LMFDB - Embedded newform 1444.2.e.g.653.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1444,2,Mod(429,1444)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1444, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("1444.429");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1444 = 2^{2} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1444.e (of order $3$, degree $2$, not 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:	$11.5303980519$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 3 x^{10} + 70 x^{9} - 15 x^{8} - 426 x^{7} + 64 x^{6} + 1659 x^{5} + 267 x^{4} + \cdots + 4161 $ x^12 - 6x^11 - 3x^10 + 70x^9 - 15x^8 - 426x^7 + 64x^6 + 1659x^5 + 267x^4 - 3969x^3 - 2088x^2 + 4446*x + 4161
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			653.6
Root			$2.75227 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	1444.653
Dual form			1444.2.e.g.429.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34598 + 2.33131i) q^{3} +(0.641102 + 1.11042i) q^{5} -3.34467 q^{7} +(-2.12333 + 3.67771i) q^{9} +O(q^{10})$	\(q+(1.34598 + 2.33131i) q^{3} +(0.641102 + 1.11042i) q^{5} -3.34467 q^{7} +(-2.12333 + 3.67771i) q^{9} -5.65641 q^{11} +(0.221039 - 0.382850i) q^{13} +(-1.72582 + 2.98921i) q^{15} +(2.37605 + 4.11545i) q^{17} +(-4.50185 - 7.79744i) q^{21} +(1.83685 - 3.18152i) q^{23} +(1.67798 - 2.90634i) q^{25} -3.35595 q^{27} +(-1.50913 + 2.61389i) q^{29} -10.7825 q^{31} +(-7.61342 - 13.1868i) q^{33} +(-2.14427 - 3.71399i) q^{35} -1.81198 q^{37} +1.19006 q^{39} +(-2.01777 - 3.49489i) q^{41} +(1.34644 + 2.33210i) q^{43} -5.44508 q^{45} +(-3.03370 + 5.25453i) q^{47} +4.18678 q^{49} +(-6.39625 + 11.0786i) q^{51} +(-0.816066 + 1.41347i) q^{53} +(-3.62634 - 6.28100i) q^{55} +(-4.27625 - 7.40668i) q^{59} +(-1.29780 + 2.24786i) q^{61} +(7.10182 - 12.3007i) q^{63} +0.566834 q^{65} +(2.01663 - 3.49290i) q^{67} +9.88947 q^{69} +(5.54707 + 9.60781i) q^{71} +(3.68232 + 6.37797i) q^{73} +9.03409 q^{75} +18.9188 q^{77} +(-5.07962 - 8.79815i) q^{79} +(1.85294 + 3.20939i) q^{81} +4.55683 q^{83} +(-3.04659 + 5.27684i) q^{85} -8.12503 q^{87} +(-6.47844 + 11.2210i) q^{89} +(-0.739300 + 1.28051i) q^{91} +(-14.5130 - 25.1372i) q^{93} +(5.95092 + 10.3073i) q^{97} +(12.0104 - 20.8027i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} + 3 q^{5} - 6 q^{7} - 9 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 + 3 * q^5 - 6 * q^7 - 9 * q^9	$ 12 q - 3 q^{3} + 3 q^{5} - 6 q^{7} - 9 q^{9} - 6 q^{11} - 12 q^{13} + 6 q^{17} - 21 q^{21} - 9 q^{25} + 18 q^{27} - 21 q^{29} - 12 q^{31} - 9 q^{33} - 3 q^{35} - 12 q^{37} + 60 q^{39} - 36 q^{41} + 18 q^{43} - 48 q^{45} - 30 q^{47} - 18 q^{49} - 24 q^{51} - 18 q^{53} + 15 q^{55} - 21 q^{59} - 9 q^{61} - 6 q^{63} + 66 q^{65} - 18 q^{67} + 66 q^{69} + 12 q^{71} + 24 q^{73} + 42 q^{75} + 24 q^{77} - 9 q^{79} + 6 q^{81} - 6 q^{83} + 12 q^{85} + 36 q^{87} - 45 q^{89} - 9 q^{91} - 15 q^{97} + 33 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 + 3 * q^5 - 6 * q^7 - 9 * q^9 - 6 * q^11 - 12 * q^13 + 6 * q^17 - 21 * q^21 - 9 * q^25 + 18 * q^27 - 21 * q^29 - 12 * q^31 - 9 * q^33 - 3 * q^35 - 12 * q^37 + 60 * q^39 - 36 * q^41 + 18 * q^43 - 48 * q^45 - 30 * q^47 - 18 * q^49 - 24 * q^51 - 18 * q^53 + 15 * q^55 - 21 * q^59 - 9 * q^61 - 6 * q^63 + 66 * q^65 - 18 * q^67 + 66 * q^69 + 12 * q^71 + 24 * q^73 + 42 * q^75 + 24 * q^77 - 9 * q^79 + 6 * q^81 - 6 * q^83 + 12 * q^85 + 36 * q^87 - 45 * q^89 - 9 * q^91 - 15 * q^97 + 33 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1444\mathbb{Z}\right)^\times$.

$n$	$723$	$1085$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	1.34598	+	2.33131i	0.777102	+	1.34598i	0.933605	+	0.358303i	$0.116645\pi$
$3$	1.34598	+	2.33131i	0.777102	+	1.34598i	−0.156503	+	0.987677i	$0.550022\pi$
$4$		0			0
$5$	0.641102	+	1.11042i	0.286710	+	0.496596i	0.973022	−	0.230711i	$-0.0741052\pi$
$5$	0.641102	+	1.11042i	0.286710	+	0.496596i	−0.686313	+	0.727307i	$0.740772\pi$
$6$		0			0
$7$	−3.34467			−1.26416			−0.632082	−	0.774901i	$-0.717800\pi$
$7$	−3.34467			−1.26416			−0.632082	+	0.774901i	$0.717800\pi$
$8$		0			0
$9$	−2.12333	+	3.67771i	−0.707776	+	1.22590i
$10$		0			0
$11$	−5.65641			−1.70547			−0.852736	−	0.522342i	$-0.825059\pi$
$11$	−5.65641			−1.70547			−0.852736	+	0.522342i	$0.825059\pi$
$12$		0			0
$13$	0.221039	−	0.382850i	0.0613051	−	0.106184i	−0.833744	−	0.552151i	$-0.813807\pi$
$13$	0.221039	−	0.382850i	0.0613051	−	0.106184i	0.895049	+	0.445968i	$0.147140\pi$
$14$		0			0
$15$	−1.72582	+	2.98921i	−0.445606	+	0.771811i
$16$		0			0
$17$	2.37605	+	4.11545i	0.576278	+	0.998142i	0.995902	+	0.0904442i	$0.0288287\pi$
$17$	2.37605	+	4.11545i	0.576278	+	0.998142i	−0.419624	+	0.907698i	$0.637838\pi$
$18$		0			0
$19$		0			0
$19$		0			0
$20$		0			0
$21$	−4.50185	−	7.79744i	−0.982385	−	1.70154i
$22$		0			0
$23$	1.83685	−	3.18152i	0.383010	−	0.663393i	−0.608481	−	0.793569i	$-0.708221\pi$
$23$	1.83685	−	3.18152i	0.383010	−	0.663393i	0.991491	+	0.130176i	$0.0415541\pi$
$24$		0			0
$25$	1.67798	−	2.90634i	0.335595	−	0.581268i
$26$		0			0
$27$	−3.35595			−0.645853
$28$		0			0
$29$	−1.50913	+	2.61389i	−0.280238	+	0.485387i	−0.971443	−	0.237272i	$-0.923747\pi$
$29$	−1.50913	+	2.61389i	−0.280238	+	0.485387i	0.691205	+	0.722659i	$0.257080\pi$
$30$		0			0
$31$	−10.7825			−1.93659			−0.968293	−	0.249817i	$-0.919629\pi$
$31$	−10.7825			−1.93659			−0.968293	+	0.249817i	$0.919629\pi$
$32$		0			0
$33$	−7.61342	−	13.1868i	−1.32533	−	2.29553i
$34$		0			0
$35$	−2.14427	−	3.71399i	−0.362448	−	0.627779i
$36$		0			0
$37$	−1.81198			−0.297888			−0.148944	−	0.988846i	$-0.547587\pi$
$37$	−1.81198			−0.297888			−0.148944	+	0.988846i	$0.547587\pi$
$38$		0			0
$39$	1.19006			0.190561
$40$		0			0
$41$	−2.01777	−	3.49489i	−0.315123	−	0.545810i	0.664340	−	0.747430i	$-0.268713\pi$
$41$	−2.01777	−	3.49489i	−0.315123	−	0.545810i	−0.979464	+	0.201621i	$0.935379\pi$
$42$		0			0
$43$	1.34644	+	2.33210i	0.205330	+	0.355642i	0.950238	−	0.311526i	$-0.100840\pi$
$43$	1.34644	+	2.33210i	0.205330	+	0.355642i	−0.744908	+	0.667167i	$0.767507\pi$
$44$		0			0
$45$	−5.44508			−0.811705
$46$		0			0
$47$	−3.03370	+	5.25453i	−0.442511	+	0.766452i	−0.997875	−	0.0651557i	$-0.979246\pi$
$47$	−3.03370	+	5.25453i	−0.442511	+	0.766452i	0.555364	+	0.831607i	$0.312579\pi$
$48$		0			0
$49$	4.18678			0.598112
$50$		0			0
$51$	−6.39625	+	11.0786i	−0.895654	+	1.55132i
$52$		0			0
$53$	−0.816066	+	1.41347i	−0.112095	+	0.194155i	−0.916615	−	0.399771i	$-0.869090\pi$
$53$	−0.816066	+	1.41347i	−0.112095	+	0.194155i	0.804520	+	0.593926i	$0.202423\pi$
$54$		0			0
