LMFDB - Embedded newform 1344.2.u.a.1231.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(559,1344)]

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, 0, 2]))

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

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

chi := DirichletCharacter("1344.559");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.u (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:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1231.18
Character	$\chi$	$=$	1344.1231
Dual form			1344.2.u.a.559.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(2.46638 - 2.46638i) q^{5} +(2.50032 + 0.865115i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{3} +(2.46638 - 2.46638i) q^{5} +(2.50032 + 0.865115i) q^{7} -1.00000i q^{9} +(-0.244455 + 0.244455i) q^{11} +(-2.35087 - 2.35087i) q^{13} -3.48798i q^{15} -5.19171i q^{17} +(-1.43102 + 1.43102i) q^{19} +(2.37972 - 1.15626i) q^{21} +6.61525 q^{23} -7.16602i q^{25} +(-0.707107 - 0.707107i) q^{27} +(-5.09187 + 5.09187i) q^{29} +1.53315 q^{31} +0.345712i q^{33} +(8.30041 - 4.03302i) q^{35} +(-2.40835 - 2.40835i) q^{37} -3.32463 q^{39} +9.55090 q^{41} +(-6.80405 + 6.80405i) q^{43} +(-2.46638 - 2.46638i) q^{45} -7.20043 q^{47} +(5.50315 + 4.32612i) q^{49} +(-3.67109 - 3.67109i) q^{51} +(5.49720 + 5.49720i) q^{53} +1.20584i q^{55} +2.02377i q^{57} +(3.45643 + 3.45643i) q^{59} +(-1.27576 - 1.27576i) q^{61} +(0.865115 - 2.50032i) q^{63} -11.5962 q^{65} +(-3.83774 - 3.83774i) q^{67} +(4.67768 - 4.67768i) q^{69} -16.0833 q^{71} +6.68392 q^{73} +(-5.06714 - 5.06714i) q^{75} +(-0.822697 + 0.399733i) q^{77} +4.09727i q^{79} -1.00000 q^{81} +(9.70907 - 9.70907i) q^{83} +(-12.8047 - 12.8047i) q^{85} +7.20100i q^{87} +11.5562 q^{89} +(-3.84414 - 7.91168i) q^{91} +(1.08410 - 1.08410i) q^{93} +7.05886i q^{95} -16.7160i q^{97} +(0.244455 + 0.244455i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 8 q^{11} + 16 q^{23} + 16 q^{29} - 24 q^{35} + 16 q^{37} + 8 q^{43} + 16 q^{53} - 56 q^{67} + 128 q^{71} - 64 q^{81} - 8 q^{91} + 8 q^{99}+O(q^{100}) $ 64 * q - 8 * q^11 + 16 * q^23 + 16 * q^29 - 24 * q^35 + 16 * q^37 + 8 * q^43 + 16 * q^53 - 56 * q^67 + 128 * q^71 - 64 * q^81 - 8 * q^91 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	2.46638	−	2.46638i	1.10300	−	1.10300i	0.108949	−	0.994047i	$-0.465251\pi$
$5$	2.46638	−	2.46638i	1.10300	−	1.10300i	0.994047	−	0.108949i	$-0.0347486\pi$
$6$		0			0
$7$	2.50032	+	0.865115i	0.945030	+	0.326983i
$7$	2.50032	+	0.865115i	0.945030	+	0.326983i
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−0.244455	+	0.244455i	−0.0737061	+	0.0737061i	−0.742999	−	0.669293i	$-0.766597\pi$
$11$	−0.244455	+	0.244455i	−0.0737061	+	0.0737061i	0.669293	+	0.742999i	$0.266597\pi$
$12$		0			0
$13$	−2.35087	−	2.35087i	−0.652014	−	0.652014i	0.301464	−	0.953478i	$-0.402525\pi$
$13$	−2.35087	−	2.35087i	−0.652014	−	0.652014i	−0.953478	+	0.301464i	$0.902525\pi$
$14$		0			0
$15$		−	3.48798i		−	0.900593i
$16$		0			0
$17$		−	5.19171i		−	1.25918i	−0.776930	−	0.629588i	$-0.783224\pi$
$17$		−	5.19171i		−	1.25918i	0.776930	−	0.629588i	$-0.216776\pi$
$18$		0			0
$19$	−1.43102	+	1.43102i	−0.328298	+	0.328298i	−0.851939	−	0.523641i	$-0.824573\pi$
$19$	−1.43102	+	1.43102i	−0.328298	+	0.328298i	0.523641	+	0.851939i	$0.324573\pi$
$20$		0			0
$21$	2.37972	−	1.15626i	0.519297	−	0.252317i
$22$		0			0
$23$	6.61525			1.37937			0.689687	−	0.724108i	$-0.257748\pi$
$23$	6.61525			1.37937			0.689687	+	0.724108i	$0.257748\pi$
$24$		0			0
$25$		−	7.16602i		−	1.43320i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$	−5.09187	+	5.09187i	−0.945537	+	0.945537i	−0.998592	−	0.0530544i	$-0.983104\pi$
$29$	−5.09187	+	5.09187i	−0.945537	+	0.945537i	0.0530544	+	0.998592i	$0.483104\pi$
$30$		0			0
$31$	1.53315			0.275363			0.137681	−	0.990477i	$-0.456035\pi$
$31$	1.53315			0.275363			0.137681	+	0.990477i	$0.456035\pi$
$32$		0			0
$33$			0.345712i			0.0601807i
$34$		0			0
$35$	8.30041	−	4.03302i	1.40303	−	0.681704i
$36$		0			0
$37$	−2.40835	−	2.40835i	−0.395930	−	0.395930i	0.480865	−	0.876795i	$-0.340323\pi$
$37$	−2.40835	−	2.40835i	−0.395930	−	0.395930i	−0.876795	+	0.480865i	$0.840323\pi$
$38$		0			0
$39$	−3.32463			−0.532367
$40$		0			0
$41$	9.55090			1.49160			0.745800	−	0.666170i	$-0.232068\pi$
$41$	9.55090			1.49160			0.745800	+	0.666170i	$0.232068\pi$
$42$		0			0
$43$	−6.80405	+	6.80405i	−1.03761	+	1.03761i	−0.0383425	+	0.999265i	$0.512208\pi$
$43$	−6.80405	+	6.80405i	−1.03761	+	1.03761i	−0.999265	+	0.0383425i	$0.987792\pi$
$44$		0			0
$45$	−2.46638	−	2.46638i	−0.367666	−	0.367666i
$46$		0			0
$47$	−7.20043			−1.05029			−0.525145	−	0.851013i	$-0.675989\pi$
$47$	−7.20043			−1.05029			−0.525145	+	0.851013i	$0.675989\pi$
$48$		0			0
$49$	5.50315	+	4.32612i	0.786165	+	0.618017i
$50$		0			0
$51$	−3.67109	−	3.67109i	−0.514056	−	0.514056i
$52$		0			0
$53$	5.49720	+	5.49720i	0.755099	+	0.755099i	0.975426	−	0.220327i	$-0.0707126\pi$
$53$	5.49720	+	5.49720i	0.755099	+	0.755099i	−0.220327	+	0.975426i	$0.570713\pi$
$54$		0			0
$55$			1.20584i			0.162595i
$56$		0			0
$57$			2.02377i			0.268055i
$58$		0			0
$59$	3.45643	+	3.45643i	0.449988	+	0.449988i	0.895351	−	0.445362i	$-0.146925\pi$
$59$	3.45643	+	3.45643i	0.449988	+	0.449988i	−0.445362	+	0.895351i	$0.646925\pi$
$60$		0			0
$61$	−1.27576	−	1.27576i	−0.163344	−	0.163344i	0.620702	−	0.784046i	$-0.286848\pi$
$61$	−1.27576	−	1.27576i	−0.163344	−	0.163344i	−0.784046	+	0.620702i	$0.786848\pi$
$62$		0			0
$63$	0.865115	−	2.50032i	0.108994	−	0.315010i
$64$		0			0
$65$	−11.5962			−1.43834
$66$		0			0
$67$	−3.83774	−	3.83774i	−0.468855	−	0.468855i	0.432689	−	0.901543i	$-0.357565\pi$
$67$	−3.83774	−	3.83774i	−0.468855	−	0.468855i	−0.901543	+	0.432689i	$0.857565\pi$
$68$		0			0
$69$	4.67768	−	4.67768i	0.563127	−	0.563127i
$70$		0			0
$71$	−16.0833			−1.90874			−0.954368	−	0.298632i	$-0.903470\pi$
$71$	−16.0833			−1.90874			−0.954368	+	0.298632i	$0.903470\pi$
$72$		0			0
$73$	6.68392			0.782293			0.391147	−	0.920328i	$-0.372079\pi$
$73$	6.68392			0.782293			0.391147	+	0.920328i	$0.372079\pi$
$74$		0			0
$75$	−5.06714	−	5.06714i	−0.585103	−	0.585103i
$76$		0			0
$77$	−0.822697	+	0.399733i	−0.0937551	+	0.0455539i
