LMFDB - Embedded newform 1035.2.j.b.323.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1035,2,Mod(323,1035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1035, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("1035.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1035 = 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1035.j (of order $4$, 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:	$8.26451660920$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.17
Character	$\chi$	$=$	1035.323
Dual form			1035.2.j.b.737.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.27425 + 1.27425i) q^{2} +1.24744i q^{4} +(-2.19469 + 0.428183i) q^{5} +(0.936657 - 0.936657i) q^{7} +(0.958947 - 0.958947i) q^{8} +O(q^{10})$	\(q+(1.27425 + 1.27425i) q^{2} +1.24744i q^{4} +(-2.19469 + 0.428183i) q^{5} +(0.936657 - 0.936657i) q^{7} +(0.958947 - 0.958947i) q^{8} +(-3.34220 - 2.25098i) q^{10} -0.533463i q^{11} +(4.37643 + 4.37643i) q^{13} +2.38708 q^{14} +4.93877 q^{16} +(-0.921166 - 0.921166i) q^{17} +7.99219i q^{19} +(-0.534134 - 2.73775i) q^{20} +(0.679767 - 0.679767i) q^{22} +(-0.707107 + 0.707107i) q^{23} +(4.63332 - 1.87946i) q^{25} +11.1534i q^{26} +(1.16843 + 1.16843i) q^{28} +9.15782 q^{29} +2.22459 q^{31} +(4.37535 + 4.37535i) q^{32} -2.34760i q^{34} +(-1.65461 + 2.45673i) q^{35} +(-2.15213 + 2.15213i) q^{37} +(-10.1841 + 10.1841i) q^{38} +(-1.69399 + 2.51520i) q^{40} -11.2956i q^{41} +(5.40825 + 5.40825i) q^{43} +0.665465 q^{44} -1.80207 q^{46} +(-1.53126 - 1.53126i) q^{47} +5.24535i q^{49} +(8.29893 + 3.50912i) q^{50} +(-5.45935 + 5.45935i) q^{52} +(-2.98095 + 2.98095i) q^{53} +(0.228420 + 1.17079i) q^{55} -1.79641i q^{56} +(11.6694 + 11.6694i) q^{58} -6.39579 q^{59} -12.6077 q^{61} +(2.83469 + 2.83469i) q^{62} +1.27307i q^{64} +(-11.4788 - 7.73098i) q^{65} +(9.65268 - 9.65268i) q^{67} +(1.14910 - 1.14910i) q^{68} +(-5.23889 + 1.02211i) q^{70} +1.85834i q^{71} +(-9.68980 - 9.68980i) q^{73} -5.48471 q^{74} -9.96981 q^{76} +(-0.499672 - 0.499672i) q^{77} -9.38659i q^{79} +(-10.8391 + 2.11470i) q^{80} +(14.3935 - 14.3935i) q^{82} +(-8.08083 + 8.08083i) q^{83} +(2.41610 + 1.62725i) q^{85} +13.7830i q^{86} +(-0.511563 - 0.511563i) q^{88} +12.2252 q^{89} +8.19842 q^{91} +(-0.882076 - 0.882076i) q^{92} -3.90243i q^{94} +(-3.42212 - 17.5404i) q^{95} +(1.22394 - 1.22394i) q^{97} +(-6.68390 + 6.68390i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 12 q^{7}+O(q^{10}) $ 44 * q + 12 * q^7	$ 44 q + 12 q^{7} - 20 q^{10} + 4 q^{13} - 44 q^{16} + 16 q^{22} - 8 q^{25} + 40 q^{28} - 32 q^{31} + 56 q^{37} - 16 q^{40} + 72 q^{43} - 4 q^{46} + 76 q^{52} + 56 q^{55} - 12 q^{58} - 96 q^{61} + 12 q^{67} - 48 q^{70} + 68 q^{73} - 112 q^{76} + 52 q^{82} + 32 q^{85} + 56 q^{88} - 176 q^{91} + 76 q^{97}+O(q^{100}) $ 44 * q + 12 * q^7 - 20 * q^10 + 4 * q^13 - 44 * q^16 + 16 * q^22 - 8 * q^25 + 40 * q^28 - 32 * q^31 + 56 * q^37 - 16 * q^40 + 72 * q^43 - 4 * q^46 + 76 * q^52 + 56 * q^55 - 12 * q^58 - 96 * q^61 + 12 * q^67 - 48 * q^70 + 68 * q^73 - 112 * q^76 + 52 * q^82 + 32 * q^85 + 56 * q^88 - 176 * q^91 + 76 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1035\mathbb{Z}\right)^\times$.

$n$	$461$	$622$	$856$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	1.27425	+	1.27425i	0.901033	+	0.901033i	0.995526	−	0.0944923i	$-0.0301228\pi$
$2$	1.27425	+	1.27425i	0.901033	+	0.901033i	−0.0944923	+	0.995526i	$0.530123\pi$
$3$		0			0
$3$		0			0
$4$			1.24744i			0.623722i
$5$	−2.19469	+	0.428183i	−0.981495	+	0.191489i
$5$	−2.19469	+	0.428183i	−0.981495	+	0.191489i
$6$		0			0
$7$	0.936657	−	0.936657i	0.354023	−	0.354023i	−0.507581	−	0.861604i	$-0.669460\pi$
$7$	0.936657	−	0.936657i	0.354023	−	0.354023i	0.861604	+	0.507581i	$0.169460\pi$
$8$	0.958947	−	0.958947i	0.339039	−	0.339039i
$9$		0			0
$10$	−3.34220	−	2.25098i	−1.05690	−	0.711821i
$11$		−	0.533463i		−	0.160845i	−0.996761	−	0.0804226i	$-0.974373\pi$
$11$		−	0.533463i		−	0.160845i	0.996761	−	0.0804226i	$-0.0256270\pi$
$12$		0			0
$13$	4.37643	+	4.37643i	1.21380	+	1.21380i	0.969766	+	0.244036i	$0.0784714\pi$
$13$	4.37643	+	4.37643i	1.21380	+	1.21380i	0.244036	+	0.969766i	$0.421529\pi$
$14$	2.38708			0.637973
$15$		0			0
$16$	4.93877			1.23469
$17$	−0.921166	−	0.921166i	−0.223416	−	0.223416i	0.586520	−	0.809935i	$-0.300498\pi$
$17$	−0.921166	−	0.921166i	−0.223416	−	0.223416i	−0.809935	+	0.586520i	$0.800498\pi$
$18$		0			0
$19$			7.99219i			1.83353i	0.399422	+	0.916767i	$0.369211\pi$
$19$			7.99219i			1.83353i	−0.399422	+	0.916767i	$0.630789\pi$
$20$	−0.534134	−	2.73775i	−0.119436	−	0.612180i
$21$		0			0
$22$	0.679767	−	0.679767i	0.144927	−	0.144927i
$23$	−0.707107	+	0.707107i	−0.147442	+	0.147442i
$23$	−0.707107	+	0.707107i	−0.147442	+	0.147442i
$24$		0			0
$25$	4.63332	−	1.87946i	0.926664	−	0.375892i
$26$			11.1534i			2.18735i
$27$		0			0
$28$	1.16843	+	1.16843i	0.220812	+	0.220812i
$29$	9.15782			1.70056			0.850282	−	0.526327i	$-0.176431\pi$
$29$	9.15782			1.70056			0.850282	+	0.526327i	$0.176431\pi$
$30$		0			0
$31$	2.22459			0.399549			0.199774	−	0.979842i	$-0.435979\pi$
$31$	2.22459			0.399549			0.199774	+	0.979842i	$0.435979\pi$
$32$	4.37535	+	4.37535i	0.773460	+	0.773460i
$33$		0			0
$34$		−	2.34760i		−	0.402610i
$35$	−1.65461	+	2.45673i	−0.279680	+	0.415263i
$36$		0			0
$37$	−2.15213	+	2.15213i	−0.353808	+	0.353808i	−0.861524	−	0.507717i	$-0.830490\pi$
$37$	−2.15213	+	2.15213i	−0.353808	+	0.353808i	0.507717	+	0.861524i	$0.330490\pi$
$38$	−10.1841	+	10.1841i	−1.65208	+	1.65208i
$39$		0			0
$40$	−1.69399	+	2.51520i	−0.267843	+	0.397687i
$41$		−	11.2956i		−	1.76408i	−0.471173	−	0.882041i	$-0.656169\pi$
$41$		−	11.2956i		−	1.76408i	0.471173	−	0.882041i	$-0.343831\pi$
$42$		0			0
$43$	5.40825	+	5.40825i	0.824750	+	0.824750i	0.986785	−	0.162035i	$-0.0518057\pi$
$43$	5.40825	+	5.40825i	0.824750	+	0.824750i	−0.162035	+	0.986785i	$0.551806\pi$
$44$	0.665465			0.100323
$45$		0			0
$46$	−1.80207			−0.265700
$47$	−1.53126	−	1.53126i	−0.223358	−	0.223358i	0.586553	−	0.809911i	$-0.300485\pi$
$47$	−1.53126	−	1.53126i	−0.223358	−	0.223358i	−0.809911	+	0.586553i	$0.800485\pi$
$48$		0			0
$49$			5.24535i			0.749335i
$50$	8.29893	+	3.50912i	1.17365	+	0.496264i
$51$		0			0
$52$	−5.45935	+	5.45935i	−0.757075	+	0.757075i
$53$	−2.98095	+	2.98095i	−0.409465	+	0.409465i	−0.881552	−	0.472087i	$-0.843501\pi$
$53$	−2.98095	+	2.98095i	−0.409465	+	0.409465i	0.472087	+	0.881552i	$0.343501\pi$
$54$		0			0
$55$	0.228420	+	1.17079i	0.0308001	+	0.157869i
$56$		−	1.79641i		−	0.240055i
$57$		0			0
$58$	11.6694	+	11.6694i	1.53227	+	1.53227i
$59$	−6.39579			−0.832660			−0.416330	−	0.909213i	$-0.636684\pi$
$59$	−6.39579			−0.832660			−0.416330	+	0.909213i	$0.636684\pi$
$60$		0			0
$61$	−12.6077			−1.61425			−0.807124	−	0.590381i	$-0.798977\pi$
$61$	−12.6077			−1.61425			−0.807124	+	0.590381i	$0.798977\pi$
$62$	2.83469	+	2.83469i	0.360007	+	0.360007i
$63$		0			0
$64$			1.27307i			0.159134i
$65$	−11.4788	−	7.73098i	−1.42377	−	0.958910i
$66$		0			0
