LMFDB - Embedded newform 352.2.u.a.95.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [352,2,Mod(63,352)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(352, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("352.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 352 = 2^{5} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	352.u (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			95.8
Character	$\chi$	$=$	352.95
Dual form			352.2.u.a.63.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.821048 + 0.266775i) q^{3} +(0.946699 - 0.687817i) q^{5} +(-1.39243 - 4.28545i) q^{7} +(-1.82410 - 1.32529i) q^{9} +(-1.25816 - 3.06872i) q^{11} +(2.26030 - 3.11103i) q^{13} +(0.960777 - 0.312175i) q^{15} +(4.70931 + 6.48181i) q^{17} +(-0.853485 + 2.62676i) q^{19} -3.89002i q^{21} +3.09605i q^{23} +(-1.12194 + 3.45297i) q^{25} +(-2.66643 - 3.67002i) q^{27} +(7.05366 - 2.29187i) q^{29} +(-0.434298 + 0.597760i) q^{31} +(-0.214353 - 2.85521i) q^{33} +(-4.26581 - 3.09929i) q^{35} +(0.572081 + 1.76068i) q^{37} +(2.68576 - 1.95132i) q^{39} +(-0.0835459 - 0.0271457i) q^{41} +8.29153 q^{43} -2.63843 q^{45} +(-2.06484 - 0.670908i) q^{47} +(-10.7631 + 7.81985i) q^{49} +(2.13739 + 6.57821i) q^{51} +(-2.64442 - 1.92129i) q^{53} +(-3.30181 - 2.03977i) q^{55} +(-1.40150 + 1.92900i) q^{57} +(5.86792 - 1.90660i) q^{59} +(-6.81768 - 9.38374i) q^{61} +(-3.13952 + 9.66245i) q^{63} -4.49988i q^{65} +9.54408i q^{67} +(-0.825948 + 2.54201i) q^{69} +(-0.138253 - 0.190289i) q^{71} +(1.49411 - 0.485466i) q^{73} +(-1.84233 + 2.53575i) q^{75} +(-11.3989 + 9.66474i) q^{77} +(12.3705 + 8.98766i) q^{79} +(0.880036 + 2.70847i) q^{81} +(3.59158 - 2.60943i) q^{83} +(8.91660 + 2.89718i) q^{85} +6.40281 q^{87} +8.42612 q^{89} +(-16.4795 - 5.35451i) q^{91} +(-0.516047 + 0.374930i) q^{93} +(0.998734 + 3.07379i) q^{95} +(-10.9895 - 7.98432i) q^{97} +(-1.77192 + 7.26507i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{9} + 4 q^{25} + 36 q^{33} + 40 q^{41} - 96 q^{45} - 4 q^{49} - 8 q^{53} + 20 q^{57} - 8 q^{69} - 40 q^{73} - 72 q^{77} - 72 q^{81} - 80 q^{85} - 40 q^{89} + 8 q^{93} + 4 q^{97}+O(q^{100}) $ 48 * q + 4 * q^9 + 4 * q^25 + 36 * q^33 + 40 * q^41 - 96 * q^45 - 4 * q^49 - 8 * q^53 + 20 * q^57 - 8 * q^69 - 40 * q^73 - 72 * q^77 - 72 * q^81 - 80 * q^85 - 40 * q^89 + 8 * q^93 + 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$.

$n$	$133$	$287$	$321$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.821048	+	0.266775i	0.474032	+	0.154022i	0.536283	−	0.844038i	$-0.319828\pi$
$3$	0.821048	+	0.266775i	0.474032	+	0.154022i	−0.0622508	+	0.998061i	$0.519828\pi$
$4$		0			0
$5$	0.946699	−	0.687817i	0.423376	−	0.307601i	−0.355618	−	0.934631i	$-0.615730\pi$
$5$	0.946699	−	0.687817i	0.423376	−	0.307601i	0.778995	+	0.627030i	$0.215730\pi$
$6$		0			0
$7$	−1.39243	−	4.28545i	−0.526288	−	1.61975i	−0.761755	−	0.647865i	$-0.775662\pi$
$7$	−1.39243	−	4.28545i	−0.526288	−	1.61975i	0.235467	−	0.971882i	$-0.424338\pi$
$8$		0			0
$9$	−1.82410	−	1.32529i	−0.608033	−	0.441762i
$10$		0			0
$11$	−1.25816	−	3.06872i	−0.379349	−	0.925254i
$11$	−1.25816	−	3.06872i	−0.379349	−	0.925254i
$12$		0			0
$13$	2.26030	−	3.11103i	0.626894	−	0.862846i	−0.370938	−	0.928658i	$-0.620964\pi$
$13$	2.26030	−	3.11103i	0.626894	−	0.862846i	0.997832	+	0.0658120i	$0.0209638\pi$
$14$		0			0
$15$	0.960777	−	0.312175i	0.248072	−	0.0806034i
$16$		0			0
$17$	4.70931	+	6.48181i	1.14218	+	1.57207i	0.762548	+	0.646932i	$0.223948\pi$
$17$	4.70931	+	6.48181i	1.14218	+	1.57207i	0.379629	+	0.925139i	$0.376052\pi$
$18$		0			0
$19$	−0.853485	+	2.62676i	−0.195803	+	0.602619i	0.804164	+	0.594408i	$0.202614\pi$
$19$	−0.853485	+	2.62676i	−0.195803	+	0.602619i	−0.999966	+	0.00821083i	$0.997386\pi$
$20$		0			0
$21$		−	3.89002i		−	0.848873i
$22$		0			0
$23$			3.09605i			0.645571i	0.946472	+	0.322785i	$0.104619\pi$
$23$			3.09605i			0.645571i	−0.946472	+	0.322785i	$0.895381\pi$
$24$		0			0
$25$	−1.12194	+	3.45297i	−0.224388	+	0.690594i
$26$		0			0
$27$	−2.66643	−	3.67002i	−0.513154	−	0.706296i
$28$		0			0
$29$	7.05366	−	2.29187i	1.30983	−	0.425590i	0.430840	−	0.902428i	$-0.358217\pi$
$29$	7.05366	−	2.29187i	1.30983	−	0.425590i	0.878991	+	0.476838i	$0.158217\pi$
$30$		0			0
$31$	−0.434298	+	0.597760i	−0.0780022	+	0.107361i	−0.846235	−	0.532809i	$-0.821136\pi$
$31$	−0.434298	+	0.597760i	−0.0780022	+	0.107361i	0.768233	+	0.640170i	$0.221136\pi$
$32$		0			0
$33$	−0.214353	−	2.85521i	−0.0373141	−	0.497028i
$34$		0			0
$35$	−4.26581	−	3.09929i	−0.721054	−	0.523876i
$36$		0			0
$37$	0.572081	+	1.76068i	0.0940495	+	0.289455i	0.987005	−	0.160691i	$-0.0513722\pi$
$37$	0.572081	+	1.76068i	0.0940495	+	0.289455i	−0.892955	+	0.450145i	$0.851372\pi$
$38$		0			0
$39$	2.68576	−	1.95132i	0.430066	−	0.312461i
$40$		0			0
$41$	−0.0835459	−	0.0271457i	−0.0130477	−	0.00423945i	0.302486	−	0.953154i	$-0.402183\pi$
$41$	−0.0835459	−	0.0271457i	−0.0130477	−	0.00423945i	−0.315534	+	0.948914i	$0.602183\pi$
$42$		0			0
$43$	8.29153			1.26445			0.632223	−	0.774786i	$-0.282142\pi$
$43$	8.29153			1.26445			0.632223	+	0.774786i	$0.282142\pi$
$44$		0			0
$45$	−2.63843			−0.393313
$46$		0			0
$47$	−2.06484	−	0.670908i	−0.301188	−	0.0978619i	0.154524	−	0.987989i	$-0.450615\pi$
$47$	−2.06484	−	0.670908i	−0.301188	−	0.0978619i	−0.455712	+	0.890127i	$0.650615\pi$
$48$		0			0
$49$	−10.7631	+	7.81985i	−1.53759	+	1.11712i
$50$		0			0
$51$	2.13739	+	6.57821i	0.299294	+	0.921133i
$52$		0			0
$53$	−2.64442	−	1.92129i	−0.363240	−	0.263909i	0.391162	−	0.920322i	$-0.372073\pi$
$53$	−2.64442	−	1.92129i	−0.363240	−	0.263909i	−0.754402	+	0.656413i	$0.772073\pi$
$54$		0			0
$55$	−3.30181	−	2.03977i	−0.445217	−	0.275042i
$56$		0			0
$57$	−1.40150	+	1.92900i	−0.185634	+	0.255503i
$58$		0			0
$59$	5.86792	−	1.90660i	0.763938	−	0.248218i	0.0989698	−	0.995090i	$-0.468445\pi$
$59$	5.86792	−	1.90660i	0.763938	−	0.248218i	0.664968	+	0.746872i	$0.268445\pi$
$60$		0			0
$61$	−6.81768	−	9.38374i	−0.872915	−	1.20146i	−0.978333	−	0.207037i	$-0.933618\pi$
$61$	−6.81768	−	9.38374i	−0.872915	−	1.20146i	0.105418	−	0.994428i	$-0.466382\pi$
$62$		0			0
$63$	−3.13952	+	9.66245i	−0.395542	+	1.21735i
$64$		0			0
$65$		−	4.49988i		−	0.558142i
$66$		0			0
$67$			9.54408i			1.16600i	0.812474	+	0.582998i	$0.198120\pi$
$67$			9.54408i			1.16600i	−0.812474	+	0.582998i	$0.801880\pi$
$68$		0			0
$69$	−0.825948	+	2.54201i	−0.0994324	+	0.306022i
$70$		0			0
$71$	−0.138253	−	0.190289i	−0.0164077	−	0.0225832i	0.800734	−	0.599020i	$-0.204443\pi$
$71$	−0.138253	−	0.190289i	−0.0164077	−	0.0225832i	−0.817142	+	0.576436i	$0.804443\pi$
$72$		0			0
$73$	1.49411	−	0.485466i	0.174873	−	0.0568195i	−0.220272	−	0.975438i	$-0.570695\pi$
