LMFDB - Embedded newform 315.2.ce.a.233.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [315,2,Mod(53,315)] 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("315.53"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(315, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.ce (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			233.10
Character	$\chi$	$=$	315.233
Dual form			315.2.ce.a.242.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.370100 - 0.0991680i) q^{2} +(-1.60491 + 0.926596i) q^{4} +(0.266643 - 2.22011i) q^{5} +(-1.13202 - 2.39134i) q^{7} +(-1.04395 + 1.04395i) q^{8} +(-0.121480 - 0.848106i) q^{10} +(3.48588 - 2.01257i) q^{11} +(-2.94019 - 2.94019i) q^{13} +(-0.656107 - 0.772776i) q^{14} +(1.57035 - 2.71993i) q^{16} +(0.510805 - 1.90635i) q^{17} +(-3.06607 - 1.77020i) q^{19} +(1.62921 + 3.81015i) q^{20} +(1.09054 - 1.09054i) q^{22} +(0.467117 + 1.74330i) q^{23} +(-4.85780 - 1.18396i) q^{25} +(-1.37974 - 0.796592i) q^{26} +(4.03261 + 2.78897i) q^{28} +7.33557 q^{29} +(1.20124 + 2.08061i) q^{31} +(1.07568 - 4.01451i) q^{32} -0.756196i q^{34} +(-5.61090 + 1.87558i) q^{35} +(2.22373 + 8.29907i) q^{37} +(-1.31030 - 0.351094i) q^{38} +(2.03933 + 2.59606i) q^{40} -5.20836i q^{41} +(-1.29106 - 1.29106i) q^{43} +(-3.72969 + 6.46001i) q^{44} +(0.345760 + 0.598874i) q^{46} +(-1.06806 + 0.286186i) q^{47} +(-4.43705 + 5.41411i) q^{49} +(-1.91528 + 0.0435568i) q^{50} +(7.44311 + 1.99437i) q^{52} +(-10.7964 - 2.89287i) q^{53} +(-3.53866 - 8.27569i) q^{55} +(3.67823 + 1.31467i) q^{56} +(2.71489 - 0.727454i) q^{58} +(7.20215 + 12.4745i) q^{59} +(-2.48813 + 4.30957i) q^{61} +(0.650911 + 0.650911i) q^{62} +4.68896i q^{64} +(-7.31153 + 5.74357i) q^{65} +(5.94931 + 1.59411i) q^{67} +(0.946620 + 3.53283i) q^{68} +(-1.89060 + 1.25058i) q^{70} +1.99948i q^{71} +(3.35751 - 12.5304i) q^{73} +(1.64601 + 2.85096i) q^{74} +6.56103 q^{76} +(-8.75886 - 6.05766i) q^{77} +(12.9543 + 7.47918i) q^{79} +(-5.61982 - 4.21161i) q^{80} +(-0.516502 - 1.92761i) q^{82} +(11.2724 - 11.2724i) q^{83} +(-4.09611 - 1.64236i) q^{85} +(-0.605851 - 0.349788i) q^{86} +(-1.53806 + 5.74013i) q^{88} +(4.22341 - 7.31516i) q^{89} +(-3.70264 + 10.3594i) q^{91} +(-2.36502 - 2.36502i) q^{92} +(-0.366909 + 0.211835i) q^{94} +(-4.74759 + 6.33502i) q^{95} +(4.46118 - 4.46118i) q^{97} +(-1.10525 + 2.44378i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{7} + 8 q^{10} + 32 q^{16} - 48 q^{22} - 16 q^{25} + 88 q^{28} + 32 q^{31} - 16 q^{37} - 40 q^{40} - 16 q^{43} - 80 q^{52} - 32 q^{55} - 88 q^{58} + 48 q^{61} - 32 q^{67} - 112 q^{70} - 88 q^{73}+ \cdots + 208 q^{97}+O(q^{100}) $ 64 * q + 8 * q^7 + 8 * q^10 + 32 * q^16 - 48 * q^22 - 16 * q^25 + 88 * q^28 + 32 * q^31 - 16 * q^37 - 40 * q^40 - 16 * q^43 - 80 * q^52 - 32 * q^55 - 88 * q^58 + 48 * q^61 - 32 * q^67 - 112 * q^70 - 88 * q^73 - 320 * q^76 - 56 * q^82 + 16 * q^85 + 120 * q^88 - 128 * q^91 + 208 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	0.370100	−	0.0991680i	0.261700	−	0.0701224i	−0.125583	−	0.992083i	$-0.540080\pi$
$2$	0.370100	−	0.0991680i	0.261700	−	0.0701224i	0.387283	+	0.921961i	$0.373414\pi$
$3$		0			0
$3$		0			0
$4$	−1.60491	+	0.926596i	−0.802456	+	0.463298i
$5$	0.266643	−	2.22011i	0.119246	−	0.992865i
$5$	0.266643	−	2.22011i	0.119246	−	0.992865i
$6$		0			0
$7$	−1.13202	−	2.39134i	−0.427864	−	0.903843i
$7$	−1.13202	−	2.39134i	−0.427864	−	0.903843i
$8$	−1.04395	+	1.04395i	−0.369093	+	0.369093i
$9$		0			0
$10$	−0.121480	−	0.848106i	−0.0384152	−	0.268195i
$11$	3.48588	−	2.01257i	1.05103	−	0.606814i	0.128095	−	0.991762i	$-0.459114\pi$
$11$	3.48588	−	2.01257i	1.05103	−	0.606814i	0.922938	+	0.384948i	$0.125781\pi$
$12$		0			0
$13$	−2.94019	−	2.94019i	−0.815462	−	0.815462i	0.169985	−	0.985447i	$-0.445628\pi$
$13$	−2.94019	−	2.94019i	−0.815462	−	0.815462i	−0.985447	+	0.169985i	$0.945628\pi$
$14$	−0.656107	−	0.772776i	−0.175352	−	0.206533i
$15$		0			0
$16$	1.57035	−	2.71993i	0.392588	−	0.679982i
$17$	0.510805	−	1.90635i	0.123888	−	0.462358i	−0.875909	−	0.482476i	$-0.839738\pi$
$17$	0.510805	−	1.90635i	0.123888	−	0.462358i	0.999798	+	0.0201182i	$0.00640424\pi$
$18$		0			0
$19$	−3.06607	−	1.77020i	−0.703406	−	0.406111i	0.105209	−	0.994450i	$-0.466449\pi$
$19$	−3.06607	−	1.77020i	−0.703406	−	0.406111i	−0.808615	+	0.588339i	$0.799782\pi$
$20$	1.62921	+	3.81015i	0.364302	+	0.851976i
$21$		0			0
$22$	1.09054	−	1.09054i	0.232504	−	0.232504i
$23$	0.467117	+	1.74330i	0.0974006	+	0.363504i	0.997372	−	0.0724439i	$-0.0230798\pi$
$23$	0.467117	+	1.74330i	0.0974006	+	0.363504i	−0.899972	+	0.435948i	$0.856413\pi$
$24$		0			0
$25$	−4.85780	−	1.18396i	−0.971561	−	0.236791i
$26$	−1.37974	−	0.796592i	−0.270589	−	0.156224i
$27$		0			0
$28$	4.03261	+	2.78897i	0.762091	+	0.527065i
$29$	7.33557			1.36218			0.681090	−	0.732199i	$-0.261506\pi$
$29$	7.33557			1.36218			0.681090	+	0.732199i	$0.261506\pi$
$30$		0			0
$31$	1.20124	+	2.08061i	0.215750	+	0.373689i	0.953504	−	0.301380i	$-0.0974472\pi$
$31$	1.20124	+	2.08061i	0.215750	+	0.373689i	−0.737755	+	0.675069i	$0.764114\pi$
$32$	1.07568	−	4.01451i	0.190156	−	0.709671i
$33$		0			0
$34$		−	0.756196i		−	0.129687i
$35$	−5.61090	+	1.87558i	−0.948415	+	0.317032i
$36$		0			0
$37$	2.22373	+	8.29907i	0.365579	+	1.36436i	0.866634	+	0.498944i	$0.166279\pi$
$37$	2.22373	+	8.29907i	0.365579	+	1.36436i	−0.501055	+	0.865415i	$0.667055\pi$
$38$	−1.31030	−	0.351094i	−0.212559	−	0.0569550i
$39$		0			0
$40$	2.03933	+	2.59606i	0.322447	+	0.410473i
$41$		−	5.20836i		−	0.813408i	−0.913560	−	0.406704i	$-0.866678\pi$
$41$		−	5.20836i		−	0.813408i	0.913560	−	0.406704i	$-0.133322\pi$
$42$		0			0
$43$	−1.29106	−	1.29106i	−0.196884	−	0.196884i	0.601779	−	0.798663i	$-0.294459\pi$
$43$	−1.29106	−	1.29106i	−0.196884	−	0.196884i	−0.798663	+	0.601779i	$0.794459\pi$
$44$	−3.72969	+	6.46001i	−0.562271	+	0.973883i
$45$		0			0
$46$	0.345760	+	0.598874i	0.0509795	+	0.0882991i
$47$	−1.06806	+	0.286186i	−0.155793	+	0.0417445i	−0.335872	−	0.941907i	$-0.609031\pi$
$47$	−1.06806	+	0.286186i	−0.155793	+	0.0417445i	0.180080	+	0.983652i	$0.442364\pi$
$48$		0			0
$49$	−4.43705	+	5.41411i	−0.633864	+	0.773445i
$50$	−1.91528	+	0.0435568i	−0.270862	+	0.00615987i
$51$		0			0
$52$	7.44311	+	1.99437i	1.03217	+	0.276570i
$53$	−10.7964	−	2.89287i	−1.48299	−	0.397367i	−0.575628	−	0.817711i	$-0.695242\pi$
$53$	−10.7964	−	2.89287i	−1.48299	−	0.397367i	−0.907364	+	0.420345i	$0.861909\pi$
$54$		0			0
$55$	−3.53866	−	8.27569i	−0.477152	−	1.11589i
$56$	3.67823	+	1.31467i	0.491524	+	0.175680i
$57$		0			0
$58$	2.71489	−	0.727454i	0.356483	−	0.0955193i
$59$	7.20215	+	12.4745i	0.937640	+	1.62404i	0.769858	+	0.638215i	$0.220327\pi$
$59$	7.20215	+	12.4745i	0.937640	+	1.62404i	0.167782	+	0.985824i	$0.446340\pi$
$60$		0			0
$61$	−2.48813	+	4.30957i	−0.318572	+	0.551783i	−0.980190	−	0.198058i	$-0.936537\pi$
$61$	−2.48813	+	4.30957i	−0.318572	+	0.551783i	0.661618	+	0.749841i	$0.269870\pi$
$62$	0.650911	+	0.650911i	0.0826657	+	0.0826657i
$63$		0			0
$64$			4.68896i			0.586120i
$65$	−7.31153	+	5.74357i	−0.906884	+	0.712402i
$66$		0			0
$67$	5.94931	+	1.59411i	0.726824	+	0.194752i	0.603214	−	0.797579i	$-0.293886\pi$
$67$	5.94931	+	1.59411i	0.726824	+	0.194752i	0.123609	+	0.992331i	$0.460553\pi$
$68$	0.946620	+	3.53283i	0.114794	+	0.428419i
$69$		0			0
$70$	−1.89060	+	1.25058i	−0.225969	+	0.149472i
$71$			1.99948i			0.237295i	0.992936	+	0.118647i	$0.0378558\pi$
$71$			1.99948i			0.237295i	−0.992936	+	0.118647i	$0.962144\pi$
$72$		0			0
$73$	3.35751	−	12.5304i	0.392966	−	1.46657i	−0.432250	−	0.901754i	$-0.642280\pi$