$67$	9.65268	−	9.65268i	1.17926	−	1.17926i	0.199330	−	0.979932i	$-0.436123\pi$
$67$	9.65268	−	9.65268i	1.17926	−	1.17926i	0.979932	−	0.199330i	$-0.0638767\pi$
$68$	1.14910	−	1.14910i	0.139349	−	0.139349i
$69$		0			0
$70$	−5.23889	+	1.02211i	−0.626167	+	0.122165i
$71$			1.85834i			0.220545i	0.993901	+	0.110272i	$0.0351723\pi$
$71$			1.85834i			0.220545i	−0.993901	+	0.110272i	$0.964828\pi$
$72$		0			0
$73$	−9.68980	−	9.68980i	−1.13411	−	1.13411i	−0.989488	−	0.144618i	$-0.953805\pi$
$73$	−9.68980	−	9.68980i	−1.13411	−	1.13411i	−0.144618	−	0.989488i	$-0.546195\pi$
$74$	−5.48471			−0.637585
$75$		0			0
$76$	−9.96981			−1.14362
$77$	−0.499672	−	0.499672i	−0.0569429	−	0.0569429i
$78$		0			0
$79$		−	9.38659i		−	1.05607i	−0.849221	−	0.528037i	$-0.822928\pi$
$79$		−	9.38659i		−	1.05607i	0.849221	−	0.528037i	$-0.177072\pi$
$80$	−10.8391	+	2.11470i	−1.21184	+	0.236431i
$81$		0			0
$82$	14.3935	−	14.3935i	1.58950	−	1.58950i
$83$	−8.08083	+	8.08083i	−0.886986	+	0.886986i	−0.994232	−	0.107246i	$-0.965797\pi$
$83$	−8.08083	+	8.08083i	−0.886986	+	0.886986i	0.107246	+	0.994232i	$0.465797\pi$
$84$		0			0
$85$	2.41610	+	1.62725i	0.262063	+	0.176500i
$86$			13.7830i			1.48625i
$87$		0			0
$88$	−0.511563	−	0.511563i	−0.0545328	−	0.0545328i
$89$	12.2252			1.29587			0.647935	−	0.761696i	$-0.275633\pi$
$89$	12.2252			1.29587			0.647935	+	0.761696i	$0.275633\pi$
$90$		0			0
$91$	8.19842			0.859428
$92$	−0.882076	−	0.882076i	−0.0919628	−	0.0919628i
$93$		0			0
$94$		−	3.90243i		−	0.402505i
$95$	−3.42212	−	17.5404i	−0.351102	−	1.79960i
$96$		0			0
$97$	1.22394	−	1.22394i	0.124272	−	0.124272i	−0.642236	−	0.766507i	$-0.721993\pi$
$97$	1.22394	−	1.22394i	0.124272	−	0.124272i	0.766507	+	0.642236i	$0.221993\pi$
$98$	−6.68390	+	6.68390i	−0.675176	+	0.675176i
$99$		0			0
$100$	2.34452	+	5.77980i	0.234452	+	0.577980i
$101$			7.20392i			0.716816i	0.933565	+	0.358408i	$0.116680\pi$
$101$			7.20392i			0.716816i	−0.933565	+	0.358408i	$0.883320\pi$
$102$		0			0
$103$	2.36308	+	2.36308i	0.232841	+	0.232841i	0.813877	−	0.581037i	$-0.197353\pi$
$103$	2.36308	+	2.36308i	0.232841	+	0.232841i	−0.581037	+	0.813877i	$0.697353\pi$
$104$	8.39352			0.823052
$105$		0			0
$106$	−7.59697			−0.737883
$107$	7.04742	+	7.04742i	0.681300	+	0.681300i	0.960293	−	0.278993i	$-0.0900007\pi$
$107$	7.04742	+	7.04742i	0.681300	+	0.681300i	−0.278993	+	0.960293i	$0.590001\pi$
$108$		0			0
$109$			1.08372i			0.103802i	0.998652	+	0.0519009i	$0.0165280\pi$
$109$			1.08372i			0.103802i	−0.998652	+	0.0519009i	$0.983472\pi$
$110$	−1.20081	+	1.78294i	−0.114493	+	0.169997i
$111$		0			0
$112$	4.62594	−	4.62594i	0.437110	−	0.437110i
$113$	−4.48424	+	4.48424i	−0.421842	+	0.421842i	−0.885837	−	0.463996i	$-0.846415\pi$
$113$	−4.48424	+	4.48424i	−0.421842	+	0.421842i	0.463996	+	0.885837i	$0.346415\pi$
$114$		0			0
$115$	1.24911	−	1.85465i	0.116480	−	0.172947i
$116$			11.4239i			1.06068i
$117$		0			0
$118$	−8.14985	−	8.14985i	−0.750255	−	0.750255i
$119$	−1.72563			−0.158189
$120$		0			0
$121$	10.7154			0.974129
$122$	−16.0654	−	16.0654i	−1.45449	−	1.45449i
$123$		0			0
$124$			2.77505i			0.249207i
$125$	−9.36394	+	6.10873i	−0.837536	+	0.546382i
$126$		0			0
$127$	10.3715	−	10.3715i	0.920319	−	0.920319i	−0.0767325	−	0.997052i	$-0.524449\pi$
$127$	10.3715	−	10.3715i	0.920319	−	0.920319i	0.997052	+	0.0767325i	$0.0244487\pi$
$128$	7.12849	−	7.12849i	0.630075	−	0.630075i
$129$		0			0
$130$	−4.77568	−	24.4781i	−0.418855	−	2.14687i
$131$		−	5.06225i		−	0.442291i	−0.975241	−	0.221145i	$-0.929020\pi$
$131$		−	5.06225i		−	0.442291i	0.975241	−	0.221145i	$-0.0709796\pi$
$132$		0			0
$133$	7.48594	+	7.48594i	0.649114	+	0.649114i
$134$	24.5999			2.12511
$135$		0			0
$136$	−1.76670			−0.151493
$137$	−9.56489	−	9.56489i	−0.817184	−	0.817184i	0.168515	−	0.985699i	$-0.446103\pi$
$137$	−9.56489	−	9.56489i	−0.817184	−	0.817184i	−0.985699	+	0.168515i	$0.946103\pi$
$138$		0			0
$139$		−	21.6316i		−	1.83477i	−0.398007	−	0.917383i	$-0.630298\pi$
$139$		−	21.6316i		−	1.83477i	0.398007	−	0.917383i	$-0.369702\pi$
$140$	−3.06464	−	2.06403i	−0.259009	−	0.174443i
$141$		0			0
$142$	−2.36800	+	2.36800i	−0.198718	+	0.198718i
$143$	2.33466	−	2.33466i	0.195234	−	0.195234i
$144$		0			0
$145$	−20.0986	+	3.92123i	−1.66910	+	0.325640i
$146$		−	24.6945i		−	2.04373i
$147$		0			0
$148$	−2.68466	−	2.68466i	−0.220678	−	0.220678i
$149$	−6.45065			−0.528458			−0.264229	−	0.964460i	$-0.585117\pi$
$149$	−6.45065			−0.528458			−0.264229	+	0.964460i	$0.585117\pi$
$150$		0			0
$151$	−22.1115			−1.79940			−0.899702	−	0.436504i	$-0.856217\pi$
$151$	−22.1115			−1.79940			−0.899702	+	0.436504i	$0.856217\pi$
$152$	7.66409	+	7.66409i	0.621640	+	0.621640i
$153$		0			0
$154$		−	1.27342i		−	0.102615i
$155$	−4.88229	+	0.952533i	−0.392155	+	0.0765093i
$156$		0			0
$157$	7.12253	−	7.12253i	0.568440	−	0.568440i	−0.363251	−	0.931691i	$-0.618333\pi$
$157$	7.12253	−	7.12253i	0.568440	−	0.568440i	0.931691	+	0.363251i	$0.118333\pi$
$158$	11.9609	−	11.9609i	0.951558	−	0.951558i
$159$		0			0
$160$	−11.4760	−	7.72909i	−0.907257	−	0.611038i
$161$			1.32463i			0.104396i
$162$		0			0
$163$	2.06765	+	2.06765i	0.161951	+	0.161951i	0.783430	−	0.621480i	$-0.213468\pi$
$163$	2.06765	+	2.06765i	0.161951	+	0.161951i	−0.621480	+	0.783430i	$0.713468\pi$
$164$	14.0907			1.10030
$165$		0			0
$166$	−20.5940			−1.59841
$167$	5.95896	+	5.95896i	0.461118	+	0.461118i	0.899022	−	0.437904i	$-0.144279\pi$
$167$	5.95896	+	5.95896i	0.461118	+	0.461118i	−0.437904	+	0.899022i	$0.644279\pi$
$168$		0			0
$169$			25.3062i			1.94663i
$170$	1.00520	+	5.15225i	0.0770955	+	0.395159i
$171$		0			0
$172$	−6.74649	+	6.74649i	−0.514415	+	0.514415i
$173$	4.72810	−	4.72810i	0.359470	−	0.359470i	−0.504147	−	0.863618i	$-0.668193\pi$
$173$	4.72810	−	4.72810i	0.359470	−	0.359470i	0.863618	+	0.504147i	$0.168193\pi$
$174$		0			0
$175$	2.57942	−	6.10024i	0.194986	−	0.461135i
$176$		−	2.63465i		−	0.198594i
$177$		0			0
$178$	15.5780	+	15.5780i	1.16762	+	1.16762i
$179$	−23.8782			−1.78474			−0.892369	−	0.451306i	$-0.850958\pi$
$179$	−23.8782			−1.78474			−0.892369	+	0.451306i	$0.850958\pi$
$180$		0			0
$181$	−23.7387			−1.76449			−0.882243	−	0.470793i	$-0.843968\pi$
$181$	−23.7387			−1.76449			−0.882243	+	0.470793i	$0.843968\pi$
$182$	10.4469	+	10.4469i	0.774373	+	0.774373i
$183$		0			0
$184$			1.35616i			0.0999772i
$185$	3.80175	−	5.64475i	0.279510	−	0.415011i
$186$		0			0
$187$	−0.491408	+	0.491408i	−0.0359353	+	0.0359353i
$188$	1.91016	−	1.91016i	0.139313	−	0.139313i
$189$		0			0
$190$	17.9902	−	26.7115i	1.30515	−	1.93786i
$191$		−	6.20979i		−	0.449325i	−0.974437	−	0.224662i	$-0.927872\pi$
$191$		−	6.20979i		−	0.449325i	0.974437	−	0.224662i	$-0.0721279\pi$
$192$		0			0
$193$	−4.80730	−	4.80730i	−0.346037	−	0.346037i	0.512594	−	0.858631i	$-0.328685\pi$
$193$	−4.80730	−	4.80730i	−0.346037	−	0.346037i	−0.858631	+	0.512594i	$0.828685\pi$
$194$	3.11921			0.223946
$195$		0			0
$196$	−6.54328			−0.467377
$197$	−2.34082	−	2.34082i	−0.166776	−	0.166776i	0.618784	−	0.785561i	$-0.287625\pi$
