LMFDB - Embedded newform 660.2.y.c.181.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [660,2,Mod(181,660)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(660, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("660.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	660.y (of order $5$, 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:	$5.27012653340$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.819390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 10x^{6} - 13x^{5} + 29x^{4} - 7x^{3} + 80x^{2} + 143x + 121 $ x^8 - 3x^7 + 10x^6 - 13x^5 + 29x^4 - 7x^3 + 80x^2 + 143*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.1
Root			$-0.575405 - 1.77091i$ of defining polynomial
Character	$\chi$	$=$	660.181
Dual form			660.2.y.c.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{5} +(-1.62844 + 1.18313i) q^{7} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{5} +(-1.62844 + 1.18313i) q^{7} +(0.309017 + 0.951057i) q^{9} +(-0.213356 + 3.30976i) q^{11} +(0.664637 + 2.04554i) q^{13} +(0.809017 - 0.587785i) q^{15} +(-0.841792 + 2.59077i) q^{17} +(5.24250 + 3.80890i) q^{19} -2.01286 q^{21} +2.57329 q^{23} +(-0.809017 - 0.587785i) q^{25} +(-0.309017 + 0.951057i) q^{27} +(4.98651 - 3.62291i) q^{29} +(1.50246 + 4.62408i) q^{31} +(-2.11803 + 2.55224i) q^{33} +(0.622007 + 1.91434i) q^{35} +(4.41111 - 3.20486i) q^{37} +(-0.664637 + 2.04554i) q^{39} +(-5.64129 - 4.09864i) q^{41} -3.46037 q^{43} +1.00000 q^{45} +(0.851646 + 0.618757i) q^{47} +(-0.911107 + 2.80410i) q^{49} +(-2.20384 + 1.60118i) q^{51} +(-2.84577 - 8.75837i) q^{53} +(3.08183 + 1.22568i) q^{55} +(2.00246 + 6.16292i) q^{57} +(6.62692 - 4.81474i) q^{59} +(-3.42460 + 10.5398i) q^{61} +(-1.62844 - 1.18313i) q^{63} +2.15081 q^{65} -14.3728 q^{67} +(2.08183 + 1.51254i) q^{69} +(2.44485 - 7.52448i) q^{71} +(-3.80504 + 2.76453i) q^{73} +(-0.309017 - 0.951057i) q^{75} +(-3.56843 - 5.64215i) q^{77} +(1.02047 + 3.14067i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-1.22588 + 3.77286i) q^{83} +(2.20384 + 1.60118i) q^{85} +6.16367 q^{87} +4.00110 q^{89} +(-3.50246 - 2.54468i) q^{91} +(-1.50246 + 4.62408i) q^{93} +(5.24250 - 3.80890i) q^{95} +(-2.37854 - 7.32040i) q^{97} +(-3.21369 + 0.819857i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - 2 q^{5} + 3 q^{7} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 - 2 * q^5 + 3 * q^7 - 2 * q^9	$ 8 q + 2 q^{3} - 2 q^{5} + 3 q^{7} - 2 q^{9} - 7 q^{11} + 2 q^{13} + 2 q^{15} + 4 q^{17} + 10 q^{19} + 12 q^{21} + 10 q^{23} - 2 q^{25} + 2 q^{27} + 4 q^{29} - 9 q^{31} - 8 q^{33} + 3 q^{35} + 7 q^{37} - 2 q^{39} - q^{41} + 4 q^{43} + 8 q^{45} + q^{47} + 21 q^{49} + 6 q^{51} - 19 q^{53} + 3 q^{55} - 5 q^{57} + 9 q^{59} - 35 q^{61} + 3 q^{63} + 2 q^{65} + 18 q^{67} - 5 q^{69} + 25 q^{71} - 19 q^{73} + 2 q^{75} - 47 q^{77} + 18 q^{79} - 2 q^{81} - 11 q^{83} - 6 q^{85} + 6 q^{87} + 8 q^{89} - 7 q^{91} + 9 q^{93} + 10 q^{95} - 9 q^{97} - 7 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 - 2 * q^5 + 3 * q^7 - 2 * q^9 - 7 * q^11 + 2 * q^13 + 2 * q^15 + 4 * q^17 + 10 * q^19 + 12 * q^21 + 10 * q^23 - 2 * q^25 + 2 * q^27 + 4 * q^29 - 9 * q^31 - 8 * q^33 + 3 * q^35 + 7 * q^37 - 2 * q^39 - q^41 + 4 * q^43 + 8 * q^45 + q^47 + 21 * q^49 + 6 * q^51 - 19 * q^53 + 3 * q^55 - 5 * q^57 + 9 * q^59 - 35 * q^61 + 3 * q^63 + 2 * q^65 + 18 * q^67 - 5 * q^69 + 25 * q^71 - 19 * q^73 + 2 * q^75 - 47 * q^77 + 18 * q^79 - 2 * q^81 - 11 * q^83 - 6 * q^85 + 6 * q^87 + 8 * q^89 - 7 * q^91 + 9 * q^93 + 10 * q^95 - 9 * q^97 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/660\mathbb{Z}\right)^\times$.

$n$	$221$	$331$	$397$	$541$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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			0
$2$		0			0
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$		0			0
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$6$		0			0
$7$	−1.62844	+	1.18313i	−0.615491	+	0.447180i	−0.851344	−	0.524608i	$-0.824212\pi$
$7$	−1.62844	+	1.18313i	−0.615491	+	0.447180i	0.235853	+	0.971789i	$0.424212\pi$
$8$		0			0
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	−0.213356	+	3.30976i	−0.0643293	+	0.997929i
$11$	−0.213356	+	3.30976i	−0.0643293	+	0.997929i
$12$		0			0
$13$	0.664637	+	2.04554i	0.184337	+	0.567331i	0.999936	−	0.0112861i	$-0.00359256\pi$
$13$	0.664637	+	2.04554i	0.184337	+	0.567331i	−0.815599	+	0.578617i	$0.803593\pi$
$14$		0			0
$15$	0.809017	−	0.587785i	0.208887	−	0.151765i
$16$		0			0
$17$	−0.841792	+	2.59077i	−0.204165	+	0.628354i	0.795582	+	0.605846i	$0.207165\pi$
$17$	−0.841792	+	2.59077i	−0.204165	+	0.628354i	−0.999747	+	0.0225082i	$0.992835\pi$
$18$		0			0
$19$	5.24250	+	3.80890i	1.20271	+	0.873821i	0.994549	−	0.104273i	$-0.0332517\pi$
$19$	5.24250	+	3.80890i	1.20271	+	0.873821i	0.208163	+	0.978094i	$0.433252\pi$
$20$		0			0
$21$	−2.01286			−0.439242
$22$		0			0
$23$	2.57329			0.536568			0.268284	−	0.963340i	$-0.413544\pi$
$23$	2.57329			0.536568			0.268284	+	0.963340i	$0.413544\pi$
$24$		0			0
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$		0			0
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$		0			0
$29$	4.98651	−	3.62291i	0.925972	−	0.672758i	−0.0190313	−	0.999819i	$-0.506058\pi$
$29$	4.98651	−	3.62291i	0.925972	−	0.672758i	0.945003	+	0.327061i	$0.106058\pi$
$30$		0			0
$31$	1.50246	+	4.62408i	0.269849	+	0.830510i	0.990536	+	0.137250i	$0.0438263\pi$
$31$	1.50246	+	4.62408i	0.269849	+	0.830510i	−0.720687	+	0.693260i	$0.756174\pi$
$32$		0			0
$33$	−2.11803	+	2.55224i	−0.368702	+	0.444288i
$34$		0			0
$35$	0.622007	+	1.91434i	0.105138	+	0.323583i
$36$		0			0
$37$	4.41111	−	3.20486i	0.725181	−	0.526875i	−0.162854	−	0.986650i	$-0.552070\pi$
$37$	4.41111	−	3.20486i	0.725181	−	0.526875i	0.888035	+	0.459775i	$0.152070\pi$
$38$		0			0
$39$	−0.664637	+	2.04554i	−0.106427	+	0.327549i
$40$		0			0
$41$	−5.64129	−	4.09864i	−0.881022	−	0.640100i	0.0524996	−	0.998621i	$-0.483281\pi$
$41$	−5.64129	−	4.09864i	−0.881022	−	0.640100i	−0.933522	+	0.358521i	$0.883281\pi$
$42$		0			0
$43$	−3.46037			−0.527702			−0.263851	−	0.964563i	$-0.584993\pi$
$43$	−3.46037			−0.527702			−0.263851	+	0.964563i	$0.584993\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	0.851646	+	0.618757i	0.124225	+	0.0902550i	0.648163	−	0.761502i	$-0.275538\pi$
$47$	0.851646	+	0.618757i	0.124225	+	0.0902550i	−0.523938	+	0.851757i	$0.675538\pi$
$48$		0			0
$49$	−0.911107	+	2.80410i	−0.130158	+	0.400585i
$50$		0			0
$51$	−2.20384	+	1.60118i	−0.308599	+	0.224211i
$52$		0			0
$53$	−2.84577	−	8.75837i	−0.390896	−	1.20305i	−0.932112	−	0.362170i	$-0.882036\pi$
$53$	−2.84577	−	8.75837i	−0.390896	−	1.20305i	0.541216	−	0.840884i	$-0.317964\pi$
$54$		0			0
$55$	3.08183	+	1.22568i	0.415554	+	0.165271i
$56$		0			0
$57$	2.00246	+	6.16292i	0.265232	+	0.816299i
$58$		0			0
$59$	6.62692	−	4.81474i	0.862751	−	0.626826i	−0.0658808	−	0.997828i	$-0.520986\pi$
