LMFDB - Embedded newform 1344.2.s.c.239.5

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			239.5
Character	$\chi$	$=$	1344.239
Dual form			1344.2.s.c.911.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26429 + 1.18388i) q^{3} +(-2.84277 - 2.84277i) q^{5} +1.00000 q^{7} +(0.196841 - 2.99354i) q^{9} +O(q^{10})$	\(q+(-1.26429 + 1.18388i) q^{3} +(-2.84277 - 2.84277i) q^{5} +1.00000 q^{7} +(0.196841 - 2.99354i) q^{9} +(3.31805 - 3.31805i) q^{11} +(-2.31290 - 2.31290i) q^{13} +(6.95958 + 0.228568i) q^{15} -0.814979i q^{17} +(-4.39281 + 4.39281i) q^{19} +(-1.26429 + 1.18388i) q^{21} +3.30328i q^{23} +11.1627i q^{25} +(3.29513 + 4.01772i) q^{27} +(3.25705 - 3.25705i) q^{29} -3.89472i q^{31} +(-0.266782 + 8.12315i) q^{33} +(-2.84277 - 2.84277i) q^{35} +(-3.65469 + 3.65469i) q^{37} +(5.66238 + 0.185965i) q^{39} +3.20387 q^{41} +(-1.63867 - 1.63867i) q^{43} +(-9.06950 + 7.95036i) q^{45} -6.70608 q^{47} +1.00000 q^{49} +(0.964840 + 1.03037i) q^{51} +(-7.69839 - 7.69839i) q^{53} -18.8649 q^{55} +(0.353196 - 10.7543i) q^{57} +(-7.31843 + 7.31843i) q^{59} +(-5.54897 - 5.54897i) q^{61} +(0.196841 - 2.99354i) q^{63} +13.1501i q^{65} +(0.0553126 - 0.0553126i) q^{67} +(-3.91070 - 4.17629i) q^{69} -6.50772i q^{71} +6.05260i q^{73} +(-13.2153 - 14.1128i) q^{75} +(3.31805 - 3.31805i) q^{77} +15.1804i q^{79} +(-8.92251 - 1.17850i) q^{81} +(4.25907 + 4.25907i) q^{83} +(-2.31680 + 2.31680i) q^{85} +(-0.261877 + 7.97380i) q^{87} +2.31624 q^{89} +(-2.31290 - 2.31290i) q^{91} +(4.61089 + 4.92404i) q^{93} +24.9755 q^{95} -15.2402 q^{97} +(-9.27958 - 10.5858i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.26429	+	1.18388i	−0.729936	+	0.683515i
$3$	−1.26429	+	1.18388i	−0.729936	+	0.683515i
$4$		0			0
$5$	−2.84277	−	2.84277i	−1.27133	−	1.27133i	−0.945393	−	0.325932i	$-0.894322\pi$
$5$	−2.84277	−	2.84277i	−1.27133	−	1.27133i	−0.325932	−	0.945393i	$-0.605678\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$		0			0
$9$	0.196841	−	2.99354i	0.0656136	−	0.997845i
$10$		0			0
$11$	3.31805	−	3.31805i	1.00043	−	1.00043i	0.000430454	−	1.00000i	$-0.499863\pi$
$11$	3.31805	−	3.31805i	1.00043	−	1.00043i	1.00000		0.000430454i	$-0.000137018\pi$
$12$		0			0
$13$	−2.31290	−	2.31290i	−0.641484	−	0.641484i	0.309436	−	0.950920i	$-0.399860\pi$
$13$	−2.31290	−	2.31290i	−0.641484	−	0.641484i	−0.950920	+	0.309436i	$0.899860\pi$
$14$		0			0
$15$	6.95958	+	0.228568i	1.79696	+	0.0590160i
$16$		0			0
$17$		−	0.814979i		−	0.197661i	−0.995104	−	0.0988307i	$-0.968490\pi$
$17$		−	0.814979i		−	0.197661i	0.995104	−	0.0988307i	$-0.0315102\pi$
$18$		0			0
$19$	−4.39281	+	4.39281i	−1.00778	+	1.00778i	−0.00780997	+	0.999970i	$0.502486\pi$
$19$	−4.39281	+	4.39281i	−1.00778	+	1.00778i	−0.999970	+	0.00780997i	$0.997514\pi$
$20$		0			0
$21$	−1.26429	+	1.18388i	−0.275890	+	0.258345i
$22$		0			0
$23$			3.30328i			0.688782i	0.938826	+	0.344391i	$0.111915\pi$
$23$			3.30328i			0.688782i	−0.938826	+	0.344391i	$0.888085\pi$
$24$		0			0
$25$			11.1627i			2.23254i
$26$		0			0
$27$	3.29513	+	4.01772i	0.634149	+	0.773211i
$28$		0			0
$29$	3.25705	−	3.25705i	0.604818	−	0.604818i	−0.336769	−	0.941587i	$-0.609334\pi$
$29$	3.25705	−	3.25705i	0.604818	−	0.604818i	0.941587	+	0.336769i	$0.109334\pi$
$30$		0			0
$31$		−	3.89472i		−	0.699513i	−0.936841	−	0.349756i	$-0.886264\pi$
$31$		−	3.89472i		−	0.699513i	0.936841	−	0.349756i	$-0.113736\pi$
$32$		0			0
$33$	−0.266782	+	8.12315i	−0.0464408	+	1.41406i
$34$		0			0
$35$	−2.84277	−	2.84277i	−0.480516	−	0.480516i
$36$		0			0
$37$	−3.65469	+	3.65469i	−0.600827	+	0.600827i	−0.940532	−	0.339705i	$-0.889673\pi$
$37$	−3.65469	+	3.65469i	−0.600827	+	0.600827i	0.339705	+	0.940532i	$0.389673\pi$
$38$		0			0
$39$	5.66238	+	0.185965i	0.906707	+	0.0297783i
$40$		0			0
$41$	3.20387			0.500360			0.250180	−	0.968199i	$-0.419510\pi$
$41$	3.20387			0.500360			0.250180	+	0.968199i	$0.419510\pi$
$42$		0			0
$43$	−1.63867	−	1.63867i	−0.249895	−	0.249895i	0.571033	−	0.820927i	$-0.306543\pi$
$43$	−1.63867	−	1.63867i	−0.249895	−	0.249895i	−0.820927	+	0.571033i	$0.806543\pi$
$44$		0			0
$45$	−9.06950	+	7.95036i	−1.35200	+	1.18517i
$46$		0			0
$47$	−6.70608			−0.978182			−0.489091	−	0.872233i	$-0.662671\pi$
$47$	−6.70608			−0.978182			−0.489091	+	0.872233i	$0.662671\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$		0			0
$51$	0.964840	+	1.03037i	0.135105	+	0.144280i
$52$		0			0
$53$	−7.69839	−	7.69839i	−1.05746	−	1.05746i	−0.998246	−	0.0592097i	$-0.981142\pi$
$53$	−7.69839	−	7.69839i	−1.05746	−	1.05746i	−0.0592097	−	0.998246i	$-0.518858\pi$
$54$		0			0
$55$	−18.8649			−2.54374
$56$		0			0
$57$	0.353196	−	10.7543i	0.0467820	−	1.42445i
$58$		0			0
$59$	−7.31843	+	7.31843i	−0.952778	+	0.952778i	−0.998934	−	0.0461561i	$-0.985303\pi$
$59$	−7.31843	+	7.31843i	−0.952778	+	0.952778i	0.0461561	+	0.998934i	$0.485303\pi$
$60$		0			0
$61$	−5.54897	−	5.54897i	−0.710473	−	0.710473i	0.256161	−	0.966634i	$-0.417542\pi$
$61$	−5.54897	−	5.54897i	−0.710473	−	0.710473i	−0.966634	+	0.256161i	$0.917542\pi$
$62$		0			0
$63$	0.196841	−	2.99354i	0.0247996	−	0.377150i
$64$		0			0
$65$			13.1501i			1.63107i
$66$		0			0
$67$	0.0553126	−	0.0553126i	0.00675751	−	0.00675751i	−0.703720	−	0.710477i	$-0.748479\pi$
$67$	0.0553126	−	0.0553126i	0.00675751	−	0.00675751i	0.710477	+	0.703720i	$0.248479\pi$
$68$		0			0
$69$	−3.91070	−	4.17629i	−0.470793	−	0.502767i
$70$		0			0
$71$		−	6.50772i		−	0.772325i	−0.922431	−	0.386162i	$-0.873800\pi$
$71$		−	6.50772i		−	0.772325i	0.922431	−	0.386162i	$-0.126200\pi$
$72$		0			0
$73$			6.05260i			0.708403i	0.935169	+	0.354201i	$0.115247\pi$
$73$			6.05260i			0.708403i	−0.935169	+	0.354201i	$0.884753\pi$
$74$		0			0
$75$	−13.2153	−	14.1128i	−1.52597	−	1.62961i
$76$		0			0
$77$	3.31805	−	3.31805i	0.378127	−	0.378127i
$78$		0			0
$79$			15.1804i			1.70792i	0.520335	+	0.853962i	$0.325807\pi$
$79$			15.1804i			1.70792i	−0.520335	+	0.853962i	$0.674193\pi$
$80$		0			0
$81$	−8.92251	−	1.17850i	−0.991390	−	0.130944i
$82$		0			0
$83$	4.25907	+	4.25907i	0.467494	+	0.467494i	0.901102	−	0.433608i	$-0.142760\pi$
$83$	4.25907	+	4.25907i	0.467494	+	0.467494i	−0.433608	+	0.901102i	$0.642760\pi$
$84$		0			0
$85$	−2.31680	+	2.31680i	−0.251292	+	0.251292i
$86$		0			0
