LMFDB - Embedded newform 968.2.i.c.729.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(9,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("968.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.i (of order $5$, degree $4$, 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:	$7.72951891566$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			729.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	968.729
Dual form			968.2.i.c.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 1.53884i) q^{3} +(-0.500000 - 0.363271i) q^{5} +(-0.500000 + 1.53884i) q^{7} +(0.309017 - 0.224514i) q^{9} +(-4.73607 + 3.44095i) q^{13} +(-0.309017 + 0.951057i) q^{15} +(-1.50000 - 1.08981i) q^{17} +(-1.50000 - 4.61653i) q^{19} +2.61803 q^{21} -4.00000 q^{23} +(-1.42705 - 4.39201i) q^{25} +(-4.42705 - 3.21644i) q^{27} +(-2.26393 + 6.96767i) q^{29} +(-0.881966 + 0.640786i) q^{31} +(0.809017 - 0.587785i) q^{35} +(-2.97214 + 9.14729i) q^{37} +(7.66312 + 5.56758i) q^{39} +(2.97214 + 9.14729i) q^{41} -1.52786 q^{43} -0.236068 q^{45} +(-3.26393 - 10.0453i) q^{47} +(3.54508 + 2.57565i) q^{49} +(-0.927051 + 2.85317i) q^{51} +(-0.500000 + 0.363271i) q^{53} +(-6.35410 + 4.61653i) q^{57} +(-0.736068 + 2.26538i) q^{59} +(-1.50000 - 1.08981i) q^{61} +(0.190983 + 0.587785i) q^{63} +3.61803 q^{65} -14.4721 q^{67} +(2.00000 + 6.15537i) q^{69} +(4.11803 + 2.99193i) q^{71} +(0.972136 - 2.99193i) q^{73} +(-6.04508 + 4.39201i) q^{75} +(-3.11803 + 2.26538i) q^{79} +(-2.38197 + 7.33094i) q^{81} +(7.59017 + 5.51458i) q^{83} +(0.354102 + 1.08981i) q^{85} +11.8541 q^{87} -4.47214 q^{89} +(-2.92705 - 9.00854i) q^{91} +(1.42705 + 1.03681i) q^{93} +(-0.927051 + 2.85317i) q^{95} +(9.97214 - 7.24518i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 2 q^{5} - 2 q^{7} - q^{9} - 10 q^{13} + q^{15} - 6 q^{17} - 6 q^{19} + 6 q^{21} - 16 q^{23} + q^{25} - 11 q^{27} - 18 q^{29} - 8 q^{31} + q^{35} + 6 q^{37} + 15 q^{39} - 6 q^{41} - 24 q^{43}+ \cdots + 22 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^5 - 2 * q^7 - q^9 - 10 * q^13 + q^15 - 6 * q^17 - 6 * q^19 + 6 * q^21 - 16 * q^23 + q^25 - 11 * q^27 - 18 * q^29 - 8 * q^31 + q^35 + 6 * q^37 + 15 * q^39 - 6 * q^41 - 24 * q^43 + 8 * q^45 - 22 * q^47 + 3 * q^49 + 3 * q^51 - 2 * q^53 - 12 * q^57 + 6 * q^59 - 6 * q^61 + 3 * q^63 + 10 * q^65 - 40 * q^67 + 8 * q^69 + 12 * q^71 - 14 * q^73 - 13 * q^75 - 8 * q^79 - 14 * q^81 + 8 * q^83 - 12 * q^85 + 34 * q^87 - 5 * q^91 - q^93 + 3 * q^95 + 22 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	−0.500000	−	1.53884i	−0.288675	−	0.888451i	−0.985273	−	0.170989i	$-0.945304\pi$
$3$	−0.500000	−	1.53884i	−0.288675	−	0.888451i	0.696598	−	0.717462i	$-0.254696\pi$
$4$		0			0
$5$	−0.500000	−	0.363271i	−0.223607	−	0.162460i	0.470342	−	0.882484i	$-0.344131\pi$
$5$	−0.500000	−	0.363271i	−0.223607	−	0.162460i	−0.693949	+	0.720024i	$0.744131\pi$
$6$		0			0
$7$	−0.500000	+	1.53884i	−0.188982	+	0.581628i	−0.999994	−	0.00340203i	$-0.998917\pi$
$7$	−0.500000	+	1.53884i	−0.188982	+	0.581628i	0.811012	+	0.585030i	$0.198917\pi$
$8$		0			0
$9$	0.309017	−	0.224514i	0.103006	−	0.0748380i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	−4.73607	+	3.44095i	−1.31355	+	0.954349i	−0.313560	+	0.949568i	$0.601522\pi$
$13$	−4.73607	+	3.44095i	−1.31355	+	0.954349i	−0.999989	+	0.00478088i	$0.998478\pi$
$14$		0			0
$15$	−0.309017	+	0.951057i	−0.0797878	+	0.245562i
$16$		0			0
$17$	−1.50000	−	1.08981i	−0.363803	−	0.264319i	0.390833	−	0.920461i	$-0.372187\pi$
$17$	−1.50000	−	1.08981i	−0.363803	−	0.264319i	−0.754637	+	0.656143i	$0.772187\pi$
$18$		0			0
$19$	−1.50000	−	4.61653i	−0.344124	−	1.05910i	−0.962051	−	0.272869i	$-0.912028\pi$
$19$	−1.50000	−	4.61653i	−0.344124	−	1.05910i	0.617928	−	0.786235i	$-0.287972\pi$
$20$		0			0
$21$	2.61803			0.571302
$22$		0			0
$23$	−4.00000			−0.834058			−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000			−0.834058			−0.417029	+	0.908893i	$0.636929\pi$
$24$		0			0
$25$	−1.42705	−	4.39201i	−0.285410	−	0.878402i
$26$		0			0
$27$	−4.42705	−	3.21644i	−0.851986	−	0.619004i
$28$		0			0
$29$	−2.26393	+	6.96767i	−0.420402	+	1.29386i	0.486928	+	0.873442i	$0.338118\pi$
$29$	−2.26393	+	6.96767i	−0.420402	+	1.29386i	−0.907329	+	0.420421i	$0.861882\pi$
$30$		0			0
$31$	−0.881966	+	0.640786i	−0.158406	+	0.115089i	−0.664165	−	0.747586i	$-0.731213\pi$
$31$	−0.881966	+	0.640786i	−0.158406	+	0.115089i	0.505759	+	0.862675i	$0.331213\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.809017	−	0.587785i	0.136749	−	0.0993538i
$36$		0			0
$37$	−2.97214	+	9.14729i	−0.488616	+	1.50381i	0.338058	+	0.941125i	$0.390230\pi$
$37$	−2.97214	+	9.14729i	−0.488616	+	1.50381i	−0.826674	+	0.562681i	$0.809770\pi$
$38$		0			0
$39$	7.66312	+	5.56758i	1.22708	+	0.891527i
$40$		0			0
$41$	2.97214	+	9.14729i	0.464170	+	1.42857i	0.860024	+	0.510254i	$0.170449\pi$
$41$	2.97214	+	9.14729i	0.464170	+	1.42857i	−0.395854	+	0.918313i	$0.629551\pi$
$42$		0			0
$43$	−1.52786			−0.232997			−0.116499	−	0.993191i	$-0.537167\pi$
$43$	−1.52786			−0.232997			−0.116499	+	0.993191i	$0.537167\pi$
$44$		0			0
$45$	−0.236068			−0.0351909
$46$		0			0
$47$	−3.26393	−	10.0453i	−0.476093	−	1.46526i	−0.844477	−	0.535591i	$-0.820089\pi$
$47$	−3.26393	−	10.0453i	−0.476093	−	1.46526i	0.368384	−	0.929674i	$-0.379911\pi$
$48$		0			0
$49$	3.54508	+	2.57565i	0.506441	+	0.367951i
$50$		0			0
$51$	−0.927051	+	2.85317i	−0.129813	+	0.399524i
$52$		0			0
$53$	−0.500000	+	0.363271i	−0.0686803	+	0.0498991i	−0.621596	−	0.783338i	$-0.713515\pi$
$53$	−0.500000	+	0.363271i	−0.0686803	+	0.0498991i	0.552915	+	0.833237i	$0.313515\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−6.35410	+	4.61653i	−0.841621	+	0.611474i
$58$		0			0
$59$	−0.736068	+	2.26538i	−0.0958279	+	0.294928i	−0.987469	−	0.157816i	$-0.949555\pi$
$59$	−0.736068	+	2.26538i	−0.0958279	+	0.294928i	0.891641	+	0.452744i	$0.149555\pi$
$60$		0			0
$61$	−1.50000	−	1.08981i	−0.192055	−	0.139536i	0.487602	−	0.873066i	$-0.337872\pi$
$61$	−1.50000	−	1.08981i	−0.192055	−	0.139536i	−0.679658	+	0.733530i	$0.737872\pi$
$62$		0			0
$63$	0.190983	+	0.587785i	0.0240616	+	0.0740540i
$64$		0			0
$65$	3.61803			0.448762
$66$		0			0
$67$	−14.4721			−1.76805			−0.884026	−	0.467437i	$-0.845177\pi$
$67$	−14.4721			−1.76805			−0.884026	+	0.467437i	$0.845177\pi$
$68$		0			0
$69$	2.00000	+	6.15537i	0.240772	+	0.741019i
$70$		0			0
$71$	4.11803	+	2.99193i	0.488721	+	0.355076i	0.804692	−	0.593692i	$-0.202330\pi$
$71$	4.11803	+	2.99193i	0.488721	+	0.355076i	−0.315971	+	0.948769i	$0.602330\pi$
$72$		0			0
$73$	0.972136	−	2.99193i	0.113780	−	0.350179i	−0.877911	−	0.478824i	$-0.841063\pi$
