LMFDB - Embedded newform 1344.2.s.c.239.15

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			239.15
Character	$\chi$	$=$	1344.239
Dual form			1344.2.s.c.911.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.714681 - 1.57773i) q^{3} +(1.31983 + 1.31983i) q^{5} +1.00000 q^{7} +(-1.97846 - 2.25515i) q^{9} +O(q^{10})$	\(q+(0.714681 - 1.57773i) q^{3} +(1.31983 + 1.31983i) q^{5} +1.00000 q^{7} +(-1.97846 - 2.25515i) q^{9} +(1.23544 - 1.23544i) q^{11} +(4.57782 + 4.57782i) q^{13} +(3.02558 - 1.13907i) q^{15} +5.82397i q^{17} +(2.27291 - 2.27291i) q^{19} +(0.714681 - 1.57773i) q^{21} -2.63707i q^{23} -1.51612i q^{25} +(-4.97198 + 1.50977i) q^{27} +(-4.30719 + 4.30719i) q^{29} +5.81364i q^{31} +(-1.06624 - 2.83213i) q^{33} +(1.31983 + 1.31983i) q^{35} +(6.99022 - 6.99022i) q^{37} +(10.4943 - 3.95088i) q^{39} +3.57004 q^{41} +(-2.12307 - 2.12307i) q^{43} +(0.365176 - 5.58763i) q^{45} +11.3696 q^{47} +1.00000 q^{49} +(9.18865 + 4.16228i) q^{51} +(-0.573389 - 0.573389i) q^{53} +3.26113 q^{55} +(-1.96163 - 5.21043i) q^{57} +(-8.42236 + 8.42236i) q^{59} +(-6.80408 - 6.80408i) q^{61} +(-1.97846 - 2.25515i) q^{63} +12.0839i q^{65} +(-1.90390 + 1.90390i) q^{67} +(-4.16058 - 1.88466i) q^{69} -13.3926i q^{71} -0.516078i q^{73} +(-2.39202 - 1.08354i) q^{75} +(1.23544 - 1.23544i) q^{77} -3.10873i q^{79} +(-1.17138 + 8.92345i) q^{81} +(-2.91252 - 2.91252i) q^{83} +(-7.68663 + 7.68663i) q^{85} +(3.71731 + 9.87385i) q^{87} +4.34348 q^{89} +(4.57782 + 4.57782i) q^{91} +(9.17236 + 4.15490i) q^{93} +5.99968 q^{95} +8.09726 q^{97} +(-5.23036 - 0.341828i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.714681	−	1.57773i	0.412621	−	0.910903i
$3$	0.714681	−	1.57773i	0.412621	−	0.910903i
$4$		0			0
$5$	1.31983	+	1.31983i	0.590244	+	0.590244i	0.937697	−	0.347453i	$-0.112953\pi$
$5$	1.31983	+	1.31983i	0.590244	+	0.590244i	−0.347453	+	0.937697i	$0.612953\pi$
$6$		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	−0.495888	−	0.868387i	$-0.665157\pi$
$11$	1.23544	−	1.23544i	0.372499	−	0.372499i	0.868387	+	0.495888i	$0.165157\pi$
$12$		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	$0.249619\pi$
$17$			5.82397i			1.41252i	−0.707952	+	0.706260i	$0.750381\pi$
$18$		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
$21$	0.714681	−	1.57773i	0.155956	−	0.344289i
$22$		0			0
$23$		−	2.63707i		−	0.549867i	−0.961463	−	0.274934i	$-0.911344\pi$
$23$		−	2.63707i		−	0.549867i	0.961463	−	0.274934i	$-0.0886558\pi$
$24$		0			0
$25$		−	1.51612i		−	0.303224i
$26$		0			0
$27$	−4.97198	+	1.50977i	−0.956858	+	0.290555i
$28$		0			0
$29$	−4.30719	+	4.30719i	−0.799825	+	0.799825i	−0.983068	−	0.183243i	$-0.941341\pi$
$29$	−4.30719	+	4.30719i	−0.799825	+	0.799825i	0.183243	+	0.983068i	$0.441341\pi$
$30$		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	$-0.410072\pi$
$41$	3.57004			0.557547			0.278773	+	0.960357i	$0.410072\pi$
$42$		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
$45$	0.365176	−	5.58763i	0.0544373	−	0.832954i
$46$		0			0
$47$	11.3696			1.65842			0.829211	−	0.558935i	$-0.188790\pi$
$47$	11.3696			1.65842			0.829211	+	0.558935i	$0.188790\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$		0			0
