LMFDB - Embedded newform 1710.2.q.b.179.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(179,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1710.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.q (of order $6$, 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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.8
Character	$\chi$	$=$	1710.179
Dual form			1710.2.q.b.449.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.79066 + 1.33924i) q^{5} +0.180093i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.79066 + 1.33924i) q^{5} +0.180093i q^{7} -1.00000i q^{8} +(-0.881135 - 2.05514i) q^{10} -1.44133i q^{11} +(-1.78765 - 3.09631i) q^{13} +(0.0900463 - 0.155965i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.50006 - 2.59818i) q^{17} +(-4.18093 - 1.23282i) q^{19} +(-0.264485 + 2.22037i) q^{20} +(-0.720664 + 1.24823i) q^{22} +(-4.69340 - 8.12920i) q^{23} +(1.41289 + 4.79622i) q^{25} +3.57531i q^{26} +(-0.155965 + 0.0900463i) q^{28} +(-3.02974 - 5.24767i) q^{29} +5.35453i q^{31} +(0.866025 - 0.500000i) q^{32} +(-2.59818 + 1.50006i) q^{34} +(-0.241187 + 0.322484i) q^{35} -10.3873 q^{37} +(3.00438 + 3.15811i) q^{38} +(1.33924 - 1.79066i) q^{40} +(5.23274 - 9.06337i) q^{41} +(-0.527413 - 0.304502i) q^{43} +(1.24823 - 0.720664i) q^{44} +9.38680i q^{46} +(0.114049 + 0.197538i) q^{47} +6.96757 q^{49} +(1.17451 - 4.86010i) q^{50} +(1.78765 - 3.09631i) q^{52} +(5.26691 - 3.04085i) q^{53} +(1.93028 - 2.58092i) q^{55} +0.180093 q^{56} +6.05949i q^{58} +(-4.94033 + 8.55691i) q^{59} +(-6.64753 - 11.5139i) q^{61} +(2.67726 - 4.63716i) q^{62} -1.00000 q^{64} +(0.945614 - 7.93851i) q^{65} +(-2.02318 - 3.50425i) q^{67} +3.00013 q^{68} +(0.370116 - 0.158686i) q^{70} +(-1.34163 + 2.32377i) q^{71} +(5.65274 + 3.26361i) q^{73} +(8.99565 + 5.19364i) q^{74} +(-1.02281 - 4.23720i) q^{76} +0.259573 q^{77} +(9.06694 + 5.23480i) q^{79} +(-2.05514 + 0.881135i) q^{80} +(-9.06337 + 5.23274i) q^{82} +16.9502 q^{83} +(6.16568 - 2.64352i) q^{85} +(0.304502 + 0.527413i) q^{86} -1.44133 q^{88} +(-1.71203 - 2.96533i) q^{89} +(0.557622 - 0.321943i) q^{91} +(4.69340 - 8.12920i) q^{92} -0.228097i q^{94} +(-5.83557 - 7.80680i) q^{95} +(-5.02338 + 8.70075i) q^{97} +(-6.03409 - 3.48378i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4}+O(q^{10}) $ 64 * q + 32 * q^4	$ 64 q + 32 q^{4} - 24 q^{10} - 32 q^{16} + 40 q^{19} - 8 q^{25} - 24 q^{34} - 24 q^{40} + 8 q^{55} + 104 q^{61} - 64 q^{64} - 48 q^{70} + 32 q^{76} + 48 q^{79} + 16 q^{85} + 96 q^{91}+O(q^{100}) $ 64 * q + 32 * q^4 - 24 * q^10 - 32 * q^16 + 40 * q^19 - 8 * q^25 - 24 * q^34 - 24 * q^40 + 8 * q^55 + 104 * q^61 - 64 * q^64 - 48 * q^70 + 32 * q^76 + 48 * q^79 + 16 * q^85 + 96 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.79066	+	1.33924i	0.800805	+	0.598925i
$5$	1.79066	+	1.33924i	0.800805	+	0.598925i
$6$		0			0
$7$			0.180093i			0.0680686i	0.999421	+	0.0340343i	$0.0108355\pi$
$7$			0.180093i			0.0680686i	−0.999421	+	0.0340343i	$0.989164\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.881135	−	2.05514i	−0.278639	−	0.649892i
$11$		−	1.44133i		−	0.434577i	−0.976107	−	0.217288i	$-0.930279\pi$
$11$		−	1.44133i		−	0.434577i	0.976107	−	0.217288i	$-0.0697212\pi$
$12$		0			0
$13$	−1.78765	−	3.09631i	−0.495806	−	0.858761i	0.504182	−	0.863597i	$-0.331794\pi$
$13$	−1.78765	−	3.09631i	−0.495806	−	0.858761i	−0.999988	+	0.00483613i	$0.998461\pi$
$14$	0.0900463	−	0.155965i	0.0240659	−	0.0416833i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.50006	−	2.59818i	0.363819	−	0.630152i	−0.624767	−	0.780811i	$-0.714806\pi$
$17$	1.50006	−	2.59818i	0.363819	−	0.630152i	0.988586	+	0.150659i	$0.0481395\pi$
$18$		0			0
$19$	−4.18093	−	1.23282i	−0.959171	−	0.282828i
$19$	−4.18093	−	1.23282i	−0.959171	−	0.282828i
$20$	−0.264485	+	2.22037i	−0.0591406	+	0.496490i
$21$		0			0
$22$	−0.720664	+	1.24823i	−0.153646	+	0.266123i
$23$	−4.69340	−	8.12920i	−0.978641	−	1.69506i	−0.667355	−	0.744740i	$-0.732574\pi$
$23$	−4.69340	−	8.12920i	−0.978641	−	1.69506i	−0.311286	−	0.950316i	$-0.600760\pi$
$24$		0			0
$25$	1.41289	+	4.79622i	0.282579	+	0.959244i
$26$			3.57531i			0.701175i
$27$		0			0
$28$	−0.155965	+	0.0900463i	−0.0294746	+	0.0170172i
$29$	−3.02974	−	5.24767i	−0.562609	−	0.974468i	−0.997268	−	0.0738722i	$-0.976464\pi$
$29$	−3.02974	−	5.24767i	−0.562609	−	0.974468i	0.434659	−	0.900595i	$-0.356869\pi$
$30$		0			0
$31$			5.35453i			0.961701i	0.876803	+	0.480851i	$0.159672\pi$
$31$			5.35453i			0.961701i	−0.876803	+	0.480851i	$0.840328\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	−2.59818	+	1.50006i	−0.445585	+	0.257259i
$35$	−0.241187	+	0.322484i	−0.0407680	+	0.0545097i
$36$		0			0
$37$	−10.3873			−1.70766			−0.853829	−	0.520554i	$-0.825726\pi$
$37$	−10.3873			−1.70766			−0.853829	+	0.520554i	$0.825726\pi$
$38$	3.00438	+	3.15811i	0.487375	+	0.512314i
$39$		0			0
$40$	1.33924	−	1.79066i	0.211752	−	0.283127i
$41$	5.23274	−	9.06337i	0.817217	−	1.41546i	−0.0905082	−	0.995896i	$-0.528849\pi$
$41$	5.23274	−	9.06337i	0.817217	−	1.41546i	0.907725	−	0.419565i	$-0.137818\pi$
$42$		0			0
$43$	−0.527413	−	0.304502i	−0.0804297	−	0.0464361i	0.459246	−	0.888309i	$-0.348120\pi$
$43$	−0.527413	−	0.304502i	−0.0804297	−	0.0464361i	−0.539675	+	0.841873i	$0.681453\pi$
$44$	1.24823	−	0.720664i	0.188177	−	0.108644i
$45$		0			0
$46$			9.38680i			1.38401i
$47$	0.114049	+	0.197538i	0.0166357	+	0.0288139i	0.874223	−	0.485524i	$-0.161371\pi$
$47$	0.114049	+	0.197538i	0.0166357	+	0.0288139i	−0.857588	+	0.514338i	$0.828038\pi$
$48$		0			0
$49$	6.96757			0.995367
$50$	1.17451	−	4.86010i	0.166101	−	0.687321i
$51$		0			0
$52$	1.78765	−	3.09631i	0.247903	−	0.429381i
$53$	5.26691	−	3.04085i	0.723465	−	0.417693i	−0.0925616	−	0.995707i	$-0.529506\pi$
$53$	5.26691	−	3.04085i	0.723465	−	0.417693i	0.816027	+	0.578014i	$0.196172\pi$
$54$		0			0
$55$	1.93028	−	2.58092i	0.260279	−	0.348011i
$56$	0.180093			0.0240659
$57$		0			0
$58$			6.05949i			0.795649i
$59$	−4.94033	+	8.55691i	−0.643176	+	1.11401i	0.341543	+	0.939866i	$0.389050\pi$
$59$	−4.94033	+	8.55691i	−0.643176	+	1.11401i	−0.984719	+	0.174148i	$0.944283\pi$
$60$		0			0
$61$	−6.64753	−	11.5139i	−0.851128	−	1.47420i	−0.880191	−	0.474620i	$-0.842585\pi$
$61$	−6.64753	−	11.5139i	−0.851128	−	1.47420i	0.0290623	−	0.999578i	$-0.490748\pi$
$62$	2.67726	−	4.63716i	0.340013	−	0.588919i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.945614	−	7.93851i	0.117289	−	0.984651i
$66$		0			0
$67$	−2.02318	−	3.50425i	−0.247171	−	0.428112i	0.715569	−	0.698542i	$-0.246167\pi$
$67$	−2.02318	−	3.50425i	−0.247171	−	0.428112i	−0.962740	+	0.270430i	$0.912834\pi$
$68$	3.00013			0.363819
$69$		0			0
$70$	0.370116	−	0.158686i	0.0442373	−	0.0189666i
$71$	−1.34163	+	2.32377i	−0.159222	+	0.275781i	−0.934588	−	0.355731i	$-0.884232\pi$
$71$	−1.34163	+	2.32377i	−0.159222	+	0.275781i	0.775366	+	0.631512i	$0.217565\pi$
$72$		0			0
$73$	5.65274	+	3.26361i	0.661603	+	0.381977i	0.792887	−	0.609368i	$-0.208577\pi$
$73$	5.65274	+	3.26361i	0.661603	+	0.381977i	−0.131284	+	0.991345i	$0.541910\pi$
$74$	8.99565	+	5.19364i	1.04572	+	0.603748i
$75$		0			0
$76$	−1.02281	−	4.23720i	−0.117325	−	0.486040i
$77$	0.259573			0.0295810
$78$		0			0
$79$	9.06694	+	5.23480i	1.02011	+	0.588961i	0.914136	−	0.405408i	$-0.132871\pi$
