LMFDB - Embedded newform 3150.2.bf.a.1601.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(1151,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("3150.1151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.bf (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:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1601.2
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	3150.1601
Dual form			3150.2.bf.a.1151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.62132 - 2.09077i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.62132 - 2.09077i) q^{7} -1.00000i q^{8} +(-2.59808 + 1.50000i) q^{11} -2.44949i q^{13} +(-2.44949 + 1.00000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.507306 + 0.878680i) q^{17} +(-0.878680 - 0.507306i) q^{19} +3.00000 q^{22} +(3.67423 + 2.12132i) q^{23} +(-1.22474 + 2.12132i) q^{26} +(2.62132 + 0.358719i) q^{28} +1.24264i q^{29} +(4.86396 - 2.80821i) q^{31} +(0.866025 - 0.500000i) q^{32} -1.01461i q^{34} +(4.12132 - 7.13834i) q^{37} +(0.507306 + 0.878680i) q^{38} +2.02922 q^{41} -8.24264 q^{43} +(-2.59808 - 1.50000i) q^{44} +(-2.12132 - 3.67423i) q^{46} +(0.507306 - 0.878680i) q^{47} +(-1.74264 - 6.77962i) q^{49} +(2.12132 - 1.22474i) q^{52} +(-1.07616 + 0.621320i) q^{53} +(-2.09077 - 1.62132i) q^{56} +(0.621320 - 1.07616i) q^{58} +(-5.76500 - 9.98528i) q^{59} +(5.12132 + 2.95680i) q^{61} -5.61642 q^{62} -1.00000 q^{64} +(-5.00000 - 8.66025i) q^{67} +(-0.507306 + 0.878680i) q^{68} +10.2426i q^{71} +(-7.24264 + 4.18154i) q^{73} +(-7.13834 + 4.12132i) q^{74} -1.01461i q^{76} +(-1.07616 + 7.86396i) q^{77} +(5.62132 - 9.73641i) q^{79} +(-1.75736 - 1.01461i) q^{82} +3.16693 q^{83} +(7.13834 + 4.12132i) q^{86} +(1.50000 + 2.59808i) q^{88} +(5.19615 - 9.00000i) q^{89} +(-5.12132 - 3.97141i) q^{91} +4.24264i q^{92} +(-0.878680 + 0.507306i) q^{94} -3.76127i q^{97} +(-1.88064 + 6.74264i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^4 - 4 * q^7	$ 8 q + 4 q^{4} - 4 q^{7} - 4 q^{16} - 24 q^{19} + 24 q^{22} + 4 q^{28} - 12 q^{31} + 16 q^{37} - 32 q^{43} + 20 q^{49} - 12 q^{58} + 24 q^{61} - 8 q^{64} - 40 q^{67} - 24 q^{73} + 28 q^{79} - 48 q^{82} + 12 q^{88} - 24 q^{91} - 24 q^{94}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^7 - 4 * q^16 - 24 * q^19 + 24 * q^22 + 4 * q^28 - 12 * q^31 + 16 * q^37 - 32 * q^43 + 20 * q^49 - 12 * q^58 + 24 * q^61 - 8 * q^64 - 40 * q^67 - 24 * q^73 + 28 * q^79 - 48 * q^82 + 12 * q^88 - 24 * q^91 - 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	−	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
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.62132	−	2.09077i	0.612801	−	0.790237i
$7$	1.62132	−	2.09077i	0.612801	−	0.790237i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$		0			0
$11$	−2.59808	+	1.50000i	−0.783349	+	0.452267i	−0.837616	−	0.546259i	$-0.816051\pi$
$11$	−2.59808	+	1.50000i	−0.783349	+	0.452267i	0.0542666	+	0.998526i	$0.482718\pi$
$12$		0			0
$13$		−	2.44949i		−	0.679366i	−0.940540	−	0.339683i	$-0.889680\pi$
$13$		−	2.44949i		−	0.679366i	0.940540	−	0.339683i	$-0.110320\pi$
$14$	−2.44949	+	1.00000i	−0.654654	+	0.267261i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.507306	+	0.878680i	0.123040	+	0.213111i	0.920965	−	0.389645i	$-0.127402\pi$
$17$	0.507306	+	0.878680i	0.123040	+	0.213111i	−0.797925	+	0.602756i	$0.794069\pi$
$18$		0			0
$19$	−0.878680	−	0.507306i	−0.201583	−	0.116384i	0.395811	−	0.918332i	$-0.370464\pi$
$19$	−0.878680	−	0.507306i	−0.201583	−	0.116384i	−0.597394	+	0.801948i	$0.703797\pi$
$20$		0			0
$21$		0			0
$22$	3.00000			0.639602
$23$	3.67423	+	2.12132i	0.766131	+	0.442326i	0.831493	−	0.555536i	$-0.187487\pi$
$23$	3.67423	+	2.12132i	0.766131	+	0.442326i	−0.0653618	+	0.997862i	$0.520820\pi$
$24$		0			0
$25$		0			0
$26$	−1.22474	+	2.12132i	−0.240192	+	0.416025i
$27$		0			0
$28$	2.62132	+	0.358719i	0.495383	+	0.0677916i
$29$			1.24264i			0.230753i	0.993322	+	0.115376i	$0.0368074\pi$
$29$			1.24264i			0.230753i	−0.993322	+	0.115376i	$0.963193\pi$
$30$		0			0
$31$	4.86396	−	2.80821i	0.873593	−	0.504369i	0.00505256	−	0.999987i	$-0.498392\pi$
$31$	4.86396	−	2.80821i	0.873593	−	0.504369i	0.868541	+	0.495618i	$0.165058\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$		−	1.01461i		−	0.174005i
$35$		0			0
$36$		0			0
$37$	4.12132	−	7.13834i	0.677541	−	1.17354i	−0.298178	−	0.954510i	$-0.596379\pi$
$37$	4.12132	−	7.13834i	0.677541	−	1.17354i	0.975719	−	0.219025i	$-0.0702877\pi$
$38$	0.507306	+	0.878680i	0.0822959	+	0.142541i
$39$		0			0
$40$		0			0
$41$	2.02922			0.316912			0.158456	−	0.987366i	$-0.449348\pi$
$41$	2.02922			0.316912			0.158456	+	0.987366i	$0.449348\pi$
$42$		0			0
$43$	−8.24264			−1.25699			−0.628495	−	0.777813i	$-0.716329\pi$
$43$	−8.24264			−1.25699			−0.628495	+	0.777813i	$0.716329\pi$
$44$	−2.59808	−	1.50000i	−0.391675	−	0.226134i
$45$		0			0
$46$	−2.12132	−	3.67423i	−0.312772	−	0.541736i
$47$	0.507306	−	0.878680i	0.0739982	−	0.128169i	−0.826652	−	0.562713i	$-0.809757\pi$
$47$	0.507306	−	0.878680i	0.0739982	−	0.128169i	0.900650	+	0.434545i	$0.143091\pi$
$48$		0			0
$49$	−1.74264	−	6.77962i	−0.248949	−	0.968517i
$50$		0			0
$51$		0			0
$52$	2.12132	−	1.22474i	0.294174	−	0.169842i
$53$	−1.07616	+	0.621320i	−0.147822	+	0.0853449i	−0.572087	−	0.820193i	$-0.693866\pi$
$53$	−1.07616	+	0.621320i	−0.147822	+	0.0853449i	0.424265	+	0.905538i	$0.360533\pi$
$54$		0			0
$55$		0			0
$56$	−2.09077	−	1.62132i	−0.279391	−	0.216658i
$57$		0			0
$58$	0.621320	−	1.07616i	0.0815834	−	0.141307i
$59$	−5.76500	−	9.98528i	−0.750540	−	1.29997i	−0.947561	−	0.319574i	$-0.896460\pi$
$59$	−5.76500	−	9.98528i	−0.750540	−	1.29997i	0.197022	−	0.980399i	$-0.436873\pi$
$60$		0			0
$61$	5.12132	+	2.95680i	0.655718	+	0.378579i	0.790643	−	0.612277i	$-0.209746\pi$
$61$	5.12132	+	2.95680i	0.655718	+	0.378579i	−0.134926	+	0.990856i	$0.543080\pi$
$62$	−5.61642			−0.713286
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	−5.00000	−	8.66025i	−0.610847	−	1.05802i	−0.991098	−	0.133135i	$-0.957496\pi$
$67$	−5.00000	−	8.66025i	−0.610847	−	1.05802i	0.380251	−	0.924883i	$-0.375838\pi$
$68$	−0.507306	+	0.878680i	−0.0615199	+	0.106556i
$69$		0			0
$70$		0			0
$71$			10.2426i			1.21558i	0.794099	+	0.607789i	$0.207943\pi$
$71$			10.2426i			1.21558i	−0.794099	+	0.607789i	$0.792057\pi$
$72$		0			0
$73$	−7.24264	+	4.18154i	−0.847687	+	0.489412i	−0.859870	−	0.510513i	$-0.829455\pi$
$73$	−7.24264	+	4.18154i	−0.847687	+	0.489412i	0.0121828	+	0.999926i	$0.496122\pi$
$74$	−7.13834	+	4.12132i	−0.829815	+	0.479094i
$75$		0			0
$76$		−	1.01461i		−	0.116384i
$77$	−1.07616	+	7.86396i	−0.122640	+	0.896182i
$78$		0			0
$79$	5.62132	−	9.73641i	0.632448	−	1.09543i	−0.354602	−	0.935017i	$-0.615384\pi$
$79$	5.62132	−	9.73641i	0.632448	−	1.09543i	0.987050	−	0.160415i	$-0.0512831\pi$
$80$		0			0
$81$		0			0