$55$	−3.62634	−	6.28100i	−0.488976	−	0.846931i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.27625	−	7.40668i	−0.556720	−	0.964267i	−0.997767	−	0.0667834i	$-0.978726\pi$
$59$	−4.27625	−	7.40668i	−0.556720	−	0.964267i	0.441048	−	0.897484i	$-0.354607\pi$
$60$		0			0
$61$	−1.29780	+	2.24786i	−0.166167	+	0.287809i	−0.937069	−	0.349144i	$-0.886472\pi$
$61$	−1.29780	+	2.24786i	−0.166167	+	0.287809i	0.770902	+	0.636954i	$0.219806\pi$
$62$		0			0
$63$	7.10182	−	12.3007i	0.894745	−	1.54974i
$64$		0			0
$65$	0.566834			0.0703071
$66$		0			0
$67$	2.01663	−	3.49290i	0.246370	−	0.426726i	−0.716146	−	0.697951i	$-0.754095\pi$
$67$	2.01663	−	3.49290i	0.246370	−	0.426726i	0.962516	+	0.271225i	$0.0874288\pi$
$68$		0			0
$69$	9.88947			1.19055
$70$		0			0
$71$	5.54707	+	9.60781i	0.658316	+	1.14024i	0.981051	+	0.193748i	$0.0620643\pi$
$71$	5.54707	+	9.60781i	0.658316	+	1.14024i	−0.322735	+	0.946489i	$0.604602\pi$
$72$		0			0
$73$	3.68232	+	6.37797i	0.430983	+	0.746484i	0.996958	−	0.0779379i	$-0.0248336\pi$
$73$	3.68232	+	6.37797i	0.430983	+	0.746484i	−0.565975	+	0.824422i	$0.691500\pi$
$74$		0			0
$75$	9.03409			1.04317
$76$		0			0
$77$	18.9188			2.15600
$78$		0			0
$79$	−5.07962	−	8.79815i	−0.571502	−	0.989870i	−0.996412	−	0.0846343i	$-0.973028\pi$
$79$	−5.07962	−	8.79815i	−0.571502	−	0.989870i	0.424911	−	0.905235i	$-0.360306\pi$
$80$		0			0
$81$	1.85294	+	3.20939i	0.205882	+	0.356598i
$82$		0			0
$83$	4.55683			0.500177			0.250089	−	0.968223i	$-0.419540\pi$
$83$	4.55683			0.500177			0.250089	+	0.968223i	$0.419540\pi$
$84$		0			0
$85$	−3.04659	+	5.27684i	−0.330449	+	0.572354i
$86$		0			0
$87$	−8.12503			−0.871095
$88$		0			0
$89$	−6.47844	+	11.2210i	−0.686713	+	1.18942i	0.286182	+	0.958175i	$0.407614\pi$
$89$	−6.47844	+	11.2210i	−0.686713	+	1.18942i	−0.972895	+	0.231247i	$0.925720\pi$
$90$		0			0
$91$	−0.739300	+	1.28051i	−0.0774997	+	0.134233i
$92$		0			0
$93$	−14.5130	−	25.1372i	−1.50493	−	2.60661i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	5.95092	+	10.3073i	0.604224	+	1.04655i	0.992174	+	0.124866i	$0.0398501\pi$
$97$	5.95092	+	10.3073i	0.604224	+	1.04655i	−0.387950	+	0.921681i	$0.626817\pi$
$98$		0			0
$99$	12.0104	−	20.8027i	1.20709	−	2.09075i
$100$		0			0
$101$	−5.09809	+	8.83015i	−0.507279	+	0.878633i	0.492686	+	0.870207i	$0.336015\pi$
$101$	−5.09809	+	8.83015i	−0.507279	+	0.878633i	−0.999965	+	0.00842530i	$0.997318\pi$
$102$		0			0
$103$	−4.52677			−0.446036			−0.223018	−	0.974814i	$-0.571591\pi$
$103$	−4.52677			−0.446036			−0.223018	+	0.974814i	$0.571591\pi$
$104$		0			0
$105$	5.77230	−	9.99792i	0.563319	−	0.975697i
$106$		0			0
$107$	1.27883			0.123629			0.0618146	−	0.998088i	$-0.480311\pi$
$107$	1.27883			0.123629			0.0618146	+	0.998088i	$0.480311\pi$
$108$		0			0
$109$	−3.21168	−	5.56279i	−0.307623	−	0.532819i	0.670219	−	0.742163i	$-0.266200\pi$
$109$	−3.21168	−	5.56279i	−0.307623	−	0.532819i	−0.977842	+	0.209345i	$0.932867\pi$
$110$		0			0
$111$	−2.43889	−	4.22428i	−0.231489	−	0.400951i
$112$		0			0
$113$	−1.77037			−0.166542			−0.0832710	−	0.996527i	$-0.526537\pi$
$113$	−1.77037			−0.166542			−0.0832710	+	0.996527i	$0.526537\pi$
$114$		0			0
$115$	4.71044			0.439251
$116$		0			0
$117$	0.938675	+	1.62583i	0.0867806	+	0.150308i
$118$		0			0
$119$	−7.94710	−	13.7648i	−0.728510	−	1.26182i
$120$		0			0
$121$	20.9950			1.90864
$122$		0			0
$123$	5.43177	−	9.40810i	0.489766	−	0.848300i
$124$		0			0
$125$	10.7140			0.958293
$126$		0			0
$127$	−6.74097	+	11.6757i	−0.598165	+	1.03605i	0.394927	+	0.918712i	$0.370770\pi$
$127$	−6.74097	+	11.6757i	−0.598165	+	1.03605i	−0.993092	+	0.117339i	$0.962563\pi$
$128$		0			0
$129$	−3.62456	+	6.27792i	−0.319125	+	0.552740i
$130$		0			0
$131$	5.06635	+	8.77518i	0.442649	+	0.766691i	0.997885	−	0.0650019i	$-0.0207054\pi$
$131$	5.06635	+	8.77518i	0.442649	+	0.766691i	−0.555236	+	0.831693i	$0.687372\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−2.15151	−	3.72652i	−0.185172	−	0.320728i
$136$		0			0
$137$	1.74834	−	3.02822i	0.149371	−	0.258718i	−0.781624	−	0.623750i	$-0.785608\pi$
$137$	1.74834	−	3.02822i	0.149371	−	0.258718i	0.930995	+	0.365031i	$0.118942\pi$
$138$		0			0
$139$	−5.32861	+	9.22942i	−0.451967	+	0.782829i	−0.998508	−	0.0546028i	$-0.982611\pi$
$139$	−5.32861	+	9.22942i	−0.451967	+	0.782829i	0.546541	+	0.837432i	$0.315944\pi$
$140$		0			0
$141$	−16.3332			−1.37551
$142$		0			0
$143$	−1.25029	+	2.16556i	−0.104554	+	0.181093i
$144$		0			0
$145$	−3.87002			−0.321388
$146$		0			0
$147$	5.63533	+	9.76068i	0.464794	+	0.805047i
$148$		0			0
$149$	4.21062	+	7.29302i	0.344948	+	0.597467i	0.985344	−	0.170577i	$-0.0545633\pi$
$149$	4.21062	+	7.29302i	0.344948	+	0.597467i	−0.640396	+	0.768045i	$0.721230\pi$
$150$		0			0
$151$	−11.3794			−0.926039			−0.463020	−	0.886348i	$-0.653234\pi$
$151$	−11.3794			−0.926039			−0.463020	+	0.886348i	$0.653234\pi$
$152$		0			0
$153$	−20.1806			−1.63150
$154$		0			0
$155$	−6.91266	−	11.9731i	−0.555238	−	0.961700i
$156$		0			0
$157$	2.33801	+	4.04955i	0.186593	+	0.323189i	0.944112	−	0.329624i	$-0.106922\pi$
$157$	2.33801	+	4.04955i	0.186593	+	0.323189i	−0.757519	+	0.652813i	$0.773589\pi$
$158$		0			0
$159$	−4.39364			−0.348438
$160$		0			0
$161$	−6.14365	+	10.6411i	−0.484188	+	0.838638i
$162$		0			0
$163$	−1.82998			−0.143335			−0.0716676	−	0.997429i	$-0.522832\pi$
$163$	−1.82998			−0.143335			−0.0716676	+	0.997429i	$0.522832\pi$
$164$		0			0
$165$	9.76197	−	16.9082i	0.759968	−	1.31630i
$166$		0			0
$167$	9.98720	−	17.2983i	0.772832	−	1.33859i	−0.163172	−	0.986598i	$-0.552173\pi$
$167$	9.98720	−	17.2983i	0.772832	−	1.33859i	0.936005	−	0.351987i	$-0.114494\pi$
$168$		0			0
$169$	6.40228	+	11.0891i	0.492483	+	0.853006i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.33669	+	4.04727i	0.177656	+	0.307708i	0.941077	−	0.338192i	$-0.109815\pi$
$173$	2.33669	+	4.04727i	0.177656	+	0.307708i	−0.763422	+	0.645901i	$0.776482\pi$
$174$		0			0
$175$	−5.61227	+	9.72073i	−0.424247	+	0.734818i
$176$		0			0
$177$	11.5115	−	19.9385i	0.865257	−	1.49867i
$178$		0			0
$179$	7.64250			0.571227			0.285613	−	0.958345i	$-0.407803\pi$
$179$	7.64250			0.571227			0.285613	+	0.958345i	$0.407803\pi$
$180$		0			0
$181$	−3.04723	+	5.27796i	−0.226499	+	0.392307i	−0.956768	−	0.290852i	$-0.906061\pi$
$181$	−3.04723	+	5.27796i	−0.226499	+	0.392307i	0.730269	+	0.683159i	$0.239395\pi$
$182$		0			0
$183$	−6.98728			−0.516515
$184$		0			0
$185$	−1.16166	−	2.01206i	−0.0854073	−	0.147930i
$186$		0			0
$187$	−13.4399	−	23.2787i	−0.982826	−	1.70230i
$188$		0			0
$189$	11.2245			0.816465
$190$		0			0
$191$	7.93272			0.573992			0.286996	−	0.957932i	$-0.407343\pi$