$79$	9.06694	+	5.23480i	1.02011	+	0.588961i	0.105974	+	0.994369i	$0.466204\pi$
$80$	−2.05514	+	0.881135i	−0.229772	+	0.0985139i
$81$		0			0
$82$	−9.06337	+	5.23274i	−1.00088	+	0.577860i
$83$	16.9502			1.86053			0.930264	−	0.366891i	$-0.119578\pi$
$83$	16.9502			1.86053			0.930264	+	0.366891i	$0.119578\pi$
$84$		0			0
$85$	6.16568	−	2.64352i	0.668762	−	0.286730i
$86$	0.304502	+	0.527413i	0.0328353	+	0.0568724i
$87$		0			0
$88$	−1.44133			−0.153646
$89$	−1.71203	−	2.96533i	−0.181475	−	0.314324i	0.760908	−	0.648860i	$-0.224754\pi$
$89$	−1.71203	−	2.96533i	−0.181475	−	0.314324i	−0.942383	+	0.334536i	$0.891421\pi$
$90$		0			0
$91$	0.557622	−	0.321943i	0.0584547	−	0.0337488i
$92$	4.69340	−	8.12920i	0.489321	−	0.847528i
$93$		0			0
$94$		−	0.228097i		−	0.0235264i
$95$	−5.83557	−	7.80680i	−0.598717	−	0.800961i
$96$		0			0
$97$	−5.02338	+	8.70075i	−0.510047	+	0.883427i	0.489886	+	0.871787i	$0.337039\pi$
$97$	−5.02338	+	8.70075i	−0.510047	+	0.883427i	−0.999932	+	0.0116401i	$0.996295\pi$
$98$	−6.03409	−	3.48378i	−0.609535	−	0.351915i
$99$		0			0
$100$	−3.44720	+	3.62171i	−0.344720	+	0.362171i
$101$	9.33315	−	5.38850i	0.928683	−	0.536176i	0.0422885	−	0.999105i	$-0.486535\pi$
$101$	9.33315	−	5.38850i	0.928683	−	0.536176i	0.886395	+	0.462930i	$0.153202\pi$
$102$		0			0
$103$	−14.6347			−1.44200			−0.721001	−	0.692934i	$-0.756318\pi$
$103$	−14.6347			−1.44200			−0.721001	+	0.692934i	$0.756318\pi$
$104$	−3.09631	+	1.78765i	−0.303618	+	0.175294i
$105$		0			0
$106$	−6.08170			−0.590707
$107$		−	9.40284i		−	0.909007i	−0.890745	−	0.454503i	$-0.849817\pi$
$107$		−	9.40284i		−	0.909007i	0.890745	−	0.454503i	$-0.150183\pi$
$108$		0			0
$109$	3.09424	+	1.78646i	0.296375	+	0.171112i	0.640813	−	0.767697i	$-0.278597\pi$
$109$	3.09424	+	1.78646i	0.296375	+	0.171112i	−0.344439	+	0.938809i	$0.611931\pi$
$110$	−2.96213	+	1.27000i	−0.282428	+	0.121090i
$111$		0			0
$112$	−0.155965	−	0.0900463i	−0.0147373	−	0.00850858i
$113$		−	8.89976i		−	0.837219i	−0.908166	−	0.418609i	$-0.862518\pi$
$113$		−	8.89976i		−	0.837219i	0.908166	−	0.418609i	$-0.137482\pi$
$114$		0			0
$115$	2.48266	−	20.8422i	0.231510	−	1.94354i
$116$	3.02974	−	5.24767i	0.281305	−	0.487234i
$117$		0			0
$118$	8.55691	−	4.94033i	0.787727	−	0.454794i
$119$	0.467914	+	0.270150i	0.0428936	+	0.0247646i
$120$		0			0
$121$	8.92257			0.811143
$122$			13.2951i			1.20368i
$123$		0			0
$124$	−4.63716	+	2.67726i	−0.416429	+	0.240425i
$125$	−3.89327	+	10.4806i	−0.348224	+	0.937411i
$126$		0			0
$127$	4.58160	+	7.93557i	0.406551	+	0.704168i	0.994501	−	0.104730i	$-0.0333979\pi$
$127$	4.58160	+	7.93557i	0.406551	+	0.704168i	−0.587949	+	0.808898i	$0.700065\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−4.78818	+	6.40214i	−0.419951	+	0.561505i
$131$	−16.9930	−	9.81092i	−1.48469	−	0.857184i	−0.484838	−	0.874604i	$-0.661122\pi$
$131$	−16.9930	−	9.81092i	−1.48469	−	0.857184i	−0.999848	+	0.0174195i	$0.994455\pi$
$132$		0			0
$133$	0.222021	−	0.752954i	0.0192517	−	0.0652894i
$134$			4.04636i			0.349552i
$135$		0			0
$136$	−2.59818	−	1.50006i	−0.222793	−	0.128629i
$137$	10.5782	+	18.3220i	0.903755	+	1.56535i	0.822580	+	0.568650i	$0.192534\pi$
$137$	10.5782	+	18.3220i	0.903755	+	1.56535i	0.0811756	+	0.996700i	$0.474133\pi$
$138$		0			0
$139$	−1.46722	−	2.54129i	−0.124448	−	0.215550i	0.797069	−	0.603888i	$-0.206383\pi$
$139$	−1.46722	−	2.54129i	−0.124448	−	0.215550i	−0.921517	+	0.388338i	$0.873049\pi$
$140$	−0.399872	−	0.0476317i	−0.0337954	−	0.00402562i
$141$		0			0
$142$	2.32377	−	1.34163i	0.195007	−	0.112587i
$143$	−4.46279	+	2.57660i	−0.373198	+	0.215466i
$144$		0			0
$145$	1.60264	−	13.4543i	0.133092	−	1.11732i
$146$	−3.26361	−	5.65274i	−0.270098	−	0.467824i
$147$		0			0
$148$	−5.19364	−	8.99565i	−0.426915	−	0.739438i
$149$	−8.00673	−	4.62269i	−0.655937	−	0.378705i	0.134790	−	0.990874i	$-0.456964\pi$
$149$	−8.00673	−	4.62269i	−0.655937	−	0.378705i	−0.790727	+	0.612169i	$0.790297\pi$
$150$		0			0
$151$		−	10.5001i		−	0.854485i	−0.904137	−	0.427242i	$-0.859485\pi$
$151$		−	10.5001i		−	0.854485i	0.904137	−	0.427242i	$-0.140515\pi$
$152$	−1.23282	+	4.18093i	−0.0999947	+	0.339118i
$153$		0			0
$154$	−0.224796	−	0.129786i	−0.0181146	−	0.0104585i
$155$	−7.17097	+	9.58811i	−0.575986	+	0.770136i
$156$		0			0
$157$	−17.9423	−	10.3590i	−1.43195	−	0.826739i	−0.434685	−	0.900583i	$-0.643140\pi$
$157$	−17.9423	−	10.3590i	−1.43195	−	0.826739i	−0.997270	+	0.0738435i	$0.976473\pi$
$158$	−5.23480	−	9.06694i	−0.416458	−	0.721327i
$159$		0			0
$160$	2.22037	+	0.264485i	0.175536	+	0.0209094i
$161$	1.46401	−	0.845246i	0.115380	−	0.0666147i
$162$		0			0
$163$			14.9423i			1.17037i	0.810900	+	0.585184i	$0.198978\pi$
$163$			14.9423i			1.17037i	−0.810900	+	0.585184i	$0.801022\pi$
$164$	10.4655			0.817217
$165$		0			0
$166$	−14.6793	−	8.47511i	−1.13934	−	0.657796i
$167$	1.75551	−	1.01355i	0.135846	−	0.0784305i	−0.430537	−	0.902573i	$-0.641676\pi$
$167$	1.75551	−	1.01355i	0.135846	−	0.0784305i	0.566383	+	0.824142i	$0.308342\pi$
$168$		0			0
$169$	0.108588	−	0.188080i	0.00835294	−	0.0144677i
$170$	−6.66139	−	0.793487i	−0.510905	−	0.0608577i
$171$		0			0
$172$		−	0.609004i		−	0.0464361i
$173$	−13.4749	−	7.77976i	−1.02448	−	0.591485i	−0.109083	−	0.994033i	$-0.534791\pi$
$173$	−13.4749	−	7.77976i	−1.02448	−	0.591485i	−0.915399	+	0.402548i	$0.868125\pi$
$174$		0			0
$175$	−0.863764	+	0.254452i	−0.0652944	+	0.0192347i
$176$	1.24823	+	0.720664i	0.0940886	+	0.0543221i
$177$		0			0
$178$			3.42407i			0.256645i
$179$	−12.3835			−0.925589			−0.462795	−	0.886465i	$-0.653153\pi$
$179$	−12.3835			−0.925589			−0.462795	+	0.886465i	$0.653153\pi$
$180$		0			0
$181$	5.25771	−	3.03554i	0.390803	−	0.225630i	−0.291705	−	0.956508i	$-0.594223\pi$
$181$	5.25771	−	3.03554i	0.390803	−	0.225630i	0.682508	+	0.730878i	$0.260889\pi$
$182$	−0.643886			−0.0477280
$183$		0			0
$184$	−8.12920	+	4.69340i	−0.599293	+	0.346002i
$185$	−18.6000	−	13.9110i	−1.36750	−	1.02276i
$186$		0			0
$187$	−3.74484	−	2.16208i	−0.273850	−	0.158107i
$188$	−0.114049	+	0.197538i	−0.00831785	+	0.0144069i
$189$		0			0
$190$	1.15035	+	9.67867i	0.0834552	+	0.702165i
$191$			11.2319i			0.812714i	0.913714	+	0.406357i	$0.133201\pi$
$191$			11.2319i			0.812714i	−0.913714	+	0.406357i	$0.866799\pi$
$192$		0			0
$193$	8.09635	−	14.0233i	0.582788	−	1.00942i	−0.412359	−	0.911021i	$-0.635295\pi$
$193$	8.09635	−	14.0233i	0.582788	−	1.00942i	0.995147	−	0.0983970i	$-0.0313715\pi$
$194$	8.70075	−	5.02338i	0.624677	−	0.360657i
$195$		0			0
$196$	3.48378	+	6.03409i	0.248842	+	0.431006i
$197$	7.70680			0.549087			0.274543	−	0.961575i	$-0.411473\pi$
$197$	7.70680			0.549087			0.274543	+	0.961575i	$0.411473\pi$
$198$		0			0
$199$	−6.95650	−	12.0490i	−0.493133	−	0.854132i	0.506835	−	0.862043i	$-0.330815\pi$
$199$	−6.95650	−	12.0490i	−0.493133	−	0.854132i	−0.999969	+	0.00791096i	$0.997482\pi$
$200$	4.79622	−	1.41289i	0.339144	−	0.0999067i
$201$		0			0
$202$	−10.7770			−0.758267
$203$	0.945066	−	0.545634i	0.0663306	−	0.0382960i
$204$		0			0
$205$	21.5080	−	9.22150i	1.50219	−	0.644058i
$206$	12.6740	+	7.31736i	0.883042	+	0.509825i
$207$		0			0
$208$	3.57531			0.247903
$209$	−1.77689	+	6.02609i	−0.122910	+	0.416833i
$210$		0			0
$211$	−9.33327	−	5.38856i	−0.642529	−	0.370964i	0.143059	−	0.989714i	$-0.454306\pi$
