082	+	8.86082i	0.805529	+	0.805529i
$122$	2.13014	−	0.882332i	0.192854	−	0.0798825i
$123$		−	0.118564i		−	0.0106905i
$124$	−0.175091	−	0.422708i	−0.0157237	−	0.0379603i
$125$	−0.923880	−	0.382683i	−0.0826343	−	0.0342282i
$126$	1.14321	−	2.75995i	0.101845	−	0.245876i
$127$	0.352520	−	0.352520i	0.0312811	−	0.0312811i	−0.691293	−	0.722574i	$-0.742959\pi$
$127$	0.352520	−	0.352520i	0.0312811	−	0.0312811i	0.722574	+	0.691293i	$0.242959\pi$
$128$	8.38878	−	8.38878i	0.741470	−	0.741470i
$129$	0.0269647	−	0.0650985i	0.00237411	−	0.00573160i
$130$	7.49378	+	3.10402i	0.657248	+	0.272241i
$131$	−7.47537	−	18.0471i	−0.653126	−	1.57679i	−0.808217	−	0.588885i	$-0.799567\pi$
$131$	−7.47537	−	18.0471i	−0.653126	−	1.57679i	0.155091	−	0.987900i	$-0.450433\pi$
$132$			0.0367815i			0.00320142i
$133$	1.49159	−	0.617838i	0.129337	−	0.0535733i
$134$	3.04531	+	3.04531i	0.263075	+	0.263075i
$135$	0.658113			0.0566414
$136$	10.6409	+	4.23371i	0.912447	+	0.363037i
$137$	−3.81724			−0.326129			−0.163065	−	0.986615i	$-0.552138\pi$
$137$	−3.81724			−0.326129			−0.163065	+	0.986615i	$0.552138\pi$
$138$	−0.518337	−	0.518337i	−0.0441238	−	0.0441238i
$139$	12.2437	−	5.07150i	1.03850	−	0.430159i	0.202725	−	0.979236i	$-0.435020\pi$
$139$	12.2437	−	5.07150i	1.03850	−	0.430159i	0.835772	+	0.549076i	$0.185020\pi$
$140$		−	0.0479537i		−	0.00405283i
$141$	0.207649	+	0.501309i	0.0174872	+	0.0422178i
$142$	−6.23061	−	2.58080i	−0.522861	−	0.216576i
$143$	−10.4681	+	25.2722i	−0.875385	+	2.11337i
$144$	−8.73258	+	8.73258i	−0.727715	+	0.727715i
$145$	−4.60056	+	4.60056i	−0.382056	+	0.382056i
$146$	3.02699	−	7.30780i	0.250516	−	0.604798i
$147$	−0.661726	−	0.274096i	−0.0545782	−	0.0226070i
$148$	0.00313184	+	0.00756094i	0.000257436	+	0.000621505i
$149$			17.4543i			1.42991i	0.699171	+	0.714955i	$0.253553\pi$
$149$			17.4543i			1.42991i	−0.699171	+	0.714955i	$0.746447\pi$
$150$	0.146056	−	0.0604983i	0.0119254	−	0.00493967i
$151$	7.97016	+	7.97016i	0.648602	+	0.648602i	0.952655	−	0.304053i	$-0.0983400\pi$
$151$	7.97016	+	7.97016i	0.648602	+	0.648602i	−0.304053	+	0.952655i	$0.598340\pi$
$152$	−6.45150			−0.523286
$153$	−11.4468	−	4.55435i	−0.925416	−	0.368197i
$154$	4.84996			0.390821
$155$	−4.68949	−	4.68949i	−0.376669	−	0.376669i
$156$	−0.0395030	+	0.0163627i	−0.00316277	+	0.00131006i
$157$		−	6.14541i		−	0.490457i	−0.969465	−	0.245229i	$-0.921137\pi$
$157$		−	6.14541i		−	0.490457i	0.969465	−	0.245229i	$-0.0788630\pi$
$158$	−8.17087	−	19.7262i	−0.650039	−	1.56933i
$159$	−1.21710	−	0.504141i	−0.0965227	−	0.0399810i
$160$	−0.149282	+	0.360399i	−0.0118018	+	0.0284920i
$161$	−2.27901	+	2.27901i	−0.179611	+	0.179611i
$162$	9.04348	−	9.04348i	0.710523	−	0.710523i
$163$	4.28650	−	10.3485i	0.335745	−	0.810560i	−0.662369	−	0.749177i	$-0.730449\pi$
$163$	4.28650	−	10.3485i	0.335745	−	0.810560i	0.998114	−	0.0613824i	$-0.0195509\pi$
$164$	−0.0687586	−	0.0284808i	−0.00536915	−	0.00222397i
$165$	0.204026	+	0.492562i	0.0158834	+	0.0383459i
$166$		−	7.24243i		−	0.562121i
$167$	−5.27168	+	2.18360i	−0.407935	+	0.168972i	−0.577208	−	0.816597i	$-0.695858\pi$
$167$	−5.27168	+	2.18360i	−0.407935	+	0.168972i	0.169273	+	0.985569i	$0.445858\pi$
$168$	−0.150041	−	0.150041i	−0.0115759	−	0.0115759i
$169$	−18.7989			−1.44607
$170$	−5.93008	+	0.0831959i	−0.454817	+	0.00638083i
$171$	6.94010			0.530723
$172$	−0.0312752	−	0.0312752i	−0.00238471	−	0.00238471i
$173$	−4.19214	+	1.73644i	−0.318722	+	0.132019i	−0.536309	−	0.844022i	$-0.680182\pi$
$173$	−4.19214	+	1.73644i	−0.318722	+	0.132019i	0.217586	+	0.976041i	$0.430182\pi$
$174$		−	1.02856i		−	0.0779750i
$175$	−0.265997	−	0.642174i	−0.0201075	−	0.0485438i
$176$	−18.5236	−	7.67272i	−1.39627	−	0.578353i
$177$	−0.417158	+	1.00711i	−0.0313555	+	0.0756990i
$178$	2.39687	−	2.39687i	0.179653	−	0.179653i
$179$	−12.9935	+	12.9935i	−0.971179	+	0.971179i	−0.999596	−	0.0284174i	$-0.990953\pi$
$179$	−12.9935	+	12.9935i	−0.971179	+	0.971179i	0.0284174	+	0.999596i	$0.490953\pi$
$180$	0.0788847	−	0.190445i	0.00587972	−	0.0141949i
$181$	−9.90234	−	4.10168i	−0.736035	−	0.304876i	−0.0170058	−	0.999855i	$-0.505413\pi$
$181$	−9.90234	−	4.10168i	−0.736035	−	0.304876i	−0.719029	+	0.694980i	$0.755413\pi$
$182$	2.15756	+	5.20881i	0.159929	+	0.386103i
$183$			0.176172i			0.0130230i
$184$	11.8988	−	4.92864i	0.877191	−	0.363344i
$185$	0.0838805	+	0.0838805i	0.00616702	+	0.00616702i
$186$	1.04844			0.0768754
$187$	−0.280571	−	19.9987i	−0.0205174	−	1.46245i
$188$	0.340604			0.0248411
$189$	0.323462	+	0.323462i	0.0235284	+	0.0235284i
$190$	3.08668	−	1.27854i	0.223931	−	0.0927553i
$191$			18.5397i			1.34149i	0.741690	+	0.670743i	$0.234024\pi$
$191$			18.5397i			1.34149i	−0.741690	+	0.670743i	$0.765976\pi$
$192$	0.324082	+	0.782404i	0.0233886	+	0.0564652i
$193$	9.13339	+	3.78317i	0.657435	+	0.272319i	0.686359	−	0.727263i	$-0.259208\pi$
$193$	9.13339	+	3.78317i	0.657435	+	0.272319i	−0.0289235	+	0.999582i	$0.509208\pi$
$194$	1.48666	−	3.58912i	0.106736	−	0.257684i
$195$	−0.438244	+	0.438244i	−0.0313833	+	0.0313833i
$196$	−0.317912	+	0.317912i	−0.0227080	+	0.0227080i
$197$	5.33973	−	12.8913i	0.380440	−	0.918464i	−0.611440	−	0.791291i	$-0.709410\pi$
$197$	5.33973	−	12.8913i	0.380440	−	0.918464i	0.991881	−	0.127173i	$-0.0405905\pi$
$198$	19.2613	+	7.97827i	1.36884	+	0.566991i
$199$	4.87410	+	11.7671i	0.345516	+	0.834148i	0.997138	+	0.0756048i	$0.0240887\pi$
$199$	4.87410	+	11.7671i	0.345516	+	0.834148i	−0.651622	+	0.758544i	$0.725911\pi$
$200$			2.77756i			0.196403i
$201$	−0.304024	+	0.125931i	−0.0214442	+	0.00888248i
$202$	−14.5471	−	14.5471i	−1.02353	−	1.02353i
$203$	−4.52235			−0.317407
$204$	0.0217941	−	0.0224143i	0.00152589	−	0.00156932i
$205$	−1.07877			−0.0753443
$206$	−11.0827	−	11.0827i	−0.772167	−	0.772167i
$207$	−12.8000	+	5.30191i	−0.889658	+	0.368509i
$208$		−	23.3075i		−	1.61608i
$209$	4.31179	+	10.4096i	0.298253	+	0.720046i
$210$	0.101521	+	0.0420515i	0.00700563	+	0.00290183i
$211$	4.92813	−	11.8976i	0.339266	−	0.819061i	−0.658520	−	0.752563i	$-0.728817\pi$
$211$	4.92813	−	11.8976i	0.339266	−	0.819061i	0.997787	−	0.0664982i	$-0.0211827\pi$
$212$	−0.584733	+	0.584733i	−0.0401596	+	0.0401596i
$213$	0.364372	−	0.364372i	0.0249664	−	0.0249664i
$214$	−9.15253	+	22.0962i	−0.625654	+	1.51046i
$215$	−0.592307	−	0.245341i	−0.0403950	−	0.0167321i
$216$	−0.699526	−	1.68881i	−0.0475967	−	0.114909i
$217$		−	4.60976i		−	0.312931i
$218$	14.0863	−	5.83472i	0.954042	−	0.395177i
$219$	0.427368	+	0.427368i	0.0288788	+	0.0288788i
$220$	0.334661			0.0225629
$221$	21.3537	−	9.19801i	1.43640	−	0.618725i
$222$	−0.0187534			−0.00125864
$223$	14.4397	+	14.4397i	0.966952	+	0.966952i	0.999471	−	0.0325195i	$-0.0103531\pi$
$223$	14.4397	+	14.4397i	0.966952	+	0.966952i	−0.0325195	+	0.999471i	$0.510353\pi$
$224$	−0.250507	+	0.103764i	−0.0167377	+	0.00693300i
$225$		−	2.98792i		−	0.199195i
$226$	6.35202	+	15.3351i	0.422530	+	1.02008i
$227$	1.12740	+	0.466985i	0.0748282	+	0.0309949i	0.419784	−	0.907624i	$-0.362106\pi$
$227$	1.12740	+	0.466985i	0.0748282	+	0.0309949i	−0.344955	+	0.938619i	$0.612106\pi$
$228$	−0.00673977	+	0.0162713i	−0.000446352	+	0.00107759i
$229$	−2.48862	+	2.48862i	−0.164453	+	0.164453i	−0.784536	−	0.620083i	$-0.787099\pi$
$229$	−2.48862	+	2.48862i	−0.164453	+	0.164453i	0.620083	+	0.784536i	$0.287099\pi$
$230$	−4.71616	+	4.71616i	−0.310974	+	0.310974i
$231$	−0.141815	+	0.342372i	−0.00933076	+	0.0225264i
$232$	16.6957	+	6.91560i	1.09613	+	0.454031i
$233$	−11.0988	−	26.7949i	−0.727107	−	1.75539i	−0.652005	−	0.758215i	$-0.726072\pi$
$233$	−11.0988	−	26.7949i	−0.727107	−	1.75539i	−0.0751019	−	0.997176i	$-0.523928\pi$