$191$	7.93272			0.573992			0.286996	+	0.957932i	$0.407343\pi$
$192$		0			0
$193$	3.42471	+	5.93177i	0.246516	+	0.426978i	0.962557	−	0.271080i	$-0.0873810\pi$
$193$	3.42471	+	5.93177i	0.246516	+	0.426978i	−0.716041	+	0.698058i	$0.754048\pi$
$194$		0			0
$195$	0.762947	+	1.32146i	0.0546358	+	0.0946319i
$196$		0			0
$197$	−25.5509			−1.82043			−0.910213	−	0.414141i	$-0.864082\pi$
$197$	−25.5509			−1.82043			−0.910213	+	0.414141i	$0.864082\pi$
$198$		0			0
$199$	3.81358	−	6.60531i	0.270337	−	0.468238i	−0.698611	−	0.715502i	$-0.746198\pi$
$199$	3.81358	−	6.60531i	0.270337	−	0.468238i	0.968948	+	0.247264i	$0.0795315\pi$
$200$		0			0
$201$	10.8574			0.765819
$202$		0			0
$203$	5.04753	−	8.74258i	0.354267	−	0.613609i
$204$		0			0
$205$	2.58720	−	4.48116i	0.180698	−	0.312978i
$206$		0			0
$207$	7.80048	+	13.5108i	0.542171	+	0.939067i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−5.73545	−	9.93410i	−0.394845	−	0.683891i	0.598237	−	0.801320i	$-0.295868\pi$
$211$	−5.73545	−	9.93410i	−0.394845	−	0.683891i	−0.993081	+	0.117428i	$0.962535\pi$
$212$		0			0
$213$	−14.9325	+	25.8639i	−1.02316	+	1.77216i
$214$		0			0
$215$	−1.72641	+	2.99023i	−0.117740	+	0.203932i
$216$		0			0
$217$	36.0637			2.44816
$218$		0			0
$219$	−9.91266	+	17.1692i	−0.669836	+	1.16019i
$220$		0			0
$221$	2.10080			0.141315
$222$		0			0
$223$	1.39939	+	2.42382i	0.0937102	+	0.162311i	0.909070	−	0.416644i	$-0.136794\pi$
$223$	1.39939	+	2.42382i	0.0937102	+	0.162311i	−0.815359	+	0.578955i	$0.803461\pi$
$224$		0			0
$225$	7.12579	+	12.3422i	0.475052	+	0.822815i
$226$		0			0
$227$	−6.05837			−0.402108			−0.201054	−	0.979580i	$-0.564437\pi$
$227$	−6.05837			−0.402108			−0.201054	+	0.979580i	$0.564437\pi$
$228$		0			0
$229$	−8.97380			−0.593005			−0.296503	−	0.955032i	$-0.595820\pi$
$229$	−8.97380			−0.593005			−0.296503	+	0.955032i	$0.595820\pi$
$230$		0			0
$231$	25.4644	+	44.1055i	1.67543	+	2.90193i
$232$		0			0
$233$	3.67029	+	6.35713i	0.240449	+	0.416469i	0.960842	−	0.277096i	$-0.0893721\pi$
$233$	3.67029	+	6.35713i	0.240449	+	0.416469i	−0.720394	+	0.693566i	$0.756039\pi$
$234$		0			0
$235$	−7.77966			−0.507489
$236$		0			0
$237$	13.6741	−	23.6843i	0.888230	−	1.53846i
$238$		0			0
$239$	−19.1710			−1.24007			−0.620036	−	0.784574i	$-0.712882\pi$
$239$	−19.1710			−1.24007			−0.620036	+	0.784574i	$0.712882\pi$
$240$		0			0
$241$	6.06367	−	10.5026i	0.390596	−	0.676531i	−0.601933	−	0.798547i	$-0.705602\pi$
$241$	6.06367	−	10.5026i	0.390596	−	0.676531i	0.992528	+	0.122016i	$0.0389358\pi$
$242$		0			0
$243$	−10.0220	+	17.3586i	−0.642910	+	1.11355i
$244$		0			0
$245$	2.68416	+	4.64910i	0.171485	+	0.297020i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	6.13341	+	10.6234i	0.388689	+	0.673229i
$250$		0			0
$251$	−7.30661	+	12.6554i	−0.461189	+	0.798803i	−0.999021	−	0.0442493i	$-0.985910\pi$
$251$	−7.30661	+	12.6554i	−0.461189	+	0.798803i	0.537831	+	0.843053i	$0.319244\pi$
$252$		0			0
$253$	−10.3900	+	17.9960i	−0.653213	+	1.13140i
$254$		0			0
$255$	−16.4026			−1.02717
$256$		0			0
$257$	−1.29560	+	2.24404i	−0.0808171	+	0.139979i	−0.903601	−	0.428375i	$-0.859086\pi$
$257$	−1.29560	+	2.24404i	−0.0808171	+	0.139979i	0.822784	+	0.568354i	$0.192420\pi$
$258$		0			0
$259$	6.06047			0.376579
$260$		0			0
$261$	−6.40875	−	11.1003i	−0.396692	−	0.687090i
$262$		0			0
$263$	11.5081	+	19.9326i	0.709619	+	1.22910i	0.964998	+	0.262256i	$0.0844664\pi$
$263$	11.5081	+	19.9326i	0.709619	+	1.22910i	−0.255379	+	0.966841i	$0.582200\pi$
$264$		0			0
$265$	−2.09273			−0.128555
$266$		0			0
$267$	−34.8794			−2.13459
$268$		0			0
$269$	−13.0914	−	22.6749i	−0.798195	−	1.38251i	−0.920790	−	0.390058i	$-0.872455\pi$
$269$	−13.0914	−	22.6749i	−0.798195	−	1.38251i	0.122595	−	0.992457i	$-0.460878\pi$
$270$		0			0
$271$	7.38808	+	12.7965i	0.448794	+	0.777334i	0.998308	−	0.0581505i	$-0.0185203\pi$
$271$	7.38808	+	12.7965i	0.448794	+	0.777334i	−0.549514	+	0.835485i	$0.685187\pi$
$272$		0			0
$273$	−3.98034			−0.240901
$274$		0			0
$275$	−9.49132	+	16.4395i	−0.572348	+	0.991336i
$276$		0			0
$277$	−14.7470			−0.886061			−0.443030	−	0.896507i	$-0.646097\pi$
$277$	−14.7470			−0.886061			−0.443030	+	0.896507i	$0.646097\pi$
$278$		0			0
$279$	22.8947	−	39.6548i	1.37067	−	2.37407i
$280$		0			0
$281$	−6.97028	+	12.0729i	−0.415812	+	0.720207i	−0.995513	−	0.0946218i	$-0.969836\pi$
$281$	−6.97028	+	12.0729i	−0.415812	+	0.720207i	0.579702	+	0.814829i	$0.303169\pi$
$282$		0			0
$283$	9.14444	+	15.8386i	0.543580	+	0.941509i	0.998695	+	0.0510759i	$0.0162651\pi$
$283$	9.14444	+	15.8386i	0.543580	+	0.941509i	−0.455114	+	0.890433i	$0.650402\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.74878	+	11.6892i	0.398368	+	0.689993i
$288$		0			0
$289$	−2.79126	+	4.83461i	−0.164192	+	0.284389i
$290$		0			0
$291$	−16.0196	+	27.7468i	−0.939088	+	1.62655i
$292$		0			0
$293$	24.7475			1.44576			0.722882	−	0.690972i	$-0.242817\pi$
$293$	24.7475			1.44576			0.722882	+	0.690972i	$0.242817\pi$
$294$		0			0
$295$	5.48302	−	9.49688i	0.319234	−	0.552929i
$296$		0			0
$297$	18.9826			1.10148
$298$		0			0
$299$	−0.812031	−	1.40648i	−0.0469609	−	0.0813387i
$300$		0			0
$301$	−4.50338	−	7.80009i	−0.259571	−	0.449590i
$302$		0			0
$303$	−27.4477			−1.57683
$304$		0			0
$305$	−3.32810			−0.190567
$306$		0			0
$307$	11.4665	+	19.8606i	0.654429	+	1.13350i	0.982037	+	0.188690i	$0.0604242\pi$
$307$	11.4665	+	19.8606i	0.654429	+	1.13350i	−0.327608	+	0.944814i	$0.606242\pi$
$308$		0			0
$309$	−6.09295	−	10.5533i	−0.346616	−	0.600356i
$310$		0			0
$311$	29.6666			1.68224			0.841119	−	0.540850i	$-0.181897\pi$
$311$	29.6666			1.68224			0.841119	+	0.540850i	$0.181897\pi$
$312$		0			0
$313$	10.3624	−	17.9482i	0.585717	−	1.01449i	−0.409069	−	0.912503i	$-0.634147\pi$
$313$	10.3624	−	17.9482i	0.585717	−	1.01449i	0.994786	−	0.101987i	$-0.0325202\pi$
$314$		0			0
$315$	18.2120			1.02613
$316$		0			0
$317$	16.2068	−	28.0710i	0.910264	−	1.57662i	0.0965731	−	0.995326i	$-0.469212\pi$
$317$	16.2068	−	28.0710i	0.910264	−	1.57662i	0.813691	−	0.581298i	$-0.197455\pi$
$318$		0			0
$319$	8.53626	−	14.7852i	0.477939	−	0.827814i
$320$		0			0
$321$	1.72128	+	2.98135i	0.0960726	+	0.166403i
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−0.741795	−	1.28483i	−0.0411474	−	0.0712693i
$326$		0			0
$327$	8.64571	−	14.9748i	0.478109	−	0.828109i
$328$		0			0
$329$	10.1467	−	17.5746i	0.559407	−	0.968921i
$330$		0			0
$331$	−21.2388			−1.16739			−0.583694	−	0.811974i	$-0.698393\pi$
$331$	−21.2388			−1.16739			−0.583694	+	0.811974i	$0.698393\pi$
$332$		0			0
$333$	3.84743	−	6.66394i	0.210838	−	0.365182i
$334$		0			0
