LMFDB - Embedded newform 672.2.bi.c.17.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(17,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 1]))

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

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

chi := DirichletCharacter("672.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bi (of order $6$, 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.11
Character	$\chi$	$=$	672.17
Dual form			672.2.bi.c.593.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.390548 + 1.68745i) q^{3} +(1.54900 - 0.894317i) q^{5} +(-2.63573 + 0.230049i) q^{7} +(-2.69494 - 1.31806i) q^{9} +O(q^{10})$	\(q+(-0.390548 + 1.68745i) q^{3} +(1.54900 - 0.894317i) q^{5} +(-2.63573 + 0.230049i) q^{7} +(-2.69494 - 1.31806i) q^{9} +(-0.501346 + 0.868358i) q^{11} -2.47302 q^{13} +(0.904151 + 2.96313i) q^{15} +(-3.32963 + 5.76708i) q^{17} +(1.85941 + 3.22059i) q^{19} +(0.641185 - 4.53750i) q^{21} +(-6.85244 + 3.95626i) q^{23} +(-0.900394 + 1.55953i) q^{25} +(3.27666 - 4.03281i) q^{27} +0.748403 q^{29} +(-2.87254 - 1.65846i) q^{31} +(-1.26951 - 1.18513i) q^{33} +(-3.87702 + 2.71353i) q^{35} +(3.22429 - 1.86155i) q^{37} +(0.965832 - 4.17308i) q^{39} +2.01044 q^{41} -9.19651i q^{43} +(-5.35324 + 0.368459i) q^{45} +(-1.19840 - 2.07569i) q^{47} +(6.89415 - 1.21270i) q^{49} +(-8.43126 - 7.87089i) q^{51} +(-6.33884 + 10.9792i) q^{53} +1.79345i q^{55} +(-6.16075 + 1.87985i) q^{57} +(7.34922 + 4.24308i) q^{59} +(2.02442 + 3.50640i) q^{61} +(7.40637 + 2.85408i) q^{63} +(-3.83071 + 2.21166i) q^{65} +(-6.89843 - 3.98281i) q^{67} +(-3.99976 - 13.1082i) q^{69} +5.46843i q^{71} +(-5.68546 - 3.28250i) q^{73} +(-2.27997 - 2.12844i) q^{75} +(1.12165 - 2.40409i) q^{77} +(-2.53988 - 4.39920i) q^{79} +(5.52545 + 7.10419i) q^{81} +5.65457i q^{83} +11.9110i q^{85} +(-0.292288 + 1.26289i) q^{87} +(-7.39495 - 12.8084i) q^{89} +(6.51821 - 0.568916i) q^{91} +(3.92043 - 4.19955i) q^{93} +(5.76045 + 3.32580i) q^{95} -1.75577i q^{97} +(2.49565 - 1.67937i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{7} - 14 q^{9}+O(q^{10}) $ 48 * q + 4 * q^7 - 14 * q^9	$ 48 q + 4 q^{7} - 14 q^{9} - 4 q^{15} - 8 q^{25} - 48 q^{31} - 42 q^{33} + 8 q^{39} - 36 q^{49} + 4 q^{57} + 6 q^{63} - 36 q^{73} + 56 q^{79} + 42 q^{81} + 132 q^{87}+O(q^{100}) $ 48 * q + 4 * q^7 - 14 * q^9 - 4 * q^15 - 8 * q^25 - 48 * q^31 - 42 * q^33 + 8 * q^39 - 36 * q^49 + 4 * q^57 + 6 * q^63 - 36 * q^73 + 56 * q^79 + 42 * q^81 + 132 * q^87

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.390548	+	1.68745i	−0.225483	+	0.974247i
$3$	−0.390548	+	1.68745i	−0.225483	+	0.974247i
$4$		0			0
$5$	1.54900	−	0.894317i	0.692735	−	0.399951i	−0.111901	−	0.993719i	$-0.535694\pi$
$5$	1.54900	−	0.894317i	0.692735	−	0.399951i	0.804636	+	0.593769i	$0.202361\pi$
$6$		0			0
$7$	−2.63573	+	0.230049i	−0.996213	+	0.0869505i
$7$	−2.63573	+	0.230049i	−0.996213	+	0.0869505i
$8$		0			0
$9$	−2.69494	−	1.31806i	−0.898315	−	0.439353i
$10$		0			0
$11$	−0.501346	+	0.868358i	−0.151162	+	0.261820i	−0.931655	−	0.363345i	$-0.881635\pi$
$11$	−0.501346	+	0.868358i	−0.151162	+	0.261820i	0.780493	+	0.625164i	$0.214968\pi$
$12$		0			0
$13$	−2.47302			−0.685891			−0.342946	−	0.939355i	$-0.611425\pi$
$13$	−2.47302			−0.685891			−0.342946	+	0.939355i	$0.611425\pi$
$14$		0			0
$15$	0.904151	+	2.96313i	0.233451	+	0.765077i
$16$		0			0
$17$	−3.32963	+	5.76708i	−0.807553	+	1.39872i	0.107001	+	0.994259i	$0.465875\pi$
$17$	−3.32963	+	5.76708i	−0.807553	+	1.39872i	−0.914554	+	0.404464i	$0.867458\pi$
$18$		0			0
$19$	1.85941	+	3.22059i	0.426577	+	0.738854i	0.996566	−	0.0827988i	$-0.0263859\pi$
$19$	1.85941	+	3.22059i	0.426577	+	0.738854i	−0.569989	+	0.821652i	$0.693053\pi$
$20$		0			0
$21$	0.641185	−	4.53750i	0.139918	−	0.990163i
$22$		0			0
$23$	−6.85244	+	3.95626i	−1.42883	+	0.824936i	−0.997029	−	0.0770314i	$-0.975456\pi$
$23$	−6.85244	+	3.95626i	−1.42883	+	0.824936i	−0.431803	+	0.901968i	$0.642123\pi$
$24$		0			0
$25$	−0.900394	+	1.55953i	−0.180079	+	0.311906i
$26$		0			0
$27$	3.27666	−	4.03281i	0.630593	−	0.776114i
$28$		0			0
$29$	0.748403			0.138975			0.0694875	−	0.997583i	$-0.477864\pi$
$29$	0.748403			0.138975			0.0694875	+	0.997583i	$0.477864\pi$
$30$		0			0
$31$	−2.87254	−	1.65846i	−0.515924	−	0.297869i	0.219341	−	0.975648i	$-0.429609\pi$
$31$	−2.87254	−	1.65846i	−0.515924	−	0.297869i	−0.735265	+	0.677779i	$0.762942\pi$
$32$		0			0
$33$	−1.26951	−	1.18513i	−0.220993	−	0.206305i
$34$		0			0
$35$	−3.87702	+	2.71353i	−0.655335	+	0.458670i
$36$		0			0
$37$	3.22429	−	1.86155i	0.530071	−	0.306036i	−0.210975	−	0.977492i	$-0.567664\pi$
$37$	3.22429	−	1.86155i	0.530071	−	0.306036i	0.741045	+	0.671455i	$0.234330\pi$
$38$		0			0
$39$	0.965832	−	4.17308i	0.154657	−	0.668228i
$40$		0			0
$41$	2.01044			0.313978			0.156989	−	0.987600i	$-0.449821\pi$
$41$	2.01044			0.313978			0.156989	+	0.987600i	$0.449821\pi$
$42$		0			0
$43$		−	9.19651i		−	1.40245i	−0.712938	−	0.701227i	$-0.752636\pi$
$43$		−	9.19651i		−	1.40245i	0.712938	−	0.701227i	$-0.247364\pi$
$44$		0			0
$45$	−5.35324	+	0.368459i	−0.798013	+	0.0549266i
$46$		0			0
$47$	−1.19840	−	2.07569i	−0.174805	−	0.302771i	0.765289	−	0.643687i	$-0.222596\pi$
$47$	−1.19840	−	2.07569i	−0.174805	−	0.302771i	−0.940094	+	0.340916i	$0.889263\pi$
$48$		0			0
$49$	6.89415	−	1.21270i	0.984879	−	0.173242i
$50$		0			0
$51$	−8.43126	−	7.87089i	−1.18061	−	1.10214i
$52$		0			0
$53$	−6.33884	+	10.9792i	−0.870707	+	1.50811i	−0.00943963	+	0.999955i	$0.503005\pi$
$53$	−6.33884	+	10.9792i	−0.870707	+	1.50811i	−0.861267	+	0.508153i	$0.830329\pi$
$54$		0			0
$55$			1.79345i			0.241829i
$56$		0			0
$57$	−6.16075	+	1.87985i	−0.816012	+	0.248993i
$58$		0			0
$59$	7.34922	+	4.24308i	0.956787	+	0.552401i	0.895183	−	0.445699i	$-0.147045\pi$
$59$	7.34922	+	4.24308i	0.956787	+	0.552401i	0.0616046	+	0.998101i	$0.480378\pi$
$60$		0			0
$61$	2.02442	+	3.50640i	0.259200	+	0.448948i	0.966028	−	0.258438i	$-0.0832077\pi$
$61$	2.02442	+	3.50640i	0.259200	+	0.448948i	−0.706828	+	0.707386i	$0.749874\pi$
$62$		0			0
$63$	7.40637	+	2.85408i	0.933114	+	0.359580i
$64$		0			0
$65$	−3.83071	+	2.21166i	−0.475141	+	0.274323i
$66$		0			0
$67$	−6.89843	−	3.98281i	−0.842777	−	0.486577i	0.0154303	−	0.999881i	$-0.495088\pi$
$67$	−6.89843	−	3.98281i	−0.842777	−	0.486577i	−0.858207	+	0.513303i	$0.828422\pi$
$68$		0			0
$69$	−3.99976	−	13.1082i	−0.481514	−	1.57804i
$70$		0			0
$71$			5.46843i			0.648984i	0.945889	+	0.324492i	$0.105193\pi$
$71$			5.46843i			0.648984i	−0.945889	+	0.324492i	$0.894807\pi$
$72$		0			0
$73$	−5.68546	−	3.28250i	−0.665433	−	0.384188i	0.128911	−	0.991656i	$-0.458852\pi$
$73$	−5.68546	−	3.28250i	−0.665433	−	0.384188i	−0.794344	+	0.607468i	$0.792185\pi$