$87$	−0.261877	+	7.97380i	−0.0280762	+	0.854881i
$88$		0			0
$89$	2.31624			0.245521			0.122761	−	0.992436i	$-0.460825\pi$
$89$	2.31624			0.245521			0.122761	+	0.992436i	$0.460825\pi$
$90$		0			0
$91$	−2.31290	−	2.31290i	−0.242458	−	0.242458i
$92$		0			0
$93$	4.61089	+	4.92404i	0.478128	+	0.510599i
$94$		0			0
$95$	24.9755			2.56243
$96$		0			0
$97$	−15.2402			−1.54741			−0.773703	−	0.633549i	$-0.781598\pi$
$97$	−15.2402			−1.54741			−0.773703	+	0.633549i	$0.781598\pi$
$98$		0			0
$99$	−9.27958	−	10.5858i	−0.932633	−	1.06392i
$100$		0			0
$101$	−1.01023	−	1.01023i	−0.100522	−	0.100522i	0.655058	−	0.755579i	$-0.272644\pi$
$101$	−1.01023	−	1.01023i	−0.100522	−	0.100522i	−0.755579	+	0.655058i	$0.772644\pi$
$102$		0			0
$103$	−5.54554			−0.546418			−0.273209	−	0.961955i	$-0.588085\pi$
$103$	−5.54554			−0.546418			−0.273209	+	0.961955i	$0.588085\pi$
$104$		0			0
$105$	6.95958	+	0.228568i	0.679186	+	0.0223060i
$106$		0			0
$107$	−6.92329	+	6.92329i	−0.669300	+	0.669300i	−0.957554	−	0.288254i	$-0.906925\pi$
$107$	−6.92329	+	6.92329i	−0.669300	+	0.669300i	0.288254	+	0.957554i	$0.406925\pi$
$108$		0			0
$109$	1.69753	+	1.69753i	0.162594	+	0.162594i	0.783715	−	0.621121i	$-0.213322\pi$
$109$	1.69753	+	1.69753i	0.162594	+	0.162594i	−0.621121	+	0.783715i	$0.713322\pi$
$110$		0			0
$111$	0.293849	−	8.94729i	0.0278909	−	0.849239i
$112$		0			0
$113$			3.05425i			0.287320i	0.989627	+	0.143660i	$0.0458871\pi$
$113$			3.05425i			0.287320i	−0.989627	+	0.143660i	$0.954113\pi$
$114$		0			0
$115$	9.39046	−	9.39046i	0.875665	−	0.875665i
$116$		0			0
$117$	−7.37904	+	6.46849i	−0.682192	+	0.598012i
$118$		0			0
$119$		−	0.814979i		−	0.0747090i
$120$		0			0
$121$		−	11.0189i		−	1.00172i
$122$		0			0
$123$	−4.05061	+	3.79301i	−0.365231	+	0.342004i
$124$		0			0
$125$	17.5191	−	17.5191i	1.56695	−	1.56695i
$126$		0			0
$127$			1.00904i			0.0895376i	0.998997	+	0.0447688i	$0.0142551\pi$
$127$			1.00904i			0.0895376i	−0.998997	+	0.0447688i	$0.985745\pi$
$128$		0			0
$129$	4.01174	+	0.131754i	0.353214	+	0.0116003i
$130$		0			0
$131$	1.25508	+	1.25508i	0.109657	+	0.109657i	0.759806	−	0.650150i	$-0.225294\pi$
$131$	1.25508	+	1.25508i	0.109657	+	0.109657i	−0.650150	+	0.759806i	$0.725294\pi$
$132$		0			0
$133$	−4.39281	+	4.39281i	−0.380905	+	0.380905i
$134$		0			0
$135$	2.05416	−	20.7888i	0.176794	−	1.78921i
$136$		0			0
$137$	−5.70652			−0.487540			−0.243770	−	0.969833i	$-0.578384\pi$
$137$	−5.70652			−0.487540			−0.243770	+	0.969833i	$0.578384\pi$
$138$		0			0
$139$	6.78446	+	6.78446i	0.575450	+	0.575450i	0.933646	−	0.358196i	$-0.116608\pi$
$139$	6.78446	+	6.78446i	0.575450	+	0.575450i	−0.358196	+	0.933646i	$0.616608\pi$
$140$		0			0
$141$	8.47840	−	7.93921i	0.714010	−	0.668602i
$142$		0			0
$143$	−15.3487			−1.28352
$144$		0			0
$145$	−18.5181			−1.53784
$146$		0			0
$147$	−1.26429	+	1.18388i	−0.104277	+	0.0976450i
$148$		0			0
$149$	4.36672	+	4.36672i	0.357736	+	0.357736i	0.862978	−	0.505242i	$-0.168597\pi$
$149$	4.36672	+	4.36672i	0.357736	+	0.357736i	−0.505242	+	0.862978i	$0.668597\pi$
$150$		0			0
$151$	−7.01244			−0.570664			−0.285332	−	0.958429i	$-0.592104\pi$
$151$	−7.01244			−0.570664			−0.285332	+	0.958429i	$0.592104\pi$
$152$		0			0
$153$	−2.43967	−	0.160421i	−0.197235	−	0.0129693i
$154$		0			0
$155$	−11.0718	+	11.0718i	−0.889308	+	0.889308i
$156$		0			0
$157$	10.3514	+	10.3514i	0.826129	+	0.826129i	0.986979	−	0.160850i	$-0.0514235\pi$
$157$	10.3514	+	10.3514i	0.826129	+	0.826129i	−0.160850	+	0.986979i	$0.551423\pi$
$158$		0			0
$159$	18.8470	+	0.618976i	1.49466	+	0.0490880i
$160$		0			0
$161$			3.30328i			0.260335i
$162$		0			0
$163$	−11.2691	+	11.2691i	−0.882661	+	0.882661i	−0.993804	−	0.111143i	$-0.964549\pi$
$163$	−11.2691	+	11.2691i	−0.882661	+	0.882661i	0.111143	+	0.993804i	$0.464549\pi$
$164$		0			0
$165$	23.8507	−	22.3339i	1.85677	−	1.73869i
$166$		0			0
$167$		−	4.10358i		−	0.317545i	−0.987315	−	0.158772i	$-0.949246\pi$
$167$		−	4.10358i		−	0.317545i	0.987315	−	0.158772i	$-0.0507536\pi$
$168$		0			0
$169$		−	2.30095i		−	0.176996i
$170$		0			0
$171$	12.2853	+	14.0147i	0.939484	+	1.07173i
$172$		0			0
$173$	−0.181676	+	0.181676i	−0.0138126	+	0.0138126i	−0.713979	−	0.700167i	$-0.753109\pi$
$173$	−0.181676	+	0.181676i	−0.0138126	+	0.0138126i	0.700167	+	0.713979i	$0.253109\pi$
$174$		0			0
$175$			11.1627i			0.843819i
$176$		0			0
$177$	0.588426	−	17.9168i	0.0442288	−	1.34671i
$178$		0			0
$179$	−8.19489	−	8.19489i	−0.612515	−	0.612515i	0.331086	−	0.943601i	$-0.392585\pi$
$179$	−8.19489	−	8.19489i	−0.612515	−	0.612515i	−0.943601	+	0.331086i	$0.892585\pi$
$180$		0			0
$181$	14.1393	−	14.1393i	1.05097	−	1.05097i	0.0523357	−	0.998630i	$-0.483333\pi$
$181$	14.1393	−	14.1393i	1.05097	−	1.05097i	0.998630	−	0.0523357i	$-0.0166666\pi$
$182$		0			0
$183$	13.5848	+	0.446156i	1.00422	+	0.0329808i
$184$		0			0
$185$	20.7789			1.52769
$186$		0			0
$187$	−2.70414	−	2.70414i	−0.197746	−	0.197746i
$188$		0			0
$189$	3.29513	+	4.01772i	0.239686	+	0.292246i
$190$		0			0
$191$	−8.99690			−0.650993			−0.325497	−	0.945543i	$-0.605531\pi$
$191$	−8.99690			−0.650993			−0.325497	+	0.945543i	$0.605531\pi$
$192$		0			0
$193$	24.9613			1.79676			0.898378	−	0.439222i	$-0.144746\pi$
$193$	24.9613			1.79676			0.898378	+	0.439222i	$0.144746\pi$
$194$		0			0
$195$	−15.5682	−	16.6255i	−1.11486	−	1.19058i
$196$		0			0
$197$	2.68965	+	2.68965i	0.191630	+	0.191630i	0.796400	−	0.604770i	$-0.206735\pi$
$197$	2.68965	+	2.68965i	0.191630	+	0.191630i	−0.604770	+	0.796400i	$0.706735\pi$
$198$		0			0
$199$	5.82077			0.412624			0.206312	−	0.978486i	$-0.433854\pi$
$199$	5.82077			0.412624			0.206312	+	0.978486i	$0.433854\pi$
$200$		0			0
$201$	−0.00444732	+	0.135415i	−0.000313690	+	0.00955142i
$202$		0			0
$203$	3.25705	−	3.25705i	0.228600	−	0.228600i
$204$		0			0
$205$	−9.10786	−	9.10786i	−0.636120	−	0.636120i
$206$		0			0
$207$	9.88849	+	0.650221i	0.687297	+	0.0451935i
$208$		0			0
$209$			29.1511i			2.01643i
$210$		0			0
$211$	5.04692	−	5.04692i	0.347444	−	0.347444i	−0.511712	−	0.859157i	$-0.670989\pi$
$211$	5.04692	−	5.04692i	0.347444	−	0.347444i	0.859157	+	0.511712i	$0.170989\pi$
$212$		0			0
$213$	7.70439	+	8.22763i	0.527896	+	0.563748i
$214$		0			0
$215$			9.31671i			0.635394i
$216$		0			0
