LMFDB - Embedded newform 572.2.n.b.313.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(53,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6, 0]))

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

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

chi := DirichletCharacter("572.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.n (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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			313.1
Character	$\chi$	$=$	572.313
Dual form			572.2.n.b.53.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.46647 - 1.79199i) q^{3} +(0.518170 - 1.59476i) q^{5} +(-2.24130 + 1.62840i) q^{7} +(1.94517 + 5.98661i) q^{9} +O(q^{10})$	\(q+(-2.46647 - 1.79199i) q^{3} +(0.518170 - 1.59476i) q^{5} +(-2.24130 + 1.62840i) q^{7} +(1.94517 + 5.98661i) q^{9} +(-3.14645 - 1.04873i) q^{11} +(-0.309017 - 0.951057i) q^{13} +(-4.13586 + 3.00487i) q^{15} +(-0.872693 + 2.68587i) q^{17} +(-0.580719 - 0.421917i) q^{19} +8.44618 q^{21} +1.69900 q^{23} +(1.77031 + 1.28621i) q^{25} +(3.10395 - 9.55299i) q^{27} +(-0.142122 + 0.103257i) q^{29} +(3.16309 + 9.73500i) q^{31} +(5.88131 + 8.22507i) q^{33} +(1.43554 + 4.41814i) q^{35} +(-0.763222 + 0.554513i) q^{37} +(-0.942106 + 2.89951i) q^{39} +(3.83201 + 2.78412i) q^{41} +4.08506 q^{43} +10.5552 q^{45} +(-1.40587 - 1.02142i) q^{47} +(0.208624 - 0.642079i) q^{49} +(6.96553 - 5.06075i) q^{51} +(-3.11897 - 9.59920i) q^{53} +(-3.30287 + 4.47443i) q^{55} +(0.676252 + 2.08129i) q^{57} +(-12.0611 + 8.76291i) q^{59} +(-4.00049 + 12.3123i) q^{61} +(-14.1083 - 10.2503i) q^{63} -1.67683 q^{65} +2.13708 q^{67} +(-4.19053 - 3.04460i) q^{69} +(1.29678 - 3.99107i) q^{71} +(-6.76042 + 4.91173i) q^{73} +(-2.06154 - 6.34478i) q^{75} +(8.75990 - 2.77317i) q^{77} +(-2.09648 - 6.45230i) q^{79} +(-9.49714 + 6.90007i) q^{81} +(-2.64082 + 8.12760i) q^{83} +(3.83113 + 2.78348i) q^{85} +0.535575 q^{87} +2.99597 q^{89} +(2.24130 + 1.62840i) q^{91} +(9.64339 - 29.6793i) q^{93} +(-0.973770 + 0.707485i) q^{95} +(-3.07878 - 9.47551i) q^{97} +(0.157939 - 20.8765i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9}+O(q^{10}) $ 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9	$ 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9} + q^{11} + 7 q^{13} - 24 q^{15} + 7 q^{17} - 7 q^{19} - 12 q^{21} + 34 q^{23} - 26 q^{25} - 11 q^{27} + 8 q^{29} - 17 q^{31} - 2 q^{33} - 6 q^{35} - 15 q^{37} + 4 q^{39} + 29 q^{41} - 8 q^{43} + 62 q^{45} - 27 q^{47} - 4 q^{49} + 69 q^{51} - 32 q^{53} + 19 q^{55} + 9 q^{57} - 37 q^{59} - 19 q^{61} + 46 q^{63} - 18 q^{65} + 10 q^{67} - 32 q^{69} - 27 q^{71} - 79 q^{75} + 13 q^{77} + 21 q^{79} - 18 q^{81} + 27 q^{83} + 7 q^{85} + 56 q^{87} + 82 q^{89} - 11 q^{91} - 53 q^{93} + 51 q^{95} - 88 q^{97} + 86 q^{99}+O(q^{100}) $ 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9 + q^11 + 7 * q^13 - 24 * q^15 + 7 * q^17 - 7 * q^19 - 12 * q^21 + 34 * q^23 - 26 * q^25 - 11 * q^27 + 8 * q^29 - 17 * q^31 - 2 * q^33 - 6 * q^35 - 15 * q^37 + 4 * q^39 + 29 * q^41 - 8 * q^43 + 62 * q^45 - 27 * q^47 - 4 * q^49 + 69 * q^51 - 32 * q^53 + 19 * q^55 + 9 * q^57 - 37 * q^59 - 19 * q^61 + 46 * q^63 - 18 * q^65 + 10 * q^67 - 32 * q^69 - 27 * q^71 - 79 * q^75 + 13 * q^77 + 21 * q^79 - 18 * q^81 + 27 * q^83 + 7 * q^85 + 56 * q^87 + 82 * q^89 - 11 * q^91 - 53 * q^93 + 51 * q^95 - 88 * q^97 + 86 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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
$3$	−2.46647	−	1.79199i	−1.42402	−	1.03461i	−0.991092	−	0.133177i	$-0.957482\pi$
$3$	−2.46647	−	1.79199i	−1.42402	−	1.03461i	−0.432923	−	0.901431i	$-0.642518\pi$
$4$		0			0
$5$	0.518170	−	1.59476i	0.231733	−	0.713200i	−0.765805	−	0.643073i	$-0.777659\pi$
$5$	0.518170	−	1.59476i	0.231733	−	0.713200i	0.997538	−	0.0701276i	$-0.0223406\pi$
$6$		0			0
$7$	−2.24130	+	1.62840i	−0.847132	+	0.615478i	−0.924354	−	0.381536i	$-0.875395\pi$
$7$	−2.24130	+	1.62840i	−0.847132	+	0.615478i	0.0772215	+	0.997014i	$0.475395\pi$
$8$		0			0
$9$	1.94517	+	5.98661i	0.648389	+	1.99554i
$10$		0			0
$11$	−3.14645	−	1.04873i	−0.948692	−	0.316203i
$11$	−3.14645	−	1.04873i	−0.948692	−	0.316203i
$12$		0			0
$13$	−0.309017	−	0.951057i	−0.0857059	−	0.263776i
$13$	−0.309017	−	0.951057i	−0.0857059	−	0.263776i
$14$		0			0
$15$	−4.13586	+	3.00487i	−1.06787	+	0.775855i
$16$		0			0
$17$	−0.872693	+	2.68587i	−0.211659	+	0.651420i	0.787715	+	0.616040i	$0.211264\pi$
$17$	−0.872693	+	2.68587i	−0.211659	+	0.651420i	−0.999374	+	0.0353797i	$0.988736\pi$
$18$		0			0
$19$	−0.580719	−	0.421917i	−0.133226	−	0.0967945i	0.519176	−	0.854667i	$-0.326239\pi$
$19$	−0.580719	−	0.421917i	−0.133226	−	0.0967945i	−0.652402	+	0.757873i	$0.726239\pi$
$20$		0			0
$21$	8.44618			1.84311
$22$		0			0
$23$	1.69900			0.354266			0.177133	−	0.984187i	$-0.443318\pi$
$23$	1.69900			0.354266			0.177133	+	0.984187i	$0.443318\pi$
$24$		0			0
$25$	1.77031	+	1.28621i	0.354063	+	0.257242i
$26$		0			0
$27$	3.10395	−	9.55299i	0.597356	−	1.83847i
$28$		0			0
$29$	−0.142122	+	0.103257i	−0.0263913	+	0.0191744i	−0.600903	−	0.799322i	$-0.705192\pi$
$29$	−0.142122	+	0.103257i	−0.0263913	+	0.0191744i	0.574511	+	0.818497i	$0.305192\pi$
$30$		0			0
$31$	3.16309	+	9.73500i	0.568108	+	1.74846i	0.658530	+	0.752554i	$0.271179\pi$
$31$	3.16309	+	9.73500i	0.568108	+	1.74846i	−0.0904215	+	0.995904i	$0.528821\pi$
$32$		0			0
$33$	5.88131	+	8.22507i	1.02381	+	1.43180i
$34$		0			0
$35$	1.43554	+	4.41814i	0.242650	+	0.746801i
$36$		0			0
$37$	−0.763222	+	0.554513i	−0.125473	+	0.0911614i	−0.648752	−	0.761000i	$-0.724709\pi$
$37$	−0.763222	+	0.554513i	−0.125473	+	0.0911614i	0.523279	+	0.852162i	$0.324709\pi$
$38$		0			0
$39$	−0.942106	+	2.89951i	−0.150858	+	0.464292i
$40$		0			0
$41$	3.83201	+	2.78412i	0.598460	+	0.434807i	0.845332	−	0.534241i	$-0.179403\pi$
$41$	3.83201	+	2.78412i	0.598460	+	0.434807i	−0.246872	+	0.969048i	$0.579403\pi$
$42$		0			0
$43$	4.08506			0.622966			0.311483	−	0.950252i	$-0.399174\pi$
$43$	4.08506			0.622966			0.311483	+	0.950252i	$0.399174\pi$
$44$		0			0
$45$	10.5552			1.57347
$46$		0			0
$47$	−1.40587	−	1.02142i	−0.205067	−	0.148990i	0.480512	−	0.876988i	$-0.340451\pi$
$47$	−1.40587	−	1.02142i	−0.205067	−	0.148990i	−0.685579	+	0.727998i	$0.740451\pi$
$48$		0			0
$49$	0.208624	−	0.642079i	0.0298034	−	0.0917256i
$50$		0			0
$51$	6.96553	−	5.06075i	0.975370	−	0.708647i
$52$		0			0
$53$	−3.11897	−	9.59920i	−0.428423	−	1.31855i	−0.899678	−	0.436554i	$-0.856199\pi$
$53$	−3.11897	−	9.59920i	−0.428423	−	1.31855i	0.471255	−	0.881997i	$-0.343801\pi$
$54$		0			0
$55$	−3.30287	+	4.47443i	−0.445359	+	0.603332i
$56$		0			0
$57$	0.676252	+	2.08129i	0.0895718	+	0.275674i
$58$		0			0
$59$	−12.0611	+	8.76291i	−1.57022	+	1.14083i	−0.643281	+	0.765630i	$0.722427\pi$
$59$	−12.0611	+	8.76291i	−1.57022	+	1.14083i	−0.926942	+	0.375204i	$0.877573\pi$
