LMFDB - Embedded newform 448.2.ba.c.81.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [448,2,Mod(81,448)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("448.81"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(448, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.ba (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.57729801055$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			81.4
Character	$\chi$	$=$	448.81
Dual form			448.2.ba.c.177.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.16533 + 0.312249i) q^{3} +(0.980942 + 0.262843i) q^{5} +(-2.60251 + 0.476386i) q^{7} +(-1.33758 + 0.772254i) q^{9} +(-0.635020 - 2.36993i) q^{11} +(-2.65786 - 2.65786i) q^{13} -1.22519 q^{15} +(-0.509128 + 0.881836i) q^{17} +(0.0250951 - 0.0936561i) q^{19} +(2.88403 - 1.36778i) q^{21} +(-1.67238 + 0.965551i) q^{23} +(-3.43697 - 1.98433i) q^{25} +(3.87683 - 3.87683i) q^{27} +(-5.05325 - 5.05325i) q^{29} +(-4.28249 + 7.41749i) q^{31} +(1.48001 + 2.56346i) q^{33} +(-2.67813 - 0.216743i) q^{35} +(-7.71428 - 2.06704i) q^{37} +(3.92719 + 2.26737i) q^{39} +8.51782i q^{41} +(4.47950 - 4.47950i) q^{43} +(-1.51507 + 0.405963i) q^{45} +(-6.02995 - 10.4442i) q^{47} +(6.54611 - 2.47960i) q^{49} +(0.317949 - 1.18660i) q^{51} +(0.381000 + 1.42191i) q^{53} -2.49167i q^{55} +0.116976i q^{57} +(1.86535 + 6.96158i) q^{59} +(-1.18609 + 4.42654i) q^{61} +(3.11318 - 2.64701i) q^{63} +(-1.90861 - 3.30580i) q^{65} +(3.38700 - 0.907543i) q^{67} +(1.64738 - 1.64738i) q^{69} +5.43131i q^{71} +(7.34303 + 4.23950i) q^{73} +(4.62480 + 1.23921i) q^{75} +(2.78165 + 5.86524i) q^{77} +(0.433595 + 0.751008i) q^{79} +(-0.990483 + 1.71557i) q^{81} +(5.44318 + 5.44318i) q^{83} +(-0.731209 + 0.731209i) q^{85} +(7.46657 + 4.31083i) q^{87} +(3.93155 - 2.26988i) q^{89} +(8.18327 + 5.65093i) q^{91} +(2.67441 - 9.98102i) q^{93} +(0.0492336 - 0.0852752i) q^{95} +16.4025 q^{97} +(2.67958 + 2.67958i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{5} + 4 q^{11} - 24 q^{13} + 40 q^{15} + 8 q^{17} + 4 q^{19} - 8 q^{21} + 24 q^{27} + 24 q^{29} - 28 q^{31} + 16 q^{33} - 28 q^{35} - 24 q^{37} + 40 q^{43} - 28 q^{45} + 20 q^{47} - 24 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) $ 48 * q + 4 * q^5 + 4 * q^11 - 24 * q^13 + 40 * q^15 + 8 * q^17 + 4 * q^19 - 8 * q^21 + 24 * q^27 + 24 * q^29 - 28 * q^31 + 16 * q^33 - 28 * q^35 - 24 * q^37 + 40 * q^43 - 28 * q^45 + 20 * q^47 - 24 * q^51 - 16 * q^53 + 20 * q^59 + 8 * q^61 + 16 * q^63 + 8 * q^65 - 48 * q^67 - 40 * q^69 + 4 * q^75 - 20 * q^77 + 36 * q^79 + 8 * q^83 - 64 * q^91 + 8 * q^93 + 4 * q^95 - 48 * q^97 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.16533	+	0.312249i	−0.672803	+	0.180277i	−0.579017	−	0.815315i	$-0.696564\pi$
$3$	−1.16533	+	0.312249i	−0.672803	+	0.180277i	−0.0937859	+	0.995592i	$0.529897\pi$
$4$		0			0
$5$	0.980942	+	0.262843i	0.438691	+	0.117547i	0.471403	−	0.881918i	$-0.343748\pi$
$5$	0.980942	+	0.262843i	0.438691	+	0.117547i	−0.0327122	+	0.999465i	$0.510414\pi$
$6$		0			0
$7$	−2.60251	+	0.476386i	−0.983656	+	0.180057i
$7$	−2.60251	+	0.476386i	−0.983656	+	0.180057i
$8$		0			0
$9$	−1.33758	+	0.772254i	−0.445861	+	0.257418i
$10$		0			0
$11$	−0.635020	−	2.36993i	−0.191466	−	0.714560i	−0.993153	−	0.116817i	$-0.962731\pi$
$11$	−0.635020	−	2.36993i	−0.191466	−	0.714560i	0.801688	−	0.597743i	$-0.203936\pi$
$12$		0			0
$13$	−2.65786	−	2.65786i	−0.737157	−	0.737157i	0.234870	−	0.972027i	$-0.424534\pi$
$13$	−2.65786	−	2.65786i	−0.737157	−	0.737157i	−0.972027	+	0.234870i	$0.924534\pi$
$14$		0			0
$15$	−1.22519			−0.316343
$16$		0			0
$17$	−0.509128	+	0.881836i	−0.123482	+	0.213877i	−0.921138	−	0.389235i	$-0.872739\pi$
$17$	−0.509128	+	0.881836i	−0.123482	+	0.213877i	0.797657	+	0.603112i	$0.206073\pi$
$18$		0			0
$19$	0.0250951	−	0.0936561i	0.00575721	−	0.0214862i	−0.962987	−	0.269546i	$-0.913126\pi$
$19$	0.0250951	−	0.0936561i	0.00575721	−	0.0214862i	0.968745	+	0.248060i	$0.0797930\pi$
$20$		0			0
$21$	2.88403	−	1.36778i	0.629347	−	0.298474i
$22$		0			0
$23$	−1.67238	+	0.965551i	−0.348716	+	0.201331i	−0.664120	−	0.747626i	$-0.731193\pi$
$23$	−1.67238	+	0.965551i	−0.348716	+	0.201331i	0.315404	+	0.948958i	$0.397860\pi$
$24$		0			0
$25$	−3.43697	−	1.98433i	−0.687393	−	0.396867i
$26$		0			0
$27$	3.87683	−	3.87683i	0.746096	−	0.746096i
$28$		0			0
$29$	−5.05325	−	5.05325i	−0.938365	−	0.938365i	0.0598432	−	0.998208i	$-0.480940\pi$
$29$	−5.05325	−	5.05325i	−0.938365	−	0.938365i	−0.998208	+	0.0598432i	$0.980940\pi$
$30$		0			0
$31$	−4.28249	+	7.41749i	−0.769158	+	1.33222i	0.168862	+	0.985640i	$0.445991\pi$
$31$	−4.28249	+	7.41749i	−0.769158	+	1.33222i	−0.938020	+	0.346581i	$0.887343\pi$
$32$		0			0
$33$	1.48001	+	2.56346i	0.257637	+	0.446241i
$34$		0			0
$35$	−2.67813	−	0.216743i	−0.452686	−	0.0366363i
$36$		0			0
$37$	−7.71428	−	2.06704i	−1.26822	−	0.339818i	−0.438871	−	0.898550i	$-0.644622\pi$
$37$	−7.71428	−	2.06704i	−1.26822	−	0.339818i	−0.829349	+	0.558732i	$0.811288\pi$
$38$		0			0
$39$	3.92719	+	2.26737i	0.628854	+	0.363069i
$40$		0			0
$41$			8.51782i			1.33026i	0.746728	+	0.665130i	$0.231624\pi$
$41$			8.51782i			1.33026i	−0.746728	+	0.665130i	$0.768376\pi$
$42$		0			0
$43$	4.47950	−	4.47950i	0.683117	−	0.683117i	−0.277584	−	0.960701i	$-0.589534\pi$
$43$	4.47950	−	4.47950i	0.683117	−	0.683117i	0.960701	+	0.277584i	$0.0895338\pi$
$44$		0			0
$45$	−1.51507	+	0.405963i	−0.225854	+	0.0605174i
$46$		0			0
$47$	−6.02995	−	10.4442i	−0.879559	−	1.52344i	−0.851826	−	0.523825i	$-0.824505\pi$
$47$	−6.02995	−	10.4442i	−0.879559	−	1.52344i	−0.0277324	−	0.999615i	$-0.508829\pi$
$48$		0			0
$49$	6.54611	−	2.47960i	0.935159	−	0.354229i
$50$		0			0
$51$	0.317949	−	1.18660i	0.0445218	−	0.166158i
$52$		0			0
$53$	0.381000	+	1.42191i	0.0523344	+	0.195315i	0.987144	−	0.159836i	$-0.0510964\pi$
$53$	0.381000	+	1.42191i	0.0523344	+	0.195315i	−0.934809	+	0.355150i	$0.884430\pi$
$54$		0			0
$55$		−	2.49167i		−	0.335977i
$56$		0			0
$57$			0.116976i			0.0154939i
$58$		0			0
$59$	1.86535	+	6.96158i	0.242848	+	0.906320i	0.974453	+	0.224592i	$0.0721048\pi$
$59$	1.86535	+	6.96158i	0.242848	+	0.906320i	−0.731605	+	0.681729i	$0.761229\pi$
$60$		0			0
$61$	−1.18609	+	4.42654i	−0.151863	+	0.566760i	0.847491	+	0.530810i	$0.178112\pi$
$61$	−1.18609	+	4.42654i	−0.151863	+	0.566760i	−0.999354	+	0.0359500i	$0.988554\pi$
$62$		0			0
$63$	3.11318	−	2.64701i	0.392224	−	0.333491i
$64$		0			0
$65$	−1.90861	−	3.30580i	−0.236734	−	0.410034i
$66$		0			0
$67$	3.38700	−	0.907543i	0.413787	−	0.110874i	−0.0459185	−	0.998945i	$-0.514621\pi$
$67$	3.38700	−	0.907543i	0.413787	−	0.110874i	0.459706	+	0.888071i	$0.347955\pi$
$68$		0			0
$69$	1.64738	−	1.64738i	0.198322	−	0.198322i
$70$		0			0
$71$			5.43131i			0.644578i	0.946641	+	0.322289i	$0.104452\pi$
$71$			5.43131i			0.644578i	−0.946641	+	0.322289i	$0.895548\pi$
$72$		0			0
$73$	7.34303	+	4.23950i	0.859436	+	0.496196i	0.863824	−	0.503795i	$-0.168063\pi$