$217$		−	3.89472i		−	0.264391i
$218$		0			0
$219$	−7.16557	−	7.65222i	−0.484204	−	0.517089i
$220$		0			0
$221$	−1.88497	+	1.88497i	−0.126797	+	0.126797i
$222$		0			0
$223$			2.61492i			0.175108i	0.996160	+	0.0875539i	$0.0279050\pi$
$223$			2.61492i			0.175108i	−0.996160	+	0.0875539i	$0.972095\pi$
$224$		0			0
$225$	33.4159	+	2.19727i	2.22772	+	0.146485i
$226$		0			0
$227$	1.46915	+	1.46915i	0.0975109	+	0.0975109i	0.754179	−	0.656668i	$-0.228035\pi$
$227$	1.46915	+	1.46915i	0.0975109	+	0.0975109i	−0.656668	+	0.754179i	$0.728035\pi$
$228$		0			0
$229$	−14.8529	+	14.8529i	−0.981505	+	0.981505i	−0.999832	−	0.0183274i	$-0.994166\pi$
$229$	−14.8529	+	14.8529i	−0.981505	+	0.981505i	0.0183274	+	0.999832i	$0.494166\pi$
$230$		0			0
$231$	−0.266782	+	8.12315i	−0.0175530	+	0.534464i
$232$		0			0
$233$	−29.3923			−1.92556			−0.962778	−	0.270295i	$-0.912879\pi$
$233$	−29.3923			−1.92556			−0.962778	+	0.270295i	$0.912879\pi$
$234$		0			0
$235$	19.0638	+	19.0638i	1.24359	+	1.24359i
$236$		0			0
$237$	−17.9718	−	19.1923i	−1.16739	−	1.24668i
$238$		0			0
$239$	−0.818139			−0.0529210			−0.0264605	−	0.999650i	$-0.508424\pi$
$239$	−0.818139			−0.0529210			−0.0264605	+	0.999650i	$0.508424\pi$
$240$		0			0
$241$	8.11229			0.522558			0.261279	−	0.965263i	$-0.415856\pi$
$241$	8.11229			0.522558			0.261279	+	0.965263i	$0.415856\pi$
$242$		0			0
$243$	12.6758	−	9.07324i	0.813154	−	0.582049i
$244$		0			0
$245$	−2.84277	−	2.84277i	−0.181618	−	0.181618i
$246$		0			0
$247$	20.3203			1.29295
$248$		0			0
$249$	−10.4269	−	0.342443i	−0.660780	−	0.0217015i
$250$		0			0
$251$	−17.1026	+	17.1026i	−1.07951	+	1.07951i	−0.0829549	+	0.996553i	$0.526436\pi$
$251$	−17.1026	+	17.1026i	−1.07951	+	1.07951i	−0.996553	+	0.0829549i	$0.973564\pi$
$252$		0			0
$253$	10.9605	+	10.9605i	0.689078	+	0.689078i
$254$		0			0
$255$	0.186278	−	5.67191i	0.0116652	−	0.355189i
$256$		0			0
$257$		−	17.1523i		−	1.06993i	−0.844874	−	0.534966i	$-0.820325\pi$
$257$		−	17.1523i		−	1.06993i	0.844874	−	0.534966i	$-0.179675\pi$
$258$		0			0
$259$	−3.65469	+	3.65469i	−0.227091	+	0.227091i
$260$		0			0
$261$	−9.10896	−	10.3912i	−0.563831	−	0.643199i
$262$		0			0
$263$		−	5.92938i		−	0.365621i	−0.983148	−	0.182811i	$-0.941480\pi$
$263$		−	5.92938i		−	0.365621i	0.983148	−	0.182811i	$-0.0585196\pi$
$264$		0			0
$265$			43.7695i			2.68874i
$266$		0			0
$267$	−2.92839	+	2.74216i	−0.179215	+	0.167818i
$268$		0			0
$269$	−4.43027	+	4.43027i	−0.270119	+	0.270119i	−0.829148	−	0.559029i	$-0.811174\pi$
$269$	−4.43027	+	4.43027i	−0.270119	+	0.270119i	0.559029	+	0.829148i	$0.311174\pi$
$270$		0			0
$271$		−	16.4128i		−	0.997006i	−0.866888	−	0.498503i	$-0.833883\pi$
$271$		−	16.4128i		−	0.997006i	0.866888	−	0.498503i	$-0.166117\pi$
$272$		0			0
$273$	5.66238	+	0.185965i	0.342703	+	0.0112551i
$274$		0			0
$275$	37.0383	+	37.0383i	2.23350	+	2.23350i
$276$		0			0
$277$	−20.2225	+	20.2225i	−1.21505	+	1.21505i	−0.245709	+	0.969344i	$0.579021\pi$
$277$	−20.2225	+	20.2225i	−1.21505	+	1.21505i	−0.969344	+	0.245709i	$0.920979\pi$
$278$		0			0
$279$	−11.6590	−	0.766640i	−0.698005	−	0.0458976i
$280$		0			0
$281$	−3.30930			−0.197416			−0.0987082	−	0.995116i	$-0.531471\pi$
$281$	−3.30930			−0.197416			−0.0987082	+	0.995116i	$0.531471\pi$
$282$		0			0
$283$	−2.67402	−	2.67402i	−0.158954	−	0.158954i	0.623149	−	0.782103i	$-0.285853\pi$
$283$	−2.67402	−	2.67402i	−0.158954	−	0.158954i	−0.782103	+	0.623149i	$0.785853\pi$
$284$		0			0
$285$	−31.5762	+	29.5681i	−1.87041	+	1.75146i
$286$		0			0
$287$	3.20387			0.189118
$288$		0			0
$289$	16.3358			0.960930
$290$		0			0
$291$	19.2680	−	18.0426i	1.12951	−	1.05768i
$292$		0			0
$293$	4.59716	+	4.59716i	0.268569	+	0.268569i	0.828523	−	0.559954i	$-0.189181\pi$
$293$	4.59716	+	4.59716i	0.268569	+	0.268569i	−0.559954	+	0.828523i	$0.689181\pi$
$294$		0			0
$295$	41.6092			2.42258
$296$		0			0
$297$	24.2644	+	2.39759i	1.40797	+	0.139122i
$298$		0			0
$299$	7.64017	−	7.64017i	0.441842	−	0.441842i
$300$		0			0
$301$	−1.63867	−	1.63867i	−0.0944513	−	0.0944513i
$302$		0			0
$303$	2.47321	+	0.0812257i	0.142082	+	0.00466630i
$304$		0			0
$305$			31.5489i			1.80648i
$306$		0			0
$307$	−10.2535	+	10.2535i	−0.585198	+	0.585198i	−0.936327	−	0.351129i	$-0.885798\pi$
$307$	−10.2535	+	10.2535i	−0.585198	+	0.585198i	0.351129	+	0.936327i	$0.385798\pi$
$308$		0			0
$309$	7.01115	−	6.56527i	0.398850	−	0.373485i
$310$		0			0
$311$		−	28.4542i		−	1.61349i	−0.590901	−	0.806744i	$-0.701228\pi$
$311$		−	28.4542i		−	1.61349i	0.590901	−	0.806744i	$-0.298772\pi$
$312$		0			0
$313$		−	23.6568i		−	1.33716i	−0.743641	−	0.668579i	$-0.766903\pi$
$313$		−	23.6568i		−	1.33716i	0.743641	−	0.668579i	$-0.233097\pi$
$314$		0			0
$315$	−9.06950	+	7.95036i	−0.511009	+	0.447952i
$316$		0			0
$317$	5.31748	−	5.31748i	0.298660	−	0.298660i	−0.541829	−	0.840489i	$-0.682268\pi$
$317$	5.31748	−	5.31748i	0.298660	−	0.298660i	0.840489	+	0.541829i	$0.182268\pi$
$318$		0			0
$319$		−	21.6141i		−	1.21016i
$320$		0			0
$321$	0.556655	−	16.9494i	0.0310695	−	0.946023i
$322$		0			0
$323$	3.58005	+	3.58005i	0.199199	+	0.199199i
$324$		0			0
$325$	25.8182	−	25.8182i	1.43214	−	1.43214i
$326$		0			0
$327$	−4.15585	−	0.136487i	−0.229819	−	0.00754776i
$328$		0			0
$329$	−6.70608			−0.369718
$330$		0			0
$331$	−6.17926	−	6.17926i	−0.339643	−	0.339643i	0.516590	−	0.856233i	$-0.327201\pi$
$331$	−6.17926	−	6.17926i	−0.339643	−	0.339643i	−0.856233	+	0.516590i	$0.827201\pi$
$332$		0			0
$333$	10.2210	+	11.6598i	0.560110	+	0.638954i
$334$		0			0
$335$	−0.314482			−0.0171820
$336$		0			0
$337$	−0.191549			−0.0104343			−0.00521717	−	0.999986i	$-0.501661\pi$
$337$	−0.191549			−0.0104343			−0.00521717	+	0.999986i	$0.501661\pi$
$338$		0			0
$339$	−3.61587	−	3.86145i	−0.196387	−	0.209725i
$340$		0			0
$341$	−12.9229	−	12.9229i	−0.699814	−	0.699814i
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	−0.755024	+	22.9895i	−0.0406491	+	1.23771i
$346$		0			0
$347$	17.6420	−	17.6420i	0.947073	−	0.947073i	−0.0515951	−	0.998668i	$-0.516431\pi$
$347$	17.6420	−	17.6420i	0.947073	−	0.947073i	0.998668	+	0.0515951i	$0.0164305\pi$
$348$		0			0
$349$	9.44916	+	9.44916i	0.505802	+	0.505802i	0.913235	−	0.407433i	$-0.133576\pi$
$349$	9.44916	+	9.44916i	0.505802	+	0.505802i	−0.407433	+	0.913235i	$0.633576\pi$