$335$	5.17146			0.282547
$336$		0			0
$337$	5.88341	+	10.1904i	0.320490	+	0.555105i	0.980589	−	0.196074i	$-0.0628192\pi$
$337$	5.88341	+	10.1904i	0.320490	+	0.555105i	−0.660099	+	0.751178i	$0.729486\pi$
$338$		0			0
$339$	−2.38288	−	4.12726i	−0.129420	−	0.224162i
$340$		0			0
$341$	60.9900			3.30279
$342$		0			0
$343$	9.40926			0.508052
$344$		0			0
$345$	6.34016	+	10.9815i	0.341343	+	0.591223i
$346$		0			0
$347$	−12.8730	−	22.2967i	−0.691059	−	1.19695i	−0.971491	−	0.237075i	$-0.923811\pi$
$347$	−12.8730	−	22.2967i	−0.691059	−	1.19695i	0.280433	−	0.959874i	$-0.409522\pi$
$348$		0			0
$349$	10.1537			0.543517			0.271759	−	0.962365i	$-0.412395\pi$
$349$	10.1537			0.543517			0.271759	+	0.962365i	$0.412395\pi$
$350$		0			0
$351$	−0.741795	+	1.28483i	−0.0395941	+	0.0685790i
$352$		0			0
$353$	15.2411			0.811201			0.405600	−	0.914050i	$-0.367062\pi$
$353$	15.2411			0.811201			0.405600	+	0.914050i	$0.367062\pi$
$354$		0			0
$355$	−7.11248	+	12.3192i	−0.377491	+	0.653834i
$356$		0			0
$357$	21.3933	−	37.0543i	1.13225	−	1.96112i
$358$		0			0
$359$	9.38264	+	16.2512i	0.495197	+	0.857706i	0.999985	−	0.00553728i	$-0.00176258\pi$
$359$	9.38264	+	16.2512i	0.495197	+	0.857706i	−0.504788	+	0.863243i	$0.668429\pi$
$360$		0			0
$361$		0			0
$362$		0			0
$363$	28.2589	+	48.9458i	1.48321	+	2.56899i
$364$		0			0
$365$	−4.72149	+	8.17786i	−0.247134	+	0.428049i
$366$		0			0
$367$	−6.05483	+	10.4873i	−0.316060	+	0.547431i	−0.979662	−	0.200654i	$-0.935693\pi$
$367$	−6.05483	+	10.4873i	−0.316060	+	0.547431i	0.663603	+	0.748085i	$0.269027\pi$
$368$		0			0
$369$	17.1376			0.892147
$370$		0			0
$371$	2.72947	−	4.72758i	0.141707	−	0.245444i
$372$		0			0
$373$	−33.1556			−1.71673			−0.858366	−	0.513038i	$-0.828520\pi$
$373$	−33.1556			−1.71673			−0.858366	+	0.513038i	$0.828520\pi$
$374$		0			0
$375$	14.4209	+	24.9777i	0.744692	+	1.28984i
$376$		0			0
$377$	0.667152	+	1.15554i	0.0343601	+	0.0595134i
$378$		0			0
$379$	−19.5956			−1.00656			−0.503280	−	0.864123i	$-0.667874\pi$
$379$	−19.5956			−1.00656			−0.503280	+	0.864123i	$0.667874\pi$
$380$		0			0
$381$	−36.2929			−1.85934
$382$		0			0
$383$	−12.5245	−	21.6931i	−0.639974	−	1.10847i	−0.985438	−	0.170036i	$-0.945612\pi$
$383$	−12.5245	−	21.6931i	−0.639974	−	1.10847i	0.345464	−	0.938432i	$-0.387722\pi$
$384$		0			0
$385$	12.1289	+	21.0079i	0.618146	+	1.07066i
$386$		0			0
$387$	−11.4357			−0.581310
$388$		0			0
$389$	8.29104	−	14.3605i	0.420372	−	0.728106i	−0.575603	−	0.817729i	$-0.695233\pi$
$389$	8.29104	−	14.3605i	0.420372	−	0.728106i	0.995976	+	0.0896226i	$0.0285661\pi$
$390$		0			0
$391$	17.4578			0.882881
$392$		0			0
$393$	−13.6384	+	23.6224i	−0.687968	+	1.19159i
$394$		0			0
$395$	6.51311	−	11.2810i	0.327710	−	0.567610i
$396$		0			0
$397$	−14.9455	−	25.8864i	−0.750095	−	1.29920i	−0.947776	−	0.318937i	$-0.896674\pi$
$397$	−14.9455	−	25.8864i	−0.750095	−	1.29920i	0.197681	−	0.980266i	$-0.436659\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−10.0942	−	17.4837i	−0.504082	−	0.873095i	−0.999989	−	0.00471960i	$-0.998498\pi$
$401$	−10.0942	−	17.4837i	−0.504082	−	0.873095i	0.495907	−	0.868376i	$-0.334836\pi$
$402$		0			0
$403$	−2.38334	+	4.12806i	−0.118723	+	0.205634i
$404$		0			0
$405$	−2.37585	+	4.11509i	−0.118057	+	0.204480i
$406$		0			0
$407$	10.2493			0.508039
$408$		0			0
$409$	5.95092	−	10.3073i	0.294254	−	0.509663i	−0.680557	−	0.732695i	$-0.738262\pi$
$409$	5.95092	−	10.3073i	0.294254	−	0.509663i	0.974811	+	0.223032i	$0.0715955\pi$
$410$		0			0
$411$	9.41295			0.464306
$412$		0			0
$413$	14.3026	+	24.7729i	0.703786	+	1.21899i
$414$		0			0
$415$	2.92140	+	5.06001i	0.143406	+	0.248386i
$416$		0			0
$417$	−28.6888			−1.40490
$418$		0			0
$419$	17.0337			0.832151			0.416076	−	0.909330i	$-0.363405\pi$
$419$	17.0337			0.832151			0.416076	+	0.909330i	$0.363405\pi$
$420$		0			0
$421$	−2.73924	−	4.74450i	−0.133502	−	0.231233i	0.791522	−	0.611141i	$-0.209289\pi$
$421$	−2.73924	−	4.74450i	−0.133502	−	0.231233i	−0.925024	+	0.379908i	$0.875956\pi$
$422$		0			0
$423$	−12.8831	−	22.3142i	−0.626397	−	1.08495i
$424$		0			0
$425$	15.9478			0.773584
$426$		0			0
$427$	4.34072	−	7.51835i	0.210062	−	0.363838i
$428$		0			0
$429$	−6.73144			−0.324997
$430$		0			0
$431$	−0.146767	+	0.254209i	−0.00706953	+	0.0122448i	−0.869539	−	0.493865i	$-0.835584\pi$
$431$	−0.146767	+	0.254209i	−0.00706953	+	0.0122448i	0.862469	+	0.506110i	$0.168917\pi$
$432$		0			0
$433$	−10.8850	+	18.8534i	−0.523101	+	0.906037i	0.476538	+	0.879154i	$0.341892\pi$
$433$	−10.8850	+	18.8534i	−0.523101	+	0.906037i	−0.999639	+	0.0268833i	$0.991442\pi$
$434$		0			0
$435$	−5.20898	−	9.02221i	−0.249751	−	0.432582i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	6.84302	+	11.8525i	0.326599	+	0.565687i	0.981835	−	0.189738i	$-0.0607639\pi$
$439$	6.84302	+	11.8525i	0.326599	+	0.565687i	−0.655235	+	0.755425i	$0.727431\pi$
$440$		0			0
$441$	−8.88992	+	15.3978i	−0.423329	+	0.733228i
$442$		0			0
$443$	4.75081	−	8.22864i	0.225718	−	0.390954i	−0.730817	−	0.682574i	$-0.760861\pi$
$443$	4.75081	−	8.22864i	0.225718	−	0.390954i	0.956535	+	0.291619i	$0.0941940\pi$
$444$		0			0
$445$	−16.6134			−0.787549
$446$		0			0
$447$	−11.3348	+	19.6325i	−0.536120	+	0.928586i
$448$		0			0
$449$	38.4822			1.81609			0.908043	−	0.418877i	$-0.137576\pi$
$449$	38.4822			1.81609			0.908043	+	0.418877i	$0.137576\pi$
$450$		0			0
$451$	11.4134	+	19.7685i	0.537434	+	0.930864i
$452$		0			0
$453$	−15.3164	−	26.5288i	−0.719627	−	1.24643i
$454$		0			0
$455$	−1.89587			−0.0888797
$456$		0			0
$457$	12.3537			0.577880			0.288940	−	0.957347i	$-0.406697\pi$
$457$	12.3537			0.577880			0.288940	+	0.957347i	$0.406697\pi$
$458$		0			0
$459$	−7.97392	−	13.8112i	−0.372191	−	0.644653i
$460$		0			0
$461$	−1.65555	−	2.86749i	−0.0771065	−	0.133552i	0.824894	−	0.565288i	$-0.191235\pi$
$461$	−1.65555	−	2.86749i	−0.0771065	−	0.133552i	−0.902000	+	0.431735i	$0.857901\pi$
$462$		0			0
$463$	−4.16441			−0.193536			−0.0967682	−	0.995307i	$-0.530851\pi$
$463$	−4.16441			−0.193536			−0.0967682	+	0.995307i	$0.530851\pi$
$464$		0			0
$465$	18.6086	−	32.2311i	0.862953	−	1.49468i
$466$		0			0
$467$	39.2187			1.81483			0.907413	−	0.420241i	$-0.138054\pi$
$467$	39.2187			1.81483			0.907413	+	0.420241i	$0.138054\pi$
$468$		0			0
$469$	−6.74494	+	11.6826i	−0.311452	+	0.539451i
$470$		0			0
$471$	−6.29383	+	10.9012i	−0.290004	+	0.502302i
$472$		0			0
$473$	−7.61601	−	13.1913i	−0.350184	−	0.606537i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−3.46555	−	6.00251i	−0.158677	−	0.274836i
$478$		0			0
$479$	3.71051	−	6.42680i	0.169538	−	0.293648i	−0.768720	−	0.639586i	$-0.779106\pi$