$73$	7.34303	+	4.23950i	0.859436	+	0.496196i	−0.00438712	+	0.999990i	$0.501396\pi$
$74$		0			0
$75$	4.62480	+	1.23921i	0.534026	+	0.143092i
$76$		0			0
$77$	2.78165	+	5.86524i	0.316998	+	0.668406i
$78$		0			0
$79$	0.433595	+	0.751008i	0.0487832	+	0.0844950i	0.889386	−	0.457157i	$-0.151132\pi$
$79$	0.433595	+	0.751008i	0.0487832	+	0.0844950i	−0.840603	+	0.541652i	$0.817799\pi$
$80$		0			0
$81$	−0.990483	+	1.71557i	−0.110054	+	0.190619i
$82$		0			0
$83$	5.44318	+	5.44318i	0.597466	+	0.597466i	0.939638	−	0.342171i	$-0.111162\pi$
$83$	5.44318	+	5.44318i	0.597466	+	0.597466i	−0.342171	+	0.939638i	$0.611162\pi$
$84$		0			0
$85$	−0.731209	+	0.731209i	−0.0793108	+	0.0793108i
$86$		0			0
$87$	7.46657	+	4.31083i	0.800500	+	0.462169i
$88$		0			0
$89$	3.93155	−	2.26988i	0.416744	−	0.240607i	−0.276939	−	0.960887i	$-0.589320\pi$
$89$	3.93155	−	2.26988i	0.416744	−	0.240607i	0.693683	+	0.720280i	$0.255987\pi$
$90$		0			0
$91$	8.18327	+	5.65093i	0.857840	+	0.592379i
$92$		0			0
$93$	2.67441	−	9.98102i	0.277323	−	1.03498i
$94$		0			0
$95$	0.0492336	−	0.0852752i	0.00505126	−	0.00874905i
$96$		0			0
$97$	16.4025			1.66542			0.832712	−	0.553706i	$-0.186787\pi$
$97$	16.4025			1.66542			0.832712	+	0.553706i	$0.186787\pi$
$98$		0			0
$99$	2.67958	+	2.67958i	0.269308	+	0.269308i
$100$		0			0
$101$	2.38049	+	8.88412i	0.236868	+	0.884003i	0.977298	+	0.211870i	$0.0679552\pi$
$101$	2.38049	+	8.88412i	0.236868	+	0.884003i	−0.740430	+	0.672134i	$0.765378\pi$
$102$		0			0
$103$	−6.69469	+	3.86518i	−0.659647	+	0.380848i	−0.792143	−	0.610336i	$-0.791034\pi$
$103$	−6.69469	+	3.86518i	−0.659647	+	0.380848i	0.132495	+	0.991184i	$0.457701\pi$
$104$		0			0
$105$	3.18858	−	0.583665i	0.311173	−	0.0569599i
$106$		0			0
$107$	−18.2555	−	4.89154i	−1.76482	−	0.472883i	−0.777137	−	0.629332i	$-0.783329\pi$
$107$	−18.2555	−	4.89154i	−1.76482	−	0.472883i	−0.987686	+	0.156449i	$0.949995\pi$
$108$		0			0
$109$	15.8026	−	4.23429i	1.51361	−	0.405571i	0.595980	−	0.802999i	$-0.296764\pi$
$109$	15.8026	−	4.23429i	1.51361	−	0.405571i	0.917633	+	0.397428i	$0.130097\pi$
$110$		0			0
$111$	9.63510			0.914524
$112$		0			0
$113$	−20.1152			−1.89228			−0.946138	−	0.323765i	$-0.895051\pi$
$113$	−20.1152			−1.89228			−0.946138	+	0.323765i	$0.895051\pi$
$114$		0			0
$115$	−1.89430	+	0.507576i	−0.176644	+	0.0473317i
$116$		0			0
$117$	5.60765	+	1.50257i	0.518428	+	0.138912i
$118$		0			0
$119$	0.904916	−	2.53753i	0.0829535	−	0.232615i
$120$		0			0
$121$	4.31298	−	2.49010i	0.392089	−	0.226373i
$122$		0			0
$123$	−2.65968	−	9.92606i	−0.239815	−	0.895003i
$124$		0			0
$125$	−6.44039	−	6.44039i	−0.576046	−	0.576046i
$126$		0			0
$127$	0.988901			0.0877508			0.0438754	−	0.999037i	$-0.486030\pi$
$127$	0.988901			0.0877508			0.0438754	+	0.999037i	$0.486030\pi$
$128$		0			0
$129$	−3.82137	+	6.61880i	−0.336453	+	0.582753i
$130$		0			0
$131$	2.03878	−	7.60883i	0.178129	−	0.664786i	−0.817869	−	0.575405i	$-0.804844\pi$
$131$	2.03878	−	7.60883i	0.178129	−	0.664786i	0.995998	−	0.0893811i	$-0.0284889\pi$
$132$		0			0
$133$	−0.0206937	+	0.255696i	−0.00179437	+	0.0221716i
$134$		0			0
$135$	4.82194	−	2.78395i	0.415007	−	0.239604i
$136$		0			0
$137$	−9.57893	−	5.53040i	−0.818383	−	0.472494i	0.0314753	−	0.999505i	$-0.489979\pi$
$137$	−9.57893	−	5.53040i	−0.818383	−	0.472494i	−0.849859	+	0.527011i	$0.823313\pi$
$138$		0			0
$139$	−12.4154	+	12.4154i	−1.05306	+	1.05306i	−0.0545473	+	0.998511i	$0.517372\pi$
$139$	−12.4154	+	12.4154i	−1.05306	+	1.05306i	−0.998511	+	0.0545473i	$0.982628\pi$
$140$		0			0
$141$	10.2881	+	10.2881i	0.866411	+	0.866411i
$142$		0			0
$143$	−4.61114	+	7.98672i	−0.385603	+	0.667883i
$144$		0			0
$145$	−3.62873	−	6.28515i	−0.301350	−	0.521954i
$146$		0			0
$147$	−6.85412	+	4.93357i	−0.565318	+	0.406914i
$148$		0			0
$149$	−5.06147	−	1.35622i	−0.414652	−	0.111106i	0.0454610	−	0.998966i	$-0.485524\pi$
$149$	−5.06147	−	1.35622i	−0.414652	−	0.111106i	−0.460113	+	0.887861i	$0.652191\pi$
$150$		0			0
$151$	−1.18073	−	0.681693i	−0.0960862	−	0.0554754i	0.451187	−	0.892429i	$-0.351001\pi$
$151$	−1.18073	−	0.681693i	−0.0960862	−	0.0554754i	−0.547273	+	0.836954i	$0.684334\pi$
$152$		0			0
$153$		−	1.57271i		−	0.127146i
$154$		0			0
$155$	−6.15051	+	6.15051i	−0.494021	+	0.494021i
$156$		0			0
$157$	0.306970	−	0.0822524i	0.0244989	−	0.00656446i	−0.246549	−	0.969130i	$-0.579297\pi$
$157$	0.306970	−	0.0822524i	0.0244989	−	0.00656446i	0.271048	+	0.962566i	$0.412630\pi$
$158$		0			0
$159$	−0.887981	−	1.53803i	−0.0704215	−	0.121974i
$160$		0			0
$161$	3.89242	−	3.30955i	0.306765	−	0.260829i
$162$		0			0
$163$	3.84175	−	14.3376i	0.300909	−	1.12301i	−0.635501	−	0.772100i	$-0.719206\pi$
$163$	3.84175	−	14.3376i	0.300909	−	1.12301i	0.936410	−	0.350907i	$-0.114127\pi$
$164$		0			0
$165$	0.778022	+	2.90362i	0.0605689	+	0.226046i
$166$		0			0
$167$		−	14.5986i		−	1.12967i	−0.825204	−	0.564836i	$-0.808940\pi$
$167$		−	14.5986i		−	1.12967i	0.825204	−	0.564836i	$-0.191060\pi$
$168$		0			0
$169$			1.12842i			0.0868018i
$170$		0			0
$171$	0.0387596	+	0.144653i	0.00296402	+	0.0110619i
$172$		0			0
$173$	−3.19660	+	11.9299i	−0.243033	+	0.907011i	0.731329	+	0.682025i	$0.238900\pi$
$173$	−3.19660	+	11.9299i	−0.243033	+	0.907011i	−0.974362	+	0.224986i	$0.927766\pi$
$174$		0			0
$175$	9.89005	+	3.52692i	0.747617	+	0.266610i
$176$		0			0
$177$	−4.34749	−	7.53008i	−0.326777	−	0.565995i
$178$		0			0
$179$	−0.455619	+	0.122083i	−0.0340545	+	0.00912489i	−0.275806	−	0.961213i	$-0.588945\pi$
$179$	−0.455619	+	0.122083i	−0.0340545	+	0.00912489i	0.241752	+	0.970338i	$0.422278\pi$
$180$		0			0
$181$	15.4654	−	15.4654i	1.14953	−	1.14953i	0.162887	−	0.986645i	$-0.447919\pi$
$181$	15.4654	−	15.4654i	1.14953	−	1.14953i	0.986645	−	0.162887i	$-0.0520807\pi$
$182$		0			0
$183$		−	5.52873i		−	0.408696i
$184$		0			0
$185$	−7.02396	−	4.05528i	−0.516412	−	0.298150i
$186$		0			0
$187$	2.41319	+	0.646613i	0.176470	+	0.0472850i
$188$		0			0
$189$	−8.24262	+	11.9364i	−0.599562	+	0.868242i
$190$		0			0
$191$	3.04108	+	5.26731i	0.220045	+	0.381129i	0.954821	−	0.297180i	$-0.0960463\pi$
$191$	3.04108	+	5.26731i	0.220045	+	0.381129i	−0.734776	+	0.678309i	$0.762713\pi$
$192$		0			0
$193$	−5.03089	+	8.71375i	−0.362131	+	0.627229i	−0.988311	−	0.152449i	$-0.951284\pi$
$193$	−5.03089	+	8.71375i	−0.362131	+	0.627229i	0.626180	+	0.779678i	$0.284617\pi$
$194$		0			0
$195$	3.25639	+	3.25639i	0.233195	+	0.233195i
$196$		0			0
$197$	−10.0837	+	10.0837i	−0.718432	+	0.718432i	−0.968284	−	0.249852i	$-0.919618\pi$
$197$	−10.0837	+	10.0837i	−0.718432	+	0.718432i	0.249852	+	0.968284i	$0.419618\pi$
$198$		0			0
$199$	−10.0980	−	5.83005i	−0.715825	−	0.413282i	0.0973893	−	0.995246i	$-0.468951\pi$
$199$	−10.0980	−	5.83005i	−0.715825	−	0.413282i	−0.813214	+	0.581965i	$0.802284\pi$
$200$		0			0
$201$	−3.66359	+	2.11517i	−0.258409	+	0.149193i
$202$		0			0
$203$	15.5584	+	10.7438i	1.09199	+	0.754069i
$204$		0			0
$205$	−2.23885	+	8.35549i	−0.156368	+	0.583572i
$206$		0			0
$207$	1.49130	−	2.58301i	0.103653	−	0.179532i
