LMFDB - Embedded newform 1064.2.q.n.457.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1064,2,Mod(305,1064)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1064, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))

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

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

chi := DirichletCharacter("1064.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1064 = 2^{3} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1064.q (of order $3$, degree $2$, 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:	$8.49608277506$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 15 x^{14} - 2 x^{13} + 159 x^{12} - 19 x^{11} + 839 x^{10} - 62 x^{9} + 3204 x^{8} + 8 x^{7} + \cdots + 256 $ x^16 + 15x^14 - 2x^13 + 159x^12 - 19x^11 + 839x^10 - 62x^9 + 3204x^8 + 8x^7 + 4560x^6 + 1376x^5 + 4688x^4 + 736x^3 + 1280x^2 - 128x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			457.1
Root			$-1.42832 - 2.47393i$ of defining polynomial
Character	$\chi$	$=$	1064.457
Dual form			1064.2.q.n.305.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.42832 - 2.47393i) q^{3} +(-0.413955 + 0.716991i) q^{5} +(0.222612 + 2.63637i) q^{7} +(-2.58022 + 4.46907i) q^{9} +O(q^{10})$	\(q+(-1.42832 - 2.47393i) q^{3} +(-0.413955 + 0.716991i) q^{5} +(0.222612 + 2.63637i) q^{7} +(-2.58022 + 4.46907i) q^{9} +(-2.85761 - 4.94952i) q^{11} -0.0340264 q^{13} +2.36505 q^{15} +(2.11767 + 3.66790i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(6.20423 - 4.31632i) q^{21} +(-2.44630 + 4.23711i) q^{23} +(2.15728 + 3.73652i) q^{25} +6.17162 q^{27} +9.29907 q^{29} +(1.26932 + 2.19853i) q^{31} +(-8.16318 + 14.1390i) q^{33} +(-1.98241 - 0.931727i) q^{35} +(-2.29292 + 3.97146i) q^{37} +(0.0486007 + 0.0841790i) q^{39} -2.00000 q^{41} +9.61156 q^{43} +(-2.13619 - 3.69999i) q^{45} +(5.66119 - 9.80547i) q^{47} +(-6.90089 + 1.17378i) q^{49} +(6.04943 - 10.4779i) q^{51} +(-1.71658 - 2.97321i) q^{53} +4.73169 q^{55} +2.85665 q^{57} +(3.67675 + 6.36832i) q^{59} +(-1.24625 + 2.15857i) q^{61} +(-12.3565 - 5.80754i) q^{63} +(0.0140854 - 0.0243966i) q^{65} +(3.49153 + 6.04751i) q^{67} +13.9764 q^{69} +12.0575 q^{71} +(-0.375646 - 0.650638i) q^{73} +(6.16260 - 10.6739i) q^{75} +(12.4126 - 8.63554i) q^{77} +(5.98262 - 10.3622i) q^{79} +(-1.07442 - 1.86095i) q^{81} -13.7727 q^{83} -3.50647 q^{85} +(-13.2821 - 23.0053i) q^{87} +(-2.69864 + 4.67419i) q^{89} +(-0.00757470 - 0.0897062i) q^{91} +(3.62601 - 6.28044i) q^{93} +(-0.413955 - 0.716991i) q^{95} +8.49448 q^{97} +29.4930 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{5} + 5 q^{7} - 6 q^{9}+O(q^{10}) $ 16 * q + q^5 + 5 * q^7 - 6 * q^9	$ 16 q + q^{5} + 5 q^{7} - 6 q^{9} - 9 q^{11} + 16 q^{15} - 4 q^{17} - 8 q^{19} - 2 q^{21} - 25 q^{23} - 15 q^{25} + 6 q^{27} + 12 q^{29} - 8 q^{33} + 5 q^{35} - 13 q^{37} + 11 q^{39} - 32 q^{41} + 34 q^{43} - 17 q^{45} + 24 q^{47} - 13 q^{49} - 5 q^{51} - 2 q^{53} + 10 q^{55} - 2 q^{59} + 13 q^{61} - 52 q^{63} + 26 q^{65} - 2 q^{67} - 22 q^{69} + 20 q^{71} - 5 q^{73} + 20 q^{75} + 28 q^{77} - 16 q^{79} + 12 q^{81} - 86 q^{83} + 48 q^{85} - 20 q^{87} - 8 q^{89} - 34 q^{91} - 2 q^{93} + q^{95} - 24 q^{97} + 74 q^{99}+O(q^{100}) $ 16 * q + q^5 + 5 * q^7 - 6 * q^9 - 9 * q^11 + 16 * q^15 - 4 * q^17 - 8 * q^19 - 2 * q^21 - 25 * q^23 - 15 * q^25 + 6 * q^27 + 12 * q^29 - 8 * q^33 + 5 * q^35 - 13 * q^37 + 11 * q^39 - 32 * q^41 + 34 * q^43 - 17 * q^45 + 24 * q^47 - 13 * q^49 - 5 * q^51 - 2 * q^53 + 10 * q^55 - 2 * q^59 + 13 * q^61 - 52 * q^63 + 26 * q^65 - 2 * q^67 - 22 * q^69 + 20 * q^71 - 5 * q^73 + 20 * q^75 + 28 * q^77 - 16 * q^79 + 12 * q^81 - 86 * q^83 + 48 * q^85 - 20 * q^87 - 8 * q^89 - 34 * q^91 - 2 * q^93 + q^95 - 24 * q^97 + 74 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times$.

$n$	$533$	$799$	$913$	$1009$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.42832	−	2.47393i	−0.824643	−	1.42832i	−0.902191	−	0.431336i	$-0.858042\pi$
$3$	−1.42832	−	2.47393i	−0.824643	−	1.42832i	0.0775480	−	0.996989i	$-0.475291\pi$
$4$		0			0
$5$	−0.413955	+	0.716991i	−0.185126	+	0.320648i	−0.943619	−	0.331033i	$-0.892603\pi$
$5$	−0.413955	+	0.716991i	−0.185126	+	0.320648i	0.758493	+	0.651681i	$0.225936\pi$
$6$		0			0
$7$	0.222612	+	2.63637i	0.0841396	+	0.996454i
$7$	0.222612	+	2.63637i	0.0841396	+	0.996454i
$8$		0			0
$9$	−2.58022	+	4.46907i	−0.860074	+	1.48969i
$10$		0			0
$11$	−2.85761	−	4.94952i	−0.861601	−	1.49234i	−0.870383	−	0.492376i	$-0.836129\pi$
$11$	−2.85761	−	4.94952i	−0.861601	−	1.49234i	0.00878126	−	0.999961i	$-0.497205\pi$
$12$		0			0
$13$	−0.0340264			−0.00943723			−0.00471861	−	0.999989i	$-0.501502\pi$
$13$	−0.0340264			−0.00943723			−0.00471861	+	0.999989i	$0.501502\pi$
$14$		0			0
$15$	2.36505			0.610653
$16$		0			0
$17$	2.11767	+	3.66790i	0.513609	+	0.889597i	0.999875	+	0.0157865i	$0.00502522\pi$
$17$	2.11767	+	3.66790i	0.513609	+	0.889597i	−0.486266	+	0.873811i	$0.661641\pi$
$18$		0			0
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$20$		0			0
$21$	6.20423	−	4.31632i	1.35387	−	0.941898i
$22$		0			0
$23$	−2.44630	+	4.23711i	−0.510088	+	0.883499i	0.489843	+	0.871810i	$0.337054\pi$
$23$	−2.44630	+	4.23711i	−0.510088	+	0.883499i	−0.999932	+	0.0116884i	$0.996279\pi$
$24$		0			0
$25$	2.15728	+	3.73652i	0.431456	+	0.747305i
$26$		0			0
$27$	6.17162			1.18773
$28$		0			0
$29$	9.29907			1.72679			0.863397	−	0.504525i	$-0.168332\pi$
$29$	9.29907			1.72679			0.863397	+	0.504525i	$0.168332\pi$
$30$		0			0
$31$	1.26932	+	2.19853i	0.227977	+	0.394868i	0.957209	−	0.289399i	$-0.0934555\pi$
$31$	1.26932	+	2.19853i	0.227977	+	0.394868i	−0.729231	+	0.684267i	$0.760122\pi$
$32$		0			0
$33$	−8.16318	+	14.1390i	−1.42103	+	2.46129i
$34$		0			0
$35$	−1.98241	−	0.931727i	−0.335088	−	0.157491i
$36$		0			0
$37$	−2.29292	+	3.97146i	−0.376954	+	0.652904i	−0.990617	−	0.136664i	$-0.956362\pi$
$37$	−2.29292	+	3.97146i	−0.376954	+	0.652904i	0.613663	+	0.789568i	$0.289695\pi$
$38$		0			0
$39$	0.0486007	+	0.0841790i	0.00778235	+	0.0134794i
$40$		0			0
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		0			0
$43$	9.61156			1.46575			0.732875	−	0.680364i	$-0.238178\pi$
$43$	9.61156			1.46575			0.732875	+	0.680364i	$0.238178\pi$
$44$		0			0
$45$	−2.13619	−	3.69999i	−0.318445	−	0.551562i
$46$		0			0
$47$	5.66119	−	9.80547i	0.825769	−	1.43027i	−0.0755607	−	0.997141i	$-0.524075\pi$
$47$	5.66119	−	9.80547i	0.825769	−	1.43027i	0.901330	−	0.433133i	$-0.142592\pi$
$48$		0			0
$49$	−6.90089	+	1.17378i	−0.985841	+	0.167682i
$50$		0			0
$51$	6.04943	−	10.4779i	0.847089	−	1.46720i
$52$		0			0
$53$	−1.71658	−	2.97321i	−0.235791	−	0.408401i	0.723712	−	0.690103i	$-0.242435\pi$