$59$	6.62692	−	4.81474i	0.862751	−	0.626826i	0.928632	+	0.371002i	$0.120986\pi$
$60$		0			0
$61$	−3.42460	+	10.5398i	−0.438475	+	1.34949i	0.451009	+	0.892519i	$0.351064\pi$
$61$	−3.42460	+	10.5398i	−0.438475	+	1.34949i	−0.889484	+	0.456967i	$0.848936\pi$
$62$		0			0
$63$	−1.62844	−	1.18313i	−0.205164	−	0.149060i
$64$		0			0
$65$	2.15081			0.266775
$66$		0			0
$67$	−14.3728			−1.75591			−0.877956	−	0.478741i	$-0.841093\pi$
$67$	−14.3728			−1.75591			−0.877956	+	0.478741i	$0.841093\pi$
$68$		0			0
$69$	2.08183	+	1.51254i	0.250623	+	0.182088i
$70$		0			0
$71$	2.44485	−	7.52448i	0.290151	−	0.892991i	−0.694657	−	0.719341i	$-0.744444\pi$
$71$	2.44485	−	7.52448i	0.290151	−	0.892991i	0.984807	−	0.173650i	$-0.0555562\pi$
$72$		0			0
$73$	−3.80504	+	2.76453i	−0.445347	+	0.323563i	−0.787756	−	0.615988i	$-0.788757\pi$
$73$	−3.80504	+	2.76453i	−0.445347	+	0.323563i	0.342409	+	0.939551i	$0.388757\pi$
$74$		0			0
$75$	−0.309017	−	0.951057i	−0.0356822	−	0.109819i
$76$		0			0
$77$	−3.56843	−	5.64215i	−0.406660	−	0.642983i
$78$		0			0
$79$	1.02047	+	3.14067i	0.114811	+	0.353353i	0.991908	−	0.126962i	$-0.0405225\pi$
$79$	1.02047	+	3.14067i	0.114811	+	0.353353i	−0.877096	+	0.480315i	$0.840522\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$		0			0
$83$	−1.22588	+	3.77286i	−0.134557	+	0.414125i	−0.995521	−	0.0945418i	$-0.969861\pi$
$83$	−1.22588	+	3.77286i	−0.134557	+	0.414125i	0.860964	+	0.508667i	$0.169861\pi$
$84$		0			0
$85$	2.20384	+	1.60118i	0.239040	+	0.173673i
$86$		0			0
$87$	6.16367			0.660814
$88$		0			0
$89$	4.00110			0.424115			0.212058	−	0.977257i	$-0.431984\pi$
$89$	4.00110			0.424115			0.212058	+	0.977257i	$0.431984\pi$
$90$		0			0
$91$	−3.50246	−	2.54468i	−0.367157	−	0.266755i
$92$		0			0
$93$	−1.50246	+	4.62408i	−0.155797	+	0.479495i
$94$		0			0
$95$	5.24250	−	3.80890i	0.537869	−	0.390785i
$96$		0			0
$97$	−2.37854	−	7.32040i	−0.241504	−	0.743274i	−0.996192	−	0.0871892i	$-0.972212\pi$
$97$	−2.37854	−	7.32040i	−0.241504	−	0.743274i	0.754688	−	0.656084i	$-0.227788\pi$
$98$		0			0
$99$	−3.21369	+	0.819857i	−0.322988	+	0.0823987i
$100$		0			0
$101$	−2.24250	−	6.90170i	−0.223137	−	0.686744i	−0.998475	−	0.0551986i	$-0.982421\pi$
$101$	−2.24250	−	6.90170i	−0.223137	−	0.686744i	0.775339	−	0.631546i	$-0.217579\pi$
$102$		0			0
$103$	7.39331	−	5.37155i	0.728484	−	0.529275i	−0.160599	−	0.987020i	$-0.551343\pi$
$103$	7.39331	−	5.37155i	0.728484	−	0.529275i	0.889084	+	0.457745i	$0.151343\pi$
$104$		0			0
$105$	−0.622007	+	1.91434i	−0.0607017	+	0.186821i
$106$		0			0
$107$	14.2155	+	10.3282i	1.37427	+	0.998463i	0.997390	+	0.0721991i	$0.0230017\pi$
$107$	14.2155	+	10.3282i	1.37427	+	0.998463i	0.376876	+	0.926264i	$0.376998\pi$
$108$		0			0
$109$	9.68055			0.927228			0.463614	−	0.886037i	$-0.346552\pi$
$109$	9.68055			0.927228			0.463614	+	0.886037i	$0.346552\pi$
$110$		0			0
$111$	5.45243			0.517522
$112$		0			0
$113$	−14.7876	−	10.7438i	−1.39110	−	1.01069i	−0.995744	−	0.0921639i	$-0.970622\pi$
$113$	−14.7876	−	10.7438i	−1.39110	−	1.01069i	−0.395355	−	0.918528i	$-0.629378\pi$
$114$		0			0
$115$	0.795190	−	2.44734i	0.0741518	−	0.228216i
$116$		0			0
$117$	−1.74004	+	1.26421i	−0.160867	+	0.116877i
$118$		0			0
$119$	−1.69441	−	5.21485i	−0.155326	−	0.478045i
$120$		0			0
$121$	−10.9090	−	1.41231i	−0.991723	−	0.128392i
$122$		0			0
$123$	−2.15478	−	6.63174i	−0.194290	−	0.597964i
$124$		0			0
$125$	−0.809017	+	0.587785i	−0.0723607	+	0.0525731i
$126$		0			0
$127$	−2.07671	+	6.39147i	−0.184278	+	0.567151i	−0.999935	−	0.0113854i	$-0.996376\pi$
$127$	−2.07671	+	6.39147i	−0.184278	+	0.567151i	0.815657	+	0.578536i	$0.196376\pi$
$128$		0			0
$129$	−2.79950	−	2.03396i	−0.246482	−	0.179080i
$130$		0			0
$131$	−2.51992			−0.220166			−0.110083	−	0.993922i	$-0.535112\pi$
$131$	−2.51992			−0.220166			−0.110083	+	0.993922i	$0.535112\pi$
$132$		0			0
$133$	−13.0435			−1.13101
$134$		0			0
$135$	0.809017	+	0.587785i	0.0696291	+	0.0505885i
$136$		0			0
$137$	4.44143	−	13.6693i	0.379457	−	1.16785i	−0.560966	−	0.827839i	$-0.689570\pi$
$137$	4.44143	−	13.6693i	0.379457	−	1.16785i	0.940422	−	0.340008i	$-0.110430\pi$
$138$		0			0
$139$	16.1913	−	11.7637i	1.37333	−	0.997781i	0.375858	−	0.926677i	$-0.377348\pi$
$139$	16.1913	−	11.7637i	1.37333	−	0.997781i	0.997469	−	0.0711036i	$-0.0226521\pi$
$140$		0			0
$141$	0.325300	+	1.00117i	0.0273952	+	0.0843138i
$142$		0			0
$143$	−6.91204	+	1.76336i	−0.578014	+	0.147459i
$144$		0			0
$145$	−1.90468	−	5.86200i	−0.158175	−	0.486812i
$146$		0			0
$147$	−2.38531	+	1.73303i	−0.196737	+	0.142938i
$148$		0			0
$149$	3.28779	−	10.1188i	0.269346	−	0.828963i	−0.721314	−	0.692608i	$-0.756461\pi$
$149$	3.28779	−	10.1188i	0.269346	−	0.828963i	0.990660	−	0.136354i	$-0.0435386\pi$
$150$		0			0
$151$	1.18392	+	0.860171i	0.0963463	+	0.0699997i	0.634915	−	0.772582i	$-0.281035\pi$
$151$	1.18392	+	0.860171i	0.0963463	+	0.0699997i	−0.538569	+	0.842581i	$0.681035\pi$
$152$		0			0
$153$	−2.72410			−0.220230
$154$		0			0
$155$	4.86205			0.390529
$156$		0			0
$157$	−8.43293	−	6.12688i	−0.673021	−	0.488979i	0.198014	−	0.980199i	$-0.436551\pi$
$157$	−8.43293	−	6.12688i	−0.673021	−	0.488979i	−0.871035	+	0.491221i	$0.836551\pi$
$158$		0			0
$159$	2.84577	−	8.75837i	0.225684	−	0.694584i
$160$		0			0
$161$	−4.19043	+	3.04453i	−0.330253	+	0.239943i
$162$		0			0
$163$	4.25653	+	13.1003i	0.333397	+	1.02609i	0.967506	+	0.252848i	$0.0813672\pi$
$163$	4.25653	+	13.1003i	0.333397	+	1.02609i	−0.634109	+	0.773244i	$0.718633\pi$
$164$		0			0
$165$	1.77282	+	2.80306i	0.138014	+	0.218218i
$166$		0			0
$167$	−2.32927	−	7.16877i	−0.180245	−	0.554736i	0.819590	−	0.572951i	$-0.194202\pi$
$167$	−2.32927	−	7.16877i	−0.180245	−	0.554736i	−0.999834	+	0.0182154i	$0.994202\pi$
$168$		0			0
$169$	6.77472	−	4.92213i	0.521133	−	0.378625i
$170$		0			0
$171$	−2.00246	+	6.16292i	−0.153132	+	0.471291i
$172$		0			0
$173$	−9.69281	−	7.04224i	−0.736931	−	0.535411i	0.154818	−	0.987943i	$-0.450521\pi$
$173$	−9.69281	−	7.04224i	−0.736931	−	0.535411i	−0.891748	+	0.452532i	$0.850521\pi$
$174$		0			0
$175$	2.01286			0.152158
$176$		0			0
$177$	8.19132			0.615697
$178$		0			0
$179$	−8.86848	−	6.44333i	−0.662861	−	0.481597i	0.204767	−	0.978811i	$-0.434356\pi$
$179$	−8.86848	−	6.44333i	−0.662861	−	0.481597i	−0.867628	+	0.497214i	$0.834356\pi$
$180$		0			0
$181$	−0.778697	+	2.39658i	−0.0578801	+	0.178137i	−0.975817	−	0.218591i	$-0.929854\pi$
$181$	−0.778697	+	2.39658i	−0.0578801	+	0.178137i	0.917937	+	0.396727i	$0.129854\pi$
$182$		0			0
$183$	−8.96571	+	6.51397i	−0.662764	+	0.481526i
$184$		0			0
$185$	−1.68489	−	5.18557i	−0.123876	−	0.381250i
$186$		0			0
$187$	−8.39521	−	3.33888i	−0.613919	−	0.244163i
$188$		0			0
$189$	−0.622007	−	1.91434i	−0.0452444	−	0.139248i
$190$		0			0
$191$	7.20972	−	5.23817i	0.521677	−	0.379021i	−0.295558	−	0.955325i	$-0.595506\pi$
$191$	7.20972	−	5.23817i	0.521677	−	0.379021i	0.817235	+	0.576304i	$0.195506\pi$