$82$	−1.75736	−	1.01461i	−0.194068	−	0.112045i
$83$	3.16693			0.347616			0.173808	−	0.984780i	$-0.444393\pi$
$83$	3.16693			0.347616			0.173808	+	0.984780i	$0.444393\pi$
$84$		0			0
$85$		0			0
$86$	7.13834	+	4.12132i	0.769747	+	0.444413i
$87$		0			0
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	5.19615	−	9.00000i	0.550791	−	0.953998i	−0.447427	−	0.894321i	$-0.647659\pi$
$89$	5.19615	−	9.00000i	0.550791	−	0.953998i	0.998218	−	0.0596775i	$-0.0190072\pi$
$90$		0			0
$91$	−5.12132	−	3.97141i	−0.536860	−	0.416317i
$92$			4.24264i			0.442326i
$93$		0			0
$94$	−0.878680	+	0.507306i	−0.0906289	+	0.0523246i
$95$		0			0
$96$		0			0
$97$		−	3.76127i		−	0.381900i	−0.981600	−	0.190950i	$-0.938843\pi$
$97$		−	3.76127i		−	0.381900i	0.981600	−	0.190950i	$-0.0611568\pi$
$98$	−1.88064	+	6.74264i	−0.189973	+	0.681110i
$99$		0			0
$100$		0			0
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	13.2426	+	7.64564i	1.30484	+	0.753348i	0.981229	−	0.192844i	$-0.0617712\pi$
$103$	13.2426	+	7.64564i	1.30484	+	0.753348i	0.323607	+	0.946192i	$0.395105\pi$
$104$	−2.44949			−0.240192
$105$		0			0
$106$	1.24264			0.120696
$107$	−4.75039	−	2.74264i	−0.459238	−	0.265141i	0.252486	−	0.967601i	$-0.418752\pi$
$107$	−4.75039	−	2.74264i	−0.459238	−	0.265141i	−0.711724	+	0.702459i	$0.752085\pi$
$108$		0			0
$109$	−0.757359	−	1.31178i	−0.0725419	−	0.125646i	0.827473	−	0.561506i	$-0.189778\pi$
$109$	−0.757359	−	1.31178i	−0.0725419	−	0.125646i	−0.900015	+	0.435860i	$0.856444\pi$
$110$		0			0
$111$		0			0
$112$	1.00000	+	2.44949i	0.0944911	+	0.231455i
$113$		−	8.48528i		−	0.798228i	−0.916901	−	0.399114i	$-0.869318\pi$
$113$		−	8.48528i		−	0.798228i	0.916901	−	0.399114i	$-0.130682\pi$
$114$		0			0
$115$		0			0
$116$	−1.07616	+	0.621320i	−0.0999188	+	0.0576881i
$117$		0			0
$118$			11.5300i			1.06142i
$119$	2.65962	+	0.363961i	0.243807	+	0.0333643i
$120$		0			0
$121$	−1.00000	+	1.73205i	−0.0909091	+	0.157459i
$122$	−2.95680	−	5.12132i	−0.267696	−	0.463663i
$123$		0			0
$124$	4.86396	+	2.80821i	0.436797	+	0.252185i
$125$		0			0
$126$		0			0
$127$	5.24264			0.465209			0.232605	−	0.972571i	$-0.425275\pi$
$127$	5.24264			0.465209			0.232605	+	0.972571i	$0.425275\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$		0			0
$131$	−2.59808	+	4.50000i	−0.226995	+	0.393167i	−0.956916	−	0.290365i	$-0.906223\pi$
$131$	−2.59808	+	4.50000i	−0.226995	+	0.393167i	0.729921	+	0.683531i	$0.239557\pi$
$132$		0			0
$133$	−2.48528	+	1.01461i	−0.215501	+	0.0879780i
$134$			10.0000i			0.863868i
$135$		0			0
$136$	0.878680	−	0.507306i	0.0753462	−	0.0435011i
$137$	−12.5446	+	7.24264i	−1.07176	+	0.618781i	−0.928662	−	0.370928i	$-0.879040\pi$
$137$	−12.5446	+	7.24264i	−1.07176	+	0.618781i	−0.143098	+	0.989709i	$0.545706\pi$
$138$		0			0
$139$		−	20.1903i		−	1.71252i	−0.516549	−	0.856258i	$-0.672783\pi$
$139$		−	20.1903i		−	1.71252i	0.516549	−	0.856258i	$-0.327217\pi$
$140$		0			0
$141$		0			0
$142$	5.12132	−	8.87039i	0.429772	−	0.744386i
$143$	3.67423	+	6.36396i	0.307255	+	0.532181i
$144$		0			0
$145$		0			0
$146$	8.36308			0.692134
$147$		0			0
$148$	8.24264			0.677541
$149$	−17.7408	−	10.2426i	−1.45338	−	0.839110i	−0.454709	−	0.890640i	$-0.650257\pi$
$149$	−17.7408	−	10.2426i	−1.45338	−	0.839110i	−0.998671	+	0.0515300i	$0.983590\pi$
$150$		0			0
$151$	1.62132	+	2.80821i	0.131941	+	0.228529i	0.924425	−	0.381364i	$-0.124546\pi$
$151$	1.62132	+	2.80821i	0.131941	+	0.228529i	−0.792484	+	0.609893i	$0.791212\pi$
$152$	−0.507306	+	0.878680i	−0.0411479	+	0.0712703i
$153$		0			0
$154$	4.86396	−	6.27231i	0.391949	−	0.505437i
$155$		0			0
$156$		0			0
$157$	12.7279	−	7.34847i	1.01580	−	0.586472i	0.102915	−	0.994690i	$-0.467183\pi$
$157$	12.7279	−	7.34847i	1.01580	−	0.586472i	0.912884	+	0.408219i	$0.133850\pi$
$158$	−9.73641	+	5.62132i	−0.774587	+	0.447208i
$159$		0			0
$160$		0			0
$161$	10.3923	−	4.24264i	0.819028	−	0.334367i
$162$		0			0
$163$	3.12132	−	5.40629i	0.244481	−	0.423453i	−0.717505	−	0.696554i	$-0.754716\pi$
$163$	3.12132	−	5.40629i	0.244481	−	0.423453i	0.961985	+	0.273101i	$0.0880492\pi$
$164$	1.01461	+	1.75736i	0.0792279	+	0.137227i
$165$		0			0
$166$	−2.74264	−	1.58346i	−0.212870	−	0.122901i
$167$	−23.0600			−1.78444			−0.892219	−	0.451603i	$-0.850852\pi$
$167$	−23.0600			−1.78444			−0.892219	+	0.451603i	$0.850852\pi$
$168$		0			0
$169$	7.00000			0.538462
$170$		0			0
$171$		0			0
$172$	−4.12132	−	7.13834i	−0.314248	−	0.544293i
$173$	10.3923	−	18.0000i	0.790112	−	1.36851i	−0.135785	−	0.990738i	$-0.543356\pi$
$173$	10.3923	−	18.0000i	0.790112	−	1.36851i	0.925897	−	0.377776i	$-0.123311\pi$
$174$		0			0
$175$		0			0
$176$		−	3.00000i		−	0.226134i
$177$		0			0
$178$	−9.00000	+	5.19615i	−0.674579	+	0.389468i
$179$	8.23999	−	4.75736i	0.615886	−	0.355582i	−0.159380	−	0.987217i	$-0.550949\pi$
$179$	8.23999	−	4.75736i	0.615886	−	0.355582i	0.775265	+	0.631636i	$0.217616\pi$
$180$		0			0
$181$			2.02922i			0.150831i	0.997152	+	0.0754155i	$0.0240283\pi$
$181$			2.02922i			0.150831i	−0.997152	+	0.0754155i	$0.975972\pi$
$182$	2.44949	+	6.00000i	0.181568	+	0.444750i
$183$		0			0
$184$	2.12132	−	3.67423i	0.156386	−	0.270868i
$185$		0			0
$186$		0			0
$187$	−2.63604	−	1.52192i	−0.192766	−	0.111294i
$188$	1.01461			0.0739982
$189$		0			0
$190$		0			0
$191$	−7.34847	−	4.24264i	−0.531717	−	0.306987i	0.209999	−	0.977702i	$-0.432654\pi$
$191$	−7.34847	−	4.24264i	−0.531717	−	0.306987i	−0.741715	+	0.670715i	$0.765987\pi$
$192$		0			0
$193$	−3.74264	−	6.48244i	−0.269401	−	0.466617i	0.699306	−	0.714822i	$-0.253492\pi$
$193$	−3.74264	−	6.48244i	−0.269401	−	0.466617i	−0.968707	+	0.248206i	$0.920159\pi$
$194$	−1.88064	+	3.25736i	−0.135022	+	0.233865i
$195$		0			0
$196$	5.00000	−	4.89898i	0.357143	−	0.349927i
$197$		−	9.51472i		−	0.677896i	−0.940805	−	0.338948i	$-0.889929\pi$
$197$		−	9.51472i		−	0.677896i	0.940805	−	0.338948i	$-0.110071\pi$
$198$		0			0
$199$	−13.9706	+	8.06591i	−0.990347	+	0.571777i	−0.905378	−	0.424607i	$-0.860412\pi$
$199$	−13.9706	+	8.06591i	−0.990347	+	0.571777i	−0.0849690	+	0.996384i	$0.527079\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.59808	+	2.01472i	0.182349	+	0.141406i
$204$		0			0
$205$		0			0
$206$	−7.64564	−	13.2426i	−0.532697	−	0.922658i
$207$		0			0
$208$	2.12132	+	1.22474i	0.147087	+	0.0849208i
$209$	3.04384			0.210547
$210$		0			0
$211$	8.24264			0.567447			0.283723	−	0.958906i	$-0.408430\pi$
$211$	8.24264			0.567447			0.283723	+	0.958906i	$0.408430\pi$
$212$	−1.07616	−	0.621320i	−0.0739109	−	0.0426725i
$213$		0			0
$214$	2.74264	+	4.75039i	0.187483	+	0.324730i
$215$		0			0
$216$		0			0
$217$	2.01472	−	14.7224i	0.136768	−	0.999424i
$218$			1.51472i			0.102590i
$219$		0			0
$220$		0			0
$221$	2.15232	−	1.24264i	0.144780	−	0.0835891i
$222$		0			0
$223$			12.5446i			0.840050i	0.907513	+	0.420025i	$0.137979\pi$
