LMFDB - Embedded newform 1568.2.i.m.1537.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1568,2,Mod(961,1568)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1568, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("1568.961");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1568 = 2^{5} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1568.i (of order $3$, 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:	$12.5205430369$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1537.2
Root			$-0.309017 + 0.535233i$ of defining polynomial
Character	$\chi$	$=$	1568.1537
Dual form			1568.2.i.m.961.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.618034 - 1.07047i) q^{3} +(-1.61803 - 2.80252i) q^{5} +(0.736068 + 1.27491i) q^{9} +O(q^{10})$	\(q+(0.618034 - 1.07047i) q^{3} +(-1.61803 - 2.80252i) q^{5} +(0.736068 + 1.27491i) q^{9} +(-3.23607 + 5.60503i) q^{11} +0.763932 q^{13} -4.00000 q^{15} +(-2.23607 + 3.87298i) q^{17} +(-0.618034 - 1.07047i) q^{19} +(2.00000 + 3.46410i) q^{23} +(-2.73607 + 4.73901i) q^{25} +5.52786 q^{27} -4.47214 q^{29} +(-1.23607 + 2.14093i) q^{31} +(4.00000 + 6.92820i) q^{33} +(2.23607 + 3.87298i) q^{37} +(0.472136 - 0.817763i) q^{39} -8.47214 q^{41} -6.47214 q^{43} +(2.38197 - 4.12569i) q^{45} +(5.23607 + 9.06914i) q^{47} +(2.76393 + 4.78727i) q^{51} +(5.00000 - 8.66025i) q^{53} +20.9443 q^{55} -1.52786 q^{57} +(-4.61803 + 7.99867i) q^{59} +(-5.61803 - 9.73072i) q^{61} +(-1.23607 - 2.14093i) q^{65} +(2.00000 - 3.46410i) q^{67} +4.94427 q^{69} +4.94427 q^{71} +(1.47214 - 2.54981i) q^{73} +(3.38197 + 5.85774i) q^{75} +(6.47214 + 11.2101i) q^{79} +(1.20820 - 2.09267i) q^{81} +9.23607 q^{83} +14.4721 q^{85} +(-2.76393 + 4.78727i) q^{87} +(3.00000 + 5.19615i) q^{89} +(1.52786 + 2.64634i) q^{93} +(-2.00000 + 3.46410i) q^{95} +12.4721 q^{97} -9.52786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 2 q^{5} - 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 2 * q^5 - 6 * q^9	$ 4 q - 2 q^{3} - 2 q^{5} - 6 q^{9} - 4 q^{11} + 12 q^{13} - 16 q^{15} + 2 q^{19} + 8 q^{23} - 2 q^{25} + 40 q^{27} + 4 q^{31} + 16 q^{33} - 16 q^{39} - 16 q^{41} - 8 q^{43} + 14 q^{45} + 12 q^{47} + 20 q^{51} + 20 q^{53} + 48 q^{55} - 24 q^{57} - 14 q^{59} - 18 q^{61} + 4 q^{65} + 8 q^{67} - 16 q^{69} - 16 q^{71} - 12 q^{73} + 18 q^{75} + 8 q^{79} - 22 q^{81} + 28 q^{83} + 40 q^{85} - 20 q^{87} + 12 q^{89} + 24 q^{93} - 8 q^{95} + 32 q^{97} - 56 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^5 - 6 * q^9 - 4 * q^11 + 12 * q^13 - 16 * q^15 + 2 * q^19 + 8 * q^23 - 2 * q^25 + 40 * q^27 + 4 * q^31 + 16 * q^33 - 16 * q^39 - 16 * q^41 - 8 * q^43 + 14 * q^45 + 12 * q^47 + 20 * q^51 + 20 * q^53 + 48 * q^55 - 24 * q^57 - 14 * q^59 - 18 * q^61 + 4 * q^65 + 8 * q^67 - 16 * q^69 - 16 * q^71 - 12 * q^73 + 18 * q^75 + 8 * q^79 - 22 * q^81 + 28 * q^83 + 40 * q^85 - 20 * q^87 + 12 * q^89 + 24 * q^93 - 8 * q^95 + 32 * q^97 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times$.

$n$	$197$	$1471$	$1473$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	0.618034	−	1.07047i	0.356822	−	0.618034i	−0.630606	−	0.776103i	$-0.717194\pi$
$3$	0.618034	−	1.07047i	0.356822	−	0.618034i	0.987428	+	0.158069i	$0.0505269\pi$
$4$		0			0
$5$	−1.61803	−	2.80252i	−0.723607	−	1.25332i	−0.959545	−	0.281556i	$-0.909150\pi$
$5$	−1.61803	−	2.80252i	−0.723607	−	1.25332i	0.235938	−	0.971768i	$-0.424184\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	0.736068	+	1.27491i	0.245356	+	0.424969i
$10$		0			0
$11$	−3.23607	+	5.60503i	−0.975711	+	1.68998i	−0.298143	+	0.954521i	$0.596367\pi$
$11$	−3.23607	+	5.60503i	−0.975711	+	1.68998i	−0.677568	+	0.735460i	$0.736966\pi$
$12$		0			0
$13$	0.763932			0.211877			0.105938	−	0.994373i	$-0.466215\pi$
$13$	0.763932			0.211877			0.105938	+	0.994373i	$0.466215\pi$
$14$		0			0
$15$	−4.00000			−1.03280
$16$		0			0
$17$	−2.23607	+	3.87298i	−0.542326	+	0.939336i	0.456444	+	0.889752i	$0.349123\pi$
$17$	−2.23607	+	3.87298i	−0.542326	+	0.939336i	−0.998770	+	0.0495842i	$0.984210\pi$
$18$		0			0
$19$	−0.618034	−	1.07047i	−0.141787	−	0.245582i	0.786383	−	0.617740i	$-0.211951\pi$
$19$	−0.618034	−	1.07047i	−0.141787	−	0.245582i	−0.928170	+	0.372158i	$0.878618\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	0.995639	−	0.0932891i	$-0.0297381\pi$
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	−0.578610	+	0.815604i	$0.696405\pi$
$24$		0			0
$25$	−2.73607	+	4.73901i	−0.547214	+	0.947802i
$26$		0			0
$27$	5.52786			1.06384
$28$		0			0
$29$	−4.47214			−0.830455			−0.415227	−	0.909718i	$-0.636298\pi$
$29$	−4.47214			−0.830455			−0.415227	+	0.909718i	$0.636298\pi$
$30$		0			0
$31$	−1.23607	+	2.14093i	−0.222004	+	0.384523i	−0.955417	−	0.295261i	$-0.904593\pi$
$31$	−1.23607	+	2.14093i	−0.222004	+	0.384523i	0.733412	+	0.679784i	$0.237927\pi$
$32$		0			0
$33$	4.00000	+	6.92820i	0.696311	+	1.20605i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.23607	+	3.87298i	0.367607	+	0.636715i	0.989191	−	0.146633i	$-0.0468437\pi$
$37$	2.23607	+	3.87298i	0.367607	+	0.636715i	−0.621584	+	0.783348i	$0.713510\pi$
$38$		0			0
$39$	0.472136	−	0.817763i	0.0756023	−	0.130947i
$40$		0			0
$41$	−8.47214			−1.32313			−0.661563	−	0.749890i	$-0.730106\pi$
$41$	−8.47214			−1.32313			−0.661563	+	0.749890i	$0.730106\pi$
$42$		0			0
$43$	−6.47214			−0.986991			−0.493496	−	0.869748i	$-0.664281\pi$
$43$	−6.47214			−0.986991			−0.493496	+	0.869748i	$0.664281\pi$
$44$		0			0
$45$	2.38197	−	4.12569i	0.355083	−	0.615021i
$46$		0			0
$47$	5.23607	+	9.06914i	0.763759	+	1.32287i	0.940900	+	0.338684i	$0.109982\pi$
$47$	5.23607	+	9.06914i	0.763759	+	1.32287i	−0.177141	+	0.984185i	$0.556685\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	2.76393	+	4.78727i	0.387028	+	0.670352i
$52$		0			0
$53$	5.00000	−	8.66025i	0.686803	−	1.18958i	−0.286064	−	0.958211i	$-0.592347\pi$
$53$	5.00000	−	8.66025i	0.686803	−	1.18958i	0.972867	−	0.231367i	$-0.0743197\pi$
$54$		0			0
$55$	20.9443			2.82413
$56$		0			0
$57$	−1.52786			−0.202371
$58$		0			0
$59$	−4.61803	+	7.99867i	−0.601217	+	1.04134i	0.391420	+	0.920212i	$0.371984\pi$
$59$	−4.61803	+	7.99867i	−0.601217	+	1.04134i	−0.992637	+	0.121126i	$0.961349\pi$
$60$		0			0
$61$	−5.61803	−	9.73072i	−0.719316	−	1.24589i	−0.961271	−	0.275604i	$-0.911122\pi$
$61$	−5.61803	−	9.73072i	−0.719316	−	1.24589i	0.241956	−	0.970287i	$-0.422211\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.23607	−	2.14093i	−0.153315	−	0.265550i