$73$	1.49411	−	0.485466i	0.174873	−	0.0568195i	0.395145	+	0.918619i	$0.370695\pi$
$74$		0			0
$75$	−1.84233	+	2.53575i	−0.212734	+	0.292803i
$76$		0			0
$77$	−11.3989	+	9.66474i	−1.29903	+	1.10140i
$78$		0			0
$79$	12.3705	+	8.98766i	1.39179	+	1.01119i	0.995667	+	0.0929915i	$0.0296430\pi$
$79$	12.3705	+	8.98766i	1.39179	+	1.01119i	0.396118	+	0.918200i	$0.370357\pi$
$80$		0			0
$81$	0.880036	+	2.70847i	0.0977817	+	0.300941i
$82$		0			0
$83$	3.59158	−	2.60943i	0.394227	−	0.286423i	−0.372959	−	0.927848i	$-0.621657\pi$
$83$	3.59158	−	2.60943i	0.394227	−	0.286423i	0.767185	+	0.641425i	$0.221657\pi$
$84$		0			0
$85$	8.91660	+	2.89718i	0.967141	+	0.314243i
$86$		0			0
$87$	6.40281			0.686453
$88$		0			0
$89$	8.42612			0.893167			0.446584	−	0.894742i	$-0.352641\pi$
$89$	8.42612			0.893167			0.446584	+	0.894742i	$0.352641\pi$
$90$		0			0
$91$	−16.4795	−	5.35451i	−1.72752	−	0.561305i
$92$		0			0
$93$	−0.516047	+	0.374930i	−0.0535116	+	0.0388784i
$94$		0			0
$95$	0.998734	+	3.07379i	0.102468	+	0.315364i
$96$		0			0
$97$	−10.9895	−	7.98432i	−1.11581	−	0.810685i	−0.132243	−	0.991217i	$-0.542218\pi$
$97$	−10.9895	−	7.98432i	−1.11581	−	0.810685i	−0.983569	+	0.180532i	$0.942218\pi$
$98$		0			0
$99$	−1.77192	+	7.26507i	−0.178085	+	0.730167i
$100$		0			0
$101$	−3.67693	+	5.06086i	−0.365869	+	0.503575i	−0.951772	−	0.306806i	$-0.900740\pi$
$101$	−3.67693	+	5.06086i	−0.365869	+	0.503575i	0.585904	+	0.810381i	$0.300740\pi$
$102$		0			0
$103$	−12.3038	+	3.99775i	−1.21233	+	0.393910i	−0.844284	−	0.535897i	$-0.819974\pi$
$103$	−12.3038	+	3.99775i	−1.21233	+	0.393910i	−0.368048	+	0.929807i	$0.619974\pi$
$104$		0			0
$105$	−2.67562	−	3.68268i	−0.261114	−	0.359393i
$106$		0			0
$107$	1.95157	−	6.00630i	0.188665	−	0.580651i	−0.811327	−	0.584592i	$-0.801255\pi$
$107$	1.95157	−	6.00630i	0.188665	−	0.580651i	0.999992	+	0.00394122i	$0.00125453\pi$
$108$		0			0
$109$			1.65134i			0.158170i	0.996868	+	0.0790849i	$0.0251998\pi$
$109$			1.65134i			0.158170i	−0.996868	+	0.0790849i	$0.974800\pi$
$110$		0			0
$111$			1.59822i			0.151697i
$112$		0			0
$113$	0.999070	−	3.07482i	0.0939846	−	0.289255i	−0.893003	−	0.450051i	$-0.851406\pi$
$113$	0.999070	−	3.07482i	0.0939846	−	0.289255i	0.986988	+	0.160796i	$0.0514060\pi$
$114$		0			0
$115$	2.12951	+	2.93103i	0.198578	+	0.273320i
$116$		0			0
$117$	−8.24602	+	2.67929i	−0.762345	+	0.247701i
$118$		0			0
$119$	21.2201	−	29.2070i	1.94524	−	2.67740i
$120$		0			0
$121$	−7.83407	+	7.72188i	−0.712188	+	0.701989i
$122$		0			0
$123$	−0.0613534	−	0.0445759i	−0.00553205	−	0.00401927i
$124$		0			0
$125$	3.12091	+	9.60517i	0.279142	+	0.859112i
$126$		0			0
$127$	−15.1368	+	10.9975i	−1.34318	+	0.975874i	−0.343855	+	0.939023i	$0.611733\pi$
$127$	−15.1368	+	10.9975i	−1.34318	+	0.975874i	−0.999321	+	0.0368512i	$0.988267\pi$
$128$		0			0
$129$	6.80775	+	2.21197i	0.599389	+	0.194753i
$130$		0			0
$131$	13.7690			1.20300			0.601500	−	0.798873i	$-0.294570\pi$
$131$	13.7690			1.20300			0.601500	+	0.798873i	$0.294570\pi$
$132$		0			0
$133$	12.4452			1.07914
$134$		0			0
$135$	−5.04861	−	1.64039i	−0.434515	−	0.141182i
$136$		0			0
$137$	10.2620	−	7.45580i	0.876744	−	0.636992i	−0.0556438	−	0.998451i	$-0.517721\pi$
$137$	10.2620	−	7.45580i	0.876744	−	0.636992i	0.932388	+	0.361459i	$0.117721\pi$
$138$		0			0
$139$	2.13372	+	6.56691i	0.180980	+	0.556998i	0.999856	−	0.0169719i	$-0.00540259\pi$
$139$	2.13372	+	6.56691i	0.180980	+	0.556998i	−0.818876	+	0.573970i	$0.805403\pi$
$140$		0			0
$141$	−1.51635	−	1.10170i	−0.127700	−	0.0927795i
$142$		0			0
$143$	−12.3907	−	3.02204i	−1.03616	−	0.252716i
$144$		0			0
$145$	5.10130	−	7.02134i	0.423640	−	0.583090i
$146$		0			0
$147$	−10.9232	+	3.54915i	−0.900927	+	0.292729i
$148$		0			0
$149$	3.42416	+	4.71295i	0.280518	+	0.386100i	0.925905	−	0.377755i	$-0.123304\pi$
$149$	3.42416	+	4.71295i	0.280518	+	0.386100i	−0.645387	+	0.763856i	$0.723304\pi$
$150$		0			0
$151$	0.610801	−	1.87985i	0.0497063	−	0.152980i	−0.923122	−	0.384506i	$-0.874372\pi$
$151$	0.610801	−	1.87985i	0.0497063	−	0.152980i	0.972829	+	0.231526i	$0.0743718\pi$
$152$		0			0
$153$		−	18.0647i		−	1.46044i
$154$		0			0
$155$			0.864616i			0.0694476i
$156$		0			0
$157$	2.27594	−	7.00462i	0.181640	−	0.559029i	−0.818235	−	0.574884i	$-0.805047\pi$
$157$	2.27594	−	7.00462i	0.181640	−	0.559029i	0.999874	+	0.0158551i	$0.00504703\pi$
$158$		0			0
$159$	−1.65865	−	2.28293i	−0.131539	−	0.181048i
$160$		0			0
$161$	13.2680	−	4.31102i	1.04566	−	0.339756i
$162$		0			0
$163$	−0.416303	+	0.572992i	−0.0326073	+	0.0448802i	−0.825009	−	0.565119i	$-0.808830\pi$
$163$	−0.416303	+	0.572992i	−0.0326073	+	0.0448802i	0.792402	+	0.609999i	$0.208830\pi$
$164$		0			0
$165$	−2.16679	−	2.55559i	−0.168684	−	0.198952i
$166$		0			0
$167$	−8.89406	−	6.46192i	−0.688243	−	0.500038i	0.187839	−	0.982200i	$-0.439852\pi$
$167$	−8.89406	−	6.46192i	−0.688243	−	0.500038i	−0.876082	+	0.482162i	$0.839852\pi$
$168$		0			0
$169$	−0.552362	−	1.70000i	−0.0424894	−	0.130769i
$170$		0			0
$171$	5.03804	−	3.66035i	0.385269	−	0.279914i
$172$		0			0
$173$	12.6386	+	4.10654i	0.960898	+	0.312215i	0.747136	−	0.664671i	$-0.231428\pi$
$173$	12.6386	+	4.10654i	0.960898	+	0.312215i	0.213762	+	0.976886i	$0.431428\pi$
$174$		0			0
$175$	16.3598			1.23668
$176$		0			0
$177$	5.32648			0.400362
$178$		0			0
$179$	−3.38857	−	1.10101i	−0.253273	−	0.0822935i	0.179629	−	0.983734i	$-0.442510\pi$
$179$	−3.38857	−	1.10101i	−0.253273	−	0.0822935i	−0.432902	+	0.901441i	$0.642510\pi$
$180$		0			0
$181$	−13.2963	+	9.66033i	−0.988306	+	0.718047i	−0.959550	−	0.281540i	$-0.909155\pi$
$181$	−13.2963	+	9.66033i	−0.988306	+	0.718047i	−0.0287567	+	0.999586i	$0.509155\pi$
$182$		0			0
$183$	−3.09430	−	9.52329i	−0.228738	−	0.703982i
$184$		0			0
$185$	1.75262	+	1.27335i	0.128855	+	0.0936185i
$186$		0			0
$187$	13.9658	−	22.6067i	1.02128	−	1.65317i
$188$		0			0
$189$	−12.0149	+	16.5371i	−0.873955	+	1.20290i
$190$		0			0
$191$	6.02166	−	1.95655i	0.435712	−	0.141571i	−0.0829446	−	0.996554i	$-0.526432\pi$
$191$	6.02166	−	1.95655i	0.435712	−	0.141571i	0.518656	+	0.854983i	$0.326432\pi$
$192$		0			0
$193$	−7.00924	−	9.64740i	−0.504536	−	0.694435i	0.478450	−	0.878115i	$-0.341199\pi$
$193$	−7.00924	−	9.64740i	−0.504536	−	0.694435i	−0.982986	+	0.183680i	$0.941199\pi$
$194$		0			0
$195$	1.20046	−	3.69462i	0.0859664	−	0.264577i
$196$		0			0
$197$		−	21.1804i		−	1.50904i	−0.656275	−	0.754522i	$-0.727869\pi$
$197$		−	21.1804i		−	1.50904i	0.656275	−	0.754522i	$-0.272131\pi$
$198$		0			0
$199$			9.63234i			0.682819i	0.939915	+	0.341409i	$0.110904\pi$
$199$			9.63234i			0.682819i	−0.939915	+	0.341409i	$0.889096\pi$
$200$		0			0
$201$	−2.54612	+	7.83615i	−0.179590	+	0.552720i