$350$		0			0
$351$	1.67128	−	16.9139i	0.0892064	−	0.902799i
$352$		0			0
$353$		−	37.3053i		−	1.98556i	−0.119950	−	0.992780i	$-0.538274\pi$
$353$		−	37.3053i		−	1.98556i	0.119950	−	0.992780i	$-0.461726\pi$
$354$		0			0
$355$	−18.5000	+	18.5000i	−0.981876	+	0.981876i
$356$		0			0
$357$	0.964840	+	1.03037i	0.0510647	+	0.0545328i
$358$		0			0
$359$		−	29.6103i		−	1.56277i	−0.624049	−	0.781385i	$-0.714514\pi$
$359$		−	29.6103i		−	1.56277i	0.624049	−	0.781385i	$-0.285486\pi$
$360$		0			0
$361$		−	19.5935i		−	1.03124i
$362$		0			0
$363$	13.0451	+	13.9311i	0.684692	+	0.731193i
$364$		0			0
$365$	17.2061	−	17.2061i	0.900611	−	0.900611i
$366$		0			0
$367$			22.1073i			1.15399i	0.816746	+	0.576997i	$0.195776\pi$
$367$			22.1073i			1.15399i	−0.816746	+	0.576997i	$0.804224\pi$
$368$		0			0
$369$	0.630652	−	9.59089i	0.0328304	−	0.499282i
$370$		0			0
$371$	−7.69839	−	7.69839i	−0.399681	−	0.399681i
$372$		0			0
$373$	−13.9397	+	13.9397i	−0.721771	+	0.721771i	−0.968966	−	0.247195i	$-0.920491\pi$
$373$	−13.9397	+	13.9397i	−0.721771	+	0.721771i	0.247195	+	0.968966i	$0.420491\pi$
$374$		0			0
$375$	−1.40859	+	42.8897i	−0.0727393	+	2.21481i
$376$		0			0
$377$	−15.0665			−0.775963
$378$		0			0
$379$	6.03251	+	6.03251i	0.309869	+	0.309869i	0.844859	−	0.534989i	$-0.179684\pi$
$379$	6.03251	+	6.03251i	0.309869	+	0.309869i	−0.534989	+	0.844859i	$0.679684\pi$
$380$		0			0
$381$	−1.19458	−	1.27571i	−0.0612003	−	0.0653567i
$382$		0			0
$383$	9.07832			0.463880			0.231940	−	0.972730i	$-0.425493\pi$
$383$	9.07832			0.463880			0.231940	+	0.972730i	$0.425493\pi$
$384$		0			0
$385$	−18.8649			−0.961445
$386$		0			0
$387$	−5.22797	+	4.58285i	−0.265753	+	0.232960i
$388$		0			0
$389$	−19.6351	−	19.6351i	−0.995538	−	0.995538i	0.00445242	−	0.999990i	$-0.498583\pi$
$389$	−19.6351	−	19.6351i	−0.995538	−	0.995538i	−0.999990	+	0.00445242i	$0.998583\pi$
$390$		0			0
$391$	2.69210			0.136146
$392$		0			0
$393$	−3.07264	−	0.100912i	−0.154994	−	0.00509035i
$394$		0			0
$395$	43.1543	−	43.1543i	2.17133	−	2.17133i
$396$		0			0
$397$	2.09474	+	2.09474i	0.105132	+	0.105132i	0.757716	−	0.652584i	$-0.226315\pi$
$397$	2.09474	+	2.09474i	0.105132	+	0.105132i	−0.652584	+	0.757716i	$0.726315\pi$
$398$		0			0
$399$	0.353196	−	10.7543i	0.0176819	−	0.538391i
$400$		0			0
$401$			3.50963i			0.175263i	0.996153	+	0.0876313i	$0.0279297\pi$
$401$			3.50963i			0.175263i	−0.996153	+	0.0876313i	$0.972070\pi$
$402$		0			0
$403$	−9.00812	+	9.00812i	−0.448726	+	0.448726i
$404$		0			0
$405$	22.0144	+	28.7148i	1.09391	+	1.42685i
$406$		0			0
$407$			24.2529i			1.20217i
$408$		0			0
$409$		−	19.5923i		−	0.968778i	−0.874853	−	0.484389i	$-0.839042\pi$
$409$		−	19.5923i		−	0.968778i	0.874853	−	0.484389i	$-0.160958\pi$
$410$		0			0
$411$	7.21467	−	6.75585i	0.355873	−	0.333241i
$412$		0			0
$413$	−7.31843	+	7.31843i	−0.360116	+	0.360116i
$414$		0			0
$415$		−	24.2151i		−	1.18867i
$416$		0			0
$417$	−16.6095	−	0.545493i	−0.813371	−	0.0267129i
$418$		0			0
$419$	3.04462	+	3.04462i	0.148739	+	0.148739i	0.777555	−	0.628815i	$-0.216460\pi$
$419$	3.04462	+	3.04462i	0.148739	+	0.148739i	−0.628815	+	0.777555i	$0.716460\pi$
$420$		0			0
$421$	25.3941	−	25.3941i	1.23763	−	1.23763i	0.276668	−	0.960965i	$-0.410770\pi$
$421$	25.3941	−	25.3941i	1.23763	−	1.23763i	0.960965	−	0.276668i	$-0.0892303\pi$
$422$		0			0
$423$	−1.32003	+	20.0749i	−0.0641821	+	0.976074i
$424$		0			0
$425$	9.09735			0.441286
$426$		0			0
$427$	−5.54897	−	5.54897i	−0.268534	−	0.268534i
$428$		0			0
$429$	19.4051	−	18.1710i	0.936888	−	0.877306i
$430$		0			0
$431$	−33.5588			−1.61647			−0.808235	−	0.588860i	$-0.799577\pi$
$431$	−33.5588			−1.61647			−0.808235	+	0.588860i	$0.799577\pi$
$432$		0			0
$433$	−23.2355			−1.11663			−0.558313	−	0.829631i	$-0.688551\pi$
$433$	−23.2355			−1.11663			−0.558313	+	0.829631i	$0.688551\pi$
$434$		0			0
$435$	23.4121	−	21.9232i	1.12253	−	1.05114i
$436$		0			0
$437$	−14.5107	−	14.5107i	−0.694140	−	0.694140i
$438$		0			0
$439$	−27.6659			−1.32042			−0.660211	−	0.751080i	$-0.729533\pi$
$439$	−27.6659			−1.32042			−0.660211	+	0.751080i	$0.729533\pi$
$440$		0			0
$441$	0.196841	−	2.99354i	0.00937338	−	0.142549i
$442$		0			0
$443$	20.5742	−	20.5742i	0.977507	−	0.977507i	−0.0222452	−	0.999753i	$-0.507081\pi$
$443$	20.5742	−	20.5742i	0.977507	−	0.977507i	0.999753	+	0.0222452i	$0.00708144\pi$
$444$		0			0
$445$	−6.58455	−	6.58455i	−0.312137	−	0.312137i
$446$		0			0
$447$	−10.6905	−	0.351099i	−0.505642	−	0.0166064i
$448$		0			0
$449$			36.3315i			1.71459i	0.514826	+	0.857294i	$0.327856\pi$
$449$			36.3315i			1.71459i	−0.514826	+	0.857294i	$0.672144\pi$
$450$		0			0
$451$	10.6306	−	10.6306i	0.500575	−	0.500575i
$452$		0			0
$453$	8.86573	−	8.30191i	0.416549	−	0.390058i
$454$		0			0
$455$			13.1501i			0.616487i
$456$		0			0
$457$		−	3.28562i		−	0.153695i	−0.997043	−	0.0768474i	$-0.975515\pi$
$457$		−	3.28562i		−	0.153695i	0.997043	−	0.0768474i	$-0.0244854\pi$
$458$		0			0
$459$	3.27436	−	2.68546i	0.152834	−	0.125347i
$460$		0			0
$461$	−15.0027	+	15.0027i	−0.698744	+	0.698744i	−0.964140	−	0.265396i	$-0.914497\pi$
$461$	−15.0027	+	15.0027i	−0.698744	+	0.698744i	0.265396	+	0.964140i	$0.414497\pi$
$462$		0			0
$463$			25.8407i			1.20092i	0.799656	+	0.600458i	$0.205015\pi$
$463$			25.8407i			1.20092i	−0.799656	+	0.600458i	$0.794985\pi$
$464$		0			0
$465$	0.890209	−	27.1056i	0.0412824	−	1.25699i
$466$		0			0
$467$	−22.0389	−	22.0389i	−1.01984	−	1.01984i	−0.999799	−	0.0200376i	$-0.993621\pi$
$467$	−22.0389	−	22.0389i	−1.01984	−	1.01984i	−0.0200376	−	0.999799i	$-0.506379\pi$
$468$		0			0
$469$	0.0553126	−	0.0553126i	0.00255410	−	0.00255410i
$470$		0			0
$471$	−25.3419	−	0.832284i	−1.16769	−	0.0383496i
$472$		0			0
$473$	−10.8744			−0.500004
$474$		0			0
$475$	−49.0355	−	49.0355i	−2.24990	−	2.24990i
$476$		0			0
$477$	−24.5608	+	21.5300i	−1.12456	+	0.985793i
$478$		0			0
$479$	−19.7108			−0.900608			−0.450304	−	0.892875i	$-0.648684\pi$
$479$	−19.7108			−0.900608			−0.450304	+	0.892875i	$0.648684\pi$
$480$		0			0
$481$	16.9059			0.770842
$482$		0			0
$483$	−3.91070	−	4.17629i	−0.177943	−	0.190028i
$484$		0			0
$485$	43.3243	+	43.3243i	1.96726	+	1.96726i
$486$		0			0