$223$			12.5446i			0.840050i	−0.907513	+	0.420025i	$0.862021\pi$
$224$	0.358719	−	2.62132i	0.0239680	−	0.175144i
$225$		0			0
$226$	−4.24264	+	7.34847i	−0.282216	+	0.488813i
$227$	−7.79423	−	13.5000i	−0.517321	−	0.896026i	−0.999798	−	0.0201176i	$-0.993596\pi$
$227$	−7.79423	−	13.5000i	−0.517321	−	0.896026i	0.482476	−	0.875909i	$-0.339737\pi$
$228$		0			0
$229$	−12.0000	−	6.92820i	−0.792982	−	0.457829i	0.0480291	−	0.998846i	$-0.484706\pi$
$229$	−12.0000	−	6.92820i	−0.792982	−	0.457829i	−0.841011	+	0.541017i	$0.818039\pi$
$230$		0			0
$231$		0			0
$232$	1.24264			0.0815834
$233$	5.82655	+	3.36396i	0.381710	+	0.220380i	0.678562	−	0.734543i	$-0.262603\pi$
$233$	5.82655	+	3.36396i	0.381710	+	0.220380i	−0.296852	+	0.954924i	$0.595937\pi$
$234$		0			0
$235$		0			0
$236$	5.76500	−	9.98528i	0.375270	−	0.649986i
$237$		0			0
$238$	−2.12132	−	1.64501i	−0.137505	−	0.106630i
$239$			12.7279i			0.823301i	0.911342	+	0.411650i	$0.135048\pi$
$239$			12.7279i			0.823301i	−0.911342	+	0.411650i	$0.864952\pi$
$240$		0			0
$241$	14.7426	−	8.51167i	0.949657	−	0.548285i	0.0566826	−	0.998392i	$-0.481948\pi$
$241$	14.7426	−	8.51167i	0.949657	−	0.548285i	0.892974	+	0.450108i	$0.148614\pi$
$242$	1.73205	−	1.00000i	0.111340	−	0.0642824i
$243$		0			0
$244$			5.91359i			0.378579i
$245$		0			0
$246$		0			0
$247$	−1.24264	+	2.15232i	−0.0790673	+	0.136949i
$248$	−2.80821	−	4.86396i	−0.178321	−	0.308862i
$249$		0			0
$250$		0			0
$251$	−17.6177			−1.11202			−0.556009	−	0.831176i	$-0.687668\pi$
$251$	−17.6177			−1.11202			−0.556009	+	0.831176i	$0.687668\pi$
$252$		0			0
$253$	−12.7279			−0.800198
$254$	−4.54026	−	2.62132i	−0.284881	−	0.164476i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.5446	−	21.7279i	0.782512	−	1.35535i	−0.147962	−	0.988993i	$-0.547271\pi$
$257$	12.5446	−	21.7279i	0.782512	−	1.35535i	0.930474	−	0.366358i	$-0.119395\pi$
$258$		0			0
$259$	−8.24264	−	20.1903i	−0.512173	−	1.25456i
$260$		0			0
$261$		0			0
$262$	4.50000	−	2.59808i	0.278011	−	0.160510i
$263$	23.5673	−	13.6066i	1.45322	−	0.839019i	0.454561	−	0.890716i	$-0.349796\pi$
$263$	23.5673	−	13.6066i	1.45322	−	0.839019i	0.998663	+	0.0516967i	$0.0164629\pi$
$264$		0			0
$265$		0			0
$266$	2.65962	+	0.363961i	0.163072	+	0.0223159i
$267$		0			0
$268$	5.00000	−	8.66025i	0.305424	−	0.529009i
$269$	5.25770	+	9.10660i	0.320568	+	0.555239i	0.980605	−	0.195993i	$-0.0627930\pi$
$269$	5.25770	+	9.10660i	0.320568	+	0.555239i	−0.660038	+	0.751232i	$0.729460\pi$
$270$		0			0
$271$	−9.62132	−	5.55487i	−0.584454	−	0.337434i	0.178448	−	0.983949i	$-0.442892\pi$
$271$	−9.62132	−	5.55487i	−0.584454	−	0.337434i	−0.762901	+	0.646515i	$0.776226\pi$
$272$	−1.01461			−0.0615199
$273$		0			0
$274$	14.4853			0.875088
$275$		0			0
$276$		0			0
$277$	−10.4853	−	18.1610i	−0.630000	−	1.09119i	−0.987551	−	0.157298i	$-0.949722\pi$
$277$	−10.4853	−	18.1610i	−0.630000	−	1.09119i	0.357552	−	0.933893i	$-0.383612\pi$
$278$	−10.0951	+	17.4853i	−0.605466	+	1.04870i
$279$		0			0
$280$		0			0
$281$		−	6.00000i		−	0.357930i	−0.983855	−	0.178965i	$-0.942725\pi$
$281$		−	6.00000i		−	0.357930i	0.983855	−	0.178965i	$-0.0572749\pi$
$282$		0			0
$283$	5.63604	−	3.25397i	0.335028	−	0.193428i	−0.323043	−	0.946384i	$-0.604706\pi$
$283$	5.63604	−	3.25397i	0.335028	−	0.193428i	0.658071	+	0.752956i	$0.271373\pi$
$284$	−8.87039	+	5.12132i	−0.526361	+	0.303894i
$285$		0			0
$286$		−	7.34847i		−	0.434524i
$287$	3.29002	−	4.24264i	0.194204	−	0.250435i
$288$		0			0
$289$	7.98528	−	13.8309i	0.469722	−	0.813583i
$290$		0			0
$291$		0			0
$292$	−7.24264	−	4.18154i	−0.423843	−	0.244706i
$293$	−4.18154			−0.244288			−0.122144	−	0.992512i	$-0.538977\pi$
$293$	−4.18154			−0.244288			−0.122144	+	0.992512i	$0.538977\pi$
$294$		0			0
$295$		0			0
$296$	−7.13834	−	4.12132i	−0.414907	−	0.239547i
$297$		0			0
$298$	10.2426	+	17.7408i	0.593340	+	1.02770i
$299$	5.19615	−	9.00000i	0.300501	−	0.520483i
$300$		0			0
$301$	−13.3640	+	17.2335i	−0.770286	+	0.993321i
$302$		−	3.24264i		−	0.186593i
$303$		0			0
$304$	0.878680	−	0.507306i	0.0503957	−	0.0290960i
$305$		0			0
$306$		0			0
$307$			24.6690i			1.40793i	0.710233	+	0.703966i	$0.248589\pi$
$307$			24.6690i			1.40793i	−0.710233	+	0.703966i	$0.751411\pi$
$308$	−7.34847	+	3.00000i	−0.418718	+	0.170941i
$309$		0			0
$310$		0			0
$311$	−9.37769	−	16.2426i	−0.531760	−	0.921036i	−0.999313	−	0.0370703i	$-0.988197\pi$
$311$	−9.37769	−	16.2426i	−0.531760	−	0.921036i	0.467552	−	0.883965i	$-0.345136\pi$
$312$		0			0
$313$	0.985281	+	0.568852i	0.0556914	+	0.0321534i	0.527587	−	0.849501i	$-0.323097\pi$
$313$	0.985281	+	0.568852i	0.0556914	+	0.0321534i	−0.471896	+	0.881654i	$0.656430\pi$
$314$	−14.6969			−0.829396
$315$		0			0
$316$	11.2426			0.632448
$317$	6.27231	+	3.62132i	0.352288	+	0.203394i	0.665693	−	0.746226i	$-0.268136\pi$
$317$	6.27231	+	3.62132i	0.352288	+	0.203394i	−0.313404	+	0.949620i	$0.601470\pi$
$318$		0			0
$319$	−1.86396	−	3.22848i	−0.104362	−	0.180760i
$320$		0			0
$321$		0			0
$322$	−11.1213	−	1.52192i	−0.619767	−	0.0848132i
$323$		−	1.02944i		−	0.0572794i
$324$		0			0
$325$		0			0
$326$	−5.40629	+	3.12132i	−0.299426	+	0.172874i
$327$		0			0
$328$		−	2.02922i		−	0.112045i
$329$	−1.01461	−	2.48528i	−0.0559374	−	0.137018i
$330$		0			0
$331$	−8.72792	+	15.1172i	−0.479730	+	0.830917i	−0.999730	−	0.0232497i	$-0.992599\pi$
$331$	−8.72792	+	15.1172i	−0.479730	+	0.830917i	0.520000	+	0.854166i	$0.325932\pi$
$332$	1.58346	+	2.74264i	0.0869039	+	0.150522i
$333$		0			0
$334$	19.9706	+	11.5300i	1.09274	+	0.630894i
$335$		0			0
$336$		0			0
$337$	5.00000			0.272367			0.136184	−	0.990684i	$-0.456516\pi$
$337$	5.00000			0.272367			0.136184	+	0.990684i	$0.456516\pi$
$338$	−6.06218	−	3.50000i	−0.329739	−	0.190375i
$339$		0			0
$340$		0			0
$341$	−8.42463	+	14.5919i	−0.456219	+	0.790195i
$342$		0			0
$343$	−17.0000	−	7.34847i	−0.917914	−	0.396780i
$344$			8.24264i			0.444413i
$345$		0			0
$346$	−18.0000	+	10.3923i	−0.967686	+	0.558694i
$347$	12.5446	−	7.24264i	0.673431	−	0.388805i	−0.123945	−	0.992289i	$-0.539555\pi$
$347$	12.5446	−	7.24264i	0.673431	−	0.388805i	0.797375	+	0.603484i	$0.206221\pi$
$348$		0			0
$349$			36.9164i			1.97609i	0.154163	+	0.988045i	$0.450732\pi$
$349$			36.9164i			1.97609i	−0.154163	+	0.988045i	$0.549268\pi$
$350$		0			0
$351$		0			0
$352$	−1.50000	+	2.59808i	−0.0799503	+	0.138478i
$353$	9.37769	+	16.2426i	0.499124	+	0.864509i	0.999999	−	0.00101095i	$-0.000321796\pi$
$353$	9.37769	+	16.2426i	0.499124	+	0.864509i	−0.500875	+	0.865519i	$0.666988\pi$
$354$		0			0
$355$		0			0
$356$	10.3923			0.550791
$357$		0			0
$358$	−9.51472			−0.502869
$359$	−15.5885	−	9.00000i	−0.822727	−	0.475002i	0.0286287	−	0.999590i	$-0.490886\pi$
$359$	−15.5885	−	9.00000i	−0.822727	−	0.475002i	−0.851356	+	0.524588i	$0.824219\pi$
$360$		0			0
$361$	−8.98528	−	15.5630i	−0.472910	−	0.819103i
$362$	1.01461	−	1.75736i	0.0533268	−	0.0923648i