$53$	−1.71658	−	2.97321i	−0.235791	−	0.408401i	−0.959502	+	0.281701i	$0.909101\pi$
$54$		0			0
$55$	4.73169			0.638020
$56$		0			0
$57$	2.85665			0.378372
$58$		0			0
$59$	3.67675	+	6.36832i	0.478673	+	0.829085i	0.999701	−	0.0244542i	$-0.00778478\pi$
$59$	3.67675	+	6.36832i	0.478673	+	0.829085i	−0.521028	+	0.853539i	$0.674451\pi$
$60$		0			0
$61$	−1.24625	+	2.15857i	−0.159566	+	0.276376i	−0.934712	−	0.355406i	$-0.884343\pi$
$61$	−1.24625	+	2.15857i	−0.159566	+	0.276376i	0.775146	+	0.631782i	$0.217676\pi$
$62$		0			0
$63$	−12.3565	−	5.80754i	−1.55678	−	0.731682i
$64$		0			0
$65$	0.0140854	−	0.0243966i	0.00174708	−	0.00302603i
$66$		0			0
$67$	3.49153	+	6.04751i	0.426559	+	0.738821i	0.996565	−	0.0828194i	$-0.0263925\pi$
$67$	3.49153	+	6.04751i	0.426559	+	0.738821i	−0.570006	+	0.821641i	$0.693059\pi$
$68$		0			0
$69$	13.9764			1.68256
$70$		0			0
$71$	12.0575			1.43097			0.715484	−	0.698630i	$-0.246206\pi$
$71$	12.0575			1.43097			0.715484	+	0.698630i	$0.246206\pi$
$72$		0			0
$73$	−0.375646	−	0.650638i	−0.0439660	−	0.0761514i	0.843205	−	0.537592i	$-0.180666\pi$
$73$	−0.375646	−	0.650638i	−0.0439660	−	0.0761514i	−0.887171	+	0.461441i	$0.847333\pi$
$74$		0			0
$75$	6.16260	−	10.6739i	0.711595	−	1.23252i
$76$		0			0
$77$	12.4126	−	8.63554i	1.41455	−	0.984111i
$78$		0			0
$79$	5.98262	−	10.3622i	0.673097	−	1.16584i	−0.303924	−	0.952696i	$-0.598297\pi$
$79$	5.98262	−	10.3622i	0.673097	−	1.16584i	0.977021	−	0.213143i	$-0.0683699\pi$
$80$		0			0
$81$	−1.07442	−	1.86095i	−0.119380	−	0.206772i
$82$		0			0
$83$	−13.7727			−1.51175			−0.755875	−	0.654716i	$-0.772788\pi$
$83$	−13.7727			−1.51175			−0.755875	+	0.654716i	$0.772788\pi$
$84$		0			0
$85$	−3.50647			−0.380330
$86$		0			0
$87$	−13.2821	−	23.0053i	−1.42399	−	2.46642i
$88$		0			0
$89$	−2.69864	+	4.67419i	−0.286056	+	0.495463i	−0.972865	−	0.231375i	$-0.925678\pi$
$89$	−2.69864	+	4.67419i	−0.286056	+	0.495463i	0.686809	+	0.726838i	$0.259011\pi$
$90$		0			0
$91$	−0.00757470	−	0.0897062i	−0.000794044	−	0.00940376i
$92$		0			0
$93$	3.62601	−	6.28044i	0.376000	−	0.651251i
$94$		0			0
$95$	−0.413955	−	0.716991i	−0.0424709	−	0.0735618i
$96$		0			0
$97$	8.49448			0.862484			0.431242	−	0.902236i	$-0.358076\pi$
$97$	8.49448			0.862484			0.431242	+	0.902236i	$0.358076\pi$
$98$		0			0
$99$	29.4930			2.96416
$100$		0			0
$101$	−6.19426	−	10.7288i	−0.616351	−	1.06755i	−0.990146	−	0.140040i	$-0.955277\pi$
$101$	−6.19426	−	10.7288i	−0.616351	−	1.06755i	0.373794	−	0.927512i	$-0.378057\pi$
$102$		0			0
$103$	−7.11356	+	12.3211i	−0.700920	+	1.21403i	0.267224	+	0.963635i	$0.413894\pi$
$103$	−7.11356	+	12.3211i	−0.700920	+	1.21403i	−0.968144	+	0.250395i	$0.919440\pi$
$104$		0			0
$105$	0.526489	+	6.23514i	0.0513801	+	0.608488i
$106$		0			0
$107$	0.204199	−	0.353683i	0.0197407	−	0.0341918i	−0.855986	−	0.516998i	$-0.827049\pi$
$107$	0.204199	−	0.353683i	0.0197407	−	0.0341918i	0.875727	+	0.482807i	$0.160383\pi$
$108$		0			0
$109$	8.14715	+	14.1113i	0.780355	+	1.35161i	0.931735	+	0.363139i	$0.118295\pi$
$109$	8.14715	+	14.1113i	0.780355	+	1.35161i	−0.151380	+	0.988476i	$0.548372\pi$
$110$		0			0
$111$	13.1002			1.24341
$112$		0			0
$113$	13.9404			1.31141			0.655704	−	0.755018i	$-0.272372\pi$
$113$	13.9404			1.31141			0.655704	+	0.755018i	$0.272372\pi$
$114$		0			0
$115$	−2.02531	−	3.50795i	−0.188862	−	0.327118i
$116$		0			0
$117$	0.0877956	−	0.152067i	0.00811671	−	0.0140586i
$118$		0			0
$119$	−9.19853	+	6.39947i	−0.843228	+	0.586638i
$120$		0			0
$121$	−10.8319	+	18.7613i	−0.984714	+	1.70557i
$122$		0			0
$123$	2.85665	+	4.94786i	0.257575	+	0.446134i
$124$		0			0
$125$	−7.71162			−0.689749
$126$		0			0
$127$	0.718299			0.0637387			0.0318694	−	0.999492i	$-0.489854\pi$
$127$	0.718299			0.0637387			0.0318694	+	0.999492i	$0.489854\pi$
$128$		0			0
$129$	−13.7284	−	23.7783i	−1.20872	−	2.09357i
$130$		0			0
$131$	−7.31225	+	12.6652i	−0.638874	+	1.10656i	0.346806	+	0.937937i	$0.387266\pi$
$131$	−7.31225	+	12.6652i	−0.638874	+	1.10656i	−0.985680	+	0.168625i	$0.946067\pi$
$132$		0			0
$133$	−2.39447	−	1.12540i	−0.207627	−	0.0975843i
$134$		0			0
$135$	−2.55478	+	4.42500i	−0.219880	+	0.380843i
$136$		0			0
$137$	8.45731	+	14.6485i	0.722557	+	1.25150i	0.959972	+	0.280096i	$0.0903665\pi$
$137$	8.45731	+	14.6485i	0.722557	+	1.25150i	−0.237415	+	0.971408i	$0.576300\pi$
$138$		0			0
$139$	−13.3401			−1.13149			−0.565744	−	0.824581i	$-0.691411\pi$
$139$	−13.3401			−1.13149			−0.565744	+	0.824581i	$0.691411\pi$
$140$		0			0
$141$	−32.3441			−2.72386
$142$		0			0
$143$	0.0972342	+	0.168414i	0.00813113	+	0.0140835i
$144$		0			0
$145$	−3.84940	+	6.66735i	−0.319675	+	0.553694i
$146$		0			0
$147$	12.7605	+	15.3958i	1.05247	+	1.26982i
$148$		0			0
$149$	5.75304	−	9.96456i	0.471307	−	0.816328i	−0.528154	−	0.849149i	$-0.677116\pi$
$149$	5.75304	−	9.96456i	0.471307	−	0.816328i	0.999461	+	0.0328203i	$0.0104489\pi$
$150$		0			0
$151$	2.62895	+	4.55347i	0.213941	+	0.370556i	0.952944	−	0.303145i	$-0.0980367\pi$
$151$	2.62895	+	4.55347i	0.213941	+	0.370556i	−0.739004	+	0.673702i	$0.764703\pi$
$152$		0			0
$153$	−21.8562			−1.76697
$154$		0			0
$155$	−2.10177			−0.168818
$156$		0			0
$157$	0.683557	+	1.18395i	0.0545538	+	0.0944899i	0.892013	−	0.452010i	$-0.149293\pi$
$157$	0.683557	+	1.18395i	0.0545538	+	0.0944899i	−0.837459	+	0.546500i	$0.815960\pi$
$158$		0			0
$159$	−4.90367	+	8.49340i	−0.388886	+	0.673571i
$160$		0			0
$161$	−11.7152	−	5.50611i	−0.923284	−	0.433942i
$162$		0			0
$163$	−5.10493	+	8.84200i	−0.399849	+	0.692559i	−0.993707	−	0.112011i	$-0.964271\pi$
$163$	−5.10493	+	8.84200i	−0.399849	+	0.692559i	0.593858	+	0.804570i	$0.297604\pi$
$164$		0			0
$165$	−6.75838	−	11.7059i	−0.526139	−	0.911300i
$166$		0			0
$167$	4.13699			0.320130			0.160065	−	0.987106i	$-0.448830\pi$
$167$	4.13699			0.320130			0.160065	+	0.987106i	$0.448830\pi$
$168$		0			0
$169$	−12.9988			−0.999911
$170$		0			0
$171$	−2.58022	−	4.46907i	−0.197314	−	0.341759i
$172$		0			0
$173$	−9.14211	+	15.8346i	−0.695062	+	1.20388i	0.275098	+	0.961416i	$0.411290\pi$
$173$	−9.14211	+	15.8346i	−0.695062	+	1.20388i	−0.970160	+	0.242466i	$0.922044\pi$
$174$		0			0
$175$	−9.37062	+	6.51919i	−0.708352	+	0.492804i
$176$		0			0
$177$	10.5032	−	18.1921i	0.789468	−	1.36740i
$178$		0			0
$179$	−0.609217	−	1.05519i	−0.0455350	−	0.0788690i	0.842360	−	0.538916i	$-0.181166\pi$
$179$	−0.609217	−	1.05519i	−0.0455350	−	0.0788690i	−0.887895	+	0.460047i	$0.847833\pi$
$180$		0			0
$181$	−14.0374			−1.04339			−0.521695	−	0.853132i	$-0.674700\pi$
$181$	−14.0374			−1.04339			−0.521695	+	0.853132i	$0.674700\pi$
$182$		0			0
$183$	7.12019			0.526340
$184$		0			0
$185$	−1.89834	−	3.28801i	−0.139568	−	0.241740i
$186$		0			0
$187$	12.1029	−	20.9629i	0.885053	−	1.53296i