$487$	−3.69188			−0.167295			−0.0836475	−	0.996495i	$-0.526657\pi$
$487$	−3.69188			−0.167295			−0.0836475	+	0.996495i	$0.526657\pi$
$488$		0			0
$489$	0.906070	−	27.5886i	0.0409739	−	1.24760i
$490$		0			0
$491$	10.5801	−	10.5801i	0.477475	−	0.477475i	−0.426848	−	0.904323i	$-0.640376\pi$
$491$	10.5801	−	10.5801i	0.477475	−	0.477475i	0.904323	+	0.426848i	$0.140376\pi$
$492$		0			0
$493$	−2.65442	−	2.65442i	−0.119549	−	0.119549i
$494$		0			0
$495$	−3.71339	+	56.4728i	−0.166904	+	2.53826i
$496$		0			0
$497$		−	6.50772i		−	0.291911i
$498$		0			0
$499$	29.1727	−	29.1727i	1.30595	−	1.30595i	0.381636	−	0.924313i	$-0.375361\pi$
$499$	29.1727	−	29.1727i	1.30595	−	1.30595i	0.924313	−	0.381636i	$-0.124639\pi$
$500$		0			0
$501$	4.85816	+	5.18810i	0.217047	+	0.231787i
$502$		0			0
$503$		−	15.0826i		−	0.672498i	−0.941773	−	0.336249i	$-0.890842\pi$
$503$		−	15.0826i		−	0.672498i	0.941773	−	0.336249i	$-0.109158\pi$
$504$		0			0
$505$			5.74369i			0.255591i
$506$		0			0
$507$	2.72405	+	2.90906i	0.120979	+	0.129196i
$508$		0			0
$509$	16.5998	−	16.5998i	0.735773	−	0.735773i	−0.235984	−	0.971757i	$-0.575831\pi$
$509$	16.5998	−	16.5998i	0.735773	−	0.735773i	0.971757	+	0.235984i	$0.0758312\pi$
$510$		0			0
$511$			6.05260i			0.267751i
$512$		0			0
$513$	−32.1240	−	3.17420i	−1.41831	−	0.140144i
$514$		0			0
$515$	15.7647	+	15.7647i	0.694675	+	0.694675i
$516$		0			0
$517$	−22.2511	+	22.2511i	−0.978603	+	0.978603i
$518$		0			0
$519$	0.0146074	−	0.444774i	0.000641193	−	0.0195234i
$520$		0			0
$521$	21.5578			0.944465			0.472232	−	0.881474i	$-0.343448\pi$
$521$	21.5578			0.944465			0.472232	+	0.881474i	$0.343448\pi$
$522$		0			0
$523$	25.5106	+	25.5106i	1.11550	+	1.11550i	0.992393	+	0.123109i	$0.0392866\pi$
$523$	25.5106	+	25.5106i	1.11550	+	1.11550i	0.123109	+	0.992393i	$0.460713\pi$
$524$		0			0
$525$	−13.2153	−	14.1128i	−0.576763	−	0.615934i
$526$		0			0
$527$	−3.17412			−0.138267
$528$		0			0
$529$	12.0883			0.525580
$530$		0			0
$531$	20.4674	+	23.3485i	0.888210	+	1.01324i
$532$		0			0
$533$	−7.41024	−	7.41024i	−0.320973	−	0.320973i
$534$		0			0
$535$	39.3626			1.70180
$536$		0			0
$537$	20.0625	+	0.658896i	0.865760	+	0.0284335i
$538$		0			0
$539$	3.31805	−	3.31805i	0.142919	−	0.142919i
$540$		0			0
$541$	7.33890	+	7.33890i	0.315524	+	0.315524i	0.847045	−	0.531521i	$-0.178379\pi$
$541$	7.33890	+	7.33890i	0.315524	+	0.315524i	−0.531521	+	0.847045i	$0.678379\pi$
$542$		0			0
$543$	−1.13685	+	34.6154i	−0.0487867	+	1.48549i
$544$		0			0
$545$		−	9.65138i		−	0.413420i
$546$		0			0
$547$	5.52913	−	5.52913i	0.236408	−	0.236408i	−0.578953	−	0.815361i	$-0.696538\pi$
$547$	5.52913	−	5.52913i	0.236408	−	0.236408i	0.815361	+	0.578953i	$0.196538\pi$
$548$		0			0
$549$	−17.7033	+	15.5188i	−0.755559	+	0.662325i
$550$		0			0
$551$			28.6152i			1.21905i
$552$		0			0
$553$			15.1804i			0.645535i
$554$		0			0
$555$	−26.2704	+	24.5997i	−1.11512	+	1.04420i
$556$		0			0
$557$	−27.8816	+	27.8816i	−1.18138	+	1.18138i	−0.201995	+	0.979386i	$0.564743\pi$
$557$	−27.8816	+	27.8816i	−1.18138	+	1.18138i	−0.979386	+	0.201995i	$0.935257\pi$
$558$		0			0
$559$			7.58017i			0.320607i
$560$		0			0
$561$	6.62020	+	0.217422i	0.279505	+	0.00917956i
$562$		0			0
$563$	−1.04328	−	1.04328i	−0.0439691	−	0.0439691i	0.684780	−	0.728749i	$-0.259898\pi$
$563$	−1.04328	−	1.04328i	−0.0439691	−	0.0439691i	−0.728749	+	0.684780i	$0.759898\pi$
$564$		0			0
$565$	8.68253	−	8.68253i	0.365277	−	0.365277i
$566$		0			0
$567$	−8.92251	−	1.17850i	−0.374710	−	0.0494924i
$568$		0			0
$569$	−22.1966			−0.930530			−0.465265	−	0.885171i	$-0.654041\pi$
$569$	−22.1966			−0.930530			−0.465265	+	0.885171i	$0.654041\pi$
$570$		0			0
$571$	−4.44290	−	4.44290i	−0.185930	−	0.185930i	0.608004	−	0.793934i	$-0.291970\pi$
$571$	−4.44290	−	4.44290i	−0.185930	−	0.185930i	−0.793934	+	0.608004i	$0.791970\pi$
$572$		0			0
$573$	11.3747	−	10.6513i	0.475183	−	0.444964i
$574$		0			0
$575$	−36.8735			−1.53773
$576$		0			0
$577$	−2.94900			−0.122768			−0.0613842	−	0.998114i	$-0.519551\pi$
$577$	−2.94900			−0.122768			−0.0613842	+	0.998114i	$0.519551\pi$
$578$		0			0
$579$	−31.5583	+	29.5513i	−1.31152	+	1.22811i
$580$		0			0
$581$	4.25907	+	4.25907i	0.176696	+	0.176696i
$582$		0			0
$583$	−51.0873			−2.11582
$584$		0			0
$585$	39.3653	+	2.58848i	1.62756	+	0.107020i
$586$		0			0
$587$	−13.8692	+	13.8692i	−0.572443	+	0.572443i	−0.932811	−	0.360367i	$-0.882651\pi$
$587$	−13.8692	+	13.8692i	−0.572443	+	0.572443i	0.360367	+	0.932811i	$0.382651\pi$
$588$		0			0
$589$	17.1088	+	17.1088i	0.704954	+	0.704954i
$590$		0			0
$591$	−6.58472	−	0.216257i	−0.270859	−	0.00889561i
$592$		0			0
$593$		−	22.9708i		−	0.943296i	−0.881787	−	0.471648i	$-0.843659\pi$
$593$		−	22.9708i		−	0.943296i	0.881787	−	0.471648i	$-0.156341\pi$
$594$		0			0
$595$	−2.31680	+	2.31680i	−0.0949794	+	0.0949794i
$596$		0			0
$597$	−7.35912	+	6.89111i	−0.301189	+	0.282035i
$598$		0			0
$599$		−	6.85784i		−	0.280204i	−0.990137	−	0.140102i	$-0.955257\pi$
$599$		−	6.85784i		−	0.280204i	0.990137	−	0.140102i	$-0.0447430\pi$
$600$		0			0
$601$		−	28.1867i		−	1.14976i	−0.818237	−	0.574881i	$-0.805048\pi$
$601$		−	28.1867i		−	1.14976i	0.818237	−	0.574881i	$-0.194952\pi$
$602$		0			0
$603$	−0.154693	−	0.176468i	−0.00629957	−	0.00718634i
$604$		0			0
$605$	−31.3243	+	31.3243i	−1.27351	+	1.27351i
$606$		0			0
$607$		−	3.92533i		−	0.159324i	−0.996822	−	0.0796620i	$-0.974616\pi$
$607$		−	3.92533i		−	0.159324i	0.996822	−	0.0796620i	$-0.0253841\pi$
$608$		0			0
$609$	−0.261877	+	7.97380i	−0.0106118	+	0.323115i
$610$		0			0
$611$	15.5105	+	15.5105i	0.627488	+	0.627488i
$612$		0			0
$613$	−11.4345	+	11.4345i	−0.461835	+	0.461835i	−0.899257	−	0.437421i	$-0.855892\pi$
$613$	−11.4345	+	11.4345i	−0.461835	+	0.461835i	0.437421	+	0.899257i	$0.355892\pi$
$614$		0			0
$615$	22.2976	+	0.732302i	0.899125	+	0.0295293i
$616$		0			0
$617$	−43.5345			−1.75263			−0.876316	−	0.481738i	$-0.840006\pi$
$617$	−43.5345			−1.75263			−0.876316	+	0.481738i	$0.840006\pi$
$618$		0			0
$619$	−23.4517	−	23.4517i	−0.942603	−	0.942603i	0.0558372	−	0.998440i	$-0.482217\pi$
$619$	−23.4517	−	23.4517i	−0.942603	−	0.942603i	−0.998440	+	0.0558372i	$0.982217\pi$
$620$		0			0
$621$	−13.2717	+	10.8847i	−0.532574	+	0.436790i
$622$		0			0
$623$	2.31624			0.0927983