$211$	−9.33327	−	5.38856i	−0.642529	−	0.370964i	−0.785588	+	0.618750i	$0.787639\pi$
$212$	5.26691	+	3.04085i	0.361733	+	0.208846i
$213$		0			0
$214$	−4.70142	+	8.14310i	−0.321382	+	0.556651i
$215$	−0.536614	−	1.25159i	−0.0365968	−	0.0853576i
$216$		0			0
$217$	−0.964310			−0.0654617
$218$	−1.78646	−	3.09424i	−0.120994	−	0.209568i
$219$		0			0
$220$	3.20028	+	0.381209i	0.215763	+	0.0257011i
$221$	−10.7264			−0.721534
$222$		0			0
$223$	10.2181	−	17.6983i	0.684255	−	1.18516i	−0.289416	−	0.957203i	$-0.593461\pi$
$223$	10.2181	−	17.6983i	0.684255	−	1.18516i	0.973670	−	0.227960i	$-0.0732056\pi$
$224$	0.0900463	+	0.155965i	0.00601647	+	0.0104208i
$225$		0			0
$226$	−4.44988	+	7.70742i	−0.296002	+	0.512690i
$227$			24.8836i			1.65159i	0.563974	+	0.825793i	$0.309272\pi$
$227$			24.8836i			1.65159i	−0.563974	+	0.825793i	$0.690728\pi$
$228$		0			0
$229$	15.8364			1.04650			0.523249	−	0.852180i	$-0.324720\pi$
$229$	15.8364			1.04650			0.523249	+	0.852180i	$0.324720\pi$
$230$	−12.5711	+	16.8085i	−0.828916	+	1.10832i
$231$		0			0
$232$	−5.24767	+	3.02974i	−0.344526	+	0.198912i
$233$	−3.23099	+	5.59623i	−0.211669	+	0.366621i	−0.952237	−	0.305360i	$-0.901223\pi$
$233$	−3.23099	+	5.59623i	−0.211669	+	0.366621i	0.740568	+	0.671981i	$0.234557\pi$
$234$		0			0
$235$	−0.0603282	+	0.506460i	−0.00393538	+	0.0330378i
$236$	−9.88066			−0.643176
$237$		0			0
$238$	−0.270150	−	0.467914i	−0.0175112	−	0.0303304i
$239$		−	3.08527i		−	0.199570i	−0.995009	−	0.0997849i	$-0.968185\pi$
$239$		−	3.08527i		−	0.199570i	0.995009	−	0.0997849i	$-0.0318155\pi$
$240$		0			0
$241$	−17.1738	+	9.91529i	−1.10626	+	0.638700i	−0.937858	−	0.347018i	$-0.887194\pi$
$241$	−17.1738	+	9.91529i	−1.10626	+	0.638700i	−0.168403	+	0.985718i	$0.553861\pi$
$242$	−7.72718	−	4.46129i	−0.496722	−	0.286782i
$243$		0			0
$244$	6.64753	−	11.5139i	0.425564	−	0.737099i
$245$	12.4765	+	9.33122i	0.797095	+	0.596150i
$246$		0			0
$247$	3.65687	+	15.1493i	0.232681	+	0.963926i
$248$	5.35453			0.340013
$249$		0			0
$250$	8.61196	−	7.12981i	0.544668	−	0.450929i
$251$	18.0919	−	10.4453i	1.14195	−	0.659304i	0.195036	−	0.980796i	$-0.437518\pi$
$251$	18.0919	−	10.4453i	1.14195	−	0.659304i	0.946912	+	0.321492i	$0.104184\pi$
$252$		0			0
$253$	−11.7168	+	6.76473i	−0.736632	+	0.425295i
$254$		−	9.16320i		−	0.574950i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.29590	+	1.90289i	−0.205592	+	0.118699i	−0.599261	−	0.800553i	$-0.704539\pi$
$257$	−3.29590	+	1.90289i	−0.205592	+	0.118699i	0.393669	+	0.919252i	$0.371206\pi$
$258$		0			0
$259$		−	1.87067i		−	0.116238i
$260$	7.34776	−	3.15033i	0.455689	−	0.195375i
$261$		0			0
$262$	9.81092	+	16.9930i	0.606121	+	1.04983i
$263$	−8.20870	+	14.2179i	−0.506170	+	0.876713i	0.493804	+	0.869573i	$0.335606\pi$
$263$	−8.20870	+	14.2179i	−0.506170	+	0.876713i	−0.999975	+	0.00713969i	$0.997727\pi$
$264$		0			0
$265$	13.5036	+	1.60852i	0.829521	+	0.0988104i
$266$	−0.568753	+	0.541067i	−0.0348725	+	0.0331749i
$267$		0			0
$268$	2.02318	−	3.50425i	0.123585	−	0.214056i
$269$	0.399470	−	0.691902i	0.0243561	−	0.0421860i	−0.853590	−	0.520945i	$-0.825580\pi$
$269$	0.399470	−	0.691902i	0.0243561	−	0.0421860i	0.877947	+	0.478759i	$0.158913\pi$
$270$		0			0
$271$	6.62871	−	11.4813i	0.402666	−	0.697437i	−0.591381	−	0.806392i	$-0.701417\pi$
$271$	6.62871	−	11.4813i	0.402666	−	0.697437i	0.994047	+	0.108955i	$0.0347504\pi$
$272$	1.50006	+	2.59818i	0.0909547	+	0.157538i
$273$		0			0
$274$		−	21.1564i		−	1.27810i
$275$	6.91293	−	2.03644i	0.416865	−	0.122802i
$276$		0			0
$277$			8.48800i			0.509994i	0.966942	+	0.254997i	$0.0820745\pi$
$277$			8.48800i			0.509994i	−0.966942	+	0.254997i	$0.917925\pi$
$278$			2.93443i			0.175995i
$279$		0			0
$280$	0.322484	+	0.241187i	0.0192721	+	0.0144137i
$281$	−12.8871	−	22.3211i	−0.768780	−	1.33157i	−0.938225	−	0.346027i	$-0.887531\pi$
$281$	−12.8871	−	22.3211i	−0.768780	−	1.33157i	0.169444	−	0.985540i	$-0.445803\pi$
$282$		0			0
$283$	18.3937	+	10.6196i	1.09339	+	0.631272i	0.934478	−	0.356020i	$-0.115867\pi$
$283$	18.3937	+	10.6196i	1.09339	+	0.631272i	0.158917	+	0.987292i	$0.449200\pi$
$284$	−2.68326			−0.159222
$285$		0			0
$286$	5.15319			0.304715
$287$	1.63225	+	0.942378i	0.0963485	+	0.0556268i
$288$		0			0
$289$	3.99962	+	6.92755i	0.235272	+	0.407503i
$290$	−8.11508	+	10.8505i	−0.476534	+	0.637160i
$291$		0			0
$292$			6.52722i			0.381977i
$293$			12.5945i			0.735778i	0.929870	+	0.367889i	$0.119919\pi$
$293$			12.5945i			0.735778i	−0.929870	+	0.367889i	$0.880081\pi$
$294$		0			0
$295$	−20.3061	+	8.70620i	−1.18227	+	0.506895i
$296$			10.3873i			0.603748i
$297$		0			0
$298$	4.62269	+	8.00673i	0.267785	+	0.463817i
$299$	−16.7803	+	29.0644i	−0.970432	+	1.68084i
$300$		0			0
$301$	0.0548385	−	0.0949831i	0.00316084	−	0.00547473i
$302$	−5.25004	+	9.09334i	−0.302106	+	0.523263i
$303$		0			0
$304$	3.15811	−	3.00438i	0.181130	−	0.172313i
$305$	3.51634	−	29.5199i	0.201345	−	1.69031i
$306$		0			0
$307$	−14.8470	+	25.7157i	−0.847361	+	1.46767i	0.0361944	+	0.999345i	$0.488476\pi$
$307$	−14.8470	+	25.7157i	−0.847361	+	1.46767i	−0.883555	+	0.468327i	$0.844857\pi$
$308$	0.129786	+	0.224796i	0.00739526	+	0.0128090i
$309$		0			0
$310$	11.0043	−	4.71806i	0.625002	−	0.267968i
$311$		−	14.2653i		−	0.808913i	−0.914557	−	0.404456i	$-0.867461\pi$
$311$		−	14.2653i		−	0.808913i	0.914557	−	0.404456i	$-0.132539\pi$
$312$		0			0
$313$	23.9295	−	13.8157i	1.35258	−	0.780911i	0.363968	−	0.931411i	$-0.381422\pi$
$313$	23.9295	−	13.8157i	1.35258	−	0.780911i	0.988610	+	0.150500i	$0.0480884\pi$
$314$	10.3590	+	17.9423i	0.584593	+	1.01254i
$315$		0			0
$316$			10.4696i			0.588961i
$317$	26.3560	−	15.2166i	1.48030	−	0.854651i	0.480548	−	0.876969i	$-0.340438\pi$
$317$	26.3560	−	15.2166i	1.48030	−	0.854651i	0.999751	+	0.0223177i	$0.00710452\pi$
$318$		0			0
$319$	−7.56361	+	4.36685i	−0.423481	+	0.244497i
$320$	−1.79066	−	1.33924i	−0.100101	−	0.0748656i
$321$		0			0
$322$	−1.69049			−0.0942075
$323$	−9.47474	+	9.01352i	−0.527189	+	0.501526i
$324$		0			0
$325$	12.3248	−	12.9487i	0.683657	−	0.718267i
$326$	7.47113	−	12.9404i	0.413788	−	0.716702i
$327$		0			0
$328$	−9.06337	−	5.23274i	−0.500441	−	0.288930i
$329$	−0.0355751	+	0.0205393i	−0.00196132	+	0.00113237i
$330$		0			0
$331$		−	20.4963i		−	1.12658i	−0.826259	−	0.563290i	$-0.809535\pi$
$331$		−	20.4963i		−	1.12658i	0.826259	−	0.563290i	$-0.190465\pi$
$332$	8.47511	+	14.6793i	0.465132	+	0.805632i
$333$		0			0
$334$	−2.02709			−0.110917
$335$	1.07020	−	8.98442i	0.0584713	−	0.490871i
$336$		0			0
$337$	−8.35340	+	14.4685i	−0.455039	+	0.788150i	−0.998690	−	0.0511610i	$-0.983708\pi$
$337$	−8.35340	+	14.4685i	−0.455039	+	0.788150i	0.543652	+	0.839311i	$0.317041\pi$
$338$	−0.188080	+	0.108588i	−0.0102302	+	0.00590642i
$339$		0			0
$340$	5.37219	+	4.01788i	0.291348	+	0.217900i
$341$	7.71763			0.417933
$342$		0			0
$343$			2.51546i			0.135822i
$344$	−0.304502	+	0.527413i	−0.0164176	+	0.0284362i
$345$		0			0
$346$	7.77976	+	13.4749i	0.418243	+	0.724418i
$347$	−6.80018	+	11.7783i	−0.365053	+	0.632290i	−0.988785	−	0.149348i	$-0.952282\pi$
$347$	−6.80018	+	11.7783i	−0.365053	+	0.632290i	0.623732	+	0.781638i	$0.285616\pi$
$348$		0			0
$349$	30.5342			1.63446			0.817228	−	0.576314i	$-0.195509\pi$