$66$		0			0
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$		0			0
$69$	4.94427			0.595220
$70$		0			0
$71$	4.94427			0.586777			0.293389	−	0.955993i	$-0.405217\pi$
$71$	4.94427			0.586777			0.293389	+	0.955993i	$0.405217\pi$
$72$		0			0
$73$	1.47214	−	2.54981i	0.172300	−	0.298433i	−0.766923	−	0.641739i	$-0.778213\pi$
$73$	1.47214	−	2.54981i	0.172300	−	0.298433i	0.939224	+	0.343306i	$0.111547\pi$
$74$		0			0
$75$	3.38197	+	5.85774i	0.390516	+	0.676393i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	6.47214	+	11.2101i	0.728172	+	1.26123i	0.957655	+	0.287918i	$0.0929632\pi$
$79$	6.47214	+	11.2101i	0.728172	+	1.26123i	−0.229483	+	0.973313i	$0.573703\pi$
$80$		0			0
$81$	1.20820	−	2.09267i	0.134245	−	0.232519i
$82$		0			0
$83$	9.23607			1.01379			0.506895	−	0.862008i	$-0.330793\pi$
$83$	9.23607			1.01379			0.506895	+	0.862008i	$0.330793\pi$
$84$		0			0
$85$	14.4721			1.56972
$86$		0			0
$87$	−2.76393	+	4.78727i	−0.296325	+	0.513249i
$88$		0			0
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.52786	+	2.64634i	0.158432	+	0.274412i
$94$		0			0
$95$	−2.00000	+	3.46410i	−0.205196	+	0.355409i
$96$		0			0
$97$	12.4721			1.26635			0.633177	−	0.774007i	$-0.281751\pi$
$97$	12.4721			1.26635			0.633177	+	0.774007i	$0.281751\pi$
$98$		0			0
$99$	−9.52786			−0.957586
$100$		0			0
$101$	0.854102	−	1.47935i	0.0849863	−	0.147201i	−0.820399	−	0.571791i	$-0.806249\pi$
$101$	0.854102	−	1.47935i	0.0849863	−	0.147201i	0.905385	+	0.424591i	$0.139582\pi$
$102$		0			0
$103$	−2.76393	−	4.78727i	−0.272338	−	0.471704i	0.697122	−	0.716953i	$-0.254464\pi$
$103$	−2.76393	−	4.78727i	−0.272338	−	0.471704i	−0.969460	+	0.245249i	$0.921130\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.47214	+	7.74597i	0.432338	+	0.748831i	0.997074	−	0.0764405i	$-0.0243555\pi$
$107$	4.47214	+	7.74597i	0.432338	+	0.748831i	−0.564736	+	0.825271i	$0.691022\pi$
$108$		0			0
$109$	−4.23607	+	7.33708i	−0.405742	+	0.702765i	−0.994407	−	0.105611i	$-0.966320\pi$
$109$	−4.23607	+	7.33708i	−0.405742	+	0.702765i	0.588666	+	0.808377i	$0.299653\pi$
$110$		0			0
$111$	5.52786			0.524682
$112$		0			0
$113$	−12.4721			−1.17328			−0.586640	−	0.809848i	$-0.699550\pi$
$113$	−12.4721			−1.17328			−0.586640	+	0.809848i	$0.699550\pi$
$114$		0			0
$115$	6.47214	−	11.2101i	0.603530	−	1.04534i
$116$		0			0
$117$	0.562306	+	0.973942i	0.0519852	+	0.0900410i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−15.4443	−	26.7503i	−1.40402	−	2.43184i
$122$		0			0
$123$	−5.23607	+	9.06914i	−0.472120	+	0.817736i
$124$		0			0
$125$	1.52786			0.136656
$126$		0			0
$127$	−8.94427			−0.793676			−0.396838	−	0.917889i	$-0.629892\pi$
$127$	−8.94427			−0.793676			−0.396838	+	0.917889i	$0.629892\pi$
$128$		0			0
$129$	−4.00000	+	6.92820i	−0.352180	+	0.609994i
$130$		0			0
$131$	5.85410	+	10.1396i	0.511475	+	0.885901i	0.999912	+	0.0133016i	$0.00423415\pi$
$131$	5.85410	+	10.1396i	0.511475	+	0.885901i	−0.488436	+	0.872600i	$0.662433\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−8.94427	−	15.4919i	−0.769800	−	1.33333i
$136$		0			0
$137$	−7.47214	+	12.9421i	−0.638388	+	1.10572i	0.347399	+	0.937717i	$0.387065\pi$
$137$	−7.47214	+	12.9421i	−0.638388	+	1.10572i	−0.985787	+	0.168002i	$0.946268\pi$
$138$		0			0
$139$	−1.23607			−0.104842			−0.0524210	−	0.998625i	$-0.516694\pi$
$139$	−1.23607			−0.104842			−0.0524210	+	0.998625i	$0.516694\pi$
$140$		0			0
$141$	12.9443			1.09010
$142$		0			0
$143$	−2.47214	+	4.28187i	−0.206730	+	0.358068i
$144$		0			0
$145$	7.23607	+	12.5332i	0.600923	+	1.04083i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.47214	−	2.54981i	−0.120602	−	0.208889i	0.799403	−	0.600795i	$-0.205149\pi$
$149$	−1.47214	−	2.54981i	−0.120602	−	0.208889i	−0.920005	+	0.391906i	$0.871816\pi$
$150$		0			0
$151$	−4.47214	+	7.74597i	−0.363937	+	0.630358i	−0.988605	−	0.150533i	$-0.951901\pi$
$151$	−4.47214	+	7.74597i	−0.363937	+	0.630358i	0.624668	+	0.780891i	$0.285234\pi$
$152$		0			0
$153$	−6.58359			−0.532252
$154$		0			0
$155$	8.00000			0.642575
$156$		0			0
$157$	−0.381966	+	0.661585i	−0.0304842	+	0.0528002i	−0.880865	−	0.473368i	$-0.843038\pi$
$157$	−0.381966	+	0.661585i	−0.0304842	+	0.0528002i	0.850381	+	0.526168i	$0.176372\pi$
$158$		0			0
$159$	−6.18034	−	10.7047i	−0.490133	−	0.848935i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1.70820	−	2.95870i	−0.133797	−	0.231743i	0.791340	−	0.611376i	$-0.209384\pi$
$163$	−1.70820	−	2.95870i	−0.133797	−	0.231743i	−0.925137	+	0.379633i	$0.876050\pi$
$164$		0			0
$165$	12.9443	−	22.4201i	1.00771	−	1.74541i
$166$		0			0
$167$	−23.4164			−1.81202			−0.906008	−	0.423261i	$-0.860886\pi$
$167$	−23.4164			−1.81202			−0.906008	+	0.423261i	$0.860886\pi$
$168$		0			0
$169$	−12.4164			−0.955108
$170$		0			0
$171$	0.909830	−	1.57587i	0.0695764	−	0.120510i
$172$		0			0
$173$	−2.85410	−	4.94345i	−0.216993	−	0.375844i	0.736894	−	0.676008i	$-0.236292\pi$
$173$	−2.85410	−	4.94345i	−0.216993	−	0.375844i	−0.953887	+	0.300165i	$0.902958\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	5.70820	+	9.88690i	0.429055	+	0.743145i
$178$		0			0
$179$	−3.52786	+	6.11044i	−0.263685	+	0.456716i	−0.967218	−	0.253947i	$-0.918271\pi$
$179$	−3.52786	+	6.11044i	−0.263685	+	0.456716i	0.703533	+	0.710662i	$0.251605\pi$
$180$		0			0
$181$	−12.1803			−0.905358			−0.452679	−	0.891674i	$-0.649532\pi$
$181$	−12.1803			−0.905358			−0.452679	+	0.891674i	$0.649532\pi$
$182$		0			0
$183$	−13.8885			−1.02667
$184$		0			0
$185$	7.23607	−	12.5332i	0.532006	−	0.921462i
$186$		0			0
$187$	−14.4721	−	25.0665i	−1.05831	−	1.83304i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.47214	+	4.28187i	0.178877	+	0.309825i	0.941496	−	0.337023i	$-0.109420\pi$
$191$	2.47214	+	4.28187i	0.178877	+	0.309825i	−0.762619	+	0.646848i	$0.776087\pi$
$192$		0			0
$193$	−0.236068	+	0.408882i	−0.0169925	+	0.0294320i	−0.874397	−	0.485212i	$-0.838742\pi$
$193$	−0.236068	+	0.408882i	−0.0169925	+	0.0294320i	0.857404	+	0.514644i	$0.172076\pi$
$194$		0			0
$195$	−3.05573			−0.218825
$196$		0			0
$197$	10.9443			0.779747			0.389874	−	0.920868i	$-0.372519\pi$
$197$	10.9443			0.779747			0.389874	+	0.920868i	$0.372519\pi$
$198$		0			0
$199$	7.70820	−	13.3510i	0.546420	−	0.946427i	−0.452096	−	0.891969i	$-0.649324\pi$
$199$	7.70820	−	13.3510i	0.546420	−	0.946427i	0.998516	−	0.0544581i	$-0.0173431\pi$
$200$		0			0