$197$	−2.34082	−	2.34082i	−0.166776	−	0.166776i	−0.785561	+	0.618784i	$0.787625\pi$
$198$		0			0
$199$			7.11166i			0.504132i	0.967710	+	0.252066i	$0.0811100\pi$
$199$			7.11166i			0.504132i	−0.967710	+	0.252066i	$0.918890\pi$
$200$	2.64081	−	6.24541i	0.186733	−	0.441617i
$201$		0			0
$202$	−9.17962	+	9.17962i	−0.645876	+	0.645876i
$203$	8.57774	−	8.57774i	0.602039	−	0.602039i
$204$		0			0
$205$	4.83660	+	24.7904i	0.337803	+	1.73144i
$206$			6.02232i			0.419595i
$207$		0			0
$208$	21.6142	+	21.6142i	1.49867	+	1.49867i
$209$	4.26354			0.294915
$210$		0			0
$211$	3.27225			0.225271			0.112636	−	0.993636i	$-0.464071\pi$
$211$	3.27225			0.225271			0.112636	+	0.993636i	$0.464071\pi$
$212$	−3.71857	−	3.71857i	−0.255392	−	0.255392i
$213$		0			0
$214$			17.9604i			1.22775i
$215$	−14.1851	−	9.55370i	−0.967419	−	0.651557i
$216$		0			0
$217$	2.08368	−	2.08368i	0.141449	−	0.141449i
$218$	−1.38094	+	1.38094i	−0.0935289	+	0.0935289i
$219$		0			0
$220$	−1.46049	+	0.284941i	−0.0984662	+	0.0192107i
$221$		−	8.06283i		−	0.542365i
$222$		0			0
$223$	10.1203	+	10.1203i	0.677702	+	0.677702i	0.959480	−	0.281778i	$-0.0909240\pi$
$223$	10.1203	+	10.1203i	0.677702	+	0.677702i	−0.281778	+	0.959480i	$0.590924\pi$
$224$	8.19641			0.547646
$225$		0			0
$226$	−11.4281			−0.760187
$227$	8.81391	+	8.81391i	0.585000	+	0.585000i	0.936273	−	0.351273i	$-0.114251\pi$
$227$	8.81391	+	8.81391i	0.585000	+	0.585000i	−0.351273	+	0.936273i	$0.614251\pi$
$228$		0			0
$229$		−	11.3572i		−	0.750503i	−0.926923	−	0.375251i	$-0.877556\pi$
$229$		−	11.3572i		−	0.750503i	0.926923	−	0.375251i	$-0.122444\pi$
$230$	3.95498	−	0.771615i	0.260783	−	0.0508788i
$231$		0			0
$232$	8.78187	−	8.78187i	0.576558	−	0.576558i
$233$	−6.49018	+	6.49018i	−0.425186	+	0.425186i	−0.886985	−	0.461799i	$-0.847204\pi$
$233$	−6.49018	+	6.49018i	−0.425186	+	0.425186i	0.461799	+	0.886985i	$0.347204\pi$
$234$		0			0
$235$	4.01631	+	2.70498i	0.261995	+	0.176454i
$236$		−	7.97838i		−	0.519349i
$237$		0			0
$238$	−2.19889	−	2.19889i	−0.142533	−	0.142533i
$239$	−6.26735			−0.405401			−0.202700	−	0.979241i	$-0.564972\pi$
$239$	−6.26735			−0.405401			−0.202700	+	0.979241i	$0.564972\pi$
$240$		0			0
$241$	−12.0303			−0.774942			−0.387471	−	0.921882i	$-0.626651\pi$
$241$	−12.0303			−0.774942			−0.387471	+	0.921882i	$0.626651\pi$
$242$	13.6542	+	13.6542i	0.877722	+	0.877722i
$243$		0			0
$244$		−	15.7274i		−	1.00684i
$245$	−2.24597	−	11.5119i	−0.143490	−	0.735469i
$246$		0			0
$247$	−34.9772	+	34.9772i	−2.22555	+	2.22555i
$248$	2.13327	−	2.13327i	0.135463	−	0.135463i
$249$		0			0
$250$	−19.7161	−	4.14796i	−1.24696	−	0.262340i
$251$			18.3955i			1.16111i	0.814221	+	0.580556i	$0.197165\pi$
$251$			18.3955i			1.16111i	−0.814221	+	0.580556i	$0.802835\pi$
$252$		0			0
$253$	0.377215	+	0.377215i	0.0237153	+	0.0237153i
$254$	26.4318			1.65848
$255$		0			0
$256$	20.7131			1.29457
$257$	6.07409	+	6.07409i	0.378891	+	0.378891i	0.870702	−	0.491811i	$-0.163665\pi$
$257$	6.07409	+	6.07409i	0.378891	+	0.378891i	−0.491811	+	0.870702i	$0.663665\pi$
$258$		0			0
$259$			4.03161i			0.250512i
$260$	9.64396	−	14.3192i	0.598093	−	0.888037i
$261$		0			0
$262$	6.45059	−	6.45059i	0.398519	−	0.398519i
$263$	15.2849	−	15.2849i	0.942506	−	0.942506i	−0.0559284	−	0.998435i	$-0.517812\pi$
$263$	15.2849	−	15.2849i	0.942506	−	0.942506i	0.998435	+	0.0559284i	$0.0178119\pi$
$264$		0			0
$265$	5.26586	−	7.81865i	0.323480	−	0.480296i
$266$			19.0780i			1.16975i
$267$		0			0
$268$	12.0412	+	12.0412i	0.735532	+	0.735532i
$269$	−16.1707			−0.985946			−0.492973	−	0.870045i	$-0.664090\pi$
$269$	−16.1707			−0.985946			−0.492973	+	0.870045i	$0.664090\pi$
$270$		0			0
$271$	−11.8291			−0.718567			−0.359283	−	0.933228i	$-0.616979\pi$
$271$	−11.8291			−0.718567			−0.359283	+	0.933228i	$0.616979\pi$
$272$	−4.54943	−	4.54943i	−0.275850	−	0.275850i
$273$		0			0
$274$		−	24.3762i		−	1.47262i
$275$	−1.00262	−	2.47170i	−0.0604603	−	0.149049i
$276$		0			0
$277$	−3.27773	+	3.27773i	−0.196940	+	0.196940i	−0.798687	−	0.601747i	$-0.794472\pi$
$277$	−3.27773	+	3.27773i	−0.196940	+	0.196940i	0.601747	+	0.798687i	$0.294472\pi$
$278$	27.5641	−	27.5641i	1.65318	−	1.65318i
$279$		0			0
$280$	0.769192	+	3.94256i	0.0459680	+	0.235613i
$281$		−	18.3950i		−	1.09735i	−0.836034	−	0.548677i	$-0.815132\pi$
$281$		−	18.3950i		−	1.09735i	0.836034	−	0.548677i	$-0.184868\pi$
$282$		0			0
$283$	8.74223	+	8.74223i	0.519671	+	0.519671i	0.917472	−	0.397800i	$-0.130226\pi$
$283$	8.74223	+	8.74223i	0.519671	+	0.519671i	−0.397800	+	0.917472i	$0.630226\pi$
$284$	−2.31818			−0.137558
$285$		0			0
$286$	5.94990			0.351825
$287$	−10.5801	−	10.5801i	−0.624526	−	0.624526i
$288$		0			0
$289$		−	15.3029i		−	0.900171i
$290$	−30.6073	−	20.6140i	−1.79732	−	1.21050i
$291$		0			0
$292$	12.0875	−	12.0875i	0.707366	−	0.707366i
$293$	10.7596	−	10.7596i	0.628584	−	0.628584i	−0.319128	−	0.947712i	$-0.603390\pi$
$293$	10.7596	−	10.7596i	0.628584	−	0.628584i	0.947712	+	0.319128i	$0.103390\pi$
$294$		0			0
$295$	14.0368	−	2.73857i	0.817252	−	0.159446i
$296$			4.12755i			0.239909i
$297$		0			0
$298$	−8.21976	−	8.21976i	−0.476158	−	0.476158i
$299$	−6.18920			−0.357931
$300$		0			0
$301$	10.1313			0.583961
$302$	−28.1756	−	28.1756i	−1.62132	−	1.62132i
$303$		0			0
$304$			39.4716i			2.26385i
$305$	27.6700	−	5.39840i	1.58438	−	0.309111i
$306$		0			0
$307$	−14.1297	+	14.1297i	−0.806424	+	0.806424i	−0.984091	−	0.177666i	$-0.943145\pi$
$307$	−14.1297	+	14.1297i	−0.806424	+	0.806424i	0.177666	+	0.984091i	$0.443145\pi$
$308$	0.623313	−	0.623313i	0.0355165	−	0.0355165i
$309$		0			0
$310$	−7.43504	−	5.00750i	−0.422282	−	0.284407i
$311$			1.21478i			0.0688838i	0.999407	+	0.0344419i	$0.0109654\pi$
$311$			1.21478i			0.0688838i	−0.999407	+	0.0344419i	$0.989035\pi$
$312$		0			0
$313$	−15.1232	−	15.1232i	−0.854813	−	0.854813i	0.135908	−	0.990721i	$-0.456605\pi$
$313$	−15.1232	−	15.1232i	−0.854813	−	0.854813i	−0.990721	+	0.135908i	$0.956605\pi$
$314$	18.1518			1.02437
$315$		0			0
$316$	11.7092			0.658696
$317$	−11.9762	−	11.9762i	−0.672653	−	0.672653i	0.285674	−	0.958327i	$-0.407783\pi$
$317$	−11.9762	−	11.9762i	−0.672653	−	0.672653i	−0.958327	+	0.285674i	$0.907783\pi$
$318$		0			0
$319$		−	4.88536i		−	0.273528i
$320$	−0.545109	−	2.79400i	−0.0304725	−	0.156189i
$321$		0			0
$322$	−1.68792	+	1.68792i	−0.0940640	+	0.0940640i
$323$	7.36214	−	7.36214i	0.409640	−	0.409640i
$324$		0			0
$325$	28.5027	+	12.0521i	1.58104	+	0.668528i
$326$			5.26942i			0.291846i
$327$		0			0
$328$	−10.8319	−	10.8319i	−0.598093	−	0.598093i
$329$	−2.86854			−0.158148
$330$		0			0
$331$	−12.8930			−0.708662			−0.354331	−	0.935120i	$-0.615291\pi$
$331$	−12.8930			−0.708662			−0.354331	+	0.935120i	$0.615291\pi$
$332$	−10.0804	−	10.0804i	−0.553233	−	0.553233i
$333$		0			0
$334$			15.1864i			0.830965i
$335$	−17.0515	+	25.3177i	−0.931624	+	1.38326i
$336$		0			0
$337$	−1.70473	+	1.70473i	−0.0928626	+	0.0928626i	−0.752012	−	0.659149i	$-0.770916\pi$
$337$	−1.70473	+	1.70473i	−0.0928626	+	0.0928626i	0.659149	+	0.752012i	$0.270916\pi$
