LMFDB - Embedded newform 2352.2.bl.t.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2352,2,Mod(31,2352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2352, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 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("2352.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2352 = 2^{4} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2352.bl (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$18.7808145554$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.339738624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 $ x^8 - 4x^6 + 14x^4 - 8*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.4
Root			$-0.662827 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	2352.31
Dual form			2352.2.bl.t.607.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{3} +(3.72153 - 2.14862i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(4.38435 + 2.53131i) q^{11} +3.37849i q^{13} -4.29725i q^{15} +(-2.39587 - 1.38326i) q^{17} +(2.35159 + 4.07308i) q^{19} +(4.18394 - 2.41560i) q^{23} +(6.73317 - 11.6622i) q^{25} -1.00000 q^{27} +2.46054 q^{29} +(-2.84882 + 4.93430i) q^{31} +(4.38435 - 2.53131i) q^{33} +(1.16765 + 2.02243i) q^{37} +(2.92586 + 1.68925i) q^{39} -5.14822i q^{41} +13.0199i q^{43} +(-3.72153 - 2.14862i) q^{45} +(2.67725 + 4.63713i) q^{47} +(-2.39587 + 1.38326i) q^{51} +(2.11185 - 3.65784i) q^{53} +21.7553 q^{55} +4.70319 q^{57} +(4.80249 - 8.31815i) q^{59} +(-3.35757 + 1.93849i) q^{61} +(7.25911 + 12.5732i) q^{65} +(-4.12524 - 2.38171i) q^{67} -4.83120i q^{69} -12.3181i q^{71} +(-9.96809 - 5.75508i) q^{73} +(-6.73317 - 11.6622i) q^{75} +(-12.0521 + 6.95830i) q^{79} +(-0.500000 + 0.866025i) q^{81} -7.32191 q^{83} -11.8884 q^{85} +(1.23027 - 2.13089i) q^{87} +(-12.1631 + 7.02239i) q^{89} +(2.84882 + 4.93430i) q^{93} +(17.5030 + 10.1054i) q^{95} -14.5716i q^{97} -5.06262i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 4 q^{9} + 24 q^{23} + 12 q^{25} - 8 q^{27} + 16 q^{29} - 16 q^{31} - 8 q^{47} - 8 q^{53} + 64 q^{55} + 24 q^{59} - 48 q^{61} + 8 q^{65} - 48 q^{67} - 48 q^{73} - 12 q^{75} - 24 q^{79} - 4 q^{81}+ \cdots + 72 q^{95}+O(q^{100}) $ 8 * q + 4 * q^3 - 4 * q^9 + 24 * q^23 + 12 * q^25 - 8 * q^27 + 16 * q^29 - 16 * q^31 - 8 * q^47 - 8 * q^53 + 64 * q^55 + 24 * q^59 - 48 * q^61 + 8 * q^65 - 48 * q^67 - 48 * q^73 - 12 * q^75 - 24 * q^79 - 4 * q^81 - 64 * q^85 + 8 * q^87 - 48 * q^89 + 16 * q^93 + 72 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times$.

$n$	$785$	$1471$	$1765$	$2257$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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			0
$2$		0			0
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	3.72153	−	2.14862i	1.66432	−	0.960894i	0.693701	−	0.720264i	$-0.255979\pi$
$5$	3.72153	−	2.14862i	1.66432	−	0.960894i	0.970617	−	0.240630i	$-0.0773542\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	4.38435	+	2.53131i	1.32193	+	0.763218i	0.984037	−	0.177966i	$-0.0569516\pi$
$11$	4.38435	+	2.53131i	1.32193	+	0.763218i	0.337896	+	0.941184i	$0.390285\pi$
$12$		0			0
$13$			3.37849i			0.937025i	0.883457	+	0.468513i	$0.155210\pi$
$13$			3.37849i			0.937025i	−0.883457	+	0.468513i	$0.844790\pi$
$14$		0			0
$15$		−	4.29725i		−	1.10954i
$16$		0			0
$17$	−2.39587	−	1.38326i	−0.581084	−	0.335489i	0.180480	−	0.983579i	$-0.442235\pi$
$17$	−2.39587	−	1.38326i	−0.581084	−	0.335489i	−0.761564	+	0.648089i	$0.775568\pi$
$18$		0			0
$19$	2.35159	+	4.07308i	0.539492	+	0.934428i	0.998931	+	0.0462188i	$0.0147172\pi$
$19$	2.35159	+	4.07308i	0.539492	+	0.934428i	−0.459439	+	0.888209i	$0.651950\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.18394	−	2.41560i	0.872412	−	0.503687i	0.00426301	−	0.999991i	$-0.498643\pi$
$23$	4.18394	−	2.41560i	0.872412	−	0.503687i	0.868149	+	0.496304i	$0.165310\pi$
$24$		0			0
$25$	6.73317	−	11.6622i	1.34663	−	2.33244i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	2.46054			0.456912			0.228456	−	0.973554i	$-0.426632\pi$
$29$	2.46054			0.456912			0.228456	+	0.973554i	$0.426632\pi$
$30$		0			0
$31$	−2.84882	+	4.93430i	−0.511663	+	0.886227i	0.488245	+	0.872706i	$0.337637\pi$
$31$	−2.84882	+	4.93430i	−0.511663	+	0.886227i	−0.999909	+	0.0135202i	$0.995696\pi$
$32$		0			0
$33$	4.38435	−	2.53131i	0.763218	−	0.440644i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.16765	+	2.02243i	0.191961	+	0.332486i	0.945900	−	0.324458i	$-0.105182\pi$
$37$	1.16765	+	2.02243i	0.191961	+	0.332486i	−0.753939	+	0.656944i	$0.771849\pi$
$38$		0			0
$39$	2.92586	+	1.68925i	0.468513	+	0.270496i
$40$		0			0
$41$		−	5.14822i		−	0.804018i	−0.915636	−	0.402009i	$-0.868312\pi$
$41$		−	5.14822i		−	0.804018i	0.915636	−	0.402009i	$-0.131688\pi$
$42$		0			0
$43$			13.0199i			1.98552i	0.120117	+	0.992760i	$0.461673\pi$
$43$			13.0199i			1.98552i	−0.120117	+	0.992760i	$0.538327\pi$
$44$		0			0
$45$	−3.72153	−	2.14862i	−0.554772	−	0.320298i
$46$		0			0
$47$	2.67725	+	4.63713i	0.390517	+	0.676395i	0.992518	−	0.122101i	$-0.0389631\pi$
$47$	2.67725	+	4.63713i	0.390517	+	0.676395i	−0.602001	+	0.798495i	$0.705630\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−2.39587	+	1.38326i	−0.335489	+	0.193695i
$52$		0			0
$53$	2.11185	−	3.65784i	0.290085	−	0.502443i	−0.683744	−	0.729722i	$-0.739650\pi$
$53$	2.11185	−	3.65784i	0.290085	−	0.502443i	0.973830	+	0.227279i	$0.0729830\pi$
$54$		0			0
$55$	21.7553			2.93349
$56$		0			0
$57$	4.70319			0.622952
$58$		0			0
$59$	4.80249	−	8.31815i	0.625231	−	1.08293i	−0.363265	−	0.931686i	$-0.618338\pi$
$59$	4.80249	−	8.31815i	0.625231	−	1.08293i	0.988496	−	0.151246i	$-0.0483285\pi$
$60$		0			0
$61$	−3.35757	+	1.93849i	−0.429892	+	0.248198i	−0.699301	−	0.714828i	$-0.746505\pi$
$61$	−3.35757	+	1.93849i	−0.429892	+	0.248198i	0.269408	+	0.963026i	$0.413172\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	7.25911	+	12.5732i	0.900382	+	1.55951i
$66$		0			0
$67$	−4.12524	−	2.38171i	−0.503978	−	0.290972i	0.226377	−	0.974040i	$-0.427312\pi$
$67$	−4.12524	−	2.38171i	−0.503978	−	0.290972i	−0.730355	+	0.683068i	$0.760645\pi$
$68$		0			0
$69$		−	4.83120i		−	0.581608i
$70$		0			0
$71$		−	12.3181i		−	1.46189i	−0.682437	−	0.730944i	$-0.739080\pi$
$71$		−	12.3181i		−	1.46189i	0.682437	−	0.730944i	$-0.260920\pi$