$202$		0			0
$203$	−19.6434	−	27.0368i	−1.37870	−	1.89761i
$204$		0			0
$205$	−0.0977640	+	0.0317655i	−0.00682814	+	0.00221860i
$206$		0			0
$207$	4.10315	−	5.64750i	0.285189	−	0.392529i
$208$		0			0
$209$	9.13459	−	0.685773i	0.631853	−	0.0474359i
$210$		0			0
$211$	−20.0237	−	14.5480i	−1.37849	−	1.00153i	−0.997020	−	0.0771453i	$-0.975419\pi$
$211$	−20.0237	−	14.5480i	−1.37849	−	1.00153i	−0.381466	−	0.924383i	$-0.624581\pi$
$212$		0			0
$213$	−0.0627483	−	0.193119i	−0.00429944	−	0.0132323i
$214$		0			0
$215$	7.84958	−	5.70306i	0.535337	−	0.388945i
$216$		0			0
$217$	3.16640	+	1.02882i	0.214949	+	0.0698412i
$218$		0			0
$219$	1.35625			0.0916467
$220$		0			0
$221$	30.8096			2.07248
$222$		0			0
$223$	5.16411	+	1.67792i	0.345814	+	0.112362i	0.476774	−	0.879026i	$-0.341806\pi$
$223$	5.16411	+	1.67792i	0.345814	+	0.112362i	−0.130960	+	0.991388i	$0.541806\pi$
$224$		0			0
$225$	6.62270	−	4.81168i	0.441514	−	0.320778i
$226$		0			0
$227$	7.02945	+	21.6344i	0.466561	+	1.43593i	0.857009	+	0.515301i	$0.172320\pi$
$227$	7.02945	+	21.6344i	0.466561	+	1.43593i	−0.390448	+	0.920625i	$0.627680\pi$
$228$		0			0
$229$	−5.54714	−	4.03023i	−0.366565	−	0.266325i	0.389220	−	0.921145i	$-0.372745\pi$
$229$	−5.54714	−	4.03023i	−0.366565	−	0.266325i	−0.755785	+	0.654820i	$0.772745\pi$
$230$		0			0
$231$	−11.9374	+	4.89427i	−0.785423	+	0.322019i
$232$		0			0
$233$	0.0558764	−	0.0769073i	0.00366059	−	0.00503837i	−0.807183	−	0.590302i	$-0.799009\pi$
$233$	0.0558764	−	0.0769073i	0.00366059	−	0.00503837i	0.810843	+	0.585263i	$0.199009\pi$
$234$		0			0
$235$	−2.41624	+	0.785085i	−0.157618	+	0.0512133i
$236$		0			0
$237$	7.75906	+	10.6794i	0.504005	+	0.693704i
$238$		0			0
$239$	−6.60521	+	20.3288i	−0.427256	+	1.31496i	0.473562	+	0.880761i	$0.342968\pi$
$239$	−6.60521	+	20.3288i	−0.427256	+	1.31496i	−0.900818	+	0.434197i	$0.857032\pi$
$240$		0			0
$241$		−	10.7913i		−	0.695130i	−0.937656	−	0.347565i	$-0.887009\pi$
$241$		−	10.7913i		−	0.695130i	0.937656	−	0.347565i	$-0.112991\pi$
$242$		0			0
$243$			16.0678i			1.03075i
$244$		0			0
$245$	−4.81079	+	14.8061i	−0.307350	+	0.945926i
$246$		0			0
$247$	6.24280	+	8.59247i	0.397220	+	0.546726i
$248$		0			0
$249$	3.64499	−	1.18433i	0.230992	−	0.0750538i
$250$		0			0
$251$	−3.62774	+	4.99316i	−0.228981	+	0.315166i	−0.908012	−	0.418944i	$-0.862400\pi$
$251$	−3.62774	+	4.99316i	−0.228981	+	0.315166i	0.679031	+	0.734110i	$0.262400\pi$
$252$		0			0
$253$	9.50090	−	3.89532i	0.597317	−	0.244897i
$254$		0			0
$255$	6.54807	+	4.75745i	0.410056	+	0.297923i
$256$		0			0
$257$	4.41700	+	13.5941i	0.275525	+	0.847978i	0.989080	+	0.147379i	$0.0470837\pi$
$257$	4.41700	+	13.5941i	0.275525	+	0.847978i	−0.713555	+	0.700599i	$0.752916\pi$
$258$		0			0
$259$	6.74874	−	4.90325i	0.419346	−	0.304673i
$260$		0			0
$261$	−15.9040	−	5.16751i	−0.984431	−	0.319861i
$262$		0			0
$263$	−22.8100			−1.40653			−0.703263	−	0.710929i	$-0.748274\pi$
$263$	−22.8100			−1.40653			−0.703263	+	0.710929i	$0.748274\pi$
$264$		0			0
$265$	−3.82497			−0.234966
$266$		0			0
$267$	6.91825	+	2.24788i	0.423390	+	0.137568i
$268$		0			0
$269$	−17.9057	+	13.0093i	−1.09173	+	0.793190i	−0.979691	−	0.200514i	$-0.935739\pi$
$269$	−17.9057	+	13.0093i	−1.09173	+	0.793190i	−0.112041	+	0.993704i	$0.535739\pi$
$270$		0			0
$271$	−4.08031	−	12.5579i	−0.247861	−	0.762839i	−0.995153	−	0.0983421i	$-0.968646\pi$
$271$	−4.08031	−	12.5579i	−0.247861	−	0.762839i	0.747291	−	0.664497i	$-0.231354\pi$
$272$		0			0
$273$	−12.1020	−	8.79262i	−0.732446	−	0.532153i
$274$		0			0
$275$	12.0078	−	0.901476i	0.724096	−	0.0543610i
$276$		0			0
$277$	15.0108	−	20.6606i	0.901912	−	1.24138i	−0.0679420	−	0.997689i	$-0.521643\pi$
$277$	15.0108	−	20.6606i	0.901912	−	1.24138i	0.969854	−	0.243686i	$-0.0783567\pi$
$278$		0			0
$279$	1.58441	−	0.514804i	0.0948559	−	0.0308205i
$280$		0			0
$281$	0.140020	+	0.192720i	0.00835286	+	0.0114967i	0.813173	−	0.582022i	$-0.197738\pi$
$281$	0.140020	+	0.192720i	0.00835286	+	0.0114967i	−0.804820	+	0.593519i	$0.797738\pi$
$282$		0			0
$283$	−6.84605	+	21.0700i	−0.406955	+	1.25248i	0.512296	+	0.858809i	$0.328795\pi$
$283$	−6.84605	+	21.0700i	−0.406955	+	1.25248i	−0.919252	+	0.393671i	$0.871205\pi$
$284$		0			0
$285$			2.79016i			0.165275i
$286$		0			0
$287$			0.395830i			0.0233651i
$288$		0			0
$289$	−14.5830	+	44.8818i	−0.857823	+	2.64011i
$290$		0			0
$291$	−6.89287	−	9.48723i	−0.404067	−	0.556151i
$292$		0			0
$293$	2.20964	−	0.717956i	0.129089	−	0.0419434i	−0.243760	−	0.969836i	$-0.578381\pi$
$293$	2.20964	−	0.717956i	0.129089	−	0.0419434i	0.372849	+	0.927892i	$0.378381\pi$
$294$		0			0
$295$	4.24376	−	5.84103i	0.247081	−	0.340078i
$296$		0			0
$297$	−7.90748	+	12.8000i	−0.458838	+	0.742731i
$298$		0			0
$299$	9.63191	+	6.99800i	0.557028	+	0.404705i
$300$		0			0
$301$	−11.5454	−	35.5329i	−0.665463	−	2.04808i
$302$		0			0
$303$	−4.36905	+	3.17430i	−0.250995	+	0.182359i
$304$		0			0
$305$	−12.9086	−	4.19425i	−0.739143	−	0.240162i
$306$		0			0
$307$	21.3506			1.21854			0.609272	−	0.792961i	$-0.291462\pi$
$307$	21.3506			1.21854			0.609272	+	0.792961i	$0.291462\pi$
$308$		0			0
$309$	−11.1685			−0.635355
$310$		0			0
$311$	22.0461	+	7.16322i	1.25012	+	0.406189i	0.857964	−	0.513709i	$-0.171729\pi$
$311$	22.0461	+	7.16322i	1.25012	+	0.406189i	0.392157	+	0.919898i	$0.371729\pi$
$312$		0			0
$313$	−18.5533	+	13.4798i	−1.04869	+	0.761921i	−0.971964	−	0.235131i	$-0.924448\pi$
$313$	−18.5533	+	13.4798i	−1.04869	+	0.761921i	−0.0767304	+	0.997052i	$0.524448\pi$
$314$		0			0
$315$	3.67382	+	11.3068i	0.206996	+	0.637068i
$316$		0			0
$317$	−21.0321	−	15.2807i	−1.18128	−	0.858249i	−0.188963	−	0.981984i	$-0.560513\pi$
$317$	−21.0321	−	15.2807i	−1.18128	−	0.858249i	−0.992315	+	0.123736i	$0.960513\pi$
$318$		0			0
$319$	−15.9077	−	18.7622i	−0.890662	−	1.05048i
$320$		0			0
$321$	3.20466	−	4.41083i	0.178867	−	0.246189i
$322$		0			0
$323$	−21.0455	+	6.83809i	−1.17100	+	0.380481i
$324$		0			0
$325$	8.20640	+	11.2951i	0.455209	+	0.626541i
$326$		0			0
$327$	−0.440536	+	1.35583i	−0.0243617	+	0.0749777i
$328$		0			0
$329$			9.78296i			0.539352i
$330$		0			0
$331$			4.78936i			0.263247i	0.991300	+	0.131624i	$0.0420190\pi$
$331$			4.78936i			0.263247i	−0.991300	+	0.131624i	$0.957981\pi$
$332$		0			0
$333$	1.28988	−	3.96983i	0.0706848	−	0.217545i
$334$		0			0
$335$	6.56458	+	9.03537i	0.358661	+	0.493655i
$336$		0			0
$337$	−2.66425	+	0.865668i	−0.145131	+	0.0471559i	−0.380682	−	0.924706i	$-0.624311\pi$
$337$	−2.66425	+	0.865668i	−0.145131	+	0.0471559i	0.235551	+	0.971862i	$0.424311\pi$
$338$		0			0
$339$	1.64057	−	2.25805i	0.0891035	−	0.122640i
$340$		0			0
$341$	2.38077	+	0.580661i	0.128926	+	0.0314446i