$208$		0			0
$209$	−0.237894			−0.0164555
$210$		0			0
$211$	−6.53423	−	6.53423i	−0.449835	−	0.449835i	0.445465	−	0.895300i	$-0.353038\pi$
$211$	−6.53423	−	6.53423i	−0.449835	−	0.449835i	−0.895300	+	0.445465i	$0.853038\pi$
$212$		0			0
$213$	−1.69592	−	6.32927i	−0.116203	−	0.433674i
$214$		0			0
$215$	5.57153	−	3.21672i	0.379975	−	0.219379i
$216$		0			0
$217$	7.61163	−	21.3442i	0.516711	−	1.44894i
$218$		0			0
$219$	−9.88082	−	2.64756i	−0.667684	−	0.178905i
$220$		0			0
$221$	3.69698	−	0.990604i	0.248686	−	0.0666352i
$222$		0			0
$223$	23.3350			1.56263			0.781315	−	0.624137i	$-0.214549\pi$
$223$	23.3350			1.56263			0.781315	+	0.624137i	$0.214549\pi$
$224$		0			0
$225$	6.12964			0.408643
$226$		0			0
$227$	−15.1161	+	4.05036i	−1.00329	+	0.268832i	−0.722824	−	0.691032i	$-0.757156\pi$
$227$	−15.1161	+	4.05036i	−1.00329	+	0.268832i	−0.280468	+	0.959863i	$0.590490\pi$
$228$		0			0
$229$	−25.8292	−	6.92092i	−1.70684	−	0.457347i	−0.732196	−	0.681094i	$-0.761504\pi$
$229$	−25.8292	−	6.92092i	−1.70684	−	0.457347i	−0.974647	+	0.223747i	$0.928171\pi$
$230$		0			0
$231$	−5.07295	−	5.96637i	−0.333775	−	0.392558i
$232$		0			0
$233$	−11.0402	+	6.37405i	−0.723267	+	0.417578i	−0.815954	−	0.578117i	$-0.803788\pi$
$233$	−11.0402	+	6.37405i	−0.723267	+	0.417578i	0.0926872	+	0.995695i	$0.470454\pi$
$234$		0			0
$235$	−3.16986	−	11.8301i	−0.206779	−	0.771708i
$236$		0			0
$237$	−0.739782	−	0.739782i	−0.0480540	−	0.0480540i
$238$		0			0
$239$	−14.9688			−0.968253			−0.484127	−	0.874998i	$-0.660863\pi$
$239$	−14.9688			−0.968253			−0.484127	+	0.874998i	$0.660863\pi$
$240$		0			0
$241$	−9.90526	+	17.1564i	−0.638054	+	1.10514i	0.347805	+	0.937567i	$0.386927\pi$
$241$	−9.90526	+	17.1564i	−0.638054	+	1.10514i	−0.985859	+	0.167575i	$0.946406\pi$
$242$		0			0
$243$	−3.63850	+	13.5791i	−0.233410	+	0.871098i
$244$		0			0
$245$	7.07310	−	0.711747i	0.451884	−	0.0454718i
$246$		0			0
$247$	−0.315624	+	0.182226i	−0.0200827	+	0.0115947i
$248$		0			0
$249$	−8.04272	−	4.64346i	−0.509686	−	0.294268i
$250$		0			0
$251$	−9.23966	+	9.23966i	−0.583202	+	0.583202i	−0.935782	−	0.352580i	$-0.885305\pi$
$251$	−9.23966	+	9.23966i	−0.583202	+	0.583202i	0.352580	+	0.935782i	$0.385305\pi$
$252$		0			0
$253$	3.35028	+	3.35028i	0.210630	+	0.210630i
$254$		0			0
$255$	0.623780	−	1.08042i	0.0390626	−	0.0676584i
$256$		0			0
$257$	−11.6109	−	20.1107i	−0.724271	−	1.25447i	−0.959273	−	0.282479i	$-0.908843\pi$
$257$	−11.6109	−	20.1107i	−0.724271	−	1.25447i	0.235003	−	0.971995i	$-0.424490\pi$
$258$		0			0
$259$	21.0612	+	1.70450i	1.30868	+	0.105913i
$260$		0			0
$261$	10.6615	+	2.85675i	0.659933	+	0.176828i
$262$		0			0
$263$	3.91454	+	2.26006i	0.241381	+	0.139361i	0.615811	−	0.787894i	$-0.288828\pi$
$263$	3.91454	+	2.26006i	0.241381	+	0.139361i	−0.374430	+	0.927255i	$0.622162\pi$
$264$		0			0
$265$			1.49496i			0.0918345i
$266$		0			0
$267$	−3.87278	+	3.87278i	−0.237011	+	0.237011i
$268$		0			0
$269$	−0.385363	+	0.103258i	−0.0234960	+	0.00629574i	−0.270548	−	0.962707i	$-0.587205\pi$
$269$	−0.385363	+	0.103258i	−0.0234960	+	0.00629574i	0.247052	+	0.969002i	$0.420538\pi$
$270$		0			0
$271$	5.31084	+	9.19864i	0.322611	+	0.558778i	0.981026	−	0.193877i	$-0.0621063\pi$
$271$	5.31084	+	9.19864i	0.322611	+	0.558778i	−0.658415	+	0.752655i	$0.728773\pi$
$272$		0			0
$273$	−11.3007	−	4.02998i	−0.683949	−	0.243906i
$274$		0			0
$275$	−2.52018	+	9.40545i	−0.151973	+	0.567170i
$276$		0			0
$277$	−2.98011	−	11.1219i	−0.179058	−	0.668252i	−0.995825	−	0.0912848i	$-0.970903\pi$
$277$	−2.98011	−	11.1219i	−0.179058	−	0.668252i	0.816767	−	0.576967i	$-0.195764\pi$
$278$		0			0
$279$		−	13.2287i		−	0.791981i
$280$		0			0
$281$		−	18.6360i		−	1.11173i	−0.831272	−	0.555866i	$-0.812387\pi$
$281$		−	18.6360i		−	1.11173i	0.831272	−	0.555866i	$-0.187613\pi$
$282$		0			0
$283$	−2.35222	−	8.77861i	−0.139825	−	0.521834i	−0.999931	−	0.0117192i	$-0.996270\pi$
$283$	−2.35222	−	8.77861i	−0.139825	−	0.521834i	0.860106	−	0.510115i	$-0.170397\pi$
$284$		0			0
$285$	−0.0307463	+	0.114747i	−0.00182125	+	0.00679701i
$286$		0			0
$287$	−4.05777	−	22.1677i	−0.239523	−	1.30852i
$288$		0			0
$289$	7.98158	+	13.8245i	0.469505	+	0.813206i
$290$		0			0
$291$	−19.1143	+	5.12167i	−1.12050	+	0.300238i
$292$		0			0
$293$	−12.0193	+	12.0193i	−0.702174	+	0.702174i	−0.964877	−	0.262703i	$-0.915386\pi$
$293$	−12.0193	+	12.0193i	−0.702174	+	0.702174i	0.262703	+	0.964877i	$0.415386\pi$
$294$		0			0
$295$			7.31920i			0.426140i
$296$		0			0
$297$	−11.6497	−	6.72594i	−0.675982	−	0.390278i
$298$		0			0
$299$	7.01125	+	1.87866i	0.405471	+	0.108646i
$300$		0			0
$301$	−9.52396	+	13.7919i	−0.548952	+	0.794952i
$302$		0			0
$303$	−5.54812	−	9.60962i	−0.318731	−	0.552058i
$304$		0			0
$305$	−2.32697	+	4.03043i	−0.133242	+	0.230781i
$306$		0			0
$307$	−17.8339	−	17.8339i	−1.01784	−	1.01784i	−0.999838	−	0.0179975i	$-0.994271\pi$
$307$	−17.8339	−	17.8339i	−1.01784	−	1.01784i	−0.0179975	−	0.999838i	$-0.505729\pi$
$308$		0			0
$309$	6.59462	−	6.59462i	0.375155	−	0.375155i
$310$		0			0
$311$	5.66778	+	3.27229i	0.321390	+	0.185555i	0.652012	−	0.758209i	$-0.273925\pi$
$311$	5.66778	+	3.27229i	0.321390	+	0.185555i	−0.330622	+	0.943763i	$0.607258\pi$
$312$		0			0
$313$	16.6047	−	9.58671i	0.938551	−	0.541873i	0.0490453	−	0.998797i	$-0.484382\pi$
$313$	16.6047	−	9.58671i	0.938551	−	0.541873i	0.889506	+	0.456924i	$0.151049\pi$
$314$		0			0
$315$	3.74960	−	1.77828i	0.211266	−	0.100195i
$316$		0			0
$317$	4.87115	−	18.1794i	0.273591	−	1.02106i	−0.683189	−	0.730242i	$-0.739407\pi$
$317$	4.87115	−	18.1794i	0.273591	−	1.02106i	0.956780	−	0.290814i	$-0.0939260\pi$
$318$		0			0
$319$	−8.76691	+	15.1847i	−0.490853	+	0.850182i
$320$		0			0
$321$	22.8010			1.27263
$322$		0			0
$323$	0.0698127	+	0.0698127i	0.00388448	+	0.00388448i
$324$		0			0
$325$	3.86089	+	14.4090i	0.214164	+	0.799270i
$326$		0			0
$327$	−17.0931	+	9.86868i	−0.945248	+	0.545739i
$328$		0			0
$329$	20.6685	+	24.3085i	1.13949	+	1.34017i
$330$		0			0
$331$	9.45985	+	2.53476i	0.519960	+	0.139323i	0.509248	−	0.860620i	$-0.329924\pi$
$331$	9.45985	+	2.53476i	0.519960	+	0.139323i	0.0107120	+	0.999943i	$0.496590\pi$
$332$		0			0
$333$	11.9148	−	3.19255i	0.652926	−	0.174951i
$334$		0			0
$335$	3.56099			0.194558
$336$		0			0
$337$	4.91600			0.267792			0.133896	−	0.990995i	$-0.457251\pi$
$337$	4.91600			0.267792			0.133896	+	0.990995i	$0.457251\pi$
$338$		0			0
$339$	23.4408	−	6.28094i	1.27313	−	0.341134i
$340$		0			0
$341$	20.2984	+	5.43893i	1.09922	+	0.294535i
$342$		0			0
$343$	−15.8551	+	9.57166i	−0.856093	+	0.516821i
$344$		0			0
$345$	2.04899	−	1.18299i	0.110314	−	0.0636898i
$346$		0			0
$347$	−2.42076	−	9.03438i	−0.129953	−	0.484991i	0.870015	−	0.493026i	$-0.164109\pi$
$347$	−2.42076	−	9.03438i	−0.129953	−	0.484991i	−0.999968	+	0.00803463i	$0.997442\pi$
$348$		0			0
$349$	−17.2061	−	17.2061i	−0.921021	−	0.921021i	0.0760810	−	0.997102i	$-0.475759\pi$
$349$	−17.2061	−	17.2061i	−0.921021	−	0.921021i	−0.997102	+	0.0760810i	$0.975759\pi$