$73$	3.35751	−	12.5304i	0.392966	−	1.46657i	0.825217	−	0.564816i	$-0.191053\pi$
$74$	1.64601	+	2.85096i	0.191344	+	0.331418i
$75$		0			0
$76$	6.56103			0.752602
$77$	−8.75886	−	6.05766i	−0.998164	−	0.690334i
$78$		0			0
$79$	12.9543	+	7.47918i	1.45747	+	0.841474i	0.998887	−	0.0471753i	$-0.0150219\pi$
$79$	12.9543	+	7.47918i	1.45747	+	0.841474i	0.458588	+	0.888649i	$0.348355\pi$
$80$	−5.61982	−	4.21161i	−0.628315	−	0.470872i
$81$		0			0
$82$	−0.516502	−	1.92761i	−0.0570381	−	0.212869i
$83$	11.2724	−	11.2724i	1.23731	−	1.23731i	0.276212	−	0.961097i	$-0.410921\pi$
$83$	11.2724	−	11.2724i	1.23731	−	1.23731i	0.961097	−	0.276212i	$-0.0890792\pi$
$84$		0			0
$85$	−4.09611	−	1.64236i	−0.444286	−	0.178139i
$86$	−0.605851	−	0.349788i	−0.0653306	−	0.0377186i
$87$		0			0
$88$	−1.53806	+	5.74013i	−0.163958	+	0.611900i
$89$	4.22341	−	7.31516i	0.447680	−	0.775405i	−0.550554	−	0.834799i	$-0.685584\pi$
$89$	4.22341	−	7.31516i	0.447680	−	0.775405i	0.998235	+	0.0593942i	$0.0189169\pi$
$90$		0			0
$91$	−3.70264	+	10.3594i	−0.388142	+	1.08596i
$92$	−2.36502	−	2.36502i	−0.246570	−	0.246570i
$93$		0			0
$94$	−0.366909	+	0.211835i	−0.0378438	+	0.0218491i
$95$	−4.74759	+	6.33502i	−0.487092	+	0.649959i
$96$		0			0
$97$	4.46118	−	4.46118i	0.452964	−	0.452964i	−0.443373	−	0.896337i	$-0.646218\pi$
$97$	4.46118	−	4.46118i	0.452964	−	0.452964i	0.896337	+	0.443373i	$0.146218\pi$
$98$	−1.10525	+	2.44378i	−0.111647	+	0.246859i
$99$		0			0
$100$	8.89339	−	2.60108i	0.889339	−	0.260108i
$101$	8.98534	−	5.18769i	0.894074	−	0.516194i	0.0188014	−	0.999823i	$-0.494015\pi$
$101$	8.98534	−	5.18769i	0.894074	−	0.516194i	0.875273	+	0.483629i	$0.160682\pi$
$102$		0			0
$103$	−3.82430	+	1.02472i	−0.376819	+	0.100968i	−0.442257	−	0.896888i	$-0.645822\pi$
$103$	−3.82430	+	1.02472i	−0.376819	+	0.100968i	0.0654380	+	0.997857i	$0.479156\pi$
$104$	6.13884			0.601963
$105$		0			0
$106$	−4.28261			−0.415964
$107$	−1.69403	+	0.453913i	−0.163768	+	0.0438815i	−0.339771	−	0.940508i	$-0.610350\pi$
$107$	−1.69403	+	0.453913i	−0.163768	+	0.0438815i	0.176003	+	0.984390i	$0.443683\pi$
$108$		0			0
$109$	−12.9603	+	7.48264i	−1.24137	+	0.716707i	−0.969374	−	0.245591i	$-0.921018\pi$
$109$	−12.9603	+	7.48264i	−1.24137	+	0.716707i	−0.271999	+	0.962298i	$0.587685\pi$
$110$	−2.13034	−	2.71191i	−0.203120	−	0.258571i
$111$		0			0
$112$	−8.28196	−	0.676228i	−0.782571	−	0.0638975i
$113$	−1.92868	+	1.92868i	−0.181435	+	0.181435i	−0.791981	−	0.610546i	$-0.790950\pi$
$113$	−1.92868	+	1.92868i	−0.181435	+	0.181435i	0.610546	+	0.791981i	$0.290950\pi$
$114$		0			0
$115$	3.99489	−	0.572213i	0.372525	−	0.0533591i
$116$	−11.7729	+	6.79711i	−1.09309	+	0.631095i
$117$		0			0
$118$	3.90259	+	3.90259i	0.359262	+	0.359262i
$119$	−5.13698	+	0.936522i	−0.470906	+	0.0858508i
$120$		0			0
$121$	2.60091	−	4.50492i	0.236447	−	0.409538i
$122$	−0.493486	+	1.84171i	−0.0446781	+	0.166741i
$123$		0			0
$124$	−3.85578	−	2.22613i	−0.346259	−	0.199913i
$125$	−3.92381	+	10.4692i	−0.350957	+	0.936392i
$126$		0			0
$127$	4.99811	−	4.99811i	0.443511	−	0.443511i	−0.449679	−	0.893190i	$-0.648462\pi$
$127$	4.99811	−	4.99811i	0.443511	−	0.443511i	0.893190	+	0.449679i	$0.148462\pi$
$128$	2.61636	+	9.76440i	0.231256	+	0.863059i
$129$		0			0
$130$	−2.13642	+	2.85077i	−0.187376	+	0.250029i
$131$	12.8763	+	7.43415i	1.12501	+	0.649525i	0.942675	−	0.333712i	$-0.108301\pi$
$131$	12.8763	+	7.43415i	1.12501	+	0.649525i	0.182335	+	0.983237i	$0.441635\pi$
$132$		0			0
$133$	−0.762287	+	9.33594i	−0.0660986	+	0.809529i
$134$	2.35992			0.203866
$135$		0			0
$136$	1.45688	+	2.52340i	0.124927	+	0.216379i
$137$	4.73094	−	17.6561i	0.404191	−	1.50846i	−0.401351	−	0.915924i	$-0.631459\pi$
$137$	4.73094	−	17.6561i	0.404191	−	1.50846i	0.805542	−	0.592538i	$-0.201874\pi$
$138$		0			0
$139$		−	16.9265i		−	1.43569i	−0.696203	−	0.717845i	$-0.745129\pi$
$139$		−	16.9265i		−	1.43569i	0.696203	−	0.717845i	$-0.254871\pi$
$140$	7.26709	−	8.20918i	0.614181	−	0.693802i
$141$		0			0
$142$	0.198285	+	0.740008i	0.0166397	+	0.0621001i
$143$	−16.1665	−	4.33180i	−1.35191	−	0.362243i
$144$		0			0
$145$	1.95598	−	16.2858i	0.162435	−	1.35246i
$146$		−	4.97045i		−	0.411358i
$147$		0			0
$148$	−11.2588	−	11.2588i	−0.925466	−	0.925466i
$149$	2.91667	−	5.05181i	0.238943	−	0.413861i	−0.721469	−	0.692447i	$-0.756533\pi$
$149$	2.91667	−	5.05181i	0.238943	−	0.413861i	0.960411	+	0.278586i	$0.0898659\pi$
$150$		0			0
$151$	−0.781346	−	1.35333i	−0.0635850	−	0.110132i	0.832480	−	0.554054i	$-0.186920\pi$
$151$	−0.781346	−	1.35333i	−0.0635850	−	0.110132i	−0.896065	+	0.443922i	$0.853587\pi$
$152$	5.04884	−	1.35283i	0.409515	−	0.109729i
$153$		0			0
$154$	−3.84238	−	1.37334i	−0.309628	−	0.110667i
$155$	4.93950	−	2.11211i	0.396750	−	0.169649i
$156$		0			0
$157$	−20.6501	−	5.53319i	−1.64806	−	0.441597i	−0.688992	−	0.724769i	$-0.741947\pi$
$157$	−20.6501	−	5.53319i	−1.64806	−	0.441597i	−0.959069	+	0.283172i	$0.908613\pi$
$158$	5.53609	+	1.48339i	0.440428	+	0.118012i
$159$		0			0
$160$	−8.62584	−	3.45858i	−0.681932	−	0.273425i
$161$	3.64005	−	3.09050i	0.286876	−	0.243565i
$162$		0			0
$163$	5.33299	−	1.42897i	0.417712	−	0.111926i	−0.0438402	−	0.999039i	$-0.513959\pi$
$163$	5.33299	−	1.42897i	0.417712	−	0.111926i	0.461553	+	0.887113i	$0.347293\pi$
$164$	4.82604	+	8.35895i	0.376850	+	0.652724i
$165$		0			0
$166$	3.05406	−	5.28979i	0.237041	−	0.410567i
$167$	9.56242	+	9.56242i	0.739962	+	0.739962i	0.972571	−	0.232608i	$-0.0747259\pi$
$167$	9.56242	+	9.56242i	0.739962	+	0.739962i	−0.232608	+	0.972571i	$0.574726\pi$
$168$		0			0
$169$			4.28942i			0.329956i
$170$	−1.67884	−	0.201634i	−0.128761	−	0.0154646i
$171$		0			0
$172$	3.26832	+	0.875743i	0.249207	+	0.0667747i
$173$	0.208360	+	0.777609i	0.0158413	+	0.0591205i	0.973394	−	0.229138i	$-0.0735906\pi$
$173$	0.208360	+	0.777609i	0.0158413	+	0.0591205i	−0.957553	+	0.288258i	$0.906924\pi$
$174$		0			0
$175$	2.66790	+	12.9569i	0.201674	+	0.979453i
$176$		−	12.6418i		−	0.952911i
$177$		0			0
$178$	0.837654	−	3.12617i	0.0627848	−	0.234316i
$179$	−4.96978	−	8.60791i	−0.371459	−	0.643385i	0.618332	−	0.785917i	$-0.287809\pi$
$179$	−4.96978	−	8.60791i	−0.371459	−	0.643385i	−0.989790	+	0.142532i	$0.954476\pi$
$180$		0			0
$181$	−10.5660			−0.785367			−0.392684	−	0.919674i	$-0.628453\pi$
$181$	−10.5660			−0.785367			−0.392684	+	0.919674i	$0.628453\pi$
$182$	−0.343030	+	4.20118i	−0.0254271	+	0.311413i
$183$		0			0
$184$	−2.30758	−	1.33228i	−0.170117	−	0.0982170i
$185$	19.0178	−	2.72404i	1.39822	−	0.200276i
$186$		0			0
$187$	−2.05607	−	7.67334i	−0.150354	−	0.561131i
$188$	1.44896	−	1.44896i	0.105677	−	0.105677i
$189$		0			0
$190$	−1.12885	+	2.81540i	−0.0818955	+	0.204251i
$191$	−3.99141	−	2.30444i	−0.288808	−	0.166743i	0.348596	−	0.937273i	$-0.386658\pi$
$191$	−3.99141	−	2.30444i	−0.288808	−	0.166743i	−0.637404	+	0.770530i	$0.719992\pi$
$192$		0			0
$193$	−0.0106297	+	0.0396705i	−0.000765141	+	0.00285555i	−0.966307	−	0.257391i	$-0.917137\pi$
$193$	−0.0106297	+	0.0396705i	−0.000765141	+	0.00285555i	0.965542	+	0.260247i	$0.0838038\pi$
$194$	1.20868	−	2.09349i	0.0867779	−	0.150304i
$195$		0			0
$196$	2.10437	−	12.8005i	0.150312	−	0.914323i
$197$	6.07098	+	6.07098i	0.432539	+	0.432539i	0.889491	−	0.456952i	$-0.151059\pi$
$197$	6.07098	+	6.07098i	0.432539	+	0.432539i	−0.456952	+	0.889491i	$0.651059\pi$
$198$		0			0
$199$	−0.549943	+	0.317510i	−0.0389845	+	0.0225077i	−0.519366	−	0.854552i	$-0.673832\pi$
$199$	−0.549943	+	0.317510i	−0.0389845	+	0.0225077i	0.480381	+	0.877060i	$0.340498\pi$
$200$	6.30731	−	3.83533i	0.445994	−	0.271198i
$201$		0			0
$202$	2.81102	−	2.81102i	0.197783	−	0.197783i
