LMFDB - Embedded newform 1176.2.u.c.521.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1176,2,Mod(521,1176)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1176, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("1176.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1176 = 2^{3} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1176.u (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.39040727770$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.23
Character	$\chi$	$=$	1176.521
Dual form			1176.2.u.c.1097.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.70977 + 0.276907i) q^{3} +(-0.655965 - 1.13616i) q^{5} +(2.84664 + 0.946897i) q^{9} +(-4.31240 - 2.48976i) q^{11} -0.733252i q^{13} +(-0.806939 - 2.12423i) q^{15} +(-0.364175 + 0.630770i) q^{17} +(6.01418 - 3.47229i) q^{19} +(6.86694 - 3.96463i) q^{23} +(1.63942 - 2.83956i) q^{25} +(4.60491 + 2.40724i) q^{27} -4.62960i q^{29} +(-1.56144 - 0.901500i) q^{31} +(-6.68379 - 5.45106i) q^{33} +(2.61211 + 4.52431i) q^{37} +(0.203043 - 1.25369i) q^{39} +7.83857 q^{41} -1.27217 q^{43} +(-0.791468 - 3.85539i) q^{45} +(2.12081 + 3.67336i) q^{47} +(-0.797322 + 0.977630i) q^{51} +(-12.4851 - 7.20830i) q^{53} +6.53279i q^{55} +(11.2444 - 4.27145i) q^{57} +(-4.67659 + 8.10009i) q^{59} +(-11.7677 + 6.79406i) q^{61} +(-0.833095 + 0.480987i) q^{65} +(3.77405 - 6.53685i) q^{67} +(12.8387 - 4.87711i) q^{69} -6.92721i q^{71} +(3.29014 + 1.89956i) q^{73} +(3.58933 - 4.40103i) q^{75} +(-6.79638 - 11.7717i) q^{79} +(7.20677 + 5.39096i) q^{81} +6.58972 q^{83} +0.955545 q^{85} +(1.28197 - 7.91557i) q^{87} +(2.18923 + 3.79185i) q^{89} +(-2.42008 - 1.97374i) q^{93} +(-7.89018 - 4.55540i) q^{95} +15.1510i q^{97} +(-9.91831 - 11.1709i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 32 q^{15} - 8 q^{25} - 16 q^{37} + 64 q^{39} + 32 q^{43} - 48 q^{51} + 96 q^{57} - 16 q^{67} - 80 q^{81} - 128 q^{85} + 32 q^{93} - 112 q^{99}+O(q^{100}) $ 48 * q - 32 * q^15 - 8 * q^25 - 16 * q^37 + 64 * q^39 + 32 * q^43 - 48 * q^51 + 96 * q^57 - 16 * q^67 - 80 * q^81 - 128 * q^85 + 32 * q^93 - 112 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times$.

$n$	$295$	$589$	$785$	$1081$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.70977	+	0.276907i	0.987138	+	0.159873i
$3$	1.70977	+	0.276907i	0.987138	+	0.159873i
$4$		0			0
$5$	−0.655965	−	1.13616i	−0.293356	−	0.508108i	0.681245	−	0.732056i	$-0.261439\pi$
$5$	−0.655965	−	1.13616i	−0.293356	−	0.508108i	−0.974601	+	0.223947i	$0.928106\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	2.84664	+	0.946897i	0.948882	+	0.315632i
$10$		0			0
$11$	−4.31240	−	2.48976i	−1.30024	−	0.750692i	−0.319792	−	0.947488i	$-0.603613\pi$
$11$	−4.31240	−	2.48976i	−1.30024	−	0.750692i	−0.980445	+	0.196796i	$0.936946\pi$
$12$		0			0
$13$		−	0.733252i		−	0.203367i	−0.994817	−	0.101684i	$-0.967577\pi$
$13$		−	0.733252i		−	0.203367i	0.994817	−	0.101684i	$-0.0324230\pi$
$14$		0			0
$15$	−0.806939	−	2.12423i	−0.208351	−	0.548473i
$16$		0			0
$17$	−0.364175	+	0.630770i	−0.0883255	+	0.152984i	−0.906803	−	0.421554i	$-0.861485\pi$
$17$	−0.364175	+	0.630770i	−0.0883255	+	0.152984i	0.818478	+	0.574538i	$0.194818\pi$
$18$		0			0
$19$	6.01418	−	3.47229i	1.37975	−	0.796597i	0.387618	−	0.921820i	$-0.373298\pi$
$19$	6.01418	−	3.47229i	1.37975	−	0.796597i	0.992129	+	0.125223i	$0.0399646\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	6.86694	−	3.96463i	1.43186	−	0.826683i	0.434594	−	0.900626i	$-0.356892\pi$
$23$	6.86694	−	3.96463i	1.43186	−	0.826683i	0.997262	+	0.0739435i	$0.0235584\pi$
$24$		0			0
$25$	1.63942	−	2.83956i	0.327884	−	0.567912i
$26$		0			0
$27$	4.60491	+	2.40724i	0.886216	+	0.463273i
$28$		0			0
$29$		−	4.62960i		−	0.859696i	−0.902901	−	0.429848i	$-0.858567\pi$
$29$		−	4.62960i		−	0.859696i	0.902901	−	0.429848i	$-0.141433\pi$
$30$		0			0
$31$	−1.56144	−	0.901500i	−0.280444	−	0.161914i	0.353181	−	0.935555i	$-0.385100\pi$
$31$	−1.56144	−	0.901500i	−0.280444	−	0.161914i	−0.633624	+	0.773641i	$0.718433\pi$
$32$		0			0
$33$	−6.68379	−	5.45106i	−1.16350	−	0.948909i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.61211	+	4.52431i	0.429429	+	0.743792i	0.996823	−	0.0796541i	$-0.0253816\pi$
$37$	2.61211	+	4.52431i	0.429429	+	0.743792i	−0.567394	+	0.823447i	$0.692048\pi$
$38$		0			0
$39$	0.203043	−	1.25369i	0.0325129	−	0.200752i
$40$		0			0
$41$	7.83857			1.22418			0.612089	−	0.790789i	$-0.290329\pi$
$41$	7.83857			1.22418			0.612089	+	0.790789i	$0.290329\pi$
$42$		0			0
$43$	−1.27217			−0.194004			−0.0970020	−	0.995284i	$-0.530925\pi$
$43$	−1.27217			−0.194004			−0.0970020	+	0.995284i	$0.530925\pi$
$44$		0			0
$45$	−0.791468	−	3.85539i	−0.117985	−	0.574727i
$46$		0			0
$47$	2.12081	+	3.67336i	0.309352	+	0.535814i	0.978221	−	0.207567i	$-0.0665544\pi$
$47$	2.12081	+	3.67336i	0.309352	+	0.535814i	−0.668868	+	0.743381i	$0.733221\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−0.797322	+	0.977630i	−0.111647	+	0.136896i
$52$		0			0
$53$	−12.4851	−	7.20830i	−1.71497	−	0.990136i	−0.927537	−	0.373732i	$-0.878078\pi$
$53$	−12.4851	−	7.20830i	−1.71497	−	0.990136i	−0.787430	−	0.616404i	$-0.788589\pi$
$54$		0			0
$55$			6.53279i			0.880882i
$56$		0			0
$57$	11.2444	−	4.27145i	1.48935	−	0.565767i
$58$		0			0
$59$	−4.67659	+	8.10009i	−0.608840	+	1.05454i	0.382592	+	0.923917i	$0.375032\pi$
$59$	−4.67659	+	8.10009i	−0.608840	+	1.05454i	−0.991432	+	0.130624i	$0.958302\pi$
$60$		0			0
$61$	−11.7677	+	6.79406i	−1.50669	+	0.869890i	−0.506725	+	0.862108i	$0.669144\pi$
$61$	−11.7677	+	6.79406i	−1.50669	+	0.869890i	−0.999970	+	0.00778252i	$0.997523\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.833095	+	0.480987i	−0.103333	+	0.0596592i
$66$		0			0
$67$	3.77405	−	6.53685i	0.461074	−	0.798604i	−0.537941	−	0.842983i	$-0.680798\pi$
$67$	3.77405	−	6.53685i	0.461074	−	0.798604i	0.999015	+	0.0443788i	$0.0141309\pi$
$68$		0			0
$69$	12.8387	−	4.87711i	1.54560	−	0.587135i
$70$		0			0
$71$		−	6.92721i		−	0.822109i	−0.911611	−	0.411055i	$-0.865161\pi$
$71$		−	6.92721i		−	0.822109i	0.911611	−	0.411055i	$-0.134839\pi$
$72$		0			0
$73$	3.29014	+	1.89956i	0.385082	+	0.222327i	0.680027	−	0.733187i	$-0.261968\pi$
$73$	3.29014	+	1.89956i	0.385082	+	0.222327i	−0.294945	+	0.955514i	$0.595301\pi$
$74$		0			0
$75$	3.58933	−	4.40103i	0.414460	−	0.508187i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−6.79638	−	11.7717i	−0.764653	−	1.32442i	−0.940430	−	0.339988i	$-0.889577\pi$