$188$		0			0
$189$	1.37388	+	16.2707i	0.0999351	+	1.18352i
$190$		0			0
$191$	−4.06906	+	7.04782i	−0.294427	+	0.509963i	−0.974851	−	0.222856i	$-0.928462\pi$
$191$	−4.06906	+	7.04782i	−0.294427	+	0.509963i	0.680424	+	0.732818i	$0.261795\pi$
$192$		0			0
$193$	3.68771	+	6.38730i	0.265447	+	0.459768i	0.967681	−	0.252179i	$-0.0811471\pi$
$193$	3.68771	+	6.38730i	0.265447	+	0.459768i	−0.702233	+	0.711947i	$0.747814\pi$
$194$		0			0
$195$	−0.0804741			−0.00576287
$196$		0			0
$197$	27.6022			1.96657			0.983287	−	0.182063i	$-0.0582774\pi$
$197$	27.6022			1.96657			0.983287	+	0.182063i	$0.0582774\pi$
$198$		0			0
$199$	−1.32357	−	2.29250i	−0.0938257	−	0.162511i	0.815292	−	0.579050i	$-0.196576\pi$
$199$	−1.32357	−	2.29250i	−0.0938257	−	0.162511i	−0.909118	+	0.416539i	$0.863243\pi$
$200$		0			0
$201$	9.97408	−	17.2756i	0.703517	−	1.21853i
$202$		0			0
$203$	2.07009	+	24.5158i	0.145292	+	1.72067i
$204$		0			0
$205$	0.827910	−	1.43398i	0.0578238	−	0.100154i
$206$		0			0
$207$	−12.6240	−	21.8654i	−0.877427	−	1.51975i
$208$		0			0
$209$	5.71522			0.395330
$210$		0			0
$211$	−12.7616			−0.878545			−0.439272	−	0.898354i	$-0.644764\pi$
$211$	−12.7616			−0.878545			−0.439272	+	0.898354i	$0.644764\pi$
$212$		0			0
$213$	−17.2221	−	29.8295i	−1.18004	−	2.04389i
$214$		0			0
$215$	−3.97875	+	6.89141i	−0.271349	+	0.469990i
$216$		0			0
$217$	−5.51358	+	3.83583i	−0.374286	+	0.260393i
$218$		0			0
$219$	−1.07309	+	1.85864i	−0.0725126	+	0.125595i
$220$		0			0
$221$	−0.0720565	−	0.124806i	−0.00484705	−	0.00839533i
$222$		0			0
$223$	−7.90397			−0.529289			−0.264645	−	0.964346i	$-0.585255\pi$
$223$	−7.90397			−0.529289			−0.264645	+	0.964346i	$0.585255\pi$
$224$		0			0
$225$	−22.2651			−1.48434
$226$		0			0
$227$	13.9074	+	24.0883i	0.923064	+	1.59879i	0.794646	+	0.607073i	$0.207657\pi$
$227$	13.9074	+	24.0883i	0.923064	+	1.59879i	0.128418	+	0.991720i	$0.459010\pi$
$228$		0			0
$229$	5.29342	−	9.16848i	0.349799	−	0.605870i	−0.636414	−	0.771347i	$-0.719583\pi$
$229$	5.29342	−	9.16848i	0.349799	−	0.605870i	0.986214	+	0.165477i	$0.0529164\pi$
$230$		0			0
$231$	−39.0930	−	18.3736i	−2.57213	−	1.20890i
$232$		0			0
$233$	−2.59851	+	4.50076i	−0.170234	+	0.294854i	−0.938502	−	0.345275i	$-0.887786\pi$
$233$	−2.59851	+	4.50076i	−0.170234	+	0.294854i	0.768267	+	0.640129i	$0.221119\pi$
$234$		0			0
$235$	4.68696	+	8.11805i	0.305743	+	0.529563i
$236$		0			0
$237$	−34.1805			−2.22026
$238$		0			0
$239$	3.63655			0.235229			0.117614	−	0.993059i	$-0.462475\pi$
$239$	3.63655			0.235229			0.117614	+	0.993059i	$0.462475\pi$
$240$		0			0
$241$	−3.83554	−	6.64335i	−0.247069	−	0.427936i	0.715642	−	0.698467i	$-0.246134\pi$
$241$	−3.83554	−	6.64335i	−0.247069	−	0.427936i	−0.962711	+	0.270531i	$0.912801\pi$
$242$		0			0
$243$	6.18820	−	10.7183i	0.396973	−	0.687578i
$244$		0			0
$245$	2.01507	−	5.43377i	0.128738	−	0.347151i
$246$		0			0
$247$	0.0170132	−	0.0294677i	0.00108252	−	0.00187499i
$248$		0			0
$249$	19.6719	+	34.0727i	1.24665	+	2.15927i
$250$		0			0
$251$	16.3670			1.03308			0.516539	−	0.856264i	$-0.327220\pi$
$251$	16.3670			1.03308			0.516539	+	0.856264i	$0.327220\pi$
$252$		0			0
$253$	27.9622			1.75797
$254$		0			0
$255$	5.00838	+	8.67477i	0.313637	+	0.543235i
$256$		0			0
$257$	7.95880	−	13.7851i	0.496457	−	0.859888i	−0.503535	−	0.863975i	$-0.667968\pi$
$257$	7.95880	−	13.7851i	0.496457	−	0.859888i	0.999992	+	0.00408679i	$0.00130087\pi$
$258$		0			0
$259$	−10.9807	−	5.16090i	−0.682306	−	0.320683i
$260$		0			0
$261$	−23.9937	+	41.5582i	−1.48517	+	2.57239i
$262$		0			0
$263$	−5.88311	−	10.1899i	−0.362768	−	0.628333i	0.625647	−	0.780106i	$-0.284835\pi$
$263$	−5.88311	−	10.1899i	−0.362768	−	0.628333i	−0.988415	+	0.151773i	$0.951502\pi$
$264$		0			0
$265$	2.84235			0.174604
$266$		0			0
$267$	15.4182			0.943576
$268$		0			0
$269$	4.98404	+	8.63261i	0.303882	+	0.526340i	0.977012	−	0.213185i	$-0.0683837\pi$
$269$	4.98404	+	8.63261i	0.303882	+	0.526340i	−0.673129	+	0.739525i	$0.735050\pi$
$270$		0			0
$271$	−6.96975	+	12.0720i	−0.423382	+	0.733320i	−0.996268	−	0.0863157i	$-0.972491\pi$
$271$	−6.96975	+	12.0720i	−0.423382	+	0.733320i	0.572886	+	0.819635i	$0.305824\pi$
$272$		0			0
$273$	−0.211108	+	0.146869i	−0.0127768	+	0.00888890i
$274$		0			0
$275$	12.3293	−	21.3550i	0.743487	−	1.28776i
$276$		0			0
$277$	2.47289	+	4.28317i	0.148582	+	0.257351i	0.930703	−	0.365775i	$-0.119196\pi$
$277$	2.47289	+	4.28317i	0.148582	+	0.257351i	−0.782122	+	0.623126i	$0.785863\pi$
$278$		0			0
$279$	−13.1005			−0.784309
$280$		0			0
$281$	−10.0464			−0.599318			−0.299659	−	0.954046i	$-0.596873\pi$
$281$	−10.0464			−0.599318			−0.299659	+	0.954046i	$0.596873\pi$
$282$		0			0
$283$	9.94275	+	17.2214i	0.591035	+	1.02370i	0.994093	+	0.108529i	$0.0346139\pi$
$283$	9.94275	+	17.2214i	0.591035	+	1.02370i	−0.403058	+	0.915174i	$0.632053\pi$
$284$		0			0
$285$	−1.18252	+	2.04819i	−0.0700467	+	0.121324i
$286$		0			0
$287$	−0.445225	−	5.27274i	−0.0262808	−	0.311240i
$288$		0			0
$289$	−0.469011	+	0.812351i	−0.0275889	+	0.0477853i
$290$		0			0
$291$	−12.1329	−	21.0148i	−0.711242	−	1.23191i
$292$		0			0
$293$	6.94575			0.405775			0.202888	−	0.979202i	$-0.434967\pi$
$293$	6.94575			0.405775			0.202888	+	0.979202i	$0.434967\pi$
$294$		0			0
$295$	−6.08804			−0.354460
$296$		0			0
$297$	−17.6361	−	30.5466i	−1.02335	−	1.77249i
$298$		0			0
$299$	0.0832387	−	0.144174i	0.00481382	−	0.00833778i
$300$		0			0
$301$	2.13965	+	25.3396i	0.123328	+	1.46055i
$302$		0			0
$303$	−17.6948	+	30.6483i	−1.01654	+	1.76070i
$304$		0			0
$305$	−1.03178	−	1.78710i	−0.0590797	−	0.102329i
$306$		0			0
$307$	−20.9772			−1.19723			−0.598617	−	0.801035i	$-0.704283\pi$
$307$	−20.9772			−1.19723			−0.598617	+	0.801035i	$0.704283\pi$
$308$		0			0
$309$	40.6419			2.31204
$310$		0			0
$311$	−3.73021	−	6.46092i	−0.211521	−	0.366365i	0.740670	−	0.671869i	$-0.234508\pi$
$311$	−3.73021	−	6.46092i	−0.211521	−	0.366365i	−0.952191	+	0.305504i	$0.901175\pi$
$312$		0			0
$313$	3.61383	−	6.25933i	0.204266	−	0.353798i	−0.745633	−	0.666357i	$-0.767853\pi$
$313$	3.61383	−	6.25933i	0.204266	−	0.353798i	0.949898	+	0.312559i	$0.101186\pi$
$314$		0			0
$315$	9.27900	−	6.45545i	0.522813	−	0.363724i
$316$		0			0
$317$	2.87984	−	4.98802i	0.161748	−	0.280155i	−0.773748	−	0.633494i	$-0.781620\pi$
$317$	2.87984	−	4.98802i	0.161748	−	0.280155i	0.935496	+	0.353338i	$0.114954\pi$
$318$		0			0
$319$	−26.5731	−	46.0260i	−1.48781	−	2.57696i
$320$		0			0
$321$	−1.16665			−0.0651160
$322$		0			0
$323$	−4.23533			−0.235660
$324$		0			0
$325$	−0.0734046	−	0.127140i	−0.00407175	−	0.00705248i
$326$		0			0
$327$	23.2735	−	40.3110i	1.28703	−	2.22920i
$328$		0			0
$329$	27.1111	+	12.7422i	1.49468	+	0.702498i
$330$		0			0
