LMFDB - Embedded newform 1344.2.s.c.239.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(239,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))

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

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

chi := DirichletCharacter("1344.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.s (of order $4$, 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:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.17
Character	$\chi$	$=$	1344.239
Dual form			1344.2.s.c.911.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.57773 - 0.714681i) q^{3} +(-1.31983 - 1.31983i) q^{5} +1.00000 q^{7} +(1.97846 - 2.25515i) q^{9} +O(q^{10})$	\(q+(1.57773 - 0.714681i) q^{3} +(-1.31983 - 1.31983i) q^{5} +1.00000 q^{7} +(1.97846 - 2.25515i) q^{9} +(-1.23544 + 1.23544i) q^{11} +(4.57782 + 4.57782i) q^{13} +(-3.02558 - 1.13907i) q^{15} -5.82397i q^{17} +(2.27291 - 2.27291i) q^{19} +(1.57773 - 0.714681i) q^{21} +2.63707i q^{23} -1.51612i q^{25} +(1.50977 - 4.97198i) q^{27} +(4.30719 - 4.30719i) q^{29} +5.81364i q^{31} +(-1.06624 + 2.83213i) q^{33} +(-1.31983 - 1.31983i) q^{35} +(6.99022 - 6.99022i) q^{37} +(10.4943 + 3.95088i) q^{39} -3.57004 q^{41} +(-2.12307 - 2.12307i) q^{43} +(-5.58763 + 0.365176i) q^{45} -11.3696 q^{47} +1.00000 q^{49} +(-4.16228 - 9.18865i) q^{51} +(0.573389 + 0.573389i) q^{53} +3.26113 q^{55} +(1.96163 - 5.21043i) q^{57} +(8.42236 - 8.42236i) q^{59} +(-6.80408 - 6.80408i) q^{61} +(1.97846 - 2.25515i) q^{63} -12.0839i q^{65} +(-1.90390 + 1.90390i) q^{67} +(1.88466 + 4.16058i) q^{69} +13.3926i q^{71} -0.516078i q^{73} +(-1.08354 - 2.39202i) q^{75} +(-1.23544 + 1.23544i) q^{77} -3.10873i q^{79} +(-1.17138 - 8.92345i) q^{81} +(2.91252 + 2.91252i) q^{83} +(-7.68663 + 7.68663i) q^{85} +(3.71731 - 9.87385i) q^{87} -4.34348 q^{89} +(4.57782 + 4.57782i) q^{91} +(4.15490 + 9.17236i) q^{93} -5.99968 q^{95} +8.09726 q^{97} +(0.341828 + 5.23036i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} + 40 q^{7}+O(q^{10}) $ 40 * q - 4 * q^3 + 40 * q^7	$ 40 q - 4 q^{3} + 40 q^{7} + 24 q^{13} - 16 q^{19} - 4 q^{21} + 32 q^{27} + 24 q^{33} - 8 q^{37} + 64 q^{39} - 24 q^{43} - 28 q^{45} + 40 q^{49} + 32 q^{51} - 16 q^{55} - 48 q^{61} - 40 q^{67} + 4 q^{69} - 40 q^{75} + 56 q^{81} - 48 q^{85} - 32 q^{87} + 24 q^{91} + 56 q^{93} + 16 q^{97} - 24 q^{99}+O(q^{100}) $ 40 * q - 4 * q^3 + 40 * q^7 + 24 * q^13 - 16 * q^19 - 4 * q^21 + 32 * q^27 + 24 * q^33 - 8 * q^37 + 64 * q^39 - 24 * q^43 - 28 * q^45 + 40 * q^49 + 32 * q^51 - 16 * q^55 - 48 * q^61 - 40 * q^67 + 4 * q^69 - 40 * q^75 + 56 * q^81 - 48 * q^85 - 32 * q^87 + 24 * q^91 + 56 * q^93 + 16 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	1.57773	−	0.714681i	0.910903	−	0.412621i
$3$	1.57773	−	0.714681i	0.910903	−	0.412621i
$4$		0			0
$5$	−1.31983	−	1.31983i	−0.590244	−	0.590244i	0.347453	−	0.937697i	$-0.387047\pi$
$5$	−1.31983	−	1.31983i	−0.590244	−	0.590244i	−0.937697	+	0.347453i	$0.887047\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$		0			0
$9$	1.97846	−	2.25515i	0.659487	−	0.751716i
$10$		0			0
$11$	−1.23544	+	1.23544i	−0.372499	+	0.372499i	−0.868387	−	0.495888i	$-0.834843\pi$
$11$	−1.23544	+	1.23544i	−0.372499	+	0.372499i	0.495888	+	0.868387i	$0.334843\pi$
$12$		0			0
$13$	4.57782	+	4.57782i	1.26966	+	1.26966i	0.946264	+	0.323396i	$0.104825\pi$
$13$	4.57782	+	4.57782i	1.26966	+	1.26966i	0.323396	+	0.946264i	$0.395175\pi$
$14$		0			0
$15$	−3.02558	−	1.13907i	−0.781202	−	0.294108i
$16$		0			0
$17$		−	5.82397i		−	1.41252i	−0.707952	−	0.706260i	$-0.750381\pi$
$17$		−	5.82397i		−	1.41252i	0.707952	−	0.706260i	$-0.249619\pi$
$18$		0			0
$19$	2.27291	−	2.27291i	0.521440	−	0.521440i	−0.396566	−	0.918006i	$-0.629798\pi$
$19$	2.27291	−	2.27291i	0.521440	−	0.521440i	0.918006	+	0.396566i	$0.129798\pi$
$20$		0			0
$21$	1.57773	−	0.714681i	0.344289	−	0.155956i
$22$		0			0
$23$			2.63707i			0.549867i	0.961463	+	0.274934i	$0.0886558\pi$
$23$			2.63707i			0.549867i	−0.961463	+	0.274934i	$0.911344\pi$
$24$		0			0
$25$		−	1.51612i		−	0.303224i
$26$		0			0
$27$	1.50977	−	4.97198i	0.290555	−	0.956858i
$28$		0			0
$29$	4.30719	−	4.30719i	0.799825	−	0.799825i	−0.183243	−	0.983068i	$-0.558659\pi$
$29$	4.30719	−	4.30719i	0.799825	−	0.799825i	0.983068	+	0.183243i	$0.0586594\pi$
$30$		0			0
$31$			5.81364i			1.04416i	0.852896	+	0.522081i	$0.174844\pi$
$31$			5.81364i			1.04416i	−0.852896	+	0.522081i	$0.825156\pi$
$32$		0			0
$33$	−1.06624	+	2.83213i	−0.185609	+	0.493011i
$34$		0			0
$35$	−1.31983	−	1.31983i	−0.223091	−	0.223091i
$36$		0			0
$37$	6.99022	−	6.99022i	1.14919	−	1.14919i	0.162472	−	0.986713i	$-0.448053\pi$
$37$	6.99022	−	6.99022i	1.14919	−	1.14919i	0.986713	−	0.162472i	$-0.0519467\pi$
$38$		0			0
$39$	10.4943	+	3.95088i	1.68043	+	0.632648i
$40$		0			0
$41$	−3.57004			−0.557547			−0.278773	−	0.960357i	$-0.589928\pi$
$41$	−3.57004			−0.557547			−0.278773	+	0.960357i	$0.589928\pi$
$42$		0			0
$43$	−2.12307	−	2.12307i	−0.323765	−	0.323765i	0.526444	−	0.850210i	$-0.323525\pi$
$43$	−2.12307	−	2.12307i	−0.323765	−	0.323765i	−0.850210	+	0.526444i	$0.823525\pi$
$44$		0			0
$45$	−5.58763	+	0.365176i	−0.832954	+	0.0544373i
$46$		0			0
$47$	−11.3696			−1.65842			−0.829211	−	0.558935i	$-0.811210\pi$
$47$	−11.3696			−1.65842			−0.829211	+	0.558935i	$0.811210\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$		0			0
$51$	−4.16228	−	9.18865i	−0.582836	−	1.28667i
$52$		0			0
$53$	0.573389	+	0.573389i	0.0787610	+	0.0787610i	0.745390	−	0.666629i	$-0.232263\pi$
$53$	0.573389	+	0.573389i	0.0787610	+	0.0787610i	−0.666629	+	0.745390i	$0.732263\pi$
$54$		0			0
$55$	3.26113			0.439730
$56$		0			0
$57$	1.96163	−	5.21043i	0.259824	−	0.690139i
$58$		0			0
$59$	8.42236	−	8.42236i	1.09650	−	1.09650i	0.101681	−	0.994817i	$-0.467578\pi$
$59$	8.42236	−	8.42236i	1.09650	−	1.09650i	0.994817	−	0.101681i	$-0.0324220\pi$
$60$		0			0
$61$	−6.80408	−	6.80408i	−0.871174	−	0.871174i	0.121427	−	0.992600i	$-0.461253\pi$
$61$	−6.80408	−	6.80408i	−0.871174	−	0.871174i	−0.992600	+	0.121427i	$0.961253\pi$
$62$		0			0
$63$	1.97846	−	2.25515i	0.249263	−	0.284122i
$64$		0			0
$65$		−	12.0839i		−	1.49882i
$66$		0			0
$67$	−1.90390	+	1.90390i	−0.232598	+	0.232598i	−0.813776	−	0.581178i	$-0.802592\pi$
$67$	−1.90390	+	1.90390i	−0.232598	+	0.232598i	0.581178	+	0.813776i	$0.302592\pi$
$68$		0			0
$69$	1.88466	+	4.16058i	0.226887	+	0.500875i
$70$		0			0