$60$		0			0
$61$	−4.00049	+	12.3123i	−0.512211	+	1.57642i	0.276090	+	0.961132i	$0.410961\pi$
$61$	−4.00049	+	12.3123i	−0.512211	+	1.57642i	−0.788301	+	0.615290i	$0.789039\pi$
$62$		0			0
$63$	−14.1083	−	10.2503i	−1.77748	−	1.29141i
$64$		0			0
$65$	−1.67683			−0.207986
$66$		0			0
$67$	2.13708			0.261086			0.130543	−	0.991443i	$-0.458328\pi$
$67$	2.13708			0.261086			0.130543	+	0.991443i	$0.458328\pi$
$68$		0			0
$69$	−4.19053	−	3.04460i	−0.504480	−	0.366526i
$70$		0			0
$71$	1.29678	−	3.99107i	0.153899	−	0.473653i	−0.844149	−	0.536109i	$-0.819893\pi$
$71$	1.29678	−	3.99107i	0.153899	−	0.473653i	0.998048	+	0.0624565i	$0.0198935\pi$
$72$		0			0
$73$	−6.76042	+	4.91173i	−0.791247	+	0.574875i	−0.908333	−	0.418247i	$-0.862645\pi$
$73$	−6.76042	+	4.91173i	−0.791247	+	0.574875i	0.117086	+	0.993122i	$0.462645\pi$
$74$		0			0
$75$	−2.06154	−	6.34478i	−0.238046	−	0.732632i
$76$		0			0
$77$	8.75990	−	2.77317i	0.998283	−	0.316033i
$78$		0			0
$79$	−2.09648	−	6.45230i	−0.235872	−	0.725941i	−0.997004	−	0.0773438i	$-0.975356\pi$
$79$	−2.09648	−	6.45230i	−0.235872	−	0.725941i	0.761132	−	0.648597i	$-0.224644\pi$
$80$		0			0
$81$	−9.49714	+	6.90007i	−1.05524	+	0.766675i
$82$		0			0
$83$	−2.64082	+	8.12760i	−0.289867	+	0.892120i	0.695030	+	0.718981i	$0.255391\pi$
$83$	−2.64082	+	8.12760i	−0.289867	+	0.892120i	−0.984897	+	0.173139i	$0.944609\pi$
$84$		0			0
$85$	3.83113	+	2.78348i	0.415544	+	0.301911i
$86$		0			0
$87$	0.535575			0.0574197
$88$		0			0
$89$	2.99597			0.317572			0.158786	−	0.987313i	$-0.449242\pi$
$89$	2.99597			0.317572			0.158786	+	0.987313i	$0.449242\pi$
$90$		0			0
$91$	2.24130	+	1.62840i	0.234952	+	0.170703i
$92$		0			0
$93$	9.64339	−	29.6793i	0.999973	−	3.07760i
$94$		0			0
$95$	−0.973770	+	0.707485i	−0.0999067	+	0.0725865i
$96$		0			0
$97$	−3.07878	−	9.47551i	−0.312603	−	0.962092i	−0.976730	−	0.214473i	$-0.931197\pi$
$97$	−3.07878	−	9.47551i	−0.312603	−	0.962092i	0.664127	−	0.747620i	$-0.268803\pi$
$98$		0			0
$99$	0.157939	−	20.8765i	0.0158735	−	2.09817i
$100$		0			0
$101$	4.42878	+	13.6304i	0.440680	+	1.35627i	0.887152	+	0.461477i	$0.152680\pi$
$101$	4.42878	+	13.6304i	0.440680	+	1.35627i	−0.446472	+	0.894797i	$0.647320\pi$
$102$		0			0
$103$	−3.92383	+	2.85083i	−0.386626	+	0.280900i	−0.764071	−	0.645132i	$-0.776803\pi$
$103$	−3.92383	+	2.85083i	−0.386626	+	0.280900i	0.377446	+	0.926032i	$0.376803\pi$
$104$		0			0
$105$	4.37656	−	13.4697i	0.427108	−	1.31450i
$106$		0			0
$107$	−8.69666	−	6.31849i	−0.840738	−	0.610832i	0.0818388	−	0.996646i	$-0.473921\pi$
$107$	−8.69666	−	6.31849i	−0.840738	−	0.610832i	−0.922577	+	0.385814i	$0.873921\pi$
$108$		0			0
$109$	−14.7139			−1.40934			−0.704668	−	0.709537i	$-0.748904\pi$
$109$	−14.7139			−1.40934			−0.704668	+	0.709537i	$0.748904\pi$
$110$		0			0
$111$	2.87614			0.272992
$112$		0			0
$113$	−14.9137	−	10.8354i	−1.40296	−	1.01931i	−0.994300	−	0.106622i	$-0.965997\pi$
$113$	−14.9137	−	10.8354i	−1.40296	−	1.01931i	−0.408659	−	0.912687i	$-0.634003\pi$
$114$		0			0
$115$	0.880371	−	2.70950i	0.0820950	−	0.252663i
$116$		0			0
$117$	5.09252	−	3.69993i	0.470803	−	0.342059i
$118$		0			0
$119$	−2.41771	−	7.44094i	−0.221631	−	0.682110i
$120$		0			0
$121$	8.80034	+	6.59954i	0.800031	+	0.599958i
$122$		0			0
$123$	−4.46241	−	13.7339i	−0.402362	−	1.23834i
$124$		0			0
$125$	9.75146	−	7.08485i	0.872197	−	0.633688i
$126$		0			0
$127$	−6.34445	+	19.5262i	−0.562979	+	1.73267i	0.110903	+	0.993831i	$0.464626\pi$
$127$	−6.34445	+	19.5262i	−0.562979	+	1.73267i	−0.673882	+	0.738839i	$0.735374\pi$
$128$		0			0
$129$	−10.0757	−	7.32040i	−0.887113	−	0.644525i
$130$		0			0
$131$	21.2697			1.85834			0.929170	−	0.369652i	$-0.120523\pi$
$131$	21.2697			1.85834			0.929170	+	0.369652i	$0.120523\pi$
$132$		0			0
$133$	1.98862			0.172435
$134$		0			0
$135$	−13.6264	−	9.90015i	−1.17277	−	0.852069i
$136$		0			0
$137$	−1.05359	+	3.24263i	−0.0900146	+	0.277036i	−0.985922	−	0.167204i	$-0.946526\pi$
$137$	−1.05359	+	3.24263i	−0.0900146	+	0.277036i	0.895908	+	0.444240i	$0.146526\pi$
$138$		0			0
$139$	−9.93701	+	7.21966i	−0.842846	+	0.612363i	−0.923164	−	0.384406i	$-0.874406\pi$
$139$	−9.93701	+	7.21966i	−0.842846	+	0.612363i	0.0803182	+	0.996769i	$0.474406\pi$
$140$		0			0
$141$	1.63714	+	5.03861i	0.137872	+	0.424327i
$142$		0			0
$143$	−0.0250909	+	3.31653i	−0.00209821	+	0.277342i
$144$		0			0
$145$	0.0910280	+	0.280156i	0.00755947	+	0.0232656i
$146$		0			0
$147$	−1.66517	+	1.20981i	−0.137340	+	0.0997837i
$148$		0			0
$149$	−1.08721	+	3.34608i	−0.0890676	+	0.274122i	−0.985662	−	0.168730i	$-0.946033\pi$
$149$	−1.08721	+	3.34608i	−0.0890676	+	0.274122i	0.896595	+	0.442852i	$0.146033\pi$
$150$		0			0
$151$	−11.7211	−	8.51585i	−0.953846	−	0.693010i	−0.00213294	−	0.999998i	$-0.500679\pi$
$151$	−11.7211	−	8.51585i	−0.953846	−	0.693010i	−0.951713	+	0.306988i	$0.900679\pi$
$152$		0			0
$153$	−17.7768			−1.43717
$154$		0			0
$155$	17.1641			1.37865
$156$		0			0
$157$	−11.6222	−	8.44400i	−0.927550	−	0.673904i	0.0178419	−	0.999841i	$-0.494320\pi$
$157$	−11.6222	−	8.44400i	−0.927550	−	0.673904i	−0.945392	+	0.325936i	$0.894320\pi$
$158$		0			0
$159$	−9.50887	+	29.2653i	−0.754102	+	2.32089i
$160$		0			0
$161$	−3.80797	+	2.76665i	−0.300110	+	0.218043i
$162$		0			0
$163$	−6.50166	−	20.0101i	−0.509249	−	1.56731i	−0.793507	−	0.608561i	$-0.791747\pi$
$163$	−6.50166	−	20.0101i	−0.509249	−	1.56731i	0.284258	−	0.958748i	$-0.408253\pi$
$164$		0			0
$165$	16.1646	−	5.11732i	1.25841	−	0.398383i
$166$		0			0
$167$	2.43845	+	7.50478i	0.188693	+	0.580738i	0.999992	−	0.00389337i	$-0.00123930\pi$
$167$	2.43845	+	7.50478i	0.188693	+	0.580738i	−0.811299	+	0.584631i	$0.801239\pi$
$168$		0			0
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$		0			0
$171$	1.39626	−	4.29724i	0.106775	−	0.328618i
$172$		0			0
$173$	6.41210	+	4.65866i	0.487503	+	0.354192i	0.804223	−	0.594327i	$-0.202582\pi$
$173$	6.41210	+	4.65866i	0.487503	+	0.354192i	−0.316720	+	0.948519i	$0.602582\pi$
$174$		0			0
$175$	−6.06227			−0.458264
$176$		0			0
$177$	45.4514			3.41634
$178$		0			0
$179$	15.8118	+	11.4880i	1.18183	+	0.858652i	0.992377	−	0.123238i	$-0.0393278\pi$
$179$	15.8118	+	11.4880i	1.18183	+	0.858652i	0.189455	+	0.981889i	$0.439328\pi$
$180$		0			0
$181$	−6.97762	+	21.4749i	−0.518643	+	1.59622i	0.257912	+	0.966168i	$0.416965\pi$
$181$	−6.97762	+	21.4749i	−0.518643	+	1.59622i	−0.776555	+	0.630050i	$0.783035\pi$
$182$		0			0
$183$	31.9305	−	23.1989i	2.36037	−	1.71491i
$184$		0			0
$185$	0.488839	+	1.50449i	0.0359401	+	0.110612i
$186$		0			0
$187$	5.56263	−	7.53576i	0.406780	−	0.551069i
$188$		0			0
$189$	8.59920	+	26.4656i	0.625500	+	1.92509i
$190$		0			0
$191$	11.2333	−	8.16144i	0.812810	−	0.590541i	−0.101834	−	0.994801i	$-0.532471\pi$
$191$	11.2333	−	8.16144i	0.812810	−	0.590541i	0.914644	+	0.404260i	$0.132471\pi$
$192$		0			0