$331$	−6.04262	+	10.4661i	−0.332133	+	0.575270i	−0.982930	−	0.183981i	$-0.941101\pi$
$331$	−6.04262	+	10.4661i	−0.332133	+	0.575270i	0.650797	+	0.759252i	$0.274435\pi$
$332$		0			0
$333$	−11.8325	−	20.4945i	−0.648417	−	1.12309i
$334$		0			0
$335$	−5.78135			−0.315869
$336$		0			0
$337$	−12.3876			−0.674794			−0.337397	−	0.941363i	$-0.609546\pi$
$337$	−12.3876			−0.674794			−0.337397	+	0.941363i	$0.609546\pi$
$338$		0			0
$339$	−19.9115	−	34.4877i	−1.08144	−	1.87311i
$340$		0			0
$341$	7.25446	−	12.5651i	0.392851	−	0.680438i
$342$		0			0
$343$	−4.63073	−	17.9320i	−0.250036	−	0.968237i
$344$		0			0
$345$	−5.78561	+	10.0210i	−0.311487	+	0.539511i
$346$		0			0
$347$	−10.7841	−	18.6786i	−0.578922	−	1.00272i	−0.995603	−	0.0936694i	$-0.970140\pi$
$347$	−10.7841	−	18.6786i	−0.578922	−	1.00272i	0.416682	−	0.909053i	$-0.363193\pi$
$348$		0			0
$349$	28.6816			1.53529			0.767645	−	0.640875i	$-0.221428\pi$
$349$	28.6816			1.53529			0.767645	+	0.640875i	$0.221428\pi$
$350$		0			0
$351$	−0.209998			−0.0112089
$352$		0			0
$353$	−7.43824	−	12.8834i	−0.395898	−	0.685715i	0.597318	−	0.802005i	$-0.296233\pi$
$353$	−7.43824	−	12.8834i	−0.395898	−	0.685715i	−0.993215	+	0.116290i	$0.962900\pi$
$354$		0			0
$355$	−4.99128	+	8.64515i	−0.264910	+	0.458837i
$356$		0			0
$357$	28.9703	+	13.6160i	1.53327	+	0.720635i
$358$		0			0
$359$	−2.04354	+	3.53952i	−0.107854	+	0.186809i	−0.914901	−	0.403679i	$-0.867731\pi$
$359$	−2.04354	+	3.53952i	−0.107854	+	0.186809i	0.807047	+	0.590488i	$0.201065\pi$
$360$		0			0
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$		0			0
$363$	61.8856			3.24815
$364$		0			0
$365$	0.622002			0.0325571
$366$		0			0
$367$	10.2759	+	17.7984i	0.536399	+	0.929071i	0.999094	+	0.0425533i	$0.0135492\pi$
$367$	10.2759	+	17.7984i	0.536399	+	0.929071i	−0.462695	+	0.886518i	$0.653117\pi$
$368$		0			0
$369$	5.16044	−	8.93815i	0.268642	−	0.465301i
$370$		0			0
$371$	7.45634	−	5.18741i	0.387114	−	0.269317i
$372$		0			0
$373$	4.20276	−	7.27939i	0.217611	−	0.376913i	−0.736466	−	0.676474i	$-0.763507\pi$
$373$	4.20276	−	7.27939i	0.217611	−	0.376913i	0.954077	+	0.299561i	$0.0968404\pi$
$374$		0			0
$375$	11.0147	+	19.0780i	0.568797	+	0.985185i
$376$		0			0
$377$	−0.316414			−0.0162962
$378$		0			0
$379$	−21.0086			−1.07914			−0.539570	−	0.841941i	$-0.681413\pi$
$379$	−21.0086			−1.07914			−0.539570	+	0.841941i	$0.681413\pi$
$380$		0			0
$381$	−1.02596	−	1.77702i	−0.0525617	−	0.0910396i
$382$		0			0
$383$	−5.30716	+	9.19227i	−0.271183	+	0.469703i	−0.969165	−	0.246412i	$-0.920748\pi$
$383$	−5.30716	+	9.19227i	−0.271183	+	0.469703i	0.697982	+	0.716115i	$0.254082\pi$
$384$		0			0
$385$	1.05333	+	12.4745i	0.0536828	+	0.635758i
$386$		0			0
$387$	−24.7999	+	42.9548i	−1.26065	+	2.18351i
$388$		0			0
$389$	−17.0131	−	29.4675i	−0.862598	−	1.49406i	−0.869413	−	0.494087i	$-0.835503\pi$
$389$	−17.0131	−	29.4675i	−0.862598	−	1.49406i	0.00681469	−	0.999977i	$-0.497831\pi$
$390$		0			0
$391$	−20.7218			−1.04794
$392$		0			0
$393$	41.7770			2.10737
$394$		0			0
$395$	4.95307	+	8.57897i	0.249216	+	0.431655i
$396$		0			0
$397$	−0.0203509	+	0.0352488i	−0.00102138	+	0.00176909i	−0.866536	−	0.499115i	$-0.833658\pi$
$397$	−0.0203509	+	0.0352488i	−0.00102138	+	0.00176909i	0.865514	+	0.500884i	$0.166992\pi$
$398$		0			0
$399$	0.635926	+	7.53118i	0.0318361	+	0.377031i
$400$		0			0
$401$	12.9792	−	22.4806i	0.648149	−	1.12263i	−0.335415	−	0.942070i	$-0.608877\pi$
$401$	12.9792	−	22.4806i	0.648149	−	1.12263i	0.983565	−	0.180557i	$-0.0577900\pi$
$402$		0			0
$403$	−0.0431905	−	0.0748082i	−0.00215147	−	0.00372646i
$404$		0			0
$405$	1.77904			0.0884013
$406$		0			0
$407$	26.2091			1.29914
$408$		0			0
$409$	−9.43289	−	16.3382i	−0.466426	−	0.807874i	0.532838	−	0.846217i	$-0.321125\pi$
$409$	−9.43289	−	16.3382i	−0.466426	−	0.807874i	−0.999265	+	0.0383432i	$0.987792\pi$
$410$		0			0
$411$	24.1596	−	41.8456i	1.19170	−	2.06409i
$412$		0			0
$413$	−15.9708	+	11.1109i	−0.785870	+	0.546734i
$414$		0			0
$415$	5.70128	−	9.87490i	0.279865	−	0.484740i
$416$		0			0
$417$	19.0539	+	33.0024i	0.933075	+	1.61613i
$418$		0			0
$419$	−31.3570			−1.53189			−0.765944	−	0.642907i	$-0.777728\pi$
$419$	−31.3570			−1.53189			−0.765944	+	0.642907i	$0.777728\pi$
$420$		0			0
$421$	9.59485			0.467624			0.233812	−	0.972282i	$-0.424880\pi$
$421$	9.59485			0.467624			0.233812	+	0.972282i	$0.424880\pi$
$422$		0			0
$423$	29.2142	+	50.6005i	1.42044	+	2.46028i
$424$		0			0
$425$	−9.13680	+	15.8254i	−0.443200	+	0.767645i
$426$		0			0
$427$	−5.96821	−	2.80505i	−0.288822	−	0.135746i
$428$		0			0
$429$	0.277764	−	0.481101i	0.0134106	−	0.0232278i
$430$		0			0
$431$	−16.1191	−	27.9191i	−0.776431	−	1.34482i	−0.933987	−	0.357308i	$-0.883695\pi$
$431$	−16.1191	−	27.9191i	−0.776431	−	1.34482i	0.157556	−	0.987510i	$-0.449639\pi$
$432$		0			0
$433$	40.2685			1.93518			0.967590	−	0.252525i	$-0.0812610\pi$
$433$	40.2685			1.93518			0.967590	+	0.252525i	$0.0812610\pi$
$434$		0			0
$435$	21.9928			1.05447
$436$		0			0
$437$	−2.44630	−	4.23711i	−0.117022	−	0.202689i
$438$		0			0
$439$	−15.1547	+	26.2487i	−0.723295	+	1.25278i	0.236378	+	0.971661i	$0.424040\pi$
$439$	−15.1547	+	26.2487i	−0.723295	+	1.25278i	−0.959672	+	0.281122i	$0.909294\pi$
$440$		0			0
$441$	12.5601	−	33.8692i	0.598101	−	1.61282i
$442$		0			0
$443$	10.3633	−	17.9498i	0.492378	−	0.852823i	−0.507584	−	0.861602i	$-0.669461\pi$
$443$	10.3633	−	17.9498i	0.492378	−	0.852823i	0.999961	+	0.00877943i	$0.00279462\pi$
$444$		0			0
$445$	−2.23424	−	3.86981i	−0.105913	−	0.183447i
$446$		0			0
$447$	−32.8688			−1.55464
$448$		0			0
$449$	−27.0998			−1.27892			−0.639459	−	0.768825i	$-0.720842\pi$
$449$	−27.0998			−1.27892			−0.639459	+	0.768825i	$0.720842\pi$
$450$		0			0
$451$	5.71522	+	9.89905i	0.269119	+	0.466128i
$452$		0			0
$453$	7.50998	−	13.0077i	0.352850	−	0.611154i
$454$		0			0
$455$	0.0674541	+	0.0317033i	0.00316230	+	0.00148628i
$456$		0			0
$457$	−12.9036	+	22.3496i	−0.603603	+	1.04547i	0.388668	+	0.921378i	$0.372935\pi$
$457$	−12.9036	+	22.3496i	−0.603603	+	1.04547i	−0.992271	+	0.124093i	$0.960398\pi$
$458$		0			0
$459$	13.0694	+	22.6369i	0.610029	+	1.05660i
$460$		0			0
$461$	−39.9222			−1.85936			−0.929681	−	0.368366i	$-0.879917\pi$
$461$	−39.9222			−1.85936			−0.929681	+	0.368366i	$0.879917\pi$
$462$		0			0
$463$	−24.7160			−1.14865			−0.574324	−	0.818628i	$-0.694735\pi$
$463$	−24.7160			−1.14865			−0.574324	+	0.818628i	$0.694735\pi$
$464$		0			0
$465$	3.00201	+	5.19964i	0.139215	+	0.241127i
$466$		0			0
$467$	−0.335830	+	0.581674i	−0.0155403	+	0.0269167i	−0.873691	−	0.486481i	$-0.838280\pi$
$467$	−0.335830	+	0.581674i	−0.0155403	+	0.0269167i	0.858151	+	0.513398i	$0.171614\pi$
$468$		0			0