$72$		0			0
$73$	−9.96809	−	5.75508i	−1.16668	−	0.673581i	−0.213782	−	0.976881i	$-0.568578\pi$
$73$	−9.96809	−	5.75508i	−1.16668	−	0.673581i	−0.952895	+	0.303300i	$0.901911\pi$
$74$		0			0
$75$	−6.73317	−	11.6622i	−0.777480	−	1.34663i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−12.0521	+	6.95830i	−1.35597	+	0.782870i	−0.989078	−	0.147393i	$-0.952912\pi$
$79$	−12.0521	+	6.95830i	−1.35597	+	0.782870i	−0.366893	+	0.930263i	$0.619578\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−7.32191			−0.803685			−0.401842	−	0.915709i	$-0.631630\pi$
$83$	−7.32191			−0.803685			−0.401842	+	0.915709i	$0.631630\pi$
$84$		0			0
$85$	−11.8884			−1.28948
$86$		0			0
$87$	1.23027	−	2.13089i	0.131899	−	0.228456i
$88$		0			0
$89$	−12.1631	+	7.02239i	−1.28929	+	0.744372i	−0.978528	−	0.206116i	$-0.933918\pi$
$89$	−12.1631	+	7.02239i	−1.28929	+	0.744372i	−0.310762	+	0.950488i	$0.600584\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	2.84882	+	4.93430i	0.295409	+	0.511663i
$94$		0			0
$95$	17.5030	+	10.1054i	1.79577	+	1.03679i
$96$		0			0
$97$		−	14.5716i		−	1.47952i	−0.672868	−	0.739762i	$-0.734938\pi$
$97$		−	14.5716i		−	1.47952i	0.672868	−	0.739762i	$-0.265062\pi$
$98$		0			0
$99$		−	5.06262i		−	0.508812i
$100$		0			0
$101$	−11.3524	−	6.55434i	−1.12961	−	0.652181i	−0.185773	−	0.982593i	$-0.559479\pi$
$101$	−11.3524	−	6.55434i	−1.12961	−	0.652181i	−0.943837	+	0.330412i	$0.892812\pi$
$102$		0			0
$103$	0.104849	+	0.181604i	0.0103311	+	0.0178939i	0.871145	−	0.491026i	$-0.163378\pi$
$103$	0.104849	+	0.181604i	0.0103311	+	0.0178939i	−0.860814	+	0.508920i	$0.830045\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.56558	+	3.21329i	−0.538044	+	0.310640i	−0.744286	−	0.667861i	$-0.767210\pi$
$107$	−5.56558	+	3.21329i	−0.538044	+	0.310640i	0.206242	+	0.978501i	$0.433877\pi$
$108$		0			0
$109$	−0.470012	+	0.814084i	−0.0450190	+	0.0779751i	−0.887657	−	0.460506i	$-0.847668\pi$
$109$	−0.470012	+	0.814084i	−0.0450190	+	0.0779751i	0.842638	+	0.538481i	$0.181001\pi$
$110$		0			0
$111$	2.33530			0.221657
$112$		0			0
$113$	1.09821			0.103311			0.0516554	−	0.998665i	$-0.483550\pi$
$113$	1.09821			0.103311			0.0516554	+	0.998665i	$0.483550\pi$
$114$		0			0
$115$	10.3804	−	17.9794i	0.967980	−	1.67659i
$116$		0			0
$117$	2.92586	−	1.68925i	0.270496	−	0.156171i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	7.31504	+	12.6700i	0.665004	+	1.15182i
$122$		0			0
$123$	−4.45849	−	2.57411i	−0.402009	−	0.232100i
$124$		0			0
$125$		−	36.3820i		−	3.25411i
$126$		0			0
$127$		−	5.22625i		−	0.463755i	−0.972745	−	0.231877i	$-0.925513\pi$
$127$		−	5.22625i		−	0.463755i	0.972745	−	0.231877i	$-0.0744868\pi$
$128$		0			0
$129$	11.2756	+	6.50996i	0.992760	+	0.573170i
$130$		0			0
$131$	0.437508	+	0.757785i	0.0382252	+	0.0662080i	0.884505	−	0.466531i	$-0.154496\pi$
$131$	0.437508	+	0.757785i	0.0382252	+	0.0662080i	−0.846280	+	0.532739i	$0.821163\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−3.72153	+	2.14862i	−0.320298	+	0.184924i
$136$		0			0
$137$	−0.118419	+	0.205108i	−0.0101172	+	0.0175235i	−0.871040	−	0.491213i	$-0.836554\pi$
$137$	−0.118419	+	0.205108i	−0.0101172	+	0.0175235i	0.860922	+	0.508736i	$0.169887\pi$
$138$		0			0
$139$	3.00555			0.254927			0.127464	−	0.991843i	$-0.459316\pi$
$139$	3.00555			0.254927			0.127464	+	0.991843i	$0.459316\pi$
$140$		0			0
$141$	5.35449			0.450930
$142$		0			0
$143$	−8.55201	+	14.8125i	−0.715155	+	1.23868i
$144$		0			0
$145$	9.15698	−	5.28679i	0.760446	−	0.439044i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.40083	+	12.8186i	0.606299	+	1.05014i	0.991845	+	0.127452i	$0.0406799\pi$
$149$	7.40083	+	12.8186i	0.606299	+	1.05014i	−0.385545	+	0.922689i	$0.625987\pi$
$150$		0			0
$151$	−10.7087	−	6.18269i	−0.871464	−	0.503140i	−0.00362965	−	0.999993i	$-0.501155\pi$
$151$	−10.7087	−	6.18269i	−0.871464	−	0.503140i	−0.867835	+	0.496853i	$0.834489\pi$
$152$		0			0
$153$			2.76652i			0.223659i
$154$		0			0
$155$			24.4842i			1.96662i
$156$		0			0
$157$	−9.43153	−	5.44530i	−0.752718	−	0.434582i	0.0739569	−	0.997261i	$-0.476437\pi$
$157$	−9.43153	−	5.44530i	−0.752718	−	0.434582i	−0.826675	+	0.562679i	$0.809771\pi$
$158$		0			0
$159$	−2.11185	−	3.65784i	−0.167481	−	0.290085i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1.30791	+	0.755120i	−0.102443	+	0.0591455i	−0.550346	−	0.834937i	$-0.685504\pi$
$163$	−1.30791	+	0.755120i	−0.102443	+	0.0591455i	0.447903	+	0.894082i	$0.352171\pi$
$164$		0			0
$165$	10.8777	−	18.8407i	0.846825	−	1.46674i
$166$		0			0
$167$	−10.3333			−0.799612			−0.399806	−	0.916600i	$-0.630922\pi$
$167$	−10.3333			−0.799612			−0.399806	+	0.916600i	$0.630922\pi$
$168$		0			0
$169$	1.58579			0.121984
$170$		0			0
$171$	2.35159	−	4.07308i	0.179831	−	0.311476i
$172$		0			0
$173$	−2.90674	+	1.67821i	−0.220996	+	0.127592i	−0.606411	−	0.795151i	$-0.707391\pi$
$173$	−2.90674	+	1.67821i	−0.220996	+	0.127592i	0.385416	+	0.922743i	$0.374058\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−4.80249	−	8.31815i	−0.360977	−	0.625231i
$178$		0			0
$179$	11.4826	+	6.62946i	0.858247	+	0.495509i	0.863425	−	0.504477i	$-0.168315\pi$
$179$	11.4826	+	6.62946i	0.858247	+	0.495509i	−0.00517789	+	0.999987i	$0.501648\pi$
$180$		0			0
$181$			11.8519i			0.880946i	0.897766	+	0.440473i	$0.145189\pi$
$181$			11.8519i			0.880946i	−0.897766	+	0.440473i	$0.854811\pi$
$182$		0			0
$183$			3.87698i			0.286595i
$184$		0			0
$185$	8.69089	+	5.01769i	0.638967	+	0.368908i
$186$		0			0
$187$	−7.00290	−	12.1294i	−0.512103	−	0.886988i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.16619	−	0.673302i	0.0843828	−	0.0487184i	−0.457215	−	0.889356i	$-0.651153\pi$
$191$	1.16619	−	0.673302i	0.0843828	−	0.0487184i	0.541598	+	0.840638i	$0.317820\pi$
$192$		0			0
$193$	13.0577	−	22.6166i	0.939912	−	1.62798i	0.174281	−	0.984696i	$-0.444240\pi$
$193$	13.0577	−	22.6166i	0.939912	−	1.62798i	0.765631	−	0.643280i	$-0.222427\pi$
$194$		0			0
$195$	14.5182			1.03967
$196$		0			0
$197$	−7.49083			−0.533699			−0.266850	−	0.963738i	$-0.585983\pi$
$197$	−7.49083			−0.533699			−0.266850	+	0.963738i	$0.585983\pi$
$198$		0			0
$199$	2.24674	−	3.89147i	0.159267	−	0.275859i	−0.775337	−	0.631547i	$-0.782420\pi$
$199$	2.24674	−	3.89147i	0.159267	−	0.275859i	0.934605	+	0.355688i	$0.115753\pi$