$79$	−6.79638	−	11.7717i	−0.764653	−	1.32442i	0.175777	−	0.984430i	$-0.443756\pi$
$80$		0			0
$81$	7.20677	+	5.39096i	0.800752	+	0.598996i
$82$		0			0
$83$	6.58972			0.723316			0.361658	−	0.932311i	$-0.382211\pi$
$83$	6.58972			0.723316			0.361658	+	0.932311i	$0.382211\pi$
$84$		0			0
$85$	0.955545			0.103643
$86$		0			0
$87$	1.28197	−	7.91557i	0.137442	−	0.848638i
$88$		0			0
$89$	2.18923	+	3.79185i	0.232057	+	0.401935i	0.958413	−	0.285383i	$-0.0921209\pi$
$89$	2.18923	+	3.79185i	0.232057	+	0.401935i	−0.726356	+	0.687319i	$0.758788\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−2.42008	−	1.97374i	−0.250951	−	0.204667i
$94$		0			0
$95$	−7.89018	−	4.55540i	−0.809515	−	0.467374i
$96$		0			0
$97$			15.1510i			1.53835i	0.639039	+	0.769174i	$0.279332\pi$
$97$			15.1510i			1.53835i	−0.639039	+	0.769174i	$0.720668\pi$
$98$		0			0
$99$	−9.91831	−	11.1709i	−0.996828	−	1.12271i
$100$		0			0
$101$	−5.49796	+	9.52275i	−0.547068	+	0.947549i	0.451406	+	0.892319i	$0.350923\pi$
$101$	−5.49796	+	9.52275i	−0.547068	+	0.947549i	−0.998474	+	0.0552302i	$0.982411\pi$
$102$		0			0
$103$	9.03199	−	5.21462i	0.889949	−	0.513812i	0.0160229	−	0.999872i	$-0.494900\pi$
$103$	9.03199	−	5.21462i	0.889949	−	0.513812i	0.873926	+	0.486060i	$0.161566\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.66747	+	1.54006i	−0.257874	+	0.148883i	−0.623364	−	0.781932i	$-0.714235\pi$
$107$	−2.66747	+	1.54006i	−0.257874	+	0.148883i	0.365491	+	0.930815i	$0.380901\pi$
$108$		0			0
$109$	−6.87562	+	11.9089i	−0.658565	+	1.14067i	0.322422	+	0.946596i	$0.395503\pi$
$109$	−6.87562	+	11.9089i	−0.658565	+	1.14067i	−0.980987	+	0.194072i	$0.937830\pi$
$110$		0			0
$111$	3.21330	+	8.45886i	0.304993	+	0.802879i
$112$		0			0
$113$			12.6414i			1.18920i	0.804022	+	0.594599i	$0.202689\pi$
$113$			12.6414i			1.18920i	−0.804022	+	0.594599i	$0.797311\pi$
$114$		0			0
$115$	−9.00895	−	5.20132i	−0.840089	−	0.485026i
$116$		0			0
$117$	0.694314	−	2.08731i	0.0641894	−	0.192972i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	6.89785	+	11.9474i	0.627077	+	1.08613i
$122$		0			0
$123$	13.4022	+	2.17056i	1.20843	+	0.195713i
$124$		0			0
$125$	−10.8613			−0.971461
$126$		0			0
$127$	3.31989			0.294593			0.147296	−	0.989092i	$-0.452943\pi$
$127$	3.31989			0.294593			0.147296	+	0.989092i	$0.452943\pi$
$128$		0			0
$129$	−2.17512	−	0.352273i	−0.191509	−	0.0310159i
$130$		0			0
$131$	8.00611	+	13.8670i	0.699497	+	1.21157i	0.968641	+	0.248465i	$0.0799261\pi$
$131$	8.00611	+	13.8670i	0.699497	+	1.21157i	−0.269143	+	0.963100i	$0.586741\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.285645	−	6.81100i	−0.0245844	−	0.586198i
$136$		0			0
$137$	−9.31267	−	5.37667i	−0.795635	−	0.459360i	0.0463076	−	0.998927i	$-0.485255\pi$
$137$	−9.31267	−	5.37667i	−0.795635	−	0.459360i	−0.841943	+	0.539567i	$0.818588\pi$
$138$		0			0
$139$		−	18.5535i		−	1.57369i	−0.617152	−	0.786844i	$-0.711714\pi$
$139$		−	18.5535i		−	1.57369i	0.617152	−	0.786844i	$-0.288286\pi$
$140$		0			0
$141$	2.60893	+	6.86787i	0.219711	+	0.578379i
$142$		0			0
$143$	−1.82562	+	3.16207i	−0.152666	+	0.264426i
$144$		0			0
$145$	−5.25999	+	3.03686i	−0.436819	+	0.252197i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.21624	−	2.43425i	0.345408	−	0.199421i	−0.317253	−	0.948341i	$-0.602760\pi$
$149$	4.21624	−	2.43425i	0.345408	−	0.199421i	0.662661	+	0.748920i	$0.269427\pi$
$150$		0			0
$151$	−0.850601	+	1.47328i	−0.0692209	+	0.119894i	−0.898559	−	0.438854i	$-0.855385\pi$
$151$	−0.850601	+	1.47328i	−0.0692209	+	0.119894i	0.829338	+	0.558748i	$0.188718\pi$
$152$		0			0
$153$	−1.63395	+	1.45074i	−0.132097	+	0.117285i
$154$		0			0
$155$			2.36541i			0.189994i
$156$		0			0
$157$	15.7423	+	9.08881i	1.25637	+	0.725366i	0.972367	−	0.233457i	$-0.0750038\pi$
$157$	15.7423	+	9.08881i	1.25637	+	0.725366i	0.284004	+	0.958823i	$0.408337\pi$
$158$		0			0
$159$	−19.3507	−	15.7818i	−1.53461	−	1.25158i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	2.51166	+	4.35032i	0.196728	+	0.340744i	0.947466	−	0.319857i	$-0.103635\pi$
$163$	2.51166	+	4.35032i	0.196728	+	0.340744i	−0.750737	+	0.660601i	$0.770302\pi$
$164$		0			0
$165$	−1.80898	+	11.1696i	−0.140829	+	0.869551i
$166$		0			0
$167$	−16.4374			−1.27196			−0.635982	−	0.771704i	$-0.719405\pi$
$167$	−16.4374			−1.27196			−0.635982	+	0.771704i	$0.719405\pi$
$168$		0			0
$169$	12.4623			0.958642
$170$		0			0
$171$	20.4081	−	4.18956i	1.56065	−	0.320384i
$172$		0			0
$173$	2.10223	+	3.64118i	0.159830	+	0.276834i	0.934807	−	0.355156i	$-0.115572\pi$
$173$	2.10223	+	3.64118i	0.159830	+	0.276834i	−0.774977	+	0.631989i	$0.782239\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−10.2389	+	12.5543i	−0.769601	+	0.943641i
$178$		0			0
$179$	7.04948	+	4.07002i	0.526903	+	0.304208i	0.739754	−	0.672877i	$-0.234942\pi$
$179$	7.04948	+	4.07002i	0.526903	+	0.304208i	−0.212851	+	0.977085i	$0.568275\pi$
$180$		0			0
$181$		−	17.8884i		−	1.32963i	−0.747007	−	0.664817i	$-0.768510\pi$
$181$		−	17.8884i		−	1.32963i	0.747007	−	0.664817i	$-0.231490\pi$
$182$		0			0
$183$	−22.0013	+	8.35775i	−1.62639	+	0.617823i
$184$		0			0
$185$	3.42691	−	5.93558i	0.251951	−	0.436393i
$186$		0			0
$187$	3.14094	−	1.81342i	0.229688	−	0.132610i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3.55972	−	2.05520i	0.257572	−	0.148709i	−0.365654	−	0.930751i	$-0.619155\pi$
$191$	3.55972	−	2.05520i	0.257572	−	0.148709i	0.623226	+	0.782041i	$0.285821\pi$
$192$		0			0
$193$	1.61460	−	2.79656i	0.116221	−	0.201301i	−0.802046	−	0.597262i	$-0.796255\pi$
$193$	1.61460	−	2.79656i	0.116221	−	0.201301i	0.918267	+	0.395961i	$0.129589\pi$
$194$		0			0
$195$	−1.55759	+	0.591689i	−0.111541	+	0.0423717i
$196$		0			0
$197$			4.70768i			0.335408i	0.985837	+	0.167704i	$0.0536353\pi$
$197$			4.70768i			0.335408i	−0.985837	+	0.167704i	$0.946365\pi$
$198$		0			0
$199$	−14.7081	−	8.49175i	−1.04263	−	0.601964i	−0.122055	−	0.992523i	$-0.538948\pi$
$199$	−14.7081	−	8.49175i	−1.04263	−	0.601964i	−0.920578	+	0.390559i	$0.872282\pi$
$200$		0			0
$201$	8.26288	−	10.1315i	0.582819	−	0.714619i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−5.14183	−	8.90590i	−0.359121	−	0.622015i
$206$		0			0
$207$	23.3018	−	4.78361i	1.61959	−	0.332484i
$208$		0			0
$209$	−34.5807			−2.39200
$210$		0			0