$51$	9.18865	+	4.16228i	1.28667	+	0.582836i
$52$		0			0
$53$	−0.573389	−	0.573389i	−0.0787610	−	0.0787610i	0.666629	−	0.745390i	$-0.267737\pi$
$53$	−0.573389	−	0.573389i	−0.0787610	−	0.0787610i	−0.745390	+	0.666629i	$0.767737\pi$
$54$		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	$0.532422\pi$
$59$	−8.42236	+	8.42236i	−1.09650	+	1.09650i	−0.994817	+	0.101681i	$0.967578\pi$
$60$		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
$69$	−4.16058	−	1.88466i	−0.500875	−	0.226887i
$70$		0			0
$71$		−	13.3926i		−	1.58941i	−0.606994	−	0.794706i	$-0.707625\pi$
$71$		−	13.3926i		−	1.58941i	0.606994	−	0.794706i	$-0.292375\pi$
$72$		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
$75$	−2.39202	−	1.08354i	−0.276207	−	0.125116i
$76$		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	0.528958	−	0.848648i	$-0.322583\pi$
$83$	−2.91252	−	2.91252i	−0.319691	−	0.319691i	−0.848648	+	0.528958i	$0.822583\pi$
$84$		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	$-0.426061\pi$
$89$	4.34348			0.460408			0.230204	+	0.973142i	$0.426061\pi$
$90$		0			0
$91$	4.57782	+	4.57782i	0.479886	+	0.479886i
$92$		0			0
$93$	9.17236	+	4.15490i	0.951129	+	0.430843i
$94$		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
$99$	−5.23036	−	0.341828i	−0.525671	−	0.0343550i
$100$		0			0
$101$	−0.961217	−	0.961217i	−0.0956447	−	0.0956447i	0.657665	−	0.753310i	$-0.271544\pi$
$101$	−0.961217	−	0.961217i	−0.0956447	−	0.0956447i	−0.753310	+	0.657665i	$0.771544\pi$
$102$		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	−0.891545	−	0.452932i	$-0.850378\pi$
$107$	−4.53705	+	4.53705i	−0.438613	+	0.438613i	0.452932	+	0.891545i	$0.350378\pi$
$108$		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	$-0.727089\pi$
$113$		−	16.0755i		−	1.51226i	0.654424	−	0.756128i	$-0.272911\pi$
$114$		0			0
$115$	3.48047	−	3.48047i	0.324556	−	0.324556i
$116$		0			0
$117$	1.26662	−	19.3807i	0.117099	−	1.79175i
$118$		0			0
$119$			5.82397i			0.533883i
$120$		0			0
$121$			7.94738i			0.722489i
$122$		0			0
$123$	2.55144	−	5.63256i	0.230056	−	0.507871i
$124$		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	$-0.945518\pi$
$131$	−13.2278	−	13.2278i	−1.15571	−	1.15571i	−0.170327	−	0.985388i	$-0.554482\pi$
$132$		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	$-0.452560\pi$
$137$	3.47597			0.296972			0.148486	+	0.988915i	$0.452560\pi$
$138$		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
$141$	8.12562	−	17.9381i	0.684300	−	1.51066i
$142$		0			0
$143$	11.3112			0.945893
$144$		0			0
$145$	−11.3695			−0.944184
$146$		0			0
$147$	0.714681	−	1.57773i	0.0589459	−	0.130129i
$148$		0			0
$149$	−3.66058	−	3.66058i	−0.299886	−	0.299886i	0.541083	−	0.840969i	$-0.318014\pi$
$149$	−3.66058	−	3.66058i	−0.299886	−	0.299886i	−0.840969	+	0.541083i	$0.818014\pi$
$150$		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
$165$	2.33067	−	5.14518i	0.181442	−	0.400552i
$166$		0			0
$167$			4.20664i			0.325519i	0.986666	+	0.162760i	$0.0520395\pi$
$167$			4.20664i			0.325519i	−0.986666	+	0.162760i	$0.947961\pi$
$168$		0			0
$169$			28.9129i			2.22407i
$170$		0			0
$171$	−9.62260	−	0.628879i	−0.735858	−	0.0480916i