$342$		0			0
$343$	22.9805	+	16.6963i	1.24083	+	0.901515i
$344$		0			0
$345$	0.966511	+	2.97461i	0.0520352	+	0.160148i
$346$		0			0
$347$	10.8961	−	7.91651i	0.584936	−	0.424981i	−0.255564	−	0.966792i	$-0.582261\pi$
$347$	10.8961	−	7.91651i	0.584936	−	0.424981i	0.840500	+	0.541811i	$0.182261\pi$
$348$		0			0
$349$	10.0828	+	3.27610i	0.539720	+	0.175366i	0.566176	−	0.824284i	$-0.308422\pi$
$349$	10.0828	+	3.27610i	0.539720	+	0.175366i	−0.0264563	+	0.999650i	$0.508422\pi$
$350$		0			0
$351$	−17.4445			−0.931118
$352$		0			0
$353$	−24.1753			−1.28672			−0.643360	−	0.765564i	$-0.722460\pi$
$353$	−24.1753			−1.28672			−0.643360	+	0.765564i	$0.722460\pi$
$354$		0			0
$355$	−0.261768	−	0.0850537i	−0.0138932	−	0.00451418i
$356$		0			0
$357$	25.2144	−	18.3193i	1.33449	−	0.969563i
$358$		0			0
$359$	0.575034	+	1.76977i	0.0303492	+	0.0934051i	0.965084	−	0.261942i	$-0.0843628\pi$
$359$	0.575034	+	1.76977i	0.0303492	+	0.0934051i	−0.934735	+	0.355347i	$0.884363\pi$
$360$		0			0
$361$	9.19992	+	6.68413i	0.484206	+	0.351796i
$362$		0			0
$363$	−8.49215	+	4.25010i	−0.445722	+	0.223072i
$364$		0			0
$365$	1.08056	−	1.48727i	0.0565592	−	0.0778470i
$366$		0			0
$367$	11.8946	−	3.86477i	0.620891	−	0.201740i	0.0183550	−	0.999832i	$-0.494157\pi$
$367$	11.8946	−	3.86477i	0.620891	−	0.201740i	0.602536	+	0.798092i	$0.294157\pi$
$368$		0			0
$369$	0.116420	+	0.160239i	0.00606059	+	0.00834169i
$370$		0			0
$371$	−4.55141	+	14.0078i	−0.236297	+	0.727248i
$372$		0			0
$373$		−	7.74672i		−	0.401110i	−0.979682	−	0.200555i	$-0.935725\pi$
$373$		−	7.74672i		−	0.401110i	0.979682	−	0.200555i	$-0.0642745\pi$
$374$		0			0
$375$			8.71888i			0.450241i
$376$		0			0
$377$	8.81328	−	27.1245i	0.453907	−	1.39698i
$378$		0			0
$379$	7.54898	+	10.3903i	0.387765	+	0.533713i	0.957621	−	0.288032i	$-0.0930009\pi$
$379$	7.54898	+	10.3903i	0.387765	+	0.533713i	−0.569856	+	0.821745i	$0.693001\pi$
$380$		0			0
$381$	−15.3619	+	4.99139i	−0.787015	+	0.255717i
$382$		0			0
$383$	9.92745	−	13.6640i	0.507269	−	0.698196i	−0.476187	−	0.879344i	$-0.657981\pi$
$383$	9.92745	−	13.6640i	0.507269	−	0.698196i	0.983456	+	0.181148i	$0.0579814\pi$
$384$		0			0
$385$	−4.14379	+	16.9900i	−0.211187	+	0.865890i
$386$		0			0
$387$	−15.1246	−	10.9887i	−0.768826	−	0.558585i
$388$		0			0
$389$	7.35307	+	22.6304i	0.372815	+	1.14741i	0.944941	+	0.327241i	$0.106119\pi$
$389$	7.35307	+	22.6304i	0.372815	+	1.14741i	−0.572126	+	0.820166i	$0.693881\pi$
$390$		0			0
$391$	−20.0680	+	14.5803i	−1.01488	+	0.737356i
$392$		0			0
$393$	11.3050	+	3.67321i	0.570261	+	0.185289i
$394$		0			0
$395$	17.8930			0.900292
$396$		0			0
$397$	−10.8989			−0.547002			−0.273501	−	0.961872i	$-0.588182\pi$
$397$	−10.8989			−0.547002			−0.273501	+	0.961872i	$0.588182\pi$
$398$		0			0
$399$	10.2181	+	3.32008i	0.511547	+	0.166212i
$400$		0			0
$401$	3.91875	−	2.84714i	0.195693	−	0.142179i	−0.485624	−	0.874168i	$-0.661408\pi$
$401$	3.91875	−	2.84714i	0.195693	−	0.142179i	0.681317	+	0.731988i	$0.261408\pi$
$402$		0			0
$403$	0.878008	+	2.70223i	0.0437367	+	0.134608i
$404$		0			0
$405$	2.69606	+	1.95880i	0.133968	+	0.0973337i
$406$		0			0
$407$	4.68327	−	3.97078i	0.232141	−	0.196824i
$408$		0			0
$409$	−11.3951	+	15.6840i	−0.563450	+	0.775523i	−0.991760	−	0.128109i	$-0.959109\pi$
$409$	−11.3951	+	15.6840i	−0.563450	+	0.775523i	0.428310	+	0.903632i	$0.359109\pi$
$410$		0			0
$411$	10.4146	−	3.38392i	0.513716	−	0.166917i
$412$		0			0
$413$	−16.3413	−	22.4919i	−0.804102	−	1.10675i
$414$		0			0
$415$	1.60533	−	4.94070i	0.0788025	−	0.242529i
$416$		0			0
$417$			5.96097i			0.291910i
$418$		0			0
$419$		−	25.7867i		−	1.25976i	−0.776691	−	0.629882i	$-0.783103\pi$
$419$		−	25.7867i		−	1.25976i	0.776691	−	0.629882i	$-0.216897\pi$
$420$		0			0
$421$	−2.92555	+	9.00393i	−0.142583	+	0.438824i	−0.996692	−	0.0812687i	$-0.974103\pi$
$421$	−2.92555	+	9.00393i	−0.142583	+	0.438824i	0.854110	+	0.520093i	$0.174103\pi$
$422$		0			0
$423$	2.87733	+	3.96031i	0.139901	+	0.192557i
$424$		0			0
$425$	−27.6651	+	8.98893i	−1.34195	+	0.436027i
$426$		0			0
$427$	−30.7204	+	42.2830i	−1.48666	+	2.04622i
$428$		0			0
$429$	−9.36716	−	5.78677i	−0.452251	−	0.279388i
$430$		0			0
$431$	6.42802	+	4.67023i	0.309627	+	0.224957i	0.731736	−	0.681588i	$-0.238710\pi$
$431$	6.42802	+	4.67023i	0.309627	+	0.224957i	−0.422110	+	0.906545i	$0.638710\pi$
$432$		0			0
$433$	−4.71114	−	14.4994i	−0.226403	−	0.696797i	−0.998146	−	0.0608624i	$-0.980615\pi$
$433$	−4.71114	−	14.4994i	−0.226403	−	0.696797i	0.771743	−	0.635934i	$-0.219385\pi$
$434$		0			0
$435$	6.06153	−	4.40396i	0.290628	−	0.211154i
$436$		0			0
$437$	−8.13256	−	2.64243i	−0.389033	−	0.126405i
$438$		0			0
$439$	−6.03531			−0.288050			−0.144025	−	0.989574i	$-0.546005\pi$
$439$	−6.03531			−0.288050			−0.144025	+	0.989574i	$0.546005\pi$
$440$		0			0
$441$	29.9965			1.42841
$442$		0			0
$443$	−27.8478	−	9.04831i	−1.32309	−	0.429898i	−0.439535	−	0.898225i	$-0.644857\pi$
$443$	−27.8478	−	9.04831i	−1.32309	−	0.429898i	−0.883555	+	0.468327i	$0.844857\pi$
$444$		0			0
$445$	7.97700	−	5.79563i	0.378146	−	0.274739i
$446$		0			0
$447$	1.55410	+	4.78304i	0.0735066	+	0.226230i
$448$		0			0
$449$	21.5716	+	15.6727i	1.01802	+	0.739638i	0.965877	−	0.259001i	$-0.0833933\pi$
$449$	21.5716	+	15.6727i	1.01802	+	0.739638i	0.0521477	+	0.998639i	$0.483393\pi$
$450$		0			0
$451$	0.0218115	+	0.290532i	0.00102706	+	0.0136806i
$452$		0			0
$453$	1.00299	−	1.38050i	0.0471248	−	0.0648617i
$454$		0			0
$455$	−19.2840	+	6.26576i	−0.904049	+	0.293743i
$456$		0			0
$457$	5.80699	+	7.99263i	0.271639	+	0.373880i	0.922942	−	0.384938i	$-0.125777\pi$
$457$	5.80699	+	7.99263i	0.271639	+	0.373880i	−0.651303	+	0.758818i	$0.725777\pi$
$458$		0			0
$459$	11.2314	−	34.5666i	0.524235	−	1.61343i
$460$		0			0
$461$		−	19.1288i		−	0.890917i	−0.895302	−	0.445459i	$-0.853041\pi$
$461$		−	19.1288i		−	0.890917i	0.895302	−	0.445459i	$-0.146959\pi$
$462$		0			0
$463$		−	32.6826i		−	1.51889i	−0.650572	−	0.759445i	$-0.725471\pi$
$463$		−	32.6826i		−	1.51889i	0.650572	−	0.759445i	$-0.274529\pi$
$464$		0			0
$465$	−0.230658	+	0.709891i	−0.0106965	+	0.0329204i
$466$		0			0
$467$	−6.44149	−	8.86594i	−0.298076	−	0.410267i	0.633540	−	0.773710i	$-0.281601\pi$
$467$	−6.44149	−	8.86594i	−0.298076	−	0.410267i	−0.931616	+	0.363443i	$0.881601\pi$
$468$		0			0
$469$	40.9007	−	13.2894i	1.88862	−	0.613649i
$470$		0			0
$471$	3.73731	−	5.14397i	0.172206	−	0.237021i
$472$		0			0
$473$	−10.4321	−	25.4444i	−0.479667	−	1.16993i
$474$		0			0
$475$	−8.11256	−	5.89412i	−0.372230	−	0.270441i
$476$		0			0
$477$	2.27744	+	7.00924i	0.104277	+	0.320931i
$478$		0			0
$479$	−9.80461	+	7.12347i	−0.447984	+	0.325479i	−0.788799	−	0.614651i	$-0.789297\pi$