$78$		0			0
$79$			4.09727i			0.460979i	0.973075	+	0.230490i	$0.0740328\pi$
$79$			4.09727i			0.460979i	−0.973075	+	0.230490i	$0.925967\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	9.70907	−	9.70907i	1.06571	−	1.06571i	0.0680257	−	0.997684i	$-0.478330\pi$
$83$	9.70907	−	9.70907i	1.06571	−	1.06571i	0.997684	−	0.0680257i	$-0.0216700\pi$
$84$		0			0
$85$	−12.8047	−	12.8047i	−1.38887	−	1.38887i
$86$		0			0
$87$			7.20100i			0.772028i
$88$		0			0
$89$	11.5562			1.22495			0.612477	−	0.790489i	$-0.290173\pi$
$89$	11.5562			1.22495			0.612477	+	0.790489i	$0.290173\pi$
$90$		0			0
$91$	−3.84414	−	7.91168i	−0.402975	−	0.829370i
$92$		0			0
$93$	1.08410	−	1.08410i	0.112416	−	0.112416i
$94$		0			0
$95$			7.05886i			0.724224i
$96$		0			0
$97$		−	16.7160i		−	1.69725i	−0.528995	−	0.848625i	$-0.677431\pi$
$97$		−	16.7160i		−	1.69725i	0.528995	−	0.848625i	$-0.322569\pi$
$98$		0			0
$99$	0.244455	+	0.244455i	0.0245687	+	0.0245687i
$100$		0			0
$101$	−10.5198	+	10.5198i	−1.04676	+	1.04676i	−0.0479051	+	0.998852i	$0.515255\pi$
$101$	−10.5198	+	10.5198i	−1.04676	+	1.04676i	−0.998852	+	0.0479051i	$0.984745\pi$
$102$		0			0
$103$			5.39742i			0.531824i	0.963997	+	0.265912i	$0.0856730\pi$
$103$			5.39742i			0.531824i	−0.963997	+	0.265912i	$0.914327\pi$
$104$		0			0
$105$	3.01751	−	8.72105i	0.294478	−	0.851088i
$106$		0			0
$107$	5.63948	−	5.63948i	0.545189	−	0.545189i	−0.379857	−	0.925045i	$-0.624027\pi$
$107$	5.63948	−	5.63948i	0.545189	−	0.545189i	0.925045	+	0.379857i	$0.124027\pi$
$108$		0			0
$109$	1.70321	−	1.70321i	0.163138	−	0.163138i	−0.620817	−	0.783955i	$-0.713199\pi$
$109$	1.70321	−	1.70321i	0.163138	−	0.163138i	0.783955	+	0.620817i	$0.213199\pi$
$110$		0			0
$111$	−3.40592			−0.323275
$112$		0			0
$113$	5.88021			0.553163			0.276582	−	0.960990i	$-0.410798\pi$
$113$	5.88021			0.553163			0.276582	+	0.960990i	$0.410798\pi$
$114$		0			0
$115$	16.3157	−	16.3157i	1.52144	−	1.52144i
$116$		0			0
$117$	−2.35087	+	2.35087i	−0.217338	+	0.217338i
$118$		0			0
$119$	4.49143	−	12.9809i	0.411729	−	1.18996i
$120$		0			0
$121$			10.8805i			0.989135i
$122$		0			0
$123$	6.75350	−	6.75350i	0.608943	−	0.608943i
$124$		0			0
$125$	−5.34221	−	5.34221i	−0.477822	−	0.477822i
$126$		0			0
$127$			2.54065i			0.225446i	0.993626	+	0.112723i	$0.0359573\pi$
$127$			2.54065i			0.225446i	−0.993626	+	0.112723i	$0.964043\pi$
$128$		0			0
$129$			9.62237i			0.847203i
$130$		0			0
$131$	−1.36457	+	1.36457i	−0.119223	+	0.119223i	−0.764201	−	0.644978i	$-0.776866\pi$
$131$	−1.36457	+	1.36457i	−0.119223	+	0.119223i	0.644978	+	0.764201i	$0.276866\pi$
$132$		0			0
$133$	−4.81600	+	2.34000i	−0.417600	+	0.202904i
$134$		0			0
$135$	−3.48798			−0.300198
$136$		0			0
$137$			8.81747i			0.753327i	0.926350	+	0.376664i	$0.122929\pi$
$137$			8.81747i			0.753327i	−0.926350	+	0.376664i	$0.877071\pi$
$138$		0			0
$139$	0.409417	+	0.409417i	0.0347263	+	0.0347263i	0.724257	−	0.689530i	$-0.242183\pi$
$139$	0.409417	+	0.409417i	0.0347263	+	0.0347263i	−0.689530	+	0.724257i	$0.742183\pi$
$140$		0			0
$141$	−5.09147	+	5.09147i	−0.428779	+	0.428779i
$142$		0			0
$143$	1.14936			0.0961147
$144$		0			0
$145$			25.1169i			2.08585i
$146$		0			0
$147$	6.95035	−	0.832287i	0.573255	−	0.0686459i
$148$		0			0
$149$	8.59190	+	8.59190i	0.703876	+	0.703876i	0.965240	−	0.261364i	$-0.0841724\pi$
$149$	8.59190	+	8.59190i	0.703876	+	0.703876i	−0.261364	+	0.965240i	$0.584172\pi$
$150$		0			0
$151$	15.8215			1.28753			0.643767	−	0.765222i	$-0.277371\pi$
$151$	15.8215			1.28753			0.643767	+	0.765222i	$0.277371\pi$
$152$		0			0
$153$	−5.19171			−0.419725
$154$		0			0
$155$	3.78134	−	3.78134i	0.303724	−	0.303724i
$156$		0			0
$157$	−13.3568	−	13.3568i	−1.06599	−	1.06599i	−0.997663	−	0.0683267i	$-0.978234\pi$
$157$	−13.3568	−	13.3568i	−1.06599	−	1.06599i	−0.0683267	−	0.997663i	$-0.521766\pi$
$158$		0			0
$159$	7.77422			0.616535
$160$		0			0
$161$	16.5402	+	5.72295i	1.30355	+	0.451031i
$162$		0			0
$163$	−11.2072	−	11.2072i	−0.877815	−	0.877815i	0.115493	−	0.993308i	$-0.463155\pi$
$163$	−11.2072	−	11.2072i	−0.877815	−	0.877815i	−0.993308	+	0.115493i	$0.963155\pi$
$164$		0			0
$165$	0.852656	+	0.852656i	0.0663792	+	0.0663792i
$166$		0			0
$167$			15.6103i			1.20796i	0.796998	+	0.603981i	$0.206420\pi$
$167$			15.6103i			1.20796i	−0.796998	+	0.603981i	$0.793580\pi$
$168$		0			0
$169$		−	1.94683i		−	0.149756i
$170$		0			0
$171$	1.43102	+	1.43102i	0.109433	+	0.109433i
$172$		0			0
$173$	−6.62694	−	6.62694i	−0.503837	−	0.503837i	0.408791	−	0.912628i	$-0.365950\pi$
$173$	−6.62694	−	6.62694i	−0.503837	−	0.503837i	−0.912628	+	0.408791i	$0.865950\pi$
$174$		0			0
$175$	6.19943	−	17.9173i	0.468633	−	1.35442i
$176$		0			0
$177$	4.88812			0.367414
$178$		0			0
$179$	1.58460	+	1.58460i	0.118439	+	0.118439i	0.763842	−	0.645403i	$-0.223311\pi$
$179$	1.58460	+	1.58460i	0.118439	+	0.118439i	−0.645403	+	0.763842i	$0.723311\pi$
$180$		0			0
$181$	7.37897	−	7.37897i	0.548475	−	0.548475i	−0.377525	−	0.925999i	$-0.623225\pi$
$181$	7.37897	−	7.37897i	0.548475	−	0.548475i	0.925999	+	0.377525i	$0.123225\pi$
$182$		0			0
$183$	−1.80419			−0.133370
$184$		0			0
$185$	−11.8798			−0.873419
$186$		0			0
$187$	1.26914	+	1.26914i	0.0928088	+	0.0928088i
$188$		0			0
$189$	−1.15626	−	2.37972i	−0.0841056	−	0.173099i
$190$		0			0
$191$			24.9642i			1.80635i	0.429274	+	0.903174i	$0.358769\pi$
$191$			24.9642i			1.80635i	−0.429274	+	0.903174i	$0.641231\pi$
$192$		0			0
$193$	−9.84108			−0.708376			−0.354188	−	0.935174i	$-0.615243\pi$
$193$	−9.84108			−0.708376			−0.354188	+	0.935174i	$0.615243\pi$
$194$		0			0
$195$	−8.19979	+	8.19979i	−0.587199	+	0.587199i
$196$		0			0
$197$	6.20883	+	6.20883i	0.442360	+	0.442360i	0.892805	−	0.450444i	$-0.148734\pi$
$197$	6.20883	+	6.20883i	0.442360	+	0.442360i	−0.450444	+	0.892805i	$0.648734\pi$
$198$		0			0
$199$		−	10.1707i		−	0.720981i	−0.932763	−	0.360491i	$-0.882609\pi$
$199$		−	10.1707i		−	0.720981i	0.932763	−	0.360491i	$-0.117391\pi$
$200$		0			0
$201$	−5.42739			−0.382818
$202$		0			0
$203$	−17.1363	+	8.32623i	−1.20274	+	0.584387i
$204$		0			0
$205$	23.5561	−	23.5561i	1.64523	−	1.64523i
$206$		0			0
$207$		−	6.61525i		−	0.459791i
$208$		0			0