$172$		0			0
$173$	−6.93594	+	6.93594i	−0.527330	+	0.527330i	−0.919775	−	0.392445i	$-0.871629\pi$
$173$	−6.93594	+	6.93594i	−0.527330	+	0.527330i	0.392445	+	0.919775i	$0.371629\pi$
$174$		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	0.682780	−	0.730624i	$-0.260771\pi$
$179$	−0.640117	−	0.640117i	−0.0478446	−	0.0478446i	−0.730624	+	0.682780i	$0.760771\pi$
$180$		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
$189$	−4.97198	+	1.50977i	−0.361658	+	0.109819i
$190$		0			0
$191$	12.2266			0.884684			0.442342	−	0.896847i	$-0.354148\pi$
$191$	12.2266			0.884684			0.442342	+	0.896847i	$0.354148\pi$
$192$		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
$195$	19.0651	+	8.63611i	1.36528	+	0.618445i
$196$		0			0
$197$	−7.69332	−	7.69332i	−0.548126	−	0.548126i	0.377772	−	0.925899i	$-0.376690\pi$
$197$	−7.69332	−	7.69332i	−0.548126	−	0.548126i	−0.925899	+	0.377772i	$0.876690\pi$
$198$		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
$213$	−21.1299	−	9.57146i	−1.44780	−	0.655825i
$214$		0			0
$215$		−	5.60417i		−	0.382201i
$216$		0			0
$217$			5.81364i			0.394656i
$218$		0			0
$219$	−0.814231	−	0.368831i	−0.0550206	−	0.0249233i
$220$		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	$-0.962532\pi$
$227$	−16.7316	−	16.7316i	−1.11052	−	1.11052i	−0.117437	−	0.993080i	$-0.537468\pi$
$228$		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	$-0.762971\pi$
$233$	−22.4485			−1.47065			−0.735326	+	0.677713i	$0.762971\pi$
$234$		0			0
$235$	15.0059	+	15.0059i	0.978874	+	0.978874i
$236$		0			0
$237$	−4.90473	−	2.22175i	−0.318596	−	0.144318i
$238$		0			0
$239$	−16.7259			−1.08191			−0.540953	−	0.841053i	$-0.681936\pi$
$239$	−16.7259			−1.08191			−0.540953	+	0.841053i	$0.681936\pi$
$240$		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
$243$	13.2416	+	8.22553i	0.849451	+	0.527668i
$244$		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	−0.635855	−	0.771808i	$-0.719353\pi$
$251$	2.15390	−	2.15390i	0.135953	−	0.135953i	0.771808	+	0.635855i	$0.219353\pi$
$252$		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	$0.274170\pi$
$257$			24.3261i			1.51742i	−0.651428	+	0.758711i	$0.725830\pi$
$258$		0			0
$259$	6.99022	−	6.99022i	0.434351	−	0.434351i
$260$		0			0
$261$	18.2350	+	1.19174i	1.12872	+	0.0737666i
$262$		0			0
$263$			8.47386i			0.522521i	0.965268	+	0.261260i	$0.0841381\pi$
$263$			8.47386i			0.522521i	−0.965268	+	0.261260i	$0.915862\pi$
$264$		0			0
$265$		−	1.51355i		−	0.0929764i
$266$		0			0
$267$	3.10420	−	6.85283i	0.189974	−	0.419387i
$268$		0			0
$269$	−0.519029	+	0.519029i	−0.0316458	+	0.0316458i	−0.722753	−	0.691107i	$-0.757123\pi$
$269$	−0.519029	+	0.519029i	−0.0316458	+	0.0316458i	0.691107	+	0.722753i	$0.257123\pi$
$270$		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	$-0.373138\pi$
$281$	13.0109			0.776163			0.388082	+	0.921625i	$0.373138\pi$
$282$		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
$285$	4.28786	−	9.46588i	0.253991	−	0.560710i
$286$		0			0
$287$	3.57004			0.210733
$288$		0			0
$289$	−16.9187			−0.995215
$290$		0			0
$291$	5.78696	−	12.7753i	0.339237	−	0.748900i
$292$		0			0