$234$			24.2356i			1.58433i
$235$	4.56122	−	1.88932i	0.297541	−	0.123246i
$236$	0.483845	+	0.483845i	0.0314956	+	0.0314956i
$237$	1.63145			0.105974
$238$	−2.95552	−	2.87374i	−0.191578	−	0.186277i
$239$	7.87133			0.509154			0.254577	−	0.967053i	$-0.418064\pi$
$239$	7.87133			0.509154			0.254577	+	0.967053i	$0.418064\pi$
$240$	−0.321217	−	0.321217i	−0.0207344	−	0.0207344i
$241$	10.7419	−	4.44945i	0.691947	−	0.286614i	−0.00886385	−	0.999961i	$-0.502821\pi$
$241$	10.7419	−	4.44945i	0.691947	−	0.286614i	0.700811	+	0.713347i	$0.252821\pi$
$242$			18.0247i			1.15867i
$243$	1.12952	+	2.72689i	0.0724585	+	0.174930i
$244$	0.102167	+	0.0423192i	0.00654060	+	0.00270921i
$245$	−2.49389	+	6.02079i	−0.159329	+	0.384654i
$246$	0.120591	−	0.120591i	0.00768862	−	0.00768862i
$247$	−9.26165	+	9.26165i	−0.589305	+	0.589305i
$248$	−7.04926	+	17.0184i	−0.447629	+	1.08067i
$249$	0.511263	+	0.211772i	0.0324000	+	0.0134205i
$250$	−0.550451	−	1.32891i	−0.0348136	−	0.0840474i
$251$			7.94692i			0.501605i	0.968038	+	0.250803i	$0.0806945\pi$
$251$			7.94692i			0.501605i	−0.968038	+	0.250803i	$0.919306\pi$
$252$	0.132375	−	0.0548316i	0.00833885	−	0.00345406i
$253$	−15.9049	−	15.9049i	−0.999930	−	0.999930i
$254$	0.717097			0.0449947
$255$	0.167526	−	0.421054i	0.0104909	−	0.0263674i
$256$	1.65381			0.103363
$257$	−5.60542	−	5.60542i	−0.349657	−	0.349657i	0.510325	−	0.859982i	$-0.329525\pi$
$257$	−5.60542	−	5.60542i	−0.349657	−	0.349657i	−0.859982	+	0.510325i	$0.829525\pi$
$258$	0.0936376	−	0.0387860i	0.00582962	−	0.00241471i
$259$			0.0824544i			0.00512347i
$260$	0.148878	+	0.359423i	0.00923302	+	0.0222905i
$261$	−17.9602	−	7.43935i	−1.11171	−	0.460484i
$262$	10.7526	−	25.9590i	0.664295	−	1.60375i
$263$	−6.03602	+	6.03602i	−0.372197	+	0.372197i	−0.868277	−	0.496080i	$-0.834772\pi$
$263$	−6.03602	+	6.03602i	−0.372197	+	0.372197i	0.496080	+	0.868277i	$0.334772\pi$
$264$	1.04711	−	1.04711i	0.0644454	−	0.0644454i
$265$	−4.58699	+	11.0740i	−0.281777	+	0.680269i
$266$	2.14550	+	0.888696i	0.131549	+	0.0544895i
$267$	0.0991163	+	0.239288i	0.00606582	+	0.0146442i
$268$			0.206563i			0.0126178i
$269$	−14.7662	+	6.11636i	−0.900311	+	0.372921i	−0.784340	−	0.620331i	$-0.786998\pi$
$269$	−14.7662	+	6.11636i	−0.900311	+	0.372921i	−0.115971	+	0.993253i	$0.536998\pi$
$270$	0.669368	+	0.669368i	0.0407364	+	0.0407364i
$271$	22.5289			1.36853			0.684266	−	0.729232i	$-0.260123\pi$
$271$	22.5289			1.36853			0.684266	+	0.729232i	$0.260123\pi$
$272$	6.74180	+	15.6514i	0.408782	+	0.949008i
$273$	−0.430793			−0.0260728
$274$	−3.88252	−	3.88252i	−0.234552	−	0.234552i
$275$	4.48163	−	1.85635i	0.270253	−	0.111942i
$276$		−	0.0351587i		−	0.00211630i
$277$	2.64132	+	6.37672i	0.158702	+	0.383140i	0.983151	−	0.182796i	$-0.0585149\pi$
$277$	2.64132	+	6.37672i	0.158702	+	0.383140i	−0.824449	+	0.565936i	$0.808515\pi$
$278$	17.6113	+	7.29484i	1.05626	+	0.437516i
$279$	7.58314	−	18.3073i	0.453991	−	1.09603i
$280$	−1.36517	+	1.36517i	−0.0815845	+	0.0815845i
$281$	6.63310	−	6.63310i	0.395698	−	0.395698i	−0.481015	−	0.876712i	$-0.659732\pi$
$281$	6.63310	−	6.63310i	0.395698	−	0.395698i	0.876712	+	0.481015i	$0.159732\pi$
$282$	−0.298682	+	0.721082i	−0.0177862	+	0.0429398i
$283$	19.0106	+	7.87443i	1.13006	+	0.468086i	0.867802	−	0.496911i	$-0.165532\pi$
$283$	19.0106	+	7.87443i	1.13006	+	0.468086i	0.262259	+	0.964997i	$0.415532\pi$
$284$	−0.123783	−	0.298838i	−0.00734515	−	0.0177328i
$285$			0.255283i			0.0151216i
$286$	−36.3515	+	15.0573i	−2.14951	+	0.890355i
$287$	−0.530213	−	0.530213i	−0.0312975	−	0.0312975i
$288$	−1.16557			−0.0686816
$289$	−11.6789	+	12.3533i	−0.686992	+	0.726665i
$290$	−9.35848			−0.549549
$291$	0.209895	+	0.209895i	0.0123043	+	0.0123043i
$292$	0.350503	−	0.145183i	0.0205117	−	0.00849620i
$293$		−	23.4539i		−	1.37019i	−0.728452	−	0.685097i	$-0.759760\pi$
$293$		−	23.4539i		−	1.37019i	0.728452	−	0.685097i	$-0.240240\pi$
$294$	−0.394259	−	0.951825i	−0.0229936	−	0.0555116i
$295$	9.16330	+	3.79557i	0.533508	+	0.220986i
$296$	0.126090	−	0.304407i	0.00732881	−	0.0176933i
$297$	−2.25739	+	2.25739i	−0.130987	+	0.130987i
$298$	−17.7528	+	17.7528i	−1.02839	+	1.02839i
$299$	10.0062	−	24.1572i	0.578675	−	1.39704i
$300$	0.00700526	+	0.00290167i	0.000404449	+	0.000167528i
$301$	−0.170533	−	0.411703i	−0.00982936	−	0.0237302i
$302$			16.2129i			0.932948i
$303$	1.45228	−	0.601555i	0.0834315	−	0.0345585i
$304$	−6.78845	−	6.78845i	−0.389344	−	0.389344i
$305$	1.60292			0.0917832
$306$	−7.01028	−	16.2747i	−0.400751	−	0.930365i
$307$	30.4260			1.73650			0.868251	−	0.496126i	$-0.165244\pi$
$307$	30.4260			1.73650			0.868251	+	0.496126i	$0.165244\pi$
$308$	0.164486	+	0.164486i	0.00937244	+	0.00937244i
$309$	1.10642	−	0.458294i	0.0629421	−	0.0260715i
$310$		−	9.53937i		−	0.541800i
$311$	0.413255	+	0.997685i	0.0234335	+	0.0565735i	0.935163	−	0.354217i	$-0.115253\pi$
$311$	0.413255	+	0.997685i	0.0234335	+	0.0565735i	−0.911730	+	0.410791i	$0.865253\pi$
$312$	1.59041	+	0.658771i	0.0900394	+	0.0372955i
$313$	1.38743	−	3.34956i	0.0784224	−	0.189328i	−0.879806	−	0.475333i	$-0.842327\pi$
$313$	1.38743	−	3.34956i	0.0784224	−	0.189328i	0.958228	+	0.286005i	$0.0923274\pi$
$314$	6.25051	−	6.25051i	0.352737	−	0.352737i
$315$	1.46856	−	1.46856i	0.0827440	−	0.0827440i
$316$	0.391898	−	0.946126i	0.0220460	−	0.0532238i
$317$	−8.12537	−	3.36564i	−0.456366	−	0.189033i	0.142645	−	0.989774i	$-0.454439\pi$
$317$	−8.12537	−	3.36564i	−0.456366	−	0.189033i	−0.599011	+	0.800741i	$0.704439\pi$
$318$	−0.725156	−	1.75068i	−0.0406647	−	0.0981733i
$319$		−	31.5607i		−	1.76706i
$320$	7.11880	−	2.94870i	0.397953	−	0.164837i
$321$	−1.29221	−	1.29221i	−0.0721239	−	0.0721239i
$322$	−4.63597			−0.258353
$323$	3.54041	−	8.89837i	0.196994	−	0.495119i
$324$	0.613417			0.0340787
$325$	3.98741	+	3.98741i	0.221182	+	0.221182i
$326$	14.8853	−	6.16570i	0.824421	−	0.341486i
$327$			1.16500i			0.0644246i
$328$	1.14665	+	2.76826i	0.0633132	+	0.152851i
$329$	3.17043	+	1.31324i	0.174792	+	0.0724010i
$330$	−0.293470	+	0.708500i	−0.0161550	+	0.0390017i
$331$	−24.8643	+	24.8643i	−1.36666	+	1.36666i	−0.501515	+	0.865149i	$0.667224\pi$
$331$	−24.8643	+	24.8643i	−1.36666	+	1.36666i	−0.865149	+	0.501515i	$0.832776\pi$
$332$	0.245626	−	0.245626i	0.0134805	−	0.0134805i
$333$	−0.135639	+	0.327462i	−0.00743297	+	0.0179448i
$334$	−7.58278	−	3.14089i	−0.414911	−	0.171862i
$335$	1.14580	+	2.76620i	0.0626016	+	0.151134i
$336$		−	0.315755i		−	0.0172259i
$337$	−29.1162	+	12.0603i	−1.58606	+	0.656968i	−0.989359	−	0.145494i	$-0.953523\pi$
$337$	−29.1162	+	12.0603i	−1.58606	+	0.656968i	−0.596702	+	0.802463i	$0.703523\pi$
$338$	−19.1204	−	19.1204i	−1.04001	−	1.04001i
$339$	−1.26829			−0.0688839
$340$	−0.203940	−	0.198296i	−0.0110602	−	0.0107541i
$341$	32.1708			1.74214
$342$	7.05879	+	7.05879i	0.381696	+	0.381696i
$343$	−8.68018	+	3.59545i	−0.468686	+	0.194136i
$344$			1.78072i			0.0960098i
$345$	−0.195024	−	0.470830i	−0.0104997	−	0.0253486i
$346$	−6.02997	−	2.49769i	−0.324173	−	0.134277i
$347$	−0.168500	+	0.406795i	−0.00904556	+	0.0218379i	−0.928338	−	0.371738i	$-0.878762\pi$
$347$	−0.168500	+	0.406795i	−0.00904556	+	0.0218379i	0.919292	+	0.393576i	$0.128762\pi$
$348$	0.0348835	−	0.0348835i	0.00186995	−	0.00186995i
$349$	−8.78380	+	8.78380i	−0.470186	+	0.470186i	−0.901975	−	0.431789i	$-0.857883\pi$
$349$	−8.78380	+	8.78380i	−0.470186	+	0.470186i	0.431789	+	0.901975i	$0.357883\pi$
$350$	0.382610	−	0.923703i	0.0204514	−	0.0493740i
$351$	−3.42864	−	1.42019i	−0.183007	−	0.0758041i
$352$	−0.724150	−	1.74825i	−0.0385973	−	0.0931821i
$353$			7.38055i			0.392827i	0.980521	+	0.196414i	$0.0629295\pi$