$349$	30.5342			1.63446			0.817228	+	0.576314i	$0.195509\pi$
$350$	0.875267	+	0.211520i	0.0467850	+	0.0113062i
$351$		0			0
$352$	−0.720664	−	1.24823i	−0.0384115	−	0.0665307i
$353$	−18.8401			−1.00276			−0.501379	−	0.865228i	$-0.667174\pi$
$353$	−18.8401			−1.00276			−0.501379	+	0.865228i	$0.667174\pi$
$354$		0			0
$355$	−5.51448	+	2.36432i	−0.292678	+	0.125485i
$356$	1.71203	−	2.96533i	0.0907376	−	0.157162i
$357$		0			0
$358$	10.7245	+	6.19177i	0.566805	+	0.327245i
$359$	10.3468	+	5.97371i	0.546082	+	0.315281i	0.747540	−	0.664217i	$-0.231235\pi$
$359$	10.3468	+	5.97371i	0.546082	+	0.315281i	−0.201458	+	0.979497i	$0.564568\pi$
$360$		0			0
$361$	15.9603	+	10.3086i	0.840017	+	0.542560i
$362$	−6.07109			−0.319089
$363$		0			0
$364$	0.557622	+	0.321943i	0.0292273	+	0.0168744i
$365$	5.75136	+	13.4144i	0.301040	+	0.702139i
$366$		0			0
$367$	−15.1070	+	8.72206i	−0.788582	+	0.455288i	−0.839463	−	0.543417i	$-0.817130\pi$
$367$	−15.1070	+	8.72206i	−0.788582	+	0.455288i	0.0508814	+	0.998705i	$0.483797\pi$
$368$	9.38680			0.489321
$369$		0			0
$370$	9.15259	+	21.3473i	0.475821	+	1.10979i
$371$	0.547634	+	0.948531i	0.0284318	+	0.0492453i
$372$		0			0
$373$	12.8141			0.663490			0.331745	−	0.943369i	$-0.392363\pi$
$373$	12.8141			0.663490			0.331745	+	0.943369i	$0.392363\pi$
$374$	2.16208	+	3.74484i	0.111799	+	0.193641i
$375$		0			0
$376$	0.197538	−	0.114049i	0.0101872	−	0.00588161i
$377$	−10.8323	+	18.7620i	−0.557890	+	0.966294i
$378$		0			0
$379$			21.0837i			1.08300i	0.840702	+	0.541498i	$0.182143\pi$
$379$			21.0837i			1.08300i	−0.840702	+	0.541498i	$0.817857\pi$
$380$	3.84310	−	8.95715i	0.197147	−	0.459492i
$381$		0			0
$382$	5.61597	−	9.72714i	0.287338	−	0.497684i
$383$	9.48787	+	5.47782i	0.484807	+	0.279904i	0.722418	−	0.691457i	$-0.243031\pi$
$383$	9.48787	+	5.47782i	0.484807	+	0.279904i	−0.237610	+	0.971361i	$0.576364\pi$
$384$		0			0
$385$	0.464805	+	0.347629i	0.0236887	+	0.0177168i
$386$	−14.0233	+	8.09635i	−0.713766	+	0.412093i
$387$		0			0
$388$	−10.0468			−0.510047
$389$	7.95264	−	4.59146i	0.403215	−	0.232796i	−0.284655	−	0.958630i	$-0.591879\pi$
$389$	7.95264	−	4.59146i	0.403215	−	0.232796i	0.687870	+	0.725834i	$0.258546\pi$
$390$		0			0
$391$	−28.1616			−1.42419
$392$		−	6.96757i		−	0.351915i
$393$		0			0
$394$	−6.67428	−	3.85340i	−0.336246	−	0.194131i
$395$	9.22513	+	21.5165i	0.464167	+	1.08261i
$396$		0			0
$397$	22.8226	+	13.1766i	1.14543	+	0.661316i	0.947770	−	0.318954i	$-0.103331\pi$
$397$	22.8226	+	13.1766i	1.14543	+	0.661316i	0.197663	+	0.980270i	$0.436665\pi$
$398$			13.9130i			0.697396i
$399$		0			0
$400$	−4.86010	−	1.17451i	−0.243005	−	0.0587254i
$401$	14.1653	−	24.5350i	0.707381	−	1.22522i	−0.258444	−	0.966026i	$-0.583210\pi$
$401$	14.1653	−	24.5350i	0.707381	−	1.22522i	0.965825	−	0.259194i	$-0.0834569\pi$
$402$		0			0
$403$	16.5793	−	9.57204i	0.825872	−	0.476817i
$404$	9.33315	+	5.38850i	0.464342	+	0.268088i
$405$		0			0
$406$	−1.09127			−0.0541587
$407$			14.9715i			0.742108i
$408$		0			0
$409$	−3.16421	+	1.82686i	−0.156460	+	0.0903324i	−0.576186	−	0.817319i	$-0.695460\pi$
$409$	−3.16421	+	1.82686i	−0.156460	+	0.0903324i	0.419726	+	0.907651i	$0.362126\pi$
$410$	−23.2373	−	2.76796i	−1.14761	−	0.136700i
$411$		0			0
$412$	−7.31736	−	12.6740i	−0.360500	−	0.624405i
$413$	−1.54104	−	0.889717i	−0.0758294	−	0.0437801i
$414$		0			0
$415$	30.3520	+	22.7003i	1.48992	+	1.11432i
$416$	−3.09631	−	1.78765i	−0.151809	−	0.0876469i
$417$		0			0
$418$	4.55188	−	4.33030i	0.222640	−	0.211802i
$419$		−	27.7675i		−	1.35653i	−0.734817	−	0.678266i	$-0.762732\pi$
$419$		−	27.7675i		−	1.35653i	0.734817	−	0.678266i	$-0.237268\pi$
$420$		0			0
$421$	0.0830135	+	0.0479279i	0.00404583	+	0.00233586i	0.502022	−	0.864855i	$-0.332590\pi$
$421$	0.0830135	+	0.0479279i	0.00404583	+	0.00233586i	−0.497976	+	0.867191i	$0.665923\pi$
$422$	5.38856	+	9.33327i	0.262311	+	0.454336i
$423$		0			0
$424$	−3.04085	−	5.26691i	−0.147677	−	0.255784i
$425$	14.5809	+	3.52367i	0.707277	+	0.170923i
$426$		0			0
$427$	2.07356	−	1.19717i	0.100347	−	0.0579351i
$428$	8.14310	−	4.70142i	0.393612	−	0.227252i
$429$		0			0
$430$	−0.161072	+	1.35221i	−0.00776759	+	0.0652095i
$431$	17.2948	+	29.9555i	0.833062	+	1.44291i	0.895598	+	0.444864i	$0.146748\pi$
$431$	17.2948	+	29.9555i	0.833062	+	1.44291i	−0.0625360	+	0.998043i	$0.519919\pi$
$432$		0			0
$433$	−0.287352	−	0.497708i	−0.0138093	−	0.0239183i	0.859038	−	0.511911i	$-0.171062\pi$
$433$	−0.287352	−	0.497708i	−0.0138093	−	0.0239183i	−0.872847	+	0.487993i	$0.837729\pi$
$434$	0.835117	+	0.482155i	0.0400869	+	0.0231442i
$435$		0			0
$436$			3.57292i			0.171112i
$437$	9.60094	+	39.7737i	0.459275	+	1.90263i
$438$		0			0
$439$	−10.1031	−	5.83303i	−0.482195	−	0.278395i	0.239136	−	0.970986i	$-0.423136\pi$
$439$	−10.1031	−	5.83303i	−0.482195	−	0.278395i	−0.721331	+	0.692591i	$0.756469\pi$
$440$	−2.58092	−	1.93028i	−0.123041	−	0.0920224i
$441$		0			0
$442$	9.28931	+	5.36319i	0.441847	+	0.255101i
$443$	−5.82209	−	10.0841i	−0.276616	−	0.479112i	0.693926	−	0.720046i	$-0.255880\pi$
$443$	−5.82209	−	10.0841i	−0.276616	−	0.479112i	−0.970541	+	0.240934i	$0.922546\pi$
$444$		0			0
$445$	0.905613	−	7.60270i	0.0429302	−	0.360403i
$446$	−17.6983	+	10.2181i	−0.838037	+	0.483841i
$447$		0			0
$448$		−	0.180093i		−	0.00850858i
$449$	−9.29191			−0.438512			−0.219256	−	0.975667i	$-0.570363\pi$
$449$	−9.29191			−0.438512			−0.219256	+	0.975667i	$0.570363\pi$
$450$		0			0
$451$	−13.0633	−	7.54210i	−0.615127	−	0.355143i
$452$	7.70742	−	4.44988i	0.362526	−	0.209305i
$453$		0			0
$454$	12.4418	−	21.5499i	0.583924	−	1.01139i
$455$	1.42967	+	0.170298i	0.0670238	+	0.00798370i
$456$		0			0
$457$		−	1.05360i		−	0.0492853i	−0.999696	−	0.0246426i	$-0.992155\pi$
$457$		−	1.05360i		−	0.0492853i	0.999696	−	0.0246426i	$-0.00784479\pi$
$458$	−13.7147	−	7.91819i	−0.640846	−	0.369993i
$459$		0			0
$460$	19.2912	−	8.27103i	0.899456	−	0.385639i
$461$	14.0950	+	8.13777i	0.656471	+	0.379014i	0.790931	−	0.611905i	$-0.209597\pi$
$461$	14.0950	+	8.13777i	0.656471	+	0.379014i	−0.134460	+	0.990919i	$0.542930\pi$
$462$		0			0
$463$		−	29.4392i		−	1.36816i	−0.729408	−	0.684079i	$-0.760205\pi$
$463$		−	29.4392i		−	1.36816i	0.729408	−	0.684079i	$-0.239795\pi$
$464$	6.05949			0.281305
$465$		0			0
$466$	5.59623	−	3.23099i	0.259240	−	0.149673i
$467$	−4.65315			−0.215322			−0.107661	−	0.994188i	$-0.534336\pi$
$467$	−4.65315			−0.215322			−0.107661	+	0.994188i	$0.534336\pi$
$468$		0			0
$469$	0.631089	−	0.364360i	0.0291410	−	0.0168246i
$470$	0.305476	−	0.408444i	0.0140906	−	0.0188401i
$471$		0			0
$472$	8.55691	+	4.94033i	0.393864	+	0.227397i
$473$	−0.438887	+	0.760174i	−0.0201800	+	0.0349529i
$474$		0			0
$475$	0.00565462	−	21.7945i	0.000259452	−	1.00000i
$476$			0.540300i			0.0247646i
$477$		0			0
$478$	−1.54264	+	2.67193i	−0.0705586	+	0.122211i
$479$	−24.0829	+	13.9043i	−1.10038	+	0.635303i	−0.936320	−	0.351147i	$-0.885792\pi$
$479$	−24.0829	+	13.9043i	−1.10038	+	0.635303i	−0.164058	+	0.986451i	$0.552458\pi$
$480$		0			0
$481$	18.5689	+	32.1622i	0.846667	+	1.46647i
$482$	19.8306			0.903259
$483$		0			0
$484$	4.46129	+	7.72718i	0.202786	+	0.351235i
$485$	−20.6475	+	8.85255i	−0.937554	+	0.401974i
$486$		0			0
$487$	−9.77903			−0.443130			−0.221565	−	0.975146i	$-0.571117\pi$