$73$	0.972136	−	2.99193i	0.113780	−	0.350179i	0.991691	+	0.128646i	$0.0410631\pi$
$74$		0			0
$75$	−6.04508	+	4.39201i	−0.698026	+	0.507146i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−3.11803	+	2.26538i	−0.350806	+	0.254876i	−0.749207	−	0.662336i	$-0.769565\pi$
$79$	−3.11803	+	2.26538i	−0.350806	+	0.254876i	0.398401	+	0.917211i	$0.369565\pi$
$80$		0			0
$81$	−2.38197	+	7.33094i	−0.264663	+	0.814549i
$82$		0			0
$83$	7.59017	+	5.51458i	0.833129	+	0.605304i	0.920443	−	0.390877i	$-0.127828\pi$
$83$	7.59017	+	5.51458i	0.833129	+	0.605304i	−0.0873136	+	0.996181i	$0.527828\pi$
$84$		0			0
$85$	0.354102	+	1.08981i	0.0384078	+	0.118207i
$86$		0			0
$87$	11.8541			1.27089
$88$		0			0
$89$	−4.47214			−0.474045			−0.237023	−	0.971504i	$-0.576172\pi$
$89$	−4.47214			−0.474045			−0.237023	+	0.971504i	$0.576172\pi$
$90$		0			0
$91$	−2.92705	−	9.00854i	−0.306838	−	0.944351i
$92$		0			0
$93$	1.42705	+	1.03681i	0.147978	+	0.107513i
$94$		0			0
$95$	−0.927051	+	2.85317i	−0.0951134	+	0.292729i
$96$		0			0
$97$	9.97214	−	7.24518i	1.01252	−	0.735637i	0.0477815	−	0.998858i	$-0.484785\pi$
$97$	9.97214	−	7.24518i	1.01252	−	0.735637i	0.964736	+	0.263221i	$0.0847849\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.50000	−	1.81636i	0.248759	−	0.180734i	−0.456417	−	0.889766i	$-0.650868\pi$
$101$	2.50000	−	1.81636i	0.248759	−	0.180734i	0.705177	+	0.709032i	$0.250868\pi$
$102$		0			0
$103$	3.73607	−	11.4984i	0.368126	−	1.13297i	−0.579875	−	0.814706i	$-0.696899\pi$
$103$	3.73607	−	11.4984i	0.368126	−	1.13297i	0.948000	−	0.318269i	$-0.103101\pi$
$104$		0			0
$105$	−1.30902	−	0.951057i	−0.127747	−	0.0928136i
$106$		0			0
$107$	−1.20820	−	3.71847i	−0.116801	−	0.359478i	0.875517	−	0.483187i	$-0.160521\pi$
$107$	−1.20820	−	3.71847i	−0.116801	−	0.359478i	−0.992319	+	0.123709i	$0.960521\pi$
$108$		0			0
$109$	−14.9443			−1.43140			−0.715701	−	0.698407i	$-0.753893\pi$
$109$	−14.9443			−1.43140			−0.715701	+	0.698407i	$0.753893\pi$
$110$		0			0
$111$	15.5623			1.47711
$112$		0			0
$113$	2.73607	+	8.42075i	0.257388	+	0.792158i	0.993350	+	0.115135i	$0.0367301\pi$
$113$	2.73607	+	8.42075i	0.257388	+	0.792158i	−0.735962	+	0.677023i	$0.763270\pi$
$114$		0			0
$115$	2.00000	+	1.45309i	0.186501	+	0.135501i
$116$		0			0
$117$	−0.690983	+	2.12663i	−0.0638814	+	0.196607i
$118$		0			0
$119$	2.42705	−	1.76336i	0.222487	−	0.161647i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	12.5902	−	9.14729i	1.13522	−	0.824784i
$124$		0			0
$125$	−1.83688	+	5.65334i	−0.164296	+	0.505650i
$126$		0			0
$127$	−4.59017	−	3.33495i	−0.407312	−	0.295929i	0.365201	−	0.930929i	$-0.381000\pi$
$127$	−4.59017	−	3.33495i	−0.407312	−	0.295929i	−0.772513	+	0.634999i	$0.781000\pi$
$128$		0			0
$129$	0.763932	+	2.35114i	0.0672605	+	0.207006i
$130$		0			0
$131$	−8.00000			−0.698963			−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000			−0.698963			−0.349482	+	0.936943i	$0.613642\pi$
$132$		0			0
$133$	7.85410			0.681037
$134$		0			0
$135$	1.04508	+	3.21644i	0.0899466	+	0.276827i
$136$		0			0
$137$	−14.2082	−	10.3229i	−1.21389	−	0.881942i	−0.218311	−	0.975879i	$-0.570055\pi$
$137$	−14.2082	−	10.3229i	−1.21389	−	0.881942i	−0.995578	+	0.0939375i	$0.970055\pi$
$138$		0			0
$139$	5.02786	−	15.4742i	0.426458	−	1.31250i	−0.475134	−	0.879914i	$-0.657600\pi$
$139$	5.02786	−	15.4742i	0.426458	−	1.31250i	0.901591	−	0.432589i	$-0.142400\pi$
$140$		0			0
$141$	−13.8262	+	10.0453i	−1.16438	+	0.845971i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	3.66312	−	2.66141i	0.304205	−	0.221018i
$146$		0			0
$147$	2.19098	−	6.74315i	0.180709	−	0.556166i
$148$		0			0
$149$	−14.4443	−	10.4944i	−1.18332	−	0.859733i	−0.190778	−	0.981633i	$-0.561101\pi$
$149$	−14.4443	−	10.4944i	−1.18332	−	0.859733i	−0.992542	+	0.121900i	$0.961101\pi$
$150$		0			0
$151$	−2.26393	−	6.96767i	−0.184236	−	0.567021i	0.815698	−	0.578478i	$-0.196353\pi$
$151$	−2.26393	−	6.96767i	−0.184236	−	0.567021i	−0.999934	+	0.0114571i	$0.996353\pi$
$152$		0			0
$153$	−0.708204			−0.0572549
$154$		0			0
$155$	0.673762			0.0541179
$156$		0			0
$157$	−0.208204	−	0.640786i	−0.0166165	−	0.0511403i	0.942404	−	0.334475i	$-0.108559\pi$
$157$	−0.208204	−	0.640786i	−0.0166165	−	0.0511403i	−0.959021	+	0.283335i	$0.908559\pi$
$158$		0			0
$159$	0.809017	+	0.587785i	0.0641592	+	0.0466144i
$160$		0			0
$161$	2.00000	−	6.15537i	0.157622	−	0.485111i
$162$		0			0
$163$	7.11803	−	5.17155i	0.557527	−	0.405067i	−0.273026	−	0.962007i	$-0.588024\pi$
$163$	7.11803	−	5.17155i	0.557527	−	0.405067i	0.830553	+	0.556939i	$0.188024\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−11.5902	+	8.42075i	−0.896874	+	0.651617i	−0.937661	−	0.347551i	$-0.887014\pi$
$167$	−11.5902	+	8.42075i	−0.896874	+	0.651617i	0.0407870	+	0.999168i	$0.487014\pi$
$168$		0			0
$169$	6.57295	−	20.2295i	0.505611	−	1.55611i
$170$		0			0
$171$	−1.50000	−	1.08981i	−0.114708	−	0.0833401i
$172$		0			0
$173$	−2.73607	−	8.42075i	−0.208019	−	0.640218i	−0.999576	−	0.0291218i	$-0.990729\pi$
$173$	−2.73607	−	8.42075i	−0.208019	−	0.640218i	0.791556	−	0.611096i	$-0.209271\pi$
$174$		0			0
$175$	7.47214			0.564840
$176$		0			0
$177$	3.85410			0.289692
$178$		0			0
$179$	7.50000	+	23.0826i	0.560576	+	1.72528i	0.680743	+	0.732523i	$0.261657\pi$
$179$	7.50000	+	23.0826i	0.560576	+	1.72528i	−0.120166	+	0.992754i	$0.538343\pi$
$180$		0			0
$181$	7.50000	+	5.44907i	0.557471	+	0.405026i	0.830532	−	0.556970i	$-0.188036\pi$
$181$	7.50000	+	5.44907i	0.557471	+	0.405026i	−0.273062	+	0.961997i	$0.588036\pi$
$182$		0			0
$183$	−0.927051	+	2.85317i	−0.0685296	+	0.210912i
$184$		0			0
$185$	4.80902	−	3.49396i	0.353566	−	0.256881i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	7.16312	−	5.20431i	0.521040	−	0.378558i
$190$		0			0
$191$	4.68034	−	14.4046i	0.338658	−	1.04228i	−0.626235	−	0.779635i	$-0.715405\pi$
$191$	4.68034	−	14.4046i	0.338658	−	1.04228i	0.964892	−	0.262646i	$-0.0845952\pi$
$192$		0			0
$193$	−5.97214	−	4.33901i	−0.429884	−	0.312329i	0.351719	−	0.936106i	$-0.385597\pi$
$193$	−5.97214	−	4.33901i	−0.429884	−	0.312329i	−0.781602	+	0.623777i	$0.785597\pi$
$194$		0			0
$195$	−1.80902	−	5.56758i	−0.129546	−	0.398703i
$196$		0			0
$197$	−0.472136			−0.0336383			−0.0168191	−	0.999859i	$-0.505354\pi$
$197$	−0.472136			−0.0336383			−0.0168191	+	0.999859i	$0.505354\pi$
$198$		0			0
$199$	20.3607			1.44333			0.721665	−	0.692242i	$-0.243377\pi$
$199$	20.3607			1.44333			0.721665	+	0.692242i	$0.243377\pi$
$200$		0			0
$201$	7.23607	+	22.2703i	0.510393	+	1.57083i
$202$		0			0
$203$	−9.59017	−	6.96767i	−0.673098	−	0.489034i
$204$		0			0
$205$	1.83688	−	5.65334i	0.128293	−	0.394846i
$206$		0			0