$350$		0			0
$351$	−20.6081			−1.09998
$352$		0			0
$353$	4.08472	−	7.07494i	0.217408	−	0.376561i	−0.736607	−	0.676321i	$-0.763573\pi$
$353$	4.08472	−	7.07494i	0.217408	−	0.376561i	0.954015	+	0.299760i	$0.0969066\pi$
$354$		0			0
$355$	−1.42758	+	5.32780i	−0.0757681	+	0.282771i
$356$		0			0
$357$	−0.262185	+	3.23961i	−0.0138763	+	0.171459i
$358$		0			0
$359$	10.0193	−	5.78465i	0.528799	−	0.305302i	−0.211728	−	0.977329i	$-0.567909\pi$
$359$	10.0193	−	5.78465i	0.528799	−	0.305302i	0.740527	+	0.672027i	$0.234576\pi$
$360$		0			0
$361$	16.4463	+	9.49530i	0.865597	+	0.499753i
$362$		0			0
$363$	−4.24851	+	4.24851i	−0.222989	+	0.222989i
$364$		0			0
$365$	6.08876	+	6.08876i	0.318700	+	0.318700i
$366$		0			0
$367$	4.25356	−	7.36738i	0.222034	−	0.384574i	−0.733392	−	0.679807i	$-0.762064\pi$
$367$	4.25356	−	7.36738i	0.222034	−	0.384574i	0.955425	+	0.295232i	$0.0953971\pi$
$368$		0			0
$369$	−6.57792	−	11.3933i	−0.342433	−	0.593111i
$370$		0			0
$371$	−1.66894	−	3.51904i	−0.0866469	−	0.182699i
$372$		0			0
$373$	−5.06649	−	1.35756i	−0.262333	−	0.0702919i	0.125255	−	0.992125i	$-0.460025\pi$
$373$	−5.06649	−	1.35756i	−0.262333	−	0.0702919i	−0.387588	+	0.921833i	$0.626692\pi$
$374$		0			0
$375$	9.51618	+	5.49417i	0.491414	+	0.283718i
$376$		0			0
$377$			26.8616i			1.38344i
$378$		0			0
$379$	3.62966	−	3.62966i	0.186443	−	0.186443i	−0.607713	−	0.794156i	$-0.707913\pi$
$379$	3.62966	−	3.62966i	0.186443	−	0.186443i	0.794156	+	0.607713i	$0.207913\pi$
$380$		0			0
$381$	−1.15239	+	0.308783i	−0.0590390	+	0.0158194i
$382$		0			0
$383$	−3.48127	−	6.02973i	−0.177884	−	0.308105i	0.763271	−	0.646078i	$-0.223592\pi$
$383$	−3.48127	−	6.02973i	−0.177884	−	0.308105i	−0.941156	+	0.337973i	$0.890259\pi$
$384$		0			0
$385$	1.18700	+	6.48460i	0.0604950	+	0.330486i
$386$		0			0
$387$	−2.53239	+	9.45101i	−0.128729	+	0.480422i
$388$		0			0
$389$	−3.41145	−	12.7317i	−0.172967	−	0.645523i	−0.996889	−	0.0788190i	$-0.974885\pi$
$389$	−3.41145	−	12.7317i	−0.172967	−	0.645523i	0.823922	−	0.566704i	$-0.191782\pi$
$390$		0			0
$391$		−	1.96636i		−	0.0994429i
$392$		0			0
$393$			9.50339i			0.479383i
$394$		0			0
$395$	0.227934	+	0.850663i	0.0114686	+	0.0428015i
$396$		0			0
$397$	1.61554	−	6.02928i	0.0810817	−	0.302601i	−0.913462	−	0.406925i	$-0.866601\pi$
$397$	1.61554	−	6.02928i	0.0810817	−	0.302601i	0.994543	+	0.104324i	$0.0332678\pi$
$398$		0			0
$399$	−0.0557258	−	0.304431i	−0.00278978	−	0.0152406i
$400$		0			0
$401$	7.95077	+	13.7711i	0.397042	+	0.687697i	0.993360	−	0.115051i	$-0.0367033\pi$
$401$	7.95077	+	13.7711i	0.397042	+	0.687697i	−0.596317	+	0.802749i	$0.703370\pi$
$402$		0			0
$403$	31.0969	−	8.33239i	1.54905	−	0.415066i
$404$		0			0
$405$	−1.42253	+	1.42253i	−0.0706861	+	0.0706861i
$406$		0			0
$407$			19.5949i			0.971282i
$408$		0			0
$409$	4.93864	+	2.85133i	0.244200	+	0.140989i	0.617106	−	0.786880i	$-0.288305\pi$
$409$	4.93864	+	2.85133i	0.244200	+	0.140989i	−0.372906	+	0.927869i	$0.621638\pi$
$410$		0			0
$411$	12.8895	+	3.45372i	0.635791	+	0.170360i
$412$		0			0
$413$	−8.17099	−	17.2289i	−0.402068	−	0.847781i
$414$		0			0
$415$	3.90874	+	6.77014i	0.191873	+	0.332333i
$416$		0			0
$417$	10.5913	−	18.3447i	0.518659	−	0.898343i
$418$		0			0
$419$	4.57142	+	4.57142i	0.223328	+	0.223328i	0.809898	−	0.586570i	$-0.199522\pi$
$419$	4.57142	+	4.57142i	0.223328	+	0.223328i	−0.586570	+	0.809898i	$0.699522\pi$
$420$		0			0
$421$	0.421252	−	0.421252i	0.0205306	−	0.0205306i	−0.696767	−	0.717298i	$-0.745379\pi$
$421$	0.421252	−	0.421252i	0.0205306	−	0.0205306i	0.717298	+	0.696767i	$0.245379\pi$
$422$		0			0
$423$	16.1311	+	9.31331i	0.784322	+	0.452829i
$424$		0			0
$425$	3.49971	−	2.02056i	0.169761	−	0.0980115i
$426$		0			0
$427$	0.978062	−	12.0852i	0.0473317	−	0.584841i
$428$		0			0
$429$	2.87964	−	10.7470i	0.139031	−	0.518869i
$430$		0			0
$431$	−10.5518	+	18.2762i	−0.508262	+	0.880336i	0.491692	+	0.870769i	$0.336379\pi$
$431$	−10.5518	+	18.2762i	−0.508262	+	0.880336i	−0.999954	+	0.00956658i	$0.996955\pi$
$432$		0			0
$433$	−13.9717			−0.671436			−0.335718	−	0.941962i	$-0.608979\pi$
$433$	−13.9717			−0.671436			−0.335718	+	0.941962i	$0.608979\pi$
$434$		0			0
$435$	6.19120	+	6.19120i	0.296845	+	0.296845i
$436$		0			0
$437$	0.0484611	+	0.180859i	0.00231821	+	0.00865168i
$438$		0			0
$439$	−4.69322	+	2.70963i	−0.223995	+	0.129324i	−0.607799	−	0.794091i	$-0.707947\pi$
$439$	−4.69322	+	2.70963i	−0.223995	+	0.129324i	0.383804	+	0.923415i	$0.374614\pi$
$440$		0			0
$441$	−6.84109	+	8.37194i	−0.325766	+	0.398664i
$442$		0			0
$443$	5.83698	+	1.56401i	0.277323	+	0.0743085i	0.394800	−	0.918767i	$-0.370814\pi$
$443$	5.83698	+	1.56401i	0.277323	+	0.0743085i	−0.117477	+	0.993076i	$0.537481\pi$
$444$		0			0
$445$	4.45325	−	1.19324i	0.211104	−	0.0565652i
$446$		0			0
$447$	6.32175			0.299009
$448$		0			0
$449$	18.4262			0.869587			0.434794	−	0.900530i	$-0.356821\pi$
$449$	18.4262			0.869587			0.434794	+	0.900530i	$0.356821\pi$
$450$		0			0
$451$	20.1866	−	5.40898i	0.950550	−	0.254699i
$452$		0			0
$453$	1.58879	+	0.425716i	0.0746480	+	0.0200019i
$454$		0			0
$455$	6.54201	+	7.69415i	0.306694	+	0.360707i
$456$		0			0
$457$	−31.1530	+	17.9862i	−1.45728	+	0.841358i	−0.998877	−	0.0473884i	$-0.984910\pi$
$457$	−31.1530	+	17.9862i	−1.45728	+	0.841358i	−0.458399	+	0.888747i	$0.651577\pi$
$458$		0			0
$459$	1.44492	+	5.39253i	0.0674433	+	0.251702i
$460$		0			0
$461$	−0.903879	−	0.903879i	−0.0420978	−	0.0420978i	0.685745	−	0.727842i	$-0.259477\pi$
$461$	−0.903879	−	0.903879i	−0.0420978	−	0.0420978i	−0.727842	+	0.685745i	$0.759477\pi$
$462$		0			0
$463$	12.5999			0.585565			0.292782	−	0.956179i	$-0.405419\pi$
$463$	12.5999			0.585565			0.292782	+	0.956179i	$0.405419\pi$
$464$		0			0
$465$	5.24687	−	9.08785i	0.243318	−	0.421439i
$466$		0			0
$467$	2.14538	−	8.00668i	0.0992765	−	0.370505i	−0.898357	−	0.439267i	$-0.855238\pi$
$467$	2.14538	−	8.00668i	0.0992765	−	0.370505i	0.997633	+	0.0687620i	$0.0219049\pi$
$468$		0			0
$469$	−8.38235	+	3.97541i	−0.387061	+	0.183567i
$470$		0			0
$471$	−0.332038	+	0.191702i	−0.0152995	+	0.00883318i
$472$		0			0
$473$	−13.4606	−	7.77151i	−0.618921	−	0.357334i
$474$		0			0
$475$	−0.272096	+	0.272096i	−0.0124846	+	0.0124846i
$476$		0			0
$477$	−1.60770	−	1.60770i	−0.0736114	−	0.0736114i
$478$		0			0
$479$	4.63918	−	8.03529i	0.211969	−	0.367142i	−0.740361	−	0.672209i	$-0.765346\pi$
$479$	4.63918	−	8.03529i	0.211969	−	0.367142i	0.952331	+	0.305067i	$0.0986789\pi$
$480$		0			0
$481$	15.0096	+	25.9974i	0.684378	+	1.18538i
$482$		0			0
$483$	−3.50254	+	5.07212i	−0.159371	+	0.230790i
$484$		0			0
$485$	16.0899	+	4.31128i	0.730606	+	0.195765i
$486$		0			0
$487$	33.5037	+	19.3434i	1.51820	+	0.876533i	0.999771	+	0.0214118i	$0.00681612\pi$
$487$	33.5037	+	19.3434i	1.51820	+	0.876533i	0.518429	+	0.855121i	$0.326517\pi$
$488$		0			0
$489$			17.9076i			0.809810i
$490$		0			0
$491$	29.8086	−	29.8086i	1.34524	−	1.34524i	0.454494	−	0.890750i	$-0.349820\pi$