$211$	−1.89126			−0.130199			−0.0650997	−	0.997879i	$-0.520737\pi$
$211$	−1.89126			−0.130199			−0.0650997	+	0.997879i	$0.520737\pi$
$212$		0			0
$213$	1.91820	−	11.8440i	0.131433	−	0.811535i
$214$		0			0
$215$	0.834498	+	1.44539i	0.0569123	+	0.0985750i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	5.09939	+	4.15889i	0.344585	+	0.281032i
$220$		0			0
$221$	0.462513	+	0.267032i	0.0311120	+	0.0179625i
$222$		0			0
$223$		−	9.29671i		−	0.622554i	−0.950319	−	0.311277i	$-0.899243\pi$
$223$		−	9.29671i		−	0.622554i	0.950319	−	0.311277i	$-0.100757\pi$
$224$		0			0
$225$	7.35562	−	6.53085i	0.490374	−	0.435390i
$226$		0			0
$227$	2.48497	−	4.30410i	0.164933	−	0.285673i	−0.771698	−	0.635989i	$-0.780592\pi$
$227$	2.48497	−	4.30410i	0.164933	−	0.285673i	0.936632	+	0.350316i	$0.113926\pi$
$228$		0			0
$229$	−4.61728	+	2.66579i	−0.305118	+	0.176160i	−0.644740	−	0.764402i	$-0.723034\pi$
$229$	−4.61728	+	2.66579i	−0.305118	+	0.176160i	0.339622	+	0.940562i	$0.389701\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.03312	+	1.75118i	−0.198707	+	0.114723i	−0.596052	−	0.802946i	$-0.703265\pi$
$233$	−3.03312	+	1.75118i	−0.198707	+	0.114723i	0.397345	+	0.917669i	$0.369931\pi$
$234$		0			0
$235$	2.78236	−	4.81919i	0.181501	−	0.314369i
$236$		0			0
$237$	−8.36061	−	22.0089i	−0.543080	−	1.42963i
$238$		0			0
$239$			23.4769i			1.51859i	0.650744	+	0.759297i	$0.274457\pi$
$239$			23.4769i			1.51859i	−0.650744	+	0.759297i	$0.725543\pi$
$240$		0			0
$241$	8.71865	+	5.03371i	0.561618	+	0.324250i	0.753794	−	0.657110i	$-0.228221\pi$
$241$	8.71865	+	5.03371i	0.561618	+	0.324250i	−0.192177	+	0.981360i	$0.561555\pi$
$242$		0			0
$243$	10.8291	+	11.2129i	0.694690	+	0.719309i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−2.54606	−	4.40991i	−0.162002	−	0.280596i
$248$		0			0
$249$	11.2669	+	1.82474i	0.714012	+	0.115638i
$250$		0			0
$251$	−19.7932			−1.24933			−0.624666	−	0.780892i	$-0.714765\pi$
$251$	−19.7932			−1.24933			−0.624666	+	0.780892i	$0.714765\pi$
$252$		0			0
$253$	−39.4840			−2.48234
$254$		0			0
$255$	1.63376	+	0.264597i	0.102310	+	0.0165697i
$256$		0			0
$257$	6.30815	+	10.9260i	0.393492	+	0.681548i	0.992907	−	0.118890i	$-0.0379336\pi$
$257$	6.30815	+	10.9260i	0.393492	+	0.681548i	−0.599416	+	0.800438i	$0.704600\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	4.38376	−	13.1788i	0.271348	−	0.815750i
$262$		0			0
$263$	5.48367	+	3.16600i	0.338137	+	0.195224i	0.659448	−	0.751750i	$-0.270790\pi$
$263$	5.48367	+	3.16600i	0.338137	+	0.195224i	−0.321311	+	0.946974i	$0.604123\pi$
$264$		0			0
$265$			18.9136i			1.16185i
$266$		0			0
$267$	2.69309	+	7.08941i	0.164814	+	0.433865i
$268$		0			0
$269$	−12.1920	+	21.1171i	−0.743356	+	1.28753i	0.207602	+	0.978213i	$0.433434\pi$
$269$	−12.1920	+	21.1171i	−0.743356	+	1.28753i	−0.950959	+	0.309318i	$0.899899\pi$
$270$		0			0
$271$	−0.297975	+	0.172036i	−0.0181007	+	0.0104504i	−0.509023	−	0.860753i	$-0.669993\pi$
$271$	−0.297975	+	0.172036i	−0.0181007	+	0.0104504i	0.490922	+	0.871203i	$0.336660\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−14.1397	+	8.16354i	−0.852654	+	0.492280i
$276$		0			0
$277$	−6.11798	+	10.5966i	−0.367594	+	0.636691i	−0.989189	−	0.146648i	$-0.953152\pi$
$277$	−6.11798	+	10.5966i	−0.367594	+	0.636691i	0.621595	+	0.783339i	$0.286485\pi$
$278$		0			0
$279$	−3.59125	−	4.04478i	−0.215002	−	0.242155i
$280$		0			0
$281$			16.6761i			0.994810i	0.867519	+	0.497405i	$0.165714\pi$
$281$			16.6761i			0.994810i	−0.867519	+	0.497405i	$0.834286\pi$
$282$		0			0
$283$	2.68606	+	1.55080i	0.159670	+	0.0921853i	0.577706	−	0.816245i	$-0.303948\pi$
$283$	2.68606	+	1.55080i	0.159670	+	0.0921853i	−0.418036	+	0.908430i	$0.637281\pi$
$284$		0			0
$285$	−12.2290	−	9.97354i	−0.724383	−	0.590782i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	8.23475	+	14.2630i	0.484397	+	0.839001i
$290$		0			0
$291$	−4.19542	+	25.9047i	−0.245940	+	1.51856i
$292$		0			0
$293$	16.2490			0.949278			0.474639	−	0.880181i	$-0.342579\pi$
$293$	16.2490			0.949278			0.474639	+	0.880181i	$0.342579\pi$
$294$		0			0
$295$	12.2707			0.714429
$296$		0			0
$297$	−13.8648	−	21.8461i	−0.804515	−	1.26764i
$298$		0			0
$299$	−2.90707	−	5.03520i	−0.168120	−	0.291193i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−12.0372	+	14.7593i	−0.691518	+	0.847900i
$304$		0			0
$305$	15.4383	+	8.91333i	0.883997	+	0.510376i
$306$		0			0
$307$		−	2.82559i		−	0.161265i	−0.996744	−	0.0806326i	$-0.974306\pi$
$307$		−	2.82559i		−	0.161265i	0.996744	−	0.0806326i	$-0.0256940\pi$
$308$		0			0
$309$	16.8866	−	6.41479i	0.960646	−	0.364925i
$310$		0			0
$311$	8.20180	−	14.2059i	0.465081	−	0.805544i	−0.534124	−	0.845406i	$-0.679358\pi$
$311$	8.20180	−	14.2059i	0.465081	−	0.805544i	0.999205	+	0.0398618i	$0.0126918\pi$
$312$		0			0
$313$	0.281285	−	0.162400i	0.0158991	−	0.00917938i	−0.492029	−	0.870579i	$-0.663745\pi$
$313$	0.281285	−	0.162400i	0.0158991	−	0.00917938i	0.507929	+	0.861399i	$0.330411\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.4345	+	6.02438i	−0.586062	+	0.338363i	−0.763539	−	0.645762i	$-0.776540\pi$
$317$	−10.4345	+	6.02438i	−0.586062	+	0.338363i	0.177477	+	0.984125i	$0.443206\pi$
$318$		0			0
$319$	−11.5266	+	19.9647i	−0.645367	+	1.11781i
$320$		0			0
$321$	−4.98721	+	1.89451i	−0.278359	+	0.105742i
$322$		0			0
$323$			5.05808i			0.281439i
$324$		0			0
$325$	−2.08211	−	1.20211i	−0.115495	−	0.0666809i
$326$		0			0
$327$	−15.0534	+	18.4576i	−0.832456	+	1.02071i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−3.50003	−	6.06222i	−0.192379	−	0.333210i	0.753659	−	0.657265i	$-0.228287\pi$
$331$	−3.50003	−	6.06222i	−0.192379	−	0.333210i	−0.946038	+	0.324055i	$0.894954\pi$
$332$		0			0
$333$	3.15170	+	15.3525i	0.172712	+	0.841313i
$334$		0			0
$335$	−9.90259			−0.541036
$336$		0			0
$337$	−12.2829			−0.669094			−0.334547	−	0.942379i	$-0.608583\pi$
$337$	−12.2829			−0.669094			−0.334547	+	0.942379i	$0.608583\pi$
$338$		0			0
$339$	−3.50048	+	21.6138i	−0.190120	+	1.17390i
$340$		0			0
$341$	4.48905	+	7.77525i	0.243095	+	0.421054i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−13.9630	−	11.3877i	−0.751741	−	0.613094i
$346$		0			0
$347$	−17.9947	−	10.3892i	−0.966006	−	0.557724i	−0.0679895	−	0.997686i	$-0.521658\pi$
$347$	−17.9947	−	10.3892i	−0.966006	−	0.557724i	−0.898016	+	0.439962i	$0.854992\pi$
$348$		0			0
$349$		−	1.72878i		−	0.0925396i	−0.998929	−	0.0462698i	$-0.985267\pi$