$203$	−8.30403	−	17.5419i	−0.582829	−	1.23120i
$204$		0			0
$205$	−11.5631	−	1.38877i	−0.807605	−	0.0969960i
$206$	−1.31375	+	0.758496i	−0.0915336	+	0.0528469i
$207$		0			0
$208$	−12.6142	+	3.37997i	−0.874640	+	0.234359i
$209$	−14.2506			−0.985737
$210$		0			0
$211$	25.5980			1.76224			0.881119	−	0.472895i	$-0.156791\pi$
$211$	25.5980			1.76224			0.881119	+	0.472895i	$0.156791\pi$
$212$	20.0077	−	5.36105i	1.37413	−	0.368198i
$213$		0			0
$214$	−0.581946	+	0.335987i	−0.0397810	+	0.0229676i
$215$	−3.21054	+	2.52204i	−0.218957	+	0.172002i
$216$		0			0
$217$	3.61563	−	5.22789i	0.245445	−	0.354892i
$218$	−4.05457	+	4.05457i	−0.274610	+	0.274610i
$219$		0			0
$220$	13.3475	+	10.0028i	0.899885	+	0.674391i
$221$	−7.10689	+	4.10317i	−0.478061	+	0.276009i
$222$		0			0
$223$	7.50244	+	7.50244i	0.502401	+	0.502401i	0.912183	−	0.409783i	$-0.134395\pi$
$223$	7.50244	+	7.50244i	0.502401	+	0.502401i	−0.409783	+	0.912183i	$0.634395\pi$
$224$	−10.8178	+	1.97218i	−0.722792	+	0.131772i
$225$		0			0
$226$	−0.522542	+	0.905069i	−0.0347590	+	0.0602043i
$227$	−3.25451	+	12.1460i	−0.216010	+	0.806159i	0.769799	+	0.638286i	$0.220356\pi$
$227$	−3.25451	+	12.1460i	−0.216010	+	0.806159i	−0.985809	+	0.167873i	$0.946310\pi$
$228$		0			0
$229$	10.1070	+	5.83527i	0.667888	+	0.385605i	0.795276	−	0.606248i	$-0.207326\pi$
$229$	10.1070	+	5.83527i	0.667888	+	0.385605i	−0.127388	+	0.991853i	$0.540659\pi$
$230$	1.42176	−	0.607941i	0.0937482	−	0.0400864i
$231$		0			0
$232$	−7.65799	+	7.65799i	−0.502772	+	0.502772i
$233$	4.19304	+	15.6486i	0.274695	+	1.02518i	0.956046	+	0.293218i	$0.0947262\pi$
$233$	4.19304	+	15.6486i	0.274695	+	1.02518i	−0.681351	+	0.731957i	$0.738607\pi$
$234$		0			0
$235$	0.350575	+	2.44753i	0.0228690	+	0.159659i
$236$	−23.1176	−	13.3470i	−1.50483	−	0.868813i
$237$		0			0
$238$	−1.80832	+	0.856031i	−0.117216	+	0.0554883i
$239$	−16.0682			−1.03936			−0.519682	−	0.854360i	$-0.673950\pi$
$239$	−16.0682			−1.03936			−0.519682	+	0.854360i	$0.673950\pi$
$240$		0			0
$241$	−1.35376	−	2.34478i	−0.0872034	−	0.151041i	0.819125	−	0.573616i	$-0.194460\pi$
$241$	−1.35376	−	2.34478i	−0.0872034	−	0.151041i	−0.906328	+	0.422575i	$0.861126\pi$
$242$	0.515855	−	1.92520i	0.0331604	−	0.123756i
$243$		0			0
$244$		−	9.22196i		−	0.590375i
$245$	10.8368	+	11.2944i	0.692340	+	0.721572i
$246$		0			0
$247$	3.81012	+	14.2196i	0.242432	+	0.904769i
$248$	−3.42611	−	0.918022i	−0.217558	−	0.0582945i
$249$		0			0
$250$	−0.413996	+	4.26376i	−0.0261834	+	0.269664i
$251$			16.0085i			1.01045i	0.862989	+	0.505223i	$0.168590\pi$
$251$			16.0085i			1.01045i	−0.862989	+	0.505223i	$0.831410\pi$
$252$		0			0
$253$	5.13684	+	5.13684i	0.322951	+	0.322951i
$254$	1.35415	−	2.34545i	0.0849668	−	0.147167i
$255$		0			0
$256$	−2.75233	−	4.76717i	−0.172021	−	0.297948i
$257$	−22.0568	+	5.91009i	−1.37586	+	0.368662i	−0.869617	−	0.493727i	$-0.835634\pi$
$257$	−22.0568	+	5.91009i	−1.37586	+	0.368662i	−0.506247	+	0.862389i	$0.668968\pi$
$258$		0			0
$259$	17.3286	−	14.7124i	1.07675	−	0.914187i
$260$	6.41239	−	15.9928i	0.397680	−	0.991829i
$261$		0			0
$262$	5.50276	+	1.47446i	0.339962	+	0.0910925i
$263$	26.7207	+	7.15980i	1.64767	+	0.441492i	0.958959	−	0.283544i	$-0.0915102\pi$
$263$	26.7207	+	7.15980i	1.64767	+	0.441492i	0.688711	+	0.725036i	$0.258177\pi$
$264$		0			0
$265$	−9.30128	+	23.1978i	−0.571373	+	1.42503i
$266$	0.643704	+	3.53083i	0.0394680	+	0.216489i
$267$		0			0
$268$	−11.0252	+	2.95420i	−0.673472	+	0.180456i
$269$	−2.20972	−	3.82735i	−0.134729	−	0.233357i	0.790765	−	0.612120i	$-0.209683\pi$
$269$	−2.20972	−	3.82735i	−0.134729	−	0.233357i	−0.925494	+	0.378762i	$0.876350\pi$
$270$		0			0
$271$	−8.32314	+	14.4161i	−0.505595	+	0.875716i	0.494384	+	0.869243i	$0.335394\pi$
$271$	−8.32314	+	14.4161i	−0.505595	+	0.875716i	−0.999979	+	0.00647219i	$0.997940\pi$
$272$	−4.38299	−	4.38299i	−0.265758	−	0.265758i
$273$		0			0
$274$		−	7.00368i		−	0.423108i
$275$	−19.3165	+	5.64956i	−1.16483	+	0.340682i
$276$		0			0
$277$	−11.3131	−	3.03132i	−0.679735	−	0.182135i	−0.0975991	−	0.995226i	$-0.531116\pi$
$277$	−11.3131	−	3.03132i	−0.679735	−	0.182135i	−0.582136	+	0.813091i	$0.697783\pi$
$278$	−1.67857	−	6.26451i	−0.100674	−	0.375720i
$279$		0			0
$280$	3.89949	−	7.81554i	0.233039	−	0.467068i
$281$			15.8649i			0.946421i	0.880949	+	0.473211i	$0.156905\pi$
$281$			15.8649i			0.946421i	−0.880949	+	0.473211i	$0.843095\pi$
$282$		0			0
$283$	1.79393	−	6.69505i	0.106638	−	0.397979i	−0.891888	−	0.452257i	$-0.850619\pi$
$283$	1.79393	−	6.69505i	0.106638	−	0.397979i	0.998526	+	0.0542777i	$0.0172856\pi$
$284$	−1.85271	−	3.20899i	−0.109938	−	0.190418i
$285$		0			0
$286$	−6.41280			−0.379197
$287$	−12.4550	+	5.89598i	−0.735193	+	0.348029i
$288$		0			0
$289$	11.3492	+	6.55245i	0.667599	+	0.385438i
$290$	−0.891122	−	6.22134i	−0.0523285	−	0.365330i
$291$		0			0
$292$	6.22210	+	23.2212i	0.364121	+	1.35892i
$293$	8.89793	−	8.89793i	0.519823	−	0.519823i	−0.397695	−	0.917518i	$-0.630190\pi$
$293$	8.89793	−	8.89793i	0.519823	−	0.519823i	0.917518	+	0.397695i	$0.130190\pi$
$294$		0			0
$295$	29.6152	−	12.6633i	1.72426	−	0.737289i
$296$	−10.9853	−	6.34237i	−0.638508	−	0.368643i
$297$		0			0
$298$	0.578480	−	2.15892i	0.0335104	−	0.125063i
$299$	3.75223	−	6.49906i	0.216997	−	0.375850i
$300$		0			0
$301$	−1.62585	+	4.54886i	−0.0937126	+	0.262192i
$302$	−0.423383	−	0.423383i	−0.0243630	−	0.0243630i
$303$		0			0
$304$	−9.62963	+	5.55967i	−0.552297	+	0.318869i
$305$	8.90428	+	6.67304i	0.509858	+	0.382097i
$306$		0			0
$307$	−8.47590	+	8.47590i	−0.483745	+	0.483745i	−0.906326	−	0.422580i	$-0.861125\pi$
$307$	−8.47590	+	8.47590i	−0.483745	+	0.483745i	0.422580	+	0.906326i	$0.361125\pi$
$308$	19.6702	+	1.60609i	1.12081	+	0.0915152i
$309$		0			0
$310$	1.61866	−	1.27153i	0.0919335	−	0.0722183i
$311$	5.89965	−	3.40617i	0.334539	−	0.193146i	−0.323316	−	0.946291i	$-0.604798\pi$
$311$	5.89965	−	3.40617i	0.334539	−	0.193146i	0.657854	+	0.753145i	$0.271464\pi$
$312$		0			0
$313$	18.3126	−	4.90685i	1.03509	−	0.277352i	0.299013	−	0.954249i	$-0.403342\pi$
$313$	18.3126	−	4.90685i	1.03509	−	0.277352i	0.736078	+	0.676897i	$0.236676\pi$
$314$	−8.19134			−0.462264
$315$		0			0
$316$	−27.7207			−1.55941
$317$	5.70405	−	1.52839i	0.320371	−	0.0858432i	−0.0950497	−	0.995473i	$-0.530301\pi$
$317$	5.70405	−	1.52839i	0.320371	−	0.0858432i	0.415421	+	0.909629i	$0.363634\pi$
$318$		0			0
$319$	25.5709	−	14.7634i	1.43170	−	0.826590i
$320$	10.4100	+	1.25028i	0.581938	+	0.0698927i
$321$		0			0
$322$	1.04070	−	1.50477i	0.0579962	−	0.0838576i
$323$	−4.94078	+	4.94078i	−0.274913	+	0.274913i
$324$		0			0
$325$	10.8018	+	17.7639i	0.599176	+	0.985364i
$326$	1.83203	−	1.05773i	0.101467	−	0.0585820i
$327$		0			0
$328$	5.43728	+	5.43728i	0.300224	+	0.300224i
$329$	1.89344	+	2.23013i	0.104389	+	0.122951i
$330$		0			0
$331$	−4.17653	+	7.23397i	−0.229563	+	0.397615i	−0.957679	−	0.287839i	$-0.907063\pi$
$331$	−4.17653	+	7.23397i	−0.229563	+	0.397615i	0.728116	+	0.685454i	$0.240396\pi$
$332$	−7.64625	+	28.5362i	−0.419643	+	1.56613i
$333$		0			0
$334$	4.48734	+	2.59077i	0.245536	+	0.141760i
$335$	5.12545	−	12.7831i	0.280033	−	0.698414i
$336$		0			0
$337$	0.454919	−	0.454919i	0.0247810	−	0.0247810i	−0.694608	−	0.719389i	$-0.744422\pi$
$337$	0.454919	−	0.454919i	0.0247810	−	0.0247810i	0.719389	+	0.694608i	$0.244422\pi$
$338$	0.425374	+	1.58752i	0.0231373	+	0.0863495i
$339$		0			0
$340$	8.09570	−	1.15960i	0.439051	−	0.0628880i
$341$	8.37478	+	4.83518i	0.453520	+	0.261840i
$342$		0			0
$343$	17.9698	+	4.48161i	0.970280	+	0.241984i
$344$	2.69560			0.145337
$345$		0			0
$346$	0.154228	+	0.267130i	0.00829134	+	0.0143610i