$192$		0			0
$193$	−2.12073	+	6.52694i	−0.152654	+	0.469819i	−0.997916	−	0.0645327i	$-0.979444\pi$
$193$	−2.12073	+	6.52694i	−0.152654	+	0.469819i	0.845262	+	0.534352i	$0.179444\pi$
$194$		0			0
$195$	1.74004	+	1.26421i	0.124607	+	0.0905322i
$196$		0			0
$197$	1.06926			0.0761819			0.0380909	−	0.999274i	$-0.487872\pi$
$197$	1.06926			0.0761819			0.0380909	+	0.999274i	$0.487872\pi$
$198$		0			0
$199$	25.4762			1.80596			0.902980	−	0.429682i	$-0.141374\pi$
$199$	25.4762			1.80596			0.902980	+	0.429682i	$0.141374\pi$
$200$		0			0
$201$	−11.6278	−	8.44810i	−0.820162	−	0.595883i
$202$		0			0
$203$	−3.83385	+	11.7994i	−0.269083	+	0.828153i
$204$		0			0
$205$	−5.64129	+	4.09864i	−0.394005	+	0.286261i
$206$		0			0
$207$	0.795190	+	2.44734i	0.0552695	+	0.170102i
$208$		0			0
$209$	−13.7250	+	16.5387i	−0.949381	+	1.14401i
$210$		0			0
$211$	−4.91568	−	15.1289i	−0.338409	−	1.04152i	−0.965018	−	0.262183i	$-0.915558\pi$
$211$	−4.91568	−	15.1289i	−0.338409	−	1.04152i	0.626609	−	0.779334i	$-0.284442\pi$
$212$		0			0
$213$	6.40070	−	4.65038i	0.438569	−	0.318639i
$214$		0			0
$215$	−1.06931	+	3.29101i	−0.0729266	+	0.224445i
$216$		0			0
$217$	−7.91754	−	5.75243i	−0.537477	−	0.390500i
$218$		0			0
$219$	−4.70329			−0.317819
$220$		0			0
$221$	−5.85901			−0.394120
$222$		0			0
$223$	−16.2017	−	11.7712i	−1.08495	−	0.788259i	−0.106407	−	0.994323i	$-0.533935\pi$
$223$	−16.2017	−	11.7712i	−1.08495	−	0.788259i	−0.978539	+	0.206064i	$0.933935\pi$
$224$		0			0
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$		0			0
$227$	−12.5306	+	9.10400i	−0.831684	+	0.604253i	−0.920035	−	0.391836i	$-0.871840\pi$
$227$	−12.5306	+	9.10400i	−0.831684	+	0.604253i	0.0883516	+	0.996089i	$0.471840\pi$
$228$		0			0
$229$	2.97666	+	9.16121i	0.196703	+	0.605390i	0.999952	+	0.00974696i	$0.00310260\pi$
$229$	2.97666	+	9.16121i	0.196703	+	0.605390i	−0.803249	+	0.595643i	$0.796897\pi$
$230$		0			0
$231$	0.429456	−	6.66207i	0.0282561	−	0.438332i
$232$		0			0
$233$	0.872502	+	2.68528i	0.0571595	+	0.175919i	0.975560	−	0.219733i	$-0.0705187\pi$
$233$	0.872502	+	2.68528i	0.0571595	+	0.175919i	−0.918401	+	0.395652i	$0.870519\pi$
$234$		0			0
$235$	0.851646	−	0.618757i	0.0555553	−	0.0403633i
$236$		0			0
$237$	−1.02047	+	3.14067i	−0.0662864	+	0.204008i
$238$		0			0
$239$	23.7235	+	17.2361i	1.53455	+	1.11491i	0.953643	+	0.300942i	$0.0973009\pi$
$239$	23.7235	+	17.2361i	1.53455	+	1.11491i	0.580904	+	0.813972i	$0.302699\pi$
$240$		0			0
$241$	14.6285			0.942307			0.471153	−	0.882051i	$-0.343838\pi$
$241$	14.6285			0.942307			0.471153	+	0.882051i	$0.343838\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	2.38531	+	1.73303i	0.152392	+	0.110719i
$246$		0			0
$247$	−4.30690	+	13.2553i	−0.274041	+	0.843413i
$248$		0			0
$249$	−3.20938	+	2.33175i	−0.203386	+	0.147769i
$250$		0			0
$251$	−1.96004	−	6.03237i	−0.123716	−	0.380760i	0.869949	−	0.493142i	$-0.164152\pi$
$251$	−1.96004	−	6.03237i	−0.123716	−	0.380760i	−0.993665	+	0.112383i	$0.964152\pi$
$252$		0			0
$253$	−0.549027	+	8.51695i	−0.0345170	+	0.535456i
$254$		0			0
$255$	0.841792	+	2.59077i	0.0527151	+	0.162240i
$256$		0			0
$257$	11.9777	−	8.70229i	0.747147	−	0.542834i	−0.147794	−	0.989018i	$-0.547217\pi$
$257$	11.9777	−	8.70229i	0.747147	−	0.542834i	0.894941	+	0.446184i	$0.147217\pi$
$258$		0			0
$259$	−3.39145	+	10.4378i	−0.210734	+	0.648574i
$260$		0			0
$261$	4.98651	+	3.62291i	0.308657	+	0.224253i
$262$		0			0
$263$	11.2975			0.696633			0.348316	−	0.937377i	$-0.386753\pi$
$263$	11.2975			0.696633			0.348316	+	0.937377i	$0.386753\pi$
$264$		0			0
$265$	−9.20909			−0.565710
$266$		0			0
$267$	3.23695	+	2.35179i	0.198098	+	0.143927i
$268$		0			0
$269$	7.02140	−	21.6097i	0.428103	−	1.31756i	−0.471889	−	0.881658i	$-0.656428\pi$
$269$	7.02140	−	21.6097i	0.428103	−	1.31756i	0.899992	−	0.435906i	$-0.143572\pi$
$270$		0			0
$271$	17.0335	−	12.3756i	1.03471	−	0.751762i	0.0654654	−	0.997855i	$-0.479147\pi$
$271$	17.0335	−	12.3756i	1.03471	−	0.751762i	0.969246	+	0.246093i	$0.0791468\pi$
$272$		0			0
$273$	−1.33782	−	4.11738i	−0.0809685	−	0.249195i
$274$		0			0
$275$	2.11803	−	2.55224i	0.127722	−	0.153906i
$276$		0			0
$277$	−5.29634	−	16.3004i	−0.318226	−	0.979399i	−0.974406	−	0.224795i	$-0.927829\pi$
$277$	−5.29634	−	16.3004i	−0.318226	−	0.979399i	0.656180	−	0.754604i	$-0.272171\pi$
$278$		0			0
$279$	−3.93348	+	2.85784i	−0.235491	+	0.171094i
$280$		0			0
$281$	−4.83688	+	14.8864i	−0.288544	+	0.888048i	0.696770	+	0.717295i	$0.254620\pi$
$281$	−4.83688	+	14.8864i	−0.288544	+	0.888048i	−0.985314	+	0.170753i	$0.945380\pi$
$282$		0			0
$283$	5.09414	+	3.70111i	0.302815	+	0.220008i	0.728808	−	0.684719i	$-0.240075\pi$
$283$	5.09414	+	3.70111i	0.302815	+	0.220008i	−0.425992	+	0.904727i	$0.640075\pi$
$284$		0			0
$285$	6.48008			0.383847
$286$		0			0
$287$	14.0357			0.828501
$288$		0			0
$289$	7.74981	+	5.63057i	0.455871	+	0.331210i
$290$		0			0
$291$	2.37854	−	7.32040i	0.139433	−	0.429129i
$292$		0			0
$293$	−13.4384	+	9.76356i	−0.785079	+	0.570393i	−0.906499	−	0.422208i	$-0.861255\pi$
$293$	−13.4384	+	9.76356i	−0.785079	+	0.570393i	0.121420	+	0.992601i	$0.461255\pi$
$294$		0			0
$295$	−2.53126	−	7.79041i	−0.147376	−	0.453575i
$296$		0			0
$297$	−3.08183	−	1.22568i	−0.178826	−	0.0711214i
$298$		0			0
$299$	1.71030	+	5.26377i	0.0989093	+	0.304411i
$300$		0			0
$301$	5.63500	−	4.09407i	0.324796	−	0.235978i
$302$		0			0
$303$	2.24250	−	6.90170i	0.128828	−	0.396492i
$304$		0			0
$305$	8.96571	+	6.51397i	0.513375	+	0.372989i
$306$		0			0
$307$	−4.51501			−0.257685			−0.128843	−	0.991665i	$-0.541126\pi$
$307$	−4.51501			−0.257685			−0.128843	+	0.991665i	$0.541126\pi$
$308$		0			0
$309$	9.13863			0.519878
$310$		0			0
$311$	19.1198	+	13.8913i	1.08418	+	0.787705i	0.978408	−	0.206685i	$-0.0662675\pi$
$311$	19.1198	+	13.8913i	1.08418	+	0.787705i	0.105775	+	0.994390i	$0.466268\pi$
$312$		0			0
$313$	−7.16029	+	22.0371i	−0.404724	+	1.24561i	0.516402	+	0.856346i	$0.327271\pi$
$313$	−7.16029	+	22.0371i	−0.404724	+	1.24561i	−0.921126	+	0.389265i	$0.872729\pi$
$314$		0			0
$315$	−1.62844	+	1.18313i	−0.0917520	+	0.0666617i
$316$		0			0
$317$	−0.901883	−	2.77571i	−0.0506548	−	0.155900i	0.922529	−	0.385927i	$-0.126118\pi$
$317$	−0.901883	−	2.77571i	−0.0506548	−	0.155900i	−0.973184	+	0.230028i	$0.926118\pi$
$318$		0			0
$319$	10.9271	+	17.2771i	0.611797	+	0.967332i
$320$		0			0
$321$	5.42985	+	16.7113i	0.303064	+	0.932736i
$322$		0			0
$323$	−14.2811	+	10.3758i	−0.794620	+	0.577325i
$324$		0			0
$325$	0.664637	−	2.04554i	0.0368674	−	0.113466i
$326$		0			0
$327$	7.83173	+	5.69008i	0.433096	+	0.314662i
$328$		0			0
$329$	−2.11892			−0.116820
$330$		0			0
$331$	−17.9833			−0.988450			−0.494225	−	0.869334i	$-0.664548\pi$
$331$	−17.9833			−0.988450			−0.494225	+	0.869334i	$0.664548\pi$
$332$		0			0
$333$	4.41111	+	3.20486i	0.241727	+	0.175625i
$334$		0			0
$335$	−4.44143	+	13.6693i	−0.242661	+	0.746834i