$469$	−15.1662	+	10.5512i	−0.700311	+	0.487210i
$470$		0			0
$471$	1.95268	−	3.38214i	0.0899748	−	0.155841i
$472$		0			0
$473$	−27.4661	−	47.5726i	−1.26289	−	2.18739i
$474$		0			0
$475$	−4.31456			−0.197966
$476$		0			0
$477$	17.7166			0.811189
$478$		0			0
$479$	8.97956	+	15.5530i	0.410286	+	0.710637i	0.994921	−	0.100660i	$-0.0320954\pi$
$479$	8.97956	+	15.5530i	0.410286	+	0.710637i	−0.584634	+	0.811297i	$0.698762\pi$
$480$		0			0
$481$	0.0780200	−	0.135135i	0.00355740	−	0.00616160i
$482$		0			0
$483$	3.11133	+	36.8470i	0.141570	+	1.67660i
$484$		0			0
$485$	−3.51633	+	6.09047i	−0.159669	+	0.276554i
$486$		0			0
$487$	14.8975	+	25.8033i	0.675072	+	1.16926i	0.976448	+	0.215753i	$0.0692206\pi$
$487$	14.8975	+	25.8033i	0.675072	+	1.16926i	−0.301376	+	0.953505i	$0.597446\pi$
$488$		0			0
$489$	29.1660			1.31893
$490$		0			0
$491$	11.8193			0.533397			0.266698	−	0.963780i	$-0.414067\pi$
$491$	11.8193			0.533397			0.266698	+	0.963780i	$0.414067\pi$
$492$		0			0
$493$	19.6923	+	34.1081i	0.886898	+	1.53615i
$494$		0			0
$495$	−12.2088	+	21.1463i	−0.548745	+	0.950454i
$496$		0			0
$497$	2.68416	+	31.7881i	0.120401	+	1.42589i
$498$		0			0
$499$	8.72131	−	15.1058i	0.390419	−	0.676226i	−0.602085	−	0.798432i	$-0.705663\pi$
$499$	8.72131	−	15.1058i	0.390419	−	0.676226i	0.992505	+	0.122205i	$0.0389967\pi$
$500$		0			0
$501$	−5.90897	−	10.2346i	−0.263993	−	0.457249i
$502$		0			0
$503$	28.8112			1.28463			0.642313	−	0.766442i	$-0.277975\pi$
$503$	28.8112			1.28463			0.642313	+	0.766442i	$0.277975\pi$
$504$		0			0
$505$	10.2566			0.456412
$506$		0			0
$507$	18.5666	+	32.1582i	0.824570	+	1.42820i
$508$		0			0
$509$	10.3216	−	17.8776i	0.457498	−	0.792410i	−0.541330	−	0.840810i	$-0.682079\pi$
$509$	10.3216	−	17.8776i	0.457498	−	0.792410i	0.998828	+	0.0484004i	$0.0154123\pi$
$510$		0			0
$511$	1.63170	−	1.13518i	0.0721821	−	0.0502175i
$512$		0			0
$513$	−3.08581	+	5.34478i	−0.136242	+	0.235978i
$514$		0			0
$515$	−5.88939	−	10.2007i	−0.259518	−	0.449498i
$516$		0			0
$517$	−64.7098			−2.84594
$518$		0			0
$519$	52.2316			2.29271
$520$		0			0
$521$	5.71164	+	9.89286i	0.250232	+	0.433414i	0.963589	−	0.267386i	$-0.0861599\pi$
$521$	5.71164	+	9.89286i	0.250232	+	0.433414i	−0.713358	+	0.700800i	$0.752827\pi$
$522$		0			0
$523$	0.780572	−	1.35199i	0.0341320	−	0.0591184i	−0.848455	−	0.529268i	$-0.822467\pi$
$523$	0.780572	−	1.35199i	0.0341320	−	0.0591184i	0.882587	+	0.470149i	$0.155800\pi$
$524$		0			0
$525$	29.5123	+	13.8707i	1.28802	+	0.605368i
$526$		0			0
$527$	−5.37601	+	9.31152i	−0.234182	+	0.405616i
$528$		0			0
$529$	−0.468741	−	0.811884i	−0.0203801	−	0.0352993i
$530$		0			0
$531$	−37.9473			−1.64677
$532$		0			0
$533$	0.0680528			0.00294769
$534$		0			0
$535$	0.169058	+	0.292818i	0.00730903	+	0.0126596i
$536$		0			0
$537$	−1.74032	+	3.01432i	−0.0751003	+	0.130078i
$538$		0			0
$539$	25.5297	+	30.8019i	1.09964	+	1.32673i
$540$		0			0
$541$	−6.18457	+	10.7120i	−0.265896	+	0.460545i	−0.967798	−	0.251729i	$-0.919001\pi$
$541$	−6.18457	+	10.7120i	−0.265896	+	0.460545i	0.701902	+	0.712273i	$0.252334\pi$
$542$		0			0
$543$	20.0499	+	34.7275i	0.860425	+	1.49030i
$544$		0			0
$545$	−13.4902			−0.577857
$546$		0			0
$547$	9.11300			0.389644			0.194822	−	0.980839i	$-0.437587\pi$
$547$	9.11300			0.389644			0.194822	+	0.980839i	$0.437587\pi$
$548$		0			0
$549$	−6.43120	−	11.1392i	−0.274477	−	0.475408i
$550$		0			0
$551$	−4.64954	+	8.05323i	−0.198077	+	0.343079i
$552$		0			0
$553$	28.6504	+	13.4656i	1.21834	+	0.572617i
$554$		0			0
$555$	−5.42288	+	9.39270i	−0.230188	+	0.398698i
$556$		0			0
$557$	9.90158	+	17.1500i	0.419543	+	0.726670i	0.995893	−	0.0905325i	$-0.0288569\pi$
$557$	9.90158	+	17.1500i	0.419543	+	0.726670i	−0.576350	+	0.817203i	$0.695524\pi$
$558$		0			0
$559$	−0.327047			−0.0138326
$560$		0			0
$561$	−69.1476			−2.91941
$562$		0			0
$563$	−7.05918	−	12.2269i	−0.297509	−	0.515301i	0.678056	−	0.735010i	$-0.262823\pi$
$563$	−7.05918	−	12.2269i	−0.297509	−	0.515301i	−0.975565	+	0.219709i	$0.929489\pi$
$564$		0			0
$565$	−5.77072	+	9.99518i	−0.242776	+	0.420500i
$566$		0			0
$567$	4.66696	−	3.24683i	0.195994	−	0.136354i
$568$		0			0
$569$	21.7911	−	37.7434i	0.913532	−	1.58228i	0.104497	−	0.994525i	$-0.466677\pi$
$569$	21.7911	−	37.7434i	0.913532	−	1.58228i	0.809036	−	0.587759i	$-0.199990\pi$
$570$		0			0
$571$	−21.2262	−	36.7648i	−0.888289	−	1.53856i	−0.841897	−	0.539638i	$-0.818561\pi$
$571$	−21.2262	−	36.7648i	−0.888289	−	1.53856i	−0.0463912	−	0.998923i	$-0.514772\pi$
$572$		0			0
$573$	23.2478			0.971189
$574$		0			0
$575$	−21.1094			−0.880324
$576$		0			0
$577$	12.2686	+	21.2499i	0.510750	+	0.884646i	0.999922	+	0.0124584i	$0.00396572\pi$
$577$	12.2686	+	21.2499i	0.510750	+	0.884646i	−0.489172	+	0.872187i	$0.662701\pi$
$578$		0			0
$579$	10.5345	−	18.2463i	0.437799	−	0.758290i
$580$		0			0
$581$	−3.06597	−	36.3099i	−0.127198	−	1.50639i
$582$		0			0
$583$	−9.81063	+	16.9925i	−0.406315	+	0.703758i
$584$		0			0
$585$	0.0726869	+	0.125897i	0.00300523	+	0.00520522i
$586$		0			0
$587$	17.6330			0.727792			0.363896	−	0.931440i	$-0.381446\pi$
$587$	17.6330			0.727792			0.363896	+	0.931440i	$0.381446\pi$
$588$		0			0
$589$	−2.53865			−0.104603
$590$		0			0
$591$	−39.4249	−	68.2859i	−1.62172	−	2.80891i
$592$		0			0
$593$	18.0694	−	31.2970i	0.742019	−	1.28522i	−0.209555	−	0.977797i	$-0.567202\pi$
$593$	18.0694	−	31.2970i	0.742019	−	1.28522i	0.951574	−	0.307418i	$-0.0994651\pi$
$594$		0			0
$595$	−0.780585	−	9.24436i	−0.0320008	−	0.378982i
$596$		0			0
$597$	−3.78099	+	6.54886i	−0.154745	+	0.268027i
$598$		0			0
$599$	4.79273	+	8.30125i	0.195826	+	0.339180i	0.947171	−	0.320729i	$-0.103928\pi$
$599$	4.79273	+	8.30125i	0.195826	+	0.339180i	−0.751345	+	0.659909i	$0.770595\pi$
$600$		0			0
$601$	11.6277			0.474303			0.237151	−	0.971473i	$-0.423786\pi$
$601$	11.6277			0.474303			0.237151	+	0.971473i	$0.423786\pi$
$602$		0			0
$603$	−36.0357			−1.46749
$604$		0			0
$605$	−8.96780	−	15.5327i	−0.364593	−	0.631494i
$606$		0			0
$607$	11.6098	−	20.1087i	0.471225	−	0.816186i	−0.528233	−	0.849100i	$-0.677145\pi$
$607$	11.6098	−	20.1087i	0.471225	−	0.816186i	0.999458	+	0.0329131i	$0.0104785\pi$
$608$		0			0
$609$	57.6936	−	40.1378i	2.33786	−	1.62646i
$610$		0			0
$611$	−0.192630	+	0.333645i	−0.00779297	+	0.0134978i
$612$		0			0
$613$	1.45232	+	2.51549i	0.0586586	+	0.101600i	0.893863	−	0.448339i	$-0.147984\pi$
$613$	1.45232	+	2.51549i	0.0586586	+	0.101600i	−0.835205	+	0.549939i	$0.814651\pi$
$614$		0			0
$615$	−4.73010			−0.190736
$616$		0			0
$617$	4.32789			0.174234			0.0871171	−	0.996198i	$-0.472235\pi$
$617$	4.32789			0.174234			0.0871171	+	0.996198i	$0.472235\pi$
$618$		0			0
$619$	13.4761	+	23.3413i	0.541651	+	0.938167i	0.998809	+	0.0487820i	$0.0155340\pi$