$491$	29.8086	−	29.8086i	1.34524	−	1.34524i	0.890750	−	0.454494i	$-0.150180\pi$
$492$		0			0
$493$	7.02889	−	1.88338i	0.316565	−	0.0848234i
$494$		0			0
$495$	1.92420	+	3.33282i	0.0864865	+	0.149799i
$496$		0			0
$497$	−2.58740	−	14.1350i	−0.116061	−	0.634044i
$498$		0			0
$499$	2.89367	−	10.7993i	0.129538	−	0.483444i	−0.870422	−	0.492306i	$-0.836154\pi$
$499$	2.89367	−	10.7993i	0.129538	−	0.483444i	0.999961	+	0.00886191i	$0.00282087\pi$
$500$		0			0
$501$	4.55839	+	17.0121i	0.203654	+	0.760046i
$502$		0			0
$503$			18.1532i			0.809409i	0.914448	+	0.404704i	$0.132626\pi$
$503$			18.1532i			0.809409i	−0.914448	+	0.404704i	$0.867374\pi$
$504$		0			0
$505$			9.34050i			0.415647i
$506$		0			0
$507$	−0.352349	−	1.31498i	−0.0156484	−	0.0584005i
$508$		0			0
$509$	0.530258	−	1.97895i	0.0235033	−	0.0877154i	−0.953178	−	0.302410i	$-0.902209\pi$
$509$	0.530258	−	1.97895i	0.0235033	−	0.0877154i	0.976681	+	0.214694i	$0.0688756\pi$
$510$		0			0
$511$	−21.1299	−	7.53522i	−0.934733	−	0.333338i
$512$		0			0
$513$	−0.265799	−	0.460378i	−0.0117353	−	0.0203262i
$514$		0			0
$515$	−7.58304	+	2.03187i	−0.334149	+	0.0895348i
$516$		0			0
$517$	−20.9228	+	20.9228i	−0.920183	+	0.920183i
$518$		0			0
$519$		−	14.9004i		−	0.654053i
$520$		0			0
$521$	−2.51905	−	1.45437i	−0.110361	−	0.0637172i	0.443803	−	0.896124i	$-0.353629\pi$
$521$	−2.51905	−	1.45437i	−0.110361	−	0.0637172i	−0.554165	+	0.832407i	$0.686962\pi$
$522$		0			0
$523$	16.0023	+	4.28781i	0.699732	+	0.187493i	0.591111	−	0.806590i	$-0.298690\pi$
$523$	16.0023	+	4.28781i	0.699732	+	0.187493i	0.108622	+	0.994083i	$0.465356\pi$
$524$		0			0
$525$	−12.6264	−	1.02187i	−0.551063	−	0.0445980i
$526$		0			0
$527$	−4.36067	−	7.55290i	−0.189954	−	0.329010i
$528$		0			0
$529$	−9.63542	+	16.6890i	−0.418931	+	0.725611i
$530$		0			0
$531$	−7.87117	−	7.87117i	−0.341580	−	0.341580i
$532$		0			0
$533$	22.6392	−	22.6392i	0.980611	−	0.980611i
$534$		0			0
$535$	−16.6219	−	9.59663i	−0.718625	−	0.414899i
$536$		0			0
$537$	0.492826	−	0.284533i	0.0212670	−	0.0122785i
$538$		0			0
$539$	−10.0334	−	13.9392i	−0.432168	−	0.600404i
$540$		0			0
$541$	1.87978	−	7.01543i	0.0808180	−	0.301617i	−0.913671	−	0.406453i	$-0.866765\pi$
$541$	1.87978	−	7.01543i	0.0808180	−	0.301617i	0.994489	+	0.104837i	$0.0334320\pi$
$542$		0			0
$543$	−13.1932	+	22.8513i	−0.566174	+	0.980643i
$544$		0			0
$545$	16.6144			0.711682
$546$		0			0
$547$	−18.2712	−	18.2712i	−0.781218	−	0.781218i	0.198818	−	0.980036i	$-0.436290\pi$
$547$	−18.2712	−	18.2712i	−0.781218	−	0.781218i	−0.980036	+	0.198818i	$0.936290\pi$
$548$		0			0
$549$	−1.83192	−	6.83683i	−0.0781846	−	0.291789i
$550$		0			0
$551$	−0.600079	+	0.346456i	−0.0255642	+	0.0147595i
$552$		0			0
$553$	−1.48621	−	1.74795i	−0.0631999	−	0.0743303i
$554$		0			0
$555$	9.45148	+	2.53252i	0.401193	+	0.107499i
$556$		0			0
$557$	−4.78640	+	1.28251i	−0.202806	+	0.0543418i	−0.358792	−	0.933417i	$-0.616811\pi$
$557$	−4.78640	+	1.28251i	−0.202806	+	0.0543418i	0.155986	+	0.987759i	$0.450145\pi$
$558$		0			0
$559$	−23.8117			−1.00713
$560$		0			0
$561$	−3.01407			−0.127254
$562$		0			0
$563$	−23.4858	+	6.29301i	−0.989809	+	0.265219i	−0.717170	−	0.696898i	$-0.754563\pi$
$563$	−23.4858	+	6.29301i	−0.989809	+	0.265219i	−0.272639	+	0.962116i	$0.587896\pi$
$564$		0			0
$565$	−19.7318	−	5.28712i	−0.830123	−	0.222431i
$566$		0			0
$567$	1.76047	−	4.93663i	0.0739327	−	0.207319i
$568$		0			0
$569$	2.33865	−	1.35022i	0.0980412	−	0.0566041i	−0.450178	−	0.892939i	$-0.648639\pi$
$569$	2.33865	−	1.35022i	0.0980412	−	0.0566041i	0.548219	+	0.836335i	$0.315306\pi$
$570$		0			0
$571$	3.43500	+	12.8196i	0.143750	+	0.536484i	0.999808	+	0.0196030i	$0.00624022\pi$
$571$	3.43500	+	12.8196i	0.143750	+	0.536484i	−0.856058	+	0.516881i	$0.827093\pi$
$572$		0			0
$573$	−5.18857	−	5.18857i	−0.216756	−	0.216756i
$574$		0			0
$575$	7.66390			0.319607
$576$		0			0
$577$	12.4461	−	21.5572i	0.518137	−	0.897439i	−0.481641	−	0.876369i	$-0.659959\pi$
$577$	12.4461	−	21.5572i	0.518137	−	0.897439i	0.999778	−	0.0210709i	$-0.00670757\pi$
$578$		0			0
$579$	3.14178	−	11.7253i	0.130568	−	0.487286i
$580$		0			0
$581$	−16.7590	−	11.5729i	−0.695279	−	0.480123i
$582$		0			0
$583$	3.12788	−	1.80589i	0.129544	−	0.0747921i
$584$		0			0
$585$	5.10584	+	2.94786i	0.211101	+	0.121879i
$586$		0			0
$587$	−23.9315	+	23.9315i	−0.987758	+	0.987758i	−0.999926	−	0.0121684i	$-0.996127\pi$
$587$	−23.9315	+	23.9315i	−0.987758	+	0.987758i	0.0121684	+	0.999926i	$0.496127\pi$
$588$		0			0
$589$	0.587224	+	0.587224i	0.0241961	+	0.0241961i
$590$		0			0
$591$	8.60218	−	14.8994i	0.353846	−	0.612880i
$592$		0			0
$593$	−0.895084	−	1.55033i	−0.0367567	−	0.0636645i	0.847062	−	0.531494i	$-0.178369\pi$
$593$	−0.895084	−	1.55033i	−0.0367567	−	0.0636645i	−0.883819	+	0.467830i	$0.845036\pi$
$594$		0			0
$595$	1.55464	−	2.25132i	0.0637341	−	0.0922950i
$596$		0			0
$597$	13.5879	+	3.64086i	0.556114	+	0.149010i
$598$		0			0
$599$	−37.3788	−	21.5806i	−1.52726	−	0.881761i	−0.999476	−	0.0323796i	$-0.989691\pi$
$599$	−37.3788	−	21.5806i	−1.52726	−	0.881761i	−0.527779	−	0.849381i	$-0.676975\pi$
$600$		0			0
$601$		−	27.6564i		−	1.12813i	−0.825730	−	0.564065i	$-0.809237\pi$
$601$		−	27.6564i		−	1.12813i	0.825730	−	0.564065i	$-0.190763\pi$
$602$		0			0
$603$	−3.82954	+	3.82954i	−0.155951	+	0.155951i
$604$		0			0
$605$	4.88529	−	1.30901i	0.198615	−	0.0532188i
$606$		0			0
$607$	−10.7968	−	18.7006i	−0.438228	−	0.759032i	0.559325	−	0.828948i	$-0.311060\pi$
$607$	−10.7968	−	18.7006i	−0.438228	−	0.759032i	−0.997553	+	0.0699158i	$0.977727\pi$
$608$		0			0
$609$	−21.4854	−	7.66199i	−0.870634	−	0.310480i
$610$		0			0
$611$	−11.7324	+	43.7859i	−0.474642	+	1.77139i
$612$		0			0
$613$	−2.56885	−	9.58708i	−0.103755	−	0.387219i	0.894446	−	0.447176i	$-0.147570\pi$
$613$	−2.56885	−	9.58708i	−0.103755	−	0.387219i	−0.998201	+	0.0599573i	$0.980904\pi$
$614$		0			0
$615$		−	10.4360i		−	0.420819i
$616$		0			0
$617$		−	14.2458i		−	0.573515i	−0.958003	−	0.286758i	$-0.907423\pi$
$617$		−	14.2458i		−	0.573515i	0.958003	−	0.286758i	$-0.0925774\pi$
$618$		0			0
$619$	−9.45579	−	35.2895i	−0.380060	−	1.41840i	−0.845808	−	0.533487i	$-0.820881\pi$
$619$	−9.45579	−	35.2895i	−0.380060	−	1.41840i	0.465748	−	0.884917i	$-0.345785\pi$
$620$		0			0
$621$	−2.74027	+	10.2268i	−0.109963	+	0.410388i
$622$		0			0
$623$	−9.15056	+	7.78033i	−0.366610	+	0.311712i
$624$		0			0
$625$	5.29682	+	9.17437i	0.211873	+	0.366975i
$626$		0			0
$627$	0.277225	−	0.0742821i	0.0110713	−	0.00296654i
$628$		0			0
$629$	5.75034	−	5.75034i	0.229281	−	0.229281i
$630$		0			0
$631$		−	4.87006i		−	0.193874i	−0.995291	−	0.0969370i	$-0.969095\pi$
$631$		−	4.87006i		−	0.193874i	0.995291	−	0.0969370i	$-0.0309045\pi$
$632$		0			0
$633$	9.65483	+	5.57422i	0.383745	+	0.221555i
$634$		0			0
$635$	0.970054	+	0.259925i	0.0384954	+	0.0103148i
$636$		0			0
$637$	−23.9891	−	10.8082i	−0.950481	−	0.428237i
$638$		0			0
$639$	−4.19436	−	7.26484i	−0.165926	−	0.287393i
$640$		0			0