$71$			13.3926i			1.58941i	0.606994	+	0.794706i	$0.292375\pi$
$71$			13.3926i			1.58941i	−0.606994	+	0.794706i	$0.707625\pi$
$72$		0			0
$73$		−	0.516078i		−	0.0604023i	−0.999544	−	0.0302012i	$-0.990385\pi$
$73$		−	0.516078i		−	0.0604023i	0.999544	−	0.0302012i	$-0.00961479\pi$
$74$		0			0
$75$	−1.08354	−	2.39202i	−0.125116	−	0.276207i
$76$		0			0
$77$	−1.23544	+	1.23544i	−0.140791	+	0.140791i
$78$		0			0
$79$		−	3.10873i		−	0.349759i	−0.984590	−	0.174879i	$-0.944046\pi$
$79$		−	3.10873i		−	0.349759i	0.984590	−	0.174879i	$-0.0559536\pi$
$80$		0			0
$81$	−1.17138	−	8.92345i	−0.130153	−	0.991494i
$82$		0			0
$83$	2.91252	+	2.91252i	0.319691	+	0.319691i	0.848648	−	0.528958i	$-0.177417\pi$
$83$	2.91252	+	2.91252i	0.319691	+	0.319691i	−0.528958	+	0.848648i	$0.677417\pi$
$84$		0			0
$85$	−7.68663	+	7.68663i	−0.833732	+	0.833732i
$86$		0			0
$87$	3.71731	−	9.87385i	0.398538	−	1.05859i
$88$		0			0
$89$	−4.34348			−0.460408			−0.230204	−	0.973142i	$-0.573939\pi$
$89$	−4.34348			−0.460408			−0.230204	+	0.973142i	$0.573939\pi$
$90$		0			0
$91$	4.57782	+	4.57782i	0.479886	+	0.479886i
$92$		0			0
$93$	4.15490	+	9.17236i	0.430843	+	0.951129i
$94$		0			0
$95$	−5.99968			−0.615554
$96$		0			0
$97$	8.09726			0.822152			0.411076	−	0.911601i	$-0.365153\pi$
$97$	8.09726			0.822152			0.411076	+	0.911601i	$0.365153\pi$
$98$		0			0
$99$	0.341828	+	5.23036i	0.0343550	+	0.525671i
$100$		0			0
$101$	0.961217	+	0.961217i	0.0956447	+	0.0956447i	0.753310	−	0.657665i	$-0.228456\pi$
$101$	0.961217	+	0.961217i	0.0956447	+	0.0956447i	−0.657665	+	0.753310i	$0.728456\pi$
$102$		0			0
$103$	−1.57772			−0.155457			−0.0777286	−	0.996975i	$-0.524767\pi$
$103$	−1.57772			−0.155457			−0.0777286	+	0.996975i	$0.524767\pi$
$104$		0			0
$105$	−3.02558	−	1.13907i	−0.295267	−	0.111162i
$106$		0			0
$107$	4.53705	−	4.53705i	0.438613	−	0.438613i	−0.452932	−	0.891545i	$-0.649622\pi$
$107$	4.53705	−	4.53705i	0.438613	−	0.438613i	0.891545	+	0.452932i	$0.149622\pi$
$108$		0			0
$109$	−2.23973	−	2.23973i	−0.214528	−	0.214528i	0.591660	−	0.806188i	$-0.298473\pi$
$109$	−2.23973	−	2.23973i	−0.214528	−	0.214528i	−0.806188	+	0.591660i	$0.798473\pi$
$110$		0			0
$111$	6.03290	−	16.0245i	0.572617	−	1.52097i
$112$		0			0
$113$			16.0755i			1.51226i	0.654424	+	0.756128i	$0.272911\pi$
$113$			16.0755i			1.51226i	−0.654424	+	0.756128i	$0.727089\pi$
$114$		0			0
$115$	3.48047	−	3.48047i	0.324556	−	0.324556i
$116$		0			0
$117$	19.3807	−	1.26662i	1.79175	−	0.117099i
$118$		0			0
$119$		−	5.82397i		−	0.533883i
$120$		0			0
$121$			7.94738i			0.722489i
$122$		0			0
$123$	−5.63256	+	2.55144i	−0.507871	+	0.230056i
$124$		0			0
$125$	−8.60014	+	8.60014i	−0.769220	+	0.769220i
$126$		0			0
$127$			12.1741i			1.08028i	0.841575	+	0.540140i	$0.181629\pi$
$127$			12.1741i			1.08028i	−0.841575	+	0.540140i	$0.818371\pi$
$128$		0			0
$129$	−4.86695	−	1.83231i	−0.428511	−	0.161326i
$130$		0			0
$131$	13.2278	+	13.2278i	1.15571	+	1.15571i	0.985388	+	0.170327i	$0.0544824\pi$
$131$	13.2278	+	13.2278i	1.15571	+	1.15571i	0.170327	+	0.985388i	$0.445518\pi$
$132$		0			0
$133$	2.27291	−	2.27291i	0.197086	−	0.197086i
$134$		0			0
$135$	−8.55478	+	4.56952i	−0.736278	+	0.393282i
$136$		0			0
$137$	−3.47597			−0.296972			−0.148486	−	0.988915i	$-0.547440\pi$
$137$	−3.47597			−0.296972			−0.148486	+	0.988915i	$0.547440\pi$
$138$		0			0
$139$	−7.82479	−	7.82479i	−0.663690	−	0.663690i	0.292558	−	0.956248i	$-0.405494\pi$
$139$	−7.82479	−	7.82479i	−0.663690	−	0.663690i	−0.956248	+	0.292558i	$0.905494\pi$
$140$		0			0
$141$	−17.9381	+	8.12562i	−1.51066	+	0.684300i
$142$		0			0
$143$	−11.3112			−0.945893
$144$		0			0
$145$	−11.3695			−0.944184
$146$		0			0
$147$	1.57773	−	0.714681i	0.130129	−	0.0589459i
$148$		0			0
$149$	3.66058	+	3.66058i	0.299886	+	0.299886i	0.840969	−	0.541083i	$-0.181986\pi$
$149$	3.66058	+	3.66058i	0.299886	+	0.299886i	−0.541083	+	0.840969i	$0.681986\pi$
$150$		0			0
$151$	−0.834525			−0.0679127			−0.0339563	−	0.999423i	$-0.510811\pi$
$151$	−0.834525			−0.0679127			−0.0339563	+	0.999423i	$0.510811\pi$
$152$		0			0
$153$	−13.1339	−	11.5225i	−1.06181	−	0.931540i
$154$		0			0
$155$	7.67300	−	7.67300i	0.616310	−	0.616310i
$156$		0			0
$157$	11.1183	+	11.1183i	0.887337	+	0.887337i	0.994267	−	0.106930i	$-0.0341020\pi$
$157$	11.1183	+	11.1183i	0.887337	+	0.887337i	−0.106930	+	0.994267i	$0.534102\pi$
$158$		0			0
$159$	1.31444	+	0.494862i	0.104242	+	0.0392451i
$160$		0			0
$161$			2.63707i			0.207830i
$162$		0			0
$163$	2.39613	−	2.39613i	0.187680	−	0.187680i	−0.607013	−	0.794692i	$-0.707632\pi$
$163$	2.39613	−	2.39613i	0.187680	−	0.187680i	0.794692	+	0.607013i	$0.207632\pi$
$164$		0			0
$165$	5.14518	−	2.33067i	0.400552	−	0.181442i
$166$		0			0
$167$		−	4.20664i		−	0.325519i	−0.986666	−	0.162760i	$-0.947961\pi$
$167$		−	4.20664i		−	0.325519i	0.986666	−	0.162760i	$-0.0520395\pi$
$168$		0			0
$169$			28.9129i			2.22407i
$170$		0			0
$171$	−0.628879	−	9.62260i	−0.0480916	−	0.735858i
$172$		0			0
$173$	6.93594	−	6.93594i	0.527330	−	0.527330i	−0.392445	−	0.919775i	$-0.628371\pi$
$173$	6.93594	−	6.93594i	0.527330	−	0.527330i	0.919775	+	0.392445i	$0.128371\pi$
$174$		0			0
$175$		−	1.51612i		−	0.114608i
$176$		0			0
$177$	7.26891	−	19.3075i	0.546364	−	1.45124i
$178$		0			0
$179$	0.640117	+	0.640117i	0.0478446	+	0.0478446i	0.730624	−	0.682780i	$-0.239229\pi$
$179$	0.640117	+	0.640117i	0.0478446	+	0.0478446i	−0.682780	+	0.730624i	$0.739229\pi$
$180$		0			0
$181$	4.43844	−	4.43844i	0.329906	−	0.329906i	−0.522644	−	0.852551i	$-0.675054\pi$
$181$	4.43844	−	4.43844i	0.329906	−	0.329906i	0.852551	+	0.522644i	$0.175054\pi$
$182$		0			0
$183$	−15.5978	−	5.87225i	−1.15302	−	0.434090i
$184$		0			0
$185$	−18.4518			−1.35660
$186$		0			0
$187$	7.19516	+	7.19516i	0.526162	+	0.526162i
$188$		0			0
$189$	1.50977	−	4.97198i	0.109819	−	0.361658i
$190$		0			0
$191$	−12.2266			−0.884684			−0.442342	−	0.896847i	$-0.645852\pi$
$191$	−12.2266			−0.884684			−0.442342	+	0.896847i	$0.645852\pi$
$192$		0			0
$193$	8.96283			0.645159			0.322579	−	0.946542i	$-0.395450\pi$
$193$	8.96283			0.645159			0.322579	+	0.946542i	$0.395450\pi$
$194$		0			0
$195$	−8.63611	−	19.0651i	−0.618445	−	1.36528i
$196$		0			0
$197$	7.69332	+	7.69332i	0.548126	+	0.548126i	0.925899	−	0.377772i	$-0.123310\pi$
$197$	7.69332	+	7.69332i	0.548126	+	0.548126i	−0.377772	+	0.925899i	$0.623310\pi$
$198$		0			0
$199$	−10.4352			−0.739734			−0.369867	−	0.929085i	$-0.620597\pi$