$363$		0			0
$364$	0.878680	−	6.42090i	0.0460553	−	0.336546i
$365$		0			0
$366$		0			0
$367$	−16.3492	+	9.43924i	−0.853424	+	0.492724i	−0.861804	−	0.507241i	$-0.830666\pi$
$367$	−16.3492	+	9.43924i	−0.853424	+	0.492724i	0.00838099	+	0.999965i	$0.497332\pi$
$368$	−3.67423	+	2.12132i	−0.191533	+	0.110581i
$369$		0			0
$370$		0			0
$371$	−0.445759	+	3.25736i	−0.0231427	+	0.169114i
$372$		0			0
$373$	10.7279	−	18.5813i	0.555471	−	0.962104i	−0.442396	−	0.896820i	$-0.645871\pi$
$373$	10.7279	−	18.5813i	0.555471	−	0.962104i	0.997867	−	0.0652837i	$-0.0207952\pi$
$374$	1.52192	+	2.63604i	0.0786965	+	0.136306i
$375$		0			0
$376$	−0.878680	−	0.507306i	−0.0453144	−	0.0261623i
$377$	3.04384			0.156766
$378$		0			0
$379$	−4.48528			−0.230393			−0.115197	−	0.993343i	$-0.536750\pi$
$379$	−4.48528			−0.230393			−0.115197	+	0.993343i	$0.536750\pi$
$380$		0			0
$381$		0			0
$382$	4.24264	+	7.34847i	0.217072	+	0.375980i
$383$	6.21076	−	10.7574i	0.317355	−	0.549675i	−0.662580	−	0.748991i	$-0.730539\pi$
$383$	6.21076	−	10.7574i	0.317355	−	0.549675i	0.979935	+	0.199316i	$0.0638719\pi$
$384$		0			0
$385$		0			0
$386$			7.48528i			0.380991i
$387$		0			0
$388$	3.25736	−	1.88064i	0.165367	−	0.0954749i
$389$	16.8493	−	9.72792i	0.854291	−	0.493225i	−0.00780525	−	0.999970i	$-0.502485\pi$
$389$	16.8493	−	9.72792i	0.854291	−	0.493225i	0.862096	+	0.506744i	$0.169151\pi$
$390$		0			0
$391$			4.30463i			0.217695i
$392$	−6.77962	+	1.74264i	−0.342422	+	0.0880166i
$393$		0			0
$394$	−4.75736	+	8.23999i	−0.239672	+	0.415125i
$395$		0			0
$396$		0			0
$397$	−12.0000	−	6.92820i	−0.602263	−	0.347717i	0.167668	−	0.985843i	$-0.446376\pi$
$397$	−12.0000	−	6.92820i	−0.602263	−	0.347717i	−0.769931	+	0.638127i	$0.779710\pi$
$398$	16.1318			0.808615
$399$		0			0
$400$		0			0
$401$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$401$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$402$		0			0
$403$	−6.87868	−	11.9142i	−0.342651	−	0.593490i
$404$		0			0
$405$		0			0
$406$	−1.24264	−	3.04384i	−0.0616712	−	0.151063i
$407$			24.7279i			1.22572i
$408$		0			0
$409$	−3.98528	+	2.30090i	−0.197059	+	0.113772i	−0.595283	−	0.803516i	$-0.702960\pi$
$409$	−3.98528	+	2.30090i	−0.197059	+	0.113772i	0.398224	+	0.917288i	$0.369627\pi$
$410$		0			0
$411$		0			0
$412$			15.2913i			0.753348i
$413$	−30.2238	−	4.13604i	−1.48722	−	0.203521i
$414$		0			0
$415$		0			0
$416$	−1.22474	−	2.12132i	−0.0600481	−	0.104006i
$417$		0			0
$418$	−2.63604	−	1.52192i	−0.128933	−	0.0744394i
$419$	4.05845			0.198268			0.0991341	−	0.995074i	$-0.468393\pi$
$419$	4.05845			0.198268			0.0991341	+	0.995074i	$0.468393\pi$
$420$		0			0
$421$	−5.75736			−0.280597			−0.140298	−	0.990109i	$-0.544806\pi$
$421$	−5.75736			−0.280597			−0.140298	+	0.990109i	$0.544806\pi$
$422$	−7.13834	−	4.12132i	−0.347489	−	0.200623i
$423$		0			0
$424$	0.621320	+	1.07616i	0.0301740	+	0.0522629i
$425$		0			0
$426$		0			0
$427$	14.4853	−	5.91359i	0.700992	−	0.286179i
$428$		−	5.48528i		−	0.265141i
$429$		0			0
$430$		0			0
$431$	−17.7408	+	10.2426i	−0.854543	+	0.493371i	−0.862181	−	0.506600i	$-0.830902\pi$
$431$	−17.7408	+	10.2426i	−0.854543	+	0.493371i	0.00763808	+	0.999971i	$0.497569\pi$
$432$		0			0
$433$			3.46410i			0.166474i	0.996530	+	0.0832370i	$0.0265259\pi$
$433$			3.46410i			0.166474i	−0.996530	+	0.0832370i	$0.973474\pi$
$434$	−9.10601	+	11.7426i	−0.437103	+	0.563665i
$435$		0			0
$436$	0.757359	−	1.31178i	0.0362709	−	0.0628231i
$437$	−2.15232	−	3.72792i	−0.102959	−	0.178331i
$438$		0			0
$439$	23.5919	+	13.6208i	1.12598	+	0.650084i	0.942921	−	0.333018i	$-0.108067\pi$
$439$	23.5919	+	13.6208i	1.12598	+	0.650084i	0.183059	+	0.983102i	$0.441400\pi$
$440$		0			0
$441$		0			0
$442$	−2.48528			−0.118213
$443$	−29.8396	−	17.2279i	−1.41772	−	0.818523i	−0.421625	−	0.906770i	$-0.638540\pi$
$443$	−29.8396	−	17.2279i	−1.41772	−	0.818523i	−0.996099	+	0.0882469i	$0.971874\pi$
$444$		0			0
$445$		0			0
$446$	6.27231	−	10.8640i	0.297003	−	0.514423i
$447$		0			0
$448$	−1.62132	+	2.09077i	−0.0766002	+	0.0987796i
$449$			10.2426i			0.483380i	0.970354	+	0.241690i	$0.0777017\pi$
$449$			10.2426i			0.483380i	−0.970354	+	0.241690i	$0.922298\pi$
$450$		0			0
$451$	−5.27208	+	3.04384i	−0.248252	+	0.143329i
$452$	7.34847	−	4.24264i	0.345643	−	0.199557i
$453$		0			0
$454$			15.5885i			0.731603i
$455$		0			0
$456$		0			0
$457$	−11.5000	+	19.9186i	−0.537947	+	0.931752i	0.461067	+	0.887365i	$0.347467\pi$
$457$	−11.5000	+	19.9186i	−0.537947	+	0.931752i	−0.999014	+	0.0443868i	$0.985867\pi$
$458$	6.92820	+	12.0000i	0.323734	+	0.560723i
$459$		0			0
$460$		0			0
$461$	22.8138			1.06255			0.531273	−	0.847201i	$-0.321714\pi$
$461$	22.8138			1.06255			0.531273	+	0.847201i	$0.321714\pi$
$462$		0			0
$463$	−21.4558			−0.997138			−0.498569	−	0.866850i	$-0.666141\pi$
$463$	−21.4558			−0.997138			−0.498569	+	0.866850i	$0.666141\pi$
$464$	−1.07616	−	0.621320i	−0.0499594	−	0.0288441i
$465$		0			0
$466$	−3.36396	−	5.82655i	−0.155832	−	0.269910i
$467$	9.50079	−	16.4558i	0.439644	−	0.761486i	−0.558018	−	0.829829i	$-0.688438\pi$
$467$	9.50079	−	16.4558i	0.439644	−	0.761486i	0.997662	+	0.0683432i	$0.0217713\pi$
$468$		0			0
$469$	−26.2132	−	3.58719i	−1.21041	−	0.165641i
$470$		0			0
$471$		0			0
$472$	−9.98528	+	5.76500i	−0.459610	+	0.265356i
$473$	21.4150	−	12.3640i	0.984663	−	0.568496i
$474$		0			0
$475$		0			0
$476$	1.01461	+	2.48528i	0.0465047	+	0.113913i
$477$		0			0
$478$	6.36396	−	11.0227i	0.291081	−	0.504167i
$479$	18.2481	+	31.6066i	0.833776	+	1.44414i	0.895023	+	0.446020i	$0.147159\pi$
$479$	18.2481	+	31.6066i	0.833776	+	1.44414i	−0.0612470	+	0.998123i	$0.519508\pi$
$480$		0			0
$481$	−17.4853	−	10.0951i	−0.797260	−	0.460298i
$482$	−17.0233			−0.775392
$483$		0			0
$484$	−2.00000			−0.0909091
$485$		0			0
$486$		0			0
$487$	14.1066	+	24.4334i	0.639231	+	1.10718i	0.985602	+	0.169083i	$0.0540806\pi$
$487$	14.1066	+	24.4334i	0.639231	+	1.10718i	−0.346371	+	0.938098i	$0.612586\pi$
$488$	2.95680	−	5.12132i	0.133848	−	0.231831i
$489$		0			0
$490$		0			0
$491$		−	19.9706i		−	0.901259i	−0.892711	−	0.450629i	$-0.851200\pi$
$491$		−	19.9706i		−	0.901259i	0.892711	−	0.450629i	$-0.148800\pi$
$492$		0			0
$493$	−1.09188	+	0.630399i	−0.0491759	+	0.0283917i
$494$	2.15232	−	1.24264i	0.0968373	−	0.0559090i
$495$		0			0
$496$			5.61642i			0.252185i
$497$	21.4150	+	16.6066i	0.960594	+	0.744908i
$498$		0			0
$499$	17.9706	−	31.1259i	0.804473	−	1.39339i	−0.112173	−	0.993689i	$-0.535781\pi$
$499$	17.9706	−	31.1259i	0.804473	−	1.39339i	0.916646	−	0.399699i	$-0.130885\pi$
$500$		0			0
$501$		0			0
$502$	15.2574	+	8.80884i	0.680969	+	0.393158i
$503$	−3.29002			−0.146695			−0.0733474	−	0.997306i	$-0.523368\pi$
$503$	−3.29002			−0.146695			−0.0733474	+	0.997306i	$0.523368\pi$
$504$		0			0
$505$		0			0
$506$	11.0227	+	6.36396i	0.490019	+	0.282913i