$641$	−17.1939	+	29.7808i	−0.679120	+	1.17627i	0.296126	+	0.955149i	$0.404305\pi$
$641$	−17.1939	+	29.7808i	−0.679120	+	1.17627i	−0.975246	+	0.221121i	$0.929028\pi$
$642$		0			0
$643$	11.9018	+	11.9018i	0.469361	+	0.469361i	0.901708	−	0.432346i	$-0.142314\pi$
$643$	11.9018	+	11.9018i	0.469361	+	0.469361i	−0.432346	+	0.901708i	$0.642314\pi$
$644$		0			0
$645$	−5.48825	+	5.48825i	−0.216099	+	0.216099i
$646$		0			0
$647$	4.56190	+	2.63381i	0.179347	+	0.103546i	0.586986	−	0.809597i	$-0.300314\pi$
$647$	4.56190	+	2.63381i	0.179347	+	0.103546i	−0.407639	+	0.913143i	$0.633648\pi$
$648$		0			0
$649$	15.3139	−	8.84148i	0.601123	−	0.347058i
$650$		0			0
$651$	−2.20535	+	27.2497i	−0.0864343	+	1.06800i
$652$		0			0
$653$	−8.87812	+	33.1336i	−0.347427	+	1.29662i	0.542323	+	0.840170i	$0.317545\pi$
$653$	−8.87812	+	33.1336i	−0.347427	+	1.29662i	−0.889751	+	0.456447i	$0.849122\pi$
$654$		0			0
$655$	3.99985	−	6.92794i	0.156287	−	0.270697i
$656$		0			0
$657$	−13.0959			−0.510919
$658$		0			0
$659$	14.4817	+	14.4817i	0.564126	+	0.564126i	0.930477	−	0.366351i	$-0.119393\pi$
$659$	14.4817	+	14.4817i	0.564126	+	0.564126i	−0.366351	+	0.930477i	$0.619393\pi$
$660$		0			0
$661$	−4.10893	−	15.3347i	−0.159819	−	0.596452i	−0.998644	−	0.0520518i	$-0.983424\pi$
$661$	−4.10893	−	15.3347i	−0.159819	−	0.596452i	0.838826	−	0.544400i	$-0.183243\pi$
$662$		0			0
$663$	−3.99889	+	2.30876i	−0.155304	+	0.0896648i
$664$		0			0
$665$	−0.0875071	+	0.245384i	−0.00339338	+	0.00951557i
$666$		0			0
$667$	13.3301	+	3.57180i	0.516145	+	0.138301i
$668$		0			0
$669$	−27.1930	+	7.28634i	−1.05134	+	0.281706i
$670$		0			0
$671$	11.2438			0.434061
$672$		0			0
$673$	−8.09831			−0.312167			−0.156083	−	0.987744i	$-0.549887\pi$
$673$	−8.09831			−0.312167			−0.156083	+	0.987744i	$0.549887\pi$
$674$		0			0
$675$	−21.0175	+	5.63161i	−0.808962	+	0.216761i
$676$		0			0
$677$	21.8750	+	5.86138i	0.840724	+	0.225271i	0.653386	−	0.757025i	$-0.273348\pi$
$677$	21.8750	+	5.86138i	0.840724	+	0.225271i	0.187337	+	0.982296i	$0.440014\pi$
$678$		0			0
$679$	−42.6877	+	7.81394i	−1.63820	+	0.299871i
$680$		0			0
$681$	16.3505	−	9.43999i	0.626554	−	0.361741i
$682$		0			0
$683$	−9.86156	−	36.8038i	−0.377342	−	1.40826i	−0.849892	−	0.526956i	$-0.823333\pi$
$683$	−9.86156	−	36.8038i	−0.377342	−	1.40826i	0.472550	−	0.881304i	$-0.343334\pi$
$684$		0			0
$685$	−7.94275	−	7.94275i	−0.303477	−	0.303477i
$686$		0			0
$687$	32.2606			1.23082
$688$		0			0
$689$	2.76660	−	4.79189i	0.105399	−	0.182556i
$690$		0			0
$691$	−6.40271	+	23.8952i	−0.243571	+	0.909018i	0.730526	+	0.682885i	$0.239275\pi$
$691$	−6.40271	+	23.8952i	−0.243571	+	0.909018i	−0.974096	+	0.226133i	$0.927392\pi$
$692$		0			0
$693$	−8.25014	−	5.69711i	−0.313397	−	0.216415i
$694$		0			0
$695$	−15.4421	+	8.91547i	−0.585750	+	0.338183i
$696$		0			0
$697$	−7.51132	−	4.33666i	−0.284511	−	0.164263i
$698$		0			0
$699$	10.8752	−	10.8752i	0.411336	−	0.411336i
$700$		0			0
$701$	−10.6300	−	10.6300i	−0.401489	−	0.401489i	0.477269	−	0.878757i	$-0.341627\pi$
$701$	−10.6300	−	10.6300i	−0.401489	−	0.401489i	−0.878757	+	0.477269i	$0.841627\pi$
$702$		0			0
$703$	−0.387181	+	0.670617i	−0.0146028	+	0.0252928i
$704$		0			0
$705$	7.38785	+	12.7961i	0.278242	+	0.481930i
$706$		0			0
$707$	−10.4275	−	21.9870i	−0.392168	−	0.826905i
$708$		0			0
$709$	3.42184	+	0.916878i	0.128510	+	0.0344341i	0.322501	−	0.946569i	$-0.395477\pi$
$709$	3.42184	+	0.916878i	0.128510	+	0.0344341i	−0.193991	+	0.981003i	$0.562143\pi$
$710$		0			0
$711$	−1.15994	−	0.669691i	−0.0435011	−	0.0251154i
$712$		0			0
$713$		−	16.5398i		−	0.619422i
$714$		0			0
$715$	−6.62251	+	6.62251i	−0.247668	+	0.247668i
$716$		0			0
$717$	17.4436	−	4.67400i	0.651444	−	0.174554i
$718$		0			0
$719$	8.10598	+	14.0400i	0.302302	+	0.523603i	0.976657	−	0.214805i	$-0.0689115\pi$
$719$	8.10598	+	14.0400i	0.302302	+	0.523603i	−0.674355	+	0.738407i	$0.735578\pi$
$720$		0			0
$721$	15.5817	−	13.2484i	0.580292	−	0.493397i
$722$		0			0
$723$	6.18582	−	23.0858i	0.230053	−	0.858569i
$724$		0			0
$725$	7.34051	+	27.3952i	0.272620	+	1.01743i
$726$		0			0
$727$			14.2822i			0.529699i	0.964290	+	0.264849i	$0.0853223\pi$
$727$			14.2822i			0.529699i	−0.964290	+	0.264849i	$0.914678\pi$
$728$		0			0
$729$		−	22.9031i		−	0.848263i
$730$		0			0
$731$	1.66954	+	6.23082i	0.0617503	+	0.230455i
$732$		0			0
$733$	−8.91206	+	33.2603i	−0.329175	+	1.22850i	0.580874	+	0.813994i	$0.302711\pi$
$733$	−8.91206	+	33.2603i	−0.329175	+	1.22850i	−0.910048	+	0.414502i	$0.863956\pi$
$734$		0			0
$735$	−8.02025	+	3.03799i	−0.295831	+	0.112058i
$736$		0			0
$737$	−4.30162	−	7.45062i	−0.158452	−	0.274447i
$738$		0			0
$739$	−20.1534	+	5.40009i	−0.741356	+	0.198646i	−0.609681	−	0.792647i	$-0.708702\pi$
$739$	−20.1534	+	5.40009i	−0.741356	+	0.198646i	−0.131675	+	0.991293i	$0.542036\pi$
$740$		0			0
$741$	0.310906	−	0.310906i	0.0114214	−	0.0114214i
$742$		0			0
$743$		−	30.1201i		−	1.10500i	−0.833513	−	0.552500i	$-0.813674\pi$
$743$		−	30.1201i		−	1.10500i	0.833513	−	0.552500i	$-0.186326\pi$
$744$		0			0
$745$	−4.60854	−	2.66074i	−0.168844	−	0.0974820i
$746$		0			0
$747$	−11.4842	−	3.07719i	−0.420186	−	0.112588i
$748$		0			0
$749$	49.8403	+	4.03362i	1.82112	+	0.147385i
$750$		0			0
$751$	22.6093	+	39.1605i	0.825026	+	1.42899i	0.901900	+	0.431946i	$0.142173\pi$
$751$	22.6093	+	39.1605i	0.825026	+	1.42899i	−0.0768741	+	0.997041i	$0.524494\pi$
$752$		0			0
$753$	7.88217	−	13.6523i	0.287242	−	0.497518i
$754$		0			0
$755$	−0.979047	−	0.979047i	−0.0356312	−	0.0356312i
$756$		0			0
$757$	−10.1353	+	10.1353i	−0.368375	+	0.368375i	−0.866884	−	0.498509i	$-0.833881\pi$
$757$	−10.1353	+	10.1353i	−0.368375	+	0.368375i	0.498509	+	0.866884i	$0.333881\pi$
$758$		0			0
$759$	−4.95030	−	2.85806i	−0.179684	−	0.103741i
$760$		0			0
$761$	−17.0843	+	9.86363i	−0.619306	+	0.357556i	−0.776599	−	0.629996i	$-0.783057\pi$
$761$	−17.0843	+	9.86363i	−0.619306	+	0.357556i	0.157293	+	0.987552i	$0.449723\pi$
$762$		0			0
$763$	−39.1092	+	18.5479i	−1.41585	+	0.671480i
$764$		0			0
$765$	0.413374	−	1.54273i	0.0149456	−	0.0557776i
$766$		0			0
$767$	13.5451	−	23.4607i	0.489084	−	0.847118i
$768$		0			0
$769$	−41.2736			−1.48837			−0.744183	−	0.667976i	$-0.767161\pi$
$769$	−41.2736			−1.48837			−0.744183	+	0.667976i	$0.767161\pi$
$770$		0			0
$771$	19.8101	+	19.8101i	0.713444	+	0.713444i
$772$		0			0
$773$	−13.8201	−	51.5773i	−0.497074	−	1.85511i	−0.518090	−	0.855326i	$-0.673357\pi$
$773$	−13.8201	−	51.5773i	−0.497074	−	1.85511i	0.0210159	−	0.999779i	$-0.493310\pi$
$774$		0			0
$775$	29.4375	−	16.9958i	1.05743	−	0.610506i
$776$		0			0
$777$	−25.0754	+	4.59003i	−0.899577	+	0.164666i
$778$		0			0
$779$	0.797746	+	0.213755i	0.0285822	+	0.00765858i
$780$		0			0
$781$	12.8718	−	3.44899i	0.460590	−	0.123415i
$782$		0			0
$783$	−39.1812			−1.40022
$784$		0			0
$785$	0.322740			0.0115191
$786$		0			0
$787$	−0.494375	+	0.132467i	−0.0176226	+	0.00472196i	−0.267620	−	0.963525i	$-0.586237\pi$