$207$	−1.23607	+	0.898056i	−0.0859127	+	0.0624192i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	10.5902	−	7.69421i	0.729057	−	0.529691i	−0.160208	−	0.987083i	$-0.551216\pi$
$211$	10.5902	−	7.69421i	0.729057	−	0.529691i	0.889265	+	0.457392i	$0.151216\pi$
$212$		0			0
$213$	2.54508	−	7.83297i	0.174386	−	0.536706i
$214$		0			0
$215$	0.763932	+	0.555029i	0.0520997	+	0.0378527i
$216$		0			0
$217$	−0.545085	−	1.67760i	−0.0370028	−	0.113883i
$218$		0			0
$219$	−5.09017			−0.343962
$220$		0			0
$221$	10.8541			0.730126
$222$		0			0
$223$	−2.97214	−	9.14729i	−0.199029	−	0.612548i	−0.999906	−	0.0137191i	$-0.995633\pi$
$223$	−2.97214	−	9.14729i	−0.199029	−	0.612548i	0.800877	−	0.598829i	$-0.204367\pi$
$224$		0			0
$225$	−1.42705	−	1.03681i	−0.0951367	−	0.0691209i
$226$		0			0
$227$	−2.20820	+	6.79615i	−0.146564	+	0.451077i	−0.997209	−	0.0746638i	$-0.976212\pi$
$227$	−2.20820	+	6.79615i	−0.146564	+	0.451077i	0.850645	+	0.525740i	$0.176212\pi$
$228$		0			0
$229$	13.2082	−	9.59632i	0.872823	−	0.634143i	−0.0585202	−	0.998286i	$-0.518638\pi$
$229$	13.2082	−	9.59632i	0.872823	−	0.634143i	0.931343	+	0.364143i	$0.118638\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	12.9721	−	9.42481i	0.849833	−	0.617440i	−0.0752671	−	0.997163i	$-0.523981\pi$
$233$	12.9721	−	9.42481i	0.849833	−	0.617440i	0.925100	+	0.379724i	$0.123981\pi$
$234$		0			0
$235$	−2.01722	+	6.20837i	−0.131589	+	0.404989i
$236$		0			0
$237$	5.04508	+	3.66547i	0.327713	+	0.238098i
$238$		0			0
$239$	7.26393	+	22.3561i	0.469865	+	1.44609i	0.852760	+	0.522303i	$0.174927\pi$
$239$	7.26393	+	22.3561i	0.469865	+	1.44609i	−0.382895	+	0.923792i	$0.625073\pi$
$240$		0			0
$241$	−1.05573			−0.0680054			−0.0340027	−	0.999422i	$-0.510825\pi$
$241$	−1.05573			−0.0680054			−0.0340027	+	0.999422i	$0.510825\pi$
$242$		0			0
$243$	−3.94427			−0.253025
$244$		0			0
$245$	−0.836881	−	2.57565i	−0.0534664	−	0.164553i
$246$		0			0
$247$	22.9894	+	16.7027i	1.46278	+	1.06277i
$248$		0			0
$249$	4.69098	−	14.4374i	0.297279	−	0.914931i
$250$		0			0
$251$	−8.59017	+	6.24112i	−0.542207	+	0.393936i	−0.824904	−	0.565273i	$-0.808771\pi$
$251$	−8.59017	+	6.24112i	−0.542207	+	0.393936i	0.282697	+	0.959209i	$0.408771\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	1.50000	−	1.08981i	0.0939336	−	0.0682468i
$256$		0			0
$257$	−0.791796	+	2.43690i	−0.0493909	+	0.152010i	−0.972710	−	0.232024i	$-0.925465\pi$
$257$	−0.791796	+	2.43690i	−0.0493909	+	0.152010i	0.923319	+	0.384033i	$0.125465\pi$
$258$		0			0
$259$	−12.5902	−	9.14729i	−0.782315	−	0.568385i
$260$		0			0
$261$	0.864745	+	2.66141i	0.0535264	+	0.164737i
$262$		0			0
$263$	−7.41641			−0.457315			−0.228658	−	0.973507i	$-0.573434\pi$
$263$	−7.41641			−0.457315			−0.228658	+	0.973507i	$0.573434\pi$
$264$		0			0
$265$	0.381966			0.0234640
$266$		0			0
$267$	2.23607	+	6.88191i	0.136845	+	0.421166i
$268$		0			0
$269$	0.736068	+	0.534785i	0.0448789	+	0.0326064i	0.609999	−	0.792403i	$-0.291170\pi$
$269$	0.736068	+	0.534785i	0.0448789	+	0.0326064i	−0.565120	+	0.825009i	$0.691170\pi$
$270$		0			0
$271$	8.15248	−	25.0907i	0.495228	−	1.52415i	−0.321374	−	0.946952i	$-0.604145\pi$
$271$	8.15248	−	25.0907i	0.495228	−	1.52415i	0.816602	−	0.577202i	$-0.195855\pi$
$272$		0			0
$273$	−12.3992	+	9.00854i	−0.750433	+	0.545221i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−2.73607	+	1.98787i	−0.164394	+	0.119440i	−0.666941	−	0.745111i	$-0.732397\pi$
$277$	−2.73607	+	1.98787i	−0.164394	+	0.119440i	0.502546	+	0.864550i	$0.332397\pi$
$278$		0			0
$279$	−0.128677	+	0.396027i	−0.00770370	+	0.0237095i
$280$		0			0
$281$	10.9721	+	7.97172i	0.654543	+	0.475553i	0.864816	−	0.502090i	$-0.167435\pi$
$281$	10.9721	+	7.97172i	0.654543	+	0.475553i	−0.210273	+	0.977643i	$0.567435\pi$
$282$		0			0
$283$	−4.26393	−	13.1230i	−0.253464	−	0.780083i	−0.994128	−	0.108208i	$-0.965489\pi$
$283$	−4.26393	−	13.1230i	−0.253464	−	0.780083i	0.740664	−	0.671876i	$-0.234511\pi$
$284$		0			0
$285$	4.85410			0.287532
$286$		0			0
$287$	−15.5623			−0.918614
$288$		0			0
$289$	−4.19098	−	12.8985i	−0.246528	−	0.758736i
$290$		0			0
$291$	−16.1353	−	11.7229i	−0.945865	−	0.687211i
$292$		0			0
$293$	3.26393	−	10.0453i	0.190681	−	0.586856i	−0.809319	−	0.587369i	$-0.800164\pi$
$293$	3.26393	−	10.0453i	0.190681	−	0.586856i	1.00000		0.000513854i	$0.000163565\pi$
$294$		0			0
$295$	1.19098	−	0.865300i	0.0693417	−	0.0503797i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	18.9443	−	13.7638i	1.09558	−	0.795982i
$300$		0			0
$301$	0.763932	−	2.35114i	0.0440323	−	0.135518i
$302$		0			0
$303$	−4.04508	−	2.93893i	−0.232384	−	0.168837i
$304$		0			0
$305$	0.354102	+	1.08981i	0.0202758	+	0.0624026i
$306$		0			0
$307$	−33.8885			−1.93412			−0.967061	−	0.254546i	$-0.918074\pi$
$307$	−33.8885			−1.93412			−0.967061	+	0.254546i	$0.918074\pi$
$308$		0			0
$309$	−19.5623			−1.11286
$310$		0			0
$311$	9.97214	+	30.6911i	0.565468	+	1.74033i	0.666557	+	0.745454i	$0.267767\pi$
$311$	9.97214	+	30.6911i	0.565468	+	1.74033i	−0.101089	+	0.994877i	$0.532233\pi$
$312$		0			0
$313$	22.4443	+	16.3067i	1.26863	+	0.921710i	0.999147	−	0.0412963i	$-0.0131487\pi$
$313$	22.4443	+	16.3067i	1.26863	+	0.921710i	0.269478	+	0.963006i	$0.413149\pi$
$314$		0			0
$315$	0.118034	−	0.363271i	0.00665046	−	0.0204680i
$316$		0			0
$317$	0.263932	−	0.191758i	0.0148239	−	0.0107702i	−0.580349	−	0.814368i	$-0.697084\pi$
$317$	0.263932	−	0.191758i	0.0148239	−	0.0107702i	0.595173	+	0.803598i	$0.297084\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−5.11803	+	3.71847i	−0.285661	+	0.207545i
$322$		0			0
$323$	−2.78115	+	8.55951i	−0.154747	+	0.476264i
$324$		0			0
$325$	21.8713	+	15.8904i	1.21320	+	0.881443i
$326$		0			0
$327$	7.47214	+	22.9969i	0.413210	+	1.27173i
$328$		0			0
$329$	17.0902			0.942212
$330$		0			0
$331$	−8.94427			−0.491622			−0.245811	−	0.969318i	$-0.579054\pi$
$331$	−8.94427			−0.491622			−0.245811	+	0.969318i	$0.579054\pi$
$332$		0			0
$333$	1.13525	+	3.49396i	0.0622116	+	0.191468i
$334$		0			0
$335$	7.23607	+	5.25731i	0.395349	+	0.287238i
$336$		0			0
$337$	−8.15248	+	25.0907i	−0.444094	+	1.36678i	0.439381	+	0.898301i	$0.355198\pi$
$337$	−8.15248	+	25.0907i	−0.444094	+	1.36678i	−0.883475	+	0.468479i	$0.844802\pi$
$338$		0			0
$339$	11.5902	−	8.42075i	0.629492	−	0.457352i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−14.8992	+	10.8249i	−0.804480	+	0.584489i
$344$		0			0
$345$	1.23607	−	3.80423i	0.0665477	−	0.204813i
$346$		0			0
$347$	−6.88197	−	5.00004i	−0.369443	−	0.268416i	0.387537	−	0.921854i	$-0.373326\pi$
$347$	−6.88197	−	5.00004i	−0.369443	−	0.268416i	−0.756980	+	0.653438i	$0.773326\pi$
$348$		0			0
$349$	−6.26393	−	19.2784i	−0.335301	−	1.03195i	−0.966574	−	0.256389i	$-0.917467\pi$