$487$	−9.77903			−0.443130			−0.221565	+	0.975146i	$0.571117\pi$
$488$	−11.5139	+	6.64753i	−0.521208	+	0.300919i
$489$		0			0
$490$	−6.13937	−	14.3193i	−0.277348	−	0.646881i
$491$	21.3038	+	12.2997i	0.961426	+	0.555080i	0.896612	−	0.442818i	$-0.146021\pi$
$491$	21.3038	+	12.2997i	0.961426	+	0.555080i	0.0648146	+	0.997897i	$0.479354\pi$
$492$		0			0
$493$	−18.1792			−0.818751
$494$	4.40770	−	14.9481i	0.198312	−	0.672547i
$495$		0			0
$496$	−4.63716	−	2.67726i	−0.208214	−	0.120213i
$497$	−0.418494	−	0.241618i	−0.0187720	−	0.0108380i
$498$		0			0
$499$	−15.2664	+	26.4422i	−0.683419	+	1.18372i	0.290512	+	0.956871i	$0.406174\pi$
$499$	−15.2664	+	26.4422i	−0.683419	+	1.18372i	−0.973931	+	0.226845i	$0.927159\pi$
$500$	−11.0231	+	1.86862i	−0.492967	+	0.0835673i
$501$		0			0
$502$	−20.8907			−0.932397
$503$	10.5841	+	18.3322i	0.471921	+	0.817392i	0.999484	−	0.0321243i	$-0.0102272\pi$
$503$	10.5841	+	18.3322i	0.471921	+	0.817392i	−0.527562	+	0.849516i	$0.676894\pi$
$504$		0			0
$505$	23.9289	+	2.85035i	1.06482	+	0.126839i
$506$	13.5295			0.601457
$507$		0			0
$508$	−4.58160	+	7.93557i	−0.203276	+	0.352084i
$509$	−3.91941	−	6.78861i	−0.173725	−	0.300900i	0.765994	−	0.642847i	$-0.222247\pi$
$509$	−3.91941	−	6.78861i	−0.173725	−	0.300900i	−0.939719	+	0.341947i	$0.888914\pi$
$510$		0			0
$511$	−0.587752	+	1.01802i	−0.0260006	+	0.0450344i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	3.80577			0.167865
$515$	−26.2057	−	19.5993i	−1.15476	−	0.863650i
$516$		0			0
$517$	0.284717	−	0.164381i	0.0125218	−	0.00722949i
$518$	−0.935336	+	1.62005i	−0.0410963	+	0.0711809i
$519$		0			0
$520$	−7.93851	−	0.945614i	−0.348127	−	0.0414679i
$521$	9.75840			0.427523			0.213762	−	0.976886i	$-0.431428\pi$
$521$	9.75840			0.427523			0.213762	+	0.976886i	$0.431428\pi$
$522$		0			0
$523$	2.14945	+	3.72297i	0.0939891	+	0.162794i	0.909186	−	0.416390i	$-0.136705\pi$
$523$	2.14945	+	3.72297i	0.0939891	+	0.162794i	−0.815197	+	0.579184i	$0.803371\pi$
$524$		−	19.6218i		−	0.857184i
$525$		0			0
$526$	14.2179	−	8.20870i	0.619930	−	0.357917i
$527$	13.9120	+	8.03212i	0.606018	+	0.349885i
$528$		0			0
$529$	−32.5560	+	56.3886i	−1.41548	+	2.45168i
$530$	−10.8902	−	8.14483i	−0.473041	−	0.353789i
$531$		0			0
$532$	0.763088	−	0.184201i	0.0330841	−	0.00798613i
$533$	−37.4173			−1.62072
$534$		0			0
$535$	12.5926	−	16.8372i	0.544427	−	0.727938i
$536$	−3.50425	+	2.02318i	−0.151360	+	0.0873880i
$537$		0			0
$538$	−0.691902	+	0.399470i	−0.0298300	+	0.0172224i
$539$		−	10.0425i		−	0.432563i
$540$		0			0
$541$	−8.31198	−	14.3968i	−0.357360	−	0.618965i	0.630159	−	0.776466i	$-0.282990\pi$
$541$	−8.31198	−	14.3968i	−0.357360	−	0.618965i	−0.987519	+	0.157501i	$0.949656\pi$
$542$	−11.4813	+	6.62871i	−0.493163	+	0.284728i
$543$		0			0
$544$		−	3.00013i		−	0.128629i
$545$	3.14823	+	7.34286i	0.134855	+	0.314533i
$546$		0			0
$547$	−9.82788	−	17.0224i	−0.420210	−	0.727824i	0.575750	−	0.817626i	$-0.304710\pi$
$547$	−9.82788	−	17.0224i	−0.420210	−	0.727824i	−0.995960	+	0.0898013i	$0.971377\pi$
$548$	−10.5782	+	18.3220i	−0.451878	+	0.782675i
$549$		0			0
$550$	−7.00499	−	1.69285i	−0.298694	−	0.0721835i
$551$	6.19772	+	25.6752i	0.264032	+	1.09380i
$552$		0			0
$553$	−0.942748	+	1.63289i	−0.0400897	+	0.0694375i
$554$	4.24400	−	7.35082i	0.180310	−	0.312306i
$555$		0			0
$556$	1.46722	−	2.54129i	0.0622238	−	0.107775i
$557$	−13.8516	−	23.9917i	−0.586913	−	1.01656i	−0.994634	−	0.103456i	$-0.967010\pi$
$557$	−13.8516	−	23.9917i	−0.586913	−	1.01656i	0.407721	−	0.913107i	$-0.366324\pi$
$558$		0			0
$559$			2.17737i			0.0920931i
$560$	−0.158686	−	0.370116i	−0.00670570	−	0.0156402i
$561$		0			0
$562$			25.7742i			1.08722i
$563$		−	41.0685i		−	1.73083i	−0.501057	−	0.865414i	$-0.667055\pi$
$563$		−	41.0685i		−	1.73083i	0.501057	−	0.865414i	$-0.332945\pi$
$564$		0			0
$565$	11.9189	−	15.9364i	0.501431	−	0.670450i
$566$	−10.6196	−	18.3937i	−0.446377	−	0.773147i
$567$		0			0
$568$	2.32377	+	1.34163i	0.0975034	+	0.0562936i
$569$	6.68022			0.280049			0.140025	−	0.990148i	$-0.455282\pi$
$569$	6.68022			0.280049			0.140025	+	0.990148i	$0.455282\pi$
$570$		0			0
$571$	18.9224			0.791876			0.395938	−	0.918277i	$-0.370420\pi$
$571$	18.9224			0.791876			0.395938	+	0.918277i	$0.370420\pi$
$572$	−4.46279	−	2.57660i	−0.186599	−	0.107733i
$573$		0			0
$574$	−0.942378	−	1.63225i	−0.0393341	−	0.0681287i
$575$	32.3582	−	33.9963i	1.34943	−	1.41774i
$576$		0			0
$577$			24.5711i			1.02291i	0.859311	+	0.511453i	$0.170893\pi$
$577$			24.5711i			1.02291i	−0.859311	+	0.511453i	$0.829107\pi$
$578$		−	7.99925i		−	0.332725i
$579$		0			0
$580$	12.4531	−	5.33922i	0.517086	−	0.221699i
$581$			3.05261i			0.126644i
$582$		0			0
$583$	−4.38286	−	7.59134i	−0.181520	−	0.314401i
$584$	3.26361	−	5.65274i	0.135049	−	0.233912i
$585$		0			0
$586$	6.29725	−	10.9072i	0.260137	−	0.450570i
$587$	1.03656	−	1.79538i	0.0427835	−	0.0741031i	−0.843841	−	0.536594i	$-0.819711\pi$
$587$	1.03656	−	1.79538i	0.0427835	−	0.0741031i	0.886624	+	0.462491i	$0.153044\pi$
$588$		0			0
$589$	6.60115	−	22.3869i	0.271996	−	0.922436i
$590$	21.9387	+	2.61328i	0.903204	+	0.107587i
$591$		0			0
$592$	5.19364	−	8.99565i	0.213457	−	0.369719i
$593$	9.43982	+	16.3502i	0.387647	+	0.671424i	0.992133	−	0.125192i	$-0.0399546\pi$
$593$	9.43982	+	16.3502i	0.387647	+	0.671424i	−0.604486	+	0.796616i	$0.706621\pi$
$594$		0			0
$595$	0.476078	+	1.11039i	0.0195173	+	0.0455217i
$596$		−	9.24537i		−	0.378705i
$597$		0			0
$598$	29.0644	−	16.7803i	1.18853	−	0.686199i
$599$	−7.49674	−	12.9847i	−0.306308	−	0.530542i	0.671243	−	0.741237i	$-0.265761\pi$
$599$	−7.49674	−	12.9847i	−0.306308	−	0.530542i	−0.977552	+	0.210695i	$0.932427\pi$
$600$		0			0
$601$			37.7223i			1.53873i	0.638812	+	0.769363i	$0.279426\pi$
$601$			37.7223i			1.53873i	−0.638812	+	0.769363i	$0.720574\pi$
$602$	−0.0949831	+	0.0548385i	−0.00387122	+	0.00223505i
$603$		0			0
$604$	9.09334	−	5.25004i	0.370003	−	0.213621i
$605$	15.9773	+	11.9494i	0.649568	+	0.485813i
$606$		0			0
$607$	−9.05962			−0.367719			−0.183859	−	0.982953i	$-0.558859\pi$
$607$	−9.05962			−0.367719			−0.183859	+	0.982953i	$0.558859\pi$
$608$	−4.23720	+	1.02281i	−0.171841	+	0.0414806i
$609$		0			0
$610$	−17.8052	+	23.8069i	−0.720912	+	0.963911i
$611$	0.407759	−	0.706259i	0.0164962	−	0.0285722i
$612$		0			0
$613$	2.58885	+	1.49467i	0.104563	+	0.0603693i	0.551369	−	0.834261i	$-0.314105\pi$
$613$	2.58885	+	1.49467i	0.104563	+	0.0603693i	−0.446807	+	0.894631i	$0.647439\pi$
$614$	25.7157	−	14.8470i	1.03780	−	0.599175i
$615$		0			0
$616$		−	0.259573i		−	0.0104585i
$617$	7.38037	+	12.7832i	0.297122	+	0.514631i	0.975476	−	0.220104i	$-0.0706397\pi$
$617$	7.38037	+	12.7832i	0.297122	+	0.514631i	−0.678354	+	0.734735i	$0.737306\pi$
$618$		0			0
$619$	−11.5664			−0.464894			−0.232447	−	0.972609i	$-0.574673\pi$
$619$	−11.5664			−0.464894			−0.232447	+	0.972609i	$0.574673\pi$
$620$	−11.8890	−	1.41619i	−0.477475	−	0.0568756i
$621$		0			0
$622$	−7.13266	+	12.3541i	−0.285994	+	0.495356i
$623$	0.534034	−	0.308325i	0.0213956	−	0.0123528i
$624$		0			0
$625$	−21.0075	+	13.5531i	−0.840299	+	0.542124i
$626$	−27.6315			−1.10438
$627$		0			0
$628$		−	20.7180i		−	0.826739i
$629$	−15.5816	+	26.9881i	−0.621278	+	1.07608i
$630$		0			0
$631$	−12.1321	−	21.0135i	−0.482973	−	0.836534i	0.516836	−	0.856085i	$-0.327110\pi$