$200$		0			0
$201$	−4.12524	+	2.38171i	−0.290972	+	0.167993i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−11.0616	−	19.1593i	−0.772576	−	1.33814i
$206$		0			0
$207$	−4.18394	−	2.41560i	−0.290804	−	0.167896i
$208$		0			0
$209$			23.8104i			1.64700i
$210$		0			0
$211$		−	5.93122i		−	0.408322i	−0.978937	−	0.204161i	$-0.934553\pi$
$211$		−	5.93122i		−	0.408322i	0.978937	−	0.204161i	$-0.0654466\pi$
$212$		0			0
$213$	−10.6678	−	6.15905i	−0.730944	−	0.422011i
$214$		0			0
$215$	27.9749	+	48.4540i	1.90787	+	3.30453i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−9.96809	+	5.75508i	−0.673581	+	0.388892i
$220$		0			0
$221$	4.67333	−	8.09444i	0.314362	−	0.544491i
$222$		0			0
$223$	−20.6163			−1.38057			−0.690286	−	0.723537i	$-0.742515\pi$
$223$	−20.6163			−1.38057			−0.690286	+	0.723537i	$0.742515\pi$
$224$		0			0
$225$	−13.4663			−0.897756
$226$		0			0
$227$	10.2455	−	17.7458i	0.680021	−	1.17783i	−0.294954	−	0.955512i	$-0.595304\pi$
$227$	10.2455	−	17.7458i	0.680021	−	1.17783i	0.974974	−	0.222318i	$-0.0713625\pi$
$228$		0			0
$229$	25.1502	−	14.5205i	1.66197	−	0.959539i	0.690197	−	0.723622i	$-0.257524\pi$
$229$	25.1502	−	14.5205i	1.66197	−	0.959539i	0.971773	−	0.235917i	$-0.0758095\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−8.86819	−	15.3602i	−0.580975	−	1.00628i	−0.995364	−	0.0961779i	$-0.969338\pi$
$233$	−8.86819	−	15.3602i	−0.580975	−	1.00628i	0.414390	−	0.910100i	$-0.363995\pi$
$234$		0			0
$235$	19.9269	+	11.5048i	1.29989	+	0.750490i
$236$		0			0
$237$			13.9166i			0.903981i
$238$		0			0
$239$			20.4248i			1.32117i	0.750750	+	0.660586i	$0.229692\pi$
$239$			20.4248i			1.32117i	−0.750750	+	0.660586i	$0.770308\pi$
$240$		0			0
$241$	2.82101	+	1.62871i	0.181717	+	0.104915i	0.588099	−	0.808789i	$-0.299876\pi$
$241$	2.82101	+	1.62871i	0.181717	+	0.104915i	−0.406382	+	0.913703i	$0.633210\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−13.7609	+	7.94484i	−0.875583	+	0.505518i
$248$		0			0
$249$	−3.66096	+	6.34096i	−0.232004	+	0.401842i
$250$		0			0
$251$	−3.95633			−0.249721			−0.124861	−	0.992174i	$-0.539848\pi$
$251$	−3.95633			−0.249721			−0.124861	+	0.992174i	$0.539848\pi$
$252$		0			0
$253$	24.4585			1.53769
$254$		0			0
$255$	−5.94420	+	10.2957i	−0.372240	+	0.644739i
$256$		0			0
$257$	4.45849	−	2.57411i	0.278113	−	0.160569i	−0.354456	−	0.935073i	$-0.615334\pi$
$257$	4.45849	−	2.57411i	0.278113	−	0.160569i	0.632569	+	0.774504i	$0.282001\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−1.23027	−	2.13089i	−0.0761519	−	0.131899i
$262$		0			0
$263$	0.0679848	+	0.0392511i	0.00419212	+	0.00242032i	0.502095	−	0.864813i	$-0.332563\pi$
$263$	0.0679848	+	0.0392511i	0.00419212	+	0.00242032i	−0.497902	+	0.867233i	$0.665896\pi$
$264$		0			0
$265$		−	18.1503i		−	1.11497i
$266$		0			0
$267$			14.0448i			0.859527i
$268$		0			0
$269$	−0.764956	−	0.441648i	−0.0466402	−	0.0269277i	0.476499	−	0.879175i	$-0.341906\pi$
$269$	−0.764956	−	0.441648i	−0.0466402	−	0.0269277i	−0.523139	+	0.852247i	$0.675239\pi$
$270$		0			0
$271$	−9.65421	−	16.7216i	−0.586451	−	1.01576i	−0.994693	−	0.102890i	$-0.967191\pi$
$271$	−9.65421	−	16.7216i	−0.586451	−	1.01576i	0.408241	−	0.912874i	$-0.366142\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	59.0412	−	34.0875i	3.56032	−	2.05555i
$276$		0			0
$277$	−8.46635	+	14.6641i	−0.508694	+	0.881083i	0.491256	+	0.871015i	$0.336538\pi$
$277$	−8.46635	+	14.6641i	−0.508694	+	0.881083i	−0.999949	+	0.0100677i	$0.996795\pi$
$278$		0			0
$279$	5.69764			0.341109
$280$		0			0
$281$	5.05417			0.301507			0.150753	−	0.988571i	$-0.451830\pi$
$281$	5.05417			0.301507			0.150753	+	0.988571i	$0.451830\pi$
$282$		0			0
$283$	−9.55781	+	16.5546i	−0.568153	+	0.984069i	0.428596	+	0.903496i	$0.359008\pi$
$283$	−9.55781	+	16.5546i	−0.568153	+	0.984069i	−0.996749	+	0.0805731i	$0.974325\pi$
$284$		0			0
$285$	17.5030	−	10.1054i	1.03679	−	0.598591i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−4.67320	−	8.09421i	−0.274894	−	0.476130i
$290$		0			0
$291$	−12.6194	−	7.28581i	−0.739762	−	0.427102i
$292$		0			0
$293$		−	2.37837i		−	0.138946i	−0.997584	−	0.0694730i	$-0.977868\pi$
$293$		−	2.37837i		−	0.138946i	0.997584	−	0.0694730i	$-0.0221318\pi$
$294$		0			0
$295$		−	41.2750i		−	2.40312i
$296$		0			0
$297$	−4.38435	−	2.53131i	−0.254406	−	0.146881i
$298$		0			0
$299$	8.16109	+	14.1354i	0.471968	+	0.817472i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−11.3524	+	6.55434i	−0.652181	+	0.376537i
$304$		0			0
$305$	−8.33018	+	14.4283i	−0.476985	+	0.826162i
$306$		0			0
$307$	−4.89599			−0.279429			−0.139714	−	0.990192i	$-0.544618\pi$
$307$	−4.89599			−0.279429			−0.139714	+	0.990192i	$0.544618\pi$
$308$		0			0
$309$	0.209698			0.0119293
$310$		0			0
$311$	5.24000	−	9.07594i	0.297133	−	0.514649i	−0.678346	−	0.734743i	$-0.737303\pi$
$311$	5.24000	−	9.07594i	0.297133	−	0.514649i	0.975479	+	0.220093i	$0.0706362\pi$
$312$		0			0
$313$	8.31534	−	4.80086i	0.470011	−	0.271361i	−0.246234	−	0.969211i	$-0.579193\pi$
$313$	8.31534	−	4.80086i	0.470011	−	0.271361i	0.716244	+	0.697850i	$0.245860\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	8.39672	+	14.5435i	0.471607	+	0.816847i	0.999472	−	0.0324809i	$-0.0103408\pi$
$317$	8.39672	+	14.5435i	0.471607	+	0.816847i	−0.527865	+	0.849328i	$0.677007\pi$
$318$		0			0
$319$	10.7879	+	6.22840i	0.604006	+	0.348723i
$320$		0			0
$321$			6.42657i			0.358696i
$322$		0			0
$323$		−	13.0114i		−	0.723976i
$324$		0			0
$325$	39.4007	+	22.7480i	2.18556	+	1.26183i
$326$		0			0
$327$	0.470012	+	0.814084i	0.0259917	+	0.0450190i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	23.2409	−	13.4181i	1.27743	−	0.737526i	0.301057	−	0.953606i	$-0.402660\pi$
$331$	23.2409	−	13.4181i	1.27743	−	0.737526i	0.976376	+	0.216080i	$0.0693271\pi$
$332$		0			0
$333$	1.16765	−	2.02243i	0.0639869	−	0.110829i
$334$		0			0
$335$	−20.4696			−1.11837
$336$		0			0
$337$	23.0827			1.25739			0.628697	−	0.777651i	$-0.283589\pi$
$337$	23.0827			1.25739			0.628697	+	0.777651i	$0.283589\pi$
$338$		0			0
$339$	0.549104	−	0.951076i	0.0298232	−	0.0516554i
$340$		0			0
$341$	−24.9805	+	14.4225i	−1.35277	+	0.781021i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−10.3804	−	17.9794i	−0.558864	−	0.967980i
$346$		0			0