$349$		−	1.72878i		−	0.0925396i	0.998929	−	0.0462698i	$-0.0147334\pi$
$350$		0			0
$351$	1.76511	−	3.37656i	0.0942146	−	0.180227i
$352$		0			0
$353$	−5.31556	+	9.20681i	−0.282919	+	0.490029i	−0.972102	−	0.234557i	$-0.924636\pi$
$353$	−5.31556	+	9.20681i	−0.282919	+	0.490029i	0.689184	+	0.724587i	$0.257969\pi$
$354$		0			0
$355$	−7.87046	+	4.54401i	−0.417720	+	0.241171i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−3.65893	+	2.11249i	−0.193111	+	0.111493i	−0.593438	−	0.804880i	$-0.702230\pi$
$359$	−3.65893	+	2.11249i	−0.193111	+	0.111493i	0.400327	+	0.916372i	$0.368897\pi$
$360$		0			0
$361$	14.6135	−	25.3114i	0.769134	−	1.33218i
$362$		0			0
$363$	8.48542	+	22.3374i	0.445369	+	1.17241i
$364$		0			0
$365$		−	4.98419i		−	0.260885i
$366$		0			0
$367$	20.8212	+	12.0212i	1.08686	+	0.627499i	0.932739	−	0.360553i	$-0.117412\pi$
$367$	20.8212	+	12.0212i	1.08686	+	0.627499i	0.154121	+	0.988052i	$0.450745\pi$
$368$		0			0
$369$	22.3136	+	7.42232i	1.16160	+	0.386390i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−16.2951	−	28.2239i	−0.843727	−	1.46138i	−0.886722	−	0.462302i	$-0.847023\pi$
$373$	−16.2951	−	28.2239i	−0.843727	−	1.46138i	0.0429957	−	0.999075i	$-0.486310\pi$
$374$		0			0
$375$	−18.5703	−	3.00756i	−0.958965	−	0.155310i
$376$		0			0
$377$	−3.39466			−0.174834
$378$		0			0
$379$	19.2333			0.987948			0.493974	−	0.869477i	$-0.335544\pi$
$379$	19.2333			0.987948			0.493974	+	0.869477i	$0.335544\pi$
$380$		0			0
$381$	5.67626	+	0.919302i	0.290804	+	0.0470973i
$382$		0			0
$383$	12.9702	+	22.4650i	0.662745	+	1.14791i	0.979891	+	0.199532i	$0.0639422\pi$
$383$	12.9702	+	22.4650i	0.662745	+	1.14791i	−0.317146	+	0.948377i	$0.602725\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.62141	−	1.20461i	−0.184087	−	0.0612339i
$388$		0			0
$389$	19.5518	+	11.2882i	0.991316	+	0.572336i	0.905667	−	0.423989i	$-0.139370\pi$
$389$	19.5518	+	11.2882i	0.991316	+	0.572336i	0.0856485	+	0.996325i	$0.472704\pi$
$390$		0			0
$391$			5.77528i			0.292069i
$392$		0			0
$393$	9.84876	+	25.9264i	0.496804	+	1.30781i
$394$		0			0
$395$	−8.91638	+	15.4436i	−0.448632	+	0.777053i
$396$		0			0
$397$	5.82800	−	3.36479i	0.292499	−	0.168874i	−0.346569	−	0.938024i	$-0.612654\pi$
$397$	5.82800	−	3.36479i	0.292499	−	0.168874i	0.639068	+	0.769150i	$0.279320\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.66935	+	3.27320i	−0.283114	+	0.163456i	−0.634832	−	0.772650i	$-0.718931\pi$
$401$	−5.66935	+	3.27320i	−0.283114	+	0.163456i	0.351719	+	0.936106i	$0.385597\pi$
$402$		0			0
$403$	−0.661027	+	1.14493i	−0.0329281	+	0.0570331i
$404$		0			0
$405$	1.39763	−	11.7244i	0.0694487	−	0.582588i
$406$		0			0
$407$		−	26.0142i		−	1.28948i
$408$		0			0
$409$	−17.5082	−	10.1084i	−0.865726	−	0.499827i	0.000199559	−	1.00000i	$-0.499936\pi$
$409$	−17.5082	−	10.1084i	−0.865726	−	0.499827i	−0.865926	+	0.500173i	$0.833270\pi$
$410$		0			0
$411$	−14.4337	−	11.7716i	−0.711962	−	0.580652i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−4.32263	−	7.48701i	−0.212189	−	0.367523i
$416$		0			0
$417$	5.13760	−	31.7223i	0.251589	−	1.55345i
$418$		0			0
$419$	13.0519			0.637627			0.318813	−	0.947817i	$-0.396716\pi$
$419$	13.0519			0.637627			0.318813	+	0.947817i	$0.396716\pi$
$420$		0			0
$421$	−33.1602			−1.61613			−0.808065	−	0.589093i	$-0.799485\pi$
$421$	−33.1602			−1.61613			−0.808065	+	0.589093i	$0.799485\pi$
$422$		0			0
$423$	2.55891	+	12.4649i	0.124418	+	0.606066i
$424$		0			0
$425$	1.19407	+	2.06819i	0.0579210	+	0.100322i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−3.99700	+	4.90090i	−0.192977	+	0.236618i
$430$		0			0
$431$	0.969987	+	0.560022i	0.0467226	+	0.0269753i	0.523179	−	0.852223i	$-0.324746\pi$
$431$	0.969987	+	0.560022i	0.0467226	+	0.0269753i	−0.476457	+	0.879198i	$0.658079\pi$
$432$		0			0
$433$			29.9594i			1.43976i	0.694100	+	0.719878i	$0.255802\pi$
$433$			29.9594i			1.43976i	−0.694100	+	0.719878i	$0.744198\pi$
$434$		0			0
$435$	−9.83432	+	3.73581i	−0.471520	+	0.179118i
$436$		0			0
$437$	27.5327	−	47.6880i	1.31707	−	2.28123i
$438$		0			0
$439$	18.7386	−	10.8187i	0.894344	−	0.516350i	0.0189834	−	0.999820i	$-0.493957\pi$
$439$	18.7386	−	10.8187i	0.894344	−	0.516350i	0.875361	+	0.483470i	$0.160624\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	6.82437	−	3.94005i	0.324236	−	0.187198i	−0.329043	−	0.944315i	$-0.606726\pi$
$443$	6.82437	−	3.94005i	0.324236	−	0.187198i	0.653279	+	0.757117i	$0.273393\pi$
$444$		0			0
$445$	2.87211	−	4.97464i	0.136151	−	0.235821i
$446$		0			0
$447$	7.88287	−	2.99450i	0.372847	−	0.141635i
$448$		0			0
$449$		−	29.5174i		−	1.39301i	−0.717550	−	0.696507i	$-0.754737\pi$
$449$		−	29.5174i		−	1.39301i	0.717550	−	0.696507i	$-0.245263\pi$
$450$		0			0
$451$	−33.8030	−	19.5162i	−1.59172	−	0.918981i
$452$		0			0
$453$	−1.86230	+	2.28344i	−0.0874983	+	0.107285i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.28872	−	2.23213i	−0.0602839	−	0.104415i	0.834308	−	0.551298i	$-0.185867\pi$
$457$	−1.28872	−	2.23213i	−0.0602839	−	0.104415i	−0.894592	+	0.446883i	$0.852534\pi$
$458$		0			0
$459$	−3.19541	+	2.02798i	−0.149149	+	0.0946582i
$460$		0			0
$461$	30.8387			1.43630			0.718151	−	0.695888i	$-0.244989\pi$
$461$	30.8387			1.43630			0.718151	+	0.695888i	$0.244989\pi$
$462$		0			0
$463$	36.6548			1.70349			0.851745	−	0.523956i	$-0.175544\pi$
$463$	36.6548			1.70349			0.851745	+	0.523956i	$0.175544\pi$
$464$		0			0
$465$	−0.655000	+	4.04431i	−0.0303749	+	0.187551i
$466$		0			0
$467$	−17.5386	−	30.3777i	−0.811588	−	1.40571i	−0.911752	−	0.410740i	$-0.865270\pi$
$467$	−17.5386	−	30.3777i	−0.811588	−	1.40571i	0.100165	−	0.994971i	$-0.468063\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	24.3990	+	19.8990i	1.12425	+	0.916896i
$472$		0			0
$473$	5.48610	+	3.16740i	0.252251	+	0.145637i
$474$		0			0
$475$		−	22.7701i		−	1.04477i
$476$		0			0
$477$	−28.7152	−	32.3416i	−1.31478	−	1.48082i
$478$		0			0
$479$	−14.3841	+	24.9141i	−0.657228	+	1.13835i	0.324102	+	0.946022i	$0.394938\pi$
$479$	−14.3841	+	24.9141i	−0.657228	+	1.13835i	−0.981330	+	0.192331i	$0.938395\pi$
$480$		0			0
$481$	3.31746	−	1.91534i	0.151263	−	0.0873318i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	17.2140	−	9.93851i	0.781648	−	0.451284i
$486$		0			0
$487$	−18.0375	+	31.2418i	−0.817356	+	1.41570i	0.0902675	+	0.995918i	$0.471228\pi$