$209$		−	0.699641i		−	0.0483952i
$210$		0			0
$211$	5.69803	+	5.69803i	0.392269	+	0.392269i	0.875495	−	0.483227i	$-0.160535\pi$
$211$	5.69803	+	5.69803i	0.392269	+	0.392269i	−0.483227	+	0.875495i	$0.660535\pi$
$212$		0			0
$213$	−11.3726	+	11.3726i	−0.779238	+	0.779238i
$214$		0			0
$215$			33.5627i			2.28895i
$216$		0			0
$217$	3.83337	+	1.32636i	0.260226	+	0.0900389i
$218$		0			0
$219$	4.72624	−	4.72624i	0.319370	−	0.319370i
$220$		0			0
$221$	−12.2050	+	12.2050i	−0.820999	+	0.820999i
$222$		0			0
$223$	−5.26554			−0.352607			−0.176303	−	0.984336i	$-0.556414\pi$
$223$	−5.26554			−0.352607			−0.176303	+	0.984336i	$0.556414\pi$
$224$		0			0
$225$	−7.16602			−0.477734
$226$		0			0
$227$	−11.3768	+	11.3768i	−0.755102	+	0.755102i	−0.975427	−	0.220325i	$-0.929288\pi$
$227$	−11.3768	+	11.3768i	−0.755102	+	0.755102i	0.220325	+	0.975427i	$0.429288\pi$
$228$		0			0
$229$	−14.8763	+	14.8763i	−0.983051	+	0.983051i	−0.999859	−	0.0168077i	$-0.994650\pi$
$229$	−14.8763	+	14.8763i	−0.983051	+	0.983051i	0.0168077	+	0.999859i	$0.494650\pi$
$230$		0			0
$231$	−0.299081	+	0.864389i	−0.0196781	+	0.0568726i
$232$		0			0
$233$		−	2.12538i		−	0.139238i	−0.997574	−	0.0696190i	$-0.977822\pi$
$233$		−	2.12538i		−	0.139238i	0.997574	−	0.0696190i	$-0.0221783\pi$
$234$		0			0
$235$	−17.7590	+	17.7590i	−1.15847	+	1.15847i
$236$		0			0
$237$	2.89721	+	2.89721i	0.188194	+	0.188194i
$238$		0			0
$239$		−	8.94355i		−	0.578510i	−0.957252	−	0.289255i	$-0.906592\pi$
$239$		−	8.94355i		−	0.578510i	0.957252	−	0.289255i	$-0.0934076\pi$
$240$		0			0
$241$		−	4.16309i		−	0.268168i	−0.990970	−	0.134084i	$-0.957191\pi$
$241$		−	4.16309i		−	0.268168i	0.990970	−	0.134084i	$-0.0428092\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	24.2427	−	2.90300i	1.54881	−	0.185466i
$246$		0			0
$247$	6.72828			0.428110
$248$		0			0
$249$		−	13.7307i		−	0.870148i
$250$		0			0
$251$	0.848419	+	0.848419i	0.0535518	+	0.0535518i	0.733376	−	0.679824i	$-0.237944\pi$
$251$	0.848419	+	0.848419i	0.0535518	+	0.0535518i	−0.679824	+	0.733376i	$0.737944\pi$
$252$		0			0
$253$	−1.61713	+	1.61713i	−0.101668	+	0.101668i
$254$		0			0
$255$	−18.1086			−1.13400
$256$		0			0
$257$			20.1074i			1.25426i	0.778913	+	0.627132i	$0.215772\pi$
$257$			20.1074i			1.25426i	−0.778913	+	0.627132i	$0.784228\pi$
$258$		0			0
$259$	−3.93813	−	8.10513i	−0.244703	−	0.503628i
$260$		0			0
$261$	5.09187	+	5.09187i	0.315179	+	0.315179i
$262$		0			0
$263$	6.57887			0.405671			0.202835	−	0.979213i	$-0.434984\pi$
$263$	6.57887			0.405671			0.202835	+	0.979213i	$0.434984\pi$
$264$		0			0
$265$	27.1163			1.66574
$266$		0			0
$267$	8.17146	−	8.17146i	0.500085	−	0.500085i
$268$		0			0
$269$	18.5658	+	18.5658i	1.13198	+	1.13198i	0.989848	+	0.142129i	$0.0453949\pi$
$269$	18.5658	+	18.5658i	1.13198	+	1.13198i	0.142129	+	0.989848i	$0.454605\pi$
$270$		0			0
$271$	−22.1109			−1.34314			−0.671569	−	0.740942i	$-0.734379\pi$
$271$	−22.1109			−1.34314			−0.671569	+	0.740942i	$0.734379\pi$
$272$		0			0
$273$	−8.31262	−	2.87619i	−0.503103	−	0.174075i
$274$		0			0
$275$	1.75177	+	1.75177i	0.105636	+	0.105636i
$276$		0			0
$277$	−14.1965	−	14.1965i	−0.852983	−	0.852983i	0.137516	−	0.990499i	$-0.456088\pi$
$277$	−14.1965	−	14.1965i	−0.852983	−	0.852983i	−0.990499	+	0.137516i	$0.956088\pi$
$278$		0			0
$279$		−	1.53315i		−	0.0917876i
$280$		0			0
$281$		−	0.533748i		−	0.0318407i	−0.999873	−	0.0159204i	$-0.994932\pi$
$281$		−	0.533748i		−	0.0318407i	0.999873	−	0.0159204i	$-0.00506782\pi$
$282$		0			0
$283$	19.5036	+	19.5036i	1.15937	+	1.15937i	0.984612	+	0.174754i	$0.0559131\pi$
$283$	19.5036	+	19.5036i	1.15937	+	1.15937i	0.174754	+	0.984612i	$0.444087\pi$
$284$		0			0
$285$	4.99137	+	4.99137i	0.295663	+	0.295663i
$286$		0			0
$287$	23.8802	+	8.26262i	1.40961	+	0.487727i
$288$		0			0
$289$	−9.95388			−0.585522
$290$		0			0
$291$	−11.8200	−	11.8200i	−0.692899	−	0.692899i
$292$		0			0
$293$	13.2601	−	13.2601i	0.774661	−	0.774661i	−0.204256	−	0.978917i	$-0.565478\pi$
$293$	13.2601	−	13.2601i	0.774661	−	0.774661i	0.978917	+	0.204256i	$0.0654775\pi$
$294$		0			0
$295$	17.0497			0.992671
$296$		0			0
$297$	0.345712			0.0200602
$298$		0			0
$299$	−15.5516	−	15.5516i	−0.899371	−	0.899371i
$300$		0			0
$301$	−22.8985	+	11.1260i	−1.31985	+	0.641291i
$302$		0			0
$303$			14.8772i			0.854674i
$304$		0			0
$305$	−6.29298			−0.360335
$306$		0			0
$307$	−8.75073	+	8.75073i	−0.499430	+	0.499430i	−0.911261	−	0.411830i	$-0.864890\pi$
$307$	−8.75073	+	8.75073i	−0.499430	+	0.499430i	0.411830	+	0.911261i	$0.364890\pi$
$308$		0			0
$309$	3.81655	+	3.81655i	0.217116	+	0.217116i
$310$		0			0
$311$		−	12.5063i		−	0.709170i	−0.935024	−	0.354585i	$-0.884622\pi$
$311$		−	12.5063i		−	0.709170i	0.935024	−	0.354585i	$-0.115378\pi$
$312$		0			0
$313$	−30.6740			−1.73380			−0.866899	−	0.498484i	$-0.833890\pi$
$313$	−30.6740			−1.73380			−0.866899	+	0.498484i	$0.833890\pi$
$314$		0			0
$315$	−4.03302	−	8.30041i	−0.227235	−	0.467675i
$316$		0			0
$317$	−6.56844	+	6.56844i	−0.368920	+	0.368920i	−0.867083	−	0.498163i	$-0.834008\pi$
$317$	−6.56844	+	6.56844i	−0.368920	+	0.368920i	0.498163	+	0.867083i	$0.334008\pi$
$318$		0			0
$319$		−	2.48947i		−	0.139384i
$320$		0			0
$321$		−	7.97542i		−	0.445145i
$322$		0			0
$323$	7.42944	+	7.42944i	0.413385	+	0.413385i
$324$		0			0
$325$	−16.8464	+	16.8464i	−0.934468	+	0.934468i
$326$		0			0
$327$		−	2.40871i		−	0.133202i
$328$		0			0
$329$	−18.0033	−	6.22920i	−0.992556	−	0.343427i
$330$		0			0
$331$	−2.86508	+	2.86508i	−0.157479	+	0.157479i	−0.781449	−	0.623969i	$-0.785519\pi$
$331$	−2.86508	+	2.86508i	−0.157479	+	0.157479i	0.623969	+	0.781449i	$0.285519\pi$
$332$		0			0
$333$	−2.40835	+	2.40835i	−0.131977	+	0.131977i
$334$		0			0
$335$	−18.9306			−1.03429
$336$		0			0
$337$	23.4976			1.28000			0.639999	−	0.768376i	$-0.278935\pi$
$337$	23.4976			1.28000			0.639999	+	0.768376i	$0.278935\pi$
$338$		0			0
$339$	4.15793	−	4.15793i	0.225828	−	0.225828i
$340$		0			0
$341$	−0.374788	+	0.374788i	−0.0202959	+	0.0202959i
$342$		0			0
$343$	10.0170	+	15.5775i	0.540868	+	0.841107i
$344$		0			0
$345$		−	23.0739i		−	1.24225i
$346$		0			0
$347$	−7.30416	+	7.30416i	−0.392108	+	0.392108i	−0.875438	−	0.483330i	$-0.839427\pi$