$349$	−6.26393	−	19.2784i	−0.335301	−	1.03195i	0.631273	−	0.775561i	$-0.282533\pi$
$350$		0			0
$351$	32.0344			1.70987
$352$		0			0
$353$	1.41641			0.0753878			0.0376939	−	0.999289i	$-0.487999\pi$
$353$	1.41641			0.0753878			0.0376939	+	0.999289i	$0.487999\pi$
$354$		0			0
$355$	−0.972136	−	2.99193i	−0.0515956	−	0.158795i
$356$		0			0
$357$	−3.92705	−	2.85317i	−0.207842	−	0.151006i
$358$		0			0
$359$	−4.79180	+	14.7476i	−0.252901	+	0.778350i	0.741335	+	0.671136i	$0.234193\pi$
$359$	−4.79180	+	14.7476i	−0.252901	+	0.778350i	−0.994236	+	0.107215i	$0.965807\pi$
$360$		0			0
$361$	−3.69098	+	2.68166i	−0.194262	+	0.141140i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.57295	+	1.14281i	−0.0823319	+	0.0598176i
$366$		0			0
$367$	−8.44427	+	25.9888i	−0.440787	+	1.35660i	0.446251	+	0.894908i	$0.352759\pi$
$367$	−8.44427	+	25.9888i	−0.440787	+	1.35660i	−0.887038	+	0.461696i	$0.847241\pi$
$368$		0			0
$369$	2.97214	+	2.15938i	0.154723	+	0.112413i
$370$		0			0
$371$	−0.309017	−	0.951057i	−0.0160434	−	0.0493764i
$372$		0			0
$373$	5.41641			0.280451			0.140225	−	0.990120i	$-0.455217\pi$
$373$	5.41641			0.280451			0.140225	+	0.990120i	$0.455217\pi$
$374$		0			0
$375$	9.61803			0.496673
$376$		0			0
$377$	−13.2533	−	40.7894i	−0.682579	−	2.10076i
$378$		0			0
$379$	−15.5902	−	11.3269i	−0.800813	−	0.581825i	0.110339	−	0.993894i	$-0.464806\pi$
$379$	−15.5902	−	11.3269i	−0.800813	−	0.581825i	−0.911153	+	0.412069i	$0.864806\pi$
$380$		0			0
$381$	−2.83688	+	8.73102i	−0.145338	+	0.447304i
$382$		0			0
$383$	1.59017	−	1.15533i	0.0812539	−	0.0590344i	−0.546417	−	0.837513i	$-0.684008\pi$
$383$	1.59017	−	1.15533i	0.0812539	−	0.0590344i	0.627671	+	0.778479i	$0.284008\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.472136	+	0.343027i	−0.0240000	+	0.0174370i
$388$		0			0
$389$	8.26393	−	25.4338i	0.418998	−	1.28954i	−0.489628	−	0.871932i	$-0.662867\pi$
$389$	8.26393	−	25.4338i	0.418998	−	1.28954i	0.908626	−	0.417612i	$-0.137133\pi$
$390$		0			0
$391$	6.00000	+	4.35926i	0.303433	+	0.220457i
$392$		0			0
$393$	4.00000	+	12.3107i	0.201773	+	0.620994i
$394$		0			0
$395$	2.38197			0.119850
$396$		0			0
$397$	−2.58359			−0.129667			−0.0648334	−	0.997896i	$-0.520652\pi$
$397$	−2.58359			−0.129667			−0.0648334	+	0.997896i	$0.520652\pi$
$398$		0			0
$399$	−3.92705	−	12.0862i	−0.196598	−	0.605068i
$400$		0			0
$401$	−5.73607	−	4.16750i	−0.286446	−	0.208115i	0.435278	−	0.900296i	$-0.356650\pi$
$401$	−5.73607	−	4.16750i	−0.286446	−	0.208115i	−0.721724	+	0.692181i	$0.756650\pi$
$402$		0			0
$403$	1.97214	−	6.06961i	0.0982391	−	0.302349i
$404$		0			0
$405$	3.85410	−	2.80017i	0.191512	−	0.139142i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	1.26393	−	0.918300i	0.0624974	−	0.0454070i	−0.556098	−	0.831117i	$-0.687702\pi$
$409$	1.26393	−	0.918300i	0.0624974	−	0.0454070i	0.618595	+	0.785710i	$0.287702\pi$
$410$		0			0
$411$	−8.78115	+	27.0256i	−0.433142	+	1.33308i
$412$		0			0
$413$	−3.11803	−	2.26538i	−0.153428	−	0.111472i
$414$		0			0
$415$	−1.79180	−	5.51458i	−0.0879558	−	0.270700i
$416$		0			0
$417$	−26.3262			−1.28920
$418$		0			0
$419$	3.05573			0.149282			0.0746410	−	0.997210i	$-0.476219\pi$
$419$	3.05573			0.149282			0.0746410	+	0.997210i	$0.476219\pi$
$420$		0			0
$421$	−2.50000	−	7.69421i	−0.121843	−	0.374993i	0.871470	−	0.490449i	$-0.163167\pi$
$421$	−2.50000	−	7.69421i	−0.121843	−	0.374993i	−0.993313	+	0.115456i	$0.963167\pi$
$422$		0			0
$423$	−3.26393	−	2.37139i	−0.158698	−	0.115301i
$424$		0			0
$425$	−2.64590	+	8.14324i	−0.128345	+	0.395005i
$426$		0			0
$427$	2.42705	−	1.76336i	0.117453	−	0.0853348i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−26.8262	+	19.4904i	−1.29217	+	0.938820i	−0.999847	−	0.0174986i	$-0.994430\pi$
$431$	−26.8262	+	19.4904i	−1.29217	+	0.938820i	−0.292328	+	0.956318i	$0.594430\pi$
$432$		0			0
$433$	−0.680340	+	2.09387i	−0.0326950	+	0.100625i	−0.966072	−	0.258272i	$-0.916847\pi$
$433$	−0.680340	+	2.09387i	−0.0326950	+	0.100625i	0.933377	+	0.358897i	$0.116847\pi$
$434$		0			0
$435$	−5.92705	−	4.30625i	−0.284180	−	0.206469i
$436$		0			0
$437$	6.00000	+	18.4661i	0.287019	+	0.883353i
$438$		0			0
$439$	0.944272			0.0450676			0.0225338	−	0.999746i	$-0.492827\pi$
$439$	0.944272			0.0450676			0.0225338	+	0.999746i	$0.492827\pi$
$440$		0			0
$441$	1.67376			0.0797030
$442$		0			0
$443$	1.79180	+	5.51458i	0.0851308	+	0.262006i	0.984556	−	0.175069i	$-0.0560147\pi$
$443$	1.79180	+	5.51458i	0.0851308	+	0.262006i	−0.899425	+	0.437074i	$0.856015\pi$
$444$		0			0
$445$	2.23607	+	1.62460i	0.106000	+	0.0770134i
$446$		0			0
$447$	−8.92705	+	27.4746i	−0.422235	+	1.29951i
$448$		0			0
$449$	−31.9164	+	23.1886i	−1.50623	+	1.09434i	−0.538412	+	0.842682i	$0.680976\pi$
$449$	−31.9164	+	23.1886i	−1.50623	+	1.09434i	−0.967816	+	0.251657i	$0.919024\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−9.59017	+	6.96767i	−0.450585	+	0.327370i
$454$		0			0
$455$	−1.80902	+	5.56758i	−0.0848080	+	0.261012i
$456$		0			0
$457$	7.73607	+	5.62058i	0.361878	+	0.262920i	0.753835	−	0.657064i	$-0.228202\pi$
$457$	7.73607	+	5.62058i	0.361878	+	0.262920i	−0.391957	+	0.919984i	$0.628202\pi$
$458$		0			0
$459$	3.13525	+	9.64932i	0.146341	+	0.450392i
$460$		0			0
$461$	30.3607			1.41404			0.707019	−	0.707195i	$-0.250040\pi$
$461$	30.3607			1.41404			0.707019	+	0.707195i	$0.250040\pi$
$462$		0			0
$463$	15.4164			0.716461			0.358231	−	0.933633i	$-0.383380\pi$
$463$	15.4164			0.716461			0.358231	+	0.933633i	$0.383380\pi$
$464$		0			0
$465$	−0.336881	−	1.03681i	−0.0156225	−	0.0480811i
$466$		0			0
$467$	2.59017	+	1.88187i	0.119859	+	0.0870825i	0.646100	−	0.763253i	$-0.276399\pi$
$467$	2.59017	+	1.88187i	0.119859	+	0.0870825i	−0.526241	+	0.850335i	$0.676399\pi$
$468$		0			0
$469$	7.23607	−	22.2703i	0.334131	−	1.02835i
$470$		0			0
$471$	−0.881966	+	0.640786i	−0.0406388	+	0.0295259i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−18.1353	+	13.1760i	−0.832103	+	0.604558i
$476$		0			0
$477$	−0.0729490	+	0.224514i	−0.00334011	+	0.0102798i
$478$		0			0
$479$	−18.5902	−	13.5065i	−0.849407	−	0.617130i	0.0755758	−	0.997140i	$-0.475921\pi$
$479$	−18.5902	−	13.5065i	−0.849407	−	0.617130i	−0.924982	+	0.380010i	$0.875921\pi$
$480$		0			0
$481$	−17.3992	−	53.5492i	−0.793335	−	2.44163i
$482$		0			0
$483$	−10.4721			−0.476499
$484$		0			0
$485$	−7.61803			−0.345917
$486$		0			0
$487$	−10.2082	−	31.4176i	−0.462578	−	1.42367i	−0.862003	−	0.506903i	$-0.830790\pi$
$487$	−10.2082	−	31.4176i	−0.462578	−	1.42367i	0.399425	−	0.916766i	$-0.369210\pi$
$488$		0			0
$489$	−11.5172	−	8.36775i	−0.520827	−	0.378403i
$490$		0			0
$491$	−6.02786	+	18.5519i	−0.272034	+	0.837234i	0.717955	+	0.696089i	$0.245078\pi$