$619$	13.4761	+	23.3413i	0.541651	+	0.938167i	−0.457158	+	0.889385i	$0.651133\pi$
$620$		0			0
$621$	−15.0976	+	26.1499i	−0.605847	+	1.04936i
$622$		0			0
$623$	−12.9236	−	6.07409i	−0.517775	−	0.243353i
$624$		0			0
$625$	−7.59415	+	13.1534i	−0.303766	+	0.526138i
$626$		0			0
$627$	−8.16318	−	14.1390i	−0.326006	−	0.564659i
$628$		0			0
$629$	−19.4226			−0.774429
$630$		0			0
$631$	−8.31113			−0.330861			−0.165430	−	0.986221i	$-0.552901\pi$
$631$	−8.31113			−0.330861			−0.165430	+	0.986221i	$0.552901\pi$
$632$		0			0
$633$	18.2277	+	31.5713i	0.724486	+	1.25485i
$634$		0			0
$635$	−0.297344	+	0.515014i	−0.0117997	+	0.0204377i
$636$		0			0
$637$	0.234812	−	0.0399394i	0.00930361	−	0.00158246i
$638$		0			0
$639$	−31.1111	+	53.8860i	−1.23074	+	2.13170i
$640$		0			0
$641$	15.5026	+	26.8513i	0.612317	+	1.06056i	0.990849	+	0.134976i	$0.0430956\pi$
$641$	15.5026	+	26.8513i	0.612317	+	1.06056i	−0.378532	+	0.925588i	$0.623571\pi$
$642$		0			0
$643$	38.6660			1.52484			0.762420	−	0.647083i	$-0.224011\pi$
$643$	38.6660			1.52484			0.762420	+	0.647083i	$0.224011\pi$
$644$		0			0
$645$	22.7318			0.895064
$646$		0			0
$647$	−16.8359	−	29.1605i	−0.661886	−	1.14642i	−0.980120	−	0.198407i	$-0.936423\pi$
$647$	−16.8359	−	29.1605i	−0.661886	−	1.14642i	0.318234	−	0.948012i	$-0.396910\pi$
$648$		0			0
$649$	21.0134	−	36.3964i	0.824850	−	1.42868i
$650$		0			0
$651$	17.3648	+	8.16141i	0.680578	+	0.319871i
$652$		0			0
$653$	9.66890	−	16.7470i	0.378373	−	0.655362i	−0.612452	−	0.790507i	$-0.709817\pi$
$653$	9.66890	−	16.7470i	0.378373	−	0.655362i	0.990826	+	0.135146i	$0.0431502\pi$
$654$		0			0
$655$	−6.05388	−	10.4856i	−0.236545	−	0.409708i
$656$		0			0
$657$	3.87700			0.151256
$658$		0			0
$659$	−33.8064			−1.31691			−0.658456	−	0.752619i	$-0.728790\pi$
$659$	−33.8064			−1.31691			−0.658456	+	0.752619i	$0.728790\pi$
$660$		0			0
$661$	−10.0974	−	17.4892i	−0.392744	−	0.680252i	0.600067	−	0.799950i	$-0.295141\pi$
$661$	−10.0974	−	17.4892i	−0.392744	−	0.680252i	−0.992810	+	0.119698i	$0.961807\pi$
$662$		0			0
$663$	−0.205840	+	0.356526i	−0.00799417	+	0.0138463i
$664$		0			0
$665$	1.79810	−	1.25095i	0.0697274	−	0.0485098i
$666$		0			0
$667$	−22.7483	+	39.4012i	−0.880818	+	1.52562i
$668$		0			0
$669$	11.2894	+	19.5539i	0.436475	+	0.755997i
$670$		0			0
$671$	14.2452			0.549929
$672$		0			0
$673$	22.7317			0.876242			0.438121	−	0.898916i	$-0.355644\pi$
$673$	22.7317			0.876242			0.438121	+	0.898916i	$0.355644\pi$
$674$		0			0
$675$	13.3139	+	23.0604i	0.512454	+	0.887596i
$676$		0			0
$677$	15.9547	−	27.6344i	0.613190	−	1.06208i	−0.377509	−	0.926006i	$-0.623219\pi$
$677$	15.9547	−	27.6344i	0.613190	−	1.06208i	0.990699	−	0.136071i	$-0.0434474\pi$
$678$		0			0
$679$	1.89098	+	22.3946i	0.0725691	+	0.859426i
$680$		0			0
$681$	39.7284	−	68.8117i	1.52240	−	2.63687i
$682$		0			0
$683$	13.3913	+	23.1944i	0.512404	+	0.887509i	0.999897	+	0.0143822i	$0.00457816\pi$
$683$	13.3913	+	23.1944i	0.512404	+	0.887509i	−0.487493	+	0.873127i	$0.662089\pi$
$684$		0			0
$685$	−14.0038			−0.535057
$686$		0			0
$687$	−30.2429			−1.15384
$688$		0			0
$689$	0.0584091	+	0.101168i	0.00222521	+	0.00385417i
$690$		0			0
$691$	20.8482	−	36.1102i	0.793104	−	1.37370i	−0.130933	−	0.991391i	$-0.541797\pi$
$691$	20.8482	−	36.1102i	0.793104	−	1.37370i	0.924036	−	0.382305i	$-0.124870\pi$
$692$		0			0
$693$	6.56552	+	77.7546i	0.249403	+	2.95365i
$694$		0			0
$695$	5.52218	−	9.56470i	0.209468	−	0.362810i
$696$		0			0
$697$	−4.23533	−	7.33581i	−0.160425	−	0.277864i
$698$		0			0
$699$	14.8461			0.561530
$700$		0			0
$701$	−23.5645			−0.890017			−0.445009	−	0.895526i	$-0.646799\pi$
$701$	−23.5645			−0.890017			−0.445009	+	0.895526i	$0.646799\pi$
$702$		0			0
$703$	−2.29292	−	3.97146i	−0.0864793	−	0.149786i
$704$		0			0
$705$	13.3890	−	23.1904i	0.504258	−	0.873401i
$706$		0			0
$707$	26.9061	−	18.7187i	1.01191	−	0.703989i
$708$		0			0
$709$	−4.12280	+	7.14091i	−0.154835	+	0.268182i	−0.932999	−	0.359879i	$-0.882818\pi$
$709$	−4.12280	+	7.14091i	−0.154835	+	0.268182i	0.778164	+	0.628061i	$0.216151\pi$
$710$		0			0
$711$	30.8730	+	53.4736i	1.15783	+	2.00541i
$712$		0			0
$713$	−12.4206			−0.465154
$714$		0			0
$715$	−0.161002			−0.00602114
$716$		0			0
$717$	−5.19417	−	8.99657i	−0.193980	−	0.335983i
$718$		0			0
$719$	8.84120	−	15.3134i	0.329721	−	0.571094i	−0.652735	−	0.757586i	$-0.726379\pi$
$719$	8.84120	−	15.3134i	0.329721	−	0.571094i	0.982456	+	0.186492i	$0.0597119\pi$
$720$		0			0
$721$	−34.0664	−	16.0112i	−1.26870	−	0.596287i
$722$		0			0
$723$	−10.9568	+	18.9777i	−0.407487	+	0.705789i
$724$		0			0
$725$	20.0607	+	34.7462i	0.745037	+	1.29044i
$726$		0			0
$727$	25.0671			0.929689			0.464844	−	0.885392i	$-0.346110\pi$
$727$	25.0671			0.929689			0.464844	+	0.885392i	$0.346110\pi$
$728$		0			0
$729$	−41.8015			−1.54821
$730$		0			0
$731$	20.3541	+	35.2543i	0.752822	+	1.30393i
$732$		0			0
$733$	0.239578	−	0.414962i	0.00884903	−	0.0153270i	−0.861567	−	0.507644i	$-0.830517\pi$
$733$	0.239578	−	0.414962i	0.00884903	−	0.0153270i	0.870416	+	0.492317i	$0.163850\pi$
$734$		0			0
$735$	−16.3209	+	2.77604i	−0.602007	+	0.102396i
$736$		0			0
$737$	19.9549	−	34.5628i	0.735047	−	1.27314i
$738$		0			0
$739$	17.3086	+	29.9793i	0.636706	+	1.10281i	0.986151	+	0.165850i	$0.0530369\pi$
$739$	17.3086	+	29.9793i	0.636706	+	1.10281i	−0.349445	+	0.936957i	$0.613630\pi$
$740$		0			0
$741$	−0.0972015			−0.00357079
$742$		0			0
$743$	30.2246			1.10883			0.554417	−	0.832239i	$-0.312941\pi$
$743$	30.2246			1.10883			0.554417	+	0.832239i	$0.312941\pi$
$744$		0			0
$745$	4.76300	+	8.24976i	0.174503	+	0.302248i
$746$		0			0
$747$	35.5366	−	61.5512i	1.30022	−	2.25204i
$748$		0			0
$749$	0.977896	+	0.459610i	0.0357315	+	0.0167938i
$750$		0			0
$751$	−13.8403	+	23.9720i	−0.505038	+	0.874752i	0.494945	+	0.868924i	$0.335188\pi$
$751$	−13.8403	+	23.9720i	−0.505038	+	0.874752i	−0.999983	+	0.00582720i	$0.998145\pi$
$752$		0			0
$753$	−23.3774	−	40.4909i	−0.851921	−	1.47557i
$754$		0			0
$755$	−4.35307			−0.158424
$756$		0			0
$757$	3.82783			0.139125			0.0695625	−	0.997578i	$-0.477840\pi$
$757$	3.82783			0.139125			0.0695625	+	0.997578i	$0.477840\pi$
$758$		0			0
$759$	−39.9391	−	69.1766i	−1.44970	−	2.51095i
$760$		0			0
$761$	−4.27395	+	7.40270i	−0.154931	+	0.268348i	−0.933034	−	0.359789i	$-0.882849\pi$
$761$	−4.27395	+	7.40270i	−0.154931	+	0.268348i	0.778103	+	0.628136i	$0.216182\pi$
$762$		0			0
$763$	−35.3889	+	24.6202i	−1.28116	+	0.891312i
$764$		0			0
$765$	9.04748	−	15.6707i	0.327112	−	0.566575i
$766$		0			0
$767$	−0.125107	−	0.216691i	−0.00451734	−	0.00782426i
$768$		0			0
$769$	−15.0750			−0.543619			−0.271810	−	0.962351i	$-0.587622\pi$