$507$		0			0
$508$	2.62132	+	4.54026i	0.116302	+	0.201441i
$509$	20.8462	−	36.1066i	0.923990	−	1.60040i	0.130812	−	0.991407i	$-0.458242\pi$
$509$	20.8462	−	36.1066i	0.923990	−	1.60040i	0.793178	−	0.608990i	$-0.208425\pi$
$510$		0			0
$511$	−3.00000	+	21.9223i	−0.132712	+	0.969786i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−21.7279	+	12.5446i	−0.958378	+	0.553320i
$515$		0			0
$516$		0			0
$517$			3.04384i			0.133868i
$518$	−2.95680	+	21.6066i	−0.129914	+	0.949340i
$519$		0			0
$520$		0			0
$521$	10.0081	+	17.3345i	0.438462	+	0.759439i	0.997571	−	0.0696551i	$-0.0221899\pi$
$521$	10.0081	+	17.3345i	0.438462	+	0.759439i	−0.559109	+	0.829094i	$0.688857\pi$
$522$		0			0
$523$	23.8492	+	13.7694i	1.04285	+	0.602092i	0.920641	−	0.390411i	$-0.127667\pi$
$523$	23.8492	+	13.7694i	1.04285	+	0.602092i	0.122214	+	0.992504i	$0.461001\pi$
$524$	−5.19615			−0.226995
$525$		0			0
$526$	−27.2132			−1.18655
$527$	4.93503	+	2.84924i	0.214973	+	0.124115i
$528$		0			0
$529$	−2.50000	−	4.33013i	−0.108696	−	0.188266i
$530$		0			0
$531$		0			0
$532$	−2.12132	−	1.64501i	−0.0919709	−	0.0713203i
$533$		−	4.97056i		−	0.215299i
$534$		0			0
$535$		0			0
$536$	−8.66025	+	5.00000i	−0.374066	+	0.215967i
$537$		0			0
$538$		−	10.5154i		−	0.453351i
$539$	14.6969	+	15.0000i	0.633042	+	0.646096i
$540$		0			0
$541$	5.36396	−	9.29065i	0.230615	−	0.399436i	−0.727374	−	0.686241i	$-0.759260\pi$
$541$	5.36396	−	9.29065i	0.230615	−	0.399436i	0.957989	+	0.286804i	$0.0925930\pi$
$542$	5.55487	+	9.62132i	0.238602	+	0.413271i
$543$		0			0
$544$	0.878680	+	0.507306i	0.0376731	+	0.0217506i
$545$		0			0
$546$		0			0
$547$	−19.6985			−0.842246			−0.421123	−	0.907003i	$-0.638364\pi$
$547$	−19.6985			−0.842246			−0.421123	+	0.907003i	$0.638364\pi$
$548$	−12.5446	−	7.24264i	−0.535880	−	0.309390i
$549$		0			0
$550$		0			0
$551$	0.630399	−	1.09188i	0.0268559	−	0.0465158i
$552$		0			0
$553$	−11.2426	−	27.5387i	−0.478086	−	1.17107i
$554$			20.9706i			0.890954i
$555$		0			0
$556$	17.4853	−	10.0951i	0.741541	−	0.428129i
$557$	13.6208	−	7.86396i	0.577131	−	0.333207i	−0.182861	−	0.983139i	$-0.558536\pi$
$557$	13.6208	−	7.86396i	0.577131	−	0.333207i	0.759992	+	0.649932i	$0.225203\pi$
$558$		0			0
$559$			20.1903i			0.853957i
$560$		0			0
$561$		0			0
$562$	−3.00000	+	5.19615i	−0.126547	+	0.219186i
$563$	12.0989	+	20.9558i	0.509906	+	0.883184i	0.999934	+	0.0114768i	$0.00365325\pi$
$563$	12.0989	+	20.9558i	0.509906	+	0.883184i	−0.490028	+	0.871707i	$0.663013\pi$
$564$		0			0
$565$		0			0
$566$	−6.50794			−0.273549
$567$		0			0
$568$	10.2426			0.429772
$569$	−1.52192	−	0.878680i	−0.0638021	−	0.0368362i	0.467760	−	0.883856i	$-0.345061\pi$
$569$	−1.52192	−	0.878680i	−0.0638021	−	0.0368362i	−0.531562	+	0.847020i	$0.678395\pi$
$570$		0			0
$571$	8.36396	+	14.4868i	0.350021	+	0.606254i	0.986253	−	0.165244i	$-0.0528412\pi$
$571$	8.36396	+	14.4868i	0.350021	+	0.606254i	−0.636232	+	0.771498i	$0.719508\pi$
$572$	−3.67423	+	6.36396i	−0.153627	+	0.266091i
$573$		0			0
$574$	−4.97056	+	2.02922i	−0.207467	+	0.0846982i
$575$		0			0
$576$		0			0
$577$	−17.7426	+	10.2437i	−0.738636	+	0.426452i	−0.821573	−	0.570103i	$-0.806903\pi$
$577$	−17.7426	+	10.2437i	−0.738636	+	0.426452i	0.0829373	+	0.996555i	$0.473570\pi$
$578$	−13.8309	+	7.98528i	−0.575290	+	0.332144i
$579$		0			0
$580$		0			0
$581$	5.13461	−	6.62132i	0.213019	−	0.274699i
$582$		0			0
$583$	1.86396	−	3.22848i	0.0771974	−	0.133710i
$584$	4.18154	+	7.24264i	0.173033	+	0.299703i
$585$		0			0
$586$	3.62132	+	2.09077i	0.149595	+	0.0863689i
$587$	−5.19615			−0.214468			−0.107234	−	0.994234i	$-0.534199\pi$
$587$	−5.19615			−0.214468			−0.107234	+	0.994234i	$0.534199\pi$
$588$		0			0
$589$	−5.69848			−0.234802
$590$		0			0
$591$		0			0
$592$	4.12132	+	7.13834i	0.169385	+	0.293384i
$593$	−15.2042	+	26.3345i	−0.624363	+	1.08143i	0.364300	+	0.931282i	$0.381308\pi$
$593$	−15.2042	+	26.3345i	−0.624363	+	1.08143i	−0.988664	+	0.150148i	$0.952025\pi$
$594$		0			0
$595$		0			0
$596$		−	20.4853i		−	0.839110i
$597$		0			0
$598$	−9.00000	+	5.19615i	−0.368037	+	0.212486i
$599$	37.6339	−	21.7279i	1.53768	−	0.887779i	0.538704	−	0.842495i	$-0.318914\pi$
$599$	37.6339	−	21.7279i	1.53768	−	0.887779i	0.998974	−	0.0452836i	$-0.0144192\pi$
$600$		0			0
$601$		−	6.03668i		−	0.246241i	−0.992392	−	0.123121i	$-0.960710\pi$
$601$		−	6.03668i		−	0.246241i	0.992392	−	0.123121i	$-0.0392902\pi$
$602$	20.1903	−	8.24264i	0.822894	−	0.335945i
$603$		0			0
$604$	−1.62132	+	2.80821i	−0.0659706	+	0.114264i
$605$		0			0
$606$		0			0
$607$	21.6213	+	12.4831i	0.877582	+	0.506672i	0.869860	−	0.493298i	$-0.164209\pi$
$607$	21.6213	+	12.4831i	0.877582	+	0.506672i	0.00772182	+	0.999970i	$0.497542\pi$
$608$	−1.01461			−0.0411479
$609$		0			0
$610$		0			0
$611$	−2.15232	−	1.24264i	−0.0870734	−	0.0502719i
$612$		0			0
$613$	2.60660	+	4.51477i	0.105280	+	0.182350i	0.913852	−	0.406046i	$-0.133093\pi$
$613$	2.60660	+	4.51477i	0.105280	+	0.182350i	−0.808573	+	0.588396i	$0.799760\pi$
$614$	12.3345	−	21.3640i	0.497779	−	0.862179i
$615$		0			0
$616$	7.86396	+	1.07616i	0.316848	+	0.0433597i
$617$			41.6985i			1.67872i	0.543578	+	0.839359i	$0.317069\pi$
$617$			41.6985i			1.67872i	−0.543578	+	0.839359i	$0.682931\pi$
$618$		0			0
$619$	−41.3345	+	23.8645i	−1.66137	+	0.959195i	−0.689315	+	0.724462i	$0.742088\pi$
$619$	−41.3345	+	23.8645i	−1.66137	+	0.959195i	−0.972060	+	0.234733i	$0.924578\pi$
$620$		0			0
$621$		0			0
$622$			18.7554i			0.752022i
$623$	−10.3923	−	25.4558i	−0.416359	−	1.01987i
$624$		0			0
$625$		0			0
$626$	−0.568852	−	0.985281i	−0.0227359	−	0.0393798i
$627$		0			0
$628$	12.7279	+	7.34847i	0.507899	+	0.293236i
$629$	8.36308			0.333458
$630$		0			0
$631$	33.2426			1.32337			0.661684	−	0.749783i	$-0.269842\pi$
$631$	33.2426			1.32337			0.661684	+	0.749783i	$0.269842\pi$
$632$	−9.73641	−	5.62132i	−0.387294	−	0.223604i
$633$		0			0
$634$	−3.62132	−	6.27231i	−0.143821	−	0.249105i
$635$		0			0
$636$		0			0
$637$	−16.6066	+	4.26858i	−0.657978	+	0.169127i
$638$			3.72792i			0.147590i
$639$		0			0
$640$		0			0
$641$	36.1119	−	20.8492i	1.42634	−	0.823496i	0.429507	−	0.903064i	$-0.358687\pi$
$641$	36.1119	−	20.8492i	1.42634	−	0.823496i	0.996829	+	0.0795681i	$0.0253541\pi$
$642$		0			0
$643$		−	2.62357i		−	0.103463i	−0.998661	−	0.0517317i	$-0.983526\pi$
$643$		−	2.62357i		−	0.103463i	0.998661	−	0.0517317i	$-0.0164741\pi$
$644$	8.87039	+	6.87868i	0.349542	+	0.271058i
$645$		0			0
$646$	−0.514719	+	0.891519i	−0.0202513	+	0.0350763i
$647$	−5.82655	−	10.0919i	−0.229065	−	0.396753i	0.728466	−	0.685082i	$-0.240234\pi$
$647$	−5.82655	−	10.0919i	−0.229065	−	0.396753i	−0.957531	+	0.288329i	$0.906900\pi$
$648$		0			0
$649$	29.9558	+	17.2950i	1.17587	+	0.678889i
$650$		0			0
$651$		0			0
$652$	6.24264			0.244481
$653$	−9.31615	−	5.37868i	−0.364569	−	0.210484i	0.306514	−	0.951866i	$-0.400837\pi$