$347$	−7.30416	+	7.30416i	−0.392108	+	0.392108i	0.483330	+	0.875438i	$0.339427\pi$
$348$		0			0
$349$	10.4160	+	10.4160i	0.557555	+	0.557555i	0.928611	−	0.371055i	$-0.121004\pi$
$349$	10.4160	+	10.4160i	0.557555	+	0.557555i	−0.371055	+	0.928611i	$0.621004\pi$
$350$		0			0
$351$			3.32463i			0.177456i
$352$		0			0
$353$			0.352884i			0.0187821i	0.999956	+	0.00939107i	$0.00298931\pi$
$353$			0.352884i			0.0187821i	−0.999956	+	0.00939107i	$0.997011\pi$
$354$		0			0
$355$	−39.6675	+	39.6675i	−2.10533	+	2.10533i
$356$		0			0
$357$	−6.00297	−	12.3548i	−0.317711	−	0.653886i
$358$		0			0
$359$	−2.93757			−0.155039			−0.0775194	−	0.996991i	$-0.524700\pi$
$359$	−2.93757			−0.155039			−0.0775194	+	0.996991i	$0.524700\pi$
$360$		0			0
$361$			14.9044i			0.784440i
$362$		0			0
$363$	7.69366	+	7.69366i	0.403813	+	0.403813i
$364$		0			0
$365$	16.4850	−	16.4850i	0.862867	−	0.862867i
$366$		0			0
$367$	−33.3562			−1.74118			−0.870589	−	0.492010i	$-0.836262\pi$
$367$	−33.3562			−1.74118			−0.870589	+	0.492010i	$0.836262\pi$
$368$		0			0
$369$		−	9.55090i		−	0.497200i
$370$		0			0
$371$	8.98902	+	18.5004i	0.466687	+	0.960495i
$372$		0			0
$373$	19.0617	+	19.0617i	0.986977	+	0.986977i	0.999916	−	0.0129389i	$-0.00411870\pi$
$373$	19.0617	+	19.0617i	0.986977	+	0.986977i	−0.0129389	+	0.999916i	$0.504119\pi$
$374$		0			0
$375$	−7.55502			−0.390140
$376$		0			0
$377$	23.9407			1.23301
$378$		0			0
$379$	8.93678	−	8.93678i	0.459051	−	0.459051i	−0.439293	−	0.898344i	$-0.644771\pi$
$379$	8.93678	−	8.93678i	0.459051	−	0.459051i	0.898344	+	0.439293i	$0.144771\pi$
$380$		0			0
$381$	1.79651	+	1.79651i	0.0920381	+	0.0920381i
$382$		0			0
$383$	30.1669			1.54145			0.770727	−	0.637165i	$-0.219893\pi$
$383$	30.1669			1.54145			0.770727	+	0.637165i	$0.219893\pi$
$384$		0			0
$385$	−1.04319	+	3.01497i	−0.0531658	+	0.153657i
$386$		0			0
$387$	6.80405	+	6.80405i	0.345869	+	0.345869i
$388$		0			0
$389$	9.88128	+	9.88128i	0.501001	+	0.501001i	0.911749	−	0.410748i	$-0.134732\pi$
$389$	9.88128	+	9.88128i	0.501001	+	0.501001i	−0.410748	+	0.911749i	$0.634732\pi$
$390$		0			0
$391$		−	34.3445i		−	1.73687i
$392$		0			0
$393$			1.92979i			0.0973451i
$394$		0			0
$395$	10.1054	+	10.1054i	0.508459	+	0.508459i
$396$		0			0
$397$	5.73434	+	5.73434i	0.287798	+	0.287798i	0.836209	−	0.548411i	$-0.184767\pi$
$397$	5.73434	+	5.73434i	0.287798	+	0.287798i	−0.548411	+	0.836209i	$0.684767\pi$
$398$		0			0
$399$	−1.75079	+	5.06006i	−0.0876492	+	0.253320i
$400$		0			0
$401$	10.0283			0.500789			0.250394	−	0.968144i	$-0.419440\pi$
$401$	10.0283			0.500789			0.250394	+	0.968144i	$0.419440\pi$
$402$		0			0
$403$	−3.60425	−	3.60425i	−0.179540	−	0.179540i
$404$		0			0
$405$	−2.46638	+	2.46638i	−0.122555	+	0.122555i
$406$		0			0
$407$	1.17747			0.0583649
$408$		0			0
$409$	16.0808			0.795145			0.397572	−	0.917571i	$-0.369853\pi$
$409$	16.0808			0.795145			0.397572	+	0.917571i	$0.369853\pi$
$410$		0			0
$411$	6.23489	+	6.23489i	0.307545	+	0.307545i
$412$		0			0
$413$	5.65195	+	11.6324i	0.278114	+	0.572391i
$414$		0			0
$415$		−	47.8924i		−	2.35095i
$416$		0			0
$417$	0.579003			0.0283539
$418$		0			0
$419$	6.59346	−	6.59346i	0.322112	−	0.322112i	−0.527465	−	0.849577i	$-0.676857\pi$
$419$	6.59346	−	6.59346i	0.322112	−	0.322112i	0.849577	+	0.527465i	$0.176857\pi$
$420$		0			0
$421$	−4.63581	−	4.63581i	−0.225936	−	0.225936i	0.585057	−	0.810992i	$-0.301072\pi$
$421$	−4.63581	−	4.63581i	−0.225936	−	0.225936i	−0.810992	+	0.585057i	$0.801072\pi$
$422$		0			0
$423$			7.20043i			0.350097i
$424$		0			0
$425$	−37.2039			−1.80465
$426$		0			0
$427$	−2.08612	−	4.29347i	−0.100954	−	0.207775i
$428$		0			0
$429$	0.812724	−	0.812724i	0.0392387	−	0.0392387i
$430$		0			0
$431$			9.22678i			0.444438i	0.974997	+	0.222219i	$0.0713301\pi$
$431$			9.22678i			0.444438i	−0.974997	+	0.222219i	$0.928670\pi$
$432$		0			0
$433$		−	20.5961i		−	0.989786i	−0.868954	−	0.494893i	$-0.835207\pi$
$433$		−	20.5961i		−	0.989786i	0.868954	−	0.494893i	$-0.164793\pi$
$434$		0			0
$435$	17.7604	+	17.7604i	0.851544	+	0.851544i
$436$		0			0
$437$	−9.46655	+	9.46655i	−0.452846	+	0.452846i
$438$		0			0
$439$			30.5005i			1.45571i	0.685731	+	0.727855i	$0.259483\pi$
$439$			30.5005i			1.45571i	−0.685731	+	0.727855i	$0.740517\pi$
$440$		0			0
$441$	4.32612	−	5.50315i	0.206006	−	0.262055i
$442$		0			0
$443$	16.6469	−	16.6469i	0.790916	−	0.790916i	−0.190727	−	0.981643i	$-0.561084\pi$
$443$	16.6469	−	16.6469i	0.790916	−	0.790916i	0.981643	+	0.190727i	$0.0610845\pi$
$444$		0			0
$445$	28.5019	−	28.5019i	1.35112	−	1.35112i
$446$		0			0
$447$	12.1508			0.574712
$448$		0			0
$449$	10.8337			0.511272			0.255636	−	0.966773i	$-0.417715\pi$
$449$	10.8337			0.511272			0.255636	+	0.966773i	$0.417715\pi$
$450$		0			0
$451$	−2.33477	+	2.33477i	−0.109940	+	0.109940i
$452$		0			0
$453$	11.1875	−	11.1875i	0.525633	−	0.525633i
$454$		0			0
$455$	−28.9943	−	10.0321i	−1.35927	−	0.470312i
$456$		0			0
$457$			35.1980i			1.64650i	0.567683	+	0.823248i	$0.307840\pi$
$457$			35.1980i			1.64650i	−0.567683	+	0.823248i	$0.692160\pi$
$458$		0			0
$459$	−3.67109	+	3.67109i	−0.171352	+	0.171352i
$460$		0			0
$461$	−27.0443	−	27.0443i	−1.25958	−	1.25958i	−0.951294	−	0.308286i	$-0.900245\pi$
$461$	−27.0443	−	27.0443i	−1.25958	−	1.25958i	−0.308286	−	0.951294i	$-0.599755\pi$
$462$		0			0
$463$			18.6030i			0.864556i	0.901740	+	0.432278i	$0.142290\pi$
$463$			18.6030i			0.864556i	−0.901740	+	0.432278i	$0.857710\pi$
$464$		0			0
$465$		−	5.34762i		−	0.247990i
$466$		0			0
$467$	−10.0714	+	10.0714i	−0.466047	+	0.466047i	−0.900631	−	0.434584i	$-0.856895\pi$
$467$	−10.0714	+	10.0714i	−0.466047	+	0.466047i	0.434584	+	0.900631i	$0.356895\pi$
$468$		0			0
$469$	−6.27547	−	12.9156i	−0.289774	−	0.596389i
$470$		0			0
$471$	−18.8894			−0.870377
$472$		0			0
$473$		−	3.32657i		−	0.152956i
$474$		0			0
$475$	10.2547	+	10.2547i	0.470518	+	0.470518i
$476$		0			0
$477$	5.49720	−	5.49720i	0.251700	−	0.251700i
$478$		0			0
$479$	−8.19876			−0.374611			−0.187305	−	0.982302i	$-0.559975\pi$
$479$	−8.19876			−0.374611			−0.187305	+	0.982302i	$0.559975\pi$
$480$		0			0
$481$			11.3234i			0.516303i
$482$		0			0