$201$	−2.47214	−	4.28187i	−0.174371	−	0.302019i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	13.7082	+	23.7433i	0.957422	+	1.65830i
$206$		0			0
$207$	−2.94427	+	5.09963i	−0.204641	+	0.354449i
$208$		0			0
$209$	8.00000			0.553372
$210$		0			0
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$		0			0
$213$	3.05573	−	5.29268i	0.209375	−	0.362648i
$214$		0			0
$215$	10.4721	+	18.1383i	0.714194	+	1.23702i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−1.81966	−	3.15174i	−0.122961	−	0.212975i
$220$		0			0
$221$	−1.70820	+	2.95870i	−0.114906	+	0.199023i
$222$		0			0
$223$	−12.9443			−0.866813			−0.433406	−	0.901199i	$-0.642688\pi$
$223$	−12.9443			−0.866813			−0.433406	+	0.901199i	$0.642688\pi$
$224$		0			0
$225$	−8.05573			−0.537049
$226$		0			0
$227$	−8.61803	+	14.9269i	−0.571999	+	0.990731i	0.424362	+	0.905493i	$0.360499\pi$
$227$	−8.61803	+	14.9269i	−0.571999	+	0.990731i	−0.996361	+	0.0852385i	$0.972835\pi$
$228$		0			0
$229$	−11.7984	−	20.4354i	−0.779658	−	1.35041i	−0.932139	−	0.362102i	$-0.882059\pi$
$229$	−11.7984	−	20.4354i	−0.779658	−	1.35041i	0.152480	−	0.988307i	$-0.451274\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.94427	+	13.7599i	0.520447	+	0.901440i	0.999717	+	0.0237728i	$0.00756784\pi$
$233$	7.94427	+	13.7599i	0.520447	+	0.901440i	−0.479271	+	0.877667i	$0.659099\pi$
$234$		0			0
$235$	16.9443	−	29.3483i	1.10532	−	1.91447i
$236$		0			0
$237$	16.0000			1.03931
$238$		0			0
$239$	13.8885			0.898375			0.449188	−	0.893437i	$-0.351713\pi$
$239$	13.8885			0.898375			0.449188	+	0.893437i	$0.351713\pi$
$240$		0			0
$241$	−6.23607	+	10.8012i	−0.401700	+	0.695766i	−0.993931	−	0.110003i	$-0.964914\pi$
$241$	−6.23607	+	10.8012i	−0.401700	+	0.695766i	0.592231	+	0.805768i	$0.298247\pi$
$242$		0			0
$243$	6.79837	+	11.7751i	0.436116	+	0.755375i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.472136	−	0.817763i	−0.0300413	−	0.0520330i
$248$		0			0
$249$	5.70820	−	9.88690i	0.361743	−	0.626557i
$250$		0			0
$251$	−4.29180			−0.270896			−0.135448	−	0.990784i	$-0.543247\pi$
$251$	−4.29180			−0.270896			−0.135448	+	0.990784i	$0.543247\pi$
$252$		0			0
$253$	−25.8885			−1.62760
$254$		0			0
$255$	8.94427	−	15.4919i	0.560112	−	0.970143i
$256$		0			0
$257$	7.00000	+	12.1244i	0.436648	+	0.756297i	0.997429	−	0.0716680i	$-0.0228322\pi$
$257$	7.00000	+	12.1244i	0.436648	+	0.756297i	−0.560781	+	0.827964i	$0.689499\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3.29180	−	5.70156i	−0.203757	−	0.352918i
$262$		0			0
$263$	5.52786	−	9.57454i	0.340863	−	0.590392i	−0.643730	−	0.765252i	$-0.722614\pi$
$263$	5.52786	−	9.57454i	0.340863	−	0.590392i	0.984593	+	0.174861i	$0.0559475\pi$
$264$		0			0
$265$	−32.3607			−1.98790
$266$		0			0
$267$	7.41641			0.453877
$268$		0			0
$269$	2.09017	−	3.62028i	0.127440	−	0.220732i	−0.795244	−	0.606289i	$-0.792657\pi$
$269$	2.09017	−	3.62028i	0.127440	−	0.220732i	0.922684	+	0.385557i	$0.125991\pi$
$270$		0			0
$271$	−12.0000	−	20.7846i	−0.728948	−	1.26258i	−0.957328	−	0.289003i	$-0.906676\pi$
$271$	−12.0000	−	20.7846i	−0.728948	−	1.26258i	0.228380	−	0.973572i	$-0.426657\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−17.7082	−	30.6715i	−1.06784	−	1.84956i
$276$		0			0
$277$	−3.94427	+	6.83168i	−0.236988	+	0.410476i	−0.959849	−	0.280518i	$-0.909494\pi$
$277$	−3.94427	+	6.83168i	−0.236988	+	0.410476i	0.722860	+	0.690994i	$0.242827\pi$
$278$		0			0
$279$	−3.63932			−0.217880
$280$		0			0
$281$	26.0000			1.55103			0.775515	−	0.631329i	$-0.217490\pi$
$281$	26.0000			1.55103			0.775515	+	0.631329i	$0.217490\pi$
$282$		0			0
$283$	−3.09017	+	5.35233i	−0.183692	+	0.318163i	−0.943135	−	0.332410i	$-0.892138\pi$
$283$	−3.09017	+	5.35233i	−0.183692	+	0.318163i	0.759443	+	0.650574i	$0.225471\pi$
$284$		0			0
$285$	2.47214	+	4.28187i	0.146437	+	0.253636i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−1.50000	−	2.59808i	−0.0882353	−	0.152828i
$290$		0			0
$291$	7.70820	−	13.3510i	0.451863	−	0.782650i
$292$		0			0
$293$	−12.7639			−0.745677			−0.372838	−	0.927896i	$-0.621615\pi$
$293$	−12.7639			−0.745677			−0.372838	+	0.927896i	$0.621615\pi$
$294$		0			0
$295$	29.8885			1.74018
$296$		0			0
$297$	−17.8885	+	30.9839i	−1.03800	+	1.79787i
$298$		0			0
$299$	1.52786	+	2.64634i	0.0883587	+	0.153042i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−1.05573	−	1.82857i	−0.0606500	−	0.105049i
$304$		0			0
$305$	−18.1803	+	31.4893i	−1.04100	+	1.80307i
$306$		0			0
$307$	−1.81966			−0.103853			−0.0519267	−	0.998651i	$-0.516536\pi$
$307$	−1.81966			−0.103853			−0.0519267	+	0.998651i	$0.516536\pi$
$308$		0			0
$309$	−6.83282			−0.388705
$310$		0			0
$311$	4.00000	−	6.92820i	0.226819	−	0.392862i	−0.730044	−	0.683400i	$-0.760501\pi$
$311$	4.00000	−	6.92820i	0.226819	−	0.392862i	0.956864	+	0.290537i	$0.0938340\pi$
$312$		0			0
$313$	4.23607	+	7.33708i	0.239437	+	0.414717i	0.960553	−	0.278098i	$-0.0897039\pi$
$313$	4.23607	+	7.33708i	0.239437	+	0.414717i	−0.721116	+	0.692814i	$0.756371\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.52786	−	7.84249i	−0.254310	−	0.440478i	0.710398	−	0.703800i	$-0.248515\pi$
$317$	−4.52786	−	7.84249i	−0.254310	−	0.440478i	−0.964708	+	0.263322i	$0.915182\pi$
$318$		0			0
$319$	14.4721	−	25.0665i	0.810284	−	1.40345i
$320$		0			0
$321$	11.0557			0.617071
$322$		0			0
$323$	5.52786			0.307579
$324$		0			0
$325$	−2.09017	+	3.62028i	−0.115942	+	0.200817i
$326$		0			0
$327$	5.23607	+	9.06914i	0.289555	+	0.501524i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	11.2361	+	19.4614i	0.617590	+	1.06970i	0.989924	+	0.141599i	$0.0452243\pi$
$331$	11.2361	+	19.4614i	0.617590	+	1.06970i	−0.372334	+	0.928099i	$0.621442\pi$
$332$		0			0
$333$	−3.29180	+	5.70156i	−0.180389	+	0.312443i
$334$		0			0
$335$	−12.9443			−0.707221
$336$		0			0
$337$	10.3607			0.564382			0.282191	−	0.959358i	$-0.408939\pi$
$337$	10.3607			0.564382			0.282191	+	0.959358i	$0.408939\pi$
$338$		0			0
$339$	−7.70820	+	13.3510i	−0.418652	+	0.725127i
$340$		0			0
$341$	−8.00000	−	13.8564i	−0.433224	−	0.750366i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−8.00000	−	13.8564i	−0.430706	−	0.746004i
$346$		0			0
$347$	3.23607	−	5.60503i	0.173721	−	0.300894i	−0.765997	−	0.642844i	$-0.777754\pi$
$347$	3.23607	−	5.60503i	0.173721	−	0.300894i	0.939718	+	0.341950i	$0.111087\pi$
$348$		0			0
$349$	26.6525			1.42667			0.713337	−	0.700821i	$-0.247183\pi$
$349$	26.6525			1.42667			0.713337	+	0.700821i	$0.247183\pi$
$350$		0			0