$74$		0			0
$75$	−2.27997	−	2.12844i	−0.263268	−	0.245771i
$76$		0			0
$77$	1.12165	−	2.40409i	0.127824	−	0.273972i
$78$		0			0
$79$	−2.53988	−	4.39920i	−0.285759	−	0.494949i	0.687034	−	0.726625i	$-0.258912\pi$
$79$	−2.53988	−	4.39920i	−0.285759	−	0.494949i	−0.972793	+	0.231676i	$0.925579\pi$
$80$		0			0
$81$	5.52545	+	7.10419i	0.613938	+	0.789354i
$82$		0			0
$83$			5.65457i			0.620669i	0.950627	+	0.310335i	$0.100441\pi$
$83$			5.65457i			0.620669i	−0.950627	+	0.310335i	$0.899559\pi$
$84$		0			0
$85$			11.9110i			1.29193i
$86$		0			0
$87$	−0.292288	+	1.26289i	−0.0313365	+	0.135396i
$88$		0			0
$89$	−7.39495	−	12.8084i	−0.783863	−	1.35769i	−0.929676	−	0.368379i	$-0.879913\pi$
$89$	−7.39495	−	12.8084i	−0.783863	−	1.35769i	0.145812	−	0.989312i	$-0.453420\pi$
$90$		0			0
$91$	6.51821	−	0.568916i	0.683294	−	0.0596386i
$92$		0			0
$93$	3.92043	−	4.19955i	0.406530	−	0.435473i
$94$		0			0
$95$	5.76045	+	3.32580i	0.591010	+	0.341220i
$96$		0			0
$97$		−	1.75577i		−	0.178271i	−0.996019	−	0.0891356i	$-0.971590\pi$
$97$		−	1.75577i		−	0.178271i	0.996019	−	0.0891356i	$-0.0284105\pi$
$98$		0			0
$99$	2.49565	−	1.67937i	0.250822	−	0.168783i
$100$		0			0
$101$	12.6803	+	7.32100i	1.26174	+	0.728467i	0.973411	−	0.229064i	$-0.0735667\pi$
$101$	12.6803	+	7.32100i	1.26174	+	0.728467i	0.288330	+	0.957531i	$0.406900\pi$
$102$		0			0
$103$	8.54056	−	4.93089i	0.841526	−	0.485855i	−0.0162566	−	0.999868i	$-0.505175\pi$
$103$	8.54056	−	4.93089i	0.841526	−	0.485855i	0.857783	+	0.514013i	$0.171842\pi$
$104$		0			0
$105$	−3.06476	−	7.60202i	−0.299090	−	0.741881i
$106$		0			0
$107$	3.48110	+	6.02945i	0.336531	+	0.582889i	0.983778	−	0.179392i	$-0.0574130\pi$
$107$	3.48110	+	6.02945i	0.336531	+	0.582889i	−0.647247	+	0.762281i	$0.724080\pi$
$108$		0			0
$109$	−2.36373	−	1.36470i	−0.226404	−	0.130715i	0.382508	−	0.923952i	$-0.375061\pi$
$109$	−2.36373	−	1.36470i	−0.226404	−	0.130715i	−0.608912	+	0.793238i	$0.708394\pi$
$110$		0			0
$111$	1.88202	+	6.16785i	0.178633	+	0.585426i
$112$		0			0
$113$			0.531154i			0.0499667i	0.999688	+	0.0249834i	$0.00795328\pi$
$113$			0.531154i			0.0499667i	−0.999688	+	0.0249834i	$0.992047\pi$
$114$		0			0
$115$	−7.07629	+	12.2565i	−0.659868	+	1.14292i
$116$		0			0
$117$	6.66464	+	3.25958i	0.616146	+	0.301348i
$118$		0			0
$119$	7.44929	−	15.9665i	0.682875	−	1.46364i
$120$		0			0
$121$	4.99730	+	8.65558i	0.454300	+	0.786871i
$122$		0			0
$123$	−0.785174	+	3.39251i	−0.0707967	+	0.305892i
$124$		0			0
$125$			12.1641i			1.08799i
$126$		0			0
$127$	4.52393			0.401434			0.200717	−	0.979649i	$-0.435673\pi$
$127$	4.52393			0.401434			0.200717	+	0.979649i	$0.435673\pi$
$128$		0			0
$129$	15.5186	+	3.59168i	1.36634	+	0.316230i
$130$		0			0
$131$	13.3927	−	7.73228i	1.17013	−	0.675573i	0.216416	−	0.976301i	$-0.430563\pi$
$131$	13.3927	−	7.73228i	1.17013	−	0.675573i	0.953710	+	0.300729i	$0.0972298\pi$
$132$		0			0
$133$	−5.64179	−	8.06085i	−0.489205	−	0.698964i
$134$		0			0
$135$	1.46894	−	9.17720i	0.126427	−	0.789847i
$136$		0			0
$137$	9.71195	+	5.60719i	0.829748	+	0.479055i	0.853766	−	0.520657i	$-0.174313\pi$
$137$	9.71195	+	5.60719i	0.829748	+	0.479055i	−0.0240187	+	0.999712i	$0.507646\pi$
$138$		0			0
$139$	17.9824			1.52525			0.762625	−	0.646840i	$-0.223910\pi$
$139$	17.9824			1.52525			0.762625	+	0.646840i	$0.223910\pi$
$140$		0			0
$141$	3.97066	−	1.21158i	0.334390	−	0.102033i
$142$		0			0
$143$	1.23984	−	2.14746i	0.103680	−	0.179580i
$144$		0			0
$145$	1.15928	−	0.669310i	0.0962728	−	0.0555831i
$146$		0			0
$147$	−0.646141	+	12.1071i	−0.0532928	+	0.998579i
$148$		0			0
$149$	−0.462495	−	0.801066i	−0.0378891	−	0.0656258i	0.846459	−	0.532454i	$-0.178730\pi$
$149$	−0.462495	−	0.801066i	−0.0378891	−	0.0656258i	−0.884348	+	0.466828i	$0.845397\pi$
$150$		0			0
$151$	−9.56720	+	16.5709i	−0.778568	+	1.34852i	0.154200	+	0.988040i	$0.450720\pi$
$151$	−9.56720	+	16.5709i	−0.778568	+	1.34852i	−0.932767	+	0.360479i	$0.882613\pi$
$152$		0			0
$153$	16.5745	−	11.1533i	1.33997	−	0.901693i
$154$		0			0
$155$	−5.93277			−0.476531
$156$		0			0
$157$	5.46873	−	9.47212i	0.436452	−	0.755957i	−0.560961	−	0.827842i	$-0.689568\pi$
$157$	5.46873	−	9.47212i	0.436452	−	0.755957i	0.997413	+	0.0718851i	$0.0229015\pi$
$158$		0			0
$159$	−16.0512	−	14.9844i	−1.27294	−	1.18834i
$160$		0			0
$161$	17.1510	−	12.0040i	1.35169	−	0.946050i
$162$		0			0
$163$	−9.21188	+	5.31848i	−0.721530	+	0.416576i	−0.815316	−	0.579017i	$-0.803437\pi$
$163$	−9.21188	+	5.31848i	−0.721530	+	0.416576i	0.0937855	+	0.995592i	$0.470103\pi$
$164$		0			0
$165$	−3.02635	−	0.700429i	−0.235601	−	0.0545283i
$166$		0			0
$167$	7.93040			0.613673			0.306836	−	0.951762i	$-0.400730\pi$
$167$	7.93040			0.613673			0.306836	+	0.951762i	$0.400730\pi$
$168$		0			0
$169$	−6.88419			−0.529553
$170$		0			0
$171$	−0.766076	−	11.1301i	−0.0585833	−	0.851141i
$172$		0			0
$173$	3.69882	−	2.13552i	0.281216	−	0.162360i	−0.352758	−	0.935715i	$-0.614756\pi$
$173$	3.69882	−	2.13552i	0.281216	−	0.162360i	0.633974	+	0.773354i	$0.281423\pi$
$174$		0			0
$175$	2.01443	−	4.31763i	0.152276	−	0.326382i
$176$		0			0
$177$	−10.0302	+	10.7443i	−0.753915	+	0.807590i
$178$		0			0
$179$	−3.77825	+	6.54412i	−0.282399	+	0.489130i	−0.971975	−	0.235083i	$-0.924464\pi$
$179$	−3.77825	+	6.54412i	−0.282399	+	0.489130i	0.689576	+	0.724214i	$0.257797\pi$
$180$		0			0
$181$	−5.00239			−0.371824			−0.185912	−	0.982566i	$-0.559524\pi$
$181$	−5.00239			−0.371824			−0.185912	+	0.982566i	$0.559524\pi$
$182$		0			0
$183$	−6.70749	+	2.04668i	−0.495832	+	0.151295i
$184$		0			0
$185$	3.32963	−	5.76708i	0.244799	−	0.424004i
$186$		0			0
$187$	−3.33859	−	5.78261i	−0.244142	−	0.422867i
$188$		0			0
$189$	−7.70864	+	11.3832i	−0.560721	+	0.828005i
$190$		0			0
$191$	−10.4891	+	6.05587i	−0.758963	+	0.438188i	−0.828923	−	0.559362i	$-0.811046\pi$
$191$	−10.4891	+	6.05587i	−0.758963	+	0.438188i	0.0699601	+	0.997550i	$0.477713\pi$
$192$		0			0
$193$	0.592437	−	1.02613i	0.0426445	−	0.0738625i	−0.843915	−	0.536476i	$-0.819755\pi$
$193$	0.592437	−	1.02613i	0.0426445	−	0.0738625i	0.886560	+	0.462614i	$0.153088\pi$
$194$		0			0
$195$	−2.23598	−	7.32787i	−0.160122	−	0.524760i
$196$		0			0
$197$	−19.5111			−1.39011			−0.695054	−	0.718957i	$-0.744620\pi$
$197$	−19.5111			−1.39011			−0.695054	+	0.718957i	$0.744620\pi$
$198$		0			0
$199$	12.7632	+	7.36884i	0.904760	+	0.522363i	0.878741	−	0.477298i	$-0.158384\pi$
$199$	12.7632	+	7.36884i	0.904760	+	0.522363i	0.0260186	+	0.999661i	$0.491717\pi$
$200$		0			0
$201$	9.41494	−	10.0852i	0.664079	−	0.711358i
$202$		0			0
$203$	−1.97259	+	0.172170i	−0.138449	+	0.0120839i
$204$		0			0
$205$	3.11418	−	1.79797i	0.217503	−	0.125576i
$206$		0			0