$338$	−32.2465	+	32.2465i	−1.75398	+	1.75398i
$339$		0			0
$340$	−2.02990	+	3.01395i	−0.110087	+	0.163454i
$341$		−	1.18674i		−	0.0642655i
$342$		0			0
$343$	11.4697	+	11.4697i	0.619305	+	0.619305i
$344$	10.3724			0.559245
$345$		0			0
$346$	12.0496			0.647790
$347$	12.0394	+	12.0394i	0.646307	+	0.646307i	0.952098	−	0.305792i	$-0.0989211\pi$
$347$	12.0394	+	12.0394i	0.646307	+	0.646307i	−0.305792	+	0.952098i	$0.598921\pi$
$348$		0			0
$349$			1.70930i			0.0914968i	0.998953	+	0.0457484i	$0.0145673\pi$
$349$			1.70930i			0.0914968i	−0.998953	+	0.0457484i	$0.985433\pi$
$350$	11.0601	−	4.48641i	0.591187	−	0.239809i
$351$		0			0
$352$	2.33409	−	2.33409i	0.124407	−	0.124407i
$353$	0.986758	−	0.986758i	0.0525198	−	0.0525198i	−0.680359	−	0.732879i	$-0.738176\pi$
$353$	0.986758	−	0.986758i	0.0525198	−	0.0525198i	0.732879	+	0.680359i	$0.238176\pi$
$354$		0			0
$355$	−0.795710	−	4.07848i	−0.0422319	−	0.216463i
$356$			15.2503i			0.808262i
$357$		0			0
$358$	−30.4269	−	30.4269i	−1.60811	−	1.60811i
$359$	8.94564			0.472133			0.236066	−	0.971737i	$-0.424142\pi$
$359$	8.94564			0.472133			0.236066	+	0.971737i	$0.424142\pi$
$360$		0			0
$361$	−44.8751			−2.36185
$362$	−30.2492	−	30.2492i	−1.58986	−	1.58986i
$363$		0			0
$364$			10.2271i			0.536044i
$365$	25.4151	+	17.1171i	1.33029	+	0.895949i
$366$		0			0
$367$	7.49247	−	7.49247i	0.391104	−	0.391104i	−0.483977	−	0.875081i	$-0.660808\pi$
$367$	7.49247	−	7.49247i	0.391104	−	0.391104i	0.875081	+	0.483977i	$0.160808\pi$
$368$	−3.49224	+	3.49224i	−0.182046	+	0.182046i
$369$		0			0
$370$	12.0372	−	2.34846i	0.625786	−	0.122091i
$371$			5.58426i			0.289920i
$372$		0			0
$373$	5.23284	+	5.23284i	0.270946	+	0.270946i	0.829481	−	0.558535i	$-0.188636\pi$
$373$	5.23284	+	5.23284i	0.270946	+	0.270946i	−0.558535	+	0.829481i	$0.688636\pi$
$374$	−1.25236			−0.0647578
$375$		0			0
$376$	−2.93680			−0.151454
$377$	40.0785	+	40.0785i	2.06415	+	2.06415i
$378$		0			0
$379$		−	7.29597i		−	0.374769i	−0.982287	−	0.187384i	$-0.939999\pi$
$379$		−	7.29597i		−	0.374769i	0.982287	−	0.187384i	$-0.0600010\pi$
$380$	21.8806	−	4.26891i	1.12245	−	0.218990i
$381$		0			0
$382$	7.91285	−	7.91285i	0.404857	−	0.404857i
$383$	7.74755	−	7.74755i	0.395881	−	0.395881i	−0.480896	−	0.876777i	$-0.659689\pi$
$383$	7.74755	−	7.74755i	0.395881	−	0.395881i	0.876777	+	0.480896i	$0.159689\pi$
$384$		0			0
$385$	1.31058	+	0.882674i	0.0667931	+	0.0449852i
$386$		−	12.2514i		−	0.623581i
$387$		0			0
$388$	1.52679	+	1.52679i	0.0775111	+	0.0775111i
$389$	24.8418			1.25953			0.629765	−	0.776786i	$-0.283151\pi$
$389$	24.8418			1.25953			0.629765	+	0.776786i	$0.283151\pi$
$390$		0			0
$391$	1.30273			0.0658817
$392$	5.03001	+	5.03001i	0.254054	+	0.254054i
$393$		0			0
$394$		−	5.96559i		−	0.300542i
$395$	4.01918	+	20.6006i	0.202227	+	1.03653i
$396$		0			0
$397$	20.2528	−	20.2528i	1.01646	−	1.01646i	0.0165980	−	0.999862i	$-0.494716\pi$
$397$	20.2528	−	20.2528i	1.01646	−	1.01646i	0.999862	−	0.0165980i	$-0.00528354\pi$
$398$	−9.06206	+	9.06206i	−0.454240	+	0.454240i
$399$		0			0
$400$	22.8829	−	9.28221i	1.14415	−	0.464111i
$401$		−	19.4537i		−	0.971473i	−0.874105	−	0.485736i	$-0.838552\pi$
$401$		−	19.4537i		−	0.971473i	0.874105	−	0.485736i	$-0.161448\pi$
$402$		0			0
$403$	9.73576	+	9.73576i	0.484973	+	0.484973i
$404$	−8.98648			−0.447094
$405$		0			0
$406$	21.8604			1.08491
$407$	1.14808	+	1.14808i	0.0569082	+	0.0569082i
$408$		0			0
$409$			20.3346i			1.00548i	0.864437	+	0.502741i	$0.167675\pi$
$409$			20.3346i			1.00548i	−0.864437	+	0.502741i	$0.832325\pi$
$410$	−25.4262	+	37.7523i	−1.25571	+	1.86445i
$411$		0			0
$412$	−2.94781	+	2.94781i	−0.145228	+	0.145228i
$413$	−5.99066	+	5.99066i	−0.294781	+	0.294781i
$414$		0			0
$415$	14.2748	−	21.1950i	0.700724	−	1.04042i
$416$			38.2968i			1.87766i
$417$		0			0
$418$	5.43283	+	5.43283i	0.265728	+	0.265728i
$419$	−28.5701			−1.39574			−0.697871	−	0.716224i	$-0.745869\pi$
$419$	−28.5701			−1.39574			−0.697871	+	0.716224i	$0.745869\pi$
$420$		0			0
$421$	3.06521			0.149389			0.0746945	−	0.997206i	$-0.476202\pi$
$421$	3.06521			0.149389			0.0746945	+	0.997206i	$0.476202\pi$
$422$	4.16968	+	4.16968i	0.202977	+	0.202977i
$423$		0			0
$424$			5.71715i			0.277649i
$425$	−5.99935	−	2.53676i	−0.291011	−	0.123051i
$426$		0			0
$427$	−11.8091	+	11.8091i	−0.571481	+	0.571481i
$428$	−8.79126	+	8.79126i	−0.424942	+	0.424942i
$429$		0			0
$430$	−5.90163	−	30.2493i	−0.284602	−	1.45875i
$431$			14.0429i			0.676421i	0.941071	+	0.338210i	$0.109822\pi$
$431$			14.0429i			0.676421i	−0.941071	+	0.338210i	$0.890178\pi$
$432$		0			0
$433$	−20.0530	−	20.0530i	−0.963687	−	0.963687i	0.0356760	−	0.999363i	$-0.488642\pi$
$433$	−20.0530	−	20.0530i	−0.963687	−	0.963687i	−0.999363	+	0.0356760i	$0.988642\pi$
$434$	5.31027			0.254901
$435$		0			0
$436$	−1.35188			−0.0647435
$437$	−5.65133	−	5.65133i	−0.270340	−	0.270340i
$438$		0			0
$439$			20.1834i			0.963300i	0.876364	+	0.481650i	$0.159962\pi$
$439$			20.1834i			0.963300i	−0.876364	+	0.481650i	$0.840038\pi$
$440$	1.34176	+	0.903679i	0.0639661	+	0.0430812i
$441$		0			0
$442$	10.2741	−	10.2741i	0.488689	−	0.488689i
$443$	0.710248	−	0.710248i	0.0337449	−	0.0337449i	−0.690033	−	0.723778i	$-0.742404\pi$
$443$	0.710248	−	0.710248i	0.0337449	−	0.0337449i	0.723778	+	0.690033i	$0.242404\pi$
$444$		0			0
$445$	−26.8305	+	5.23463i	−1.27189	+	0.248145i
$446$			25.7915i			1.22126i
$447$		0			0
$448$	1.19243	+	1.19243i	0.0563372	+	0.0563372i
$449$	−31.2791			−1.47615			−0.738077	−	0.674716i	$-0.764266\pi$
$449$	−31.2791			−1.47615			−0.738077	+	0.674716i	$0.764266\pi$
$450$		0			0
$451$	−6.02581			−0.283744
$452$	−5.59384	−	5.59384i	−0.263112	−	0.263112i
$453$		0			0
$454$			22.4623i			1.05421i
$455$	−17.9930	+	3.51043i	−0.843524	+	0.164571i
$456$		0			0
$457$	8.50810	−	8.50810i	0.397992	−	0.397992i	−0.479532	−	0.877524i	$-0.659194\pi$
$457$	8.50810	−	8.50810i	0.397992	−	0.397992i	0.877524	+	0.479532i	$0.159194\pi$
$458$	14.4719	−	14.4719i	0.676228	−	0.676228i
$459$		0			0
$460$	2.31357	+	1.55819i	0.107871	+	0.0726511i
$461$			2.35109i			0.109501i	0.998500	+	0.0547505i	$0.0174363\pi$
$461$			2.35109i			0.109501i	−0.998500	+	0.0547505i	$0.982564\pi$
$462$		0			0
$463$	5.92380	+	5.92380i	0.275303	+	0.275303i	0.831230	−	0.555928i	$-0.187637\pi$
$463$	5.92380	+	5.92380i	0.275303	+	0.275303i	−0.555928	+	0.831230i	$0.687637\pi$
$464$	45.2284			2.09968
$465$		0			0
$466$	−16.5403			−0.766213
$467$	−20.1333	−	20.1333i	−0.931658	−	0.931658i	0.0661517	−	0.997810i	$-0.478928\pi$
$467$	−20.1333	−	20.1333i	−0.931658	−	0.931658i	−0.997810	+	0.0661517i	$0.978928\pi$
$468$		0			0
$469$		−	18.0825i		−	0.834973i
$470$	1.67096	+	8.56463i	0.0770755	+	0.395057i
$471$		0			0
$472$	−6.13322	+	6.13322i	−0.282304	+	0.282304i
$473$	2.88510	−	2.88510i	0.132657	−	0.132657i
$474$		0			0
$475$	15.0210	+	37.0304i	0.689210	+	1.69907i
$476$		−	2.15263i		−	0.0986657i
$477$		0			0
$478$	−7.98619	−	7.98619i	−0.365280	−	0.365280i