$487$	−18.0375	+	31.2418i	−0.817356	+	1.41570i	−0.907624	+	0.419785i	$0.862106\pi$
$488$		0			0
$489$	3.08973	+	8.13356i	0.139723	+	0.367812i
$490$		0			0
$491$			26.0949i			1.17764i	0.808263	+	0.588822i	$0.200408\pi$
$491$			26.0949i			1.17764i	−0.808263	+	0.588822i	$0.799592\pi$
$492$		0			0
$493$	2.92022	+	1.68599i	0.131520	+	0.0759330i
$494$		0			0
$495$	−6.18588	+	18.5965i	−0.278035	+	0.835852i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	9.27200	+	16.0596i	0.415072	+	0.718925i	0.995436	−	0.0954319i	$-0.0304232\pi$
$499$	9.27200	+	16.0596i	0.415072	+	0.718925i	−0.580364	+	0.814357i	$0.697090\pi$
$500$		0			0
$501$	−28.1042	−	4.55164i	−1.25560	−	0.203352i
$502$		0			0
$503$	19.2682			0.859126			0.429563	−	0.903037i	$-0.358668\pi$
$503$	19.2682			0.859126			0.429563	+	0.903037i	$0.358668\pi$
$504$		0			0
$505$	14.4259			0.641943
$506$		0			0
$507$	21.3078	+	3.45091i	0.946311	+	0.153260i
$508$		0			0
$509$	−12.9656	−	22.4570i	−0.574688	−	0.995389i	−0.996075	−	0.0885081i	$-0.971790\pi$
$509$	−12.9656	−	22.4570i	−0.574688	−	0.995389i	0.421387	−	0.906881i	$-0.361543\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	36.0534	−	1.51203i	1.59180	−	0.0667578i
$514$		0			0
$515$	−11.8493	−	6.84122i	−0.522144	−	0.301460i
$516$		0			0
$517$		−	21.1213i		−	0.928914i
$518$		0			0
$519$	2.58607	+	6.80771i	0.113516	+	0.298825i
$520$		0			0
$521$	−5.53584	+	9.58836i	−0.242530	+	0.420074i	−0.961434	−	0.275035i	$-0.911310\pi$
$521$	−5.53584	+	9.58836i	−0.242530	+	0.420074i	0.718905	+	0.695109i	$0.244644\pi$
$522$		0			0
$523$	−30.7081	+	17.7293i	−1.34277	+	0.775249i	−0.987213	−	0.159405i	$-0.949042\pi$
$523$	−30.7081	+	17.7293i	−1.34277	+	0.775249i	−0.355558	+	0.934654i	$0.615709\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.13728	−	0.656608i	0.0495406	−	0.0286023i
$528$		0			0
$529$	19.9366	−	34.5312i	0.866809	−	1.50136i
$530$		0			0
$531$	−20.9825	+	18.6298i	−0.910565	+	0.808466i
$532$		0			0
$533$		−	5.74764i		−	0.248958i
$534$		0			0
$535$	3.49953	+	2.02045i	0.151298	+	0.0873518i
$536$		0			0
$537$	10.9260	+	8.91086i	0.471491	+	0.384532i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	4.02456	+	6.97075i	0.173029	+	0.299696i	0.939478	−	0.342610i	$-0.111311\pi$
$541$	4.02456	+	6.97075i	0.173029	+	0.299696i	−0.766448	+	0.642306i	$0.777978\pi$
$542$		0			0
$543$	4.95343	−	30.5851i	0.212572	−	1.31253i
$544$		0			0
$545$	18.0407			0.772777
$546$		0			0
$547$	15.3821			0.657690			0.328845	−	0.944384i	$-0.393341\pi$
$547$	15.3821			0.657690			0.328845	+	0.944384i	$0.393341\pi$
$548$		0			0
$549$	−39.9316	+	8.19751i	−1.70424	+	0.349861i
$550$		0			0
$551$	−16.0753	−	27.8433i	−0.684831	−	1.18616i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	7.50284	−	9.19956i	0.318478	−	0.390500i
$556$		0			0
$557$	−29.5356	−	17.0524i	−1.25147	−	0.722534i	−0.280065	−	0.959981i	$-0.590356\pi$
$557$	−29.5356	−	17.0524i	−1.25147	−	0.722534i	−0.971400	+	0.237447i	$0.923689\pi$
$558$		0			0
$559$			0.932820i			0.0394541i
$560$		0			0
$561$	5.87244	−	2.23079i	0.247934	−	0.0941840i
$562$		0			0
$563$	16.3328	−	28.2892i	0.688343	−	1.19225i	−0.284030	−	0.958815i	$-0.591672\pi$
$563$	16.3328	−	28.2892i	0.688343	−	1.19225i	0.972374	−	0.233430i	$-0.0749951\pi$
$564$		0			0
$565$	14.3627	−	8.29228i	0.604242	−	0.348859i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	20.7309	−	11.9690i	0.869084	−	0.501766i	0.00203998	−	0.999998i	$-0.499351\pi$
$569$	20.7309	−	11.9690i	0.869084	−	0.501766i	0.867044	+	0.498232i	$0.166017\pi$
$570$		0			0
$571$	12.4750	−	21.6074i	0.522065	−	0.904242i	−0.477606	−	0.878574i	$-0.658495\pi$
$571$	12.4750	−	21.6074i	0.522065	−	0.904242i	0.999671	−	0.0256682i	$-0.00817134\pi$
$572$		0			0
$573$	6.65540	−	2.52822i	0.278034	−	0.105618i
$574$		0			0
$575$		−	25.9988i		−	1.08422i
$576$		0			0
$577$	18.0068	+	10.3962i	0.749633	+	0.432801i	0.825561	−	0.564313i	$-0.190859\pi$
$577$	18.0068	+	10.3962i	0.749633	+	0.432801i	−0.0759284	+	0.997113i	$0.524192\pi$
$578$		0			0
$579$	3.53498	−	4.33439i	0.146909	−	0.180131i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	35.8939	+	62.1701i	1.48658	+	2.57482i
$584$		0			0
$585$	−2.82697	+	0.580345i	−0.116881	+	0.0239943i
$586$		0			0
$587$	11.7010			0.482951			0.241475	−	0.970407i	$-0.422369\pi$
$587$	11.7010			0.482951			0.241475	+	0.970407i	$0.422369\pi$
$588$		0			0
$589$	−12.5211			−0.515922
$590$		0			0
$591$	−1.30359	+	8.04906i	−0.0536226	+	0.331094i
$592$		0			0
$593$	−16.8227	−	29.1378i	−0.690826	−	1.19655i	−0.971567	−	0.236763i	$-0.923914\pi$
$593$	−16.8227	−	29.1378i	−0.690826	−	1.19655i	0.280741	−	0.959784i	$-0.409420\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−22.7962	−	18.5918i	−0.932985	−	0.760910i
$598$		0			0
$599$	9.70331	+	5.60221i	0.396467	+	0.228900i	0.684958	−	0.728582i	$-0.259820\pi$
$599$	9.70331	+	5.60221i	0.396467	+	0.228900i	−0.288492	+	0.957482i	$0.593154\pi$
$600$		0			0
$601$			6.08245i			0.248108i	0.992275	+	0.124054i	$0.0395897\pi$
$601$			6.08245i			0.248108i	−0.992275	+	0.124054i	$0.960410\pi$
$602$		0			0
$603$	16.9331	−	15.0345i	0.689570	−	0.612251i
$604$		0			0
$605$	9.04950	−	15.6742i	0.367914	−	0.637246i
$606$		0			0
$607$	6.00021	−	3.46422i	0.243541	−	0.140608i	−0.373262	−	0.927726i	$-0.621761\pi$
$607$	6.00021	−	3.46422i	0.243541	−	0.140608i	0.616803	+	0.787117i	$0.288427\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.69349	−	1.55509i	0.108967	−	0.0629122i
$612$		0			0
$613$	−6.76156	+	11.7114i	−0.273097	+	0.473018i	−0.969653	−	0.244484i	$-0.921381\pi$
$613$	−6.76156	+	11.7114i	−0.273097	+	0.473018i	0.696556	+	0.717502i	$0.254715\pi$
$614$		0			0
$615$	−6.32524	−	16.6509i	−0.255058	−	0.671428i
$616$		0			0
$617$		−	3.82786i		−	0.154104i	−0.997027	−	0.0770519i	$-0.975449\pi$
$617$		−	3.82786i		−	0.154104i	0.997027	−	0.0770519i	$-0.0245507\pi$
$618$		0			0
$619$	5.10279	+	2.94610i	0.205099	+	0.118414i	0.599031	−	0.800726i	$-0.295552\pi$
$619$	5.10279	+	2.94610i	0.205099	+	0.118414i	−0.393933	+	0.919139i	$0.628886\pi$
$620$		0			0
$621$	41.1655	−	1.72643i	1.65191	−	0.0692791i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−1.07249	−	1.85761i	−0.0428997	−	0.0743044i
$626$		0			0
$627$	−59.1251	−	9.57565i	−2.36123	−	0.382415i
$628$		0			0
$629$	−3.80507			−0.151718
$630$		0			0
$631$	−3.83697			−0.152747			−0.0763737	−	0.997079i	$-0.524334\pi$
$631$	−3.83697			−0.152747			−0.0763737	+	0.997079i	$0.524334\pi$