$653$	−9.31615	−	5.37868i	−0.364569	−	0.210484i	−0.671083	+	0.741382i	$0.734171\pi$
$654$		0			0
$655$		0			0
$656$	−1.01461	+	1.75736i	−0.0396139	+	0.0686134i
$657$		0			0
$658$	−0.363961	+	2.65962i	−0.0141887	+	0.103683i
$659$		−	6.00000i		−	0.233727i	−0.993148	−	0.116863i	$-0.962716\pi$
$659$		−	6.00000i		−	0.233727i	0.993148	−	0.116863i	$-0.0372840\pi$
$660$		0			0
$661$	35.1213	−	20.2773i	1.36606	−	0.788696i	0.375639	−	0.926766i	$-0.377423\pi$
$661$	35.1213	−	20.2773i	1.36606	−	0.788696i	0.990422	+	0.138071i	$0.0440901\pi$
$662$	15.1172	−	8.72792i	0.587547	−	0.339220i
$663$		0			0
$664$		−	3.16693i		−	0.122901i
$665$		0			0
$666$		0			0
$667$	−2.63604	+	4.56575i	−0.102068	+	0.176787i
$668$	−11.5300	−	19.9706i	−0.446109	−	0.772684i
$669$		0			0
$670$		0			0
$671$	−17.7408			−0.684875
$672$		0			0
$673$	15.9706			0.615620			0.307810	−	0.951448i	$-0.400404\pi$
$673$	15.9706			0.615620			0.307810	+	0.951448i	$0.400404\pi$
$674$	−4.33013	−	2.50000i	−0.166790	−	0.0962964i
$675$		0			0
$676$	3.50000	+	6.06218i	0.134615	+	0.233161i
$677$	6.27231	−	10.8640i	0.241064	−	0.417536i	−0.719953	−	0.694023i	$-0.755837\pi$
$677$	6.27231	−	10.8640i	0.241064	−	0.417536i	0.961018	+	0.276487i	$0.0891701\pi$
$678$		0			0
$679$	−7.86396	−	6.09823i	−0.301791	−	0.234029i
$680$		0			0
$681$		0			0
$682$	14.5919	−	8.42463i	0.558752	−	0.322596i
$683$	−22.4912	+	12.9853i	−0.860601	+	0.496868i	−0.864213	−	0.503125i	$-0.832183\pi$
$683$	−22.4912	+	12.9853i	−0.860601	+	0.496868i	0.00361277	+	0.999993i	$0.498850\pi$
$684$		0			0
$685$		0			0
$686$	11.0482	+	14.8640i	0.421822	+	0.567509i
$687$		0			0
$688$	4.12132	−	7.13834i	0.157124	−	0.272147i
$689$	1.52192	+	2.63604i	0.0579805	+	0.100425i
$690$		0			0
$691$	−0.727922	−	0.420266i	−0.0276915	−	0.0159877i	0.486090	−	0.873909i	$-0.338423\pi$
$691$	−0.727922	−	0.420266i	−0.0276915	−	0.0159877i	−0.513782	+	0.857921i	$0.671756\pi$
$692$	20.7846			0.790112
$693$		0			0
$694$	−14.4853			−0.549854
$695$		0			0
$696$		0			0
$697$	1.02944	+	1.78304i	0.0389927	+	0.0675374i
$698$	18.4582	−	31.9706i	0.698654	−	1.21010i
$699$		0			0
$700$		0			0
$701$			38.6985i			1.46162i	0.682580	+	0.730811i	$0.260858\pi$
$701$			38.6985i			1.46162i	−0.682580	+	0.730811i	$0.739142\pi$
$702$		0			0
$703$	−7.24264	+	4.18154i	−0.273161	+	0.157710i
$704$	2.59808	−	1.50000i	0.0979187	−	0.0565334i
$705$		0			0
$706$		−	18.7554i		−	0.705868i
$707$		0			0
$708$		0			0
$709$	3.48528	−	6.03668i	0.130892	−	0.226712i	−0.793128	−	0.609055i	$-0.791549\pi$
$709$	3.48528	−	6.03668i	0.130892	−	0.226712i	0.924021	+	0.382342i	$0.124882\pi$
$710$		0			0
$711$		0			0
$712$	−9.00000	−	5.19615i	−0.337289	−	0.194734i
$713$	23.8284			0.892382
$714$		0			0
$715$		0			0
$716$	8.23999	+	4.75736i	0.307943	+	0.177791i
$717$		0			0
$718$	9.00000	+	15.5885i	0.335877	+	0.581756i
$719$	11.5300	−	19.9706i	0.429997	−	0.744776i	−0.566876	−	0.823803i	$-0.691848\pi$
$719$	11.5300	−	19.9706i	0.429997	−	0.744776i	0.996872	+	0.0790270i	$0.0251813\pi$
$720$		0			0
$721$	37.4558	−	15.2913i	1.39493	−	0.569477i
$722$			17.9706i			0.668795i
$723$		0			0
$724$	−1.75736	+	1.01461i	−0.0653117	+	0.0377078i
$725$		0			0
$726$		0			0
$727$			26.4010i			0.979160i	0.871958	+	0.489580i	$0.162850\pi$
$727$			26.4010i			0.979160i	−0.871958	+	0.489580i	$0.837150\pi$
$728$	−3.97141	+	5.12132i	−0.147190	+	0.189809i
$729$		0			0
$730$		0			0
$731$	−4.18154	−	7.24264i	−0.154660	−	0.267879i
$732$		0			0
$733$	34.0919	+	19.6830i	1.25921	+	0.727007i	0.972921	−	0.231136i	$-0.0742443\pi$
$733$	34.0919	+	19.6830i	1.25921	+	0.727007i	0.286291	+	0.958143i	$0.407578\pi$
$734$	18.8785			0.696817
$735$		0			0
$736$	4.24264			0.156386
$737$	25.9808	+	15.0000i	0.957014	+	0.552532i
$738$		0			0
$739$	17.7279	+	30.7057i	0.652132	+	1.12953i	0.982605	+	0.185710i	$0.0594586\pi$
$739$	17.7279	+	30.7057i	0.652132	+	1.12953i	−0.330472	+	0.943816i	$0.607208\pi$
$740$		0			0
$741$		0			0
$742$	2.01472	−	2.59808i	0.0739626	−	0.0953784i
$743$			21.5147i			0.789298i	0.918832	+	0.394649i	$0.129134\pi$
$743$			21.5147i			0.789298i	−0.918832	+	0.394649i	$0.870866\pi$
$744$		0			0
$745$		0			0
$746$	−18.5813	+	10.7279i	−0.680310	+	0.392777i
$747$		0			0
$748$		−	3.04384i		−	0.111294i
$749$	−13.4361	+	5.48528i	−0.490946	+	0.200428i
$750$		0			0
$751$	−13.3787	+	23.1726i	−0.488195	+	0.845578i	−0.999908	−	0.0135781i	$-0.995678\pi$
$751$	−13.3787	+	23.1726i	−0.488195	+	0.845578i	0.511713	+	0.859157i	$0.329011\pi$
$752$	0.507306	+	0.878680i	0.0184995	+	0.0320422i
$753$		0			0
$754$	−2.63604	−	1.52192i	−0.0959989	−	0.0554250i
$755$		0			0
$756$		0			0
$757$	42.2426			1.53533			0.767667	−	0.640848i	$-0.221417\pi$
$757$	42.2426			1.53533			0.767667	+	0.640848i	$0.221417\pi$
$758$	3.88437	+	2.24264i	0.141087	+	0.0814564i
$759$		0			0
$760$		0			0
$761$	−2.53653	+	4.39340i	−0.0919491	+	0.159261i	−0.908331	−	0.418252i	$-0.862643\pi$
$761$	−2.53653	+	4.39340i	−0.0919491	+	0.159261i	0.816382	+	0.577512i	$0.195976\pi$
$762$		0			0
$763$	−3.97056	−	0.543359i	−0.143744	−	0.0196709i
$764$		−	8.48528i		−	0.306987i
$765$		0			0
$766$	−10.7574	+	6.21076i	−0.388679	+	0.224404i
$767$	−24.4588	+	14.1213i	−0.883158	+	0.509891i
$768$		0			0
$769$			49.0408i			1.76846i	0.467056	+	0.884228i	$0.345315\pi$
$769$			49.0408i			1.76846i	−0.467056	+	0.884228i	$0.654685\pi$
$770$		0			0
$771$		0			0
$772$	3.74264	−	6.48244i	0.134701	−	0.233308i
$773$	11.5300	+	19.9706i	0.414706	+	0.718291i	0.995398	−	0.0958322i	$-0.0305512\pi$
$773$	11.5300	+	19.9706i	0.414706	+	0.718291i	−0.580692	+	0.814123i	$0.697218\pi$
$774$		0			0
$775$		0			0
$776$	−3.76127			−0.135022
$777$		0			0
$778$	−19.4558			−0.697526
$779$	−1.78304	−	1.02944i	−0.0638840	−	0.0368834i
$780$		0			0
$781$	−15.3640	−	26.6112i	−0.549766	−	0.952222i
$782$	2.15232	−	3.72792i	0.0769667	−	0.133310i
$783$		0			0
$784$	6.74264	+	1.88064i	0.240809	+	0.0671656i
$785$		0			0
$786$		0			0
$787$	−32.1213	+	18.5453i	−1.14500	+	0.661067i	−0.947664	−	0.319269i	$-0.896563\pi$
$787$	−32.1213	+	18.5453i	−1.14500	+	0.661067i	−0.197337	+	0.980336i	$0.563229\pi$
$788$	8.23999	−	4.75736i	0.293537	−	0.169474i
$789$		0			0
$790$		0			0
$791$	−17.7408	−	13.7574i	−0.630789	−	0.489155i
$792$		0			0
$793$	7.24264	−	12.5446i	0.257194	−	0.445473i
$794$	6.92820	+	12.0000i	0.245873	+	0.425864i
$795$		0			0
$796$	−13.9706	−	8.06591i	−0.495173	−	0.285889i
$797$	37.6339			1.33306			0.666530	−	0.745478i	$-0.267779\pi$
$797$	37.6339			1.33306			0.666530	+	0.745478i	$0.267779\pi$
$798$		0			0
$799$	1.02944			0.0364189
$800$		0			0
$801$		0			0
$802$		0			0
$803$	12.5446	−	21.7279i	0.442690	−	0.766762i
$804$		0			0
$805$		0			0
$806$			13.7574i			0.484582i
$807$		0			0
$808$		0			0
$809$	−35.4815	+	20.4853i	−1.24746	+	0.720224i	−0.970603	−	0.240686i	$-0.922628\pi$