$479$	−9.80461	+	7.12347i	−0.447984	+	0.325479i	0.340815	+	0.940130i	$0.389297\pi$
$480$		0			0
$481$	6.77062	+	2.19991i	0.308714	+	0.100307i
$482$		0			0
$483$	12.0437			0.548008
$484$		0			0
$485$	−15.8955			−0.721776
$486$		0			0
$487$	−31.7555	−	10.3180i	−1.43898	−	0.467553i	−0.517400	−	0.855743i	$-0.673100\pi$
$487$	−31.7555	−	10.3180i	−1.43898	−	0.467553i	−0.921579	+	0.388191i	$0.873100\pi$
$488$		0			0
$489$	−0.494664	+	0.359395i	−0.0223695	+	0.0162524i
$490$		0			0
$491$	−0.933713	−	2.87367i	−0.0421379	−	0.129687i	0.927774	−	0.373141i	$-0.121719\pi$
$491$	−0.933713	−	2.87367i	−0.0421379	−	0.129687i	−0.969912	+	0.243454i	$0.921719\pi$
$492$		0			0
$493$	48.0734	+	34.9274i	2.16512	+	1.57305i
$494$		0			0
$495$	3.31956	+	8.09659i	0.149203	+	0.363915i
$496$		0			0
$497$	−0.622968	+	0.857442i	−0.0279439	+	0.0384615i
$498$		0			0
$499$	39.3585	−	12.7883i	1.76193	−	0.572485i	0.764530	−	0.644588i	$-0.222971\pi$
$499$	39.3585	−	12.7883i	1.76193	−	0.572485i	0.997397	+	0.0721028i	$0.0229710\pi$
$500$		0			0
$501$	−5.57858	−	7.67826i	−0.249233	−	0.343039i
$502$		0			0
$503$	6.83618	−	21.0396i	0.304810	−	0.938109i	−0.674938	−	0.737875i	$-0.735830\pi$
$503$	6.83618	−	21.0396i	0.304810	−	0.938109i	0.979748	−	0.200235i	$-0.0641704\pi$
$504$		0			0
$505$			7.32017i			0.325743i
$506$		0			0
$507$		−	1.54314i		−	0.0685331i
$508$		0			0
$509$	3.10119	−	9.54450i	0.137458	−	0.423052i	−0.858506	−	0.512803i	$-0.828607\pi$
$509$	3.10119	−	9.54450i	0.137458	−	0.423052i	0.995964	+	0.0897508i	$0.0286071\pi$
$510$		0			0
$511$	−4.16088	−	5.72696i	−0.184067	−	0.253346i
$512$		0			0
$513$	11.9160	−	3.87175i	0.526105	−	0.170942i
$514$		0			0
$515$	−8.89829	+	12.2474i	−0.392105	+	0.539687i
$516$		0			0
$517$	0.539073	+	7.18053i	0.0237084	+	0.315799i
$518$		0			0
$519$	9.28142	+	6.74334i	0.407409	+	0.296000i
$520$		0			0
$521$	0.550645	+	1.69471i	0.0241242	+	0.0742467i	0.962394	−	0.271658i	$-0.0875720\pi$
$521$	0.550645	+	1.69471i	0.0241242	+	0.0742467i	−0.938270	+	0.345905i	$0.887572\pi$
$522$		0			0
$523$	−12.4675	+	9.05816i	−0.545165	+	0.396086i	−0.826000	−	0.563671i	$-0.809389\pi$
$523$	−12.4675	+	9.05816i	−0.545165	+	0.396086i	0.280835	+	0.959756i	$0.409389\pi$
$524$		0			0
$525$	13.4321	+	4.36437i	0.586227	+	0.190477i
$526$		0			0
$527$	−5.91981			−0.257871
$528$		0			0
$529$	13.4145			0.583238
$530$		0			0
$531$	−13.2305	−	4.29884i	−0.574153	−	0.186554i
$532$		0			0
$533$	−0.273290	+	0.198557i	−0.0118375	+	0.00860044i
$534$		0			0
$535$	−2.28369	−	7.02848i	−0.0987325	−	0.303867i
$536$		0			0
$537$	−2.48845	−	1.80797i	−0.107385	−	0.0780195i
$538$		0			0
$539$	37.5386	+	23.1903i	1.61690	+	0.998877i
$540$		0			0
$541$	9.04600	−	12.4508i	0.388918	−	0.535300i	−0.569002	−	0.822336i	$-0.692670\pi$
$541$	9.04600	−	12.4508i	0.388918	−	0.535300i	0.957920	+	0.287037i	$0.0926702\pi$
$542$		0			0
$543$	−13.4940	+	4.38448i	−0.579085	+	0.188156i
$544$		0			0
$545$	1.13582	+	1.56332i	0.0486532	+	0.0669654i
$546$		0			0
$547$	10.0471	−	30.9217i	0.429582	−	1.32212i	−0.468956	−	0.883221i	$-0.655370\pi$
$547$	10.0471	−	30.9217i	0.429582	−	1.32212i	0.898538	−	0.438895i	$-0.144630\pi$
$548$		0			0
$549$			26.1523i			1.11615i
$550$		0			0
$551$			20.4843i			0.872661i
$552$		0			0
$553$	21.2912	−	65.5276i	0.905395	−	2.78652i
$554$		0			0
$555$	1.09928	+	1.51304i	0.0466620	+	0.0642248i
$556$		0			0
$557$	−10.3610	+	3.36648i	−0.439008	+	0.142642i	−0.520178	−	0.854058i	$-0.674134\pi$
$557$	−10.3610	+	3.36648i	−0.439008	+	0.142642i	0.0811697	+	0.996700i	$0.474134\pi$
$558$		0			0
$559$	18.7413	−	25.7952i	0.792674	−	1.09102i
$560$		0			0
$561$	17.4975	−	14.8355i	0.738745	−	0.626355i
$562$		0			0
$563$	−7.04716	−	5.12006i	−0.297002	−	0.215785i	0.429297	−	0.903163i	$-0.358761\pi$
$563$	−7.04716	−	5.12006i	−0.297002	−	0.215785i	−0.726299	+	0.687379i	$0.758761\pi$
$564$		0			0
$565$	−1.16910	−	3.59811i	−0.0491842	−	0.151374i
$566$		0			0
$567$	10.3816	−	7.54270i	0.435987	−	0.316763i
$568$		0			0
$569$	13.3128	+	4.32558i	0.558100	+	0.181338i	0.574466	−	0.818528i	$-0.305210\pi$
$569$	13.3128	+	4.32558i	0.558100	+	0.181338i	−0.0163661	+	0.999866i	$0.505210\pi$
$570$		0			0
$571$	−29.5709			−1.23751			−0.618753	−	0.785586i	$-0.712362\pi$
$571$	−29.5709			−1.23751			−0.618753	+	0.785586i	$0.712362\pi$
$572$		0			0
$573$	5.46603			0.228347
$574$		0			0
$575$	−10.6906	−	3.47358i	−0.445828	−	0.144858i
$576$		0			0
$577$	−7.64850	+	5.55696i	−0.318411	+	0.231339i	−0.735497	−	0.677528i	$-0.763051\pi$
$577$	−7.64850	+	5.55696i	−0.318411	+	0.231339i	0.417086	+	0.908867i	$0.363051\pi$
$578$		0			0
$579$	−3.18125	−	9.79087i	−0.132208	−	0.406895i
$580$		0			0
$581$	−16.1836	−	11.7581i	−0.671409	−	0.487807i
$582$		0			0
$583$	−2.56878	+	10.5323i	−0.106388	+	0.436202i
$584$		0			0
$585$	−5.96363	+	8.20823i	−0.246566	+	0.339369i
$586$		0			0
$587$	−27.7154	+	9.00528i	−1.14394	+	0.371688i	−0.818856	−	0.573998i	$-0.805392\pi$
$587$	−27.7154	+	9.00528i	−1.14394	+	0.371688i	−0.325081	+	0.945686i	$0.605392\pi$
$588$		0			0
$589$	−1.19950	−	1.65097i	−0.0494246	−	0.0680272i
$590$		0			0
$591$	5.65041	−	17.3902i	0.232427	−	0.715336i
$592$		0			0
$593$			19.7983i			0.813018i	0.913647	+	0.406509i	$0.133254\pi$
$593$			19.7983i			0.813018i	−0.913647	+	0.406509i	$0.866746\pi$
$594$		0			0
$595$		−	42.2458i		−	1.73191i
$596$		0			0
$597$	−2.56967	+	7.90862i	−0.105169	+	0.323678i
$598$		0			0
$599$	19.2444	+	26.4876i	0.786305	+	1.08226i	0.994558	+	0.104181i	$0.0332220\pi$
$599$	19.2444	+	26.4876i	0.786305	+	1.08226i	−0.208254	+	0.978075i	$0.566778\pi$
$600$		0			0
$601$	−14.6558	+	4.76196i	−0.597823	+	0.194245i	−0.592269	−	0.805740i	$-0.701768\pi$
$601$	−14.6558	+	4.76196i	−0.597823	+	0.194245i	−0.00555393	+	0.999985i	$0.501768\pi$
$602$		0			0
$603$	12.6486	−	17.4094i	0.515092	−	0.708964i
$604$		0			0
$605$	−2.10527	+	12.6987i	−0.0855913	+	0.516275i
$606$		0			0
$607$	−5.82959	−	4.23544i	−0.236616	−	0.171911i	0.463159	−	0.886275i	$-0.346716\pi$
$607$	−5.82959	−	4.23544i	−0.236616	−	0.171911i	−0.699774	+	0.714364i	$0.746716\pi$
$608$		0			0
$609$	−8.91544	−	27.4389i	−0.361272	−	1.11188i
$610$		0			0
$611$	−6.75437	+	4.90734i	−0.273253	+	0.198530i
$612$		0			0
$613$	−32.9602	−	10.7094i	−1.33125	−	0.432550i	−0.444907	−	0.895577i	$-0.646763\pi$
$613$	−32.9602	−	10.7094i	−1.33125	−	0.432550i	−0.886344	+	0.463027i	$0.846763\pi$
$614$		0			0
$615$	−0.0887432			−0.00357847
$616$		0			0
$617$	1.08499			0.0436801			0.0218400	−	0.999761i	$-0.493048\pi$
$617$	1.08499			0.0436801			0.0218400	+	0.999761i	$0.493048\pi$
$618$		0			0
$619$	28.5161	+	9.26544i	1.14616	+	0.372409i	0.819695	−	0.572800i	$-0.194143\pi$