$293$	6.14398	+	6.14398i	0.358935	+	0.358935i	0.863420	−	0.504485i	$-0.168318\pi$
$293$	6.14398	+	6.14398i	0.358935	+	0.358935i	−0.504485	+	0.863420i	$0.668318\pi$
$294$		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
$309$	−1.12757	+	2.48921i	−0.0641449	+	0.141606i
$310$		0			0
$311$			27.0587i			1.53436i	0.641432	+	0.767180i	$0.278341\pi$
$311$			27.0587i			1.53436i	−0.641432	+	0.767180i	$0.721659\pi$
$312$		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
$315$	0.365176	−	5.58763i	0.0205754	−	0.314827i
$316$		0			0
$317$	17.8168	−	17.8168i	1.00069	−	1.00069i	0.000690694	−	1.00000i	$-0.499780\pi$
$317$	17.8168	−	17.8168i	1.00069	−	1.00069i	1.00000		0.000690694i	$-0.000219855\pi$
$318$		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
$333$	−29.5939	−	1.93409i	−1.62173	−	0.105987i
$334$		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
$339$	−25.3628	−	11.4889i	−1.37752	−	0.623989i
$340$		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	−0.539115	−	0.842232i	$-0.681241\pi$
$347$	5.64644	−	5.64644i	0.303117	−	0.303117i	0.842232	+	0.539115i	$0.181241\pi$
$348$		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	$-0.654354\pi$
$353$		−	33.2445i		−	1.76943i	0.466136	−	0.884713i	$-0.345646\pi$
$354$		0			0
$355$	17.6759	−	17.6759i	0.938142	−	0.938142i
$356$		0			0
$357$	9.18865	+	4.16228i	0.486315	+	0.220291i
$358$		0			0
$359$		−	22.1409i		−	1.16855i	−0.811555	−	0.584276i	$-0.801379\pi$
$359$		−	22.1409i		−	1.16855i	0.811555	−	0.584276i	$-0.198621\pi$
$360$		0			0
$361$			8.66780i			0.456200i
$362$		0			0
$363$	12.5388	+	5.67984i	0.658117	+	0.298115i
$364$		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
$381$	19.2075	+	8.70062i	0.984030	+	0.445746i
$382$		0			0
$383$	11.3881			0.581902			0.290951	−	0.956738i	$-0.406028\pi$
$383$	11.3881			0.581902			0.290951	+	0.956738i	$0.406028\pi$
$384$		0			0
$385$	3.26113			0.166203
$386$		0			0
$387$	−0.587422	+	8.98825i	−0.0298604	+	0.456899i
$388$		0			0
$389$	2.70246	+	2.70246i	0.137020	+	0.137020i	0.772290	−	0.635270i	$-0.219111\pi$
$389$	2.70246	+	2.70246i	0.137020	+	0.137020i	−0.635270	+	0.772290i	$0.719111\pi$
$390$		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	$-0.825798\pi$
$401$		−	20.8404i		−	1.04072i	0.853947	−	0.520360i	$-0.174202\pi$
$402$		0			0
$403$	−26.6138	+	26.6138i	−1.32573	+	1.32573i
$404$		0			0
$405$	−13.3234	+	10.2314i	−0.662046	+	0.508402i
$406$		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
$411$	2.48421	−	5.48414i	0.122537	−	0.270513i
$412$		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	0.863355	−	0.504598i	$-0.168359\pi$
$419$	7.34358	+	7.34358i	0.358757	+	0.358757i	−0.504598	+	0.863355i	$0.668359\pi$
$420$		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
$429$	8.08393	−	17.8461i	0.390296	−	0.861617i
$430$		0			0
$431$	24.7167			1.19056			0.595280	−	0.803518i	$-0.297041\pi$
$431$	24.7167			1.19056			0.595280	+	0.803518i	$0.297041\pi$
$432$		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
$435$	−8.12555	+	17.9380i	−0.389591	+	0.860060i
$436$		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	$0.520813\pi$
$443$	−22.3778	+	22.3778i	−1.06320	+	1.06320i	−0.997863	+	0.0653386i	$0.979187\pi$