$787$	−0.494375	+	0.132467i	−0.0176226	+	0.00472196i	0.249997	+	0.968247i	$0.419570\pi$
$788$		0			0
$789$	−5.26743	−	1.41140i	−0.187526	−	0.0502473i
$790$		0			0
$791$	52.3499	−	9.58259i	1.86135	−	0.340718i
$792$		0			0
$793$	14.9176	−	8.61266i	0.529739	−	0.305845i
$794$		0			0
$795$	−0.466799	−	1.74212i	−0.0165556	−	0.0617865i
$796$		0			0
$797$	35.5605	+	35.5605i	1.25962	+	1.25962i	0.951276	+	0.308341i	$0.0997736\pi$
$797$	35.5605	+	35.5605i	1.25962	+	1.25962i	0.308341	+	0.951276i	$0.400226\pi$
$798$		0			0
$799$	12.2801			0.434438
$800$		0			0
$801$	−3.50586	+	6.07232i	−0.123873	+	0.214555i
$802$		0			0
$803$	5.38433	−	20.0946i	0.190009	−	0.709123i
$804$		0			0
$805$	4.68813	−	2.22339i	0.165235	−	0.0783641i
$806$		0			0
$807$	0.416833	−	0.240659i	0.0146732	−	0.00847158i
$808$		0			0
$809$	−1.17802	−	0.680131i	−0.0414170	−	0.0239121i	0.479149	−	0.877734i	$-0.340946\pi$
$809$	−1.17802	−	0.680131i	−0.0414170	−	0.0239121i	−0.520566	+	0.853822i	$0.674279\pi$
$810$		0			0
$811$	−12.4370	+	12.4370i	−0.436722	+	0.436722i	−0.890907	−	0.454186i	$-0.849930\pi$
$811$	−12.4370	+	12.4370i	−0.436722	+	0.436722i	0.454186	+	0.890907i	$0.349930\pi$
$812$		0			0
$813$	−9.06114	−	9.06114i	−0.317788	−	0.317788i
$814$		0			0
$815$	7.53706	−	13.0546i	0.264012	−	0.457282i
$816$		0			0
$817$	−0.307119	−	0.531945i	−0.0107447	−	0.0186104i
$818$		0			0
$819$	−15.3098	−	1.23903i	−0.534967	−	0.0432953i
$820$		0			0
$821$	5.33567	+	1.42969i	0.186216	+	0.0498965i	0.350722	−	0.936480i	$-0.385936\pi$
$821$	5.33567	+	1.42969i	0.186216	+	0.0498965i	−0.164506	+	0.986376i	$0.552603\pi$
$822$		0			0
$823$	−16.5082	−	9.53100i	−0.575439	−	0.332230i	0.183880	−	0.982949i	$-0.441134\pi$
$823$	−16.5082	−	9.53100i	−0.575439	−	0.332230i	−0.759319	+	0.650719i	$0.774468\pi$
$824$		0			0
$825$		−	11.7474i		−	0.408991i
$826$		0			0
$827$	−3.94521	+	3.94521i	−0.137188	+	0.137188i	−0.772366	−	0.635178i	$-0.780927\pi$
$827$	−3.94521	+	3.94521i	−0.137188	+	0.137188i	0.635178	+	0.772366i	$0.280927\pi$
$828$		0			0
$829$	25.9036	−	6.94085i	0.899669	−	0.241066i	0.220795	−	0.975320i	$-0.429135\pi$
$829$	25.9036	−	6.94085i	0.899669	−	0.241066i	0.678874	+	0.734255i	$0.262468\pi$
$830$		0			0
$831$	6.94562	+	12.0302i	0.240941	+	0.417322i
$832$		0			0
$833$	−1.14621	+	7.03503i	−0.0397138	+	0.243749i
$834$		0			0
$835$	3.83713	−	14.3203i	0.132789	−	0.495576i
$836$		0			0
$837$	12.1539	+	45.3588i	0.420099	+	1.56783i
$838$		0			0
$839$		−	5.34140i		−	0.184406i	−0.995740	−	0.0922028i	$-0.970609\pi$
$839$		−	5.34140i		−	0.184406i	0.995740	−	0.0922028i	$-0.0293908\pi$
$840$		0			0
$841$			22.0706i			0.761056i
$842$		0			0
$843$	5.81908	+	21.7171i	0.200420	+	0.747976i
$844$		0			0
$845$	−0.296598	+	1.10692i	−0.0102033	+	0.0380791i
$846$		0			0
$847$	−10.0383	+	8.53515i	−0.344921	+	0.293271i
$848$		0			0
$849$	5.48222	+	9.49549i	0.188149	+	0.325884i
$850$		0			0
$851$	14.8971	−	3.99165i	0.510664	−	0.136832i
$852$		0			0
$853$	1.42841	−	1.42841i	0.0489078	−	0.0489078i	−0.682230	−	0.731138i	$-0.738990\pi$
$853$	1.42841	−	1.42841i	0.0489078	−	0.0489078i	0.731138	+	0.682230i	$0.238990\pi$
$854$		0			0
$855$			0.152084i			0.00520115i
$856$		0			0
$857$	−22.1543	−	12.7908i	−0.756778	−	0.436926i	0.0713599	−	0.997451i	$-0.477266\pi$
$857$	−22.1543	−	12.7908i	−0.756778	−	0.436926i	−0.828138	+	0.560525i	$0.810599\pi$
$858$		0			0
$859$	−44.0264	−	11.7968i	−1.50216	−	0.402503i	−0.588337	−	0.808616i	$-0.700217\pi$
$859$	−44.0264	−	11.7968i	−1.50216	−	0.402503i	−0.913823	+	0.406113i	$0.866884\pi$
$860$		0			0
$861$	11.6505	+	24.5656i	0.397047	+	0.837194i
$862$		0			0
$863$	19.7223	+	34.1601i	0.671356	+	1.16282i	0.977520	+	0.210843i	$0.0676210\pi$
$863$	19.7223	+	34.1601i	0.671356	+	1.16282i	−0.306164	+	0.951979i	$0.599046\pi$
$864$		0			0
$865$	−6.27135	+	10.8623i	−0.213232	+	0.369329i
$866$		0			0
$867$	−13.6178	−	13.6178i	−0.462486	−	0.462486i
$868$		0			0
$869$	1.50449	−	1.50449i	0.0510364	−	0.0510364i
$870$		0			0
$871$	−11.4143	−	6.59004i	−0.386758	−	0.223295i
$872$		0			0
$873$	−21.9398	+	12.6669i	−0.742548	+	0.428710i
$874$		0			0
$875$	19.8293	+	13.6931i	0.670353	+	0.462910i
$876$		0			0
$877$	−2.72833	+	10.1823i	−0.0921292	+	0.343831i	−0.996569	−	0.0827714i	$-0.973623\pi$
$877$	−2.72833	+	10.1823i	−0.0921292	+	0.343831i	0.904439	+	0.426602i	$0.140290\pi$
$878$		0			0
$879$	10.2534	−	17.7594i	0.345839	−	0.599011i
$880$		0			0
$881$	−15.4426			−0.520274			−0.260137	−	0.965572i	$-0.583768\pi$
$881$	−15.4426			−0.520274			−0.260137	+	0.965572i	$0.583768\pi$
$882$		0			0
$883$	−10.0224	−	10.0224i	−0.337280	−	0.337280i	0.518063	−	0.855343i	$-0.326653\pi$
$883$	−10.0224	−	10.0224i	−0.337280	−	0.337280i	−0.855343	+	0.518063i	$0.826653\pi$
$884$		0			0
$885$	−2.28541	−	8.52927i	−0.0768233	−	0.286708i
$886$		0			0
$887$	37.9027	−	21.8831i	1.27265	−	0.734763i	0.297162	−	0.954827i	$-0.403960\pi$
$887$	37.9027	−	21.8831i	1.27265	−	0.734763i	0.975485	+	0.220064i	$0.0706267\pi$
$888$		0			0
$889$	−2.57362	+	0.471099i	−0.0863166	+	0.0158001i
$890$		0			0
$891$	4.69474	+	1.25795i	0.157280	+	0.0421430i
$892$		0			0
$893$	−1.12948	+	0.302644i	−0.0377967	+	0.0101276i
$894$		0			0
$895$	−0.479024			−0.0160120
$896$		0			0
$897$	−8.75703			−0.292389
$898$		0			0
$899$	59.1229	−	15.8419i	1.97186	−	0.528358i
$900$		0			0
$901$	−1.44787	−	0.387956i	−0.0482356	−	0.0129247i
$902$		0			0
$903$	6.79204	−	19.0460i	0.226025	−	0.633810i
$904$		0			0
$905$	19.2356	−	11.1057i	0.639413	−	0.369165i
$906$		0			0
$907$	12.5599	+	46.8743i	0.417045	+	1.55643i	0.780703	+	0.624902i	$0.214861\pi$
$907$	12.5599	+	46.8743i	0.417045	+	1.55643i	−0.363658	+	0.931533i	$0.618472\pi$
$908$		0			0
$909$	−10.0449	−	10.0449i	−0.333169	−	0.333169i
$910$		0			0
$911$	35.2525			1.16797			0.583983	−	0.811766i	$-0.301493\pi$
$911$	35.2525			1.16797			0.583983	+	0.811766i	$0.301493\pi$
$912$		0			0
$913$	9.44340	−	16.3564i	0.312531	−	0.541319i
$914$		0			0
$915$	1.45319	−	5.42336i	0.0480409	−	0.179291i
$916$		0			0
$917$	−1.68120	+	20.7733i	−0.0555181	+	0.685994i
$918$		0			0
$919$	22.1228	−	12.7726i	0.729763	−	0.421329i	−0.0885726	−	0.996070i	$-0.528231\pi$
$919$	22.1228	−	12.7726i	0.729763	−	0.421329i	0.818335	+	0.574741i	$0.194897\pi$
$920$		0			0
$921$	26.3510	+	15.2138i	0.868295	+	0.501310i
$922$		0			0
$923$	14.4357	−	14.4357i	0.475156	−	0.475156i
$924$		0			0
$925$	22.4120	+	22.4120i	0.736903	+	0.736903i
$926$		0			0
$927$	5.96981	−	10.3400i	0.196074	−	0.339610i
$928$		0			0
$929$	−1.98515	−	3.43838i	−0.0651306	−	0.112810i	0.831621	−	0.555343i	$-0.187413\pi$
$929$	−1.98515	−	3.43838i	−0.0651306	−	0.112810i	−0.896752	+	0.442534i	$0.854080\pi$
$930$		0			0
$931$	−0.0679545	−	0.675309i	−0.00222712	−	0.0221324i
$932$		0			0
$933$	−7.62660	−	2.04354i	−0.249684	−	0.0669025i
$934$		0			0
$935$	2.19724	+	1.26858i	0.0718576	+	0.0414870i
$936$		0			0
$937$		−	18.3326i		−	0.598899i	−0.954112	−	0.299450i	$-0.903197\pi$
$937$		−	18.3326i		−	0.598899i	0.954112	−	0.299450i	$-0.0968031\pi$