$479$	−20.8959			−0.954759			−0.477380	−	0.878697i	$-0.658413\pi$
$479$	−20.8959			−0.954759			−0.477380	+	0.878697i	$0.658413\pi$
$480$		0			0
$481$	−18.8373			−0.858905
$482$	−15.3297	−	15.3297i	−0.698249	−	0.698249i
$483$		0			0
$484$			13.3669i			0.607586i
$485$	−2.16209	+	3.21023i	−0.0981754	+	0.145769i
$486$		0			0
$487$	12.4452	−	12.4452i	0.563945	−	0.563945i	−0.366481	−	0.930426i	$-0.619437\pi$
$487$	12.4452	−	12.4452i	0.563945	−	0.563945i	0.930426	+	0.366481i	$0.119437\pi$
$488$	−12.0901	+	12.0901i	−0.547293	+	0.547293i
$489$		0			0
$490$	11.8072	−	17.5310i	0.533393	−	0.791971i
$491$			11.6286i			0.524793i	0.964960	+	0.262397i	$0.0845129\pi$
$491$			11.6286i			0.524793i	−0.964960	+	0.262397i	$0.915487\pi$
$492$		0			0
$493$	−8.43587	−	8.43587i	−0.379933	−	0.379933i
$494$	−89.1397			−4.01059
$495$		0			0
$496$	10.9868			0.493320
$497$	1.74063	+	1.74063i	0.0780779	+	0.0780779i
$498$		0			0
$499$		−	30.2364i		−	1.35357i	−0.736182	−	0.676784i	$-0.763373\pi$
$499$		−	30.2364i		−	1.35357i	0.736182	−	0.676784i	$-0.236627\pi$
$500$	−7.62030	−	11.6810i	−0.340790	−	0.522390i
$501$		0			0
$502$	−23.4405	+	23.4405i	−1.04620	+	1.04620i
$503$	−22.8361	+	22.8361i	−1.01821	+	1.01821i	−0.0183783	+	0.999831i	$0.505850\pi$
$503$	−22.8361	+	22.8361i	−1.01821	+	1.01821i	−0.999831	+	0.0183783i	$0.994150\pi$
$504$		0			0
$505$	−3.08460	−	15.8104i	−0.137263	−	0.703552i
$506$			0.961336i			0.0427366i
$507$		0			0
$508$	12.9378	+	12.9378i	0.574023	+	0.574023i
$509$	3.97176			0.176045			0.0880225	−	0.996118i	$-0.471945\pi$
$509$	3.97176			0.176045			0.0880225	+	0.996118i	$0.471945\pi$
$510$		0			0
$511$	−18.1520			−0.802999
$512$	12.1368	+	12.1368i	0.536377	+	0.536377i
$513$		0			0
$514$			15.4799i			0.682787i
$515$	−6.19805	−	4.17439i	−0.273119	−	0.183946i
$516$		0			0
$517$	−0.816872	+	0.816872i	−0.0359260	+	0.0359260i
$518$	−5.13729	+	5.13729i	−0.225720	+	0.225720i
$519$		0			0
$520$	−18.4212	+	3.59396i	−0.807822	+	0.157606i
$521$			11.5247i			0.504904i	0.967609	+	0.252452i	$0.0812370\pi$
$521$			11.5247i			0.504904i	−0.967609	+	0.252452i	$0.918763\pi$
$522$		0			0
$523$	8.87857	+	8.87857i	0.388233	+	0.388233i	0.874057	−	0.485824i	$-0.161480\pi$
$523$	8.87857	+	8.87857i	0.388233	+	0.388233i	−0.485824	+	0.874057i	$0.661480\pi$
$524$	6.31488			0.275867
$525$		0			0
$526$	38.9536			1.69846
$527$	−2.04922	−	2.04922i	−0.0892654	−	0.0892654i
$528$		0			0
$529$		−	1.00000i		−	0.0434783i
$530$	16.6730	−	3.25290i	0.724228	−	0.141297i
$531$		0			0
$532$	−9.33829	+	9.33829i	−0.404866	+	0.404866i
$533$	49.4345	−	49.4345i	2.14125	−	2.14125i
$534$		0			0
$535$	−18.4845	−	12.4493i	−0.799154	−	0.538230i
$536$		−	18.5128i		−	0.799632i
$537$		0			0
$538$	−20.6056	−	20.6056i	−0.888370	−	0.888370i
$539$	2.79820			0.120527
$540$		0			0
$541$	7.01221			0.301479			0.150739	−	0.988574i	$-0.451835\pi$
$541$	7.01221			0.301479			0.150739	+	0.988574i	$0.451835\pi$
$542$	−15.0733	−	15.0733i	−0.647453	−	0.647453i
$543$		0			0
$544$		−	8.06085i		−	0.345606i
$545$	−0.464032	−	2.37844i	−0.0198769	−	0.101881i
$546$		0			0
$547$	2.87026	−	2.87026i	0.122723	−	0.122723i	−0.643078	−	0.765801i	$-0.722343\pi$
$547$	2.87026	−	2.87026i	0.122723	−	0.122723i	0.765801	+	0.643078i	$0.222343\pi$
$548$	11.9317	−	11.9317i	0.509695	−	0.509695i
$549$		0			0
$550$	1.87198	−	4.42717i	0.0798217	−	0.188775i
$551$			73.1911i			3.11804i
$552$		0			0
$553$	−8.79202	−	8.79202i	−0.373875	−	0.373875i
$554$	−8.35332			−0.354899
$555$		0			0
$556$	26.9842			1.14438
$557$	−19.8219	−	19.8219i	−0.839881	−	0.839881i	0.148962	−	0.988843i	$-0.452407\pi$
$557$	−19.8219	−	19.8219i	−0.839881	−	0.839881i	−0.988843	+	0.148962i	$0.952407\pi$
$558$		0			0
$559$			47.3376i			2.00217i
$560$	−8.17174	+	12.1332i	−0.345319	+	0.512723i
$561$		0			0
$562$	23.4399	−	23.4399i	0.988753	−	0.988753i
$563$	−2.74958	+	2.74958i	−0.115881	+	0.115881i	−0.762669	−	0.646789i	$-0.776112\pi$
$563$	−2.74958	+	2.74958i	−0.115881	+	0.115881i	0.646789	+	0.762669i	$0.276112\pi$
$564$		0			0
$565$	7.92143	−	11.7616i	0.333257	−	0.494814i
$566$			22.2796i			0.936483i
$567$		0			0
$568$	1.78205	+	1.78205i	0.0747732	+	0.0747732i
$569$	−13.9469			−0.584686			−0.292343	−	0.956314i	$-0.594435\pi$
$569$	−13.9469			−0.584686			−0.292343	+	0.956314i	$0.594435\pi$
$570$		0			0
$571$	29.8881			1.25078			0.625389	−	0.780313i	$-0.284940\pi$
$571$	29.8881			1.25078			0.625389	+	0.780313i	$0.284940\pi$
$572$	2.91236	+	2.91236i	0.121772	+	0.121772i
$573$		0			0
$574$		−	26.9636i		−	1.12544i
$575$	−1.94727	+	4.60523i	−0.0812069	+	0.192051i
$576$		0			0
$577$	−9.19787	+	9.19787i	−0.382912	+	0.382912i	−0.872150	−	0.489238i	$-0.837275\pi$
$577$	−9.19787	+	9.19787i	−0.382912	+	0.382912i	0.489238	+	0.872150i	$0.337275\pi$
$578$	19.4998	−	19.4998i	0.811084	−	0.811084i
$579$		0			0
$580$	−4.89151	−	25.0718i	−0.203109	−	1.04105i
$581$			15.1379i			0.628027i
$582$		0			0
$583$	1.59023	+	1.59023i	0.0658605	+	0.0658605i
$584$	−18.5840			−0.769012
$585$		0			0
$586$	27.4210			1.13275
$587$	30.6312	+	30.6312i	1.26428	+	1.26428i	0.948996	+	0.315289i	$0.102101\pi$
$587$	30.6312	+	30.6312i	1.26428	+	1.26428i	0.315289	+	0.948996i	$0.397899\pi$
$588$		0			0
$589$			17.7794i			0.732586i
$590$	21.3760	+	14.3968i	0.880037	+	0.592705i
$591$		0			0
$592$	−10.6289	+	10.6289i	−0.436844	+	0.436844i
$593$	−9.47498	+	9.47498i	−0.389091	+	0.389091i	−0.874363	−	0.485272i	$-0.838720\pi$
$593$	−9.47498	+	9.47498i	−0.389091	+	0.389091i	0.485272	+	0.874363i	$0.338720\pi$
$594$		0			0
$595$	3.78723	−	0.738887i	0.155261	−	0.0302914i
$596$		−	8.04682i		−	0.329611i
$597$		0			0
$598$	−7.88661	−	7.88661i	−0.322507	−	0.322507i
$599$	15.3900			0.628820			0.314410	−	0.949287i	$-0.398193\pi$
$599$	15.3900			0.628820			0.314410	+	0.949287i	$0.398193\pi$
$600$		0			0
$601$	0.231410			0.00943942			0.00471971	−	0.999989i	$-0.498498\pi$
$601$	0.231410			0.00943942			0.00471971	+	0.999989i	$0.498498\pi$
$602$	12.9099	+	12.9099i	0.526168	+	0.526168i
$603$		0			0
$604$		−	27.5828i		−	1.12233i
$605$	−23.5170	+	4.58816i	−0.956102	+	0.186535i
$606$		0			0
$607$	−1.30895	+	1.30895i	−0.0531288	+	0.0531288i	−0.733172	−	0.680043i	$-0.761961\pi$
$607$	−1.30895	+	1.30895i	−0.0531288	+	0.0531288i	0.680043	+	0.733172i	$0.261961\pi$
$608$	−34.9687	+	34.9687i	−1.41817	+	1.41817i
$609$		0			0
$610$	42.1375	+	28.3796i	1.70610	+	1.14906i
$611$		−	13.4029i		−	0.542224i
$612$		0			0
$613$	5.44641	+	5.44641i	0.219978	+	0.219978i	0.808489	−	0.588511i	$-0.200286\pi$
$613$	5.44641	+	5.44641i	0.219978	+	0.219978i	−0.588511	+	0.808489i	$0.700286\pi$
$614$	−36.0096			−1.45323
$615$		0			0
$616$	−0.958318			−0.0386117
$617$	1.38033	+	1.38033i	0.0555700	+	0.0555700i	0.734346	−	0.678776i	$-0.237489\pi$
$617$	1.38033	+	1.38033i	0.0555700	+	0.0555700i	−0.678776	+	0.734346i	$0.737489\pi$
$618$		0			0
$619$		−	13.4436i		−	0.540345i	−0.962812	−	0.270172i	$-0.912919\pi$
$619$		−	13.4436i		−	0.540345i	0.962812	−	0.270172i	$-0.0870807\pi$
$620$	−1.18823	−	6.09038i	−0.0477205	−	0.244596i
$621$		0			0