$199$	−10.4352			−0.739734			−0.369867	+	0.929085i	$0.620597\pi$
$200$		0			0
$201$	−1.64315	+	4.36451i	−0.115899	+	0.307849i
$202$		0			0
$203$	4.30719	−	4.30719i	0.302305	−	0.302305i
$204$		0			0
$205$	4.71183	+	4.71183i	0.329089	+	0.329089i
$206$		0			0
$207$	5.94698	+	5.21734i	0.413344	+	0.362630i
$208$		0			0
$209$			5.61607i			0.388472i
$210$		0			0
$211$	−17.9097	+	17.9097i	−1.23295	+	1.23295i	−0.270127	+	0.962825i	$0.587066\pi$
$211$	−17.9097	+	17.9097i	−1.23295	+	1.23295i	−0.962825	+	0.270127i	$0.912934\pi$
$212$		0			0
$213$	9.57146	+	21.1299i	0.655825	+	1.44780i
$214$		0			0
$215$			5.60417i			0.382201i
$216$		0			0
$217$			5.81364i			0.394656i
$218$		0			0
$219$	−0.368831	−	0.814231i	−0.0249233	−	0.0550206i
$220$		0			0
$221$	26.6611	−	26.6611i	1.79342	−	1.79342i
$222$		0			0
$223$			8.27899i			0.554402i	0.960812	+	0.277201i	$0.0894068\pi$
$223$			8.27899i			0.554402i	−0.960812	+	0.277201i	$0.910593\pi$
$224$		0			0
$225$	−3.41907	−	2.99958i	−0.227938	−	0.199972i
$226$		0			0
$227$	16.7316	+	16.7316i	1.11052	+	1.11052i	0.993080	+	0.117437i	$0.0374679\pi$
$227$	16.7316	+	16.7316i	1.11052	+	1.11052i	0.117437	+	0.993080i	$0.462532\pi$
$228$		0			0
$229$	−3.32761	+	3.32761i	−0.219894	+	0.219894i	−0.808454	−	0.588560i	$-0.799695\pi$
$229$	−3.32761	+	3.32761i	−0.219894	+	0.219894i	0.588560	+	0.808454i	$0.299695\pi$
$230$		0			0
$231$	−1.06624	+	2.83213i	−0.0701537	+	0.186341i
$232$		0			0
$233$	22.4485			1.47065			0.735326	−	0.677713i	$-0.237029\pi$
$233$	22.4485			1.47065			0.735326	+	0.677713i	$0.237029\pi$
$234$		0			0
$235$	15.0059	+	15.0059i	0.978874	+	0.978874i
$236$		0			0
$237$	−2.22175	−	4.90473i	−0.144318	−	0.318596i
$238$		0			0
$239$	16.7259			1.08191			0.540953	−	0.841053i	$-0.318064\pi$
$239$	16.7259			1.08191			0.540953	+	0.841053i	$0.318064\pi$
$240$		0			0
$241$	−19.0542			−1.22739			−0.613693	−	0.789545i	$-0.710317\pi$
$241$	−19.0542			−1.22739			−0.613693	+	0.789545i	$0.710317\pi$
$242$		0			0
$243$	−8.22553	−	13.2416i	−0.527668	−	0.849451i
$244$		0			0
$245$	−1.31983	−	1.31983i	−0.0843206	−	0.0843206i
$246$		0			0
$247$	20.8099			1.32410
$248$		0			0
$249$	6.67670	+	2.51365i	0.423118	+	0.159296i
$250$		0			0
$251$	−2.15390	+	2.15390i	−0.135953	+	0.135953i	−0.771808	−	0.635855i	$-0.780647\pi$
$251$	−2.15390	+	2.15390i	−0.135953	+	0.135953i	0.635855	+	0.771808i	$0.280647\pi$
$252$		0			0
$253$	−3.25794	−	3.25794i	−0.204825	−	0.204825i
$254$		0			0
$255$	−6.63394	+	17.6209i	−0.415433	+	1.10346i
$256$		0			0
$257$		−	24.3261i		−	1.51742i	−0.651428	−	0.758711i	$-0.725830\pi$
$257$		−	24.3261i		−	1.51742i	0.651428	−	0.758711i	$-0.274170\pi$
$258$		0			0
$259$	6.99022	−	6.99022i	0.434351	−	0.434351i
$260$		0			0
$261$	−1.19174	−	18.2350i	−0.0737666	−	1.12872i
$262$		0			0
$263$		−	8.47386i		−	0.522521i	−0.965268	−	0.261260i	$-0.915862\pi$
$263$		−	8.47386i		−	0.522521i	0.965268	−	0.261260i	$-0.0841381\pi$
$264$		0			0
$265$		−	1.51355i		−	0.0929764i
$266$		0			0
$267$	−6.85283	+	3.10420i	−0.419387	+	0.189974i
$268$		0			0
$269$	0.519029	−	0.519029i	0.0316458	−	0.0316458i	−0.691107	−	0.722753i	$-0.742877\pi$
$269$	0.519029	−	0.519029i	0.0316458	−	0.0316458i	0.722753	+	0.691107i	$0.242877\pi$
$270$		0			0
$271$			0.444161i			0.0269809i	0.999909	+	0.0134904i	$0.00429427\pi$
$271$			0.444161i			0.0269809i	−0.999909	+	0.0134904i	$0.995706\pi$
$272$		0			0
$273$	10.4943	+	3.95088i	0.635141	+	0.239118i
$274$		0			0
$275$	1.87307	+	1.87307i	0.112950	+	0.112950i
$276$		0			0
$277$	−20.3609	+	20.3609i	−1.22337	+	1.22337i	−0.256939	+	0.966428i	$0.582714\pi$
$277$	−20.3609	+	20.3609i	−1.22337	+	1.22337i	−0.966428	+	0.256939i	$0.917286\pi$
$278$		0			0
$279$	13.1106	+	11.5021i	0.784913	+	0.688611i
$280$		0			0
$281$	−13.0109			−0.776163			−0.388082	−	0.921625i	$-0.626862\pi$
$281$	−13.0109			−0.776163			−0.388082	+	0.921625i	$0.626862\pi$
$282$		0			0
$283$	−10.7492	−	10.7492i	−0.638976	−	0.638976i	0.311327	−	0.950303i	$-0.399227\pi$
$283$	−10.7492	−	10.7492i	−0.638976	−	0.638976i	−0.950303	+	0.311327i	$0.899227\pi$
$284$		0			0
$285$	−9.46588	+	4.28786i	−0.560710	+	0.253991i
$286$		0			0
$287$	−3.57004			−0.210733
$288$		0			0
$289$	−16.9187			−0.995215
$290$		0			0
$291$	12.7753	−	5.78696i	0.748900	−	0.339237i
$292$		0			0
$293$	−6.14398	−	6.14398i	−0.358935	−	0.358935i	0.504485	−	0.863420i	$-0.331682\pi$
$293$	−6.14398	−	6.14398i	−0.358935	−	0.358935i	−0.863420	+	0.504485i	$0.831682\pi$
$294$		0			0
$295$	−22.2321			−1.29440
$296$		0			0
$297$	4.27735	+	8.00780i	0.248197	+	0.464660i
$298$		0			0
$299$	−12.0720	+	12.0720i	−0.698144	+	0.698144i
$300$		0			0
$301$	−2.12307	−	2.12307i	−0.122372	−	0.122372i
$302$		0			0
$303$	2.20350	+	0.829577i	0.126588	+	0.0476580i
$304$		0			0
$305$			17.9604i			1.02841i
$306$		0			0
$307$	−21.4360	+	21.4360i	−1.22342	+	1.22342i	−0.257010	+	0.966409i	$0.582737\pi$
$307$	−21.4360	+	21.4360i	−1.22342	+	1.22342i	−0.966409	+	0.257010i	$0.917263\pi$
$308$		0			0
$309$	−2.48921	+	1.12757i	−0.141606	+	0.0641449i
$310$		0			0
$311$		−	27.0587i		−	1.53436i	−0.641432	−	0.767180i	$-0.721659\pi$
$311$		−	27.0587i		−	1.53436i	0.641432	−	0.767180i	$-0.278341\pi$
$312$		0			0
$313$		−	19.5559i		−	1.10537i	−0.833392	−	0.552683i	$-0.813604\pi$
$313$		−	19.5559i		−	1.10537i	0.833392	−	0.552683i	$-0.186396\pi$
$314$		0			0
$315$	−5.58763	+	0.365176i	−0.314827	+	0.0205754i
$316$		0			0
$317$	−17.8168	+	17.8168i	−1.00069	+	1.00069i	−0.000690694		1.00000i	$0.500220\pi$
$317$	−17.8168	+	17.8168i	−1.00069	+	1.00069i	−1.00000		0.000690694i	$0.999780\pi$
$318$		0			0
$319$			10.6425i			0.595868i
$320$		0			0
$321$	3.91569	−	10.4008i	0.218553	−	0.580515i
$322$		0			0
$323$	−13.2373	−	13.2373i	−0.736545	−	0.736545i
$324$		0			0
$325$	6.94052	−	6.94052i	0.384991	−	0.384991i
$326$		0			0
$327$	−5.13439	−	1.93300i	−0.283932	−	0.106895i
$328$		0			0
$329$	−11.3696			−0.626825
$330$		0			0
$331$	1.41507	+	1.41507i	0.0777791	+	0.0777791i	0.744926	−	0.667147i	$-0.232485\pi$
$331$	1.41507	+	1.41507i	0.0777791	+	0.0777791i	−0.667147	+	0.744926i	$0.732485\pi$
$332$		0			0
$333$	−1.93409	−	29.5939i	−0.105987	−	1.62173i
$334$		0			0
$335$	5.02562			0.274579
$336$		0			0
$337$	−29.1493			−1.58786			−0.793931	−	0.608008i	$-0.791969\pi$
$337$	−29.1493			−1.58786			−0.793931	+	0.608008i	$0.791969\pi$
$338$		0			0
$339$	11.4889	+	25.3628i	0.623989	+	1.37752i
$340$		0			0
$341$	−7.18240	−	7.18240i	−0.388949	−	0.388949i