$336$		0			0
$337$	8.48034	−	6.16133i	0.461953	−	0.335629i	−0.332344	−	0.943158i	$-0.607839\pi$
$337$	8.48034	−	6.16133i	0.461953	−	0.335629i	0.794297	+	0.607530i	$0.207839\pi$
$338$		0			0
$339$	−5.64835	−	17.3838i	−0.306776	−	0.944161i
$340$		0			0
$341$	−15.6251	+	3.98618i	−0.846149	+	0.215864i
$342$		0			0
$343$	−6.18798	−	19.0446i	−0.334119	−	1.02831i
$344$		0			0
$345$	2.08183	−	1.51254i	0.112082	−	0.0814324i
$346$		0			0
$347$	−9.04903	+	27.8500i	−0.485777	+	1.49507i	0.345075	+	0.938575i	$0.387854\pi$
$347$	−9.04903	+	27.8500i	−0.485777	+	1.49507i	−0.830852	+	0.556493i	$0.812146\pi$
$348$		0			0
$349$	25.7932	+	18.7398i	1.38068	+	1.00312i	0.996817	+	0.0797292i	$0.0254055\pi$
$349$	25.7932	+	18.7398i	1.38068	+	1.00312i	0.383860	+	0.923391i	$0.374594\pi$
$350$		0			0
$351$	−2.15081			−0.114802
$352$		0			0
$353$	28.1814			1.49995			0.749973	−	0.661468i	$-0.230066\pi$
$353$	28.1814			1.49995			0.749973	+	0.661468i	$0.230066\pi$
$354$		0			0
$355$	−6.40070	−	4.65038i	−0.339714	−	0.246817i
$356$		0			0
$357$	1.69441	−	5.21485i	0.0896776	−	0.275999i
$358$		0			0
$359$	−10.1949	+	7.40701i	−0.538065	+	0.390927i	−0.823366	−	0.567511i	$-0.807906\pi$
$359$	−10.1949	+	7.40701i	−0.538065	+	0.390927i	0.285301	+	0.958438i	$0.407906\pi$
$360$		0			0
$361$	7.10475	+	21.8662i	0.373934	+	1.15085i
$362$		0			0
$363$	−7.99540	−	7.55471i	−0.419649	−	0.396519i
$364$		0			0
$365$	1.45340	+	4.47310i	0.0760743	+	0.234133i
$366$		0			0
$367$	−3.50157	+	2.54404i	−0.182780	+	0.132798i	−0.675413	−	0.737440i	$-0.736035\pi$
$367$	−3.50157	+	2.54404i	−0.182780	+	0.132798i	0.492633	+	0.870237i	$0.336035\pi$
$368$		0			0
$369$	2.15478	−	6.63174i	0.112173	−	0.345235i
$370$		0			0
$371$	14.9964	+	10.8955i	0.778575	+	0.565668i
$372$		0			0
$373$	31.4190			1.62681			0.813406	−	0.581696i	$-0.197611\pi$
$373$	31.4190			1.62681			0.813406	+	0.581696i	$0.197611\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	10.7250	+	7.79219i	0.552367	+	0.401318i
$378$		0			0
$379$	−2.49645	+	7.68327i	−0.128234	+	0.394663i	−0.994476	−	0.104961i	$-0.966528\pi$
$379$	−2.49645	+	7.68327i	−0.128234	+	0.394663i	0.866243	+	0.499624i	$0.166528\pi$
$380$		0			0
$381$	−5.43691	+	3.95014i	−0.278541	+	0.202372i
$382$		0			0
$383$	3.13029	+	9.63405i	0.159950	+	0.492277i	0.998629	−	0.0523502i	$-0.0166712\pi$
$383$	3.13029	+	9.63405i	0.159950	+	0.492277i	−0.838678	+	0.544627i	$0.816671\pi$
$384$		0			0
$385$	−6.46871	+	1.65026i	−0.329676	+	0.0841048i
$386$		0			0
$387$	−1.06931	−	3.29101i	−0.0543563	−	0.167292i
$388$		0			0
$389$	−8.69255	+	6.31551i	−0.440730	+	0.320209i	−0.785925	−	0.618322i	$-0.787813\pi$
$389$	−8.69255	+	6.31551i	−0.440730	+	0.320209i	0.345195	+	0.938531i	$0.387813\pi$
$390$		0			0
$391$	−2.16617	+	6.66680i	−0.109548	+	0.337154i
$392$		0			0
$393$	−2.03866	−	1.48117i	−0.102837	−	0.0747152i
$394$		0			0
$395$	3.30230			0.166157
$396$		0			0
$397$	2.91584			0.146342			0.0731708	−	0.997319i	$-0.476688\pi$
$397$	2.91584			0.146342			0.0731708	+	0.997319i	$0.476688\pi$
$398$		0			0
$399$	−10.5524	−	7.66677i	−0.528281	−	0.383818i
$400$		0			0
$401$	−10.0620	+	30.9677i	−0.502473	+	1.54645i	0.302505	+	0.953148i	$0.402177\pi$
$401$	−10.0620	+	30.9677i	−0.502473	+	1.54645i	−0.804978	+	0.593305i	$0.797823\pi$
$402$		0			0
$403$	−8.46017	+	6.14667i	−0.421431	+	0.306187i
$404$		0			0
$405$	0.309017	+	0.951057i	0.0153552	+	0.0472584i
$406$		0			0
$407$	9.66615	+	15.2835i	0.479133	+	0.757573i
$408$		0			0
$409$	−6.79837	−	20.9232i	−0.336158	−	1.03459i	−0.966149	−	0.257985i	$-0.916941\pi$
$409$	−6.79837	−	20.9232i	−0.336158	−	1.03459i	0.629991	−	0.776603i	$-0.283059\pi$
$410$		0			0
$411$	11.6278	−	8.44810i	0.573557	−	0.416714i
$412$		0			0
$413$	−5.09506	+	15.6810i	−0.250712	+	0.771611i
$414$		0			0
$415$	3.20938	+	2.33175i	0.157542	+	0.114461i
$416$		0			0
$417$	20.0135			0.980067
$418$		0			0
$419$	−23.6277			−1.15429			−0.577144	−	0.816642i	$-0.695833\pi$
$419$	−23.6277			−1.15429			−0.577144	+	0.816642i	$0.695833\pi$
$420$		0			0
$421$	−20.3301	−	14.7707i	−0.990830	−	0.719880i	−0.0307272	−	0.999528i	$-0.509782\pi$
$421$	−20.3301	−	14.7707i	−0.990830	−	0.719880i	−0.960103	+	0.279648i	$0.909782\pi$
$422$		0			0
$423$	−0.325300	+	1.00117i	−0.0158166	+	0.0486786i
$424$		0			0
$425$	2.20384	−	1.60118i	0.106902	−	0.0776688i
$426$		0			0
$427$	−6.89322	−	21.2152i	−0.333586	−	1.02667i
$428$		0			0
$429$	−6.62844	−	2.63621i	−0.320024	−	0.127278i
$430$		0			0
$431$	−4.01252	−	12.3493i	−0.193276	−	0.594843i	−0.999992	−	0.00390396i	$-0.998757\pi$
$431$	−4.01252	−	12.3493i	−0.193276	−	0.594843i	0.806716	−	0.590939i	$-0.201243\pi$
$432$		0			0
$433$	32.1267	−	23.3414i	1.54391	−	1.12172i	0.596086	−	0.802921i	$-0.296722\pi$
$433$	32.1267	−	23.3414i	1.54391	−	1.12172i	0.947824	−	0.318795i	$-0.103278\pi$
$434$		0			0
$435$	1.90468	−	5.86200i	0.0913223	−	0.281061i
$436$		0			0
$437$	13.4905	+	9.80139i	0.645336	+	0.468864i
$438$		0			0
$439$	−40.4303			−1.92963			−0.964816	−	0.262928i	$-0.915312\pi$
$439$	−40.4303			−1.92963			−0.964816	+	0.262928i	$0.915312\pi$
$440$		0			0
$441$	−2.94840			−0.140400
$442$		0			0
$443$	−22.7029	−	16.4946i	−1.07865	−	0.783684i	−0.101201	−	0.994866i	$-0.532269\pi$
$443$	−22.7029	−	16.4946i	−1.07865	−	0.783684i	−0.977447	+	0.211182i	$0.932269\pi$
$444$		0			0
$445$	1.23641	−	3.80527i	0.0586113	−	0.180387i
$446$		0			0
$447$	8.60755	−	6.25375i	0.407123	−	0.295792i
$448$		0			0
$449$	−3.74917	−	11.5387i	−0.176934	−	0.544547i	0.822782	−	0.568357i	$-0.192421\pi$
$449$	−3.74917	−	11.5387i	−0.176934	−	0.544547i	−0.999717	+	0.0238093i	$0.992421\pi$
$450$		0			0
$451$	14.7691	−	17.7968i	0.695450	−	0.838020i
$452$		0			0
$453$	0.452218	+	1.39179i	0.0212471	+	0.0653918i
$454$		0			0
$455$	−3.50246	+	2.54468i	−0.164198	+	0.119297i
$456$		0			0
$457$	−9.18113	+	28.2566i	−0.429475	+	1.32179i	0.469168	+	0.883109i	$0.344554\pi$
$457$	−9.18113	+	28.2566i	−0.429475	+	1.32179i	−0.898643	+	0.438680i	$0.855446\pi$
$458$		0			0
$459$	−2.20384	−	1.60118i	−0.102866	−	0.0747369i
$460$		0			0
$461$	−19.6451			−0.914964			−0.457482	−	0.889219i	$-0.651249\pi$
$461$	−19.6451			−0.914964			−0.457482	+	0.889219i	$0.651249\pi$
$462$		0			0
$463$	36.4450			1.69374			0.846871	−	0.531798i	$-0.178483\pi$
$463$	36.4450			1.69374			0.846871	+	0.531798i	$0.178483\pi$
$464$		0			0
$465$	3.93348	+	2.85784i	0.182411	+	0.132529i
$466$		0			0
$467$	−5.01383	+	15.4310i	−0.232012	+	0.714060i	0.765491	+	0.643446i	$0.222496\pi$
$467$	−5.01383	+	15.4310i	−0.232012	+	0.714060i	−0.997504	+	0.0706142i	$0.977504\pi$
$468$		0			0
$469$	23.4051	−	17.0048i	1.08075	−	0.785209i
$470$		0			0
$471$	−3.22109	−	9.91351i	−0.148420	−	0.456790i
$472$		0			0
$473$	0.738292	−	11.4530i	0.0339467	−	0.526609i
$474$		0			0
$475$	−2.00246	−	6.16292i	−0.0918790	−	0.282774i
$476$		0			0
$477$	7.45031	−	5.41297i	0.341126	−	0.247843i
$478$		0			0