$622$	−1.54794	+	1.54794i	−0.0620666	+	0.0620666i
$623$	11.4508	−	11.4508i	0.458768	−	0.458768i
$624$		0			0
$625$	17.9353	−	17.4163i	0.717411	−	0.696650i
$626$		−	38.5415i		−	1.54043i
$627$		0			0
$628$	8.88496	+	8.88496i	0.354548	+	0.354548i
$629$	3.96493			0.158092
$630$		0			0
$631$	26.4123			1.05146			0.525729	−	0.850652i	$-0.323792\pi$
$631$	26.4123			1.05146			0.525729	+	0.850652i	$0.323792\pi$
$632$	−9.00124	−	9.00124i	−0.358050	−	0.358050i
$633$		0			0
$634$		−	30.5216i		−	1.21217i
$635$	−18.3213	+	27.2030i	−0.727057	+	1.07952i
$636$		0			0
$637$	−22.9559	+	22.9559i	−0.909545	+	0.909545i
$638$	6.22519	−	6.22519i	0.246458	−	0.246458i
$639$		0			0
$640$	−12.5925	+	18.6971i	−0.497763	+	0.739068i
$641$			5.22599i			0.206414i	0.994660	+	0.103207i	$0.0329105\pi$
$641$			5.22599i			0.206414i	−0.994660	+	0.103207i	$0.967090\pi$
$642$		0			0
$643$	−26.2399	−	26.2399i	−1.03480	−	1.03480i	−0.999372	−	0.0354298i	$-0.988720\pi$
$643$	−26.2399	−	26.2399i	−1.03480	−	1.03480i	−0.0354298	−	0.999372i	$-0.511280\pi$
$644$	−1.65241			−0.0651139
$645$		0			0
$646$	18.7625			0.738199
$647$	30.7754	+	30.7754i	1.20991	+	1.20991i	0.971056	+	0.238850i	$0.0767704\pi$
$647$	30.7754	+	30.7754i	1.20991	+	1.20991i	0.238850	+	0.971056i	$0.423230\pi$
$648$		0			0
$649$			3.41192i			0.133929i
$650$	20.9622	+	51.6770i	0.822207	+	2.02694i
$651$		0			0
$652$	−2.57928	+	2.57928i	−0.101012	+	0.101012i
$653$	18.9530	−	18.9530i	0.741687	−	0.741687i	−0.231215	−	0.972903i	$-0.574270\pi$
$653$	18.9530	−	18.9530i	0.741687	−	0.741687i	0.972903	+	0.231215i	$0.0742702\pi$
$654$		0			0
$655$	2.16757	+	11.1101i	0.0846940	+	0.434106i
$656$		−	55.7866i		−	2.17810i
$657$		0			0
$658$	−3.65524	−	3.65524i	−0.142496	−	0.142496i
$659$	−36.5329			−1.42312			−0.711560	−	0.702625i	$-0.752011\pi$
$659$	−36.5329			−1.42312			−0.711560	+	0.702625i	$0.752011\pi$
$660$		0			0
$661$	9.23098			0.359044			0.179522	−	0.983754i	$-0.442545\pi$
$661$	9.23098			0.359044			0.179522	+	0.983754i	$0.442545\pi$
$662$	−16.4289	−	16.4289i	−0.638528	−	0.638528i
$663$		0			0
$664$			15.4982i			0.601446i
$665$	−19.6347	−	13.2240i	−0.761400	−	0.512803i
$666$		0			0
$667$	−6.47556	+	6.47556i	−0.250735	+	0.250735i
$668$	−7.43347	+	7.43347i	−0.287609	+	0.287609i
$669$		0			0
$670$	−53.9892	+	10.5333i	−2.08578	+	0.406936i
$671$			6.72574i			0.259644i
$672$		0			0
$673$	22.0039	+	22.0039i	0.848188	+	0.848188i	0.989907	−	0.141719i	$-0.0452628\pi$
$673$	22.0039	+	22.0039i	0.848188	+	0.848188i	−0.141719	+	0.989907i	$0.545263\pi$
$674$	−4.34452			−0.167345
$675$		0			0
$676$	−31.5681			−1.21416
$677$	31.5949	+	31.5949i	1.21429	+	1.21429i	0.969602	+	0.244687i	$0.0786852\pi$
$677$	31.5949	+	31.5949i	1.21429	+	1.21429i	0.244687	+	0.969602i	$0.421315\pi$
$678$		0			0
$679$		−	2.29282i		−	0.0879902i
$680$	3.87735	−	0.756471i	0.148690	−	0.0290093i
$681$		0			0
$682$	1.51221	−	1.51221i	0.0579053	−	0.0579053i
$683$	3.30866	−	3.30866i	0.126602	−	0.126602i	−0.640967	−	0.767569i	$-0.721466\pi$
$683$	3.30866	−	3.30866i	0.126602	−	0.126602i	0.767569	+	0.640967i	$0.221466\pi$
$684$		0			0
$685$	25.0875	+	16.8964i	0.958544	+	0.645580i
$686$			29.2306i			1.11603i
$687$		0			0
$688$	26.7101	+	26.7101i	1.01831	+	1.01831i
$689$	−26.0918			−0.994019
$690$		0			0
$691$	25.0658			0.953549			0.476775	−	0.879026i	$-0.341806\pi$
$691$	25.0658			0.953549			0.476775	+	0.879026i	$0.341806\pi$
$692$	5.89803	+	5.89803i	0.224210	+	0.224210i
$693$		0			0
$694$			30.6824i			1.16469i
$695$	9.26227	+	47.4745i	0.351338	+	1.80081i
$696$		0			0
$697$	−10.4052	+	10.4052i	−0.394123	+	0.394123i
$698$	−2.17808	+	2.17808i	−0.0824417	+	0.0824417i
$699$		0			0
$700$	7.60970	+	3.21769i	0.287620	+	0.121617i
$701$		−	48.9894i		−	1.85030i	−0.379596	−	0.925152i	$-0.623937\pi$
$701$		−	48.9894i		−	1.85030i	0.379596	−	0.925152i	$-0.376063\pi$
$702$		0			0
$703$	−17.2002	−	17.2002i	−0.648718	−	0.648718i
$704$	0.679138			0.0255960
$705$		0			0
$706$	2.51476			0.0946443
$707$	6.74760	+	6.74760i	0.253770	+	0.253770i
$708$		0			0
$709$		−	20.4113i		−	0.766561i	−0.923632	−	0.383280i	$-0.874794\pi$
$709$		−	20.4113i		−	0.766561i	0.923632	−	0.383280i	$-0.125206\pi$
$710$	4.18308	−	6.21095i	0.156988	−	0.233093i
$711$		0			0
$712$	11.7233	−	11.7233i	0.439350	−	0.439350i
$713$	−1.57302	+	1.57302i	−0.0589102	+	0.0589102i
$714$		0			0
$715$	−4.12419	+	6.12352i	−0.154236	+	0.229007i
$716$		−	29.7867i		−	1.11318i
$717$		0			0
$718$	11.3990	+	11.3990i	0.425407	+	0.425407i
$719$	25.8313			0.963344			0.481672	−	0.876352i	$-0.340030\pi$
$719$	25.8313			0.963344			0.481672	+	0.876352i	$0.340030\pi$
$720$		0			0
$721$	4.42679			0.164862
$722$	−57.1823	−	57.1823i	−2.12810	−	2.12810i
$723$		0			0
$724$		−	29.6128i		−	1.10055i
$725$	42.4311	−	17.2117i	1.57585	−	0.639228i
$726$		0			0
$727$	20.2221	−	20.2221i	0.749998	−	0.749998i	−0.224481	−	0.974479i	$-0.572069\pi$
$727$	20.2221	−	20.2221i	0.749998	−	0.749998i	0.974479	+	0.224481i	$0.0720686\pi$
$728$	7.86185	−	7.86185i	0.291380	−	0.291380i
$729$		0			0
$730$	10.5738	+	54.1968i	0.391353	+	2.00591i
$731$		−	9.96379i		−	0.368524i
$732$		0			0
$733$	−31.9757	−	31.9757i	−1.18105	−	1.18105i	−0.979473	−	0.201575i	$-0.935394\pi$
$733$	−31.9757	−	31.9757i	−1.18105	−	1.18105i	−0.201575	−	0.979473i	$-0.564606\pi$
$734$	19.0946			0.704795
$735$		0			0
$736$	−6.18768			−0.228081
$737$	−5.14935	−	5.14935i	−0.189679	−	0.189679i
$738$		0			0
$739$			7.36651i			0.270981i	0.990779	+	0.135491i	$0.0432611\pi$
$739$			7.36651i			0.270981i	−0.990779	+	0.135491i	$0.956739\pi$
$740$	7.04152	+	4.74246i	0.258851	+	0.174336i
$741$		0			0
$742$	−7.11576	+	7.11576i	−0.261228	+	0.261228i
$743$	−7.01455	+	7.01455i	−0.257339	+	0.257339i	−0.823971	−	0.566632i	$-0.808246\pi$
$743$	−7.01455	+	7.01455i	−0.257339	+	0.257339i	0.566632	+	0.823971i	$0.308246\pi$
$744$		0			0
$745$	14.1572	−	2.76206i	0.518678	−	0.101194i
$746$			13.3359i			0.488263i
$747$		0			0
$748$	−0.613004	−	0.613004i	−0.0224137	−	0.0224137i
$749$	13.2020			0.482392
$750$		0			0
$751$	−40.8717			−1.49143			−0.745715	−	0.666265i	$-0.767892\pi$
$751$	−40.8717			−1.49143			−0.745715	+	0.666265i	$0.767892\pi$
$752$	−7.56256	−	7.56256i	−0.275778	−	0.275778i
$753$		0			0
$754$			102.140i			3.71973i
$755$	48.5278	−	9.46775i	1.76611	−	0.344567i
$756$		0			0
$757$	1.64597	−	1.64597i	0.0598239	−	0.0598239i	−0.676562	−	0.736386i	$-0.736531\pi$
$757$	1.64597	−	1.64597i	0.0598239	−	0.0598239i	0.736386	+	0.676562i	$0.236531\pi$
$758$	9.29692	−	9.29692i	0.337679	−	0.337679i
$759$		0			0
$760$	−20.1019	−	13.5387i	−0.729174	−	0.491099i
$761$		−	30.0718i		−	1.09010i	−0.838403	−	0.545050i	$-0.816511\pi$
$761$		−	30.0718i		−	1.09010i	0.838403	−	0.545050i	$-0.183489\pi$
$762$		0			0
$763$	1.01508	+	1.01508i	0.0367483	+	0.0367483i
$764$	7.74637			0.280254
$765$		0			0
$766$	19.7447			0.713404
$767$	−27.9907	−	27.9907i	−1.01068	−	1.01068i
$768$		0			0
$769$		−	18.3204i		−	0.660652i	−0.943867	−	0.330326i	$-0.892841\pi$
$769$		−	18.3204i		−	0.660652i	0.943867	−	0.330326i	$-0.107159\pi$