$351$	4.22291			0.225402
$352$		0			0
$353$	7.94427	−	13.7599i	0.422831	−	0.732365i	−0.573384	−	0.819287i	$-0.694370\pi$
$353$	7.94427	−	13.7599i	0.422831	−	0.732365i	0.996215	+	0.0869220i	$0.0277031\pi$
$354$		0			0
$355$	−8.00000	−	13.8564i	−0.424596	−	0.735422i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−8.47214	−	14.6742i	−0.447142	−	0.774473i	0.551056	−	0.834468i	$-0.314225\pi$
$359$	−8.47214	−	14.6742i	−0.447142	−	0.774473i	−0.998199	+	0.0599949i	$0.980892\pi$
$360$		0			0
$361$	8.73607	−	15.1313i	0.459793	−	0.796385i
$362$		0			0
$363$	−38.1803			−2.00395
$364$		0			0
$365$	−9.52786			−0.498711
$366$		0			0
$367$	−11.4164	+	19.7738i	−0.595932	+	1.03218i	0.397483	+	0.917610i	$0.369884\pi$
$367$	−11.4164	+	19.7738i	−0.595932	+	1.03218i	−0.993415	+	0.114574i	$0.963450\pi$
$368$		0			0
$369$	−6.23607	−	10.8012i	−0.324637	−	0.562287i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−1.47214	−	2.54981i	−0.0762243	−	0.132024i	0.825394	−	0.564558i	$-0.190953\pi$
$373$	−1.47214	−	2.54981i	−0.0762243	−	0.132024i	−0.901618	+	0.432533i	$0.857620\pi$
$374$		0			0
$375$	0.944272	−	1.63553i	0.0487620	−	0.0844582i
$376$		0			0
$377$	−3.41641			−0.175954
$378$		0			0
$379$	4.58359			0.235443			0.117722	−	0.993047i	$-0.462441\pi$
$379$	4.58359			0.235443			0.117722	+	0.993047i	$0.462441\pi$
$380$		0			0
$381$	−5.52786	+	9.57454i	−0.283201	+	0.490519i
$382$		0			0
$383$	−7.70820	−	13.3510i	−0.393871	−	0.682204i	0.599086	−	0.800685i	$-0.295531\pi$
$383$	−7.70820	−	13.3510i	−0.393871	−	0.682204i	−0.992956	+	0.118481i	$0.962198\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−4.76393	−	8.25137i	−0.242164	−	0.419441i
$388$		0			0
$389$	2.23607	−	3.87298i	0.113373	−	0.196368i	−0.803755	−	0.594960i	$-0.797168\pi$
$389$	2.23607	−	3.87298i	0.113373	−	0.196368i	0.917128	+	0.398592i	$0.130501\pi$
$390$		0			0
$391$	−17.8885			−0.904663
$392$		0			0
$393$	14.4721			0.730023
$394$		0			0
$395$	20.9443	−	36.2765i	1.05382	−	1.82527i
$396$		0			0
$397$	7.61803	+	13.1948i	0.382338	+	0.662229i	0.991396	−	0.130897i	$-0.0417856\pi$
$397$	7.61803	+	13.1948i	0.382338	+	0.662229i	−0.609058	+	0.793126i	$0.708452\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	11.7639	+	20.3757i	0.587463	+	1.01752i	0.994563	+	0.104132i	$0.0332065\pi$
$401$	11.7639	+	20.3757i	0.587463	+	1.01752i	−0.407101	+	0.913383i	$0.633460\pi$
$402$		0			0
$403$	−0.944272	+	1.63553i	−0.0470375	+	0.0814714i
$404$		0			0
$405$	−7.81966			−0.388562
$406$		0			0
$407$	−28.9443			−1.43471
$408$		0			0
$409$	10.7082	−	18.5472i	0.529487	−	0.917098i	−0.469922	−	0.882708i	$-0.655718\pi$
$409$	10.7082	−	18.5472i	0.529487	−	0.917098i	0.999408	−	0.0343897i	$-0.0109487\pi$
$410$		0			0
$411$	9.23607	+	15.9973i	0.455582	+	0.789091i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−14.9443	−	25.8842i	−0.733585	−	1.27061i
$416$		0			0
$417$	−0.763932	+	1.32317i	−0.0374099	+	0.0647959i
$418$		0			0
$419$	−22.1803			−1.08358			−0.541790	−	0.840514i	$-0.682253\pi$
$419$	−22.1803			−1.08358			−0.541790	+	0.840514i	$0.682253\pi$
$420$		0			0
$421$	−2.00000			−0.0974740			−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000			−0.0974740			−0.0487370	+	0.998812i	$0.515520\pi$
$422$		0			0
$423$	−7.70820	+	13.3510i	−0.374786	+	0.649148i
$424$		0			0
$425$	−12.2361	−	21.1935i	−0.593536	−	1.02804i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	3.05573	+	5.29268i	0.147532	+	0.255533i
$430$		0			0
$431$	−14.0000	+	24.2487i	−0.674356	+	1.16802i	0.302300	+	0.953213i	$0.402245\pi$
$431$	−14.0000	+	24.2487i	−0.674356	+	1.16802i	−0.976657	+	0.214807i	$0.931088\pi$
$432$		0			0
$433$	9.41641			0.452524			0.226262	−	0.974067i	$-0.427349\pi$
$433$	9.41641			0.452524			0.226262	+	0.974067i	$0.427349\pi$
$434$		0			0
$435$	17.8885			0.857690
$436$		0			0
$437$	2.47214	−	4.28187i	0.118258	−	0.204829i
$438$		0			0
$439$	−16.0000	−	27.7128i	−0.763638	−	1.32266i	−0.940963	−	0.338508i	$-0.890078\pi$
$439$	−16.0000	−	27.7128i	−0.763638	−	1.32266i	0.177325	−	0.984152i	$-0.443256\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6.94427	−	12.0278i	−0.329932	−	0.571460i	0.652566	−	0.757732i	$-0.273693\pi$
$443$	−6.94427	−	12.0278i	−0.329932	−	0.571460i	−0.982498	+	0.186273i	$0.940359\pi$
$444$		0			0
$445$	9.70820	−	16.8151i	0.460213	−	0.797112i
$446$		0			0
$447$	−3.63932			−0.172134
$448$		0			0
$449$	−7.88854			−0.372283			−0.186142	−	0.982523i	$-0.559598\pi$
$449$	−7.88854			−0.372283			−0.186142	+	0.982523i	$0.559598\pi$
$450$		0			0
$451$	27.4164	−	47.4866i	1.29099	−	2.23606i
$452$		0			0
$453$	5.52786	+	9.57454i	0.259722	+	0.449851i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.76393	+	6.51932i	0.176069	+	0.304961i	0.940531	−	0.339708i	$-0.110328\pi$
$457$	3.76393	+	6.51932i	0.176069	+	0.304961i	−0.764462	+	0.644669i	$0.776995\pi$
$458$		0			0
$459$	−12.3607	+	21.4093i	−0.576947	+	0.999302i
$460$		0			0
$461$	21.7082			1.01105			0.505526	−	0.862811i	$-0.331298\pi$
$461$	21.7082			1.01105			0.505526	+	0.862811i	$0.331298\pi$
$462$		0			0
$463$	35.7771			1.66270			0.831351	−	0.555748i	$-0.187568\pi$
$463$	35.7771			1.66270			0.831351	+	0.555748i	$0.187568\pi$
$464$		0			0
$465$	4.94427	−	8.56373i	0.229285	−	0.397133i
$466$		0			0
$467$	−16.0344	−	27.7725i	−0.741985	−	1.28516i	−0.951590	−	0.307370i	$-0.900551\pi$
$467$	−16.0344	−	27.7725i	−0.741985	−	1.28516i	0.209605	−	0.977786i	$-0.432782\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	0.472136	+	0.817763i	0.0217549	+	0.0376806i
$472$		0			0
$473$	20.9443	−	36.2765i	0.963019	−	1.66800i
$474$		0			0
$475$	6.76393			0.310350
$476$		0			0
$477$	14.7214			0.674045
$478$		0			0
$479$	−4.29180	+	7.43361i	−0.196097	+	0.339650i	−0.947260	−	0.320467i	$-0.896160\pi$
$479$	−4.29180	+	7.43361i	−0.196097	+	0.339650i	0.751162	+	0.660117i	$0.229493\pi$
$480$		0			0
$481$	1.70820	+	2.95870i	0.0778874	+	0.134905i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−20.1803	−	34.9534i	−0.916342	−	1.58715i
$486$		0			0
$487$	10.0000	−	17.3205i	0.453143	−	0.784867i	−0.545436	−	0.838152i	$-0.683636\pi$
$487$	10.0000	−	17.3205i	0.453143	−	0.784867i	0.998579	+	0.0532853i	$0.0169693\pi$
$488$		0			0
$489$	−4.22291			−0.190967
$490$		0			0
$491$	−37.8885			−1.70989			−0.854943	−	0.518722i	$-0.826408\pi$
$491$	−37.8885			−1.70989			−0.854943	+	0.518722i	$0.826408\pi$
$492$		0			0
$493$	10.0000	−	17.3205i	0.450377	−	0.780076i