$479$	−0.969471	+	2.98372i	−0.0442963	+	0.136330i	−0.970759	−	0.240057i	$-0.922834\pi$
$479$	−0.969471	+	2.98372i	−0.0442963	+	0.136330i	0.926462	+	0.376387i	$0.122834\pi$
$480$		0			0
$481$	9.48745	+	6.89304i	0.432590	+	0.314295i
$482$		0			0
$483$	−5.17966			−0.235683
$484$		0			0
$485$	−7.69712			−0.349508
$486$		0			0
$487$	−21.6405	−	15.7227i	−0.980625	−	0.712466i	−0.0227767	−	0.999741i	$-0.507251\pi$
$487$	−21.6405	−	15.7227i	−0.980625	−	0.712466i	−0.957848	+	0.287275i	$0.907251\pi$
$488$		0			0
$489$	−4.25653	+	13.1003i	−0.192487	+	0.592414i
$490$		0			0
$491$	−4.10729	+	2.98412i	−0.185360	+	0.134672i	−0.676595	−	0.736355i	$-0.736545\pi$
$491$	−4.10729	+	2.98412i	−0.185360	+	0.134672i	0.491236	+	0.871027i	$0.336545\pi$
$492$		0			0
$493$	5.18853	+	15.9686i	0.233680	+	0.719192i
$494$		0			0
$495$	−0.213356	+	3.30976i	−0.00958964	+	0.148762i
$496$		0			0
$497$	4.92114	+	15.1457i	0.220743	+	0.679378i
$498$		0			0
$499$	−2.63043	+	1.91112i	−0.117754	+	0.0855533i	−0.645104	−	0.764095i	$-0.723186\pi$
$499$	−2.63043	+	1.91112i	−0.117754	+	0.0855533i	0.527350	+	0.849648i	$0.323186\pi$
$500$		0			0
$501$	2.32927	−	7.16877i	0.104064	−	0.320277i
$502$		0			0
$503$	−0.138290	−	0.100474i	−0.00616606	−	0.00447990i	0.584698	−	0.811251i	$-0.301213\pi$
$503$	−0.138290	−	0.100474i	−0.00616606	−	0.00447990i	−0.590864	+	0.806771i	$0.701213\pi$
$504$		0			0
$505$	−7.25687			−0.322927
$506$		0			0
$507$	8.37402			0.371903
$508$		0			0
$509$	−15.5891	−	11.3261i	−0.690973	−	0.502021i	0.186007	−	0.982548i	$-0.440445\pi$
$509$	−15.5891	−	11.3261i	−0.690973	−	0.502021i	−0.876980	+	0.480527i	$0.840445\pi$
$510$		0			0
$511$	2.92548	−	9.00371i	0.129416	−	0.398301i
$512$		0			0
$513$	−5.24250	+	3.80890i	−0.231462	+	0.168167i
$514$		0			0
$515$	−2.82399	−	8.69135i	−0.124440	−	0.382987i
$516$		0			0
$517$	−2.22964	+	2.68673i	−0.0980594	+	0.118162i
$518$		0			0
$519$	−3.70232	−	11.3946i	−0.162514	−	0.500167i
$520$		0			0
$521$	24.6849	−	17.9346i	1.08146	−	0.785729i	0.103526	−	0.994627i	$-0.466988\pi$
$521$	24.6849	−	17.9346i	1.08146	−	0.785729i	0.977938	+	0.208898i	$0.0669875\pi$
$522$		0			0
$523$	1.54707	−	4.76140i	0.0676488	−	0.208201i	−0.911518	−	0.411261i	$-0.865088\pi$
$523$	1.54707	−	4.76140i	0.0676488	−	0.208201i	0.979166	+	0.203060i	$0.0650885\pi$
$524$		0			0
$525$	1.62844	+	1.18313i	0.0710708	+	0.0516359i
$526$		0			0
$527$	−13.2447			−0.576948
$528$		0			0
$529$	−16.3782			−0.712095
$530$		0			0
$531$	6.62692	+	4.81474i	0.287584	+	0.208942i
$532$		0			0
$533$	4.63453	−	14.2636i	0.200744	−	0.617825i
$534$		0			0
$535$	14.2155	−	10.3282i	0.614591	−	0.446526i
$536$		0			0
$537$	−3.38746	−	10.4255i	−0.146180	−	0.449894i
$538$		0			0
$539$	−9.08649	−	3.61381i	−0.391383	−	0.155658i
$540$		0			0
$541$	3.70731	+	11.4099i	0.159390	+	0.490552i	0.998579	−	0.0532878i	$-0.0169701\pi$
$541$	3.70731	+	11.4099i	0.159390	+	0.490552i	−0.839189	+	0.543839i	$0.816970\pi$
$542$		0			0
$543$	−2.03866	+	1.48117i	−0.0874871	+	0.0635631i
$544$		0			0
$545$	2.99145	−	9.20675i	0.128140	−	0.394374i
$546$		0			0
$547$	−33.4732	−	24.3197i	−1.43121	−	1.03984i	−0.989790	−	0.142535i	$-0.954475\pi$
$547$	−33.4732	−	24.3197i	−1.43121	−	1.03984i	−0.441421	−	0.897300i	$-0.645525\pi$
$548$		0			0
$549$	−11.0822			−0.472978
$550$		0			0
$551$	39.9411			1.70155
$552$		0			0
$553$	−5.37758	−	3.90704i	−0.228678	−	0.166144i
$554$		0			0
$555$	1.68489	−	5.18557i	0.0715197	−	0.220115i
$556$		0			0
$557$	−9.83262	+	7.14381i	−0.416621	+	0.302693i	−0.776277	−	0.630392i	$-0.782894\pi$
$557$	−9.83262	+	7.14381i	−0.416621	+	0.302693i	0.359656	+	0.933085i	$0.382894\pi$
$558$		0			0
$559$	−2.29989	−	7.07834i	−0.0972750	−	0.299382i
$560$		0			0
$561$	−4.82932	−	7.63580i	−0.203894	−	0.322384i
$562$		0			0
$563$	0.742256	+	2.28443i	0.0312824	+	0.0962772i	0.965479	−	0.260482i	$-0.0838816\pi$
$563$	0.742256	+	2.28443i	0.0312824	+	0.0962772i	−0.934196	+	0.356759i	$0.883882\pi$
$564$		0			0
$565$	−14.7876	+	10.7438i	−0.622118	+	0.451995i
$566$		0			0
$567$	0.622007	−	1.91434i	0.0261218	−	0.0803948i
$568$		0			0
$569$	−3.71767	−	2.70104i	−0.155853	−	0.113234i	0.507126	−	0.861872i	$-0.330708\pi$
$569$	−3.71767	−	2.70104i	−0.155853	−	0.113234i	−0.662979	+	0.748638i	$0.730708\pi$
$570$		0			0
$571$	−31.4402			−1.31573			−0.657867	−	0.753134i	$-0.728541\pi$
$571$	−31.4402			−1.31573			−0.657867	+	0.753134i	$0.728541\pi$
$572$		0			0
$573$	8.91171			0.372292
$574$		0			0
$575$	−2.08183	−	1.51254i	−0.0868185	−	0.0630773i
$576$		0			0
$577$	10.4701	−	32.2237i	0.435876	−	1.34149i	−0.456310	−	0.889821i	$-0.650829\pi$
$577$	10.4701	−	32.2237i	0.435876	−	1.34149i	0.892186	−	0.451668i	$-0.149171\pi$
$578$		0			0
$579$	−5.55214	+	4.03387i	−0.230739	+	0.167642i
$580$		0			0
$581$	−2.46751	−	7.59422i	−0.102370	−	0.315061i
$582$		0			0
$583$	29.5952	−	7.55014i	1.22571	−	0.312695i
$584$		0			0
$585$	0.664637	+	2.04554i	0.0274793	+	0.0845727i
$586$		0			0
$587$	−9.65306	+	7.01336i	−0.398424	+	0.289472i	−0.768899	−	0.639370i	$-0.779195\pi$
$587$	−9.65306	+	7.01336i	−0.398424	+	0.289472i	0.370475	+	0.928843i	$0.379195\pi$
$588$		0			0
$589$	−9.73604	+	29.9644i	−0.401166	+	1.23466i
$590$		0			0
$591$	0.865052	+	0.628497i	0.0355835	+	0.0258529i
$592$		0			0
$593$	29.5627			1.21400			0.606998	−	0.794704i	$-0.292374\pi$
$593$	29.5627			1.21400			0.606998	+	0.794704i	$0.292374\pi$
$594$		0			0
$595$	−5.48322			−0.224790
$596$		0			0
$597$	20.6107	+	14.9745i	0.843539	+	0.612867i
$598$		0			0
$599$	−3.52765	+	10.8570i	−0.144136	+	0.443605i	−0.996899	−	0.0786932i	$-0.974925\pi$
$599$	−3.52765	+	10.8570i	−0.144136	+	0.443605i	0.852763	+	0.522298i	$0.174925\pi$
$600$		0			0
$601$	−7.03003	+	5.10761i	−0.286761	+	0.208344i	−0.721861	−	0.692038i	$-0.756713\pi$
$601$	−7.03003	+	5.10761i	−0.286761	+	0.208344i	0.435100	+	0.900382i	$0.356713\pi$
$602$		0			0
$603$	−4.44143	−	13.6693i	−0.180869	−	0.556657i
$604$		0			0
$605$	−4.71424	+	9.93861i	−0.191661	+	0.404062i
$606$		0			0
$607$	−8.84040	−	27.2080i	−0.358821	−	1.10434i	−0.953761	−	0.300567i	$-0.902824\pi$
$607$	−8.84040	−	27.2080i	−0.358821	−	1.10434i	0.594940	−	0.803770i	$-0.297176\pi$
$608$		0			0
$609$	−10.0371	+	7.29241i	−0.406725	+	0.295503i
$610$		0			0
$611$	−0.699658	+	2.15333i	−0.0283051	+	0.0871143i
$612$		0			0
$613$	−4.33693	−	3.15097i	−0.175167	−	0.127266i	0.496747	−	0.867895i	$-0.334528\pi$
$613$	−4.33693	−	3.15097i	−0.175167	−	0.127266i	−0.671914	+	0.740629i	$0.734528\pi$
$614$		0			0
$615$	−6.97302			−0.281179
$616$		0			0
$617$	18.7506			0.754870			0.377435	−	0.926036i	$-0.376806\pi$
$617$	18.7506			0.754870			0.377435	+	0.926036i	$0.376806\pi$
$618$		0			0
$619$	−3.24859	−	2.36024i	−0.130572	−	0.0948659i	0.520582	−	0.853811i	$-0.325715\pi$
$619$	−3.24859	−	2.36024i	−0.130572	−	0.0948659i	−0.651154	+	0.758946i	$0.725715\pi$
$620$		0			0
$621$	−0.795190	+	2.44734i	−0.0319099	+	0.0982085i
$622$		0			0
$623$	−6.51553	+	4.73381i	−0.261039	+	0.189656i