$809$	−35.4815	+	20.4853i	−1.24746	+	0.720224i	−0.276862	+	0.960910i	$0.589294\pi$
$810$		0			0
$811$			31.1769i			1.09477i	0.836881	+	0.547385i	$0.184377\pi$
$811$			31.1769i			1.09477i	−0.836881	+	0.547385i	$0.815623\pi$
$812$	−0.445759	+	3.25736i	−0.0156431	+	0.114311i
$813$		0			0
$814$	12.3640	−	21.4150i	0.433357	−	0.750596i
$815$		0			0
$816$		0			0
$817$	7.24264	+	4.18154i	0.253388	+	0.146294i
$818$	4.60181			0.160898
$819$		0			0
$820$		0			0
$821$	42.6454	+	24.6213i	1.48833	+	0.859290i	0.999911	−	0.0133172i	$-0.00423912\pi$
$821$	42.6454	+	24.6213i	1.48833	+	0.859290i	0.488423	+	0.872607i	$0.337572\pi$
$822$		0			0
$823$	−18.9706	−	32.8580i	−0.661272	−	1.14536i	−0.980282	−	0.197606i	$-0.936683\pi$
$823$	−18.9706	−	32.8580i	−0.661272	−	1.14536i	0.319009	−	0.947752i	$-0.396650\pi$
$824$	7.64564	−	13.2426i	0.266349	−	0.461329i
$825$		0			0
$826$	24.1066	+	18.6938i	0.838776	+	0.650442i
$827$			4.02944i			0.140117i	0.997543	+	0.0700586i	$0.0223186\pi$
$827$			4.02944i			0.140117i	−0.997543	+	0.0700586i	$0.977681\pi$
$828$		0			0
$829$	−35.3345	+	20.4004i	−1.22722	+	0.708535i	−0.966447	−	0.256865i	$-0.917310\pi$
$829$	−35.3345	+	20.4004i	−1.22722	+	0.708535i	−0.260772	+	0.965401i	$0.583977\pi$
$830$		0			0
$831$		0			0
$832$			2.44949i			0.0849208i
$833$	5.07306	−	4.97056i	0.175771	−	0.172220i
$834$		0			0
$835$		0			0
$836$	1.52192	+	2.63604i	0.0526366	+	0.0911693i
$837$		0			0
$838$	−3.51472	−	2.02922i	−0.121414	−	0.0700984i
$839$	−24.0746			−0.831149			−0.415574	−	0.909559i	$-0.636419\pi$
$839$	−24.0746			−0.831149			−0.415574	+	0.909559i	$0.636419\pi$
$840$		0			0
$841$	27.4558			0.946753
$842$	4.98602	+	2.87868i	0.171830	+	0.0992059i
$843$		0			0
$844$	4.12132	+	7.13834i	0.141862	+	0.245712i
$845$		0			0
$846$		0			0
$847$	2.00000	+	4.89898i	0.0687208	+	0.168331i
$848$		−	1.24264i		−	0.0426725i
$849$		0			0
$850$		0			0
$851$	30.2854	−	17.4853i	1.03817	−	0.599388i
$852$		0			0
$853$			2.27541i			0.0779085i	0.999241	+	0.0389543i	$0.0124027\pi$
$853$			2.27541i			0.0779085i	−0.999241	+	0.0389543i	$0.987597\pi$
$854$	−15.5014	−	2.12132i	−0.530448	−	0.0725901i
$855$		0			0
$856$	−2.74264	+	4.75039i	−0.0937415	+	0.162365i
$857$	10.0081	+	17.3345i	0.341870	+	0.592136i	0.984780	−	0.173806i	$-0.0556064\pi$
$857$	10.0081	+	17.3345i	0.341870	+	0.592136i	−0.642910	+	0.765942i	$0.722273\pi$
$858$		0			0
$859$	3.87868	+	2.23936i	0.132339	+	0.0764059i	0.564708	−	0.825291i	$-0.308989\pi$
$859$	3.87868	+	2.23936i	0.132339	+	0.0764059i	−0.432369	+	0.901697i	$0.642322\pi$
$860$		0			0
$861$		0			0
$862$	20.4853			0.697731
$863$	−43.7215	−	25.2426i	−1.48830	−	0.859269i	−0.488388	−	0.872627i	$-0.662415\pi$
$863$	−43.7215	−	25.2426i	−1.48830	−	0.859269i	−0.999911	+	0.0133573i	$0.995748\pi$
$864$		0			0
$865$		0			0
$866$	1.73205	−	3.00000i	0.0588575	−	0.101944i
$867$		0			0
$868$	13.7574	−	5.61642i	0.466955	−	0.190634i
$869$			33.7279i			1.14414i
$870$		0			0
$871$	−21.2132	+	12.2474i	−0.718782	+	0.414989i
$872$	−1.31178	+	0.757359i	−0.0444226	+	0.0256474i
$873$		0			0
$874$			4.30463i			0.145606i
$875$		0			0
$876$		0			0
$877$	−6.24264	+	10.8126i	−0.210799	+	0.365115i	−0.951965	−	0.306207i	$-0.900940\pi$
$877$	−6.24264	+	10.8126i	−0.210799	+	0.365115i	0.741166	+	0.671322i	$0.234273\pi$
$878$	−13.6208	−	23.5919i	−0.459679	−	0.796187i
$879$		0			0
$880$		0			0
$881$	−39.7862			−1.34043			−0.670215	−	0.742167i	$-0.733798\pi$
$881$	−39.7862			−1.34043			−0.670215	+	0.742167i	$0.733798\pi$
$882$		0			0
$883$	9.45584			0.318214			0.159107	−	0.987261i	$-0.449138\pi$
$883$	9.45584			0.318214			0.159107	+	0.987261i	$0.449138\pi$
$884$	2.15232	+	1.24264i	0.0723902	+	0.0417945i
$885$		0			0
$886$	17.2279	+	29.8396i	0.578783	+	1.00248i
$887$	−22.4296	+	38.8492i	−0.753113	+	1.30443i	0.193194	+	0.981161i	$0.438115\pi$
$887$	−22.4296	+	38.8492i	−0.753113	+	1.30443i	−0.946307	+	0.323269i	$0.895218\pi$
$888$		0			0
$889$	8.50000	−	10.9612i	0.285081	−	0.367625i
$890$		0			0
$891$		0			0
$892$	−10.8640	+	6.27231i	−0.363752	+	0.210012i
$893$	−0.891519	+	0.514719i	−0.0298335	+	0.0172244i
$894$		0			0
$895$		0			0
$896$	2.44949	−	1.00000i	0.0818317	−	0.0334077i
$897$		0			0
$898$	5.12132	−	8.87039i	0.170901	−	0.296009i
$899$	3.48960	+	6.04416i	0.116385	+	0.201584i
$900$		0			0
$901$	−1.09188	−	0.630399i	−0.0363759	−	0.0210016i
$902$	6.08767			0.202697
$903$		0			0
$904$	−8.48528			−0.282216
$905$		0			0
$906$		0			0
$907$	13.8492	+	23.9876i	0.459857	+	0.796495i	0.998953	−	0.0457492i	$-0.0145675\pi$
$907$	13.8492	+	23.9876i	0.459857	+	0.796495i	−0.539096	+	0.842244i	$0.681234\pi$
$908$	7.79423	−	13.5000i	0.258661	−	0.448013i
$909$		0			0
$910$		0			0
$911$		−	18.7279i		−	0.620484i	−0.950658	−	0.310242i	$-0.899590\pi$
$911$		−	18.7279i		−	0.620484i	0.950658	−	0.310242i	$-0.100410\pi$
$912$		0			0
$913$	−8.22792	+	4.75039i	−0.272304	+	0.157215i
$914$	19.9186	−	11.5000i	0.658848	−	0.380386i
$915$		0			0
$916$		−	13.8564i		−	0.457829i
$917$	5.19615	+	12.7279i	0.171592	+	0.420313i
$918$		0			0
$919$	−9.75736	+	16.9002i	−0.321866	+	0.557488i	−0.980873	−	0.194649i	$-0.937643\pi$
$919$	−9.75736	+	16.9002i	−0.321866	+	0.557488i	0.659007	+	0.752136i	$0.270977\pi$
$920$		0			0
$921$		0			0
$922$	−19.7574	−	11.4069i	−0.650674	−	0.375667i
$923$	25.0892			0.825823
$924$		0			0
$925$		0			0
$926$	18.5813	+	10.7279i	0.610620	+	0.352541i
$927$		0			0
$928$	0.621320	+	1.07616i	0.0203958	+	0.0353266i
$929$	1.64501	−	2.84924i	0.0539711	−	0.0934806i	−0.837778	−	0.546012i	$-0.816145\pi$
$929$	1.64501	−	2.84924i	0.0539711	−	0.0934806i	0.891749	+	0.452531i	$0.149479\pi$
$930$		0			0
$931$	−1.90812	+	6.84116i	−0.0625360	+	0.224210i
$932$			6.72792i			0.220380i
$933$		0			0
$934$	−16.4558	+	9.50079i	−0.538452	+	0.310875i
$935$		0			0
$936$		0			0
$937$		−	4.00746i		−	0.130918i	−0.997855	−	0.0654590i	$-0.979149\pi$
$937$		−	4.00746i		−	0.130918i	0.997855	−	0.0654590i	$-0.0208512\pi$
$938$	20.9077	+	16.2132i	0.682661	+	0.529380i
$939$		0			0
$940$		0			0
$941$	26.0423	+	45.1066i	0.848955	+	1.47043i	0.882142	+	0.470984i	$0.156101\pi$
$941$	26.0423	+	45.1066i	0.848955	+	1.47043i	−0.0331867	+	0.999449i	$0.510566\pi$
$942$		0			0
$943$	7.45584	+	4.30463i	0.242796	+	0.140178i
$944$	11.5300			0.375270
$945$		0			0
$946$	−24.7279			−0.803974
$947$	−19.8931	−	11.4853i	−0.646439	−	0.373221i	0.140652	−	0.990059i	$-0.455080\pi$
$947$	−19.8931	−	11.4853i	−0.646439	−	0.373221i	−0.787090	+	0.616838i	$0.788414\pi$
$948$		0			0
$949$	10.2426	+	17.7408i	0.332490	+	0.575890i
$950$		0			0
$951$		0			0
$952$	0.363961	−	2.65962i	0.0117960	−	0.0861989i
$953$			41.6985i			1.35075i	0.737476	+	0.675373i	$0.236017\pi$
$953$			41.6985i			1.35075i	−0.737476	+	0.675373i	$0.763983\pi$
$954$		0			0
$955$		0			0
$956$	−11.0227	+	6.36396i	−0.356500	+	0.205825i
$957$		0			0
$958$		−	36.4962i		−	1.17914i