$347$	1.13181	+	0.653449i	0.0607586	+	0.0350790i	0.530072	−	0.847953i	$-0.322165\pi$
$347$	1.13181	+	0.653449i	0.0607586	+	0.0350790i	−0.469313	+	0.883032i	$0.655498\pi$
$348$		0			0
$349$			26.5489i			1.42113i	0.703633	+	0.710564i	$0.251560\pi$
$349$			26.5489i			1.42113i	−0.703633	+	0.710564i	$0.748440\pi$
$350$		0			0
$351$		−	3.37849i		−	0.180331i
$352$		0			0
$353$	−14.6266	−	8.44466i	−0.778494	−	0.449464i	0.0574020	−	0.998351i	$-0.481718\pi$
$353$	−14.6266	−	8.44466i	−0.778494	−	0.449464i	−0.835896	+	0.548887i	$0.815052\pi$
$354$		0			0
$355$	−26.4670	−	45.8421i	−1.40472	−	2.43305i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−29.0899	+	16.7950i	−1.53530	+	0.886408i	−0.536200	+	0.844091i	$0.680141\pi$
$359$	−29.0899	+	16.7950i	−1.53530	+	0.886408i	−0.999104	+	0.0423171i	$0.986526\pi$
$360$		0			0
$361$	−1.55998	+	2.70196i	−0.0821040	+	0.142208i
$362$		0			0
$363$	14.6301			0.767880
$364$		0			0
$365$	−49.4620			−2.58896
$366$		0			0
$367$	−3.67989	+	6.37376i	−0.192089	+	0.332708i	−0.945942	−	0.324335i	$-0.894859\pi$
$367$	−3.67989	+	6.37376i	−0.192089	+	0.332708i	0.753854	+	0.657043i	$0.228193\pi$
$368$		0			0
$369$	−4.45849	+	2.57411i	−0.232100	+	0.134003i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−1.81504	−	3.14374i	−0.0939791	−	0.162777i	0.815203	−	0.579175i	$-0.196625\pi$
$373$	−1.81504	−	3.14374i	−0.0939791	−	0.162777i	−0.909182	+	0.416399i	$0.863292\pi$
$374$		0			0
$375$	−31.5077	−	18.1910i	−1.62705	−	0.939379i
$376$		0			0
$377$			8.31293i			0.428138i
$378$		0			0
$379$		−	13.6647i		−	0.701908i	−0.936393	−	0.350954i	$-0.885857\pi$
$379$		−	13.6647i		−	0.701908i	0.936393	−	0.350954i	$-0.114143\pi$
$380$		0			0
$381$	−4.52607	−	2.61313i	−0.231877	−	0.133874i
$382$		0			0
$383$	−6.82843	−	11.8272i	−0.348916	−	0.604341i	0.637141	−	0.770747i	$-0.280117\pi$
$383$	−6.82843	−	11.8272i	−0.348916	−	0.604341i	−0.986057	+	0.166407i	$0.946784\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	11.2756	−	6.50996i	0.573170	−	0.330920i
$388$		0			0
$389$	−13.4540	+	23.3030i	−0.682144	+	1.18151i	0.292181	+	0.956363i	$0.405619\pi$
$389$	−13.4540	+	23.3030i	−0.682144	+	1.18151i	−0.974325	+	0.225145i	$0.927714\pi$
$390$		0			0
$391$	−13.3656			−0.675927
$392$		0			0
$393$	0.875015			0.0441387
$394$		0			0
$395$	−29.9016	+	51.7910i	−1.50451	+	2.60589i
$396$		0			0
$397$	−31.8041	+	18.3621i	−1.59620	+	0.921568i	−0.603994	+	0.796989i	$0.706425\pi$
$397$	−31.8041	+	18.3621i	−1.59620	+	0.921568i	−0.992210	+	0.124579i	$0.960242\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	13.8408	+	23.9730i	0.691176	+	1.19715i	0.971453	+	0.237233i	$0.0762405\pi$
$401$	13.8408	+	23.9730i	0.691176	+	1.19715i	−0.280276	+	0.959919i	$0.590426\pi$
$402$		0			0
$403$	−16.6705	−	9.62472i	−0.830417	−	0.479441i
$404$		0			0
$405$			4.29725i			0.213532i
$406$		0			0
$407$			11.8227i			0.586032i
$408$		0			0
$409$	7.29903	+	4.21410i	0.360914	+	0.208374i	0.669482	−	0.742829i	$-0.266516\pi$
$409$	7.29903	+	4.21410i	0.360914	+	0.208374i	−0.308568	+	0.951202i	$0.599850\pi$
$410$		0			0
$411$	0.118419	+	0.205108i	0.00584118	+	0.0101172i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−27.2487	+	15.7320i	−1.33759	+	0.772256i
$416$		0			0
$417$	1.50277	−	2.60288i	0.0735911	−	0.127464i
$418$		0			0
$419$	18.3029			0.894154			0.447077	−	0.894495i	$-0.352465\pi$
$419$	18.3029			0.894154			0.447077	+	0.894495i	$0.352465\pi$
$420$		0			0
$421$	22.6274			1.10279			0.551396	−	0.834243i	$-0.314095\pi$
$421$	22.6274			1.10279			0.551396	+	0.834243i	$0.314095\pi$
$422$		0			0
$423$	2.67725	−	4.63713i	0.130172	−	0.225465i
$424$		0			0
$425$	−32.2636	+	18.6274i	−1.56502	+	0.903563i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	8.55201	+	14.8125i	0.412895	+	0.715155i
$430$		0			0
$431$	−3.85300	−	2.22453i	−0.185592	−	0.107152i	0.404325	−	0.914615i	$-0.367506\pi$
$431$	−3.85300	−	2.22453i	−0.185592	−	0.107152i	−0.589918	+	0.807464i	$0.700840\pi$
$432$		0			0
$433$		−	1.66205i		−	0.0798730i	−0.999202	−	0.0399365i	$-0.987284\pi$
$433$		−	1.66205i		−	0.0798730i	0.999202	−	0.0399365i	$-0.0127156\pi$
$434$		0			0
$435$		−	10.5736i		−	0.506964i
$436$		0			0
$437$	19.6779	+	11.3610i	0.941319	+	0.543471i
$438$		0			0
$439$	9.37753	+	16.2424i	0.447565	+	0.775206i	0.998227	−	0.0595229i	$-0.0189579\pi$
$439$	9.37753	+	16.2424i	0.447565	+	0.775206i	−0.550662	+	0.834728i	$0.685625\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	28.6060	−	16.5157i	1.35911	−	0.784684i	0.369609	−	0.929187i	$-0.379492\pi$
$443$	28.6060	−	16.5157i	1.35911	−	0.784684i	0.989504	+	0.144503i	$0.0461584\pi$
$444$		0			0
$445$	−30.1770	+	52.2680i	−1.43053	+	2.47774i
$446$		0			0
$447$	14.8017			0.700094
$448$		0			0
$449$	9.29441			0.438630			0.219315	−	0.975654i	$-0.429618\pi$
$449$	9.29441			0.438630			0.219315	+	0.975654i	$0.429618\pi$
$450$		0			0
$451$	13.0317	−	22.5716i	0.613641	−	1.06286i
$452$		0			0
$453$	−10.7087	+	6.18269i	−0.503140	+	0.290488i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	13.7224	+	23.7679i	0.641906	+	1.11181i	0.985007	+	0.172515i	$0.0551893\pi$
$457$	13.7224	+	23.7679i	0.641906	+	1.11181i	−0.343101	+	0.939298i	$0.611477\pi$
$458$		0			0
$459$	2.39587	+	1.38326i	0.111830	+	0.0645649i
$460$		0			0
$461$		−	4.28209i		−	0.199437i	−0.995016	−	0.0997183i	$-0.968206\pi$
$461$		−	4.28209i		−	0.199437i	0.995016	−	0.0997183i	$-0.0317942\pi$
$462$		0			0
$463$			16.1278i			0.749521i	0.927122	+	0.374760i	$0.122275\pi$
$463$			16.1278i			0.749521i	−0.927122	+	0.374760i	$0.877725\pi$
$464$		0			0
$465$	21.2039	+	12.2421i	0.983308	+	0.567713i
$466$		0			0
$467$	13.7702	+	23.8506i	0.637207	+	1.10368i	0.986043	+	0.166491i	$0.0532438\pi$
$467$	13.7702	+	23.8506i	0.637207	+	1.10368i	−0.348836	+	0.937184i	$0.613423\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−9.43153	+	5.44530i	−0.434582	+	0.250906i
$472$		0			0
$473$	−32.9574	+	57.0839i	−1.51538	+	2.62472i
$474$		0			0
$475$	63.3347			2.90600
$476$		0			0
$477$	−4.22371			−0.193390
$478$		0			0
$479$	−9.77545	+	16.9316i	−0.446652	+	0.773624i	−0.998166	−	0.0605420i	$-0.980717\pi$
$479$	−9.77545	+	16.9316i	−0.446652	+	0.773624i	0.551514	+	0.834166i	$0.314050\pi$
$480$		0			0