$624$		0			0
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$		0			0
$627$	−20.8250	+	5.31274i	−0.831671	+	0.212170i
$628$		0			0
$629$	4.58981	+	14.1260i	0.183008	+	0.563240i
$630$		0			0
$631$	16.9303	−	12.3006i	0.673985	−	0.489679i	−0.197372	−	0.980329i	$-0.563241\pi$
$631$	16.9303	−	12.3006i	0.673985	−	0.489679i	0.871357	+	0.490650i	$0.163241\pi$
$632$		0			0
$633$	4.91568	−	15.1289i	0.195381	−	0.601320i
$634$		0			0
$635$	5.43691	+	3.95014i	0.215757	+	0.156757i
$636$		0			0
$637$	−6.34145			−0.251258
$638$		0			0
$639$	7.91171			0.312982
$640$		0			0
$641$	−6.97569	−	5.06813i	−0.275523	−	0.200179i	0.441439	−	0.897291i	$-0.354468\pi$
$641$	−6.97569	−	5.06813i	−0.275523	−	0.200179i	−0.716962	+	0.697112i	$0.754468\pi$
$642$		0			0
$643$	−3.65834	+	11.2592i	−0.144271	+	0.444020i	−0.996916	−	0.0784698i	$-0.974997\pi$
$643$	−3.65834	+	11.2592i	−0.144271	+	0.444020i	0.852646	+	0.522489i	$0.174997\pi$
$644$		0			0
$645$	−2.79950	+	2.03396i	−0.110230	+	0.0800870i
$646$		0			0
$647$	1.31189	+	4.03759i	0.0515758	+	0.158734i	0.973527	−	0.228572i	$-0.0734057\pi$
$647$	1.31189	+	4.03759i	0.0515758	+	0.158734i	−0.921951	+	0.387306i	$0.873406\pi$
$648$		0			0
$649$	14.5217	+	22.9607i	0.570027	+	0.901288i
$650$		0			0
$651$	−3.02423	−	9.30762i	−0.118529	−	0.364794i
$652$		0			0
$653$	36.4108	−	26.4540i	1.42486	−	1.03522i	0.433920	−	0.900952i	$-0.357130\pi$
$653$	36.4108	−	26.4540i	1.42486	−	1.03522i	0.990944	−	0.134273i	$-0.0428698\pi$
$654$		0			0
$655$	−0.778697	+	2.39658i	−0.0304262	+	0.0936423i
$656$		0			0
$657$	−3.80504	−	2.76453i	−0.148449	−	0.107854i
$658$		0			0
$659$	−43.1606			−1.68130			−0.840649	−	0.541581i	$-0.817826\pi$
$659$	−43.1606			−1.68130			−0.840649	+	0.541581i	$0.817826\pi$
$660$		0			0
$661$	22.6808			0.882181			0.441090	−	0.897463i	$-0.354592\pi$
$661$	22.6808			0.882181			0.441090	+	0.897463i	$0.354592\pi$
$662$		0			0
$663$	−4.74004	−	3.44384i	−0.184088	−	0.133748i
$664$		0			0
$665$	−4.03066	+	12.4051i	−0.156302	+	0.481049i
$666$		0			0
$667$	12.8317	−	9.32280i	0.496847	−	0.360980i
$668$		0			0
$669$	−6.18850	−	19.0462i	−0.239261	−	0.736370i
$670$		0			0
$671$	−34.1536	−	13.5833i	−1.31848	−	0.524378i
$672$		0			0
$673$	−12.3653	−	38.0564i	−0.476646	−	1.46696i	−0.843725	−	0.536775i	$-0.819642\pi$
$673$	−12.3653	−	38.0564i	−0.476646	−	1.46696i	0.367079	−	0.930190i	$-0.380358\pi$
$674$		0			0
$675$	0.809017	−	0.587785i	0.0311391	−	0.0226239i
$676$		0			0
$677$	9.87909	−	30.4047i	0.379684	−	1.16855i	−0.560579	−	0.828101i	$-0.689422\pi$
$677$	9.87909	−	30.4047i	0.379684	−	1.16855i	0.940264	−	0.340447i	$-0.110578\pi$
$678$		0			0
$679$	12.5343	+	9.10668i	0.481021	+	0.349482i
$680$		0			0
$681$	−15.4886			−0.593526
$682$		0			0
$683$	7.96754			0.304869			0.152435	−	0.988314i	$-0.451289\pi$
$683$	7.96754			0.304869			0.152435	+	0.988314i	$0.451289\pi$
$684$		0			0
$685$	−11.6278	−	8.44810i	−0.444276	−	0.322785i
$686$		0			0
$687$	−2.97666	+	9.16121i	−0.113567	+	0.349522i
$688$		0			0
$689$	16.0242	−	11.6423i	0.610473	−	0.443535i
$690$		0			0
$691$	7.44579	+	22.9158i	0.283251	+	0.871758i	0.986917	+	0.161227i	$0.0515451\pi$
$691$	7.44579	+	22.9158i	0.283251	+	0.871758i	−0.703666	+	0.710531i	$0.748455\pi$
$692$		0			0
$693$	4.26330	−	5.13730i	0.161949	−	0.195150i
$694$		0			0
$695$	−6.18452	−	19.0340i	−0.234592	−	0.722001i
$696$		0			0
$697$	15.3674	−	11.1651i	0.582083	−	0.422908i
$698$		0			0
$699$	−0.872502	+	2.68528i	−0.0330010	+	0.101567i
$700$		0			0
$701$	−38.8666	−	28.2383i	−1.46797	−	1.06654i	−0.981195	−	0.193019i	$-0.938172\pi$
$701$	−38.8666	−	28.2383i	−1.46797	−	1.06654i	−0.486777	−	0.873526i	$-0.661828\pi$
$702$		0			0
$703$	35.3322			1.33258
$704$		0			0
$705$	1.05269			0.0396467
$706$		0			0
$707$	11.8174	+	8.58581i	0.444437	+	0.322903i
$708$		0			0
$709$	9.00289	−	27.7081i	0.338111	−	1.04060i	−0.627059	−	0.778972i	$-0.715741\pi$
$709$	9.00289	−	27.7081i	0.338111	−	1.04060i	0.965169	−	0.261626i	$-0.0842586\pi$
$710$		0			0
$711$	−2.67161	+	1.94104i	−0.100193	+	0.0727947i
$712$		0			0
$713$	3.86625	+	11.8991i	0.144792	+	0.445625i
$714$		0			0
$715$	−0.458888	+	7.11865i	−0.0171614	+	0.266222i
$716$		0			0
$717$	9.06158	+	27.8887i	0.338411	+	1.04152i
$718$		0			0
$719$	−28.0468	+	20.3772i	−1.04597	+	0.759942i	−0.971442	−	0.237277i	$-0.923745\pi$
$719$	−28.0468	+	20.3772i	−1.04597	+	0.759942i	−0.0745281	+	0.997219i	$0.523745\pi$
$720$		0			0
$721$	−5.68429	+	17.4945i	−0.211694	+	0.651528i
$722$		0			0
$723$	11.8347	+	8.59844i	0.440138	+	0.319779i
$724$		0			0
$725$	−6.16367			−0.228913
$726$		0			0
$727$	−51.4262			−1.90729			−0.953647	−	0.300929i	$-0.902703\pi$
$727$	−51.4262			−1.90729			−0.953647	+	0.300929i	$0.902703\pi$
$728$		0			0
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	2.91292	−	8.96504i	0.107738	−	0.331584i
$732$		0			0
$733$	9.37956	−	6.81465i	0.346442	−	0.251705i	−0.400933	−	0.916107i	$-0.631314\pi$
$733$	9.37956	−	6.81465i	0.346442	−	0.251705i	0.747375	+	0.664403i	$0.231314\pi$
$734$		0			0
$735$	0.911107	+	2.80410i	0.0336067	+	0.103431i
$736$		0			0
$737$	3.06652	−	47.5703i	0.112957	−	1.75227i
$738$		0			0
$739$	−7.20948	−	22.1885i	−0.265205	−	0.816217i	−0.991646	−	0.128988i	$-0.958827\pi$
$739$	−7.20948	−	22.1885i	−0.265205	−	0.816217i	0.726441	−	0.687229i	$-0.241173\pi$
$740$		0			0
$741$	−11.2756	+	8.19221i	−0.414220	+	0.300948i
$742$		0			0
$743$	9.78125	−	30.1036i	0.358839	−	1.10439i	−0.594910	−	0.803792i	$-0.702812\pi$
$743$	9.78125	−	30.1036i	0.358839	−	1.10439i	0.953750	−	0.300602i	$-0.0971875\pi$
$744$		0			0
$745$	−8.60755	−	6.25375i	−0.315356	−	0.229120i
$746$		0			0
$747$	−3.96702			−0.145146
$748$		0			0
$749$	−35.3686			−1.29234
$750$		0			0
$751$	20.7906	+	15.1052i	0.758659	+	0.551198i	0.898499	−	0.438976i	$-0.144659\pi$
$751$	20.7906	+	15.1052i	0.758659	+	0.551198i	−0.139840	+	0.990174i	$0.544659\pi$
$752$		0			0
$753$	1.96004	−	6.03237i	0.0714277	−	0.219832i
$754$		0			0
$755$	1.18392	−	0.860171i	0.0430874	−	0.0313048i
$756$		0			0
$757$	10.4531	+	32.1714i	0.379925	+	1.16929i	0.940096	+	0.340911i	$0.110735\pi$
$757$	10.4531	+	32.1714i	0.379925	+	1.16929i	−0.560171	+	0.828377i	$0.689265\pi$
$758$		0			0
$759$	−5.45031	+	6.56765i	−0.197834	+	0.238391i
$760$		0			0
$761$	12.8060	+	39.4127i	0.464215	+	1.42871i	0.859967	+	0.510350i	$0.170484\pi$
$761$	12.8060	+	39.4127i	0.464215	+	1.42871i	−0.395751	+	0.918358i	$0.629516\pi$
$762$		0			0
$763$	−15.7642	+	11.4533i	−0.570701	+	0.414638i
$764$		0			0
$765$	−0.841792	+	2.59077i	−0.0304351	+	0.0936695i
$766$		0			0
$767$	14.2532	+	10.3556i	0.514655	+	0.373918i
$768$		0			0
$769$	15.2490			0.549894			0.274947	−	0.961459i	$-0.411340\pi$
$769$	15.2490			0.549894			0.274947	+	0.961459i	$0.411340\pi$
$770$		0			0
$771$	14.8052			0.533197
$772$		0			0
$773$	28.2150	+	20.4994i	1.01482	+	0.737312i	0.965215	−	0.261456i	$-0.0842027\pi$