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	3.00382	−	7.97868i	0.161720	−	0.429557i
$346$		0			0
$347$	−5.64644	+	5.64644i	−0.303117	+	0.303117i	−0.842232	−	0.539115i	$-0.818759\pi$
$347$	−5.64644	+	5.64644i	−0.303117	+	0.303117i	0.539115	+	0.842232i	$0.318759\pi$
$348$		0			0
$349$	2.91855	+	2.91855i	0.156226	+	0.156226i	0.780892	−	0.624666i	$-0.214765\pi$
$349$	2.91855	+	2.91855i	0.156226	+	0.156226i	−0.624666	+	0.780892i	$0.714765\pi$
$350$		0			0
$351$	29.6723	−	15.8494i	1.58379	−	0.845979i
$352$		0			0
$353$			33.2445i			1.76943i	0.466136	+	0.884713i	$0.345646\pi$
$353$			33.2445i			1.76943i	−0.466136	+	0.884713i	$0.654354\pi$
$354$		0			0
$355$	17.6759	−	17.6759i	0.938142	−	0.938142i
$356$		0			0
$357$	−4.16228	−	9.18865i	−0.220291	−	0.486315i
$358$		0			0
$359$			22.1409i			1.16855i	0.811555	+	0.584276i	$0.198621\pi$
$359$			22.1409i			1.16855i	−0.811555	+	0.584276i	$0.801379\pi$
$360$		0			0
$361$			8.66780i			0.456200i
$362$		0			0
$363$	5.67984	+	12.5388i	0.298115	+	0.658117i
$364$		0			0
$365$	−0.681133	+	0.681133i	−0.0356521	+	0.0356521i
$366$		0			0
$367$			13.1466i			0.686245i	0.939291	+	0.343123i	$0.111485\pi$
$367$			13.1466i			0.686245i	−0.939291	+	0.343123i	$0.888515\pi$
$368$		0			0
$369$	−7.06319	+	8.05097i	−0.367695	+	0.419117i
$370$		0			0
$371$	0.573389	+	0.573389i	0.0297688	+	0.0297688i
$372$		0			0
$373$	−6.88134	+	6.88134i	−0.356302	+	0.356302i	−0.862448	−	0.506146i	$-0.831070\pi$
$373$	−6.88134	+	6.88134i	−0.356302	+	0.356302i	0.506146	+	0.862448i	$0.331070\pi$
$374$		0			0
$375$	−7.42234	+	19.7151i	−0.383288	+	1.01808i
$376$		0			0
$377$	39.4351			2.03101
$378$		0			0
$379$	8.62629	+	8.62629i	0.443103	+	0.443103i	0.893053	−	0.449951i	$-0.148558\pi$
$379$	8.62629	+	8.62629i	0.443103	+	0.443103i	−0.449951	+	0.893053i	$0.648558\pi$
$380$		0			0
$381$	8.70062	+	19.2075i	0.445746	+	0.984030i
$382$		0			0
$383$	−11.3881			−0.581902			−0.290951	−	0.956738i	$-0.593972\pi$
$383$	−11.3881			−0.581902			−0.290951	+	0.956738i	$0.593972\pi$
$384$		0			0
$385$	3.26113			0.166203
$386$		0			0
$387$	−8.98825	+	0.587422i	−0.456899	+	0.0298604i
$388$		0			0
$389$	−2.70246	−	2.70246i	−0.137020	−	0.137020i	0.635270	−	0.772290i	$-0.280889\pi$
$389$	−2.70246	−	2.70246i	−0.137020	−	0.137020i	−0.772290	+	0.635270i	$0.780889\pi$
$390$		0			0
$391$	15.3582			0.776699
$392$		0			0
$393$	30.3235	+	11.4162i	1.52962	+	0.575871i
$394$		0			0
$395$	−4.10298	+	4.10298i	−0.206443	+	0.206443i
$396$		0			0
$397$	13.4550	+	13.4550i	0.675285	+	0.675285i	0.958929	−	0.283645i	$-0.0915437\pi$
$397$	13.4550	+	13.4550i	0.675285	+	0.675285i	−0.283645	+	0.958929i	$0.591544\pi$
$398$		0			0
$399$	1.96163	−	5.21043i	0.0982042	−	0.260848i
$400$		0			0
$401$			20.8404i			1.04072i	0.853947	+	0.520360i	$0.174202\pi$
$401$			20.8404i			1.04072i	−0.853947	+	0.520360i	$0.825798\pi$
$402$		0			0
$403$	−26.6138	+	26.6138i	−1.32573	+	1.32573i
$404$		0			0
$405$	−10.2314	+	13.3234i	−0.508402	+	0.662046i
$406$		0			0
$407$			17.2720i			0.856140i
$408$		0			0
$409$			5.40841i			0.267429i	0.991020	+	0.133714i	$0.0426904\pi$
$409$			5.40841i			0.267429i	−0.991020	+	0.133714i	$0.957310\pi$
$410$		0			0
$411$	−5.48414	+	2.48421i	−0.270513	+	0.122537i
$412$		0			0
$413$	8.42236	−	8.42236i	0.414437	−	0.414437i
$414$		0			0
$415$		−	7.68804i		−	0.377391i
$416$		0			0
$417$	−17.9376	−	6.75317i	−0.878409	−	0.330704i
$418$		0			0
$419$	−7.34358	−	7.34358i	−0.358757	−	0.358757i	0.504598	−	0.863355i	$-0.331641\pi$
$419$	−7.34358	−	7.34358i	−0.358757	−	0.358757i	−0.863355	+	0.504598i	$0.831641\pi$
$420$		0			0
$421$	−27.6477	+	27.6477i	−1.34746	+	1.34746i	−0.459059	+	0.888406i	$0.651813\pi$
$421$	−27.6477	+	27.6477i	−1.34746	+	1.34746i	−0.888406	+	0.459059i	$0.848187\pi$
$422$		0			0
$423$	−22.4943	+	25.6401i	−1.09371	+	1.24666i
$424$		0			0
$425$	−8.82983			−0.428310
$426$		0			0
$427$	−6.80408	−	6.80408i	−0.329273	−	0.329273i
$428$		0			0
$429$	−17.8461	+	8.08393i	−0.861617	+	0.390296i
$430$		0			0
$431$	−24.7167			−1.19056			−0.595280	−	0.803518i	$-0.702959\pi$
$431$	−24.7167			−1.19056			−0.595280	+	0.803518i	$0.702959\pi$
$432$		0			0
$433$	8.30731			0.399224			0.199612	−	0.979875i	$-0.436032\pi$
$433$	8.30731			0.399224			0.199612	+	0.979875i	$0.436032\pi$
$434$		0			0
$435$	−17.9380	+	8.12555i	−0.860060	+	0.389591i
$436$		0			0
$437$	5.99381	+	5.99381i	0.286723	+	0.286723i
$438$		0			0
$439$	11.3849			0.543372			0.271686	−	0.962386i	$-0.412419\pi$
$439$	11.3849			0.543372			0.271686	+	0.962386i	$0.412419\pi$
$440$		0			0
$441$	1.97846	−	2.25515i	0.0942125	−	0.107388i
$442$		0			0
$443$	22.3778	−	22.3778i	1.06320	−	1.06320i	0.0653386	−	0.997863i	$-0.479187\pi$
$443$	22.3778	−	22.3778i	1.06320	−	1.06320i	0.997863	−	0.0653386i	$-0.0208128\pi$
$444$		0			0
$445$	5.73263	+	5.73263i	0.271753	+	0.271753i
$446$		0			0
$447$	8.39155	+	3.15926i	0.396906	+	0.149428i
$448$		0			0
$449$			1.78966i			0.0844591i	0.999108	+	0.0422296i	$0.0134461\pi$
$449$			1.78966i			0.0844591i	−0.999108	+	0.0422296i	$0.986554\pi$
$450$		0			0
$451$	4.41057	−	4.41057i	0.207685	−	0.207685i
$452$		0			0
$453$	−1.31665	+	0.596419i	−0.0618618	+	0.0280222i
$454$		0			0
$455$		−	12.0839i		−	0.566500i
$456$		0			0
$457$		−	39.7567i		−	1.85974i	−0.367891	−	0.929869i	$-0.619920\pi$
$457$		−	39.7567i		−	1.85974i	0.367891	−	0.929869i	$-0.380080\pi$
$458$		0			0
$459$	−28.9567	−	8.79284i	−1.35158	−	0.410415i
$460$		0			0
$461$	1.66514	−	1.66514i	0.0775534	−	0.0775534i	−0.667266	−	0.744819i	$-0.732536\pi$
$461$	1.66514	−	1.66514i	0.0775534	−	0.0775534i	0.744819	+	0.667266i	$0.232536\pi$
$462$		0			0
$463$		−	6.79248i		−	0.315674i	−0.987465	−	0.157837i	$-0.949548\pi$
$463$		−	6.79248i		−	0.315674i	0.987465	−	0.157837i	$-0.0504520\pi$
$464$		0			0
$465$	6.62217	−	17.5897i	0.307096	−	0.815701i
$466$		0			0
$467$	8.95396	+	8.95396i	0.414340	+	0.414340i	0.883247	−	0.468907i	$-0.155352\pi$
$467$	8.95396	+	8.95396i	0.414340	+	0.414340i	−0.468907	+	0.883247i	$0.655352\pi$
$468$		0			0
$469$	−1.90390	+	1.90390i	−0.0879138	+	0.0879138i
$470$		0			0
$471$	25.4877	+	9.59563i	1.17441	+	0.442143i
$472$		0			0
$473$	5.24585			0.241204
$474$		0			0
$475$	−3.44599	−	3.44599i	−0.158113	−	0.158113i
$476$		0			0
$477$	2.42750	−	0.158648i	0.111148	−	0.00726400i
$478$		0			0
$479$	−17.2099			−0.786340			−0.393170	−	0.919466i	$-0.628622\pi$
$479$	−17.2099			−0.786340			−0.393170	+	0.919466i	$0.628622\pi$
$480$		0			0
$481$	64.0000			2.91815