$479$	3.71051	−	6.42680i	0.169538	−	0.293648i	0.938257	+	0.345938i	$0.112439\pi$
$480$		0			0
$481$	−0.400518	+	0.693717i	−0.0182620	+	0.0316308i
$482$		0			0
$483$	−33.0770			−1.50505
$484$		0			0
$485$	−7.63029	+	13.2161i	−0.346474	+	0.600110i
$486$		0			0
$487$	32.6140			1.47788			0.738940	−	0.673771i	$-0.235327\pi$
$487$	32.6140			1.47788			0.738940	+	0.673771i	$0.235327\pi$
$488$		0			0
$489$	−2.46312	−	4.26625i	−0.111386	−	0.192926i
$490$		0			0
$491$	12.0636	+	20.8948i	0.544423	+	0.942969i	0.998643	+	0.0520789i	$0.0165847\pi$
$491$	12.0636	+	20.8948i	0.544423	+	0.942969i	−0.454220	+	0.890890i	$0.650082\pi$
$492$		0			0
$493$	−14.3431			−0.645980
$494$		0			0
$495$	30.7996			1.38434
$496$		0			0
$497$	−18.5531	−	32.1349i	−0.832220	−	1.44145i
$498$		0			0
$499$	−8.56139	−	14.8288i	−0.383260	−	0.663826i	0.608266	−	0.793733i	$-0.291865\pi$
$499$	−8.56139	−	14.8288i	−0.383260	−	0.663826i	−0.991526	+	0.129907i	$0.958532\pi$
$500$		0			0
$501$	53.7703			2.40228
$502$		0			0
$503$	−12.5324	+	21.7068i	−0.558794	+	0.967860i	0.438803	+	0.898583i	$0.355402\pi$
$503$	−12.5324	+	21.7068i	−0.558794	+	0.967860i	−0.997597	+	0.0692766i	$0.977931\pi$
$504$		0			0
$505$	−13.0736			−0.581767
$506$		0			0
$507$	−17.2347	+	29.8514i	−0.765420	+	1.32575i
$508$		0			0
$509$	6.52941	−	11.3093i	0.289411	−	0.501275i	−0.684258	−	0.729240i	$-0.739874\pi$
$509$	6.52941	−	11.3093i	0.289411	−	0.501275i	0.973669	+	0.227965i	$0.0732072\pi$
$510$		0			0
$511$	−12.3161	−	21.3322i	−0.544833	−	0.943679i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.90213	−	5.02663i	−0.127883	−	0.221500i
$516$		0			0
$517$	17.1599	−	29.7218i	0.754690	−	1.30716i
$518$		0			0
$519$	−6.29029	+	10.8951i	−0.276113	+	0.478242i
$520$		0			0
$521$	19.1979			0.841076			0.420538	−	0.907275i	$-0.361841\pi$
$521$	19.1979			0.841076			0.420538	+	0.907275i	$0.361841\pi$
$522$		0			0
$523$	−21.1144	+	36.5712i	−0.923269	+	1.59915i	−0.128947	+	0.991651i	$0.541160\pi$
$523$	−21.1144	+	36.5712i	−0.923269	+	1.59915i	−0.794322	+	0.607497i	$0.792174\pi$
$524$		0			0
$525$	−30.2160			−1.31873
$526$		0			0
$527$	−25.6197	−	44.3746i	−1.11601	−	1.93299i
$528$		0			0
$529$	4.75195	+	8.23062i	0.206606	+	0.357853i
$530$		0			0
$531$	36.3195			1.57613
$532$		0			0
$533$	−1.78402			−0.0772747
$534$		0			0
$535$	0.819862	+	1.42004i	0.0354457	+	0.0613938i
$536$		0			0
$537$	10.2867	+	17.8170i	0.443902	+	0.768860i
$538$		0			0
$539$	−23.6822			−1.02006
$540$		0			0
$541$	−0.454016	+	0.786378i	−0.0195197	+	0.0338090i	−0.875620	−	0.483000i	$-0.839547\pi$
$541$	−0.454016	+	0.786378i	−0.0195197	+	0.0338090i	0.856101	+	0.516809i	$0.172880\pi$
$542$		0			0
$543$	−16.4060			−0.704051
$544$		0			0
$545$	4.11803	−	7.13264i	0.176397	−	0.305529i
$546$		0			0
$547$	−17.3044	+	29.9722i	−0.739885	+	1.28152i	0.212662	+	0.977126i	$0.431787\pi$
$547$	−17.3044	+	29.9722i	−0.739885	+	1.28152i	−0.952547	+	0.304392i	$0.901547\pi$
$548$		0			0
$549$	−5.51133	−	9.54590i	−0.235218	−	0.407409i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	16.9896	+	29.4269i	0.722472	+	1.25136i
$554$		0			0
$555$	3.12716	−	5.41639i	0.132740	−	0.229913i
$556$		0			0
$557$	−3.63484	+	6.29573i	−0.154013	+	0.266759i	−0.932699	−	0.360655i	$-0.882553\pi$
$557$	−3.63484	+	6.29573i	−0.154013	+	0.266759i	0.778686	+	0.627414i	$0.215887\pi$
$558$		0			0
$559$	1.19046			0.0503511
$560$		0			0
$561$	36.1798	−	62.6653i	1.52751	−	2.64573i
$562$		0			0
$563$	−2.45317			−0.103389			−0.0516944	−	0.998663i	$-0.516462\pi$
$563$	−2.45317			−0.103389			−0.0516944	+	0.998663i	$0.516462\pi$
$564$		0			0
$565$	−1.13499	−	1.96585i	−0.0477492	−	0.0827040i
$566$		0			0
$567$	−6.19746	−	10.7343i	−0.260269	−	0.450799i
$568$		0			0
$569$	18.1326			0.760159			0.380080	−	0.924954i	$-0.375897\pi$
$569$	18.1326			0.760159			0.380080	+	0.924954i	$0.375897\pi$
$570$		0			0
$571$	−25.1171			−1.05112			−0.525560	−	0.850757i	$-0.676144\pi$
$571$	−25.1171			−1.05112			−0.525560	+	0.850757i	$0.676144\pi$
$572$		0			0
$573$	10.6773	+	18.4936i	0.446050	+	0.772582i
$574$		0			0
$575$	−6.16439	−	10.6770i	−0.257073	−	0.445263i
$576$		0			0
$577$	−20.6753			−0.860722			−0.430361	−	0.902657i	$-0.641614\pi$
$577$	−20.6753			−0.860722			−0.430361	+	0.902657i	$0.641614\pi$
$578$		0			0
$579$	−9.21918	+	15.9681i	−0.383136	+	0.663611i
$580$		0			0
$581$	−15.2411			−0.632307
$582$		0			0
$583$	4.61601	−	7.99516i	0.191175	−	0.331126i
$584$		0			0
$585$	−1.20357	+	2.08465i	−0.0497617	+	0.0861897i
$586$		0			0
$587$	12.5077	+	21.6639i	0.516247	+	0.894165i	0.999822	+	0.0188627i	$0.00600453\pi$
$587$	12.5077	+	21.6639i	0.516247	+	0.894165i	−0.483575	+	0.875303i	$0.660662\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	−34.3910	−	59.5670i	−1.41466	−	2.45026i
$592$		0			0
$593$	18.7268	−	32.4357i	0.769016	−	1.33198i	−0.169081	−	0.985602i	$-0.554080\pi$
$593$	18.7268	−	32.4357i	0.769016	−	1.33198i	0.938097	−	0.346373i	$-0.112587\pi$
$594$		0			0
$595$	10.1898	−	17.6493i	0.417742	−	0.723550i
$596$		0			0
$597$	20.5320			0.840319
$598$		0			0
$599$	20.9584	−	36.3010i	0.856336	−	1.48322i	−0.0190640	−	0.999818i	$-0.506069\pi$
$599$	20.9584	−	36.3010i	0.856336	−	1.48322i	0.875400	−	0.483399i	$-0.160598\pi$
$600$		0			0
$601$	−24.3133			−0.991760			−0.495880	−	0.868391i	$-0.665154\pi$
$601$	−24.3133			−0.991760			−0.495880	+	0.868391i	$0.665154\pi$
$602$		0			0
$603$	8.56392	+	14.8331i	0.348750	+	0.604052i
$604$		0			0
$605$	13.4600	+	23.3133i	0.547225	+	0.947821i
$606$		0			0
$607$	−19.2612			−0.781790			−0.390895	−	0.920435i	$-0.627834\pi$
$607$	−19.2612			−0.781790			−0.390895	+	0.920435i	$0.627834\pi$
$608$		0			0
$609$	27.1755			1.10121
$610$		0			0
$611$	1.34113	+	2.32291i	0.0542564	+	0.0939748i
$612$		0			0
$613$	−8.04796	−	13.9395i	−0.325054	−	0.563010i	0.656469	−	0.754353i	$-0.272049\pi$
$613$	−8.04796	−	13.9395i	−0.325054	−	0.563010i	−0.981523	+	0.191343i	$0.938716\pi$
$614$		0			0
$615$	13.9293			0.561683
$616$		0			0
$617$	−11.5094	+	19.9348i	−0.463350	+	0.802546i	−0.999125	−	0.0418148i	$-0.986686\pi$
$617$	−11.5094	+	19.9348i	−0.463350	+	0.802546i	0.535775	+	0.844361i	$0.320019\pi$
$618$		0			0
$619$	3.28899			0.132196			0.0660979	−	0.997813i	$-0.478945\pi$
$619$	3.28899			0.132196			0.0660979	+	0.997813i	$0.478945\pi$
$620$		0			0
$621$	−6.16439	+	10.6770i	−0.247368	+	0.428454i
$622$		0			0
$623$	21.6682	−	37.5304i	0.868118	−	1.50362i
$624$		0			0
$625$	−1.52108	−	2.63459i	−0.0608432	−	0.105384i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−4.30536	−	7.45711i	−0.171666	−	0.297334i
$630$		0			0