$483$	15.7424	−	7.64895i	0.716305	−	0.348039i
$484$		0			0
$485$	−41.2279	−	41.2279i	−1.87206	−	1.87206i
$486$		0			0
$487$	−18.4865			−0.837705			−0.418852	−	0.908054i	$-0.637568\pi$
$487$	−18.4865			−0.837705			−0.418852	+	0.908054i	$0.637568\pi$
$488$		0			0
$489$	−15.8494			−0.716733
$490$		0			0
$491$	7.92543	−	7.92543i	0.357670	−	0.357670i	−0.505284	−	0.862953i	$-0.668612\pi$
$491$	7.92543	−	7.92543i	0.357670	−	0.357670i	0.862953	+	0.505284i	$0.168612\pi$
$492$		0			0
$493$	26.4355	+	26.4355i	1.19060	+	1.19060i
$494$		0			0
$495$	1.20584			0.0541984
$496$		0			0
$497$	−40.2133	−	13.9139i	−1.80381	−	0.624124i
$498$		0			0
$499$	2.98057	+	2.98057i	0.133429	+	0.133429i	0.770667	−	0.637238i	$-0.219923\pi$
$499$	2.98057	+	2.98057i	0.133429	+	0.133429i	−0.637238	+	0.770667i	$0.719923\pi$
$500$		0			0
$501$	11.0382	+	11.0382i	0.493149	+	0.493149i
$502$		0			0
$503$			4.63846i			0.206819i	0.994639	+	0.103409i	$0.0329751\pi$
$503$			4.63846i			0.206819i	−0.994639	+	0.103409i	$0.967025\pi$
$504$		0			0
$505$			51.8914i			2.30914i
$506$		0			0
$507$	−1.37662	−	1.37662i	−0.0611378	−	0.0611378i
$508$		0			0
$509$	6.96054	+	6.96054i	0.308520	+	0.308520i	0.844335	−	0.535815i	$-0.179996\pi$
$509$	6.96054	+	6.96054i	0.308520	+	0.308520i	−0.535815	+	0.844335i	$0.679996\pi$
$510$		0			0
$511$	16.7119	+	5.78236i	0.739291	+	0.255796i
$512$		0			0
$513$	2.02377			0.0893515
$514$		0			0
$515$	13.3121	+	13.3121i	0.586600	+	0.586600i
$516$		0			0
$517$	1.76018	−	1.76018i	0.0774127	−	0.0774127i
$518$		0			0
$519$	−9.37191			−0.411381
$520$		0			0
$521$	−11.4231			−0.500457			−0.250229	−	0.968187i	$-0.580506\pi$
$521$	−11.4231			−0.500457			−0.250229	+	0.968187i	$0.580506\pi$
$522$		0			0
$523$	6.27518	+	6.27518i	0.274394	+	0.274394i	0.830866	−	0.556472i	$-0.187845\pi$
$523$	6.27518	+	6.27518i	0.274394	+	0.274394i	−0.556472	+	0.830866i	$0.687845\pi$
$524$		0			0
$525$	−8.28579	−	17.0531i	−0.361621	−	0.744258i
$526$		0			0
$527$		−	7.95970i		−	0.346730i
$528$		0			0
$529$	20.7615			0.902673
$530$		0			0
$531$	3.45643	−	3.45643i	0.149996	−	0.149996i
$532$		0			0
$533$	−22.4529	−	22.4529i	−0.972543	−	0.972543i
$534$		0			0
$535$		−	27.8181i		−	1.20268i
$536$		0			0
$537$	2.24097			0.0967049
$538$		0			0
$539$	−2.40282	+	0.287732i	−0.103497	+	0.0123935i
$540$		0			0
$541$	−28.9885	+	28.9885i	−1.24631	+	1.24631i	−0.288978	+	0.957336i	$0.593315\pi$
$541$	−28.9885	+	28.9885i	−1.24631	+	1.24631i	−0.957336	+	0.288978i	$0.906685\pi$
$542$		0			0
$543$		−	10.4354i		−	0.447828i
$544$		0			0
$545$		−	8.40153i		−	0.359882i
$546$		0			0
$547$	−1.24129	−	1.24129i	−0.0530738	−	0.0530738i	0.680072	−	0.733146i	$-0.261949\pi$
$547$	−1.24129	−	1.24129i	−0.0530738	−	0.0530738i	−0.733146	+	0.680072i	$0.761949\pi$
$548$		0			0
$549$	−1.27576	+	1.27576i	−0.0544479	+	0.0544479i
$550$		0			0
$551$		−	14.5731i		−	0.620837i
$552$		0			0
$553$	−3.54461	+	10.2445i	−0.150732	+	0.435639i
$554$		0			0
$555$	−8.40027	+	8.40027i	−0.356572	+	0.356572i
$556$		0			0
$557$	−18.6847	+	18.6847i	−0.791695	+	0.791695i	−0.981770	−	0.190075i	$-0.939127\pi$
$557$	−18.6847	+	18.6847i	−0.791695	+	0.791695i	0.190075	+	0.981770i	$0.439127\pi$
$558$		0			0
$559$	31.9908			1.35307
$560$		0			0
$561$	1.79484			0.0757781
$562$		0			0
$563$	−0.450781	+	0.450781i	−0.0189981	+	0.0189981i	−0.716542	−	0.697544i	$-0.754276\pi$
$563$	−0.450781	+	0.450781i	−0.0189981	+	0.0189981i	0.697544	+	0.716542i	$0.254276\pi$
$564$		0			0
$565$	14.5028	−	14.5028i	0.610137	−	0.610137i
$566$		0			0
$567$	−2.50032	−	0.865115i	−0.105003	−	0.0363314i
$568$		0			0
$569$		−	19.8762i		−	0.833254i	−0.909077	−	0.416627i	$-0.863212\pi$
$569$		−	19.8762i		−	0.833254i	0.909077	−	0.416627i	$-0.136788\pi$
$570$		0			0
$571$	−0.229081	+	0.229081i	−0.00958675	+	0.00958675i	−0.711884	−	0.702297i	$-0.752158\pi$
$571$	−0.229081	+	0.229081i	−0.00958675	+	0.00958675i	0.702297	+	0.711884i	$0.252158\pi$
$572$		0			0
$573$	17.6524	+	17.6524i	0.737439	+	0.737439i
$574$		0			0
$575$		−	47.4050i		−	1.97692i
$576$		0			0
$577$		−	44.9253i		−	1.87026i	−0.354300	−	0.935132i	$-0.615281\pi$
$577$		−	44.9253i		−	1.87026i	0.354300	−	0.935132i	$-0.384719\pi$
$578$		0			0
$579$	−6.95869	+	6.95869i	−0.289193	+	0.289193i
$580$		0			0
$581$	32.6752	−	15.8763i	1.35560	−	0.658659i
$582$		0			0
$583$	−2.68764			−0.111311
$584$		0			0
$585$			11.5962i			0.479446i
$586$		0			0
$587$	−22.6986	−	22.6986i	−0.936871	−	0.936871i	0.0612514	−	0.998122i	$-0.480491\pi$
$587$	−22.6986	−	22.6986i	−0.936871	−	0.936871i	−0.998122	+	0.0612514i	$0.980491\pi$
$588$		0			0
$589$	−2.19397	+	2.19397i	−0.0904011	+	0.0904011i
$590$		0			0
$591$	8.78060			0.361186
$592$		0			0
$593$			17.6514i			0.724855i	0.932012	+	0.362427i	$0.118052\pi$
$593$			17.6514i			0.724855i	−0.932012	+	0.362427i	$0.881948\pi$
$594$		0			0
$595$	−20.9383	−	43.0934i	−0.858385	−	1.76666i
$596$		0			0
$597$	−7.19176	−	7.19176i	−0.294339	−	0.294339i
$598$		0			0
$599$	−13.0847			−0.534627			−0.267314	−	0.963610i	$-0.586136\pi$
$599$	−13.0847			−0.534627			−0.267314	+	0.963610i	$0.586136\pi$
$600$		0			0
$601$	−42.5370			−1.73512			−0.867560	−	0.497333i	$-0.834313\pi$
$601$	−42.5370			−1.73512			−0.867560	+	0.497333i	$0.834313\pi$
$602$		0			0
$603$	−3.83774	+	3.83774i	−0.156285	+	0.156285i
$604$		0			0
$605$	26.8354	+	26.8354i	1.09101	+	1.09101i
$606$		0			0
$607$	29.5855			1.20084			0.600419	−	0.799686i	$-0.295001\pi$
$607$	29.5855			1.20084			0.600419	+	0.799686i	$0.295001\pi$
$608$		0			0
$609$	−6.22969	+	18.0048i	−0.252440	+	0.729590i
$610$		0			0
$611$	16.9273	+	16.9273i	0.684804	+	0.684804i
$612$		0			0
$613$	−20.2489	−	20.2489i	−0.817847	−	0.817847i	0.167949	−	0.985796i	$-0.446286\pi$
$613$	−20.2489	−	20.2489i	−0.817847	−	0.817847i	−0.985796	+	0.167949i	$0.946286\pi$
$614$		0			0
$615$		−	33.3133i		−	1.34332i
$616$		0			0
$617$		−	32.9416i		−	1.32618i	−0.748541	−	0.663089i	$-0.769245\pi$
$617$		−	32.9416i		−	1.32618i	0.748541	−	0.663089i	$-0.230755\pi$
$618$		0			0
$619$	−20.5109	−	20.5109i	−0.824404	−	0.824404i	0.162333	−	0.986736i	$-0.448098\pi$
$619$	−20.5109	−	20.5109i	−0.824404	−	0.824404i	−0.986736	+	0.162333i	$0.948098\pi$
$620$		0			0
$621$	−4.67768	−	4.67768i	−0.187709	−	0.187709i