$347$	−9.25852	+	34.5533i	−0.497023	+	1.85492i	0.0213654	+	0.999772i	$0.493199\pi$
$347$	−9.25852	+	34.5533i	−0.497023	+	1.85492i	−0.518389	+	0.855145i	$0.673468\pi$
$348$		0			0
$349$			14.2309i			0.761762i	0.924624	+	0.380881i	$0.124379\pi$
$349$			14.2309i			0.761762i	−0.924624	+	0.380881i	$0.875621\pi$
$350$	2.27230	+	4.53079i	0.121460	+	0.242181i
$351$		0			0
$352$	−4.32979	−	16.1590i	−0.230779	−	0.861277i
$353$	−25.2551	−	6.76709i	−1.34419	−	0.360176i	−0.486206	−	0.873844i	$-0.661619\pi$
$353$	−25.2551	−	6.76709i	−1.34419	−	0.360176i	−0.857989	+	0.513669i	$0.828286\pi$
$354$		0			0
$355$	4.43907	+	0.533148i	0.235602	+	0.0282965i
$356$			15.6536i			0.829638i
$357$		0			0
$358$	−2.69294	−	2.69294i	−0.142327	−	0.142327i
$359$	14.8840	−	25.7798i	0.785545	−	1.36060i	−0.143128	−	0.989704i	$-0.545716\pi$
$359$	14.8840	−	25.7798i	0.785545	−	1.36060i	0.928673	−	0.370899i	$-0.120951\pi$
$360$		0			0
$361$	−3.23279	−	5.59936i	−0.170147	−	0.294703i
$362$	−3.91049	+	1.04781i	−0.205531	+	0.0550718i
$363$		0			0
$364$	−3.65653	−	20.0567i	−0.191654	−	1.05126i
$365$	−26.9236	−	10.7952i	−1.40925	−	0.565045i
$366$		0			0
$367$	−14.2575	−	3.82028i	−0.744234	−	0.199417i	−0.133275	−	0.991079i	$-0.542549\pi$
$367$	−14.2575	−	3.82028i	−0.744234	−	0.199417i	−0.610959	+	0.791662i	$0.709216\pi$
$368$	5.47520	+	1.46708i	0.285414	+	0.0764766i
$369$		0			0
$370$	6.76836	−	2.89413i	0.351870	−	0.150459i
$371$	5.30386	+	29.0926i	0.275363	+	1.51041i
$372$		0			0
$373$	−35.3044	+	9.45979i	−1.82799	+	0.489809i	−0.997716	−	0.0675413i	$-0.978485\pi$
$373$	−35.3044	+	9.45979i	−1.82799	+	0.489809i	−0.830277	+	0.557351i	$0.811818\pi$
$374$	−1.52190	−	2.63601i	−0.0786956	−	0.136305i
$375$		0			0
$376$	0.816241	−	1.41377i	0.0420944	−	0.0729097i
$377$	−21.5680	−	21.5680i	−1.11081	−	1.11081i
$378$		0			0
$379$			14.2298i			0.730936i	0.930824	+	0.365468i	$0.119091\pi$
$379$			14.2298i			0.730936i	−0.930824	+	0.365468i	$0.880909\pi$
$380$	1.74945	−	14.5662i	0.0897451	−	0.747232i
$381$		0			0
$382$	−1.70575	−	0.457053i	−0.0872736	−	0.0233849i
$383$	7.22126	+	26.9501i	0.368989	+	1.37709i	0.861932	+	0.507025i	$0.169255\pi$
$383$	7.22126	+	26.9501i	0.368989	+	1.37709i	−0.492942	+	0.870062i	$0.664079\pi$
$384$		0			0
$385$	−15.7842	+	17.8304i	−0.804436	+	0.908722i
$386$			0.0157362i			0.000800951i
$387$		0			0
$388$	−3.02608	+	11.2935i	−0.153626	+	0.573341i
$389$	−11.9954	−	20.7767i	−0.608191	−	1.05342i	−0.991538	−	0.129814i	$-0.958562\pi$
$389$	−11.9954	−	20.7767i	−0.608191	−	1.05342i	0.383347	−	0.923604i	$-0.374771\pi$
$390$		0			0
$391$	3.56195			0.180136
$392$	−1.02001	−	10.2841i	−0.0515182	−	0.519428i
$393$		0			0
$394$	2.84892	+	1.64482i	0.143526	+	0.0828649i
$395$	20.0588	−	26.7658i	1.00927	−	1.34673i
$396$		0			0
$397$	−1.14584	−	4.27635i	−0.0575083	−	0.214624i	0.931192	−	0.364529i	$-0.118770\pi$
$397$	−1.14584	−	4.27635i	−0.0575083	−	0.214624i	−0.988700	+	0.149905i	$0.952103\pi$
$398$	−0.172047	+	0.172047i	−0.00862395	+	0.00862395i
$399$		0			0
$400$	−10.8487	+	11.3536i	−0.542436	+	0.567682i
$401$	−8.36213	−	4.82788i	−0.417585	−	0.241093i	0.276459	−	0.961026i	$-0.410839\pi$
$401$	−8.36213	−	4.82788i	−0.417585	−	0.241093i	−0.694044	+	0.719933i	$0.744172\pi$
$402$		0			0
$403$	2.58552	−	9.64928i	0.128794	−	0.480665i
$404$	−9.61378	+	16.6516i	−0.478303	+	0.828446i
$405$		0			0
$406$	−4.81291	−	5.66875i	−0.238861	−	0.281335i
$407$	24.4542	+	24.4542i	1.21215	+	1.21215i
$408$		0			0
$409$	−5.80046	+	3.34890i	−0.286814	+	0.165592i	−0.636504	−	0.771273i	$-0.719620\pi$
$409$	−5.80046	+	3.34890i	−0.286814	+	0.165592i	0.349690	+	0.936865i	$0.386287\pi$
$410$	−4.41724	+	0.632709i	−0.218152	+	0.0312473i
$411$		0			0
$412$	5.18816	−	5.18816i	0.255602	−	0.255602i
$413$	21.6778	−	31.3442i	1.06669	−	1.54235i
$414$		0			0
$415$	−22.0203	−	28.0318i	−1.08094	−	1.37602i
$416$	−14.9661	+	8.64070i	−0.733775	+	0.423645i
$417$		0			0
$418$	−5.27416	+	1.41321i	−0.257968	+	0.0691222i
$419$	−28.3239			−1.38371			−0.691855	−	0.722036i	$-0.743206\pi$
$419$	−28.3239			−1.38371			−0.691855	+	0.722036i	$0.743206\pi$
$420$		0			0
$421$	3.09516			0.150849			0.0754244	−	0.997152i	$-0.475969\pi$
$421$	3.09516			0.150849			0.0754244	+	0.997152i	$0.475969\pi$
$422$	9.47381	−	2.53850i	0.461178	−	0.123572i
$423$		0			0
$424$	14.2909	−	8.25086i	0.694028	−	0.400697i
$425$	−4.73842	+	8.65590i	−0.229847	+	0.419873i
$426$		0			0
$427$	13.1223	+	1.07144i	0.635031	+	0.0518508i
$428$	2.29817	−	2.29817i	0.111086	−	0.111086i
$429$		0			0
$430$	−0.938116	+	1.25179i	−0.0452400	+	0.0603666i
$431$	3.56921	−	2.06068i	0.171923	−	0.0992597i	−0.411569	−	0.911378i	$-0.635019\pi$
$431$	3.56921	−	2.06068i	0.171923	−	0.0992597i	0.583492	+	0.812119i	$0.301686\pi$
$432$		0			0
$433$	17.3170	+	17.3170i	0.832201	+	0.832201i	0.987818	−	0.155616i	$-0.0497364\pi$
$433$	17.3170	+	17.3170i	0.832201	+	0.832201i	−0.155616	+	0.987818i	$0.549736\pi$
$434$	0.819705	−	2.29340i	0.0393471	−	0.110087i
$435$		0			0
$436$	13.8668	−	24.0179i	0.664097	−	1.15025i
$437$	1.65378	−	6.17199i	0.0791110	−	0.295246i
$438$		0			0
$439$	−18.3960	−	10.6209i	−0.877993	−	0.506909i	−0.00799680	−	0.999968i	$-0.502545\pi$
$439$	−18.3960	−	10.6209i	−0.877993	−	0.506909i	−0.869996	+	0.493059i	$0.835879\pi$
$440$	12.3336	+	4.94524i	0.587983	+	0.235755i
$441$		0			0
$442$	−2.22336	+	2.22336i	−0.105754	+	0.105754i
$443$	−1.79350	−	6.69343i	−0.0852117	−	0.318015i	0.910142	−	0.414295i	$-0.135972\pi$
$443$	−1.79350	−	6.69343i	−0.0852117	−	0.318015i	−0.995354	+	0.0962809i	$0.969305\pi$
$444$		0			0
$445$	−15.1143	−	11.3270i	−0.716488	−	0.536950i
$446$	3.52066	+	2.03265i	0.166708	+	0.0962489i
$447$		0			0
$448$	11.2129	−	5.30801i	0.529761	−	0.250780i
$449$	16.8279			0.794159			0.397080	−	0.917784i	$-0.370024\pi$
$449$	16.8279			0.794159			0.397080	+	0.917784i	$0.370024\pi$
$450$		0			0
$451$	−10.4822	−	18.1557i	−0.493588	−	0.854919i
$452$	1.30825	−	4.88247i	0.0615351	−	0.229652i
$453$		0			0
$454$			4.81798i			0.226119i
$455$	22.0117	+	10.9825i	1.03192	+	0.514869i
$456$		0			0
$457$	−4.00916	−	14.9624i	−0.187540	−	0.699910i	−0.994072	−	0.108720i	$-0.965325\pi$
$457$	−4.00916	−	14.9624i	−0.187540	−	0.699910i	0.806532	−	0.591190i	$-0.201342\pi$
$458$	4.31927	+	1.15734i	0.201826	+	0.0540791i
$459$		0			0
$460$	−5.88123	+	4.61999i	−0.274214	+	0.215408i
$461$			8.02877i			0.373937i	0.982366	+	0.186968i	$0.0598662\pi$
$461$			8.02877i			0.373937i	−0.982366	+	0.186968i	$0.940134\pi$
$462$		0			0
$463$	5.00172	+	5.00172i	0.232450	+	0.232450i	0.813715	−	0.581265i	$-0.197442\pi$
$463$	5.00172	+	5.00172i	0.232450	+	0.232450i	−0.581265	+	0.813715i	$0.697442\pi$
$464$	11.5194	−	19.9522i	0.534776	−	0.926258i
$465$		0			0
$466$	3.10369	+	5.37574i	0.143775	+	0.249026i
$467$	34.2874	−	9.18727i	1.58663	−	0.425136i	0.645660	−	0.763625i	$-0.276582\pi$
$467$	34.2874	−	9.18727i	1.58663	−	0.425136i	0.940970	+	0.338489i	$0.109916\pi$
$468$		0			0
$469$	−2.92268	−	16.0314i	−0.134957	−	0.740262i
$470$	0.372464	+	0.871064i	0.0171805	+	0.0401792i
$471$		0			0
$472$	−20.5415	−	5.50407i	−0.945498	−	0.253346i
$473$	−7.09881	−	1.90212i	−0.326404	−	0.0874596i
$474$		0			0
$475$	12.7985	+	12.2294i	0.587238	+	0.561122i
$476$	7.37662	−	6.26294i	0.338107	−	0.287061i
$477$		0			0
$478$	−5.94684	+	1.59345i	−0.272002	+	0.0728827i
$479$	−2.23639	−	3.87354i	−0.102183	−	0.176986i	0.810401	−	0.585876i	$-0.199249\pi$
$479$	−2.23639	−	3.87354i	−0.102183	−	0.176986i	−0.912584	+	0.408890i	$0.865916\pi$
$480$		0			0
$481$	17.8627	−	30.9390i	0.814467	−	1.41070i
$482$	−0.733554	−	0.733554i	−0.0334125	−	0.0334125i
$483$		0			0