$773$	28.2150	+	20.4994i	1.01482	+	0.737312i	0.0496083	+	0.998769i	$0.484203\pi$
$774$		0			0
$775$	1.50246	−	4.62408i	0.0539698	−	0.166102i
$776$		0			0
$777$	−8.87893	+	6.45092i	−0.318530	+	0.231425i
$778$		0			0
$779$	−13.9632	−	42.9742i	−0.500282	−	1.53971i
$780$		0			0
$781$	24.3826	+	9.69725i	0.872477	+	0.346995i
$782$		0			0
$783$	1.90468	+	5.86200i	0.0680676	+	0.209491i
$784$		0			0
$785$	−8.43293	+	6.12688i	−0.300984	+	0.218678i
$786$		0			0
$787$	−6.73092	+	20.7156i	−0.239931	+	0.738432i	0.756498	+	0.653996i	$0.226909\pi$
$787$	−6.73092	+	20.7156i	−0.239931	+	0.738432i	−0.996429	+	0.0844360i	$0.973091\pi$
$788$		0			0
$789$	9.13986	+	6.64050i	0.325388	+	0.236408i
$790$		0			0
$791$	36.7919			1.30817
$792$		0			0
$793$	−23.8357			−0.846432
$794$		0			0
$795$	−7.45031	−	5.41297i	−0.264235	−	0.191978i
$796$		0			0
$797$	−2.74801	+	8.45750i	−0.0973394	+	0.299580i	−0.987856	−	0.155370i	$-0.950343\pi$
$797$	−2.74801	+	8.45750i	−0.0973394	+	0.299580i	0.890517	+	0.454950i	$0.150343\pi$
$798$		0			0
$799$	−2.31997	+	1.68555i	−0.0820745	+	0.0596306i
$800$		0			0
$801$	1.23641	+	3.80527i	0.0436863	+	0.134453i
$802$		0			0
$803$	−8.33808	−	13.1836i	−0.294244	−	0.465239i
$804$		0			0
$805$	1.60060	+	4.92615i	0.0564139	+	0.173624i
$806$		0			0
$807$	18.3823	−	13.3555i	0.647087	−	0.470136i
$808$		0			0
$809$	−6.96727	+	21.4431i	−0.244956	+	0.753898i	0.750687	+	0.660658i	$0.229722\pi$
$809$	−6.96727	+	21.4431i	−0.244956	+	0.753898i	−0.995644	+	0.0932403i	$0.970278\pi$
$810$		0			0
$811$	−1.45691	−	1.05850i	−0.0511589	−	0.0371691i	0.561912	−	0.827197i	$-0.310066\pi$
$811$	−1.45691	−	1.05850i	−0.0511589	−	0.0371691i	−0.613071	+	0.790028i	$0.710066\pi$
$812$		0			0
$813$	21.0546			0.738416
$814$		0			0
$815$	13.7744			0.482497
$816$		0			0
$817$	−18.1410	−	13.1802i	−0.634673	−	0.461117i
$818$		0			0
$819$	1.33782	−	4.11738i	0.0467472	−	0.143873i
$820$		0			0
$821$	10.4015	−	7.55710i	0.363013	−	0.263745i	−0.391294	−	0.920266i	$-0.627973\pi$
$821$	10.4015	−	7.55710i	0.363013	−	0.263745i	0.754308	+	0.656521i	$0.227973\pi$
$822$		0			0
$823$	3.26815	+	10.0583i	0.113920	+	0.350611i	0.991720	−	0.128416i	$-0.0409894\pi$
$823$	3.26815	+	10.0583i	0.113920	+	0.350611i	−0.877800	+	0.479027i	$0.840989\pi$
$824$		0			0
$825$	3.21369	−	0.819857i	0.111886	−	0.0285438i
$826$		0			0
$827$	−11.2262	−	34.5507i	−0.390374	−	1.20145i	−0.932506	−	0.361154i	$-0.882383\pi$
$827$	−11.2262	−	34.5507i	−0.390374	−	1.20145i	0.542133	−	0.840293i	$-0.317617\pi$
$828$		0			0
$829$	−35.8279	+	26.0305i	−1.24436	+	0.904077i	−0.997881	−	0.0650721i	$-0.979272\pi$
$829$	−35.8279	+	26.0305i	−1.24436	+	0.904077i	−0.246475	+	0.969149i	$0.579272\pi$
$830$		0			0
$831$	5.29634	−	16.3004i	0.183728	−	0.565456i
$832$		0			0
$833$	−6.49781	−	4.72094i	−0.225136	−	0.163571i
$834$		0			0
$835$	−7.53769			−0.260852
$836$		0			0
$837$	−4.86205			−0.168057
$838$		0			0
$839$	7.16892	+	5.20852i	0.247499	+	0.179818i	0.704617	−	0.709587i	$-0.251119\pi$
$839$	7.16892	+	5.20852i	0.247499	+	0.179818i	−0.457119	+	0.889406i	$0.651119\pi$
$840$		0			0
$841$	2.77831	−	8.55075i	0.0958037	−	0.294853i
$842$		0			0
$843$	−12.6631	+	9.20029i	−0.436141	+	0.316875i
$844$		0			0
$845$	−2.58771	−	7.96417i	−0.0890201	−	0.273976i
$846$		0			0
$847$	19.4355	−	10.6068i	0.667811	−	0.364455i
$848$		0			0
$849$	1.94579	+	5.98852i	0.0667793	+	0.205526i
$850$		0			0
$851$	11.3510	−	8.24702i	0.389109	−	0.282704i
$852$		0			0
$853$	−5.41027	+	16.6511i	−0.185244	+	0.570123i	−0.999952	−	0.00974824i	$-0.996897\pi$
$853$	−5.41027	+	16.6511i	−0.185244	+	0.570123i	0.814708	+	0.579871i	$0.196897\pi$
$854$		0			0
$855$	5.24250	+	3.80890i	0.179290	+	0.130262i
$856$		0			0
$857$	−8.06429			−0.275471			−0.137735	−	0.990469i	$-0.543982\pi$
$857$	−8.06429			−0.275471			−0.137735	+	0.990469i	$0.543982\pi$
$858$		0			0
$859$	−34.1476			−1.16510			−0.582551	−	0.812794i	$-0.697945\pi$
$859$	−34.1476			−1.16510			−0.582551	+	0.812794i	$0.697945\pi$
$860$		0			0
$861$	11.3551	+	8.24998i	0.386982	+	0.281159i
$862$		0			0
$863$	−4.15399	+	12.7847i	−0.141404	+	0.435195i	−0.996531	−	0.0832224i	$-0.973479\pi$
$863$	−4.15399	+	12.7847i	−0.141404	+	0.435195i	0.855127	+	0.518418i	$0.173479\pi$
$864$		0			0
$865$	−9.69281	+	7.04224i	−0.329565	+	0.239443i
$866$		0			0
$867$	2.96017	+	9.11045i	0.100532	+	0.309407i
$868$		0			0
$869$	−10.6126	+	2.70741i	−0.360007	+	0.0918426i
$870$		0			0
$871$	−9.55266	−	29.4001i	−0.323680	−	0.996183i
$872$		0			0
$873$	6.22710	−	4.52425i	0.210755	−	0.153123i
$874$		0			0
$875$	0.622007	−	1.91434i	0.0210277	−	0.0647166i
$876$		0			0
$877$	0.361627	+	0.262737i	0.0122113	+	0.00887201i	0.593874	−	0.804558i	$-0.297598\pi$
$877$	0.361627	+	0.262737i	0.0122113	+	0.00887201i	−0.581663	+	0.813430i	$0.697598\pi$
$878$		0			0
$879$	−16.6108			−0.560267
$880$		0			0
$881$	−2.95373			−0.0995138			−0.0497569	−	0.998761i	$-0.515845\pi$
$881$	−2.95373			−0.0995138			−0.0497569	+	0.998761i	$0.515845\pi$
$882$		0			0
$883$	46.9966	+	34.1450i	1.58156	+	1.14907i	0.914878	+	0.403730i	$0.132287\pi$
$883$	46.9966	+	34.1450i	1.58156	+	1.14907i	0.666683	+	0.745341i	$0.267713\pi$
$884$		0			0
$885$	2.53126	−	7.79041i	0.0850873	−	0.261872i
$886$		0			0
$887$	−14.4810	+	10.5211i	−0.486225	+	0.353263i	−0.803731	−	0.594993i	$-0.797155\pi$
$887$	−14.4810	+	10.5211i	−0.486225	+	0.353263i	0.317506	+	0.948256i	$0.397155\pi$
$888$		0			0
$889$	−4.18013	−	12.8651i	−0.140197	−	0.431482i
$890$		0			0
$891$	−1.77282	−	2.80306i	−0.0593916	−	0.0939059i
$892$		0			0
$893$	2.10797	+	6.48767i	0.0705405	+	0.217101i
$894$		0			0
$895$	−8.86848	+	6.44333i	−0.296441	+	0.215377i
$896$		0			0
$897$	−1.71030	+	5.26377i	−0.0571053	+	0.175752i
$898$		0			0
$899$	24.2447	+	17.6148i	0.808605	+	0.587486i
$900$		0			0
$901$	25.0865			0.835751
$902$		0			0
$903$	6.96524			0.231789
$904$		0			0
$905$	2.03866	+	1.48117i	0.0677672	+	0.0492358i
$906$		0			0
$907$	−12.9165	+	39.7529i	−0.428885	+	1.31997i	0.470340	+	0.882485i	$0.344131\pi$
$907$	−12.9165	+	39.7529i	−0.428885	+	1.31997i	−0.899225	+	0.437487i	$0.855869\pi$
$908$		0			0
$909$	5.87093	−	4.26548i	0.194727	−	0.141477i
$910$		0			0
$911$	0.332036	+	1.02190i	0.0110008	+	0.0338571i	0.956406	−	0.292039i	$-0.0943339\pi$
$911$	0.332036	+	1.02190i	0.0110008	+	0.0338571i	−0.945405	+	0.325897i	$0.894334\pi$
$912$		0			0
$913$	−12.2257	−	4.86231i	−0.404611	−	0.160919i
$914$		0			0
$915$	3.42460	+	10.5398i	0.113214	+	0.348436i
$916$		0			0
$917$	4.10352	−	2.98139i	0.135510	−	0.0984540i
$918$		0			0
$919$	3.32426	−	10.2310i	0.109657	−	0.337491i	−0.881138	−	0.472859i	$-0.843222\pi$
$919$	3.32426	−	10.2310i	0.109657	−	0.337491i	0.990795	+	0.135369i	$0.0432219\pi$
$920$		0			0
$921$	−3.65272	−	2.65385i	−0.120361	−	0.0874475i
$922$		0			0
$923$	17.0166			0.560107
$924$		0			0
$925$	−5.45243			−0.179275
$926$		0			0
$927$	7.39331	+	5.37155i	0.242828	+	0.176425i
$928$		0			0