$481$	−6.83277	+	3.94490i	−0.311548	+	0.179872i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−31.3089	−	54.2287i	−1.42167	−	2.46240i
$486$		0			0
$487$	−32.7285	−	18.8958i	−1.48307	−	0.856252i	−0.483257	−	0.875479i	$-0.660546\pi$
$487$	−32.7285	−	18.8958i	−1.48307	−	0.856252i	−0.999815	+	0.0192268i	$0.993880\pi$
$488$		0			0
$489$			1.51024i			0.0682954i
$490$		0			0
$491$			29.2605i			1.32051i	0.751042	+	0.660254i	$0.229551\pi$
$491$			29.2605i			1.32051i	−0.751042	+	0.660254i	$0.770449\pi$
$492$		0			0
$493$	−5.89515	−	3.40357i	−0.265504	−	0.153289i
$494$		0			0
$495$	−10.8777	−	18.8407i	−0.488914	−	0.846825i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	10.9485	−	6.32111i	0.490122	−	0.282972i	−0.234503	−	0.972115i	$-0.575346\pi$
$499$	10.9485	−	6.32111i	0.490122	−	0.282972i	0.724625	+	0.689143i	$0.242013\pi$
$500$		0			0
$501$	−5.16663	+	8.94887i	−0.230828	+	0.399806i
$502$		0			0
$503$	−27.0714			−1.20706			−0.603528	−	0.797342i	$-0.706239\pi$
$503$	−27.0714			−1.20706			−0.603528	+	0.797342i	$0.706239\pi$
$504$		0			0
$505$	−56.3312			−2.50671
$506$		0			0
$507$	0.792893	−	1.37333i	0.0352136	−	0.0609918i
$508$		0			0
$509$	−10.1311	+	5.84917i	−0.449051	+	0.259260i	−0.707429	−	0.706784i	$-0.750145\pi$
$509$	−10.1311	+	5.84917i	−0.449051	+	0.259260i	0.258378	+	0.966044i	$0.416812\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−2.35159	−	4.07308i	−0.103825	−	0.179831i
$514$		0			0
$515$	0.780396	+	0.450562i	0.0343884	+	0.0198541i
$516$		0			0
$517$			27.1077i			1.19220i
$518$		0			0
$519$			3.35642i			0.147330i
$520$		0			0
$521$	−6.24095	−	3.60322i	−0.273421	−	0.157860i	0.357020	−	0.934097i	$-0.383793\pi$
$521$	−6.24095	−	3.60322i	−0.273421	−	0.157860i	−0.630441	+	0.776237i	$0.717126\pi$
$522$		0			0
$523$	−8.85727	−	15.3412i	−0.387301	−	0.670825i	0.604784	−	0.796389i	$-0.293259\pi$
$523$	−8.85727	−	15.3412i	−0.387301	−	0.670825i	−0.992086	+	0.125564i	$0.959926\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	13.6508	−	7.88130i	0.594639	−	0.343315i
$528$		0			0
$529$	0.170243	−	0.294869i	0.00740185	−	0.0128204i
$530$		0			0
$531$	−9.60498			−0.416821
$532$		0			0
$533$	17.3932			0.753385
$534$		0			0
$535$	−13.8083	+	23.9167i	−0.596984	+	1.03401i
$536$		0			0
$537$	11.4826	−	6.62946i	0.495509	−	0.286082i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−11.5590	−	20.0208i	−0.496961	−	0.860761i	0.503033	−	0.864267i	$-0.332217\pi$
$541$	−11.5590	−	20.0208i	−0.496961	−	0.860761i	−0.999994	+	0.00350600i	$0.998884\pi$
$542$		0			0
$543$	10.2641	+	5.92596i	0.440473	+	0.254307i
$544$		0			0
$545$			4.03951i			0.173034i
$546$		0			0
$547$		−	16.0524i		−	0.686351i	−0.939271	−	0.343176i	$-0.888497\pi$
$547$		−	16.0524i		−	0.686351i	0.939271	−	0.343176i	$-0.111503\pi$
$548$		0			0
$549$	3.35757	+	1.93849i	0.143297	+	0.0827328i
$550$		0			0
$551$	5.78620	+	10.0220i	0.246500	+	0.426951i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	8.69089	−	5.01769i	0.368908	−	0.212989i
$556$		0			0
$557$	6.29041	−	10.8953i	0.266533	−	0.461649i	−0.701431	−	0.712738i	$-0.747455\pi$
$557$	6.29041	−	10.8953i	0.266533	−	0.461649i	0.967964	+	0.251088i	$0.0807884\pi$
$558$		0			0
$559$	−43.9877			−1.86048
$560$		0			0
$561$	−14.0058			−0.591325
$562$		0			0
$563$	18.2974	−	31.6921i	0.771144	−	1.33566i	−0.165792	−	0.986161i	$-0.553018\pi$
$563$	18.2974	−	31.6921i	0.771144	−	1.33566i	0.936936	−	0.349500i	$-0.113649\pi$
$564$		0			0
$565$	4.08701	−	2.35964i	0.171942	−	0.0992707i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	12.2495	+	21.2167i	0.513524	+	0.889450i	0.999877	+	0.0156875i	$0.00499368\pi$
$569$	12.2495	+	21.2167i	0.513524	+	0.889450i	−0.486353	+	0.873763i	$0.661673\pi$
$570$		0			0
$571$	−28.3990	−	16.3962i	−1.18846	−	0.686159i	−0.230506	−	0.973071i	$-0.574038\pi$
$571$	−28.3990	−	16.3962i	−1.18846	−	0.686159i	−0.957957	+	0.286912i	$0.907371\pi$
$572$		0			0
$573$		−	1.34660i		−	0.0562552i
$574$		0			0
$575$		−	65.0586i		−	2.71313i
$576$		0			0
$577$	−16.6398	−	9.60699i	−0.692724	−	0.399944i	0.111908	−	0.993719i	$-0.464304\pi$
$577$	−16.6398	−	9.60699i	−0.692724	−	0.399944i	−0.804632	+	0.593774i	$0.797637\pi$
$578$		0			0
$579$	−13.0577	−	22.6166i	−0.542659	−	0.939912i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	18.5182	−	10.6915i	0.766946	−	0.442797i
$584$		0			0
$585$	7.25911	−	12.5732i	0.300127	−	0.519836i
$586$		0			0
$587$	−24.1451			−0.996573			−0.498286	−	0.867012i	$-0.666037\pi$
$587$	−24.1451			−0.996573			−0.498286	+	0.867012i	$0.666037\pi$
$588$		0			0
$589$	−26.7971			−1.10415
$590$		0			0
$591$	−3.74541	+	6.48725i	−0.154066	+	0.266850i
$592$		0			0
$593$	−2.20475	+	1.27291i	−0.0905380	+	0.0522722i	−0.544585	−	0.838705i	$-0.683313\pi$
$593$	−2.20475	+	1.27291i	−0.0905380	+	0.0522722i	0.454047	+	0.890978i	$0.349980\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−2.24674	−	3.89147i	−0.0919531	−	0.159267i
$598$		0			0
$599$	−12.9816	−	7.49493i	−0.530414	−	0.306234i	0.210771	−	0.977535i	$-0.432402\pi$
$599$	−12.9816	−	7.49493i	−0.530414	−	0.306234i	−0.741185	+	0.671301i	$0.765736\pi$
$600$		0			0
$601$			24.3343i			0.992618i	0.868146	+	0.496309i	$0.165312\pi$
$601$			24.3343i			0.992618i	−0.868146	+	0.496309i	$0.834688\pi$
$602$		0			0
$603$			4.76342i			0.193981i
$604$		0			0
$605$	54.4462	+	31.4345i	2.21355	+	1.27800i
$606$		0			0
$607$	4.45644	+	7.71878i	0.180881	+	0.313296i	0.942181	−	0.335105i	$-0.108772\pi$
$607$	4.45644	+	7.71878i	0.180881	+	0.313296i	−0.761300	+	0.648400i	$0.775438\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−15.6665	+	9.04506i	−0.633799	+	0.365924i
$612$		0			0
$613$	8.58741	−	14.8738i	0.346842	−	0.600748i	−0.638844	−	0.769336i	$-0.720587\pi$
$613$	8.58741	−	14.8738i	0.346842	−	0.600748i	0.985687	+	0.168588i	$0.0539206\pi$
$614$		0			0
$615$	−22.1232			−0.892094
$616$		0			0
$617$	35.9980			1.44922			0.724612	−	0.689157i	$-0.242019\pi$
$617$	35.9980			1.44922			0.724612	+	0.689157i	$0.242019\pi$
$618$		0			0
$619$	−2.05562	+	3.56043i	−0.0826222	+	0.143106i	−0.904376	−	0.426738i	$-0.859663\pi$
$619$	−2.05562	+	3.56043i	−0.0826222	+	0.143106i	0.821753	+	0.569843i	$0.192996\pi$
$620$		0			0
$621$	−4.18394	+	2.41560i	−0.167896	+	0.0969347i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−44.5054	−	77.0856i	−1.78022	−	3.08342i
$626$		0			0