$631$	−21.0206	+	36.4087i	−0.836816	+	1.44941i	0.0557279	+	0.998446i	$0.482252\pi$
$631$	−21.0206	+	36.4087i	−0.836816	+	1.44941i	−0.892544	+	0.450961i	$0.851081\pi$
$632$		0			0
$633$	15.4396	−	26.7422i	0.613670	−	1.06291i
$634$		0			0
$635$	−17.2866			−0.685999
$636$		0			0
$637$	0.925441	−	1.60291i	0.0366673	−	0.0635097i
$638$		0			0
$639$	−47.1130			−1.86376
$640$		0			0
$641$	−9.40617	−	16.2920i	−0.371521	−	0.643494i	0.618279	−	0.785959i	$-0.287830\pi$
$641$	−9.40617	−	16.2920i	−0.371521	−	0.643494i	−0.989800	+	0.142465i	$0.954497\pi$
$642$		0			0
$643$	−7.91179	−	13.7036i	−0.312010	−	0.540418i	0.666787	−	0.745248i	$-0.267669\pi$
$643$	−7.91179	−	13.7036i	−0.312010	−	0.540418i	−0.978797	+	0.204830i	$0.934336\pi$
$644$		0			0
$645$	−9.29485			−0.365984
$646$		0			0
$647$	−8.04659			−0.316344			−0.158172	−	0.987412i	$-0.550560\pi$
$647$	−8.04659			−0.316344			−0.158172	+	0.987412i	$0.550560\pi$
$648$		0			0
$649$	24.1882	+	41.8952i	0.949471	+	1.64453i
$650$		0			0
$651$	48.5410	+	84.0756i	1.90247	+	3.29518i
$652$		0			0
$653$	−41.3583			−1.61848			−0.809238	−	0.587481i	$-0.800120\pi$
$653$	−41.3583			−1.61848			−0.809238	+	0.587481i	$0.800120\pi$
$654$		0			0
$655$	−6.49610	+	11.2516i	−0.253824	+	0.439635i
$656$		0			0
$657$	−31.2751			−1.22016
$658$		0			0
$659$	−0.838048	+	1.45154i	−0.0326457	+	0.0565441i	−0.881887	−	0.471461i	$-0.843727\pi$
$659$	−0.838048	+	1.45154i	−0.0326457	+	0.0565441i	0.849241	+	0.528006i	$0.177060\pi$
$660$		0			0
$661$	−5.55601	+	9.62329i	−0.216104	+	0.374303i	−0.953613	−	0.301034i	$-0.902668\pi$
$661$	−5.55601	+	9.62329i	−0.216104	+	0.374303i	0.737510	+	0.675337i	$0.236002\pi$
$662$		0			0
$663$	2.82764	+	4.89761i	0.109816	+	0.190207i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	5.54409	+	9.60265i	0.214668	+	0.371816i
$668$		0			0
$669$	−3.76711	+	6.52482i	−0.145645	+	0.252264i
$670$		0			0
$671$	7.34092	−	12.7148i	0.283393	−	0.490851i
$672$		0			0
$673$	−50.1601			−1.93353			−0.966764	−	0.255669i	$-0.917704\pi$
$673$	−50.1601			−1.93353			−0.966764	+	0.255669i	$0.917704\pi$
$674$		0			0
$675$	−5.63120	+	9.75353i	−0.216745	+	0.375414i
$676$		0			0
$677$	24.5938			0.945218			0.472609	−	0.881272i	$-0.343312\pi$
$677$	24.5938			0.945218			0.472609	+	0.881272i	$0.343312\pi$
$678$		0			0
$679$	−19.9038	−	34.4744i	−0.763839	−	1.32301i
$680$		0			0
$681$	−8.15445	−	14.1239i	−0.312479	−	0.541230i
$682$		0			0
$683$	40.1865			1.53769			0.768846	−	0.639434i	$-0.220831\pi$
$683$	40.1865			1.53769			0.768846	+	0.639434i	$0.220831\pi$
$684$		0			0
$685$	4.48347			0.171305
$686$		0			0
$687$	−12.0786	−	20.9207i	−0.460826	−	0.798173i
$688$		0			0
$689$	0.360764	+	0.624862i	0.0137440	+	0.0238054i
$690$		0			0
$691$	−9.38100			−0.356870			−0.178435	−	0.983952i	$-0.557103\pi$
$691$	−9.38100			−0.356870			−0.178435	+	0.983952i	$0.557103\pi$
$692$		0			0
$693$	−40.1708	+	69.5779i	−1.52596	+	2.64305i
$694$		0			0
$695$	−13.6647			−0.518333
$696$		0			0
$697$	9.58868	−	16.6081i	0.363197	−	0.629076i
$698$		0			0
$699$	−9.88027	+	17.1131i	−0.373706	+	0.647278i
$700$		0			0
$701$	18.5874	+	32.1943i	0.702036	+	1.21596i	0.967750	+	0.251911i	$0.0810589\pi$
$701$	18.5874	+	32.1943i	0.702036	+	1.21596i	−0.265714	+	0.964052i	$0.585608\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−10.4713	−	18.1368i	−0.394371	−	0.683070i
$706$		0			0
$707$	17.0514	−	29.5339i	0.641284	−	1.11074i
$708$		0			0
$709$	15.6366	−	27.0834i	0.587246	−	1.01714i	−0.407346	−	0.913274i	$-0.633546\pi$
$709$	15.6366	−	27.0834i	0.587246	−	1.01714i	0.994591	−	0.103865i	$-0.0331211\pi$
$710$		0			0
$711$	43.1428			1.61798
$712$		0			0
$713$	−19.8058	+	34.3046i	−0.741732	+	1.28472i
$714$		0			0
$715$	−3.20625			−0.119907
$716$		0			0
$717$	−25.8038	−	44.6936i	−0.963662	−	1.66911i
$718$		0			0
$719$	−13.0243	−	22.5588i	−0.485725	−	0.841301i	0.514140	−	0.857706i	$-0.328111\pi$
$719$	−13.0243	−	22.5588i	−0.485725	−	0.841301i	−0.999865	+	0.0164054i	$0.994778\pi$
$720$		0			0
$721$	15.1405			0.563863
$722$		0			0
$723$	32.6463			1.21413
$724$		0			0
$725$	5.06456	+	8.77208i	0.188093	+	0.325787i
$726$		0			0
$727$	1.03986	+	1.80110i	0.0385664	+	0.0667990i	0.884664	−	0.466229i	$-0.154388\pi$
$727$	1.03986	+	1.80110i	0.0385664	+	0.0667990i	−0.846098	+	0.533027i	$0.821054\pi$
$728$		0			0
$729$	−42.8399			−1.58666
$730$		0			0
$731$	−6.39842	+	11.0824i	−0.236654	+	0.409897i
$732$		0			0
$733$	−6.92827			−0.255901			−0.127951	−	0.991781i	$-0.540840\pi$
$733$	−6.92827			−0.255901			−0.127951	+	0.991781i	$0.540840\pi$
$734$		0			0
$735$	−7.22565	+	12.5152i	−0.266522	+	0.461630i
$736$		0			0
$737$	−11.4069	+	19.7573i	−0.420178	+	0.727769i
$738$		0			0
$739$	−8.66052	−	15.0005i	−0.318582	−	0.551801i	0.661610	−	0.749848i	$-0.269873\pi$
$739$	−8.66052	−	15.0005i	−0.318582	−	0.551801i	−0.980192	+	0.198047i	$0.936540\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−26.0775	−	45.1675i	−0.956690	−	1.65704i	−0.730452	−	0.682964i	$-0.760691\pi$
$743$	−26.0775	−	45.1675i	−0.956690	−	1.65704i	−0.226238	−	0.974072i	$-0.572643\pi$
$744$		0			0
$745$	−5.39888	+	9.35114i	−0.197800	+	0.342599i
$746$		0			0
$747$	−9.67565	+	16.7587i	−0.354014	+	0.613170i
$748$		0			0
$749$	−4.27726			−0.156288
$750$		0			0
$751$	−5.80991	+	10.0631i	−0.212006	+	0.367206i	−0.952342	−	0.305031i	$-0.901333\pi$
$751$	−5.80991	+	10.0631i	−0.212006	+	0.367206i	0.740336	+	0.672237i	$0.234666\pi$
$752$		0			0
$753$	−39.3382			−1.43357
$754$		0			0
$755$	−7.29534	−	12.6359i	−0.265504	−	0.459867i
$756$		0			0
$757$	13.6310	+	23.6096i	0.495428	+	0.858106i	0.999986	−	0.00527146i	$-0.00167796\pi$
$757$	13.6310	+	23.6096i	0.495428	+	0.858106i	−0.504558	+	0.863378i	$0.668345\pi$
$758$		0			0
$759$	−55.9389			−2.03045
$760$		0			0
$761$	32.8211			1.18976			0.594882	−	0.803813i	$-0.297199\pi$
$761$	32.8211			1.18976			0.594882	+	0.803813i	$0.297199\pi$
$762$		0			0
$763$	10.7420	+	18.6057i	0.388886	+	0.673570i
$764$		0			0
$765$	−12.9378	−	22.4089i	−0.467768	−	0.810197i
$766$		0			0
$767$	−3.78086			−0.136519
$768$		0			0
$769$	−1.22615	+	2.12375i	−0.0442159	+	0.0765843i	−0.887286	−	0.461219i	$-0.847412\pi$
$769$	−1.22615	+	2.12375i	−0.0442159	+	0.0765843i	0.843070	+	0.537803i	$0.180746\pi$
$770$		0			0
$771$	−6.97539			−0.251213
$772$		0			0
$773$	−4.85405	+	8.40746i	−0.174588	+	0.302395i	−0.940019	−	0.341123i	$-0.889193\pi$
$773$	−4.85405	+	8.40746i	−0.174588	+	0.302395i	0.765431	+	0.643518i	$0.222526\pi$
$774$		0			0
$775$	−18.0927	+	31.3375i	−0.649909	+	1.12568i
$776$		0			0
$777$	8.15727	+	14.1288i	0.292640	+	0.506868i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	−31.3765	−	54.3457i	−1.12274	−	1.94464i