$622$		0			0
$623$	28.8941	+	9.99743i	1.15762	+	0.400539i
$624$		0			0
$625$	9.47829			0.379132
$626$		0			0
$627$	−0.494721	−	0.494721i	−0.0197572	−	0.0197572i
$628$		0			0
$629$	−12.5034	+	12.5034i	−0.498545	+	0.498545i
$630$		0			0
$631$	1.92496			0.0766314			0.0383157	−	0.999266i	$-0.487801\pi$
$631$	1.92496			0.0766314			0.0383157	+	0.999266i	$0.487801\pi$
$632$		0			0
$633$	8.05823			0.320286
$634$		0			0
$635$	6.26620	+	6.26620i	0.248666	+	0.248666i
$636$		0			0
$637$	−2.76705	−	23.1073i	−0.109634	−	0.915546i
$638$		0			0
$639$			16.0833i			0.636246i
$640$		0			0
$641$	0.665171			0.0262727			0.0131363	−	0.999914i	$-0.495818\pi$
$641$	0.665171			0.0262727			0.0131363	+	0.999914i	$0.495818\pi$
$642$		0			0
$643$	10.5926	−	10.5926i	0.417733	−	0.417733i	−0.466689	−	0.884422i	$-0.654553\pi$
$643$	10.5926	−	10.5926i	0.417733	−	0.417733i	0.884422	+	0.466689i	$0.154553\pi$
$644$		0			0
$645$	23.7324	+	23.7324i	0.934462	+	0.934462i
$646$		0			0
$647$		−	40.4129i		−	1.58880i	−0.607397	−	0.794398i	$-0.707786\pi$
$647$		−	40.4129i		−	1.58880i	0.607397	−	0.794398i	$-0.292214\pi$
$648$		0			0
$649$	−1.68988			−0.0663337
$650$		0			0
$651$	3.64848	−	1.77273i	0.142995	−	0.0694787i
$652$		0			0
$653$	6.72324	−	6.72324i	0.263101	−	0.263101i	−0.563212	−	0.826313i	$-0.690435\pi$
$653$	6.72324	−	6.72324i	0.263101	−	0.263101i	0.826313	+	0.563212i	$0.190435\pi$
$654$		0			0
$655$			6.73108i			0.263005i
$656$		0			0
$657$		−	6.68392i		−	0.260764i
$658$		0			0
$659$	−33.6058	−	33.6058i	−1.30910	−	1.30910i	−0.922067	−	0.387029i	$-0.873501\pi$
$659$	−33.6058	−	33.6058i	−1.30910	−	1.30910i	−0.387029	−	0.922067i	$-0.626499\pi$
$660$		0			0
$661$	−8.66416	+	8.66416i	−0.336997	+	0.336997i	−0.855236	−	0.518239i	$-0.826588\pi$
$661$	−8.66416	+	8.66416i	−0.336997	+	0.336997i	0.518239	+	0.855236i	$0.326588\pi$
$662$		0			0
$663$			17.2605i			0.670343i
$664$		0			0
$665$	−6.10673	+	17.6494i	−0.236809	+	0.684414i
$666$		0			0
$667$	−33.6840	+	33.6840i	−1.30425	+	1.30425i
$668$		0			0
$669$	−3.72330	+	3.72330i	−0.143951	+	0.143951i
$670$		0			0
$671$	0.623731			0.0240789
$672$		0			0
$673$	5.60669			0.216122			0.108061	−	0.994144i	$-0.465536\pi$
$673$	5.60669			0.216122			0.108061	+	0.994144i	$0.465536\pi$
$674$		0			0
$675$	−5.06714	+	5.06714i	−0.195034	+	0.195034i
$676$		0			0
$677$	−1.76989	+	1.76989i	−0.0680223	+	0.0680223i	−0.740300	−	0.672277i	$-0.765316\pi$
$677$	−1.76989	+	1.76989i	−0.0680223	+	0.0680223i	0.672277	+	0.740300i	$0.265316\pi$
$678$		0			0
$679$	14.4612	−	41.7952i	0.554971	−	1.60395i
$680$		0			0
$681$			16.0892i			0.616538i
$682$		0			0
$683$	28.4450	−	28.4450i	1.08842	−	1.08842i	0.0927272	−	0.995692i	$-0.470442\pi$
$683$	28.4450	−	28.4450i	1.08842	−	1.08842i	0.995692	−	0.0927272i	$-0.0295584\pi$
$684$		0			0
$685$	21.7472	+	21.7472i	0.830917	+	0.830917i
$686$		0			0
$687$			21.0382i			0.802658i
$688$		0			0
$689$		−	25.8464i		−	0.984669i
$690$		0			0
$691$	10.4240	−	10.4240i	0.396547	−	0.396547i	−0.480466	−	0.877013i	$-0.659533\pi$
$691$	10.4240	−	10.4240i	0.396547	−	0.396547i	0.877013	+	0.480466i	$0.159533\pi$
$692$		0			0
$693$	0.399733	+	0.822697i	0.0151846	+	0.0312517i
$694$		0			0
$695$	2.01955			0.0766060
$696$		0			0
$697$		−	49.5855i		−	1.87818i
$698$		0			0
$699$	−1.50287	−	1.50287i	−0.0568437	−	0.0568437i
$700$		0			0
$701$	37.1588	−	37.1588i	1.40347	−	1.40347i	0.614732	−	0.788736i	$-0.289264\pi$
$701$	37.1588	−	37.1588i	1.40347	−	1.40347i	0.788736	−	0.614732i	$-0.210736\pi$
$702$		0			0
$703$	6.89278			0.259966
$704$		0			0
$705$			25.1150i			0.945884i
$706$		0			0
$707$	−35.4036	+	17.2019i	−1.33149	+	0.646946i
$708$		0			0
$709$	−2.24522	−	2.24522i	−0.0843210	−	0.0843210i	0.663688	−	0.748009i	$-0.268990\pi$
$709$	−2.24522	−	2.24522i	−0.0843210	−	0.0843210i	−0.748009	+	0.663688i	$0.768990\pi$
$710$		0			0
$711$	4.09727			0.153660
$712$		0			0
$713$	10.1422			0.379828
$714$		0			0
$715$	2.83477	−	2.83477i	0.106014	−	0.106014i
$716$		0			0
$717$	−6.32405	−	6.32405i	−0.236176	−	0.236176i
$718$		0			0
$719$	−19.0248			−0.709506			−0.354753	−	0.934960i	$-0.615435\pi$
$719$	−19.0248			−0.709506			−0.354753	+	0.934960i	$0.615435\pi$
$720$		0			0
$721$	−4.66939	+	13.4953i	−0.173897	+	0.502590i
$722$		0			0
$723$	−2.94375	−	2.94375i	−0.109479	−	0.109479i
$724$		0			0
$725$	36.4884	+	36.4884i	1.35515	+	1.35515i
$726$		0			0
$727$		−	40.7707i		−	1.51210i	−0.654513	−	0.756050i	$-0.727126\pi$
$727$		−	40.7707i		−	1.51210i	0.654513	−	0.756050i	$-0.272874\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	35.3246	+	35.3246i	1.30653	+	1.30653i
$732$		0			0
$733$	−6.53739	−	6.53739i	−0.241464	−	0.241464i	0.575992	−	0.817456i	$-0.304616\pi$
$733$	−6.53739	−	6.53739i	−0.241464	−	0.241464i	−0.817456	+	0.575992i	$0.804616\pi$
$734$		0			0
$735$	15.0894	−	19.1949i	0.556582	−	0.708014i
$736$		0			0
$737$	1.87631			0.0691149
$738$		0			0
$739$	25.7167	+	25.7167i	0.946003	+	0.946003i	0.998615	−	0.0526125i	$-0.0167548\pi$
$739$	25.7167	+	25.7167i	0.946003	+	0.946003i	−0.0526125	+	0.998615i	$0.516755\pi$
$740$		0			0
$741$	4.75761	−	4.75761i	0.174775	−	0.174775i
$742$		0			0
$743$	−9.46009			−0.347057			−0.173529	−	0.984829i	$-0.555517\pi$
$743$	−9.46009			−0.347057			−0.173529	+	0.984829i	$0.555517\pi$
$744$		0			0
$745$	42.3817			1.55275
$746$		0			0
$747$	−9.70907	−	9.70907i	−0.355236	−	0.355236i
$748$		0			0
$749$	18.9793	−	9.22167i	0.693487	−	0.336953i
$750$		0			0
$751$		−	26.5634i		−	0.969313i	−0.874705	−	0.484656i	$-0.838945\pi$
$751$		−	26.5634i		−	0.969313i	0.874705	−	0.484656i	$-0.161055\pi$
$752$		0			0
$753$	1.19985			0.0437248
$754$		0			0
$755$	39.0217	−	39.0217i	1.42015	−	1.42015i
$756$		0			0
$757$	7.83618	+	7.83618i	0.284811	+	0.284811i	0.835024	−	0.550213i	$-0.185454\pi$
$757$	7.83618	+	7.83618i	0.284811	+	0.284811i	−0.550213	+	0.835024i	$0.685454\pi$
$758$		0			0
$759$			2.28697i			0.0830118i
$760$		0			0
$761$	−22.5355			−0.816910			−0.408455	−	0.912778i	$-0.633932\pi$
$761$	−22.5355			−0.816910			−0.408455	+	0.912778i	$0.633932\pi$
$762$		0			0
$763$	5.73204	−	2.78509i	0.207514	−	0.100827i
$764$		0			0
$765$	−12.8047	+	12.8047i	−0.462955	+	0.462955i
$766$		0			0