$627$	20.6204	+	11.9052i	0.823501	+	0.475448i
$628$		0			0
$629$		−	6.46065i		−	0.257603i
$630$		0			0
$631$			34.8970i			1.38923i	0.719383	+	0.694613i	$0.244425\pi$
$631$			34.8970i			1.38923i	−0.719383	+	0.694613i	$0.755575\pi$
$632$		0			0
$633$	−5.13659	−	2.96561i	−0.204161	−	0.117872i
$634$		0			0
$635$	−11.2293	−	19.4496i	−0.445619	−	0.771835i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−10.6678	+	6.15905i	−0.422011	+	0.243648i
$640$		0			0
$641$	−3.66368	+	6.34567i	−0.144707	+	0.250639i	−0.929263	−	0.369418i	$-0.879557\pi$
$641$	−3.66368	+	6.34567i	−0.144707	+	0.250639i	0.784557	+	0.620057i	$0.212890\pi$
$642$		0			0
$643$	−9.24275			−0.364498			−0.182249	−	0.983252i	$-0.558338\pi$
$643$	−9.24275			−0.364498			−0.182249	+	0.983252i	$0.558338\pi$
$644$		0			0
$645$	55.9498			2.20302
$646$		0			0
$647$	−7.59013	+	13.1465i	−0.298399	+	0.516842i	−0.975770	−	0.218800i	$-0.929786\pi$
$647$	−7.59013	+	13.1465i	−0.298399	+	0.516842i	0.677371	+	0.735642i	$0.263119\pi$
$648$		0			0
$649$	42.1116	−	24.3132i	1.65303	−	0.954375i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.06425	+	1.84333i	0.0416471	+	0.0721349i	0.886098	−	0.463499i	$-0.153406\pi$
$653$	1.06425	+	1.84333i	0.0416471	+	0.0721349i	−0.844450	+	0.535634i	$0.820073\pi$
$654$		0			0
$655$	3.25639	+	1.88008i	0.127238	+	0.0734608i
$656$		0			0
$657$			11.5102i			0.449054i
$658$		0			0
$659$		−	13.0520i		−	0.508436i	−0.967147	−	0.254218i	$-0.918182\pi$
$659$		−	13.0520i		−	0.508436i	0.967147	−	0.254218i	$-0.0818180\pi$
$660$		0			0
$661$	−16.6958	−	9.63931i	−0.649390	−	0.374926i	0.138832	−	0.990316i	$-0.455665\pi$
$661$	−16.6958	−	9.63931i	−0.649390	−	0.374926i	−0.788223	+	0.615390i	$0.788998\pi$
$662$		0			0
$663$	−4.67333	−	8.09444i	−0.181497	−	0.314362i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	10.2948	−	5.94369i	0.398615	−	0.230141i
$668$		0			0
$669$	−10.3082	+	17.8543i	−0.398537	+	0.690286i
$670$		0			0
$671$	−19.6277			−0.757718
$672$		0			0
$673$	−7.08216			−0.272997			−0.136499	−	0.990640i	$-0.543585\pi$
$673$	−7.08216			−0.272997			−0.136499	+	0.990640i	$0.543585\pi$
$674$		0			0
$675$	−6.73317	+	11.6622i	−0.259160	+	0.448878i
$676$		0			0
$677$	31.6135	−	18.2521i	1.21501	−	0.701485i	0.251161	−	0.967945i	$-0.419188\pi$
$677$	31.6135	−	18.2521i	1.21501	−	0.701485i	0.963846	+	0.266461i	$0.0858542\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−10.2455	−	17.7458i	−0.392610	−	0.680021i
$682$		0			0
$683$	26.0852	+	15.0603i	0.998124	+	0.576267i	0.907693	−	0.419636i	$-0.137842\pi$
$683$	26.0852	+	15.0603i	0.998124	+	0.576267i	0.0904313	+	0.995903i	$0.471175\pi$
$684$		0			0
$685$			1.01775i			0.0388863i
$686$		0			0
$687$		−	29.0409i		−	1.10798i
$688$		0			0
$689$	12.3580	+	7.13488i	0.470801	+	0.271817i
$690$		0			0
$691$	19.9057	+	34.4776i	0.757247	+	1.31159i	0.944249	+	0.329231i	$0.106789\pi$
$691$	19.9057	+	34.4776i	0.757247	+	1.31159i	−0.187002	+	0.982359i	$0.559877\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	11.1852	−	6.45779i	0.424280	−	0.244958i
$696$		0			0
$697$	−7.12132	+	12.3345i	−0.269739	+	0.467202i
$698$		0			0
$699$	−17.7364			−0.670852
$700$		0			0
$701$	28.0795			1.06055			0.530275	−	0.847826i	$-0.322089\pi$
$701$	28.0795			1.06055			0.530275	+	0.847826i	$0.322089\pi$
$702$		0			0
$703$	−5.49168	+	9.51187i	−0.207123	+	0.358747i
$704$		0			0
$705$	19.9269	−	11.5048i	0.750490	−	0.433296i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	18.4738	+	31.9975i	0.693797	+	1.20169i	0.970585	+	0.240761i	$0.0773969\pi$
$709$	18.4738	+	31.9975i	0.693797	+	1.20169i	−0.276787	+	0.960931i	$0.589270\pi$
$710$		0			0
$711$	12.0521	+	6.95830i	0.451990	+	0.260957i
$712$		0			0
$713$			27.5264i			1.03087i
$714$		0			0
$715$			73.5002i			2.74875i
$716$		0			0
$717$	17.6884	+	10.2124i	0.660586	+	0.381389i
$718$		0			0
$719$	9.35449	+	16.2025i	0.348864	+	0.604250i	0.986048	−	0.166462i	$-0.0532343\pi$
$719$	9.35449	+	16.2025i	0.348864	+	0.604250i	−0.637184	+	0.770712i	$0.719901\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	2.82101	−	1.62871i	0.104915	−	0.0605724i
$724$		0			0
$725$	16.5673	−	28.6954i	0.615293	−	1.06572i
$726$		0			0
$727$	31.2078			1.15743			0.578716	−	0.815529i	$-0.303554\pi$
$727$	31.2078			1.15743			0.578716	+	0.815529i	$0.303554\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	18.0099	−	31.1941i	0.666120	−	1.15375i
$732$		0			0
$733$	−3.52383	+	2.03449i	−0.130156	+	0.0751455i	−0.563664	−	0.826004i	$-0.690609\pi$
$733$	−3.52383	+	2.03449i	−0.130156	+	0.0751455i	0.433508	+	0.901150i	$0.357275\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.0577	−	20.8845i	−0.444150	−	0.769291i
$738$		0			0
$739$	−34.5566	−	19.9513i	−1.27119	−	0.733919i	−0.295974	−	0.955196i	$-0.595644\pi$
$739$	−34.5566	−	19.9513i	−1.27119	−	0.733919i	−0.975211	+	0.221277i	$0.928978\pi$
$740$		0			0
$741$			15.8897i			0.583722i
$742$		0			0
$743$			41.7530i			1.53177i	0.642979	+	0.765884i	$0.277698\pi$
$743$			41.7530i			1.53177i	−0.642979	+	0.765884i	$0.722302\pi$
$744$		0			0
$745$	55.0847	+	31.8032i	2.01815	+	1.16518i
$746$		0			0
$747$	3.66096	+	6.34096i	0.133947	+	0.232004i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−7.88020	+	4.54963i	−0.287552	+	0.166019i	−0.636838	−	0.770998i	$-0.719758\pi$
$751$	−7.88020	+	4.54963i	−0.287552	+	0.166019i	0.349285	+	0.937017i	$0.386424\pi$
$752$		0			0
$753$	−1.97816	+	3.42628i	−0.0720883	+	0.124861i
$754$		0			0
$755$	−53.1371			−1.93386
$756$		0			0
$757$	−0.902155			−0.0327894			−0.0163947	−	0.999866i	$-0.505219\pi$
$757$	−0.902155			−0.0327894			−0.0163947	+	0.999866i	$0.505219\pi$
$758$		0			0
$759$	12.2293	−	21.1817i	0.443894	−	0.768847i
$760$		0			0
$761$	20.5924	−	11.8891i	0.746475	−	0.430978i	−0.0779436	−	0.996958i	$-0.524835\pi$
$761$	20.5924	−	11.8891i	0.746475	−	0.430978i	0.824419	+	0.565980i	$0.191502\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	5.94420	+	10.2957i	0.214913	+	0.372240i
$766$		0			0
$767$	28.1028	+	16.2252i	1.01473	+	0.585857i
$768$		0			0
$769$			16.3028i			0.587895i	0.955822	+	0.293948i	$0.0949691\pi$
$769$			16.3028i			0.587895i	−0.955822	+	0.293948i	$0.905031\pi$
$770$		0			0
$771$		−	5.14822i		−	0.185409i
$772$		0			0
$773$	−21.7270	−	12.5441i	−0.781465	−	0.451179i	0.0554845	−	0.998460i	$-0.482330\pi$