$491$	−6.02786	+	18.5519i	−0.272034	+	0.837234i	−0.989989	+	0.141144i	$0.954922\pi$
$492$		0			0
$493$	10.9894	−	7.98424i	0.494936	−	0.359592i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.66312	+	4.84104i	−0.298882	+	0.217150i
$498$		0			0
$499$	−3.68034	+	11.3269i	−0.164755	+	0.507063i	−0.999018	−	0.0443033i	$-0.985893\pi$
$499$	−3.68034	+	11.3269i	−0.164755	+	0.507063i	0.834263	+	0.551366i	$0.185893\pi$
$500$		0			0
$501$	18.7533	+	13.6251i	0.837835	+	0.608723i
$502$		0			0
$503$	2.50000	+	7.69421i	0.111469	+	0.343068i	0.991194	−	0.132415i	$-0.0422733\pi$
$503$	2.50000	+	7.69421i	0.111469	+	0.343068i	−0.879725	+	0.475483i	$0.842273\pi$
$504$		0			0
$505$	−1.90983			−0.0849863
$506$		0			0
$507$	−34.4164			−1.52849
$508$		0			0
$509$	−6.02786	−	18.5519i	−0.267180	−	0.822297i	−0.991183	−	0.132500i	$-0.957700\pi$
$509$	−6.02786	−	18.5519i	−0.267180	−	0.822297i	0.724003	−	0.689797i	$-0.242300\pi$
$510$		0			0
$511$	4.11803	+	2.99193i	0.182171	+	0.132355i
$512$		0			0
$513$	−8.20820	+	25.2623i	−0.362401	+	1.11536i
$514$		0			0
$515$	−6.04508	+	4.39201i	−0.266378	+	0.193535i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−11.5902	+	8.42075i	−0.508752	+	0.369630i
$520$		0			0
$521$	−7.73607	+	23.8092i	−0.338923	+	1.04310i	0.625834	+	0.779956i	$0.284759\pi$
$521$	−7.73607	+	23.8092i	−0.338923	+	1.04310i	−0.964757	+	0.263142i	$0.915241\pi$
$522$		0			0
$523$	−10.1180	−	7.35118i	−0.442431	−	0.321445i	0.344169	−	0.938908i	$-0.388161\pi$
$523$	−10.1180	−	7.35118i	−0.442431	−	0.321445i	−0.786600	+	0.617463i	$0.788161\pi$
$524$		0			0
$525$	−3.73607	−	11.4984i	−0.163055	−	0.501833i
$526$		0			0
$527$	2.02129			0.0880486
$528$		0			0
$529$	−7.00000			−0.304348
$530$		0			0
$531$	0.281153	+	0.865300i	0.0122010	+	0.0375508i
$532$		0			0
$533$	−45.5517	−	33.0952i	−1.97306	−	1.43351i
$534$		0			0
$535$	−0.746711	+	2.29814i	−0.0322831	+	0.0993573i
$536$		0			0
$537$	31.7705	−	23.0826i	1.37100	−	0.996089i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	2.20820	−	1.60435i	0.0949381	−	0.0689766i	−0.539304	−	0.842111i	$-0.681312\pi$
$541$	2.20820	−	1.60435i	0.0949381	−	0.0689766i	0.634242	+	0.773135i	$0.281312\pi$
$542$		0			0
$543$	4.63525	−	14.2658i	0.198918	−	0.612206i
$544$		0			0
$545$	7.47214	+	5.42882i	0.320071	+	0.232545i
$546$		0			0
$547$	3.15248	+	9.70232i	0.134790	+	0.414841i	0.995557	−	0.0941575i	$-0.0300157\pi$
$547$	3.15248	+	9.70232i	0.134790	+	0.414841i	−0.860767	+	0.508999i	$0.830016\pi$
$548$		0			0
$549$	−0.708204			−0.0302254
$550$		0			0
$551$	35.5623			1.51501
$552$		0			0
$553$	−1.92705	−	5.93085i	−0.0819465	−	0.252206i
$554$		0			0
$555$	−7.78115	−	5.65334i	−0.330292	−	0.239971i
$556$		0			0
$557$	−10.1525	+	31.2461i	−0.430174	+	1.32394i	0.467778	+	0.883846i	$0.345055\pi$
$557$	−10.1525	+	31.2461i	−0.430174	+	1.32394i	−0.897952	+	0.440094i	$0.854945\pi$
$558$		0			0
$559$	7.23607	−	5.25731i	0.306053	−	0.222361i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	12.5902	−	9.14729i	0.530612	−	0.385512i	−0.289974	−	0.957034i	$-0.593647\pi$
$563$	12.5902	−	9.14729i	0.530612	−	0.385512i	0.820587	+	0.571522i	$0.193647\pi$
$564$		0			0
$565$	1.69098	−	5.20431i	0.0711402	−	0.218947i
$566$		0			0
$567$	−10.0902	−	7.33094i	−0.423747	−	0.307870i
$568$		0			0
$569$	−7.97214	−	24.5357i	−0.334209	−	1.02859i	−0.967110	−	0.254358i	$-0.918136\pi$
$569$	−7.97214	−	24.5357i	−0.334209	−	1.02859i	0.632901	−	0.774233i	$-0.281864\pi$
$570$		0			0
$571$	30.8328			1.29031			0.645157	−	0.764050i	$-0.276792\pi$
$571$	30.8328			1.29031			0.645157	+	0.764050i	$0.276792\pi$
$572$		0			0
$573$	−24.5066			−1.02378
$574$		0			0
$575$	5.70820	+	17.5680i	0.238049	+	0.732638i
$576$		0			0
$577$	15.6803	+	11.3924i	0.652781	+	0.474273i	0.864217	−	0.503119i	$-0.167814\pi$
$577$	15.6803	+	11.3924i	0.652781	+	0.474273i	−0.211436	+	0.977392i	$0.567814\pi$
$578$		0			0
$579$	−3.69098	+	11.3597i	−0.153392	+	0.472092i
$580$		0			0
$581$	−12.2812	+	8.92278i	−0.509508	+	0.370179i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	1.11803	−	0.812299i	0.0462250	−	0.0335844i
$586$		0			0
$587$	0.0278640	−	0.0857567i	0.00115007	−	0.00353956i	−0.950480	−	0.310786i	$-0.899408\pi$
$587$	0.0278640	−	0.0857567i	0.00115007	−	0.00353956i	0.951630	+	0.307247i	$0.0994077\pi$
$588$		0			0
$589$	4.28115	+	3.11044i	0.176402	+	0.128163i
$590$		0			0
$591$	0.236068	+	0.726543i	0.00971054	+	0.0298860i
$592$		0			0
$593$	−0.472136			−0.0193883			−0.00969415	−	0.999953i	$-0.503086\pi$
$593$	−0.472136			−0.0193883			−0.00969415	+	0.999953i	$0.503086\pi$
$594$		0			0
$595$	−1.85410			−0.0760108
$596$		0			0
$597$	−10.1803	−	31.3319i	−0.416654	−	1.28233i
$598$		0			0
$599$	20.2984	+	14.7476i	0.829369	+	0.602572i	0.919381	−	0.393369i	$-0.128690\pi$
$599$	20.2984	+	14.7476i	0.829369	+	0.602572i	−0.0900117	+	0.995941i	$0.528690\pi$
$600$		0			0
$601$	9.62461	−	29.6215i	0.392596	−	1.20829i	−0.538222	−	0.842803i	$-0.680904\pi$
$601$	9.62461	−	29.6215i	0.392596	−	1.20829i	0.930818	−	0.365483i	$-0.119096\pi$
$602$		0			0
$603$	−4.47214	+	3.24920i	−0.182119	+	0.132318i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−23.7705	+	17.2703i	−0.964815	+	0.700979i	−0.954264	−	0.298965i	$-0.903359\pi$
$607$	−23.7705	+	17.2703i	−0.964815	+	0.700979i	−0.0105512	+	0.999944i	$0.503359\pi$
$608$		0			0
$609$	−5.92705	+	18.2416i	−0.240176	+	0.739186i
$610$		0			0
$611$	50.0238	+	36.3444i	2.02375	+	1.47034i
$612$		0			0
$613$	12.9721	+	39.9241i	0.523940	+	1.61252i	0.766403	+	0.642360i	$0.222045\pi$
$613$	12.9721	+	39.9241i	0.523940	+	1.61252i	−0.242464	+	0.970161i	$0.577955\pi$
$614$		0			0
$615$	−9.61803			−0.387837
$616$		0			0
$617$	−25.4164			−1.02323			−0.511613	−	0.859216i	$-0.670952\pi$
$617$	−25.4164			−1.02323			−0.511613	+	0.859216i	$0.670952\pi$
$618$		0			0
$619$	−2.20820	−	6.79615i	−0.0887552	−	0.273160i	0.896821	−	0.442394i	$-0.145871\pi$
$619$	−2.20820	−	6.79615i	−0.0887552	−	0.273160i	−0.985576	+	0.169234i	$0.945871\pi$
$620$		0			0
$621$	17.7082	+	12.8658i	0.710606	+	0.516285i
$622$		0			0
$623$	2.23607	−	6.88191i	0.0895862	−	0.275718i
$624$		0			0
$625$	−15.7082	+	11.4127i	−0.628328	+	0.456507i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	14.4271	−	10.4819i	0.575244	−	0.417939i
$630$		0			0
$631$	3.73607	−	11.4984i	0.148731	−	0.457745i	−0.848741	−	0.528808i	$-0.822639\pi$
$631$	3.73607	−	11.4984i	0.148731	−	0.457745i	0.997472	+	0.0710628i	$0.0226391\pi$
$632$		0			0
$633$	−17.1353	−	12.4495i	−0.681065	−	0.494823i
$634$		0			0
$635$	1.08359	+	3.33495i	0.0430010	+	0.132344i
$636$		0			0
$637$	−25.6525			−1.01639
$638$		0			0
$639$	1.94427			0.0769142
$640$		0			0
$641$	4.15248	+	12.7800i	0.164013	+	0.504780i	0.998962	−	0.0455470i	$-0.0145031\pi$