$929$	16.0150	−	49.2892i	0.525436	−	1.61713i	−0.238016	−	0.971261i	$-0.576497\pi$
$929$	16.0150	−	49.2892i	0.525436	−	1.61713i	0.763452	−	0.645864i	$-0.223503\pi$
$930$		0			0
$931$	−15.4570	+	11.2302i	−0.506583	+	0.368054i
$932$		0			0
$933$	7.30310	+	22.4766i	0.239093	+	0.735852i
$934$		0			0
$935$	−5.76973	+	6.95255i	−0.188690	+	0.227373i
$936$		0			0
$937$	6.23267	+	19.1822i	0.203613	+	0.626655i	0.999768	+	0.0215623i	$0.00686402\pi$
$937$	6.23267	+	19.1822i	0.203613	+	0.626655i	−0.796155	+	0.605093i	$0.793136\pi$
$938$		0			0
$939$	−18.7459	+	13.6197i	−0.611749	+	0.444462i
$940$		0			0
$941$	−5.14948	+	15.8485i	−0.167868	+	0.516645i	−0.999236	−	0.0390769i	$-0.987558\pi$
$941$	−5.14948	+	15.8485i	−0.167868	+	0.516645i	0.831368	+	0.555722i	$0.187558\pi$
$942$		0			0
$943$	−14.5167	−	10.5470i	−0.472728	−	0.343457i
$944$		0			0
$945$	−2.01286			−0.0654783
$946$		0			0
$947$	54.9492			1.78561			0.892805	−	0.450444i	$-0.148734\pi$
$947$	54.9492			1.78561			0.892805	+	0.450444i	$0.148734\pi$
$948$		0			0
$949$	−8.18392	−	5.94597i	−0.265661	−	0.193014i
$950$		0			0
$951$	0.901883	−	2.77571i	0.0292456	−	0.0900086i
$952$		0			0
$953$	−48.2163	+	35.0312i	−1.56188	+	1.13477i	−0.627433	+	0.778670i	$0.715895\pi$
$953$	−48.2163	+	35.0312i	−1.56188	+	1.13477i	−0.934447	+	0.356102i	$0.884105\pi$
$954$		0			0
$955$	−2.75387	−	8.47554i	−0.0891131	−	0.274262i
$956$		0			0
$957$	−1.31506	+	20.4002i	−0.0425097	+	0.659446i
$958$		0			0
$959$	8.93996	+	27.5144i	0.288686	+	0.888485i
$960$		0			0
$961$	5.95476	−	4.32638i	0.192089	−	0.139561i
$962$		0			0
$963$	−5.42985	+	16.7113i	−0.174974	+	0.538516i
$964$		0			0
$965$	5.55214	+	4.03387i	0.178730	+	0.129855i
$966$		0			0
$967$	−10.7122			−0.344482			−0.172241	−	0.985055i	$-0.555101\pi$
$967$	−10.7122			−0.344482			−0.172241	+	0.985055i	$0.555101\pi$
$968$		0			0
$969$	−17.6524			−0.567076
$970$		0			0
$971$	23.6394	+	17.1750i	0.758623	+	0.551172i	0.898488	−	0.438999i	$-0.144667\pi$
$971$	23.6394	+	17.1750i	0.758623	+	0.551172i	−0.139865	+	0.990171i	$0.544667\pi$
$972$		0			0
$973$	−12.4486	+	38.3127i	−0.399083	+	1.22825i
$974$		0			0
$975$	1.74004	−	1.26421i	0.0557259	−	0.0404872i
$976$		0			0
$977$	12.4195	+	38.2234i	0.397336	+	1.22287i	0.927128	+	0.374746i	$0.122270\pi$
$977$	12.4195	+	38.2234i	0.397336	+	1.22287i	−0.529792	+	0.848128i	$0.677730\pi$
$978$		0			0
$979$	−0.853658	+	13.2426i	−0.0272830	+	0.423237i
$980$		0			0
$981$	2.99145	+	9.20675i	0.0955098	+	0.293949i
$982$		0			0
$983$	35.1343	−	25.5266i	1.12061	−	0.814172i	0.136310	−	0.990666i	$-0.456476\pi$
$983$	35.1343	−	25.5266i	1.12061	−	0.814172i	0.984302	+	0.176495i	$0.0564758\pi$
$984$		0			0
$985$	0.330421	−	1.01693i	0.0105281	−	0.0324021i
$986$		0			0
$987$	−1.71424	−	1.24547i	−0.0545650	−	0.0396438i
$988$		0			0
$989$	−8.90454			−0.283148
$990$		0			0
$991$	−7.55212			−0.239901			−0.119951	−	0.992780i	$-0.538274\pi$
$991$	−7.55212			−0.239901			−0.119951	+	0.992780i	$0.538274\pi$
$992$		0			0
$993$	−14.5488	−	10.5703i	−0.461691	−	0.335438i
$994$		0			0
$995$	7.87258	−	24.2293i	0.249578	−	0.768121i
$996$		0			0
$997$	42.4618	−	30.8503i	1.34478	−	0.977040i	0.345526	−	0.938409i	$-0.387700\pi$
$997$	42.4618	−	30.8503i	1.34478	−	0.977040i	0.999254	−	0.0386305i	$-0.0122995\pi$
$998$		0			0
$999$	1.68489	+	5.18557i	0.0533077	+	0.164064i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	660.2.y.c.181.1	✓	8
3.2	odd	2		1980.2.z.f.181.1		8
11.3	even	5		7260.2.a.bc.1.4		4
11.8	odd	10		7260.2.a.bd.1.1		4
11.9	even	5	inner	660.2.y.c.361.1	yes	8
33.20	odd	10		1980.2.z.f.361.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
660.2.y.c.181.1	✓	8	1.1	even	1	trivial
660.2.y.c.361.1	yes	8	11.9	even	5	inner
1980.2.z.f.181.1		8	3.2	odd	2
1980.2.z.f.361.1		8	33.20	odd	10
7260.2.a.bc.1.4		4	11.3	even	5
7260.2.a.bd.1.1		4	11.8	odd	10

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:	\( N \)	\(=\)	\( 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	660.y (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{5} +(-1.62844 + 1.18313i) q^{7} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{5} +(-1.62844 + 1.18313i) q^{7} +(0.309017 + 0.951057i) q^{9} +(-0.213356 + 3.30976i) q^{11} +(0.664637 + 2.04554i) q^{13} +(0.809017 - 0.587785i) q^{15} +(-0.841792 + 2.59077i) q^{17} +(5.24250 + 3.80890i) q^{19} -2.01286 q^{21} +2.57329 q^{23} +(-0.809017 - 0.587785i) q^{25} +(-0.309017 + 0.951057i) q^{27} +(4.98651 - 3.62291i) q^{29} +(1.50246 + 4.62408i) q^{31} +(-2.11803 + 2.55224i) q^{33} +(0.622007 + 1.91434i) q^{35} +(4.41111 - 3.20486i) q^{37} +(-0.664637 + 2.04554i) q^{39} +(-5.64129 - 4.09864i) q^{41} -3.46037 q^{43} +1.00000 q^{45} +(0.851646 + 0.618757i) q^{47} +(-0.911107 + 2.80410i) q^{49} +(-2.20384 + 1.60118i) q^{51} +(-2.84577 - 8.75837i) q^{53} +(3.08183 + 1.22568i) q^{55} +(2.00246 + 6.16292i) q^{57} +(6.62692 - 4.81474i) q^{59} +(-3.42460 + 10.5398i) q^{61} +(-1.62844 - 1.18313i) q^{63} +2.15081 q^{65} -14.3728 q^{67} +(2.08183 + 1.51254i) q^{69} +(2.44485 - 7.52448i) q^{71} +(-3.80504 + 2.76453i) q^{73} +(-0.309017 - 0.951057i) q^{75} +(-3.56843 - 5.64215i) q^{77} +(1.02047 + 3.14067i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-1.22588 + 3.77286i) q^{83} +(2.20384 + 1.60118i) q^{85} +6.16367 q^{87} +4.00110 q^{89} +(-3.50246 - 2.54468i) q^{91} +(-1.50246 + 4.62408i) q^{93} +(5.24250 - 3.80890i) q^{95} +(-2.37854 - 7.32040i) q^{97} +(-3.21369 + 0.819857i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 2 q^{5} + 3 q^{7} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 - 2 * q^5 + 3 * q^7 - 2 * q^9	\( 8 q + 2 q^{3} - 2 q^{5} + 3 q^{7} - 2 q^{9} - 7 q^{11} + 2 q^{13} + 2 q^{15} + 4 q^{17} + 10 q^{19} + 12 q^{21} + 10 q^{23} - 2 q^{25} + 2 q^{27} + 4 q^{29} - 9 q^{31} - 8 q^{33} + 3 q^{35} + 7 q^{37} - 2 q^{39} - q^{41} + 4 q^{43} + 8 q^{45} + q^{47} + 21 q^{49} + 6 q^{51} - 19 q^{53} + 3 q^{55} - 5 q^{57} + 9 q^{59} - 35 q^{61} + 3 q^{63} + 2 q^{65} + 18 q^{67} - 5 q^{69} + 25 q^{71} - 19 q^{73} + 2 q^{75} - 47 q^{77} + 18 q^{79} - 2 q^{81} - 11 q^{83} - 6 q^{85} + 6 q^{87} + 8 q^{89} - 7 q^{91} + 9 q^{93} + 10 q^{95} - 9 q^{97} - 7 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 - 2 * q^5 + 3 * q^7 - 2 * q^9 - 7 * q^11 + 2 * q^13 + 2 * q^15 + 4 * q^17 + 10 * q^19 + 12 * q^21 + 10 * q^23 - 2 * q^25 + 2 * q^27 + 4 * q^29 - 9 * q^31 - 8 * q^33 + 3 * q^35 + 7 * q^37 - 2 * q^39 - q^41 + 4 * q^43 + 8 * q^45 + q^47 + 21 * q^49 + 6 * q^51 - 19 * q^53 + 3 * q^55 - 5 * q^57 + 9 * q^59 - 35 * q^61 + 3 * q^63 + 2 * q^65 + 18 * q^67 - 5 * q^69 + 25 * q^71 - 19 * q^73 + 2 * q^75 - 47 * q^77 + 18 * q^79 - 2 * q^81 - 11 * q^83 - 6 * q^85 + 6 * q^87 + 8 * q^89 - 7 * q^91 + 9 * q^93 + 10 * q^95 - 9 * q^97 - 7 * q^99

Introduction

L-functions

Modular forms

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Database

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