$631$	−12.1321	−	21.0135i	−0.482973	−	0.836534i	−0.999809	+	0.0195506i	$0.993776\pi$
$632$	5.23480	−	9.06694i	0.208229	−	0.360663i
$633$		0			0
$634$	−30.4333			−1.20866
$635$	−2.42353	+	20.3457i	−0.0961747	+	0.807395i
$636$		0			0
$637$	−12.4556	−	21.5737i	−0.493509	−	0.854782i
$638$	8.73371			0.345771
$639$		0			0
$640$	0.881135	+	2.05514i	0.0348299	+	0.0812365i
$641$	−14.4986	+	25.1123i	−0.572660	+	0.991876i	0.423632	+	0.905834i	$0.360755\pi$
$641$	−14.4986	+	25.1123i	−0.572660	+	0.991876i	−0.996292	+	0.0860414i	$0.972578\pi$
$642$		0			0
$643$	−15.7266	−	9.07976i	−0.620197	−	0.358071i	0.156749	−	0.987638i	$-0.449899\pi$
$643$	−15.7266	−	9.07976i	−0.620197	−	0.358071i	−0.776946	+	0.629568i	$0.783232\pi$
$644$	1.46401	+	0.845246i	0.0576900	+	0.0333074i
$645$		0			0
$646$	12.7121	−	3.06857i	0.500152	−	0.120731i
$647$	5.44787			0.214178			0.107089	−	0.994249i	$-0.465847\pi$
$647$	5.44787			0.214178			0.107089	+	0.994249i	$0.465847\pi$
$648$		0			0
$649$	12.3333	+	7.12064i	0.484125	+	0.279510i
$650$	−17.1480	+	5.05153i	−0.672598	+	0.198137i
$651$		0			0
$652$	−12.9404	+	7.47113i	−0.506785	+	0.292592i
$653$	5.23730			0.204952			0.102476	−	0.994735i	$-0.467324\pi$
$653$	5.23730			0.204952			0.102476	+	0.994735i	$0.467324\pi$
$654$		0			0
$655$	−17.2895	−	40.3256i	−0.675556	−	1.57565i
$656$	5.23274	+	9.06337i	0.204304	+	0.353865i
$657$		0			0
$658$	0.0410786			0.00160141
$659$	10.1507	+	17.5815i	0.395416	+	0.684880i	0.993154	−	0.116811i	$-0.0372672\pi$
$659$	10.1507	+	17.5815i	0.395416	+	0.684880i	−0.597739	+	0.801691i	$0.703934\pi$
$660$		0			0
$661$	6.29651	−	3.63529i	0.244906	−	0.141397i	−0.372524	−	0.928023i	$-0.621507\pi$
$661$	6.29651	−	3.63529i	0.244906	−	0.141397i	0.617430	+	0.786626i	$0.288174\pi$
$662$	−10.2482	+	17.7503i	−0.398306	+	0.689887i
$663$		0			0
$664$		−	16.9502i		−	0.657796i
$665$	1.40595	−	1.05094i	0.0545203	−	0.0407538i
$666$		0			0
$667$	−28.4396	+	49.2588i	−1.10118	+	1.90731i
$668$	1.75551	+	1.01355i	0.0679228	+	0.0392152i
$669$		0			0
$670$	−5.41903	+	7.24563i	−0.209355	+	0.279923i
$671$	−16.5952	+	9.58127i	−0.640652	+	0.369881i
$672$		0			0
$673$	−4.82113			−0.185841			−0.0929204	−	0.995674i	$-0.529620\pi$
$673$	−4.82113			−0.185841			−0.0929204	+	0.995674i	$0.529620\pi$
$674$	14.4685	−	8.35340i	0.557306	−	0.321761i
$675$		0			0
$676$	0.217176			0.00835294
$677$		−	9.34397i		−	0.359118i	−0.983747	−	0.179559i	$-0.942533\pi$
$677$		−	9.34397i		−	0.359118i	0.983747	−	0.179559i	$-0.0574670\pi$
$678$		0			0
$679$	−1.56694	−	0.904673i	−0.0601336	−	0.0347182i
$680$	−2.64352	−	6.16568i	−0.101374	−	0.236443i
$681$		0			0
$682$	−6.68366	−	3.85881i	−0.255931	−	0.147762i
$683$		−	2.62811i		−	0.100562i	−0.998735	−	0.0502809i	$-0.983988\pi$
$683$		−	2.62811i		−	0.100562i	0.998735	−	0.0502809i	$-0.0160117\pi$
$684$		0			0
$685$	−5.59554	+	46.9750i	−0.213794	+	1.79482i
$686$	1.25773	−	2.17845i	0.0480203	−	0.0831735i
$687$		0			0
$688$	0.527413	−	0.304502i	0.0201074	−	0.0116090i
$689$	−18.8308	−	10.8720i	−0.717397	−	0.414189i
$690$		0			0
$691$	6.77060			0.257566			0.128783	−	0.991673i	$-0.458893\pi$
$691$	6.77060			0.257566			0.128783	+	0.991673i	$0.458893\pi$
$692$		−	15.5595i		−	0.591485i
$693$		0			0
$694$	11.7783	−	6.80018i	0.447096	−	0.258131i
$695$	0.776112	−	6.51552i	0.0294396	−	0.247148i
$696$		0			0
$697$	−15.6989	−	27.1913i	−0.594637	−	1.02994i
$698$	−26.4434	−	15.2671i	−1.00090	−	0.577868i
$699$		0			0
$700$	−0.652244	−	0.620816i	−0.0246525	−	0.0234646i
$701$	−27.0371	−	15.6099i	−1.02118	−	0.589577i	−0.106732	−	0.994288i	$-0.534039\pi$
$701$	−27.0371	−	15.6099i	−1.02118	−	0.589577i	−0.914445	+	0.404711i	$0.867372\pi$
$702$		0			0
$703$	43.4285	+	12.8056i	1.63794	+	0.482973i
$704$			1.44133i			0.0543221i
$705$		0			0
$706$	16.3160	+	9.42006i	0.614061	+	0.354528i
$707$	0.970429	+	1.68083i	0.0364967	+	0.0632142i
$708$		0			0
$709$	5.19610	+	8.99990i	0.195143	+	0.337998i	0.946948	−	0.321388i	$-0.104149\pi$
$709$	5.19610	+	8.99990i	0.195143	+	0.337998i	−0.751804	+	0.659387i	$0.770816\pi$
$710$	5.95784	+	0.709682i	0.223594	+	0.0266339i
$711$		0			0
$712$	−2.96533	+	1.71203i	−0.111130	+	0.0641612i
$713$	43.5280	−	25.1309i	1.63014	−	0.941160i
$714$		0			0
$715$	−11.4420	−	1.36294i	−0.427906	−	0.0509711i
$716$	−6.19177	−	10.7245i	−0.231397	−	0.400792i
$717$		0			0
$718$	−5.97371	−	10.3468i	−0.222937	−	0.386138i
$719$	5.55424	+	3.20674i	0.207138	+	0.119591i	0.599981	−	0.800015i	$-0.295175\pi$
$719$	5.55424	+	3.20674i	0.207138	+	0.119591i	−0.392843	+	0.919606i	$0.628508\pi$
$720$		0			0
$721$		−	2.63560i		−	0.0981550i
$722$	−8.66773	−	16.9077i	−0.322579	−	0.629240i
$723$		0			0
$724$	5.25771	+	3.03554i	0.195401	+	0.112815i
$725$	20.8883	−	21.9457i	0.775771	−	0.815043i
$726$		0			0
$727$	−12.6659	−	7.31268i	−0.469754	−	0.271212i	0.246383	−	0.969173i	$-0.420758\pi$
$727$	−12.6659	−	7.31268i	−0.469754	−	0.271212i	−0.716137	+	0.697960i	$0.754091\pi$
$728$	−0.321943	−	0.557622i	−0.0119320	−	0.0206668i
$729$		0			0
$730$	1.72635	−	14.4929i	0.0638951	−	0.536404i
$731$	−1.58230	+	0.913543i	−0.0585236	+	0.0337886i
$732$		0			0
$733$		−	2.68842i		−	0.0992989i	−0.998767	−	0.0496495i	$-0.984190\pi$
$733$		−	2.68842i		−	0.0992989i	0.998767	−	0.0496495i	$-0.0158104\pi$
$734$	17.4441			0.643874
$735$		0			0
$736$	−8.12920	−	4.69340i	−0.299646	−	0.173001i
$737$	−5.05077	+	2.91606i	−0.186048	+	0.107415i
$738$		0			0
$739$	−4.75454	+	8.23510i	−0.174899	+	0.302933i	−0.940126	−	0.340827i	$-0.889293\pi$
$739$	−4.75454	+	8.23510i	−0.174899	+	0.302933i	0.765228	+	0.643760i	$0.222626\pi$
$740$	2.74728	−	23.0636i	0.100992	−	0.847835i
$741$		0			0
$742$		−	1.09527i		−	0.0402086i
$743$	−35.4706	−	20.4790i	−1.30129	−	0.751300i	−0.320664	−	0.947193i	$-0.603906\pi$
$743$	−35.4706	−	20.4790i	−1.30129	−	0.751300i	−0.980625	+	0.195893i	$0.937239\pi$
$744$		0			0
$745$	−8.14642	−	19.0005i	−0.298462	−	0.696126i
$746$	−11.0974	−	6.40706i	−0.406303	−	0.234579i
$747$		0			0
$748$		−	4.32416i		−	0.158107i
$749$	1.69338			0.0618748
$750$		0			0
$751$	17.7798	−	10.2652i	0.648793	−	0.374581i	−0.139201	−	0.990264i	$-0.544453\pi$
$751$	17.7798	−	10.2652i	0.648793	−	0.374581i	0.787994	+	0.615683i	$0.211120\pi$
$752$	−0.228097			−0.00831785
$753$		0			0
$754$	18.7620	−	10.8323i	0.683273	−	0.394488i
$755$	14.0621	−	18.8020i	0.511772	−	0.684276i
$756$		0			0
$757$	24.7371	+	14.2820i	0.899086	+	0.519088i	0.876904	−	0.480666i	$-0.159605\pi$
$757$	24.7371	+	14.2820i	0.899086	+	0.519088i	0.0221825	+	0.999754i	$0.492939\pi$
$758$	10.5419	−	18.2590i	0.382897	−	0.663197i
$759$		0			0
$760$	−7.80680	+	5.83557i	−0.283182	+	0.211678i
$761$		−	34.6620i		−	1.25650i	−0.778013	−	0.628248i	$-0.783772\pi$
$761$		−	34.6620i		−	1.25650i	0.778013	−	0.628248i	$-0.216228\pi$
$762$		0			0
$763$	−0.321728	+	0.557250i	−0.0116474	+	0.0201738i
$764$	−9.72714	+	5.61597i	−0.351916	+	0.203179i
$765$		0			0
$766$	−5.47782	−	9.48787i	−0.197922	−	0.342811i
$767$	35.3264			1.27556
$768$		0			0
$769$	11.0245	+	19.0949i	0.397552	+	0.688581i	0.993423	−	0.114499i	$-0.0365264\pi$
$769$	11.0245	+	19.0949i	0.397552	+	0.688581i	−0.595871	+	0.803080i	$0.703193\pi$
$770$	−0.228718	−	0.533458i	−0.00824244	−	0.0192245i
$771$		0			0
$772$	16.1927			0.582788