$767$		−	16.2512i		−	0.586797i
$768$		0			0
$769$		−	5.25162i		−	0.189378i	−0.995507	−	0.0946892i	$-0.969814\pi$
$769$		−	5.25162i		−	0.189378i	0.995507	−	0.0946892i	$-0.0301857\pi$
$770$		0			0
$771$	14.2181	+	14.2181i	0.512052	+	0.512052i
$772$		0			0
$773$	−10.2035	+	10.2035i	−0.366995	+	0.366995i	−0.866380	−	0.499385i	$-0.833559\pi$
$773$	−10.2035	+	10.2035i	−0.366995	+	0.366995i	0.499385	+	0.866380i	$0.333559\pi$
$774$		0			0
$775$		−	10.9866i		−	0.394651i
$776$		0			0
$777$	−8.51587	−	2.94651i	−0.305505	−	0.105705i
$778$		0			0
$779$	−13.6675	+	13.6675i	−0.489690	+	0.489690i
$780$		0			0
$781$	3.93165	−	3.93165i	0.140685	−	0.140685i
$782$		0			0
$783$	7.20100			0.257343
$784$		0			0
$785$	−65.8858			−2.35157
$786$		0			0
$787$	−9.39612	+	9.39612i	−0.334936	+	0.334936i	−0.854457	−	0.519522i	$-0.826110\pi$
$787$	−9.39612	+	9.39612i	−0.334936	+	0.334936i	0.519522	+	0.854457i	$0.326110\pi$
$788$		0			0
$789$	4.65196	−	4.65196i	0.165614	−	0.165614i
$790$		0			0
$791$	14.7024	+	5.08706i	0.522756	+	0.180875i
$792$		0			0
$793$			5.99827i			0.213005i
$794$		0			0
$795$	19.1741	−	19.1741i	0.680036	−	0.680036i
$796$		0			0
$797$	15.0117	+	15.0117i	0.531741	+	0.531741i	0.921090	−	0.389349i	$-0.127300\pi$
$797$	15.0117	+	15.0117i	0.531741	+	0.531741i	−0.389349	+	0.921090i	$0.627300\pi$
$798$		0			0
$799$			37.3825i			1.32250i
$800$		0			0
$801$		−	11.5562i		−	0.408318i
$802$		0			0
$803$	−1.63392	+	1.63392i	−0.0576597	+	0.0576597i
$804$		0			0
$805$	54.9093	−	26.6794i	1.93530	−	0.940325i
$806$		0			0
$807$	26.2560			0.924256
$808$		0			0
$809$			9.85392i			0.346445i	0.984883	+	0.173223i	$0.0554180\pi$
$809$			9.85392i			0.346445i	−0.984883	+	0.173223i	$0.944582\pi$
$810$		0			0
$811$	5.99202	+	5.99202i	0.210408	+	0.210408i	0.804441	−	0.594033i	$-0.202465\pi$
$811$	5.99202	+	5.99202i	0.210408	+	0.210408i	−0.594033	+	0.804441i	$0.702465\pi$
$812$		0			0
$813$	−15.6347	+	15.6347i	−0.548334	+	0.548334i
$814$		0			0
$815$	−55.2823			−1.93645
$816$		0			0
$817$		−	19.4734i		−	0.681290i
$818$		0			0
$819$	−7.91168	+	3.84414i	−0.276457	+	0.134325i
$820$		0			0
$821$	7.92158	+	7.92158i	0.276465	+	0.276465i	0.831696	−	0.555231i	$-0.187370\pi$
$821$	7.92158	+	7.92158i	0.276465	+	0.276465i	−0.555231	+	0.831696i	$0.687370\pi$
$822$		0			0
$823$	31.5025			1.09811			0.549055	−	0.835786i	$-0.314988\pi$
$823$	31.5025			1.09811			0.549055	+	0.835786i	$0.314988\pi$
$824$		0			0
$825$	2.47738			0.0862512
$826$		0			0
$827$	−2.82748	+	2.82748i	−0.0983211	+	0.0983211i	−0.754556	−	0.656235i	$-0.772148\pi$
$827$	−2.82748	+	2.82748i	−0.0983211	+	0.0983211i	0.656235	+	0.754556i	$0.272148\pi$
$828$		0			0
$829$	−5.54898	−	5.54898i	−0.192724	−	0.192724i	0.604148	−	0.796872i	$-0.293514\pi$
$829$	−5.54898	−	5.54898i	−0.192724	−	0.192724i	−0.796872	+	0.604148i	$0.793514\pi$
$830$		0			0
$831$	−20.0768			−0.696458
$832$		0			0
$833$	22.4600	−	28.5708i	0.778192	−	0.989919i
$834$		0			0
$835$	38.5009	+	38.5009i	1.33238	+	1.33238i
$836$		0			0
$837$	−1.08410	−	1.08410i	−0.0374721	−	0.0374721i
$838$		0			0
$839$		−	25.5143i		−	0.880850i	−0.897789	−	0.440425i	$-0.854828\pi$
$839$		−	25.5143i		−	0.880850i	0.897789	−	0.440425i	$-0.145172\pi$
$840$		0			0
$841$		−	22.8544i		−	0.788081i
$842$		0			0
$843$	−0.377417	−	0.377417i	−0.0129989	−	0.0129989i
$844$		0			0
$845$	−4.80162	−	4.80162i	−0.165181	−	0.165181i
$846$		0			0
$847$	−9.41287	+	27.2046i	−0.323430	+	0.934762i
$848$		0			0
$849$	27.5822			0.946619
$850$		0			0
$851$	−15.9318	−	15.9318i	−0.546135	−	0.546135i
$852$		0			0
$853$	9.34018	−	9.34018i	0.319802	−	0.319802i	−0.528889	−	0.848691i	$-0.677391\pi$
$853$	9.34018	−	9.34018i	0.319802	−	0.319802i	0.848691	+	0.528889i	$0.177391\pi$
$854$		0			0
$855$	7.05886			0.241408
$856$		0			0
$857$	14.6466			0.500317			0.250159	−	0.968205i	$-0.419517\pi$
$857$	14.6466			0.500317			0.250159	+	0.968205i	$0.419517\pi$
$858$		0			0
$859$	−35.4037	−	35.4037i	−1.20796	−	1.20796i	−0.971687	−	0.236272i	$-0.924074\pi$
$859$	−35.4037	−	35.4037i	−1.20796	−	1.20796i	−0.236272	−	0.971687i	$-0.575926\pi$
$860$		0			0
$861$	22.7284	−	11.0433i	0.774583	−	0.376356i
$862$		0			0
$863$		−	31.2983i		−	1.06541i	−0.846302	−	0.532703i	$-0.821176\pi$
$863$		−	31.2983i		−	1.06541i	0.846302	−	0.532703i	$-0.178824\pi$
$864$		0			0
$865$	−32.6890			−1.11146
$866$		0			0
$867$	−7.03845	+	7.03845i	−0.239038	+	0.239038i
$868$		0			0
$869$	−1.00160	−	1.00160i	−0.0339770	−	0.0339770i
$870$		0			0
$871$			18.0440i			0.611399i
$872$		0			0
$873$	−16.7160			−0.565750
$874$		0			0
$875$	−8.73558	−	17.9788i	−0.295317	−	0.607795i
$876$		0			0
$877$	14.5201	−	14.5201i	0.490310	−	0.490310i	−0.418094	−	0.908404i	$-0.637302\pi$
$877$	14.5201	−	14.5201i	0.490310	−	0.490310i	0.908404	+	0.418094i	$0.137302\pi$
$878$		0			0
$879$		−	18.7526i		−	0.632508i
$880$		0			0
$881$		−	10.6714i		−	0.359529i	−0.983710	−	0.179764i	$-0.942466\pi$
$881$		−	10.6714i		−	0.359529i	0.983710	−	0.179764i	$-0.0575335\pi$
$882$		0			0
$883$	−35.8490	−	35.8490i	−1.20641	−	1.20641i	−0.972180	−	0.234235i	$-0.924742\pi$
$883$	−35.8490	−	35.8490i	−1.20641	−	1.20641i	−0.234235	−	0.972180i	$-0.575258\pi$
$884$		0			0
$885$	12.0560	−	12.0560i	0.405256	−	0.405256i
$886$		0			0
$887$			4.16513i			0.139852i	0.997552	+	0.0699258i	$0.0222762\pi$
$887$			4.16513i			0.139852i	−0.997552	+	0.0699258i	$0.977724\pi$
$888$		0			0
$889$	−2.19795	+	6.35243i	−0.0737170	+	0.213054i
$890$		0			0
$891$	0.244455	−	0.244455i	0.00818956	−	0.00818956i
$892$		0			0
$893$	10.3040	−	10.3040i	0.344809	−	0.344809i
$894$		0			0
$895$	7.81645			0.261275
$896$		0			0
$897$	−21.9932			−0.734333
$898$		0			0
$899$	−7.80663	+	7.80663i	−0.260366	+	0.260366i
$900$		0			0
$901$	28.5399	−	28.5399i	0.950801	−	0.950801i
$902$		0			0
$903$	−8.32446	+	24.0590i	−0.277021	+	0.800632i
$904$		0			0
$905$		−	36.3986i		−	1.20993i
$906$		0			0
$907$	−7.88170	+	7.88170i	−0.261708	+	0.261708i	−0.825747	−	0.564040i	$-0.809246\pi$
$907$	−7.88170	+	7.88170i	−0.261708	+	0.261708i	0.564040	+	0.825747i	$0.309246\pi$
$908$		0			0
$909$	10.5198	+	10.5198i	0.348919	+	0.348919i
$910$		0			0
$911$			22.4309i			0.743169i	0.928399	+	0.371585i	$0.121185\pi$