$641$	4.15248	+	12.7800i	0.164013	+	0.504780i	−0.834949	+	0.550327i	$0.814503\pi$
$642$		0			0
$643$	21.5344	+	15.6457i	0.849235	+	0.617006i	0.924935	−	0.380125i	$-0.124119\pi$
$643$	21.5344	+	15.6457i	0.849235	+	0.617006i	−0.0756997	+	0.997131i	$0.524119\pi$
$644$		0			0
$645$	0.472136	−	1.45309i	0.0185903	−	0.0572152i
$646$		0			0
$647$	10.0623	−	7.31069i	0.395590	−	0.287413i	−0.372152	−	0.928172i	$-0.621380\pi$
$647$	10.0623	−	7.31069i	0.395590	−	0.287413i	0.767742	+	0.640759i	$0.221380\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−2.30902	+	1.67760i	−0.0904975	+	0.0657503i
$652$		0			0
$653$	−12.0279	+	37.0180i	−0.470687	+	1.44862i	0.381001	+	0.924575i	$0.375580\pi$
$653$	−12.0279	+	37.0180i	−0.470687	+	1.44862i	−0.851688	+	0.524050i	$0.824420\pi$
$654$		0			0
$655$	4.00000	+	2.90617i	0.156293	+	0.113553i
$656$		0			0
$657$	−0.371323	−	1.14281i	−0.0144867	−	0.0445854i
$658$		0			0
$659$	−32.0000			−1.24654			−0.623272	−	0.782006i	$-0.714197\pi$
$659$	−32.0000			−1.24654			−0.623272	+	0.782006i	$0.714197\pi$
$660$		0			0
$661$	6.94427			0.270101			0.135050	−	0.990839i	$-0.456880\pi$
$661$	6.94427			0.270101			0.135050	+	0.990839i	$0.456880\pi$
$662$		0			0
$663$	−5.42705	−	16.7027i	−0.210769	−	0.648681i
$664$		0			0
$665$	−3.92705	−	2.85317i	−0.152285	−	0.110641i
$666$		0			0
$667$	9.05573	−	27.8707i	0.350639	−	1.07916i
$668$		0			0
$669$	−12.5902	+	9.14729i	−0.486764	+	0.353655i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−6.26393	+	4.55101i	−0.241457	+	0.175429i	−0.701932	−	0.712244i	$-0.747679\pi$
$673$	−6.26393	+	4.55101i	−0.241457	+	0.175429i	0.460475	+	0.887673i	$0.347679\pi$
$674$		0			0
$675$	−7.80902	+	24.0337i	−0.300569	+	0.925057i
$676$		0			0
$677$	−16.4443	−	11.9475i	−0.632005	−	0.459178i	0.225089	−	0.974338i	$-0.427733\pi$
$677$	−16.4443	−	11.9475i	−0.632005	−	0.459178i	−0.857094	+	0.515160i	$0.827733\pi$
$678$		0			0
$679$	6.16312	+	18.9681i	0.236519	+	0.727930i
$680$		0			0
$681$	11.5623			0.443069
$682$		0			0
$683$	−0.944272			−0.0361316			−0.0180658	−	0.999837i	$-0.505751\pi$
$683$	−0.944272			−0.0361316			−0.0180658	+	0.999837i	$0.505751\pi$
$684$		0			0
$685$	3.35410	+	10.3229i	0.128154	+	0.394416i
$686$		0			0
$687$	−21.3713	−	15.5272i	−0.815367	−	0.592399i
$688$		0			0
$689$	1.11803	−	3.44095i	0.0425937	−	0.131090i
$690$		0			0
$691$	−19.0623	+	13.8496i	−0.725164	+	0.526863i	−0.888030	−	0.459786i	$-0.847926\pi$
$691$	−19.0623	+	13.8496i	−0.725164	+	0.526863i	0.162866	+	0.986648i	$0.447926\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−8.13525	+	5.91061i	−0.308588	+	0.224202i
$696$		0			0
$697$	5.51064	−	16.9600i	0.208730	−	0.642406i
$698$		0			0
$699$	−20.9894	−	15.2497i	−0.793890	−	0.576795i
$700$		0			0
$701$	4.86068	+	14.9596i	0.183585	+	0.565018i	0.999921	−	0.0125600i	$-0.00399809\pi$
$701$	4.86068	+	14.9596i	0.183585	+	0.565018i	−0.816336	+	0.577578i	$0.803998\pi$
$702$		0			0
$703$	46.6869			1.76083
$704$		0			0
$705$	10.5623			0.397799
$706$		0			0
$707$	1.54508	+	4.75528i	0.0581089	+	0.178841i
$708$		0			0
$709$	15.9721	+	11.6044i	0.599846	+	0.435814i	0.845824	−	0.533462i	$-0.179109\pi$
$709$	15.9721	+	11.6044i	0.599846	+	0.435814i	−0.245978	+	0.969275i	$0.579109\pi$
$710$		0			0
$711$	−0.454915	+	1.40008i	−0.0170606	+	0.0525073i
$712$		0			0
$713$	3.52786	−	2.56314i	0.132120	−	0.0959905i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	30.7705	−	22.3561i	1.14915	−	0.834903i
$718$		0			0
$719$	0.0278640	−	0.0857567i	0.00103915	−	0.00319819i	−0.950536	−	0.310616i	$-0.899465\pi$
$719$	0.0278640	−	0.0857567i	0.00103915	−	0.00319819i	0.951575	+	0.307417i	$0.0994648\pi$
$720$		0			0
$721$	15.8262	+	11.4984i	0.589400	+	0.428224i
$722$		0			0
$723$	0.527864	+	1.62460i	0.0196315	+	0.0604195i
$724$		0			0
$725$	33.8328			1.25652
$726$		0			0
$727$	−28.9443			−1.07348			−0.536742	−	0.843747i	$-0.680345\pi$
$727$	−28.9443			−1.07348			−0.536742	+	0.843747i	$0.680345\pi$
$728$		0			0
$729$	9.11803	+	28.0624i	0.337705	+	1.03935i
$730$		0			0
$731$	2.29180	+	1.66509i	0.0847651	+	0.0615855i
$732$		0			0
$733$	4.02786	−	12.3965i	0.148773	−	0.457875i	−0.848704	−	0.528868i	$-0.822617\pi$
$733$	4.02786	−	12.3965i	0.148773	−	0.457875i	0.997477	+	0.0709929i	$0.0226168\pi$
$734$		0			0
$735$	−3.54508	+	2.57565i	−0.130762	+	0.0950045i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	6.59017	−	4.78804i	0.242423	−	0.176131i	−0.459939	−	0.887951i	$-0.652129\pi$
$739$	6.59017	−	4.78804i	0.242423	−	0.176131i	0.702362	+	0.711820i	$0.252129\pi$
$740$		0			0
$741$	14.2082	−	43.7284i	0.521951	−	1.60640i
$742$		0			0
$743$	37.7705	+	27.4419i	1.38567	+	1.00674i	0.996325	+	0.0856511i	$0.0272970\pi$
$743$	37.7705	+	27.4419i	1.38567	+	1.00674i	0.389340	+	0.921094i	$0.372703\pi$
$744$		0			0
$745$	3.40983	+	10.4944i	0.124927	+	0.384484i
$746$		0			0
$747$	3.58359			0.131117
$748$		0			0
$749$	6.32624			0.231156
$750$		0			0
$751$	1.02786	+	3.16344i	0.0375073	+	0.115436i	0.968057	−	0.250730i	$-0.0806705\pi$
$751$	1.02786	+	3.16344i	0.0375073	+	0.115436i	−0.930550	+	0.366165i	$0.880671\pi$
$752$		0			0
$753$	13.8992	+	10.0984i	0.506515	+	0.368004i
$754$		0			0
$755$	−1.39919	+	4.30625i	−0.0509216	+	0.156721i
$756$		0			0
$757$	21.9721	−	15.9637i	0.798591	−	0.580210i	−0.111910	−	0.993718i	$-0.535697\pi$
$757$	21.9721	−	15.9637i	0.798591	−	0.580210i	0.910500	+	0.413508i	$0.135697\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	5.26393	−	3.82447i	0.190817	−	0.138637i	−0.488275	−	0.872690i	$-0.662374\pi$
$761$	5.26393	−	3.82447i	0.190817	−	0.138637i	0.679092	+	0.734053i	$0.262374\pi$
$762$		0			0
$763$	7.47214	−	22.9969i	0.270509	−	0.832543i
$764$		0			0
$765$	0.354102	+	0.257270i	0.0128026	+	0.00930162i
$766$		0			0
$767$	−4.30902	−	13.2618i	−0.155590	−	0.478856i
$768$		0			0
$769$	−36.2492			−1.30718			−0.653590	−	0.756849i	$-0.726738\pi$
$769$	−36.2492			−1.30718			−0.653590	+	0.756849i	$0.726738\pi$
$770$		0			0
$771$	4.14590			0.149311
$772$		0			0
$773$	12.5557	+	38.6426i	0.451598	+	1.38988i	0.875083	+	0.483973i	$0.160807\pi$
$773$	12.5557	+	38.6426i	0.451598	+	1.38988i	−0.423485	+	0.905903i	$0.639193\pi$
$774$		0			0
$775$	4.07295	+	2.95917i	0.146305	+	0.106297i
$776$		0			0
$777$	−7.78115	+	23.9479i	−0.279147	+	0.859127i
$778$		0			0
$779$	37.7705	−	27.4419i	1.35327	−	0.983207i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	32.4336	−	23.5644i	1.15908	−	0.842123i
$784$		0			0
$785$	−0.128677	+	0.396027i	−0.00459268	+	0.0141348i
$786$		0			0
$787$	−19.0623	−	13.8496i	−0.679498	−	0.493684i	0.193693	−	0.981062i	$-0.437953\pi$
$787$	−19.0623	−	13.8496i	−0.679498	−	0.493684i	−0.873191	+	0.487378i	$0.837953\pi$