$207$	23.6815	−	1.62998i	1.64598	−	0.113291i
$208$		0			0
$209$	−3.72883			−0.257929
$210$		0			0
$211$			14.9240i			1.02741i	0.857967	+	0.513704i	$0.171727\pi$
$211$			14.9240i			1.02741i	−0.857967	+	0.513704i	$0.828273\pi$
$212$		0			0
$213$	−9.22768	−	2.13569i	−0.632270	−	0.146335i
$214$		0			0
$215$	−8.22459	−	14.2454i	−0.560913	−	0.971529i
$216$		0			0
$217$	7.95278	+	3.71044i	0.539870	+	0.251881i
$218$		0			0
$219$	7.75949	−	8.31193i	0.524338	−	0.561668i
$220$		0			0
$221$	8.23422	−	14.2621i	0.553894	−	0.959372i
$222$		0			0
$223$			7.62187i			0.510398i	0.966889	+	0.255199i	$0.0821410\pi$
$223$			7.62187i			0.510398i	−0.966889	+	0.255199i	$0.917859\pi$
$224$		0			0
$225$	4.48206	−	3.01607i	0.298804	−	0.201071i
$226$		0			0
$227$	−13.6531	−	7.88264i	−0.906190	−	0.523189i	−0.0269870	−	0.999636i	$-0.508591\pi$
$227$	−13.6531	−	7.88264i	−0.906190	−	0.523189i	−0.879203	+	0.476446i	$0.841925\pi$
$228$		0			0
$229$	−8.82193	−	15.2800i	−0.582970	−	1.00973i	−0.995125	−	0.0986198i	$-0.968557\pi$
$229$	−8.82193	−	15.2800i	−0.582970	−	1.00973i	0.412155	−	0.911114i	$-0.364776\pi$
$230$		0			0
$231$	3.61871	+	2.83164i	0.238094	+	0.186308i
$232$		0			0
$233$	−15.7079	+	9.06896i	−1.02906	+	0.594127i	−0.916715	−	0.399542i	$-0.869169\pi$
$233$	−15.7079	+	9.06896i	−1.02906	+	0.594127i	−0.112344	+	0.993669i	$0.535836\pi$
$234$		0			0
$235$	−3.71266	−	2.14350i	−0.242187	−	0.139827i
$236$		0			0
$237$	8.41536	−	2.56781i	0.546637	−	0.166797i
$238$		0			0
$239$		−	5.41040i		−	0.349970i	−0.984571	−	0.174985i	$-0.944012\pi$
$239$		−	5.41040i		−	0.349970i	0.984571	−	0.174985i	$-0.0559877\pi$
$240$		0			0
$241$	−18.6025	−	10.7401i	−1.19829	−	0.691834i	−0.238117	−	0.971236i	$-0.576530\pi$
$241$	−18.6025	−	10.7401i	−1.19829	−	0.691834i	−0.960174	+	0.279403i	$0.909863\pi$
$242$		0			0
$243$	−14.1459	+	6.54936i	−0.907459	+	0.420142i
$244$		0			0
$245$	9.59453	−	8.04403i	0.612972	−	0.513914i
$246$		0			0
$247$	−4.59834	−	7.96457i	−0.292586	−	0.506773i
$248$		0			0
$249$	−9.54177	−	2.20838i	−0.604685	−	0.139951i
$250$		0			0
$251$			19.8553i			1.25325i	0.779319	+	0.626627i	$0.215565\pi$
$251$			19.8553i			1.25325i	−0.779319	+	0.626627i	$0.784435\pi$
$252$		0			0
$253$		−	7.93382i		−	0.498795i
$254$		0			0
$255$	−20.0991	−	4.65181i	−1.25865	−	0.291308i
$256$		0			0
$257$	−4.36616	−	7.56240i	−0.272353	−	0.471730i	0.697111	−	0.716964i	$-0.254469\pi$
$257$	−4.36616	−	7.56240i	−0.272353	−	0.471730i	−0.969464	+	0.245234i	$0.921135\pi$
$258$		0			0
$259$	−8.07012	+	5.64828i	−0.501453	+	0.350967i
$260$		0			0
$261$	−2.01690	−	0.986439i	−0.124843	−	0.0610590i
$262$		0			0
$263$	17.1429	+	9.89747i	1.05708	+	0.610304i	0.924623	−	0.380885i	$-0.124381\pi$
$263$	17.1429	+	9.89747i	1.05708	+	0.610304i	0.132455	+	0.991189i	$0.457714\pi$
$264$		0			0
$265$			22.6757i			1.39296i
$266$		0			0
$267$	24.5016	−	7.47627i	1.49947	−	0.457540i
$268$		0			0
$269$	−0.805574	−	0.465098i	−0.0491167	−	0.0283575i	0.475241	−	0.879856i	$-0.342361\pi$
$269$	−0.805574	−	0.465098i	−0.0491167	−	0.0283575i	−0.524357	+	0.851498i	$0.675694\pi$
$270$		0			0
$271$	7.45646	−	4.30499i	0.452948	−	0.261509i	−0.256127	−	0.966643i	$-0.582446\pi$
$271$	7.45646	−	4.30499i	0.452948	−	0.261509i	0.709074	+	0.705134i	$0.249113\pi$
$272$		0			0
$273$	−1.58566	+	11.2213i	−0.0959685	+	0.679144i
$274$		0			0
$275$	−0.902819	−	1.56373i	−0.0544420	−	0.0942964i
$276$		0			0
$277$	25.5583	+	14.7561i	1.53565	+	0.886607i	0.999086	+	0.0427456i	$0.0136105\pi$
$277$	25.5583	+	14.7561i	1.53565	+	0.886607i	0.536562	+	0.843861i	$0.319723\pi$
$278$		0			0
$279$	5.55539	+	8.25565i	0.332593	+	0.494253i
$280$		0			0
$281$			21.3260i			1.27220i	0.771605	+	0.636102i	$0.219454\pi$
$281$			21.3260i			1.27220i	−0.771605	+	0.636102i	$0.780546\pi$
$282$		0			0
$283$	10.4247	−	18.0561i	0.619684	−	1.07332i	−0.369860	−	0.929088i	$-0.620594\pi$
$283$	10.4247	−	18.0561i	0.619684	−	1.07332i	0.989543	−	0.144236i	$-0.0460724\pi$
$284$		0			0
$285$	−7.86184	+	8.42156i	−0.465695	+	0.498850i
$286$		0			0
$287$	−5.29898	+	0.462500i	−0.312789	+	0.0273005i
$288$		0			0
$289$	−13.6728	−	23.6820i	−0.804284	−	1.39306i
$290$		0			0
$291$	2.96276	+	0.685712i	0.173680	+	0.0401972i
$292$		0			0
$293$			13.1058i			0.765652i	0.923821	+	0.382826i	$0.125049\pi$
$293$			13.1058i			0.765652i	−0.923821	+	0.382826i	$0.874951\pi$
$294$		0			0
$295$	15.1786			0.883733
$296$		0			0
$297$	1.85918	+	4.86714i	0.107880	+	0.282420i
$298$		0			0
$299$	16.9462	−	9.78389i	0.980023	−	0.565817i
$300$		0			0
$301$	2.11565	+	24.2395i	0.121944	+	1.39714i
$302$		0			0
$303$	−17.3061	+	18.5382i	−0.994208	+	1.06499i
$304$		0			0
$305$	6.27166	+	3.62094i	0.359114	+	0.207335i
$306$		0			0
$307$	−18.6425			−1.06398			−0.531992	−	0.846750i	$-0.678556\pi$
$307$	−18.6425			−1.06398			−0.531992	+	0.846750i	$0.678556\pi$
$308$		0			0
$309$	4.98511	+	16.3375i	0.283593	+	0.929406i
$310$		0			0
$311$	−9.92896	+	17.1975i	−0.563020	+	0.975179i	0.434211	+	0.900811i	$0.357027\pi$
$311$	−9.92896	+	17.1975i	−0.563020	+	0.975179i	−0.997231	+	0.0743677i	$0.976306\pi$
$312$		0			0
$313$	2.33108	−	1.34585i	0.131760	−	0.0760718i	−0.432671	−	0.901552i	$-0.642429\pi$
$313$	2.33108	−	1.34585i	0.131760	−	0.0760718i	0.564431	+	0.825480i	$0.309096\pi$
$314$		0			0
$315$	14.0249	−	2.20267i	0.790215	−	0.124106i
$316$		0			0
$317$	−5.35288	−	9.27147i	−0.300648	−	0.520737i	0.675635	−	0.737236i	$-0.263870\pi$
$317$	−5.35288	−	9.27147i	−0.300648	−	0.520737i	−0.976283	+	0.216499i	$0.930536\pi$
$318$		0			0
$319$	−0.375209	+	0.649881i	−0.0210077	+	0.0363864i
$320$		0			0
$321$	−11.5339	+	3.51938i	−0.643760	+	0.196433i
$322$		0			0
$323$	−24.7645			−1.37794
$324$		0			0
$325$	2.22669	−	3.85674i	0.123514	−	0.213933i
$326$		0			0
$327$	3.22601	−	3.45569i	0.178399	−	0.191100i
$328$		0			0
$329$	3.63618	+	5.19528i	0.200469	+	0.286425i
$330$		0			0
$331$	18.8525	−	10.8845i	1.03623	−	0.598266i	0.117465	−	0.993077i	$-0.462523\pi$
$331$	18.8525	−	10.8845i	1.03623	−	0.598266i	0.918762	+	0.394811i	$0.129190\pi$
$332$		0			0
$333$	−11.1429	+	0.766958i	−0.610628	+	0.0420290i
$334$		0			0
$335$	−14.2476			−0.778428
$336$		0			0
$337$	−11.3104			−0.616116			−0.308058	−	0.951368i	$-0.599679\pi$
$337$	−11.3104			−0.616116			−0.308058	+	0.951368i	$0.599679\pi$
$338$		0			0
$339$	−0.896293	−	0.207441i	−0.0486799	−	0.0112667i
$340$		0			0
$341$	2.88028	−	1.66293i	0.155976	−	0.0900527i
$342$		0			0
$343$	−17.8922	+	4.78234i	−0.966086	+	0.258222i
$344$		0			0
$345$	−17.9185	−	16.7276i	−0.964702	−	0.900585i
$346$		0			0
$347$	9.94032	−	17.2171i	0.533624	−	0.924265i	−0.465604	−	0.884993i	$-0.654163\pi$
$347$	9.94032	−	17.2171i	0.533624	−	0.924265i	0.999229	−	0.0392715i	$-0.0125037\pi$
$348$		0			0