$193$	−7.57045	+	23.2995i	−0.544933	+	1.67713i	0.176216	+	0.984352i	$0.443614\pi$
$193$	−7.57045	+	23.2995i	−0.544933	+	1.67713i	−0.721149	+	0.692780i	$0.756386\pi$
$194$		0			0
$195$	4.13586	+	3.00487i	0.296175	+	0.215184i
$196$		0			0
$197$	−18.5024			−1.31824			−0.659120	−	0.752038i	$-0.729071\pi$
$197$	−18.5024			−1.31824			−0.659120	+	0.752038i	$0.729071\pi$
$198$		0			0
$199$	0.431688			0.0306015			0.0153008	−	0.999883i	$-0.495129\pi$
$199$	0.431688			0.0306015			0.0153008	+	0.999883i	$0.495129\pi$
$200$		0			0
$201$	−5.27104	−	3.82963i	−0.371790	−	0.270121i
$202$		0			0
$203$	0.150393	−	0.462862i	0.0105555	−	0.0324866i
$204$		0			0
$205$	6.42565	−	4.66851i	0.448787	−	0.326063i
$206$		0			0
$207$	3.30484	+	10.1713i	0.229702	+	0.706951i
$208$		0			0
$209$	1.38473	+	1.93656i	0.0957838	+	0.133955i
$210$		0			0
$211$	3.96056	+	12.1894i	0.272656	+	0.839150i	0.989830	+	0.142256i	$0.0454355\pi$
$211$	3.96056	+	12.1894i	0.272656	+	0.839150i	−0.717173	+	0.696895i	$0.754564\pi$
$212$		0			0
$213$	−10.3504	+	7.52003i	−0.709200	+	0.515264i
$214$		0			0
$215$	2.11676	−	6.51471i	0.144362	−	0.444299i
$216$		0			0
$217$	−22.9419	−	16.6683i	−1.55740	−	1.13152i
$218$		0			0
$219$	25.4761			1.72152
$220$		0			0
$221$	2.82409			0.189969
$222$		0			0
$223$	−1.00189	−	0.727914i	−0.0670914	−	0.0487447i	0.553734	−	0.832694i	$-0.313202\pi$
$223$	−1.00189	−	0.727914i	−0.0670914	−	0.0487447i	−0.620825	+	0.783949i	$0.713202\pi$
$224$		0			0
$225$	−4.25647	+	13.1001i	−0.283765	+	0.873338i
$226$		0			0
$227$	0.816844	−	0.593472i	0.0542159	−	0.0393901i	−0.560347	−	0.828258i	$-0.689332\pi$
$227$	0.816844	−	0.593472i	0.0542159	−	0.0393901i	0.614563	+	0.788868i	$0.289332\pi$
$228$		0			0
$229$	3.25863	+	10.0290i	0.215336	+	0.662736i	0.999130	+	0.0417147i	$0.0132821\pi$
$229$	3.25863	+	10.0290i	0.215336	+	0.662736i	−0.783794	+	0.621022i	$0.786718\pi$
$230$		0			0
$231$	−26.5755	−	8.85773i	−1.74854	−	0.582796i
$232$		0			0
$233$	−7.99640	−	24.6104i	−0.523862	−	1.61228i	−0.766556	−	0.642178i	$-0.778031\pi$
$233$	−7.99640	−	24.6104i	−0.523862	−	1.61228i	0.242694	−	0.970103i	$-0.421969\pi$
$234$		0			0
$235$	−2.35741	+	1.71276i	−0.153780	+	0.111728i
$236$		0			0
$237$	−6.39158	+	19.6713i	−0.415178	+	1.27779i
$238$		0			0
$239$	14.7088	+	10.6866i	0.951434	+	0.691258i	0.951146	−	0.308742i	$-0.0999081\pi$
$239$	14.7088	+	10.6866i	0.951434	+	0.691258i	0.000288738		1.00000i	$0.499908\pi$
$240$		0			0
$241$	−21.0469			−1.35575			−0.677876	−	0.735176i	$-0.737099\pi$
$241$	−21.0469			−1.35575			−0.677876	+	0.735176i	$0.737099\pi$
$242$		0			0
$243$	5.65544			0.362797
$244$		0			0
$245$	−0.915862	−	0.665412i	−0.0585122	−	0.0425116i
$246$		0			0
$247$	−0.221815	+	0.682676i	−0.0141138	+	0.0434377i
$248$		0			0
$249$	21.0781	−	15.3141i	1.33577	−	0.970494i
$250$		0			0
$251$	−6.32954	−	19.4803i	−0.399517	−	1.22959i	−0.925387	−	0.379022i	$-0.876260\pi$
$251$	−6.32954	−	19.4803i	−0.399517	−	1.22959i	0.525870	−	0.850565i	$-0.323740\pi$
$252$		0			0
$253$	−5.34582	−	1.78179i	−0.336089	−	0.112020i
$254$		0			0
$255$	−4.46138	−	13.7307i	−0.279382	−	0.859851i
$256$		0			0
$257$	1.21819	−	0.885070i	0.0759889	−	0.0552091i	−0.549142	−	0.835729i	$-0.685045\pi$
$257$	1.21819	−	0.885070i	0.0759889	−	0.0552091i	0.625131	+	0.780520i	$0.285045\pi$
$258$		0			0
$259$	0.807640	−	2.48566i	0.0501843	−	0.154451i
$260$		0			0
$261$	−0.894613	−	0.649974i	−0.0553751	−	0.0402324i
$262$		0			0
$263$	20.2058			1.24594			0.622971	−	0.782245i	$-0.285925\pi$
$263$	20.2058			1.24594			0.622971	+	0.782245i	$0.285925\pi$
$264$		0			0
$265$	−16.9246			−1.03967
$266$		0			0
$267$	−7.38945	−	5.36875i	−0.452227	−	0.328562i
$268$		0			0
$269$	3.29140	−	10.1299i	0.200680	−	0.617630i	−0.799183	−	0.601088i	$-0.794734\pi$
$269$	3.29140	−	10.1299i	0.200680	−	0.617630i	0.999863	−	0.0165421i	$-0.00526574\pi$
$270$		0			0
$271$	15.3728	−	11.1690i	0.933832	−	0.678469i	−0.0130962	−	0.999914i	$-0.504169\pi$
$271$	15.3728	−	11.1690i	0.933832	−	0.678469i	0.946928	+	0.321446i	$0.104169\pi$
$272$		0			0
$273$	−2.61001	−	8.03279i	−0.157965	−	0.486167i
$274$		0			0
$275$	−4.22133	−	5.90357i	−0.254556	−	0.355999i
$276$		0			0
$277$	5.99188	+	18.4411i	0.360017	+	1.10802i	0.953043	+	0.302836i	$0.0979334\pi$
$277$	5.99188	+	18.4411i	0.360017	+	1.10802i	−0.593025	+	0.805184i	$0.702067\pi$
$278$		0			0
$279$	−52.1269	+	37.8724i	−3.12076	+	2.26736i
$280$		0			0
$281$	4.80494	−	14.7881i	0.286639	−	0.882183i	−0.699264	−	0.714863i	$-0.746489\pi$
$281$	4.80494	−	14.7881i	0.286639	−	0.882183i	0.985903	−	0.167319i	$-0.0535111\pi$
$282$		0			0
$283$	4.06726	+	2.95504i	0.241773	+	0.175659i	0.702073	−	0.712105i	$-0.252258\pi$
$283$	4.06726	+	2.95504i	0.241773	+	0.175659i	−0.460300	+	0.887764i	$0.652258\pi$
$284$		0			0
$285$	3.66958			0.217367
$286$		0			0
$287$	−13.1224			−0.774589
$288$		0			0
$289$	7.30097	+	5.30447i	0.429469	+	0.312027i
$290$		0			0
$291$	−9.38634	+	28.8882i	−0.550237	+	1.69345i
$292$		0			0
$293$	−0.0735232	+	0.0534177i	−0.00429527	+	0.00312070i	−0.589931	−	0.807454i	$-0.700845\pi$
$293$	−0.0735232	+	0.0534177i	−0.00429527	+	0.00312070i	0.585636	+	0.810574i	$0.300845\pi$
$294$		0			0
$295$	7.72507	+	23.7753i	0.449771	+	1.38425i
$296$		0			0
$297$	−19.7849	+	26.8028i	−1.14804	+	1.55526i
$298$		0			0
$299$	−0.525020	−	1.61584i	−0.0303627	−	0.0934467i
$300$		0			0
$301$	−9.15585	+	6.65212i	−0.527735	+	0.383422i
$302$		0			0
$303$	13.5021	−	41.5552i	0.775676	−	2.38729i
$304$		0			0
$305$	17.5622	+	12.7597i	1.00561	+	0.730617i
$306$		0			0
$307$	18.7704			1.07128			0.535642	−	0.844445i	$-0.320070\pi$
$307$	18.7704			1.07128			0.535642	+	0.844445i	$0.320070\pi$
$308$		0			0
$309$	14.7866			0.841183
$310$		0			0
$311$	−3.18080	−	2.31099i	−0.180367	−	0.131044i	0.493939	−	0.869497i	$-0.335557\pi$
$311$	−3.18080	−	2.31099i	−0.180367	−	0.131044i	−0.674305	+	0.738453i	$0.735557\pi$
$312$		0			0
$313$	7.37436	−	22.6959i	0.416823	−	1.28285i	−0.493786	−	0.869583i	$-0.664388\pi$
$313$	7.37436	−	22.6959i	0.416823	−	1.28285i	0.910610	−	0.413267i	$-0.135612\pi$
$314$		0			0
$315$	−23.6573	+	17.1880i	−1.33294	+	0.968436i
$316$		0			0
$317$	−2.87320	−	8.84280i	−0.161375	−	0.496661i	0.837376	−	0.546627i	$-0.184089\pi$
$317$	−2.87320	−	8.84280i	−0.161375	−	0.496661i	−0.998751	+	0.0499663i	$0.984089\pi$
$318$		0			0
$319$	0.555468	−	0.175848i	0.0311003	−	0.00984560i
$320$		0			0
$321$	10.1273	+	31.1687i	0.565252	+	1.73967i
$322$		0			0
$323$	1.64001	−	1.19153i	0.0912523	−	0.0662987i
$324$		0			0
$325$	0.676199	−	2.08113i	0.0375088	−	0.115440i
$326$		0			0
$327$	36.2914	+	26.3672i	2.00692	+	1.45811i
$328$		0			0
$329$	4.81426			0.265419
$330$		0			0
$331$	−25.2234			−1.38640			−0.693201	−	0.720744i	$-0.743800\pi$
$331$	−25.2234			−1.38640			−0.693201	+	0.720744i	$0.743800\pi$
$332$		0			0
$333$	−4.80425	−	3.49049i	−0.263271	−	0.191278i
$334$		0			0