$353$			7.38055i			0.392827i	−0.980521	+	0.196414i	$0.937071\pi$
$354$	−1.44862	+	0.600040i	−0.0769935	+	0.0318918i
$355$	−3.31529	−	3.31529i	−0.175957	−	0.175957i
$356$	0.162579			0.00861668
$357$	0.289286	−	0.124609i	0.0153107	−	0.00659501i
$358$	−26.4314			−1.39694
$359$	−4.98636	−	4.98636i	−0.263170	−	0.263170i	0.563171	−	0.826341i	$-0.309581\pi$
$359$	−4.98636	−	4.98636i	−0.263170	−	0.263170i	−0.826341	+	0.563171i	$0.809581\pi$
$360$	−7.66740	+	3.17594i	−0.404107	+	0.167387i
$361$		−	13.6050i		−	0.716051i
$362$	−5.89986	−	14.2435i	−0.310090	−	0.748622i
$363$	−1.27241	−	0.527051i	−0.0667844	−	0.0276630i
$364$	−0.103483	+	0.249830i	−0.00542397	+	0.0130946i
$365$	3.88846	−	3.88846i	0.203531	−	0.203531i
$366$	−0.179185	+	0.179185i	−0.00936615	+	0.00936615i
$367$	−6.24413	+	15.0747i	−0.325941	+	0.786891i	0.672945	+	0.739693i	$0.265029\pi$
$367$	−6.24413	+	15.0747i	−0.325941	+	0.786891i	−0.998886	+	0.0471982i	$0.984971\pi$
$368$	17.7063	+	7.33419i	0.923005	+	0.382321i
$369$	−1.23349	−	2.97791i	−0.0642130	−	0.155024i
$370$			0.170630i			0.00887063i
$371$	−7.69735	+	3.18835i	−0.399626	+	0.165531i
$372$	0.0355577	+	0.0355577i	0.00184358	+	0.00184358i
$373$	18.3821			0.951787			0.475893	−	0.879503i	$-0.342125\pi$
$373$	18.3821			0.951787			0.475893	+	0.879503i	$0.342125\pi$
$374$	20.0554	−	20.6261i	1.03704	−	1.06655i
$375$	0.109907			0.00567556
$376$	−9.69648	−	9.69648i	−0.500058	−	0.500058i
$377$	33.8960	−	14.0402i	1.74573	−	0.723105i
$378$			0.657987i			0.0338432i
$379$	−6.31254	−	15.2398i	−0.324253	−	0.782817i	−0.998998	−	0.0447652i	$-0.985746\pi$
$379$	−6.31254	−	15.2398i	−0.324253	−	0.782817i	0.674744	−	0.738052i	$-0.264254\pi$
$380$	0.148046	+	0.0613226i	0.00759460	+	0.00314579i
$381$	−0.0209683	+	0.0506219i	−0.00107424	+	0.00259344i
$382$	−18.8567	+	18.8567i	−0.964795	+	0.964795i
$383$	−25.6981	+	25.6981i	−1.31311	+	1.31311i	−0.394002	+	0.919110i	$0.628910\pi$
$383$	−25.6981	+	25.6981i	−1.31311	+	1.31311i	−0.919110	+	0.394002i	$0.871090\pi$
$384$	−0.498974	+	1.20463i	−0.0254631	+	0.0614735i
$385$	3.11511	+	1.29032i	0.158761	+	0.0657609i
$386$	5.44171	+	13.1374i	0.276976	+	0.668678i
$387$		−	1.91558i		−	0.0973744i
$388$	0.172144	−	0.0713045i	0.00873930	−	0.00361994i
$389$	−4.50312	−	4.50312i	−0.228317	−	0.228317i	0.583672	−	0.811989i	$-0.301615\pi$
$389$	−4.50312	−	4.50312i	−0.228317	−	0.228317i	−0.811989	+	0.583672i	$0.801615\pi$
$390$	−0.891477			−0.0451417
$391$	0.268192	+	19.1164i	0.0135631	+	0.966757i
$392$	18.1010			0.914237
$393$	1.51811	+	1.51811i	0.0765784	+	0.0765784i
$394$	18.5428	−	7.68066i	0.934171	−	0.386946i
$395$		−	14.8439i		−	0.746880i
$396$	0.382661	+	0.923825i	0.0192294	+	0.0464240i
$397$	−30.8370	−	12.7731i	−1.54767	−	0.641065i	−0.564774	−	0.825245i	$-0.691037\pi$
$397$	−30.8370	−	12.7731i	−1.54767	−	0.641065i	−0.982892	+	0.184181i	$0.941037\pi$
$398$	−7.01089	+	16.9258i	−0.351424	+	0.848413i
$399$	−0.125471	+	0.125471i	−0.00628142	+	0.00628142i
$400$	−2.92263	+	2.92263i	−0.146131	+	0.146131i
$401$	−4.49654	+	10.8556i	−0.224547	+	0.542104i	−0.995497	−	0.0947914i	$-0.969782\pi$
$401$	−4.49654	+	10.8556i	−0.224547	+	0.542104i	0.770950	+	0.636895i	$0.219782\pi$
$402$	−0.437307	−	0.181139i	−0.0218109	−	0.00903438i
$403$	14.3115	+	34.5511i	0.712909	+	1.72111i
$404$		−	0.986724i		−	0.0490914i
$405$	8.21461	−	3.40260i	0.408187	−	0.169077i
$406$	−4.59968	−	4.59968i	−0.228278	−	0.228278i
$407$	−0.575436			−0.0285233
$408$	−1.25855	+	0.0176567i	−0.0623074	+	0.000874139i
$409$	12.6834			0.627154			0.313577	−	0.949563i	$-0.398473\pi$
$409$	12.6834			0.627154			0.313577	+	0.949563i	$0.398473\pi$
$410$	−1.09721	−	1.09721i	−0.0541876	−	0.0541876i
$411$	0.387605	−	0.160551i	0.0191192	−	0.00791941i
$412$		−	0.751735i		−	0.0370353i
$413$	2.63824	+	6.36927i	0.129819	+	0.313411i
$414$	−18.4114	−	7.62626i	−0.904872	−	0.374810i
$415$	1.92684	−	4.65179i	0.0945846	−	0.228347i
$416$	1.55546	−	1.55546i	0.0762627	−	0.0762627i
$417$	−1.02993	+	1.02993i	−0.0504358	+	0.0504358i
$418$	−6.20207	+	14.9731i	−0.303353	+	0.732359i
$419$	32.3564	+	13.4025i	1.58072	+	0.654754i	0.988527	−	0.151045i	$-0.0482639\pi$
$419$	32.3564	+	13.4025i	1.58072	+	0.654754i	0.592189	+	0.805799i	$0.298264\pi$
$420$	0.00201691	+	0.00486925i	9.84150e−5	+	0.000237595i
$421$			10.0231i			0.488497i	0.969713	+	0.244248i	$0.0785412\pi$
$421$			10.0231i			0.488497i	−0.969713	+	0.244248i	$0.921459\pi$
$422$	17.1134	−	7.08861i	0.833068	−	0.345068i
$423$	10.4308	+	10.4308i	0.507165	+	0.507165i
$424$	33.2929			1.61685
$425$	−3.83101	−	1.52425i	−0.185831	−	0.0739371i
$426$	0.741207			0.0359116
$427$	0.787836	+	0.787836i	0.0381260	+	0.0381260i
$428$	−1.05980	+	0.438982i	−0.0512271	+	0.0212190i
$429$		−	3.00643i		−	0.145152i
$430$	−0.352899	−	0.851973i	−0.0170183	−	0.0410858i
$431$	21.9385	+	9.08724i	1.05674	+	0.437717i	0.842294	−	0.539019i	$-0.181205\pi$
$431$	21.9385	+	9.08724i	1.05674	+	0.437717i	0.214448	+	0.976735i	$0.431205\pi$
$432$	1.04095	−	2.51307i	0.0500826	−	0.120910i
$433$	22.8337	−	22.8337i	1.09732	−	1.09732i	0.102592	−	0.994724i	$-0.467286\pi$
$433$	22.8337	−	22.8337i	1.09732	−	1.09732i	0.994724	−	0.102592i	$-0.0327135\pi$
$434$	4.68859	−	4.68859i	0.225059	−	0.225059i
$435$	0.273647	−	0.660642i	0.0131204	−	0.0316753i
$436$	0.675618	+	0.279850i	0.0323562	+	0.0134024i
$437$	−4.12155	−	9.95030i	−0.197160	−	0.475987i
$438$			0.869353i			0.0415393i
$439$	−19.7035	+	8.16145i	−0.940396	+	0.389525i	−0.799613	−	0.600515i	$-0.794962\pi$
$439$	−19.7035	+	8.16145i	−0.940396	+	0.389525i	−0.140783	+	0.990040i	$0.544962\pi$
$440$	−9.52730	−	9.52730i	−0.454196	−	0.454196i
$441$	−19.4719			−0.927231
$442$	31.0741	+	12.3635i	1.47805	+	0.588073i
$443$	−13.8187			−0.656546			−0.328273	−	0.944583i	$-0.606467\pi$
$443$	−13.8187			−0.656546			−0.328273	+	0.944583i	$0.606467\pi$
$444$	−0.000636019	0	0.000636019i	−3.01841e−5	0	3.01841e-5i
$445$	2.17719	−	0.901821i	0.103209	−	0.0427504i
$446$			29.3732i			1.39086i
$447$	−0.734118	−	1.77232i	−0.0347226	−	0.0838277i
$448$	4.94817	+	2.04960i	0.233779	+	0.0968344i
$449$	−2.53099	+	6.11035i	−0.119445	+	0.288365i	−0.972282	−	0.233812i	$-0.924880\pi$
$449$	−2.53099	+	6.11035i	−0.119445	+	0.288365i	0.852837	+	0.522177i	$0.174880\pi$
$450$	3.03902	−	3.03902i	0.143261	−	0.143261i
$451$	3.70027	−	3.70027i	0.174239	−	0.174239i
$452$	−0.304661	+	0.735517i	−0.0143301	+	0.0345958i
$453$	−1.14452	−	0.474074i	−0.0537740	−	0.0222739i
$454$	0.671710	+	1.62165i	0.0315249	+	0.0761079i
$455$			3.91962i			0.183755i
$456$	0.655089	−	0.271347i	0.0306774	−	0.0127070i
$457$	−3.54288	−	3.54288i	−0.165729	−	0.165729i	0.619370	−	0.785099i	$-0.287388\pi$
$457$	−3.54288	−	3.54288i	−0.165729	−	0.165729i	−0.785099	+	0.619370i	$0.787388\pi$
$458$	−5.06236			−0.236548
$459$	2.71320	−	0.0380648i	0.126641	−	0.00177671i
$460$	−0.319896			−0.0149152
$461$	11.5839	+	11.5839i	0.539518	+	0.539518i	0.923387	−	0.383869i	$-0.125409\pi$
$461$	11.5839	+	11.5839i	0.539518	+	0.539518i	−0.383869	+	0.923387i	$0.625409\pi$
$462$	−0.492468	+	0.203987i	−0.0229117	+	0.00949032i
$463$		−	27.3768i		−	1.27231i	−0.771563	−	0.636153i	$-0.780525\pi$
$463$		−	27.3768i		−	1.27231i	0.771563	−	0.636153i	$-0.219475\pi$
$464$	10.2909	+	24.8445i	0.477744	+	1.15338i
$465$	0.673411	+	0.278936i	0.0312287	+	0.0129353i
$466$	15.9645	−	38.5417i	0.739541	−	1.78541i
$467$	0.457032	−	0.457032i	0.0211489	−	0.0211489i	−0.696453	−	0.717602i	$-0.745240\pi$
$467$	0.457032	−	0.457032i	0.0211489	−	0.0211489i	0.717602	+	0.696453i	$0.245240\pi$
$468$	−0.821949	+	0.821949i	−0.0379946	+	0.0379946i
$469$	−0.796426	+	1.92274i	−0.0367755	+	0.0887840i