$349$	−9.45348			−0.506033			−0.253017	−	0.967462i	$-0.581423\pi$
$349$	−9.45348			−0.506033			−0.253017	+	0.967462i	$0.581423\pi$
$350$		0			0
$351$	−8.10323	+	9.97319i	−0.432518	+	0.532330i
$352$		0			0
$353$	−8.48135	+	14.6901i	−0.451417	+	0.781877i	−0.998474	−	0.0552182i	$-0.982415\pi$
$353$	−8.48135	+	14.6901i	−0.451417	+	0.781877i	0.547057	+	0.837095i	$0.315748\pi$
$354$		0			0
$355$	4.89051	+	8.47062i	0.259561	+	0.449574i
$356$		0			0
$357$	24.0332	+	18.8059i	1.27197	+	0.995316i
$358$		0			0
$359$	−18.2162	+	10.5171i	−0.961413	+	0.555072i	−0.896608	−	0.442826i	$-0.853976\pi$
$359$	−18.2162	+	10.5171i	−0.961413	+	0.555072i	−0.0648056	+	0.997898i	$0.520643\pi$
$360$		0			0
$361$	2.58521	−	4.47771i	0.136064	−	0.235669i
$362$		0			0
$363$	−16.5575	+	5.05225i	−0.869044	+	0.265174i
$364$		0			0
$365$	−11.7424			−0.614625
$366$		0			0
$367$	−1.24875	−	0.720966i	−0.0651842	−	0.0376341i	0.467054	−	0.884229i	$-0.345315\pi$
$367$	−1.24875	−	0.720966i	−0.0651842	−	0.0376341i	−0.532238	+	0.846595i	$0.678649\pi$
$368$		0			0
$369$	−5.41802	−	2.64988i	−0.282051	−	0.137947i
$370$		0			0
$371$	14.1817	−	30.3964i	0.736278	−	1.57810i
$372$		0			0
$373$	−18.8362	+	10.8751i	−0.975302	+	0.563091i	−0.900848	−	0.434134i	$-0.857055\pi$
$373$	−18.8362	+	10.8751i	−0.975302	+	0.563091i	−0.0744535	+	0.997224i	$0.523721\pi$
$374$		0			0
$375$	−20.5263	−	4.75068i	−1.05997	−	0.245324i
$376$		0			0
$377$	−1.85081			−0.0953217
$378$		0			0
$379$		−	1.82298i		−	0.0936402i	−0.998903	−	0.0468201i	$-0.985091\pi$
$379$		−	1.82298i		−	0.0936402i	0.998903	−	0.0468201i	$-0.0149087\pi$
$380$		0			0
$381$	−1.76681	+	7.63389i	−0.0905167	+	0.391096i
$382$		0			0
$383$	4.81069	+	8.33236i	0.245815	+	0.425763i	0.962360	−	0.271777i	$-0.0876112\pi$
$383$	4.81069	+	8.33236i	0.245815	+	0.425763i	−0.716546	+	0.697540i	$0.754278\pi$
$384$		0			0
$385$	−0.412582	−	4.72705i	−0.0210271	−	0.240913i
$386$		0			0
$387$	−12.1215	+	24.7841i	−0.616172	+	1.25984i
$388$		0			0
$389$	14.0629	−	24.3576i	0.713017	−	1.23498i	−0.250703	−	0.968064i	$-0.580662\pi$
$389$	14.0629	−	24.3576i	0.713017	−	1.23498i	0.963719	−	0.266917i	$-0.0860050\pi$
$390$		0			0
$391$		−	52.6914i		−	2.66472i
$392$		0			0
$393$	7.81730	+	25.6193i	0.394331	+	1.29232i
$394$		0			0
$395$	−7.86857	−	4.54292i	−0.395911	−	0.228579i
$396$		0			0
$397$	9.42646	+	16.3271i	0.473101	+	0.819434i	0.999526	−	0.0307871i	$-0.00980139\pi$
$397$	9.42646	+	16.3271i	0.473101	+	0.819434i	−0.526425	+	0.850221i	$0.676468\pi$
$398$		0			0
$399$	15.8056	−	6.37206i	0.791271	−	0.319002i
$400$		0			0
$401$	−5.22718	+	3.01791i	−0.261033	+	0.150707i	−0.624806	−	0.780780i	$-0.714822\pi$
$401$	−5.22718	+	3.01791i	−0.261033	+	0.150707i	0.363773	+	0.931488i	$0.381488\pi$
$402$		0			0
$403$	7.10385	+	4.10141i	0.353868	+	0.204306i
$404$		0			0
$405$	14.9123	+	6.06290i	0.740999	+	0.301268i
$406$		0			0
$407$			3.73312i			0.185044i
$408$		0			0
$409$	22.6629	+	13.0844i	1.12061	+	0.646984i	0.941556	−	0.336856i	$-0.109364\pi$
$409$	22.6629	+	13.0844i	1.12061	+	0.646984i	0.179052	+	0.983840i	$0.442697\pi$
$410$		0			0
$411$	−13.2548	+	14.1985i	−0.653812	+	0.700360i
$412$		0			0
$413$	−20.3467	−	9.49292i	−1.00120	−	0.467116i
$414$		0			0
$415$	5.05698	+	8.75894i	0.248237	+	0.429959i
$416$		0			0
$417$	−7.02301	+	30.3444i	−0.343918	+	1.48597i
$418$		0			0
$419$		−	2.51866i		−	0.123045i	−0.998106	−	0.0615223i	$-0.980404\pi$
$419$		−	2.51866i		−	0.123045i	0.998106	−	0.0615223i	$-0.0195955\pi$
$420$		0			0
$421$		−	33.4873i		−	1.63207i	−0.578003	−	0.816034i	$-0.696168\pi$
$421$		−	33.4873i		−	1.63207i	0.578003	−	0.816034i	$-0.303832\pi$
$422$		0			0
$423$	0.493742	+	7.17345i	0.0240066	+	0.348785i
$424$		0			0
$425$	−5.99595	−	10.3853i	−0.290846	−	0.503761i
$426$		0			0
$427$	−6.14247	−	8.77620i	−0.297255	−	0.424710i
$428$		0			0
$429$	3.13951	+	2.93085i	0.151577	+	0.141503i
$430$		0			0
$431$	12.0003	+	6.92836i	0.578033	+	0.333727i	0.760351	−	0.649512i	$-0.225027\pi$
$431$	12.0003	+	6.92836i	0.578033	+	0.333727i	−0.182319	+	0.983240i	$0.558360\pi$
$432$		0			0
$433$		−	9.79368i		−	0.470654i	−0.971916	−	0.235327i	$-0.924384\pi$
$433$		−	9.79368i		−	0.470654i	0.971916	−	0.235327i	$-0.0756161\pi$
$434$		0			0
$435$	0.676669	+	2.21762i	0.0324438	+	0.106327i
$436$		0			0
$437$	−25.4829	−	14.7126i	−1.21901	−	0.703798i
$438$		0			0
$439$	−6.99463	+	4.03835i	−0.333835	+	0.192740i	−0.657543	−	0.753417i	$-0.728404\pi$
$439$	−6.99463	+	4.03835i	−0.333835	+	0.192740i	0.323707	+	0.946157i	$0.395071\pi$
$440$		0			0
$441$	−20.1778	−	5.81875i	−0.960846	−	0.277083i
$442$		0			0
$443$	−8.84884	−	15.3266i	−0.420421	−	0.728191i	0.575559	−	0.817760i	$-0.304784\pi$
$443$	−8.84884	−	15.3266i	−0.420421	−	0.728191i	−0.995981	+	0.0895692i	$0.971451\pi$
$444$		0			0
$445$	−22.9096	−	13.2269i	−1.08602	−	0.627014i
$446$		0			0
$447$	1.53238	−	0.467581i	0.0724791	−	0.0221158i
$448$		0			0
$449$		−	19.4650i		−	0.918609i	−0.888279	−	0.459305i	$-0.848099\pi$
$449$		−	19.4650i		−	0.918609i	0.888279	−	0.459305i	$-0.151901\pi$
$450$		0			0
$451$	−1.00793	+	1.74578i	−0.0474614	+	0.0822056i
$452$		0			0
$453$	−24.2260	−	22.6159i	−1.13824	−	1.06259i
$454$		0			0
$455$	9.58793	−	6.71059i	0.449489	−	0.314597i
$456$		0			0
$457$	7.75626	+	13.4342i	0.362823	+	0.628427i	0.988424	−	0.151715i	$-0.0484797\pi$
$457$	7.75626	+	13.4342i	0.362823	+	0.628427i	−0.625601	+	0.780143i	$0.715146\pi$
$458$		0			0
$459$	12.3475	+	32.3245i	0.576331	+	1.50878i
$460$		0			0
$461$		−	0.857290i		−	0.0399280i	−0.999801	−	0.0199640i	$-0.993645\pi$
$461$		−	0.857290i		−	0.0399280i	0.999801	−	0.0199640i	$-0.00635516\pi$
$462$		0			0
$463$	−37.5731			−1.74617			−0.873086	−	0.487566i	$-0.837885\pi$
$463$	−37.5731			−1.74617			−0.873086	+	0.487566i	$0.837885\pi$
$464$		0			0
$465$	2.31703	−	10.0112i	0.107450	−	0.464259i
$466$		0			0
$467$	−8.69155	+	5.01807i	−0.402197	+	0.232208i	−0.687431	−	0.726249i	$-0.741262\pi$
$467$	−8.69155	+	5.01807i	−0.402197	+	0.232208i	0.285235	+	0.958458i	$0.407928\pi$
$468$		0			0
$469$	19.0986	+	8.91063i	0.881893	+	0.411455i
$470$		0			0
$471$	13.8479	+	12.9275i	0.638076	+	0.595668i
$472$		0			0
$473$	7.98586	+	4.61064i	0.367190	+	0.211997i
$474$		0			0
$475$	−6.69680			−0.307270
$476$		0			0
$477$	31.5540	−	21.2333i	1.44476	−	0.972208i
$478$		0			0
$479$	11.0594	−	19.1555i	0.505318	−	0.875237i	−0.494663	−	0.869085i	$-0.664708\pi$
$479$	11.0594	−	19.1555i	0.505318	−	0.875237i	0.999981	−	0.00615194i	$-0.00195824\pi$
$480$		0			0
$481$	−7.97373	+	4.60364i	−0.363571	+	0.209908i
$482$		0			0
$483$	13.5578	+	33.6296i	0.616902	+	1.53020i
$484$		0			0
$485$	−1.57021	−	2.71969i	−0.0712997	−	0.123495i
$486$		0			0
$487$	−11.2659	+	19.5131i	−0.510506	+	0.884223i	0.489419	+	0.872049i	$0.337209\pi$