$335$	1.10737	−	3.40814i	0.0605022	−	0.186206i
$336$		0			0
$337$	10.6556	−	7.74176i	0.580448	−	0.421720i	−0.258437	−	0.966028i	$-0.583208\pi$
$337$	10.6556	−	7.74176i	0.580448	−	0.421720i	0.838886	+	0.544308i	$0.183208\pi$
$338$		0			0
$339$	17.3671	+	53.4503i	0.943249	+	2.90302i
$340$		0			0
$341$	0.256830	−	33.9480i	0.0139081	−	1.83838i
$342$		0			0
$343$	−5.41473	−	16.6648i	−0.292368	−	0.899817i
$344$		0			0
$345$	−7.02682	+	5.10528i	−0.378311	+	0.274859i
$346$		0			0
$347$	−3.38478	+	10.4173i	−0.181704	+	0.559229i	−0.999876	−	0.0157454i	$-0.994988\pi$
$347$	−3.38478	+	10.4173i	−0.181704	+	0.559229i	0.818172	+	0.574974i	$0.194988\pi$
$348$		0			0
$349$	9.98093	+	7.25157i	0.534267	+	0.388168i	0.821951	−	0.569558i	$-0.192885\pi$
$349$	9.98093	+	7.25157i	0.534267	+	0.388168i	−0.287684	+	0.957725i	$0.592885\pi$
$350$		0			0
$351$	−10.0446			−0.536141
$352$		0			0
$353$	−9.55653			−0.508643			−0.254321	−	0.967120i	$-0.581852\pi$
$353$	−9.55653			−0.508643			−0.254321	+	0.967120i	$0.581852\pi$
$354$		0			0
$355$	−5.69286	−	4.13611i	−0.302146	−	0.219522i
$356$		0			0
$357$	−7.37092	+	22.6854i	−0.390110	+	1.20064i
$358$		0			0
$359$	−20.6309	+	14.9892i	−1.08885	+	0.791099i	−0.979205	−	0.202871i	$-0.934973\pi$
$359$	−20.6309	+	14.9892i	−1.08885	+	0.791099i	−0.109649	+	0.993970i	$0.534973\pi$
$360$		0			0
$361$	−5.71210	−	17.5800i	−0.300637	−	0.925265i
$362$		0			0
$363$	−9.87942	−	32.0477i	−0.518535	−	1.68207i
$364$		0			0
$365$	4.33000	+	13.3264i	0.226643	+	0.697535i
$366$		0			0
$367$	−2.50293	+	1.81848i	−0.130652	+	0.0949241i	−0.651192	−	0.758913i	$-0.725731\pi$
$367$	−2.50293	+	1.81848i	−0.130652	+	0.0949241i	0.520540	+	0.853837i	$0.325731\pi$
$368$		0			0
$369$	−9.21354	+	28.3564i	−0.479638	+	1.47617i
$370$		0			0
$371$	22.6219	+	16.4358i	1.17447	+	0.853303i
$372$		0			0
$373$	33.2436			1.72129			0.860645	−	0.509205i	$-0.170061\pi$
$373$	33.2436			1.72129			0.860645	+	0.509205i	$0.170061\pi$
$374$		0			0
$375$	−36.7476			−1.89764
$376$		0			0
$377$	0.142122	+	0.103257i	0.00731964	+	0.00531803i
$378$		0			0
$379$	−5.33607	+	16.4227i	−0.274096	+	0.843580i	0.715362	+	0.698754i	$0.246262\pi$
$379$	−5.33607	+	16.4227i	−0.274096	+	0.843580i	−0.989457	+	0.144825i	$0.953738\pi$
$380$		0			0
$381$	50.6392	−	36.7915i	2.59432	−	1.88489i
$382$		0			0
$383$	6.06437	+	18.6642i	0.309875	+	0.953696i	0.977813	+	0.209479i	$0.0671769\pi$
$383$	6.06437	+	18.6642i	0.309875	+	0.953696i	−0.667938	+	0.744217i	$0.732823\pi$
$384$		0			0
$385$	0.116560	−	15.4069i	0.00594044	−	0.785211i
$386$		0			0
$387$	7.94613	+	24.4557i	0.403924	+	1.24315i
$388$		0			0
$389$	10.5069	−	7.63374i	0.532723	−	0.387046i	−0.288652	−	0.957434i	$-0.593207\pi$
$389$	10.5069	−	7.63374i	0.532723	−	0.387046i	0.821375	+	0.570388i	$0.193207\pi$
$390$		0			0
$391$	−1.48271	+	4.56330i	−0.0749836	+	0.230776i
$392$		0			0
$393$	−52.4610	−	38.1151i	−2.64631	−	1.92265i
$394$		0			0
$395$	−11.3762			−0.572400
$396$		0			0
$397$	13.9429			0.699774			0.349887	−	0.936792i	$-0.386220\pi$
$397$	13.9429			0.699774			0.349887	+	0.936792i	$0.386220\pi$
$398$		0			0
$399$	−4.90486	−	3.56359i	−0.245550	−	0.178403i
$400$		0			0
$401$	0.525108	−	1.61612i	0.0262226	−	0.0807050i	−0.937089	−	0.349091i	$-0.886490\pi$
$401$	0.525108	−	1.61612i	0.0262226	−	0.0807050i	0.963311	+	0.268386i	$0.0864903\pi$
$402$		0			0
$403$	8.28109	−	6.01656i	0.412510	−	0.299706i
$404$		0			0
$405$	6.08286	+	18.7211i	0.302260	+	0.930259i
$406$		0			0
$407$	2.98297	−	0.944338i	0.147861	−	0.0468091i
$408$		0			0
$409$	−2.48484	−	7.64756i	−0.122868	−	0.378148i	0.870639	−	0.491923i	$-0.163706\pi$
$409$	−2.48484	−	7.64756i	−0.122868	−	0.378148i	−0.993507	+	0.113775i	$0.963706\pi$
$410$		0			0
$411$	8.40942	−	6.10980i	0.414806	−	0.301374i
$412$		0			0
$413$	12.7631	−	39.2807i	0.628029	−	1.93287i
$414$		0			0
$415$	11.5932	+	8.42296i	0.569088	+	0.413467i
$416$		0			0
$417$	37.4469			1.83378
$418$		0			0
$419$	−25.0551			−1.22402			−0.612010	−	0.790850i	$-0.709639\pi$
$419$	−25.0551			−1.22402			−0.612010	+	0.790850i	$0.709639\pi$
$420$		0			0
$421$	3.39338	+	2.46543i	0.165383	+	0.120158i	0.667398	−	0.744701i	$-0.267408\pi$
$421$	3.39338	+	2.46543i	0.165383	+	0.120158i	−0.502015	+	0.864859i	$0.667408\pi$
$422$		0			0
$423$	3.38021	−	10.4032i	0.164351	−	0.505822i
$424$		0			0
$425$	−4.99953	+	3.63237i	−0.242513	+	0.176196i
$426$		0			0
$427$	−11.0830	−	34.1099i	−0.536342	−	1.65069i
$428$		0			0
$429$	6.00508	−	8.13515i	0.289928	−	0.392769i
$430$		0			0
$431$	6.83141	+	21.0249i	0.329058	+	1.01274i	0.969576	+	0.244792i	$0.0787197\pi$
$431$	6.83141	+	21.0249i	0.329058	+	1.01274i	−0.640518	+	0.767943i	$0.721280\pi$
$432$		0			0
$433$	−15.3928	+	11.1836i	−0.739733	+	0.537447i	−0.892627	−	0.450795i	$-0.851141\pi$
$433$	−15.3928	+	11.1836i	−0.739733	+	0.537447i	0.152895	+	0.988243i	$0.451141\pi$
$434$		0			0
$435$	0.277519	−	0.854116i	0.0133060	−	0.0409517i
$436$		0			0
$437$	−0.986642	−	0.716837i	−0.0471975	−	0.0342910i
$438$		0			0
$439$	32.3324			1.54314			0.771570	−	0.636144i	$-0.219472\pi$
$439$	32.3324			1.54314			0.771570	+	0.636144i	$0.219472\pi$
$440$		0			0
$441$	4.24969			0.202366
$442$		0			0
$443$	27.0304	+	19.6388i	1.28425	+	0.933065i	0.999673	−	0.0255863i	$-0.00814527\pi$
$443$	27.0304	+	19.6388i	1.28425	+	0.933065i	0.284582	+	0.958652i	$0.408145\pi$
$444$		0			0
$445$	1.55242	−	4.77786i	0.0735918	−	0.226492i
$446$		0			0
$447$	8.67772	−	6.30473i	0.410442	−	0.298204i
$448$		0			0
$449$	−9.11666	−	28.0582i	−0.430242	−	1.32415i	−0.897885	−	0.440231i	$-0.854897\pi$
$449$	−9.11666	−	28.0582i	−0.430242	−	1.32415i	0.467643	−	0.883918i	$-0.345103\pi$
$450$		0			0
$451$	−9.13747	−	12.7788i	−0.430267	−	0.601732i
$452$		0			0
$453$	13.6493	+	42.0081i	0.641298	+	1.97371i
$454$		0			0
$455$	3.75829	−	2.73056i	0.176191	−	0.128011i
$456$		0			0
$457$	−9.12886	+	28.0957i	−0.427030	+	1.31426i	0.474007	+	0.880521i	$0.342807\pi$
$457$	−9.12886	+	28.0957i	−0.427030	+	1.31426i	−0.901037	+	0.433742i	$0.857193\pi$
$458$		0			0
$459$	22.9493	+	16.6736i	1.07118	+	0.778259i
$460$		0			0
$461$	−0.188230			−0.00876672			−0.00438336	−	0.999990i	$-0.501395\pi$
$461$	−0.188230			−0.00876672			−0.00438336	+	0.999990i	$0.501395\pi$
$462$		0			0
$463$	6.17260			0.286865			0.143433	−	0.989660i	$-0.454186\pi$
$463$	6.17260			0.286865			0.143433	+	0.989660i	$0.454186\pi$
$464$		0			0
$465$	−42.3346	−	30.7579i	−1.96322	−	1.42636i
$466$		0			0
$467$	3.28211	−	10.1013i	0.151878	−	0.467432i	−0.845953	−	0.533257i	$-0.820968\pi$
$467$	3.28211	−	10.1013i	0.151878	−	0.467432i	0.997831	+	0.0658247i	$0.0209678\pi$
$468$		0			0
$469$	−4.78984	+	3.48002i	−0.221174	+	0.160693i
$470$		0			0
$471$	13.5341	+	41.6537i	0.623618	+	1.91930i
$472$		0			0
$473$	−12.8535	−	4.28411i	−0.591003	−	0.196984i
$474$		0			0
$475$	−0.485382	−	1.49385i	−0.0222708	−	0.0685426i
$476$		0			0