$444$		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	$-0.986554\pi$
$449$		−	1.78966i		−	0.0844591i	0.999108	−	0.0422296i	$-0.0134461\pi$
$450$		0			0
$451$	4.41057	−	4.41057i	0.207685	−	0.207685i
$452$		0			0
$453$	−0.596419	+	1.31665i	−0.0280222	+	0.0618618i
$454$		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
$459$	−8.79284	−	28.9567i	−0.410415	−	1.35158i
$460$		0			0
$461$	−1.66514	+	1.66514i	−0.0775534	+	0.0775534i	−0.744819	−	0.667266i	$-0.767464\pi$
$461$	−1.66514	+	1.66514i	−0.0775534	+	0.0775534i	0.667266	+	0.744819i	$0.267464\pi$
$462$		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	0.468907	−	0.883247i	$-0.344648\pi$
$467$	−8.95396	−	8.95396i	−0.414340	−	0.414340i	−0.883247	+	0.468907i	$0.844648\pi$
$468$		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
$477$	−0.158648	+	2.42750i	−0.00726400	+	0.111148i
$478$		0			0
$479$	17.2099			0.786340			0.393170	−	0.919466i	$-0.371378\pi$
$479$	17.2099			0.786340			0.393170	+	0.919466i	$0.371378\pi$
$480$		0			0
$481$	64.0000			2.91815
$482$		0			0
$483$	−4.16058	−	1.88466i	−0.189313	−	0.0857552i
$484$		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	−0.567974	−	0.823047i	$-0.692272\pi$
$491$	5.65204	−	5.65204i	0.255073	−	0.255073i	0.823047	+	0.567974i	$0.192272\pi$
$492$		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
$501$	6.63693	+	3.00640i	0.296516	+	0.134316i
$502$		0			0
$503$			16.9039i			0.753707i	0.926273	+	0.376854i	$0.122994\pi$
$503$			16.9039i			0.753707i	−0.926273	+	0.376854i	$0.877006\pi$
$504$		0			0
$505$		−	2.53728i		−	0.112907i
$506$		0			0
$507$	45.6168	+	20.6635i	2.02591	+	0.917699i
$508$		0			0
$509$	−22.6903	+	22.6903i	−1.00573	+	1.00573i	−0.00574435	+	0.999984i	$0.501828\pi$
$509$	−22.6903	+	22.6903i	−1.00573	+	1.00573i	−0.999984	+	0.00574435i	$0.998172\pi$
$510$		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	$-0.551307\pi$
$521$	−7.32638			−0.320974			−0.160487	+	0.987038i	$0.551307\pi$
$522$		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
$525$	−2.39202	−	1.08354i	−0.104396	−	0.0472896i
$526$		0			0
$527$	−33.8585			−1.47490
$528$		0			0
$529$	16.0459			0.697646
$530$		0			0
$531$	35.6570	+	2.33034i	1.54738	+	0.101128i
$532$		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
$549$	−1.88259	+	28.8058i	−0.0803469	+	1.22940i
$550$		0			0
$551$			19.5797i			0.834122i
$552$		0			0
$553$		−	3.10873i		−	0.132196i
$554$		0			0
$555$	13.1871	−	29.1119i	0.559762	−	1.23573i
$556$		0			0
$557$	19.4928	−	19.4928i	0.825938	−	0.825938i	−0.161014	−	0.986952i	$-0.551477\pi$
$557$	19.4928	−	19.4928i	0.825938	−	0.825938i	0.986952	+	0.161014i	$0.0514766\pi$
$558$		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	0.504261	−	0.863551i	$-0.331765\pi$
$563$	−8.52509	−	8.52509i	−0.359290	−	0.359290i	−0.863551	+	0.504261i	$0.831765\pi$
$564$		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	$-0.553810\pi$
$569$	−8.02648			−0.336488			−0.168244	+	0.985745i	$0.553810\pi$
$570$		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
$573$	8.73810	−	19.2902i	0.365039	−	0.805861i
$574$		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