$494$		0			0
$495$	15.4164	+	26.7020i	0.692916	+	1.20017i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	10.9443	+	18.9560i	0.489933	+	0.848589i	0.999933	−	0.0115857i	$-0.00368794\pi$
$499$	10.9443	+	18.9560i	0.489933	+	0.848589i	−0.510000	+	0.860174i	$0.670355\pi$
$500$		0			0
$501$	−14.4721	+	25.0665i	−0.646567	+	1.11989i
$502$		0			0
$503$	4.94427			0.220454			0.110227	−	0.993906i	$-0.464842\pi$
$503$	4.94427			0.220454			0.110227	+	0.993906i	$0.464842\pi$
$504$		0			0
$505$	−5.52786			−0.245987
$506$		0			0
$507$	−7.67376	+	13.2913i	−0.340804	+	0.590289i
$508$		0			0
$509$	20.5623	+	35.6150i	0.911408	+	1.57861i	0.812077	+	0.583551i	$0.198337\pi$
$509$	20.5623	+	35.6150i	0.911408	+	1.57861i	0.0993316	+	0.995054i	$0.468330\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−3.41641	−	5.91739i	−0.150838	−	0.261259i
$514$		0			0
$515$	−8.94427	+	15.4919i	−0.394132	+	0.682656i
$516$		0			0
$517$	−67.7771			−2.98083
$518$		0			0
$519$	−7.05573			−0.309712
$520$		0			0
$521$	3.29180	−	5.70156i	0.144216	−	0.249790i	−0.784864	−	0.619668i	$-0.787267\pi$
$521$	3.29180	−	5.70156i	0.144216	−	0.249790i	0.929080	+	0.369878i	$0.120601\pi$
$522$		0			0
$523$	−2.14590	−	3.71680i	−0.0938336	−	0.162525i	0.815288	−	0.579056i	$-0.196579\pi$
$523$	−2.14590	−	3.71680i	−0.0938336	−	0.162525i	−0.909121	+	0.416532i	$0.863245\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.52786	−	9.57454i	−0.240798	−	0.417074i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$		0			0
$531$	−13.5967			−0.590049
$532$		0			0
$533$	−6.47214			−0.280339
$534$		0			0
$535$	14.4721	−	25.0665i	0.625685	−	1.08372i
$536$		0			0
$537$	4.36068	+	7.55292i	0.188177	+	0.325933i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	2.52786	+	4.37839i	0.108681	+	0.188242i	0.915236	−	0.402917i	$-0.132004\pi$
$541$	2.52786	+	4.37839i	0.108681	+	0.188242i	−0.806555	+	0.591159i	$0.798671\pi$
$542$		0			0
$543$	−7.52786	+	13.0386i	−0.323052	+	0.559542i
$544$		0			0
$545$	27.4164			1.17439
$546$		0			0
$547$	4.58359			0.195980			0.0979901	−	0.995187i	$-0.468759\pi$
$547$	4.58359			0.195980			0.0979901	+	0.995187i	$0.468759\pi$
$548$		0			0
$549$	8.27051	−	14.3249i	0.352977	−	0.611374i
$550$		0			0
$551$	2.76393	+	4.78727i	0.117747	+	0.203945i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−8.94427	−	15.4919i	−0.379663	−	0.657596i
$556$		0			0
$557$	−4.52786	+	7.84249i	−0.191852	+	0.332297i	−0.945864	−	0.324563i	$-0.894783\pi$
$557$	−4.52786	+	7.84249i	−0.191852	+	0.332297i	0.754012	+	0.656860i	$0.228116\pi$
$558$		0			0
$559$	−4.94427			−0.209120
$560$		0			0
$561$	−35.7771			−1.51051
$562$		0			0
$563$	−8.90983	+	15.4323i	−0.375505	+	0.650393i	−0.990402	−	0.138214i	$-0.955864\pi$
$563$	−8.90983	+	15.4323i	−0.375505	+	0.650393i	0.614898	+	0.788607i	$0.289197\pi$
$564$		0			0
$565$	20.1803	+	34.9534i	0.848993	+	1.47050i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−13.1803	−	22.8290i	−0.552549	−	0.957042i	−0.998090	−	0.0617808i	$-0.980322\pi$
$569$	−13.1803	−	22.8290i	−0.552549	−	0.957042i	0.445541	−	0.895261i	$-0.353011\pi$
$570$		0			0
$571$	−7.23607	+	12.5332i	−0.302820	+	0.524500i	−0.976774	−	0.214274i	$-0.931261\pi$
$571$	−7.23607	+	12.5332i	−0.302820	+	0.524500i	0.673954	+	0.738774i	$0.264595\pi$
$572$		0			0
$573$	6.11146			0.255310
$574$		0			0
$575$	−21.8885			−0.912815
$576$		0			0
$577$	3.00000	−	5.19615i	0.124892	−	0.216319i	−0.796799	−	0.604245i	$-0.793475\pi$
$577$	3.00000	−	5.19615i	0.124892	−	0.216319i	0.921691	+	0.387926i	$0.126808\pi$
$578$		0			0
$579$	0.291796	+	0.505406i	0.0121266	+	0.0210039i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	32.3607	+	56.0503i	1.34024	+	2.32137i
$584$		0			0
$585$	1.81966	−	3.15174i	0.0752337	−	0.130309i
$586$		0			0
$587$	3.70820			0.153054			0.0765270	−	0.997068i	$-0.475617\pi$
$587$	3.70820			0.153054			0.0765270	+	0.997068i	$0.475617\pi$
$588$		0			0
$589$	3.05573			0.125909
$590$		0			0
$591$	6.76393	−	11.7155i	0.278231	−	0.481910i
$592$		0			0
$593$	−16.4164	−	28.4341i	−0.674141	−	1.16765i	−0.976719	−	0.214522i	$-0.931181\pi$
$593$	−16.4164	−	28.4341i	−0.674141	−	1.16765i	0.302578	−	0.953125i	$-0.402153\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−9.52786	−	16.5027i	−0.389950	−	0.675412i
$598$		0			0
$599$	8.94427	−	15.4919i	0.365453	−	0.632983i	−0.623396	−	0.781907i	$-0.714247\pi$
$599$	8.94427	−	15.4919i	0.365453	−	0.632983i	0.988849	+	0.148923i	$0.0475807\pi$
$600$		0			0
$601$	29.7771			1.21463			0.607316	−	0.794460i	$-0.292246\pi$
$601$	29.7771			1.21463			0.607316	+	0.794460i	$0.292246\pi$
$602$		0			0
$603$	5.88854			0.239800
$604$		0			0
$605$	−49.9787	+	86.5657i	−2.03192	+	3.51940i
$606$		0			0
$607$	4.94427	+	8.56373i	0.200682	+	0.347591i	0.948748	−	0.316033i	$-0.102351\pi$
$607$	4.94427	+	8.56373i	0.200682	+	0.347591i	−0.748066	+	0.663624i	$0.769018\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	4.00000	+	6.92820i	0.161823	+	0.280285i
$612$		0			0
$613$	−14.7082	+	25.4754i	−0.594059	+	1.02894i	0.399620	+	0.916681i	$0.369142\pi$
$613$	−14.7082	+	25.4754i	−0.594059	+	1.02894i	−0.993679	+	0.112259i	$0.964191\pi$
$614$		0			0
$615$	33.8885			1.36652
$616$		0			0
$617$	34.3607			1.38331			0.691654	−	0.722229i	$-0.256882\pi$
$617$	34.3607			1.38331			0.691654	+	0.722229i	$0.256882\pi$
$618$		0			0
$619$	−24.0344	+	41.6289i	−0.966026	+	1.67321i	−0.259192	+	0.965826i	$0.583456\pi$
$619$	−24.0344	+	41.6289i	−0.966026	+	1.67321i	−0.706833	+	0.707380i	$0.749877\pi$
$620$		0			0
$621$	11.0557	+	19.1491i	0.443651	+	0.768426i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	11.2082	+	19.4132i	0.448328	+	0.776527i
$626$		0			0
$627$	4.94427	−	8.56373i	0.197455	−	0.342002i
$628$		0			0
$629$	−20.0000			−0.797452
$630$		0			0
$631$	44.9443			1.78920			0.894602	−	0.446865i	$-0.147459\pi$
$631$	44.9443			1.78920			0.894602	+	0.446865i	$0.147459\pi$
$632$		0			0
$633$	7.41641	−	12.8456i	0.294776	−	0.510567i
$634$		0			0
$635$	14.4721	+	25.0665i	0.574309	+	0.994733i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	3.63932	+	6.30349i	0.143969	+	0.249362i
$640$		0			0
$641$	−7.29180	+	12.6298i	−0.288009	+	0.498846i	−0.973334	−	0.229391i	$-0.926327\pi$
$641$	−7.29180	+	12.6298i	−0.288009	+	0.498846i	0.685326	+	0.728237i	$0.259660\pi$
$642$		0			0
$643$	43.7082			1.72368			0.861842	−	0.507177i	$-0.169311\pi$
$643$	43.7082			1.72368			0.861842	+	0.507177i	$0.169311\pi$