$477$	51.3998	−	37.3441i	2.35343	−	1.70987i
$478$		0			0
$479$	9.57562	−	29.4707i	0.437521	−	1.34655i	−0.452960	−	0.891531i	$-0.649632\pi$
$479$	9.57562	−	29.4707i	0.437521	−	1.34655i	0.890481	−	0.455021i	$-0.150368\pi$
$480$		0			0
$481$	0.763222	+	0.554513i	0.0347999	+	0.0252836i
$482$		0			0
$483$	14.3501			0.652950
$484$		0			0
$485$	−16.7065			−0.758605
$486$		0			0
$487$	9.68328	+	7.03532i	0.438791	+	0.318801i	0.785155	−	0.619300i	$-0.212583\pi$
$487$	9.68328	+	7.03532i	0.438791	+	0.318801i	−0.346363	+	0.938101i	$0.612583\pi$
$488$		0			0
$489$	−19.8217	+	61.0051i	−0.896370	+	2.75874i
$490$		0			0
$491$	−2.10383	+	1.52853i	−0.0949447	+	0.0689814i	−0.634245	−	0.773132i	$-0.718689\pi$
$491$	−2.10383	+	1.52853i	−0.0949447	+	0.0689814i	0.539300	+	0.842114i	$0.318689\pi$
$492$		0			0
$493$	−0.153308	−	0.471833i	−0.00690463	−	0.0212503i
$494$		0			0
$495$	−33.2113	−	11.0695i	−1.49274	−	0.497536i
$496$		0			0
$497$	3.59259	+	11.0569i	0.161150	+	0.495968i
$498$		0			0
$499$	−4.61860	+	3.35561i	−0.206757	+	0.150218i	−0.686345	−	0.727276i	$-0.740786\pi$
$499$	−4.61860	+	3.35561i	−0.206757	+	0.150218i	0.479588	+	0.877494i	$0.340786\pi$
$500$		0			0
$501$	7.43416	−	22.8800i	0.332134	−	1.02220i
$502$		0			0
$503$	−23.4642	−	17.0477i	−1.04622	−	0.760120i	−0.0747261	−	0.997204i	$-0.523808\pi$
$503$	−23.4642	−	17.0477i	−1.04622	−	0.760120i	−0.971489	+	0.237084i	$0.923808\pi$
$504$		0			0
$505$	24.0321			1.06941
$506$		0			0
$507$	3.04872			0.135398
$508$		0			0
$509$	−11.9043	−	8.64897i	−0.527648	−	0.383359i	0.291829	−	0.956470i	$-0.405736\pi$
$509$	−11.9043	−	8.64897i	−0.527648	−	0.383359i	−0.819477	+	0.573112i	$0.805736\pi$
$510$		0			0
$511$	7.15387	−	22.0173i	0.316468	−	0.973990i
$512$		0			0
$513$	−5.83310	+	4.23799i	−0.257538	+	0.187112i
$514$		0			0
$515$	2.51319	+	7.73479i	0.110744	+	0.340836i
$516$		0			0
$517$	3.35230	+	4.68823i	0.147434	+	0.206188i
$518$		0			0
$519$	−7.46694	−	22.9809i	−0.327762	−	1.00875i
$520$		0			0
$521$	2.87119	−	2.08604i	0.125789	−	0.0913912i	−0.523112	−	0.852264i	$-0.675229\pi$
$521$	2.87119	−	2.08604i	0.125789	−	0.0913912i	0.648901	+	0.760873i	$0.275229\pi$
$522$		0			0
$523$	3.14044	−	9.66528i	0.137322	−	0.422633i	−0.858622	−	0.512609i	$-0.828679\pi$
$523$	3.14044	−	9.66528i	0.137322	−	0.422633i	0.995944	+	0.0899760i	$0.0286790\pi$
$524$		0			0
$525$	14.9524	+	10.8635i	0.652575	+	0.474124i
$526$		0			0
$527$	−28.9074			−1.25923
$528$		0			0
$529$	−20.1134			−0.874496
$530$		0			0
$531$	−75.9210	−	55.1599i	−3.29469	−	2.39373i
$532$		0			0
$533$	1.46370	−	4.50480i	0.0633999	−	0.195125i
$534$		0			0
$535$	−14.5829	+	10.5951i	−0.630472	+	0.458065i
$536$		0			0
$537$	−18.4130	−	56.6694i	−0.794580	−	2.44547i
$538$		0			0
$539$	−1.32979	+	1.80148i	−0.0572782	+	0.0775953i
$540$		0			0
$541$	−10.4158	−	32.0566i	−0.447810	−	1.37822i	−0.879372	−	0.476135i	$-0.842037\pi$
$541$	−10.4158	−	32.0566i	−0.447810	−	1.37822i	0.431561	−	0.902084i	$-0.357963\pi$
$542$		0			0
$543$	55.6930	−	40.4633i	2.39001	−	1.73645i
$544$		0			0
$545$	−7.62431	+	23.4652i	−0.326590	+	1.00514i
$546$		0			0
$547$	−20.8604	−	15.1560i	−0.891926	−	0.648022i	0.0444537	−	0.999011i	$-0.485845\pi$
$547$	−20.8604	−	15.1560i	−0.891926	−	0.648022i	−0.936379	+	0.350990i	$0.885845\pi$
$548$		0			0
$549$	−81.4903			−3.47792
$550$		0			0
$551$	0.126099			0.00537199
$552$		0			0
$553$	15.2058	+	11.0476i	0.646615	+	0.469794i
$554$		0			0
$555$	1.49033	−	4.58677i	0.0632611	−	0.194698i
$556$		0			0
$557$	−12.5074	+	9.08714i	−0.529955	+	0.385035i	−0.820341	−	0.571875i	$-0.806216\pi$
$557$	−12.5074	+	9.08714i	−0.529955	+	0.385035i	0.290386	+	0.956910i	$0.406216\pi$
$558$		0			0
$559$	−1.26235	−	3.88512i	−0.0533919	−	0.164323i
$560$		0			0
$561$	−27.2241	+	8.61849i	−1.14940	+	0.363873i
$562$		0			0
$563$	3.29640	+	10.1453i	0.138927	+	0.427572i	0.996180	−	0.0873224i	$-0.0278310\pi$
$563$	3.29640	+	10.1453i	0.138927	+	0.427572i	−0.857253	+	0.514895i	$0.827831\pi$
$564$		0			0
$565$	−25.0077	+	18.1692i	−1.05208	+	0.764383i
$566$		0			0
$567$	10.0499	−	30.9303i	0.422055	−	1.29895i
$568$		0			0
$569$	−23.7067	−	17.2239i	−0.993836	−	0.722064i	−0.0330780	−	0.999453i	$-0.510531\pi$
$569$	−23.7067	−	17.2239i	−0.993836	−	0.722064i	−0.960758	+	0.277389i	$0.910531\pi$
$570$		0			0
$571$	−26.4775			−1.10805			−0.554024	−	0.832501i	$-0.686908\pi$
$571$	−26.4775			−1.10805			−0.554024	+	0.832501i	$0.686908\pi$
$572$		0			0
$573$	−42.3317			−1.76843
$574$		0			0
$575$	3.00776	+	2.18527i	0.125432	+	0.0911319i
$576$		0			0
$577$	−11.1647	+	34.3614i	−0.464793	+	1.43048i	0.394451	+	0.918917i	$0.370935\pi$
$577$	−11.1647	+	34.3614i	−0.464793	+	1.43048i	−0.859243	+	0.511567i	$0.829065\pi$
$578$		0			0
$579$	60.4247	−	43.9011i	2.51117	−	1.82447i
$580$		0			0
$581$	−7.31612	−	22.5167i	−0.303524	−	0.934151i
$582$		0			0
$583$	−0.253247	+	33.4744i	−0.0104884	+	1.38637i
$584$		0			0
$585$	−3.26172	−	10.0386i	−0.134856	−	0.415043i
$586$		0			0
$587$	−35.6512	+	25.9021i	−1.47148	+	1.06909i	−0.491299	+	0.870991i	$0.663478\pi$
$587$	−35.6512	+	25.9021i	−1.47148	+	1.06909i	−0.980181	+	0.198103i	$0.936522\pi$
$588$		0			0
$589$	2.27050	−	6.98787i	0.0935542	−	0.287930i
$590$		0			0
$591$	45.6355	+	33.1561i	1.87719	+	1.36386i
$592$		0			0
$593$	−9.43372			−0.387396			−0.193698	−	0.981061i	$-0.562048\pi$
$593$	−9.43372			−0.387396			−0.193698	+	0.981061i	$0.562048\pi$
$594$		0			0
$595$	−13.1193			−0.537840
$596$		0			0
$597$	−1.06474	−	0.773582i	−0.0435771	−	0.0316606i
$598$		0			0
$599$	10.7762	−	33.1657i	0.440304	−	1.35512i	−0.447249	−	0.894409i	$-0.647596\pi$
$599$	10.7762	−	33.1657i	0.440304	−	1.35512i	0.887553	−	0.460706i	$-0.152404\pi$
$600$		0			0
$601$	1.04337	−	0.758053i	0.0425600	−	0.0309216i	−0.566302	−	0.824198i	$-0.691626\pi$
$601$	1.04337	−	0.758053i	0.0425600	−	0.0309216i	0.608862	+	0.793276i	$0.291626\pi$
$602$		0			0
$603$	4.15698	+	12.7939i	0.169285	+	0.521007i
$604$		0			0
$605$	15.0848	−	10.6148i	0.613284	−	0.431552i
$606$		0			0
$607$	0.0425506	+	0.130957i	0.00172707	+	0.00531539i	0.951916	−	0.306358i	$-0.0991105\pi$
$607$	0.0425506	+	0.130957i	0.00172707	+	0.00531539i	−0.950189	+	0.311673i	$0.899110\pi$
$608$		0			0
$609$	−1.20039	+	0.872131i	−0.0486421	+	0.0353405i
$610$		0			0
$611$	−0.536993	+	1.65270i	−0.0217244	+	0.0668609i
$612$		0			0
$613$	−15.1761	−	11.0261i	−0.612957	−	0.445340i	0.237497	−	0.971388i	$-0.423673\pi$
$613$	−15.1761	−	11.0261i	−0.612957	−	0.445340i	−0.850454	+	0.526049i	$0.823673\pi$
$614$		0			0
$615$	−24.2146			−0.976427
$616$		0			0
$617$	28.2853			1.13872			0.569362	−	0.822087i	$-0.307190\pi$
$617$	28.2853			1.13872			0.569362	+	0.822087i	$0.307190\pi$
$618$		0			0
$619$	2.84698	+	2.06845i	0.114430	+	0.0831382i	0.643528	−	0.765422i	$-0.277470\pi$
$619$	2.84698	+	2.06845i	0.114430	+	0.0831382i	−0.529099	+	0.848560i	$0.677470\pi$