$470$	6.56085	+	2.71759i	0.302629	+	0.125353i
$471$	0.258473	+	0.624009i	0.0119098	+	0.0287528i
$472$		−	27.5487i		−	1.26803i
$473$	2.87321	−	1.19012i	0.132110	−	0.0547219i
$474$	1.65935	+	1.65935i	0.0762165	+	0.0762165i
$475$	2.32272			0.106574
$476$	−0.00277360	−	0.197699i	−0.000127128	−	0.00906150i
$477$	−35.8144			−1.63983
$478$	8.00594	+	8.00594i	0.366183	+	0.366183i
$479$	−12.5323	+	5.19106i	−0.572616	+	0.237185i	−0.650152	−	0.759804i	$-0.725295\pi$
$479$	−12.5323	+	5.19106i	−0.572616	+	0.237185i	0.0775357	+	0.996990i	$0.475295\pi$
$480$		−	0.0428738i		−	0.00195691i
$481$	−0.255989	−	0.618013i	−0.0116721	−	0.0281790i
$482$	15.4511	+	6.40008i	0.703781	+	0.291515i
$483$	0.135558	−	0.327266i	0.00616811	−	0.0148911i
$484$	−0.611305	+	0.611305i	−0.0277866	+	0.0277866i
$485$	1.90976	−	1.90976i	0.0867176	−	0.0867176i
$486$	−1.62469	+	3.92236i	−0.0736976	+	0.177922i
$487$	−26.8238	−	11.1108i	−1.21550	−	0.503478i	−0.319527	−	0.947577i	$-0.603524\pi$
$487$	−26.8238	−	11.1108i	−1.21550	−	0.503478i	−0.895978	+	0.444099i	$0.853524\pi$
$488$	−1.70379	−	4.11332i	−0.0771270	−	0.186201i
$489$			1.23108i			0.0556716i
$490$	−8.66030	+	3.58721i	−0.391232	+	0.162054i
$491$	−9.28419	−	9.28419i	−0.418990	−	0.418990i	0.465866	−	0.884855i	$-0.345743\pi$
$491$	−9.28419	−	9.28419i	−0.418990	−	0.418990i	−0.884855	+	0.465866i	$0.845743\pi$
$492$	0.00817968			0.000368768
$493$	−18.7007	+	19.2328i	−0.842235	+	0.866204i
$494$	−18.8401			−0.847655
$495$	10.2488	+	10.2488i	0.460651	+	0.460651i
$496$	−25.3247	+	10.4898i	−1.13711	+	0.471007i
$497$		−	3.25892i		−	0.146183i
$498$	0.304613	+	0.735400i	0.0136500	+	0.0329541i
$499$	10.4777	+	4.34000i	0.469045	+	0.194285i	0.604671	−	0.796475i	$-0.293305\pi$
$499$	10.4777	+	4.34000i	0.469045	+	0.194285i	−0.135626	+	0.990760i	$0.543305\pi$
$500$	0.0264012	−	0.0637382i	0.00118070	−	0.00285046i
$501$	0.443449	−	0.443449i	0.0198118	−	0.0198118i
$502$	−8.08282	+	8.08282i	−0.360754	+	0.360754i
$503$	7.86171	−	18.9798i	0.350536	−	0.846269i	−0.646018	−	0.763322i	$-0.723567\pi$
$503$	7.86171	−	18.9798i	0.350536	−	0.846269i	0.996554	−	0.0829468i	$-0.0264332\pi$
$504$	−5.32949	−	2.20755i	−0.237394	−	0.0983320i
$505$	−5.47332	−	13.2138i	−0.243560	−	0.588005i
$506$		−	32.3537i		−	1.43830i
$507$	1.90886	−	0.790674i	0.0847753	−	0.0351151i
$508$	0.0243203	+	0.0243203i	0.00107904	+	0.00107904i
$509$	−8.40900			−0.372722			−0.186361	−	0.982481i	$-0.559669\pi$
$509$	−8.40900			−0.372722			−0.186361	+	0.982481i	$0.559669\pi$
$510$	0.598645	−	0.257864i	0.0265085	−	0.0114184i
$511$	3.82235			0.169091
$512$	−15.0955	−	15.0955i	−0.667132	−	0.667132i
$513$	−1.41225	+	0.584975i	−0.0623525	+	0.0258273i
$514$		−	11.4026i		−	0.502946i
$515$	−4.16985	−	10.0669i	−0.183745	−	0.443601i
$516$	0.00449113	+	0.00186029i	0.000197711	+	8.18945e-5i
$517$	−9.16486	+	22.1259i	−0.403070	+	0.973098i
$518$	−0.0838644	+	0.0838644i	−0.00368479	+	0.00368479i
$519$	0.352639	−	0.352639i	0.0154791	−	0.0154791i
$520$	5.99390	−	14.4706i	0.262850	−	0.634576i
$521$	−19.7304	−	8.17262i	−0.864406	−	0.358049i	−0.0939770	−	0.995574i	$-0.529958\pi$
$521$	−19.7304	−	8.17262i	−0.864406	−	0.358049i	−0.770429	+	0.637526i	$0.779958\pi$
$522$	−10.7007	−	25.8339i	−0.468359	−	1.13072i
$523$			24.4644i			1.06975i	0.844930	+	0.534877i	$0.179642\pi$
$523$			24.4644i			1.06975i	−0.844930	+	0.534877i	$0.820358\pi$
$524$	1.24507	−	0.515723i	0.0543910	−	0.0225295i
$525$	0.0540191	+	0.0540191i	0.00235759	+	0.00235759i
$526$	−12.2785			−0.535367
$527$	−19.6046	−	19.0621i	−0.853989	−	0.830359i
$528$	2.20361			0.0958996
$529$	−1.06033	−	1.06033i	−0.0461012	−	0.0461012i
$530$	−15.9288	+	6.59792i	−0.691902	+	0.286595i
$531$			29.6351i			1.28605i
$532$	0.0426244	+	0.102904i	0.00184800	+	0.00446148i
$533$	5.62017	+	2.32795i	0.243436	+	0.100835i
$534$	−0.142569	+	0.344191i	−0.00616955	+	0.0148946i
$535$	−11.7573	+	11.7573i	−0.508312	+	0.508312i
$536$	5.88053	−	5.88053i	0.254000	−	0.254000i
$537$	0.772867	−	1.86587i	0.0333517	−	0.0805181i
$538$	−21.2397	−	8.79776i	−0.915708	−	0.379299i
$539$	−12.0976	−	29.2062i	−0.521080	−	1.25800i
$540$			0.0454030i			0.00195384i
$541$	1.77760	−	0.736307i	0.0764251	−	0.0316563i	−0.344143	−	0.938917i	$-0.611831\pi$
$541$	1.77760	−	0.736307i	0.0764251	−	0.0316563i	0.420569	+	0.907261i	$0.361831\pi$
$542$	22.9142	+	22.9142i	0.984248	+	0.984248i
$543$	1.17800			0.0505530
$544$	−0.594600	+	1.49445i	−0.0254932	+	0.0640740i
$545$	10.5999			0.454049
$546$	−0.438160	−	0.438160i	−0.0187515	−	0.0187515i
$547$	13.6015	−	5.63393i	0.581559	−	0.240890i	−0.0724556	−	0.997372i	$-0.523084\pi$
$547$	13.6015	−	5.63393i	0.581559	−	0.240890i	0.654014	+	0.756482i	$0.273084\pi$
$548$		−	0.263350i		−	0.0112498i
$549$	1.83283	+	4.42484i	0.0782232	+	0.188847i
$550$	6.44637	+	2.67018i	0.274874	+	0.113857i
$551$	5.78313	−	13.9617i	0.246369	−	0.594789i
$552$	−1.00092	+	1.00092i	−0.0426018	+	0.0426018i
$553$	7.29579	−	7.29579i	0.310248	−	0.310248i
$554$	−3.79928	+	9.17226i	−0.161416	+	0.389692i
$555$	−0.0120452	−	0.00498931i	−0.000511292	−	0.000211784i
$556$	0.349882	+	0.844689i	0.0148383	+	0.0358228i
$557$			24.3617i			1.03224i	0.856517	+	0.516119i	$0.172624\pi$
$557$			24.3617i			1.03224i	−0.856517	+	0.516119i	$0.827376\pi$
$558$	26.3332	−	10.9076i	1.11477	−	0.461754i
$559$	2.55636	+	2.55636i	0.108123	+	0.108123i
$560$	−2.87294			−0.121404
$561$	0.869627	+	2.01888i	0.0367157	+	0.0852374i
$562$	13.4931			0.569171
$563$	−21.7224	−	21.7224i	−0.915488	−	0.915488i	0.0812090	−	0.996697i	$-0.474122\pi$
$563$	−21.7224	−	21.7224i	−0.915488	−	0.915488i	−0.996697	+	0.0812090i	$0.974122\pi$
$564$	−0.0345851	+	0.0143256i	−0.00145630	+	0.000603218i
$565$			11.5397i			0.485477i
$566$	11.3266	+	27.3448i	0.476091	+	1.14939i
$567$	5.70985	+	2.36510i	0.239791	+	0.0993247i
$568$	−4.98356	+	12.0314i	−0.209105	+	0.504825i
$569$	−3.78820	+	3.78820i	−0.158809	+	0.158809i	−0.782039	−	0.623230i	$-0.785820\pi$
$569$	−3.78820	+	3.78820i	−0.158809	+	0.158809i	0.623230	+	0.782039i	$0.285820\pi$
$570$	−0.259648	+	0.259648i	−0.0108755	+	0.0108755i
$571$	13.7904	−	33.2930i	0.577110	−	1.39327i	−0.318285	−	0.947995i	$-0.603107\pi$
$571$	13.7904	−	33.2930i	0.577110	−	1.39327i	0.895395	−	0.445272i	$-0.146893\pi$
$572$	−1.74352	−	0.722190i	−0.0729003	−	0.0301963i
$573$	−0.779770	−	1.88253i	−0.0325754	−	0.0786439i
$574$		−	1.07856i		−	0.0450182i
$575$	−4.28390	+	1.77445i	−0.178651	+	0.0739997i
$576$	16.2797	+	16.2797i	0.678319	+	0.678319i
$577$	39.5472			1.64637			0.823186	−	0.567772i	$-0.192194\pi$
$577$	39.5472			1.64637			0.823186	+	0.567772i	$0.192194\pi$
$578$	−24.4431	+	0.685983i	−1.01670	+	0.0285331i
$579$	−1.08653			−0.0451546
$580$	−0.317392	−	0.317392i	−0.0131790	−	0.0131790i
$581$	3.23339	−	1.33931i	0.134144	−	0.0555641i
$582$			0.426969i			0.0176984i
$583$	−22.2510	−	53.7186i	−0.921541	−	2.22480i
$584$	−14.1114	−	5.84515i	−0.583936	−	0.241874i
$585$	−6.44785	+	15.5665i	−0.266586	+	0.643595i
$586$	23.8550	−	23.8550i	0.985442	−	0.985442i
$587$	12.6771	−	12.6771i	0.523242	−	0.523242i	−0.395307	−	0.918549i	$-0.629362\pi$
$587$	12.6771	−	12.6771i	0.523242	−	0.523242i	0.918549	+	0.395307i	$0.129362\pi$
$588$	0.0189098	−	0.0456523i	0.000779827	−	0.00188267i
$589$	14.2316	+	5.89491i	0.586401	+	0.242895i
$590$	5.45953	+	13.1805i	0.224765	+	0.542632i
$591$			1.53357i			0.0630827i
$592$	0.452981	−	0.187631i	0.0186174	−	0.00771158i
$593$	10.8169	+	10.8169i	0.444199	+	0.444199i	0.893420	−	0.449222i	$-0.148299\pi$
$593$	10.8169	+	10.8169i	0.444199	+	0.444199i	−0.449222	+	0.893420i	$0.648299\pi$
$594$	−4.59199			−0.188412