$644$		0			0
$645$	25.8885			1.01936
$646$		0			0
$647$	−10.1803	+	17.6329i	−0.400230	+	0.693219i	−0.993753	−	0.111598i	$-0.964403\pi$
$647$	−10.1803	+	17.6329i	−0.400230	+	0.693219i	0.593523	+	0.804817i	$0.297737\pi$
$648$		0			0
$649$	−29.8885	−	51.7685i	−1.17323	−	2.03209i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4.70820	+	8.15485i	0.184246	+	0.319124i	0.943322	−	0.331878i	$-0.107682\pi$
$653$	4.70820	+	8.15485i	0.184246	+	0.319124i	−0.759076	+	0.651002i	$0.774349\pi$
$654$		0			0
$655$	18.9443	−	32.8124i	0.740214	−	1.28209i
$656$		0			0
$657$	4.33437			0.169100
$658$		0			0
$659$	−37.3050			−1.45319			−0.726597	−	0.687064i	$-0.758899\pi$
$659$	−37.3050			−1.45319			−0.726597	+	0.687064i	$0.758899\pi$
$660$		0			0
$661$	11.3262	−	19.6176i	0.440540	−	0.763037i	−0.557190	−	0.830385i	$-0.688120\pi$
$661$	11.3262	−	19.6176i	0.440540	−	0.763037i	0.997730	+	0.0673481i	$0.0214538\pi$
$662$		0			0
$663$	2.11146	+	3.65715i	0.0820022	+	0.142032i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−8.94427	−	15.4919i	−0.346324	−	0.599850i
$668$		0			0
$669$	−8.00000	+	13.8564i	−0.309298	+	0.535720i
$670$		0			0
$671$	72.7214			2.80738
$672$		0			0
$673$	−2.94427			−0.113493			−0.0567467	−	0.998389i	$-0.518073\pi$
$673$	−2.94427			−0.113493			−0.0567467	+	0.998389i	$0.518073\pi$
$674$		0			0
$675$	−15.1246	+	26.1966i	−0.582147	+	1.00831i
$676$		0			0
$677$	−9.90983	−	17.1643i	−0.380866	−	0.659679i	0.610321	−	0.792155i	$-0.291041\pi$
$677$	−9.90983	−	17.1643i	−0.380866	−	0.659679i	−0.991186	+	0.132476i	$0.957707\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	10.6525	+	18.4506i	0.408204	+	0.707030i
$682$		0			0
$683$	11.8885	−	20.5916i	0.454902	−	0.787914i	−0.543780	−	0.839228i	$-0.683007\pi$
$683$	11.8885	−	20.5916i	0.454902	−	0.787914i	0.998683	+	0.0513135i	$0.0163408\pi$
$684$		0			0
$685$	48.3607			1.84777
$686$		0			0
$687$	−29.1672			−1.11280
$688$		0			0
$689$	3.81966	−	6.61585i	0.145517	−	0.252044i
$690$		0			0
$691$	−7.09017	−	12.2805i	−0.269723	−	0.467174i	0.699067	−	0.715056i	$-0.253599\pi$
$691$	−7.09017	−	12.2805i	−0.269723	−	0.467174i	−0.968790	+	0.247882i	$0.920265\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.00000	+	3.46410i	0.0758643	+	0.131401i
$696$		0			0
$697$	18.9443	−	32.8124i	0.717565	−	1.24286i
$698$		0			0
$699$	19.6393			0.742827
$700$		0			0
$701$	−41.4164			−1.56428			−0.782138	−	0.623105i	$-0.785871\pi$
$701$	−41.4164			−1.56428			−0.782138	+	0.623105i	$0.785871\pi$
$702$		0			0
$703$	2.76393	−	4.78727i	0.104244	−	0.180555i
$704$		0			0
$705$	−20.9443	−	36.2765i	−0.788807	−	1.36625i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.819660	−	1.41969i	−0.0307830	−	0.0533177i	0.850223	−	0.526422i	$-0.176467\pi$
$709$	−0.819660	−	1.41969i	−0.0307830	−	0.0533177i	−0.881006	+	0.473104i	$0.843133\pi$
$710$		0			0
$711$	−9.52786	+	16.5027i	−0.357323	+	0.618901i
$712$		0			0
$713$	−9.88854			−0.370329
$714$		0			0
$715$	16.0000			0.598366
$716$		0			0
$717$	8.58359	−	14.8672i	0.320560	−	0.555226i
$718$		0			0
$719$	25.5967	+	44.3349i	0.954598	+	1.65341i	0.735286	+	0.677757i	$0.237048\pi$
$719$	25.5967	+	44.3349i	0.954598	+	1.65341i	0.219311	+	0.975655i	$0.429619\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	7.70820	+	13.3510i	0.286671	+	0.496529i
$724$		0			0
$725$	12.2361	−	21.1935i	0.454436	−	0.787107i
$726$		0			0
$727$	−12.3607			−0.458432			−0.229216	−	0.973376i	$-0.573616\pi$
$727$	−12.3607			−0.458432			−0.229216	+	0.973376i	$0.573616\pi$
$728$		0			0
$729$	24.0557			0.890953
$730$		0			0
$731$	14.4721	−	25.0665i	0.535271	−	0.927117i
$732$		0			0
$733$	2.38197	+	4.12569i	0.0879799	+	0.152386i	0.906657	−	0.421868i	$-0.138626\pi$
$733$	2.38197	+	4.12569i	0.0879799	+	0.152386i	−0.818677	+	0.574254i	$0.805292\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	12.9443	+	22.4201i	0.476808	+	0.825856i
$738$		0			0
$739$	−1.70820	+	2.95870i	−0.0628373	+	0.108837i	−0.895733	−	0.444593i	$-0.853348\pi$
$739$	−1.70820	+	2.95870i	−0.0628373	+	0.108837i	0.832895	+	0.553431i	$0.186682\pi$
$740$		0			0
$741$	−1.16718			−0.0428776
$742$		0			0
$743$	−24.9443			−0.915117			−0.457558	−	0.889180i	$-0.651276\pi$
$743$	−24.9443			−0.915117			−0.457558	+	0.889180i	$0.651276\pi$
$744$		0			0
$745$	−4.76393	+	8.25137i	−0.174537	+	0.302307i
$746$		0			0
$747$	6.79837	+	11.7751i	0.248739	+	0.430829i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	18.0000	+	31.1769i	0.656829	+	1.13766i	0.981432	+	0.191811i	$0.0614361\pi$
$751$	18.0000	+	31.1769i	0.656829	+	1.13766i	−0.324603	+	0.945851i	$0.605231\pi$
$752$		0			0
$753$	−2.65248	+	4.59422i	−0.0966616	+	0.167423i
$754$		0			0
$755$	28.9443			1.05339
$756$		0			0
$757$	39.3050			1.42856			0.714281	−	0.699859i	$-0.246754\pi$
$757$	39.3050			1.42856			0.714281	+	0.699859i	$0.246754\pi$
$758$		0			0
$759$	−16.0000	+	27.7128i	−0.580763	+	1.00591i
$760$		0			0
$761$	1.76393	+	3.05522i	0.0639425	+	0.110752i	0.896224	−	0.443601i	$-0.146299\pi$
$761$	1.76393	+	3.05522i	0.0639425	+	0.110752i	−0.832282	+	0.554353i	$0.812966\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	10.6525	+	18.4506i	0.385141	+	0.667084i
$766$		0			0
$767$	−3.52786	+	6.11044i	−0.127384	+	0.220635i
$768$		0			0
$769$	−18.3607			−0.662103			−0.331052	−	0.943613i	$-0.607403\pi$
$769$	−18.3607			−0.662103			−0.331052	+	0.943613i	$0.607403\pi$
$770$		0			0
$771$	17.3050			0.623223
$772$		0			0
$773$	−20.0902	+	34.7972i	−0.722593	+	1.25157i	0.237364	+	0.971421i	$0.423717\pi$
$773$	−20.0902	+	34.7972i	−0.722593	+	1.25157i	−0.959957	+	0.280147i	$0.909617\pi$
$774$		0			0
$775$	−6.76393	−	11.7155i	−0.242968	−	0.420832i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	5.23607	+	9.06914i	0.187602	+	0.324936i
$780$		0			0
$781$	−16.0000	+	27.7128i	−0.572525	+	0.991642i
$782$		0			0
$783$	−24.7214			−0.883469
$784$		0			0
$785$	2.47214			0.0882343
$786$		0			0
$787$	−6.14590	+	10.6450i	−0.219078	+	0.379454i	−0.954526	−	0.298127i	$-0.903638\pi$
$787$	−6.14590	+	10.6450i	−0.219078	+	0.379454i	0.735449	+	0.677580i	$0.236971\pi$
$788$		0			0
$789$	−6.83282	−	11.8348i	−0.243255	−	0.421329i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−4.29180	−	7.43361i	−0.152406	−	0.263975i
$794$		0			0
$795$	−20.0000	+	34.6410i	−0.709327	+	1.22859i
$796$		0			0
$797$	−52.1803			−1.84832			−0.924161	−	0.382003i	$-0.875235\pi$
$797$	−52.1803			−1.84832			−0.924161	+	0.382003i	$0.875235\pi$