$620$		0			0
$621$	5.27362	−	16.2305i	0.211623	−	0.651309i
$622$		0			0
$623$	−6.71486	+	4.87863i	−0.269025	+	0.195458i
$624$		0			0
$625$	−2.86475	−	8.81679i	−0.114590	−	0.352672i
$626$		0			0
$627$	0.0549088	−	7.25789i	0.00219285	−	0.289852i
$628$		0			0
$629$	−0.823293	−	2.53384i	−0.0328268	−	0.101031i
$630$		0			0
$631$	5.89131	−	4.28029i	0.234529	−	0.170396i	−0.464313	−	0.885671i	$-0.653699\pi$
$631$	5.89131	−	4.28029i	0.234529	−	0.170396i	0.698843	+	0.715276i	$0.253699\pi$
$632$		0			0
$633$	12.0747	−	37.1620i	0.479924	−	1.47706i
$634$		0			0
$635$	27.8522	+	20.2358i	1.10528	+	0.803033i
$636$		0			0
$637$	−0.675122			−0.0267493
$638$		0			0
$639$	26.4154			1.04498
$640$		0			0
$641$	−2.40426	−	1.74680i	−0.0949627	−	0.0689944i	0.539291	−	0.842120i	$-0.318692\pi$
$641$	−2.40426	−	1.74680i	−0.0949627	−	0.0689944i	−0.634253	+	0.773125i	$0.718692\pi$
$642$		0			0
$643$	−2.75207	+	8.46999i	−0.108531	+	0.334024i	−0.990543	−	0.137203i	$-0.956189\pi$
$643$	−2.75207	+	8.46999i	−0.108531	+	0.334024i	0.882012	+	0.471227i	$0.156189\pi$
$644$		0			0
$645$	−16.8952	+	12.2751i	−0.665249	+	0.483331i
$646$		0			0
$647$	7.31169	+	22.5031i	0.287452	+	0.884686i	0.985653	+	0.168785i	$0.0539842\pi$
$647$	7.31169	+	22.5031i	0.287452	+	0.884686i	−0.698201	+	0.715902i	$0.746016\pi$
$648$		0			0
$649$	47.1396	−	14.9233i	1.85039	−	0.585790i
$650$		0			0
$651$	26.7161	+	82.2236i	1.04708	+	3.22260i
$652$		0			0
$653$	37.0949	−	26.9510i	1.45164	−	1.05467i	0.466190	−	0.884685i	$-0.345626\pi$
$653$	37.0949	−	26.9510i	1.45164	−	1.05467i	0.985446	−	0.169990i	$-0.0543735\pi$
$654$		0			0
$655$	11.0213	−	33.9201i	0.430638	−	1.32537i
$656$		0			0
$657$	−42.5548	−	30.9178i	−1.66022	−	1.20622i
$658$		0			0
$659$	9.09980			0.354478			0.177239	−	0.984168i	$-0.443283\pi$
$659$	9.09980			0.354478			0.177239	+	0.984168i	$0.443283\pi$
$660$		0			0
$661$	−12.7359			−0.495369			−0.247684	−	0.968841i	$-0.579670\pi$
$661$	−12.7359			−0.495369			−0.247684	+	0.968841i	$0.579670\pi$
$662$		0			0
$663$	−6.96553	−	5.06075i	−0.270519	−	0.196543i
$664$		0			0
$665$	1.03044	−	3.17138i	0.0399588	−	0.122981i
$666$		0			0
$667$	−0.241465	+	0.175434i	−0.00934955	+	0.00679285i
$668$		0			0
$669$	1.16671	+	3.59075i	0.0451074	+	0.138826i
$670$		0			0
$671$	25.4996	−	34.5445i	0.984399	−	1.33358i
$672$		0			0
$673$	−1.08411	−	3.33656i	−0.0417895	−	0.128615i	0.927985	−	0.372617i	$-0.121540\pi$
$673$	−1.08411	−	3.33656i	−0.0417895	−	0.128615i	−0.969775	+	0.244002i	$0.921540\pi$
$674$		0			0
$675$	17.7821	−	12.9194i	0.684433	−	0.497270i
$676$		0			0
$677$	−9.44769	+	29.0770i	−0.363104	+	1.11752i	0.588055	+	0.808821i	$0.299894\pi$
$677$	−9.44769	+	29.0770i	−0.363104	+	1.11752i	−0.951160	+	0.308699i	$0.900106\pi$
$678$		0			0
$679$	22.3304	+	16.2240i	0.856962	+	0.622619i
$680$		0			0
$681$	−3.07822			−0.117958
$682$		0			0
$683$	−40.0563			−1.53271			−0.766355	−	0.642417i	$-0.777932\pi$
$683$	−40.0563			−1.53271			−0.766355	+	0.642417i	$0.777932\pi$
$684$		0			0
$685$	4.62529	+	3.36047i	0.176723	+	0.128397i
$686$		0			0
$687$	9.93464	−	30.5757i	0.379030	−	1.16653i
$688$		0			0
$689$	−8.16557	+	5.93263i	−0.311083	+	0.226015i
$690$		0			0
$691$	−6.87556	−	21.1608i	−0.261559	−	0.804994i	−0.992466	−	0.122518i	$-0.960903\pi$
$691$	−6.87556	−	21.1608i	−0.261559	−	0.804994i	0.730908	−	0.682476i	$-0.239097\pi$
$692$		0			0
$693$	33.6414	+	47.0478i	1.27793	+	1.78720i
$694$		0			0
$695$	6.36459	+	19.5882i	0.241423	+	0.743023i
$696$		0			0
$697$	−10.8220	+	7.86262i	−0.409911	+	0.297818i
$698$		0			0
$699$	−24.3788	+	75.0302i	−0.922091	+	2.83790i
$700$		0			0
$701$	31.7404	+	23.0607i	1.19882	+	0.870992i	0.994168	−	0.107843i	$-0.0343945\pi$
$701$	31.7404	+	23.0607i	1.19882	+	0.870992i	0.204650	+	0.978835i	$0.434394\pi$
$702$		0			0
$703$	0.677176			0.0255402
$704$		0			0
$705$	8.88371			0.334580
$706$		0			0
$707$	−32.1220	−	23.3380i	−1.20807	−	0.877715i
$708$		0			0
$709$	4.41194	−	13.5786i	0.165694	−	0.509953i	−0.833393	−	0.552681i	$-0.813605\pi$
$709$	4.41194	−	13.5786i	0.165694	−	0.509953i	0.999087	+	0.0427276i	$0.0136048\pi$
$710$		0			0
$711$	34.5494	−	25.1016i	1.29570	−	0.941384i
$712$		0			0
$713$	5.37410	+	16.5398i	0.201262	+	0.619419i
$714$		0			0
$715$	5.27608	+	1.75854i	0.197314	+	0.0657657i
$716$		0			0
$717$	−17.1285	−	52.7162i	−0.639677	−	1.96872i
$718$		0			0
$719$	−7.59495	+	5.51805i	−0.283244	+	0.205789i	−0.720331	−	0.693630i	$-0.756010\pi$
$719$	−7.59495	+	5.51805i	−0.283244	+	0.205789i	0.437087	+	0.899419i	$0.356010\pi$
$720$		0			0
$721$	4.15219	−	12.7791i	0.154636	−	0.475919i
$722$		0			0
$723$	51.9116	+	37.7160i	1.93061	+	1.40267i
$724$		0			0
$725$	−0.384410			−0.0142766
$726$		0			0
$727$	39.9566			1.48191			0.740955	−	0.671555i	$-0.234373\pi$
$727$	39.9566			1.48191			0.740955	+	0.671555i	$0.234373\pi$
$728$		0			0
$729$	14.5425	+	10.5657i	0.538610	+	0.391323i
$730$		0			0
$731$	−3.56500	+	10.9720i	−0.131856	+	0.405812i
$732$		0			0
$733$	−21.7118	+	15.7745i	−0.801943	+	0.582646i	−0.911484	−	0.411336i	$-0.865062\pi$
$733$	−21.7118	+	15.7745i	−0.801943	+	0.582646i	0.109540	+	0.993982i	$0.465062\pi$
$734$		0			0
$735$	1.06653	+	3.28243i	0.0393395	+	0.121074i
$736$		0			0
$737$	−6.72422	−	2.24121i	−0.247690	−	0.0825562i
$738$		0			0
$739$	4.94635	+	15.2233i	0.181954	+	0.559998i	0.999883	−	0.0153224i	$-0.00487745\pi$
$739$	4.94635	+	15.2233i	0.181954	+	0.559998i	−0.817928	+	0.575320i	$0.804877\pi$
$740$		0			0
$741$	1.77045	−	1.28631i	0.0650391	−	0.0472537i
$742$		0			0
$743$	3.31878	−	10.2141i	0.121754	−	0.374721i	−0.871542	−	0.490322i	$-0.836879\pi$
$743$	3.31878	−	10.2141i	0.121754	−	0.374721i	0.993296	+	0.115601i	$0.0368793\pi$
$744$		0			0
$745$	4.77285	+	3.46768i	0.174864	+	0.127046i
$746$		0			0
$747$	−53.7936			−1.96821
$748$		0			0
$749$	29.7809			1.08817
$750$		0			0
$751$	5.51661	+	4.00805i	0.201304	+	0.146256i	0.683870	−	0.729603i	$-0.260295\pi$
$751$	5.51661	+	4.00805i	0.201304	+	0.146256i	−0.482567	+	0.875859i	$0.660295\pi$
$752$		0			0
$753$	−19.2970	+	59.3901i	−0.703222	+	2.16429i
$754$		0			0
$755$	−19.6543	+	14.2797i	−0.715292	+	0.519690i
$756$		0			0
$757$	12.3507	+	38.0114i	0.448892	+	1.38155i	0.878158	+	0.478371i	$0.158772\pi$
$757$	12.3507	+	38.0114i	0.448892	+	1.38155i	−0.429266	+	0.903178i	$0.641228\pi$
$758$		0			0
$759$	9.99235	+	13.9744i	0.362699	+	0.507239i
$760$		0			0
$761$	7.60387	+	23.4023i	0.275640	+	0.848333i	0.989049	+	0.147585i	$0.0471501\pi$
$761$	7.60387	+	23.4023i	0.275640	+	0.848333i	−0.713409	+	0.700748i	$0.752850\pi$
$762$		0			0
$763$	32.9783	−	23.9601i	1.19389	−	0.867415i
$764$		0			0
$765$	−9.21141	+	28.3498i	−0.333039	+	1.02499i
$766$		0			0
$767$	12.0611	+	8.76291i	0.435502	+	0.316410i
$768$		0			0
$769$	−0.401429			−0.0144759			−0.00723795	−	0.999974i	$-0.502304\pi$
$769$	−0.401429			−0.0144759			−0.00723795	+	0.999974i	$0.502304\pi$