$782$		0			0
$783$	5.06456	−	8.77208i	0.180993	−	0.313489i
$784$		0			0
$785$	−2.99781	+	5.19235i	−0.106996	+	0.185323i
$786$		0			0
$787$	32.4028			1.15503			0.577517	−	0.816379i	$-0.304022\pi$
$787$	32.4028			1.15503			0.577517	+	0.816379i	$0.304022\pi$
$788$		0			0
$789$	−30.9793	+	53.6578i	−1.10289	+	1.91027i
$790$		0			0
$791$	5.92128			0.210536
$792$		0			0
$793$	0.573730	+	0.993729i	0.0203737	+	0.0352884i
$794$		0			0
$795$	−2.81677	−	4.87879i	−0.0999006	−	0.173033i
$796$		0			0
$797$	−14.1556			−0.501417			−0.250708	−	0.968063i	$-0.580664\pi$
$797$	−14.1556			−0.501417			−0.250708	+	0.968063i	$0.580664\pi$
$798$		0			0
$799$	−28.8330			−1.02004
$800$		0			0
$801$	−27.5117	−	47.6517i	−0.972078	−	1.68369i
$802$		0			0
$803$	−20.8287	−	36.0764i	−0.735030	−	1.27311i
$804$		0			0
$805$	−15.7548			−0.555285
$806$		0			0
$807$	35.2415	−	61.0400i	1.24056	−	2.14871i
$808$		0			0
$809$	−4.19788			−0.147589			−0.0737947	−	0.997273i	$-0.523511\pi$
$809$	−4.19788			−0.147589			−0.0737947	+	0.997273i	$0.523511\pi$
$810$		0			0
$811$	−22.8282	+	39.5396i	−0.801607	+	1.38842i	0.116951	+	0.993138i	$0.462688\pi$
$811$	−22.8282	+	39.5396i	−0.801607	+	1.38842i	−0.918558	+	0.395286i	$0.870646\pi$
$812$		0			0
$813$	−19.8884	+	34.4478i	−0.697518	+	1.20814i
$814$		0			0
$815$	−1.17321	−	2.03205i	−0.0410956	−	0.0711796i
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−3.13955	−	5.43787i	−0.109705	−	0.190014i
$820$		0			0
$821$	−2.07846	+	3.60000i	−0.0725388	+	0.125641i	−0.900013	−	0.435862i	$-0.856443\pi$
$821$	−2.07846	+	3.60000i	−0.0725388	+	0.125641i	0.827475	+	0.561503i	$0.189777\pi$
$822$		0			0
$823$	23.1810	−	40.1506i	0.808037	−	1.39956i	−0.106184	−	0.994347i	$-0.533863\pi$
$823$	23.1810	−	40.1506i	0.808037	−	1.39956i	0.914221	−	0.405215i	$-0.132803\pi$
$824$		0			0
$825$	−51.1005			−1.77909
$826$		0			0
$827$	15.2540	−	26.4207i	0.530434	−	0.918739i	−0.468935	−	0.883232i	$-0.655362\pi$
$827$	15.2540	−	26.4207i	0.530434	−	0.918739i	0.999369	−	0.0355062i	$-0.0113043\pi$
$828$		0			0
$829$	7.28342			0.252964			0.126482	−	0.991969i	$-0.459631\pi$
$829$	7.28342			0.252964			0.126482	+	0.991969i	$0.459631\pi$
$830$		0			0
$831$	−19.8492	−	34.3798i	−0.688560	−	1.19262i
$832$		0			0
$833$	9.94803	+	17.2305i	0.344679	+	0.597001i
$834$		0			0
$835$	25.6113			0.886314
$836$		0			0
$837$	36.1854			1.25075
$838$		0			0
$839$	6.64967	+	11.5176i	0.229572	+	0.397631i	0.957681	−	0.287830i	$-0.0929340\pi$
$839$	6.64967	+	11.5176i	0.229572	+	0.397631i	−0.728109	+	0.685461i	$0.759601\pi$
$840$		0			0
$841$	9.94506	+	17.2254i	0.342933	+	0.593978i
$842$		0			0
$843$	−37.5274			−1.29251
$844$		0			0
$845$	−8.20904	+	14.2185i	−0.282400	+	0.489130i
$846$		0			0
$847$	−70.2213			−2.41283
$848$		0			0
$849$	−24.6165	+	42.6370i	−0.844835	+	1.46330i
$850$		0			0
$851$	−3.32834	+	5.76485i	−0.114094	+	0.197617i
$852$		0			0
$853$	−8.18244	−	14.1724i	−0.280161	−	0.485254i	0.691263	−	0.722603i	$-0.257055\pi$
$853$	−8.18244	−	14.1724i	−0.280161	−	0.485254i	−0.971424	+	0.237350i	$0.923721\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−14.3044	−	24.7759i	−0.488628	−	0.846328i	0.511287	−	0.859410i	$-0.329169\pi$
$857$	−14.3044	−	24.7759i	−0.488628	−	0.846328i	−0.999914	+	0.0130823i	$0.995836\pi$
$858$		0			0
$859$	2.70384	−	4.68319i	0.0922538	−	0.159788i	−0.816205	−	0.577762i	$-0.803926\pi$
$859$	2.70384	−	4.68319i	0.0922538	−	0.159788i	0.908459	+	0.417974i	$0.137260\pi$
$860$		0			0
$861$	−18.1675	+	31.4670i	−0.619145	+	1.07239i
$862$		0			0
$863$	−42.0613			−1.43178			−0.715892	−	0.698211i	$-0.753980\pi$
$863$	−42.0613			−1.43178			−0.715892	+	0.698211i	$0.753980\pi$
$864$		0			0
$865$	−2.99612	+	5.18943i	−0.101871	+	0.176446i
$866$		0			0
$867$	−15.0280			−0.510376
$868$		0			0
$869$	28.7324	+	49.7660i	0.974680	+	1.68820i
$870$		0			0
$871$	−0.891505	−	1.54413i	−0.0302075	−	0.0523209i
$872$		0			0
$873$	−50.5430			−1.71062
$874$		0			0
$875$	−35.8349			−1.21144
$876$		0			0
$877$	−5.86744	−	10.1627i	−0.198129	−	0.343170i	0.749792	−	0.661673i	$-0.230153\pi$
$877$	−5.86744	−	10.1627i	−0.198129	−	0.343170i	−0.947922	+	0.318503i	$0.896820\pi$
$878$		0			0
$879$	33.3096	+	57.6940i	1.12351	+	1.94597i
$880$		0			0
$881$	23.5318			0.792806			0.396403	−	0.918077i	$-0.370258\pi$
$881$	23.5318			0.792806			0.396403	+	0.918077i	$0.370258\pi$
$882$		0			0
$883$	1.78102	−	3.08482i	0.0599361	−	0.103812i	−0.834500	−	0.551007i	$-0.814244\pi$
$883$	1.78102	−	3.08482i	0.0599361	−	0.103812i	0.894437	+	0.447195i	$0.147577\pi$
$884$		0			0
$885$	29.5202			0.992310
$886$		0			0
$887$	12.2959	−	21.2971i	0.412856	−	0.715087i	−0.582345	−	0.812942i	$-0.697865\pi$
$887$	12.2959	−	21.2971i	0.412856	−	0.715087i	0.995201	+	0.0978548i	$0.0311981\pi$
$888$		0			0
$889$	22.5463	−	39.0513i	0.756179	−	1.30974i
$890$		0			0
$891$	−10.4810	−	18.1536i	−0.351126	−	0.608169i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	4.89962	+	8.48639i	0.163776	+	0.283669i
$896$		0			0
$897$	2.18596	−	3.78619i	0.0729869	−	0.126417i
$898$		0			0
$899$	16.2721	−	28.1841i	0.542705	−	0.939993i
$900$		0			0
$901$	−7.75607			−0.258392
$902$		0			0
$903$	12.1229	−	20.9975i	0.403426	−	0.698754i
$904$		0			0
$905$	−7.81434			−0.259758
$906$		0			0
$907$	−1.48186	−	2.56666i	−0.0492044	−	0.0852246i	0.840374	−	0.542007i	$-0.182335\pi$
$907$	−1.48186	−	2.56666i	−0.0492044	−	0.0852246i	−0.889579	+	0.456782i	$0.849002\pi$
$908$		0			0
$909$	−21.6498	−	37.4986i	−0.718080	−	1.24375i
$910$		0			0
$911$	31.6411			1.04832			0.524158	−	0.851621i	$-0.324380\pi$
$911$	31.6411			1.04832			0.524158	+	0.851621i	$0.324380\pi$
$912$		0			0
$913$	−25.7753			−0.853039
$914$		0			0
$915$	−4.47956	−	7.75883i	−0.148090	−	0.256499i
$916$		0			0
$917$	−16.9453	−	29.3500i	−0.559581	−	0.969224i
$918$		0			0
$919$	39.8066			1.31310			0.656549	−	0.754284i	$-0.272016\pi$
$919$	39.8066			1.31310			0.656549	+	0.754284i	$0.272016\pi$
$920$		0			0
$921$	−30.8674	+	53.4640i	−1.01712	+	1.76170i
$922$		0			0
$923$	4.90447			0.161433
$924$		0			0
$925$	−3.04046	+	5.26623i	−0.0999696	+	0.173152i
$926$		0			0
$927$	9.61183	−	16.6482i	0.315694	−	0.546798i
$928$		0			0
$929$	1.21002	+	2.09582i	0.0396996	+	0.0687617i	0.885192	−	0.465225i	$-0.154027\pi$
$929$	1.21002	+	2.09582i	0.0396996	+	0.0687617i	−0.845493	+	0.533987i	$0.820693\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	39.9307	+	69.1619i	1.30727	+	2.26426i
$934$		0			0
$935$	17.2328	−	29.8480i	0.563571	−	0.976134i
$936$		0			0
$937$	−7.40769	+	12.8305i	−0.241999	+	0.419154i	−0.961284	−	0.275561i	$-0.911136\pi$