$482$		0			0
$483$	1.88466	+	4.16058i	0.0857552	+	0.189313i
$484$		0			0
$485$	−10.6870	−	10.6870i	−0.485270	−	0.485270i
$486$		0			0
$487$	−27.8022			−1.25984			−0.629918	−	0.776662i	$-0.716911\pi$
$487$	−27.8022			−1.25984			−0.629918	+	0.776662i	$0.716911\pi$
$488$		0			0
$489$	2.06798	−	5.49292i	0.0935172	−	0.248398i
$490$		0			0
$491$	−5.65204	+	5.65204i	−0.255073	+	0.255073i	−0.823047	−	0.567974i	$-0.807728\pi$
$491$	−5.65204	+	5.65204i	−0.255073	+	0.255073i	0.567974	+	0.823047i	$0.307728\pi$
$492$		0			0
$493$	−25.0850	−	25.0850i	−1.12977	−	1.12977i
$494$		0			0
$495$	6.45202	−	7.35432i	0.289997	−	0.330552i
$496$		0			0
$497$			13.3926i			0.600741i
$498$		0			0
$499$	15.1120	−	15.1120i	0.676506	−	0.676506i	−0.282701	−	0.959208i	$-0.591231\pi$
$499$	15.1120	−	15.1120i	0.676506	−	0.676506i	0.959208	+	0.282701i	$0.0912306\pi$
$500$		0			0
$501$	−3.00640	−	6.63693i	−0.134316	−	0.296516i
$502$		0			0
$503$		−	16.9039i		−	0.753707i	−0.926273	−	0.376854i	$-0.877006\pi$
$503$		−	16.9039i		−	0.753707i	0.926273	−	0.376854i	$-0.122994\pi$
$504$		0			0
$505$		−	2.53728i		−	0.112907i
$506$		0			0
$507$	20.6635	+	45.6168i	0.917699	+	2.02591i
$508$		0			0
$509$	22.6903	−	22.6903i	1.00573	−	1.00573i	0.00574435	−	0.999984i	$-0.498172\pi$
$509$	22.6903	−	22.6903i	1.00573	−	1.00573i	0.999984	−	0.00574435i	$-0.00182849\pi$
$510$		0			0
$511$		−	0.516078i		−	0.0228299i
$512$		0			0
$513$	−7.86929	−	14.7324i	−0.347438	−	0.650452i
$514$		0			0
$515$	2.08231	+	2.08231i	0.0917577	+	0.0917577i
$516$		0			0
$517$	14.0464	−	14.0464i	0.617760	−	0.617760i
$518$		0			0
$519$	5.98606	−	15.9000i	0.262759	−	0.697934i
$520$		0			0
$521$	7.32638			0.320974			0.160487	−	0.987038i	$-0.448693\pi$
$521$	7.32638			0.320974			0.160487	+	0.987038i	$0.448693\pi$
$522$		0			0
$523$	−14.9784	−	14.9784i	−0.654958	−	0.654958i	0.299225	−	0.954183i	$-0.403272\pi$
$523$	−14.9784	−	14.9784i	−0.654958	−	0.654958i	−0.954183	+	0.299225i	$0.903272\pi$
$524$		0			0
$525$	−1.08354	−	2.39202i	−0.0472896	−	0.104396i
$526$		0			0
$527$	33.8585			1.47490
$528$		0			0
$529$	16.0459			0.697646
$530$		0			0
$531$	−2.33034	−	35.6570i	−0.101128	−	1.54738i
$532$		0			0
$533$	−16.3430	−	16.3430i	−0.707895	−	0.707895i
$534$		0			0
$535$	−11.9762			−0.517778
$536$		0			0
$537$	1.46741	+	0.552452i	0.0633234	+	0.0238401i
$538$		0			0
$539$	−1.23544	+	1.23544i	−0.0532141	+	0.0532141i
$540$		0			0
$541$	−4.34392	−	4.34392i	−0.186760	−	0.186760i	0.607534	−	0.794294i	$-0.292159\pi$
$541$	−4.34392	−	4.34392i	−0.186760	−	0.186760i	−0.794294	+	0.607534i	$0.792159\pi$
$542$		0			0
$543$	3.83059	−	10.1747i	0.164386	−	0.436639i
$544$		0			0
$545$			5.91212i			0.253247i
$546$		0			0
$547$	−21.3206	+	21.3206i	−0.911603	+	0.911603i	−0.996398	−	0.0847958i	$-0.972976\pi$
$547$	−21.3206	+	21.3206i	−0.911603	+	0.911603i	0.0847958	+	0.996398i	$0.472976\pi$
$548$		0			0
$549$	−28.8058	+	1.88259i	−1.22940	+	0.0803469i
$550$		0			0
$551$		−	19.5797i		−	0.834122i
$552$		0			0
$553$		−	3.10873i		−	0.132196i
$554$		0			0
$555$	−29.1119	+	13.1871i	−1.23573	+	0.559762i
$556$		0			0
$557$	−19.4928	+	19.4928i	−0.825938	+	0.825938i	−0.986952	−	0.161014i	$-0.948523\pi$
$557$	−19.4928	+	19.4928i	−0.825938	+	0.825938i	0.161014	+	0.986952i	$0.448523\pi$
$558$		0			0
$559$		−	19.4381i		−	0.822144i
$560$		0			0
$561$	16.4943	+	6.20977i	0.696388	+	0.262177i
$562$		0			0
$563$	8.52509	+	8.52509i	0.359290	+	0.359290i	0.863551	−	0.504261i	$-0.168235\pi$
$563$	8.52509	+	8.52509i	0.359290	+	0.359290i	−0.504261	+	0.863551i	$0.668235\pi$
$564$		0			0
$565$	21.2169	−	21.2169i	0.892600	−	0.892600i
$566$		0			0
$567$	−1.17138	−	8.92345i	−0.0491932	−	0.374749i
$568$		0			0
$569$	8.02648			0.336488			0.168244	−	0.985745i	$-0.446190\pi$
$569$	8.02648			0.336488			0.168244	+	0.985745i	$0.446190\pi$
$570$		0			0
$571$	14.7516	+	14.7516i	0.617337	+	0.617337i	0.944848	−	0.327511i	$-0.106210\pi$
$571$	14.7516	+	14.7516i	0.617337	+	0.617337i	−0.327511	+	0.944848i	$0.606210\pi$
$572$		0			0
$573$	−19.2902	+	8.73810i	−0.805861	+	0.365039i
$574$		0			0
$575$	3.99811			0.166733
$576$		0			0
$577$	8.97453			0.373614			0.186807	−	0.982397i	$-0.440186\pi$
$577$	8.97453			0.373614			0.186807	+	0.982397i	$0.440186\pi$
$578$		0			0
$579$	14.1409	−	6.40557i	0.587677	−	0.266206i
$580$		0			0
$581$	2.91252	+	2.91252i	0.120832	+	0.120832i
$582$		0			0
$583$	−1.41677			−0.0586767
$584$		0			0
$585$	−27.2509	−	23.9075i	−1.12669	−	0.988452i
$586$		0			0
$587$	10.9929	−	10.9929i	0.453727	−	0.453727i	−0.442863	−	0.896589i	$-0.646037\pi$
$587$	10.9929	−	10.9929i	0.453727	−	0.453727i	0.896589	+	0.442863i	$0.146037\pi$
$588$		0			0
$589$	13.2139	+	13.2139i	0.544468	+	0.544468i
$590$		0			0
$591$	17.6362	+	6.63971i	0.725458	+	0.273121i
$592$		0			0
$593$			31.8111i			1.30632i	0.757218	+	0.653162i	$0.226558\pi$
$593$			31.8111i			1.30632i	−0.757218	+	0.653162i	$0.773442\pi$
$594$		0			0
$595$	−7.68663	+	7.68663i	−0.315121	+	0.315121i
$596$		0			0
$597$	−16.4640	+	7.45786i	−0.673826	+	0.305230i
$598$		0			0
$599$		−	30.5728i		−	1.24917i	−0.780957	−	0.624585i	$-0.785268\pi$
$599$		−	30.5728i		−	1.24917i	0.780957	−	0.624585i	$-0.214732\pi$
$600$		0			0
$601$		−	24.7270i		−	1.00863i	−0.863519	−	0.504317i	$-0.831744\pi$
$601$		−	24.7270i		−	1.00863i	0.863519	−	0.504317i	$-0.168256\pi$
$602$		0			0
$603$	0.526780	+	8.06035i	0.0214521	+	0.328243i
$604$		0			0
$605$	10.4892	−	10.4892i	0.426445	−	0.426445i
$606$		0			0
$607$		−	23.2149i		−	0.942264i	−0.882063	−	0.471132i	$-0.843846\pi$
$607$		−	23.2149i		−	0.942264i	0.882063	−	0.471132i	$-0.156154\pi$
$608$		0			0
$609$	3.71731	−	9.87385i	0.150633	−	0.400109i
$610$		0			0
$611$	−52.0479	−	52.0479i	−2.10563	−	2.10563i
$612$		0			0
$613$	4.54522	−	4.54522i	0.183580	−	0.183580i	−0.609334	−	0.792914i	$-0.708563\pi$
$613$	4.54522	−	4.54522i	0.183580	−	0.183580i	0.792914	+	0.609334i	$0.208563\pi$
$614$		0			0
$615$	10.8015	+	4.06654i	0.435557	+	0.163979i
$616$		0			0
$617$	15.7116			0.632526			0.316263	−	0.948671i	$-0.397572\pi$
$617$	15.7116			0.632526			0.316263	+	0.948671i	$0.397572\pi$
$618$		0			0
$619$	−25.9169	−	25.9169i	−1.04169	−	1.04169i	−0.999092	−	0.0425971i	$-0.986437\pi$
$619$	−25.9169	−	25.9169i	−1.04169	−	1.04169i	−0.0425971	−	0.999092i	$-0.513563\pi$
$620$		0			0
$621$	13.1115	+	3.98136i	0.526145	+	0.159767i
$622$		0			0
$623$	−4.34348			−0.174018
$624$		0			0
$625$	15.1208			0.604832
$626$		0			0