$769$	−15.0750			−0.543619			−0.271810	+	0.962351i	$0.587622\pi$
$770$		0			0
$771$	−45.4710			−1.63760
$772$		0			0
$773$	0.0816036	+	0.141342i	0.00293508	+	0.00508370i	0.867489	−	0.497456i	$-0.165732\pi$
$773$	0.0816036	+	0.141342i	0.00293508	+	0.00508370i	−0.864554	+	0.502540i	$0.832399\pi$
$774$		0			0
$775$	−5.47658	+	9.48572i	−0.196725	+	0.340737i
$776$		0			0
$777$	2.91626	+	34.5369i	0.104620	+	1.23900i
$778$		0			0
$779$	1.00000	−	1.73205i	0.0358287	−	0.0620572i
$780$		0			0
$781$	−34.4557	−	59.6791i	−1.23292	−	2.13549i
$782$		0			0
$783$	57.3904			2.05096
$784$		0			0
$785$	−1.13185			−0.0403974
$786$		0			0
$787$	−20.4952	−	35.4986i	−0.730573	−	1.26539i	−0.956639	−	0.291278i	$-0.905920\pi$
$787$	−20.4952	−	35.4986i	−0.730573	−	1.26539i	0.226065	−	0.974112i	$-0.427414\pi$
$788$		0			0
$789$	−16.8060	+	29.1088i	−0.598309	+	1.03630i
$790$		0			0
$791$	3.10332	+	36.7522i	0.110341	+	1.30676i
$792$		0			0
$793$	0.0424054	−	0.0734483i	0.00150586	−	0.00260822i
$794$		0			0
$795$	−4.05980	−	7.03178i	−0.143986	−	0.249391i
$796$		0			0
$797$	36.3930			1.28911			0.644554	−	0.764559i	$-0.277043\pi$
$797$	36.3930			1.28911			0.644554	+	0.764559i	$0.277043\pi$
$798$		0			0
$799$	47.9540			1.69649
$800$		0			0
$801$	−13.9262	−	24.1209i	−0.492058	−	0.852269i
$802$		0			0
$803$	−2.14690	+	3.71854i	−0.0757624	+	0.131224i
$804$		0			0
$805$	8.79739	−	6.12039i	0.310067	−	0.215715i
$806$		0			0
$807$	14.2377	−	24.6603i	0.501189	−	0.868085i
$808$		0			0
$809$	14.0279	+	24.2970i	0.493193	+	0.854236i	0.999969	−	0.00784176i	$-0.00249614\pi$
$809$	14.0279	+	24.2970i	0.493193	+	0.854236i	−0.506776	+	0.862078i	$0.669163\pi$
$810$		0			0
$811$	53.7818			1.88853			0.944267	−	0.329179i	$-0.106772\pi$
$811$	53.7818			1.88853			0.944267	+	0.329179i	$0.106772\pi$
$812$		0			0
$813$	39.8203			1.39656
$814$		0			0
$815$	−4.22642	−	7.32038i	−0.148045	−	0.256422i
$816$		0			0
$817$	−4.80578	+	8.32386i	−0.168133	+	0.291215i
$818$		0			0
$819$	0.420448	+	0.197610i	0.0146916	+	0.00690505i
$820$		0			0
$821$	17.5835	−	30.4554i	0.613667	−	1.06290i	−0.376950	−	0.926234i	$-0.623027\pi$
$821$	17.5835	−	30.4554i	0.613667	−	1.06290i	0.990617	−	0.136669i	$-0.0436395\pi$
$822$		0			0
$823$	−20.1838	−	34.9594i	−0.703563	−	1.21861i	−0.967208	−	0.253987i	$-0.918258\pi$
$823$	−20.1838	−	34.9594i	−0.703563	−	1.21861i	0.263645	−	0.964620i	$-0.415075\pi$
$824$		0			0
$825$	−70.4412			−2.45245
$826$		0			0
$827$	52.9629			1.84170			0.920851	−	0.389914i	$-0.127495\pi$
$827$	52.9629			1.84170			0.920851	+	0.389914i	$0.127495\pi$
$828$		0			0
$829$	−10.9035	−	18.8855i	−0.378696	−	0.655920i	0.612177	−	0.790721i	$-0.290294\pi$
$829$	−10.9035	−	18.8855i	−0.378696	−	0.655920i	−0.990873	+	0.134800i	$0.956961\pi$
$830$		0			0
$831$	7.06418	−	12.2355i	0.245054	−	0.424446i
$832$		0			0
$833$	−18.9191	−	22.8261i	−0.655507	−	0.790878i
$834$		0			0
$835$	−1.71253	+	2.96619i	−0.0592645	+	0.102649i
$836$		0			0
$837$	7.83379	+	13.5685i	0.270775	+	0.468997i
$838$		0			0
$839$	−33.8346			−1.16810			−0.584051	−	0.811717i	$-0.698533\pi$
$839$	−33.8346			−1.16810			−0.584051	+	0.811717i	$0.698533\pi$
$840$		0			0
$841$	57.4728			1.98182
$842$		0			0
$843$	14.3495	+	24.8541i	0.494223	+	0.856020i
$844$		0			0
$845$	5.38094	−	9.32006i	0.185110	−	0.320620i
$846$		0			0
$847$	−51.8731	−	24.3803i	−1.78238	−	0.837716i
$848$		0			0
$849$	28.4030	−	49.1954i	0.974787	−	1.68838i
$850$		0			0
$851$	−11.2183	−	19.4307i	−0.384560	−	0.666077i
$852$		0			0
$853$	−58.1329			−1.99043			−0.995217	−	0.0976929i	$-0.968854\pi$
$853$	−58.1329			−1.99043			−0.995217	+	0.0976929i	$0.968854\pi$
$854$		0			0
$855$	4.27238			0.146112
$856$		0			0
$857$	−9.36630	−	16.2229i	−0.319947	−	0.554164i	0.660530	−	0.750800i	$-0.270332\pi$
$857$	−9.36630	−	16.2229i	−0.319947	−	0.554164i	−0.980477	+	0.196636i	$0.936998\pi$
$858$		0			0
$859$	11.7150	−	20.2910i	0.399711	−	0.692320i	−0.593979	−	0.804480i	$-0.702444\pi$
$859$	11.7150	−	20.2910i	0.399711	−	0.692320i	0.993690	+	0.112161i	$0.0357772\pi$
$860$		0			0
$861$	−12.4085	+	8.63264i	−0.422879	+	0.294199i
$862$		0			0
$863$	−16.3626	+	28.3409i	−0.556991	+	0.964736i	0.440755	+	0.897627i	$0.354711\pi$
$863$	−16.3626	+	28.3409i	−0.556991	+	0.964736i	−0.997746	+	0.0671087i	$0.978623\pi$
$864$		0			0
$865$	−7.56885	−	13.1096i	−0.257349	−	0.445741i
$866$		0			0
$867$	2.67960			0.0910039
$868$		0			0
$869$	−68.3840			−2.31977
$870$		0			0
$871$	−0.118804	−	0.205775i	−0.00402553	−	0.00697242i
$872$		0			0
$873$	−21.9176	+	37.9625i	−0.741800	+	1.28483i
$874$		0			0
$875$	−1.71670	−	20.3307i	−0.0580352	−	0.687303i
$876$		0			0
$877$	−0.0631859	+	0.109441i	−0.00213363	+	0.00369556i	−0.867090	−	0.498151i	$-0.834012\pi$
$877$	−0.0631859	+	0.109441i	−0.00213363	+	0.00369556i	0.864957	+	0.501847i	$0.167346\pi$
$878$		0			0
$879$	−9.92079	−	17.1833i	−0.334620	−	0.579579i
$880$		0			0
$881$	−24.2852			−0.818190			−0.409095	−	0.912492i	$-0.634156\pi$
$881$	−24.2852			−0.818190			−0.409095	+	0.912492i	$0.634156\pi$
$882$		0			0
$883$	−53.0218			−1.78432			−0.892162	−	0.451715i	$-0.850812\pi$
$883$	−53.0218			−1.78432			−0.892162	+	0.451715i	$0.850812\pi$
$884$		0			0
$885$	8.69570	+	15.0614i	0.292303	+	0.506283i
$886$		0			0
$887$	−0.263045	+	0.455607i	−0.00883218	+	0.0152978i	−0.870408	−	0.492332i	$-0.836145\pi$
$887$	−0.263045	+	0.455607i	−0.00883218	+	0.0152978i	0.861576	+	0.507629i	$0.169478\pi$
$888$		0			0
$889$	0.159902	+	1.89370i	0.00536295	+	0.0635127i
$890$		0			0
$891$	−6.14053	+	10.6357i	−0.205715	+	0.356310i
$892$		0			0
$893$	5.66119	+	9.80547i	0.189444	+	0.328127i
$894$		0			0
$895$	1.00875			0.0337189
$896$		0			0
$897$	−0.475568			−0.0158787
$898$		0			0
$899$	11.8035	+	20.4443i	0.393670	+	0.681856i
$900$		0			0
$901$	7.27029	−	12.5925i	0.242208	−	0.419517i
$902$		0			0
$903$	59.6323	−	41.4866i	1.98444	−	1.38059i
$904$		0			0
$905$	5.81084	−	10.0647i	0.193159	−	0.334561i
$906$		0			0
$907$	−5.80939	−	10.0622i	−0.192898	−	0.334108i	0.753312	−	0.657664i	$-0.228455\pi$
$907$	−5.80939	−	10.0622i	−0.192898	−	0.334108i	−0.946209	+	0.323555i	$0.895122\pi$
$908$		0			0
$909$	63.9302			2.12043
$910$		0			0
$911$	2.23613			0.0740862			0.0370431	−	0.999314i	$-0.488206\pi$
$911$	2.23613			0.0740862			0.0370431	+	0.999314i	$0.488206\pi$
$912$		0			0
$913$	39.3570	+	68.1683i	1.30253	+	2.25604i
$914$		0			0
$915$	−2.94744	+	5.10512i	−0.0974393	+	0.168770i
$916$		0			0
$917$	−35.0179	−	16.4584i	−1.15639	−	0.543503i
$918$		0			0
$919$	18.9942	−	32.8989i	0.626561	−	1.08524i	−0.361676	−	0.932304i	$-0.617795\pi$
$919$	18.9942	−	32.8989i	0.626561	−	1.08524i	0.988237	−	0.152931i	$-0.0488713\pi$
$920$		0			0
$921$	29.9623	+	51.8962i	0.987291	+	1.71004i