$619$	28.5161	+	9.26544i	1.14616	+	0.372409i	0.326463	+	0.945210i	$0.394143\pi$
$620$		0			0
$621$	11.3626	−	8.25539i	0.455964	−	0.331277i
$622$		0			0
$623$	−11.7328	−	36.1097i	−0.470063	−	1.44671i
$624$		0			0
$625$	−5.12521	−	3.72369i	−0.205009	−	0.148947i
$626$		0			0
$627$	7.68289	+	1.87383i	0.306825	+	0.0748334i
$628$		0			0
$629$	−8.71832	+	11.9997i	−0.347622	+	0.478461i
$630$		0			0
$631$	37.8220	−	12.2891i	1.50567	−	0.489222i	0.564005	−	0.825771i	$-0.309260\pi$
$631$	37.8220	−	12.2891i	1.50567	−	0.489222i	0.941666	+	0.336549i	$0.109260\pi$
$632$		0			0
$633$	−12.5593	−	17.2864i	−0.499189	−	0.687075i
$634$		0			0
$635$	−6.76571	+	20.8227i	−0.268489	+	0.826324i
$636$		0			0
$637$			51.1596i			2.02702i
$638$		0			0
$639$			0.530332i			0.0209796i
$640$		0			0
$641$	8.52476	−	26.2365i	0.336708	−	1.03628i	−0.629167	−	0.777270i	$-0.716604\pi$
$641$	8.52476	−	26.2365i	0.336708	−	1.03628i	0.965875	−	0.259010i	$-0.0833963\pi$
$642$		0			0
$643$	−19.7858	−	27.2328i	−0.780277	−	1.07396i	−0.995251	−	0.0973391i	$-0.968967\pi$
$643$	−19.7858	−	27.2328i	−0.780277	−	1.07396i	0.214975	−	0.976620i	$-0.431033\pi$
$644$		0			0
$645$	7.96632	−	2.58841i	0.313673	−	0.101919i
$646$		0			0
$647$	−17.7392	+	24.4160i	−0.697402	+	0.959891i	0.302576	+	0.953125i	$0.402154\pi$
$647$	−17.7392	+	24.4160i	−0.697402	+	0.959891i	−0.999977	+	0.00676544i	$0.997846\pi$
$648$		0			0
$649$	−13.2336	−	15.6082i	−0.519464	−	0.612674i
$650$		0			0
$651$	2.32530	+	1.68943i	0.0911357	+	0.0662140i
$652$		0			0
$653$	5.80704	+	17.8722i	0.227247	+	0.699394i	0.998056	+	0.0623276i	$0.0198524\pi$
$653$	5.80704	+	17.8722i	0.227247	+	0.699394i	−0.770809	+	0.637067i	$0.780148\pi$
$654$		0			0
$655$	13.0351	−	9.47052i	0.509322	−	0.370044i
$656$		0			0
$657$	−3.36879	−	1.09459i	−0.131429	−	0.0427039i
$658$		0			0
$659$	−35.7219			−1.39153			−0.695763	−	0.718272i	$-0.744934\pi$
$659$	−35.7219			−1.39153			−0.695763	+	0.718272i	$0.744934\pi$
$660$		0			0
$661$	−43.4094			−1.68843			−0.844215	−	0.536005i	$-0.819933\pi$
$661$	−43.4094			−1.68843			−0.844215	+	0.536005i	$0.819933\pi$
$662$		0			0
$663$	25.2962	+	8.21922i	0.982422	+	0.319208i
$664$		0			0
$665$	11.7819	−	8.56005i	0.456882	−	0.331944i
$666$		0			0
$667$	7.09575	+	21.8385i	0.274749	+	0.845589i
$668$		0			0
$669$	3.79236	+	2.75531i	0.146621	+	0.106526i
$670$		0			0
$671$	−20.2183	+	32.7278i	−0.780519	+	1.26344i
$672$		0			0
$673$	11.9404	−	16.4346i	0.460269	−	0.633506i	−0.514296	−	0.857613i	$-0.671947\pi$
$673$	11.9404	−	16.4346i	0.460269	−	0.633506i	0.974564	+	0.224107i	$0.0719466\pi$
$674$		0			0
$675$	15.6641	−	5.08956i	0.602910	−	0.195897i
$676$		0			0
$677$	13.9695	+	19.2274i	0.536892	+	0.738969i	0.988161	−	0.153419i	$-0.0490285\pi$
$677$	13.9695	+	19.2274i	0.536892	+	0.738969i	−0.451269	+	0.892388i	$0.649029\pi$
$678$		0			0
$679$	−18.9144	+	58.2124i	−0.725867	+	2.23399i
$680$		0			0
$681$			19.6382i			0.752536i
$682$		0			0
$683$			37.5222i			1.43575i	0.696173	+	0.717874i	$0.254885\pi$
$683$			37.5222i			1.43575i	−0.696173	+	0.717874i	$0.745115\pi$
$684$		0			0
$685$	4.58682	−	14.1168i	0.175254	−	0.539375i
$686$		0			0
$687$	−3.47930	−	4.78885i	−0.132744	−	0.182706i
$688$		0			0
$689$	−11.9544	+	3.88421i	−0.455425	+	0.147977i
$690$		0			0
$691$	−15.2949	+	21.0517i	−0.581847	+	0.800843i	−0.993896	−	0.110318i	$-0.964813\pi$
$691$	−15.2949	+	21.0517i	−0.581847	+	0.800843i	0.412050	+	0.911161i	$0.364813\pi$
$692$		0			0
$693$	33.6014	−	2.52260i	1.27641	−	0.0958256i
$694$		0			0
$695$	6.53682	+	4.74928i	0.247956	+	0.180150i
$696$		0			0
$697$	−0.217490	−	0.669367i	−0.00823804	−	0.0253541i
$698$		0			0
$699$	0.0663942	−	0.0482382i	0.00251126	−	0.00182454i
$700$		0			0
$701$	−14.6243	−	4.75173i	−0.552353	−	0.179470i	0.0195246	−	0.999809i	$-0.493785\pi$
$701$	−14.6243	−	4.75173i	−0.552353	−	0.179470i	−0.571878	+	0.820339i	$0.693785\pi$
$702$		0			0
$703$	−5.11315			−0.192846
$704$		0			0
$705$	−2.19329			−0.0826042
$706$		0			0
$707$	26.8079	+	8.71043i	1.00822	+	0.327589i
$708$		0			0
$709$	0.994218	−	0.722342i	0.0373386	−	0.0271281i	−0.568959	−	0.822366i	$-0.692654\pi$
$709$	0.994218	−	0.722342i	0.0373386	−	0.0271281i	0.606298	+	0.795237i	$0.292654\pi$
$710$		0			0
$711$	−10.6537	−	32.7888i	−0.399546	−	1.22968i
$712$		0			0
$713$	−1.85069	−	1.34461i	−0.0693090	−	0.0503560i
$714$		0			0
$715$	−13.8089	+	5.66157i	−0.516423	+	0.211731i
$716$		0			0
$717$	−10.8464	+	14.9288i	−0.405066	+	0.557526i
$718$		0			0
$719$	15.6222	−	5.07597i	0.582611	−	0.189302i	−0.00285891	−	0.999996i	$-0.500910\pi$
$719$	15.6222	−	5.07597i	0.582611	−	0.189302i	0.585470	+	0.810694i	$0.300910\pi$
$720$		0			0
$721$	34.2643	+	47.1608i	1.27607	+	1.75636i
$722$		0			0
$723$	2.87885	−	8.86020i	0.107066	−	0.329514i
$724$		0			0
$725$			26.9274i			1.00006i
$726$		0			0
$727$		−	22.9858i		−	0.852496i	−0.904606	−	0.426248i	$-0.859835\pi$
$727$		−	22.9858i		−	0.852496i	0.904606	−	0.426248i	$-0.140165\pi$
$728$		0			0
$729$	−1.64636	+	5.06699i	−0.0609764	+	0.187666i
$730$		0			0
$731$	39.0474	+	53.7442i	1.44422	+	1.98780i
$732$		0			0
$733$	−31.8479	+	10.3480i	−1.17633	+	0.382212i	−0.831002	−	0.556270i	$-0.812232\pi$
$733$	−31.8479	+	10.3480i	−1.17633	+	0.382212i	−0.345327	+	0.938482i	$0.612232\pi$
$734$		0			0
$735$	−7.89978	+	10.8731i	−0.291388	+	0.401061i
$736$		0			0
$737$	29.2881	−	12.0080i	1.07884	−	0.442320i
$738$		0			0
$739$	22.1277	+	16.0767i	0.813979	+	0.591391i	0.914982	−	0.403496i	$-0.132205\pi$
$739$	22.1277	+	16.0767i	0.813979	+	0.591391i	−0.101002	+	0.994886i	$0.532205\pi$
$740$		0			0
$741$	2.83338	+	8.72025i	0.104087	+	0.320346i
$742$		0			0
$743$	−20.4711	+	14.8731i	−0.751011	+	0.545642i	−0.896140	−	0.443771i	$-0.853640\pi$
$743$	−20.4711	+	14.8731i	−0.751011	+	0.545642i	0.145129	+	0.989413i	$0.453640\pi$
$744$		0			0
$745$	6.48330	+	2.10655i	0.237530	+	0.0771781i
$746$		0			0
$747$	−10.0096			−0.366234
$748$		0			0
$749$	−28.4571			−1.03980
$750$		0			0
$751$	19.6946	+	6.39918i	0.718668	+	0.233509i	0.645445	−	0.763806i	$-0.276672\pi$
$751$	19.6946	+	6.39918i	0.718668	+	0.233509i	0.0732222	+	0.997316i	$0.476672\pi$
$752$		0			0
$753$	−4.31060	+	3.13184i	−0.157087	+	0.114130i
$754$		0			0
$755$	−0.714749	−	2.19977i	−0.0260124	−	0.0800579i
$756$		0			0
$757$	−13.0963	−	9.51499i	−0.475992	−	0.345828i	0.323780	−	0.946132i	$-0.395046\pi$
$757$	−13.0963	−	9.51499i	−0.475992	−	0.345828i	−0.799772	+	0.600304i	$0.795046\pi$
$758$		0			0
$759$	8.83987	−	0.663648i	0.320867	−	0.0240889i
$760$		0			0
$761$	−9.50090	+	13.0769i	−0.344407	+	0.474036i	−0.945722	−	0.324976i	$-0.894644\pi$
$761$	−9.50090	+	13.0769i	−0.344407	+	0.474036i	0.601315	+	0.799012i	$0.294644\pi$
$762$		0			0