$770$	0.545256	+	2.79476i	0.0196497	+	0.100716i
$771$		0			0
$772$	5.99683	−	5.99683i	0.215831	−	0.215831i
$773$	16.5056	−	16.5056i	0.593665	−	0.593665i	−0.344955	−	0.938619i	$-0.612106\pi$
$773$	16.5056	−	16.5056i	0.593665	−	0.593665i	0.938619	+	0.344955i	$0.112106\pi$
$774$		0			0
$775$	10.3072	−	4.18103i	0.370247	−	0.150187i
$776$		−	2.34738i		−	0.0842660i
$777$		0			0
$778$	31.6548	+	31.6548i	1.13488	+	1.13488i
$779$	90.2769			3.23451
$780$		0			0
$781$	0.991357			0.0354735
$782$	1.66000	+	1.66000i	0.0593616	+	0.0593616i
$783$		0			0
$784$			25.9056i			0.925199i
$785$	−12.5820	+	18.6815i	−0.449070	+	0.666771i
$786$		0			0
$787$	14.3206	−	14.3206i	0.510474	−	0.510474i	−0.404197	−	0.914672i	$-0.632449\pi$
$787$	14.3206	−	14.3206i	0.510474	−	0.510474i	0.914672	+	0.404197i	$0.132449\pi$
$788$	2.92004	−	2.92004i	0.104022	−	0.104022i
$789$		0			0
$790$	−21.1290	+	31.3719i	−0.751736	+	1.11616i
$791$			8.40039i			0.298683i
$792$		0			0
$793$	−55.1766	−	55.1766i	−1.95938	−	1.95938i
$794$	51.6145			1.83173
$795$		0			0
$796$	−8.87140			−0.314438
$797$	25.4177	+	25.4177i	0.900340	+	0.900340i	0.995465	−	0.0951258i	$-0.0303253\pi$
$797$	25.4177	+	25.4177i	0.900340	+	0.900340i	−0.0951258	+	0.995465i	$0.530325\pi$
$798$		0			0
$799$			2.82109i			0.0998031i
$800$	28.4957	+	12.0491i	1.00747	+	0.426000i
$801$		0			0
$802$	24.7890	−	24.7890i	0.875329	−	0.875329i
$803$	−5.16915	+	5.16915i	−0.182415	+	0.182415i
$804$		0			0
$805$	−0.567186	−	2.90716i	−0.0199907	−	0.102464i
$806$			24.8117i			0.873953i
$807$		0			0
$808$	6.90818	+	6.90818i	0.243029	+	0.243029i
$809$	−34.5728			−1.21551			−0.607757	−	0.794123i	$-0.707931\pi$
$809$	−34.5728			−1.21551			−0.607757	+	0.794123i	$0.707931\pi$
$810$		0			0
$811$	−22.5482			−0.791776			−0.395888	−	0.918299i	$-0.629563\pi$
$811$	−22.5482			−0.791776			−0.395888	+	0.918299i	$0.629563\pi$
$812$	10.7002	+	10.7002i	0.375505	+	0.375505i
$813$		0			0
$814$			2.92589i			0.102552i
$815$	−5.42318	−	3.65251i	−0.189966	−	0.127942i
$816$		0			0
$817$	−43.2238	+	43.2238i	−1.51221	+	1.51221i
$818$	−25.9114	+	25.9114i	−0.905972	+	0.905972i
$819$		0			0
$820$	−30.9246	+	6.03339i	−1.07994	+	0.210695i
$821$			15.2633i			0.532694i	0.963877	+	0.266347i	$0.0858167\pi$
$821$			15.2633i			0.532694i	−0.963877	+	0.266347i	$0.914183\pi$
$822$		0			0
$823$	30.5973	+	30.5973i	1.06655	+	1.06655i	0.997621	+	0.0689332i	$0.0219595\pi$
$823$	30.5973	+	30.5973i	1.06655	+	1.06655i	0.0689332	+	0.997621i	$0.478040\pi$
$824$	4.53213			0.157884
$825$		0			0
$826$	−15.2672			−0.531215
$827$	−11.7841	−	11.7841i	−0.409774	−	0.409774i	0.471886	−	0.881660i	$-0.343574\pi$
$827$	−11.7841	−	11.7841i	−0.409774	−	0.409774i	−0.881660	+	0.471886i	$0.843574\pi$
$828$		0			0
$829$		−	14.4792i		−	0.502884i	−0.967872	−	0.251442i	$-0.919095\pi$
$829$		−	14.4792i		−	0.502884i	0.967872	−	0.251442i	$-0.0809047\pi$
$830$	45.1975	−	8.81802i	1.56883	−	0.306078i
$831$		0			0
$832$	−5.57151	+	5.57151i	−0.193157	+	0.193157i
$833$	4.83184	−	4.83184i	0.167413	−	0.167413i
$834$		0			0
$835$	−15.6296	−	10.5265i	−0.540884	−	0.364286i
$836$			5.31853i			0.183945i
$837$		0			0
$838$	−36.4056	−	36.4056i	−1.25761	−	1.25761i
$839$	3.80885			0.131496			0.0657481	−	0.997836i	$-0.479057\pi$
$839$	3.80885			0.131496			0.0657481	+	0.997836i	$0.479057\pi$
$840$		0			0
$841$	54.8657			1.89192
$842$	3.90585	+	3.90585i	0.134604	+	0.134604i
$843$		0			0
$844$			4.08195i			0.140507i
$845$	−10.8357	−	55.5392i	−0.372759	−	1.91061i
$846$		0			0
$847$	10.0367	−	10.0367i	0.344864	−	0.344864i
$848$	−14.7222	+	14.7222i	−0.505563	+	0.505563i
$849$		0			0
$850$	−4.41221	−	10.8772i	−0.151338	−	0.373084i
$851$		−	3.04357i		−	0.104332i
$852$		0			0
$853$	−4.73842	−	4.73842i	−0.162241	−	0.162241i	0.621318	−	0.783559i	$-0.286598\pi$
$853$	−4.73842	−	4.73842i	−0.162241	−	0.162241i	−0.783559	+	0.621318i	$0.786598\pi$
$854$	−30.0955			−1.02985
$855$		0			0
$856$	13.5162			0.461974
$857$	−23.0285	−	23.0285i	−0.786639	−	0.786639i	0.194303	−	0.980942i	$-0.437756\pi$
$857$	−23.0285	−	23.0285i	−0.786639	−	0.786639i	−0.980942	+	0.194303i	$0.937756\pi$
$858$		0			0
$859$			40.7742i			1.39120i	0.718430	+	0.695599i	$0.244861\pi$
$859$			40.7742i			1.39120i	−0.718430	+	0.695599i	$0.755139\pi$
$860$	11.9177	−	17.6952i	0.406390	−	0.603400i
$861$		0			0
$862$	−17.8942	+	17.8942i	−0.609478	+	0.609478i
$863$	25.6459	−	25.6459i	0.872997	−	0.872997i	−0.119801	−	0.992798i	$-0.538226\pi$
$863$	25.6459	−	25.6459i	0.872997	−	0.872997i	0.992798	+	0.119801i	$0.0382257\pi$
$864$		0			0
$865$	−8.35221	+	12.4012i	−0.283984	+	0.421653i
$866$		−	51.1053i		−	1.73663i
$867$		0			0
$868$	2.59927	+	2.59927i	0.0882251	+	0.0882251i
$869$	−5.00740			−0.169864
$870$		0			0
$871$	84.4885			2.86278
$872$	1.03923	+	1.03923i	0.0351929	+	0.0351929i
$873$		0			0
$874$		−	14.4025i		−	0.487171i
$875$	−3.04901	+	14.4926i	−0.103075	+	0.489939i
$876$		0			0
$877$	2.94407	−	2.94407i	0.0994143	−	0.0994143i	−0.655650	−	0.755065i	$-0.727605\pi$
$877$	2.94407	−	2.94407i	0.0994143	−	0.0994143i	0.755065	+	0.655650i	$0.227605\pi$
$878$	−25.7187	+	25.7187i	−0.867965	+	0.867965i
$879$		0			0
$880$	1.12811	+	5.78224i	0.0380287	+	0.194919i
$881$		−	15.3837i		−	0.518291i	−0.965838	−	0.259145i	$-0.916559\pi$
$881$		−	15.3837i		−	0.518291i	0.965838	−	0.259145i	$-0.0834409\pi$
$882$		0			0
$883$	5.60224	+	5.60224i	0.188530	+	0.188530i	0.795061	−	0.606530i	$-0.207439\pi$
$883$	5.60224	+	5.60224i	0.188530	+	0.188530i	−0.606530	+	0.795061i	$0.707439\pi$
$884$	10.0579			0.338285
$885$		0			0
$886$	1.81007			0.0608106
$887$	40.4544	+	40.4544i	1.35833	+	1.35833i	0.875982	+	0.482344i	$0.160214\pi$
$887$	40.4544	+	40.4544i	1.35833	+	1.35833i	0.482344	+	0.875982i	$0.339786\pi$
$888$		0			0
$889$		−	19.4290i		−	0.651629i
$890$	−40.8591	−	27.5187i	−1.36960	−	0.922428i
$891$		0			0
$892$	−12.6244	+	12.6244i	−0.422698	+	0.422698i
$893$	12.2381	−	12.2381i	0.409534	−	0.409534i
$894$		0			0
$895$	52.4052	−	10.2242i	1.75171	−	0.341758i
$896$		−	13.3539i		−	0.446122i
$897$		0			0
$898$	−39.8576	−	39.8576i	−1.33006	−	1.33006i
$899$	20.3724			0.679458
$900$		0			0
$901$	5.49190			0.182962
$902$	−7.67840	−	7.67840i	−0.255663	−	0.255663i
$903$		0			0
$904$			8.60030i			0.286042i
$905$	52.0992	−	10.1645i	1.73183	−	0.337880i
$906$		0			0
$907$	8.28320	−	8.28320i	0.275039	−	0.275039i	−0.556086	−	0.831125i	$-0.687697\pi$
$907$	8.28320	−	8.28320i	0.275039	−	0.275039i	0.831125	+	0.556086i	$0.187697\pi$
$908$	−10.9949	+	10.9949i	−0.364877	+	0.364877i
$909$		0			0
$910$	−27.4008	−	18.4544i	−0.908327	−	0.611759i
$911$		−	26.5779i		−	0.880564i	−0.897860	−	0.440282i	$-0.854878\pi$
$911$		−	26.5779i		−	0.880564i	0.897860	−	0.440282i	$-0.145122\pi$
$912$		0			0
$913$	4.31082	+	4.31082i	0.142667	+	0.142667i
$914$	21.6829			0.717208
$915$		0			0
$916$	14.1674			0.468105
$917$	−4.74159	−	4.74159i	−0.156581	−	0.156581i
$918$		0			0
$919$			28.5501i			0.941780i	0.882192	+	0.470890i	$0.156067\pi$
$919$			28.5501i			0.941780i	−0.882192	+	0.470890i	$0.843933\pi$