$484$			9.63999i			0.438181i
$485$	−8.71477	−	11.0939i	−0.395718	−	0.503746i
$486$		0			0
$487$	16.2736	+	4.36050i	0.737428	+	0.197593i	0.607934	−	0.793987i	$-0.291998\pi$
$487$	16.2736	+	4.36050i	0.737428	+	0.197593i	0.129493	+	0.991580i	$0.458665\pi$
$488$	−1.90149	−	7.09648i	−0.0860766	−	0.321242i
$489$		0			0
$490$	5.13075	+	3.10538i	0.231784	+	0.140287i
$491$		−	13.8498i		−	0.625034i	−0.949912	−	0.312517i	$-0.898828\pi$
$491$		−	13.8498i		−	0.625034i	0.949912	−	0.312517i	$-0.101172\pi$
$492$		0			0
$493$	3.74704	−	13.9842i	0.168758	−	0.629815i
$494$	2.82025	+	4.88482i	0.126889	+	0.219778i
$495$		0			0
$496$	7.54549			0.338803
$497$	4.78145	−	2.26346i	0.214477	−	0.101530i
$498$		0			0
$499$	−30.2262	−	17.4511i	−1.35311	−	0.781220i	−0.364428	−	0.931232i	$-0.618735\pi$
$499$	−30.2262	−	17.4511i	−1.35311	−	0.781220i	−0.988684	+	0.150012i	$0.952069\pi$
$500$	−3.40333	−	20.4379i	−0.152201	−	0.914010i
$501$		0			0
$502$	1.58753	+	5.92473i	0.0708548	+	0.264434i
$503$	7.45879	−	7.45879i	0.332571	−	0.332571i	−0.520991	−	0.853562i	$-0.674438\pi$
$503$	7.45879	−	7.45879i	0.332571	−	0.332571i	0.853562	+	0.520991i	$0.174438\pi$
$504$		0			0
$505$	−9.12137	−	21.3317i	−0.405896	−	0.949249i
$506$	2.41056	+	1.39174i	0.107162	+	0.0618702i
$507$		0			0
$508$	−3.39029	+	12.6528i	−0.150420	+	0.561375i
$509$	7.98917	−	13.8376i	0.354114	−	0.613343i	−0.632852	−	0.774273i	$-0.718116\pi$
$509$	7.98917	−	13.8376i	0.354114	−	0.613343i	0.986966	+	0.160930i	$0.0514492\pi$
$510$		0			0
$511$	−33.7652	+	6.15573i	−1.49369	+	0.272313i
$512$	−15.7875	−	15.7875i	−0.697714	−	0.697714i
$513$		0			0
$514$	−7.57712	+	4.37465i	−0.334213	+	0.192958i
$515$	1.25527	+	8.76361i	0.0553137	+	0.386171i
$516$		0			0
$517$	−3.14716	+	3.14716i	−0.138412	+	0.138412i
$518$	4.95432	−	7.16352i	0.217680	−	0.314747i
$519$		0			0
$520$	1.63688	−	13.6289i	0.0717819	−	0.597668i
$521$	33.0945	−	19.1071i	1.44990	−	0.837098i	0.451421	−	0.892311i	$-0.350917\pi$
$521$	33.0945	−	19.1071i	1.44990	−	0.837098i	0.998475	+	0.0552134i	$0.0175839\pi$
$522$		0			0
$523$	5.99602	−	1.60663i	0.262188	−	0.0702529i	−0.125331	−	0.992115i	$-0.539999\pi$
$523$	5.99602	−	1.60663i	0.262188	−	0.0702529i	0.387518	+	0.921862i	$0.373332\pi$
$524$	−27.5538			−1.20369
$525$		0			0
$526$	10.5994			0.462154
$527$	4.57998	−	1.22720i	0.199507	−	0.0534578i
$528$		0			0
$529$	17.0977	−	9.87135i	0.743377	−	0.429189i
$530$	−1.14193	+	9.50788i	−0.0496022	+	0.412996i
$531$		0			0
$532$	−7.42724	−	15.6897i	−0.322012	−	0.680234i
$533$	−15.3135	+	15.3135i	−0.663303	+	0.663303i
$534$		0			0
$535$	0.556038	+	3.88197i	0.0240396	+	0.167832i
$536$	−7.87498	+	4.54662i	−0.340147	+	0.196384i
$537$		0			0
$538$	−1.19737	−	1.19737i	−0.0516222	−	0.0516222i
$539$	−4.57072	+	27.8028i	−0.196875	+	1.19755i
$540$		0			0
$541$	−3.79619	+	6.57520i	−0.163211	+	0.282690i	−0.936019	−	0.351951i	$-0.885518\pi$
$541$	−3.79619	+	6.57520i	−0.163211	+	0.282690i	0.772808	+	0.634640i	$0.218852\pi$
$542$	−1.65078	+	6.16079i	−0.0709070	+	0.264629i
$543$		0			0
$544$	−7.10359	−	4.10126i	−0.304564	−	0.175840i
$545$	13.1565	+	30.7685i	0.563564	+	1.31798i
$546$		0			0
$547$	−19.3606	+	19.3606i	−0.827801	+	0.827801i	−0.987212	−	0.159411i	$-0.949040\pi$
$547$	−19.3606	+	19.3606i	−0.827801	+	0.827801i	0.159411	+	0.987212i	$0.449040\pi$
$548$	8.76734	+	32.7201i	0.374522	+	1.39774i
$549$		0			0
$550$	−6.58879	+	4.00649i	−0.280947	+	0.170837i
$551$	−22.4914	−	12.9854i	−0.958165	−	0.553197i
$552$		0			0
$553$	3.22070	−	39.4448i	0.136958	−	1.67736i
$554$	−4.48757			−0.190659
$555$		0			0
$556$	15.6840	+	27.1656i	0.665152	+	1.15208i
$557$	−6.50195	+	24.2656i	−0.275496	+	1.02817i	0.680012	+	0.733201i	$0.261975\pi$
$557$	−6.50195	+	24.2656i	−0.275496	+	1.02817i	−0.955508	+	0.294965i	$0.904692\pi$
$558$		0			0
$559$			7.59189i			0.321103i
$560$	−3.70963	+	18.2066i	−0.156760	+	0.769368i
$561$		0			0
$562$	1.57329	+	5.87161i	0.0663653	+	0.247679i
$563$	−31.5627	−	8.45719i	−1.33021	−	0.356428i	−0.477415	−	0.878678i	$-0.658426\pi$
$563$	−31.5627	−	8.45719i	−1.33021	−	0.356428i	−0.852792	+	0.522250i	$0.825093\pi$
$564$		0			0
$565$	3.76762	+	4.79616i	0.158505	+	0.201776i
$566$		−	2.65574i		−	0.111629i
$567$		0			0
$568$	−2.08736	−	2.08736i	−0.0875839	−	0.0875839i
$569$	8.07272	−	13.9824i	0.338426	−	0.586171i	−0.645711	−	0.763582i	$-0.723439\pi$
$569$	8.07272	−	13.9824i	0.338426	−	0.586171i	0.984137	+	0.177411i	$0.0567722\pi$
$570$		0			0
$571$	4.99553	+	8.65252i	0.209057	+	0.362097i	0.951418	−	0.307904i	$-0.0996274\pi$
$571$	4.99553	+	8.65252i	0.209057	+	0.362097i	−0.742361	+	0.670000i	$0.766294\pi$
$572$	29.9596	−	8.02766i	1.25267	−	0.335653i
$573$		0			0
$574$	−4.02489	+	3.41724i	−0.167996	+	0.142633i
$575$	−0.205168	−	9.02167i	−0.00855611	−	0.376230i
$576$		0			0
$577$	−15.2049	−	4.07415i	−0.632990	−	0.169609i	−0.0719636	−	0.997407i	$-0.522927\pi$
$577$	−15.2049	−	4.07415i	−0.632990	−	0.169609i	−0.561026	+	0.827798i	$0.689593\pi$
$578$	4.85013	+	1.29959i	0.201739	+	0.0540557i
$579$		0			0
$580$	11.9512	+	27.9496i	0.496245	+	1.16055i
$581$	−39.7169	−	14.1956i	−1.64773	−	0.588932i
$582$		0			0
$583$	−43.4569	+	11.6442i	−1.79980	+	0.482255i
$584$	9.57605	+	16.5862i	0.396260	+	0.686342i
$585$		0			0
$586$	2.41073	−	4.17552i	0.0995865	−	0.172489i
$587$	−24.7394	−	24.7394i	−1.02110	−	1.02110i	−0.999772	−	0.0213323i	$-0.993209\pi$
$587$	−24.7394	−	24.7394i	−1.02110	−	1.02110i	−0.0213323	−	0.999772i	$-0.506791\pi$
$588$		0			0
$589$		−	8.50575i		−	0.350474i
$590$	9.70478	−	7.62358i	0.399539	−	0.313858i
$591$		0			0
$592$	26.0649	+	6.98407i	1.07126	+	0.287044i
$593$	4.55376	+	16.9949i	0.187001	+	0.697896i	0.994193	+	0.107608i	$0.0343192\pi$
$593$	4.55376	+	16.9949i	0.187001	+	0.697896i	−0.807193	+	0.590288i	$0.799014\pi$
$594$		0			0
$595$	0.709445	+	11.6544i	0.0290844	+	0.477784i
$596$			10.8103i			0.442806i
$597$		0			0
$598$	0.744203	−	2.77740i	0.0304327	−	0.113576i
$599$	4.40720	+	7.63350i	0.180073	+	0.311896i	0.941905	−	0.335878i	$-0.109033\pi$
$599$	4.40720	+	7.63350i	0.180073	+	0.311896i	−0.761832	+	0.647775i	$0.775700\pi$
$600$		0			0
$601$	−11.8686			−0.484131			−0.242066	−	0.970260i	$-0.577825\pi$
$601$	−11.8686			−0.484131			−0.242066	+	0.970260i	$0.577825\pi$
$602$	−0.150627	+	1.84477i	−0.00613908	+	0.0751871i
$603$		0			0
$604$	2.50798	+	1.44798i	0.102048	+	0.0589176i
$605$	−9.30791	−	6.97553i	−0.378420	−	0.283596i
$606$		0			0
$607$	1.03290	+	3.85482i	0.0419239	+	0.156462i	0.983715	−	0.179738i	$-0.0575249\pi$
$607$	1.03290	+	3.85482i	0.0419239	+	0.156462i	−0.941791	+	0.336200i	$0.890858\pi$
$608$	−10.4046	+	10.4046i	−0.421962	+	0.421962i
$609$		0			0
$610$	3.95723	+	1.58667i	0.160223	+	0.0642425i
$611$	3.98174	+	2.29886i	0.161084	+	0.0930019i
$612$		0			0
$613$	−7.20520	+	26.8902i	−0.291015	+	1.08608i	0.653315	+	0.757086i	$0.273378\pi$
$613$	−7.20520	+	26.8902i	−0.291015	+	1.08608i	−0.944331	+	0.328998i	$0.893289\pi$
$614$	−2.29639	+	3.97747i	−0.0926749	+	0.160518i
$615$		0			0
$616$	15.4677	−	2.81992i	0.623213	−	0.113618i
$617$	16.3933	+	16.3933i	0.659968	+	0.659968i	0.955372	−	0.295405i	$-0.0954544\pi$
$617$	16.3933	+	16.3933i	0.659968	+	0.659968i	−0.295405	+	0.955372i	$0.595454\pi$
$618$		0			0
$619$	−18.6355	+	10.7592i	−0.749023	+	0.432448i	−0.825341	−	0.564635i	$-0.809017\pi$
$619$	−18.6355	+	10.7592i	−0.749023	+	0.432448i	0.0763180	+	0.997084i	$0.475684\pi$
$620$	−5.97038	+	7.96668i	−0.239776	+	0.319949i
$621$		0			0
$622$	1.84568	−	1.84568i	0.0740050	−	0.0740050i
$623$	−22.2741	−	1.81869i	−0.892391	−	0.0728644i
$624$		0			0
$625$	22.1965	+	11.5028i	0.887860	+	0.460114i