$487$	−11.2659	+	19.5131i	−0.510506	+	0.884223i	−0.999926	+	0.0121746i	$0.996125\pi$
$488$		0			0
$489$	−5.37696	−	17.6217i	−0.243155	−	0.796879i
$490$		0			0
$491$	−25.1085			−1.13313			−0.566565	−	0.824017i	$-0.691728\pi$
$491$	−25.1085			−1.13313			−0.566565	+	0.824017i	$0.691728\pi$
$492$		0			0
$493$	−2.49190	+	4.31610i	−0.112230	+	0.194387i
$494$		0			0
$495$	2.36387	−	4.83325i	0.106248	−	0.217238i
$496$		0			0
$497$	−1.25801	−	14.4133i	−0.0564295	−	0.646526i
$498$		0			0
$499$	9.19695	−	5.30986i	0.411712	−	0.237702i	−0.279813	−	0.960054i	$-0.590273\pi$
$499$	9.19695	−	5.30986i	0.411712	−	0.237702i	0.691525	+	0.722353i	$0.256939\pi$
$500$		0			0
$501$	−3.09721	+	13.3821i	−0.138373	+	0.597869i
$502$		0			0
$503$	13.3046			0.593223			0.296612	−	0.954998i	$-0.404143\pi$
$503$	13.3046			0.593223			0.296612	+	0.954998i	$0.404143\pi$
$504$		0			0
$505$	26.1892			1.16540
$506$		0			0
$507$	2.68861	−	11.6167i	0.119405	−	0.515916i
$508$		0			0
$509$	20.2595	−	11.6968i	0.897985	−	0.518452i	0.0214392	−	0.999770i	$-0.493175\pi$
$509$	20.2595	−	11.6968i	0.897985	−	0.518452i	0.876546	+	0.481318i	$0.159842\pi$
$510$		0			0
$511$	15.7405	+	7.34385i	0.696318	+	0.324873i
$512$		0			0
$513$	19.0806	+	3.05413i	0.842431	+	0.134843i
$514$		0			0
$515$	8.81956	−	15.2759i	0.388636	−	0.673138i
$516$		0			0
$517$	2.40326			0.105695
$518$		0			0
$519$	2.15900	+	7.07558i	0.0947695	+	0.310584i
$520$		0			0
$521$	0.735700	−	1.27427i	0.0322316	−	0.0558267i	−0.849460	−	0.527654i	$-0.823072\pi$
$521$	0.735700	−	1.27427i	0.0322316	−	0.0558267i	0.881691	+	0.471827i	$0.156405\pi$
$522$		0			0
$523$	5.30372	+	9.18631i	0.231915	+	0.401689i	0.958372	−	0.285523i	$-0.0921674\pi$
$523$	5.30372	+	9.18631i	0.231915	+	0.401689i	−0.726456	+	0.687213i	$0.758834\pi$
$524$		0			0
$525$	6.49904	+	5.08548i	0.283641	+	0.221949i
$526$		0			0
$527$	19.1290	−	11.0441i	0.833272	−	0.481090i
$528$		0			0
$529$	19.8039	−	34.3014i	0.861040	−	1.49137i
$530$		0			0
$531$	−14.2131	−	21.1216i	−0.616797	−	0.916597i
$532$		0			0
$533$	−4.97185			−0.215355
$534$		0			0
$535$	10.7845	+	6.22642i	0.466254	+	0.269192i
$536$		0			0
$537$	−9.56725	−	8.93138i	−0.412857	−	0.385417i
$538$		0			0
$539$	−2.40331	+	6.59457i	−0.103518	+	0.284048i
$540$		0			0
$541$	14.0009	−	8.08343i	0.601946	−	0.347534i	−0.167861	−	0.985811i	$-0.553686\pi$
$541$	14.0009	−	8.08343i	0.601946	−	0.347534i	0.769807	+	0.638277i	$0.220353\pi$
$542$		0			0
$543$	1.95367	−	8.44125i	0.0838402	−	0.362249i
$544$		0			0
$545$	−4.88190			−0.209118
$546$		0			0
$547$			12.4170i			0.530914i	0.964123	+	0.265457i	$0.0855228\pi$
$547$			12.4170i			0.530914i	−0.964123	+	0.265457i	$0.914477\pi$
$548$		0			0
$549$	−0.834061	−	12.1178i	−0.0355969	−	0.517177i
$550$		0			0
$551$	1.39159	+	2.41030i	0.0592836	+	0.102682i
$552$		0			0
$553$	7.70648	+	11.0108i	0.327713	+	0.468228i
$554$		0			0
$555$	8.43126	+	7.87089i	0.357887	+	0.334101i
$556$		0			0
$557$	−10.7167	+	18.5619i	−0.454081	+	0.786492i	−0.998635	−	0.0522341i	$-0.983366\pi$
$557$	−10.7167	+	18.5619i	−0.454081	+	0.786492i	0.544554	+	0.838726i	$0.316699\pi$
$558$		0			0
$559$			22.7431i			0.961931i
$560$		0			0
$561$	11.0617	−	3.37530i	0.467026	−	0.142505i
$562$		0			0
$563$	17.9430	+	10.3594i	0.756205	+	0.436595i	0.827932	−	0.560829i	$-0.189517\pi$
$563$	17.9430	+	10.3594i	0.756205	+	0.436595i	−0.0717262	+	0.997424i	$0.522851\pi$
$564$		0			0
$565$	0.475020	+	0.822758i	0.0199842	+	0.0346137i
$566$		0			0
$567$	−16.1979	−	17.4536i	−0.680248	−	0.732982i
$568$		0			0
$569$	23.8691	−	13.7808i	1.00064	−	0.577722i	0.0922056	−	0.995740i	$-0.470608\pi$
$569$	23.8691	−	13.7808i	1.00064	−	0.577722i	0.908439	+	0.418018i	$0.137275\pi$
$570$		0			0
$571$	−0.339940	−	0.196264i	−0.0142260	−	0.00821340i	0.492870	−	0.870103i	$-0.335948\pi$
$571$	−0.339940	−	0.196264i	−0.0142260	−	0.00821340i	−0.507096	+	0.861889i	$0.669281\pi$
$572$		0			0
$573$	−6.12246	−	20.0649i	−0.255770	−	0.838222i
$574$		0			0
$575$		−	14.2488i		−	0.594214i
$576$		0			0
$577$	−12.7927	−	7.38589i	−0.532569	−	0.307479i	0.209493	−	0.977810i	$-0.432819\pi$
$577$	−12.7927	−	7.38589i	−0.532569	−	0.307479i	−0.742062	+	0.670331i	$0.766152\pi$
$578$		0			0
$579$	1.50016	+	1.40046i	0.0623447	+	0.0582011i
$580$		0			0
$581$	−1.30083	−	14.9039i	−0.0539675	−	0.618319i
$582$		0			0
$583$	−6.35591	−	11.0088i	−0.263235	−	0.455936i
$584$		0			0
$585$	13.2386	−	0.911205i	0.547350	−	0.0376737i
$586$		0			0
$587$		−	3.51421i		−	0.145047i	−0.997367	−	0.0725236i	$-0.976895\pi$
$587$		−	3.51421i		−	0.145047i	0.997367	−	0.0725236i	$-0.0231052\pi$
$588$		0			0
$589$		−	12.3350i		−	0.508256i
$590$		0			0
$591$	7.62003	−	32.9239i	0.313446	−	1.35431i
$592$		0			0
$593$	17.8824	+	30.9732i	0.734342	+	1.27192i	0.955012	+	0.296568i	$0.0958423\pi$
$593$	17.8824	+	30.9732i	0.734342	+	1.27192i	−0.220670	+	0.975349i	$0.570824\pi$
$594$		0			0
$595$	−2.74011	−	31.3941i	−0.112334	−	1.28703i
$596$		0			0
$597$	−17.4192	+	18.6593i	−0.712919	+	0.763676i
$598$		0			0
$599$	−35.4819	−	20.4855i	−1.44975	−	0.837014i	−0.451284	−	0.892380i	$-0.649034\pi$
$599$	−35.4819	−	20.4855i	−1.44975	−	0.837014i	−0.998466	+	0.0553669i	$0.982367\pi$
$600$		0			0
$601$			36.1540i			1.47475i	0.675482	+	0.737377i	$0.263936\pi$
$601$			36.1540i			1.47475i	−0.675482	+	0.737377i	$0.736064\pi$
$602$		0			0
$603$	13.3413	+	19.8260i	0.543300	+	0.807376i
$604$		0			0
$605$	15.4817	+	8.93835i	0.629419	+	0.363395i
$606$		0			0
$607$	−9.04038	+	5.21946i	−0.366938	+	0.211851i	−0.672120	−	0.740443i	$-0.734616\pi$
$607$	−9.04038	+	5.21946i	−0.366938	+	0.211851i	0.305182	+	0.952294i	$0.401283\pi$
$608$		0			0
$609$	0.479865	−	3.39588i	0.0194451	−	0.137608i
$610$		0			0
$611$	2.96367	+	5.13323i	0.119897	+	0.207668i
$612$		0			0
$613$	5.37925	+	3.10571i	0.217266	+	0.125439i	0.604684	−	0.796466i	$-0.293300\pi$
$613$	5.37925	+	3.10571i	0.217266	+	0.125439i	−0.387418	+	0.921904i	$0.626633\pi$
$614$		0			0
$615$	1.81774	+	5.95720i	0.0732984	+	0.240217i
$616$		0			0
$617$		−	22.4963i		−	0.905669i	−0.891595	−	0.452834i	$-0.850413\pi$
$617$		−	22.4963i		−	0.905669i	0.891595	−	0.452834i	$-0.149587\pi$
$618$		0			0
$619$	−14.1624	+	24.5300i	−0.569235	+	0.985943i	0.427407	+	0.904059i	$0.359427\pi$
$619$	−14.1624	+	24.5300i	−0.569235	+	0.985943i	−0.996642	+	0.0818842i	$0.973906\pi$
$620$		0			0
$621$	−6.49827	+	40.5978i	−0.260767	+	1.62914i
$622$		0			0
$623$	22.4377	+	32.0584i	0.898947	+	1.28439i
$624$		0			0
$625$	6.37661	+	11.0446i	0.255064	+	0.441785i
$626$		0			0
$627$	1.45629	−	6.29220i	0.0581585	−	0.251286i
$628$		0			0
$629$			24.7930i			0.988563i
$630$		0			0
$631$	−8.51542			−0.338993			−0.169497	−	0.985531i	$-0.554214\pi$