$937$	−7.40769	+	12.8305i	−0.241999	+	0.419154i	0.719285	+	0.694715i	$0.244470\pi$
$938$		0			0
$939$	55.7903			1.82065
$940$		0			0
$941$	−7.38687	+	12.7944i	−0.240805	+	0.417087i	−0.960944	−	0.276743i	$-0.910745\pi$
$941$	−7.38687	+	12.7944i	−0.240805	+	0.417087i	0.720139	+	0.693830i	$0.244078\pi$
$942$		0			0
$943$	−14.8254			−0.482782
$944$		0			0
$945$	7.19607	+	12.4640i	0.234088	+	0.405453i
$946$		0			0
$947$	−25.0224	−	43.3401i	−0.813119	−	1.40836i	−0.910670	−	0.413134i	$-0.864434\pi$
$947$	−25.0224	−	43.3401i	−0.813119	−	1.40836i	0.0975511	−	0.995231i	$-0.468899\pi$
$948$		0			0
$949$	3.25574			0.105686
$950$		0			0
$951$	87.2561			2.82947
$952$		0			0
$953$	−2.89468	−	5.01374i	−0.0937680	−	0.162411i	0.815326	−	0.579003i	$-0.196558\pi$
$953$	−2.89468	−	5.01374i	−0.0937680	−	0.162411i	−0.909094	+	0.416592i	$0.863225\pi$
$954$		0			0
$955$	5.08569	+	8.80867i	0.164569	+	0.285042i
$956$		0			0
$957$	45.9585			1.48563
$958$		0			0
$959$	−5.84762	+	10.1284i	−0.188830	+	0.327062i
$960$		0			0
$961$	85.2613			2.75037
$962$		0			0
$963$	−2.71538	+	4.70317i	−0.0875018	+	0.151558i
$964$		0			0
$965$	−4.39117	+	7.60574i	−0.141357	+	0.244837i
$966$		0			0
$967$	−15.8640	−	27.4772i	−0.510151	−	0.883607i	−0.999931	−	0.0117610i	$-0.996256\pi$
$967$	−15.8640	−	27.4772i	−0.510151	−	0.883607i	0.489780	−	0.871846i	$-0.337077\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	4.50837	+	7.80872i	0.144680	+	0.250594i	0.929254	−	0.369442i	$-0.120451\pi$
$971$	4.50837	+	7.80872i	0.144680	+	0.250594i	−0.784573	+	0.620036i	$0.787118\pi$
$972$		0			0
$973$	17.8224	−	30.8693i	0.571360	−	0.989625i
$974$		0			0
$975$	1.99688	−	3.45870i	0.0639514	−	0.110767i
$976$		0			0
$977$	−42.4099			−1.35681			−0.678407	−	0.734686i	$-0.737329\pi$
$977$	−42.4099			−1.35681			−0.678407	+	0.734686i	$0.737329\pi$
$978$		0			0
$979$	36.6447	−	63.4705i	1.17117	−	2.02853i
$980$		0			0
$981$	27.2778			0.870913
$982$		0			0
$983$	25.3762	+	43.9528i	0.809374	+	1.40188i	0.913298	+	0.407291i	$0.133526\pi$
$983$	25.3762	+	43.9528i	0.809374	+	1.40188i	−0.103925	+	0.994585i	$0.533140\pi$
$984$		0			0
$985$	−16.3807	−	28.3723i	−0.521934	−	0.904016i
$986$		0			0
$987$	54.6292			1.73887
$988$		0			0
$989$	9.89283			0.314574
$990$		0			0
$991$	5.03480	+	8.72053i	0.159936	+	0.277017i	0.934845	−	0.355055i	$-0.115538\pi$
$991$	5.03480	+	8.72053i	0.159936	+	0.277017i	−0.774910	+	0.632072i	$0.782205\pi$
$992$		0			0
$993$	−28.5870	−	49.5141i	−0.907180	−	1.57128i
$994$		0			0
$995$	9.77957			0.310033
$996$		0			0
$997$	16.3705	−	28.3545i	0.518458	−	0.897995i	−0.481312	−	0.876549i	$-0.659840\pi$
$997$	16.3705	−	28.3545i	0.518458	−	0.897995i	0.999770	−	0.0214459i	$-0.00682696\pi$
$998$		0			0
$999$	6.08092			0.192392

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1444.2.e.g.653.6		12
19.5	even	9		76.2.i.a.61.1	yes	12
19.6	even	9		76.2.i.a.5.1	✓	12
19.7	even	3		1444.2.a.h.1.1		6
19.8	odd	6		1444.2.e.h.429.1		12
19.11	even	3	inner	1444.2.e.g.429.6		12
19.12	odd	6		1444.2.a.g.1.6		6
19.18	odd	2		1444.2.e.h.653.1		12
57.5	odd	18		684.2.bo.c.289.2		12
57.44	odd	18		684.2.bo.c.613.2		12
76.7	odd	6		5776.2.a.bw.1.6		6
76.31	even	6		5776.2.a.by.1.1		6
76.43	odd	18		304.2.u.e.289.2		12
76.63	odd	18		304.2.u.e.81.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.i.a.5.1	✓	12	19.6	even	9
76.2.i.a.61.1	yes	12	19.5	even	9
304.2.u.e.81.2		12	76.63	odd	18
304.2.u.e.289.2		12	76.43	odd	18
684.2.bo.c.289.2		12	57.5	odd	18
684.2.bo.c.613.2		12	57.44	odd	18
1444.2.a.g.1.6		6	19.12	odd	6
1444.2.a.h.1.1		6	19.7	even	3
1444.2.e.g.429.6		12	19.11	even	3	inner
1444.2.e.g.653.6		12	1.1	even	1	trivial
1444.2.e.h.429.1		12	19.8	odd	6
1444.2.e.h.653.1		12	19.18	odd	2
5776.2.a.bw.1.6		6	76.7	odd	6
5776.2.a.by.1.1		6	76.31	even	6

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:	\( N \)	\(=\)	\( 1444 = 2^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1444.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.34598 + 2.33131i) q^{3} +(0.641102 + 1.11042i) q^{5} -3.34467 q^{7} +(-2.12333 + 3.67771i) q^{9} +O(q^{10})\)	\(q+(1.34598 + 2.33131i) q^{3} +(0.641102 + 1.11042i) q^{5} -3.34467 q^{7} +(-2.12333 + 3.67771i) q^{9} -5.65641 q^{11} +(0.221039 - 0.382850i) q^{13} +(-1.72582 + 2.98921i) q^{15} +(2.37605 + 4.11545i) q^{17} +(-4.50185 - 7.79744i) q^{21} +(1.83685 - 3.18152i) q^{23} +(1.67798 - 2.90634i) q^{25} -3.35595 q^{27} +(-1.50913 + 2.61389i) q^{29} -10.7825 q^{31} +(-7.61342 - 13.1868i) q^{33} +(-2.14427 - 3.71399i) q^{35} -1.81198 q^{37} +1.19006 q^{39} +(-2.01777 - 3.49489i) q^{41} +(1.34644 + 2.33210i) q^{43} -5.44508 q^{45} +(-3.03370 + 5.25453i) q^{47} +4.18678 q^{49} +(-6.39625 + 11.0786i) q^{51} +(-0.816066 + 1.41347i) q^{53} +(-3.62634 - 6.28100i) q^{55} +(-4.27625 - 7.40668i) q^{59} +(-1.29780 + 2.24786i) q^{61} +(7.10182 - 12.3007i) q^{63} +0.566834 q^{65} +(2.01663 - 3.49290i) q^{67} +9.88947 q^{69} +(5.54707 + 9.60781i) q^{71} +(3.68232 + 6.37797i) q^{73} +9.03409 q^{75} +18.9188 q^{77} +(-5.07962 - 8.79815i) q^{79} +(1.85294 + 3.20939i) q^{81} +4.55683 q^{83} +(-3.04659 + 5.27684i) q^{85} -8.12503 q^{87} +(-6.47844 + 11.2210i) q^{89} +(-0.739300 + 1.28051i) q^{91} +(-14.5130 - 25.1372i) q^{93} +(5.95092 + 10.3073i) q^{97} +(12.0104 - 20.8027i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} + 3 q^{5} - 6 q^{7} - 9 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 + 3 * q^5 - 6 * q^7 - 9 * q^9	\( 12 q - 3 q^{3} + 3 q^{5} - 6 q^{7} - 9 q^{9} - 6 q^{11} - 12 q^{13} + 6 q^{17} - 21 q^{21} - 9 q^{25} + 18 q^{27} - 21 q^{29} - 12 q^{31} - 9 q^{33} - 3 q^{35} - 12 q^{37} + 60 q^{39} - 36 q^{41} + 18 q^{43} - 48 q^{45} - 30 q^{47} - 18 q^{49} - 24 q^{51} - 18 q^{53} + 15 q^{55} - 21 q^{59} - 9 q^{61} - 6 q^{63} + 66 q^{65} - 18 q^{67} + 66 q^{69} + 12 q^{71} + 24 q^{73} + 42 q^{75} + 24 q^{77} - 9 q^{79} + 6 q^{81} - 6 q^{83} + 12 q^{85} + 36 q^{87} - 45 q^{89} - 9 q^{91} - 15 q^{97} + 33 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 + 3 * q^5 - 6 * q^7 - 9 * q^9 - 6 * q^11 - 12 * q^13 + 6 * q^17 - 21 * q^21 - 9 * q^25 + 18 * q^27 - 21 * q^29 - 12 * q^31 - 9 * q^33 - 3 * q^35 - 12 * q^37 + 60 * q^39 - 36 * q^41 + 18 * q^43 - 48 * q^45 - 30 * q^47 - 18 * q^49 - 24 * q^51 - 18 * q^53 + 15 * q^55 - 21 * q^59 - 9 * q^61 - 6 * q^63 + 66 * q^65 - 18 * q^67 + 66 * q^69 + 12 * q^71 + 24 * q^73 + 42 * q^75 + 24 * q^77 - 9 * q^79 + 6 * q^81 - 6 * q^83 + 12 * q^85 + 36 * q^87 - 45 * q^89 - 9 * q^91 - 15 * q^97 + 33 * q^99

Introduction

L-functions

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