$938$		0			0
$939$	−16.3565	+	16.3565i	−0.533773	+	0.533773i
$940$		0			0
$941$	−28.7932	+	7.71512i	−0.938632	+	0.251506i	−0.695531	−	0.718496i	$-0.744831\pi$
$941$	−28.7932	+	7.71512i	−0.938632	+	0.251506i	−0.243100	+	0.970001i	$0.578164\pi$
$942$		0			0
$943$	−8.22438	−	14.2451i	−0.267823	−	0.463883i
$944$		0			0
$945$	−11.2229	+	9.54236i	−0.365081	+	0.310413i
$946$		0			0
$947$	−7.28394	+	27.1840i	−0.236696	+	0.883362i	0.740681	+	0.671857i	$0.234503\pi$
$947$	−7.28394	+	27.1840i	−0.236696	+	0.883362i	−0.977377	+	0.211505i	$0.932163\pi$
$948$		0			0
$949$	−8.24874	−	30.7847i	−0.267765	−	0.999314i
$950$		0			0
$951$			22.7060i			0.736291i
$952$		0			0
$953$			9.54510i			0.309196i	0.987977	+	0.154598i	$0.0494083\pi$
$953$			9.54510i			0.309196i	−0.987977	+	0.154598i	$0.950592\pi$
$954$		0			0
$955$	1.59865	+	5.96625i	0.0517311	+	0.193063i
$956$		0			0
$957$	5.47492	−	20.4327i	0.176979	−	0.660495i
$958$		0			0
$959$	27.5639	+	9.82964i	0.890084	+	0.317416i
$960$		0			0
$961$	−21.1794	−	36.6839i	−0.683208	−	1.18335i
$962$		0			0
$963$	28.1957	−	7.55502i	0.908595	−	0.243457i
$964$		0			0
$965$	−7.22535	+	7.22535i	−0.232592	+	0.232592i
$966$		0			0
$967$			54.0255i			1.73734i	0.495388	+	0.868672i	$0.335026\pi$
$967$			54.0255i			1.73734i	−0.495388	+	0.868672i	$0.664974\pi$
$968$		0			0
$969$	−0.103154	−	0.0595558i	−0.00331377	−	0.00191321i
$970$		0			0
$971$	5.75433	+	1.54187i	0.184665	+	0.0494809i	0.349966	−	0.936762i	$-0.386193\pi$
$971$	5.75433	+	1.54187i	0.184665	+	0.0494809i	−0.165301	+	0.986243i	$0.552860\pi$
$972$		0			0
$973$	26.3966	−	38.2257i	0.846237	−	1.22546i
$974$		0			0
$975$	−8.99842	−	15.5857i	−0.288180	−	0.499143i
$976$		0			0
$977$	14.6499	−	25.3743i	0.468690	−	0.811795i	−0.530669	−	0.847579i	$-0.678059\pi$
$977$	14.6499	−	25.3743i	0.468690	−	0.811795i	0.999360	+	0.0357835i	$0.0113927\pi$
$978$		0			0
$979$	−7.87607	−	7.87607i	−0.251720	−	0.251720i
$980$		0			0
$981$	−17.8673	+	17.8673i	−0.570460	+	0.570460i
$982$		0			0
$983$	−13.8442	−	7.99296i	−0.441562	−	0.254936i	0.262698	−	0.964878i	$-0.415388\pi$
$983$	−13.8442	−	7.99296i	−0.441562	−	0.254936i	−0.704260	+	0.709942i	$0.748721\pi$
$984$		0			0
$985$	−12.5419	+	7.24108i	−0.399619	+	0.230720i
$986$		0			0
$987$	−31.6759	−	21.8737i	−1.00825	−	0.696247i
$988$		0			0
$989$	−3.16625	+	11.8166i	−0.100681	+	0.375746i
$990$		0			0
$991$	10.3826	−	17.9832i	0.329814	−	0.571255i	−0.652661	−	0.757650i	$-0.726347\pi$
$991$	10.3826	−	17.9832i	0.329814	−	0.571255i	0.982475	+	0.186396i	$0.0596806\pi$
$992$		0			0
$993$	−11.8153			−0.374948
$994$		0			0
$995$	−8.37312	−	8.37312i	−0.265446	−	0.265446i
$996$		0			0
$997$	12.8681	+	48.0242i	0.407535	+	1.52094i	0.799331	+	0.600890i	$0.205187\pi$
$997$	12.8681	+	48.0242i	0.407535	+	1.52094i	−0.391796	+	0.920052i	$0.628146\pi$
$998$		0			0
$999$	−37.9205	+	21.8934i	−1.19975	+	0.692677i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.2.ba.c.81.4		48
4.3	odd	2		112.2.w.c.109.5	yes	48
7.2	even	3	inner	448.2.ba.c.401.9		48
8.3	odd	2		896.2.ba.f.417.4		48
8.5	even	2		896.2.ba.e.417.9		48
16.3	odd	4		896.2.ba.f.865.9		48
16.5	even	4	inner	448.2.ba.c.305.9		48
16.11	odd	4		112.2.w.c.53.12	yes	48
16.13	even	4		896.2.ba.e.865.4		48
28.3	even	6		784.2.m.k.589.5		24
28.11	odd	6		784.2.m.j.589.5		24
28.19	even	6		784.2.x.o.765.12		48
28.23	odd	6		112.2.w.c.93.12	yes	48
28.27	even	2		784.2.x.o.557.5		48
56.37	even	6		896.2.ba.e.289.4		48
56.51	odd	6		896.2.ba.f.289.9		48
112.11	odd	12		784.2.m.j.197.5		24
112.27	even	4		784.2.x.o.165.12		48
112.37	even	12	inner	448.2.ba.c.177.4		48
112.51	odd	12		896.2.ba.f.737.4		48
112.59	even	12		784.2.m.k.197.5		24
112.75	even	12		784.2.x.o.373.5		48
112.93	even	12		896.2.ba.e.737.9		48
112.107	odd	12		112.2.w.c.37.5	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.5	✓	48	112.107	odd	12
112.2.w.c.53.12	yes	48	16.11	odd	4
112.2.w.c.93.12	yes	48	28.23	odd	6
112.2.w.c.109.5	yes	48	4.3	odd	2
448.2.ba.c.81.4		48	1.1	even	1	trivial
448.2.ba.c.177.4		48	112.37	even	12	inner
448.2.ba.c.305.9		48	16.5	even	4	inner
448.2.ba.c.401.9		48	7.2	even	3	inner
784.2.m.j.197.5		24	112.11	odd	12
784.2.m.j.589.5		24	28.11	odd	6
784.2.m.k.197.5		24	112.59	even	12
784.2.m.k.589.5		24	28.3	even	6
784.2.x.o.165.12		48	112.27	even	4
784.2.x.o.373.5		48	112.75	even	12
784.2.x.o.557.5		48	28.27	even	2
784.2.x.o.765.12		48	28.19	even	6
896.2.ba.e.289.4		48	56.37	even	6
896.2.ba.e.417.9		48	8.5	even	2
896.2.ba.e.737.9		48	112.93	even	12
896.2.ba.e.865.4		48	16.13	even	4
896.2.ba.f.289.9		48	56.51	odd	6
896.2.ba.f.417.4		48	8.3	odd	2
896.2.ba.f.737.4		48	112.51	odd	12
896.2.ba.f.865.9		48	16.3	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.ba (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.16533 + 0.312249i) q^{3} +(0.980942 + 0.262843i) q^{5} +(-2.60251 + 0.476386i) q^{7} +(-1.33758 + 0.772254i) q^{9} +(-0.635020 - 2.36993i) q^{11} +(-2.65786 - 2.65786i) q^{13} -1.22519 q^{15} +(-0.509128 + 0.881836i) q^{17} +(0.0250951 - 0.0936561i) q^{19} +(2.88403 - 1.36778i) q^{21} +(-1.67238 + 0.965551i) q^{23} +(-3.43697 - 1.98433i) q^{25} +(3.87683 - 3.87683i) q^{27} +(-5.05325 - 5.05325i) q^{29} +(-4.28249 + 7.41749i) q^{31} +(1.48001 + 2.56346i) q^{33} +(-2.67813 - 0.216743i) q^{35} +(-7.71428 - 2.06704i) q^{37} +(3.92719 + 2.26737i) q^{39} +8.51782i q^{41} +(4.47950 - 4.47950i) q^{43} +(-1.51507 + 0.405963i) q^{45} +(-6.02995 - 10.4442i) q^{47} +(6.54611 - 2.47960i) q^{49} +(0.317949 - 1.18660i) q^{51} +(0.381000 + 1.42191i) q^{53} -2.49167i q^{55} +0.116976i q^{57} +(1.86535 + 6.96158i) q^{59} +(-1.18609 + 4.42654i) q^{61} +(3.11318 - 2.64701i) q^{63} +(-1.90861 - 3.30580i) q^{65} +(3.38700 - 0.907543i) q^{67} +(1.64738 - 1.64738i) q^{69} +5.43131i q^{71} +(7.34303 + 4.23950i) q^{73} +(4.62480 + 1.23921i) q^{75} +(2.78165 + 5.86524i) q^{77} +(0.433595 + 0.751008i) q^{79} +(-0.990483 + 1.71557i) q^{81} +(5.44318 + 5.44318i) q^{83} +(-0.731209 + 0.731209i) q^{85} +(7.46657 + 4.31083i) q^{87} +(3.93155 - 2.26988i) q^{89} +(8.18327 + 5.65093i) q^{91} +(2.67441 - 9.98102i) q^{93} +(0.0492336 - 0.0852752i) q^{95} +16.4025 q^{97} +(2.67958 + 2.67958i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{5} + 4 q^{11} - 24 q^{13} + 40 q^{15} + 8 q^{17} + 4 q^{19} - 8 q^{21} + 24 q^{27} + 24 q^{29} - 28 q^{31} + 16 q^{33} - 28 q^{35} - 24 q^{37} + 40 q^{43} - 28 q^{45} + 20 q^{47} - 24 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) \) 48 * q + 4 * q^5 + 4 * q^11 - 24 * q^13 + 40 * q^15 + 8 * q^17 + 4 * q^19 - 8 * q^21 + 24 * q^27 + 24 * q^29 - 28 * q^31 + 16 * q^33 - 28 * q^35 - 24 * q^37 + 40 * q^43 - 28 * q^45 + 20 * q^47 - 24 * q^51 - 16 * q^53 + 20 * q^59 + 8 * q^61 + 16 * q^63 + 8 * q^65 - 48 * q^67 - 40 * q^69 + 4 * q^75 - 20 * q^77 + 36 * q^79 + 8 * q^83 - 64 * q^91 + 8 * q^93 + 4 * q^95 - 48 * q^97 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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