$773$	−21.7270	−	12.5441i	−0.781465	−	0.451179i	−0.836949	+	0.547281i	$0.815663\pi$
$774$		0			0
$775$	38.3632	+	66.4470i	1.37805	+	2.38685i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	20.9691	−	12.1065i	0.751297	−	0.433761i
$780$		0			0
$781$	31.1809	−	54.0069i	1.11574	−	1.93252i
$782$		0			0
$783$	−2.46054			−0.0879327
$784$		0			0
$785$	−46.7996			−1.67035
$786$		0			0
$787$	−2.23565	+	3.87226i	−0.0796924	+	0.138031i	−0.903117	−	0.429394i	$-0.858727\pi$
$787$	−2.23565	+	3.87226i	−0.0796924	+	0.138031i	0.823425	+	0.567425i	$0.192060\pi$
$788$		0			0
$789$	0.0679848	−	0.0392511i	0.00242032	−	0.00139737i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−6.54918	−	11.3435i	−0.232568	−	0.402820i
$794$		0			0
$795$	−15.7186	−	9.07516i	−0.557483	−	0.321863i
$796$		0			0
$797$			6.62320i			0.234606i	0.993096	+	0.117303i	$0.0374248\pi$
$797$			6.62320i			0.234606i	−0.993096	+	0.117303i	$0.962575\pi$
$798$		0			0
$799$		−	14.8133i		−	0.524056i
$800$		0			0
$801$	12.1631	+	7.02239i	0.429763	+	0.248124i
$802$		0			0
$803$	−29.1358	−	50.4646i	−1.02818	−	1.78086i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.764956	+	0.441648i	−0.0269277	+	0.0155467i
$808$		0			0
$809$	4.18522	−	7.24901i	0.147144	−	0.254862i	−0.783027	−	0.621988i	$-0.786325\pi$
$809$	4.18522	−	7.24901i	0.147144	−	0.254862i	0.930171	+	0.367127i	$0.119658\pi$
$810$		0			0
$811$	1.20944			0.0424692			0.0212346	−	0.999775i	$-0.493240\pi$
$811$	1.20944			0.0424692			0.0212346	+	0.999775i	$0.493240\pi$
$812$		0			0
$813$	−19.3084			−0.677176
$814$		0			0
$815$	−3.24494	+	5.62040i	−0.113665	+	0.196874i
$816$		0			0
$817$	−53.0312	+	30.6176i	−1.85533	+	1.07117i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−25.6260	−	44.3855i	−0.894353	−	1.54906i	−0.834604	−	0.550851i	$-0.814303\pi$
$821$	−25.6260	−	44.3855i	−0.894353	−	1.54906i	−0.0597490	−	0.998213i	$-0.519030\pi$
$822$		0			0
$823$	27.3271	+	15.7773i	0.952563	+	0.549962i	0.893876	−	0.448314i	$-0.147975\pi$
$823$	27.3271	+	15.7773i	0.952563	+	0.549962i	0.0586866	+	0.998276i	$0.481309\pi$
$824$		0			0
$825$		−	68.1749i		−	2.37355i
$826$		0			0
$827$			23.4800i			0.816480i	0.912875	+	0.408240i	$0.133857\pi$
$827$			23.4800i			0.816480i	−0.912875	+	0.408240i	$0.866143\pi$
$828$		0			0
$829$	−14.9510	−	8.63194i	−0.519268	−	0.299800i	0.217367	−	0.976090i	$-0.430253\pi$
$829$	−14.9510	−	8.63194i	−0.519268	−	0.299800i	−0.736635	+	0.676290i	$0.763587\pi$
$830$		0			0
$831$	8.46635	+	14.6641i	0.293694	+	0.508694i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−38.4555	+	22.2023i	−1.33081	+	0.768342i
$836$		0			0
$837$	2.84882	−	4.93430i	0.0984696	−	0.170554i
$838$		0			0
$839$	37.4781			1.29389			0.646943	−	0.762538i	$-0.276047\pi$
$839$	37.4781			1.29389			0.646943	+	0.762538i	$0.276047\pi$
$840$		0			0
$841$	−22.9457			−0.791232
$842$		0			0
$843$	2.52709	−	4.37704i	0.0870375	−	0.150753i
$844$		0			0
$845$	5.90155	−	3.40726i	0.203019	−	0.117213i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	9.55781	+	16.5546i	0.328023	+	0.568153i
$850$		0			0
$851$	9.77077	+	5.64116i	0.334938	+	0.193376i
$852$		0			0
$853$			9.50115i			0.325313i	0.986683	+	0.162657i	$0.0520063\pi$
$853$			9.50115i			0.325313i	−0.986683	+	0.162657i	$0.947994\pi$
$854$		0			0
$855$		−	20.2108i		−	0.691193i
$856$		0			0
$857$	−28.3880	−	16.3898i	−0.969717	−	0.559866i	−0.0705668	−	0.997507i	$-0.522481\pi$
$857$	−28.3880	−	16.3898i	−0.969717	−	0.559866i	−0.899150	+	0.437641i	$0.855814\pi$
$858$		0			0
$859$	2.68653	+	4.65321i	0.0916633	+	0.158765i	0.908211	−	0.418512i	$-0.137448\pi$
$859$	2.68653	+	4.65321i	0.0916633	+	0.158765i	−0.816548	+	0.577278i	$0.804115\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−25.7057	+	14.8412i	−0.875031	+	0.505200i	−0.869017	−	0.494782i	$-0.835248\pi$
$863$	−25.7057	+	14.8412i	−0.875031	+	0.505200i	−0.00601431	+	0.999982i	$0.501914\pi$
$864$		0			0
$865$	−7.21169	+	12.4910i	−0.245205	+	0.424707i
$866$		0			0
$867$	−9.34639			−0.317420
$868$		0			0
$869$	−70.4544			−2.39000
$870$		0			0
$871$	8.04659	−	13.9371i	0.272648	−	0.472241i
$872$		0			0
$873$	−12.6194	+	7.28581i	−0.427102	+	0.246587i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	15.1621	+	26.2615i	0.511988	+	0.886789i	0.999903	+	0.0138982i	$0.00442409\pi$
$877$	15.1621	+	26.2615i	0.511988	+	0.886789i	−0.487915	+	0.872891i	$0.662243\pi$
$878$		0			0
$879$	−2.05973	−	1.18919i	−0.0694730	−	0.0401103i
$880$		0			0
$881$			16.5012i			0.555939i	0.960590	+	0.277969i	$0.0896614\pi$
$881$			16.5012i			0.555939i	−0.960590	+	0.277969i	$0.910339\pi$
$882$		0			0
$883$			22.5909i			0.760245i	0.924936	+	0.380122i	$0.124118\pi$
$883$			22.5909i			0.760245i	−0.924936	+	0.380122i	$0.875882\pi$
$884$		0			0
$885$	−35.7452	−	20.6375i	−1.20156	−	0.693722i
$886$		0			0
$887$	−19.3018	−	33.4317i	−0.648090	−	1.12253i	−0.983578	−	0.180481i	$-0.942235\pi$
$887$	−19.3018	−	33.4317i	−0.648090	−	1.12253i	0.335488	−	0.942044i	$-0.391099\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−4.38435	+	2.53131i	−0.146881	+	0.0848020i
$892$		0			0
$893$	−12.5916	+	21.8093i	−0.421361	+	0.729819i
$894$		0			0
$895$	56.9769			1.90453
$896$		0			0
$897$	16.3222			0.544981
$898$		0			0
$899$	−7.00965	+	12.1411i	−0.233785	+	0.404927i
$900$		0			0
$901$	−10.1195	+	5.84247i	−0.337128	+	0.194641i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	25.4653	+	44.1072i	0.846496	+	1.46617i
$906$		0			0
$907$	−31.7609	−	18.3371i	−1.05460	−	0.608875i	−0.130668	−	0.991426i	$-0.541712\pi$
$907$	−31.7609	−	18.3371i	−1.05460	−	0.608875i	−0.923934	+	0.382551i	$0.875046\pi$
$908$		0			0
$909$			13.1087i			0.434787i
$910$		0			0
$911$		−	52.6835i		−	1.74548i	−0.488185	−	0.872740i	$-0.662341\pi$
$911$		−	52.6835i		−	1.74548i	0.488185	−	0.872740i	$-0.337659\pi$
$912$		0			0
$913$	−32.1019	−	18.5340i	−1.06242	−	0.613387i
$914$		0			0
$915$	8.33018	+	14.4283i	0.275387	+	0.476985i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	4.43074	−	2.55809i	0.146157	−	0.0843836i	−0.425138	−	0.905128i	$-0.639775\pi$
$919$	4.43074	−	2.55809i	0.146157	−	0.0843836i	0.571295	+	0.820745i	$0.306441\pi$
$920$		0			0
$921$	−2.44799	+	4.24005i	−0.0806642	+	0.139714i
$922$		0			0
$923$	41.6166			1.36983