$770$		0			0
$771$	−4.59067			−0.165329
$772$		0			0
$773$	−10.9712	−	7.97104i	−0.394607	−	0.286698i	0.372734	−	0.927938i	$-0.378420\pi$
$773$	−10.9712	−	7.97104i	−0.394607	−	0.286698i	−0.767341	+	0.641240i	$0.778420\pi$
$774$		0			0
$775$	−6.92157	+	21.3024i	−0.248630	+	0.765205i
$776$		0			0
$777$	−6.44631	+	4.68352i	−0.231260	+	0.168020i
$778$		0			0
$779$	−1.05066	−	3.23359i	−0.0376437	−	0.115855i
$780$		0			0
$781$	−8.26579	+	11.1978i	−0.295773	+	0.400687i
$782$		0			0
$783$	0.545278	+	1.67819i	0.0194866	+	0.0599737i
$784$		0			0
$785$	−19.4884	+	14.1592i	−0.695572	+	0.505363i
$786$		0			0
$787$	−2.75519	+	8.47960i	−0.0982119	+	0.302265i	−0.988077	−	0.153958i	$-0.950798\pi$
$787$	−2.75519	+	8.47960i	−0.0982119	+	0.302265i	0.889866	+	0.456223i	$0.150798\pi$
$788$		0			0
$789$	−49.8369	−	36.2086i	−1.77424	−	1.28906i
$790$		0			0
$791$	51.0704			1.81585
$792$		0			0
$793$	12.9459			0.459721
$794$		0			0
$795$	41.7440	+	30.3288i	1.48051	+	1.07565i
$796$		0			0
$797$	9.28212	−	28.5674i	0.328790	−	1.01191i	−0.640911	−	0.767615i	$-0.721443\pi$
$797$	9.28212	−	28.5674i	0.328790	−	1.01191i	0.969701	−	0.244296i	$-0.0785567\pi$
$798$		0			0
$799$	3.97030	−	2.88459i	0.140459	−	0.102050i
$800$		0			0
$801$	5.82766	+	17.9357i	0.205910	+	0.633726i
$802$		0			0
$803$	26.4224	−	8.36470i	0.932426	−	0.295184i
$804$		0			0
$805$	2.43898	+	7.50641i	0.0859628	+	0.264566i
$806$		0			0
$807$	−26.2708	+	19.0868i	−0.924776	+	0.671889i
$808$		0			0
$809$	−2.33837	+	7.19676i	−0.0822127	+	0.253025i	−0.983711	−	0.179758i	$-0.942468\pi$
$809$	−2.33837	+	7.19676i	−0.0822127	+	0.253025i	0.901498	+	0.432783i	$0.142468\pi$
$810$		0			0
$811$	−32.0223	−	23.2655i	−1.12445	−	0.816964i	−0.139576	−	0.990211i	$-0.544574\pi$
$811$	−32.0223	−	23.2655i	−1.12445	−	0.816964i	−0.984878	+	0.173248i	$0.944574\pi$
$812$		0			0
$813$	−57.9313			−2.03174
$814$		0			0
$815$	−35.2803			−1.23581
$816$		0			0
$817$	−2.37227	−	1.72356i	−0.0829954	−	0.0602997i
$818$		0			0
$819$	−5.38890	+	16.5853i	−0.188303	+	0.579538i
$820$		0			0
$821$	7.32739	−	5.32366i	0.255728	−	0.185797i	−0.452534	−	0.891747i	$-0.649480\pi$
$821$	7.32739	−	5.32366i	0.255728	−	0.185797i	0.708261	+	0.705950i	$0.249480\pi$
$822$		0			0
$823$	0.859506	+	2.64529i	0.0299605	+	0.0922089i	0.964919	−	0.262549i	$-0.0845632\pi$
$823$	0.859506	+	2.64529i	0.0299605	+	0.0922089i	−0.934958	+	0.354758i	$0.884563\pi$
$824$		0			0
$825$	−0.167389	+	22.1255i	−0.00582772	+	0.770312i
$826$		0			0
$827$	−11.5588	−	35.5743i	−0.401938	−	1.23704i	−0.923425	−	0.383779i	$-0.874623\pi$
$827$	−11.5588	−	35.5743i	−0.401938	−	1.23704i	0.521487	−	0.853259i	$-0.325377\pi$
$828$		0			0
$829$	18.8154	−	13.6702i	0.653486	−	0.474785i	−0.210971	−	0.977492i	$-0.567663\pi$
$829$	18.8154	−	13.6702i	0.653486	−	0.474785i	0.864457	+	0.502707i	$0.167663\pi$
$830$		0			0
$831$	18.2676	−	56.2218i	0.633695	−	1.95031i
$832$		0			0
$833$	1.54248	+	1.12068i	0.0534437	+	0.0388291i
$834$		0			0
$835$	13.2319			0.457909
$836$		0			0
$837$	102.816			3.55386
$838$		0			0
$839$	41.3780	+	30.0629i	1.42853	+	1.03789i	0.990288	+	0.139028i	$0.0443977\pi$
$839$	41.3780	+	30.0629i	1.42853	+	1.03789i	0.438239	+	0.898858i	$0.355602\pi$
$840$		0			0
$841$	−8.95196	+	27.5513i	−0.308688	+	0.950044i
$842$		0			0
$843$	−38.3513	+	27.8639i	−1.32089	+	0.959683i
$844$		0			0
$845$	0.518170	+	1.59476i	0.0178256	+	0.0548616i
$846$		0			0
$847$	−30.4709	−	0.461076i	−1.04699	−	0.0158428i
$848$		0			0
$849$	−4.73635	−	14.5770i	−0.162551	−	0.500281i
$850$		0			0
$851$	−1.29671	+	0.942118i	−0.0444508	+	0.0322954i
$852$		0			0
$853$	−11.5433	+	35.5265i	−0.395234	+	1.21640i	0.533546	+	0.845771i	$0.320859\pi$
$853$	−11.5433	+	35.5265i	−0.395234	+	1.21640i	−0.928779	+	0.370633i	$0.879141\pi$
$854$		0			0
$855$	−6.12959	−	4.45340i	−0.209627	−	0.152303i
$856$		0			0
$857$	0.313785			0.0107187			0.00535935	−	0.999986i	$-0.498294\pi$
$857$	0.313785			0.0107187			0.00535935	+	0.999986i	$0.498294\pi$
$858$		0			0
$859$	−31.6420			−1.07961			−0.539806	−	0.841789i	$-0.681502\pi$
$859$	−31.6420			−1.07961			−0.539806	+	0.841789i	$0.681502\pi$
$860$		0			0
$861$	32.3659	+	23.5152i	1.10303	+	0.801395i
$862$		0			0
$863$	−7.10701	+	21.8731i	−0.241925	+	0.744570i	0.754202	+	0.656643i	$0.228024\pi$
$863$	−7.10701	+	21.8731i	−0.241925	+	0.744570i	−0.996127	+	0.0879268i	$0.971976\pi$
$864$		0			0
$865$	10.7520	−	7.81180i	0.365580	−	0.265609i
$866$		0			0
$867$	−8.50204	−	26.1666i	−0.288744	−	0.888664i
$868$		0			0
$869$	−0.170225	+	22.5005i	−0.00577450	+	0.763277i
$870$		0			0
$871$	−0.660394	−	2.03248i	−0.0223766	−	0.0688681i
$872$		0			0
$873$	50.7374	−	36.8629i	1.71720	−	1.24762i
$874$		0			0
$875$	−10.3190	+	31.7586i	−0.348845	+	1.07364i
$876$		0			0
$877$	−7.68650	−	5.58457i	−0.259555	−	0.188577i	0.450396	−	0.892829i	$-0.351283\pi$
$877$	−7.68650	−	5.58457i	−0.259555	−	0.188577i	−0.709951	+	0.704251i	$0.751283\pi$
$878$		0			0
$879$	0.277067			0.00934523
$880$		0			0
$881$	−17.3412			−0.584238			−0.292119	−	0.956382i	$-0.594360\pi$
$881$	−17.3412			−0.584238			−0.292119	+	0.956382i	$0.594360\pi$
$882$		0			0
$883$	42.3359	+	30.7588i	1.42472	+	1.03512i	0.990970	+	0.134082i	$0.0428085\pi$
$883$	42.3359	+	30.7588i	1.42472	+	1.03512i	0.433746	+	0.901035i	$0.357191\pi$
$884$		0			0
$885$	23.5516	−	72.4843i	0.791677	−	2.43653i
$886$		0			0
$887$	−7.28386	+	5.29203i	−0.244568	+	0.177689i	−0.703316	−	0.710877i	$-0.748298\pi$
$887$	−7.28386	+	5.29203i	−0.244568	+	0.177689i	0.458748	+	0.888566i	$0.348298\pi$
$888$		0			0
$889$	−17.5767	−	54.0954i	−0.589502	−	1.81430i
$890$		0			0
$891$	37.1186	−	11.7509i	1.24352	−	0.393669i
$892$		0			0
$893$	0.385458	+	1.18632i	0.0128989	+	0.0396987i
$894$		0			0
$895$	26.5138	−	19.2634i	0.886260	−	0.643905i
$896$		0			0
$897$	−1.60064	+	4.92626i	−0.0534438	+	0.164483i
$898$		0			0
$899$	−1.45476	−	1.05694i	−0.0485188	−	0.0352510i
$900$		0			0
$901$	28.5041			0.949610
$902$		0			0
$903$	34.5032			1.14819
$904$		0			0
$905$	30.6318	+	22.2553i	1.01824	+	0.739792i
$906$		0			0
$907$	3.20866	−	9.87525i	0.106542	−	0.327902i	−0.883547	−	0.468342i	$-0.844852\pi$
$907$	3.20866	−	9.87525i	0.106542	−	0.327902i	0.990089	+	0.140440i	$0.0448516\pi$
$908$		0			0
$909$	−72.9851	+	53.0268i	−2.42076	+	1.75879i
$910$		0			0
$911$	7.68504	+	23.6521i	0.254617	+	0.783630i	0.993905	+	0.110241i	$0.0351622\pi$
$911$	7.68504	+	23.6521i	0.254617	+	0.783630i	−0.739288	+	0.673389i	$0.764838\pi$
$912$		0			0
$913$	16.8328	−	22.8036i	0.557086	−	0.754690i
$914$		0			0
$915$	−20.4513	−	62.9427i	−0.676100	−	2.08082i
$916$		0			0
$917$	−47.6718	+	34.6356i	−1.57426	+	1.14377i
$918$		0			0
$919$	−13.7278	+	42.2497i	−0.452837	+	1.39369i	0.420820	+	0.907144i	$0.361743\pi$
$919$	−13.7278	+	42.2497i	−0.452837	+	1.39369i	−0.873656	+	0.486544i	$0.838257\pi$
$920$		0			0