$773$	28.9739	−	16.7281i	1.04212	−	0.601667i	0.121685	−	0.992569i	$-0.461170\pi$
$773$	28.9739	−	16.7281i	1.04212	−	0.601667i	0.920432	+	0.390902i	$0.127837\pi$
$774$		0			0
$775$	−25.6815	+	7.56537i	−0.922506	+	0.271756i
$776$	8.70075	+	5.02338i	0.312339	+	0.180329i
$777$		0			0
$778$	−9.18292			−0.329224
$779$	−33.0512	+	31.4423i	−1.18418	+	1.12654i
$780$		0			0
$781$	3.34932	+	1.93373i	0.119848	+	0.0691943i
$782$	24.3886	+	14.0808i	0.872136	+	0.503528i
$783$		0			0
$784$	−3.48378	+	6.03409i	−0.124421	+	0.215503i
$785$	−18.2554	−	42.5784i	−0.651562	−	1.51969i
$786$		0			0
$787$	13.5946			0.484594			0.242297	−	0.970202i	$-0.422099\pi$
$787$	13.5946			0.484594			0.242297	+	0.970202i	$0.422099\pi$
$788$	3.85340	+	6.67428i	0.137272	+	0.237761i
$789$		0			0
$790$	2.76905	−	23.2464i	0.0985183	−	0.827069i
$791$	1.60278			0.0569883
$792$		0			0
$793$	−23.7669	+	41.1656i	−0.843989	+	1.46183i
$794$	−13.1766	−	22.8226i	−0.467621	−	0.809944i
$795$		0			0
$796$	6.95650	−	12.0490i	0.246567	−	0.427066i
$797$		−	35.2320i		−	1.24798i	−0.781432	−	0.623990i	$-0.785511\pi$
$797$		−	35.2320i		−	1.24798i	0.781432	−	0.623990i	$-0.214489\pi$
$798$		0			0
$799$	0.684320			0.0242095
$800$	3.62171	+	3.44720i	0.128047	+	0.121877i
$801$		0			0
$802$	−24.5350	+	14.1653i	−0.866361	+	0.500194i
$803$	4.70393	−	8.14745i	0.165998	−	0.287517i
$804$		0			0
$805$	3.75352	+	0.447109i	0.132294	+	0.0157585i
$806$	−19.1441			−0.674321
$807$		0			0
$808$	−5.38850	−	9.33315i	−0.189567	−	0.328339i
$809$			12.4394i			0.437345i	0.975798	+	0.218673i	$0.0701727\pi$
$809$			12.4394i			0.437345i	−0.975798	+	0.218673i	$0.929827\pi$
$810$		0			0
$811$	−32.6423	+	18.8460i	−1.14623	+	0.661774i	−0.947965	−	0.318375i	$-0.896863\pi$
$811$	−32.6423	+	18.8460i	−1.14623	+	0.661774i	−0.198261	+	0.980149i	$0.563529\pi$
$812$	0.945066	+	0.545634i	0.0331653	+	0.0191480i
$813$		0			0
$814$	7.48574	−	12.9657i	0.262375	−	0.454447i
$815$	−20.0112	+	26.7565i	−0.700963	+	0.937238i
$816$		0			0
$817$	1.82968	+	1.92330i	0.0640124	+	0.0672879i
$818$	3.65372			0.127749
$819$		0			0
$820$	18.7401	+	14.0158i	0.654432	+	0.489451i
$821$	−40.5107	+	23.3889i	−1.41383	+	0.816277i	−0.995747	−	0.0921304i	$-0.970632\pi$
$821$	−40.5107	+	23.3889i	−1.41383	+	0.816277i	−0.418086	+	0.908407i	$0.637299\pi$
$822$		0			0
$823$	−27.2503	+	15.7330i	−0.949887	+	0.548418i	−0.893046	−	0.449966i	$-0.851436\pi$
$823$	−27.2503	+	15.7330i	−0.949887	+	0.548418i	−0.0568412	+	0.998383i	$0.518103\pi$
$824$			14.6347i			0.509825i
$825$		0			0
$826$	0.889717	+	1.54104i	0.0309572	+	0.0536195i
$827$	41.5264	−	23.9753i	1.44402	−	0.833703i	0.445902	−	0.895082i	$-0.352883\pi$
$827$	41.5264	−	23.9753i	1.44402	−	0.833703i	0.998115	+	0.0613789i	$0.0195498\pi$
$828$		0			0
$829$		−	8.97169i		−	0.311600i	−0.987789	−	0.155800i	$-0.950205\pi$
$829$		−	8.97169i		−	0.311600i	0.987789	−	0.155800i	$-0.0497955\pi$
$830$	−14.9354	−	34.8351i	−0.518416	−	1.20914i
$831$		0			0
$832$	1.78765	+	3.09631i	0.0619757	+	0.107345i
$833$	10.4518	−	18.1030i	0.362133	−	0.627233i
$834$		0			0
$835$	4.50089	+	0.536134i	0.155760	+	0.0185537i
$836$	−6.10719	+	1.47421i	−0.211222	+	0.0509866i
$837$		0			0
$838$	−13.8838	+	24.0474i	−0.479606	+	0.830703i
$839$	−9.67512	+	16.7578i	−0.334022	+	0.578543i	−0.983297	−	0.182011i	$-0.941739\pi$
$839$	−9.67512	+	16.7578i	−0.334022	+	0.578543i	0.649274	+	0.760554i	$0.275073\pi$
$840$		0			0
$841$	−3.85868	+	6.68343i	−0.133058	+	0.230463i
$842$	−0.0479279	−	0.0830135i	−0.00165170	−	0.00286084i
$843$		0			0
$844$		−	10.7771i		−	0.370964i
$845$	0.446328	−	0.191362i	0.0153542	−	0.00658305i
$846$		0			0
$847$			1.60689i			0.0552134i
$848$			6.08170i			0.208846i
$849$		0			0
$850$	−10.8656	−	10.3420i	−0.372687	−	0.354729i
$851$	48.7516	+	84.4403i	1.67118	+	2.89458i
$852$		0			0
$853$	−15.6617	−	9.04231i	−0.536248	−	0.309603i	0.207309	−	0.978275i	$-0.433529\pi$
$853$	−15.6617	−	9.04231i	−0.536248	−	0.309603i	−0.743557	+	0.668673i	$0.766863\pi$
$854$	−2.39434			−0.0819326
$855$		0			0
$856$	−9.40284			−0.321382
$857$	−2.36232	−	1.36389i	−0.0806953	−	0.0465895i	0.459109	−	0.888380i	$-0.348169\pi$
$857$	−2.36232	−	1.36389i	−0.0806953	−	0.0465895i	−0.539805	+	0.841790i	$0.681502\pi$
$858$		0			0
$859$	−21.5489	−	37.3239i	−0.735240	−	1.27347i	−0.954618	−	0.297834i	$-0.903736\pi$
$859$	−21.5489	−	37.3239i	−0.735240	−	1.27347i	0.219377	−	0.975640i	$-0.429597\pi$
$860$	0.815599	−	1.09052i	0.0278117	−	0.0371863i
$861$		0			0
$862$		−	34.5896i		−	1.17813i
$863$			5.91290i			0.201277i	0.994923	+	0.100639i	$0.0320886\pi$
$863$			5.91290i			0.201277i	−0.994923	+	0.100639i	$0.967911\pi$
$864$		0			0
$865$	−13.7100	−	31.9770i	−0.466156	−	1.08725i
$866$			0.574704i			0.0195292i
$867$		0			0
$868$	−0.482155	−	0.835117i	−0.0163654	−	0.0283457i
$869$	7.54506	−	13.0684i	0.255949	−	0.443316i
$870$		0			0
$871$	−7.23349	+	12.5288i	−0.245097	+	0.424521i
$872$	1.78646	−	3.09424i	0.0604972	−	0.104784i
$873$		0			0
$874$	11.5722	−	39.2455i	0.391435	−	1.32750i
$875$	−1.88747	−	0.701148i	−0.0638083	−	0.0237031i
$876$		0			0
$877$	13.2277	−	22.9110i	0.446667	−	0.773649i	−0.551500	−	0.834175i	$-0.685944\pi$
$877$	13.2277	−	22.9110i	0.446667	−	0.773649i	0.998167	+	0.0605257i	$0.0192777\pi$
$878$	5.83303	+	10.1031i	0.196855	+	0.340963i
$879$		0			0
$880$	1.27000	+	2.96213i	0.0428118	+	0.0998534i
$881$		−	13.8132i		−	0.465378i	−0.972551	−	0.232689i	$-0.925248\pi$
$881$		−	13.8132i		−	0.465378i	0.972551	−	0.232689i	$-0.0747525\pi$
$882$		0			0
$883$	11.5596	−	6.67395i	0.389012	−	0.224596i	−0.292720	−	0.956198i	$-0.594560\pi$
$883$	11.5596	−	6.67395i	0.389012	−	0.224596i	0.681732	+	0.731602i	$0.261227\pi$
$884$	−5.36319	−	9.28931i	−0.180383	−	0.312433i
$885$		0			0
$886$			11.6442i			0.391194i
$887$	13.8812	−	8.01431i	0.466085	−	0.269094i	−0.248514	−	0.968628i	$-0.579942\pi$
$887$	13.8812	−	8.01431i	0.466085	−	0.269094i	0.714599	+	0.699534i	$0.246609\pi$
$888$		0			0
$889$	−1.42914	+	0.825112i	−0.0479317	+	0.0276734i
$890$	−4.58563	+	6.13132i	−0.153711	+	0.205522i
$891$		0			0
$892$	20.4362			0.684255
$893$	−0.233301	−	0.966493i	−0.00780712	−	0.0323425i
$894$		0			0
$895$	−22.1747	−	16.5845i	−0.741217	−	0.554358i
$896$	−0.0900463	+	0.155965i	−0.00300824	+	0.00521042i
$897$		0			0
$898$	8.04703	+	4.64595i	0.268533	+	0.155037i
$899$	28.0988	−	16.2228i	0.937147	−	0.541062i
$900$		0			0
$901$		−	18.2459i		−	0.607858i
$902$	7.54210	+	13.0633i	0.251124	+	0.434960i
$903$		0			0
$904$	−8.89976			−0.296002
$905$	13.4801	+	1.60571i	0.448092	+	0.0533756i
$906$		0			0
$907$	−2.63465	+	4.56335i	−0.0874821	+	0.151523i	−0.906446	−	0.422321i	$-0.861215\pi$
$907$	−2.63465	+	4.56335i	−0.0874821	+	0.151523i	0.818964	+	0.573845i	$0.194549\pi$
$908$	−21.5499	+	12.4418i	−0.715157	+	0.412896i
$909$		0			0
$910$	−1.15298	−	0.862316i	−0.0382209	−	0.0285855i
$911$	2.99139			0.0991091			0.0495546	−	0.998771i	$-0.484220\pi$
$911$	2.99139			0.0991091			0.0495546	+	0.998771i	$0.484220\pi$
$912$		0			0
$913$		−	24.4308i		−	0.808542i
$914$	−0.526799	+	0.912443i	−0.0174250	+	0.0301809i
$915$		0			0
$916$	7.91819	+	13.7147i	0.261624	+	0.453147i
$917$	1.76687	−	3.06032i	0.0583473	−	0.101061i
$918$		0			0
$919$	−19.8625			−0.655205			−0.327602	−	0.944816i	$-0.606241\pi$