$788$		0			0
$789$	3.70820	+	11.4127i	0.132016	+	0.406302i
$790$		0			0
$791$	−14.3262			−0.509382
$792$		0			0
$793$	10.8541			0.385440
$794$		0			0
$795$	−0.190983	−	0.587785i	−0.00677347	−	0.0208466i
$796$		0			0
$797$	−9.26393	−	6.73064i	−0.328145	−	0.238412i	0.411498	−	0.911411i	$-0.365006\pi$
$797$	−9.26393	−	6.73064i	−0.328145	−	0.238412i	−0.739643	+	0.672999i	$0.765006\pi$
$798$		0			0
$799$	−6.05166	+	18.6251i	−0.214092	+	0.658909i
$800$		0			0
$801$	−1.38197	+	1.00406i	−0.0488294	+	0.0354766i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−3.23607	+	2.35114i	−0.114056	+	0.0828668i
$806$		0			0
$807$	0.454915	−	1.40008i	0.0160138	−	0.0492853i
$808$		0			0
$809$	−1.20820	−	0.877812i	−0.0424782	−	0.0308622i	0.566344	−	0.824169i	$-0.308358\pi$
$809$	−1.20820	−	0.877812i	−0.0424782	−	0.0308622i	−0.608822	+	0.793307i	$0.708358\pi$
$810$		0			0
$811$	−13.2082	−	40.6507i	−0.463803	−	1.42744i	−0.860482	−	0.509481i	$-0.829837\pi$
$811$	−13.2082	−	40.6507i	−0.463803	−	1.42744i	0.396679	−	0.917957i	$-0.370163\pi$
$812$		0			0
$813$	−42.6869			−1.49710
$814$		0			0
$815$	−5.43769			−0.190474
$816$		0			0
$817$	2.29180	+	7.05342i	0.0801798	+	0.246768i
$818$		0			0
$819$	−2.92705	−	2.12663i	−0.102279	−	0.0743104i
$820$		0			0
$821$	14.3885	−	44.2834i	0.502164	−	1.54550i	−0.303324	−	0.952888i	$-0.598096\pi$
$821$	14.3885	−	44.2834i	0.502164	−	1.54550i	0.805487	−	0.592613i	$-0.201904\pi$
$822$		0			0
$823$	−11.0623	+	8.03724i	−0.385608	+	0.280160i	−0.763653	−	0.645627i	$-0.776596\pi$
$823$	−11.0623	+	8.03724i	−0.385608	+	0.280160i	0.378046	+	0.925787i	$0.376596\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	11.0623	−	8.03724i	0.384674	−	0.279482i	−0.378595	−	0.925562i	$-0.623593\pi$
$827$	11.0623	−	8.03724i	0.384674	−	0.279482i	0.763270	+	0.646080i	$0.223593\pi$
$828$		0			0
$829$	−5.26393	+	16.2007i	−0.182824	+	0.562674i	−0.999904	−	0.0138499i	$-0.995591\pi$
$829$	−5.26393	+	16.2007i	−0.182824	+	0.562674i	0.817080	+	0.576524i	$0.195591\pi$
$830$		0			0
$831$	4.42705	+	3.21644i	0.153573	+	0.111577i
$832$		0			0
$833$	−2.51064	−	7.72696i	−0.0869886	−	0.267723i
$834$		0			0
$835$	8.85410			0.306409
$836$		0			0
$837$	5.96556			0.206200
$838$		0			0
$839$	5.86068	+	18.0373i	0.202333	+	0.622717i	0.999812	+	0.0193710i	$0.00616635\pi$
$839$	5.86068	+	18.0373i	0.202333	+	0.622717i	−0.797479	+	0.603346i	$0.793834\pi$
$840$		0			0
$841$	−19.9615	−	14.5029i	−0.688327	−	0.500099i
$842$		0			0
$843$	6.78115	−	20.8702i	0.233555	−	0.718809i
$844$		0			0
$845$	−10.6353	+	7.72696i	−0.365864	+	0.265816i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−18.0623	+	13.1230i	−0.619897	+	0.450381i
$850$		0			0
$851$	11.8885	−	36.5892i	0.407534	−	1.25426i
$852$		0			0
$853$	−26.6246	−	19.3439i	−0.911609	−	0.662323i	0.0298120	−	0.999556i	$-0.490509\pi$
$853$	−26.6246	−	19.3439i	−0.911609	−	0.662323i	−0.941421	+	0.337233i	$0.890509\pi$
$854$		0			0
$855$	0.354102	+	1.08981i	0.0121100	+	0.0372708i
$856$		0			0
$857$	26.3607			0.900464			0.450232	−	0.892912i	$-0.351341\pi$
$857$	26.3607			0.900464			0.450232	+	0.892912i	$0.351341\pi$
$858$		0			0
$859$	13.8885			0.473871			0.236935	−	0.971525i	$-0.423857\pi$
$859$	13.8885			0.473871			0.236935	+	0.971525i	$0.423857\pi$
$860$		0			0
$861$	7.78115	+	23.9479i	0.265181	+	0.816143i
$862$		0			0
$863$	10.1180	+	7.35118i	0.344422	+	0.250237i	0.746525	−	0.665357i	$-0.231721\pi$
$863$	10.1180	+	7.35118i	0.344422	+	0.250237i	−0.402103	+	0.915594i	$0.631721\pi$
$864$		0			0
$865$	−1.69098	+	5.20431i	−0.0574951	+	0.176952i
$866$		0			0
$867$	−17.7533	+	12.8985i	−0.602933	+	0.438057i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	68.5410	−	49.7980i	2.32242	−	1.68734i
$872$		0			0
$873$	1.45492	−	4.47777i	0.0492414	−	0.151549i
$874$		0			0
$875$	−7.78115	−	5.65334i	−0.263051	−	0.191118i
$876$		0			0
$877$	−5.86068	−	18.0373i	−0.197901	−	0.609077i	−0.999930	−	0.0117923i	$-0.996246\pi$
$877$	−5.86068	−	18.0373i	−0.197901	−	0.609077i	0.802029	−	0.597285i	$-0.203754\pi$
$878$		0			0
$879$	−17.0902			−0.576437
$880$		0			0
$881$	31.5279			1.06220			0.531100	−	0.847309i	$-0.321779\pi$
$881$	31.5279			1.06220			0.531100	+	0.847309i	$0.321779\pi$
$882$		0			0
$883$	3.97214	+	12.2250i	0.133673	+	0.411403i	0.995381	−	0.0960009i	$-0.0306052\pi$
$883$	3.97214	+	12.2250i	0.133673	+	0.411403i	−0.861708	+	0.507404i	$0.830605\pi$
$884$		0			0
$885$	−1.92705	−	1.40008i	−0.0647771	−	0.0470633i
$886$		0			0
$887$	15.3197	−	47.1491i	0.514384	−	1.58311i	−0.270016	−	0.962856i	$-0.587029\pi$
$887$	15.3197	−	47.1491i	0.514384	−	1.58311i	0.784400	−	0.620255i	$-0.212971\pi$
$888$		0			0
$889$	7.42705	−	5.39607i	0.249095	−	0.180978i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−41.4787	+	30.1360i	−1.38803	+	1.00846i
$894$		0			0
$895$	4.63525	−	14.2658i	0.154939	−	0.476855i
$896$		0			0
$897$	−30.6525	−	22.2703i	−1.02346	−	0.743585i
$898$		0			0
$899$	−2.46807	−	7.59594i	−0.0823148	−	0.253339i
$900$		0			0
$901$	1.14590			0.0381754
$902$		0			0
$903$	−4.00000			−0.133112
$904$		0			0
$905$	−1.77051	−	5.44907i	−0.0588537	−	0.181133i
$906$		0			0
$907$	−22.0623	−	16.0292i	−0.732567	−	0.532241i	0.157808	−	0.987470i	$-0.449557\pi$
$907$	−22.0623	−	16.0292i	−0.732567	−	0.532241i	−0.890374	+	0.455229i	$0.849557\pi$
$908$		0			0
$909$	0.364745	−	1.12257i	0.0120978	−	0.0372333i
$910$		0			0
$911$	−38.0066	+	27.6134i	−1.25921	+	0.914873i	−0.998719	−	0.0506025i	$-0.983886\pi$
$911$	−38.0066	+	27.6134i	−1.25921	+	0.914873i	−0.260495	+	0.965475i	$0.583886\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	1.50000	−	1.08981i	0.0495885	−	0.0360281i
$916$		0			0
$917$	4.00000	−	12.3107i	0.132092	−	0.406536i
$918$		0			0
$919$	−15.0623	−	10.9434i	−0.496860	−	0.360990i	0.310957	−	0.950424i	$-0.399351\pi$
$919$	−15.0623	−	10.9434i	−0.496860	−	0.360990i	−0.807816	+	0.589434i	$0.799351\pi$
$920$		0			0
$921$	16.9443	+	52.1491i	0.558333	+	1.71837i
$922$		0			0
$923$	−29.7984			−0.980825
$924$		0			0
$925$	44.4164			1.46040
$926$		0			0
$927$	−1.42705	−	4.39201i	−0.0468705	−	0.144253i
$928$		0			0
$929$	11.6803	+	8.48626i	0.383220	+	0.278425i	0.762671	−	0.646786i	$-0.223887\pi$
$929$	11.6803	+	8.48626i	0.383220	+	0.278425i	−0.379452	+	0.925211i	$0.623887\pi$
$930$		0			0
$931$	6.57295	−	20.2295i	0.215420	−	0.662994i
$932$		0			0
$933$	42.2426	−	30.6911i	1.38296	−	1.00478i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	1.26393	−	0.918300i	0.0412909	−	0.0299996i	−0.566948	−	0.823753i	$-0.691876\pi$
$937$	1.26393	−	0.918300i	0.0412909	−	0.0299996i	0.608239	+	0.793754i	$0.291876\pi$
$938$		0			0
$939$	13.8713	−	42.6915i	0.452674	−	1.39319i
$940$		0			0