$798$		0			0
$799$	−46.8328			−1.65683
$800$		0			0
$801$	−4.41641	+	7.64944i	−0.156046	+	0.270280i
$802$		0			0
$803$	9.52786	+	16.5027i	0.336231	+	0.582369i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−2.58359	−	4.47491i	−0.0909468	−	0.157524i
$808$		0			0
$809$	8.70820	−	15.0831i	0.306164	−	0.530292i	−0.671356	−	0.741135i	$-0.734288\pi$
$809$	8.70820	−	15.0831i	0.306164	−	0.530292i	0.977520	+	0.210843i	$0.0676210\pi$
$810$		0			0
$811$	53.0132			1.86154			0.930772	−	0.365601i	$-0.119136\pi$
$811$	53.0132			1.86154			0.930772	+	0.365601i	$0.119136\pi$
$812$		0			0
$813$	−29.6656			−1.04042
$814$		0			0
$815$	−5.52786	+	9.57454i	−0.193633	+	0.335382i
$816$		0			0
$817$	4.00000	+	6.92820i	0.139942	+	0.242387i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−2.05573	−	3.56063i	−0.0717454	−	0.124267i	0.827921	−	0.560845i	$-0.189524\pi$
$821$	−2.05573	−	3.56063i	−0.0717454	−	0.124267i	−0.899666	+	0.436578i	$0.856190\pi$
$822$		0			0
$823$	−9.88854	+	17.1275i	−0.344693	+	0.597026i	−0.985298	−	0.170845i	$-0.945350\pi$
$823$	−9.88854	+	17.1275i	−0.344693	+	0.597026i	0.640605	+	0.767871i	$0.278684\pi$
$824$		0			0
$825$	−43.7771			−1.52412
$826$		0			0
$827$	−15.0557			−0.523539			−0.261769	−	0.965130i	$-0.584306\pi$
$827$	−15.0557			−0.523539			−0.261769	+	0.965130i	$0.584306\pi$
$828$		0			0
$829$	−5.61803	+	9.73072i	−0.195122	+	0.337962i	−0.946941	−	0.321409i	$-0.895844\pi$
$829$	−5.61803	+	9.73072i	−0.195122	+	0.337962i	0.751818	+	0.659370i	$0.229177\pi$
$830$		0			0
$831$	4.87539	+	8.44442i	0.169125	+	0.292934i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	37.8885	+	65.6249i	1.31119	+	2.27104i
$836$		0			0
$837$	−6.83282	+	11.8348i	−0.236177	+	0.409070i
$838$		0			0
$839$	21.5279			0.743224			0.371612	−	0.928388i	$-0.378805\pi$
$839$	21.5279			0.743224			0.371612	+	0.928388i	$0.378805\pi$
$840$		0			0
$841$	−9.00000			−0.310345
$842$		0			0
$843$	16.0689	−	27.8321i	0.553442	−	0.958589i
$844$		0			0
$845$	20.0902	+	34.7972i	0.691123	+	1.19706i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	3.81966	+	6.61585i	0.131090	+	0.227055i
$850$		0			0
$851$	−8.94427	+	15.4919i	−0.306606	+	0.531057i
$852$		0			0
$853$	13.7082			0.469360			0.234680	−	0.972073i	$-0.424596\pi$
$853$	13.7082			0.469360			0.234680	+	0.972073i	$0.424596\pi$
$854$		0			0
$855$	−5.88854			−0.201384
$856$		0			0
$857$	13.7639	−	23.8398i	0.470167	−	0.814353i	−0.529251	−	0.848465i	$-0.677527\pi$
$857$	13.7639	−	23.8398i	0.470167	−	0.814353i	0.999418	+	0.0341122i	$0.0108604\pi$
$858$		0			0
$859$	−16.9098	−	29.2887i	−0.576956	−	0.999317i	−0.995826	−	0.0912709i	$-0.970907\pi$
$859$	−16.9098	−	29.2887i	−0.576956	−	0.999317i	0.418870	−	0.908046i	$-0.362426\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−10.4721	−	18.1383i	−0.356476	−	0.617434i	0.630894	−	0.775869i	$-0.282688\pi$
$863$	−10.4721	−	18.1383i	−0.356476	−	0.617434i	−0.987369	+	0.158435i	$0.949355\pi$
$864$		0			0
$865$	−9.23607	+	15.9973i	−0.314036	+	0.543926i
$866$		0			0
$867$	−3.70820			−0.125937
$868$		0			0
$869$	−83.7771			−2.84194
$870$		0			0
$871$	1.52786	−	2.64634i	0.0517697	−	0.0896677i
$872$		0			0
$873$	9.18034	+	15.9008i	0.310707	+	0.538161i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−6.70820	−	11.6190i	−0.226520	−	0.392344i	0.730254	−	0.683175i	$-0.239402\pi$
$877$	−6.70820	−	11.6190i	−0.226520	−	0.392344i	−0.956774	+	0.290831i	$0.906068\pi$
$878$		0			0
$879$	−7.88854	+	13.6634i	−0.266074	+	0.460854i
$880$		0			0
$881$	24.8328			0.836639			0.418319	−	0.908300i	$-0.362619\pi$
$881$	24.8328			0.836639			0.418319	+	0.908300i	$0.362619\pi$
$882$		0			0
$883$	−23.0557			−0.775887			−0.387944	−	0.921683i	$-0.626814\pi$
$883$	−23.0557			−0.775887			−0.387944	+	0.921683i	$0.626814\pi$
$884$		0			0
$885$	18.4721	−	31.9947i	0.620934	−	1.07549i
$886$		0			0
$887$	−16.6525	−	28.8429i	−0.559135	−	0.968451i	−0.997569	−	0.0696873i	$-0.977800\pi$
$887$	−16.6525	−	28.8429i	−0.559135	−	0.968451i	0.438433	−	0.898764i	$-0.355533\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	7.81966	+	13.5440i	0.261968	+	0.453743i
$892$		0			0
$893$	6.47214	−	11.2101i	0.216582	−	0.375131i
$894$		0			0
$895$	22.8328			0.763217
$896$		0			0
$897$	3.77709			0.126113
$898$		0			0
$899$	5.52786	−	9.57454i	0.184365	−	0.319329i
$900$		0			0
$901$	22.3607	+	38.7298i	0.744942	+	1.29028i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	19.7082	+	34.1356i	0.655123	+	1.13471i
$906$		0			0
$907$	0.472136	−	0.817763i	0.0156770	−	0.0271534i	−0.858080	−	0.513515i	$-0.828343\pi$
$907$	0.472136	−	0.817763i	0.0156770	−	0.0271534i	0.873757	+	0.486362i	$0.161676\pi$
$908$		0			0
$909$	2.51471			0.0834076
$910$		0			0
$911$	34.8328			1.15406			0.577031	−	0.816722i	$-0.304211\pi$
$911$	34.8328			1.15406			0.577031	+	0.816722i	$0.304211\pi$
$912$		0			0
$913$	−29.8885	+	51.7685i	−0.989166	+	1.71329i
$914$		0			0
$915$	22.4721	+	38.9229i	0.742906	+	1.28675i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−17.8885	−	30.9839i	−0.590089	−	1.02206i	−0.994220	−	0.107362i	$-0.965759\pi$
$919$	−17.8885	−	30.9839i	−0.590089	−	1.02206i	0.404131	−	0.914701i	$-0.367574\pi$
$920$		0			0
$921$	−1.12461	+	1.94788i	−0.0370572	+	0.0641850i
$922$		0			0
$923$	3.77709			0.124324
$924$		0			0
$925$	−24.4721			−0.804639
$926$		0			0
$927$	4.06888	−	7.04751i	0.133640	−	0.231471i
$928$		0			0
$929$	23.6525	+	40.9673i	0.776013	+	1.34409i	0.934224	+	0.356688i	$0.116094\pi$
$929$	23.6525	+	40.9673i	0.776013	+	1.34409i	−0.158211	+	0.987405i	$0.550573\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−4.94427	−	8.56373i	−0.161868	−	0.280364i
$934$		0			0
$935$	−46.8328	+	81.1168i	−1.53160	+	2.65280i
$936$		0			0
$937$	−9.05573			−0.295838			−0.147919	−	0.988999i	$-0.547257\pi$
$937$	−9.05573			−0.295838			−0.147919	+	0.988999i	$0.547257\pi$
$938$		0			0
$939$	10.4721			0.341745
$940$		0			0
$941$	17.7984	−	30.8277i	0.580210	−	1.00495i	−0.415244	−	0.909710i	$-0.636304\pi$
$941$	17.7984	−	30.8277i	0.580210	−	1.00495i	0.995454	−	0.0952436i	$-0.0303630\pi$
$942$		0			0
$943$	−16.9443	−	29.3483i	−0.551781	−	0.955713i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−2.29180	−	3.96951i	−0.0744734	−	0.128992i	0.826384	−	0.563107i	$-0.190394\pi$
$947$	−2.29180	−	3.96951i	−0.0744734	−	0.128992i	−0.900857	+	0.434116i	$0.857061\pi$
$948$		0			0
$949$	1.12461	−	1.94788i	0.0365064	−	0.0632310i