$627$	4.01370	+	8.86064i	0.160292	+	0.353860i
$628$		0			0
$629$	−40.7109	−	40.7109i	−1.62325	−	1.62325i
$630$		0			0
$631$	30.9855			1.23351			0.616756	−	0.787154i	$-0.288446\pi$
$631$	30.9855			1.23351			0.616756	+	0.787154i	$0.288446\pi$
$632$		0			0
$633$	−15.4569	+	41.0563i	−0.614357	+	1.63184i
$634$		0			0
$635$	16.0677	−	16.0677i	0.637629	−	0.637629i
$636$		0			0
$637$	4.57782	+	4.57782i	0.181380	+	0.181380i
$638$		0			0
$639$	30.2023	+	26.4968i	1.19479	+	1.04820i
$640$		0			0
$641$			36.3928i			1.43743i	0.695306	+	0.718714i	$0.255269\pi$
$641$			36.3928i			1.43743i	−0.695306	+	0.718714i	$0.744731\pi$
$642$		0			0
$643$	33.1871	−	33.1871i	1.30877	−	1.30877i	0.386468	−	0.922303i	$-0.373695\pi$
$643$	33.1871	−	33.1871i	1.30877	−	1.30877i	0.922303	−	0.386468i	$-0.126305\pi$
$644$		0			0
$645$	4.00519	+	8.84187i	0.157704	+	0.348148i
$646$		0			0
$647$		−	21.9570i		−	0.863217i	−0.902061	−	0.431608i	$-0.857946\pi$
$647$		−	21.9570i		−	0.863217i	0.902061	−	0.431608i	$-0.142054\pi$
$648$		0			0
$649$			20.8106i			0.816888i
$650$		0			0
$651$	4.15490	+	9.17236i	0.162843	+	0.359493i
$652$		0			0
$653$	−28.1079	+	28.1079i	−1.09995	+	1.09995i	−0.105532	+	0.994416i	$0.533655\pi$
$653$	−28.1079	+	28.1079i	−1.09995	+	1.09995i	−0.994416	+	0.105532i	$0.966345\pi$
$654$		0			0
$655$		−	34.9167i		−	1.36431i
$656$		0			0
$657$	−1.16383	−	1.02104i	−0.0454054	−	0.0398346i
$658$		0			0
$659$	27.8370	+	27.8370i	1.08438	+	1.08438i	0.996096	+	0.0882817i	$0.0281376\pi$
$659$	27.8370	+	27.8370i	1.08438	+	1.08438i	0.0882817	+	0.996096i	$0.471862\pi$
$660$		0			0
$661$	25.8418	−	25.8418i	1.00513	−	1.00513i	0.00514248	−	0.999987i	$-0.498363\pi$
$661$	25.8418	−	25.8418i	1.00513	−	1.00513i	0.999987	−	0.00514248i	$-0.00163691\pi$
$662$		0			0
$663$	23.0098	−	61.1182i	0.893628	−	2.37364i
$664$		0			0
$665$	−5.99968			−0.232658
$666$		0			0
$667$	11.3584	+	11.3584i	0.439797	+	0.439797i
$668$		0			0
$669$	5.91684	+	13.0620i	0.228758	+	0.505006i
$670$		0			0
$671$	16.8121			0.649022
$672$		0			0
$673$	−22.1619			−0.854277			−0.427139	−	0.904186i	$-0.640478\pi$
$673$	−22.1619			−0.854277			−0.427139	+	0.904186i	$0.640478\pi$
$674$		0			0
$675$	−7.53811	−	2.28898i	−0.290142	−	0.0881031i
$676$		0			0
$677$	−22.4728	−	22.4728i	−0.863700	−	0.863700i	0.128065	−	0.991766i	$-0.459123\pi$
$677$	−22.4728	−	22.4728i	−0.863700	−	0.863700i	−0.991766	+	0.128065i	$0.959123\pi$
$678$		0			0
$679$	8.09726			0.310744
$680$		0			0
$681$	38.3558	+	14.4402i	1.46980	+	0.553350i
$682$		0			0
$683$	−8.67868	+	8.67868i	−0.332080	+	0.332080i	−0.853376	−	0.521296i	$-0.825449\pi$
$683$	−8.67868	+	8.67868i	−0.332080	+	0.332080i	0.521296	+	0.853376i	$0.325449\pi$
$684$		0			0
$685$	4.58767	+	4.58767i	0.175286	+	0.175286i
$686$		0			0
$687$	−2.87189	+	7.62824i	−0.109569	+	0.291035i
$688$		0			0
$689$			5.24974i			0.199999i
$690$		0			0
$691$	10.6368	−	10.6368i	0.404644	−	0.404644i	−0.475222	−	0.879866i	$-0.657632\pi$
$691$	10.6368	−	10.6368i	0.404644	−	0.404644i	0.879866	+	0.475222i	$0.157632\pi$
$692$		0			0
$693$	0.341828	+	5.23036i	0.0129850	+	0.198685i
$694$		0			0
$695$			20.6547i			0.783478i
$696$		0			0
$697$			20.7918i			0.787546i
$698$		0			0
$699$	35.4177	−	16.0435i	1.33962	−	0.606822i
$700$		0			0
$701$	27.3460	−	27.3460i	1.03285	−	1.03285i	0.0334040	−	0.999442i	$-0.489365\pi$
$701$	27.3460	−	27.3460i	1.03285	−	1.03285i	0.999442	−	0.0334040i	$-0.0106348\pi$
$702$		0			0
$703$		−	31.7762i		−	1.19846i
$704$		0			0
$705$	34.3996	+	12.9508i	1.29556	+	0.487755i
$706$		0			0
$707$	0.961217	+	0.961217i	0.0361503	+	0.0361503i
$708$		0			0
$709$	−3.83200	+	3.83200i	−0.143914	+	0.143914i	−0.775393	−	0.631479i	$-0.782448\pi$
$709$	−3.83200	+	3.83200i	−0.143914	+	0.143914i	0.631479	+	0.775393i	$0.282448\pi$
$710$		0			0
$711$	−7.01063	−	6.15049i	−0.262919	−	0.230662i
$712$		0			0
$713$	−15.3310			−0.574150
$714$		0			0
$715$	14.9289	+	14.9289i	0.558308	+	0.558308i
$716$		0			0
$717$	26.3889	−	11.9537i	0.985512	−	0.446418i
$718$		0			0
$719$	−28.2350			−1.05299			−0.526494	−	0.850179i	$-0.676494\pi$
$719$	−28.2350			−1.05299			−0.526494	+	0.850179i	$0.676494\pi$
$720$		0			0
$721$	−1.57772			−0.0587573
$722$		0			0
$723$	−30.0623	+	13.6176i	−1.11803	+	0.506446i
$724$		0			0
$725$	−6.53021	−	6.53021i	−0.242526	−	0.242526i
$726$		0			0
$727$	−8.86990			−0.328966			−0.164483	−	0.986380i	$-0.552596\pi$
$727$	−8.86990			−0.328966			−0.164483	+	0.986380i	$0.552596\pi$
$728$		0			0
$729$	−22.4412	−	15.0131i	−0.831156	−	0.556040i
$730$		0			0
$731$	−12.3647	+	12.3647i	−0.457325	+	0.457325i
$732$		0			0
$733$	−21.0124	−	21.0124i	−0.776112	−	0.776112i	0.203055	−	0.979167i	$-0.434913\pi$
$733$	−21.0124	−	21.0124i	−0.776112	−	0.776112i	−0.979167	+	0.203055i	$0.934913\pi$
$734$		0			0
$735$	−3.02558	−	1.13907i	−0.111600	−	0.0420154i
$736$		0			0
$737$		−	4.70429i		−	0.173285i
$738$		0			0
$739$	20.4672	−	20.4672i	0.752898	−	0.752898i	−0.222121	−	0.975019i	$-0.571298\pi$
$739$	20.4672	−	20.4672i	0.752898	−	0.752898i	0.975019	+	0.222121i	$0.0712980\pi$
$740$		0			0
$741$	32.8324	−	14.8725i	1.20613	−	0.546353i
$742$		0			0
$743$		−	1.56551i		−	0.0574330i	−0.999588	−	0.0287165i	$-0.990858\pi$
$743$		−	1.56551i		−	0.0574330i	0.999588	−	0.0287165i	$-0.00914200\pi$
$744$		0			0
$745$		−	9.66265i		−	0.354012i
$746$		0			0
$747$	12.3305	−	0.805852i	0.451149	−	0.0294846i
$748$		0			0
$749$	4.53705	−	4.53705i	0.165780	−	0.165780i
$750$		0			0
$751$		−	33.8650i		−	1.23575i	−0.786275	−	0.617876i	$-0.787993\pi$
$751$		−	33.8650i		−	1.23575i	0.786275	−	0.617876i	$-0.212007\pi$
$752$		0			0
$753$	−1.85892	+	4.93762i	−0.0677428	+	0.179937i
$754$		0			0
$755$	1.10143	+	1.10143i	0.0400851	+	0.0400851i
$756$		0			0
$757$	12.4442	−	12.4442i	0.452291	−	0.452291i	−0.443823	−	0.896114i	$-0.646378\pi$
$757$	12.4442	−	12.4442i	0.452291	−	0.452291i	0.896114	+	0.443823i	$0.146378\pi$
$758$		0			0
$759$	−7.46853	−	2.81176i	−0.271091	−	0.102060i
$760$		0			0
$761$	−46.8851			−1.69958			−0.849791	−	0.527119i	$-0.823272\pi$
$761$	−46.8851			−1.69958			−0.849791	+	0.527119i	$0.823272\pi$
$762$		0			0
$763$	−2.23973	−	2.23973i	−0.0810838	−	0.0810838i
$764$		0			0
$765$	2.12678	+	32.5422i	0.0768938	+	1.17657i
$766$		0			0
$767$	77.1121			2.78436
$768$		0			0
$769$	12.9505			0.467005			0.233503	−	0.972356i	$-0.424981\pi$
$769$	12.9505			0.467005			0.233503	+	0.972356i	$0.424981\pi$
$770$		0			0
$771$	−17.3854	−	38.3800i	−0.626121	−	1.38222i