$631$	−8.51542			−0.338993			−0.169497	+	0.985531i	$0.554214\pi$
$632$		0			0
$633$	−25.1834	−	5.82853i	−1.00095	−	0.231663i
$634$		0			0
$635$	7.00758	−	4.04583i	0.278087	−	0.160554i
$636$		0			0
$637$	−17.0494	+	2.99902i	−0.675520	+	0.118825i
$638$		0			0
$639$	7.20771	−	14.7371i	0.285133	−	0.582992i
$640$		0			0
$641$	0.0793494	+	0.0458124i	0.00313411	+	0.00180948i	0.501566	−	0.865119i	$-0.332757\pi$
$641$	0.0793494	+	0.0458124i	0.00313411	+	0.00180948i	−0.498432	+	0.866929i	$0.666091\pi$
$642$		0			0
$643$	5.89351			0.232417			0.116209	−	0.993225i	$-0.462926\pi$
$643$	5.89351			0.232417			0.116209	+	0.993225i	$0.462926\pi$
$644$		0			0
$645$	27.2505	−	8.31503i	1.07299	−	0.327404i
$646$		0			0
$647$	4.05903	−	7.03045i	0.159577	−	0.276396i	−0.775139	−	0.631791i	$-0.782320\pi$
$647$	4.05903	−	7.03045i	0.159577	−	0.276396i	0.934716	+	0.355395i	$0.115654\pi$
$648$		0			0
$649$	−7.36901	+	4.25450i	−0.289259	+	0.167004i
$650$		0			0
$651$	−9.36710	+	11.9708i	−0.367126	+	0.469172i
$652$		0			0
$653$	16.7312	+	28.9792i	0.654741	+	1.13404i	0.981959	+	0.189095i	$0.0605555\pi$
$653$	16.7312	+	28.9792i	0.654741	+	1.13404i	−0.327218	+	0.944949i	$0.606111\pi$
$654$		0			0
$655$	13.8302	−	23.9547i	0.540392	−	0.935986i
$656$		0			0
$657$	10.9955	+	16.3399i	0.428974	+	0.637481i
$658$		0			0
$659$	15.5448			0.605540			0.302770	−	0.953064i	$-0.402089\pi$
$659$	15.5448			0.605540			0.302770	+	0.953064i	$0.402089\pi$
$660$		0			0
$661$	−15.4190	+	26.7065i	−0.599731	+	1.03876i	0.393130	+	0.919483i	$0.371392\pi$
$661$	−15.4190	+	26.7065i	−0.599731	+	1.03876i	−0.992861	+	0.119281i	$0.961941\pi$
$662$		0			0
$663$	20.8506	+	19.4648i	0.809772	+	0.755952i
$664$		0			0
$665$	−15.9481	−	7.44072i	−0.618441	−	0.288539i
$666$		0			0
$667$	−5.12838	+	2.96087i	−0.198572	+	0.114646i
$668$		0			0
$669$	−12.8615	−	2.97671i	−0.497254	−	0.115086i
$670$		0			0
$671$	−4.05974			−0.156725
$672$		0			0
$673$	3.84855			0.148351			0.0741753	−	0.997245i	$-0.476368\pi$
$673$	3.84855			0.148351			0.0741753	+	0.997245i	$0.476368\pi$
$674$		0			0
$675$	3.33899	+	8.74115i	0.128518	+	0.336447i
$676$		0			0
$677$	32.5497	−	18.7926i	1.25099	−	0.722257i	0.279680	−	0.960093i	$-0.409772\pi$
$677$	32.5497	−	18.7926i	1.25099	−	0.722257i	0.971305	+	0.237836i	$0.0764382\pi$
$678$		0			0
$679$	0.403913	+	4.62773i	0.0155008	+	0.177596i
$680$		0			0
$681$	18.6337	−	19.9604i	0.714046	−	0.764883i
$682$		0			0
$683$	−1.02051	+	1.76757i	−0.0390487	+	0.0676343i	−0.884889	−	0.465802i	$-0.845766\pi$
$683$	−1.02051	+	1.76757i	−0.0390487	+	0.0676343i	0.845841	+	0.533436i	$0.179099\pi$
$684$		0			0
$685$	20.0584			0.766394
$686$		0			0
$687$	29.2296	−	8.91894i	1.11518	−	0.340279i
$688$		0			0
$689$	15.6761	−	27.1517i	0.597210	−	1.03440i
$690$		0			0
$691$	−11.7334	−	20.3229i	−0.446360	−	0.773119i	0.551786	−	0.833986i	$-0.313947\pi$
$691$	−11.7334	−	20.3229i	−0.446360	−	0.773119i	−0.998146	+	0.0608673i	$0.980613\pi$
$692$		0			0
$693$	−6.19151	+	5.00049i	−0.235196	+	0.189953i
$694$		0			0
$695$	27.8548	−	16.0820i	1.05659	−	0.610025i
$696$		0			0
$697$	−6.69401	+	11.5944i	−0.253554	+	0.439168i
$698$		0			0
$699$	−9.16868	−	30.0481i	−0.346791	−	1.13652i
$700$		0			0
$701$	−15.4603			−0.583926			−0.291963	−	0.956430i	$-0.594308\pi$
$701$	−15.4603			−0.583926			−0.291963	+	0.956430i	$0.594308\pi$
$702$		0			0
$703$	11.9906	+	6.92275i	0.452232	+	0.261096i
$704$		0			0
$705$	5.06702	−	5.42777i	0.190835	−	0.204421i
$706$		0			0
$707$	−35.1062	−	16.3791i	−1.32030	−	0.615999i
$708$		0			0
$709$	−41.7153	+	24.0843i	−1.56665	+	0.904505i	−0.570093	+	0.821580i	$0.693093\pi$
$709$	−41.7153	+	24.0843i	−1.56665	+	0.904505i	−0.996556	+	0.0829254i	$0.973574\pi$
$710$		0			0
$711$	1.04643	+	15.2033i	0.0392443	+	0.570169i
$712$		0			0
$713$	26.2452			0.982891
$714$		0			0
$715$		−	4.43523i		−	0.165868i
$716$		0			0
$717$	9.12976	+	2.11302i	0.340957	+	0.0789123i
$718$		0			0
$719$	−6.49021	−	11.2414i	−0.242044	−	0.419232i	0.719252	−	0.694749i	$-0.244484\pi$
$719$	−6.49021	−	11.2414i	−0.242044	−	0.419232i	−0.961296	+	0.275517i	$0.911151\pi$
$720$		0			0
$721$	−21.3763	+	14.9613i	−0.796094	+	0.557186i
$722$		0			0
$723$	25.3886	−	27.1961i	0.944211	−	1.01143i
$724$		0			0
$725$	−0.673858	+	1.16716i	−0.0250264	+	0.0433471i
$726$		0			0
$727$		−	12.0095i		−	0.445406i	−0.974886	−	0.222703i	$-0.928512\pi$
$727$		−	12.0095i		−	0.445406i	0.974886	−	0.222703i	$-0.0714880\pi$
$728$		0			0
$729$	−5.52704	−	26.4282i	−0.204705	−	0.978824i
$730$		0			0
$731$	53.0370	+	30.6209i	1.96164	+	1.13256i
$732$		0			0
$733$	4.29808	+	7.44449i	0.158753	+	0.274968i	0.934419	−	0.356175i	$-0.115919\pi$
$733$	4.29808	+	7.44449i	0.158753	+	0.274968i	−0.775666	+	0.631143i	$0.782586\pi$
$734$		0			0
$735$	9.82673	+	19.3318i	0.362465	+	0.713065i
$736$		0			0
$737$	6.91700	−	3.99353i	0.254791	−	0.147104i
$738$		0			0
$739$	2.25350	+	1.30106i	0.0828963	+	0.0478602i	0.540875	−	0.841103i	$-0.318093\pi$
$739$	2.25350	+	1.30106i	0.0828963	+	0.0478602i	−0.457979	+	0.888963i	$0.651426\pi$
$740$		0			0
$741$	15.2356	−	4.64891i	0.559695	−	0.170782i
$742$		0			0
$743$		−	13.4061i		−	0.491823i	−0.969292	−	0.245911i	$-0.920913\pi$
$743$		−	13.4061i		−	0.491823i	0.969292	−	0.245911i	$-0.0790872\pi$
$744$		0			0
$745$	−1.43281	−	0.827235i	−0.0524942	−	0.0303075i
$746$		0			0
$747$	7.45305	−	15.2387i	0.272693	−	0.557556i
$748$		0			0
$749$	−10.5623	−	15.0912i	−0.385939	−	0.551420i
$750$		0			0
$751$	7.86182	+	13.6171i	0.286882	+	0.496894i	0.973064	−	0.230536i	$-0.0740480\pi$
$751$	7.86182	+	13.6171i	0.286882	+	0.496894i	−0.686182	+	0.727430i	$0.740715\pi$
$752$		0			0
$753$	−33.5047	−	7.75445i	−1.22098	−	0.282588i
$754$		0			0
$755$			34.2244i			1.24555i
$756$		0			0
$757$			48.7626i			1.77231i	0.463391	+	0.886154i	$0.346633\pi$
$757$			48.7626i			1.77231i	−0.463391	+	0.886154i	$0.653367\pi$
$758$		0			0
$759$	13.3879	+	3.09854i	0.485950	+	0.112470i
$760$		0			0
$761$	21.7170	+	37.6149i	0.787240	+	1.36354i	0.927652	+	0.373447i	$0.121824\pi$
$761$	21.7170	+	37.6149i	0.787240	+	1.36354i	−0.140411	+	0.990093i	$0.544842\pi$
$762$		0			0
$763$	6.54411	+	3.05321i	0.236913	+	0.110534i
$764$		0			0
$765$	15.6993	−	32.0994i	0.567611	−	1.16056i
$766$		0			0
$767$	−18.1747	−	10.4932i	−0.656252	−	0.378887i
$768$		0			0
$769$		−	23.9226i		−	0.862670i	−0.902192	−	0.431335i	$-0.858043\pi$
$769$		−	23.9226i		−	0.862670i	0.902192	−	0.431335i	$-0.141957\pi$
$770$		0			0
$771$	14.4663	−	4.41417i	0.520993	−	0.158972i
$772$		0			0
$773$	14.3402	+	8.27930i	0.515780	+	0.297786i	0.735206	−	0.677843i	$-0.237085\pi$
$773$	14.3402	+	8.27930i	0.515780	+	0.297786i	−0.219427	+	0.975629i	$0.570419\pi$
$774$		0			0
$775$	5.17284	−	2.98654i	0.185814	−	0.107280i