$624$		0			0
$625$	−43.7920			−1.75168
$626$		0			0
$627$	−34.5115	−	36.8554i	−1.37826	−	1.47186i
$628$		0			0
$629$	2.97849	+	2.97849i	0.118760	+	0.118760i
$630$		0			0
$631$	−25.1262			−1.00026			−0.500129	−	0.865951i	$-0.666714\pi$
$631$	−25.1262			−1.00026			−0.500129	+	0.865951i	$0.666714\pi$
$632$		0			0
$633$	−0.405789	+	12.3557i	−0.0161287	+	0.491096i
$634$		0			0
$635$	2.86846	−	2.86846i	0.113831	−	0.113831i
$636$		0			0
$637$	−2.31290	−	2.31290i	−0.0916406	−	0.0916406i
$638$		0			0
$639$	−19.4811	−	1.28099i	−0.770661	−	0.0506750i
$640$		0			0
$641$		−	33.0405i		−	1.30502i	−0.757779	−	0.652511i	$-0.773716\pi$
$641$		−	33.0405i		−	1.30502i	0.757779	−	0.652511i	$-0.226284\pi$
$642$		0			0
$643$	2.66006	−	2.66006i	0.104902	−	0.104902i	−0.652708	−	0.757610i	$-0.726367\pi$
$643$	2.66006	−	2.66006i	0.104902	−	0.104902i	0.757610	+	0.652708i	$0.226367\pi$
$644$		0			0
$645$	−11.0299	−	11.7790i	−0.434302	−	0.463797i
$646$		0			0
$647$			36.7484i			1.44473i	0.691512	+	0.722365i	$0.256945\pi$
$647$			36.7484i			1.44473i	−0.691512	+	0.722365i	$0.743055\pi$
$648$		0			0
$649$			48.5658i			1.90638i
$650$		0			0
$651$	4.61089	+	4.92404i	0.180715	+	0.192988i
$652$		0			0
$653$	21.7533	−	21.7533i	0.851271	−	0.851271i	−0.139019	−	0.990290i	$-0.544395\pi$
$653$	21.7533	−	21.7533i	0.851271	−	0.851271i	0.990290	+	0.139019i	$0.0443949\pi$
$654$		0			0
$655$		−	7.13579i		−	0.278818i
$656$		0			0
$657$	18.1187	+	1.19140i	0.706876	+	0.0464809i
$658$		0			0
$659$	11.3925	+	11.3925i	0.443790	+	0.443790i	0.893283	−	0.449494i	$-0.148396\pi$
$659$	11.3925	+	11.3925i	0.443790	+	0.443790i	−0.449494	+	0.893283i	$0.648396\pi$
$660$		0			0
$661$	13.7678	−	13.7678i	0.535506	−	0.535506i	−0.386700	−	0.922206i	$-0.626385\pi$
$661$	13.7678	−	13.7678i	0.535506	−	0.535506i	0.922206	+	0.386700i	$0.126385\pi$
$662$		0			0
$663$	0.151558	−	4.61472i	0.00588601	−	0.179221i
$664$		0			0
$665$	24.9755			0.968508
$666$		0			0
$667$	10.7589	+	10.7589i	0.416588	+	0.416588i
$668$		0			0
$669$	−3.09576	−	3.30600i	−0.119689	−	0.127818i
$670$		0			0
$671$	−36.8236			−1.42156
$672$		0			0
$673$	23.8933			0.921019			0.460509	−	0.887655i	$-0.347667\pi$
$673$	23.8933			0.921019			0.460509	+	0.887655i	$0.347667\pi$
$674$		0			0
$675$	−44.8486	+	36.7825i	−1.72622	+	1.41576i
$676$		0			0
$677$	30.9999	+	30.9999i	1.19142	+	1.19142i	0.976668	+	0.214755i	$0.0688951\pi$
$677$	30.9999	+	30.9999i	1.19142	+	1.19142i	0.214755	+	0.976668i	$0.431105\pi$
$678$		0			0
$679$	−15.2402			−0.584864
$680$		0			0
$681$	−3.59673	−	0.118125i	−0.137827	−	0.00452654i
$682$		0			0
$683$	−22.6478	+	22.6478i	−0.866595	+	0.866595i	−0.992094	−	0.125498i	$-0.959947\pi$
$683$	−22.6478	+	22.6478i	−0.866595	+	0.866595i	0.125498	+	0.992094i	$0.459947\pi$
$684$		0			0
$685$	16.2223	+	16.2223i	0.619823	+	0.619823i
$686$		0			0
$687$	1.19422	−	36.3623i	0.0455623	−	1.38731i
$688$		0			0
$689$			35.6113i			1.35668i
$690$		0			0
$691$	14.7567	−	14.7567i	0.561372	−	0.561372i	−0.368325	−	0.929697i	$-0.620069\pi$
$691$	14.7567	−	14.7567i	0.561372	−	0.561372i	0.929697	+	0.368325i	$0.120069\pi$
$692$		0			0
$693$	−9.27958	−	10.5858i	−0.352502	−	0.402123i
$694$		0			0
$695$		−	38.5733i		−	1.46317i
$696$		0			0
$697$		−	2.61108i		−	0.0989019i
$698$		0			0
$699$	37.1603	−	34.7971i	1.40553	−	1.31615i
$700$		0			0
$701$	21.8411	−	21.8411i	0.824928	−	0.824928i	−0.161882	−	0.986810i	$-0.551756\pi$
$701$	21.8411	−	21.8411i	0.824928	−	0.824928i	0.986810	+	0.161882i	$0.0517564\pi$
$702$		0			0
$703$		−	32.1087i		−	1.21100i
$704$		0			0
$705$	−46.6715	−	1.53279i	−1.75775	−	0.0577284i
$706$		0			0
$707$	−1.01023	−	1.01023i	−0.0379936	−	0.0379936i
$708$		0			0
$709$	2.48004	−	2.48004i	0.0931400	−	0.0931400i	−0.659002	−	0.752142i	$-0.729021\pi$
$709$	2.48004	−	2.48004i	0.0931400	−	0.0931400i	0.752142	+	0.659002i	$0.229021\pi$
$710$		0			0
$711$	45.4430	+	2.98812i	1.70424	+	0.112063i
$712$		0			0
$713$	12.8654			0.481811
$714$		0			0
$715$	43.6327	+	43.6327i	1.63177	+	1.63177i
$716$		0			0
$717$	1.03436	−	0.968582i	0.0386290	−	0.0361723i
$718$		0			0
$719$	−35.4163			−1.32080			−0.660402	−	0.750912i	$-0.729614\pi$
$719$	−35.4163			−1.32080			−0.660402	+	0.750912i	$0.729614\pi$
$720$		0			0
$721$	−5.54554			−0.206527
$722$		0			0
$723$	−10.2563	+	9.60400i	−0.381434	+	0.357177i
$724$		0			0
$725$	36.3574	+	36.3574i	1.35028	+	1.35028i
$726$		0			0
$727$	−10.1700			−0.377184			−0.188592	−	0.982056i	$-0.560392\pi$
$727$	−10.1700			−0.377184			−0.188592	+	0.982056i	$0.560392\pi$
$728$		0			0
$729$	−5.28420	+	26.4779i	−0.195711	+	0.980662i
$730$		0			0
$731$	−1.33548	+	1.33548i	−0.0493945	+	0.0493945i
$732$		0			0
$733$	−14.9007	−	14.9007i	−0.550371	−	0.550371i	0.376177	−	0.926548i	$-0.377239\pi$
$733$	−14.9007	−	14.9007i	−0.550371	−	0.550371i	−0.926548	+	0.376177i	$0.877239\pi$
$734$		0			0
$735$	6.95958	+	0.228568i	0.256708	+	0.00843086i
$736$		0			0
$737$		−	0.367060i		−	0.0135208i
$738$		0			0
$739$	−30.2894	+	30.2894i	−1.11421	+	1.11421i	−0.121640	+	0.992574i	$0.538815\pi$
$739$	−30.2894	+	30.2894i	−1.11421	+	1.11421i	−0.992574	+	0.121640i	$0.961185\pi$
$740$		0			0
$741$	−25.6907	+	24.0569i	−0.943770	+	0.883751i
$742$		0			0
$743$		−	0.334889i		−	0.0122859i	−0.999981	−	0.00614294i	$-0.998045\pi$
$743$		−	0.334889i		−	0.0122859i	0.999981	−	0.00614294i	$-0.00195537\pi$
$744$		0			0
$745$		−	24.8272i		−	0.909597i
$746$		0			0
$747$	13.5880	−	11.9113i	0.497161	−	0.435813i
$748$		0			0
$749$	−6.92329	+	6.92329i	−0.252972	+	0.252972i
$750$		0			0
$751$		−	22.8597i		−	0.834164i	−0.908869	−	0.417082i	$-0.863053\pi$
$751$		−	22.8597i		−	0.834164i	0.908869	−	0.417082i	$-0.136947\pi$
$752$		0			0
$753$	1.37511	−	41.8701i	0.0501117	−	1.52583i
$754$		0			0
$755$	19.9348	+	19.9348i	0.725500	+	0.725500i
$756$		0			0
$757$	5.43514	−	5.43514i	0.197544	−	0.197544i	−0.601403	−	0.798946i	$-0.705391\pi$
$757$	5.43514	−	5.43514i	0.197544	−	0.197544i	0.798946	+	0.601403i	$0.205391\pi$
$758$		0			0
$759$	−26.8331	−	0.881257i	−0.973978	−	0.0319876i
$760$		0			0
$761$	23.2552			0.843000			0.421500	−	0.906828i	$-0.361504\pi$
$761$	23.2552			0.843000			0.421500	+	0.906828i	$0.361504\pi$
$762$		0			0
$763$	1.69753	+	1.69753i	0.0614548	+	0.0614548i