$595$	−1.13377	−	2.63211i	−0.0464800	−	0.107906i
$596$	−1.20416			−0.0493245
$597$	−0.989838	−	0.989838i	−0.0405114	−	0.0405114i
$598$	34.7476	−	14.3929i	1.42094	−	0.588571i
$599$			34.6498i			1.41575i	0.706336	+	0.707877i	$0.250347\pi$
$599$			34.6498i			1.41575i	−0.706336	+	0.707877i	$0.749653\pi$
$600$	−0.116823	−	0.282035i	−0.00476927	−	0.0115140i
$601$	−14.8154	−	6.13675i	−0.604333	−	0.250323i	0.0594701	−	0.998230i	$-0.481059\pi$
$601$	−14.8154	−	6.13675i	−0.604333	−	0.250323i	−0.663804	+	0.747907i	$0.731059\pi$
$602$	0.245294	−	0.592193i	0.00999746	−	0.0241360i
$603$	−6.32590	+	6.32590i	−0.257610	+	0.257610i
$604$	−0.549859	+	0.549859i	−0.0223734	+	0.0223734i
$605$	−4.79544	+	11.5772i	−0.194962	+	0.470681i
$606$	2.08896	+	0.865276i	0.0848583	+	0.0351494i
$607$	13.9725	+	33.7326i	0.567126	+	1.36916i	0.903967	+	0.427602i	$0.140641\pi$
$607$	13.9725	+	33.7326i	0.567126	+	1.36916i	−0.336841	+	0.941561i	$0.609359\pi$
$608$		−	0.906076i		−	0.0367462i
$609$	0.459202	−	0.190208i	0.0186078	−	0.00770760i
$610$	1.63034	+	1.63034i	0.0660104	+	0.0660104i
$611$	−27.8402			−1.12629
$612$	0.314203	−	0.789709i	0.0127009	−	0.0319221i
$613$	33.2758			1.34400			0.671998	−	0.740553i	$-0.265436\pi$
$613$	33.2758			1.34400			0.671998	+	0.740553i	$0.265436\pi$
$614$	30.9463	+	30.9463i	1.24889	+	1.24889i
$615$	0.109539	−	0.0453724i	0.00441702	−	0.00182959i
$616$		−	9.36532i		−	0.377339i
$617$	12.1343	+	29.2948i	0.488508	+	1.17936i	0.955471	+	0.295086i	$0.0953483\pi$
$617$	12.1343	+	29.2948i	0.488508	+	1.17936i	−0.466963	+	0.884277i	$0.654652\pi$
$618$	1.59147	+	0.659210i	0.0640185	+	0.0265173i
$619$	−15.6250	+	37.7222i	−0.628023	+	1.51618i	0.214052	+	0.976822i	$0.431334\pi$
$619$	−15.6250	+	37.7222i	−0.628023	+	1.51618i	−0.842075	+	0.539360i	$0.818666\pi$
$620$	0.323526	−	0.323526i	0.0129931	−	0.0129931i
$621$	2.15779	−	2.15779i	0.0865892	−	0.0865892i
$622$	−0.594425	+	1.43507i	−0.0238343	+	0.0575410i
$623$	1.51333	+	0.626842i	0.0606303	+	0.0251139i
$624$	0.980300	+	2.36665i	0.0392434	+	0.0947420i
$625$		−	1.00000i		−	0.0400000i
$626$	4.81800	−	1.99568i	0.192566	−	0.0797635i
$627$	−0.875644	−	0.875644i	−0.0349698	−	0.0349698i
$628$	0.423970			0.0169183
$629$	0.350666	+	0.340963i	0.0139820	+	0.0135951i
$630$	2.98735			0.119019
$631$	−11.1724	−	11.1724i	−0.444764	−	0.444764i	0.448845	−	0.893610i	$-0.351835\pi$
$631$	−11.1724	−	11.1724i	−0.444764	−	0.444764i	−0.893610	+	0.448845i	$0.851835\pi$
$632$	−38.0915	+	15.7780i	−1.51520	+	0.627616i
$633$			1.41536i			0.0562555i
$634$	−4.84113	−	11.6875i	−0.192266	−	0.464171i
$635$	0.460590	+	0.190782i	0.0182779	+	0.00757097i
$636$	0.0347806	−	0.0839677i	0.00137914	−	0.00332954i
$637$	25.9854	−	25.9854i	1.02958	−	1.02958i
$638$	32.1005	−	32.1005i	1.27087	−	1.27087i
$639$	5.36099	−	12.9426i	0.212077	−	0.512000i
$640$	10.9605	+	4.53997i	0.433250	+	0.179458i
$641$	9.54180	+	23.0359i	0.376878	+	0.909865i	0.992547	+	0.121860i	$0.0388859\pi$
$641$	9.54180	+	23.0359i	0.376878	+	0.909865i	−0.615669	+	0.788005i	$0.711114\pi$
$642$		−	2.62861i		−	0.103743i
$643$	22.1880	−	9.19057i	0.875009	−	0.362441i	0.100450	−	0.994942i	$-0.467972\pi$
$643$	22.1880	−	9.19057i	0.875009	−	0.362441i	0.774559	+	0.632501i	$0.217972\pi$
$644$	−0.157228	−	0.157228i	−0.00619567	−	0.00619567i
$645$	0.0704621			0.00277444
$646$	12.6515	−	5.44959i	0.497767	−	0.214411i
$647$	−23.8307			−0.936882			−0.468441	−	0.883495i	$-0.655184\pi$
$647$	−23.8307			−0.936882			−0.468441	+	0.883495i	$0.655184\pi$
$648$	−17.4631	−	17.4631i	−0.686014	−	0.686014i
$649$	−44.4501	+	18.4119i	−1.74482	+	0.722728i
$650$			8.11121i			0.318148i
$651$	0.193884	+	0.468078i	0.00759892	+	0.0183454i
$652$	0.713942	+	0.295725i	0.0279601	+	0.0115815i
$653$	6.32157	−	15.2616i	0.247382	−	0.597234i	−0.750598	−	0.660759i	$-0.770234\pi$
$653$	6.32157	−	15.2616i	0.247382	−	0.597234i	0.997980	+	0.0635255i	$0.0202344\pi$
$654$	−1.18492	+	1.18492i	−0.0463341	+	0.0463341i
$655$	13.8127	−	13.8127i	0.539706	−	0.539706i
$656$	−1.70630	+	4.11938i	−0.0666199	+	0.160835i
$657$	15.1802	+	6.28783i	0.592235	+	0.245312i
$658$	1.88896	+	4.56034i	0.0736392	+	0.177781i
$659$		−	10.2510i		−	0.399324i	−0.979865	−	0.199662i	$-0.936016\pi$
$659$		−	10.2510i		−	0.399324i	0.979865	−	0.199662i	$-0.0639843\pi$
$660$	−0.0339817	+	0.0140757i	−0.00132274	+	0.000547895i
$661$	15.0908	+	15.0908i	0.586962	+	0.586962i	0.936808	−	0.349845i	$-0.113766\pi$
$661$	15.0908	+	15.0908i	0.586962	+	0.586962i	−0.349845	+	0.936808i	$0.613766\pi$
$662$	−50.5790			−1.96581
$663$	−1.78140	+	1.83210i	−0.0691839	+	0.0711527i
$664$	−13.9852			−0.542731
$665$	1.14161	+	1.14161i	0.0442699	+	0.0442699i
$666$	−0.471020	+	0.195103i	−0.0182517	+	0.00756009i
$667$			30.1683i			1.16812i
$668$	−0.150646	−	0.363692i	−0.00582867	−	0.0140717i
$669$	−2.07354	−	0.858887i	−0.0801676	−	0.0332065i
$670$	−1.64811	+	3.97889i	−0.0636721	+	0.153718i
$671$	−5.49818	+	5.49818i	−0.212255	+	0.212255i
$672$	0.0210724	−	0.0210724i	0.000812887	−	0.000812887i
$673$	−10.5299	+	25.4214i	−0.405898	+	0.979924i	0.580308	+	0.814397i	$0.302932\pi$
$673$	−10.5299	+	25.4214i	−0.405898	+	0.979924i	−0.986205	+	0.165526i	$0.947068\pi$
$674$	−41.8807	−	17.3476i	−1.61319	−	0.668203i
$675$	0.251849	+	0.608017i	0.00969367	+	0.0234026i
$676$		−	1.29693i		−	0.0498821i
$677$	15.7463	−	6.52233i	0.605180	−	0.250674i	−0.0589863	−	0.998259i	$-0.518787\pi$
$677$	15.7463	−	6.52233i	0.605180	−	0.250674i	0.664166	+	0.747585i	$0.268787\pi$
$678$	−1.28998	−	1.28998i	−0.0495412	−	0.0495412i
$679$	1.87729			0.0720437
$680$	0.160652	+	11.4511i	0.00616072	+	0.439128i
$681$	−0.134118			−0.00513942
$682$	32.7209	+	32.7209i	1.25295	+	1.25295i
$683$	−2.88510	+	1.19505i	−0.110395	+	0.0457273i	−0.437198	−	0.899366i	$-0.644029\pi$
$683$	−2.88510	+	1.19505i	−0.110395	+	0.0457273i	0.326802	+	0.945093i	$0.394029\pi$
$684$			0.478796i			0.0183072i
$685$	−1.46080	−	3.52667i	−0.0558141	−	0.134747i
$686$	−12.4856	−	5.17169i	−0.476701	−	0.197456i
$687$	0.148026	−	0.357366i	0.00564754	−	0.0136344i
$688$	−1.87372	+	1.87372i	−0.0714349	+	0.0714349i
$689$	47.7947	−	47.7947i	1.82083	−	1.82083i
$690$	0.280522	−	0.677241i	0.0106793	−	0.0257821i
$691$	−33.3778	−	13.8255i	−1.26975	−	0.525948i	−0.356862	−	0.934157i	$-0.616153\pi$
$691$	−33.3778	−	13.8255i	−1.26975	−	0.525948i	−0.912888	+	0.408210i	$0.866153\pi$
$692$	−0.119797	−	0.289214i	−0.00455398	−	0.0109943i
$693$			10.0746i			0.382702i
$694$	−0.585134	+	0.242370i	−0.0222114	+	0.00920025i
$695$	9.37092	+	9.37092i	0.355459	+	0.355459i
$696$	−1.98616			−0.0752852
$697$	−4.44743	+	0.0623950i	−0.168458	+	0.00236338i
$698$	−17.8680			−0.676315
$699$	2.25396	+	2.25396i	0.0852525	+	0.0852525i
$700$	0.0443034	−	0.0183511i	0.00167451	−	0.000693606i
$701$		−	18.1677i		−	0.686185i	−0.939302	−	0.343093i	$-0.888526\pi$
$701$		−	18.1677i		−	0.686185i	0.939302	−	0.343093i	$-0.111474\pi$
$702$	−2.04280	−	4.93175i	−0.0771005	−	0.186137i
$703$	−0.254559	−	0.105442i	−0.00960087	−	0.00397681i
$704$	−14.3038	+	34.5325i	−0.539095	+	1.30149i
$705$	−0.383685	+	0.383685i	−0.0144504	+	0.0144504i
$706$	−7.50677	+	7.50677i	−0.282521	+	0.282521i
$707$	3.80442	−	9.18469i	0.143080	−	0.345426i
$708$	−0.0694802	−	0.0287796i	−0.00261123	−	0.00108160i
$709$	4.44086	+	10.7212i	0.166780	+	0.402643i	0.985068	−	0.172166i	$-0.0550765\pi$
$709$	4.44086	+	10.7212i	0.166780	+	0.402643i	−0.818288	+	0.574809i	$0.805077\pi$
$710$		−	6.74396i		−	0.253096i
$711$	40.9764	−	16.9730i	1.53674	−	0.636536i
$712$	−4.62839	−	4.62839i	−0.173456	−	0.173456i
$713$	−30.7514			−1.15165
$714$	0.420974	+	0.167494i	0.0157545	+	0.00626829i
$715$	−27.3544			−1.02300