$776$		0			0
$777$	−6.37940	−	15.8238i	−0.228860	−	0.567676i
$778$		0			0
$779$	3.73823	+	6.47480i	0.133936	+	0.231984i
$780$		0			0
$781$	−4.74856	−	2.74158i	−0.169917	−	0.0981014i
$782$		0			0
$783$	2.45226	−	3.01816i	0.0876366	−	0.107860i
$784$		0			0
$785$		−	19.5631i		−	0.698237i
$786$		0			0
$787$	5.81161	−	10.0660i	0.207162	−	0.358814i	−0.743658	−	0.668561i	$-0.766911\pi$
$787$	5.81161	−	10.0660i	0.207162	−	0.358814i	0.950819	+	0.309746i	$0.100244\pi$
$788$		0			0
$789$	−23.3966	+	25.0623i	−0.832940	+	0.892242i
$790$		0			0
$791$	−0.122192	−	1.39998i	−0.00434463	−	0.0497775i
$792$		0			0
$793$	−5.00642	−	8.67137i	−0.177783	−	0.307930i
$794$		0			0
$795$	−38.2641	−	8.85597i	−1.35709	−	0.314089i
$796$		0			0
$797$			2.35681i			0.0834824i	0.999128	+	0.0417412i	$0.0132905\pi$
$797$			2.35681i			0.0834824i	−0.999128	+	0.0417412i	$0.986709\pi$
$798$		0			0
$799$	15.9609			0.564657
$800$		0			0
$801$	3.04672	+	44.2650i	0.107651	+	1.56403i
$802$		0			0
$803$	5.70077	−	3.29134i	0.201176	−	0.116149i
$804$		0			0
$805$	15.8316	−	33.9327i	0.557991	−	1.19597i
$806$		0			0
$807$	1.09944	−	1.17772i	0.0387022	−	0.0414576i
$808$		0			0
$809$	−39.6070	−	22.8671i	−1.39251	−	0.803964i	−0.398914	−	0.916988i	$-0.630613\pi$
$809$	−39.6070	−	22.8671i	−1.39251	−	0.803964i	−0.993592	+	0.113024i	$0.963946\pi$
$810$		0			0
$811$	−0.844573			−0.0296570			−0.0148285	−	0.999890i	$-0.504720\pi$
$811$	−0.844573			−0.0296570			−0.0148285	+	0.999890i	$0.504720\pi$
$812$		0			0
$813$	4.35233	+	14.2637i	0.152643	+	0.500249i
$814$		0			0
$815$	−9.51282	+	16.4767i	−0.333219	+	0.577153i
$816$		0			0
$817$	29.6182	−	17.1000i	1.03621	−	0.598255i
$818$		0			0
$819$	−18.3161	−	7.05818i	−0.640015	−	0.246633i
$820$		0			0
$821$	−18.4890	−	32.0239i	−0.645272	−	1.11764i	−0.984239	−	0.176845i	$-0.943411\pi$
$821$	−18.4890	−	32.0239i	−0.645272	−	1.11764i	0.338967	−	0.940798i	$-0.389922\pi$
$822$		0			0
$823$	3.62518	−	6.27899i	0.126366	−	0.218872i	−0.795900	−	0.605428i	$-0.793002\pi$
$823$	3.62518	−	6.27899i	0.126366	−	0.218872i	0.922266	+	0.386556i	$0.126335\pi$
$824$		0			0
$825$	2.99130	−	0.912746i	0.104144	−	0.0317777i
$826$		0			0
$827$	−43.4014			−1.50921			−0.754607	−	0.656176i	$-0.772173\pi$
$827$	−43.4014			−1.50921			−0.754607	+	0.656176i	$0.772173\pi$
$828$		0			0
$829$	12.7789	−	22.1338i	0.443830	−	0.768737i	−0.554139	−	0.832424i	$-0.686953\pi$
$829$	12.7789	−	22.1338i	0.443830	−	0.768737i	0.997970	+	0.0636869i	$0.0202859\pi$
$830$		0			0
$831$	−34.8818	+	37.3652i	−1.21004	+	1.29619i
$832$		0			0
$833$	−15.9612	+	43.7970i	−0.553024	+	1.51748i
$834$		0			0
$835$	12.2842	−	7.09229i	0.425113	−	0.245439i
$836$		0			0
$837$	−16.1006	+	6.15019i	−0.556518	+	0.212582i
$838$		0			0
$839$	−19.2288			−0.663854			−0.331927	−	0.943305i	$-0.607699\pi$
$839$	−19.2288			−0.663854			−0.331927	+	0.943305i	$0.607699\pi$
$840$		0			0
$841$	−28.4399			−0.980686
$842$		0			0
$843$	−35.9865	−	8.32884i	−1.23944	−	0.286860i
$844$		0			0
$845$	−10.6636	+	6.15665i	−0.366840	+	0.211795i
$846$		0			0
$847$	−15.1628	−	21.6642i	−0.520999	−	0.744389i
$848$		0			0
$849$	26.3973	+	24.6429i	0.905954	+	0.845741i
$850$		0			0
$851$	−14.7295	+	25.5123i	−0.504921	+	0.874549i
$852$		0			0
$853$	43.5472			1.49103			0.745514	−	0.666489i	$-0.232204\pi$
$853$	43.5472			1.49103			0.745514	+	0.666489i	$0.232204\pi$
$854$		0			0
$855$	−11.1405	−	16.5555i	−0.380997	−	0.566185i
$856$		0			0
$857$	−4.41603	+	7.64878i	−0.150849	+	0.261277i	−0.931540	−	0.363640i	$-0.881534\pi$
$857$	−4.41603	+	7.64878i	−0.150849	+	0.261277i	0.780691	+	0.624917i	$0.214867\pi$
$858$		0			0
$859$	2.94564	+	5.10200i	0.100504	+	0.174078i	0.911892	−	0.410429i	$-0.134621\pi$
$859$	2.94564	+	5.10200i	0.100504	+	0.174078i	−0.811388	+	0.584507i	$0.801288\pi$
$860$		0			0
$861$	1.28906	−	9.12236i	0.0439311	−	0.310889i
$862$		0			0
$863$	2.80835	−	1.62140i	0.0955974	−	0.0551932i	−0.451439	−	0.892302i	$-0.649089\pi$
$863$	2.80835	−	1.62140i	0.0955974	−	0.0551932i	0.547037	+	0.837109i	$0.315756\pi$
$864$		0			0
$865$	3.81966	−	6.61584i	0.129872	−	0.224945i
$866$		0			0
$867$	45.3020	−	13.8232i	1.53854	−	0.469460i
$868$		0			0
$869$	5.09344			0.172783
$870$		0			0
$871$	17.0599	+	9.84955i	0.578053	+	0.333739i
$872$		0			0
$873$	−2.31420	+	4.73170i	−0.0783240	+	0.160144i
$874$		0			0
$875$	−2.79835	−	32.0614i	−0.0946015	−	1.08387i
$876$		0			0
$877$	39.1526	−	22.6048i	1.32209	−	0.763309i	0.338028	−	0.941136i	$-0.390240\pi$
$877$	39.1526	−	22.6048i	1.32209	−	0.763309i	0.984062	+	0.177828i	$0.0569070\pi$
$878$		0			0
$879$	−22.1154	−	5.11847i	−0.745934	−	0.172642i
$880$		0			0
$881$	−28.1014			−0.946759			−0.473380	−	0.880859i	$-0.656966\pi$
$881$	−28.1014			−0.946759			−0.473380	+	0.880859i	$0.656966\pi$
$882$		0			0
$883$		−	5.45102i		−	0.183442i	−0.995785	−	0.0917208i	$-0.970763\pi$
$883$		−	5.45102i		−	0.183442i	0.995785	−	0.0917208i	$-0.0292367\pi$
$884$		0			0
$885$	−5.92799	+	25.6131i	−0.199267	+	0.860975i
$886$		0			0
$887$	25.3783	+	43.9566i	0.852122	+	1.47592i	0.879290	+	0.476287i	$0.158018\pi$
$887$	25.3783	+	43.9566i	0.852122	+	1.47592i	−0.0271684	+	0.999631i	$0.508649\pi$
$888$		0			0
$889$	−11.9239	+	1.04073i	−0.399914	+	0.0349049i
$890$		0			0
$891$	−8.93914	+	1.23640i	−0.299472	+	0.0414211i
$892$		0			0
$893$	4.45664	−	7.71912i	0.149136	−	0.258311i
$894$		0			0
$895$			13.5158i			0.451783i
$896$		0			0
$897$	9.89147	+	32.4168i	0.330266	+	1.08237i
$898$		0			0
$899$	−2.14982	−	1.24120i	−0.0717005	−	0.0413963i
$900$		0			0
$901$	−42.2119	−	73.1132i	−1.40628	−	2.43575i
$902$		0			0
$903$	−41.7291	−	5.89666i	−1.38866	−	0.196228i
$904$		0			0
$905$	−7.74871	+	4.47372i	−0.257576	+	0.148711i
$906$		0			0
$907$	−8.66652	−	5.00362i	−0.287767	−	0.166142i	0.349167	−	0.937060i	$-0.386464\pi$
$907$	−8.66652	−	5.00362i	−0.287767	−	0.166142i	−0.636934	+	0.770918i	$0.719798\pi$
$908$		0			0
$909$	−24.5233	−	36.4431i	−0.813387	−	1.20874i
$910$		0			0
$911$			14.5940i			0.483521i	0.970336	+	0.241761i	$0.0777249\pi$
$911$			14.5940i			0.483521i	−0.970336	+	0.241761i	$0.922275\pi$
$912$		0			0
$913$	−4.91019	−	2.83490i	−0.162503	−	0.0938214i
$914$		0			0
$915$	−8.55953	+	9.16893i	−0.282969	+	0.303115i
$916$		0			0
$917$	−33.5208	+	23.4612i	−1.10695	+	0.774757i
$918$		0			0
$919$	1.14316	+	1.98001i	0.0377093	+	0.0653145i	0.884264	−	0.466987i	$-0.154661\pi$
$919$	1.14316	+	1.98001i	0.0377093	+	0.0653145i	−0.846555	+	0.532302i	$0.821327\pi$
$920$		0			0
$921$	7.28079	−	31.4582i	0.239910	−	1.03658i
$922$		0			0
$923$		−	13.5235i		−	0.445132i
$924$		0			0
$925$			6.70450i			0.220443i
$926$		0			0
$927$	−29.5155	+	2.03153i	−0.969417	+	0.0667242i
$928$		0			0