$632$		0			0
$633$	−3.23362	−	0.523703i	−0.128525	−	0.0208153i
$634$		0			0
$635$	−2.17773	−	3.77194i	−0.0864207	−	0.149685i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	6.55936	−	19.7193i	0.259484	−	0.780084i
$640$		0			0
$641$	3.45196	+	1.99299i	0.136344	+	0.0787183i	0.566621	−	0.823979i	$-0.308251\pi$
$641$	3.45196	+	1.99299i	0.136344	+	0.0787183i	−0.430276	+	0.902697i	$0.641584\pi$
$642$		0			0
$643$			15.4887i			0.610814i	0.952222	+	0.305407i	$0.0987925\pi$
$643$			15.4887i			0.610814i	−0.952222	+	0.305407i	$0.901207\pi$
$644$		0			0
$645$	1.02656	+	2.70237i	0.0404209	+	0.106406i
$646$		0			0
$647$	10.3128	−	17.8623i	0.405437	−	0.702238i	−0.588935	−	0.808180i	$-0.700453\pi$
$647$	10.3128	−	17.8623i	0.405437	−	0.702238i	0.994372	+	0.105943i	$0.0337860\pi$
$648$		0			0
$649$	40.3346	−	23.2872i	1.58327	−	0.914103i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	43.5115	−	25.1214i	1.70274	−	0.983075i	0.759767	−	0.650196i	$-0.225313\pi$
$653$	43.5115	−	25.1214i	1.70274	−	0.983075i	0.942969	−	0.332879i	$-0.108020\pi$
$654$		0			0
$655$	10.5035	−	18.1925i	0.410404	−	0.710841i
$656$		0			0
$657$	7.56717	+	8.52281i	0.295224	+	0.332507i
$658$		0			0
$659$		−	34.6160i		−	1.34845i	−0.738528	−	0.674223i	$-0.764479\pi$
$659$		−	34.6160i		−	1.34845i	0.738528	−	0.674223i	$-0.235521\pi$
$660$		0			0
$661$	8.65013	+	4.99416i	0.336451	+	0.194250i	0.658702	−	0.752404i	$-0.271106\pi$
$661$	8.65013	+	4.99416i	0.336451	+	0.194250i	−0.322250	+	0.946654i	$0.604439\pi$
$662$		0			0
$663$	0.716849	+	0.584637i	0.0278401	+	0.0227054i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−18.3547	−	31.7912i	−0.710696	−	1.23096i
$668$		0			0
$669$	2.57433	−	15.8953i	0.0995292	−	0.614546i
$670$		0			0
$671$	67.6624			2.61208
$672$		0			0
$673$	−8.78901			−0.338791			−0.169396	−	0.985548i	$-0.554182\pi$
$673$	−8.78901			−0.338791			−0.169396	+	0.985548i	$0.554182\pi$
$674$		0			0
$675$	14.3849	−	9.12945i	0.553674	−	0.351393i
$676$		0			0
$677$	2.37938	+	4.12120i	0.0914468	+	0.158391i	0.908120	−	0.418710i	$-0.137518\pi$
$677$	2.37938	+	4.12120i	0.0914468	+	0.158391i	−0.816673	+	0.577100i	$0.804184\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	5.44057	−	6.67092i	0.208483	−	0.255630i
$682$		0			0
$683$	22.5997	+	13.0479i	0.864752	+	0.499265i	0.865601	−	0.500735i	$-0.166937\pi$
$683$	22.5997	+	13.0479i	0.864752	+	0.499265i	−0.000848961		1.00000i	$0.500270\pi$
$684$		0			0
$685$			14.1076i			0.539025i
$686$		0			0
$687$	−8.63267	+	3.27933i	−0.329357	+	0.125114i
$688$		0			0
$689$	−5.28550	+	9.15475i	−0.201361	+	0.348768i
$690$		0			0
$691$	−26.5047	+	15.3025i	−1.00829	+	0.582134i	−0.910689	−	0.413092i	$-0.864449\pi$
$691$	−26.5047	+	15.3025i	−1.00829	+	0.582134i	−0.0975962	+	0.995226i	$0.531115\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−21.0798	+	12.1704i	−0.799604	+	0.461651i
$696$		0			0
$697$	−2.85461	+	4.94433i	−0.108126	+	0.187280i
$698$		0			0
$699$	−5.67087	+	2.15422i	−0.214492	+	0.0814800i
$700$		0			0
$701$		−	45.8510i		−	1.73177i	−0.500246	−	0.865884i	$-0.666757\pi$
$701$		−	45.8510i		−	1.73177i	0.500246	−	0.865884i	$-0.333243\pi$
$702$		0			0
$703$	31.4194	+	18.1400i	1.18501	+	0.684163i
$704$		0			0
$705$	6.09167	−	7.46926i	0.229426	−	0.281309i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	3.66229	+	6.34327i	0.137540	+	0.238227i	0.926565	−	0.376135i	$-0.122747\pi$
$709$	3.66229	+	6.34327i	0.137540	+	0.238227i	−0.789025	+	0.614361i	$0.789414\pi$
$710$		0			0
$711$	−8.20032	−	39.9453i	−0.307536	−	1.49806i
$712$		0			0
$713$	−14.2965			−0.535407
$714$		0			0
$715$	4.79018			0.179143
$716$		0			0
$717$	−6.50092	+	40.1401i	−0.242781	+	1.49906i
$718$		0			0
$719$	−9.32123	−	16.1448i	−0.347623	−	0.602101i	0.638204	−	0.769868i	$-0.279678\pi$
$719$	−9.32123	−	16.1448i	−0.347623	−	0.602101i	−0.985827	+	0.167767i	$0.946344\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	13.5130	+	11.0208i	0.502555	+	0.409867i
$724$		0			0
$725$	−13.1460	−	7.58986i	−0.488231	−	0.281880i
$726$		0			0
$727$		−	4.44113i		−	0.164712i	−0.996603	−	0.0823562i	$-0.973755\pi$
$727$		−	4.44113i		−	0.164712i	0.996603	−	0.0823562i	$-0.0262445\pi$
$728$		0			0
$729$	15.4104	+	22.1702i	0.570757	+	0.821119i
$730$		0			0
$731$	0.463292	−	0.802446i	0.0171355	−	0.0296795i
$732$		0			0
$733$	−32.3277	+	18.6644i	−1.19405	+	0.689385i	−0.959223	−	0.282652i	$-0.908786\pi$
$733$	−32.3277	+	18.6644i	−1.19405	+	0.689385i	−0.234827	+	0.972037i	$0.575452\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−32.5505	+	18.7930i	−1.19901	+	0.692249i
$738$		0			0
$739$	−7.85335	+	13.6024i	−0.288890	+	0.500373i	−0.973545	−	0.228495i	$-0.926620\pi$
$739$	−7.85335	+	13.6024i	−0.288890	+	0.500373i	0.684655	+	0.728867i	$0.259953\pi$
$740$		0			0
$741$	−3.13205	−	8.24496i	−0.115059	−	0.302886i
$742$		0			0
$743$			41.4427i			1.52039i	0.649697	+	0.760193i	$0.274896\pi$
$743$			41.4427i			1.52039i	−0.649697	+	0.760193i	$0.725104\pi$
$744$		0			0
$745$	−5.53141	−	3.19356i	−0.202655	−	0.117003i
$746$		0			0
$747$	18.7586	+	6.23979i	0.686341	+	0.228302i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−5.95974	−	10.3226i	−0.217474	−	0.376676i	0.736561	−	0.676371i	$-0.236448\pi$
$751$	−5.95974	−	10.3226i	−0.217474	−	0.376676i	−0.954035	+	0.299695i	$0.903115\pi$
$752$		0			0
$753$	−33.8418	−	5.48087i	−1.23326	−	0.199734i
$754$		0			0
$755$	2.23186			0.0812256
$756$		0			0
$757$	20.9855			0.762731			0.381365	−	0.924424i	$-0.375454\pi$
$757$	20.9855			0.762731			0.381365	+	0.924424i	$0.375454\pi$
$758$		0			0
$759$	−67.5086	−	10.9334i	−2.45041	−	0.396858i
$760$		0			0
$761$	13.2481	+	22.9464i	0.480245	+	0.831808i	0.999743	−	0.0226633i	$-0.00721457\pi$
$761$	13.2481	+	22.9464i	0.480245	+	0.831808i	−0.519499	+	0.854471i	$0.673881\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	2.72010	+	0.904803i	0.0983453	+	0.0327132i
$766$		0			0
$767$	5.93940	+	3.42912i	0.214459	+	0.123818i
$768$		0			0
$769$			49.5271i			1.78599i	0.450062	+	0.892997i	$0.351402\pi$
$769$			49.5271i			1.78599i	−0.450062	+	0.892997i	$0.648598\pi$
$770$		0			0
$771$	7.76001	+	20.4278i	0.279470	+	0.735690i
$772$		0			0
$773$	−3.68724	+	6.38649i	−0.132621	+	0.229706i	−0.924686	−	0.380730i	$-0.875673\pi$
$773$	−3.68724	+	6.38649i	−0.132621	+	0.229706i	0.792065	+	0.610436i	$0.209006\pi$
$774$		0			0