$764$		0			0
$765$	6.47937	+	7.39146i	0.234262	+	0.267239i
$766$		0			0
$767$	33.8536			1.22238
$768$		0			0
$769$	13.2676			0.478443			0.239221	−	0.970965i	$-0.423108\pi$
$769$	13.2676			0.478443			0.239221	+	0.970965i	$0.423108\pi$
$770$		0			0
$771$	20.3063	+	21.6854i	0.731314	+	0.780981i
$772$		0			0
$773$	−3.63940	−	3.63940i	−0.130900	−	0.130900i	0.638621	−	0.769521i	$-0.279505\pi$
$773$	−3.63940	−	3.63940i	−0.130900	−	0.130900i	−0.769521	+	0.638621i	$0.779505\pi$
$774$		0			0
$775$	43.4755			1.56169
$776$		0			0
$777$	0.293849	−	8.94729i	0.0105418	−	0.320982i
$778$		0			0
$779$	−14.0740	+	14.0740i	−0.504253	+	0.504253i
$780$		0			0
$781$	−21.5930	−	21.5930i	−0.772657	−	0.772657i
$782$		0			0
$783$	23.8183	+	2.35351i	0.851197	+	0.0841076i
$784$		0			0
$785$		−	58.8531i		−	2.10056i
$786$		0			0
$787$	28.7316	−	28.7316i	1.02417	−	1.02417i	0.0244694	−	0.999701i	$-0.492210\pi$
$787$	28.7316	−	28.7316i	1.02417	−	1.02417i	0.999701	−	0.0244694i	$-0.00778964\pi$
$788$		0			0
$789$	7.01970	+	7.49644i	0.249908	+	0.266880i
$790$		0			0
$791$			3.05425i			0.108597i
$792$		0			0
$793$			25.6685i			0.911514i
$794$		0			0
$795$	−51.8180	−	55.3372i	−1.83779	−	1.96261i
$796$		0			0
$797$	28.8804	−	28.8804i	1.02300	−	1.02300i	0.0232677	−	0.999729i	$-0.492593\pi$
$797$	28.8804	−	28.8804i	1.02300	−	1.02300i	0.999729	−	0.0232677i	$-0.00740700\pi$
$798$		0			0
$799$			5.46531i			0.193349i
$800$		0			0
$801$	0.455931	−	6.93376i	0.0161095	−	0.244992i
$802$		0			0
$803$	20.0828	+	20.0828i	0.708708	+	0.708708i
$804$		0			0
$805$	9.39046	−	9.39046i	0.330970	−	0.330970i
$806$		0			0
$807$	0.356209	−	10.8461i	0.0125391	−	0.381799i
$808$		0			0
$809$	23.8315			0.837870			0.418935	−	0.908016i	$-0.362403\pi$
$809$	23.8315			0.837870			0.418935	+	0.908016i	$0.362403\pi$
$810$		0			0
$811$	−0.597878	−	0.597878i	−0.0209943	−	0.0209943i	0.696532	−	0.717526i	$-0.254726\pi$
$811$	−0.597878	−	0.597878i	−0.0209943	−	0.0209943i	−0.717526	+	0.696532i	$0.754726\pi$
$812$		0			0
$813$	19.4308	+	20.7505i	0.681469	+	0.727750i
$814$		0			0
$815$	64.0707			2.24430
$816$		0			0
$817$	14.3967			0.503677
$818$		0			0
$819$	−7.37904	+	6.46849i	−0.257844	+	0.226027i
$820$		0			0
$821$	−9.64131	−	9.64131i	−0.336484	−	0.336484i	0.518558	−	0.855042i	$-0.326469\pi$
$821$	−9.64131	−	9.64131i	−0.336484	−	0.336484i	−0.855042	+	0.518558i	$0.826469\pi$
$822$		0			0
$823$	−11.2582			−0.392436			−0.196218	−	0.980560i	$-0.562866\pi$
$823$	−11.2582			−0.392436			−0.196218	+	0.980560i	$0.562866\pi$
$824$		0			0
$825$	−90.6762	−	2.97801i	−3.15694	−	0.103681i
$826$		0			0
$827$	19.4759	−	19.4759i	0.677245	−	0.677245i	−0.282131	−	0.959376i	$-0.591041\pi$
$827$	19.4759	−	19.4759i	0.677245	−	0.677245i	0.959376	+	0.282131i	$0.0910413\pi$
$828$		0			0
$829$	−31.7146	−	31.7146i	−1.10149	−	1.10149i	−0.994231	−	0.107263i	$-0.965791\pi$
$829$	−31.7146	−	31.7146i	−1.10149	−	1.10149i	−0.107263	−	0.994231i	$-0.534209\pi$
$830$		0			0
$831$	1.62596	−	49.5081i	0.0564038	−	1.71742i
$832$		0			0
$833$		−	0.814979i		−	0.0282373i
$834$		0			0
$835$	−11.6655	+	11.6655i	−0.403703	+	0.403703i
$836$		0			0
$837$	15.6479	−	12.8336i	0.540871	−	0.443595i
$838$		0			0
$839$		−	26.3441i		−	0.909498i	−0.890620	−	0.454749i	$-0.849729\pi$
$839$		−	26.3441i		−	0.909498i	0.890620	−	0.454749i	$-0.150271\pi$
$840$		0			0
$841$			7.78330i			0.268390i
$842$		0			0
$843$	4.18391	−	3.91783i	0.144101	−	0.134937i
$844$		0			0
$845$	−6.54106	+	6.54106i	−0.225019	+	0.225019i
$846$		0			0
$847$		−	11.0189i		−	0.378615i
$848$		0			0
$849$	6.54647	+	0.215000i	0.224674	+	0.00737879i
$850$		0			0
$851$	−12.0725	−	12.0725i	−0.413838	−	0.413838i
$852$		0			0
$853$	−33.6622	+	33.6622i	−1.15257	+	1.15257i	−0.166538	+	0.986035i	$0.553259\pi$
$853$	−33.6622	+	33.6622i	−1.15257	+	1.15257i	−0.986035	+	0.166538i	$0.946741\pi$
$854$		0			0
$855$	4.91620	−	74.7650i	0.168130	−	2.55691i
$856$		0			0
$857$	−25.7318			−0.878982			−0.439491	−	0.898247i	$-0.644841\pi$
$857$	−25.7318			−0.878982			−0.439491	+	0.898247i	$0.644841\pi$
$858$		0			0
$859$	−19.5545	−	19.5545i	−0.667189	−	0.667189i	0.289875	−	0.957064i	$-0.406386\pi$
$859$	−19.5545	−	19.5545i	−0.667189	−	0.667189i	−0.957064	+	0.289875i	$0.906386\pi$
$860$		0			0
$861$	−4.05061	+	3.79301i	−0.138044	+	0.129265i
$862$		0			0
$863$	−44.8475			−1.52663			−0.763314	−	0.646028i	$-0.776429\pi$
$863$	−44.8475			−1.52663			−0.763314	+	0.646028i	$0.776429\pi$
$864$		0			0
$865$	1.03293			0.0351206
$866$		0			0
$867$	−20.6531	+	19.3397i	−0.701418	+	0.656810i
$868$		0			0
$869$	50.3693	+	50.3693i	1.70866	+	1.70866i
$870$		0			0
$871$	−0.255866			−0.00866968
$872$		0			0
$873$	−2.99989	+	45.6220i	−0.101531	+	1.54407i
$874$		0			0
$875$	17.5191	−	17.5191i	0.592253	−	0.592253i
$876$		0			0
$877$	−37.7902	−	37.7902i	−1.27608	−	1.27608i	−0.942841	−	0.333244i	$-0.891857\pi$
$877$	−37.7902	−	37.7902i	−1.27608	−	1.27608i	−0.333244	−	0.942841i	$-0.608143\pi$
$878$		0			0
$879$	−11.2546	−	0.369627i	−0.379609	−	0.0124672i
$880$		0			0
$881$			1.93495i			0.0651903i	0.999469	+	0.0325951i	$0.0103772\pi$
$881$			1.93495i			0.0651903i	−0.999469	+	0.0325951i	$0.989623\pi$
$882$		0			0
$883$	−3.35788	+	3.35788i	−0.113002	+	0.113002i	−0.761347	−	0.648345i	$-0.775461\pi$
$883$	−3.35788	+	3.35788i	−0.113002	+	0.113002i	0.648345	+	0.761347i	$0.275461\pi$
$884$		0			0
$885$	−52.6060	+	49.2604i	−1.76833	+	1.65587i
$886$		0			0
$887$			17.6612i			0.593005i	0.955032	+	0.296502i	$0.0958202\pi$
$887$			17.6612i			0.593005i	−0.955032	+	0.296502i	$0.904180\pi$
$888$		0			0
$889$			1.00904i			0.0338420i
$890$		0			0
$891$	−33.5157	+	25.6950i	−1.12282	+	0.860816i
$892$		0			0
$893$	29.4585	−	29.4585i	0.985791	−	0.985791i
$894$		0			0
$895$			46.5924i			1.55741i
$896$		0			0
$897$	−0.614295	+	18.7044i	−0.0205107	+	0.624523i
$898$		0			0
$899$	−12.6853	−	12.6853i	−0.423078	−	0.423078i
$900$		0			0
$901$	−6.27403	+	6.27403i	−0.209018	+	0.209018i
$902$		0			0
$903$	4.01174	+	0.131754i	0.133502	+	0.00438451i
$904$		0			0
$905$	−80.3895			−2.67224
$906$		0			0
$907$	−6.00083	−	6.00083i	−0.199254	−	0.199254i	0.600426	−	0.799680i	$-0.294998\pi$
$907$	−6.00083	−	6.00083i	−0.199254	−	0.199254i	−0.799680	+	0.600426i	$0.794998\pi$
$908$		0			0