$579$	6.40557	−	14.1409i	0.266206	−	0.587677i
$580$		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	−0.896589	−	0.442863i	$-0.853963\pi$
$587$	−10.9929	+	10.9929i	−0.453727	+	0.453727i	0.442863	+	0.896589i	$0.353963\pi$
$588$		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	$-0.773442\pi$
$593$		−	31.8111i		−	1.30632i	0.757218	−	0.653162i	$-0.226558\pi$
$594$		0			0
$595$	−7.68663	+	7.68663i	−0.315121	+	0.315121i
$596$		0			0
$597$	−7.45786	+	16.4640i	−0.305230	+	0.673826i
$598$		0			0
$599$			30.5728i			1.24917i	0.780957	+	0.624585i	$0.214732\pi$
$599$			30.5728i			1.24917i	−0.780957	+	0.624585i	$0.785268\pi$
$600$		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
$603$	8.06035	+	0.526780i	0.328243	+	0.0214521i
$604$		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	$-0.602428\pi$
$617$	−15.7116			−0.632526			−0.316263	+	0.948671i	$0.602428\pi$
$618$		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
$621$	3.98136	+	13.1115i	0.159767	+	0.526145i
$622$		0			0
$623$	4.34348			0.174018
$624$		0			0
$625$	15.1208			0.604832
$626$		0			0
$627$	−8.86064	−	4.01370i	−0.353860	−	0.160292i
$628$		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	$-0.744731\pi$
$641$		−	36.3928i		−	1.43743i	0.695306	−	0.718714i	$-0.255269\pi$
$642$		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
$645$	−8.84187	−	4.00519i	−0.348148	−	0.157704i
$646$		0			0
$647$			21.9570i			0.863217i	0.902061	+	0.431608i	$0.142054\pi$
$647$			21.9570i			0.863217i	−0.902061	+	0.431608i	$0.857946\pi$
$648$		0			0
$649$			20.8106i			0.816888i
$650$		0			0
$651$	9.17236	+	4.15490i	0.359493	+	0.162843i
$652$		0			0
$653$	28.1079	−	28.1079i	1.09995	−	1.09995i	0.105532	−	0.994416i	$-0.466345\pi$
$653$	28.1079	−	28.1079i	1.09995	−	1.09995i	0.994416	−	0.105532i	$-0.0336546\pi$
$654$		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	$-0.971862\pi$
$659$	−27.8370	−	27.8370i	−1.08438	−	1.08438i	−0.0882817	−	0.996096i	$-0.528138\pi$
$660$		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
$669$	13.0620	+	5.91684i	0.505006	+	0.228758i
$670$		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
$675$	2.28898	+	7.53811i	0.0881031	+	0.290142i
$676$		0			0
$677$	22.4728	+	22.4728i	0.863700	+	0.863700i	0.991766	−	0.128065i	$-0.0408767\pi$
$677$	22.4728	+	22.4728i	0.863700	+	0.863700i	−0.128065	+	0.991766i	$0.540877\pi$
$678$		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	−0.521296	−	0.853376i	$-0.674551\pi$
$683$	8.67868	−	8.67868i	0.332080	−	0.332080i	0.853376	+	0.521296i	$0.174551\pi$
$684$		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
$693$	−5.23036	−	0.341828i	−0.198685	−	0.0129850i
$694$		0			0
$695$		−	20.6547i		−	0.783478i
$696$		0			0
$697$			20.7918i			0.787546i
$698$		0			0
$699$	−16.0435	+	35.4177i	−0.606822	+	1.33962i
$700$		0			0
$701$	−27.3460	+	27.3460i	−1.03285	+	1.03285i	−0.0334040	+	0.999442i	$0.510635\pi$
$701$	−27.3460	+	27.3460i	−1.03285	+	1.03285i	−0.999442	+	0.0334040i	$0.989365\pi$
$702$		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
$717$	−11.9537	+	26.3889i	−0.446418	+	0.985512i
$718$		0			0
$719$	28.2350			1.05299			0.526494	−	0.850179i	$-0.323506\pi$