$919$	−19.8625			−0.655205			−0.327602	+	0.944816i	$0.606241\pi$
$920$	−20.8422	−	2.48266i	−0.687146	−	0.0818510i
$921$		0			0
$922$	−8.13777	−	14.0950i	−0.268003	−	0.464195i
$923$	9.59349			0.315774
$924$		0			0
$925$	−14.6761	−	49.8197i	−0.482548	−	1.63806i
$926$	−14.7196	+	25.4951i	−0.483717	+	0.837822i
$927$		0			0
$928$	−5.24767	−	3.02974i	−0.172263	−	0.0994562i
$929$	−1.24568	−	0.719194i	−0.0408695	−	0.0235960i	0.479426	−	0.877582i	$-0.340845\pi$
$929$	−1.24568	−	0.719194i	−0.0408695	−	0.0235960i	−0.520296	+	0.853986i	$0.674178\pi$
$930$		0			0
$931$	−29.1309	−	8.58973i	−0.954727	−	0.281517i
$932$	−6.46197			−0.211669
$933$		0			0
$934$	4.02974	+	2.32657i	0.131857	+	0.0761278i
$935$	−3.81017	−	8.88676i	−0.124606	−	0.290628i
$936$		0			0
$937$	−4.80731	+	2.77550i	−0.157048	+	0.0906716i	−0.576464	−	0.817122i	$-0.695568\pi$
$937$	−4.80731	+	2.77550i	−0.157048	+	0.0906716i	0.419416	+	0.907794i	$0.362235\pi$
$938$	−0.728719			−0.0237935
$939$		0			0
$940$	−0.468772	+	0.200984i	−0.0152896	+	0.00655539i
$941$	−2.33675	−	4.04737i	−0.0761758	−	0.131940i	0.825421	−	0.564517i	$-0.190938\pi$
$941$	−2.33675	−	4.04737i	−0.0761758	−	0.131940i	−0.901597	+	0.432577i	$0.857604\pi$
$942$		0			0
$943$	−98.2373			−3.19905
$944$	−4.94033	−	8.55691i	−0.160794	−	0.278504i
$945$		0			0
$946$	0.760174	−	0.438887i	0.0247154	−	0.0142694i
$947$	−20.9430	+	36.2744i	−0.680557	+	1.17876i	0.294254	+	0.955727i	$0.404929\pi$
$947$	−20.9430	+	36.2744i	−0.680557	+	1.17876i	−0.974811	+	0.223032i	$0.928405\pi$
$948$		0			0
$949$		−	23.3368i		−	0.757545i
$950$	−10.9021	+	18.8718i	−0.353712	+	0.612281i
$951$		0			0
$952$	0.270150	−	0.467914i	0.00875562	−	0.0151652i
$953$	5.56862	+	3.21504i	0.180385	+	0.104145i	0.587474	−	0.809243i	$-0.300123\pi$
$953$	5.56862	+	3.21504i	0.180385	+	0.104145i	−0.407088	+	0.913389i	$0.633456\pi$
$954$		0			0
$955$	−15.0422	+	20.1125i	−0.486754	+	0.650826i
$956$	2.67193	−	1.54264i	0.0864162	−	0.0498924i
$957$		0			0
$958$	27.8086			0.898455
$959$	−3.29965	+	1.90505i	−0.106551	+	0.0615174i
$960$		0			0
$961$	2.32906			0.0751309
$962$		−	37.1377i		−	1.19737i
$963$		0			0
$964$	−17.1738	−	9.91529i	−0.553131	−	0.319350i
$965$	33.2783	−	14.2680i	1.07127	−	0.459302i
$966$		0			0
$967$	4.59646	+	2.65377i	0.147812	+	0.0853395i	0.572082	−	0.820196i	$-0.306136\pi$
$967$	4.59646	+	2.65377i	0.147812	+	0.0853395i	−0.424270	+	0.905536i	$0.639469\pi$
$968$		−	8.92257i		−	0.286782i
$969$		0			0
$970$	22.3075	+	2.65721i	0.716251	+	0.0853180i
$971$	−4.56626	+	7.90899i	−0.146538	+	0.253812i	−0.929946	−	0.367697i	$-0.880146\pi$
$971$	−4.56626	+	7.90899i	−0.146538	+	0.253812i	0.783408	+	0.621508i	$0.213480\pi$
$972$		0			0
$973$	0.457668	−	0.264235i	0.0146722	−	0.00847097i
$974$	8.46889	+	4.88951i	0.271361	+	0.156670i
$975$		0			0
$976$	13.2951			0.425564
$977$		−	35.8425i		−	1.14670i	−0.819309	−	0.573352i	$-0.805643\pi$
$977$		−	35.8425i		−	1.14670i	0.819309	−	0.573352i	$-0.194357\pi$
$978$		0			0
$979$	−4.27401	+	2.46760i	−0.136598	+	0.0788649i
$980$	−1.84281	+	15.4706i	−0.0588666	+	0.494190i
$981$		0			0
$982$	−12.2997	−	21.3038i	−0.392501	−	0.679831i
$983$	−24.3706	−	14.0704i	−0.777301	−	0.448775i	0.0581717	−	0.998307i	$-0.481473\pi$
$983$	−24.3706	−	14.0704i	−0.777301	−	0.448775i	−0.835473	+	0.549531i	$0.814806\pi$
$984$		0			0
$985$	13.8002	+	10.3212i	0.439712	+	0.328861i
$986$	15.7437	+	9.08961i	0.501380	+	0.289472i
$987$		0			0
$988$	−11.2912	+	10.7416i	−0.359222	+	0.341735i
$989$			5.71659i			0.181777i
$990$		0			0
$991$	46.4410	+	26.8127i	1.47525	+	0.851735i	0.999611	−	0.0279062i	$-0.00888397\pi$
$991$	46.4410	+	26.8127i	1.47525	+	0.851735i	0.475638	+	0.879641i	$0.342217\pi$
$992$	2.67726	+	4.63716i	0.0850032	+	0.147230i
$993$		0			0
$994$	0.241618	+	0.418494i	0.00766365	+	0.0132738i
$995$	3.67978	−	30.8920i	0.116657	−	0.979343i
$996$		0			0
$997$	−8.49728	+	4.90591i	−0.269111	+	0.155372i	−0.628484	−	0.777823i	$-0.716324\pi$
$997$	−8.49728	+	4.90591i	−0.269111	+	0.155372i	0.359372	+	0.933194i	$0.382991\pi$
$998$	26.4422	−	15.2664i	0.837014	−	0.483250i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.q.b.179.8	yes	64
3.2	odd	2	inner	1710.2.q.b.179.21	yes	64
5.4	even	2	inner	1710.2.q.b.179.22	yes	64
15.14	odd	2	inner	1710.2.q.b.179.7	✓	64
19.12	odd	6	inner	1710.2.q.b.449.7	yes	64
57.50	even	6	inner	1710.2.q.b.449.22	yes	64
95.69	odd	6	inner	1710.2.q.b.449.21	yes	64
285.164	even	6	inner	1710.2.q.b.449.8	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1710.2.q.b.179.7	✓	64	15.14	odd	2	inner
1710.2.q.b.179.8	yes	64	1.1	even	1	trivial
1710.2.q.b.179.21	yes	64	3.2	odd	2	inner
1710.2.q.b.179.22	yes	64	5.4	even	2	inner
1710.2.q.b.449.7	yes	64	19.12	odd	6	inner
1710.2.q.b.449.8	yes	64	285.164	even	6	inner
1710.2.q.b.449.21	yes	64	95.69	odd	6	inner
1710.2.q.b.449.22	yes	64	57.50	even	6	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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.79066 + 1.33924i) q^{5} +0.180093i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.79066 + 1.33924i) q^{5} +0.180093i q^{7} -1.00000i q^{8} +(-0.881135 - 2.05514i) q^{10} -1.44133i q^{11} +(-1.78765 - 3.09631i) q^{13} +(0.0900463 - 0.155965i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.50006 - 2.59818i) q^{17} +(-4.18093 - 1.23282i) q^{19} +(-0.264485 + 2.22037i) q^{20} +(-0.720664 + 1.24823i) q^{22} +(-4.69340 - 8.12920i) q^{23} +(1.41289 + 4.79622i) q^{25} +3.57531i q^{26} +(-0.155965 + 0.0900463i) q^{28} +(-3.02974 - 5.24767i) q^{29} +5.35453i q^{31} +(0.866025 - 0.500000i) q^{32} +(-2.59818 + 1.50006i) q^{34} +(-0.241187 + 0.322484i) q^{35} -10.3873 q^{37} +(3.00438 + 3.15811i) q^{38} +(1.33924 - 1.79066i) q^{40} +(5.23274 - 9.06337i) q^{41} +(-0.527413 - 0.304502i) q^{43} +(1.24823 - 0.720664i) q^{44} +9.38680i q^{46} +(0.114049 + 0.197538i) q^{47} +6.96757 q^{49} +(1.17451 - 4.86010i) q^{50} +(1.78765 - 3.09631i) q^{52} +(5.26691 - 3.04085i) q^{53} +(1.93028 - 2.58092i) q^{55} +0.180093 q^{56} +6.05949i q^{58} +(-4.94033 + 8.55691i) q^{59} +(-6.64753 - 11.5139i) q^{61} +(2.67726 - 4.63716i) q^{62} -1.00000 q^{64} +(0.945614 - 7.93851i) q^{65} +(-2.02318 - 3.50425i) q^{67} +3.00013 q^{68} +(0.370116 - 0.158686i) q^{70} +(-1.34163 + 2.32377i) q^{71} +(5.65274 + 3.26361i) q^{73} +(8.99565 + 5.19364i) q^{74} +(-1.02281 - 4.23720i) q^{76} +0.259573 q^{77} +(9.06694 + 5.23480i) q^{79} +(-2.05514 + 0.881135i) q^{80} +(-9.06337 + 5.23274i) q^{82} +16.9502 q^{83} +(6.16568 - 2.64352i) q^{85} +(0.304502 + 0.527413i) q^{86} -1.44133 q^{88} +(-1.71203 - 2.96533i) q^{89} +(0.557622 - 0.321943i) q^{91} +(4.69340 - 8.12920i) q^{92} -0.228097i q^{94} +(-5.83557 - 7.80680i) q^{95} +(-5.02338 + 8.70075i) q^{97} +(-6.03409 - 3.48378i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4}+O(q^{10}) \) 64 * q + 32 * q^4	\( 64 q + 32 q^{4} - 24 q^{10} - 32 q^{16} + 40 q^{19} - 8 q^{25} - 24 q^{34} - 24 q^{40} + 8 q^{55} + 104 q^{61} - 64 q^{64} - 48 q^{70} + 32 q^{76} + 48 q^{79} + 16 q^{85} + 96 q^{91}+O(q^{100}) \) 64 * q + 32 * q^4 - 24 * q^10 - 32 * q^16 + 40 * q^19 - 8 * q^25 - 24 * q^34 - 24 * q^40 + 8 * q^55 + 104 * q^61 - 64 * q^64 - 48 * q^70 + 32 * q^76 + 48 * q^79 + 16 * q^85 + 96 * q^91

Introduction

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