$909$	−3.22301	+	2.82530i	−0.106900	+	0.0937093i
$910$		0			0
$911$	21.4940			0.712127			0.356064	−	0.934462i	$-0.384119\pi$
$911$	21.4940			0.712127			0.356064	+	0.934462i	$0.384119\pi$
$912$		0			0
$913$	28.2636			0.935390
$914$		0			0
$915$	−37.3502	−	39.8868i	−1.23476	−	1.31862i
$916$		0			0
$917$	1.25508	+	1.25508i	0.0414463	+	0.0414463i
$918$		0			0
$919$	−29.2110			−0.963582			−0.481791	−	0.876286i	$-0.660014\pi$
$919$	−29.2110			−0.963582			−0.481791	+	0.876286i	$0.660014\pi$
$920$		0			0
$921$	0.824416	−	25.1023i	0.0271654	−	0.827150i
$922$		0			0
$923$	−15.0517	+	15.0517i	−0.495434	+	0.495434i
$924$		0			0
$925$	−40.7961	−	40.7961i	−1.34137	−	1.34137i
$926$		0			0
$927$	−1.09159	+	16.6008i	−0.0358525	+	0.545241i
$928$		0			0
$929$			37.2301i			1.22148i	0.791831	+	0.610741i	$0.209128\pi$
$929$			37.2301i			1.22148i	−0.791831	+	0.610741i	$0.790872\pi$
$930$		0			0
$931$	−4.39281	+	4.39281i	−0.143968	+	0.143968i
$932$		0			0
$933$	33.6864	+	35.9742i	1.10284	+	1.17774i
$934$		0			0
$935$			15.3745i			0.502800i
$936$		0			0
$937$		−	28.8582i		−	0.942755i	−0.881931	−	0.471378i	$-0.843757\pi$
$937$		−	28.8582i		−	0.942755i	0.881931	−	0.471378i	$-0.156243\pi$
$938$		0			0
$939$	28.0068	+	29.9089i	0.913969	+	0.976041i
$940$		0			0
$941$	−36.5463	+	36.5463i	−1.19138	+	1.19138i	−0.214696	+	0.976681i	$0.568876\pi$
$941$	−36.5463	+	36.5463i	−1.19138	+	1.19138i	−0.976681	+	0.214696i	$0.931124\pi$
$942$		0			0
$943$			10.5833i			0.344639i
$944$		0			0
$945$	2.05416	−	20.7888i	0.0668217	−	0.676259i
$946$		0			0
$947$	−11.9514	−	11.9514i	−0.388367	−	0.388367i	0.485738	−	0.874105i	$-0.338551\pi$
$947$	−11.9514	−	11.9514i	−0.388367	−	0.388367i	−0.874105	+	0.485738i	$0.838551\pi$
$948$		0			0
$949$	13.9991	−	13.9991i	0.454429	−	0.454429i
$950$		0			0
$951$	−0.427543	+	13.0181i	−0.0138640	+	0.422141i
$952$		0			0
$953$	51.5749			1.67068			0.835338	−	0.549737i	$-0.185272\pi$
$953$	51.5749			1.67068			0.835338	+	0.549737i	$0.185272\pi$
$954$		0			0
$955$	25.5761	+	25.5761i	0.827624	+	0.827624i
$956$		0			0
$957$	25.5886	+	27.3264i	0.827161	+	0.883337i
$958$		0			0
$959$	−5.70652			−0.184273
$960$		0			0
$961$	15.8311			0.510682
$962$		0			0
$963$	19.3623	+	22.0879i	0.623942	+	0.711773i
$964$		0			0
$965$	−70.9594	−	70.9594i	−2.28426	−	2.28426i
$966$		0			0
$967$	−2.76614			−0.0889531			−0.0444766	−	0.999010i	$-0.514162\pi$
$967$	−2.76614			−0.0889531			−0.0444766	+	0.999010i	$0.514162\pi$
$968$		0			0
$969$	−8.76456	−	0.287848i	−0.281558	−	0.00924700i
$970$		0			0
$971$	−26.6491	+	26.6491i	−0.855210	+	0.855210i	−0.990769	−	0.135559i	$-0.956717\pi$
$971$	−26.6491	+	26.6491i	−0.855210	+	0.855210i	0.135559	+	0.990769i	$0.456717\pi$
$972$		0			0
$973$	6.78446	+	6.78446i	0.217500	+	0.217500i
$974$		0			0
$975$	−2.07587	+	63.2074i	−0.0664810	+	2.02426i
$976$		0			0
$977$			15.9054i			0.508859i	0.967091	+	0.254429i	$0.0818877\pi$
$977$			15.9054i			0.508859i	−0.967091	+	0.254429i	$0.918112\pi$
$978$		0			0
$979$	7.68542	−	7.68542i	0.245627	−	0.245627i
$980$		0			0
$981$	5.41576	−	4.74748i	0.172912	−	0.151575i
$982$		0			0
$983$			58.2649i			1.85836i	0.369625	+	0.929181i	$0.379486\pi$
$983$			58.2649i			1.85836i	−0.369625	+	0.929181i	$0.620514\pi$
$984$		0			0
$985$		−	15.2921i		−	0.487247i
$986$		0			0
$987$	8.47840	−	7.93921i	0.269870	−	0.252708i
$988$		0			0
$989$	5.41298	−	5.41298i	0.172123	−	0.172123i
$990$		0			0
$991$		−	5.20415i		−	0.165315i	−0.996578	−	0.0826576i	$-0.973659\pi$
$991$		−	5.20415i		−	0.165315i	0.996578	−	0.0826576i	$-0.0263408\pi$
$992$		0			0
$993$	15.1279	+	0.496833i	0.480069	+	0.0157665i
$994$		0			0
$995$	−16.5471	−	16.5471i	−0.524579	−	0.524579i
$996$		0			0
$997$	23.8283	−	23.8283i	0.754650	−	0.754650i	−0.220693	−	0.975343i	$-0.570832\pi$
$997$	23.8283	−	23.8283i	0.754650	−	0.754650i	0.975343	+	0.220693i	$0.0708319\pi$
$998$		0			0
$999$	−26.7262	−	2.64084i	−0.845579	−	0.0835525i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.s.c.239.5		40
3.2	odd	2	inner	1344.2.s.c.239.6		40
4.3	odd	2		336.2.s.c.323.11	yes	40
12.11	even	2		336.2.s.c.323.10	yes	40
16.5	even	4		336.2.s.c.155.10	✓	40
16.11	odd	4	inner	1344.2.s.c.911.6		40
48.5	odd	4		336.2.s.c.155.11	yes	40
48.11	even	4	inner	1344.2.s.c.911.5		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.c.155.10	✓	40	16.5	even	4
336.2.s.c.155.11	yes	40	48.5	odd	4
336.2.s.c.323.10	yes	40	12.11	even	2
336.2.s.c.323.11	yes	40	4.3	odd	2
1344.2.s.c.239.5		40	1.1	even	1	trivial
1344.2.s.c.239.6		40	3.2	odd	2	inner
1344.2.s.c.911.5		40	48.11	even	4	inner
1344.2.s.c.911.6		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)

\(f(q)\)	\(=\)	\(q+(-1.26429 + 1.18388i) q^{3} +(-2.84277 - 2.84277i) q^{5} +1.00000 q^{7} +(0.196841 - 2.99354i) q^{9} +O(q^{10})\)	\(q+(-1.26429 + 1.18388i) q^{3} +(-2.84277 - 2.84277i) q^{5} +1.00000 q^{7} +(0.196841 - 2.99354i) q^{9} +(3.31805 - 3.31805i) q^{11} +(-2.31290 - 2.31290i) q^{13} +(6.95958 + 0.228568i) q^{15} -0.814979i q^{17} +(-4.39281 + 4.39281i) q^{19} +(-1.26429 + 1.18388i) q^{21} +3.30328i q^{23} +11.1627i q^{25} +(3.29513 + 4.01772i) q^{27} +(3.25705 - 3.25705i) q^{29} -3.89472i q^{31} +(-0.266782 + 8.12315i) q^{33} +(-2.84277 - 2.84277i) q^{35} +(-3.65469 + 3.65469i) q^{37} +(5.66238 + 0.185965i) q^{39} +3.20387 q^{41} +(-1.63867 - 1.63867i) q^{43} +(-9.06950 + 7.95036i) q^{45} -6.70608 q^{47} +1.00000 q^{49} +(0.964840 + 1.03037i) q^{51} +(-7.69839 - 7.69839i) q^{53} -18.8649 q^{55} +(0.353196 - 10.7543i) q^{57} +(-7.31843 + 7.31843i) q^{59} +(-5.54897 - 5.54897i) q^{61} +(0.196841 - 2.99354i) q^{63} +13.1501i q^{65} +(0.0553126 - 0.0553126i) q^{67} +(-3.91070 - 4.17629i) q^{69} -6.50772i q^{71} +6.05260i q^{73} +(-13.2153 - 14.1128i) q^{75} +(3.31805 - 3.31805i) q^{77} +15.1804i q^{79} +(-8.92251 - 1.17850i) q^{81} +(4.25907 + 4.25907i) q^{83} +(-2.31680 + 2.31680i) q^{85} +(-0.261877 + 7.97380i) q^{87} +2.31624 q^{89} +(-2.31290 - 2.31290i) q^{91} +(4.61089 + 4.92404i) q^{93} +24.9755 q^{95} -15.2402 q^{97} +(-9.27958 - 10.5858i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} + 40 q^{7}+O(q^{10}) \) 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

Properties

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