$763$	7.07674	−	2.29937i	0.256195	−	0.0832429i
$764$		0			0
$765$	−12.4252	−	17.1018i	−0.449233	−	0.618317i
$766$		0			0
$767$	7.33174	−	22.5648i	0.264734	−	0.814767i
$768$		0			0
$769$		−	28.0773i		−	1.01249i	−0.862389	−	0.506247i	$-0.831032\pi$
$769$		−	28.0773i		−	1.01249i	0.862389	−	0.506247i	$-0.168968\pi$
$770$		0			0
$771$			12.3398i			0.444406i
$772$		0			0
$773$	−9.80799	+	30.1859i	−0.352769	+	1.08571i	0.604523	+	0.796588i	$0.293364\pi$
$773$	−9.80799	+	30.1859i	−0.352769	+	1.08571i	−0.957292	+	0.289123i	$0.906636\pi$
$774$		0			0
$775$	−1.57679	−	2.17027i	−0.0566401	−	0.0779583i
$776$		0			0
$777$	6.84910	−	2.22541i	0.245710	−	0.0798361i
$778$		0			0
$779$	0.142610	−	0.196286i	0.00510954	−	0.00703268i
$780$		0			0
$781$	−0.410000	+	0.663675i	−0.0146709	+	0.0237482i
$782$		0			0
$783$	−27.2193	−	19.7760i	−0.972738	−	0.706736i
$784$		0			0
$785$	−2.66327	−	8.19669i	−0.0950560	−	0.292552i
$786$		0			0
$787$	14.2814	−	10.3761i	0.509077	−	0.369866i	−0.303396	−	0.952865i	$-0.598121\pi$
$787$	14.2814	−	10.3761i	0.509077	−	0.369866i	0.812474	+	0.582998i	$0.198121\pi$
$788$		0			0
$789$	−18.7281	−	6.08514i	−0.666739	−	0.216637i
$790$		0			0
$791$	−14.5681			−0.517983
$792$		0			0
$793$	−44.6031			−1.58390
$794$		0			0
$795$	−3.14048	−	1.02040i	−0.111381	−	0.0361900i
$796$		0			0
$797$	−11.7546	+	8.54018i	−0.416368	+	0.302509i	−0.776175	−	0.630518i	$-0.782843\pi$
$797$	−11.7546	+	8.54018i	−0.416368	+	0.302509i	0.359807	+	0.933027i	$0.382843\pi$
$798$		0			0
$799$	−5.37529	−	16.5434i	−0.190164	−	0.585265i
$800$		0			0
$801$	−15.3701	−	11.1670i	−0.543075	−	0.394567i
$802$		0			0
$803$	−3.36959	−	3.97421i	−0.118910	−	0.140247i
$804$		0			0
$805$	9.59557	−	13.2072i	0.338199	−	0.465491i
$806$		0			0
$807$	−18.1720	+	5.90445i	−0.639686	+	0.207846i
$808$		0			0
$809$	−26.2723	−	36.1607i	−0.923684	−	1.27134i	−0.962273	−	0.272087i	$-0.912286\pi$
$809$	−26.2723	−	36.1607i	−0.923684	−	1.27134i	0.0385881	−	0.999255i	$-0.487714\pi$
$810$		0			0
$811$	10.0922	−	31.0607i	0.354386	−	1.09069i	−0.601978	−	0.798513i	$-0.705620\pi$
$811$	10.0922	−	31.0607i	0.354386	−	1.09069i	0.956364	−	0.292177i	$-0.0943795\pi$
$812$		0			0
$813$		−	11.3992i		−	0.399786i
$814$		0			0
$815$			0.828790i			0.0290313i
$816$		0			0
$817$	−7.07669	+	21.7798i	−0.247582	+	0.761980i
$818$		0			0
$819$	22.9640	+	31.6072i	0.802426	+	1.10444i
$820$		0			0
$821$	13.8070	−	4.48616i	0.481867	−	0.156568i	−0.0580034	−	0.998316i	$-0.518473\pi$
$821$	13.8070	−	4.48616i	0.481867	−	0.156568i	0.539870	+	0.841748i	$0.318473\pi$
$822$		0			0
$823$	−32.2755	+	44.4235i	−1.12505	+	1.54850i	−0.327918	+	0.944706i	$0.606347\pi$
$823$	−32.2755	+	44.4235i	−1.12505	+	1.54850i	−0.797137	+	0.603799i	$0.793653\pi$
$824$		0			0
$825$	10.0995	+	2.46322i	0.351618	+	0.0857582i
$826$		0			0
$827$	−42.4910	−	30.8715i	−1.47756	−	1.07351i	−0.978334	−	0.207033i	$-0.933619\pi$
$827$	−42.4910	−	30.8715i	−1.47756	−	1.07351i	−0.499222	−	0.866474i	$-0.666381\pi$
$828$		0			0
$829$	3.91359	+	12.0448i	0.135925	+	0.418333i	0.995733	−	0.0922841i	$-0.0294168\pi$
$829$	3.91359	+	12.0448i	0.135925	+	0.418333i	−0.859808	+	0.510618i	$0.829417\pi$
$830$		0			0
$831$	17.8363	−	12.9588i	0.618735	−	0.449538i
$832$		0			0
$833$	−101.374	−	32.9383i	−3.51239	−	1.14124i
$834$		0			0
$835$	−12.8646			−0.445198
$836$		0			0
$837$	3.35182			0.115856
$838$		0			0
$839$	25.2353	+	8.19943i	0.871218	+	0.283076i	0.710306	−	0.703893i	$-0.248557\pi$
$839$	25.2353	+	8.19943i	0.871218	+	0.283076i	0.160912	+	0.986969i	$0.448557\pi$
$840$		0			0
$841$	21.0399	−	15.2864i	0.725515	−	0.527117i
$842$		0			0
$843$	0.0635499	+	0.195586i	0.00218877	+	0.00673635i
$844$		0			0
$845$	−1.69221	−	1.22946i	−0.0582137	−	0.0422947i
$846$		0			0
$847$	44.0001	+	22.8204i	1.51186	+	0.784117i
$848$		0			0
$849$	−11.2419	+	15.4731i	−0.385820	+	0.531036i
$850$		0			0
$851$	−5.45116	+	1.77119i	−0.186863	+	0.0607156i
$852$		0			0
$853$	34.2960	+	47.2044i	1.17427	+	1.61625i	0.625127	+	0.780523i	$0.285047\pi$
$853$	34.2960	+	47.2044i	1.17427	+	1.61625i	0.549147	+	0.835726i	$0.314953\pi$
$854$		0			0
$855$	2.25186	−	6.93050i	0.0770119	−	0.237018i
$856$		0			0
$857$			33.7944i			1.15440i	0.816604	+	0.577198i	$0.195854\pi$
$857$			33.7944i			1.15440i	−0.816604	+	0.577198i	$0.804146\pi$
$858$		0			0
$859$			9.44116i			0.322128i	0.986944	+	0.161064i	$0.0514926\pi$
$859$			9.44116i			0.322128i	−0.986944	+	0.161064i	$0.948507\pi$
$860$		0			0
$861$	−0.105597	+	0.324996i	−0.00359875	+	0.0110758i
$862$		0			0
$863$	26.6232	+	36.6436i	0.906263	+	1.24736i	0.968427	+	0.249298i	$0.0801998\pi$
$863$	26.6232	+	36.6436i	0.906263	+	1.24736i	−0.0621641	+	0.998066i	$0.519800\pi$
$864$		0			0
$865$	14.7895	−	4.80541i	0.502859	−	0.163389i
$866$		0			0
$867$	−23.9467	+	32.9598i	−0.813272	+	1.11937i
$868$		0			0
$869$	12.0166	−	49.2694i	0.407635	−	1.67135i
$870$		0			0
$871$	29.6920	+	21.5725i	1.00607	+	0.730956i
$872$		0			0
$873$	9.46439	+	29.1284i	0.320321	+	0.985847i
$874$		0			0
$875$	36.8168	−	26.7490i	1.24464	−	0.904281i
$876$		0			0
$877$	9.07699	+	2.94929i	0.306508	+	0.0995905i	0.458233	−	0.888832i	$-0.348483\pi$
$877$	9.07699	+	2.94929i	0.306508	+	0.0995905i	−0.151724	+	0.988423i	$0.548483\pi$
$878$		0			0
$879$	2.00575			0.0676524
$880$		0			0
$881$	−22.4843			−0.757514			−0.378757	−	0.925496i	$-0.623648\pi$
$881$	−22.4843			−0.757514			−0.378757	+	0.925496i	$0.623648\pi$
$882$		0			0
$883$	−1.78032	−	0.578460i	−0.0599124	−	0.0194667i	0.278907	−	0.960318i	$-0.410028\pi$
$883$	−1.78032	−	0.578460i	−0.0599124	−	0.0194667i	−0.338820	+	0.940851i	$0.610028\pi$
$884$		0			0
$885$	5.04257	−	3.66364i	0.169504	−	0.123152i
$886$		0			0
$887$	13.3179	+	40.9883i	0.447172	+	1.37625i	0.880084	+	0.474818i	$0.157486\pi$
$887$	13.3179	+	40.9883i	0.447172	+	1.37625i	−0.432912	+	0.901436i	$0.642514\pi$
$888$		0			0
$889$	68.2063	+	49.5548i	2.28757	+	1.66201i
$890$		0			0
$891$	7.20431	−	6.10827i	0.241353	−	0.204635i
$892$		0			0
$893$	3.52462	−	4.85122i	0.117947	−	0.162340i
$894$		0			0
$895$	−3.96524	+	1.28839i	−0.132543	+	0.0430660i
$896$		0			0
$897$	6.04138	+	8.31524i	0.201716	+	0.277638i
$898$		0			0
$899$	−1.69340	+	5.21175i	−0.0564781	+	0.173822i
$900$		0			0
$901$		−	26.1886i		−	0.872469i
$902$		0			0
$903$		−	32.2543i		−	1.07335i
$904$		0			0
$905$	−5.94305	+	18.2908i	−0.197554	+	0.608008i
$906$		0			0
$907$	−22.4567	−	30.9090i	−0.745662	−	1.02632i	−0.998273	−	0.0587480i	$-0.981289\pi$
$907$	−22.4567	−	30.9090i	−0.745662	−	1.02632i	0.252611	−	0.967568i	$-0.418711\pi$
$908$		0			0
$909$	13.4142	−	4.35853i	0.444920	−	0.144563i
$910$		0			0
$911$	−17.7625	+	24.4480i	−0.588497	+	0.809997i	−0.994595	−	0.103833i	$-0.966889\pi$