$922$		0			0
$923$	−0.410275			−0.0135044
$924$		0			0
$925$	−19.7859			−0.650558
$926$		0			0
$927$	−36.7091	−	63.5821i	−1.20569	−	2.08831i
$928$		0			0
$929$	−10.3899	+	17.9958i	−0.340881	+	0.590423i	−0.984597	−	0.174842i	$-0.944059\pi$
$929$	−10.3899	+	17.9958i	−0.340881	+	0.590423i	0.643716	+	0.765265i	$0.277392\pi$
$930$		0			0
$931$	2.43392	−	6.56323i	0.0797686	−	0.215101i
$932$		0			0
$933$	−10.6559	+	18.4566i	−0.348859	+	0.604241i
$934$		0			0
$935$	10.0201	+	17.3554i	0.327693	+	0.567581i
$936$		0			0
$937$	−39.6999			−1.29694			−0.648470	−	0.761240i	$-0.724591\pi$
$937$	−39.6999			−1.29694			−0.648470	+	0.761240i	$0.724591\pi$
$938$		0			0
$939$	−20.6469			−0.673785
$940$		0			0
$941$	21.7946	+	37.7494i	0.710485	+	1.23060i	0.964675	+	0.263442i	$0.0848576\pi$
$941$	21.7946	+	37.7494i	0.710485	+	1.23060i	−0.254191	+	0.967154i	$0.581809\pi$
$942$		0			0
$943$	4.89259	−	8.47422i	0.159325	−	0.275959i
$944$		0			0
$945$	−12.2347	−	5.75027i	−0.397994	−	0.187056i
$946$		0			0
$947$	−28.1191	+	48.7037i	−0.913747	+	1.58266i	−0.105022	+	0.994470i	$0.533491\pi$
$947$	−28.1191	+	48.7037i	−0.913747	+	1.58266i	−0.808725	+	0.588187i	$0.799842\pi$
$948$		0			0
$949$	0.0127819	+	0.0221389i	0.000414917	+	0.000718658i
$950$		0			0
$951$	−16.4534			−0.533537
$952$		0			0
$953$	−8.77476			−0.284242			−0.142121	−	0.989849i	$-0.545392\pi$
$953$	−8.77476			−0.284242			−0.142121	+	0.989849i	$0.545392\pi$
$954$		0			0
$955$	−3.36882	−	5.83496i	−0.109012	−	0.188815i
$956$		0			0
$957$	−75.9100	+	131.480i	−2.45382	+	4.25015i
$958$		0			0
$959$	−36.7361	+	25.5575i	−1.18627	+	0.825295i
$960$		0			0
$961$	12.2776	−	21.2655i	0.396053	−	0.685983i
$962$		0			0
$963$	1.05376	+	1.82516i	0.0339568	+	0.0588150i
$964$		0			0
$965$	−6.10619			−0.196565
$966$		0			0
$967$	56.7355			1.82449			0.912245	−	0.409644i	$-0.134347\pi$
$967$	56.7355			1.82449			0.912245	+	0.409644i	$0.134347\pi$
$968$		0			0
$969$	6.04943	+	10.4779i	0.194336	+	0.336599i
$970$		0			0
$971$	−17.4868	+	30.2881i	−0.561179	+	0.971991i	0.436215	+	0.899843i	$0.356319\pi$
$971$	−17.4868	+	30.2881i	−0.561179	+	0.971991i	−0.997394	+	0.0721481i	$0.977015\pi$
$972$		0			0
$973$	−2.96966	−	35.1693i	−0.0952030	−	1.12748i
$974$		0			0
$975$	−0.209691	+	0.363196i	−0.00671549	+	0.0116316i
$976$		0			0
$977$	−18.6286	−	32.2657i	−0.595982	−	1.03227i	−0.993408	−	0.114637i	$-0.963430\pi$
$977$	−18.6286	−	32.2657i	−0.595982	−	1.03227i	0.397426	−	0.917634i	$-0.369904\pi$
$978$		0			0
$979$	30.8467			0.985864
$980$		0			0
$981$	−84.0858			−2.68465
$982$		0			0
$983$	−10.4038	−	18.0199i	−0.331829	−	0.574744i	0.651042	−	0.759042i	$-0.274332\pi$
$983$	−10.4038	−	18.0199i	−0.331829	−	0.574744i	−0.982870	+	0.184298i	$0.940999\pi$
$984$		0			0
$985$	−11.4261	+	19.7905i	−0.364065	+	0.630578i
$986$		0			0
$987$	−7.20019	−	85.2709i	−0.229185	−	2.71420i
$988$		0			0
$989$	−23.5127	+	40.7253i	−0.747661	+	1.29499i
$990$		0			0
$991$	8.11095	+	14.0486i	0.257653	+	0.446268i	0.965613	−	0.259985i	$-0.0837176\pi$
$991$	8.11095	+	14.0486i	0.257653	+	0.446268i	−0.707960	+	0.706253i	$0.750384\pi$
$992$		0			0
$993$	34.5233			1.09556
$994$		0			0
$995$	2.19160			0.0694784
$996$		0			0
$997$	2.82999	+	4.90170i	0.0896268	+	0.155238i	0.907353	−	0.420369i	$-0.138099\pi$
$997$	2.82999	+	4.90170i	0.0896268	+	0.155238i	−0.817727	+	0.575607i	$0.804766\pi$
$998$		0			0
$999$	−14.1511	+	24.5104i	−0.447720	+	0.775474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1064.2.q.n.457.1	yes	16
7.2	even	3		7448.2.a.bq.1.8		8
7.4	even	3	inner	1064.2.q.n.305.1	✓	16
7.5	odd	6		7448.2.a.br.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1064.2.q.n.305.1	✓	16	7.4	even	3	inner
1064.2.q.n.457.1	yes	16	1.1	even	1	trivial
7448.2.a.bq.1.8		8	7.2	even	3
7448.2.a.br.1.1		8	7.5	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:	\( N \)	\(=\)	\( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1064.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.42832 - 2.47393i) q^{3} +(-0.413955 + 0.716991i) q^{5} +(0.222612 + 2.63637i) q^{7} +(-2.58022 + 4.46907i) q^{9} +O(q^{10})\)	\(q+(-1.42832 - 2.47393i) q^{3} +(-0.413955 + 0.716991i) q^{5} +(0.222612 + 2.63637i) q^{7} +(-2.58022 + 4.46907i) q^{9} +(-2.85761 - 4.94952i) q^{11} -0.0340264 q^{13} +2.36505 q^{15} +(2.11767 + 3.66790i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(6.20423 - 4.31632i) q^{21} +(-2.44630 + 4.23711i) q^{23} +(2.15728 + 3.73652i) q^{25} +6.17162 q^{27} +9.29907 q^{29} +(1.26932 + 2.19853i) q^{31} +(-8.16318 + 14.1390i) q^{33} +(-1.98241 - 0.931727i) q^{35} +(-2.29292 + 3.97146i) q^{37} +(0.0486007 + 0.0841790i) q^{39} -2.00000 q^{41} +9.61156 q^{43} +(-2.13619 - 3.69999i) q^{45} +(5.66119 - 9.80547i) q^{47} +(-6.90089 + 1.17378i) q^{49} +(6.04943 - 10.4779i) q^{51} +(-1.71658 - 2.97321i) q^{53} +4.73169 q^{55} +2.85665 q^{57} +(3.67675 + 6.36832i) q^{59} +(-1.24625 + 2.15857i) q^{61} +(-12.3565 - 5.80754i) q^{63} +(0.0140854 - 0.0243966i) q^{65} +(3.49153 + 6.04751i) q^{67} +13.9764 q^{69} +12.0575 q^{71} +(-0.375646 - 0.650638i) q^{73} +(6.16260 - 10.6739i) q^{75} +(12.4126 - 8.63554i) q^{77} +(5.98262 - 10.3622i) q^{79} +(-1.07442 - 1.86095i) q^{81} -13.7727 q^{83} -3.50647 q^{85} +(-13.2821 - 23.0053i) q^{87} +(-2.69864 + 4.67419i) q^{89} +(-0.00757470 - 0.0897062i) q^{91} +(3.62601 - 6.28044i) q^{93} +(-0.413955 - 0.716991i) q^{95} +8.49448 q^{97} +29.4930 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{5} + 5 q^{7} - 6 q^{9}+O(q^{10}) \) 16 * q + q^5 + 5 * q^7 - 6 * q^9	\( 16 q + q^{5} + 5 q^{7} - 6 q^{9} - 9 q^{11} + 16 q^{15} - 4 q^{17} - 8 q^{19} - 2 q^{21} - 25 q^{23} - 15 q^{25} + 6 q^{27} + 12 q^{29} - 8 q^{33} + 5 q^{35} - 13 q^{37} + 11 q^{39} - 32 q^{41} + 34 q^{43} - 17 q^{45} + 24 q^{47} - 13 q^{49} - 5 q^{51} - 2 q^{53} + 10 q^{55} - 2 q^{59} + 13 q^{61} - 52 q^{63} + 26 q^{65} - 2 q^{67} - 22 q^{69} + 20 q^{71} - 5 q^{73} + 20 q^{75} + 28 q^{77} - 16 q^{79} + 12 q^{81} - 86 q^{83} + 48 q^{85} - 20 q^{87} - 8 q^{89} - 34 q^{91} - 2 q^{93} + q^{95} - 24 q^{97} + 74 q^{99}+O(q^{100}) \) 16 * q + q^5 + 5 * q^7 - 6 * q^9 - 9 * q^11 + 16 * q^15 - 4 * q^17 - 8 * q^19 - 2 * q^21 - 25 * q^23 - 15 * q^25 + 6 * q^27 + 12 * q^29 - 8 * q^33 + 5 * q^35 - 13 * q^37 + 11 * q^39 - 32 * q^41 + 34 * q^43 - 17 * q^45 + 24 * q^47 - 13 * q^49 - 5 * q^51 - 2 * q^53 + 10 * q^55 - 2 * q^59 + 13 * q^61 - 52 * q^63 + 26 * q^65 - 2 * q^67 - 22 * q^69 + 20 * q^71 - 5 * q^73 + 20 * q^75 + 28 * q^77 - 16 * q^79 + 12 * q^81 - 86 * q^83 + 48 * q^85 - 20 * q^87 - 8 * q^89 - 34 * q^91 - 2 * q^93 + q^95 - 24 * q^97 + 74 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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