$719$	28.2350			1.05299			0.526494	+	0.850179i	$0.323506\pi$
$720$		0			0
$721$	−1.57772			−0.0587573
$722$		0			0
$723$	−13.6176	+	30.0623i	−0.506446	+	1.11803i
$724$		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
$741$	14.8725	−	32.8324i	0.546353	−	1.20613i
$742$		0			0
$743$			1.56551i			0.0574330i	0.999588	+	0.0287165i	$0.00914200\pi$
$743$			1.56551i			0.0574330i	−0.999588	+	0.0287165i	$0.990858\pi$
$744$		0			0
$745$		−	9.66265i		−	0.354012i
$746$		0			0
$747$	−0.805852	+	12.3305i	−0.0294846	+	0.451149i
$748$		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	$-0.176728\pi$
$761$	46.8851			1.69958			0.849791	+	0.527119i	$0.176728\pi$
$762$		0			0
$763$	−2.23973	−	2.23973i	−0.0810838	−	0.0810838i
$764$		0			0
$765$	32.5422	+	2.12678i	1.17657	+	0.0768938i
$766$		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
$771$	38.3800	+	17.3854i	1.38222	+	0.626121i
$772$		0			0
$773$	−17.9424	−	17.9424i	−0.645342	−	0.645342i	0.306522	−	0.951864i	$-0.400835\pi$
$773$	−17.9424	−	17.9424i	−0.645342	−	0.645342i	−0.951864	+	0.306522i	$0.900835\pi$
$774$		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
$789$	13.3695	+	6.05611i	0.475966	+	0.215603i
$790$		0			0
$791$		−	16.0755i		−	0.571579i
$792$		0			0
$793$		−	62.2958i		−	2.21219i
$794$		0			0
$795$	−2.38797	−	1.08170i	−0.0846925	−	0.0383641i
$796$		0			0
$797$	6.78134	−	6.78134i	0.240207	−	0.240207i	−0.576729	−	0.816936i	$-0.695671\pi$
$797$	6.78134	−	6.78134i	0.240207	−	0.240207i	0.816936	+	0.576729i	$0.195671\pi$
$798$		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	$-0.491409\pi$
$809$	1.53506			0.0539699			0.0269849	+	0.999636i	$0.491409\pi$
$810$		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
$813$	0.700766	+	0.317434i	0.0245769	+	0.0111329i
$814$		0			0
$815$	6.32495			0.221553
$816$		0			0
$817$	−9.65108			−0.337649
$818$		0			0
$819$	1.26662	−	19.3807i	0.0442591	−	0.677217i
$820$		0			0
$821$	−35.7226	−	35.7226i	−1.24673	−	1.24673i	−0.957156	−	0.289571i	$-0.906487\pi$
$821$	−35.7226	−	35.7226i	−1.24673	−	1.24673i	−0.289571	−	0.957156i	$-0.593513\pi$
$822$		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	−0.363256	−	0.931689i	$-0.618335\pi$
$827$	16.3468	−	16.3468i	0.568434	−	0.568434i	0.931689	+	0.363256i	$0.118335\pi$
$828$		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
$837$	−8.77725	−	28.9053i	−0.303386	−	0.999115i
$838$		0			0
$839$		−	27.8332i		−	0.960907i	−0.877020	−	0.480454i	$-0.840472\pi$
$839$		−	27.8332i		−	0.960907i	0.877020	−	0.480454i	$-0.159528\pi$
$840$		0			0
$841$		−	8.10376i		−	0.279440i
$842$		0			0
$843$	9.29862	−	20.5276i	0.320261	−	0.707009i
$844$		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	$-0.592167\pi$
$857$	−16.7170			−0.571043			−0.285521	+	0.958372i	$0.592167\pi$
$858$		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
$861$	2.55144	−	5.63256i	0.0869529	−	0.191957i
$862$		0			0
$863$	4.35836			0.148360			0.0741802	−	0.997245i	$-0.476366\pi$
$863$	4.35836			0.148360			0.0741802	+	0.997245i	$0.476366\pi$
$864$		0			0
$865$	−18.3085			−0.622507
$866$		0			0
$867$	−12.0914	+	26.6931i	−0.410647	+	0.906544i
$868$		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	$0.151753\pi$