$911$	−17.7625	+	24.4480i	−0.588497	+	0.809997i	0.406098	+	0.913830i	$0.366889\pi$
$912$		0			0
$913$	−12.5264	−	7.73846i	−0.414563	−	0.256106i
$914$		0			0
$915$	−9.47965	−	6.88737i	−0.313388	−	0.227689i
$916$		0			0
$917$	−19.1723	−	59.0062i	−0.633124	−	1.94856i
$918$		0			0
$919$	−0.719399	+	0.522674i	−0.0237308	+	0.0172414i	−0.599587	−	0.800309i	$-0.704669\pi$
$919$	−0.719399	+	0.522674i	−0.0237308	+	0.0172414i	0.575857	+	0.817551i	$0.304669\pi$
$920$		0			0
$921$	17.5299	+	5.69581i	0.577630	+	0.187683i
$922$		0			0
$923$	−0.904491			−0.0297717
$924$		0			0
$925$	−6.72143			−0.220999
$926$		0			0
$927$	27.7416	+	9.01378i	0.911152	+	0.296051i
$928$		0			0
$929$	25.3394	−	18.4102i	0.831359	−	0.604017i	−0.0885847	−	0.996069i	$-0.528234\pi$
$929$	25.3394	−	18.4102i	0.831359	−	0.604017i	0.919943	+	0.392051i	$0.128234\pi$
$930$		0			0
$931$	−11.3547	−	34.9462i	−0.372135	−	1.14531i
$932$		0			0
$933$	16.1900	+	11.7627i	0.530036	+	0.385093i
$934$		0			0
$935$	−2.32788	−	31.0077i	−0.0761298	−	1.01406i
$936$		0			0
$937$	28.0472	−	38.6036i	0.916262	−	1.26113i	−0.0487208	−	0.998812i	$-0.515514\pi$
$937$	28.0472	−	38.6036i	0.916262	−	1.26113i	0.964983	−	0.262314i	$-0.0844855\pi$
$938$		0			0
$939$	−18.8292	+	6.11798i	−0.614468	+	0.199653i
$940$		0			0
$941$	−15.9015	−	21.8865i	−0.518373	−	0.713479i	0.466930	−	0.884294i	$-0.345360\pi$
$941$	−15.9015	−	21.8865i	−0.518373	−	0.713479i	−0.985303	+	0.170815i	$0.945360\pi$
$942$		0			0
$943$	0.0840444	−	0.258662i	0.00273686	−	0.00842320i
$944$		0			0
$945$			23.9197i			0.778107i
$946$		0			0
$947$		−	19.7824i		−	0.642843i	−0.946936	−	0.321421i	$-0.895839\pi$
$947$		−	19.7824i		−	0.642843i	0.946936	−	0.321421i	$-0.104161\pi$
$948$		0			0
$949$	1.86684	−	5.74553i	0.0606001	−	0.186508i
$950$		0			0
$951$	−13.1918	−	18.1570i	−0.427774	−	0.588781i
$952$		0			0
$953$	7.79671	−	2.53331i	0.252560	−	0.0820618i	−0.180001	−	0.983666i	$-0.557610\pi$
$953$	7.79671	−	2.53331i	0.252560	−	0.0820618i	0.432561	+	0.901605i	$0.357610\pi$
$954$		0			0
$955$	4.35494	−	5.99406i	0.140923	−	0.193963i
$956$		0			0
$957$	−8.05575	−	19.6484i	−0.260406	−	0.635143i
$958$		0			0
$959$	−46.2406	−	33.5958i	−1.49319	−	1.08486i
$960$		0			0
$961$	9.41082	+	28.9635i	0.303575	+	0.934308i
$962$		0			0
$963$	−11.5199	+	8.36971i	−0.371224	+	0.269710i
$964$		0			0
$965$	−13.2713	−	4.31210i	−0.427218	−	0.138811i
$966$		0			0
$967$	−38.3279			−1.23254			−0.616272	−	0.787534i	$-0.711358\pi$
$967$	−38.3279			−1.23254			−0.616272	+	0.787534i	$0.711358\pi$
$968$		0			0
$969$	−19.1036			−0.613695
$970$		0			0
$971$	12.1455	+	3.94630i	0.389767	+	0.126643i	0.497343	−	0.867554i	$-0.334309\pi$
$971$	12.1455	+	3.94630i	0.389767	+	0.126643i	−0.107576	+	0.994197i	$0.534309\pi$
$972$		0			0
$973$	25.1711	−	18.2879i	0.806949	−	0.586283i
$974$		0			0
$975$	3.72459	+	11.4631i	0.119282	+	0.367113i
$976$		0			0
$977$	−9.03513	−	6.56440i	−0.289059	−	0.210014i	0.433800	−	0.901009i	$-0.357172\pi$
$977$	−9.03513	−	6.56440i	−0.289059	−	0.210014i	−0.722859	+	0.690995i	$0.757172\pi$
$978$		0			0
$979$	−10.6014	−	25.8574i	−0.338822	−	0.826406i
$980$		0			0
$981$	2.18850	−	3.01221i	0.0698734	−	0.0961725i
$982$		0			0
$983$	19.3378	−	6.28323i	0.616780	−	0.200404i	0.0160700	−	0.999871i	$-0.494885\pi$
$983$	19.3378	−	6.28323i	0.616780	−	0.200404i	0.600710	+	0.799467i	$0.294885\pi$
$984$		0			0
$985$	−14.5683	−	20.0515i	−0.464184	−	0.638894i
$986$		0			0
$987$	−2.60985	+	8.03228i	−0.0830724	+	0.255670i
$988$		0			0
$989$			25.6710i			0.816290i
$990$		0			0
$991$		−	48.9495i		−	1.55493i	−0.628924	−	0.777467i	$-0.716504\pi$
$991$		−	48.9495i		−	1.55493i	0.628924	−	0.777467i	$-0.283496\pi$
$992$		0			0
$993$	−1.27768	+	3.93230i	−0.0405460	+	0.124788i
$994$		0			0
$995$	6.62529	+	9.11892i	0.210036	+	0.289089i
$996$		0			0
$997$	−33.7192	+	10.9560i	−1.06790	+	0.346981i	−0.789668	−	0.613534i	$-0.789747\pi$
$997$	−33.7192	+	10.9560i	−1.06790	+	0.346981i	−0.278229	+	0.960515i	$0.589747\pi$
$998$		0			0
$999$	4.93634	−	6.79429i	0.156179	−	0.214962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.u.a.95.8	yes	48
4.3	odd	2	inner	352.2.u.a.95.5	yes	48
8.3	odd	2		704.2.u.d.447.8		48
8.5	even	2		704.2.u.d.447.5		48
11.8	odd	10	inner	352.2.u.a.63.5	✓	48
44.19	even	10	inner	352.2.u.a.63.8	yes	48
88.19	even	10		704.2.u.d.63.5		48
88.85	odd	10		704.2.u.d.63.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.2.u.a.63.5	✓	48	11.8	odd	10	inner
352.2.u.a.63.8	yes	48	44.19	even	10	inner
352.2.u.a.95.5	yes	48	4.3	odd	2	inner
352.2.u.a.95.8	yes	48	1.1	even	1	trivial
704.2.u.d.63.5		48	88.19	even	10
704.2.u.d.63.8		48	88.85	odd	10
704.2.u.d.447.5		48	8.5	even	2
704.2.u.d.447.8		48	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.821048 + 0.266775i) q^{3} +(0.946699 - 0.687817i) q^{5} +(-1.39243 - 4.28545i) q^{7} +(-1.82410 - 1.32529i) q^{9} +(-1.25816 - 3.06872i) q^{11} +(2.26030 - 3.11103i) q^{13} +(0.960777 - 0.312175i) q^{15} +(4.70931 + 6.48181i) q^{17} +(-0.853485 + 2.62676i) q^{19} -3.89002i q^{21} +3.09605i q^{23} +(-1.12194 + 3.45297i) q^{25} +(-2.66643 - 3.67002i) q^{27} +(7.05366 - 2.29187i) q^{29} +(-0.434298 + 0.597760i) q^{31} +(-0.214353 - 2.85521i) q^{33} +(-4.26581 - 3.09929i) q^{35} +(0.572081 + 1.76068i) q^{37} +(2.68576 - 1.95132i) q^{39} +(-0.0835459 - 0.0271457i) q^{41} +8.29153 q^{43} -2.63843 q^{45} +(-2.06484 - 0.670908i) q^{47} +(-10.7631 + 7.81985i) q^{49} +(2.13739 + 6.57821i) q^{51} +(-2.64442 - 1.92129i) q^{53} +(-3.30181 - 2.03977i) q^{55} +(-1.40150 + 1.92900i) q^{57} +(5.86792 - 1.90660i) q^{59} +(-6.81768 - 9.38374i) q^{61} +(-3.13952 + 9.66245i) q^{63} -4.49988i q^{65} +9.54408i q^{67} +(-0.825948 + 2.54201i) q^{69} +(-0.138253 - 0.190289i) q^{71} +(1.49411 - 0.485466i) q^{73} +(-1.84233 + 2.53575i) q^{75} +(-11.3989 + 9.66474i) q^{77} +(12.3705 + 8.98766i) q^{79} +(0.880036 + 2.70847i) q^{81} +(3.59158 - 2.60943i) q^{83} +(8.91660 + 2.89718i) q^{85} +6.40281 q^{87} +8.42612 q^{89} +(-16.4795 - 5.35451i) q^{91} +(-0.516047 + 0.374930i) q^{93} +(0.998734 + 3.07379i) q^{95} +(-10.9895 - 7.98432i) q^{97} +(-1.77192 + 7.26507i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{9} + 4 q^{25} + 36 q^{33} + 40 q^{41} - 96 q^{45} - 4 q^{49} - 8 q^{53} + 20 q^{57} - 8 q^{69} - 40 q^{73} - 72 q^{77} - 72 q^{81} - 80 q^{85} - 40 q^{89} + 8 q^{93} + 4 q^{97}+O(q^{100}) \) 48 * q + 4 * q^9 + 4 * q^25 + 36 * q^33 + 40 * q^41 - 96 * q^45 - 4 * q^49 - 8 * q^53 + 20 * q^57 - 8 * q^69 - 40 * q^73 - 72 * q^77 - 72 * q^81 - 80 * q^85 - 40 * q^89 + 8 * q^93 + 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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