$921$	−46.2966	−	33.6364i	−1.52552	−	1.10836i
$922$		0			0
$923$	−4.19646			−0.138128
$924$		0			0
$925$	−2.06436			−0.0678757
$926$		0			0
$927$	−24.6993	−	17.9451i	−0.811231	−	0.589394i
$928$		0			0
$929$	−6.88474	+	21.1891i	−0.225881	+	0.695191i	0.772320	+	0.635234i	$0.219096\pi$
$929$	−6.88474	+	21.1891i	−0.225881	+	0.695191i	−0.998201	+	0.0599567i	$0.980904\pi$
$930$		0			0
$931$	−0.392056	+	0.284846i	−0.0128491	+	0.00933543i
$932$		0			0
$933$	3.70407	+	11.3999i	0.121266	+	0.373217i
$934$		0			0
$935$	−9.13536	−	12.7759i	−0.298758	−	0.417816i
$936$		0			0
$937$	−5.34037	−	16.4360i	−0.174462	−	0.536939i	0.825146	−	0.564919i	$-0.191093\pi$
$937$	−5.34037	−	16.4360i	−0.174462	−	0.536939i	−0.999608	+	0.0279797i	$0.991093\pi$
$938$		0			0
$939$	−58.8596	+	42.7640i	−1.92081	+	1.39555i
$940$		0			0
$941$	−3.43325	+	10.5665i	−0.111921	+	0.344457i	−0.991292	−	0.131679i	$-0.957963\pi$
$941$	−3.43325	+	10.5665i	−0.111921	+	0.344457i	0.879371	+	0.476136i	$0.157963\pi$
$942$		0			0
$943$	6.51059	+	4.73022i	0.212014	+	0.154037i
$944$		0			0
$945$	46.6622			1.51792
$946$		0			0
$947$	−39.0016			−1.26738			−0.633691	−	0.773586i	$-0.718461\pi$
$947$	−39.0016			−1.26738			−0.633691	+	0.773586i	$0.718461\pi$
$948$		0			0
$949$	6.76042	+	4.91173i	0.219452	+	0.159442i
$950$		0			0
$951$	−8.75958	+	26.9592i	−0.284049	+	0.874213i
$952$		0			0
$953$	−18.9926	+	13.7990i	−0.615232	+	0.446992i	−0.851253	−	0.524756i	$-0.824157\pi$
$953$	−18.9926	+	13.7990i	−0.615232	+	0.446992i	0.236021	+	0.971748i	$0.424157\pi$
$954$		0			0
$955$	−7.19483	−	22.1434i	−0.232819	−	0.716544i
$956$		0			0
$957$	−1.68516	−	0.561672i	−0.0544736	−	0.0181563i
$958$		0			0
$959$	−2.91888	−	8.98338i	−0.0942555	−	0.290088i
$960$		0			0
$961$	−59.6856	+	43.3641i	−1.92534	+	1.39884i
$962$		0			0
$963$	20.9099	−	64.3541i	0.673812	−	2.07378i
$964$		0			0
$965$	33.2344	+	24.1462i	1.06985	+	0.777293i
$966$		0			0
$967$	16.6731			0.536171			0.268086	−	0.963395i	$-0.413609\pi$
$967$	16.6731			0.536171			0.268086	+	0.963395i	$0.413609\pi$
$968$		0			0
$969$	−6.18024			−0.198538
$970$		0			0
$971$	−28.2825	−	20.5484i	−0.907629	−	0.659431i	0.0327851	−	0.999462i	$-0.489562\pi$
$971$	−28.2825	−	20.5484i	−0.907629	−	0.659431i	−0.940414	+	0.340031i	$0.889562\pi$
$972$		0			0
$973$	10.5153	−	32.3629i	0.337106	−	1.03751i
$974$		0			0
$975$	−5.39719	+	3.92129i	−0.172848	+	0.125582i
$976$		0			0
$977$	5.70656	+	17.5630i	0.182569	+	0.561890i	0.999898	−	0.0142815i	$-0.00454609\pi$
$977$	5.70656	+	17.5630i	0.182569	+	0.561890i	−0.817329	+	0.576171i	$0.804546\pi$
$978$		0			0
$979$	−9.42667	−	3.14195i	−0.301278	−	0.100417i
$980$		0			0
$981$	−28.6210	−	88.0864i	−0.913799	−	2.81238i
$982$		0			0
$983$	−33.8097	+	24.5642i	−1.07836	+	0.783475i	−0.977396	−	0.211415i	$-0.932193\pi$
$983$	−33.8097	+	24.5642i	−1.07836	+	0.783475i	−0.100964	+	0.994890i	$0.532193\pi$
$984$		0			0
$985$	−9.58738	+	29.5069i	−0.305479	+	0.940169i
$986$		0			0
$987$	−11.8742	−	8.62711i	−0.377960	−	0.274604i
$988$		0			0
$989$	6.94052			0.220696
$990$		0			0
$991$	20.6562			0.656165			0.328082	−	0.944649i	$-0.393598\pi$
$991$	20.6562			0.656165			0.328082	+	0.944649i	$0.393598\pi$
$992$		0			0
$993$	62.2126	+	45.2001i	1.97426	+	1.43438i
$994$		0			0
$995$	0.223688	−	0.688440i	0.00709138	−	0.0218250i
$996$		0			0
$997$	−17.0530	+	12.3897i	−0.540072	+	0.392386i	−0.824112	−	0.566427i	$-0.808325\pi$
$997$	−17.0530	+	12.3897i	−0.540072	+	0.392386i	0.284040	+	0.958813i	$0.408325\pi$
$998$		0			0
$999$	2.92825	+	9.01223i	0.0926458	+	0.285134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.n.b.313.1	yes	28
11.3	even	5		6292.2.a.z.1.12		14
11.8	odd	10		6292.2.a.y.1.12		14
11.9	even	5	inner	572.2.n.b.53.1	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.n.b.53.1	✓	28	11.9	even	5	inner
572.2.n.b.313.1	yes	28	1.1	even	1	trivial
6292.2.a.y.1.12		14	11.8	odd	10
6292.2.a.z.1.12		14	11.3	even	5

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.46647 - 1.79199i) q^{3} +(0.518170 - 1.59476i) q^{5} +(-2.24130 + 1.62840i) q^{7} +(1.94517 + 5.98661i) q^{9} +O(q^{10})\)	\(q+(-2.46647 - 1.79199i) q^{3} +(0.518170 - 1.59476i) q^{5} +(-2.24130 + 1.62840i) q^{7} +(1.94517 + 5.98661i) q^{9} +(-3.14645 - 1.04873i) q^{11} +(-0.309017 - 0.951057i) q^{13} +(-4.13586 + 3.00487i) q^{15} +(-0.872693 + 2.68587i) q^{17} +(-0.580719 - 0.421917i) q^{19} +8.44618 q^{21} +1.69900 q^{23} +(1.77031 + 1.28621i) q^{25} +(3.10395 - 9.55299i) q^{27} +(-0.142122 + 0.103257i) q^{29} +(3.16309 + 9.73500i) q^{31} +(5.88131 + 8.22507i) q^{33} +(1.43554 + 4.41814i) q^{35} +(-0.763222 + 0.554513i) q^{37} +(-0.942106 + 2.89951i) q^{39} +(3.83201 + 2.78412i) q^{41} +4.08506 q^{43} +10.5552 q^{45} +(-1.40587 - 1.02142i) q^{47} +(0.208624 - 0.642079i) q^{49} +(6.96553 - 5.06075i) q^{51} +(-3.11897 - 9.59920i) q^{53} +(-3.30287 + 4.47443i) q^{55} +(0.676252 + 2.08129i) q^{57} +(-12.0611 + 8.76291i) q^{59} +(-4.00049 + 12.3123i) q^{61} +(-14.1083 - 10.2503i) q^{63} -1.67683 q^{65} +2.13708 q^{67} +(-4.19053 - 3.04460i) q^{69} +(1.29678 - 3.99107i) q^{71} +(-6.76042 + 4.91173i) q^{73} +(-2.06154 - 6.34478i) q^{75} +(8.75990 - 2.77317i) q^{77} +(-2.09648 - 6.45230i) q^{79} +(-9.49714 + 6.90007i) q^{81} +(-2.64082 + 8.12760i) q^{83} +(3.83113 + 2.78348i) q^{85} +0.535575 q^{87} +2.99597 q^{89} +(2.24130 + 1.62840i) q^{91} +(9.64339 - 29.6793i) q^{93} +(-0.973770 + 0.707485i) q^{95} +(-3.07878 - 9.47551i) q^{97} +(0.157939 - 20.8765i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9}+O(q^{10}) \) 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9	\( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9} + q^{11} + 7 q^{13} - 24 q^{15} + 7 q^{17} - 7 q^{19} - 12 q^{21} + 34 q^{23} - 26 q^{25} - 11 q^{27} + 8 q^{29} - 17 q^{31} - 2 q^{33} - 6 q^{35} - 15 q^{37} + 4 q^{39} + 29 q^{41} - 8 q^{43} + 62 q^{45} - 27 q^{47} - 4 q^{49} + 69 q^{51} - 32 q^{53} + 19 q^{55} + 9 q^{57} - 37 q^{59} - 19 q^{61} + 46 q^{63} - 18 q^{65} + 10 q^{67} - 32 q^{69} - 27 q^{71} - 79 q^{75} + 13 q^{77} + 21 q^{79} - 18 q^{81} + 27 q^{83} + 7 q^{85} + 56 q^{87} + 82 q^{89} - 11 q^{91} - 53 q^{93} + 51 q^{95} - 88 q^{97} + 86 q^{99}+O(q^{100}) \) 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9 + q^11 + 7 * q^13 - 24 * q^15 + 7 * q^17 - 7 * q^19 - 12 * q^21 + 34 * q^23 - 26 * q^25 - 11 * q^27 + 8 * q^29 - 17 * q^31 - 2 * q^33 - 6 * q^35 - 15 * q^37 + 4 * q^39 + 29 * q^41 - 8 * q^43 + 62 * q^45 - 27 * q^47 - 4 * q^49 + 69 * q^51 - 32 * q^53 + 19 * q^55 + 9 * q^57 - 37 * q^59 - 19 * q^61 + 46 * q^63 - 18 * q^65 + 10 * q^67 - 32 * q^69 - 27 * q^71 - 79 * q^75 + 13 * q^77 + 21 * q^79 - 18 * q^81 + 27 * q^83 + 7 * q^85 + 56 * q^87 + 82 * q^89 - 11 * q^91 - 53 * q^93 + 51 * q^95 - 88 * q^97 + 86 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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