$775$	−5.11972	+	2.95587i	−0.183906	+	0.106178i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	47.1425	−	27.2177i	1.68906	−	0.975177i
$780$		0			0
$781$	−17.2471	+	29.8729i	−0.617151	+	1.06894i
$782$		0			0
$783$	11.1445	−	21.3189i	0.398274	−	0.761876i
$784$		0			0
$785$		−	23.8478i		−	0.851164i
$786$		0			0
$787$	−31.2674	−	18.0523i	−1.11456	−	0.643493i	−0.174556	−	0.984647i	$-0.555849\pi$
$787$	−31.2674	−	18.0523i	−1.11456	−	0.643493i	−0.940007	+	0.341154i	$0.889182\pi$
$788$		0			0
$789$	8.49914	+	6.93160i	0.302577	+	0.246772i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	4.98176	+	8.62866i	0.176907	+	0.306413i
$794$		0			0
$795$	−5.23731	+	32.3379i	−0.185748	+	1.14691i
$796$		0			0
$797$	25.6502			0.908576			0.454288	−	0.890855i	$-0.349894\pi$
$797$	25.6502			0.908576			0.454288	+	0.890855i	$0.349894\pi$
$798$		0			0
$799$	−3.08939			−0.109295
$800$		0			0
$801$	2.64145	+	12.8670i	0.0933312	+	0.454634i
$802$		0			0
$803$	−9.45893	−	16.3834i	−0.333799	−	0.578156i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−26.6929	+	32.7294i	−0.939636	+	1.15213i
$808$		0			0
$809$	28.2515	+	16.3110i	0.993269	+	0.573464i	0.906250	−	0.422742i	$-0.138932\pi$
$809$	28.2515	+	16.3110i	0.993269	+	0.573464i	0.0870195	+	0.996207i	$0.472266\pi$
$810$		0			0
$811$			12.7234i			0.446779i	0.974729	+	0.223390i	$0.0717122\pi$
$811$			12.7234i			0.446779i	−0.974729	+	0.223390i	$0.928288\pi$
$812$		0			0
$813$	−0.557107	+	0.211631i	−0.0195386	+	0.00742221i
$814$		0			0
$815$	3.29512	−	5.70732i	0.115423	−	0.199919i
$816$		0			0
$817$	−7.65105	+	4.41734i	−0.267676	+	0.154543i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−45.7231	+	26.3982i	−1.59575	+	0.921305i	−0.603452	+	0.797399i	$0.706209\pi$
$821$	−45.7231	+	26.3982i	−1.59575	+	0.921305i	−0.992294	+	0.123905i	$0.960458\pi$
$822$		0			0
$823$	−6.33692	+	10.9759i	−0.220891	+	0.382595i	−0.955079	−	0.296352i	$-0.904230\pi$
$823$	−6.33692	+	10.9759i	−0.220891	+	0.382595i	0.734188	+	0.678947i	$0.237563\pi$
$824$		0			0
$825$	−26.4361	+	10.0424i	−0.920388	+	0.349632i
$826$		0			0
$827$		−	30.4839i		−	1.06003i	−0.847988	−	0.530015i	$-0.822186\pi$
$827$		−	30.4839i		−	1.06003i	0.847988	−	0.530015i	$-0.177814\pi$
$828$		0			0
$829$	−6.89227	−	3.97925i	−0.239378	−	0.138205i	0.375513	−	0.926817i	$-0.377467\pi$
$829$	−6.89227	−	3.97925i	−0.239378	−	0.138205i	−0.614891	+	0.788612i	$0.710800\pi$
$830$		0			0
$831$	−13.3946	+	16.4237i	−0.464655	+	0.569733i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	10.7824	+	18.6756i	0.373139	+	0.646296i
$836$		0			0
$837$	−5.02019	−	7.91009i	−0.173523	−	0.273413i
$838$		0			0
$839$	15.9255			0.549808			0.274904	−	0.961472i	$-0.411354\pi$
$839$	15.9255			0.549808			0.274904	+	0.961472i	$0.411354\pi$
$840$		0			0
$841$	7.56677			0.260923
$842$		0			0
$843$	−4.61772	+	28.5123i	−0.159043	+	0.982014i
$844$		0			0
$845$	−8.17486	−	14.1593i	−0.281224	−	0.487094i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	4.16312	+	3.39530i	0.142878	+	0.116526i
$850$		0			0
$851$	35.8745	+	20.7121i	1.22976	+	0.710003i
$852$		0			0
$853$		−	24.3170i		−	0.832597i	−0.909228	−	0.416298i	$-0.863327\pi$
$853$		−	24.3170i		−	0.832597i	0.909228	−	0.416298i	$-0.136673\pi$
$854$		0			0
$855$	−18.1470	−	20.4388i	−0.620616	−	0.698992i
$856$		0			0
$857$	22.1459	−	38.3579i	0.756491	−	1.31028i	−0.188139	−	0.982142i	$-0.560246\pi$
$857$	22.1459	−	38.3579i	0.756491	−	1.31028i	0.944630	−	0.328138i	$-0.106421\pi$
$858$		0			0
$859$	−19.8175	+	11.4417i	−0.676166	+	0.390385i	−0.798409	−	0.602116i	$-0.794325\pi$
$859$	−19.8175	+	11.4417i	−0.676166	+	0.390385i	0.122243	+	0.992500i	$0.460991\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−20.4926	+	11.8314i	−0.697575	+	0.402745i	−0.806443	−	0.591311i	$-0.798610\pi$
$863$	−20.4926	+	11.8314i	−0.697575	+	0.402745i	0.108869	+	0.994056i	$0.465277\pi$
$864$		0			0
$865$	2.75798	−	4.77697i	0.0937743	−	0.162422i
$866$		0			0
$867$	10.1300	+	26.6668i	0.344034	+	0.905651i
$868$		0			0
$869$			67.6856i			2.29608i
$870$		0			0
$871$	−4.79316	−	2.76733i	−0.162410	−	0.0937675i
$872$		0			0
$873$	−14.3464	+	43.1294i	−0.485553	+	1.45971i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−14.7579	−	25.5615i	−0.498340	−	0.863150i	0.501658	−	0.865066i	$-0.332724\pi$
$877$	−14.7579	−	25.5615i	−0.498340	−	0.863150i	−0.999998	+	0.00191559i	$0.999390\pi$
$878$		0			0
$879$	27.7821	+	4.49947i	0.937068	+	0.151763i
$880$		0			0
$881$	12.0113			0.404673			0.202336	−	0.979316i	$-0.435147\pi$
$881$	12.0113			0.404673			0.202336	+	0.979316i	$0.435147\pi$
$882$		0			0
$883$	−26.4428			−0.889871			−0.444935	−	0.895563i	$-0.646773\pi$
$883$	−26.4428			−0.889871			−0.444935	+	0.895563i	$0.646773\pi$
$884$		0			0
$885$	20.9801	+	3.39785i	0.705239	+	0.114218i
$886$		0			0
$887$	−1.56238	−	2.70612i	−0.0524596	−	0.0908628i	0.838603	−	0.544743i	$-0.183373\pi$
$887$	−1.56238	−	2.70612i	−0.0524596	−	0.0908628i	−0.891063	+	0.453880i	$0.850039\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−17.6562	−	41.1911i	−0.591506	−	1.37995i
$892$		0			0
$893$	25.5099	+	14.7281i	0.853656	+	0.492858i
$894$		0			0
$895$		−	10.6792i		−	0.356965i
$896$		0			0
$897$	−3.57615	−	9.41403i	−0.119404	−	0.314325i
$898$		0			0
$899$	−4.17359	+	7.22887i	−0.139197	+	0.241096i
$900$		0			0
$901$	9.09356	−	5.25017i	0.302950	−	0.174909i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−20.3242	+	11.7342i	−0.675598	+	0.390057i
$906$		0			0
$907$	28.9904	−	50.2128i	0.962610	−	1.66729i	0.246708	−	0.969090i	$-0.420651\pi$
$907$	28.9904	−	50.2128i	0.962610	−	1.66729i	0.715903	−	0.698200i	$-0.246015\pi$
$908$		0			0
$909$	−24.6678	+	21.9019i	−0.818180	+	0.726439i
$910$		0			0
$911$			0.434872i			0.0144079i	0.999974	+	0.00720397i	$0.00229312\pi$
$911$			0.434872i			0.0144079i	−0.999974	+	0.00720397i	$0.997707\pi$
$912$		0			0
$913$	−28.4175	−	16.4068i	−0.940482	−	0.542987i
$914$		0			0
$915$	23.9279	+	19.5148i	0.791032	+	0.645138i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−20.0768	−	34.7740i	−0.662271	−	1.14709i	−0.980017	−	0.198912i	$-0.936259\pi$
$919$	−20.0768	−	34.7740i	−0.662271	−	1.14709i	0.317746	−	0.948176i	$-0.397074\pi$
$920$		0			0
$921$	0.782428	−	4.83112i	0.0257819	−	0.159191i
$922$		0			0
$923$	−5.07939			−0.167190
$924$		0			0
$925$	17.1294			0.563211
$926$		0			0
$927$	30.6486	−	6.29181i	1.00663	−	0.206650i