$881$			27.2412i			0.917780i	−0.888493	+	0.458890i	$0.848247\pi$
$882$		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
$885$	−15.8889	+	35.0762i	−0.534098	+	1.17908i
$886$		0			0
$887$			5.06180i			0.169959i	0.996383	+	0.0849793i	$0.0270824\pi$
$887$			5.06180i			0.169959i	−0.996383	+	0.0849793i	$0.972918\pi$
$888$		0			0
$889$			12.1741i			0.408307i
$890$		0			0
$891$	9.57720	+	12.4715i	0.320848	+	0.417812i
$892$		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
$909$	−0.265955	+	4.06942i	−0.00882115	+	0.134974i
$910$		0			0
$911$	28.5053			0.944423			0.472211	−	0.881485i	$-0.343456\pi$
$911$	28.5053			0.944423			0.472211	+	0.881485i	$0.343456\pi$
$912$		0			0
$913$	−7.19648			−0.238169
$914$		0			0
$915$	−28.3367	−	12.8360i	−0.936782	−	0.424344i
$916$		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	$0.132714\pi$
$929$			24.6859i			0.809917i	−0.914335	+	0.404958i	$0.867286\pi$
$930$		0			0
$931$	2.27291	−	2.27291i	0.0744915	−	0.0744915i
$932$		0			0
$933$	42.6914	+	19.3384i	1.39765	+	0.633110i
$934$		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
$939$	−30.8540	−	13.9762i	−1.00688	−	0.456097i
$940$		0			0
$941$	−17.0730	+	17.0730i	−0.556564	+	0.556564i	−0.928328	−	0.371763i	$-0.878753\pi$
$941$	−17.0730	+	17.0730i	−0.556564	+	0.556564i	0.371763	+	0.928328i	$0.378753\pi$
$942$		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	$0.0483634\pi$
$947$	35.0765	+	35.0765i	1.13983	+	1.13983i	0.151354	+	0.988480i	$0.451637\pi$
$948$		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	$-0.646437\pi$
$953$	−27.4125			−0.887979			−0.443990	+	0.896032i	$0.646437\pi$
$954$		0			0
$955$	16.1369	+	16.1369i	0.522179	+	0.522179i
$956$		0			0
$957$	16.7910	+	7.60602i	0.542777	+	0.245868i
$958$		0			0
$959$	3.47597			0.112245
$960$		0			0
$961$	−2.79846			−0.0902730
$962$		0			0
$963$	19.2081	+	1.25533i	0.618972	+	0.0404526i
$964$		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	−0.575738	−	0.817634i	$-0.695285\pi$
$971$	7.53771	−	7.53771i	0.241897	−	0.241897i	0.817634	+	0.575738i	$0.195285\pi$
$972$		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	$0.000386255\pi$
$977$			0.0758580i			0.00242691i	−0.999999	+	0.00121346i	$0.999614\pi$
$978$		0			0
$979$	5.36610	−	5.36610i	0.171501	−	0.171501i
$980$		0			0
$981$	−0.619701	+	9.48216i	−0.0197855	+	0.302742i
$982$		0			0
$983$			17.1286i			0.546318i	0.961969	+	0.273159i	$0.0880684\pi$
$983$			17.1286i			0.546318i	−0.961969	+	0.273159i	$0.911932\pi$
$984$		0			0
$985$		−	20.3077i		−	0.647057i
$986$		0			0
$987$	8.12562	−	17.9381i	0.258641	−	0.570976i
$988$		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.239.15		40
3.2	odd	2	inner	1344.2.s.c.239.17		40
4.3	odd	2		336.2.s.c.323.12	yes	40
12.11	even	2		336.2.s.c.323.9	yes	40
16.5	even	4		336.2.s.c.155.9	✓	40
16.11	odd	4	inner	1344.2.s.c.911.17		40
48.5	odd	4		336.2.s.c.155.12	yes	40
48.11	even	4	inner	1344.2.s.c.911.15		40

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

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

Fields

Representations

Groups

Database

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