$626$	6.29090	−	3.63205i	0.251435	−	0.145166i
$627$		0			0
$628$	38.2687	−	10.2541i	1.52709	−	0.409182i
$629$	16.9568			0.676113
$630$		0			0
$631$	5.55021			0.220950			0.110475	−	0.993879i	$-0.464763\pi$
$631$	5.55021			0.220950			0.110475	+	0.993879i	$0.464763\pi$
$632$	−21.3316	+	5.71579i	−0.848526	+	0.227362i
$633$		0			0
$634$	1.95950	−	1.13132i	0.0778217	−	0.0449304i
$635$	−9.76366	−	12.4291i	−0.387459	−	0.493233i
$636$		0			0
$637$	28.9643	−	2.87275i	1.14761	−	0.113823i
$638$	7.99975	−	7.99975i	0.316713	−	0.316713i
$639$		0			0
$640$	22.3757	−	3.20501i	0.884477	−	0.126689i
$641$	38.9210	−	22.4710i	1.53729	−	0.887553i	0.538290	−	0.842760i	$-0.319070\pi$
$641$	38.9210	−	22.4710i	1.53729	−	0.887553i	0.998996	−	0.0447931i	$-0.0142629\pi$
$642$		0			0
$643$	−14.2388	−	14.2388i	−0.561523	−	0.561523i	0.368217	−	0.929740i	$-0.379968\pi$
$643$	−14.2388	−	14.2388i	−0.561523	−	0.561523i	−0.929740	+	0.368217i	$0.879968\pi$
$644$	−2.97832	+	8.33283i	−0.117362	+	0.328359i
$645$		0			0
$646$	−1.33862	+	2.31855i	−0.0526672	+	0.0912222i
$647$	1.83522	−	6.84915i	0.0721501	−	0.269268i	−0.920422	−	0.390926i	$-0.872155\pi$
$647$	1.83522	−	6.84915i	0.0721501	−	0.269268i	0.992572	+	0.121659i	$0.0388213\pi$
$648$		0			0
$649$	50.2117	+	28.9897i	1.97098	+	1.13795i
$650$	5.75936	+	5.50323i	0.225901	+	0.215854i
$651$		0			0
$652$	−7.23490	+	7.23490i	−0.283341	+	0.283341i
$653$	−0.431788	−	1.61146i	−0.0168972	−	0.0630611i	0.956962	−	0.290212i	$-0.0937257\pi$
$653$	−0.431788	−	1.61146i	−0.0168972	−	0.0630611i	−0.973860	+	0.227151i	$0.927059\pi$
$654$		0			0
$655$	19.9380	−	26.6046i	0.779044	−	1.03953i
$656$	−14.1664	−	8.17895i	−0.553103	−	0.319334i
$657$		0			0
$658$	0.921920	+	0.637603i	0.0359402	+	0.0248564i
$659$	−6.89018			−0.268403			−0.134202	−	0.990954i	$-0.542847\pi$
$659$	−6.89018			−0.268403			−0.134202	+	0.990954i	$0.542847\pi$
$660$		0			0
$661$	18.8965	+	32.7297i	0.734989	+	1.27304i	0.954728	+	0.297479i	$0.0961458\pi$
$661$	18.8965	+	32.7297i	0.734989	+	1.27304i	−0.219740	+	0.975559i	$0.570521\pi$
$662$	−0.828357	+	3.09147i	−0.0321950	+	0.120153i
$663$		0			0
$664$			23.5358i			0.913364i
$665$	20.5236	+	4.18173i	0.795871	+	0.162160i
$666$		0			0
$667$	3.42657	+	12.7881i	0.132677	+	0.495158i
$668$	−24.2073	−	6.48634i	−0.936610	−	0.250964i
$669$		0			0
$670$	0.629257	−	5.23930i	0.0243103	−	0.202412i
$671$			20.0302i			0.773257i
$672$		0			0
$673$	−5.36449	−	5.36449i	−0.206786	−	0.206786i	0.596114	−	0.802900i	$-0.296711\pi$
$673$	−5.36449	−	5.36449i	−0.206786	−	0.206786i	−0.802900	+	0.596114i	$0.796711\pi$
$674$	0.123252	−	0.213479i	0.00474749	−	0.00822290i
$675$		0			0
$676$	−3.97456	−	6.88414i	−0.152868	−	0.264775i
$677$	−33.3312	+	8.93106i	−1.28102	+	0.343249i	−0.834243	−	0.551396i	$-0.814095\pi$
$677$	−33.3312	+	8.93106i	−1.28102	+	0.343249i	−0.446778	+	0.894645i	$0.647429\pi$
$678$		0			0
$679$	−15.7184	−	5.61805i	−0.603215	−	0.215601i
$680$	5.99069	−	2.56160i	0.229733	−	0.0982329i
$681$		0			0
$682$	3.57900	+	0.958991i	0.137047	+	0.0367217i
$683$	43.8433	+	11.7478i	1.67762	+	0.449516i	0.967148	−	0.254213i	$-0.0818166\pi$
$683$	43.8433	+	11.7478i	1.67762	+	0.449516i	0.710468	+	0.703729i	$0.248483\pi$
$684$		0			0
$685$	−37.9371	−	15.2111i	−1.44950	−	0.581186i
$686$	7.09507	−	0.123391i	0.270891	−	0.00471107i
$687$		0			0
$688$	−5.53899	+	1.48417i	−0.211172	+	0.0565834i
$689$	23.2377	+	40.2489i	0.885286	+	1.53336i
$690$		0			0
$691$	−11.6039	+	20.0985i	−0.441433	+	0.764584i	−0.997796	−	0.0663550i	$-0.978863\pi$
$691$	−11.6039	+	20.0985i	−0.441433	+	0.764584i	0.556363	+	0.830939i	$0.312196\pi$
$692$	−1.05493	−	1.05493i	−0.0401023	−	0.0401023i
$693$		0			0
$694$			13.7063i			0.520285i
$695$	−37.5788	−	4.51334i	−1.42545	−	0.171201i
$696$		0			0
$697$	−9.92895	−	2.66045i	−0.376086	−	0.100772i
$698$	1.41125	+	5.26686i	0.0534166	+	0.199353i
$699$		0			0
$700$	−16.2876	−	18.3227i	−0.615613	−	0.692532i
$701$		−	33.8131i		−	1.27710i	−0.769580	−	0.638551i	$-0.779534\pi$
$701$		−	33.8131i		−	1.27710i	0.769580	−	0.638551i	$-0.220466\pi$
$702$		0			0
$703$	7.87289	−	29.3820i	0.296932	−	1.10816i
$704$	9.43689	+	16.3452i	0.355666	+	0.616032i
$705$		0			0
$706$	−10.0180			−0.377032
$707$	−22.5771	−	15.6144i	−0.849101	−	0.587242i
$708$		0			0
$709$	7.53269	+	4.34900i	0.282896	+	0.163330i	0.634734	−	0.772731i	$-0.281110\pi$
$709$	7.53269	+	4.34900i	0.282896	+	0.163330i	−0.351838	+	0.936061i	$0.614443\pi$
$710$	1.69577	−	0.242896i	0.0636412	−	0.00911573i
$711$		0			0
$712$	3.22764	+	12.0457i	0.120961	+	0.451433i
$713$	−3.06602	+	3.06602i	−0.114823	+	0.114823i
$714$		0			0
$715$	−13.9278	+	34.7364i	−0.520869	+	1.29907i
$716$	15.9521	+	9.20995i	0.596158	+	0.344192i
$717$		0			0
$718$	2.95202	−	11.0171i	0.110169	−	0.411155i
$719$	−4.14644	+	7.18185i	−0.154636	+	0.267838i	−0.932926	−	0.360067i	$-0.882754\pi$
$719$	−4.14644	+	7.18185i	−0.154636	+	0.267838i	0.778290	+	0.627905i	$0.216087\pi$
$720$		0			0
$721$	6.77965	+	7.98521i	0.252487	+	0.297385i
$722$	−1.75174	−	1.75174i	−0.0651928	−	0.0651928i
$723$		0			0
$724$	16.9575	−	9.79044i	0.630222	−	0.363859i
$725$	−35.6347	−	8.68498i	−1.32344	−	0.322552i
$726$		0			0
$727$	18.4277	−	18.4277i	0.683447	−	0.683447i	−0.277328	−	0.960775i	$-0.589449\pi$
$727$	18.4277	−	18.4277i	0.683447	−	0.683447i	0.960775	+	0.277328i	$0.0894490\pi$
$728$	−6.94931	−	14.6801i	−0.257558	−	0.544080i
$729$		0			0
$730$	−11.0350	−	1.32534i	−0.408422	−	0.0490529i
$731$	−3.12068	+	1.80173i	−0.115423	+	0.0666393i
$732$		0			0
$733$	−44.6895	+	11.9745i	−1.65065	+	0.442289i	−0.959793	−	0.280707i	$-0.909431\pi$
$733$	−44.6895	+	11.9745i	−1.65065	+	0.442289i	−0.690852	+	0.722996i	$0.742764\pi$
$734$	−5.65554			−0.208750
$735$		0			0
$736$	7.50098			0.276490
$737$	23.9469	−	6.41654i	0.882094	−	0.236356i
$738$		0			0
$739$	6.02263	−	3.47717i	0.221546	−	0.127910i	−0.385120	−	0.922867i	$-0.625840\pi$
$739$	6.02263	−	3.47717i	0.221546	−	0.127910i	0.606666	+	0.794957i	$0.292507\pi$
$740$	−27.9978	+	21.9937i	−1.02922	+	0.808504i
$741$		0			0
$742$	4.84801	+	10.2412i	0.177976	+	0.375966i
$743$	4.69627	−	4.69627i	0.172289	−	0.172289i	−0.615695	−	0.787985i	$-0.711125\pi$
$743$	4.69627	−	4.69627i	0.172289	−	0.172289i	0.787985	+	0.615695i	$0.211125\pi$
$744$		0			0
$745$	−10.4379	−	7.82236i	−0.382415	−	0.286589i
$746$	−12.1281	+	7.00214i	−0.444040	+	0.256367i
$747$		0			0
$748$	10.4099	+	10.4099i	0.380623	+	0.380623i
$749$	3.00314	+	3.53716i	0.109732	+	0.129245i
$750$		0			0
$751$	−6.61449	+	11.4566i	−0.241366	+	0.418059i	−0.961104	−	0.276188i	$-0.910929\pi$
$751$	−6.61449	+	11.4566i	−0.241366	+	0.418059i	0.719737	+	0.694246i	$0.244262\pi$
$752$	−0.898825	+	3.35446i	−0.0327768	+	0.122325i
$753$		0			0
$754$	−10.1212	−	5.84345i	−0.368591	−	0.212806i
$755$	−3.21289	+	1.37382i	−0.116929	+	0.0499984i
$756$		0			0
$757$	30.1565	−	30.1565i	1.09606	−	1.09606i	0.101190	−	0.994867i	$-0.467735\pi$
$757$	30.1565	−	30.1565i	1.09606	−	1.09606i	0.994867	−	0.101190i	$-0.0322649\pi$
$758$	1.41114	+	5.26645i	0.0512550	+	0.191286i
$759$		0			0
$760$	−1.65720	−	11.5697i	−0.0601131	−	0.419678i
$761$	18.9022	+	10.9132i	0.685205	+	0.395603i	0.801813	−	0.597575i	$-0.203869\pi$
$761$	18.9022	+	10.9132i	0.685205	+	0.395603i	−0.116608	+	0.993178i	$0.537202\pi$
$762$		0			0
$763$	32.5649	+	22.5220i	1.17893	+	0.815352i
$764$	8.54114			0.309007
$765$		0			0
$766$	5.34518	+	9.25812i	0.193129	+	0.334510i
$767$	15.5017	−	57.8530i	0.559733	−	2.08895i
$768$		0			0
$769$		−	6.13772i		−	0.221332i	−0.993858	−	0.110666i	$-0.964702\pi$
$769$		−	6.13772i		−	0.221332i	0.993858	−	0.110666i	$-0.0352983\pi$