$928$		0			0
$929$	−14.0683	−	24.3670i	−0.461566	−	0.799456i	0.537473	−	0.843281i	$-0.319379\pi$
$929$	−14.0683	−	24.3670i	−0.461566	−	0.799456i	−0.999039	+	0.0438250i	$0.986046\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	17.9569	−	22.0178i	0.587884	−	0.720829i
$934$		0			0
$935$	−4.12069	−	2.37908i	−0.134761	−	0.0778043i
$936$		0			0
$937$		−	57.1209i		−	1.86606i	−0.359801	−	0.933029i	$-0.617156\pi$
$937$		−	57.1209i		−	1.86606i	0.359801	−	0.933029i	$-0.382844\pi$
$938$		0			0
$939$	0.525902	−	0.199777i	0.0171622	−	0.00651947i
$940$		0			0
$941$	−5.01759	+	8.69073i	−0.163569	+	0.283310i	−0.936146	−	0.351611i	$-0.885634\pi$
$941$	−5.01759	+	8.69073i	−0.163569	+	0.283310i	0.772577	+	0.634921i	$0.218967\pi$
$942$		0			0
$943$	53.8270	−	31.0770i	1.75285	−	1.01201i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−15.5402	+	8.97213i	−0.504988	+	0.291555i	−0.730771	−	0.682623i	$-0.760839\pi$
$947$	−15.5402	+	8.97213i	−0.504988	+	0.291555i	0.225783	+	0.974178i	$0.427506\pi$
$948$		0			0
$949$	1.39286	−	2.41250i	0.0452141	−	0.0783131i
$950$		0			0
$951$	−19.5089	+	7.41092i	−0.632618	+	0.240316i
$952$		0			0
$953$		−	1.76188i		−	0.0570730i	−0.999593	−	0.0285365i	$-0.990915\pi$
$953$		−	1.76188i		−	0.0570730i	0.999593	−	0.0285365i	$-0.00908469\pi$
$954$		0			0
$955$	−4.67010	−	2.69628i	−0.151121	−	0.0872496i
$956$		0			0
$957$	−25.2363	+	30.9433i	−0.815773	+	1.00025i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−13.8746	−	24.0315i	−0.447568	−	0.775210i
$962$		0			0
$963$	−9.05161	+	1.85819i	−0.291684	+	0.0598794i
$964$		0			0
$965$	−4.23647			−0.136377
$966$		0			0
$967$	−20.8379			−0.670102			−0.335051	−	0.942200i	$-0.608754\pi$
$967$	−20.8379			−0.670102			−0.335051	+	0.942200i	$0.608754\pi$
$968$		0			0
$969$	−1.40062	+	8.64817i	−0.0449944	+	0.277819i
$970$		0			0
$971$	11.3816	+	19.7136i	0.365254	+	0.632639i	0.988817	−	0.149134i	$-0.0476487\pi$
$971$	11.3816	+	19.7136i	0.365254	+	0.632639i	−0.623563	+	0.781773i	$0.714315\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−3.22706	−	2.63188i	−0.103349	−	0.0842877i
$976$		0			0
$977$	−0.460396	−	0.265810i	−0.0147294	−	0.00850401i	0.492617	−	0.870246i	$-0.336040\pi$
$977$	−0.460396	−	0.265810i	−0.0147294	−	0.00850401i	−0.507347	+	0.861742i	$0.669374\pi$
$978$		0			0
$979$		−	21.8026i		−	0.696815i
$980$		0			0
$981$	−30.8490	+	27.3900i	−0.984932	+	0.874495i
$982$		0			0
$983$	−4.83659	+	8.37723i	−0.154263	+	0.267192i	−0.932791	−	0.360419i	$-0.882634\pi$
$983$	−4.83659	+	8.37723i	−0.154263	+	0.267192i	0.778527	+	0.627611i	$0.215967\pi$
$984$		0			0
$985$	5.34870	−	3.08807i	0.170424	−	0.0983942i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−8.73591	+	5.04368i	−0.277786	+	0.160380i
$990$		0			0
$991$	−2.07358	+	3.59155i	−0.0658695	+	0.114089i	−0.897079	−	0.441869i	$-0.854315\pi$
$991$	−2.07358	+	3.59155i	−0.0658695	+	0.114089i	0.831210	+	0.555959i	$0.187649\pi$
$992$		0			0
$993$	−4.30557	−	11.3342i	−0.136633	−	0.359680i
$994$		0			0
$995$			22.2812i			0.706361i
$996$		0			0
$997$	−3.79822	−	2.19290i	−0.120291	−	0.0694500i	0.438647	−	0.898659i	$-0.355458\pi$
$997$	−3.79822	−	2.19290i	−0.120291	−	0.0694500i	−0.558938	+	0.829209i	$0.688791\pi$
$998$		0			0
$999$	1.13746	+	27.1220i	0.0359878	+	0.858103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1176.2.u.c.521.23		48
3.2	odd	2	inner	1176.2.u.c.521.19		48
7.2	even	3	inner	1176.2.u.c.1097.6		48
7.3	odd	6		1176.2.k.b.881.16	yes	24
7.4	even	3		1176.2.k.b.881.9	✓	24
7.5	odd	6	inner	1176.2.u.c.1097.19		48
7.6	odd	2	inner	1176.2.u.c.521.2		48
21.2	odd	6	inner	1176.2.u.c.1097.2		48
21.5	even	6	inner	1176.2.u.c.1097.23		48
21.11	odd	6		1176.2.k.b.881.15	yes	24
21.17	even	6		1176.2.k.b.881.10	yes	24
21.20	even	2	inner	1176.2.u.c.521.6		48
28.3	even	6		2352.2.k.j.881.9		24
28.11	odd	6		2352.2.k.j.881.16		24
84.11	even	6		2352.2.k.j.881.10		24
84.59	odd	6		2352.2.k.j.881.15		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1176.2.k.b.881.9	✓	24	7.4	even	3
1176.2.k.b.881.10	yes	24	21.17	even	6
1176.2.k.b.881.15	yes	24	21.11	odd	6
1176.2.k.b.881.16	yes	24	7.3	odd	6
1176.2.u.c.521.2		48	7.6	odd	2	inner
1176.2.u.c.521.6		48	21.20	even	2	inner
1176.2.u.c.521.19		48	3.2	odd	2	inner
1176.2.u.c.521.23		48	1.1	even	1	trivial
1176.2.u.c.1097.2		48	21.2	odd	6	inner
1176.2.u.c.1097.6		48	7.2	even	3	inner
1176.2.u.c.1097.19		48	7.5	odd	6	inner
1176.2.u.c.1097.23		48	21.5	even	6	inner
2352.2.k.j.881.9		24	28.3	even	6
2352.2.k.j.881.10		24	84.11	even	6
2352.2.k.j.881.15		24	84.59	odd	6
2352.2.k.j.881.16		24	28.11	odd	6

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:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1176.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.70977 + 0.276907i) q^{3} +(-0.655965 - 1.13616i) q^{5} +(2.84664 + 0.946897i) q^{9} +(-4.31240 - 2.48976i) q^{11} -0.733252i q^{13} +(-0.806939 - 2.12423i) q^{15} +(-0.364175 + 0.630770i) q^{17} +(6.01418 - 3.47229i) q^{19} +(6.86694 - 3.96463i) q^{23} +(1.63942 - 2.83956i) q^{25} +(4.60491 + 2.40724i) q^{27} -4.62960i q^{29} +(-1.56144 - 0.901500i) q^{31} +(-6.68379 - 5.45106i) q^{33} +(2.61211 + 4.52431i) q^{37} +(0.203043 - 1.25369i) q^{39} +7.83857 q^{41} -1.27217 q^{43} +(-0.791468 - 3.85539i) q^{45} +(2.12081 + 3.67336i) q^{47} +(-0.797322 + 0.977630i) q^{51} +(-12.4851 - 7.20830i) q^{53} +6.53279i q^{55} +(11.2444 - 4.27145i) q^{57} +(-4.67659 + 8.10009i) q^{59} +(-11.7677 + 6.79406i) q^{61} +(-0.833095 + 0.480987i) q^{65} +(3.77405 - 6.53685i) q^{67} +(12.8387 - 4.87711i) q^{69} -6.92721i q^{71} +(3.29014 + 1.89956i) q^{73} +(3.58933 - 4.40103i) q^{75} +(-6.79638 - 11.7717i) q^{79} +(7.20677 + 5.39096i) q^{81} +6.58972 q^{83} +0.955545 q^{85} +(1.28197 - 7.91557i) q^{87} +(2.18923 + 3.79185i) q^{89} +(-2.42008 - 1.97374i) q^{93} +(-7.89018 - 4.55540i) q^{95} +15.1510i q^{97} +(-9.91831 - 11.1709i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 32 q^{15} - 8 q^{25} - 16 q^{37} + 64 q^{39} + 32 q^{43} - 48 q^{51} + 96 q^{57} - 16 q^{67} - 80 q^{81} - 128 q^{85} + 32 q^{93} - 112 q^{99}+O(q^{100}) \) 48 * q - 32 * q^15 - 8 * q^25 - 16 * q^37 + 64 * q^39 + 32 * q^43 - 48 * q^51 + 96 * q^57 - 16 * q^67 - 80 * q^81 - 128 * q^85 + 32 * q^93 - 112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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