$929$	9.71753	+	16.8313i	0.318822	+	0.552216i	0.980242	−	0.197799i	$-0.0633795\pi$
$929$	9.71753	+	16.8313i	0.318822	+	0.552216i	−0.661421	+	0.750015i	$0.730046\pi$
$930$		0			0
$931$	16.7246	+	19.9483i	0.548128	+	0.653780i
$932$		0			0
$933$	−25.1420	−	23.4710i	−0.823114	−	0.768407i
$934$		0			0
$935$	−10.3430	−	5.97152i	−0.338252	−	0.195290i
$936$		0			0
$937$		−	21.6552i		−	0.707445i	−0.935350	−	0.353723i	$-0.884916\pi$
$937$		−	21.6552i		−	0.707445i	0.935350	−	0.353723i	$-0.115084\pi$
$938$		0			0
$939$	1.36065	+	4.45918i	0.0444030	+	0.145520i
$940$		0			0
$941$	5.82024	+	3.36032i	0.189735	+	0.109543i	0.591858	−	0.806042i	$-0.298395\pi$
$941$	5.82024	+	3.36032i	0.189735	+	0.109543i	−0.402124	+	0.915585i	$0.631728\pi$
$942$		0			0
$943$	−13.7764	+	7.95381i	−0.448622	+	0.259012i
$944$		0			0
$945$	−1.76053	+	24.5265i	−0.0572701	+	0.797849i
$946$		0			0
$947$	10.5673	+	18.3031i	0.343392	+	0.594772i	0.985060	−	0.172210i	$-0.0550908\pi$
$947$	10.5673	+	18.3031i	0.343392	+	0.594772i	−0.641668	+	0.766982i	$0.721757\pi$
$948$		0			0
$949$	14.0602	+	8.11768i	0.456414	+	0.263511i
$950$		0			0
$951$	17.7357	−	5.41174i	0.575118	−	0.175488i
$952$		0			0
$953$			2.18327i			0.0707230i	0.999375	+	0.0353615i	$0.0112583\pi$
$953$			2.18327i			0.0707230i	−0.999375	+	0.0353615i	$0.988742\pi$
$954$		0			0
$955$	−10.8317	+	18.7611i	−0.350507	+	0.607096i
$956$		0			0
$957$	−0.950102	−	0.886955i	−0.0307124	−	0.0286712i
$958$		0			0
$959$	−26.8880	−	12.5448i	−0.868259	−	0.405094i
$960$		0			0
$961$	−9.99900	−	17.3188i	−0.322548	−	0.558670i
$962$		0			0
$963$	−1.43422	−	20.8373i	−0.0462170	−	0.671473i
$964$		0			0
$965$		−	2.11931i		−	0.0682229i
$966$		0			0
$967$	25.1413			0.808490			0.404245	−	0.914651i	$-0.367534\pi$
$967$	25.1413			0.808490			0.404245	+	0.914651i	$0.367534\pi$
$968$		0			0
$969$	9.67175	−	41.7888i	0.310701	−	1.34245i
$970$		0			0
$971$	−30.0100	+	17.3263i	−0.963065	+	0.556026i	−0.897115	−	0.441797i	$-0.854341\pi$
$971$	−30.0100	+	17.3263i	−0.963065	+	0.556026i	−0.0659503	+	0.997823i	$0.521008\pi$
$972$		0			0
$973$	−47.3969	+	4.13685i	−1.51947	+	0.132621i
$974$		0			0
$975$	5.63841	+	5.26366i	0.180574	+	0.168572i
$976$		0			0
$977$	3.22538	+	1.86218i	0.103189	+	0.0595763i	0.550706	−	0.834699i	$-0.314358\pi$
$977$	3.22538	+	1.86218i	0.103189	+	0.0595763i	−0.447517	+	0.894275i	$0.647692\pi$
$978$		0			0
$979$	14.8297			0.473960
$980$		0			0
$981$	4.57137	+	6.79333i	0.145953	+	0.216894i
$982$		0			0
$983$	−27.3018	+	47.2881i	−0.870792	+	1.50826i	−0.00961355	+	0.999954i	$0.503060\pi$
$983$	−27.3018	+	47.2881i	−0.870792	+	1.50826i	−0.861179	+	0.508302i	$0.830273\pi$
$984$		0			0
$985$	−30.2227	+	17.4491i	−0.962977	+	0.555975i
$986$		0			0
$987$	−10.1869	+	4.10685i	−0.324251	+	0.130722i
$988$		0			0
$989$	36.3837	+	63.0185i	1.15694	+	2.00387i
$990$		0			0
$991$	25.1790	−	43.6114i	0.799839	−	1.38536i	−0.119882	−	0.992788i	$-0.538252\pi$
$991$	25.1790	−	43.6114i	0.799839	−	1.38536i	0.919721	−	0.392573i	$-0.128415\pi$
$992$		0			0
$993$	11.0042	+	36.0635i	0.349207	+	1.14444i
$994$		0			0
$995$	26.3603			0.835679
$996$		0			0
$997$	12.7609	−	22.1025i	0.404141	−	0.699993i	−0.590080	−	0.807345i	$-0.700904\pi$
$997$	12.7609	−	22.1025i	0.404141	−	0.699993i	0.994221	+	0.107352i	$0.0342372\pi$
$998$		0			0
$999$	3.05765	−	19.1026i	0.0967398	−	0.604380i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bi.c.17.11		48
3.2	odd	2	inner	672.2.bi.c.17.5		48
4.3	odd	2		168.2.ba.c.101.7	yes	48
7.5	odd	6	inner	672.2.bi.c.593.20		48
8.3	odd	2		168.2.ba.c.101.15	yes	48
8.5	even	2	inner	672.2.bi.c.17.14		48
12.11	even	2		168.2.ba.c.101.18	yes	48
21.5	even	6	inner	672.2.bi.c.593.14		48
24.5	odd	2	inner	672.2.bi.c.17.20		48
24.11	even	2		168.2.ba.c.101.10	yes	48
28.19	even	6		168.2.ba.c.5.10	yes	48
56.5	odd	6	inner	672.2.bi.c.593.5		48
56.19	even	6		168.2.ba.c.5.18	yes	48
84.47	odd	6		168.2.ba.c.5.15	yes	48
168.5	even	6	inner	672.2.bi.c.593.11		48
168.131	odd	6		168.2.ba.c.5.7	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.7	✓	48	168.131	odd	6
168.2.ba.c.5.10	yes	48	28.19	even	6
168.2.ba.c.5.15	yes	48	84.47	odd	6
168.2.ba.c.5.18	yes	48	56.19	even	6
168.2.ba.c.101.7	yes	48	4.3	odd	2
168.2.ba.c.101.10	yes	48	24.11	even	2
168.2.ba.c.101.15	yes	48	8.3	odd	2
168.2.ba.c.101.18	yes	48	12.11	even	2
672.2.bi.c.17.5		48	3.2	odd	2	inner
672.2.bi.c.17.11		48	1.1	even	1	trivial
672.2.bi.c.17.14		48	8.5	even	2	inner
672.2.bi.c.17.20		48	24.5	odd	2	inner
672.2.bi.c.593.5		48	56.5	odd	6	inner
672.2.bi.c.593.11		48	168.5	even	6	inner
672.2.bi.c.593.14		48	21.5	even	6	inner
672.2.bi.c.593.20		48	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.390548 + 1.68745i) q^{3} +(1.54900 - 0.894317i) q^{5} +(-2.63573 + 0.230049i) q^{7} +(-2.69494 - 1.31806i) q^{9} +O(q^{10})\)	\(q+(-0.390548 + 1.68745i) q^{3} +(1.54900 - 0.894317i) q^{5} +(-2.63573 + 0.230049i) q^{7} +(-2.69494 - 1.31806i) q^{9} +(-0.501346 + 0.868358i) q^{11} -2.47302 q^{13} +(0.904151 + 2.96313i) q^{15} +(-3.32963 + 5.76708i) q^{17} +(1.85941 + 3.22059i) q^{19} +(0.641185 - 4.53750i) q^{21} +(-6.85244 + 3.95626i) q^{23} +(-0.900394 + 1.55953i) q^{25} +(3.27666 - 4.03281i) q^{27} +0.748403 q^{29} +(-2.87254 - 1.65846i) q^{31} +(-1.26951 - 1.18513i) q^{33} +(-3.87702 + 2.71353i) q^{35} +(3.22429 - 1.86155i) q^{37} +(0.965832 - 4.17308i) q^{39} +2.01044 q^{41} -9.19651i q^{43} +(-5.35324 + 0.368459i) q^{45} +(-1.19840 - 2.07569i) q^{47} +(6.89415 - 1.21270i) q^{49} +(-8.43126 - 7.87089i) q^{51} +(-6.33884 + 10.9792i) q^{53} +1.79345i q^{55} +(-6.16075 + 1.87985i) q^{57} +(7.34922 + 4.24308i) q^{59} +(2.02442 + 3.50640i) q^{61} +(7.40637 + 2.85408i) q^{63} +(-3.83071 + 2.21166i) q^{65} +(-6.89843 - 3.98281i) q^{67} +(-3.99976 - 13.1082i) q^{69} +5.46843i q^{71} +(-5.68546 - 3.28250i) q^{73} +(-2.27997 - 2.12844i) q^{75} +(1.12165 - 2.40409i) q^{77} +(-2.53988 - 4.39920i) q^{79} +(5.52545 + 7.10419i) q^{81} +5.65457i q^{83} +11.9110i q^{85} +(-0.292288 + 1.26289i) q^{87} +(-7.39495 - 12.8084i) q^{89} +(6.51821 - 0.568916i) q^{91} +(3.92043 - 4.19955i) q^{93} +(5.76045 + 3.32580i) q^{95} -1.75577i q^{97} +(2.49565 - 1.67937i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7} - 14 q^{9}+O(q^{10}) \) 48 * q + 4 * q^7 - 14 * q^9	\( 48 q + 4 q^{7} - 14 q^{9} - 4 q^{15} - 8 q^{25} - 48 q^{31} - 42 q^{33} + 8 q^{39} - 36 q^{49} + 4 q^{57} + 6 q^{63} - 36 q^{73} + 56 q^{79} + 42 q^{81} + 132 q^{87}+O(q^{100}) \) 48 * q + 4 * q^7 - 14 * q^9 - 4 * q^15 - 8 * q^25 - 48 * q^31 - 42 * q^33 + 8 * q^39 - 36 * q^49 + 4 * q^57 + 6 * q^63 - 36 * q^73 + 56 * q^79 + 42 * q^81 + 132 * q^87

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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