$941$	−23.6803	−	17.2048i	−0.771957	−	0.560860i	0.130597	−	0.991435i	$-0.458310\pi$
$941$	−23.6803	−	17.2048i	−0.771957	−	0.560860i	−0.902554	+	0.430576i	$0.858310\pi$
$942$		0			0
$943$	−11.8885	−	36.5892i	−0.387144	−	1.19151i
$944$		0			0
$945$	−5.47214			−0.178009
$946$		0			0
$947$	18.8328			0.611984			0.305992	−	0.952034i	$-0.401012\pi$
$947$	18.8328			0.611984			0.305992	+	0.952034i	$0.401012\pi$
$948$		0			0
$949$	5.69098	+	17.5150i	0.184737	+	0.568562i
$950$		0			0
$951$	−0.427051	−	0.310271i	−0.0138481	−	0.0100612i
$952$		0			0
$953$	9.26393	−	28.5115i	0.300088	−	0.923576i	−0.681376	−	0.731933i	$-0.738618\pi$
$953$	9.26393	−	28.5115i	0.300088	−	0.923576i	0.981465	−	0.191643i	$-0.0613817\pi$
$954$		0			0
$955$	−7.57295	+	5.50207i	−0.245055	+	0.178043i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	22.9894	−	16.7027i	0.742365	−	0.539360i
$960$		0			0
$961$	−9.21227	+	28.3524i	−0.297170	+	0.914595i
$962$		0			0
$963$	−1.20820	−	0.877812i	−0.0389338	−	0.0282871i
$964$		0			0
$965$	1.40983	+	4.33901i	0.0453840	+	0.139678i
$966$		0			0
$967$	−33.3050			−1.07102			−0.535508	−	0.844530i	$-0.679880\pi$
$967$	−33.3050			−1.07102			−0.535508	+	0.844530i	$0.679880\pi$
$968$		0			0
$969$	14.5623			0.467809
$970$		0			0
$971$	−3.44427	−	10.6004i	−0.110532	−	0.340182i	0.880457	−	0.474126i	$-0.157236\pi$
$971$	−3.44427	−	10.6004i	−0.110532	−	0.340182i	−0.990989	+	0.133944i	$0.957236\pi$
$972$		0			0
$973$	21.2984	+	15.4742i	0.682795	+	0.496079i
$974$		0			0
$975$	13.5172	−	41.6017i	0.432898	−	1.33232i
$976$		0			0
$977$	7.02786	−	5.10604i	0.224841	−	0.163357i	−0.469662	−	0.882846i	$-0.655624\pi$
$977$	7.02786	−	5.10604i	0.224841	−	0.163357i	0.694503	+	0.719490i	$0.255624\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−4.61803	+	3.35520i	−0.147442	+	0.107123i
$982$		0			0
$983$	2.50000	−	7.69421i	0.0797376	−	0.245407i	−0.903239	−	0.429138i	$-0.858817\pi$
$983$	2.50000	−	7.69421i	0.0797376	−	0.245407i	0.982977	+	0.183731i	$0.0588174\pi$
$984$		0			0
$985$	0.236068	+	0.171513i	0.00752175	+	0.00546487i
$986$		0			0
$987$	−8.54508	−	26.2991i	−0.271993	−	0.837109i
$988$		0			0
$989$	6.11146			0.194333
$990$		0			0
$991$	27.0557			0.859454			0.429727	−	0.902959i	$-0.358610\pi$
$991$	27.0557			0.859454			0.429727	+	0.902959i	$0.358610\pi$
$992$		0			0
$993$	4.47214	+	13.7638i	0.141919	+	0.436782i
$994$		0			0
$995$	−10.1803	−	7.39645i	−0.322738	−	0.234483i
$996$		0			0
$997$	−8.84752	+	27.2299i	−0.280204	+	0.862379i	0.707591	+	0.706622i	$0.249782\pi$
$997$	−8.84752	+	27.2299i	−0.280204	+	0.862379i	−0.987795	+	0.155757i	$0.950218\pi$
$998$		0			0
$999$	42.5795	−	30.9358i	1.34716	−	0.978767i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.i.c.729.1		4
11.2	odd	10		968.2.a.i.1.1		2
11.3	even	5		968.2.i.k.753.1		4
11.4	even	5	inner	968.2.i.c.81.1		4
11.5	even	5		968.2.i.k.9.1		4
11.6	odd	10		88.2.i.a.9.1	✓	4
11.7	odd	10		968.2.i.d.81.1		4
11.8	odd	10		88.2.i.a.49.1	yes	4
11.9	even	5		968.2.a.h.1.1		2
11.10	odd	2		968.2.i.d.729.1		4
33.2	even	10		8712.2.a.bp.1.1		2
33.8	even	10		792.2.r.b.577.1		4
33.17	even	10		792.2.r.b.361.1		4
33.20	odd	10		8712.2.a.bm.1.1		2
44.19	even	10		176.2.m.a.49.1		4
44.31	odd	10		1936.2.a.u.1.2		2
44.35	even	10		1936.2.a.t.1.2		2
44.39	even	10		176.2.m.a.97.1		4
88.13	odd	10		7744.2.a.cr.1.2		2
88.19	even	10		704.2.m.g.577.1		4
88.35	even	10		7744.2.a.cb.1.1		2
88.53	even	10		7744.2.a.cq.1.2		2
88.61	odd	10		704.2.m.b.449.1		4
88.75	odd	10		7744.2.a.cc.1.1		2
88.83	even	10		704.2.m.g.449.1		4
88.85	odd	10		704.2.m.b.577.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.i.a.9.1	✓	4	11.6	odd	10
88.2.i.a.49.1	yes	4	11.8	odd	10
176.2.m.a.49.1		4	44.19	even	10
176.2.m.a.97.1		4	44.39	even	10
704.2.m.b.449.1		4	88.61	odd	10
704.2.m.b.577.1		4	88.85	odd	10
704.2.m.g.449.1		4	88.83	even	10
704.2.m.g.577.1		4	88.19	even	10
792.2.r.b.361.1		4	33.17	even	10
792.2.r.b.577.1		4	33.8	even	10
968.2.a.h.1.1		2	11.9	even	5
968.2.a.i.1.1		2	11.2	odd	10
968.2.i.c.81.1		4	11.4	even	5	inner
968.2.i.c.729.1		4	1.1	even	1	trivial
968.2.i.d.81.1		4	11.7	odd	10
968.2.i.d.729.1		4	11.10	odd	2
968.2.i.k.9.1		4	11.5	even	5
968.2.i.k.753.1		4	11.3	even	5
1936.2.a.t.1.2		2	44.35	even	10
1936.2.a.u.1.2		2	44.31	odd	10
7744.2.a.cb.1.1		2	88.35	even	10
7744.2.a.cc.1.1		2	88.75	odd	10
7744.2.a.cq.1.2		2	88.53	even	10
7744.2.a.cr.1.2		2	88.13	odd	10
8712.2.a.bm.1.1		2	33.20	odd	10
8712.2.a.bp.1.1		2	33.2	even	10

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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.i (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 1.53884i) q^{3} +(-0.500000 - 0.363271i) q^{5} +(-0.500000 + 1.53884i) q^{7} +(0.309017 - 0.224514i) q^{9} +(-4.73607 + 3.44095i) q^{13} +(-0.309017 + 0.951057i) q^{15} +(-1.50000 - 1.08981i) q^{17} +(-1.50000 - 4.61653i) q^{19} +2.61803 q^{21} -4.00000 q^{23} +(-1.42705 - 4.39201i) q^{25} +(-4.42705 - 3.21644i) q^{27} +(-2.26393 + 6.96767i) q^{29} +(-0.881966 + 0.640786i) q^{31} +(0.809017 - 0.587785i) q^{35} +(-2.97214 + 9.14729i) q^{37} +(7.66312 + 5.56758i) q^{39} +(2.97214 + 9.14729i) q^{41} -1.52786 q^{43} -0.236068 q^{45} +(-3.26393 - 10.0453i) q^{47} +(3.54508 + 2.57565i) q^{49} +(-0.927051 + 2.85317i) q^{51} +(-0.500000 + 0.363271i) q^{53} +(-6.35410 + 4.61653i) q^{57} +(-0.736068 + 2.26538i) q^{59} +(-1.50000 - 1.08981i) q^{61} +(0.190983 + 0.587785i) q^{63} +3.61803 q^{65} -14.4721 q^{67} +(2.00000 + 6.15537i) q^{69} +(4.11803 + 2.99193i) q^{71} +(0.972136 - 2.99193i) q^{73} +(-6.04508 + 4.39201i) q^{75} +(-3.11803 + 2.26538i) q^{79} +(-2.38197 + 7.33094i) q^{81} +(7.59017 + 5.51458i) q^{83} +(0.354102 + 1.08981i) q^{85} +11.8541 q^{87} -4.47214 q^{89} +(-2.92705 - 9.00854i) q^{91} +(1.42705 + 1.03681i) q^{93} +(-0.927051 + 2.85317i) q^{95} +(9.97214 - 7.24518i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{5} - 2 q^{7} - q^{9} - 10 q^{13} + q^{15} - 6 q^{17} - 6 q^{19} + 6 q^{21} - 16 q^{23} + q^{25} - 11 q^{27} - 18 q^{29} - 8 q^{31} + q^{35} + 6 q^{37} + 15 q^{39} - 6 q^{41} - 24 q^{43}+ \cdots + 22 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^5 - 2 * q^7 - q^9 - 10 * q^13 + q^15 - 6 * q^17 - 6 * q^19 + 6 * q^21 - 16 * q^23 + q^25 - 11 * q^27 - 18 * q^29 - 8 * q^31 + q^35 + 6 * q^37 + 15 * q^39 - 6 * q^41 - 24 * q^43 + 8 * q^45 - 22 * q^47 + 3 * q^49 + 3 * q^51 - 2 * q^53 - 12 * q^57 + 6 * q^59 - 6 * q^61 + 3 * q^63 + 10 * q^65 - 40 * q^67 + 8 * q^69 + 12 * q^71 - 14 * q^73 - 13 * q^75 - 8 * q^79 - 14 * q^81 + 8 * q^83 - 12 * q^85 + 34 * q^87 - 5 * q^91 - q^93 + 3 * q^95 + 22 * q^97

Introduction

L-functions

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