$924$		0			0
$925$	31.4480			1.03400
$926$		0			0
$927$	0.104849	−	0.181604i	0.00344369	−	0.00596465i
$928$		0			0
$929$	30.6308	−	17.6847i	1.00496	−	0.580217i	0.0952512	−	0.995453i	$-0.469635\pi$
$929$	30.6308	−	17.6847i	1.00496	−	0.580217i	0.909713	+	0.415237i	$0.136301\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−5.24000	−	9.07594i	−0.171550	−	0.297133i
$934$		0			0
$935$	−52.1230	−	30.0932i	−1.70460	−	0.984153i
$936$		0			0
$937$		−	23.6290i		−	0.771924i	−0.922515	−	0.385962i	$-0.873870\pi$
$937$		−	23.6290i		−	0.771924i	0.922515	−	0.385962i	$-0.126130\pi$
$938$		0			0
$939$		−	9.60172i		−	0.313340i
$940$		0			0
$941$	16.6438	+	9.60933i	0.542574	+	0.313255i	0.746121	−	0.665810i	$-0.231914\pi$
$941$	16.6438	+	9.60933i	0.542574	+	0.313255i	−0.203548	+	0.979065i	$0.565247\pi$
$942$		0			0
$943$	−12.4360	−	21.5399i	−0.404973	−	0.701435i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−24.0892	+	13.9079i	−0.782795	+	0.451947i	−0.837420	−	0.546560i	$-0.815937\pi$
$947$	−24.0892	+	13.9079i	−0.782795	+	0.451947i	0.0546249	+	0.998507i	$0.482604\pi$
$948$		0			0
$949$	19.4435	−	33.6771i	0.631162	−	1.09321i
$950$		0			0
$951$	16.7934			0.544565
$952$		0			0
$953$	56.8087			1.84021			0.920107	−	0.391668i	$-0.128102\pi$
$953$	56.8087			1.84021			0.920107	+	0.391668i	$0.128102\pi$
$954$		0			0
$955$	2.89335	−	5.01142i	0.0936264	−	0.162166i
$956$		0			0
$957$	10.7879	−	6.22840i	0.348723	−	0.201335i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.731549	−	1.26708i	−0.0235984	−	0.0408736i
$962$		0			0
$963$	5.56558	+	3.21329i	0.179348	+	0.103547i
$964$		0			0
$965$		−	112.224i		−	3.61262i
$966$		0			0
$967$			20.3860i			0.655570i	0.944752	+	0.327785i	$0.106302\pi$
$967$			20.3860i			0.655570i	−0.944752	+	0.327785i	$0.893698\pi$
$968$		0			0
$969$	−11.2682	−	6.50572i	−0.361988	−	0.208994i
$970$		0			0
$971$	5.61437	+	9.72437i	0.180174	+	0.312070i	0.941940	−	0.335782i	$-0.109001\pi$
$971$	5.61437	+	9.72437i	0.180174	+	0.312070i	−0.761766	+	0.647852i	$0.775667\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	39.4007	−	22.7480i	1.26183	−	0.728518i
$976$		0			0
$977$	6.09164	−	10.5510i	0.194889	−	0.337557i	−0.751975	−	0.659191i	$-0.770899\pi$
$977$	6.09164	−	10.5510i	0.194889	−	0.337557i	0.946864	+	0.321634i	$0.104232\pi$
$978$		0			0
$979$	−71.1033			−2.27247
$980$		0			0
$981$	0.940024			0.0300126
$982$		0			0
$983$	−4.53187	+	7.84943i	−0.144544	+	0.250358i	−0.929203	−	0.369570i	$-0.879505\pi$
$983$	−4.53187	+	7.84943i	−0.144544	+	0.250358i	0.784659	+	0.619928i	$0.212838\pi$
$984$		0			0
$985$	−27.8773	+	16.0950i	−0.888245	+	0.512829i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	31.4509	+	54.4746i	1.00008	+	1.73219i
$990$		0			0
$991$	4.65193	+	2.68579i	0.147773	+	0.0853170i	0.572064	−	0.820209i	$-0.306143\pi$
$991$	4.65193	+	2.68579i	0.147773	+	0.0853170i	−0.424290	+	0.905526i	$0.639476\pi$
$992$		0			0
$993$		−	26.8362i		−	0.851622i
$994$		0			0
$995$		−	19.3096i		−	0.612157i
$996$		0			0
$997$	12.4222	+	7.17199i	0.393417	+	0.227139i	0.683639	−	0.729820i	$-0.260396\pi$
$997$	12.4222	+	7.17199i	0.393417	+	0.227139i	−0.290223	+	0.956959i	$0.593729\pi$
$998$		0			0
$999$	−1.16765	−	2.02243i	−0.0369429	−	0.0639869i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2352.2.bl.t.31.4		8
4.3	odd	2		2352.2.bl.o.31.4		8
7.2	even	3		2352.2.bl.r.607.1		8
7.3	odd	6		2352.2.b.l.1567.1	yes	8
7.4	even	3		2352.2.b.k.1567.8	yes	8
7.5	odd	6		2352.2.bl.o.607.4		8
7.6	odd	2		2352.2.bl.q.31.1		8
21.11	odd	6		7056.2.b.x.1567.1		8
21.17	even	6		7056.2.b.w.1567.8		8
28.3	even	6		2352.2.b.k.1567.1	✓	8
28.11	odd	6		2352.2.b.l.1567.8	yes	8
28.19	even	6	inner	2352.2.bl.t.607.4		8
28.23	odd	6		2352.2.bl.q.607.1		8
28.27	even	2		2352.2.bl.r.31.1		8
84.11	even	6		7056.2.b.w.1567.1		8
84.59	odd	6		7056.2.b.x.1567.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2352.2.b.k.1567.1	✓	8	28.3	even	6
2352.2.b.k.1567.8	yes	8	7.4	even	3
2352.2.b.l.1567.1	yes	8	7.3	odd	6
2352.2.b.l.1567.8	yes	8	28.11	odd	6
2352.2.bl.o.31.4		8	4.3	odd	2
2352.2.bl.o.607.4		8	7.5	odd	6
2352.2.bl.q.31.1		8	7.6	odd	2
2352.2.bl.q.607.1		8	28.23	odd	6
2352.2.bl.r.31.1		8	28.27	even	2
2352.2.bl.r.607.1		8	7.2	even	3
2352.2.bl.t.31.4		8	1.1	even	1	trivial
2352.2.bl.t.607.4		8	28.19	even	6	inner
7056.2.b.w.1567.1		8	84.11	even	6
7056.2.b.w.1567.8		8	21.17	even	6
7056.2.b.x.1567.1		8	21.11	odd	6
7056.2.b.x.1567.8		8	84.59	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2352.bl (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(3.72153 - 2.14862i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(4.38435 + 2.53131i) q^{11} +3.37849i q^{13} -4.29725i q^{15} +(-2.39587 - 1.38326i) q^{17} +(2.35159 + 4.07308i) q^{19} +(4.18394 - 2.41560i) q^{23} +(6.73317 - 11.6622i) q^{25} -1.00000 q^{27} +2.46054 q^{29} +(-2.84882 + 4.93430i) q^{31} +(4.38435 - 2.53131i) q^{33} +(1.16765 + 2.02243i) q^{37} +(2.92586 + 1.68925i) q^{39} -5.14822i q^{41} +13.0199i q^{43} +(-3.72153 - 2.14862i) q^{45} +(2.67725 + 4.63713i) q^{47} +(-2.39587 + 1.38326i) q^{51} +(2.11185 - 3.65784i) q^{53} +21.7553 q^{55} +4.70319 q^{57} +(4.80249 - 8.31815i) q^{59} +(-3.35757 + 1.93849i) q^{61} +(7.25911 + 12.5732i) q^{65} +(-4.12524 - 2.38171i) q^{67} -4.83120i q^{69} -12.3181i q^{71} +(-9.96809 - 5.75508i) q^{73} +(-6.73317 - 11.6622i) q^{75} +(-12.0521 + 6.95830i) q^{79} +(-0.500000 + 0.866025i) q^{81} -7.32191 q^{83} -11.8884 q^{85} +(1.23027 - 2.13089i) q^{87} +(-12.1631 + 7.02239i) q^{89} +(2.84882 + 4.93430i) q^{93} +(17.5030 + 10.1054i) q^{95} -14.5716i q^{97} -5.06262i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 4 q^{9} + 24 q^{23} + 12 q^{25} - 8 q^{27} + 16 q^{29} - 16 q^{31} - 8 q^{47} - 8 q^{53} + 64 q^{55} + 24 q^{59} - 48 q^{61} + 8 q^{65} - 48 q^{67} - 48 q^{73} - 12 q^{75} - 24 q^{79} - 4 q^{81}+ \cdots + 72 q^{95}+O(q^{100}) \) 8 * q + 4 * q^3 - 4 * q^9 + 24 * q^23 + 12 * q^25 - 8 * q^27 + 16 * q^29 - 16 * q^31 - 8 * q^47 - 8 * q^53 + 64 * q^55 + 24 * q^59 - 48 * q^61 + 8 * q^65 - 48 * q^67 - 48 * q^73 - 12 * q^75 - 24 * q^79 - 4 * q^81 - 64 * q^85 + 8 * q^87 - 48 * q^89 + 16 * q^93 + 72 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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