$772$		0			0
$773$	17.9424	+	17.9424i	0.645342	+	0.645342i	0.951864	−	0.306522i	$-0.0991653\pi$
$773$	17.9424	+	17.9424i	0.645342	+	0.645342i	−0.306522	+	0.951864i	$0.599165\pi$
$774$		0			0
$775$	8.81417			0.316614
$776$		0			0
$777$	6.03290	−	16.0245i	0.216429	−	0.574874i
$778$		0			0
$779$	−8.11437	+	8.11437i	−0.290727	+	0.290727i
$780$		0			0
$781$	−16.5458	−	16.5458i	−0.592054	−	0.592054i
$782$		0			0
$783$	−14.9124	−	27.9181i	−0.532926	−	0.997712i
$784$		0			0
$785$		−	29.3484i		−	1.04749i
$786$		0			0
$787$	25.3110	−	25.3110i	0.902240	−	0.902240i	−0.0933900	−	0.995630i	$-0.529770\pi$
$787$	25.3110	−	25.3110i	0.902240	−	0.902240i	0.995630	+	0.0933900i	$0.0297703\pi$
$788$		0			0
$789$	−6.05611	−	13.3695i	−0.215603	−	0.475966i
$790$		0			0
$791$			16.0755i			0.571579i
$792$		0			0
$793$		−	62.2958i		−	2.21219i
$794$		0			0
$795$	−1.08170	−	2.38797i	−0.0383641	−	0.0846925i
$796$		0			0
$797$	−6.78134	+	6.78134i	−0.240207	+	0.240207i	−0.816936	−	0.576729i	$-0.804329\pi$
$797$	−6.78134	+	6.78134i	−0.240207	+	0.240207i	0.576729	+	0.816936i	$0.304329\pi$
$798$		0			0
$799$			66.2161i			2.34256i
$800$		0			0
$801$	−8.59340	+	9.79518i	−0.303633	+	0.346096i
$802$		0			0
$803$	0.637582	+	0.637582i	0.0224998	+	0.0224998i
$804$		0			0
$805$	3.48047	−	3.48047i	0.122671	−	0.122671i
$806$		0			0
$807$	0.447948	−	1.18983i	0.0157685	−	0.0418839i
$808$		0			0
$809$	−1.53506			−0.0539699			−0.0269849	−	0.999636i	$-0.508591\pi$
$809$	−1.53506			−0.0539699			−0.0269849	+	0.999636i	$0.508591\pi$
$810$		0			0
$811$	14.5930	+	14.5930i	0.512428	+	0.512428i	0.915270	−	0.402842i	$-0.131978\pi$
$811$	14.5930	+	14.5930i	0.512428	+	0.512428i	−0.402842	+	0.915270i	$0.631978\pi$
$812$		0			0
$813$	0.317434	+	0.700766i	0.0111329	+	0.0245769i
$814$		0			0
$815$	−6.32495			−0.221553
$816$		0			0
$817$	−9.65108			−0.337649
$818$		0			0
$819$	19.3807	−	1.26662i	0.677217	−	0.0442591i
$820$		0			0
$821$	35.7226	+	35.7226i	1.24673	+	1.24673i	0.957156	+	0.289571i	$0.0935127\pi$
$821$	35.7226	+	35.7226i	1.24673	+	1.24673i	0.289571	+	0.957156i	$0.406487\pi$
$822$		0			0
$823$	1.22131			0.0425722			0.0212861	−	0.999773i	$-0.493224\pi$
$823$	1.22131			0.0425722			0.0212861	+	0.999773i	$0.493224\pi$
$824$		0			0
$825$	4.29385	+	1.61655i	0.149493	+	0.0562811i
$826$		0			0
$827$	−16.3468	+	16.3468i	−0.568434	+	0.568434i	−0.931689	−	0.363256i	$-0.881665\pi$
$827$	−16.3468	+	16.3468i	−0.568434	+	0.568434i	0.363256	+	0.931689i	$0.381665\pi$
$828$		0			0
$829$	−19.0692	−	19.0692i	−0.662299	−	0.662299i	0.293622	−	0.955921i	$-0.405139\pi$
$829$	−19.0692	−	19.0692i	−0.662299	−	0.662299i	−0.955921	+	0.293622i	$0.905139\pi$
$830$		0			0
$831$	−17.5724	+	46.6755i	−0.609581	+	1.61915i
$832$		0			0
$833$		−	5.82397i		−	0.201789i
$834$		0			0
$835$	−5.55203	+	5.55203i	−0.192136	+	0.192136i
$836$		0			0
$837$	28.9053	+	8.77725i	0.999115	+	0.303386i
$838$		0			0
$839$			27.8332i			0.960907i	0.877020	+	0.480454i	$0.159528\pi$
$839$			27.8332i			0.960907i	−0.877020	+	0.480454i	$0.840472\pi$
$840$		0			0
$841$		−	8.10376i		−	0.279440i
$842$		0			0
$843$	−20.5276	+	9.29862i	−0.707009	+	0.320261i
$844$		0			0
$845$	38.1600	−	38.1600i	1.31275	−	1.31275i
$846$		0			0
$847$			7.94738i			0.273075i
$848$		0			0
$849$	−24.6417	−	9.27711i	−0.845700	−	0.318390i
$850$		0			0
$851$	18.4337	+	18.4337i	0.631899	+	0.631899i
$852$		0			0
$853$	5.17015	−	5.17015i	0.177023	−	0.177023i	−0.613034	−	0.790057i	$-0.710051\pi$
$853$	5.17015	−	5.17015i	0.177023	−	0.177023i	0.790057	+	0.613034i	$0.210051\pi$
$854$		0			0
$855$	−11.8701	+	13.5302i	−0.405950	+	0.462722i
$856$		0			0
$857$	16.7170			0.571043			0.285521	−	0.958372i	$-0.407833\pi$
$857$	16.7170			0.571043			0.285521	+	0.958372i	$0.407833\pi$
$858$		0			0
$859$	23.6679	+	23.6679i	0.807538	+	0.807538i	0.984261	−	0.176723i	$-0.0565496\pi$
$859$	23.6679	+	23.6679i	0.807538	+	0.807538i	−0.176723	+	0.984261i	$0.556550\pi$
$860$		0			0
$861$	−5.63256	+	2.55144i	−0.191957	+	0.0869529i
$862$		0			0
$863$	−4.35836			−0.148360			−0.0741802	−	0.997245i	$-0.523634\pi$
$863$	−4.35836			−0.148360			−0.0741802	+	0.997245i	$0.523634\pi$
$864$		0			0
$865$	−18.3085			−0.622507
$866$		0			0
$867$	−26.6931	+	12.0914i	−0.906544	+	0.410647i
$868$		0			0
$869$	3.84064	+	3.84064i	0.130285	+	0.130285i
$870$		0			0
$871$	−17.4314			−0.590640
$872$		0			0
$873$	16.0201	−	18.2605i	0.542199	−	0.618025i
$874$		0			0
$875$	−8.60014	+	8.60014i	−0.290738	+	0.290738i
$876$		0			0
$877$	17.3529	+	17.3529i	0.585967	+	0.585967i	0.936537	−	0.350570i	$-0.114012\pi$
$877$	17.3529	+	17.3529i	0.585967	+	0.585967i	−0.350570	+	0.936537i	$0.614012\pi$
$878$		0			0
$879$	−14.0845	−	5.30255i	−0.475059	−	0.178851i
$880$		0			0
$881$		−	27.2412i		−	0.917780i	−0.888493	−	0.458890i	$-0.848247\pi$
$881$		−	27.2412i		−	0.917780i	0.888493	−	0.458890i	$-0.151753\pi$
$882$		0			0
$883$	19.7164	−	19.7164i	0.663509	−	0.663509i	−0.292696	−	0.956205i	$-0.594552\pi$
$883$	19.7164	−	19.7164i	0.663509	−	0.663509i	0.956205	+	0.292696i	$0.0945524\pi$
$884$		0			0
$885$	−35.0762	+	15.8889i	−1.17908	+	0.534098i
$886$		0			0
$887$		−	5.06180i		−	0.169959i	−0.996383	−	0.0849793i	$-0.972918\pi$
$887$		−	5.06180i		−	0.169959i	0.996383	−	0.0849793i	$-0.0270824\pi$
$888$		0			0
$889$			12.1741i			0.408307i
$890$		0			0
$891$	12.4715	+	9.57720i	0.417812	+	0.320848i
$892$		0			0
$893$	−25.8420	+	25.8420i	−0.864768	+	0.864768i
$894$		0			0
$895$		−	1.68969i		−	0.0564800i
$896$		0			0
$897$	−10.4188	+	27.6741i	−0.347872	+	0.924010i
$898$		0			0
$899$	25.0405	+	25.0405i	0.835146	+	0.835146i
$900$		0			0
$901$	3.33940	−	3.33940i	0.111252	−	0.111252i
$902$		0			0
$903$	−4.86695	−	1.83231i	−0.161962	−	0.0609756i
$904$		0			0
$905$	−11.7159			−0.389451
$906$		0			0
$907$	−19.9916	−	19.9916i	−0.663812	−	0.663812i	0.292465	−	0.956276i	$-0.405525\pi$
$907$	−19.9916	−	19.9916i	−0.663812	−	0.663812i	−0.956276	+	0.292465i	$0.905525\pi$
$908$		0			0
$909$	4.06942	−	0.265955i	0.134974	−	0.00882115i
$910$		0			0
$911$	−28.5053			−0.944423			−0.472211	−	0.881485i	$-0.656544\pi$
$911$	−28.5053			−0.944423			−0.472211	+	0.881485i	$0.656544\pi$
$912$		0			0
$913$	−7.19648			−0.238169
$914$		0			0
$915$	12.8360	+	28.3367i	0.424344	+	0.936782i
$916$		0			0
$917$	13.2278	+	13.2278i	0.436819	+	0.436819i
$918$		0			0
$919$	7.25783			0.239414			0.119707	−	0.992809i	$-0.461805\pi$
$919$	7.25783			0.239414			0.119707	+	0.992809i	$0.461805\pi$