$770$	−4.07352	+	8.16432i	−0.146799	+	0.294222i
$771$		0			0
$772$	−0.0196988	−	0.0735171i	−0.000708977	−	0.00264594i
$773$	−4.08084	−	1.09346i	−0.146778	−	0.0393290i	0.184682	−	0.982798i	$-0.440874\pi$
$773$	−4.08084	−	1.09346i	−0.146778	−	0.0393290i	−0.331460	+	0.943469i	$0.607541\pi$
$774$		0			0
$775$	−3.37205	−	11.5294i	−0.121128	−	0.414149i
$776$			9.31452i			0.334372i
$777$		0			0
$778$	−6.49988	−	6.49988i	−0.233032	−	0.233032i
$779$	−9.21982	+	15.9692i	−0.330334	+	0.572156i
$780$		0			0
$781$	4.02410	+	6.96995i	0.143994	+	0.249405i
$782$	1.31828	−	0.353232i	0.0471416	−	0.0126315i
$783$		0			0
$784$	7.75827	+	20.5705i	0.277081	+	0.734661i
$785$	−17.7905	+	44.3703i	−0.634971	+	1.58364i
$786$		0			0
$787$	21.8845	+	5.86394i	0.780099	+	0.209027i	0.626828	−	0.779157i	$-0.284353\pi$
$787$	21.8845	+	5.86394i	0.780099	+	0.209027i	0.153271	+	0.988184i	$0.451019\pi$
$788$	−15.3687	−	4.11804i	−0.547488	−	0.146699i
$789$		0			0
$790$	4.76946	−	11.8952i	0.169690	−	0.423213i
$791$	6.79545	+	2.42883i	0.241618	+	0.0863592i
$792$		0			0
$793$	19.9865	−	5.35537i	0.709742	−	0.190175i
$794$	−0.848154	−	1.46905i	−0.0300999	−	0.0521345i
$795$		0			0
$796$	0.588407	−	1.01915i	0.0208555	−	0.0361228i
$797$	−26.3704	−	26.3704i	−0.934088	−	0.934088i	0.0638707	−	0.997958i	$-0.479655\pi$
$797$	−26.3704	−	26.3704i	−0.934088	−	0.934088i	−0.997958	+	0.0638707i	$0.979655\pi$
$798$		0			0
$799$			2.18228i			0.0772037i
$800$	−9.97846	+	18.2281i	−0.352792	+	0.644462i
$801$		0			0
$802$	−3.57360	−	0.957543i	−0.126188	−	0.0338120i
$803$	−13.5145	−	50.4367i	−0.476915	−	1.77987i
$804$		0			0
$805$	−5.89066	−	8.90539i	−0.207618	−	0.313874i
$806$		−	3.82760i		−	0.134821i
$807$		0			0
$808$	−3.96457	+	14.7960i	−0.139473	+	0.520521i
$809$	3.26224	+	5.65037i	0.114694	+	0.198656i	0.917657	−	0.397372i	$-0.130078\pi$
$809$	3.26224	+	5.65037i	0.114694	+	0.198656i	−0.802963	+	0.596029i	$0.796744\pi$
$810$		0			0
$811$	−23.6047			−0.828872			−0.414436	−	0.910078i	$-0.636021\pi$
$811$	−23.6047			−0.828872			−0.414436	+	0.910078i	$0.636021\pi$
$812$	29.5814	+	20.4586i	1.03811	+	0.717958i
$813$		0			0
$814$	11.4756	+	6.62542i	0.402218	+	0.232221i
$815$	−1.75047	−	12.2209i	−0.0613164	−	0.428079i
$816$		0			0
$817$	1.67305	+	6.24390i	0.0585325	+	0.218446i
$818$	−1.81465	+	1.81465i	−0.0634477	+	0.0634477i
$819$		0			0
$820$	19.8446	−	8.48550i	0.693005	−	0.296327i
$821$	−28.7605	−	16.6049i	−1.00375	−	0.579514i	−0.0943923	−	0.995535i	$-0.530091\pi$
$821$	−28.7605	−	16.6049i	−1.00375	−	0.579514i	−0.909355	+	0.416021i	$0.863424\pi$
$822$		0			0
$823$	−1.35423	+	5.05406i	−0.0472055	+	0.176173i	−0.985504	−	0.169654i	$-0.945735\pi$
$823$	−1.35423	+	5.05406i	−0.0472055	+	0.176173i	0.938298	+	0.345827i	$0.112402\pi$
$824$	2.92263	−	5.06215i	0.101815	−	0.176348i
$825$		0			0
$826$	4.91461	−	13.7502i	0.171001	−	0.478432i
$827$	−2.58727	−	2.58727i	−0.0899681	−	0.0899681i	0.660690	−	0.750658i	$-0.270264\pi$
$827$	−2.58727	−	2.58727i	−0.0899681	−	0.0899681i	−0.750658	+	0.660690i	$0.770264\pi$
$828$		0			0
$829$	−35.3778	+	20.4254i	−1.22872	+	0.709403i	−0.966762	−	0.255676i	$-0.917702\pi$
$829$	−35.3778	+	20.4254i	−1.22872	+	0.709403i	−0.261959	+	0.965079i	$0.584369\pi$
$830$	−10.9296	−	8.19084i	−0.379371	−	0.284308i
$831$		0			0
$832$	13.7864	−	13.7864i	0.477959	−	0.477959i
$833$	8.05473	+	11.2241i	0.279080	+	0.388893i
$834$		0			0
$835$	23.7794	−	18.6799i	0.822920	−	0.646445i
$836$	22.8710	−	13.2046i	0.791010	−	0.456690i
$837$		0			0
$838$	−10.4827	+	2.80882i	−0.362118	+	0.0970291i
$839$	36.4857			1.25963			0.629813	−	0.776746i	$-0.283131\pi$
$839$	36.4857			1.25963			0.629813	+	0.776746i	$0.283131\pi$
$840$		0			0
$841$	24.8105			0.855536
$842$	1.14552	−	0.306941i	0.0394772	−	0.0105779i
$843$		0			0
$844$	−41.0825	+	23.7190i	−1.41412	+	0.816441i
$845$	9.52300	+	1.14374i	0.327601	+	0.0393460i
$846$		0			0
$847$	−13.7171	−	1.12001i	−0.471325	−	0.0384841i
$848$	−24.8225	+	24.8225i	−0.852407	+	0.852407i
$849$		0			0
$850$	−0.895302	+	3.67345i	−0.0307086	+	0.125998i
$851$	−13.4291	+	7.75327i	−0.460342	+	0.265779i
$852$		0			0
$853$	11.2358	+	11.2358i	0.384707	+	0.384707i	0.872795	−	0.488087i	$-0.162305\pi$
$853$	11.2358	+	11.2358i	0.384707	+	0.384707i	−0.488087	+	0.872795i	$0.662305\pi$
$854$	4.96281	−	0.904768i	0.169824	−	0.0309605i
$855$		0			0
$856$	1.29462	−	2.24235i	0.0442492	−	0.0766419i
$857$	−6.66759	+	24.8838i	−0.227761	+	0.850014i	0.753519	+	0.657426i	$0.228355\pi$
$857$	−6.66759	+	24.8838i	−0.227761	+	0.850014i	−0.981280	+	0.192588i	$0.938312\pi$
$858$		0			0
$859$	−28.3695	−	16.3792i	−0.967956	−	0.558850i	−0.0693435	−	0.997593i	$-0.522090\pi$
$859$	−28.3695	−	16.3792i	−0.967956	−	0.558850i	−0.898612	+	0.438743i	$0.855424\pi$
$860$	2.81572	−	7.02252i	0.0960153	−	0.239466i
$861$		0			0
$862$	1.11661	−	1.11661i	0.0380319	−	0.0380319i
$863$	−3.95435	−	14.7578i	−0.134608	−	0.502362i	−0.999999	−	0.00126606i	$-0.999597\pi$
$863$	−3.95435	−	14.7578i	−0.134608	−	0.502362i	0.865392	−	0.501096i	$-0.167070\pi$
$864$		0			0
$865$	1.78194	−	0.255238i	0.0605877	−	0.00867835i
$866$	8.12631	+	4.69173i	0.276143	+	0.159431i
$867$		0			0
$868$	−0.958623	+	11.7405i	−0.0325378	+	0.398499i
$869$	60.2096			2.04247
$870$		0			0
$871$	−12.8051	−	22.1791i	−0.433884	−	0.751510i
$872$	5.71843	−	21.3415i	0.193651	−	0.722714i
$873$		0			0
$874$		−	2.44826i		−	0.0828135i
$875$	29.4772	−	2.46817i	0.996513	−	0.0834392i
$876$		0			0
$877$	1.51081	+	5.63841i	0.0510163	+	0.190396i	0.986731	−	0.162361i	$-0.0519110\pi$
$877$	1.51081	+	5.63841i	0.0510163	+	0.190396i	−0.935715	+	0.352757i	$0.885244\pi$
$878$	−7.86162	−	2.10651i	−0.265317	−	0.0710914i
$879$		0			0
$880$	−28.0662	−	3.37085i	−0.946112	−	0.113631i
$881$		−	20.5062i		−	0.690871i	−0.938442	−	0.345436i	$-0.887731\pi$
$881$		−	20.5062i		−	0.690871i	0.938442	−	0.345436i	$-0.112269\pi$
$882$		0			0
$883$	1.83466	+	1.83466i	0.0617412	+	0.0617412i	0.737303	−	0.675562i	$-0.236099\pi$
$883$	1.83466	+	1.83466i	0.0617412	+	0.0617412i	−0.675562	+	0.737303i	$0.736099\pi$
$884$	7.60395	−	13.1704i	0.255749	−	0.442970i
$885$		0			0
$886$	−1.32755	−	2.29938i	−0.0445999	−	0.0772492i
$887$	20.9870	−	5.62344i	0.704673	−	0.188817i	0.111350	−	0.993781i	$-0.464482\pi$
$887$	20.9870	−	5.62344i	0.704673	−	0.188817i	0.593323	+	0.804965i	$0.297816\pi$
$888$		0			0
$889$	−17.6102	−	6.29422i	−0.590626	−	0.211102i
$890$	−6.71709	−	2.69326i	−0.225157	−	0.0902782i
$891$		0			0
$892$	−18.9925	−	5.08902i	−0.635915	−	0.170393i
$893$	3.78136	+	1.01321i	0.126538	+	0.0339059i
$894$		0			0
$895$	−20.4357	+	8.73823i	−0.683089	+	0.292087i
$896$	20.3883	−	17.3101i	0.681124	−	0.578291i
$897$		0			0
$898$	6.22802	−	1.66879i	0.207832	−	0.0556883i
$899$	8.81180	+	15.2625i	0.293890	+	0.509032i
$900$		0			0
$901$	−11.0297	+	19.1039i	−0.367451	+	0.636444i
$902$	−5.67993	−	5.67993i	−0.189121	−	0.189121i
$903$		0			0
$904$		−	4.02691i		−	0.133933i
$905$	−2.81736	+	23.4578i	−0.0936522	+	0.779763i
$906$		0			0
$907$	−42.0555	−	11.2687i	−1.39643	−	0.374172i	−0.519369	−	0.854550i	$-0.673833\pi$
$907$	−42.0555	−	11.2687i	−1.39643	−	0.374172i	−0.877062	+	0.480378i	$0.840500\pi$
$908$	−6.03124	−	22.5089i	−0.200154	−	0.746984i
$909$		0			0
$910$	9.23564	+	1.88178i	0.306158	+	0.0623805i
$911$			7.86365i			0.260534i	0.991479	+	0.130267i	$0.0415835\pi$
$911$			7.86365i			0.260534i	−0.991479	+	0.130267i	$0.958417\pi$
$912$		0			0
$913$	16.6077	−	61.9809i	0.549636	−	2.05127i
$914$	−2.96758	−	5.14000i	−0.0981587	−	0.170016i
$915$		0			0
$916$	−21.6277			−0.714600
$917$	3.20131	−	39.2074i	0.105717	−	1.29474i
$918$		0			0