$716$	−0.896417	−	0.896417i	−0.0335007	−	0.0335007i
$717$	−0.799260	+	0.331064i	−0.0298489	+	0.0123638i
$718$		−	10.1433i		−	0.378543i
$719$	−9.86790	−	23.8232i	−0.368011	−	0.888456i	−0.994076	−	0.108686i	$-0.965336\pi$
$719$	−9.86790	−	23.8232i	−0.368011	−	0.888456i	0.626066	−	0.779770i	$-0.284664\pi$
$720$	−11.4097	−	4.72604i	−0.425213	−	0.176129i
$721$	2.89840	−	6.99735i	0.107942	−	0.260595i
$722$	13.8376	−	13.8376i	0.514983	−	0.514983i
$723$	−0.903599	+	0.903599i	−0.0336052	+	0.0336052i
$724$	0.282974	−	0.683160i	0.0105166	−	0.0253894i
$725$	−6.01093	−	2.48981i	−0.223240	−	0.0924691i
$726$	−0.758110	−	1.83024i	−0.0281361	−	0.0679265i
$727$		−	17.7430i		−	0.658051i	−0.944321	−	0.329025i	$-0.893280\pi$
$727$		−	17.7430i		−	0.658051i	0.944321	−	0.329025i	$-0.106720\pi$
$728$	10.0583	−	4.16627i	0.372784	−	0.154412i
$729$	18.6322	+	18.6322i	0.690081	+	0.690081i
$730$	7.90991			0.292759
$731$	−2.45609	−	0.977211i	−0.0908419	−	0.0361434i
$732$	−0.0121541			−0.000449227
$733$	−18.9661	−	18.9661i	−0.700527	−	0.700527i	0.263996	−	0.964524i	$-0.414959\pi$
$733$	−18.9661	−	18.9661i	−0.700527	−	0.700527i	−0.964524	+	0.263996i	$0.914959\pi$
$734$	−21.6834	+	8.98155i	−0.800348	+	0.331515i
$735$		−	0.716247i		−	0.0264192i
$736$	0.692200	+	1.67112i	0.0255148	+	0.0615982i
$737$	−13.4185	−	5.55813i	−0.494277	−	0.204736i
$738$	1.77425	−	4.28342i	0.0653111	−	0.157675i
$739$	−0.319229	+	0.319229i	−0.0117430	+	0.0117430i	−0.712954	−	0.701211i	$-0.752643\pi$
$739$	−0.319229	+	0.319229i	−0.0117430	+	0.0117430i	0.701211	+	0.712954i	$0.252643\pi$
$740$	−0.00578689	+	0.00578689i	−0.000212730	+	0.000212730i
$741$	0.550893	−	1.32997i	0.0202376	−	0.0488578i
$742$	−11.0719	−	4.58611i	−0.406460	−	0.168361i
$743$	7.90111	+	19.0750i	0.289864	+	0.699793i	0.999991	−	0.00428071i	$-0.00136260\pi$
$743$	7.90111	+	19.0750i	0.289864	+	0.699793i	−0.710127	+	0.704073i	$0.751363\pi$
$744$		−	2.02455i		−	0.0742236i
$745$	−16.1256	+	6.67946i	−0.590798	+	0.244716i
$746$	18.6964	+	18.6964i	0.684524	+	0.684524i
$747$	15.0444			0.550445
$748$	1.37971	−	0.0193565i	0.0504471	−	0.000707745i
$749$	−11.5574			−0.422298
$750$	0.111786	+	0.111786i	0.00408186	+	0.00408186i
$751$	24.6731	−	10.2199i	0.900333	−	0.372930i	0.115985	−	0.993251i	$-0.462998\pi$
$751$	24.6731	−	10.2199i	0.900333	−	0.372930i	0.784348	+	0.620321i	$0.212998\pi$
$752$		−	20.4058i		−	0.744123i
$753$	−0.334243	−	0.806935i	−0.0121805	−	0.0294064i
$754$	48.7559	+	20.1953i	1.77558	+	0.735471i
$755$	−4.31342	+	10.4135i	−0.156981	+	0.378986i
$756$	−0.0223155	+	0.0223155i	−0.000811609	+	0.000811609i
$757$	13.6672	−	13.6672i	0.496742	−	0.496742i	−0.413680	−	0.910422i	$-0.635757\pi$
$757$	13.6672	−	13.6672i	0.496742	−	0.496742i	0.910422	+	0.413680i	$0.135757\pi$
$758$	9.07995	−	21.9209i	0.329799	−	0.796204i
$759$	2.28394	+	0.946039i	0.0829018	+	0.0343390i
$760$	−2.46888	−	5.96041i	−0.0895558	−	0.216207i
$761$			9.52382i			0.345238i	0.984989	+	0.172619i	$0.0552230\pi$
$761$			9.52382i			0.345238i	−0.984989	+	0.172619i	$0.944777\pi$
$762$	−0.0728145	+	0.0301607i	−0.00263779	+	0.00109261i
$763$	5.20984	+	5.20984i	0.188609	+	0.188609i
$764$	−1.27905			−0.0462743
$765$	−0.172819	−	12.3183i	−0.00624828	−	0.445369i
$766$	−52.2751			−1.88878
$767$	−39.5483	−	39.5483i	−1.42801	−	1.42801i
$768$	−0.167928	+	0.0695582i	−0.00605960	+	0.00250997i
$769$			21.8393i			0.787544i	0.919208	+	0.393772i	$0.128830\pi$
$769$			21.8393i			0.787544i	−0.919208	+	0.393772i	$0.871170\pi$
$770$	1.85600	+	4.48078i	0.0668855	+	0.161476i
$771$	0.804939	+	0.333417i	0.0289892	+	0.0120077i
$772$	−0.261000	+	0.630110i	−0.00939359	+	0.0226781i
$773$	12.8920	−	12.8920i	0.463693	−	0.463693i	−0.436171	−	0.899864i	$-0.643666\pi$
$773$	12.8920	−	12.8920i	0.463693	−	0.463693i	0.899864	+	0.436171i	$0.143666\pi$
$774$	1.94834	−	1.94834i	0.0700316	−	0.0700316i
$775$	2.53793	−	6.12711i	0.0911652	−	0.220092i
$776$	−6.93062	−	2.87076i	−0.248795	−	0.103054i
$777$	−0.00346799	−	0.00837247i	−0.000124413	−	0.000300361i
$778$		−	9.16025i		−	0.328411i
$779$	2.31494	−	0.958880i	0.0829413	−	0.0343554i
$780$	−0.0302343	−	0.0302343i	−0.00108256	−	0.00108256i
$781$	22.7435			0.813826
$782$	−19.1705	+	19.7161i	−0.685536	+	0.705045i
$783$	4.28180			0.153019
$784$	19.0463	+	19.0463i	0.680227	+	0.680227i
$785$	5.67762	−	2.35175i	0.202643	−	0.0839375i
$786$			3.08814i			0.110150i
$787$	3.86446	+	9.32964i	0.137753	+	0.332566i	0.977669	−	0.210151i	$-0.0673956\pi$
$787$	3.86446	+	9.32964i	0.137753	+	0.332566i	−0.839916	+	0.542717i	$0.817396\pi$
$788$	0.889364	+	0.368387i	0.0316823	+	0.0131232i
$789$	0.359029	−	0.866773i	0.0127818	−	0.0308579i
$790$	15.0978	−	15.0978i	0.537156	−	0.537156i
$791$	−5.67173	+	5.67173i	−0.201664	+	0.201664i
$792$	15.4061	−	37.1937i	0.547433	−	1.32162i
$793$	−8.35093	−	3.45907i	−0.296550	−	0.122835i
$794$	−18.3728	−	44.3559i	−0.652028	−	1.57413i
$795$		−	1.31738i		−	0.0467228i
$796$	−0.811810	+	0.336263i	−0.0287738	+	0.0119185i
$797$	21.3651	+	21.3651i	0.756792	+	0.756792i	0.975737	−	0.218945i	$-0.0702615\pi$
$797$	21.3651	+	21.3651i	0.756792	+	0.756792i	−0.218945	+	0.975737i	$0.570262\pi$
$798$	−0.255234			−0.00903518
$799$	18.6953	−	8.05291i	0.661390	−	0.284891i
$800$	−0.390093			−0.0137919
$801$	4.97892	+	4.97892i	0.175921	+	0.175921i
$802$	−15.6147	+	6.46782i	−0.551374	+	0.228387i
$803$			26.6756i			0.941360i
$804$	−0.00868793	−	0.0209745i	−0.000306400	−	0.000739714i
$805$	−2.97767	−	1.23339i	−0.104949	−	0.0434714i
$806$	−20.5857	+	49.6983i	−0.725100	+	1.75055i
$807$	1.24212	−	1.24212i	0.0437246	−	0.0437246i
$808$	−28.0905	+	28.0905i	−0.988222	+	0.988222i
$809$	9.87604	−	23.8429i	0.347223	−	0.838270i	−0.649723	−	0.760171i	$-0.725115\pi$
$809$	9.87604	−	23.8429i	0.347223	−	0.838270i	0.996946	−	0.0780990i	$-0.0248850\pi$
$810$	11.8159	+	4.89430i	0.415168	+	0.171968i
$811$	−18.0534	−	43.5848i	−0.633941	−	1.53047i	−0.834628	−	0.550814i	$-0.814317\pi$
$811$	−18.0534	−	43.5848i	−0.633941	−	1.53047i	0.200686	−	0.979656i	$-0.435683\pi$
$812$		−	0.311995i		−	0.0109489i
$813$	−2.28760	+	0.947554i	−0.0802296	+	0.0332322i
$814$	−0.585277	−	0.585277i	−0.0205139	−	0.0205139i
$815$	11.2012			0.392360
$816$	−1.34286	−	1.30570i	−0.0470095	−	0.0457087i
$817$	1.48911			0.0520975
$818$	12.9003	+	12.9003i	0.451049	+	0.451049i
$819$	−10.8200	+	4.48180i	−0.378082	+	0.156607i
$820$		−	0.0744238i		−	0.00259899i
$821$	−13.3232	−	32.1651i	−0.464983	−	1.12257i	−0.966326	−	0.257320i	$-0.917161\pi$
$821$	−13.3232	−	32.1651i	−0.464983	−	1.12257i	0.501343	−	0.865249i	$-0.332839\pi$
$822$	0.557531	+	0.230937i	0.0194461	+	0.00805484i
$823$	4.56508	−	11.0211i	0.159129	−	0.384171i	−0.824126	−	0.566406i	$-0.808333\pi$
$823$	4.56508	−	11.0211i	0.159129	−	0.384171i	0.983255	+	0.182236i	$0.0583334\pi$
$824$	−21.4008	+	21.4008i	−0.745531	+	0.745531i
$825$	−0.376991	+	0.376991i	−0.0131251	+	0.0131251i
$826$	−3.79484	+	9.16155i	−0.132039	+	0.318771i
$827$	−7.00545	−	2.90175i	−0.243603	−	0.100904i	0.257541	−	0.966267i	$-0.417088\pi$
$827$	−7.00545	−	2.90175i	−0.243603	−	0.100904i	−0.501145	+	0.865363i	$0.667088\pi$
$828$	−0.365778	−	0.883065i	−0.0127116	−	0.0306886i
$829$		−	24.5064i		−	0.851141i	−0.904925	−	0.425570i	$-0.860073\pi$
$829$		−	24.5064i		−	0.851141i	0.904925	−	0.425570i	$-0.139927\pi$
$830$	6.69113	−	2.77156i	0.232252	−	0.0962021i
$831$	−0.536403	−	0.536403i	−0.0186076	−	0.0186076i
$832$	−43.4508			−1.50639
$833$	−9.93334	+	24.9662i	−0.344170	+	0.865026i
$834$	−2.09508			−0.0725467
$835$	−4.03477	−	4.03477i	−0.139629	−	0.139629i
$836$	−0.718154	+	0.297469i	−0.0248379	+	0.0102882i
$837$			4.36456i			0.150861i