$959$	−5.19615	+	37.9706i	−0.167793	+	1.22613i
$960$		0			0
$961$	0.272078	−	0.471253i	0.00877671	−	0.0152017i
$962$	10.0951	+	17.4853i	0.325480	+	0.563748i
$963$		0			0
$964$	14.7426	+	8.51167i	0.474828	+	0.274142i
$965$		0			0
$966$		0			0
$967$	−22.2721			−0.716222			−0.358111	−	0.933679i	$-0.616579\pi$
$967$	−22.2721			−0.716222			−0.358111	+	0.933679i	$0.616579\pi$
$968$	1.73205	+	1.00000i	0.0556702	+	0.0321412i
$969$		0			0
$970$		0			0
$971$	−25.6581	+	44.4411i	−0.823407	+	1.42618i	0.0797229	+	0.996817i	$0.474596\pi$
$971$	−25.6581	+	44.4411i	−0.823407	+	1.42618i	−0.903130	+	0.429367i	$0.858737\pi$
$972$		0			0
$973$	−42.2132	−	32.7349i	−1.35329	−	1.04943i
$974$		−	28.2132i		−	0.904009i
$975$		0			0
$976$	−5.12132	+	2.95680i	−0.163929	+	0.0946447i
$977$	27.5027	−	15.8787i	0.879889	−	0.508004i	0.00926698	−	0.999957i	$-0.497050\pi$
$977$	27.5027	−	15.8787i	0.879889	−	0.508004i	0.870622	+	0.491953i	$0.163717\pi$
$978$		0			0
$979$			31.1769i			0.996419i
$980$		0			0
$981$		0			0
$982$	−9.98528	+	17.2950i	−0.318643	+	0.551906i
$983$	4.05845	+	7.02944i	0.129444	+	0.224204i	0.923461	−	0.383691i	$-0.125347\pi$
$983$	4.05845	+	7.02944i	0.129444	+	0.224204i	−0.794017	+	0.607895i	$0.792014\pi$
$984$		0			0
$985$		0			0
$986$	1.26080			0.0401520
$987$		0			0
$988$	−2.48528			−0.0790673
$989$	−30.2854	−	17.4853i	−0.963020	−	0.556000i
$990$		0			0
$991$	−4.89340	−	8.47561i	−0.155444	−	0.269237i	0.777777	−	0.628541i	$-0.216347\pi$
$991$	−4.89340	−	8.47561i	−0.155444	−	0.269237i	−0.933221	+	0.359304i	$0.883014\pi$
$992$	2.80821	−	4.86396i	0.0891607	−	0.154431i
$993$		0			0
$994$	−10.2426	−	25.0892i	−0.324877	−	0.795782i
$995$		0			0
$996$		0			0
$997$	8.27208	−	4.77589i	0.261979	−	0.151254i	−0.363258	−	0.931689i	$-0.618336\pi$
$997$	8.27208	−	4.77589i	0.261979	−	0.151254i	0.625237	+	0.780435i	$0.285002\pi$
$998$	−31.1259	+	17.9706i	−0.985274	+	0.568848i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bf.a.1601.2		8
3.2	odd	2	inner	3150.2.bf.a.1601.4		8
5.2	odd	4		3150.2.bp.e.1349.4		8
5.3	odd	4		3150.2.bp.b.1349.1		8
5.4	even	2		126.2.k.a.89.4	yes	8
7.3	odd	6	inner	3150.2.bf.a.1151.4		8
15.2	even	4		3150.2.bp.b.1349.4		8
15.8	even	4		3150.2.bp.e.1349.1		8
15.14	odd	2		126.2.k.a.89.1	yes	8
20.19	odd	2		1008.2.bt.c.593.4		8
21.17	even	6	inner	3150.2.bf.a.1151.2		8
35.3	even	12		3150.2.bp.b.899.4		8
35.4	even	6		882.2.k.a.521.2		8
35.9	even	6		882.2.d.a.881.1		8
35.17	even	12		3150.2.bp.e.899.1		8
35.19	odd	6		882.2.d.a.881.4		8
35.24	odd	6		126.2.k.a.17.1	✓	8
35.34	odd	2		882.2.k.a.215.3		8
45.4	even	6		1134.2.t.e.593.1		8
45.14	odd	6		1134.2.t.e.593.4		8
45.29	odd	6		1134.2.l.f.215.3		8
45.34	even	6		1134.2.l.f.215.2		8
60.59	even	2		1008.2.bt.c.593.1		8
105.17	odd	12		3150.2.bp.b.899.1		8
105.38	odd	12		3150.2.bp.e.899.4		8
105.44	odd	6		882.2.d.a.881.8		8
105.59	even	6		126.2.k.a.17.4	yes	8
105.74	odd	6		882.2.k.a.521.3		8
105.89	even	6		882.2.d.a.881.5		8
105.104	even	2		882.2.k.a.215.2		8
140.19	even	6		7056.2.k.f.881.8		8
140.59	even	6		1008.2.bt.c.17.1		8
140.79	odd	6		7056.2.k.f.881.2		8
315.59	even	6		1134.2.l.f.269.4		8
315.94	odd	6		1134.2.l.f.269.1		8
315.164	even	6		1134.2.t.e.1025.1		8
315.304	odd	6		1134.2.t.e.1025.4		8
420.59	odd	6		1008.2.bt.c.17.4		8
420.299	odd	6		7056.2.k.f.881.1		8
420.359	even	6		7056.2.k.f.881.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.k.a.17.1	✓	8	35.24	odd	6
126.2.k.a.17.4	yes	8	105.59	even	6
126.2.k.a.89.1	yes	8	15.14	odd	2
126.2.k.a.89.4	yes	8	5.4	even	2
882.2.d.a.881.1		8	35.9	even	6
882.2.d.a.881.4		8	35.19	odd	6
882.2.d.a.881.5		8	105.89	even	6
882.2.d.a.881.8		8	105.44	odd	6
882.2.k.a.215.2		8	105.104	even	2
882.2.k.a.215.3		8	35.34	odd	2
882.2.k.a.521.2		8	35.4	even	6
882.2.k.a.521.3		8	105.74	odd	6
1008.2.bt.c.17.1		8	140.59	even	6
1008.2.bt.c.17.4		8	420.59	odd	6
1008.2.bt.c.593.1		8	60.59	even	2
1008.2.bt.c.593.4		8	20.19	odd	2
1134.2.l.f.215.2		8	45.34	even	6
1134.2.l.f.215.3		8	45.29	odd	6
1134.2.l.f.269.1		8	315.94	odd	6
1134.2.l.f.269.4		8	315.59	even	6
1134.2.t.e.593.1		8	45.4	even	6
1134.2.t.e.593.4		8	45.14	odd	6
1134.2.t.e.1025.1		8	315.164	even	6
1134.2.t.e.1025.4		8	315.304	odd	6
3150.2.bf.a.1151.2		8	21.17	even	6	inner
3150.2.bf.a.1151.4		8	7.3	odd	6	inner
3150.2.bf.a.1601.2		8	1.1	even	1	trivial
3150.2.bf.a.1601.4		8	3.2	odd	2	inner
3150.2.bp.b.899.1		8	105.17	odd	12
3150.2.bp.b.899.4		8	35.3	even	12
3150.2.bp.b.1349.1		8	5.3	odd	4
3150.2.bp.b.1349.4		8	15.2	even	4
3150.2.bp.e.899.1		8	35.17	even	12
3150.2.bp.e.899.4		8	105.38	odd	12
3150.2.bp.e.1349.1		8	15.8	even	4
3150.2.bp.e.1349.4		8	5.2	odd	4
7056.2.k.f.881.1		8	420.299	odd	6
7056.2.k.f.881.2		8	140.79	odd	6
7056.2.k.f.881.7		8	420.359	even	6
7056.2.k.f.881.8		8	140.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.62132 - 2.09077i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.62132 - 2.09077i) q^{7} -1.00000i q^{8} +(-2.59808 + 1.50000i) q^{11} -2.44949i q^{13} +(-2.44949 + 1.00000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.507306 + 0.878680i) q^{17} +(-0.878680 - 0.507306i) q^{19} +3.00000 q^{22} +(3.67423 + 2.12132i) q^{23} +(-1.22474 + 2.12132i) q^{26} +(2.62132 + 0.358719i) q^{28} +1.24264i q^{29} +(4.86396 - 2.80821i) q^{31} +(0.866025 - 0.500000i) q^{32} -1.01461i q^{34} +(4.12132 - 7.13834i) q^{37} +(0.507306 + 0.878680i) q^{38} +2.02922 q^{41} -8.24264 q^{43} +(-2.59808 - 1.50000i) q^{44} +(-2.12132 - 3.67423i) q^{46} +(0.507306 - 0.878680i) q^{47} +(-1.74264 - 6.77962i) q^{49} +(2.12132 - 1.22474i) q^{52} +(-1.07616 + 0.621320i) q^{53} +(-2.09077 - 1.62132i) q^{56} +(0.621320 - 1.07616i) q^{58} +(-5.76500 - 9.98528i) q^{59} +(5.12132 + 2.95680i) q^{61} -5.61642 q^{62} -1.00000 q^{64} +(-5.00000 - 8.66025i) q^{67} +(-0.507306 + 0.878680i) q^{68} +10.2426i q^{71} +(-7.24264 + 4.18154i) q^{73} +(-7.13834 + 4.12132i) q^{74} -1.01461i q^{76} +(-1.07616 + 7.86396i) q^{77} +(5.62132 - 9.73641i) q^{79} +(-1.75736 - 1.01461i) q^{82} +3.16693 q^{83} +(7.13834 + 4.12132i) q^{86} +(1.50000 + 2.59808i) q^{88} +(5.19615 - 9.00000i) q^{89} +(-5.12132 - 3.97141i) q^{91} +4.24264i q^{92} +(-0.878680 + 0.507306i) q^{94} -3.76127i q^{97} +(-1.88064 + 6.74264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^4 - 4 * q^7	\( 8 q + 4 q^{4} - 4 q^{7} - 4 q^{16} - 24 q^{19} + 24 q^{22} + 4 q^{28} - 12 q^{31} + 16 q^{37} - 32 q^{43} + 20 q^{49} - 12 q^{58} + 24 q^{61} - 8 q^{64} - 40 q^{67} - 24 q^{73} + 28 q^{79} - 48 q^{82} + 12 q^{88} - 24 q^{91} - 24 q^{94}+O(q^{100}) \) 8 * q + 4 * q^4 - 4 * q^7 - 4 * q^16 - 24 * q^19 + 24 * q^22 + 4 * q^28 - 12 * q^31 + 16 * q^37 - 32 * q^43 + 20 * q^49 - 12 * q^58 + 24 * q^61 - 8 * q^64 - 40 * q^67 - 24 * q^73 + 28 * q^79 - 48 * q^82 + 12 * q^88 - 24 * q^91 - 24 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more