$920$	−0.580683	−	2.97634i	−0.0191446	−	0.0981270i
$921$		0			0
$922$	−2.99588	+	2.99588i	−0.0986641	+	0.0986641i
$923$	−8.13289	+	8.13289i	−0.267697	+	0.267697i
$924$		0			0
$925$	−5.92666	+	14.0163i	−0.194867	+	0.460854i
$926$			15.0969i			0.496113i
$927$		0			0
$928$	40.0687	+	40.0687i	1.31532	+	1.31532i
$929$	−28.6982			−0.941558			−0.470779	−	0.882251i	$-0.656027\pi$
$929$	−28.6982			−0.941558			−0.470779	+	0.882251i	$0.656027\pi$
$930$		0			0
$931$	−41.9218			−1.37393
$932$	−8.09613	−	8.09613i	−0.265198	−	0.265198i
$933$		0			0
$934$		−	51.3098i		−	1.67891i
$935$	0.868075	−	1.28890i	0.0283891	−	0.0421516i
$936$		0			0
$937$	−6.97047	+	6.97047i	−0.227715	+	0.227715i	−0.811738	−	0.584022i	$-0.801478\pi$
$937$	−6.97047	+	6.97047i	−0.227715	+	0.227715i	0.584022	+	0.811738i	$0.301478\pi$
$938$	23.0417	−	23.0417i	0.752338	−	0.752338i
$939$		0			0
$940$	−3.37432	+	5.01012i	−0.110058	+	0.163412i
$941$			3.95058i			0.128785i	0.997925	+	0.0643926i	$0.0205110\pi$
$941$			3.95058i			0.128785i	−0.997925	+	0.0643926i	$0.979489\pi$
$942$		0			0
$943$	7.98722	+	7.98722i	0.260100	+	0.260100i
$944$	−31.5873			−1.02808
$945$		0			0
$946$	7.35270			0.239057
$947$	30.9548	+	30.9548i	1.00590	+	1.00590i	0.999983	+	0.00591493i	$0.00188279\pi$
$947$	30.9548	+	30.9548i	1.00590	+	1.00590i	0.00591493	+	0.999983i	$0.498117\pi$
$948$		0			0
$949$		−	84.8134i		−	2.75316i
$950$	−28.0455	+	66.3266i	−0.909917	+	2.15192i
$951$		0			0
$952$	−1.65479	+	1.65479i	−0.0536321	+	0.0536321i
$953$	−25.2755	+	25.2755i	−0.818755	+	0.818755i	−0.985928	−	0.167173i	$-0.946536\pi$
$953$	−25.2755	+	25.2755i	−0.818755	+	0.818755i	0.167173	+	0.985928i	$0.446536\pi$
$954$		0			0
$955$	2.65893	+	13.6286i	0.0860409	+	0.441010i
$956$		−	7.81816i		−	0.252857i
$957$		0			0
$958$	−26.6267	−	26.6267i	−0.860270	−	0.860270i
$959$	−17.9180			−0.578604
$960$		0			0
$961$	−26.0512			−0.840361
$962$	−24.0034	−	24.0034i	−0.773902	−	0.773902i
$963$		0			0
$964$		−	15.0072i		−	0.483349i
$965$	12.6089	+	8.49212i	0.405896	+	0.273371i
$966$		0			0
$967$	−21.9378	+	21.9378i	−0.705471	+	0.705471i	−0.965579	−	0.260108i	$-0.916242\pi$
$967$	−21.9378	+	21.9378i	−0.705471	+	0.705471i	0.260108	+	0.965579i	$0.416242\pi$
$968$	10.2755	−	10.2755i	0.330268	−	0.330268i
$969$		0			0
$970$	−6.84569	+	1.33559i	−0.219802	+	0.0428833i
$971$			36.2865i			1.16449i	0.813014	+	0.582244i	$0.197825\pi$
$971$			36.2865i			1.16449i	−0.813014	+	0.582244i	$0.802175\pi$
$972$		0			0
$973$	−20.2614	−	20.2614i	−0.649549	−	0.649549i
$974$	31.7166			1.01627
$975$		0			0
$976$	−62.2665			−1.99310
$977$	−23.9738	−	23.9738i	−0.766990	−	0.766990i	0.210586	−	0.977575i	$-0.432463\pi$
$977$	−23.9738	−	23.9738i	−0.766990	−	0.766990i	−0.977575	+	0.210586i	$0.932463\pi$
$978$		0			0
$979$		−	6.52170i		−	0.208434i
$980$	14.3605	−	2.80172i	0.458728	−	0.0894977i
$981$		0			0
$982$	−14.8178	+	14.8178i	−0.472856	+	0.472856i
$983$	7.07002	−	7.07002i	0.225499	−	0.225499i	−0.585311	−	0.810809i	$-0.699027\pi$
$983$	7.07002	−	7.07002i	0.225499	−	0.225499i	0.810809	+	0.585311i	$0.199027\pi$
$984$		0			0
$985$	6.13967	+	4.13507i	0.195626	+	0.131754i
$986$		−	21.4989i		−	0.684664i
$987$		0			0
$988$	−43.6321	−	43.6321i	−1.38812	−	1.38812i
$989$	−7.64842			−0.243206
$990$		0			0
$991$	−52.2948			−1.66120			−0.830600	−	0.556869i	$-0.812002\pi$
$991$	−52.2948			−1.66120			−0.830600	+	0.556869i	$0.812002\pi$
$992$	9.73337	+	9.73337i	0.309035	+	0.309035i
$993$		0			0
$994$			4.43600i			0.140701i
$995$	−3.04509	−	15.6079i	−0.0965359	−	0.494803i
$996$		0			0
$997$	22.0522	−	22.0522i	0.698399	−	0.698399i	−0.265666	−	0.964065i	$-0.585592\pi$
$997$	22.0522	−	22.0522i	0.698399	−	0.698399i	0.964065	+	0.265666i	$0.0855919\pi$
$998$	38.5288	−	38.5288i	1.21961	−	1.21961i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1035.2.j.b.323.17	yes	44
3.2	odd	2	inner	1035.2.j.b.323.6	✓	44
5.2	odd	4	inner	1035.2.j.b.737.6	yes	44
15.2	even	4	inner	1035.2.j.b.737.17	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1035.2.j.b.323.6	✓	44	3.2	odd	2	inner
1035.2.j.b.323.17	yes	44	1.1	even	1	trivial
1035.2.j.b.737.6	yes	44	5.2	odd	4	inner
1035.2.j.b.737.17	yes	44	15.2	even	4	inner

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:	\( N \)	\(=\)	\( 1035 = 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1035.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.27425 + 1.27425i) q^{2} +1.24744i q^{4} +(-2.19469 + 0.428183i) q^{5} +(0.936657 - 0.936657i) q^{7} +(0.958947 - 0.958947i) q^{8} +O(q^{10})\)	\(q+(1.27425 + 1.27425i) q^{2} +1.24744i q^{4} +(-2.19469 + 0.428183i) q^{5} +(0.936657 - 0.936657i) q^{7} +(0.958947 - 0.958947i) q^{8} +(-3.34220 - 2.25098i) q^{10} -0.533463i q^{11} +(4.37643 + 4.37643i) q^{13} +2.38708 q^{14} +4.93877 q^{16} +(-0.921166 - 0.921166i) q^{17} +7.99219i q^{19} +(-0.534134 - 2.73775i) q^{20} +(0.679767 - 0.679767i) q^{22} +(-0.707107 + 0.707107i) q^{23} +(4.63332 - 1.87946i) q^{25} +11.1534i q^{26} +(1.16843 + 1.16843i) q^{28} +9.15782 q^{29} +2.22459 q^{31} +(4.37535 + 4.37535i) q^{32} -2.34760i q^{34} +(-1.65461 + 2.45673i) q^{35} +(-2.15213 + 2.15213i) q^{37} +(-10.1841 + 10.1841i) q^{38} +(-1.69399 + 2.51520i) q^{40} -11.2956i q^{41} +(5.40825 + 5.40825i) q^{43} +0.665465 q^{44} -1.80207 q^{46} +(-1.53126 - 1.53126i) q^{47} +5.24535i q^{49} +(8.29893 + 3.50912i) q^{50} +(-5.45935 + 5.45935i) q^{52} +(-2.98095 + 2.98095i) q^{53} +(0.228420 + 1.17079i) q^{55} -1.79641i q^{56} +(11.6694 + 11.6694i) q^{58} -6.39579 q^{59} -12.6077 q^{61} +(2.83469 + 2.83469i) q^{62} +1.27307i q^{64} +(-11.4788 - 7.73098i) q^{65} +(9.65268 - 9.65268i) q^{67} +(1.14910 - 1.14910i) q^{68} +(-5.23889 + 1.02211i) q^{70} +1.85834i q^{71} +(-9.68980 - 9.68980i) q^{73} -5.48471 q^{74} -9.96981 q^{76} +(-0.499672 - 0.499672i) q^{77} -9.38659i q^{79} +(-10.8391 + 2.11470i) q^{80} +(14.3935 - 14.3935i) q^{82} +(-8.08083 + 8.08083i) q^{83} +(2.41610 + 1.62725i) q^{85} +13.7830i q^{86} +(-0.511563 - 0.511563i) q^{88} +12.2252 q^{89} +8.19842 q^{91} +(-0.882076 - 0.882076i) q^{92} -3.90243i q^{94} +(-3.42212 - 17.5404i) q^{95} +(1.22394 - 1.22394i) q^{97} +(-6.68390 + 6.68390i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 12 q^{7}+O(q^{10}) \) 44 * q + 12 * q^7	\( 44 q + 12 q^{7} - 20 q^{10} + 4 q^{13} - 44 q^{16} + 16 q^{22} - 8 q^{25} + 40 q^{28} - 32 q^{31} + 56 q^{37} - 16 q^{40} + 72 q^{43} - 4 q^{46} + 76 q^{52} + 56 q^{55} - 12 q^{58} - 96 q^{61} + 12 q^{67} - 48 q^{70} + 68 q^{73} - 112 q^{76} + 52 q^{82} + 32 q^{85} + 56 q^{88} - 176 q^{91} + 76 q^{97}+O(q^{100}) \) 44 * q + 12 * q^7 - 20 * q^10 + 4 * q^13 - 44 * q^16 + 16 * q^22 - 8 * q^25 + 40 * q^28 - 32 * q^31 + 56 * q^37 - 16 * q^40 + 72 * q^43 - 4 * q^46 + 76 * q^52 + 56 * q^55 - 12 * q^58 - 96 * q^61 + 12 * q^67 - 48 * q^70 + 68 * q^73 - 112 * q^76 + 52 * q^82 + 32 * q^85 + 56 * q^88 - 176 * q^91 + 76 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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