$838$	19.2781	+	46.5415i	0.665951	+	1.60775i
$839$	−12.9110	−	5.34790i	−0.445737	−	0.184630i	0.148514	−	0.988910i	$-0.452551\pi$
$839$	−12.9110	−	5.34790i	−0.445737	−	0.184630i	−0.594250	+	0.804280i	$0.702551\pi$
$840$	0.0812018	−	0.196038i	0.00280173	−	0.00676397i
$841$	−9.42601	+	9.42601i	−0.325035	+	0.325035i
$842$	−10.1945	+	10.1945i	−0.351326	+	0.351326i
$843$	−0.394544	+	0.952514i	−0.0135888	+	0.0328063i
$844$	0.820809	+	0.339990i	0.0282534	+	0.0117029i
$845$	−7.19405	−	17.3680i	−0.247483	−	0.597476i
$846$			21.2184i			0.729505i
$847$	−8.04714	+	3.33324i	−0.276503	+	0.114531i
$848$	35.0317	+	35.0317i	1.20299	+	1.20299i
$849$	−2.26154			−0.0776158
$850$	−2.34621	−	5.44685i	−0.0804743	−	0.186825i
$851$	0.550047			0.0188554
$852$	0.0251379	+	0.0251379i	0.000861212	+	0.000861212i
$853$	−6.83679	+	2.83189i	−0.234087	+	0.0969621i	−0.496644	−	0.867955i	$-0.665434\pi$
$853$	−6.83679	+	2.83189i	−0.234087	+	0.0969621i	0.262556	+	0.964917i	$0.415434\pi$
$854$			1.60262i			0.0548404i
$855$	2.65586	+	6.41182i	0.0908286	+	0.219280i
$856$	42.6679	+	17.6736i	1.45836	+	0.604072i
$857$	18.4907	−	44.6404i	0.631629	−	1.52489i	−0.205944	−	0.978564i	$-0.566027\pi$
$857$	18.4907	−	44.6404i	0.631629	−	1.52489i	0.837574	−	0.546324i	$-0.183973\pi$
$858$	3.05785	−	3.05785i	0.104393	−	0.104393i
$859$	−3.68462	+	3.68462i	−0.125718	+	0.125718i	−0.767166	−	0.641448i	$-0.778334\pi$
$859$	−3.68462	+	3.68462i	−0.125718	+	0.125718i	0.641448	+	0.767166i	$0.278334\pi$
$860$	0.0169260	−	0.0408631i	0.000577173	−	0.00139342i
$861$	0.0761386	+	0.0315377i	0.00259480	+	0.00107480i
$862$	13.0711	+	31.5564i	0.445202	+	1.07481i
$863$		−	7.90307i		−	0.269024i	−0.990912	−	0.134512i	$-0.957053\pi$
$863$		−	7.90307i		−	0.269024i	0.990912	−	0.134512i	$-0.0429466\pi$
$864$	0.237183	−	0.0982444i	0.00806913	−	0.00334234i
$865$	−3.20852	−	3.20852i	−0.109093	−	0.109093i
$866$	46.4483			1.57838
$867$	0.666305	−	1.74557i	0.0226289	−	0.0592827i
$868$	0.318026			0.0107945
$869$	50.9161	+	50.9161i	1.72721	+	1.72721i
$870$	0.950266	−	0.393613i	0.0322170	−	0.0133447i
$871$		−	16.8840i		−	0.572091i
$872$	−11.2669	−	27.2007i	−0.381546	−	0.921133i
$873$	7.45551	+	3.08817i	0.252331	+	0.104519i
$874$	5.92843	−	14.3125i	0.200532	−	0.484127i
$875$	0.491499	−	0.491499i	0.0166157	−	0.0166157i
$876$	−0.0294840	+	0.0294840i	−0.000996172	+	0.000996172i
$877$	−10.5262	+	25.4126i	−0.355445	+	0.858121i	0.640483	+	0.767972i	$0.278734\pi$
$877$	−10.5262	+	25.4126i	−0.355445	+	0.858121i	−0.995928	+	0.0901488i	$0.971266\pi$
$878$	−28.3415	−	11.7394i	−0.956478	−	0.396186i
$879$	0.986461	+	2.38153i	0.0332725	+	0.0803269i
$880$		−	20.0498i		−	0.675878i
$881$	18.2295	−	7.55089i	0.614166	−	0.254396i	−0.0538426	−	0.998549i	$-0.517147\pi$
$881$	18.2295	−	7.55089i	0.614166	−	0.254396i	0.668009	+	0.744154i	$0.267147\pi$
$882$	−19.8048	−	19.8048i	−0.666864	−	0.666864i
$883$	−21.8566			−0.735534			−0.367767	−	0.929918i	$-0.619878\pi$
$883$	−21.8566			−0.735534			−0.367767	+	0.929918i	$0.619878\pi$
$884$	0.634568	+	1.47318i	0.0213428	+	0.0495485i
$885$	−1.09009			−0.0366429
$886$	−14.0550	−	14.0550i	−0.472187	−	0.472187i
$887$	2.56722	−	1.06338i	0.0861989	−	0.0357048i	−0.339167	−	0.940726i	$-0.610145\pi$
$887$	2.56722	−	1.06338i	0.0861989	−	0.0357048i	0.425366	+	0.905021i	$0.360145\pi$
$888$			0.0362130i			0.00121523i
$889$	0.132610	+	0.320149i	0.00444759	+	0.0107374i
$890$	3.13167	+	1.29718i	0.104974	+	0.0434815i
$891$	−16.5056	+	39.8481i	−0.552960	+	1.33496i
$892$	−0.996188	+	0.996188i	−0.0333549	+	0.0333549i
$893$	−8.10863	+	8.10863i	−0.271345	+	0.271345i
$894$	1.05595	−	2.54930i	0.0353164	−	0.0852613i
$895$	−16.9768	−	7.03202i	−0.567472	−	0.235055i
$896$	3.15567	+	7.61845i	0.105423	+	0.254515i
$897$			2.87379i			0.0959530i
$898$	−8.78912	+	3.64057i	−0.293297	+	0.121488i
$899$	−30.5107	−	30.5107i	−1.01759	−	1.01759i
$900$	0.206136			0.00687119
$901$	−18.2703	+	45.9200i	−0.608671	+	1.52982i
$902$	7.52710			0.250625
$903$	0.0346321	+	0.0346321i	0.00115248	+	0.00115248i
$904$	29.6123	−	12.2658i	0.984890	−	0.407955i
$905$		−	10.7182i		−	0.356286i
$906$	−0.681907	−	1.64627i	−0.0226548	−	0.0546936i
$907$	39.2435	+	16.2552i	1.30306	+	0.539745i	0.922851	−	0.385156i	$-0.125853\pi$
$907$	39.2435	+	16.2552i	1.30306	+	0.539745i	0.380208	+	0.924901i	$0.375853\pi$
$908$	−0.0322171	+	0.0777791i	−0.00106916	+	0.00258119i
$909$	30.2180	−	30.2180i	1.00227	−	1.00227i
$910$	−3.98665	+	3.98665i	−0.132156	+	0.132156i
$911$	−22.6043	+	54.5717i	−0.748915	+	1.80804i	−0.183933	+	0.982939i	$0.558883\pi$
$911$	−22.6043	+	54.5717i	−0.748915	+	1.80804i	−0.564982	+	0.825103i	$0.691117\pi$
$912$	0.974822	+	0.403784i	0.0322796	+	0.0133706i
$913$	9.34686	+	22.5653i	0.309336	+	0.746803i
$914$		−	7.20694i		−	0.238384i
$915$	−0.162762	+	0.0674182i	−0.00538074	+	0.00222878i
$916$	−0.171689	−	0.171689i	−0.00567277	−	0.00567277i
$917$	13.5778			0.448380
$918$	2.79832	+	2.72089i	0.0923582	+	0.0898026i
$919$	26.5657			0.876323			0.438161	−	0.898896i	$-0.355630\pi$
$919$	26.5657			0.876323			0.438161	+	0.898896i	$0.355630\pi$
$920$	9.10695	+	9.10695i	0.300247	+	0.300247i
$921$	−3.08947	+	1.27970i	−0.101802	+	0.0421676i
$922$			23.5641i			0.776042i
$923$	10.1177	+	24.4263i	0.333028	+	0.804001i
$924$	−0.0236202	−	0.00978379i	−0.000777046	−	0.000321863i
$925$	−0.0453958	+	0.109595i	−0.00149260	+	0.00360347i
$926$	27.8450	−	27.8450i	0.915042	−	0.915042i
$927$	23.0215	−	23.0215i	0.756127	−	0.756127i
$928$	−0.971255	+	2.34482i	−0.0318830	+	0.0769724i
$929$	36.0284	+	14.9234i	1.18205	+	0.489622i	0.885159	−	0.465288i	$-0.154049\pi$
$929$	36.0284	+	14.9234i	1.18205	+	0.489622i	0.296894	+	0.954911i	$0.404049\pi$
$930$	0.401221	+	0.968633i	0.0131566	+	0.0317627i
$931$		−	15.1368i		−	0.496090i
$932$	1.84857	−	0.765703i	0.0605519	−	0.0250814i
$933$	−0.0839243	−	0.0839243i	−0.00274756	−	0.00274756i
$934$	0.929695			0.0304206
$935$	18.3691	−	7.91240i	0.600732	−	0.258763i
$936$	46.7993			1.52968
$937$	6.93328	+	6.93328i	0.226500	+	0.226500i	0.811229	−	0.584729i	$-0.198799\pi$
$937$	6.93328	+	6.93328i	0.226500	+	0.226500i	−0.584729	+	0.811229i	$0.698799\pi$
$938$	−2.76567	+	1.14558i	−0.0903023	+	0.0374044i
$939$			0.398471i			0.0130036i
$940$	0.130344	+	0.314677i	0.00425134	+	0.0102636i
$941$	−45.4770	−	18.8372i	−1.48251	−	0.614075i	−0.512837	−	0.858486i	$-0.671405\pi$
$941$	−45.4770	−	18.8372i	−1.48251	−	0.614075i	−0.969672	+	0.244411i	$0.921405\pi$
$942$	−0.371787	+	0.897574i	−0.0121135	+	0.0292445i
$943$	−3.53701	+	3.53701i	−0.115181	+	0.115181i
$944$	28.9875	−	28.9875i	0.943462	−	0.943462i
$945$	−0.175056	+	0.422623i	−0.00569458	+	0.0137479i
$946$	4.13282	+	1.71187i	0.134370	+	0.0556577i
$947$	6.96387	+	16.8123i	0.226295	+	0.546326i	0.995721	−	0.0924110i	$-0.0294574\pi$
$947$	6.96387	+	16.8123i	0.226295	+	0.546326i	−0.769425	+	0.638737i	$0.779457\pi$
$948$			0.112553i			0.00365556i
$949$	−28.6493	+	11.8669i	−0.929996	+	0.385217i
$950$	2.36244	+	2.36244i	0.0766477	+	0.0766477i
$951$	0.966612			0.0313445
$952$	−5.54922	+	5.70714i	−0.179851	+	0.184970i
$953$	−5.23591			−0.169608			−0.0848039	−	0.996398i	$-0.527026\pi$
$953$	−5.23591			−0.169608			−0.0848039	+	0.996398i	$0.527026\pi$
$954$	−36.4268	−	36.4268i	−1.17936	−	1.17936i
$955$	−17.1284	+	7.09483i	−0.554263	+	0.229583i
$956$			0.543041i			0.0175632i
$957$	1.32743	+	3.20470i	0.0429097	+	0.103593i
$958$	−18.0265	−	7.46681i	−0.582409	−	0.241242i
$959$	1.01538	−	2.45134i	0.0327882	−	0.0791578i
$960$	−0.598826	+	0.598826i	−0.0193270	+	0.0193270i
$961$	9.18007	−	9.18007i	0.296131	−	0.296131i
$962$	0.368215	−	0.888949i	0.0118717	−	0.0286609i