$920$		0			0
$921$	−18.5003	+	49.1402i	−0.609607	+	1.61922i
$922$		0			0
$923$	−61.3091	+	61.3091i	−2.01801	+	2.01801i
$924$		0			0
$925$	−10.5980	−	10.5980i	−0.348460	−	0.348460i
$926$		0			0
$927$	−3.12146	+	3.55799i	−0.102522	+	0.116860i
$928$		0			0
$929$		−	24.6859i		−	0.809917i	−0.914335	−	0.404958i	$-0.867286\pi$
$929$		−	24.6859i		−	0.809917i	0.914335	−	0.404958i	$-0.132714\pi$
$930$		0			0
$931$	2.27291	−	2.27291i	0.0744915	−	0.0744915i
$932$		0			0
$933$	−19.3384	−	42.6914i	−0.633110	−	1.39765i
$934$		0			0
$935$		−	18.9927i		−	0.621128i
$936$		0			0
$937$			47.2256i			1.54279i	0.636354	+	0.771397i	$0.280442\pi$
$937$			47.2256i			1.54279i	−0.636354	+	0.771397i	$0.719558\pi$
$938$		0			0
$939$	−13.9762	−	30.8540i	−0.456097	−	1.00688i
$940$		0			0
$941$	17.0730	−	17.0730i	0.556564	−	0.556564i	−0.371763	−	0.928328i	$-0.621247\pi$
$941$	17.0730	−	17.0730i	0.556564	−	0.556564i	0.928328	+	0.371763i	$0.121247\pi$
$942$		0			0
$943$		−	9.41445i		−	0.306577i
$944$		0			0
$945$	−8.55478	+	4.56952i	−0.278287	+	0.148647i
$946$		0			0
$947$	−35.0765	−	35.0765i	−1.13983	−	1.13983i	−0.988480	−	0.151354i	$-0.951637\pi$
$947$	−35.0765	−	35.0765i	−1.13983	−	1.13983i	−0.151354	−	0.988480i	$-0.548363\pi$
$948$		0			0
$949$	2.36251	−	2.36251i	0.0766904	−	0.0766904i
$950$		0			0
$951$	−15.3768	+	40.8434i	−0.498625	+	1.32444i
$952$		0			0
$953$	27.4125			0.887979			0.443990	−	0.896032i	$-0.353563\pi$
$953$	27.4125			0.887979			0.443990	+	0.896032i	$0.353563\pi$
$954$		0			0
$955$	16.1369	+	16.1369i	0.522179	+	0.522179i
$956$		0			0
$957$	7.60602	+	16.7910i	0.245868	+	0.542777i
$958$		0			0
$959$	−3.47597			−0.112245
$960$		0			0
$961$	−2.79846			−0.0902730
$962$		0			0
$963$	−1.25533	−	19.2081i	−0.0404526	−	0.618972i
$964$		0			0
$965$	−11.8294	−	11.8294i	−0.380801	−	0.380801i
$966$		0			0
$967$	−9.02426			−0.290201			−0.145100	−	0.989417i	$-0.546350\pi$
$967$	−9.02426			−0.290201			−0.145100	+	0.989417i	$0.546350\pi$
$968$		0			0
$969$	−30.3454	−	11.4245i	−0.974836	−	0.367007i
$970$		0			0
$971$	−7.53771	+	7.53771i	−0.241897	+	0.241897i	−0.817634	−	0.575738i	$-0.804715\pi$
$971$	−7.53771	+	7.53771i	−0.241897	+	0.241897i	0.575738	+	0.817634i	$0.304715\pi$
$972$		0			0
$973$	−7.82479	−	7.82479i	−0.250851	−	0.250851i
$974$		0			0
$975$	5.99000	−	15.9105i	0.191834	−	0.509544i
$976$		0			0
$977$		−	0.0758580i		−	0.00242691i	−0.999999	−	0.00121346i	$-0.999614\pi$
$977$		−	0.0758580i		−	0.00242691i	0.999999	−	0.00121346i	$-0.000386255\pi$
$978$		0			0
$979$	5.36610	−	5.36610i	0.171501	−	0.171501i
$980$		0			0
$981$	−9.48216	+	0.619701i	−0.302742	+	0.0197855i
$982$		0			0
$983$		−	17.1286i		−	0.546318i	−0.961969	−	0.273159i	$-0.911932\pi$
$983$		−	17.1286i		−	0.546318i	0.961969	−	0.273159i	$-0.0880684\pi$
$984$		0			0
$985$		−	20.3077i		−	0.647057i
$986$		0			0
$987$	−17.9381	+	8.12562i	−0.570976	+	0.258641i
$988$		0			0
$989$	5.59869	−	5.59869i	0.178028	−	0.178028i
$990$		0			0
$991$			52.2548i			1.65993i	0.557816	+	0.829965i	$0.311639\pi$
$991$			52.2548i			1.65993i	−0.557816	+	0.829965i	$0.688361\pi$
$992$		0			0
$993$	3.24391	+	1.22127i	0.102942	+	0.0387559i
$994$		0			0
$995$	13.7727	+	13.7727i	0.436624	+	0.436624i
$996$		0			0
$997$	−14.7204	+	14.7204i	−0.466200	+	0.466200i	−0.900681	−	0.434481i	$-0.856932\pi$
$997$	−14.7204	+	14.7204i	−0.466200	+	0.466200i	0.434481	+	0.900681i	$0.356932\pi$
$998$		0			0
$999$	−24.2016	−	45.3089i	−0.765706	−	1.43351i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.s.c.239.17		40
3.2	odd	2	inner	1344.2.s.c.239.15		40
4.3	odd	2		336.2.s.c.323.9	yes	40
12.11	even	2		336.2.s.c.323.12	yes	40
16.5	even	4		336.2.s.c.155.12	yes	40
16.11	odd	4	inner	1344.2.s.c.911.15		40
48.5	odd	4		336.2.s.c.155.9	✓	40
48.11	even	4	inner	1344.2.s.c.911.17		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.c.155.9	✓	40	48.5	odd	4
336.2.s.c.155.12	yes	40	16.5	even	4
336.2.s.c.323.9	yes	40	4.3	odd	2
336.2.s.c.323.12	yes	40	12.11	even	2
1344.2.s.c.239.15		40	3.2	odd	2	inner
1344.2.s.c.239.17		40	1.1	even	1	trivial
1344.2.s.c.911.15		40	16.11	odd	4	inner
1344.2.s.c.911.17		40	48.11	even	4	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:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.57773 - 0.714681i) q^{3} +(-1.31983 - 1.31983i) q^{5} +1.00000 q^{7} +(1.97846 - 2.25515i) q^{9} +O(q^{10})\)	\(q+(1.57773 - 0.714681i) q^{3} +(-1.31983 - 1.31983i) q^{5} +1.00000 q^{7} +(1.97846 - 2.25515i) q^{9} +(-1.23544 + 1.23544i) q^{11} +(4.57782 + 4.57782i) q^{13} +(-3.02558 - 1.13907i) q^{15} -5.82397i q^{17} +(2.27291 - 2.27291i) q^{19} +(1.57773 - 0.714681i) q^{21} +2.63707i q^{23} -1.51612i q^{25} +(1.50977 - 4.97198i) q^{27} +(4.30719 - 4.30719i) q^{29} +5.81364i q^{31} +(-1.06624 + 2.83213i) q^{33} +(-1.31983 - 1.31983i) q^{35} +(6.99022 - 6.99022i) q^{37} +(10.4943 + 3.95088i) q^{39} -3.57004 q^{41} +(-2.12307 - 2.12307i) q^{43} +(-5.58763 + 0.365176i) q^{45} -11.3696 q^{47} +1.00000 q^{49} +(-4.16228 - 9.18865i) q^{51} +(0.573389 + 0.573389i) q^{53} +3.26113 q^{55} +(1.96163 - 5.21043i) q^{57} +(8.42236 - 8.42236i) q^{59} +(-6.80408 - 6.80408i) q^{61} +(1.97846 - 2.25515i) q^{63} -12.0839i q^{65} +(-1.90390 + 1.90390i) q^{67} +(1.88466 + 4.16058i) q^{69} +13.3926i q^{71} -0.516078i q^{73} +(-1.08354 - 2.39202i) q^{75} +(-1.23544 + 1.23544i) q^{77} -3.10873i q^{79} +(-1.17138 - 8.92345i) q^{81} +(2.91252 + 2.91252i) q^{83} +(-7.68663 + 7.68663i) q^{85} +(3.71731 - 9.87385i) q^{87} -4.34348 q^{89} +(4.57782 + 4.57782i) q^{91} +(4.15490 + 9.17236i) q^{93} -5.99968 q^{95} +8.09726 q^{97} +(0.341828 + 5.23036i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} + 40 q^{7}+O(q^{10}) \) 40 * q - 4 * q^3 + 40 * q^7	\( 40 q - 4 q^{3} + 40 q^{7} + 24 q^{13} - 16 q^{19} - 4 q^{21} + 32 q^{27} + 24 q^{33} - 8 q^{37} + 64 q^{39} - 24 q^{43} - 28 q^{45} + 40 q^{49} + 32 q^{51} - 16 q^{55} - 48 q^{61} - 40 q^{67} + 4 q^{69} - 40 q^{75} + 56 q^{81} - 48 q^{85} - 32 q^{87} + 24 q^{91} + 56 q^{93} + 16 q^{97} - 24 q^{99}+O(q^{100}) \) 40 * q - 4 * q^3 + 40 * q^7 + 24 * q^13 - 16 * q^19 - 4 * q^21 + 32 * q^27 + 24 * q^33 - 8 * q^37 + 64 * q^39 - 24 * q^43 - 28 * q^45 + 40 * q^49 + 32 * q^51 - 16 * q^55 - 48 * q^61 - 40 * q^67 + 4 * q^69 - 40 * q^75 + 56 * q^81 - 48 * q^85 - 32 * q^87 + 24 * q^91 + 56 * q^93 + 16 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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