$950$		0			0
$951$	−11.1935			−0.362974
$952$		0			0
$953$	51.8885			1.68083			0.840417	−	0.541940i	$-0.182310\pi$
$953$	51.8885			1.68083			0.840417	+	0.541940i	$0.182310\pi$
$954$		0			0
$955$	8.00000	−	13.8564i	0.258874	−	0.448383i
$956$		0			0
$957$	−17.8885	−	30.9839i	−0.578254	−	1.00157i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	12.4443	+	21.5541i	0.401428	+	0.695294i
$962$		0			0
$963$	−6.58359	+	11.4031i	−0.212153	+	0.367460i
$964$		0			0
$965$	1.52786			0.0491837
$966$		0			0
$967$	−29.8885			−0.961151			−0.480575	−	0.876953i	$-0.659572\pi$
$967$	−29.8885			−0.961151			−0.480575	+	0.876953i	$0.659572\pi$
$968$		0			0
$969$	3.41641	−	5.91739i	0.109751	−	0.190094i
$970$		0			0
$971$	11.3820	+	19.7141i	0.365265	+	0.632657i	0.988819	−	0.149123i	$-0.0476452\pi$
$971$	11.3820	+	19.7141i	0.365265	+	0.632657i	−0.623554	+	0.781780i	$0.714312\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	2.58359	+	4.47491i	0.0827412	+	0.143312i
$976$		0			0
$977$	6.41641	−	11.1135i	0.205279	−	0.355554i	−0.744943	−	0.667129i	$-0.767523\pi$
$977$	6.41641	−	11.1135i	0.205279	−	0.355554i	0.950222	+	0.311575i	$0.100856\pi$
$978$		0			0
$979$	−38.8328			−1.24110
$980$		0			0
$981$	−12.4721			−0.398205
$982$		0			0
$983$	−2.76393	+	4.78727i	−0.0881557	+	0.152690i	−0.906732	−	0.421708i	$-0.861431\pi$
$983$	−2.76393	+	4.78727i	−0.0881557	+	0.152690i	0.818576	+	0.574398i	$0.194764\pi$
$984$		0			0
$985$	−17.7082	−	30.6715i	−0.564230	−	0.977276i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−12.9443	−	22.4201i	−0.411604	−	0.712919i
$990$		0			0
$991$	−12.0000	+	20.7846i	−0.381193	+	0.660245i	−0.991233	−	0.132125i	$-0.957820\pi$
$991$	−12.0000	+	20.7846i	−0.381193	+	0.660245i	0.610040	+	0.792370i	$0.291153\pi$
$992$		0			0
$993$	27.7771			0.881479
$994$		0			0
$995$	−49.8885			−1.58157
$996$		0			0
$997$	−9.03444	+	15.6481i	−0.286124	+	0.495581i	−0.972881	−	0.231306i	$-0.925700\pi$
$997$	−9.03444	+	15.6481i	−0.286124	+	0.495581i	0.686757	+	0.726887i	$0.259033\pi$
$998$		0			0
$999$	12.3607	+	21.4093i	0.391075	+	0.677361i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1568.2.i.m.1537.2		4
4.3	odd	2		1568.2.i.v.1537.1		4
7.2	even	3	inner	1568.2.i.m.961.2		4
7.3	odd	6		1568.2.a.k.1.2		2
7.4	even	3		224.2.a.d.1.1	yes	2
7.5	odd	6		1568.2.i.w.961.1		4
7.6	odd	2		1568.2.i.w.1537.1		4
21.11	odd	6		2016.2.a.o.1.1		2
28.3	even	6		1568.2.a.v.1.1		2
28.11	odd	6		224.2.a.c.1.2	✓	2
28.19	even	6		1568.2.i.n.961.2		4
28.23	odd	6		1568.2.i.v.961.1		4
28.27	even	2		1568.2.i.n.1537.2		4
35.4	even	6		5600.2.a.z.1.2		2
56.3	even	6		3136.2.a.bf.1.2		2
56.11	odd	6		448.2.a.j.1.1		2
56.45	odd	6		3136.2.a.by.1.1		2
56.53	even	6		448.2.a.i.1.2		2
84.11	even	6		2016.2.a.r.1.1		2
112.11	odd	12		1792.2.b.k.897.2		4
112.53	even	12		1792.2.b.m.897.3		4
112.67	odd	12		1792.2.b.k.897.3		4
112.109	even	12		1792.2.b.m.897.2		4
140.39	odd	6		5600.2.a.bk.1.1		2
168.11	even	6		4032.2.a.bw.1.2		2
168.53	odd	6		4032.2.a.bv.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.a.c.1.2	✓	2	28.11	odd	6
224.2.a.d.1.1	yes	2	7.4	even	3
448.2.a.i.1.2		2	56.53	even	6
448.2.a.j.1.1		2	56.11	odd	6
1568.2.a.k.1.2		2	7.3	odd	6
1568.2.a.v.1.1		2	28.3	even	6
1568.2.i.m.961.2		4	7.2	even	3	inner
1568.2.i.m.1537.2		4	1.1	even	1	trivial
1568.2.i.n.961.2		4	28.19	even	6
1568.2.i.n.1537.2		4	28.27	even	2
1568.2.i.v.961.1		4	28.23	odd	6
1568.2.i.v.1537.1		4	4.3	odd	2
1568.2.i.w.961.1		4	7.5	odd	6
1568.2.i.w.1537.1		4	7.6	odd	2
1792.2.b.k.897.2		4	112.11	odd	12
1792.2.b.k.897.3		4	112.67	odd	12
1792.2.b.m.897.2		4	112.109	even	12
1792.2.b.m.897.3		4	112.53	even	12
2016.2.a.o.1.1		2	21.11	odd	6
2016.2.a.r.1.1		2	84.11	even	6
3136.2.a.bf.1.2		2	56.3	even	6
3136.2.a.by.1.1		2	56.45	odd	6
4032.2.a.bv.1.2		2	168.53	odd	6
4032.2.a.bw.1.2		2	168.11	even	6
5600.2.a.z.1.2		2	35.4	even	6
5600.2.a.bk.1.1		2	140.39	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:	\( N \)	\(=\)	\( 1568 = 2^{5} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1568.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.618034 - 1.07047i) q^{3} +(-1.61803 - 2.80252i) q^{5} +(0.736068 + 1.27491i) q^{9} +O(q^{10})\)	\(q+(0.618034 - 1.07047i) q^{3} +(-1.61803 - 2.80252i) q^{5} +(0.736068 + 1.27491i) q^{9} +(-3.23607 + 5.60503i) q^{11} +0.763932 q^{13} -4.00000 q^{15} +(-2.23607 + 3.87298i) q^{17} +(-0.618034 - 1.07047i) q^{19} +(2.00000 + 3.46410i) q^{23} +(-2.73607 + 4.73901i) q^{25} +5.52786 q^{27} -4.47214 q^{29} +(-1.23607 + 2.14093i) q^{31} +(4.00000 + 6.92820i) q^{33} +(2.23607 + 3.87298i) q^{37} +(0.472136 - 0.817763i) q^{39} -8.47214 q^{41} -6.47214 q^{43} +(2.38197 - 4.12569i) q^{45} +(5.23607 + 9.06914i) q^{47} +(2.76393 + 4.78727i) q^{51} +(5.00000 - 8.66025i) q^{53} +20.9443 q^{55} -1.52786 q^{57} +(-4.61803 + 7.99867i) q^{59} +(-5.61803 - 9.73072i) q^{61} +(-1.23607 - 2.14093i) q^{65} +(2.00000 - 3.46410i) q^{67} +4.94427 q^{69} +4.94427 q^{71} +(1.47214 - 2.54981i) q^{73} +(3.38197 + 5.85774i) q^{75} +(6.47214 + 11.2101i) q^{79} +(1.20820 - 2.09267i) q^{81} +9.23607 q^{83} +14.4721 q^{85} +(-2.76393 + 4.78727i) q^{87} +(3.00000 + 5.19615i) q^{89} +(1.52786 + 2.64634i) q^{93} +(-2.00000 + 3.46410i) q^{95} +12.4721 q^{97} -9.52786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{5} - 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 2 * q^5 - 6 * q^9	\( 4 q - 2 q^{3} - 2 q^{5} - 6 q^{9} - 4 q^{11} + 12 q^{13} - 16 q^{15} + 2 q^{19} + 8 q^{23} - 2 q^{25} + 40 q^{27} + 4 q^{31} + 16 q^{33} - 16 q^{39} - 16 q^{41} - 8 q^{43} + 14 q^{45} + 12 q^{47} + 20 q^{51} + 20 q^{53} + 48 q^{55} - 24 q^{57} - 14 q^{59} - 18 q^{61} + 4 q^{65} + 8 q^{67} - 16 q^{69} - 16 q^{71} - 12 q^{73} + 18 q^{75} + 8 q^{79} - 22 q^{81} + 28 q^{83} + 40 q^{85} - 20 q^{87} + 12 q^{89} + 24 q^{93} - 8 q^{95} + 32 q^{97} - 56 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^5 - 6 * q^9 - 4 * q^11 + 12 * q^13 - 16 * q^15 + 2 * q^19 + 8 * q^23 - 2 * q^25 + 40 * q^27 + 4 * q^31 + 16 * q^33 - 16 * q^39 - 16 * q^41 - 8 * q^43 + 14 * q^45 + 12 * q^47 + 20 * q^51 + 20 * q^53 + 48 * q^55 - 24 * q^57 - 14 * q^59 - 18 * q^61 + 4 * q^65 + 8 * q^67 - 16 * q^69 - 16 * q^71 - 12 * q^73 + 18 * q^75 + 8 * q^79 - 22 * q^81 + 28 * q^83 + 40 * q^85 - 20 * q^87 + 12 * q^89 + 24 * q^93 - 8 * q^95 + 32 * q^97 - 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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