$963$	−45.8994	−	19.0121i	−1.47909	−	0.612658i
$964$	0.306966	+	0.741081i	0.00988671	+	0.0238686i
$965$			9.88591i			0.318239i
$966$	0.470740	−	0.194987i	0.0151458	−	0.00627359i
$967$	−2.25894	−	2.25894i	−0.0726426	−	0.0726426i	0.669852	−	0.742495i	$-0.266358\pi$
$967$	−2.25894	−	2.25894i	−0.0726426	−	0.0726426i	−0.742495	+	0.669852i	$0.766358\pi$
$968$	34.8059			1.11870
$969$	0.0147654	+	1.05245i	0.000474332	+	0.0338097i
$970$	3.88483			0.124734
$971$	−19.2766	−	19.2766i	−0.618617	−	0.618617i	0.326560	−	0.945176i	$-0.394110\pi$
$971$	−19.2766	−	19.2766i	−0.618617	−	0.618617i	−0.945176	+	0.326560i	$0.894110\pi$
$972$	−0.188128	+	0.0779250i	−0.00603419	+	0.00249944i
$973$			9.21160i			0.295310i
$974$	−15.9818	−	38.5834i	−0.512089	−	1.23629i
$975$	−0.572593	−	0.237176i	−0.0183377	−	0.00759571i
$976$	2.53537	−	6.12092i	0.0811552	−	0.195926i
$977$	−5.66117	+	5.66117i	−0.181117	+	0.181117i	−0.791842	−	0.610726i	$-0.790878\pi$
$977$	−5.66117	+	5.66117i	−0.181117	+	0.181117i	0.610726	+	0.791842i	$0.290878\pi$
$978$	−1.25214	+	1.25214i	−0.0400390	+	0.0400390i
$979$	−4.37463	+	10.5613i	−0.139814	+	0.337540i
$980$	−0.415373	−	0.172053i	−0.0132686	−	0.00549603i
$981$	12.1202	+	29.2608i	0.386969	+	0.934225i
$982$		−	18.8859i		−	0.602674i
$983$	10.1132	−	4.18902i	0.322561	−	0.133609i	−0.215527	−	0.976498i	$-0.569147\pi$
$983$	10.1132	−	4.18902i	0.322561	−	0.133609i	0.538088	+	0.842889i	$0.319147\pi$
$984$	−0.232863	−	0.232863i	−0.00742341	−	0.00742341i
$985$	13.9534			0.444592
$986$	−38.5822	+	0.541287i	−1.22871	+	0.0172381i
$987$	−0.377162			−0.0120052
$988$	−0.638958	−	0.638958i	−0.0203280	−	0.0203280i
$989$	−2.74644	+	1.13761i	−0.0873318	+	0.0361740i
$990$			20.8482i			0.662600i
$991$	−11.1297	−	26.8695i	−0.353547	−	0.853539i	−0.996177	−	0.0873614i	$-0.972157\pi$
$991$	−11.1297	−	26.8695i	−0.353547	−	0.853539i	0.642629	−	0.766177i	$-0.277843\pi$
$992$	−2.39014	−	0.990028i	−0.0758870	−	0.0314334i
$993$	1.47895	−	3.57051i	0.0469332	−	0.113307i
$994$	3.31465	−	3.31465i	0.105134	−	0.105134i
$995$	−9.00616	+	9.00616i	−0.285514	+	0.285514i
$996$	−0.0146101	+	0.0352719i	−0.000462939	+	0.00111763i
$997$	12.6531	+	5.24110i	0.400728	+	0.165987i	0.573940	−	0.818898i	$-0.305414\pi$
$997$	12.6531	+	5.24110i	0.400728	+	0.165987i	−0.173211	+	0.984885i	$0.555414\pi$
$998$	6.24264	+	15.0711i	0.197607	+	0.477067i
$999$		−	0.0780686i		−	0.00246998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.l.a.36.5	yes	24
3.2	odd	2		765.2.be.b.631.2		24
5.2	odd	4		425.2.n.c.274.2		24
5.3	odd	4		425.2.n.f.274.5		24
5.4	even	2		425.2.m.b.376.2		24
17.3	odd	16		1445.2.a.q.1.10		12
17.5	odd	16		1445.2.d.j.866.5		24
17.9	even	8	inner	85.2.l.a.26.5	✓	24
17.12	odd	16		1445.2.d.j.866.6		24
17.14	odd	16		1445.2.a.p.1.10		12
51.26	odd	8		765.2.be.b.451.2		24
85.9	even	8		425.2.m.b.26.2		24
85.14	odd	16		7225.2.a.bs.1.3		12
85.43	odd	8		425.2.n.c.349.2		24
85.54	odd	16		7225.2.a.bq.1.3		12
85.77	odd	8		425.2.n.f.349.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.5	✓	24	17.9	even	8	inner
85.2.l.a.36.5	yes	24	1.1	even	1	trivial
425.2.m.b.26.2		24	85.9	even	8
425.2.m.b.376.2		24	5.4	even	2
425.2.n.c.274.2		24	5.2	odd	4
425.2.n.c.349.2		24	85.43	odd	8
425.2.n.f.274.5		24	5.3	odd	4
425.2.n.f.349.5		24	85.77	odd	8
765.2.be.b.451.2		24	51.26	odd	8
765.2.be.b.631.2		24	3.2	odd	2
1445.2.a.p.1.10		12	17.14	odd	16
1445.2.a.q.1.10		12	17.3	odd	16
1445.2.d.j.866.5		24	17.5	odd	16
1445.2.d.j.866.6		24	17.12	odd	16
7225.2.a.bq.1.3		12	85.54	odd	16
7225.2.a.bs.1.3		12	85.14	odd	16

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:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.01710 + 1.01710i) q^{2} +(-0.101541 + 0.0420595i) q^{3} +0.0689897i q^{4} +(0.382683 + 0.923880i) q^{5} +(-0.146056 - 0.0604983i) q^{6} +(-0.265997 + 0.642174i) q^{7} +(1.96403 - 1.96403i) q^{8} +(-2.11278 + 2.11278i) q^{9} +(-0.550451 + 1.32891i) q^{10} +(-4.48163 - 1.85635i) q^{11} +(-0.00290167 - 0.00700526i) q^{12} -5.63906i q^{13} +(-0.923703 + 0.382610i) q^{14} +(-0.0777158 - 0.0777158i) q^{15} +4.13322 q^{16} +(1.63113 + 3.78674i) q^{17} -4.29782 q^{18} +(-1.64241 - 1.64241i) q^{19} +(-0.0637382 + 0.0264012i) q^{20} -0.0763945i q^{21} +(-2.67018 - 6.44637i) q^{22} +(4.28390 + 1.77445i) q^{23} +(-0.116823 + 0.282035i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(5.73549 - 5.73549i) q^{26} +(0.251849 - 0.608017i) q^{27} +(-0.0443034 - 0.0183511i) q^{28} +(2.48981 + 6.01093i) q^{29} -0.158090i q^{30} +(-6.12711 + 2.53793i) q^{31} +(0.275837 + 0.275837i) q^{32} +0.533145 q^{33} +(-2.19248 + 5.51052i) q^{34} -0.695085 q^{35} +(-0.145760 - 0.145760i) q^{36} +(0.109595 - 0.0453958i) q^{37} -3.34100i q^{38} +(0.237176 + 0.572593i) q^{39} +(2.56613 + 1.06293i) q^{40} +(-0.412826 + 0.996650i) q^{41} +(0.0777010 - 0.0777010i) q^{42} +(-0.453332 + 0.453332i) q^{43} +(0.128069 - 0.309187i) q^{44} +(-2.76048 - 1.14343i) q^{45} +(2.55237 + 6.16195i) q^{46} -4.93703i q^{47} +(-0.419690 + 0.173841i) q^{48} +(4.60811 + 4.60811i) q^{49} -1.43840 q^{50} +(-0.324894 - 0.315904i) q^{51} +0.389037 q^{52} +(8.47565 + 8.47565i) q^{53} +(0.874571 - 0.362259i) q^{54} -4.85089i q^{55} +(0.738824 + 1.78368i) q^{56} +(0.235850 + 0.0976925i) q^{57} +(-3.58134 + 8.64611i) q^{58} +(7.01329 - 7.01329i) q^{59} +(0.00536159 - 0.00536159i) q^{60} +(0.613413 - 1.48091i) q^{61} +(-8.81322 - 3.65056i) q^{62} +(-0.794779 - 1.91877i) q^{63} -7.70533i q^{64} +(5.20981 - 2.15797i) q^{65} +(0.542263 + 0.542263i) q^{66} +2.99411 q^{67} +(-0.261246 + 0.112531i) q^{68} -0.509622 q^{69} +(-0.706971 - 0.706971i) q^{70} +(-4.33163 + 1.79422i) q^{71} +8.29913i q^{72} +(-2.10442 - 5.08052i) q^{73} +(0.157641 + 0.0652972i) q^{74} +(0.0420595 - 0.101541i) q^{75} +(0.113309 - 0.113309i) q^{76} +(2.38421 - 2.38421i) q^{77} +(-0.341153 + 0.823617i) q^{78} +(-13.7140 - 5.68053i) q^{79} +(1.58171 + 3.81860i) q^{80} -8.89143i q^{81} +(-1.43358 + 0.593808i) q^{82} +(-3.56033 - 3.56033i) q^{83} +0.00527044 q^{84} +(-2.87429 + 2.95609i) q^{85} -0.922169 q^{86} +(-0.505633 - 0.505633i) q^{87} +(-12.4480 + 5.15614i) q^{88} -2.35657i q^{89} +(-1.64470 - 3.97067i) q^{90} +(3.62126 + 1.49997i) q^{91} +(-0.122419 + 0.295545i) q^{92} +(0.515406 - 0.515406i) q^{93} +(5.02145 - 5.02145i) q^{94} +(0.888867 - 2.14591i) q^{95} +(-0.0396102 - 0.0164071i) q^{96} +(-1.03355 - 2.49522i) q^{97} +9.37384i q^{98} +(13.3908 - 5.54664i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} + 24 q^{12} - 8 q^{15} - 24 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 32 q^{22} - 16 q^{23} - 8 q^{24} + 16 q^{26} + 24 q^{27} + 48 q^{28} - 8 q^{29} + 16 q^{34} - 32 q^{35}+ \cdots - 8 q^{99}+O(q^{100}) \) 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 + 24 * q^12 - 8 * q^15 - 24 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 32 * q^22 - 16 * q^23 - 8 * q^24 + 16 * q^26 + 24 * q^27 + 48 * q^28 - 8 * q^29 + 16 * q^34 - 32 * q^35 - 24 * q^36 + 24 * q^37 + 8 * q^39 + 16 * q^40 + 16 * q^41 - 24 * q^42 + 8 * q^43 + 16 * q^44 + 16 * q^45 + 8 * q^46 + 80 * q^48 + 8 * q^50 - 56 * q^51 - 48 * q^52 + 24 * q^53 - 32 * q^54 + 64 * q^56 + 32 * q^57 - 64 * q^58 + 32 * q^59 + 24 * q^60 + 32 * q^61 - 32 * q^62 - 56 * q^63 + 8 * q^65 + 96 * q^66 + 16 * q^67 - 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^75 - 8 * q^76 + 24 * q^77 - 112 * q^78 - 32 * q^80 - 80 * q^82 - 96 * q^83 - 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 + 80 * q^92 + 64 * q^93 + 56 * q^94 - 16 * q^95 - 168 * q^96 - 40 * q^97 - 8 * q^99

Introduction

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