$919$	11.4005	+	6.58211i	0.376069	+	0.217124i	0.676107	−	0.736804i	$-0.263666\pi$
$919$	11.4005	+	6.58211i	0.376069	+	0.217124i	−0.300037	+	0.953927i	$0.596999\pi$
$920$	−3.57311	+	4.76784i	−0.117802	+	0.157191i
$921$		0			0
$922$	0.796197	+	2.97145i	0.0262213	+	0.0978594i
$923$	5.87885	−	5.87885i	0.193505	−	0.193505i
$924$		0			0
$925$	−0.976712	−	42.9481i	−0.0321141	−	1.41212i
$926$	2.34715	+	1.35513i	0.0771321	+	0.0445322i
$927$		0			0
$928$	7.89075	−	29.4487i	0.259027	−	0.966701i
$929$	−6.03017	+	10.4446i	−0.197843	+	0.342675i	−0.947829	−	0.318779i	$-0.896727\pi$
$929$	−6.03017	+	10.4446i	−0.197843	+	0.342675i	0.749986	+	0.661454i	$0.230060\pi$
$930$		0			0
$931$	23.1884	−	8.74561i	0.759968	−	0.286626i
$932$	−21.2294	−	21.2294i	−0.695392	−	0.695392i
$933$		0			0
$934$	11.7787	−	6.80042i	0.385410	−	0.222517i
$935$	−17.5839	+	2.51866i	−0.575056	+	0.0823689i
$936$		0			0
$937$	18.1175	−	18.1175i	0.591874	−	0.591874i	−0.346264	−	0.938137i	$-0.612550\pi$
$937$	18.1175	−	18.1175i	0.591874	−	0.591874i	0.938137	+	0.346264i	$0.112550\pi$
$938$	−2.67149	−	5.64339i	−0.0872272	−	0.184263i
$939$		0			0
$940$	−2.83051	−	3.60322i	−0.0923210	−	0.117524i
$941$	−14.8155	+	8.55376i	−0.482973	+	0.278844i	−0.721655	−	0.692253i	$-0.756618\pi$
$941$	−14.8155	+	8.55376i	−0.482973	+	0.278844i	0.238682	+	0.971098i	$0.423285\pi$
$942$		0			0
$943$	9.07975	−	2.43291i	0.295677	−	0.0792265i
$944$	45.2396			1.47242
$945$		0			0
$946$	−2.81590			−0.0915528
$947$	44.5651	−	11.9412i	1.44817	−	0.388036i	0.552784	−	0.833324i	$-0.313565\pi$
$947$	44.5651	−	11.9412i	1.44817	−	0.388036i	0.895387	+	0.445288i	$0.146899\pi$
$948$		0			0
$949$	−46.7134	+	26.9700i	−1.51638	+	0.875483i
$950$	5.94951	+	3.25688i	0.193027	+	0.105667i
$951$		0			0
$952$	4.38508	−	6.34045i	0.142121	−	0.205495i
$953$	−7.69282	+	7.69282i	−0.249195	+	0.249195i	−0.820640	−	0.571445i	$-0.806383\pi$
$953$	−7.69282	+	7.69282i	−0.249195	+	0.249195i	0.571445	+	0.820640i	$0.306383\pi$
$954$		0			0
$955$	−6.18040	+	8.24691i	−0.199993	+	0.266864i
$956$	25.7880	−	14.8887i	0.834044	−	0.481535i
$957$		0			0
$958$	−1.21182	−	1.21182i	−0.0391521	−	0.0391521i
$959$	−47.5773	+	8.67382i	−1.53635	+	0.280092i
$960$		0			0
$961$	12.6140	−	21.8481i	0.406904	−	0.704779i
$962$	3.54281	−	13.2219i	0.114225	−	0.426293i
$963$		0			0
$964$	4.34533	+	2.50878i	0.139954	+	0.0808023i
$965$	0.0852387	+	0.0341770i	0.00274393	+	0.00110020i
$966$		0			0
$967$	−27.7133	+	27.7133i	−0.891200	+	0.891200i	−0.994636	−	0.103436i	$-0.967016\pi$
$967$	−27.7133	+	27.7133i	−0.891200	+	0.891200i	0.103436	+	0.994636i	$0.467016\pi$
$968$	1.98769	+	7.41815i	0.0638867	+	0.238429i
$969$		0			0
$970$	−4.32549	−	3.24161i	−0.138883	−	0.104082i
$971$	28.8000	+	16.6277i	0.924237	+	0.533608i	0.884984	−	0.465621i	$-0.154169\pi$
$971$	28.8000	+	16.6277i	0.924237	+	0.533608i	0.0392525	+	0.999229i	$0.487502\pi$
$972$		0			0
$973$	−40.4771	+	19.1612i	−1.29764	+	0.614280i
$974$	6.45529			0.206841
$975$		0			0
$976$	7.81447	+	13.5351i	0.250135	+	0.433247i
$977$	−2.47403	+	9.23319i	−0.0791511	+	0.295396i	−0.994142	−	0.108077i	$-0.965531\pi$
$977$	−2.47403	+	9.23319i	−0.0791511	+	0.295396i	0.914991	+	0.403473i	$0.132197\pi$
$978$		0			0
$979$		−	33.9997i		−	1.08664i
$980$	−27.8575	−	8.08512i	−0.889875	−	0.258270i
$981$		0			0
$982$	−1.37346	−	5.12582i	−0.0438289	−	0.163572i
$983$	15.6808	+	4.20165i	0.500139	+	0.134012i	0.500064	−	0.865988i	$-0.333310\pi$
$983$	15.6808	+	4.20165i	0.500139	+	0.134012i	7.42785e−5		1.00000i	$0.499976\pi$
$984$		0			0
$985$	15.0970	−	11.8595i	0.481032	−	0.377874i
$986$		−	5.54713i		−	0.176656i
$987$		0			0
$988$	−19.2907	−	19.2907i	−0.613718	−	0.613718i
$989$	1.64763	−	2.85378i	0.0523915	−	0.0907448i
$990$		0			0
$991$	−15.3019	−	26.5037i	−0.486082	−	0.841919i	0.513790	−	0.857916i	$-0.328241\pi$
$991$	−15.3019	−	26.5037i	−0.486082	−	0.841919i	−0.999872	+	0.0159973i	$0.994908\pi$
$992$	9.64480	−	2.58432i	0.306223	−	0.0820521i
$993$		0			0
$994$	1.54515	−	1.31187i	0.0490092	−	0.0416101i
$995$	0.558270	+	1.30560i	0.0176983	+	0.0413903i
$996$		0			0
$997$	39.0130	+	10.4535i	1.23555	+	0.331065i	0.816739	−	0.577007i	$-0.195779\pi$
$997$	39.0130	+	10.4535i	1.23555	+	0.331065i	0.418814	+	0.908072i	$0.362446\pi$
$998$	−12.9173	−	3.46119i	−0.408891	−	0.109562i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.ce.a.233.10	yes	64
3.2	odd	2	inner	315.2.ce.a.233.7	yes	64
5.2	odd	4	inner	315.2.ce.a.107.10	yes	64
7.4	even	3	inner	315.2.ce.a.53.7	✓	64
15.2	even	4	inner	315.2.ce.a.107.7	yes	64
21.11	odd	6	inner	315.2.ce.a.53.10	yes	64
35.32	odd	12	inner	315.2.ce.a.242.7	yes	64
105.32	even	12	inner	315.2.ce.a.242.10	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.ce.a.53.7	✓	64	7.4	even	3	inner
315.2.ce.a.53.10	yes	64	21.11	odd	6	inner
315.2.ce.a.107.7	yes	64	15.2	even	4	inner
315.2.ce.a.107.10	yes	64	5.2	odd	4	inner
315.2.ce.a.233.7	yes	64	3.2	odd	2	inner
315.2.ce.a.233.10	yes	64	1.1	even	1	trivial
315.2.ce.a.242.7	yes	64	35.32	odd	12	inner
315.2.ce.a.242.10	yes	64	105.32	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.370100 - 0.0991680i) q^{2} +(-1.60491 + 0.926596i) q^{4} +(0.266643 - 2.22011i) q^{5} +(-1.13202 - 2.39134i) q^{7} +(-1.04395 + 1.04395i) q^{8} +(-0.121480 - 0.848106i) q^{10} +(3.48588 - 2.01257i) q^{11} +(-2.94019 - 2.94019i) q^{13} +(-0.656107 - 0.772776i) q^{14} +(1.57035 - 2.71993i) q^{16} +(0.510805 - 1.90635i) q^{17} +(-3.06607 - 1.77020i) q^{19} +(1.62921 + 3.81015i) q^{20} +(1.09054 - 1.09054i) q^{22} +(0.467117 + 1.74330i) q^{23} +(-4.85780 - 1.18396i) q^{25} +(-1.37974 - 0.796592i) q^{26} +(4.03261 + 2.78897i) q^{28} +7.33557 q^{29} +(1.20124 + 2.08061i) q^{31} +(1.07568 - 4.01451i) q^{32} -0.756196i q^{34} +(-5.61090 + 1.87558i) q^{35} +(2.22373 + 8.29907i) q^{37} +(-1.31030 - 0.351094i) q^{38} +(2.03933 + 2.59606i) q^{40} -5.20836i q^{41} +(-1.29106 - 1.29106i) q^{43} +(-3.72969 + 6.46001i) q^{44} +(0.345760 + 0.598874i) q^{46} +(-1.06806 + 0.286186i) q^{47} +(-4.43705 + 5.41411i) q^{49} +(-1.91528 + 0.0435568i) q^{50} +(7.44311 + 1.99437i) q^{52} +(-10.7964 - 2.89287i) q^{53} +(-3.53866 - 8.27569i) q^{55} +(3.67823 + 1.31467i) q^{56} +(2.71489 - 0.727454i) q^{58} +(7.20215 + 12.4745i) q^{59} +(-2.48813 + 4.30957i) q^{61} +(0.650911 + 0.650911i) q^{62} +4.68896i q^{64} +(-7.31153 + 5.74357i) q^{65} +(5.94931 + 1.59411i) q^{67} +(0.946620 + 3.53283i) q^{68} +(-1.89060 + 1.25058i) q^{70} +1.99948i q^{71} +(3.35751 - 12.5304i) q^{73} +(1.64601 + 2.85096i) q^{74} +6.56103 q^{76} +(-8.75886 - 6.05766i) q^{77} +(12.9543 + 7.47918i) q^{79} +(-5.61982 - 4.21161i) q^{80} +(-0.516502 - 1.92761i) q^{82} +(11.2724 - 11.2724i) q^{83} +(-4.09611 - 1.64236i) q^{85} +(-0.605851 - 0.349788i) q^{86} +(-1.53806 + 5.74013i) q^{88} +(4.22341 - 7.31516i) q^{89} +(-3.70264 + 10.3594i) q^{91} +(-2.36502 - 2.36502i) q^{92} +(-0.366909 + 0.211835i) q^{94} +(-4.74759 + 6.33502i) q^{95} +(4.46118 - 4.46118i) q^{97} +(-1.10525 + 2.44378i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{7} + 8 q^{10} + 32 q^{16} - 48 q^{22} - 16 q^{25} + 88 q^{28} + 32 q^{31} - 16 q^{37} - 40 q^{40} - 16 q^{43} - 80 q^{52} - 32 q^{55} - 88 q^{58} + 48 q^{61} - 32 q^{67} - 112 q^{70} - 88 q^{73}+ \cdots + 208 q^{97}+O(q^{100}) \) 64 * q + 8 * q^7 + 8 * q^10 + 32 * q^16 - 48 * q^22 - 16 * q^25 + 88 * q^28 + 32 * q^31 - 16 * q^37 - 40 * q^40 - 16 * q^43 - 80 * q^52 - 32 * q^55 - 88 * q^58 + 48 * q^61 - 32 * q^67 - 112 * q^70 - 88 * q^73 - 320 * q^76 - 56 * q^82 + 16 * q^85 + 120 * q^88 - 128 * q^91 + 208 * q^97

Introduction

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