$911$			22.4309i			0.743169i	−0.928399	+	0.371585i	$0.878815\pi$
$912$		0			0
$913$			4.74687i			0.157098i
$914$		0			0
$915$	−4.44981	+	4.44981i	−0.147106	+	0.147106i
$916$		0			0
$917$	−4.59236	+	2.23134i	−0.151653	+	0.0736855i
$918$		0			0
$919$	−38.3187			−1.26402			−0.632009	−	0.774961i	$-0.717770\pi$
$919$	−38.3187			−1.26402			−0.632009	+	0.774961i	$0.717770\pi$
$920$		0			0
$921$			12.3754i			0.407783i
$922$		0			0
$923$	37.8097	+	37.8097i	1.24452	+	1.24452i
$924$		0			0
$925$	−17.2583	+	17.2583i	−0.567448	+	0.567448i
$926$		0			0
$927$	5.39742			0.177275
$928$		0			0
$929$			28.5117i			0.935438i	0.883877	+	0.467719i	$0.154924\pi$
$929$			28.5117i			0.935438i	−0.883877	+	0.467719i	$0.845076\pi$
$930$		0			0
$931$	−14.0659	+	1.68436i	−0.460991	+	0.0552025i
$932$		0			0
$933$	−8.84332	−	8.84332i	−0.289517	−	0.289517i
$934$		0			0
$935$	6.26036			0.204736
$936$		0			0
$937$	−16.8510			−0.550499			−0.275250	−	0.961373i	$-0.588760\pi$
$937$	−16.8510			−0.550499			−0.275250	+	0.961373i	$0.588760\pi$
$938$		0			0
$939$	−21.6898	+	21.6898i	−0.707820	+	0.707820i
$940$		0			0
$941$	−28.9571	−	28.9571i	−0.943975	−	0.943975i	0.0545372	−	0.998512i	$-0.482632\pi$
$941$	−28.9571	−	28.9571i	−0.943975	−	0.943975i	−0.998512	+	0.0545372i	$0.982632\pi$
$942$		0			0
$943$	63.1815			2.05747
$944$		0			0
$945$	−8.72105	−	3.01751i	−0.283696	−	0.0981595i
$946$		0			0
$947$	−42.0974	−	42.0974i	−1.36798	−	1.36798i	−0.863315	−	0.504666i	$-0.831616\pi$
$947$	−42.0974	−	42.0974i	−1.36798	−	1.36798i	−0.504666	−	0.863315i	$-0.668384\pi$
$948$		0			0
$949$	−15.7130	−	15.7130i	−0.510066	−	0.510066i
$950$		0			0
$951$			9.28918i			0.301222i
$952$		0			0
$953$		−	20.9090i		−	0.677308i	−0.940911	−	0.338654i	$-0.890028\pi$
$953$		−	20.9090i		−	0.677308i	0.940911	−	0.338654i	$-0.109972\pi$
$954$		0			0
$955$	61.5712	+	61.5712i	1.99240	+	1.99240i
$956$		0			0
$957$	−1.76032	−	1.76032i	−0.0569031	−	0.0569031i
$958$		0			0
$959$	−7.62812	+	22.0465i	−0.246325	+	0.711917i
$960$		0			0
$961$	−28.6494			−0.924175
$962$		0			0
$963$	−5.63948	−	5.63948i	−0.181730	−	0.181730i
$964$		0			0
$965$	−24.2718	+	24.2718i	−0.781337	+	0.781337i
$966$		0			0
$967$	19.1350			0.615340			0.307670	−	0.951493i	$-0.400451\pi$
$967$	19.1350			0.615340			0.307670	+	0.951493i	$0.400451\pi$
$968$		0			0
$969$	10.5068			0.337528
$970$		0			0
$971$	−13.3830	−	13.3830i	−0.429480	−	0.429480i	0.458971	−	0.888451i	$-0.348218\pi$
$971$	−13.3830	−	13.3830i	−0.429480	−	0.429480i	−0.888451	+	0.458971i	$0.848218\pi$
$972$		0			0
$973$	0.669479	+	1.37787i	0.0214625	+	0.0441723i
$974$		0			0
$975$			23.8244i			0.762990i
$976$		0			0
$977$	36.3850			1.16406			0.582029	−	0.813168i	$-0.302259\pi$
$977$	36.3850			1.16406			0.582029	+	0.813168i	$0.302259\pi$
$978$		0			0
$979$	−2.82497	+	2.82497i	−0.0902865	+	0.0902865i
$980$		0			0
$981$	−1.70321	−	1.70321i	−0.0543794	−	0.0543794i
$982$		0			0
$983$			13.6512i			0.435406i	0.976015	+	0.217703i	$0.0698563\pi$
$983$			13.6512i			0.435406i	−0.976015	+	0.217703i	$0.930144\pi$
$984$		0			0
$985$	30.6266			0.975844
$986$		0			0
$987$	−17.1350	+	8.32557i	−0.545413	+	0.265006i
$988$		0			0
$989$	−45.0104	+	45.0104i	−1.43125	+	1.43125i
$990$		0			0
$991$			14.6044i			0.463926i	0.972725	+	0.231963i	$0.0745148\pi$
$991$			14.6044i			0.463926i	−0.972725	+	0.231963i	$0.925485\pi$
$992$		0			0
$993$			4.05184i			0.128581i
$994$		0			0
$995$	−25.0847	−	25.0847i	−0.795240	−	0.795240i
$996$		0			0
$997$	−33.5387	+	33.5387i	−1.06218	+	1.06218i	−0.0642464	+	0.997934i	$0.520464\pi$
$997$	−33.5387	+	33.5387i	−1.06218	+	1.06218i	−0.997934	+	0.0642464i	$0.979536\pi$
$998$		0			0
$999$			3.40592i			0.107758i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.u.a.1231.18		64
4.3	odd	2		336.2.u.a.139.15	✓	64
7.6	odd	2	inner	1344.2.u.a.1231.15		64
16.3	odd	4	inner	1344.2.u.a.559.15		64
16.13	even	4		336.2.u.a.307.16	yes	64
28.27	even	2		336.2.u.a.139.16	yes	64
112.13	odd	4		336.2.u.a.307.15	yes	64
112.83	even	4	inner	1344.2.u.a.559.18		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.u.a.139.15	✓	64	4.3	odd	2
336.2.u.a.139.16	yes	64	28.27	even	2
336.2.u.a.307.15	yes	64	112.13	odd	4
336.2.u.a.307.16	yes	64	16.13	even	4
1344.2.u.a.559.15		64	16.3	odd	4	inner
1344.2.u.a.559.18		64	112.83	even	4	inner
1344.2.u.a.1231.15		64	7.6	odd	2	inner
1344.2.u.a.1231.18		64	1.1	even	1	trivial

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.u (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(2.46638 - 2.46638i) q^{5} +(2.50032 + 0.865115i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(2.46638 - 2.46638i) q^{5} +(2.50032 + 0.865115i) q^{7} -1.00000i q^{9} +(-0.244455 + 0.244455i) q^{11} +(-2.35087 - 2.35087i) q^{13} -3.48798i q^{15} -5.19171i q^{17} +(-1.43102 + 1.43102i) q^{19} +(2.37972 - 1.15626i) q^{21} +6.61525 q^{23} -7.16602i q^{25} +(-0.707107 - 0.707107i) q^{27} +(-5.09187 + 5.09187i) q^{29} +1.53315 q^{31} +0.345712i q^{33} +(8.30041 - 4.03302i) q^{35} +(-2.40835 - 2.40835i) q^{37} -3.32463 q^{39} +9.55090 q^{41} +(-6.80405 + 6.80405i) q^{43} +(-2.46638 - 2.46638i) q^{45} -7.20043 q^{47} +(5.50315 + 4.32612i) q^{49} +(-3.67109 - 3.67109i) q^{51} +(5.49720 + 5.49720i) q^{53} +1.20584i q^{55} +2.02377i q^{57} +(3.45643 + 3.45643i) q^{59} +(-1.27576 - 1.27576i) q^{61} +(0.865115 - 2.50032i) q^{63} -11.5962 q^{65} +(-3.83774 - 3.83774i) q^{67} +(4.67768 - 4.67768i) q^{69} -16.0833 q^{71} +6.68392 q^{73} +(-5.06714 - 5.06714i) q^{75} +(-0.822697 + 0.399733i) q^{77} +4.09727i q^{79} -1.00000 q^{81} +(9.70907 - 9.70907i) q^{83} +(-12.8047 - 12.8047i) q^{85} +7.20100i q^{87} +11.5562 q^{89} +(-3.84414 - 7.91168i) q^{91} +(1.08410 - 1.08410i) q^{93} +7.05886i q^{95} -16.7160i q^{97} +(0.244455 + 0.244455i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 8 q^{11} + 16 q^{23} + 16 q^{29} - 24 q^{35} + 16 q^{37} + 8 q^{43} + 16 q^{53} - 56 q^{67} + 128 q^{71} - 64 q^{81} - 8 q^{91} + 8 q^{99}+O(q^{100}) \) 64 * q - 8 * q^11 + 16 * q^23 + 16 * q^29 - 24 * q^35 + 16 * q^37 + 8 * q^43 + 16 * q^53 - 56 * q^67 + 128 * q^71 - 64 * q^81 - 8 * q^91 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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